Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(364,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, 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("1815.364");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.c (of order \(2\), degree \(1\), 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: | \(14.4928479669\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 364.13 | ||
Character | \(\chi\) | \(=\) | 1815.364 |
Dual form | 1815.2.c.j.364.12 |
$q$-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 \(\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times\).
\(n\) | \(727\) | \(1211\) | \(1696\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.288813i | 0.204221i | 0.994773 | + | 0.102111i | \(0.0325596\pi\) | ||||
−0.994773 | + | 0.102111i | \(0.967440\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 1.91659 | 0.958294 | ||||||||
\(5\) | −0.407156 | − | 2.19869i | −0.182086 | − | 0.983283i | ||||
\(6\) | 0.288813 | 0.117907 | ||||||||
\(7\) | 3.66740i | 1.38615i | 0.720867 | + | 0.693074i | \(0.243744\pi\) | ||||
−0.720867 | + | 0.693074i | \(0.756256\pi\) | |||||||
\(8\) | 1.13116i | 0.399926i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.635009 | − | 0.117592i | 0.200807 | − | 0.0371859i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | − | 1.91659i | − | 0.553271i | ||||||
\(13\) | 4.82569i | 1.33840i | 0.743080 | + | 0.669202i | \(0.233364\pi\) | ||||
−0.743080 | + | 0.669202i | \(0.766636\pi\) | |||||||
\(14\) | −1.05919 | −0.283081 | ||||||||
\(15\) | −2.19869 | + | 0.407156i | −0.567698 | + | 0.105127i | ||||
\(16\) | 3.50648 | 0.876620 | ||||||||
\(17\) | − | 3.84013i | − | 0.931369i | −0.884951 | − | 0.465685i | \(-0.845808\pi\) | ||
0.884951 | − | 0.465685i | \(-0.154192\pi\) | |||||||
\(18\) | − | 0.288813i | − | 0.0680738i | ||||||
\(19\) | 6.96183 | 1.59715 | 0.798576 | − | 0.601894i | \(-0.205587\pi\) | ||||
0.798576 | + | 0.601894i | \(0.205587\pi\) | |||||||
\(20\) | −0.780351 | − | 4.21397i | −0.174492 | − | 0.942273i | ||||
\(21\) | 3.66740 | 0.800293 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.20633i | − | 0.251537i | −0.992060 | − | 0.125769i | \(-0.959860\pi\) | ||
0.992060 | − | 0.125769i | \(-0.0401397\pi\) | |||||||
\(24\) | 1.13116 | 0.230897 | ||||||||
\(25\) | −4.66845 | + | 1.79042i | −0.933689 | + | 0.358084i | ||||
\(26\) | −1.39372 | −0.273331 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 7.02890i | 1.32834i | ||||||||
\(29\) | −4.94672 | −0.918583 | −0.459292 | − | 0.888286i | \(-0.651897\pi\) | ||||
−0.459292 | + | 0.888286i | \(0.651897\pi\) | |||||||
\(30\) | −0.117592 | − | 0.635009i | −0.0214693 | − | 0.115936i | ||||
\(31\) | 7.36932 | 1.32357 | 0.661784 | − | 0.749694i | \(-0.269800\pi\) | ||||
0.661784 | + | 0.749694i | \(0.269800\pi\) | |||||||
\(32\) | 3.27504i | 0.578950i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.10908 | 0.190206 | ||||||||
\(35\) | 8.06347 | − | 1.49321i | 1.36297 | − | 0.252398i | ||||
\(36\) | −1.91659 | −0.319431 | ||||||||
\(37\) | 2.38692i | 0.392407i | 0.980563 | + | 0.196204i | \(0.0628614\pi\) | ||||
−0.980563 | + | 0.196204i | \(0.937139\pi\) | |||||||
\(38\) | 2.01066i | 0.326173i | ||||||||
\(39\) | 4.82569 | 0.772728 | ||||||||
\(40\) | 2.48707 | − | 0.460559i | 0.393240 | − | 0.0728208i | ||||
\(41\) | 4.30563 | 0.672427 | 0.336213 | − | 0.941786i | \(-0.390854\pi\) | ||||
0.336213 | + | 0.941786i | \(0.390854\pi\) | |||||||
\(42\) | 1.05919i | 0.163437i | ||||||||
\(43\) | 0.772454i | 0.117798i | 0.998264 | + | 0.0588990i | \(0.0187590\pi\) | ||||
−0.998264 | + | 0.0588990i | \(0.981241\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.407156 | + | 2.19869i | 0.0606953 | + | 0.327761i | ||||
\(46\) | 0.348403 | 0.0513693 | ||||||||
\(47\) | 6.47068i | 0.943846i | 0.881640 | + | 0.471923i | \(0.156440\pi\) | ||||
−0.881640 | + | 0.471923i | \(0.843560\pi\) | |||||||
\(48\) | − | 3.50648i | − | 0.506117i | ||||||
\(49\) | −6.44984 | −0.921405 | ||||||||
\(50\) | −0.517096 | − | 1.34831i | −0.0731284 | − | 0.190679i | ||||
\(51\) | −3.84013 | −0.537726 | ||||||||
\(52\) | 9.24885i | 1.28258i | ||||||||
\(53\) | 10.7562i | 1.47748i | 0.673989 | + | 0.738741i | \(0.264580\pi\) | ||||
−0.673989 | + | 0.738741i | \(0.735420\pi\) | |||||||
\(54\) | −0.288813 | −0.0393024 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.14842 | −0.554356 | ||||||||
\(57\) | − | 6.96183i | − | 0.922116i | ||||||
\(58\) | − | 1.42868i | − | 0.187594i | ||||||
\(59\) | 14.4979 | 1.88746 | 0.943730 | − | 0.330717i | \(-0.107291\pi\) | ||||
0.943730 | + | 0.330717i | \(0.107291\pi\) | |||||||
\(60\) | −4.21397 | + | 0.780351i | −0.544022 | + | 0.100743i | ||||
\(61\) | −1.83091 | −0.234424 | −0.117212 | − | 0.993107i | \(-0.537396\pi\) | ||||
−0.117212 | + | 0.993107i | \(0.537396\pi\) | |||||||
\(62\) | 2.12835i | 0.270301i | ||||||||
\(63\) | − | 3.66740i | − | 0.462049i | ||||||
\(64\) | 6.06709 | 0.758386 | ||||||||
\(65\) | 10.6102 | − | 1.96481i | 1.31603 | − | 0.243705i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6.10784i | − | 0.746191i | −0.927793 | − | 0.373096i | \(-0.878296\pi\) | ||
0.927793 | − | 0.373096i | \(-0.121704\pi\) | |||||||
\(68\) | − | 7.35995i | − | 0.892525i | ||||||
\(69\) | −1.20633 | −0.145225 | ||||||||
\(70\) | 0.431257 | + | 2.32883i | 0.0515451 | + | 0.278349i | ||||
\(71\) | −3.29108 | −0.390579 | −0.195289 | − | 0.980746i | \(-0.562565\pi\) | ||||
−0.195289 | + | 0.980746i | \(0.562565\pi\) | |||||||
\(72\) | − | 1.13116i | − | 0.133309i | ||||||
\(73\) | 0.191521i | 0.0224158i | 0.999937 | + | 0.0112079i | \(0.00356767\pi\) | ||||
−0.999937 | + | 0.0112079i | \(0.996432\pi\) | |||||||
\(74\) | −0.689373 | −0.0801380 | ||||||||
\(75\) | 1.79042 | + | 4.66845i | 0.206740 | + | 0.539066i | ||||
\(76\) | 13.3429 | 1.53054 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.39372i | 0.157808i | ||||||||
\(79\) | 3.15994 | 0.355522 | 0.177761 | − | 0.984074i | \(-0.443115\pi\) | ||||
0.177761 | + | 0.984074i | \(0.443115\pi\) | |||||||
\(80\) | −1.42769 | − | 7.70965i | −0.159620 | − | 0.861965i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.24352i | 0.137324i | ||||||||
\(83\) | 1.53041i | 0.167985i | 0.996466 | + | 0.0839923i | \(0.0267671\pi\) | ||||
−0.996466 | + | 0.0839923i | \(0.973233\pi\) | |||||||
\(84\) | 7.02890 | 0.766915 | ||||||||
\(85\) | −8.44325 | + | 1.56354i | −0.915799 | + | 0.169589i | ||||
\(86\) | −0.223095 | −0.0240569 | ||||||||
\(87\) | 4.94672i | 0.530344i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.04594 | 0.322869 | 0.161434 | − | 0.986883i | \(-0.448388\pi\) | ||||
0.161434 | + | 0.986883i | \(0.448388\pi\) | |||||||
\(90\) | −0.635009 | + | 0.117592i | −0.0669358 | + | 0.0123953i | ||||
\(91\) | −17.6977 | −1.85523 | ||||||||
\(92\) | − | 2.31204i | − | 0.241046i | ||||||
\(93\) | − | 7.36932i | − | 0.764163i | ||||||
\(94\) | −1.86882 | −0.192754 | ||||||||
\(95\) | −2.83455 | − | 15.3069i | −0.290819 | − | 1.57045i | ||||
\(96\) | 3.27504 | 0.334257 | ||||||||
\(97\) | − | 13.7770i | − | 1.39885i | −0.714708 | − | 0.699423i | \(-0.753440\pi\) | ||
0.714708 | − | 0.699423i | \(-0.246560\pi\) | |||||||
\(98\) | − | 1.86280i | − | 0.188171i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.94749 | + | 3.43149i | −0.894749 | + | 0.343149i | ||||
\(101\) | −4.65928 | −0.463616 | −0.231808 | − | 0.972762i | \(-0.574464\pi\) | ||||
−0.231808 | + | 0.972762i | \(0.574464\pi\) | |||||||
\(102\) | − | 1.10908i | − | 0.109815i | ||||||
\(103\) | − | 9.81701i | − | 0.967299i | −0.875262 | − | 0.483649i | \(-0.839311\pi\) | ||
0.875262 | − | 0.483649i | \(-0.160689\pi\) | |||||||
\(104\) | −5.45863 | −0.535262 | ||||||||
\(105\) | −1.49321 | − | 8.06347i | −0.145722 | − | 0.786914i | ||||
\(106\) | −3.10654 | −0.301734 | ||||||||
\(107\) | − | 11.8016i | − | 1.14090i | −0.821331 | − | 0.570452i | \(-0.806768\pi\) | ||
0.821331 | − | 0.570452i | \(-0.193232\pi\) | |||||||
\(108\) | 1.91659i | 0.184424i | ||||||||
\(109\) | 10.4450 | 1.00045 | 0.500226 | − | 0.865895i | \(-0.333250\pi\) | ||||
0.500226 | + | 0.865895i | \(0.333250\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.38692 | 0.226556 | ||||||||
