Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(1,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("845.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.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: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 17x^{7} - 9x^{6} + 59x^{5} + 32x^{4} - 44x^{3} - 23x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.07331\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.271374 | 0.191890 | 0.0959451 | − | 0.995387i | \(-0.469413\pi\) | ||||
0.0959451 | + | 0.995387i | \(0.469413\pi\) | |||||||
\(3\) | −0.319618 | −0.184531 | −0.0922656 | − | 0.995734i | \(-0.529411\pi\) | ||||
−0.0922656 | + | 0.995734i | \(0.529411\pi\) | |||||||
\(4\) | −1.92636 | −0.963178 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.0867358 | −0.0354098 | ||||||||
\(7\) | 3.38151 | 1.27809 | 0.639046 | − | 0.769168i | \(-0.279329\pi\) | ||||
0.639046 | + | 0.769168i | \(0.279329\pi\) | |||||||
\(8\) | −1.06551 | −0.376715 | ||||||||
\(9\) | −2.89784 | −0.965948 | ||||||||
\(10\) | −0.271374 | −0.0858159 | ||||||||
\(11\) | 1.75204 | 0.528261 | 0.264131 | − | 0.964487i | \(-0.414915\pi\) | ||||
0.264131 | + | 0.964487i | \(0.414915\pi\) | |||||||
\(12\) | 0.615697 | 0.177736 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.917654 | 0.245253 | ||||||||
\(15\) | 0.319618 | 0.0825249 | ||||||||
\(16\) | 3.56356 | 0.890890 | ||||||||
\(17\) | 1.95419 | 0.473960 | 0.236980 | − | 0.971514i | \(-0.423842\pi\) | ||||
0.236980 | + | 0.971514i | \(0.423842\pi\) | |||||||
\(18\) | −0.786399 | −0.185356 | ||||||||
\(19\) | −7.13261 | −1.63633 | −0.818167 | − | 0.574981i | \(-0.805010\pi\) | ||||
−0.818167 | + | 0.574981i | \(0.805010\pi\) | |||||||
\(20\) | 1.92636 | 0.430746 | ||||||||
\(21\) | −1.08079 | −0.235848 | ||||||||
\(22\) | 0.475459 | 0.101368 | ||||||||
\(23\) | 7.61420 | 1.58767 | 0.793835 | − | 0.608133i | \(-0.208081\pi\) | ||||
0.793835 | + | 0.608133i | \(0.208081\pi\) | |||||||
\(24\) | 0.340556 | 0.0695157 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.88505 | 0.362779 | ||||||||
\(28\) | −6.51400 | −1.23103 | ||||||||
\(29\) | 3.98380 | 0.739773 | 0.369886 | − | 0.929077i | \(-0.379397\pi\) | ||||
0.369886 | + | 0.929077i | \(0.379397\pi\) | |||||||
\(30\) | 0.0867358 | 0.0158357 | ||||||||
\(31\) | 4.86923 | 0.874540 | 0.437270 | − | 0.899330i | \(-0.355945\pi\) | ||||
0.437270 | + | 0.899330i | \(0.355945\pi\) | |||||||
\(32\) | 3.09808 | 0.547668 | ||||||||
\(33\) | −0.559984 | −0.0974807 | ||||||||
\(34\) | 0.530316 | 0.0909484 | ||||||||
\(35\) | −3.38151 | −0.571580 | ||||||||
\(36\) | 5.58228 | 0.930380 | ||||||||
\(37\) | 10.5010 | 1.72635 | 0.863176 | − | 0.504903i | \(-0.168472\pi\) | ||||
0.863176 | + | 0.504903i | \(0.168472\pi\) | |||||||
\(38\) | −1.93560 | −0.313997 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.06551 | 0.168472 | ||||||||
\(41\) | 0.911110 | 0.142292 | 0.0711458 | − | 0.997466i | \(-0.477334\pi\) | ||||
0.0711458 | + | 0.997466i | \(0.477334\pi\) | |||||||
\(42\) | −0.293298 | −0.0452569 | ||||||||
\(43\) | 4.58553 | 0.699286 | 0.349643 | − | 0.936883i | \(-0.386303\pi\) | ||||
0.349643 | + | 0.936883i | \(0.386303\pi\) | |||||||
\(44\) | −3.37506 | −0.508810 | ||||||||
\(45\) | 2.89784 | 0.431985 | ||||||||
\(46\) | 2.06629 | 0.304658 | ||||||||
\(47\) | −8.58491 | −1.25224 | −0.626119 | − | 0.779728i | \(-0.715357\pi\) | ||||
−0.626119 | + | 0.779728i | \(0.715357\pi\) | |||||||
\(48\) | −1.13898 | −0.164397 | ||||||||
\(49\) | 4.43464 | 0.633520 | ||||||||
\(50\) | 0.271374 | 0.0383781 | ||||||||
\(51\) | −0.624593 | −0.0874605 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.9646 | 1.64347 | 0.821734 | − | 0.569871i | \(-0.193007\pi\) | ||||
0.821734 | + | 0.569871i | \(0.193007\pi\) | |||||||
\(54\) | 0.511554 | 0.0696137 | ||||||||
\(55\) | −1.75204 | −0.236246 | ||||||||
\(56\) | −3.60304 | −0.481476 | ||||||||
\(57\) | 2.27971 | 0.301955 | ||||||||
\(58\) | 1.08110 | 0.141955 | ||||||||
\(59\) | 3.82297 | 0.497708 | 0.248854 | − | 0.968541i | \(-0.419946\pi\) | ||||
0.248854 | + | 0.968541i | \(0.419946\pi\) | |||||||
\(60\) | −0.615697 | −0.0794862 | ||||||||
\(61\) | 7.98476 | 1.02234 | 0.511172 | − | 0.859479i | \(-0.329212\pi\) | ||||
0.511172 | + | 0.859479i | \(0.329212\pi\) | |||||||
\(62\) | 1.32138 | 0.167816 | ||||||||
\(63\) | −9.79910 | −1.23457 | ||||||||
\(64\) | −6.28638 | −0.785798 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.151965 | −0.0187056 | ||||||||
\(67\) | 0.472749 | 0.0577554 | 0.0288777 | − | 0.999583i | \(-0.490807\pi\) | ||||
0.0288777 | + | 0.999583i | \(0.490807\pi\) | |||||||
\(68\) | −3.76446 | −0.456508 | ||||||||
\(69\) | −2.43363 | −0.292975 | ||||||||
\(70\) | −0.917654 | −0.109681 | ||||||||
\(71\) | −5.50312 | −0.653101 | −0.326550 | − | 0.945180i | \(-0.605886\pi\) | ||||
−0.326550 | + | 0.945180i | \(0.605886\pi\) | |||||||
\(72\) | 3.08768 | 0.363887 | ||||||||
\(73\) | 2.93857 | 0.343934 | 0.171967 | − | 0.985103i | \(-0.444988\pi\) | ||||
0.171967 | + | 0.985103i | \(0.444988\pi\) | |||||||
\(74\) | 2.84969 | 0.331270 | ||||||||
\(75\) | −0.319618 | −0.0369063 | ||||||||
\(76\) | 13.7400 | 1.57608 | ||||||||
\(77\) | 5.92456 | 0.675167 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.09938 | 0.461216 | 0.230608 | − | 0.973047i | \(-0.425928\pi\) | ||||
0.230608 | + | 0.973047i | \(0.425928\pi\) | |||||||
\(80\) | −3.56356 | −0.398418 | ||||||||
\(81\) | 8.09104 | 0.899004 | ||||||||
\(82\) | 0.247252 | 0.0273044 | ||||||||
\(83\) | −11.7733 | −1.29229 | −0.646144 | − | 0.763215i | \(-0.723619\pi\) | ||||
−0.646144 | + | 0.763215i | \(0.723619\pi\) | |||||||
\(84\) | 2.08199 | 0.227164 | ||||||||
\(85\) | −1.95419 | −0.211961 | ||||||||
\(86\) | 1.24439 | 0.134186 | ||||||||
\(87\) | −1.27329 | −0.136511 | ||||||||
\(88\) | −1.86682 | −0.199004 | ||||||||
\(89\) | −3.85992 | −0.409151 | −0.204576 | − | 0.978851i | \(-0.565581\pi\) | ||||
−0.204576 | + | 0.978851i | \(0.565581\pi\) | |||||||
\(90\) | 0.786399 | 0.0828937 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −14.6677 | −1.52921 | ||||||||
\(93\) | −1.55629 | −0.161380 | ||||||||
\(94\) | −2.32972 | −0.240292 | ||||||||
\(95\) | 7.13261 | 0.731791 | ||||||||
\(96\) | −0.990200 | −0.101062 | ||||||||
\(97\) | −6.95775 | −0.706453 | −0.353226 | − | 0.935538i | \(-0.614915\pi\) | ||||
−0.353226 | + | 0.935538i | \(0.614915\pi\) | |||||||
\(98\) | 1.20345 | 0.121566 | ||||||||
\(99\) | −5.07715 | −0.510273 | ||||||||
\(100\) | −1.92636 | −0.192636 | ||||||||
\(101\) | −17.8923 | −1.78035 | −0.890175 | − | 0.455619i | \(-0.849418\pi\) | ||||
−0.890175 | + | 0.455619i | \(0.849418\pi\) | |||||||
\(102\) | −0.169498 | −0.0167828 | ||||||||
\(103\) | 10.2561 | 1.01056 | 0.505281 | − | 0.862955i | \(-0.331389\pi\) | ||||
0.505281 | + | 0.862955i | \(0.331389\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.08079 | 0.105474 | ||||||||
\(106\) | 3.24689 | 0.315366 | ||||||||
\(107\) | 12.8986 | 1.24696 | 0.623478 | − | 0.781841i | \(-0.285719\pi\) | ||||
0.623478 | + | 0.781841i | \(0.285719\pi\) | |||||||
\(108\) | −3.63129 | −0.349421 | ||||||||
\(109\) | 10.4476 | 1.00070 | 0.500348 | − | 0.865825i | \(-0.333206\pi\) | ||||
0.500348 | + | 0.865825i | \(0.333206\pi\) | |||||||
