Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(107,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.be (of order \(6\), 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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.8 | ||
Character | \(\chi\) | \(=\) | 756.107 |
Dual form | 756.2.be.e.431.8 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.04167 | + | 0.956516i | −0.736572 | + | 0.676359i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.170154 | − | 1.99275i | 0.0850769 | − | 0.996374i | ||||
\(5\) | 0.835158 | + | 0.482179i | 0.373494 | + | 0.215637i | 0.674984 | − | 0.737833i | \(-0.264151\pi\) |
−0.301490 | + | 0.953469i | \(0.597484\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.03771 | − | 1.68753i | 0.770181 | − | 0.637825i | ||||
\(8\) | 1.72885 | + | 2.23854i | 0.611242 | + | 0.791444i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.33117 | + | 0.296571i | −0.420953 | + | 0.0937840i | ||||
\(11\) | 1.63178 | + | 2.82633i | 0.492001 | + | 0.852170i | 0.999958 | − | 0.00921230i | \(-0.00293241\pi\) |
−0.507957 | + | 0.861383i | \(0.669599\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.66851 | −0.740113 | −0.370056 | − | 0.929009i | \(-0.620662\pi\) | ||||
−0.370056 | + | 0.929009i | \(0.620662\pi\) | |||||||
\(14\) | −0.508474 | + | 3.70695i | −0.135895 | + | 0.990723i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.94210 | − | 0.678147i | −0.985524 | − | 0.169537i | ||||
\(17\) | −0.713843 | + | 0.412137i | −0.173132 | + | 0.0999580i | −0.584062 | − | 0.811709i | \(-0.698538\pi\) |
0.410930 | + | 0.911667i | \(0.365204\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.31465 | + | 2.49107i | 0.989849 | + | 0.571490i | 0.905229 | − | 0.424924i | \(-0.139699\pi\) |
0.0846201 | + | 0.996413i | \(0.473032\pi\) | |||||||
\(20\) | 1.10297 | − | 1.58222i | 0.246631 | − | 0.353794i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.40321 | − | 1.38328i | −0.938767 | − | 0.294916i | ||||
\(23\) | 4.08549 | − | 7.07628i | 0.851884 | − | 1.47551i | −0.0276221 | − | 0.999618i | \(-0.508794\pi\) |
0.879506 | − | 0.475888i | \(-0.157873\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.03501 | − | 3.52474i | −0.407002 | − | 0.704947i | ||||
\(26\) | 2.77971 | − | 2.55248i | 0.545146 | − | 0.500582i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.01609 | − | 4.34778i | −0.569988 | − | 0.821653i | ||||
\(29\) | 7.71232i | 1.43214i | 0.698028 | + | 0.716071i | \(0.254061\pi\) | ||||
−0.698028 | + | 0.716071i | \(0.745939\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.98679 | − | 4.03382i | 1.25486 | − | 0.724496i | 0.282793 | − | 0.959181i | \(-0.408739\pi\) |
0.972071 | + | 0.234685i | \(0.0754059\pi\) | |||||||
\(32\) | 4.75502 | − | 3.06427i | 0.840577 | − | 0.541692i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.349373 | − | 1.11211i | 0.0599170 | − | 0.190726i | ||||
\(35\) | 2.51550 | − | 0.426812i | 0.425197 | − | 0.0721443i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.46063 | − | 4.26194i | 0.404526 | − | 0.700659i | −0.589740 | − | 0.807593i | \(-0.700770\pi\) |
0.994266 | + | 0.106934i | \(0.0341033\pi\) | |||||||
\(38\) | −6.87719 | + | 1.53217i | −1.11563 | + | 0.248550i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.364488 | + | 2.70315i | 0.0576306 | + | 0.427406i | ||||
\(41\) | 5.35061i | 0.835624i | 0.908533 | + | 0.417812i | \(0.137203\pi\) | ||||
−0.908533 | + | 0.417812i | \(0.862797\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.09044i | 1.23378i | 0.787049 | + | 0.616890i | \(0.211608\pi\) | ||||
−0.787049 | + | 0.616890i | \(0.788392\pi\) | |||||||
\(44\) | 5.90982 | − | 2.77082i | 0.890938 | − | 0.417717i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.51284 | + | 11.2790i | 0.370498 | + | 1.66300i | ||||
\(47\) | −0.910519 | + | 1.57706i | −0.132813 | + | 0.230038i | −0.924760 | − | 0.380551i | \(-0.875734\pi\) |
0.791947 | + | 0.610590i | \(0.209068\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.30451 | − | 6.87737i | 0.186359 | − | 0.982482i | ||||
\(50\) | 5.49127 | + | 1.72510i | 0.776583 | + | 0.243965i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.454058 | + | 5.31768i | −0.0629664 | + | 0.737429i | ||||
\(53\) | 7.39839 | − | 4.27147i | 1.01625 | − | 0.586731i | 0.103233 | − | 0.994657i | \(-0.467081\pi\) |
0.913015 | + | 0.407926i | \(0.133748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.14724i | 0.424374i | ||||||||
\(56\) | 7.30049 | + | 1.64401i | 0.975570 | + | 0.219690i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.37696 | − | 8.03369i | −0.968642 | − | 1.05488i | ||||
\(59\) | 0.238238 | + | 0.412641i | 0.0310160 | + | 0.0537213i | 0.881117 | − | 0.472899i | \(-0.156792\pi\) |
−0.850101 | + | 0.526620i | \(0.823459\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.09383 | + | 3.62661i | −0.268087 | + | 0.464340i | −0.968368 | − | 0.249527i | \(-0.919725\pi\) |
0.700281 | + | 0.713867i | \(0.253058\pi\) | |||||||
\(62\) | −3.41951 | + | 10.8849i | −0.434278 | + | 1.38238i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.02214 | + | 7.74022i | −0.252767 | + | 0.967527i | ||||
\(65\) | −2.22863 | − | 1.28670i | −0.276428 | − | 0.159596i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.36654 | − | 4.25307i | 0.899966 | − | 0.519596i | 0.0227769 | − | 0.999741i | \(-0.492749\pi\) |
0.877189 | + | 0.480145i | \(0.159416\pi\) | |||||||
\(68\) | 0.699823 | + | 1.49264i | 0.0848661 | + | 0.181009i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.21207 | + | 2.85071i | −0.264393 | + | 0.340725i | ||||
\(71\) | −7.12475 | −0.845553 | −0.422776 | − | 0.906234i | \(-0.638944\pi\) | ||||
−0.422776 | + | 0.906234i | \(0.638944\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.84578 | + | 10.1252i | 0.684197 | + | 1.18506i | 0.973688 | + | 0.227883i | \(0.0731805\pi\) |
−0.289491 | + | 0.957181i | \(0.593486\pi\) | |||||||
\(74\) | 1.51345 | + | 6.79317i | 0.175935 | + | 0.789691i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.69822 | − | 8.17416i | 0.653631 | − | 0.937640i | ||||
\(77\) | 8.09460 | + | 3.00556i | 0.922465 | + | 0.342515i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.28159 | + | 1.89463i | 0.369208 | + | 0.213162i | 0.673112 | − | 0.739540i | \(-0.264957\pi\) |
−0.303905 | + | 0.952702i | \(0.598290\pi\) | |||||||
\(80\) | −2.96528 | − | 2.46715i | −0.331529 | − | 0.275836i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.11794 | − | 5.57357i | −0.565182 | − | 0.615497i | ||||
\(83\) | 0.0674837 | 0.00740730 | 0.00370365 | − | 0.999993i | \(-0.498821\pi\) | ||||
0.00370365 | + | 0.999993i | \(0.498821\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.794896 | −0.0862185 | ||||||||
\(86\) | −7.73863 | − | 8.42757i | −0.834478 | − | 0.908768i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.50575 | + | 8.53912i | −0.373714 | + | 0.910273i | ||||
\(89\) | −13.7441 | − | 7.93517i | −1.45687 | − | 0.841126i | −0.458018 | − | 0.888943i | \(-0.651440\pi\) |
−0.998856 | + | 0.0478167i | \(0.984774\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.43765 | + | 4.50319i | −0.570021 | + | 0.472062i | ||||
\(92\) | −13.4061 | − | 9.34541i | −1.39768 | − | 0.974327i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.560027 | − | 2.51371i | −0.0577624 | − | 0.259269i | ||||
\(95\) | 2.40228 | + | 4.16087i | 0.246469 | + | 0.426896i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.41403 | 0.752781 | 0.376390 | − | 0.926461i | \(-0.377165\pi\) | ||||
0.376390 | + | 0.926461i | \(0.377165\pi\) | |||||||
\(98\) | 5.21945 | + | 8.41174i | 0.527244 | + | 0.849714i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.37018 | + | 3.45551i | −0.737018 | + | 0.345551i | ||||
\(101\) | −1.87642 | + | 1.08335i | −0.186711 | + | 0.107797i | −0.590442 | − | 0.807080i | \(-0.701046\pi\) |
0.403731 | + | 0.914878i | \(0.367713\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.2933 | + | 8.82956i | 1.50689 | + | 0.870003i | 0.999968 | + | 0.00801027i | \(0.00254978\pi\) |
0.506921 | + | 0.861992i | \(0.330784\pi\) | |||||||
\(104\) | −4.61347 | − | 5.97358i | −0.452388 | − | 0.585758i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.62096 | + | 11.5261i | −0.351699 | + | 1.11952i | ||||
\(107\) | −1.77753 | + | 3.07877i | −0.171840 | + | 0.297636i | −0.939063 | − | 0.343744i | \(-0.888305\pi\) |
0.767223 | + | 0.641381i | \(0.221638\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.39239 | − | 2.41168i | −0.133366 | − | 0.230997i | 0.791606 | − | 0.611032i | \(-0.209245\pi\) |
−0.924972 | + | 0.380035i | \(0.875912\pi\) | |||||||
\(110\) | −3.01039 | − | 3.27839i | −0.287029 | − | 0.312582i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.17723 | + | 5.27052i | −0.867167 | + | 0.498018i | ||||
\(113\) | 3.09703i | 0.291344i | 0.989333 | + | 0.145672i | \(0.0465344\pi\) | ||||