\(112\) | 12.8597i | 1.21513i | ||||||||
\(113\) | − | 12.8654i | − | 1.21028i | −0.796120 | − | 0.605139i | \(-0.793118\pi\) | ||
0.796120 | − | 0.605139i | \(-0.206882\pi\) | |||||||
\(114\) | 2.01066 | 0.188316 | ||||||||
\(115\) | −2.65234 | + | 0.491165i | −0.247332 | + | 0.0458014i | ||||
\(116\) | −9.48082 | −0.880272 | ||||||||
\(117\) | − | 4.82569i | − | 0.446135i | ||||||
\(118\) | 4.18717i | 0.385460i | ||||||||
\(119\) | 14.0833 | 1.29102 | ||||||||
\(120\) | −0.460559 | − | 2.48707i | −0.0420431 | − | 0.227037i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 0.528791i | − | 0.0478745i | ||||||
\(123\) | − | 4.30563i | − | 0.388226i | ||||||
\(124\) | 14.1239 | 1.26837 | ||||||||
\(125\) | 5.83736 | + | 9.53547i | 0.522109 | + | 0.852879i | ||||
\(126\) | 1.05919 | 0.0943604 | ||||||||
\(127\) | − | 0.185919i | − | 0.0164977i | −0.999966 | − | 0.00824884i | \(-0.997374\pi\) | ||
0.999966 | − | 0.00824884i | \(-0.00262572\pi\) | |||||||
\(128\) | 8.30233i | 0.733829i | ||||||||
\(129\) | 0.772454 | 0.0680108 | ||||||||
\(130\) | 0.567462 | + | 3.06435i | 0.0497697 | + | 0.268762i | ||||
\(131\) | −9.27143 | −0.810048 | −0.405024 | − | 0.914306i | \(-0.632737\pi\) | ||||
−0.405024 | + | 0.914306i | \(0.632737\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 25.5318i | 2.21389i | ||||||||
\(134\) | 1.76402 | 0.152388 | ||||||||
\(135\) | 2.19869 | − | 0.407156i | 0.189233 | − | 0.0350425i | ||||
\(136\) | 4.34381 | 0.372479 | ||||||||
\(137\) | − | 0.438101i | − | 0.0374295i | −0.999825 | − | 0.0187147i | \(-0.994043\pi\) | ||
0.999825 | − | 0.0187147i | \(-0.00595744\pi\) | |||||||
\(138\) | − | 0.348403i | − | 0.0296581i | ||||||
\(139\) | −8.60433 | −0.729810 | −0.364905 | − | 0.931045i | \(-0.618898\pi\) | ||||
−0.364905 | + | 0.931045i | \(0.618898\pi\) | |||||||
\(140\) | 15.4543 | − | 2.86186i | 1.30613 | − | 0.241871i | ||||
\(141\) | 6.47068 | 0.544930 | ||||||||
\(142\) | − | 0.950505i | − | 0.0797646i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.50648 | −0.292207 | ||||||||
\(145\) | 2.01409 | + | 10.8763i | 0.167261 | + | 0.903227i | ||||
\(146\) | −0.0553137 | −0.00457780 | ||||||||
\(147\) | 6.44984i | 0.531974i | ||||||||
\(148\) | 4.57474i | 0.376041i | ||||||||
\(149\) | 15.3241 | 1.25540 | 0.627700 | − | 0.778455i | \(-0.283996\pi\) | ||||
0.627700 | + | 0.778455i | \(0.283996\pi\) | |||||||
\(150\) | −1.34831 | + | 0.517096i | −0.110089 | + | 0.0422207i | ||||
\(151\) | −1.05059 | −0.0854958 | −0.0427479 | − | 0.999086i | \(-0.513611\pi\) | ||||
−0.0427479 | + | 0.999086i | \(0.513611\pi\) | |||||||
\(152\) | 7.87494i | 0.638742i | ||||||||
\(153\) | 3.84013i | 0.310456i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.00047 | − | 16.2028i | −0.241003 | − | 1.30144i | ||||
\(156\) | 9.24885 | 0.740501 | ||||||||
\(157\) | − | 4.93869i | − | 0.394150i | −0.980388 | − | 0.197075i | \(-0.936856\pi\) | ||
0.980388 | − | 0.197075i | \(-0.0631443\pi\) | |||||||
\(158\) | 0.912632i | 0.0726051i | ||||||||
\(159\) | 10.7562 | 0.853025 | ||||||||
\(160\) | 7.20078 | − | 1.33345i | 0.569272 | − | 0.105419i | ||||
\(161\) | 4.42410 | 0.348668 | ||||||||
\(162\) | 0.288813i | 0.0226913i | ||||||||
\(163\) | − | 9.62856i | − | 0.754167i | −0.926179 | − | 0.377083i | \(-0.876927\pi\) | ||
0.926179 | − | 0.377083i | \(-0.123073\pi\) | |||||||
\(164\) | 8.25212 | 0.644382 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.442003 | −0.0343061 | ||||||||
\(167\) | 9.34416i | 0.723073i | 0.932358 | + | 0.361536i | \(0.117748\pi\) | ||||
−0.932358 | + | 0.361536i | \(0.882252\pi\) | |||||||
\(168\) | 4.14842i | 0.320058i | ||||||||
\(169\) | −10.2873 | −0.791327 | ||||||||
\(170\) | −0.451569 | − | 2.43852i | −0.0346338 | − | 0.187026i | ||||
\(171\) | −6.96183 | −0.532384 | ||||||||
\(172\) | 1.48047i | 0.112885i | ||||||||
\(173\) | 0.344694i | 0.0262066i | 0.999914 | + | 0.0131033i | \(0.00417103\pi\) | ||||
−0.999914 | + | 0.0131033i | \(0.995829\pi\) | |||||||
\(174\) | −1.42868 | −0.108308 | ||||||||
\(175\) | −6.56619 | − | 17.1211i | −0.496357 | − | 1.29423i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 14.4979i | − | 1.08973i | ||||||
\(178\) | 0.879706i | 0.0659368i | ||||||||
\(179\) | −16.0740 | −1.20143 | −0.600713 | − | 0.799465i | \(-0.705117\pi\) | ||||
−0.600713 | + | 0.799465i | \(0.705117\pi\) | |||||||
\(180\) | 0.780351 | + | 4.21397i | 0.0581639 | + | 0.314091i | ||||
\(181\) | −10.7349 | −0.797922 | −0.398961 | − | 0.916968i | \(-0.630629\pi\) | ||||
−0.398961 | + | 0.916968i | \(0.630629\pi\) | |||||||
\(182\) | − | 5.11133i | − | 0.378877i | ||||||
\(183\) | 1.83091i | 0.135345i | ||||||||
\(184\) | 1.36455 | 0.100596 | ||||||||
\(185\) | 5.24809 | − | 0.971850i | 0.385847 | − | 0.0714518i | ||||
\(186\) | 2.12835 | 0.156058 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.4016i | 0.904481i | ||||||||
\(189\) | −3.66740 | −0.266764 | ||||||||
\(190\) | 4.42082 | − | 0.818655i | 0.320720 | − | 0.0593915i | ||||
\(191\) | −13.5985 | −0.983954 | −0.491977 | − | 0.870608i | \(-0.663726\pi\) | ||||
−0.491977 | + | 0.870608i | \(0.663726\pi\) | |||||||
\(192\) | − | 6.06709i | − | 0.437854i | ||||||
\(193\) | 25.9081i | 1.86490i | 0.361296 | + | 0.932451i | \(0.382334\pi\) | ||||
−0.361296 | + | 0.932451i | \(0.617666\pi\) | |||||||
\(194\) | 3.97899 | 0.285674 | ||||||||
\(195\) | −1.96481 | − | 10.6102i | −0.140703 | − | 0.759810i | ||||
\(196\) | −12.3617 | −0.882977 | ||||||||
\(197\) | − | 1.18346i | − | 0.0843177i | −0.999111 | − | 0.0421588i | \(-0.986576\pi\) | ||
0.999111 | − | 0.0421588i | \(-0.0134236\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.13466 | −0.222210 | −0.111105 | − | 0.993809i | \(-0.535439\pi\) | ||||
−0.111105 | + | 0.993809i | \(0.535439\pi\) | |||||||
\(200\) | −2.02525 | − | 5.28076i | −0.143207 | − | 0.373406i | ||||
\(201\) | −6.10784 | −0.430814 | ||||||||
\(202\) | − | 1.34566i | − | 0.0946804i | ||||||
\(203\) | − | 18.1416i | − | 1.27329i | ||||||
\(204\) | −7.35995 | −0.515300 | ||||||||
\(205\) | −1.75307 | − | 9.46674i | −0.122439 | − | 0.661186i | ||||
\(206\) | 2.83528 | 0.197543 | ||||||||
\(207\) | 1.20633i | 0.0838457i | ||||||||
\(208\) | 16.9212i | 1.17327i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.32883 | − | 0.431257i | 0.160705 | − | 0.0297596i | ||||
\(211\) | −3.02303 | −0.208114 | −0.104057 | − | 0.994571i | \(-0.533182\pi\) | ||||
−0.104057 | + | 0.994571i | \(0.533182\pi\) | |||||||
\(212\) | 20.6153i | 1.41586i | ||||||||
\(213\) | 3.29108i | 0.225501i | ||||||||
\(214\) | 3.40846 | 0.232997 | ||||||||
\(215\) | 1.69838 | − | 0.314510i | 0.115829 | − | 0.0214494i | ||||
\(216\) | −1.13116 | −0.0769657 | ||||||||
\(217\) | 27.0262i | 1.83466i | ||||||||
\(218\) | 3.01666i | 0.204314i | ||||||||
\(219\) | 0.191521 | 0.0129418 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.5313 | 1.24655 | ||||||||
\(222\) | 0.689373i | 0.0462677i | ||||||||
\(223\) | 0.0459708i | 0.00307843i | 0.999999 | + | 0.00153922i | \(0.000489948\pi\) | ||||
−0.999999 | + | 0.00153922i | \(0.999510\pi\) | |||||||
\(224\) | −12.0109 | −0.802511 | ||||||||
\(225\) | 4.66845 | − | 1.79042i | 0.311230 | − | 0.119361i | ||||
\(226\) | 3.71570 | 0.247165 | ||||||||
\(227\) | 6.14586i | 0.407915i | 0.978980 | + | 0.203958i | \(0.0653805\pi\) | ||||
−0.978980 | + | 0.203958i | \(0.934620\pi\) | |||||||
\(228\) | − | 13.3429i | − | 0.883658i | ||||||
\(229\) | −11.7365 | −0.775570 | −0.387785 | − | 0.921750i | \(-0.626760\pi\) | ||||
−0.387785 | + | 0.921750i | \(0.626760\pi\) | |||||||
\(230\) | −0.141855 | − | 0.766030i | −0.00935362 | − | 0.0505105i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 5.59554i | − | 0.367365i | ||||||
\(233\) | − | 10.6588i | − | 0.698280i | −0.937071 | − | 0.349140i | \(-0.886474\pi\) | ||
0.937071 | − | 0.349140i | \(-0.113526\pi\) | |||||||
\(234\) | 1.39372 | 0.0911103 | ||||||||
\(235\) | 14.2270 | − | 2.63458i | 0.928067 | − | 0.171861i | ||||
\(236\) | 27.7864 | 1.80874 | ||||||||
\(237\) | − | 3.15994i | − | 0.205260i | ||||||
\(238\) | 4.06744i | 0.263653i | ||||||||
