Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,2,Mod(6,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.6");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.c (of order \(3\), 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: | \(0.343356728692\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 36.2 | ||
Root | \(0.809017 + 1.40126i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.36 |
Dual form | 43.2.c.b.6.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.381966 | −0.270091 | −0.135045 | − | 0.990839i | \(-0.543118\pi\) | ||||
−0.135045 | + | 0.990839i | \(0.543118\pi\) | |||||||
\(3\) | 1.30902 | + | 2.26728i | 0.755761 | + | 1.30902i | 0.944995 | + | 0.327085i | \(0.106066\pi\) |
−0.189234 | + | 0.981932i | \(0.560600\pi\) | |||||||
\(4\) | −1.85410 | −0.927051 | ||||||||
\(5\) | −0.618034 | − | 1.07047i | −0.276393 | − | 0.478727i | 0.694092 | − | 0.719886i | \(-0.255806\pi\) |
−0.970486 | + | 0.241159i | \(0.922473\pi\) | |||||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | 2.11803 | − | 3.66854i | 0.800542 | − | 1.38658i | −0.118718 | − | 0.992928i | \(-0.537879\pi\) |
0.919260 | − | 0.393651i | \(-0.128788\pi\) | |||||||
\(8\) | 1.47214 | 0.520479 | ||||||||
\(9\) | −1.92705 | + | 3.33775i | −0.642350 | + | 1.11258i | ||||
\(10\) | 0.236068 | + | 0.408882i | 0.0746512 | + | 0.129300i | ||||
\(11\) | −3.61803 | −1.09088 | −0.545439 | − | 0.838150i | \(-0.683637\pi\) | ||||
−0.545439 | + | 0.838150i | \(0.683637\pi\) | |||||||
\(12\) | −2.42705 | − | 4.20378i | −0.700629 | − | 1.21353i | ||||
\(13\) | −0.690983 | + | 1.19682i | −0.191644 | + | 0.331937i | −0.945795 | − | 0.324763i | \(-0.894715\pi\) |
0.754151 | + | 0.656701i | \(0.228049\pi\) | |||||||
\(14\) | −0.809017 | + | 1.40126i | −0.216219 | + | 0.374502i | ||||
\(15\) | 1.61803 | − | 2.80252i | 0.417775 | − | 0.723607i | ||||
\(16\) | 3.14590 | 0.786475 | ||||||||
\(17\) | −3.04508 | + | 5.27424i | −0.738542 | + | 1.27919i | 0.214610 | + | 0.976700i | \(0.431152\pi\) |
−0.953152 | + | 0.302492i | \(0.902182\pi\) | |||||||
\(18\) | 0.736068 | − | 1.27491i | 0.173493 | − | 0.300498i | ||||
\(19\) | 0.618034 | + | 1.07047i | 0.141787 | + | 0.245582i | 0.928170 | − | 0.372158i | \(-0.121382\pi\) |
−0.786383 | + | 0.617740i | \(0.788049\pi\) | |||||||
\(20\) | 1.14590 | + | 1.98475i | 0.256231 | + | 0.443804i | ||||
\(21\) | 11.0902 | 2.42007 | ||||||||
\(22\) | 1.38197 | 0.294636 | ||||||||
\(23\) | −2.19098 | − | 3.79489i | −0.456852 | − | 0.791290i | 0.541941 | − | 0.840417i | \(-0.317690\pi\) |
−0.998793 | + | 0.0491264i | \(0.984356\pi\) | |||||||
\(24\) | 1.92705 | + | 3.33775i | 0.393358 | + | 0.681315i | ||||
\(25\) | 1.73607 | − | 3.00696i | 0.347214 | − | 0.601392i | ||||
\(26\) | 0.263932 | − | 0.457144i | 0.0517613 | − | 0.0896533i | ||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | −3.92705 | + | 6.80185i | −0.742143 | + | 1.28543i | ||||
\(29\) | −1.50000 | + | 2.59808i | −0.278543 | + | 0.482451i | −0.971023 | − | 0.238987i | \(-0.923185\pi\) |
0.692480 | + | 0.721437i | \(0.256518\pi\) | |||||||
\(30\) | −0.618034 | + | 1.07047i | −0.112837 | + | 0.195440i | ||||
\(31\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(32\) | −4.14590 | −0.732898 | ||||||||
\(33\) | −4.73607 | − | 8.20311i | −0.824444 | − | 1.42798i | ||||
\(34\) | 1.16312 | − | 2.01458i | 0.199473 | − | 0.345498i | ||||
\(35\) | −5.23607 | −0.885057 | ||||||||
\(36\) | 3.57295 | − | 6.18853i | 0.595492 | − | 1.03142i | ||||
\(37\) | 2.42705 | + | 4.20378i | 0.399005 | + | 0.691096i | 0.993603 | − | 0.112926i | \(-0.0360224\pi\) |
−0.594599 | + | 0.804023i | \(0.702689\pi\) | |||||||
\(38\) | −0.236068 | − | 0.408882i | −0.0382953 | − | 0.0663294i | ||||
\(39\) | −3.61803 | −0.579349 | ||||||||
\(40\) | −0.909830 | − | 1.57587i | −0.143857 | − | 0.249167i | ||||
\(41\) | 9.47214 | 1.47930 | 0.739650 | − | 0.672992i | \(-0.234991\pi\) | ||||
0.739650 | + | 0.672992i | \(0.234991\pi\) | |||||||
\(42\) | −4.23607 | −0.653639 | ||||||||
\(43\) | −6.50000 | − | 0.866025i | −0.991241 | − | 0.132068i | ||||
\(44\) | 6.70820 | 1.01130 | ||||||||
\(45\) | 4.76393 | 0.710165 | ||||||||
\(46\) | 0.836881 | + | 1.44952i | 0.123391 | + | 0.213720i | ||||
\(47\) | 1.14590 | 0.167146 | 0.0835732 | − | 0.996502i | \(-0.473367\pi\) | ||||
0.0835732 | + | 0.996502i | \(0.473367\pi\) | |||||||
\(48\) | 4.11803 | + | 7.13264i | 0.594387 | + | 1.02951i | ||||
\(49\) | −5.47214 | − | 9.47802i | −0.781734 | − | 1.35400i | ||||
\(50\) | −0.663119 | + | 1.14856i | −0.0937792 | + | 0.162430i | ||||
\(51\) | −15.9443 | −2.23264 | ||||||||
\(52\) | 1.28115 | − | 2.21902i | 0.177664 | − | 0.307723i | ||||
\(53\) | 0.690983 | + | 1.19682i | 0.0949138 | + | 0.164396i | 0.909573 | − | 0.415545i | \(-0.136409\pi\) |
−0.814659 | + | 0.579941i | \(0.803076\pi\) | |||||||
\(54\) | 0.854102 | 0.116229 | ||||||||
\(55\) | 2.23607 | + | 3.87298i | 0.301511 | + | 0.522233i | ||||
\(56\) | 3.11803 | − | 5.40059i | 0.416665 | − | 0.721685i | ||||
\(57\) | −1.61803 | + | 2.80252i | −0.214314 | + | 0.371202i | ||||
\(58\) | 0.572949 | − | 0.992377i | 0.0752319 | − | 0.130305i | ||||
\(59\) | 5.09017 | 0.662684 | 0.331342 | − | 0.943511i | \(-0.392499\pi\) | ||||
0.331342 | + | 0.943511i | \(0.392499\pi\) | |||||||
\(60\) | −3.00000 | + | 5.19615i | −0.387298 | + | 0.670820i | ||||
\(61\) | −1.42705 | + | 2.47172i | −0.182715 | + | 0.316472i | −0.942804 | − | 0.333347i | \(-0.891822\pi\) |
0.760089 | + | 0.649819i | \(0.225155\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.16312 | + | 14.1389i | 1.02846 | + | 1.78134i | ||||
\(64\) | −4.70820 | −0.588525 | ||||||||
\(65\) | 1.70820 | 0.211877 | ||||||||
\(66\) | 1.80902 | + | 3.13331i | 0.222675 | + | 0.385684i | ||||
\(67\) | 1.92705 | + | 3.33775i | 0.235427 | + | 0.407771i | 0.959397 | − | 0.282061i | \(-0.0910179\pi\) |
−0.723970 | + | 0.689832i | \(0.757685\pi\) | |||||||
\(68\) | 5.64590 | − | 9.77898i | 0.684666 | − | 1.18588i | ||||
\(69\) | 5.73607 | − | 9.93516i | 0.690541 | − | 1.19605i | ||||
\(70\) | 2.00000 | 0.239046 | ||||||||
\(71\) | 5.39919 | − | 9.35167i | 0.640766 | − | 1.10984i | −0.344497 | − | 0.938788i | \(-0.611950\pi\) |
0.985262 | − | 0.171051i | \(-0.0547163\pi\) | |||||||
\(72\) | −2.83688 | + | 4.91362i | −0.334330 | + | 0.579076i | ||||
\(73\) | −0.927051 | + | 1.60570i | −0.108503 | + | 0.187933i | −0.915164 | − | 0.403082i | \(-0.867939\pi\) |
0.806661 | + | 0.591015i | \(0.201272\pi\) | |||||||
\(74\) | −0.927051 | − | 1.60570i | −0.107767 | − | 0.186659i | ||||
\(75\) | 9.09017 | 1.04964 | ||||||||
\(76\) | −1.14590 | − | 1.98475i | −0.131444 | − | 0.227667i | ||||
\(77\) | −7.66312 | + | 13.2729i | −0.873293 | + | 1.51259i | ||||
\(78\) | 1.38197 | 0.156477 | ||||||||
\(79\) | 0.690983 | − | 1.19682i | 0.0777417 | − | 0.134653i | −0.824534 | − | 0.565813i | \(-0.808562\pi\) |
0.902275 | + | 0.431161i | \(0.141896\pi\) | |||||||
\(80\) | −1.94427 | − | 3.36758i | −0.217376 | − | 0.376507i | ||||
\(81\) | 2.85410 | + | 4.94345i | 0.317122 | + | 0.549272i | ||||
\(82\) | −3.61803 | −0.399545 | ||||||||
\(83\) | −8.01722 | − | 13.8862i | −0.880004 | − | 1.52421i | −0.851335 | − | 0.524623i | \(-0.824206\pi\) |
−0.0286698 | − | 0.999589i | \(-0.509127\pi\) | |||||||
\(84\) | −20.5623 | −2.24353 | ||||||||
\(85\) | 7.52786 | 0.816511 | ||||||||
\(86\) | 2.48278 | + | 0.330792i | 0.267725 | + | 0.0356702i | ||||
\(87\) | −7.85410 | −0.842048 | ||||||||
\(88\) | −5.32624 | −0.567779 | ||||||||
\(89\) | 0.927051 | + | 1.60570i | 0.0982672 | + | 0.170204i | 0.910968 | − | 0.412478i | \(-0.135337\pi\) |
−0.812700 | + | 0.582682i | \(0.802003\pi\) | |||||||
\(90\) | −1.81966 | −0.191809 | ||||||||
\(91\) | 2.92705 | + | 5.06980i | 0.306838 | + | 0.531460i | ||||
\(92\) | 4.06231 | + | 7.03612i | 0.423525 | + | 0.733566i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.437694 | −0.0451447 | ||||||||
\(95\) | 0.763932 | − | 1.32317i | 0.0783778 | − | 0.135754i | ||||
\(96\) | −5.42705 | − | 9.39993i | −0.553896 | − | 0.959376i | ||||
\(97\) | −9.23607 | −0.937781 | −0.468890 | − | 0.883256i | \(-0.655346\pi\) | ||||
−0.468890 | + | 0.883256i | \(0.655346\pi\) | |||||||
\(98\) | 2.09017 | + | 3.62028i | 0.211139 | + | 0.365704i | ||||
\(99\) | 6.97214 | − | 12.0761i | 0.700726 | − | 1.21369i | ||||
\(100\) | −3.21885 | + | 5.57521i | −0.321885 | + | 0.557521i | ||||
\(101\) | −1.88197 | + | 3.25966i | −0.187263 | + | 0.324348i | −0.944337 | − | 0.328981i | \(-0.893295\pi\) |
0.757074 | + | 0.653329i | \(0.226628\pi\) | |||||||
\(102\) | 6.09017 | 0.603017 | ||||||||
\(103\) | 8.20820 | − | 14.2170i | 0.808778 | − | 1.40085i | −0.104932 | − | 0.994479i | \(-0.533463\pi\) |
0.913710 | − | 0.406366i | \(-0.133204\pi\) | |||||||
\(104\) | −1.01722 | + | 1.76188i | −0.0997467 | + | 0.172766i | ||||
\(105\) | −6.85410 | − | 11.8717i | −0.668892 | − | 1.15855i | ||||
\(106\) | −0.263932 | − | 0.457144i | −0.0256353 | − | 0.0444017i | ||||
\(107\) | 7.52786 | 0.727746 | 0.363873 | − | 0.931449i | \(-0.381454\pi\) | ||||
0.363873 | + | 0.931449i | \(0.381454\pi\) | |||||||
\(108\) | 4.14590 | 0.398939 | ||||||||
\(109\) | 6.92705 | + | 11.9980i | 0.663491 | + | 1.14920i | 0.979692 | + | 0.200508i | \(0.0642593\pi\) |
−0.316201 | + | 0.948692i | \(0.602407\pi\) | |||||||
\(110\) | −0.854102 | − | 1.47935i | −0.0814354 | − | 0.141050i | ||||
\(111\) | −6.35410 | + | 11.0056i | −0.603105 | + | 1.04461i | ||||
