Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [555,2,Mod(454,555)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(555, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("555.454");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 555 = 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 555.bb (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: | \(4.43169731218\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 454.5 | ||
Character | \(\chi\) | \(=\) | 555.454 |
Dual form | 555.2.bb.a.544.5 |
$q$-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 \(\left(\mathbb{Z}/555\mathbb{Z}\right)^\times\).
\(n\) | \(76\) | \(112\) | \(371\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.96173 | − | 1.13261i | −1.38715 | − | 0.800873i | −0.394160 | − | 0.919042i | \(-0.628964\pi\) |
−0.992994 | + | 0.118169i | \(0.962298\pi\) | |||||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 1.56559 | + | 2.71168i | 0.782796 | + | 1.35584i | ||||
\(5\) | 0.414545 | + | 2.19731i | 0.185390 | + | 0.982665i | ||||
\(6\) | 2.26521 | 0.924769 | ||||||||
\(7\) | 1.72326 | − | 0.994927i | 0.651332 | − | 0.376047i | −0.137634 | − | 0.990483i | \(-0.543950\pi\) |
0.788967 | + | 0.614436i | \(0.210616\pi\) | |||||||
\(8\) | − | 2.56237i | − | 0.905935i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 1.67546 | − | 4.78004i | 0.529826 | − | 1.51158i | ||||
\(11\) | −0.139104 | −0.0419415 | −0.0209708 | − | 0.999780i | \(-0.506676\pi\) | ||||
−0.0209708 | + | 0.999780i | \(0.506676\pi\) | |||||||
\(12\) | −2.71168 | − | 1.56559i | −0.782796 | − | 0.451947i | ||||
\(13\) | 1.16325 | − | 0.671601i | 0.322627 | − | 0.186269i | −0.329936 | − | 0.944003i | \(-0.607027\pi\) |
0.652563 | + | 0.757735i | \(0.273694\pi\) | |||||||
\(14\) | −4.50744 | −1.20466 | ||||||||
\(15\) | −1.45766 | − | 1.69565i | −0.376366 | − | 0.437815i | ||||
\(16\) | 0.229029 | − | 0.396689i | 0.0572572 | − | 0.0991723i | ||||
\(17\) | 1.17935 | + | 0.680898i | 0.286034 | + | 0.165142i | 0.636152 | − | 0.771564i | \(-0.280525\pi\) |
−0.350118 | + | 0.936706i | \(0.613858\pi\) | |||||||
\(18\) | −1.96173 | + | 1.13261i | −0.462384 | + | 0.266958i | ||||
\(19\) | −0.744884 | − | 1.29018i | −0.170888 | − | 0.295987i | 0.767843 | − | 0.640639i | \(-0.221330\pi\) |
−0.938731 | + | 0.344652i | \(0.887997\pi\) | |||||||
\(20\) | −5.30939 | + | 4.56420i | −1.18722 | + | 1.02059i | ||||
\(21\) | −0.994927 | + | 1.72326i | −0.217111 | + | 0.376047i | ||||
\(22\) | 0.272885 | + | 0.157550i | 0.0581793 | + | 0.0335899i | ||||
\(23\) | 5.72279i | 1.19328i | 0.802507 | + | 0.596642i | \(0.203499\pi\) | ||||
−0.802507 | + | 0.596642i | \(0.796501\pi\) | |||||||
\(24\) | 1.28118 | + | 2.21908i | 0.261521 | + | 0.452967i | ||||
