Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(253,1110)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.o (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 | 253.18 | ||
Character | \(\chi\) | \(=\) | 1110.253 |
Dual form | 1110.2.o.a.487.18 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.64803 | + | 1.51129i | −0.737022 | + | 0.675869i | ||||
\(6\) | −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 | \(-0.0140270\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 1.64803 | − | 1.51129i | 0.521153 | − | 0.477912i | ||||
\(11\) | 0.350472i | 0.105671i | 0.998603 | + | 0.0528356i | \(0.0168259\pi\) | ||||
−0.998603 | + | 0.0528356i | \(0.983174\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | 3.27075 | 0.907143 | 0.453572 | − | 0.891220i | \(-0.350150\pi\) | ||||
0.453572 | + | 0.891220i | \(0.350150\pi\) | |||||||
\(14\) | −2.75974 | + | 2.75974i | −0.737570 | + | 0.737570i | ||||
\(15\) | −0.0966903 | + | 2.23398i | −0.0249653 | + | 0.576810i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.07368i | 1.71562i | 0.513967 | + | 0.857810i | \(0.328176\pi\) | ||||
−0.513967 | + | 0.857810i | \(0.671824\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 2.01227 | + | 2.01227i | 0.461647 | + | 0.461647i | 0.899195 | − | 0.437548i | \(-0.144153\pi\) |
−0.437548 | + | 0.899195i | \(0.644153\pi\) | |||||||
\(20\) | −1.64803 | + | 1.51129i | −0.368511 | + | 0.337935i | ||||
\(21\) | − | 3.90286i | − | 0.851673i | ||||||
\(22\) | − | 0.350472i | − | 0.0747209i | ||||||
\(23\) | −1.24836 | −0.260301 | −0.130150 | − | 0.991494i | \(-0.541546\pi\) | ||||
−0.130150 | + | 0.991494i | \(0.541546\pi\) | |||||||
\(24\) | −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 | 0.153165 | − | 0.988201i | \(-0.451053\pi\) |
0.988201 | − | 0.153165i | \(-0.0489467\pi\) | |||||||
\(30\) | 0.0966903 | − | 2.23398i | 0.0176532 | − | 0.407866i | ||||
\(31\) | −2.76854 | − | 2.76854i | −0.497244 | − | 0.497244i | 0.413335 | − | 0.910579i | \(-0.364364\pi\) |
−0.910579 | + | 0.413335i | \(0.864364\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.247821 | + | 0.247821i | 0.0431401 | + | 0.0431401i | ||||
\(34\) | − | 7.07368i | − | 1.21313i | ||||||
\(35\) | −0.377368 | + | 8.71889i | −0.0637869 | + | 1.47376i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | −3.58895 | + | 4.91116i | −0.590019 | + | 0.807389i | ||||
\(38\) | −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 | \(-0.856539\pi\) | ||
0.900144 | − | 0.435592i | \(-0.143461\pi\) | |||||||
\(42\) | 3.90286i | 0.602224i | ||||||||
\(43\) | 3.23195 | 0.492868 | 0.246434 | − | 0.969160i | \(-0.420741\pi\) | ||||
0.246434 | + | 0.969160i | \(0.420741\pi\) | |||||||
\(44\) | 0.350472i | 0.0528356i | ||||||||
\(45\) | 1.51129 | + | 1.64803i | 0.225290 | + | 0.245674i | ||||
\(46\) | 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 | ||||||
\(50\) | −0.432008 | + | 4.98130i | −0.0610951 | + | 0.704462i | ||||
\(51\) | 5.00185 | + | 5.00185i | 0.700399 | + | 0.700399i | ||||
\(52\) | 3.27075 | 0.453572 | ||||||||
\(53\) | −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 | ||||
\(55\) | −0.529665 | − | 0.577588i | −0.0714200 | − | 0.0778820i | ||||
\(56\) | −2.75974 | + | 2.75974i | −0.368785 | + | 0.368785i | ||||
\(57\) | 2.84578 | 0.376933 | ||||||||
\(58\) | −6.14644 | + | 6.14644i | −0.807068 | + | 0.807068i | ||||
\(59\) | 10.6205 | + | 10.6205i | 1.38267 | + | 1.38267i | 0.839841 | + | 0.542832i | \(0.182648\pi\) |
0.542832 | + | 0.839841i | \(0.317352\pi\) | |||||||
\(60\) | −0.0966903 | + | 2.23398i | −0.0124827 | + | 0.288405i | ||||
\(61\) | 1.30384 | + | 1.30384i | 0.166940 | + | 0.166940i | 0.785633 | − | 0.618693i | \(-0.212338\pi\) |
−0.618693 | + | 0.785633i | \(0.712338\pi\) | |||||||
\(62\) | 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 | \(0.119527\pi\) |
0.366744 | + | 0.930322i | \(0.380473\pi\) | |||||||
\(68\) | 7.07368i | 0.857810i | ||||||||
\(69\) | −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 | \(0.107633\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 0.998067 | − | 0.998067i | 0.116815 | − | 0.116815i | −0.646283 | − | 0.763098i | \(-0.723677\pi\) |
0.763098 | + | 0.646283i | \(0.223677\pi\) | |||||||
\(74\) | 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 | \(-0.186990\pi\) |
−0.554237 | + | 0.832359i | \(0.686990\pi\) | |||||||
\(80\) | −1.64803 | + | 1.51129i | −0.184255 | + | 0.168967i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 5.57830i | 0.616020i | ||||||||
\(83\) | −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 | ||||||||
\(87\) | − | 8.69238i | − | 0.931921i | ||||||
\(88\) | − | 0.350472i | − | 0.0373604i | ||||||
\(89\) | 3.03601 | − | 3.03601i | 0.321816 | − | 0.321816i | −0.527647 | − | 0.849464i | \(-0.676926\pi\) |
0.849464 | + | 0.527647i | \(0.176926\pi\) | |||||||
\(90\) | −1.51129 | − | 1.64803i | −0.159304 | − | 0.173718i | ||||
\(91\) | 9.02641 | − | 9.02641i | 0.946225 | − | 0.946225i | ||||
\(92\) | −1.24836 | −0.130150 | ||||||||
\(93\) | −3.91530 | −0.405998 | ||||||||
\(94\) | −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 | ||||
\(97\) | − | 7.94277i | − | 0.806466i | −0.915097 | − | 0.403233i | \(-0.867886\pi\) | ||
0.915097 | − | 0.403233i | \(-0.132114\pi\) | |||||||
\(98\) | 8.23228i | 0.831586i | ||||||||
\(99\) | 0.350472 | 0.0352238 | ||||||||
\(100\) | 0.432008 | − | 4.98130i | 0.0432008 | − | 0.498130i | ||||
\(101\) | − | 0.514124i | − | 0.0511573i | −0.999673 | − | 0.0255786i | \(-0.991857\pi\) | ||
0.999673 | − | 0.0255786i | \(-0.00814282\pi\) | |||||||
\(102\) | −5.00185 | − | 5.00185i | −0.495257 | − | 0.495257i | ||||
\(103\) | − | 9.07861i | − | 0.894542i | −0.894398 | − | 0.447271i | \(-0.852396\pi\) | ||
0.894398 | − | 0.447271i | \(-0.147604\pi\) | |||||||
\(104\) | −3.27075 | −0.320724 | ||||||||
\(105\) | 5.89834 | + | 6.43202i | 0.575620 | + | 0.627701i | ||||
\(106\) | 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 | \(-0.299990\pi\) |
−0.808998 | + | 0.587812i | \(0.799990\pi\) | |||||||
\(110\) | 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 | ||||
\(113\) | − | 7.85255i | − | 0.738705i | −0.929289 | − | 0.369353i | \(-0.879579\pi\) | ||
0.929289 | − | 0.369353i | \(-0.120421\pi\) | |||||||
\(114\) | −2.84578 | −0.266532 | ||||||||
\(115\) | 2.05733 | − | 1.88663i | 0.191847 | − | 0.175929i | ||||
\(116\) | 6.14644 | − | 6.14644i | 0.570683 | − | 0.570683i | ||||
\(117\) | − | 3.27075i | − | 0.302381i | ||||||
\(118\) | −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 | ||||
\(125\) | 6.81623 | + | 8.86223i | 0.609662 | + | 0.792662i | ||||
