Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [78,3,Mod(7,78)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(78, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 11]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("78.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 78 = 2 \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 78.l (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.12534606201\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 78.37 |
Dual form | 78.3.l.a.19.1 |
$q$-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 \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(67\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{7}{12}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | − | 1.36603i | 0.183013 | − | 0.683013i | ||||
\(3\) | −0.866025 | − | 1.50000i | −0.288675 | − | 0.500000i | ||||
\(4\) | −1.73205 | − | 1.00000i | −0.433013 | − | 0.250000i | ||||
\(5\) | −1.26795 | − | 1.26795i | −0.253590 | − | 0.253590i | 0.568851 | − | 0.822441i | \(-0.307388\pi\) |
−0.822441 | + | 0.568851i | \(0.807388\pi\) | |||||||
\(6\) | −2.36603 | + | 0.633975i | −0.394338 | + | 0.105662i | ||||
\(7\) | −2.50000 | − | 9.33013i | −0.357143 | − | 1.33288i | −0.877766 | − | 0.479089i | \(-0.840967\pi\) |
0.520624 | − | 0.853786i | \(-0.325700\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | −1.50000 | + | 2.59808i | −0.166667 | + | 0.288675i | ||||
\(10\) | −2.19615 | + | 1.26795i | −0.219615 | + | 0.126795i | ||||
\(11\) | 9.92820 | + | 2.66025i | 0.902564 | + | 0.241841i | 0.680117 | − | 0.733104i | \(-0.261929\pi\) |
0.222447 | + | 0.974945i | \(0.428596\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | −11.2583 | − | 6.50000i | −0.866025 | − | 0.500000i | ||||
\(14\) | −13.6603 | −0.975732 | ||||||||
\(15\) | −0.803848 | + | 3.00000i | −0.0535898 | + | 0.200000i | ||||
\(16\) | 2.00000 | + | 3.46410i | 0.125000 | + | 0.216506i | ||||
\(17\) | 16.3923 | + | 9.46410i | 0.964253 | + | 0.556712i | 0.897479 | − | 0.441056i | \(-0.145396\pi\) |
0.0667738 | + | 0.997768i | \(0.478729\pi\) | |||||||
\(18\) | 3.00000 | + | 3.00000i | 0.166667 | + | 0.166667i | ||||
\(19\) | 31.9545 | − | 8.56218i | 1.68181 | − | 0.450641i | 0.713558 | − | 0.700597i | \(-0.247083\pi\) |
0.968257 | + | 0.249956i | \(0.0804160\pi\) | |||||||
\(20\) | 0.928203 | + | 3.46410i | 0.0464102 | + | 0.173205i | ||||
\(21\) | −11.8301 | + | 11.8301i | −0.563339 | + | 0.563339i | ||||
\(22\) | 7.26795 | − | 12.5885i | 0.330361 | − | 0.572203i | ||||
\(23\) | −3.58846 | + | 2.07180i | −0.156020 | + | 0.0900781i | −0.575977 | − | 0.817466i | \(-0.695378\pi\) |
0.419957 | + | 0.907544i | \(0.362045\pi\) | |||||||
\(24\) | 4.73205 | + | 1.26795i | 0.197169 | + | 0.0528312i | ||||
\(25\) | − | 21.7846i | − | 0.871384i | ||||||
\(26\) | −13.0000 | + | 13.0000i | −0.500000 | + | 0.500000i | ||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | −5.00000 | + | 18.6603i | −0.178571 | + | 0.666438i | ||||
\(29\) | 8.66025 | + | 15.0000i | 0.298629 | + | 0.517241i | 0.975823 | − | 0.218564i | \(-0.0701372\pi\) |
−0.677193 | + | 0.735805i | \(0.736804\pi\) | |||||||
\(30\) | 3.80385 | + | 2.19615i | 0.126795 | + | 0.0732051i | ||||
\(31\) | 22.1699 | + | 22.1699i | 0.715157 | + | 0.715157i | 0.967609 | − | 0.252452i | \(-0.0812370\pi\) |
−0.252452 | + | 0.967609i | \(0.581237\pi\) | |||||||
\(32\) | 5.46410 | − | 1.46410i | 0.170753 | − | 0.0457532i | ||||
\(33\) | −4.60770 | − | 17.1962i | −0.139627 | − | 0.521096i | ||||
\(34\) | 18.9282 | − | 18.9282i | 0.556712 | − | 0.556712i | ||||
\(35\) | −8.66025 | + | 15.0000i | −0.247436 | + | 0.428571i | ||||
\(36\) | 5.19615 | − | 3.00000i | 0.144338 | − | 0.0833333i | ||||
\(37\) | −35.7583 | − | 9.58142i | −0.966441 | − | 0.258957i | −0.259117 | − | 0.965846i | \(-0.583431\pi\) |
−0.707325 | + | 0.706889i | \(0.750098\pi\) | |||||||
\(38\) | − | 46.7846i | − | 1.23117i | ||||||
\(39\) | 22.5167i | 0.577350i | ||||||||
\(40\) | 5.07180 | 0.126795 | ||||||||
\(41\) | −6.67949 | + | 24.9282i | −0.162914 | + | 0.608005i | 0.835383 | + | 0.549669i | \(0.185246\pi\) |
−0.998297 | + | 0.0583360i | \(0.981421\pi\) | |||||||
\(42\) | 11.8301 | + | 20.4904i | 0.281670 | + | 0.487866i | ||||
\(43\) | −13.2846 | − | 7.66987i | −0.308944 | − | 0.178369i | 0.337510 | − | 0.941322i | \(-0.390415\pi\) |
−0.646454 | + | 0.762953i | \(0.723749\pi\) | |||||||
\(44\) | −14.5359 | − | 14.5359i | −0.330361 | − | 0.330361i | ||||
\(45\) | 5.19615 | − | 1.39230i | 0.115470 | − | 0.0309401i | ||||
\(46\) | 1.51666 | + | 5.66025i | 0.0329709 | + | 0.123049i | ||||
\(47\) | 7.01924 | − | 7.01924i | 0.149345 | − | 0.149345i | −0.628480 | − | 0.777826i | \(-0.716323\pi\) |
0.777826 | + | 0.628480i | \(0.216323\pi\) | |||||||
\(48\) | 3.46410 | − | 6.00000i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −38.3660 | + | 22.1506i | −0.782980 | + | 0.452054i | ||||
\(50\) | −29.7583 | − | 7.97372i | −0.595167 | − | 0.159474i | ||||
\(51\) | − | 32.7846i | − | 0.642835i | ||||||
\(52\) | 13.0000 | + | 22.5167i | 0.250000 | + | 0.433013i | ||||
\(53\) | −61.6743 | −1.16367 | −0.581833 | − | 0.813308i | \(-0.697664\pi\) | ||||
−0.581833 | + | 0.813308i | \(0.697664\pi\) | |||||||
\(54\) | 1.90192 | − | 7.09808i | 0.0352208 | − | 0.131446i | ||||
\(55\) | −9.21539 | − | 15.9615i | −0.167553 | − | 0.290210i | ||||
\(56\) | 23.6603 | + | 13.6603i | 0.422505 | + | 0.243933i | ||||
\(57\) | −40.5167 | − | 40.5167i | −0.710819 | − | 0.710819i | ||||
\(58\) | 23.6603 | − | 6.33975i | 0.407935 | − | 0.109306i | ||||
\(59\) | −17.1051 | − | 63.8372i | −0.289917 | − | 1.08199i | −0.945171 | − | 0.326577i | \(-0.894105\pi\) |
0.655253 | − | 0.755409i | \(-0.272562\pi\) | |||||||
\(60\) | 4.39230 | − | 4.39230i | 0.0732051 | − | 0.0732051i | ||||
\(61\) | 3.65064 | − | 6.32309i | 0.0598465 | − | 0.103657i | −0.834550 | − | 0.550932i | \(-0.814272\pi\) |
0.894396 | + | 0.447275i | \(0.147606\pi\) | |||||||
\(62\) | 38.3993 | − | 22.1699i | 0.619344 | − | 0.357579i | ||||
\(63\) | 27.9904 | + | 7.50000i | 0.444292 | + | 0.119048i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 6.03332 | + | 22.5167i | 0.0928203 | + | 0.346410i | ||||
\(66\) | −25.1769 | −0.381468 | ||||||||
\(67\) | −10.1532 | + | 37.8923i | −0.151540 | + | 0.565557i | 0.847836 | + | 0.530258i | \(0.177905\pi\) |
−0.999377 | + | 0.0352988i | \(0.988762\pi\) | |||||||
\(68\) | −18.9282 | − | 32.7846i | −0.278356 | − | 0.482127i | ||||
\(69\) | 6.21539 | + | 3.58846i | 0.0900781 | + | 0.0520066i | ||||
\(70\) | 17.3205 | + | 17.3205i | 0.247436 | + | 0.247436i | ||||
\(71\) | 103.890 | − | 27.8372i | 1.46324 | − | 0.392073i | 0.562630 | − | 0.826709i | \(-0.309790\pi\) |
0.900606 | + | 0.434636i | \(0.143123\pi\) | |||||||
\(72\) | −2.19615 | − | 8.19615i | −0.0305021 | − | 0.113835i | ||||
\(73\) | −67.4186 | + | 67.4186i | −0.923542 | + | 0.923542i | −0.997278 | − | 0.0737356i | \(-0.976508\pi\) |
0.0737356 | + | 0.997278i | \(0.476508\pi\) | |||||||
\(74\) | −26.1769 | + | 45.3397i | −0.353742 | + | 0.612699i | ||||
\(75\) | −32.6769 | + | 18.8660i | −0.435692 | + | 0.251547i | ||||
\(76\) | −63.9090 | − | 17.1244i | −0.840907 | − | 0.225320i | ||||
\(77\) | − | 99.2820i | − | 1.28938i | ||||||
\(78\) | 30.7583 | + | 8.24167i | 0.394338 | + | 0.105662i | ||||
\(79\) | 11.8756 | 0.150325 | 0.0751623 | − | 0.997171i | \(-0.476053\pi\) | ||||
0.0751623 | + | 0.997171i | \(0.476053\pi\) | |||||||
\(80\) | 1.85641 | − | 6.92820i | 0.0232051 | − | 0.0866025i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 31.6077 | + | 18.2487i | 0.385460 | + | 0.222545i | ||||
\(83\) | 111.033 | + | 111.033i | 1.33775 | + | 1.33775i | 0.898235 | + | 0.439516i | \(0.144850\pi\) |
0.439516 | + | 0.898235i | \(0.355150\pi\) | |||||||
\(84\) | 32.3205 | − | 8.66025i | 0.384768 | − | 0.103098i | ||||
\(85\) | −8.78461 | − | 32.7846i | −0.103348 | − | 0.385701i | ||||
\(86\) | −15.3397 | + | 15.3397i | −0.178369 | + | 0.178369i | ||||
\(87\) | 15.0000 | − | 25.9808i | 0.172414 | − | 0.298629i | ||||
\(88\) | −25.1769 | + | 14.5359i | −0.286101 | + | 0.165181i | ||||
\(89\) | 162.067 | + | 43.4256i | 1.82097 | + | 0.487928i | 0.996909 | − | 0.0785673i | \(-0.0250346\pi\) |
0.824065 | + | 0.566496i | \(0.191701\pi\) | |||||||
\(90\) | − | 7.60770i | − | 0.0845299i | ||||||
\(91\) | −32.5000 | + | 121.292i | −0.357143 | + | 1.33288i | ||||
\(92\) | 8.28719 | 0.0900781 | ||||||||
\(93\) | 14.0551 | − | 52.4545i | 0.151130 | − | 0.564027i | ||||
\(94\) | −7.01924 | − | 12.1577i | −0.0746727 | − | 0.129337i | ||||
\(95\) | −51.3731 | − | 29.6603i | −0.540769 | − | 0.312213i | ||||
\(96\) | −6.92820 | − | 6.92820i | −0.0721688 | − | 0.0721688i | ||||
\(97\) | 150.246 | − | 40.2583i | 1.54893 | − | 0.415034i | 0.619791 | − | 0.784767i | \(-0.287217\pi\) |
0.929138 | + | 0.369733i | \(0.120551\pi\) | |||||||
\(98\) | 16.2154 | + | 60.5167i | 0.165463 | + | 0.617517i | ||||
\(99\) | −21.8038 | + | 21.8038i | −0.220241 | + | 0.220241i | ||||
\(100\) | −21.7846 | + | 37.7321i | −0.217846 | + | 0.377321i | ||||
\(101\) | −161.785 | + | 93.4064i | −1.60183 | + | 0.924816i | −0.610706 | + | 0.791857i | \(0.709114\pi\) |
−0.991122 | + | 0.132958i | \(0.957552\pi\) | |||||||
\(102\) | −44.7846 | − | 12.0000i | −0.439065 | − | 0.117647i | ||||
\(103\) | 83.2628i | 0.808377i | 0.914676 | + | 0.404188i | \(0.132446\pi\) | ||||
−0.914676 | + | 0.404188i | \(0.867554\pi\) | |||||||
\(104\) | 35.5167 | − | 9.51666i | 0.341506 | − | 0.0915064i | ||||
\(105\) | 30.0000 | 0.285714 | ||||||||
\(106\) | −22.5744 | + | 84.2487i | −0.212966 | + | 0.794799i | ||||
\(107\) | −51.2487 | − | 88.7654i | −0.478960 | − | 0.829583i | 0.520749 | − | 0.853710i | \(-0.325653\pi\) |
−0.999709 | + | 0.0241269i | \(0.992319\pi\) | |||||||
\(108\) | −9.00000 | − | 5.19615i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | 48.1891 | + | 48.1891i | 0.442102 | + | 0.442102i | 0.892718 | − | 0.450616i | \(-0.148796\pi\) |
−0.450616 | + | 0.892718i | \(0.648796\pi\) | |||||||
\(110\) | −25.1769 | + | 6.74613i | −0.228881 | + | 0.0613285i | ||||
\(111\) | 16.5955 | + | 61.9352i | 0.149509 | + | 0.557975i | ||||