\(110\) | −0.475459 | −0.0453332 | ||||||||
\(111\) | −3.35630 | −0.318566 | ||||||||
\(112\) | 12.0502 | 1.13864 | ||||||||
\(113\) | −18.9766 | −1.78516 | −0.892582 | − | 0.450884i | \(-0.851109\pi\) | ||||
−0.892582 | + | 0.450884i | \(0.851109\pi\) | |||||||
\(114\) | 0.618653 | 0.0579422 | ||||||||
\(115\) | −7.61420 | −0.710028 | ||||||||
\(116\) | −7.67421 | −0.712533 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.03745 | 0.0955054 | ||||||||
\(119\) | 6.60812 | 0.605765 | ||||||||
\(120\) | −0.340556 | −0.0310883 | ||||||||
\(121\) | −7.93034 | −0.720940 | ||||||||
\(122\) | 2.16685 | 0.196178 | ||||||||
\(123\) | −0.291207 | −0.0262572 | ||||||||
\(124\) | −9.37987 | −0.842337 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.65922 | −0.236902 | ||||||||
\(127\) | −9.88489 | −0.877142 | −0.438571 | − | 0.898697i | \(-0.644515\pi\) | ||||
−0.438571 | + | 0.898697i | \(0.644515\pi\) | |||||||
\(128\) | −7.90212 | −0.698455 | ||||||||
\(129\) | −1.46561 | −0.129040 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.4705 | −1.00218 | −0.501089 | − | 0.865396i | \(-0.667067\pi\) | ||||
−0.501089 | + | 0.865396i | \(0.667067\pi\) | |||||||
\(132\) | 1.07873 | 0.0938913 | ||||||||
\(133\) | −24.1190 | −2.09139 | ||||||||
\(134\) | 0.128292 | 0.0110827 | ||||||||
\(135\) | −1.88505 | −0.162240 | ||||||||
\(136\) | −2.08221 | −0.178548 | ||||||||
\(137\) | −13.0826 | −1.11772 | −0.558861 | − | 0.829261i | \(-0.688761\pi\) | ||||
−0.558861 | + | 0.829261i | \(0.688761\pi\) | |||||||
\(138\) | −0.660424 | −0.0562190 | ||||||||
\(139\) | 11.9762 | 1.01581 | 0.507904 | − | 0.861414i | \(-0.330421\pi\) | ||||
0.507904 | + | 0.861414i | \(0.330421\pi\) | |||||||
\(140\) | 6.51400 | 0.550534 | ||||||||
\(141\) | 2.74389 | 0.231077 | ||||||||
\(142\) | −1.49340 | −0.125324 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −10.3266 | −0.860554 | ||||||||
\(145\) | −3.98380 | −0.330836 | ||||||||
\(146\) | 0.797452 | 0.0659976 | ||||||||
\(147\) | −1.41739 | −0.116904 | ||||||||
\(148\) | −20.2287 | −1.66278 | ||||||||
\(149\) | 16.3052 | 1.33577 | 0.667887 | − | 0.744262i | \(-0.267199\pi\) | ||||
0.667887 | + | 0.744262i | \(0.267199\pi\) | |||||||
\(150\) | −0.0867358 | −0.00708195 | ||||||||
\(151\) | 8.75415 | 0.712402 | 0.356201 | − | 0.934409i | \(-0.384072\pi\) | ||||
0.356201 | + | 0.934409i | \(0.384072\pi\) | |||||||
\(152\) | 7.59987 | 0.616431 | ||||||||
\(153\) | −5.66293 | −0.457821 | ||||||||
\(154\) | 1.60777 | 0.129558 | ||||||||
\(155\) | −4.86923 | −0.391106 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.48821 | 0.517816 | 0.258908 | − | 0.965902i | \(-0.416637\pi\) | ||||
0.258908 | + | 0.965902i | \(0.416637\pi\) | |||||||
\(158\) | 1.11246 | 0.0885029 | ||||||||
\(159\) | −3.82411 | −0.303271 | ||||||||
\(160\) | −3.09808 | −0.244925 | ||||||||
\(161\) | 25.7475 | 2.02919 | ||||||||
\(162\) | 2.19570 | 0.172510 | ||||||||
\(163\) | −3.84933 | −0.301503 | −0.150751 | − | 0.988572i | \(-0.548169\pi\) | ||||
−0.150751 | + | 0.988572i | \(0.548169\pi\) | |||||||
\(164\) | −1.75512 | −0.137052 | ||||||||
\(165\) | 0.559984 | 0.0435947 | ||||||||
\(166\) | −3.19497 | −0.247977 | ||||||||
\(167\) | −6.85894 | −0.530760 | −0.265380 | − | 0.964144i | \(-0.585497\pi\) | ||||
−0.265380 | + | 0.964144i | \(0.585497\pi\) | |||||||
\(168\) | 1.15159 | 0.0888474 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.530316 | −0.0406733 | ||||||||
\(171\) | 20.6692 | 1.58061 | ||||||||
\(172\) | −8.83336 | −0.673537 | ||||||||
\(173\) | 16.0204 | 1.21801 | 0.609005 | − | 0.793166i | \(-0.291569\pi\) | ||||
0.609005 | + | 0.793166i | \(0.291569\pi\) | |||||||
\(174\) | −0.345538 | −0.0261952 | ||||||||
\(175\) | 3.38151 | 0.255618 | ||||||||
\(176\) | 6.24352 | 0.470623 | ||||||||
\(177\) | −1.22189 | −0.0918428 | ||||||||
\(178\) | −1.04748 | −0.0785121 | ||||||||
\(179\) | −8.08309 | −0.604158 | −0.302079 | − | 0.953283i | \(-0.597681\pi\) | ||||
−0.302079 | + | 0.953283i | \(0.597681\pi\) | |||||||
\(180\) | −5.58228 | −0.416079 | ||||||||
\(181\) | 11.0898 | 0.824298 | 0.412149 | − | 0.911117i | \(-0.364778\pi\) | ||||
0.412149 | + | 0.911117i | \(0.364778\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.55207 | −0.188654 | ||||||||
\(184\) | −8.11301 | −0.598099 | ||||||||
\(185\) | −10.5010 | −0.772048 | ||||||||
\(186\) | −0.422337 | −0.0309672 | ||||||||
\(187\) | 3.42382 | 0.250375 | ||||||||
\(188\) | 16.5376 | 1.20613 | ||||||||
\(189\) | 6.37434 | 0.463665 | ||||||||
\(190\) | 1.93560 | 0.140424 | ||||||||
\(191\) | 21.7532 | 1.57401 | 0.787003 | − | 0.616949i | \(-0.211631\pi\) | ||||
0.787003 | + | 0.616949i | \(0.211631\pi\) | |||||||
\(192\) | 2.00924 | 0.145004 | ||||||||
\(193\) | −22.5285 | −1.62164 | −0.810820 | − | 0.585296i | \(-0.800978\pi\) | ||||
−0.810820 | + | 0.585296i | \(0.800978\pi\) | |||||||
\(194\) | −1.88815 | −0.135561 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.54270 | −0.610193 | ||||||||
\(197\) | 17.2749 | 1.23078 | 0.615392 | − | 0.788221i | \(-0.288998\pi\) | ||||
0.615392 | + | 0.788221i | \(0.288998\pi\) | |||||||
\(198\) | −1.37781 | −0.0979164 | ||||||||
\(199\) | 17.4901 | 1.23984 | 0.619919 | − | 0.784666i | \(-0.287166\pi\) | ||||
0.619919 | + | 0.784666i | \(0.287166\pi\) | |||||||
\(200\) | −1.06551 | −0.0753430 | ||||||||
\(201\) | −0.151099 | −0.0106577 | ||||||||
\(202\) | −4.85550 | −0.341632 | ||||||||
\(203\) | 13.4713 | 0.945498 | ||||||||
\(204\) | 1.20319 | 0.0842400 | ||||||||
\(205\) | −0.911110 | −0.0636347 | ||||||||
\(206\) | 2.78323 | 0.193917 | ||||||||
\(207\) | −22.0648 | −1.53361 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.4967 | −0.864412 | ||||||||
\(210\) | 0.293298 | 0.0202395 | ||||||||
\(211\) | 6.33563 | 0.436163 | 0.218081 | − | 0.975931i | \(-0.430020\pi\) | ||||
0.218081 | + | 0.975931i | \(0.430020\pi\) | |||||||
\(212\) | −23.0481 | −1.58295 | ||||||||
\(213\) | 1.75889 | 0.120517 | ||||||||
\(214\) | 3.50034 | 0.239279 | ||||||||
\(215\) | −4.58553 | −0.312730 | ||||||||
\(216\) | −2.00855 | −0.136664 | ||||||||
\(217\) | 16.4654 | 1.11774 | ||||||||
\(218\) | 2.83520 | 0.192024 | ||||||||
\(219\) | −0.939220 | −0.0634666 | ||||||||
\(220\) | 3.37506 | 0.227547 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.910812 | −0.0611297 | ||||||||
\(223\) | −23.4948 | −1.57333 | −0.786664 | − | 0.617381i | \(-0.788194\pi\) | ||||
−0.786664 | + | 0.617381i | \(0.788194\pi\) | |||||||
\(224\) | 10.4762 | 0.699970 | ||||||||
\(225\) | −2.89784 | −0.193190 | ||||||||
\(226\) | −5.14974 | −0.342556 | ||||||||
\(227\) | −9.59397 | −0.636774 | −0.318387 | − | 0.947961i | \(-0.603141\pi\) | ||||
−0.318387 | + | 0.947961i | \(0.603141\pi\) | |||||||
\(228\) | −4.39153 | −0.290836 | ||||||||
\(229\) | 7.23000 | 0.477772 | 0.238886 | − | 0.971048i | \(-0.423218\pi\) | ||||
0.238886 | + | 0.971048i | \(0.423218\pi\) | |||||||
\(230\) | −2.06629 | −0.136247 | ||||||||
\(231\) | −1.89359 | −0.124589 | ||||||||
\(232\) | −4.24478 | −0.278683 | ||||||||
\(233\) | −0.429924 | −0.0281652 | −0.0140826 | − | 0.999901i | \(-0.504483\pi\) | ||||
−0.0140826 | + | 0.999901i | \(0.504483\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.58491 | 0.560017 | ||||||||
\(236\) | −7.36440 | −0.479382 | ||||||||