\(126\) | 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 | \(0.879225\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.28533 | − | 2.28533i | 0.201212 | − | 0.201212i | ||||
\(130\) | 5.39030 | − | 4.94305i | 0.472760 | − | 0.433534i | ||||
\(131\) | −3.62929 | − | 3.62929i | −0.317093 | − | 0.317093i | 0.530557 | − | 0.847649i | \(-0.321983\pi\) |
−0.847649 | + | 0.530557i | \(0.821983\pi\) | |||||||
\(132\) | 0.247821 | + | 0.247821i | 0.0215701 | + | 0.0215701i | ||||
\(133\) | 11.1067 | 0.963070 | ||||||||
\(134\) | −10.6169 | − | 10.6169i | −0.917164 | − | 0.917164i | ||||
\(135\) | 2.23398 | + | 0.0966903i | 0.192270 | + | 0.00832178i | ||||
\(136\) | − | 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 | \(-0.450306\pi\) | ||||
0.155486 | + | 0.987838i | \(0.450306\pi\) | |||||||
\(140\) | −0.377368 | + | 8.71889i | −0.0318934 | + | 0.736880i | ||||
\(141\) | − | 8.14998i | − | 0.686352i | ||||||
\(142\) | −15.8980 | −1.33413 | ||||||||
\(143\) | 1.14631i | 0.0958590i | ||||||||
\(144\) | − | 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 | ||||
\(148\) | −3.58895 | + | 4.91116i | −0.295010 | + | 0.403695i | ||||
\(149\) | − | 16.9433i | − | 1.38805i | −0.719951 | − | 0.694025i | \(-0.755836\pi\) | ||
0.719951 | − | 0.694025i | \(-0.244164\pi\) | |||||||
\(150\) | 3.21684 | + | 3.82779i | 0.262654 | + | 0.312538i | ||||
\(151\) | 10.7953i | 0.878510i | 0.898362 | + | 0.439255i | \(0.144758\pi\) | ||||
−0.898362 | + | 0.439255i | \(0.855242\pi\) | |||||||
\(152\) | −2.01227 | − | 2.01227i | −0.163217 | − | 0.163217i | ||||
\(153\) | 7.07368 | 0.571873 | ||||||||
\(154\) | −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 | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | − | 7.00131i | − | 0.548385i | −0.961675 | − | 0.274193i | \(-0.911589\pi\) | ||
0.961675 | − | 0.274193i | \(-0.0884106\pi\) | |||||||
\(164\) | − | 5.57830i | − | 0.435592i | ||||||
\(165\) | −0.782946 | − | 0.0338872i | −0.0609523 | − | 0.00263812i | ||||
\(166\) | 10.6094 | + | 10.6094i | 0.823451 | + | 0.823451i | ||||
\(167\) | 14.7018i | 1.13766i | 0.822455 | + | 0.568830i | \(0.192604\pi\) | ||||
−0.822455 | + | 0.568830i | \(0.807396\pi\) | |||||||
\(168\) | 3.90286i | 0.301112i | ||||||||
\(169\) | −2.30219 | −0.177091 | ||||||||
\(170\) | 10.6904 | + | 11.6576i | 0.819915 | + | 0.894101i | ||||
\(171\) | 2.01227 | − | 2.01227i | 0.153882 | − | 0.153882i | ||||
\(172\) | 3.23195 | 0.246434 | ||||||||
\(173\) | 3.00005 | − | 3.00005i | 0.228090 | − | 0.228090i | −0.583805 | − | 0.811894i | \(-0.698437\pi\) |
0.811894 | + | 0.583805i | \(0.198437\pi\) | |||||||
\(174\) | 8.69238i | 0.658968i | ||||||||
\(175\) | −12.5548 | − | 14.9393i | −0.949057 | − | 1.12931i | ||||
\(176\) | 0.350472i | 0.0264178i | ||||||||
\(177\) | 15.0197 | 1.12895 | ||||||||
\(178\) | −3.03601 | + | 3.03601i | −0.227559 | + | 0.227559i | ||||
\(179\) | −9.62402 | + | 9.62402i | −0.719333 | + | 0.719333i | −0.968469 | − | 0.249136i | \(-0.919853\pi\) |
0.249136 | + | 0.968469i | \(0.419853\pi\) | |||||||
\(180\) | 1.51129 | + | 1.64803i | 0.112645 | + | 0.122837i | ||||
\(181\) | 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 | ||||
\(183\) | 1.84391 | 0.136306 | ||||||||
\(184\) | 1.24836 | 0.0920302 | ||||||||
\(185\) | −1.50749 | − | 13.5177i | −0.110833 | − | 0.993839i | ||||
\(186\) | 3.91530 | 0.287084 | ||||||||
\(187\) | −2.47913 | −0.181292 | ||||||||
\(188\) | 5.76291 | − | 5.76291i | 0.420303 | − | 0.420303i | ||||
\(189\) | −3.90286 | −0.283891 | ||||||||
\(190\) | 6.35741 | + | 0.275159i | 0.461215 | + | 0.0199622i | ||||
\(191\) | 2.11691 | − | 2.11691i | 0.153174 | − | 0.153174i | −0.626360 | − | 0.779534i | \(-0.715456\pi\) |
0.779534 | + | 0.626360i | \(0.215456\pi\) | |||||||
\(192\) | 0.707107 | − | 0.707107i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | −20.7874 | −1.49631 | −0.748154 | − | 0.663525i | \(-0.769060\pi\) | ||||
−0.748154 | + | 0.663525i | \(0.769060\pi\) | |||||||
\(194\) | 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 | \(0.453733\pi\) | |||||||
\(198\) | −0.350472 | −0.0249070 | ||||||||
\(199\) | −6.76638 | + | 6.76638i | −0.479656 | + | 0.479656i | −0.905022 | − | 0.425366i | \(-0.860146\pi\) |
0.425366 | + | 0.905022i | \(0.360146\pi\) | |||||||
\(200\) | −0.432008 | + | 4.98130i | −0.0305476 | + | 0.352231i | ||||
\(201\) | 15.0146 | 1.05905 | ||||||||
\(202\) | 0.514124i | 0.0361737i | ||||||||
\(203\) | − | 33.9251i | − | 2.38108i | ||||||
\(204\) | 5.00185 | + | 5.00185i | 0.350200 | + | 0.350200i | ||||
\(205\) | 8.43043 | + | 9.19321i | 0.588807 | + | 0.642082i | ||||
\(206\) | 9.07861i | 0.632537i | ||||||||
\(207\) | 1.24836i | 0.0867669i | ||||||||
\(208\) | 3.27075 | 0.226786 | ||||||||
\(209\) | −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 | ||||
\(217\) | −15.2809 | −1.03733 | ||||||||
\(218\) | 2.30925 | + | 2.30925i | 0.156402 | + | 0.156402i | ||||
\(219\) | − | 1.41148i | − | 0.0953790i | ||||||
\(220\) | −0.529665 | − | 0.577588i | −0.0357100 | − | 0.0389410i | ||||
\(221\) | 23.1363i | 1.55631i | ||||||||
\(222\) | −0.934944 | − | 6.01048i | −0.0627494 | − | 0.403397i | ||||
\(223\) | −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 | ||||||||
\(227\) | 16.6142i | 1.10273i | 0.834265 | + | 0.551363i | \(0.185892\pi\) | ||||
−0.834265 | + | 0.551363i | \(0.814108\pi\) | |||||||
\(228\) | 2.84578 | 0.188466 | ||||||||
\(229\) | − | 2.86631i | − | 0.189411i | −0.995505 | − | 0.0947056i | \(-0.969809\pi\) | ||
0.995505 | − | 0.0947056i | \(-0.0301910\pi\) | |||||||
\(230\) | −2.05733 | + | 1.88663i | −0.135656 | + | 0.124401i | ||||
\(231\) | 1.36784 | 0.0899974 | ||||||||
\(232\) | −6.14644 | + | 6.14644i | −0.403534 | + | 0.403534i | ||||
\(233\) | −8.37425 | + | 8.37425i | −0.548615 | + | 0.548615i | −0.926040 | − | 0.377425i | \(-0.876810\pi\) |
0.377425 | + | 0.926040i | \(0.376810\pi\) | |||||||
\(234\) | 3.27075i | 0.213816i | ||||||||
\(235\) | −0.788024 | + | 18.2069i | −0.0514050 | + | 1.18769i | ||||
\(236\) | 10.6205 | + | 10.6205i | 0.691337 | + | 0.691337i | ||||
\(237\) | 3.49594 | 0.227085 | ||||||||
\(238\) | −19.5215 | − | 19.5215i | −1.26539 | − | 1.26539i | ||||
\(239\) | −16.9584 | − | 16.9584i | −1.09695 | − | 1.09695i | −0.994765 | − | 0.102185i | \(-0.967417\pi\) |
−0.102185 | − | 0.994765i | \(-0.532583\pi\) | |||||||
\(240\) | −0.0966903 | + | 2.23398i | −0.00624133 | + | 0.144203i | ||||
\(241\) | 9.32818 | − | 9.32818i | 0.600881 | − | 0.600881i | −0.339665 | − | 0.940546i | \(-0.610314\pi\) |
0.940546 | + | 0.339665i | \(0.110314\pi\) | |||||||
\(242\) | −10.8772 | −0.699211 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 1.30384 | + | 1.30384i | 0.0834698 | + | 0.0834698i | ||||