\(112\) | 27.3205 | − | 27.3205i | 0.243933 | − | 0.243933i | ||||
\(113\) | 22.6077 | − | 39.1577i | 0.200068 | − | 0.346528i | −0.748482 | − | 0.663155i | \(-0.769217\pi\) |
0.948550 | + | 0.316627i | \(0.102550\pi\) | |||||||
\(114\) | −70.1769 | + | 40.5167i | −0.615587 | + | 0.355409i | ||||
\(115\) | 7.17691 | + | 1.92305i | 0.0624080 | + | 0.0167222i | ||||
\(116\) | − | 34.6410i | − | 0.298629i | ||||||
\(117\) | 33.7750 | − | 19.5000i | 0.288675 | − | 0.166667i | ||||
\(118\) | −93.4641 | −0.792069 | ||||||||
\(119\) | 47.3205 | − | 176.603i | 0.397651 | − | 1.48405i | ||||
\(120\) | −4.39230 | − | 7.60770i | −0.0366025 | − | 0.0633975i | ||||
\(121\) | −13.2968 | − | 7.67691i | −0.109891 | − | 0.0634456i | ||||
\(122\) | −7.30127 | − | 7.30127i | −0.0598465 | − | 0.0598465i | ||||
\(123\) | 43.1769 | − | 11.5692i | 0.351032 | − | 0.0940587i | ||||
\(124\) | −16.2295 | − | 60.5692i | −0.130883 | − | 0.488461i | ||||
\(125\) | −59.3205 | + | 59.3205i | −0.474564 | + | 0.474564i | ||||
\(126\) | 20.4904 | − | 35.4904i | 0.162622 | − | 0.281670i | ||||
\(127\) | 205.115 | − | 118.423i | 1.61508 | − | 0.932465i | 0.626908 | − | 0.779093i | \(-0.284320\pi\) |
0.988169 | − | 0.153372i | \(-0.0490132\pi\) | |||||||
\(128\) | −10.9282 | − | 2.92820i | −0.0853766 | − | 0.0228766i | ||||
\(129\) | 26.5692i | 0.205963i | ||||||||
\(130\) | 32.9667 | 0.253590 | ||||||||
\(131\) | −209.636 | −1.60027 | −0.800137 | − | 0.599817i | \(-0.795240\pi\) | ||||
−0.800137 | + | 0.599817i | \(0.795240\pi\) | |||||||
\(132\) | −9.21539 | + | 34.3923i | −0.0698136 | + | 0.260548i | ||||
\(133\) | −159.772 | − | 276.734i | −1.20130 | − | 2.08071i | ||||
\(134\) | 48.0455 | + | 27.7391i | 0.358549 | + | 0.207008i | ||||
\(135\) | −6.58846 | − | 6.58846i | −0.0488034 | − | 0.0488034i | ||||
\(136\) | −51.7128 | + | 13.8564i | −0.380241 | + | 0.101885i | ||||
\(137\) | 29.4782 | + | 110.014i | 0.215169 | + | 0.803023i | 0.986107 | + | 0.166112i | \(0.0531213\pi\) |
−0.770938 | + | 0.636911i | \(0.780212\pi\) | |||||||
\(138\) | 7.17691 | − | 7.17691i | 0.0520066 | − | 0.0520066i | ||||
\(139\) | 47.8538 | − | 82.8853i | 0.344272 | − | 0.596297i | −0.640949 | − | 0.767583i | \(-0.721459\pi\) |
0.985221 | + | 0.171287i | \(0.0547924\pi\) | |||||||
\(140\) | 30.0000 | − | 17.3205i | 0.214286 | − | 0.123718i | ||||
\(141\) | −16.6077 | − | 4.45002i | −0.117785 | − | 0.0315604i | ||||
\(142\) | − | 152.105i | − | 1.07116i | ||||||
\(143\) | −94.4833 | − | 94.4833i | −0.660723 | − | 0.660723i | ||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 8.03848 | − | 30.0000i | 0.0554378 | − | 0.206897i | ||||
\(146\) | 67.4186 | + | 116.772i | 0.461771 | + | 0.799811i | ||||
\(147\) | 66.4519 | + | 38.3660i | 0.452054 | + | 0.260993i | ||||
\(148\) | 52.3538 | + | 52.3538i | 0.353742 | + | 0.353742i | ||||
\(149\) | −54.9282 | + | 14.7180i | −0.368646 | + | 0.0987783i | −0.438386 | − | 0.898787i | \(-0.644450\pi\) |
0.0697402 | + | 0.997565i | \(0.477783\pi\) | |||||||
\(150\) | 13.8109 | + | 51.5429i | 0.0920726 | + | 0.343620i | ||||
\(151\) | −55.0385 | + | 55.0385i | −0.364493 | + | 0.364493i | −0.865464 | − | 0.500971i | \(-0.832976\pi\) |
0.500971 | + | 0.865464i | \(0.332976\pi\) | |||||||
\(152\) | −46.7846 | + | 81.0333i | −0.307793 | + | 0.533114i | ||||
\(153\) | −49.1769 | + | 28.3923i | −0.321418 | + | 0.185571i | ||||
\(154\) | −135.622 | − | 36.3397i | −0.880661 | − | 0.235972i | ||||
\(155\) | − | 56.2205i | − | 0.362713i | ||||||
\(156\) | 22.5167 | − | 39.0000i | 0.144338 | − | 0.250000i | ||||
\(157\) | 55.4308 | 0.353062 | 0.176531 | − | 0.984295i | \(-0.443512\pi\) | ||||
0.176531 | + | 0.984295i | \(0.443512\pi\) | |||||||
\(158\) | 4.34679 | − | 16.2224i | 0.0275113 | − | 0.102674i | ||||
\(159\) | 53.4115 | + | 92.5115i | 0.335922 | + | 0.581833i | ||||
\(160\) | −8.78461 | − | 5.07180i | −0.0549038 | − | 0.0316987i | ||||
\(161\) | 28.3013 | + | 28.3013i | 0.175784 | + | 0.175784i | ||||
\(162\) | −12.2942 | + | 3.29423i | −0.0758903 | + | 0.0203347i | ||||
\(163\) | −52.9468 | − | 197.600i | −0.324827 | − | 1.21227i | −0.914486 | − | 0.404618i | \(-0.867405\pi\) |
0.589659 | − | 0.807652i | \(-0.299262\pi\) | |||||||
\(164\) | 36.4974 | − | 36.4974i | 0.222545 | − | 0.222545i | ||||
\(165\) | −15.9615 | + | 27.6462i | −0.0967365 | + | 0.167553i | ||||
\(166\) | 192.315 | − | 111.033i | 1.15853 | − | 0.668875i | ||||
\(167\) | −156.315 | − | 41.8846i | −0.936020 | − | 0.250806i | −0.241600 | − | 0.970376i | \(-0.577672\pi\) |
−0.694420 | + | 0.719570i | \(0.744339\pi\) | |||||||
\(168\) | − | 47.3205i | − | 0.281670i | ||||||
\(169\) | 84.5000 | + | 146.358i | 0.500000 | + | 0.866025i | ||||
\(170\) | −48.0000 | −0.282353 | ||||||||
\(171\) | −25.6865 | + | 95.8634i | −0.150214 | + | 0.560605i | ||||
\(172\) | 15.3397 | + | 26.5692i | 0.0891846 | + | 0.154472i | ||||
\(173\) | 232.492 | + | 134.229i | 1.34389 | + | 0.775893i | 0.987375 | − | 0.158398i | \(-0.0506330\pi\) |
0.356511 | + | 0.934291i | \(0.383966\pi\) | |||||||
\(174\) | −30.0000 | − | 30.0000i | −0.172414 | − | 0.172414i | ||||
\(175\) | −203.253 | + | 54.4615i | −1.16145 | + | 0.311209i | ||||
\(176\) | 10.6410 | + | 39.7128i | 0.0604603 | + | 0.225641i | ||||
\(177\) | −80.9423 | + | 80.9423i | −0.457301 | + | 0.457301i | ||||
\(178\) | 118.641 | − | 205.492i | 0.666523 | − | 1.15445i | ||||
\(179\) | −247.492 | + | 142.890i | −1.38264 | + | 0.798267i | −0.992471 | − | 0.122477i | \(-0.960916\pi\) |
−0.390167 | + | 0.920744i | \(0.627583\pi\) | |||||||
\(180\) | −10.3923 | − | 2.78461i | −0.0577350 | − | 0.0154701i | ||||
\(181\) | 177.646i | 0.981471i | 0.871309 | + | 0.490735i | \(0.163272\pi\) | ||||
−0.871309 | + | 0.490735i | \(0.836728\pi\) | |||||||
\(182\) | 153.792 | + | 88.7917i | 0.845009 | + | 0.487866i | ||||
\(183\) | −12.6462 | −0.0691048 | ||||||||
\(184\) | 3.03332 | − | 11.3205i | 0.0164854 | − | 0.0615245i | ||||
\(185\) | 33.1910 | + | 57.4885i | 0.179411 | + | 0.310749i | ||||
\(186\) | −66.5096 | − | 38.3993i | −0.357579 | − | 0.206448i | ||||
\(187\) | 137.569 | + | 137.569i | 0.735664 | + | 0.735664i | ||||
\(188\) | −19.1769 | + | 5.13844i | −0.102005 | + | 0.0273321i | ||||
\(189\) | −12.9904 | − | 48.4808i | −0.0687322 | − | 0.256512i | ||||
\(190\) | −59.3205 | + | 59.3205i | −0.312213 | + | 0.312213i | ||||
\(191\) | −98.6603 | + | 170.885i | −0.516546 | + | 0.894684i | 0.483270 | + | 0.875472i | \(0.339449\pi\) |
−0.999815 | + | 0.0192120i | \(0.993884\pi\) | |||||||
\(192\) | −12.0000 | + | 6.92820i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −20.2846 | − | 5.43524i | −0.105102 | − | 0.0281619i | 0.205885 | − | 0.978576i | \(-0.433993\pi\) |
−0.310987 | + | 0.950414i | \(0.600659\pi\) | |||||||
\(194\) | − | 219.976i | − | 1.13389i | ||||||
\(195\) | 28.5500 | − | 28.5500i | 0.146410 | − | 0.146410i | ||||
\(196\) | 88.6025 | 0.452054 | ||||||||
\(197\) | 39.1487 | − | 146.105i | 0.198725 | − | 0.741650i | −0.792547 | − | 0.609811i | \(-0.791245\pi\) |
0.991271 | − | 0.131839i | \(-0.0420882\pi\) | |||||||
\(198\) | 21.8038 | + | 37.7654i | 0.110120 | + | 0.190734i | ||||
\(199\) | 19.2391 | + | 11.1077i | 0.0966789 | + | 0.0558176i | 0.547560 | − | 0.836766i | \(-0.315557\pi\) |
−0.450881 | + | 0.892584i | \(0.648890\pi\) | |||||||
\(200\) | 43.5692 | + | 43.5692i | 0.217846 | + | 0.217846i | ||||
\(201\) | 65.6314 | − | 17.5859i | 0.326524 | − | 0.0874919i | ||||
\(202\) | 68.3782 | + | 255.191i | 0.338506 | + | 1.26332i | ||||
\(203\) | 118.301 | − | 118.301i | 0.582765 | − | 0.582765i | ||||
\(204\) | −32.7846 | + | 56.7846i | −0.160709 | + | 0.278356i | ||||
\(205\) | 40.0770 | − | 23.1384i | 0.195497 | − | 0.112870i | ||||
\(206\) | 113.739 | + | 30.4763i | 0.552132 | + | 0.147943i | ||||
\(207\) | − | 12.4308i | − | 0.0600521i | ||||||
\(208\) | − | 52.0000i | − | 0.250000i | ||||||
\(209\) | 340.028 | 1.62693 | ||||||||
\(210\) | 10.9808 | − | 40.9808i | 0.0522893 | − | 0.195146i | ||||
\(211\) | −32.1007 | − | 55.6000i | −0.152136 | − | 0.263507i | 0.779877 | − | 0.625933i | \(-0.215282\pi\) |
−0.932012 | + | 0.362426i | \(0.881948\pi\) | |||||||
\(212\) | 106.823 | + | 61.6743i | 0.503882 | + | 0.290917i | ||||
\(213\) | −131.727 | − | 131.727i | −0.618436 | − | 0.618436i | ||||
\(214\) | −140.014 | + | 37.5167i | −0.654271 | + | 0.175311i | ||||
\(215\) | 7.11920 | + | 26.5692i | 0.0331126 | + | 0.123578i | ||||
\(216\) | −10.3923 | + | 10.3923i | −0.0481125 | + | 0.0481125i | ||||
\(217\) | 151.423 | − | 262.272i | 0.697802 | − | 1.20863i | ||||
\(218\) | 83.4660 | − | 48.1891i | 0.382872 | − | 0.221051i | ||||
\(219\) | 159.514 | + | 42.7417i | 0.728375 | + | 0.195167i | ||||
\(220\) | 36.8616i | 0.167553i | ||||||||
\(221\) | −123.033 | − | 213.100i | −0.556712 | − | 0.964253i | ||||
\(222\) | 90.6795 | 0.408466 | ||||||||
\(223\) | −56.5622 | + | 211.093i | −0.253642 | + | 0.946605i | 0.715199 | + | 0.698921i | \(0.246336\pi\) |
−0.968841 | + | 0.247684i | \(0.920331\pi\) | |||||||
\(224\) | −27.3205 | − | 47.3205i | −0.121967 | − | 0.211252i | ||||
\(225\) | 56.5981 | + | 32.6769i | 0.251547 | + | 0.145231i | ||||
\(226\) | −45.2154 | − | 45.2154i | −0.200068 | − | 0.200068i | ||||
\(227\) | 62.4449 | − | 16.7321i | 0.275088 | − | 0.0737095i | −0.118638 | − | 0.992938i | \(-0.537853\pi\) |
0.393725 | + | 0.919228i | \(0.371186\pi\) | |||||||
\(228\) | 29.6603 | + | 110.694i | 0.130089 | + | 0.485498i | ||||
\(229\) | 58.6846 | − | 58.6846i | 0.256265 | − | 0.256265i | −0.567268 | − | 0.823533i | \(-0.692000\pi\) |
0.823533 | + | 0.567268i | \(0.192000\pi\) | |||||||
\(230\) | 5.25387 | − | 9.09996i | 0.0228429 | − | 0.0395651i | ||||
\(231\) | −148.923 | + | 85.9808i | −0.644689 | + | 0.372211i | ||||
\(232\) | −47.3205 | − | 12.6795i | −0.203968 | − | 0.0546530i | ||||
\(233\) | 380.669i | 1.63377i | 0.576798 | + | 0.816887i | \(0.304302\pi\) | ||||
−0.576798 | + | 0.816887i | \(0.695698\pi\) | |||||||
\(234\) | −14.2750 | − | 53.2750i | −0.0610042 | − | 0.227671i | ||||
\(235\) | −17.8001 | −0.0757450 | ||||||||
\(236\) | −34.2102 | + | 127.674i | −0.144959 | + | 0.540993i | ||||
\(237\) | −10.2846 | − | 17.8135i | −0.0433950 | − | 0.0751623i | ||||
