Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(71,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.n (of order \(5\), 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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 10 x^{10} - 9 x^{9} + 27 x^{8} - 26 x^{7} + 47 x^{6} + 46 x^{5} + 137 x^{4} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 421.2 | ||
Root | \(0.248272 + 0.764103i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.421 |
Dual form | 770.2.n.g.631.2 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | + | 0.587785i | −0.572061 | + | 0.415627i | ||||
\(3\) | −0.248272 | − | 0.764103i | −0.143340 | − | 0.441155i | 0.853454 | − | 0.521168i | \(-0.174504\pi\) |
−0.996794 | + | 0.0800135i | \(0.974504\pi\) | |||||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | −0.809017 | − | 0.587785i | −0.361803 | − | 0.262866i | ||||
\(6\) | 0.649985 | + | 0.472241i | 0.265355 | + | 0.192792i | ||||
\(7\) | −0.309017 | + | 0.951057i | −0.116797 | + | 0.359466i | ||||
\(8\) | 0.309017 | + | 0.951057i | 0.109254 | + | 0.336249i | ||||
\(9\) | 1.90484 | − | 1.38395i | 0.634946 | − | 0.461315i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −3.22166 | − | 0.787978i | −0.971367 | − | 0.237584i | ||||
\(12\) | −0.803425 | −0.231929 | ||||||||
\(13\) | 2.13834 | − | 1.55360i | 0.593070 | − | 0.430890i | −0.250343 | − | 0.968157i | \(-0.580543\pi\) |
0.843412 | + | 0.537267i | \(0.180543\pi\) | |||||||
\(14\) | −0.309017 | − | 0.951057i | −0.0825883 | − | 0.254181i | ||||
\(15\) | −0.248272 | + | 0.764103i | −0.0641036 | + | 0.197290i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −1.29806 | − | 0.943099i | −0.314827 | − | 0.228735i | 0.419138 | − | 0.907923i | \(-0.362332\pi\) |
−0.733965 | + | 0.679187i | \(0.762332\pi\) | |||||||
\(18\) | −0.727583 | + | 2.23927i | −0.171493 | + | 0.527801i | ||||
\(19\) | 0.590037 | + | 1.81595i | 0.135364 | + | 0.416607i | 0.995646 | − | 0.0932105i | \(-0.0297130\pi\) |
−0.860283 | + | 0.509817i | \(0.829713\pi\) | |||||||
\(20\) | −0.809017 | + | 0.587785i | −0.180902 | + | 0.131433i | ||||
\(21\) | 0.803425 | 0.175322 | ||||||||
\(22\) | 3.06954 | − | 1.25616i | 0.654428 | − | 0.267813i | ||||
\(23\) | −4.22916 | −0.881840 | −0.440920 | − | 0.897546i | \(-0.645348\pi\) | ||||
−0.440920 | + | 0.897546i | \(0.645348\pi\) | |||||||
\(24\) | 0.649985 | − | 0.472241i | 0.132678 | − | 0.0963959i | ||||
\(25\) | 0.309017 | + | 0.951057i | 0.0618034 | + | 0.190211i | ||||
\(26\) | −0.816775 | + | 2.51377i | −0.160183 | + | 0.492992i | ||||
\(27\) | −3.48035 | − | 2.52862i | −0.669793 | − | 0.486633i | ||||
\(28\) | 0.809017 | + | 0.587785i | 0.152890 | + | 0.111081i | ||||
\(29\) | 2.77477 | − | 8.53988i | 0.515263 | − | 1.58582i | −0.267541 | − | 0.963546i | \(-0.586211\pi\) |
0.782804 | − | 0.622269i | \(-0.213789\pi\) | |||||||
\(30\) | −0.248272 | − | 0.764103i | −0.0453281 | − | 0.139505i | ||||
\(31\) | −2.00312 | + | 1.45536i | −0.359772 | + | 0.261389i | −0.752957 | − | 0.658070i | \(-0.771373\pi\) |
0.393185 | + | 0.919459i | \(0.371373\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.197752 | + | 2.65731i | 0.0344242 | + | 0.462579i | ||||
\(34\) | 1.60450 | 0.275169 | ||||||||
\(35\) | 0.809017 | − | 0.587785i | 0.136749 | − | 0.0993538i | ||||
\(36\) | −0.727583 | − | 2.23927i | −0.121264 | − | 0.373212i | ||||
\(37\) | −1.73320 | + | 5.33426i | −0.284937 | + | 0.876946i | 0.701480 | + | 0.712689i | \(0.252523\pi\) |
−0.986418 | + | 0.164257i | \(0.947477\pi\) | |||||||
\(38\) | −1.54474 | − | 1.12232i | −0.250589 | − | 0.182064i | ||||
\(39\) | −1.71800 | − | 1.24820i | −0.275100 | − | 0.199872i | ||||
\(40\) | 0.309017 | − | 0.951057i | 0.0488599 | − | 0.150375i | ||||
\(41\) | −2.99616 | − | 9.22125i | −0.467922 | − | 1.44012i | −0.855270 | − | 0.518183i | \(-0.826609\pi\) |
0.387348 | − | 0.921934i | \(-0.373391\pi\) | |||||||
\(42\) | −0.649985 | + | 0.472241i | −0.100295 | + | 0.0728684i | ||||
\(43\) | −4.00169 | −0.610252 | −0.305126 | − | 0.952312i | \(-0.598699\pi\) | ||||
−0.305126 | + | 0.952312i | \(0.598699\pi\) | |||||||
\(44\) | −1.74496 | + | 2.82048i | −0.263062 | + | 0.425204i | ||||
\(45\) | −2.35451 | −0.350989 | ||||||||
\(46\) | 3.42146 | − | 2.48584i | 0.504467 | − | 0.366516i | ||||
\(47\) | −2.02252 | − | 6.22469i | −0.295015 | − | 0.907964i | −0.983216 | − | 0.182444i | \(-0.941599\pi\) |
0.688201 | − | 0.725520i | \(-0.258401\pi\) | |||||||
\(48\) | −0.248272 | + | 0.764103i | −0.0358350 | + | 0.110289i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | −0.809017 | − | 0.587785i | −0.114412 | − | 0.0831254i | ||||
\(51\) | −0.398351 | + | 1.22600i | −0.0557804 | + | 0.171674i | ||||
\(52\) | −0.816775 | − | 2.51377i | −0.113266 | − | 0.348598i | ||||
\(53\) | −8.12885 | + | 5.90596i | −1.11658 | + | 0.811246i | −0.983688 | − | 0.179884i | \(-0.942428\pi\) |
−0.132896 | + | 0.991130i | \(0.542428\pi\) | |||||||
\(54\) | 4.30195 | 0.585421 | ||||||||
\(55\) | 2.14322 | + | 2.53113i | 0.288991 | + | 0.341298i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 1.24108 | − | 0.901698i | 0.164385 | − | 0.119433i | ||||
\(58\) | 2.77477 | + | 8.53988i | 0.364346 | + | 1.12134i | ||||
\(59\) | 1.28756 | − | 3.96270i | 0.167626 | − | 0.515900i | −0.831594 | − | 0.555384i | \(-0.812571\pi\) |
0.999220 | + | 0.0394838i | \(0.0125714\pi\) | |||||||
\(60\) | 0.649985 | + | 0.472241i | 0.0839126 | + | 0.0609661i | ||||
\(61\) | −10.7299 | − | 7.79571i | −1.37382 | − | 0.998139i | −0.997428 | − | 0.0716784i | \(-0.977164\pi\) |
−0.376392 | − | 0.926460i | \(-0.622836\pi\) | |||||||
\(62\) | 0.765125 | − | 2.35481i | 0.0971710 | − | 0.299062i | ||||
\(63\) | 0.727583 | + | 2.23927i | 0.0916668 | + | 0.282122i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | −2.64314 | −0.327841 | ||||||||
\(66\) | −1.72191 | − | 2.03357i | −0.211953 | − | 0.250316i | ||||
\(67\) | −10.5029 | −1.28314 | −0.641570 | − | 0.767065i | \(-0.721716\pi\) | ||||
−0.641570 | + | 0.767065i | \(0.721716\pi\) | |||||||
\(68\) | −1.29806 | + | 0.943099i | −0.157413 | + | 0.114368i | ||||
\(69\) | 1.04998 | + | 3.23151i | 0.126403 | + | 0.389028i | ||||
\(70\) | −0.309017 | + | 0.951057i | −0.0369346 | + | 0.113673i | ||||
\(71\) | −3.70925 | − | 2.69493i | −0.440207 | − | 0.319829i | 0.345510 | − | 0.938415i | \(-0.387706\pi\) |
−0.785717 | + | 0.618586i | \(0.787706\pi\) | |||||||
\(72\) | 1.90484 | + | 1.38395i | 0.224487 | + | 0.163099i | ||||
\(73\) | 1.14118 | − | 3.51218i | 0.133565 | − | 0.411070i | −0.861799 | − | 0.507249i | \(-0.830662\pi\) |
0.995364 | + | 0.0961797i | \(0.0306623\pi\) | |||||||
\(74\) | −1.73320 | − | 5.33426i | −0.201481 | − | 0.620095i | ||||
\(75\) | 0.649985 | − | 0.472241i | 0.0750538 | − | 0.0545297i | ||||
\(76\) | 1.90940 | 0.219023 | ||||||||
\(77\) | 1.74496 | − | 2.82048i | 0.198857 | − | 0.321424i | ||||
\(78\) | 2.12356 | 0.240446 | ||||||||
\(79\) | 11.2839 | − | 8.19826i | 1.26954 | − | 0.922376i | 0.270357 | − | 0.962760i | \(-0.412858\pi\) |
0.999184 | + | 0.0403841i | \(0.0128582\pi\) | |||||||
\(80\) | 0.309017 | + | 0.951057i | 0.0345492 | + | 0.106331i | ||||
\(81\) | 1.11470 | − | 3.43068i | 0.123855 | − | 0.381187i | ||||
\(82\) | 7.84406 | + | 5.69904i | 0.866232 | + | 0.629354i | ||||
\(83\) | 10.9705 | + | 7.97052i | 1.20417 | + | 0.874878i | 0.994688 | − | 0.102936i | \(-0.0328236\pi\) |
0.209478 | + | 0.977813i | \(0.432824\pi\) | |||||||
\(84\) | 0.248272 | − | 0.764103i | 0.0270887 | − | 0.0833704i | ||||
\(85\) | 0.495817 | + | 1.52597i | 0.0537789 | + | 0.165514i | ||||
\(86\) | 3.23744 | − | 2.35214i | 0.349102 | − | 0.253637i | ||||
\(87\) | −7.21424 | −0.773448 | ||||||||
\(88\) | −0.246136 | − | 3.30748i | −0.0262382 | − | 0.352578i | ||||
\(89\) | −3.41009 | −0.361469 | −0.180735 | − | 0.983532i | \(-0.557847\pi\) | ||||
−0.180735 | + | 0.983532i | \(0.557847\pi\) | |||||||
\(90\) | 1.90484 | − | 1.38395i | 0.200787 | − | 0.145881i | ||||
\(91\) | 0.816775 | + | 2.51377i | 0.0856212 | + | 0.263515i | ||||
\(92\) | −1.30688 | + | 4.02217i | −0.136252 | + | 0.419340i | ||||
\(93\) | 1.60936 | + | 1.16927i | 0.166883 | + | 0.121248i | ||||
\(94\) | 5.29503 | + | 3.84707i | 0.546141 | + | 0.396795i | ||||
\(95\) | 0.590037 | − | 1.81595i | 0.0605365 | − | 0.186312i | ||||
\(96\) | −0.248272 | − | 0.764103i | −0.0253392 | − | 0.0779859i | ||||
\(97\) | 14.1345 | − | 10.2693i | 1.43515 | − | 1.04269i | 0.446116 | − | 0.894975i | \(-0.352807\pi\) |
0.989029 | − | 0.147719i | \(-0.0471930\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −7.22725 | + | 2.95763i | −0.726366 | + | 0.297253i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 8.61553 | − | 6.25955i | 0.857278 | − | 0.622849i | −0.0698652 | − | 0.997556i | \(-0.522257\pi\) |
0.927143 | + | 0.374708i | \(0.122257\pi\) | |||||||
\(102\) | −0.398351 | − | 1.22600i | −0.0394427 | − | 0.121392i | ||||
\(103\) | −2.12192 | + | 6.53058i | −0.209079 | + | 0.643478i | 0.790443 | + | 0.612536i | \(0.209851\pi\) |
−0.999521 | + | 0.0309416i | \(0.990149\pi\) | |||||||
\(104\) | 2.13834 | + | 1.55360i | 0.209682 | + | 0.152343i | ||||
\(105\) | −0.649985 | − | 0.472241i | −0.0634320 | − | 0.0460860i | ||||
\(106\) | 3.10495 | − | 9.55604i | 0.301579 | − | 0.928165i | ||||
\(107\) | −0.890804 | − | 2.74161i | −0.0861172 | − | 0.265042i | 0.898720 | − | 0.438523i | \(-0.144498\pi\) |
−0.984837 | + | 0.173482i | \(0.944498\pi\) | |||||||
\(108\) | −3.48035 | + | 2.52862i | −0.334897 | + | 0.243317i | ||||
\(109\) | −18.4938 | −1.77139 | −0.885693 | − | 0.464271i | \(-0.846316\pi\) | ||||
−0.885693 | + | 0.464271i | \(0.846316\pi\) | |||||||
\(110\) | −3.22166 | − | 0.787978i | −0.307173 | − | 0.0751307i | ||||
\(111\) | 4.50623 | 0.427712 | ||||||||
\(112\) | 0.809017 | − | 0.587785i | 0.0764449 | − | 0.0555405i | ||||
\(113\) | 3.69479 | + | 11.3714i | 0.347577 | + | 1.06973i | 0.960190 | + | 0.279348i | \(0.0901184\pi\) |
−0.612613 | + | 0.790383i | \(0.709882\pi\) | |||||||
\(114\) | −0.474051 | + | 1.45898i | −0.0443989 | + | 0.136646i | ||||
