Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [990,2,Mod(91,990)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(990, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("990.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 990.n (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.90518980011\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 330) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(-0.309017 - 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 990.361 |
Dual form | 990.2.n.a.181.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/990\mathbb{Z}\right)^\times\).
\(n\) | \(397\) | \(541\) | \(551\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | − | 0.951057i | 0.218508 | − | 0.672499i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.809017 | − | 0.587785i | −0.404508 | − | 0.293893i | ||||
\(5\) | 0.309017 | + | 0.951057i | 0.138197 | + | 0.425325i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.92705 | − | 2.12663i | −1.10632 | − | 0.803789i | −0.124241 | − | 0.992252i | \(-0.539650\pi\) |
−0.982080 | + | 0.188463i | \(0.939650\pi\) | |||||||
\(8\) | −0.809017 | + | 0.587785i | −0.286031 | + | 0.207813i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −2.80902 | + | 1.76336i | −0.846950 | + | 0.531672i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.190983 | − | 0.587785i | 0.0529692 | − | 0.163022i | −0.921073 | − | 0.389391i | \(-0.872685\pi\) |
0.974042 | + | 0.226369i | \(0.0726855\pi\) | |||||||
\(14\) | −2.92705 | + | 2.12663i | −0.782287 | + | 0.568365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.309017 | + | 0.951057i | 0.0772542 | + | 0.237764i | ||||
\(17\) | 2.00000 | + | 6.15537i | 0.485071 | + | 1.49290i | 0.831878 | + | 0.554959i | \(0.187266\pi\) |
−0.346806 | + | 0.937937i | \(0.612734\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.500000 | − | 0.363271i | 0.114708 | − | 0.0833401i | −0.528952 | − | 0.848651i | \(-0.677415\pi\) |
0.643660 | + | 0.765311i | \(0.277415\pi\) | |||||||
\(20\) | 0.309017 | − | 0.951057i | 0.0690983 | − | 0.212663i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.809017 | + | 3.21644i | 0.172483 | + | 0.685747i | ||||
\(23\) | −4.85410 | −1.01215 | −0.506075 | − | 0.862489i | \(-0.668904\pi\) | ||||
−0.506075 | + | 0.862489i | \(0.668904\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.809017 | + | 0.587785i | −0.161803 | + | 0.117557i | ||||
\(26\) | −0.500000 | − | 0.363271i | −0.0980581 | − | 0.0712434i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.11803 | + | 3.44095i | 0.211289 | + | 0.650279i | ||||
\(29\) | 3.00000 | + | 2.17963i | 0.557086 | + | 0.404747i | 0.830391 | − | 0.557181i | \(-0.188117\pi\) |
−0.273305 | + | 0.961927i | \(0.588117\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.85410 | + | 8.78402i | −0.512612 | + | 1.57766i | 0.274974 | + | 0.961452i | \(0.411331\pi\) |
−0.787586 | + | 0.616205i | \(0.788669\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.47214 | 1.10996 | ||||||||
\(35\) | 1.11803 | − | 3.44095i | 0.188982 | − | 0.581628i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.500000 | + | 0.363271i | 0.0821995 | + | 0.0597214i | 0.628126 | − | 0.778112i | \(-0.283822\pi\) |
−0.545927 | + | 0.837833i | \(0.683822\pi\) | |||||||
\(38\) | −0.190983 | − | 0.587785i | −0.0309815 | − | 0.0953514i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.809017 | − | 0.587785i | −0.127917 | − | 0.0929370i | ||||
\(41\) | −7.54508 | + | 5.48183i | −1.17834 | + | 0.856117i | −0.991984 | − | 0.126364i | \(-0.959669\pi\) |
−0.186360 | + | 0.982481i | \(0.559669\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.763932 | 0.116499 | 0.0582493 | − | 0.998302i | \(-0.481448\pi\) | ||||
0.0582493 | + | 0.998302i | \(0.481448\pi\) | |||||||
\(44\) | 3.30902 | + | 0.224514i | 0.498853 | + | 0.0338468i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.50000 | + | 4.61653i | −0.221163 | + | 0.680670i | ||||
\(47\) | −2.11803 | + | 1.53884i | −0.308947 | + | 0.224463i | −0.731445 | − | 0.681901i | \(-0.761154\pi\) |
0.422498 | + | 0.906364i | \(0.361154\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.88197 | + | 5.79210i | 0.268852 | + | 0.827442i | ||||
\(50\) | 0.309017 | + | 0.951057i | 0.0437016 | + | 0.134500i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.500000 | + | 0.363271i | −0.0693375 | + | 0.0503767i | ||||
\(53\) | 1.88197 | − | 5.79210i | 0.258508 | − | 0.795606i | −0.734610 | − | 0.678489i | \(-0.762635\pi\) |
0.993118 | − | 0.117116i | \(-0.0373650\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.54508 | − | 2.12663i | −0.343179 | − | 0.286754i | ||||
\(56\) | 3.61803 | 0.483480 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.00000 | − | 2.17963i | 0.393919 | − | 0.286199i | ||||
\(59\) | −11.8262 | − | 8.59226i | −1.53965 | − | 1.11862i | −0.950558 | − | 0.310548i | \(-0.899487\pi\) |
−0.589087 | − | 0.808069i | \(-0.700513\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.47214 | + | 10.6861i | 0.444561 | + | 1.36822i | 0.882964 | + | 0.469441i | \(0.155544\pi\) |
−0.438403 | + | 0.898779i | \(0.644456\pi\) | |||||||
\(62\) | 7.47214 | + | 5.42882i | 0.948962 | + | 0.689461i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.309017 | − | 0.951057i | 0.0386271 | − | 0.118882i | ||||
\(65\) | 0.618034 | 0.0766577 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.18034 | −0.999388 | −0.499694 | − | 0.866202i | \(-0.666554\pi\) | ||||
−0.499694 | + | 0.866202i | \(0.666554\pi\) | |||||||
\(68\) | 2.00000 | − | 6.15537i | 0.242536 | − | 0.746448i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.92705 | − | 2.12663i | −0.349850 | − | 0.254181i | ||||
\(71\) | 0.0901699 | + | 0.277515i | 0.0107012 | + | 0.0329349i | 0.956265 | − | 0.292503i | \(-0.0944882\pi\) |
−0.945563 | + | 0.325438i | \(0.894488\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.85410 | − | 6.43288i | −1.03629 | − | 0.752912i | −0.0667355 | − | 0.997771i | \(-0.521258\pi\) |
−0.969559 | + | 0.244859i | \(0.921258\pi\) | |||||||
\(74\) | 0.500000 | − | 0.363271i | 0.0581238 | − | 0.0422294i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.618034 | −0.0708934 | ||||||||
\(77\) | 11.9721 | + | 0.812299i | 1.36435 | + | 0.0925701i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.38197 | + | 4.25325i | −0.155483 | + | 0.478528i | −0.998210 | − | 0.0598139i | \(-0.980949\pi\) |
0.842726 | + | 0.538342i | \(0.180949\pi\) | |||||||
\(80\) | −0.809017 | + | 0.587785i | −0.0904508 | + | 0.0657164i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.88197 | + | 8.86978i | 0.318260 | + | 0.979503i | ||||
\(83\) | 1.52786 | + | 4.70228i | 0.167705 | + | 0.516143i | 0.999225 | − | 0.0393515i | \(-0.0125292\pi\) |
−0.831521 | + | 0.555494i | \(0.812529\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.23607 | + | 3.80423i | −0.567931 | + | 0.412626i | ||||
\(86\) | 0.236068 | − | 0.726543i | 0.0254559 | − | 0.0783451i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.23607 | − | 3.07768i | 0.131765 | − | 0.328082i | ||||
\(89\) | 5.14590 | 0.545464 | 0.272732 | − | 0.962090i | \(-0.412073\pi\) | ||||
0.272732 | + | 0.962090i | \(0.412073\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.80902 | + | 1.31433i | −0.189637 | + | 0.137779i | ||||
\(92\) | 3.92705 | + | 2.85317i | 0.409423 | + | 0.297463i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.809017 | + | 2.48990i | 0.0834437 | + | 0.256813i | ||||
\(95\) | 0.500000 | + | 0.363271i | 0.0512989 | + | 0.0372708i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.61803 | − | 14.2128i | 0.468890 | − | 1.44310i | −0.385133 | − | 0.922861i | \(-0.625844\pi\) |
0.854023 | − | 0.520235i | \(-0.174156\pi\) | |||||||
\(98\) | 6.09017 | 0.615200 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −1.23607 | + | 3.80423i | −0.122993 | + | 0.378535i | −0.993530 | − | 0.113569i | \(-0.963772\pi\) |
0.870537 | + | 0.492103i | \(0.163772\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.97214 | + | 5.79210i | 0.785518 | + | 0.570712i | 0.906630 | − | 0.421927i | \(-0.138646\pi\) |
−0.121112 | + | 0.992639i | \(0.538646\pi\) | |||||||
\(104\) | 0.190983 | + | 0.587785i | 0.0187274 | + | 0.0576371i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.92705 | − | 3.57971i | −0.478557 | − | 0.347692i | ||||
\(107\) | 14.4721 | − | 10.5146i | 1.39907 | − | 1.01649i | 0.404274 | − | 0.914638i | \(-0.367524\pi\) |
0.994800 | − | 0.101849i | \(-0.0324759\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000 | 0.383131 | 0.191565 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(110\) | −2.80902 | + | 1.76336i | −0.267829 | + | 0.168129i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.11803 | − | 3.44095i | 0.105644 | − | 0.325140i | ||||
