Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(113,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.ba (of order \(10\), degree \(4\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 113.10 | ||
Character | \(\chi\) | \(=\) | 1148.113 |
Dual form | 1148.2.ba.a.701.11 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) |
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 | 0 | ||||||||
\(3\) | 0.268055i | 0.154762i | 0.997002 | + | 0.0773809i | \(0.0246558\pi\) | ||||
−0.997002 | + | 0.0773809i | \(0.975344\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.725265 | + | 2.23214i | 0.324348 | + | 0.998242i | 0.971734 | + | 0.236079i | \(0.0758624\pi\) |
−0.647385 | + | 0.762163i | \(0.724138\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.587785 | + | 0.809017i | 0.222162 | + | 0.305780i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.92815 | 0.976049 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.13064 | + | 1.66705i | 1.54695 | + | 0.502633i | 0.953283 | − | 0.302080i | \(-0.0976808\pi\) |
0.593664 | + | 0.804713i | \(0.297681\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.29047 | − | 1.77618i | 0.357912 | − | 0.492623i | −0.591654 | − | 0.806192i | \(-0.701525\pi\) |
0.949565 | + | 0.313569i | \(0.101525\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.598336 | + | 0.194411i | −0.154490 | + | 0.0501967i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.13726 | − | 0.694437i | −0.518361 | − | 0.168426i | 0.0381402 | − | 0.999272i | \(-0.487857\pi\) |
−0.556501 | + | 0.830847i | \(0.687857\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.234325 | + | 0.322520i | 0.0537578 | + | 0.0739913i | 0.835050 | − | 0.550175i | \(-0.185439\pi\) |
−0.781292 | + | 0.624166i | \(0.785439\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.216861 | + | 0.157559i | −0.0473230 | + | 0.0343822i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.94523 | − | 3.59292i | −1.03115 | − | 0.749176i | −0.0626134 | − | 0.998038i | \(-0.519943\pi\) |
−0.968539 | + | 0.248862i | \(0.919943\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.411339 | + | 0.298855i | −0.0822677 | + | 0.0597710i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.58907i | 0.305817i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.796559 | + | 0.258818i | −0.147917 | + | 0.0480612i | −0.382040 | − | 0.924146i | \(-0.624778\pi\) |
0.234123 | + | 0.972207i | \(0.424778\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.226552 | + | 0.697256i | −0.0406900 | + | 0.125231i | −0.969338 | − | 0.245731i | \(-0.920972\pi\) |
0.928648 | + | 0.370962i | \(0.120972\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.446861 | + | 1.37530i | −0.0777885 | + | 0.239408i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.37954 | + | 1.89877i | −0.233184 | + | 0.320950i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.56018 | − | 4.80173i | −0.256491 | − | 0.789400i | −0.993532 | − | 0.113551i | \(-0.963777\pi\) |
0.737041 | − | 0.675848i | \(-0.236223\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.476114 | + | 0.345917i | 0.0762393 | + | 0.0553911i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.06679 | + | 3.91505i | 0.791300 | + | 0.611428i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.26016 | + | 4.54827i | 0.954665 | + | 0.693605i | 0.951906 | − | 0.306391i | \(-0.0991217\pi\) |
0.00275940 | + | 0.999996i | \(0.499122\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.12368 | + | 6.53602i | 0.316580 | + | 0.974333i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.50692 | + | 7.57962i | −0.803267 | + | 1.10560i | 0.189061 | + | 0.981965i | \(0.439456\pi\) |
−0.992328 | + | 0.123636i | \(0.960544\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.309017 | + | 0.951057i | −0.0441453 | + | 0.135865i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.186148 | − | 0.572903i | 0.0260659 | − | 0.0802225i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.775030 | + | 0.251822i | −0.106459 | + | 0.0345905i | −0.361762 | − | 0.932271i | \(-0.617825\pi\) |
0.255303 | + | 0.966861i | \(0.417825\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.6613i | 1.70726i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0864533 | + | 0.0628120i | −0.0114510 | + | 0.00831965i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.625846 | + | 0.454704i | 0.0814782 | + | 0.0591974i | 0.627779 | − | 0.778392i | \(-0.283964\pi\) |
−0.546300 | + | 0.837589i | \(0.683964\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.04444 | − | 2.93846i | 0.517837 | − | 0.376231i | −0.297951 | − | 0.954581i | \(-0.596303\pi\) |
0.815788 | + | 0.578350i | \(0.196303\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.72112 | + | 2.36892i | 0.216841 | + | 0.298456i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.90061 | + | 1.59230i | 0.607845 | + | 0.197501i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.57518 | − | 1.16165i | 0.436777 | − | 0.141918i | −0.0823709 | − | 0.996602i | \(-0.526249\pi\) |
0.519148 | + | 0.854684i | \(0.326249\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.963102 | − | 1.32560i | 0.115944 | − | 0.159583i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.416251 | + | 0.135248i | 0.0493999 | + | 0.0160510i | 0.333613 | − | 0.942710i | \(-0.391732\pi\) |
−0.284213 | + | 0.958761i | \(0.591732\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.48431 | −0.641890 | −0.320945 | − | 0.947098i | \(-0.604000\pi\) | ||||
−0.320945 | + | 0.947098i | \(0.604000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.0801097 | − | 0.110262i | −0.00925027 | − | 0.0127319i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.66705 | + | 5.13064i | 0.189978 | + | 0.584691i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.94695i | 0.669084i | 0.942381 | + | 0.334542i | \(0.108582\pi\) | ||||
−0.942381 | + | 0.334542i | \(0.891418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.35848 | 0.928720 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.84125 | −0.531396 | −0.265698 | − | 0.964056i | \(-0.585602\pi\) | ||||
−0.265698 | + | 0.964056i | \(0.585602\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 5.27430i | − | 0.572078i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.0693775 | − | 0.213522i | −0.00743805 | − | 0.0228920i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.57065 | − | 4.91458i | −0.378488 | − | 0.520944i | 0.576695 | − | 0.816959i | \(-0.304342\pi\) |
−0.955183 | + | 0.296015i | \(0.904342\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.19548 | 0.230149 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.186903 | − | 0.0607285i | −0.0193809 | − | 0.00629725i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.549962 | + | 0.756958i | −0.0564249 | + | 0.0776622i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.29839 | + | 1.39663i | −0.436435 | + | 0.141806i | −0.518990 | − | 0.854780i | \(-0.673692\pi\) |
0.0825551 | + | 0.996586i | \(0.473692\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.0233 | + | 4.88136i | 1.50990 | + | 0.490595i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.09357 | − | 11.1398i | −0.805340 | − | 1.10846i | −0.992026 | − | 0.126036i | \(-0.959774\pi\) |
0.186685 | − | 0.982420i | \(-0.440226\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.50643 | + | 2.54757i | −0.345499 | + | 0.251020i | −0.746978 | − | 0.664848i | \(-0.768496\pi\) |
0.401479 | + | 0.915868i | \(0.368496\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.508975 | − | 0.369792i | −0.0496709 | − | 0.0360880i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.3514 | + | 10.4269i | −1.38741 | + | 1.00801i | −0.391262 | + | 0.920279i | \(0.627962\pi\) |
−0.996144 | + | 0.0877308i | \(0.972038\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.0446i | − | 1.05789i | −0.848658 | − | 0.528943i | \(-0.822589\pi\) | ||
