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: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.682515625.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 \) |
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 | 421.1 | ||
Root | \(-0.390899 - 1.20306i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.421 |
Dual form | 770.2.n.e.631.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(1\) |
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 | ||||
\(3\) | −0.632489 | − | 1.94660i | −0.365167 | − | 1.12387i | −0.949876 | − | 0.312626i | \(-0.898791\pi\) |
0.584709 | − | 0.811243i | \(-0.301209\pi\) | |||||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 0.809017 | + | 0.587785i | 0.361803 | + | 0.262866i | ||||
\(6\) | −1.65588 | − | 1.20306i | −0.676009 | − | 0.491149i | ||||
\(7\) | −0.309017 | + | 0.951057i | −0.116797 | + | 0.359466i | ||||
\(8\) | −0.309017 | − | 0.951057i | −0.109254 | − | 0.336249i | ||||
\(9\) | −0.962157 | + | 0.699048i | −0.320719 | + | 0.233016i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −2.40640 | − | 2.28238i | −0.725557 | − | 0.688162i | ||||
\(12\) | −2.04678 | −0.590853 | ||||||||
\(13\) | 2.83240 | − | 2.05786i | 0.785568 | − | 0.570748i | −0.121077 | − | 0.992643i | \(-0.538635\pi\) |
0.906645 | + | 0.421895i | \(0.138635\pi\) | |||||||
\(14\) | 0.309017 | + | 0.951057i | 0.0825883 | + | 0.254181i | ||||
\(15\) | 0.632489 | − | 1.94660i | 0.163308 | − | 0.502610i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −3.46489 | − | 2.51739i | −0.840360 | − | 0.610557i | 0.0821111 | − | 0.996623i | \(-0.473834\pi\) |
−0.922471 | + | 0.386066i | \(0.873834\pi\) | |||||||
\(18\) | −0.367511 | + | 1.13108i | −0.0866233 | + | 0.266599i | ||||
\(19\) | −1.37408 | − | 4.22898i | −0.315235 | − | 0.970194i | −0.975658 | − | 0.219300i | \(-0.929623\pi\) |
0.660423 | − | 0.750894i | \(-0.270377\pi\) | |||||||
\(20\) | 0.809017 | − | 0.587785i | 0.180902 | − | 0.131433i | ||||
\(21\) | 2.04678 | 0.446643 | ||||||||
\(22\) | −3.28837 | − | 0.432036i | −0.701082 | − | 0.0921103i | ||||
\(23\) | −2.00000 | −0.417029 | −0.208514 | − | 0.978019i | \(-0.566863\pi\) | ||||
−0.208514 | + | 0.978019i | \(0.566863\pi\) | |||||||
\(24\) | −1.65588 | + | 1.20306i | −0.338004 | + | 0.245575i | ||||
\(25\) | 0.309017 | + | 0.951057i | 0.0618034 | + | 0.190211i | ||||
\(26\) | 1.08188 | − | 3.32969i | 0.212175 | − | 0.653006i | ||||
\(27\) | −2.99831 | − | 2.17840i | −0.577025 | − | 0.419233i | ||||
\(28\) | 0.809017 | + | 0.587785i | 0.152890 | + | 0.111081i | ||||
\(29\) | −0.403663 | + | 1.24235i | −0.0749583 | + | 0.230698i | −0.981515 | − | 0.191387i | \(-0.938702\pi\) |
0.906556 | + | 0.422085i | \(0.138702\pi\) | |||||||
\(30\) | −0.632489 | − | 1.94660i | −0.115476 | − | 0.355399i | ||||
\(31\) | 4.61803 | − | 3.35520i | 0.829423 | − | 0.602611i | −0.0899727 | − | 0.995944i | \(-0.528678\pi\) |
0.919396 | + | 0.393333i | \(0.128678\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.92085 | + | 6.12787i | −0.508455 | + | 1.06673i | ||||
\(34\) | −4.28284 | −0.734502 | ||||||||
\(35\) | −0.809017 | + | 0.587785i | −0.136749 | + | 0.0993538i | ||||
\(36\) | 0.367511 | + | 1.13108i | 0.0612519 | + | 0.188514i | ||||
\(37\) | −0.101212 | + | 0.311499i | −0.0166392 | + | 0.0512102i | −0.959031 | − | 0.283300i | \(-0.908571\pi\) |
0.942392 | + | 0.334510i | \(0.108571\pi\) | |||||||
\(38\) | −3.59738 | − | 2.61365i | −0.583572 | − | 0.423990i | ||||
\(39\) | −5.79730 | − | 4.21198i | −0.928311 | − | 0.674457i | ||||
\(40\) | 0.309017 | − | 0.951057i | 0.0488599 | − | 0.150375i | ||||
\(41\) | 1.19755 | + | 3.68568i | 0.187026 | + | 0.575606i | 0.999977 | − | 0.00672509i | \(-0.00214068\pi\) |
−0.812952 | + | 0.582331i | \(0.802141\pi\) | |||||||
\(42\) | 1.65588 | − | 1.20306i | 0.255507 | − | 0.185637i | ||||
\(43\) | 2.63928 | 0.402487 | 0.201243 | − | 0.979541i | \(-0.435502\pi\) | ||||
0.201243 | + | 0.979541i | \(0.435502\pi\) | |||||||
\(44\) | −2.91429 | + | 1.58333i | −0.439345 | + | 0.238696i | ||||
\(45\) | −1.18929 | −0.177289 | ||||||||
\(46\) | −1.61803 | + | 1.17557i | −0.238566 | + | 0.173328i | ||||
\(47\) | 3.77797 | + | 11.6274i | 0.551073 | + | 1.69603i | 0.706094 | + | 0.708118i | \(0.250456\pi\) |
−0.155021 | + | 0.987911i | \(0.549544\pi\) | |||||||
\(48\) | −0.632489 | + | 1.94660i | −0.0912919 | + | 0.280967i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | 0.809017 | + | 0.587785i | 0.114412 | + | 0.0831254i | ||||
\(51\) | −2.70885 | + | 8.33698i | −0.379315 | + | 1.16741i | ||||
\(52\) | −1.08188 | − | 3.32969i | −0.150030 | − | 0.461745i | ||||
\(53\) | −0.883011 | + | 0.641545i | −0.121291 | + | 0.0881230i | −0.646777 | − | 0.762679i | \(-0.723884\pi\) |
0.525486 | + | 0.850802i | \(0.323884\pi\) | |||||||
\(54\) | −3.70611 | −0.504338 | ||||||||
\(55\) | −0.605270 | − | 3.26093i | −0.0816146 | − | 0.439703i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −7.36304 | + | 5.34956i | −0.975258 | + | 0.708566i | ||||
\(58\) | 0.403663 | + | 1.24235i | 0.0530035 | + | 0.163128i | ||||
\(59\) | 3.10910 | − | 9.56883i | 0.404770 | − | 1.24576i | −0.516316 | − | 0.856398i | \(-0.672697\pi\) |
0.921087 | − | 0.389357i | \(-0.127303\pi\) | |||||||
\(60\) | −1.65588 | − | 1.20306i | −0.213773 | − | 0.155315i | ||||
\(61\) | 10.5189 | + | 7.64244i | 1.34681 | + | 0.978514i | 0.999164 | + | 0.0408875i | \(0.0130185\pi\) |
0.347645 | + | 0.937626i | \(0.386981\pi\) | |||||||
\(62\) | 1.76393 | − | 5.42882i | 0.224020 | − | 0.689461i | ||||
\(63\) | −0.367511 | − | 1.13108i | −0.0463021 | − | 0.142503i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 3.50105 | 0.434251 | ||||||||
\(66\) | 1.23885 | + | 6.67439i | 0.152492 | + | 0.821560i | ||||
\(67\) | −8.44661 | −1.03192 | −0.515959 | − | 0.856613i | \(-0.672564\pi\) | ||||
−0.515959 | + | 0.856613i | \(0.672564\pi\) | |||||||
\(68\) | −3.46489 | + | 2.51739i | −0.420180 | + | 0.305279i | ||||
\(69\) | 1.26498 | + | 3.89320i | 0.152285 | + | 0.468686i | ||||
\(70\) | −0.309017 | + | 0.951057i | −0.0369346 | + | 0.113673i | ||||
\(71\) | 4.75672 | + | 3.45596i | 0.564519 | + | 0.410147i | 0.833110 | − | 0.553107i | \(-0.186558\pi\) |
−0.268591 | + | 0.963254i | \(0.586558\pi\) | |||||||
\(72\) | 0.962157 | + | 0.699048i | 0.113391 | + | 0.0823836i | ||||
\(73\) | 2.29967 | − | 7.07764i | 0.269156 | − | 0.828375i | −0.721551 | − | 0.692361i | \(-0.756571\pi\) |
0.990707 | − | 0.136015i | \(-0.0434294\pi\) | |||||||
\(74\) | 0.101212 | + | 0.311499i | 0.0117657 | + | 0.0362111i | ||||
\(75\) | 1.65588 | − | 1.20306i | 0.191204 | − | 0.138918i | ||||
\(76\) | −4.44661 | −0.510061 | ||||||||
\(77\) | 2.91429 | − | 1.58333i | 0.332114 | − | 0.180437i | ||||
\(78\) | −7.16586 | −0.811373 | ||||||||
\(79\) | 0.403663 | − | 0.293278i | 0.0454156 | − | 0.0329964i | −0.564846 | − | 0.825196i | \(-0.691064\pi\) |
0.610261 | + | 0.792200i | \(0.291064\pi\) | |||||||
\(80\) | −0.309017 | − | 0.951057i | −0.0345492 | − | 0.106331i | ||||
\(81\) | −3.44661 | + | 10.6076i | −0.382957 | + | 1.17862i | ||||
\(82\) | 3.13522 | + | 2.27787i | 0.346228 | + | 0.251549i | ||||
\(83\) | −10.2037 | − | 7.41342i | −1.12000 | − | 0.813729i | −0.135792 | − | 0.990737i | \(-0.543358\pi\) |
−0.984209 | + | 0.177009i | \(0.943358\pi\) | |||||||
\(84\) | 0.632489 | − | 1.94660i | 0.0690102 | − | 0.212391i | ||||
\(85\) | −1.32347 | − | 4.07323i | −0.143551 | − | 0.441803i | ||||
\(86\) | 2.13522 | − | 1.55133i | 0.230247 | − | 0.167284i | ||||
\(87\) | 2.67366 | 0.286647 | ||||||||
\(88\) | −1.42705 | + | 2.99391i | −0.152124 | + | 0.319152i | ||||
\(89\) | 1.39645 | 0.148023 | 0.0740117 | − | 0.997257i | \(-0.476420\pi\) | ||||
0.0740117 | + | 0.997257i | \(0.476420\pi\) | |||||||
\(90\) | −0.962157 | + | 0.699048i | −0.101420 | + | 0.0736862i | ||||
\(91\) | 1.08188 | + | 3.32969i | 0.113412 | + | 0.349047i | ||||
\(92\) | −0.618034 | + | 1.90211i | −0.0644345 | + | 0.198309i | ||||
\(93\) | −9.45208 | − | 6.86734i | −0.980135 | − | 0.712110i | ||||
\(94\) | 9.89085 | + | 7.18612i | 1.02016 | + | 0.741192i | ||||
\(95\) | 1.37408 | − | 4.22898i | 0.140977 | − | 0.433884i | ||||
\(96\) | 0.632489 | + | 1.94660i | 0.0645531 | + | 0.198674i | ||||
\(97\) | 7.92705 | − | 5.75934i | 0.804870 | − | 0.584772i | −0.107469 | − | 0.994208i | \(-0.534275\pi\) |
0.912339 | + | 0.409436i | \(0.134275\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 3.91083 | + | 0.513816i | 0.393053 | + | 0.0516405i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 14.0667 | − | 10.2201i | 1.39969 | − | 1.01694i | 0.404970 | − | 0.914330i | \(-0.367282\pi\) |
0.994722 | − | 0.102606i | \(-0.0327181\pi\) | |||||||
\(102\) | 2.70885 | + | 8.33698i | 0.268216 | + | 0.825484i | ||||
\(103\) | 2.12291 | − | 6.53364i | 0.209176 | − | 0.643779i | −0.790340 | − | 0.612669i | \(-0.790096\pi\) |
0.999516 | − | 0.0311098i | \(-0.00990416\pi\) | |||||||
\(104\) | −2.83240 | − | 2.05786i | −0.277740 | − | 0.201790i | ||||
\(105\) | 1.65588 | + | 1.20306i | 0.161597 | + | 0.117407i | ||||
\(106\) | −0.337280 | + | 1.03804i | −0.0327596 | + | 0.100824i | ||||
\(107\) | −0.540856 | − | 1.66458i | −0.0522865 | − | 0.160921i | 0.921504 | − | 0.388370i | \(-0.126962\pi\) |
−0.973790 | + | 0.227448i | \(0.926962\pi\) | |||||||
\(108\) | −2.99831 | + | 2.17840i | −0.288512 | + | 0.209617i | ||||
\(109\) | 5.88436 | 0.563620 | 0.281810 | − | 0.959470i | \(-0.409065\pi\) | ||||
0.281810 | + | 0.959470i | \(0.409065\pi\) | |||||||
\(110\) | −2.40640 | − | 2.28238i | −0.229441 | − | 0.217616i | ||||
\(111\) | 0.670380 | 0.0636297 | ||||||||
\(112\) | 0.809017 | − | 0.587785i | 0.0764449 | − | 0.0555405i | ||||
\(113\) | 5.29282 | + | 16.2896i | 0.497907 | + | 1.53240i | 0.812377 | + | 0.583132i | \(0.198173\pi\) |
−0.314470 | + | 0.949267i | \(0.601827\pi\) | |||||||
\(114\) | −2.81243 | + | 8.65577i | −0.263408 | + | 0.810687i | ||||
\(115\) | −1.61803 | − | 1.17557i | −0.150882 | − | 0.109623i | ||||
\(116\) | 1.05680 | + | 0.767813i | 0.0981217 | + | 0.0712896i | ||||
