Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(43,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.l (of order \(4\), degree \(2\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.1 | ||
Character | \(\chi\) | \(=\) | 1110.43 |
Dual form | 1110.2.l.a.697.1 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.51129 | − | 1.64803i | −0.675869 | − | 0.737022i | ||||
\(6\) | −0.707107 | − | 0.707107i | −0.288675 | − | 0.288675i | ||||
\(7\) | 2.75974 | − | 2.75974i | 1.04308 | − | 1.04308i | 0.0440528 | − | 0.999029i | \(-0.485973\pi\) |
0.999029 | − | 0.0440528i | \(-0.0140270\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 1.64803 | − | 1.51129i | 0.521153 | − | 0.477912i | ||||
\(11\) | − | 0.350472i | − | 0.105671i | −0.998603 | − | 0.0528356i | \(-0.983174\pi\) | ||
0.998603 | − | 0.0528356i | \(-0.0168259\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | 3.27075i | 0.907143i | 0.891220 | + | 0.453572i | \(0.149850\pi\) | ||||
−0.891220 | + | 0.453572i | \(0.850150\pi\) | |||||||
\(14\) | 2.75974 | + | 2.75974i | 0.737570 | + | 0.737570i | ||||
\(15\) | 2.23398 | + | 0.0966903i | 0.576810 | + | 0.0249653i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.07368 | −1.71562 | −0.857810 | − | 0.513967i | \(-0.828176\pi\) | ||||
−0.857810 | + | 0.513967i | \(0.828176\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −2.01227 | + | 2.01227i | −0.461647 | + | 0.461647i | −0.899195 | − | 0.437548i | \(-0.855847\pi\) |
0.437548 | + | 0.899195i | \(0.355847\pi\) | |||||||
\(20\) | 1.51129 | + | 1.64803i | 0.337935 | + | 0.368511i | ||||
\(21\) | 3.90286i | 0.851673i | ||||||||
\(22\) | 0.350472 | 0.0747209 | ||||||||
\(23\) | − | 1.24836i | − | 0.260301i | −0.991494 | − | 0.130150i | \(-0.958454\pi\) | ||
0.991494 | − | 0.130150i | \(-0.0415460\pi\) | |||||||
\(24\) | 0.707107 | + | 0.707107i | 0.144338 | + | 0.144338i | ||||
\(25\) | −0.432008 | + | 4.98130i | −0.0864015 | + | 0.996260i | ||||
\(26\) | −3.27075 | −0.641447 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | −2.75974 | + | 2.75974i | −0.521541 | + | 0.521541i | ||||
\(29\) | −6.14644 | − | 6.14644i | −1.14137 | − | 1.14137i | −0.988201 | − | 0.153165i | \(-0.951053\pi\) |
−0.153165 | − | 0.988201i | \(-0.548947\pi\) | |||||||
\(30\) | −0.0966903 | + | 2.23398i | −0.0176532 | + | 0.407866i | ||||
\(31\) | −2.76854 | + | 2.76854i | −0.497244 | + | 0.497244i | −0.910579 | − | 0.413335i | \(-0.864364\pi\) |
0.413335 | + | 0.910579i | \(0.364364\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0.247821 | + | 0.247821i | 0.0431401 | + | 0.0431401i | ||||
\(34\) | − | 7.07368i | − | 1.21313i | ||||||
\(35\) | −8.71889 | − | 0.377368i | −1.47376 | − | 0.0637869i | ||||
\(36\) | 1.00000i | 0.166667i | ||||||||
\(37\) | −4.91116 | + | 3.58895i | −0.807389 | + | 0.590019i | ||||
\(38\) | −2.01227 | − | 2.01227i | −0.326433 | − | 0.326433i | ||||
\(39\) | −2.31277 | − | 2.31277i | −0.370340 | − | 0.370340i | ||||
\(40\) | −1.64803 | + | 1.51129i | −0.260576 | + | 0.238956i | ||||
\(41\) | 5.57830i | 0.871185i | 0.900144 | + | 0.435592i | \(0.143461\pi\) | ||||
−0.900144 | + | 0.435592i | \(0.856539\pi\) | |||||||
\(42\) | −3.90286 | −0.602224 | ||||||||
\(43\) | 3.23195i | 0.492868i | 0.969160 | + | 0.246434i | \(0.0792588\pi\) | ||||
−0.969160 | + | 0.246434i | \(0.920741\pi\) | |||||||
\(44\) | 0.350472i | 0.0528356i | ||||||||
\(45\) | −1.64803 | + | 1.51129i | −0.245674 | + | 0.225290i | ||||
\(46\) | 1.24836 | 0.184060 | ||||||||
\(47\) | 5.76291 | − | 5.76291i | 0.840606 | − | 0.840606i | −0.148331 | − | 0.988938i | \(-0.547390\pi\) |
0.988938 | + | 0.148331i | \(0.0473902\pi\) | |||||||
\(48\) | −0.707107 | + | 0.707107i | −0.102062 | + | 0.102062i | ||||
\(49\) | − | 8.23228i | − | 1.17604i | ||||||
\(50\) | −4.98130 | − | 0.432008i | −0.704462 | − | 0.0610951i | ||||
\(51\) | 5.00185 | − | 5.00185i | 0.700399 | − | 0.700399i | ||||
\(52\) | − | 3.27075i | − | 0.453572i | ||||||
\(53\) | −3.45760 | − | 3.45760i | −0.474938 | − | 0.474938i | 0.428571 | − | 0.903508i | \(-0.359017\pi\) |
−0.903508 | + | 0.428571i | \(0.859017\pi\) | |||||||
\(54\) | −0.707107 | + | 0.707107i | −0.0962250 | + | 0.0962250i | ||||
\(55\) | −0.577588 | + | 0.529665i | −0.0778820 | + | 0.0714200i | ||||
\(56\) | −2.75974 | − | 2.75974i | −0.368785 | − | 0.368785i | ||||
\(57\) | − | 2.84578i | − | 0.376933i | ||||||
\(58\) | 6.14644 | − | 6.14644i | 0.807068 | − | 0.807068i | ||||
\(59\) | −10.6205 | + | 10.6205i | −1.38267 | + | 1.38267i | −0.542832 | + | 0.839841i | \(0.682648\pi\) |
−0.839841 | + | 0.542832i | \(0.817352\pi\) | |||||||
\(60\) | −2.23398 | − | 0.0966903i | −0.288405 | − | 0.0124827i | ||||
\(61\) | 1.30384 | − | 1.30384i | 0.166940 | − | 0.166940i | −0.618693 | − | 0.785633i | \(-0.712338\pi\) |
0.785633 | + | 0.618693i | \(0.212338\pi\) | |||||||
\(62\) | −2.76854 | − | 2.76854i | −0.351605 | − | 0.351605i | ||||
\(63\) | −2.75974 | − | 2.75974i | −0.347694 | − | 0.347694i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 5.39030 | − | 4.94305i | 0.668584 | − | 0.613110i | ||||
\(66\) | −0.247821 | + | 0.247821i | −0.0305047 | + | 0.0305047i | ||||
\(67\) | −10.6169 | − | 10.6169i | −1.29707 | − | 1.29707i | −0.930322 | − | 0.366744i | \(-0.880473\pi\) |
−0.366744 | − | 0.930322i | \(-0.619527\pi\) | |||||||
\(68\) | 7.07368 | 0.857810 | ||||||||
\(69\) | 0.882722 | + | 0.882722i | 0.106267 | + | 0.106267i | ||||
\(70\) | 0.377368 | − | 8.71889i | 0.0451041 | − | 1.04211i | ||||
\(71\) | 15.8980 | 1.88675 | 0.943373 | − | 0.331733i | \(-0.107633\pi\) | ||||
0.943373 | + | 0.331733i | \(0.107633\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −0.998067 | + | 0.998067i | −0.116815 | + | 0.116815i | −0.763098 | − | 0.646283i | \(-0.776323\pi\) |
0.646283 | + | 0.763098i | \(0.276323\pi\) | |||||||
\(74\) | −3.58895 | − | 4.91116i | −0.417207 | − | 0.570910i | ||||
\(75\) | −3.21684 | − | 3.82779i | −0.371448 | − | 0.441995i | ||||
\(76\) | 2.01227 | − | 2.01227i | 0.230823 | − | 0.230823i | ||||
\(77\) | −0.967210 | − | 0.967210i | −0.110224 | − | 0.110224i | ||||
\(78\) | 2.31277 | − | 2.31277i | 0.261870 | − | 0.261870i | ||||
\(79\) | −2.47200 | + | 2.47200i | −0.278122 | + | 0.278122i | −0.832359 | − | 0.554237i | \(-0.813010\pi\) |
0.554237 | + | 0.832359i | \(0.313010\pi\) | |||||||
\(80\) | −1.51129 | − | 1.64803i | −0.168967 | − | 0.184255i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −5.57830 | −0.616020 | ||||||||
\(83\) | −10.6094 | − | 10.6094i | −1.16454 | − | 1.16454i | −0.983471 | − | 0.181065i | \(-0.942046\pi\) |
−0.181065 | − | 0.983471i | \(-0.557954\pi\) | |||||||
\(84\) | − | 3.90286i | − | 0.425836i | ||||||
\(85\) | 10.6904 | + | 11.6576i | 1.15954 | + | 1.26445i | ||||
\(86\) | −3.23195 | −0.348510 | ||||||||
\(87\) | 8.69238 | 0.931921 | ||||||||
\(88\) | −0.350472 | −0.0373604 | ||||||||
\(89\) | −3.03601 | − | 3.03601i | −0.321816 | − | 0.321816i | 0.527647 | − | 0.849464i | \(-0.323074\pi\) |
−0.849464 | + | 0.527647i | \(0.823074\pi\) | |||||||
\(90\) | −1.51129 | − | 1.64803i | −0.159304 | − | 0.173718i | ||||
\(91\) | 9.02641 | + | 9.02641i | 0.946225 | + | 0.946225i | ||||
\(92\) | 1.24836i | 0.130150i | ||||||||
\(93\) | − | 3.91530i | − | 0.405998i | ||||||
\(94\) | 5.76291 | + | 5.76291i | 0.594398 | + | 0.594398i | ||||
\(95\) | 6.35741 | + | 0.275159i | 0.652256 | + | 0.0282308i | ||||
\(96\) | −0.707107 | − | 0.707107i | −0.0721688 | − | 0.0721688i | ||||
\(97\) | 7.94277 | 0.806466 | 0.403233 | − | 0.915097i | \(-0.367886\pi\) | ||||
0.403233 | + | 0.915097i | \(0.367886\pi\) | |||||||
\(98\) | 8.23228 | 0.831586 | ||||||||
\(99\) | −0.350472 | −0.0352238 | ||||||||
\(100\) | 0.432008 | − | 4.98130i | 0.0432008 | − | 0.498130i | ||||
\(101\) | 0.514124i | 0.0511573i | 0.999673 | + | 0.0255786i | \(0.00814282\pi\) | ||||
−0.999673 | + | 0.0255786i | \(0.991857\pi\) | |||||||
\(102\) | 5.00185 | + | 5.00185i | 0.495257 | + | 0.495257i | ||||
\(103\) | −9.07861 | −0.894542 | −0.447271 | − | 0.894398i | \(-0.647604\pi\) | ||||
−0.447271 | + | 0.894398i | \(0.647604\pi\) | |||||||
\(104\) | 3.27075 | 0.320724 | ||||||||
\(105\) | 6.43202 | − | 5.89834i | 0.627701 | − | 0.575620i | ||||
\(106\) | 3.45760 | − | 3.45760i | 0.335832 | − | 0.335832i | ||||
\(107\) | 1.33354 | − | 1.33354i | 0.128919 | − | 0.128919i | −0.639703 | − | 0.768622i | \(-0.720943\pi\) |
0.768622 | + | 0.639703i | \(0.220943\pi\) | |||||||
\(108\) | −0.707107 | − | 0.707107i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | 2.30925 | − | 2.30925i | 0.221186 | − | 0.221186i | −0.587812 | − | 0.808998i | \(-0.700010\pi\) |
0.808998 | + | 0.587812i | \(0.200010\pi\) | |||||||
\(110\) | −0.529665 | − | 0.577588i | −0.0505015 | − | 0.0550709i | ||||
\(111\) | 0.934944 | − | 6.01048i | 0.0887410 | − | 0.570490i | ||||
\(112\) | 2.75974 | − | 2.75974i | 0.260770 | − | 0.260770i | ||||
\(113\) | −7.85255 | −0.738705 | −0.369353 | − | 0.929289i | \(-0.620421\pi\) | ||||
−0.369353 | + | 0.929289i | \(0.620421\pi\) | |||||||
\(114\) | 2.84578 | 0.266532 | ||||||||
\(115\) | −2.05733 | + | 1.88663i | −0.191847 | + | 0.175929i | ||||
\(116\) | 6.14644 | + | 6.14644i | 0.570683 | + | 0.570683i | ||||
\(117\) | 3.27075 | 0.302381 | ||||||||
\(118\) | −10.6205 | − | 10.6205i | −0.977698 | − | 0.977698i | ||||
\(119\) | −19.5215 | + | 19.5215i | −1.78953 | + | 1.78953i | ||||