\(25\) | −4.65631 | + | 1.82176i | −0.931261 | + | 0.364353i | ||||
\(26\) | −3.04264 | −0.596710 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 5.39585 | + | 3.11530i | 1.01972 | + | 0.588736i | ||||
\(29\) | −3.64762 | −0.677347 | −0.338673 | − | 0.940904i | \(-0.609978\pi\) | ||||
−0.338673 | + | 0.940904i | \(0.609978\pi\) | |||||||
\(30\) | 0.939032 | + | 4.97736i | 0.171443 | + | 0.908738i | ||||
\(31\) | 7.21023 | 1.29500 | 0.647498 | − | 0.762067i | \(-0.275815\pi\) | ||||
0.647498 | + | 0.762067i | \(0.275815\pi\) | |||||||
\(32\) | −5.33674 | + | 3.08117i | −0.943411 | + | 0.544679i | ||||
\(33\) | 0.120468 | − | 0.0695522i | 0.0209708 | − | 0.0121075i | ||||
\(34\) | −1.54238 | − | 2.67148i | −0.264515 | − | 0.458154i | ||||
\(35\) | 2.90053 | + | 3.37410i | 0.490279 | + | 0.570326i | ||||
\(36\) | 3.13118 | 0.521864 | ||||||||
\(37\) | 4.12279 | + | 4.47243i | 0.677782 | + | 0.735263i | ||||
\(38\) | 3.37464i | 0.547439i | ||||||||
\(39\) | −0.671601 | + | 1.16325i | −0.107542 | + | 0.186269i | ||||
\(40\) | 5.63031 | − | 1.06222i | 0.890230 | − | 0.167951i | ||||
\(41\) | 1.54324 | + | 2.67297i | 0.241013 | + | 0.417447i | 0.961003 | − | 0.276537i | \(-0.0891869\pi\) |
−0.719990 | + | 0.693985i | \(0.755854\pi\) | |||||||
\(42\) | 3.90356 | − | 2.25372i | 0.602332 | − | 0.347756i | ||||
\(43\) | 2.43821i | 0.371823i | 0.982567 | + | 0.185911i | \(0.0595237\pi\) | ||||
−0.982567 | + | 0.185911i | \(0.940476\pi\) | |||||||
\(44\) | −0.217781 | − | 0.377207i | −0.0328317 | − | 0.0568661i | ||||
\(45\) | 2.11020 | + | 0.739647i | 0.314569 | + | 0.110260i | ||||
\(46\) | 6.48167 | − | 11.2266i | 0.955670 | − | 1.65527i | ||||
\(47\) | − | 4.92965i | − | 0.719064i | −0.933133 | − | 0.359532i | \(-0.882936\pi\) | ||
0.933133 | − | 0.359532i | \(-0.117064\pi\) | |||||||
\(48\) | 0.458057i | 0.0661149i | ||||||||
\(49\) | −1.52024 | + | 2.63314i | −0.217177 | + | 0.376162i | ||||
\(50\) | 11.1978 | + | 1.69995i | 1.58360 | + | 0.240409i | ||||
\(51\) | −1.36180 | −0.190689 | ||||||||
\(52\) | 3.64234 | + | 2.10291i | 0.505102 | + | 0.291621i | ||||
\(53\) | 7.32836 | + | 4.23103i | 1.00663 | + | 0.581177i | 0.910203 | − | 0.414163i | \(-0.135926\pi\) |
0.0964253 | + | 0.995340i | \(0.469259\pi\) | |||||||
\(54\) | 1.13261 | − | 1.96173i | 0.154128 | − | 0.266958i | ||||
\(55\) | −0.0576650 | − | 0.305655i | −0.00777554 | − | 0.0412145i | ||||
\(56\) | −2.54937 | − | 4.41564i | −0.340674 | − | 0.590064i | ||||
\(57\) | 1.29018 | + | 0.744884i | 0.170888 | + | 0.0986623i | ||||
\(58\) | 7.15566 | + | 4.13132i | 0.939584 | + | 0.542469i | ||||
\(59\) | 2.53188 | − | 4.38534i | 0.329623 | − | 0.570923i | −0.652814 | − | 0.757518i | \(-0.726412\pi\) |
0.982437 | + | 0.186595i | \(0.0597451\pi\) | |||||||
\(60\) | 2.31597 | − | 6.60741i | 0.298990 | − | 0.853013i | ||||
