Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.a (trivial) |
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: | yes |
Analytic conductor: | \(28.3389076774\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.121819537.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 25x^{4} + 55x^{3} + 224x^{2} - 252x - 728 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.06987\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.24698 | −0.881748 | −0.440874 | − | 0.897569i | \(-0.645331\pi\) | ||||
−0.440874 | + | 0.897569i | \(0.645331\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.445042 | −0.222521 | ||||||||
\(5\) | 3.06987 | 1.37289 | 0.686443 | − | 0.727183i | \(-0.259171\pi\) | ||||
0.686443 | + | 0.727183i | \(0.259171\pi\) | |||||||
\(6\) | 1.24698 | 0.509077 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 3.04892 | 1.07796 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.82806 | −1.21054 | ||||||||
\(11\) | −3.50559 | −1.05697 | −0.528487 | − | 0.848941i | \(-0.677240\pi\) | ||||
−0.528487 | + | 0.848941i | \(0.677240\pi\) | |||||||
\(12\) | 0.445042 | 0.128473 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.24698 | −0.333269 | ||||||||
\(15\) | −3.06987 | −0.792637 | ||||||||
\(16\) | −2.91185 | −0.727963 | ||||||||
\(17\) | 7.13559 | 1.73063 | 0.865317 | − | 0.501225i | \(-0.167117\pi\) | ||||
0.865317 | + | 0.501225i | \(0.167117\pi\) | |||||||
\(18\) | −1.24698 | −0.293916 | ||||||||
\(19\) | −3.36622 | −0.772264 | −0.386132 | − | 0.922444i | \(-0.626189\pi\) | ||||
−0.386132 | + | 0.922444i | \(0.626189\pi\) | |||||||
\(20\) | −1.36622 | −0.305496 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 4.37139 | 0.931984 | ||||||||
\(23\) | −1.88076 | −0.392166 | −0.196083 | − | 0.980587i | \(-0.562822\pi\) | ||||
−0.196083 | + | 0.980587i | \(0.562822\pi\) | |||||||
\(24\) | −3.04892 | −0.622358 | ||||||||
\(25\) | 4.42409 | 0.884818 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.445042 | −0.0841050 | ||||||||
\(29\) | −4.40064 | −0.817178 | −0.408589 | − | 0.912718i | \(-0.633979\pi\) | ||||
−0.408589 | + | 0.912718i | \(0.633979\pi\) | |||||||
\(30\) | 3.82806 | 0.698905 | ||||||||
\(31\) | −2.60803 | −0.468415 | −0.234208 | − | 0.972187i | \(-0.575250\pi\) | ||||
−0.234208 | + | 0.972187i | \(0.575250\pi\) | |||||||
\(32\) | −2.46681 | −0.436075 | ||||||||
\(33\) | 3.50559 | 0.610244 | ||||||||
\(34\) | −8.89793 | −1.52598 | ||||||||
\(35\) | 3.06987 | 0.518902 | ||||||||
\(36\) | −0.445042 | −0.0741736 | ||||||||
\(37\) | −5.25483 | −0.863888 | −0.431944 | − | 0.901900i | \(-0.642172\pi\) | ||||
−0.431944 | + | 0.901900i | \(0.642172\pi\) | |||||||
\(38\) | 4.19761 | 0.680942 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 9.35977 | 1.47991 | ||||||||
\(41\) | 6.41744 | 1.00224 | 0.501118 | − | 0.865379i | \(-0.332922\pi\) | ||||
0.501118 | + | 0.865379i | \(0.332922\pi\) | |||||||
\(42\) | 1.24698 | 0.192413 | ||||||||
\(43\) | −10.3388 | −1.57666 | −0.788328 | − | 0.615255i | \(-0.789053\pi\) | ||||
−0.788328 | + | 0.615255i | \(0.789053\pi\) | |||||||
\(44\) | 1.56013 | 0.235199 | ||||||||
\(45\) | 3.06987 | 0.457629 | ||||||||
\(46\) | 2.34527 | 0.345791 | ||||||||
\(47\) | −12.1076 | −1.76608 | −0.883039 | − | 0.469300i | \(-0.844506\pi\) | ||||
−0.883039 | + | 0.469300i | \(0.844506\pi\) | |||||||
\(48\) | 2.91185 | 0.420290 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −5.51675 | −0.780186 | ||||||||
\(51\) | −7.13559 | −0.999182 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.3647 | −1.42371 | −0.711854 | − | 0.702328i | \(-0.752144\pi\) | ||||
−0.711854 | + | 0.702328i | \(0.752144\pi\) | |||||||
\(54\) | 1.24698 | 0.169692 | ||||||||
\(55\) | −10.7617 | −1.45111 | ||||||||
\(56\) | 3.04892 | 0.407429 | ||||||||
\(57\) | 3.36622 | 0.445867 | ||||||||
\(58\) | 5.48751 | 0.720545 | ||||||||
\(59\) | 12.6505 | 1.64695 | 0.823477 | − | 0.567350i | \(-0.192031\pi\) | ||||
0.823477 | + | 0.567350i | \(0.192031\pi\) | |||||||
\(60\) | 1.36622 | 0.176378 | ||||||||
\(61\) | −12.5783 | −1.61049 | −0.805245 | − | 0.592943i | \(-0.797966\pi\) | ||||
−0.805245 | + | 0.592943i | \(0.797966\pi\) | |||||||
\(62\) | 3.25215 | 0.413024 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 8.89977 | 1.11247 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.37139 | −0.538081 | ||||||||
\(67\) | 1.93301 | 0.236155 | 0.118077 | − | 0.993004i | \(-0.462327\pi\) | ||||
0.118077 | + | 0.993004i | \(0.462327\pi\) | |||||||
\(68\) | −3.17563 | −0.385102 | ||||||||
\(69\) | 1.88076 | 0.226417 | ||||||||
\(70\) | −3.82806 | −0.457541 | ||||||||
\(71\) | −11.4790 | −1.36231 | −0.681154 | − | 0.732140i | \(-0.738522\pi\) | ||||
−0.681154 | + | 0.732140i | \(0.738522\pi\) | |||||||
\(72\) | 3.04892 | 0.359318 | ||||||||
\(73\) | 4.91575 | 0.575346 | 0.287673 | − | 0.957729i | \(-0.407118\pi\) | ||||
0.287673 | + | 0.957729i | \(0.407118\pi\) | |||||||
\(74\) | 6.55266 | 0.761732 | ||||||||
\(75\) | −4.42409 | −0.510850 | ||||||||
\(76\) | 1.49811 | 0.171845 | ||||||||
\(77\) | −3.50559 | −0.399499 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.41810 | −0.384566 | −0.192283 | − | 0.981339i | \(-0.561589\pi\) | ||||
−0.192283 | + | 0.981339i | \(0.561589\pi\) | |||||||
\(80\) | −8.93901 | −0.999411 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.00242 | −0.883719 | ||||||||
\(83\) | 7.10798 | 0.780202 | 0.390101 | − | 0.920772i | \(-0.372440\pi\) | ||||
0.390101 | + | 0.920772i | \(0.372440\pi\) | |||||||
\(84\) | 0.445042 | 0.0485580 | ||||||||
\(85\) | 21.9053 | 2.37596 | ||||||||
\(86\) | 12.8923 | 1.39021 | ||||||||
\(87\) | 4.40064 | 0.471798 | ||||||||
\(88\) | −10.6882 | −1.13937 | ||||||||
\(89\) | −0.730586 | −0.0774420 | −0.0387210 | − | 0.999250i | \(-0.512328\pi\) | ||||
−0.0387210 | + | 0.999250i | \(0.512328\pi\) | |||||||
\(90\) | −3.82806 | −0.403513 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.837017 | 0.0872650 | ||||||||
\(93\) | 2.60803 | 0.270440 | ||||||||
\(94\) | 15.0980 | 1.55724 | ||||||||
\(95\) | −10.3339 | −1.06023 | ||||||||
\(96\) | 2.46681 | 0.251768 | ||||||||
\(97\) | −6.18414 | −0.627904 | −0.313952 | − | 0.949439i | \(-0.601653\pi\) | ||||
−0.313952 | + | 0.949439i | \(0.601653\pi\) | |||||||
\(98\) | −1.24698 | −0.125964 | ||||||||
\(99\) | −3.50559 | −0.352325 | ||||||||
\(100\) | −1.96891 | −0.196891 | ||||||||
\(101\) | 11.6216 | 1.15639 | 0.578197 | − | 0.815897i | \(-0.303757\pi\) | ||||
0.578197 | + | 0.815897i | \(0.303757\pi\) | |||||||
\(102\) | 8.89793 | 0.881026 | ||||||||
\(103\) | 12.3453 | 1.21642 | 0.608208 | − | 0.793778i | \(-0.291889\pi\) | ||||
0.608208 | + | 0.793778i | \(0.291889\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.06987 | −0.299588 | ||||||||
\(106\) | 12.9246 | 1.25535 | ||||||||
\(107\) | −10.5138 | −1.01641 | −0.508203 | − | 0.861237i | \(-0.669690\pi\) | ||||
−0.508203 | + | 0.861237i | \(0.669690\pi\) | |||||||
\(108\) | 0.445042 | 0.0428242 | ||||||||
\(109\) | −0.707801 | −0.0677950 | −0.0338975 | − | 0.999425i | \(-0.510792\pi\) | ||||