\(120\) | 0.0966903 | − | 2.23398i | 0.00882658 | − | 0.203933i | ||||
\(121\) | 10.8772 | 0.988834 | ||||||||
\(122\) | 1.30384 | + | 1.30384i | 0.118044 | + | 0.118044i | ||||
\(123\) | −3.94446 | − | 3.94446i | −0.355660 | − | 0.355660i | ||||
\(124\) | 2.76854 | − | 2.76854i | 0.248622 | − | 0.248622i | ||||
\(125\) | 8.86223 | − | 6.81623i | 0.792662 | − | 0.609662i | ||||
\(126\) | 2.75974 | − | 2.75974i | 0.245857 | − | 0.245857i | ||||
\(127\) | −14.6420 | + | 14.6420i | −1.29927 | + | 1.29927i | −0.370388 | + | 0.928877i | \(0.620775\pi\) |
−0.928877 | + | 0.370388i | \(0.879225\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −2.28533 | − | 2.28533i | −0.201212 | − | 0.201212i | ||||
\(130\) | 4.94305 | + | 5.39030i | 0.433534 | + | 0.472760i | ||||
\(131\) | −3.62929 | + | 3.62929i | −0.317093 | + | 0.317093i | −0.847649 | − | 0.530557i | \(-0.821983\pi\) |
0.530557 | + | 0.847649i | \(0.321983\pi\) | |||||||
\(132\) | −0.247821 | − | 0.247821i | −0.0215701 | − | 0.0215701i | ||||
\(133\) | 11.1067i | 0.963070i | ||||||||
\(134\) | 10.6169 | − | 10.6169i | 0.917164 | − | 0.917164i | ||||
\(135\) | 0.0966903 | − | 2.23398i | 0.00832178 | − | 0.192270i | ||||
\(136\) | 7.07368i | 0.606563i | ||||||||
\(137\) | −12.5315 | + | 12.5315i | −1.07064 | + | 1.07064i | −0.0733326 | + | 0.997308i | \(0.523363\pi\) |
−0.997308 | + | 0.0733326i | \(0.976637\pi\) | |||||||
\(138\) | −0.882722 | + | 0.882722i | −0.0751423 | + | 0.0751423i | ||||
\(139\) | −3.66631 | −0.310972 | −0.155486 | − | 0.987838i | \(-0.549694\pi\) | ||||
−0.155486 | + | 0.987838i | \(0.549694\pi\) | |||||||
\(140\) | 8.71889 | + | 0.377368i | 0.736880 | + | 0.0318934i | ||||
\(141\) | 8.14998i | 0.686352i | ||||||||
\(142\) | 15.8980i | 1.33413i | ||||||||
\(143\) | 1.14631 | 0.0958590 | ||||||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | −0.840469 | + | 19.4186i | −0.0697972 | + | 1.61263i | ||||
\(146\) | −0.998067 | − | 0.998067i | −0.0826007 | − | 0.0826007i | ||||
\(147\) | 5.82110 | + | 5.82110i | 0.480116 | + | 0.480116i | ||||
\(148\) | 4.91116 | − | 3.58895i | 0.403695 | − | 0.295010i | ||||
\(149\) | − | 16.9433i | − | 1.38805i | −0.719951 | − | 0.694025i | \(-0.755836\pi\) | ||
0.719951 | − | 0.694025i | \(-0.244164\pi\) | |||||||
\(150\) | 3.82779 | − | 3.21684i | 0.312538 | − | 0.262654i | ||||
\(151\) | − | 10.7953i | − | 0.878510i | −0.898362 | − | 0.439255i | \(-0.855242\pi\) | ||
0.898362 | − | 0.439255i | \(-0.144758\pi\) | |||||||
\(152\) | 2.01227 | + | 2.01227i | 0.163217 | + | 0.163217i | ||||
\(153\) | 7.07368i | 0.571873i | ||||||||
\(154\) | 0.967210 | − | 0.967210i | 0.0779400 | − | 0.0779400i | ||||
\(155\) | 8.74670 | + | 0.378572i | 0.702552 | + | 0.0304076i | ||||
\(156\) | 2.31277 | + | 2.31277i | 0.185170 | + | 0.185170i | ||||
\(157\) | 6.59408 | − | 6.59408i | 0.526265 | − | 0.526265i | −0.393192 | − | 0.919457i | \(-0.628629\pi\) |
0.919457 | + | 0.393192i | \(0.128629\pi\) | |||||||
\(158\) | −2.47200 | − | 2.47200i | −0.196662 | − | 0.196662i | ||||
\(159\) | 4.88978 | 0.387785 | ||||||||
\(160\) | 1.64803 | − | 1.51129i | 0.130288 | − | 0.119478i | ||||
\(161\) | −3.44514 | − | 3.44514i | −0.271515 | − | 0.271515i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −7.00131 | −0.548385 | −0.274193 | − | 0.961675i | \(-0.588411\pi\) | ||||
−0.274193 | + | 0.961675i | \(0.588411\pi\) | |||||||
\(164\) | − | 5.57830i | − | 0.435592i | ||||||
\(165\) | 0.0338872 | − | 0.782946i | 0.00263812 | − | 0.0609523i | ||||
\(166\) | 10.6094 | − | 10.6094i | 0.823451 | − | 0.823451i | ||||
\(167\) | −14.7018 | −1.13766 | −0.568830 | − | 0.822455i | \(-0.692604\pi\) | ||||
−0.568830 | + | 0.822455i | \(0.692604\pi\) | |||||||
\(168\) | 3.90286 | 0.301112 | ||||||||
\(169\) | 2.30219 | 0.177091 | ||||||||
\(170\) | −11.6576 | + | 10.6904i | −0.894101 | + | 0.819915i | ||||
\(171\) | 2.01227 | + | 2.01227i | 0.153882 | + | 0.153882i | ||||
\(172\) | − | 3.23195i | − | 0.246434i | ||||||
\(173\) | −3.00005 | + | 3.00005i | −0.228090 | + | 0.228090i | −0.811894 | − | 0.583805i | \(-0.801563\pi\) |
0.583805 | + | 0.811894i | \(0.301563\pi\) | |||||||
\(174\) | 8.69238i | 0.658968i | ||||||||
\(175\) | 12.5548 | + | 14.9393i | 0.949057 | + | 1.12931i | ||||
\(176\) | − | 0.350472i | − | 0.0264178i | ||||||
\(177\) | − | 15.0197i | − | 1.12895i | ||||||
\(178\) | 3.03601 | − | 3.03601i | 0.227559 | − | 0.227559i | ||||
\(179\) | 9.62402 | + | 9.62402i | 0.719333 | + | 0.719333i | 0.968469 | − | 0.249136i | \(-0.0801466\pi\) |
−0.249136 | + | 0.968469i | \(0.580147\pi\) | |||||||
\(180\) | 1.64803 | − | 1.51129i | 0.122837 | − | 0.112645i | ||||
\(181\) | 14.0878 | 1.04713 | 0.523567 | − | 0.851984i | \(-0.324601\pi\) | ||||
0.523567 | + | 0.851984i | \(0.324601\pi\) | |||||||
\(182\) | −9.02641 | + | 9.02641i | −0.669082 | + | 0.669082i | ||||
\(183\) | 1.84391i | 0.136306i | ||||||||
\(184\) | −1.24836 | −0.0920302 | ||||||||
\(185\) | 13.3369 | + | 2.66980i | 0.980546 | + | 0.196288i | ||||
\(186\) | 3.91530 | 0.287084 | ||||||||
\(187\) | 2.47913i | 0.181292i | ||||||||
\(188\) | −5.76291 | + | 5.76291i | −0.420303 | + | 0.420303i | ||||
\(189\) | 3.90286 | 0.283891 | ||||||||
\(190\) | −0.275159 | + | 6.35741i | −0.0199622 | + | 0.461215i | ||||
\(191\) | 2.11691 | + | 2.11691i | 0.153174 | + | 0.153174i | 0.779534 | − | 0.626360i | \(-0.215456\pi\) |
−0.626360 | + | 0.779534i | \(0.715456\pi\) | |||||||
\(192\) | 0.707107 | − | 0.707107i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | − | 20.7874i | − | 1.49631i | −0.663525 | − | 0.748154i | \(-0.730940\pi\) | ||
0.663525 | − | 0.748154i | \(-0.269060\pi\) | |||||||
\(194\) | 7.94277i | 0.570257i | ||||||||
\(195\) | −0.316250 | + | 7.30678i | −0.0226471 | + | 0.523249i | ||||
\(196\) | 8.23228i | 0.588020i | ||||||||
\(197\) | −11.8547 | + | 11.8547i | −0.844614 | + | 0.844614i | −0.989455 | − | 0.144841i | \(-0.953733\pi\) |
0.144841 | + | 0.989455i | \(0.453733\pi\) | |||||||
\(198\) | − | 0.350472i | − | 0.0249070i | ||||||
\(199\) | 6.76638 | + | 6.76638i | 0.479656 | + | 0.479656i | 0.905022 | − | 0.425366i | \(-0.139854\pi\) |
−0.425366 | + | 0.905022i | \(0.639854\pi\) | |||||||
\(200\) | 4.98130 | + | 0.432008i | 0.352231 | + | 0.0305476i | ||||
\(201\) | 15.0146 | 1.05905 | ||||||||
\(202\) | −0.514124 | −0.0361737 | ||||||||
\(203\) | −33.9251 | −2.38108 | ||||||||
\(204\) | −5.00185 | + | 5.00185i | −0.350200 | + | 0.350200i | ||||
\(205\) | 9.19321 | − | 8.43043i | 0.642082 | − | 0.588807i | ||||
\(206\) | − | 9.07861i | − | 0.632537i | ||||||
\(207\) | −1.24836 | −0.0867669 | ||||||||
\(208\) | 3.27075i | 0.226786i | ||||||||
\(209\) | 0.705244 | + | 0.705244i | 0.0487828 | + | 0.0487828i | ||||
\(210\) | 5.89834 | + | 6.43202i | 0.407024 | + | 0.443852i | ||||
\(211\) | −9.92928 | −0.683560 | −0.341780 | − | 0.939780i | \(-0.611030\pi\) | ||||
−0.341780 | + | 0.939780i | \(0.611030\pi\) | |||||||
\(212\) | 3.45760 | + | 3.45760i | 0.237469 | + | 0.237469i | ||||
\(213\) | −11.2416 | + | 11.2416i | −0.770261 | + | 0.770261i | ||||
\(214\) | 1.33354 | + | 1.33354i | 0.0911592 | + | 0.0911592i | ||||
\(215\) | 5.32635 | − | 4.88441i | 0.363254 | − | 0.333114i | ||||
\(216\) | 0.707107 | − | 0.707107i | 0.0481125 | − | 0.0481125i | ||||
\(217\) | 15.2809i | 1.03733i | ||||||||
\(218\) | 2.30925 | + | 2.30925i | 0.156402 | + | 0.156402i | ||||
\(219\) | − | 1.41148i | − | 0.0953790i | ||||||
\(220\) | 0.577588 | − | 0.529665i | 0.0389410 | − | 0.0357100i | ||||
\(221\) | − | 23.1363i | − | 1.55631i | ||||||
\(222\) | 6.01048 | + | 0.934944i | 0.403397 | + | 0.0627494i | ||||
\(223\) | −6.49659 | − | 6.49659i | −0.435044 | − | 0.435044i | 0.455296 | − | 0.890340i | \(-0.349533\pi\) |
−0.890340 | + | 0.455296i | \(0.849533\pi\) | |||||||
\(224\) | 2.75974 | + | 2.75974i | 0.184393 | + | 0.184393i | ||||
\(225\) | 4.98130 | + | 0.432008i | 0.332087 | + | 0.0288005i | ||||
\(226\) | − | 7.85255i | − | 0.522344i | ||||||
\(227\) | −16.6142 | −1.10273 | −0.551363 | − | 0.834265i | \(-0.685892\pi\) | ||||
−0.551363 | + | 0.834265i | \(0.685892\pi\) | |||||||
\(228\) | 2.84578i | 0.188466i | ||||||||
\(229\) | − | 2.86631i | − | 0.189411i | −0.995505 | − | 0.0947056i | \(-0.969809\pi\) | ||
0.995505 | − | 0.0947056i | \(-0.0301910\pi\) | |||||||
\(230\) | −1.88663 | − | 2.05733i | −0.124401 | − | 0.135656i | ||||
\(231\) | 1.36784 | 0.0899974 | ||||||||
\(232\) | −6.14644 | + | 6.14644i | −0.403534 | + | 0.403534i | ||||
\(233\) | 8.37425 | − | 8.37425i | 0.548615 | − | 0.548615i | −0.377425 | − | 0.926040i | \(-0.623190\pi\) |
0.926040 | + | 0.377425i | \(0.123190\pi\) | |||||||
\(234\) | 3.27075i | 0.213816i | ||||||||
\(235\) | −18.2069 | − | 0.788024i | −1.18769 | − | 0.0514050i | ||||
\(236\) | 10.6205 | − | 10.6205i | 0.691337 | − | 0.691337i | ||||
\(237\) | − | 3.49594i | − | 0.227085i | ||||||
\(238\) | −19.5215 | − | 19.5215i | −1.26539 | − | 1.26539i | ||||
\(239\) | 16.9584 | − | 16.9584i | 1.09695 | − | 1.09695i | 0.102185 | − | 0.994765i | \(-0.467417\pi\) |
0.994765 | − | 0.102185i | \(-0.0325834\pi\) | |||||||
\(240\) | 2.23398 | + | 0.0966903i | 0.144203 | + | 0.00624133i | ||||
\(241\) | 9.32818 | + | 9.32818i | 0.600881 | + | 0.600881i | 0.940546 | − | 0.339665i | \(-0.110314\pi\) |
−0.339665 | + | 0.940546i | \(0.610314\pi\) | |||||||