\(117\) | −1.28667 | + | 3.95998i | −0.118953 | + | 0.366100i | ||||
\(118\) | −3.10910 | − | 9.56883i | −0.286216 | − | 0.880882i | ||||
\(119\) | 3.46489 | − | 2.51739i | 0.317626 | − | 0.230769i | ||||
\(120\) | −2.04678 | −0.186844 | ||||||||
\(121\) | 0.581513 | + | 10.9846i | 0.0528649 | + | 0.998602i | ||||
\(122\) | 13.0021 | 1.17715 | ||||||||
\(123\) | 6.41710 | − | 4.66230i | 0.578611 | − | 0.420385i | ||||
\(124\) | −1.76393 | − | 5.42882i | −0.158406 | − | 0.487523i | ||||
\(125\) | −0.309017 | + | 0.951057i | −0.0276393 | + | 0.0850651i | ||||
\(126\) | −0.962157 | − | 0.699048i | −0.0857158 | − | 0.0622762i | ||||
\(127\) | −8.04339 | − | 5.84387i | −0.713736 | − | 0.518559i | 0.170641 | − | 0.985333i | \(-0.445416\pi\) |
−0.884377 | + | 0.466774i | \(0.845416\pi\) | |||||||
\(128\) | −0.309017 | + | 0.951057i | −0.0273135 | + | 0.0840623i | ||||
\(129\) | −1.66932 | − | 5.13763i | −0.146975 | − | 0.452343i | ||||
\(130\) | 2.83240 | − | 2.05786i | 0.248418 | − | 0.180486i | ||||
\(131\) | 7.65112 | 0.668482 | 0.334241 | − | 0.942488i | \(-0.391520\pi\) | ||||
0.334241 | + | 0.942488i | \(0.391520\pi\) | |||||||
\(132\) | 4.92536 | + | 4.67151i | 0.428698 | + | 0.406603i | ||||
\(133\) | 4.44661 | 0.385570 | ||||||||
\(134\) | −6.83345 | + | 4.96479i | −0.590320 | + | 0.428893i | ||||
\(135\) | −1.14525 | − | 3.52472i | −0.0985676 | − | 0.303360i | ||||
\(136\) | −1.32347 | + | 4.07323i | −0.113487 | + | 0.349276i | ||||
\(137\) | −1.74779 | − | 1.26984i | −0.149323 | − | 0.108490i | 0.510615 | − | 0.859809i | \(-0.329418\pi\) |
−0.659939 | + | 0.751320i | \(0.729418\pi\) | |||||||
\(138\) | 3.31175 | + | 2.40613i | 0.281915 | + | 0.204823i | ||||
\(139\) | 6.52995 | − | 20.0971i | 0.553863 | − | 1.70462i | −0.145062 | − | 0.989423i | \(-0.546338\pi\) |
0.698926 | − | 0.715194i | \(-0.253662\pi\) | |||||||
\(140\) | 0.309017 | + | 0.951057i | 0.0261167 | + | 0.0803789i | ||||
\(141\) | 20.2444 | − | 14.7084i | 1.70488 | − | 1.23867i | ||||
\(142\) | 5.87963 | 0.493408 | ||||||||
\(143\) | −11.5127 | − | 1.51258i | −0.962742 | − | 0.126488i | ||||
\(144\) | 1.18929 | 0.0991077 | ||||||||
\(145\) | −1.05680 | + | 0.767813i | −0.0877627 | + | 0.0637634i | ||||
\(146\) | −2.29967 | − | 7.07764i | −0.190322 | − | 0.585750i | ||||
\(147\) | −0.632489 | + | 1.94660i | −0.0521668 | + | 0.160553i | ||||
\(148\) | 0.264977 | + | 0.192517i | 0.0217810 | + | 0.0158248i | ||||
\(149\) | 12.9515 | + | 9.40980i | 1.06103 | + | 0.770881i | 0.974278 | − | 0.225349i | \(-0.0723522\pi\) |
0.0867488 | + | 0.996230i | \(0.472352\pi\) | |||||||
\(150\) | 0.632489 | − | 1.94660i | 0.0516425 | − | 0.158939i | ||||
\(151\) | 3.99826 | + | 12.3054i | 0.325374 | + | 1.00140i | 0.971272 | + | 0.237974i | \(0.0764832\pi\) |
−0.645898 | + | 0.763424i | \(0.723517\pi\) | |||||||
\(152\) | −3.59738 | + | 2.61365i | −0.291786 | + | 0.211995i | ||||
\(153\) | 5.09355 | 0.411789 | ||||||||
\(154\) | 1.42705 | − | 2.99391i | 0.114995 | − | 0.241257i | ||||
\(155\) | 5.70820 | 0.458494 | ||||||||
\(156\) | −5.79730 | + | 4.21198i | −0.464155 | + | 0.337229i | ||||
\(157\) | 5.71542 | + | 17.5902i | 0.456140 | + | 1.40385i | 0.869792 | + | 0.493419i | \(0.164253\pi\) |
−0.413652 | + | 0.910435i | \(0.635747\pi\) | |||||||
\(158\) | 0.154186 | − | 0.474534i | 0.0122663 | − | 0.0377519i | ||||
\(159\) | 1.80733 | + | 1.31310i | 0.143330 | + | 0.104136i | ||||
\(160\) | −0.809017 | − | 0.587785i | −0.0639584 | − | 0.0464685i | ||||
\(161\) | 0.618034 | − | 1.90211i | 0.0487079 | − | 0.149908i | ||||
\(162\) | 3.44661 | + | 10.6076i | 0.270791 | + | 0.833410i | ||||
\(163\) | −5.28225 | + | 3.83778i | −0.413738 | + | 0.300598i | −0.775113 | − | 0.631822i | \(-0.782307\pi\) |
0.361376 | + | 0.932420i | \(0.382307\pi\) | |||||||
\(164\) | 3.87535 | 0.302614 | ||||||||
\(165\) | −5.96489 | + | 3.24072i | −0.464366 | + | 0.252290i | ||||
\(166\) | −12.6125 | −0.978917 | ||||||||
\(167\) | 9.70820 | − | 7.05342i | 0.751243 | − | 0.545810i | −0.144969 | − | 0.989436i | \(-0.546308\pi\) |
0.896212 | + | 0.443626i | \(0.146308\pi\) | |||||||
\(168\) | −0.632489 | − | 1.94660i | −0.0487976 | − | 0.150183i | ||||
\(169\) | −0.229502 | + | 0.706334i | −0.0176540 | + | 0.0543334i | ||||
\(170\) | −3.46489 | − | 2.51739i | −0.265745 | − | 0.193075i | ||||
\(171\) | 4.27834 | + | 3.10839i | 0.327173 | + | 0.237705i | ||||
\(172\) | 0.815583 | − | 2.51011i | 0.0621876 | − | 0.191394i | ||||
\(173\) | −2.33108 | − | 7.17434i | −0.177229 | − | 0.545455i | 0.822499 | − | 0.568766i | \(-0.192579\pi\) |
−0.999728 | + | 0.0233115i | \(0.992579\pi\) | |||||||
\(174\) | 2.16304 | − | 1.57154i | 0.163980 | − | 0.119138i | ||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0.605270 | + | 3.26093i | 0.0456240 | + | 0.245802i | ||||
\(177\) | −20.5931 | −1.54788 | ||||||||
\(178\) | 1.12975 | − | 0.820813i | 0.0846785 | − | 0.0615225i | ||||
\(179\) | 2.06058 | + | 6.34183i | 0.154015 | + | 0.474010i | 0.998060 | − | 0.0622628i | \(-0.0198317\pi\) |
−0.844044 | + | 0.536273i | \(0.819832\pi\) | |||||||
\(180\) | −0.367511 | + | 1.13108i | −0.0273927 | + | 0.0843060i | ||||
\(181\) | 2.63928 | + | 1.91755i | 0.196176 | + | 0.142530i | 0.681537 | − | 0.731783i | \(-0.261312\pi\) |
−0.485361 | + | 0.874314i | \(0.661312\pi\) | |||||||
\(182\) | 2.83240 | + | 2.05786i | 0.209952 | + | 0.152539i | ||||
\(183\) | 8.22367 | − | 25.3099i | 0.607911 | − | 1.87096i | ||||
\(184\) | 0.618034 | + | 1.90211i | 0.0455621 | + | 0.140226i | ||||
\(185\) | −0.264977 | + | 0.192517i | −0.0194815 | + | 0.0141541i | ||||
\(186\) | −11.6834 | −0.856670 | ||||||||
\(187\) | 2.59228 | + | 13.9660i | 0.189566 | + | 1.02130i | ||||
\(188\) | 12.2258 | 0.891655 | ||||||||
\(189\) | 2.99831 | − | 2.17840i | 0.218095 | − | 0.158455i | ||||
\(190\) | −1.37408 | − | 4.22898i | −0.0996861 | − | 0.306802i | ||||
\(191\) | −4.23460 | + | 13.0328i | −0.306405 | + | 0.943018i | 0.672744 | + | 0.739875i | \(0.265116\pi\) |
−0.979149 | + | 0.203143i | \(0.934884\pi\) | |||||||
\(192\) | 1.65588 | + | 1.20306i | 0.119503 | + | 0.0868237i | ||||
\(193\) | −9.01787 | − | 6.55186i | −0.649120 | − | 0.471613i | 0.213851 | − | 0.976866i | \(-0.431399\pi\) |
−0.862971 | + | 0.505253i | \(0.831399\pi\) | |||||||
\(194\) | 3.02786 | − | 9.31881i | 0.217388 | − | 0.669051i | ||||
\(195\) | −2.21437 | − | 6.81513i | −0.158574 | − | 0.488042i | ||||
\(196\) | −0.809017 | + | 0.587785i | −0.0577869 | + | 0.0419847i | ||||
\(197\) | −3.51254 | −0.250258 | −0.125129 | − | 0.992140i | \(-0.539935\pi\) | ||||
−0.125129 | + | 0.992140i | \(0.539935\pi\) | |||||||
\(198\) | 3.46594 | − | 1.88304i | 0.246314 | − | 0.133822i | ||||
\(199\) | 19.5167 | 1.38350 | 0.691752 | − | 0.722135i | \(-0.256839\pi\) | ||||
0.691752 | + | 0.722135i | \(0.256839\pi\) | |||||||
\(200\) | 0.809017 | − | 0.587785i | 0.0572061 | − | 0.0415627i | ||||
\(201\) | 5.34238 | + | 16.4422i | 0.376823 | + | 1.15974i | ||||
\(202\) | 5.37301 | − | 16.5364i | 0.378044 | − | 1.16350i | ||||
\(203\) | −1.05680 | − | 0.767813i | −0.0741731 | − | 0.0538899i | ||||
\(204\) | 7.09186 | + | 5.15254i | 0.496530 | + | 0.360750i | ||||
\(205\) | −1.19755 | + | 3.68568i | −0.0836405 | + | 0.257419i | ||||
\(206\) | −2.12291 | − | 6.53364i | −0.147910 | − | 0.455220i | ||||
\(207\) | 1.92431 | − | 1.39810i | 0.133749 | − | 0.0971744i | ||||
\(208\) | −3.50105 | −0.242754 | ||||||||
\(209\) | −6.34554 | + | 13.3128i | −0.438930 | + | 0.920863i | ||||
\(210\) | 2.04678 | 0.141241 | ||||||||
\(211\) | 11.6090 | − | 8.43443i | 0.799197 | − | 0.580650i | −0.111482 | − | 0.993766i | \(-0.535560\pi\) |
0.910678 | + | 0.413116i | \(0.135560\pi\) | |||||||
\(212\) | 0.337280 | + | 1.03804i | 0.0231645 | + | 0.0712930i | ||||
\(213\) | 3.71880 | − | 11.4453i | 0.254808 | − | 0.784218i | ||||
\(214\) | −1.41598 | − | 1.02877i | −0.0967943 | − | 0.0703252i | ||||
\(215\) | 2.13522 | + | 1.55133i | 0.145621 | + | 0.105800i | ||||
\(216\) | −1.14525 | + | 3.52472i | −0.0779245 | + | 0.239827i | ||||
\(217\) | 1.76393 | + | 5.42882i | 0.119744 | + | 0.368533i | ||||
\(218\) | 4.76055 | − | 3.45874i | 0.322425 | − | 0.234256i | ||||
\(219\) | −15.2319 | −1.02927 | ||||||||
\(220\) | −3.28837 | − | 0.432036i | −0.221702 | − | 0.0291278i | ||||
\(221\) | −14.9944 | −1.00863 | ||||||||
\(222\) | 0.542349 | − | 0.394039i | 0.0364001 | − | 0.0264462i | ||||
\(223\) | 4.10933 | + | 12.6472i | 0.275181 | + | 0.846920i | 0.989171 | + | 0.146765i | \(0.0468860\pi\) |
−0.713990 | + | 0.700155i | \(0.753114\pi\) | |||||||
\(224\) | 0.309017 | − | 0.951057i | 0.0206471 | − | 0.0635451i | ||||
\(225\) | −0.962157 | − | 0.699048i | −0.0641438 | − | 0.0466032i | ||||
\(226\) | 13.8568 | + | 10.0675i | 0.921740 | + | 0.669683i | ||||
\(227\) | −5.84475 | + | 17.9883i | −0.387930 | + | 1.19392i | 0.546403 | + | 0.837523i | \(0.315997\pi\) |
−0.934333 | + | 0.356402i | \(0.884003\pi\) | |||||||
\(228\) | 2.81243 | + | 8.65577i | 0.186258 | + | 0.573242i | ||||
\(229\) | −3.14799 | + | 2.28715i | −0.208025 | + | 0.151139i | −0.686920 | − | 0.726733i | \(-0.741038\pi\) |
0.478895 | + | 0.877872i | \(0.341038\pi\) | |||||||
\(230\) | −2.00000 | −0.131876 | ||||||||
\(231\) | −4.92536 | − | 4.67151i | −0.324065 | − | 0.307363i | ||||
\(232\) | 1.30628 | 0.0857615 | ||||||||
\(233\) | −5.60189 | + | 4.07001i | −0.366992 | + | 0.266635i | −0.755962 | − | 0.654615i | \(-0.772831\pi\) |
0.388971 | + | 0.921250i | \(0.372831\pi\) | |||||||
\(234\) | 1.28667 | + | 3.95998i | 0.0841125 | + | 0.258872i | ||||
\(235\) | −3.77797 | + | 11.6274i | −0.246448 | + | 0.758487i | ||||
\(236\) | −8.13973 | − | 5.91386i | −0.529851 | − | 0.384960i | ||||
\(237\) | −0.826208 | − | 0.600275i | −0.0536680 | − | 0.0389921i | ||||
\(238\) | 1.32347 | − | 4.07323i | 0.0857879 | − | 0.264028i | ||||
\(239\) | −8.23460 | − | 25.3435i | −0.532652 | − | 1.63934i | −0.748668 | − | 0.662945i | \(-0.769306\pi\) |
0.216015 | − | 0.976390i | \(-0.430694\pi\) | |||||||
