Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(229,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.229");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.k (of order \(6\), 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: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 229.3 | ||
Character | \(\chi\) | \(=\) | 966.229 |
Dual form | 966.2.k.b.367.3 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.320775 | + | 0.555599i | −0.143455 | + | 0.248472i | −0.928796 | − | 0.370593i | \(-0.879155\pi\) |
0.785340 | + | 0.619064i | \(0.212488\pi\) | |||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | −2.04200 | + | 1.68233i | −0.771804 | + | 0.635860i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0.320775 | + | 0.555599i | 0.101438 | + | 0.175696i | ||||
\(11\) | 1.26628 | − | 0.731086i | 0.381797 | − | 0.220431i | −0.296803 | − | 0.954939i | \(-0.595920\pi\) |
0.678600 | + | 0.734508i | \(0.262587\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | − | 3.75315i | − | 1.04094i | −0.853881 | − | 0.520468i | \(-0.825757\pi\) | ||
0.853881 | − | 0.520468i | \(-0.174243\pi\) | |||||||
\(14\) | 0.435938 | + | 2.60959i | 0.116509 | + | 0.697442i | ||||
\(15\) | − | 0.641551i | − | 0.165648i | ||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.24804 | + | 2.16166i | 0.302693 | + | 0.524280i | 0.976745 | − | 0.214404i | \(-0.0687809\pi\) |
−0.674052 | + | 0.738684i | \(0.735448\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | 1.74685 | − | 3.02564i | 0.400756 | − | 0.694129i | −0.593062 | − | 0.805157i | \(-0.702081\pi\) |
0.993817 | + | 0.111028i | \(0.0354143\pi\) | |||||||
\(20\) | 0.641551 | 0.143455 | ||||||||
\(21\) | 0.927261 | − | 2.47794i | 0.202345 | − | 0.540731i | ||||
\(22\) | − | 1.46217i | − | 0.311736i | ||||||
\(23\) | 4.68603 | − | 1.02035i | 0.977105 | − | 0.212759i | ||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 2.29421 | + | 3.97368i | 0.458841 | + | 0.794736i | ||||
\(26\) | −3.25032 | − | 1.87658i | −0.637441 | − | 0.368027i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 2.47794 | + | 0.927261i | 0.468287 | + | 0.175236i | ||||
\(29\) | 3.12287 | 0.579902 | 0.289951 | − | 0.957042i | \(-0.406361\pi\) | ||||
0.289951 | + | 0.957042i | \(0.406361\pi\) | |||||||
\(30\) | −0.555599 | − | 0.320775i | −0.101438 | − | 0.0585653i | ||||
\(31\) | 5.79664 | − | 3.34669i | 1.04111 | − | 0.601083i | 0.120960 | − | 0.992657i | \(-0.461403\pi\) |
0.920147 | + | 0.391574i | \(0.128069\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −0.731086 | + | 1.26628i | −0.127266 | + | 0.220431i | ||||
\(34\) | 2.49607 | 0.428073 | ||||||||
\(35\) | −0.279676 | − | 1.67418i | −0.0472739 | − | 0.282989i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 8.00310 | + | 4.62059i | 1.31570 | + | 0.759621i | 0.983034 | − | 0.183423i | \(-0.0587179\pi\) |
0.332668 | + | 0.943044i | \(0.392051\pi\) | |||||||
\(38\) | −1.74685 | − | 3.02564i | −0.283377 | − | 0.490824i | ||||
\(39\) | 1.87658 | + | 3.25032i | 0.300493 | + | 0.520468i | ||||
\(40\) | 0.320775 | − | 0.555599i | 0.0507190 | − | 0.0878479i | ||||
\(41\) | − | 11.5475i | − | 1.80341i | −0.432350 | − | 0.901706i | \(-0.642315\pi\) | ||
0.432350 | − | 0.901706i | \(-0.357685\pi\) | |||||||
\(42\) | −1.68233 | − | 2.04200i | −0.259589 | − | 0.315088i | ||||
\(43\) | 5.63040i | 0.858629i | 0.903155 | + | 0.429314i | \(0.141245\pi\) | ||||
−0.903155 | + | 0.429314i | \(0.858755\pi\) | |||||||
\(44\) | −1.26628 | − | 0.731086i | −0.190899 | − | 0.110215i | ||||
\(45\) | 0.320775 | + | 0.555599i | 0.0478184 | + | 0.0828238i | ||||
\(46\) | 1.45936 | − | 4.56840i | 0.215171 | − | 0.673574i | ||||
\(47\) | −1.64885 | − | 0.951961i | −0.240509 | − | 0.138858i | 0.374902 | − | 0.927065i | \(-0.377676\pi\) |
−0.615411 | + | 0.788207i | \(0.711010\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 1.33954 | − | 6.87063i | 0.191363 | − | 0.981519i | ||||
\(50\) | 4.58841 | 0.648900 | ||||||||
\(51\) | −2.16166 | − | 1.24804i | −0.302693 | − | 0.174760i | ||||
\(52\) | −3.25032 | + | 1.87658i | −0.450739 | + | 0.260234i | ||||
\(53\) | 11.9760 | − | 6.91435i | 1.64503 | − | 0.949759i | 0.666023 | − | 0.745931i | \(-0.267995\pi\) |
0.979007 | − | 0.203828i | \(-0.0653382\pi\) | |||||||
\(54\) | 0.866025 | + | 0.500000i | 0.117851 | + | 0.0680414i | ||||
\(55\) | 0.938058i | 0.126488i | ||||||||
\(56\) | 2.04200 | − | 1.68233i | 0.272874 | − | 0.224811i | ||||
\(57\) | 3.49371i | 0.462753i | ||||||||
\(58\) | 1.56143 | − | 2.70448i | 0.205026 | − | 0.355116i | ||||
\(59\) | −10.4694 | + | 6.04453i | −1.36300 | + | 0.786931i | −0.990023 | − | 0.140908i | \(-0.954998\pi\) |
−0.372981 | + | 0.927839i | \(0.621664\pi\) | |||||||
\(60\) | −0.555599 | + | 0.320775i | −0.0717276 | + | 0.0414119i | ||||
\(61\) | −4.60070 | + | 7.96865i | −0.589060 | + | 1.02028i | 0.405296 | + | 0.914186i | \(0.367168\pi\) |
−0.994356 | + | 0.106096i | \(0.966165\pi\) | |||||||
\(62\) | − | 6.69338i | − | 0.850060i | ||||||
\(63\) | 0.435938 | + | 2.60959i | 0.0549230 | + | 0.328777i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.08525 | + | 1.20392i | 0.258643 | + | 0.149328i | ||||
\(66\) | 0.731086 | + | 1.26628i | 0.0899905 | + | 0.155868i | ||||
\(67\) | 6.42953 | − | 3.71209i | 0.785492 | − | 0.453504i | −0.0528814 | − | 0.998601i | \(-0.516841\pi\) |
0.838373 | + | 0.545097i | \(0.183507\pi\) | |||||||
\(68\) | 1.24804 | − | 2.16166i | 0.151347 | − | 0.262140i | ||||
\(69\) | −3.54804 | + | 3.22667i | −0.427134 | + | 0.388445i | ||||
\(70\) | −1.58972 | − | 0.594885i | −0.190008 | − | 0.0711024i | ||||
\(71\) | −3.43645 | −0.407831 | −0.203916 | − | 0.978988i | \(-0.565367\pi\) | ||||
−0.203916 | + | 0.978988i | \(0.565367\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 7.21510 | − | 4.16564i | 0.844464 | − | 0.487552i | −0.0143151 | − | 0.999898i | \(-0.504557\pi\) |
0.858779 | + | 0.512346i | \(0.171223\pi\) | |||||||
\(74\) | 8.00310 | − | 4.62059i | 0.930342 | − | 0.537133i | ||||
\(75\) | −3.97368 | − | 2.29421i | −0.458841 | − | 0.264912i | ||||
\(76\) | −3.49371 | −0.400756 | ||||||||
\(77\) | −1.35582 | + | 3.62318i | −0.154510 | + | 0.412899i | ||||
\(78\) | 3.75315 | 0.424961 | ||||||||
\(79\) | −12.2606 | − | 7.07864i | −1.37942 | − | 0.796410i | −0.387332 | − | 0.921940i | \(-0.626603\pi\) |
−0.992090 | + | 0.125530i | \(0.959937\pi\) | |||||||
\(80\) | −0.320775 | − | 0.555599i | −0.0358638 | − | 0.0621179i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −10.0004 | − | 5.77374i | −1.10436 | − | 0.637602i | ||||
\(83\) | −10.5288 | −1.15569 | −0.577844 | − | 0.816147i | \(-0.696106\pi\) | ||||
−0.577844 | + | 0.816147i | \(0.696106\pi\) | |||||||
\(84\) | −2.60959 | + | 0.435938i | −0.284730 | + | 0.0475647i | ||||
\(85\) | −1.60136 | −0.173692 | ||||||||
\(86\) | 4.87607 | + | 2.81520i | 0.525801 | + | 0.303571i | ||||
\(87\) | −2.70448 | + | 1.56143i | −0.289951 | + | 0.167403i | ||||
\(88\) | −1.26628 | + | 0.731086i | −0.134986 | + | 0.0779341i | ||||
\(89\) | 0.915023 | − | 1.58487i | 0.0969923 | − | 0.167996i | −0.813446 | − | 0.581640i | \(-0.802411\pi\) |
0.910438 | + | 0.413645i | \(0.135744\pi\) | |||||||
\(90\) | 0.641551 | 0.0676254 | ||||||||
\(91\) | 6.31403 | + | 7.66394i | 0.661890 | + | 0.803399i | ||||
\(92\) | −3.22667 | − | 3.54804i | −0.336403 | − | 0.369909i | ||||
\(93\) | −3.34669 | + | 5.79664i | −0.347036 | + | 0.601083i | ||||
\(94\) | −1.64885 | + | 0.951961i | −0.170065 | + | 0.0981873i | ||||
\(95\) | 1.12070 | + | 1.94110i | 0.114981 | + | 0.199153i | ||||
\(96\) | −0.866025 | − | 0.500000i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | 11.5594 | 1.17368 | 0.586841 | − | 0.809702i | \(-0.300371\pi\) | ||||
0.586841 | + | 0.809702i | \(0.300371\pi\) | |||||||
\(98\) | −5.28037 | − | 4.59540i | −0.533398 | − | 0.464205i | ||||
\(99\) | − | 1.46217i | − | 0.146954i | ||||||
\(100\) | 2.29421 | − | 3.97368i | 0.229421 | − | 0.397368i | ||||
\(101\) | 14.3329 | − | 8.27511i | 1.42618 | − | 0.823404i | 0.429361 | − | 0.903133i | \(-0.358739\pi\) |
0.996817 | + | 0.0797294i | \(0.0254056\pi\) | |||||||
\(102\) | −2.16166 | + | 1.24804i | −0.214037 | + | 0.123574i | ||||
\(103\) | −4.77542 | + | 8.27128i | −0.470536 | + | 0.814993i | −0.999432 | − | 0.0336937i | \(-0.989273\pi\) |
0.528896 | + | 0.848687i | \(0.322606\pi\) | |||||||
\(104\) | 3.75315i | 0.368027i | ||||||||
\(105\) | 1.07930 | + | 1.31005i | 0.105329 | + | 0.127848i | ||||
\(106\) | − | 13.8287i | − | 1.34316i | ||||||
\(107\) | −3.03603 | − | 1.75285i | −0.293504 | − | 0.169455i | 0.346017 | − | 0.938228i | \(-0.387534\pi\) |
−0.639521 | + | 0.768774i | \(0.720867\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | −13.6070 | + | 7.85601i | −1.30332 | + | 0.752470i | −0.980971 | − | 0.194153i | \(-0.937804\pi\) |
−0.322344 | + | 0.946622i | \(0.604471\pi\) | |||||||
\(110\) | 0.812382 | + | 0.469029i | 0.0774576 | + | 0.0447202i | ||||
\(111\) | −9.24119 | −0.877135 | ||||||||
\(112\) | −0.435938 | − | 2.60959i | −0.0411923 | − | 0.246583i | ||||
\(113\) | − | 6.33088i | − | 0.595559i | −0.954635 | − | 0.297779i | \(-0.903754\pi\) | ||
0.954635 | − | 0.297779i | \(-0.0962460\pi\) | |||||||
\(114\) | 3.02564 | + | 1.74685i | 0.283377 | + | 0.163608i | ||||
\(115\) | −0.936255 | + | 2.93086i | −0.0873062 | + | 0.273304i | ||||
\(116\) | −1.56143 | − | 2.70448i | −0.144975 | − | 0.251105i | ||||
\(117\) | −3.25032 | − | 1.87658i | −0.300493 | − | 0.173489i | ||||
\(118\) | 12.0891i | 1.11289i | ||||||||
\(119\) | −6.18512 | − | 2.31451i | −0.566989 | − | 0.212171i | ||||
\(120\) | 0.641551i | 0.0585653i | ||||||||