\(242\) | 10.8772i | 0.699211i | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −1.30384 | + | 1.30384i | −0.0834698 | + | 0.0834698i | ||||
\(245\) | −13.5670 | + | 12.4414i | −0.866767 | + | 0.794849i | ||||
\(246\) | 3.94446 | − | 3.94446i | 0.251489 | − | 0.251489i | ||||
\(247\) | −6.58164 | − | 6.58164i | −0.418780 | − | 0.418780i | ||||
\(248\) | 2.76854 | + | 2.76854i | 0.175802 | + | 0.175802i | ||||
\(249\) | 15.0040 | 0.950840 | ||||||||
\(250\) | 6.81623 | + | 8.86223i | 0.431096 | + | 0.560496i | ||||
\(251\) | −21.5270 | + | 21.5270i | −1.35877 | + | 1.35877i | −0.483333 | + | 0.875437i | \(0.660574\pi\) |
−0.875437 | + | 0.483333i | \(0.839426\pi\) | |||||||
\(252\) | 2.75974 | + | 2.75974i | 0.173847 | + | 0.173847i | ||||
\(253\) | −0.437515 | −0.0275063 | ||||||||
\(254\) | −14.6420 | − | 14.6420i | −0.918719 | − | 0.918719i | ||||
\(255\) | −15.8024 | − | 0.683957i | −0.989587 | − | 0.0428310i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.409575 | −0.0255486 | −0.0127743 | − | 0.999918i | \(-0.504066\pi\) | ||||
−0.0127743 | + | 0.999918i | \(0.504066\pi\) | |||||||
\(258\) | 2.28533 | − | 2.28533i | 0.142279 | − | 0.142279i | ||||
\(259\) | −3.64895 | + | 23.4580i | −0.226735 | + | 1.45761i | ||||
\(260\) | −5.39030 | + | 4.94305i | −0.334292 | + | 0.306555i | ||||
\(261\) | −6.14644 | + | 6.14644i | −0.380455 | + | 0.380455i | ||||
\(262\) | −3.62929 | − | 3.62929i | −0.224218 | − | 0.224218i | ||||
\(263\) | 10.0366 | − | 10.0366i | 0.618882 | − | 0.618882i | −0.326362 | − | 0.945245i | \(-0.605823\pi\) |
0.945245 | + | 0.326362i | \(0.105823\pi\) | |||||||
\(264\) | 0.247821 | − | 0.247821i | 0.0152523 | − | 0.0152523i | ||||
\(265\) | −0.472795 | + | 10.9237i | −0.0290435 | + | 0.671035i | ||||
\(266\) | −11.1067 | −0.680994 | ||||||||
\(267\) | 4.29357 | 0.262762 | ||||||||
\(268\) | 10.6169 | + | 10.6169i | 0.648533 | + | 0.648533i | ||||
\(269\) | 19.9758i | 1.21794i | 0.793192 | + | 0.608972i | \(0.208418\pi\) | ||||
−0.793192 | + | 0.608972i | \(0.791582\pi\) | |||||||
\(270\) | 2.23398 | + | 0.0966903i | 0.135955 | + | 0.00588438i | ||||
\(271\) | 11.0572 | 0.671678 | 0.335839 | − | 0.941919i | \(-0.390980\pi\) | ||||
0.335839 | + | 0.941919i | \(0.390980\pi\) | |||||||
\(272\) | −7.07368 | −0.428905 | ||||||||
\(273\) | −12.7653 | −0.772589 | ||||||||
\(274\) | −12.5315 | − | 12.5315i | −0.757057 | − | 0.757057i | ||||
\(275\) | 1.74581 | + | 0.151407i | 0.105276 | + | 0.00913016i | ||||
\(276\) | −0.882722 | − | 0.882722i | −0.0531336 | − | 0.0531336i | ||||
\(277\) | − | 24.4538i | − | 1.46929i | −0.678453 | − | 0.734644i | \(-0.737349\pi\) | ||
0.678453 | − | 0.734644i | \(-0.262651\pi\) | |||||||
\(278\) | − | 3.66631i | − | 0.219890i | ||||||
\(279\) | 2.76854 | + | 2.76854i | 0.165748 | + | 0.165748i | ||||
\(280\) | −0.377368 | + | 8.71889i | −0.0225521 | + | 0.521053i | ||||
\(281\) | −7.23968 | − | 7.23968i | −0.431883 | − | 0.431883i | 0.457385 | − | 0.889269i | \(-0.348786\pi\) |
−0.889269 | + | 0.457385i | \(0.848786\pi\) | |||||||
\(282\) | −8.14998 | −0.485324 | ||||||||
\(283\) | 30.2054 | 1.79552 | 0.897761 | − | 0.440483i | \(-0.145193\pi\) | ||||
0.897761 | + | 0.440483i | \(0.145193\pi\) | |||||||
\(284\) | −15.8980 | −0.943373 | ||||||||
\(285\) | −4.68993 | + | 4.30080i | −0.277808 | + | 0.254757i | ||||
\(286\) | 1.14631i | 0.0677825i | ||||||||
\(287\) | 15.3946 | + | 15.3946i | 0.908717 | + | 0.908717i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 33.0370 | 1.94335 | ||||||||
\(290\) | −19.4186 | − | 0.840469i | −1.14030 | − | 0.0493540i | ||||
\(291\) | −5.61638 | + | 5.61638i | −0.329238 | + | 0.329238i | ||||
\(292\) | 0.998067 | − | 0.998067i | 0.0584075 | − | 0.0584075i | ||||
\(293\) | −0.618270 | − | 0.618270i | −0.0361197 | − | 0.0361197i | 0.688816 | − | 0.724936i | \(-0.258131\pi\) |
−0.724936 | + | 0.688816i | \(0.758131\pi\) | |||||||
\(294\) | −5.82110 | + | 5.82110i | −0.339494 | + | 0.339494i | ||||
\(295\) | 33.5536 | + | 1.45226i | 1.95357 | + | 0.0845537i | ||||
\(296\) | 3.58895 | + | 4.91116i | 0.208603 | + | 0.285455i | ||||
\(297\) | 0.247821 | − | 0.247821i | 0.0143800 | − | 0.0143800i | ||||
\(298\) | 16.9433 | 0.981499 | ||||||||
\(299\) | 4.08307 | 0.236130 | ||||||||
\(300\) | 3.21684 | + | 3.82779i | 0.185724 | + | 0.220997i | ||||
\(301\) | 8.91933 | + | 8.91933i | 0.514101 | + | 0.514101i | ||||
\(302\) | 10.7953 | 0.621201 | ||||||||
\(303\) | −0.363541 | − | 0.363541i | −0.0208849 | − | 0.0208849i | ||||
\(304\) | −2.01227 | + | 2.01227i | −0.115412 | + | 0.115412i | ||||
\(305\) | −4.11925 | − | 0.178288i | −0.235867 | − | 0.0102087i | ||||
\(306\) | −7.07368 | −0.404376 | ||||||||
\(307\) | 8.55841 | + | 8.55841i | 0.488454 | + | 0.488454i | 0.907818 | − | 0.419364i | \(-0.137747\pi\) |
−0.419364 | + | 0.907818i | \(0.637747\pi\) | |||||||
\(308\) | 0.967210 | + | 0.967210i | 0.0551119 | + | 0.0551119i | ||||
\(309\) | 6.41955 | − | 6.41955i | 0.365195 | − | 0.365195i | ||||
\(310\) | −0.378572 | + | 8.74670i | −0.0215014 | + | 0.496779i | ||||
\(311\) | 7.07966 | − | 7.07966i | 0.401451 | − | 0.401451i | −0.477293 | − | 0.878744i | \(-0.658382\pi\) |
0.878744 | + | 0.477293i | \(0.158382\pi\) | |||||||
\(312\) | −2.31277 | + | 2.31277i | −0.130935 | + | 0.130935i | ||||
\(313\) | − | 21.8518i | − | 1.23514i | −0.786518 | − | 0.617568i | \(-0.788118\pi\) | ||
0.786518 | − | 0.617568i | \(-0.211882\pi\) | |||||||
\(314\) | 6.59408 | + | 6.59408i | 0.372126 | + | 0.372126i | ||||
\(315\) | −0.377368 | + | 8.71889i | −0.0212623 | + | 0.491254i | ||||
\(316\) | 2.47200 | − | 2.47200i | 0.139061 | − | 0.139061i | ||||
\(317\) | 19.1074 | + | 19.1074i | 1.07318 | + | 1.07318i | 0.997102 | + | 0.0760779i | \(0.0242398\pi\) |
0.0760779 | + | 0.997102i | \(0.475760\pi\) | |||||||
\(318\) | 4.88978i | 0.274205i | ||||||||
\(319\) | −2.15416 | + | 2.15416i | −0.120610 | + | 0.120610i | ||||
\(320\) | 1.51129 | + | 1.64803i | 0.0844837 | + | 0.0921277i | ||||
\(321\) | 1.88592i | 0.105262i | ||||||||
\(322\) | 3.44514 | − | 3.44514i | 0.191990 | − | 0.191990i | ||||
\(323\) | 14.2342 | − | 14.2342i | 0.792010 | − | 0.792010i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −16.2926 | − | 1.41299i | −0.903751 | − | 0.0783786i | ||||
\(326\) | − | 7.00131i | − | 0.387767i | ||||||
\(327\) | 3.26578i | 0.180598i | ||||||||
\(328\) | 5.57830 | 0.308010 | ||||||||
\(329\) | − | 31.8082i | − | 1.75364i | ||||||
\(330\) | 0.782946 | + | 0.0338872i | 0.0430998 | + | 0.00186543i | ||||
\(331\) | 2.84439 | + | 2.84439i | 0.156342 | + | 0.156342i | 0.780943 | − | 0.624602i | \(-0.214739\pi\) |
−0.624602 | + | 0.780943i | \(0.714739\pi\) | |||||||
\(332\) | 10.6094 | + | 10.6094i | 0.582268 | + | 0.582268i | ||||
\(333\) | 3.58895 | + | 4.91116i | 0.196673 | + | 0.269130i | ||||
\(334\) | − | 14.7018i | − | 0.804447i | ||||||
\(335\) | −1.45177 | + | 33.5423i | −0.0793186 | + | 1.83261i | ||||
\(336\) | 3.90286i | 0.212918i | ||||||||
\(337\) | −12.4436 | − | 12.4436i | −0.677844 | − | 0.677844i | 0.281668 | − | 0.959512i | \(-0.409112\pi\) |
−0.959512 | + | 0.281668i | \(0.909112\pi\) | |||||||
\(338\) | 2.30219i | 0.125222i | ||||||||
\(339\) | 5.55259 | − | 5.55259i | 0.301575 | − | 0.301575i | ||||
\(340\) | −10.6904 | − | 11.6576i | −0.579768 | − | 0.632225i | ||||
\(341\) | 0.970295 | + | 0.970295i | 0.0525444 | + | 0.0525444i | ||||
\(342\) | −2.01227 | + | 2.01227i | −0.108811 | + | 0.108811i | ||||
\(343\) | −3.40077 | − | 3.40077i | −0.183624 | − | 0.183624i | ||||
\(344\) | 3.23195 | 0.174255 | ||||||||
\(345\) | 0.120704 | − | 2.78880i | 0.00649849 | − | 0.150144i | ||||
\(346\) | −3.00005 | − | 3.00005i | −0.161284 | − | 0.161284i | ||||
\(347\) | 13.9100i | 0.746727i | 0.927685 | + | 0.373363i | \(0.121796\pi\) | ||||
−0.927685 | + | 0.373363i | \(0.878204\pi\) | |||||||
\(348\) | −8.69238 | −0.465961 | ||||||||
\(349\) | − | 0.414422i | − | 0.0221835i | −0.999938 | − | 0.0110918i | \(-0.996469\pi\) | ||
0.999938 | − | 0.0110918i | \(-0.00353069\pi\) | |||||||
\(350\) | −14.9393 | + | 12.5548i | −0.798539 | + | 0.671085i | ||||
\(351\) | −2.31277 | + | 2.31277i | −0.123447 | + | 0.123447i | ||||
\(352\) | 0.350472 | 0.0186802 | ||||||||
\(353\) | 29.7855 | 1.58532 | 0.792662 | − | 0.609661i | \(-0.208695\pi\) | ||||
0.792662 | + | 0.609661i | \(0.208695\pi\) | |||||||
\(354\) | 15.0197 | 0.798287 | ||||||||
\(355\) | −24.0265 | − | 26.2004i | −1.27519 | − | 1.39057i | ||||
\(356\) | 3.03601 | + | 3.03601i | 0.160908 | + | 0.160908i | ||||
\(357\) | − | 27.6076i | − | 1.46115i | ||||||
\(358\) | −9.62402 | + | 9.62402i | −0.508645 | + | 0.508645i | ||||
\(359\) | − | 8.57788i | − | 0.452723i | −0.974043 | − | 0.226362i | \(-0.927317\pi\) | ||
0.974043 | − | 0.226362i | \(-0.0726831\pi\) | |||||||
\(360\) | 1.51129 | + | 1.64803i | 0.0796520 | + | 0.0868588i | ||||
\(361\) | 10.9015i | 0.573765i | ||||||||
\(362\) | 14.0878i | 0.740436i | ||||||||
\(363\) | −7.69132 | + | 7.69132i | −0.403690 | + | 0.403690i | ||||
\(364\) | −9.02641 | − | 9.02641i | −0.473112 | − | 0.473112i | ||||
\(365\) | 3.15321 | + | 0.136476i | 0.165047 | + | 0.00714350i | ||||
\(366\) | −1.84391 | −0.0963826 | ||||||||
\(367\) | −9.30759 | + | 9.30759i | −0.485852 | + | 0.485852i | −0.906995 | − | 0.421142i | \(-0.861629\pi\) |
0.421142 | + | 0.906995i | \(0.361629\pi\) | |||||||