\(238\) | −223.923 | − | 129.282i | −0.940853 | − | 0.543202i | ||||
\(239\) | −167.138 | − | 167.138i | −0.699324 | − | 0.699324i | 0.264941 | − | 0.964265i | \(-0.414648\pi\) |
−0.964265 | + | 0.264941i | \(0.914648\pi\) | |||||||
\(240\) | −12.0000 | + | 3.21539i | −0.0500000 | + | 0.0133975i | ||||
\(241\) | 0.796806 | + | 2.97372i | 0.00330625 | + | 0.0123391i | 0.967559 | − | 0.252644i | \(-0.0813002\pi\) |
−0.964253 | + | 0.264983i | \(0.914634\pi\) | |||||||
\(242\) | −15.3538 | + | 15.3538i | −0.0634456 | + | 0.0634456i | ||||
\(243\) | −7.79423 | + | 13.5000i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −12.6462 | + | 7.30127i | −0.0518286 | + | 0.0299232i | ||||
\(245\) | 76.7321 | + | 20.5603i | 0.313192 | + | 0.0839196i | ||||
\(246\) | − | 63.2154i | − | 0.256973i | ||||||
\(247\) | −415.408 | − | 111.308i | −1.68181 | − | 0.450641i | ||||
\(248\) | −88.6795 | −0.357579 | ||||||||
\(249\) | 70.3923 | − | 262.708i | 0.282700 | − | 1.05505i | ||||
\(250\) | 59.3205 | + | 102.746i | 0.237282 | + | 0.410985i | ||||
\(251\) | −180.746 | − | 104.354i | −0.720104 | − | 0.415752i | 0.0946869 | − | 0.995507i | \(-0.469815\pi\) |
−0.814791 | + | 0.579755i | \(0.803148\pi\) | |||||||
\(252\) | −40.9808 | − | 40.9808i | −0.162622 | − | 0.162622i | ||||
\(253\) | −41.1384 | + | 11.0230i | −0.162603 | + | 0.0435692i | ||||
\(254\) | −86.6917 | − | 323.538i | −0.341306 | − | 1.27377i | ||||
\(255\) | −41.5692 | + | 41.5692i | −0.163017 | + | 0.163017i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 64.2769 | − | 37.1103i | 0.250105 | − | 0.144398i | −0.369708 | − | 0.929148i | \(-0.620542\pi\) |
0.619812 | + | 0.784750i | \(0.287209\pi\) | |||||||
\(258\) | 36.2942 | + | 9.72501i | 0.140675 | + | 0.0376938i | ||||
\(259\) | 357.583i | 1.38063i | ||||||||
\(260\) | 12.0666 | − | 45.0333i | 0.0464102 | − | 0.173205i | ||||
\(261\) | −51.9615 | −0.199086 | ||||||||
\(262\) | −76.7321 | + | 286.368i | −0.292870 | + | 1.09301i | ||||
\(263\) | 12.1821 | + | 21.1000i | 0.0463197 | + | 0.0802280i | 0.888256 | − | 0.459349i | \(-0.151917\pi\) |
−0.841936 | + | 0.539577i | \(0.818584\pi\) | |||||||
\(264\) | 43.6077 | + | 25.1769i | 0.165181 | + | 0.0953671i | ||||
\(265\) | 78.1999 | + | 78.1999i | 0.295094 | + | 0.295094i | ||||
\(266\) | −436.506 | + | 116.962i | −1.64100 | + | 0.439705i | ||||
\(267\) | −75.2154 | − | 280.708i | −0.281706 | − | 1.05134i | ||||
\(268\) | 55.4782 | − | 55.4782i | 0.207008 | − | 0.207008i | ||||
\(269\) | 87.8705 | − | 152.196i | 0.326656 | − | 0.565785i | −0.655190 | − | 0.755464i | \(-0.727411\pi\) |
0.981846 | + | 0.189679i | \(0.0607448\pi\) | |||||||
\(270\) | −11.4115 | + | 6.58846i | −0.0422650 | + | 0.0244017i | ||||
\(271\) | 269.169 | + | 72.1237i | 0.993244 | + | 0.266139i | 0.718613 | − | 0.695411i | \(-0.244777\pi\) |
0.274632 | + | 0.961550i | \(0.411444\pi\) | |||||||
\(272\) | 75.7128i | 0.278356i | ||||||||
\(273\) | 210.083 | − | 56.2917i | 0.769536 | − | 0.206197i | ||||
\(274\) | 161.072 | 0.587853 | ||||||||
\(275\) | 57.9526 | − | 216.282i | 0.210737 | − | 0.786480i | ||||
\(276\) | −7.17691 | − | 12.4308i | −0.0260033 | − | 0.0450391i | ||||
\(277\) | −387.100 | − | 223.492i | −1.39747 | − | 0.806831i | −0.403345 | − | 0.915048i | \(-0.632153\pi\) |
−0.994127 | + | 0.108216i | \(0.965486\pi\) | |||||||
\(278\) | −95.7077 | − | 95.7077i | −0.344272 | − | 0.344272i | ||||
\(279\) | −90.8538 | + | 24.3442i | −0.325641 | + | 0.0872552i | ||||
\(280\) | −12.6795 | − | 47.3205i | −0.0452839 | − | 0.169002i | ||||
\(281\) | −5.54483 | + | 5.54483i | −0.0197325 | + | 0.0197325i | −0.716904 | − | 0.697172i | \(-0.754442\pi\) |
0.697172 | + | 0.716904i | \(0.254442\pi\) | |||||||
\(282\) | −12.1577 | + | 21.0577i | −0.0431123 | + | 0.0746727i | ||||
\(283\) | 14.4160 | − | 8.32309i | 0.0509400 | − | 0.0294102i | −0.474314 | − | 0.880356i | \(-0.657304\pi\) |
0.525254 | + | 0.850946i | \(0.323970\pi\) | |||||||
\(284\) | −207.779 | − | 55.6743i | −0.731618 | − | 0.196036i | ||||
\(285\) | 102.746i | 0.360513i | ||||||||
\(286\) | −163.650 | + | 94.4833i | −0.572203 | + | 0.330361i | ||||
\(287\) | 249.282 | 0.868579 | ||||||||
\(288\) | −4.39230 | + | 16.3923i | −0.0152511 | + | 0.0569177i | ||||
\(289\) | 34.6384 | + | 59.9955i | 0.119856 | + | 0.207597i | ||||
\(290\) | −38.0385 | − | 21.9615i | −0.131167 | − | 0.0757294i | ||||
\(291\) | −190.504 | − | 190.504i | −0.654655 | − | 0.654655i | ||||
\(292\) | 184.191 | − | 49.3538i | 0.630791 | − | 0.169020i | ||||
\(293\) | 48.4885 | + | 180.962i | 0.165490 | + | 0.617616i | 0.997977 | + | 0.0635723i | \(0.0202493\pi\) |
−0.832487 | + | 0.554044i | \(0.813084\pi\) | |||||||
\(294\) | 76.7321 | − | 76.7321i | 0.260993 | − | 0.260993i | ||||
\(295\) | −59.2539 | + | 102.631i | −0.200861 | + | 0.347901i | ||||
\(296\) | 90.6795 | − | 52.3538i | 0.306350 | − | 0.176871i | ||||
\(297\) | 51.5885 | + | 13.8231i | 0.173699 | + | 0.0465424i | ||||
\(298\) | 80.4205i | 0.269867i | ||||||||
\(299\) | 53.8667 | 0.180156 | ||||||||
\(300\) | 75.4641 | 0.251547 | ||||||||
\(301\) | −38.3494 | + | 143.122i | −0.127407 | + | 0.475488i | ||||
\(302\) | 55.0385 | + | 95.3294i | 0.182247 | + | 0.315660i | ||||
\(303\) | 280.219 | + | 161.785i | 0.924816 | + | 0.533943i | ||||
\(304\) | 93.5692 | + | 93.5692i | 0.307793 | + | 0.307793i | ||||
\(305\) | −12.6462 | + | 3.38853i | −0.0414629 | + | 0.0111099i | ||||
\(306\) | 20.7846 | + | 77.5692i | 0.0679236 | + | 0.253494i | ||||
\(307\) | 375.069 | − | 375.069i | 1.22172 | − | 1.22172i | 0.254702 | − | 0.967020i | \(-0.418023\pi\) |
0.967020 | − | 0.254702i | \(-0.0819774\pi\) | |||||||
\(308\) | −99.2820 | + | 171.962i | −0.322344 | + | 0.558317i | ||||
\(309\) | 124.894 | − | 72.1077i | 0.404188 | − | 0.233358i | ||||
\(310\) | −76.7987 | − | 20.5781i | −0.247738 | − | 0.0663811i | ||||
\(311\) | − | 296.238i | − | 0.952535i | −0.879300 | − | 0.476268i | \(-0.841989\pi\) | ||
0.879300 | − | 0.476268i | \(-0.158011\pi\) | |||||||
\(312\) | −45.0333 | − | 45.0333i | −0.144338 | − | 0.144338i | ||||
\(313\) | 118.286 | 0.377910 | 0.188955 | − | 0.981986i | \(-0.439490\pi\) | ||||
0.188955 | + | 0.981986i | \(0.439490\pi\) | |||||||
\(314\) | 20.2891 | − | 75.7199i | 0.0646149 | − | 0.241146i | ||||
\(315\) | −25.9808 | − | 45.0000i | −0.0824786 | − | 0.142857i | ||||
\(316\) | −20.5692 | − | 11.8756i | −0.0650925 | − | 0.0375812i | ||||
\(317\) | −280.708 | − | 280.708i | −0.885513 | − | 0.885513i | 0.108575 | − | 0.994088i | \(-0.465371\pi\) |
−0.994088 | + | 0.108575i | \(0.965371\pi\) | |||||||
\(318\) | 145.923 | − | 39.1000i | 0.458878 | − | 0.122956i | ||||
\(319\) | 46.0770 | + | 171.962i | 0.144442 | + | 0.539064i | ||||
\(320\) | −10.1436 | + | 10.1436i | −0.0316987 | + | 0.0316987i | ||||
\(321\) | −88.7654 | + | 153.746i | −0.276528 | + | 0.478960i | ||||
\(322\) | 49.0192 | − | 28.3013i | 0.152234 | − | 0.0878921i | ||||
\(323\) | 604.841 | + | 162.067i | 1.87257 | + | 0.501754i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | −141.600 | + | 245.258i | −0.435692 | + | 0.754641i | ||||
\(326\) | −289.306 | −0.887443 | ||||||||
\(327\) | 30.5507 | − | 114.017i | 0.0934271 | − | 0.348675i | ||||
\(328\) | −36.4974 | − | 63.2154i | −0.111273 | − | 0.192730i | ||||
\(329\) | −83.0385 | − | 47.9423i | −0.252397 | − | 0.145721i | ||||
\(330\) | 31.9230 | + | 31.9230i | 0.0967365 | + | 0.0967365i | ||||
\(331\) | −137.454 | + | 36.8308i | −0.415270 | + | 0.111271i | −0.460404 | − | 0.887710i | \(-0.652295\pi\) |
0.0451334 | + | 0.998981i | \(0.485629\pi\) | |||||||
\(332\) | −81.2820 | − | 303.349i | −0.244825 | − | 0.913701i | ||||
\(333\) | 78.5307 | − | 78.5307i | 0.235828 | − | 0.235828i | ||||
\(334\) | −114.431 | + | 198.200i | −0.342607 | + | 0.593413i | ||||
\(335\) | 60.9193 | − | 35.1718i | 0.181849 | − | 0.104990i | ||||
\(336\) | −64.6410 | − | 17.3205i | −0.192384 | − | 0.0515491i | ||||
\(337\) | 347.508i | 1.03118i | 0.856835 | + | 0.515590i | \(0.172427\pi\) | ||||
−0.856835 | + | 0.515590i | \(0.827573\pi\) | |||||||
\(338\) | 230.858 | − | 61.8583i | 0.683013 | − | 0.183013i | ||||
\(339\) | −78.3154 | −0.231019 | ||||||||
\(340\) | −17.5692 | + | 65.5692i | −0.0516742 | + | 0.192851i | ||||
\(341\) | 161.130 | + | 279.084i | 0.472521 | + | 0.818430i | ||||
\(342\) | 121.550 | + | 70.1769i | 0.355409 | + | 0.205196i | ||||
\(343\) | −32.0929 | − | 32.0929i | −0.0935654 | − | 0.0935654i | ||||
\(344\) | 41.9090 | − | 11.2295i | 0.121828 | − | 0.0326438i | ||||
\(345\) | −3.33082 | − | 12.4308i | −0.00965454 | − | 0.0360312i | ||||
\(346\) | 268.459 | − | 268.459i | 0.775893 | − | 0.775893i | ||||
\(347\) | −218.851 | + | 379.061i | −0.630695 | + | 1.09240i | 0.356715 | + | 0.934213i | \(0.383897\pi\) |
−0.987410 | + | 0.158183i | \(0.949436\pi\) | |||||||
\(348\) | −51.9615 | + | 30.0000i | −0.149315 | + | 0.0862069i | ||||
\(349\) | −432.889 | − | 115.992i | −1.24037 | − | 0.332356i | −0.421761 | − | 0.906707i | \(-0.638588\pi\) |
−0.818609 | + | 0.574351i | \(0.805254\pi\) | |||||||
\(350\) | 297.583i | 0.850238i | ||||||||
\(351\) | −58.5000 | − | 33.7750i | −0.166667 | − | 0.0962250i | ||||
\(352\) | 58.1436 | 0.165181 | ||||||||
\(353\) | −151.914 | + | 566.951i | −0.430352 | + | 1.60609i | 0.321600 | + | 0.946876i | \(0.395779\pi\) |
−0.751951 | + | 0.659218i | \(0.770887\pi\) | |||||||
\(354\) | 80.9423 | + | 140.196i | 0.228651 | + | 0.396034i | ||||
\(355\) | −167.023 | − | 96.4308i | −0.470487 | − | 0.271636i | ||||
\(356\) | −237.282 | − | 237.282i | −0.666523 | − | 0.666523i | ||||
\(357\) | −305.885 | + | 81.9615i | −0.856820 | + | 0.229584i | ||||
\(358\) | 104.603 | + | 390.382i | 0.292186 | + | 1.09045i | ||||
\(359\) | 64.2769 | − | 64.2769i | 0.179044 | − | 0.179044i | −0.611895 | − | 0.790939i | \(-0.709592\pi\) |
0.790939 | + | 0.611895i | \(0.209592\pi\) | |||||||
\(360\) | −7.60770 | + | 13.1769i | −0.0211325 | + | 0.0366025i | ||||
\(361\) | 635.143 | − | 366.700i | 1.75940 | − | 1.01579i | ||||
\(362\) | 242.669 | + | 65.0230i | 0.670357 | + | 0.179622i | ||||
\(363\) | 26.5936i | 0.0732606i | ||||||||
\(364\) | 177.583 | − | 177.583i | 0.487866 | − | 0.487866i | ||||
\(365\) | 170.967 | 0.468402 | ||||||||