\(240\) | −1.65588 | + | 1.20306i | −0.106886 | + | 0.0776575i | ||||
\(241\) | −0.0928140 | −0.00597868 | −0.00298934 | − | 0.999996i | \(-0.500952\pi\) | ||||
−0.00298934 | + | 0.999996i | \(0.500952\pi\) | |||||||
\(242\) | 6.92705 | + | 8.54494i | 0.445288 | + | 0.549289i | ||||
\(243\) | 11.7103 | 0.751216 | ||||||||
\(244\) | 10.5189 | − | 7.64244i | 0.673404 | − | 0.489257i | ||||
\(245\) | −0.309017 | − | 0.951057i | −0.0197424 | − | 0.0607608i | ||||
\(246\) | 2.45112 | − | 7.54376i | 0.156277 | − | 0.480972i | ||||
\(247\) | −12.5946 | − | 9.15051i | −0.801375 | − | 0.582233i | ||||
\(248\) | −4.61803 | − | 3.35520i | −0.293245 | − | 0.213055i | ||||
\(249\) | −7.97724 | + | 24.5514i | −0.505537 | + | 1.55588i | ||||
\(250\) | 0.309017 | + | 0.951057i | 0.0195440 | + | 0.0601501i | ||||
\(251\) | −16.9944 | + | 12.3472i | −1.07268 | + | 0.779347i | −0.976392 | − | 0.216007i | \(-0.930697\pi\) |
−0.0962870 | + | 0.995354i | \(0.530697\pi\) | |||||||
\(252\) | −1.18929 | −0.0749184 | ||||||||
\(253\) | 4.81280 | + | 4.56475i | 0.302578 | + | 0.286984i | ||||
\(254\) | −9.94218 | −0.623828 | ||||||||
\(255\) | −7.09186 | + | 5.15254i | −0.444110 | + | 0.322664i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | −1.30733 | + | 4.02354i | −0.0815488 | + | 0.250981i | −0.983515 | − | 0.180824i | \(-0.942123\pi\) |
0.901967 | + | 0.431806i | \(0.142123\pi\) | |||||||
\(258\) | −4.37033 | − | 3.17523i | −0.272085 | − | 0.197681i | ||||
\(259\) | −0.264977 | − | 0.192517i | −0.0164649 | − | 0.0119624i | ||||
\(260\) | 1.08188 | − | 3.32969i | 0.0670955 | − | 0.206499i | ||||
\(261\) | −0.480073 | − | 1.47751i | −0.0297158 | − | 0.0914558i | ||||
\(262\) | 6.18989 | − | 4.49722i | 0.382413 | − | 0.277839i | ||||
\(263\) | −16.4789 | −1.01613 | −0.508066 | − | 0.861318i | \(-0.669639\pi\) | ||||
−0.508066 | + | 0.861318i | \(0.669639\pi\) | |||||||
\(264\) | 6.73055 | + | 0.884280i | 0.414237 | + | 0.0544237i | ||||
\(265\) | −1.09146 | −0.0670480 | ||||||||
\(266\) | 3.59738 | − | 2.61365i | 0.220570 | − | 0.160253i | ||||
\(267\) | −0.883239 | − | 2.71833i | −0.0540534 | − | 0.166359i | ||||
\(268\) | −2.61015 | + | 8.03320i | −0.159440 | + | 0.490706i | ||||
\(269\) | −16.4108 | − | 11.9231i | −1.00058 | − | 0.726966i | −0.0383697 | − | 0.999264i | \(-0.512216\pi\) |
−0.962213 | + | 0.272298i | \(0.912216\pi\) | |||||||
\(270\) | −2.99831 | − | 2.17840i | −0.182471 | − | 0.132573i | ||||
\(271\) | −4.27811 | + | 13.1667i | −0.259877 | + | 0.799818i | 0.732953 | + | 0.680279i | \(0.238142\pi\) |
−0.992830 | + | 0.119539i | \(0.961858\pi\) | |||||||
\(272\) | 1.32347 | + | 4.07323i | 0.0802473 | + | 0.246976i | ||||
\(273\) | 5.79730 | − | 4.21198i | 0.350868 | − | 0.254921i | ||||
\(274\) | −2.16038 | −0.130513 | ||||||||
\(275\) | 1.42705 | − | 2.99391i | 0.0860544 | − | 0.180540i | ||||
\(276\) | 4.09355 | 0.246403 | ||||||||
\(277\) | −6.87963 | + | 4.99834i | −0.413357 | + | 0.300321i | −0.774959 | − | 0.632011i | \(-0.782230\pi\) |
0.361603 | + | 0.932332i | \(0.382230\pi\) | |||||||
\(278\) | −6.52995 | − | 20.0971i | −0.391641 | − | 1.20535i | ||||
\(279\) | −2.09783 | + | 6.45646i | −0.125594 | + | 0.386538i | ||||
\(280\) | 0.809017 | + | 0.587785i | 0.0483480 | + | 0.0351269i | ||||
\(281\) | 1.66856 | + | 1.21228i | 0.0995380 | + | 0.0723186i | 0.636441 | − | 0.771325i | \(-0.280406\pi\) |
−0.536903 | + | 0.843644i | \(0.680406\pi\) | |||||||
\(282\) | 7.73266 | − | 23.7987i | 0.460473 | − | 1.41719i | ||||
\(283\) | −8.44278 | − | 25.9842i | −0.501871 | − | 1.54460i | −0.805968 | − | 0.591959i | \(-0.798355\pi\) |
0.304097 | − | 0.952641i | \(-0.401645\pi\) | |||||||
\(284\) | 4.75672 | − | 3.45596i | 0.282259 | − | 0.205073i | ||||
\(285\) | −9.10121 | −0.539109 | ||||||||
\(286\) | −10.2031 | + | 5.54330i | −0.603319 | + | 0.327782i | ||||
\(287\) | −3.87535 | −0.228755 | ||||||||
\(288\) | 0.962157 | − | 0.699048i | 0.0566957 | − | 0.0411918i | ||||
\(289\) | 0.414933 | + | 1.27703i | 0.0244078 | + | 0.0751196i | ||||
\(290\) | −0.403663 | + | 1.24235i | −0.0237039 | + | 0.0729531i | ||||
\(291\) | −16.2249 | − | 11.7881i | −0.951120 | − | 0.691029i | ||||
\(292\) | −6.02060 | − | 4.37422i | −0.352329 | − | 0.255982i | ||||
\(293\) | −5.88984 | + | 18.1271i | −0.344088 | + | 1.05899i | 0.617982 | + | 0.786192i | \(0.287950\pi\) |
−0.962070 | + | 0.272802i | \(0.912050\pi\) | |||||||
\(294\) | 0.632489 | + | 1.94660i | 0.0368875 | + | 0.113528i | ||||
\(295\) | 8.13973 | − | 5.91386i | 0.473913 | − | 0.344318i | ||||
\(296\) | 0.327530 | 0.0190373 | ||||||||
\(297\) | 2.24320 | + | 12.0854i | 0.130164 | + | 0.701264i | ||||
\(298\) | 16.0089 | 0.927372 | ||||||||
\(299\) | −5.66481 | + | 4.11573i | −0.327604 | + | 0.238019i | ||||
\(300\) | −0.632489 | − | 1.94660i | −0.0365167 | − | 0.112387i | ||||
\(301\) | −0.815583 | + | 2.51011i | −0.0470094 | + | 0.144680i | ||||
\(302\) | 10.4676 | + | 7.60514i | 0.602342 | + | 0.437627i | ||||
\(303\) | −28.7915 | − | 20.9182i | −1.65403 | − | 1.20172i | ||||
\(304\) | −1.37408 | + | 4.22898i | −0.0788088 | + | 0.242548i | ||||
\(305\) | 4.01787 | + | 12.3657i | 0.230062 | + | 0.708059i | ||||
\(306\) | 4.12077 | − | 2.99391i | 0.235569 | − | 0.171151i | ||||
\(307\) | 27.8834 | 1.59139 | 0.795694 | − | 0.605699i | \(-0.207106\pi\) | ||||
0.795694 | + | 0.605699i | \(0.207106\pi\) | |||||||
\(308\) | −0.605270 | − | 3.26093i | −0.0344885 | − | 0.185809i | ||||
\(309\) | −14.0611 | −0.799908 | ||||||||
\(310\) | 4.61803 | − | 3.35520i | 0.262287 | − | 0.190562i | ||||
\(311\) | 6.49975 | + | 20.0042i | 0.368567 | + | 1.13433i | 0.947717 | + | 0.319112i | \(0.103385\pi\) |
−0.579150 | + | 0.815221i | \(0.696615\pi\) | |||||||
\(312\) | −2.21437 | + | 6.81513i | −0.125364 | + | 0.385831i | ||||
\(313\) | −3.19417 | − | 2.32070i | −0.180545 | − | 0.131174i | 0.493842 | − | 0.869552i | \(-0.335592\pi\) |
−0.674387 | + | 0.738378i | \(0.735592\pi\) | |||||||
\(314\) | 14.9632 | + | 10.8714i | 0.844420 | + | 0.613507i | ||||
\(315\) | 0.367511 | − | 1.13108i | 0.0207069 | − | 0.0637294i | ||||
\(316\) | −0.154186 | − | 0.474534i | −0.00867361 | − | 0.0266946i | ||||
\(317\) | 22.7516 | − | 16.5300i | 1.27786 | − | 0.928417i | 0.278371 | − | 0.960474i | \(-0.410206\pi\) |
0.999486 | + | 0.0320561i | \(0.0102055\pi\) | |||||||
\(318\) | 2.23398 | 0.125275 | ||||||||
\(319\) | 3.80688 | − | 2.06827i | 0.213144 | − | 0.115801i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −2.89819 | + | 2.10566i | −0.161761 | + | 0.117526i | ||||
\(322\) | −0.618034 | − | 1.90211i | −0.0344417 | − | 0.106001i | ||||
\(323\) | −5.88496 | + | 18.1120i | −0.327448 | + | 1.00778i | ||||
\(324\) | 9.02334 | + | 6.55584i | 0.501297 | + | 0.364213i | ||||
\(325\) | 2.83240 | + | 2.05786i | 0.157114 | + | 0.114150i | ||||
\(326\) | −2.01764 | + | 6.20965i | −0.111747 | + | 0.343921i | ||||
\(327\) | −3.72179 | − | 11.4545i | −0.205816 | − | 0.633435i | ||||
\(328\) | 3.13522 | − | 2.27787i | 0.173114 | − | 0.125775i | ||||
\(329\) | −12.2258 | −0.674028 | ||||||||
\(330\) | −2.92085 | + | 6.12787i | −0.160788 | + | 0.337328i | ||||
\(331\) | 30.2738 | 1.66400 | 0.831999 | − | 0.554777i | \(-0.187196\pi\) | ||||
0.831999 | + | 0.554777i | \(0.187196\pi\) | |||||||
\(332\) | −10.2037 | + | 7.41342i | −0.560001 | + | 0.406864i | ||||
\(333\) | −0.120371 | − | 0.370464i | −0.00659629 | − | 0.0203013i | ||||
\(334\) | 3.70820 | − | 11.4127i | 0.202904 | − | 0.624474i | ||||
\(335\) | −6.83345 | − | 4.96479i | −0.373351 | − | 0.271256i | ||||
\(336\) | −1.65588 | − | 1.20306i | −0.0903355 | − | 0.0656326i | ||||
\(337\) | 9.91215 | − | 30.5065i | 0.539949 | − | 1.66179i | −0.192756 | − | 0.981247i | \(-0.561743\pi\) |
0.732705 | − | 0.680546i | \(-0.238257\pi\) | |||||||
\(338\) | 0.229502 | + | 0.706334i | 0.0124832 | + | 0.0384195i | ||||
\(339\) | 28.3617 | − | 20.6060i | 1.54040 | − | 1.11916i | ||||
\(340\) | −4.28284 | −0.232270 | ||||||||
\(341\) | −18.7707 | − | 2.46615i | −1.01649 | − | 0.133549i | ||||
\(342\) | 5.28832 | 0.285959 | ||||||||
\(343\) | 0.809017 | − | 0.587785i | 0.0436828 | − | 0.0317374i | ||||
\(344\) | −0.815583 | − | 2.51011i | −0.0439733 | − | 0.135336i | ||||
\(345\) | −1.26498 | + | 3.89320i | −0.0681041 | + | 0.209603i | ||||
\(346\) | −6.10285 | − | 4.43398i | −0.328091 | − | 0.238372i | ||||
\(347\) | 13.4770 | + | 9.79162i | 0.723484 | + | 0.525642i | 0.887495 | − | 0.460817i | \(-0.152443\pi\) |
−0.164012 | + | 0.986458i | \(0.552443\pi\) | |||||||
\(348\) | 0.826208 | − | 2.54281i | 0.0442894 | − | 0.136309i | ||||
\(349\) | 1.68397 | + | 5.18272i | 0.0901408 | + | 0.277425i | 0.985957 | − | 0.167000i | \(-0.0534080\pi\) |
−0.895816 | + | 0.444425i | \(0.853408\pi\) | |||||||
\(350\) | −0.809017 | + | 0.587785i | −0.0432438 | + | 0.0314184i | ||||
\(351\) | −12.9753 | −0.692569 | ||||||||
\(352\) | 2.40640 | + | 2.28238i | 0.128262 | + | 0.121651i | ||||
\(353\) | 12.9302 | 0.688207 | 0.344104 | − | 0.938932i | \(-0.388183\pi\) | ||||
0.344104 | + | 0.938932i | \(0.388183\pi\) | |||||||
\(354\) | −16.6602 | + | 12.1043i | −0.885480 | + | 0.643339i | ||||
\(355\) | 1.81691 | + | 5.59186i | 0.0964313 | + | 0.296785i | ||||
\(356\) | 0.431527 | − | 1.32810i | 0.0228709 | − | 0.0703894i | ||||
\(357\) | −7.09186 | − | 5.15254i | −0.375341 | − | 0.272701i | ||||
\(358\) | 5.39468 | + | 3.91946i | 0.285118 | + | 0.207150i | ||||
\(359\) | −9.43574 | + | 29.0402i | −0.497999 | + | 1.53268i | 0.314231 | + | 0.949347i | \(0.398253\pi\) |
−0.812230 | + | 0.583337i | \(0.801747\pi\) | |||||||
\(360\) | 0.367511 | + | 1.13108i | 0.0193696 | + | 0.0596134i | ||||
\(361\) | −0.624828 | + | 0.453964i | −0.0328857 | + | 0.0238929i | ||||
\(362\) | 3.26233 | 0.171464 | ||||||||
\(363\) | 21.0149 | − | 8.07962i | 1.10299 | − | 0.424070i | ||||
\(364\) | 3.50105 | 0.183505 | ||||||||
\(365\) | 6.02060 | − | 4.37422i | 0.315133 | − | 0.228957i | ||||
\(366\) | −8.22367 | − | 25.3099i | −0.429858 | − | 1.32297i | ||||
\(367\) | 8.60418 | − | 26.4809i | 0.449134 | − | 1.38229i | −0.428751 | − | 0.903423i | \(-0.641046\pi\) |