\(112\) | 6.66312 | − | 11.5409i | 0.629606 | − | 1.09051i | ||||
\(113\) | −15.6180 | −1.46922 | −0.734611 | − | 0.678489i | \(-0.762635\pi\) | ||||
−0.734611 | + | 0.678489i | \(0.762635\pi\) | |||||||
\(114\) | 0.618034 | − | 1.07047i | 0.0578842 | − | 0.100258i | ||||
\(115\) | −2.70820 | + | 4.69075i | −0.252541 | + | 0.437414i | ||||
\(116\) | 2.78115 | − | 4.81710i | 0.258224 | − | 0.447256i | ||||
\(117\) | −2.66312 | − | 4.61266i | −0.246205 | − | 0.426440i | ||||
\(118\) | −1.94427 | −0.178985 | ||||||||
\(119\) | 12.8992 | + | 22.3420i | 1.18247 | + | 2.04809i | ||||
\(120\) | 2.38197 | − | 4.12569i | 0.217443 | − | 0.376622i | ||||
\(121\) | 2.09017 | 0.190015 | ||||||||
\(122\) | 0.545085 | − | 0.944115i | 0.0493497 | − | 0.0854761i | ||||
\(123\) | 12.3992 | + | 21.4760i | 1.11800 | + | 1.93643i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.4721 | −0.936656 | ||||||||
\(126\) | −3.11803 | − | 5.40059i | −0.277777 | − | 0.481123i | ||||
\(127\) | −14.6525 | −1.30020 | −0.650098 | − | 0.759850i | \(-0.725272\pi\) | ||||
−0.650098 | + | 0.759850i | \(0.725272\pi\) | |||||||
\(128\) | 10.0902 | 0.891853 | ||||||||
\(129\) | −6.54508 | − | 15.8710i | −0.576263 | − | 1.39736i | ||||
\(130\) | −0.652476 | −0.0572259 | ||||||||
\(131\) | 9.94427 | 0.868835 | 0.434418 | − | 0.900712i | \(-0.356954\pi\) | ||||
0.434418 | + | 0.900712i | \(0.356954\pi\) | |||||||
\(132\) | 8.78115 | + | 15.2094i | 0.764301 | + | 1.32381i | ||||
\(133\) | 5.23607 | 0.454025 | ||||||||
\(134\) | −0.736068 | − | 1.27491i | −0.0635866 | − | 0.110135i | ||||
\(135\) | 1.38197 | + | 2.39364i | 0.118941 | + | 0.206011i | ||||
\(136\) | −4.48278 | + | 7.76440i | −0.384395 | + | 0.665792i | ||||
\(137\) | 3.70820 | 0.316813 | 0.158407 | − | 0.987374i | \(-0.449364\pi\) | ||||
0.158407 | + | 0.987374i | \(0.449364\pi\) | |||||||
\(138\) | −2.19098 | + | 3.79489i | −0.186509 | + | 0.323043i | ||||
\(139\) | 2.64590 | + | 4.58283i | 0.224422 | + | 0.388711i | 0.956146 | − | 0.292891i | \(-0.0946172\pi\) |
−0.731724 | + | 0.681601i | \(0.761284\pi\) | |||||||
\(140\) | 9.70820 | 0.820493 | ||||||||
\(141\) | 1.50000 | + | 2.59808i | 0.126323 | + | 0.218797i | ||||
\(142\) | −2.06231 | + | 3.57202i | −0.173065 | + | 0.299757i | ||||
\(143\) | 2.50000 | − | 4.33013i | 0.209061 | − | 0.362103i | ||||
\(144\) | −6.06231 | + | 10.5002i | −0.505192 | + | 0.875018i | ||||
\(145\) | 3.70820 | 0.307950 | ||||||||
\(146\) | 0.354102 | − | 0.613323i | 0.0293057 | − | 0.0507589i | ||||
\(147\) | 14.3262 | − | 24.8138i | 1.18161 | − | 2.04661i | ||||
\(148\) | −4.50000 | − | 7.79423i | −0.369898 | − | 0.640682i | ||||
\(149\) | −4.50000 | − | 7.79423i | −0.368654 | − | 0.638528i | 0.620701 | − | 0.784047i | \(-0.286848\pi\) |
−0.989355 | + | 0.145519i | \(0.953515\pi\) | |||||||
\(150\) | −3.47214 | −0.283499 | ||||||||
\(151\) | −8.85410 | −0.720537 | −0.360268 | − | 0.932849i | \(-0.617315\pi\) | ||||
−0.360268 | + | 0.932849i | \(0.617315\pi\) | |||||||
\(152\) | 0.909830 | + | 1.57587i | 0.0737970 | + | 0.127820i | ||||
\(153\) | −11.7361 | − | 20.3275i | −0.948805 | − | 1.64338i | ||||
\(154\) | 2.92705 | − | 5.06980i | 0.235868 | − | 0.408536i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.70820 | 0.537086 | ||||||||
\(157\) | 2.57295 | − | 4.45648i | 0.205344 | − | 0.355666i | −0.744898 | − | 0.667178i | \(-0.767502\pi\) |
0.950242 | + | 0.311512i | \(0.100835\pi\) | |||||||
\(158\) | −0.263932 | + | 0.457144i | −0.0209973 | + | 0.0363684i | ||||
\(159\) | −1.80902 | + | 3.13331i | −0.143464 | + | 0.248488i | ||||
\(160\) | 2.56231 | + | 4.43804i | 0.202568 | + | 0.350858i | ||||
\(161\) | −18.5623 | −1.46291 | ||||||||
\(162\) | −1.09017 | − | 1.88823i | −0.0856518 | − | 0.148353i | ||||
\(163\) | −7.00000 | + | 12.1244i | −0.548282 | + | 0.949653i | 0.450110 | + | 0.892973i | \(0.351385\pi\) |
−0.998392 | + | 0.0566798i | \(0.981949\pi\) | |||||||
\(164\) | −17.5623 | −1.37139 | ||||||||
\(165\) | −5.85410 | + | 10.1396i | −0.455741 | + | 0.789367i | ||||
\(166\) | 3.06231 | + | 5.30407i | 0.237681 | + | 0.411676i | ||||
\(167\) | −7.11803 | − | 12.3288i | −0.550810 | − | 0.954031i | −0.998216 | − | 0.0597001i | \(-0.980986\pi\) |
0.447406 | − | 0.894331i | \(-0.352348\pi\) | |||||||
\(168\) | 16.3262 | 1.25960 | ||||||||
\(169\) | 5.54508 | + | 9.60437i | 0.426545 | + | 0.738798i | ||||
\(170\) | −2.87539 | −0.220532 | ||||||||
\(171\) | −4.76393 | −0.364307 | ||||||||
\(172\) | 12.0517 | + | 1.60570i | 0.918931 | + | 0.122433i | ||||
\(173\) | −3.76393 | −0.286166 | −0.143083 | − | 0.989711i | \(-0.545702\pi\) | ||||
−0.143083 | + | 0.989711i | \(0.545702\pi\) | |||||||
\(174\) | 3.00000 | 0.227429 | ||||||||
\(175\) | −7.35410 | − | 12.7377i | −0.555918 | − | 0.962878i | ||||
\(176\) | −11.3820 | −0.857948 | ||||||||
\(177\) | 6.66312 | + | 11.5409i | 0.500831 | + | 0.867464i | ||||
\(178\) | −0.354102 | − | 0.613323i | −0.0265411 | − | 0.0459705i | ||||
\(179\) | −4.82624 | + | 8.35929i | −0.360730 | + | 0.624803i | −0.988081 | − | 0.153934i | \(-0.950806\pi\) |
0.627351 | + | 0.778736i | \(0.284139\pi\) | |||||||
\(180\) | −8.83282 | −0.658359 | ||||||||
\(181\) | 9.69098 | − | 16.7853i | 0.720325 | − | 1.24764i | −0.240544 | − | 0.970638i | \(-0.577326\pi\) |
0.960869 | − | 0.277002i | \(-0.0893407\pi\) | |||||||
\(182\) | −1.11803 | − | 1.93649i | −0.0828742 | − | 0.143542i | ||||
\(183\) | −7.47214 | −0.552356 | ||||||||
\(184\) | −3.22542 | − | 5.58660i | −0.237781 | − | 0.411850i | ||||
\(185\) | 3.00000 | − | 5.19615i | 0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.0172 | − | 19.0824i | 0.805659 | − | 1.39544i | ||||
\(188\) | −2.12461 | −0.154953 | ||||||||
\(189\) | −4.73607 | + | 8.20311i | −0.344498 | + | 0.596688i | ||||
\(190\) | −0.291796 | + | 0.505406i | −0.0211691 | + | 0.0366660i | ||||
\(191\) | 7.26393 | + | 12.5815i | 0.525600 | + | 0.910365i | 0.999555 | + | 0.0298167i | \(0.00949234\pi\) |
−0.473956 | + | 0.880549i | \(0.657174\pi\) | |||||||
\(192\) | −6.16312 | − | 10.6748i | −0.444785 | − | 0.770390i | ||||
\(193\) | 2.70820 | 0.194941 | 0.0974704 | − | 0.995238i | \(-0.468925\pi\) | ||||
0.0974704 | + | 0.995238i | \(0.468925\pi\) | |||||||
\(194\) | 3.52786 | 0.253286 | ||||||||
\(195\) | 2.23607 | + | 3.87298i | 0.160128 | + | 0.277350i | ||||
\(196\) | 10.1459 | + | 17.5732i | 0.724707 | + | 1.25523i | ||||
\(197\) | 1.47214 | − | 2.54981i | 0.104885 | − | 0.181667i | −0.808806 | − | 0.588076i | \(-0.799886\pi\) |
0.913691 | + | 0.406409i | \(0.133219\pi\) | |||||||
\(198\) | −2.66312 | + | 4.61266i | −0.189260 | + | 0.327807i | ||||
\(199\) | 1.94427 | 0.137826 | 0.0689129 | − | 0.997623i | \(-0.478047\pi\) | ||||
0.0689129 | + | 0.997623i | \(0.478047\pi\) | |||||||
\(200\) | 2.55573 | − | 4.42665i | 0.180717 | − | 0.313011i | ||||
\(201\) | −5.04508 | + | 8.73834i | −0.355853 | + | 0.616355i | ||||
\(202\) | 0.718847 | − | 1.24508i | 0.0505779 | − | 0.0876035i | ||||
\(203\) | 6.35410 | + | 11.0056i | 0.445971 | + | 0.772444i | ||||
\(204\) | 29.5623 | 2.06978 | ||||||||
\(205\) | −5.85410 | − | 10.1396i | −0.408868 | − | 0.708181i | ||||
\(206\) | −3.13525 | + | 5.43042i | −0.218444 | + | 0.378355i | ||||
\(207\) | 16.8885 | 1.17383 | ||||||||
\(208\) | −2.17376 | + | 3.76507i | −0.150723 | + | 0.261060i | ||||
\(209\) | −2.23607 | − | 3.87298i | −0.154672 | − | 0.267900i | ||||
\(210\) | 2.61803 | + | 4.53457i | 0.180662 | + | 0.312915i | ||||
\(211\) | −9.23607 | −0.635837 | −0.317919 | − | 0.948118i | \(-0.602984\pi\) | ||||
−0.317919 | + | 0.948118i | \(0.602984\pi\) | |||||||
\(212\) | −1.28115 | − | 2.21902i | −0.0879899 | − | 0.152403i | ||||
\(213\) | 28.2705 | 1.93706 | ||||||||
\(214\) | −2.87539 | −0.196557 | ||||||||
\(215\) | 3.09017 | + | 7.49326i | 0.210748 | + | 0.511036i | ||||
\(216\) | −3.29180 | −0.223978 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.64590 | − | 4.58283i | −0.179203 | − | 0.310388i | ||||
\(219\) | −4.85410 | −0.328010 | ||||||||
\(220\) | −4.14590 | − | 7.18091i | −0.279516 | − | 0.484137i | ||||
\(221\) | −4.20820 | − | 7.28882i | −0.283074 | − | 0.490299i | ||||
\(222\) | 2.42705 | − | 4.20378i | 0.162893 | − | 0.282139i | ||||
\(223\) | 2.76393 | 0.185087 | 0.0925433 | − | 0.995709i | \(-0.470500\pi\) | ||||
0.0925433 | + | 0.995709i | \(0.470500\pi\) | |||||||
\(224\) | −8.78115 | + | 15.2094i | −0.586715 | + | 1.01622i | ||||
\(225\) | 6.69098 | + | 11.5891i | 0.446066 | + | 0.772608i | ||||
\(226\) | 5.96556 | 0.396823 | ||||||||
\(227\) | 0.736068 | + | 1.27491i | 0.0488545 | + | 0.0846186i | 0.889419 | − | 0.457094i | \(-0.151110\pi\) |
−0.840564 | + | 0.541712i | \(0.817776\pi\) | |||||||
\(228\) | 3.00000 | − | 5.19615i | 0.198680 | − | 0.344124i | ||||
\(229\) | 1.14590 | − | 1.98475i | 0.0757231 | − | 0.131156i | −0.825677 | − | 0.564143i | \(-0.809207\pi\) |
0.901400 | + | 0.432986i | \(0.142540\pi\) | |||||||
\(230\) | 1.03444 | − | 1.79171i | 0.0682091 | − | 0.118142i | ||||
\(231\) | −40.1246 | −2.64001 | ||||||||
\(232\) | −2.20820 | + | 3.82472i | −0.144976 | + | 0.251105i | ||||
\(233\) | −9.01722 | + | 15.6183i | −0.590738 | + | 1.02319i | 0.403395 | + | 0.915026i | \(0.367830\pi\) |
−0.994133 | + | 0.108162i | \(0.965503\pi\) | |||||||
\(234\) | 1.01722 | + | 1.76188i | 0.0664978 | + | 0.115178i | ||||
\(235\) | −0.708204 | − | 1.22665i | −0.0461981 | − | 0.0800175i | ||||
\(236\) | −9.43769 | −0.614342 | ||||||||
\(237\) | 3.61803 | 0.235017 | ||||||||