\(115\) | 3.42146 | + | 2.48584i | 0.319053 | + | 0.231805i | ||||
\(116\) | −7.26445 | − | 5.27793i | −0.674487 | − | 0.490044i | ||||
\(117\) | 1.92310 | − | 5.91870i | 0.177791 | − | 0.547184i | ||||
\(118\) | 1.28756 | + | 3.96270i | 0.118530 | + | 0.364796i | ||||
\(119\) | 1.29806 | − | 0.943099i | 0.118993 | − | 0.0864538i | ||||
\(120\) | −0.803425 | −0.0733423 | ||||||||
\(121\) | 9.75818 | + | 5.07719i | 0.887107 | + | 0.461563i | ||||
\(122\) | 13.2629 | 1.20076 | ||||||||
\(123\) | −6.30212 | + | 4.57875i | −0.568243 | + | 0.412852i | ||||
\(124\) | 0.765125 | + | 2.35481i | 0.0687103 | + | 0.211469i | ||||
\(125\) | 0.309017 | − | 0.951057i | 0.0276393 | − | 0.0850651i | ||||
\(126\) | −1.90484 | − | 1.38395i | −0.169696 | − | 0.123292i | ||||
\(127\) | 10.8477 | + | 7.88134i | 0.962581 | + | 0.699356i | 0.953749 | − | 0.300605i | \(-0.0971886\pi\) |
0.00883223 | + | 0.999961i | \(0.497189\pi\) | |||||||
\(128\) | 0.309017 | − | 0.951057i | 0.0273135 | − | 0.0840623i | ||||
\(129\) | 0.993508 | + | 3.05770i | 0.0874735 | + | 0.269216i | ||||
\(130\) | 2.13834 | − | 1.55360i | 0.187545 | − | 0.136260i | ||||
\(131\) | −8.49928 | −0.742585 | −0.371293 | − | 0.928516i | \(-0.621085\pi\) | ||||
−0.371293 | + | 0.928516i | \(0.621085\pi\) | |||||||
\(132\) | 2.58836 | + | 0.633081i | 0.225288 | + | 0.0551026i | ||||
\(133\) | −1.90940 | −0.165566 | ||||||||
\(134\) | 8.49706 | − | 6.17348i | 0.734035 | − | 0.533307i | ||||
\(135\) | 1.32937 | + | 4.09139i | 0.114414 | + | 0.352131i | ||||
\(136\) | 0.495817 | − | 1.52597i | 0.0425159 | − | 0.130851i | ||||
\(137\) | −8.15058 | − | 5.92174i | −0.696351 | − | 0.505929i | 0.182391 | − | 0.983226i | \(-0.441616\pi\) |
−0.878742 | + | 0.477298i | \(0.841616\pi\) | |||||||
\(138\) | −2.74889 | − | 1.99718i | −0.234001 | − | 0.170011i | ||||
\(139\) | 4.27063 | − | 13.1436i | 0.362230 | − | 1.11483i | −0.589467 | − | 0.807792i | \(-0.700662\pi\) |
0.951697 | − | 0.307037i | \(-0.0993376\pi\) | |||||||
\(140\) | −0.309017 | − | 0.951057i | −0.0261167 | − | 0.0803789i | ||||
\(141\) | −4.25416 | + | 3.09083i | −0.358265 | + | 0.260295i | ||||
\(142\) | 4.58489 | 0.384755 | ||||||||
\(143\) | −8.11322 | + | 3.32019i | −0.678461 | + | 0.277649i | ||||
\(144\) | −2.35451 | −0.196209 | ||||||||
\(145\) | −7.26445 | + | 5.27793i | −0.603280 | + | 0.438309i | ||||
\(146\) | 1.14118 | + | 3.51218i | 0.0944444 | + | 0.290670i | ||||
\(147\) | −0.248272 | + | 0.764103i | −0.0204771 | + | 0.0630221i | ||||
\(148\) | 4.53759 | + | 3.29675i | 0.372987 | + | 0.270991i | ||||
\(149\) | 14.8566 | + | 10.7940i | 1.21710 | + | 0.884278i | 0.995856 | − | 0.0909401i | \(-0.0289872\pi\) |
0.221247 | + | 0.975218i | \(0.428987\pi\) | |||||||
\(150\) | −0.248272 | + | 0.764103i | −0.0202713 | + | 0.0623887i | ||||
\(151\) | 6.35704 | + | 19.5650i | 0.517329 | + | 1.59217i | 0.779005 | + | 0.627018i | \(0.215725\pi\) |
−0.261676 | + | 0.965156i | \(0.584275\pi\) | |||||||
\(152\) | −1.54474 | + | 1.12232i | −0.125295 | + | 0.0910319i | ||||
\(153\) | −3.77780 | −0.305417 | ||||||||
\(154\) | 0.246136 | + | 3.30748i | 0.0198342 | + | 0.266524i | ||||
\(155\) | 2.47600 | 0.198877 | ||||||||
\(156\) | −1.71800 | + | 1.24820i | −0.137550 | + | 0.0999359i | ||||
\(157\) | −1.43658 | − | 4.42133i | −0.114651 | − | 0.352860i | 0.877223 | − | 0.480083i | \(-0.159394\pi\) |
−0.991874 | + | 0.127223i | \(0.959394\pi\) | |||||||
\(158\) | −4.31008 | + | 13.2651i | −0.342891 | + | 1.05531i | ||||
\(159\) | 6.53093 | + | 4.74499i | 0.517936 | + | 0.376303i | ||||
\(160\) | −0.809017 | − | 0.587785i | −0.0639584 | − | 0.0464685i | ||||
\(161\) | 1.30688 | − | 4.02217i | 0.102997 | − | 0.316991i | ||||
\(162\) | 1.11470 | + | 3.43068i | 0.0875788 | + | 0.269540i | ||||
\(163\) | −4.04023 | + | 2.93540i | −0.316455 | + | 0.229918i | −0.734661 | − | 0.678434i | \(-0.762659\pi\) |
0.418206 | + | 0.908352i | \(0.362659\pi\) | |||||||
\(164\) | −9.69579 | −0.757114 | ||||||||
\(165\) | 1.40194 | − | 2.26605i | 0.109141 | − | 0.176411i | ||||
\(166\) | −13.5603 | −1.05248 | ||||||||
\(167\) | 1.51162 | − | 1.09826i | 0.116973 | − | 0.0849857i | −0.527761 | − | 0.849393i | \(-0.676968\pi\) |
0.644734 | + | 0.764407i | \(0.276968\pi\) | |||||||
\(168\) | 0.248272 | + | 0.764103i | 0.0191546 | + | 0.0589518i | ||||
\(169\) | −1.85837 | + | 5.71949i | −0.142952 | + | 0.439960i | ||||
\(170\) | −1.29806 | − | 0.943099i | −0.0995570 | − | 0.0723324i | ||||
\(171\) | 3.63710 | + | 2.64250i | 0.278136 | + | 0.202077i | ||||
\(172\) | −1.23659 | + | 3.80583i | −0.0942891 | + | 0.290192i | ||||
\(173\) | −3.64020 | − | 11.2034i | −0.276760 | − | 0.851779i | −0.988748 | − | 0.149588i | \(-0.952205\pi\) |
0.711989 | − | 0.702191i | \(-0.247795\pi\) | |||||||
\(174\) | 5.83644 | − | 4.24042i | 0.442460 | − | 0.321466i | ||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 2.14322 | + | 2.53113i | 0.161551 | + | 0.190791i | ||||
\(177\) | −3.34758 | −0.251619 | ||||||||
\(178\) | 2.75882 | − | 2.00440i | 0.206782 | − | 0.150236i | ||||
\(179\) | −3.20466 | − | 9.86294i | −0.239528 | − | 0.737191i | −0.996488 | − | 0.0837303i | \(-0.973317\pi\) |
0.756961 | − | 0.653460i | \(-0.226683\pi\) | |||||||
\(180\) | −0.727583 | + | 2.23927i | −0.0542308 | + | 0.166905i | ||||
\(181\) | 18.3435 | + | 13.3273i | 1.36346 | + | 0.990611i | 0.998216 | + | 0.0596985i | \(0.0190139\pi\) |
0.365242 | + | 0.930912i | \(0.380986\pi\) | |||||||
\(182\) | −2.13834 | − | 1.55360i | −0.158505 | − | 0.115160i | ||||
\(183\) | −3.29280 | + | 10.1342i | −0.243411 | + | 0.749141i | ||||
\(184\) | −1.30688 | − | 4.02217i | −0.0963446 | − | 0.296518i | ||||
\(185\) | 4.53759 | − | 3.29675i | 0.333610 | − | 0.242382i | ||||
\(186\) | −1.98928 | −0.145861 | ||||||||
\(187\) | 3.43878 | + | 4.06119i | 0.251469 | + | 0.296984i | ||||
\(188\) | −6.54502 | −0.477345 | ||||||||
\(189\) | 3.48035 | − | 2.52862i | 0.253158 | − | 0.183930i | ||||
\(190\) | 0.590037 | + | 1.81595i | 0.0428058 | + | 0.131743i | ||||
\(191\) | −2.62245 | + | 8.07107i | −0.189754 | + | 0.584002i | −0.999998 | − | 0.00209040i | \(-0.999335\pi\) |
0.810244 | + | 0.586093i | \(0.199335\pi\) | |||||||
\(192\) | 0.649985 | + | 0.472241i | 0.0469086 | + | 0.0340811i | ||||
\(193\) | 20.3531 | + | 14.7874i | 1.46505 | + | 1.06442i | 0.982011 | + | 0.188822i | \(0.0604668\pi\) |
0.483038 | + | 0.875599i | \(0.339533\pi\) | |||||||
\(194\) | −5.39891 | + | 16.6161i | −0.387619 | + | 1.19297i | ||||
\(195\) | 0.656217 | + | 2.01963i | 0.0469927 | + | 0.144629i | ||||
\(196\) | −0.809017 | + | 0.587785i | −0.0577869 | + | 0.0419847i | ||||
\(197\) | −13.2603 | −0.944757 | −0.472379 | − | 0.881396i | \(-0.656604\pi\) | ||||
−0.472379 | + | 0.881396i | \(0.656604\pi\) | |||||||
\(198\) | 4.10852 | − | 6.64085i | 0.291980 | − | 0.471944i | ||||
\(199\) | 3.59813 | 0.255065 | 0.127532 | − | 0.991834i | \(-0.459294\pi\) | ||||
0.127532 | + | 0.991834i | \(0.459294\pi\) | |||||||
\(200\) | −0.809017 | + | 0.587785i | −0.0572061 | + | 0.0415627i | ||||
\(201\) | 2.60759 | + | 8.02533i | 0.183925 | + | 0.566063i | ||||
\(202\) | −3.29084 | + | 10.1282i | −0.231543 | + | 0.712615i | ||||
\(203\) | 7.26445 | + | 5.27793i | 0.509865 | + | 0.370438i | ||||
\(204\) | 1.04290 | + | 0.757710i | 0.0730174 | + | 0.0530503i | ||||
\(205\) | −2.99616 | + | 9.22125i | −0.209261 | + | 0.644040i | ||||
\(206\) | −2.12192 | − | 6.53058i | −0.147841 | − | 0.455007i | ||||
\(207\) | −8.05585 | + | 5.85292i | −0.559920 | + | 0.406806i | ||||
\(208\) | −2.64314 | −0.183269 | ||||||||
\(209\) | −0.469972 | − | 6.31530i | −0.0325087 | − | 0.436838i | ||||
\(210\) | 0.803425 | 0.0554416 | ||||||||
\(211\) | 8.09486 | − | 5.88126i | 0.557273 | − | 0.404883i | −0.273187 | − | 0.961961i | \(-0.588078\pi\) |
0.830460 | + | 0.557078i | \(0.188078\pi\) | |||||||
\(212\) | 3.10495 | + | 9.55604i | 0.213249 | + | 0.656312i | ||||
\(213\) | −1.13830 | + | 3.50332i | −0.0779950 | + | 0.240044i | ||||
\(214\) | 2.33215 | + | 1.69441i | 0.159423 | + | 0.115827i | ||||
\(215\) | 3.23744 | + | 2.35214i | 0.220791 | + | 0.160414i | ||||
\(216\) | 1.32937 | − | 4.09139i | 0.0904525 | − | 0.278384i | ||||
\(217\) | −0.765125 | − | 2.35481i | −0.0519401 | − | 0.159855i | ||||
\(218\) | 14.9618 | − | 10.8704i | 1.01334 | − | 0.736236i | ||||
\(219\) | −2.96699 | −0.200491 | ||||||||
\(220\) | 3.06954 | − | 1.25616i | 0.206948 | − | 0.0846901i | ||||
\(221\) | −4.24090 | −0.285274 | ||||||||
\(222\) | −3.64561 | + | 2.64869i | −0.244678 | + | 0.177769i | ||||
\(223\) | 7.73769 | + | 23.8142i | 0.518154 | + | 1.59471i | 0.777469 | + | 0.628922i | \(0.216503\pi\) |
−0.259315 | + | 0.965793i | \(0.583497\pi\) | |||||||
\(224\) | −0.309017 | + | 0.951057i | −0.0206471 | + | 0.0635451i | ||||
\(225\) | 1.90484 | + | 1.38395i | 0.126989 | + | 0.0922630i | ||||
\(226\) | −9.67309 | − | 7.02791i | −0.643444 | − | 0.467490i | ||||
\(227\) | −0.0565265 | + | 0.173971i | −0.00375180 | + | 0.0115468i | −0.952915 | − | 0.303238i | \(-0.901932\pi\) |
0.949163 | + | 0.314785i | \(0.101932\pi\) | |||||||
\(228\) | −0.474051 | − | 1.45898i | −0.0313948 | − | 0.0966232i | ||||
\(229\) | 0.108709 | − | 0.0789815i | 0.00718367 | − | 0.00521924i | −0.584188 | − | 0.811619i | \(-0.698587\pi\) |
0.591371 | + | 0.806399i | \(0.298587\pi\) | |||||||
\(230\) | −4.22916 | −0.278862 | ||||||||
\(231\) | −2.58836 | − | 0.633081i | −0.170302 | − | 0.0416537i | ||||
\(232\) | 8.97936 | 0.589524 | ||||||||
\(233\) | 2.37050 | − | 1.72227i | 0.155296 | − | 0.112830i | −0.507423 | − | 0.861697i | \(-0.669402\pi\) |
0.662720 | + | 0.748867i | \(0.269402\pi\) | |||||||
\(234\) | 1.92310 | + | 5.91870i | 0.125717 | + | 0.386918i | ||||
\(235\) | −2.02252 | + | 6.22469i | −0.131935 | + | 0.406054i | ||||
\(236\) | −3.37088 | − | 2.44909i | −0.219425 | − | 0.159422i | ||||
\(237\) | −9.06579 | − | 6.58669i | −0.588887 | − | 0.427851i | ||||
\(238\) | −0.495817 | + | 1.52597i | −0.0321390 | + | 0.0989137i | ||||
\(239\) | 2.55684 | + | 7.86914i | 0.165388 | + | 0.509012i | 0.999065 | − | 0.0432406i | \(-0.0137682\pi\) |
