Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,2,Mod(85,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.85");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.w (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.68297350792\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 85.7 | ||
Character | \(\chi\) | \(=\) | 336.85 |
Dual form | 336.2.w.b.253.7 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.371814 | − | 1.36446i | −0.262912 | − | 0.964820i | ||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | −1.72351 | + | 1.01465i | −0.861754 | + | 0.507326i | ||||
\(5\) | 0.116928 | + | 0.116928i | 0.0522919 | + | 0.0522919i | 0.732769 | − | 0.680477i | \(-0.238228\pi\) |
−0.680477 | + | 0.732769i | \(0.738228\pi\) | |||||||
\(6\) | 1.22773 | + | 0.701908i | 0.501219 | + | 0.286553i | ||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 2.02528 | + | 1.97440i | 0.716044 | + | 0.698056i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0.116068 | − | 0.203020i | 0.0367041 | − | 0.0642004i | ||||
\(11\) | −0.842648 | − | 0.842648i | −0.254068 | − | 0.254068i | 0.568568 | − | 0.822636i | \(-0.307498\pi\) |
−0.822636 | + | 0.568568i | \(0.807498\pi\) | |||||||
\(12\) | 0.501238 | − | 1.93617i | 0.144695 | − | 0.558925i | ||||
\(13\) | 5.06549 | − | 5.06549i | 1.40491 | − | 1.40491i | 0.621495 | − | 0.783418i | \(-0.286526\pi\) |
0.783418 | − | 0.621495i | \(-0.213474\pi\) | |||||||
\(14\) | −1.36446 | + | 0.371814i | −0.364668 | + | 0.0993715i | ||||
\(15\) | −0.165361 | −0.0426961 | ||||||||
\(16\) | 1.94096 | − | 3.49752i | 0.485241 | − | 0.874380i | ||||
\(17\) | −0.448406 | −0.108755 | −0.0543773 | − | 0.998520i | \(-0.517317\pi\) | ||||
−0.0543773 | + | 0.998520i | \(0.517317\pi\) | |||||||
\(18\) | −1.36446 | + | 0.371814i | −0.321607 | + | 0.0876374i | ||||
\(19\) | 1.66164 | − | 1.66164i | 0.381206 | − | 0.381206i | −0.490330 | − | 0.871537i | \(-0.663124\pi\) |
0.871537 | + | 0.490330i | \(0.163124\pi\) | |||||||
\(20\) | −0.320168 | − | 0.0828854i | −0.0715918 | − | 0.0185337i | ||||
\(21\) | 0.707107 | + | 0.707107i | 0.154303 | + | 0.154303i | ||||
\(22\) | −0.836452 | + | 1.46307i | −0.178332 | + | 0.311927i | ||||
\(23\) | − | 2.66931i | − | 0.556590i | −0.960496 | − | 0.278295i | \(-0.910231\pi\) | ||
0.960496 | − | 0.278295i | \(-0.0897694\pi\) | |||||||
\(24\) | −2.82820 | + | 0.0359761i | −0.577304 | + | 0.00734359i | ||||
\(25\) | − | 4.97266i | − | 0.994531i | ||||||
\(26\) | −8.79508 | − | 5.02824i | −1.72486 | − | 0.986119i | ||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 1.01465 | + | 1.72351i | 0.191751 | + | 0.325713i | ||||
\(29\) | 0.858643 | − | 0.858643i | 0.159446 | − | 0.159446i | −0.622875 | − | 0.782321i | \(-0.714036\pi\) |
0.782321 | + | 0.622875i | \(0.214036\pi\) | |||||||
\(30\) | 0.0614837 | + | 0.225629i | 0.0112253 | + | 0.0411941i | ||||
\(31\) | −1.40070 | −0.251573 | −0.125787 | − | 0.992057i | \(-0.540145\pi\) | ||||
−0.125787 | + | 0.992057i | \(0.540145\pi\) | |||||||
\(32\) | −5.49391 | − | 1.34794i | −0.971195 | − | 0.238285i | ||||
\(33\) | 1.19168 | 0.207445 | ||||||||
\(34\) | 0.166724 | + | 0.611833i | 0.0285929 | + | 0.104929i | ||||
\(35\) | 0.116928 | − | 0.116928i | 0.0197645 | − | 0.0197645i | ||||
\(36\) | 1.01465 | + | 1.72351i | 0.169109 | + | 0.287251i | ||||
\(37\) | 5.76957 | + | 5.76957i | 0.948512 | + | 0.948512i | 0.998738 | − | 0.0502262i | \(-0.0159942\pi\) |
−0.0502262 | + | 0.998738i | \(0.515994\pi\) | |||||||
\(38\) | −2.88506 | − | 1.64942i | −0.468019 | − | 0.267572i | ||||
\(39\) | 7.16368i | 1.14711i | ||||||||
\(40\) | 0.00594906 | + | 0.467675i | 0.000940629 | + | 0.0739459i | ||||
\(41\) | − | 5.42377i | − | 0.847051i | −0.905884 | − | 0.423525i | \(-0.860792\pi\) | ||
0.905884 | − | 0.423525i | \(-0.139208\pi\) | |||||||
\(42\) | 0.701908 | − | 1.22773i | 0.108307 | − | 0.189443i | ||||
\(43\) | 3.30205 | + | 3.30205i | 0.503558 | + | 0.503558i | 0.912542 | − | 0.408984i | \(-0.134117\pi\) |
−0.408984 | + | 0.912542i | \(0.634117\pi\) | |||||||
\(44\) | 2.30730 | + | 0.597317i | 0.347839 | + | 0.0900489i | ||||
\(45\) | 0.116928 | − | 0.116928i | 0.0174306 | − | 0.0174306i | ||||
\(46\) | −3.64218 | + | 0.992488i | −0.537009 | + | 0.146334i | ||||
\(47\) | −12.4218 | −1.81190 | −0.905950 | − | 0.423385i | \(-0.860842\pi\) | ||||
−0.905950 | + | 0.423385i | \(0.860842\pi\) | |||||||
\(48\) | 1.10065 | + | 3.84559i | 0.158865 | + | 0.555063i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −6.78500 | + | 1.84890i | −0.959543 | + | 0.261474i | ||||
\(51\) | 0.317071 | − | 0.317071i | 0.0443988 | − | 0.0443988i | ||||
\(52\) | −3.59071 | + | 13.8701i | −0.497941 | + | 1.92344i | ||||
\(53\) | 7.71727 | + | 7.71727i | 1.06005 | + | 1.06005i | 0.998078 | + | 0.0619700i | \(0.0197383\pi\) |
0.0619700 | + | 0.998078i | \(0.480262\pi\) | |||||||
\(54\) | 0.701908 | − | 1.22773i | 0.0955175 | − | 0.167073i | ||||
\(55\) | − | 0.197059i | − | 0.0265714i | ||||||
\(56\) | 1.97440 | − | 2.02528i | 0.263840 | − | 0.270639i | ||||
\(57\) | 2.34991i | 0.311254i | ||||||||
\(58\) | −1.49084 | − | 0.852330i | −0.195757 | − | 0.111916i | ||||
\(59\) | −2.01752 | − | 2.01752i | −0.262659 | − | 0.262659i | 0.563475 | − | 0.826133i | \(-0.309464\pi\) |
−0.826133 | + | 0.563475i | \(0.809464\pi\) | |||||||
\(60\) | 0.285002 | − | 0.167784i | 0.0367936 | − | 0.0216609i | ||||
\(61\) | 6.02230 | − | 6.02230i | 0.771076 | − | 0.771076i | −0.207219 | − | 0.978295i | \(-0.566441\pi\) |
0.978295 | + | 0.207219i | \(0.0664412\pi\) | |||||||
\(62\) | 0.520800 | + | 1.91120i | 0.0661417 | + | 0.242723i | ||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0.203495 | + | 7.99741i | 0.0254369 | + | 0.999676i | ||||
\(65\) | 1.18460 | 0.146931 | ||||||||
\(66\) | −0.443085 | − | 1.62601i | −0.0545399 | − | 0.200148i | ||||
\(67\) | −3.55703 | + | 3.55703i | −0.434561 | + | 0.434561i | −0.890177 | − | 0.455616i | \(-0.849419\pi\) |
0.455616 | + | 0.890177i | \(0.349419\pi\) | |||||||
\(68\) | 0.772832 | − | 0.454976i | 0.0937197 | − | 0.0551740i | ||||
\(69\) | 1.88749 | + | 1.88749i | 0.227227 | + | 0.227227i | ||||
\(70\) | −0.203020 | − | 0.116068i | −0.0242655 | − | 0.0138728i | ||||
\(71\) | 11.1040i | 1.31780i | 0.752228 | + | 0.658902i | \(0.228979\pi\) | ||||
−0.752228 | + | 0.658902i | \(0.771021\pi\) | |||||||
\(72\) | 1.97440 | − | 2.02528i | 0.232685 | − | 0.238681i | ||||
\(73\) | − | 8.39873i | − | 0.982997i | −0.870878 | − | 0.491499i | \(-0.836449\pi\) | ||
0.870878 | − | 0.491499i | \(-0.163551\pi\) | |||||||
\(74\) | 5.72715 | − | 10.0176i | 0.665768 | − | 1.16452i | ||||
\(75\) | 3.51620 | + | 3.51620i | 0.406016 | + | 0.406016i | ||||
\(76\) | −1.17787 | + | 4.54984i | −0.135110 | + | 0.521902i | ||||
\(77\) | −0.842648 | + | 0.842648i | −0.0960286 | + | 0.0960286i | ||||
\(78\) | 9.77456 | − | 2.66356i | 1.10675 | − | 0.301588i | ||||
\(79\) | 8.06582 | 0.907475 | 0.453738 | − | 0.891135i | \(-0.350090\pi\) | ||||
0.453738 | + | 0.891135i | \(0.350090\pi\) | |||||||
\(80\) | 0.635912 | − | 0.182005i | 0.0710972 | − | 0.0203488i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −7.40053 | + | 2.01663i | −0.817251 | + | 0.222700i | ||||
\(83\) | 7.48793 | − | 7.48793i | 0.821907 | − | 0.821907i | −0.164475 | − | 0.986381i | \(-0.552593\pi\) |
0.986381 | + | 0.164475i | \(0.0525929\pi\) | |||||||
\(84\) | −1.93617 | − | 0.501238i | −0.211254 | − | 0.0546895i | ||||
\(85\) | −0.0524314 | − | 0.0524314i | −0.00568698 | − | 0.00568698i | ||||
\(86\) | 3.27777 | − | 5.73327i | 0.353451 | − | 0.618234i | ||||
\(87\) | 1.21430i | 0.130187i | ||||||||
\(88\) | −0.0428721 | − | 3.37032i | −0.00457019 | − | 0.359277i | ||||
\(89\) | 8.82635i | 0.935592i | 0.883837 | + | 0.467796i | \(0.154952\pi\) | ||||
−0.883837 | + | 0.467796i | \(0.845048\pi\) | |||||||
\(90\) | −0.203020 | − | 0.116068i | −0.0214001 | − | 0.0122347i | ||||
\(91\) | −5.06549 | − | 5.06549i | −0.531007 | − | 0.531007i | ||||
\(92\) | 2.70842 | + | 4.60059i | 0.282373 | + | 0.479644i | ||||
\(93\) | 0.990445 | − | 0.990445i | 0.102704 | − | 0.102704i | ||||
\(94\) | 4.61858 | + | 16.9490i | 0.476370 | + | 1.74816i | ||||
\(95\) | 0.388585 | 0.0398680 | ||||||||
\(96\) | 4.83792 | − | 2.93164i | 0.493768 | − | 0.299209i | ||||
\(97\) | −2.19995 | −0.223372 | −0.111686 | − | 0.993744i | \(-0.535625\pi\) | ||||
−0.111686 | + | 0.993744i | \(0.535625\pi\) | |||||||
\(98\) | 0.371814 | + | 1.36446i | 0.0375589 | + | 0.137831i | ||||
\(99\) | −0.842648 | + | 0.842648i | −0.0846893 | + | 0.0846893i | ||||
\(100\) | 5.04551 | + | 8.57042i | 0.504551 | + | 0.857042i | ||||
\(101\) | −6.15886 | − | 6.15886i | −0.612829 | − | 0.612829i | 0.330853 | − | 0.943682i | \(-0.392664\pi\) |
−0.943682 | + | 0.330853i | \(0.892664\pi\) | |||||||
\(102\) | −0.550523 | − | 0.314740i | −0.0545099 | − | 0.0311639i | ||||
\(103\) | 12.8752i | 1.26863i | 0.773073 | + | 0.634317i | \(0.218718\pi\) | ||||
−0.773073 | + | 0.634317i | \(0.781282\pi\) | |||||||
\(104\) | 20.2603 | − | 0.257721i | 1.98669 | − | 0.0252717i | ||||
\(105\) | 0.165361i | 0.0161376i | ||||||||
\(106\) | 7.66052 | − | 13.3993i | 0.744056 | − | 1.30145i | ||||
\(107\) | 1.60576 | + | 1.60576i | 0.155235 | + | 0.155235i | 0.780451 | − | 0.625217i | \(-0.214989\pi\) |
−0.625217 | + | 0.780451i | \(0.714989\pi\) | |||||||
\(108\) | −1.93617 | − | 0.501238i | −0.186308 | − | 0.0482316i | ||||
\(109\) | −4.74644 | + | 4.74644i | −0.454626 | + | 0.454626i | −0.896887 | − | 0.442260i | \(-0.854177\pi\) |
0.442260 | + | 0.896887i | \(0.354177\pi\) | |||||||
\(110\) | −0.268879 | + | 0.0732691i | −0.0256366 | + | 0.00698594i | ||||
\(111\) | −8.15941 | −0.774457 | ||||||||
\(112\) | −3.49752 | − | 1.94096i | −0.330485 | − | 0.183404i | ||||
\(113\) | −16.0799 | −1.51267 | −0.756336 | − | 0.654183i | \(-0.773013\pi\) | ||||
−0.756336 | + | 0.654183i | \(0.773013\pi\) | |||||||
\(114\) | 3.20637 | − | 0.873731i | 0.300304 | − | 0.0818324i | ||||