0.877885 | − | 0.478871i | \(-0.158954\pi\) | |||||||
\(368\) | 1.61803 | + | 1.17557i | 0.0843459 | + | 0.0612808i | ||||
\(369\) | −3.72870 | − | 2.70906i | −0.194108 | − | 0.141028i | ||||
\(370\) | −0.101212 | + | 0.311499i | −0.00526177 | + | 0.0161941i | ||||
\(371\) | −0.337280 | − | 1.03804i | −0.0175107 | − | 0.0538924i | ||||
\(372\) | −9.45208 | + | 6.86734i | −0.490068 | + | 0.356055i | ||||
\(373\) | 14.5146 | 0.751539 | 0.375770 | − | 0.926713i | \(-0.377378\pi\) | ||||
0.375770 | + | 0.926713i | \(0.377378\pi\) | |||||||
\(374\) | 10.3062 | + | 9.77506i | 0.532923 | + | 0.505456i | ||||
\(375\) | 2.04678 | 0.105695 | ||||||||
\(376\) | 9.89085 | − | 7.18612i | 0.510082 | − | 0.370596i | ||||
\(377\) | 1.41324 | + | 4.34951i | 0.0727857 | + | 0.224011i | ||||
\(378\) | 1.14525 | − | 3.52472i | 0.0589054 | − | 0.181292i | ||||
\(379\) | 9.64411 | + | 7.00686i | 0.495385 | + | 0.359918i | 0.807251 | − | 0.590208i | \(-0.200954\pi\) |
−0.311867 | + | 0.950126i | \(0.600954\pi\) | |||||||
\(380\) | −3.59738 | − | 2.61365i | −0.184542 | − | 0.134077i | ||||
\(381\) | −6.28832 | + | 19.3534i | −0.322160 | + | 0.991507i | ||||
\(382\) | 4.23460 | + | 13.0328i | 0.216661 | + | 0.666815i | ||||
\(383\) | −25.7208 | + | 18.6872i | −1.31427 | + | 0.954874i | −0.314286 | + | 0.949328i | \(0.601765\pi\) |
−0.999985 | + | 0.00554556i | \(0.998235\pi\) | |||||||
\(384\) | 2.04678 | 0.104449 | ||||||||
\(385\) | 3.28837 | + | 0.432036i | 0.167591 | + | 0.0220186i | ||||
\(386\) | −11.1467 | −0.567352 | ||||||||
\(387\) | −2.53941 | + | 1.84499i | −0.129085 | + | 0.0937859i | ||||
\(388\) | −3.02786 | − | 9.31881i | −0.153717 | − | 0.473091i | ||||
\(389\) | 0.937276 | − | 2.88464i | 0.0475218 | − | 0.146257i | −0.924480 | − | 0.381231i | \(-0.875500\pi\) |
0.972002 | + | 0.234974i | \(0.0755004\pi\) | |||||||
\(390\) | −5.79730 | − | 4.21198i | −0.293558 | − | 0.213282i | ||||
\(391\) | 6.92979 | + | 5.03479i | 0.350454 | + | 0.254620i | ||||
\(392\) | −0.309017 | + | 0.951057i | −0.0156077 | + | 0.0480356i | ||||
\(393\) | −4.83925 | − | 14.8937i | −0.244108 | − | 0.751286i | ||||
\(394\) | −2.84171 | + | 2.06462i | −0.143163 | + | 0.104014i | ||||
\(395\) | 0.498955 | 0.0251051 | ||||||||
\(396\) | 1.69718 | − | 3.56064i | 0.0852865 | − | 0.178929i | ||||
\(397\) | −28.8927 | −1.45008 | −0.725041 | − | 0.688706i | \(-0.758179\pi\) | ||||
−0.725041 | + | 0.688706i | \(0.758179\pi\) | |||||||
\(398\) | 15.7894 | − | 11.4716i | 0.791449 | − | 0.575021i | ||||
\(399\) | −2.81243 | − | 8.65577i | −0.140798 | − | 0.433330i | ||||
\(400\) | 0.309017 | − | 0.951057i | 0.0154508 | − | 0.0475528i | ||||
\(401\) | −29.3557 | − | 21.3282i | −1.46595 | − | 1.06508i | −0.981762 | − | 0.190116i | \(-0.939114\pi\) |
−0.484192 | − | 0.874962i | \(-0.660886\pi\) | |||||||
\(402\) | 13.9865 | + | 10.1618i | 0.697585 | + | 0.506825i | ||||
\(403\) | 6.17561 | − | 19.0066i | 0.307629 | − | 0.946784i | ||||
\(404\) | −5.37301 | − | 16.5364i | −0.267317 | − | 0.822718i | ||||
\(405\) | −9.02334 | + | 6.55584i | −0.448373 | + | 0.325762i | ||||
\(406\) | −1.30628 | −0.0648296 | ||||||||
\(407\) | 0.954516 | − | 0.518587i | 0.0473136 | − | 0.0257054i | ||||
\(408\) | 8.76602 | 0.433983 | ||||||||
\(409\) | −4.81071 | + | 3.49518i | −0.237874 | + | 0.172826i | −0.700336 | − | 0.713814i | \(-0.746966\pi\) |
0.462461 | + | 0.886639i | \(0.346966\pi\) | |||||||
\(410\) | 1.19755 | + | 3.68568i | 0.0591427 | + | 0.182023i | ||||
\(411\) | −1.36642 | + | 4.20540i | −0.0674004 | + | 0.207437i | ||||
\(412\) | −5.55785 | − | 4.03801i | −0.273816 | − | 0.198939i | ||||
\(413\) | 8.13973 | + | 5.91386i | 0.400530 | + | 0.291002i | ||||
\(414\) | 0.735023 | − | 2.26217i | 0.0361244 | − | 0.111179i | ||||
\(415\) | −3.89747 | − | 11.9952i | −0.191319 | − | 0.588820i | ||||
\(416\) | −2.83240 | + | 2.05786i | −0.138870 | + | 0.100895i | ||||
\(417\) | −43.2512 | −2.11802 | ||||||||
\(418\) | 2.69140 | + | 14.5001i | 0.131641 | + | 0.709222i | ||||
\(419\) | 7.10047 | 0.346881 | 0.173440 | − | 0.984844i | \(-0.444512\pi\) | ||||
0.173440 | + | 0.984844i | \(0.444512\pi\) | |||||||
\(420\) | 1.65588 | − | 1.20306i | 0.0807985 | − | 0.0587035i | ||||
\(421\) | −6.71987 | − | 20.6816i | −0.327507 | − | 1.00796i | −0.970296 | − | 0.241919i | \(-0.922223\pi\) |
0.642790 | − | 0.766043i | \(-0.277777\pi\) | |||||||
\(422\) | 4.43424 | − | 13.6472i | 0.215856 | − | 0.664335i | ||||
\(423\) | −11.7631 | − | 8.54640i | −0.571942 | − | 0.415540i | ||||
\(424\) | 0.883011 | + | 0.641545i | 0.0428828 | + | 0.0311562i | ||||
\(425\) | 1.32347 | − | 4.07323i | 0.0641978 | − | 0.197581i | ||||
\(426\) | −3.71880 | − | 11.4453i | −0.180176 | − | 0.554526i | ||||
\(427\) | −10.5189 | + | 7.64244i | −0.509046 | + | 0.369843i | ||||
\(428\) | −1.75025 | −0.0846013 | ||||||||
\(429\) | 4.33728 | + | 23.3673i | 0.209406 | + | 1.12819i | ||||
\(430\) | 2.63928 | 0.127278 | ||||||||
\(431\) | 15.2047 | − | 11.0469i | 0.732384 | − | 0.532108i | −0.157933 | − | 0.987450i | \(-0.550483\pi\) |
0.890317 | + | 0.455342i | \(0.150483\pi\) | |||||||
\(432\) | 1.14525 | + | 3.52472i | 0.0551010 | + | 0.169583i | ||||
\(433\) | −10.0272 | + | 30.8606i | −0.481877 | + | 1.48307i | 0.354576 | + | 0.935027i | \(0.384625\pi\) |
−0.836453 | + | 0.548039i | \(0.815375\pi\) | |||||||
\(434\) | 4.61803 | + | 3.35520i | 0.221673 | + | 0.161055i | ||||
\(435\) | 2.16304 | + | 1.57154i | 0.103710 | + | 0.0753496i | ||||
\(436\) | 1.81837 | − | 5.59636i | 0.0870840 | − | 0.268017i | ||||
\(437\) | 2.74816 | + | 8.45795i | 0.131462 | + | 0.404599i | ||||
\(438\) | −12.3228 | + | 8.95306i | −0.588807 | + | 0.427794i | ||||
\(439\) | −17.1535 | −0.818690 | −0.409345 | − | 0.912380i | \(-0.634243\pi\) | ||||
−0.409345 | + | 0.912380i | \(0.634243\pi\) | |||||||
\(440\) | −2.91429 | + | 1.58333i | −0.138933 | + | 0.0754822i | ||||
\(441\) | 1.18929 | 0.0566330 | ||||||||
\(442\) | −12.1307 | + | 8.81350i | −0.577001 | + | 0.419216i | ||||
\(443\) | 1.30980 | + | 4.03116i | 0.0622307 | + | 0.191526i | 0.977338 | − | 0.211683i | \(-0.0678945\pi\) |
−0.915108 | + | 0.403210i | \(0.867895\pi\) | |||||||
\(444\) | 0.207159 | − | 0.637569i | 0.00983132 | − | 0.0302577i | ||||
\(445\) | 1.12975 | + | 0.820813i | 0.0535554 | + | 0.0389103i | ||||
\(446\) | 10.7584 | + | 7.81641i | 0.509423 | + | 0.370118i | ||||
\(447\) | 10.1255 | − | 31.1629i | 0.478918 | − | 1.47396i | ||||
\(448\) | −0.309017 | − | 0.951057i | −0.0145997 | − | 0.0449332i | ||||
\(449\) | −10.6458 | + | 7.73463i | −0.502406 | + | 0.365020i | −0.809935 | − | 0.586519i | \(-0.800498\pi\) |
0.307529 | + | 0.951539i | \(0.400498\pi\) | |||||||
\(450\) | −1.18929 | −0.0560638 | ||||||||
\(451\) | 5.53032 | − | 11.6025i | 0.260413 | − | 0.546339i | ||||
\(452\) | 17.1279 | 0.805630 | ||||||||
\(453\) | 21.4248 | − | 15.5660i | 1.00662 | − | 0.731356i | ||||
\(454\) | 5.84475 | + | 17.9883i | 0.274308 | + | 0.844232i | ||||
\(455\) | −1.08188 | + | 3.32969i | −0.0507194 | + | 0.156098i | ||||
\(456\) | 7.36304 | + | 5.34956i | 0.344806 | + | 0.250516i | ||||
\(457\) | 0.549640 | + | 0.399337i | 0.0257111 | + | 0.0186802i | 0.600567 | − | 0.799575i | \(-0.294942\pi\) |
−0.574855 | + | 0.818255i | \(0.694942\pi\) | |||||||
\(458\) | −1.20242 | + | 3.70068i | −0.0561856 | + | 0.172922i | ||||
\(459\) | 4.90494 | + | 15.0958i | 0.228943 | + | 0.704614i | ||||
\(460\) | −1.61803 | + | 1.17557i | −0.0754412 | + | 0.0548113i | ||||
\(461\) | −33.9310 | −1.58033 | −0.790163 | − | 0.612897i | \(-0.790004\pi\) | ||||
−0.790163 | + | 0.612897i | \(0.790004\pi\) | |||||||
\(462\) | −6.73055 | − | 0.884280i | −0.313133 | − | 0.0411404i | ||||
\(463\) | −8.67985 | −0.403387 | −0.201693 | − | 0.979449i | \(-0.564644\pi\) | ||||
−0.201693 | + | 0.979449i | \(0.564644\pi\) | |||||||
\(464\) | 1.05680 | − | 0.767813i | 0.0490609 | − | 0.0356448i | ||||
\(465\) | −3.61037 | − | 11.1116i | −0.167427 | − | 0.515288i | ||||
\(466\) | −2.13973 | + | 6.58541i | −0.0991211 | + | 0.305063i | ||||
\(467\) | −3.70656 | − | 2.69297i | −0.171519 | − | 0.124616i | 0.498714 | − | 0.866767i | \(-0.333806\pi\) |
−0.670233 | + | 0.742151i | \(0.733806\pi\) | |||||||
\(468\) | 3.36856 | + | 2.44740i | 0.155712 | + | 0.113131i | ||||
\(469\) | 2.61015 | − | 8.03320i | 0.120525 | − | 0.370939i | ||||
\(470\) | 3.77797 | + | 11.6274i | 0.174265 | + | 0.536332i | ||||
\(471\) | 30.6262 | − | 22.2513i | 1.41118 | − | 1.02528i | ||||
\(472\) | −10.0613 | −0.463107 | ||||||||
\(473\) | −6.35117 | − | 6.02384i | −0.292027 | − | 0.276976i | ||||
\(474\) | −1.02125 | −0.0469075 | ||||||||
\(475\) | 3.59738 | − | 2.61365i | 0.165059 | − | 0.119923i | ||||
\(476\) | −1.32347 | − | 4.07323i | −0.0606612 | − | 0.186696i | ||||
\(477\) | 0.401125 | − | 1.23453i | 0.0183662 | − | 0.0565255i | ||||
\(478\) | −21.5585 | − | 15.6631i | −0.986062 | − | 0.716416i | ||||
\(479\) | −31.4651 | − | 22.8607i | −1.43768 | − | 1.04453i | −0.988521 | − | 0.151081i | \(-0.951725\pi\) |
−0.449156 | − | 0.893453i | \(-0.648275\pi\) | |||||||
\(480\) | −0.632489 | + | 1.94660i | −0.0288690 | + | 0.0888497i | ||||
\(481\) | 0.354349 | + | 1.09057i | 0.0161569 | + | 0.0497259i | ||||
\(482\) | −0.0750881 | + | 0.0545547i | −0.00342017 | + | 0.00248490i | ||||
\(483\) | −4.09355 | −0.186263 | ||||||||
\(484\) | 10.6267 | + | 2.84138i | 0.483031 | + | 0.129154i | ||||
\(485\) | 9.79837 | 0.444921 | ||||||||
\(486\) | 9.47383 | − | 6.88314i | 0.429742 | − | 0.312225i | ||||
\(487\) | 6.10595 | + | 18.7922i | 0.276687 | + | 0.851555i | 0.988768 | + | 0.149458i | \(0.0477527\pi\) |
−0.712081 | + | 0.702097i | \(0.752247\pi\) | |||||||
\(488\) | 4.01787 | − | 12.3657i | 0.181880 | − | 0.559770i | ||||
\(489\) | 10.8116 | + | 7.85507i | 0.488916 | + | 0.355219i | ||||
\(490\) | −0.809017 | − | 0.587785i | −0.0365477 | − | 0.0265534i | ||||
\(491\) | −9.48935 | + | 29.2052i | −0.428248 | + | 1.31801i | 0.471601 | + | 0.881812i | \(0.343676\pi\) |