\(239\) | −4.59328 | −0.297115 | −0.148557 | − | 0.988904i | \(-0.547463\pi\) | ||||
−0.148557 | + | 0.988904i | \(0.547463\pi\) | |||||||
\(240\) | −7.70965 | + | 1.42769i | −0.497656 | + | 0.0921568i | ||||
\(241\) | −18.8716 | −1.21563 | −0.607814 | − | 0.794079i | \(-0.707953\pi\) | ||||
−0.607814 | + | 0.794079i | \(0.707953\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −3.50911 | −0.224647 | ||||||||
\(245\) | 2.62609 | + | 14.1812i | 0.167775 | + | 0.906002i | ||||
\(246\) | 1.24352 | 0.0792841 | ||||||||
\(247\) | 33.5956i | 2.13764i | ||||||||
\(248\) | 8.33588i | 0.529329i | ||||||||
\(249\) | 1.53041 | 0.0969860 | ||||||||
\(250\) | −2.75397 | + | 1.68590i | −0.174176 | + | 0.106626i | ||||
\(251\) | −19.4907 | −1.23024 | −0.615120 | − | 0.788434i | \(-0.710892\pi\) | ||||
−0.615120 | + | 0.788434i | \(0.710892\pi\) | |||||||
\(252\) | − | 7.02890i | − | 0.442779i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.0536959 | 0.00336918 | ||||||||
\(255\) | 1.56354 | + | 8.44325i | 0.0979124 | + | 0.528737i | ||||
\(256\) | 9.73636 | 0.608522 | ||||||||
\(257\) | 13.1814i | 0.822234i | 0.911582 | + | 0.411117i | \(0.134861\pi\) | ||||
−0.911582 | + | 0.411117i | \(0.865139\pi\) | |||||||
\(258\) | 0.223095i | 0.0138893i | ||||||||
\(259\) | −8.75380 | −0.543934 | ||||||||
\(260\) | 20.3353 | − | 3.76573i | 1.26114 | − | 0.233541i | ||||
\(261\) | 4.94672 | 0.306194 | ||||||||
\(262\) | − | 2.67771i | − | 0.165429i | ||||||
\(263\) | 29.8396i | 1.83999i | 0.391935 | + | 0.919993i | \(0.371806\pi\) | ||||
−0.391935 | + | 0.919993i | \(0.628194\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.6496 | − | 4.37947i | 1.45278 | − | 0.269029i | ||||
\(266\) | −7.37391 | −0.452124 | ||||||||
\(267\) | − | 3.04594i | − | 0.186408i | ||||||
\(268\) | − | 11.7062i | − | 0.715070i | ||||||
\(269\) | −0.251857 | −0.0153560 | −0.00767800 | − | 0.999971i | \(-0.502444\pi\) | ||||
−0.00767800 | + | 0.999971i | \(0.502444\pi\) | |||||||
\(270\) | 0.117592 | + | 0.635009i | 0.00715642 | + | 0.0386454i | ||||
\(271\) | −12.0897 | −0.734400 | −0.367200 | − | 0.930142i | \(-0.619684\pi\) | ||||
−0.367200 | + | 0.930142i | \(0.619684\pi\) | |||||||
\(272\) | − | 13.4654i | − | 0.816457i | ||||||
\(273\) | 17.6977i | 1.07112i | ||||||||
\(274\) | 0.126529 | 0.00764391 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.31204 | −0.139168 | ||||||||
\(277\) | − | 16.4655i | − | 0.989318i | −0.869087 | − | 0.494659i | \(-0.835293\pi\) | ||
0.869087 | − | 0.494659i | \(-0.164707\pi\) | |||||||
\(278\) | − | 2.48504i | − | 0.149043i | ||||||
\(279\) | −7.36932 | −0.441189 | ||||||||
\(280\) | 1.68906 | + | 9.12108i | 0.100940 | + | 0.545089i | ||||
\(281\) | 12.6017 | 0.751756 | 0.375878 | − | 0.926669i | \(-0.377341\pi\) | ||||
0.375878 | + | 0.926669i | \(0.377341\pi\) | |||||||
\(282\) | 1.86882i | 0.111286i | ||||||||
\(283\) | 17.8478i | 1.06094i | 0.847703 | + | 0.530472i | \(0.177985\pi\) | ||||
−0.847703 | + | 0.530472i | \(0.822015\pi\) | |||||||
\(284\) | −6.30763 | −0.374289 | ||||||||
\(285\) | −15.3069 | + | 2.83455i | −0.906701 | + | 0.167904i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.7905i | 0.932083i | ||||||||
\(288\) | − | 3.27504i | − | 0.192983i | ||||||
\(289\) | 2.25337 | 0.132551 | ||||||||
\(290\) | −3.14121 | + | 0.581695i | −0.184458 | + | 0.0341583i | ||||
\(291\) | −13.7770 | −0.807624 | ||||||||
\(292\) | 0.367067i | 0.0214810i | ||||||||
\(293\) | 9.90674i | 0.578758i | 0.957215 | + | 0.289379i | \(0.0934488\pi\) | ||||
−0.957215 | + | 0.289379i | \(0.906551\pi\) | |||||||
\(294\) | −1.86280 | −0.108640 | ||||||||
\(295\) | −5.90289 | − | 31.8762i | −0.343680 | − | 1.85591i | ||||
\(296\) | −2.69999 | −0.156934 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.42580i | 0.256380i | ||||||||
\(299\) | 5.82137 | 0.336658 | ||||||||
\(300\) | 3.43149 | + | 8.94749i | 0.198117 | + | 0.516583i | ||||
\(301\) | −2.83290 | −0.163286 | ||||||||
\(302\) | − | 0.303424i | − | 0.0174601i | ||||||
\(303\) | 4.65928i | 0.267669i | ||||||||
\(304\) | 24.4115 | 1.40010 | ||||||||
\(305\) | 0.745468 | + | 4.02561i | 0.0426854 | + | 0.230505i | ||||
\(306\) | −1.10908 | −0.0634019 | ||||||||
\(307\) | − | 23.2505i | − | 1.32698i | −0.748186 | − | 0.663489i | \(-0.769075\pi\) | ||
0.748186 | − | 0.663489i | \(-0.230925\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.81701 | −0.558470 | ||||||||
\(310\) | 4.67958 | − | 0.866573i | 0.265782 | − | 0.0492180i | ||||
\(311\) | 29.8628 | 1.69336 | 0.846681 | − | 0.532100i | \(-0.178597\pi\) | ||||
0.846681 | + | 0.532100i | \(0.178597\pi\) | |||||||
\(312\) | 5.45863i | 0.309034i | ||||||||
\(313\) | 25.6366i | 1.44907i | 0.689240 | + | 0.724533i | \(0.257945\pi\) | ||||
−0.689240 | + | 0.724533i | \(0.742055\pi\) | |||||||
\(314\) | 1.42636 | 0.0804940 | ||||||||
\(315\) | −8.06347 | + | 1.49321i | −0.454325 | + | 0.0841327i | ||||
\(316\) | 6.05631 | 0.340694 | ||||||||
\(317\) | − | 1.12070i | − | 0.0629448i | −0.999505 | − | 0.0314724i | \(-0.989980\pi\) | ||
0.999505 | − | 0.0314724i | \(-0.0100196\pi\) | |||||||
\(318\) | 3.10654i | 0.174206i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −2.47025 | − | 13.3396i | −0.138091 | − | 0.745708i | ||||
\(321\) | −11.8016 | −0.658702 | ||||||||
\(322\) | 1.27774i | 0.0712054i | ||||||||
\(323\) | − | 26.7343i | − | 1.48754i | ||||||
\(324\) | 1.91659 | 0.106477 | ||||||||
\(325\) | −8.64000 | − | 22.5285i | −0.479261 | − | 1.24965i | ||||
\(326\) | 2.78085 | 0.154017 | ||||||||
\(327\) | − | 10.4450i | − | 0.577612i | ||||||
\(328\) | 4.87036i | 0.268921i | ||||||||
\(329\) | −23.7306 | −1.30831 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9379 | −0.601200 | −0.300600 | − | 0.953750i | \(-0.597187\pi\) | ||||
−0.300600 | + | 0.953750i | \(0.597187\pi\) | |||||||
\(332\) | 2.93317i | 0.160979i | ||||||||
\(333\) | − | 2.38692i | − | 0.130802i | ||||||
\(334\) | −2.69871 | −0.147667 | ||||||||
\(335\) | −13.4292 | + | 2.48685i | −0.733717 | + | 0.135871i | ||||
\(336\) | 12.8597 | 0.701553 | ||||||||
\(337\) | − | 21.8160i | − | 1.18839i | −0.804320 | − | 0.594196i | \(-0.797470\pi\) | ||
0.804320 | − | 0.594196i | \(-0.202530\pi\) | |||||||
\(338\) | − | 2.97109i | − | 0.161606i | ||||||
\(339\) | −12.8654 | −0.698754 | ||||||||
\(340\) | −16.1822 | + | 2.99665i | −0.877605 | + | 0.162516i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − | 2.01066i | − | 0.108724i | ||||||
\(343\) | 2.01767i | 0.108944i | ||||||||
\(344\) | −0.873769 | −0.0471105 | ||||||||
\(345\) | 0.491165 | + | 2.65234i | 0.0264434 | + | 0.142797i | ||||
\(346\) | −0.0995521 | −0.00535195 | ||||||||
\(347\) | − | 25.3859i | − | 1.36279i | −0.731917 | − | 0.681394i | \(-0.761374\pi\) | ||
0.731917 | − | 0.681394i | \(-0.238626\pi\) | |||||||
\(348\) | 9.48082i | 0.508225i | ||||||||
\(349\) | −32.1887 | −1.72302 | −0.861511 | − | 0.507739i | \(-0.830482\pi\) | ||||
−0.861511 | + | 0.507739i | \(0.830482\pi\) | |||||||
\(350\) | 4.94479 | − | 1.89640i | 0.264310 | − | 0.101367i | ||||
\(351\) | −4.82569 | −0.257576 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10.2135i | − | 0.543611i | −0.962352 | − | 0.271806i | \(-0.912379\pi\) | ||
0.962352 | − | 0.271806i | \(-0.0876208\pi\) | |||||||
\(354\) | 4.18717 | 0.222545 | ||||||||
\(355\) | 1.33998 | + | 7.23604i | 0.0711189 | + | 0.384049i | ||||
\(356\) | 5.83781 | 0.309403 | ||||||||
\(357\) | − | 14.0833i | − | 0.745368i | ||||||
\(358\) | − | 4.64237i | − | 0.245357i | ||||||
\(359\) | −32.2585 | −1.70254 | −0.851270 | − | 0.524727i | \(-0.824167\pi\) | ||||
−0.851270 | + | 0.524727i | \(0.824167\pi\) | |||||||
\(360\) | −2.48707 | + | 0.460559i | −0.131080 | + | 0.0242736i | ||||
\(361\) | 29.4670 | 1.55090 | ||||||||
\(362\) | − | 3.10039i | − | 0.162953i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −33.9193 | −1.77785 | ||||||||
\(365\) | 0.421095 | − | 0.0779790i | 0.0220411 | − | 0.00408161i | ||||
\(366\) | −0.528791 | −0.0276404 | ||||||||
\(367\) | − | 15.2516i | − | 0.796125i | −0.917358 | − | 0.398063i | \(-0.869683\pi\) | ||
0.917358 | − | 0.398063i | \(-0.130317\pi\) | |||||||
