Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.4 | ||
Root | \(0.403032 + 0.403032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.2.c.g.199.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.193937i | 0.137134i | 0.997647 | + | 0.0685669i | \(0.0218427\pi\) | ||||
−0.997647 | + | 0.0685669i | \(0.978157\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.96239 | 0.981194 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.193937 | −0.0791743 | ||||||||
\(7\) | − 3.35026i | − 1.26628i | −0.774037 | − | 0.633140i | \(-0.781766\pi\) | ||||
0.774037 | − | 0.633140i | \(-0.218234\pi\) | |||||||
\(8\) | 0.768452i | 0.271689i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.96239i | 0.566493i | ||||||||
\(13\) | 2.96239i | 0.821619i | 0.911721 | + | 0.410809i | \(0.134754\pi\) | ||||
−0.911721 | + | 0.410809i | \(0.865246\pi\) | |||||||
\(14\) | 0.649738 | 0.173650 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.77575 | 0.943937 | ||||||||
\(17\) | 4.57452i | 1.10948i | 0.832023 | + | 0.554741i | \(0.187183\pi\) | ||||
−0.832023 | + | 0.554741i | \(0.812817\pi\) | |||||||
\(18\) | − 0.193937i | − 0.0457113i | ||||||||
\(19\) | 4.31265 | 0.989390 | 0.494695 | − | 0.869067i | \(-0.335280\pi\) | ||||
0.494695 | + | 0.869067i | \(0.335280\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.35026 | 0.731087 | ||||||||
\(22\) | 0.193937i | 0.0413474i | ||||||||
\(23\) | − 6.70052i | − 1.39716i | −0.715534 | − | 0.698578i | \(-0.753817\pi\) | ||||
0.715534 | − | 0.698578i | \(-0.246183\pi\) | |||||||
\(24\) | −0.768452 | −0.156860 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.574515 | −0.112672 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | − 6.57452i | − 1.24247i | ||||||||
\(29\) | 3.61213 | 0.670755 | 0.335378 | − | 0.942084i | \(-0.391136\pi\) | ||||
0.335378 | + | 0.942084i | \(0.391136\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.92478 | 1.78254 | 0.891271 | − | 0.453470i | \(-0.149814\pi\) | ||||
0.891271 | + | 0.453470i | \(0.149814\pi\) | |||||||
\(32\) | 2.26916i | 0.401134i | ||||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | −0.887166 | −0.152148 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.96239 | −0.327065 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 0.836381i | 0.135679i | ||||||||
\(39\) | −2.96239 | −0.474362 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.38787 | −0.685271 | −0.342635 | − | 0.939468i | \(-0.611320\pi\) | ||||
−0.342635 | + | 0.939468i | \(0.611320\pi\) | |||||||
\(42\) | 0.649738i | 0.100257i | ||||||||
\(43\) | − 9.27504i | − 1.41443i | −0.706998 | − | 0.707215i | \(-0.749951\pi\) | ||||
0.706998 | − | 0.707215i | \(-0.250049\pi\) | |||||||
\(44\) | 1.96239 | 0.295841 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.29948 | 0.191597 | ||||||||
\(47\) | 9.92478i | 1.44768i | 0.689969 | + | 0.723839i | \(0.257624\pi\) | ||||
−0.689969 | + | 0.723839i | \(0.742376\pi\) | |||||||
\(48\) | 3.77575i | 0.544982i | ||||||||
\(49\) | −4.22425 | −0.603465 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.57452 | −0.640560 | ||||||||
\(52\) | 5.81336i | 0.806168i | ||||||||
\(53\) | 4.70052i | 0.645667i | 0.946456 | + | 0.322833i | \(0.104635\pi\) | ||||
−0.946456 | + | 0.322833i | \(0.895365\pi\) | |||||||
\(54\) | 0.193937 | 0.0263914 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.57452 | 0.344034 | ||||||||
\(57\) | 4.31265i | 0.571224i | ||||||||
\(58\) | 0.700523i | 0.0919832i | ||||||||
\(59\) | −10.7005 | −1.39309 | −0.696545 | − | 0.717513i | \(-0.745280\pi\) | ||||
−0.696545 | + | 0.717513i | \(0.745280\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.70052 | −1.11399 | −0.556994 | − | 0.830517i | \(-0.688045\pi\) | ||||
−0.556994 | + | 0.830517i | \(0.688045\pi\) | |||||||
\(62\) | 1.92478i | 0.244447i | ||||||||
\(63\) | 3.35026i | 0.422093i | ||||||||
\(64\) | 7.11142 | 0.888927 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.193937 | −0.0238719 | ||||||||
\(67\) | − 5.92478i | − 0.723827i | −0.932212 | − | 0.361913i | \(-0.882124\pi\) | ||||
0.932212 | − | 0.361913i | \(-0.117876\pi\) | |||||||
\(68\) | 8.97698i | 1.08862i | ||||||||
\(69\) | 6.70052 | 0.806648 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.92478 | 1.17785 | 0.588927 | − | 0.808186i | \(-0.299550\pi\) | ||||
0.588927 | + | 0.808186i | \(0.299550\pi\) | |||||||
\(72\) | − 0.768452i | − 0.0905629i | ||||||||
\(73\) | − 7.73813i | − 0.905680i | −0.891592 | − | 0.452840i | \(-0.850411\pi\) | ||||
0.891592 | − | 0.452840i | \(-0.149589\pi\) | |||||||
\(74\) | −0.387873 | −0.0450893 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.46310 | 0.970784 | ||||||||
\(77\) | − 3.35026i | − 0.381798i | ||||||||
\(78\) | − 0.574515i | − 0.0650511i | ||||||||
\(79\) | −11.5369 | −1.29800 | −0.649002 | − | 0.760787i | \(-0.724813\pi\) | ||||
−0.649002 | + | 0.760787i | \(0.724813\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 0.850969i | − 0.0939738i | ||||||||
\(83\) | 10.8872i | 1.19502i | 0.801861 | + | 0.597511i | \(0.203844\pi\) | ||||
−0.801861 | + | 0.597511i | \(0.796156\pi\) | |||||||
\(84\) | 6.57452 | 0.717338 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.79877 | 0.193966 | ||||||||
\(87\) | 3.61213i | 0.387261i | ||||||||
\(88\) | 0.768452i | 0.0819173i | ||||||||
\(89\) | 2.77575 | 0.294229 | 0.147114 | − | 0.989120i | \(-0.453001\pi\) | ||||
0.147114 | + | 0.989120i | \(0.453001\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.92478 | 1.04040 | ||||||||
\(92\) | − 13.1490i | − 1.37088i | ||||||||
\(93\) | 9.92478i | 1.02915i | ||||||||
\(94\) | −1.92478 | −0.198526 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.26916 | −0.231595 | ||||||||
\(97\) | − 0.0752228i | − 0.00763772i | −0.999993 | − | 0.00381886i | \(-0.998784\pi\) | ||||
0.999993 | − | 0.00381886i | \(-0.00121558\pi\) | |||||||
\(98\) | − 0.819237i | − 0.0827555i | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.0884 | −1.50135 | −0.750676 | − | 0.660671i | \(-0.770272\pi\) | ||||
−0.750676 | + | 0.660671i | \(0.770272\pi\) | |||||||
\(102\) | − 0.887166i | − 0.0878425i | ||||||||
\(103\) | − 3.22425i | − 0.317695i | −0.987303 | − | 0.158848i | \(-0.949222\pi\) | ||||
0.987303 | − | 0.158848i | \(-0.0507778\pi\) | |||||||
\(104\) | −2.27645 | −0.223225 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.911603 | −0.0885427 | ||||||||
\(107\) | 0.962389i | 0.0930376i | 0.998917 | + | 0.0465188i | \(0.0148127\pi\) | ||||
−0.998917 | + | 0.0465188i | \(0.985187\pi\) | |||||||
\(108\) | − 1.96239i | − 0.188831i | ||||||||
\(109\) | −11.4010 | −1.09202 | −0.546011 | − | 0.837778i | \(-0.683854\pi\) | ||||
−0.546011 | + | 0.837778i | \(0.683854\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | − 12.6497i | − 1.19529i | ||||||||
\(113\) | − 6.00000i | − 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | −0.836381 | −0.0783342 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.08840 | 0.658141 | ||||||||
\(117\) | − 2.96239i | − 0.273873i | ||||||||
\(118\) | − 2.07522i | − 0.191040i | ||||||||