−0.899850 | + | 0.436200i | \(0.856324\pi\) | |||||||
\(492\) | −2.45112 | − | 7.54376i | −0.110505 | − | 0.340099i | ||||
\(493\) | 4.52612 | − | 3.28842i | 0.203846 | − | 0.148103i | ||||
\(494\) | −15.5678 | −0.700427 | ||||||||
\(495\) | 2.86191 | + | 2.71441i | 0.128633 | + | 0.122004i | ||||
\(496\) | −5.70820 | −0.256306 | ||||||||
\(497\) | −4.75672 | + | 3.45596i | −0.213368 | + | 0.155021i | ||||
\(498\) | 7.97724 | + | 24.5514i | 0.357469 | + | 1.10018i | ||||
\(499\) | −5.74711 | + | 17.6878i | −0.257276 | + | 0.791814i | 0.736097 | + | 0.676876i | \(0.236667\pi\) |
−0.993373 | + | 0.114938i | \(0.963333\pi\) | |||||||
\(500\) | 0.809017 | + | 0.587785i | 0.0361803 | + | 0.0262866i | ||||
\(501\) | −19.8705 | − | 14.4368i | −0.887749 | − | 0.644988i | ||||
\(502\) | −6.49129 | + | 19.9782i | −0.289721 | + | 0.891668i | ||||
\(503\) | −0.474891 | − | 1.46156i | −0.0211743 | − | 0.0651679i | 0.939911 | − | 0.341420i | \(-0.110908\pi\) |
−0.961085 | + | 0.276252i | \(0.910908\pi\) | |||||||
\(504\) | −0.962157 | + | 0.699048i | −0.0428579 | + | 0.0311381i | ||||
\(505\) | 17.3874 | 0.773731 | ||||||||
\(506\) | 6.57673 | + | 0.864071i | 0.292371 | + | 0.0384127i | ||||
\(507\) | 1.52011 | 0.0675103 | ||||||||
\(508\) | −8.04339 | + | 5.84387i | −0.356868 | + | 0.259280i | ||||
\(509\) | −5.88639 | − | 18.1165i | −0.260910 | − | 0.802998i | −0.992608 | − | 0.121369i | \(-0.961272\pi\) |
0.731698 | − | 0.681629i | \(-0.238728\pi\) | |||||||
\(510\) | −2.70885 | + | 8.33698i | −0.119950 | + | 0.369168i | ||||
\(511\) | 6.02060 | + | 4.37422i | 0.266336 | + | 0.193504i | ||||
\(512\) | 0.809017 | + | 0.587785i | 0.0357538 | + | 0.0259767i | ||||
\(513\) | −5.09249 | + | 15.6731i | −0.224839 | + | 0.691983i | ||||
\(514\) | 1.30733 | + | 4.02354i | 0.0576637 | + | 0.177471i | ||||
\(515\) | 5.55785 | − | 4.03801i | 0.244908 | − | 0.177936i | ||||
\(516\) | −5.40202 | −0.237811 | ||||||||
\(517\) | 17.4468 | − | 36.6029i | 0.767309 | − | 1.60979i | ||||
\(518\) | −0.327530 | −0.0143908 | ||||||||
\(519\) | −12.4912 | + | 9.07537i | −0.548302 | + | 0.398365i | ||||
\(520\) | −1.08188 | − | 3.32969i | −0.0474437 | − | 0.146017i | ||||
\(521\) | 5.61697 | − | 17.2873i | 0.246084 | − | 0.757368i | −0.749372 | − | 0.662149i | \(-0.769645\pi\) |
0.995456 | − | 0.0952196i | \(-0.0303553\pi\) | |||||||
\(522\) | −1.25685 | − | 0.913153i | −0.0550107 | − | 0.0399676i | ||||
\(523\) | −13.9907 | − | 10.1649i | −0.611772 | − | 0.444478i | 0.238266 | − | 0.971200i | \(-0.423421\pi\) |
−0.850038 | + | 0.526722i | \(0.823421\pi\) | |||||||
\(524\) | 2.36433 | − | 7.27665i | 0.103286 | − | 0.317882i | ||||
\(525\) | 0.632489 | + | 1.94660i | 0.0276041 | + | 0.0849566i | ||||
\(526\) | −13.3317 | + | 9.68605i | −0.581290 | + | 0.422332i | ||||
\(527\) | −24.4473 | −1.06494 | ||||||||
\(528\) | 5.96489 | − | 3.24072i | 0.259589 | − | 0.141034i | ||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | −0.883011 | + | 0.641545i | −0.0383556 | + | 0.0278669i | ||||
\(531\) | 3.69763 | + | 11.3801i | 0.160463 | + | 0.493856i | ||||
\(532\) | 1.37408 | − | 4.22898i | 0.0595738 | − | 0.183349i | ||||
\(533\) | 10.9766 | + | 7.97494i | 0.475448 | + | 0.345433i | ||||
\(534\) | −2.31235 | − | 1.68002i | −0.100065 | − | 0.0727016i | ||||
\(535\) | 0.540856 | − | 1.66458i | 0.0233832 | − | 0.0719662i | ||||
\(536\) | 2.61015 | + | 8.03320i | 0.112741 | + | 0.346981i | ||||
\(537\) | 11.0417 | − | 8.02227i | 0.476485 | − | 0.346186i | ||||
\(538\) | −20.2848 | −0.874541 | ||||||||
\(539\) | 0.605270 | + | 3.26093i | 0.0260708 | + | 0.140458i | ||||
\(540\) | −3.70611 | −0.159486 | ||||||||
\(541\) | 19.8034 | − | 14.3880i | 0.851415 | − | 0.618589i | −0.0741211 | − | 0.997249i | \(-0.523615\pi\) |
0.925536 | + | 0.378660i | \(0.123615\pi\) | |||||||
\(542\) | 4.27811 | + | 13.1667i | 0.183761 | + | 0.565557i | ||||
\(543\) | 2.06339 | − | 6.35046i | 0.0885485 | − | 0.272524i | ||||
\(544\) | 3.46489 | + | 2.51739i | 0.148556 | + | 0.107932i | ||||
\(545\) | 4.76055 | + | 3.45874i | 0.203920 | + | 0.148156i | ||||
\(546\) | 2.21437 | − | 6.81513i | 0.0947663 | − | 0.291661i | ||||
\(547\) | −12.3052 | − | 37.8714i | −0.526131 | − | 1.61926i | −0.762069 | − | 0.647495i | \(-0.775817\pi\) |
0.235939 | − | 0.971768i | \(-0.424183\pi\) | |||||||
\(548\) | −1.74779 | + | 1.26984i | −0.0746617 | + | 0.0542449i | ||||
\(549\) | −15.4633 | −0.659957 | ||||||||
\(550\) | −0.605270 | − | 3.26093i | −0.0258088 | − | 0.139046i | ||||
\(551\) | 5.80852 | 0.247451 | ||||||||
\(552\) | 3.31175 | − | 2.40613i | 0.140958 | − | 0.102412i | ||||
\(553\) | 0.154186 | + | 0.474534i | 0.00655664 | + | 0.0201793i | ||||
\(554\) | −2.62778 | + | 8.08749i | −0.111644 | + | 0.343604i | ||||
\(555\) | 0.542349 | + | 0.394039i | 0.0230214 | + | 0.0167260i | ||||
\(556\) | −17.0956 | − | 12.4207i | −0.725017 | − | 0.526755i | ||||
\(557\) | −7.09355 | + | 21.8317i | −0.300563 | + | 0.925039i | 0.680732 | + | 0.732532i | \(0.261662\pi\) |
−0.981296 | + | 0.192507i | \(0.938338\pi\) | |||||||
\(558\) | 2.09783 | + | 6.45646i | 0.0888082 | + | 0.273324i | ||||
\(559\) | 7.47552 | − | 5.43128i | 0.316181 | − | 0.229719i | ||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 25.5467 | − | 13.8795i | 1.07858 | − | 0.585993i | ||||
\(562\) | 2.06245 | 0.0869994 | ||||||||
\(563\) | −12.8747 | + | 9.35402i | −0.542604 | + | 0.394225i | −0.825051 | − | 0.565058i | \(-0.808854\pi\) |
0.282447 | + | 0.959283i | \(0.408854\pi\) | |||||||
\(564\) | −7.73266 | − | 23.7987i | −0.325604 | − | 1.00210i | ||||
\(565\) | −5.29282 | + | 16.2896i | −0.222671 | + | 0.685310i | ||||
\(566\) | −22.1035 | − | 16.0591i | −0.929079 | − | 0.675015i | ||||
\(567\) | −9.02334 | − | 6.55584i | −0.378945 | − | 0.275319i | ||||
\(568\) | 1.81691 | − | 5.59186i | 0.0762357 | − | 0.234629i | ||||
\(569\) | −5.48037 | − | 16.8669i | −0.229749 | − | 0.707095i | −0.997775 | − | 0.0666761i | \(-0.978761\pi\) |
0.768025 | − | 0.640419i | \(-0.221239\pi\) | |||||||
\(570\) | −7.36304 | + | 5.34956i | −0.308404 | + | 0.224068i | ||||
\(571\) | −1.05280 | −0.0440584 | −0.0220292 | − | 0.999757i | \(-0.507013\pi\) | ||||
−0.0220292 | + | 0.999757i | \(0.507013\pi\) | |||||||
\(572\) | −4.99617 | + | 10.4818i | −0.208900 | + | 0.438267i | ||||
\(573\) | 28.0479 | 1.17172 | ||||||||
\(574\) | −3.13522 | + | 2.27787i | −0.130862 | + | 0.0950766i | ||||
\(575\) | −0.618034 | − | 1.90211i | −0.0257738 | − | 0.0793236i | ||||
\(576\) | 0.367511 | − | 1.13108i | 0.0153130 | − | 0.0471285i | ||||
\(577\) | 10.3734 | + | 7.53674i | 0.431852 | + | 0.313759i | 0.782389 | − | 0.622790i | \(-0.214001\pi\) |
−0.350537 | + | 0.936549i | \(0.614001\pi\) | |||||||
\(578\) | 1.08631 | + | 0.789250i | 0.0451845 | + | 0.0328285i | ||||
\(579\) | −7.05016 | + | 21.6982i | −0.292995 | + | 0.901745i | ||||
\(580\) | 0.403663 | + | 1.24235i | 0.0167612 | + | 0.0515856i | ||||
\(581\) | 10.2037 | − | 7.41342i | 0.423321 | − | 0.307560i | ||||
\(582\) | −20.0551 | −0.831310 | ||||||||
\(583\) | 3.58912 | + | 0.471550i | 0.148646 | + | 0.0195296i | ||||
\(584\) | −7.44187 | −0.307947 | ||||||||
\(585\) | −3.36856 | + | 2.44740i | −0.139273 | + | 0.101188i | ||||
\(586\) | 5.88984 | + | 18.1271i | 0.243307 | + | 0.748822i | ||||
\(587\) | −3.01612 | + | 9.28265i | −0.124488 | + | 0.383136i | −0.993808 | − | 0.111115i | \(-0.964558\pi\) |
0.869319 | + | 0.494251i | \(0.164558\pi\) | |||||||
\(588\) | 1.65588 | + | 1.20306i | 0.0682872 | + | 0.0496136i | ||||
\(589\) | −20.5346 | − | 14.9193i | −0.846113 | − | 0.614737i | ||||
\(590\) | 3.10910 | − | 9.56883i | 0.128000 | − | 0.393942i | ||||
\(591\) | 2.22164 | + | 6.83752i | 0.0913862 | + | 0.281258i | ||||
\(592\) | 0.264977 | − | 0.192517i | 0.0108905 | − | 0.00791241i | ||||
\(593\) | −25.4142 | −1.04364 | −0.521818 | − | 0.853057i | \(-0.674746\pi\) | ||||
−0.521818 | + | 0.853057i | \(0.674746\pi\) | |||||||
\(594\) | 8.91839 | + | 8.45875i | 0.365926 | + | 0.347067i | ||||
\(595\) | 4.28284 | 0.175579 | ||||||||
\(596\) | 12.9515 | − | 9.40980i | 0.530513 | − | 0.385441i | ||||
\(597\) | −12.3441 | − | 37.9912i | −0.505211 | − | 1.55488i | ||||
\(598\) | −2.16376 | + | 6.65938i | −0.0884829 | + | 0.272322i | ||||
\(599\) | 33.4386 | + | 24.2945i | 1.36626 | + | 0.992648i | 0.998019 | + | 0.0629192i | \(0.0200411\pi\) |
0.368244 | + | 0.929729i | \(0.379959\pi\) | |||||||
\(600\) | −1.65588 | − | 1.20306i | −0.0676009 | − | 0.0491149i | ||||
\(601\) | −12.1265 | + | 37.3215i | −0.494650 | + | 1.52238i | 0.322851 | + | 0.946450i | \(0.395359\pi\) |
−0.817501 | + | 0.575927i | \(0.804641\pi\) | |||||||
\(602\) | 0.815583 | + | 2.51011i | 0.0332407 | + | 0.102304i | ||||
\(603\) | 8.12697 | − | 5.90459i | 0.330956 | − | 0.240453i | ||||
\(604\) | 12.9386 | 0.526466 | ||||||||
\(605\) | −5.98614 | + | 9.22855i | −0.243371 | + | 0.375194i | ||||
\(606\) | −35.5882 | −1.44567 | ||||||||
\(607\) | 6.32725 | − | 4.59702i | 0.256815 | − | 0.186587i | −0.451927 | − | 0.892055i | \(-0.649263\pi\) |
0.708742 | + | 0.705468i | \(0.249263\pi\) | |||||||
\(608\) | 1.37408 | + | 4.22898i | 0.0557262 | + | 0.171508i | ||||
\(609\) | −0.826208 | + | 2.54281i | −0.0334796 | + | 0.103040i | ||||
\(610\) | 10.5189 | + | 7.64244i | 0.425898 | + | 0.309433i | ||||
\(611\) | 34.6283 | + | 25.1589i | 1.40091 | + | 1.01782i | ||||
\(612\) | 1.57399 | − | 4.84426i | 0.0636249 | − | 0.195817i | ||||
\(613\) | −0.379876 | − | 1.16914i | −0.0153430 | − | 0.0472210i | 0.943092 | − | 0.332532i | \(-0.107903\pi\) |
−0.958435 | + | 0.285311i | \(0.907903\pi\) | |||||||
\(614\) | 22.5581 | − | 16.3894i | 0.910372 | − | 0.661424i | ||||
\(615\) | 7.93198 | 0.319848 | ||||||||
\(616\) | −2.40640 | − | 2.28238i | −0.0969566 | − | 0.0919596i | ||||
\(617\) | −8.43129 | −0.339431 | −0.169715 | − | 0.985493i | \(-0.554285\pi\) | ||||
−0.169715 | + | 0.985493i | \(0.554285\pi\) | |||||||
\(618\) | −11.3757 | + | 8.26491i | −0.457597 | + | 0.332463i | ||||
\(619\) | 2.22345 | + | 6.84306i | 0.0893678 | + | 0.275046i | 0.985745 | − | 0.168246i | \(-0.0538104\pi\) |