\(121\) | −4.43103 | + | 7.67476i | −0.402821 | + | 0.697706i | ||||
\(122\) | 4.60070 | + | 7.96865i | 0.416528 | + | 0.721448i | ||||
\(123\) | 5.77374 | + | 10.0004i | 0.520600 | + | 0.901706i | ||||
\(124\) | −5.79664 | − | 3.34669i | −0.520553 | − | 0.300542i | ||||
\(125\) | −6.15145 | −0.550203 | ||||||||
\(126\) | 2.47794 | + | 0.927261i | 0.220752 | + | 0.0826070i | ||||
\(127\) | 20.0911 | 1.78280 | 0.891400 | − | 0.453217i | \(-0.149724\pi\) | ||||
0.891400 | + | 0.453217i | \(0.149724\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −2.81520 | − | 4.87607i | −0.247865 | − | 0.429314i | ||||
\(130\) | 2.08525 | − | 1.20392i | 0.182888 | − | 0.105591i | ||||
\(131\) | 2.29470 | + | 1.32484i | 0.200489 | + | 0.115752i | 0.596883 | − | 0.802328i | \(-0.296405\pi\) |
−0.396395 | + | 0.918080i | \(0.629739\pi\) | |||||||
\(132\) | 1.46217 | 0.127266 | ||||||||
\(133\) | 1.52304 | + | 9.11714i | 0.132064 | + | 0.790557i | ||||
\(134\) | − | 7.42418i | − | 0.641351i | ||||||
\(135\) | −0.555599 | − | 0.320775i | −0.0478184 | − | 0.0276079i | ||||
\(136\) | −1.24804 | − | 2.16166i | −0.107018 | − | 0.185361i | ||||
\(137\) | 19.8373 | − | 11.4530i | 1.69481 | − | 0.978500i | 0.744281 | − | 0.667866i | \(-0.232792\pi\) |
0.950530 | − | 0.310634i | \(-0.100541\pi\) | |||||||
\(138\) | 1.02035 | + | 4.68603i | 0.0868584 | + | 0.398901i | ||||
\(139\) | 7.19533i | 0.610300i | 0.952304 | + | 0.305150i | \(0.0987065\pi\) | ||||
−0.952304 | + | 0.305150i | \(0.901293\pi\) | |||||||
\(140\) | −1.31005 | + | 1.07930i | −0.110719 | + | 0.0912174i | ||||
\(141\) | 1.90392 | 0.160339 | ||||||||
\(142\) | −1.71822 | + | 2.97605i | −0.144190 | + | 0.249745i | ||||
\(143\) | −2.74388 | − | 4.75253i | −0.229455 | − | 0.397427i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −1.00174 | + | 1.73506i | −0.0831899 | + | 0.144089i | ||||
\(146\) | − | 8.33128i | − | 0.689502i | ||||||
\(147\) | 2.27524 | + | 6.61992i | 0.187659 | + | 0.546001i | ||||
\(148\) | − | 9.24119i | − | 0.759621i | ||||||
\(149\) | −4.73532 | − | 2.73394i | −0.387933 | − | 0.223973i | 0.293331 | − | 0.956011i | \(-0.405236\pi\) |
−0.681264 | + | 0.732038i | \(0.738569\pi\) | |||||||
\(150\) | −3.97368 | + | 2.29421i | −0.324450 | + | 0.187321i | ||||
\(151\) | 8.72726 | + | 15.1161i | 0.710215 | + | 1.23013i | 0.964776 | + | 0.263071i | \(0.0847355\pi\) |
−0.254562 | + | 0.967057i | \(0.581931\pi\) | |||||||
\(152\) | −1.74685 | + | 3.02564i | −0.141689 | + | 0.245412i | ||||
\(153\) | 2.49607 | 0.201796 | ||||||||
\(154\) | 2.45985 | + | 2.98576i | 0.198221 | + | 0.240599i | ||||
\(155\) | 4.29414i | 0.344914i | ||||||||
\(156\) | 1.87658 | − | 3.25032i | 0.150246 | − | 0.260234i | ||||
\(157\) | −2.89797 | − | 5.01943i | −0.231283 | − | 0.400594i | 0.726903 | − | 0.686740i | \(-0.240959\pi\) |
−0.958186 | + | 0.286146i | \(0.907626\pi\) | |||||||
\(158\) | −12.2606 | + | 7.07864i | −0.975399 | + | 0.563147i | ||||
\(159\) | −6.91435 | + | 11.9760i | −0.548343 | + | 0.949759i | ||||
\(160\) | −0.641551 | −0.0507190 | ||||||||
\(161\) | −7.85231 | + | 9.96701i | −0.618849 | + | 0.785510i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −0.565971 | + | 0.980291i | −0.0443303 | + | 0.0767823i | −0.887339 | − | 0.461117i | \(-0.847449\pi\) |
0.843009 | + | 0.537900i | \(0.180782\pi\) | |||||||
\(164\) | −10.0004 | + | 5.77374i | −0.780900 | + | 0.450853i | ||||
\(165\) | −0.469029 | − | 0.812382i | −0.0365139 | − | 0.0632438i | ||||
\(166\) | −5.26441 | + | 9.11823i | −0.408598 | + | 0.707712i | ||||
\(167\) | − | 1.49172i | − | 0.115433i | −0.998333 | − | 0.0577164i | \(-0.981618\pi\) | ||
0.998333 | − | 0.0577164i | \(-0.0183819\pi\) | |||||||
\(168\) | −0.927261 | + | 2.47794i | −0.0715398 | + | 0.191177i | ||||
\(169\) | −1.08614 | −0.0835492 | ||||||||
\(170\) | −0.800679 | + | 1.38682i | −0.0614093 | + | 0.106364i | ||||
\(171\) | −1.74685 | − | 3.02564i | −0.133585 | − | 0.231376i | ||||
\(172\) | 4.87607 | − | 2.81520i | 0.371797 | − | 0.214657i | ||||
\(173\) | −17.1380 | − | 9.89462i | −1.30298 | − | 0.752274i | −0.322064 | − | 0.946718i | \(-0.604376\pi\) |
−0.980914 | + | 0.194444i | \(0.937710\pi\) | |||||||
\(174\) | 3.12287i | 0.236744i | ||||||||
\(175\) | −11.3698 | − | 4.25466i | −0.859477 | − | 0.321622i | ||||
\(176\) | 1.46217i | 0.110215i | ||||||||
\(177\) | 6.04453 | − | 10.4694i | 0.454335 | − | 0.786931i | ||||
\(178\) | −0.915023 | − | 1.58487i | −0.0685839 | − | 0.118791i | ||||
\(179\) | 11.2078 | + | 19.4125i | 0.837713 | + | 1.45096i | 0.891802 | + | 0.452426i | \(0.149441\pi\) |
−0.0540890 | + | 0.998536i | \(0.517225\pi\) | |||||||
\(180\) | 0.320775 | − | 0.555599i | 0.0239092 | − | 0.0414119i | ||||
\(181\) | −19.7000 | −1.46429 | −0.732145 | − | 0.681148i | \(-0.761481\pi\) | ||||
−0.732145 | + | 0.681148i | \(0.761481\pi\) | |||||||
\(182\) | 9.79418 | − | 1.63614i | 0.725993 | − | 0.121279i | ||||
\(183\) | − | 9.20141i | − | 0.680188i | ||||||
\(184\) | −4.68603 | + | 1.02035i | −0.345459 | + | 0.0752216i | ||||
\(185\) | −5.13440 | + | 2.96434i | −0.377488 | + | 0.217943i | ||||
\(186\) | 3.34669 | + | 5.79664i | 0.245391 | + | 0.425030i | ||||
\(187\) | 3.16072 | + | 1.82484i | 0.231135 | + | 0.133446i | ||||
\(188\) | 1.90392i | 0.138858i | ||||||||
\(189\) | −1.68233 | − | 2.04200i | −0.122371 | − | 0.148534i | ||||
\(190\) | 2.24139 | 0.162608 | ||||||||
\(191\) | −18.2187 | − | 10.5186i | −1.31826 | − | 0.761097i | −0.334811 | − | 0.942285i | \(-0.608672\pi\) |
−0.983448 | + | 0.181188i | \(0.942006\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 5.41719 | + | 9.38285i | 0.389938 | + | 0.675392i | 0.992441 | − | 0.122724i | \(-0.0391631\pi\) |
−0.602503 | + | 0.798117i | \(0.705830\pi\) | |||||||
\(194\) | 5.77972 | − | 10.0108i | 0.414960 | − | 0.718731i | ||||
\(195\) | −2.40784 | −0.172429 | ||||||||
\(196\) | −6.61992 | + | 2.27524i | −0.472851 | + | 0.162517i | ||||
\(197\) | −11.8314 | −0.842956 | −0.421478 | − | 0.906839i | \(-0.638488\pi\) | ||||
−0.421478 | + | 0.906839i | \(0.638488\pi\) | |||||||
\(198\) | −1.26628 | − | 0.731086i | −0.0899905 | − | 0.0519560i | ||||
\(199\) | 7.17383 | + | 12.4254i | 0.508539 | + | 0.880816i | 0.999951 | + | 0.00988879i | \(0.00314775\pi\) |
−0.491412 | + | 0.870927i | \(0.663519\pi\) | |||||||
\(200\) | −2.29421 | − | 3.97368i | −0.162225 | − | 0.280982i | ||||
\(201\) | −3.71209 | + | 6.42953i | −0.261831 | + | 0.453504i | ||||
\(202\) | − | 16.5502i | − | 1.16447i | ||||||
\(203\) | −6.37690 | + | 5.25369i | −0.447571 | + | 0.368737i | ||||
\(204\) | 2.49607i | 0.174760i | ||||||||
\(205\) | 6.41577 | + | 3.70414i | 0.448097 | + | 0.258709i | ||||
\(206\) | 4.77542 | + | 8.27128i | 0.332720 | + | 0.576287i | ||||
\(207\) | 1.45936 | − | 4.56840i | 0.101433 | − | 0.317526i | ||||
\(208\) | 3.25032 | + | 1.87658i | 0.225369 | + | 0.130117i | ||||
\(209\) | − | 5.10840i | − | 0.353356i | ||||||
\(210\) | 1.67418 | − | 0.279676i | 0.115530 | − | 0.0192995i | ||||
\(211\) | 7.50209 | 0.516465 | 0.258233 | − | 0.966083i | \(-0.416860\pi\) | ||||
0.258233 | + | 0.966083i | \(0.416860\pi\) | |||||||
\(212\) | −11.9760 | − | 6.91435i | −0.822515 | − | 0.474879i | ||||
\(213\) | 2.97605 | − | 1.71822i | 0.203916 | − | 0.117731i | ||||
\(214\) | −3.03603 | + | 1.75285i | −0.207539 | + | 0.119823i | ||||
\(215\) | −3.12825 | − | 1.80609i | −0.213345 | − | 0.123175i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −6.20651 | + | 16.5858i | −0.421326 | + | 1.12592i | ||||
\(218\) | 15.7120i | 1.06415i | ||||||||
\(219\) | −4.16564 | + | 7.21510i | −0.281488 | + | 0.487552i | ||||
\(220\) | 0.812382 | − | 0.469029i | 0.0547708 | − | 0.0316219i | ||||
\(221\) | 8.11305 | − | 4.68407i | 0.545743 | − | 0.315085i | ||||
\(222\) | −4.62059 | + | 8.00310i | −0.310114 | + | 0.537133i | ||||
\(223\) | 15.4435i | 1.03417i | 0.855933 | + | 0.517087i | \(0.172984\pi\) | ||||
−0.855933 | + | 0.517087i | \(0.827016\pi\) | |||||||
\(224\) | −2.47794 | − | 0.927261i | −0.165564 | − | 0.0619553i | ||||
\(225\) | 4.58841 | 0.305894 | ||||||||
\(226\) | −5.48270 | − | 3.16544i | −0.364704 | − | 0.210562i | ||||
\(227\) | −5.87255 | − | 10.1715i | −0.389775 | − | 0.675109i | 0.602644 | − | 0.798010i | \(-0.294114\pi\) |
−0.992419 | + | 0.122900i | \(0.960780\pi\) | |||||||
\(228\) | 3.02564 | − | 1.74685i | 0.200378 | − | 0.115688i | ||||
\(229\) | 1.20025 | − | 2.07889i | 0.0793146 | − | 0.137377i | −0.823640 | − | 0.567113i | \(-0.808060\pi\) |
0.902954 | + | 0.429736i | \(0.141394\pi\) | |||||||
\(230\) | 2.07007 | + | 2.27625i | 0.136496 | + | 0.150091i | ||||
\(231\) | −0.637417 | − | 3.81567i | −0.0419389 | − | 0.251053i | ||||
\(232\) | −3.12287 | −0.205026 | ||||||||
\(233\) | 11.5129 | − | 19.9410i | 0.754236 | − | 1.30638i | −0.191517 | − | 0.981489i | \(-0.561341\pi\) |
0.945753 | − | 0.324887i | \(-0.105326\pi\) | |||||||
\(234\) | −3.25032 | + | 1.87658i | −0.212480 | + | 0.122676i | ||||
\(235\) | 1.05782 | − | 0.610731i | 0.0690044 | − | 0.0398397i | ||||
\(236\) | 10.4694 | + | 6.04453i | 0.681502 | + | 0.393465i | ||||
\(237\) | 14.1573 | 0.919615 | ||||||||
\(238\) | −5.09699 | + | 4.19921i | −0.330389 | + | 0.272195i | ||||
\(239\) | −24.8829 | −1.60954 | −0.804772 | − | 0.593584i | \(-0.797713\pi\) | ||||
−0.804772 | + | 0.593584i | \(0.797713\pi\) | |||||||
\(240\) | 0.555599 | + | 0.320775i | 0.0358638 | + | 0.0207060i | ||||
\(241\) | 3.92849 | + | 6.80434i | 0.253056 | + | 0.438306i | 0.964366 | − | 0.264573i | \(-0.0852309\pi\) |
−0.711310 | + | 0.702879i | \(0.751898\pi\) | |||||||
\(242\) | 4.43103 | + | 7.67476i | 0.284837 | + | 0.493352i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 9.20141 | 0.589060 | ||||||||