\(237\) | −1.31023 | −0.0851088 | ||||||||
\(238\) | 1.79327 | 0.116240 | ||||||||
\(239\) | 12.7450 | 0.824405 | 0.412203 | − | 0.911092i | \(-0.364760\pi\) | ||||
0.412203 | + | 0.911092i | \(0.364760\pi\) | |||||||
\(240\) | 1.13898 | 0.0735206 | ||||||||
\(241\) | −19.1338 | −1.23252 | −0.616258 | − | 0.787545i | \(-0.711352\pi\) | ||||
−0.616258 | + | 0.787545i | \(0.711352\pi\) | |||||||
\(242\) | −2.15209 | −0.138341 | ||||||||
\(243\) | −8.24120 | −0.528673 | ||||||||
\(244\) | −15.3815 | −0.984699 | ||||||||
\(245\) | −4.43464 | −0.283319 | ||||||||
\(246\) | −0.0790259 | −0.00503851 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5.18821 | −0.329452 | ||||||||
\(249\) | 3.76295 | 0.238468 | ||||||||
\(250\) | −0.271374 | −0.0171632 | ||||||||
\(251\) | 0.411815 | 0.0259935 | 0.0129968 | − | 0.999916i | \(-0.495863\pi\) | ||||
0.0129968 | + | 0.999916i | \(0.495863\pi\) | |||||||
\(252\) | 18.8766 | 1.18911 | ||||||||
\(253\) | 13.3404 | 0.838705 | ||||||||
\(254\) | −2.68250 | −0.168315 | ||||||||
\(255\) | 0.624593 | 0.0391135 | ||||||||
\(256\) | 10.4283 | 0.651771 | ||||||||
\(257\) | −2.47556 | −0.154421 | −0.0772105 | − | 0.997015i | \(-0.524601\pi\) | ||||
−0.0772105 | + | 0.997015i | \(0.524601\pi\) | |||||||
\(258\) | −0.397729 | −0.0247616 | ||||||||
\(259\) | 35.5093 | 2.20644 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.5444 | −0.714582 | ||||||||
\(262\) | −3.11278 | −0.192308 | ||||||||
\(263\) | −11.3591 | −0.700430 | −0.350215 | − | 0.936669i | \(-0.613892\pi\) | ||||
−0.350215 | + | 0.936669i | \(0.613892\pi\) | |||||||
\(264\) | 0.596669 | 0.0367224 | ||||||||
\(265\) | −11.9646 | −0.734981 | ||||||||
\(266\) | −6.54527 | −0.401317 | ||||||||
\(267\) | 1.23370 | 0.0755012 | ||||||||
\(268\) | −0.910682 | −0.0556288 | ||||||||
\(269\) | −29.6888 | −1.81016 | −0.905078 | − | 0.425245i | \(-0.860188\pi\) | ||||
−0.905078 | + | 0.425245i | \(0.860188\pi\) | |||||||
\(270\) | −0.511554 | −0.0311322 | ||||||||
\(271\) | 14.7761 | 0.897583 | 0.448792 | − | 0.893636i | \(-0.351855\pi\) | ||||
0.448792 | + | 0.893636i | \(0.351855\pi\) | |||||||
\(272\) | 6.96387 | 0.422247 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.55028 | −0.214480 | ||||||||
\(275\) | 1.75204 | 0.105652 | ||||||||
\(276\) | 4.68804 | 0.282187 | ||||||||
\(277\) | −1.94652 | −0.116955 | −0.0584774 | − | 0.998289i | \(-0.518625\pi\) | ||||
−0.0584774 | + | 0.998289i | \(0.518625\pi\) | |||||||
\(278\) | 3.25002 | 0.194924 | ||||||||
\(279\) | −14.1103 | −0.844760 | ||||||||
\(280\) | 3.60304 | 0.215323 | ||||||||
\(281\) | −18.5256 | −1.10515 | −0.552573 | − | 0.833464i | \(-0.686354\pi\) | ||||
−0.552573 | + | 0.833464i | \(0.686354\pi\) | |||||||
\(282\) | 0.744619 | 0.0443414 | ||||||||
\(283\) | 13.0952 | 0.778427 | 0.389214 | − | 0.921148i | \(-0.372747\pi\) | ||||
0.389214 | + | 0.921148i | \(0.372747\pi\) | |||||||
\(284\) | 10.6010 | 0.629052 | ||||||||
\(285\) | −2.27971 | −0.135038 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.08093 | 0.181862 | ||||||||
\(288\) | −8.97775 | −0.529019 | ||||||||
\(289\) | −13.1811 | −0.775362 | ||||||||
\(290\) | −1.08110 | −0.0634843 | ||||||||
\(291\) | 2.22382 | 0.130363 | ||||||||
\(292\) | −5.66074 | −0.331270 | ||||||||
\(293\) | 1.20753 | 0.0705445 | 0.0352722 | − | 0.999378i | \(-0.488770\pi\) | ||||
0.0352722 | + | 0.999378i | \(0.488770\pi\) | |||||||
\(294\) | −0.384642 | −0.0224328 | ||||||||
\(295\) | −3.82297 | −0.222582 | ||||||||
\(296\) | −11.1889 | −0.650342 | ||||||||
\(297\) | 3.30270 | 0.191642 | ||||||||
\(298\) | 4.42481 | 0.256322 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.615697 | 0.0355473 | ||||||||
\(301\) | 15.5060 | 0.893752 | ||||||||
\(302\) | 2.37565 | 0.136703 | ||||||||
\(303\) | 5.71869 | 0.328530 | ||||||||
\(304\) | −25.4175 | −1.45779 | ||||||||
\(305\) | −7.98476 | −0.457206 | ||||||||
\(306\) | −1.53677 | −0.0878514 | ||||||||
\(307\) | 21.9275 | 1.25147 | 0.625733 | − | 0.780037i | \(-0.284800\pi\) | ||||
0.625733 | + | 0.780037i | \(0.284800\pi\) | |||||||
\(308\) | −11.4128 | −0.650306 | ||||||||
\(309\) | −3.27802 | −0.186480 | ||||||||
\(310\) | −1.32138 | −0.0750494 | ||||||||
\(311\) | −12.5966 | −0.714288 | −0.357144 | − | 0.934049i | \(-0.616249\pi\) | ||||
−0.357144 | + | 0.934049i | \(0.616249\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.8268 | 1.51634 | 0.758169 | − | 0.652058i | \(-0.226094\pi\) | ||||
0.758169 | + | 0.652058i | \(0.226094\pi\) | |||||||
\(314\) | 1.76073 | 0.0993638 | ||||||||
\(315\) | 9.79910 | 0.552117 | ||||||||
\(316\) | −7.89687 | −0.444234 | ||||||||
\(317\) | −17.1279 | −0.961999 | −0.481000 | − | 0.876721i | \(-0.659726\pi\) | ||||
−0.481000 | + | 0.876721i | \(0.659726\pi\) | |||||||
\(318\) | −1.03776 | −0.0581948 | ||||||||
\(319\) | 6.97979 | 0.390793 | ||||||||
\(320\) | 6.28638 | 0.351420 | ||||||||
\(321\) | −4.12262 | −0.230102 | ||||||||
\(322\) | 6.98720 | 0.389382 | ||||||||
\(323\) | −13.9385 | −0.775557 | ||||||||
\(324\) | −15.5862 | −0.865901 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.04461 | −0.0578555 | ||||||||
\(327\) | −3.33923 | −0.184660 | ||||||||
\(328\) | −0.970798 | −0.0536033 | ||||||||
\(329\) | −29.0300 | −1.60047 | ||||||||
\(330\) | 0.151965 | 0.00836540 | ||||||||
\(331\) | 1.43062 | 0.0786338 | 0.0393169 | − | 0.999227i | \(-0.487482\pi\) | ||||
0.0393169 | + | 0.999227i | \(0.487482\pi\) | |||||||
\(332\) | 22.6796 | 1.24470 | ||||||||
\(333\) | −30.4302 | −1.66757 | ||||||||
\(334\) | −1.86134 | −0.101848 | ||||||||
\(335\) | −0.472749 | −0.0258290 | ||||||||
\(336\) | −3.85147 | −0.210115 | ||||||||
\(337\) | −7.48872 | −0.407937 | −0.203968 | − | 0.978977i | \(-0.565384\pi\) | ||||
−0.203968 | + | 0.978977i | \(0.565384\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.06524 | 0.329419 | ||||||||
\(340\) | 3.76446 | 0.204157 | ||||||||
\(341\) | 8.53111 | 0.461985 | ||||||||
\(342\) | 5.60908 | 0.303304 | ||||||||
\(343\) | −8.67480 | −0.468395 | ||||||||
\(344\) | −4.88593 | −0.263431 | ||||||||
\(345\) | 2.43363 | 0.131022 | ||||||||
\(346\) | 4.34752 | 0.233724 | ||||||||
\(347\) | 6.96813 | 0.374069 | 0.187034 | − | 0.982353i | \(-0.440112\pi\) | ||||
0.187034 | + | 0.982353i | \(0.440112\pi\) | |||||||
\(348\) | 2.45281 | 0.131485 | ||||||||
\(349\) | 21.9738 | 1.17623 | 0.588116 | − | 0.808777i | \(-0.299870\pi\) | ||||
0.588116 | + | 0.808777i | \(0.299870\pi\) | |||||||
\(350\) | 0.917654 | 0.0490507 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.42797 | 0.289312 | ||||||||
\(353\) | 13.0184 | 0.692899 | 0.346450 | − | 0.938069i | \(-0.387387\pi\) | ||||
0.346450 | + | 0.938069i | \(0.387387\pi\) | |||||||
\(354\) | −0.331589 | −0.0176237 | ||||||||
\(355\) | 5.50312 | 0.292075 | ||||||||
\(356\) | 7.43559 | 0.394085 | ||||||||
\(357\) | −2.11207 | −0.111783 | ||||||||
\(358\) | −2.19354 | −0.115932 | ||||||||
\(359\) | 9.99211 | 0.527363 | 0.263682 | − | 0.964610i | \(-0.415063\pi\) | ||||
0.263682 | + | 0.964610i | \(0.415063\pi\) | |||||||
\(360\) | −3.08768 | −0.162735 | ||||||||
\(361\) | 31.8742 | 1.67759 | ||||||||
\(362\) | 3.00948 | 0.158175 | ||||||||
\(363\) | 2.53468 | 0.133036 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.93857 | −0.153812 | ||||||||
\(366\) | −0.692564 | −0.0362009 | ||||||||