−0.0338975 | + | 0.999425i | \(0.510792\pi\) | |||||||
\(110\) | 13.4196 | 1.27951 | ||||||||
\(111\) | 5.25483 | 0.498766 | ||||||||
\(112\) | −2.91185 | −0.275144 | ||||||||
\(113\) | −6.54416 | −0.615623 | −0.307812 | − | 0.951447i | \(-0.599597\pi\) | ||||
−0.307812 | + | 0.951447i | \(0.599597\pi\) | |||||||
\(114\) | −4.19761 | −0.393142 | ||||||||
\(115\) | −5.77368 | −0.538399 | ||||||||
\(116\) | 1.95847 | 0.181839 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15.7749 | −1.45220 | ||||||||
\(119\) | 7.13559 | 0.654118 | ||||||||
\(120\) | −9.35977 | −0.854427 | ||||||||
\(121\) | 1.28913 | 0.117194 | ||||||||
\(122\) | 15.6849 | 1.42005 | ||||||||
\(123\) | −6.41744 | −0.578641 | ||||||||
\(124\) | 1.16068 | 0.104232 | ||||||||
\(125\) | −1.76796 | −0.158132 | ||||||||
\(126\) | −1.24698 | −0.111090 | ||||||||
\(127\) | −3.11279 | −0.276216 | −0.138108 | − | 0.990417i | \(-0.544102\pi\) | ||||
−0.138108 | + | 0.990417i | \(0.544102\pi\) | |||||||
\(128\) | −6.16421 | −0.544844 | ||||||||
\(129\) | 10.3388 | 0.910283 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.35550 | −0.467913 | −0.233956 | − | 0.972247i | \(-0.575167\pi\) | ||||
−0.233956 | + | 0.972247i | \(0.575167\pi\) | |||||||
\(132\) | −1.56013 | −0.135792 | ||||||||
\(133\) | −3.36622 | −0.291888 | ||||||||
\(134\) | −2.41042 | −0.208229 | ||||||||
\(135\) | −3.06987 | −0.264212 | ||||||||
\(136\) | 21.7558 | 1.86555 | ||||||||
\(137\) | 15.6533 | 1.33735 | 0.668674 | − | 0.743556i | \(-0.266862\pi\) | ||||
0.668674 | + | 0.743556i | \(0.266862\pi\) | |||||||
\(138\) | −2.34527 | −0.199643 | ||||||||
\(139\) | −7.69765 | −0.652907 | −0.326453 | − | 0.945213i | \(-0.605854\pi\) | ||||
−0.326453 | + | 0.945213i | \(0.605854\pi\) | |||||||
\(140\) | −1.36622 | −0.115467 | ||||||||
\(141\) | 12.1076 | 1.01965 | ||||||||
\(142\) | 14.3141 | 1.20121 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.91185 | −0.242654 | ||||||||
\(145\) | −13.5094 | −1.12189 | ||||||||
\(146\) | −6.12985 | −0.507310 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 2.33862 | 0.192233 | ||||||||
\(149\) | 14.3574 | 1.17620 | 0.588101 | − | 0.808787i | \(-0.299876\pi\) | ||||
0.588101 | + | 0.808787i | \(0.299876\pi\) | |||||||
\(150\) | 5.51675 | 0.450441 | ||||||||
\(151\) | 18.2801 | 1.48762 | 0.743808 | − | 0.668394i | \(-0.233018\pi\) | ||||
0.743808 | + | 0.668394i | \(0.233018\pi\) | |||||||
\(152\) | −10.2633 | −0.832466 | ||||||||
\(153\) | 7.13559 | 0.576878 | ||||||||
\(154\) | 4.37139 | 0.352257 | ||||||||
\(155\) | −8.00629 | −0.643081 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.14988 | 0.730240 | 0.365120 | − | 0.930960i | \(-0.381028\pi\) | ||||
0.365120 | + | 0.930960i | \(0.381028\pi\) | |||||||
\(158\) | 4.26230 | 0.339090 | ||||||||
\(159\) | 10.3647 | 0.821978 | ||||||||
\(160\) | −7.57279 | −0.598681 | ||||||||
\(161\) | −1.88076 | −0.148225 | ||||||||
\(162\) | −1.24698 | −0.0979720 | ||||||||
\(163\) | −13.6215 | −1.06691 | −0.533457 | − | 0.845827i | \(-0.679108\pi\) | ||||
−0.533457 | + | 0.845827i | \(0.679108\pi\) | |||||||
\(164\) | −2.85603 | −0.223018 | ||||||||
\(165\) | 10.7617 | 0.837796 | ||||||||
\(166\) | −8.86350 | −0.687941 | ||||||||
\(167\) | −3.58810 | −0.277655 | −0.138828 | − | 0.990317i | \(-0.544333\pi\) | ||||
−0.138828 | + | 0.990317i | \(0.544333\pi\) | |||||||
\(168\) | −3.04892 | −0.235229 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −27.3155 | −2.09500 | ||||||||
\(171\) | −3.36622 | −0.257421 | ||||||||
\(172\) | 4.60121 | 0.350839 | ||||||||
\(173\) | −5.00471 | −0.380501 | −0.190251 | − | 0.981736i | \(-0.560930\pi\) | ||||
−0.190251 | + | 0.981736i | \(0.560930\pi\) | |||||||
\(174\) | −5.48751 | −0.416007 | ||||||||
\(175\) | 4.42409 | 0.334430 | ||||||||
\(176\) | 10.2078 | 0.769438 | ||||||||
\(177\) | −12.6505 | −0.950869 | ||||||||
\(178\) | 0.911026 | 0.0682843 | ||||||||
\(179\) | −6.82831 | −0.510372 | −0.255186 | − | 0.966892i | \(-0.582137\pi\) | ||||
−0.255186 | + | 0.966892i | \(0.582137\pi\) | |||||||
\(180\) | −1.36622 | −0.101832 | ||||||||
\(181\) | 25.1122 | 1.86658 | 0.933289 | − | 0.359125i | \(-0.116925\pi\) | ||||
0.933289 | + | 0.359125i | \(0.116925\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.5783 | 0.929817 | ||||||||
\(184\) | −5.73428 | −0.422737 | ||||||||
\(185\) | −16.1316 | −1.18602 | ||||||||
\(186\) | −3.25215 | −0.238460 | ||||||||
\(187\) | −25.0144 | −1.82924 | ||||||||
\(188\) | 5.38840 | 0.392989 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 12.8861 | 0.934856 | ||||||||
\(191\) | −17.4749 | −1.26444 | −0.632218 | − | 0.774790i | \(-0.717855\pi\) | ||||
−0.632218 | + | 0.774790i | \(0.717855\pi\) | |||||||
\(192\) | −8.89977 | −0.642286 | ||||||||
\(193\) | 7.75149 | 0.557964 | 0.278982 | − | 0.960296i | \(-0.410003\pi\) | ||||
0.278982 | + | 0.960296i | \(0.410003\pi\) | |||||||
\(194\) | 7.71150 | 0.553653 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.445042 | −0.0317887 | ||||||||
\(197\) | −10.0904 | −0.718908 | −0.359454 | − | 0.933163i | \(-0.617037\pi\) | ||||
−0.359454 | + | 0.933163i | \(0.617037\pi\) | |||||||
\(198\) | 4.37139 | 0.310661 | ||||||||
\(199\) | 21.9594 | 1.55666 | 0.778331 | − | 0.627854i | \(-0.216067\pi\) | ||||
0.778331 | + | 0.627854i | \(0.216067\pi\) | |||||||
\(200\) | 13.4887 | 0.953794 | ||||||||
\(201\) | −1.93301 | −0.136344 | ||||||||
\(202\) | −14.4919 | −1.01965 | ||||||||
\(203\) | −4.40064 | −0.308864 | ||||||||
\(204\) | 3.17563 | 0.222339 | ||||||||
\(205\) | 19.7007 | 1.37596 | ||||||||
\(206\) | −15.3943 | −1.07257 | ||||||||
\(207\) | −1.88076 | −0.130722 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.8006 | 0.816263 | ||||||||
\(210\) | 3.82806 | 0.264161 | ||||||||
\(211\) | −19.3081 | −1.32922 | −0.664612 | − | 0.747189i | \(-0.731403\pi\) | ||||
−0.664612 | + | 0.747189i | \(0.731403\pi\) | |||||||
\(212\) | 4.61274 | 0.316805 | ||||||||
\(213\) | 11.4790 | 0.786529 | ||||||||
\(214\) | 13.1105 | 0.896214 | ||||||||
\(215\) | −31.7388 | −2.16457 | ||||||||
\(216\) | −3.04892 | −0.207453 | ||||||||
\(217\) | −2.60803 | −0.177044 | ||||||||
\(218\) | 0.882613 | 0.0597781 | ||||||||
\(219\) | −4.91575 | −0.332176 | ||||||||
\(220\) | 4.78940 | 0.322901 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.55266 | −0.439786 | ||||||||
\(223\) | 18.9063 | 1.26606 | 0.633031 | − | 0.774126i | \(-0.281810\pi\) | ||||
0.633031 | + | 0.774126i | \(0.281810\pi\) | |||||||
\(224\) | −2.46681 | −0.164821 | ||||||||
\(225\) | 4.42409 | 0.294939 | ||||||||
\(226\) | 8.16044 | 0.542824 | ||||||||
\(227\) | 9.41062 | 0.624605 | 0.312302 | − | 0.949983i | \(-0.398900\pi\) | ||||
0.312302 | + | 0.949983i | \(0.398900\pi\) | |||||||
\(228\) | −1.49811 | −0.0992147 | ||||||||
\(229\) | −10.7573 | −0.710861 | −0.355431 | − | 0.934703i | \(-0.615666\pi\) | ||||
−0.355431 | + | 0.934703i | \(0.615666\pi\) | |||||||
\(230\) | 7.19967 | 0.474732 | ||||||||
\(231\) | 3.50559 | 0.230651 | ||||||||
\(232\) | −13.4172 | −0.880881 | ||||||||