0.848658 | − | 0.528943i | \(-0.177411\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.28713 | − | 0.418214i | 0.122169 | − | 0.0396951i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.76483 | − | 14.6646i | 0.448237 | − | 1.37953i | −0.430657 | − | 0.902516i | \(-0.641718\pi\) |
0.878894 | − | 0.477017i | \(-0.158282\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.43329 | − | 13.6443i | 0.413406 | − | 1.27233i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.77868 | − | 5.20091i | 0.349339 | − | 0.480825i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.694437 | − | 2.13726i | −0.0636590 | − | 0.195922i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.6453 | + | 10.6404i | 1.33139 | + | 0.967309i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.04945 | + | 1.35818i | −0.0946257 | + | 0.122463i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.52843 | + | 6.19627i | 0.762806 | + | 0.554211i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.96524 | − | 15.2814i | −0.440593 | − | 1.35601i | −0.887245 | − | 0.461299i | \(-0.847384\pi\) |
0.446651 | − | 0.894708i | \(-0.352616\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.21919 | + | 1.67807i | −0.107344 | + | 0.147746i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.48979 | + | 13.8182i | −0.392275 | + | 1.20730i | 0.538788 | + | 0.842441i | \(0.318882\pi\) |
−0.931063 | + | 0.364857i | \(0.881118\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.123192 | + | 0.379146i | −0.0106821 | + | 0.0328761i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.54702 | + | 1.15250i | −0.305279 | + | 0.0991912i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.9508i | 1.78995i | 0.446115 | + | 0.894975i | \(0.352807\pi\) | ||||
−0.446115 | + | 0.894975i | \(0.647193\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.65109 | + | 4.10576i | −0.479320 | + | 0.348246i | −0.801062 | − | 0.598581i | \(-0.795731\pi\) |
0.321743 | + | 0.946827i | \(0.395731\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.03176 | − | 1.47616i | −0.171105 | − | 0.124315i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.58191 | − | 6.96167i | 0.801280 | − | 0.582164i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.15543 | − | 1.59032i | −0.0959535 | − | 0.132069i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.254936 | − | 0.0828336i | −0.0210267 | − | 0.00683200i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.39980 | − | 2.40434i | 0.606216 | − | 0.196971i | 0.0102050 | − | 0.999948i | \(-0.496752\pi\) |
0.596011 | + | 0.802977i | \(0.296752\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.68258 | − | 6.44502i | 0.381063 | − | 0.524489i | −0.574803 | − | 0.818292i | \(-0.694921\pi\) |
0.955866 | + | 0.293804i | \(0.0949212\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.25820 | − | 2.03341i | −0.505946 | − | 0.164392i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.72068 | −0.138208 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.64994 | − | 7.77648i | −0.450914 | − | 0.620630i | 0.521679 | − | 0.853142i | \(-0.325306\pi\) |
−0.972594 | + | 0.232511i | \(0.925306\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.0675024 | − | 0.207751i | −0.00535328 | − | 0.0164757i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.11264i | − | 0.481744i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.3496 | −0.810646 | −0.405323 | − | 0.914174i | \(-0.632841\pi\) | ||||
−0.405323 | + | 0.914174i | \(0.632841\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.39394 | −0.264218 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.73356i | 0.366294i | 0.983086 | + | 0.183147i | \(0.0586284\pi\) | ||||
−0.983086 | + | 0.183147i | \(0.941372\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.52772 | + | 7.77952i | 0.194440 | + | 0.598425i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.686137 | + | 0.944387i | 0.0524702 | + | 0.0722191i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.05189 | 0.536145 | 0.268073 | − | 0.963399i | \(-0.413613\pi\) | ||||
0.268073 | + | 0.963399i | \(0.413613\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.483558 | − | 0.157117i | −0.0365535 | − | 0.0118770i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.121886 | + | 0.167761i | −0.00916150 | + | 0.0126097i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.99974 | + | 1.94943i | −0.448441 | + | 0.145707i | −0.524527 | − | 0.851394i | \(-0.675758\pi\) |
0.0760856 | + | 0.997101i | \(0.475758\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.70107 | − | 1.85239i | −0.423757 | − | 0.137687i | 0.0893722 | − | 0.995998i | \(-0.471514\pi\) |
−0.513129 | + | 0.858311i | \(0.671514\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.787669 | + | 1.08413i | 0.0582261 | + | 0.0801414i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.58657 | − | 6.96505i | 0.704819 | − | 0.512081i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.80785 | − | 7.12582i | −0.717221 | − | 0.521091i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.28559 | + | 0.934033i | −0.0935126 | + | 0.0679409i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.58946i | 0.404439i | 0.979340 | + | 0.202219i | \(0.0648154\pi\) | ||||
−0.979340 | + | 0.202219i | \(0.935185\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.35051 | − | 1.73849i | 0.385138 | − | 0.125139i | −0.110047 | − | 0.993926i | \(-0.535100\pi\) |
0.495185 | + | 0.868787i | \(0.335100\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.426825 | + | 1.31363i | −0.0305656 | + | 0.0940713i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.63619 | − | 17.3464i | 0.401562 | − | 1.23588i | −0.522170 | − | 0.852841i | \(-0.674877\pi\) |
0.923732 | − | 0.383039i | \(-0.125123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.38976 | − | 10.1711i | 0.523846 | − | 0.721013i | −0.462331 | − | 0.886708i | \(-0.652987\pi\) |
0.986177 | + | 0.165695i | \(0.0529867\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.311385 | + | 0.958345i | 0.0219634 | + | 0.0675965i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.677594 | − | 0.492301i | −0.0475578 | − | 0.0345527i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.06415 | + | 14.1492i | −0.353696 | + | 0.988225i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.4804 | − | 10.5206i | −1.00646 | − | 0.731232i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.664580 | + | 2.04537i | 0.0459700 | + | 0.141481i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.36629 | − | 10.1388i | 0.507116 | − | 0.697986i | −0.476313 | − | 0.879276i | \(-0.658027\pi\) |
0.983430 | + | 0.181290i | \(0.0580272\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.0362540 | + | 0.111578i | −0.00248408 | + | 0.00764523i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.61209 | + | 17.2722i | −0.382741 | + | 1.17796i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.697256 | + | 0.226552i | −0.0473328 | + | 0.0153794i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1.47010i | − | 0.0993400i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.99151 | + | 2.90000i | −0.268498 | + | 0.195075i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.5571 | − | 12.0294i | −1.10874 | − | 0.805548i | −0.126277 | − | 0.991995i | \(-0.540303\pi\) |
−0.982465 | + | 0.186447i | \(0.940303\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.20446 | + | 0.875091i | −0.0802973 | + | 0.0583394i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.8844 | − | 20.4866i | −0.987913 | − | 1.35974i | −0.932456 | − | 0.361284i | \(-0.882339\pi\) |
−0.0554567 | − | 0.998461i | \(-0.517661\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.1772 | − | 5.25628i | −1.06902 | − | 0.347345i | −0.278912 | − | 0.960317i | \(-0.589974\pi\) |
−0.790105 | + | 0.612972i | \(0.789974\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.37530 | + | 0.446861i | −0.0904878 | + | 0.0294013i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.05700 | + | 2.83121i | −0.134758 | + | 0.185479i | −0.871063 | − | 0.491171i | \(-0.836569\pi\) |