\(368\) | − | 4.22997i | − | 0.220503i | ||||||
\(369\) | −4.30563 | −0.224142 | ||||||||
\(370\) | 0.280683 | + | 1.51572i | 0.0145920 | + | 0.0787983i | ||||
\(371\) | −39.4474 | −2.04801 | ||||||||
\(372\) | − | 14.1239i | − | 0.732292i | ||||||
\(373\) | − | 14.4355i | − | 0.747440i | −0.927542 | − | 0.373720i | \(-0.878082\pi\) | ||
0.927542 | − | 0.373720i | \(-0.121918\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.53547 | − | 5.83736i | 0.492410 | − | 0.301440i | ||||
\(376\) | −7.31938 | −0.377468 | ||||||||
\(377\) | − | 23.8713i | − | 1.22944i | ||||||
\(378\) | − | 1.05919i | − | 0.0544790i | ||||||
\(379\) | 20.1384 | 1.03444 | 0.517220 | − | 0.855852i | \(-0.326967\pi\) | ||||
0.517220 | + | 0.855852i | \(0.326967\pi\) | |||||||
\(380\) | −5.43267 | − | 29.3370i | −0.278690 | − | 1.50495i | ||||
\(381\) | −0.185919 | −0.00952494 | ||||||||
\(382\) | − | 3.92743i | − | 0.200945i | ||||||
\(383\) | 9.23909i | 0.472096i | 0.971741 | + | 0.236048i | \(0.0758522\pi\) | ||||
−0.971741 | + | 0.236048i | \(0.924148\pi\) | |||||||
\(384\) | 8.30233 | 0.423676 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.48258 | −0.380853 | ||||||||
\(387\) | − | 0.772454i | − | 0.0392660i | ||||||
\(388\) | − | 26.4049i | − | 1.34051i | ||||||
\(389\) | −20.5859 | −1.04375 | −0.521874 | − | 0.853023i | \(-0.674767\pi\) | ||||
−0.521874 | + | 0.853023i | \(0.674767\pi\) | |||||||
\(390\) | 3.06435 | − | 0.567462i | 0.155170 | − | 0.0287346i | ||||
\(391\) | −4.63247 | −0.234274 | ||||||||
\(392\) | − | 7.29580i | − | 0.368494i | ||||||
\(393\) | 9.27143i | 0.467682i | ||||||||
\(394\) | 0.341797 | 0.0172195 | ||||||||
\(395\) | −1.28659 | − | 6.94773i | −0.0647355 | − | 0.349578i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.1311i | 1.01035i | 0.863017 | + | 0.505176i | \(0.168572\pi\) | ||||
−0.863017 | + | 0.505176i | \(0.831428\pi\) | |||||||
\(398\) | − | 0.905331i | − | 0.0453801i | ||||||
\(399\) | 25.5318 | 1.27819 | ||||||||
\(400\) | −16.3698 | + | 6.27807i | −0.818491 | + | 0.313904i | ||||
\(401\) | 0.648927 | 0.0324059 | 0.0162029 | − | 0.999869i | \(-0.494842\pi\) | ||||
0.0162029 | + | 0.999869i | \(0.494842\pi\) | |||||||
\(402\) | − | 1.76402i | − | 0.0879814i | ||||||
\(403\) | 35.5620i | 1.77147i | ||||||||
\(404\) | −8.92992 | −0.444280 | ||||||||
\(405\) | −0.407156 | − | 2.19869i | −0.0202318 | − | 0.109254i | ||||
\(406\) | 5.23953 | 0.260034 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | − | 4.34381i | − | 0.215051i | ||||||
\(409\) | −13.1101 | −0.648255 | −0.324128 | − | 0.946013i | \(-0.605071\pi\) | ||||
−0.324128 | + | 0.946013i | \(0.605071\pi\) | |||||||
\(410\) | 2.73412 | − | 0.506308i | 0.135028 | − | 0.0250048i | ||||
\(411\) | −0.438101 | −0.0216099 | ||||||||
\(412\) | − | 18.8152i | − | 0.926956i | ||||||
\(413\) | 53.1695i | 2.61630i | ||||||||
\(414\) | −0.348403 | −0.0171231 | ||||||||
\(415\) | 3.36490 | − | 0.623118i | 0.165176 | − | 0.0305876i | ||||
\(416\) | −15.8043 | −0.774870 | ||||||||
\(417\) | 8.60433i | 0.421356i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.0462 | 1.61441 | 0.807206 | − | 0.590270i | \(-0.200979\pi\) | ||||
0.807206 | + | 0.590270i | \(0.200979\pi\) | |||||||
\(420\) | −2.86186 | − | 15.4543i | −0.139644 | − | 0.754095i | ||||
\(421\) | 8.71780 | 0.424879 | 0.212440 | − | 0.977174i | \(-0.431859\pi\) | ||||
0.212440 | + | 0.977174i | \(0.431859\pi\) | |||||||
\(422\) | − | 0.873091i | − | 0.0425014i | ||||||
\(423\) | − | 6.47068i | − | 0.314615i | ||||||
\(424\) | −12.1670 | −0.590883 | ||||||||
\(425\) | 6.87545 | + | 17.9275i | 0.333508 | + | 0.869610i | ||||
\(426\) | −0.950505 | −0.0460521 | ||||||||
\(427\) | − | 6.71470i | − | 0.324947i | ||||||
\(428\) | − | 22.6188i | − | 1.09332i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.0908344 | + | 0.490515i | 0.00438042 | + | 0.0236547i | ||||
\(431\) | −16.3875 | −0.789358 | −0.394679 | − | 0.918819i | \(-0.629144\pi\) | ||||
−0.394679 | + | 0.918819i | \(0.629144\pi\) | |||||||
\(432\) | 3.50648i | 0.168706i | ||||||||
\(433\) | − | 34.9874i | − | 1.68139i | −0.541510 | − | 0.840695i | \(-0.682147\pi\) | ||
0.541510 | − | 0.840695i | \(-0.317853\pi\) | |||||||
\(434\) | −7.80553 | −0.374677 | ||||||||
\(435\) | 10.8763 | − | 2.01409i | 0.521478 | − | 0.0965682i | ||||
\(436\) | 20.0188 | 0.958728 | ||||||||
\(437\) | − | 8.39826i | − | 0.401743i | ||||||
\(438\) | 0.0553137i | 0.00264299i | ||||||||
\(439\) | −18.5657 | −0.886091 | −0.443046 | − | 0.896499i | \(-0.646102\pi\) | ||||
−0.443046 | + | 0.896499i | \(0.646102\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.44984 | 0.307135 | ||||||||
\(442\) | 5.35207i | 0.254572i | ||||||||
\(443\) | 8.85169i | 0.420556i | 0.977642 | + | 0.210278i | \(0.0674370\pi\) | ||||
−0.977642 | + | 0.210278i | \(0.932563\pi\) | |||||||
\(444\) | 4.57474 | 0.217108 | ||||||||
\(445\) | −1.24017 | − | 6.69706i | −0.0587899 | − | 0.317471i | ||||
\(446\) | −0.0132770 | −0.000628682 | ||||||||
\(447\) | − | 15.3241i | − | 0.724806i | ||||||
\(448\) | 22.2505i | 1.05124i | ||||||||
\(449\) | −3.18109 | −0.150125 | −0.0750624 | − | 0.997179i | \(-0.523916\pi\) | ||||
−0.0750624 | + | 0.997179i | \(0.523916\pi\) | |||||||
\(450\) | 0.517096 | + | 1.34831i | 0.0243761 | + | 0.0635598i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 24.6577i | − | 1.15980i | ||||||
\(453\) | 1.05059i | 0.0493610i | ||||||||
\(454\) | −1.77500 | −0.0833051 | ||||||||
\(455\) | 7.20575 | + | 38.9118i | 0.337811 | + | 1.82421i | ||||
\(456\) | 7.87494 | 0.368778 | ||||||||
\(457\) | − | 3.52754i | − | 0.165011i | −0.996591 | − | 0.0825056i | \(-0.973708\pi\) | ||
0.996591 | − | 0.0825056i | \(-0.0262922\pi\) | |||||||
\(458\) | − | 3.38965i | − | 0.158388i | ||||||
\(459\) | 3.84013 | 0.179242 | ||||||||
\(460\) | −5.08344 | + | 0.941360i | −0.237017 | + | 0.0438912i | ||||
\(461\) | −18.1321 | −0.844496 | −0.422248 | − | 0.906480i | \(-0.638759\pi\) | ||||
−0.422248 | + | 0.906480i | \(0.638759\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.0104i | 0.837013i | 0.908214 | + | 0.418506i | \(0.137446\pi\) | ||||
−0.908214 | + | 0.418506i | \(0.862554\pi\) | |||||||
\(464\) | −17.3456 | −0.805248 | ||||||||
\(465\) | −16.2028 | + | 3.00047i | −0.751388 | + | 0.139143i | ||||
\(466\) | 3.07839 | 0.142604 | ||||||||
\(467\) | − | 26.7217i | − | 1.23653i | −0.785969 | − | 0.618266i | \(-0.787835\pi\) | ||
0.785969 | − | 0.618266i | \(-0.212165\pi\) | |||||||
\(468\) | − | 9.24885i | − | 0.427528i | ||||||
\(469\) | 22.3999 | 1.03433 | ||||||||
\(470\) | 0.760900 | + | 4.10894i | 0.0350977 | + | 0.189531i | ||||
\(471\) | −4.93869 | −0.227563 | ||||||||
\(472\) | 16.3994i | 0.754844i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.912632 | 0.0419186 | ||||||||
\(475\) | −32.5009 | + | 12.4646i | −1.49124 | + | 0.571914i | ||||
\(476\) | 26.9919 | 1.23717 | ||||||||
\(477\) | − | 10.7562i | − | 0.492494i | ||||||
\(478\) | − | 1.32660i | − | 0.0606772i | ||||||
\(479\) | −22.7687 | −1.04033 | −0.520163 | − | 0.854067i | \(-0.674129\pi\) | ||||
−0.520163 | + | 0.854067i | \(0.674129\pi\) | |||||||
\(480\) | −1.33345 | − | 7.20078i | −0.0608635 | − | 0.328669i | ||||
\(481\) | −11.5185 | −0.525200 | ||||||||
\(482\) | − | 5.45037i | − | 0.248257i | ||||||
\(483\) | − | 4.42410i | − | 0.201303i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −30.2914 | + | 5.60941i | −1.37546 | + | 0.254710i | ||||
\(486\) | 0.288813 | 0.0131008 | ||||||||
\(487\) | 13.5507i | 0.614039i | 0.951703 | + | 0.307020i | \(0.0993318\pi\) | ||||
−0.951703 | + | 0.307020i | \(0.900668\pi\) | |||||||
\(488\) | − | 2.07106i | − | 0.0937523i | ||||||
\(489\) | −9.62856 | −0.435418 | ||||||||
\(490\) | −4.09570 | + | 0.758449i | −0.185025 | + | 0.0342633i | ||||
\(491\) | 19.0361 | 0.859088 | 0.429544 | − | 0.903046i | \(-0.358674\pi\) | ||||
0.429544 | + | 0.903046i | \(0.358674\pi\) | |||||||
\(492\) | − | 8.25212i | − | 0.372034i | ||||||
\(493\) | 18.9961i | 0.855540i | ||||||||
\(494\) | −9.70284 | −0.436551 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 25.8404 | 1.16027 | ||||||||
\(497\) | − | 12.0697i | − | 0.541400i | ||||||
