Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4235,2,Mod(1,4235)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4235, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4235.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4235 = 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4235.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: | \(33.8166452560\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.288385.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 7x^{3} - 2x^{2} + 10x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.90452\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4235.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.90452 | −1.34670 | −0.673348 | − | 0.739326i | \(-0.735144\pi\) | ||||
−0.673348 | + | 0.739326i | \(0.735144\pi\) | |||||||
\(3\) | 0.214998 | 0.124129 | 0.0620646 | − | 0.998072i | \(-0.480232\pi\) | ||||
0.0620646 | + | 0.998072i | \(0.480232\pi\) | |||||||
\(4\) | 1.62718 | 0.813589 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.409467 | −0.167164 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0.710046 | 0.251039 | ||||||||
\(9\) | −2.95378 | −0.984592 | ||||||||
\(10\) | −1.90452 | −0.602261 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.349840 | 0.100990 | ||||||||
\(13\) | −4.56834 | −1.26703 | −0.633514 | − | 0.773731i | \(-0.718388\pi\) | ||||
−0.633514 | + | 0.773731i | \(0.718388\pi\) | |||||||
\(14\) | −1.90452 | −0.509003 | ||||||||
\(15\) | 0.214998 | 0.0555123 | ||||||||
\(16\) | −4.60665 | −1.15166 | ||||||||
\(17\) | 3.25164 | 0.788639 | 0.394320 | − | 0.918973i | \(-0.370980\pi\) | ||||
0.394320 | + | 0.918973i | \(0.370980\pi\) | |||||||
\(18\) | 5.62551 | 1.32595 | ||||||||
\(19\) | 5.02403 | 1.15259 | 0.576296 | − | 0.817241i | \(-0.304498\pi\) | ||||
0.576296 | + | 0.817241i | \(0.304498\pi\) | |||||||
\(20\) | 1.62718 | 0.363848 | ||||||||
\(21\) | 0.214998 | 0.0469164 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.292666 | 0.0610252 | 0.0305126 | − | 0.999534i | \(-0.490286\pi\) | ||||
0.0305126 | + | 0.999534i | \(0.490286\pi\) | |||||||
\(24\) | 0.152659 | 0.0311613 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 8.70047 | 1.70630 | ||||||||
\(27\) | −1.28005 | −0.246346 | ||||||||
\(28\) | 1.62718 | 0.307508 | ||||||||
\(29\) | 1.00271 | 0.186199 | 0.0930995 | − | 0.995657i | \(-0.470323\pi\) | ||||
0.0930995 | + | 0.995657i | \(0.470323\pi\) | |||||||
\(30\) | −0.409467 | −0.0747581 | ||||||||
\(31\) | −6.62551 | −1.18998 | −0.594988 | − | 0.803734i | \(-0.702843\pi\) | ||||
−0.594988 | + | 0.803734i | \(0.702843\pi\) | |||||||
\(32\) | 7.35334 | 1.29990 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.19280 | −1.06206 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −4.80632 | −0.801053 | ||||||||
\(37\) | −4.62822 | −0.760875 | −0.380438 | − | 0.924807i | \(-0.624227\pi\) | ||||
−0.380438 | + | 0.924807i | \(0.624227\pi\) | |||||||
\(38\) | −9.56834 | −1.55219 | ||||||||
\(39\) | −0.982183 | −0.157275 | ||||||||
\(40\) | 0.710046 | 0.112268 | ||||||||
\(41\) | 2.69743 | 0.421268 | 0.210634 | − | 0.977565i | \(-0.432447\pi\) | ||||
0.210634 | + | 0.977565i | \(0.432447\pi\) | |||||||
\(42\) | −0.409467 | −0.0631821 | ||||||||
\(43\) | 0.193423 | 0.0294968 | 0.0147484 | − | 0.999891i | \(-0.495305\pi\) | ||||
0.0147484 | + | 0.999891i | \(0.495305\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.95378 | −0.440323 | ||||||||
\(46\) | −0.557388 | −0.0821823 | ||||||||
\(47\) | −4.29620 | −0.626665 | −0.313333 | − | 0.949643i | \(-0.601445\pi\) | ||||
−0.313333 | + | 0.949643i | \(0.601445\pi\) | |||||||
\(48\) | −0.990420 | −0.142955 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.90452 | −0.269339 | ||||||||
\(51\) | 0.699097 | 0.0978931 | ||||||||
\(52\) | −7.43350 | −1.03084 | ||||||||
\(53\) | 2.78333 | 0.382320 | 0.191160 | − | 0.981559i | \(-0.438775\pi\) | ||||
0.191160 | + | 0.981559i | \(0.438775\pi\) | |||||||
\(54\) | 2.43787 | 0.331753 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.710046 | 0.0948839 | ||||||||
\(57\) | 1.08016 | 0.143070 | ||||||||
\(58\) | −1.90968 | −0.250753 | ||||||||
\(59\) | −0.846879 | −0.110254 | −0.0551271 | − | 0.998479i | \(-0.517556\pi\) | ||||
−0.0551271 | + | 0.998479i | \(0.517556\pi\) | |||||||
\(60\) | 0.349840 | 0.0451641 | ||||||||
\(61\) | 0.963356 | 0.123345 | 0.0616725 | − | 0.998096i | \(-0.480357\pi\) | ||||
0.0616725 | + | 0.998096i | \(0.480357\pi\) | |||||||
\(62\) | 12.6184 | 1.60254 | ||||||||
\(63\) | −2.95378 | −0.372141 | ||||||||
\(64\) | −4.79125 | −0.598906 | ||||||||
\(65\) | −4.56834 | −0.566632 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.95848 | 0.483605 | 0.241803 | − | 0.970325i | \(-0.422261\pi\) | ||||
0.241803 | + | 0.970325i | \(0.422261\pi\) | |||||||
\(68\) | 5.29100 | 0.641628 | ||||||||
\(69\) | 0.0629227 | 0.00757500 | ||||||||
\(70\) | −1.90452 | −0.227633 | ||||||||
\(71\) | 5.54264 | 0.657791 | 0.328895 | − | 0.944366i | \(-0.393324\pi\) | ||||
0.328895 | + | 0.944366i | \(0.393324\pi\) | |||||||
\(72\) | −2.09732 | −0.247171 | ||||||||
\(73\) | 11.7502 | 1.37526 | 0.687628 | − | 0.726063i | \(-0.258652\pi\) | ||||
0.687628 | + | 0.726063i | \(0.258652\pi\) | |||||||
\(74\) | 8.81452 | 1.02467 | ||||||||
\(75\) | 0.214998 | 0.0248258 | ||||||||
\(76\) | 8.17499 | 0.937735 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.87058 | 0.211802 | ||||||||
\(79\) | −9.39619 | −1.05715 | −0.528577 | − | 0.848885i | \(-0.677274\pi\) | ||||
−0.528577 | + | 0.848885i | \(0.677274\pi\) | |||||||
\(80\) | −4.60665 | −0.515039 | ||||||||
\(81\) | 8.58612 | 0.954013 | ||||||||
\(82\) | −5.13730 | −0.567319 | ||||||||
\(83\) | 9.07799 | 0.996439 | 0.498220 | − | 0.867051i | \(-0.333987\pi\) | ||||
0.498220 | + | 0.867051i | \(0.333987\pi\) | |||||||
\(84\) | 0.349840 | 0.0381707 | ||||||||
\(85\) | 3.25164 | 0.352690 | ||||||||
\(86\) | −0.368378 | −0.0397232 | ||||||||
\(87\) | 0.215581 | 0.0231127 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.30633 | 0.456470 | 0.228235 | − | 0.973606i | \(-0.426705\pi\) | ||||
0.228235 | + | 0.973606i | \(0.426705\pi\) | |||||||
\(90\) | 5.62551 | 0.592981 | ||||||||
\(91\) | −4.56834 | −0.478892 | ||||||||
\(92\) | 0.476220 | 0.0496494 | ||||||||
\(93\) | −1.42447 | −0.147711 | ||||||||
\(94\) | 8.18218 | 0.843927 | ||||||||
\(95\) | 5.02403 | 0.515454 | ||||||||
\(96\) | 1.58095 | 0.161355 | ||||||||
\(97\) | 1.09820 | 0.111505 | 0.0557525 | − | 0.998445i | \(-0.482244\pi\) | ||||
0.0557525 | + | 0.998445i | \(0.482244\pi\) | |||||||
\(98\) | −1.90452 | −0.192385 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.62718 | 0.162718 | ||||||||
\(101\) | 4.61577 | 0.459286 | 0.229643 | − | 0.973275i | \(-0.426244\pi\) | ||||
0.229643 | + | 0.973275i | \(0.426244\pi\) | |||||||
\(102\) | −1.33144 | −0.131832 | ||||||||
\(103\) | 13.8643 | 1.36609 | 0.683044 | − | 0.730377i | \(-0.260656\pi\) | ||||
0.683044 | + | 0.730377i | \(0.260656\pi\) | |||||||
\(104\) | −3.24373 | −0.318074 | ||||||||
\(105\) | 0.214998 | 0.0209817 | ||||||||
\(106\) | −5.30090 | −0.514869 | ||||||||