\(366\) | −4.62882 | + | 17.2750i | −0.0126470 | + | 0.0471994i | ||||
\(367\) | 108.892 | + | 188.607i | 0.296709 | + | 0.513916i | 0.975381 | − | 0.220526i | \(-0.0707774\pi\) |
−0.678672 | + | 0.734442i | \(0.737444\pi\) | |||||||
\(368\) | −14.3538 | − | 8.28719i | −0.0390050 | − | 0.0225195i | ||||
\(369\) | −54.7461 | − | 54.7461i | −0.148364 | − | 0.148364i | ||||
\(370\) | 90.6795 | − | 24.2975i | 0.245080 | − | 0.0656689i | ||||
\(371\) | 154.186 | + | 575.429i | 0.415595 | + | 1.55102i | ||||
\(372\) | −76.7987 | + | 76.7987i | −0.206448 | + | 0.206448i | ||||
\(373\) | 109.803 | − | 190.185i | 0.294378 | − | 0.509878i | −0.680462 | − | 0.732784i | \(-0.738221\pi\) |
0.974840 | + | 0.222905i | \(0.0715541\pi\) | |||||||
\(374\) | 238.277 | − | 137.569i | 0.637104 | − | 0.367832i | ||||
\(375\) | 140.354 | + | 37.6077i | 0.374277 | + | 0.100287i | ||||
\(376\) | 28.0770i | 0.0746727i | ||||||||
\(377\) | − | 225.167i | − | 0.597259i | ||||||
\(378\) | −70.9808 | −0.187780 | ||||||||
\(379\) | 50.1846 | − | 187.292i | 0.132413 | − | 0.494173i | −0.867582 | − | 0.497294i | \(-0.834327\pi\) |
0.999995 | + | 0.00312126i | \(0.000993528\pi\) | |||||||
\(380\) | 59.3205 | + | 102.746i | 0.156107 | + | 0.270385i | ||||
\(381\) | −355.269 | − | 205.115i | −0.932465 | − | 0.538359i | ||||
\(382\) | 197.321 | + | 197.321i | 0.516546 | + | 0.516546i | ||||
\(383\) | 188.172 | − | 50.4205i | 0.491310 | − | 0.131646i | −0.00465401 | − | 0.999989i | \(-0.501481\pi\) |
0.495964 | + | 0.868343i | \(0.334815\pi\) | |||||||
\(384\) | 5.07180 | + | 18.9282i | 0.0132078 | + | 0.0492922i | ||||
\(385\) | −125.885 | + | 125.885i | −0.326973 | + | 0.326973i | ||||
\(386\) | −14.8494 | + | 25.7199i | −0.0384699 | + | 0.0666317i | ||||
\(387\) | 39.8538 | − | 23.0096i | 0.102981 | − | 0.0594564i | ||||
\(388\) | −300.492 | − | 80.5167i | −0.774465 | − | 0.207517i | ||||
\(389\) | − | 17.7513i | − | 0.0456331i | −0.999740 | − | 0.0228166i | \(-0.992737\pi\) | ||
0.999740 | − | 0.0228166i | \(-0.00726337\pi\) | |||||||
\(390\) | −28.5500 | − | 49.4500i | −0.0732051 | − | 0.126795i | ||||
\(391\) | −78.4308 | −0.200590 | ||||||||
\(392\) | 32.4308 | − | 121.033i | 0.0827316 | − | 0.308758i | ||||
\(393\) | 181.550 | + | 314.454i | 0.461959 | + | 0.800137i | ||||
\(394\) | −185.254 | − | 106.956i | −0.470187 | − | 0.271463i | ||||
\(395\) | −15.0577 | − | 15.0577i | −0.0381208 | − | 0.0381208i | ||||
\(396\) | 59.5692 | − | 15.9615i | 0.150427 | − | 0.0403069i | ||||
\(397\) | −87.3494 | − | 325.992i | −0.220024 | − | 0.821139i | −0.984337 | − | 0.176295i | \(-0.943589\pi\) |
0.764314 | − | 0.644844i | \(-0.223078\pi\) | |||||||
\(398\) | 22.2154 | − | 22.2154i | 0.0558176 | − | 0.0558176i | ||||
\(399\) | −276.734 | + | 479.317i | −0.693569 | + | 1.20130i | ||||
\(400\) | 75.4641 | − | 43.5692i | 0.188660 | − | 0.108923i | ||||
\(401\) | −496.435 | − | 133.019i | −1.23799 | − | 0.331719i | −0.420305 | − | 0.907383i | \(-0.638077\pi\) |
−0.817686 | + | 0.575664i | \(0.804744\pi\) | |||||||
\(402\) | − | 96.0910i | − | 0.239032i | ||||||
\(403\) | −105.492 | − | 393.700i | −0.261766 | − | 0.976923i | ||||
\(404\) | 373.626 | 0.924816 | ||||||||
\(405\) | −4.17691 | + | 15.5885i | −0.0103134 | + | 0.0384900i | ||||
\(406\) | −118.301 | − | 204.904i | −0.291382 | − | 0.504689i | ||||
\(407\) | −329.527 | − | 190.252i | −0.809649 | − | 0.467451i | ||||
\(408\) | 65.5692 | + | 65.5692i | 0.160709 | + | 0.160709i | ||||
\(409\) | −562.838 | + | 150.812i | −1.37613 | + | 0.368734i | −0.869715 | − | 0.493554i | \(-0.835697\pi\) |
−0.506418 | + | 0.862288i | \(0.669031\pi\) | |||||||
\(410\) | −16.9385 | − | 63.2154i | −0.0413134 | − | 0.154184i | ||||
\(411\) | 139.492 | − | 139.492i | 0.339397 | − | 0.339397i | ||||
\(412\) | 83.2628 | − | 144.215i | 0.202094 | − | 0.350037i | ||||
\(413\) | −552.846 | + | 319.186i | −1.33861 | + | 0.772847i | ||||
\(414\) | −16.9808 | − | 4.54998i | −0.0410163 | − | 0.0109903i | ||||
\(415\) | − | 281.569i | − | 0.678480i | ||||||
\(416\) | −71.0333 | − | 19.0333i | −0.170753 | − | 0.0457532i | ||||
\(417\) | −165.771 | −0.397531 | ||||||||
\(418\) | 124.459 | − | 464.487i | 0.297749 | − | 1.11121i | ||||
\(419\) | 391.177 | + | 677.538i | 0.933596 | + | 1.61704i | 0.777118 | + | 0.629355i | \(0.216681\pi\) |
0.156479 | + | 0.987681i | \(0.449986\pi\) | |||||||
\(420\) | −51.9615 | − | 30.0000i | −0.123718 | − | 0.0714286i | ||||
\(421\) | −27.0352 | − | 27.0352i | −0.0642166 | − | 0.0642166i | 0.674269 | − | 0.738486i | \(-0.264459\pi\) |
−0.738486 | + | 0.674269i | \(0.764459\pi\) | |||||||
\(422\) | −87.7006 | + | 23.4993i | −0.207821 | + | 0.0556856i | ||||
\(423\) | 7.70766 | + | 28.7654i | 0.0182214 | + | 0.0680032i | ||||
\(424\) | 123.349 | − | 123.349i | 0.290917 | − | 0.290917i | ||||
\(425\) | 206.172 | − | 357.100i | 0.485110 | − | 0.840235i | ||||
\(426\) | −228.158 | + | 131.727i | −0.535581 | + | 0.309218i | ||||
\(427\) | −68.1218 | − | 18.2532i | −0.159536 | − | 0.0427475i | ||||
\(428\) | 204.995i | 0.478960i | ||||||||
\(429\) | −59.9000 | + | 223.550i | −0.139627 | + | 0.521096i | ||||
\(430\) | 38.9000 | 0.0904652 | ||||||||
\(431\) | 162.995 | − | 608.305i | 0.378178 | − | 1.41138i | −0.470467 | − | 0.882418i | \(-0.655914\pi\) |
0.848645 | − | 0.528963i | \(-0.177419\pi\) | |||||||
\(432\) | 10.3923 | + | 18.0000i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −205.928 | − | 118.892i | −0.475583 | − | 0.274578i | 0.242991 | − | 0.970029i | \(-0.421872\pi\) |
−0.718574 | + | 0.695451i | \(0.755205\pi\) | |||||||
\(434\) | −302.846 | − | 302.846i | −0.697802 | − | 0.697802i | ||||
\(435\) | −51.9615 | + | 13.9230i | −0.119452 | + | 0.0320070i | ||||
\(436\) | −35.2769 | − | 131.655i | −0.0809103 | − | 0.301961i | ||||
\(437\) | −96.9282 | + | 96.9282i | −0.221804 | + | 0.221804i | ||||
\(438\) | 116.772 | − | 202.256i | 0.266604 | − | 0.461771i | ||||
\(439\) | 597.092 | − | 344.731i | 1.36012 | − | 0.785265i | 0.370480 | − | 0.928841i | \(-0.379193\pi\) |
0.989639 | + | 0.143576i | \(0.0458600\pi\) | |||||||
\(440\) | 50.3538 | + | 13.4923i | 0.114441 | + | 0.0306642i | ||||
\(441\) | − | 132.904i | − | 0.301369i | ||||||
\(442\) | −336.133 | + | 90.0666i | −0.760483 | + | 0.203771i | ||||
\(443\) | −304.028 | −0.686294 | −0.343147 | − | 0.939282i | \(-0.611493\pi\) | ||||
−0.343147 | + | 0.939282i | \(0.611493\pi\) | |||||||
\(444\) | 33.1910 | − | 123.870i | 0.0747545 | − | 0.278988i | ||||
\(445\) | −150.431 | − | 260.554i | −0.338047 | − | 0.585514i | ||||
\(446\) | 267.655 | + | 154.531i | 0.600124 | + | 0.346481i | ||||
\(447\) | 69.6462 | + | 69.6462i | 0.155808 | + | 0.155808i | ||||
\(448\) | −74.6410 | + | 20.0000i | −0.166609 | + | 0.0446429i | ||||
\(449\) | −73.4589 | − | 274.153i | −0.163606 | − | 0.610585i | −0.998214 | − | 0.0597407i | \(-0.980973\pi\) |
0.834608 | − | 0.550844i | \(-0.185694\pi\) | |||||||
\(450\) | 65.3538 | − | 65.3538i | 0.145231 | − | 0.145231i | ||||
\(451\) | −132.631 | + | 229.723i | −0.294081 | + | 0.509364i | ||||
\(452\) | −78.3154 | + | 45.2154i | −0.173264 | + | 0.100034i | ||||
\(453\) | 130.222 | + | 34.8930i | 0.287467 | + | 0.0770265i | ||||
\(454\) | − | 91.4256i | − | 0.201378i | ||||||
\(455\) | 195.000 | − | 112.583i | 0.428571 | − | 0.247436i | ||||
\(456\) | 162.067 | 0.355409 | ||||||||
\(457\) | −37.1584 | + | 138.677i | −0.0813093 | + | 0.303451i | −0.994590 | − | 0.103881i | \(-0.966874\pi\) |
0.913280 | + | 0.407331i | \(0.133541\pi\) | |||||||
\(458\) | −58.6846 | − | 101.645i | −0.128132 | − | 0.221932i | ||||
\(459\) | 85.1769 | + | 49.1769i | 0.185571 | + | 0.107139i | ||||
\(460\) | −10.5077 | − | 10.5077i | −0.0228429 | − | 0.0228429i | ||||
\(461\) | 568.435 | − | 152.312i | 1.23305 | − | 0.330394i | 0.417282 | − | 0.908777i | \(-0.362983\pi\) |
0.815765 | + | 0.578383i | \(0.196316\pi\) | |||||||
\(462\) | 62.9423 | + | 234.904i | 0.136239 | + | 0.508450i | ||||
\(463\) | −169.599 | + | 169.599i | −0.366305 | + | 0.366305i | −0.866128 | − | 0.499823i | \(-0.833399\pi\) |
0.499823 | + | 0.866128i | \(0.333399\pi\) | |||||||
\(464\) | −34.6410 | + | 60.0000i | −0.0746574 | + | 0.129310i | ||||
\(465\) | −84.3308 | + | 48.6884i | −0.181357 | + | 0.104706i | ||||
\(466\) | 520.004 | + | 139.335i | 1.11589 | + | 0.299001i | ||||
\(467\) | 732.649i | 1.56884i | 0.620230 | + | 0.784420i | \(0.287039\pi\) | ||||
−0.620230 | + | 0.784420i | \(0.712961\pi\) | |||||||
\(468\) | −78.0000 | −0.166667 | ||||||||
\(469\) | 378.923 | 0.807938 | ||||||||
\(470\) | −6.51528 | + | 24.3154i | −0.0138623 | + | 0.0517348i | ||||
\(471\) | −48.0045 | − | 83.1462i | −0.101920 | − | 0.176531i | ||||
\(472\) | 161.885 | + | 93.4641i | 0.342976 | + | 0.198017i | ||||
\(473\) | −111.488 | − | 111.488i | −0.235705 | − | 0.235705i | ||||
\(474\) | −28.0981 | + | 7.52886i | −0.0592786 | + | 0.0158837i | ||||
\(475\) | −186.524 | − | 696.116i | −0.392681 | − | 1.46551i | ||||
\(476\) | −258.564 | + | 258.564i | −0.543202 | + | 0.543202i | ||||
\(477\) | 92.5115 | − | 160.235i | 0.193944 | − | 0.335922i | ||||
\(478\) | −289.492 | + | 167.138i | −0.605632 | + | 0.349662i | ||||
\(479\) | −357.167 | − | 95.7025i | −0.745651 | − | 0.199796i | −0.134063 | − | 0.990973i | \(-0.542802\pi\) |
−0.611588 | + | 0.791176i | \(0.709469\pi\) | |||||||
\(480\) | 17.5692i | 0.0366025i | ||||||||
\(481\) | 340.300 | + | 340.300i | 0.707484 | + | 0.707484i | ||||
\(482\) | 4.35383 | 0.00903284 | ||||||||
\(483\) | 17.9423 | − | 66.9615i | 0.0371476 | − | 0.138637i | ||||
\(484\) | 15.3538 | + | 26.5936i | 0.0317228 | + | 0.0549455i | ||||
\(485\) | −241.550 | − | 139.459i | −0.498041 | − | 0.287544i | ||||
\(486\) | 15.5885 | + | 15.5885i | 0.0320750 | + | 0.0320750i | ||||
\(487\) | 187.145 | − | 50.1455i | 0.384282 | − | 0.102968i | −0.0615056 | − | 0.998107i | \(-0.519590\pi\) |
0.445788 | + | 0.895139i | \(0.352924\pi\) | |||||||
\(488\) | 5.34490 | + | 19.9474i | 0.0109527 | + | 0.0408759i | ||||
\(489\) | −250.547 | + | 250.547i | −0.512365 | + | 0.512365i | ||||
\(490\) | 56.1718 | − | 97.2923i | 0.114636 | − | 0.198556i | ||||