\(245\) | 3.38763 | + | 2.94818i | 0.216428 | + | 0.188352i | ||||
\(246\) | 11.5475 | 0.736240 | ||||||||
\(247\) | −11.3557 | − | 6.55620i | −0.722545 | − | 0.417161i | ||||
\(248\) | −5.79664 | + | 3.34669i | −0.368087 | + | 0.212515i | ||||
\(249\) | 9.11823 | − | 5.26441i | 0.577844 | − | 0.333619i | ||||
\(250\) | −3.07573 | + | 5.32731i | −0.194526 | + | 0.336929i | ||||
\(251\) | 20.1145 | 1.26961 | 0.634807 | − | 0.772671i | \(-0.281080\pi\) | ||||
0.634807 | + | 0.772671i | \(0.281080\pi\) | |||||||
\(252\) | 2.04200 | − | 1.68233i | 0.128634 | − | 0.105977i | ||||
\(253\) | 5.18785 | − | 4.71795i | 0.326157 | − | 0.296615i | ||||
\(254\) | 10.0456 | − | 17.3994i | 0.630315 | − | 1.09174i | ||||
\(255\) | 1.38682 | − | 0.800679i | 0.0868458 | − | 0.0501405i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 15.6917 | + | 9.05958i | 0.978819 | + | 0.565121i | 0.901913 | − | 0.431917i | \(-0.142163\pi\) |
0.0769055 | + | 0.997038i | \(0.475496\pi\) | |||||||
\(258\) | −5.63040 | −0.350534 | ||||||||
\(259\) | −24.1157 | + | 4.02859i | −1.49848 | + | 0.250324i | ||||
\(260\) | − | 2.40784i | − | 0.149328i | ||||||
\(261\) | 1.56143 | − | 2.70448i | 0.0966503 | − | 0.167403i | ||||
\(262\) | 2.29470 | − | 1.32484i | 0.141767 | − | 0.0818492i | ||||
\(263\) | −2.45403 | + | 1.41683i | −0.151322 | + | 0.0873657i | −0.573749 | − | 0.819031i | \(-0.694512\pi\) |
0.422427 | + | 0.906397i | \(0.361178\pi\) | |||||||
\(264\) | 0.731086 | − | 1.26628i | 0.0449952 | − | 0.0779341i | ||||
\(265\) | 8.87181i | 0.544991i | ||||||||
\(266\) | 8.65720 | + | 3.23958i | 0.530807 | + | 0.198631i | ||||
\(267\) | 1.83005i | 0.111997i | ||||||||
\(268\) | −6.42953 | − | 3.71209i | −0.392746 | − | 0.226752i | ||||
\(269\) | −9.06271 | + | 5.23236i | −0.552563 | + | 0.319023i | −0.750155 | − | 0.661262i | \(-0.770021\pi\) |
0.197592 | + | 0.980284i | \(0.436688\pi\) | |||||||
\(270\) | −0.555599 | + | 0.320775i | −0.0338127 | + | 0.0195218i | ||||
\(271\) | 0.476714 | + | 0.275231i | 0.0289583 | + | 0.0167191i | 0.514409 | − | 0.857545i | \(-0.328011\pi\) |
−0.485451 | + | 0.874264i | \(0.661345\pi\) | |||||||
\(272\) | −2.49607 | −0.151347 | ||||||||
\(273\) | −9.30008 | − | 3.48015i | −0.562867 | − | 0.210628i | ||||
\(274\) | − | 22.9061i | − | 1.38381i | ||||||
\(275\) | 5.81021 | + | 3.35453i | 0.350369 | + | 0.202286i | ||||
\(276\) | 4.56840 | + | 1.45936i | 0.274985 | + | 0.0878433i | ||||
\(277\) | −2.25153 | − | 3.89976i | −0.135281 | − | 0.234314i | 0.790424 | − | 0.612561i | \(-0.209860\pi\) |
−0.925705 | + | 0.378247i | \(0.876527\pi\) | |||||||
\(278\) | 6.23134 | + | 3.59766i | 0.373731 | + | 0.215773i | ||||
\(279\) | − | 6.69338i | − | 0.400722i | ||||||
\(280\) | 0.279676 | + | 1.67418i | 0.0167139 | + | 0.100052i | ||||
\(281\) | 11.9701i | 0.714079i | 0.934089 | + | 0.357040i | \(0.116214\pi\) | ||||
−0.934089 | + | 0.357040i | \(0.883786\pi\) | |||||||
\(282\) | 0.951961 | − | 1.64885i | 0.0566885 | − | 0.0981873i | ||||
\(283\) | −10.7059 | − | 18.5431i | −0.636398 | − | 1.10227i | −0.986217 | − | 0.165457i | \(-0.947090\pi\) |
0.349819 | − | 0.936817i | \(-0.386243\pi\) | |||||||
\(284\) | 1.71822 | + | 2.97605i | 0.101958 | + | 0.176596i | ||||
\(285\) | −1.94110 | − | 1.12070i | −0.114981 | − | 0.0663843i | ||||
\(286\) | −5.48775 | −0.324498 | ||||||||
\(287\) | 19.4266 | + | 23.5800i | 1.14672 | + | 1.39188i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 5.38481 | − | 9.32676i | 0.316753 | − | 0.548633i | ||||
\(290\) | 1.00174 | + | 1.73506i | 0.0588241 | + | 0.101886i | ||||
\(291\) | −10.0108 | + | 5.77972i | −0.586841 | + | 0.338813i | ||||
\(292\) | −7.21510 | − | 4.16564i | −0.422232 | − | 0.243776i | ||||
\(293\) | −5.03581 | −0.294195 | −0.147098 | − | 0.989122i | \(-0.546993\pi\) | ||||
−0.147098 | + | 0.989122i | \(0.546993\pi\) | |||||||
\(294\) | 6.87063 | + | 1.33954i | 0.400704 | + | 0.0781237i | ||||
\(295\) | − | 7.75575i | − | 0.451557i | ||||||
\(296\) | −8.00310 | − | 4.62059i | −0.465171 | − | 0.268567i | ||||
\(297\) | 0.731086 | + | 1.26628i | 0.0424219 | + | 0.0734769i | ||||
\(298\) | −4.73532 | + | 2.73394i | −0.274310 | + | 0.158373i | ||||
\(299\) | −3.82955 | − | 17.5874i | −0.221468 | − | 1.01710i | ||||
\(300\) | 4.58841i | 0.264912i | ||||||||
\(301\) | −9.47219 | − | 11.4973i | −0.545968 | − | 0.662693i | ||||
\(302\) | 17.4545 | 1.00440 | ||||||||
\(303\) | −8.27511 | + | 14.3329i | −0.475392 | + | 0.823404i | ||||
\(304\) | 1.74685 | + | 3.02564i | 0.100189 | + | 0.173532i | ||||
\(305\) | −2.95159 | − | 5.11230i | −0.169007 | − | 0.292729i | ||||
\(306\) | 1.24804 | − | 2.16166i | 0.0713455 | − | 0.123574i | ||||
\(307\) | 9.89753i | 0.564882i | 0.959285 | + | 0.282441i | \(0.0911441\pi\) | ||||
−0.959285 | + | 0.282441i | \(0.908856\pi\) | |||||||
\(308\) | 3.81567 | − | 0.637417i | 0.217418 | − | 0.0363202i | ||||
\(309\) | − | 9.55085i | − | 0.543329i | ||||||
\(310\) | 3.71884 | + | 2.14707i | 0.211216 | + | 0.121945i | ||||
\(311\) | 22.5520 | − | 13.0204i | 1.27880 | − | 0.738318i | 0.302176 | − | 0.953252i | \(-0.402287\pi\) |
0.976629 | + | 0.214934i | \(0.0689535\pi\) | |||||||
\(312\) | −1.87658 | − | 3.25032i | −0.106240 | − | 0.184013i | ||||
\(313\) | −6.92894 | + | 12.0013i | −0.391647 | + | 0.678352i | −0.992667 | − | 0.120882i | \(-0.961428\pi\) |
0.601020 | + | 0.799234i | \(0.294761\pi\) | |||||||
\(314\) | −5.79594 | −0.327084 | ||||||||
\(315\) | −1.58972 | − | 0.594885i | −0.0895708 | − | 0.0335180i | ||||
\(316\) | 14.1573i | 0.796410i | ||||||||
\(317\) | 5.09880 | − | 8.83138i | 0.286377 | − | 0.496020i | −0.686565 | − | 0.727068i | \(-0.740882\pi\) |
0.972942 | + | 0.231049i | \(0.0742157\pi\) | |||||||
\(318\) | 6.91435 | + | 11.9760i | 0.387737 | + | 0.671581i | ||||
\(319\) | 3.95442 | − | 2.28309i | 0.221405 | − | 0.127828i | ||||
\(320\) | −0.320775 | + | 0.555599i | −0.0179319 | + | 0.0310589i | ||||
\(321\) | 3.50571 | 0.195670 | ||||||||
\(322\) | 4.70553 | + | 11.7838i | 0.262229 | + | 0.656686i | ||||
\(323\) | 8.72055 | 0.485224 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 14.9138 | − | 8.61050i | 0.827270 | − | 0.477625i | ||||
\(326\) | 0.565971 | + | 0.980291i | 0.0313462 | + | 0.0542933i | ||||
\(327\) | 7.85601 | − | 13.6070i | 0.434439 | − | 0.752470i | ||||
\(328\) | 11.5475i | 0.637602i | ||||||||
\(329\) | 4.96846 | − | 0.829992i | 0.273920 | − | 0.0457590i | ||||
\(330\) | −0.938058 | −0.0516384 | ||||||||
\(331\) | 4.96632 | − | 8.60191i | 0.272973 | − | 0.472804i | −0.696648 | − | 0.717413i | \(-0.745326\pi\) |
0.969622 | + | 0.244609i | \(0.0786595\pi\) | |||||||
\(332\) | 5.26441 | + | 9.11823i | 0.288922 | + | 0.500428i | ||||
\(333\) | 8.00310 | − | 4.62059i | 0.438567 | − | 0.253207i | ||||
\(334\) | −1.29187 | − | 0.745861i | −0.0706879 | − | 0.0408117i | ||||
\(335\) | 4.76299i | 0.260230i | ||||||||
\(336\) | 1.68233 | + | 2.04200i | 0.0917785 | + | 0.111400i | ||||
\(337\) | 25.7788i | 1.40426i | 0.712049 | + | 0.702130i | \(0.247767\pi\) | ||||
−0.712049 | + | 0.702130i | \(0.752233\pi\) | |||||||
\(338\) | −0.543069 | + | 0.940624i | −0.0295391 | + | 0.0511632i | ||||
\(339\) | 3.16544 | + | 5.48270i | 0.171923 | + | 0.297779i | ||||
\(340\) | 0.800679 | + | 1.38682i | 0.0434229 | + | 0.0752107i | ||||
\(341\) | 4.89344 | − | 8.47568i | 0.264995 | − | 0.458984i | ||||
\(342\) | −3.49371 | −0.188918 | ||||||||
\(343\) | 8.82331 | + | 16.2834i | 0.476414 | + | 0.879221i | ||||
\(344\) | − | 5.63040i | − | 0.303571i | ||||||
\(345\) | −0.654609 | − | 3.00633i | −0.0352430 | − | 0.161855i | ||||
\(346\) | −17.1380 | + | 9.89462i | −0.921344 | + | 0.531938i | ||||
\(347\) | 2.22541 | + | 3.85452i | 0.119466 | + | 0.206921i | 0.919556 | − | 0.392958i | \(-0.128548\pi\) |
−0.800090 | + | 0.599880i | \(0.795215\pi\) | |||||||
\(348\) | 2.70448 | + | 1.56143i | 0.144975 | + | 0.0837016i | ||||
\(349\) | − | 22.9293i | − | 1.22738i | −0.789548 | − | 0.613689i | \(-0.789685\pi\) | ||
0.789548 | − | 0.613689i | \(-0.210315\pi\) | |||||||
\(350\) | −9.36955 | + | 7.71922i | −0.500823 | + | 0.412609i | ||||
\(351\) | 3.75315 | 0.200328 | ||||||||
\(352\) | 1.26628 | + | 0.731086i | 0.0674929 | + | 0.0389670i | ||||
\(353\) | −2.19435 | + | 1.26691i | −0.116794 | + | 0.0674308i | −0.557259 | − | 0.830339i | \(-0.688147\pi\) |
0.440465 | + | 0.897770i | \(0.354814\pi\) | |||||||
\(354\) | −6.04453 | − | 10.4694i | −0.321263 | − | 0.556444i | ||||
\(355\) | 1.10233 | − | 1.90929i | 0.0585055 | − | 0.101334i | ||||
\(356\) | −1.83005 | −0.0969923 | ||||||||
\(357\) | 6.51373 | − | 1.08813i | 0.344743 | − | 0.0575901i | ||||
\(358\) | 22.4157 | 1.18471 | ||||||||
\(359\) | −9.78344 | − | 5.64847i | −0.516350 | − | 0.298115i | 0.219090 | − | 0.975705i | \(-0.429691\pi\) |
−0.735440 | + | 0.677590i | \(0.763025\pi\) | |||||||
\(360\) | −0.320775 | − | 0.555599i | −0.0169063 | − | 0.0292826i | ||||
\(361\) | 3.39700 | + | 5.88378i | 0.178790 | + | 0.309673i | ||||
\(362\) | −9.85001 | + | 17.0607i | −0.517705 | + | 0.896691i | ||||
\(363\) | − | 8.86205i | − | 0.465137i | ||||||
\(364\) | 3.48015 | − | 9.30008i | 0.182409 | − | 0.487457i | ||||
\(365\) | 5.34494i | 0.279767i | ||||||||
\(366\) | −7.96865 | − | 4.60070i | −0.416528 | − | 0.240483i | ||||
\(367\) | −9.30564 | − | 16.1178i | −0.485751 | − | 0.841345i | 0.514115 | − | 0.857721i | \(-0.328120\pi\) |
−0.999866 | + | 0.0163765i | \(0.994787\pi\) | |||||||
\(368\) | −1.45936 | + | 4.56840i | −0.0760745 | + | 0.238144i | ||||
\(369\) | −10.0004 | − | 5.77374i | −0.520600 | − | 0.300569i | ||||
\(370\) | 5.92869i | 0.308218i | ||||||||
\(371\) | −12.8228 | + | 34.2667i | −0.665727 | + | 1.77904i | ||||