\(61\) | −0.665693 | − | 1.15301i | −0.0852333 | − | 0.147628i | 0.820257 | − | 0.571995i | \(-0.193830\pi\) |
−0.905491 | + | 0.424366i | \(0.860497\pi\) | |||||||
\(62\) | −14.1445 | − | 8.16635i | −1.79636 | − | 1.03713i | ||||
\(63\) | − | 1.98985i | − | 0.250698i | ||||||
\(64\) | 13.0429 | 1.63036 | ||||||||
\(65\) | 1.95793 | + | 2.27760i | 0.242851 | + | 0.282502i | ||||
\(66\) | −0.315101 | −0.0387862 | ||||||||
\(67\) | 5.66355 | − | 3.26985i | 0.691913 | − | 0.399476i | −0.112415 | − | 0.993661i | \(-0.535859\pi\) |
0.804328 | + | 0.594185i | \(0.202525\pi\) | |||||||
\(68\) | 4.26403i | 0.517090i | ||||||||
\(69\) | −2.86140 | − | 4.95608i | −0.344472 | − | 0.596642i | ||||
\(70\) | −1.86854 | − | 9.90422i | −0.223333 | − | 1.18378i | ||||
\(71\) | 3.69038 | + | 6.39193i | 0.437968 | + | 0.758582i | 0.997533 | − | 0.0702042i | \(-0.0223651\pi\) |
−0.559565 | + | 0.828786i | \(0.689032\pi\) | |||||||
\(72\) | −2.21908 | − | 1.28118i | −0.261521 | − | 0.150989i | ||||
\(73\) | 7.96602i | 0.932352i | 0.884692 | + | 0.466176i | \(0.154369\pi\) | ||||
−0.884692 | + | 0.466176i | \(0.845631\pi\) | |||||||
\(74\) | −3.02231 | − | 13.4432i | −0.351336 | − | 1.56274i | ||||
\(75\) | 3.12160 | − | 3.90585i | 0.360451 | − | 0.451008i | ||||
\(76\) | 2.33237 | − | 4.03978i | 0.267541 | − | 0.463394i | ||||
\(77\) | −0.239713 | + | 0.138399i | −0.0273179 | + | 0.0157720i | ||||
\(78\) | 2.63500 | − | 1.52132i | 0.298355 | − | 0.172255i | ||||
\(79\) | 3.57273 | + | 6.18814i | 0.401963 | + | 0.696221i | 0.993963 | − | 0.109718i | \(-0.0349947\pi\) |
−0.592000 | + | 0.805938i | \(0.701661\pi\) | |||||||
\(80\) | 0.966590 | + | 0.338800i | 0.108068 | + | 0.0378790i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | − | 6.99152i | − | 0.772084i | ||||||
\(83\) | −5.18475 | − | 2.99342i | −0.569100 | − | 0.328570i | 0.187690 | − | 0.982228i | \(-0.439900\pi\) |
−0.756790 | + | 0.653658i | \(0.773233\pi\) | |||||||
\(84\) | −6.23060 | −0.679814 | ||||||||
\(85\) | −1.00725 | + | 2.87365i | −0.109251 | + | 0.311691i | ||||
\(86\) | 2.76153 | − | 4.78310i | 0.297783 | − | 0.515775i | ||||
\(87\) | 3.15893 | − | 1.82381i | 0.338673 | − | 0.195533i | ||||
\(88\) | 0.356437i | 0.0379963i | ||||||||
\(89\) | −7.58937 | + | 13.1452i | −0.804472 | + | 1.39339i | 0.112175 | + | 0.993688i | \(0.464218\pi\) |
−0.916647 | + | 0.399698i | \(0.869115\pi\) | |||||||
\(90\) | −3.30191 | − | 3.84101i | −0.348052 | − | 0.404878i | ||||
\(91\) | 1.33639 | − | 2.31469i | 0.140091 | − | 0.242646i | ||||
\(92\) | −15.5184 | + | 8.95956i | −1.61791 | + | 0.934098i | ||||
\(93\) | −6.24424 | + | 3.60512i | −0.647498 | + | 0.373833i | ||||
\(94\) | −5.58335 | + | 9.67065i | −0.575879 | + | 0.997452i | ||||