\(233\) | −22.6327 | −1.48272 | −0.741358 | − | 0.671110i | \(-0.765818\pi\) | ||||
−0.741358 | + | 0.671110i | \(0.765818\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −37.1688 | −2.42463 | ||||||||
\(236\) | −5.63000 | −0.366482 | ||||||||
\(237\) | 3.41810 | 0.222029 | ||||||||
\(238\) | −8.89793 | −0.576767 | ||||||||
\(239\) | −21.6067 | −1.39762 | −0.698810 | − | 0.715308i | \(-0.746287\pi\) | ||||
−0.698810 | + | 0.715308i | \(0.746287\pi\) | |||||||
\(240\) | 8.93901 | 0.577010 | ||||||||
\(241\) | 2.91822 | 0.187979 | 0.0939895 | − | 0.995573i | \(-0.470038\pi\) | ||||
0.0939895 | + | 0.995573i | \(0.470038\pi\) | |||||||
\(242\) | −1.60752 | −0.103336 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 5.59788 | 0.358368 | ||||||||
\(245\) | 3.06987 | 0.196127 | ||||||||
\(246\) | 8.00242 | 0.510215 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7.95165 | −0.504930 | ||||||||
\(249\) | −7.10798 | −0.450450 | ||||||||
\(250\) | 2.20462 | 0.139432 | ||||||||
\(251\) | −18.4508 | −1.16460 | −0.582302 | − | 0.812973i | \(-0.697848\pi\) | ||||
−0.582302 | + | 0.812973i | \(0.697848\pi\) | |||||||
\(252\) | −0.445042 | −0.0280350 | ||||||||
\(253\) | 6.59317 | 0.414509 | ||||||||
\(254\) | 3.88159 | 0.243552 | ||||||||
\(255\) | −21.9053 | −1.37176 | ||||||||
\(256\) | −10.1129 | −0.632056 | ||||||||
\(257\) | −15.6082 | −0.973615 | −0.486807 | − | 0.873509i | \(-0.661839\pi\) | ||||
−0.486807 | + | 0.873509i | \(0.661839\pi\) | |||||||
\(258\) | −12.8923 | −0.802640 | ||||||||
\(259\) | −5.25483 | −0.326519 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.40064 | −0.272393 | ||||||||
\(262\) | 6.67820 | 0.412581 | ||||||||
\(263\) | −16.8076 | −1.03640 | −0.518200 | − | 0.855259i | \(-0.673398\pi\) | ||||
−0.518200 | + | 0.855259i | \(0.673398\pi\) | |||||||
\(264\) | 10.6882 | 0.657816 | ||||||||
\(265\) | −31.8184 | −1.95459 | ||||||||
\(266\) | 4.19761 | 0.257372 | ||||||||
\(267\) | 0.730586 | 0.0447111 | ||||||||
\(268\) | −0.860271 | −0.0525494 | ||||||||
\(269\) | −20.3448 | −1.24045 | −0.620223 | − | 0.784426i | \(-0.712958\pi\) | ||||
−0.620223 | + | 0.784426i | \(0.712958\pi\) | |||||||
\(270\) | 3.82806 | 0.232968 | ||||||||
\(271\) | 5.26295 | 0.319702 | 0.159851 | − | 0.987141i | \(-0.448899\pi\) | ||||
0.159851 | + | 0.987141i | \(0.448899\pi\) | |||||||
\(272\) | −20.7778 | −1.25984 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.5193 | −1.17920 | ||||||||
\(275\) | −15.5090 | −0.935230 | ||||||||
\(276\) | −0.837017 | −0.0503825 | ||||||||
\(277\) | −27.0717 | −1.62658 | −0.813292 | − | 0.581856i | \(-0.802327\pi\) | ||||
−0.813292 | + | 0.581856i | \(0.802327\pi\) | |||||||
\(278\) | 9.59882 | 0.575699 | ||||||||
\(279\) | −2.60803 | −0.156138 | ||||||||
\(280\) | 9.35977 | 0.559354 | ||||||||
\(281\) | −22.6562 | −1.35156 | −0.675779 | − | 0.737104i | \(-0.736193\pi\) | ||||
−0.675779 | + | 0.737104i | \(0.736193\pi\) | |||||||
\(282\) | −15.0980 | −0.899070 | ||||||||
\(283\) | 2.68158 | 0.159403 | 0.0797016 | − | 0.996819i | \(-0.474603\pi\) | ||||
0.0797016 | + | 0.996819i | \(0.474603\pi\) | |||||||
\(284\) | 5.10864 | 0.303142 | ||||||||
\(285\) | 10.3339 | 0.612125 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.41744 | 0.378810 | ||||||||
\(288\) | −2.46681 | −0.145358 | ||||||||
\(289\) | 33.9166 | 1.99509 | ||||||||
\(290\) | 16.8459 | 0.989227 | ||||||||
\(291\) | 6.18414 | 0.362521 | ||||||||
\(292\) | −2.18772 | −0.128026 | ||||||||
\(293\) | −24.8294 | −1.45055 | −0.725276 | − | 0.688458i | \(-0.758288\pi\) | ||||
−0.725276 | + | 0.688458i | \(0.758288\pi\) | |||||||
\(294\) | 1.24698 | 0.0727253 | ||||||||
\(295\) | 38.8353 | 2.26108 | ||||||||
\(296\) | −16.0215 | −0.931233 | ||||||||
\(297\) | 3.50559 | 0.203415 | ||||||||
\(298\) | −17.9034 | −1.03711 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.96891 | 0.113675 | ||||||||
\(301\) | −10.3388 | −0.595920 | ||||||||
\(302\) | −22.7949 | −1.31170 | ||||||||
\(303\) | −11.6216 | −0.667644 | ||||||||
\(304\) | 9.80194 | 0.562180 | ||||||||
\(305\) | −38.6138 | −2.21102 | ||||||||
\(306\) | −8.89793 | −0.508661 | ||||||||
\(307\) | −22.7954 | −1.30100 | −0.650501 | − | 0.759505i | \(-0.725441\pi\) | ||||
−0.650501 | + | 0.759505i | \(0.725441\pi\) | |||||||
\(308\) | 1.56013 | 0.0888968 | ||||||||
\(309\) | −12.3453 | −0.702298 | ||||||||
\(310\) | 9.98368 | 0.567035 | ||||||||
\(311\) | 23.1401 | 1.31216 | 0.656078 | − | 0.754693i | \(-0.272214\pi\) | ||||
0.656078 | + | 0.754693i | \(0.272214\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.5357 | −0.991175 | −0.495588 | − | 0.868558i | \(-0.665047\pi\) | ||||
−0.495588 | + | 0.868558i | \(0.665047\pi\) | |||||||
\(314\) | −11.4097 | −0.643887 | ||||||||
\(315\) | 3.06987 | 0.172967 | ||||||||
\(316\) | 1.52120 | 0.0855741 | ||||||||
\(317\) | 21.1340 | 1.18700 | 0.593500 | − | 0.804834i | \(-0.297746\pi\) | ||||
0.593500 | + | 0.804834i | \(0.297746\pi\) | |||||||
\(318\) | −12.9246 | −0.724777 | ||||||||
\(319\) | 15.4268 | 0.863736 | ||||||||
\(320\) | 27.3211 | 1.52730 | ||||||||
\(321\) | 10.5138 | 0.586823 | ||||||||
\(322\) | 2.34527 | 0.130697 | ||||||||
\(323\) | −24.0200 | −1.33651 | ||||||||
\(324\) | −0.445042 | −0.0247245 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.9857 | 0.940750 | ||||||||
\(327\) | 0.707801 | 0.0391415 | ||||||||
\(328\) | 19.5662 | 1.08037 | ||||||||
\(329\) | −12.1076 | −0.667515 | ||||||||
\(330\) | −13.4196 | −0.738725 | ||||||||
\(331\) | −19.6453 | −1.07980 | −0.539901 | − | 0.841728i | \(-0.681538\pi\) | ||||
−0.539901 | + | 0.841728i | \(0.681538\pi\) | |||||||
\(332\) | −3.16335 | −0.173611 | ||||||||
\(333\) | −5.25483 | −0.287963 | ||||||||
\(334\) | 4.47428 | 0.244822 | ||||||||
\(335\) | 5.93409 | 0.324214 | ||||||||
\(336\) | 2.91185 | 0.158855 | ||||||||
\(337\) | 0.587432 | 0.0319994 | 0.0159997 | − | 0.999872i | \(-0.494907\pi\) | ||||
0.0159997 | + | 0.999872i | \(0.494907\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.54416 | 0.355430 | ||||||||
\(340\) | −9.74878 | −0.528702 | ||||||||
\(341\) | 9.14266 | 0.495103 | ||||||||
\(342\) | 4.19761 | 0.226981 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −31.5222 | −1.69956 | ||||||||
\(345\) | 5.77368 | 0.310845 | ||||||||
\(346\) | 6.24077 | 0.335506 | ||||||||
\(347\) | −16.4236 | −0.881663 | −0.440831 | − | 0.897590i | \(-0.645316\pi\) | ||||
−0.440831 | + | 0.897590i | \(0.645316\pi\) | |||||||
\(348\) | −1.95847 | −0.104985 | ||||||||
\(349\) | 34.5166 | 1.84763 | 0.923815 | − | 0.382838i | \(-0.125053\pi\) | ||||
0.923815 | + | 0.382838i | \(0.125053\pi\) | |||||||
\(350\) | −5.51675 | −0.294883 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.64762 | 0.460920 | ||||||||
\(353\) | 29.2191 | 1.55518 | 0.777589 | − | 0.628773i | \(-0.216443\pi\) | ||||
0.777589 | + | 0.628773i | \(0.216443\pi\) | |||||||
\(354\) | 15.7749 | 0.838427 | ||||||||
\(355\) | −35.2391 | −1.87030 | ||||||||
\(356\) | 0.325141 | 0.0172325 | ||||||||
\(357\) | −7.13559 | −0.377655 | ||||||||
\(358\) | 8.51477 | 0.450019 | ||||||||