−0.989333 | + | 0.145672i | \(0.953466\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.82406 | − | 3.93987i | 0.636347 | − | 0.367395i | ||||
\(116\) | 15.3687 | + | 1.31228i | 1.42695 | + | 0.121842i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.642864 | − | 0.201957i | −0.0591804 | − | 0.0185917i | ||||
\(119\) | −0.759111 | + | 2.04444i | −0.0695876 | + | 0.187414i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.174577 | − | 0.302376i | 0.0158706 | − | 0.0274887i | ||||
\(122\) | −1.28784 | − | 5.78051i | −0.116595 | − | 0.523343i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.84957 | − | 14.6093i | −0.615109 | − | 1.31195i | ||||
\(125\) | − | 8.74674i | − | 0.782332i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.308166i | − | 0.0273454i | −0.999907 | − | 0.0136727i | \(-0.995648\pi\) | ||
0.999907 | − | 0.0136727i | \(-0.00435228\pi\) | |||||||
\(128\) | −5.29724 | − | 9.99696i | −0.468214 | − | 0.883615i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.55225 | − | 0.791404i | 0.311553 | − | 0.0694107i | ||||
\(131\) | −1.18854 | + | 2.05862i | −0.103843 | + | 0.179862i | −0.913265 | − | 0.407366i | \(-0.866447\pi\) |
0.809422 | + | 0.587228i | \(0.199781\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.9957 | − | 2.20502i | 1.12687 | − | 0.191200i | ||||
\(134\) | −3.60537 | + | 11.4765i | −0.311457 | + | 0.991420i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.15672 | − | 0.885443i | −0.184937 | − | 0.0759261i | ||||
\(137\) | −2.58499 | + | 1.49245i | −0.220851 | + | 0.127508i | −0.606344 | − | 0.795202i | \(-0.707365\pi\) |
0.385493 | + | 0.922711i | \(0.374031\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 11.6534i | − | 0.988427i | −0.869340 | − | 0.494214i | \(-0.835456\pi\) | ||
0.869340 | − | 0.494214i | \(-0.164544\pi\) | |||||||
\(140\) | −0.422507 | − | 5.08538i | −0.0357084 | − | 0.429793i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.42164 | − | 6.81494i | 0.622811 | − | 0.571897i | ||||
\(143\) | −4.35443 | − | 7.54210i | −0.364136 | − | 0.630702i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.71871 | + | 6.44100i | −0.308822 | + | 0.534896i | ||||
\(146\) | −15.7743 | − | 4.95553i | −1.30549 | − | 0.410122i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.07430 | − | 5.62861i | −0.663703 | − | 0.462669i | ||||
\(149\) | −10.3895 | − | 5.99838i | −0.851142 | − | 0.491407i | 0.00989432 | − | 0.999951i | \(-0.496850\pi\) |
−0.861036 | + | 0.508544i | \(0.830184\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.42801 | + | 5.44327i | −0.767241 | + | 0.442967i | −0.831889 | − | 0.554941i | \(-0.812741\pi\) |
0.0646486 | + | 0.997908i | \(0.479407\pi\) | |||||||
\(152\) | 1.88304 | + | 13.9652i | 0.152735 | + | 1.13273i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11.3068 | + | 4.61181i | −0.911125 | + | 0.371631i | ||||
\(155\) | 7.78009 | 0.624912 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.33931 | − | 5.78386i | −0.266506 | − | 0.461602i | 0.701451 | − | 0.712718i | \(-0.252536\pi\) |
−0.967957 | + | 0.251115i | \(0.919203\pi\) | |||||||
\(158\) | −5.23058 | + | 1.16532i | −0.416122 | + | 0.0927077i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.44872 | − | 0.266381i | 0.430759 | − | 0.0210593i | ||||
\(161\) | −3.61637 | − | 21.3138i | −0.285010 | − | 1.67976i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.41872 | + | 0.819098i | 0.111123 | + | 0.0641567i | 0.554531 | − | 0.832163i | \(-0.312898\pi\) |
−0.443409 | + | 0.896320i | \(0.646231\pi\) | |||||||
\(164\) | 10.6624 | + | 0.910425i | 0.832595 | + | 0.0710923i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.0702957 | + | 0.0645492i | −0.00545601 | + | 0.00500999i | ||||
\(167\) | −22.9045 | −1.77240 | −0.886201 | − | 0.463302i | \(-0.846665\pi\) | ||||
−0.886201 | + | 0.463302i | \(0.846665\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.87903 | −0.452233 | ||||||||
\(170\) | 0.828019 | − | 0.760330i | 0.0635062 | − | 0.0583147i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 16.1222 | + | 1.37662i | 1.22931 | + | 0.104966i | ||||
\(173\) | 19.6628 | + | 11.3524i | 1.49494 | + | 0.863103i | 0.999983 | − | 0.00581508i | \(-0.00185101\pi\) |
0.494956 | + | 0.868918i | \(0.335184\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.0948 | − | 3.74826i | −0.763098 | − | 0.283341i | ||||
\(176\) | −4.51597 | − | 12.2482i | −0.340404 | − | 0.923246i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 21.9070 | − | 4.88064i | 1.64200 | − | 0.365819i | ||||
\(179\) | 2.13289 | + | 3.69428i | 0.159420 | + | 0.276123i | 0.934660 | − | 0.355544i | \(-0.115704\pi\) |
−0.775240 | + | 0.631667i | \(0.782371\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.8046 | −1.47206 | −0.736032 | − | 0.676947i | \(-0.763303\pi\) | ||||
−0.736032 | + | 0.676947i | \(0.763303\pi\) | |||||||
\(182\) | 1.35687 | − | 9.89204i | 0.100578 | − | 0.733247i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 22.9038 | − | 3.08830i | 1.68849 | − | 0.227672i | ||||
\(185\) | 4.11004 | − | 2.37293i | 0.302176 | − | 0.174461i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.32967 | − | 1.34504i | −0.170363 | − | 0.0983588i | ||||
\(188\) | 2.98776 | + | 2.08278i | 0.217905 | + | 0.151902i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.48232 | − | 2.03643i | −0.470277 | − | 0.147738i | ||||
\(191\) | 9.06556 | − | 15.7020i | 0.655961 | − | 1.13616i | −0.325691 | − | 0.945476i | \(-0.605597\pi\) |
0.981652 | − | 0.190681i | \(-0.0610697\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.9282 | − | 20.6602i | −0.858610 | − | 1.48716i | −0.873255 | − | 0.487263i | \(-0.837995\pi\) |
0.0146458 | − | 0.999893i | \(-0.495338\pi\) | |||||||
\(194\) | −7.72297 | + | 7.09164i | −0.554477 | + | 0.509150i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.4829 | − | 3.76977i | −0.963065 | − | 0.269269i | ||||
\(197\) | − | 17.9765i | − | 1.28077i | −0.768052 | − | 0.640387i | \(-0.778774\pi\) | ||
0.768052 | − | 0.640387i | \(-0.221226\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.86082 | − | 2.22904i | 0.273686 | − | 0.158013i | −0.356876 | − | 0.934152i | \(-0.616158\pi\) |
0.630562 | + | 0.776139i | \(0.282825\pi\) | |||||||
\(200\) | 4.37204 | − | 10.6492i | 0.309150 | − | 0.753012i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.918367 | − | 2.92332i | 0.0646161 | − | 0.205684i | ||||
\(203\) | 13.0147 | + | 15.7155i | 0.913456 | + | 1.10301i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.57995 | + | 4.46860i | −0.180191 | + | 0.312101i | ||||
\(206\) | −24.3761 | + | 5.43075i | −1.69837 | + | 0.378378i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.5195 | + | 1.80965i | 0.729399 | + | 0.125476i | ||||
\(209\) | 16.2595i | 1.12469i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1.53384i | − | 0.105594i | −0.998605 | − | 0.0527970i | \(-0.983186\pi\) | ||
0.998605 | − | 0.0527970i | \(-0.0168136\pi\) | |||||||
\(212\) | −7.25309 | − | 15.4699i | −0.498144 | − | 1.06248i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.09330 | − | 4.90730i | −0.0747362 | − | 0.335456i | ||||
\(215\) | −3.90104 | + | 6.75679i | −0.266048 | + | 0.460809i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.42985 | − | 20.0101i | 0.504371 | − | 1.35838i | ||||
\(218\) | 3.75722 | + | 1.18034i | 0.254471 | + | 0.0799426i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.27166 | + | 0.535515i | 0.422835 | + | 0.0361044i | ||||
\(221\) | 1.90490 | − | 1.09979i | 0.128137 | − | 0.0739802i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 0.996362i | − | 0.0667213i | −0.999443 | − | 0.0333607i | \(-0.989379\pi\) | ||
0.999443 | − | 0.0333607i | \(-0.0106210\pi\) | |||||||
\(224\) | 4.51831 | − | 14.2683i | 0.301892 | − | 0.953342i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.96236 | − | 3.22608i | −0.197053 | − | 0.214596i | ||||
\(227\) | −14.2085 | − | 24.6099i | −0.943053 | − | 1.63342i | −0.759603 | − | 0.650387i | \(-0.774607\pi\) |
−0.183450 | − | 0.983029i | \(-0.558727\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.5125 | + | 23.4043i | −0.892932 | + | 1.54660i | −0.0565877 | + | 0.998398i | \(0.518022\pi\) |
−0.836344 | + | 0.548205i | \(0.815311\pi\) | |||||||
\(230\) | −3.33987 | + | 10.6314i | −0.220224 | + | 0.701012i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −17.2643 | + | 13.3335i | −1.13346 | + | 0.875384i | ||||
\(233\) | −15.9500 | − | 9.20872i | −1.04492 | − | 0.603283i | −0.123695 | − | 0.992320i | \(-0.539475\pi\) |
−0.921222 | + | 0.389037i | \(0.872808\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.52085 | + | 0.878065i | −0.0992095 | + | 0.0572787i | ||||
\(236\) | 0.862827 | − | 0.404537i | 0.0561653 | − | 0.0263331i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.16480 | − | 2.85574i | −0.0755028 | − | 0.185110i | ||||