−0.833677 | + | 0.552253i | \(0.813768\pi\) | |||||||
\(240\) | 0.649985 | − | 0.472241i | 0.0419563 | − | 0.0304831i | ||||
\(241\) | 16.5842 | 1.06828 | 0.534142 | − | 0.845395i | \(-0.320635\pi\) | ||||
0.534142 | + | 0.845395i | \(0.320635\pi\) | |||||||
\(242\) | −10.8788 | + | 1.62818i | −0.699318 | + | 0.104663i | ||||
\(243\) | −15.8040 | −1.01383 | ||||||||
\(244\) | −10.7299 | + | 7.79571i | −0.686910 | + | 0.499069i | ||||
\(245\) | 0.309017 | + | 0.951057i | 0.0197424 | + | 0.0607608i | ||||
\(246\) | 2.40719 | − | 7.40858i | 0.153477 | − | 0.472354i | ||||
\(247\) | 4.08295 | + | 2.96644i | 0.259792 | + | 0.188750i | ||||
\(248\) | −2.00312 | − | 1.45536i | −0.127199 | − | 0.0924151i | ||||
\(249\) | 3.36663 | − | 10.3614i | 0.213352 | − | 0.656629i | ||||
\(250\) | 0.309017 | + | 0.951057i | 0.0195440 | + | 0.0601501i | ||||
\(251\) | 10.9610 | − | 7.96366i | 0.691855 | − | 0.502662i | −0.185415 | − | 0.982660i | \(-0.559363\pi\) |
0.877269 | + | 0.479998i | \(0.159363\pi\) | |||||||
\(252\) | 2.35451 | 0.148320 | ||||||||
\(253\) | 13.6249 | + | 3.33248i | 0.856590 | + | 0.209511i | ||||
\(254\) | −13.4085 | −0.841327 | ||||||||
\(255\) | 1.04290 | − | 0.757710i | 0.0653088 | − | 0.0474496i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | 5.69288 | − | 17.5209i | 0.355112 | − | 1.09292i | −0.600832 | − | 0.799375i | \(-0.705164\pi\) |
0.955944 | − | 0.293548i | \(-0.0948360\pi\) | |||||||
\(258\) | −2.60104 | − | 1.88976i | −0.161934 | − | 0.117652i | ||||
\(259\) | −4.53759 | − | 3.29675i | −0.281952 | − | 0.204850i | ||||
\(260\) | −0.816775 | + | 2.51377i | −0.0506542 | + | 0.155898i | ||||
\(261\) | −6.53323 | − | 20.1072i | −0.404397 | − | 1.24460i | ||||
\(262\) | 6.87606 | − | 4.99575i | 0.424804 | − | 0.308638i | ||||
\(263\) | −19.1658 | −1.18181 | −0.590907 | − | 0.806740i | \(-0.701230\pi\) | ||||
−0.590907 | + | 0.806740i | \(0.701230\pi\) | |||||||
\(264\) | −2.46614 | + | 1.00923i | −0.151781 | + | 0.0621137i | ||||
\(265\) | 10.0478 | 0.617232 | ||||||||
\(266\) | 1.54474 | − | 1.12232i | 0.0947139 | − | 0.0688137i | ||||
\(267\) | 0.846630 | + | 2.60566i | 0.0518129 | + | 0.159464i | ||||
\(268\) | −3.24559 | + | 9.98890i | −0.198256 | + | 0.610169i | ||||
\(269\) | −7.35126 | − | 5.34100i | −0.448214 | − | 0.325647i | 0.340676 | − | 0.940181i | \(-0.389344\pi\) |
−0.788890 | + | 0.614534i | \(0.789344\pi\) | |||||||
\(270\) | −3.48035 | − | 2.52862i | −0.211807 | − | 0.153887i | ||||
\(271\) | 5.92506 | − | 18.2355i | 0.359922 | − | 1.10773i | −0.593178 | − | 0.805071i | \(-0.702127\pi\) |
0.953100 | − | 0.302655i | \(-0.0978729\pi\) | |||||||
\(272\) | 0.495817 | + | 1.52597i | 0.0300633 | + | 0.0925253i | ||||
\(273\) | 1.71800 | − | 1.24820i | 0.103978 | − | 0.0755445i | ||||
\(274\) | 10.0747 | 0.608633 | ||||||||
\(275\) | −0.246136 | − | 3.30748i | −0.0148426 | − | 0.199448i | ||||
\(276\) | 3.39781 | 0.204524 | ||||||||
\(277\) | 16.7217 | − | 12.1490i | 1.00471 | − | 0.729964i | 0.0416161 | − | 0.999134i | \(-0.486749\pi\) |
0.963093 | + | 0.269170i | \(0.0867493\pi\) | |||||||
\(278\) | 4.27063 | + | 13.1436i | 0.256135 | + | 0.788303i | ||||
\(279\) | −1.80149 | + | 5.54443i | −0.107853 | + | 0.331936i | ||||
\(280\) | 0.809017 | + | 0.587785i | 0.0483480 | + | 0.0351269i | ||||
\(281\) | 1.10959 | + | 0.806163i | 0.0661925 | + | 0.0480916i | 0.620389 | − | 0.784294i | \(-0.286975\pi\) |
−0.554197 | + | 0.832386i | \(0.686975\pi\) | |||||||
\(282\) | 1.62495 | − | 5.00107i | 0.0967641 | − | 0.297809i | ||||
\(283\) | −1.98856 | − | 6.12017i | −0.118208 | − | 0.363806i | 0.874395 | − | 0.485215i | \(-0.161259\pi\) |
−0.992603 | + | 0.121409i | \(0.961259\pi\) | |||||||
\(284\) | −3.70925 | + | 2.69493i | −0.220104 | + | 0.159915i | ||||
\(285\) | −1.53406 | −0.0908699 | ||||||||
\(286\) | 4.61217 | − | 7.45492i | 0.272723 | − | 0.440819i | ||||
\(287\) | 9.69579 | 0.572324 | ||||||||
\(288\) | 1.90484 | − | 1.38395i | 0.112244 | − | 0.0815497i | ||||
\(289\) | −4.45775 | − | 13.7196i | −0.262221 | − | 0.807033i | ||||
\(290\) | 2.77477 | − | 8.53988i | 0.162940 | − | 0.501479i | ||||
\(291\) | −11.3560 | − | 8.25065i | −0.665703 | − | 0.483662i | ||||
\(292\) | −2.98764 | − | 2.17065i | −0.174838 | − | 0.127028i | ||||
\(293\) | 1.42065 | − | 4.37230i | 0.0829951 | − | 0.255433i | −0.900945 | − | 0.433934i | \(-0.857125\pi\) |
0.983940 | + | 0.178502i | \(0.0571250\pi\) | |||||||
\(294\) | −0.248272 | − | 0.764103i | −0.0144795 | − | 0.0445634i | ||||
\(295\) | −3.37088 | + | 2.44909i | −0.196260 | + | 0.142591i | ||||
\(296\) | −5.60877 | −0.326003 | ||||||||
\(297\) | 9.22000 | + | 10.8888i | 0.534999 | + | 0.631832i | ||||
\(298\) | −18.3638 | −1.06379 | ||||||||
\(299\) | −9.04339 | + | 6.57041i | −0.522993 | + | 0.379976i | ||||
\(300\) | −0.248272 | − | 0.764103i | −0.0143340 | − | 0.0441155i | ||||
\(301\) | 1.23659 | − | 3.80583i | 0.0712759 | − | 0.219365i | ||||
\(302\) | −16.6429 | − | 12.0918i | −0.957694 | − | 0.695805i | ||||
\(303\) | −6.92194 | − | 5.02908i | −0.397655 | − | 0.288913i | ||||
\(304\) | 0.590037 | − | 1.81595i | 0.0338409 | − | 0.104152i | ||||
\(305\) | 4.09845 | + | 12.6137i | 0.234676 | + | 0.722260i | ||||
\(306\) | 3.05630 | − | 2.22053i | 0.174717 | − | 0.126940i | ||||
\(307\) | −24.8042 | −1.41565 | −0.707825 | − | 0.706388i | \(-0.750323\pi\) | ||||
−0.707825 | + | 0.706388i | \(0.750323\pi\) | |||||||
\(308\) | −2.14322 | − | 2.53113i | −0.122121 | − | 0.144225i | ||||
\(309\) | 5.51685 | 0.313843 | ||||||||
\(310\) | −2.00312 | + | 1.45536i | −0.113770 | + | 0.0826586i | ||||
\(311\) | 7.97333 | + | 24.5394i | 0.452126 | + | 1.39150i | 0.874476 | + | 0.485069i | \(0.161205\pi\) |
−0.422350 | + | 0.906433i | \(0.638795\pi\) | |||||||
\(312\) | 0.656217 | − | 2.01963i | 0.0371510 | − | 0.114339i | ||||
\(313\) | −13.3553 | − | 9.70322i | −0.754888 | − | 0.548458i | 0.142450 | − | 0.989802i | \(-0.454502\pi\) |
−0.897338 | + | 0.441344i | \(0.854502\pi\) | |||||||
\(314\) | 3.76101 | + | 2.73253i | 0.212246 | + | 0.154206i | ||||
\(315\) | 0.727583 | − | 2.23927i | 0.0409947 | − | 0.126169i | ||||
\(316\) | −4.31008 | − | 13.2651i | −0.242461 | − | 0.746218i | ||||
\(317\) | −1.88569 | + | 1.37004i | −0.105911 | + | 0.0769489i | −0.639480 | − | 0.768808i | \(-0.720850\pi\) |
0.533569 | + | 0.845756i | \(0.320850\pi\) | |||||||
\(318\) | −8.07267 | −0.452693 | ||||||||
\(319\) | −15.6686 | + | 25.3261i | −0.877274 | + | 1.41799i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −1.87371 | + | 1.36133i | −0.104580 | + | 0.0759821i | ||||
\(322\) | 1.30688 | + | 4.02217i | 0.0728296 | + | 0.224147i | ||||
\(323\) | 0.946712 | − | 2.91368i | 0.0526765 | − | 0.162122i | ||||
\(324\) | −2.91831 | − | 2.12028i | −0.162128 | − | 0.117793i | ||||
\(325\) | 2.13834 | + | 1.55360i | 0.118614 | + | 0.0861781i | ||||
\(326\) | 1.54323 | − | 4.74958i | 0.0854716 | − | 0.263055i | ||||
\(327\) | 4.59150 | + | 14.1312i | 0.253910 | + | 0.781456i | ||||
\(328\) | 7.84406 | − | 5.69904i | 0.433116 | − | 0.314677i | ||||
\(329\) | 6.54502 | 0.360839 | ||||||||
\(330\) | 0.197752 | + | 2.65731i | 0.0108859 | + | 0.146280i | ||||
\(331\) | 6.54411 | 0.359697 | 0.179848 | − | 0.983694i | \(-0.442439\pi\) | ||||
0.179848 | + | 0.983694i | \(0.442439\pi\) | |||||||
\(332\) | 10.9705 | − | 7.97052i | 0.602083 | − | 0.437439i | ||||
\(333\) | 4.08084 | + | 12.5595i | 0.223629 | + | 0.688259i | ||||
\(334\) | −0.577388 | + | 1.77702i | −0.0315933 | + | 0.0972341i | ||||
\(335\) | 8.49706 | + | 6.17348i | 0.464244 | + | 0.337293i | ||||
\(336\) | −0.649985 | − | 0.472241i | −0.0354596 | − | 0.0257629i | ||||
\(337\) | 5.15321 | − | 15.8600i | 0.280713 | − | 0.863947i | −0.706938 | − | 0.707276i | \(-0.749924\pi\) |
0.987651 | − | 0.156671i | \(-0.0500761\pi\) | |||||||
\(338\) | −1.85837 | − | 5.71949i | −0.101082 | − | 0.311099i | ||||
\(339\) | 7.77160 | − | 5.64640i | 0.422096 | − | 0.306670i | ||||
\(340\) | 1.60450 | 0.0870160 | ||||||||
\(341\) | 7.60017 | − | 3.11024i | 0.411572 | − | 0.168429i | ||||
\(342\) | −4.49570 | −0.243099 | ||||||||
\(343\) | 0.809017 | − | 0.587785i | 0.0436828 | − | 0.0317374i | ||||
\(344\) | −1.23659 | − | 3.80583i | −0.0666725 | − | 0.205197i | ||||
\(345\) | 1.04998 | − | 3.23151i | 0.0565291 | − | 0.173979i | ||||
\(346\) | 9.53018 | + | 6.92408i | 0.512346 | + | 0.372241i | ||||
\(347\) | −23.6893 | − | 17.2113i | −1.27171 | − | 0.923950i | −0.272439 | − | 0.962173i | \(-0.587830\pi\) |
−0.999269 | + | 0.0382231i | \(0.987830\pi\) | |||||||
\(348\) | −2.22932 | + | 6.86115i | −0.119504 | + | 0.367796i | ||||
\(349\) | −5.18642 | − | 15.9622i | −0.277623 | − | 0.854435i | −0.988514 | − | 0.151132i | \(-0.951708\pi\) |
0.710891 | − | 0.703302i | \(-0.248292\pi\) | |||||||
\(350\) | 0.809017 | − | 0.587785i | 0.0432438 | − | 0.0314184i | ||||
\(351\) | −11.3706 | −0.606920 | ||||||||
\(352\) | −3.22166 | − | 0.787978i | −0.171715 | − | 0.0419994i | ||||
\(353\) | 22.9110 | 1.21943 | 0.609715 | − | 0.792621i | \(-0.291284\pi\) | ||||
0.609715 | + | 0.792621i | \(0.291284\pi\) | |||||||
\(354\) | 2.70825 | − | 1.96766i | 0.143942 | − | 0.104580i | ||||
\(355\) | 1.41681 | + | 4.36049i | 0.0751963 | + | 0.231431i | ||||
\(356\) | −1.05378 | + | 3.24319i | −0.0558500 | + | 0.171889i | ||||
\(357\) | −1.04290 | − | 0.757710i | −0.0551960 | − | 0.0401022i | ||||
\(358\) | 8.38992 | + | 6.09563i | 0.443421 | + | 0.322164i | ||||
\(359\) | 2.58498 | − | 7.95576i | 0.136430 | − | 0.419889i | −0.859380 | − | 0.511338i | \(-0.829150\pi\) |
0.995810 | + | 0.0914492i | \(0.0291499\pi\) | |||||||
\(360\) | −0.727583 | − | 2.23927i | −0.0383470 | − | 0.118020i | ||||
\(361\) | 12.4218 | − | 9.02497i | 0.653779 | − | 0.474998i | ||||
\(362\) | −22.6738 | −1.19171 | ||||||||
\(363\) | 1.45681 | − | 8.71678i | 0.0764629 | − | 0.457512i | ||||
\(364\) | 2.64314 | 0.138538 | ||||||||
\(365\) | −2.98764 | + | 2.17065i | −0.156380 | + | 0.113617i | ||||
\(366\) | −3.29280 | − | 10.1342i | −0.172117 | − | 0.529722i | ||||