\(115\) | 0.312118 | − | 0.312118i | 0.0291052 | − | 0.0291052i | ||||
\(116\) | −0.608656 | + | 2.35110i | −0.0565122 | + | 0.218294i | ||||
\(117\) | −5.06549 | − | 5.06549i | −0.468304 | − | 0.468304i | ||||
\(118\) | −2.00269 | + | 3.50297i | −0.184362 | + | 0.322475i | ||||
\(119\) | 0.448406i | 0.0411053i | ||||||||
\(120\) | −0.334903 | − | 0.326490i | −0.0305723 | − | 0.0298043i | ||||
\(121\) | − | 9.57989i | − | 0.870899i | ||||||
\(122\) | −10.4564 | − | 5.97802i | −0.946675 | − | 0.541224i | ||||
\(123\) | 3.83519 | + | 3.83519i | 0.345807 | + | 0.345807i | ||||
\(124\) | 2.41412 | − | 1.42122i | 0.216794 | − | 0.127630i | ||||
\(125\) | 1.16608 | − | 1.16608i | 0.104298 | − | 0.104298i | ||||
\(126\) | 0.371814 | + | 1.36446i | 0.0331238 | + | 0.121556i | ||||
\(127\) | −3.72584 | −0.330615 | −0.165307 | − | 0.986242i | \(-0.552862\pi\) | ||||
−0.165307 | + | 0.986242i | \(0.552862\pi\) | |||||||
\(128\) | 10.8365 | − | 3.25121i | 0.957820 | − | 0.287369i | ||||
\(129\) | −4.66980 | −0.411153 | ||||||||
\(130\) | −0.440450 | − | 1.61634i | −0.0386300 | − | 0.141762i | ||||
\(131\) | −0.420527 | + | 0.420527i | −0.0367416 | + | 0.0367416i | −0.725239 | − | 0.688497i | \(-0.758271\pi\) |
0.688497 | + | 0.725239i | \(0.258271\pi\) | |||||||
\(132\) | −2.05388 | + | 1.20914i | −0.178767 | + | 0.105242i | ||||
\(133\) | −1.66164 | − | 1.66164i | −0.144082 | − | 0.144082i | ||||
\(134\) | 6.17599 | + | 3.53088i | 0.533524 | + | 0.305022i | ||||
\(135\) | 0.165361i | 0.0142320i | ||||||||
\(136\) | −0.908147 | − | 0.885333i | −0.0778730 | − | 0.0759167i | ||||
\(137\) | 15.0365i | 1.28465i | 0.766432 | + | 0.642326i | \(0.222030\pi\) | ||||
−0.766432 | + | 0.642326i | \(0.777970\pi\) | |||||||
\(138\) | 1.87361 | − | 3.27720i | 0.159492 | − | 0.278974i | ||||
\(139\) | −14.5884 | − | 14.5884i | −1.23737 | − | 1.23737i | −0.961070 | − | 0.276304i | \(-0.910890\pi\) |
−0.276304 | − | 0.961070i | \(-0.589110\pi\) | |||||||
\(140\) | −0.0828854 | + | 0.320168i | −0.00700510 | + | 0.0270592i | ||||
\(141\) | 8.78351 | − | 8.78351i | 0.739705 | − | 0.739705i | ||||
\(142\) | 15.1510 | − | 4.12863i | 1.27144 | − | 0.346467i | ||||
\(143\) | −8.53684 | −0.713886 | ||||||||
\(144\) | −3.49752 | − | 1.94096i | −0.291460 | − | 0.161747i | ||||
\(145\) | 0.200799 | 0.0166755 | ||||||||
\(146\) | −11.4597 | + | 3.12277i | −0.948415 | + | 0.258442i | ||||
\(147\) | 0.707107 | − | 0.707107i | 0.0583212 | − | 0.0583212i | ||||
\(148\) | −15.7980 | − | 4.08980i | −1.29859 | − | 0.336180i | ||||
\(149\) | 15.4379 | + | 15.4379i | 1.26472 | + | 1.26472i | 0.948778 | + | 0.315944i | \(0.102321\pi\) |
0.315944 | + | 0.948778i | \(0.397679\pi\) | |||||||
\(150\) | 3.49034 | − | 6.10509i | 0.284985 | − | 0.498478i | ||||
\(151\) | 7.81338i | 0.635844i | 0.948117 | + | 0.317922i | \(0.102985\pi\) | ||||
−0.948117 | + | 0.317922i | \(0.897015\pi\) | |||||||
\(152\) | 6.64602 | − | 0.0845408i | 0.539064 | − | 0.00685716i | ||||
\(153\) | 0.448406i | 0.0362515i | ||||||||
\(154\) | 1.46307 | + | 0.836452i | 0.117897 | + | 0.0674032i | ||||
\(155\) | −0.163781 | − | 0.163781i | −0.0131552 | − | 0.0131552i | ||||
\(156\) | −7.26864 | − | 12.3467i | −0.581957 | − | 0.988524i | ||||
\(157\) | −12.5393 | + | 12.5393i | −1.00074 | + | 1.00074i | −0.000741791 | 1.00000i | \(0.500236\pi\) | |
−1.00000 | 0.000741791i | \(0.999764\pi\) | ||||||||
\(158\) | −2.99898 | − | 11.0055i | −0.238586 | − | 0.875550i | ||||
\(159\) | −10.9139 | −0.865526 | ||||||||
\(160\) | −0.484780 | − | 0.800006i | −0.0383253 | − | 0.0632460i | ||||
\(161\) | −2.66931 | −0.210371 | ||||||||
\(162\) | 0.371814 | + | 1.36446i | 0.0292125 | + | 0.107202i | ||||
\(163\) | −4.28825 | + | 4.28825i | −0.335881 | + | 0.335881i | −0.854815 | − | 0.518933i | \(-0.826329\pi\) |
0.518933 | + | 0.854815i | \(0.326329\pi\) | |||||||
\(164\) | 5.50324 | + | 9.34792i | 0.429731 | + | 0.729950i | ||||
\(165\) | 0.139341 | + | 0.139341i | 0.0108477 | + | 0.0108477i | ||||
\(166\) | −13.0011 | − | 7.43287i | −1.00908 | − | 0.576902i | ||||
\(167\) | − | 15.3880i | − | 1.19076i | −0.803444 | − | 0.595380i | \(-0.797001\pi\) | ||
0.803444 | − | 0.595380i | \(-0.202999\pi\) | |||||||
\(168\) | 0.0359761 | + | 2.82820i | 0.00277562 | + | 0.218200i | ||||
\(169\) | − | 38.3183i | − | 2.94756i | ||||||
\(170\) | −0.0520458 | + | 0.0910353i | −0.00399173 | + | 0.00698209i | ||||
\(171\) | −1.66164 | − | 1.66164i | −0.127069 | − | 0.127069i | ||||
\(172\) | −9.04154 | − | 2.34068i | −0.689411 | − | 0.178475i | ||||
\(173\) | −11.9143 | + | 11.9143i | −0.905825 | + | 0.905825i | −0.995932 | − | 0.0901075i | \(-0.971279\pi\) |
0.0901075 | + | 0.995932i | \(0.471279\pi\) | |||||||
\(174\) | 1.65687 | − | 0.451496i | 0.125607 | − | 0.0342278i | ||||
\(175\) | −4.97266 | −0.375897 | ||||||||
\(176\) | −4.58273 | + | 1.31163i | −0.345436 | + | 0.0988677i | ||||
\(177\) | 2.85320 | 0.214460 | ||||||||
\(178\) | 12.0432 | − | 3.28176i | 0.902677 | − | 0.245978i | ||||
\(179\) | 16.4795 | − | 16.4795i | 1.23174 | − | 1.23174i | 0.268444 | − | 0.963295i | \(-0.413491\pi\) |
0.963295 | − | 0.268444i | \(-0.0865093\pi\) | |||||||
\(180\) | −0.0828854 | + | 0.320168i | −0.00617791 | + | 0.0238639i | ||||
\(181\) | 5.69994 | + | 5.69994i | 0.423673 | + | 0.423673i | 0.886466 | − | 0.462793i | \(-0.153153\pi\) |
−0.462793 | + | 0.886466i | \(0.653153\pi\) | |||||||
\(182\) | −5.02824 | + | 8.79508i | −0.372718 | + | 0.651935i | ||||
\(183\) | 8.51681i | 0.629581i | ||||||||
\(184\) | 5.27029 | − | 5.40610i | 0.388531 | − | 0.398543i | ||||
\(185\) | 1.34925i | 0.0991989i | ||||||||
\(186\) | −1.71969 | − | 0.983163i | −0.126093 | − | 0.0720890i | ||||
\(187\) | 0.377849 | + | 0.377849i | 0.0276310 | + | 0.0276310i | ||||
\(188\) | 21.4090 | − | 12.6038i | 1.56141 | − | 0.919223i | ||||
\(189\) | 0.707107 | − | 0.707107i | 0.0514344 | − | 0.0514344i | ||||
\(190\) | −0.144481 | − | 0.530209i | −0.0104818 | − | 0.0384654i | ||||
\(191\) | −5.58350 | −0.404008 | −0.202004 | − | 0.979385i | \(-0.564745\pi\) | ||||
−0.202004 | + | 0.979385i | \(0.564745\pi\) | |||||||
\(192\) | −5.79892 | − | 5.51113i | −0.418501 | − | 0.397732i | ||||
\(193\) | −8.17034 | −0.588114 | −0.294057 | − | 0.955788i | \(-0.595006\pi\) | ||||
−0.294057 | + | 0.955788i | \(0.595006\pi\) | |||||||
\(194\) | 0.817974 | + | 3.00175i | 0.0587271 | + | 0.215513i | ||||
\(195\) | −0.837636 | + | 0.837636i | −0.0599844 | + | 0.0599844i | ||||
\(196\) | 1.72351 | − | 1.01465i | 0.123108 | − | 0.0724751i | ||||
\(197\) | −7.94570 | − | 7.94570i | −0.566108 | − | 0.566108i | 0.364928 | − | 0.931036i | \(-0.381094\pi\) |
−0.931036 | + | 0.364928i | \(0.881094\pi\) | |||||||
\(198\) | 1.46307 | + | 0.836452i | 0.103976 | + | 0.0594440i | ||||
\(199\) | 2.13313i | 0.151213i | 0.997138 | + | 0.0756066i | \(0.0240893\pi\) | ||||
−0.997138 | + | 0.0756066i | \(0.975911\pi\) | |||||||
\(200\) | 9.81801 | − | 10.0710i | 0.694238 | − | 0.712128i | ||||
\(201\) | − | 5.03041i | − | 0.354818i | ||||||
\(202\) | −6.11357 | + | 10.6935i | −0.430150 | + | 0.752390i | ||||
\(203\) | −0.858643 | − | 0.858643i | −0.0602649 | − | 0.0602649i | ||||
\(204\) | −0.224758 | + | 0.868192i | −0.0157362 | + | 0.0607856i | ||||
\(205\) | 0.634192 | − | 0.634192i | 0.0442939 | − | 0.0442939i | ||||
\(206\) | 17.5677 | − | 4.78719i | 1.22400 | − | 0.333539i | ||||
\(207\) | −2.66931 | −0.185530 | ||||||||
\(208\) | −7.88472 | − | 27.5486i | −0.546707 | − | 1.91015i | ||||
\(209\) | −2.80035 | −0.193705 | ||||||||
\(210\) | 0.225629 | − | 0.0614837i | 0.0155699 | − | 0.00424278i | ||||
\(211\) | 6.94940 | − | 6.94940i | 0.478416 | − | 0.478416i | −0.426208 | − | 0.904625i | \(-0.640151\pi\) |
0.904625 | + | 0.426208i | \(0.140151\pi\) | |||||||
\(212\) | −21.1311 | − | 5.47044i | −1.45129 | − | 0.375711i | ||||
\(213\) | −7.85173 | − | 7.85173i | −0.537992 | − | 0.537992i | ||||
\(214\) | 1.59395 | − | 2.78804i | 0.108960 | − | 0.190586i | ||||
\(215\) | 0.772206i | 0.0526640i | ||||||||
\(216\) | 0.0359761 | + | 2.82820i | 0.00244786 | + | 0.192435i | ||||
\(217\) | 1.40070i | 0.0950858i | ||||||||
\(218\) | 8.24112 | + | 4.71154i | 0.558159 | + | 0.319106i | ||||
\(219\) | 5.93880 | + | 5.93880i | 0.401307 | + | 0.401307i | ||||
\(220\) | 0.199946 | + | 0.339632i | 0.0134803 | + | 0.0228980i | ||||
\(221\) | −2.27140 | + | 2.27140i | −0.152791 | + | 0.152791i | ||||
\(222\) | 3.03378 | + | 11.1332i | 0.203614 | + | 0.747211i | ||||
\(223\) | 9.83111 | 0.658340 | 0.329170 | − | 0.944271i | \(-0.393231\pi\) | ||||
0.329170 | + | 0.944271i | \(0.393231\pi\) | |||||||
\(224\) | −1.34794 | + | 5.49391i | −0.0900633 | + | 0.367077i | ||||
\(225\) | −4.97266 | −0.331510 | ||||||||
\(226\) | 5.97874 | + | 21.9404i | 0.397700 | + | 1.45946i | ||||
\(227\) | 10.8974 | − | 10.8974i | 0.723283 | − | 0.723283i | −0.245989 | − | 0.969273i | \(-0.579113\pi\) |
0.969273 | + | 0.245989i | \(0.0791129\pi\) | |||||||
\(228\) | −2.38434 | − | 4.05010i | −0.157907 | − | 0.268224i | ||||
\(229\) | 18.3016 | + | 18.3016i | 1.20940 | + | 1.20940i | 0.971221 | + | 0.238181i | \(0.0765512\pi\) |
0.238181 | + | 0.971221i | \(0.423449\pi\) | |||||||
\(230\) | −0.541923 | − | 0.309823i | −0.0357333 | − | 0.0204291i | ||||
\(231\) | − | 1.19168i | − | 0.0784070i | ||||||
\(232\) | 3.43430 | − | 0.0436860i | 0.225473 | − | 0.00286812i | ||||
\(233\) | 20.4162i | 1.33751i | 0.743483 | + | 0.668755i | \(0.233172\pi\) | ||||
−0.743483 | + | 0.668755i | \(0.766828\pi\) | |||||||
\(234\) | −5.02824 | + | 8.79508i | −0.328706 | + | 0.574952i | ||||
\(235\) | −1.45245 | − | 1.45245i | −0.0947477 | − | 0.0947477i | ||||
\(236\) | 5.52429 | + | 1.43013i | 0.359601 | + | 0.0930938i | ||||
\(237\) | −5.70339 | + | 5.70339i | −0.370475 | + | 0.370475i | ||||
\(238\) | 0.611833 | − | 0.166724i | 0.0396593 | − | 0.0108071i | ||||
\(239\) | 22.7723 | 1.47302 | 0.736510 | − | 0.676427i | \(-0.236473\pi\) | ||||
0.736510 | + | 0.676427i | \(0.236473\pi\) | |||||||