\(359\) | −8.37106 | −0.441808 | −0.220904 | − | 0.975296i | \(-0.570901\pi\) | ||||
−0.220904 | + | 0.975296i | \(0.570901\pi\) | |||||||
\(360\) | 9.35977 | 0.493303 | ||||||||
\(361\) | −7.66856 | −0.403609 | ||||||||
\(362\) | −31.3145 | −1.64585 | ||||||||
\(363\) | −1.28913 | −0.0676620 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.0907 | 0.789884 | ||||||||
\(366\) | −15.6849 | −0.819864 | ||||||||
\(367\) | −3.23730 | −0.168986 | −0.0844928 | − | 0.996424i | \(-0.526927\pi\) | ||||
−0.0844928 | + | 0.996424i | \(0.526927\pi\) | |||||||
\(368\) | 5.47650 | 0.285482 | ||||||||
\(369\) | 6.41744 | 0.334079 | ||||||||
\(370\) | 20.1158 | 1.04577 | ||||||||
\(371\) | −10.3647 | −0.538111 | ||||||||
\(372\) | −1.16068 | −0.0601785 | ||||||||
\(373\) | 20.8028 | 1.07713 | 0.538564 | − | 0.842585i | \(-0.318967\pi\) | ||||
0.538564 | + | 0.842585i | \(0.318967\pi\) | |||||||
\(374\) | 31.1925 | 1.61292 | ||||||||
\(375\) | 1.76796 | 0.0912973 | ||||||||
\(376\) | −36.9151 | −1.90375 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.24698 | 0.0641377 | ||||||||
\(379\) | 34.5507 | 1.77475 | 0.887375 | − | 0.461049i | \(-0.152527\pi\) | ||||
0.887375 | + | 0.461049i | \(0.152527\pi\) | |||||||
\(380\) | 4.59900 | 0.235924 | ||||||||
\(381\) | 3.11279 | 0.159473 | ||||||||
\(382\) | 21.7908 | 1.11491 | ||||||||
\(383\) | 19.7920 | 1.01132 | 0.505662 | − | 0.862732i | \(-0.331248\pi\) | ||||
0.505662 | + | 0.862732i | \(0.331248\pi\) | |||||||
\(384\) | 6.16421 | 0.314566 | ||||||||
\(385\) | −10.7617 | −0.548466 | ||||||||
\(386\) | −9.66595 | −0.491984 | ||||||||
\(387\) | −10.3388 | −0.525552 | ||||||||
\(388\) | 2.75220 | 0.139722 | ||||||||
\(389\) | −31.7604 | −1.61032 | −0.805159 | − | 0.593059i | \(-0.797920\pi\) | ||||
−0.805159 | + | 0.593059i | \(0.797920\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.4203 | −0.678695 | ||||||||
\(392\) | 3.04892 | 0.153994 | ||||||||
\(393\) | 5.35550 | 0.270149 | ||||||||
\(394\) | 12.5825 | 0.633896 | ||||||||
\(395\) | −10.4931 | −0.527966 | ||||||||
\(396\) | 1.56013 | 0.0783996 | ||||||||
\(397\) | 2.45734 | 0.123330 | 0.0616651 | − | 0.998097i | \(-0.480359\pi\) | ||||
0.0616651 | + | 0.998097i | \(0.480359\pi\) | |||||||
\(398\) | −27.3829 | −1.37258 | ||||||||
\(399\) | 3.36622 | 0.168522 | ||||||||
\(400\) | −12.8823 | −0.644115 | ||||||||
\(401\) | 7.91185 | 0.395099 | 0.197549 | − | 0.980293i | \(-0.436702\pi\) | ||||
0.197549 | + | 0.980293i | \(0.436702\pi\) | |||||||
\(402\) | 2.41042 | 0.120221 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −5.17210 | −0.257322 | ||||||||
\(405\) | 3.06987 | 0.152543 | ||||||||
\(406\) | 5.48751 | 0.272340 | ||||||||
\(407\) | 18.4212 | 0.913107 | ||||||||
\(408\) | −21.7558 | −1.07707 | ||||||||
\(409\) | 0.291281 | 0.0144029 | 0.00720147 | − | 0.999974i | \(-0.497708\pi\) | ||||
0.00720147 | + | 0.999974i | \(0.497708\pi\) | |||||||
\(410\) | −24.5664 | −1.21325 | ||||||||
\(411\) | −15.6533 | −0.772118 | ||||||||
\(412\) | −5.49416 | −0.270678 | ||||||||
\(413\) | 12.6505 | 0.622490 | ||||||||
\(414\) | 2.34527 | 0.115264 | ||||||||
\(415\) | 21.8206 | 1.07113 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.69765 | 0.376956 | ||||||||
\(418\) | −14.7151 | −0.719738 | ||||||||
\(419\) | −25.9101 | −1.26579 | −0.632895 | − | 0.774238i | \(-0.718134\pi\) | ||||
−0.632895 | + | 0.774238i | \(0.718134\pi\) | |||||||
\(420\) | 1.36622 | 0.0666647 | ||||||||
\(421\) | −29.4450 | −1.43506 | −0.717530 | − | 0.696527i | \(-0.754727\pi\) | ||||
−0.717530 | + | 0.696527i | \(0.754727\pi\) | |||||||
\(422\) | 24.0768 | 1.17204 | ||||||||
\(423\) | −12.1076 | −0.588693 | ||||||||
\(424\) | −31.6012 | −1.53469 | ||||||||
\(425\) | 31.5685 | 1.53130 | ||||||||
\(426\) | −14.3141 | −0.693520 | ||||||||
\(427\) | −12.5783 | −0.608708 | ||||||||
\(428\) | 4.67908 | 0.226172 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 39.5777 | 1.90860 | ||||||||
\(431\) | −13.6974 | −0.659778 | −0.329889 | − | 0.944020i | \(-0.607011\pi\) | ||||
−0.329889 | + | 0.944020i | \(0.607011\pi\) | |||||||
\(432\) | 2.91185 | 0.140097 | ||||||||
\(433\) | 11.0908 | 0.532989 | 0.266494 | − | 0.963836i | \(-0.414135\pi\) | ||||
0.266494 | + | 0.963836i | \(0.414135\pi\) | |||||||
\(434\) | 3.25215 | 0.156108 | ||||||||
\(435\) | 13.5094 | 0.647725 | ||||||||
\(436\) | 0.315001 | 0.0150858 | ||||||||
\(437\) | 6.33105 | 0.302855 | ||||||||
\(438\) | 6.12985 | 0.292895 | ||||||||
\(439\) | −5.41203 | −0.258302 | −0.129151 | − | 0.991625i | \(-0.541225\pi\) | ||||
−0.129151 | + | 0.991625i | \(0.541225\pi\) | |||||||
\(440\) | −32.8115 | −1.56423 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.5902 | 1.45339 | 0.726693 | − | 0.686962i | \(-0.241056\pi\) | ||||
0.726693 | + | 0.686962i | \(0.241056\pi\) | |||||||
\(444\) | −2.33862 | −0.110986 | ||||||||
\(445\) | −2.24280 | −0.106319 | ||||||||
\(446\) | −23.5758 | −1.11635 | ||||||||
\(447\) | −14.3574 | −0.679081 | ||||||||
\(448\) | 8.89977 | 0.420475 | ||||||||
\(449\) | 9.50119 | 0.448389 | 0.224195 | − | 0.974544i | \(-0.428025\pi\) | ||||
0.224195 | + | 0.974544i | \(0.428025\pi\) | |||||||
\(450\) | −5.51675 | −0.260062 | ||||||||
\(451\) | −22.4969 | −1.05934 | ||||||||
\(452\) | 2.91243 | 0.136989 | ||||||||
\(453\) | −18.2801 | −0.858875 | ||||||||
\(454\) | −11.7349 | −0.550744 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.2633 | 0.480624 | ||||||||
\(457\) | −26.5823 | −1.24347 | −0.621734 | − | 0.783229i | \(-0.713571\pi\) | ||||
−0.621734 | + | 0.783229i | \(0.713571\pi\) | |||||||
\(458\) | 13.4141 | 0.626800 | ||||||||
\(459\) | −7.13559 | −0.333061 | ||||||||
\(460\) | 2.56953 | 0.119805 | ||||||||
\(461\) | 11.1580 | 0.519679 | 0.259839 | − | 0.965652i | \(-0.416330\pi\) | ||||
0.259839 | + | 0.965652i | \(0.416330\pi\) | |||||||
\(462\) | −4.37139 | −0.203376 | ||||||||
\(463\) | 2.23413 | 0.103829 | 0.0519144 | − | 0.998652i | \(-0.483468\pi\) | ||||
0.0519144 | + | 0.998652i | \(0.483468\pi\) | |||||||
\(464\) | 12.8140 | 0.594876 | ||||||||
\(465\) | 8.00629 | 0.371283 | ||||||||
\(466\) | 28.2225 | 1.30738 | ||||||||
\(467\) | −19.9539 | −0.923355 | −0.461677 | − | 0.887048i | \(-0.652752\pi\) | ||||
−0.461677 | + | 0.887048i | \(0.652752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.93301 | 0.0892581 | ||||||||
\(470\) | 46.3487 | 2.13791 | ||||||||
\(471\) | −9.14988 | −0.421604 | ||||||||
\(472\) | 38.5703 | 1.77534 | ||||||||
\(473\) | 36.2436 | 1.66648 | ||||||||
\(474\) | −4.26230 | −0.195774 | ||||||||
\(475\) | −14.8925 | −0.683313 | ||||||||
\(476\) | −3.17563 | −0.145555 | ||||||||
\(477\) | −10.3647 | −0.474569 | ||||||||
\(478\) | 26.9431 | 1.23235 | ||||||||
\(479\) | −8.85542 | −0.404614 | −0.202307 | − | 0.979322i | \(-0.564844\pi\) | ||||
−0.202307 | + | 0.979322i | \(0.564844\pi\) | |||||||
\(480\) | 7.57279 | 0.345649 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −3.63896 | −0.165750 | ||||||||
\(483\) | 1.88076 | 0.0855775 | ||||||||
\(484\) | −0.573718 | −0.0260781 | ||||||||
\(485\) | −18.9845 | −0.862041 | ||||||||