\(368\) | − | 1.24836i | − | 0.0650752i | ||||||
\(369\) | 5.57830 | 0.290395 | ||||||||
\(370\) | −2.66980 | + | 13.3369i | −0.138796 | + | 0.693351i | ||||
\(371\) | −19.0841 | −0.990798 | ||||||||
\(372\) | 3.91530i | 0.202999i | ||||||||
\(373\) | 18.3349 | − | 18.3349i | 0.949345 | − | 0.949345i | −0.0494321 | − | 0.998777i | \(-0.515741\pi\) |
0.998777 | + | 0.0494321i | \(0.0157411\pi\) | |||||||
\(374\) | −2.47913 | −0.128193 | ||||||||
\(375\) | −1.44674 | + | 11.0863i | −0.0747093 | + | 0.572496i | ||||
\(376\) | −5.76291 | − | 5.76291i | −0.297199 | − | 0.297199i | ||||
\(377\) | 20.1035 | − | 20.1035i | 1.03538 | − | 1.03538i | ||||
\(378\) | 3.90286i | 0.200741i | ||||||||
\(379\) | 0.736373i | 0.0378249i | 0.999821 | + | 0.0189125i | \(0.00602038\pi\) | ||||
−0.999821 | + | 0.0189125i | \(0.993980\pi\) | |||||||
\(380\) | −6.35741 | − | 0.275159i | −0.326128 | − | 0.0141154i | ||||
\(381\) | − | 20.7069i | − | 1.06085i | ||||||
\(382\) | −2.11691 | + | 2.11691i | −0.108311 | + | 0.108311i | ||||
\(383\) | 2.85854i | 0.146065i | 0.997330 | + | 0.0730323i | \(0.0232676\pi\) | ||||
−0.997330 | + | 0.0730323i | \(0.976732\pi\) | |||||||
\(384\) | 0.707107 | + | 0.707107i | 0.0360844 | + | 0.0360844i | ||||
\(385\) | −0.132257 | + | 3.05573i | −0.00674044 | + | 0.155734i | ||||
\(386\) | 20.7874 | 1.05805 | ||||||||
\(387\) | 3.23195 | 0.164289 | ||||||||
\(388\) | −7.94277 | −0.403233 | ||||||||
\(389\) | −14.3095 | + | 14.3095i | −0.725519 | + | 0.725519i | −0.969724 | − | 0.244205i | \(-0.921473\pi\) |
0.244205 | + | 0.969724i | \(0.421473\pi\) | |||||||
\(390\) | −7.30678 | − | 0.316250i | −0.369993 | − | 0.0160139i | ||||
\(391\) | 8.83049i | 0.446577i | ||||||||
\(392\) | −8.23228 | −0.415793 | ||||||||
\(393\) | − | 5.13259i | − | 0.258905i | ||||||
\(394\) | −11.8547 | − | 11.8547i | −0.597233 | − | 0.597233i | ||||
\(395\) | 7.80984 | + | 0.338023i | 0.392956 | + | 0.0170078i | ||||
\(396\) | 0.350472 | 0.0176119 | ||||||||
\(397\) | 0.498839 | + | 0.498839i | 0.0250360 | + | 0.0250360i | 0.719514 | − | 0.694478i | \(-0.244365\pi\) |
−0.694478 | + | 0.719514i | \(0.744365\pi\) | |||||||
\(398\) | −6.76638 | + | 6.76638i | −0.339168 | + | 0.339168i | ||||
\(399\) | −7.85360 | − | 7.85360i | −0.393172 | − | 0.393172i | ||||
\(400\) | −0.432008 | + | 4.98130i | −0.0216004 | + | 0.249065i | ||||
\(401\) | 10.8582 | − | 10.8582i | 0.542234 | − | 0.542234i | −0.381949 | − | 0.924183i | \(-0.624747\pi\) |
0.924183 | + | 0.381949i | \(0.124747\pi\) | |||||||
\(402\) | 15.0146i | 0.748861i | ||||||||
\(403\) | −9.05520 | − | 9.05520i | −0.451072 | − | 0.451072i | ||||
\(404\) | − | 0.514124i | − | 0.0255786i | ||||||
\(405\) | 1.51129 | + | 1.64803i | 0.0750966 | + | 0.0818913i | ||||
\(406\) | − | 33.9251i | − | 1.68368i | ||||||
\(407\) | 1.25783 | + | 1.72122i | 0.0623481 | + | 0.0853179i | ||||
\(408\) | −5.00185 | − | 5.00185i | −0.247628 | − | 0.247628i | ||||
\(409\) | −7.92408 | − | 7.92408i | −0.391820 | − | 0.391820i | 0.483515 | − | 0.875336i | \(-0.339360\pi\) |
−0.875336 | + | 0.483515i | \(0.839360\pi\) | |||||||
\(410\) | 8.43043 | + | 9.19321i | 0.416349 | + | 0.454020i | ||||
\(411\) | − | 17.7222i | − | 0.874174i | ||||||
\(412\) | 9.07861 | 0.447271 | ||||||||
\(413\) | 58.6196i | 2.88448i | ||||||||
\(414\) | − | 1.24836i | − | 0.0613535i | ||||||
\(415\) | −1.45074 | + | 33.5186i | −0.0712141 | + | 1.64536i | ||||
\(416\) | −3.27075 | −0.160362 | ||||||||
\(417\) | 2.59247 | − | 2.59247i | 0.126954 | − | 0.126954i | ||||
\(418\) | −0.705244 | + | 0.705244i | −0.0344946 | + | 0.0344946i | ||||
\(419\) | 13.1368i | 0.641775i | 0.947117 | + | 0.320887i | \(0.103981\pi\) | ||||
−0.947117 | + | 0.320887i | \(0.896019\pi\) | |||||||
\(420\) | −6.43202 | + | 5.89834i | −0.313851 | + | 0.287810i | ||||
\(421\) | 10.6585 | − | 10.6585i | 0.519461 | − | 0.519461i | −0.397947 | − | 0.917408i | \(-0.630277\pi\) |
0.917408 | + | 0.397947i | \(0.130277\pi\) | |||||||
\(422\) | − | 9.92928i | − | 0.483350i | ||||||
\(423\) | −5.76291 | − | 5.76291i | −0.280202 | − | 0.280202i | ||||
\(424\) | −3.45760 | + | 3.45760i | −0.167916 | + | 0.167916i | ||||
\(425\) | 3.05589 | − | 35.2362i | 0.148232 | − | 1.70920i | ||||
\(426\) | −11.2416 | − | 11.2416i | −0.544657 | − | 0.544657i | ||||
\(427\) | − | 7.19651i | − | 0.348263i | ||||||
\(428\) | −1.33354 | + | 1.33354i | −0.0644593 | + | 0.0644593i | ||||
\(429\) | −0.810561 | + | 0.810561i | −0.0391343 | + | 0.0391343i | ||||
\(430\) | 4.88441 | + | 5.32635i | 0.235547 | + | 0.256859i | ||||
\(431\) | −13.6585 | + | 13.6585i | −0.657907 | + | 0.657907i | −0.954884 | − | 0.296978i | \(-0.904021\pi\) |
0.296978 | + | 0.954884i | \(0.404021\pi\) | |||||||
\(432\) | 0.707107 | + | 0.707107i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | −16.2196 | − | 16.2196i | −0.779466 | − | 0.779466i | 0.200274 | − | 0.979740i | \(-0.435817\pi\) |
−0.979740 | + | 0.200274i | \(0.935817\pi\) | |||||||
\(434\) | −15.2809 | −0.733505 | ||||||||
\(435\) | −13.1367 | − | 14.3253i | −0.629857 | − | 0.686846i | ||||
\(436\) | −2.30925 | + | 2.30925i | −0.110593 | + | 0.110593i | ||||
\(437\) | 2.51203 | + | 2.51203i | 0.120167 | + | 0.120167i | ||||
\(438\) | 1.41148 | 0.0674431 | ||||||||
\(439\) | 4.52525 | + | 4.52525i | 0.215979 | + | 0.215979i | 0.806801 | − | 0.590823i | \(-0.201197\pi\) |
−0.590823 | + | 0.806801i | \(0.701197\pi\) | |||||||
\(440\) | 0.529665 | + | 0.577588i | 0.0252508 | + | 0.0275354i | ||||
\(441\) | −8.23228 | −0.392013 | ||||||||
\(442\) | 23.1363 | 1.10048 | ||||||||
\(443\) | −17.5292 | + | 17.5292i | −0.832839 | + | 0.832839i | −0.987904 | − | 0.155066i | \(-0.950441\pi\) |
0.155066 | + | 0.987904i | \(0.450441\pi\) | |||||||
\(444\) | −0.934944 | + | 6.01048i | −0.0443705 | + | 0.285245i | ||||
\(445\) | −0.415146 | + | 9.59172i | −0.0196798 | + | 0.454691i | ||||
\(446\) | 6.49659 | − | 6.49659i | 0.307623 | − | 0.307623i | ||||
\(447\) | 11.9807 | + | 11.9807i | 0.566669 | + | 0.566669i | ||||
\(448\) | −2.75974 | + | 2.75974i | −0.130385 | + | 0.130385i | ||||
\(449\) | 24.1689 | − | 24.1689i | 1.14060 | − | 1.14060i | 0.152263 | − | 0.988340i | \(-0.451344\pi\) |
0.988340 | − | 0.152263i | \(-0.0486561\pi\) | |||||||
\(450\) | −0.432008 | + | 4.98130i | −0.0203650 | + | 0.234821i | ||||
\(451\) | 1.95504 | 0.0920592 | ||||||||
\(452\) | 7.85255 | 0.369353 | ||||||||
\(453\) | 7.63344 | + | 7.63344i | 0.358650 | + | 0.358650i | ||||
\(454\) | − | 16.6142i | − | 0.779745i | ||||||
\(455\) | 1.23428 | − | 28.5173i | 0.0578638 | − | 1.33691i | ||||
\(456\) | −2.84578 | −0.133266 | ||||||||
\(457\) | −15.3091 | −0.716131 | −0.358065 | − | 0.933697i | \(-0.616564\pi\) | ||||
−0.358065 | + | 0.933697i | \(0.616564\pi\) | |||||||
\(458\) | 2.86631 | 0.133934 | ||||||||
\(459\) | −5.00185 | − | 5.00185i | −0.233466 | − | 0.233466i | ||||
\(460\) | 2.05733 | − | 1.88663i | 0.0959236 | − | 0.0879646i | ||||
\(461\) | 19.6061 | + | 19.6061i | 0.913145 | + | 0.913145i | 0.996518 | − | 0.0833730i | \(-0.0265693\pi\) |
−0.0833730 | + | 0.996518i | \(0.526569\pi\) | |||||||
\(462\) | 1.36784i | 0.0636377i | ||||||||
\(463\) | − | 25.4617i | − | 1.18331i | −0.806192 | − | 0.591653i | \(-0.798475\pi\) | ||
0.806192 | − | 0.591653i | \(-0.201525\pi\) | |||||||
\(464\) | −6.14644 | − | 6.14644i | −0.285341 | − | 0.285341i | ||||
\(465\) | −6.45254 | + | 5.91716i | −0.299229 | + | 0.274402i | ||||
\(466\) | 8.37425 | + | 8.37425i | 0.387930 | + | 0.387930i | ||||
\(467\) | 18.9252 | 0.875752 | 0.437876 | − | 0.899035i | \(-0.355731\pi\) | ||||
0.437876 | + | 0.899035i | \(0.355731\pi\) | |||||||
\(468\) | −3.27075 | −0.151191 | ||||||||
\(469\) | −58.5999 | −2.70589 | ||||||||
\(470\) | 0.788024 | − | 18.2069i | 0.0363488 | − | 0.839820i | ||||
\(471\) | 9.32544i | 0.429694i | ||||||||
\(472\) | 10.6205 | + | 10.6205i | 0.488849 | + | 0.488849i | ||||
\(473\) | 1.13271 | 0.0520820 | ||||||||
\(474\) | 3.49594 | 0.160574 | ||||||||
\(475\) | −9.15441 | − | 10.8930i | −0.420033 | − | 0.499807i | ||||
\(476\) | 19.5215 | − | 19.5215i | 0.894766 | − | 0.894766i | ||||
\(477\) | −3.45760 | + | 3.45760i | −0.158313 | + | 0.158313i | ||||
\(478\) | 16.9584 | + | 16.9584i | 0.775661 | + | 0.775661i | ||||
\(479\) | 3.00653 | − | 3.00653i | 0.137372 | − | 0.137372i | −0.635077 | − | 0.772449i | \(-0.719032\pi\) |
0.772449 | + | 0.635077i | \(0.219032\pi\) | |||||||
\(480\) | −0.0966903 | + | 2.23398i | −0.00441329 | + | 0.101967i | ||||
\(481\) | −11.7386 | − | 16.0632i | −0.535232 | − | 0.732418i | ||||
\(482\) | −9.32818 | + | 9.32818i | −0.424887 | + | 0.424887i | ||||
\(483\) | 4.87216 | 0.221691 | ||||||||
\(484\) | −10.8772 | −0.494417 | ||||||||
\(485\) | −12.0038 | − | 13.0899i | −0.545065 | − | 0.594383i | ||||
\(486\) | 0.707107 | + | 0.707107i | 0.0320750 | + | 0.0320750i | ||||
\(487\) | −42.0200 | −1.90411 | −0.952054 | − | 0.305929i | \(-0.901033\pi\) | ||||
−0.952054 | + | 0.305929i | \(0.901033\pi\) | |||||||
\(488\) | −1.30384 | − | 1.30384i | −0.0590221 | − | 0.0590221i | ||||
\(489\) | 4.95068 | − | 4.95068i | 0.223877 | − | 0.223877i | ||||
\(490\) | −12.4414 | − | 13.5670i | −0.562043 | − | 0.612897i | ||||
\(491\) | 14.2813 | 0.644507 | 0.322254 | − | 0.946653i | \(-0.395560\pi\) | ||||
0.322254 | + | 0.946653i | \(0.395560\pi\) | |||||||
\(492\) | 3.94446 | + | 3.94446i | 0.177830 | + | 0.177830i | ||||