\(240\) | −0.320961 | + | 0.578355i | −0.0207179 | + | 0.0373327i | ||||
\(241\) | 7.04377 | 0.453729 | 0.226864 | − | 0.973926i | \(-0.427153\pi\) | ||||
0.226864 | + | 0.973926i | \(0.427153\pi\) | |||||||
\(242\) | −13.0714 | + | 3.56194i | −0.840261 | + | 0.228970i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −4.26895 | + | 16.4900i | −0.273291 | + | 1.05566i | ||||
\(245\) | −0.116928 | − | 0.116928i | −0.00747027 | − | 0.00747027i | ||||
\(246\) | 3.80699 | − | 6.65894i | 0.242725 | − | 0.424558i | ||||
\(247\) | − | 16.8340i | − | 1.07112i | ||||||
\(248\) | −2.83681 | − | 2.76554i | −0.180137 | − | 0.175612i | ||||
\(249\) | 10.5895i | 0.671084i | ||||||||
\(250\) | −2.02464 | − | 1.15751i | −0.128050 | − | 0.0732074i | ||||
\(251\) | −0.962935 | − | 0.962935i | −0.0607799 | − | 0.0607799i | 0.676063 | − | 0.736843i | \(-0.263685\pi\) |
−0.736843 | + | 0.676063i | \(0.763685\pi\) | |||||||
\(252\) | 1.72351 | − | 1.01465i | 0.108571 | − | 0.0639170i | ||||
\(253\) | −2.24929 | + | 2.24929i | −0.141412 | + | 0.141412i | ||||
\(254\) | 1.38532 | + | 5.08376i | 0.0869226 | + | 0.318983i | ||||
\(255\) | 0.0741491 | 0.00464340 | ||||||||
\(256\) | −8.46531 | − | 13.5771i | −0.529082 | − | 0.848571i | ||||
\(257\) | 14.1715 | 0.883994 | 0.441997 | − | 0.897016i | \(-0.354270\pi\) | ||||
0.441997 | + | 0.897016i | \(0.354270\pi\) | |||||||
\(258\) | 1.73630 | + | 6.37177i | 0.108097 | + | 0.396689i | ||||
\(259\) | 5.76957 | − | 5.76957i | 0.358504 | − | 0.358504i | ||||
\(260\) | −2.04166 | + | 1.20195i | −0.126619 | + | 0.0745419i | ||||
\(261\) | −0.858643 | − | 0.858643i | −0.0531487 | − | 0.0531487i | ||||
\(262\) | 0.730150 | + | 0.417435i | 0.0451088 | + | 0.0257892i | ||||
\(263\) | 20.3221i | 1.25311i | 0.779376 | + | 0.626557i | \(0.215536\pi\) | ||||
−0.779376 | + | 0.626557i | \(0.784464\pi\) | |||||||
\(264\) | 2.41349 | + | 2.35286i | 0.148540 | + | 0.144808i | ||||
\(265\) | 1.80473i | 0.110864i | ||||||||
\(266\) | −1.64942 | + | 2.88506i | −0.101133 | + | 0.176895i | ||||
\(267\) | −6.24117 | − | 6.24117i | −0.381954 | − | 0.381954i | ||||
\(268\) | 2.52143 | − | 9.73973i | 0.154021 | − | 0.594949i | ||||
\(269\) | 8.72963 | − | 8.72963i | 0.532255 | − | 0.532255i | −0.388988 | − | 0.921243i | \(-0.627175\pi\) |
0.921243 | + | 0.388988i | \(0.127175\pi\) | |||||||
\(270\) | 0.225629 | − | 0.0614837i | 0.0137314 | − | 0.00374178i | ||||
\(271\) | 24.7011 | 1.50049 | 0.750244 | − | 0.661161i | \(-0.229936\pi\) | ||||
0.750244 | + | 0.661161i | \(0.229936\pi\) | |||||||
\(272\) | −0.870341 | + | 1.56831i | −0.0527722 | + | 0.0950928i | ||||
\(273\) | 7.16368 | 0.433566 | ||||||||
\(274\) | 20.5167 | − | 5.59077i | 1.23946 | − | 0.337750i | ||||
\(275\) | −4.19020 | + | 4.19020i | −0.252678 | + | 0.252678i | ||||
\(276\) | −5.16825 | − | 1.33796i | −0.311092 | − | 0.0805358i | ||||
\(277\) | 1.69928 | + | 1.69928i | 0.102100 | + | 0.102100i | 0.756311 | − | 0.654212i | \(-0.226999\pi\) |
−0.654212 | + | 0.756311i | \(0.726999\pi\) | |||||||
\(278\) | −14.4812 | + | 25.3295i | −0.868522 | + | 1.51916i | ||||
\(279\) | 1.40070i | 0.0838578i | ||||||||
\(280\) | 0.467675 | − | 0.00594906i | 0.0279489 | − | 0.000355525i | ||||
\(281\) | − | 1.77758i | − | 0.106042i | −0.998593 | − | 0.0530208i | \(-0.983115\pi\) | ||
0.998593 | − | 0.0530208i | \(-0.0168850\pi\) | |||||||
\(282\) | −15.2506 | − | 8.71893i | −0.908159 | − | 0.519205i | ||||
\(283\) | 12.6599 | + | 12.6599i | 0.752553 | + | 0.752553i | 0.974955 | − | 0.222402i | \(-0.0713897\pi\) |
−0.222402 | + | 0.974955i | \(0.571390\pi\) | |||||||
\(284\) | −11.2667 | − | 19.1379i | −0.668556 | − | 1.13562i | ||||
\(285\) | −0.274771 | + | 0.274771i | −0.0162760 | + | 0.0162760i | ||||
\(286\) | 3.17412 | + | 11.6482i | 0.187689 | + | 0.688772i | ||||
\(287\) | −5.42377 | −0.320155 | ||||||||
\(288\) | −1.34794 | + | 5.49391i | −0.0794284 | + | 0.323732i | ||||
\(289\) | −16.7989 | −0.988172 | ||||||||
\(290\) | −0.0746600 | − | 0.273983i | −0.00438418 | − | 0.0160888i | ||||
\(291\) | 1.55560 | − | 1.55560i | 0.0911911 | − | 0.0911911i | ||||
\(292\) | 8.52178 | + | 14.4753i | 0.498700 | + | 0.847102i | ||||
\(293\) | 10.9894 | + | 10.9894i | 0.642008 | + | 0.642008i | 0.951049 | − | 0.309041i | \(-0.100008\pi\) |
−0.309041 | + | 0.951049i | \(0.600008\pi\) | |||||||
\(294\) | −1.22773 | − | 0.701908i | −0.0716028 | − | 0.0409361i | ||||
\(295\) | − | 0.471810i | − | 0.0274698i | ||||||
\(296\) | 0.293544 | + | 23.0764i | 0.0170619 | + | 1.34129i | ||||
\(297\) | − | 1.19168i | − | 0.0691485i | ||||||
\(298\) | 15.3244 | − | 26.8044i | 0.887718 | − | 1.55274i | ||||
\(299\) | −13.5214 | − | 13.5214i | −0.781961 | − | 0.781961i | ||||
\(300\) | −9.62791 | − | 2.49248i | −0.555868 | − | 0.143904i | ||||
\(301\) | 3.30205 | − | 3.30205i | 0.190327 | − | 0.190327i | ||||
\(302\) | 10.6611 | − | 2.90512i | 0.613475 | − | 0.167171i | ||||
\(303\) | 8.70994 | 0.500373 | ||||||||
\(304\) | −2.58644 | − | 9.03681i | −0.148342 | − | 0.518296i | ||||
\(305\) | 1.40835 | 0.0806420 | ||||||||
\(306\) | 0.611833 | − | 0.166724i | 0.0349762 | − | 0.00953096i | ||||
\(307\) | −17.8158 | + | 17.8158i | −1.01680 | + | 1.01680i | −0.0169469 | + | 0.999856i | \(0.505395\pi\) |
−0.999856 | + | 0.0169469i | \(0.994605\pi\) | |||||||
\(308\) | 0.597317 | − | 2.30730i | 0.0340353 | − | 0.131471i | ||||
\(309\) | −9.10416 | − | 9.10416i | −0.517917 | − | 0.517917i | ||||
\(310\) | −0.162577 | + | 0.284370i | −0.00923377 | + | 0.0161511i | ||||
\(311\) | − | 13.3582i | − | 0.757476i | −0.925504 | − | 0.378738i | \(-0.876358\pi\) | ||
0.925504 | − | 0.378738i | \(-0.123642\pi\) | |||||||
\(312\) | −14.1440 | + | 14.5084i | −0.800744 | + | 0.821378i | ||||
\(313\) | 15.5358i | 0.878137i | 0.898454 | + | 0.439068i | \(0.144691\pi\) | ||||
−0.898454 | + | 0.439068i | \(0.855309\pi\) | |||||||
\(314\) | 21.7716 | + | 12.4471i | 1.22864 | + | 0.702428i | ||||
\(315\) | −0.116928 | − | 0.116928i | −0.00658816 | − | 0.00658816i | ||||
\(316\) | −13.9015 | + | 8.18399i | −0.782021 | + | 0.460386i | ||||
\(317\) | −7.90981 | + | 7.90981i | −0.444259 | + | 0.444259i | −0.893441 | − | 0.449181i | \(-0.851716\pi\) |
0.449181 | + | 0.893441i | \(0.351716\pi\) | |||||||
\(318\) | 4.05793 | + | 14.8915i | 0.227557 | + | 0.835076i | ||||
\(319\) | −1.44707 | −0.0810202 | ||||||||
\(320\) | −0.911329 | + | 0.958917i | −0.0509448 | + | 0.0536051i | ||||
\(321\) | −2.27089 | −0.126748 | ||||||||
\(322\) | 0.992488 | + | 3.64218i | 0.0553092 | + | 0.202971i | ||||
\(323\) | −0.745090 | + | 0.745090i | −0.0414579 | + | 0.0414579i | ||||
\(324\) | 1.72351 | − | 1.01465i | 0.0957505 | − | 0.0563695i | ||||
\(325\) | −25.1889 | − | 25.1889i | −1.39723 | − | 1.39723i | ||||
\(326\) | 7.44558 | + | 4.25672i | 0.412372 | + | 0.235758i | ||||
\(327\) | − | 6.71248i | − | 0.371201i | ||||||
\(328\) | 10.7087 | − | 10.9846i | 0.591288 | − | 0.606525i | ||||
\(329\) | 12.4218i | 0.684834i | ||||||||
\(330\) | 0.138317 | − | 0.241935i | 0.00761409 | − | 0.0133181i | ||||
\(331\) | −7.23397 | − | 7.23397i | −0.397615 | − | 0.397615i | 0.479776 | − | 0.877391i | \(-0.340718\pi\) |
−0.877391 | + | 0.479776i | \(0.840718\pi\) | |||||||
\(332\) | −5.30787 | + | 20.5031i | −0.291307 | + | 1.12526i | ||||
\(333\) | 5.76957 | − | 5.76957i | 0.316171 | − | 0.316171i | ||||
\(334\) | −20.9964 | + | 5.72148i | −1.14887 | + | 0.313065i | ||||
\(335\) | −0.831835 | −0.0454480 | ||||||||
\(336\) | 3.84559 | − | 1.10065i | 0.209794 | − | 0.0600455i | ||||
\(337\) | −10.6952 | −0.582602 | −0.291301 | − | 0.956631i | \(-0.594088\pi\) | ||||
−0.291301 | + | 0.956631i | \(0.594088\pi\) | |||||||
\(338\) | −52.2838 | + | 14.2473i | −2.84387 | + | 0.774950i | ||||
\(339\) | 11.3702 | − | 11.3702i | 0.617546 | − | 0.617546i | ||||
\(340\) | 0.143565 | + | 0.0371664i | 0.00778593 | + | 0.00201563i | ||||
\(341\) | 1.18030 | + | 1.18030i | 0.0639167 | + | 0.0639167i | ||||
\(342\) | −1.64942 | + | 2.88506i | −0.0891905 | + | 0.156006i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0.168001 | + | 13.2071i | 0.00905803 | + | 0.712081i | ||||
\(345\) | 0.441402i | 0.0237643i | ||||||||
\(346\) | 20.6864 | + | 11.8267i | 1.11211 | + | 0.635805i | ||||
\(347\) | 21.2763 | + | 21.2763i | 1.14217 | + | 1.14217i | 0.988052 | + | 0.154121i | \(0.0492547\pi\) |
0.154121 | + | 0.988052i | \(0.450745\pi\) | |||||||
\(348\) | −1.23210 | − | 2.09287i | −0.0660473 | − | 0.112189i | ||||
\(349\) | −3.09709 | + | 3.09709i | −0.165783 | + | 0.165783i | −0.785123 | − | 0.619340i | \(-0.787400\pi\) |
0.619340 | + | 0.785123i | \(0.287400\pi\) | |||||||
\(350\) | 1.84890 | + | 6.78500i | 0.0988280 | + | 0.362673i | ||||
\(351\) | 7.16368 | 0.382369 | ||||||||
\(352\) | 3.49359 | + | 5.76527i | 0.186209 | + | 0.307290i | ||||
\(353\) | 24.0364 | 1.27933 | 0.639665 | − | 0.768654i | \(-0.279073\pi\) | ||||
0.639665 | + | 0.768654i | \(0.279073\pi\) | |||||||
\(354\) | −1.06086 | − | 3.89309i | −0.0563841 | − | 0.206915i | ||||
\(355\) | −1.29837 | + | 1.29837i | −0.0689105 | + | 0.0689105i | ||||
\(356\) | −8.95567 | − | 15.2123i | −0.474650 | − | 0.806250i | ||||
\(357\) | −0.317071 | − | 0.317071i | −0.0167812 | − | 0.0167812i | ||||
\(358\) | −28.6130 | − | 16.3584i | −1.51225 | − | 0.864567i | ||||
\(359\) | − | 25.2131i | − | 1.33070i | −0.746532 | − | 0.665349i | \(-0.768283\pi\) | ||
0.746532 | − | 0.665349i | \(-0.231717\pi\) | |||||||
\(360\) | 0.467675 | − | 0.00594906i | 0.0246486 | − | 0.000313543i | ||||
\(361\) | 13.4779i | 0.709363i | ||||||||
\(362\) | 5.65803 | − | 9.89667i | 0.297380 | − | 0.520157i | ||||
\(363\) | 6.77401 | + | 6.77401i | 0.355543 | + | 0.355543i | ||||
\(364\) | 13.8701 | + | 3.59071i | 0.726991 | + | 0.188204i | ||||
\(365\) | 0.982049 | − | 0.982049i | 0.0514028 | − | 0.0514028i | ||||
\(366\) | 11.6209 | − | 3.16667i | 0.607432 | − | 0.165524i | ||||
\(367\) | 9.37796 | 0.489526 | 0.244763 | − | 0.969583i | \(-0.421290\pi\) | ||||