\(372\) | 6.69338 | 0.347036 | ||||||||
\(373\) | 12.2660 | + | 7.08177i | 0.635109 | + | 0.366680i | 0.782728 | − | 0.622364i | \(-0.213828\pi\) |
−0.147619 | + | 0.989044i | \(0.547161\pi\) | |||||||
\(374\) | 3.16072 | − | 1.82484i | 0.163437 | − | 0.0943605i | ||||
\(375\) | 5.32731 | − | 3.07573i | 0.275101 | − | 0.158830i | ||||
\(376\) | 1.64885 | + | 0.951961i | 0.0850327 | + | 0.0490936i | ||||
\(377\) | − | 11.7206i | − | 0.603641i | ||||||
\(378\) | −2.60959 | + | 0.435938i | −0.134223 | + | 0.0224222i | ||||
\(379\) | − | 29.9100i | − | 1.53638i | −0.640224 | − | 0.768188i | \(-0.721159\pi\) | ||
0.640224 | − | 0.768188i | \(-0.278841\pi\) | |||||||
\(380\) | 1.12070 | − | 1.94110i | 0.0574905 | − | 0.0995764i | ||||
\(381\) | −17.3994 | + | 10.0456i | −0.891400 | + | 0.514650i | ||||
\(382\) | −18.2187 | + | 10.5186i | −0.932150 | + | 0.538177i | ||||
\(383\) | −15.3684 | + | 26.6188i | −0.785287 | + | 1.36016i | 0.143541 | + | 0.989644i | \(0.454151\pi\) |
−0.928828 | + | 0.370512i | \(0.879182\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | −1.57812 | − | 1.91552i | −0.0804285 | − | 0.0976237i | ||||
\(386\) | 10.8344 | 0.551456 | ||||||||
\(387\) | 4.87607 | + | 2.81520i | 0.247865 | + | 0.143105i | ||||
\(388\) | −5.77972 | − | 10.0108i | −0.293421 | − | 0.508220i | ||||
\(389\) | 19.7850 | − | 11.4229i | 1.00314 | − | 0.579163i | 0.0939645 | − | 0.995576i | \(-0.470046\pi\) |
0.909176 | + | 0.416412i | \(0.136713\pi\) | |||||||
\(390\) | −1.20392 | + | 2.08525i | −0.0609628 | + | 0.105591i | ||||
\(391\) | 8.05400 | + | 8.85618i | 0.407308 | + | 0.447876i | ||||
\(392\) | −1.33954 | + | 6.87063i | −0.0676571 | + | 0.347019i | ||||
\(393\) | −2.64969 | −0.133659 | ||||||||
\(394\) | −5.91572 | + | 10.2463i | −0.298030 | + | 0.516203i | ||||
\(395\) | 7.86578 | − | 4.54131i | 0.395770 | − | 0.228498i | ||||
\(396\) | −1.26628 | + | 0.731086i | −0.0636329 | + | 0.0367385i | ||||
\(397\) | −2.75666 | − | 1.59156i | −0.138353 | − | 0.0798780i | 0.429226 | − | 0.903197i | \(-0.358786\pi\) |
−0.567579 | + | 0.823319i | \(0.692120\pi\) | |||||||
\(398\) | 14.3477 | 0.719183 | ||||||||
\(399\) | −5.87756 | − | 7.13416i | −0.294246 | − | 0.357155i | ||||
\(400\) | −4.58841 | −0.229421 | ||||||||
\(401\) | −7.09790 | − | 4.09797i | −0.354452 | − | 0.204643i | 0.312192 | − | 0.950019i | \(-0.398937\pi\) |
−0.666644 | + | 0.745376i | \(0.732270\pi\) | |||||||
\(402\) | 3.71209 | + | 6.42953i | 0.185142 | + | 0.320676i | ||||
\(403\) | −12.5606 | − | 21.7557i | −0.625690 | − | 1.08373i | ||||
\(404\) | −14.3329 | − | 8.27511i | −0.713089 | − | 0.411702i | ||||
\(405\) | 0.641551 | 0.0318789 | ||||||||
\(406\) | 1.36138 | + | 8.14940i | 0.0675640 | + | 0.404448i | ||||
\(407\) | 13.5122 | 0.669775 | ||||||||
\(408\) | 2.16166 | + | 1.24804i | 0.107018 | + | 0.0617870i | ||||
\(409\) | −14.7694 | + | 8.52713i | −0.730301 | + | 0.421639i | −0.818532 | − | 0.574461i | \(-0.805212\pi\) |
0.0882313 | + | 0.996100i | \(0.471879\pi\) | |||||||
\(410\) | 6.41577 | − | 3.70414i | 0.316852 | − | 0.182935i | ||||
\(411\) | −11.4530 | + | 19.8373i | −0.564937 | + | 0.978500i | ||||
\(412\) | 9.55085 | 0.470536 | ||||||||
\(413\) | 11.2097 | − | 29.9560i | 0.551594 | − | 1.47404i | ||||
\(414\) | −3.22667 | − | 3.54804i | −0.158582 | − | 0.174377i | ||||
\(415\) | 3.37739 | − | 5.84981i | 0.165789 | − | 0.287156i | ||||
\(416\) | 3.25032 | − | 1.87658i | 0.159360 | − | 0.0920067i | ||||
\(417\) | −3.59766 | − | 6.23134i | −0.176178 | − | 0.305150i | ||||
\(418\) | −4.42401 | − | 2.55420i | −0.216385 | − | 0.124930i | ||||
\(419\) | −26.4920 | −1.29422 | −0.647110 | − | 0.762397i | \(-0.724022\pi\) | ||||
−0.647110 | + | 0.762397i | \(0.724022\pi\) | |||||||
\(420\) | 0.594885 | − | 1.58972i | 0.0290274 | − | 0.0775706i | ||||
\(421\) | − | 27.2139i | − | 1.32632i | −0.748476 | − | 0.663162i | \(-0.769214\pi\) | ||
0.748476 | − | 0.663162i | \(-0.230786\pi\) | |||||||
\(422\) | 3.75105 | − | 6.49700i | 0.182598 | − | 0.316269i | ||||
\(423\) | −1.64885 | + | 0.951961i | −0.0801696 | + | 0.0462859i | ||||
\(424\) | −11.9760 | + | 6.91435i | −0.581606 | + | 0.335790i | ||||
\(425\) | −5.72651 | + | 9.91860i | −0.277776 | + | 0.481123i | ||||
\(426\) | − | 3.43645i | − | 0.166496i | ||||||
\(427\) | −4.01125 | − | 24.0119i | −0.194118 | − | 1.16202i | ||||
\(428\) | 3.50571i | 0.169455i | ||||||||
\(429\) | 4.75253 | + | 2.74388i | 0.229455 | + | 0.132476i | ||||
\(430\) | −3.12825 | + | 1.80609i | −0.150858 | + | 0.0870976i | ||||
\(431\) | 7.87094 | − | 4.54429i | 0.379130 | − | 0.218891i | −0.298310 | − | 0.954469i | \(-0.596423\pi\) |
0.677440 | + | 0.735578i | \(0.263090\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | 38.2940 | 1.84029 | 0.920147 | − | 0.391572i | \(-0.128069\pi\) | ||||
0.920147 | + | 0.391572i | \(0.128069\pi\) | |||||||
\(434\) | 11.2605 | + | 13.6679i | 0.540520 | + | 0.656080i | ||||
\(435\) | − | 2.00348i | − | 0.0960594i | ||||||
\(436\) | 13.6070 | + | 7.85601i | 0.651658 | + | 0.376235i | ||||
\(437\) | 5.09858 | − | 15.9606i | 0.243898 | − | 0.763501i | ||||
\(438\) | 4.16564 | + | 7.21510i | 0.199042 | + | 0.344751i | ||||
\(439\) | −8.56977 | − | 4.94776i | −0.409013 | − | 0.236144i | 0.281353 | − | 0.959604i | \(-0.409217\pi\) |
−0.690366 | + | 0.723461i | \(0.742550\pi\) | |||||||
\(440\) | − | 0.938058i | − | 0.0447202i | ||||||
\(441\) | −5.28037 | − | 4.59540i | −0.251446 | − | 0.218828i | ||||
\(442\) | − | 9.36814i | − | 0.445597i | ||||||
\(443\) | −0.732011 | + | 1.26788i | −0.0347789 | + | 0.0602388i | −0.882891 | − | 0.469578i | \(-0.844406\pi\) |
0.848112 | + | 0.529817i | \(0.177739\pi\) | |||||||
\(444\) | 4.62059 | + | 8.00310i | 0.219284 | + | 0.379810i | ||||
\(445\) | 0.587034 | + | 1.01677i | 0.0278281 | + | 0.0481996i | ||||
\(446\) | 13.3745 | + | 7.72176i | 0.633300 | + | 0.365636i | ||||
\(447\) | 5.46788 | 0.258622 | ||||||||
\(448\) | −2.04200 | + | 1.68233i | −0.0964755 | + | 0.0794825i | ||||
\(449\) | −14.7310 | −0.695198 | −0.347599 | − | 0.937643i | \(-0.613003\pi\) | ||||
−0.347599 | + | 0.937643i | \(0.613003\pi\) | |||||||
\(450\) | 2.29421 | − | 3.97368i | 0.108150 | − | 0.187321i | ||||
\(451\) | −8.44220 | − | 14.6223i | −0.397528 | − | 0.688538i | ||||
\(452\) | −5.48270 | + | 3.16544i | −0.257885 | + | 0.148890i | ||||
\(453\) | −15.1161 | − | 8.72726i | −0.710215 | − | 0.410043i | ||||
\(454\) | −11.7451 | −0.551224 | ||||||||
\(455\) | −6.28346 | + | 1.04967i | −0.294573 | + | 0.0492092i | ||||
\(456\) | − | 3.49371i | − | 0.163608i | ||||||
\(457\) | −13.3608 | − | 7.71386i | −0.624992 | − | 0.360839i | 0.153818 | − | 0.988099i | \(-0.450843\pi\) |
−0.778810 | + | 0.627260i | \(0.784176\pi\) | |||||||
\(458\) | −1.20025 | − | 2.07889i | −0.0560839 | − | 0.0971401i | ||||
\(459\) | −2.16166 | + | 1.24804i | −0.100898 | + | 0.0582534i | ||||
\(460\) | 3.00633 | − | 0.654609i | 0.140171 | − | 0.0305213i | ||||
\(461\) | − | 4.48982i | − | 0.209112i | −0.994519 | − | 0.104556i | \(-0.966658\pi\) | ||
0.994519 | − | 0.104556i | \(-0.0333421\pi\) | |||||||
\(462\) | −3.62318 | − | 1.35582i | −0.168565 | − | 0.0630783i | ||||
\(463\) | −30.3409 | −1.41006 | −0.705031 | − | 0.709177i | \(-0.749067\pi\) | ||||
−0.705031 | + | 0.709177i | \(0.749067\pi\) | |||||||
\(464\) | −1.56143 | + | 2.70448i | −0.0724877 | + | 0.125552i | ||||
\(465\) | −2.14707 | − | 3.71884i | −0.0995681 | − | 0.172457i | ||||
\(466\) | −11.5129 | − | 19.9410i | −0.533326 | − | 0.923747i | ||||
\(467\) | 8.55783 | − | 14.8226i | 0.396009 | − | 0.685908i | −0.597220 | − | 0.802077i | \(-0.703728\pi\) |
0.993229 | + | 0.116169i | \(0.0370614\pi\) | |||||||
\(468\) | 3.75315i | 0.173489i | ||||||||
\(469\) | −6.88415 | + | 18.3967i | −0.317881 | + | 0.849479i | ||||
\(470\) | − | 1.22146i | − | 0.0563419i | ||||||
\(471\) | 5.01943 | + | 2.89797i | 0.231283 | + | 0.133531i | ||||
\(472\) | 10.4694 | − | 6.04453i | 0.481895 | − | 0.278222i | ||||
\(473\) | 4.11631 | + | 7.12966i | 0.189268 | + | 0.327822i | ||||
\(474\) | 7.07864 | − | 12.2606i | 0.325133 | − | 0.563147i | ||||
\(475\) | 16.0306 | 0.735533 | ||||||||
\(476\) | 1.08813 | + | 6.51373i | 0.0498745 | + | 0.298556i | ||||
\(477\) | − | 13.8287i | − | 0.633172i | ||||||
\(478\) | −12.4415 | + | 21.5493i | −0.569060 | + | 0.985641i | ||||
\(479\) | −9.60766 | − | 16.6409i | −0.438985 | − | 0.760344i | 0.558626 | − | 0.829419i | \(-0.311329\pi\) |
−0.997611 | + | 0.0690750i | \(0.977995\pi\) | |||||||
\(480\) | 0.555599 | − | 0.320775i | 0.0253595 | − | 0.0146413i | ||||
\(481\) | 17.3418 | − | 30.0368i | 0.790717 | − | 1.36956i | ||||
\(482\) | 7.85698 | 0.357875 | ||||||||
\(483\) | 1.81680 | − | 12.5578i | 0.0826671 | − | 0.571401i | ||||
\(484\) | 8.86205 | 0.402821 | ||||||||
\(485\) | −3.70798 | + | 6.42241i | −0.168371 | + | 0.291627i | ||||
\(486\) | 0.866025 | − | 0.500000i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | −0.744901 | − | 1.29021i | −0.0337547 | − | 0.0584649i | 0.848655 | − | 0.528948i | \(-0.177413\pi\) |
−0.882409 | + | 0.470483i | \(0.844080\pi\) | |||||||
\(488\) | 4.60070 | − | 7.96865i | 0.208264 | − | 0.360724i | ||||
\(489\) | − | 1.13194i | − | 0.0511882i | ||||||
\(490\) | 4.24701 | − | 1.45968i | 0.191860 | − | 0.0659417i | ||||
\(491\) | −10.2935 | −0.464537 | −0.232269 | − | 0.972652i | \(-0.574615\pi\) | ||||
−0.232269 | + | 0.972652i | \(0.574615\pi\) | |||||||
\(492\) | 5.77374 | − | 10.0004i | 0.260300 | − | 0.450853i | ||||
\(493\) | 3.89745 | + | 6.75059i | 0.175532 | + | 0.304031i | ||||
\(494\) | −11.3557 | + | 6.55620i | −0.510916 | + | 0.294978i | ||||