\(245\) | 12.4414 | + | 13.5670i | 0.794849 | + | 0.866767i | ||||
\(246\) | 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 | −0.875437 | − | 0.483333i | \(-0.839426\pi\) |
−0.483333 | − | 0.875437i | \(-0.660574\pi\) | |||||||
\(252\) | −2.75974 | − | 2.75974i | −0.173847 | − | 0.173847i | ||||
\(253\) | − | 0.437515i | − | 0.0275063i | ||||||
\(254\) | 14.6420 | − | 14.6420i | 0.918719 | − | 0.918719i | ||||
\(255\) | −15.8024 | − | 0.683957i | −0.989587 | − | 0.0428310i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.409575i | 0.0255486i | 0.999918 | + | 0.0127743i | \(0.00406630\pi\) | ||||
−0.999918 | + | 0.0127743i | \(0.995934\pi\) | |||||||
\(258\) | −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 | −0.945245 | − | 0.326362i | \(-0.894177\pi\) |
0.326362 | + | 0.945245i | \(0.394177\pi\) | |||||||
\(264\) | −0.247821 | − | 0.247821i | −0.0152523 | − | 0.0152523i | ||||
\(265\) | 10.9237 | + | 0.472795i | 0.671035 | + | 0.0290435i | ||||
\(266\) | −11.1067 | −0.680994 | ||||||||
\(267\) | − | 4.29357i | − | 0.262762i | ||||||
\(268\) | 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 | \(0.390980\pi\) | |||||||
\(272\) | 7.07368i | 0.428905i | ||||||||
\(273\) | − | 12.7653i | − | 0.772589i | ||||||
\(274\) | 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 | ||||
\(277\) | 24.4538 | 1.46929 | 0.734644 | − | 0.678453i | \(-0.237349\pi\) | ||||
0.734644 | + | 0.678453i | \(0.237349\pi\) | |||||||
\(278\) | −3.66631 | −0.219890 | ||||||||
\(279\) | −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 | −0.889269 | − | 0.457385i | \(-0.848786\pi\) |
0.457385 | + | 0.889269i | \(0.348786\pi\) | |||||||
\(282\) | 8.14998i | 0.485324i | ||||||||
\(283\) | 30.2054i | 1.79552i | 0.440483 | + | 0.897761i | \(0.354807\pi\) | ||||
−0.440483 | + | 0.897761i | \(0.645193\pi\) | |||||||
\(284\) | 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 | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −33.0370 | −1.94335 | ||||||||
\(290\) | 0.840469 | − | 19.4186i | 0.0493540 | − | 1.14030i | ||||
\(291\) | −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 | ||||
\(298\) | 16.9433i | 0.981499i | ||||||||
\(299\) | −4.08307 | −0.236130 | ||||||||
\(300\) | −3.21684 | − | 3.82779i | −0.185724 | − | 0.220997i | ||||
\(301\) | 8.91933 | − | 8.91933i | 0.514101 | − | 0.514101i | ||||
\(302\) | − | 10.7953i | − | 0.621201i | ||||||
\(303\) | −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 | 0.419364 | − | 0.907818i | \(-0.362253\pi\) |
−0.907818 | + | 0.419364i | \(0.862253\pi\) | |||||||
\(308\) | 0.967210 | + | 0.967210i | 0.0551119 | + | 0.0551119i | ||||
\(309\) | −6.41955 | − | 6.41955i | −0.365195 | − | 0.365195i | ||||
\(310\) | −8.74670 | − | 0.378572i | −0.496779 | − | 0.0215014i | ||||
\(311\) | 7.07966 | + | 7.07966i | 0.401451 | + | 0.401451i | 0.878744 | − | 0.477293i | \(-0.158382\pi\) |
−0.477293 | + | 0.878744i | \(0.658382\pi\) | |||||||
\(312\) | −2.31277 | + | 2.31277i | −0.130935 | + | 0.130935i | ||||
\(313\) | −21.8518 | −1.23514 | −0.617568 | − | 0.786518i | \(-0.711882\pi\) | ||||
−0.617568 | + | 0.786518i | \(0.711882\pi\) | |||||||
\(314\) | −6.59408 | + | 6.59408i | −0.372126 | + | 0.372126i | ||||
\(315\) | 8.71889 | + | 0.377368i | 0.491254 | + | 0.0212623i | ||||
\(316\) | 2.47200 | + | 2.47200i | 0.139061 | + | 0.139061i | ||||
\(317\) | −19.1074 | − | 19.1074i | −1.07318 | − | 1.07318i | −0.997102 | − | 0.0760779i | \(-0.975760\pi\) |
−0.0760779 | − | 0.997102i | \(-0.524240\pi\) | |||||||
\(318\) | 4.88978 | 0.274205 | ||||||||
\(319\) | 2.15416 | + | 2.15416i | 0.120610 | + | 0.120610i | ||||
\(320\) | −1.64803 | + | 1.51129i | −0.0921277 | + | 0.0844837i | ||||
\(321\) | − | 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 | ||||||||
\(325\) | 1.41299 | − | 16.2926i | 0.0783786 | − | 0.903751i | ||||
\(326\) | 7.00131i | 0.387767i | ||||||||
\(327\) | −3.26578 | −0.180598 | ||||||||
\(328\) | 5.57830i | 0.308010i | ||||||||
\(329\) | − | 31.8082i | − | 1.75364i | ||||||
\(330\) | 0.782946 | + | 0.0338872i | 0.0430998 | + | 0.00186543i | ||||
\(331\) | 2.84439 | − | 2.84439i | 0.156342 | − | 0.156342i | −0.624602 | − | 0.780943i | \(-0.714739\pi\) |
0.780943 | + | 0.624602i | \(0.214739\pi\) | |||||||
\(332\) | −10.6094 | − | 10.6094i | −0.582268 | − | 0.582268i | ||||
\(333\) | 4.91116 | + | 3.58895i | 0.269130 | + | 0.196673i | ||||
\(334\) | − | 14.7018i | − | 0.804447i | ||||||
\(335\) | −33.5423 | − | 1.45177i | −1.83261 | − | 0.0793186i | ||||
\(336\) | − | 3.90286i | − | 0.212918i | ||||||
\(337\) | 12.4436 | + | 12.4436i | 0.677844 | + | 0.677844i | 0.959512 | − | 0.281668i | \(-0.0908876\pi\) |
−0.281668 | + | 0.959512i | \(0.590888\pi\) | |||||||
\(338\) | 2.30219 | 0.125222 | ||||||||
\(339\) | −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 | ||||
\(347\) | −13.9100 | −0.746727 | −0.373363 | − | 0.927685i | \(-0.621796\pi\) | ||||
−0.373363 | + | 0.927685i | \(0.621796\pi\) | |||||||
\(348\) | − | 8.69238i | − | 0.465961i | ||||||
\(349\) | − | 0.414422i | − | 0.0221835i | −0.999938 | − | 0.0110918i | \(-0.996469\pi\) | ||
0.999938 | − | 0.0110918i | \(-0.00353069\pi\) | |||||||
\(350\) | 12.5548 | + | 14.9393i | 0.671085 | + | 0.798539i | ||||
\(351\) | −2.31277 | − | 2.31277i | −0.123447 | − | 0.123447i | ||||
\(352\) | − | 0.350472i | − | 0.0186802i | ||||||
\(353\) | 29.7855i | 1.58532i | 0.609661 | + | 0.792662i | \(0.291305\pi\) | ||||
−0.609661 | + | 0.792662i | \(0.708695\pi\) | |||||||
\(354\) | −15.0197 | −0.798287 | ||||||||
\(355\) | −26.2004 | + | 24.0265i | −1.39057 | + | 1.27519i | ||||
\(356\) | 3.03601 | − | 3.03601i | 0.160908 | − | 0.160908i | ||||
\(357\) | 27.6076 | 1.46115 | ||||||||
\(358\) | 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 | ||||||
\(362\) | −14.0878 | −0.740436 | ||||||||
\(363\) | 7.69132 | − | 7.69132i | 0.403690 | − | 0.403690i | ||||
\(364\) | 9.02641 | − | 9.02641i | 0.473112 | − | 0.473112i | ||||
\(365\) | −0.136476 | + | 3.15321i | −0.00714350 | + | 0.165047i | ||||
\(366\) | −1.84391 | −0.0963826 | ||||||||
\(367\) | −9.30759 | + | 9.30759i | −0.485852 | + | 0.485852i | −0.906995 | − | 0.421142i | \(-0.861629\pi\) |
0.421142 | + | 0.906995i | \(0.361629\pi\) | |||||||
\(368\) | −1.24836 | −0.0650752 | ||||||||
\(369\) | −5.57830 | −0.290395 | ||||||||
\(370\) | 1.50749 | + | 13.5177i | 0.0783706 | + | 0.702750i | ||||
\(371\) | −19.0841 | −0.990798 | ||||||||
\(372\) | −3.91530 | −0.202999 | ||||||||
\(373\) | −18.3349 | + | 18.3349i | −0.949345 | + | 0.949345i | −0.998777 | − | 0.0494321i | \(-0.984259\pi\) |
0.0494321 | + | 0.998777i | \(0.484259\pi\) | |||||||
\(374\) | 2.47913 | 0.128193 | ||||||||