0.736305 | + | 0.676650i | \(0.236569\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.9127 | − | 6.79496i | −1.36420 | − | 0.443254i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.59411 | −0.103549 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.5349 | − | 15.8765i | −0.746133 | − | 1.02696i | −0.998242 | − | 0.0592652i | \(-0.981124\pi\) |
0.252109 | − | 0.967699i | \(-0.418876\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.93700 | − | 5.96147i | −0.124773 | − | 0.384012i | 0.869087 | − | 0.494660i | \(-0.164707\pi\) |
−0.993860 | + | 0.110648i | \(0.964707\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.00775i | 0.449547i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.34701 | −0.149945 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.875243 | 0.0556904 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1.29772i | − | 0.0822399i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.06229 | + | 9.42475i | 0.193290 | + | 0.594885i | 0.999992 | + | 0.00392715i | \(0.00125005\pi\) |
−0.806702 | + | 0.590958i | \(0.798750\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.3827 | − | 26.6779i | −1.21858 | − | 1.67723i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.41380 | 0.0885359 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.2916 | + | 6.59315i | 1.26576 | + | 0.411269i | 0.863542 | − | 0.504277i | \(-0.168241\pi\) |
0.402214 | + | 0.915546i | \(0.368241\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.96763 | − | 4.08460i | 0.184400 | − | 0.253804i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.33244 | + | 0.757856i | −0.144375 | + | 0.0469101i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.6774 | + | 6.06864i | 1.15170 | + | 0.374209i | 0.821782 | − | 0.569802i | \(-0.192980\pi\) |
0.329914 | + | 0.944011i | \(0.392980\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.12420 | − | 1.54733i | −0.0690593 | − | 0.0950520i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.31738 | − | 0.957132i | 0.0806223 | − | 0.0585755i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.01337 | + | 3.64243i | 0.305671 | + | 0.222083i | 0.730037 | − | 0.683408i | \(-0.239503\pi\) |
−0.424366 | + | 0.905491i | \(0.639503\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.4513 | + | 12.6791i | −1.06009 | + | 0.770202i | −0.974105 | − | 0.226095i | \(-0.927404\pi\) |
−0.0859862 | + | 0.996296i | \(0.527404\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.588510i | 0.0356182i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.60864 | + | 0.847597i | −0.157307 | + | 0.0511120i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.63130 | − | 26.5644i | 0.518604 | − | 1.59610i | −0.258022 | − | 0.966139i | \(-0.583071\pi\) |
0.776627 | − | 0.629961i | \(-0.216929\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.663378 | + | 2.04167i | −0.0397154 | + | 0.122231i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.7505 | − | 23.0551i | 0.999250 | − | 1.37535i | 0.0734655 | − | 0.997298i | \(-0.476594\pi\) |
0.925784 | − | 0.378052i | \(-0.123406\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.28398 | + | 13.1847i | 0.254656 | + | 0.783751i | 0.993897 | + | 0.110310i | \(0.0351844\pi\) |
−0.739241 | + | 0.673441i | \(0.764816\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.202907 | − | 0.147420i | −0.0120191 | − | 0.00873242i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.189155 | + | 6.40033i | −0.0111654 | + | 0.377800i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.66766 | − | 7.02397i | −0.568686 | − | 0.413174i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.374374 | − | 1.15221i | −0.0219462 | − | 0.0675435i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.88596 | − | 8.10133i | 0.343861 | − | 0.473285i | −0.601703 | − | 0.798720i | \(-0.705511\pi\) |
0.945564 | + | 0.325435i | \(0.105511\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.561057 | + | 1.72675i | −0.0326660 | + | 0.100536i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.64906 | + | 8.15295i | −0.153714 | + | 0.473082i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.7633 | + | 4.14706i | −0.738123 | + | 0.239831i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.73798i | 0.446010i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.98609 | − | 2.16952i | 0.171547 | − | 0.124636i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.49232 | + | 6.89658i | 0.543529 | + | 0.394897i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.91481 | − | 4.29736i | 0.337576 | − | 0.245263i | −0.406062 | − | 0.913845i | \(-0.633098\pi\) |
0.743638 | + | 0.668582i | \(0.233098\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.682891 | − | 0.939918i | −0.0388483 | − | 0.0534701i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.1389 | + | 8.49305i | 1.48220 | + | 0.481597i | 0.934770 | − | 0.355253i | \(-0.115605\pi\) |
0.547432 | + | 0.836850i | \(0.315605\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.85284 | − | 0.926943i | 0.161252 | − | 0.0523939i | −0.227279 | − | 0.973830i | \(-0.572983\pi\) |
0.388531 | + | 0.921436i | \(0.372983\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.03948 | + | 5.55987i | −0.227599 | + | 0.313263i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.59992 | + | 1.81952i | 0.314523 | + | 0.102195i | 0.462025 | − | 0.886867i | \(-0.347123\pi\) |
−0.147502 | + | 0.989062i | \(0.547123\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.51832 | −0.252977 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.79500 | − | 3.84698i | −0.156001 | − | 0.214718i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.276842 | − | 0.852033i | −0.0154039 | − | 0.0474084i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.11627i | 0.0619198i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.96058 | 0.163720 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.36893 | −0.516526 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 23.6626i | − | 1.30062i | −0.759670 | − | 0.650308i | \(-0.774640\pi\) | ||
0.759670 | − | 0.650308i | \(-0.225360\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.56843 | − | 14.0602i | −0.250348 | − | 0.770492i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.18590 | + | 7.13778i | 0.283336 | + | 0.389979i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4217 | −0.622181 | −0.311090 | − | 0.950380i | \(-0.600694\pi\) | ||||
−0.311090 | + | 0.950380i | \(0.600694\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.93093 | + | 1.27724i | 0.213499 | + | 0.0693700i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.32471 | + | 3.19970i | −0.125890 | + | 0.173273i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.951057 | + | 0.309017i | −0.0513522 | + | 0.0166853i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.65742 | + | 1.18837i | 0.196909 | + | 0.0639795i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.10033 | − | 12.5255i | −0.488531 | − | 0.672406i | 0.491585 | − | 0.870830i | \(-0.336418\pi\) |
−0.980116 | + | 0.198424i | \(0.936418\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.727151 | − | 0.528306i | 0.0389235 | − | 0.0282796i | −0.568153 | − | 0.822923i | \(-0.692342\pi\) |
0.607077 | + | 0.794643i | \(0.292342\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.82247 | + | 2.05065i | 0.150653 | + | 0.109455i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.98026 | − | 6.52454i | 0.477971 | − | 0.347266i | −0.322569 | − | 0.946546i | \(-0.604546\pi\) |
0.800540 | + | 0.599280i | \(0.204546\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.02722i | 0.0545192i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.572903 | − | 0.186148i | 0.0303213 | − | 0.00985198i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.58197 | + | 4.86879i | −0.0834929 | + | 0.256965i | −0.984084 | − | 0.177702i | \(-0.943134\pi\) |