\(486\) | 1.24698 | 0.0565641 | ||||||||
\(487\) | 16.7789 | 0.760323 | 0.380161 | − | 0.924920i | \(-0.375868\pi\) | ||||
0.380161 | + | 0.924920i | \(0.375868\pi\) | |||||||
\(488\) | −38.3503 | −1.73604 | ||||||||
\(489\) | 13.6215 | 0.615983 | ||||||||
\(490\) | −3.82806 | −0.172934 | ||||||||
\(491\) | −6.15382 | −0.277718 | −0.138859 | − | 0.990312i | \(-0.544343\pi\) | ||||
−0.138859 | + | 0.990312i | \(0.544343\pi\) | |||||||
\(492\) | 2.85603 | 0.128760 | ||||||||
\(493\) | −31.4011 | −1.41424 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.7617 | −0.483702 | ||||||||
\(496\) | 7.59419 | 0.340989 | ||||||||
\(497\) | −11.4790 | −0.514904 | ||||||||
\(498\) | 8.86350 | 0.397183 | ||||||||
\(499\) | 32.9818 | 1.47647 | 0.738234 | − | 0.674544i | \(-0.235660\pi\) | ||||
0.738234 | + | 0.674544i | \(0.235660\pi\) | |||||||
\(500\) | 0.786818 | 0.0351876 | ||||||||
\(501\) | 3.58810 | 0.160304 | ||||||||
\(502\) | 23.0078 | 1.02689 | ||||||||
\(503\) | 30.6076 | 1.36473 | 0.682363 | − | 0.731013i | \(-0.260952\pi\) | ||||
0.682363 | + | 0.731013i | \(0.260952\pi\) | |||||||
\(504\) | 3.04892 | 0.135810 | ||||||||
\(505\) | 35.6768 | 1.58760 | ||||||||
\(506\) | −8.22154 | −0.365492 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.38532 | 0.0614638 | ||||||||
\(509\) | −0.286603 | −0.0127035 | −0.00635174 | − | 0.999980i | \(-0.502022\pi\) | ||||
−0.00635174 | + | 0.999980i | \(0.502022\pi\) | |||||||
\(510\) | 27.3155 | 1.20955 | ||||||||
\(511\) | 4.91575 | 0.217460 | ||||||||
\(512\) | 24.9390 | 1.10216 | ||||||||
\(513\) | 3.36622 | 0.148622 | ||||||||
\(514\) | 19.4631 | 0.858483 | ||||||||
\(515\) | 37.8984 | 1.67000 | ||||||||
\(516\) | −4.60121 | −0.202557 | ||||||||
\(517\) | 42.4443 | 1.86670 | ||||||||
\(518\) | 6.55266 | 0.287907 | ||||||||
\(519\) | 5.00471 | 0.219683 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.3464 | −0.672339 | −0.336169 | − | 0.941802i | \(-0.609131\pi\) | ||||
−0.336169 | + | 0.941802i | \(0.609131\pi\) | |||||||
\(522\) | 5.48751 | 0.240182 | ||||||||
\(523\) | 24.4508 | 1.06916 | 0.534580 | − | 0.845118i | \(-0.320470\pi\) | ||||
0.534580 | + | 0.845118i | \(0.320470\pi\) | |||||||
\(524\) | 2.38342 | 0.104120 | ||||||||
\(525\) | −4.42409 | −0.193083 | ||||||||
\(526\) | 20.9587 | 0.913844 | ||||||||
\(527\) | −18.6098 | −0.810655 | ||||||||
\(528\) | −10.2078 | −0.444236 | ||||||||
\(529\) | −19.4627 | −0.846206 | ||||||||
\(530\) | 39.6769 | 1.72345 | ||||||||
\(531\) | 12.6505 | 0.548985 | ||||||||
\(532\) | 1.49811 | 0.0649513 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.911026 | −0.0394239 | ||||||||
\(535\) | −32.2760 | −1.39541 | ||||||||
\(536\) | 5.89359 | 0.254564 | ||||||||
\(537\) | 6.82831 | 0.294663 | ||||||||
\(538\) | 25.3696 | 1.09376 | ||||||||
\(539\) | −3.50559 | −0.150996 | ||||||||
\(540\) | 1.36622 | 0.0587927 | ||||||||
\(541\) | 8.48224 | 0.364680 | 0.182340 | − | 0.983236i | \(-0.441633\pi\) | ||||
0.182340 | + | 0.983236i | \(0.441633\pi\) | |||||||
\(542\) | −6.56280 | −0.281896 | ||||||||
\(543\) | −25.1122 | −1.07767 | ||||||||
\(544\) | −17.6022 | −0.754686 | ||||||||
\(545\) | −2.17286 | −0.0930749 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.2091 | 0.992352 | 0.496176 | − | 0.868222i | \(-0.334737\pi\) | ||||
0.496176 | + | 0.868222i | \(0.334737\pi\) | |||||||
\(548\) | −6.96635 | −0.297588 | ||||||||
\(549\) | −12.5783 | −0.536830 | ||||||||
\(550\) | 19.3394 | 0.824637 | ||||||||
\(551\) | 14.8135 | 0.631077 | ||||||||
\(552\) | 5.73428 | 0.244067 | ||||||||
\(553\) | −3.41810 | −0.145352 | ||||||||
\(554\) | 33.7579 | 1.43424 | ||||||||
\(555\) | 16.1316 | 0.684749 | ||||||||
\(556\) | 3.42578 | 0.145285 | ||||||||
\(557\) | 23.1593 | 0.981292 | 0.490646 | − | 0.871359i | \(-0.336761\pi\) | ||||
0.490646 | + | 0.871359i | \(0.336761\pi\) | |||||||
\(558\) | 3.25215 | 0.137675 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −8.93901 | −0.377742 | ||||||||
\(561\) | 25.0144 | 1.05611 | ||||||||
\(562\) | 28.2519 | 1.19173 | ||||||||
\(563\) | −45.3459 | −1.91110 | −0.955552 | − | 0.294824i | \(-0.904739\pi\) | ||||
−0.955552 | + | 0.294824i | \(0.904739\pi\) | |||||||
\(564\) | −5.38840 | −0.226892 | ||||||||
\(565\) | −20.0897 | −0.845181 | ||||||||
\(566\) | −3.34387 | −0.140553 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −34.9986 | −1.46851 | ||||||||
\(569\) | 1.97526 | 0.0828073 | 0.0414037 | − | 0.999143i | \(-0.486817\pi\) | ||||
0.0414037 | + | 0.999143i | \(0.486817\pi\) | |||||||
\(570\) | −12.8861 | −0.539739 | ||||||||
\(571\) | 25.0965 | 1.05025 | 0.525127 | − | 0.851024i | \(-0.324018\pi\) | ||||
0.525127 | + | 0.851024i | \(0.324018\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.4749 | 0.730023 | ||||||||
\(574\) | −8.00242 | −0.334014 | ||||||||
\(575\) | −8.32065 | −0.346995 | ||||||||
\(576\) | 8.89977 | 0.370824 | ||||||||
\(577\) | −21.2775 | −0.885793 | −0.442897 | − | 0.896573i | \(-0.646049\pi\) | ||||
−0.442897 | + | 0.896573i | \(0.646049\pi\) | |||||||
\(578\) | −42.2933 | −1.75917 | ||||||||
\(579\) | −7.75149 | −0.322141 | ||||||||
\(580\) | 6.01224 | 0.249645 | ||||||||
\(581\) | 7.10798 | 0.294889 | ||||||||
\(582\) | −7.71150 | −0.319652 | ||||||||
\(583\) | 36.3345 | 1.50482 | ||||||||
\(584\) | 14.9877 | 0.620197 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.9618 | 1.27902 | ||||||||
\(587\) | −22.4224 | −0.925470 | −0.462735 | − | 0.886497i | \(-0.653132\pi\) | ||||
−0.462735 | + | 0.886497i | \(0.653132\pi\) | |||||||
\(588\) | 0.445042 | 0.0183532 | ||||||||
\(589\) | 8.77919 | 0.361740 | ||||||||
\(590\) | −48.4269 | −1.99370 | ||||||||
\(591\) | 10.0904 | 0.415062 | ||||||||
\(592\) | 15.3013 | 0.628879 | ||||||||
\(593\) | 11.0541 | 0.453937 | 0.226969 | − | 0.973902i | \(-0.427119\pi\) | ||||
0.226969 | + | 0.973902i | \(0.427119\pi\) | |||||||
\(594\) | −4.37139 | −0.179360 | ||||||||
\(595\) | 21.9053 | 0.898030 | ||||||||
\(596\) | −6.38964 | −0.261730 | ||||||||
\(597\) | −21.9594 | −0.898739 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.6837 | −1.09027 | −0.545134 | − | 0.838349i | \(-0.683521\pi\) | ||||
−0.545134 | + | 0.838349i | \(0.683521\pi\) | |||||||
\(600\) | −13.4887 | −0.550673 | ||||||||
\(601\) | 21.0761 | 0.859714 | 0.429857 | − | 0.902897i | \(-0.358564\pi\) | ||||
0.429857 | + | 0.902897i | \(0.358564\pi\) | |||||||
\(602\) | 12.8923 | 0.525451 | ||||||||
\(603\) | 1.93301 | 0.0787183 | ||||||||
\(604\) | −8.13542 | −0.331026 | ||||||||
\(605\) | 3.95747 | 0.160894 | ||||||||
\(606\) | 14.4919 | 0.588694 | ||||||||
\(607\) | 16.7427 | 0.679564 | 0.339782 | − | 0.940504i | \(-0.389647\pi\) | ||||
0.339782 | + | 0.940504i | \(0.389647\pi\) | |||||||
\(608\) | 8.30383 | 0.336765 | ||||||||
\(609\) | 4.40064 | 0.178323 | ||||||||
\(610\) | 48.1506 | 1.94956 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.17563 | −0.128367 | ||||||||
\(613\) | −40.9378 | −1.65346 | −0.826730 | − | 0.562598i | \(-0.809802\pi\) | ||||
−0.826730 | + | 0.562598i | \(0.809802\pi\) | |||||||