\(107\) | 14.5598 | 1.40755 | 0.703775 | − | 0.710423i | \(-0.251496\pi\) | ||||
0.703775 | + | 0.710423i | \(0.251496\pi\) | |||||||
\(108\) | −2.08287 | −0.200424 | ||||||||
\(109\) | 19.4350 | 1.86154 | 0.930768 | − | 0.365611i | \(-0.119140\pi\) | ||||
0.930768 | + | 0.365611i | \(0.119140\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.995059 | −0.0944468 | ||||||||
\(112\) | −4.60665 | −0.435287 | ||||||||
\(113\) | −17.1884 | −1.61695 | −0.808474 | − | 0.588532i | \(-0.799706\pi\) | ||||
−0.808474 | + | 0.588532i | \(0.799706\pi\) | |||||||
\(114\) | −2.05717 | −0.192672 | ||||||||
\(115\) | 0.292666 | 0.0272913 | ||||||||
\(116\) | 1.63159 | 0.151489 | ||||||||
\(117\) | 13.4938 | 1.24751 | ||||||||
\(118\) | 1.61289 | 0.148479 | ||||||||
\(119\) | 3.25164 | 0.298078 | ||||||||
\(120\) | 0.152659 | 0.0139358 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.83473 | −0.166108 | ||||||||
\(123\) | 0.579942 | 0.0522916 | ||||||||
\(124\) | −10.7809 | −0.968152 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 5.62551 | 0.501160 | ||||||||
\(127\) | 3.06459 | 0.271938 | 0.135969 | − | 0.990713i | \(-0.456585\pi\) | ||||
0.135969 | + | 0.990713i | \(0.456585\pi\) | |||||||
\(128\) | −5.58167 | −0.493355 | ||||||||
\(129\) | 0.0415857 | 0.00366141 | ||||||||
\(130\) | 8.70047 | 0.763081 | ||||||||
\(131\) | −14.6745 | −1.28212 | −0.641059 | − | 0.767492i | \(-0.721505\pi\) | ||||
−0.641059 | + | 0.767492i | \(0.721505\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.02403 | 0.435638 | ||||||||
\(134\) | −7.53898 | −0.651269 | ||||||||
\(135\) | −1.28005 | −0.110169 | ||||||||
\(136\) | 2.30882 | 0.197979 | ||||||||
\(137\) | −15.7705 | −1.34737 | −0.673683 | − | 0.739020i | \(-0.735289\pi\) | ||||
−0.673683 | + | 0.739020i | \(0.735289\pi\) | |||||||
\(138\) | −0.119837 | −0.0102012 | ||||||||
\(139\) | −9.60769 | −0.814914 | −0.407457 | − | 0.913224i | \(-0.633584\pi\) | ||||
−0.407457 | + | 0.913224i | \(0.633584\pi\) | |||||||
\(140\) | 1.62718 | 0.137522 | ||||||||
\(141\) | −0.923674 | −0.0777874 | ||||||||
\(142\) | −10.5560 | −0.885844 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 13.6070 | 1.13392 | ||||||||
\(145\) | 1.00271 | 0.0832707 | ||||||||
\(146\) | −22.3784 | −1.85205 | ||||||||
\(147\) | 0.214998 | 0.0177327 | ||||||||
\(148\) | −7.53094 | −0.619039 | ||||||||
\(149\) | 1.39502 | 0.114284 | 0.0571422 | − | 0.998366i | \(-0.481801\pi\) | ||||
0.0571422 | + | 0.998366i | \(0.481801\pi\) | |||||||
\(150\) | −0.409467 | −0.0334328 | ||||||||
\(151\) | 11.9950 | 0.976136 | 0.488068 | − | 0.872805i | \(-0.337702\pi\) | ||||
0.488068 | + | 0.872805i | \(0.337702\pi\) | |||||||
\(152\) | 3.56729 | 0.289346 | ||||||||
\(153\) | −9.60462 | −0.776488 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.62551 | −0.532174 | ||||||||
\(156\) | −1.59819 | −0.127957 | ||||||||
\(157\) | −24.4749 | −1.95331 | −0.976657 | − | 0.214807i | \(-0.931088\pi\) | ||||
−0.976657 | + | 0.214807i | \(0.931088\pi\) | |||||||
\(158\) | 17.8952 | 1.42367 | ||||||||
\(159\) | 0.598412 | 0.0474571 | ||||||||
\(160\) | 7.35334 | 0.581332 | ||||||||
\(161\) | 0.292666 | 0.0230653 | ||||||||
\(162\) | −16.3524 | −1.28477 | ||||||||
\(163\) | 1.83205 | 0.143497 | 0.0717485 | − | 0.997423i | \(-0.477142\pi\) | ||||
0.0717485 | + | 0.997423i | \(0.477142\pi\) | |||||||
\(164\) | 4.38920 | 0.342739 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.2892 | −1.34190 | ||||||||
\(167\) | −6.88977 | −0.533146 | −0.266573 | − | 0.963815i | \(-0.585891\pi\) | ||||
−0.266573 | + | 0.963815i | \(0.585891\pi\) | |||||||
\(168\) | 0.152659 | 0.0117779 | ||||||||
\(169\) | 7.86970 | 0.605362 | ||||||||
\(170\) | −6.19280 | −0.474966 | ||||||||
\(171\) | −14.8399 | −1.13483 | ||||||||
\(172\) | 0.314734 | 0.0239983 | ||||||||
\(173\) | −8.34496 | −0.634456 | −0.317228 | − | 0.948349i | \(-0.602752\pi\) | ||||
−0.317228 | + | 0.948349i | \(0.602752\pi\) | |||||||
\(174\) | −0.410578 | −0.0311258 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.182077 | −0.0136858 | ||||||||
\(178\) | −8.20147 | −0.614726 | ||||||||
\(179\) | 7.34255 | 0.548808 | 0.274404 | − | 0.961614i | \(-0.411519\pi\) | ||||
0.274404 | + | 0.961614i | \(0.411519\pi\) | |||||||
\(180\) | −4.80632 | −0.358242 | ||||||||
\(181\) | 0.127426 | 0.00947148 | 0.00473574 | − | 0.999989i | \(-0.498493\pi\) | ||||
0.00473574 | + | 0.999989i | \(0.498493\pi\) | |||||||
\(182\) | 8.70047 | 0.644921 | ||||||||
\(183\) | 0.207120 | 0.0153107 | ||||||||
\(184\) | 0.207807 | 0.0153197 | ||||||||
\(185\) | −4.62822 | −0.340274 | ||||||||
\(186\) | 2.71293 | 0.198922 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.99068 | −0.509848 | ||||||||
\(189\) | −1.28005 | −0.0931099 | ||||||||
\(190\) | −9.56834 | −0.694160 | ||||||||
\(191\) | 23.0237 | 1.66594 | 0.832968 | − | 0.553321i | \(-0.186640\pi\) | ||||
0.832968 | + | 0.553321i | \(0.186640\pi\) | |||||||
\(192\) | −1.03011 | −0.0743417 | ||||||||
\(193\) | −17.8948 | −1.28809 | −0.644047 | − | 0.764986i | \(-0.722746\pi\) | ||||
−0.644047 | + | 0.764986i | \(0.722746\pi\) | |||||||
\(194\) | −2.09153 | −0.150163 | ||||||||
\(195\) | −0.982183 | −0.0703356 | ||||||||
\(196\) | 1.62718 | 0.116227 | ||||||||
\(197\) | −21.6655 | −1.54360 | −0.771801 | − | 0.635864i | \(-0.780644\pi\) | ||||
−0.771801 | + | 0.635864i | \(0.780644\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.8072 | 1.75853 | 0.879267 | − | 0.476330i | \(-0.158033\pi\) | ||||
0.879267 | + | 0.476330i | \(0.158033\pi\) | |||||||
\(200\) | 0.710046 | 0.0502078 | ||||||||
\(201\) | 0.851065 | 0.0600295 | ||||||||
\(202\) | −8.79080 | −0.618518 | ||||||||
\(203\) | 1.00271 | 0.0703766 | ||||||||
\(204\) | 1.13755 | 0.0796447 | ||||||||
\(205\) | 2.69743 | 0.188397 | ||||||||
\(206\) | −26.4047 | −1.83970 | ||||||||
\(207\) | −0.864471 | −0.0600849 | ||||||||
\(208\) | 21.0447 | 1.45919 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.409467 | −0.0282559 | ||||||||
\(211\) | 21.0959 | 1.45230 | 0.726150 | − | 0.687536i | \(-0.241308\pi\) | ||||
0.726150 | + | 0.687536i | \(0.241308\pi\) | |||||||
\(212\) | 4.52898 | 0.311052 | ||||||||
\(213\) | 1.19166 | 0.0816510 | ||||||||
\(214\) | −27.7294 | −1.89554 | ||||||||
\(215\) | 0.193423 | 0.0131914 | ||||||||
\(216\) | −0.908895 | −0.0618424 | ||||||||
\(217\) | −6.62551 | −0.449769 | ||||||||
\(218\) | −37.0143 | −2.50692 | ||||||||
\(219\) | 2.52627 | 0.170709 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.8546 | −0.999228 | ||||||||
\(222\) | 1.89510 | 0.127191 | ||||||||
\(223\) | 13.0233 | 0.872105 | 0.436053 | − | 0.899921i | \(-0.356376\pi\) | ||||
0.436053 | + | 0.899921i | \(0.356376\pi\) | |||||||
\(224\) | 7.35334 | 0.491316 | ||||||||
\(225\) | −2.95378 | −0.196918 | ||||||||
\(226\) | 32.7355 | 2.17754 | ||||||||
\(227\) | 12.1441 | 0.806032 | 0.403016 | − | 0.915193i | \(-0.367962\pi\) | ||||
0.403016 | + | 0.915193i | \(0.367962\pi\) | |||||||
\(228\) | 1.75761 | 0.116400 | ||||||||
\(229\) | 18.8096 | 1.24297 | 0.621487 | − | 0.783424i | \(-0.286529\pi\) | ||||
0.621487 | + | 0.783424i | \(0.286529\pi\) | |||||||