\(491\) | −31.9808 | + | 18.4641i | −0.0651339 | + | 0.0376051i | −0.532213 | − | 0.846610i | \(-0.678640\pi\) |
0.467079 | + | 0.884215i | \(0.345306\pi\) | |||||||
\(492\) | −86.3538 | − | 23.1384i | −0.175516 | − | 0.0470293i | ||||
\(493\) | 327.846i | 0.665002i | ||||||||
\(494\) | −304.100 | + | 526.717i | −0.615587 | + | 1.06623i | ||||
\(495\) | 55.2923 | 0.111702 | ||||||||
\(496\) | −32.4589 | + | 121.138i | −0.0654414 | + | 0.244231i | ||||
\(497\) | −519.449 | − | 899.711i | −1.04517 | − | 1.81028i | ||||
\(498\) | −333.100 | − | 192.315i | −0.668875 | − | 0.386175i | ||||
\(499\) | 462.769 | + | 462.769i | 0.927393 | + | 0.927393i | 0.997537 | − | 0.0701438i | \(-0.0223458\pi\) |
−0.0701438 | + | 0.997537i | \(0.522346\pi\) | |||||||
\(500\) | 162.067 | − | 43.4256i | 0.324133 | − | 0.0868513i | ||||
\(501\) | 72.5462 | + | 270.746i | 0.144803 | + | 0.540411i | ||||
\(502\) | −208.708 | + | 208.708i | −0.415752 | + | 0.415752i | ||||
\(503\) | 179.378 | − | 310.692i | 0.356617 | − | 0.617678i | −0.630777 | − | 0.775965i | \(-0.717264\pi\) |
0.987393 | + | 0.158286i | \(0.0505969\pi\) | |||||||
\(504\) | −70.9808 | + | 40.9808i | −0.140835 | + | 0.0813110i | ||||
\(505\) | 323.569 | + | 86.7001i | 0.640731 | + | 0.171683i | ||||
\(506\) | 60.2309i | 0.119033i | ||||||||
\(507\) | 146.358 | − | 253.500i | 0.288675 | − | 0.500000i | ||||
\(508\) | −473.692 | −0.932465 | ||||||||
\(509\) | −190.972 | + | 712.717i | −0.375190 | + | 1.40023i | 0.477876 | + | 0.878427i | \(0.341407\pi\) |
−0.853067 | + | 0.521802i | \(0.825260\pi\) | |||||||
\(510\) | 41.5692 | + | 72.0000i | 0.0815083 | + | 0.141176i | ||||
\(511\) | 797.570 | + | 460.477i | 1.56080 | + | 0.901130i | ||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 166.040 | − | 44.4904i | 0.323665 | − | 0.0867259i | ||||
\(514\) | −27.1666 | − | 101.387i | −0.0528533 | − | 0.197251i | ||||
\(515\) | 105.573 | − | 105.573i | 0.204996 | − | 0.204996i | ||||
\(516\) | 26.5692 | − | 46.0192i | 0.0514907 | − | 0.0891846i | ||||
\(517\) | 88.3614 | − | 51.0155i | 0.170912 | − | 0.0986759i | ||||
\(518\) | 488.468 | + | 130.885i | 0.942988 | + | 0.252673i | ||||
\(519\) | − | 464.985i | − | 0.895924i | ||||||
\(520\) | −57.1000 | − | 32.9667i | −0.109808 | − | 0.0633975i | ||||
\(521\) | 156.049 | 0.299518 | 0.149759 | − | 0.988723i | \(-0.452150\pi\) | ||||
0.149759 | + | 0.988723i | \(0.452150\pi\) | |||||||
\(522\) | −19.0192 | + | 70.9808i | −0.0364353 | + | 0.135978i | ||||
\(523\) | −20.9615 | − | 36.3064i | −0.0400794 | − | 0.0694196i | 0.845290 | − | 0.534308i | \(-0.179428\pi\) |
−0.885369 | + | 0.464888i | \(0.846094\pi\) | |||||||
\(524\) | 363.100 | + | 209.636i | 0.692939 | + | 0.400068i | ||||
\(525\) | 257.715 | + | 257.715i | 0.490885 | + | 0.490885i | ||||
\(526\) | 33.2820 | − | 8.91789i | 0.0632738 | − | 0.0169542i | ||||
\(527\) | 153.597 | + | 573.233i | 0.291456 | + | 1.08773i | ||||
\(528\) | 50.3538 | − | 50.3538i | 0.0953671 | − | 0.0953671i | ||||
\(529\) | −255.915 | + | 443.258i | −0.483772 | + | 0.837917i | ||||
\(530\) | 135.446 | − | 78.1999i | 0.255559 | − | 0.147547i | ||||
\(531\) | 191.512 | + | 51.3154i | 0.360662 | + | 0.0966391i | ||||
\(532\) | 639.090i | 1.20130i | ||||||||
\(533\) | 237.233 | − | 237.233i | 0.445091 | − | 0.445091i | ||||
\(534\) | −410.985 | −0.769634 | ||||||||
\(535\) | −47.5692 | + | 177.531i | −0.0889144 | + | 0.331833i | ||||
\(536\) | −55.4782 | − | 96.0910i | −0.103504 | − | 0.179274i | ||||
\(537\) | 428.669 | + | 247.492i | 0.798267 | + | 0.460879i | ||||
\(538\) | −175.741 | − | 175.741i | −0.326656 | − | 0.326656i | ||||
\(539\) | −439.832 | + | 117.853i | −0.816015 | + | 0.218651i | ||||
\(540\) | 4.82309 | + | 18.0000i | 0.00893164 | + | 0.0333333i | ||||
\(541\) | −4.44298 | + | 4.44298i | −0.00821253 | + | 0.00821253i | −0.711201 | − | 0.702989i | \(-0.751848\pi\) |
0.702989 | + | 0.711201i | \(0.251848\pi\) | |||||||
\(542\) | 197.046 | − | 341.293i | 0.363553 | − | 0.629692i | ||||
\(543\) | 266.469 | − | 153.846i | 0.490735 | − | 0.283326i | ||||
\(544\) | 103.426 | + | 27.7128i | 0.190121 | + | 0.0509427i | ||||
\(545\) | − | 122.203i | − | 0.224225i | ||||||
\(546\) | − | 307.583i | − | 0.563339i | ||||||
\(547\) | −101.508 | −0.185572 | −0.0927859 | − | 0.995686i | \(-0.529577\pi\) | ||||
−0.0927859 | + | 0.995686i | \(0.529577\pi\) | |||||||
\(548\) | 58.9564 | − | 220.028i | 0.107585 | − | 0.401511i | ||||
\(549\) | 10.9519 | + | 18.9693i | 0.0199488 | + | 0.0345524i | ||||
\(550\) | −274.235 | − | 158.329i | −0.498608 | − | 0.287872i | ||||
\(551\) | 405.167 | + | 405.167i | 0.735330 | + | 0.735330i | ||||
\(552\) | −19.6077 | + | 5.25387i | −0.0355212 | + | 0.00951787i | ||||
\(553\) | −29.6891 | − | 110.801i | −0.0536874 | − | 0.200364i | ||||
\(554\) | −446.985 | + | 446.985i | −0.806831 | + | 0.806831i | ||||
\(555\) | 57.4885 | − | 99.5730i | 0.103583 | − | 0.179411i | ||||
\(556\) | −165.771 | + | 95.7077i | −0.298148 | + | 0.172136i | ||||
\(557\) | −636.358 | − | 170.512i | −1.14247 | − | 0.306125i | −0.362528 | − | 0.931973i | \(-0.618086\pi\) |
−0.779945 | + | 0.625848i | \(0.784753\pi\) | |||||||
\(558\) | 133.019i | 0.238386i | ||||||||
\(559\) | 99.7083 | + | 172.700i | 0.178369 | + | 0.308944i | ||||
\(560\) | −69.2820 | −0.123718 | ||||||||
\(561\) | 87.2154 | − | 325.492i | 0.155464 | − | 0.580200i | ||||
\(562\) | 5.54483 | + | 9.60392i | 0.00986624 | + | 0.0170888i | ||||
\(563\) | 76.8385 | + | 44.3628i | 0.136481 | + | 0.0787971i | 0.566686 | − | 0.823934i | \(-0.308225\pi\) |
−0.430205 | + | 0.902731i | \(0.641559\pi\) | |||||||
\(564\) | 24.3154 | + | 24.3154i | 0.0431123 | + | 0.0431123i | ||||
\(565\) | −78.3154 | + | 20.9845i | −0.138611 | + | 0.0371408i | ||||
\(566\) | −6.09292 | − | 22.7391i | −0.0107649 | − | 0.0401751i | ||||
\(567\) | −61.4711 | + | 61.4711i | −0.108415 | + | 0.108415i | ||||
\(568\) | −152.105 | + | 263.454i | −0.267791 | + | 0.463827i | ||||
\(569\) | −373.750 | + | 215.785i | −0.656854 | + | 0.379235i | −0.791077 | − | 0.611716i | \(-0.790479\pi\) |
0.134223 | + | 0.990951i | \(0.457146\pi\) | |||||||
\(570\) | 140.354 | + | 37.6077i | 0.246235 | + | 0.0659784i | ||||
\(571\) | − | 959.892i | − | 1.68107i | −0.541756 | − | 0.840536i | \(-0.682240\pi\) | ||
0.541756 | − | 0.840536i | \(-0.317760\pi\) | |||||||
\(572\) | 69.1666 | + | 258.133i | 0.120921 | + | 0.451282i | ||||
\(573\) | 341.769 | 0.596456 | ||||||||
\(574\) | 91.2436 | − | 340.526i | 0.158961 | − | 0.593250i | ||||
\(575\) | 45.1333 | + | 78.1731i | 0.0784927 | + | 0.135953i | ||||
\(576\) | 20.7846 | + | 12.0000i | 0.0360844 | + | 0.0208333i | ||||
\(577\) | −313.669 | − | 313.669i | −0.543621 | − | 0.543621i | 0.380968 | − | 0.924588i | \(-0.375591\pi\) |
−0.924588 | + | 0.380968i | \(0.875591\pi\) | |||||||
\(578\) | 94.6340 | − | 25.3571i | 0.163727 | − | 0.0438704i | ||||
\(579\) | 9.41412 | + | 35.1340i | 0.0162593 | + | 0.0606804i | ||||
\(580\) | −43.9230 | + | 43.9230i | −0.0757294 | + | 0.0757294i | ||||
\(581\) | 758.372 | − | 1313.54i | 1.30529 | − | 2.26082i | ||||
\(582\) | −329.963 | + | 190.504i | −0.566947 | + | 0.327327i | ||||
\(583\) | −612.315 | − | 164.069i | −1.05028 | − | 0.281423i | ||||
\(584\) | − | 269.674i | − | 0.461771i | ||||||
\(585\) | −67.5500 | − | 18.1000i | −0.115470 | − | 0.0309401i | ||||
\(586\) | 264.946 | 0.452126 | ||||||||
\(587\) | −58.5654 | + | 218.569i | −0.0997708 | + | 0.372350i | −0.997700 | − | 0.0677912i | \(-0.978405\pi\) |
0.897929 | + | 0.440141i | \(0.145071\pi\) | |||||||
\(588\) | −76.7321 | − | 132.904i | −0.130497 | − | 0.226027i | ||||
\(589\) | 898.249 | + | 518.604i | 1.52504 | + | 0.880483i | ||||
\(590\) | 118.508 | + | 118.508i | 0.200861 | + | 0.200861i | ||||
\(591\) | −253.061 | + | 67.8076i | −0.428192 | + | 0.114734i | ||||
\(592\) | −38.3257 | − | 143.033i | −0.0647393 | − | 0.241610i | ||||
\(593\) | 335.229 | − | 335.229i | 0.565311 | − | 0.565311i | −0.365500 | − | 0.930811i | \(-0.619102\pi\) |
0.930811 | + | 0.365500i | \(0.119102\pi\) | |||||||
\(594\) | 37.7654 | − | 65.4115i | 0.0635781 | − | 0.110120i | ||||
\(595\) | −283.923 | + | 163.923i | −0.477182 | + | 0.275501i | ||||
\(596\) | 109.856 | + | 29.4359i | 0.184323 | + | 0.0493892i | ||||
\(597\) | − | 38.4782i | − | 0.0644526i | ||||||
\(598\) | 19.7166 | − | 73.5833i | 0.0329709 | − | 0.123049i | ||||
\(599\) | 136.908 | 0.228560 | 0.114280 | − | 0.993449i | \(-0.463544\pi\) | ||||
0.114280 | + | 0.993449i | \(0.463544\pi\) | |||||||
\(600\) | 27.6218 | − | 103.086i | 0.0460363 | − | 0.171810i | ||||
\(601\) | 8.78461 | + | 15.2154i | 0.0146167 | + | 0.0253168i | 0.873241 | − | 0.487288i | \(-0.162014\pi\) |
−0.858625 | + | 0.512605i | \(0.828681\pi\) | |||||||
\(602\) | 181.471 | + | 104.772i | 0.301447 | + | 0.174041i | ||||
\(603\) | −83.2173 | − | 83.2173i | −0.138005 | − | 0.138005i | ||||
\(604\) | 150.368 | − | 40.2910i | 0.248953 | − | 0.0667069i | ||||
\(605\) | 7.12574 | + | 26.5936i | 0.0117781 | + | 0.0439564i | ||||
\(606\) | 323.569 | − | 323.569i | 0.533943 | − | 0.533943i | ||||
\(607\) | −422.300 | + | 731.445i | −0.695716 | + | 1.20502i | 0.274222 | + | 0.961666i | \(0.411580\pi\) |
−0.969939 | + | 0.243350i | \(0.921754\pi\) | |||||||
\(608\) | 162.067 | − | 93.5692i | 0.266557 | − | 0.153897i | ||||
\(609\) | −279.904 | − | 75.0000i | −0.459612 | − | 0.123153i | ||||
\(610\) | 18.5153i | 0.0303529i | ||||||||
\(611\) | −124.650 | + | 33.3999i | −0.204010 | + | 0.0546642i | ||||
\(612\) | 113.569 | 0.185571 | ||||||||
\(613\) | −163.158 | + | 608.915i | −0.266164 | + | 0.993337i | 0.695370 | + | 0.718651i | \(0.255240\pi\) |
−0.961534 | + | 0.274685i | \(0.911426\pi\) | |||||||
\(614\) | −375.069 | − | 649.638i | −0.610861 | − | 1.05804i | ||||
\(615\) | −69.4153 | − | 40.0770i | −0.112870 | − | 0.0651658i | ||||
\(616\) | 198.564 | + | 198.564i | 0.322344 | + | 0.322344i | ||||
\(617\) | 107.014 | − | 28.6743i | 0.173443 | − | 0.0464738i | −0.171053 | − | 0.985262i | \(-0.554717\pi\) |
0.344495 | + | 0.938788i | \(0.388050\pi\) | |||||||
\(618\) | −52.7865 | − | 197.002i | −0.0854150 | − | 0.318773i | ||||
\(619\) | −111.970 | + | 111.970i | −0.180888 | + | 0.180888i | −0.791743 | − | 0.610854i | \(-0.790826\pi\) |