\(113\) | −10.0902 | + | 7.33094i | −0.949203 | + | 0.689637i | −0.950618 | − | 0.310362i | \(-0.899550\pi\) |
0.00141497 | + | 0.999999i | \(0.499550\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.50000 | − | 4.61653i | −0.139876 | − | 0.430493i | ||||
\(116\) | −1.14590 | − | 3.52671i | −0.106394 | − | 0.327447i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.8262 | + | 8.59226i | −1.08869 | + | 0.790982i | ||||
\(119\) | 7.23607 | − | 22.2703i | 0.663329 | − | 2.04152i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.78115 | − | 9.90659i | 0.434650 | − | 0.900599i | ||||
\(122\) | 11.2361 | 1.01727 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.47214 | − | 5.42882i | 0.671018 | − | 0.487523i | ||||
\(125\) | −0.809017 | − | 0.587785i | −0.0723607 | − | 0.0525731i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.89919 | + | 12.0005i | 0.345997 | + | 1.06487i | 0.961048 | + | 0.276382i | \(0.0891354\pi\) |
−0.615051 | + | 0.788487i | \(0.710865\pi\) | |||||||
\(128\) | −0.809017 | − | 0.587785i | −0.0715077 | − | 0.0519534i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.190983 | − | 0.587785i | 0.0167503 | − | 0.0515522i | ||||
\(131\) | −20.9443 | −1.82991 | −0.914955 | − | 0.403556i | \(-0.867774\pi\) | ||||
−0.914955 | + | 0.403556i | \(0.867774\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.23607 | −0.193892 | ||||||||
\(134\) | −2.52786 | + | 7.77997i | −0.218374 | + | 0.672087i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.23607 | − | 3.80423i | −0.448989 | − | 0.326210i | ||||
\(137\) | −4.76393 | − | 14.6619i | −0.407010 | − | 1.25265i | −0.919205 | − | 0.393779i | \(-0.871167\pi\) |
0.512195 | − | 0.858869i | \(-0.328833\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.16312 | + | 4.47777i | 0.522749 | + | 0.379799i | 0.817638 | − | 0.575732i | \(-0.195283\pi\) |
−0.294890 | + | 0.955531i | \(0.595283\pi\) | |||||||
\(140\) | −2.92705 | + | 2.12663i | −0.247381 | + | 0.179733i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.291796 | 0.0244870 | ||||||||
\(143\) | 0.500000 | + | 1.98787i | 0.0418121 | + | 0.166234i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.14590 | + | 3.52671i | −0.0951617 | + | 0.292877i | ||||
\(146\) | −8.85410 | + | 6.43288i | −0.732771 | + | 0.532389i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.190983 | − | 0.587785i | −0.0156987 | − | 0.0483157i | ||||
\(149\) | 2.76393 | + | 8.50651i | 0.226430 | + | 0.696880i | 0.998143 | + | 0.0609095i | \(0.0194001\pi\) |
−0.771713 | + | 0.635971i | \(0.780600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0902 | − | 7.33094i | 0.821126 | − | 0.596583i | −0.0959085 | − | 0.995390i | \(-0.530576\pi\) |
0.917035 | + | 0.398807i | \(0.130576\pi\) | |||||||
\(152\) | −0.190983 | + | 0.587785i | −0.0154908 | + | 0.0476757i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.47214 | − | 11.1352i | 0.360375 | − | 0.897297i | ||||
\(155\) | −9.23607 | −0.741859 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.54508 | − | 3.30220i | 0.362737 | − | 0.263544i | −0.391456 | − | 0.920197i | \(-0.628028\pi\) |
0.754193 | + | 0.656653i | \(0.228028\pi\) | |||||||
\(158\) | 3.61803 | + | 2.62866i | 0.287835 | + | 0.209125i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.309017 | + | 0.951057i | 0.0244299 | + | 0.0751876i | ||||
\(161\) | 14.2082 | + | 10.3229i | 1.11976 | + | 0.813556i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.52786 | − | 17.0130i | 0.432976 | − | 1.33256i | −0.462171 | − | 0.886791i | \(-0.652929\pi\) |
0.895147 | − | 0.445771i | \(-0.147071\pi\) | |||||||
\(164\) | 9.32624 | 0.728257 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.94427 | 0.383750 | ||||||||
\(167\) | 3.57295 | − | 10.9964i | 0.276483 | − | 0.850927i | −0.712340 | − | 0.701834i | \(-0.752365\pi\) |
0.988823 | − | 0.149093i | \(-0.0476354\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.2082 | + | 7.41669i | 0.785246 | + | 0.570515i | ||||
\(170\) | 2.00000 | + | 6.15537i | 0.153393 | + | 0.472095i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.618034 | − | 0.449028i | −0.0471246 | − | 0.0342381i | ||||
\(173\) | −19.8713 | + | 14.4374i | −1.51079 | + | 1.09765i | −0.544963 | + | 0.838460i | \(0.683456\pi\) |
−0.965826 | + | 0.259192i | \(0.916544\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.61803 | 0.273498 | ||||||||
\(176\) | −2.54508 | − | 2.12663i | −0.191843 | − | 0.160301i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.59017 | − | 4.89404i | 0.119188 | − | 0.366824i | ||||
\(179\) | −9.01722 | + | 6.55139i | −0.673979 | + | 0.489674i | −0.871355 | − | 0.490654i | \(-0.836758\pi\) |
0.197376 | + | 0.980328i | \(0.436758\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.52786 | − | 23.1684i | −0.559542 | − | 1.72209i | −0.683637 | − | 0.729822i | \(-0.739603\pi\) |
0.124095 | − | 0.992270i | \(-0.460397\pi\) | |||||||
\(182\) | 0.690983 | + | 2.12663i | 0.0512191 | + | 0.157636i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.92705 | − | 2.85317i | 0.289506 | − | 0.210338i | ||||
\(185\) | −0.190983 | + | 0.587785i | −0.0140413 | + | 0.0432148i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.4721 | − | 13.7638i | −1.20456 | − | 1.00651i | ||||
\(188\) | 2.61803 | 0.190940 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.500000 | − | 0.363271i | 0.0362738 | − | 0.0263545i | ||||
\(191\) | −11.0902 | − | 8.05748i | −0.802457 | − | 0.583019i | 0.109177 | − | 0.994022i | \(-0.465178\pi\) |
−0.911634 | + | 0.411004i | \(0.865178\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.14590 | − | 3.52671i | −0.0824835 | − | 0.253858i | 0.901307 | − | 0.433182i | \(-0.142609\pi\) |
−0.983790 | + | 0.179323i | \(0.942609\pi\) | |||||||
\(194\) | −12.0902 | − | 8.78402i | −0.868024 | − | 0.630656i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.88197 | − | 5.79210i | 0.134426 | − | 0.413721i | ||||
\(197\) | −3.61803 | −0.257774 | −0.128887 | − | 0.991659i | \(-0.541140\pi\) | ||||
−0.128887 | + | 0.991659i | \(0.541140\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.9443 | −0.917595 | −0.458798 | − | 0.888541i | \(-0.651720\pi\) | ||||
−0.458798 | + | 0.888541i | \(0.651720\pi\) | |||||||
\(200\) | 0.309017 | − | 0.951057i | 0.0218508 | − | 0.0672499i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.23607 | + | 2.35114i | 0.227689 | + | 0.165426i | ||||
\(203\) | −4.14590 | − | 12.7598i | −0.290985 | − | 0.895560i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.54508 | − | 5.48183i | −0.526972 | − | 0.382867i | ||||
\(206\) | 7.97214 | − | 5.79210i | 0.555445 | − | 0.403554i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.618034 | 0.0428529 | ||||||||
\(209\) | −0.763932 | + | 1.90211i | −0.0528423 | + | 0.131572i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.23607 | + | 22.2703i | −0.498151 | + | 1.53315i | 0.313836 | + | 0.949477i | \(0.398386\pi\) |
−0.811987 | + | 0.583675i | \(0.801614\pi\) | |||||||
\(212\) | −4.92705 | + | 3.57971i | −0.338391 | + | 0.245856i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.52786 | − | 17.0130i | −0.377877 | − | 1.16299i | ||||
\(215\) | 0.236068 | + | 0.726543i | 0.0160997 | + | 0.0495498i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.0344 | − | 19.6417i | 1.83522 | − | 1.33336i | ||||
\(218\) | 1.23607 | − | 3.80423i | 0.0837171 | − | 0.257655i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.809017 | + | 3.21644i | 0.0545439 | + | 0.216852i | ||||
\(221\) | 4.00000 | 0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.16312 | + | 4.47777i | −0.412713 | + | 0.299854i | −0.774699 | − | 0.632330i | \(-0.782099\pi\) |
0.361986 | + | 0.932183i | \(0.382099\pi\) | |||||||
\(224\) | −2.92705 | − | 2.12663i | −0.195572 | − | 0.142091i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.85410 | + | 11.8617i | 0.256371 | + | 0.789029i | ||||
\(227\) | −3.38197 | − | 2.45714i | −0.224469 | − | 0.163086i | 0.469867 | − | 0.882737i | \(-0.344302\pi\) |
−0.694336 | + | 0.719651i | \(0.744302\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.56231 | + | 10.9637i | −0.235404 | + | 0.724498i | 0.761664 | + | 0.647972i | \(0.224383\pi\) |
−0.997068 | + | 0.0765260i | \(0.975617\pi\) | |||||||
\(230\) | −4.85410 | −0.320070 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.70820 | −0.243456 | ||||||||
\(233\) | 5.03444 | − | 15.4944i | 0.329817 | − | 1.01507i | −0.639402 | − | 0.768873i | \(-0.720818\pi\) |
0.969219 | − | 0.246200i | \(-0.0791821\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.11803 | − | 1.53884i | −0.138165 | − | 0.100383i | ||||