\(367\) | 25.2882 | 1.32004 | 0.660018 | − | 0.751250i | \(-0.270549\pi\) | ||||
0.660018 | + | 0.751250i | \(0.270549\pi\) | |||||||
\(368\) | 27.1337 | 1.41444 | ||||||||
\(369\) | −2.64026 | −0.137446 | ||||||||
\(370\) | −2.84969 | −0.148149 | ||||||||
\(371\) | 40.4586 | 2.10050 | ||||||||
\(372\) | 2.99797 | 0.155438 | ||||||||
\(373\) | 14.2703 | 0.738887 | 0.369444 | − | 0.929253i | \(-0.379548\pi\) | ||||
0.369444 | + | 0.929253i | \(0.379548\pi\) | |||||||
\(374\) | 0.929136 | 0.0480445 | ||||||||
\(375\) | 0.319618 | 0.0165050 | ||||||||
\(376\) | 9.14730 | 0.471736 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.72983 | 0.0889728 | ||||||||
\(379\) | 7.01341 | 0.360255 | 0.180127 | − | 0.983643i | \(-0.442349\pi\) | ||||
0.180127 | + | 0.983643i | \(0.442349\pi\) | |||||||
\(380\) | −13.7400 | −0.704845 | ||||||||
\(381\) | 3.15938 | 0.161860 | ||||||||
\(382\) | 5.90325 | 0.302036 | ||||||||
\(383\) | 4.69336 | 0.239820 | 0.119910 | − | 0.992785i | \(-0.461739\pi\) | ||||
0.119910 | + | 0.992785i | \(0.461739\pi\) | |||||||
\(384\) | 2.52565 | 0.128887 | ||||||||
\(385\) | −5.92456 | −0.301944 | ||||||||
\(386\) | −6.11365 | −0.311177 | ||||||||
\(387\) | −13.2881 | −0.675474 | ||||||||
\(388\) | 13.4031 | 0.680440 | ||||||||
\(389\) | −9.34682 | −0.473902 | −0.236951 | − | 0.971522i | \(-0.576148\pi\) | ||||
−0.236951 | + | 0.971522i | \(0.576148\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.8796 | 0.752493 | ||||||||
\(392\) | −4.72515 | −0.238656 | ||||||||
\(393\) | 3.66616 | 0.184933 | ||||||||
\(394\) | 4.68795 | 0.236176 | ||||||||
\(395\) | −4.09938 | −0.206262 | ||||||||
\(396\) | 9.78041 | 0.491484 | ||||||||
\(397\) | −21.2133 | −1.06467 | −0.532334 | − | 0.846535i | \(-0.678685\pi\) | ||||
−0.532334 | + | 0.846535i | \(0.678685\pi\) | |||||||
\(398\) | 4.74634 | 0.237913 | ||||||||
\(399\) | 7.70887 | 0.385926 | ||||||||
\(400\) | 3.56356 | 0.178178 | ||||||||
\(401\) | 18.2172 | 0.909725 | 0.454863 | − | 0.890562i | \(-0.349688\pi\) | ||||
0.454863 | + | 0.890562i | \(0.349688\pi\) | |||||||
\(402\) | −0.0410042 | −0.00204511 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 34.4669 | 1.71479 | ||||||||
\(405\) | −8.09104 | −0.402047 | ||||||||
\(406\) | 3.65575 | 0.181432 | ||||||||
\(407\) | 18.3982 | 0.911965 | ||||||||
\(408\) | 0.665510 | 0.0329477 | ||||||||
\(409\) | −4.36136 | −0.215655 | −0.107828 | − | 0.994170i | \(-0.534389\pi\) | ||||
−0.107828 | + | 0.994170i | \(0.534389\pi\) | |||||||
\(410\) | −0.247252 | −0.0122109 | ||||||||
\(411\) | 4.18143 | 0.206255 | ||||||||
\(412\) | −19.7569 | −0.973351 | ||||||||
\(413\) | 12.9274 | 0.636117 | ||||||||
\(414\) | −5.98780 | −0.294284 | ||||||||
\(415\) | 11.7733 | 0.577929 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.82780 | −0.187448 | ||||||||
\(418\) | −3.39127 | −0.165872 | ||||||||
\(419\) | 17.0555 | 0.833214 | 0.416607 | − | 0.909087i | \(-0.363219\pi\) | ||||
0.416607 | + | 0.909087i | \(0.363219\pi\) | |||||||
\(420\) | −2.08199 | −0.101591 | ||||||||
\(421\) | 1.27996 | 0.0623816 | 0.0311908 | − | 0.999513i | \(-0.490070\pi\) | ||||
0.0311908 | + | 0.999513i | \(0.490070\pi\) | |||||||
\(422\) | 1.71932 | 0.0836954 | ||||||||
\(423\) | 24.8777 | 1.20960 | ||||||||
\(424\) | −12.7484 | −0.619119 | ||||||||
\(425\) | 1.95419 | 0.0947921 | ||||||||
\(426\) | 0.477318 | 0.0231261 | ||||||||
\(427\) | 27.0006 | 1.30665 | ||||||||
\(428\) | −24.8473 | −1.20104 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.24439 | −0.0600099 | ||||||||
\(431\) | −32.8733 | −1.58345 | −0.791725 | − | 0.610878i | \(-0.790817\pi\) | ||||
−0.791725 | + | 0.610878i | \(0.790817\pi\) | |||||||
\(432\) | 6.71751 | 0.323196 | ||||||||
\(433\) | −28.2622 | −1.35819 | −0.679097 | − | 0.734048i | \(-0.737628\pi\) | ||||
−0.679097 | + | 0.734048i | \(0.737628\pi\) | |||||||
\(434\) | 4.46827 | 0.214484 | ||||||||
\(435\) | 1.27329 | 0.0610497 | ||||||||
\(436\) | −20.1257 | −0.963848 | ||||||||
\(437\) | −54.3091 | −2.59796 | ||||||||
\(438\) | −0.254880 | −0.0121786 | ||||||||
\(439\) | 26.2621 | 1.25342 | 0.626711 | − | 0.779252i | \(-0.284401\pi\) | ||||
0.626711 | + | 0.779252i | \(0.284401\pi\) | |||||||
\(440\) | 1.86682 | 0.0889972 | ||||||||
\(441\) | −12.8509 | −0.611948 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.0477 | −0.667427 | −0.333714 | − | 0.942674i | \(-0.608302\pi\) | ||||
−0.333714 | + | 0.942674i | \(0.608302\pi\) | |||||||
\(444\) | 6.46543 | 0.306836 | ||||||||
\(445\) | 3.85992 | 0.182978 | ||||||||
\(446\) | −6.37588 | −0.301906 | ||||||||
\(447\) | −5.21143 | −0.246492 | ||||||||
\(448\) | −21.2575 | −1.00432 | ||||||||
\(449\) | 4.45904 | 0.210435 | 0.105218 | − | 0.994449i | \(-0.466446\pi\) | ||||
0.105218 | + | 0.994449i | \(0.466446\pi\) | |||||||
\(450\) | −0.786399 | −0.0370712 | ||||||||
\(451\) | 1.59631 | 0.0751671 | ||||||||
\(452\) | 36.5556 | 1.71943 | ||||||||
\(453\) | −2.79798 | −0.131461 | ||||||||
\(454\) | −2.60355 | −0.122191 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.42905 | −0.113751 | ||||||||
\(457\) | −16.4149 | −0.767855 | −0.383927 | − | 0.923363i | \(-0.625429\pi\) | ||||
−0.383927 | + | 0.923363i | \(0.625429\pi\) | |||||||
\(458\) | 1.96203 | 0.0916798 | ||||||||
\(459\) | 3.68375 | 0.171943 | ||||||||
\(460\) | 14.6677 | 0.683883 | ||||||||
\(461\) | −20.5455 | −0.956899 | −0.478449 | − | 0.878115i | \(-0.658801\pi\) | ||||
−0.478449 | + | 0.878115i | \(0.658801\pi\) | |||||||
\(462\) | −0.513872 | −0.0239075 | ||||||||
\(463\) | −1.58359 | −0.0735958 | −0.0367979 | − | 0.999323i | \(-0.511716\pi\) | ||||
−0.0367979 | + | 0.999323i | \(0.511716\pi\) | |||||||
\(464\) | 14.1965 | 0.659056 | ||||||||
\(465\) | 1.55629 | 0.0721713 | ||||||||
\(466\) | −0.116670 | −0.00540463 | ||||||||
\(467\) | 5.14277 | 0.237979 | 0.118990 | − | 0.992896i | \(-0.462034\pi\) | ||||
0.118990 | + | 0.992896i | \(0.462034\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.59861 | 0.0738168 | ||||||||
\(470\) | 2.32972 | 0.107462 | ||||||||
\(471\) | −2.07375 | −0.0955532 | ||||||||
\(472\) | −4.07341 | −0.187494 | ||||||||
\(473\) | 8.03405 | 0.369406 | ||||||||
\(474\) | −0.355563 | −0.0163316 | ||||||||
\(475\) | −7.13261 | −0.327267 | ||||||||
\(476\) | −12.7296 | −0.583460 | ||||||||
\(477\) | −34.6716 | −1.58751 | ||||||||
\(478\) | 3.45866 | 0.158195 | ||||||||
\(479\) | −22.2914 | −1.01852 | −0.509260 | − | 0.860613i | \(-0.670081\pi\) | ||||
−0.509260 | + | 0.860613i | \(0.670081\pi\) | |||||||
\(480\) | 0.990200 | 0.0451962 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −5.19241 | −0.236508 | ||||||||
\(483\) | −8.22936 | −0.374449 | ||||||||
\(484\) | 15.2767 | 0.694394 | ||||||||
\(485\) | 6.95775 | 0.315935 | ||||||||
\(486\) | −2.23645 | −0.101447 | ||||||||
\(487\) | 23.4185 | 1.06119 | 0.530597 | − | 0.847624i | \(-0.321968\pi\) | ||||
0.530597 | + | 0.847624i | \(0.321968\pi\) | |||||||
\(488\) | −8.50784 | −0.385132 | ||||||||
\(489\) | 1.23031 | 0.0556367 | ||||||||
\(490\) | −1.20345 | −0.0543661 | ||||||||
\(491\) | 3.39791 | 0.153345 | 0.0766727 | − | 0.997056i | \(-0.475570\pi\) | ||||
0.0766727 | + | 0.997056i | \(0.475570\pi\) | |||||||
\(492\) | 0.560968 | 0.0252904 | ||||||||