\(367\) | −0.557226 | + | 1.71496i | −0.0290869 | + | 0.0895204i | −0.964546 | − | 0.263914i | \(-0.914986\pi\) |
0.935459 | + | 0.353435i | \(0.114986\pi\) | |||||||
\(368\) | 3.42146 | + | 2.48584i | 0.178356 | + | 0.129583i | ||||
\(369\) | −18.4689 | − | 13.4184i | −0.961453 | − | 0.698536i | ||||
\(370\) | −1.73320 | + | 5.33426i | −0.0901050 | + | 0.277315i | ||||
\(371\) | −3.10495 | − | 9.55604i | −0.161201 | − | 0.496125i | ||||
\(372\) | 1.60936 | − | 1.16927i | 0.0834415 | − | 0.0606238i | ||||
\(373\) | 9.60451 | 0.497303 | 0.248651 | − | 0.968593i | \(-0.420013\pi\) | ||||
0.248651 | + | 0.968593i | \(0.420013\pi\) | |||||||
\(374\) | −5.16914 | − | 1.26431i | −0.267290 | − | 0.0653758i | ||||
\(375\) | −0.803425 | −0.0414887 | ||||||||
\(376\) | 5.29503 | − | 3.84707i | 0.273071 | − | 0.198397i | ||||
\(377\) | −7.33411 | − | 22.5721i | −0.377726 | − | 1.16252i | ||||
\(378\) | −1.32937 | + | 4.09139i | −0.0683756 | + | 0.210439i | ||||
\(379\) | 4.80593 | + | 3.49171i | 0.246864 | + | 0.179357i | 0.704336 | − | 0.709867i | \(-0.251245\pi\) |
−0.457472 | + | 0.889224i | \(0.651245\pi\) | |||||||
\(380\) | −1.54474 | − | 1.12232i | −0.0792433 | − | 0.0575737i | ||||
\(381\) | 3.32897 | − | 10.2455i | 0.170548 | − | 0.524893i | ||||
\(382\) | −2.62245 | − | 8.07107i | −0.134176 | − | 0.412952i | ||||
\(383\) | 23.8060 | − | 17.2960i | 1.21643 | − | 0.883786i | 0.220629 | − | 0.975358i | \(-0.429189\pi\) |
0.995799 | + | 0.0915714i | \(0.0291890\pi\) | |||||||
\(384\) | −0.803425 | −0.0409996 | ||||||||
\(385\) | −3.06954 | + | 1.25616i | −0.156438 | + | 0.0640197i | ||||
\(386\) | −25.1578 | −1.28050 | ||||||||
\(387\) | −7.62257 | + | 5.53812i | −0.387477 | + | 0.281519i | ||||
\(388\) | −5.39891 | − | 16.6161i | −0.274088 | − | 0.843557i | ||||
\(389\) | −5.82858 | + | 17.9385i | −0.295520 | + | 0.909519i | 0.687526 | + | 0.726160i | \(0.258697\pi\) |
−0.983046 | + | 0.183358i | \(0.941303\pi\) | |||||||
\(390\) | −1.71800 | − | 1.24820i | −0.0869943 | − | 0.0632050i | ||||
\(391\) | 5.48972 | + | 3.98851i | 0.277627 | + | 0.201708i | ||||
\(392\) | 0.309017 | − | 0.951057i | 0.0156077 | − | 0.0480356i | ||||
\(393\) | 2.11013 | + | 6.49432i | 0.106442 | + | 0.327595i | ||||
\(394\) | 10.7278 | − | 7.79421i | 0.540459 | − | 0.392667i | ||||
\(395\) | −13.9477 | −0.701785 | ||||||||
\(396\) | 0.579529 | + | 7.78749i | 0.0291225 | + | 0.391336i | ||||
\(397\) | 25.4542 | 1.27751 | 0.638756 | − | 0.769409i | \(-0.279449\pi\) | ||||
0.638756 | + | 0.769409i | \(0.279449\pi\) | |||||||
\(398\) | −2.91095 | + | 2.11493i | −0.145913 | + | 0.106012i | ||||
\(399\) | 0.474051 | + | 1.45898i | 0.0237322 | + | 0.0730402i | ||||
\(400\) | 0.309017 | − | 0.951057i | 0.0154508 | − | 0.0475528i | ||||
\(401\) | −12.1245 | − | 8.80895i | −0.605467 | − | 0.439898i | 0.242348 | − | 0.970189i | \(-0.422082\pi\) |
−0.847815 | + | 0.530292i | \(0.822082\pi\) | |||||||
\(402\) | −6.82675 | − | 4.95993i | −0.340488 | − | 0.247379i | ||||
\(403\) | −2.02233 | + | 6.22410i | −0.100740 | + | 0.310044i | ||||
\(404\) | −3.29084 | − | 10.1282i | −0.163725 | − | 0.503895i | ||||
\(405\) | −2.91831 | + | 2.12028i | −0.145012 | + | 0.105357i | ||||
\(406\) | −8.97936 | −0.445638 | ||||||||
\(407\) | 9.78707 | − | 15.8194i | 0.485127 | − | 0.784140i | ||||
\(408\) | −1.28909 | −0.0638196 | ||||||||
\(409\) | −3.93000 | + | 2.85531i | −0.194326 | + | 0.141186i | −0.680694 | − | 0.732568i | \(-0.738322\pi\) |
0.486368 | + | 0.873754i | \(0.338322\pi\) | |||||||
\(410\) | −2.99616 | − | 9.22125i | −0.147970 | − | 0.455405i | ||||
\(411\) | −2.50126 | + | 7.69808i | −0.123378 | + | 0.379718i | ||||
\(412\) | 5.55525 | + | 4.03612i | 0.273687 | + | 0.198846i | ||||
\(413\) | 3.37088 | + | 2.44909i | 0.165870 | + | 0.120512i | ||||
\(414\) | 3.07706 | − | 9.47022i | 0.151229 | − | 0.465436i | ||||
\(415\) | −4.19035 | − | 12.8966i | −0.205696 | − | 0.633068i | ||||
\(416\) | 2.13834 | − | 1.55360i | 0.104841 | − | 0.0761714i | ||||
\(417\) | −11.1034 | −0.543734 | ||||||||
\(418\) | 4.09226 | + | 4.83294i | 0.200159 | + | 0.236387i | ||||
\(419\) | −1.77493 | −0.0867109 | −0.0433554 | − | 0.999060i | \(-0.513805\pi\) | ||||
−0.0433554 | + | 0.999060i | \(0.513805\pi\) | |||||||
\(420\) | −0.649985 | + | 0.472241i | −0.0317160 | + | 0.0230430i | ||||
\(421\) | −5.22997 | − | 16.0962i | −0.254893 | − | 0.784480i | −0.993851 | − | 0.110728i | \(-0.964682\pi\) |
0.738958 | − | 0.673752i | \(-0.235318\pi\) | |||||||
\(422\) | −3.09196 | + | 9.51608i | −0.150514 | + | 0.463236i | ||||
\(423\) | −12.4672 | − | 9.05795i | −0.606176 | − | 0.440413i | ||||
\(424\) | −8.12885 | − | 5.90596i | −0.394772 | − | 0.286819i | ||||
\(425\) | 0.495817 | − | 1.52597i | 0.0240506 | − | 0.0740202i | ||||
\(426\) | −1.13830 | − | 3.50332i | −0.0551508 | − | 0.169737i | ||||
\(427\) | 10.7299 | − | 7.79571i | 0.519255 | − | 0.377261i | ||||
\(428\) | −2.88270 | −0.139341 | ||||||||
\(429\) | 4.55125 | + | 5.37502i | 0.219737 | + | 0.259508i | ||||
\(430\) | −4.00169 | −0.192979 | ||||||||
\(431\) | −3.36245 | + | 2.44296i | −0.161963 | + | 0.117673i | −0.665815 | − | 0.746117i | \(-0.731916\pi\) |
0.503851 | + | 0.863790i | \(0.331916\pi\) | |||||||
\(432\) | 1.32937 | + | 4.09139i | 0.0639596 | + | 0.196847i | ||||
\(433\) | 6.87285 | − | 21.1525i | 0.330288 | − | 1.01652i | −0.638709 | − | 0.769449i | \(-0.720531\pi\) |
0.968997 | − | 0.247073i | \(-0.0794689\pi\) | |||||||
\(434\) | 2.00312 | + | 1.45536i | 0.0961531 | + | 0.0698593i | ||||
\(435\) | 5.83644 | + | 4.24042i | 0.279836 | + | 0.203313i | ||||
\(436\) | −5.71490 | + | 17.5887i | −0.273694 | + | 0.842344i | ||||
\(437\) | −2.49536 | − | 7.67992i | −0.119369 | − | 0.367381i | ||||
\(438\) | 2.40034 | − | 1.74395i | 0.114693 | − | 0.0833293i | ||||
\(439\) | −21.6172 | −1.03173 | −0.515866 | − | 0.856669i | \(-0.672530\pi\) | ||||
−0.515866 | + | 0.856669i | \(0.672530\pi\) | |||||||
\(440\) | −1.74496 | + | 2.82048i | −0.0831877 | + | 0.134461i | ||||
\(441\) | −2.35451 | −0.112119 | ||||||||
\(442\) | 3.43096 | − | 2.49274i | 0.163194 | − | 0.118568i | ||||
\(443\) | −4.00059 | − | 12.3126i | −0.190074 | − | 0.584987i | 0.809925 | − | 0.586534i | \(-0.199508\pi\) |
−0.999999 | + | 0.00154626i | \(0.999508\pi\) | |||||||
\(444\) | 1.39250 | − | 4.28567i | 0.0660851 | − | 0.203389i | ||||
\(445\) | 2.75882 | + | 2.00440i | 0.130781 | + | 0.0950178i | ||||
\(446\) | −20.2575 | − | 14.7180i | −0.959222 | − | 0.696916i | ||||
\(447\) | 4.55922 | − | 14.0318i | 0.215644 | − | 0.663684i | ||||
\(448\) | −0.309017 | − | 0.951057i | −0.0145997 | − | 0.0449332i | ||||
\(449\) | −11.2098 | + | 8.14441i | −0.529024 | + | 0.384359i | −0.819993 | − | 0.572374i | \(-0.806023\pi\) |
0.290968 | + | 0.956733i | \(0.406023\pi\) | |||||||
\(450\) | −2.35451 | −0.110993 | ||||||||
\(451\) | 2.38648 | + | 32.0686i | 0.112375 | + | 1.51005i | ||||
\(452\) | 11.9566 | 0.562391 | ||||||||
\(453\) | 13.3714 | − | 9.71486i | 0.628241 | − | 0.456444i | ||||
\(454\) | −0.0565265 | − | 0.173971i | −0.00265292 | − | 0.00816485i | ||||
\(455\) | 0.816775 | − | 2.51377i | 0.0382910 | − | 0.117848i | ||||
\(456\) | 1.24108 | + | 0.901698i | 0.0581189 | + | 0.0422259i | ||||
\(457\) | 8.08043 | + | 5.87077i | 0.377986 | + | 0.274623i | 0.760515 | − | 0.649321i | \(-0.224947\pi\) |
−0.382528 | + | 0.923944i | \(0.624947\pi\) | |||||||
\(458\) | −0.0415230 | + | 0.127795i | −0.00194024 | + | 0.00597145i | ||||
\(459\) | 2.13298 | + | 6.56463i | 0.0995588 | + | 0.306410i | ||||
\(460\) | 3.42146 | − | 2.48584i | 0.159526 | − | 0.115903i | ||||
\(461\) | 27.8198 | 1.29570 | 0.647850 | − | 0.761768i | \(-0.275668\pi\) | ||||
0.647850 | + | 0.761768i | \(0.275668\pi\) | |||||||
\(462\) | 2.46614 | − | 1.00923i | 0.114735 | − | 0.0469535i | ||||
\(463\) | −10.2727 | −0.477413 | −0.238707 | − | 0.971092i | \(-0.576723\pi\) | ||||
−0.238707 | + | 0.971092i | \(0.576723\pi\) | |||||||
\(464\) | −7.26445 | + | 5.27793i | −0.337244 | + | 0.245022i | ||||
\(465\) | −0.614721 | − | 1.89192i | −0.0285070 | − | 0.0877355i | ||||
\(466\) | −0.905450 | + | 2.78669i | −0.0419441 | + | 0.129091i | ||||
\(467\) | −7.31181 | − | 5.31234i | −0.338350 | − | 0.245826i | 0.405615 | − | 0.914044i | \(-0.367057\pi\) |
−0.743965 | + | 0.668218i | \(0.767057\pi\) | |||||||
\(468\) | −5.03475 | − | 3.65796i | −0.232731 | − | 0.169089i | ||||
\(469\) | 3.24559 | − | 9.98890i | 0.149867 | − | 0.461244i | ||||
\(470\) | −2.02252 | − | 6.22469i | −0.0932920 | − | 0.287123i | ||||
\(471\) | −3.02169 | + | 2.19538i | −0.139232 | + | 0.101158i | ||||
\(472\) | 4.16663 | 0.191785 | ||||||||
\(473\) | 12.8921 | + | 3.15324i | 0.592779 | + | 0.144986i | ||||
\(474\) | 11.2059 | 0.514706 | ||||||||
\(475\) | −1.54474 | + | 1.12232i | −0.0708774 | + | 0.0514954i | ||||
\(476\) | −0.495817 | − | 1.52597i | −0.0227257 | − | 0.0699426i | ||||
\(477\) | −7.31062 | + | 22.4998i | −0.334730 | + | 1.03019i | ||||
\(478\) | −6.69389 | − | 4.86340i | −0.306171 | − | 0.222447i | ||||
\(479\) | 31.8995 | + | 23.1764i | 1.45753 | + | 1.05895i | 0.983999 | + | 0.178176i | \(0.0570196\pi\) |
0.473528 | + | 0.880779i | \(0.342980\pi\) | |||||||
\(480\) | −0.248272 | + | 0.764103i | −0.0113320 | + | 0.0348764i | ||||
\(481\) | 4.58110 | + | 14.0992i | 0.208880 | + | 0.642867i | ||||
\(482\) | −13.4169 | + | 9.74797i | −0.611124 | + | 0.444008i | ||||
\(483\) | −3.39781 | −0.154606 | ||||||||
\(484\) | 7.84414 | − | 7.71164i | 0.356552 | − | 0.350529i | ||||
\(485\) | −17.4713 | −0.793329 | ||||||||
\(486\) | 12.7857 | − | 9.28935i | 0.579971 | − | 0.421373i | ||||
\(487\) | −5.84616 | − | 17.9926i | −0.264915 | − | 0.815323i | −0.991713 | − | 0.128473i | \(-0.958993\pi\) |
0.726798 | − | 0.686851i | \(-0.241007\pi\) | |||||||
\(488\) | 4.09845 | − | 12.6137i | 0.185528 | − | 0.570997i | ||||
\(489\) | 3.24602 | + | 2.35837i | 0.146790 | + | 0.106649i | ||||
\(490\) | −0.809017 | − | 0.587785i | −0.0365477 | − | 0.0265534i | ||||