0.900591 | + | 0.434667i | \(0.143134\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.82221 | − | 17.9189i | 0.306432 | − | 0.943101i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.85222 | + | 3.92574i | −0.149702 | + | 0.206048i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.97758 | − | 12.2417i | −0.208196 | − | 0.640761i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.06146 | + | 4.40391i | 0.316405 | + | 0.229882i | 0.734640 | − | 0.678457i | \(-0.237351\pi\) |
−0.418235 | + | 0.908339i | \(0.637351\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.8363 | + | 11.4638i | 0.772348 | + | 0.596783i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.659280 | − | 0.478995i | −0.0342281 | − | 0.0248682i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.79750 | − | 14.7652i | −0.248405 | − | 0.764512i | −0.995058 | − | 0.0992981i | \(-0.968340\pi\) |
0.746653 | − | 0.665214i | \(-0.231660\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.66094 | + | 2.28609i | −0.0857707 | + | 0.118053i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.568229 | + | 1.74883i | −0.0292653 | + | 0.0900692i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.29566 | − | 10.1430i | 0.169286 | − | 0.521010i | −0.830040 | − | 0.557704i | \(-0.811683\pi\) |
0.999327 | + | 0.0366936i | \(0.0116825\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.09627 | − | 1.33096i | 0.209858 | − | 0.0681870i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.4885i | 0.995817i | 0.867230 | + | 0.497908i | \(0.165898\pi\) | ||||
−0.867230 | + | 0.497908i | \(0.834102\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.2432 | + | 7.44215i | −0.522044 | + | 0.379287i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.3307 | + | 13.3180i | 0.931800 | + | 0.676992i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.2827 | + | 12.5566i | −0.876266 | + | 0.636645i | −0.932261 | − | 0.361786i | \(-0.882167\pi\) |
0.0559947 | + | 0.998431i | \(0.482167\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.07418 | + | 11.1132i | 0.408329 | + | 0.562016i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.70403 | − | 1.20351i | −0.186844 | − | 0.0607092i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.2744 | + | 4.31311i | −0.667907 | + | 0.217016i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.643695 | − | 0.885970i | 0.0323061 | − | 0.0444656i | −0.792558 | − | 0.609796i | \(-0.791251\pi\) |
0.824865 | + | 0.565330i | \(0.191251\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.101632 | − | 0.0330222i | −0.00508796 | − | 0.00165318i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.31994 | −0.165790 | −0.0828949 | − | 0.996558i | \(-0.526417\pi\) | ||||
−0.0828949 | + | 0.996558i | \(0.526417\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.946092 | + | 1.30218i | 0.0471282 | + | 0.0648664i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.06211 | + | 18.6573i | 0.301229 | + | 0.927087i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 27.2368i | − | 1.35008i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.3385 | 0.758438 | 0.379219 | − | 0.925307i | \(-0.376193\pi\) | ||||
0.379219 | + | 0.925307i | \(0.376193\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.61598 | −0.277016 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.773588i | 0.0380658i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.51119 | − | 10.8063i | −0.172358 | − | 0.530462i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.10057 | − | 1.51481i | −0.0538952 | − | 0.0741804i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.3488 | −1.67805 | −0.839026 | − | 0.544092i | \(-0.816874\pi\) | ||||
−0.839026 | + | 0.544092i | \(0.816874\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.9075 | + | 3.54407i | 0.531601 | + | 0.172728i | 0.562504 | − | 0.826795i | \(-0.309838\pi\) |
−0.0309027 | + | 0.999522i | \(0.509838\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.1251 | + | 22.1942i | −0.784027 | + | 1.07912i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.08667 | − | 0.353081i | 0.0527114 | − | 0.0171270i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.75452 | + | 1.54484i | 0.230087 | + | 0.0747599i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.86611 | + | 2.56848i | 0.0900967 | + | 0.124007i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.06821 | + | 2.95573i | −0.195959 | + | 0.142373i | −0.681438 | − | 0.731876i | \(-0.738645\pi\) |
0.485479 | + | 0.874248i | \(0.338645\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.9426 | − | 19.5749i | −1.29478 | − | 0.940712i | −0.294889 | − | 0.955532i | \(-0.595283\pi\) |
−0.999890 | + | 0.0148196i | \(0.995283\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.426293 | − | 0.309720i | 0.0204392 | − | 0.0148499i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2.43685i | − | 0.116570i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.1951 | − | 3.31258i | 0.486584 | − | 0.158101i | −0.0554430 | − | 0.998462i | \(-0.517657\pi\) |
0.542027 | + | 0.840361i | \(0.317657\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.904847 | + | 2.78483i | −0.0430880 | + | 0.132611i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.60957 | − | 8.03143i | 0.123984 | − | 0.381585i | −0.869730 | − | 0.493527i | \(-0.835707\pi\) |
0.993715 | + | 0.111943i | \(0.0357073\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.38034 | − | 11.5345i | 0.397266 | − | 0.546790i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.644497 | + | 1.98356i | 0.0304837 | + | 0.0938190i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.30924 | + | 6.03702i | 0.392137 | + | 0.284904i | 0.766331 | − | 0.642446i | \(-0.222080\pi\) |
−0.374193 | + | 0.927351i | \(0.622080\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.4693 | + | 28.5333i | 0.916775 | + | 1.34358i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.72762 | + | 1.25519i | 0.0811708 | + | 0.0589740i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.59230 | + | 4.90061i | 0.0746483 | + | 0.229744i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.6659 | + | 20.1859i | −0.686041 | + | 0.944254i | −0.999987 | − | 0.00518651i | \(-0.998349\pi\) |
0.313946 | + | 0.949441i | \(0.398349\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.10351 | − | 3.39626i | 0.0515074 | − | 0.158524i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.83030 | + | 8.71077i | −0.131820 | + | 0.405701i | −0.995082 | − | 0.0990557i | \(-0.968418\pi\) |
0.863262 | + | 0.504757i | \(0.168418\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.53349 | − | 0.498261i | 0.0712673 | − | 0.0231561i | −0.273166 | − | 0.961967i | \(-0.588071\pi\) |
0.344434 | + | 0.938811i | \(0.388071\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 0.461237i | − | 0.0213894i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.1091 | − | 16.0632i | 1.02309 | − | 0.743315i | 0.0561720 | − | 0.998421i | \(-0.482110\pi\) |
0.966913 | + | 0.255106i | \(0.0821105\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.04123 | + | 2.20958i | 0.140431 | + | 0.102029i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.08453 | − | 1.51450i | 0.0960499 | − | 0.0697843i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.5364 | + | 33.7715i | 1.12819 | + | 1.55282i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.192774 | − | 0.0626360i | −0.00884506 | − | 0.00287394i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.26940 | + | 0.737373i | −0.103909 | + | 0.0337620i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.84871 | − | 6.67368i | 0.221543 | − | 0.304928i | −0.683749 | − | 0.729717i | \(-0.739652\pi\) |
0.905292 | + | 0.424789i | \(0.139652\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.5421 | − | 3.42533i | −0.480678 | − | 0.156182i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.63853 | 0.0745555 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.23494 | − | 8.58166i | −0.283114 | − | 0.389673i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.59539 | − | 26.4539i | −0.389494 | − | 1.19874i | −0.933167 | − | 0.359443i | \(-0.882967\pi\) |