\(498\) | 0.442003i | 0.0198066i | ||||||||
\(499\) | 23.1094 | 1.03452 | 0.517258 | − | 0.855829i | \(-0.326953\pi\) | ||||
0.517258 | + | 0.855829i | \(0.326953\pi\) | |||||||
\(500\) | 11.1878 | + | 18.2756i | 0.500334 | + | 0.817308i | ||||
\(501\) | 9.34416 | 0.417466 | ||||||||
\(502\) | − | 5.62915i | − | 0.251241i | ||||||
\(503\) | − | 26.6808i | − | 1.18964i | −0.803859 | − | 0.594820i | \(-0.797224\pi\) | ||
0.803859 | − | 0.594820i | \(-0.202776\pi\) | |||||||
\(504\) | 4.14842 | 0.184785 | ||||||||
\(505\) | 1.89706 | + | 10.2443i | 0.0844180 | + | 0.455866i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.2873i | 0.456873i | ||||||||
\(508\) | − | 0.356331i | − | 0.0158096i | ||||||
\(509\) | −8.67668 | −0.384587 | −0.192294 | − | 0.981337i | \(-0.561593\pi\) | ||||
−0.192294 | + | 0.981337i | \(0.561593\pi\) | |||||||
\(510\) | −2.43852 | + | 0.451569i | −0.107979 | + | 0.0199958i | ||||
\(511\) | −0.702385 | −0.0310717 | ||||||||
\(512\) | 19.4166i | 0.858102i | ||||||||
\(513\) | 6.96183i | 0.307372i | ||||||||
\(514\) | −3.80696 | −0.167918 | ||||||||
\(515\) | −21.5845 | + | 3.99706i | −0.951128 | + | 0.176132i | ||||
\(516\) | 1.48047 | 0.0651743 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 2.52821i | − | 0.111083i | ||||||
\(519\) | 0.344694 | 0.0151304 | ||||||||
\(520\) | 2.22252 | + | 12.0018i | 0.0974637 | + | 0.526314i | ||||
\(521\) | −6.51721 | −0.285524 | −0.142762 | − | 0.989757i | \(-0.545598\pi\) | ||||
−0.142762 | + | 0.989757i | \(0.545598\pi\) | |||||||
\(522\) | 1.42868i | 0.0625315i | ||||||||
\(523\) | 36.8608i | 1.61181i | 0.592045 | + | 0.805905i | \(0.298321\pi\) | ||||
−0.592045 | + | 0.805905i | \(0.701679\pi\) | |||||||
\(524\) | −17.7695 | −0.776264 | ||||||||
\(525\) | −17.1211 | + | 6.56619i | −0.747225 | + | 0.286572i | ||||
\(526\) | −8.61805 | −0.375765 | ||||||||
\(527\) | − | 28.2992i | − | 1.23273i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.5448 | 0.936729 | ||||||||
\(530\) | 1.26485 | + | 6.83031i | 0.0549415 | + | 0.296690i | ||||
\(531\) | −14.4979 | −0.629153 | ||||||||
\(532\) | 48.9339i | 2.12156i | ||||||||
\(533\) | 20.7776i | 0.899979i | ||||||||
\(534\) | 0.879706 | 0.0380686 | ||||||||
\(535\) | −25.9480 | + | 4.80510i | −1.12183 | + | 0.207743i | ||||
\(536\) | 6.90895 | 0.298421 | ||||||||
\(537\) | 16.0740i | 0.693644i | ||||||||
\(538\) | − | 0.0727396i | − | 0.00313603i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.21397 | − | 0.780351i | 0.181341 | − | 0.0335810i | ||||
\(541\) | 20.3681 | 0.875691 | 0.437846 | − | 0.899050i | \(-0.355742\pi\) | ||||
0.437846 | + | 0.899050i | \(0.355742\pi\) | |||||||
\(542\) | − | 3.49167i | − | 0.149980i | ||||||
\(543\) | 10.7349i | 0.460680i | ||||||||
\(544\) | 12.5766 | 0.539217 | ||||||||
\(545\) | −4.25276 | − | 22.9654i | −0.182168 | − | 0.983728i | ||||
\(546\) | −5.11133 | −0.218745 | ||||||||
\(547\) | − | 24.0697i | − | 1.02915i | −0.857447 | − | 0.514573i | \(-0.827950\pi\) | ||
0.857447 | − | 0.514573i | \(-0.172050\pi\) | |||||||
\(548\) | − | 0.839659i | − | 0.0358684i | ||||||
\(549\) | 1.83091 | 0.0781415 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.4382 | −1.46712 | ||||||||
\(552\) | − | 1.36455i | − | 0.0580792i | ||||||
\(553\) | 11.5888i | 0.492805i | ||||||||
\(554\) | 4.75546 | 0.202040 | ||||||||
\(555\) | −0.971850 | − | 5.24809i | −0.0412527 | − | 0.222769i | ||||
\(556\) | −16.4909 | −0.699372 | ||||||||
\(557\) | − | 38.0312i | − | 1.61144i | −0.592300 | − | 0.805718i | \(-0.701780\pi\) | ||
0.592300 | − | 0.805718i | \(-0.298220\pi\) | |||||||
\(558\) | − | 2.12835i | − | 0.0901004i | ||||||
\(559\) | −3.72762 | −0.157662 | ||||||||
\(560\) | 28.2744 | − | 5.23590i | 1.19481 | − | 0.221257i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.63954i | 0.153525i | ||||||||
\(563\) | 1.45960i | 0.0615147i | 0.999527 | + | 0.0307574i | \(0.00979192\pi\) | ||||
−0.999527 | + | 0.0307574i | \(0.990208\pi\) | |||||||
\(564\) | 12.4016 | 0.522203 | ||||||||
\(565\) | −28.2870 | + | 5.23824i | −1.19004 | + | 0.220374i | ||||
\(566\) | −5.15468 | −0.216668 | ||||||||
\(567\) | 3.66740i | 0.154016i | ||||||||
\(568\) | − | 3.72273i | − | 0.156202i | ||||||
\(569\) | 1.06880 | 0.0448064 | 0.0224032 | − | 0.999749i | \(-0.492868\pi\) | ||||
0.0224032 | + | 0.999749i | \(0.492868\pi\) | |||||||
\(570\) | −0.818655 | − | 4.42082i | −0.0342897 | − | 0.185168i | ||||
\(571\) | −4.25241 | −0.177958 | −0.0889789 | − | 0.996034i | \(-0.528360\pi\) | ||||
−0.0889789 | + | 0.996034i | \(0.528360\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.5985i | 0.568086i | ||||||||
\(574\) | −4.56050 | −0.190351 | ||||||||
\(575\) | 2.15984 | + | 5.63169i | 0.0900714 | + | 0.234858i | ||||
\(576\) | −6.06709 | −0.252795 | ||||||||
\(577\) | − | 3.03655i | − | 0.126413i | −0.998000 | − | 0.0632065i | \(-0.979867\pi\) | ||
0.998000 | − | 0.0632065i | \(-0.0201327\pi\) | |||||||
\(578\) | 0.650801i | 0.0270698i | ||||||||
\(579\) | 25.9081 | 1.07670 | ||||||||
\(580\) | 3.86018 | + | 20.8454i | 0.160285 | + | 0.865556i | ||||
\(581\) | −5.61264 | −0.232852 | ||||||||
\(582\) | − | 3.97899i | − | 0.164934i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.216641 | −0.00896467 | ||||||||
\(585\) | −10.6102 | + | 1.96481i | −0.438677 | + | 0.0812349i | ||||
\(586\) | −2.86119 | −0.118195 | ||||||||
\(587\) | 2.54270i | 0.104949i | 0.998622 | + | 0.0524743i | \(0.0167108\pi\) | ||||
−0.998622 | + | 0.0524743i | \(0.983289\pi\) | |||||||
\(588\) | 12.3617i | 0.509787i | ||||||||
\(589\) | 51.3039 | 2.11394 | ||||||||
\(590\) | 9.20627 | − | 1.70483i | 0.379016 | − | 0.0701868i | ||||
\(591\) | −1.18346 | −0.0486808 | ||||||||
\(592\) | 8.36969i | 0.343992i | ||||||||
\(593\) | 40.7468i | 1.67327i | 0.547760 | + | 0.836636i | \(0.315481\pi\) | ||||
−0.547760 | + | 0.836636i | \(0.684519\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.73411 | − | 30.9648i | −0.235076 | − | 1.26943i | ||||
\(596\) | 29.3700 | 1.20304 | ||||||||
\(597\) | 3.13466i | 0.128293i | ||||||||
\(598\) | 1.68129i | 0.0687529i | ||||||||
\(599\) | −6.76111 | −0.276251 | −0.138126 | − | 0.990415i | \(-0.544108\pi\) | ||||
−0.138126 | + | 0.990415i | \(0.544108\pi\) | |||||||
\(600\) | −5.28076 | + | 2.02525i | −0.215586 | + | 0.0826805i | ||||
\(601\) | −15.0937 | −0.615685 | −0.307843 | − | 0.951437i | \(-0.599607\pi\) | ||||
−0.307843 | + | 0.951437i | \(0.599607\pi\) | |||||||
\(602\) | − | 0.818177i | − | 0.0333464i | ||||||
\(603\) | 6.10784i | 0.248730i | ||||||||
\(604\) | −2.01355 | −0.0819301 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.34566 | −0.0546637 | ||||||||
\(607\) | 7.86639i | 0.319287i | 0.987175 | + | 0.159643i | \(0.0510344\pi\) | ||||
−0.987175 | + | 0.159643i | \(0.948966\pi\) | |||||||
\(608\) | 22.8002i | 0.924672i | ||||||||
\(609\) | −18.1416 | −0.735135 | ||||||||
\(610\) | −1.16265 | + | 0.215301i | −0.0470742 | + | 0.00871727i | ||||
\(611\) | −31.2255 | −1.26325 | ||||||||
\(612\) | 7.35995i | 0.297508i | ||||||||
\(613\) | − | 27.1001i | − | 1.09456i | −0.836948 | − | 0.547282i | \(-0.815662\pi\) | ||
0.836948 | − | 0.547282i | \(-0.184338\pi\) | |||||||
\(614\) | 6.71505 | 0.270997 | ||||||||
\(615\) | −9.46674 | + | 1.75307i | −0.381736 | + | 0.0706905i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3.61737i | − | 0.145630i | −0.997345 | − | 0.0728149i | \(-0.976802\pi\) | ||
0.997345 | − | 0.0728149i | \(-0.0231982\pi\) | |||||||
\(618\) | − | 2.83528i | − | 0.114052i | ||||||
\(619\) | 16.5624 | 0.665698 | 0.332849 | − | 0.942980i | \(-0.391990\pi\) | ||||
0.332849 | + | 0.942980i | \(0.391990\pi\) | |||||||
\(620\) | −5.75065 | − | 31.0541i | −0.230952 | − | 1.24716i | ||||
\(621\) | 1.20633 | 0.0484083 | ||||||||
\(622\) | 8.62475i | 0.345821i | ||||||||
\(623\) | 11.1707i | 0.447544i | ||||||||
\(624\) | 16.9212 | 0.677389 | ||||||||
\(625\) | 18.5888 | − | 16.7170i | 0.743552 | − | 0.668678i | ||||
\(626\) | −7.40418 | −0.295931 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 9.46543i | − | 0.377712i | ||||||
\(629\) | 9.16609 | 0.365476 | ||||||||
\(630\) | −0.431257 | − | 2.32883i | −0.0171817 | − | 0.0927829i | ||||