\(375\) | 11.0863 | + | 1.44674i | 0.572496 | + | 0.0747093i | ||||
\(376\) | −5.76291 | + | 5.76291i | −0.297199 | + | 0.297199i | ||||
\(377\) | 20.1035 | − | 20.1035i | 1.03538 | − | 1.03538i | ||||
\(378\) | 3.90286 | 0.200741 | ||||||||
\(379\) | 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 | ||||
\(383\) | 2.85854 | 0.146065 | 0.0730323 | − | 0.997330i | \(-0.476732\pi\) | ||||
0.0730323 | + | 0.997330i | \(0.476732\pi\) | |||||||
\(384\) | −0.707107 | + | 0.707107i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | −3.05573 | − | 0.132257i | −0.155734 | − | 0.00674044i | ||||
\(386\) | 20.7874 | 1.05805 | ||||||||
\(387\) | − | 3.23195i | − | 0.164289i | ||||||
\(388\) | − | 7.94277i | − | 0.403233i | ||||||
\(389\) | 14.3095 | + | 14.3095i | 0.725519 | + | 0.725519i | 0.969724 | − | 0.244205i | \(-0.0785269\pi\) |
−0.244205 | + | 0.969724i | \(0.578527\pi\) | |||||||
\(390\) | 0.316250 | − | 7.30678i | 0.0160139 | − | 0.369993i | ||||
\(391\) | − | 8.83049i | − | 0.446577i | ||||||
\(392\) | 8.23228i | 0.415793i | ||||||||
\(393\) | −5.13259 | −0.258905 | ||||||||
\(394\) | 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 | 0.694478 | − | 0.719514i | \(-0.255635\pi\) |
−0.719514 | + | 0.694478i | \(0.755635\pi\) | |||||||
\(398\) | 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 | 0.924183 | − | 0.381949i | \(-0.124747\pi\) |
−0.381949 | + | 0.924183i | \(0.624747\pi\) | |||||||
\(402\) | −15.0146 | −0.748861 | ||||||||
\(403\) | −9.05520 | − | 9.05520i | −0.451072 | − | 0.451072i | ||||
\(404\) | − | 0.514124i | − | 0.0255786i | ||||||
\(405\) | 1.64803 | − | 1.51129i | 0.0818913 | − | 0.0750966i | ||||
\(406\) | 33.9251i | 1.68368i | ||||||||
\(407\) | −1.72122 | − | 1.25783i | −0.0853179 | − | 0.0623481i | ||||
\(408\) | −5.00185 | − | 5.00185i | −0.247628 | − | 0.247628i | ||||
\(409\) | 7.92408 | − | 7.92408i | 0.391820 | − | 0.391820i | −0.483515 | − | 0.875336i | \(-0.660640\pi\) |
0.875336 | + | 0.483515i | \(0.160640\pi\) | |||||||
\(410\) | −8.43043 | − | 9.19321i | −0.416349 | − | 0.454020i | ||||
\(411\) | 17.7222i | 0.874174i | ||||||||
\(412\) | − | 9.07861i | − | 0.447271i | ||||||
\(413\) | 58.6196 | 2.88448 | ||||||||
\(414\) | − | 1.24836i | − | 0.0613535i | ||||||
\(415\) | 33.5186 | + | 1.45074i | 1.64536 | + | 0.0712141i | ||||
\(416\) | −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 | \(0.896019\pi\) | |||||||
\(420\) | 5.89834 | + | 6.43202i | 0.287810 | + | 0.313851i | ||||
\(421\) | 10.6585 | + | 10.6585i | 0.519461 | + | 0.519461i | 0.917408 | − | 0.397947i | \(-0.130277\pi\) |
−0.397947 | + | 0.917408i | \(0.630277\pi\) | |||||||
\(422\) | 9.92928 | 0.483350 | ||||||||
\(423\) | −5.76291 | − | 5.76291i | −0.280202 | − | 0.280202i | ||||
\(424\) | 3.45760 | + | 3.45760i | 0.167916 | + | 0.167916i | ||||
\(425\) | 35.2362 | + | 3.05589i | 1.70920 | + | 0.148232i | ||||
\(426\) | −11.2416 | + | 11.2416i | −0.544657 | + | 0.544657i | ||||
\(427\) | 7.19651 | 0.348263 | ||||||||
\(428\) | 1.33354 | − | 1.33354i | 0.0644593 | − | 0.0644593i | ||||
\(429\) | 0.810561 | + | 0.810561i | 0.0391343 | + | 0.0391343i | ||||
\(430\) | 5.32635 | − | 4.88441i | 0.256859 | − | 0.235547i | ||||
\(431\) | −13.6585 | − | 13.6585i | −0.657907 | − | 0.657907i | 0.296978 | − | 0.954884i | \(-0.404021\pi\) |
−0.954884 | + | 0.296978i | \(0.904021\pi\) | |||||||
\(432\) | −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 | ||||
\(438\) | 1.41148i | 0.0674431i | ||||||||
\(439\) | −4.52525 | + | 4.52525i | −0.215979 | + | 0.215979i | −0.806801 | − | 0.590823i | \(-0.798803\pi\) |
0.590823 | + | 0.806801i | \(0.298803\pi\) | |||||||
\(440\) | 0.529665 | + | 0.577588i | 0.0252508 | + | 0.0275354i | ||||
\(441\) | −8.23228 | −0.392013 | ||||||||
\(442\) | − | 23.1363i | − | 1.10048i | ||||||
\(443\) | 17.5292 | − | 17.5292i | 0.832839 | − | 0.832839i | −0.155066 | − | 0.987904i | \(-0.549559\pi\) |
0.987904 | + | 0.155066i | \(0.0495589\pi\) | |||||||
\(444\) | 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 | −0.988340 | − | 0.152263i | \(-0.951344\pi\) |
−0.152263 | − | 0.988340i | \(-0.548656\pi\) | |||||||
\(450\) | 4.98130 | + | 0.432008i | 0.234821 | + | 0.0203650i | ||||
\(451\) | 1.95504 | 0.0920592 | ||||||||
\(452\) | − | 7.85255i | − | 0.369353i | ||||||
\(453\) | 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 | ||||||||
\(457\) | 15.3091i | 0.716131i | 0.933697 | + | 0.358065i | \(0.116564\pi\) | ||||
−0.933697 | + | 0.358065i | \(0.883436\pi\) | |||||||
\(458\) | 2.86631i | 0.133934i | ||||||||
\(459\) | 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 | −0.0833730 | − | 0.996518i | \(-0.526569\pi\) |
0.996518 | + | 0.0833730i | \(0.0265693\pi\) | |||||||
\(462\) | −1.36784 | −0.0636377 | ||||||||
\(463\) | −25.4617 | −1.18331 | −0.591653 | − | 0.806192i | \(-0.701525\pi\) | ||||
−0.591653 | + | 0.806192i | \(0.701525\pi\) | |||||||
\(464\) | 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 | ||||
\(467\) | − | 18.9252i | − | 0.875752i | −0.899035 | − | 0.437876i | \(-0.855731\pi\) | ||
0.899035 | − | 0.437876i | \(-0.144269\pi\) | |||||||
\(468\) | − | 3.27075i | − | 0.151191i | ||||||
\(469\) | 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 | ||||
\(473\) | 1.13271i | 0.0520820i | ||||||||
\(474\) | −3.49594 | −0.160574 | ||||||||
\(475\) | 10.8930 | − | 9.15441i | 0.499807 | − | 0.420033i | ||||
\(476\) | 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 | \(-0.280968\pi\) |
−0.772449 | + | 0.635077i | \(0.780968\pi\) | |||||||
\(480\) | 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 | ||||
\(483\) | 4.87216i | 0.221691i | ||||||||
\(484\) | 10.8772 | 0.494417 | ||||||||
\(485\) | 12.0038 | + | 13.0899i | 0.545065 | + | 0.594383i | ||||
\(486\) | 0.707107 | − | 0.707107i | 0.0320750 | − | 0.0320750i | ||||
\(487\) | 42.0200i | 1.90411i | 0.305929 | + | 0.952054i | \(0.401033\pi\) | ||||
−0.305929 | + | 0.952054i | \(0.598967\pi\) | |||||||
\(488\) | −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 | ||||
\(495\) | −0.577588 | + | 0.529665i | −0.0259607 | + | 0.0238067i | ||||
\(496\) | −2.76854 | − | 2.76854i | −0.124311 | − | 0.124311i | ||||
\(497\) | 43.8743 | − | 43.8743i | 1.96803 | − | 1.96803i | ||||
\(498\) | 15.0040 | 0.672345 | ||||||||
\(499\) | 4.58214 | − | 4.58214i | 0.205125 | − | 0.205125i | −0.597067 | − | 0.802192i | \(-0.703667\pi\) |
0.802192 | + | 0.597067i | \(0.203667\pi\) | |||||||
\(500\) | 6.81623 | + | 8.86223i | 0.304831 | + | 0.396331i | ||||
\(501\) | 10.3957 | + | 10.3957i | 0.464447 | + | 0.464447i | ||||
\(502\) | 21.5270 | + | 21.5270i | 0.960795 | + | 0.960795i | ||||
\(503\) | 4.41445 | 0.196831 | 0.0984153 | − | 0.995145i | \(-0.468623\pi\) | ||||