\(614\) | 28.4254 | 1.14716 | ||||||||
\(615\) | −19.7007 | −0.794409 | ||||||||
\(616\) | −10.6882 | −0.430642 | ||||||||
\(617\) | −7.98627 | −0.321515 | −0.160758 | − | 0.986994i | \(-0.551394\pi\) | ||||
−0.160758 | + | 0.986994i | \(0.551394\pi\) | |||||||
\(618\) | 15.3943 | 0.619250 | ||||||||
\(619\) | 11.7272 | 0.471357 | 0.235679 | − | 0.971831i | \(-0.424269\pi\) | ||||
0.235679 | + | 0.971831i | \(0.424269\pi\) | |||||||
\(620\) | 3.56314 | 0.143099 | ||||||||
\(621\) | 1.88076 | 0.0754723 | ||||||||
\(622\) | −28.8552 | −1.15699 | ||||||||
\(623\) | −0.730586 | −0.0292703 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.5479 | −1.10191 | ||||||||
\(626\) | 21.8666 | 0.873967 | ||||||||
\(627\) | −11.8006 | −0.471270 | ||||||||
\(628\) | −4.07208 | −0.162494 | ||||||||
\(629\) | −37.4963 | −1.49507 | ||||||||
\(630\) | −3.82806 | −0.152514 | ||||||||
\(631\) | 23.2438 | 0.925320 | 0.462660 | − | 0.886536i | \(-0.346895\pi\) | ||||
0.462660 | + | 0.886536i | \(0.346895\pi\) | |||||||
\(632\) | −10.4215 | −0.414545 | ||||||||
\(633\) | 19.3081 | 0.767428 | ||||||||
\(634\) | −26.3536 | −1.04664 | ||||||||
\(635\) | −9.55586 | −0.379213 | ||||||||
\(636\) | −4.61274 | −0.182907 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −19.2369 | −0.761597 | ||||||||
\(639\) | −11.4790 | −0.454103 | ||||||||
\(640\) | −18.9233 | −0.748010 | ||||||||
\(641\) | −2.88394 | −0.113909 | −0.0569544 | − | 0.998377i | \(-0.518139\pi\) | ||||
−0.0569544 | + | 0.998377i | \(0.518139\pi\) | |||||||
\(642\) | −13.1105 | −0.517430 | ||||||||
\(643\) | 2.36239 | 0.0931636 | 0.0465818 | − | 0.998914i | \(-0.485167\pi\) | ||||
0.0465818 | + | 0.998914i | \(0.485167\pi\) | |||||||
\(644\) | 0.837017 | 0.0329831 | ||||||||
\(645\) | 31.7388 | 1.24972 | ||||||||
\(646\) | 29.9524 | 1.17846 | ||||||||
\(647\) | 7.21370 | 0.283600 | 0.141800 | − | 0.989895i | \(-0.454711\pi\) | ||||
0.141800 | + | 0.989895i | \(0.454711\pi\) | |||||||
\(648\) | 3.04892 | 0.119773 | ||||||||
\(649\) | −44.3474 | −1.74079 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.60803 | 0.102217 | ||||||||
\(652\) | 6.06212 | 0.237411 | ||||||||
\(653\) | −9.44736 | −0.369704 | −0.184852 | − | 0.982766i | \(-0.559181\pi\) | ||||
−0.184852 | + | 0.982766i | \(0.559181\pi\) | |||||||
\(654\) | −0.882613 | −0.0345129 | ||||||||
\(655\) | −16.4407 | −0.642391 | ||||||||
\(656\) | −18.6866 | −0.729591 | ||||||||
\(657\) | 4.91575 | 0.191782 | ||||||||
\(658\) | 15.0980 | 0.588580 | ||||||||
\(659\) | −25.1033 | −0.977884 | −0.488942 | − | 0.872316i | \(-0.662617\pi\) | ||||
−0.488942 | + | 0.872316i | \(0.662617\pi\) | |||||||
\(660\) | −4.78940 | −0.186427 | ||||||||
\(661\) | 30.8959 | 1.20171 | 0.600855 | − | 0.799358i | \(-0.294827\pi\) | ||||
0.600855 | + | 0.799358i | \(0.294827\pi\) | |||||||
\(662\) | 24.4973 | 0.952113 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 21.6716 | 0.841023 | ||||||||
\(665\) | −10.3339 | −0.400730 | ||||||||
\(666\) | 6.55266 | 0.253911 | ||||||||
\(667\) | 8.27654 | 0.320469 | ||||||||
\(668\) | 1.59685 | 0.0617841 | ||||||||
\(669\) | −18.9063 | −0.730961 | ||||||||
\(670\) | −7.39969 | −0.285875 | ||||||||
\(671\) | 44.0944 | 1.70225 | ||||||||
\(672\) | 2.46681 | 0.0951593 | ||||||||
\(673\) | 5.84117 | 0.225161 | 0.112580 | − | 0.993643i | \(-0.464088\pi\) | ||||
0.112580 | + | 0.993643i | \(0.464088\pi\) | |||||||
\(674\) | −0.732515 | −0.0282154 | ||||||||
\(675\) | −4.42409 | −0.170283 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.7932 | 0.683848 | 0.341924 | − | 0.939728i | \(-0.388921\pi\) | ||||
0.341924 | + | 0.939728i | \(0.388921\pi\) | |||||||
\(678\) | −8.16044 | −0.313400 | ||||||||
\(679\) | −6.18414 | −0.237325 | ||||||||
\(680\) | 66.7875 | 2.56118 | ||||||||
\(681\) | −9.41062 | −0.360616 | ||||||||
\(682\) | −11.4007 | −0.436556 | ||||||||
\(683\) | −26.0580 | −0.997081 | −0.498541 | − | 0.866866i | \(-0.666131\pi\) | ||||
−0.498541 | + | 0.866866i | \(0.666131\pi\) | |||||||
\(684\) | 1.49811 | 0.0572816 | ||||||||
\(685\) | 48.0534 | 1.83603 | ||||||||
\(686\) | −1.24698 | −0.0476099 | ||||||||
\(687\) | 10.7573 | 0.410416 | ||||||||
\(688\) | 30.1051 | 1.14775 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −7.19967 | −0.274087 | ||||||||
\(691\) | 30.3760 | 1.15556 | 0.577779 | − | 0.816193i | \(-0.303920\pi\) | ||||
0.577779 | + | 0.816193i | \(0.303920\pi\) | |||||||
\(692\) | 2.22731 | 0.0846695 | ||||||||
\(693\) | −3.50559 | −0.133166 | ||||||||
\(694\) | 20.4798 | 0.777404 | ||||||||
\(695\) | −23.6308 | −0.896367 | ||||||||
\(696\) | 13.4172 | 0.508577 | ||||||||
\(697\) | 45.7922 | 1.73450 | ||||||||
\(698\) | −43.0415 | −1.62914 | ||||||||
\(699\) | 22.6327 | 0.856046 | ||||||||
\(700\) | −1.96891 | −0.0744176 | ||||||||
\(701\) | −11.1900 | −0.422641 | −0.211321 | − | 0.977417i | \(-0.567776\pi\) | ||||
−0.211321 | + | 0.977417i | \(0.567776\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.6889 | 0.667150 | ||||||||
\(704\) | −31.1989 | −1.17585 | ||||||||
\(705\) | 37.1688 | 1.39986 | ||||||||
\(706\) | −36.4357 | −1.37127 | ||||||||
\(707\) | 11.6216 | 0.437076 | ||||||||
\(708\) | 5.63000 | 0.211588 | ||||||||
\(709\) | −48.9630 | −1.83884 | −0.919422 | − | 0.393273i | \(-0.871343\pi\) | ||||
−0.919422 | + | 0.393273i | \(0.871343\pi\) | |||||||
\(710\) | 43.9424 | 1.64913 | ||||||||
\(711\) | −3.41810 | −0.128189 | ||||||||
\(712\) | −2.22750 | −0.0834790 | ||||||||
\(713\) | 4.90507 | 0.183696 | ||||||||
\(714\) | 8.89793 | 0.332997 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.03888 | 0.113568 | ||||||||
\(717\) | 21.6067 | 0.806916 | ||||||||
\(718\) | 10.4385 | 0.389563 | ||||||||
\(719\) | −13.9878 | −0.521655 | −0.260828 | − | 0.965385i | \(-0.583995\pi\) | ||||
−0.260828 | + | 0.965385i | \(0.583995\pi\) | |||||||
\(720\) | −8.93901 | −0.333137 | ||||||||
\(721\) | 12.3453 | 0.459762 | ||||||||
\(722\) | 9.56254 | 0.355881 | ||||||||
\(723\) | −2.91822 | −0.108530 | ||||||||
\(724\) | −11.1760 | −0.415353 | ||||||||
\(725\) | −19.4688 | −0.723054 | ||||||||
\(726\) | 1.60752 | 0.0596608 | ||||||||
\(727\) | −10.7215 | −0.397640 | −0.198820 | − | 0.980036i | \(-0.563711\pi\) | ||||
−0.198820 | + | 0.980036i | \(0.563711\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −18.8178 | −0.696479 | ||||||||
\(731\) | −73.7736 | −2.72861 | ||||||||
\(732\) | −5.59788 | −0.206904 | ||||||||
\(733\) | −16.6709 | −0.615753 | −0.307877 | − | 0.951426i | \(-0.599618\pi\) | ||||
−0.307877 | + | 0.951426i | \(0.599618\pi\) | |||||||
\(734\) | 4.03684 | 0.149003 | ||||||||
\(735\) | −3.06987 | −0.113234 | ||||||||
\(736\) | 4.63948 | 0.171014 | ||||||||
\(737\) | −6.77633 | −0.249609 | ||||||||
\(738\) | −8.00242 | −0.294573 | ||||||||
\(739\) | −40.7050 | −1.49736 | −0.748678 | − | 0.662934i | \(-0.769311\pi\) | ||||
−0.748678 | + | 0.662934i | \(0.769311\pi\) | |||||||
\(740\) | 7.17925 | 0.263914 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.9246 | 0.474478 | ||||||||
\(743\) | 47.9898 | 1.76057 | 0.880287 | − | 0.474442i | \(-0.157350\pi\) | ||||