\(493\) | 43.4780 | + | 43.4780i | 1.95815 | + | 1.95815i | ||||
\(494\) | 6.58164 | − | 6.58164i | 0.296122 | − | 0.296122i | ||||
\(495\) | 0.529665 | + | 0.577588i | 0.0238067 | + | 0.0259607i | ||||
\(496\) | −2.76854 | + | 2.76854i | −0.124311 | + | 0.124311i | ||||
\(497\) | 43.8743 | − | 43.8743i | 1.96803 | − | 1.96803i | ||||
\(498\) | 15.0040i | 0.672345i | ||||||||
\(499\) | −4.58214 | − | 4.58214i | −0.205125 | − | 0.205125i | 0.597067 | − | 0.802192i | \(-0.296333\pi\) |
−0.802192 | + | 0.597067i | \(0.796333\pi\) | |||||||
\(500\) | −8.86223 | + | 6.81623i | −0.396331 | + | 0.304831i | ||||
\(501\) | 10.3957 | − | 10.3957i | 0.464447 | − | 0.464447i | ||||
\(502\) | −21.5270 | − | 21.5270i | −0.960795 | − | 0.960795i | ||||
\(503\) | 4.41445i | 0.196831i | 0.995145 | + | 0.0984153i | \(0.0313774\pi\) | ||||
−0.995145 | + | 0.0984153i | \(0.968623\pi\) | |||||||
\(504\) | −2.75974 | + | 2.75974i | −0.122928 | + | 0.122928i | ||||
\(505\) | 0.847293 | − | 0.776991i | 0.0377040 | − | 0.0345756i | ||||
\(506\) | − | 0.437515i | − | 0.0194499i | ||||||
\(507\) | −1.62789 | + | 1.62789i | −0.0722972 | + | 0.0722972i | ||||
\(508\) | 14.6420 | − | 14.6420i | 0.649633 | − | 0.649633i | ||||
\(509\) | −23.7000 | −1.05048 | −0.525242 | − | 0.850953i | \(-0.676025\pi\) | ||||
−0.525242 | + | 0.850953i | \(0.676025\pi\) | |||||||
\(510\) | 0.683957 | − | 15.8024i | 0.0302861 | − | 0.699744i | ||||
\(511\) | 5.50880i | 0.243695i | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −2.84578 | −0.125644 | ||||||||
\(514\) | − | 0.409575i | − | 0.0180656i | ||||||
\(515\) | 13.7204 | + | 14.9618i | 0.604594 | + | 0.659297i | ||||
\(516\) | 2.28533 | + | 2.28533i | 0.100606 | + | 0.100606i | ||||
\(517\) | −2.01974 | − | 2.01974i | −0.0888279 | − | 0.0888279i | ||||
\(518\) | −23.4580 | − | 3.64895i | −1.03069 | − | 0.160326i | ||||
\(519\) | − | 4.24271i | − | 0.186234i | ||||||
\(520\) | −4.94305 | − | 5.39030i | −0.216767 | − | 0.236380i | ||||
\(521\) | − | 22.6223i | − | 0.991100i | −0.868579 | − | 0.495550i | \(-0.834966\pi\) | ||
0.868579 | − | 0.495550i | \(-0.165034\pi\) | |||||||
\(522\) | −6.14644 | − | 6.14644i | −0.269023 | − | 0.269023i | ||||
\(523\) | − | 38.2884i | − | 1.67424i | −0.547023 | − | 0.837118i | \(-0.684239\pi\) | ||
0.547023 | − | 0.837118i | \(-0.315761\pi\) | |||||||
\(524\) | 3.62929 | − | 3.62929i | 0.158546 | − | 0.158546i | ||||
\(525\) | −19.4413 | − | 1.68606i | −0.848488 | − | 0.0735858i | ||||
\(526\) | 10.0366 | + | 10.0366i | 0.437616 | + | 0.437616i | ||||
\(527\) | 19.5838 | − | 19.5838i | 0.853082 | − | 0.853082i | ||||
\(528\) | 0.247821 | + | 0.247821i | 0.0107850 | + | 0.0107850i | ||||
\(529\) | 21.4416 | 0.932244 | ||||||||
\(530\) | −10.9237 | − | 0.472795i | −0.474494 | − | 0.0205369i | ||||
\(531\) | 10.6205 | + | 10.6205i | 0.460891 | + | 0.460891i | ||||
\(532\) | − | 11.1067i | − | 0.481535i | ||||||
\(533\) | −18.2452 | −0.790289 | ||||||||
\(534\) | 4.29357i | 0.185801i | ||||||||
\(535\) | −4.21309 | − | 0.182350i | −0.182148 | − | 0.00788367i | ||||
\(536\) | −10.6169 | + | 10.6169i | −0.458582 | + | 0.458582i | ||||
\(537\) | −13.6104 | −0.587333 | ||||||||
\(538\) | −19.9758 | −0.861217 | ||||||||
\(539\) | −2.88518 | −0.124274 | ||||||||
\(540\) | −0.0966903 | + | 2.23398i | −0.00416089 | + | 0.0961350i | ||||
\(541\) | 8.89780 | + | 8.89780i | 0.382546 | + | 0.382546i | 0.872019 | − | 0.489472i | \(-0.162811\pi\) |
−0.489472 | + | 0.872019i | \(0.662811\pi\) | |||||||
\(542\) | 11.0572i | 0.474948i | ||||||||
\(543\) | −9.96155 | + | 9.96155i | −0.427491 | + | 0.427491i | ||||
\(544\) | − | 7.07368i | − | 0.303282i | ||||||
\(545\) | −7.29567 | − | 0.315769i | −0.312512 | − | 0.0135260i | ||||
\(546\) | − | 12.7653i | − | 0.546303i | ||||||
\(547\) | − | 7.12339i | − | 0.304574i | −0.988336 | − | 0.152287i | \(-0.951336\pi\) | ||
0.988336 | − | 0.152287i | \(-0.0486638\pi\) | |||||||
\(548\) | 12.5315 | − | 12.5315i | 0.535320 | − | 0.535320i | ||||
\(549\) | −1.30384 | − | 1.30384i | −0.0556465 | − | 0.0556465i | ||||
\(550\) | −0.151407 | + | 1.74581i | −0.00645600 | + | 0.0744414i | ||||
\(551\) | 24.7366 | 1.05382 | ||||||||
\(552\) | 0.882722 | − | 0.882722i | 0.0375712 | − | 0.0375712i | ||||
\(553\) | 13.6441i | 0.580208i | ||||||||
\(554\) | 24.4538 | 1.03894 | ||||||||
\(555\) | −11.3184 | + | 7.54276i | −0.480440 | + | 0.320172i | ||||
\(556\) | 3.66631 | 0.155486 | ||||||||
\(557\) | − | 45.3868i | − | 1.92310i | −0.274626 | − | 0.961551i | \(-0.588554\pi\) | ||
0.274626 | − | 0.961551i | \(-0.411446\pi\) | |||||||
\(558\) | −2.76854 | + | 2.76854i | −0.117202 | + | 0.117202i | ||||
\(559\) | −10.5709 | −0.447102 | ||||||||
\(560\) | −8.71889 | − | 0.377368i | −0.368440 | − | 0.0159467i | ||||
\(561\) | −1.75301 | − | 1.75301i | −0.0740121 | − | 0.0740121i | ||||
\(562\) | 7.23968 | − | 7.23968i | 0.305388 | − | 0.305388i | ||||
\(563\) | 5.35148i | 0.225538i | 0.993621 | + | 0.112769i | \(0.0359720\pi\) | ||||
−0.993621 | + | 0.112769i | \(0.964028\pi\) | |||||||
\(564\) | − | 8.14998i | − | 0.343176i | ||||||
\(565\) | 11.8675 | + | 12.9412i | 0.499268 | + | 0.544442i | ||||
\(566\) | 30.2054i | 1.26963i | ||||||||
\(567\) | −2.75974 | + | 2.75974i | −0.115898 | + | 0.115898i | ||||
\(568\) | − | 15.8980i | − | 0.667066i | ||||||
\(569\) | 13.2588 | + | 13.2588i | 0.555837 | + | 0.555837i | 0.928119 | − | 0.372283i | \(-0.121425\pi\) |
−0.372283 | + | 0.928119i | \(0.621425\pi\) | |||||||
\(570\) | −4.30080 | − | 4.68993i | −0.180141 | − | 0.196440i | ||||
\(571\) | −39.9897 | −1.67352 | −0.836758 | − | 0.547574i | \(-0.815552\pi\) | ||||
−0.836758 | + | 0.547574i | \(0.815552\pi\) | |||||||
\(572\) | −1.14631 | −0.0479295 | ||||||||
\(573\) | −2.99376 | −0.125066 | ||||||||
\(574\) | −15.3946 | + | 15.3946i | −0.642560 | + | 0.642560i | ||||
\(575\) | 6.21845 | + | 0.539300i | 0.259327 | + | 0.0224904i | ||||
\(576\) | 1.00000i | 0.0416667i | ||||||||
\(577\) | 2.19671 | 0.0914503 | 0.0457251 | − | 0.998954i | \(-0.485440\pi\) | ||||
0.0457251 | + | 0.998954i | \(0.485440\pi\) | |||||||
\(578\) | 33.0370i | 1.37416i | ||||||||
\(579\) | 14.6989 | + | 14.6989i | 0.610865 | + | 0.610865i | ||||
\(580\) | 0.840469 | − | 19.4186i | 0.0348986 | − | 0.806313i | ||||
\(581\) | −58.5584 | −2.42941 | ||||||||
\(582\) | −5.61638 | − | 5.61638i | −0.232807 | − | 0.232807i | ||||
\(583\) | −1.21179 | + | 1.21179i | −0.0501873 | + | 0.0501873i | ||||
\(584\) | 0.998067 | + | 0.998067i | 0.0413003 | + | 0.0413003i | ||||
\(585\) | −4.94305 | − | 5.39030i | −0.204370 | − | 0.222861i | ||||
\(586\) | 0.618270 | − | 0.618270i | 0.0255405 | − | 0.0255405i | ||||
\(587\) | − | 40.3393i | − | 1.66498i | −0.554041 | − | 0.832490i | \(-0.686915\pi\) | ||
0.554041 | − | 0.832490i | \(-0.313085\pi\) | |||||||
\(588\) | −5.82110 | − | 5.82110i | −0.240058 | − | 0.240058i | ||||
\(589\) | − | 11.1421i | − | 0.459102i | ||||||
\(590\) | −1.45226 | + | 33.5536i | −0.0597885 | + | 1.38138i | ||||
\(591\) | − | 16.7651i | − | 0.689625i | ||||||
\(592\) | −4.91116 | + | 3.58895i | −0.201847 | + | 0.147505i | ||||
\(593\) | −14.1348 | − | 14.1348i | −0.580448 | − | 0.580448i | 0.354579 | − | 0.935026i | \(-0.384624\pi\) |
−0.935026 | + | 0.354579i | \(0.884624\pi\) | |||||||
\(594\) | 0.247821 | + | 0.247821i | 0.0101682 | + | 0.0101682i | ||||
\(595\) | 61.6747 | + | 2.66938i | 2.52841 | + | 0.109434i | ||||
\(596\) | 16.9433i | 0.694025i | ||||||||
\(597\) | −9.56911 | −0.391638 | ||||||||
\(598\) | 4.08307i | 0.166969i | ||||||||
\(599\) | − | 23.9120i | − | 0.977016i | −0.872559 | − | 0.488508i | \(-0.837541\pi\) | ||
0.872559 | − | 0.488508i | \(-0.162459\pi\) | |||||||
\(600\) | −3.82779 | + | 3.21684i | −0.156269 | + | 0.131327i | ||||
\(601\) | −24.5648 | −1.00202 | −0.501009 | − | 0.865442i | \(-0.667038\pi\) | ||||
−0.501009 | + | 0.865442i | \(0.667038\pi\) | |||||||
\(602\) | −8.91933 | + | 8.91933i | −0.363525 | + | 0.363525i | ||||
\(603\) | −10.6169 | + | 10.6169i | −0.432355 | + | 0.432355i | ||||
\(604\) | 10.7953i | 0.439255i | ||||||||
\(605\) | −16.4386 | − | 17.9259i | −0.668322 | − | 0.728792i | ||||
\(606\) | 0.363541 | − | 0.363541i | 0.0147678 | − | 0.0147678i | ||||
\(607\) | 28.5020i | 1.15686i | 0.815732 | + | 0.578430i | \(0.196334\pi\) | ||||
−0.815732 | + | 0.578430i | \(0.803666\pi\) | |||||||
\(608\) | −2.01227 | − | 2.01227i | −0.0816084 | − | 0.0816084i | ||||
\(609\) | 23.9887 | − | 23.9887i | 0.972070 | − | 0.972070i | ||||
\(610\) | 0.178288 | − | 4.11925i | 0.00721867 | − | 0.166783i | ||||
\(611\) | 18.8490 | + | 18.8490i | 0.762550 | + | 0.762550i | ||||
\(612\) | − | 7.07368i | − | 0.285937i | ||||||
\(613\) | −20.5098 | + | 20.5098i | −0.828384 | + | 0.828384i | −0.987293 | − | 0.158909i | \(-0.949202\pi\) |
0.158909 | + | 0.987293i | \(0.449202\pi\) | |||||||
\(614\) | −8.55841 | + | 8.55841i | −0.345389 | + | 0.345389i | ||||
\(615\) | −0.539368 | + | 12.4618i | −0.0217494 | + | 0.502508i | ||||
\(616\) | −0.967210 | + | 0.967210i | −0.0389700 | + | 0.0389700i | ||||
\(617\) | −14.5571 | − | 14.5571i | −0.586047 | − | 0.586047i | 0.350511 | − | 0.936559i | \(-0.386008\pi\) |
−0.936559 | + | 0.350511i | \(0.886008\pi\) | |||||||
\(618\) | 6.41955 | + | 6.41955i | 0.258232 | + | 0.258232i | ||||
\(619\) | −22.6423 | −0.910070 | −0.455035 | − | 0.890474i | \(-0.650373\pi\) | ||||