\(239\) | −0.547163 | −0.0353930 | −0.0176965 | − | 0.999843i | \(-0.505633\pi\) | ||||
−0.0176965 | + | 0.999843i | \(0.505633\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.94128 | + | 10.2906i | 0.382712 | + | 0.662876i | 0.991449 | − | 0.130496i | \(-0.0416569\pi\) |
−0.608737 | + | 0.793372i | \(0.708324\pi\) | |||||||
\(242\) | 0.107376 | + | 0.481962i | 0.00690240 | + | 0.0309817i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.87066 | + | 4.78955i | 0.439849 | + | 0.306620i | ||||
\(245\) | 4.40559 | − | 5.11469i | 0.281463 | − | 0.326765i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.5137 | − | 6.64744i | −0.732600 | − | 0.422967i | ||||
\(248\) | 21.1090 | + | 8.66633i | 1.34042 | + | 0.550313i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.36639 | + | 9.11121i | 0.529137 | + | 0.576244i | ||||
\(251\) | −20.1885 | −1.27429 | −0.637143 | − | 0.770746i | \(-0.719884\pi\) | ||||
−0.637143 | + | 0.770746i | \(0.719884\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.6665 | 1.67651 | ||||||||
\(254\) | 0.294766 | + | 0.321008i | 0.0184953 | + | 0.0201418i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.0802 | + | 5.34664i | 0.942515 | + | 0.334165i | ||||
\(257\) | −7.44631 | − | 4.29913i | −0.464488 | − | 0.268172i | 0.249442 | − | 0.968390i | \(-0.419753\pi\) |
−0.713929 | + | 0.700218i | \(0.753086\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.17809 | − | 12.8370i | −0.135340 | − | 0.797651i | ||||
\(260\) | −2.94328 | + | 4.22216i | −0.182534 | + | 0.261847i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.731030 | − | 3.28126i | −0.0451632 | − | 0.202717i | ||||
\(263\) | 8.76014 | + | 15.1730i | 0.540173 | + | 0.935607i | 0.998894 | + | 0.0470268i | \(0.0149746\pi\) |
−0.458720 | + | 0.888581i | \(0.651692\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.23844 | 0.506083 | ||||||||
\(266\) | −11.4281 | + | 14.7275i | −0.700704 | + | 0.903004i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.22186 | − | 15.4033i | −0.441145 | − | 0.940909i | ||||
\(269\) | −6.65653 | + | 3.84315i | −0.405856 | + | 0.234321i | −0.689008 | − | 0.724754i | \(-0.741953\pi\) |
0.283152 | + | 0.959075i | \(0.408620\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.4624 | − | 11.8140i | −1.24300 | − | 0.717649i | −0.273300 | − | 0.961929i | \(-0.588115\pi\) |
−0.969705 | + | 0.244280i | \(0.921448\pi\) | |||||||
\(272\) | 3.09353 | − | 1.14059i | 0.187573 | − | 0.0691587i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.26516 | − | 4.02722i | 0.0764312 | − | 0.243294i | ||||
\(275\) | 6.64138 | − | 11.5032i | 0.400490 | − | 0.693669i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.9596 | − | 20.7147i | −0.718584 | − | 1.24462i | −0.961561 | − | 0.274592i | \(-0.911457\pi\) |
0.242977 | − | 0.970032i | \(-0.421876\pi\) | |||||||
\(278\) | 11.1467 | + | 12.1390i | 0.668532 | + | 0.728048i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.30436 | + | 4.89315i | 0.316996 | + | 0.292422i | ||||
\(281\) | − | 2.87579i | − | 0.171555i | −0.996314 | − | 0.0857777i | \(-0.972663\pi\) | ||
0.996314 | − | 0.0857777i | \(-0.0273375\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.2157 | + | 5.89802i | −0.607258 | + | 0.350601i | −0.771892 | − | 0.635754i | \(-0.780689\pi\) |
0.164633 | + | 0.986355i | \(0.447356\pi\) | |||||||
\(284\) | −1.21230 | + | 14.1978i | −0.0719370 | + | 0.842487i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.7500 | + | 3.69129i | 0.694793 | + | 0.218271i | ||||
\(287\) | 9.02929 | + | 10.9030i | 0.532982 | + | 0.643582i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.16029 | + | 14.1340i | −0.480017 | + | 0.831413i | ||||
\(290\) | −2.28725 | − | 10.2664i | −0.134312 | − | 0.602864i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 21.1716 | − | 9.92633i | 1.23898 | − | 0.580895i | ||||
\(293\) | 29.0652i | 1.69801i | 0.528387 | + | 0.849003i | \(0.322797\pi\) | ||||
−0.528387 | + | 0.849003i | \(0.677203\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.459494i | 0.0267528i | ||||||||
\(296\) | 13.7946 | − | 1.86004i | 0.801795 | − | 0.108113i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.5600 | − | 3.68939i | 0.959295 | − | 0.213721i | ||||
\(299\) | −10.9022 | + | 18.8831i | −0.630490 | + | 1.09204i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.6528 | + | 16.4859i | 0.786936 | + | 0.950234i | ||||
\(302\) | 4.61431 | − | 14.6881i | 0.265524 | − | 0.845207i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −15.3195 | − | 12.7460i | −0.878632 | − | 0.731033i | ||||
\(305\) | −3.49735 | + | 2.01920i | −0.200258 | + | 0.115619i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.4085i | 1.73551i | 0.496995 | + | 0.867754i | \(0.334437\pi\) | ||||
−0.496995 | + | 0.867754i | \(0.665563\pi\) | |||||||
\(308\) | 7.36665 | − | 15.6191i | 0.419754 | − | 0.889981i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.10429 | + | 7.44179i | −0.460293 | + | 0.422665i | ||||
\(311\) | 12.8735 | + | 22.2975i | 0.729988 | + | 1.26438i | 0.956888 | + | 0.290458i | \(0.0938077\pi\) |
−0.226900 | + | 0.973918i | \(0.572859\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.5546 | + | 25.2092i | −0.822673 | + | 1.42491i | 0.0810126 | + | 0.996713i | \(0.474185\pi\) |
−0.903685 | + | 0.428198i | \(0.859149\pi\) | |||||||
\(314\) | 9.01082 | + | 2.83077i | 0.508510 | + | 0.159750i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.33389 | − | 6.21701i | 0.243800 | − | 0.349734i | ||||
\(317\) | 23.3028 | + | 13.4539i | 1.30881 | + | 0.755644i | 0.981898 | − | 0.189410i | \(-0.0606576\pi\) |
0.326915 | + | 0.945054i | \(0.393991\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.7975 | + | 12.5848i | −1.22043 | + | 0.704615i | ||||
\(320\) | −5.42097 | + | 5.48927i | −0.303042 | + | 0.306860i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 24.1540 | + | 18.7428i | 1.34605 | + | 1.04450i | ||||
\(323\) | −4.10665 | −0.228500 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.43045 | + | 9.40581i | 0.301227 | + | 0.521740i | ||||
\(326\) | −2.26132 | + | 0.503798i | −0.125243 | + | 0.0279028i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −11.9776 | + | 9.25041i | −0.661350 | + | 0.510768i | ||||
\(329\) | 0.805967 | + | 4.75012i | 0.0444344 | + | 0.261883i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.1236 | − | 7.57689i | −0.721336 | − | 0.416464i | 0.0939082 | − | 0.995581i | \(-0.470064\pi\) |
−0.815244 | + | 0.579117i | \(0.803397\pi\) | |||||||
\(332\) | 0.0114826 | − | 0.134478i | 0.000630189 | − | 0.00738044i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 23.8589 | − | 21.9085i | 1.30550 | − | 1.19878i | ||||
\(335\) | 8.20296 | 0.448176 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.6582 | 0.907429 | 0.453715 | − | 0.891147i | \(-0.350099\pi\) | ||||
0.453715 | + | 0.891147i | \(0.350099\pi\) | |||||||
\(338\) | 6.12401 | − | 5.62339i | 0.333103 | − | 0.305872i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.135254 | + | 1.58403i | −0.00733520 | + | 0.0859059i | ||||
\(341\) | 22.8018 | + | 13.1646i | 1.23479 | + | 0.712905i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.94754 | − | 16.2155i | −0.483122 | − | 0.875553i | ||||
\(344\) | −18.1108 | + | 13.9872i | −0.976468 | + | 0.754138i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −31.3409 | + | 6.98243i | −1.68490 | + | 0.375378i | ||||
\(347\) | −10.2420 | − | 17.7397i | −0.549822 | − | 0.952319i | −0.998286 | − | 0.0585187i | \(-0.981362\pi\) |
0.448464 | − | 0.893801i | \(-0.351971\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.97866 | −0.373559 | −0.186780 | − | 0.982402i | \(-0.559805\pi\) | ||||
−0.186780 | + | 0.982402i | \(0.559805\pi\) | |||||||
\(350\) | 14.1008 | − | 5.75143i | 0.753717 | − | 0.307427i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.4198 | + | 8.43903i | 0.875178 | + | 0.449802i | ||||
\(353\) | −25.7521 | + | 14.8680i | −1.37064 | + | 0.791342i | −0.991009 | − | 0.133794i | \(-0.957284\pi\) |
−0.379635 | + | 0.925136i | \(0.623951\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.95029 | − | 3.43540i | −0.315809 | − | 0.182332i | ||||
\(356\) | −18.1514 | + | 26.0384i | −0.962023 | + | 1.38003i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.75541 | − | 1.80807i | −0.304183 | − | 0.0955597i | ||||
\(359\) | 1.93429 | − | 3.35029i | 0.102088 | − | 0.176821i | −0.810457 | − | 0.585798i | \(-0.800781\pi\) |
0.912545 | + | 0.408977i | \(0.134114\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.91082 | + | 5.04169i | 0.153201 | + | 0.265352i | ||||
\(362\) | 20.6298 | − | 18.9434i | 1.08428 | − | 0.995643i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.04848 | + | 11.6021i | 0.421855 | + | 0.608116i | ||||