\(491\) | −0.469465 | + | 1.44487i | −0.0211867 | + | 0.0652059i | −0.961091 | − | 0.276232i | \(-0.910914\pi\) |
0.939904 | + | 0.341438i | \(0.110914\pi\) | |||||||
\(492\) | 2.40719 | + | 7.40858i | 0.108525 | + | 0.334005i | ||||
\(493\) | −11.6558 | + | 8.46842i | −0.524950 | + | 0.381399i | ||||
\(494\) | −5.04681 | −0.227067 | ||||||||
\(495\) | 7.58542 | + | 1.85530i | 0.340939 | + | 0.0833895i | ||||
\(496\) | 2.47600 | 0.111176 | ||||||||
\(497\) | 3.70925 | − | 2.69493i | 0.166383 | − | 0.120884i | ||||
\(498\) | 3.36663 | + | 10.3614i | 0.150862 | + | 0.464307i | ||||
\(499\) | 3.65173 | − | 11.2389i | 0.163474 | − | 0.503120i | −0.835447 | − | 0.549571i | \(-0.814791\pi\) |
0.998921 | + | 0.0464508i | \(0.0147911\pi\) | |||||||
\(500\) | −0.809017 | − | 0.587785i | −0.0361803 | − | 0.0262866i | ||||
\(501\) | −1.21448 | − | 0.882368i | −0.0542588 | − | 0.0394213i | ||||
\(502\) | −4.18675 | + | 12.8855i | −0.186864 | + | 0.575107i | ||||
\(503\) | −4.95943 | − | 15.2636i | −0.221130 | − | 0.680568i | −0.998661 | − | 0.0517242i | \(-0.983528\pi\) |
0.777531 | − | 0.628844i | \(-0.216472\pi\) | |||||||
\(504\) | −1.90484 | + | 1.38395i | −0.0848482 | + | 0.0616458i | ||||
\(505\) | −10.6494 | −0.473891 | ||||||||
\(506\) | −12.9816 | + | 5.31248i | −0.577101 | + | 0.236169i | ||||
\(507\) | 4.83166 | 0.214581 | ||||||||
\(508\) | 10.8477 | − | 7.88134i | 0.481290 | − | 0.349678i | ||||
\(509\) | 12.4461 | + | 38.3052i | 0.551665 | + | 1.69785i | 0.704593 | + | 0.709612i | \(0.251130\pi\) |
−0.152929 | + | 0.988237i | \(0.548870\pi\) | |||||||
\(510\) | −0.398351 | + | 1.22600i | −0.0176393 | + | 0.0542882i | ||||
\(511\) | 2.98764 | + | 2.17065i | 0.132165 | + | 0.0960238i | ||||
\(512\) | −0.809017 | − | 0.587785i | −0.0357538 | − | 0.0259767i | ||||
\(513\) | 2.53831 | − | 7.81211i | 0.112069 | − | 0.344913i | ||||
\(514\) | 5.69288 | + | 17.5209i | 0.251102 | + | 0.772813i | ||||
\(515\) | 5.55525 | − | 4.03612i | 0.244793 | − | 0.177853i | ||||
\(516\) | 3.21506 | 0.141535 | ||||||||
\(517\) | 1.61097 | + | 21.6475i | 0.0708502 | + | 0.952057i | ||||
\(518\) | 5.60877 | 0.246435 | ||||||||
\(519\) | −7.65679 | + | 5.56298i | −0.336096 | + | 0.244188i | ||||
\(520\) | −0.816775 | − | 2.51377i | −0.0358179 | − | 0.110236i | ||||
\(521\) | −8.49492 | + | 26.1447i | −0.372169 | + | 1.14542i | 0.573200 | + | 0.819416i | \(0.305702\pi\) |
−0.945369 | + | 0.326003i | \(0.894298\pi\) | |||||||
\(522\) | 17.1042 | + | 12.4269i | 0.748631 | + | 0.543912i | ||||
\(523\) | −16.3716 | − | 11.8946i | −0.715879 | − | 0.520117i | 0.169186 | − | 0.985584i | \(-0.445886\pi\) |
−0.885065 | + | 0.465468i | \(0.845886\pi\) | |||||||
\(524\) | −2.62642 | + | 8.08329i | −0.114736 | + | 0.353120i | ||||
\(525\) | 0.248272 | + | 0.764103i | 0.0108355 | + | 0.0333482i | ||||
\(526\) | 15.5055 | − | 11.2654i | 0.676070 | − | 0.491193i | ||||
\(527\) | 3.97273 | 0.173055 | ||||||||
\(528\) | 1.40194 | − | 2.26605i | 0.0610118 | − | 0.0986170i | ||||
\(529\) | −5.11424 | −0.222358 | ||||||||
\(530\) | −8.12885 | + | 5.90596i | −0.353095 | + | 0.256538i | ||||
\(531\) | −3.03157 | − | 9.33022i | −0.131559 | − | 0.404897i | ||||
\(532\) | −0.590037 | + | 1.81595i | −0.0255814 | + | 0.0787313i | ||||
\(533\) | −20.7329 | − | 15.0634i | −0.898043 | − | 0.652466i | ||||
\(534\) | −2.21651 | − | 1.61039i | −0.0959177 | − | 0.0696883i | ||||
\(535\) | −0.890804 | + | 2.74161i | −0.0385128 | + | 0.118530i | ||||
\(536\) | −3.24559 | − | 9.98890i | −0.140188 | − | 0.431455i | ||||
\(537\) | −6.74067 | + | 4.89738i | −0.290881 | + | 0.211338i | ||||
\(538\) | 9.08666 | 0.391754 | ||||||||
\(539\) | 2.14322 | + | 2.53113i | 0.0923148 | + | 0.109024i | ||||
\(540\) | 4.30195 | 0.185126 | ||||||||
\(541\) | −21.4595 | + | 15.5913i | −0.922617 | + | 0.670320i | −0.944174 | − | 0.329447i | \(-0.893138\pi\) |
0.0215570 | + | 0.999768i | \(0.493138\pi\) | |||||||
\(542\) | 5.92506 | + | 18.2355i | 0.254503 | + | 0.783281i | ||||
\(543\) | 5.62926 | − | 17.3251i | 0.241575 | − | 0.743491i | ||||
\(544\) | −1.29806 | − | 0.943099i | −0.0556541 | − | 0.0404350i | ||||
\(545\) | 14.9618 | + | 10.8704i | 0.640894 | + | 0.465637i | ||||
\(546\) | −0.656217 | + | 2.01963i | −0.0280835 | + | 0.0864321i | ||||
\(547\) | 0.981371 | + | 3.02035i | 0.0419604 | + | 0.129141i | 0.969842 | − | 0.243734i | \(-0.0783722\pi\) |
−0.927882 | + | 0.372874i | \(0.878372\pi\) | |||||||
\(548\) | −8.15058 | + | 5.92174i | −0.348175 | + | 0.252964i | ||||
\(549\) | −31.2275 | −1.33276 | ||||||||
\(550\) | 2.14322 | + | 2.53113i | 0.0913870 | + | 0.107928i | ||||
\(551\) | 17.1452 | 0.730409 | ||||||||
\(552\) | −2.74889 | + | 1.99718i | −0.117000 | + | 0.0850057i | ||||
\(553\) | 4.31008 | + | 13.2651i | 0.183283 | + | 0.564088i | ||||
\(554\) | −6.38712 | + | 19.6575i | −0.271363 | + | 0.835168i | ||||
\(555\) | −3.64561 | − | 2.64869i | −0.154748 | − | 0.112431i | ||||
\(556\) | −11.1807 | − | 8.12322i | −0.474165 | − | 0.344501i | ||||
\(557\) | −9.03031 | + | 27.7924i | −0.382626 | + | 1.17760i | 0.555561 | + | 0.831476i | \(0.312503\pi\) |
−0.938188 | + | 0.346127i | \(0.887497\pi\) | |||||||
\(558\) | −1.80149 | − | 5.54443i | −0.0762633 | − | 0.234714i | ||||
\(559\) | −8.55699 | + | 6.21702i | −0.361922 | + | 0.262952i | ||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 2.24941 | − | 3.63586i | 0.0949703 | − | 0.153506i | ||||
\(562\) | −1.37153 | −0.0578543 | ||||||||
\(563\) | 4.97934 | − | 3.61770i | 0.209854 | − | 0.152468i | −0.477894 | − | 0.878418i | \(-0.658600\pi\) |
0.687748 | + | 0.725950i | \(0.258600\pi\) | |||||||
\(564\) | 1.62495 | + | 5.00107i | 0.0684226 | + | 0.210583i | ||||
\(565\) | 3.69479 | − | 11.3714i | 0.155441 | − | 0.478398i | ||||
\(566\) | 5.20613 | + | 3.78247i | 0.218830 | + | 0.158989i | ||||
\(567\) | 2.91831 | + | 2.12028i | 0.122558 | + | 0.0890433i | ||||
\(568\) | 1.41681 | − | 4.36049i | 0.0594479 | − | 0.182962i | ||||
\(569\) | −1.10952 | − | 3.41474i | −0.0465133 | − | 0.143153i | 0.925103 | − | 0.379717i | \(-0.123979\pi\) |
−0.971616 | + | 0.236564i | \(0.923979\pi\) | |||||||
\(570\) | 1.24108 | − | 0.901698i | 0.0519831 | − | 0.0377680i | ||||
\(571\) | −28.1128 | −1.17649 | −0.588243 | − | 0.808684i | \(-0.700180\pi\) | ||||
−0.588243 | + | 0.808684i | \(0.700180\pi\) | |||||||
\(572\) | 0.650572 | + | 8.74212i | 0.0272018 | + | 0.365527i | ||||
\(573\) | 6.81821 | 0.284835 | ||||||||
\(574\) | −7.84406 | + | 5.69904i | −0.327405 | + | 0.237873i | ||||
\(575\) | −1.30688 | − | 4.02217i | −0.0545007 | − | 0.167736i | ||||
\(576\) | −0.727583 | + | 2.23927i | −0.0303160 | + | 0.0933029i | ||||
\(577\) | −23.0876 | − | 16.7741i | −0.961149 | − | 0.698315i | −0.00773133 | − | 0.999970i | \(-0.502461\pi\) |
−0.953417 | + | 0.301655i | \(0.902461\pi\) | |||||||
\(578\) | 11.6705 | + | 8.47915i | 0.485431 | + | 0.352686i | ||||
\(579\) | 6.24599 | − | 19.2232i | 0.259574 | − | 0.798888i | ||||
\(580\) | 2.77477 | + | 8.53988i | 0.115216 | + | 0.354599i | ||||
\(581\) | −10.9705 | + | 7.97052i | −0.455132 | + | 0.330673i | ||||
\(582\) | 14.0368 | 0.581846 | ||||||||
\(583\) | 30.8422 | − | 12.6216i | 1.27735 | − | 0.522734i | ||||
\(584\) | 3.69293 | 0.152814 | ||||||||
\(585\) | −5.03475 | + | 3.65796i | −0.208161 | + | 0.151238i | ||||
\(586\) | 1.42065 | + | 4.37230i | 0.0586864 | + | 0.180618i | ||||
\(587\) | −6.02913 | + | 18.5557i | −0.248849 | + | 0.765878i | 0.746131 | + | 0.665799i | \(0.231909\pi\) |
−0.994980 | + | 0.100078i | \(0.968091\pi\) | |||||||
\(588\) | 0.649985 | + | 0.472241i | 0.0268049 | + | 0.0194749i | ||||
\(589\) | −3.82477 | − | 2.77886i | −0.157597 | − | 0.114501i | ||||
\(590\) | 1.28756 | − | 3.96270i | 0.0530080 | − | 0.163142i | ||||
\(591\) | 3.29216 | + | 10.1322i | 0.135421 | + | 0.416784i | ||||
\(592\) | 4.53759 | − | 3.29675i | 0.186494 | − | 0.135496i | ||||
\(593\) | 4.84298 | 0.198877 | 0.0994386 | − | 0.995044i | \(-0.468295\pi\) | ||||
0.0994386 | + | 0.995044i | \(0.468295\pi\) | |||||||
\(594\) | −13.8594 | − | 3.38984i | −0.568658 | − | 0.139087i | ||||
\(595\) | −1.60450 | −0.0657779 | ||||||||
\(596\) | 14.8566 | − | 10.7940i | 0.608552 | − | 0.442139i | ||||
\(597\) | −0.893315 | − | 2.74934i | −0.0365610 | − | 0.112523i | ||||
\(598\) | 3.45427 | − | 10.6311i | 0.141255 | − | 0.434740i | ||||
\(599\) | 2.97029 | + | 2.15805i | 0.121363 | + | 0.0881753i | 0.646811 | − | 0.762650i | \(-0.276102\pi\) |
−0.525448 | + | 0.850826i | \(0.676102\pi\) | |||||||
\(600\) | 0.649985 | + | 0.472241i | 0.0265355 | + | 0.0192792i | ||||
\(601\) | −0.535752 | + | 1.64887i | −0.0218538 | + | 0.0672590i | −0.961389 | − | 0.275194i | \(-0.911258\pi\) |
0.939535 | + | 0.342453i | \(0.111258\pi\) | |||||||
\(602\) | 1.23659 | + | 3.80583i | 0.0503997 | + | 0.155114i | ||||
\(603\) | −20.0064 | + | 14.5355i | −0.814724 | + | 0.591932i | ||||
\(604\) | 20.5718 | 0.837055 | ||||||||
\(605\) | −4.91024 | − | 9.84325i | −0.199629 | − | 0.400185i | ||||
\(606\) | 8.55598 | 0.347563 | ||||||||
\(607\) | 23.0237 | − | 16.7277i | 0.934504 | − | 0.678957i | −0.0125871 | − | 0.999921i | \(-0.504007\pi\) |
0.947092 | + | 0.320964i | \(0.104007\pi\) | |||||||
\(608\) | 0.590037 | + | 1.81595i | 0.0239292 | + | 0.0736464i | ||||
\(609\) | 2.22932 | − | 6.86115i | 0.0903367 | − | 0.278028i | ||||
\(610\) | −10.7299 | − | 7.79571i | −0.434440 | − | 0.315639i | ||||
\(611\) | −13.9955 | − | 10.1683i | −0.566198 | − | 0.411367i | ||||
\(612\) | −1.16740 | + | 3.59290i | −0.0471895 | + | 0.145234i | ||||
\(613\) | −2.49656 | − | 7.68362i | −0.100835 | − | 0.310339i | 0.887895 | − | 0.460046i | \(-0.152167\pi\) |
−0.988730 | + | 0.149707i | \(0.952167\pi\) | |||||||
\(614\) | 20.0670 | − | 14.5795i | 0.809839 | − | 0.588382i | ||||
\(615\) | 7.78984 | 0.314117 | ||||||||
\(616\) | 3.22166 | + | 0.787978i | 0.129804 | + | 0.0317485i | ||||
\(617\) | 2.53152 | 0.101915 | 0.0509577 | − | 0.998701i | \(-0.483773\pi\) | ||||
0.0509577 | + | 0.998701i | \(0.483773\pi\) | |||||||
\(618\) | −4.46323 | + | 3.24272i | −0.179537 | + | 0.130441i | ||||