0.244763 | + | 0.969583i | \(0.421290\pi\) | |||||||
\(368\) | −9.33598 | − | 5.18104i | −0.486672 | − | 0.270081i | ||||
\(369\) | −5.42377 | −0.282350 | ||||||||
\(370\) | 1.84100 | − | 0.501670i | 0.0957091 | − | 0.0260806i | ||||
\(371\) | 7.71727 | − | 7.71727i | 0.400661 | − | 0.400661i | ||||
\(372\) | −0.702084 | + | 2.71200i | −0.0364014 | + | 0.140611i | ||||
\(373\) | 11.0512 | + | 11.0512i | 0.572209 | + | 0.572209i | 0.932745 | − | 0.360536i | \(-0.117406\pi\) |
−0.360536 | + | 0.932745i | \(0.617406\pi\) | |||||||
\(374\) | 0.375070 | − | 0.656049i | 0.0193944 | − | 0.0339235i | ||||
\(375\) | 1.64909i | 0.0851588i | ||||||||
\(376\) | −25.1575 | − | 24.5255i | −1.29740 | − | 1.26481i | ||||
\(377\) | − | 8.69889i | − | 0.448016i | ||||||
\(378\) | −1.22773 | − | 0.701908i | −0.0631477 | − | 0.0361022i | ||||
\(379\) | 19.6856 | + | 19.6856i | 1.01118 | + | 1.01118i | 0.999937 | + | 0.0112441i | \(0.00357920\pi\) |
0.0112441 | + | 0.999937i | \(0.496421\pi\) | |||||||
\(380\) | −0.669730 | + | 0.394279i | −0.0343564 | + | 0.0202261i | ||||
\(381\) | 2.63456 | − | 2.63456i | 0.134973 | − | 0.134973i | ||||
\(382\) | 2.07602 | + | 7.61847i | 0.106219 | + | 0.389795i | ||||
\(383\) | 1.50314 | 0.0768067 | 0.0384034 | − | 0.999262i | \(-0.487773\pi\) | ||||
0.0384034 | + | 0.999262i | \(0.487773\pi\) | |||||||
\(384\) | −5.36361 | + | 9.96151i | −0.273710 | + | 0.508346i | ||||
\(385\) | −0.197059 | −0.0100430 | ||||||||
\(386\) | 3.03785 | + | 11.1481i | 0.154622 | + | 0.567424i | ||||
\(387\) | 3.30205 | − | 3.30205i | 0.167853 | − | 0.167853i | ||||
\(388\) | 3.79164 | − | 2.23219i | 0.192491 | − | 0.113322i | ||||
\(389\) | −24.4743 | − | 24.4743i | −1.24090 | − | 1.24090i | −0.959630 | − | 0.281266i | \(-0.909246\pi\) |
−0.281266 | − | 0.959630i | \(-0.590754\pi\) | |||||||
\(390\) | 1.45437 | + | 0.831477i | 0.0736447 | + | 0.0421035i | ||||
\(391\) | 1.19694i | 0.0605317i | ||||||||
\(392\) | −2.02528 | − | 1.97440i | −0.102292 | − | 0.0997222i | ||||
\(393\) | − | 0.594714i | − | 0.0299994i | ||||||
\(394\) | −7.88728 | + | 13.7959i | −0.397356 | + | 0.695029i | ||||
\(395\) | 0.943122 | + | 0.943122i | 0.0474536 | + | 0.0474536i | ||||
\(396\) | 0.597317 | − | 2.30730i | 0.0300163 | − | 0.115946i | ||||
\(397\) | −16.2293 | + | 16.2293i | −0.814527 | + | 0.814527i | −0.985309 | − | 0.170782i | \(-0.945371\pi\) |
0.170782 | + | 0.985309i | \(0.445371\pi\) | |||||||
\(398\) | 2.91057 | − | 0.793126i | 0.145894 | − | 0.0397558i | ||||
\(399\) | 2.34991 | 0.117643 | ||||||||
\(400\) | −17.3920 | − | 9.65175i | −0.869598 | − | 0.482587i | ||||
\(401\) | −8.45753 | −0.422349 | −0.211174 | − | 0.977448i | \(-0.567729\pi\) | ||||
−0.211174 | + | 0.977448i | \(0.567729\pi\) | |||||||
\(402\) | −6.86379 | + | 1.87038i | −0.342335 | + | 0.0932858i | ||||
\(403\) | −7.09523 | + | 7.09523i | −0.353439 | + | 0.353439i | ||||
\(404\) | 16.8639 | + | 4.36575i | 0.839012 | + | 0.217204i | ||||
\(405\) | −0.116928 | − | 0.116928i | −0.00581021 | − | 0.00581021i | ||||
\(406\) | −0.852330 | + | 1.49084i | −0.0423004 | + | 0.0739892i | ||||
\(407\) | − | 9.72343i | − | 0.481973i | ||||||
\(408\) | 1.26818 | − | 0.0161319i | 0.0627844 | − | 0.000798649i | ||||
\(409\) | − | 2.90076i | − | 0.143433i | −0.997425 | − | 0.0717166i | \(-0.977152\pi\) | ||
0.997425 | − | 0.0717166i | \(-0.0228477\pi\) | |||||||
\(410\) | −1.10113 | − | 0.629529i | −0.0543810 | − | 0.0310902i | ||||
\(411\) | −10.6324 | − | 10.6324i | −0.524457 | − | 0.524457i | ||||
\(412\) | −13.0639 | − | 22.1906i | −0.643610 | − | 1.09325i | ||||
\(413\) | −2.01752 | + | 2.01752i | −0.0992757 | + | 0.0992757i | ||||
\(414\) | 0.992488 | + | 3.64218i | 0.0487781 | + | 0.179003i | ||||
\(415\) | 1.75110 | 0.0859581 | ||||||||
\(416\) | −34.6573 | + | 21.0013i | −1.69921 | + | 1.02968i | ||||
\(417\) | 20.6312 | 1.01031 | ||||||||
\(418\) | 1.04121 | + | 3.82097i | 0.0509273 | + | 0.186890i | ||||
\(419\) | 8.22993 | − | 8.22993i | 0.402058 | − | 0.402058i | −0.476900 | − | 0.878958i | \(-0.658239\pi\) |
0.878958 | + | 0.476900i | \(0.158239\pi\) | |||||||
\(420\) | −0.167784 | − | 0.285002i | −0.00818703 | − | 0.0139067i | ||||
\(421\) | 12.1183 | + | 12.1183i | 0.590609 | + | 0.590609i | 0.937796 | − | 0.347187i | \(-0.112863\pi\) |
−0.347187 | + | 0.937796i | \(0.612863\pi\) | |||||||
\(422\) | −12.0661 | − | 6.89830i | −0.587367 | − | 0.335804i | ||||
\(423\) | 12.4218i | 0.603967i | ||||||||
\(424\) | 0.392638 | + | 30.8666i | 0.0190682 | + | 1.49901i | ||||
\(425\) | 2.22977i | 0.108160i | ||||||||
\(426\) | −7.79400 | + | 13.6328i | −0.377620 | + | 0.660509i | ||||
\(427\) | −6.02230 | − | 6.02230i | −0.291439 | − | 0.291439i | ||||
\(428\) | −4.39682 | − | 1.13825i | −0.212529 | − | 0.0550196i | ||||
\(429\) | 6.03646 | − | 6.03646i | 0.291443 | − | 0.291443i | ||||
\(430\) | 1.05364 | − | 0.287117i | 0.0508113 | − | 0.0138460i | ||||
\(431\) | 23.4181 | 1.12801 | 0.564005 | − | 0.825771i | \(-0.309260\pi\) | ||||
0.564005 | + | 0.825771i | \(0.309260\pi\) | |||||||
\(432\) | 3.84559 | − | 1.10065i | 0.185021 | − | 0.0529551i | ||||
\(433\) | −17.2436 | −0.828673 | −0.414336 | − | 0.910124i | \(-0.635986\pi\) | ||||
−0.414336 | + | 0.910124i | \(0.635986\pi\) | |||||||
\(434\) | 1.91120 | − | 0.520800i | 0.0917406 | − | 0.0249992i | ||||
\(435\) | −0.141987 | + | 0.141987i | −0.00680773 | + | 0.00680773i | ||||
\(436\) | 3.36455 | − | 12.9965i | 0.161133 | − | 0.622420i | ||||
\(437\) | −4.43544 | − | 4.43544i | −0.212176 | − | 0.212176i | ||||
\(438\) | 5.89513 | − | 10.3114i | 0.281680 | − | 0.492697i | ||||
\(439\) | − | 15.7763i | − | 0.752961i | −0.926424 | − | 0.376481i | \(-0.877134\pi\) | ||
0.926424 | − | 0.376481i | \(-0.122866\pi\) | |||||||
\(440\) | 0.389072 | − | 0.399098i | 0.0185483 | − | 0.0190263i | ||||
\(441\) | 1.00000i | 0.0476190i | ||||||||
\(442\) | 3.94377 | + | 2.25470i | 0.187586 | + | 0.107245i | ||||
\(443\) | −2.04057 | − | 2.04057i | −0.0969506 | − | 0.0969506i | 0.656968 | − | 0.753919i | \(-0.271839\pi\) |
−0.753919 | + | 0.656968i | \(0.771839\pi\) | |||||||
\(444\) | 14.0628 | − | 8.27895i | 0.667391 | − | 0.392902i | ||||
\(445\) | −1.03205 | + | 1.03205i | −0.0489238 | + | 0.0489238i | ||||
\(446\) | −3.65534 | − | 13.4142i | −0.173085 | − | 0.635179i | ||||
\(447\) | −21.8325 | −1.03264 | ||||||||
\(448\) | 7.99741 | − | 0.203495i | 0.377842 | − | 0.00961424i | ||||
\(449\) | −30.1235 | −1.42162 | −0.710809 | − | 0.703385i | \(-0.751671\pi\) | ||||
−0.710809 | + | 0.703385i | \(0.751671\pi\) | |||||||
\(450\) | 1.84890 | + | 6.78500i | 0.0871581 | + | 0.319848i | ||||
\(451\) | −4.57033 | + | 4.57033i | −0.215208 | + | 0.215208i | ||||
\(452\) | 27.7139 | − | 16.3155i | 1.30355 | − | 0.767418i | ||||
\(453\) | −5.52489 | − | 5.52489i | −0.259582 | − | 0.259582i | ||||
\(454\) | −18.9208 | − | 10.8172i | −0.887998 | − | 0.507678i | ||||
\(455\) | − | 1.18460i | − | 0.0555347i | ||||||
\(456\) | −4.63967 | + | 4.75923i | −0.217272 | + | 0.222871i | ||||
\(457\) | − | 15.3037i | − | 0.715876i | −0.933745 | − | 0.357938i | \(-0.883480\pi\) | ||
0.933745 | − | 0.357938i | \(-0.116520\pi\) | |||||||
\(458\) | 18.1670 | − | 31.7766i | 0.848888 | − | 1.48482i | ||||
\(459\) | −0.317071 | − | 0.317071i | −0.0147996 | − | 0.0147996i | ||||
\(460\) | −0.221247 | + | 0.854629i | −0.0103157 | + | 0.0398473i | ||||
\(461\) | 3.13603 | − | 3.13603i | 0.146060 | − | 0.146060i | −0.630296 | − | 0.776355i | \(-0.717066\pi\) |
0.776355 | + | 0.630296i | \(0.217066\pi\) | |||||||
\(462\) | −1.62601 | + | 0.443085i | −0.0756486 | + | 0.0206142i | ||||
\(463\) | 26.1517 | 1.21537 | 0.607686 | − | 0.794178i | \(-0.292098\pi\) | ||||
0.607686 | + | 0.794178i | \(0.292098\pi\) | |||||||
\(464\) | −1.33653 | − | 4.66972i | −0.0620467 | − | 0.216786i | ||||
\(465\) | 0.231622 | 0.0107412 | ||||||||
\(466\) | 27.8571 | − | 7.59103i | 1.29046 | − | 0.351647i | ||||
\(467\) | 8.99017 | − | 8.99017i | 0.416015 | − | 0.416015i | −0.467812 | − | 0.883828i | \(-0.654958\pi\) |
0.883828 | + | 0.467812i | \(0.154958\pi\) | |||||||
\(468\) | 13.8701 | + | 3.59071i | 0.641146 | + | 0.165980i | ||||
\(469\) | 3.55703 | + | 3.55703i | 0.164249 | + | 0.164249i | ||||
\(470\) | −1.44177 | + | 2.52186i | −0.0665041 | + | 0.116325i | ||||
\(471\) | − | 17.7332i | − | 0.817102i | ||||||
\(472\) | −0.102647 | − | 8.06943i | −0.00472472 | − | 0.371426i | ||||
\(473\) | − | 5.56493i | − | 0.255876i | ||||||
\(474\) | 9.90266 | + | 5.66146i | 0.454844 | + | 0.260039i | ||||
\(475\) | −8.26276 | − | 8.26276i | −0.379122 | − | 0.379122i | ||||
\(476\) | −0.454976 | − | 0.772832i | −0.0208538 | − | 0.0354227i | ||||
\(477\) | 7.71727 | − | 7.71727i | 0.353349 | − | 0.353349i | ||||
\(478\) | −8.46707 | − | 31.0720i | −0.387275 | − | 1.42120i | ||||
\(479\) | −24.8217 | −1.13413 | −0.567066 | − | 0.823672i | \(-0.691922\pi\) | ||||
−0.567066 | + | 0.823672i | \(0.691922\pi\) | |||||||
\(480\) | 0.908481 | + | 0.222898i | 0.0414663 | + | 0.0101739i | ||||
\(481\) | 58.4514 | 2.66515 | ||||||||
\(482\) | −2.61897 | − | 9.61095i | −0.119291 | − | 0.437767i | ||||
\(483\) | 1.88749 | − | 1.88749i | 0.0858838 | − | 0.0858838i | ||||
\(484\) | 9.72025 | + | 16.5110i | 0.441830 | + | 0.750501i | ||||
\(485\) | −0.257237 | − | 0.257237i | −0.0116805 | − | 0.0116805i | ||||
\(486\) | −1.22773 | − | 0.701908i | −0.0556911 | − | 0.0318392i | ||||
\(487\) | 12.6249i | 0.572087i | 0.958217 | + | 0.286043i | \(0.0923401\pi\) | ||||
−0.958217 | + | 0.286043i | \(0.907660\pi\) | |||||||
\(488\) | 24.0872 | − | 0.306402i | 1.09038 | − | 0.0138702i | ||||
\(489\) | − | 6.06450i | − | 0.274246i | ||||||
\(490\) | −0.116068 | + | 0.203020i | −0.00524344 | + | 0.00917149i | ||||
\(491\) | 13.7916 | + | 13.7916i | 0.622407 | + | 0.622407i | 0.946146 | − | 0.323739i | \(-0.104940\pi\) |
−0.323739 | + | 0.946146i | \(0.604940\pi\) | |||||||
\(492\) | −10.5014 | − | 2.71860i | −0.473438 | − | 0.122564i | ||||