\(365\) | 11.2748i | 0.590152i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.5077 | + | 6.64395i | −0.600695 | + | 0.346811i | −0.769315 | − | 0.638870i | \(-0.779402\pi\) |
0.168620 | + | 0.985681i | \(0.446069\pi\) | |||||||
\(368\) | −20.9042 | + | 25.1248i | −1.08970 | + | 1.30972i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.01156 | + | 6.40313i | −0.104576 | + | 0.332883i | ||||
\(371\) | 7.86756 | − | 21.1890i | 0.408463 | − | 1.10008i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.708016 | + | 1.22632i | −0.0366597 | + | 0.0634964i | −0.883773 | − | 0.467916i | \(-0.845005\pi\) |
0.847113 | + | 0.531412i | \(0.178338\pi\) | |||||||
\(374\) | 3.71330 | − | 0.827284i | 0.192010 | − | 0.0427778i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.10448 | + | 0.688278i | −0.263243 | + | 0.0354952i | ||||
\(377\) | − | 20.5804i | − | 1.05995i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 32.9449i | − | 1.69227i | −0.532972 | − | 0.846133i | \(-0.678925\pi\) | ||
0.532972 | − | 0.846133i | \(-0.321075\pi\) | |||||||
\(380\) | 8.70032 | − | 4.07915i | 0.446317 | − | 0.209256i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.57590 | + | 25.0277i | 0.285288 | + | 1.28053i | ||||
\(383\) | 18.6554 | − | 32.3121i | 0.953245 | − | 1.65107i | 0.214911 | − | 0.976634i | \(-0.431054\pi\) |
0.738334 | − | 0.674435i | \(-0.235613\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.31105 | + | 6.41316i | 0.270676 | + | 0.326845i | ||||
\(386\) | 32.1871 | + | 10.1116i | 1.63828 | + | 0.514669i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.26152 | − | 14.7743i | 0.0640442 | − | 0.750051i | ||||
\(389\) | 14.4005 | − | 8.31416i | 0.730136 | − | 0.421545i | −0.0883356 | − | 0.996091i | \(-0.528155\pi\) |
0.818472 | + | 0.574546i | \(0.194821\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.73514i | 0.340611i | ||||||||
\(392\) | 17.6506 | − | 8.96976i | 0.891489 | − | 0.453041i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 17.1948 | + | 18.7256i | 0.866264 | + | 0.943383i | ||||
\(395\) | 1.82710 | + | 3.16463i | 0.0919313 | + | 0.159230i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.47847 | − | 7.75695i | 0.224768 | − | 0.389310i | −0.731482 | − | 0.681861i | \(-0.761171\pi\) |
0.956250 | + | 0.292551i | \(0.0945042\pi\) | |||||||
\(398\) | −1.88958 | + | 6.01486i | −0.0947161 | + | 0.301498i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.63190 | + | 15.2749i | 0.281595 | + | 0.763744i | ||||
\(401\) | −13.8311 | − | 7.98541i | −0.690694 | − | 0.398772i | 0.113178 | − | 0.993575i | \(-0.463897\pi\) |
−0.803872 | + | 0.594802i | \(0.797230\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.6443 | + | 10.7643i | −0.928741 | + | 0.536209i | ||||
\(404\) | 1.83957 | + | 3.92357i | 0.0915218 | + | 0.195205i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −28.5891 | − | 3.92151i | −1.41886 | − | 0.194621i | ||||
\(407\) | 16.0609 | 0.796108 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.5816 | + | 20.0600i | 0.572674 | + | 0.991901i | 0.996290 | + | 0.0860589i | \(0.0274273\pi\) |
−0.423616 | + | 0.905842i | \(0.639239\pi\) | |||||||
\(410\) | −1.58683 | − | 7.12257i | −0.0783681 | − | 0.351759i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 20.1973 | − | 28.9732i | 0.995050 | − | 1.42741i | ||||
\(413\) | 1.18180 | + | 0.438809i | 0.0581527 | + | 0.0215924i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.0563595 | + | 0.0325392i | 0.00276658 | + | 0.00159729i | ||||
\(416\) | −12.6888 | + | 8.17705i | −0.622122 | + | 0.400913i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −15.5525 | − | 16.9370i | −0.760697 | − | 0.828418i | ||||
\(419\) | 8.76342 | 0.428121 | 0.214061 | − | 0.976820i | \(-0.431331\pi\) | ||||
0.214061 | + | 0.976820i | \(0.431331\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.2524 | 0.743356 | 0.371678 | − | 0.928362i | \(-0.378782\pi\) | ||||
0.371678 | + | 0.928362i | \(0.378782\pi\) | |||||||
\(422\) | 1.46714 | + | 1.59776i | 0.0714195 | + | 0.0777776i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 22.3526 | + | 9.17688i | 1.08554 | + | 0.445669i | ||||
\(425\) | 2.90535 | + | 1.67741i | 0.140930 | + | 0.0813661i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.85340 | + | 10.9234i | 0.0896922 | + | 0.528619i | ||||
\(428\) | 5.83277 | + | 4.06604i | 0.281938 | + | 0.196539i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.39939 | − | 10.7698i | −0.115709 | − | 0.519364i | ||||
\(431\) | 1.89646 | + | 3.28476i | 0.0913492 | + | 0.158221i | 0.908079 | − | 0.418799i | \(-0.137549\pi\) |
−0.816730 | + | 0.577020i | \(0.804215\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −39.7504 | −1.91028 | −0.955142 | − | 0.296147i | \(-0.904298\pi\) | ||||
−0.955142 | + | 0.296147i | \(0.904298\pi\) | |||||||
\(434\) | 11.4006 | + | 27.9507i | 0.547245 | + | 1.34168i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.04280 | + | 2.36432i | −0.241506 | + | 0.113230i | ||||
\(437\) | 35.2550 | − | 20.3545i | 1.68647 | − | 0.973686i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.349336 | + | 0.201689i | 0.0166729 | + | 0.00962611i | 0.508313 | − | 0.861172i | \(-0.330269\pi\) |
−0.491640 | + | 0.870798i | \(0.663603\pi\) | |||||||
\(440\) | −7.04523 | + | 5.44112i | −0.335868 | + | 0.259395i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.932306 | + | 2.96769i | −0.0443453 | + | 0.141159i | ||||
\(443\) | 2.07536 | − | 3.59463i | 0.0986032 | − | 0.170786i | −0.812504 | − | 0.582956i | \(-0.801896\pi\) |
0.911107 | + | 0.412171i | \(0.135229\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.65234 | − | 13.2542i | −0.362756 | − | 0.628311i | ||||
\(446\) | 0.953036 | + | 1.03788i | 0.0451276 | + | 0.0491451i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.94129 | + | 19.1847i | 0.422436 | + | 0.906393i | ||||
\(449\) | 21.3129i | 1.00582i | 0.864339 | + | 0.502910i | \(0.167737\pi\) | ||||
−0.864339 | + | 0.502910i | \(0.832263\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.1226 | + | 8.73102i | −0.712094 | + | 0.411128i | ||||
\(452\) | 6.17160 | + | 0.526971i | 0.290288 | + | 0.0247866i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 38.3404 | + | 12.0447i | 1.79940 | + | 0.565286i | ||||
\(455\) | −6.71264 | + | 1.13895i | −0.314693 | + | 0.0533949i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.15571 | − | 15.8582i | 0.428286 | − | 0.741813i | −0.568435 | − | 0.822728i | \(-0.692451\pi\) |
0.996721 | + | 0.0809150i | \(0.0257842\pi\) | |||||||
\(458\) | −8.31106 | − | 37.3045i | −0.388350 | − | 1.74313i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.69004 | − | 14.2690i | −0.311925 | − | 0.665297i | ||||
\(461\) | 13.5275i | 0.630040i | 0.949085 | + | 0.315020i | \(0.102011\pi\) | ||||
−0.949085 | + | 0.315020i | \(0.897989\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.7296i | 0.545121i | 0.962139 | + | 0.272560i | \(0.0878704\pi\) | ||||
−0.962139 | + | 0.272560i | \(0.912130\pi\) | |||||||
\(464\) | 5.23009 | − | 30.4027i | 0.242801 | − | 1.41141i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25.4229 | − | 5.66396i | 1.17769 | − | 0.262378i | ||||
\(467\) | 2.64703 | − | 4.58479i | 0.122490 | − | 0.212159i | −0.798259 | − | 0.602314i | \(-0.794245\pi\) |
0.920749 | + | 0.390155i | \(0.127579\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.83368 | − | 21.0978i | 0.361726 | − | 0.974204i | ||||
\(470\) | 0.744344 | − | 2.36938i | 0.0343340 | − | 0.109291i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.511835 | + | 1.24670i | −0.0235591 | + | 0.0573841i | ||||
\(473\) | −22.8662 | + | 13.2018i | −1.05139 | + | 0.607021i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 20.2774i | − | 0.930389i | ||||||
\(476\) | 3.94490 | + | 1.86059i | 0.180814 | + | 0.0852799i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.569963 | − | 0.523370i | 0.0260695 | − | 0.0239384i | ||||
\(479\) | −1.19209 | − | 2.06475i | −0.0544678 | − | 0.0943410i | 0.837506 | − | 0.546428i | \(-0.184013\pi\) |
−0.891974 | + | 0.452087i | \(0.850680\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.56624 | + | 11.3731i | −0.299395 | + | 0.518567i | ||||
\(482\) | −16.0320 | − | 5.03648i | −0.730237 | − | 0.229406i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.572855 | − | 0.399339i | −0.0260389 | − | 0.0181518i | ||||
\(485\) | 6.19189 | + | 3.57489i | 0.281159 | + | 0.162327i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.7730 | − | 11.9933i | 0.941314 | − | 0.543468i | 0.0509423 | − | 0.998702i | \(-0.483778\pi\) |
0.890372 | + | 0.455233i | \(0.150444\pi\) | |||||||
\(488\) | −11.7382 | + | 1.58276i | −0.531365 | + | 0.0716482i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.303103 | + | 9.54184i | 0.0136928 | + | 0.431056i | ||||
\(491\) | −19.8907 | −0.897654 | −0.448827 | − | 0.893619i | \(-0.648158\pi\) | ||||