\(238\) | −4.92705 | − | 8.53390i | −0.319373 | − | 0.553171i | ||||
\(239\) | 4.14590 | + | 7.18091i | 0.268176 | + | 0.464494i | 0.968391 | − | 0.249438i | \(-0.0802458\pi\) |
−0.700215 | + | 0.713932i | \(0.746913\pi\) | |||||||
\(240\) | 5.09017 | − | 8.81643i | 0.328569 | − | 0.569098i | ||||
\(241\) | −2.13525 | + | 3.69837i | −0.137544 | + | 0.238233i | −0.926566 | − | 0.376131i | \(-0.877254\pi\) |
0.789022 | + | 0.614364i | \(0.210587\pi\) | |||||||
\(242\) | −0.798374 | −0.0513214 | ||||||||
\(243\) | −10.8262 | + | 18.7516i | −0.694503 | + | 1.20292i | ||||
\(244\) | 2.64590 | − | 4.58283i | 0.169386 | − | 0.293386i | ||||
\(245\) | −6.76393 | + | 11.7155i | −0.432132 | + | 0.748474i | ||||
\(246\) | −4.73607 | − | 8.20311i | −0.301961 | − | 0.523011i | ||||
\(247\) | −1.70820 | −0.108690 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.9894 | − | 36.3546i | 1.33015 | − | 2.30388i | ||||
\(250\) | 4.00000 | 0.252982 | ||||||||
\(251\) | 14.5902 | − | 25.2709i | 0.920923 | − | 1.59509i | 0.122934 | − | 0.992415i | \(-0.460770\pi\) |
0.797990 | − | 0.602671i | \(-0.205897\pi\) | |||||||
\(252\) | −15.1353 | − | 26.2150i | −0.953431 | − | 1.65139i | ||||
\(253\) | 7.92705 | + | 13.7301i | 0.498369 | + | 0.863201i | ||||
\(254\) | 5.59675 | 0.351171 | ||||||||
\(255\) | 9.85410 | + | 17.0678i | 0.617088 | + | 1.06883i | ||||
\(256\) | 5.56231 | 0.347644 | ||||||||
\(257\) | 3.43769 | 0.214437 | 0.107219 | − | 0.994235i | \(-0.465805\pi\) | ||||
0.107219 | + | 0.994235i | \(0.465805\pi\) | |||||||
\(258\) | 2.50000 | + | 6.06218i | 0.155643 | + | 0.377415i | ||||
\(259\) | 20.5623 | 1.27768 | ||||||||
\(260\) | −3.16718 | −0.196420 | ||||||||
\(261\) | −5.78115 | − | 10.0133i | −0.357844 | − | 0.619805i | ||||
\(262\) | −3.79837 | −0.234664 | ||||||||
\(263\) | −13.7533 | − | 23.8214i | −0.848064 | − | 1.46889i | −0.882933 | − | 0.469498i | \(-0.844435\pi\) |
0.0348693 | − | 0.999392i | \(-0.488899\pi\) | |||||||
\(264\) | −6.97214 | − | 12.0761i | −0.429105 | − | 0.743232i | ||||
\(265\) | 0.854102 | − | 1.47935i | 0.0524671 | − | 0.0908756i | ||||
\(266\) | −2.00000 | −0.122628 | ||||||||
\(267\) | −2.42705 | + | 4.20378i | −0.148533 | + | 0.257267i | ||||
\(268\) | −3.57295 | − | 6.18853i | −0.218253 | − | 0.378025i | ||||
\(269\) | 11.5623 | 0.704966 | 0.352483 | − | 0.935818i | \(-0.385337\pi\) | ||||
0.352483 | + | 0.935818i | \(0.385337\pi\) | |||||||
\(270\) | −0.527864 | − | 0.914287i | −0.0321248 | − | 0.0556418i | ||||
\(271\) | −6.92705 | + | 11.9980i | −0.420788 | + | 0.728827i | −0.996017 | − | 0.0891660i | \(-0.971580\pi\) |
0.575228 | + | 0.817993i | \(0.304913\pi\) | |||||||
\(272\) | −9.57953 | + | 16.5922i | −0.580844 | + | 1.00605i | ||||
\(273\) | −7.66312 | + | 13.2729i | −0.463793 | + | 0.803313i | ||||
\(274\) | −1.41641 | −0.0855683 | ||||||||
\(275\) | −6.28115 | + | 10.8793i | −0.378768 | + | 0.656045i | ||||
\(276\) | −10.6353 | + | 18.4208i | −0.640167 | + | 1.10880i | ||||
\(277\) | 6.23607 | + | 10.8012i | 0.374689 | + | 0.648980i | 0.990280 | − | 0.139085i | \(-0.0444161\pi\) |
−0.615591 | + | 0.788065i | \(0.711083\pi\) | |||||||
\(278\) | −1.01064 | − | 1.75049i | −0.0606143 | − | 0.104987i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.70820 | −0.460653 | ||||||||
\(281\) | −3.73607 | − | 6.47106i | −0.222875 | − | 0.386031i | 0.732805 | − | 0.680439i | \(-0.238211\pi\) |
−0.955680 | + | 0.294408i | \(0.904878\pi\) | |||||||
\(282\) | −0.572949 | − | 0.992377i | −0.0341186 | − | 0.0590952i | ||||
\(283\) | −5.38197 | + | 9.32184i | −0.319925 | + | 0.554126i | −0.980472 | − | 0.196659i | \(-0.936991\pi\) |
0.660547 | + | 0.750784i | \(0.270324\pi\) | |||||||
\(284\) | −10.0106 | + | 17.3389i | −0.594022 | + | 1.02888i | ||||
\(285\) | 4.00000 | 0.236940 | ||||||||
\(286\) | −0.954915 | + | 1.65396i | −0.0564653 | + | 0.0978008i | ||||
\(287\) | 20.0623 | − | 34.7489i | 1.18424 | − | 2.05116i | ||||
\(288\) | 7.98936 | − | 13.8380i | 0.470777 | − | 0.815410i | ||||
\(289\) | −10.0451 | − | 17.3986i | −0.590887 | − | 1.02345i | ||||
\(290\) | −1.41641 | −0.0831743 | ||||||||
\(291\) | −12.0902 | − | 20.9408i | −0.708738 | − | 1.22757i | ||||
\(292\) | 1.71885 | − | 2.97713i | 0.100588 | − | 0.174223i | ||||
\(293\) | −12.0902 | −0.706315 | −0.353158 | − | 0.935564i | \(-0.614892\pi\) | ||||
−0.353158 | + | 0.935564i | \(0.614892\pi\) | |||||||
\(294\) | −5.47214 | + | 9.47802i | −0.319141 | + | 0.552769i | ||||
\(295\) | −3.14590 | − | 5.44886i | −0.183161 | − | 0.317245i | ||||
\(296\) | 3.57295 | + | 6.18853i | 0.207673 | + | 0.359701i | ||||
\(297\) | 8.09017 | 0.469439 | ||||||||
\(298\) | 1.71885 | + | 2.97713i | 0.0995701 | + | 0.172461i | ||||
\(299\) | 6.05573 | 0.350212 | ||||||||
\(300\) | −16.8541 | −0.973072 | ||||||||
\(301\) | −16.9443 | + | 22.0113i | −0.976652 | + | 1.26871i | ||||
\(302\) | 3.38197 | 0.194610 | ||||||||
\(303\) | −9.85410 | −0.566103 | ||||||||
\(304\) | 1.94427 | + | 3.36758i | 0.111512 | + | 0.193144i | ||||
\(305\) | 3.52786 | 0.202005 | ||||||||
\(306\) | 4.48278 | + | 7.76440i | 0.256263 | + | 0.443861i | ||||
\(307\) | 11.6074 | + | 20.1046i | 0.662469 | + | 1.14743i | 0.979965 | + | 0.199170i | \(0.0638246\pi\) |
−0.317496 | + | 0.948260i | \(0.602842\pi\) | |||||||
\(308\) | 14.2082 | − | 24.6093i | 0.809588 | − | 1.40225i | ||||
\(309\) | 42.9787 | 2.44497 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.9164 | + | 25.8360i | 0.845832 | + | 1.46502i | 0.884897 | + | 0.465787i | \(0.154229\pi\) |
−0.0390649 | + | 0.999237i | \(0.512438\pi\) | |||||||
\(312\) | −5.32624 | −0.301539 | ||||||||
\(313\) | −6.56231 | − | 11.3662i | −0.370923 | − | 0.642458i | 0.618784 | − | 0.785561i | \(-0.287625\pi\) |
−0.989708 | + | 0.143103i | \(0.954292\pi\) | |||||||
\(314\) | −0.982779 | + | 1.70222i | −0.0554614 | + | 0.0960620i | ||||
\(315\) | 10.0902 | − | 17.4767i | 0.568517 | − | 0.984700i | ||||
\(316\) | −1.28115 | + | 2.21902i | −0.0720705 | + | 0.124830i | ||||
\(317\) | 33.3050 | 1.87059 | 0.935296 | − | 0.353866i | \(-0.115133\pi\) | ||||
0.935296 | + | 0.353866i | \(0.115133\pi\) | |||||||
\(318\) | 0.690983 | − | 1.19682i | 0.0387484 | − | 0.0671142i | ||||
\(319\) | 5.42705 | − | 9.39993i | 0.303857 | − | 0.526295i | ||||
\(320\) | 2.90983 | + | 5.03997i | 0.162664 | + | 0.281743i | ||||
\(321\) | 9.85410 | + | 17.0678i | 0.550002 | + | 0.952632i | ||||
\(322\) | 7.09017 | 0.395120 | ||||||||
\(323\) | −7.52786 | −0.418862 | ||||||||
\(324\) | −5.29180 | − | 9.16566i | −0.293989 | − | 0.509203i | ||||
\(325\) | 2.39919 | + | 4.15551i | 0.133083 | + | 0.230506i | ||||
\(326\) | 2.67376 | − | 4.63109i | 0.148086 | − | 0.256492i | ||||
\(327\) | −18.1353 | + | 31.4112i | −1.00288 | + | 1.73704i | ||||
\(328\) | 13.9443 | 0.769944 | ||||||||
\(329\) | 2.42705 | − | 4.20378i | 0.133808 | − | 0.231762i | ||||
\(330\) | 2.23607 | − | 3.87298i | 0.123091 | − | 0.213201i | ||||
\(331\) | 2.73607 | − | 4.73901i | 0.150388 | − | 0.260479i | −0.780982 | − | 0.624553i | \(-0.785281\pi\) |
0.931370 | + | 0.364074i | \(0.118614\pi\) | |||||||
\(332\) | 14.8647 | + | 25.7465i | 0.815809 | + | 1.41302i | ||||
\(333\) | −18.7082 | −1.02520 | ||||||||
\(334\) | 2.71885 | + | 4.70918i | 0.148769 | + | 0.257675i | ||||
\(335\) | 2.38197 | − | 4.12569i | 0.130141 | − | 0.225410i | ||||
\(336\) | 34.8885 | 1.90333 | ||||||||
\(337\) | −14.0000 | + | 24.2487i | −0.762629 | + | 1.32091i | 0.178863 | + | 0.983874i | \(0.442758\pi\) |
−0.941491 | + | 0.337037i | \(0.890575\pi\) | |||||||
\(338\) | −2.11803 | − | 3.66854i | −0.115206 | − | 0.199542i | ||||
\(339\) | −20.4443 | − | 35.4105i | −1.11038 | − | 1.92324i | ||||
\(340\) | −13.9574 | −0.756948 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.81966 | 0.0983959 | ||||||||
\(343\) | −16.7082 | −0.902158 | ||||||||
\(344\) | −9.56888 | − | 1.27491i | −0.515920 | − | 0.0687384i | ||||
\(345\) | −14.1803 | −0.763444 | ||||||||
\(346\) | 1.43769 | 0.0772909 | ||||||||
\(347\) | −5.04508 | − | 8.73834i | −0.270834 | − | 0.469099i | 0.698241 | − | 0.715862i | \(-0.253966\pi\) |
−0.969076 | + | 0.246764i | \(0.920633\pi\) | |||||||
\(348\) | 14.5623 | 0.780622 | ||||||||
\(349\) | −10.3541 | − | 17.9338i | −0.554242 | − | 0.959976i | −0.997962 | − | 0.0638103i | \(-0.979675\pi\) |
0.443720 | − | 0.896166i | \(-0.353659\pi\) | |||||||
\(350\) | 2.80902 | + | 4.86536i | 0.150148 | + | 0.260064i | ||||
\(351\) | 1.54508 | − | 2.67617i | 0.0824705 | − | 0.142843i | ||||
\(352\) | 15.0000 | 0.799503 | ||||||||
\(353\) | 8.61803 | − | 14.9269i | 0.458692 | − | 0.794477i | −0.540200 | − | 0.841536i | \(-0.681652\pi\) |
0.998892 | + | 0.0470591i | \(0.0149849\pi\) | |||||||
\(354\) | −2.54508 | − | 4.40822i | −0.135270 | − | 0.234294i | ||||
\(355\) | −13.3475 | −0.708413 | ||||||||
\(356\) | −1.71885 | − | 2.97713i | −0.0910987 | − | 0.157788i | ||||
\(357\) | −33.7705 | + | 58.4922i | −1.78732 | + | 3.09574i | ||||
\(358\) | 1.84346 | − | 3.19296i | 0.0974298 | − | 0.168753i | ||||
\(359\) | 2.67376 | − | 4.63109i | 0.141116 | − | 0.244420i | −0.786801 | − | 0.617206i | \(-0.788264\pi\) |
0.927917 | + | 0.372787i | \(0.121598\pi\) | |||||||
\(360\) | 7.01316 | 0.369626 | ||||||||
\(361\) | 8.73607 | − | 15.1313i | 0.459793 | − | 0.796385i | ||||
\(362\) | −3.70163 | + | 6.41140i | −0.194553 | + | 0.336976i | ||||
\(363\) | 2.73607 | + | 4.73901i | 0.143606 | + | 0.248733i | ||||
\(364\) | −5.42705 | − | 9.39993i | −0.284455 | − | 0.492690i | ||||