\(119\) | 15.3258 | 1.40492 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − 1.68735i | − 0.152765i | ||||||||
\(123\) | − 4.38787i | − 0.395641i | ||||||||
\(124\) | 19.4763 | 1.74902 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.649738 | −0.0578833 | ||||||||
\(127\) | 14.5745i | 1.29328i | 0.762796 | + | 0.646640i | \(0.223826\pi\) | ||||
−0.762796 | + | 0.646640i | \(0.776174\pi\) | |||||||
\(128\) | 5.91748i | 0.523037i | ||||||||
\(129\) | 9.27504 | 0.816622 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.92478 | −0.517650 | −0.258825 | − | 0.965924i | \(-0.583335\pi\) | ||||
−0.258825 | + | 0.965924i | \(0.583335\pi\) | |||||||
\(132\) | 1.96239i | 0.170804i | ||||||||
\(133\) | − 14.4485i | − 1.25284i | ||||||||
\(134\) | 1.14903 | 0.0992612 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.51530 | −0.301434 | ||||||||
\(137\) | − 13.8496i | − 1.18325i | −0.806214 | − | 0.591624i | \(-0.798487\pi\) | ||||
0.806214 | − | 0.591624i | \(-0.201513\pi\) | |||||||
\(138\) | 1.29948i | 0.110619i | ||||||||
\(139\) | −13.6121 | −1.15457 | −0.577283 | − | 0.816544i | \(-0.695887\pi\) | ||||
−0.577283 | + | 0.816544i | \(0.695887\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.92478 | −0.835817 | ||||||||
\(142\) | 1.92478i | 0.161524i | ||||||||
\(143\) | 2.96239i | 0.247727i | ||||||||
\(144\) | −3.77575 | −0.314646 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.50071 | 0.124199 | ||||||||
\(147\) | − 4.22425i | − 0.348411i | ||||||||
\(148\) | 3.92478i | 0.322615i | ||||||||
\(149\) | −1.53690 | −0.125908 | −0.0629540 | − | 0.998016i | \(-0.520052\pi\) | ||||
−0.0629540 | + | 0.998016i | \(0.520052\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.76116 | −0.550215 | −0.275108 | − | 0.961413i | \(-0.588713\pi\) | ||||
−0.275108 | + | 0.961413i | \(0.588713\pi\) | |||||||
\(152\) | 3.31406i | 0.268806i | ||||||||
\(153\) | − 4.57452i | − 0.369828i | ||||||||
\(154\) | 0.649738 | 0.0523574 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.81336 | −0.465441 | ||||||||
\(157\) | 5.47627i | 0.437054i | 0.975831 | + | 0.218527i | \(0.0701252\pi\) | ||||
−0.975831 | + | 0.218527i | \(0.929875\pi\) | |||||||
\(158\) | − 2.23743i | − 0.178000i | ||||||||
\(159\) | −4.70052 | −0.372776 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.4485 | −1.76919 | ||||||||
\(162\) | 0.193937i | 0.0152371i | ||||||||
\(163\) | 12.6253i | 0.988890i | 0.869209 | + | 0.494445i | \(0.164629\pi\) | ||||
−0.869209 | + | 0.494445i | \(0.835371\pi\) | |||||||
\(164\) | −8.61071 | −0.672384 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.11142 | −0.163878 | ||||||||
\(167\) | − 18.3634i | − 1.42101i | −0.703695 | − | 0.710503i | \(-0.748468\pi\) | ||||
0.703695 | − | 0.710503i | \(-0.251532\pi\) | |||||||
\(168\) | 2.57452i | 0.198628i | ||||||||
\(169\) | 4.22425 | 0.324943 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.31265 | −0.329797 | ||||||||
\(172\) | − 18.2012i | − 1.38783i | ||||||||
\(173\) | − 8.57452i | − 0.651908i | −0.945386 | − | 0.325954i | \(-0.894314\pi\) | ||||
0.945386 | − | 0.325954i | \(-0.105686\pi\) | |||||||
\(174\) | −0.700523 | −0.0531065 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.77575 | 0.284608 | ||||||||
\(177\) | − 10.7005i | − 0.804301i | ||||||||
\(178\) | 0.538319i | 0.0403487i | ||||||||
\(179\) | −14.1768 | −1.05962 | −0.529812 | − | 0.848115i | \(-0.677737\pi\) | ||||
−0.529812 | + | 0.848115i | \(0.677737\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.22425 | −0.388316 | −0.194158 | − | 0.980970i | \(-0.562197\pi\) | ||||
−0.194158 | + | 0.980970i | \(0.562197\pi\) | |||||||
\(182\) | 1.92478i | 0.142674i | ||||||||
\(183\) | − 8.70052i | − 0.643161i | ||||||||
\(184\) | 5.14903 | 0.379592 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.92478 | −0.141132 | ||||||||
\(187\) | 4.57452i | 0.334522i | ||||||||
\(188\) | 19.4763i | 1.42045i | ||||||||
\(189\) | −3.35026 | −0.243696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.6253 | −1.20296 | −0.601482 | − | 0.798886i | \(-0.705423\pi\) | ||||
−0.601482 | + | 0.798886i | \(0.705423\pi\) | |||||||
\(192\) | 7.11142i | 0.513222i | ||||||||
\(193\) | − 16.3634i | − 1.17787i | −0.808182 | − | 0.588933i | \(-0.799548\pi\) | ||||
0.808182 | − | 0.588933i | \(-0.200452\pi\) | |||||||
\(194\) | 0.0145884 | 0.00104739 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.28963 | −0.592116 | ||||||||
\(197\) | 20.4241i | 1.45515i | 0.686026 | + | 0.727577i | \(0.259354\pi\) | ||||
−0.686026 | + | 0.727577i | \(0.740646\pi\) | |||||||
\(198\) | − 0.193937i | − 0.0137825i | ||||||||
\(199\) | 8.62530 | 0.611431 | 0.305716 | − | 0.952123i | \(-0.401104\pi\) | ||||
0.305716 | + | 0.952123i | \(0.401104\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.92478 | 0.417902 | ||||||||
\(202\) | − 2.92619i | − 0.205886i | ||||||||
\(203\) | − 12.1016i | − 0.849364i | ||||||||
\(204\) | −8.97698 | −0.628514 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.625301 | 0.0435668 | ||||||||
\(207\) | 6.70052i | 0.465719i | ||||||||
\(208\) | 11.1852i | 0.775556i | ||||||||
\(209\) | 4.31265 | 0.298312 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.08840 | 0.625671 | 0.312836 | − | 0.949807i | \(-0.398721\pi\) | ||||
0.312836 | + | 0.949807i | \(0.398721\pi\) | |||||||
\(212\) | 9.22425i | 0.633524i | ||||||||
\(213\) | 9.92478i | 0.680035i | ||||||||
\(214\) | −0.186642 | −0.0127586 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.768452 | 0.0522865 | ||||||||
\(217\) | − 33.2506i | − 2.25720i | ||||||||
\(218\) | − 2.21108i | − 0.149753i | ||||||||
\(219\) | 7.73813 | 0.522895 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.5515 | −0.911572 | ||||||||
\(222\) | − 0.387873i | − 0.0260323i | ||||||||
\(223\) | − 6.70052i | − 0.448700i | −0.974509 | − | 0.224350i | \(-0.927974\pi\) | ||||
0.974509 | − | 0.224350i | \(-0.0720259\pi\) | |||||||
\(224\) | 7.60228 | 0.507949 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.16362 | 0.0774028 | ||||||||
\(227\) | − 16.9624i | − 1.12583i | −0.826514 | − | 0.562917i | \(-0.809679\pi\) | ||||
0.826514 | − | 0.562917i | \(-0.190321\pi\) | |||||||
\(228\) | 8.46310i | 0.560482i | ||||||||
\(229\) | −25.8496 | −1.70819 | −0.854093 | − | 0.520120i | \(-0.825887\pi\) | ||||
−0.854093 | + | 0.520120i | \(0.825887\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.35026 | 0.220431 | ||||||||
\(232\) | 2.77575i | 0.182237i | ||||||||
\(233\) | − 19.2750i | − 1.26275i | −0.775478 | − | 0.631375i | \(-0.782491\pi\) | ||||
0.775478 | − | 0.631375i | \(-0.217509\pi\) | |||||||
\(234\) | 0.574515 | 0.0375573 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −20.9986 | −1.36689 | ||||||||
\(237\) | − 11.5369i | − 0.749402i | ||||||||
\(238\) | 2.97224i | 0.192662i | ||||||||
\(239\) | −26.5501 | −1.71738 | −0.858691 | − | 0.512494i | \(-0.828722\pi\) | ||||
−0.858691 | + | 0.512494i | \(0.828722\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.5501 | 1.83907 | 0.919536 | − | 0.393006i | \(-0.128565\pi\) | ||||
0.919536 | + | 0.393006i | \(0.128565\pi\) | |||||||