\(495\) | 0.812382 | + | 0.469029i | 0.0365139 | + | 0.0210813i | ||||
\(496\) | 6.69338i | 0.300542i | ||||||||
\(497\) | 7.01723 | − | 5.78123i | 0.314766 | − | 0.259324i | ||||
\(498\) | − | 10.5288i | − | 0.471808i | ||||||
\(499\) | 6.36607 | − | 11.0264i | 0.284984 | − | 0.493608i | −0.687621 | − | 0.726070i | \(-0.741345\pi\) |
0.972605 | + | 0.232462i | \(0.0746782\pi\) | |||||||
\(500\) | 3.07573 | + | 5.32731i | 0.137551 | + | 0.238245i | ||||
\(501\) | 0.745861 | + | 1.29187i | 0.0333226 | + | 0.0577164i | ||||
\(502\) | 10.0572 | − | 17.4196i | 0.448876 | − | 0.777476i | ||||
\(503\) | −22.8522 | −1.01893 | −0.509465 | − | 0.860491i | \(-0.670157\pi\) | ||||
−0.509465 | + | 0.860491i | \(0.670157\pi\) | |||||||
\(504\) | −0.435938 | − | 2.60959i | −0.0194182 | − | 0.116240i | ||||
\(505\) | 10.6178i | 0.472486i | ||||||||
\(506\) | −1.49193 | − | 6.85178i | −0.0663246 | − | 0.304599i | ||||
\(507\) | 0.940624 | − | 0.543069i | 0.0417746 | − | 0.0241186i | ||||
\(508\) | −10.0456 | − | 17.3994i | −0.445700 | − | 0.771975i | ||||
\(509\) | −3.25906 | − | 1.88162i | −0.144455 | − | 0.0834012i | 0.426030 | − | 0.904709i | \(-0.359912\pi\) |
−0.570486 | + | 0.821308i | \(0.693245\pi\) | |||||||
\(510\) | − | 1.60136i | − | 0.0709093i | ||||||
\(511\) | −7.72528 | + | 20.6444i | −0.341746 | + | 0.913255i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.02564 | + | 1.74685i | 0.133585 | + | 0.0771255i | ||||
\(514\) | 15.6917 | − | 9.05958i | 0.692129 | − | 0.399601i | ||||
\(515\) | −3.06368 | − | 5.30644i | −0.135002 | − | 0.233830i | ||||
\(516\) | −2.81520 | + | 4.87607i | −0.123932 | + | 0.214657i | ||||
\(517\) | −2.78386 | −0.122434 | ||||||||
\(518\) | −8.56899 | + | 22.8991i | −0.376500 | + | 1.00613i | ||||
\(519\) | 19.7892 | 0.868651 | ||||||||
\(520\) | −2.08525 | − | 1.20392i | −0.0914442 | − | 0.0527953i | ||||
\(521\) | 14.6312 | + | 25.3419i | 0.641003 | + | 1.11025i | 0.985209 | + | 0.171356i | \(0.0548147\pi\) |
−0.344206 | + | 0.938894i | \(0.611852\pi\) | |||||||
\(522\) | −1.56143 | − | 2.70448i | −0.0683421 | − | 0.118372i | ||||
\(523\) | −19.2011 | + | 33.2572i | −0.839603 | + | 1.45424i | 0.0506233 | + | 0.998718i | \(0.483879\pi\) |
−0.890227 | + | 0.455518i | \(0.849454\pi\) | |||||||
\(524\) | − | 2.64969i | − | 0.115752i | ||||||
\(525\) | 11.9739 | − | 2.00026i | 0.522583 | − | 0.0872987i | ||||
\(526\) | 2.83367i | 0.123554i | ||||||||
\(527\) | 14.4688 | + | 8.35358i | 0.630272 | + | 0.363888i | ||||
\(528\) | −0.731086 | − | 1.26628i | −0.0318164 | − | 0.0551077i | ||||
\(529\) | 20.9178 | − | 9.56283i | 0.909467 | − | 0.415775i | ||||
\(530\) | 7.68321 | + | 4.43590i | 0.333737 | + | 0.192683i | ||||
\(531\) | 12.0891i | 0.524621i | ||||||||
\(532\) | 7.13416 | − | 5.87756i | 0.309305 | − | 0.254825i | ||||
\(533\) | −43.3394 | −1.87724 | ||||||||
\(534\) | 1.58487 | + | 0.915023i | 0.0685839 | + | 0.0395969i | ||||
\(535\) | 1.94777 | − | 1.12454i | 0.0842094 | − | 0.0486183i | ||||
\(536\) | −6.42953 | + | 3.71209i | −0.277713 | + | 0.160338i | ||||
\(537\) | −19.4125 | − | 11.2078i | −0.837713 | − | 0.483654i | ||||
\(538\) | 10.4647i | 0.451166i | ||||||||
\(539\) | −3.32679 | − | 9.67946i | −0.143295 | − | 0.416924i | ||||
\(540\) | 0.641551i | 0.0276079i | ||||||||
\(541\) | 3.78930 | − | 6.56326i | 0.162915 | − | 0.282177i | −0.772998 | − | 0.634408i | \(-0.781244\pi\) |
0.935913 | + | 0.352232i | \(0.114577\pi\) | |||||||
\(542\) | 0.476714 | − | 0.275231i | 0.0204766 | − | 0.0118222i | ||||
\(543\) | 17.0607 | − | 9.85001i | 0.732145 | − | 0.422704i | ||||
\(544\) | −1.24804 | + | 2.16166i | −0.0535091 | + | 0.0926805i | ||||
\(545\) | − | 10.0801i | − | 0.431782i | ||||||
\(546\) | −7.66394 | + | 6.31403i | −0.327986 | + | 0.270216i | ||||
\(547\) | −14.8688 | −0.635746 | −0.317873 | − | 0.948133i | \(-0.602968\pi\) | ||||
−0.317873 | + | 0.948133i | \(0.602968\pi\) | |||||||
\(548\) | −19.8373 | − | 11.4530i | −0.847406 | − | 0.489250i | ||||
\(549\) | 4.60070 | + | 7.96865i | 0.196353 | + | 0.340094i | ||||
\(550\) | 5.81021 | − | 3.35453i | 0.247748 | − | 0.143037i | ||||
\(551\) | 5.45519 | − | 9.44867i | 0.232399 | − | 0.402527i | ||||
\(552\) | 3.54804 | − | 3.22667i | 0.151015 | − | 0.137336i | ||||
\(553\) | 36.9447 | − | 6.17170i | 1.57105 | − | 0.262447i | ||||
\(554\) | −4.50306 | −0.191317 | ||||||||
\(555\) | 2.96434 | − | 5.13440i | 0.125829 | − | 0.217943i | ||||
\(556\) | 6.23134 | − | 3.59766i | 0.264267 | − | 0.152575i | ||||
\(557\) | −7.57642 | + | 4.37425i | −0.321023 | + | 0.185343i | −0.651849 | − | 0.758349i | \(-0.726006\pi\) |
0.330825 | + | 0.943692i | \(0.392673\pi\) | |||||||
\(558\) | −5.79664 | − | 3.34669i | −0.245391 | − | 0.141677i | ||||
\(559\) | 21.1318 | 0.893778 | ||||||||
\(560\) | 1.58972 | + | 0.594885i | 0.0671781 | + | 0.0251385i | ||||
\(561\) | −3.64969 | −0.154090 | ||||||||
\(562\) | 10.3665 | + | 5.98507i | 0.437282 | + | 0.252465i | ||||
\(563\) | −7.69223 | − | 13.3233i | −0.324189 | − | 0.561512i | 0.657159 | − | 0.753752i | \(-0.271758\pi\) |
−0.981348 | + | 0.192240i | \(0.938425\pi\) | |||||||
\(564\) | −0.951961 | − | 1.64885i | −0.0400848 | − | 0.0694289i | ||||
\(565\) | 3.51743 | + | 2.03079i | 0.147979 | + | 0.0854359i | ||||
\(566\) | −21.4118 | −0.900003 | ||||||||
\(567\) | 2.47794 | + | 0.927261i | 0.104064 | + | 0.0389413i | ||||
\(568\) | 3.43645 | 0.144190 | ||||||||
\(569\) | 9.48688 | + | 5.47725i | 0.397711 | + | 0.229618i | 0.685496 | − | 0.728077i | \(-0.259586\pi\) |
−0.287785 | + | 0.957695i | \(0.592919\pi\) | |||||||
\(570\) | −1.94110 | + | 1.12070i | −0.0813038 | + | 0.0469408i | ||||
\(571\) | 12.1074 | − | 6.99022i | 0.506680 | − | 0.292532i | −0.224788 | − | 0.974408i | \(-0.572169\pi\) |
0.731468 | + | 0.681876i | \(0.238836\pi\) | |||||||
\(572\) | −2.74388 | + | 4.75253i | −0.114727 | + | 0.198713i | ||||
\(573\) | 21.0371 | 0.878840 | ||||||||
\(574\) | 30.1342 | − | 5.03398i | 1.25778 | − | 0.210114i | ||||
\(575\) | 14.8053 | + | 16.2799i | 0.617423 | + | 0.678918i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 37.3087 | − | 21.5402i | 1.55318 | − | 0.896731i | 0.555303 | − | 0.831648i | \(-0.312602\pi\) |
0.997880 | − | 0.0650829i | \(-0.0207312\pi\) | |||||||
\(578\) | −5.38481 | − | 9.32676i | −0.223979 | − | 0.387942i | ||||
\(579\) | −9.38285 | − | 5.41719i | −0.389938 | − | 0.225131i | ||||
\(580\) | 2.00348 | 0.0831899 | ||||||||
\(581\) | 21.4999 | − | 17.7129i | 0.891966 | − | 0.734857i | ||||
\(582\) | 11.5594i | 0.479154i | ||||||||
\(583\) | 10.1100 | − | 17.5110i | 0.418712 | − | 0.725231i | ||||
\(584\) | −7.21510 | + | 4.16564i | −0.298563 | + | 0.172375i | ||||
\(585\) | 2.08525 | − | 1.20392i | 0.0862144 | − | 0.0497759i | ||||
\(586\) | −2.51791 | + | 4.36114i | −0.104014 | + | 0.180157i | ||||
\(587\) | − | 1.59131i | − | 0.0656803i | −0.999461 | − | 0.0328402i | \(-0.989545\pi\) | ||
0.999461 | − | 0.0328402i | \(-0.0104552\pi\) | |||||||
\(588\) | 4.59540 | − | 5.28037i | 0.189511 | − | 0.217759i | ||||
\(589\) | − | 23.3847i | − | 0.963550i | ||||||
\(590\) | −6.71667 | − | 3.87787i | −0.276521 | − | 0.159649i | ||||
\(591\) | 10.2463 | − | 5.91572i | 0.421478 | − | 0.243340i | ||||
\(592\) | −8.00310 | + | 4.62059i | −0.328925 | + | 0.189905i | ||||
\(593\) | −3.60850 | − | 2.08337i | −0.148183 | − | 0.0855538i | 0.424075 | − | 0.905627i | \(-0.360599\pi\) |
−0.572259 | + | 0.820073i | \(0.693933\pi\) | |||||||
\(594\) | 1.46217 | 0.0599937 | ||||||||
\(595\) | 3.26998 | − | 2.69401i | 0.134056 | − | 0.110444i | ||||
\(596\) | 5.46788i | 0.223973i | ||||||||
\(597\) | −12.4254 | − | 7.17383i | −0.508539 | − | 0.293605i | ||||
\(598\) | −17.1459 | − | 5.47720i | −0.701147 | − | 0.223980i | ||||
\(599\) | 17.4240 | + | 30.1793i | 0.711925 | + | 1.23309i | 0.964133 | + | 0.265418i | \(0.0855099\pi\) |
−0.252208 | + | 0.967673i | \(0.581157\pi\) | |||||||
\(600\) | 3.97368 | + | 2.29421i | 0.162225 | + | 0.0936606i | ||||
\(601\) | 13.8276i | 0.564041i | 0.959408 | + | 0.282020i | \(0.0910046\pi\) | ||||
−0.959408 | + | 0.282020i | \(0.908995\pi\) | |||||||
\(602\) | −14.6930 | + | 2.45451i | −0.598844 | + | 0.100038i | ||||
\(603\) | − | 7.42418i | − | 0.302336i | ||||||
\(604\) | 8.72726 | − | 15.1161i | 0.355107 | − | 0.615064i | ||||
\(605\) | −2.84273 | − | 4.92375i | −0.115573 | − | 0.200179i | ||||
\(606\) | 8.27511 | + | 14.3329i | 0.336153 | + | 0.582234i | ||||
\(607\) | −31.8009 | − | 18.3602i | −1.29076 | − | 0.745219i | −0.311969 | − | 0.950092i | \(-0.600989\pi\) |
−0.978789 | + | 0.204873i | \(0.934322\pi\) | |||||||
\(608\) | 3.49371 | 0.141689 | ||||||||
\(609\) | 2.89571 | − | 7.73828i | 0.117340 | − | 0.313571i | ||||
\(610\) | −5.90317 | −0.239012 | ||||||||
\(611\) | −3.57285 | + | 6.18836i | −0.144542 | + | 0.250354i | ||||
\(612\) | −1.24804 | − | 2.16166i | −0.0504489 | − | 0.0873800i | ||||
\(613\) | −25.6063 | + | 14.7838i | −1.03423 | + | 0.597112i | −0.918193 | − | 0.396133i | \(-0.870352\pi\) |
−0.116036 | + | 0.993245i | \(0.537019\pi\) | |||||||
\(614\) | 8.57151 | + | 4.94877i | 0.345918 | + | 0.199716i | ||||
\(615\) | −7.40829 | −0.298731 | ||||||||
\(616\) | 1.35582 | − | 3.62318i | 0.0546274 | − | 0.145982i | ||||
\(617\) | 21.0301i | 0.846639i | 0.905981 | + | 0.423319i | \(0.139135\pi\) | ||||
−0.905981 | + | 0.423319i | \(0.860865\pi\) | |||||||
\(618\) | −8.27128 | − | 4.77542i | −0.332720 | − | 0.192096i | ||||
\(619\) | −0.785602 | − | 1.36070i | −0.0315760 | − | 0.0546912i | 0.849806 | − | 0.527096i | \(-0.176719\pi\) |
−0.881382 | + | 0.472405i | \(0.843386\pi\) | |||||||
\(620\) | 3.71884 | − | 2.14707i | 0.149352 | − | 0.0862285i | ||||
\(621\) | 1.02035 | + | 4.68603i | 0.0409454 | + | 0.188044i | ||||