−0.896377 | + | 0.443292i | \(0.853810\pi\) | |||||||
\(620\) | 1.76393 | − | 5.42882i | 0.0708412 | − | 0.218027i | ||||
\(621\) | 5.99662 | + | 4.35680i | 0.240636 | + | 0.174832i | ||||
\(622\) | 17.0166 | + | 12.3633i | 0.682302 | + | 0.495722i | ||||
\(623\) | −0.431527 | + | 1.32810i | −0.0172888 | + | 0.0532093i | ||||
\(624\) | 2.21437 | + | 6.81513i | 0.0886458 | + | 0.272824i | ||||
\(625\) | −0.809017 | + | 0.587785i | −0.0323607 | + | 0.0235114i | ||||
\(626\) | −3.94821 | −0.157802 | ||||||||
\(627\) | 29.9281 | + | 3.93205i | 1.19521 | + | 0.157031i | ||||
\(628\) | 18.4955 | 0.738050 | ||||||||
\(629\) | 1.13486 | − | 0.824521i | 0.0452497 | − | 0.0328758i | ||||
\(630\) | −0.367511 | − | 1.13108i | −0.0146420 | − | 0.0450635i | ||||
\(631\) | 2.83111 | − | 8.71327i | 0.112705 | − | 0.346870i | −0.878757 | − | 0.477270i | \(-0.841626\pi\) |
0.991461 | + | 0.130400i | \(0.0416263\pi\) | |||||||
\(632\) | −0.403663 | − | 0.293278i | −0.0160569 | − | 0.0116660i | ||||
\(633\) | −23.7610 | − | 17.2634i | −0.944416 | − | 0.686158i | ||||
\(634\) | 8.69034 | − | 26.7461i | 0.345137 | − | 1.06222i | ||||
\(635\) | −3.07230 | − | 9.45558i | −0.121921 | − | 0.375233i | ||||
\(636\) | 1.80733 | − | 1.31310i | 0.0716651 | − | 0.0520678i | ||||
\(637\) | −3.50105 | −0.138716 | ||||||||
\(638\) | 1.86413 | − | 3.91089i | 0.0738016 | − | 0.154834i | ||||
\(639\) | −6.99260 | −0.276623 | ||||||||
\(640\) | −0.809017 | + | 0.587785i | −0.0319792 | + | 0.0232343i | ||||
\(641\) | −2.41847 | − | 7.44328i | −0.0955237 | − | 0.293992i | 0.891866 | − | 0.452300i | \(-0.149396\pi\) |
−0.987390 | + | 0.158308i | \(0.949396\pi\) | |||||||
\(642\) | −1.10701 | + | 3.40703i | −0.0436902 | + | 0.134465i | ||||
\(643\) | 34.0742 | + | 24.7564i | 1.34376 | + | 0.976296i | 0.999297 | + | 0.0374945i | \(0.0119377\pi\) |
0.344459 | + | 0.938801i | \(0.388062\pi\) | |||||||
\(644\) | −1.61803 | − | 1.17557i | −0.0637595 | − | 0.0463240i | ||||
\(645\) | 1.66932 | − | 5.13763i | 0.0657293 | − | 0.202294i | ||||
\(646\) | 5.88496 | + | 18.1120i | 0.231541 | + | 0.712609i | ||||
\(647\) | 16.6237 | − | 12.0778i | 0.653545 | − | 0.474828i | −0.210932 | − | 0.977501i | \(-0.567650\pi\) |
0.864477 | + | 0.502673i | \(0.167650\pi\) | |||||||
\(648\) | 11.1535 | 0.438149 | ||||||||
\(649\) | −29.3214 | + | 15.9303i | −1.15097 | + | 0.625318i | ||||
\(650\) | 3.50105 | 0.137322 | ||||||||
\(651\) | 9.45208 | − | 6.86734i | 0.370456 | − | 0.269152i | ||||
\(652\) | 2.01764 | + | 6.20965i | 0.0790168 | + | 0.243189i | ||||
\(653\) | −8.98293 | + | 27.6466i | −0.351529 | + | 1.08190i | 0.606465 | + | 0.795110i | \(0.292587\pi\) |
−0.957995 | + | 0.286786i | \(0.907413\pi\) | |||||||
\(654\) | −9.74378 | − | 7.07927i | −0.381012 | − | 0.276821i | ||||
\(655\) | 6.18989 | + | 4.49722i | 0.241859 | + | 0.175721i | ||||
\(656\) | 1.19755 | − | 3.68568i | 0.0467564 | − | 0.143902i | ||||
\(657\) | 2.73497 | + | 8.41738i | 0.106701 | + | 0.328393i | ||||
\(658\) | −9.89085 | + | 7.18612i | −0.385585 | + | 0.280144i | ||||
\(659\) | −16.3882 | −0.638395 | −0.319198 | − | 0.947688i | \(-0.603413\pi\) | ||||
−0.319198 | + | 0.947688i | \(0.603413\pi\) | |||||||
\(660\) | 1.23885 | + | 6.67439i | 0.0482223 | + | 0.259800i | ||||
\(661\) | 37.7386 | 1.46786 | 0.733932 | − | 0.679223i | \(-0.237683\pi\) | ||||
0.733932 | + | 0.679223i | \(0.237683\pi\) | |||||||
\(662\) | 24.4920 | − | 17.7945i | 0.951909 | − | 0.691602i | ||||
\(663\) | 9.48381 | + | 29.1882i | 0.368320 | + | 1.13357i | ||||
\(664\) | −3.89747 | + | 11.9952i | −0.151251 | + | 0.465503i | ||||
\(665\) | 3.59738 | + | 2.61365i | 0.139500 | + | 0.101353i | ||||
\(666\) | −0.315135 | − | 0.228959i | −0.0122112 | − | 0.00887199i | ||||
\(667\) | 0.807326 | − | 2.48469i | 0.0312598 | − | 0.0962077i | ||||
\(668\) | −3.70820 | − | 11.4127i | −0.143475 | − | 0.441570i | ||||
\(669\) | 22.0200 | − | 15.9984i | 0.851341 | − | 0.618535i | ||||
\(670\) | −8.44661 | −0.326321 | ||||||||
\(671\) | −7.86978 | − | 42.3989i | −0.303810 | − | 1.63679i | ||||
\(672\) | −2.04678 | −0.0789561 | ||||||||
\(673\) | 17.0102 | − | 12.3587i | 0.655697 | − | 0.476392i | −0.209510 | − | 0.977806i | \(-0.567187\pi\) |
0.865207 | + | 0.501415i | \(0.167187\pi\) | |||||||
\(674\) | −9.91215 | − | 30.5065i | −0.381802 | − | 1.17506i | ||||
\(675\) | 1.14525 | − | 3.52472i | 0.0440808 | − | 0.135667i | ||||
\(676\) | 0.600843 | + | 0.436538i | 0.0231094 | + | 0.0167899i | ||||
\(677\) | −5.57572 | − | 4.05099i | −0.214292 | − | 0.155692i | 0.475461 | − | 0.879737i | \(-0.342281\pi\) |
−0.689754 | + | 0.724044i | \(0.742281\pi\) | |||||||
\(678\) | 10.8332 | − | 33.3412i | 0.416047 | − | 1.28046i | ||||
\(679\) | 3.02786 | + | 9.31881i | 0.116199 | + | 0.357623i | ||||
\(680\) | −3.46489 | + | 2.51739i | −0.132873 | + | 0.0965376i | ||||
\(681\) | 38.7127 | 1.48348 | ||||||||
\(682\) | −16.6353 | + | 9.03796i | −0.637000 | + | 0.346081i | ||||
\(683\) | −1.37212 | −0.0525026 | −0.0262513 | − | 0.999655i | \(-0.508357\pi\) | ||||
−0.0262513 | + | 0.999655i | \(0.508357\pi\) | |||||||
\(684\) | 4.27834 | − | 3.10839i | 0.163586 | − | 0.118852i | ||||
\(685\) | −0.667595 | − | 2.05465i | −0.0255075 | − | 0.0785040i | ||||
\(686\) | 0.309017 | − | 0.951057i | 0.0117983 | − | 0.0363115i | ||||
\(687\) | 6.44323 | + | 4.68128i | 0.245824 | + | 0.178602i | ||||
\(688\) | −2.13522 | − | 1.55133i | −0.0814047 | − | 0.0591440i | ||||
\(689\) | −1.18083 | + | 3.63423i | −0.0449862 | + | 0.138453i | ||||
\(690\) | 1.26498 | + | 3.89320i | 0.0481569 | + | 0.148212i | ||||
\(691\) | 7.60212 | − | 5.52326i | 0.289198 | − | 0.210115i | −0.433721 | − | 0.901047i | \(-0.642800\pi\) |
0.722919 | + | 0.690932i | \(0.242800\pi\) | |||||||
\(692\) | −7.54354 | −0.286762 | ||||||||
\(693\) | −1.69718 | + | 3.56064i | −0.0644705 | + | 0.135257i | ||||
\(694\) | 16.6585 | 0.632348 | ||||||||
\(695\) | 17.0956 | − | 12.4207i | 0.648475 | − | 0.471144i | ||||
\(696\) | −0.826208 | − | 2.54281i | −0.0313173 | − | 0.0963848i | ||||
\(697\) | 5.12892 | − | 15.7852i | 0.194272 | − | 0.597906i | ||||
\(698\) | 4.40869 | + | 3.20310i | 0.166871 | + | 0.121239i | ||||
\(699\) | 11.4658 | + | 8.33040i | 0.433677 | + | 0.315085i | ||||
\(700\) | −0.309017 | + | 0.951057i | −0.0116797 | + | 0.0359466i | ||||
\(701\) | −4.18191 | − | 12.8706i | −0.157949 | − | 0.486116i | 0.840499 | − | 0.541813i | \(-0.182262\pi\) |
−0.998448 | + | 0.0556970i | \(0.982262\pi\) | |||||||
\(702\) | −10.4972 | + | 7.62667i | −0.396192 | + | 0.287850i | ||||
\(703\) | 1.45640 | 0.0549290 | ||||||||
\(704\) | 3.28837 | + | 0.432036i | 0.123935 | + | 0.0162830i | ||||
\(705\) | 25.0234 | 0.942436 | ||||||||
\(706\) | 10.4608 | − | 7.60021i | 0.393697 | − | 0.286038i | ||||
\(707\) | 5.37301 | + | 16.5364i | 0.202073 | + | 0.621917i | ||||
\(708\) | −6.36363 | + | 19.5852i | −0.239160 | + | 0.736059i | ||||
\(709\) | 32.5027 | + | 23.6146i | 1.22067 | + | 0.886866i | 0.996155 | − | 0.0876056i | \(-0.0279215\pi\) |
0.224511 | + | 0.974472i | \(0.427922\pi\) | |||||||
\(710\) | 4.75672 | + | 3.45596i | 0.178517 | + | 0.129700i | ||||
\(711\) | −0.183372 | + | 0.564360i | −0.00687697 | + | 0.0211651i | ||||
\(712\) | −0.431527 | − | 1.32810i | −0.0161722 | − | 0.0497728i | ||||
\(713\) | −9.23607 | + | 6.71040i | −0.345893 | + | 0.251306i | ||||
\(714\) | −8.76602 | −0.328060 | ||||||||
\(715\) | −8.42491 | − | 7.99070i | −0.315074 | − | 0.298835i | ||||
\(716\) | 6.66819 | 0.249202 | ||||||||
\(717\) | −44.1254 | + | 32.0590i | −1.64789 | + | 1.19726i | ||||
\(718\) | 9.43574 | + | 29.0402i | 0.352139 | + | 1.08377i | ||||
\(719\) | 4.07405 | − | 12.5386i | 0.151936 | − | 0.467612i | −0.845901 | − | 0.533340i | \(-0.820937\pi\) |
0.997838 | + | 0.0657273i | \(0.0209368\pi\) | |||||||
\(720\) | 0.962157 | + | 0.699048i | 0.0358575 | + | 0.0260520i | ||||
\(721\) | 5.55785 | + | 4.03801i | 0.206985 | + | 0.150383i | ||||
\(722\) | −0.238663 | + | 0.734530i | −0.00888212 | + | 0.0273364i | ||||
\(723\) | 0.0587038 | + | 0.180672i | 0.00218322 | + | 0.00671925i | ||||
\(724\) | 2.63928 | − | 1.91755i | 0.0980882 | − | 0.0712652i | ||||
\(725\) | −1.30628 | −0.0485141 | ||||||||
\(726\) | 12.2523 | − | 18.8888i | 0.454725 | − | 0.701028i | ||||
\(727\) | −40.5403 | −1.50356 | −0.751779 | − | 0.659415i | \(-0.770804\pi\) | ||||
−0.751779 | + | 0.659415i | \(0.770804\pi\) | |||||||
\(728\) | 2.83240 | − | 2.05786i | 0.104976 | − | 0.0762695i | ||||
\(729\) | 2.93320 | + | 9.02746i | 0.108637 | + | 0.334350i | ||||
\(730\) | 2.29967 | − | 7.07764i | 0.0851144 | − | 0.261955i | ||||
\(731\) | −9.14483 | − | 6.64411i | −0.338234 | − | 0.245741i | ||||
\(732\) | −21.5299 | − | 15.6424i | −0.795766 | − | 0.578158i | ||||
\(733\) | −7.07029 | + | 21.7601i | −0.261147 | + | 0.803728i | 0.731409 | + | 0.681939i | \(0.238863\pi\) |
−0.992556 | + | 0.121789i | \(0.961137\pi\) | |||||||
\(734\) | −8.60418 | − | 26.4809i | −0.317586 | − | 0.977429i | ||||
\(735\) | −1.65588 | + | 1.20306i | −0.0610779 | + | 0.0443757i | ||||
\(736\) | 2.00000 | 0.0737210 | ||||||||
\(737\) | 20.3259 | + | 19.2783i | 0.748715 | + | 0.710127i | ||||
\(738\) | −4.60892 | −0.169657 | ||||||||
\(739\) | 24.3545 | − | 17.6945i | 0.895893 | − | 0.650904i | −0.0415148 | − | 0.999138i | \(-0.513218\pi\) |
0.937408 | + | 0.348234i | \(0.113218\pi\) | |||||||
\(740\) | 0.101212 | + | 0.311499i | 0.00372064 | + | 0.0114509i | ||||
\(741\) | −9.84644 | + | 30.3042i | −0.361718 | + | 1.11325i | ||||
\(742\) | −0.883011 | − | 0.641545i | −0.0324164 | − | 0.0235519i | ||||
\(743\) | −23.9999 | − | 17.4369i | −0.880471 | − | 0.639700i | 0.0529050 | − | 0.998600i | \(-0.483152\pi\) |
−0.933376 | + | 0.358900i | \(0.883152\pi\) | |||||||
\(744\) | −3.61037 | + | 11.1116i | −0.132363 | + | 0.407371i | ||||
\(745\) | 4.94703 | + | 15.2254i | 0.181245 | + | 0.557815i | ||||
\(746\) | 11.7426 | − | 8.53149i | 0.429927 | − | 0.312360i | ||||
\(747\) | 14.9999 | 0.548818 | ||||||||