0.0984153 | + | 0.995145i | \(0.468623\pi\) | |||||||
\(504\) | 2.75974 | + | 2.75974i | 0.122928 | + | 0.122928i | ||||
\(505\) | 0.776991 | + | 0.847293i | 0.0345756 | + | 0.0377040i | ||||
\(506\) | 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 | \(-0.323975\pi\) | ||||
0.525242 | + | 0.850953i | \(0.323975\pi\) | |||||||
\(510\) | 15.8024 | + | 0.683957i | 0.699744 | + | 0.0302861i | ||||
\(511\) | − | 5.50880i | − | 0.243695i | ||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | − | 2.84578i | − | 0.125644i | ||||||
\(514\) | − | 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 | ||||
\(518\) | −3.64895 | − | 23.4580i | −0.160326 | − | 1.03069i | ||||
\(519\) | − | 4.24271i | − | 0.186234i | ||||||
\(520\) | 5.39030 | − | 4.94305i | 0.236380 | − | 0.216767i | ||||
\(521\) | 22.6223i | 0.991100i | 0.868579 | + | 0.495550i | \(0.165034\pi\) | ||||
−0.868579 | + | 0.495550i | \(0.834966\pi\) | |||||||
\(522\) | 6.14644 | + | 6.14644i | 0.269023 | + | 0.269023i | ||||
\(523\) | −38.2884 | −1.67424 | −0.837118 | − | 0.547023i | \(-0.815761\pi\) | ||||
−0.837118 | + | 0.547023i | \(0.815761\pi\) | |||||||
\(524\) | −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 | ||||
\(532\) | 11.1067 | 0.481535 | ||||||||
\(533\) | − | 18.2452i | − | 0.790289i | ||||||
\(534\) | 4.29357i | 0.185801i | ||||||||
\(535\) | −0.182350 | + | 4.21309i | −0.00788367 | + | 0.182148i | ||||
\(536\) | −10.6169 | − | 10.6169i | −0.458582 | − | 0.458582i | ||||
\(537\) | 13.6104i | 0.587333i | ||||||||
\(538\) | − | 19.9758i | − | 0.861217i | ||||||
\(539\) | 2.88518 | 0.124274 | ||||||||
\(540\) | 2.23398 | + | 0.0966903i | 0.0961350 | + | 0.00416089i | ||||
\(541\) | 8.89780 | − | 8.89780i | 0.382546 | − | 0.382546i | −0.489472 | − | 0.872019i | \(-0.662811\pi\) |
0.872019 | + | 0.489472i | \(0.162811\pi\) | |||||||
\(542\) | −11.0572 | −0.474948 | ||||||||
\(543\) | 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 | ||||||||
\(547\) | 7.12339 | 0.304574 | 0.152287 | − | 0.988336i | \(-0.451336\pi\) | ||||
0.152287 | + | 0.988336i | \(0.451336\pi\) | |||||||
\(548\) | −12.5315 | + | 12.5315i | −0.535320 | + | 0.535320i | ||||
\(549\) | 1.30384 | − | 1.30384i | 0.0556465 | − | 0.0556465i | ||||
\(550\) | −1.74581 | − | 0.151407i | −0.0744414 | − | 0.00645600i | ||||
\(551\) | 24.7366 | 1.05382 | ||||||||
\(552\) | 0.882722 | − | 0.882722i | 0.0375712 | − | 0.0375712i | ||||
\(553\) | 13.6441 | 0.580208 | ||||||||
\(554\) | −24.4538 | −1.03894 | ||||||||
\(555\) | −10.6244 | − | 8.49248i | −0.450980 | − | 0.360486i | ||||
\(556\) | 3.66631 | 0.155486 | ||||||||
\(557\) | 45.3868 | 1.92310 | 0.961551 | − | 0.274626i | \(-0.0885539\pi\) | ||||
0.961551 | + | 0.274626i | \(0.0885539\pi\) | |||||||
\(558\) | 2.76854 | − | 2.76854i | 0.117202 | − | 0.117202i | ||||
\(559\) | 10.5709 | 0.447102 | ||||||||
\(560\) | −0.377368 | + | 8.71889i | −0.0159467 | + | 0.368440i | ||||
\(561\) | −1.75301 | + | 1.75301i | −0.0740121 | + | 0.0740121i | ||||
\(562\) | 7.23968 | − | 7.23968i | 0.305388 | − | 0.305388i | ||||
\(563\) | 5.35148 | 0.225538 | 0.112769 | − | 0.993621i | \(-0.464028\pi\) | ||||
0.112769 | + | 0.993621i | \(0.464028\pi\) | |||||||
\(564\) | − | 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 | ||||
\(568\) | −15.8980 | −0.667066 | ||||||||
\(569\) | −13.2588 | + | 13.2588i | −0.555837 | + | 0.555837i | −0.928119 | − | 0.372283i | \(-0.878575\pi\) |
0.372283 | + | 0.928119i | \(0.378575\pi\) | |||||||
\(570\) | 4.68993 | − | 4.30080i | 0.196440 | − | 0.180141i | ||||
\(571\) | −39.9897 | −1.67352 | −0.836758 | − | 0.547574i | \(-0.815552\pi\) | ||||
−0.836758 | + | 0.547574i | \(0.815552\pi\) | |||||||
\(572\) | 1.14631i | 0.0479295i | ||||||||
\(573\) | − | 2.99376i | − | 0.125066i | ||||||
\(574\) | 15.3946 | + | 15.3946i | 0.642560 | + | 0.642560i | ||||
\(575\) | −0.539300 | + | 6.21845i | −0.0224904 | + | 0.259327i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | − | 2.19671i | − | 0.0914503i | −0.998954 | − | 0.0457251i | \(-0.985440\pi\) | ||
0.998954 | − | 0.0457251i | \(-0.0145598\pi\) | |||||||
\(578\) | 33.0370 | 1.37416 | ||||||||
\(579\) | −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 | ||||
\(587\) | 40.3393 | 1.66498 | 0.832490 | − | 0.554041i | \(-0.186915\pi\) | ||||
0.832490 | + | 0.554041i | \(0.186915\pi\) | |||||||
\(588\) | −5.82110 | − | 5.82110i | −0.240058 | − | 0.240058i | ||||
\(589\) | − | 11.1421i | − | 0.459102i | ||||||
\(590\) | 33.5536 | + | 1.45226i | 1.38138 | + | 0.0597885i | ||||
\(591\) | 16.7651i | 0.689625i | ||||||||
\(592\) | −3.58895 | + | 4.91116i | −0.147505 | + | 0.201847i | ||||
\(593\) | −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 | ||||||
\(597\) | 9.56911i | 0.391638i | ||||||||
\(598\) | 4.08307 | 0.166969 | ||||||||
\(599\) | − | 23.9120i | − | 0.977016i | −0.872559 | − | 0.488508i | \(-0.837541\pi\) | ||
0.872559 | − | 0.488508i | \(-0.162459\pi\) | |||||||
\(600\) | 3.21684 | + | 3.82779i | 0.131327 | + | 0.156269i | ||||
\(601\) | −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 | ||||||||
\(605\) | −17.9259 | + | 16.4386i | −0.728792 | + | 0.668322i | ||||
\(606\) | 0.363541 | + | 0.363541i | 0.0147678 | + | 0.0147678i | ||||
\(607\) | −28.5020 | −1.15686 | −0.578430 | − | 0.815732i | \(-0.696334\pi\) | ||||
−0.578430 | + | 0.815732i | \(0.696334\pi\) | |||||||
\(608\) | −2.01227 | − | 2.01227i | −0.0816084 | − | 0.0816084i | ||||
\(609\) | −23.9887 | − | 23.9887i | −0.972070 | − | 0.972070i | ||||
\(610\) | 4.11925 | + | 0.178288i | 0.166783 | + | 0.00721867i | ||||
\(611\) | 18.8490 | − | 18.8490i | 0.762550 | − | 0.762550i | ||||
\(612\) | 7.07368 | 0.285937 | ||||||||
\(613\) | 20.5098 | − | 20.5098i | 0.828384 | − | 0.828384i | −0.158909 | − | 0.987293i | \(-0.550798\pi\) |
0.987293 | + | 0.158909i | \(0.0507978\pi\) | |||||||
\(614\) | 8.55841 | + | 8.55841i | 0.345389 | + | 0.345389i | ||||
\(615\) | 12.4618 | + | 0.539368i | 0.502508 | + | 0.0217494i | ||||
\(616\) | −0.967210 | − | 0.967210i | −0.0389700 | − | 0.0389700i | ||||
\(617\) | 14.5571 | + | 14.5571i | 0.586047 | + | 0.586047i | 0.936559 | − | 0.350511i | \(-0.113992\pi\) |
−0.350511 | + | 0.936559i | \(0.613992\pi\) | |||||||
\(618\) | 6.41955 | + | 6.41955i | 0.258232 | + | 0.258232i | ||||
\(619\) | 22.6423 | 0.910070 | 0.455035 | − | 0.890474i | \(-0.349627\pi\) | ||||
0.455035 | + | 0.890474i | \(0.349627\pi\) | |||||||
\(620\) | 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 | ||||
\(623\) | − | 16.7572i | − | 0.671362i | ||||||
\(624\) | 2.31277 | − | 2.31277i | 0.0925849 | − | 0.0925849i | ||||
\(625\) | −24.6267 | − | 4.30392i | −0.985070 | − | 0.172157i | ||||