\(230\) | −0.557388 | −0.0367530 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.711972 | 0.0467433 | ||||||||
\(233\) | 23.4069 | 1.53344 | 0.766719 | − | 0.641983i | \(-0.221888\pi\) | ||||
0.766719 | + | 0.641983i | \(0.221888\pi\) | |||||||
\(234\) | −25.6992 | −1.68001 | ||||||||
\(235\) | −4.29620 | −0.280253 | ||||||||
\(236\) | −1.37802 | −0.0897016 | ||||||||
\(237\) | −2.02016 | −0.131224 | ||||||||
\(238\) | −6.19280 | −0.401420 | ||||||||
\(239\) | 15.0841 | 0.975710 | 0.487855 | − | 0.872925i | \(-0.337779\pi\) | ||||
0.487855 | + | 0.872925i | \(0.337779\pi\) | |||||||
\(240\) | −0.990420 | −0.0639314 | ||||||||
\(241\) | −0.499627 | −0.0321838 | −0.0160919 | − | 0.999871i | \(-0.505122\pi\) | ||||
−0.0160919 | + | 0.999871i | \(0.505122\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.68615 | 0.364767 | ||||||||
\(244\) | 1.56755 | 0.100352 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −1.10451 | −0.0704209 | ||||||||
\(247\) | −22.9515 | −1.46037 | ||||||||
\(248\) | −4.70442 | −0.298731 | ||||||||
\(249\) | 1.95175 | 0.123687 | ||||||||
\(250\) | −1.90452 | −0.120452 | ||||||||
\(251\) | −20.8388 | −1.31533 | −0.657666 | − | 0.753310i | \(-0.728456\pi\) | ||||
−0.657666 | + | 0.753310i | \(0.728456\pi\) | |||||||
\(252\) | −4.80632 | −0.302770 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.83656 | −0.366218 | ||||||||
\(255\) | 0.699097 | 0.0437791 | ||||||||
\(256\) | 20.2129 | 1.26330 | ||||||||
\(257\) | −9.23887 | −0.576305 | −0.288152 | − | 0.957585i | \(-0.593041\pi\) | ||||
−0.288152 | + | 0.957585i | \(0.593041\pi\) | |||||||
\(258\) | −0.0792005 | −0.00493081 | ||||||||
\(259\) | −4.62822 | −0.287584 | ||||||||
\(260\) | −7.43350 | −0.461006 | ||||||||
\(261\) | −2.96179 | −0.183330 | ||||||||
\(262\) | 27.9478 | 1.72662 | ||||||||
\(263\) | 3.90063 | 0.240523 | 0.120262 | − | 0.992742i | \(-0.461627\pi\) | ||||
0.120262 | + | 0.992742i | \(0.461627\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.78333 | 0.170979 | ||||||||
\(266\) | −9.56834 | −0.586672 | ||||||||
\(267\) | 0.925852 | 0.0566612 | ||||||||
\(268\) | 6.44115 | 0.393456 | ||||||||
\(269\) | 27.9577 | 1.70461 | 0.852307 | − | 0.523043i | \(-0.175203\pi\) | ||||
0.852307 | + | 0.523043i | \(0.175203\pi\) | |||||||
\(270\) | 2.43787 | 0.148364 | ||||||||
\(271\) | 24.0897 | 1.46335 | 0.731673 | − | 0.681655i | \(-0.238740\pi\) | ||||
0.731673 | + | 0.681655i | \(0.238740\pi\) | |||||||
\(272\) | −14.9792 | −0.908246 | ||||||||
\(273\) | −0.982183 | −0.0594444 | ||||||||
\(274\) | 30.0352 | 1.81449 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.102386 | 0.00616294 | ||||||||
\(277\) | 27.1882 | 1.63358 | 0.816790 | − | 0.576935i | \(-0.195751\pi\) | ||||
0.816790 | + | 0.576935i | \(0.195751\pi\) | |||||||
\(278\) | 18.2980 | 1.09744 | ||||||||
\(279\) | 19.5703 | 1.17164 | ||||||||
\(280\) | 0.710046 | 0.0424334 | ||||||||
\(281\) | 19.4935 | 1.16289 | 0.581443 | − | 0.813587i | \(-0.302488\pi\) | ||||
0.581443 | + | 0.813587i | \(0.302488\pi\) | |||||||
\(282\) | 1.75915 | 0.104756 | ||||||||
\(283\) | −2.43412 | −0.144693 | −0.0723466 | − | 0.997380i | \(-0.523049\pi\) | ||||
−0.0723466 | + | 0.997380i | \(0.523049\pi\) | |||||||
\(284\) | 9.01886 | 0.535171 | ||||||||
\(285\) | 1.08016 | 0.0639829 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.69743 | 0.159224 | ||||||||
\(288\) | −21.7201 | −1.27987 | ||||||||
\(289\) | −6.42682 | −0.378048 | ||||||||
\(290\) | −1.90968 | −0.112140 | ||||||||
\(291\) | 0.236110 | 0.0138410 | ||||||||
\(292\) | 19.1196 | 1.11889 | ||||||||
\(293\) | −24.4918 | −1.43083 | −0.715413 | − | 0.698702i | \(-0.753761\pi\) | ||||
−0.715413 | + | 0.698702i | \(0.753761\pi\) | |||||||
\(294\) | −0.409467 | −0.0238806 | ||||||||
\(295\) | −0.846879 | −0.0493072 | ||||||||
\(296\) | −3.28625 | −0.191009 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.65683 | −0.153906 | ||||||||
\(299\) | −1.33700 | −0.0773206 | ||||||||
\(300\) | 0.349840 | 0.0201980 | ||||||||
\(301\) | 0.193423 | 0.0111487 | ||||||||
\(302\) | −22.8446 | −1.31456 | ||||||||
\(303\) | 0.992381 | 0.0570108 | ||||||||
\(304\) | −23.1439 | −1.32740 | ||||||||
\(305\) | 0.963356 | 0.0551616 | ||||||||
\(306\) | 18.2921 | 1.04569 | ||||||||
\(307\) | −23.0511 | −1.31559 | −0.657797 | − | 0.753195i | \(-0.728512\pi\) | ||||
−0.657797 | + | 0.753195i | \(0.728512\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.98079 | 0.169571 | ||||||||
\(310\) | 12.6184 | 0.716676 | ||||||||
\(311\) | 18.7222 | 1.06164 | 0.530819 | − | 0.847485i | \(-0.321884\pi\) | ||||
0.530819 | + | 0.847485i | \(0.321884\pi\) | |||||||
\(312\) | −0.697395 | −0.0394822 | ||||||||
\(313\) | 15.4725 | 0.874555 | 0.437277 | − | 0.899327i | \(-0.355943\pi\) | ||||
0.437277 | + | 0.899327i | \(0.355943\pi\) | |||||||
\(314\) | 46.6129 | 2.63052 | ||||||||
\(315\) | −2.95378 | −0.166426 | ||||||||
\(316\) | −15.2893 | −0.860089 | ||||||||
\(317\) | 12.8989 | 0.724476 | 0.362238 | − | 0.932086i | \(-0.382013\pi\) | ||||
0.362238 | + | 0.932086i | \(0.382013\pi\) | |||||||
\(318\) | −1.13968 | −0.0639103 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −4.79125 | −0.267839 | ||||||||
\(321\) | 3.13033 | 0.174718 | ||||||||
\(322\) | −0.557388 | −0.0310620 | ||||||||
\(323\) | 16.3363 | 0.908978 | ||||||||
\(324\) | 13.9711 | 0.776174 | ||||||||
\(325\) | −4.56834 | −0.253406 | ||||||||
\(326\) | −3.48916 | −0.193247 | ||||||||
\(327\) | 4.17849 | 0.231071 | ||||||||
\(328\) | 1.91530 | 0.105755 | ||||||||
\(329\) | −4.29620 | −0.236857 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.28642 | −0.455463 | −0.227731 | − | 0.973724i | \(-0.573131\pi\) | ||||
−0.227731 | + | 0.973724i | \(0.573131\pi\) | |||||||
\(332\) | 14.7715 | 0.810692 | ||||||||
\(333\) | 13.6707 | 0.749152 | ||||||||
\(334\) | 13.1217 | 0.717986 | ||||||||
\(335\) | 3.95848 | 0.216275 | ||||||||
\(336\) | −0.990420 | −0.0540319 | ||||||||
\(337\) | −33.6591 | −1.83353 | −0.916763 | − | 0.399431i | \(-0.869208\pi\) | ||||
−0.916763 | + | 0.399431i | \(0.869208\pi\) | |||||||
\(338\) | −14.9880 | −0.815238 | ||||||||
\(339\) | −3.69547 | −0.200710 | ||||||||
\(340\) | 5.29100 | 0.286945 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 28.2627 | 1.52827 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0.137340 | 0.00740485 | ||||||||
\(345\) | 0.0629227 | 0.00338764 | ||||||||
\(346\) | 15.8931 | 0.854419 | ||||||||
\(347\) | −19.8757 | −1.06698 | −0.533492 | − | 0.845805i | \(-0.679121\pi\) | ||||
−0.533492 | + | 0.845805i | \(0.679121\pi\) | |||||||
\(348\) | 0.350789 | 0.0188043 | ||||||||
\(349\) | 18.7227 | 1.00221 | 0.501103 | − | 0.865388i | \(-0.332928\pi\) | ||||
0.501103 | + | 0.865388i | \(0.332928\pi\) | |||||||
\(350\) | −1.90452 | −0.101801 | ||||||||
\(351\) | 5.84770 | 0.312127 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.9588 | 0.742951 | 0.371476 | − | 0.928443i | \(-0.378852\pi\) | ||||
0.371476 | + | 0.928443i | \(0.378852\pi\) | |||||||
\(354\) | 0.346769 | 0.0184306 | ||||||||
\(355\) | 5.54264 | 0.294173 | ||||||||
\(356\) | 7.00716 | 0.371379 | ||||||||