\(236\) | 4.51722 | + | 13.9026i | 0.294046 | + | 0.904981i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −18.9443 | − | 13.7638i | −1.22797 | − | 0.892176i | ||||
\(239\) | 17.9443 | − | 13.0373i | 1.16072 | − | 0.843311i | 0.170850 | − | 0.985297i | \(-0.445349\pi\) |
0.989869 | + | 0.141986i | \(0.0453487\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.6180 | −1.65020 | −0.825101 | − | 0.564985i | \(-0.808882\pi\) | ||||
−0.825101 | + | 0.564985i | \(0.808882\pi\) | |||||||
\(242\) | −7.94427 | − | 7.60845i | −0.510677 | − | 0.489090i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.47214 | − | 10.6861i | 0.222281 | − | 0.684110i | ||||
\(245\) | −4.92705 | + | 3.57971i | −0.314778 | + | 0.228699i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.118034 | − | 0.363271i | −0.00751032 | − | 0.0231144i | ||||
\(248\) | −2.85410 | − | 8.78402i | −0.181236 | − | 0.557786i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.809017 | + | 0.587785i | −0.0511667 | + | 0.0371748i | ||||
\(251\) | −3.55573 | + | 10.9434i | −0.224436 | + | 0.690742i | 0.773913 | + | 0.633292i | \(0.218297\pi\) |
−0.998348 | + | 0.0574495i | \(0.981703\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.6353 | − | 8.55951i | 0.857241 | − | 0.538132i | ||||
\(254\) | 12.6180 | 0.791726 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | −4.09017 | − | 2.97168i | −0.255138 | − | 0.185368i | 0.452863 | − | 0.891580i | \(-0.350403\pi\) |
−0.708001 | + | 0.706212i | \(0.750403\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.690983 | − | 2.12663i | −0.0429356 | − | 0.132142i | ||||
\(260\) | −0.500000 | − | 0.363271i | −0.0310087 | − | 0.0225291i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.47214 | + | 19.9192i | −0.399850 | + | 1.23061i | ||||
\(263\) | 8.14590 | 0.502298 | 0.251149 | − | 0.967948i | \(-0.419192\pi\) | ||||
0.251149 | + | 0.967948i | \(0.419192\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.09017 | 0.374116 | ||||||||
\(266\) | −0.690983 | + | 2.12663i | −0.0423669 | + | 0.130392i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.61803 | + | 4.80828i | 0.404261 | + | 0.293713i | ||||
\(269\) | 7.65248 | + | 23.5519i | 0.466580 | + | 1.43598i | 0.856985 | + | 0.515341i | \(0.172335\pi\) |
−0.390405 | + | 0.920643i | \(0.627665\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.527864 | − | 0.383516i | −0.0320655 | − | 0.0232969i | 0.571637 | − | 0.820507i | \(-0.306309\pi\) |
−0.603703 | + | 0.797210i | \(0.706309\pi\) | |||||||
\(272\) | −5.23607 | + | 3.80423i | −0.317483 | + | 0.230665i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.4164 | −0.931339 | ||||||||
\(275\) | 1.23607 | − | 3.07768i | 0.0745377 | − | 0.185591i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.55573 | + | 7.86572i | −0.153559 | + | 0.472605i | −0.998012 | − | 0.0630239i | \(-0.979926\pi\) |
0.844453 | + | 0.535629i | \(0.179926\pi\) | |||||||
\(278\) | 6.16312 | − | 4.47777i | 0.369639 | − | 0.268559i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.11803 | + | 3.44095i | 0.0668153 | + | 0.205636i | ||||
\(281\) | −2.43769 | − | 7.50245i | −0.145421 | − | 0.447559i | 0.851644 | − | 0.524120i | \(-0.175606\pi\) |
−0.997065 | + | 0.0765616i | \(0.975606\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.00000 | + | 2.17963i | −0.178331 | + | 0.129565i | −0.673370 | − | 0.739306i | \(-0.735154\pi\) |
0.495039 | + | 0.868871i | \(0.335154\pi\) | |||||||
\(284\) | 0.0901699 | − | 0.277515i | 0.00535060 | − | 0.0164675i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.04508 | + | 0.138757i | 0.120928 | + | 0.00820489i | ||||
\(287\) | 33.7426 | 1.99177 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −20.1353 | + | 14.6291i | −1.18443 | + | 0.860536i | ||||
\(290\) | 3.00000 | + | 2.17963i | 0.176166 | + | 0.127992i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.38197 | + | 10.4086i | 0.197915 | + | 0.609118i | ||||
\(293\) | 8.92705 | + | 6.48588i | 0.521524 | + | 0.378909i | 0.817178 | − | 0.576386i | \(-0.195537\pi\) |
−0.295654 | + | 0.955295i | \(0.595537\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.51722 | − | 13.9026i | 0.263003 | − | 0.809439i | ||||
\(296\) | −0.618034 | −0.0359225 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.94427 | 0.518128 | ||||||||
\(299\) | −0.927051 | + | 2.85317i | −0.0536127 | + | 0.165003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.23607 | − | 1.62460i | −0.128885 | − | 0.0936403i | ||||
\(302\) | −3.85410 | − | 11.8617i | −0.221779 | − | 0.682564i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.500000 | + | 0.363271i | 0.0286770 | + | 0.0208350i | ||||
\(305\) | −9.09017 | + | 6.60440i | −0.520502 | + | 0.378167i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.8328 | 1.53143 | 0.765715 | − | 0.643180i | \(-0.222385\pi\) | ||||
0.765715 | + | 0.643180i | \(0.222385\pi\) | |||||||
\(308\) | −9.20820 | − | 7.69421i | −0.524686 | − | 0.438418i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.85410 | + | 8.78402i | −0.162102 | + | 0.498899i | ||||
\(311\) | −22.5623 | + | 16.3925i | −1.27939 | + | 0.929532i | −0.999534 | − | 0.0305099i | \(-0.990287\pi\) |
−0.279857 | + | 0.960042i | \(0.590287\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.76393 | + | 5.42882i | 0.0997033 | + | 0.306855i | 0.988451 | − | 0.151542i | \(-0.0484238\pi\) |
−0.888748 | + | 0.458397i | \(0.848424\pi\) | |||||||
\(314\) | −1.73607 | − | 5.34307i | −0.0979720 | − | 0.301527i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.61803 | − | 2.62866i | 0.203530 | − | 0.147873i | ||||
\(317\) | −3.37132 | + | 10.3759i | −0.189352 | + | 0.582767i | −0.999996 | − | 0.00277297i | \(-0.999117\pi\) |
0.810644 | + | 0.585540i | \(0.199117\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.2705 | − | 0.832544i | −0.687017 | − | 0.0466135i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 14.2082 | − | 10.3229i | 0.791792 | − | 0.575271i | ||||
\(323\) | 3.23607 | + | 2.35114i | 0.180060 | + | 0.130821i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.190983 | + | 0.587785i | 0.0105938 | + | 0.0326045i | ||||
\(326\) | −14.4721 | − | 10.5146i | −0.801537 | − | 0.582351i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.88197 | − | 8.86978i | 0.159130 | − | 0.489752i | ||||
\(329\) | 9.47214 | 0.522216 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.67376 | 0.421788 | 0.210894 | − | 0.977509i | \(-0.432362\pi\) | ||||
0.210894 | + | 0.977509i | \(0.432362\pi\) | |||||||
\(332\) | 1.52786 | − | 4.70228i | 0.0838524 | − | 0.258071i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.35410 | − | 6.79615i | −0.511834 | − | 0.371869i | ||||
\(335\) | −2.52786 | − | 7.77997i | −0.138112 | − | 0.425065i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.1803 | + | 11.7557i | 0.881399 | + | 0.640374i | 0.933621 | − | 0.358261i | \(-0.116630\pi\) |
−0.0522220 | + | 0.998635i | \(0.516630\pi\) | |||||||
\(338\) | 10.2082 | − | 7.41669i | 0.555253 | − | 0.403415i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.47214 | 0.351001 | ||||||||
\(341\) | −7.47214 | − | 29.7073i | −0.404639 | − | 1.60874i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.01722 | + | 3.13068i | −0.0549248 | + | 0.169041i | ||||
\(344\) | −0.618034 | + | 0.449028i | −0.0333222 | + | 0.0242100i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.59017 | + | 23.3601i | 0.408050 | + | 1.25585i | ||||
\(347\) | −1.18034 | − | 3.63271i | −0.0633640 | − | 0.195014i | 0.914363 | − | 0.404896i | \(-0.132692\pi\) |
−0.977727 | + | 0.209881i | \(0.932692\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.09017 | + | 5.87785i | −0.433057 | + | 0.314634i | −0.782870 | − | 0.622185i | \(-0.786245\pi\) |
0.349813 | + | 0.936819i | \(0.386245\pi\) | |||||||
\(350\) | 1.11803 | − | 3.44095i | 0.0597614 | − | 0.183927i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.80902 | + | 1.76336i | −0.149721 | + | 0.0939872i | ||||
\(353\) | 24.6525 | 1.31212 | 0.656059 | − | 0.754709i | \(-0.272222\pi\) | ||||
0.656059 | + | 0.754709i | \(0.272222\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.236068 | + | 0.171513i | −0.0125292 | + | 0.00910299i | ||||
\(356\) | −4.16312 | − | 3.02468i | −0.220645 | − | 0.160308i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.44427 | + | 10.6004i | 0.182035 | + | 0.560247i | ||||
\(359\) | 20.4164 | + | 14.8334i | 1.07754 | + | 0.782876i | 0.977252 | − | 0.212082i | \(-0.0680245\pi\) |
0.100285 | + | 0.994959i | \(0.468025\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.75329 | + | 17.7068i | −0.302805 | + | 0.931937i | ||||
\(362\) | −24.3607 | −1.28037 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.23607 | 0.117202 | ||||||||