\(242\) | 0.193937i | 0.0124667i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −17.0738 | −1.09304 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.850969 | 0.0542558 | ||||||||
\(247\) | 12.7757i | 0.812901i | ||||||||
\(248\) | 7.62672i | 0.484297i | ||||||||
\(249\) | −10.8872 | −0.689946 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.9248 | 1.88884 | 0.944418 | − | 0.328748i | \(-0.106627\pi\) | ||||
0.944418 | + | 0.328748i | \(0.106627\pi\) | |||||||
\(252\) | 6.57452i | 0.414156i | ||||||||
\(253\) | − 6.70052i | − 0.421258i | ||||||||
\(254\) | −2.82653 | −0.177352 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.0752 | 0.817201 | ||||||||
\(257\) | − 8.70052i | − 0.542724i | −0.962477 | − | 0.271362i | \(-0.912526\pi\) | ||||
0.962477 | − | 0.271362i | \(-0.0874740\pi\) | |||||||
\(258\) | 1.79877i | 0.111986i | ||||||||
\(259\) | 6.70052 | 0.416350 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.61213 | −0.223585 | ||||||||
\(262\) | − 1.14903i | − 0.0709874i | ||||||||
\(263\) | 12.2882i | 0.757724i | 0.925453 | + | 0.378862i | \(0.123684\pi\) | ||||
−0.925453 | + | 0.378862i | \(0.876316\pi\) | |||||||
\(264\) | −0.768452 | −0.0472950 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.80209 | 0.171807 | ||||||||
\(267\) | 2.77575i | 0.169873i | ||||||||
\(268\) | − 11.6267i | − 0.710215i | ||||||||
\(269\) | 5.84955 | 0.356654 | 0.178327 | − | 0.983971i | \(-0.442932\pi\) | ||||
0.178327 | + | 0.983971i | \(0.442932\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.08840 | −0.309098 | −0.154549 | − | 0.987985i | \(-0.549392\pi\) | ||||
−0.154549 | + | 0.987985i | \(0.549392\pi\) | |||||||
\(272\) | 17.2722i | 1.04728i | ||||||||
\(273\) | 9.92478i | 0.600675i | ||||||||
\(274\) | 2.68594 | 0.162263 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 13.1490 | 0.791479 | ||||||||
\(277\) | − 1.41090i | − 0.0847725i | −0.999101 | − | 0.0423863i | \(-0.986504\pi\) | ||||
0.999101 | − | 0.0423863i | \(-0.0134960\pi\) | |||||||
\(278\) | − 2.63989i | − 0.158330i | ||||||||
\(279\) | −9.92478 | −0.594181 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.38787 | −0.261759 | −0.130879 | − | 0.991398i | \(-0.541780\pi\) | ||||
−0.130879 | + | 0.991398i | \(0.541780\pi\) | |||||||
\(282\) | − 1.92478i | − 0.114619i | ||||||||
\(283\) | 26.5745i | 1.57969i | 0.613306 | + | 0.789845i | \(0.289839\pi\) | ||||
−0.613306 | + | 0.789845i | \(0.710161\pi\) | |||||||
\(284\) | 19.4763 | 1.15570 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.574515 | −0.0339718 | ||||||||
\(287\) | 14.7005i | 0.867744i | ||||||||
\(288\) | − 2.26916i | − 0.133711i | ||||||||
\(289\) | −3.92619 | −0.230952 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0752228 | 0.00440964 | ||||||||
\(292\) | − 15.1852i | − 0.888648i | ||||||||
\(293\) | − 3.42548i | − 0.200119i | −0.994981 | − | 0.100059i | \(-0.968097\pi\) | ||||
0.994981 | − | 0.100059i | \(-0.0319033\pi\) | |||||||
\(294\) | 0.819237 | 0.0477789 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.53690 | −0.0893307 | ||||||||
\(297\) | − 1.00000i | − 0.0580259i | ||||||||
\(298\) | − 0.298062i | − 0.0172663i | ||||||||
\(299\) | 19.8496 | 1.14793 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −31.0738 | −1.79106 | ||||||||
\(302\) | − 1.31124i | − 0.0754531i | ||||||||
\(303\) | − 15.0884i | − 0.866806i | ||||||||
\(304\) | 16.2835 | 0.933921 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.887166 | 0.0507159 | ||||||||
\(307\) | 16.6497i | 0.950251i | 0.879918 | + | 0.475125i | \(0.157597\pi\) | ||||
−0.879918 | + | 0.475125i | \(0.842403\pi\) | |||||||
\(308\) | − 6.57452i | − 0.374618i | ||||||||
\(309\) | 3.22425 | 0.183421 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.9986 | 1.87118 | 0.935589 | − | 0.353091i | \(-0.114869\pi\) | ||||
0.935589 | + | 0.353091i | \(0.114869\pi\) | |||||||
\(312\) | − 2.27645i | − 0.128879i | ||||||||
\(313\) | 15.4010i | 0.870519i | 0.900305 | + | 0.435259i | \(0.143343\pi\) | ||||
−0.900305 | + | 0.435259i | \(0.856657\pi\) | |||||||
\(314\) | −1.06205 | −0.0599349 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −22.6399 | −1.27359 | ||||||||
\(317\) | − 2.15045i | − 0.120781i | −0.998175 | − | 0.0603905i | \(-0.980765\pi\) | ||||
0.998175 | − | 0.0603905i | \(-0.0192346\pi\) | |||||||
\(318\) | − 0.911603i | − 0.0511202i | ||||||||
\(319\) | 3.61213 | 0.202240 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.962389 | −0.0537153 | ||||||||
\(322\) | − 4.35359i | − 0.242616i | ||||||||
\(323\) | 19.7283i | 1.09771i | ||||||||
\(324\) | 1.96239 | 0.109022 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.44851 | −0.135610 | ||||||||
\(327\) | − 11.4010i | − 0.630479i | ||||||||
\(328\) | − 3.37187i | − 0.186180i | ||||||||
\(329\) | 33.2506 | 1.83316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.5501 | −0.799745 | −0.399872 | − | 0.916571i | \(-0.630946\pi\) | ||||
−0.399872 | + | 0.916571i | \(0.630946\pi\) | |||||||
\(332\) | 21.3649i | 1.17255i | ||||||||
\(333\) | − 2.00000i | − 0.109599i | ||||||||
\(334\) | 3.56134 | 0.194868 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 12.6497 | 0.690100 | ||||||||
\(337\) | − 16.2619i | − 0.885840i | −0.896561 | − | 0.442920i | \(-0.853943\pi\) | ||||
0.896561 | − | 0.442920i | \(-0.146057\pi\) | |||||||
\(338\) | 0.819237i | 0.0445606i | ||||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.92478 | 0.537457 | ||||||||
\(342\) | − 0.836381i | − 0.0452263i | ||||||||
\(343\) | − 9.29948i | − 0.502125i | ||||||||
\(344\) | 7.12742 | 0.384285 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.66291 | 0.0893987 | ||||||||
\(347\) | 0.962389i | 0.0516637i | 0.999666 | + | 0.0258319i | \(0.00822345\pi\) | ||||
−0.999666 | + | 0.0258319i | \(0.991777\pi\) | |||||||
\(348\) | 7.08840i | 0.379978i | ||||||||
\(349\) | −20.7005 | −1.10807 | −0.554037 | − | 0.832492i | \(-0.686913\pi\) | ||||
−0.554037 | + | 0.832492i | \(0.686913\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.96239 | 0.158121 | ||||||||
\(352\) | 2.26916i | 0.120947i | ||||||||
\(353\) | 20.5501i | 1.09377i | 0.837208 | + | 0.546885i | \(0.184187\pi\) | ||||
−0.837208 | + | 0.546885i | \(0.815813\pi\) | |||||||
\(354\) | 2.07522 | 0.110297 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.44709 | 0.288695 | ||||||||
\(357\) | 15.3258i | 0.811129i | ||||||||
\(358\) | − 2.74940i | − 0.145310i | ||||||||
\(359\) | −17.9248 | −0.946034 | −0.473017 | − | 0.881053i | \(-0.656835\pi\) | ||||
−0.473017 | + | 0.881053i | \(0.656835\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.401047 | −0.0211077 | ||||||||
\(362\) | − 1.01317i | − 0.0532512i | ||||||||
\(363\) | 1.00000i | 0.0524864i | ||||||||
\(364\) | 19.4763 | 1.02083 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.68735 | 0.0881992 | ||||||||
\(367\) | 29.6531i | 1.54788i | 0.633261 | + | 0.773939i | \(0.281716\pi\) | ||||
−0.633261 | + | 0.773939i | \(0.718284\pi\) | |||||||
\(368\) | − 25.2995i | − 1.31883i | ||||||||
\(369\) | 4.38787 | 0.228424 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.7480 | 0.817595 | ||||||||