\(357\) | 0.699097 | 0.0370001 | ||||||||
\(358\) | −13.9840 | −0.739078 | ||||||||
\(359\) | −30.4147 | −1.60523 | −0.802613 | − | 0.596501i | \(-0.796557\pi\) | ||||
−0.802613 | + | 0.596501i | \(0.796557\pi\) | |||||||
\(360\) | −2.09732 | −0.110538 | ||||||||
\(361\) | 6.24086 | 0.328466 | ||||||||
\(362\) | −0.242684 | −0.0127552 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.43350 | −0.389621 | ||||||||
\(365\) | 11.7502 | 0.615033 | ||||||||
\(366\) | −0.394462 | −0.0206189 | ||||||||
\(367\) | −22.8152 | −1.19094 | −0.595471 | − | 0.803377i | \(-0.703035\pi\) | ||||
−0.595471 | + | 0.803377i | \(0.703035\pi\) | |||||||
\(368\) | −1.34821 | −0.0702804 | ||||||||
\(369\) | −7.96760 | −0.414777 | ||||||||
\(370\) | 8.81452 | 0.458245 | ||||||||
\(371\) | 2.78333 | 0.144504 | ||||||||
\(372\) | −2.31787 | −0.120176 | ||||||||
\(373\) | 25.0369 | 1.29636 | 0.648180 | − | 0.761487i | \(-0.275530\pi\) | ||||
0.648180 | + | 0.761487i | \(0.275530\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.214998 | 0.0111025 | ||||||||
\(376\) | −3.05050 | −0.157318 | ||||||||
\(377\) | −4.58073 | −0.235920 | ||||||||
\(378\) | 2.43787 | 0.125391 | ||||||||
\(379\) | 24.0173 | 1.23369 | 0.616843 | − | 0.787086i | \(-0.288411\pi\) | ||||
0.616843 | + | 0.787086i | \(0.288411\pi\) | |||||||
\(380\) | 8.17499 | 0.419368 | ||||||||
\(381\) | 0.658881 | 0.0337555 | ||||||||
\(382\) | −43.8490 | −2.24351 | ||||||||
\(383\) | 7.78788 | 0.397942 | 0.198971 | − | 0.980005i | \(-0.436240\pi\) | ||||
0.198971 | + | 0.980005i | \(0.436240\pi\) | |||||||
\(384\) | −1.20005 | −0.0612397 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 34.0809 | 1.73467 | ||||||||
\(387\) | −0.571329 | −0.0290423 | ||||||||
\(388\) | 1.78696 | 0.0907193 | ||||||||
\(389\) | 12.4598 | 0.631735 | 0.315867 | − | 0.948803i | \(-0.397705\pi\) | ||||
0.315867 | + | 0.948803i | \(0.397705\pi\) | |||||||
\(390\) | 1.87058 | 0.0947207 | ||||||||
\(391\) | 0.951647 | 0.0481268 | ||||||||
\(392\) | 0.710046 | 0.0358627 | ||||||||
\(393\) | −3.15499 | −0.159148 | ||||||||
\(394\) | 41.2623 | 2.07876 | ||||||||
\(395\) | −9.39619 | −0.472774 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.78212 | −0.0894419 | −0.0447209 | − | 0.999000i | \(-0.514240\pi\) | ||||
−0.0447209 | + | 0.999000i | \(0.514240\pi\) | |||||||
\(398\) | −47.2456 | −2.36821 | ||||||||
\(399\) | 1.08016 | 0.0540754 | ||||||||
\(400\) | −4.60665 | −0.230332 | ||||||||
\(401\) | −32.5153 | −1.62373 | −0.811867 | − | 0.583842i | \(-0.801549\pi\) | ||||
−0.811867 | + | 0.583842i | \(0.801549\pi\) | |||||||
\(402\) | −1.62087 | −0.0808415 | ||||||||
\(403\) | 30.2676 | 1.50773 | ||||||||
\(404\) | 7.51067 | 0.373670 | ||||||||
\(405\) | 8.58612 | 0.426648 | ||||||||
\(406\) | −1.90968 | −0.0947759 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.496391 | 0.0245750 | ||||||||
\(409\) | 25.7104 | 1.27130 | 0.635648 | − | 0.771979i | \(-0.280733\pi\) | ||||
0.635648 | + | 0.771979i | \(0.280733\pi\) | |||||||
\(410\) | −5.13730 | −0.253713 | ||||||||
\(411\) | −3.39063 | −0.167248 | ||||||||
\(412\) | 22.5596 | 1.11143 | ||||||||
\(413\) | −0.846879 | −0.0416722 | ||||||||
\(414\) | 1.64640 | 0.0809160 | ||||||||
\(415\) | 9.07799 | 0.445621 | ||||||||
\(416\) | −33.5925 | −1.64701 | ||||||||
\(417\) | −2.06564 | −0.101155 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.6850 | 0.912822 | 0.456411 | − | 0.889769i | \(-0.349135\pi\) | ||||
0.456411 | + | 0.889769i | \(0.349135\pi\) | |||||||
\(420\) | 0.349840 | 0.0170704 | ||||||||
\(421\) | 8.91435 | 0.434459 | 0.217229 | − | 0.976121i | \(-0.430298\pi\) | ||||
0.217229 | + | 0.976121i | \(0.430298\pi\) | |||||||
\(422\) | −40.1774 | −1.95581 | ||||||||
\(423\) | 12.6900 | 0.617009 | ||||||||
\(424\) | 1.97630 | 0.0959774 | ||||||||
\(425\) | 3.25164 | 0.157728 | ||||||||
\(426\) | −2.26953 | −0.109959 | ||||||||
\(427\) | 0.963356 | 0.0466200 | ||||||||
\(428\) | 23.6914 | 1.14517 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.368378 | −0.0177648 | ||||||||
\(431\) | 25.5710 | 1.23171 | 0.615856 | − | 0.787859i | \(-0.288810\pi\) | ||||
0.615856 | + | 0.787859i | \(0.288810\pi\) | |||||||
\(432\) | 5.89674 | 0.283707 | ||||||||
\(433\) | 21.0251 | 1.01040 | 0.505201 | − | 0.863002i | \(-0.331418\pi\) | ||||
0.505201 | + | 0.863002i | \(0.331418\pi\) | |||||||
\(434\) | 12.6184 | 0.605702 | ||||||||
\(435\) | 0.215581 | 0.0103363 | ||||||||
\(436\) | 31.6242 | 1.51452 | ||||||||
\(437\) | 1.47036 | 0.0703371 | ||||||||
\(438\) | −4.81131 | −0.229893 | ||||||||
\(439\) | 23.6556 | 1.12902 | 0.564510 | − | 0.825426i | \(-0.309065\pi\) | ||||
0.564510 | + | 0.825426i | \(0.309065\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.95378 | −0.140656 | ||||||||
\(442\) | 28.2908 | 1.34566 | ||||||||
\(443\) | 33.3347 | 1.58378 | 0.791889 | − | 0.610665i | \(-0.209098\pi\) | ||||
0.791889 | + | 0.610665i | \(0.209098\pi\) | |||||||
\(444\) | −1.61914 | −0.0768409 | ||||||||
\(445\) | 4.30633 | 0.204140 | ||||||||
\(446\) | −24.8031 | −1.17446 | ||||||||
\(447\) | 0.299926 | 0.0141860 | ||||||||
\(448\) | −4.79125 | −0.226365 | ||||||||
\(449\) | −27.5835 | −1.30175 | −0.650873 | − | 0.759187i | \(-0.725597\pi\) | ||||
−0.650873 | + | 0.759187i | \(0.725597\pi\) | |||||||
\(450\) | 5.62551 | 0.265189 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −27.9686 | −1.31553 | ||||||||
\(453\) | 2.57889 | 0.121167 | ||||||||
\(454\) | −23.1286 | −1.08548 | ||||||||
\(455\) | −4.56834 | −0.214167 | ||||||||
\(456\) | 0.766961 | 0.0359162 | ||||||||
\(457\) | 12.8605 | 0.601591 | 0.300795 | − | 0.953689i | \(-0.402748\pi\) | ||||
0.300795 | + | 0.953689i | \(0.402748\pi\) | |||||||
\(458\) | −35.8232 | −1.67391 | ||||||||
\(459\) | −4.16227 | −0.194278 | ||||||||
\(460\) | 0.476220 | 0.0222039 | ||||||||
\(461\) | −26.6291 | −1.24024 | −0.620119 | − | 0.784507i | \(-0.712916\pi\) | ||||
−0.620119 | + | 0.784507i | \(0.712916\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.2976 | 0.896836 | 0.448418 | − | 0.893824i | \(-0.351988\pi\) | ||||
0.448418 | + | 0.893824i | \(0.351988\pi\) | |||||||
\(464\) | −4.61914 | −0.214438 | ||||||||
\(465\) | −1.42447 | −0.0660583 | ||||||||
\(466\) | −44.5788 | −2.06507 | ||||||||
\(467\) | −35.9799 | −1.66495 | −0.832475 | − | 0.554063i | \(-0.813077\pi\) | ||||
−0.832475 | + | 0.554063i | \(0.813077\pi\) | |||||||
\(468\) | 21.9569 | 1.01496 | ||||||||
\(469\) | 3.95848 | 0.182786 | ||||||||
\(470\) | 8.18218 | 0.377416 | ||||||||
\(471\) | −5.26206 | −0.242463 | ||||||||
\(472\) | −0.601323 | −0.0276781 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.84743 | 0.176718 | ||||||||
\(475\) | 5.02403 | 0.230518 | ||||||||
\(476\) | 5.29100 | 0.242513 | ||||||||
\(477\) | −8.22135 | −0.376430 | ||||||||
\(478\) | −28.7279 | −1.31398 | ||||||||
\(479\) | 27.9003 | 1.27480 | 0.637399 | − | 0.770534i | \(-0.280010\pi\) | ||||
0.637399 | + | 0.770534i | \(0.280010\pi\) | |||||||
\(480\) | 1.58095 | 0.0721603 | ||||||||
\(481\) | 21.1433 | 0.964051 | ||||||||
\(482\) | 0.951547 | 0.0433418 | ||||||||