\(365\) | 2.29180 | 0.119958 | ||||||||
\(366\) | 2.85410 | 0.149186 | ||||||||
\(367\) | −9.59017 | − | 16.6107i | −0.500603 | − | 0.867069i | −1.00000 | 0.000696189i | \(-0.999778\pi\) | |
0.499397 | − | 0.866373i | \(-0.333555\pi\) | |||||||
\(368\) | −6.89261 | − | 11.9383i | −0.359302 | − | 0.622329i | ||||
\(369\) | −18.2533 | + | 31.6156i | −0.950228 | + | 1.64584i | ||||
\(370\) | −1.14590 | + | 1.98475i | −0.0595724 | + | 0.103182i | ||||
\(371\) | 5.85410 | 0.303930 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.00000 | + | 5.19615i | −0.155334 | + | 0.269047i | −0.933181 | − | 0.359408i | \(-0.882979\pi\) |
0.777847 | + | 0.628454i | \(0.216312\pi\) | |||||||
\(374\) | −4.20820 | + | 7.28882i | −0.217601 | + | 0.376896i | ||||
\(375\) | −13.7082 | − | 23.7433i | −0.707889 | − | 1.22610i | ||||
\(376\) | 1.68692 | 0.0869961 | ||||||||
\(377\) | −2.07295 | − | 3.59045i | −0.106762 | − | 0.184918i | ||||
\(378\) | 1.80902 | − | 3.13331i | 0.0930458 | − | 0.161160i | ||||
\(379\) | −27.3607 | −1.40542 | −0.702712 | − | 0.711475i | \(-0.748028\pi\) | ||||
−0.702712 | + | 0.711475i | \(0.748028\pi\) | |||||||
\(380\) | −1.41641 | + | 2.45329i | −0.0726602 | + | 0.125851i | ||||
\(381\) | −19.1803 | − | 33.2213i | −0.982639 | − | 1.70198i | ||||
\(382\) | −2.77458 | − | 4.80571i | −0.141960 | − | 0.245881i | ||||
\(383\) | 38.1246 | 1.94808 | 0.974038 | − | 0.226383i | \(-0.0726901\pi\) | ||||
0.974038 | + | 0.226383i | \(0.0726901\pi\) | |||||||
\(384\) | 13.2082 | + | 22.8773i | 0.674028 | + | 1.16745i | ||||
\(385\) | 18.9443 | 0.965489 | ||||||||
\(386\) | −1.03444 | −0.0526517 | ||||||||
\(387\) | 15.4164 | − | 20.0265i | 0.783660 | − | 1.01800i | ||||
\(388\) | 17.1246 | 0.869370 | ||||||||
\(389\) | −35.0689 | −1.77806 | −0.889031 | − | 0.457846i | \(-0.848621\pi\) | ||||
−0.889031 | + | 0.457846i | \(0.848621\pi\) | |||||||
\(390\) | −0.854102 | − | 1.47935i | −0.0432491 | − | 0.0749097i | ||||
\(391\) | 26.6869 | 1.34962 | ||||||||
\(392\) | −8.05573 | − | 13.9529i | −0.406876 | − | 0.704729i | ||||
\(393\) | 13.0172 | + | 22.5465i | 0.656632 | + | 1.13732i | ||||
\(394\) | −0.562306 | + | 0.973942i | −0.0283286 | + | 0.0490665i | ||||
\(395\) | −1.70820 | −0.0859491 | ||||||||
\(396\) | −12.9271 | + | 22.3903i | −0.649609 | + | 1.12516i | ||||
\(397\) | −16.2082 | − | 28.0734i | −0.813466 | − | 1.40897i | −0.910424 | − | 0.413677i | \(-0.864244\pi\) |
0.0969574 | − | 0.995289i | \(-0.469089\pi\) | |||||||
\(398\) | −0.742646 | −0.0372255 | ||||||||
\(399\) | 6.85410 | + | 11.8717i | 0.343134 | + | 0.594326i | ||||
\(400\) | 5.46149 | − | 9.45958i | 0.273075 | − | 0.472979i | ||||
\(401\) | 12.7082 | − | 22.0113i | 0.634617 | − | 1.09919i | −0.351979 | − | 0.936008i | \(-0.614491\pi\) |
0.986596 | − | 0.163182i | \(-0.0521756\pi\) | |||||||
\(402\) | 1.92705 | − | 3.33775i | 0.0961126 | − | 0.166472i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3.48936 | − | 6.04374i | 0.173602 | − | 0.300687i | ||||
\(405\) | 3.52786 | − | 6.11044i | 0.175301 | − | 0.303630i | ||||
\(406\) | −2.42705 | − | 4.20378i | −0.120453 | − | 0.208630i | ||||
\(407\) | −8.78115 | − | 15.2094i | −0.435266 | − | 0.753902i | ||||
\(408\) | −23.4721 | −1.16204 | ||||||||
\(409\) | 8.90983 | 0.440563 | 0.220281 | − | 0.975436i | \(-0.429302\pi\) | ||||
0.220281 | + | 0.975436i | \(0.429302\pi\) | |||||||
\(410\) | 2.23607 | + | 3.87298i | 0.110432 | + | 0.191273i | ||||
\(411\) | 4.85410 | + | 8.40755i | 0.239435 | + | 0.414714i | ||||
\(412\) | −15.2188 | + | 26.3598i | −0.749779 | + | 1.29865i | ||||
\(413\) | 10.7812 | − | 18.6735i | 0.530506 | − | 0.918863i | ||||
\(414\) | −6.45085 | −0.317042 | ||||||||
\(415\) | −9.90983 | + | 17.1643i | −0.486454 | + | 0.842564i | ||||
\(416\) | 2.86475 | − | 4.96188i | 0.140456 | − | 0.243276i | ||||
\(417\) | −6.92705 | + | 11.9980i | −0.339219 | + | 0.587545i | ||||
\(418\) | 0.854102 | + | 1.47935i | 0.0417755 | + | 0.0723573i | ||||
\(419\) | −10.2361 | −0.500065 | −0.250032 | − | 0.968237i | \(-0.580441\pi\) | ||||
−0.250032 | + | 0.968237i | \(0.580441\pi\) | |||||||
\(420\) | 12.7082 | + | 22.0113i | 0.620097 | + | 1.07404i | ||||
\(421\) | 3.82624 | − | 6.62724i | 0.186479 | − | 0.322992i | −0.757595 | − | 0.652725i | \(-0.773626\pi\) |
0.944074 | + | 0.329734i | \(0.106959\pi\) | |||||||
\(422\) | 3.52786 | 0.171734 | ||||||||
\(423\) | −2.20820 | + | 3.82472i | −0.107367 | + | 0.185964i | ||||
\(424\) | 1.01722 | + | 1.76188i | 0.0494006 | + | 0.0855644i | ||||
\(425\) | 10.5729 | + | 18.3129i | 0.512863 | + | 0.888305i | ||||
\(426\) | −10.7984 | −0.523183 | ||||||||
\(427\) | 6.04508 | + | 10.4704i | 0.292542 | + | 0.506698i | ||||
\(428\) | −13.9574 | −0.674658 | ||||||||
\(429\) | 13.0902 | 0.631999 | ||||||||
\(430\) | −1.18034 | − | 2.86217i | −0.0569210 | − | 0.138026i | ||||
\(431\) | −24.7984 | −1.19450 | −0.597248 | − | 0.802057i | \(-0.703739\pi\) | ||||
−0.597248 | + | 0.802057i | \(0.703739\pi\) | |||||||
\(432\) | −7.03444 | −0.338445 | ||||||||
\(433\) | 17.3541 | + | 30.0582i | 0.833985 | + | 1.44450i | 0.894854 | + | 0.446359i | \(0.147279\pi\) |
−0.0608693 | + | 0.998146i | \(0.519387\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.85410 | + | 8.40755i | 0.232736 | + | 0.403111i | ||||
\(436\) | −12.8435 | − | 22.2455i | −0.615090 | − | 1.06537i | ||||
\(437\) | 2.70820 | − | 4.69075i | 0.129551 | − | 0.224389i | ||||
\(438\) | 1.85410 | 0.0885924 | ||||||||
\(439\) | −0.572949 | + | 0.992377i | −0.0273454 | + | 0.0473636i | −0.879374 | − | 0.476131i | \(-0.842039\pi\) |
0.852029 | + | 0.523495i | \(0.175372\pi\) | |||||||
\(440\) | 3.29180 | + | 5.70156i | 0.156930 | + | 0.271811i | ||||
\(441\) | 42.1803 | 2.00859 | ||||||||
\(442\) | 1.60739 | + | 2.78408i | 0.0764558 | + | 0.132425i | ||||
\(443\) | −1.23607 | + | 2.14093i | −0.0587274 | + | 0.101719i | −0.893894 | − | 0.448278i | \(-0.852038\pi\) |
0.835167 | + | 0.549996i | \(0.185371\pi\) | |||||||
\(444\) | 11.7812 | − | 20.4056i | 0.559109 | − | 0.968405i | ||||
\(445\) | 1.14590 | − | 1.98475i | 0.0543208 | − | 0.0940863i | ||||
\(446\) | −1.05573 | −0.0499902 | ||||||||
\(447\) | 11.7812 | − | 20.4056i | 0.557229 | − | 0.965150i | ||||
\(448\) | −9.97214 | + | 17.2722i | −0.471139 | + | 0.816037i | ||||
\(449\) | 16.4164 | + | 28.4341i | 0.774738 | + | 1.34189i | 0.934942 | + | 0.354802i | \(0.115452\pi\) |
−0.160203 | + | 0.987084i | \(0.551215\pi\) | |||||||
\(450\) | −2.55573 | − | 4.42665i | −0.120478 | − | 0.208674i | ||||
\(451\) | −34.2705 | −1.61374 | ||||||||
\(452\) | 28.9574 | 1.36204 | ||||||||
\(453\) | −11.5902 | − | 20.0748i | −0.544554 | − | 0.943195i | ||||
\(454\) | −0.281153 | − | 0.486971i | −0.0131952 | − | 0.0228547i | ||||
\(455\) | 3.61803 | − | 6.26662i | 0.169616 | − | 0.293784i | ||||
\(456\) | −2.38197 | + | 4.12569i | −0.111546 | + | 0.193203i | ||||
\(457\) | −15.7082 | −0.734799 | −0.367399 | − | 0.930063i | \(-0.619752\pi\) | ||||
−0.367399 | + | 0.930063i | \(0.619752\pi\) | |||||||
\(458\) | −0.437694 | + | 0.758108i | −0.0204521 | + | 0.0354241i | ||||
\(459\) | 6.80902 | − | 11.7936i | 0.317818 | − | 0.550476i | ||||
\(460\) | 5.02129 | − | 8.69712i | 0.234119 | − | 0.405505i | ||||
\(461\) | 15.7984 | + | 27.3636i | 0.735804 | + | 1.27445i | 0.954370 | + | 0.298627i | \(0.0965287\pi\) |
−0.218566 | + | 0.975822i | \(0.570138\pi\) | |||||||
\(462\) | 15.3262 | 0.713041 | ||||||||
\(463\) | 14.9164 | + | 25.8360i | 0.693224 | + | 1.20070i | 0.970776 | + | 0.239989i | \(0.0771438\pi\) |
−0.277551 | + | 0.960711i | \(0.589523\pi\) | |||||||
\(464\) | −4.71885 | + | 8.17328i | −0.219067 | + | 0.379435i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.44427 | − | 5.96565i | 0.159553 | − | 0.276354i | ||||
\(467\) | 7.52786 | + | 13.0386i | 0.348348 | + | 0.603356i | 0.985956 | − | 0.167004i | \(-0.0534094\pi\) |
−0.637608 | + | 0.770361i | \(0.720076\pi\) | |||||||
\(468\) | 4.93769 | + | 8.55234i | 0.228245 | + | 0.395332i | ||||
\(469\) | 16.3262 | 0.753876 | ||||||||
\(470\) | 0.270510 | + | 0.468537i | 0.0124777 | + | 0.0216120i | ||||
\(471\) | 13.4721 | 0.620763 | ||||||||
\(472\) | 7.49342 | 0.344913 | ||||||||
\(473\) | 23.5172 | + | 3.13331i | 1.08132 | + | 0.144070i | ||||
\(474\) | −1.38197 | −0.0634758 | ||||||||
\(475\) | 4.29180 | 0.196921 | ||||||||
\(476\) | −23.9164 | − | 41.4244i | −1.09621 | − | 1.89869i | ||||
\(477\) | −5.32624 | −0.243872 | ||||||||
\(478\) | −1.58359 | − | 2.74286i | −0.0724318 | − | 0.125456i | ||||
\(479\) | 6.90983 | + | 11.9682i | 0.315718 | + | 0.546840i | 0.979590 | − | 0.201007i | \(-0.0644212\pi\) |
−0.663872 | + | 0.747846i | \(0.731088\pi\) | |||||||
\(480\) | −6.70820 | + | 11.6190i | −0.306186 | + | 0.530330i | ||||
\(481\) | −6.70820 | −0.305868 | ||||||||
\(482\) | 0.815595 | − | 1.41265i | 0.0371493 | − | 0.0643445i | ||||
\(483\) | −24.2984 | − | 42.0860i | −1.10561 | − | 1.91498i | ||||
\(484\) | −3.87539 | −0.176154 | ||||||||
\(485\) | 5.70820 | + | 9.88690i | 0.259196 | + | 0.448941i | ||||
\(486\) | 4.13525 | − | 7.16247i | 0.187579 | − | 0.324896i | ||||
\(487\) | −0.663119 | + | 1.14856i | −0.0300488 | + | 0.0520460i | −0.880659 | − | 0.473751i | \(-0.842900\pi\) |
0.850610 | + | 0.525797i | \(0.176233\pi\) | |||||||
\(488\) | −2.10081 | + | 3.63871i | −0.0950993 | + | 0.164717i | ||||
\(489\) | −36.6525 | −1.65748 | ||||||||
\(490\) | 2.58359 | − | 4.47491i | 0.116715 | − | 0.202156i | ||||