\(365\) | 3.38197 | − | 10.4086i | 0.177020 | − | 0.544812i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.76393 | − | 4.91428i | −0.353074 | − | 0.256524i | 0.397083 | − | 0.917783i | \(-0.370022\pi\) |
−0.750158 | + | 0.661259i | \(0.770022\pi\) | |||||||
\(368\) | −1.50000 | − | 4.61653i | −0.0781929 | − | 0.240653i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.500000 | + | 0.363271i | 0.0259938 | + | 0.0188856i | ||||
\(371\) | −17.8262 | + | 12.9515i | −0.925492 | + | 0.672409i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.8541 | −0.717338 | −0.358669 | − | 0.933465i | \(-0.616769\pi\) | ||||
−0.358669 | + | 0.933465i | \(0.616769\pi\) | |||||||
\(374\) | −18.1803 | + | 11.4127i | −0.940083 | + | 0.590136i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.809017 | − | 2.48990i | 0.0417219 | − | 0.128407i | ||||
\(377\) | 1.85410 | − | 1.34708i | 0.0954911 | − | 0.0693784i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.1180 | − | 31.1401i | −0.519728 | − | 1.59956i | −0.774510 | − | 0.632561i | \(-0.782004\pi\) |
0.254782 | − | 0.966999i | \(-0.417996\pi\) | |||||||
\(380\) | −0.190983 | − | 0.587785i | −0.00979722 | − | 0.0301527i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.0902 | + | 8.05748i | −0.567422 | + | 0.412257i | ||||
\(383\) | 8.79180 | − | 27.0584i | 0.449240 | − | 1.38262i | −0.428527 | − | 0.903529i | \(-0.640967\pi\) |
0.877766 | − | 0.479089i | \(-0.159033\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.92705 | + | 11.6372i | 0.149176 | + | 0.593086i | ||||
\(386\) | −3.70820 | −0.188743 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.0902 | + | 8.78402i | −0.613785 | + | 0.445941i | ||||
\(389\) | 2.85410 | + | 2.07363i | 0.144709 | + | 0.105137i | 0.657784 | − | 0.753206i | \(-0.271494\pi\) |
−0.513075 | + | 0.858344i | \(0.671494\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.70820 | − | 29.8788i | −0.490965 | − | 1.51103i | ||||
\(392\) | −4.92705 | − | 3.57971i | −0.248854 | − | 0.180803i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.11803 | + | 3.44095i | −0.0563257 | + | 0.173353i | ||||
\(395\) | −4.47214 | −0.225018 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.6738 | 0.636078 | 0.318039 | − | 0.948078i | \(-0.396976\pi\) | ||||
0.318039 | + | 0.948078i | \(0.396976\pi\) | |||||||
\(398\) | −4.00000 | + | 12.3107i | −0.200502 | + | 0.617081i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.809017 | − | 0.587785i | −0.0404508 | − | 0.0293893i | ||||
\(401\) | 0.517221 | + | 1.59184i | 0.0258288 | + | 0.0794928i | 0.963140 | − | 0.269001i | \(-0.0866934\pi\) |
−0.937311 | + | 0.348493i | \(0.886693\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.61803 | + | 3.35520i | 0.230041 | + | 0.167134i | ||||
\(404\) | 3.23607 | − | 2.35114i | 0.161000 | − | 0.116974i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.4164 | −0.665845 | ||||||||
\(407\) | −2.04508 | − | 0.138757i | −0.101371 | − | 0.00687794i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.39261 | − | 13.5191i | 0.217201 | − | 0.668475i | −0.781790 | − | 0.623542i | \(-0.785693\pi\) |
0.998990 | − | 0.0449321i | \(-0.0143071\pi\) | |||||||
\(410\) | −7.54508 | + | 5.48183i | −0.372625 | + | 0.270728i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.04508 | − | 9.37181i | −0.150021 | − | 0.461716i | ||||
\(413\) | 16.3435 | + | 50.3000i | 0.804209 | + | 2.47510i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.00000 | + | 2.90617i | −0.196352 | + | 0.142658i | ||||
\(416\) | 0.190983 | − | 0.587785i | 0.00936371 | − | 0.0288185i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.57295 | + | 1.31433i | 0.0769355 | + | 0.0642859i | ||||
\(419\) | 11.2016 | 0.547235 | 0.273618 | − | 0.961839i | \(-0.411780\pi\) | ||||
0.273618 | + | 0.961839i | \(0.411780\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.7984 | + | 15.8374i | −1.06239 | + | 0.771870i | −0.974529 | − | 0.224263i | \(-0.928003\pi\) |
−0.0878591 | + | 0.996133i | \(0.528003\pi\) | |||||||
\(422\) | 18.9443 | + | 13.7638i | 0.922193 | + | 0.670012i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.88197 | + | 5.79210i | 0.0913963 | + | 0.281289i | ||||
\(425\) | −5.23607 | − | 3.80423i | −0.253987 | − | 0.184532i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.5623 | − | 38.6628i | 0.607933 | − | 1.87102i | ||||
\(428\) | −17.8885 | −0.864675 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.763932 | 0.0368401 | ||||||||
\(431\) | −0.673762 | + | 2.07363i | −0.0324540 | + | 0.0998831i | −0.965971 | − | 0.258649i | \(-0.916723\pi\) |
0.933517 | + | 0.358532i | \(0.116723\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.7984 | + | 19.4702i | 1.28785 | + | 0.935676i | 0.999760 | − | 0.0219278i | \(-0.00698040\pi\) |
0.288088 | + | 0.957604i | \(0.406980\pi\) | |||||||
\(434\) | −10.3262 | − | 31.7809i | −0.495675 | − | 1.52553i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.23607 | − | 2.35114i | −0.154980 | − | 0.112599i | ||||
\(437\) | −2.42705 | + | 1.76336i | −0.116102 | + | 0.0843527i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.1803 | 0.963155 | 0.481578 | − | 0.876403i | \(-0.340064\pi\) | ||||
0.481578 | + | 0.876403i | \(0.340064\pi\) | |||||||
\(440\) | 3.30902 | + | 0.224514i | 0.157751 | + | 0.0107033i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.23607 | − | 3.80423i | 0.0587938 | − | 0.180949i | ||||
\(443\) | 23.3262 | − | 16.9475i | 1.10826 | − | 0.805200i | 0.125874 | − | 0.992046i | \(-0.459827\pi\) |
0.982389 | + | 0.186846i | \(0.0598266\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.59017 | + | 4.89404i | 0.0753813 | + | 0.232000i | ||||
\(446\) | 2.35410 | + | 7.24518i | 0.111470 | + | 0.343069i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.92705 | + | 2.12663i | −0.138290 | + | 0.100474i | ||||
\(449\) | 5.75329 | − | 17.7068i | 0.271514 | − | 0.835636i | −0.718606 | − | 0.695417i | \(-0.755220\pi\) |
0.990121 | − | 0.140218i | \(-0.0447805\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.5279 | − | 28.7032i | 0.542826 | − | 1.35158i | ||||
\(452\) | 12.4721 | 0.586640 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.38197 | + | 2.45714i | −0.158724 | + | 0.115319i | ||||
\(455\) | −1.80902 | − | 1.31433i | −0.0848080 | − | 0.0616166i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.05573 | + | 9.40456i | 0.142941 | + | 0.439927i | 0.996740 | − | 0.0806750i | \(-0.0257076\pi\) |
−0.853800 | + | 0.520602i | \(0.825708\pi\) | |||||||
\(458\) | 9.32624 | + | 6.77591i | 0.435786 | + | 0.316617i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.50000 | + | 4.61653i | −0.0699379 | + | 0.215247i | ||||
\(461\) | 24.7639 | 1.15337 | 0.576686 | − | 0.816966i | \(-0.304346\pi\) | ||||
0.576686 | + | 0.816966i | \(0.304346\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.38197 | −0.157173 | −0.0785866 | − | 0.996907i | \(-0.525041\pi\) | ||||
−0.0785866 | + | 0.996907i | \(0.525041\pi\) | |||||||
\(464\) | −1.14590 | + | 3.52671i | −0.0531970 | + | 0.163723i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.1803 | − | 9.57608i | −0.610567 | − | 0.443603i | ||||
\(467\) | −2.18034 | − | 6.71040i | −0.100894 | − | 0.310520i | 0.887851 | − | 0.460131i | \(-0.152198\pi\) |
−0.988745 | + | 0.149611i | \(0.952198\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.9443 | + | 17.3965i | 1.10564 | + | 0.803297i | ||||
\(470\) | −2.11803 | + | 1.53884i | −0.0976976 | + | 0.0709815i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 14.6180 | 0.672850 | ||||||||
\(473\) | −2.14590 | + | 1.34708i | −0.0986685 | + | 0.0619390i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.190983 | + | 0.587785i | −0.00876290 | + | 0.0269694i | ||||
\(476\) | −18.9443 | + | 13.7638i | −0.868309 | + | 0.630864i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.85410 | − | 21.0948i | −0.313499 | − | 0.964852i | ||||
\(479\) | 12.0557 | + | 37.1037i | 0.550840 | + | 1.69531i | 0.706683 | + | 0.707530i | \(0.250191\pi\) |
−0.155843 | + | 0.987782i | \(0.549809\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.309017 | − | 0.224514i | 0.0140900 | − | 0.0102370i | ||||
\(482\) | −7.91641 | + | 24.3642i | −0.360582 | + | 1.10976i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.69098 | + | 5.20431i | −0.440499 | + | 0.236560i | ||||
\(485\) | 14.9443 | 0.678584 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.6525 | + | 23.7234i | −1.47962 | + | 1.07501i | −0.501948 | + | 0.864898i | \(0.667383\pi\) |
−0.977677 | + | 0.210112i | \(0.932617\pi\) | |||||||
\(488\) | −9.09017 | − | 6.60440i | −0.411493 | − | 0.298967i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.88197 | + | 5.79210i | 0.0850186 | + | 0.261660i | ||||