0.543673 | − | 0.839297i | \(-0.317033\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 2.77427i | − | 0.125457i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.08168 | −0.184204 | −0.0921018 | − | 0.995750i | \(-0.529359\pi\) | ||||
−0.0921018 | + | 0.995750i | \(0.529359\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.88219 | 0.0847694 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 37.0743i | 1.66636i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.135248 | + | 0.416251i | 0.00606671 | + | 0.0186714i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.0488 | + | 31.7240i | 1.03181 | + | 1.42016i | 0.903582 | + | 0.428414i | \(0.140928\pi\) |
0.128224 | + | 0.991745i | \(0.459072\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.26886 | −0.0566883 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.0120 | + | 11.7010i | 1.60570 | + | 0.521723i | 0.968507 | − | 0.248985i | \(-0.0800969\pi\) |
0.637189 | + | 0.770707i | \(0.280097\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.9957 | − | 26.1453i | 0.845296 | − | 1.16345i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.08534 | + | 0.677569i | −0.0926133 | + | 0.0300919i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.7148 | − | 11.2795i | −1.53871 | − | 0.499956i | −0.587688 | − | 0.809088i | \(-0.699962\pi\) |
−0.951019 | + | 0.309132i | \(0.899962\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.22359 | − | 4.43690i | −0.142603 | − | 0.196277i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.512508 | + | 0.372359i | −0.0226278 | + | 0.0164400i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.22963 | − | 5.97917i | −0.362641 | − | 0.263474i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −40.8896 | + | 29.7080i | −1.79832 | + | 1.30656i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.89030i | 0.0829748i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.4368 | + | 5.66557i | −0.763922 | + | 0.248213i | −0.664961 | − | 0.746878i | \(-0.731552\pi\) |
−0.0989608 | + | 0.995091i | \(0.531552\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.59764 | + | 23.3831i | −0.332222 | + | 1.02247i | 0.635853 | + | 0.771811i | \(0.280649\pi\) |
−0.968074 | + | 0.250663i | \(0.919351\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.0421161 | − | 0.129620i | 0.00183810 | − | 0.00565709i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.968401 | − | 1.33289i | 0.0421842 | − | 0.0580616i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.43885 | + | 13.6614i | 0.192993 | + | 0.593973i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.83257 | + | 1.33144i | 0.0795267 | + | 0.0577796i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.4924 | − | 3.94728i | 0.584419 | − | 0.170976i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −33.6829 | − | 24.4721i | −1.45624 | − | 1.05802i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.522556 | − | 1.60826i | −0.0225499 | − | 0.0694016i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.17091 | + | 4.36438i | −0.136581 | + | 0.187987i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.37077 | + | 16.5295i | −0.230907 | + | 0.710660i | 0.766731 | + | 0.641969i | \(0.221882\pi\) |
−0.997638 | + | 0.0686909i | \(0.978118\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.496543 | − | 1.52820i | 0.0213087 | − | 0.0655814i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.6532 | − | 8.01030i | 1.05603 | − | 0.343123i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.75938i | − | 0.0752256i | −0.999292 | − | 0.0376128i | \(-0.988025\pi\) | ||
0.999292 | − | 0.0376128i | \(-0.0119754\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.8427 | − | 8.60423i | 0.505434 | − | 0.367219i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.270128 | − | 0.196259i | −0.0115078 | − | 0.00836092i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.81118 | + | 3.49553i | −0.204592 | + | 0.148645i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.86702 | + | 2.56973i | 0.0792506 | + | 0.109079i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.536030 | − | 0.174167i | −0.0227123 | − | 0.00737967i | 0.297639 | − | 0.954679i | \(-0.403801\pi\) |
−0.320351 | + | 0.947299i | \(0.603801\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.1571 | − | 5.24976i | 0.683372 | − | 0.222041i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.91011 | − | 2.62905i | 0.0806450 | − | 0.110998i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.3769 | + | 11.4946i | 1.49096 | + | 0.484441i | 0.937366 | − | 0.348347i | \(-0.113257\pi\) |
0.553592 | + | 0.832788i | \(0.313257\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 36.1892 | 1.52249 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.91299 | + | 6.76215i | 0.206326 | + | 0.283984i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.46796 | + | 7.59559i | 0.103462 | + | 0.318424i | 0.989366 | − | 0.145444i | \(-0.0464612\pi\) |
−0.885904 | + | 0.463868i | \(0.846461\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.04634i | 0.211183i | 0.994410 | + | 0.105591i | \(0.0336735\pi\) | ||||
−0.994410 | + | 0.105591i | \(0.966326\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.49828 | −0.0625917 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.10793 | 0.129610 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 39.2379i | − | 1.63349i | −0.576996 | − | 0.816747i | \(-0.695775\pi\) | ||
0.576996 | − | 0.816747i | \(-0.304225\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.466010 | + | 1.43423i | 0.0193667 | + | 0.0596047i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.84562 | − | 3.91665i | −0.118056 | − | 0.162490i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.39620 | −0.182072 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.3497 | + | 4.66250i | 0.593287 | + | 0.192771i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.64847 | + | 5.02169i | −0.150589 | + | 0.207267i | −0.877646 | − | 0.479309i | \(-0.840887\pi\) |
0.727058 | + | 0.686576i | \(0.240887\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.277966 | + | 0.0903166i | −0.0114534 | + | 0.00372143i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.64980 | + | 1.51081i | 0.191267 | + | 0.0621464i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.95699 | + | 12.3282i | 0.367820 | + | 0.506260i | 0.952307 | − | 0.305143i | \(-0.0987042\pi\) |
−0.584487 | + | 0.811403i | \(0.698704\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.26700 | − | 3.10016i | 0.174930 | − | 0.127094i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.72643 | + | 1.98087i | 0.111585 | + | 0.0810714i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.28459 | − | 5.29256i | 0.297640 | − | 0.216248i | −0.428935 | − | 0.903335i | \(-0.641111\pi\) |
0.726575 | + | 0.687087i | \(0.241111\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.5966i | 1.85992i | 0.367655 | + | 0.929962i | \(0.380161\pi\) | ||||
−0.367655 | + | 0.929962i | \(0.619839\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.4686 | − | 3.40147i | 0.426316 | − | 0.138518i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.1291 | + | 40.4073i | −0.533775 | + | 1.64279i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.8922 | + | 36.6003i | −0.482688 | + | 1.48556i | 0.352615 | + | 0.935769i | \(0.385293\pi\) |
−0.835302 | + | 0.549791i | \(0.814707\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.131964 | − | 0.181633i | 0.00534744 | − | 0.00736012i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.35626 | + | 19.5625i | 0.257147 | + | 0.791416i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.3274 | + | 8.95636i | 0.497898 | + | 0.361744i | 0.808213 | − | 0.588890i | \(-0.200435\pi\) |