\(372\) | 19.4763i | 1.00980i | ||||||||
\(373\) | − 9.13918i | − 0.473209i | −0.971606 | − | 0.236604i | \(-0.923965\pi\) | ||||
0.971606 | − | 0.236604i | \(-0.0760345\pi\) | |||||||
\(374\) | −0.887166 | −0.0458743 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.62672 | −0.393318 | ||||||||
\(377\) | 10.7005i | 0.551105i | ||||||||
\(378\) | − 0.649738i | − 0.0334189i | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.5745 | −0.746675 | ||||||||
\(382\) | − 3.22425i | − 0.164967i | ||||||||
\(383\) | − 34.9234i | − 1.78450i | −0.451541 | − | 0.892250i | \(-0.649126\pi\) | ||||
0.451541 | − | 0.892250i | \(-0.350874\pi\) | |||||||
\(384\) | −5.91748 | −0.301975 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.17347 | 0.161525 | ||||||||
\(387\) | 9.27504i | 0.471477i | ||||||||
\(388\) | − 0.147616i | − 0.00749408i | ||||||||
\(389\) | −2.77575 | −0.140736 | −0.0703680 | − | 0.997521i | \(-0.522417\pi\) | ||||
−0.0703680 | + | 0.997521i | \(0.522417\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.6516 | 1.55012 | ||||||||
\(392\) | − 3.24614i | − 0.163955i | ||||||||
\(393\) | − 5.92478i | − 0.298865i | ||||||||
\(394\) | −3.96097 | −0.199551 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.96239 | −0.0986137 | ||||||||
\(397\) | 19.9248i | 0.999996i | 0.866027 | + | 0.499998i | \(0.166666\pi\) | ||||
−0.866027 | + | 0.499998i | \(0.833334\pi\) | |||||||
\(398\) | 1.67276i | 0.0838479i | ||||||||
\(399\) | 14.4485 | 0.723330 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | 1.14903i | 0.0573085i | ||||||||
\(403\) | 29.4010i | 1.46457i | ||||||||
\(404\) | −29.6093 | −1.47312 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.34694 | 0.116477 | ||||||||
\(407\) | 2.00000i | 0.0991363i | ||||||||
\(408\) | − 3.51530i | − 0.174033i | ||||||||
\(409\) | 13.0738 | 0.646458 | 0.323229 | − | 0.946321i | \(-0.395232\pi\) | ||||
0.323229 | + | 0.946321i | \(0.395232\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.8496 | 0.683148 | ||||||||
\(412\) | − 6.32724i | − 0.311721i | ||||||||
\(413\) | 35.8496i | 1.76404i | ||||||||
\(414\) | −1.29948 | −0.0638658 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.72213 | −0.329580 | ||||||||
\(417\) | − 13.6121i | − 0.666589i | ||||||||
\(418\) | 0.836381i | 0.0409087i | ||||||||
\(419\) | −7.22425 | −0.352928 | −0.176464 | − | 0.984307i | \(-0.556466\pi\) | ||||
−0.176464 | + | 0.984307i | \(0.556466\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.6253 | 1.49259 | 0.746293 | − | 0.665618i | \(-0.231832\pi\) | ||||
0.746293 | + | 0.665618i | \(0.231832\pi\) | |||||||
\(422\) | 1.76257i | 0.0858007i | ||||||||
\(423\) | − 9.92478i | − 0.482559i | ||||||||
\(424\) | −3.61213 | −0.175420 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.92478 | −0.0932558 | ||||||||
\(427\) | 29.1490i | 1.41062i | ||||||||
\(428\) | 1.88858i | 0.0912880i | ||||||||
\(429\) | −2.96239 | −0.143025 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.8759 | −1.63174 | −0.815872 | − | 0.578232i | \(-0.803743\pi\) | ||||
−0.815872 | + | 0.578232i | \(0.803743\pi\) | |||||||
\(432\) | − 3.77575i | − 0.181661i | ||||||||
\(433\) | − 9.47627i | − 0.455400i | −0.973731 | − | 0.227700i | \(-0.926879\pi\) | ||||
0.973731 | − | 0.227700i | \(-0.0731206\pi\) | |||||||
\(434\) | 6.44851 | 0.309538 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −22.3733 | −1.07149 | ||||||||
\(437\) | − 28.8970i | − 1.38233i | ||||||||
\(438\) | 1.50071i | 0.0717066i | ||||||||
\(439\) | 29.4617 | 1.40613 | 0.703065 | − | 0.711126i | \(-0.251814\pi\) | ||||
0.703065 | + | 0.711126i | \(0.251814\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.22425 | 0.201155 | ||||||||
\(442\) | − 2.62813i | − 0.125007i | ||||||||
\(443\) | − 19.0738i | − 0.906224i | −0.891454 | − | 0.453112i | \(-0.850314\pi\) | ||||
0.891454 | − | 0.453112i | \(-0.149686\pi\) | |||||||
\(444\) | −3.92478 | −0.186262 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.29948 | 0.0615320 | ||||||||
\(447\) | − 1.53690i | − 0.0726931i | ||||||||
\(448\) | − 23.8251i | − 1.12563i | ||||||||
\(449\) | −35.8759 | −1.69309 | −0.846544 | − | 0.532318i | \(-0.821321\pi\) | ||||
−0.846544 | + | 0.532318i | \(0.821321\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.38787 | −0.206617 | ||||||||
\(452\) | − 11.7743i | − 0.553818i | ||||||||
\(453\) | − 6.76116i | − 0.317667i | ||||||||
\(454\) | 3.28963 | 0.154390 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.31406 | −0.155195 | ||||||||
\(457\) | − 5.28963i | − 0.247438i | −0.992317 | − | 0.123719i | \(-0.960518\pi\) | ||||
0.992317 | − | 0.123719i | \(-0.0394822\pi\) | |||||||
\(458\) | − 5.01317i | − 0.234250i | ||||||||
\(459\) | 4.57452 | 0.213520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.3390 | 1.69248 | 0.846238 | − | 0.532805i | \(-0.178862\pi\) | ||||
0.846238 | + | 0.532805i | \(0.178862\pi\) | |||||||
\(462\) | 0.649738i | 0.0302286i | ||||||||
\(463\) | 10.5501i | 0.490304i | 0.969485 | + | 0.245152i | \(0.0788378\pi\) | ||||
−0.969485 | + | 0.245152i | \(0.921162\pi\) | |||||||
\(464\) | 13.6385 | 0.633150 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.73813 | 0.173166 | ||||||||
\(467\) | − 18.7005i | − 0.865357i | −0.901548 | − | 0.432679i | \(-0.857569\pi\) | ||||
0.901548 | − | 0.432679i | \(-0.142431\pi\) | |||||||
\(468\) | − 5.81336i | − 0.268723i | ||||||||
\(469\) | −19.8496 | −0.916567 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.47627 | −0.252333 | ||||||||
\(472\) | − 8.22284i | − 0.378487i | ||||||||
\(473\) | − 9.27504i | − 0.426467i | ||||||||
\(474\) | 2.23743 | 0.102768 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 30.0752 | 1.37850 | ||||||||
\(477\) | − 4.70052i | − 0.215222i | ||||||||
\(478\) | − 5.14903i | − 0.235511i | ||||||||
\(479\) | 9.29948 | 0.424904 | 0.212452 | − | 0.977172i | \(-0.431855\pi\) | ||||
0.212452 | + | 0.977172i | \(0.431855\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.92478 | −0.270147 | ||||||||
\(482\) | 5.53690i | 0.252199i | ||||||||
\(483\) | − 22.4485i | − 1.02144i | ||||||||
\(484\) | 1.96239 | 0.0891995 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.193937 | −0.00879714 | ||||||||
\(487\) | 35.4763i | 1.60758i | 0.594911 | + | 0.803792i | \(0.297187\pi\) | ||||
−0.594911 | + | 0.803792i | \(0.702813\pi\) | |||||||
\(488\) | − 6.68594i | − 0.302658i | ||||||||
\(489\) | −12.6253 | −0.570936 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.7757 | 1.11811 | 0.559057 | − | 0.829129i | \(-0.311163\pi\) | ||||
0.559057 | + | 0.829129i | \(0.311163\pi\) | |||||||
\(492\) | − 8.61071i | − 0.388201i | ||||||||
\(493\) | 16.5237i | 0.744191i | ||||||||
\(494\) | −2.47768 | −0.111476 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 37.4734 | 1.68261 | ||||||||
\(497\) | − 33.2506i | − 1.49149i | ||||||||
\(498\) | − 2.11142i | − 0.0946150i | ||||||||
\(499\) | −14.1768 | −0.634640 | −0.317320 | − | 0.948318i | \(-0.602783\pi\) | ||||
−0.317320 | + | 0.948318i | \(0.602783\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.3634 | 0.820418 | ||||||||