\(748\) | 14.0836 | + | 1.85034i | 0.514946 | + | 0.0676552i | ||||
\(749\) | 1.75025 | 0.0639526 | ||||||||
\(750\) | 1.65588 | − | 1.20306i | 0.0604641 | − | 0.0439297i | ||||
\(751\) | 14.6575 | + | 45.1113i | 0.534861 | + | 1.64613i | 0.743949 | + | 0.668236i | \(0.232951\pi\) |
−0.209088 | + | 0.977897i | \(0.567049\pi\) | |||||||
\(752\) | 3.77797 | − | 11.6274i | 0.137768 | − | 0.424007i | ||||
\(753\) | 34.7838 | + | 25.2719i | 1.26759 | + | 0.920959i | ||||
\(754\) | 3.69992 | + | 2.68815i | 0.134743 | + | 0.0978965i | ||||
\(755\) | −3.99826 | + | 12.3054i | −0.145512 | + | 0.447839i | ||||
\(756\) | −1.14525 | − | 3.52472i | −0.0416524 | − | 0.128193i | ||||
\(757\) | 21.4809 | − | 15.6068i | 0.780736 | − | 0.567238i | −0.124464 | − | 0.992224i | \(-0.539721\pi\) |
0.905200 | + | 0.424986i | \(0.139721\pi\) | |||||||
\(758\) | 11.9208 | 0.432982 | ||||||||
\(759\) | 5.84171 | − | 12.2557i | 0.212041 | − | 0.444855i | ||||
\(760\) | −4.44661 | −0.161295 | ||||||||
\(761\) | 39.4370 | − | 28.6526i | 1.42959 | − | 1.03866i | 0.439496 | − | 0.898245i | \(-0.355157\pi\) |
0.990093 | − | 0.140412i | \(-0.0448428\pi\) | |||||||
\(762\) | 6.28832 | + | 19.3534i | 0.227802 | + | 0.701101i | ||||
\(763\) | −1.81837 | + | 5.59636i | −0.0658294 | + | 0.202602i | ||||
\(764\) | 11.0863 | + | 8.05470i | 0.401090 | + | 0.291409i | ||||
\(765\) | 4.12077 | + | 2.99391i | 0.148987 | + | 0.108245i | ||||
\(766\) | −9.82447 | + | 30.2366i | −0.354972 | + | 1.09249i | ||||
\(767\) | −10.8851 | − | 33.5009i | −0.393038 | − | 1.20965i | ||||
\(768\) | 1.65588 | − | 1.20306i | 0.0597513 | − | 0.0434119i | ||||
\(769\) | −25.8289 | −0.931415 | −0.465708 | − | 0.884939i | \(-0.654200\pi\) | ||||
−0.465708 | + | 0.884939i | \(0.654200\pi\) | |||||||
\(770\) | 2.91429 | − | 1.58333i | 0.105024 | − | 0.0570592i | ||||
\(771\) | 8.65908 | 0.311849 | ||||||||
\(772\) | −9.01787 | + | 6.55186i | −0.324560 | + | 0.235807i | ||||
\(773\) | 11.9360 | + | 36.7352i | 0.429308 | + | 1.32127i | 0.898809 | + | 0.438341i | \(0.144434\pi\) |
−0.469501 | + | 0.882932i | \(0.655566\pi\) | |||||||
\(774\) | −0.969967 | + | 2.98525i | −0.0348647 | + | 0.107303i | ||||
\(775\) | 4.61803 | + | 3.35520i | 0.165885 | + | 0.120522i | ||||
\(776\) | −7.92705 | − | 5.75934i | −0.284565 | − | 0.206748i | ||||
\(777\) | −0.207159 | + | 0.637569i | −0.00743178 | + | 0.0228727i | ||||
\(778\) | −0.937276 | − | 2.88464i | −0.0336030 | − | 0.103419i | ||||
\(779\) | 13.9411 | − | 10.1288i | 0.499492 | − | 0.362902i | ||||
\(780\) | −7.16586 | −0.256579 | ||||||||
\(781\) | −3.55877 | − | 19.1730i | −0.127343 | − | 0.686065i | ||||
\(782\) | 8.56569 | 0.306308 | ||||||||
\(783\) | 3.91663 | − | 2.84560i | 0.139969 | − | 0.101693i | ||||
\(784\) | 0.309017 | + | 0.951057i | 0.0110363 | + | 0.0339663i | ||||
\(785\) | −5.71542 | + | 17.5902i | −0.203992 | + | 0.627823i | ||||
\(786\) | −12.6693 | − | 9.20480i | −0.451900 | − | 0.328324i | ||||
\(787\) | −8.55225 | − | 6.21357i | −0.304855 | − | 0.221490i | 0.424831 | − | 0.905273i | \(-0.360334\pi\) |
−0.729686 | + | 0.683783i | \(0.760334\pi\) | |||||||
\(788\) | −1.08544 | + | 3.34063i | −0.0386670 | + | 0.119005i | ||||
\(789\) | 10.4227 | + | 32.0778i | 0.371059 | + | 1.14200i | ||||
\(790\) | 0.403663 | − | 0.293278i | 0.0143617 | − | 0.0104344i | ||||
\(791\) | −17.1279 | −0.608999 | ||||||||
\(792\) | −0.719843 | − | 3.87819i | −0.0255785 | − | 0.137806i | ||||
\(793\) | 45.5209 | 1.61649 | ||||||||
\(794\) | −23.3747 | + | 16.9827i | −0.829536 | + | 0.602693i | ||||
\(795\) | 0.690337 | + | 2.12464i | 0.0244837 | + | 0.0753532i | ||||
\(796\) | 6.03100 | − | 18.5615i | 0.213763 | − | 0.657895i | ||||
\(797\) | 32.6059 | + | 23.6896i | 1.15496 | + | 0.839128i | 0.989132 | − | 0.147027i | \(-0.0469705\pi\) |
0.165828 | + | 0.986155i | \(0.446971\pi\) | |||||||
\(798\) | −7.36304 | − | 5.34956i | −0.260649 | − | 0.189372i | ||||
\(799\) | 16.1805 | − | 49.7983i | 0.572423 | − | 1.76174i | ||||
\(800\) | −0.309017 | − | 0.951057i | −0.0109254 | − | 0.0336249i | ||||
\(801\) | −1.34361 | + | 0.976187i | −0.0474740 | + | 0.0344919i | ||||
\(802\) | −36.2856 | −1.28129 | ||||||||
\(803\) | −21.6878 | + | 11.7829i | −0.765344 | + | 0.415811i | ||||
\(804\) | 17.2883 | 0.609712 | ||||||||
\(805\) | 1.61803 | − | 1.17557i | 0.0570282 | − | 0.0414334i | ||||
\(806\) | −6.17561 | − | 19.0066i | −0.217526 | − | 0.669478i | ||||
\(807\) | −12.8299 | + | 39.4865i | −0.451635 | + | 1.38999i | ||||
\(808\) | −14.0667 | − | 10.2201i | −0.494866 | − | 0.359541i | ||||
\(809\) | −11.9721 | − | 8.69827i | −0.420918 | − | 0.305815i | 0.357089 | − | 0.934070i | \(-0.383769\pi\) |
−0.778007 | + | 0.628256i | \(0.783769\pi\) | |||||||
\(810\) | −3.44661 | + | 10.6076i | −0.121101 | + | 0.372712i | ||||
\(811\) | −9.51905 | − | 29.2966i | −0.334259 | − | 1.02874i | −0.967086 | − | 0.254450i | \(-0.918105\pi\) |
0.632827 | − | 0.774293i | \(-0.281895\pi\) | |||||||
\(812\) | −1.05680 | + | 0.767813i | −0.0370865 | + | 0.0269449i | ||||
\(813\) | 28.3361 | 0.993790 | ||||||||
\(814\) | 0.467402 | − | 0.980596i | 0.0163824 | − | 0.0343699i | ||||
\(815\) | −6.52922 | −0.228708 | ||||||||
\(816\) | 7.09186 | − | 5.15254i | 0.248265 | − | 0.180375i | ||||
\(817\) | −3.62658 | − | 11.1615i | −0.126878 | − | 0.390490i | ||||
\(818\) | −1.83753 | + | 5.65533i | −0.0642476 | + | 0.197734i | ||||
\(819\) | −3.36856 | − | 2.44740i | −0.117707 | − | 0.0855191i | ||||
\(820\) | 3.13522 | + | 2.27787i | 0.109487 | + | 0.0795468i | ||||
\(821\) | 8.20169 | − | 25.2422i | 0.286241 | − | 0.880960i | −0.699783 | − | 0.714356i | \(-0.746720\pi\) |
0.986024 | − | 0.166604i | \(-0.0532801\pi\) | |||||||
\(822\) | 1.36642 | + | 4.20540i | 0.0476593 | + | 0.146680i | ||||
\(823\) | −32.2338 | + | 23.4192i | −1.12360 | + | 0.816342i | −0.984751 | − | 0.173971i | \(-0.944340\pi\) |
−0.138848 | + | 0.990314i | \(0.544340\pi\) | |||||||
\(824\) | −6.86988 | −0.239324 | ||||||||
\(825\) | −6.73055 | − | 0.884280i | −0.234328 | − | 0.0307867i | ||||
\(826\) | 10.0613 | 0.350076 | ||||||||
\(827\) | −29.6818 | + | 21.5651i | −1.03214 | + | 0.749892i | −0.968736 | − | 0.248096i | \(-0.920195\pi\) |
−0.0634026 | + | 0.997988i | \(0.520195\pi\) | |||||||
\(828\) | −0.735023 | − | 2.26217i | −0.0255438 | − | 0.0786158i | ||||
\(829\) | 5.21685 | − | 16.0558i | 0.181189 | − | 0.557641i | −0.818673 | − | 0.574260i | \(-0.805290\pi\) |
0.999862 | + | 0.0166183i | \(0.00529001\pi\) | |||||||
\(830\) | −10.2037 | − | 7.41342i | −0.354176 | − | 0.257324i | ||||
\(831\) | 14.0811 | + | 10.2305i | 0.488467 | + | 0.354892i | ||||
\(832\) | −1.08188 | + | 3.32969i | −0.0375075 | + | 0.115436i | ||||
\(833\) | 1.32347 | + | 4.07323i | 0.0458556 | + | 0.141129i | ||||
\(834\) | −34.9910 | + | 25.4224i | −1.21164 | + | 0.880306i | ||||
\(835\) | 12.0000 | 0.415277 | ||||||||
\(836\) | 10.7003 | + | 10.1488i | 0.370078 | + | 0.351005i | ||||
\(837\) | −21.1553 | −0.731233 | ||||||||
\(838\) | 5.74440 | − | 4.17355i | 0.198437 | − | 0.144173i | ||||
\(839\) | −12.6107 | − | 38.8118i | −0.435370 | − | 1.33993i | −0.892707 | − | 0.450638i | \(-0.851196\pi\) |
0.457336 | − | 0.889294i | \(-0.348804\pi\) | |||||||
\(840\) | 0.632489 | − | 1.94660i | 0.0218229 | − | 0.0671641i | ||||
\(841\) | 22.0810 | + | 16.0428i | 0.761414 | + | 0.553200i | ||||
\(842\) | −17.5929 | − | 12.7820i | −0.606290 | − | 0.440495i | ||||
\(843\) | 1.30448 | − | 4.01477i | 0.0449286 | − | 0.138276i | ||||
\(844\) | −4.43424 | − | 13.6472i | −0.152633 | − | 0.469756i | ||||
\(845\) | −0.600843 | + | 0.436538i | −0.0206696 | + | 0.0150174i | ||||
\(846\) | −14.5400 | −0.499896 | ||||||||
\(847\) | −10.6267 | − | 2.84138i | −0.365137 | − | 0.0976310i | ||||
\(848\) | 1.09146 | 0.0374810 | ||||||||
\(849\) | −45.2409 | + | 32.8694i | −1.55266 | + | 1.12808i | ||||
\(850\) | −1.32347 | − | 4.07323i | −0.0453947 | − | 0.139711i | ||||
\(851\) | 0.202425 | − | 0.622999i | 0.00693902 | − | 0.0213561i | ||||
\(852\) | −9.73594 | − | 7.07357i | −0.333548 | − | 0.242337i | ||||
\(853\) | 0.0773273 | + | 0.0561816i | 0.00264764 | + | 0.00192362i | 0.589108 | − | 0.808054i | \(-0.299479\pi\) |
−0.586461 | + | 0.809978i | \(0.699479\pi\) | |||||||
\(854\) | −4.01787 | + | 12.3657i | −0.137489 | + | 0.423146i | ||||
\(855\) | 1.63418 | + | 5.02949i | 0.0558878 | + | 0.172005i | ||||
\(856\) | −1.41598 | + | 1.02877i | −0.0483971 | + | 0.0351626i | ||||
\(857\) | 51.9594 | 1.77490 | 0.887449 | − | 0.460906i | \(-0.152475\pi\) | ||||
0.887449 | + | 0.460906i | \(0.152475\pi\) | |||||||
\(858\) | 17.2439 | + | 16.3552i | 0.588697 | + | 0.558357i | ||||
\(859\) | 35.1186 | 1.19823 | 0.599115 | − | 0.800663i | \(-0.295519\pi\) | ||||
0.599115 | + | 0.800663i | \(0.295519\pi\) | |||||||
\(860\) | 2.13522 | − | 1.55133i | 0.0728106 | − | 0.0529000i | ||||
\(861\) | 2.45112 | + | 7.54376i | 0.0835338 | + | 0.257091i | ||||
\(862\) | 5.80768 | − | 17.8742i | 0.197810 | − | 0.608797i | ||||
\(863\) | 18.6337 | + | 13.5382i | 0.634299 | + | 0.460845i | 0.857887 | − | 0.513839i | \(-0.171777\pi\) |
−0.223588 | + | 0.974684i | \(0.571777\pi\) | |||||||
\(864\) | 2.99831 | + | 2.17840i | 0.102005 | + | 0.0741106i | ||||
\(865\) | 2.33108 | − | 7.17434i | 0.0792592 | − | 0.243935i | ||||
\(866\) | 10.0272 | + | 30.8606i | 0.340739 | + | 1.04869i | ||||
\(867\) | 2.22343 | − | 1.61542i | 0.0755117 | − | 0.0548625i | ||||
\(868\) | 5.70820 | 0.193749 | ||||||||
\(869\) | −1.64075 | − | 0.215566i | −0.0556585 | − | 0.00731259i | ||||
\(870\) | 2.67366 | 0.0906457 | ||||||||
\(871\) | −23.9242 | + | 17.3820i | −0.810641 | + | 0.588965i | ||||
\(872\) | −1.81837 | − | 5.59636i | −0.0615777 | − | 0.189517i | ||||
\(873\) | −3.60101 | + | 11.0828i | −0.121876 | + | 0.375095i | ||||
\(874\) | 7.19476 | + | 5.22730i | 0.243367 | + | 0.176816i | ||||
\(875\) | −0.809017 | − | 0.587785i | −0.0273498 | − | 0.0198708i | ||||
\(876\) | −4.70690 | + | 14.4864i | −0.159031 | + | 0.489448i | ||||