−0.310316 | + | 0.950634i | \(0.600435\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.79277 | − | 1.35747i | −0.152939 | − | 0.0547386i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.9743 | − | 8.69981i | −0.482066 | − | 0.350241i | 0.320059 | − | 0.947398i | \(-0.396297\pi\) |
−0.802125 | + | 0.597156i | \(0.796297\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.4967 | − | 44.6162i | −0.582671 | − | 1.79328i | −0.608429 | − | 0.793608i | \(-0.708200\pi\) |
0.0257586 | − | 0.999668i | \(-0.491800\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.70941 | − | 7.85833i | 0.229111 | − | 0.315344i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.87720 | − | 5.77743i | 0.0752085 | − | 0.231468i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.43113 | + | 25.9483i | −0.337245 | + | 1.03793i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.548272 | + | 0.178144i | −0.0218959 | + | 0.00711440i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.3460i | 0.452394i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.217394 | − | 0.157946i | 0.00865431 | − | 0.00628773i | −0.583450 | − | 0.812149i | \(-0.698297\pi\) |
0.592104 | + | 0.805862i | \(0.298297\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.71777 | + | 1.97457i | 0.108022 | + | 0.0784822i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 30.5091 | − | 22.1662i | 1.21072 | − | 0.879638i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.29047 | + | 1.77618i | 0.0511303 | + | 0.0703748i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.21884 | + | 0.396027i | 0.0482168 | + | 0.0156666i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.7902 | − | 11.9539i | 1.45313 | − | 0.472149i | 0.527164 | − | 0.849764i | \(-0.323255\pi\) |
0.925963 | + | 0.377614i | \(0.123255\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.647437 | + | 0.891121i | −0.0255324 | + | 0.0351424i | −0.821592 | − | 0.570075i | \(-0.806914\pi\) |
0.796060 | + | 0.605218i | \(0.206914\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.62991 | − | 1.50435i | −0.182303 | − | 0.0592337i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.7824 | 0.817042 | 0.408521 | − | 0.912749i | \(-0.366045\pi\) | ||||
0.408521 | + | 0.912749i | \(0.366045\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.45298 | + | 3.37624i | 0.0962879 | + | 0.132529i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0607285 | − | 0.186903i | −0.00238014 | − | 0.00732531i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1.53742i | − | 0.0601637i | −0.999547 | − | 0.0300819i | \(-0.990423\pi\) | ||
0.999547 | − | 0.0300819i | \(-0.00957680\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −34.1003 | −1.33241 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.0589 | −0.626516 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.7164i | 1.58608i | 0.609167 | + | 0.793042i | \(0.291504\pi\) | ||||
−0.609167 | + | 0.793042i | \(0.708496\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.2305 | − | 31.4864i | −0.397922 | − | 1.22468i | −0.926662 | − | 0.375895i | \(-0.877335\pi\) |
0.528740 | − | 0.848784i | \(-0.322665\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.777361 | − | 1.06995i | −0.0301902 | − | 0.0415533i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.935651 | −0.0362830 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.86908 | + | 1.58206i | 0.188532 | + | 0.0612576i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.22455 | − | 4.43821i | 0.124668 | − | 0.171591i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.6491 | − | 8.33390i | 0.990172 | − | 0.321727i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.9855 | + | 4.21925i | 0.500555 | + | 0.162640i | 0.548403 | − | 0.836214i | \(-0.315236\pi\) |
−0.0478475 | + | 0.998855i | \(0.515236\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.474902 | − | 0.653646i | −0.0182790 | − | 0.0251589i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.8643 | + | 28.9631i | −1.53211 | + | 1.11314i | −0.577058 | + | 0.816703i | \(0.695799\pi\) |
−0.955052 | + | 0.296439i | \(0.904201\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.65643 | − | 2.65655i | −0.140321 | − | 0.101949i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.49155 | − | 3.98984i | 0.210437 | − | 0.152891i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.72624i | 0.180844i | 0.995904 | + | 0.0904222i | \(0.0288217\pi\) | ||||
−0.995904 | + | 0.0904222i | \(0.971178\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −46.7651 | + | 15.1949i | −1.78680 | + | 0.580568i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.40897 | − | 4.33637i | 0.0537557 | − | 0.165443i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.552871 | + | 1.70156i | −0.0210627 | + | 0.0648243i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.7958 | − | 42.3868i | 1.17153 | − | 1.61247i | 0.518737 | − | 0.854934i | \(-0.326402\pi\) |
0.652792 | − | 0.757538i | \(-0.273598\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.88136 | + | 15.0233i | 0.185427 | + | 0.570687i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.2632 | − | 9.63625i | −0.503100 | − | 0.365524i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.11029 | − | 11.8860i | −0.307199 | − | 0.450216i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.758921 | − | 0.551389i | −0.0287050 | − | 0.0208554i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.2511 | + | 31.5497i | 0.387180 | + | 1.19162i | 0.934886 | + | 0.354947i | \(0.115501\pi\) |
−0.547707 | + | 0.836671i | \(0.684499\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.18307 | − | 1.62835i | 0.0446203 | − | 0.0614145i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.82142 | − | 5.60577i | 0.0685988 | − | 0.211125i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.25504 | − | 13.0957i | 0.160027 | − | 0.492513i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.95914 | − | 1.93624i | 0.223800 | − | 0.0727171i | −0.194970 | − | 0.980809i | \(-0.562461\pi\) |
0.418771 | + | 0.908092i | \(0.362461\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.4135i | 0.653059i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.62554 | − | 2.63411i | 0.135777 | − | 0.0986481i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.4888 | + | 16.3391i | 0.841034 | + | 0.611047i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.25577 | − | 3.09200i | 0.158935 | − | 0.115473i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.0800 | − | 20.7558i | −0.562387 | − | 0.774060i | 0.429240 | − | 0.903190i | \(-0.358781\pi\) |
−0.991628 | + | 0.129131i | \(0.958781\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.12206 | − | 1.33934i | −0.153514 | − | 0.0498796i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.59800 | − | 0.519223i | 0.0594304 | − | 0.0193101i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.250307 | − | 0.344517i | 0.00929615 | − | 0.0127951i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.5765 | + | 10.5848i | 1.20820 | + | 0.392567i | 0.842770 | − | 0.538274i | \(-0.180923\pi\) |
0.365426 | + | 0.930840i | \(0.380923\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.1970 | 0.859147 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.2211 | − | 14.0681i | −0.378040 | − | 0.520328i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.32088 | − | 13.2983i | −0.159595 | − | 0.491184i | 0.839002 | − | 0.544128i | \(-0.183140\pi\) |
−0.998597 | + | 0.0529440i | \(0.983140\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 0.629128i | − | 0.0232057i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.2795 | 0.747004 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.1333 | −0.961329 | −0.480665 | − | 0.876904i | \(-0.659605\pi\) | ||||
−0.480665 | + | 0.876904i | \(0.659605\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.234614i | 0.00861874i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.40117 | + | 4.31237i | 0.0514041 | + | 0.158206i | 0.973463 | − | 0.228843i | \(-0.0734944\pi\) |