\(493\) | 7.78509 | 0.350623 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.07715 | 0.228201 | ||||||||
\(496\) | 17.3518 | 0.779119 | ||||||||
\(497\) | −18.6089 | −0.834723 | ||||||||
\(498\) | 1.02117 | 0.0457596 | ||||||||
\(499\) | 4.87712 | 0.218330 | 0.109165 | − | 0.994024i | \(-0.465182\pi\) | ||||
0.109165 | + | 0.994024i | \(0.465182\pi\) | |||||||
\(500\) | 1.92636 | 0.0861493 | ||||||||
\(501\) | 2.19224 | 0.0979419 | ||||||||
\(502\) | 0.111756 | 0.00498791 | ||||||||
\(503\) | −13.9853 | −0.623572 | −0.311786 | − | 0.950152i | \(-0.600927\pi\) | ||||
−0.311786 | + | 0.950152i | \(0.600927\pi\) | |||||||
\(504\) | 10.4410 | 0.465081 | ||||||||
\(505\) | 17.8923 | 0.796196 | ||||||||
\(506\) | 3.62024 | 0.160939 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 19.0418 | 0.844844 | ||||||||
\(509\) | −37.0157 | −1.64069 | −0.820347 | − | 0.571866i | \(-0.806220\pi\) | ||||
−0.820347 | + | 0.571866i | \(0.806220\pi\) | |||||||
\(510\) | 0.169498 | 0.00750550 | ||||||||
\(511\) | 9.93683 | 0.439579 | ||||||||
\(512\) | 18.6342 | 0.823524 | ||||||||
\(513\) | −13.4454 | −0.593627 | ||||||||
\(514\) | −0.671801 | −0.0296319 | ||||||||
\(515\) | −10.2561 | −0.451937 | ||||||||
\(516\) | 2.82330 | 0.124289 | ||||||||
\(517\) | −15.0411 | −0.661508 | ||||||||
\(518\) | 9.63628 | 0.423394 | ||||||||
\(519\) | −5.12041 | −0.224761 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.5328 | 0.943370 | 0.471685 | − | 0.881767i | \(-0.343646\pi\) | ||||
0.471685 | + | 0.881767i | \(0.343646\pi\) | |||||||
\(522\) | −3.13286 | −0.137121 | ||||||||
\(523\) | 36.0055 | 1.57441 | 0.787204 | − | 0.616692i | \(-0.211528\pi\) | ||||
0.787204 | + | 0.616692i | \(0.211528\pi\) | |||||||
\(524\) | 22.0962 | 0.965277 | ||||||||
\(525\) | −1.08079 | −0.0471696 | ||||||||
\(526\) | −3.08255 | −0.134406 | ||||||||
\(527\) | 9.51539 | 0.414497 | ||||||||
\(528\) | −1.99554 | −0.0868446 | ||||||||
\(529\) | 34.9760 | 1.52070 | ||||||||
\(530\) | −3.24689 | −0.141036 | ||||||||
\(531\) | −11.0784 | −0.480761 | ||||||||
\(532\) | 46.4619 | 2.01438 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.334794 | 0.0144879 | ||||||||
\(535\) | −12.8986 | −0.557656 | ||||||||
\(536\) | −0.503718 | −0.0217573 | ||||||||
\(537\) | 2.58350 | 0.111486 | ||||||||
\(538\) | −8.05676 | −0.347351 | ||||||||
\(539\) | 7.76969 | 0.334664 | ||||||||
\(540\) | 3.63129 | 0.156266 | ||||||||
\(541\) | −0.123280 | −0.00530020 | −0.00265010 | − | 0.999996i | \(-0.500844\pi\) | ||||
−0.00265010 | + | 0.999996i | \(0.500844\pi\) | |||||||
\(542\) | 4.00984 | 0.172238 | ||||||||
\(543\) | −3.54449 | −0.152109 | ||||||||
\(544\) | 6.05423 | 0.259573 | ||||||||
\(545\) | −10.4476 | −0.447525 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.52166 | 0.107818 | 0.0539092 | − | 0.998546i | \(-0.482832\pi\) | ||||
0.0539092 | + | 0.998546i | \(0.482832\pi\) | |||||||
\(548\) | 25.2018 | 1.07657 | ||||||||
\(549\) | −23.1386 | −0.987531 | ||||||||
\(550\) | 0.475459 | 0.0202736 | ||||||||
\(551\) | −28.4149 | −1.21052 | ||||||||
\(552\) | 2.59306 | 0.110368 | ||||||||
\(553\) | 13.8621 | 0.589477 | ||||||||
\(554\) | −0.528233 | −0.0224425 | ||||||||
\(555\) | 3.35630 | 0.142467 | ||||||||
\(556\) | −23.0704 | −0.978403 | ||||||||
\(557\) | 0.974960 | 0.0413104 | 0.0206552 | − | 0.999787i | \(-0.493425\pi\) | ||||
0.0206552 | + | 0.999787i | \(0.493425\pi\) | |||||||
\(558\) | −3.82916 | −0.162101 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −12.0502 | −0.509215 | ||||||||
\(561\) | −1.09431 | −0.0462020 | ||||||||
\(562\) | −5.02737 | −0.212067 | ||||||||
\(563\) | −31.5376 | −1.32915 | −0.664576 | − | 0.747220i | \(-0.731388\pi\) | ||||
−0.664576 | + | 0.747220i | \(0.731388\pi\) | |||||||
\(564\) | −5.28570 | −0.222568 | ||||||||
\(565\) | 18.9766 | 0.798350 | ||||||||
\(566\) | 3.55369 | 0.149373 | ||||||||
\(567\) | 27.3600 | 1.14901 | ||||||||
\(568\) | 5.86363 | 0.246033 | ||||||||
\(569\) | 24.8762 | 1.04287 | 0.521433 | − | 0.853292i | \(-0.325398\pi\) | ||||
0.521433 | + | 0.853292i | \(0.325398\pi\) | |||||||
\(570\) | −0.618653 | −0.0259125 | ||||||||
\(571\) | −7.92958 | −0.331843 | −0.165921 | − | 0.986139i | \(-0.553060\pi\) | ||||
−0.165921 | + | 0.986139i | \(0.553060\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.95271 | −0.290453 | ||||||||
\(574\) | 0.836085 | 0.0348975 | ||||||||
\(575\) | 7.61420 | 0.317534 | ||||||||
\(576\) | 18.2170 | 0.759040 | ||||||||
\(577\) | −19.0769 | −0.794180 | −0.397090 | − | 0.917780i | \(-0.629980\pi\) | ||||
−0.397090 | + | 0.917780i | \(0.629980\pi\) | |||||||
\(578\) | −3.57702 | −0.148784 | ||||||||
\(579\) | 7.20051 | 0.299243 | ||||||||
\(580\) | 7.67421 | 0.318654 | ||||||||
\(581\) | −39.8116 | −1.65166 | ||||||||
\(582\) | 0.603487 | 0.0250153 | ||||||||
\(583\) | 20.9626 | 0.868181 | ||||||||
\(584\) | −3.13108 | −0.129565 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.327691 | 0.0135368 | ||||||||
\(587\) | 19.1196 | 0.789149 | 0.394574 | − | 0.918864i | \(-0.370892\pi\) | ||||
0.394574 | + | 0.918864i | \(0.370892\pi\) | |||||||
\(588\) | 2.73040 | 0.112600 | ||||||||
\(589\) | −34.7303 | −1.43104 | ||||||||
\(590\) | −1.03745 | −0.0427113 | ||||||||
\(591\) | −5.52136 | −0.227118 | ||||||||
\(592\) | 37.4209 | 1.53799 | ||||||||
\(593\) | 36.9354 | 1.51676 | 0.758379 | − | 0.651814i | \(-0.225992\pi\) | ||||
0.758379 | + | 0.651814i | \(0.225992\pi\) | |||||||
\(594\) | 0.896266 | 0.0367742 | ||||||||
\(595\) | −6.60812 | −0.270906 | ||||||||
\(596\) | −31.4096 | −1.28659 | ||||||||
\(597\) | −5.59013 | −0.228789 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.19953 | −0.212447 | −0.106224 | − | 0.994342i | \(-0.533876\pi\) | ||||
−0.106224 | + | 0.994342i | \(0.533876\pi\) | |||||||
\(600\) | 0.340556 | 0.0139031 | ||||||||
\(601\) | −28.3207 | −1.15523 | −0.577613 | − | 0.816311i | \(-0.696016\pi\) | ||||
−0.577613 | + | 0.816311i | \(0.696016\pi\) | |||||||
\(602\) | 4.20793 | 0.171502 | ||||||||
\(603\) | −1.36995 | −0.0557887 | ||||||||
\(604\) | −16.8636 | −0.686170 | ||||||||
\(605\) | 7.93034 | 0.322414 | ||||||||
\(606\) | 1.55190 | 0.0630417 | ||||||||
\(607\) | 20.1615 | 0.818332 | 0.409166 | − | 0.912460i | \(-0.365820\pi\) | ||||
0.409166 | + | 0.912460i | \(0.365820\pi\) | |||||||
\(608\) | −22.0974 | −0.896168 | ||||||||
\(609\) | −4.30565 | −0.174474 | ||||||||
\(610\) | −2.16685 | −0.0877333 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 10.9088 | 0.440963 | ||||||||
\(613\) | 18.8190 | 0.760094 | 0.380047 | − | 0.924967i | \(-0.375908\pi\) | ||||
0.380047 | + | 0.924967i | \(0.375908\pi\) | |||||||
\(614\) | 5.95054 | 0.240144 | ||||||||
\(615\) | 0.291207 | 0.0117426 | ||||||||
\(616\) | −6.31268 | −0.254345 | ||||||||
\(617\) | −2.82492 | −0.113727 | −0.0568634 | − | 0.998382i | \(-0.518110\pi\) | ||||
−0.0568634 | + | 0.998382i | \(0.518110\pi\) | |||||||
\(618\) | −0.889570 | −0.0357837 | ||||||||
\(619\) | 15.6686 | 0.629773 | 0.314886 | − | 0.949129i | \(-0.398034\pi\) | ||||
0.314886 | + | 0.949129i | \(0.398034\pi\) | |||||||
\(620\) | 9.37987 | 0.376705 | ||||||||
\(621\) | 14.3532 | 0.575973 | ||||||||
\(622\) | −3.41839 | −0.137065 | ||||||||
\(623\) | −13.0524 | −0.522933 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 7.28008 | 0.290971 | ||||||||