\(626\) | 21.8518 | 0.873372 | ||||||||
\(627\) | 0.997366i | 0.0398310i | ||||||||
\(628\) | 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 | 0.996989 | − | 0.0775462i | \(-0.0247085\pi\) |
−0.0775462 | + | 0.996989i | \(0.524709\pi\) | |||||||
\(632\) | −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 | ||||
\(635\) | 2.00215 | − | 46.2587i | 0.0794531 | − | 1.83572i | ||||
\(636\) | −4.88978 | −0.193893 | ||||||||
\(637\) | − | 26.9257i | − | 1.06684i | ||||||
\(638\) | −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 | \(0.817944\pi\) | |||||||
\(642\) | 1.88592i | 0.0744312i | ||||||||
\(643\) | 19.1904i | 0.756794i | 0.925643 | + | 0.378397i | \(0.123525\pi\) | ||||
−0.925643 | + | 0.378397i | \(0.876475\pi\) | |||||||
\(644\) | −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 | ||||
\(647\) | −28.2302 | −1.10984 | −0.554921 | − | 0.831903i | \(-0.687251\pi\) | ||||
−0.554921 | + | 0.831903i | \(0.687251\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −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 | ||||
\(652\) | − | 7.00131i | − | 0.274193i | ||||||
\(653\) | 5.24225i | 0.205145i | 0.994726 | + | 0.102573i | \(0.0327074\pi\) | ||||
−0.994726 | + | 0.102573i | \(0.967293\pi\) | |||||||
\(654\) | 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 | ||||
\(658\) | 31.8082i | 1.24001i | ||||||||
\(659\) | 30.0925 | 1.17224 | 0.586119 | − | 0.810225i | \(-0.300655\pi\) | ||||
0.586119 | + | 0.810225i | \(0.300655\pi\) | |||||||
\(660\) | −0.782946 | − | 0.0338872i | −0.0304761 | − | 0.00131906i | ||||
\(661\) | −32.5054 | − | 32.5054i | −1.26432 | − | 1.26432i | −0.948981 | − | 0.315335i | \(-0.897883\pi\) |
−0.315335 | − | 0.948981i | \(-0.602117\pi\) | |||||||
\(662\) | −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 | ||||
\(668\) | 14.7018i | 0.568830i | ||||||||
\(669\) | −9.18757 | −0.355212 | ||||||||
\(670\) | 33.5423 | + | 1.45177i | 1.29585 | + | 0.0560867i | ||||
\(671\) | −0.456959 | + | 0.456959i | −0.0176407 | + | 0.0176407i | ||||
\(672\) | 3.90286i | 0.150556i | ||||||||
\(673\) | −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 | 0.215329 | − | 0.976542i | \(-0.430918\pi\) |
−0.976542 | + | 0.215329i | \(0.930918\pi\) | |||||||
\(678\) | 5.55259 | + | 5.55259i | 0.213246 | + | 0.213246i | ||||
\(679\) | −21.9199 | − | 21.9199i | −0.841210 | − | 0.841210i | ||||
\(680\) | 10.6904 | + | 11.6576i | 0.409958 | + | 0.447050i | ||||
\(681\) | 11.7480 | + | 11.7480i | 0.450186 | + | 0.450186i | ||||
\(682\) | −0.970295 | + | 0.970295i | −0.0371545 | + | 0.0371545i | ||||
\(683\) | −9.00362 | −0.344514 | −0.172257 | − | 0.985052i | \(-0.555106\pi\) | ||||
−0.172257 | + | 0.985052i | \(0.555106\pi\) | |||||||
\(684\) | 2.01227 | − | 2.01227i | 0.0769411 | − | 0.0769411i | ||||
\(685\) | 1.71357 | − | 39.5911i | 0.0654721 | − | 1.51270i | ||||
\(686\) | 3.40077 | + | 3.40077i | 0.129842 | + | 0.129842i | ||||
\(687\) | −2.02679 | − | 2.02679i | −0.0773268 | − | 0.0773268i | ||||
\(688\) | 3.23195 | 0.123217 | ||||||||
\(689\) | −11.3089 | − | 11.3089i | −0.430837 | − | 0.430837i | ||||
\(690\) | −0.120704 | + | 2.78880i | −0.00459513 | + | 0.106168i | ||||
\(691\) | − | 8.79710i | − | 0.334657i | −0.985901 | − | 0.167329i | \(-0.946486\pi\) | ||
0.985901 | − | 0.167329i | \(-0.0535141\pi\) | |||||||
\(692\) | 3.00005 | − | 3.00005i | 0.114045 | − | 0.114045i | ||||
\(693\) | 0.967210 | − | 0.967210i | 0.0367413 | − | 0.0367413i | ||||
\(694\) | 13.9100 | 0.528016 | ||||||||
\(695\) | −6.04219 | + | 5.54085i | −0.229193 | + | 0.210176i | ||||
\(696\) | 8.69238i | 0.329484i | ||||||||
\(697\) | 39.4592 | 1.49462 | ||||||||
\(698\) | 0.414422i | 0.0156861i | ||||||||
\(699\) | 11.8430i | 0.447943i | ||||||||
\(700\) | −12.5548 | − | 14.9393i | −0.474529 | − | 0.564653i | ||||
\(701\) | 6.74494 | − | 6.74494i | 0.254753 | − | 0.254753i | −0.568163 | − | 0.822916i | \(-0.692346\pi\) |
0.822916 | + | 0.568163i | \(0.192346\pi\) | |||||||
\(702\) | 2.31277 | + | 2.31277i | 0.0872899 | + | 0.0872899i | ||||
\(703\) | −17.1045 | + | 2.66065i | −0.645109 | + | 0.100348i | ||||
\(704\) | 0.350472i | 0.0132089i | ||||||||
\(705\) | 12.3170 | + | 13.4314i | 0.463884 | + | 0.505856i | ||||
\(706\) | − | 29.7855i | − | 1.12099i | ||||||
\(707\) | −1.41885 | − | 1.41885i | −0.0533612 | − | 0.0533612i | ||||
\(708\) | 15.0197 | 0.564474 | ||||||||
\(709\) | 27.6225 | + | 27.6225i | 1.03739 | + | 1.03739i | 0.999273 | + | 0.0381132i | \(0.0121347\pi\) |
0.0381132 | + | 0.999273i | \(0.487865\pi\) | |||||||
\(710\) | 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 | ||||
\(717\) | −23.9829 | −0.895656 | ||||||||
\(718\) | 8.57788i | 0.320124i | ||||||||
\(719\) | 11.0173i | 0.410878i | 0.978670 | + | 0.205439i | \(0.0658622\pi\) | ||||
−0.978670 | + | 0.205439i | \(0.934138\pi\) | |||||||
\(720\) | 1.51129 | + | 1.64803i | 0.0563224 | + | 0.0614185i | ||||
\(721\) | −25.0546 | − | 25.0546i | −0.933081 | − | 0.933081i | ||||
\(722\) | 10.9015i | 0.405713i | ||||||||
\(723\) | − | 13.1920i | − | 0.490617i | ||||||
\(724\) | 14.0878 | 0.523567 | ||||||||
\(725\) | −27.9620 | − | 33.2726i | −1.03848 | − | 1.23571i | ||||
\(726\) | −7.69132 | + | 7.69132i | −0.285452 | + | 0.285452i | ||||
\(727\) | 8.80697 | 0.326632 | 0.163316 | − | 0.986574i | \(-0.447781\pi\) | ||||
0.163316 | + | 0.986574i | \(0.447781\pi\) | |||||||
\(728\) | −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 | ||||||||
\(732\) | 1.84391 | 0.0681528 | ||||||||
\(733\) | 11.9215 | − | 11.9215i | 0.440331 | − | 0.440331i | −0.451792 | − | 0.892123i | \(-0.649215\pi\) |
0.892123 | + | 0.451792i | \(0.149215\pi\) | |||||||
\(734\) | 9.30759 | − | 9.30759i | 0.343549 | − | 0.343549i | ||||
\(735\) | 18.3907 | + | 0.795982i | 0.678352 | + | 0.0293602i | ||||
\(736\) | 1.24836 | 0.0460151 | ||||||||
\(737\) | −3.72094 | + | 3.72094i | −0.137063 | + | 0.137063i | ||||
\(738\) | 5.57830 | 0.205340 | ||||||||
\(739\) | −1.03649 | −0.0381277 | −0.0190639 | − | 0.999818i | \(-0.506069\pi\) | ||||
−0.0190639 | + | 0.999818i | \(0.506069\pi\) | |||||||
\(740\) | −1.50749 | − | 13.5177i | −0.0554164 | − | 0.496920i | ||||
\(741\) | 9.30784 | 0.341932 | ||||||||
\(742\) | 19.0841 | 0.700600 | ||||||||
\(743\) | 16.2854 | − | 16.2854i | 0.597453 | − | 0.597453i | −0.342181 | − | 0.939634i | \(-0.611166\pi\) |
0.939634 | + | 0.342181i | \(0.111166\pi\) | |||||||
\(744\) | 3.91530 | 0.143542 | ||||||||
\(745\) | 25.6062 | + | 27.9231i | 0.938140 | + | 1.02302i | ||||
\(746\) | 18.3349 | − | 18.3349i | 0.671289 | − | 0.671289i | ||||
\(747\) | −10.6094 | + | 10.6094i | −0.388179 | + | 0.388179i | ||||
\(748\) | −2.47913 | −0.0906459 | ||||||||