−0.455035 | + | 0.890474i | \(0.650373\pi\) | |||||||
\(620\) | −8.74670 | − | 0.378572i | −0.351276 | − | 0.0152038i | ||||
\(621\) | 0.882722 | − | 0.882722i | 0.0354224 | − | 0.0354224i | ||||
\(622\) | 7.07966 | + | 7.07966i | 0.283869 | + | 0.283869i | ||||
\(623\) | −16.7572 | −0.671362 | ||||||||
\(624\) | −2.31277 | − | 2.31277i | −0.0925849 | − | 0.0925849i | ||||
\(625\) | −24.6267 | − | 4.30392i | −0.985070 | − | 0.172157i | ||||
\(626\) | 21.8518 | 0.873372 | ||||||||
\(627\) | −0.997366 | −0.0398310 | ||||||||
\(628\) | −6.59408 | + | 6.59408i | −0.263132 | + | 0.263132i | ||||
\(629\) | 34.7400 | − | 25.3871i | 1.38517 | − | 1.01225i | ||||
\(630\) | −8.71889 | − | 0.377368i | −0.347369 | − | 0.0150347i | ||||
\(631\) | 23.0961 | − | 23.0961i | 0.919443 | − | 0.919443i | −0.0775462 | − | 0.996989i | \(-0.524709\pi\) |
0.996989 | + | 0.0775462i | \(0.0247085\pi\) | |||||||
\(632\) | 2.47200 | + | 2.47200i | 0.0983309 | + | 0.0983309i | ||||
\(633\) | 7.02106 | − | 7.02106i | 0.279062 | − | 0.279062i | ||||
\(634\) | −19.1074 | + | 19.1074i | −0.758853 | + | 0.758853i | ||||
\(635\) | 46.2587 | + | 2.00215i | 1.83572 | + | 0.0794531i | ||||
\(636\) | −4.88978 | −0.193893 | ||||||||
\(637\) | 26.9257 | 1.06684 | ||||||||
\(638\) | −2.15416 | − | 2.15416i | −0.0852839 | − | 0.0852839i | ||||
\(639\) | − | 15.8980i | − | 0.628916i | ||||||
\(640\) | −1.64803 | + | 1.51129i | −0.0651441 | + | 0.0597390i | ||||
\(641\) | −42.5772 | −1.68170 | −0.840849 | − | 0.541269i | \(-0.817944\pi\) | ||||
−0.840849 | + | 0.541269i | \(0.817944\pi\) | |||||||
\(642\) | −1.88592 | −0.0744312 | ||||||||
\(643\) | 19.1904 | 0.756794 | 0.378397 | − | 0.925643i | \(-0.376475\pi\) | ||||
0.378397 | + | 0.925643i | \(0.376475\pi\) | |||||||
\(644\) | 3.44514 | + | 3.44514i | 0.135757 | + | 0.135757i | ||||
\(645\) | −0.312498 | + | 7.22010i | −0.0123046 | + | 0.284291i | ||||
\(646\) | 14.2342 | + | 14.2342i | 0.560036 | + | 0.560036i | ||||
\(647\) | 28.2302i | 1.10984i | 0.831903 | + | 0.554921i | \(0.187251\pi\) | ||||
−0.831903 | + | 0.554921i | \(0.812749\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 3.72219 | + | 3.72219i | 0.146109 | + | 0.146109i | ||||
\(650\) | 1.41299 | − | 16.2926i | 0.0554220 | − | 0.639048i | ||||
\(651\) | −10.8052 | − | 10.8052i | −0.423489 | − | 0.423489i | ||||
\(652\) | 7.00131 | 0.274193 | ||||||||
\(653\) | 5.24225 | 0.205145 | 0.102573 | − | 0.994726i | \(-0.467293\pi\) | ||||
0.102573 | + | 0.994726i | \(0.467293\pi\) | |||||||
\(654\) | −3.26578 | −0.127702 | ||||||||
\(655\) | 11.4661 | + | 0.496272i | 0.448017 | + | 0.0193910i | ||||
\(656\) | 5.57830i | 0.217796i | ||||||||
\(657\) | 0.998067 | + | 0.998067i | 0.0389383 | + | 0.0389383i | ||||
\(658\) | 31.8082 | 1.24001 | ||||||||
\(659\) | −30.0925 | −1.17224 | −0.586119 | − | 0.810225i | \(-0.699345\pi\) | ||||
−0.586119 | + | 0.810225i | \(0.699345\pi\) | |||||||
\(660\) | −0.0338872 | + | 0.782946i | −0.00131906 | + | 0.0304761i | ||||
\(661\) | −32.5054 | + | 32.5054i | −1.26432 | + | 1.26432i | −0.315335 | + | 0.948981i | \(0.602117\pi\) |
−0.948981 | + | 0.315335i | \(0.897883\pi\) | |||||||
\(662\) | −2.84439 | + | 2.84439i | −0.110550 | + | 0.110550i | ||||
\(663\) | 16.3598 | + | 16.3598i | 0.635362 | + | 0.635362i | ||||
\(664\) | −10.6094 | + | 10.6094i | −0.411726 | + | 0.411726i | ||||
\(665\) | 18.3041 | − | 16.7854i | 0.709804 | − | 0.650910i | ||||
\(666\) | −4.91116 | + | 3.58895i | −0.190303 | + | 0.139069i | ||||
\(667\) | −7.67296 | + | 7.67296i | −0.297098 | + | 0.297098i | ||||
\(668\) | 14.7018 | 0.568830 | ||||||||
\(669\) | 9.18757 | 0.355212 | ||||||||
\(670\) | −33.5423 | − | 1.45177i | −1.29585 | − | 0.0560867i | ||||
\(671\) | −0.456959 | − | 0.456959i | −0.0176407 | − | 0.0176407i | ||||
\(672\) | −3.90286 | −0.150556 | ||||||||
\(673\) | −9.11977 | − | 9.11977i | −0.351541 | − | 0.351541i | 0.509141 | − | 0.860683i | \(-0.329963\pi\) |
−0.860683 | + | 0.509141i | \(0.829963\pi\) | |||||||
\(674\) | 12.4436 | − | 12.4436i | 0.479308 | − | 0.479308i | ||||
\(675\) | −3.82779 | + | 3.21684i | −0.147332 | + | 0.123816i | ||||
\(676\) | −2.30219 | −0.0885456 | ||||||||
\(677\) | 19.8062 | + | 19.8062i | 0.761213 | + | 0.761213i | 0.976542 | − | 0.215329i | \(-0.0690823\pi\) |
−0.215329 | + | 0.976542i | \(0.569082\pi\) | |||||||
\(678\) | 5.55259 | + | 5.55259i | 0.213246 | + | 0.213246i | ||||
\(679\) | 21.9199 | − | 21.9199i | 0.841210 | − | 0.841210i | ||||
\(680\) | 11.6576 | − | 10.6904i | 0.447050 | − | 0.409958i | ||||
\(681\) | 11.7480 | − | 11.7480i | 0.450186 | − | 0.450186i | ||||
\(682\) | −0.970295 | + | 0.970295i | −0.0371545 | + | 0.0371545i | ||||
\(683\) | − | 9.00362i | − | 0.344514i | −0.985052 | − | 0.172257i | \(-0.944894\pi\) | ||
0.985052 | − | 0.172257i | \(-0.0551060\pi\) | |||||||
\(684\) | −2.01227 | − | 2.01227i | −0.0769411 | − | 0.0769411i | ||||
\(685\) | 39.5911 | + | 1.71357i | 1.51270 | + | 0.0654721i | ||||
\(686\) | 3.40077 | − | 3.40077i | 0.129842 | − | 0.129842i | ||||
\(687\) | 2.02679 | + | 2.02679i | 0.0773268 | + | 0.0773268i | ||||
\(688\) | 3.23195i | 0.123217i | ||||||||
\(689\) | 11.3089 | − | 11.3089i | 0.430837 | − | 0.430837i | ||||
\(690\) | 2.78880 | + | 0.120704i | 0.106168 | + | 0.00459513i | ||||
\(691\) | 8.79710i | 0.334657i | 0.985901 | + | 0.167329i | \(0.0535141\pi\) | ||||
−0.985901 | + | 0.167329i | \(0.946486\pi\) | |||||||
\(692\) | 3.00005 | − | 3.00005i | 0.114045 | − | 0.114045i | ||||
\(693\) | −0.967210 | + | 0.967210i | −0.0367413 | + | 0.0367413i | ||||
\(694\) | −13.9100 | −0.528016 | ||||||||
\(695\) | 5.54085 | + | 6.04219i | 0.210176 | + | 0.229193i | ||||
\(696\) | − | 8.69238i | − | 0.329484i | ||||||
\(697\) | − | 39.4592i | − | 1.49462i | ||||||
\(698\) | 0.414422 | 0.0156861 | ||||||||
\(699\) | 11.8430i | 0.447943i | ||||||||
\(700\) | −12.5548 | − | 14.9393i | −0.474529 | − | 0.564653i | ||||
\(701\) | 6.74494 | + | 6.74494i | 0.254753 | + | 0.254753i | 0.822916 | − | 0.568163i | \(-0.192346\pi\) |
−0.568163 | + | 0.822916i | \(0.692346\pi\) | |||||||
\(702\) | −2.31277 | − | 2.31277i | −0.0872899 | − | 0.0872899i | ||||
\(703\) | 2.66065 | − | 17.1045i | 0.100348 | − | 0.645109i | ||||
\(704\) | 0.350472i | 0.0132089i | ||||||||
\(705\) | 13.4314 | − | 12.3170i | 0.505856 | − | 0.463884i | ||||
\(706\) | 29.7855i | 1.12099i | ||||||||
\(707\) | 1.41885 | + | 1.41885i | 0.0533612 | + | 0.0533612i | ||||
\(708\) | 15.0197i | 0.564474i | ||||||||
\(709\) | −27.6225 | + | 27.6225i | −1.03739 | + | 1.03739i | −0.0381132 | + | 0.999273i | \(0.512135\pi\) |
−0.999273 | + | 0.0381132i | \(0.987865\pi\) | |||||||
\(710\) | 26.2004 | − | 24.0265i | 0.983284 | − | 0.901698i | ||||
\(711\) | 2.47200 | + | 2.47200i | 0.0927072 | + | 0.0927072i | ||||
\(712\) | −3.03601 | + | 3.03601i | −0.113779 | + | 0.113779i | ||||
\(713\) | 3.45613 | + | 3.45613i | 0.129433 | + | 0.129433i | ||||
\(714\) | 27.6076 | 1.03319 | ||||||||
\(715\) | −1.73240 | − | 1.88915i | −0.0647881 | − | 0.0706501i | ||||
\(716\) | −9.62402 | − | 9.62402i | −0.359666 | − | 0.359666i | ||||
\(717\) | 23.9829i | 0.895656i | ||||||||
\(718\) | 8.57788 | 0.320124 | ||||||||
\(719\) | 11.0173i | 0.410878i | 0.978670 | + | 0.205439i | \(0.0658622\pi\) | ||||
−0.978670 | + | 0.205439i | \(0.934138\pi\) | |||||||
\(720\) | −1.64803 | + | 1.51129i | −0.0614185 | + | 0.0563224i | ||||
\(721\) | −25.0546 | + | 25.0546i | −0.933081 | + | 0.933081i | ||||
\(722\) | −10.9015 | −0.405713 | ||||||||
\(723\) | −13.1920 | −0.490617 | ||||||||
\(724\) | −14.0878 | −0.523567 | ||||||||
\(725\) | 33.2726 | − | 27.9620i | 1.23571 | − | 1.03848i | ||||
\(726\) | −7.69132 | − | 7.69132i | −0.285452 | − | 0.285452i | ||||
\(727\) | − | 8.80697i | − | 0.326632i | −0.986574 | − | 0.163316i | \(-0.947781\pi\) | ||
0.986574 | − | 0.163316i | \(-0.0522191\pi\) | |||||||
\(728\) | 9.02641 | − | 9.02641i | 0.334541 | − | 0.334541i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −0.136476 | + | 3.15321i | −0.00505122 | + | 0.116706i | ||||
\(731\) | − | 22.8618i | − | 0.845574i | ||||||
\(732\) | − | 1.84391i | − | 0.0681528i | ||||||
\(733\) | −11.9215 | + | 11.9215i | −0.440331 | + | 0.440331i | −0.892123 | − | 0.451792i | \(-0.850785\pi\) |
0.451792 | + | 0.892123i | \(0.350785\pi\) | |||||||
\(734\) | −9.30759 | − | 9.30759i | −0.343549 | − | 0.343549i | ||||
\(735\) | 0.795982 | − | 18.3907i | 0.0293602 | − | 0.678352i | ||||
\(736\) | 1.24836 | 0.0460151 | ||||||||
\(737\) | −3.72094 | + | 3.72094i | −0.137063 | + | 0.137063i | ||||
\(738\) | 5.57830i | 0.205340i | ||||||||
\(739\) | 1.03649 | 0.0381277 | 0.0190639 | − | 0.999818i | \(-0.493931\pi\) | ||||
0.0190639 | + | 0.999818i | \(0.493931\pi\) | |||||||
\(740\) | −13.3369 | − | 2.66980i | −0.490273 | − | 0.0981438i | ||||
\(741\) | 9.30784 | 0.341932 | ||||||||
\(742\) | − | 19.0841i | − | 0.700600i | ||||||
\(743\) | −16.2854 | + | 16.2854i | −0.597453 | + | 0.597453i | −0.939634 | − | 0.342181i | \(-0.888834\pi\) |
0.342181 | + | 0.939634i | \(0.388834\pi\) | |||||||
\(744\) | −3.91530 | −0.143542 | ||||||||
\(745\) | −27.9231 | + | 25.6062i | −1.02302 | + | 0.938140i | ||||
\(746\) | 18.3349 | + | 18.3349i | 0.671289 | + | 0.671289i | ||||
\(747\) | −10.6094 | + | 10.6094i | −0.388179 | + | 0.388179i | ||||
\(748\) | − | 2.47913i | − | 0.0906459i | ||||||