−0.448827 | + | 0.893619i | \(0.648158\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.17854 | − | 5.50538i | −0.143154 | − | 0.247950i | ||||
\(494\) | 18.3519 | − | 4.08861i | 0.825690 | − | 0.183955i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −30.2781 | + | 11.1636i | −1.35953 | + | 0.501263i | ||||
\(497\) | −14.5182 | + | 12.0232i | −0.651229 | + | 0.539315i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.70480 | − | 4.44837i | −0.344914 | − | 0.199136i | 0.317529 | − | 0.948249i | \(-0.397147\pi\) |
−0.662443 | + | 0.749112i | \(0.730480\pi\) | |||||||
\(500\) | −17.4300 | − | 1.48829i | −0.779495 | − | 0.0665583i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21.0297 | − | 19.3106i | 0.938604 | − | 0.861875i | ||||
\(503\) | 21.6446 | 0.965086 | 0.482543 | − | 0.875872i | \(-0.339713\pi\) | ||||
0.482543 | + | 0.875872i | \(0.339713\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.08947 | −0.0929804 | ||||||||
\(506\) | −27.7777 | + | 25.5070i | −1.23487 | + | 1.13392i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.614098 | − | 0.0524357i | −0.0272462 | − | 0.00232646i | ||||
\(509\) | 17.7650 | + | 10.2566i | 0.787421 | + | 0.454618i | 0.839054 | − | 0.544048i | \(-0.183109\pi\) |
−0.0516327 | + | 0.998666i | \(0.516443\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.9985 | + | 10.7673i | 1.28282 | + | 0.476316i | ||||
\(512\) | −20.8228 | + | 8.85505i | −0.920246 | + | 0.391342i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.8688 | − | 2.64424i | 0.523509 | − | 0.116632i | ||||
\(515\) | 8.51485 | + | 14.7482i | 0.375209 | + | 0.649882i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.94307 | −0.261376 | ||||||||
\(518\) | 14.5476 | + | 11.2885i | 0.639186 | + | 0.495989i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.972640 | − | 7.21340i | −0.0426531 | − | 0.316328i | ||||
\(521\) | −13.5376 | + | 7.81591i | −0.593091 | + | 0.342421i | −0.766319 | − | 0.642460i | \(-0.777914\pi\) |
0.173228 | + | 0.984882i | \(0.444580\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.5412 | + | 13.0142i | 0.985657 | + | 0.569069i | 0.903973 | − | 0.427589i | \(-0.140637\pi\) |
0.0816838 | + | 0.996658i | \(0.473970\pi\) | |||||||
\(524\) | 3.90007 | + | 2.71875i | 0.170375 | + | 0.118769i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23.6384 | − | 7.42605i | −1.03068 | − | 0.323791i | ||||
\(527\) | −3.32498 | + | 5.75903i | −0.144838 | + | 0.250867i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.8825 | − | 37.9016i | −0.951412 | − | 1.64789i | ||||
\(530\) | −8.58174 | + | 7.88020i | −0.372767 | + | 0.342294i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.18279 | − | 26.2724i | −0.0946358 | − | 1.13906i | ||||
\(533\) | − | 14.2782i | − | 0.618456i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.96904 | + | 1.71417i | −0.128363 | + | 0.0741102i | ||||
\(536\) | 22.2563 | + | 9.13737i | 0.961328 | + | 0.394674i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.25788 | − | 10.3704i | 0.140457 | − | 0.447099i | ||||
\(539\) | 21.5664 | − | 7.53540i | 0.928930 | − | 0.324573i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0968 | + | 31.3446i | −0.778044 | + | 1.34761i | 0.155024 | + | 0.987911i | \(0.450455\pi\) |
−0.933068 | + | 0.359701i | \(0.882879\pi\) | |||||||
\(542\) | 32.6154 | − | 7.26637i | 1.40095 | − | 0.312117i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.13144 | + | 4.14713i | −0.0913847 | + | 0.177807i | ||||
\(545\) | − | 2.68551i | − | 0.115035i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 32.5689i | − | 1.39255i | −0.717777 | − | 0.696273i | \(-0.754840\pi\) | ||
0.717777 | − | 0.696273i | \(-0.245160\pi\) | |||||||
\(548\) | 2.53422 | + | 5.40519i | 0.108257 | + | 0.230898i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.08487 | + | 18.3351i | 0.174180 | + | 0.781812i | ||||
\(551\) | −19.2119 | + | 33.2760i | −0.818454 | + | 1.41760i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.88416 | − | 1.67707i | 0.420317 | − | 0.0713164i | ||||
\(554\) | 32.2719 | + | 10.1383i | 1.37110 | + | 0.430735i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −23.2223 | − | 1.98287i | −0.984844 | − | 0.0840923i | ||||
\(557\) | 15.6704 | − | 9.04732i | 0.663977 | − | 0.383347i | −0.129814 | − | 0.991538i | \(-0.541438\pi\) |
0.793791 | + | 0.608191i | \(0.208105\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 21.5894i | − | 0.913136i | ||||||
\(560\) | −10.2058 | − | 0.0233456i | −0.431273 | − | 0.000986532i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.75074 | + | 2.99563i | 0.116033 | + | 0.126363i | ||||
\(563\) | 9.24225 | + | 16.0081i | 0.389515 | + | 0.674659i | 0.992384 | − | 0.123181i | \(-0.0393094\pi\) |
−0.602870 | + | 0.797840i | \(0.705976\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.49332 | + | 2.58651i | −0.0628245 | + | 0.108815i | ||||
\(566\) | 4.99980 | − | 15.9152i | 0.210157 | − | 0.668967i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.3176 | − | 15.9491i | −0.516837 | − | 0.669208i | ||||
\(569\) | −38.6356 | − | 22.3063i | −1.61969 | − | 0.935127i | −0.987000 | − | 0.160719i | \(-0.948619\pi\) |
−0.632687 | − | 0.774407i | \(-0.718048\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.2316 | + | 12.8354i | −0.930363 | + | 0.537145i | −0.886926 | − | 0.461911i | \(-0.847164\pi\) |
−0.0434368 | + | 0.999056i | \(0.513831\pi\) | |||||||
\(572\) | −15.7704 | + | 7.39397i | −0.659395 | + | 0.309158i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19.8344 | − | 2.72064i | −0.827872 | − | 0.113557i | ||||
\(575\) | −33.2560 | −1.38687 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.0417 | − | 20.8568i | −0.501302 | − | 0.868281i | −0.999999 | − | 0.00150416i | \(-0.999521\pi\) |
0.498697 | − | 0.866777i | \(-0.333812\pi\) | |||||||
\(578\) | −5.01910 | − | 22.5284i | −0.208767 | − | 0.937060i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12.2025 | + | 8.50642i | 0.506683 | + | 0.353210i | ||||
\(581\) | 0.137512 | − | 0.113880i | 0.00570496 | − | 0.00472456i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.1451 | + | 13.9402i | 0.999989 | + | 0.577344i | ||||
\(584\) | −12.5592 | + | 30.5910i | −0.519702 | + | 1.26586i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27.8013 | − | 30.2764i | −1.14846 | − | 1.25070i | ||||
\(587\) | −13.1811 | −0.544044 | −0.272022 | − | 0.962291i | \(-0.587692\pi\) | ||||
−0.272022 | + | 0.962291i | \(0.587692\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 40.1941 | 1.65617 | ||||||||
\(590\) | −0.439513 | − | 0.478641i | −0.0180945 | − | 0.0197053i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.5903 | + | 15.1323i | −0.517457 | + | 0.621934i | ||||
\(593\) | −13.8913 | − | 8.02017i | −0.570449 | − | 0.329349i | 0.186879 | − | 0.982383i | \(-0.440163\pi\) |
−0.757329 | + | 0.653034i | \(0.773496\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.61977 | + | 1.34141i | −0.0664039 | + | 0.0549923i | ||||
\(596\) | −13.7211 | + | 19.6830i | −0.562038 | + | 0.806248i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.70555 | − | 30.0981i | −0.274210 | − | 1.23080i | ||||
\(599\) | 2.93188 | + | 5.07816i | 0.119793 | + | 0.207488i | 0.919686 | − | 0.392655i | \(-0.128444\pi\) |
−0.799892 | + | 0.600143i | \(0.795110\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.63145 | −0.270503 | −0.135251 | − | 0.990811i | \(-0.543184\pi\) | ||||
−0.135251 | + | 0.990811i | \(0.543184\pi\) | |||||||
\(602\) | −29.9908 | − | 4.11378i | −1.22233 | − | 0.167665i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.24285 | + | 19.7139i | 0.376086 | + | 0.802145i | ||||
\(605\) | 0.291599 | − | 0.168355i | 0.0118552 | − | 0.00684459i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.127387 | + | 0.0735469i | 0.00517048 | + | 0.00298518i | 0.502583 | − | 0.864529i | \(-0.332383\pi\) |
−0.497413 | + | 0.867514i | \(0.665716\pi\) | |||||||
\(608\) | 28.1496 | − | 1.37620i | 1.14162 | − | 0.0558121i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.71169 | − | 5.44861i | 0.0693044 | − | 0.220608i | ||||
\(611\) | 2.42973 | − | 4.20842i | 0.0982964 | − | 0.170254i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.2920 | − | 19.5583i | −0.456080 | − | 0.789954i | 0.542669 | − | 0.839946i | \(-0.317414\pi\) |
−0.998750 | + | 0.0499922i | \(0.984080\pi\) | |||||||
\(614\) | −29.0863 | − | 31.6757i | −1.17383 | − | 1.27833i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.26630 | + | 23.3163i | 0.292767 | + | 0.939439i | ||||
\(617\) | − | 35.8659i | − | 1.44391i | −0.691941 | − | 0.721954i | \(-0.743244\pi\) | ||
0.691941 | − | 0.721954i | \(-0.256756\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.40387 | − | 5.42933i | 0.377973 | − | 0.218223i | −0.298963 | − | 0.954265i | \(-0.596641\pi\) |
0.676936 | + | 0.736042i | \(0.263307\pi\) | |||||||