\(502\) | 5.80351i | 0.259023i | ||||||||
\(503\) | − 8.43866i | − 0.376261i | −0.982144 | − | 0.188131i | \(-0.939757\pi\) | ||||
0.982144 | − | 0.188131i | \(-0.0602428\pi\) | |||||||
\(504\) | −2.57452 | −0.114678 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.29948 | 0.0577688 | ||||||||
\(507\) | 4.22425i | 0.187606i | ||||||||
\(508\) | 28.6009i | 1.26896i | ||||||||
\(509\) | −1.10299 | −0.0488890 | −0.0244445 | − | 0.999701i | \(-0.507782\pi\) | ||||
−0.0244445 | + | 0.999701i | \(0.507782\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.9248 | −1.14684 | ||||||||
\(512\) | 14.3707i | 0.635103i | ||||||||
\(513\) | − 4.31265i | − 0.190408i | ||||||||
\(514\) | 1.68735 | 0.0744258 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 18.2012 | 0.801265 | ||||||||
\(517\) | 9.92478i | 0.436491i | ||||||||
\(518\) | 1.29948i | 0.0570957i | ||||||||
\(519\) | 8.57452 | 0.376379 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.4485 | −0.545379 | −0.272690 | − | 0.962102i | \(-0.587913\pi\) | ||||
−0.272690 | + | 0.962102i | \(0.587913\pi\) | |||||||
\(522\) | − 0.700523i | − 0.0306611i | ||||||||
\(523\) | 30.0508i | 1.31403i | 0.753878 | + | 0.657015i | \(0.228181\pi\) | ||||
−0.753878 | + | 0.657015i | \(0.771819\pi\) | |||||||
\(524\) | −11.6267 | −0.507915 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.38313 | −0.103910 | ||||||||
\(527\) | 45.4010i | 1.97770i | ||||||||
\(528\) | 3.77575i | 0.164318i | ||||||||
\(529\) | −21.8970 | −0.952044 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.7005 | 0.464363 | ||||||||
\(532\) | − 28.3536i | − 1.22928i | ||||||||
\(533\) | − 12.9986i | − 0.563031i | ||||||||
\(534\) | −0.538319 | −0.0232953 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.55291 | 0.196656 | ||||||||
\(537\) | − 14.1768i | − 0.611774i | ||||||||
\(538\) | 1.13444i | 0.0489093i | ||||||||
\(539\) | −4.22425 | −0.181951 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0000 | −0.773880 | −0.386940 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386940 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(542\) | − 0.986826i | − 0.0423878i | ||||||||
\(543\) | − 5.22425i | − 0.224194i | ||||||||
\(544\) | −10.3803 | −0.445052 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.92478 | −0.0823729 | ||||||||
\(547\) | 14.3028i | 0.611544i | 0.952105 | + | 0.305772i | \(0.0989145\pi\) | ||||
−0.952105 | + | 0.305772i | \(0.901086\pi\) | |||||||
\(548\) | − 27.1782i | − 1.16100i | ||||||||
\(549\) | 8.70052 | 0.371329 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.5778 | 0.663638 | ||||||||
\(552\) | 5.14903i | 0.219157i | ||||||||
\(553\) | 38.6516i | 1.64364i | ||||||||
\(554\) | 0.273624 | 0.0116252 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −26.7123 | −1.13285 | ||||||||
\(557\) | 11.7988i | 0.499930i | 0.968255 | + | 0.249965i | \(0.0804191\pi\) | ||||
−0.968255 | + | 0.249965i | \(0.919581\pi\) | |||||||
\(558\) | − 1.92478i | − 0.0814823i | ||||||||
\(559\) | 27.4763 | 1.16212 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.57452 | −0.193136 | ||||||||
\(562\) | − 0.850969i | − 0.0358960i | ||||||||
\(563\) | 30.4847i | 1.28478i | 0.766379 | + | 0.642389i | \(0.222056\pi\) | ||||
−0.766379 | + | 0.642389i | \(0.777944\pi\) | |||||||
\(564\) | −19.4763 | −0.820099 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.15377 | −0.216629 | ||||||||
\(567\) | − 3.35026i | − 0.140698i | ||||||||
\(568\) | 7.62672i | 0.320010i | ||||||||
\(569\) | 27.0884 | 1.13560 | 0.567802 | − | 0.823165i | \(-0.307794\pi\) | ||||
0.567802 | + | 0.823165i | \(0.307794\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.28489 | 0.304863 | 0.152432 | − | 0.988314i | \(-0.451290\pi\) | ||||
0.152432 | + | 0.988314i | \(0.451290\pi\) | |||||||
\(572\) | 5.81336i | 0.243069i | ||||||||
\(573\) | − 16.6253i | − 0.694532i | ||||||||
\(574\) | −2.85097 | −0.118997 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.11142 | −0.296309 | ||||||||
\(577\) | 31.6239i | 1.31652i | 0.752791 | + | 0.658260i | \(0.228707\pi\) | ||||
−0.752791 | + | 0.658260i | \(0.771293\pi\) | |||||||
\(578\) | − 0.761432i | − 0.0316714i | ||||||||
\(579\) | 16.3634 | 0.680041 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.4749 | 1.51323 | ||||||||
\(582\) | 0.0145884i | 0 0.000604711i | ||||||||
\(583\) | 4.70052i | 0.194676i | ||||||||
\(584\) | 5.94639 | 0.246063 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.664327 | 0.0274431 | ||||||||
\(587\) | − 33.1490i | − 1.36821i | −0.729385 | − | 0.684103i | \(-0.760194\pi\) | ||||
0.729385 | − | 0.684103i | \(-0.239806\pi\) | |||||||
\(588\) | − 8.28963i | − 0.341858i | ||||||||
\(589\) | 42.8021 | 1.76363 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.4241 | −0.840134 | ||||||||
\(592\) | 7.55149i | 0.310364i | ||||||||
\(593\) | 34.4993i | 1.41672i | 0.705853 | + | 0.708358i | \(0.250564\pi\) | ||||
−0.705853 | + | 0.708358i | \(0.749436\pi\) | |||||||
\(594\) | 0.193937 | 0.00795731 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.01600 | −0.123540 | ||||||||
\(597\) | 8.62530i | 0.353010i | ||||||||
\(598\) | 3.84955i | 0.157420i | ||||||||
\(599\) | 14.4485 | 0.590350 | 0.295175 | − | 0.955443i | \(-0.404622\pi\) | ||||
0.295175 | + | 0.955443i | \(0.404622\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.9248 | −0.649585 | −0.324793 | − | 0.945785i | \(-0.605295\pi\) | ||||
−0.324793 | + | 0.945785i | \(0.605295\pi\) | |||||||
\(602\) | − 6.02635i | − 0.245616i | ||||||||
\(603\) | 5.92478i | 0.241276i | ||||||||
\(604\) | −13.2680 | −0.539868 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.92619 | 0.118868 | ||||||||
\(607\) | 14.5745i | 0.591561i | 0.955256 | + | 0.295781i | \(0.0955798\pi\) | ||||
−0.955256 | + | 0.295781i | \(0.904420\pi\) | |||||||
\(608\) | 9.78609i | 0.396878i | ||||||||
\(609\) | 12.1016 | 0.490380 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.4010 | −1.18944 | ||||||||
\(612\) | − 8.97698i | − 0.362873i | ||||||||
\(613\) | 16.4123i | 0.662887i | 0.943475 | + | 0.331443i | \(0.107536\pi\) | ||||
−0.943475 | + | 0.331443i | \(0.892464\pi\) | |||||||
\(614\) | −3.22899 | −0.130312 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.57452 | 0.103730 | ||||||||
\(617\) | 17.8496i | 0.718596i | 0.933223 | + | 0.359298i | \(0.116984\pi\) | ||||
−0.933223 | + | 0.359298i | \(0.883016\pi\) | |||||||
\(618\) | 0.625301i | 0.0251533i | ||||||||
\(619\) | 0.402462 | 0.0161763 | 0.00808815 | − | 0.999967i | \(-0.497425\pi\) | ||||
0.00808815 | + | 0.999967i | \(0.497425\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.70052 | −0.268883 | ||||||||
\(622\) | 6.39963i | 0.256602i | ||||||||
\(623\) | − 9.29948i | − 0.372576i | ||||||||
\(624\) | −11.1852 | −0.447767 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.98683 | −0.119378 | ||||||||
\(627\) | 4.31265i | 0.172231i | ||||||||
\(628\) | 10.7466i | 0.428835i | ||||||||
\(629\) | −9.14903 | −0.364796 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.0263 | −1.51380 | −0.756902 | − | 0.653528i | \(-0.773288\pi\) | ||||