\(483\) | 0.0629227 | 0.00286308 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.09820 | 0.0498666 | ||||||||
\(486\) | −10.8294 | −0.491230 | ||||||||
\(487\) | 23.1099 | 1.04721 | 0.523606 | − | 0.851961i | \(-0.324586\pi\) | ||||
0.523606 | + | 0.851961i | \(0.324586\pi\) | |||||||
\(488\) | 0.684027 | 0.0309644 | ||||||||
\(489\) | 0.393886 | 0.0178122 | ||||||||
\(490\) | −1.90452 | −0.0860372 | ||||||||
\(491\) | −16.1116 | −0.727107 | −0.363553 | − | 0.931573i | \(-0.618437\pi\) | ||||
−0.363553 | + | 0.931573i | \(0.618437\pi\) | |||||||
\(492\) | 0.943669 | 0.0425439 | ||||||||
\(493\) | 3.26046 | 0.146844 | ||||||||
\(494\) | 43.7114 | 1.96667 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.5214 | 1.37045 | ||||||||
\(497\) | 5.54264 | 0.248621 | ||||||||
\(498\) | −3.71714 | −0.166569 | ||||||||
\(499\) | −16.4187 | −0.735003 | −0.367501 | − | 0.930023i | \(-0.619787\pi\) | ||||
−0.367501 | + | 0.930023i | \(0.619787\pi\) | |||||||
\(500\) | 1.62718 | 0.0727696 | ||||||||
\(501\) | −1.48129 | −0.0661790 | ||||||||
\(502\) | 39.6878 | 1.77135 | ||||||||
\(503\) | −11.4726 | −0.511536 | −0.255768 | − | 0.966738i | \(-0.582328\pi\) | ||||
−0.255768 | + | 0.966738i | \(0.582328\pi\) | |||||||
\(504\) | −2.09732 | −0.0934219 | ||||||||
\(505\) | 4.61577 | 0.205399 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.69197 | 0.0751430 | ||||||||
\(508\) | 4.98663 | 0.221246 | ||||||||
\(509\) | 30.6084 | 1.35669 | 0.678346 | − | 0.734743i | \(-0.262697\pi\) | ||||
0.678346 | + | 0.734743i | \(0.262697\pi\) | |||||||
\(510\) | −1.33144 | −0.0589572 | ||||||||
\(511\) | 11.7502 | 0.519798 | ||||||||
\(512\) | −27.3324 | −1.20793 | ||||||||
\(513\) | −6.43101 | −0.283936 | ||||||||
\(514\) | 17.5956 | 0.776107 | ||||||||
\(515\) | 13.8643 | 0.610933 | ||||||||
\(516\) | 0.0676672 | 0.00297888 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 8.81452 | 0.387288 | ||||||||
\(519\) | −1.79415 | −0.0787545 | ||||||||
\(520\) | −3.24373 | −0.142247 | ||||||||
\(521\) | −7.28080 | −0.318978 | −0.159489 | − | 0.987200i | \(-0.550985\pi\) | ||||
−0.159489 | + | 0.987200i | \(0.550985\pi\) | |||||||
\(522\) | 5.64077 | 0.246890 | ||||||||
\(523\) | 18.5202 | 0.809832 | 0.404916 | − | 0.914354i | \(-0.367301\pi\) | ||||
0.404916 | + | 0.914354i | \(0.367301\pi\) | |||||||
\(524\) | −23.8780 | −1.04312 | ||||||||
\(525\) | 0.214998 | 0.00938328 | ||||||||
\(526\) | −7.42881 | −0.323912 | ||||||||
\(527\) | −21.5438 | −0.938462 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9143 | −0.996276 | ||||||||
\(530\) | −5.30090 | −0.230257 | ||||||||
\(531\) | 2.50149 | 0.108555 | ||||||||
\(532\) | 8.17499 | 0.354431 | ||||||||
\(533\) | −12.3228 | −0.533758 | ||||||||
\(534\) | −1.76330 | −0.0763054 | ||||||||
\(535\) | 14.5598 | 0.629475 | ||||||||
\(536\) | 2.81070 | 0.121404 | ||||||||
\(537\) | 1.57863 | 0.0681231 | ||||||||
\(538\) | −53.2459 | −2.29559 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.08287 | −0.0896324 | ||||||||
\(541\) | 13.2331 | 0.568933 | 0.284467 | − | 0.958686i | \(-0.408183\pi\) | ||||
0.284467 | + | 0.958686i | \(0.408183\pi\) | |||||||
\(542\) | −45.8792 | −1.97068 | ||||||||
\(543\) | 0.0273963 | 0.00117569 | ||||||||
\(544\) | 23.9104 | 1.02515 | ||||||||
\(545\) | 19.4350 | 0.832504 | ||||||||
\(546\) | 1.87058 | 0.0800536 | ||||||||
\(547\) | −21.7449 | −0.929745 | −0.464872 | − | 0.885378i | \(-0.653900\pi\) | ||||
−0.464872 | + | 0.885378i | \(0.653900\pi\) | |||||||
\(548\) | −25.6614 | −1.09620 | ||||||||
\(549\) | −2.84554 | −0.121445 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.03766 | 0.214611 | ||||||||
\(552\) | 0.0446780 | 0.00190162 | ||||||||
\(553\) | −9.39619 | −0.399567 | ||||||||
\(554\) | −51.7803 | −2.19994 | ||||||||
\(555\) | −0.995059 | −0.0422379 | ||||||||
\(556\) | −15.6334 | −0.663005 | ||||||||
\(557\) | 22.5249 | 0.954412 | 0.477206 | − | 0.878792i | \(-0.341650\pi\) | ||||
0.477206 | + | 0.878792i | \(0.341650\pi\) | |||||||
\(558\) | −37.2719 | −1.57784 | ||||||||
\(559\) | −0.883623 | −0.0373733 | ||||||||
\(560\) | −4.60665 | −0.194666 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −37.1257 | −1.56605 | ||||||||
\(563\) | 2.07905 | 0.0876213 | 0.0438107 | − | 0.999040i | \(-0.486050\pi\) | ||||
0.0438107 | + | 0.999040i | \(0.486050\pi\) | |||||||
\(564\) | −1.50298 | −0.0632870 | ||||||||
\(565\) | −17.1884 | −0.723121 | ||||||||
\(566\) | 4.63581 | 0.194858 | ||||||||
\(567\) | 8.58612 | 0.360583 | ||||||||
\(568\) | 3.93553 | 0.165131 | ||||||||
\(569\) | 40.5323 | 1.69920 | 0.849602 | − | 0.527425i | \(-0.176842\pi\) | ||||
0.849602 | + | 0.527425i | \(0.176842\pi\) | |||||||
\(570\) | −2.05717 | −0.0861655 | ||||||||
\(571\) | 45.1005 | 1.88740 | 0.943698 | − | 0.330807i | \(-0.107321\pi\) | ||||
0.943698 | + | 0.330807i | \(0.107321\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.95005 | 0.206791 | ||||||||
\(574\) | −5.13730 | −0.214427 | ||||||||
\(575\) | 0.292666 | 0.0122050 | ||||||||
\(576\) | 14.1523 | 0.589678 | ||||||||
\(577\) | 11.0837 | 0.461420 | 0.230710 | − | 0.973023i | \(-0.425895\pi\) | ||||
0.230710 | + | 0.973023i | \(0.425895\pi\) | |||||||
\(578\) | 12.2400 | 0.509116 | ||||||||
\(579\) | −3.84734 | −0.159890 | ||||||||
\(580\) | 1.63159 | 0.0677481 | ||||||||
\(581\) | 9.07799 | 0.376619 | ||||||||
\(582\) | −0.449676 | −0.0186397 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 8.34318 | 0.345243 | ||||||||
\(585\) | 13.4938 | 0.557902 | ||||||||
\(586\) | 46.6450 | 1.92689 | ||||||||
\(587\) | −25.9005 | −1.06903 | −0.534513 | − | 0.845160i | \(-0.679505\pi\) | ||||
−0.534513 | + | 0.845160i | \(0.679505\pi\) | |||||||
\(588\) | 0.349840 | 0.0144272 | ||||||||
\(589\) | −33.2868 | −1.37156 | ||||||||
\(590\) | 1.61289 | 0.0664018 | ||||||||
\(591\) | −4.65804 | −0.191606 | ||||||||
\(592\) | 21.3206 | 0.876271 | ||||||||
\(593\) | 2.48445 | 0.102024 | 0.0510122 | − | 0.998698i | \(-0.483755\pi\) | ||||
0.0510122 | + | 0.998698i | \(0.483755\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.25164 | 0.133304 | ||||||||
\(596\) | 2.26994 | 0.0929805 | ||||||||
\(597\) | 5.33349 | 0.218285 | ||||||||
\(598\) | 2.54633 | 0.104127 | ||||||||
\(599\) | −5.73493 | −0.234323 | −0.117161 | − | 0.993113i | \(-0.537379\pi\) | ||||
−0.117161 | + | 0.993113i | \(0.537379\pi\) | |||||||
\(600\) | 0.152659 | 0.00623226 | ||||||||
\(601\) | −25.8331 | −1.05375 | −0.526877 | − | 0.849942i | \(-0.676637\pi\) | ||||
−0.526877 | + | 0.849942i | \(0.676637\pi\) | |||||||
\(602\) | −0.368378 | −0.0150140 | ||||||||
\(603\) | −11.6925 | −0.476154 | ||||||||
\(604\) | 19.5179 | 0.794174 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.89000 | −0.0767761 | ||||||||
\(607\) | 13.1269 | 0.532804 | 0.266402 | − | 0.963862i | \(-0.414165\pi\) | ||||
0.266402 | + | 0.963862i | \(0.414165\pi\) | |||||||
\(608\) | 36.9434 | 1.49825 | ||||||||
\(609\) | 0.215581 | 0.00873579 | ||||||||
\(610\) | −1.83473 | −0.0742858 | ||||||||
\(611\) | 19.6265 | 0.794003 | ||||||||
\(612\) | −15.6284 | −0.631742 | ||||||||
\(613\) | 13.8513 | 0.559450 | 0.279725 | − | 0.960080i | \(-0.409757\pi\) | ||||