\(749\) | − | 7.36046i | − | 0.268945i | ||||||
\(750\) | −11.0863 | − | 1.44674i | −0.404816 | − | 0.0528274i | ||||
\(751\) | − | 44.5447i | − | 1.62546i | −0.582641 | − | 0.812729i | \(-0.697981\pi\) | ||
0.582641 | − | 0.812729i | \(-0.302019\pi\) | |||||||
\(752\) | 5.76291 | − | 5.76291i | 0.210152 | − | 0.210152i | ||||
\(753\) | − | 30.4437i | − | 1.10943i | ||||||
\(754\) | 20.1035 | + | 20.1035i | 0.732126 | + | 0.732126i | ||||
\(755\) | −17.7910 | + | 16.3148i | −0.647481 | + | 0.593758i | ||||
\(756\) | −3.90286 | −0.141945 | ||||||||
\(757\) | −6.50328 | −0.236366 | −0.118183 | − | 0.992992i | \(-0.537707\pi\) | ||||
−0.118183 | + | 0.992992i | \(0.537707\pi\) | |||||||
\(758\) | −0.736373 | −0.0267463 | ||||||||
\(759\) | 0.309369 | − | 0.309369i | 0.0112294 | − | 0.0112294i | ||||
\(760\) | 0.275159 | − | 6.35741i | 0.00998108 | − | 0.230607i | ||||
\(761\) | − | 30.3235i | − | 1.09923i | −0.835419 | − | 0.549613i | \(-0.814775\pi\) | ||
0.835419 | − | 0.549613i | \(-0.185225\pi\) | |||||||
\(762\) | 20.7069 | 0.750131 | ||||||||
\(763\) | − | 12.7459i | − | 0.461431i | ||||||
\(764\) | −2.11691 | − | 2.11691i | −0.0765871 | − | 0.0765871i | ||||
\(765\) | 11.6576 | − | 10.6904i | 0.421483 | − | 0.386512i | ||||
\(766\) | −2.85854 | −0.103283 | ||||||||
\(767\) | −34.7371 | − | 34.7371i | −1.25428 | − | 1.25428i | ||||
\(768\) | −0.707107 | + | 0.707107i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | 20.4408 | + | 20.4408i | 0.737113 | + | 0.737113i | 0.972018 | − | 0.234906i | \(-0.0754781\pi\) |
−0.234906 | + | 0.972018i | \(0.575478\pi\) | |||||||
\(770\) | −3.05573 | − | 0.132257i | −0.110121 | − | 0.00476621i | ||||
\(771\) | 0.289614 | − | 0.289614i | 0.0104302 | − | 0.0104302i | ||||
\(772\) | 20.7874i | 0.748154i | ||||||||
\(773\) | −12.8496 | − | 12.8496i | −0.462167 | − | 0.462167i | 0.437198 | − | 0.899365i | \(-0.355971\pi\) |
−0.899365 | + | 0.437198i | \(0.855971\pi\) | |||||||
\(774\) | 3.23195i | 0.116170i | ||||||||
\(775\) | −12.5949 | − | 14.9870i | −0.452422 | − | 0.538347i | ||||
\(776\) | − | 7.94277i | − | 0.285129i | ||||||
\(777\) | −14.0071 | − | 19.1675i | −0.502503 | − | 0.687632i | ||||
\(778\) | −14.3095 | − | 14.3095i | −0.513019 | − | 0.513019i | ||||
\(779\) | −11.2251 | − | 11.2251i | −0.402179 | − | 0.402179i | ||||
\(780\) | 0.316250 | − | 7.30678i | 0.0113236 | − | 0.261625i | ||||
\(781\) | − | 5.57181i | − | 0.199375i | ||||||
\(782\) | −8.83049 | −0.315778 | ||||||||
\(783\) | − | 8.69238i | − | 0.310640i | ||||||
\(784\) | − | 8.23228i | − | 0.294010i | ||||||
\(785\) | −20.8328 | − | 0.901679i | −0.743555 | − | 0.0321823i | ||||
\(786\) | 5.13259 | 0.183074 | ||||||||
\(787\) | −20.2540 | + | 20.2540i | −0.721978 | + | 0.721978i | −0.969008 | − | 0.247030i | \(-0.920545\pi\) |
0.247030 | + | 0.969008i | \(0.420545\pi\) | |||||||
\(788\) | 11.8547 | − | 11.8547i | 0.422307 | − | 0.422307i | ||||
\(789\) | 14.1939i | 0.505315i | ||||||||
\(790\) | −0.338023 | + | 7.80984i | −0.0120263 | + | 0.277862i | ||||
\(791\) | −21.6709 | + | 21.6709i | −0.770530 | + | 0.770530i | ||||
\(792\) | 0.350472i | 0.0124535i | ||||||||
\(793\) | 4.26454 | + | 4.26454i | 0.151438 | + | 0.151438i | ||||
\(794\) | −0.498839 | + | 0.498839i | −0.0177031 | + | 0.0177031i | ||||
\(795\) | −7.38988 | − | 8.05851i | −0.262092 | − | 0.285806i | ||||
\(796\) | −6.76638 | − | 6.76638i | −0.239828 | − | 0.239828i | ||||
\(797\) | 33.9189i | 1.20147i | 0.799449 | + | 0.600734i | \(0.205125\pi\) | ||||
−0.799449 | + | 0.600734i | \(0.794875\pi\) | |||||||
\(798\) | 7.85360 | − | 7.85360i | 0.278014 | − | 0.278014i | ||||
\(799\) | −40.7650 | + | 40.7650i | −1.44216 | + | 1.44216i | ||||
\(800\) | −4.98130 | − | 0.432008i | −0.176116 | − | 0.0152738i | ||||
\(801\) | −3.03601 | + | 3.03601i | −0.107272 | + | 0.107272i | ||||
\(802\) | 10.8582 | + | 10.8582i | 0.383417 | + | 0.383417i | ||||
\(803\) | 0.349795 | + | 0.349795i | 0.0123440 | + | 0.0123440i | ||||
\(804\) | −15.0146 | −0.529525 | ||||||||
\(805\) | −0.471091 | + | 10.8843i | −0.0166038 | + | 0.383621i | ||||
\(806\) | 9.05520 | − | 9.05520i | 0.318956 | − | 0.318956i | ||||
\(807\) | −14.1250 | − | 14.1250i | −0.497224 | − | 0.497224i | ||||
\(808\) | 0.514124 | 0.0180868 | ||||||||
\(809\) | −11.7103 | − | 11.7103i | −0.411713 | − | 0.411713i | 0.470622 | − | 0.882335i | \(-0.344030\pi\) |
−0.882335 | + | 0.470622i | \(0.844030\pi\) | |||||||
\(810\) | −1.64803 | + | 1.51129i | −0.0579059 | + | 0.0531013i | ||||
\(811\) | 12.1269 | 0.425834 | 0.212917 | − | 0.977070i | \(-0.431704\pi\) | ||||
0.212917 | + | 0.977070i | \(0.431704\pi\) | |||||||
\(812\) | 33.9251 | 1.19054 | ||||||||
\(813\) | −7.81863 | + | 7.81863i | −0.274211 | + | 0.274211i | ||||
\(814\) | −1.72122 | + | 1.25783i | −0.0603288 | + | 0.0440867i | ||||
\(815\) | 10.5810 | + | 11.5384i | 0.370637 | + | 0.404172i | ||||
\(816\) | 5.00185 | − | 5.00185i | 0.175100 | − | 0.175100i | ||||
\(817\) | −6.50356 | − | 6.50356i | −0.227531 | − | 0.227531i | ||||
\(818\) | 7.92408 | − | 7.92408i | 0.277059 | − | 0.277059i | ||||
\(819\) | 9.02641 | − | 9.02641i | 0.315408 | − | 0.315408i | ||||
\(820\) | −9.19321 | + | 8.43043i | −0.321041 | + | 0.294403i | ||||
\(821\) | 29.1034 | 1.01571 | 0.507857 | − | 0.861441i | \(-0.330438\pi\) | ||||
0.507857 | + | 0.861441i | \(0.330438\pi\) | |||||||
\(822\) | 17.7222 | 0.618134 | ||||||||
\(823\) | −17.5087 | − | 17.5087i | −0.610316 | − | 0.610316i | 0.332712 | − | 0.943028i | \(-0.392036\pi\) |
−0.943028 | + | 0.332712i | \(0.892036\pi\) | |||||||
\(824\) | 9.07861i | 0.316268i | ||||||||
\(825\) | −1.34153 | + | 1.12741i | −0.0467062 | + | 0.0392514i | ||||
\(826\) | −58.6196 | −2.03964 | ||||||||
\(827\) | −14.9493 | −0.519837 | −0.259918 | − | 0.965631i | \(-0.583696\pi\) | ||||
−0.259918 | + | 0.965631i | \(0.583696\pi\) | |||||||
\(828\) | 1.24836 | 0.0433834 | ||||||||
\(829\) | −8.25148 | − | 8.25148i | −0.286586 | − | 0.286586i | 0.549143 | − | 0.835729i | \(-0.314954\pi\) |
−0.835729 | + | 0.549143i | \(0.814954\pi\) | |||||||
\(830\) | −33.5186 | − | 1.45074i | −1.16345 | − | 0.0503560i | ||||
\(831\) | 17.2915 | + | 17.2915i | 0.599834 | + | 0.599834i | ||||
\(832\) | − | 3.27075i | − | 0.113393i | ||||||
\(833\) | 58.2326i | 2.01764i | ||||||||
\(834\) | 2.59247 | + | 2.59247i | 0.0897699 | + | 0.0897699i | ||||
\(835\) | 22.2187 | + | 24.2290i | 0.768909 | + | 0.838479i | ||||
\(836\) | −0.705244 | − | 0.705244i | −0.0243914 | − | 0.0243914i | ||||
\(837\) | −3.91530 | −0.135333 | ||||||||
\(838\) | −13.1368 | −0.453803 | ||||||||
\(839\) | −12.0705 | −0.416720 | −0.208360 | − | 0.978052i | \(-0.566813\pi\) | ||||
−0.208360 | + | 0.978052i | \(0.566813\pi\) | |||||||
\(840\) | −5.89834 | − | 6.43202i | −0.203512 | − | 0.221926i | ||||
\(841\) | 46.5575i | 1.60543i | ||||||||
\(842\) | 10.6585 | + | 10.6585i | 0.367315 | + | 0.367315i | ||||
\(843\) | 10.2385 | 0.352631 | ||||||||
\(844\) | 9.92928 | 0.341780 | ||||||||
\(845\) | −3.47927 | − | 3.79407i | −0.119691 | − | 0.130520i | ||||
\(846\) | 5.76291 | − | 5.76291i | 0.198133 | − | 0.198133i | ||||
\(847\) | 30.0181 | − | 30.0181i | 1.03143 | − | 1.03143i | ||||
\(848\) | −3.45760 | − | 3.45760i | −0.118734 | − | 0.118734i | ||||
\(849\) | −21.3584 | + | 21.3584i | −0.733019 | + | 0.733019i | ||||
\(850\) | 35.2362 | + | 3.05589i | 1.20859 | + | 0.104816i | ||||
\(851\) | 4.48029 | + | 6.13088i | 0.153582 | + | 0.210164i | ||||
\(852\) | 11.2416 | − | 11.2416i | 0.385131 | − | 0.385131i | ||||
\(853\) | −55.2308 | −1.89107 | −0.945533 | − | 0.325527i | \(-0.894458\pi\) | ||||
−0.945533 | + | 0.325527i | \(0.894458\pi\) | |||||||
\(854\) | 7.19651 | 0.246259 | ||||||||
\(855\) | 0.275159 | − | 6.35741i | 0.00941025 | − | 0.217419i | ||||
\(856\) | −1.33354 | − | 1.33354i | −0.0455796 | − | 0.0455796i | ||||
\(857\) | 42.6736 | 1.45770 | 0.728851 | − | 0.684672i | \(-0.240054\pi\) | ||||
0.728851 | + | 0.684672i | \(0.240054\pi\) | |||||||
\(858\) | −0.810561 | − | 0.810561i | −0.0276721 | − | 0.0276721i | ||||
\(859\) | 37.8772 | − | 37.8772i | 1.29235 | − | 1.29235i | 0.359028 | − | 0.933327i | \(-0.383108\pi\) |
0.933327 | − | 0.359028i | \(-0.116892\pi\) | |||||||
\(860\) | −5.32635 | + | 4.88441i | −0.181627 | + | 0.166557i | ||||
\(861\) | −21.7713 | −0.741964 | ||||||||
\(862\) | −13.6585 | − | 13.6585i | −0.465210 | − | 0.465210i | ||||
\(863\) | 27.1162 | + | 27.1162i | 0.923047 | + | 0.923047i | 0.997244 | − | 0.0741970i | \(-0.0236394\pi\) |
−0.0741970 | + | 0.997244i | \(0.523639\pi\) | |||||||
\(864\) | −0.707107 | + | 0.707107i | −0.0240563 | + | 0.0240563i | ||||
\(865\) | 9.47812 | + | 0.410229i | 0.322266 | + | 0.0139482i | ||||
\(866\) | 16.2196 | − | 16.2196i | 0.551166 | − | 0.551166i | ||||
\(867\) | −23.3607 | + | 23.3607i | −0.793371 | + | 0.793371i | ||||
\(868\) | − | 15.2809i | − | 0.518666i | ||||||
\(869\) | 0.866367 | + | 0.866367i | 0.0293895 | + | 0.0293895i | ||||
\(870\) | 14.3253 | − | 13.1367i | 0.485674 | − | 0.445376i | ||||
\(871\) | 34.7254 | − | 34.7254i | 1.17662 | − | 1.17662i | ||||
\(872\) | −2.30925 | − | 2.30925i | −0.0782011 | − | 0.0782011i | ||||
\(873\) | − | 7.94277i | − | 0.268822i | ||||||
\(874\) | −2.51203 | + | 2.51203i | −0.0849708 | + | 0.0849708i | ||||
\(875\) | 5.64641 | − | 43.2684i | 0.190884 | − | 1.46274i | ||||