\(620\) | 1.32381 | − | 15.5038i | 0.0531656 | − | 0.622646i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −34.7379 | − | 10.9130i | −1.39286 | − | 0.437570i | ||||
\(623\) | −41.3973 | + | 7.02400i | −1.65855 | + | 0.281411i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.95755 | + | 10.3188i | −0.238302 | + | 0.412751i | ||||
\(626\) | −8.95199 | − | 40.1814i | −0.357794 | − | 1.60597i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.0940 | + | 5.67027i | −0.482602 | + | 0.226268i | ||||
\(629\) | 4.05648i | 0.161742i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 22.1335i | − | 0.881121i | −0.897723 | − | 0.440561i | \(-0.854780\pi\) | ||
0.897723 | − | 0.440561i | \(-0.145220\pi\) | |||||||
\(632\) | 1.43218 | + | 10.6215i | 0.0569692 | + | 0.422501i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −37.1426 | + | 8.27498i | −1.47512 | + | 0.328642i | ||||
\(635\) | 0.148591 | − | 0.257368i | 0.00589667 | − | 0.0102133i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.48110 | + | 18.3524i | −0.137926 | + | 0.727147i | ||||
\(638\) | 10.6683 | − | 33.9589i | 0.422361 | − | 1.34445i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.396290 | − | 10.9033i | 0.0156647 | − | 0.430989i | ||||
\(641\) | 18.3363 | − | 10.5865i | 0.724242 | − | 0.418141i | −0.0920699 | − | 0.995753i | \(-0.529348\pi\) |
0.816312 | + | 0.577611i | \(0.196015\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.5277i | 0.572917i | 0.958093 | + | 0.286458i | \(0.0924780\pi\) | ||||
−0.958093 | + | 0.286458i | \(0.907522\pi\) | |||||||
\(644\) | −43.0883 | + | 3.57989i | −1.69792 | + | 0.141068i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.27777 | − | 3.92807i | 0.168307 | − | 0.154548i | ||||
\(647\) | −12.9409 | − | 22.4143i | −0.508760 | − | 0.881198i | −0.999949 | − | 0.0101447i | \(-0.996771\pi\) |
0.491189 | − | 0.871053i | \(-0.336563\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.777506 | + | 1.34668i | −0.0305198 | + | 0.0528618i | ||||
\(650\) | −14.6535 | − | 4.60344i | −0.574759 | − | 0.180562i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.87366 | − | 2.68778i | 0.0733780 | − | 0.105262i | ||||
\(653\) | 18.1532 | + | 10.4808i | 0.710390 | + | 0.410144i | 0.811205 | − | 0.584762i | \(-0.198812\pi\) |
−0.100816 | + | 0.994905i | \(0.532145\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.98524 | + | 1.14618i | −0.0775698 | + | 0.0447849i | ||||
\(656\) | 3.62850 | − | 21.0926i | 0.141669 | − | 0.823528i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.38312 | − | 4.17714i | −0.209856 | − | 0.162842i | ||||
\(659\) | 16.0912 | 0.626826 | 0.313413 | − | 0.949617i | \(-0.398528\pi\) | ||||
0.313413 | + | 0.949617i | \(0.398528\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.274559 | + | 0.475551i | 0.0106791 | + | 0.0184968i | 0.871316 | − | 0.490723i | \(-0.163267\pi\) |
−0.860636 | + | 0.509220i | \(0.829934\pi\) | |||||||
\(662\) | 20.9178 | − | 4.66028i | 0.812995 | − | 0.181127i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.116669 | + | 0.151065i | 0.00452765 | + | 0.00586246i | ||||
\(665\) | 11.9167 | + | 4.42473i | 0.462110 | + | 0.171584i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 54.5745 | + | 31.5086i | 2.11313 | + | 1.22002i | ||||
\(668\) | −3.89728 | + | 45.6429i | −0.150790 | + | 1.76598i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.54478 | + | 7.84627i | −0.330114 | + | 0.303128i | ||||
\(671\) | −13.6667 | −0.527596 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.5345 | 1.33121 | 0.665604 | − | 0.746305i | \(-0.268174\pi\) | ||||
0.665604 | + | 0.746305i | \(0.268174\pi\) | |||||||
\(674\) | −17.3523 | + | 15.9338i | −0.668387 | + | 0.613748i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.00034 | + | 11.7154i | −0.0384746 | + | 0.450594i | ||||
\(677\) | −25.6248 | − | 14.7945i | −0.984841 | − | 0.568598i | −0.0811126 | − | 0.996705i | \(-0.525847\pi\) |
−0.903728 | + | 0.428107i | \(0.859181\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.1076 | − | 12.5114i | 0.579778 | − | 0.480142i | ||||
\(680\) | −1.37426 | − | 1.77941i | −0.0527004 | − | 0.0682371i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −36.3442 | + | 8.09710i | −1.39169 | + | 0.310054i | ||||
\(683\) | −2.69521 | − | 4.66823i | −0.103129 | − | 0.178625i | 0.809843 | − | 0.586647i | \(-0.199552\pi\) |
−0.912972 | + | 0.408021i | \(0.866219\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.87850 | −0.109982 | ||||||||
\(686\) | 24.8307 | + | 8.33271i | 0.948042 | + | 0.318144i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.48651 | − | 31.8933i | 0.209171 | − | 1.21592i | ||||
\(689\) | −19.7427 | + | 11.3985i | −0.752138 | + | 0.434247i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.9683 | + | 19.6116i | 1.29221 | + | 0.746060i | 0.979046 | − | 0.203638i | \(-0.0652766\pi\) |
0.313167 | + | 0.949698i | \(0.398610\pi\) | |||||||
\(692\) | 25.9681 | − | 37.2515i | 0.987159 | − | 1.41609i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.6372 | + | 8.68228i | 1.04909 | + | 0.329575i | ||||
\(695\) | 5.61901 | − | 9.73242i | 0.213141 | − | 0.369172i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.20519 | − | 3.81949i | −0.0835273 | − | 0.144674i | ||||
\(698\) | 7.26946 | − | 6.67520i | 0.275153 | − | 0.252660i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.18701 | + | 19.4787i | −0.347236 | + | 0.736225i | ||||
\(701\) | 30.7510i | 1.16145i | 0.814100 | + | 0.580725i | \(0.197231\pi\) | ||||
−0.814100 | + | 0.580725i | \(0.802769\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.2336 | − | 12.2592i | 0.800839 | − | 0.462365i | ||||
\(704\) | −25.1761 | + | 6.91511i | −0.948859 | + | 0.260623i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.6037 | − | 40.1198i | 0.474347 | − | 1.50993i | ||||
\(707\) | −1.99541 | + | 5.37406i | −0.0750451 | + | 0.202112i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.00634 | + | 12.1353i | −0.263129 | + | 0.455752i | −0.967072 | − | 0.254504i | \(-0.918088\pi\) |
0.703943 | + | 0.710256i | \(0.251421\pi\) | |||||||
\(710\) | 9.48426 | − | 2.11299i | 0.355938 | − | 0.0792993i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.99834 | − | 44.4855i | −0.224797 | − | 1.66717i | ||||
\(713\) | − | 65.9206i | − | 2.46875i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 8.39846i | − | 0.314084i | ||||||
\(716\) | 7.72469 | − | 3.62172i | 0.288685 | − | 0.135350i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.18971 | + | 5.34007i | 0.0443997 | + | 0.199290i | ||||
\(719\) | 18.1147 | − | 31.3756i | 0.675565 | − | 1.17011i | −0.300739 | − | 0.953707i | \(-0.597233\pi\) |
0.976304 | − | 0.216406i | \(-0.0694334\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 46.0633 | − | 7.81569i | 1.71549 | − | 0.291072i | ||||
\(722\) | −7.85458 | − | 2.46753i | −0.292317 | − | 0.0918320i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.36982 | + | 39.4656i | −0.125239 | + | 1.46673i | ||||
\(725\) | 27.1839 | − | 15.6946i | 1.00958 | − | 0.582884i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.5723i | 0.911336i | 0.890150 | + | 0.455668i | \(0.150600\pi\) | ||||
−0.890150 | + | 0.455668i | \(0.849400\pi\) | |||||||
\(728\) | −19.4815 | − | 4.38707i | −0.722031 | − | 0.162596i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.7846 | − | 11.7447i | −0.399155 | − | 0.434690i | ||||
\(731\) | −3.33437 | − | 5.77530i | −0.123326 | − | 0.213607i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.84390 | − | 3.19373i | 0.0681061 | − | 0.117963i | −0.829962 | − | 0.557821i | \(-0.811638\pi\) |
0.898068 | + | 0.439857i | \(0.144971\pi\) | |||||||
\(734\) | 5.63214 | − | 17.9281i | 0.207886 | − | 0.661737i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.25704 | − | 46.1669i | −0.0831957 | − | 1.70174i | ||||
\(737\) | 24.0412 | + | 13.8802i | 0.885568 | + | 0.511283i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.61163 | − | 0.930477i | 0.0592849 | − | 0.0342282i | −0.470065 | − | 0.882632i | \(-0.655769\pi\) |
0.529349 | + | 0.848404i | \(0.322436\pi\) | |||||||
\(740\) | −4.02932 | − | 8.59403i | −0.148121 | − | 0.315923i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.0722 | + | 29.5974i | 0.443185 | + | 1.08655i | ||||
\(743\) | −13.7224 | −0.503425 | −0.251713 | − | 0.967802i | \(-0.580994\pi\) | ||||
−0.251713 | + | 0.967802i | \(0.580994\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.78459 | − | 10.0192i | −0.211931 | − | 0.367075i | ||||
\(746\) | −0.435475 | − | 1.95465i | −0.0159439 | − | 0.0715648i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.07672 | + | 4.41359i | −0.112496 | + | 0.161377i | ||||
\(749\) | 1.57342 | + | 9.27327i | 0.0574916 | + | 0.338838i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.6535 | + | 21.1619i | 1.33751 | + | 0.772210i | 0.986437 | − | 0.164140i | \(-0.0524849\pi\) |