\(491\) | −1.88197 | − | 1.36733i | −0.0849319 | − | 0.0617067i | 0.544509 | − | 0.838755i | \(-0.316716\pi\) |
−0.629441 | + | 0.777048i | \(0.716716\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.41641 | + | 22.8254i | −0.334018 | + | 1.02800i | ||||
\(494\) | −0.381966 | −0.0171855 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.23607 | −0.414712 | ||||||||
\(497\) | 0.326238 | − | 1.00406i | 0.0146338 | − | 0.0450381i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.2533 | + | 19.8007i | 1.22002 | + | 0.886400i | 0.996102 | − | 0.0882071i | \(-0.0281137\pi\) |
0.223923 | + | 0.974607i | \(0.428114\pi\) | |||||||
\(500\) | 0.309017 | + | 0.951057i | 0.0138197 | + | 0.0425325i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.30902 | + | 6.76340i | 0.415482 | + | 0.301865i | ||||
\(503\) | −3.88197 | + | 2.82041i | −0.173088 | + | 0.125756i | −0.670957 | − | 0.741497i | \(-0.734116\pi\) |
0.497868 | + | 0.867253i | \(0.334116\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.00000 | −0.177998 | ||||||||
\(506\) | −3.92705 | − | 15.6129i | −0.174579 | − | 0.694079i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.89919 | − | 12.0005i | 0.172998 | − | 0.532434i | ||||
\(509\) | −20.5623 | + | 14.9394i | −0.911408 | + | 0.662177i | −0.941371 | − | 0.337374i | \(-0.890461\pi\) |
0.0299624 | + | 0.999551i | \(0.490461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.2361 | + | 37.6587i | 0.541292 | + | 1.66592i | ||||
\(512\) | 0.309017 | + | 0.951057i | 0.0136568 | + | 0.0420312i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.09017 | + | 2.97168i | −0.180410 | + | 0.131075i | ||||
\(515\) | −3.04508 | + | 9.37181i | −0.134182 | + | 0.412971i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.23607 | − | 8.05748i | 0.142322 | − | 0.354368i | ||||
\(518\) | −2.23607 | −0.0982472 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.500000 | + | 0.363271i | −0.0219265 | + | 0.0159305i | ||||
\(521\) | 30.1976 | + | 21.9398i | 1.32298 | + | 0.961201i | 0.999890 | + | 0.0148321i | \(0.00472138\pi\) |
0.323089 | + | 0.946369i | \(0.395279\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.708204 | + | 2.17963i | 0.0309676 | + | 0.0953085i | 0.965346 | − | 0.260975i | \(-0.0840439\pi\) |
−0.934378 | + | 0.356283i | \(0.884044\pi\) | |||||||
\(524\) | 16.9443 | + | 12.3107i | 0.740214 | + | 0.537797i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.51722 | − | 7.74721i | 0.109756 | − | 0.337794i | ||||
\(527\) | −59.7771 | −2.60393 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.562306 | 0.0244481 | ||||||||
\(530\) | 1.88197 | − | 5.79210i | 0.0817474 | − | 0.251593i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.80902 | + | 1.31433i | 0.0784308 | + | 0.0569833i | ||||
\(533\) | 1.78115 | + | 5.48183i | 0.0771503 | + | 0.237444i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.4721 | + | 10.5146i | 0.625685 | + | 0.454587i | ||||
\(536\) | 6.61803 | − | 4.80828i | 0.285856 | − | 0.207686i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24.7639 | 1.06765 | ||||||||
\(539\) | −15.5000 | − | 12.9515i | −0.667632 | − | 0.557861i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.65248 | + | 14.3188i | −0.200026 | + | 0.615615i | 0.799856 | + | 0.600193i | \(0.204909\pi\) |
−0.999881 | + | 0.0154228i | \(0.995091\pi\) | |||||||
\(542\) | −0.527864 | + | 0.383516i | −0.0226737 | + | 0.0164734i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.00000 | + | 6.15537i | 0.0857493 | + | 0.263909i | ||||
\(545\) | 1.23607 | + | 3.80423i | 0.0529473 | + | 0.162955i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.5623 | − | 11.3067i | 0.665396 | − | 0.483439i | −0.203085 | − | 0.979161i | \(-0.565097\pi\) |
0.868481 | + | 0.495723i | \(0.165097\pi\) | |||||||
\(548\) | −4.76393 | + | 14.6619i | −0.203505 | + | 0.626324i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.54508 | − | 2.12663i | −0.108523 | − | 0.0906797i | ||||
\(551\) | 2.29180 | 0.0976338 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.0902 | − | 9.51057i | 0.556651 | − | 0.404430i | ||||
\(554\) | 6.69098 | + | 4.86128i | 0.284273 | + | 0.206536i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.35410 | − | 7.24518i | −0.0998362 | − | 0.307264i | ||||
\(557\) | 11.0623 | + | 8.03724i | 0.468725 | + | 0.340549i | 0.796944 | − | 0.604053i | \(-0.206448\pi\) |
−0.328219 | + | 0.944602i | \(0.606448\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.145898 | − | 0.449028i | 0.00617083 | − | 0.0189919i | ||||
\(560\) | 3.61803 | 0.152890 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.88854 | −0.332758 | ||||||||
\(563\) | −14.0000 | + | 43.0876i | −0.590030 | + | 1.81592i | −0.0119724 | + | 0.999928i | \(0.503811\pi\) |
−0.578057 | + | 0.815996i | \(0.696189\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.0902 | − | 7.33094i | −0.424497 | − | 0.308415i | ||||
\(566\) | 1.14590 | + | 3.52671i | 0.0481657 | + | 0.148239i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.236068 | − | 0.171513i | −0.00990519 | − | 0.00719654i | ||||
\(569\) | 12.0172 | − | 8.73102i | 0.503788 | − | 0.366023i | −0.306674 | − | 0.951815i | \(-0.599216\pi\) |
0.810462 | + | 0.585791i | \(0.199216\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.5066 | −0.900022 | −0.450011 | − | 0.893023i | \(-0.648580\pi\) | ||||
−0.450011 | + | 0.893023i | \(0.648580\pi\) | |||||||
\(572\) | 0.763932 | − | 1.90211i | 0.0319416 | − | 0.0795313i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.4271 | − | 32.0912i | 0.435217 | − | 1.33946i | ||||
\(575\) | 3.92705 | − | 2.85317i | 0.163769 | − | 0.118985i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.20163 | − | 6.77591i | −0.0916549 | − | 0.282085i | 0.894713 | − | 0.446642i | \(-0.147380\pi\) |
−0.986367 | + | 0.164558i | \(0.947380\pi\) | |||||||
\(578\) | 7.69098 | + | 23.6704i | 0.319903 | + | 0.984559i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.00000 | − | 2.17963i | 0.124568 | − | 0.0905041i | ||||
\(581\) | 5.52786 | − | 17.0130i | 0.229334 | − | 0.705819i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.92705 | + | 19.5887i | 0.204058 | + | 0.811280i | ||||
\(584\) | 10.9443 | 0.452877 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.92705 | − | 6.48588i | 0.368773 | − | 0.267929i | ||||
\(587\) | 28.1803 | + | 20.4742i | 1.16313 | + | 0.845061i | 0.990170 | − | 0.139868i | \(-0.0446678\pi\) |
0.172957 | + | 0.984929i | \(0.444668\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.76393 | + | 5.42882i | 0.0726816 | + | 0.223691i | ||||
\(590\) | −11.8262 | − | 8.59226i | −0.486879 | − | 0.353738i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.190983 | + | 0.587785i | −0.00784935 | + | 0.0241578i | ||||
\(593\) | 2.58359 | 0.106095 | 0.0530477 | − | 0.998592i | \(-0.483106\pi\) | ||||
0.0530477 | + | 0.998592i | \(0.483106\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.4164 | 0.959979 | ||||||||
\(596\) | 2.76393 | − | 8.50651i | 0.113215 | − | 0.348440i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.42705 | + | 1.76336i | 0.0992495 | + | 0.0721090i | ||||
\(599\) | 1.32624 | + | 4.08174i | 0.0541886 | + | 0.166775i | 0.974488 | − | 0.224439i | \(-0.0720550\pi\) |
−0.920299 | + | 0.391215i | \(0.872055\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.3885 | + | 20.6255i | 1.15799 | + | 0.841331i | 0.989523 | − | 0.144376i | \(-0.0461174\pi\) |
0.168470 | + | 0.985707i | \(0.446117\pi\) | |||||||
\(602\) | −2.23607 | + | 1.62460i | −0.0911353 | + | 0.0662137i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12.4721 | −0.507484 | ||||||||
\(605\) | 10.8992 | + | 1.48584i | 0.443115 | + | 0.0604080i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.05573 | + | 15.5599i | −0.205206 | + | 0.631558i | 0.794499 | + | 0.607265i | \(0.207733\pi\) |
−0.999705 | + | 0.0242929i | \(0.992267\pi\) | |||||||
\(608\) | 0.500000 | − | 0.363271i | 0.0202777 | − | 0.0147326i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.47214 | + | 10.6861i | 0.140583 | + | 0.432669i | ||||
\(611\) | 0.500000 | + | 1.53884i | 0.0202278 | + | 0.0622549i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.7426 | + | 26.6951i | −1.48402 | + | 1.07820i | −0.507788 | + | 0.861482i | \(0.669537\pi\) |
−0.976233 | + | 0.216723i | \(0.930463\pi\) | |||||||
\(614\) | 8.29180 | − | 25.5195i | 0.334630 | − | 1.02988i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.1631 | + | 6.37988i | −0.409484 | + | 0.257053i | ||||
\(617\) | −23.0557 | −0.928189 | −0.464094 | − | 0.885786i | \(-0.653620\pi\) | ||||