\(622\) | − | 26.0408i | − | 1.04414i | ||||||
\(623\) | 0.797787 | + | 4.77567i | 0.0319627 | + | 0.191333i | ||||
\(624\) | −3.75315 | −0.150246 | ||||||||
\(625\) | −9.49780 | + | 16.4507i | −0.379912 | + | 0.658027i | ||||
\(626\) | 6.92894 | + | 12.0013i | 0.276936 | + | 0.479667i | ||||
\(627\) | 2.55420 | + | 4.42401i | 0.102005 | + | 0.176678i | ||||
\(628\) | −2.89797 | + | 5.01943i | −0.115642 | + | 0.200297i | ||||
\(629\) | 23.0667i | 0.919729i | ||||||||
\(630\) | −1.31005 | + | 1.07930i | −0.0521936 | + | 0.0430003i | ||||
\(631\) | 37.7541i | 1.50297i | 0.659752 | + | 0.751484i | \(0.270661\pi\) | ||||
−0.659752 | + | 0.751484i | \(0.729339\pi\) | |||||||
\(632\) | 12.2606 | + | 7.07864i | 0.487699 | + | 0.281573i | ||||
\(633\) | −6.49700 | + | 3.75105i | −0.258233 | + | 0.149091i | ||||
\(634\) | −5.09880 | − | 8.83138i | −0.202499 | − | 0.350739i | ||||
\(635\) | −6.44474 | + | 11.1626i | −0.255752 | + | 0.442975i | ||||
\(636\) | 13.8287 | 0.548343 | ||||||||
\(637\) | −25.7865 | − | 5.02751i | −1.02170 | − | 0.199197i | ||||
\(638\) | − | 4.56617i | − | 0.180776i | ||||||
\(639\) | −1.71822 | + | 2.97605i | −0.0679719 | + | 0.117731i | ||||
\(640\) | 0.320775 | + | 0.555599i | 0.0126798 | + | 0.0219620i | ||||
\(641\) | −20.0875 | + | 11.5975i | −0.793408 | + | 0.458074i | −0.841161 | − | 0.540785i | \(-0.818127\pi\) |
0.0477531 | + | 0.998859i | \(0.484794\pi\) | |||||||
\(642\) | 1.75285 | − | 3.03603i | 0.0691796 | − | 0.119823i | ||||
\(643\) | 40.1024 | 1.58148 | 0.790742 | − | 0.612150i | \(-0.209695\pi\) | ||||
0.790742 | + | 0.612150i | \(0.209695\pi\) | |||||||
\(644\) | 12.5578 | + | 1.81680i | 0.494848 | + | 0.0715918i | ||||
\(645\) | 3.61219 | 0.142230 | ||||||||
\(646\) | 4.36027 | − | 7.55222i | 0.171553 | − | 0.297138i | ||||
\(647\) | 19.8504 | − | 11.4606i | 0.780400 | − | 0.450564i | −0.0561717 | − | 0.998421i | \(-0.517889\pi\) |
0.836572 | + | 0.547857i | \(0.184556\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −8.83815 | + | 15.3081i | −0.346928 | + | 0.600896i | ||||
\(650\) | − | 17.2210i | − | 0.675463i | ||||||
\(651\) | −2.91790 | − | 17.4670i | −0.114362 | − | 0.684585i | ||||
\(652\) | 1.13194 | 0.0443303 | ||||||||
\(653\) | −9.19997 | + | 15.9348i | −0.360023 | + | 0.623577i | −0.987964 | − | 0.154683i | \(-0.950564\pi\) |
0.627942 | + | 0.778261i | \(0.283898\pi\) | |||||||
\(654\) | −7.85601 | − | 13.6070i | −0.307194 | − | 0.532076i | ||||
\(655\) | −1.47217 | + | 0.849955i | −0.0575223 | + | 0.0332105i | ||||
\(656\) | 10.0004 | + | 5.77374i | 0.390450 | + | 0.225427i | ||||
\(657\) | − | 8.33128i | − | 0.325034i | ||||||
\(658\) | 1.76543 | − | 4.71781i | 0.0688238 | − | 0.183919i | ||||
\(659\) | 31.2706i | 1.21813i | 0.793120 | + | 0.609065i | \(0.208455\pi\) | ||||
−0.793120 | + | 0.609065i | \(0.791545\pi\) | |||||||
\(660\) | −0.469029 | + | 0.812382i | −0.0182569 | + | 0.0316219i | ||||
\(661\) | −10.2933 | − | 17.8285i | −0.400362 | − | 0.693447i | 0.593408 | − | 0.804902i | \(-0.297782\pi\) |
−0.993769 | + | 0.111455i | \(0.964449\pi\) | |||||||
\(662\) | −4.96632 | − | 8.60191i | −0.193021 | − | 0.334323i | ||||
\(663\) | −4.68407 | + | 8.11305i | −0.181914 | + | 0.315085i | ||||
\(664\) | 10.5288 | 0.408598 | ||||||||
\(665\) | −5.55403 | − | 2.07835i | −0.215376 | − | 0.0805951i | ||||
\(666\) | − | 9.24119i | − | 0.358089i | ||||||
\(667\) | 14.6338 | − | 3.18643i | 0.566625 | − | 0.123379i | ||||
\(668\) | −1.29187 | + | 0.745861i | −0.0499839 | + | 0.0288582i | ||||
\(669\) | −7.72176 | − | 13.3745i | −0.298541 | − | 0.517087i | ||||
\(670\) | 4.12487 | + | 2.38149i | 0.159358 | + | 0.0920051i | ||||
\(671\) | 13.4540i | 0.519388i | ||||||||
\(672\) | 2.60959 | − | 0.435938i | 0.100667 | − | 0.0168167i | ||||
\(673\) | 47.3232 | 1.82418 | 0.912088 | − | 0.409993i | \(-0.134469\pi\) | ||||
0.912088 | + | 0.409993i | \(0.134469\pi\) | |||||||
\(674\) | 22.3251 | + | 12.8894i | 0.859930 | + | 0.496481i | ||||
\(675\) | −3.97368 | + | 2.29421i | −0.152947 | + | 0.0883040i | ||||
\(676\) | 0.543069 | + | 0.940624i | 0.0208873 | + | 0.0361778i | ||||
\(677\) | 0.689148 | − | 1.19364i | 0.0264861 | − | 0.0458753i | −0.852479 | − | 0.522762i | \(-0.824902\pi\) |
0.878965 | + | 0.476887i | \(0.158235\pi\) | |||||||
\(678\) | 6.33088 | 0.243136 | ||||||||
\(679\) | −23.6044 | + | 19.4468i | −0.905853 | + | 0.746298i | ||||
\(680\) | 1.60136 | 0.0614093 | ||||||||
\(681\) | 10.1715 | + | 5.87255i | 0.389775 | + | 0.225036i | ||||
\(682\) | −4.89344 | − | 8.47568i | −0.187379 | − | 0.324551i | ||||
\(683\) | −11.0026 | − | 19.0571i | −0.421004 | − | 0.729201i | 0.575034 | − | 0.818130i | \(-0.304989\pi\) |
−0.996038 | + | 0.0889287i | \(0.971656\pi\) | |||||||
\(684\) | −1.74685 | + | 3.02564i | −0.0667926 | + | 0.115688i | ||||
\(685\) | 14.6954i | 0.561483i | ||||||||
\(686\) | 18.5135 | + | 0.500486i | 0.706849 | + | 0.0191086i | ||||
\(687\) | 2.40050i | 0.0915846i | ||||||||
\(688\) | −4.87607 | − | 2.81520i | −0.185899 | − | 0.107329i | ||||
\(689\) | −25.9506 | − | 44.9477i | −0.988638 | − | 1.71237i | ||||
\(690\) | −2.93086 | − | 0.936255i | −0.111576 | − | 0.0356426i | ||||
\(691\) | −8.91888 | − | 5.14932i | −0.339290 | − | 0.195889i | 0.320668 | − | 0.947192i | \(-0.396093\pi\) |
−0.659958 | + | 0.751302i | \(0.729426\pi\) | |||||||
\(692\) | 19.7892i | 0.752274i | ||||||||
\(693\) | 2.45985 | + | 2.98576i | 0.0934421 | + | 0.113420i | ||||
\(694\) | 4.45082 | 0.168951 | ||||||||
\(695\) | −3.99772 | − | 2.30808i | −0.151642 | − | 0.0875506i | ||||
\(696\) | 2.70448 | − | 1.56143i | 0.102513 | − | 0.0591860i | ||||
\(697\) | 24.9617 | − | 14.4117i | 0.945493 | − | 0.545881i | ||||
\(698\) | −19.8574 | − | 11.4646i | −0.751612 | − | 0.433943i | ||||
\(699\) | 23.0258i | 0.870917i | ||||||||
\(700\) | 2.00026 | + | 11.9739i | 0.0756029 | + | 0.452570i | ||||
\(701\) | 43.7655i | 1.65300i | 0.562936 | + | 0.826500i | \(0.309672\pi\) | ||||
−0.562936 | + | 0.826500i | \(0.690328\pi\) | |||||||
\(702\) | 1.87658 | − | 3.25032i | 0.0708268 | − | 0.122676i | ||||
\(703\) | 27.9605 | − | 16.1430i | 1.05455 | − | 0.608845i | ||||
\(704\) | 1.26628 | − | 0.731086i | 0.0477247 | − | 0.0275539i | ||||
\(705\) | −0.610731 | + | 1.05782i | −0.0230015 | + | 0.0398397i | ||||
\(706\) | 2.53382i | 0.0953615i | ||||||||
\(707\) | −15.3464 | + | 41.0104i | −0.577160 | + | 1.54236i | ||||
\(708\) | −12.0891 | −0.454335 | ||||||||
\(709\) | −44.5820 | − | 25.7394i | −1.67431 | − | 0.966664i | −0.965179 | − | 0.261589i | \(-0.915753\pi\) |
−0.709132 | − | 0.705075i | \(-0.750913\pi\) | |||||||
\(710\) | −1.10233 | − | 1.90929i | −0.0413696 | − | 0.0716543i | ||||
\(711\) | −12.2606 | + | 7.07864i | −0.459807 | + | 0.265470i | ||||
\(712\) | −0.915023 | + | 1.58487i | −0.0342920 | + | 0.0593954i | ||||
\(713\) | 23.7484 | − | 21.5973i | 0.889385 | − | 0.808826i | ||||
\(714\) | 2.31451 | − | 6.18512i | 0.0866184 | − | 0.231472i | ||||
\(715\) | 3.52067 | 0.131666 | ||||||||
\(716\) | 11.2078 | − | 19.4125i | 0.418857 | − | 0.725481i | ||||
\(717\) | 21.5493 | − | 12.4415i | 0.804772 | − | 0.464635i | ||||
\(718\) | −9.78344 | + | 5.64847i | −0.365115 | + | 0.210799i | ||||
\(719\) | 15.8322 | + | 9.14071i | 0.590440 | + | 0.340891i | 0.765272 | − | 0.643708i | \(-0.222605\pi\) |
−0.174831 | + | 0.984598i | \(0.555938\pi\) | |||||||
\(720\) | −0.641551 | −0.0239092 | ||||||||
\(721\) | −4.16358 | − | 24.9238i | −0.155060 | − | 0.928211i | ||||
\(722\) | 6.79401 | 0.252847 | ||||||||
\(723\) | −6.80434 | − | 3.92849i | −0.253056 | − | 0.146102i | ||||
\(724\) | 9.85001 | + | 17.0607i | 0.366073 | + | 0.634057i | ||||
\(725\) | 7.16450 | + | 12.4093i | 0.266083 | + | 0.460869i | ||||
\(726\) | −7.67476 | − | 4.43103i | −0.284837 | − | 0.164451i | ||||
\(727\) | 38.4180 | 1.42484 | 0.712422 | − | 0.701751i | \(-0.247598\pi\) | ||||
0.712422 | + | 0.701751i | \(0.247598\pi\) | |||||||
\(728\) | −6.31403 | − | 7.66394i | −0.234014 | − | 0.284045i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 4.62886 | + | 2.67247i | 0.171322 | + | 0.0989126i | ||||
\(731\) | −12.1710 | + | 7.02695i | −0.450162 | + | 0.259901i | ||||
\(732\) | −7.96865 | + | 4.60070i | −0.294530 | + | 0.170047i | ||||
\(733\) | 2.37885 | − | 4.12028i | 0.0878647 | − | 0.152186i | −0.818744 | − | 0.574159i | \(-0.805329\pi\) |
0.906608 | + | 0.421973i | \(0.138662\pi\) | |||||||
\(734\) | −18.6113 | −0.686955 | ||||||||
\(735\) | −4.40786 | − | 0.859385i | −0.162586 | − | 0.0316989i | ||||
\(736\) | 3.22667 | + | 3.54804i | 0.118937 | + | 0.130783i | ||||
\(737\) | 5.42771 | − | 9.40108i | 0.199932 | − | 0.346293i | ||||
\(738\) | −10.0004 | + | 5.77374i | −0.368120 | + | 0.212534i | ||||
\(739\) | −12.4961 | − | 21.6439i | −0.459676 | − | 0.796182i | 0.539268 | − | 0.842134i | \(-0.318701\pi\) |
−0.998944 | + | 0.0459523i | \(0.985368\pi\) | |||||||
\(740\) | 5.13440 | + | 2.96434i | 0.188744 | + | 0.108971i | ||||
\(741\) | 13.1124 | 0.481696 | ||||||||
\(742\) | 23.2644 | + | 28.2382i | 0.854063 | + | 1.03666i | ||||
\(743\) | 8.94675i | 0.328224i | 0.986442 | + | 0.164112i | \(0.0524759\pi\) | ||||
−0.986442 | + | 0.164112i | \(0.947524\pi\) | |||||||
\(744\) | 3.34669 | − | 5.79664i | 0.122696 | − | 0.212515i | ||||
\(745\) | 3.03795 | − | 1.75396i | 0.111302 | − | 0.0642602i | ||||
\(746\) | 12.2660 | − | 7.08177i | 0.449090 | − | 0.259282i | ||||
\(747\) | −5.26441 | + | 9.11823i | −0.192615 | + | 0.333619i | ||||
\(748\) | − | 3.64969i | − | 0.133446i | ||||||
\(749\) | 9.14846 | − | 1.52827i | 0.334277 | − | 0.0558418i | ||||
\(750\) | − | 6.15145i | − | 0.224619i | ||||||