0.880287 | + | 0.474442i | \(0.157350\pi\) | |||||||
\(744\) | 7.95165 | 0.291522 | ||||||||
\(745\) | 44.0753 | 1.61479 | ||||||||
\(746\) | −25.9407 | −0.949755 | ||||||||
\(747\) | 7.10798 | 0.260067 | ||||||||
\(748\) | 11.1325 | 0.407043 | ||||||||
\(749\) | −10.5138 | −0.384166 | ||||||||
\(750\) | −2.20462 | −0.0805012 | ||||||||
\(751\) | −8.38503 | −0.305974 | −0.152987 | − | 0.988228i | \(-0.548889\pi\) | ||||
−0.152987 | + | 0.988228i | \(0.548889\pi\) | |||||||
\(752\) | 35.2556 | 1.28564 | ||||||||
\(753\) | 18.4508 | 0.672384 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 56.1176 | 2.04233 | ||||||||
\(756\) | 0.445042 | 0.0161860 | ||||||||
\(757\) | −25.8828 | −0.940727 | −0.470363 | − | 0.882473i | \(-0.655877\pi\) | ||||
−0.470363 | + | 0.882473i | \(0.655877\pi\) | |||||||
\(758\) | −43.0840 | −1.56488 | ||||||||
\(759\) | −6.59317 | −0.239317 | ||||||||
\(760\) | −31.5071 | −1.14288 | ||||||||
\(761\) | 31.1680 | 1.12984 | 0.564920 | − | 0.825146i | \(-0.308907\pi\) | ||||
0.564920 | + | 0.825146i | \(0.308907\pi\) | |||||||
\(762\) | −3.88159 | −0.140615 | ||||||||
\(763\) | −0.707801 | −0.0256241 | ||||||||
\(764\) | 7.77705 | 0.281364 | ||||||||
\(765\) | 21.9053 | 0.791988 | ||||||||
\(766\) | −24.6802 | −0.891732 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 10.1129 | 0.364918 | ||||||||
\(769\) | 6.07920 | 0.219222 | 0.109611 | − | 0.993975i | \(-0.465040\pi\) | ||||
0.109611 | + | 0.993975i | \(0.465040\pi\) | |||||||
\(770\) | 13.4196 | 0.483609 | ||||||||
\(771\) | 15.6082 | 0.562117 | ||||||||
\(772\) | −3.44974 | −0.124159 | ||||||||
\(773\) | −18.9735 | −0.682428 | −0.341214 | − | 0.939986i | \(-0.610838\pi\) | ||||
−0.341214 | + | 0.939986i | \(0.610838\pi\) | |||||||
\(774\) | 12.8923 | 0.463404 | ||||||||
\(775\) | −11.5381 | −0.414462 | ||||||||
\(776\) | −18.8549 | −0.676853 | ||||||||
\(777\) | 5.25483 | 0.188516 | ||||||||
\(778\) | 39.6046 | 1.41989 | ||||||||
\(779\) | −21.6025 | −0.773990 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.2407 | 1.43992 | ||||||||
\(782\) | 16.7349 | 0.598438 | ||||||||
\(783\) | 4.40064 | 0.157266 | ||||||||
\(784\) | −2.91185 | −0.103995 | ||||||||
\(785\) | 28.0889 | 1.00254 | ||||||||
\(786\) | −6.67820 | −0.238204 | ||||||||
\(787\) | 11.5758 | 0.412634 | 0.206317 | − | 0.978485i | \(-0.433852\pi\) | ||||
0.206317 | + | 0.978485i | \(0.433852\pi\) | |||||||
\(788\) | 4.49063 | 0.159972 | ||||||||
\(789\) | 16.8076 | 0.598366 | ||||||||
\(790\) | 13.0847 | 0.465533 | ||||||||
\(791\) | −6.54416 | −0.232684 | ||||||||
\(792\) | −10.6882 | −0.379790 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −3.06425 | −0.108746 | ||||||||
\(795\) | 31.8184 | 1.12848 | ||||||||
\(796\) | −9.77286 | −0.346390 | ||||||||
\(797\) | 24.5622 | 0.870039 | 0.435020 | − | 0.900421i | \(-0.356741\pi\) | ||||
0.435020 | + | 0.900421i | \(0.356741\pi\) | |||||||
\(798\) | −4.19761 | −0.148594 | ||||||||
\(799\) | −86.3950 | −3.05643 | ||||||||
\(800\) | −10.9134 | −0.385847 | ||||||||
\(801\) | −0.730586 | −0.0258140 | ||||||||
\(802\) | −9.86591 | −0.348378 | ||||||||
\(803\) | −17.2326 | −0.608125 | ||||||||
\(804\) | 0.860271 | 0.0303394 | ||||||||
\(805\) | −5.77368 | −0.203496 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.3448 | 0.716172 | ||||||||
\(808\) | 35.4333 | 1.24654 | ||||||||
\(809\) | −1.70053 | −0.0597876 | −0.0298938 | − | 0.999553i | \(-0.509517\pi\) | ||||
−0.0298938 | + | 0.999553i | \(0.509517\pi\) | |||||||
\(810\) | −3.82806 | −0.134504 | ||||||||
\(811\) | −8.85787 | −0.311042 | −0.155521 | − | 0.987833i | \(-0.549706\pi\) | ||||
−0.155521 | + | 0.987833i | \(0.549706\pi\) | |||||||
\(812\) | 1.95847 | 0.0687288 | ||||||||
\(813\) | −5.26295 | −0.184580 | ||||||||
\(814\) | −22.9709 | −0.805130 | ||||||||
\(815\) | −41.8161 | −1.46475 | ||||||||
\(816\) | 20.7778 | 0.727368 | ||||||||
\(817\) | 34.8028 | 1.21759 | ||||||||
\(818\) | −0.363222 | −0.0126998 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.76763 | −0.306179 | ||||||||
\(821\) | 34.4523 | 1.20239 | 0.601197 | − | 0.799101i | \(-0.294691\pi\) | ||||
0.601197 | + | 0.799101i | \(0.294691\pi\) | |||||||
\(822\) | 19.5193 | 0.680813 | ||||||||
\(823\) | 38.6660 | 1.34781 | 0.673906 | − | 0.738817i | \(-0.264615\pi\) | ||||
0.673906 | + | 0.738817i | \(0.264615\pi\) | |||||||
\(824\) | 37.6397 | 1.31124 | ||||||||
\(825\) | 15.5090 | 0.539955 | ||||||||
\(826\) | −15.7749 | −0.548879 | ||||||||
\(827\) | 18.0478 | 0.627582 | 0.313791 | − | 0.949492i | \(-0.398401\pi\) | ||||
0.313791 | + | 0.949492i | \(0.398401\pi\) | |||||||
\(828\) | 0.837017 | 0.0290883 | ||||||||
\(829\) | −42.3679 | −1.47150 | −0.735749 | − | 0.677254i | \(-0.763170\pi\) | ||||
−0.735749 | + | 0.677254i | \(0.763170\pi\) | |||||||
\(830\) | −27.2098 | −0.944466 | ||||||||
\(831\) | 27.0717 | 0.939108 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.13559 | 0.247233 | ||||||||
\(834\) | −9.59882 | −0.332380 | ||||||||
\(835\) | −11.0150 | −0.381189 | ||||||||
\(836\) | −5.25175 | −0.181636 | ||||||||
\(837\) | 2.60803 | 0.0901465 | ||||||||
\(838\) | 32.3093 | 1.11611 | ||||||||
\(839\) | 16.0041 | 0.552523 | 0.276262 | − | 0.961082i | \(-0.410904\pi\) | ||||
0.276262 | + | 0.961082i | \(0.410904\pi\) | |||||||
\(840\) | −9.35977 | −0.322943 | ||||||||
\(841\) | −9.63438 | −0.332220 | ||||||||
\(842\) | 36.7173 | 1.26536 | ||||||||
\(843\) | 22.6562 | 0.780323 | ||||||||
\(844\) | 8.59291 | 0.295780 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 15.0980 | 0.519078 | ||||||||
\(847\) | 1.28913 | 0.0442952 | ||||||||
\(848\) | 30.1806 | 1.03641 | ||||||||
\(849\) | −2.68158 | −0.0920315 | ||||||||
\(850\) | −39.3653 | −1.35022 | ||||||||
\(851\) | 9.88307 | 0.338787 | ||||||||
\(852\) | −5.10864 | −0.175019 | ||||||||
\(853\) | −45.4092 | −1.55478 | −0.777391 | − | 0.629017i | \(-0.783457\pi\) | ||||
−0.777391 | + | 0.629017i | \(0.783457\pi\) | |||||||
\(854\) | 15.6849 | 0.536727 | ||||||||
\(855\) | −10.3339 | −0.353410 | ||||||||
\(856\) | −32.0557 | −1.09564 | ||||||||
\(857\) | 4.77756 | 0.163198 | 0.0815991 | − | 0.996665i | \(-0.473997\pi\) | ||||
0.0815991 | + | 0.996665i | \(0.473997\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.175468 | 0.00598688 | 0.00299344 | − | 0.999996i | \(-0.499047\pi\) | ||||
0.00299344 | + | 0.999996i | \(0.499047\pi\) | |||||||
\(860\) | 14.1251 | 0.481662 | ||||||||
\(861\) | −6.41744 | −0.218706 | ||||||||
\(862\) | 17.0803 | 0.581758 | ||||||||
\(863\) | −23.4266 | −0.797450 | −0.398725 | − | 0.917071i | \(-0.630547\pi\) | ||||
−0.398725 | + | 0.917071i | \(0.630547\pi\) | |||||||
\(864\) | 2.46681 | 0.0839227 | ||||||||
\(865\) | −15.3638 | −0.522385 | ||||||||
\(866\) | −13.8300 | −0.469962 | ||||||||
\(867\) | −33.9166 | −1.15187 | ||||||||
\(868\) | 1.16068 | 0.0393961 | ||||||||
\(869\) | 11.9824 | 0.406477 | ||||||||
\(870\) | −16.8459 | −0.571130 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −2.15803 | −0.0730800 | ||||||||
\(873\) | −6.18414 | −0.209301 | ||||||||