\(631\) | 3.98943 | 0.158817 | 0.0794083 | − | 0.996842i | \(-0.474697\pi\) | ||||
0.0794083 | + | 0.996842i | \(0.474697\pi\) | |||||||
\(632\) | 3.57440i | 0.142182i | ||||||||
\(633\) | 3.02303i | 0.120155i | ||||||||
\(634\) | 0.323672 | 0.0128547 | ||||||||
\(635\) | −0.408779 | + | 0.0756983i | −0.0162219 | + | 0.00300400i | ||||
\(636\) | 20.6153 | 0.817448 | ||||||||
\(637\) | − | 31.1249i | − | 1.23321i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.29108 | 0.130193 | ||||||||
\(640\) | 18.2542 | − | 3.38035i | 0.721561 | − | 0.133620i | ||||
\(641\) | −34.2580 | −1.35311 | −0.676554 | − | 0.736393i | \(-0.736527\pi\) | ||||
−0.676554 | + | 0.736393i | \(0.736527\pi\) | |||||||
\(642\) | − | 3.40846i | − | 0.134521i | ||||||
\(643\) | − | 41.5718i | − | 1.63943i | −0.572771 | − | 0.819716i | \(-0.694131\pi\) | ||
0.572771 | − | 0.819716i | \(-0.305869\pi\) | |||||||
\(644\) | 8.47917 | 0.334126 | ||||||||
\(645\) | −0.314510 | − | 1.69838i | −0.0123838 | − | 0.0668738i | ||||
\(646\) | 7.72122 | 0.303787 | ||||||||
\(647\) | 9.86886i | 0.387985i | 0.981003 | + | 0.193993i | \(0.0621438\pi\) | ||||
−0.981003 | + | 0.193993i | \(0.937856\pi\) | |||||||
\(648\) | 1.13116i | 0.0444362i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 6.50651 | − | 2.49534i | 0.255206 | − | 0.0978754i | ||||
\(651\) | 27.0262 | 1.05924 | ||||||||
\(652\) | − | 18.4540i | − | 0.722713i | ||||||
\(653\) | − | 20.7327i | − | 0.811335i | −0.914021 | − | 0.405667i | \(-0.867039\pi\) | ||
0.914021 | − | 0.405667i | \(-0.132961\pi\) | |||||||
\(654\) | 3.01666 | 0.117961 | ||||||||
\(655\) | 3.77492 | + | 20.3850i | 0.147498 | + | 0.796507i | ||||
\(656\) | 15.0976 | 0.589463 | ||||||||
\(657\) | − | 0.191521i | − | 0.00747195i | ||||||
\(658\) | − | 6.85370i | − | 0.267185i | ||||||
\(659\) | −26.4580 | −1.03066 | −0.515329 | − | 0.856992i | \(-0.672330\pi\) | ||||
−0.515329 | + | 0.856992i | \(0.672330\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.75931 | 0.224011 | 0.112006 | − | 0.993708i | \(-0.464273\pi\) | ||||
0.112006 | + | 0.993708i | \(0.464273\pi\) | |||||||
\(662\) | − | 3.15900i | − | 0.122778i | ||||||
\(663\) | − | 18.5313i | − | 0.719696i | ||||||
\(664\) | −1.73114 | −0.0671814 | ||||||||
\(665\) | 56.1365 | − | 10.3954i | 2.17688 | − | 0.403118i | ||||
\(666\) | 0.689373 | 0.0267127 | ||||||||
\(667\) | 5.96738i | 0.231058i | ||||||||
\(668\) | 17.9089i | 0.692916i | ||||||||
\(669\) | 0.0459708 | 0.00177733 | ||||||||
\(670\) | −0.718233 | − | 3.87853i | −0.0277478 | − | 0.149841i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 12.0109i | 0.463330i | ||||||||
\(673\) | − | 15.8591i | − | 0.611323i | −0.952140 | − | 0.305662i | \(-0.901122\pi\) | ||
0.952140 | − | 0.305662i | \(-0.0988776\pi\) | |||||||
\(674\) | 6.30074 | 0.242695 | ||||||||
\(675\) | −1.79042 | − | 4.66845i | −0.0689133 | − | 0.179689i | ||||
\(676\) | −19.7164 | −0.758324 | ||||||||
\(677\) | − | 14.5303i | − | 0.558446i | −0.960226 | − | 0.279223i | \(-0.909923\pi\) | ||
0.960226 | − | 0.279223i | \(-0.0900768\pi\) | |||||||
\(678\) | − | 3.71570i | − | 0.142701i | ||||||
\(679\) | 50.5259 | 1.93901 | ||||||||
\(680\) | −1.76861 | − | 9.55067i | −0.0678231 | − | 0.366252i | ||||
\(681\) | 6.14586 | 0.235510 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 48.0516i | 1.83864i | 0.393509 | + | 0.919321i | \(0.371261\pi\) | ||||
−0.393509 | + | 0.919321i | \(0.628739\pi\) | |||||||
\(684\) | −13.3429 | −0.510180 | ||||||||
\(685\) | −0.963247 | + | 0.178376i | −0.0368038 | + | 0.00681538i | ||||
\(686\) | −0.582728 | −0.0222486 | ||||||||
\(687\) | 11.7365i | 0.447776i | ||||||||
\(688\) | 2.70859i | 0.103264i | ||||||||
\(689\) | −51.9062 | −1.97747 | ||||||||
\(690\) | −0.766030 | + | 0.141855i | −0.0291623 | + | 0.00540032i | ||||
\(691\) | −28.1864 | −1.07226 | −0.536131 | − | 0.844135i | \(-0.680115\pi\) | ||||
−0.536131 | + | 0.844135i | \(0.680115\pi\) | |||||||
\(692\) | 0.660636i | 0.0251136i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.33178 | 0.278310 | ||||||||
\(695\) | 3.50331 | + | 18.9182i | 0.132888 | + | 0.717609i | ||||
\(696\) | −5.59554 | −0.212098 | ||||||||
\(697\) | − | 16.5342i | − | 0.626278i | ||||||
\(698\) | − | 9.29651i | − | 0.351878i | ||||||
\(699\) | −10.6588 | −0.403152 | ||||||||
\(700\) | −12.5847 | − | 32.8140i | −0.475656 | − | 1.24025i | ||||
\(701\) | 29.7610 | 1.12406 | 0.562029 | − | 0.827117i | \(-0.310021\pi\) | ||||
0.562029 | + | 0.827117i | \(0.310021\pi\) | |||||||
\(702\) | − | 1.39372i | − | 0.0526026i | ||||||
\(703\) | 16.6173i | 0.626734i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.63458 | − | 14.2270i | −0.0992240 | − | 0.535820i | ||||
\(706\) | 2.94980 | 0.111017 | ||||||||
\(707\) | − | 17.0875i | − | 0.642640i | ||||||
\(708\) | − | 27.7864i | − | 1.04428i | ||||||
\(709\) | 2.53577 | 0.0952328 | 0.0476164 | − | 0.998866i | \(-0.484838\pi\) | ||||
0.0476164 | + | 0.998866i | \(0.484838\pi\) | |||||||
\(710\) | −2.08986 | + | 0.387004i | −0.0784311 | + | 0.0145240i | ||||
\(711\) | −3.15994 | −0.118507 | ||||||||
\(712\) | 3.44545i | 0.129124i | ||||||||
\(713\) | − | 8.88983i | − | 0.332927i | ||||||
\(714\) | 4.06744 | 0.152220 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −30.8072 | −1.15132 | ||||||||
\(717\) | 4.59328i | 0.171539i | ||||||||
\(718\) | − | 9.31668i | − | 0.347695i | ||||||
\(719\) | 37.9483 | 1.41523 | 0.707617 | − | 0.706597i | \(-0.249770\pi\) | ||||
0.707617 | + | 0.706597i | \(0.249770\pi\) | |||||||
\(720\) | 1.42769 | + | 7.70965i | 0.0532067 | + | 0.287322i | ||||
\(721\) | 36.0029 | 1.34082 | ||||||||
\(722\) | 8.51045i | 0.316726i | ||||||||
\(723\) | 18.8716i | 0.701843i | ||||||||
\(724\) | −20.5744 | −0.764643 | ||||||||
\(725\) | 23.0935 | − | 8.85670i | 0.857671 | − | 0.328930i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 10.1521i | − | 0.376520i | −0.982119 | − | 0.188260i | \(-0.939715\pi\) | ||
0.982119 | − | 0.188260i | \(-0.0602848\pi\) | |||||||
\(728\) | − | 20.0190i | − | 0.741953i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0.0225213 | + | 0.121618i | 0.000833552 | + | 0.00450127i | ||||
\(731\) | 2.96633 | 0.109714 | ||||||||
\(732\) | 3.50911i | 0.129700i | ||||||||
\(733\) | 13.8705i | 0.512320i | 0.966634 | + | 0.256160i | \(0.0824574\pi\) | ||||
−0.966634 | + | 0.256160i | \(0.917543\pi\) | |||||||
\(734\) | 4.40485 | 0.162586 | ||||||||
\(735\) | 14.1812 | − | 2.62609i | 0.523080 | − | 0.0968649i | ||||
\(736\) | 3.95077 | 0.145627 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 1.24352i | − | 0.0457747i | ||||||
\(739\) | −3.89107 | −0.143135 | −0.0715677 | − | 0.997436i | \(-0.522800\pi\) | ||||
−0.0715677 | + | 0.997436i | \(0.522800\pi\) | |||||||
\(740\) | 10.0584 | − | 1.86264i | 0.369755 | − | 0.0684718i | ||||
\(741\) | 33.5956 | 1.23416 | ||||||||
\(742\) | − | 11.3929i | − | 0.418248i | ||||||
\(743\) | − | 42.0524i | − | 1.54275i | −0.636379 | − | 0.771376i | \(-0.719569\pi\) | ||
0.636379 | − | 0.771376i | \(-0.280431\pi\) | |||||||
\(744\) | 8.33588 | 0.305608 | ||||||||
\(745\) | −6.23932 | − | 33.6929i | −0.228591 | − | 1.23441i | ||||
\(746\) | 4.16915 | 0.152643 | ||||||||
\(747\) | − | 1.53041i | − | 0.0559949i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 43.2812 | 1.58146 | ||||||||
\(750\) | 1.68590 | + | 2.75397i | 0.0615605 | + | 0.100561i | ||||
\(751\) | −5.01553 | −0.183019 | −0.0915096 | − | 0.995804i | \(-0.529169\pi\) | ||||
−0.0915096 | + | 0.995804i | \(0.529169\pi\) | |||||||
\(752\) | 22.6893i | 0.827394i | ||||||||
\(753\) | 19.4907i | 0.710279i | ||||||||
\(754\) | 6.89435 | 0.251077 | ||||||||
\(755\) | 0.427755 | + | 2.30992i | 0.0155676 | + | 0.0840665i | ||||
\(756\) | −7.02890 | −0.255638 | ||||||||
\(757\) | 35.4560i | 1.28867i | 0.764743 | + | 0.644335i | \(0.222866\pi\) | ||||
−0.764743 | + | 0.644335i | \(0.777134\pi\) | |||||||
\(758\) | 5.81623i | 0.211255i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 17.3145 | − | 3.20633i | 0.628064 | − | 0.116306i | ||||
\(761\) | 14.3160 | 0.518954 | 0.259477 | − | 0.965749i | \(-0.416450\pi\) | ||||