−0.922059 | + | 0.387049i | \(0.873494\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.7336 | + | 14.7736i | 0.393250 | + | 0.541262i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.1759 | −0.518669 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.8711 | − | 5.48176i | −0.616458 | − | 0.200299i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.6864 | + | 27.0961i | −0.718369 | + | 0.988750i | 0.281208 | + | 0.959647i | \(0.409265\pi\) |
−0.999576 | + | 0.0291028i | \(0.990735\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.52635 | + | 0.820862i | −0.0920655 | + | 0.0299139i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.7823 | + | 5.77781i | 0.647164 | + | 0.210276i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.08577 | + | 4.24719i | 0.112154 | + | 0.154367i | 0.861404 | − | 0.507921i | \(-0.169586\pi\) |
−0.749250 | + | 0.662288i | \(0.769586\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.15116 | − | 5.19562i | 0.259571 | − | 0.188589i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.1565 | + | 29.9019i | 1.49192 | + | 1.08394i | 0.973464 | + | 0.228841i | \(0.0734935\pi\) |
0.518457 | + | 0.855104i | \(0.326507\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.93531 | − | 6.49188i | 0.323480 | − | 0.235022i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 15.4439i | − | 0.558376i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.61527 | − | 0.524833i | 0.0583241 | − | 0.0189506i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.61771 | − | 8.05648i | 0.0943970 | − | 0.290524i | −0.892699 | − | 0.450653i | \(-0.851191\pi\) |
0.987096 | + | 0.160129i | \(0.0511911\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.76733 | + | 5.43928i | −0.0636488 | + | 0.195891i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.5562 | + | 26.9168i | −0.703388 | + | 0.968130i | 0.296527 | + | 0.955025i | \(0.404172\pi\) |
−0.999914 | + | 0.0131053i | \(0.995828\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.115189 | − | 0.354514i | −0.00413770 | − | 0.0127345i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.09490 | + | 0.795490i | 0.0392792 | + | 0.0285380i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.0754078 | + | 2.55154i | −0.00270177 | + | 0.0914183i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.91017 | + | 1.38782i | 0.0683513 | + | 0.0496601i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.411280 | − | 1.26579i | −0.0146979 | − | 0.0452356i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.2605 | − | 18.2514i | 0.473286 | − | 0.651422i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.11987 | − | 28.0681i | 0.325088 | − | 1.00052i | −0.646313 | − | 0.763073i | \(-0.723690\pi\) |
0.971401 | − | 0.237446i | \(-0.0763102\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.62673 | + | 5.00657i | −0.0579132 | + | 0.178238i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.6646 | − | 4.76483i | 0.521414 | − | 0.169418i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 10.9756i | − | 0.389756i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.414771 | − | 0.301349i | 0.0147104 | − | 0.0106877i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.2755 | + | 17.6372i | 0.859883 | + | 0.624742i | 0.927853 | − | 0.372946i | \(-0.121652\pi\) |
−0.0679700 | + | 0.997687i | \(0.521652\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.0333 | − | 12.3754i | 0.602594 | − | 0.437810i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.4554 | − | 14.3906i | −0.369423 | − | 0.508467i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −28.1380 | − | 9.14260i | −0.992969 | − | 0.322635i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.6443 | − | 4.43329i | 0.480897 | − | 0.156253i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.976372 | + | 1.34386i | −0.0343699 | + | 0.0473061i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.8633 | + | 13.9271i | 1.50699 | + | 0.489652i | 0.942049 | − | 0.335476i | \(-0.108897\pi\) |
0.564945 | + | 0.825128i | \(0.308897\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.2281 | 0.640075 | 0.320038 | − | 0.947405i | \(-0.396304\pi\) | ||||
0.320038 | + | 0.947405i | \(0.396304\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.39870 | − | 4.67792i | −0.119198 | − | 0.164062i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.50623 | − | 23.1018i | −0.262932 | − | 0.809220i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.08480i | 0.107924i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.42868 | 0.224636 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.4234 | −0.922183 | −0.461091 | − | 0.887353i | \(-0.652542\pi\) | ||||
−0.461091 | + | 0.887353i | \(0.652542\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 21.5393i | − | 0.750814i | −0.926860 | − | 0.375407i | \(-0.877503\pi\) | ||
0.926860 | − | 0.375407i | \(-0.122497\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.227203 | − | 0.699259i | −0.00791019 | − | 0.0243451i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.0711 | − | 22.1199i | −0.558845 | − | 0.769185i | 0.432334 | − | 0.901714i | \(-0.357690\pi\) |
−0.991179 | + | 0.132529i | \(0.957690\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −53.6232 | −1.86241 | −0.931205 | − | 0.364497i | \(-0.881241\pi\) | ||||
−0.931205 | + | 0.364497i | \(0.881241\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.12073 | + | 2.31366i | 0.247015 | + | 0.0802601i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.32090 | − | 1.81806i | 0.0457664 | − | 0.0629921i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.5660 | + | 3.43309i | −0.365650 | + | 0.118807i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.10799 | − | 0.360007i | −0.0382977 | − | 0.0124437i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.92670 | + | 5.40464i | 0.135565 | + | 0.186589i | 0.871402 | − | 0.490569i | \(-0.163211\pi\) |
−0.735837 | + | 0.677158i | \(0.763211\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.8940 | + | 16.6334i | −0.789447 | + | 0.573567i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.18003 | + | 4.49006i | 0.212852 | + | 0.154646i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.5317 | + | 11.2844i | −0.534306 | + | 0.388196i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.1025i | 0.622010i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.53424 | + | 1.14834i | −0.121295 | + | 0.0394110i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.53680 | + | 29.3513i | −0.326917 | + | 1.00615i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.49219 | − | 7.67017i | 0.0853309 | − | 0.262622i | −0.899282 | − | 0.437368i | \(-0.855911\pi\) |
0.984613 | + | 0.174747i | \(0.0559106\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.61037 | + | 2.21648i | −0.0550735 | + | 0.0758021i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.53976 | − | 4.73888i | −0.0525971 | − | 0.161877i | 0.921308 | − | 0.388834i | \(-0.127122\pi\) |
−0.973905 | + | 0.226957i | \(0.927122\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.6824 | − | 18.6594i | −0.876273 | − | 0.636650i | 0.0559899 | − | 0.998431i | \(-0.482169\pi\) |
−0.932263 | + | 0.361782i | \(0.882169\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.71564 | − | 0.0507039i | −0.0584689 | − | 0.00172798i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.2296 | − | 26.3223i | −1.23327 | − | 0.896022i | −0.236138 | − | 0.971719i | \(-0.575882\pi\) |
−0.997131 | + | 0.0756970i | \(0.975882\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.11449 | + | 15.7408i | 0.173898 | + | 0.535203i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.88281 | − | 2.59147i | 0.0639436 | − | 0.0880109i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.91384 | + | 30.5117i | −0.336304 | + | 1.03504i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.55037 | − | 7.84922i | 0.0864159 | − | 0.265961i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.5863 | + | 4.08954i | −0.425982 | + | 0.138410i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.5417i | 0.356375i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.5352 | + | 22.9117i | −1.06487 | + | 0.773672i | −0.974983 | − | 0.222280i | \(-0.928650\pi\) |