\(493\) | −0.385021 | + | 0.385021i | −0.0173405 | + | 0.0173405i | ||||
\(494\) | −22.9694 | + | 6.25913i | −1.03344 | + | 0.281611i | ||||
\(495\) | −0.197059 | −0.00885712 | ||||||||
\(496\) | −2.71871 | + | 4.89898i | −0.122074 | + | 0.219971i | ||||
\(497\) | 11.1040 | 0.498083 | ||||||||
\(498\) | 14.4490 | − | 3.93733i | 0.647475 | − | 0.176436i | ||||
\(499\) | −26.6980 | + | 26.6980i | −1.19516 | + | 1.19516i | −0.219567 | + | 0.975597i | \(0.570465\pi\) |
−0.975597 | + | 0.219567i | \(0.929535\pi\) | |||||||
\(500\) | −0.826588 | + | 3.19293i | −0.0369661 | + | 0.142792i | ||||
\(501\) | 10.8810 | + | 10.8810i | 0.486126 | + | 0.486126i | ||||
\(502\) | −0.955855 | + | 1.67192i | −0.0426619 | + | 0.0746215i | ||||
\(503\) | − | 29.5574i | − | 1.31790i | −0.752186 | − | 0.658951i | \(-0.771001\pi\) | ||
0.752186 | − | 0.658951i | \(-0.228999\pi\) | |||||||
\(504\) | −2.02528 | − | 1.97440i | −0.0902130 | − | 0.0879467i | ||||
\(505\) | − | 1.44029i | − | 0.0640920i | ||||||
\(506\) | 3.90539 | + | 2.23275i | 0.173616 | + | 0.0992580i | ||||
\(507\) | 27.0951 | + | 27.0951i | 1.20334 | + | 1.20334i | ||||
\(508\) | 6.42151 | − | 3.78043i | 0.284909 | − | 0.167729i | ||||
\(509\) | 13.2978 | − | 13.2978i | 0.589413 | − | 0.589413i | −0.348060 | − | 0.937472i | \(-0.613159\pi\) |
0.937472 | + | 0.348060i | \(0.113159\pi\) | |||||||
\(510\) | −0.0275697 | − | 0.101174i | −0.00122081 | − | 0.00448004i | ||||
\(511\) | −8.39873 | −0.371538 | ||||||||
\(512\) | −15.3779 | + | 16.5988i | −0.679616 | + | 0.733568i | ||||
\(513\) | 2.34991 | 0.103751 | ||||||||
\(514\) | −5.26917 | − | 19.3365i | −0.232413 | − | 0.852895i | ||||
\(515\) | −1.50548 | + | 1.50548i | −0.0663392 | + | 0.0663392i | ||||
\(516\) | 8.04845 | − | 4.73822i | 0.354313 | − | 0.208589i | ||||
\(517\) | 10.4672 | + | 10.4672i | 0.460345 | + | 0.460345i | ||||
\(518\) | −10.0176 | − | 5.72715i | −0.440146 | − | 0.251636i | ||||
\(519\) | − | 16.8493i | − | 0.739603i | ||||||
\(520\) | 2.39914 | + | 2.33887i | 0.105209 | + | 0.102566i | ||||
\(521\) | 13.4541i | 0.589435i | 0.955584 | + | 0.294717i | \(0.0952255\pi\) | ||||
−0.955584 | + | 0.294717i | \(0.904774\pi\) | |||||||
\(522\) | −0.852330 | + | 1.49084i | −0.0373055 | + | 0.0652523i | ||||
\(523\) | 4.26642 | + | 4.26642i | 0.186558 | + | 0.186558i | 0.794206 | − | 0.607648i | \(-0.207887\pi\) |
−0.607648 | + | 0.794206i | \(0.707887\pi\) | |||||||
\(524\) | 0.298093 | − | 1.15147i | 0.0130223 | − | 0.0503022i | ||||
\(525\) | 3.51620 | − | 3.51620i | 0.153459 | − | 0.153459i | ||||
\(526\) | 27.7287 | − | 7.55604i | 1.20903 | − | 0.329459i | ||||
\(527\) | 0.628083 | 0.0273597 | ||||||||
\(528\) | 2.31302 | − | 4.16794i | 0.100661 | − | 0.181386i | ||||
\(529\) | 15.8748 | 0.690207 | ||||||||
\(530\) | 2.46249 | − | 0.671025i | 0.106964 | − | 0.0291474i | ||||
\(531\) | −2.01752 | + | 2.01752i | −0.0875529 | + | 0.0875529i | ||||
\(532\) | 4.54984 | + | 1.17787i | 0.197260 | + | 0.0510669i | ||||
\(533\) | −27.4740 | − | 27.4740i | −1.19003 | − | 1.19003i | ||||
\(534\) | −6.19528 | + | 10.8364i | −0.268096 | + | 0.468937i | ||||
\(535\) | 0.375517i | 0.0162350i | ||||||||
\(536\) | −14.2270 | + | 0.180974i | −0.614512 | + | 0.00781691i | ||||
\(537\) | 23.3056i | 1.00571i | ||||||||
\(538\) | −15.1570 | − | 8.66544i | −0.653467 | − | 0.373594i | ||||
\(539\) | 0.842648 | + | 0.842648i | 0.0362954 | + | 0.0362954i | ||||
\(540\) | −0.167784 | − | 0.285002i | −0.00722028 | − | 0.0122645i | ||||
\(541\) | −22.8454 | + | 22.8454i | −0.982202 | + | 0.982202i | −0.999844 | − | 0.0176425i | \(-0.994384\pi\) |
0.0176425 | + | 0.999844i | \(0.494384\pi\) | |||||||
\(542\) | −9.18423 | − | 33.7038i | −0.394496 | − | 1.44770i | ||||
\(543\) | −8.06094 | −0.345928 | ||||||||
\(544\) | 2.46350 | + | 0.604427i | 0.105622 | + | 0.0259146i | ||||
\(545\) | −1.10999 | −0.0475465 | ||||||||
\(546\) | −2.66356 | − | 9.77456i | −0.113990 | − | 0.418313i | ||||
\(547\) | −31.0153 | + | 31.0153i | −1.32612 | + | 1.32612i | −0.417391 | + | 0.908727i | \(0.637055\pi\) |
−0.908727 | + | 0.417391i | \(0.862945\pi\) | |||||||
\(548\) | −15.2568 | − | 25.9155i | −0.651737 | − | 1.10705i | ||||
\(549\) | −6.02230 | − | 6.02230i | −0.257025 | − | 0.257025i | ||||
\(550\) | 7.27533 | + | 4.15939i | 0.310221 | + | 0.177357i | ||||
\(551\) | − | 2.85351i | − | 0.121564i | ||||||
\(552\) | 0.0960316 | + | 7.54935i | 0.00408737 | + | 0.321322i | ||||
\(553\) | − | 8.06582i | − | 0.342993i | ||||||
\(554\) | 1.68678 | − | 2.95041i | 0.0716645 | − | 0.125351i | ||||
\(555\) | −0.954065 | − | 0.954065i | −0.0404978 | − | 0.0404978i | ||||
\(556\) | 39.9454 | + | 10.3411i | 1.69406 | + | 0.438561i | ||||
\(557\) | 17.9517 | − | 17.9517i | 0.760638 | − | 0.760638i | −0.215799 | − | 0.976438i | \(-0.569236\pi\) |
0.976438 | + | 0.215799i | \(0.0692358\pi\) | |||||||
\(558\) | 1.91120 | − | 0.520800i | 0.0809076 | − | 0.0220472i | ||||
\(559\) | 33.4530 | 1.41491 | ||||||||
\(560\) | −0.182005 | − | 0.635912i | −0.00769113 | − | 0.0268722i | ||||
\(561\) | −0.534359 | −0.0225606 | ||||||||
\(562\) | −2.42544 | + | 0.660930i | −0.102311 | + | 0.0278796i | ||||
\(563\) | −14.0454 | + | 14.0454i | −0.591943 | + | 0.591943i | −0.938156 | − | 0.346213i | \(-0.887467\pi\) |
0.346213 | + | 0.938156i | \(0.387467\pi\) | |||||||
\(564\) | −6.22625 | + | 24.0507i | −0.262173 | + | 1.01272i | ||||
\(565\) | −1.88020 | − | 1.88020i | −0.0791005 | − | 0.0791005i | ||||
\(566\) | 12.5668 | − | 21.9811i | 0.528223 | − | 0.923934i | ||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | −21.9238 | + | 22.4887i | −0.919901 | + | 0.943606i | ||||
\(569\) | − | 25.5548i | − | 1.07131i | −0.844436 | − | 0.535657i | \(-0.820064\pi\) | ||
0.844436 | − | 0.535657i | \(-0.179936\pi\) | |||||||
\(570\) | 0.477078 | + | 0.272751i | 0.0199826 | + | 0.0114243i | ||||
\(571\) | −24.6646 | − | 24.6646i | −1.03218 | − | 1.03218i | −0.999465 | − | 0.0327177i | \(-0.989584\pi\) |
−0.0327177 | − | 0.999465i | \(-0.510416\pi\) | |||||||
\(572\) | 14.7133 | − | 8.66192i | 0.615195 | − | 0.362173i | ||||
\(573\) | 3.94813 | − | 3.94813i | 0.164936 | − | 0.164936i | ||||
\(574\) | 2.01663 | + | 7.40053i | 0.0841727 | + | 0.308892i | ||||
\(575\) | −13.2736 | −0.553547 | ||||||||
\(576\) | 7.99741 | − | 0.203495i | 0.333225 | − | 0.00847897i | ||||
\(577\) | −23.4856 | −0.977720 | −0.488860 | − | 0.872362i | \(-0.662587\pi\) | ||||
−0.488860 | + | 0.872362i | \(0.662587\pi\) | |||||||
\(578\) | 6.24608 | + | 22.9215i | 0.259803 | + | 0.953408i | ||||
\(579\) | 5.77730 | − | 5.77730i | 0.240097 | − | 0.240097i | ||||
\(580\) | −0.346079 | + | 0.203741i | −0.0143702 | + | 0.00845989i | ||||
\(581\) | −7.48793 | − | 7.48793i | −0.310651 | − | 0.310651i | ||||
\(582\) | −2.70095 | − | 1.54417i | −0.111958 | − | 0.0640077i | ||||
\(583\) | − | 13.0059i | − | 0.538648i | ||||||
\(584\) | 16.5824 | − | 17.0098i | 0.686187 | − | 0.703869i | ||||
\(585\) | − | 1.18460i | − | 0.0489770i | ||||||
\(586\) | 10.9086 | − | 19.0806i | 0.450630 | − | 0.788214i | ||||
\(587\) | −20.3478 | − | 20.3478i | −0.839842 | − | 0.839842i | 0.148996 | − | 0.988838i | \(-0.452396\pi\) |
−0.988838 | + | 0.148996i | \(0.952396\pi\) | |||||||
\(588\) | −0.501238 | + | 1.93617i | −0.0206707 | + | 0.0798464i | ||||
\(589\) | −2.32746 | + | 2.32746i | −0.0959013 | + | 0.0959013i | ||||
\(590\) | −0.643767 | + | 0.175426i | −0.0265035 | + | 0.00722216i | ||||
\(591\) | 11.2369 | 0.462225 | ||||||||
\(592\) | 31.3777 | − | 8.98066i | 1.28962 | − | 0.369103i | ||||
\(593\) | 3.34815 | 0.137492 | 0.0687459 | − | 0.997634i | \(-0.478100\pi\) | ||||
0.0687459 | + | 0.997634i | \(0.478100\pi\) | |||||||
\(594\) | −1.62601 | + | 0.443085i | −0.0667158 | + | 0.0181800i | ||||
\(595\) | −0.0524314 | + | 0.0524314i | −0.00214948 | + | 0.00214948i | ||||
\(596\) | −42.2714 | − | 10.9433i | −1.73151 | − | 0.448254i | ||||
\(597\) | −1.50835 | − | 1.50835i | −0.0617325 | − | 0.0617325i | ||||
\(598\) | −13.4220 | + | 23.4768i | −0.548865 | + | 0.960039i | ||||
\(599\) | − | 1.10888i | − | 0.0453078i | −0.999743 | − | 0.0226539i | \(-0.992788\pi\) | ||
0.999743 | − | 0.0226539i | \(-0.00721158\pi\) | |||||||
\(600\) | 0.178897 | + | 14.0637i | 0.00730343 | + | 0.574146i | ||||
\(601\) | 33.3043i | 1.35851i | 0.733901 | + | 0.679256i | \(0.237697\pi\) | ||||
−0.733901 | + | 0.679256i | \(0.762303\pi\) | |||||||
\(602\) | −5.73327 | − | 3.27777i | −0.233671 | − | 0.133592i | ||||
\(603\) | 3.55703 | + | 3.55703i | 0.144854 | + | 0.144854i | ||||
\(604\) | −7.92786 | − | 13.4664i | −0.322580 | − | 0.547941i | ||||
\(605\) | 1.12016 | − | 1.12016i | 0.0455410 | − | 0.0455410i | ||||
\(606\) | −3.23848 | − | 11.8844i | −0.131554 | − | 0.482770i | ||||
\(607\) | −20.3798 | −0.827193 | −0.413596 | − | 0.910460i | \(-0.635727\pi\) | ||||
−0.413596 | + | 0.910460i | \(0.635727\pi\) | |||||||
\(608\) | −11.3687 | + | 6.88910i | −0.461062 | + | 0.279390i | ||||
\(609\) | 1.21430 | 0.0492061 | ||||||||
\(610\) | −0.523645 | − | 1.92164i | −0.0212018 | − | 0.0778050i | ||||
\(611\) | −62.9222 | + | 62.9222i | −2.54556 | + | 2.54556i | ||||
\(612\) | −0.454976 | − | 0.772832i | −0.0183913 | − | 0.0312399i | ||||
\(613\) | −16.5645 | − | 16.5645i | −0.669033 | − | 0.669033i | 0.288460 | − | 0.957492i | \(-0.406857\pi\) |
−0.957492 | + | 0.288460i | \(0.906857\pi\) | |||||||
\(614\) | 30.9332 | + | 17.6848i | 1.24836 | + | 0.713702i | ||||
\(615\) | 0.896883i | 0.0361658i | ||||||||
\(616\) | −3.37032 | + | 0.0428721i | −0.135794 | + | 0.00172737i | ||||
\(617\) | 0.0743739i | 0.00299418i | 0.999999 | + | 0.00149709i | \(0.000476539\pi\) | ||||
−0.999999 | + | 0.00149709i | \(0.999523\pi\) | |||||||
\(618\) | −9.03721 | + | 15.8073i | −0.363530 | + | 0.635864i | ||||
\(619\) | −15.5469 | − | 15.5469i | −0.624884 | − | 0.624884i | 0.321892 | − | 0.946776i | \(-0.395681\pi\) |
−0.946776 | + | 0.321892i | \(0.895681\pi\) | |||||||