−0.756902 | + | 0.653528i | \(0.773288\pi\) | |||||||
\(632\) | − 8.86556i | − 0.352653i | ||||||||
\(633\) | 9.08840i | 0.361231i | ||||||||
\(634\) | 0.417050 | 0.0165632 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9.22425 | −0.365765 | ||||||||
\(637\) | − 12.5139i | − 0.495818i | ||||||||
\(638\) | 0.700523i | 0.0277340i | ||||||||
\(639\) | −9.92478 | −0.392618 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.0263 | −1.10697 | −0.553487 | − | 0.832858i | \(-0.686703\pi\) | ||||
−0.553487 | + | 0.832858i | \(0.686703\pi\) | |||||||
\(642\) | − 0.186642i | − 0.00736619i | ||||||||
\(643\) | − 4.62530i | − 0.182404i | −0.995832 | − | 0.0912020i | \(-0.970929\pi\) | ||||
0.995832 | − | 0.0912020i | \(-0.0290709\pi\) | |||||||
\(644\) | −44.0527 | −1.73592 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.82604 | −0.150533 | ||||||||
\(647\) | − 23.5778i | − 0.926941i | −0.886112 | − | 0.463470i | \(-0.846604\pi\) | ||||
0.886112 | − | 0.463470i | \(-0.153396\pi\) | |||||||
\(648\) | 0.768452i | 0.0301876i | ||||||||
\(649\) | −10.7005 | −0.420032 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 33.2506 | 1.30319 | ||||||||
\(652\) | 24.7757i | 0.970293i | ||||||||
\(653\) | − 2.25202i | − 0.0881282i | −0.999029 | − | 0.0440641i | \(-0.985969\pi\) | ||||
0.999029 | − | 0.0440641i | \(-0.0140306\pi\) | |||||||
\(654\) | 2.21108 | 0.0864601 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −16.5675 | −0.646852 | ||||||||
\(657\) | 7.73813i | 0.301893i | ||||||||
\(658\) | 6.44851i | 0.251389i | ||||||||
\(659\) | 41.4010 | 1.61276 | 0.806378 | − | 0.591401i | \(-0.201425\pi\) | ||||
0.806378 | + | 0.591401i | \(0.201425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.40105 | 0.132285 | 0.0661427 | − | 0.997810i | \(-0.478931\pi\) | ||||
0.0661427 | + | 0.997810i | \(0.478931\pi\) | |||||||
\(662\) | − 2.82179i | − 0.109672i | ||||||||
\(663\) | − 13.5515i | − 0.526296i | ||||||||
\(664\) | −8.36626 | −0.324674 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.387873 | 0.0150298 | ||||||||
\(667\) | − 24.2031i | − 0.937149i | ||||||||
\(668\) | − 36.0362i | − 1.39428i | ||||||||
\(669\) | 6.70052 | 0.259057 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.70052 | −0.335880 | ||||||||
\(672\) | 7.60228i | 0.293264i | ||||||||
\(673\) | 0.887166i | 0.0341977i | 0.999854 | + | 0.0170989i | \(0.00544300\pi\) | ||||
−0.999854 | + | 0.0170989i | \(0.994557\pi\) | |||||||
\(674\) | 3.15377 | 0.121479 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.28963 | 0.318832 | ||||||||
\(677\) | − 18.9018i | − 0.726453i | −0.931701 | − | 0.363227i | \(-0.881675\pi\) | ||||
0.931701 | − | 0.363227i | \(-0.118325\pi\) | |||||||
\(678\) | 1.16362i | 0.0446885i | ||||||||
\(679\) | −0.252016 | −0.00967149 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.9624 | 0.650000 | ||||||||
\(682\) | 1.92478i | 0.0737035i | ||||||||
\(683\) | − 20.8773i | − 0.798848i | −0.916766 | − | 0.399424i | \(-0.869210\pi\) | ||||
0.916766 | − | 0.399424i | \(-0.130790\pi\) | |||||||
\(684\) | −8.46310 | −0.323595 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.80351 | 0.0688583 | ||||||||
\(687\) | − 25.8496i | − 0.986222i | ||||||||
\(688\) | − 35.0202i | − 1.33513i | ||||||||
\(689\) | −13.9248 | −0.530492 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.44851 | −0.0931456 | −0.0465728 | − | 0.998915i | \(-0.514830\pi\) | ||||
−0.0465728 | + | 0.998915i | \(0.514830\pi\) | |||||||
\(692\) | − 16.8265i | − 0.639649i | ||||||||
\(693\) | 3.35026i | 0.127266i | ||||||||
\(694\) | −0.186642 | −0.00708485 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.77575 | −0.105214 | ||||||||
\(697\) | − 20.0724i | − 0.760296i | ||||||||
\(698\) | − 4.01459i | − 0.151954i | ||||||||
\(699\) | 19.2750 | 0.729049 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.98683 | −0.112811 | −0.0564054 | − | 0.998408i | \(-0.517964\pi\) | ||||
−0.0564054 | + | 0.998408i | \(0.517964\pi\) | |||||||
\(702\) | 0.574515i | 0.0216837i | ||||||||
\(703\) | 8.62530i | 0.325309i | ||||||||
\(704\) | 7.11142 | 0.268022 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.98541 | −0.149993 | ||||||||
\(707\) | 50.5501i | 1.90113i | ||||||||
\(708\) | − 20.9986i | − 0.789175i | ||||||||
\(709\) | −24.1768 | −0.907979 | −0.453989 | − | 0.891007i | \(-0.650000\pi\) | ||||
−0.453989 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.5369 | 0.432668 | ||||||||
\(712\) | 2.13303i | 0.0799386i | ||||||||
\(713\) | − 66.5012i | − 2.49049i | ||||||||
\(714\) | −2.97224 | −0.111233 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −27.8204 | −1.03970 | ||||||||
\(717\) | − 26.5501i | − 0.991531i | ||||||||
\(718\) | − 3.47627i | − 0.129733i | ||||||||
\(719\) | 30.0263 | 1.11979 | 0.559897 | − | 0.828562i | \(-0.310841\pi\) | ||||
0.559897 | + | 0.828562i | \(0.310841\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.8021 | −0.402291 | ||||||||
\(722\) | − 0.0777777i | − 0.00289459i | ||||||||
\(723\) | 28.5501i | 1.06179i | ||||||||
\(724\) | −10.2520 | −0.381013 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.193937 | −0.00719766 | ||||||||
\(727\) | − 14.9525i | − 0.554559i | −0.960789 | − | 0.277279i | \(-0.910567\pi\) | ||||
0.960789 | − | 0.277279i | \(-0.0894328\pi\) | |||||||
\(728\) | 7.62672i | 0.282665i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 42.4288 | 1.56929 | ||||||||
\(732\) | − 17.0738i | − 0.631066i | ||||||||
\(733\) | − 19.1128i | − 0.705949i | −0.935633 | − | 0.352974i | \(-0.885170\pi\) | ||||
0.935633 | − | 0.352974i | \(-0.114830\pi\) | |||||||
\(734\) | −5.75081 | −0.212266 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.2046 | 0.560447 | ||||||||
\(737\) | − 5.92478i | − 0.218242i | ||||||||
\(738\) | 0.850969i | 0.0313246i | ||||||||
\(739\) | 3.31406 | 0.121910 | 0.0609549 | − | 0.998141i | \(-0.480585\pi\) | ||||
0.0609549 | + | 0.998141i | \(0.480585\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.7757 | −0.469329 | ||||||||
\(742\) | 3.05411i | 0.112120i | ||||||||
\(743\) | − 34.9887i | − 1.28361i | −0.766867 | − | 0.641806i | \(-0.778185\pi\) | ||||
0.766867 | − | 0.641806i | \(-0.221815\pi\) | |||||||
\(744\) | −7.62672 | −0.279609 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.77242 | 0.0648930 | ||||||||
\(747\) | − 10.8872i | − 0.398341i | ||||||||
\(748\) | 8.97698i | 0.328231i | ||||||||
\(749\) | 3.22425 | 0.117812 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.9234 | −0.982447 | −0.491224 | − | 0.871033i | \(-0.663450\pi\) | ||||
−0.491224 | + | 0.871033i | \(0.663450\pi\) | |||||||
\(752\) | 37.4734i | 1.36652i | ||||||||
\(753\) | 29.9248i | 1.09052i | ||||||||
\(754\) | −2.07522 | −0.0755752 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −6.57452 | −0.239113 | ||||||||
\(757\) | − 15.9248i | − 0.578796i | −0.957209 | − | 0.289398i | \(-0.906545\pi\) | ||||
0.957209 | − | 0.289398i | \(-0.0934551\pi\) | |||||||
\(758\) | 3.87873i | 0.140882i | ||||||||