\(491\) | −10.8262 | + | 18.7516i | −0.488581 | + | 0.846248i | −0.999914 | − | 0.0131354i | \(-0.995819\pi\) |
0.511332 | + | 0.859383i | \(0.329152\pi\) | |||||||
\(492\) | −22.9894 | − | 39.8187i | −1.03644 | − | 1.79517i | ||||
\(493\) | −9.13525 | − | 15.8227i | −0.411431 | − | 0.712620i | ||||
\(494\) | 0.652476 | 0.0293563 | ||||||||
\(495\) | −17.2361 | −0.774704 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.8713 | − | 39.6143i | −1.02592 | − | 1.77694i | ||||
\(498\) | −8.01722 | + | 13.8862i | −0.359260 | + | 0.622257i | ||||
\(499\) | −6.92705 | + | 11.9980i | −0.310097 | + | 0.537104i | −0.978383 | − | 0.206800i | \(-0.933695\pi\) |
0.668286 | + | 0.743905i | \(0.267028\pi\) | |||||||
\(500\) | 19.4164 | 0.868328 | ||||||||
\(501\) | 18.6353 | − | 32.2772i | 0.832562 | − | 1.44204i | ||||
\(502\) | −5.57295 | + | 9.65263i | −0.248733 | + | 0.430818i | ||||
\(503\) | 6.73607 | − | 11.6672i | 0.300346 | − | 0.520215i | −0.675868 | − | 0.737023i | \(-0.736231\pi\) |
0.976214 | + | 0.216807i | \(0.0695644\pi\) | |||||||
\(504\) | 12.0172 | + | 20.8144i | 0.535290 | + | 0.927149i | ||||
\(505\) | 4.65248 | 0.207032 | ||||||||
\(506\) | −3.02786 | − | 5.24441i | −0.134605 | − | 0.233143i | ||||
\(507\) | −14.5172 | + | 25.1446i | −0.644732 | + | 1.11671i | ||||
\(508\) | 27.1672 | 1.20535 | ||||||||
\(509\) | −9.35410 | + | 16.2018i | −0.414613 | + | 0.718131i | −0.995388 | − | 0.0959332i | \(-0.969416\pi\) |
0.580774 | + | 0.814064i | \(0.302750\pi\) | |||||||
\(510\) | −3.76393 | − | 6.51932i | −0.166670 | − | 0.288680i | ||||
\(511\) | 3.92705 | + | 6.80185i | 0.173723 | + | 0.300896i | ||||
\(512\) | −22.3050 | −0.985749 | ||||||||
\(513\) | −1.38197 | − | 2.39364i | −0.0610153 | − | 0.105682i | ||||
\(514\) | −1.31308 | −0.0579176 | ||||||||
\(515\) | −20.2918 | −0.894163 | ||||||||
\(516\) | 12.1353 | + | 29.4264i | 0.534225 | + | 1.29543i | ||||
\(517\) | −4.14590 | −0.182336 | ||||||||
\(518\) | −7.85410 | −0.345089 | ||||||||
\(519\) | −4.92705 | − | 8.53390i | −0.216274 | − | 0.374597i | ||||
\(520\) | 2.51471 | 0.110277 | ||||||||
\(521\) | 11.0172 | + | 19.0824i | 0.482673 | + | 0.836015i | 0.999802 | − | 0.0198930i | \(-0.00633256\pi\) |
−0.517129 | + | 0.855908i | \(0.672999\pi\) | |||||||
\(522\) | 2.20820 | + | 3.82472i | 0.0966505 | + | 0.167404i | ||||
\(523\) | −17.9164 | + | 31.0321i | −0.783430 | + | 1.35694i | 0.146503 | + | 0.989210i | \(0.453198\pi\) |
−0.929933 | + | 0.367730i | \(0.880135\pi\) | |||||||
\(524\) | −18.4377 | −0.805454 | ||||||||
\(525\) | 19.2533 | − | 33.3477i | 0.840282 | − | 1.45541i | ||||
\(526\) | 5.25329 | + | 9.09896i | 0.229054 | + | 0.396734i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −14.8992 | − | 25.8061i | −0.648404 | − | 1.12307i | ||||
\(529\) | 1.89919 | − | 3.28949i | 0.0825733 | − | 0.143021i | ||||
\(530\) | −0.326238 | + | 0.565061i | −0.0141709 | + | 0.0245447i | ||||
\(531\) | −9.80902 | + | 16.9897i | −0.425675 | + | 0.737291i | ||||
\(532\) | −9.70820 | −0.420904 | ||||||||
\(533\) | −6.54508 | + | 11.3364i | −0.283499 | + | 0.491035i | ||||
\(534\) | 0.927051 | − | 1.60570i | 0.0401174 | − | 0.0694854i | ||||
\(535\) | −4.65248 | − | 8.05832i | −0.201144 | − | 0.348392i | ||||
\(536\) | 2.83688 | + | 4.91362i | 0.122535 | + | 0.212236i | ||||
\(537\) | −25.2705 | −1.09050 | ||||||||
\(538\) | −4.41641 | −0.190405 | ||||||||
\(539\) | 19.7984 | + | 34.2918i | 0.852776 | + | 1.47705i | ||||
\(540\) | −2.56231 | − | 4.43804i | −0.110264 | − | 0.190983i | ||||
\(541\) | 18.9721 | − | 32.8607i | 0.815676 | − | 1.41279i | −0.0931658 | − | 0.995651i | \(-0.529699\pi\) |
0.908842 | − | 0.417141i | \(-0.136968\pi\) | |||||||
\(542\) | 2.64590 | − | 4.58283i | 0.113651 | − | 0.196849i | ||||
\(543\) | 50.7426 | 2.17758 | ||||||||
\(544\) | 12.6246 | − | 21.8665i | 0.541276 | − | 0.937517i | ||||
\(545\) | 8.56231 | − | 14.8303i | 0.366769 | − | 0.635262i | ||||
\(546\) | 2.92705 | − | 5.06980i | 0.125266 | − | 0.216967i | ||||
\(547\) | −10.5000 | − | 18.1865i | −0.448948 | − | 0.777600i | 0.549370 | − | 0.835579i | \(-0.314868\pi\) |
−0.998318 | + | 0.0579790i | \(0.981534\pi\) | |||||||
\(548\) | −6.87539 | −0.293702 | ||||||||
\(549\) | −5.50000 | − | 9.52628i | −0.234734 | − | 0.406572i | ||||
\(550\) | 2.39919 | − | 4.15551i | 0.102302 | − | 0.177192i | ||||
\(551\) | −3.70820 | −0.157975 | ||||||||
\(552\) | 8.44427 | − | 14.6259i | 0.359412 | − | 0.622520i | ||||
\(553\) | −2.92705 | − | 5.06980i | −0.124471 | − | 0.215590i | ||||
\(554\) | −2.38197 | − | 4.12569i | −0.101200 | − | 0.175284i | ||||
\(555\) | 15.7082 | 0.666776 | ||||||||
\(556\) | −4.90576 | − | 8.49703i | −0.208051 | − | 0.360354i | ||||
\(557\) | −38.5623 | −1.63394 | −0.816969 | − | 0.576682i | \(-0.804347\pi\) | ||||
−0.816969 | + | 0.576682i | \(0.804347\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.52786 | − | 7.18091i | 0.233804 | − | 0.303720i | ||||
\(560\) | −16.4721 | −0.696075 | ||||||||
\(561\) | 57.6869 | 2.43554 | ||||||||
\(562\) | 1.42705 | + | 2.47172i | 0.0601965 | + | 0.104263i | ||||
\(563\) | −1.32624 | −0.0558943 | −0.0279471 | − | 0.999609i | \(-0.508897\pi\) | ||||
−0.0279471 | + | 0.999609i | \(0.508897\pi\) | |||||||
\(564\) | −2.78115 | − | 4.81710i | −0.117108 | − | 0.202836i | ||||
\(565\) | 9.65248 | + | 16.7186i | 0.406083 | + | 0.703356i | ||||
\(566\) | 2.05573 | − | 3.56063i | 0.0864087 | − | 0.149664i | ||||
\(567\) | 24.1803 | 1.01548 | ||||||||
\(568\) | 7.94834 | − | 13.7669i | 0.333505 | − | 0.577647i | ||||
\(569\) | 12.9721 | + | 22.4684i | 0.543820 | + | 0.941924i | 0.998680 | + | 0.0513613i | \(0.0163560\pi\) |
−0.454860 | + | 0.890563i | \(0.650311\pi\) | |||||||
\(570\) | −1.52786 | −0.0639952 | ||||||||
\(571\) | 21.5902 | + | 37.3953i | 0.903520 | + | 1.56494i | 0.822891 | + | 0.568199i | \(0.192360\pi\) |
0.0806295 | + | 0.996744i | \(0.474307\pi\) | |||||||
\(572\) | −4.63525 | + | 8.02850i | −0.193810 | + | 0.335688i | ||||
\(573\) | −19.0172 | + | 32.9388i | −0.794456 | + | 1.37604i | ||||
\(574\) | −7.66312 | + | 13.2729i | −0.319852 | + | 0.554001i | ||||
\(575\) | −15.2148 | −0.634500 | ||||||||
\(576\) | 9.07295 | − | 15.7148i | 0.378040 | − | 0.654784i | ||||
\(577\) | 14.1074 | − | 24.4347i | 0.587298 | − | 1.01723i | −0.407286 | − | 0.913301i | \(-0.633525\pi\) |
0.994585 | − | 0.103930i | \(-0.0331418\pi\) | |||||||
\(578\) | 3.83688 | + | 6.64567i | 0.159593 | + | 0.276424i | ||||
\(579\) | 3.54508 | + | 6.14027i | 0.147329 | + | 0.255181i | ||||
\(580\) | −6.87539 | −0.285485 | ||||||||
\(581\) | −67.9230 | −2.81792 | ||||||||
\(582\) | 4.61803 | + | 7.99867i | 0.191424 | + | 0.331556i | ||||
\(583\) | −2.50000 | − | 4.33013i | −0.103539 | − | 0.179336i | ||||
\(584\) | −1.36475 | + | 2.36381i | −0.0564736 | + | 0.0978151i | ||||
\(585\) | −3.29180 | + | 5.70156i | −0.136099 | + | 0.235730i | ||||
\(586\) | 4.61803 | 0.190769 | ||||||||
\(587\) | −7.87132 | + | 13.6335i | −0.324884 | + | 0.562716i | −0.981489 | − | 0.191519i | \(-0.938659\pi\) |
0.656605 | + | 0.754235i | \(0.271992\pi\) | |||||||
\(588\) | −26.5623 | + | 46.0073i | −1.09541 | + | 1.89731i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.20163 | + | 2.08128i | 0.0494702 | + | 0.0856848i | ||||
\(591\) | 7.70820 | 0.317073 | ||||||||
\(592\) | 7.63525 | + | 13.2246i | 0.313807 | + | 0.543530i | ||||
\(593\) | 15.2361 | − | 26.3896i | 0.625670 | − | 1.08369i | −0.362741 | − | 0.931890i | \(-0.618159\pi\) |
0.988411 | − | 0.151803i | \(-0.0485078\pi\) | |||||||
\(594\) | −3.09017 | −0.126791 | ||||||||
\(595\) | 15.9443 | − | 27.6163i | 0.653651 | − | 1.13216i | ||||
\(596\) | 8.34346 | + | 14.4513i | 0.341761 | + | 0.591948i | ||||
\(597\) | 2.54508 | + | 4.40822i | 0.104163 | + | 0.180416i | ||||
\(598\) | −2.31308 | −0.0945890 | ||||||||
\(599\) | −18.1180 | − | 31.3814i | −0.740283 | − | 1.28221i | −0.952366 | − | 0.304956i | \(-0.901358\pi\) |
0.212084 | − | 0.977252i | \(-0.431975\pi\) | |||||||
\(600\) | 13.3820 | 0.546316 | ||||||||
\(601\) | 29.4164 | 1.19992 | 0.599960 | − | 0.800030i | \(-0.295183\pi\) | ||||
0.599960 | + | 0.800030i | \(0.295183\pi\) | |||||||
\(602\) | 6.47214 | − | 8.40755i | 0.263785 | − | 0.342666i | ||||
\(603\) | −14.8541 | −0.604906 | ||||||||
\(604\) | 16.4164 | 0.667974 | ||||||||
\(605\) | −1.29180 | − | 2.23746i | −0.0525190 | − | 0.0909655i | ||||
\(606\) | 3.76393 | 0.152899 | ||||||||
\(607\) | 11.9271 | + | 20.6583i | 0.484104 | + | 0.838493i | 0.999833 | − | 0.0182588i | \(-0.00581228\pi\) |
−0.515729 | + | 0.856752i | \(0.672479\pi\) | |||||||
\(608\) | −2.56231 | − | 4.43804i | −0.103915 | − | 0.179986i | ||||
\(609\) | −16.6353 | + | 28.8131i | −0.674095 | + | 1.16757i | ||||
\(610\) | −1.34752 | −0.0545597 | ||||||||
\(611\) | −0.791796 | + | 1.37143i | −0.0320326 | + | 0.0554822i | ||||
\(612\) | 21.7599 | + | 37.6892i | 0.879590 | + | 1.52350i | ||||
\(613\) | 5.20163 | 0.210092 | 0.105046 | − | 0.994467i | \(-0.466501\pi\) | ||||
0.105046 | + | 0.994467i | \(0.466501\pi\) | |||||||
\(614\) | −4.43363 | − | 7.67927i | −0.178927 | − | 0.309910i | ||||
\(615\) | 15.3262 | − | 26.5458i | 0.618014 | − | 1.07043i | ||||
\(616\) | −11.2812 | + | 19.5395i | −0.454531 | + | 0.787270i | ||||
\(617\) | −4.85410 | + | 8.40755i | −0.195419 | + | 0.338475i | −0.947038 | − | 0.321122i | \(-0.895940\pi\) |
0.751619 | + | 0.659598i | \(0.229273\pi\) | |||||||
\(618\) | −16.4164 | −0.660365 | ||||||||