0.279725 | + | 0.960080i | \(0.409757\pi\) | |||||||
\(614\) | 43.9011 | 1.77170 | ||||||||
\(615\) | 0.579942 | 0.0233855 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.619693 | −0.0249479 | −0.0124739 | − | 0.999922i | \(-0.503971\pi\) | ||||
−0.0124739 | + | 0.999922i | \(0.503971\pi\) | |||||||
\(618\) | −5.67696 | −0.228361 | ||||||||
\(619\) | 29.7025 | 1.19385 | 0.596923 | − | 0.802299i | \(-0.296390\pi\) | ||||
0.596923 | + | 0.802299i | \(0.296390\pi\) | |||||||
\(620\) | −10.7809 | −0.432971 | ||||||||
\(621\) | −0.374628 | −0.0150333 | ||||||||
\(622\) | −35.6567 | −1.42970 | ||||||||
\(623\) | 4.30633 | 0.172529 | ||||||||
\(624\) | 4.52457 | 0.181128 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −29.4675 | −1.17776 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −39.8251 | −1.58919 | ||||||||
\(629\) | −15.0493 | −0.600056 | ||||||||
\(630\) | 5.62551 | 0.224126 | ||||||||
\(631\) | 20.4025 | 0.812212 | 0.406106 | − | 0.913826i | \(-0.366886\pi\) | ||||
0.406106 | + | 0.913826i | \(0.366886\pi\) | |||||||
\(632\) | −6.67173 | −0.265387 | ||||||||
\(633\) | 4.53557 | 0.180273 | ||||||||
\(634\) | −24.5662 | −0.975649 | ||||||||
\(635\) | 3.06459 | 0.121615 | ||||||||
\(636\) | 0.973722 | 0.0386106 | ||||||||
\(637\) | −4.56834 | −0.181004 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.3717 | −0.647655 | ||||||||
\(640\) | −5.58167 | −0.220635 | ||||||||
\(641\) | −0.905192 | −0.0357529 | −0.0178765 | − | 0.999840i | \(-0.505691\pi\) | ||||
−0.0178765 | + | 0.999840i | \(0.505691\pi\) | |||||||
\(642\) | −5.96176 | −0.235292 | ||||||||
\(643\) | 34.8958 | 1.37616 | 0.688078 | − | 0.725637i | \(-0.258455\pi\) | ||||
0.688078 | + | 0.725637i | \(0.258455\pi\) | |||||||
\(644\) | 0.476220 | 0.0187657 | ||||||||
\(645\) | 0.0415857 | 0.00163743 | ||||||||
\(646\) | −31.1128 | −1.22412 | ||||||||
\(647\) | −44.8587 | −1.76358 | −0.881788 | − | 0.471646i | \(-0.843660\pi\) | ||||
−0.881788 | + | 0.471646i | \(0.843660\pi\) | |||||||
\(648\) | 6.09654 | 0.239495 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 8.70047 | 0.341260 | ||||||||
\(651\) | −1.42447 | −0.0558294 | ||||||||
\(652\) | 2.98107 | 0.116748 | ||||||||
\(653\) | 42.4290 | 1.66037 | 0.830187 | − | 0.557485i | \(-0.188233\pi\) | ||||
0.830187 | + | 0.557485i | \(0.188233\pi\) | |||||||
\(654\) | −7.95799 | −0.311182 | ||||||||
\(655\) | −14.6745 | −0.573381 | ||||||||
\(656\) | −12.4261 | −0.485158 | ||||||||
\(657\) | −34.7074 | −1.35407 | ||||||||
\(658\) | 8.18218 | 0.318974 | ||||||||
\(659\) | −12.8671 | −0.501232 | −0.250616 | − | 0.968087i | \(-0.580633\pi\) | ||||
−0.250616 | + | 0.968087i | \(0.580633\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.4320 | 0.950293 | 0.475147 | − | 0.879907i | \(-0.342395\pi\) | ||||
0.475147 | + | 0.879907i | \(0.342395\pi\) | |||||||
\(662\) | 15.7816 | 0.613370 | ||||||||
\(663\) | −3.19371 | −0.124033 | ||||||||
\(664\) | 6.44579 | 0.250145 | ||||||||
\(665\) | 5.02403 | 0.194823 | ||||||||
\(666\) | −26.0361 | −1.00888 | ||||||||
\(667\) | 0.293460 | 0.0113628 | ||||||||
\(668\) | −11.2109 | −0.433762 | ||||||||
\(669\) | 2.79999 | 0.108254 | ||||||||
\(670\) | −7.53898 | −0.291256 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.58095 | 0.0609866 | ||||||||
\(673\) | 24.1166 | 0.929628 | 0.464814 | − | 0.885408i | \(-0.346121\pi\) | ||||
0.464814 | + | 0.885408i | \(0.346121\pi\) | |||||||
\(674\) | 64.1042 | 2.46920 | ||||||||
\(675\) | −1.28005 | −0.0492691 | ||||||||
\(676\) | 12.8054 | 0.492515 | ||||||||
\(677\) | 8.27910 | 0.318192 | 0.159096 | − | 0.987263i | \(-0.449142\pi\) | ||||
0.159096 | + | 0.987263i | \(0.449142\pi\) | |||||||
\(678\) | 7.03808 | 0.270296 | ||||||||
\(679\) | 1.09820 | 0.0421450 | ||||||||
\(680\) | 2.30882 | 0.0885391 | ||||||||
\(681\) | 2.61096 | 0.100052 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.6483 | −1.28752 | −0.643758 | − | 0.765229i | \(-0.722626\pi\) | ||||
−0.643758 | + | 0.765229i | \(0.722626\pi\) | |||||||
\(684\) | −24.1471 | −0.923286 | ||||||||
\(685\) | −15.7705 | −0.602561 | ||||||||
\(686\) | −1.90452 | −0.0727147 | ||||||||
\(687\) | 4.04403 | 0.154289 | ||||||||
\(688\) | −0.891034 | −0.0339703 | ||||||||
\(689\) | −12.7152 | −0.484411 | ||||||||
\(690\) | −0.119837 | −0.00456213 | ||||||||
\(691\) | −9.01062 | −0.342780 | −0.171390 | − | 0.985203i | \(-0.554826\pi\) | ||||
−0.171390 | + | 0.985203i | \(0.554826\pi\) | |||||||
\(692\) | −13.5787 | −0.516186 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 37.8536 | 1.43690 | ||||||||
\(695\) | −9.60769 | −0.364441 | ||||||||
\(696\) | 0.153073 | 0.00580220 | ||||||||
\(697\) | 8.77108 | 0.332228 | ||||||||
\(698\) | −35.6578 | −1.34967 | ||||||||
\(699\) | 5.03244 | 0.190344 | ||||||||
\(700\) | 1.62718 | 0.0615015 | ||||||||
\(701\) | 38.6147 | 1.45846 | 0.729228 | − | 0.684271i | \(-0.239879\pi\) | ||||
0.729228 | + | 0.684271i | \(0.239879\pi\) | |||||||
\(702\) | −11.1370 | −0.420340 | ||||||||
\(703\) | −23.2523 | −0.876978 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.923674 | −0.0347876 | ||||||||
\(706\) | −26.5847 | −1.00053 | ||||||||
\(707\) | 4.61577 | 0.173594 | ||||||||
\(708\) | −0.296272 | −0.0111346 | ||||||||
\(709\) | 45.5575 | 1.71095 | 0.855475 | − | 0.517845i | \(-0.173265\pi\) | ||||
0.855475 | + | 0.517845i | \(0.173265\pi\) | |||||||
\(710\) | −10.5560 | −0.396161 | ||||||||
\(711\) | 27.7543 | 1.04087 | ||||||||
\(712\) | 3.05769 | 0.114592 | ||||||||
\(713\) | −1.93906 | −0.0726185 | ||||||||
\(714\) | −1.33144 | −0.0498279 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.9476 | 0.446504 | ||||||||
\(717\) | 3.24306 | 0.121114 | ||||||||
\(718\) | 57.9252 | 2.16175 | ||||||||
\(719\) | −9.27727 | −0.345984 | −0.172992 | − | 0.984923i | \(-0.555343\pi\) | ||||
−0.172992 | + | 0.984923i | \(0.555343\pi\) | |||||||
\(720\) | 13.6070 | 0.507103 | ||||||||
\(721\) | 13.8643 | 0.516333 | ||||||||
\(722\) | −11.8858 | −0.442344 | ||||||||
\(723\) | −0.107419 | −0.00399495 | ||||||||
\(724\) | 0.207344 | 0.00770589 | ||||||||
\(725\) | 1.00271 | 0.0372398 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.13982 | −0.338977 | −0.169489 | − | 0.985532i | \(-0.554212\pi\) | ||||
−0.169489 | + | 0.985532i | \(0.554212\pi\) | |||||||
\(728\) | −3.24373 | −0.120221 | ||||||||
\(729\) | −24.5358 | −0.908735 | ||||||||
\(730\) | −22.3784 | −0.828262 | ||||||||
\(731\) | 0.628944 | 0.0232623 | ||||||||
\(732\) | 0.337020 | 0.0124566 | ||||||||
\(733\) | 29.5930 | 1.09304 | 0.546520 | − | 0.837446i | \(-0.315952\pi\) | ||||
0.546520 | + | 0.837446i | \(0.315952\pi\) | |||||||
\(734\) | 43.4519 | 1.60384 | ||||||||
\(735\) | 0.214998 | 0.00793032 | ||||||||
\(736\) | 2.15208 | 0.0793265 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 15.1744 | 0.558578 | ||||||||
\(739\) | −18.9094 | −0.695594 | −0.347797 | − | 0.937570i | \(-0.613070\pi\) | ||||
−0.347797 | + | 0.937570i | \(0.613070\pi\) | |||||||
\(740\) | −7.53094 | −0.276843 | ||||||||
\(741\) | −4.93452 | −0.181274 | ||||||||
\(742\) | −5.30090 | −0.194602 | ||||||||