\(620\) | 0.448460 | + | 0.116098i | 0.0180106 | + | 0.00466260i | ||||
\(621\) | 1.88749 | − | 1.88749i | 0.0757424 | − | 0.0757424i | ||||
\(622\) | −18.2268 | + | 4.96678i | −0.730828 | + | 0.199150i | ||||
\(623\) | 8.82635 | 0.353620 | ||||||||
\(624\) | 25.0551 | + | 13.9044i | 1.00301 | + | 0.556623i | ||||
\(625\) | −24.5906 | −0.983623 | ||||||||
\(626\) | 21.1980 | − | 5.77644i | 0.847244 | − | 0.230873i | ||||
\(627\) | 1.98015 | − | 1.98015i | 0.0790795 | − | 0.0790795i | ||||
\(628\) | 8.88854 | − | 34.3345i | 0.354691 | − | 1.37010i | ||||
\(629\) | −2.58711 | − | 2.58711i | −0.103155 | − | 0.103155i | ||||
\(630\) | −0.116068 | + | 0.203020i | −0.00462428 | + | 0.00808849i | ||||
\(631\) | 28.4423i | 1.13227i | 0.824313 | + | 0.566134i | \(0.191562\pi\) | ||||
−0.824313 | + | 0.566134i | \(0.808438\pi\) | |||||||
\(632\) | 16.3355 | + | 15.9251i | 0.649792 | + | 0.633468i | ||||
\(633\) | 9.82794i | 0.390625i | ||||||||
\(634\) | 13.7336 | + | 7.85165i | 0.545431 | + | 0.311829i | ||||
\(635\) | −0.435655 | − | 0.435655i | −0.0172885 | − | 0.0172885i | ||||
\(636\) | 18.8101 | − | 11.0738i | 0.745870 | − | 0.439103i | ||||
\(637\) | −5.06549 | + | 5.06549i | −0.200702 | + | 0.200702i | ||||
\(638\) | 0.538040 | + | 1.97447i | 0.0213012 | + | 0.0781699i | ||||
\(639\) | 11.1040 | 0.439268 | ||||||||
\(640\) | 1.64725 | + | 0.886934i | 0.0651133 | + | 0.0350591i | ||||
\(641\) | −17.6510 | −0.697171 | −0.348585 | − | 0.937277i | \(-0.613338\pi\) | ||||
−0.348585 | + | 0.937277i | \(0.613338\pi\) | |||||||
\(642\) | 0.844347 | + | 3.09854i | 0.0333237 | + | 0.122289i | ||||
\(643\) | −33.7930 | + | 33.7930i | −1.33266 | + | 1.33266i | −0.429685 | + | 0.902979i | \(0.641375\pi\) |
−0.902979 | + | 0.429685i | \(0.858625\pi\) | |||||||
\(644\) | 4.60059 | − | 2.70842i | 0.181288 | − | 0.106727i | ||||
\(645\) | −0.546032 | − | 0.546032i | −0.0215000 | − | 0.0215000i | ||||
\(646\) | 1.29368 | + | 0.739611i | 0.0508992 | + | 0.0290996i | ||||
\(647\) | 36.6980i | 1.44275i | 0.692547 | + | 0.721373i | \(0.256488\pi\) | ||||
−0.692547 | + | 0.721373i | \(0.743512\pi\) | |||||||
\(648\) | −2.02528 | − | 1.97440i | −0.0795604 | − | 0.0775617i | ||||
\(649\) | 3.40012i | 0.133466i | ||||||||
\(650\) | −25.0037 | + | 43.7349i | −0.980726 | + | 1.71542i | ||||
\(651\) | −0.990445 | − | 0.990445i | −0.0388186 | − | 0.0388186i | ||||
\(652\) | 3.03976 | − | 11.7419i | 0.119046 | − | 0.459849i | ||||
\(653\) | 25.5329 | − | 25.5329i | 0.999179 | − | 0.999179i | −0.000820971 | − | 1.00000i | \(-0.500261\pi\) |
1.00000 | 0.000820971i | \(0.000261323\pi\) | ||||||||
\(654\) | −9.15891 | + | 2.49579i | −0.358142 | + | 0.0975932i | ||||
\(655\) | −0.0983429 | −0.00384257 | ||||||||
\(656\) | −18.9698 | − | 10.5273i | −0.740645 | − | 0.411024i | ||||
\(657\) | −8.39873 | −0.327666 | ||||||||
\(658\) | 16.9490 | − | 4.61858i | 0.660741 | − | 0.180051i | ||||
\(659\) | −8.93401 | + | 8.93401i | −0.348020 | + | 0.348020i | −0.859371 | − | 0.511352i | \(-0.829145\pi\) |
0.511352 | + | 0.859371i | \(0.329145\pi\) | |||||||
\(660\) | −0.381539 | − | 0.0987732i | −0.0148514 | − | 0.00384474i | ||||
\(661\) | −15.8744 | − | 15.8744i | −0.617442 | − | 0.617442i | 0.327433 | − | 0.944875i | \(-0.393817\pi\) |
−0.944875 | + | 0.327433i | \(0.893817\pi\) | |||||||
\(662\) | −7.18078 | + | 12.5602i | −0.279089 | + | 0.488165i | ||||
\(663\) | − | 3.21224i | − | 0.124753i | ||||||
\(664\) | 29.9493 | − | 0.380970i | 1.16226 | − | 0.0147845i | ||||
\(665\) | − | 0.388585i | − | 0.0150687i | ||||||
\(666\) | −10.0176 | − | 5.72715i | −0.388173 | − | 0.221923i | ||||
\(667\) | −2.29199 | − | 2.29199i | −0.0887462 | − | 0.0887462i | ||||
\(668\) | 15.6135 | + | 26.5214i | 0.604103 | + | 1.02614i | ||||
\(669\) | −6.95164 | + | 6.95164i | −0.268766 | + | 0.268766i | ||||
\(670\) | 0.309288 | + | 1.13501i | 0.0119488 | + | 0.0438492i | ||||
\(671\) | −10.1493 | −0.391811 | ||||||||
\(672\) | −2.93164 | − | 4.83792i | −0.113090 | − | 0.186627i | ||||
\(673\) | 17.4999 | 0.674572 | 0.337286 | − | 0.941402i | \(-0.390491\pi\) | ||||
0.337286 | + | 0.941402i | \(0.390491\pi\) | |||||||
\(674\) | 3.97661 | + | 14.5931i | 0.153173 | + | 0.562106i | ||||
\(675\) | 3.51620 | − | 3.51620i | 0.135339 | − | 0.135339i | ||||
\(676\) | 38.8797 | + | 66.0419i | 1.49537 | + | 2.54007i | ||||
\(677\) | −22.5939 | − | 22.5939i | −0.868353 | − | 0.868353i | 0.123937 | − | 0.992290i | \(-0.460448\pi\) |
−0.992290 | + | 0.123937i | \(0.960448\pi\) | |||||||
\(678\) | −19.7418 | − | 11.2866i | −0.758181 | − | 0.433460i | ||||
\(679\) | 2.19995i | 0.0844265i | ||||||||
\(680\) | −0.00266760 | − | 0.209708i | −0.000102298 | − | 0.00804195i | ||||
\(681\) | 15.4112i | 0.590558i | ||||||||
\(682\) | 1.17162 | − | 2.04932i | 0.0448636 | − | 0.0784726i | ||||
\(683\) | 18.1651 | + | 18.1651i | 0.695067 | + | 0.695067i | 0.963342 | − | 0.268275i | \(-0.0864537\pi\) |
−0.268275 | + | 0.963342i | \(0.586454\pi\) | |||||||
\(684\) | 4.54984 | + | 1.17787i | 0.173967 | + | 0.0450368i | ||||
\(685\) | −1.75819 | + | 1.75819i | −0.0671768 | + | 0.0671768i | ||||
\(686\) | 1.36446 | − | 0.371814i | 0.0520954 | − | 0.0141959i | ||||
\(687\) | −25.8823 | −0.987473 | ||||||||
\(688\) | 17.9582 | − | 5.13983i | 0.684648 | − | 0.195954i | ||||
\(689\) | 78.1834 | 2.97855 | ||||||||
\(690\) | 0.602275 | − | 0.164119i | 0.0229282 | − | 0.00624792i | ||||
\(691\) | 31.4362 | − | 31.4362i | 1.19589 | − | 1.19589i | 0.220505 | − | 0.975386i | \(-0.429230\pi\) |
0.975386 | − | 0.220505i | \(-0.0707705\pi\) | |||||||
\(692\) | 8.44551 | − | 32.6232i | 0.321050 | − | 1.24015i | ||||
\(693\) | 0.842648 | + | 0.842648i | 0.0320095 | + | 0.0320095i | ||||
\(694\) | 21.1199 | − | 36.9416i | 0.801700 | − | 1.40228i | ||||
\(695\) | − | 3.41160i | − | 0.129409i | ||||||
\(696\) | −2.39752 | + | 2.45930i | −0.0908779 | + | 0.0932197i | ||||
\(697\) | 2.43205i | 0.0921206i | ||||||||
\(698\) | 5.37740 | + | 3.07432i | 0.203538 | + | 0.116365i | ||||
\(699\) | −14.4364 | − | 14.4364i | −0.546036 | − | 0.546036i | ||||
\(700\) | 8.57042 | − | 5.04551i | 0.323931 | − | 0.190702i | ||||
\(701\) | −8.84023 | + | 8.84023i | −0.333891 | + | 0.333891i | −0.854062 | − | 0.520171i | \(-0.825868\pi\) |
0.520171 | + | 0.854062i | \(0.325868\pi\) | |||||||
\(702\) | −2.66356 | − | 9.77456i | −0.100529 | − | 0.368917i | ||||
\(703\) | 19.1739 | 0.723157 | ||||||||
\(704\) | 6.56752 | − | 6.91047i | 0.247523 | − | 0.260448i | ||||
\(705\) | 2.05408 | 0.0773611 | ||||||||
\(706\) | −8.93708 | − | 32.7968i | −0.336351 | − | 1.23432i | ||||
\(707\) | −6.15886 | + | 6.15886i | −0.231628 | + | 0.231628i | ||||
\(708\) | −4.91752 | + | 2.89501i | −0.184812 | + | 0.108801i | ||||
\(709\) | 17.9508 | + | 17.9508i | 0.674156 | + | 0.674156i | 0.958671 | − | 0.284515i | \(-0.0918327\pi\) |
−0.284515 | + | 0.958671i | \(0.591833\pi\) | |||||||
\(710\) | 2.25433 | + | 1.28883i | 0.0846036 | + | 0.0483688i | ||||
\(711\) | − | 8.06582i | − | 0.302492i | ||||||
\(712\) | −17.4267 | + | 17.8758i | −0.653095 | + | 0.669924i | ||||
\(713\) | 3.73891i | 0.140023i | ||||||||
\(714\) | −0.314740 | + | 0.550523i | −0.0117788 | + | 0.0206028i | ||||
\(715\) | −0.998197 | − | 0.998197i | −0.0373305 | − | 0.0373305i | ||||
\(716\) | −11.6816 | + | 45.1236i | −0.436564 | + | 1.68635i | ||||
\(717\) | −16.1025 | + | 16.1025i | −0.601358 | + | 0.601358i | ||||
\(718\) | −34.4023 | + | 9.37460i | −1.28388 | + | 0.349857i | ||||
\(719\) | −50.0437 | −1.86631 | −0.933157 | − | 0.359470i | \(-0.882958\pi\) | ||||
−0.933157 | + | 0.359470i | \(0.882958\pi\) | |||||||
\(720\) | −0.182005 | − | 0.635912i | −0.00678294 | − | 0.0236991i | ||||
\(721\) | 12.8752 | 0.479498 | ||||||||
\(722\) | 18.3901 | − | 5.01127i | 0.684408 | − | 0.186500i | ||||
\(723\) | −4.98070 | + | 4.98070i | −0.185234 | + | 0.185234i | ||||
\(724\) | −15.6074 | − | 4.04045i | −0.580043 | − | 0.150162i | ||||
\(725\) | −4.26974 | − | 4.26974i | −0.158574 | − | 0.158574i | ||||
\(726\) | 6.72420 | − | 11.7615i | 0.249558 | − | 0.436512i | ||||
\(727\) | − | 47.5239i | − | 1.76256i | −0.472592 | − | 0.881281i | \(-0.656682\pi\) | ||
0.472592 | − | 0.881281i | \(-0.343318\pi\) | |||||||
\(728\) | −0.257721 | − | 20.2603i | −0.00955179 | − | 0.750897i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −1.70511 | − | 0.974828i | −0.0631088 | − | 0.0360800i | ||||
\(731\) | −1.48066 | − | 1.48066i | −0.0547642 | − | 0.0547642i | ||||
\(732\) | −8.64160 | − | 14.6788i | −0.319403 | − | 0.542544i | ||||
\(733\) | 10.4370 | − | 10.4370i | 0.385498 | − | 0.385498i | −0.487580 | − | 0.873078i | \(-0.662120\pi\) |
0.873078 | + | 0.487580i | \(0.162120\pi\) | |||||||
\(734\) | −3.48686 | − | 12.7959i | −0.128702 | − | 0.472304i | ||||
\(735\) | 0.165361 | 0.00609945 | ||||||||
\(736\) | −3.59809 | + | 14.6650i | −0.132627 | + | 0.540558i | ||||
\(737\) | 5.99465 | 0.220816 | ||||||||
\(738\) | 2.01663 | + | 7.40053i | 0.0742333 | + | 0.272417i | ||||
\(739\) | −12.4092 | + | 12.4092i | −0.456480 | + | 0.456480i | −0.897498 | − | 0.441018i | \(-0.854617\pi\) |
0.441018 | + | 0.897498i | \(0.354617\pi\) | |||||||
\(740\) | −1.36902 | − | 2.32545i | −0.0503262 | − | 0.0854851i | ||||
\(741\) | 11.9035 | + | 11.9035i | 0.437284 | + | 0.437284i | ||||
\(742\) | −13.3993 | − | 7.66052i | −0.491904 | − | 0.281227i | ||||
\(743\) | 47.1053i | 1.72812i | 0.503385 | + | 0.864062i | \(0.332088\pi\) | ||||
−0.503385 | + | 0.864062i | \(0.667912\pi\) | |||||||
\(744\) | 3.96146 | − | 0.0503918i | 0.145234 | − | 0.00184745i | ||||
\(745\) | 3.61025i | 0.132269i | ||||||||
\(746\) | 10.9699 | − | 19.1879i | 0.401638 | − | 0.702519i | ||||
\(747\) | −7.48793 | − | 7.48793i | −0.273969 | − | 0.273969i | ||||
\(748\) | −1.03461 | − | 0.267841i | −0.0378291 | − | 0.00979323i | ||||
\(749\) | 1.60576 | − | 1.60576i | 0.0586732 | − | 0.0586732i | ||||
\(750\) | 2.25012 | − | 0.613156i | 0.0821629 | − | 0.0223893i | ||||