\(619\) | 15.1353 | − | 26.2150i | 0.608337 | − | 1.05367i | −0.383177 | − | 0.923675i | \(-0.625170\pi\) |
0.991514 | − | 0.129996i | \(-0.0414965\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.89919 | + | 8.48564i | 0.196598 | + | 0.340517i | ||||
\(622\) | −5.69756 | − | 9.86846i | −0.228451 | − | 0.395689i | ||||
\(623\) | 7.85410 | 0.314668 | ||||||||
\(624\) | −11.3820 | −0.455643 | ||||||||
\(625\) | −2.20820 | − | 3.82472i | −0.0883282 | − | 0.152989i | ||||
\(626\) | 2.50658 | + | 4.34152i | 0.100183 | + | 0.173522i | ||||
\(627\) | 5.85410 | − | 10.1396i | 0.233790 | − | 0.404937i | ||||
\(628\) | −4.77051 | + | 8.26277i | −0.190364 | + | 0.329720i | ||||
\(629\) | −29.5623 | −1.17873 | ||||||||
\(630\) | −3.85410 | + | 6.67550i | −0.153551 | + | 0.265958i | ||||
\(631\) | 13.5451 | − | 23.4608i | 0.539221 | − | 0.933959i | −0.459725 | − | 0.888061i | \(-0.652052\pi\) |
0.998946 | − | 0.0458973i | \(-0.0146147\pi\) | |||||||
\(632\) | 1.01722 | − | 1.76188i | 0.0404629 | − | 0.0700838i | ||||
\(633\) | −12.0902 | − | 20.9408i | −0.480541 | − | 0.832322i | ||||
\(634\) | −12.7214 | −0.505230 | ||||||||
\(635\) | 9.05573 | + | 15.6850i | 0.359366 | + | 0.622439i | ||||
\(636\) | 3.35410 | − | 5.80948i | 0.132999 | − | 0.230361i | ||||
\(637\) | 15.1246 | 0.599259 | ||||||||
\(638\) | −2.07295 | + | 3.59045i | −0.0820688 | + | 0.142147i | ||||
\(639\) | 20.8090 | + | 36.0423i | 0.823192 | + | 1.42581i | ||||
\(640\) | −6.23607 | − | 10.8012i | −0.246502 | − | 0.426954i | ||||
\(641\) | 10.8197 | 0.427351 | 0.213675 | − | 0.976905i | \(-0.431457\pi\) | ||||
0.213675 | + | 0.976905i | \(0.431457\pi\) | |||||||
\(642\) | −3.76393 | − | 6.51932i | −0.148551 | − | 0.257297i | ||||
\(643\) | 9.43769 | 0.372186 | 0.186093 | − | 0.982532i | \(-0.440417\pi\) | ||||
0.186093 | + | 0.982532i | \(0.440417\pi\) | |||||||
\(644\) | 34.4164 | 1.35620 | ||||||||
\(645\) | −12.9443 | + | 16.8151i | −0.509680 | + | 0.662094i | ||||
\(646\) | 2.87539 | 0.113131 | ||||||||
\(647\) | −21.6738 | −0.852084 | −0.426042 | − | 0.904703i | \(-0.640092\pi\) | ||||
−0.426042 | + | 0.904703i | \(0.640092\pi\) | |||||||
\(648\) | 4.20163 | + | 7.27743i | 0.165055 | + | 0.285884i | ||||
\(649\) | −18.4164 | −0.722907 | ||||||||
\(650\) | −0.916408 | − | 1.58726i | −0.0359445 | − | 0.0622577i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.9787 | − | 22.4798i | 0.508286 | − | 0.880377i | ||||
\(653\) | −32.8885 | −1.28703 | −0.643514 | − | 0.765434i | \(-0.722524\pi\) | ||||
−0.643514 | + | 0.765434i | \(0.722524\pi\) | |||||||
\(654\) | 6.92705 | − | 11.9980i | 0.270869 | − | 0.469159i | ||||
\(655\) | −6.14590 | − | 10.6450i | −0.240140 | − | 0.415935i | ||||
\(656\) | 29.7984 | 1.16343 | ||||||||
\(657\) | −3.57295 | − | 6.18853i | −0.139394 | − | 0.241438i | ||||
\(658\) | −0.927051 | + | 1.60570i | −0.0361402 | + | 0.0625967i | ||||
\(659\) | 14.6803 | − | 25.4271i | 0.571865 | − | 0.990499i | −0.424510 | − | 0.905423i | \(-0.639553\pi\) |
0.996375 | − | 0.0850756i | \(-0.0271132\pi\) | |||||||
\(660\) | 10.8541 | − | 18.7999i | 0.422495 | − | 0.731783i | ||||
\(661\) | −43.3951 | −1.68787 | −0.843937 | − | 0.536442i | \(-0.819768\pi\) | ||||
−0.843937 | + | 0.536442i | \(0.819768\pi\) | |||||||
\(662\) | −1.04508 | + | 1.81014i | −0.0406184 | + | 0.0703531i | ||||
\(663\) | 11.0172 | − | 19.0824i | 0.427873 | − | 0.741098i | ||||
\(664\) | −11.8024 | − | 20.4424i | −0.458023 | − | 0.793320i | ||||
\(665\) | −3.23607 | − | 5.60503i | −0.125489 | − | 0.217354i | ||||
\(666\) | 7.14590 | 0.276898 | ||||||||
\(667\) | 13.1459 | 0.509011 | ||||||||
\(668\) | 13.1976 | + | 22.8588i | 0.510629 | + | 0.884435i | ||||
\(669\) | 3.61803 | + | 6.26662i | 0.139881 | + | 0.242281i | ||||
\(670\) | −0.909830 | + | 1.57587i | −0.0351498 | + | 0.0608812i | ||||
\(671\) | 5.16312 | − | 8.94278i | 0.199320 | − | 0.345232i | ||||
\(672\) | −45.9787 | −1.77367 | ||||||||
\(673\) | −6.91641 | + | 11.9796i | −0.266608 | + | 0.461778i | −0.967984 | − | 0.251013i | \(-0.919236\pi\) |
0.701376 | + | 0.712792i | \(0.252570\pi\) | |||||||
\(674\) | 5.34752 | − | 9.26218i | 0.205979 | − | 0.356766i | ||||
\(675\) | −3.88197 | + | 6.72376i | −0.149417 | + | 0.258798i | ||||
\(676\) | −10.2812 | − | 17.8075i | −0.395429 | − | 0.684903i | ||||
\(677\) | −31.7639 | −1.22079 | −0.610394 | − | 0.792098i | \(-0.708989\pi\) | ||||
−0.610394 | + | 0.792098i | \(0.708989\pi\) | |||||||
\(678\) | 7.80902 | + | 13.5256i | 0.299903 | + | 0.519448i | ||||
\(679\) | −19.5623 | + | 33.8829i | −0.750732 | + | 1.30031i | ||||
\(680\) | 11.0820 | 0.424977 | ||||||||
\(681\) | −1.92705 | + | 3.33775i | −0.0738448 | + | 0.127903i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.56231 | + | 9.63420i | 0.212836 | + | 0.368642i | 0.952601 | − | 0.304223i | \(-0.0983968\pi\) |
−0.739765 | + | 0.672865i | \(0.765063\pi\) | |||||||
\(684\) | 8.83282 | 0.337731 | ||||||||
\(685\) | −2.29180 | − | 3.96951i | −0.0875650 | − | 0.151667i | ||||
\(686\) | 6.38197 | 0.243665 | ||||||||
\(687\) | 6.00000 | 0.228914 | ||||||||
\(688\) | −20.4483 | − | 2.72443i | −0.779586 | − | 0.103868i | ||||
\(689\) | −1.90983 | −0.0727587 | ||||||||
\(690\) | 5.41641 | 0.206199 | ||||||||
\(691\) | −7.86475 | − | 13.6221i | −0.299189 | − | 0.518211i | 0.676762 | − | 0.736202i | \(-0.263383\pi\) |
−0.975951 | + | 0.217992i | \(0.930049\pi\) | |||||||
\(692\) | 6.97871 | 0.265291 | ||||||||
\(693\) | −29.5344 | − | 51.1552i | −1.12192 | − | 1.94322i | ||||
\(694\) | 1.92705 | + | 3.33775i | 0.0731499 | + | 0.126699i | ||||
\(695\) | 3.27051 | − | 5.66469i | 0.124058 | − | 0.214874i | ||||
\(696\) | −11.5623 | −0.438268 | ||||||||
\(697\) | −28.8435 | + | 49.9583i | −1.09252 | + | 1.89231i | ||||
\(698\) | 3.95492 | + | 6.85011i | 0.149696 | + | 0.259281i | ||||
\(699\) | −47.2148 | −1.78583 | ||||||||
\(700\) | 13.6353 | + | 23.6170i | 0.515364 | + | 0.892637i | ||||
\(701\) | 7.25329 | − | 12.5631i | 0.273953 | − | 0.474500i | −0.695917 | − | 0.718122i | \(-0.745002\pi\) |
0.969870 | + | 0.243621i | \(0.0783354\pi\) | |||||||
\(702\) | −0.590170 | + | 1.02220i | −0.0222745 | + | 0.0385806i | ||||
\(703\) | −3.00000 | + | 5.19615i | −0.113147 | + | 0.195977i | ||||
\(704\) | 17.0344 | 0.642010 | ||||||||
\(705\) | 1.85410 | − | 3.21140i | 0.0698295 | − | 0.120948i | ||||
\(706\) | −3.29180 | + | 5.70156i | −0.123888 | + | 0.214581i | ||||
\(707\) | 7.97214 | + | 13.8081i | 0.299823 | + | 0.519309i | ||||
\(708\) | −12.3541 | − | 21.3979i | −0.464296 | − | 0.804184i | ||||
\(709\) | 28.8885 | 1.08493 | 0.542466 | − | 0.840078i | \(-0.317491\pi\) | ||||
0.542466 | + | 0.840078i | \(0.317491\pi\) | |||||||
\(710\) | 5.09830 | 0.191336 | ||||||||
\(711\) | 2.66312 | + | 4.61266i | 0.0998748 | + | 0.172988i | ||||
\(712\) | 1.36475 | + | 2.36381i | 0.0511460 | + | 0.0885874i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 12.8992 | − | 22.3420i | 0.482740 | − | 0.836130i | ||||
\(715\) | −6.18034 | −0.231132 | ||||||||
\(716\) | 8.94834 | − | 15.4990i | 0.334415 | − | 0.579224i | ||||
\(717\) | −10.8541 | + | 18.7999i | −0.405354 | + | 0.702093i | ||||
\(718\) | −1.02129 | + | 1.76892i | −0.0381141 | + | 0.0660155i | ||||
\(719\) | 5.39919 | + | 9.35167i | 0.201356 | + | 0.348758i | 0.948965 | − | 0.315380i | \(-0.102132\pi\) |
−0.747610 | + | 0.664138i | \(0.768799\pi\) | |||||||
\(720\) | 14.9868 | 0.558527 | ||||||||
\(721\) | −34.7705 | − | 60.2243i | −1.29492 | − | 2.24287i | ||||
\(722\) | −3.33688 | + | 5.77965i | −0.124186 | + | 0.215096i | ||||
\(723\) | −11.1803 | −0.415801 | ||||||||
\(724\) | −17.9681 | + | 31.1216i | −0.667778 | + | 1.15663i | ||||
\(725\) | 5.20820 | + | 9.02087i | 0.193428 | + | 0.335027i | ||||
\(726\) | −1.04508 | − | 1.81014i | −0.0387867 | − | 0.0671806i | ||||
\(727\) | −17.9787 | −0.666794 | −0.333397 | − | 0.942787i | \(-0.608195\pi\) | ||||
−0.333397 | + | 0.942787i | \(0.608195\pi\) | |||||||
\(728\) | 4.30902 | + | 7.46344i | 0.159703 | + | 0.276613i | ||||
\(729\) | −39.5623 | −1.46527 | ||||||||
\(730\) | −0.875388 | −0.0323996 | ||||||||
\(731\) | 24.3607 | − | 31.6455i | 0.901012 | − | 1.17045i | ||||
\(732\) | 13.8541 | 0.512062 | ||||||||
\(733\) | 24.5410 | 0.906443 | 0.453222 | − | 0.891398i | \(-0.350275\pi\) | ||||
0.453222 | + | 0.891398i | \(0.350275\pi\) | |||||||
\(734\) | 3.66312 | + | 6.34471i | 0.135208 | + | 0.234187i | ||||
\(735\) | −35.4164 | −1.30635 | ||||||||
\(736\) | 9.08359 | + | 15.7332i | 0.334826 | + | 0.579935i | ||||
\(737\) | −6.97214 | − | 12.0761i | −0.256822 | − | 0.444829i | ||||
\(738\) | 6.97214 | − | 12.0761i | 0.256648 | − | 0.444527i | ||||
\(739\) | 49.5410 | 1.82240 | 0.911198 | − | 0.411969i | \(-0.135159\pi\) | ||||
0.911198 | + | 0.411969i | \(0.135159\pi\) | |||||||
\(740\) | −5.56231 | + | 9.63420i | −0.204474 | + | 0.354160i | ||||
\(741\) | −2.23607 | − | 3.87298i | −0.0821440 | − | 0.142278i | ||||
\(742\) | −2.23607 | −0.0820886 | ||||||||
\(743\) | −16.6803 | − | 28.8912i | −0.611942 | − | 1.05992i | −0.990913 | − | 0.134506i | \(-0.957055\pi\) |
0.378970 | − | 0.925409i | \(-0.376278\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.56231 | + | 9.63420i | −0.203787 | + | 0.352970i | ||||
\(746\) | 1.14590 | − | 1.98475i | 0.0419543 | − | 0.0726670i | ||||
\(747\) | 61.7984 | 2.26108 | ||||||||
\(748\) | −20.4271 | + | 35.3807i | −0.746887 | + | 1.29365i | ||||
\(749\) | 15.9443 | − | 27.6163i | 0.582591 | − | 1.00908i | ||||
\(750\) | 5.23607 | + | 9.06914i | 0.191194 | + | 0.331158i | ||||