0.351069 | + | 0.936350i | \(0.385818\pi\) | |||||||
\(752\) | 4.65883 | − | 5.59947i | 0.169890 | − | 0.204192i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 19.6855 | + | 21.4380i | 0.716904 | + | 0.780726i | ||||
\(755\) | −10.4985 | −0.382080 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.7909 | 0.646622 | 0.323311 | − | 0.946293i | \(-0.395204\pi\) | ||||
0.323311 | + | 0.946293i | \(0.395204\pi\) | |||||||
\(758\) | 31.5123 | + | 34.3177i | 1.14458 | + | 1.24648i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.16109 | + | 12.5711i | −0.187212 | + | 0.456003i | ||||
\(761\) | −32.0604 | − | 18.5101i | −1.16219 | − | 0.670991i | −0.210362 | − | 0.977624i | \(-0.567464\pi\) |
−0.951828 | + | 0.306633i | \(0.900798\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.90705 | − | 2.56462i | −0.250052 | − | 0.0928454i | ||||
\(764\) | −29.7476 | − | 20.7371i | −1.07623 | − | 0.750243i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.4743 | + | 51.5027i | 0.414582 | + | 1.86087i | ||||
\(767\) | −0.635743 | − | 1.10114i | −0.0229553 | − | 0.0397598i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.9042 | −0.609583 | −0.304791 | − | 0.952419i | \(-0.598587\pi\) | ||||
−0.304791 | + | 0.952419i | \(0.598587\pi\) | |||||||
\(770\) | −11.6667 | − | 1.60029i | −0.420437 | − | 0.0576704i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −43.2003 | + | 20.2545i | −1.55481 | + | 0.728974i | ||||
\(773\) | 4.25588 | − | 2.45713i | 0.153073 | − | 0.0883769i | −0.421507 | − | 0.906825i | \(-0.638499\pi\) |
0.574580 | + | 0.818448i | \(0.305165\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.4363 | − | 16.4177i | −1.02146 | − | 0.589742i | ||||
\(776\) | 12.8178 | + | 16.5966i | 0.460131 | + | 0.595784i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.04799 | + | 22.4350i | −0.252683 | + | 0.804332i | ||||
\(779\) | −13.3287 | + | 23.0860i | −0.477551 | + | 0.827142i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.6260 | − | 20.1369i | −0.416013 | − | 0.720555i | ||||
\(782\) | −6.44227 | − | 7.01579i | −0.230375 | − | 0.250884i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.80637 | + | 26.2266i | −0.350228 | + | 0.936665i | ||||
\(785\) | − | 6.44058i | − | 0.229874i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.4861 | − | 7.78620i | 0.480727 | − | 0.277548i | −0.239992 | − | 0.970775i | \(-0.577145\pi\) |
0.720719 | + | 0.693227i | \(0.243812\pi\) | |||||||
\(788\) | −35.8227 | − | 3.05877i | −1.27613 | − | 0.108964i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.93025 | − | 1.54885i | −0.175410 | − | 0.0551055i | ||||
\(791\) | 5.22632 | + | 6.31084i | 0.185827 | + | 0.224388i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.58740 | − | 9.67767i | 0.198415 | − | 0.343664i | ||||
\(794\) | 2.75455 | + | 12.3639i | 0.0977553 | + | 0.438779i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.78499 | − | 8.07292i | −0.134155 | − | 0.286137i | ||||
\(797\) | − | 30.5378i | − | 1.08170i | −0.841118 | − | 0.540852i | \(-0.818102\pi\) | ||
0.841118 | − | 0.540852i | \(-0.181898\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.50104i | − | 0.0531028i | ||||||
\(800\) | −20.4773 | − | 10.5244i | −0.723980 | − | 0.372093i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22.0457 | − | 4.91154i | 0.778459 | − | 0.173433i | ||||
\(803\) | −19.0781 | + | 33.0442i | −0.673251 | + | 1.16610i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.25681 | − | 19.5441i | 0.255769 | − | 0.688839i | ||||
\(806\) | 9.12501 | − | 29.0465i | 0.321415 | − | 1.02312i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.66918 | − | 2.32749i | −0.199441 | − | 0.0818807i | ||||
\(809\) | −23.8487 | + | 13.7690i | −0.838474 | + | 0.484093i | −0.856745 | − | 0.515740i | \(-0.827517\pi\) |
0.0182712 | + | 0.999833i | \(0.494184\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.3302i | 1.55665i | 0.627865 | + | 0.778323i | \(0.283929\pi\) | ||||
−0.627865 | + | 0.778323i | \(0.716071\pi\) | |||||||
\(812\) | 33.5315 | − | 23.2611i | 1.17672 | − | 0.816303i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.7301 | + | 15.3625i | −0.586391 | + | 0.538455i | ||||
\(815\) | 0.789903 | + | 1.36815i | 0.0276691 | + | 0.0479243i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.1538 | + | 34.9074i | −0.705093 | + | 1.22126i | ||||
\(818\) | −31.2519 | − | 9.81785i | −1.09270 | − | 0.343273i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.46581 | + | 5.90154i | 0.295639 | + | 0.206091i | ||||
\(821\) | −8.92840 | − | 5.15482i | −0.311603 | − | 0.179904i | 0.336040 | − | 0.941848i | \(-0.390912\pi\) |
−0.647644 | + | 0.761943i | \(0.724245\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.74721 | − | 5.05020i | 0.304908 | − | 0.176039i | −0.339737 | − | 0.940520i | \(-0.610338\pi\) |
0.644646 | + | 0.764481i | \(0.277005\pi\) | |||||||
\(824\) | 6.67443 | + | 49.4996i | 0.232515 | + | 1.72440i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.65078 | + | 0.673320i | −0.0574379 | + | 0.0234278i | ||||
\(827\) | 20.6380 | 0.717653 | 0.358827 | − | 0.933404i | \(-0.383177\pi\) | ||||
0.358827 | + | 0.933404i | \(0.383177\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.0292908 | − | 0.0507332i | −0.00101731 | − | 0.00176204i | 0.865516 | − | 0.500881i | \(-0.166990\pi\) |
−0.866534 | + | 0.499119i | \(0.833657\pi\) | |||||||
\(830\) | −0.0898323 | + | 0.0200137i | −0.00311812 | + | 0.000694685i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.39611 | − | 20.6549i | 0.187076 | − | 0.716079i | ||||
\(833\) | 1.90321 | + | 5.44700i | 0.0659422 | + | 0.188727i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.1289 | − | 11.0440i | −0.661981 | − | 0.382195i | ||||
\(836\) | 32.4011 | + | 2.76662i | 1.12062 | + | 0.0956854i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.12859 | + | 8.38235i | −0.315342 | + | 0.289564i | ||||
\(839\) | 13.8295 | 0.477447 | 0.238724 | − | 0.971088i | \(-0.423271\pi\) | ||||
0.238724 | + | 0.971088i | \(0.423271\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.4798 | −1.05103 | ||||||||
\(842\) | −15.8880 | + | 14.5892i | −0.547536 | + | 0.502776i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.05656 | − | 0.260989i | −0.105211 | − | 0.00898361i | ||||
\(845\) | −4.90992 | − | 2.83474i | −0.168906 | − | 0.0975182i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.154531 | − | 0.910758i | −0.00530974 | − | 0.0312940i | ||||
\(848\) | −32.0619 | + | 11.8213i | −1.10101 | + | 0.405946i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.63088 | + | 1.03171i | −0.158838 | + | 0.0353874i | ||||
\(851\) | −20.1058 | − | 34.8243i | −0.689218 | − | 1.19376i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.8632 | 1.50185 | 0.750923 | − | 0.660389i | \(-0.229609\pi\) | ||||
0.750923 | + | 0.660389i | \(0.229609\pi\) | |||||||
\(854\) | −12.3790 | − | 9.60574i | −0.423601 | − | 0.328702i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.96505 | + | 1.34367i | −0.340598 | + | 0.0459256i | ||||
\(857\) | 10.8122 | − | 6.24242i | 0.369337 | − | 0.213237i | −0.303832 | − | 0.952726i | \(-0.598266\pi\) |
0.673169 | + | 0.739489i | \(0.264933\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.19286 | + | 4.73015i | 0.279537 | + | 0.161391i | 0.633214 | − | 0.773977i | \(-0.281735\pi\) |
−0.353677 | + | 0.935368i | \(0.615069\pi\) | |||||||
\(860\) | 12.8008 | + | 8.92348i | 0.436504 | + | 0.304288i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.11741 | − | 1.60765i | −0.174300 | − | 0.0547566i | ||||
\(863\) | −22.9830 | + | 39.8077i | −0.782350 | + | 1.35507i | 0.148220 | + | 0.988954i | \(0.452646\pi\) |
−0.930570 | + | 0.366115i | \(0.880688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.9477 | + | 18.9620i | 0.372234 | + | 0.644728i | ||||
\(866\) | 41.4069 | − | 38.0219i | 1.40706 | − | 1.29204i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −38.6110 | − | 18.2106i | −1.31054 | − | 0.618109i | ||||
\(869\) | 12.3665i | 0.419504i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.6577 | + | 11.3494i | −0.666076 | + | 0.384559i | ||||
\(872\) | 2.99142 | − | 7.28636i | 0.101302 | − | 0.246747i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −17.2547 | + | 54.9246i | −0.583648 | + | 1.85785i | ||||
\(875\) | −14.7603 | − | 17.8233i | −0.498991 | − | 0.602537i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.82605 | − | 10.0910i | 0.196732 | − | 0.340749i | −0.750735 | − | 0.660603i | \(-0.770301\pi\) |
0.947467 | + | 0.319854i | \(0.103634\pi\) | |||||||
\(878\) | −0.556812 | + | 0.124052i | −0.0187915 | + | 0.00418655i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.13429 | − | 12.4067i | 0.0719470 | − | 0.418231i | ||||
\(881\) | 49.9833i | 1.68398i | 0.539493 | + | 0.841990i | \(0.318616\pi\) | ||||