\(627\) | 3.99415 | 0.159511 | ||||||||
\(628\) | −12.4986 | −0.498749 | ||||||||
\(629\) | 20.5209 | 0.818223 | ||||||||
\(630\) | 2.65922 | 0.105946 | ||||||||
\(631\) | 10.1149 | 0.402667 | 0.201333 | − | 0.979523i | \(-0.435473\pi\) | ||||
0.201333 | + | 0.979523i | \(0.435473\pi\) | |||||||
\(632\) | −4.36793 | −0.173747 | ||||||||
\(633\) | −2.02498 | −0.0804857 | ||||||||
\(634\) | −4.64807 | −0.184598 | ||||||||
\(635\) | 9.88489 | 0.392270 | ||||||||
\(636\) | 7.36659 | 0.292104 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.89413 | 0.0749894 | ||||||||
\(639\) | 15.9472 | 0.630861 | ||||||||
\(640\) | 7.90212 | 0.312359 | ||||||||
\(641\) | −17.6173 | −0.695843 | −0.347922 | − | 0.937524i | \(-0.613112\pi\) | ||||
−0.347922 | + | 0.937524i | \(0.613112\pi\) | |||||||
\(642\) | −1.11877 | −0.0441544 | ||||||||
\(643\) | −19.0312 | −0.750519 | −0.375260 | − | 0.926920i | \(-0.622446\pi\) | ||||
−0.375260 | + | 0.926920i | \(0.622446\pi\) | |||||||
\(644\) | −49.5989 | −1.95447 | ||||||||
\(645\) | 1.46561 | 0.0577085 | ||||||||
\(646\) | −3.78254 | −0.148822 | ||||||||
\(647\) | −26.6972 | −1.04957 | −0.524787 | − | 0.851233i | \(-0.675855\pi\) | ||||
−0.524787 | + | 0.851233i | \(0.675855\pi\) | |||||||
\(648\) | −8.62108 | −0.338668 | ||||||||
\(649\) | 6.69802 | 0.262920 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.26262 | −0.206258 | ||||||||
\(652\) | 7.41518 | 0.290401 | ||||||||
\(653\) | −3.16076 | −0.123690 | −0.0618451 | − | 0.998086i | \(-0.519698\pi\) | ||||
−0.0618451 | + | 0.998086i | \(0.519698\pi\) | |||||||
\(654\) | −0.906178 | −0.0354344 | ||||||||
\(655\) | 11.4705 | 0.448188 | ||||||||
\(656\) | 3.24680 | 0.126766 | ||||||||
\(657\) | −8.51553 | −0.332222 | ||||||||
\(658\) | −7.87798 | −0.307116 | ||||||||
\(659\) | −18.0060 | −0.701413 | −0.350706 | − | 0.936486i | \(-0.614058\pi\) | ||||
−0.350706 | + | 0.936486i | \(0.614058\pi\) | |||||||
\(660\) | −1.07873 | −0.0419895 | ||||||||
\(661\) | −3.51786 | −0.136829 | −0.0684145 | − | 0.997657i | \(-0.521794\pi\) | ||||
−0.0684145 | + | 0.997657i | \(0.521794\pi\) | |||||||
\(662\) | 0.388232 | 0.0150891 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.5446 | 0.486824 | ||||||||
\(665\) | 24.1190 | 0.935296 | ||||||||
\(666\) | −8.25797 | −0.319990 | ||||||||
\(667\) | 30.3334 | 1.17452 | ||||||||
\(668\) | 13.2128 | 0.511217 | ||||||||
\(669\) | 7.50935 | 0.290328 | ||||||||
\(670\) | −0.128292 | −0.00495634 | ||||||||
\(671\) | 13.9896 | 0.540064 | ||||||||
\(672\) | −3.34838 | −0.129166 | ||||||||
\(673\) | −26.0032 | −1.00235 | −0.501175 | − | 0.865346i | \(-0.667099\pi\) | ||||
−0.501175 | + | 0.865346i | \(0.667099\pi\) | |||||||
\(674\) | −2.03224 | −0.0782791 | ||||||||
\(675\) | 1.88505 | 0.0725558 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28.5157 | −1.09595 | −0.547975 | − | 0.836495i | \(-0.684601\pi\) | ||||
−0.547975 | + | 0.836495i | \(0.684601\pi\) | |||||||
\(678\) | 1.64595 | 0.0632122 | ||||||||
\(679\) | −23.5277 | −0.902912 | ||||||||
\(680\) | 2.08221 | 0.0798490 | ||||||||
\(681\) | 3.06640 | 0.117505 | ||||||||
\(682\) | 2.31512 | 0.0886505 | ||||||||
\(683\) | −28.9493 | −1.10771 | −0.553857 | − | 0.832612i | \(-0.686845\pi\) | ||||
−0.553857 | + | 0.832612i | \(0.686845\pi\) | |||||||
\(684\) | −39.8163 | −1.52241 | ||||||||
\(685\) | 13.0826 | 0.499861 | ||||||||
\(686\) | −2.35411 | −0.0898805 | ||||||||
\(687\) | −2.31084 | −0.0881639 | ||||||||
\(688\) | 16.3408 | 0.622987 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.660424 | 0.0251419 | ||||||||
\(691\) | −21.6566 | −0.823854 | −0.411927 | − | 0.911217i | \(-0.635144\pi\) | ||||
−0.411927 | + | 0.911217i | \(0.635144\pi\) | |||||||
\(692\) | −30.8611 | −1.17316 | ||||||||
\(693\) | −17.1685 | −0.652176 | ||||||||
\(694\) | 1.89097 | 0.0717801 | ||||||||
\(695\) | −11.9762 | −0.454283 | ||||||||
\(696\) | 1.35671 | 0.0514258 | ||||||||
\(697\) | 1.78048 | 0.0674405 | ||||||||
\(698\) | 5.96312 | 0.225707 | ||||||||
\(699\) | 0.137411 | 0.00519737 | ||||||||
\(700\) | −6.51400 | −0.246206 | ||||||||
\(701\) | 25.0376 | 0.945656 | 0.472828 | − | 0.881155i | \(-0.343233\pi\) | ||||
0.472828 | + | 0.881155i | \(0.343233\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −74.8995 | −2.82489 | ||||||||
\(704\) | −11.0140 | −0.415107 | ||||||||
\(705\) | −2.74389 | −0.103341 | ||||||||
\(706\) | 3.53285 | 0.132961 | ||||||||
\(707\) | −60.5030 | −2.27545 | ||||||||
\(708\) | 2.35379 | 0.0884610 | ||||||||
\(709\) | −25.6247 | −0.962355 | −0.481178 | − | 0.876623i | \(-0.659791\pi\) | ||||
−0.481178 | + | 0.876623i | \(0.659791\pi\) | |||||||
\(710\) | 1.49340 | 0.0560464 | ||||||||
\(711\) | −11.8794 | −0.445511 | ||||||||
\(712\) | 4.11279 | 0.154133 | ||||||||
\(713\) | 37.0753 | 1.38848 | ||||||||
\(714\) | −0.573160 | −0.0214500 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.5709 | 0.581912 | ||||||||
\(717\) | −4.07352 | −0.152129 | ||||||||
\(718\) | 2.71160 | 0.101196 | ||||||||
\(719\) | 14.8064 | 0.552186 | 0.276093 | − | 0.961131i | \(-0.410960\pi\) | ||||
0.276093 | + | 0.961131i | \(0.410960\pi\) | |||||||
\(720\) | 10.3266 | 0.384851 | ||||||||
\(721\) | 34.6811 | 1.29159 | ||||||||
\(722\) | 8.64982 | 0.321913 | ||||||||
\(723\) | 6.11549 | 0.227438 | ||||||||
\(724\) | −21.3629 | −0.793945 | ||||||||
\(725\) | 3.98380 | 0.147955 | ||||||||
\(726\) | 0.687845 | 0.0255283 | ||||||||
\(727\) | −30.1688 | −1.11890 | −0.559449 | − | 0.828865i | \(-0.688987\pi\) | ||||
−0.559449 | + | 0.828865i | \(0.688987\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.6391 | −0.801447 | ||||||||
\(730\) | −0.797452 | −0.0295150 | ||||||||
\(731\) | 8.96098 | 0.331434 | ||||||||
\(732\) | 4.91619 | 0.181708 | ||||||||
\(733\) | 49.8997 | 1.84309 | 0.921544 | − | 0.388275i | \(-0.126929\pi\) | ||||
0.921544 | + | 0.388275i | \(0.126929\pi\) | |||||||
\(734\) | 6.86257 | 0.253302 | ||||||||
\(735\) | 1.41739 | 0.0522812 | ||||||||
\(736\) | 23.5894 | 0.869516 | ||||||||
\(737\) | 0.828276 | 0.0305100 | ||||||||
\(738\) | −0.716496 | −0.0263746 | ||||||||
\(739\) | −31.5796 | −1.16167 | −0.580836 | − | 0.814020i | \(-0.697274\pi\) | ||||
−0.580836 | + | 0.814020i | \(0.697274\pi\) | |||||||
\(740\) | 20.2287 | 0.743620 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.9794 | 0.403066 | ||||||||
\(743\) | 1.60448 | 0.0588625 | 0.0294312 | − | 0.999567i | \(-0.490630\pi\) | ||||
0.0294312 | + | 0.999567i | \(0.490630\pi\) | |||||||
\(744\) | 1.65824 | 0.0607942 | ||||||||
\(745\) | −16.3052 | −0.597377 | ||||||||
\(746\) | 3.87258 | 0.141785 | ||||||||
\(747\) | 34.1172 | 1.24828 | ||||||||
\(748\) | −6.59551 | −0.241156 | ||||||||
\(749\) | 43.6168 | 1.59372 | ||||||||
\(750\) | 0.0867358 | 0.00316714 | ||||||||
\(751\) | 10.7873 | 0.393634 | 0.196817 | − | 0.980440i | \(-0.436940\pi\) | ||||
0.196817 | + | 0.980440i | \(0.436940\pi\) | |||||||
\(752\) | −30.5928 | −1.11561 | ||||||||
\(753\) | −0.131623 | −0.00479662 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.75415 | −0.318596 | ||||||||
\(756\) | −12.2792 | −0.446592 | ||||||||
\(757\) | −6.40389 | −0.232753 | −0.116377 | − | 0.993205i | \(-0.537128\pi\) | ||||
−0.116377 | + | 0.993205i | \(0.537128\pi\) | |||||||
\(758\) | 1.90326 | 0.0691294 | ||||||||