\(749\) | − | 7.36046i | − | 0.268945i | ||||||
\(750\) | −11.0863 | − | 1.44674i | −0.404816 | − | 0.0528274i | ||||
\(751\) | 44.5447i | 1.62546i | 0.582641 | + | 0.812729i | \(0.302019\pi\) | ||||
−0.582641 | + | 0.812729i | \(0.697981\pi\) | |||||||
\(752\) | 5.76291 | − | 5.76291i | 0.210152 | − | 0.210152i | ||||
\(753\) | −30.4437 | −1.10943 | ||||||||
\(754\) | −20.1035 | + | 20.1035i | −0.732126 | + | 0.732126i | ||||
\(755\) | −16.3148 | − | 17.7910i | −0.593758 | − | 0.647481i | ||||
\(756\) | −3.90286 | −0.141945 | ||||||||
\(757\) | 6.50328i | 0.236366i | 0.992992 | + | 0.118183i | \(0.0377069\pi\) | ||||
−0.992992 | + | 0.118183i | \(0.962293\pi\) | |||||||
\(758\) | − | 0.736373i | − | 0.0267463i | ||||||
\(759\) | −0.309369 | − | 0.309369i | −0.0112294 | − | 0.0112294i | ||||
\(760\) | 6.35741 | + | 0.275159i | 0.230607 | + | 0.00998108i | ||||
\(761\) | 30.3235i | 1.09923i | 0.835419 | + | 0.549613i | \(0.185225\pi\) | ||||
−0.835419 | + | 0.549613i | \(0.814775\pi\) | |||||||
\(762\) | − | 20.7069i | − | 0.750131i | ||||||
\(763\) | −12.7459 | −0.461431 | ||||||||
\(764\) | 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 | \(-0.924522\pi\) |
0.234906 | + | 0.972018i | \(0.424522\pi\) | |||||||
\(770\) | 3.05573 | + | 0.132257i | 0.110121 | + | 0.00476621i | ||||
\(771\) | 0.289614 | + | 0.289614i | 0.0104302 | + | 0.0104302i | ||||
\(772\) | −20.7874 | −0.748154 | ||||||||
\(773\) | −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 | ||||||||
\(775\) | −14.9870 | + | 12.5949i | −0.538347 | + | 0.452422i | ||||
\(776\) | 7.94277i | 0.285129i | ||||||||
\(777\) | 19.1675 | + | 14.0071i | 0.687632 | + | 0.502503i | ||||
\(778\) | −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 | ||||||||
\(782\) | 8.83049i | 0.315778i | ||||||||
\(783\) | −8.69238 | −0.310640 | ||||||||
\(784\) | − | 8.23228i | − | 0.294010i | ||||||
\(785\) | −0.901679 | + | 20.8328i | −0.0321823 | + | 0.743555i | ||||
\(786\) | 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 | ||||||||
\(790\) | 7.80984 | + | 0.338023i | 0.277862 | + | 0.0120263i | ||||
\(791\) | −21.6709 | − | 21.6709i | −0.770530 | − | 0.770530i | ||||
\(792\) | −0.350472 | −0.0124535 | ||||||||
\(793\) | 4.26454 | + | 4.26454i | 0.151438 | + | 0.151438i | ||||
\(794\) | 0.498839 | + | 0.498839i | 0.0177031 | + | 0.0177031i | ||||
\(795\) | 8.05851 | − | 7.38988i | 0.285806 | − | 0.262092i | ||||
\(796\) | −6.76638 | + | 6.76638i | −0.239828 | + | 0.239828i | ||||
\(797\) | −33.9189 | −1.20147 | −0.600734 | − | 0.799449i | \(-0.705125\pi\) | ||||
−0.600734 | + | 0.799449i | \(0.705125\pi\) | |||||||
\(798\) | −7.85360 | + | 7.85360i | −0.278014 | + | 0.278014i | ||||
\(799\) | 40.7650 | + | 40.7650i | 1.44216 | + | 1.44216i | ||||
\(800\) | −0.432008 | + | 4.98130i | −0.0152738 | + | 0.176116i | ||||
\(801\) | −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 | ||||
\(808\) | 0.514124i | 0.0180868i | ||||||||
\(809\) | 11.7103 | − | 11.7103i | 0.411713 | − | 0.411713i | −0.470622 | − | 0.882335i | \(-0.655970\pi\) |
0.882335 | + | 0.470622i | \(0.155970\pi\) | |||||||
\(810\) | −1.64803 | + | 1.51129i | −0.0579059 | + | 0.0531013i | ||||
\(811\) | 12.1269 | 0.425834 | 0.212917 | − | 0.977070i | \(-0.431704\pi\) | ||||
0.212917 | + | 0.977070i | \(0.431704\pi\) | |||||||
\(812\) | − | 33.9251i | − | 1.19054i | ||||||
\(813\) | 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 | ||||
\(820\) | 8.43043 | + | 9.19321i | 0.294403 | + | 0.321041i | ||||
\(821\) | 29.1034 | 1.01571 | 0.507857 | − | 0.861441i | \(-0.330438\pi\) | ||||
0.507857 | + | 0.861441i | \(0.330438\pi\) | |||||||
\(822\) | − | 17.7222i | − | 0.618134i | ||||||
\(823\) | −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 | ||||||||
\(827\) | 14.9493i | 0.519837i | 0.965631 | + | 0.259918i | \(0.0836956\pi\) | ||||
−0.965631 | + | 0.259918i | \(0.916304\pi\) | |||||||
\(828\) | 1.24836i | 0.0433834i | ||||||||
\(829\) | 8.25148 | − | 8.25148i | 0.286586 | − | 0.286586i | −0.549143 | − | 0.835729i | \(-0.685046\pi\) |
0.835729 | + | 0.549143i | \(0.185046\pi\) | |||||||
\(830\) | −33.5186 | − | 1.45074i | −1.16345 | − | 0.0503560i | ||||
\(831\) | 17.2915 | − | 17.2915i | 0.599834 | − | 0.599834i | ||||
\(832\) | 3.27075 | 0.113393 | ||||||||
\(833\) | 58.2326 | 2.01764 | ||||||||
\(834\) | −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 | ||||
\(837\) | 3.91530i | 0.135333i | ||||||||
\(838\) | − | 13.1368i | − | 0.453803i | ||||||
\(839\) | 12.0705 | 0.416720 | 0.208360 | − | 0.978052i | \(-0.433187\pi\) | ||||
0.208360 | + | 0.978052i | \(0.433187\pi\) | |||||||
\(840\) | −5.89834 | − | 6.43202i | −0.203512 | − | 0.221926i | ||||
\(841\) | − | 46.5575i | − | 1.60543i | ||||||
\(842\) | −10.6585 | − | 10.6585i | −0.367315 | − | 0.367315i | ||||
\(843\) | 10.2385i | 0.352631i | ||||||||
\(844\) | −9.92928 | −0.341780 | ||||||||
\(845\) | 3.79407 | − | 3.47927i | 0.130520 | − | 0.119691i | ||||
\(846\) | 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 | ||||
\(853\) | − | 55.2308i | − | 1.89107i | −0.325527 | − | 0.945533i | \(-0.605542\pi\) | ||
0.325527 | − | 0.945533i | \(-0.394458\pi\) | |||||||
\(854\) | −7.19651 | −0.246259 | ||||||||
\(855\) | −0.275159 | + | 6.35741i | −0.00941025 | + | 0.217419i | ||||
\(856\) | −1.33354 | + | 1.33354i | −0.0455796 | + | 0.0455796i | ||||
\(857\) | − | 42.6736i | − | 1.45770i | −0.684672 | − | 0.728851i | \(-0.740054\pi\) | ||
0.684672 | − | 0.728851i | \(-0.259946\pi\) | |||||||
\(858\) | −0.810561 | − | 0.810561i | −0.0276721 | − | 0.0276721i | ||||
\(859\) | −37.8772 | − | 37.8772i | −1.29235 | − | 1.29235i | −0.933327 | − | 0.359028i | \(-0.883108\pi\) |
−0.359028 | − | 0.933327i | \(-0.616892\pi\) | |||||||
\(860\) | −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 | ||||
\(865\) | −0.410229 | + | 9.47812i | −0.0139482 | + | 0.322266i | ||||
\(866\) | 16.2196 | + | 16.2196i | 0.551166 | + | 0.551166i | ||||
\(867\) | −23.3607 | + | 23.3607i | −0.793371 | + | 0.793371i | ||||
\(868\) | −15.2809 | −0.518666 | ||||||||
\(869\) | −0.866367 | + | 0.866367i | −0.0293895 | + | 0.0293895i | ||||
\(870\) | −13.1367 | − | 14.3253i | −0.445376 | − | 0.485674i | ||||
\(871\) | 34.7254 | + | 34.7254i | 1.17662 | + | 1.17662i | ||||
\(872\) | 2.30925 | + | 2.30925i | 0.0782011 | + | 0.0782011i | ||||
\(873\) | −7.94277 | −0.268822 | ||||||||
\(874\) | 2.51203 | + | 2.51203i | 0.0849708 | + | 0.0849708i | ||||
\(875\) | 43.2684 | + | 5.64641i | 1.46274 | + | 0.190884i | ||||
\(876\) | − | 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 | ||||||||
\(880\) | −0.529665 | − | 0.577588i | −0.0178550 | − | 0.0194705i | ||||