\(751\) | −16.2432 | −0.592722 | −0.296361 | − | 0.955076i | \(-0.595773\pi\) | ||||
−0.296361 | + | 0.955076i | \(0.595773\pi\) | |||||||
\(752\) | −24.1102 | + | 43.4454i | −0.879208 | + | 1.58429i | ||||
\(753\) | 1.36180 | 0.0496266 | ||||||||
\(754\) | −11.8693 | + | 3.23437i | −0.432254 | + | 0.117789i | ||||
\(755\) | −0.913605 | + | 0.913605i | −0.0332495 | + | 0.0332495i | ||||
\(756\) | −0.501238 | + | 1.93617i | −0.0182298 | + | 0.0704179i | ||||
\(757\) | 4.11102 | + | 4.11102i | 0.149418 | + | 0.149418i | 0.777858 | − | 0.628440i | \(-0.216306\pi\) |
−0.628440 | + | 0.777858i | \(0.716306\pi\) | |||||||
\(758\) | 19.5408 | − | 34.1796i | 0.709756 | − | 1.24146i | ||||
\(759\) | − | 3.18098i | − | 0.115462i | ||||||
\(760\) | 0.786993 | + | 0.767222i | 0.0285472 | + | 0.0278301i | ||||
\(761\) | 45.8114i | 1.66066i | 0.557272 | + | 0.830330i | \(0.311848\pi\) | ||||
−0.557272 | + | 0.830330i | \(0.688152\pi\) | |||||||
\(762\) | −4.57433 | − | 2.61519i | −0.165710 | − | 0.0947385i | ||||
\(763\) | 4.74644 | + | 4.74644i | 0.171833 | + | 0.171833i | ||||
\(764\) | 9.62321 | − | 5.66531i | 0.348156 | − | 0.204964i | ||||
\(765\) | −0.0524314 | + | 0.0524314i | −0.00189566 | + | 0.00189566i | ||||
\(766\) | −0.558887 | − | 2.05097i | −0.0201934 | − | 0.0741046i | ||||
\(767\) | −20.4394 | −0.738026 | ||||||||
\(768\) | 15.5864 | + | 3.61460i | 0.562424 | + | 0.130431i | ||||
\(769\) | 48.3860 | 1.74484 | 0.872422 | − | 0.488753i | \(-0.162548\pi\) | ||||
0.872422 | + | 0.488753i | \(0.162548\pi\) | |||||||
\(770\) | 0.0732691 | + | 0.268879i | 0.00264044 | + | 0.00968972i | ||||
\(771\) | −10.0208 | + | 10.0208i | −0.360889 | + | 0.360889i | ||||
\(772\) | 14.0817 | − | 8.29005i | 0.506810 | − | 0.298365i | ||||
\(773\) | 12.3922 | + | 12.3922i | 0.445715 | + | 0.445715i | 0.893927 | − | 0.448212i | \(-0.147939\pi\) |
−0.448212 | + | 0.893927i | \(0.647939\pi\) | |||||||
\(774\) | −5.73327 | − | 3.27777i | −0.206078 | − | 0.117817i | ||||
\(775\) | 6.96520i | 0.250198i | ||||||||
\(776\) | −4.45552 | − | 4.34359i | −0.159944 | − | 0.155926i | ||||
\(777\) | 8.15941i | 0.292717i | ||||||||
\(778\) | −24.2943 | + | 42.4941i | −0.870994 | + | 1.52349i | ||||
\(779\) | −9.01235 | − | 9.01235i | −0.322901 | − | 0.322901i | ||||
\(780\) | 0.593765 | − | 2.29358i | 0.0212602 | − | 0.0821234i | ||||
\(781\) | 9.35678 | − | 9.35678i | 0.334812 | − | 0.334812i | ||||
\(782\) | 1.63317 | − | 0.445038i | 0.0584022 | − | 0.0159145i | ||||
\(783\) | 1.21430 | 0.0433957 | ||||||||
\(784\) | −1.94096 | + | 3.49752i | −0.0693202 | + | 0.124911i | ||||
\(785\) | −2.93239 | −0.104661 | ||||||||
\(786\) | −0.811465 | + | 0.221123i | −0.0289440 | + | 0.00788720i | ||||
\(787\) | 15.5433 | − | 15.5433i | 0.554059 | − | 0.554059i | −0.373551 | − | 0.927610i | \(-0.621860\pi\) |
0.927610 | + | 0.373551i | \(0.121860\pi\) | |||||||
\(788\) | 21.7566 | + | 5.63237i | 0.775047 | + | 0.200645i | ||||
\(789\) | −14.3699 | − | 14.3699i | −0.511581 | − | 0.511581i | ||||
\(790\) | 0.936187 | − | 1.63752i | 0.0333080 | − | 0.0582603i | ||||
\(791\) | 16.0799i | 0.571736i | ||||||||
\(792\) | −3.37032 | + | 0.0428721i | −0.119759 | + | 0.00152340i | ||||
\(793\) | − | 61.0117i | − | 2.16659i | ||||||
\(794\) | 28.1786 | + | 16.1100i | 1.00002 | + | 0.571723i | ||||
\(795\) | −1.27614 | − | 1.27614i | −0.0452600 | − | 0.0452600i | ||||
\(796\) | −2.16438 | − | 3.67646i | −0.0767144 | − | 0.130309i | ||||
\(797\) | −9.99655 | + | 9.99655i | −0.354096 | + | 0.354096i | −0.861631 | − | 0.507535i | \(-0.830557\pi\) |
0.507535 | + | 0.861631i | \(0.330557\pi\) | |||||||
\(798\) | −0.873731 | − | 3.20637i | −0.0309297 | − | 0.113504i | ||||
\(799\) | 5.57000 | 0.197052 | ||||||||
\(800\) | −6.70286 | + | 27.3193i | −0.236982 | + | 0.965884i | ||||
\(801\) | 8.82635 | 0.311864 | ||||||||
\(802\) | 3.14463 | + | 11.5400i | 0.111041 | + | 0.407491i | ||||
\(803\) | −7.07717 | + | 7.07717i | −0.249748 | + | 0.249748i | ||||
\(804\) | 5.10411 | + | 8.66995i | 0.180008 | + | 0.305766i | ||||
\(805\) | −0.312118 | − | 0.312118i | −0.0110007 | − | 0.0110007i | ||||
\(806\) | 12.3193 | + | 7.04306i | 0.433928 | + | 0.248081i | ||||
\(807\) | 12.3456i | 0.434584i | ||||||||
\(808\) | −0.313350 | − | 24.6334i | −0.0110236 | − | 0.866601i | ||||
\(809\) | − | 55.0628i | − | 1.93590i | −0.251133 | − | 0.967952i | \(-0.580803\pi\) | ||
0.251133 | − | 0.967952i | \(-0.419197\pi\) | |||||||
\(810\) | −0.116068 | + | 0.203020i | −0.00407823 | + | 0.00713338i | ||||
\(811\) | 12.2961 | + | 12.2961i | 0.431773 | + | 0.431773i | 0.889231 | − | 0.457458i | \(-0.151240\pi\) |
−0.457458 | + | 0.889231i | \(0.651240\pi\) | |||||||
\(812\) | 2.35110 | + | 0.608656i | 0.0825075 | + | 0.0213596i | ||||
\(813\) | −17.4663 | + | 17.4663i | −0.612571 | + | 0.612571i | ||||
\(814\) | −13.2672 | + | 3.61531i | −0.465017 | + | 0.126716i | ||||
\(815\) | −1.00283 | −0.0351277 | ||||||||
\(816\) | −0.493539 | − | 1.72439i | −0.0172773 | − | 0.0603656i | ||||
\(817\) | 10.9736 | 0.383919 | ||||||||
\(818\) | −3.95797 | + | 1.07854i | −0.138387 | + | 0.0377103i | ||||
\(819\) | −5.06549 | + | 5.06549i | −0.177002 | + | 0.177002i | ||||
\(820\) | −0.449552 | + | 1.73652i | −0.0156990 | + | 0.0606419i | ||||
\(821\) | 24.4022 | + | 24.4022i | 0.851643 | + | 0.851643i | 0.990336 | − | 0.138692i | \(-0.0442899\pi\) |
−0.138692 | + | 0.990336i | \(0.544290\pi\) | |||||||
\(822\) | −10.5542 | + | 18.4607i | −0.368120 | + | 0.643892i | ||||
\(823\) | − | 20.7268i | − | 0.722492i | −0.932471 | − | 0.361246i | \(-0.882351\pi\) | ||
0.932471 | − | 0.361246i | \(-0.117649\pi\) | |||||||
\(824\) | −25.4208 | + | 26.0759i | −0.885576 | + | 0.908397i | ||||
\(825\) | − | 5.92583i | − | 0.206311i | ||||||
\(826\) | 3.50297 | + | 2.00269i | 0.121884 | + | 0.0696824i | ||||
\(827\) | 17.1915 | + | 17.1915i | 0.597808 | + | 0.597808i | 0.939729 | − | 0.341921i | \(-0.111077\pi\) |
−0.341921 | + | 0.939729i | \(0.611077\pi\) | |||||||
\(828\) | 4.60059 | − | 2.70842i | 0.159881 | − | 0.0941242i | ||||
\(829\) | 6.26159 | − | 6.26159i | 0.217474 | − | 0.217474i | −0.589959 | − | 0.807433i | \(-0.700856\pi\) |
0.807433 | + | 0.589959i | \(0.200856\pi\) | |||||||
\(830\) | −0.651083 | − | 2.38931i | −0.0225994 | − | 0.0829341i | ||||
\(831\) | −2.40314 | −0.0833640 | ||||||||
\(832\) | 41.5416 | + | 39.4800i | 1.44020 | + | 1.36872i | ||||
\(833\) | 0.448406 | 0.0155364 | ||||||||
\(834\) | −7.67095 | − | 28.1504i | −0.265623 | − | 0.974769i | ||||
\(835\) | 1.79929 | − | 1.79929i | 0.0622671 | − | 0.0622671i | ||||
\(836\) | 4.82643 | − | 2.84138i | 0.166926 | − | 0.0982713i | ||||
\(837\) | −0.990445 | − | 0.990445i | −0.0342348 | − | 0.0342348i | ||||
\(838\) | −14.2894 | − | 8.16942i | −0.493620 | − | 0.282208i | ||||
\(839\) | 22.4991i | 0.776754i | 0.921501 | + | 0.388377i | \(0.126964\pi\) | ||||
−0.921501 | + | 0.388377i | \(0.873036\pi\) | |||||||
\(840\) | −0.326490 | + | 0.334903i | −0.0112650 | + | 0.0115552i | ||||
\(841\) | 27.5255i | 0.949154i | ||||||||
\(842\) | 12.0292 | − | 21.0407i | 0.414553 | − | 0.725110i | ||||
\(843\) | 1.25694 | + | 1.25694i | 0.0432913 | + | 0.0432913i | ||||
\(844\) | −4.92613 | + | 19.0286i | −0.169565 | + | 0.654990i | ||||
\(845\) | 4.48049 | − | 4.48049i | 0.154134 | − | 0.154134i | ||||
\(846\) | 16.9490 | − | 4.61858i | 0.582719 | − | 0.158790i | ||||
\(847\) | −9.57989 | −0.329169 | ||||||||
\(848\) | 41.9702 | − | 12.0124i | 1.44126 | − | 0.412506i | ||||
\(849\) | −17.9038 | −0.614457 | ||||||||
\(850\) | 3.04244 | − | 0.829060i | 0.104355 | − | 0.0284365i | ||||
\(851\) | 15.4008 | − | 15.4008i | 0.527933 | − | 0.527933i | ||||
\(852\) | 21.4993 | + | 5.56575i | 0.736554 | + | 0.190680i | ||||
\(853\) | 7.92257 | + | 7.92257i | 0.271264 | + | 0.271264i | 0.829609 | − | 0.558345i | \(-0.188563\pi\) |
−0.558345 | + | 0.829609i | \(0.688563\pi\) | |||||||
\(854\) | −5.97802 | + | 10.4564i | −0.204563 | + | 0.357809i | ||||
\(855\) | − | 0.388585i | − | 0.0132893i | ||||||
\(856\) | 0.0816977 | + | 6.42252i | 0.00279237 | + | 0.219517i | ||||
\(857\) | − | 8.87592i | − | 0.303196i | −0.988442 | − | 0.151598i | \(-0.951558\pi\) | ||
0.988442 | − | 0.151598i | \(-0.0484419\pi\) | |||||||
\(858\) | −10.4809 | − | 5.99207i | −0.357814 | − | 0.204566i | ||||
\(859\) | 20.6928 | + | 20.6928i | 0.706030 | + | 0.706030i | 0.965698 | − | 0.259668i | \(-0.0836130\pi\) |
−0.259668 | + | 0.965698i | \(0.583613\pi\) | |||||||
\(860\) | −0.783520 | − | 1.33090i | −0.0267178 | − | 0.0453834i | ||||
\(861\) | 3.83519 | − | 3.83519i | 0.130703 | − | 0.130703i | ||||
\(862\) | −8.70718 | − | 31.9531i | −0.296568 | − | 1.08833i | ||||
\(863\) | 45.9301 | 1.56348 | 0.781740 | − | 0.623605i | \(-0.214333\pi\) | ||||
0.781740 | + | 0.623605i | \(0.214333\pi\) | |||||||
\(864\) | −2.93164 | − | 4.83792i | −0.0997364 | − | 0.164589i | ||||
\(865\) | −2.78623 | −0.0947346 | ||||||||
\(866\) | 6.41140 | + | 23.5282i | 0.217868 | + | 0.799520i | ||||
\(867\) | 11.8786 | − | 11.8786i | 0.403420 | − | 0.403420i | ||||
\(868\) | −1.42122 | − | 2.41412i | −0.0482395 | − | 0.0819406i | ||||
\(869\) | −6.79664 | − | 6.79664i | −0.230560 | − | 0.230560i | ||||
\(870\) | 0.246528 | + | 0.140943i | 0.00835807 | + | 0.00477840i | ||||
\(871\) | 36.0362i | 1.22104i | ||||||||
\(872\) | −18.9842 | + | 0.241489i | −0.642887 | + | 0.00817784i | ||||
\(873\) | 2.19995i | 0.0744572i | ||||||||
\(874\) | −4.40283 | + | 7.70114i | −0.148928 | + | 0.260495i | ||||
\(875\) | −1.16608 | − | 1.16608i | −0.0394209 | − | 0.0394209i | ||||
\(876\) | −16.2614 | − | 4.20976i | −0.549421 | − | 0.142235i | ||||
\(877\) | 1.95490 | − | 1.95490i | 0.0660123 | − | 0.0660123i | −0.673330 | − | 0.739342i | \(-0.735137\pi\) |
0.739342 | + | 0.673330i | \(0.235137\pi\) | |||||||
\(878\) | −21.5261 | + | 5.86585i | −0.726472 | + | 0.197963i | ||||
\(879\) | −15.5414 | −0.524197 | ||||||||
\(880\) | −0.689216 | − | 0.382484i | −0.0232335 | − | 0.0128935i | ||||