\(759\) | −4.26383 | −0.154767 | ||||||||
\(760\) | −7.59987 | −0.275676 | ||||||||
\(761\) | −50.2655 | −1.82212 | −0.911062 | − | 0.412269i | \(-0.864736\pi\) | ||||
−0.911062 | + | 0.412269i | \(0.864736\pi\) | |||||||
\(762\) | 0.857374 | 0.0310594 | ||||||||
\(763\) | 35.3286 | 1.27898 | ||||||||
\(764\) | −41.9044 | −1.51605 | ||||||||
\(765\) | 5.66293 | 0.204744 | ||||||||
\(766\) | 1.27366 | 0.0460191 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −3.33308 | −0.120272 | ||||||||
\(769\) | −4.10457 | −0.148015 | −0.0740074 | − | 0.997258i | \(-0.523579\pi\) | ||||
−0.0740074 | + | 0.997258i | \(0.523579\pi\) | |||||||
\(770\) | −1.60777 | −0.0579401 | ||||||||
\(771\) | 0.791232 | 0.0284955 | ||||||||
\(772\) | 43.3980 | 1.56193 | ||||||||
\(773\) | 1.17851 | 0.0423882 | 0.0211941 | − | 0.999775i | \(-0.493253\pi\) | ||||
0.0211941 | + | 0.999775i | \(0.493253\pi\) | |||||||
\(774\) | −3.60605 | −0.129617 | ||||||||
\(775\) | 4.86923 | 0.174908 | ||||||||
\(776\) | 7.41356 | 0.266131 | ||||||||
\(777\) | −11.3494 | −0.407157 | ||||||||
\(778\) | −2.53648 | −0.0909373 | ||||||||
\(779\) | −6.49860 | −0.232836 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.64172 | −0.345008 | ||||||||
\(782\) | 4.03793 | 0.144396 | ||||||||
\(783\) | 7.50968 | 0.268374 | ||||||||
\(784\) | 15.8031 | 0.564397 | ||||||||
\(785\) | −6.48821 | −0.231574 | ||||||||
\(786\) | 0.994900 | 0.0354869 | ||||||||
\(787\) | −33.4916 | −1.19385 | −0.596923 | − | 0.802298i | \(-0.703610\pi\) | ||||
−0.596923 | + | 0.802298i | \(0.703610\pi\) | |||||||
\(788\) | −33.2776 | −1.18546 | ||||||||
\(789\) | 3.63056 | 0.129251 | ||||||||
\(790\) | −1.11246 | −0.0395797 | ||||||||
\(791\) | −64.1695 | −2.28161 | ||||||||
\(792\) | 5.40976 | 0.192227 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −5.75675 | −0.204299 | ||||||||
\(795\) | 3.82411 | 0.135627 | ||||||||
\(796\) | −33.6921 | −1.19418 | ||||||||
\(797\) | −24.9394 | −0.883400 | −0.441700 | − | 0.897163i | \(-0.645624\pi\) | ||||
−0.441700 | + | 0.897163i | \(0.645624\pi\) | |||||||
\(798\) | 2.09198 | 0.0740555 | ||||||||
\(799\) | −16.7765 | −0.593511 | ||||||||
\(800\) | 3.09808 | 0.109534 | ||||||||
\(801\) | 11.1855 | 0.395219 | ||||||||
\(802\) | 4.94368 | 0.174567 | ||||||||
\(803\) | 5.14851 | 0.181687 | ||||||||
\(804\) | 0.291070 | 0.0102652 | ||||||||
\(805\) | −25.7475 | −0.907481 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.48906 | 0.334031 | ||||||||
\(808\) | 19.0644 | 0.670684 | ||||||||
\(809\) | 12.8221 | 0.450802 | 0.225401 | − | 0.974266i | \(-0.427631\pi\) | ||||
0.225401 | + | 0.974266i | \(0.427631\pi\) | |||||||
\(810\) | −2.19570 | −0.0771489 | ||||||||
\(811\) | −29.8424 | −1.04791 | −0.523954 | − | 0.851746i | \(-0.675544\pi\) | ||||
−0.523954 | + | 0.851746i | \(0.675544\pi\) | |||||||
\(812\) | −25.9505 | −0.910683 | ||||||||
\(813\) | −4.72270 | −0.165632 | ||||||||
\(814\) | 4.99279 | 0.174997 | ||||||||
\(815\) | 3.84933 | 0.134836 | ||||||||
\(816\) | −2.22577 | −0.0779177 | ||||||||
\(817\) | −32.7068 | −1.14427 | ||||||||
\(818\) | −1.18356 | −0.0413822 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.75512 | 0.0612916 | ||||||||
\(821\) | −19.6918 | −0.687249 | −0.343624 | − | 0.939107i | \(-0.611655\pi\) | ||||
−0.343624 | + | 0.939107i | \(0.611655\pi\) | |||||||
\(822\) | 1.13473 | 0.0395783 | ||||||||
\(823\) | 41.9069 | 1.46078 | 0.730390 | − | 0.683030i | \(-0.239338\pi\) | ||||
0.730390 | + | 0.683030i | \(0.239338\pi\) | |||||||
\(824\) | −10.9280 | −0.380693 | ||||||||
\(825\) | −0.559984 | −0.0194961 | ||||||||
\(826\) | 3.50817 | 0.122065 | ||||||||
\(827\) | −21.7734 | −0.757134 | −0.378567 | − | 0.925574i | \(-0.623583\pi\) | ||||
−0.378567 | + | 0.925574i | \(0.623583\pi\) | |||||||
\(828\) | 42.5046 | 1.47714 | ||||||||
\(829\) | −5.87683 | −0.204111 | −0.102055 | − | 0.994779i | \(-0.532542\pi\) | ||||
−0.102055 | + | 0.994779i | \(0.532542\pi\) | |||||||
\(830\) | 3.19497 | 0.110899 | ||||||||
\(831\) | 0.622141 | 0.0215818 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.66612 | 0.300263 | ||||||||
\(834\) | −1.03876 | −0.0359695 | ||||||||
\(835\) | 6.85894 | 0.237363 | ||||||||
\(836\) | 24.0730 | 0.832583 | ||||||||
\(837\) | 9.17876 | 0.317265 | ||||||||
\(838\) | 4.62841 | 0.159886 | ||||||||
\(839\) | 54.1116 | 1.86814 | 0.934069 | − | 0.357092i | \(-0.116232\pi\) | ||||
0.934069 | + | 0.357092i | \(0.116232\pi\) | |||||||
\(840\) | −1.15159 | −0.0397338 | ||||||||
\(841\) | −13.1294 | −0.452736 | ||||||||
\(842\) | 0.347348 | 0.0119704 | ||||||||
\(843\) | 5.92112 | 0.203934 | ||||||||
\(844\) | −12.2047 | −0.420103 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.75116 | 0.232110 | ||||||||
\(847\) | −26.8166 | −0.921428 | ||||||||
\(848\) | 42.6367 | 1.46415 | ||||||||
\(849\) | −4.18545 | −0.143644 | ||||||||
\(850\) | 0.530316 | 0.0181897 | ||||||||
\(851\) | 79.9567 | 2.74088 | ||||||||
\(852\) | −3.38826 | −0.116080 | ||||||||
\(853\) | −10.8001 | −0.369787 | −0.184893 | − | 0.982759i | \(-0.559194\pi\) | ||||
−0.184893 | + | 0.982759i | \(0.559194\pi\) | |||||||
\(854\) | 7.32725 | 0.250733 | ||||||||
\(855\) | −20.6692 | −0.706872 | ||||||||
\(856\) | −13.7436 | −0.469747 | ||||||||
\(857\) | −12.0558 | −0.411817 | −0.205908 | − | 0.978571i | \(-0.566015\pi\) | ||||
−0.205908 | + | 0.978571i | \(0.566015\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.6819 | −1.62688 | −0.813442 | − | 0.581646i | \(-0.802409\pi\) | ||||
−0.813442 | + | 0.581646i | \(0.802409\pi\) | |||||||
\(860\) | 8.83336 | 0.301215 | ||||||||
\(861\) | −0.984720 | −0.0335592 | ||||||||
\(862\) | −8.92095 | −0.303849 | ||||||||
\(863\) | 46.2292 | 1.57366 | 0.786831 | − | 0.617169i | \(-0.211721\pi\) | ||||
0.786831 | + | 0.617169i | \(0.211721\pi\) | |||||||
\(864\) | 5.84005 | 0.198682 | ||||||||
\(865\) | −16.0204 | −0.544711 | ||||||||
\(866\) | −7.66962 | −0.260624 | ||||||||
\(867\) | 4.21293 | 0.143078 | ||||||||
\(868\) | −31.7182 | −1.07658 | ||||||||
\(869\) | 7.18230 | 0.243643 | ||||||||
\(870\) | 0.345538 | 0.0117148 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −11.1320 | −0.376977 | ||||||||
\(873\) | 20.1625 | 0.682397 | ||||||||
\(874\) | −14.7381 | −0.498523 | ||||||||
\(875\) | −3.38151 | −0.114316 | ||||||||
\(876\) | 1.80927 | 0.0611296 | ||||||||
\(877\) | 25.2281 | 0.851893 | 0.425947 | − | 0.904748i | \(-0.359941\pi\) | ||||
0.425947 | + | 0.904748i | \(0.359941\pi\) | |||||||
\(878\) | 7.12684 | 0.240519 | ||||||||
\(879\) | −0.385947 | −0.0130177 | ||||||||
\(880\) | −6.24352 | −0.210469 | ||||||||
\(881\) | −12.5086 | −0.421425 | −0.210712 | − | 0.977548i | \(-0.567578\pi\) | ||||
−0.210712 | + | 0.977548i | \(0.567578\pi\) | |||||||
\(882\) | −3.48740 | −0.117427 | ||||||||
\(883\) | −11.2289 | −0.377881 | −0.188941 | − | 0.981989i | \(-0.560505\pi\) | ||||
−0.188941 | + | 0.981989i | \(0.560505\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.22189 | 0.0410733 | ||||||||
\(886\) | −3.81218 | −0.128073 | ||||||||
\(887\) | −54.5383 | −1.83122 | −0.915609 | − | 0.402069i | \(-0.868291\pi\) | ||||
−0.915609 | + | 0.402069i | \(0.868291\pi\) | |||||||
\(888\) | 3.57617 | 0.120009 | ||||||||
\(889\) | −33.4259 | −1.12107 | ||||||||
\(890\) | 1.04748 | 0.0351117 | ||||||||