\(874\) | −7.89469 | −0.267042 | ||||||||
\(875\) | −1.76796 | −0.0597681 | ||||||||
\(876\) | 2.18772 | 0.0739161 | ||||||||
\(877\) | −42.1109 | −1.42199 | −0.710993 | − | 0.703200i | \(-0.751754\pi\) | ||||
−0.710993 | + | 0.703200i | \(0.751754\pi\) | |||||||
\(878\) | 6.74868 | 0.227757 | ||||||||
\(879\) | 24.8294 | 0.837477 | ||||||||
\(880\) | 31.3365 | 1.05635 | ||||||||
\(881\) | 38.1193 | 1.28427 | 0.642137 | − | 0.766590i | \(-0.278048\pi\) | ||||
0.642137 | + | 0.766590i | \(0.278048\pi\) | |||||||
\(882\) | −1.24698 | −0.0419880 | ||||||||
\(883\) | 53.4646 | 1.79923 | 0.899614 | − | 0.436686i | \(-0.143848\pi\) | ||||
0.899614 | + | 0.436686i | \(0.143848\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −38.8353 | −1.30544 | ||||||||
\(886\) | −38.1454 | −1.28152 | ||||||||
\(887\) | 16.2289 | 0.544913 | 0.272457 | − | 0.962168i | \(-0.412164\pi\) | ||||
0.272457 | + | 0.962168i | \(0.412164\pi\) | |||||||
\(888\) | 16.0215 | 0.537647 | ||||||||
\(889\) | −3.11279 | −0.104400 | ||||||||
\(890\) | 2.79673 | 0.0937466 | ||||||||
\(891\) | −3.50559 | −0.117442 | ||||||||
\(892\) | −8.41411 | −0.281725 | ||||||||
\(893\) | 40.7569 | 1.36388 | ||||||||
\(894\) | 17.9034 | 0.598778 | ||||||||
\(895\) | −20.9620 | −0.700683 | ||||||||
\(896\) | −6.16421 | −0.205932 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.8478 | −0.395366 | ||||||||
\(899\) | 11.4770 | 0.382779 | ||||||||
\(900\) | −1.96891 | −0.0656302 | ||||||||
\(901\) | −73.9585 | −2.46392 | ||||||||
\(902\) | 28.0532 | 0.934068 | ||||||||
\(903\) | 10.3388 | 0.344055 | ||||||||
\(904\) | −19.9526 | −0.663614 | ||||||||
\(905\) | 77.0913 | 2.56260 | ||||||||
\(906\) | 22.7949 | 0.757311 | ||||||||
\(907\) | −38.3992 | −1.27503 | −0.637513 | − | 0.770440i | \(-0.720037\pi\) | ||||
−0.637513 | + | 0.770440i | \(0.720037\pi\) | |||||||
\(908\) | −4.18812 | −0.138988 | ||||||||
\(909\) | 11.6216 | 0.385465 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.7816 | 0.920447 | 0.460223 | − | 0.887803i | \(-0.347769\pi\) | ||||
0.460223 | + | 0.887803i | \(0.347769\pi\) | |||||||
\(912\) | −9.80194 | −0.324575 | ||||||||
\(913\) | −24.9176 | −0.824653 | ||||||||
\(914\) | 33.1476 | 1.09642 | ||||||||
\(915\) | 38.6138 | 1.27653 | ||||||||
\(916\) | 4.78744 | 0.158182 | ||||||||
\(917\) | −5.35550 | −0.176854 | ||||||||
\(918\) | 8.89793 | 0.293675 | ||||||||
\(919\) | −2.60876 | −0.0860550 | −0.0430275 | − | 0.999074i | \(-0.513700\pi\) | ||||
−0.0430275 | + | 0.999074i | \(0.513700\pi\) | |||||||
\(920\) | −17.6035 | −0.580370 | ||||||||
\(921\) | 22.7954 | 0.751134 | ||||||||
\(922\) | −13.9138 | −0.458226 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.56013 | −0.0513246 | ||||||||
\(925\) | −23.2478 | −0.764384 | ||||||||
\(926\) | −2.78591 | −0.0915508 | ||||||||
\(927\) | 12.3453 | 0.405472 | ||||||||
\(928\) | 10.8555 | 0.356351 | ||||||||
\(929\) | 1.72935 | 0.0567381 | 0.0283690 | − | 0.999598i | \(-0.490969\pi\) | ||||
0.0283690 | + | 0.999598i | \(0.490969\pi\) | |||||||
\(930\) | −9.98368 | −0.327378 | ||||||||
\(931\) | −3.36622 | −0.110323 | ||||||||
\(932\) | 10.0725 | 0.329935 | ||||||||
\(933\) | −23.1401 | −0.757573 | ||||||||
\(934\) | 24.8821 | 0.814166 | ||||||||
\(935\) | −76.7910 | −2.51133 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.0417 | −0.328047 | −0.164023 | − | 0.986456i | \(-0.552447\pi\) | ||||
−0.164023 | + | 0.986456i | \(0.552447\pi\) | |||||||
\(938\) | −2.41042 | −0.0787032 | ||||||||
\(939\) | 17.5357 | 0.572255 | ||||||||
\(940\) | 16.5417 | 0.539530 | ||||||||
\(941\) | −41.5696 | −1.35513 | −0.677565 | − | 0.735463i | \(-0.736965\pi\) | ||||
−0.677565 | + | 0.735463i | \(0.736965\pi\) | |||||||
\(942\) | 11.4097 | 0.371749 | ||||||||
\(943\) | −12.0697 | −0.393042 | ||||||||
\(944\) | −36.8364 | −1.19892 | ||||||||
\(945\) | −3.06987 | −0.0998628 | ||||||||
\(946\) | −45.1951 | −1.46942 | ||||||||
\(947\) | 3.83868 | 0.124740 | 0.0623701 | − | 0.998053i | \(-0.480134\pi\) | ||||
0.0623701 | + | 0.998053i | \(0.480134\pi\) | |||||||
\(948\) | −1.52120 | −0.0494062 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 18.5706 | 0.602510 | ||||||||
\(951\) | −21.1340 | −0.685315 | ||||||||
\(952\) | 21.7558 | 0.705110 | ||||||||
\(953\) | 53.5364 | 1.73421 | 0.867107 | − | 0.498121i | \(-0.165977\pi\) | ||||
0.867107 | + | 0.498121i | \(0.165977\pi\) | |||||||
\(954\) | 12.9246 | 0.418450 | ||||||||
\(955\) | −53.6455 | −1.73593 | ||||||||
\(956\) | 9.61587 | 0.311000 | ||||||||
\(957\) | −15.4268 | −0.498678 | ||||||||
\(958\) | 11.0425 | 0.356768 | ||||||||
\(959\) | 15.6533 | 0.505470 | ||||||||
\(960\) | −27.3211 | −0.881786 | ||||||||
\(961\) | −24.1982 | −0.780587 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.5138 | −0.338802 | ||||||||
\(964\) | −1.29873 | −0.0418293 | ||||||||
\(965\) | 23.7961 | 0.766022 | ||||||||
\(966\) | −2.34527 | −0.0754578 | ||||||||
\(967\) | 34.8048 | 1.11925 | 0.559624 | − | 0.828747i | \(-0.310946\pi\) | ||||
0.559624 | + | 0.828747i | \(0.310946\pi\) | |||||||
\(968\) | 3.93046 | 0.126330 | ||||||||
\(969\) | 24.0200 | 0.771632 | ||||||||
\(970\) | 23.6733 | 0.760103 | ||||||||
\(971\) | 0.107800 | 0.00345946 | 0.00172973 | − | 0.999999i | \(-0.499449\pi\) | ||||
0.00172973 | + | 0.999999i | \(0.499449\pi\) | |||||||
\(972\) | 0.445042 | 0.0142747 | ||||||||
\(973\) | −7.69765 | −0.246775 | ||||||||
\(974\) | −20.9229 | −0.670413 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 36.6262 | 1.17238 | ||||||||
\(977\) | 18.3161 | 0.585985 | 0.292992 | − | 0.956115i | \(-0.405349\pi\) | ||||
0.292992 | + | 0.956115i | \(0.405349\pi\) | |||||||
\(978\) | −16.9857 | −0.543142 | ||||||||
\(979\) | 2.56113 | 0.0818541 | ||||||||
\(980\) | −1.36622 | −0.0436423 | ||||||||
\(981\) | −0.707801 | −0.0225983 | ||||||||
\(982\) | 7.67369 | 0.244877 | ||||||||
\(983\) | 25.6401 | 0.817791 | 0.408896 | − | 0.912581i | \(-0.365914\pi\) | ||||
0.408896 | + | 0.912581i | \(0.365914\pi\) | |||||||
\(984\) | −19.5662 | −0.623749 | ||||||||
\(985\) | −30.9761 | −0.986980 | ||||||||
\(986\) | 39.1566 | 1.24700 | ||||||||
\(987\) | 12.1076 | 0.385390 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.4448 | 0.618310 | ||||||||
\(990\) | 13.4196 | 0.426503 | ||||||||
\(991\) | 38.2347 | 1.21457 | 0.607283 | − | 0.794486i | \(-0.292260\pi\) | ||||
0.607283 | + | 0.794486i | \(0.292260\pi\) | |||||||
\(992\) | 6.43351 | 0.204264 | ||||||||
\(993\) | 19.6453 | 0.623424 | ||||||||
\(994\) | 14.3141 | 0.454016 | ||||||||
\(995\) | 67.4125 | 2.13712 | ||||||||
\(996\) | 3.16335 | 0.100235 | ||||||||
\(997\) | 45.5428 | 1.44235 | 0.721177 | − | 0.692751i | \(-0.243602\pi\) | ||||
0.721177 | + | 0.692751i | \(0.243602\pi\) | |||||||
\(998\) | −41.1276 | −1.30187 | ||||||||
\(999\) | 5.25483 | 0.166255 |
(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 | 3549.2.a.z.1.2 | yes | 6 | |
13.12 | even | 2 | 3549.2.a.y.1.5 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.y.1.5 | ✓ | 6 | 13.12 | even | 2 | ||
3549.2.a.z.1.2 | yes | 6 | 1.1 | even | 1 | trivial |