\(881\) | − | 35.1647i | − | 1.18473i | −0.805670 | − | 0.592364i | \(-0.798195\pi\) | ||
0.805670 | − | 0.592364i | \(-0.201805\pi\) | |||||||
\(882\) | 8.23228 | 0.277195 | ||||||||
\(883\) | 28.4200i | 0.956410i | 0.878248 | + | 0.478205i | \(0.158712\pi\) | ||||
−0.878248 | + | 0.478205i | \(0.841288\pi\) | |||||||
\(884\) | 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 | \(-0.995375\pi\) |
−0.0145284 | − | 0.999894i | \(-0.504625\pi\) | |||||||
\(888\) | −0.934944 | − | 6.01048i | −0.0313747 | − | 0.201699i | ||||
\(889\) | 80.8160i | 2.71048i | ||||||||
\(890\) | 0.415146 | − | 9.59172i | 0.0139157 | − | 0.321515i | ||||
\(891\) | − | 0.350472i | − | 0.0117413i | ||||||
\(892\) | −6.49659 | − | 6.49659i | −0.217522 | − | 0.217522i | ||||
\(893\) | 23.1931 | 0.776126 | ||||||||
\(894\) | 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 | ||||
\(902\) | −1.95504 | −0.0650957 | ||||||||
\(903\) | − | 12.6138i | − | 0.419762i | ||||||
\(904\) | 7.85255i | 0.261172i | ||||||||
\(905\) | −23.2171 | + | 21.2907i | −0.771761 | + | 0.707726i | ||||
\(906\) | −7.63344 | − | 7.63344i | −0.253604 | − | 0.253604i | ||||
\(907\) | 13.2909i | 0.441317i | 0.975351 | + | 0.220658i | \(0.0708206\pi\) | ||||
−0.975351 | + | 0.220658i | \(0.929179\pi\) | |||||||
\(908\) | 16.6142i | 0.551363i | ||||||||
\(909\) | −0.514124 | −0.0170524 | ||||||||
\(910\) | 1.23428 | − | 28.5173i | 0.0409159 | − | 0.945340i | ||||
\(911\) | −31.5562 | + | 31.5562i | −1.04550 | + | 1.04550i | −0.0465896 | + | 0.998914i | \(0.514835\pi\) |
−0.998914 | + | 0.0465896i | \(0.985165\pi\) | |||||||
\(912\) | 2.84578 | 0.0942332 | ||||||||
\(913\) | 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 | ||||||
\(917\) | −20.0318 | −0.661507 | ||||||||
\(918\) | −5.00185 | + | 5.00185i | −0.165086 | + | 0.165086i | ||||
\(919\) | 1.91721 | − | 1.91721i | 0.0632431 | − | 0.0632431i | −0.674778 | − | 0.738021i | \(-0.735761\pi\) |
0.738021 | + | 0.674778i | \(0.235761\pi\) | |||||||
\(920\) | −2.05733 | + | 1.88663i | −0.0678282 | + | 0.0622004i | ||||
\(921\) | −12.1034 | −0.398821 | ||||||||
\(922\) | −19.6061 | + | 19.6061i | −0.645691 | + | 0.645691i | ||||
\(923\) | 51.9984 | 1.71155 | ||||||||
\(924\) | 1.36784 | 0.0449987 | ||||||||
\(925\) | 22.9135 | + | 19.9993i | 0.753391 | + | 0.657572i | ||||
\(926\) | 25.4617 | 0.836724 | ||||||||
\(927\) | −9.07861 | −0.298181 | ||||||||
\(928\) | −6.14644 | + | 6.14644i | −0.201767 | + | 0.201767i | ||||
\(929\) | −53.6670 | −1.76076 | −0.880378 | − | 0.474273i | \(-0.842711\pi\) | ||||
−0.880378 | + | 0.474273i | \(0.842711\pi\) | |||||||
\(930\) | −6.45254 | + | 5.91716i | −0.211587 | + | 0.194031i | ||||
\(931\) | 16.5656 | − | 16.5656i | 0.542915 | − | 0.542915i | ||||
\(932\) | −8.37425 | + | 8.37425i | −0.274308 | + | 0.274308i | ||||
\(933\) | 10.0122 | 0.327783 | ||||||||
\(934\) | 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 | \(0.107659\pi\) | |||||||
\(938\) | −58.5999 | −1.91335 | ||||||||
\(939\) | −15.4515 | + | 15.4515i | −0.504242 | + | 0.504242i | ||||
\(940\) | −0.788024 | + | 18.2069i | −0.0257025 | + | 0.593843i | ||||
\(941\) | 12.7400 | 0.415313 | 0.207657 | − | 0.978202i | \(-0.433416\pi\) | ||||
0.207657 | + | 0.978202i | \(0.433416\pi\) | |||||||
\(942\) | 9.32544i | 0.303839i | ||||||||
\(943\) | 6.96372i | 0.226770i | ||||||||
\(944\) | 10.6205 | + | 10.6205i | 0.345668 | + | 0.345668i | ||||
\(945\) | 6.43202 | − | 5.89834i | 0.209234 | − | 0.191873i | ||||
\(946\) | − | 1.13271i | − | 0.0368275i | ||||||
\(947\) | 13.4498i | 0.437059i | 0.975830 | + | 0.218529i | \(0.0701260\pi\) | ||||
−0.975830 | + | 0.218529i | \(0.929874\pi\) | |||||||
\(948\) | 3.49594 | 0.113543 | ||||||||
\(949\) | 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 | −0.718507 | − | 0.695520i | \(-0.755174\pi\) |
0.695520 | + | 0.718507i | \(0.255174\pi\) | |||||||
\(954\) | 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 | ||||
\(957\) | 3.04644 | 0.0984773 | ||||||||
\(958\) | 3.00653 | + | 3.00653i | 0.0971366 | + | 0.0971366i | ||||
\(959\) | 69.1674i | 2.23353i | ||||||||
\(960\) | −0.0966903 | + | 2.23398i | −0.00312067 | + | 0.0721013i | ||||
\(961\) | − | 15.6704i | − | 0.505496i | ||||||
\(962\) | 11.7386 | − | 16.0632i | 0.378466 | − | 0.517898i | ||||
\(963\) | −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 | ||||||
\(967\) | 4.89161i | 0.157304i | 0.996902 | + | 0.0786519i | \(0.0250615\pi\) | ||||
−0.996902 | + | 0.0786519i | \(0.974938\pi\) | |||||||
\(968\) | −10.8772 | −0.349605 | ||||||||
\(969\) | 20.1302i | 0.646674i | ||||||||
\(970\) | −12.0038 | − | 13.0899i | −0.385419 | − | 0.420292i | ||||
\(971\) | −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 | ||||||
\(975\) | −10.5215 | − | 12.5197i | −0.336957 | − | 0.400953i | ||||
\(976\) | 1.30384 | + | 1.30384i | 0.0417349 | + | 0.0417349i | ||||
\(977\) | −56.6245 | −1.81158 | −0.905790 | − | 0.423727i | \(-0.860721\pi\) | ||||
−0.905790 | + | 0.423727i | \(0.860721\pi\) | |||||||
\(978\) | 4.95068 | + | 4.95068i | 0.158305 | + | 0.158305i | ||||
\(979\) | 1.06404 | + | 1.06404i | 0.0340067 | + | 0.0340067i | ||||
\(980\) | 12.4414 | + | 13.5670i | 0.397425 | + | 0.433383i | ||||
\(981\) | −2.30925 | + | 2.30925i | −0.0737287 | + | 0.0737287i | ||||
\(982\) | −14.2813 | −0.455735 | ||||||||
\(983\) | 38.4422 | − | 38.4422i | 1.22612 | − | 1.22612i | 0.260694 | − | 0.965422i | \(-0.416049\pi\) |
0.965422 | − | 0.260694i | \(-0.0839512\pi\) | |||||||
\(984\) | 3.94446 | + | 3.94446i | 0.125745 | + | 0.125745i | ||||
\(985\) | 1.62102 | − | 37.4529i | 0.0516501 | − | 1.19335i | ||||
\(986\) | −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 | −0.999539 | − | 0.0303674i | \(-0.990332\pi\) |
−0.0303674 | − | 0.999539i | \(-0.509668\pi\) | |||||||
\(992\) | 2.76854 | + | 2.76854i | 0.0879012 | + | 0.0879012i | ||||
\(993\) | − | 4.02257i | − | 0.127652i | ||||||
\(994\) | −43.8743 | + | 43.8743i | −1.39161 | + | 1.39161i | ||||
\(995\) | 0.925240 | − | 21.3772i | 0.0293321 | − | 0.677702i | ||||
\(996\) | −15.0040 | −0.475420 | ||||||||
\(997\) | 6.92720i | 0.219387i | 0.993965 | + | 0.109693i | \(0.0349869\pi\) | ||||
−0.993965 | + | 0.109693i | \(0.965013\pi\) | |||||||
\(998\) | −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.o.a.253.18 | yes | 36 | |
5.2 | odd | 4 | 1110.2.l.a.697.1 | yes | 36 | ||
37.6 | odd | 4 | 1110.2.l.a.43.1 | ✓ | 36 | ||
185.117 | even | 4 | inner | 1110.2.o.a.487.18 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.1 | ✓ | 36 | 37.6 | odd | 4 | ||
1110.2.l.a.697.1 | yes | 36 | 5.2 | odd | 4 | ||
1110.2.o.a.253.18 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.o.a.487.18 | yes | 36 | 185.117 | even | 4 | inner |