−0.464094 | + | 0.885786i | \(0.653620\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.2082 | + | 13.9556i | −0.772043 | + | 0.560922i | −0.902580 | − | 0.430521i | \(-0.858330\pi\) |
0.130537 | + | 0.991443i | \(0.458330\pi\) | |||||||
\(620\) | 7.47214 | + | 5.42882i | 0.300088 | + | 0.218027i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.61803 | + | 26.5236i | 0.345552 | + | 1.06350i | ||||
\(623\) | −15.0623 | − | 10.9434i | −0.603459 | − | 0.438438i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.309017 | − | 0.951057i | 0.0123607 | − | 0.0380423i | ||||
\(626\) | 5.70820 | 0.228146 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.61803 | −0.224184 | ||||||||
\(629\) | −1.23607 | + | 3.80423i | −0.0492853 | + | 0.151684i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.38197 | − | 1.00406i | −0.0550152 | − | 0.0399709i | 0.559938 | − | 0.828535i | \(-0.310825\pi\) |
−0.614953 | + | 0.788564i | \(0.710825\pi\) | |||||||
\(632\) | −1.38197 | − | 4.25325i | −0.0549717 | − | 0.169185i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.82624 | + | 6.41264i | 0.350535 | + | 0.254678i | ||||
\(635\) | −10.2082 | + | 7.41669i | −0.405100 | + | 0.294323i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.76393 | 0.149132 | ||||||||
\(638\) | −4.58359 | + | 11.4127i | −0.181466 | + | 0.451832i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.309017 | − | 0.951057i | 0.0122150 | − | 0.0375938i | ||||
\(641\) | 30.2984 | − | 22.0131i | 1.19671 | − | 0.869463i | 0.202756 | − | 0.979229i | \(-0.435010\pi\) |
0.993957 | + | 0.109766i | \(0.0350101\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.05573 | − | 3.24920i | −0.0416339 | − | 0.128136i | 0.928079 | − | 0.372383i | \(-0.121459\pi\) |
−0.969713 | + | 0.244247i | \(0.921459\pi\) | |||||||
\(644\) | −5.42705 | − | 16.7027i | −0.213856 | − | 0.658180i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.23607 | − | 2.35114i | 0.127321 | − | 0.0925044i | ||||
\(647\) | 9.52786 | − | 29.3238i | 0.374579 | − | 1.15284i | −0.569183 | − | 0.822211i | \(-0.692741\pi\) |
0.943762 | − | 0.330625i | \(-0.107259\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.3713 | + | 3.28195i | 1.89874 | + | 0.128828i | ||||
\(650\) | 0.618034 | 0.0242413 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.4721 | + | 10.5146i | −0.566773 | + | 0.411784i | ||||
\(653\) | −12.8262 | − | 9.31881i | −0.501929 | − | 0.364673i | 0.307824 | − | 0.951443i | \(-0.400399\pi\) |
−0.809754 | + | 0.586770i | \(0.800399\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.47214 | − | 19.9192i | −0.252887 | − | 0.778307i | ||||
\(656\) | −7.54508 | − | 5.48183i | −0.294586 | − | 0.214029i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.92705 | − | 9.00854i | 0.114108 | − | 0.351189i | ||||
\(659\) | −28.2705 | −1.10126 | −0.550631 | − | 0.834749i | \(-0.685613\pi\) | ||||
−0.550631 | + | 0.834749i | \(0.685613\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.4853 | 1.61359 | 0.806795 | − | 0.590831i | \(-0.201200\pi\) | ||||
0.806795 | + | 0.590831i | \(0.201200\pi\) | |||||||
\(662\) | 2.37132 | − | 7.29818i | 0.0921641 | − | 0.283652i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.00000 | − | 2.90617i | −0.155230 | − | 0.112781i | ||||
\(665\) | −0.690983 | − | 2.12663i | −0.0267952 | − | 0.0824671i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.5623 | − | 10.5801i | −0.563855 | − | 0.409664i | ||||
\(668\) | −9.35410 | + | 6.79615i | −0.361921 | + | 0.262951i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.18034 | −0.316034 | ||||||||
\(671\) | −28.5967 | − | 23.8949i | −1.10397 | − | 0.922453i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.0902 | + | 43.3651i | −0.543136 | + | 1.67160i | 0.182245 | + | 0.983253i | \(0.441664\pi\) |
−0.725381 | + | 0.688348i | \(0.758336\pi\) | |||||||
\(674\) | 16.1803 | − | 11.7557i | 0.623243 | − | 0.452813i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.89919 | − | 12.0005i | −0.149969 | − | 0.461556i | ||||
\(677\) | −4.43769 | − | 13.6578i | −0.170554 | − | 0.524913i | 0.828848 | − | 0.559474i | \(-0.188997\pi\) |
−0.999403 | + | 0.0345610i | \(0.988997\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −43.7426 | + | 31.7809i | −1.67869 | + | 1.21964i | ||||
\(680\) | 2.00000 | − | 6.15537i | 0.0766965 | − | 0.236048i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −30.5623 | − | 2.07363i | −1.17029 | − | 0.0794033i | ||||
\(683\) | −31.1246 | −1.19095 | −0.595475 | − | 0.803374i | \(-0.703036\pi\) | ||||
−0.595475 | + | 0.803374i | \(0.703036\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.4721 | − | 9.06154i | 0.476536 | − | 0.346224i | ||||
\(686\) | 2.66312 | + | 1.93487i | 0.101678 | + | 0.0738736i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.236068 | + | 0.726543i | 0.00900001 | + | 0.0276992i | ||||
\(689\) | −3.04508 | − | 2.21238i | −0.116008 | − | 0.0842851i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.465558 | + | 1.43284i | −0.0177107 | + | 0.0545078i | −0.959521 | − | 0.281636i | \(-0.909123\pi\) |
0.941811 | + | 0.336144i | \(0.109123\pi\) | |||||||
\(692\) | 24.5623 | 0.933719 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.81966 | −0.144992 | ||||||||
\(695\) | −2.35410 | + | 7.24518i | −0.0892962 | + | 0.274825i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −48.8328 | − | 35.4791i | −1.84967 | − | 1.34387i | ||||
\(698\) | 3.09017 | + | 9.51057i | 0.116965 | + | 0.359980i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.92705 | − | 2.12663i | −0.110632 | − | 0.0803789i | ||||
\(701\) | −16.2361 | + | 11.7962i | −0.613228 | + | 0.445536i | −0.850549 | − | 0.525895i | \(-0.823730\pi\) |
0.237322 | + | 0.971431i | \(0.423730\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.381966 | 0.0144061 | ||||||||
\(704\) | 0.809017 | + | 3.21644i | 0.0304910 | + | 0.121224i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.61803 | − | 23.4459i | 0.286708 | − | 0.882398i | ||||
\(707\) | 11.7082 | − | 8.50651i | 0.440332 | − | 0.319920i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.61803 | − | 23.4459i | −0.286101 | − | 0.880529i | −0.986066 | − | 0.166352i | \(-0.946801\pi\) |
0.699965 | − | 0.714177i | \(-0.253199\pi\) | |||||||
\(710\) | 0.0901699 | + | 0.277515i | 0.00338402 | + | 0.0104149i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.16312 | + | 3.02468i | −0.156019 | + | 0.113355i | ||||
\(713\) | 13.8541 | − | 42.6385i | 0.518840 | − | 1.59683i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.73607 | + | 1.08981i | −0.0649253 | + | 0.0407567i | ||||
\(716\) | 11.1459 | 0.416542 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 20.4164 | − | 14.8334i | 0.761934 | − | 0.553577i | ||||
\(719\) | −19.3262 | − | 14.0413i | −0.720747 | − | 0.523653i | 0.165876 | − | 0.986147i | \(-0.446955\pi\) |
−0.886623 | + | 0.462493i | \(0.846955\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.0172 | − | 33.9075i | −0.410303 | − | 1.26278i | ||||
\(722\) | 15.0623 | + | 10.9434i | 0.560561 | + | 0.407271i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.52786 | + | 23.1684i | −0.279771 | + | 0.861046i | ||||
\(725\) | −3.70820 | −0.137719 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −46.6312 | −1.72946 | −0.864728 | − | 0.502241i | \(-0.832509\pi\) | ||||
−0.864728 | + | 0.502241i | \(0.832509\pi\) | |||||||
\(728\) | 0.690983 | − | 2.12663i | 0.0256095 | − | 0.0788180i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.85410 | − | 6.43288i | −0.327705 | − | 0.238092i | ||||
\(731\) | 1.52786 | + | 4.70228i | 0.0565101 | + | 0.173920i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.0344 | + | 16.7355i | 0.850797 | + | 0.618140i | 0.925366 | − | 0.379076i | \(-0.123758\pi\) |
−0.0745690 | + | 0.997216i | \(0.523758\pi\) | |||||||
\(734\) | −6.76393 | + | 4.91428i | −0.249661 | + | 0.181390i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.85410 | −0.178925 | ||||||||
\(737\) | 22.9787 | − | 14.4248i | 0.846432 | − | 0.531346i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.53444 | − | 26.2663i | 0.313945 | − | 0.966222i | −0.662242 | − | 0.749290i | \(-0.730395\pi\) |
0.976187 | − | 0.216932i | \(-0.0696050\pi\) | |||||||
\(740\) | 0.500000 | − | 0.363271i | 0.0183804 | − | 0.0133541i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.80902 | + | 20.9560i | 0.249967 | + | 0.769319i | ||||
\(743\) | 2.20820 | + | 6.79615i | 0.0810111 | + | 0.249327i | 0.983356 | − | 0.181687i | \(-0.0581559\pi\) |
−0.902345 | + | 0.431014i | \(0.858156\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.23607 | + | 5.25731i | −0.265109 | + | 0.192613i | ||||
\(746\) | −4.28115 | + | 13.1760i | −0.156744 | + | 0.482409i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.23607 | + | 20.8172i | 0.191450 | + | 0.761154i | ||||