\(751\) | 1.84512 | + | 1.06528i | 0.0673294 | + | 0.0388727i | 0.533287 | − | 0.845935i | \(-0.320957\pi\) |
−0.465957 | + | 0.884807i | \(0.654290\pi\) | |||||||
\(752\) | 1.64885 | − | 0.951961i | 0.0601272 | − | 0.0347145i | ||||
\(753\) | −17.4196 | + | 10.0572i | −0.634807 | + | 0.366506i | ||||
\(754\) | −10.1503 | − | 5.86030i | −0.369653 | − | 0.213419i | ||||
\(755\) | −11.1980 | −0.407536 | ||||||||
\(756\) | −0.927261 | + | 2.47794i | −0.0337242 | + | 0.0901218i | ||||
\(757\) | 22.6608i | 0.823622i | 0.911269 | + | 0.411811i | \(0.135104\pi\) | ||||
−0.911269 | + | 0.411811i | \(0.864896\pi\) | |||||||
\(758\) | −25.9029 | − | 14.9550i | −0.940834 | − | 0.543191i | ||||
\(759\) | −2.13384 | + | 6.67979i | −0.0774534 | + | 0.242461i | ||||
\(760\) | −1.12070 | − | 1.94110i | −0.0406519 | − | 0.0704111i | ||||
\(761\) | 25.7830 | + | 14.8858i | 0.934634 | + | 0.539611i | 0.888274 | − | 0.459314i | \(-0.151905\pi\) |
0.0463598 | + | 0.998925i | \(0.485238\pi\) | |||||||
\(762\) | 20.0911i | 0.727825i | ||||||||
\(763\) | 14.5692 | − | 38.9335i | 0.527439 | − | 1.40949i | ||||
\(764\) | 21.0371i | 0.761097i | ||||||||
\(765\) | −0.800679 | + | 1.38682i | −0.0289486 | + | 0.0501405i | ||||
\(766\) | 15.3684 | + | 26.6188i | 0.555282 | + | 0.961776i | ||||
\(767\) | 22.6860 | + | 39.2934i | 0.819145 | + | 1.41880i | ||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | −12.3151 | −0.444093 | −0.222047 | − | 0.975036i | \(-0.571274\pi\) | ||||
−0.222047 | + | 0.975036i | \(0.571274\pi\) | |||||||
\(770\) | −2.44795 | + | 0.408935i | −0.0882179 | + | 0.0147370i | ||||
\(771\) | −18.1192 | −0.652546 | ||||||||
\(772\) | 5.41719 | − | 9.38285i | 0.194969 | − | 0.337696i | ||||
\(773\) | 1.77489 | + | 3.07420i | 0.0638383 | + | 0.110571i | 0.896178 | − | 0.443695i | \(-0.146332\pi\) |
−0.832340 | + | 0.554266i | \(0.812999\pi\) | |||||||
\(774\) | 4.87607 | − | 2.81520i | 0.175267 | − | 0.101190i | ||||
\(775\) | 26.5974 | + | 15.3560i | 0.955406 | + | 0.551604i | ||||
\(776\) | −11.5594 | −0.414960 | ||||||||
\(777\) | 18.8705 | − | 15.5467i | 0.676976 | − | 0.557735i | ||||
\(778\) | − | 22.8458i | − | 0.819061i | ||||||
\(779\) | −34.9385 | − | 20.1717i | −1.25180 | − | 0.722728i | ||||
\(780\) | 1.20392 | + | 2.08525i | 0.0431072 | + | 0.0746638i | ||||
\(781\) | −4.35150 | + | 2.51234i | −0.155709 | + | 0.0898985i | ||||
\(782\) | 11.6967 | − | 2.54688i | 0.418272 | − | 0.0910763i | ||||
\(783\) | 3.12287i | 0.111602i | ||||||||
\(784\) | 5.28037 | + | 4.59540i | 0.188585 | + | 0.164121i | ||||
\(785\) | 3.71839 | 0.132715 | ||||||||
\(786\) | −1.32484 | + | 2.29470i | −0.0472557 | + | 0.0818492i | ||||
\(787\) | 23.6118 | + | 40.8968i | 0.841668 | + | 1.45781i | 0.888483 | + | 0.458909i | \(0.151759\pi\) |
−0.0468152 | + | 0.998904i | \(0.514907\pi\) | |||||||
\(788\) | 5.91572 | + | 10.2463i | 0.210739 | + | 0.365010i | ||||
\(789\) | 1.41683 | − | 2.45403i | 0.0504406 | − | 0.0873657i | ||||
\(790\) | − | 9.08262i | − | 0.323145i | ||||||
\(791\) | 10.6506 | + | 12.9277i | 0.378692 | + | 0.459655i | ||||
\(792\) | 1.46217i | 0.0519560i | ||||||||
\(793\) | 29.9076 | + | 17.2671i | 1.06205 | + | 0.613174i | ||||
\(794\) | −2.75666 | + | 1.59156i | −0.0978302 | + | 0.0564823i | ||||
\(795\) | −4.43590 | − | 7.68321i | −0.157325 | − | 0.272495i | ||||
\(796\) | 7.17383 | − | 12.4254i | 0.254270 | − | 0.440408i | ||||
\(797\) | −34.7174 | −1.22975 | −0.614877 | − | 0.788623i | \(-0.710794\pi\) | ||||
−0.614877 | + | 0.788623i | \(0.710794\pi\) | |||||||
\(798\) | −9.11714 | + | 1.52304i | −0.322743 | + | 0.0539150i | ||||
\(799\) | − | 4.75233i | − | 0.168125i | ||||||
\(800\) | −2.29421 | + | 3.97368i | −0.0811124 | + | 0.140491i | ||||
\(801\) | −0.915023 | − | 1.58487i | −0.0323308 | − | 0.0559985i | ||||
\(802\) | −7.09790 | + | 4.09797i | −0.250636 | + | 0.144705i | ||||
\(803\) | 6.09089 | − | 10.5497i | 0.214943 | − | 0.372292i | ||||
\(804\) | 7.42418 | 0.261831 | ||||||||
\(805\) | −3.01883 | − | 7.55991i | −0.106400 | − | 0.266452i | ||||
\(806\) | −25.1213 | −0.884859 | ||||||||
\(807\) | 5.23236 | − | 9.06271i | 0.184188 | − | 0.319023i | ||||
\(808\) | −14.3329 | + | 8.27511i | −0.504230 | + | 0.291117i | ||||
\(809\) | 3.74043 | + | 6.47861i | 0.131506 | + | 0.227776i | 0.924257 | − | 0.381770i | \(-0.124685\pi\) |
−0.792751 | + | 0.609546i | \(0.791352\pi\) | |||||||
\(810\) | 0.320775 | − | 0.555599i | 0.0112709 | − | 0.0195218i | ||||
\(811\) | 33.4013i | 1.17288i | 0.809994 | + | 0.586438i | \(0.199470\pi\) | ||||
−0.809994 | + | 0.586438i | \(0.800530\pi\) | |||||||
\(812\) | 7.73828 | + | 2.89571i | 0.271560 | + | 0.101620i | ||||
\(813\) | −0.550462 | −0.0193056 | ||||||||
\(814\) | 6.75610 | − | 11.7019i | 0.236801 | − | 0.410152i | ||||
\(815\) | −0.363099 | − | 0.628906i | −0.0127188 | − | 0.0220296i | ||||
\(816\) | 2.16166 | − | 1.24804i | 0.0756733 | − | 0.0436900i | ||||
\(817\) | 17.0356 | + | 9.83549i | 0.595999 | + | 0.344100i | ||||
\(818\) | 17.0543i | 0.596288i | ||||||||
\(819\) | 9.79418 | − | 1.63614i | 0.342236 | − | 0.0571714i | ||||
\(820\) | − | 7.40829i | − | 0.258709i | ||||||
\(821\) | −9.50836 | + | 16.4690i | −0.331844 | + | 0.574771i | −0.982873 | − | 0.184282i | \(-0.941004\pi\) |
0.651029 | + | 0.759053i | \(0.274337\pi\) | |||||||
\(822\) | 11.4530 | + | 19.8373i | 0.399471 | + | 0.691904i | ||||
\(823\) | −2.20184 | − | 3.81370i | −0.0767514 | − | 0.132937i | 0.825095 | − | 0.564994i | \(-0.191121\pi\) |
−0.901847 | + | 0.432056i | \(0.857788\pi\) | |||||||
\(824\) | 4.77542 | − | 8.27128i | 0.166360 | − | 0.288144i | ||||
\(825\) | −6.70905 | −0.233579 | ||||||||
\(826\) | −20.3378 | − | 24.6859i | −0.707641 | − | 0.858932i | ||||
\(827\) | − | 29.6423i | − | 1.03076i | −0.856961 | − | 0.515381i | \(-0.827650\pi\) | ||
0.856961 | − | 0.515381i | \(-0.172350\pi\) | |||||||
\(828\) | −4.68603 | + | 1.02035i | −0.162851 | + | 0.0354598i | ||||
\(829\) | −40.6106 | + | 23.4466i | −1.41047 | + | 0.814333i | −0.995432 | − | 0.0954730i | \(-0.969564\pi\) |
−0.415034 | + | 0.909806i | \(0.636230\pi\) | |||||||
\(830\) | −3.37739 | − | 5.84981i | −0.117231 | − | 0.203050i | ||||
\(831\) | 3.89976 | + | 2.25153i | 0.135281 | + | 0.0781047i | ||||
\(832\) | − | 3.75315i | − | 0.130117i | ||||||
\(833\) | 16.5238 | − | 5.67916i | 0.572516 | − | 0.196771i | ||||
\(834\) | −7.19533 | −0.249154 | ||||||||
\(835\) | 0.828799 | + | 0.478507i | 0.0286818 | + | 0.0165594i | ||||
\(836\) | −4.42401 | + | 2.55420i | −0.153007 | + | 0.0883389i | ||||
\(837\) | 3.34669 | + | 5.79664i | 0.115679 | + | 0.200361i | ||||
\(838\) | −13.2460 | + | 22.9427i | −0.457576 | + | 0.792544i | ||||
\(839\) | −44.9952 | −1.55341 | −0.776703 | − | 0.629867i | \(-0.783110\pi\) | ||||
−0.776703 | + | 0.629867i | \(0.783110\pi\) | |||||||
\(840\) | −1.07930 | − | 1.31005i | −0.0372394 | − | 0.0452009i | ||||
\(841\) | −19.2477 | −0.663714 | ||||||||
\(842\) | −23.5679 | − | 13.6070i | −0.812205 | − | 0.468927i | ||||
\(843\) | −5.98507 | − | 10.3665i | −0.206137 | − | 0.357040i | ||||
\(844\) | −3.75105 | − | 6.49700i | −0.129116 | − | 0.223636i | ||||
\(845\) | 0.348407 | − | 0.603458i | 0.0119856 | − | 0.0207596i | ||||
\(846\) | 1.90392i | 0.0654582i | ||||||||
\(847\) | −3.86331 | − | 23.1263i | −0.132745 | − | 0.794630i | ||||
\(848\) | 13.8287i | 0.474879i | ||||||||
\(849\) | 18.5431 | + | 10.7059i | 0.636398 | + | 0.367425i | ||||
\(850\) | 5.72651 | + | 9.91860i | 0.196418 | + | 0.340205i | ||||
\(851\) | 42.2174 | + | 13.4862i | 1.44719 | + | 0.462302i | ||||
\(852\) | −2.97605 | − | 1.71822i | −0.101958 | − | 0.0588654i | ||||
\(853\) | 48.3358i | 1.65499i | 0.561476 | + | 0.827493i | \(0.310234\pi\) | ||||
−0.561476 | + | 0.827493i | \(0.689766\pi\) | |||||||
\(854\) | −22.8005 | − | 8.53211i | −0.780218 | − | 0.291963i | ||||
\(855\) | 2.24139 | 0.0766539 | ||||||||
\(856\) | 3.03603 | + | 1.75285i | 0.103769 | + | 0.0599113i | ||||
\(857\) | −25.5120 | + | 14.7294i | −0.871474 | + | 0.503145i | −0.867838 | − | 0.496848i | \(-0.834491\pi\) |
−0.00363592 | + | 0.999993i | \(0.501157\pi\) | |||||||
\(858\) | 4.75253 | − | 2.74388i | 0.162249 | − | 0.0936744i | ||||
\(859\) | −8.29866 | − | 4.79123i | −0.283147 | − | 0.163475i | 0.351700 | − | 0.936113i | \(-0.385604\pi\) |
−0.634847 | + | 0.772638i | \(0.718937\pi\) | |||||||
\(860\) | 3.61219i | 0.123175i | ||||||||
\(861\) | −28.6139 | − | 10.7075i | −0.975161 | − | 0.364911i | ||||
\(862\) | − | 9.08858i | − | 0.309558i | ||||||
\(863\) | 1.00927 | − | 1.74811i | 0.0343560 | − | 0.0595063i | −0.848336 | − | 0.529458i | \(-0.822395\pi\) |
0.882692 | + | 0.469952i | \(0.155729\pi\) | |||||||
\(864\) | −0.866025 | + | 0.500000i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 10.9949 | − | 6.34790i | 0.373837 | − | 0.215835i | ||||
\(866\) | 19.1470 | − | 33.1636i | 0.650642 | − | 1.12695i | ||||
\(867\) | 10.7696i | 0.365755i | ||||||||
\(868\) | 17.4670 | − | 2.91790i | 0.592868 | − | 0.0990400i | ||||
\(869\) | −20.7004 | −0.702213 | ||||||||
\(870\) | −1.73506 | − | 1.00174i | −0.0588241 | − | 0.0339621i | ||||
\(871\) | −13.9320 | − | 24.1310i | −0.472069 | − | 0.817647i | ||||
\(872\) | 13.6070 | − | 7.85601i | 0.460792 | − | 0.266038i | ||||
\(873\) | 5.77972 | − | 10.0108i | 0.195614 | − | 0.338813i | ||||
\(874\) | −11.2730 | − | 12.3958i | −0.381316 | − | 0.419295i | ||||
\(875\) | 12.5613 | − | 10.3488i | 0.424649 | − | 0.349852i | ||||
\(876\) | 8.33128 | 0.281488 | ||||||||
\(877\) | −5.11265 | + | 8.85537i | −0.172642 | + | 0.299024i | −0.939343 | − | 0.342980i | \(-0.888564\pi\) |
0.766701 | + | 0.642005i | \(0.221897\pi\) | |||||||