−0.539493 | + | 0.841990i | \(0.681384\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 57.7771i | 1.94435i | 0.234250 | + | 0.972176i | \(0.424737\pi\) | ||||
−0.234250 | + | 0.972176i | \(0.575263\pi\) | |||||||
\(884\) | −1.86749 | − | 3.98312i | −0.0628104 | − | 0.133967i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.27648 | + | 5.72953i | 0.0428841 | + | 0.192487i | ||||
\(887\) | 24.9323 | − | 43.1840i | 0.837144 | − | 1.44998i | −0.0551292 | − | 0.998479i | \(-0.517557\pi\) |
0.892273 | − | 0.451496i | \(-0.149110\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.520039 | − | 0.627953i | −0.0174416 | − | 0.0210609i | ||||
\(890\) | 20.6491 | + | 6.48696i | 0.692160 | + | 0.217443i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.98550 | − | 0.169535i | −0.0664794 | − | 0.00567644i | ||||
\(893\) | −7.85714 | + | 4.53632i | −0.262929 | + | 0.151802i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.11374i | 0.137507i | ||||||||
\(896\) | −27.6644 | − | 11.4317i | −0.924202 | − | 0.381905i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.3862 | − | 22.2011i | −0.680295 | − | 0.740859i | ||||
\(899\) | 31.1101 | + | 53.8843i | 1.03758 | + | 1.79714i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.52086 | + | 6.09831i | −0.117297 | + | 0.203164i | ||||
\(902\) | 7.40137 | − | 23.5598i | 0.246439 | − | 0.784456i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.93283 | + | 5.35431i | −0.230583 | + | 0.178082i | ||||
\(905\) | −16.5400 | − | 9.54935i | −0.549807 | − | 0.317431i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.1632 | − | 12.7960i | 0.735918 | − | 0.424883i | −0.0846650 | − | 0.996409i | \(-0.526982\pi\) |
0.820583 | + | 0.571527i | \(0.193649\pi\) | |||||||
\(908\) | −51.4590 | + | 24.1266i | −1.70773 | + | 0.800668i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.90293 | − | 7.60716i | 0.195680 | − | 0.252175i | ||||
\(911\) | 40.5778 | 1.34440 | 0.672201 | − | 0.740369i | \(-0.265349\pi\) | ||||
0.672201 | + | 0.740369i | \(0.265349\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.110119 | + | 0.190731i | 0.00364439 | + | 0.00631228i | ||||
\(914\) | 5.63135 | + | 25.2766i | 0.186269 | + | 0.836074i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 44.3398 | + | 30.9094i | 1.46503 | + | 1.02127i | ||||
\(917\) | 1.05207 | + | 6.20055i | 0.0347423 | + | 0.204760i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.8189 | − | 13.1745i | −0.752725 | − | 0.434586i | 0.0739526 | − | 0.997262i | \(-0.476439\pi\) |
−0.826678 | + | 0.562676i | \(0.809772\pi\) | |||||||
\(920\) | 20.6174 | + | 8.46449i | 0.679734 | + | 0.279066i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.9393 | − | 14.0912i | −0.426133 | − | 0.464070i | ||||
\(923\) | 19.0125 | 0.625804 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.0296 | −0.658570 | ||||||||
\(926\) | −11.2196 | − | 12.2184i | −0.368697 | − | 0.401521i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 23.6326 | + | 36.6722i | 0.775779 | + | 1.20383i | ||||
\(929\) | 16.7968 | + | 9.69765i | 0.551086 | + | 0.318170i | 0.749560 | − | 0.661936i | \(-0.230265\pi\) |
−0.198474 | + | 0.980106i | \(0.563598\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.7605 | − | 26.4239i | 0.745945 | − | 0.866007i | ||||
\(932\) | −21.0646 | + | 30.2174i | −0.689995 | + | 0.989804i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.62810 | + | 7.30777i | 0.0532729 | + | 0.239118i | ||||
\(935\) | −1.29710 | − | 2.24664i | −0.0424196 | − | 0.0734729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.4703 | −0.342048 | −0.171024 | − | 0.985267i | \(-0.554708\pi\) | ||||
−0.171024 | + | 0.985267i | \(0.554708\pi\) | |||||||
\(938\) | 12.0202 | + | 29.4699i | 0.392474 | + | 0.962228i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.49098 | + | 3.18009i | 0.0486306 | + | 0.103723i | ||||
\(941\) | 8.83717 | − | 5.10214i | 0.288083 | − | 0.166325i | −0.348994 | − | 0.937125i | \(-0.613477\pi\) |
0.637077 | + | 0.770800i | \(0.280143\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 37.8624 | + | 21.8599i | 1.23297 | + | 0.711855i | ||||
\(944\) | −0.659327 | − | 1.78823i | −0.0214593 | − | 0.0582020i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.1913 | − | 35.6239i | 0.363861 | − | 1.15823i | ||||
\(947\) | −16.2233 | + | 28.0997i | −0.527188 | + | 0.913116i | 0.472310 | + | 0.881432i | \(0.343420\pi\) |
−0.999498 | + | 0.0316837i | \(0.989913\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.5995 | − | 27.0192i | −0.506383 | − | 0.877081i | ||||
\(950\) | 19.3956 | + | 21.1223i | 0.629277 | + | 0.685298i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.88897 | + | 1.83524i | −0.190863 | + | 0.0594805i | ||||
\(953\) | − | 4.47642i | − | 0.145005i | −0.997368 | − | 0.0725027i | \(-0.976901\pi\) | ||
0.997368 | − | 0.0725027i | \(-0.0230986\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.1423 | − | 8.74244i | 0.489995 | − | 0.282899i | ||||
\(956\) | −0.0931018 | + | 1.09036i | −0.00301113 | + | 0.0352647i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.21673 | + | 1.01054i | 0.103928 | + | 0.0326491i | ||||
\(959\) | −2.74892 | + | 7.40341i | −0.0887672 | + | 0.239069i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.0435 | − | 29.5201i | 0.549789 | − | 0.952263i | ||||
\(962\) | −4.03866 | − | 18.1277i | −0.130212 | − | 0.584460i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 21.5175 | − | 10.0885i | 0.693033 | − | 0.324929i | ||||
\(965\) | − | 23.0061i | − | 0.740591i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.9578i | 0.770430i | 0.922827 | + | 0.385215i | \(0.125873\pi\) | ||||
−0.922827 | + | 0.385215i | \(0.874127\pi\) | |||||||
\(968\) | 0.978700 | − | 0.131966i | 0.0314566 | − | 0.00424155i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.86934 | + | 2.19879i | −0.316885 | + | 0.0705987i | ||||
\(971\) | 10.6584 | − | 18.4609i | 0.342045 | − | 0.592440i | −0.642767 | − | 0.766062i | \(-0.722214\pi\) |
0.984812 | + | 0.173622i | \(0.0555470\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.6654 | − | 23.7462i | −0.630444 | − | 0.761268i | ||||
\(974\) | −10.1668 | + | 32.3628i | −0.325766 | + | 1.03697i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.7134 | − | 12.8765i | 0.342929 | − | 0.412168i | ||||
\(977\) | −20.6125 | + | 11.9006i | −0.659453 | + | 0.380735i | −0.792068 | − | 0.610432i | \(-0.790996\pi\) |
0.132616 | + | 0.991168i | \(0.457662\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 51.7939i | − | 1.65534i | ||||||
\(980\) | −9.44265 | − | 9.64952i | −0.301635 | − | 0.308243i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 20.7195 | − | 19.0258i | 0.661187 | − | 0.607137i | ||||
\(983\) | −31.1545 | − | 53.9613i | −0.993676 | − | 1.72110i | −0.594082 | − | 0.804404i | \(-0.702485\pi\) |
−0.399594 | − | 0.916692i | \(-0.630849\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.66790 | − | 15.0132i | 0.276182 | − | 0.478362i | ||||
\(986\) | 8.57697 | + | 2.69447i | 0.273147 | + | 0.0858096i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15.2058 | + | 21.8128i | −0.483761 | + | 0.693959i | ||||
\(989\) | 57.2502 | + | 33.0534i | 1.82045 | + | 1.05104i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.83336 | − | 2.21319i | 0.121771 | − | 0.0703044i | −0.437877 | − | 0.899035i | \(-0.644270\pi\) |
0.559648 | + | 0.828730i | \(0.310936\pi\) | |||||||
\(992\) | 20.8616 | − | 40.5903i | 0.662356 | − | 1.28874i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.62275 | − | 26.4111i | 0.114907 | − | 0.837709i | ||||
\(995\) | 4.29919 | 0.136293 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.7597 | + | 22.1004i | 0.404103 | + | 0.699928i | 0.994217 | − | 0.107393i | \(-0.0342502\pi\) |
−0.590113 | + | 0.807320i | \(0.700917\pi\) | |||||||
\(998\) | 12.2808 | − | 2.73603i | 0.388742 | − | 0.0866076i | ||||
\(999\) | 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 | 756.2.be.e.107.8 | ✓ | 64 | |
3.2 | odd | 2 | inner | 756.2.be.e.107.25 | yes | 64 | |
4.3 | odd | 2 | inner | 756.2.be.e.107.19 | yes | 64 | |
7.4 | even | 3 | inner | 756.2.be.e.431.14 | yes | 64 | |
12.11 | even | 2 | inner | 756.2.be.e.107.14 | yes | 64 | |
21.11 | odd | 6 | inner | 756.2.be.e.431.19 | yes | 64 | |
28.11 | odd | 6 | inner | 756.2.be.e.431.25 | yes | 64 | |
84.11 | even | 6 | inner | 756.2.be.e.431.8 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.be.e.107.8 | ✓ | 64 | 1.1 | even | 1 | trivial | |
756.2.be.e.107.14 | yes | 64 | 12.11 | even | 2 | inner | |
756.2.be.e.107.19 | yes | 64 | 4.3 | odd | 2 | inner | |
756.2.be.e.107.25 | yes | 64 | 3.2 | odd | 2 | inner | |
756.2.be.e.431.8 | yes | 64 | 84.11 | even | 6 | inner | |
756.2.be.e.431.14 | yes | 64 | 7.4 | even | 3 | inner | |
756.2.be.e.431.19 | yes | 64 | 21.11 | odd | 6 | inner | |
756.2.be.e.431.25 | yes | 64 | 28.11 | odd | 6 | inner |