\(749\) | −64.7214 | −2.36487 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.4721 | − | 17.7800i | 0.893001 | − | 0.648803i | −0.0436578 | − | 0.999047i | \(-0.513901\pi\) |
0.936659 | + | 0.350243i | \(0.113901\pi\) | |||||||
\(752\) | −2.11803 | − | 1.53884i | −0.0772368 | − | 0.0561158i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.708204 | − | 2.17963i | −0.0257913 | − | 0.0793774i | ||||
\(755\) | 10.0902 | + | 7.33094i | 0.367219 | + | 0.266800i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.572949 | − | 1.76336i | 0.0208242 | − | 0.0640903i | −0.940104 | − | 0.340887i | \(-0.889273\pi\) |
0.960929 | + | 0.276796i | \(0.0892728\pi\) | |||||||
\(758\) | −32.7426 | −1.18927 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.618034 | −0.0224184 | ||||||||
\(761\) | 2.43769 | − | 7.50245i | 0.0883663 | − | 0.271964i | −0.897102 | − | 0.441824i | \(-0.854332\pi\) |
0.985468 | + | 0.169860i | \(0.0543316\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.7082 | − | 8.50651i | −0.423865 | − | 0.307956i | ||||
\(764\) | 4.23607 | + | 13.0373i | 0.153256 | + | 0.471672i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.0172 | − | 16.7230i | −0.831646 | − | 0.604226i | ||||
\(767\) | −7.30902 | + | 5.31031i | −0.263913 | + | 0.191744i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.7984 | −1.25486 | −0.627431 | − | 0.778672i | \(-0.715893\pi\) | ||||
−0.627431 | + | 0.778672i | \(0.715893\pi\) | |||||||
\(770\) | 11.9721 | + | 0.812299i | 0.431446 | + | 0.0292732i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.14590 | + | 3.52671i | −0.0412418 | + | 0.126929i | ||||
\(773\) | 3.07295 | − | 2.23263i | 0.110526 | − | 0.0803021i | −0.531149 | − | 0.847278i | \(-0.678240\pi\) |
0.641675 | + | 0.766976i | \(0.278240\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.85410 | − | 8.78402i | −0.102522 | − | 0.315531i | ||||
\(776\) | 4.61803 | + | 14.2128i | 0.165778 | + | 0.510211i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.85410 | − | 2.07363i | 0.102325 | − | 0.0743431i | ||||
\(779\) | −1.78115 | + | 5.48183i | −0.0638164 | + | 0.196407i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.742646 | − | 0.620541i | −0.0265740 | − | 0.0222047i | ||||
\(782\) | −31.4164 | −1.12345 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.92705 | + | 3.57971i | −0.175966 | + | 0.127847i | ||||
\(785\) | 4.54508 | + | 3.30220i | 0.162221 | + | 0.117860i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.61803 | − | 17.2905i | −0.200261 | − | 0.616341i | −0.999875 | − | 0.0158258i | \(-0.994962\pi\) |
0.799613 | − | 0.600515i | \(-0.205038\pi\) | |||||||
\(788\) | 2.92705 | + | 2.12663i | 0.104272 | + | 0.0757580i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.38197 | + | 4.25325i | −0.0491681 | + | 0.151324i | ||||
\(791\) | 45.1246 | 1.60445 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.94427 | 0.246598 | ||||||||
\(794\) | 3.91641 | − | 12.0535i | 0.138988 | − | 0.427761i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.4721 | + | 7.60845i | 0.371175 | + | 0.269674i | ||||
\(797\) | −4.24671 | − | 13.0700i | −0.150426 | − | 0.462964i | 0.847243 | − | 0.531206i | \(-0.178261\pi\) |
−0.997669 | + | 0.0682419i | \(0.978261\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.7082 | − | 9.95959i | −0.484961 | − | 0.352345i | ||||
\(800\) | −0.809017 | + | 0.587785i | −0.0286031 | + | 0.0207813i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.67376 | 0.0591026 | ||||||||
\(803\) | 36.2148 | + | 2.45714i | 1.27799 | + | 0.0867107i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.42705 | + | 16.7027i | −0.191278 | + | 0.588694i | ||||
\(806\) | 4.61803 | − | 3.35520i | 0.162663 | − | 0.118182i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.23607 | − | 3.80423i | −0.0434847 | − | 0.133832i | ||||
\(809\) | 1.07953 | + | 3.32244i | 0.0379541 | + | 0.116811i | 0.968239 | − | 0.250028i | \(-0.0804399\pi\) |
−0.930284 | + | 0.366839i | \(0.880440\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.2533 | + | 15.4414i | −0.746304 | + | 0.542222i | −0.894679 | − | 0.446710i | \(-0.852596\pi\) |
0.148375 | + | 0.988931i | \(0.452596\pi\) | |||||||
\(812\) | −4.14590 | + | 12.7598i | −0.145492 | + | 0.447780i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.763932 | + | 1.90211i | −0.0267758 | + | 0.0666690i | ||||
\(815\) | 17.8885 | 0.626608 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.381966 | − | 0.277515i | 0.0133633 | − | 0.00970901i | ||||
\(818\) | −11.5000 | − | 8.35524i | −0.402088 | − | 0.292134i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.88197 | + | 8.86978i | 0.100643 | + | 0.309746i | ||||
\(821\) | 10.3262 | + | 7.50245i | 0.360388 | + | 0.261837i | 0.753214 | − | 0.657776i | \(-0.228502\pi\) |
−0.392826 | + | 0.919613i | \(0.628502\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.1697 | − | 31.2991i | 0.354493 | − | 1.09102i | −0.601809 | − | 0.798640i | \(-0.705553\pi\) |
0.956303 | − | 0.292379i | \(-0.0944467\pi\) | |||||||
\(824\) | −9.85410 | −0.343284 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 52.8885 | 1.84023 | ||||||||
\(827\) | 3.00000 | − | 9.23305i | 0.104320 | − | 0.321065i | −0.885250 | − | 0.465115i | \(-0.846013\pi\) |
0.989570 | + | 0.144051i | \(0.0460128\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.8541 | + | 13.6983i | 0.654830 | + | 0.475762i | 0.864913 | − | 0.501922i | \(-0.167373\pi\) |
−0.210083 | + | 0.977684i | \(0.567373\pi\) | |||||||
\(830\) | 1.52786 | + | 4.70228i | 0.0530329 | + | 0.163219i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.500000 | − | 0.363271i | −0.0173344 | − | 0.0125942i | ||||
\(833\) | −31.8885 | + | 23.1684i | −1.10487 | + | 0.802737i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.5623 | 0.400130 | ||||||||
\(836\) | 1.73607 | − | 1.08981i | 0.0600432 | − | 0.0376920i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.46149 | − | 10.6534i | 0.119575 | − | 0.368015i | ||||
\(839\) | 26.7984 | − | 19.4702i | 0.925183 | − | 0.672185i | −0.0196260 | − | 0.999807i | \(-0.506248\pi\) |
0.944809 | + | 0.327623i | \(0.106248\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.71227 | − | 14.5029i | −0.162492 | − | 0.500099i | ||||
\(842\) | 8.32624 | + | 25.6255i | 0.286941 | + | 0.883114i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.9443 | − | 13.7638i | 0.652089 | − | 0.473770i | ||||
\(845\) | −3.89919 | + | 12.0005i | −0.134136 | + | 0.412828i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −35.0623 | + | 18.8294i | −1.20476 | + | 0.646985i | ||||
\(848\) | 6.09017 | 0.209137 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.23607 | + | 3.80423i | −0.179596 | + | 0.130484i | ||||
\(851\) | −2.42705 | − | 1.76336i | −0.0831982 | − | 0.0604471i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.0836 | + | 46.4225i | 0.516452 | + | 1.58948i | 0.780624 | + | 0.625001i | \(0.214902\pi\) |
−0.264171 | + | 0.964476i | \(0.585098\pi\) | |||||||
\(854\) | −32.8885 | − | 23.8949i | −1.12542 | − | 0.817668i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.52786 | + | 17.0130i | −0.188939 | + | 0.581493i | ||||
\(857\) | −55.2361 | −1.88683 | −0.943414 | − | 0.331617i | \(-0.892406\pi\) | ||||
−0.943414 | + | 0.331617i | \(0.892406\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.0344 | 1.74127 | 0.870636 | − | 0.491927i | \(-0.163707\pi\) | ||||
0.870636 | + | 0.491927i | \(0.163707\pi\) | |||||||
\(860\) | 0.236068 | − | 0.726543i | 0.00804985 | − | 0.0247749i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.76393 | + | 1.28157i | 0.0600798 | + | 0.0436505i | ||||
\(863\) | 0.0450850 | + | 0.138757i | 0.00153471 | + | 0.00472335i | 0.951821 | − | 0.306654i | \(-0.0992096\pi\) |
−0.950286 | + | 0.311378i | \(0.899210\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.8713 | − | 14.4374i | −0.675645 | − | 0.490885i | ||||
\(866\) | 26.7984 | − | 19.4702i | 0.910646 | − | 0.661623i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −33.4164 | −1.13423 | ||||||||
\(869\) | −3.61803 | − | 14.3844i | −0.122733 | − | 0.487956i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.56231 | + | 4.80828i | −0.0529367 | + | 0.162922i | ||||
\(872\) | −3.23607 | + | 2.35114i | −0.109587 | + | 0.0796197i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.927051 | + | 2.85317i | 0.0313580 | + | 0.0965099i | ||||
\(875\) | 1.11803 | + | 3.44095i | 0.0377964 | + | 0.116326i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.9164 | − | 13.7436i | 0.638762 | − | 0.464088i | −0.220663 | − | 0.975350i | \(-0.570822\pi\) |
0.859425 | + | 0.511263i | \(0.170822\pi\) | |||||||