\(743\) | −15.0087 | −0.550617 | −0.275309 | − | 0.961356i | \(-0.588780\pi\) | ||||
−0.275309 | + | 0.961356i | \(0.588780\pi\) | |||||||
\(744\) | −1.01144 | −0.0370812 | ||||||||
\(745\) | 1.39502 | 0.0511095 | ||||||||
\(746\) | −47.6831 | −1.74580 | ||||||||
\(747\) | −26.8144 | −0.981086 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.5598 | 0.532004 | ||||||||
\(750\) | −0.409467 | −0.0149516 | ||||||||
\(751\) | 15.7351 | 0.574182 | 0.287091 | − | 0.957903i | \(-0.407312\pi\) | ||||
0.287091 | + | 0.957903i | \(0.407312\pi\) | |||||||
\(752\) | 19.7911 | 0.721706 | ||||||||
\(753\) | −4.48030 | −0.163271 | ||||||||
\(754\) | 8.72407 | 0.317712 | ||||||||
\(755\) | 11.9950 | 0.436541 | ||||||||
\(756\) | −2.08287 | −0.0757532 | ||||||||
\(757\) | −16.8017 | −0.610668 | −0.305334 | − | 0.952245i | \(-0.598768\pi\) | ||||
−0.305334 | + | 0.952245i | \(0.598768\pi\) | |||||||
\(758\) | −45.7413 | −1.66140 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.56729 | 0.129399 | ||||||||
\(761\) | −7.79540 | −0.282583 | −0.141292 | − | 0.989968i | \(-0.545125\pi\) | ||||
−0.141292 | + | 0.989968i | \(0.545125\pi\) | |||||||
\(762\) | −1.25485 | −0.0454584 | ||||||||
\(763\) | 19.4350 | 0.703594 | ||||||||
\(764\) | 37.4636 | 1.35539 | ||||||||
\(765\) | −9.60462 | −0.347256 | ||||||||
\(766\) | −14.8321 | −0.535907 | ||||||||
\(767\) | 3.86883 | 0.139695 | ||||||||
\(768\) | 4.34573 | 0.156813 | ||||||||
\(769\) | −16.8739 | −0.608490 | −0.304245 | − | 0.952594i | \(-0.598404\pi\) | ||||
−0.304245 | + | 0.952594i | \(0.598404\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.98634 | −0.0715362 | ||||||||
\(772\) | −29.1180 | −1.04798 | ||||||||
\(773\) | 9.22274 | 0.331719 | 0.165859 | − | 0.986149i | \(-0.446960\pi\) | ||||
0.165859 | + | 0.986149i | \(0.446960\pi\) | |||||||
\(774\) | 1.08811 | 0.0391111 | ||||||||
\(775\) | −6.62551 | −0.237995 | ||||||||
\(776\) | 0.779771 | 0.0279921 | ||||||||
\(777\) | −0.995059 | −0.0356975 | ||||||||
\(778\) | −23.7298 | −0.850754 | ||||||||
\(779\) | 13.5520 | 0.485549 | ||||||||
\(780\) | −1.59819 | −0.0572243 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.81243 | −0.0648122 | ||||||||
\(783\) | −1.28352 | −0.0458693 | ||||||||
\(784\) | −4.60665 | −0.164523 | ||||||||
\(785\) | −24.4749 | −0.873548 | ||||||||
\(786\) | 6.00873 | 0.214324 | ||||||||
\(787\) | −30.9722 | −1.10404 | −0.552020 | − | 0.833831i | \(-0.686143\pi\) | ||||
−0.552020 | + | 0.833831i | \(0.686143\pi\) | |||||||
\(788\) | −35.2536 | −1.25586 | ||||||||
\(789\) | 0.838628 | 0.0298560 | ||||||||
\(790\) | 17.8952 | 0.636682 | ||||||||
\(791\) | −17.1884 | −0.611149 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.40093 | −0.156282 | ||||||||
\(794\) | 3.39407 | 0.120451 | ||||||||
\(795\) | 0.598412 | 0.0212235 | ||||||||
\(796\) | 40.3657 | 1.43072 | ||||||||
\(797\) | 34.4892 | 1.22167 | 0.610835 | − | 0.791758i | \(-0.290834\pi\) | ||||
0.610835 | + | 0.791758i | \(0.290834\pi\) | |||||||
\(798\) | −2.05717 | −0.0728232 | ||||||||
\(799\) | −13.9697 | −0.494213 | ||||||||
\(800\) | 7.35334 | 0.259980 | ||||||||
\(801\) | −12.7199 | −0.449437 | ||||||||
\(802\) | 61.9258 | 2.18668 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1.38483 | 0.0488393 | ||||||||
\(805\) | 0.292666 | 0.0103151 | ||||||||
\(806\) | −57.6450 | −2.03046 | ||||||||
\(807\) | 6.01086 | 0.211592 | ||||||||
\(808\) | 3.27741 | 0.115299 | ||||||||
\(809\) | 28.9150 | 1.01660 | 0.508298 | − | 0.861181i | \(-0.330275\pi\) | ||||
0.508298 | + | 0.861181i | \(0.330275\pi\) | |||||||
\(810\) | −16.3524 | −0.574565 | ||||||||
\(811\) | 4.85554 | 0.170501 | 0.0852506 | − | 0.996360i | \(-0.472831\pi\) | ||||
0.0852506 | + | 0.996360i | \(0.472831\pi\) | |||||||
\(812\) | 1.63159 | 0.0572576 | ||||||||
\(813\) | 5.17924 | 0.181644 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.83205 | 0.0641738 | ||||||||
\(816\) | −3.22049 | −0.112740 | ||||||||
\(817\) | 0.971765 | 0.0339977 | ||||||||
\(818\) | −48.9658 | −1.71205 | ||||||||
\(819\) | 13.4938 | 0.471513 | ||||||||
\(820\) | 4.38920 | 0.153277 | ||||||||
\(821\) | −18.6341 | −0.650335 | −0.325167 | − | 0.945656i | \(-0.605421\pi\) | ||||
−0.325167 | + | 0.945656i | \(0.605421\pi\) | |||||||
\(822\) | 6.45751 | 0.225231 | ||||||||
\(823\) | −17.9622 | −0.626122 | −0.313061 | − | 0.949733i | \(-0.601354\pi\) | ||||
−0.313061 | + | 0.949733i | \(0.601354\pi\) | |||||||
\(824\) | 9.84428 | 0.342942 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.61289 | 0.0561198 | ||||||||
\(827\) | 24.9389 | 0.867212 | 0.433606 | − | 0.901103i | \(-0.357241\pi\) | ||||
0.433606 | + | 0.901103i | \(0.357241\pi\) | |||||||
\(828\) | −1.40665 | −0.0488844 | ||||||||
\(829\) | −8.99336 | −0.312352 | −0.156176 | − | 0.987729i | \(-0.549917\pi\) | ||||
−0.156176 | + | 0.987729i | \(0.549917\pi\) | |||||||
\(830\) | −17.2892 | −0.600116 | ||||||||
\(831\) | 5.84541 | 0.202775 | ||||||||
\(832\) | 21.8880 | 0.758831 | ||||||||
\(833\) | 3.25164 | 0.112663 | ||||||||
\(834\) | 3.93403 | 0.136224 | ||||||||
\(835\) | −6.88977 | −0.238430 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.48098 | 0.293146 | ||||||||
\(838\) | −35.5859 | −1.22929 | ||||||||
\(839\) | −46.9822 | −1.62201 | −0.811003 | − | 0.585041i | \(-0.801078\pi\) | ||||
−0.811003 | + | 0.585041i | \(0.801078\pi\) | |||||||
\(840\) | 0.152659 | 0.00526722 | ||||||||
\(841\) | −27.9946 | −0.965330 | ||||||||
\(842\) | −16.9775 | −0.585084 | ||||||||
\(843\) | 4.19107 | 0.144348 | ||||||||
\(844\) | 34.3267 | 1.18157 | ||||||||
\(845\) | 7.86970 | 0.270726 | ||||||||
\(846\) | −24.1683 | −0.830924 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −12.8218 | −0.440304 | ||||||||
\(849\) | −0.523330 | −0.0179606 | ||||||||
\(850\) | −6.19280 | −0.212411 | ||||||||
\(851\) | −1.35453 | −0.0464325 | ||||||||
\(852\) | 1.93904 | 0.0664303 | ||||||||
\(853\) | −49.4824 | −1.69425 | −0.847123 | − | 0.531397i | \(-0.821667\pi\) | ||||
−0.847123 | + | 0.531397i | \(0.821667\pi\) | |||||||
\(854\) | −1.83473 | −0.0627830 | ||||||||
\(855\) | −14.8399 | −0.507512 | ||||||||
\(856\) | 10.3381 | 0.353350 | ||||||||
\(857\) | −29.2713 | −0.999890 | −0.499945 | − | 0.866057i | \(-0.666646\pi\) | ||||
−0.499945 | + | 0.866057i | \(0.666646\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.2734 | −1.40823 | −0.704115 | − | 0.710086i | \(-0.748656\pi\) | ||||
−0.704115 | + | 0.710086i | \(0.748656\pi\) | |||||||
\(860\) | 0.314734 | 0.0107323 | ||||||||
\(861\) | 0.579942 | 0.0197644 | ||||||||
\(862\) | −48.7003 | −1.65874 | ||||||||
\(863\) | 29.3160 | 0.997928 | 0.498964 | − | 0.866623i | \(-0.333714\pi\) | ||||
0.498964 | + | 0.866623i | \(0.333714\pi\) | |||||||
\(864\) | −9.41264 | −0.320225 | ||||||||
\(865\) | −8.34496 | −0.283737 | ||||||||
\(866\) | −40.0426 | −1.36070 | ||||||||
\(867\) | −1.38175 | −0.0469268 | ||||||||
\(868\) | −10.7809 | −0.365927 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.410578 | −0.0139199 | ||||||||
\(871\) | −18.0837 | −0.612742 | ||||||||
\(872\) | 13.7997 | 0.467318 | ||||||||
\(873\) | −3.24383 | −0.109787 | ||||||||