0.259477 | + | 0.965749i | \(0.416450\pi\) | |||||||
\(762\) | − | 0.0536959i | − | 0.00194520i | ||||||
\(763\) | 38.3061i | 1.38678i | ||||||||
\(764\) | −26.0627 | −0.942917 | ||||||||
\(765\) | 8.44325 | − | 1.56354i | 0.305266 | − | 0.0565298i | ||||
\(766\) | −2.66837 | −0.0964121 | ||||||||
\(767\) | 69.9621i | 2.52619i | ||||||||
\(768\) | − | 9.73636i | − | 0.351331i | ||||||
\(769\) | 29.6869 | 1.07054 | 0.535269 | − | 0.844682i | \(-0.320210\pi\) | ||||
0.535269 | + | 0.844682i | \(0.320210\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.1814 | 0.474717 | ||||||||
\(772\) | 49.6550i | 1.78712i | ||||||||
\(773\) | − | 48.2367i | − | 1.73495i | −0.497477 | − | 0.867477i | \(-0.665740\pi\) | ||
0.497477 | − | 0.867477i | \(-0.334260\pi\) | |||||||
\(774\) | 0.223095 | 0.00801897 | ||||||||
\(775\) | −34.4033 | + | 13.1942i | −1.23580 | + | 0.473948i | ||||
\(776\) | 15.5840 | 0.559434 | ||||||||
\(777\) | 8.75380i | 0.314041i | ||||||||
\(778\) | − | 5.94548i | − | 0.213156i | ||||||
\(779\) | 29.9751 | 1.07397 | ||||||||
\(780\) | −3.76573 | − | 20.3353i | −0.134835 | − | 0.728121i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 1.33792i | − | 0.0478438i | ||||||
\(783\) | − | 4.94672i | − | 0.176781i | ||||||
\(784\) | −22.6162 | −0.807723 | ||||||||
\(785\) | −10.8586 | + | 2.01082i | −0.387561 | + | 0.0717692i | ||||
\(786\) | −2.67771 | −0.0955106 | ||||||||
\(787\) | − | 51.4339i | − | 1.83342i | −0.399551 | − | 0.916711i | \(-0.630834\pi\) | ||
0.399551 | − | 0.916711i | \(-0.369166\pi\) | |||||||
\(788\) | − | 2.26819i | − | 0.0808011i | ||||||
\(789\) | 29.8396 | 1.06232 | ||||||||
\(790\) | 2.00659 | − | 0.371584i | 0.0713914 | − | 0.0132204i | ||||
\(791\) | 47.1827 | 1.67762 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 8.83542i | − | 0.313755i | ||||||
\(794\) | −5.81412 | −0.206335 | ||||||||
\(795\) | −4.37947 | − | 23.6496i | −0.155324 | − | 0.838765i | ||||
\(796\) | −6.00785 | −0.212943 | ||||||||
\(797\) | 37.8789i | 1.34174i | 0.741575 | + | 0.670869i | \(0.234079\pi\) | ||||
−0.741575 | + | 0.670869i | \(0.765921\pi\) | |||||||
\(798\) | 7.37391i | 0.261034i | ||||||||
\(799\) | 24.8483 | 0.879069 | ||||||||
\(800\) | −5.86369 | − | 15.2893i | −0.207313 | − | 0.540560i | ||||
\(801\) | −3.04594 | −0.107623 | ||||||||
\(802\) | 0.187419i | 0.00661798i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −11.7062 | −0.412846 | ||||||||
\(805\) | −1.80130 | − | 9.72720i | −0.0634875 | − | 0.342839i | ||||
\(806\) | −10.2708 | −0.361772 | ||||||||
\(807\) | 0.251857i | 0.00886580i | ||||||||
\(808\) | − | 5.27040i | − | 0.185412i | ||||||
\(809\) | 33.8214 | 1.18910 | 0.594549 | − | 0.804060i | \(-0.297331\pi\) | ||||
0.594549 | + | 0.804060i | \(0.297331\pi\) | |||||||
\(810\) | 0.635009 | − | 0.117592i | 0.0223119 | − | 0.00413176i | ||||
\(811\) | −8.81396 | −0.309500 | −0.154750 | − | 0.987954i | \(-0.549457\pi\) | ||||
−0.154750 | + | 0.987954i | \(0.549457\pi\) | |||||||
\(812\) | − | 34.7700i | − | 1.22019i | ||||||
\(813\) | 12.0897i | 0.424006i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.1702 | + | 3.92033i | −0.741559 | + | 0.137323i | ||||
\(816\) | −13.4654 | −0.471382 | ||||||||
\(817\) | 5.37769i | 0.188141i | ||||||||
\(818\) | − | 3.78638i | − | 0.132388i | ||||||
\(819\) | 17.6977 | 0.618409 | ||||||||
\(820\) | −3.35990 | − | 18.1438i | −0.117333 | − | 0.633610i | ||||
\(821\) | 38.7028 | 1.35074 | 0.675369 | − | 0.737480i | \(-0.263984\pi\) | ||||
0.675369 | + | 0.737480i | \(0.263984\pi\) | |||||||
\(822\) | − | 0.126529i | − | 0.00441321i | ||||||
\(823\) | − | 6.85406i | − | 0.238918i | −0.992839 | − | 0.119459i | \(-0.961884\pi\) | ||
0.992839 | − | 0.119459i | \(-0.0381159\pi\) | |||||||
\(824\) | 11.1046 | 0.386848 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.3560 | −0.534304 | ||||||||
\(827\) | − | 38.0969i | − | 1.32476i | −0.749169 | − | 0.662379i | \(-0.769547\pi\) | ||
0.749169 | − | 0.662379i | \(-0.230453\pi\) | |||||||
\(828\) | 2.31204i | 0.0803488i | ||||||||
\(829\) | −7.42028 | −0.257717 | −0.128859 | − | 0.991663i | \(-0.541131\pi\) | ||||
−0.128859 | + | 0.991663i | \(0.541131\pi\) | |||||||
\(830\) | 0.179964 | + | 0.971826i | 0.00624665 | + | 0.0337326i | ||||
\(831\) | −16.4655 | −0.571183 | ||||||||
\(832\) | 29.2779i | 1.01503i | ||||||||
\(833\) | 24.7682i | 0.858169i | ||||||||
\(834\) | −2.48504 | −0.0860499 | ||||||||
\(835\) | 20.5449 | − | 3.80453i | 0.710985 | − | 0.131661i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.36932i | 0.254721i | ||||||||
\(838\) | 9.54416i | 0.329698i | ||||||||
\(839\) | −55.1922 | −1.90545 | −0.952723 | − | 0.303840i | \(-0.901731\pi\) | ||||
−0.952723 | + | 0.303840i | \(0.901731\pi\) | |||||||
\(840\) | 9.12108 | − | 1.68906i | 0.314707 | − | 0.0582780i | ||||
\(841\) | −4.52995 | −0.156205 | ||||||||
\(842\) | 2.51781i | 0.0867695i | ||||||||
\(843\) | − | 12.6017i | − | 0.434026i | ||||||
\(844\) | −5.79391 | −0.199435 | ||||||||
\(845\) | 4.18852 | + | 22.6185i | 0.144090 | + | 0.778098i | ||||
\(846\) | 1.86882 | 0.0642512 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 37.7165i | 1.29519i | ||||||||
\(849\) | 17.8478 | 0.612536 | ||||||||
\(850\) | −5.17768 | + | 1.98572i | −0.177593 | + | 0.0681096i | ||||
\(851\) | 2.87941 | 0.0987050 | ||||||||
\(852\) | 6.30763i | 0.216096i | ||||||||
\(853\) | − | 3.32152i | − | 0.113727i | −0.998382 | − | 0.0568634i | \(-0.981890\pi\) | ||
0.998382 | − | 0.0568634i | \(-0.0181099\pi\) | |||||||
\(854\) | 1.93929 | 0.0663611 | ||||||||
\(855\) | 2.83455 | + | 15.3069i | 0.0969396 | + | 0.523484i | ||||
\(856\) | 13.3495 | 0.456277 | ||||||||
\(857\) | 34.6080i | 1.18219i | 0.806603 | + | 0.591094i | \(0.201304\pi\) | ||||
−0.806603 | + | 0.591094i | \(0.798696\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.0606 | −1.33273 | −0.666366 | − | 0.745625i | \(-0.732151\pi\) | ||||
−0.666366 | + | 0.745625i | \(0.732151\pi\) | |||||||
\(860\) | 3.25510 | − | 0.602785i | 0.110998 | − | 0.0205548i | ||||
\(861\) | 15.7905 | 0.538138 | ||||||||
\(862\) | − | 4.73292i | − | 0.161204i | ||||||
\(863\) | − | 0.520603i | − | 0.0177215i | −0.999961 | − | 0.00886077i | \(-0.997179\pi\) | ||
0.999961 | − | 0.00886077i | \(-0.00282051\pi\) | |||||||
\(864\) | −3.27504 | −0.111419 | ||||||||
\(865\) | 0.757874 | − | 0.140344i | 0.0257685 | − | 0.00477185i | ||||
\(866\) | 10.1048 | 0.343376 | ||||||||
\(867\) | − | 2.25337i | − | 0.0765283i | ||||||
\(868\) | 51.7982i | 1.75814i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.581695 | + | 3.14121i | 0.0197213 | + | 0.106497i | ||||
\(871\) | 29.4745 | 0.998706 | ||||||||
\(872\) | 11.8150i | 0.400107i | ||||||||
\(873\) | 13.7770i | 0.466282i | ||||||||
\(874\) | 2.42552 | 0.0820446 | ||||||||
\(875\) | −34.9704 | + | 21.4079i | −1.18222 | + | 0.723721i | ||||
\(876\) | 0.367067 | 0.0124020 | ||||||||
\(877\) | − | 42.7795i | − | 1.44456i | −0.691601 | − | 0.722280i | \(-0.743094\pi\) | ||
0.691601 | − | 0.722280i | \(-0.256906\pi\) | |||||||
\(878\) | − | 5.36200i | − | 0.180959i | ||||||
\(879\) | 9.90674 | 0.334146 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.2644 | 1.12071 | 0.560353 | − | 0.828254i | \(-0.310665\pi\) | ||||
0.560353 | + | 0.828254i | \(0.310665\pi\) | |||||||
\(882\) | 1.86280i | 0.0627236i | ||||||||
\(883\) | 37.2817i | 1.25463i | 0.778766 | + | 0.627314i | \(0.215846\pi\) | ||||
−0.778766 | + | 0.627314i | \(0.784154\pi\) | |||||||
\(884\) | 35.5168 | 1.19456 | ||||||||
\(885\) | −31.8762 | + | 5.90289i | −1.07151 | + | 0.198424i | ||||
\(886\) | −2.55648 | −0.0858867 | ||||||||
\(887\) | − | 47.7445i | − | 1.60310i | −0.597926 | − | 0.801551i | \(-0.704008\pi\) | ||
0.597926 | − | 0.801551i | \(-0.295992\pi\) | |||||||
\(888\) | 2.69999i | 0.0906057i | ||||||||
\(889\) | 0.681841 | 0.0228682 | ||||||||
\(890\) | 1.93420 | − | 0.358178i | 0.0648345 | − | 0.0120062i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.0881070i | 0.00295004i | ||||||||
\(893\) | 45.0477i | 1.50747i | ||||||||
\(894\) | 4.42580 | 0.148021 | ||||||||
\(895\) | 6.54463 | + | 35.3417i | 0.218763 | + | 1.18134i | ||||