\(878\) | 6.23607 | − | 19.1926i | 0.210457 | − | 0.647720i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.23607 | − | 3.07768i | 0.0416678 | − | 0.103749i | ||||
\(881\) | −7.79837 | −0.262734 | −0.131367 | − | 0.991334i | \(-0.541937\pi\) | ||||
−0.131367 | + | 0.991334i | \(0.541937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.4721 | + | 14.8739i | −0.688942 | + | 0.500546i | −0.876312 | − | 0.481744i | \(-0.840004\pi\) |
0.187370 | + | 0.982289i | \(0.440004\pi\) | |||||||
\(884\) | −3.23607 | − | 2.35114i | −0.108841 | − | 0.0790774i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.90983 | − | 27.4216i | −0.299332 | − | 0.921248i | ||||
\(887\) | 1.01722 | + | 0.739054i | 0.0341549 | + | 0.0248150i | 0.604732 | − | 0.796429i | \(-0.293280\pi\) |
−0.570577 | + | 0.821244i | \(0.693280\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.1074 | − | 43.4181i | 0.473147 | − | 1.45620i | ||||
\(890\) | 5.14590 | 0.172491 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.61803 | 0.255071 | ||||||||
\(893\) | −0.500000 | + | 1.53884i | −0.0167319 | + | 0.0514954i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.01722 | − | 6.55139i | −0.301412 | − | 0.218989i | ||||
\(896\) | 1.11803 | + | 3.44095i | 0.0373509 | + | 0.114954i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.0623 | − | 10.9434i | −0.502636 | − | 0.365186i | ||||
\(899\) | −27.7082 | + | 20.1312i | −0.924120 | + | 0.671413i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39.4164 | 1.31315 | ||||||||
\(902\) | −23.7361 | − | 19.8334i | −0.790325 | − | 0.660381i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.85410 | − | 11.8617i | 0.128186 | − | 0.394514i | ||||
\(905\) | 19.7082 | − | 14.3188i | 0.655123 | − | 0.475975i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.23607 | + | 28.4257i | 0.306679 | + | 0.943860i | 0.979045 | + | 0.203642i | \(0.0652777\pi\) |
−0.672367 | + | 0.740218i | \(0.734722\pi\) | |||||||
\(908\) | 1.29180 | + | 3.97574i | 0.0428698 | + | 0.131940i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.80902 | + | 1.31433i | −0.0599683 | + | 0.0435695i | ||||
\(911\) | 3.29180 | − | 10.1311i | 0.109062 | − | 0.335659i | −0.881600 | − | 0.471997i | \(-0.843533\pi\) |
0.990662 | + | 0.136338i | \(0.0435334\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.5836 | − | 10.5146i | −0.416456 | − | 0.347983i | ||||
\(914\) | 9.88854 | 0.327084 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.32624 | − | 6.77591i | 0.308148 | − | 0.223882i | ||||
\(917\) | 61.3050 | + | 44.5407i | 2.02447 | + | 1.47086i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.58359 | − | 17.1845i | −0.184186 | − | 0.566865i | 0.815748 | − | 0.578408i | \(-0.196326\pi\) |
−0.999933 | + | 0.0115426i | \(0.996326\pi\) | |||||||
\(920\) | 3.92705 | + | 2.85317i | 0.129471 | + | 0.0940662i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.65248 | − | 23.5519i | 0.252021 | − | 0.775640i | ||||
\(923\) | 0.180340 | 0.00593596 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.618034 | −0.0203208 | ||||||||
\(926\) | −1.04508 | + | 3.21644i | −0.0343436 | + | 0.105699i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.00000 | + | 2.17963i | 0.0984798 | + | 0.0715498i | ||||
\(929\) | 2.17376 | + | 6.69015i | 0.0713188 | + | 0.219497i | 0.980362 | − | 0.197204i | \(-0.0631862\pi\) |
−0.909044 | + | 0.416701i | \(0.863186\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.04508 | + | 2.21238i | 0.0997986 | + | 0.0725079i | ||||
\(932\) | −13.1803 | + | 9.57608i | −0.431736 | + | 0.313675i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.05573 | −0.230870 | ||||||||
\(935\) | 8.00000 | − | 19.9192i | 0.261628 | − | 0.651427i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.9443 | − | 45.9937i | 0.488208 | − | 1.50255i | −0.339072 | − | 0.940760i | \(-0.610113\pi\) |
0.827280 | − | 0.561790i | \(-0.189887\pi\) | |||||||
\(938\) | 23.9443 | − | 17.3965i | 0.781808 | − | 0.568017i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.809017 | + | 2.48990i | 0.0263872 | + | 0.0812115i | ||||
\(941\) | −3.41641 | − | 10.5146i | −0.111372 | − | 0.342767i | 0.879801 | − | 0.475342i | \(-0.157676\pi\) |
−0.991173 | + | 0.132575i | \(0.957676\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.6246 | − | 26.6093i | 1.19266 | − | 0.866519i | ||||
\(944\) | 4.51722 | − | 13.9026i | 0.147023 | − | 0.452490i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.618034 | + | 2.45714i | 0.0200940 | + | 0.0798886i | ||||
\(947\) | 3.30495 | 0.107396 | 0.0536982 | − | 0.998557i | \(-0.482899\pi\) | ||||
0.0536982 | + | 0.998557i | \(0.482899\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.47214 | + | 3.97574i | −0.177633 | + | 0.129058i | ||||
\(950\) | 0.500000 | + | 0.363271i | 0.0162221 | + | 0.0117861i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.23607 | + | 22.2703i | 0.234522 | + | 0.721785i | ||||
\(953\) | −36.2148 | − | 26.3116i | −1.17311 | − | 0.852316i | −0.181734 | − | 0.983348i | \(-0.558171\pi\) |
−0.991378 | + | 0.131032i | \(0.958171\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.23607 | − | 13.0373i | 0.137076 | − | 0.421876i | ||||
\(956\) | −22.1803 | −0.717363 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 39.0132 | 1.26046 | ||||||||
\(959\) | −17.2361 | + | 53.0472i | −0.556582 | + | 1.71298i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −43.9336 | − | 31.9196i | −1.41721 | − | 1.02967i | ||||
\(962\) | −0.118034 | − | 0.363271i | −0.00380557 | − | 0.0117123i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.7254 | + | 15.0579i | 0.667521 | + | 0.484982i | ||||
\(965\) | 3.00000 | − | 2.17963i | 0.0965734 | − | 0.0701647i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.25735 | −0.136907 | −0.0684536 | − | 0.997654i | \(-0.521807\pi\) | ||||
−0.0684536 | + | 0.997654i | \(0.521807\pi\) | |||||||
\(968\) | 1.95492 | + | 10.8249i | 0.0628333 | + | 0.347925i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.61803 | − | 14.2128i | 0.148276 | − | 0.456347i | ||||
\(971\) | 4.69098 | − | 3.40820i | 0.150541 | − | 0.109374i | −0.509965 | − | 0.860195i | \(-0.670342\pi\) |
0.660506 | + | 0.750821i | \(0.270342\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.51722 | − | 26.2133i | −0.273050 | − | 0.840360i | ||||
\(974\) | 12.4721 | + | 38.3853i | 0.399633 | + | 1.22994i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.09017 | + | 6.60440i | −0.290969 | + | 0.211402i | ||||
\(977\) | 7.67376 | − | 23.6174i | 0.245505 | − | 0.755588i | −0.750048 | − | 0.661384i | \(-0.769969\pi\) |
0.995553 | − | 0.0942040i | \(-0.0300306\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.4549 | + | 9.07405i | −0.461981 | + | 0.290008i | ||||
\(980\) | 6.09017 | 0.194543 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.88197 | + | 1.36733i | −0.0600559 | + | 0.0436332i | ||||
\(983\) | −26.7254 | − | 19.4172i | −0.852409 | − | 0.619311i | 0.0734004 | − | 0.997303i | \(-0.476615\pi\) |
−0.925809 | + | 0.377991i | \(0.876615\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.11803 | − | 3.44095i | −0.0356235 | − | 0.109638i | ||||
\(986\) | 19.4164 | + | 14.1068i | 0.618344 | + | 0.449254i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.118034 | + | 0.363271i | −0.00375516 | + | 0.0115572i | ||||
\(989\) | −3.70820 | −0.117914 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.94427 | 0.284124 | 0.142062 | − | 0.989858i | \(-0.454627\pi\) | ||||
0.142062 | + | 0.989858i | \(0.454627\pi\) | |||||||
\(992\) | −2.85410 | + | 8.78402i | −0.0906178 | + | 0.278893i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.854102 | − | 0.620541i | −0.0270905 | − | 0.0196824i | ||||
\(995\) | −4.00000 | − | 12.3107i | −0.126809 | − | 0.390277i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.1459 | + | 8.09797i | 0.352994 | + | 0.256465i | 0.750124 | − | 0.661297i | \(-0.229994\pi\) |
−0.397130 | + | 0.917762i | \(0.629994\pi\) | |||||||
\(998\) | 27.2533 | − | 19.8007i | 0.862688 | − | 0.626779i | ||||
\(999\) | 0 | 0 |
(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 | 990.2.n.a.361.1 | 4 | ||
3.2 | odd | 2 | 330.2.m.d.31.1 | ✓ | 4 | ||
11.5 | even | 5 | inner | 990.2.n.a.181.1 | 4 | ||
33.5 | odd | 10 | 330.2.m.d.181.1 | yes | 4 | ||
33.26 | odd | 10 | 3630.2.a.bc.1.2 | 2 | |||
33.29 | even | 10 | 3630.2.a.bi.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
330.2.m.d.31.1 | ✓ | 4 | 3.2 | odd | 2 | ||
330.2.m.d.181.1 | yes | 4 | 33.5 | odd | 10 | ||
990.2.n.a.181.1 | 4 | 11.5 | even | 5 | inner | ||
990.2.n.a.361.1 | 4 | 1.1 | even | 1 | trivial | ||
3630.2.a.bc.1.2 | 2 | 33.26 | odd | 10 | |||
3630.2.a.bi.1.1 | 2 | 33.29 | even | 10 |