\(876\) | 1.41148i | 0.0476895i | ||||||||
\(877\) | 3.65778 | − | 3.65778i | 0.123514 | − | 0.123514i | −0.642648 | − | 0.766162i | \(-0.722164\pi\) |
0.766162 | + | 0.642648i | \(0.222164\pi\) | |||||||
\(878\) | −4.52525 | + | 4.52525i | −0.152720 | + | 0.152720i | ||||
\(879\) | 0.874366 | 0.0294916 | ||||||||
\(880\) | −0.577588 | + | 0.529665i | −0.0194705 | + | 0.0178550i | ||||
\(881\) | 35.1647i | 1.18473i | 0.805670 | + | 0.592364i | \(0.201805\pi\) | ||||
−0.805670 | + | 0.592364i | \(0.798195\pi\) | |||||||
\(882\) | − | 8.23228i | − | 0.277195i | ||||||
\(883\) | 28.4200 | 0.956410 | 0.478205 | − | 0.878248i | \(-0.341288\pi\) | ||||
0.478205 | + | 0.878248i | \(0.341288\pi\) | |||||||
\(884\) | 23.1363i | 0.778157i | ||||||||
\(885\) | −24.7529 | + | 22.6991i | −0.832059 | + | 0.763021i | ||||
\(886\) | −17.5292 | − | 17.5292i | −0.588906 | − | 0.588906i | ||||
\(887\) | 30.2121 | + | 30.2121i | 1.01442 | + | 1.01442i | 0.999894 | + | 0.0145284i | \(0.00462470\pi\) |
0.0145284 | + | 0.999894i | \(0.495375\pi\) | |||||||
\(888\) | −6.01048 | − | 0.934944i | −0.201699 | − | 0.0313747i | ||||
\(889\) | 80.8160i | 2.71048i | ||||||||
\(890\) | −9.59172 | − | 0.415146i | −0.321515 | − | 0.0139157i | ||||
\(891\) | 0.350472i | 0.0117413i | ||||||||
\(892\) | 6.49659 | + | 6.49659i | 0.217522 | + | 0.217522i | ||||
\(893\) | 23.1931i | 0.776126i | ||||||||
\(894\) | −11.9807 | + | 11.9807i | −0.400695 | + | 0.400695i | ||||
\(895\) | 1.31599 | − | 30.4053i | 0.0439889 | − | 1.01634i | ||||
\(896\) | −2.75974 | − | 2.75974i | −0.0921963 | − | 0.0921963i | ||||
\(897\) | −2.88717 | + | 2.88717i | −0.0963997 | + | 0.0963997i | ||||
\(898\) | 24.1689 | + | 24.1689i | 0.806528 | + | 0.806528i | ||||
\(899\) | 34.0333 | 1.13508 | ||||||||
\(900\) | −4.98130 | − | 0.432008i | −0.166043 | − | 0.0144003i | ||||
\(901\) | 24.4580 | + | 24.4580i | 0.814813 | + | 0.814813i | ||||
\(902\) | 1.95504i | 0.0650957i | ||||||||
\(903\) | −12.6138 | −0.419762 | ||||||||
\(904\) | 7.85255i | 0.261172i | ||||||||
\(905\) | −21.2907 | − | 23.2171i | −0.707726 | − | 0.771761i | ||||
\(906\) | −7.63344 | + | 7.63344i | −0.253604 | + | 0.253604i | ||||
\(907\) | −13.2909 | −0.441317 | −0.220658 | − | 0.975351i | \(-0.570821\pi\) | ||||
−0.220658 | + | 0.975351i | \(0.570821\pi\) | |||||||
\(908\) | 16.6142 | 0.551363 | ||||||||
\(909\) | 0.514124 | 0.0170524 | ||||||||
\(910\) | 28.5173 | + | 1.23428i | 0.945340 | + | 0.0409159i | ||||
\(911\) | −31.5562 | − | 31.5562i | −1.04550 | − | 1.04550i | −0.998914 | − | 0.0465896i | \(-0.985165\pi\) |
−0.0465896 | − | 0.998914i | \(-0.514835\pi\) | |||||||
\(912\) | − | 2.84578i | − | 0.0942332i | ||||||
\(913\) | −3.71831 | + | 3.71831i | −0.123058 | + | 0.123058i | ||||
\(914\) | − | 15.3091i | − | 0.506381i | ||||||
\(915\) | 3.03882 | − | 2.78668i | 0.100460 | − | 0.0921248i | ||||
\(916\) | 2.86631i | 0.0947056i | ||||||||
\(917\) | 20.0318i | 0.661507i | ||||||||
\(918\) | 5.00185 | − | 5.00185i | 0.165086 | − | 0.165086i | ||||
\(919\) | −1.91721 | − | 1.91721i | −0.0632431 | − | 0.0632431i | 0.674778 | − | 0.738021i | \(-0.264239\pi\) |
−0.738021 | + | 0.674778i | \(0.764239\pi\) | |||||||
\(920\) | 1.88663 | + | 2.05733i | 0.0622004 | + | 0.0678282i | ||||
\(921\) | −12.1034 | −0.398821 | ||||||||
\(922\) | −19.6061 | + | 19.6061i | −0.645691 | + | 0.645691i | ||||
\(923\) | 51.9984i | 1.71155i | ||||||||
\(924\) | −1.36784 | −0.0449987 | ||||||||
\(925\) | −15.7560 | − | 26.0144i | −0.518053 | − | 0.855349i | ||||
\(926\) | 25.4617 | 0.836724 | ||||||||
\(927\) | 9.07861i | 0.298181i | ||||||||
\(928\) | 6.14644 | − | 6.14644i | 0.201767 | − | 0.201767i | ||||
\(929\) | 53.6670 | 1.76076 | 0.880378 | − | 0.474273i | \(-0.157289\pi\) | ||||
0.880378 | + | 0.474273i | \(0.157289\pi\) | |||||||
\(930\) | −5.91716 | − | 6.45254i | −0.194031 | − | 0.211587i | ||||
\(931\) | 16.5656 | + | 16.5656i | 0.542915 | + | 0.542915i | ||||
\(932\) | −8.37425 | + | 8.37425i | −0.274308 | + | 0.274308i | ||||
\(933\) | 10.0122i | 0.327783i | ||||||||
\(934\) | 18.9252i | 0.619250i | ||||||||
\(935\) | 4.08568 | − | 3.74668i | 0.133616 | − | 0.122530i | ||||
\(936\) | − | 3.27075i | − | 0.106908i | ||||||
\(937\) | 18.7194 | − | 18.7194i | 0.611538 | − | 0.611538i | −0.331809 | − | 0.943347i | \(-0.607659\pi\) |
0.943347 | + | 0.331809i | \(0.107659\pi\) | |||||||
\(938\) | − | 58.5999i | − | 1.91335i | ||||||
\(939\) | 15.4515 | + | 15.4515i | 0.504242 | + | 0.504242i | ||||
\(940\) | 18.2069 | + | 0.788024i | 0.593843 | + | 0.0257025i | ||||
\(941\) | 12.7400 | 0.415313 | 0.207657 | − | 0.978202i | \(-0.433416\pi\) | ||||
0.207657 | + | 0.978202i | \(0.433416\pi\) | |||||||
\(942\) | −9.32544 | −0.303839 | ||||||||
\(943\) | 6.96372 | 0.226770 | ||||||||
\(944\) | −10.6205 | + | 10.6205i | −0.345668 | + | 0.345668i | ||||
\(945\) | −5.89834 | − | 6.43202i | −0.191873 | − | 0.209234i | ||||
\(946\) | 1.13271i | 0.0368275i | ||||||||
\(947\) | −13.4498 | −0.437059 | −0.218529 | − | 0.975830i | \(-0.570126\pi\) | ||||
−0.218529 | + | 0.975830i | \(0.570126\pi\) | |||||||
\(948\) | 3.49594i | 0.113543i | ||||||||
\(949\) | −3.26443 | − | 3.26443i | −0.105968 | − | 0.105968i | ||||
\(950\) | 10.8930 | − | 9.15441i | 0.353417 | − | 0.297008i | ||||
\(951\) | −27.0220 | −0.876248 | ||||||||
\(952\) | 19.5215 | + | 19.5215i | 0.632695 | + | 0.632695i | ||||
\(953\) | 0.709621 | − | 0.709621i | 0.0229869 | − | 0.0229869i | −0.695520 | − | 0.718507i | \(-0.744826\pi\) |
0.718507 | + | 0.695520i | \(0.244826\pi\) | |||||||
\(954\) | −3.45760 | − | 3.45760i | −0.111944 | − | 0.111944i | ||||
\(955\) | 0.289468 | − | 6.68799i | 0.00936696 | − | 0.216418i | ||||
\(956\) | −16.9584 | + | 16.9584i | −0.548475 | + | 0.548475i | ||||
\(957\) | − | 3.04644i | − | 0.0984773i | ||||||
\(958\) | 3.00653 | + | 3.00653i | 0.0971366 | + | 0.0971366i | ||||
\(959\) | 69.1674i | 2.23353i | ||||||||
\(960\) | −2.23398 | − | 0.0966903i | −0.0721013 | − | 0.00312067i | ||||
\(961\) | 15.6704i | 0.505496i | ||||||||
\(962\) | 16.0632 | − | 11.7386i | 0.517898 | − | 0.378466i | ||||
\(963\) | −1.33354 | − | 1.33354i | −0.0429729 | − | 0.0429729i | ||||
\(964\) | −9.32818 | − | 9.32818i | −0.300441 | − | 0.300441i | ||||
\(965\) | −34.2582 | + | 31.4158i | −1.10281 | + | 1.01131i | ||||
\(966\) | 4.87216i | 0.156759i | ||||||||
\(967\) | −4.89161 | −0.157304 | −0.0786519 | − | 0.996902i | \(-0.525062\pi\) | ||||
−0.0786519 | + | 0.996902i | \(0.525062\pi\) | |||||||
\(968\) | − | 10.8772i | − | 0.349605i | ||||||
\(969\) | 20.1302i | 0.646674i | ||||||||
\(970\) | 13.0899 | − | 12.0038i | 0.420292 | − | 0.385419i | ||||
\(971\) | −50.8953 | −1.63331 | −0.816654 | − | 0.577128i | \(-0.804173\pi\) | ||||
−0.816654 | + | 0.577128i | \(0.804173\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | −10.1180 | + | 10.1180i | −0.324369 | + | 0.324369i | ||||
\(974\) | − | 42.0200i | − | 1.34641i | ||||||
\(975\) | 12.5197 | − | 10.5215i | 0.400953 | − | 0.336957i | ||||
\(976\) | 1.30384 | − | 1.30384i | 0.0417349 | − | 0.0417349i | ||||
\(977\) | 56.6245i | 1.81158i | 0.423727 | + | 0.905790i | \(0.360721\pi\) | ||||
−0.423727 | + | 0.905790i | \(0.639279\pi\) | |||||||
\(978\) | 4.95068 | + | 4.95068i | 0.158305 | + | 0.158305i | ||||
\(979\) | −1.06404 | + | 1.06404i | −0.0340067 | + | 0.0340067i | ||||
\(980\) | 13.5670 | − | 12.4414i | 0.433383 | − | 0.397425i | ||||
\(981\) | −2.30925 | − | 2.30925i | −0.0737287 | − | 0.0737287i | ||||
\(982\) | 14.2813i | 0.455735i | ||||||||
\(983\) | −38.4422 | + | 38.4422i | −1.22612 | + | 1.22612i | −0.260694 | + | 0.965422i | \(0.583951\pi\) |
−0.965422 | + | 0.260694i | \(0.916049\pi\) | |||||||
\(984\) | −3.94446 | + | 3.94446i | −0.125745 | + | 0.125745i | ||||
\(985\) | 37.4529 | + | 1.62102i | 1.19335 | + | 0.0516501i | ||||
\(986\) | −43.4780 | + | 43.4780i | −1.38462 | + | 1.38462i | ||||
\(987\) | 22.4918 | + | 22.4918i | 0.715922 | + | 0.715922i | ||||
\(988\) | 6.58164 | + | 6.58164i | 0.209390 | + | 0.209390i | ||||
\(989\) | 4.03463 | 0.128294 | ||||||||
\(990\) | −0.577588 | + | 0.529665i | −0.0183570 | + | 0.0168338i | ||||
\(991\) | −32.4216 | + | 32.4216i | −1.02991 | + | 1.02991i | −0.0303674 | + | 0.999539i | \(0.509668\pi\) |
−0.999539 | + | 0.0303674i | \(0.990332\pi\) | |||||||
\(992\) | −2.76854 | − | 2.76854i | −0.0879012 | − | 0.0879012i | ||||
\(993\) | −4.02257 | −0.127652 | ||||||||
\(994\) | 43.8743 | + | 43.8743i | 1.39161 | + | 1.39161i | ||||
\(995\) | 0.925240 | − | 21.3772i | 0.0293321 | − | 0.677702i | ||||
\(996\) | −15.0040 | −0.475420 | ||||||||
\(997\) | −6.92720 | −0.219387 | −0.109693 | − | 0.993965i | \(-0.534987\pi\) | ||||
−0.109693 | + | 0.993965i | \(0.534987\pi\) | |||||||
\(998\) | 4.58214 | − | 4.58214i | 0.145045 | − | 0.145045i | ||||
\(999\) | −6.01048 | − | 0.934944i | −0.190163 | − | 0.0295803i |
(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 | 1110.2.l.a.43.1 | ✓ | 36 | |
5.2 | odd | 4 | 1110.2.o.a.487.18 | yes | 36 | ||
37.31 | odd | 4 | 1110.2.o.a.253.18 | yes | 36 | ||
185.142 | even | 4 | inner | 1110.2.l.a.697.1 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.1 | ✓ | 36 | 1.1 | even | 1 | trivial | |
1110.2.l.a.697.1 | yes | 36 | 185.142 | even | 4 | inner | |
1110.2.o.a.253.18 | yes | 36 | 37.31 | odd | 4 | ||
1110.2.o.a.487.18 | yes | 36 | 5.2 | odd | 4 |