0.610854 | + | 0.791743i | \(0.290826\pi\) | |||||||
\(620\) | −56.2205 | + | 97.3768i | −0.0906783 | + | 0.157059i | ||||
\(621\) | −18.6462 | + | 10.7654i | −0.0300260 | + | 0.0173355i | ||||
\(622\) | −404.669 | − | 108.431i | −0.650594 | − | 0.174326i | ||||
\(623\) | − | 1620.67i | − | 2.60139i | ||||||
\(624\) | −78.0000 | + | 45.0333i | −0.125000 | + | 0.0721688i | ||||
\(625\) | −394.184 | −0.630695 | ||||||||
\(626\) | 43.2956 | − | 161.581i | 0.0691623 | − | 0.258117i | ||||
\(627\) | −294.473 | − | 510.042i | −0.469654 | − | 0.813465i | ||||
\(628\) | −96.0089 | − | 55.4308i | −0.152880 | − | 0.0882656i | ||||
\(629\) | −495.482 | − | 495.482i | −0.787730 | − | 0.787730i | ||||
\(630\) | −70.9808 | + | 19.0192i | −0.112668 | + | 0.0301893i | ||||
\(631\) | 283.101 | + | 1056.55i | 0.448654 | + | 1.67440i | 0.706104 | + | 0.708108i | \(0.250451\pi\) |
−0.257450 | + | 0.966292i | \(0.582882\pi\) | |||||||
\(632\) | −23.7513 | + | 23.7513i | −0.0375812 | + | 0.0375812i | ||||
\(633\) | −55.6000 | + | 96.3020i | −0.0878356 | + | 0.152136i | ||||
\(634\) | −486.200 | + | 280.708i | −0.766877 | + | 0.442757i | ||||
\(635\) | −410.229 | − | 109.921i | −0.646031 | − | 0.173103i | ||||
\(636\) | − | 213.646i | − | 0.335922i | ||||||
\(637\) | 575.917 | 0.904108 | ||||||||
\(638\) | 251.769 | 0.394622 | ||||||||
\(639\) | −83.5115 | + | 311.669i | −0.130691 | + | 0.487745i | ||||
\(640\) | 10.1436 | + | 17.5692i | 0.0158494 | + | 0.0274519i | ||||
\(641\) | −353.869 | − | 204.306i | −0.552058 | − | 0.318731i | 0.197894 | − | 0.980223i | \(-0.436590\pi\) |
−0.749952 | + | 0.661493i | \(0.769923\pi\) | |||||||
\(642\) | 177.531 | + | 177.531i | 0.276528 | + | 0.276528i | ||||
\(643\) | −432.661 | + | 115.931i | −0.672879 | + | 0.180297i | −0.579052 | − | 0.815291i | \(-0.696577\pi\) |
−0.0938279 | + | 0.995588i | \(0.529910\pi\) | |||||||
\(644\) | −20.7180 | − | 77.3205i | −0.0321708 | − | 0.120063i | ||||
\(645\) | 33.6884 | − | 33.6884i | 0.0522301 | − | 0.0522301i | ||||
\(646\) | 442.774 | − | 766.908i | 0.685409 | − | 1.18716i | ||||
\(647\) | −279.588 | + | 161.420i | −0.432131 | + | 0.249491i | −0.700254 | − | 0.713894i | \(-0.746930\pi\) |
0.268123 | + | 0.963385i | \(0.413597\pi\) | |||||||
\(648\) | 24.5885 | + | 6.58846i | 0.0379452 | + | 0.0101674i | ||||
\(649\) | − | 679.292i | − | 1.04668i | ||||||
\(650\) | 283.200 | + | 283.200i | 0.435692 | + | 0.435692i | ||||
\(651\) | −524.545 | −0.805752 | ||||||||
\(652\) | −105.894 | + | 395.200i | −0.162413 | + | 0.606135i | ||||
\(653\) | 510.424 | + | 884.081i | 0.781660 | + | 1.35388i | 0.930974 | + | 0.365086i | \(0.118960\pi\) |
−0.149314 | + | 0.988790i | \(0.547706\pi\) | |||||||
\(654\) | −144.567 | − | 83.4660i | −0.221051 | − | 0.127624i | ||||
\(655\) | 265.808 | + | 265.808i | 0.405813 | + | 0.405813i | ||||
\(656\) | −99.7128 | + | 26.7180i | −0.152001 | + | 0.0407286i | ||||
\(657\) | −74.0307 | − | 276.286i | −0.112680 | − | 0.420527i | ||||
\(658\) | −95.8846 | + | 95.8846i | −0.145721 | + | 0.145721i | ||||
\(659\) | −113.842 | + | 197.181i | −0.172750 | + | 0.299212i | −0.939380 | − | 0.342877i | \(-0.888599\pi\) |
0.766630 | + | 0.642089i | \(0.221932\pi\) | |||||||
\(660\) | 55.2923 | − | 31.9230i | 0.0837763 | − | 0.0483683i | ||||
\(661\) | 146.181 | + | 39.1692i | 0.221152 | + | 0.0592575i | 0.367693 | − | 0.929947i | \(-0.380148\pi\) |
−0.146542 | + | 0.989205i | \(0.546814\pi\) | |||||||
\(662\) | 201.247i | 0.303999i | ||||||||
\(663\) | −213.100 | + | 369.100i | −0.321418 | + | 0.556712i | ||||
\(664\) | −444.133 | −0.668875 | ||||||||
\(665\) | −148.301 | + | 553.468i | −0.223009 | + | 0.832283i | ||||
\(666\) | −78.5307 | − | 136.019i | −0.117914 | − | 0.204233i | ||||
\(667\) | −62.1539 | − | 35.8846i | −0.0931843 | − | 0.0538000i | ||||
\(668\) | 228.862 | + | 228.862i | 0.342607 | + | 0.342607i | ||||
\(669\) | 365.624 | − | 97.9686i | 0.546523 | − | 0.146440i | ||||
\(670\) | −25.7475 | − | 96.0910i | −0.0384291 | − | 0.143419i | ||||
\(671\) | 53.0653 | − | 53.0653i | 0.0790838 | − | 0.0790838i | ||||
\(672\) | −47.3205 | + | 81.9615i | −0.0704174 | + | 0.121967i | ||||
\(673\) | −613.138 | + | 353.996i | −0.911052 | + | 0.525996i | −0.880770 | − | 0.473545i | \(-0.842974\pi\) |
−0.0302828 | + | 0.999541i | \(0.509641\pi\) | |||||||
\(674\) | 474.704 | + | 127.197i | 0.704309 | + | 0.188719i | ||||
\(675\) | − | 113.196i | − | 0.167698i | ||||||
\(676\) | − | 338.000i | − | 0.500000i | ||||||
\(677\) | −754.592 | −1.11461 | −0.557306 | − | 0.830307i | \(-0.688165\pi\) | ||||
−0.557306 | + | 0.830307i | \(0.688165\pi\) | |||||||
\(678\) | −28.6654 | + | 106.981i | −0.0422794 | + | 0.157789i | ||||
\(679\) | −751.231 | − | 1301.17i | −1.10638 | − | 1.91630i | ||||
\(680\) | 83.1384 | + | 48.0000i | 0.122262 | + | 0.0705882i | ||||
\(681\) | −79.1769 | − | 79.1769i | −0.116266 | − | 0.116266i | ||||
\(682\) | 440.214 | − | 117.955i | 0.645475 | − | 0.172955i | ||||
\(683\) | −37.2168 | − | 138.895i | −0.0544901 | − | 0.203360i | 0.933314 | − | 0.359061i | \(-0.116903\pi\) |
−0.987804 | + | 0.155701i | \(0.950236\pi\) | |||||||
\(684\) | 140.354 | − | 140.354i | 0.205196 | − | 0.205196i | ||||
\(685\) | 102.115 | − | 176.869i | 0.149074 | − | 0.258203i | ||||
\(686\) | −55.5866 | + | 32.0929i | −0.0810300 | + | 0.0467827i | ||||
\(687\) | −138.849 | − | 37.2046i | −0.202110 | − | 0.0541551i | ||||
\(688\) | − | 61.3590i | − | 0.0891846i | ||||||
\(689\) | 694.350 | + | 400.883i | 1.00776 | + | 0.581833i | ||||
\(690\) | −18.1999 | −0.0263767 | ||||||||
\(691\) | 140.931 | − | 525.961i | 0.203952 | − | 0.761159i | −0.785815 | − | 0.618462i | \(-0.787756\pi\) |
0.989766 | − | 0.142697i | \(-0.0455774\pi\) | |||||||
\(692\) | −268.459 | − | 464.985i | −0.387946 | − | 0.671943i | ||||
\(693\) | 257.942 | + | 148.923i | 0.372211 | + | 0.214896i | ||||
\(694\) | 437.703 | + | 437.703i | 0.630695 | + | 0.630695i | ||||
\(695\) | −165.771 | + | 44.4181i | −0.238519 | + | 0.0639109i | ||||
\(696\) | 21.9615 | + | 81.9615i | 0.0315539 | + | 0.117761i | ||||
\(697\) | −345.415 | + | 345.415i | −0.495574 | + | 0.495574i | ||||
\(698\) | −316.897 | + | 548.881i | −0.454007 | + | 0.786363i | ||||
\(699\) | 571.004 | − | 329.669i | 0.816887 | − | 0.471630i | ||||
\(700\) | 406.506 | + | 108.923i | 0.580723 | + | 0.155604i | ||||
\(701\) | − | 568.344i | − | 0.810761i | −0.914148 | − | 0.405381i | \(-0.867139\pi\) | ||
0.914148 | − | 0.405381i | \(-0.132861\pi\) | |||||||
\(702\) | −67.5500 | + | 67.5500i | −0.0962250 | + | 0.0962250i | ||||
\(703\) | −1224.68 | −1.74207 | ||||||||
\(704\) | 21.2820 | − | 79.4256i | 0.0302302 | − | 0.112820i | ||||
\(705\) | 15.4153 | + | 26.7001i | 0.0218657 | + | 0.0378725i | ||||
\(706\) | 718.865 | + | 415.037i | 1.01822 | + | 0.587871i | ||||
\(707\) | 1275.95 | + | 1275.95i | 1.80475 | + | 1.80475i | ||||
\(708\) | 221.138 | − | 59.2539i | 0.312342 | − | 0.0836919i | ||||
\(709\) | 94.9538 | + | 354.372i | 0.133926 | + | 0.499820i | 1.00000 | 9.64632e-5i | \(-3.07052e-5\pi\) | |
−0.866074 | + | 0.499916i | \(0.833364\pi\) | |||||||
\(710\) | −192.862 | + | 192.862i | −0.271636 | + | 0.271636i | ||||
\(711\) | −17.8135 | + | 30.8538i | −0.0250541 | + | 0.0433950i | ||||
\(712\) | −410.985 | + | 237.282i | −0.577225 | + | 0.333261i | ||||
\(713\) | −125.487 | − | 33.6242i | −0.175999 | − | 0.0471587i | ||||
\(714\) | 447.846i | 0.627235i | ||||||||
\(715\) | 239.600i | 0.335105i | ||||||||
\(716\) | 571.559 | 0.798267 | ||||||||
\(717\) | −105.962 | + | 395.454i | −0.147785 | + | 0.551539i | ||||
\(718\) | −64.2769 | − | 111.331i | −0.0895221 | − | 0.155057i | ||||
\(719\) | 228.215 | + | 131.760i | 0.317407 | + | 0.183255i | 0.650236 | − | 0.759732i | \(-0.274670\pi\) |
−0.332829 | + | 0.942987i | \(0.608003\pi\) | |||||||
\(720\) | 15.2154 | + | 15.2154i | 0.0211325 | + | 0.0211325i | ||||
\(721\) | 776.852 | − | 208.157i | 1.07747 | − | 0.288706i | ||||
\(722\) | −268.443 | − | 1001.84i | −0.371805 | − | 1.38759i | ||||
\(723\) | 3.77053 | − | 3.77053i | 0.00521511 | − | 0.00521511i | ||||
\(724\) | 177.646 | − | 307.692i | 0.245368 | − | 0.424989i | ||||
\(725\) | 326.769 | − | 188.660i | 0.450716 | − | 0.260221i | ||||
\(726\) | 36.3275 | + | 9.73394i | 0.0500379 | + | 0.0134076i | ||||
\(727\) | − | 878.415i | − | 1.20827i | −0.796880 | − | 0.604137i | \(-0.793518\pi\) | ||
0.796880 | − | 0.604137i | \(-0.206482\pi\) | |||||||
\(728\) | −177.583 | − | 307.583i | −0.243933 | − | 0.422505i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 62.5781 | − | 233.545i | 0.0857235 | − | 0.319924i | ||||
\(731\) | −145.177 | − | 251.454i | −0.198600 | − | 0.343986i | ||||
\(732\) | 21.9038 | + | 12.6462i | 0.0299232 | + | 0.0172762i | ||||
\(733\) | −146.627 | − | 146.627i | −0.200037 | − | 0.200037i | 0.599979 | − | 0.800016i | \(-0.295176\pi\) |
−0.800016 | + | 0.599979i | \(0.795176\pi\) | |||||||
\(734\) | 297.499 | − | 79.7147i | 0.405312 | − | 0.108603i | ||||
\(735\) | −35.6115 | − | 132.904i | −0.0484510 | − | 0.180822i | ||||
\(736\) | −16.5744 | + | 16.5744i | −0.0225195 | + | 0.0225195i | ||||
\(737\) | −201.606 | + | 349.192i | −0.273550 | + | 0.473802i | ||||
\(738\) | −94.8231 | + | 54.7461i | −0.128487 | + | 0.0741818i | ||||
\(739\) | 621.762 | + | 166.601i | 0.841356 | + | 0.225441i | 0.653662 | − | 0.756787i | \(-0.273232\pi\) |
0.187694 | + | 0.982227i | \(0.439899\pi\) | |||||||
\(740\) | − | 132.764i | − | 0.179411i | ||||||
\(741\) | 192.792 | + | 719.508i | 0.260178 | + | 0.970996i | ||||
\(742\) | 842.487 | 1.13543 | ||||||||
\(743\) | −3.52835 | + | 13.1680i | −0.00474879 | + | 0.0177227i | −0.968260 | − | 0.249947i | \(-0.919587\pi\) |
0.963511 | + | 0.267670i | \(0.0862535\pi\) | |||||||
\(744\) | 76.7987 | + | 133.019i | 0.103224 | + | 0.178789i | ||||
\(745\) | 88.3078 | + | 50.9845i | 0.118534 | + | 0.0684356i | ||||
\(746\) | −219.606 | − | 219.606i | −0.294378 | − | 0.294378i | ||||
\(747\) | −455.023 | + | 121.923i | −0.609134 | + | 0.163217i | ||||
\(748\) | −100.708 | − | 375.846i | −0.134636 | − | 0.502468i | ||||
\(749\) | −700.070 | + | 700.070i | −0.934673 | + | 0.934673i | ||||