\(877\) | −9.49468 | − | 29.2216i | −0.320612 | − | 0.986744i | −0.973382 | − | 0.229187i | \(-0.926393\pi\) |
0.652770 | − | 0.757556i | \(-0.273607\pi\) | |||||||
\(878\) | −13.8774 | + | 10.0826i | −0.468341 | + | 0.340270i | ||||
\(879\) | 39.0114 | 1.31582 | ||||||||
\(880\) | −1.42705 | + | 2.99391i | −0.0481059 | + | 0.100925i | ||||
\(881\) | −42.3788 | −1.42778 | −0.713890 | − | 0.700258i | \(-0.753068\pi\) | ||||
−0.713890 | + | 0.700258i | \(0.753068\pi\) | |||||||
\(882\) | 0.962157 | − | 0.699048i | 0.0323975 | − | 0.0235382i | ||||
\(883\) | 11.8437 | + | 36.4510i | 0.398571 | + | 1.22667i | 0.926146 | + | 0.377166i | \(0.123101\pi\) |
−0.527575 | + | 0.849509i | \(0.676899\pi\) | |||||||
\(884\) | −4.63353 | + | 14.2606i | −0.155843 | + | 0.479634i | ||||
\(885\) | −16.6602 | − | 12.1043i | −0.560027 | − | 0.406883i | ||||
\(886\) | 3.42911 | + | 2.49139i | 0.115203 | + | 0.0837001i | ||||
\(887\) | −7.90516 | + | 24.3296i | −0.265429 | + | 0.816908i | 0.726165 | + | 0.687521i | \(0.241301\pi\) |
−0.991594 | + | 0.129387i | \(0.958699\pi\) | |||||||
\(888\) | −0.207159 | − | 0.637569i | −0.00695179 | − | 0.0213954i | ||||
\(889\) | 8.04339 | − | 5.84387i | 0.269767 | − | 0.195997i | ||||
\(890\) | 1.39645 | 0.0468091 | ||||||||
\(891\) | 32.5044 | − | 17.6596i | 1.08894 | − | 0.591619i | ||||
\(892\) | 13.2981 | 0.445252 | ||||||||
\(893\) | 43.9807 | − | 31.9539i | 1.47176 | − | 1.06930i | ||||
\(894\) | −10.1255 | − | 31.1629i | −0.338646 | − | 1.04224i | ||||
\(895\) | −2.06058 | + | 6.34183i | −0.0688777 | + | 0.211984i | ||||
\(896\) | −0.809017 | − | 0.587785i | −0.0270274 | − | 0.0196365i | ||||
\(897\) | 11.5946 | + | 8.42397i | 0.387132 | + | 0.281268i | ||||
\(898\) | −4.06633 | + | 12.5149i | −0.135695 | + | 0.417627i | ||||
\(899\) | 2.30419 | + | 7.09157i | 0.0768491 | + | 0.236517i | ||||
\(900\) | −0.962157 | + | 0.699048i | −0.0320719 | + | 0.0233016i | ||||
\(901\) | 4.67456 | 0.155732 | ||||||||
\(902\) | −2.34564 | − | 12.6372i | −0.0781011 | − | 0.420774i | ||||
\(903\) | 5.40202 | 0.179768 | ||||||||
\(904\) | 13.8568 | − | 10.0675i | 0.460870 | − | 0.334842i | ||||
\(905\) | 1.00812 | + | 3.10266i | 0.0335109 | + | 0.103136i | ||||
\(906\) | 8.18354 | − | 25.1864i | 0.271880 | − | 0.836761i | ||||
\(907\) | 40.2697 | + | 29.2576i | 1.33713 | + | 0.971483i | 0.999544 | + | 0.0301892i | \(0.00961099\pi\) |
0.337588 | + | 0.941294i | \(0.390389\pi\) | |||||||
\(908\) | 15.3018 | + | 11.1174i | 0.507807 | + | 0.368943i | ||||
\(909\) | −6.39008 | + | 19.6667i | −0.211946 | + | 0.652302i | ||||
\(910\) | 1.08188 | + | 3.32969i | 0.0358641 | + | 0.110378i | ||||
\(911\) | −18.0622 | + | 13.1229i | −0.598427 | + | 0.434782i | −0.845320 | − | 0.534260i | \(-0.820590\pi\) |
0.246893 | + | 0.969043i | \(0.420590\pi\) | |||||||
\(912\) | 9.10121 | 0.301371 | ||||||||
\(913\) | 7.63395 | + | 41.1283i | 0.252647 | + | 1.36115i | ||||
\(914\) | 0.679393 | 0.0224723 | ||||||||
\(915\) | 21.5299 | − | 15.6424i | 0.711755 | − | 0.517120i | ||||
\(916\) | 1.20242 | + | 3.70068i | 0.0397292 | + | 0.122274i | ||||
\(917\) | −2.36433 | + | 7.27665i | −0.0780770 | + | 0.240296i | ||||
\(918\) | 12.8413 | + | 9.32974i | 0.423826 | + | 0.307927i | ||||
\(919\) | 14.5356 | + | 10.5607i | 0.479485 | + | 0.348367i | 0.801126 | − | 0.598495i | \(-0.204234\pi\) |
−0.321641 | + | 0.946862i | \(0.604234\pi\) | |||||||
\(920\) | −0.618034 | + | 1.90211i | −0.0203760 | + | 0.0627108i | ||||
\(921\) | −17.6359 | − | 54.2778i | −0.581123 | − | 1.78851i | ||||
\(922\) | −27.4508 | + | 19.9442i | −0.904044 | + | 0.656826i | ||||
\(923\) | 20.5848 | 0.677558 | ||||||||
\(924\) | −5.96489 | + | 3.24072i | −0.196231 | + | 0.106612i | ||||
\(925\) | −0.327530 | −0.0107691 | ||||||||
\(926\) | −7.02215 | + | 5.10189i | −0.230762 | + | 0.167658i | ||||
\(927\) | 2.52476 | + | 7.77041i | 0.0829240 | + | 0.255214i | ||||
\(928\) | 0.403663 | − | 1.24235i | 0.0132509 | − | 0.0407820i | ||||
\(929\) | −11.1232 | − | 8.08149i | −0.364941 | − | 0.265145i | 0.390169 | − | 0.920743i | \(-0.372417\pi\) |
−0.755110 | + | 0.655598i | \(0.772417\pi\) | |||||||
\(930\) | −9.45208 | − | 6.86734i | −0.309946 | − | 0.225189i | ||||
\(931\) | −1.37408 | + | 4.22898i | −0.0450336 | + | 0.138599i | ||||
\(932\) | 2.13973 | + | 6.58541i | 0.0700892 | + | 0.215712i | ||||
\(933\) | 34.8291 | − | 25.3048i | 1.14025 | − | 0.828443i | ||||
\(934\) | −4.58156 | −0.149913 | ||||||||
\(935\) | −6.11184 | + | 12.8225i | −0.199878 | + | 0.419340i | ||||
\(936\) | 4.16376 | 0.136097 | ||||||||
\(937\) | 6.78623 | − | 4.93048i | 0.221696 | − | 0.161072i | −0.471394 | − | 0.881923i | \(-0.656249\pi\) |
0.693090 | + | 0.720851i | \(0.256249\pi\) | |||||||
\(938\) | −2.61015 | − | 8.03320i | −0.0852243 | − | 0.262293i | ||||
\(939\) | −2.49720 | + | 7.68558i | −0.0814929 | + | 0.250809i | ||||
\(940\) | 9.89085 | + | 7.18612i | 0.322604 | + | 0.234386i | ||||
\(941\) | 22.7860 | + | 16.5550i | 0.742802 | + | 0.539677i | 0.893587 | − | 0.448889i | \(-0.148180\pi\) |
−0.150786 | + | 0.988566i | \(0.548180\pi\) | |||||||
\(942\) | 11.6982 | − | 36.0033i | 0.381147 | − | 1.17305i | ||||
\(943\) | −2.39510 | − | 7.37136i | −0.0779951 | − | 0.240044i | ||||
\(944\) | −8.13973 | + | 5.91386i | −0.264926 | + | 0.192480i | ||||
\(945\) | 3.70611 | 0.120560 | ||||||||
\(946\) | −8.67893 | − | 1.14026i | −0.282176 | − | 0.0370732i | ||||
\(947\) | −0.901036 | −0.0292797 | −0.0146399 | − | 0.999893i | \(-0.504660\pi\) | ||||
−0.0146399 | + | 0.999893i | \(0.504660\pi\) | |||||||
\(948\) | −0.826208 | + | 0.600275i | −0.0268340 | + | 0.0194960i | ||||
\(949\) | −8.05123 | − | 24.7791i | −0.261354 | − | 0.804365i | ||||
\(950\) | 1.37408 | − | 4.22898i | 0.0445810 | − | 0.137206i | ||||
\(951\) | −46.5674 | − | 33.8332i | −1.51005 | − | 1.09712i | ||||
\(952\) | −3.46489 | − | 2.51739i | −0.112298 | − | 0.0815892i | ||||
\(953\) | −1.68675 | + | 5.19129i | −0.0546393 | + | 0.168163i | −0.974652 | − | 0.223726i | \(-0.928178\pi\) |
0.920013 | + | 0.391888i | \(0.128178\pi\) | |||||||
\(954\) | −0.401125 | − | 1.23453i | −0.0129869 | − | 0.0399695i | ||||
\(955\) | −11.0863 | + | 8.05470i | −0.358746 | + | 0.260644i | ||||
\(956\) | −26.6477 | −0.861850 | ||||||||
\(957\) | −6.43390 | − | 6.10231i | −0.207979 | − | 0.197260i | ||||
\(958\) | −38.8930 | −1.25658 | ||||||||
\(959\) | 1.74779 | − | 1.26984i | 0.0564390 | − | 0.0410053i | ||||
\(960\) | 0.632489 | + | 1.94660i | 0.0204135 | + | 0.0628262i | ||||
\(961\) | 0.489357 | − | 1.50609i | 0.0157857 | − | 0.0485834i | ||||
\(962\) | 0.927697 | + | 0.674011i | 0.0299101 | + | 0.0217310i | ||||
\(963\) | 1.68401 | + | 1.22351i | 0.0542665 | + | 0.0394269i | ||||
\(964\) | −0.0286811 | + | 0.0882714i | −0.000923756 | + | 0.00284303i | ||||
\(965\) | −3.44452 | − | 10.6011i | −0.110883 | − | 0.341263i | ||||
\(966\) | −3.31175 | + | 2.40613i | −0.106554 | + | 0.0774159i | ||||
\(967\) | −36.7612 | −1.18216 | −0.591079 | − | 0.806613i | \(-0.701298\pi\) | ||||
−0.591079 | + | 0.806613i | \(0.701298\pi\) | |||||||
\(968\) | 10.2673 | − | 3.94749i | 0.330003 | − | 0.126877i | ||||
\(969\) | 38.9791 | 1.25219 | ||||||||
\(970\) | 7.92705 | − | 5.75934i | 0.254522 | − | 0.184921i | ||||
\(971\) | −14.6120 | − | 44.9711i | −0.468922 | − | 1.44319i | −0.853983 | − | 0.520301i | \(-0.825820\pi\) |
0.385061 | − | 0.922891i | \(-0.374180\pi\) | |||||||
\(972\) | 3.61868 | − | 11.1372i | 0.116069 | − | 0.357224i | ||||
\(973\) | 17.0956 | + | 12.4207i | 0.548061 | + | 0.398190i | ||||
\(974\) | 15.9856 | + | 11.6142i | 0.512211 | + | 0.372143i | ||||
\(975\) | 2.21437 | − | 6.81513i | 0.0709166 | − | 0.218259i | ||||
\(976\) | −4.01787 | − | 12.3657i | −0.128609 | − | 0.395817i | ||||
\(977\) | 35.8403 | − | 26.0395i | 1.14663 | − | 0.833078i | 0.158604 | − | 0.987342i | \(-0.449301\pi\) |
0.988030 | + | 0.154264i | \(0.0493008\pi\) | |||||||
\(978\) | 13.3638 | 0.427329 | ||||||||
\(979\) | −3.36042 | − | 3.18723i | −0.107399 | − | 0.101864i | ||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −5.66168 | + | 4.11345i | −0.180764 | + | 0.131332i | ||||
\(982\) | 9.48935 | + | 29.2052i | 0.302817 | + | 0.931975i | ||||
\(983\) | −0.922119 | + | 2.83799i | −0.0294110 | + | 0.0905178i | −0.964685 | − | 0.263408i | \(-0.915153\pi\) |
0.935274 | + | 0.353926i | \(0.115153\pi\) | |||||||
\(984\) | −6.41710 | − | 4.66230i | −0.204570 | − | 0.148629i | ||||
\(985\) | −2.84171 | − | 2.06462i | −0.0905443 | − | 0.0657843i | ||||
\(986\) | 1.72883 | − | 5.32078i | 0.0550570 | − | 0.169448i | ||||
\(987\) | 7.73266 | + | 23.7987i | 0.246133 | + | 0.757520i | ||||
\(988\) | −12.5946 | + | 9.15051i | −0.400688 | + | 0.291117i | ||||
\(989\) | −5.27857 | −0.167849 | ||||||||
\(990\) | 3.91083 | + | 0.513816i | 0.124294 | + | 0.0163302i | ||||
\(991\) | −47.4047 | −1.50586 | −0.752930 | − | 0.658100i | \(-0.771360\pi\) | ||||
−0.752930 | + | 0.658100i | \(0.771360\pi\) | |||||||
\(992\) | −4.61803 | + | 3.35520i | −0.146623 | + | 0.106528i | ||||
\(993\) | −19.1478 | − | 58.9310i | −0.607638 | − | 1.87012i | ||||
\(994\) | −1.81691 | + | 5.59186i | −0.0576287 | + | 0.177363i | ||||
\(995\) | 15.7894 | + | 11.4716i | 0.500556 | + | 0.363676i | ||||
\(996\) | 20.8847 | + | 15.1736i | 0.661757 | + | 0.480794i | ||||
\(997\) | 5.17522 | − | 15.9277i | 0.163901 | − | 0.504435i | −0.835053 | − | 0.550170i | \(-0.814563\pi\) |
0.998954 | + | 0.0457350i | \(0.0145630\pi\) | |||||||
\(998\) | 5.74711 | + | 17.6878i | 0.181922 | + | 0.559897i | ||||
\(999\) | 0.982035 | − | 0.713490i | 0.0310702 | − | 0.0225738i |
(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.e.421.1 | ✓ | 8 | |
11.2 | odd | 10 | 8470.2.a.ct.1.1 | 4 | |||
11.4 | even | 5 | inner | 770.2.n.e.631.1 | yes | 8 | |
11.9 | even | 5 | 8470.2.a.cq.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.e.421.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
770.2.n.e.631.1 | yes | 8 | 11.4 | even | 5 | inner | |
8470.2.a.cq.1.1 | 4 | 11.9 | even | 5 | |||
8470.2.a.ct.1.1 | 4 | 11.2 | odd | 10 |