−0.0898856 | + | 0.995952i | \(0.528650\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.17160 | + | 1.57776i | 0.0732464 | + | 0.0532166i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.55257 | − | 1.85455i | 0.0859982 | − | 0.0624813i | −0.543955 | − | 0.839114i | \(-0.683074\pi\) |
0.629954 | + | 0.776633i | \(0.283074\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.22050 | − | 4.43263i | −0.108378 | − | 0.149170i | 0.751382 | − | 0.659867i | \(-0.229387\pi\) |
−0.859761 | + | 0.510697i | \(0.829387\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.462866 | − | 0.150394i | −0.0155591 | − | 0.00505545i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.0956 | + | 7.50420i | −0.775473 | + | 0.251966i | −0.669906 | − | 0.742446i | \(-0.733666\pi\) |
−0.105567 | + | 0.994412i | \(0.533666\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.44444 | − | 12.9992i | 0.316756 | − | 0.435978i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 42.8844 | + | 13.9340i | 1.43668 | + | 0.466806i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.73499 | −0.124987 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.70280 | − | 11.9784i | −0.290902 | − | 0.400393i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.11164 | − | 3.42128i | −0.0371167 | − | 0.114233i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 0.614041i | − | 0.0204794i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.83131 | 0.0610099 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.07421 | −0.0690253 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 14.0690i | − | 0.467671i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.1219 | − | 31.1520i | −0.336092 | − | 1.03439i | −0.966181 | − | 0.257863i | \(-0.916982\pi\) |
0.630089 | − | 0.776523i | \(-0.283018\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −23.6992 | − | 32.6191i | −0.786051 | − | 1.08191i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.8127 | −0.656423 | −0.328212 | − | 0.944604i | \(-0.606446\pi\) | ||||
−0.328212 | + | 0.944604i | \(0.606446\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.8387 | − | 8.07059i | −0.822042 | − | 0.267098i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.84866 | + | 2.54447i | −0.0611149 | + | 0.0841175i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.8182 | + | 4.48979i | −0.456316 | + | 0.148266i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.2724 | − | 3.98755i | −0.404829 | − | 0.131537i | 0.0995225 | − | 0.995035i | \(-0.468268\pi\) |
−0.504352 | + | 0.863498i | \(0.668268\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.15193 | + | 1.58550i | 0.0379574 | + | 0.0522439i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.777385 | − | 0.564803i | 0.0255879 | − | 0.0185907i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.07678 | + | 1.50887i | 0.0682842 | + | 0.0496114i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.2674 | + | 7.45967i | −0.337224 | + | 0.245008i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 3.88667i | − | 0.127518i | −0.997965 | − | 0.0637588i | \(-0.979691\pi\) | ||
0.997965 | − | 0.0637588i | \(-0.0203088\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.379146 | + | 0.123192i | −0.0124260 | + | 0.00403745i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.27661 | + | 7.00668i | −0.0745328 | + | 0.229388i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.79251 | − | 27.0606i | 0.287546 | − | 0.884975i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.55430 | − | 13.1504i | 0.312125 | − | 0.429604i | −0.623917 | − | 0.781490i | \(-0.714460\pi\) |
0.936043 | + | 0.351887i | \(0.114460\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.248472 | + | 0.764718i | 0.00810858 | + | 0.0249556i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.7230 | + | 15.7827i | 0.708148 | + | 0.514500i | 0.882576 | − | 0.470170i | \(-0.155807\pi\) |
−0.174428 | + | 0.984670i | \(0.555807\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.9900 | − | 37.5654i | −0.357884 | − | 1.22330i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.01728 | − | 2.19218i | −0.0981521 | − | 0.0713117i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.38642 | − | 25.8108i | −0.272522 | − | 0.838737i | −0.989864 | − | 0.142016i | \(-0.954642\pi\) |
0.717342 | − | 0.696721i | \(-0.245358\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.07733 | + | 9.74111i | −0.229740 | + | 0.316210i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.487733 | + | 1.50109i | −0.0158158 | + | 0.0486761i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.53445 | − | 10.8779i | 0.114492 | − | 0.352371i | −0.877349 | − | 0.479854i | \(-0.840690\pi\) |
0.991841 | + | 0.127483i | \(0.0406898\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.4764 | + | 4.05384i | −0.403728 | + | 0.131179i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 1.21116i | − | 0.0391512i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.9496 | + | 12.3146i | −0.547331 | + | 0.397659i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.6447 | + | 17.9054i | 0.794990 | + | 0.577594i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −42.0231 | + | 30.5316i | −1.35418 | + | 0.983867i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.76108 | + | 10.6822i | 0.249838 | + | 0.343872i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.2769 | − | 13.4117i | −1.32737 | − | 0.431290i | −0.442353 | − | 0.896841i | \(-0.645856\pi\) |
−0.885021 | + | 0.465551i | \(0.845856\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.228392 | − | 0.0742091i | 0.00733701 | − | 0.00238394i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.49435 | − | 3.43318i | 0.0800474 | − | 0.110176i | −0.767116 | − | 0.641509i | \(-0.778309\pi\) |
0.847163 | + | 0.531333i | \(0.178309\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.64326 | − | 2.15853i | −0.212973 | − | 0.0691992i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.299223 | −0.00958281 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.23046 | + | 8.57549i | 0.199330 | + | 0.274354i | 0.896967 | − | 0.442097i | \(-0.145765\pi\) |
−0.697637 | + | 0.716451i | \(0.745765\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.1269 | − | 31.1674i | −0.323657 | − | 0.996114i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 32.3403i | − | 1.03255i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.0887 | 0.672626 | 0.336313 | − | 0.941750i | \(-0.390820\pi\) | ||||
0.336313 | + | 0.941750i | \(0.390820\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 42.8073 | 1.36395 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 2.51139i | − | 0.0799385i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.6164 | − | 44.9845i | −0.464773 | − | 1.43042i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.5328 | + | 40.6484i | 0.938140 | + | 1.29124i | 0.956599 | + | 0.291409i | \(0.0941240\pi\) |
−0.0184590 | + | 0.999830i | \(0.505876\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.34290 | 0.201286 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.0629 | + | 9.11819i | 0.889654 | + | 0.289066i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.5644 | + | 15.9170i | −0.366248 | + | 0.504097i | −0.951876 | − | 0.306483i | \(-0.900848\pi\) |
0.585628 | + | 0.810580i | \(0.300848\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.63029 | − | 2.47923i | 0.241412 | − | 0.0784394i |
(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 | 1148.2.ba.a.113.10 | ✓ | 80 | |
41.4 | even | 10 | inner | 1148.2.ba.a.701.11 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.ba.a.113.10 | ✓ | 80 | 1.1 | even | 1 | trivial | |
1148.2.ba.a.701.11 | yes | 80 | 41.4 | even | 10 | inner |