\(750\) | 102.746 | − | 177.962i | 0.136995 | − | 0.237282i | ||||
\(751\) | −138.631 | + | 80.0385i | −0.184595 | + | 0.106576i | −0.589450 | − | 0.807805i | \(-0.700655\pi\) |
0.404855 | + | 0.914381i | \(0.367322\pi\) | |||||||
\(752\) | 38.3538 | + | 10.2769i | 0.0510024 | + | 0.0136661i | ||||
\(753\) | 361.492i | 0.480069i | ||||||||
\(754\) | −307.583 | − | 82.4167i | −0.407935 | − | 0.109306i | ||||
\(755\) | 139.572 | 0.184864 | ||||||||
\(756\) | −25.9808 | + | 96.9615i | −0.0343661 | + | 0.128256i | ||||
\(757\) | 733.692 | + | 1270.79i | 0.969210 | + | 1.67872i | 0.697850 | + | 0.716244i | \(0.254140\pi\) |
0.271360 | + | 0.962478i | \(0.412527\pi\) | |||||||
\(758\) | −237.476 | − | 137.107i | −0.313293 | − | 0.180880i | ||||
\(759\) | 52.1615 | + | 52.1615i | 0.0687239 | + | 0.0687239i | ||||
\(760\) | 162.067 | − | 43.4256i | 0.213246 | − | 0.0571390i | ||||
\(761\) | 47.3514 | + | 176.718i | 0.0622227 | + | 0.232218i | 0.990033 | − | 0.140833i | \(-0.0449782\pi\) |
−0.927811 | + | 0.373051i | \(0.878312\pi\) | |||||||
\(762\) | −410.229 | + | 410.229i | −0.538359 | + | 0.538359i | ||||
\(763\) | 329.138 | − | 570.083i | 0.431373 | − | 0.747160i | ||||
\(764\) | 341.769 | − | 197.321i | 0.447342 | − | 0.258273i | ||||
\(765\) | 98.3538 | + | 26.3538i | 0.128567 | + | 0.0344494i | ||||
\(766\) | − | 275.503i | − | 0.359664i | ||||||
\(767\) | −222.367 | + | 829.883i | −0.289917 | + | 1.08199i | ||||
\(768\) | 27.7128 | 0.0360844 | ||||||||
\(769\) | 351.866 | − | 1313.18i | 0.457563 | − | 1.70765i | −0.222879 | − | 0.974846i | \(-0.571546\pi\) |
0.680442 | − | 0.732802i | \(-0.261788\pi\) | |||||||
\(770\) | 125.885 | + | 218.038i | 0.163486 | + | 0.283167i | ||||
\(771\) | −111.331 | − | 64.2769i | −0.144398 | − | 0.0833682i | ||||
\(772\) | 29.6987 | + | 29.6987i | 0.0384699 | + | 0.0384699i | ||||
\(773\) | 945.606 | − | 253.374i | 1.22329 | − | 0.327781i | 0.411329 | − | 0.911487i | \(-0.365065\pi\) |
0.811965 | + | 0.583706i | \(0.198398\pi\) | |||||||
\(774\) | −16.8442 | − | 62.8634i | −0.0217625 | − | 0.0812189i | ||||
\(775\) | 482.962 | − | 482.962i | 0.623177 | − | 0.623177i | ||||
\(776\) | −219.976 | + | 381.009i | −0.283474 | + | 0.490991i | ||||
\(777\) | 536.375 | − | 309.676i | 0.690315 | − | 0.398554i | ||||
\(778\) | −24.2487 | − | 6.49742i | −0.0311680 | − | 0.00835144i | ||||
\(779\) | 853.759i | 1.09597i | ||||||||
\(780\) | −78.0000 | + | 20.9000i | −0.100000 | + | 0.0267949i | ||||
\(781\) | 1105.49 | 1.41548 | ||||||||
\(782\) | −28.7077 | + | 107.138i | −0.0367106 | + | 0.137006i | ||||
\(783\) | 45.0000 | + | 77.9423i | 0.0574713 | + | 0.0995431i | ||||
\(784\) | −153.464 | − | 88.6025i | −0.195745 | − | 0.113013i | ||||
\(785\) | −70.2834 | − | 70.2834i | −0.0895330 | − | 0.0895330i | ||||
\(786\) | 496.004 | − | 132.904i | 0.631048 | − | 0.169089i | ||||
\(787\) | 30.5460 | + | 113.999i | 0.0388132 | + | 0.144853i | 0.982613 | − | 0.185664i | \(-0.0594436\pi\) |
−0.943800 | + | 0.330517i | \(0.892777\pi\) | |||||||
\(788\) | −213.913 | + | 213.913i | −0.271463 | + | 0.271463i | ||||
\(789\) | 21.1000 | − | 36.5462i | 0.0267427 | − | 0.0463197i | ||||
\(790\) | −26.0807 | + | 15.0577i | −0.0330136 | + | 0.0190604i | ||||
\(791\) | −421.865 | − | 113.038i | −0.533332 | − | 0.142906i | ||||
\(792\) | − | 87.2154i | − | 0.110120i | ||||||
\(793\) | −82.2001 | + | 47.4583i | −0.103657 | + | 0.0598465i | ||||
\(794\) | −477.286 | −0.601116 | ||||||||
\(795\) | 49.5768 | − | 185.023i | 0.0623607 | − | 0.232733i | ||||
\(796\) | −22.2154 | − | 38.4782i | −0.0279088 | − | 0.0483394i | ||||
\(797\) | 491.138 | + | 283.559i | 0.616234 | + | 0.355783i | 0.775401 | − | 0.631469i | \(-0.217548\pi\) |
−0.159167 | + | 0.987252i | \(0.550881\pi\) | |||||||
\(798\) | 553.468 | + | 553.468i | 0.693569 | + | 0.693569i | ||||
\(799\) | 181.492 | − | 48.6307i | 0.227149 | − | 0.0608645i | ||||
\(800\) | −31.8949 | − | 119.033i | −0.0398686 | − | 0.148792i | ||||
\(801\) | −355.923 | + | 355.923i | −0.444348 | + | 0.444348i | ||||
\(802\) | −363.415 | + | 629.454i | −0.453136 | + | 0.784855i | ||||
\(803\) | −848.696 | + | 489.995i | −1.05691 | + | 0.610205i | ||||
\(804\) | −131.263 | − | 35.1718i | −0.163262 | − | 0.0437460i | ||||
\(805\) | − | 71.7691i | − | 0.0891542i | ||||||
\(806\) | −576.417 | −0.715157 | ||||||||
\(807\) | −304.392 | −0.377190 | ||||||||
\(808\) | 136.756 | − | 510.382i | 0.169253 | − | 0.631661i | ||||
\(809\) | −43.7231 | − | 75.7307i | −0.0540459 | − | 0.0936102i | 0.837737 | − | 0.546074i | \(-0.183878\pi\) |
−0.891783 | + | 0.452464i | \(0.850545\pi\) | |||||||
\(810\) | 19.7654 | + | 11.4115i | 0.0244017 | + | 0.0140883i | ||||
\(811\) | −519.193 | − | 519.193i | −0.640189 | − | 0.640189i | 0.310413 | − | 0.950602i | \(-0.399533\pi\) |
−0.950602 | + | 0.310413i | \(0.899533\pi\) | |||||||
\(812\) | −323.205 | + | 86.6025i | −0.398036 | + | 0.106653i | ||||
\(813\) | −124.922 | − | 466.215i | −0.153655 | − | 0.573450i | ||||
\(814\) | −380.505 | + | 380.505i | −0.467451 | + | 0.467451i | ||||
\(815\) | −183.413 | + | 317.681i | −0.225047 | + | 0.389792i | ||||
\(816\) | 113.569 | − | 65.5692i | 0.139178 | − | 0.0803544i | ||||
\(817\) | −490.174 | − | 131.342i | −0.599968 | − | 0.160761i | ||||
\(818\) | 824.053i | 1.00740i | ||||||||
\(819\) | −266.375 | − | 266.375i | −0.325244 | − | 0.325244i | ||||
\(820\) | −92.5538 | −0.112870 | ||||||||
\(821\) | 148.881 | − | 555.631i | 0.181341 | − | 0.676773i | −0.814044 | − | 0.580804i | \(-0.802738\pi\) |
0.995384 | − | 0.0959692i | \(-0.0305950\pi\) | |||||||
\(822\) | −139.492 | − | 241.608i | −0.169699 | − | 0.293927i | ||||
\(823\) | −285.069 | − | 164.585i | −0.346378 | − | 0.199981i | 0.316711 | − | 0.948522i | \(-0.397422\pi\) |
−0.663089 | + | 0.748541i | \(0.730755\pi\) | |||||||
\(824\) | −166.526 | − | 166.526i | −0.202094 | − | 0.202094i | ||||
\(825\) | −374.611 | + | 100.377i | −0.454075 | + | 0.121669i | ||||
\(826\) | 233.660 | + | 872.032i | 0.282882 | + | 1.05573i | ||||
\(827\) | 514.410 | − | 514.410i | 0.622020 | − | 0.622020i | −0.324028 | − | 0.946048i | \(-0.605037\pi\) |
0.946048 | + | 0.324028i | \(0.105037\pi\) | |||||||
\(828\) | −12.4308 | + | 21.5307i | −0.0150130 | + | 0.0260033i | ||||
\(829\) | −816.742 | + | 471.546i | −0.985213 | + | 0.568813i | −0.903840 | − | 0.427871i | \(-0.859264\pi\) |
−0.0813731 | + | 0.996684i | \(0.525931\pi\) | |||||||
\(830\) | −384.631 | − | 103.061i | −0.463410 | − | 0.124170i | ||||
\(831\) | 774.200i | 0.931649i | ||||||||
\(832\) | −52.0000 | + | 90.0666i | −0.0625000 | + | 0.108253i | ||||
\(833\) | −838.543 | −1.00665 | ||||||||
\(834\) | −60.6762 | + | 226.447i | −0.0727533 | + | 0.271519i | ||||
\(835\) | 145.092 | + | 251.307i | 0.173763 | + | 0.300967i | ||||
\(836\) | −588.946 | − | 340.028i | −0.704481 | − | 0.406732i | ||||
\(837\) | 115.198 | + | 115.198i | 0.137632 | + | 0.137632i | ||||
\(838\) | 1068.72 | − | 286.361i | 1.27532 | − | 0.341720i | ||||
\(839\) | −203.536 | − | 759.606i | −0.242593 | − | 0.905371i | −0.974578 | − | 0.224050i | \(-0.928072\pi\) |
0.731984 | − | 0.681321i | \(-0.238594\pi\) | |||||||
\(840\) | −60.0000 | + | 60.0000i | −0.0714286 | + | 0.0714286i | ||||
\(841\) | 270.500 | − | 468.520i | 0.321641 | − | 0.557098i | ||||
\(842\) | −46.8264 | + | 27.0352i | −0.0556132 | + | 0.0321083i | ||||
\(843\) | 13.1192 | + | 3.51528i | 0.0155625 | + | 0.00416996i | ||||
\(844\) | 128.403i | 0.152136i | ||||||||
\(845\) | 78.4332 | − | 292.717i | 0.0928203 | − | 0.346410i | ||||
\(846\) | 42.1154 | 0.0497818 | ||||||||
\(847\) | −38.3846 | + | 143.253i | −0.0453183 | + | 0.169130i | ||||
\(848\) | −123.349 | − | 213.646i | −0.145458 | − | 0.251941i | ||||
\(849\) | −24.9693 | − | 14.4160i | −0.0294102 | − | 0.0169800i | ||||
\(850\) | −412.344 | − | 412.344i | −0.485110 | − | 0.485110i | ||||
\(851\) | 148.168 | − | 39.7015i | 0.174110 | − | 0.0466528i | ||||
\(852\) | 96.4308 | + | 359.885i | 0.113182 | + | 0.422400i | ||||
\(853\) | 472.527 | − | 472.527i | 0.553960 | − | 0.553960i | −0.373622 | − | 0.927581i | \(-0.621884\pi\) |
0.927581 | + | 0.373622i | \(0.121884\pi\) | |||||||
\(854\) | −49.8686 | + | 86.3750i | −0.0583941 | + | 0.101142i | ||||
\(855\) | 154.119 | − | 88.9808i | 0.180256 | − | 0.104071i | ||||
\(856\) | 280.028 | + | 75.0333i | 0.327136 | + | 0.0876557i | ||||
\(857\) | − | 436.543i | − | 0.509386i | −0.967022 | − | 0.254693i | \(-0.918026\pi\) | ||
0.967022 | − | 0.254693i | \(-0.0819743\pi\) | |||||||
\(858\) | 283.450 | + | 163.650i | 0.330361 | + | 0.190734i | ||||
\(859\) | −1238.40 | −1.44167 | −0.720837 | − | 0.693104i | \(-0.756243\pi\) | ||||
−0.720837 | + | 0.693104i | \(0.756243\pi\) | |||||||
\(860\) | 14.2384 | − | 53.1384i | 0.0165563 | − | 0.0617889i | ||||
\(861\) | −215.885 | − | 373.923i | −0.250737 | − | 0.434289i | ||||
\(862\) | −771.300 | − | 445.310i | −0.894779 | − | 0.516601i | ||||
\(863\) | 729.373 | + | 729.373i | 0.845160 | + | 0.845160i | 0.989525 | − | 0.144365i | \(-0.0461138\pi\) |
−0.144365 | + | 0.989525i | \(0.546114\pi\) | |||||||
\(864\) | 28.3923 | − | 7.60770i | 0.0328615 | − | 0.00880520i | ||||
\(865\) | −124.592 | − | 464.985i | −0.144037 | − | 0.537554i | ||||
\(866\) | −237.785 | + | 237.785i | −0.274578 | + | 0.274578i | ||||
\(867\) | 59.9955 | − | 103.915i | 0.0691990 | − | 0.119856i | ||||
\(868\) | −524.545 | + | 302.846i | −0.604314 | + | 0.348901i | ||||
\(869\) | 117.904 | + | 31.5922i | 0.135678 | + | 0.0363547i | ||||
\(870\) | 76.0770i | 0.0874448i | ||||||||
\(871\) | 360.608 | − | 360.608i | 0.414016 | − | 0.414016i | ||||
\(872\) | −192.756 | −0.221051 | ||||||||
\(873\) | −120.775 | + | 450.738i | −0.138345 | + | 0.516310i | ||||
\(874\) | 96.9282 | + | 167.885i | 0.110902 | + | 0.192088i | ||||
\(875\) | 701.769 | + | 405.167i | 0.802022 | + | 0.463048i | ||||
\(876\) | −233.545 | − | 233.545i | −0.266604 | − | 0.266604i | ||||
\(877\) | 1314.21 | − | 352.142i | 1.49853 | − | 0.401530i | 0.585923 | − | 0.810367i | \(-0.300732\pi\) |
0.912607 | + | 0.408837i | \(0.134066\pi\) | |||||||
\(878\) | −252.361 | − | 941.824i | −0.287427 | − | 1.07269i | ||||
\(879\) | 229.450 | − | 229.450i | 0.261035 | − | 0.261035i | ||||