\(881\) | −11.8155 | −0.398075 | −0.199037 | − | 0.979992i | \(-0.563782\pi\) | ||||
−0.199037 | + | 0.979992i | \(0.563782\pi\) | |||||||
\(882\) | 1.36446 | − | 0.371814i | 0.0459438 | − | 0.0125196i | ||||
\(883\) | 22.8916 | − | 22.8916i | 0.770362 | − | 0.770362i | −0.207808 | − | 0.978170i | \(-0.566633\pi\) |
0.978170 | + | 0.207808i | \(0.0666328\pi\) | |||||||
\(884\) | 1.61010 | − | 6.21945i | 0.0541534 | − | 0.209183i | ||||
\(885\) | 0.333620 | + | 0.333620i | 0.0112145 | + | 0.0112145i | ||||
\(886\) | −2.02557 | + | 3.54300i | −0.0680504 | + | 0.119029i | ||||
\(887\) | − | 2.71951i | − | 0.0913123i | −0.998957 | − | 0.0456562i | \(-0.985462\pi\) | ||
0.998957 | − | 0.0456562i | \(-0.0145379\pi\) | |||||||
\(888\) | −16.5251 | − | 16.1099i | −0.554545 | − | 0.540614i | ||||
\(889\) | 3.72584i | 0.124961i | ||||||||
\(890\) | 1.79192 | + | 1.02446i | 0.0600654 | + | 0.0343400i | ||||
\(891\) | 0.842648 | + | 0.842648i | 0.0282298 | + | 0.0282298i | ||||
\(892\) | −16.9440 | + | 9.97515i | −0.567327 | + | 0.333993i | ||||
\(893\) | −20.6405 | + | 20.6405i | −0.690708 | + | 0.690708i | ||||
\(894\) | 8.11762 | + | 29.7896i | 0.271494 | + | 0.996312i | ||||
\(895\) | 3.85385 | 0.128820 | ||||||||
\(896\) | −3.25121 | − | 10.8365i | −0.108615 | − | 0.362022i | ||||
\(897\) | 19.1221 | 0.638469 | ||||||||
\(898\) | 11.2004 | + | 41.1024i | 0.373761 | + | 1.37161i | ||||
\(899\) | −1.20270 | + | 1.20270i | −0.0401124 | + | 0.0401124i | ||||
\(900\) | 8.57042 | − | 5.04551i | 0.285681 | − | 0.168184i | ||||
\(901\) | −3.46047 | − | 3.46047i | −0.115285 | − | 0.115285i | ||||
\(902\) | 7.93535 | + | 4.53672i | 0.264218 | + | 0.151056i | ||||
\(903\) | 4.66980i | 0.155401i | ||||||||
\(904\) | −32.5663 | − | 31.7482i | −1.08314 | − | 1.05593i | ||||
\(905\) | 1.33297i | 0.0443094i | ||||||||
\(906\) | −5.48427 | + | 9.59274i | −0.182203 | + | 0.318697i | ||||
\(907\) | −19.6178 | − | 19.6178i | −0.651399 | − | 0.651399i | 0.301931 | − | 0.953330i | \(-0.402369\pi\) |
−0.953330 | + | 0.301931i | \(0.902369\pi\) | |||||||
\(908\) | −7.72467 | + | 29.8387i | −0.256352 | + | 0.990232i | ||||
\(909\) | −6.15886 | + | 6.15886i | −0.204276 | + | 0.204276i | ||||
\(910\) | −1.61634 | + | 0.440450i | −0.0535810 | + | 0.0146008i | ||||
\(911\) | 40.6590 | 1.34709 | 0.673547 | − | 0.739145i | \(-0.264770\pi\) | ||||
0.673547 | + | 0.739145i | \(0.264770\pi\) | |||||||
\(912\) | 8.21887 | + | 4.56110i | 0.272154 | + | 0.151033i | ||||
\(913\) | −12.6194 | −0.417640 | ||||||||
\(914\) | −20.8813 | + | 5.69013i | −0.690692 | + | 0.188213i | ||||
\(915\) | −0.995856 | + | 0.995856i | −0.0329220 | + | 0.0329220i | ||||
\(916\) | −50.1126 | − | 12.9732i | −1.65577 | − | 0.428647i | ||||
\(917\) | 0.420527 | + | 0.420527i | 0.0138870 | + | 0.0138870i | ||||
\(918\) | −0.314740 | + | 0.550523i | −0.0103880 | + | 0.0181700i | ||||
\(919\) | − | 52.2631i | − | 1.72400i | −0.506907 | − | 0.862001i | \(-0.669211\pi\) | ||
0.506907 | − | 0.862001i | \(-0.330789\pi\) | |||||||
\(920\) | 1.24837 | − | 0.0158799i | 0.0411576 | − | 0.000523545i | ||||
\(921\) | − | 25.1954i | − | 0.830216i | ||||||
\(922\) | −5.44501 | − | 3.11297i | −0.179322 | − | 0.102520i | ||||
\(923\) | 56.2473 | + | 56.2473i | 1.85140 | + | 1.85140i | ||||
\(924\) | 1.20914 | + | 2.05388i | 0.0397779 | + | 0.0675676i | ||||
\(925\) | 28.6901 | − | 28.6901i | 0.943324 | − | 0.943324i | ||||
\(926\) | −9.72356 | − | 35.6829i | −0.319536 | − | 1.17261i | ||||
\(927\) | 12.8752 | 0.422878 | ||||||||
\(928\) | −5.87471 | + | 3.55991i | −0.192847 | + | 0.116860i | ||||
\(929\) | 8.53368 | 0.279981 | 0.139991 | − | 0.990153i | \(-0.455293\pi\) | ||||
0.139991 | + | 0.990153i | \(0.455293\pi\) | |||||||
\(930\) | −0.0861203 | − | 0.316039i | −0.00282400 | − | 0.0103633i | ||||
\(931\) | −1.66164 | + | 1.66164i | −0.0544580 | + | 0.0544580i | ||||
\(932\) | −20.7153 | − | 35.1875i | −0.678553 | − | 1.15260i | ||||
\(933\) | 9.44570 | + | 9.44570i | 0.309238 | + | 0.309238i | ||||
\(934\) | −15.6094 | − | 8.92407i | −0.510755 | − | 0.292004i | ||||
\(935\) | 0.0883623i | 0.00288976i | ||||||||
\(936\) | −0.257721 | − | 20.2603i | −0.00842389 | − | 0.662229i | ||||
\(937\) | 9.87941i | 0.322746i | 0.986893 | + | 0.161373i | \(0.0515923\pi\) | ||||
−0.986893 | + | 0.161373i | \(0.948408\pi\) | |||||||
\(938\) | 3.53088 | − | 6.17599i | 0.115287 | − | 0.201653i | ||||
\(939\) | −10.9855 | − | 10.9855i | −0.358498 | − | 0.358498i | ||||
\(940\) | 3.97705 | + | 1.02958i | 0.129717 | + | 0.0335813i | ||||
\(941\) | 15.4288 | − | 15.4288i | 0.502963 | − | 0.502963i | −0.409394 | − | 0.912358i | \(-0.634260\pi\) |
0.912358 | + | 0.409394i | \(0.134260\pi\) | |||||||
\(942\) | −24.1962 | + | 6.59345i | −0.788356 | + | 0.214826i | ||||
\(943\) | −14.4777 | −0.471460 | ||||||||
\(944\) | −10.9723 | + | 3.14038i | −0.357117 | + | 0.102211i | ||||
\(945\) | 0.165361 | 0.00537921 | ||||||||
\(946\) | −7.59313 | + | 2.06912i | −0.246874 | + | 0.0672728i | ||||
\(947\) | 10.3348 | − | 10.3348i | 0.335837 | − | 0.335837i | −0.518961 | − | 0.854798i | \(-0.673681\pi\) |
0.854798 | + | 0.518961i | \(0.173681\pi\) | |||||||
\(948\) | 4.04289 | − | 15.6168i | 0.131307 | − | 0.507210i | ||||
\(949\) | −42.5437 | − | 42.5437i | −1.38103 | − | 1.38103i | ||||
\(950\) | −8.20201 | + | 14.3464i | −0.266108 | + | 0.465460i | ||||
\(951\) | − | 11.1862i | − | 0.362736i | ||||||
\(952\) | −0.885333 | + | 0.908147i | −0.0286938 | + | 0.0294332i | ||||
\(953\) | − | 21.8196i | − | 0.706807i | −0.935471 | − | 0.353404i | \(-0.885024\pi\) | ||
0.935471 | − | 0.353404i | \(-0.114976\pi\) | |||||||
\(954\) | −13.3993 | − | 7.66052i | −0.433818 | − | 0.248019i | ||||
\(955\) | −0.652869 | − | 0.652869i | −0.0211263 | − | 0.0211263i | ||||
\(956\) | −39.2483 | + | 23.1060i | −1.26938 | + | 0.747300i | ||||
\(957\) | 1.02323 | − | 1.02323i | 0.0330764 | − | 0.0330764i | ||||
\(958\) | 9.22905 | + | 33.8682i | 0.298177 | + | 1.09423i | ||||
\(959\) | 15.0365 | 0.485553 | ||||||||
\(960\) | −0.0336503 | − | 1.32246i | −0.00108606 | − | 0.0426823i | ||||
\(961\) | −29.0380 | −0.936711 | ||||||||
\(962\) | −21.7330 | − | 79.7546i | −0.700701 | − | 2.57139i | ||||
\(963\) | 1.60576 | − | 1.60576i | 0.0517449 | − | 0.0517449i | ||||
\(964\) | −12.1400 | + | 7.14697i | −0.391003 | + | 0.230188i | ||||
\(965\) | −0.955344 | − | 0.955344i | −0.0307536 | − | 0.0307536i | ||||
\(966\) | −3.27720 | − | 1.87361i | −0.105442 | − | 0.0602825i | ||||
\(967\) | − | 17.9595i | − | 0.577540i | −0.957399 | − | 0.288770i | \(-0.906754\pi\) | ||
0.957399 | − | 0.288770i | \(-0.0932463\pi\) | |||||||
\(968\) | 18.9145 | − | 19.4019i | 0.607936 | − | 0.623602i | ||||
\(969\) | − | 1.05372i | − | 0.0338502i | ||||||
\(970\) | −0.255345 | + | 0.446634i | −0.00819865 | + | 0.0143405i | ||||
\(971\) | −35.0162 | − | 35.0162i | −1.12372 | − | 1.12372i | −0.991177 | − | 0.132548i | \(-0.957684\pi\) |
−0.132548 | − | 0.991177i | \(-0.542316\pi\) | |||||||
\(972\) | −0.501238 | + | 1.93617i | −0.0160772 | + | 0.0621027i | ||||
\(973\) | −14.5884 | + | 14.5884i | −0.467683 | + | 0.467683i | ||||
\(974\) | 17.2261 | − | 4.69410i | 0.551960 | − | 0.150409i | ||||
\(975\) | 35.6225 | 1.14083 | ||||||||
\(976\) | −9.37404 | − | 32.7522i | −0.300056 | − | 1.04837i | ||||
\(977\) | 42.2799 | 1.35265 | 0.676327 | − | 0.736601i | \(-0.263571\pi\) | ||||
0.676327 | + | 0.736601i | \(0.263571\pi\) | |||||||
\(978\) | −8.27477 | + | 2.25486i | −0.264598 | + | 0.0721026i | ||||
\(979\) | 7.43750 | − | 7.43750i | 0.237704 | − | 0.237704i | ||||
\(980\) | 0.320168 | + | 0.0828854i | 0.0102274 | + | 0.00264768i | ||||
\(981\) | 4.74644 | + | 4.74644i | 0.151542 | + | 0.151542i | ||||
\(982\) | 13.6902 | − | 23.9460i | 0.436872 | − | 0.764149i | ||||
\(983\) | 31.1172i | 0.992484i | 0.868184 | + | 0.496242i | \(0.165287\pi\) | ||||
−0.868184 | + | 0.496242i | \(0.834713\pi\) | |||||||
\(984\) | 0.195126 | + | 15.3395i | 0.00622040 | + | 0.489005i | ||||
\(985\) | − | 1.85815i | − | 0.0592057i | ||||||
\(986\) | 0.668503 | + | 0.382190i | 0.0212895 | + | 0.0121714i | ||||
\(987\) | −8.78351 | − | 8.78351i | −0.279582 | − | 0.279582i | ||||
\(988\) | 17.0807 | + | 29.0136i | 0.543409 | + | 0.923045i | ||||
\(989\) | 8.81421 | − | 8.81421i | 0.280276 | − | 0.280276i | ||||
\(990\) | 0.0732691 | + | 0.268879i | 0.00232865 | + | 0.00854553i | ||||
\(991\) | 4.94685 | 0.157142 | 0.0785709 | − | 0.996909i | \(-0.474964\pi\) | ||||
0.0785709 | + | 0.996909i | \(0.474964\pi\) | |||||||
\(992\) | 7.69533 | + | 1.88807i | 0.244327 | + | 0.0599462i | ||||
\(993\) | 10.2304 | 0.324651 | ||||||||
\(994\) | −4.12863 | − | 15.1510i | −0.130952 | − | 0.480561i | ||||
\(995\) | −0.249423 | + | 0.249423i | −0.00790722 | + | 0.00790722i | ||||
\(996\) | −10.7447 | − | 18.2511i | −0.340458 | − | 0.578309i | ||||
\(997\) | −22.2296 | − | 22.2296i | −0.704018 | − | 0.704018i | 0.261252 | − | 0.965271i | \(-0.415864\pi\) |
−0.965271 | + | 0.261252i | \(0.915864\pi\) | |||||||
\(998\) | 46.3550 | + | 26.5017i | 1.46734 | + | 0.838895i | ||||
\(999\) | 8.15941i | 0.258152i |
(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 | 336.2.w.b.85.7 | ✓ | 28 | |
4.3 | odd | 2 | 1344.2.w.b.1009.11 | 28 | |||
8.3 | odd | 2 | 2688.2.w.c.2017.4 | 28 | |||
8.5 | even | 2 | 2688.2.w.d.2017.11 | 28 | |||
16.3 | odd | 4 | 1344.2.w.b.337.11 | 28 | |||
16.5 | even | 4 | 2688.2.w.d.673.11 | 28 | |||
16.11 | odd | 4 | 2688.2.w.c.673.4 | 28 | |||
16.13 | even | 4 | inner | 336.2.w.b.253.7 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.w.b.85.7 | ✓ | 28 | 1.1 | even | 1 | trivial | |
336.2.w.b.253.7 | yes | 28 | 16.13 | even | 4 | inner | |
1344.2.w.b.337.11 | 28 | 16.3 | odd | 4 | |||
1344.2.w.b.1009.11 | 28 | 4.3 | odd | 2 | |||
2688.2.w.c.673.4 | 28 | 16.11 | odd | 4 | |||
2688.2.w.c.2017.4 | 28 | 8.3 | odd | 2 | |||
2688.2.w.d.673.11 | 28 | 16.5 | even | 4 | |||
2688.2.w.d.2017.11 | 28 | 8.5 | even | 2 |