\(874\) | −2.80033 | −0.0947226 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 4.11069 | 0.138887 | ||||||||
\(877\) | 21.1875 | 0.715450 | 0.357725 | − | 0.933827i | \(-0.383553\pi\) | ||||
0.357725 | + | 0.933827i | \(0.383553\pi\) | |||||||
\(878\) | −45.0524 | −1.52045 | ||||||||
\(879\) | −5.26568 | −0.177607 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.9158 | −0.839435 | −0.419717 | − | 0.907655i | \(-0.637871\pi\) | ||||
−0.419717 | + | 0.907655i | \(0.637871\pi\) | |||||||
\(882\) | 5.62551 | 0.189421 | ||||||||
\(883\) | −36.1441 | −1.21635 | −0.608174 | − | 0.793804i | \(-0.708098\pi\) | ||||
−0.608174 | + | 0.793804i | \(0.708098\pi\) | |||||||
\(884\) | −24.1711 | −0.812961 | ||||||||
\(885\) | −0.182077 | −0.00612046 | ||||||||
\(886\) | −63.4864 | −2.13287 | ||||||||
\(887\) | −12.2613 | −0.411694 | −0.205847 | − | 0.978584i | \(-0.565995\pi\) | ||||
−0.205847 | + | 0.978584i | \(0.565995\pi\) | |||||||
\(888\) | −0.706538 | −0.0237098 | ||||||||
\(889\) | 3.06459 | 0.102783 | ||||||||
\(890\) | −8.20147 | −0.274914 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21.1912 | 0.709535 | ||||||||
\(893\) | −21.5842 | −0.722289 | ||||||||
\(894\) | −0.571214 | −0.0191043 | ||||||||
\(895\) | 7.34255 | 0.245435 | ||||||||
\(896\) | −5.58167 | −0.186471 | ||||||||
\(897\) | −0.287452 | −0.00959775 | ||||||||
\(898\) | 52.5332 | 1.75306 | ||||||||
\(899\) | −6.64348 | −0.221573 | ||||||||
\(900\) | −4.80632 | −0.160211 | ||||||||
\(901\) | 9.05041 | 0.301513 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.0415857 | 0.00138388 | ||||||||
\(904\) | −12.2045 | −0.405917 | ||||||||
\(905\) | 0.127426 | 0.00423578 | ||||||||
\(906\) | −4.91154 | −0.163175 | ||||||||
\(907\) | −3.37290 | −0.111995 | −0.0559977 | − | 0.998431i | \(-0.517834\pi\) | ||||
−0.0559977 | + | 0.998431i | \(0.517834\pi\) | |||||||
\(908\) | 19.7606 | 0.655778 | ||||||||
\(909\) | −13.6339 | −0.452209 | ||||||||
\(910\) | 8.70047 | 0.288418 | ||||||||
\(911\) | −9.30964 | −0.308442 | −0.154221 | − | 0.988036i | \(-0.549287\pi\) | ||||
−0.154221 | + | 0.988036i | \(0.549287\pi\) | |||||||
\(912\) | −4.97590 | −0.164768 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −24.4931 | −0.810160 | ||||||||
\(915\) | 0.207120 | 0.00684716 | ||||||||
\(916\) | 30.6066 | 1.01127 | ||||||||
\(917\) | −14.6745 | −0.484595 | ||||||||
\(918\) | 7.92710 | 0.261633 | ||||||||
\(919\) | −57.5454 | −1.89825 | −0.949123 | − | 0.314905i | \(-0.898027\pi\) | ||||
−0.949123 | + | 0.314905i | \(0.898027\pi\) | |||||||
\(920\) | 0.207807 | 0.00685118 | ||||||||
\(921\) | −4.95593 | −0.163304 | ||||||||
\(922\) | 50.7154 | 1.67022 | ||||||||
\(923\) | −25.3207 | −0.833440 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.62822 | −0.152175 | ||||||||
\(926\) | −36.7526 | −1.20776 | ||||||||
\(927\) | −40.9520 | −1.34504 | ||||||||
\(928\) | 7.37328 | 0.242040 | ||||||||
\(929\) | 3.71259 | 0.121806 | 0.0609031 | − | 0.998144i | \(-0.480602\pi\) | ||||
0.0609031 | + | 0.998144i | \(0.480602\pi\) | |||||||
\(930\) | 2.71293 | 0.0889604 | ||||||||
\(931\) | 5.02403 | 0.164656 | ||||||||
\(932\) | 38.0872 | 1.24759 | ||||||||
\(933\) | 4.02524 | 0.131780 | ||||||||
\(934\) | 68.5242 | 2.24218 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.58125 | 0.313173 | ||||||||
\(937\) | 35.7607 | 1.16825 | 0.584126 | − | 0.811663i | \(-0.301438\pi\) | ||||
0.584126 | + | 0.811663i | \(0.301438\pi\) | |||||||
\(938\) | −7.53898 | −0.246157 | ||||||||
\(939\) | 3.32655 | 0.108558 | ||||||||
\(940\) | −6.99068 | −0.228011 | ||||||||
\(941\) | 2.30778 | 0.0752316 | 0.0376158 | − | 0.999292i | \(-0.488024\pi\) | ||||
0.0376158 | + | 0.999292i | \(0.488024\pi\) | |||||||
\(942\) | 10.0217 | 0.326524 | ||||||||
\(943\) | 0.789447 | 0.0257079 | ||||||||
\(944\) | 3.90127 | 0.126976 | ||||||||
\(945\) | −1.28005 | −0.0416400 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −55.9447 | −1.81796 | −0.908979 | − | 0.416842i | \(-0.863137\pi\) | ||||
−0.908979 | + | 0.416842i | \(0.863137\pi\) | |||||||
\(948\) | −3.28716 | −0.106762 | ||||||||
\(949\) | −53.6788 | −1.74249 | ||||||||
\(950\) | −9.56834 | −0.310438 | ||||||||
\(951\) | 2.77324 | 0.0899286 | ||||||||
\(952\) | 2.30882 | 0.0748292 | ||||||||
\(953\) | −21.2762 | −0.689203 | −0.344602 | − | 0.938749i | \(-0.611986\pi\) | ||||
−0.344602 | + | 0.938749i | \(0.611986\pi\) | |||||||
\(954\) | 15.6577 | 0.506936 | ||||||||
\(955\) | 23.0237 | 0.745029 | ||||||||
\(956\) | 24.5445 | 0.793827 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −53.1365 | −1.71676 | ||||||||
\(959\) | −15.7705 | −0.509257 | ||||||||
\(960\) | −1.03011 | −0.0332466 | ||||||||
\(961\) | 12.8974 | 0.416045 | ||||||||
\(962\) | −40.2677 | −1.29828 | ||||||||
\(963\) | −43.0064 | −1.38586 | ||||||||
\(964\) | −0.812981 | −0.0261844 | ||||||||
\(965\) | −17.8948 | −0.576053 | ||||||||
\(966\) | −0.119837 | −0.00385570 | ||||||||
\(967\) | 1.52052 | 0.0488966 | 0.0244483 | − | 0.999701i | \(-0.492217\pi\) | ||||
0.0244483 | + | 0.999701i | \(0.492217\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.51228 | 0.112831 | ||||||||
\(970\) | −2.09153 | −0.0671551 | ||||||||
\(971\) | −0.577620 | −0.0185367 | −0.00926835 | − | 0.999957i | \(-0.502950\pi\) | ||||
−0.00926835 | + | 0.999957i | \(0.502950\pi\) | |||||||
\(972\) | 9.25237 | 0.296770 | ||||||||
\(973\) | −9.60769 | −0.308009 | ||||||||
\(974\) | −44.0132 | −1.41028 | ||||||||
\(975\) | −0.982183 | −0.0314550 | ||||||||
\(976\) | −4.43784 | −0.142052 | ||||||||
\(977\) | 14.1855 | 0.453836 | 0.226918 | − | 0.973914i | \(-0.427135\pi\) | ||||
0.226918 | + | 0.973914i | \(0.427135\pi\) | |||||||
\(978\) | −0.750163 | −0.0239876 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.62718 | 0.0519783 | ||||||||
\(981\) | −57.4066 | −1.83285 | ||||||||
\(982\) | 30.6848 | 0.979192 | ||||||||
\(983\) | 10.1642 | 0.324186 | 0.162093 | − | 0.986775i | \(-0.448175\pi\) | ||||
0.162093 | + | 0.986775i | \(0.448175\pi\) | |||||||
\(984\) | 0.411786 | 0.0131272 | ||||||||
\(985\) | −21.6655 | −0.690320 | ||||||||
\(986\) | −6.20960 | −0.197754 | ||||||||
\(987\) | −0.923674 | −0.0294009 | ||||||||
\(988\) | −37.3461 | −1.18814 | ||||||||
\(989\) | 0.0566085 | 0.00180005 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.0016 | −1.77895 | −0.889475 | − | 0.456983i | \(-0.848930\pi\) | ||||
−0.889475 | + | 0.456983i | \(0.848930\pi\) | |||||||
\(992\) | −48.7196 | −1.54685 | ||||||||
\(993\) | −1.78156 | −0.0565362 | ||||||||
\(994\) | −10.5560 | −0.334817 | ||||||||
\(995\) | 24.8072 | 0.786440 | ||||||||
\(996\) | 3.17584 | 0.100630 | ||||||||
\(997\) | 38.8222 | 1.22951 | 0.614756 | − | 0.788717i | \(-0.289254\pi\) | ||||
0.614756 | + | 0.788717i | \(0.289254\pi\) | |||||||
\(998\) | 31.2697 | 0.989825 | ||||||||
\(999\) | 5.92436 | 0.187438 |
(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 | 4235.2.a.bd.1.1 | yes | 5 | |
11.10 | odd | 2 | 4235.2.a.bc.1.5 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4235.2.a.bc.1.5 | ✓ | 5 | 11.10 | odd | 2 | ||
4235.2.a.bd.1.1 | yes | 5 | 1.1 | even | 1 | trivial |