\(880\) | 36.8616 | − | 63.8461i | 0.0418881 | − | 0.0725524i | ||||
\(881\) | 1354.17 | − | 781.832i | 1.53709 | − | 0.887437i | 0.538079 | − | 0.842895i | \(-0.319150\pi\) |
0.999007 | − | 0.0445423i | \(-0.0141829\pi\) | |||||||
\(882\) | −181.550 | − | 48.6462i | −0.205839 | − | 0.0551544i | ||||
\(883\) | − | 452.723i | − | 0.512710i | −0.966583 | − | 0.256355i | \(-0.917478\pi\) | ||
0.966583 | − | 0.256355i | \(-0.0825216\pi\) | |||||||
\(884\) | 492.133i | 0.556712i | ||||||||
\(885\) | 205.261 | 0.231934 | ||||||||
\(886\) | −111.282 | + | 415.310i | −0.125600 | + | 0.468747i | ||||
\(887\) | −455.469 | − | 788.896i | −0.513494 | − | 0.889398i | −0.999877 | − | 0.0156524i | \(-0.995017\pi\) |
0.486383 | − | 0.873745i | \(-0.338316\pi\) | |||||||
\(888\) | −157.061 | − | 90.6795i | −0.176871 | − | 0.102117i | ||||
\(889\) | −1617.69 | − | 1617.69i | −1.81967 | − | 1.81967i | ||||
\(890\) | −410.985 | + | 110.123i | −0.461780 | + | 0.123734i | ||||
\(891\) | −23.9423 | − | 89.3538i | −0.0268713 | − | 0.100285i | ||||
\(892\) | 309.061 | − | 309.061i | 0.346481 | − | 0.346481i | ||||
\(893\) | 164.196 | − | 284.396i | 0.183870 | − | 0.318473i | ||||
\(894\) | 120.631 | − | 69.6462i | 0.134934 | − | 0.0779040i | ||||
\(895\) | 494.985 | + | 132.631i | 0.553055 | + | 0.148191i | ||||
\(896\) | 109.282i | 0.121967i | ||||||||
\(897\) | −46.6499 | − | 80.8001i | −0.0520066 | − | 0.0900781i | ||||
\(898\) | −401.387 | −0.446979 | ||||||||
\(899\) | −140.551 | + | 524.545i | −0.156342 | + | 0.583476i | ||||
\(900\) | −65.3538 | − | 113.196i | −0.0726154 | − | 0.125774i | ||||
\(901\) | −1010.98 | − | 583.692i | −1.12207 | − | 0.647827i | ||||
\(902\) | 265.261 | + | 265.261i | 0.294081 | + | 0.294081i | ||||
\(903\) | 247.894 | − | 66.4230i | 0.274523 | − | 0.0735582i | ||||
\(904\) | 33.1000 | + | 123.531i | 0.0366150 | + | 0.136649i | ||||
\(905\) | 225.246 | − | 225.246i | 0.248891 | − | 0.248891i | ||||
\(906\) | 95.3294 | − | 165.115i | 0.105220 | − | 0.182247i | ||||
\(907\) | 385.501 | − | 222.569i | 0.425029 | − | 0.245391i | −0.272198 | − | 0.962241i | \(-0.587750\pi\) |
0.697227 | + | 0.716851i | \(0.254417\pi\) | |||||||
\(908\) | −124.890 | − | 33.4641i | −0.137544 | − | 0.0368547i | ||||
\(909\) | − | 560.438i | − | 0.616544i | ||||||
\(910\) | −82.4167 | − | 307.583i | −0.0905678 | − | 0.338004i | ||||
\(911\) | 717.233 | 0.787303 | 0.393652 | − | 0.919260i | \(-0.371212\pi\) | ||||
0.393652 | + | 0.919260i | \(0.371212\pi\) | |||||||
\(912\) | 59.3205 | − | 221.387i | 0.0650444 | − | 0.242749i | ||||
\(913\) | 806.985 | + | 1397.74i | 0.883882 | + | 1.53093i | ||||
\(914\) | 175.835 | + | 101.519i | 0.192380 | + | 0.111071i | ||||
\(915\) | 16.0347 | + | 16.0347i | 0.0175243 | + | 0.0175243i | ||||
\(916\) | −160.329 | + | 42.9601i | −0.175032 | + | 0.0468997i | ||||
\(917\) | 524.090 | + | 1955.93i | 0.571526 | + | 2.13297i | ||||
\(918\) | 98.3538 | − | 98.3538i | 0.107139 | − | 0.107139i | ||||
\(919\) | −371.569 | + | 643.577i | −0.404319 | + | 0.700301i | −0.994242 | − | 0.107158i | \(-0.965825\pi\) |
0.589923 | + | 0.807460i | \(0.299158\pi\) | |||||||
\(920\) | −18.1999 | + | 10.5077i | −0.0197825 | + | 0.0114214i | ||||
\(921\) | −887.422 | − | 237.784i | −0.963541 | − | 0.258180i | ||||
\(922\) | − | 832.246i | − | 0.902653i | ||||||
\(923\) | −1350.57 | − | 361.883i | −1.46324 | − | 0.392073i | ||||
\(924\) | 343.923 | 0.372211 | ||||||||
\(925\) | −208.727 | + | 778.981i | −0.225651 | + | 0.842142i | ||||
\(926\) | 169.599 | + | 293.755i | 0.183153 | + | 0.317230i | ||||
\(927\) | −216.323 | − | 124.894i | −0.233358 | − | 0.134729i | ||||
\(928\) | 69.2820 | + | 69.2820i | 0.0746574 | + | 0.0746574i | ||||
\(929\) | 1424.14 | − | 381.597i | 1.53298 | − | 0.410761i | 0.608992 | − | 0.793176i | \(-0.291574\pi\) |
0.923991 | + | 0.382415i | \(0.124908\pi\) | |||||||
\(930\) | 35.6424 | + | 133.019i | 0.0383252 | + | 0.143031i | ||||
\(931\) | −1036.31 | + | 1036.31i | −1.11311 | + | 1.11311i | ||||
\(932\) | 380.669 | − | 659.338i | 0.408443 | − | 0.707445i | ||||
\(933\) | −444.358 | + | 256.550i | −0.476268 | + | 0.274973i | ||||
\(934\) | 1000.82 | + | 268.168i | 1.07154 | + | 0.287118i | ||||
\(935\) | − | 348.862i | − | 0.373114i | ||||||
\(936\) | −28.5500 | + | 106.550i | −0.0305021 | + | 0.113835i | ||||
\(937\) | −172.477 | −0.184073 | −0.0920367 | − | 0.995756i | \(-0.529338\pi\) | ||||
−0.0920367 | + | 0.995756i | \(0.529338\pi\) | |||||||
\(938\) | 138.695 | − | 517.619i | 0.147863 | − | 0.551832i | ||||
\(939\) | −102.439 | − | 177.429i | −0.109093 | − | 0.188955i | ||||
\(940\) | 30.8306 | + | 17.8001i | 0.0327985 | + | 0.0189362i | ||||
\(941\) | 145.055 | + | 145.055i | 0.154150 | + | 0.154150i | 0.779969 | − | 0.625819i | \(-0.215235\pi\) |
−0.625819 | + | 0.779969i | \(0.715235\pi\) | |||||||
\(942\) | −131.151 | + | 35.1417i | −0.139226 | + | 0.0373054i | ||||
\(943\) | −27.6771 | − | 103.292i | −0.0293501 | − | 0.109536i | ||||
\(944\) | 186.928 | − | 186.928i | 0.198017 | − | 0.198017i | ||||
\(945\) | −45.0000 | + | 77.9423i | −0.0476190 | + | 0.0824786i | ||||
\(946\) | −193.104 | + | 111.488i | −0.204127 | + | 0.117853i | ||||
\(947\) | −665.902 | − | 178.428i | −0.703170 | − | 0.188414i | −0.110520 | − | 0.993874i | \(-0.535252\pi\) |
−0.592650 | + | 0.805460i | \(0.701918\pi\) | |||||||
\(948\) | 41.1384i | 0.0433950i | ||||||||
\(949\) | 1197.24 | − | 320.800i | 1.26158 | − | 0.338040i | ||||
\(950\) | −1019.18 | −1.07283 | ||||||||
\(951\) | −177.962 | + | 664.161i | −0.187131 | + | 0.698382i | ||||
\(952\) | 258.564 | + | 447.846i | 0.271601 | + | 0.470427i | ||||
\(953\) | −1044.96 | − | 603.309i | −1.09650 | − | 0.633063i | −0.161198 | − | 0.986922i | \(-0.551536\pi\) |
−0.935299 | + | 0.353859i | \(0.884869\pi\) | |||||||
\(954\) | −185.023 | − | 185.023i | −0.193944 | − | 0.193944i | ||||
\(955\) | 341.769 | − | 91.5768i | 0.357873 | − | 0.0958919i | ||||
\(956\) | 122.354 | + | 456.631i | 0.127985 | + | 0.477647i | ||||
\(957\) | 218.038 | − | 218.038i | 0.227835 | − | 0.227835i | ||||
\(958\) | −261.464 | + | 452.869i | −0.272927 | + | 0.472723i | ||||
\(959\) | 952.750 | − | 550.070i | 0.993483 | − | 0.573588i | ||||
\(960\) | 24.0000 | + | 6.43078i | 0.0250000 | + | 0.00669873i | ||||
\(961\) | 22.0065i | 0.0228996i | ||||||||
\(962\) | 589.417 | − | 340.300i | 0.612699 | − | 0.353742i | ||||
\(963\) | 307.492 | 0.319307 | ||||||||
\(964\) | 1.59361 | − | 5.94744i | 0.00165312 | − | 0.00616954i | ||||
\(965\) | 18.8282 | + | 32.6115i | 0.0195111 | + | 0.0337943i | ||||
\(966\) | −84.9038 | − | 49.0192i | −0.0878921 | − | 0.0507446i | ||||
\(967\) | −169.831 | − | 169.831i | −0.175626 | − | 0.175626i | 0.613820 | − | 0.789446i | \(-0.289632\pi\) |
−0.789446 | + | 0.613820i | \(0.789632\pi\) | |||||||
\(968\) | 41.9474 | − | 11.2398i | 0.0433341 | − | 0.0116113i | ||||
\(969\) | −280.708 | − | 1047.62i | −0.289688 | − | 1.08113i | ||||
\(970\) | −278.918 | + | 278.918i | −0.287544 | + | 0.287544i | ||||
\(971\) | −373.850 | + | 647.527i | −0.385015 | + | 0.666866i | −0.991771 | − | 0.128022i | \(-0.959137\pi\) |
0.606756 | + | 0.794888i | \(0.292471\pi\) | |||||||
\(972\) | 27.0000 | − | 15.5885i | 0.0277778 | − | 0.0160375i | ||||
\(973\) | −892.965 | − | 239.269i | −0.917744 | − | 0.245909i | ||||
\(974\) | − | 274.000i | − | 0.281314i | ||||||
\(975\) | 490.517 | 0.503094 | ||||||||
\(976\) | 29.2051 | 0.0299232 | ||||||||
\(977\) | −55.9897 | + | 208.956i | −0.0573078 | + | 0.213876i | −0.988642 | − | 0.150290i | \(-0.951979\pi\) |
0.931334 | + | 0.364166i | \(0.118646\pi\) | |||||||
\(978\) | 250.547 | + | 433.960i | 0.256183 | + | 0.443722i | ||||
\(979\) | 1493.51 | + | 862.277i | 1.52554 | + | 0.880773i | ||||
\(980\) | −112.344 | − | 112.344i | −0.114636 | − | 0.114636i | ||||
\(981\) | −197.483 | + | 52.9153i | −0.201307 | + | 0.0539402i | ||||
\(982\) | 13.5167 | + | 50.4449i | 0.0137644 | + | 0.0513695i | ||||
\(983\) | 1367.93 | − | 1367.93i | 1.39158 | − | 1.39158i | 0.569801 | − | 0.821783i | \(-0.307020\pi\) |
0.821783 | − | 0.569801i | \(-0.192980\pi\) | |||||||
\(984\) | −63.2154 | + | 109.492i | −0.0642433 | + | 0.111273i | ||||
\(985\) | −234.892 | + | 135.615i | −0.238470 | + | 0.137680i | ||||
\(986\) | 447.846 | + | 120.000i | 0.454205 | + | 0.121704i | ||||
\(987\) | 166.077i | 0.168264i | ||||||||
\(988\) | 608.200 | + | 608.200i | 0.615587 | + | 0.615587i | ||||
\(989\) | 63.5617 | 0.0642686 | ||||||||
\(990\) | 20.2384 | − | 75.5307i | 0.0204428 | − | 0.0762937i | ||||
\(991\) | 935.631 | + | 1620.56i | 0.944128 | + | 1.63528i | 0.757488 | + | 0.652849i | \(0.226426\pi\) |
0.186640 | + | 0.982428i | \(0.440240\pi\) | |||||||
\(992\) | 153.597 | + | 88.6795i | 0.154836 | + | 0.0893946i | ||||
\(993\) | 174.285 | + | 174.285i | 0.175514 | + | 0.175514i | ||||
\(994\) | −1419.16 | + | 380.263i | −1.42773 | + | 0.382558i | ||||
\(995\) | −10.3102 | − | 38.4782i | −0.0103620 | − | 0.0386715i | ||||
\(996\) | −384.631 | + | 384.631i | −0.386175 | + | 0.386175i | ||||
\(997\) | −768.584 | + | 1331.23i | −0.770897 | + | 1.33523i | 0.166175 | + | 0.986096i | \(0.446858\pi\) |
−0.937072 | + | 0.349137i | \(0.886475\pi\) | |||||||
\(998\) | 801.540 | − | 462.769i | 0.803146 | − | 0.463697i | ||||
\(999\) | −185.806 | − | 49.7865i | −0.185992 | − | 0.0498363i |
(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 | 78.3.l.a.37.1 | yes | 4 | |
3.2 | odd | 2 | 234.3.bb.c.37.1 | 4 | |||
13.2 | odd | 12 | 1014.3.f.e.577.2 | 4 | |||
13.3 | even | 3 | 1014.3.f.e.775.2 | 4 | |||
13.6 | odd | 12 | inner | 78.3.l.a.19.1 | ✓ | 4 | |
13.10 | even | 6 | 1014.3.f.d.775.2 | 4 | |||
13.11 | odd | 12 | 1014.3.f.d.577.2 | 4 | |||
39.32 | even | 12 | 234.3.bb.c.19.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.3.l.a.19.1 | ✓ | 4 | 13.6 | odd | 12 | inner | |
78.3.l.a.37.1 | yes | 4 | 1.1 | even | 1 | trivial | |
234.3.bb.c.19.1 | 4 | 39.32 | even | 12 | |||
234.3.bb.c.37.1 | 4 | 3.2 | odd | 2 | |||
1014.3.f.d.577.2 | 4 | 13.11 | odd | 12 | |||
1014.3.f.d.775.2 | 4 | 13.10 | even | 6 | |||
1014.3.f.e.577.2 | 4 | 13.2 | odd | 12 | |||
1014.3.f.e.775.2 | 4 | 13.3 | even | 3 |