\(619\) | −8.53828 | − | 26.2781i | −0.343183 | − | 1.05621i | −0.962550 | − | 0.271106i | \(-0.912611\pi\) |
0.619367 | − | 0.785102i | \(-0.287389\pi\) | |||||||
\(620\) | 0.765125 | − | 2.35481i | 0.0307282 | − | 0.0945716i | ||||
\(621\) | 14.7189 | + | 10.6939i | 0.590650 | + | 0.429133i | ||||
\(622\) | −20.8745 | − | 15.1662i | −0.836990 | − | 0.608109i | ||||
\(623\) | 1.05378 | − | 3.24319i | 0.0422187 | − | 0.129936i | ||||
\(624\) | 0.656217 | + | 2.01963i | 0.0262697 | + | 0.0808499i | ||||
\(625\) | −0.809017 | + | 0.587785i | −0.0323607 | + | 0.0235114i | ||||
\(626\) | 16.5081 | 0.659797 | ||||||||
\(627\) | −4.70886 | + | 1.92702i | −0.188054 | + | 0.0769577i | ||||
\(628\) | −4.64886 | −0.185510 | ||||||||
\(629\) | 7.28054 | − | 5.28962i | 0.290294 | − | 0.210911i | ||||
\(630\) | 0.727583 | + | 2.23927i | 0.0289876 | + | 0.0892147i | ||||
\(631\) | −9.98071 | + | 30.7175i | −0.397326 | + | 1.22284i | 0.529809 | + | 0.848117i | \(0.322263\pi\) |
−0.927135 | + | 0.374727i | \(0.877737\pi\) | |||||||
\(632\) | 11.2839 | + | 8.19826i | 0.448851 | + | 0.326109i | ||||
\(633\) | −6.50362 | − | 4.72515i | −0.258496 | − | 0.187808i | ||||
\(634\) | 0.720270 | − | 2.21676i | 0.0286056 | − | 0.0880389i | ||||
\(635\) | −4.14347 | − | 12.7523i | −0.164428 | − | 0.506059i | ||||
\(636\) | 6.53093 | − | 4.74499i | 0.258968 | − | 0.188151i | ||||
\(637\) | −2.64314 | −0.104725 | ||||||||
\(638\) | −2.21014 | − | 29.6990i | −0.0875004 | − | 1.17580i | ||||
\(639\) | −10.7952 | −0.427050 | ||||||||
\(640\) | −0.809017 | + | 0.587785i | −0.0319792 | + | 0.0232343i | ||||
\(641\) | 9.70231 | + | 29.8606i | 0.383218 | + | 1.17942i | 0.937765 | + | 0.347272i | \(0.112892\pi\) |
−0.554546 | + | 0.832153i | \(0.687108\pi\) | |||||||
\(642\) | 0.715694 | − | 2.20268i | 0.0282462 | − | 0.0869328i | ||||
\(643\) | −3.33755 | − | 2.42487i | −0.131620 | − | 0.0956275i | 0.520027 | − | 0.854150i | \(-0.325922\pi\) |
−0.651647 | + | 0.758522i | \(0.725922\pi\) | |||||||
\(644\) | −3.42146 | − | 2.48584i | −0.134824 | − | 0.0979556i | ||||
\(645\) | 0.993508 | − | 3.05770i | 0.0391193 | − | 0.120397i | ||||
\(646\) | 0.946712 | + | 2.91368i | 0.0372479 | + | 0.114637i | ||||
\(647\) | −16.9317 | + | 12.3016i | −0.665655 | + | 0.483626i | −0.868568 | − | 0.495570i | \(-0.834959\pi\) |
0.202913 | + | 0.979197i | \(0.434959\pi\) | |||||||
\(648\) | 3.60723 | 0.141705 | ||||||||
\(649\) | −7.27060 | + | 11.7519i | −0.285396 | + | 0.461303i | ||||
\(650\) | −2.64314 | −0.103672 | ||||||||
\(651\) | −1.60936 | + | 1.16927i | −0.0630758 | + | 0.0458273i | ||||
\(652\) | 1.54323 | + | 4.74958i | 0.0604376 | + | 0.186008i | ||||
\(653\) | −0.620662 | + | 1.91020i | −0.0242884 | + | 0.0747519i | −0.962466 | − | 0.271402i | \(-0.912513\pi\) |
0.938178 | + | 0.346154i | \(0.112513\pi\) | |||||||
\(654\) | −12.0207 | − | 8.73355i | −0.470046 | − | 0.341509i | ||||
\(655\) | 6.87606 | + | 4.99575i | 0.268670 | + | 0.195200i | ||||
\(656\) | −2.99616 | + | 9.22125i | −0.116981 | + | 0.360029i | ||||
\(657\) | −2.68691 | − | 8.26946i | −0.104826 | − | 0.322622i | ||||
\(658\) | −5.29503 | + | 3.84707i | −0.206422 | + | 0.149974i | ||||
\(659\) | 11.7132 | 0.456282 | 0.228141 | − | 0.973628i | \(-0.426735\pi\) | ||||
0.228141 | + | 0.973628i | \(0.426735\pi\) | |||||||
\(660\) | −1.72191 | − | 2.03357i | −0.0670254 | − | 0.0791568i | ||||
\(661\) | 35.8654 | 1.39500 | 0.697502 | − | 0.716583i | \(-0.254295\pi\) | ||||
0.697502 | + | 0.716583i | \(0.254295\pi\) | |||||||
\(662\) | −5.29429 | + | 3.84653i | −0.205769 | + | 0.149500i | ||||
\(663\) | 1.05290 | + | 3.24049i | 0.0408912 | + | 0.125850i | ||||
\(664\) | −4.19035 | + | 12.8966i | −0.162617 | + | 0.500484i | ||||
\(665\) | 1.54474 | + | 1.12232i | 0.0599023 | + | 0.0435216i | ||||
\(666\) | −10.6838 | − | 7.76223i | −0.413988 | − | 0.300780i | ||||
\(667\) | −11.7350 | + | 36.1165i | −0.454379 | + | 1.39844i | ||||
\(668\) | −0.577388 | − | 1.77702i | −0.0223398 | − | 0.0687549i | ||||
\(669\) | 16.2754 | − | 11.8248i | 0.629244 | − | 0.457172i | ||||
\(670\) | −10.5029 | −0.405764 | ||||||||
\(671\) | 28.4252 | + | 33.5700i | 1.09734 | + | 1.29596i | ||||
\(672\) | 0.803425 | 0.0309928 | ||||||||
\(673\) | 26.9902 | − | 19.6095i | 1.04039 | − | 0.755891i | 0.0700317 | − | 0.997545i | \(-0.477690\pi\) |
0.970362 | + | 0.241654i | \(0.0776900\pi\) | |||||||
\(674\) | 5.15321 | + | 15.8600i | 0.198494 | + | 0.610902i | ||||
\(675\) | 1.32937 | − | 4.09139i | 0.0511676 | − | 0.157478i | ||||
\(676\) | 4.86528 | + | 3.53484i | 0.187126 | + | 0.135955i | ||||
\(677\) | 10.7383 | + | 7.80184i | 0.412707 | + | 0.299849i | 0.774697 | − | 0.632333i | \(-0.217903\pi\) |
−0.361990 | + | 0.932182i | \(0.617903\pi\) | |||||||
\(678\) | −2.96849 | + | 9.13607i | −0.114004 | + | 0.350869i | ||||
\(679\) | 5.39891 | + | 16.6161i | 0.207191 | + | 0.637669i | ||||
\(680\) | −1.29806 | + | 0.943099i | −0.0497785 | + | 0.0361662i | ||||
\(681\) | 0.146965 | 0.00563173 | ||||||||
\(682\) | −4.32052 | + | 6.98351i | −0.165441 | + | 0.267412i | ||||
\(683\) | −15.3702 | −0.588123 | −0.294061 | − | 0.955787i | \(-0.595007\pi\) | ||||
−0.294061 | + | 0.955787i | \(0.595007\pi\) | |||||||
\(684\) | 3.63710 | − | 2.64250i | 0.139068 | − | 0.101039i | ||||
\(685\) | 3.11324 | + | 9.58158i | 0.118951 | + | 0.366093i | ||||
\(686\) | −0.309017 | + | 0.951057i | −0.0117983 | + | 0.0363115i | ||||
\(687\) | −0.0873393 | − | 0.0634557i | −0.00333220 | − | 0.00242099i | ||||
\(688\) | 3.23744 | + | 2.35214i | 0.123426 | + | 0.0896743i | ||||
\(689\) | −8.20680 | + | 25.2579i | −0.312654 | + | 0.962251i | ||||
\(690\) | 1.04998 | + | 3.23151i | 0.0399721 | + | 0.123021i | ||||
\(691\) | −16.8112 | + | 12.2141i | −0.639529 | + | 0.464645i | −0.859688 | − | 0.510819i | \(-0.829342\pi\) |
0.220159 | + | 0.975464i | \(0.429342\pi\) | |||||||
\(692\) | −11.7799 | −0.447806 | ||||||||
\(693\) | −0.579529 | − | 7.78749i | −0.0220145 | − | 0.295822i | ||||
\(694\) | 29.2816 | 1.11151 | ||||||||
\(695\) | −11.1807 | + | 8.12322i | −0.424106 | + | 0.308131i | ||||
\(696\) | −2.22932 | − | 6.86115i | −0.0845023 | − | 0.260071i | ||||
\(697\) | −4.80733 | + | 14.7955i | −0.182091 | + | 0.560418i | ||||
\(698\) | 13.5782 | + | 9.86516i | 0.513943 | + | 0.373402i | ||||
\(699\) | −1.90452 | − | 1.38371i | −0.0720355 | − | 0.0523368i | ||||
\(700\) | −0.309017 | + | 0.951057i | −0.0116797 | + | 0.0359466i | ||||
\(701\) | −1.29353 | − | 3.98108i | −0.0488560 | − | 0.150363i | 0.923652 | − | 0.383232i | \(-0.125189\pi\) |
−0.972508 | + | 0.232868i | \(0.925189\pi\) | |||||||
\(702\) | 9.19904 | − | 6.68349i | 0.347195 | − | 0.252252i | ||||
\(703\) | −10.7094 | −0.403912 | ||||||||
\(704\) | 3.06954 | − | 1.25616i | 0.115688 | − | 0.0473432i | ||||
\(705\) | 5.25844 | 0.198044 | ||||||||
\(706\) | −18.5354 | + | 13.4667i | −0.697588 | + | 0.506828i | ||||
\(707\) | 3.29084 | + | 10.1282i | 0.123765 | + | 0.380909i | ||||
\(708\) | −1.03446 | + | 3.18374i | −0.0388773 | + | 0.119652i | ||||
\(709\) | −4.43769 | − | 3.22417i | −0.166661 | − | 0.121086i | 0.501328 | − | 0.865257i | \(-0.332845\pi\) |
−0.667989 | + | 0.744171i | \(0.732845\pi\) | |||||||
\(710\) | −3.70925 | − | 2.69493i | −0.139206 | − | 0.101139i | ||||
\(711\) | 10.1481 | − | 31.2327i | 0.380584 | − | 1.17132i | ||||
\(712\) | −1.05378 | − | 3.24319i | −0.0394919 | − | 0.121544i | ||||
\(713\) | 8.47153 | − | 6.15492i | 0.317261 | − | 0.230504i | ||||
\(714\) | 1.28909 | 0.0482431 | ||||||||
\(715\) | 8.51529 | + | 2.08273i | 0.318454 | + | 0.0778898i | ||||
\(716\) | −10.3705 | −0.387564 | ||||||||
\(717\) | 5.37804 | − | 3.90738i | 0.200847 | − | 0.145924i | ||||
\(718\) | 2.58498 | + | 7.95576i | 0.0964707 | + | 0.296906i | ||||
\(719\) | −5.13007 | + | 15.7887i | −0.191319 | + | 0.588820i | 0.808681 | + | 0.588248i | \(0.200182\pi\) |
−1.00000 | 0.000572186i | \(0.999818\pi\) | ||||||||
\(720\) | 1.90484 | + | 1.38395i | 0.0709891 | + | 0.0515766i | ||||
\(721\) | −5.55525 | − | 4.03612i | −0.206888 | − | 0.150313i | ||||
\(722\) | −4.74471 | + | 14.6027i | −0.176580 | + | 0.543456i | ||||
\(723\) | −4.11740 | − | 12.6721i | −0.153128 | − | 0.471279i | ||||
\(724\) | 18.3435 | − | 13.3273i | 0.681729 | − | 0.495305i | ||||
\(725\) | 8.97936 | 0.333485 | ||||||||
\(726\) | 3.94501 | + | 7.90831i | 0.146413 | + | 0.293505i | ||||
\(727\) | −22.9499 | −0.851164 | −0.425582 | − | 0.904920i | \(-0.639931\pi\) | ||||
−0.425582 | + | 0.904920i | \(0.639931\pi\) | |||||||
\(728\) | −2.13834 | + | 1.55360i | −0.0792523 | + | 0.0575802i | ||||
\(729\) | 0.579598 | + | 1.78382i | 0.0214666 | + | 0.0660673i | ||||
\(730\) | 1.14118 | − | 3.51218i | 0.0422368 | − | 0.129992i | ||||
\(731\) | 5.19445 | + | 3.77399i | 0.192124 | + | 0.139586i | ||||
\(732\) | 8.62065 | + | 6.26327i | 0.318629 | + | 0.231497i | ||||
\(733\) | −4.92826 | + | 15.1676i | −0.182029 | + | 0.560229i | −0.999885 | − | 0.0151952i | \(-0.995163\pi\) |
0.817855 | + | 0.575424i | \(0.195163\pi\) | |||||||
\(734\) | −0.557226 | − | 1.71496i | −0.0205676 | − | 0.0633005i | ||||
\(735\) | 0.649985 | − | 0.472241i | 0.0239750 | − | 0.0174189i | ||||
\(736\) | −4.22916 | −0.155889 | ||||||||
\(737\) | 33.8369 | + | 8.27609i | 1.24640 | + | 0.304854i | ||||
\(738\) | 22.8288 | 0.840340 | ||||||||
\(739\) | 33.7005 | − | 24.4848i | 1.23969 | − | 0.900688i | 0.242114 | − | 0.970248i | \(-0.422159\pi\) |
0.997578 | + | 0.0695594i | \(0.0221594\pi\) | |||||||
\(740\) | −1.73320 | − | 5.33426i | −0.0637139 | − | 0.196091i | ||||
\(741\) | 1.25298 | − | 3.85628i | 0.0460294 | − | 0.141664i | ||||
\(742\) | 8.12885 | + | 5.90596i | 0.298420 | + | 0.216815i | ||||
\(743\) | 33.9657 | + | 24.6775i | 1.24608 | + | 0.905330i | 0.997988 | − | 0.0634061i | \(-0.0201963\pi\) |
0.248092 | + | 0.968736i | \(0.420196\pi\) | |||||||
\(744\) | −0.614721 | + | 1.89192i | −0.0225368 | + | 0.0693610i | ||||
\(745\) | −5.67473 | − | 17.4650i | −0.207906 | − | 0.639869i | ||||
\(746\) | −7.77021 | + | 5.64539i | −0.284488 | + | 0.206692i | ||||