\(759\) | 6.70052 | 0.243214 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.9380 | −1.12150 | −0.560750 | − | 0.827985i | \(-0.689487\pi\) | ||||
−0.560750 | + | 0.827985i | \(0.689487\pi\) | |||||||
\(762\) | − 2.82653i | − 0.102394i | ||||||||
\(763\) | 38.1965i | 1.38281i | ||||||||
\(764\) | −32.6253 | −1.18034 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.77292 | 0.244715 | ||||||||
\(767\) | − 31.6991i | − 1.14459i | ||||||||
\(768\) | 13.0752i | 0.471811i | ||||||||
\(769\) | −9.32582 | −0.336298 | −0.168149 | − | 0.985762i | \(-0.553779\pi\) | ||||
−0.168149 | + | 0.985762i | \(0.553779\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.70052 | 0.313342 | ||||||||
\(772\) | − 32.1114i | − 1.15572i | ||||||||
\(773\) | 44.7005i | 1.60777i | 0.594787 | + | 0.803883i | \(0.297236\pi\) | ||||
−0.594787 | + | 0.803883i | \(0.702764\pi\) | |||||||
\(774\) | −1.79877 | −0.0646554 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.0578051 | 0.00207508 | ||||||||
\(777\) | 6.70052i | 0.240380i | ||||||||
\(778\) | − 0.538319i | − 0.0192997i | ||||||||
\(779\) | −18.9234 | −0.678000 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.92478 | 0.355136 | ||||||||
\(782\) | 5.94448i | 0.212574i | ||||||||
\(783\) | − 3.61213i | − 0.129087i | ||||||||
\(784\) | −15.9497 | −0.569633 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.14903 | 0.0409846 | ||||||||
\(787\) | − 21.6775i | − 0.772719i | −0.922348 | − | 0.386360i | \(-0.873732\pi\) | ||||
0.922348 | − | 0.386360i | \(-0.126268\pi\) | |||||||
\(788\) | 40.0800i | 1.42779i | ||||||||
\(789\) | −12.2882 | −0.437472 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.1016 | −0.714730 | ||||||||
\(792\) | − 0.768452i | − 0.0273058i | ||||||||
\(793\) | − 25.7743i | − 0.915273i | ||||||||
\(794\) | −3.86414 | −0.137133 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.9262 | 0.599933 | ||||||||
\(797\) | − 22.7466i | − 0.805725i | −0.915261 | − | 0.402862i | \(-0.868015\pi\) | ||||
0.915261 | − | 0.402862i | \(-0.131985\pi\) | |||||||
\(798\) | 2.80209i | 0.0991930i | ||||||||
\(799\) | −45.4010 | −1.60617 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.77575 | −0.0980762 | ||||||||
\(802\) | 0.387873i | 0.0136963i | ||||||||
\(803\) | − 7.73813i | − 0.273073i | ||||||||
\(804\) | 11.6267 | 0.410043 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.70194 | −0.200842 | ||||||||
\(807\) | 5.84955i | 0.205914i | ||||||||
\(808\) | − 11.5947i | − 0.407900i | ||||||||
\(809\) | 23.6121 | 0.830158 | 0.415079 | − | 0.909785i | \(-0.363754\pi\) | ||||
0.415079 | + | 0.909785i | \(0.363754\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.0870 | −0.916038 | −0.458019 | − | 0.888942i | \(-0.651441\pi\) | ||||
−0.458019 | + | 0.888942i | \(0.651441\pi\) | |||||||
\(812\) | − 23.7480i | − 0.833391i | ||||||||
\(813\) | − 5.08840i | − 0.178458i | ||||||||
\(814\) | −0.387873 | −0.0135949 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −17.2722 | −0.604648 | ||||||||
\(817\) | − 40.0000i | − 1.39942i | ||||||||
\(818\) | 2.53549i | 0.0886513i | ||||||||
\(819\) | −9.92478 | −0.346800 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.4142 | −1.89907 | −0.949535 | − | 0.313662i | \(-0.898444\pi\) | ||||
−0.949535 | + | 0.313662i | \(0.898444\pi\) | |||||||
\(822\) | 2.68594i | 0.0936827i | ||||||||
\(823\) | 0.121269i | 0.00422716i | 0.999998 | + | 0.00211358i | \(0.000672774\pi\) | ||||
−0.999998 | + | 0.00211358i | \(0.999327\pi\) | |||||||
\(824\) | 2.47768 | 0.0863142 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.95254 | −0.241910 | ||||||||
\(827\) | 18.2130i | 0.633328i | 0.948538 | + | 0.316664i | \(0.102563\pi\) | ||||
−0.948538 | + | 0.316664i | \(0.897437\pi\) | |||||||
\(828\) | 13.1490i | 0.456960i | ||||||||
\(829\) | −13.0738 | −0.454072 | −0.227036 | − | 0.973886i | \(-0.572904\pi\) | ||||
−0.227036 | + | 0.973886i | \(0.572904\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.41090 | 0.0489434 | ||||||||
\(832\) | 21.0668i | 0.730359i | ||||||||
\(833\) | − 19.3239i | − 0.669534i | ||||||||
\(834\) | 2.63989 | 0.0914119 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.46310 | 0.292702 | ||||||||
\(837\) | − 9.92478i | − 0.343050i | ||||||||
\(838\) | − 1.40105i | − 0.0483984i | ||||||||
\(839\) | 26.5501 | 0.916610 | 0.458305 | − | 0.888795i | \(-0.348457\pi\) | ||||
0.458305 | + | 0.888795i | \(0.348457\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9525 | −0.550088 | ||||||||
\(842\) | 5.93937i | 0.204684i | ||||||||
\(843\) | − 4.38787i | − 0.151126i | ||||||||
\(844\) | 17.8350 | 0.613905 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.92478 | 0.0661752 | ||||||||
\(847\) | − 3.35026i | − 0.115116i | ||||||||
\(848\) | 17.7480i | 0.609468i | ||||||||
\(849\) | −26.5745 | −0.912035 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.4010 | 0.459382 | ||||||||
\(852\) | 19.4763i | 0.667246i | ||||||||
\(853\) | 40.6155i | 1.39065i | 0.718697 | + | 0.695323i | \(0.244739\pi\) | ||||
−0.718697 | + | 0.695323i | \(0.755261\pi\) | |||||||
\(854\) | −5.65306 | −0.193444 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.739549 | −0.0252773 | ||||||||
\(857\) | − 20.1721i | − 0.689064i | −0.938775 | − | 0.344532i | \(-0.888038\pi\) | ||||
0.938775 | − | 0.344532i | \(-0.111962\pi\) | |||||||
\(858\) | − 0.574515i | − 0.0196136i | ||||||||
\(859\) | −21.8035 | −0.743926 | −0.371963 | − | 0.928248i | \(-0.621315\pi\) | ||||
−0.371963 | + | 0.928248i | \(0.621315\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.7005 | −0.500993 | ||||||||
\(862\) | − 6.56978i | − 0.223767i | ||||||||
\(863\) | 35.4274i | 1.20596i | 0.797755 | + | 0.602981i | \(0.206021\pi\) | ||||
−0.797755 | + | 0.602981i | \(0.793979\pi\) | |||||||
\(864\) | 2.26916 | 0.0771984 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.83780 | 0.0624508 | ||||||||
\(867\) | − 3.92619i | − 0.133340i | ||||||||
\(868\) | − 65.2506i | − 2.21475i | ||||||||
\(869\) | −11.5369 | −0.391363 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.5515 | 0.594710 | ||||||||
\(872\) | − 8.76116i | − 0.296690i | ||||||||
\(873\) | 0.0752228i | 0.00254591i | ||||||||
\(874\) | 5.60419 | 0.189564 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 15.1852 | 0.513061 | ||||||||
\(877\) | 14.0362i | 0.473969i | 0.971513 | + | 0.236984i | \(0.0761590\pi\) | ||||
−0.971513 | + | 0.236984i | \(0.923841\pi\) | |||||||
\(878\) | 5.71370i | 0.192828i | ||||||||
\(879\) | 3.42548 | 0.115539 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.0738 | −0.709995 | −0.354997 | − | 0.934867i | \(-0.615518\pi\) | ||||
−0.354997 | + | 0.934867i | \(0.615518\pi\) | |||||||
\(882\) | 0.819237i | 0.0275852i | ||||||||
\(883\) | − 42.1476i | − 1.41838i | −0.705017 | − | 0.709190i | \(-0.749061\pi\) | ||||
0.705017 | − | 0.709190i | \(-0.250939\pi\) | |||||||
\(884\) | −26.5933 | −0.894429 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.69911 | 0.124274 | ||||||||
\(887\) | − 6.93604i | − 0.232889i | −0.993197 | − | 0.116445i | \(-0.962850\pi\) | ||||
0.993197 | − | 0.116445i | \(-0.0371498\pi\) | |||||||