\(896\) | −30.4480 | −1.01720 | ||||||||
\(897\) | − | 5.82137i | − | 0.194370i | ||||||
\(898\) | − | 0.918739i | − | 0.0306587i | ||||||
\(899\) | −36.4540 | −1.21581 | ||||||||
\(900\) | 8.94749 | − | 3.43149i | 0.298250 | − | 0.114383i | ||||
\(901\) | 41.3054 | 1.37608 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.83290i | 0.0942730i | ||||||||
\(904\) | 14.5529 | 0.484021 | ||||||||
\(905\) | 4.37080 | + | 23.6028i | 0.145290 | + | 0.784583i | ||||
\(906\) | −0.303424 | −0.0100806 | ||||||||
\(907\) | 12.2824i | 0.407830i | 0.978989 | + | 0.203915i | \(0.0653665\pi\) | ||||
−0.978989 | + | 0.203915i | \(0.934633\pi\) | |||||||
\(908\) | 11.7791i | 0.390903i | ||||||||
\(909\) | 4.65928 | 0.154539 | ||||||||
\(910\) | −11.2382 | + | 2.08111i | −0.372543 | + | 0.0689882i | ||||
\(911\) | 43.2323 | 1.43235 | 0.716174 | − | 0.697921i | \(-0.245892\pi\) | ||||
0.716174 | + | 0.697921i | \(0.245892\pi\) | |||||||
\(912\) | − | 24.4115i | − | 0.808346i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.01880 | 0.0336988 | ||||||||
\(915\) | 4.02561 | − | 0.745468i | 0.133082 | − | 0.0246444i | ||||
\(916\) | −22.4940 | −0.743224 | ||||||||
\(917\) | − | 34.0021i | − | 1.12285i | ||||||
\(918\) | 1.10908i | 0.0366051i | ||||||||
\(919\) | −55.4515 | −1.82917 | −0.914587 | − | 0.404388i | \(-0.867484\pi\) | ||||
−0.914587 | + | 0.404388i | \(0.867484\pi\) | |||||||
\(920\) | −0.555586 | − | 3.00022i | −0.0183171 | − | 0.0989144i | ||||
\(921\) | −23.2505 | −0.766131 | ||||||||
\(922\) | − | 5.23678i | − | 0.172464i | ||||||
\(923\) | − | 15.8817i | − | 0.522753i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.27359 | − | 11.1432i | −0.140515 | − | 0.366387i | ||||
\(926\) | −5.20162 | −0.170936 | ||||||||
\(927\) | 9.81701i | 0.322433i | ||||||||
\(928\) | − | 16.2007i | − | 0.531814i | ||||||
\(929\) | −47.3061 | −1.55206 | −0.776032 | − | 0.630694i | \(-0.782770\pi\) | ||||
−0.776032 | + | 0.630694i | \(0.782770\pi\) | |||||||
\(930\) | −0.866573 | − | 4.67958i | −0.0284160 | − | 0.153450i | ||||
\(931\) | −44.9026 | −1.47162 | ||||||||
\(932\) | − | 20.4285i | − | 0.669157i | ||||||
\(933\) | − | 29.8628i | − | 0.977663i | ||||||
\(934\) | 7.71757 | 0.252527 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.45863 | 0.178421 | ||||||||
\(937\) | − | 34.6722i | − | 1.13269i | −0.824168 | − | 0.566346i | \(-0.808357\pi\) | ||
0.824168 | − | 0.566346i | \(-0.191643\pi\) | |||||||
\(938\) | 6.46938i | 0.211233i | ||||||||
\(939\) | 25.6366 | 0.836619 | ||||||||
\(940\) | 27.2673 | − | 5.04940i | 0.889361 | − | 0.164693i | ||||
\(941\) | 22.0532 | 0.718913 | 0.359456 | − | 0.933162i | \(-0.382962\pi\) | ||||
0.359456 | + | 0.933162i | \(0.382962\pi\) | |||||||
\(942\) | − | 1.42636i | − | 0.0464732i | ||||||
\(943\) | − | 5.19401i | − | 0.169140i | ||||||
\(944\) | 50.8364 | 1.65459 | ||||||||
\(945\) | 1.49321 | + | 8.06347i | 0.0485740 | + | 0.262305i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 58.6395i | − | 1.90553i | −0.303711 | − | 0.952764i | \(-0.598226\pi\) | ||
0.303711 | − | 0.952764i | \(-0.401774\pi\) | |||||||
\(948\) | − | 6.05631i | − | 0.196700i | ||||||
\(949\) | −0.924221 | −0.0300015 | ||||||||
\(950\) | −3.59993 | − | 9.38668i | −0.116797 | − | 0.304544i | ||||
\(951\) | −1.12070 | −0.0363412 | ||||||||
\(952\) | 15.9305i | 0.516310i | ||||||||
\(953\) | 43.3834i | 1.40533i | 0.711523 | + | 0.702663i | \(0.248006\pi\) | ||||
−0.711523 | + | 0.702663i | \(0.751994\pi\) | |||||||
\(954\) | 3.10654 | 0.100578 | ||||||||
\(955\) | 5.53673 | + | 29.8989i | 0.179164 | + | 0.967505i | ||||
\(956\) | −8.80342 | −0.284723 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 6.57588i | − | 0.212457i | ||||||
\(959\) | 1.60669 | 0.0518828 | ||||||||
\(960\) | −13.3396 | + | 2.47025i | −0.430535 | + | 0.0797271i | ||||
\(961\) | 23.3068 | 0.751833 | ||||||||
\(962\) | − | 3.32670i | − | 0.107257i | ||||||
\(963\) | 11.8016i | 0.380302i | ||||||||
\(964\) | −36.1691 | −1.16493 | ||||||||
\(965\) | 56.9637 | − | 10.5486i | 1.83373 | − | 0.339572i | ||||
\(966\) | 1.27774 | 0.0411105 | ||||||||
\(967\) | 39.9415i | 1.28443i | 0.766523 | + | 0.642217i | \(0.221985\pi\) | ||||
−0.766523 | + | 0.642217i | \(0.778015\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −26.7343 | −0.858831 | ||||||||
\(970\) | −1.62007 | − | 8.74854i | −0.0520173 | − | 0.280899i | ||||
\(971\) | 41.7596 | 1.34013 | 0.670065 | − | 0.742302i | \(-0.266266\pi\) | ||||
0.670065 | + | 0.742302i | \(0.266266\pi\) | |||||||
\(972\) | − | 1.91659i | − | 0.0614746i | ||||||
\(973\) | − | 31.5555i | − | 1.01162i | ||||||
\(974\) | −3.91361 | −0.125400 | ||||||||
\(975\) | −22.5285 | + | 8.64000i | −0.721488 | + | 0.276702i | ||||
\(976\) | −6.42006 | −0.205501 | ||||||||
\(977\) | − | 31.7877i | − | 1.01698i | −0.861068 | − | 0.508489i | \(-0.830204\pi\) | ||
0.861068 | − | 0.508489i | \(-0.169796\pi\) | |||||||
\(978\) | − | 2.78085i | − | 0.0889218i | ||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 5.03314 | + | 27.1795i | 0.160778 | + | 0.868216i | ||||
\(981\) | −10.4450 | −0.333484 | ||||||||
\(982\) | 5.49787i | 0.175444i | ||||||||
\(983\) | 23.9900i | 0.765161i | 0.923922 | + | 0.382580i | \(0.124965\pi\) | ||||
−0.923922 | + | 0.382580i | \(0.875035\pi\) | |||||||
\(984\) | 4.87036 | 0.155261 | ||||||||
\(985\) | −2.60205 | + | 0.481851i | −0.0829081 | + | 0.0153531i | ||||
\(986\) | −5.48631 | −0.174720 | ||||||||
\(987\) | 23.7306i | 0.755353i | ||||||||
\(988\) | 64.3889i | 2.04848i | ||||||||
\(989\) | 0.931834 | 0.0296306 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.1684 | −0.450074 | −0.225037 | − | 0.974350i | \(-0.572250\pi\) | ||||
−0.225037 | + | 0.974350i | \(0.572250\pi\) | |||||||
\(992\) | 24.1348i | 0.766280i | ||||||||
\(993\) | 10.9379i | 0.347103i | ||||||||
\(994\) | 3.48588 | 0.110565 | ||||||||
\(995\) | 1.27630 | + | 6.89214i | 0.0404614 | + | 0.218496i | ||||
\(996\) | 2.93317 | 0.0929411 | ||||||||
\(997\) | 7.30718i | 0.231421i | 0.993283 | + | 0.115710i | \(0.0369144\pi\) | ||||
−0.993283 | + | 0.115710i | \(0.963086\pi\) | |||||||
\(998\) | 6.67428i | 0.211271i | ||||||||
\(999\) | −2.38692 | −0.0755188 |
(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 | 1815.2.c.j.364.13 | 24 | ||
5.2 | odd | 4 | 9075.2.a.dz.1.5 | 12 | |||
5.3 | odd | 4 | 9075.2.a.dy.1.8 | 12 | |||
5.4 | even | 2 | inner | 1815.2.c.j.364.12 | 24 | ||
11.5 | even | 5 | 165.2.s.a.124.6 | yes | 48 | ||
11.9 | even | 5 | 165.2.s.a.4.7 | yes | 48 | ||
11.10 | odd | 2 | 1815.2.c.k.364.12 | 24 | |||
33.5 | odd | 10 | 495.2.ba.c.289.7 | 48 | |||
33.20 | odd | 10 | 495.2.ba.c.334.6 | 48 | |||
55.9 | even | 10 | 165.2.s.a.4.6 | ✓ | 48 | ||
55.27 | odd | 20 | 825.2.n.o.751.4 | 24 | |||
55.32 | even | 4 | 9075.2.a.dx.1.8 | 12 | |||
55.38 | odd | 20 | 825.2.n.p.751.3 | 24 | |||
55.42 | odd | 20 | 825.2.n.o.301.4 | 24 | |||
55.43 | even | 4 | 9075.2.a.ea.1.5 | 12 | |||
55.49 | even | 10 | 165.2.s.a.124.7 | yes | 48 | ||
55.53 | odd | 20 | 825.2.n.p.301.3 | 24 | |||
55.54 | odd | 2 | 1815.2.c.k.364.13 | 24 | |||
165.104 | odd | 10 | 495.2.ba.c.289.6 | 48 | |||
165.119 | odd | 10 | 495.2.ba.c.334.7 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.s.a.4.6 | ✓ | 48 | 55.9 | even | 10 | ||
165.2.s.a.4.7 | yes | 48 | 11.9 | even | 5 | ||
165.2.s.a.124.6 | yes | 48 | 11.5 | even | 5 | ||
165.2.s.a.124.7 | yes | 48 | 55.49 | even | 10 | ||
495.2.ba.c.289.6 | 48 | 165.104 | odd | 10 | |||
495.2.ba.c.289.7 | 48 | 33.5 | odd | 10 | |||
495.2.ba.c.334.6 | 48 | 33.20 | odd | 10 | |||
495.2.ba.c.334.7 | 48 | 165.119 | odd | 10 | |||
825.2.n.o.301.4 | 24 | 55.42 | odd | 20 | |||
825.2.n.o.751.4 | 24 | 55.27 | odd | 20 | |||
825.2.n.p.301.3 | 24 | 55.53 | odd | 20 | |||
825.2.n.p.751.3 | 24 | 55.38 | odd | 20 | |||
1815.2.c.j.364.12 | 24 | 5.4 | even | 2 | inner | ||
1815.2.c.j.364.13 | 24 | 1.1 | even | 1 | trivial | ||
1815.2.c.k.364.12 | 24 | 11.10 | odd | 2 | |||
1815.2.c.k.364.13 | 24 | 55.54 | odd | 2 | |||
9075.2.a.dx.1.8 | 12 | 55.32 | even | 4 | |||
9075.2.a.dy.1.8 | 12 | 5.3 | odd | 4 | |||
9075.2.a.dz.1.5 | 12 | 5.2 | odd | 4 | |||
9075.2.a.ea.1.5 | 12 | 55.43 | even | 4 |