\(891\) | 14.1759 | 0.474909 | ||||||||
\(892\) | 45.2594 | 1.51540 | ||||||||
\(893\) | 61.2328 | 2.04908 | ||||||||
\(894\) | −1.41425 | −0.0472995 | ||||||||
\(895\) | 8.08309 | 0.270188 | ||||||||
\(896\) | −26.7211 | −0.892690 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.21007 | 0.0403805 | ||||||||
\(899\) | 19.3980 | 0.646960 | ||||||||
\(900\) | 5.58228 | 0.186076 | ||||||||
\(901\) | 23.3811 | 0.778939 | ||||||||
\(902\) | 0.433196 | 0.0144238 | ||||||||
\(903\) | −4.95600 | −0.164925 | ||||||||
\(904\) | 20.2197 | 0.672498 | ||||||||
\(905\) | −11.0898 | −0.368637 | ||||||||
\(906\) | −0.759298 | −0.0252260 | ||||||||
\(907\) | 28.9083 | 0.959883 | 0.479942 | − | 0.877300i | \(-0.340658\pi\) | ||||
0.479942 | + | 0.877300i | \(0.340658\pi\) | |||||||
\(908\) | 18.4814 | 0.613327 | ||||||||
\(909\) | 51.8491 | 1.71973 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.04371 | −0.233369 | −0.116684 | − | 0.993169i | \(-0.537227\pi\) | ||||
−0.116684 | + | 0.993169i | \(0.537227\pi\) | |||||||
\(912\) | 8.12388 | 0.269009 | ||||||||
\(913\) | −20.6274 | −0.682666 | ||||||||
\(914\) | −4.45456 | −0.147344 | ||||||||
\(915\) | 2.55207 | 0.0843688 | ||||||||
\(916\) | −13.9276 | −0.460180 | ||||||||
\(917\) | −38.7875 | −1.28088 | ||||||||
\(918\) | 0.999674 | 0.0329942 | ||||||||
\(919\) | −17.3638 | −0.572780 | −0.286390 | − | 0.958113i | \(-0.592455\pi\) | ||||
−0.286390 | + | 0.958113i | \(0.592455\pi\) | |||||||
\(920\) | 8.11301 | 0.267478 | ||||||||
\(921\) | −7.00840 | −0.230935 | ||||||||
\(922\) | −5.57551 | −0.183620 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.64774 | 0.120002 | ||||||||
\(925\) | 10.5010 | 0.345271 | ||||||||
\(926\) | −0.429745 | −0.0141223 | ||||||||
\(927\) | −29.7205 | −0.976150 | ||||||||
\(928\) | 12.3421 | 0.405150 | ||||||||
\(929\) | 30.9381 | 1.01504 | 0.507522 | − | 0.861639i | \(-0.330561\pi\) | ||||
0.507522 | + | 0.861639i | \(0.330561\pi\) | |||||||
\(930\) | 0.422337 | 0.0138490 | ||||||||
\(931\) | −31.6306 | −1.03665 | ||||||||
\(932\) | 0.828186 | 0.0271281 | ||||||||
\(933\) | 4.02610 | 0.131808 | ||||||||
\(934\) | 1.39561 | 0.0456659 | ||||||||
\(935\) | −3.42382 | −0.111971 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.5009 | 0.996422 | 0.498211 | − | 0.867056i | \(-0.333990\pi\) | ||||
0.498211 | + | 0.867056i | \(0.333990\pi\) | |||||||
\(938\) | 0.433820 | 0.0141647 | ||||||||
\(939\) | −8.57431 | −0.279812 | ||||||||
\(940\) | −16.5376 | −0.539397 | ||||||||
\(941\) | −32.0423 | −1.04455 | −0.522275 | − | 0.852777i | \(-0.674917\pi\) | ||||
−0.522275 | + | 0.852777i | \(0.674917\pi\) | |||||||
\(942\) | −0.562761 | −0.0183357 | ||||||||
\(943\) | 6.93738 | 0.225912 | ||||||||
\(944\) | 13.6234 | 0.443404 | ||||||||
\(945\) | −6.37434 | −0.207357 | ||||||||
\(946\) | 2.18023 | 0.0708854 | ||||||||
\(947\) | −8.63395 | −0.280566 | −0.140283 | − | 0.990111i | \(-0.544801\pi\) | ||||
−0.140283 | + | 0.990111i | \(0.544801\pi\) | |||||||
\(948\) | 2.52398 | 0.0819750 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.93560 | −0.0627993 | ||||||||
\(951\) | 5.47438 | 0.177519 | ||||||||
\(952\) | −7.04102 | −0.228201 | ||||||||
\(953\) | −32.4260 | −1.05038 | −0.525191 | − | 0.850984i | \(-0.676006\pi\) | ||||
−0.525191 | + | 0.850984i | \(0.676006\pi\) | |||||||
\(954\) | −9.40897 | −0.304627 | ||||||||
\(955\) | −21.7532 | −0.703917 | ||||||||
\(956\) | −24.5514 | −0.794049 | ||||||||
\(957\) | −2.23086 | −0.0721136 | ||||||||
\(958\) | −6.04930 | −0.195444 | ||||||||
\(959\) | −44.2390 | −1.42855 | ||||||||
\(960\) | −2.00924 | −0.0648479 | ||||||||
\(961\) | −7.29060 | −0.235181 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −37.3782 | −1.20449 | ||||||||
\(964\) | 36.8585 | 1.18713 | ||||||||
\(965\) | 22.5285 | 0.725219 | ||||||||
\(966\) | −2.23323 | −0.0718531 | ||||||||
\(967\) | −27.0744 | −0.870656 | −0.435328 | − | 0.900272i | \(-0.643368\pi\) | ||||
−0.435328 | + | 0.900272i | \(0.643368\pi\) | |||||||
\(968\) | 8.44986 | 0.271589 | ||||||||
\(969\) | 4.45498 | 0.143115 | ||||||||
\(970\) | 1.88815 | 0.0606249 | ||||||||
\(971\) | 31.8039 | 1.02063 | 0.510317 | − | 0.859986i | \(-0.329528\pi\) | ||||
0.510317 | + | 0.859986i | \(0.329528\pi\) | |||||||
\(972\) | 15.8755 | 0.509207 | ||||||||
\(973\) | 40.4977 | 1.29830 | ||||||||
\(974\) | 6.35517 | 0.203633 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 28.4542 | 0.910796 | ||||||||
\(977\) | −31.3672 | −1.00353 | −0.501763 | − | 0.865005i | \(-0.667315\pi\) | ||||
−0.501763 | + | 0.865005i | \(0.667315\pi\) | |||||||
\(978\) | 0.333875 | 0.0106761 | ||||||||
\(979\) | −6.76276 | −0.216139 | ||||||||
\(980\) | 8.54270 | 0.272886 | ||||||||
\(981\) | −30.2754 | −0.966620 | ||||||||
\(982\) | 0.922103 | 0.0294255 | ||||||||
\(983\) | 35.5044 | 1.13241 | 0.566207 | − | 0.824263i | \(-0.308410\pi\) | ||||
0.566207 | + | 0.824263i | \(0.308410\pi\) | |||||||
\(984\) | 0.310284 | 0.00989149 | ||||||||
\(985\) | −17.2749 | −0.550424 | ||||||||
\(986\) | 2.11267 | 0.0672811 | ||||||||
\(987\) | 9.27849 | 0.295338 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.9151 | 1.11024 | ||||||||
\(990\) | 1.37781 | 0.0437896 | ||||||||
\(991\) | −41.0638 | −1.30443 | −0.652217 | − | 0.758032i | \(-0.726161\pi\) | ||||
−0.652217 | + | 0.758032i | \(0.726161\pi\) | |||||||
\(992\) | 15.0853 | 0.478957 | ||||||||
\(993\) | −0.457250 | −0.0145104 | ||||||||
\(994\) | −5.04997 | −0.160175 | ||||||||
\(995\) | −17.4901 | −0.554472 | ||||||||
\(996\) | −7.24879 | −0.229687 | ||||||||
\(997\) | −44.7904 | −1.41853 | −0.709264 | − | 0.704943i | \(-0.750972\pi\) | ||||
−0.709264 | + | 0.704943i | \(0.750972\pi\) | |||||||
\(998\) | 1.32352 | 0.0418954 | ||||||||
\(999\) | 19.7949 | 0.626284 |
(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 | 845.2.a.n.1.6 | ✓ | 9 | |
3.2 | odd | 2 | 7605.2.a.cs.1.4 | 9 | |||
5.4 | even | 2 | 4225.2.a.bt.1.4 | 9 | |||
13.2 | odd | 12 | 845.2.m.j.316.11 | 36 | |||
13.3 | even | 3 | 845.2.e.p.191.4 | 18 | |||
13.4 | even | 6 | 845.2.e.o.146.6 | 18 | |||
13.5 | odd | 4 | 845.2.c.h.506.8 | 18 | |||
13.6 | odd | 12 | 845.2.m.j.361.8 | 36 | |||
13.7 | odd | 12 | 845.2.m.j.361.11 | 36 | |||
13.8 | odd | 4 | 845.2.c.h.506.11 | 18 | |||
13.9 | even | 3 | 845.2.e.p.146.4 | 18 | |||
13.10 | even | 6 | 845.2.e.o.191.6 | 18 | |||
13.11 | odd | 12 | 845.2.m.j.316.8 | 36 | |||
13.12 | even | 2 | 845.2.a.o.1.4 | yes | 9 | ||
39.38 | odd | 2 | 7605.2.a.cp.1.6 | 9 | |||
65.64 | even | 2 | 4225.2.a.bs.1.6 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
845.2.a.n.1.6 | ✓ | 9 | 1.1 | even | 1 | trivial | |
845.2.a.o.1.4 | yes | 9 | 13.12 | even | 2 | ||
845.2.c.h.506.8 | 18 | 13.5 | odd | 4 | |||
845.2.c.h.506.11 | 18 | 13.8 | odd | 4 | |||
845.2.e.o.146.6 | 18 | 13.4 | even | 6 | |||
845.2.e.o.191.6 | 18 | 13.10 | even | 6 | |||
845.2.e.p.146.4 | 18 | 13.9 | even | 3 | |||
845.2.e.p.191.4 | 18 | 13.3 | even | 3 | |||
845.2.m.j.316.8 | 36 | 13.11 | odd | 12 | |||
845.2.m.j.316.11 | 36 | 13.2 | odd | 12 | |||
845.2.m.j.361.8 | 36 | 13.6 | odd | 12 | |||
845.2.m.j.361.11 | 36 | 13.7 | odd | 12 | |||
4225.2.a.bs.1.6 | 9 | 65.64 | even | 2 | |||
4225.2.a.bt.1.4 | 9 | 5.4 | even | 2 | |||
7605.2.a.cp.1.6 | 9 | 39.38 | odd | 2 | |||
7605.2.a.cs.1.4 | 9 | 3.2 | odd | 2 |