\(878\) | −8.56977 | + | 4.94776i | −0.289216 | + | 0.166979i | ||||
\(879\) | 4.36114 | − | 2.51791i | 0.147098 | − | 0.0849268i | ||||
\(880\) | −0.812382 | − | 0.469029i | −0.0273854 | − | 0.0158110i | ||||
\(881\) | 11.0718 | 0.373019 | 0.186509 | − | 0.982453i | \(-0.440282\pi\) | ||||
0.186509 | + | 0.982453i | \(0.440282\pi\) | |||||||
\(882\) | −6.61992 | + | 2.27524i | −0.222904 | + | 0.0766113i | ||||
\(883\) | 9.94740 | 0.334757 | 0.167378 | − | 0.985893i | \(-0.446470\pi\) | ||||
0.167378 | + | 0.985893i | \(0.446470\pi\) | |||||||
\(884\) | −8.11305 | − | 4.68407i | −0.272871 | − | 0.157542i | ||||
\(885\) | 3.87787 | + | 6.71667i | 0.130353 | + | 0.225778i | ||||
\(886\) | 0.732011 | + | 1.26788i | 0.0245924 | + | 0.0425953i | ||||
\(887\) | −11.8399 | − | 6.83578i | −0.397546 | − | 0.229523i | 0.287879 | − | 0.957667i | \(-0.407050\pi\) |
−0.685424 | + | 0.728144i | \(0.740383\pi\) | |||||||
\(888\) | 9.24119 | 0.310114 | ||||||||
\(889\) | −41.0262 | + | 33.7999i | −1.37597 | + | 1.13361i | ||||
\(890\) | 1.17407 | 0.0393548 | ||||||||
\(891\) | −1.26628 | − | 0.731086i | −0.0424219 | − | 0.0244923i | ||||
\(892\) | 13.3745 | − | 7.72176i | 0.447811 | − | 0.258544i | ||||
\(893\) | −5.76058 | + | 3.32587i | −0.192771 | + | 0.111296i | ||||
\(894\) | 2.73394 | − | 4.73532i | 0.0914367 | − | 0.158373i | ||||
\(895\) | −14.3808 | −0.480697 | ||||||||
\(896\) | 0.435938 | + | 2.60959i | 0.0145637 | + | 0.0871803i | ||||
\(897\) | 12.1102 | + | 13.3163i | 0.404347 | + | 0.444620i | ||||
\(898\) | −7.36550 | + | 12.7574i | −0.245790 | + | 0.425720i | ||||
\(899\) | 18.1021 | − | 10.4513i | 0.603740 | − | 0.348569i | ||||
\(900\) | −2.29421 | − | 3.97368i | −0.0764735 | − | 0.132456i | ||||
\(901\) | 29.8930 | + | 17.2587i | 0.995879 | + | 0.574971i | ||||
\(902\) | −16.8844 | −0.562189 | ||||||||
\(903\) | 13.9518 | + | 5.22086i | 0.464287 | + | 0.173739i | ||||
\(904\) | 6.33088i | 0.210562i | ||||||||
\(905\) | 6.31928 | − | 10.9453i | 0.210060 | − | 0.363835i | ||||
\(906\) | −15.1161 | + | 8.72726i | −0.502198 | + | 0.289944i | ||||
\(907\) | 6.76394 | − | 3.90516i | 0.224593 | − | 0.129669i | −0.383482 | − | 0.923548i | \(-0.625275\pi\) |
0.608075 | + | 0.793879i | \(0.291942\pi\) | |||||||
\(908\) | −5.87255 | + | 10.1715i | −0.194887 | + | 0.337555i | ||||
\(909\) | − | 16.5502i | − | 0.548936i | ||||||
\(910\) | −2.23269 | + | 5.96647i | −0.0740131 | + | 0.197787i | ||||
\(911\) | − | 17.1377i | − | 0.567798i | −0.958854 | − | 0.283899i | \(-0.908372\pi\) | ||
0.958854 | − | 0.283899i | \(-0.0916280\pi\) | |||||||
\(912\) | −3.02564 | − | 1.74685i | −0.100189 | − | 0.0578441i | ||||
\(913\) | −13.3324 | + | 7.69748i | −0.441239 | + | 0.254749i | ||||
\(914\) | −13.3608 | + | 7.71386i | −0.441936 | + | 0.255152i | ||||
\(915\) | 5.11230 | + | 2.95159i | 0.169007 | + | 0.0975764i | ||||
\(916\) | −2.40050 | −0.0793146 | ||||||||
\(917\) | −6.91460 | + | 1.15510i | −0.228340 | + | 0.0381448i | ||||
\(918\) | 2.49607i | 0.0823827i | ||||||||
\(919\) | 10.1476 | + | 5.85873i | 0.334739 | + | 0.193262i | 0.657943 | − | 0.753068i | \(-0.271427\pi\) |
−0.323204 | + | 0.946329i | \(0.604760\pi\) | |||||||
\(920\) | 0.936255 | − | 2.93086i | 0.0308674 | − | 0.0966276i | ||||
\(921\) | −4.94877 | − | 8.57151i | −0.163067 | − | 0.282441i | ||||
\(922\) | −3.88829 | − | 2.24491i | −0.128054 | − | 0.0739321i | ||||
\(923\) | 12.8975i | 0.424526i | ||||||||
\(924\) | −2.98576 | + | 2.45985i | −0.0982243 | + | 0.0809233i | ||||
\(925\) | 42.4024i | 1.39418i | ||||||||
\(926\) | −15.1705 | + | 26.2760i | −0.498532 | + | 0.863483i | ||||
\(927\) | 4.77542 | + | 8.27128i | 0.156845 | + | 0.271664i | ||||
\(928\) | 1.56143 | + | 2.70448i | 0.0512566 | + | 0.0887790i | ||||
\(929\) | 23.3818 | + | 13.4995i | 0.767130 | + | 0.442903i | 0.831850 | − | 0.555001i | \(-0.187282\pi\) |
−0.0647195 | + | 0.997903i | \(0.520615\pi\) | |||||||
\(930\) | −4.29414 | −0.140811 | ||||||||
\(931\) | −18.4481 | − | 16.0550i | −0.604611 | − | 0.526180i | ||||
\(932\) | −23.0258 | −0.754236 | ||||||||
\(933\) | −13.0204 | + | 22.5520i | −0.426268 | + | 0.738318i | ||||
\(934\) | −8.55783 | − | 14.8226i | −0.280021 | − | 0.485010i | ||||
\(935\) | −2.02776 | + | 1.17073i | −0.0663150 | + | 0.0382870i | ||||
\(936\) | 3.25032 | + | 1.87658i | 0.106240 | + | 0.0613378i | ||||
\(937\) | −30.4938 | −0.996190 | −0.498095 | − | 0.867122i | \(-0.665967\pi\) | ||||
−0.498095 | + | 0.867122i | \(0.665967\pi\) | |||||||
\(938\) | 12.4899 | + | 15.1602i | 0.407810 | + | 0.494998i | ||||
\(939\) | − | 13.8579i | − | 0.452235i | ||||||
\(940\) | −1.05782 | − | 0.610731i | −0.0345022 | − | 0.0199199i | ||||
\(941\) | 3.43393 | + | 5.94774i | 0.111943 | + | 0.193891i | 0.916554 | − | 0.399912i | \(-0.130959\pi\) |
−0.804611 | + | 0.593803i | \(0.797626\pi\) | |||||||
\(942\) | 5.01943 | − | 2.89797i | 0.163542 | − | 0.0944209i | ||||
\(943\) | −11.7825 | − | 54.1118i | −0.383692 | − | 1.76212i | ||||
\(944\) | − | 12.0891i | − | 0.393465i | ||||||
\(945\) | 1.67418 | − | 0.279676i | 0.0544612 | − | 0.00909787i | ||||
\(946\) | 8.23262 | 0.267666 | ||||||||
\(947\) | −9.11070 | + | 15.7802i | −0.296058 | + | 0.512787i | −0.975230 | − | 0.221191i | \(-0.929005\pi\) |
0.679173 | + | 0.733979i | \(0.262339\pi\) | |||||||
\(948\) | −7.07864 | − | 12.2606i | −0.229904 | − | 0.398205i | ||||
\(949\) | −15.6343 | − | 27.0794i | −0.507510 | − | 0.879034i | ||||
\(950\) | 8.01529 | − | 13.8829i | 0.260050 | − | 0.450420i | ||||
\(951\) | 10.1976i | 0.330680i | ||||||||
\(952\) | 6.18512 | + | 2.31451i | 0.200461 | + | 0.0750138i | ||||
\(953\) | − | 35.2554i | − | 1.14204i | −0.820938 | − | 0.571018i | \(-0.806549\pi\) | ||
0.820938 | − | 0.571018i | \(-0.193451\pi\) | |||||||
\(954\) | −11.9760 | − | 6.91435i | −0.387737 | − | 0.223860i | ||||
\(955\) | 11.6882 | − | 6.74820i | 0.378222 | − | 0.218367i | ||||
\(956\) | 12.4415 | + | 21.5493i | 0.402386 | + | 0.696953i | ||||
\(957\) | −2.28309 | + | 3.95442i | −0.0738017 | + | 0.127828i | ||||
\(958\) | −19.2153 | −0.620819 | ||||||||
\(959\) | −21.2399 | + | 56.7599i | −0.685873 | + | 1.83287i | ||||
\(960\) | − | 0.641551i | − | 0.0207060i | ||||||
\(961\) | 6.90067 | − | 11.9523i | 0.222602 | − | 0.385559i | ||||
\(962\) | −17.3418 | − | 30.0368i | −0.559121 | − | 0.968427i | ||||
\(963\) | −3.03603 | + | 1.75285i | −0.0978348 | + | 0.0564849i | ||||
\(964\) | 3.92849 | − | 6.80434i | 0.126528 | − | 0.219153i | ||||
\(965\) | −6.95081 | −0.223754 | ||||||||
\(966\) | −9.96701 | − | 7.85231i | −0.320683 | − | 0.252644i | ||||
\(967\) | −20.1479 | −0.647913 | −0.323956 | − | 0.946072i | \(-0.605013\pi\) | ||||
−0.323956 | + | 0.946072i | \(0.605013\pi\) | |||||||
\(968\) | 4.43103 | − | 7.67476i | 0.142419 | − | 0.246676i | ||||
\(969\) | −7.55222 | + | 4.36027i | −0.242612 | + | 0.140072i | ||||
\(970\) | 3.70798 | + | 6.42241i | 0.119056 | + | 0.206211i | ||||
\(971\) | −20.4746 | + | 35.4630i | −0.657061 | + | 1.13806i | 0.324312 | + | 0.945950i | \(0.394867\pi\) |
−0.981373 | + | 0.192113i | \(0.938466\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | −12.1049 | − | 14.6929i | −0.388065 | − | 0.471032i | ||||
\(974\) | −1.48980 | −0.0477364 | ||||||||
\(975\) | −8.61050 | + | 14.9138i | −0.275757 | + | 0.477625i | ||||
\(976\) | −4.60070 | − | 7.96865i | −0.147265 | − | 0.255070i | ||||
\(977\) | −44.2956 | + | 25.5741i | −1.41714 | + | 0.818186i | −0.996047 | − | 0.0888306i | \(-0.971687\pi\) |
−0.421094 | + | 0.907017i | \(0.638354\pi\) | |||||||
\(978\) | −0.980291 | − | 0.565971i | −0.0313462 | − | 0.0180978i | ||||
\(979\) | − | 2.67584i | − | 0.0855203i | ||||||
\(980\) | 0.859385 | − | 4.40786i | 0.0274520 | − | 0.140804i | ||||
\(981\) | 15.7120i | 0.501646i | ||||||||
\(982\) | −5.14673 | + | 8.91440i | −0.164239 | + | 0.284470i | ||||
\(983\) | −8.45720 | − | 14.6483i | −0.269743 | − | 0.467208i | 0.699052 | − | 0.715070i | \(-0.253605\pi\) |
−0.968795 | + | 0.247862i | \(0.920272\pi\) | |||||||
\(984\) | −5.77374 | − | 10.0004i | −0.184060 | − | 0.318801i | ||||
\(985\) | 3.79524 | − | 6.57354i | 0.120926 | − | 0.209450i | ||||
\(986\) | 7.79491 | 0.248240 | ||||||||
\(987\) | −3.88781 | + | 3.20302i | −0.123750 | + | 0.101953i | ||||
\(988\) | 13.1124i | 0.417161i | ||||||||
\(989\) | 5.74501 | + | 26.3842i | 0.182681 | + | 0.838970i | ||||
\(990\) | 0.812382 | − | 0.469029i | 0.0258192 | − | 0.0149067i | ||||
\(991\) | −2.62618 | − | 4.54868i | −0.0834233 | − | 0.144493i | 0.821295 | − | 0.570504i | \(-0.193252\pi\) |
−0.904718 | + | 0.426010i | \(0.859919\pi\) | |||||||
\(992\) | 5.79664 | + | 3.34669i | 0.184043 | + | 0.106258i | ||||
\(993\) | 9.93263i | 0.315203i | ||||||||
\(994\) | −1.49808 | − | 8.96771i | −0.0475161 | − | 0.284439i | ||||
\(995\) | −9.20475 | −0.291810 | ||||||||
\(996\) | −9.11823 | − | 5.26441i | −0.288922 | − | 0.166809i | ||||
\(997\) | −6.38803 | + | 3.68813i | −0.202311 | + | 0.116804i | −0.597733 | − | 0.801695i | \(-0.703932\pi\) |
0.395422 | + | 0.918500i | \(0.370598\pi\) | |||||||
\(998\) | −6.36607 | − | 11.0264i | −0.201514 | − | 0.349033i | ||||
\(999\) | −4.62059 | + | 8.00310i | −0.146189 | + | 0.253207i |
(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 | 966.2.k.b.229.3 | ✓ | 32 | |
7.3 | odd | 6 | inner | 966.2.k.b.367.6 | yes | 32 | |
23.22 | odd | 2 | inner | 966.2.k.b.229.6 | yes | 32 | |
161.45 | even | 6 | inner | 966.2.k.b.367.3 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.k.b.229.3 | ✓ | 32 | 1.1 | even | 1 | trivial | |
966.2.k.b.229.6 | yes | 32 | 23.22 | odd | 2 | inner | |
966.2.k.b.367.3 | yes | 32 | 161.45 | even | 6 | inner | |
966.2.k.b.367.6 | yes | 32 | 7.3 | odd | 6 | inner |