\(751\) | 18.9894 | + | 32.8905i | 0.692931 | + | 1.20019i | 0.970873 | + | 0.239595i | \(0.0770145\pi\) |
−0.277942 | + | 0.960598i | \(0.589652\pi\) | |||||||
\(752\) | 3.60488 | 0.131456 | ||||||||
\(753\) | 76.3951 | 2.78399 | ||||||||
\(754\) | 0.791796 | + | 1.37143i | 0.0288355 | + | 0.0499446i | ||||
\(755\) | 5.47214 | + | 9.47802i | 0.199151 | + | 0.344940i | ||||
\(756\) | 8.78115 | − | 15.2094i | 0.319367 | − | 0.553161i | ||||
\(757\) | 15.4894 | − | 26.8284i | 0.562970 | − | 0.975093i | −0.434265 | − | 0.900785i | \(-0.642992\pi\) |
0.997235 | − | 0.0743080i | \(-0.0236748\pi\) | |||||||
\(758\) | 10.4508 | 0.379592 | ||||||||
\(759\) | −20.7533 | + | 35.9458i | −0.753297 | + | 1.30475i | ||||
\(760\) | 1.12461 | − | 1.94788i | 0.0407940 | − | 0.0706572i | ||||
\(761\) | −0.545085 | + | 0.944115i | −0.0197593 | + | 0.0342241i | −0.875736 | − | 0.482790i | \(-0.839623\pi\) |
0.855977 | + | 0.517014i | \(0.172957\pi\) | |||||||
\(762\) | 7.32624 | + | 12.6894i | 0.265402 | + | 0.459689i | ||||
\(763\) | 58.6869 | 2.12461 | ||||||||
\(764\) | −13.4681 | − | 23.3274i | −0.487258 | − | 0.843955i | ||||
\(765\) | −14.5066 | + | 25.1261i | −0.524486 | + | 0.908437i | ||||
\(766\) | −14.5623 | −0.526157 | ||||||||
\(767\) | −3.51722 | + | 6.09201i | −0.126999 | + | 0.219970i | ||||
\(768\) | 7.28115 | + | 12.6113i | 0.262736 | + | 0.455072i | ||||
\(769\) | −9.94427 | − | 17.2240i | −0.358600 | − | 0.621113i | 0.629128 | − | 0.777302i | \(-0.283412\pi\) |
−0.987727 | + | 0.156189i | \(0.950079\pi\) | |||||||
\(770\) | −7.23607 | −0.260770 | ||||||||
\(771\) | 4.50000 | + | 7.79423i | 0.162064 | + | 0.280702i | ||||
\(772\) | −5.02129 | −0.180720 | ||||||||
\(773\) | 15.5967 | 0.560976 | 0.280488 | − | 0.959858i | \(-0.409504\pi\) | ||||
0.280488 | + | 0.959858i | \(0.409504\pi\) | |||||||
\(774\) | −5.88854 | + | 7.64944i | −0.211659 | + | 0.274954i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.5967 | −0.488095 | ||||||||
\(777\) | 26.9164 | + | 46.6206i | 0.965621 | + | 1.67250i | ||||
\(778\) | 13.3951 | 0.480238 | ||||||||
\(779\) | 5.85410 | + | 10.1396i | 0.209745 | + | 0.363289i | ||||
\(780\) | −4.14590 | − | 7.18091i | −0.148447 | − | 0.257118i | ||||
\(781\) | −19.5344 | + | 33.8346i | −0.698997 | + | 1.21070i | ||||
\(782\) | −10.1935 | −0.364519 | ||||||||
\(783\) | 3.35410 | − | 5.80948i | 0.119866 | − | 0.207614i | ||||
\(784\) | −17.2148 | − | 29.8169i | −0.614814 | − | 1.06489i | ||||
\(785\) | −6.36068 | −0.227022 | ||||||||
\(786\) | −4.97214 | − | 8.61199i | −0.177350 | − | 0.307180i | ||||
\(787\) | −5.22542 | + | 9.05070i | −0.186266 | + | 0.322623i | −0.944002 | − | 0.329938i | \(-0.892972\pi\) |
0.757736 | + | 0.652561i | \(0.226305\pi\) | |||||||
\(788\) | −2.72949 | + | 4.72762i | −0.0972341 | + | 0.168414i | ||||
\(789\) | 36.0066 | − | 62.3652i | 1.28187 | − | 2.22026i | ||||
\(790\) | 0.652476 | 0.0232140 | ||||||||
\(791\) | −33.0795 | + | 57.2954i | −1.17617 | + | 2.03719i | ||||
\(792\) | 10.2639 | − | 17.7777i | 0.364713 | − | 0.631701i | ||||
\(793\) | −1.97214 | − | 3.41584i | −0.0700326 | − | 0.121300i | ||||
\(794\) | 6.19098 | + | 10.7231i | 0.219710 | + | 0.380548i | ||||
\(795\) | 4.47214 | 0.158610 | ||||||||
\(796\) | −3.60488 | −0.127772 | ||||||||
\(797\) | 4.11803 | + | 7.13264i | 0.145868 | + | 0.252651i | 0.929697 | − | 0.368326i | \(-0.120069\pi\) |
−0.783828 | + | 0.620978i | \(0.786736\pi\) | |||||||
\(798\) | −2.61803 | − | 4.53457i | −0.0926774 | − | 0.160522i | ||||
\(799\) | −3.48936 | + | 6.04374i | −0.123445 | + | 0.213812i | ||||
\(800\) | −7.19756 | + | 12.4665i | −0.254472 | + | 0.440759i | ||||
\(801\) | −7.14590 | −0.252488 | ||||||||
\(802\) | −4.85410 | + | 8.40755i | −0.171404 | + | 0.296881i | ||||
\(803\) | 3.35410 | − | 5.80948i | 0.118364 | − | 0.205012i | ||||
\(804\) | 9.35410 | − | 16.2018i | 0.329894 | − | 0.571393i | ||||
\(805\) | 11.4721 | + | 19.8703i | 0.404340 | + | 0.700337i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.1353 | + | 26.2150i | 0.532786 | + | 0.922813i | ||||
\(808\) | −2.77051 | + | 4.79866i | −0.0974662 | + | 0.168816i | ||||
\(809\) | 4.74265 | 0.166743 | 0.0833713 | − | 0.996519i | \(-0.473431\pi\) | ||||
0.0833713 | + | 0.996519i | \(0.473431\pi\) | |||||||
\(810\) | −1.34752 | + | 2.33398i | −0.0473472 | + | 0.0820077i | ||||
\(811\) | −23.6976 | − | 41.0454i | −0.832134 | − | 1.44130i | −0.896343 | − | 0.443362i | \(-0.853786\pi\) |
0.0642089 | − | 0.997936i | \(-0.479548\pi\) | |||||||
\(812\) | −11.7812 | − | 20.4056i | −0.413437 | − | 0.716095i | ||||
\(813\) | −36.2705 | −1.27206 | ||||||||
\(814\) | 3.35410 | + | 5.80948i | 0.117561 | + | 0.203622i | ||||
\(815\) | 17.3050 | 0.606166 | ||||||||
\(816\) | −50.1591 | −1.75592 | ||||||||
\(817\) | −3.09017 | − | 7.49326i | −0.108111 | − | 0.262156i | ||||
\(818\) | −3.40325 | −0.118992 | ||||||||
\(819\) | −22.5623 | −0.788391 | ||||||||
\(820\) | 10.8541 | + | 18.7999i | 0.379042 | + | 0.656519i | ||||
\(821\) | 0.326238 | 0.0113858 | 0.00569289 | − | 0.999984i | \(-0.498188\pi\) | ||||
0.00569289 | + | 0.999984i | \(0.498188\pi\) | |||||||
\(822\) | −1.85410 | − | 3.21140i | −0.0646692 | − | 0.112010i | ||||
\(823\) | −26.0066 | − | 45.0447i | −0.906532 | − | 1.57016i | −0.818847 | − | 0.574012i | \(-0.805386\pi\) |
−0.0876853 | − | 0.996148i | \(-0.527947\pi\) | |||||||
\(824\) | 12.0836 | − | 20.9294i | 0.420952 | − | 0.729110i | ||||
\(825\) | −32.8885 | −1.14503 | ||||||||
\(826\) | −4.11803 | + | 7.13264i | −0.143285 | + | 0.248176i | ||||
\(827\) | −4.59017 | − | 7.95041i | −0.159616 | − | 0.276463i | 0.775114 | − | 0.631821i | \(-0.217692\pi\) |
−0.934730 | + | 0.355358i | \(0.884359\pi\) | |||||||
\(828\) | −31.3131 | −1.08820 | ||||||||
\(829\) | −14.0795 | − | 24.3865i | −0.489002 | − | 0.846977i | 0.510918 | − | 0.859630i | \(-0.329306\pi\) |
−0.999920 | + | 0.0126530i | \(0.995972\pi\) | |||||||
\(830\) | 3.78522 | − | 6.55619i | 0.131387 | − | 0.227569i | ||||
\(831\) | −16.3262 | + | 28.2779i | −0.566351 | + | 0.980949i | ||||
\(832\) | 3.25329 | − | 5.63486i | 0.112787 | − | 0.195354i | ||||
\(833\) | 66.6525 | 2.30937 | ||||||||
\(834\) | 2.64590 | − | 4.58283i | 0.0916200 | − | 0.158690i | ||||
\(835\) | −8.79837 | + | 15.2392i | −0.304480 | + | 0.527375i | ||||
\(836\) | 4.14590 | + | 7.18091i | 0.143389 | + | 0.248357i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.90983 | 0.135063 | ||||||||
\(839\) | 25.8885 | 0.893772 | 0.446886 | − | 0.894591i | \(-0.352533\pi\) | ||||
0.446886 | + | 0.894591i | \(0.352533\pi\) | |||||||
\(840\) | −10.0902 | − | 17.4767i | −0.348144 | − | 0.603003i | ||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | −1.46149 | + | 2.53138i | −0.0503664 | + | 0.0872371i | ||||
\(843\) | 9.78115 | − | 16.9415i | 0.336881 | − | 0.583495i | ||||
\(844\) | 17.1246 | 0.589453 | ||||||||
\(845\) | 6.85410 | − | 11.8717i | 0.235788 | − | 0.408397i | ||||
\(846\) | 0.843459 | − | 1.46091i | 0.0289987 | − | 0.0502272i | ||||
\(847\) | 4.42705 | − | 7.66788i | 0.152115 | − | 0.263471i | ||||
\(848\) | 2.17376 | + | 3.76507i | 0.0746473 | + | 0.129293i | ||||
\(849\) | −28.1803 | −0.967147 | ||||||||
\(850\) | −4.03851 | − | 6.99490i | −0.138520 | − | 0.239923i | ||||
\(851\) | 10.6353 | − | 18.4208i | 0.364572 | − | 0.631457i | ||||
\(852\) | −52.4164 | −1.79576 | ||||||||
\(853\) | −5.62868 | + | 9.74915i | −0.192722 | + | 0.333805i | −0.946151 | − | 0.323724i | \(-0.895065\pi\) |
0.753429 | + | 0.657529i | \(0.228398\pi\) | |||||||
\(854\) | −2.30902 | − | 3.99933i | −0.0790129 | − | 0.136854i | ||||
\(855\) | 2.94427 | + | 5.09963i | 0.100692 | + | 0.174404i | ||||
\(856\) | 11.0820 | 0.378776 | ||||||||
\(857\) | 18.0902 | + | 31.3331i | 0.617948 | + | 1.07032i | 0.989860 | + | 0.142050i | \(0.0453693\pi\) |
−0.371911 | + | 0.928268i | \(0.621297\pi\) | |||||||
\(858\) | −5.00000 | −0.170697 | ||||||||
\(859\) | −49.4164 | −1.68607 | −0.843033 | − | 0.537862i | \(-0.819232\pi\) | ||||
−0.843033 | + | 0.537862i | \(0.819232\pi\) | |||||||
\(860\) | −5.72949 | − | 13.8933i | −0.195374 | − | 0.473757i | ||||
\(861\) | 105.048 | 3.58001 | ||||||||
\(862\) | 9.47214 | 0.322622 | ||||||||
\(863\) | −4.75329 | − | 8.23294i | −0.161804 | − | 0.280252i | 0.773712 | − | 0.633538i | \(-0.218398\pi\) |
−0.935516 | + | 0.353285i | \(0.885065\pi\) | |||||||
\(864\) | 9.27051 | 0.315389 | ||||||||
\(865\) | 2.32624 | + | 4.02916i | 0.0790945 | + | 0.136996i | ||||
\(866\) | −6.62868 | − | 11.4812i | −0.225252 | − | 0.390147i | ||||
\(867\) | 26.2984 | − | 45.5501i | 0.893140 | − | 1.54696i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.50000 | + | 4.33013i | −0.0848067 | + | 0.146889i | ||||
\(870\) | −1.85410 | − | 3.21140i | −0.0628599 | − | 0.108877i | ||||
\(871\) | −5.32624 | −0.180473 | ||||||||
\(872\) | 10.1976 | + | 17.6627i | 0.345333 | + | 0.598134i | ||||
\(873\) | 17.7984 | − | 30.8277i | 0.602384 | − | 1.04336i | ||||
\(874\) | −1.03444 | + | 1.79171i | −0.0349905 | + | 0.0606054i | ||||
\(875\) | −22.1803 | + | 38.4175i | −0.749832 | + | 1.29875i | ||||
\(876\) | 9.00000 | 0.304082 | ||||||||
\(877\) | 3.82624 | − | 6.62724i | 0.129203 | − | 0.223786i | −0.794165 | − | 0.607702i | \(-0.792091\pi\) |
0.923368 | + | 0.383916i | \(0.125425\pi\) | |||||||
\(878\) | 0.218847 | − | 0.379054i | 0.00738573 | − | 0.0127925i | ||||
\(879\) | −15.8262 | − | 27.4118i | −0.533806 | − | 0.924579i | ||||