\(888\) | − 1.53690i | − 0.0515751i | ||||||||
\(889\) | 48.8284 | 1.63765 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | − 13.1490i | − 0.440262i | ||||||||
\(893\) | 42.8021i | 1.43232i | ||||||||
\(894\) | 0.298062 | 0.00996868 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 19.8251 | 0.662311 | ||||||||
\(897\) | 19.8496i | 0.662757i | ||||||||
\(898\) | − 6.95765i | − 0.232180i | ||||||||
\(899\) | 35.8496 | 1.19565 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.5026 | −0.716356 | ||||||||
\(902\) | − 0.850969i | − 0.0283342i | ||||||||
\(903\) | − 31.0738i | − 1.03407i | ||||||||
\(904\) | 4.61071 | 0.153350 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.31124 | 0.0435629 | ||||||||
\(907\) | − 53.2017i | − 1.76653i | −0.468870 | − | 0.883267i | \(-0.655339\pi\) | ||||
0.468870 | − | 0.883267i | \(-0.344661\pi\) | |||||||
\(908\) | − 33.2868i | − 1.10466i | ||||||||
\(909\) | 15.0884 | 0.500451 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.4749 | 1.20847 | 0.604233 | − | 0.796808i | \(-0.293480\pi\) | ||||
0.604233 | + | 0.796808i | \(0.293480\pi\) | |||||||
\(912\) | 16.2835i | 0.539200i | ||||||||
\(913\) | 10.8872i | 0.360313i | ||||||||
\(914\) | 1.02585 | 0.0339322 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −50.7269 | −1.67606 | ||||||||
\(917\) | 19.8496i | 0.655490i | ||||||||
\(918\) | 0.887166i | 0.0292808i | ||||||||
\(919\) | −9.73340 | −0.321075 | −0.160538 | − | 0.987030i | \(-0.551323\pi\) | ||||
−0.160538 | + | 0.987030i | \(0.551323\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.6497 | −0.548628 | ||||||||
\(922\) | 7.04746i | 0.232096i | ||||||||
\(923\) | 29.4010i | 0.967747i | ||||||||
\(924\) | 6.57452 | 0.216286 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.04605 | −0.0672372 | ||||||||
\(927\) | 3.22425i | 0.105898i | ||||||||
\(928\) | 8.19649i | 0.269063i | ||||||||
\(929\) | 24.1768 | 0.793215 | 0.396607 | − | 0.917988i | \(-0.370187\pi\) | ||||
0.396607 | + | 0.917988i | \(0.370187\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.2177 | −0.597062 | ||||||||
\(932\) | − 37.8251i | − 1.23900i | ||||||||
\(933\) | 32.9986i | 1.08033i | ||||||||
\(934\) | 3.62672 | 0.118670 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.27645 | 0.0744082 | ||||||||
\(937\) | 7.48612i | 0.244561i | 0.992496 | + | 0.122280i | \(0.0390207\pi\) | ||||
−0.992496 | + | 0.122280i | \(0.960979\pi\) | |||||||
\(938\) | − 3.84955i | − 0.125692i | ||||||||
\(939\) | −15.4010 | −0.502594 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.2360 | −0.692274 | −0.346137 | − | 0.938184i | \(-0.612507\pi\) | ||||
−0.346137 | + | 0.938184i | \(0.612507\pi\) | |||||||
\(942\) | − 1.06205i | − 0.0346034i | ||||||||
\(943\) | 29.4010i | 0.957430i | ||||||||
\(944\) | −40.4025 | −1.31499 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.79877 | 0.0584830 | ||||||||
\(947\) | 15.4763i | 0.502911i | 0.967869 | + | 0.251456i | \(0.0809092\pi\) | ||||
−0.967869 | + | 0.251456i | \(0.919091\pi\) | |||||||
\(948\) | − 22.6399i | − 0.735309i | ||||||||
\(949\) | 22.9234 | 0.744124 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.15045 | 0.0697330 | ||||||||
\(952\) | 11.7772i | 0.381700i | ||||||||
\(953\) | − 32.0508i | − 1.03823i | −0.854705 | − | 0.519113i | \(-0.826262\pi\) | ||||
0.854705 | − | 0.519113i | \(-0.173738\pi\) | |||||||
\(954\) | 0.911603 | 0.0295142 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −52.1016 | −1.68509 | ||||||||
\(957\) | 3.61213i | 0.116763i | ||||||||
\(958\) | 1.80351i | 0.0582687i | ||||||||
\(959\) | −46.3996 | −1.49832 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 67.5012 | 2.17746 | ||||||||
\(962\) | − 1.14903i | − 0.0370462i | ||||||||
\(963\) | − 0.962389i | − 0.0310125i | ||||||||
\(964\) | 56.0263 | 1.80449 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.35359 | 0.140074 | ||||||||
\(967\) | 17.3766i | 0.558794i | 0.960176 | + | 0.279397i | \(0.0901346\pi\) | ||||
−0.960176 | + | 0.279397i | \(0.909865\pi\) | |||||||
\(968\) | 0.768452i | 0.0246990i | ||||||||
\(969\) | −19.7283 | −0.633764 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.2031 | 1.16181 | 0.580907 | − | 0.813970i | \(-0.302698\pi\) | ||||
0.580907 | + | 0.813970i | \(0.302698\pi\) | |||||||
\(972\) | 1.96239i | 0.0629436i | ||||||||
\(973\) | 45.6042i | 1.46200i | ||||||||
\(974\) | −6.88015 | −0.220454 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −32.8510 | −1.05153 | ||||||||
\(977\) | 28.1476i | 0.900522i | 0.892897 | + | 0.450261i | \(0.148669\pi\) | ||||
−0.892897 | + | 0.450261i | \(0.851331\pi\) | |||||||
\(978\) | − 2.44851i | − 0.0782946i | ||||||||
\(979\) | 2.77575 | 0.0887132 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.4010 | 0.364007 | ||||||||
\(982\) | 4.80492i | 0.153331i | ||||||||
\(983\) | 7.07381i | 0.225619i | 0.993617 | + | 0.112810i | \(0.0359851\pi\) | ||||
−0.993617 | + | 0.112810i | \(0.964015\pi\) | |||||||
\(984\) | 3.37187 | 0.107491 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.20456 | −0.102054 | ||||||||
\(987\) | 33.2506i | 1.05838i | ||||||||
\(988\) | 25.0710i | 0.797614i | ||||||||
\(989\) | −62.1476 | −1.97618 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.4260 | 1.41124 | 0.705619 | − | 0.708592i | \(-0.250669\pi\) | ||||
0.705619 | + | 0.708592i | \(0.250669\pi\) | |||||||
\(992\) | 22.5209i | 0.715039i | ||||||||
\(993\) | − 14.5501i | − 0.461733i | ||||||||
\(994\) | 6.44851 | 0.204534 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −21.3649 | −0.676971 | ||||||||
\(997\) | 28.4847i | 0.902120i | 0.892494 | + | 0.451060i | \(0.148954\pi\) | ||||
−0.892494 | + | 0.451060i | \(0.851046\pi\) | |||||||
\(998\) | − 2.74940i | − 0.0870307i | ||||||||
\(999\) | 2.00000 | 0.0632772 |
(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 | 825.2.c.g.199.4 | 6 | ||
3.2 | odd | 2 | 2475.2.c.r.199.3 | 6 | |||
5.2 | odd | 4 | 165.2.a.c.1.2 | ✓ | 3 | ||
5.3 | odd | 4 | 825.2.a.k.1.2 | 3 | |||
5.4 | even | 2 | inner | 825.2.c.g.199.3 | 6 | ||
15.2 | even | 4 | 495.2.a.e.1.2 | 3 | |||
15.8 | even | 4 | 2475.2.a.bb.1.2 | 3 | |||
15.14 | odd | 2 | 2475.2.c.r.199.4 | 6 | |||
20.7 | even | 4 | 2640.2.a.be.1.1 | 3 | |||
35.27 | even | 4 | 8085.2.a.bk.1.2 | 3 | |||
55.32 | even | 4 | 1815.2.a.m.1.2 | 3 | |||
55.43 | even | 4 | 9075.2.a.cf.1.2 | 3 | |||
60.47 | odd | 4 | 7920.2.a.cj.1.1 | 3 | |||
165.32 | odd | 4 | 5445.2.a.z.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.a.c.1.2 | ✓ | 3 | 5.2 | odd | 4 | ||
495.2.a.e.1.2 | 3 | 15.2 | even | 4 | |||
825.2.a.k.1.2 | 3 | 5.3 | odd | 4 | |||
825.2.c.g.199.3 | 6 | 5.4 | even | 2 | inner | ||
825.2.c.g.199.4 | 6 | 1.1 | even | 1 | trivial | ||
1815.2.a.m.1.2 | 3 | 55.32 | even | 4 | |||
2475.2.a.bb.1.2 | 3 | 15.8 | even | 4 | |||
2475.2.c.r.199.3 | 6 | 3.2 | odd | 2 | |||
2475.2.c.r.199.4 | 6 | 15.14 | odd | 2 | |||
2640.2.a.be.1.1 | 3 | 20.7 | even | 4 | |||
5445.2.a.z.1.2 | 3 | 165.32 | odd | 4 | |||
7920.2.a.cj.1.1 | 3 | 60.47 | odd | 4 | |||
8085.2.a.bk.1.2 | 3 | 35.27 | even | 4 | |||
9075.2.a.cf.1.2 | 3 | 55.43 | even | 4 |