\(747\) | 31.9277 | 1.16817 | ||||||||
\(748\) | 4.92506 | − | 2.01550i | 0.180078 | − | 0.0736939i | ||||
\(749\) | 2.88270 | 0.105332 | ||||||||
\(750\) | 0.649985 | − | 0.472241i | 0.0237341 | − | 0.0172438i | ||||
\(751\) | 9.56603 | + | 29.4412i | 0.349070 | + | 1.07433i | 0.959369 | + | 0.282155i | \(0.0910492\pi\) |
−0.610299 | + | 0.792171i | \(0.708951\pi\) | |||||||
\(752\) | −2.02252 | + | 6.22469i | −0.0737538 | + | 0.226991i | ||||
\(753\) | −8.80638 | − | 6.39821i | −0.320922 | − | 0.233164i | ||||
\(754\) | 19.2009 | + | 13.9503i | 0.699257 | + | 0.508040i | ||||
\(755\) | 6.35704 | − | 19.5650i | 0.231356 | − | 0.712042i | ||||
\(756\) | −1.32937 | − | 4.09139i | −0.0483489 | − | 0.148803i | ||||
\(757\) | −16.1658 | + | 11.7452i | −0.587557 | + | 0.426885i | −0.841441 | − | 0.540349i | \(-0.818292\pi\) |
0.253883 | + | 0.967235i | \(0.418292\pi\) | |||||||
\(758\) | −5.94046 | −0.215767 | ||||||||
\(759\) | −0.836324 | − | 11.2382i | −0.0303566 | − | 0.407920i | ||||
\(760\) | 1.90940 | 0.0692612 | ||||||||
\(761\) | −6.73485 | + | 4.89316i | −0.244138 | + | 0.177377i | −0.703125 | − | 0.711066i | \(-0.748213\pi\) |
0.458987 | + | 0.888443i | \(0.348213\pi\) | |||||||
\(762\) | 3.32897 | + | 10.2455i | 0.120596 | + | 0.371155i | ||||
\(763\) | 5.71490 | − | 17.5887i | 0.206893 | − | 0.636753i | ||||
\(764\) | 6.86567 | + | 4.98820i | 0.248391 | + | 0.180467i | ||||
\(765\) | 3.05630 | + | 2.22053i | 0.110501 | + | 0.0802836i | ||||
\(766\) | −9.09307 | + | 27.9856i | −0.328546 | + | 1.01116i | ||||
\(767\) | −3.40320 | − | 10.4740i | −0.122882 | − | 0.378193i | ||||
\(768\) | 0.649985 | − | 0.472241i | 0.0234543 | − | 0.0170405i | ||||
\(769\) | −38.3934 | −1.38450 | −0.692251 | − | 0.721657i | \(-0.743381\pi\) | ||||
−0.692251 | + | 0.721657i | \(0.743381\pi\) | |||||||
\(770\) | 1.74496 | − | 2.82048i | 0.0628840 | − | 0.101643i | ||||
\(771\) | −14.8011 | −0.533050 | ||||||||
\(772\) | 20.3531 | − | 14.7874i | 0.732525 | − | 0.532210i | ||||
\(773\) | 8.68995 | + | 26.7449i | 0.312556 | + | 0.961948i | 0.976749 | + | 0.214387i | \(0.0687753\pi\) |
−0.664193 | + | 0.747561i | \(0.731225\pi\) | |||||||
\(774\) | 2.91156 | − | 8.96087i | 0.104654 | − | 0.322092i | ||||
\(775\) | −2.00312 | − | 1.45536i | −0.0719544 | − | 0.0522779i | ||||
\(776\) | 14.1345 | + | 10.2693i | 0.507400 | + | 0.368648i | ||||
\(777\) | −1.39250 | + | 4.28567i | −0.0499557 | + | 0.153748i | ||||
\(778\) | −5.82858 | − | 17.9385i | −0.208965 | − | 0.643127i | ||||
\(779\) | 14.9774 | − | 10.8818i | 0.536623 | − | 0.389879i | ||||
\(780\) | 2.12356 | 0.0760358 | ||||||||
\(781\) | 9.82640 | + | 11.6049i | 0.351616 | + | 0.415258i | ||||
\(782\) | −6.78566 | −0.242655 | ||||||||
\(783\) | −31.2513 | + | 22.7054i | −1.11683 | + | 0.811424i | ||||
\(784\) | 0.309017 | + | 0.951057i | 0.0110363 | + | 0.0339663i | ||||
\(785\) | −1.43658 | + | 4.42133i | −0.0512736 | + | 0.157804i | ||||
\(786\) | −5.52440 | − | 4.01371i | −0.197049 | − | 0.143164i | ||||
\(787\) | 24.4296 | + | 17.7491i | 0.870821 | + | 0.632688i | 0.930807 | − | 0.365511i | \(-0.119106\pi\) |
−0.0599865 | + | 0.998199i | \(0.519106\pi\) | |||||||
\(788\) | −4.09766 | + | 12.6113i | −0.145973 | + | 0.449259i | ||||
\(789\) | 4.75833 | + | 14.6446i | 0.169401 | + | 0.521363i | ||||
\(790\) | 11.2839 | − | 8.19826i | 0.401464 | − | 0.291681i | ||||
\(791\) | −11.9566 | −0.425128 | ||||||||
\(792\) | −5.04622 | − | 5.95957i | −0.179310 | − | 0.211764i | ||||
\(793\) | −35.0556 | −1.24486 | ||||||||
\(794\) | −20.5929 | + | 14.9616i | −0.730815 | + | 0.530968i | ||||
\(795\) | −2.49459 | − | 7.67756i | −0.0884740 | − | 0.272295i | ||||
\(796\) | 1.11188 | − | 3.42203i | 0.0394097 | − | 0.121290i | ||||
\(797\) | −37.5565 | − | 27.2864i | −1.33032 | − | 0.966533i | −0.999741 | − | 0.0227544i | \(-0.992756\pi\) |
−0.330578 | − | 0.943779i | \(-0.607244\pi\) | |||||||
\(798\) | −1.24108 | − | 0.901698i | −0.0439338 | − | 0.0319198i | ||||
\(799\) | −3.24513 | + | 9.98748i | −0.114804 | + | 0.353332i | ||||
\(800\) | 0.309017 | + | 0.951057i | 0.0109254 | + | 0.0336249i | ||||
\(801\) | −6.49567 | + | 4.71938i | −0.229513 | + | 0.166751i | ||||
\(802\) | 14.9867 | 0.529198 | ||||||||
\(803\) | −6.44400 | + | 10.4158i | −0.227404 | + | 0.367567i | ||||
\(804\) | 8.43833 | 0.297597 | ||||||||
\(805\) | −3.42146 | + | 2.48584i | −0.120591 | + | 0.0876142i | ||||
\(806\) | −2.02233 | − | 6.22410i | −0.0712336 | − | 0.219235i | ||||
\(807\) | −2.25596 | + | 6.94314i | −0.0794136 | + | 0.244410i | ||||
\(808\) | 8.61553 | + | 6.25955i | 0.303093 | + | 0.220210i | ||||
\(809\) | 9.76308 | + | 7.09329i | 0.343251 | + | 0.249387i | 0.746032 | − | 0.665910i | \(-0.231956\pi\) |
−0.402781 | + | 0.915296i | \(0.631956\pi\) | |||||||
\(810\) | 1.11470 | − | 3.43068i | 0.0391664 | − | 0.120542i | ||||
\(811\) | 4.62097 | + | 14.2219i | 0.162264 | + | 0.499398i | 0.998824 | − | 0.0484772i | \(-0.0154368\pi\) |
−0.836560 | + | 0.547875i | \(0.815437\pi\) | |||||||
\(812\) | 7.26445 | − | 5.27793i | 0.254932 | − | 0.185219i | ||||
\(813\) | −15.4048 | −0.540270 | ||||||||
\(814\) | 1.38052 | + | 18.5509i | 0.0483872 | + | 0.650208i | ||||
\(815\) | 4.99400 | 0.174932 | ||||||||
\(816\) | 1.04290 | − | 0.757710i | 0.0365087 | − | 0.0265251i | ||||
\(817\) | −2.36115 | − | 7.26686i | −0.0826060 | − | 0.254235i | ||||
\(818\) | 1.50113 | − | 4.61999i | 0.0524857 | − | 0.161534i | ||||
\(819\) | 5.03475 | + | 3.65796i | 0.175928 | + | 0.127819i | ||||
\(820\) | 7.84406 | + | 5.69904i | 0.273926 | + | 0.199019i | ||||
\(821\) | 7.37291 | − | 22.6915i | 0.257316 | − | 0.791938i | −0.736048 | − | 0.676929i | \(-0.763310\pi\) |
0.993364 | − | 0.115009i | \(-0.0366897\pi\) | |||||||
\(822\) | −2.50126 | − | 7.69808i | −0.0872414 | − | 0.268501i | ||||
\(823\) | 34.2941 | − | 24.9162i | 1.19542 | − | 0.868523i | 0.201592 | − | 0.979470i | \(-0.435388\pi\) |
0.993826 | + | 0.110947i | \(0.0353884\pi\) | |||||||
\(824\) | −6.86666 | −0.239212 | ||||||||
\(825\) | −2.46614 | + | 1.00923i | −0.0858601 | + | 0.0351368i | ||||
\(826\) | −4.16663 | −0.144976 | ||||||||
\(827\) | 42.8451 | − | 31.1288i | 1.48987 | − | 1.08245i | 0.515665 | − | 0.856790i | \(-0.327545\pi\) |
0.974205 | − | 0.225664i | \(-0.0724550\pi\) | |||||||
\(828\) | 3.07706 | + | 9.47022i | 0.106935 | + | 0.329113i | ||||
\(829\) | 13.8461 | − | 42.6138i | 0.480894 | − | 1.48004i | −0.356947 | − | 0.934125i | \(-0.616182\pi\) |
0.837841 | − | 0.545914i | \(-0.183818\pi\) | |||||||
\(830\) | 10.9705 | + | 7.97052i | 0.380791 | + | 0.276661i | ||||
\(831\) | −13.4346 | − | 9.76083i | −0.466042 | − | 0.338599i | ||||
\(832\) | −0.816775 | + | 2.51377i | −0.0283166 | + | 0.0871494i | ||||
\(833\) | 0.495817 | + | 1.52597i | 0.0171790 | + | 0.0528716i | ||||
\(834\) | 8.98282 | − | 6.52640i | 0.311049 | − | 0.225991i | ||||
\(835\) | −1.86847 | −0.0646610 | ||||||||
\(836\) | −6.15144 | − | 1.50456i | −0.212752 | − | 0.0520365i | ||||
\(837\) | 10.6516 | 0.368174 | ||||||||
\(838\) | 1.43595 | − | 1.04328i | 0.0496039 | − | 0.0360394i | ||||
\(839\) | −12.5495 | − | 38.6233i | −0.433255 | − | 1.33342i | −0.894864 | − | 0.446339i | \(-0.852728\pi\) |
0.461609 | − | 0.887084i | \(-0.347272\pi\) | |||||||
\(840\) | 0.248272 | − | 0.764103i | 0.00856620 | − | 0.0263640i | ||||
\(841\) | −41.7686 | − | 30.3467i | −1.44030 | − | 1.04644i | ||||
\(842\) | 13.6922 | + | 9.94799i | 0.471866 | + | 0.342830i | ||||
\(843\) | 0.340511 | − | 1.04799i | 0.0117278 | − | 0.0360946i | ||||
\(844\) | −3.09196 | − | 9.51608i | −0.106430 | − | 0.327557i | ||||
\(845\) | 4.86528 | − | 3.53484i | 0.167371 | − | 0.121602i | ||||
\(846\) | 15.4103 | 0.529817 | ||||||||
\(847\) | −7.84414 | + | 7.71164i | −0.269528 | + | 0.264975i | ||||
\(848\) | 10.0478 | 0.345043 | ||||||||
\(849\) | −4.18273 | + | 3.03893i | −0.143551 | + | 0.104296i | ||||
\(850\) | 0.495817 | + | 1.52597i | 0.0170064 | + | 0.0523402i | ||||
\(851\) | 7.32999 | − | 22.5594i | 0.251269 | − | 0.773326i | ||||
\(852\) | 2.98011 | + | 2.16517i | 0.102097 | + | 0.0741776i | ||||
\(853\) | 0.0945276 | + | 0.0686783i | 0.00323656 | + | 0.00235150i | 0.589402 | − | 0.807840i | \(-0.299363\pi\) |
−0.586166 | + | 0.810191i | \(0.699363\pi\) | |||||||
\(854\) | −4.09845 | + | 12.6137i | −0.140246 | + | 0.431633i | ||||
\(855\) | −1.38925 | − | 4.27566i | −0.0475112 | − | 0.146225i | ||||
\(856\) | 2.33215 | − | 1.69441i | 0.0797114 | − | 0.0579137i | ||||
\(857\) | 22.2623 | 0.760465 | 0.380233 | − | 0.924891i | \(-0.375844\pi\) | ||||
0.380233 | + | 0.924891i | \(0.375844\pi\) | |||||||
\(858\) | −6.84140 | − | 1.67332i | −0.233561 | − | 0.0571262i | ||||
\(859\) | 37.0142 | 1.26291 | 0.631454 | − | 0.775413i | \(-0.282458\pi\) | ||||
0.631454 | + | 0.775413i | \(0.282458\pi\) | |||||||
\(860\) | 3.23744 | − | 2.35214i | 0.110396 | − | 0.0802071i | ||||
\(861\) | −2.40719 | − | 7.40858i | −0.0820369 | − | 0.252484i | ||||
\(862\) | 1.28434 | − | 3.95279i | 0.0437448 | − | 0.134633i | ||||
\(863\) | −35.6176 | − | 25.8777i | −1.21244 | − | 0.880886i | −0.216986 | − | 0.976175i | \(-0.569623\pi\) |
−0.995450 | + | 0.0952888i | \(0.969623\pi\) | |||||||
\(864\) | −3.48035 | − | 2.52862i | −0.118404 | − | 0.0860254i | ||||
\(865\) | −3.64020 | + | 11.2034i | −0.123771 | + | 0.380927i | ||||
\(866\) | 6.87285 | + | 21.1525i | 0.233549 | + | 0.718790i | ||||
\(867\) | −9.37641 | + | 6.81236i | −0.318440 | + | 0.231360i | ||||
\(868\) | −2.47600 | −0.0840408 | ||||||||
\(869\) | −42.8130 | + | 17.5205i | −1.45233 | + | 0.594342i | ||||
\(870\) | −7.21424 | −0.244586 | ||||||||
\(871\) | −22.4589 | + | 16.3174i | −0.760991 | + | 0.552892i | ||||
\(872\) | −5.71490 | − | 17.5887i | −0.193531 | − | 0.595627i | ||||
\(873\) | 12.7118 | − | 39.1229i | 0.430229 | − | 1.32411i | ||||
\(874\) | 6.53293 | + | 4.74645i | 0.220980 | + | 0.160551i | ||||
\(875\) | 0.809017 | + | 0.587785i | 0.0273498 | + | 0.0198708i | ||||
\(876\) | −0.916850 | + | 2.82177i | −0.0309775 | + | 0.0953389i | ||||