\(880\) | 7.03444 | + | 12.1840i | 0.237131 | + | 0.410723i | ||||
\(881\) | 33.7639 | 1.13754 | 0.568768 | − | 0.822498i | \(-0.307420\pi\) | ||||
0.568768 | + | 0.822498i | \(0.307420\pi\) | |||||||
\(882\) | −16.1115 | −0.542501 | ||||||||
\(883\) | −6.56231 | − | 11.3662i | −0.220839 | − | 0.382505i | 0.734224 | − | 0.678907i | \(-0.237546\pi\) |
−0.955063 | + | 0.296403i | \(0.904213\pi\) | |||||||
\(884\) | 7.80244 | + | 13.5142i | 0.262424 | + | 0.454532i | ||||
\(885\) | 8.23607 | − | 14.2653i | 0.276852 | − | 0.479522i | ||||
\(886\) | 0.472136 | − | 0.817763i | 0.0158617 | − | 0.0274733i | ||||
\(887\) | −52.9574 | −1.77814 | −0.889068 | − | 0.457775i | \(-0.848647\pi\) | ||||
−0.889068 | + | 0.457775i | \(0.848647\pi\) | |||||||
\(888\) | −9.35410 | + | 16.2018i | −0.313903 | + | 0.543696i | ||||
\(889\) | −31.0344 | + | 53.7532i | −1.04086 | + | 1.80283i | ||||
\(890\) | −0.437694 | + | 0.758108i | −0.0146715 | + | 0.0254119i | ||||
\(891\) | −10.3262 | − | 17.8856i | −0.345942 | − | 0.599189i | ||||
\(892\) | −5.12461 | −0.171585 | ||||||||
\(893\) | 0.708204 | + | 1.22665i | 0.0236991 | + | 0.0410481i | ||||
\(894\) | −4.50000 | + | 7.79423i | −0.150503 | + | 0.260678i | ||||
\(895\) | 11.9311 | 0.398813 | ||||||||
\(896\) | 21.3713 | − | 37.0162i | 0.713966 | − | 1.23663i | ||||
\(897\) | 7.92705 | + | 13.7301i | 0.264677 | + | 0.458433i | ||||
\(898\) | −6.27051 | − | 10.8608i | −0.209250 | − | 0.362431i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −12.4058 | − | 21.4874i | −0.413525 | − | 0.716247i | ||||
\(901\) | −8.41641 | −0.280391 | ||||||||
\(902\) | 13.0902 | 0.435855 | ||||||||
\(903\) | −72.0861 | − | 9.60437i | −2.39888 | − | 0.319613i | ||||
\(904\) | −22.9919 | −0.764698 | ||||||||
\(905\) | −23.9574 | −0.796372 | ||||||||
\(906\) | 4.42705 | + | 7.66788i | 0.147079 | + | 0.254748i | ||||
\(907\) | −21.7082 | −0.720809 | −0.360405 | − | 0.932796i | \(-0.617361\pi\) | ||||
−0.360405 | + | 0.932796i | \(0.617361\pi\) | |||||||
\(908\) | −1.36475 | − | 2.36381i | −0.0452907 | − | 0.0784457i | ||||
\(909\) | −7.25329 | − | 12.5631i | −0.240576 | − | 0.416691i | ||||
\(910\) | −1.38197 | + | 2.39364i | −0.0458117 | + | 0.0793482i | ||||
\(911\) | −42.9787 | −1.42395 | −0.711974 | − | 0.702206i | \(-0.752199\pi\) | ||||
−0.711974 | + | 0.702206i | \(0.752199\pi\) | |||||||
\(912\) | −5.09017 | + | 8.81643i | −0.168552 | + | 0.291941i | ||||
\(913\) | 29.0066 | + | 50.2409i | 0.959978 | + | 1.66273i | ||||
\(914\) | 6.00000 | 0.198462 | ||||||||
\(915\) | 4.61803 | + | 7.99867i | 0.152667 | + | 0.264428i | ||||
\(916\) | −2.12461 | + | 3.67994i | −0.0701991 | + | 0.121588i | ||||
\(917\) | 21.0623 | − | 36.4810i | 0.695539 | − | 1.20471i | ||||
\(918\) | −2.60081 | + | 4.50474i | −0.0858396 | + | 0.148679i | ||||
\(919\) | 29.3951 | 0.969656 | 0.484828 | − | 0.874610i | \(-0.338882\pi\) | ||||
0.484828 | + | 0.874610i | \(0.338882\pi\) | |||||||
\(920\) | −3.98684 | + | 6.90542i | −0.131442 | + | 0.227665i | ||||
\(921\) | −30.3885 | + | 52.6345i | −1.00134 | + | 1.73437i | ||||
\(922\) | −6.03444 | − | 10.4520i | −0.198734 | − | 0.344217i | ||||
\(923\) | 7.46149 | + | 12.9237i | 0.245598 | + | 0.425388i | ||||
\(924\) | 74.3951 | 2.44742 | ||||||||
\(925\) | 16.8541 | 0.554159 | ||||||||
\(926\) | −5.69756 | − | 9.86846i | −0.187233 | − | 0.324298i | ||||
\(927\) | 31.6353 | + | 54.7939i | 1.03904 | + | 1.79967i | ||||
\(928\) | 6.21885 | − | 10.7714i | 0.204144 | − | 0.353587i | ||||
\(929\) | −17.6180 | + | 30.5153i | −0.578029 | + | 1.00118i | 0.417676 | + | 0.908596i | \(0.362845\pi\) |
−0.995705 | + | 0.0925796i | \(0.970489\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.76393 | − | 11.7155i | 0.221679 | − | 0.383959i | ||||
\(932\) | 16.7188 | − | 28.9579i | 0.547644 | − | 0.948547i | ||||
\(933\) | −39.0517 | + | 67.6395i | −1.27849 | + | 2.21442i | ||||
\(934\) | −2.87539 | − | 4.98032i | −0.0940856 | − | 0.162961i | ||||
\(935\) | −27.2361 | −0.890715 | ||||||||
\(936\) | −3.92047 | − | 6.79046i | −0.128145 | − | 0.221953i | ||||
\(937\) | 27.6631 | − | 47.9139i | 0.903715 | − | 1.56528i | 0.0810814 | − | 0.996707i | \(-0.474163\pi\) |
0.822633 | − | 0.568572i | \(-0.192504\pi\) | |||||||
\(938\) | −6.23607 | −0.203615 | ||||||||
\(939\) | 17.1803 | − | 29.7572i | 0.560659 | − | 0.971090i | ||||
\(940\) | 1.31308 | + | 2.27433i | 0.0428280 | + | 0.0741803i | ||||
\(941\) | 13.1180 | + | 22.7211i | 0.427636 | + | 0.740687i | 0.996663 | − | 0.0816322i | \(-0.0260133\pi\) |
−0.569027 | + | 0.822319i | \(0.692680\pi\) | |||||||
\(942\) | −5.14590 | −0.167662 | ||||||||
\(943\) | −20.7533 | − | 35.9458i | −0.675820 | − | 1.17055i | ||||
\(944\) | 16.0132 | 0.521184 | ||||||||
\(945\) | 11.7082 | 0.380868 | ||||||||
\(946\) | −8.98278 | − | 1.19682i | −0.292055 | − | 0.0389119i | ||||
\(947\) | 25.3607 | 0.824111 | 0.412056 | − | 0.911159i | \(-0.364811\pi\) | ||||
0.412056 | + | 0.911159i | \(0.364811\pi\) | |||||||
\(948\) | −6.70820 | −0.217872 | ||||||||
\(949\) | −1.28115 | − | 2.21902i | −0.0415880 | − | 0.0720325i | ||||
\(950\) | −1.63932 | −0.0531866 | ||||||||
\(951\) | 43.5967 | + | 75.5118i | 1.41372 | + | 2.44864i | ||||
\(952\) | 18.9894 | + | 32.8905i | 0.615449 | + | 1.06599i | ||||
\(953\) | 19.4443 | − | 33.6785i | 0.629862 | − | 1.09095i | −0.357717 | − | 0.933830i | \(-0.616445\pi\) |
0.987579 | − | 0.157123i | \(-0.0502218\pi\) | |||||||
\(954\) | 2.03444 | 0.0658675 | ||||||||
\(955\) | 8.97871 | − | 15.5516i | 0.290544 | − | 0.503238i | ||||
\(956\) | −7.68692 | − | 13.3141i | −0.248613 | − | 0.430610i | ||||
\(957\) | 28.4164 | 0.918572 | ||||||||
\(958\) | −2.63932 | − | 4.57144i | −0.0852726 | − | 0.147696i | ||||
\(959\) | 7.85410 | − | 13.6037i | 0.253622 | − | 0.439287i | ||||
\(960\) | −7.61803 | + | 13.1948i | −0.245871 | + | 0.425861i | ||||
\(961\) | 15.5000 | − | 26.8468i | 0.500000 | − | 0.866025i | ||||
\(962\) | 2.56231 | 0.0826121 | ||||||||
\(963\) | −14.5066 | + | 25.1261i | −0.467468 | + | 0.809678i | ||||
\(964\) | 3.95898 | − | 6.85716i | 0.127510 | − | 0.220854i | ||||
\(965\) | −1.67376 | − | 2.89904i | −0.0538803 | − | 0.0933234i | ||||
\(966\) | 9.28115 | + | 16.0754i | 0.298616 | + | 0.517218i | ||||
\(967\) | 38.1033 | 1.22532 | 0.612660 | − | 0.790346i | \(-0.290099\pi\) | ||||
0.612660 | + | 0.790346i | \(0.290099\pi\) | |||||||
\(968\) | 3.07701 | 0.0988990 | ||||||||
\(969\) | −9.85410 | − | 17.0678i | −0.316559 | − | 0.548297i | ||||
\(970\) | −2.18034 | − | 3.77646i | −0.0700065 | − | 0.121255i | ||||
\(971\) | 8.68034 | − | 15.0348i | 0.278565 | − | 0.482489i | −0.692463 | − | 0.721453i | \(-0.743474\pi\) |
0.971028 | + | 0.238964i | \(0.0768078\pi\) | |||||||
\(972\) | 20.0729 | − | 34.7674i | 0.643840 | − | 1.11516i | ||||
\(973\) | 22.4164 | 0.718637 | ||||||||
\(974\) | 0.253289 | − | 0.438709i | 0.00811590 | − | 0.0140572i | ||||
\(975\) | −6.28115 | + | 10.8793i | −0.201158 | + | 0.348416i | ||||
\(976\) | −4.48936 | + | 7.77579i | −0.143701 | + | 0.248897i | ||||
\(977\) | −20.6180 | − | 35.7115i | −0.659629 | − | 1.14251i | −0.980712 | − | 0.195460i | \(-0.937380\pi\) |
0.321082 | − | 0.947051i | \(-0.395953\pi\) | |||||||
\(978\) | 14.0000 | 0.447671 | ||||||||
\(979\) | −3.35410 | − | 5.80948i | −0.107198 | − | 0.185672i | ||||
\(980\) | 12.5410 | − | 21.7217i | 0.400608 | − | 0.693874i | ||||
\(981\) | −53.3951 | −1.70478 | ||||||||
\(982\) | 4.13525 | − | 7.16247i | 0.131961 | − | 0.228564i | ||||
\(983\) | 5.23607 | + | 9.06914i | 0.167005 | + | 0.289261i | 0.937365 | − | 0.348348i | \(-0.113257\pi\) |
−0.770361 | + | 0.637608i | \(0.779924\pi\) | |||||||
\(984\) | 18.2533 | + | 31.6156i | 0.581894 | + | 1.00787i | ||||
\(985\) | −3.63932 | −0.115958 | ||||||||
\(986\) | 3.48936 | + | 6.04374i | 0.111124 | + | 0.192472i | ||||
\(987\) | 12.7082 | 0.404507 | ||||||||
\(988\) | 3.16718 | 0.100762 | ||||||||
\(989\) | 10.9549 | + | 26.5643i | 0.348346 | + | 0.844694i | ||||
\(990\) | 6.58359 | 0.209240 | ||||||||
\(991\) | −10.8197 | −0.343698 | −0.171849 | − | 0.985123i | \(-0.554974\pi\) | ||||
−0.171849 | + | 0.985123i | \(0.554974\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.3262 | 0.454629 | ||||||||
\(994\) | 8.73607 | + | 15.1313i | 0.277091 | + | 0.479936i | ||||
\(995\) | −1.20163 | − | 2.08128i | −0.0380941 | − | 0.0659809i | ||||
\(996\) | −38.9164 | + | 67.4052i | −1.23311 | + | 2.13582i | ||||
\(997\) | −19.4508 | −0.616015 | −0.308007 | − | 0.951384i | \(-0.599662\pi\) | ||||
−0.308007 | + | 0.951384i | \(0.599662\pi\) | |||||||
\(998\) | 2.64590 | − | 4.58283i | 0.0837544 | − | 0.145067i | ||||
\(999\) | −5.42705 | − | 9.39993i | −0.171704 | − | 0.297401i |
(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 | 43.2.c.b.36.2 | yes | 4 | |
3.2 | odd | 2 | 387.2.h.d.208.1 | 4 | |||
4.3 | odd | 2 | 688.2.i.e.337.1 | 4 | |||
43.6 | even | 3 | inner | 43.2.c.b.6.2 | ✓ | 4 | |
43.7 | odd | 6 | 1849.2.a.h.1.1 | 2 | |||
43.36 | even | 3 | 1849.2.a.e.1.2 | 2 | |||
129.92 | odd | 6 | 387.2.h.d.307.1 | 4 | |||
172.135 | odd | 6 | 688.2.i.e.49.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.c.b.6.2 | ✓ | 4 | 43.6 | even | 3 | inner | |
43.2.c.b.36.2 | yes | 4 | 1.1 | even | 1 | trivial | |
387.2.h.d.208.1 | 4 | 3.2 | odd | 2 | |||
387.2.h.d.307.1 | 4 | 129.92 | odd | 6 | |||
688.2.i.e.49.1 | 4 | 172.135 | odd | 6 | |||
688.2.i.e.337.1 | 4 | 4.3 | odd | 2 | |||
1849.2.a.e.1.2 | 2 | 43.36 | even | 3 | |||
1849.2.a.h.1.1 | 2 | 43.7 | odd | 6 |