\(877\) | −9.08815 | − | 27.9704i | −0.306885 | − | 0.944495i | −0.978967 | − | 0.204018i | \(-0.934600\pi\) |
0.672082 | − | 0.740477i | \(-0.265400\pi\) | |||||||
\(878\) | 17.4887 | − | 12.7063i | 0.590214 | − | 0.428816i | ||||
\(879\) | −3.69359 | −0.124582 | ||||||||
\(880\) | −0.246136 | − | 3.30748i | −0.00829725 | − | 0.111495i | ||||
\(881\) | 34.0756 | 1.14804 | 0.574019 | − | 0.818842i | \(-0.305384\pi\) | ||||
0.574019 | + | 0.818842i | \(0.305384\pi\) | |||||||
\(882\) | 1.90484 | − | 1.38395i | 0.0641392 | − | 0.0465999i | ||||
\(883\) | −5.69682 | − | 17.5330i | −0.191713 | − | 0.590033i | −0.999999 | − | 0.00124270i | \(-0.999604\pi\) |
0.808286 | − | 0.588790i | \(-0.200396\pi\) | |||||||
\(884\) | −1.31051 | + | 4.03334i | −0.0440773 | + | 0.135656i | ||||
\(885\) | 2.70825 | + | 1.96766i | 0.0910367 | + | 0.0661421i | ||||
\(886\) | 10.4737 | + | 7.60958i | 0.351870 | + | 0.255649i | ||||
\(887\) | 0.678672 | − | 2.08874i | 0.0227876 | − | 0.0701329i | −0.939016 | − | 0.343873i | \(-0.888261\pi\) |
0.961804 | + | 0.273740i | \(0.0882609\pi\) | |||||||
\(888\) | 1.39250 | + | 4.28567i | 0.0467292 | + | 0.143818i | ||||
\(889\) | −10.8477 | + | 7.88134i | −0.363821 | + | 0.264332i | ||||
\(890\) | −3.41009 | −0.114307 | ||||||||
\(891\) | −6.29447 | + | 10.1741i | −0.210873 | + | 0.340846i | ||||
\(892\) | 25.0397 | 0.838391 | ||||||||
\(893\) | 10.1103 | − | 7.34559i | 0.338330 | − | 0.245811i | ||||
\(894\) | 4.55922 | + | 14.0318i | 0.152483 | + | 0.469295i | ||||
\(895\) | −3.20466 | + | 9.86294i | −0.107120 | + | 0.329682i | ||||
\(896\) | 0.809017 | + | 0.587785i | 0.0270274 | + | 0.0196365i | ||||
\(897\) | 7.26569 | + | 5.27883i | 0.242594 | + | 0.176255i | ||||
\(898\) | 4.28177 | − | 13.1779i | 0.142885 | − | 0.439753i | ||||
\(899\) | 6.87033 | + | 21.1447i | 0.229138 | + | 0.705216i | ||||
\(900\) | 1.90484 | − | 1.38395i | 0.0634946 | − | 0.0461315i | ||||
\(901\) | 16.1217 | 0.537091 | ||||||||
\(902\) | −20.7802 | − | 24.5413i | −0.691904 | − | 0.817137i | ||||
\(903\) | −3.21506 | −0.106990 | ||||||||
\(904\) | −9.67309 | + | 7.02791i | −0.321722 | + | 0.233745i | ||||
\(905\) | −7.00658 | − | 21.5640i | −0.232907 | − | 0.716813i | ||||
\(906\) | −5.10741 | + | 15.7190i | −0.169682 | + | 0.522228i | ||||
\(907\) | −3.92055 | − | 2.84844i | −0.130180 | − | 0.0945810i | 0.520790 | − | 0.853685i | \(-0.325637\pi\) |
−0.650970 | + | 0.759104i | \(0.725637\pi\) | |||||||
\(908\) | 0.147988 | + | 0.107520i | 0.00491117 | + | 0.00356817i | ||||
\(909\) | 7.74831 | − | 23.8469i | 0.256995 | − | 0.790950i | ||||
\(910\) | 0.816775 | + | 2.51377i | 0.0270758 | + | 0.0833308i | ||||
\(911\) | −48.2638 | + | 35.0657i | −1.59905 | + | 1.16178i | −0.709749 | + | 0.704455i | \(0.751192\pi\) |
−0.889301 | + | 0.457323i | \(0.848808\pi\) | |||||||
\(912\) | −1.53406 | −0.0507978 | ||||||||
\(913\) | −29.0625 | − | 34.3228i | −0.961830 | − | 1.13592i | ||||
\(914\) | −9.98796 | −0.330372 | ||||||||
\(915\) | 8.62065 | − | 6.26327i | 0.284990 | − | 0.207057i | ||||
\(916\) | −0.0415230 | − | 0.127795i | −0.00137196 | − | 0.00422246i | ||||
\(917\) | 2.62642 | − | 8.08329i | 0.0867321 | − | 0.266934i | ||||
\(918\) | −5.58420 | − | 4.05716i | −0.184306 | − | 0.133906i | ||||
\(919\) | 13.6856 | + | 9.94317i | 0.451446 | + | 0.327995i | 0.790167 | − | 0.612892i | \(-0.209994\pi\) |
−0.338720 | + | 0.940887i | \(0.609994\pi\) | |||||||
\(920\) | −1.30688 | + | 4.02217i | −0.0430866 | + | 0.132607i | ||||
\(921\) | 6.15819 | + | 18.9530i | 0.202919 | + | 0.624521i | ||||
\(922\) | −22.5067 | + | 16.3521i | −0.741220 | + | 0.538528i | ||||
\(923\) | −12.1185 | −0.398885 | ||||||||
\(924\) | −1.40194 | + | 2.26605i | −0.0461206 | + | 0.0745474i | ||||
\(925\) | −5.60877 | −0.184415 | ||||||||
\(926\) | 8.31079 | − | 6.03815i | 0.273110 | − | 0.198426i | ||||
\(927\) | 4.99607 | + | 15.3763i | 0.164092 | + | 0.505024i | ||||
\(928\) | 2.77477 | − | 8.53988i | 0.0910864 | − | 0.280335i | ||||
\(929\) | −19.4102 | − | 14.1024i | −0.636829 | − | 0.462683i | 0.221931 | − | 0.975062i | \(-0.428764\pi\) |
−0.858759 | + | 0.512379i | \(0.828764\pi\) | |||||||
\(930\) | 1.60936 | + | 1.16927i | 0.0527730 | + | 0.0383418i | ||||
\(931\) | 0.590037 | − | 1.81595i | 0.0193377 | − | 0.0595153i | ||||
\(932\) | −0.905450 | − | 2.78669i | −0.0296590 | − | 0.0912810i | ||||
\(933\) | 16.7711 | − | 12.1849i | 0.549060 | − | 0.398915i | ||||
\(934\) | 9.03790 | 0.295729 | ||||||||
\(935\) | −0.394924 | − | 5.30684i | −0.0129154 | − | 0.173552i | ||||
\(936\) | 6.22329 | 0.203415 | ||||||||
\(937\) | −24.6885 | + | 17.9373i | −0.806539 | + | 0.585985i | −0.912825 | − | 0.408351i | \(-0.866104\pi\) |
0.106286 | + | 0.994336i | \(0.466104\pi\) | |||||||
\(938\) | 3.24559 | + | 9.98890i | 0.105972 | + | 0.326149i | ||||
\(939\) | −4.09850 | + | 12.6139i | −0.133750 | + | 0.411639i | ||||
\(940\) | 5.29503 | + | 3.84707i | 0.172705 | + | 0.125478i | ||||
\(941\) | −14.2918 | − | 10.3836i | −0.465898 | − | 0.338495i | 0.329942 | − | 0.944001i | \(-0.392971\pi\) |
−0.795841 | + | 0.605506i | \(0.792971\pi\) | |||||||
\(942\) | 1.15418 | − | 3.55221i | 0.0376053 | − | 0.115737i | ||||
\(943\) | 12.6712 | + | 38.9981i | 0.412633 | + | 1.26995i | ||||
\(944\) | −3.37088 | + | 2.44909i | −0.109713 | + | 0.0797109i | ||||
\(945\) | −4.30195 | −0.139942 | ||||||||
\(946\) | −12.2833 | + | 5.02675i | −0.399366 | + | 0.163434i | ||||
\(947\) | 4.02455 | 0.130780 | 0.0653902 | − | 0.997860i | \(-0.479171\pi\) | ||||
0.0653902 | + | 0.997860i | \(0.479171\pi\) | |||||||
\(948\) | −9.06579 | + | 6.58669i | −0.294443 | + | 0.213926i | ||||
\(949\) | −3.01629 | − | 9.28318i | −0.0979128 | − | 0.301345i | ||||
\(950\) | 0.590037 | − | 1.81595i | 0.0191433 | − | 0.0589171i | ||||
\(951\) | 1.51501 | + | 1.10072i | 0.0491276 | + | 0.0356933i | ||||
\(952\) | 1.29806 | + | 0.943099i | 0.0420705 | + | 0.0305660i | ||||
\(953\) | −15.9308 | + | 49.0300i | −0.516049 | + | 1.58824i | 0.265316 | + | 0.964162i | \(0.414524\pi\) |
−0.781365 | + | 0.624075i | \(0.785476\pi\) | |||||||
\(954\) | −7.31062 | − | 22.4998i | −0.236690 | − | 0.728457i | ||||
\(955\) | 6.86567 | − | 4.98820i | 0.222168 | − | 0.161414i | ||||
\(956\) | 8.27410 | 0.267604 | ||||||||
\(957\) | 23.2418 | + | 5.68466i | 0.751302 | + | 0.183759i | ||||
\(958\) | −39.4300 | −1.27392 | ||||||||
\(959\) | 8.15058 | − | 5.92174i | 0.263196 | − | 0.191223i | ||||
\(960\) | −0.248272 | − | 0.764103i | −0.00801294 | − | 0.0246613i | ||||
\(961\) | −7.68508 | + | 23.6522i | −0.247906 | + | 0.762975i | ||||
\(962\) | −11.9935 | − | 8.71377i | −0.386685 | − | 0.280943i | ||||
\(963\) | −5.49108 | − | 3.98950i | −0.176947 | − | 0.128560i | ||||
\(964\) | 5.12481 | − | 15.7725i | 0.165059 | − | 0.508000i | ||||
\(965\) | −7.77420 | − | 23.9265i | −0.250260 | − | 0.770222i | ||||
\(966\) | 2.74889 | − | 1.99718i | 0.0884440 | − | 0.0642583i | ||||
\(967\) | 25.3238 | 0.814359 | 0.407179 | − | 0.913348i | \(-0.366512\pi\) | ||||
0.407179 | + | 0.913348i | \(0.366512\pi\) | |||||||
\(968\) | −1.81325 | + | 10.8495i | −0.0582802 | + | 0.348717i | ||||
\(969\) | −2.46139 | −0.0790713 | ||||||||
\(970\) | 14.1345 | − | 10.2693i | 0.453833 | − | 0.329729i | ||||
\(971\) | −12.7509 | − | 39.2431i | −0.409195 | − | 1.25937i | −0.917341 | − | 0.398102i | \(-0.869669\pi\) |
0.508146 | − | 0.861271i | \(-0.330331\pi\) | |||||||
\(972\) | −4.88370 | + | 15.0305i | −0.156645 | + | 0.482103i | ||||
\(973\) | 11.1807 | + | 8.12322i | 0.358435 | + | 0.260418i | ||||
\(974\) | 15.3054 | + | 11.1201i | 0.490418 | + | 0.356309i | ||||
\(975\) | 0.656217 | − | 2.01963i | 0.0210158 | − | 0.0646799i | ||||
\(976\) | 4.09845 | + | 12.6137i | 0.131188 | + | 0.403756i | ||||
\(977\) | −11.3840 | + | 8.27097i | −0.364207 | + | 0.264612i | −0.754805 | − | 0.655950i | \(-0.772268\pi\) |
0.390598 | + | 0.920561i | \(0.372268\pi\) | |||||||
\(978\) | −4.01230 | −0.128299 | ||||||||
\(979\) | 10.9862 | + | 2.68708i | 0.351119 | + | 0.0858794i | ||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −35.2277 | + | 25.5944i | −1.12473 | + | 0.817167i | ||||
\(982\) | −0.469465 | − | 1.44487i | −0.0149812 | − | 0.0461075i | ||||
\(983\) | 15.8842 | − | 48.8867i | 0.506629 | − | 1.55924i | −0.291386 | − | 0.956605i | \(-0.594117\pi\) |
0.798015 | − | 0.602637i | \(-0.205883\pi\) | |||||||
\(984\) | −6.30212 | − | 4.57875i | −0.200904 | − | 0.145965i | ||||
\(985\) | 10.7278 | + | 7.79421i | 0.341816 | + | 0.248344i | ||||
\(986\) | 4.45211 | − | 13.7022i | 0.141784 | − | 0.436367i | ||||
\(987\) | −1.62495 | − | 5.00107i | −0.0517226 | − | 0.159186i | ||||
\(988\) | 4.08295 | − | 2.96644i | 0.129896 | − | 0.0943750i | ||||
\(989\) | 16.9238 | 0.538145 | ||||||||
\(990\) | −7.22725 | + | 2.95763i | −0.229697 | + | 0.0939997i | ||||
\(991\) | 45.9460 | 1.45952 | 0.729761 | − | 0.683702i | \(-0.239631\pi\) | ||||
0.729761 | + | 0.683702i | \(0.239631\pi\) | |||||||
\(992\) | −2.00312 | + | 1.45536i | −0.0635993 | + | 0.0462076i | ||||
\(993\) | −1.62472 | − | 5.00037i | −0.0515589 | − | 0.158682i | ||||
\(994\) | −1.41681 | + | 4.36049i | −0.0449384 | + | 0.138306i | ||||
\(995\) | −2.91095 | − | 2.11493i | −0.0922833 | − | 0.0670477i | ||||
\(996\) | −8.81395 | − | 6.40371i | −0.279281 | − | 0.202909i | ||||
\(997\) | 3.77275 | − | 11.6113i | 0.119484 | − | 0.367734i | −0.873372 | − | 0.487054i | \(-0.838071\pi\) |
0.992856 | + | 0.119320i | \(0.0380714\pi\) | |||||||
\(998\) | 3.65173 | + | 11.2389i | 0.115593 | + | 0.355760i | ||||
\(999\) | 19.5205 | − | 14.1824i | 0.617600 | − | 0.448713i |
(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 | 770.2.n.g.421.2 | ✓ | 12 | |
11.2 | odd | 10 | 8470.2.a.cv.1.3 | 6 | |||
11.4 | even | 5 | inner | 770.2.n.g.631.2 | yes | 12 | |
11.9 | even | 5 | 8470.2.a.db.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.g.421.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
770.2.n.g.631.2 | yes | 12 | 11.4 | even | 5 | inner | |
8470.2.a.cv.1.3 | 6 | 11.2 | odd | 10 | |||
8470.2.a.db.1.3 | 6 | 11.9 | even | 5 |