\(95\) | 2.52612 | − | 2.17157i | 0.259175 | − | 0.222799i | ||||
\(96\) | 3.08117 | − | 5.33674i | 0.314470 | − | 0.544679i | ||||
\(97\) | 10.2833i | 1.04411i | 0.852912 | + | 0.522055i | \(0.174835\pi\) | ||||
−0.852912 | + | 0.522055i | \(0.825165\pi\) | |||||||
\(98\) | 5.96461 | − | 3.44367i | 0.602517 | − | 0.347863i | ||||
\(99\) | −0.0695522 | + | 0.120468i | −0.00699026 | + | 0.0121075i | ||||
\(100\) | −12.2299 | − | 9.77429i | −1.22299 | − | 0.977429i | ||||
\(101\) | −4.47080 | −0.444862 | −0.222431 | − | 0.974948i | \(-0.571399\pi\) | ||||
−0.222431 | + | 0.974948i | \(0.571399\pi\) | |||||||
\(102\) | 2.67148 | + | 1.54238i | 0.264515 | + | 0.152718i | ||||
\(103\) | 17.0377i | 1.67878i | 0.543531 | + | 0.839389i | \(0.317087\pi\) | ||||
−0.543531 | + | 0.839389i | \(0.682913\pi\) | |||||||
\(104\) | −1.72089 | − | 2.98067i | −0.168747 | − | 0.292279i | ||||
\(105\) | −4.19898 | − | 1.47179i | −0.409778 | − | 0.143632i | ||||
\(106\) | −9.58418 | − | 16.6003i | −0.930898 | − | 1.61236i | ||||
\(107\) | 7.81698 | − | 4.51314i | 0.755696 | − | 0.436301i | −0.0720523 | − | 0.997401i | \(-0.522955\pi\) |
0.827748 | + | 0.561100i | \(0.189622\pi\) | |||||||
\(108\) | −2.71168 | + | 1.56559i | −0.260932 | + | 0.150649i | ||||
\(109\) | −2.31790 | + | 4.01473i | −0.222015 | + | 0.384541i | −0.955420 | − | 0.295251i | \(-0.904597\pi\) |
0.733405 | + | 0.679792i | \(0.237930\pi\) | |||||||
\(110\) | −0.233063 | + | 0.664924i | −0.0222217 | + | 0.0633980i | ||||
\(111\) | −5.80665 | − | 1.81184i | −0.551143 | − | 0.171972i | ||||
\(112\) | − | 0.911467i | − | 0.0861255i | ||||||
\(113\) | 3.79159 | + | 2.18907i | 0.356683 | + | 0.205931i | 0.667625 | − | 0.744498i | \(-0.267311\pi\) |
−0.310942 | + | 0.950429i | \(0.600644\pi\) | |||||||
\(114\) | −1.68732 | − | 2.92252i | −0.158032 | − | 0.273719i | ||||
\(115\) | −12.5747 | + | 2.37235i | −1.17260 | + | 0.221223i | ||||
\(116\) | −5.71069 | − | 9.89120i | −0.530224 | − | 0.918375i | ||||
\(117\) | − | 1.34320i | − | 0.124179i | ||||||
\(118\) | −9.93373 | + | 5.73524i | −0.914474 | + | 0.527972i | ||||
\(119\) | 2.70977 | 0.248404 | ||||||||
\(120\) | −4.34488 | + | 3.73506i | −0.396632 | + | 0.340963i | ||||
\(121\) | −10.9806 | −0.998241 | ||||||||
\(122\) | 3.01587i | 0.273044i | ||||||||
\(123\) | −2.67297 | − | 1.54324i | −0.241013 | − | 0.139149i | ||||
\(124\) | 11.2883 | + | 19.5519i | 1.01372 | + | 1.75581i | ||||
\(125\) | −5.93322 | − | 9.47612i | −0.530683 | − | 0.847570i | ||||
\(126\) | −2.25372 | + | 3.90356i | −0.200777 | + | 0.347756i | ||||
\(127\) | −4.66716 | − | 2.69459i | −0.414144 | − | 0.239106i | 0.278425 | − | 0.960458i | \(-0.410188\pi\) |
−0.692569 | + | 0.721352i | \(0.743521\pi\) | |||||||
\(128\) | −14.9131 | − | 8.61011i | −1.31815 | − | 0.761033i | ||||
\(129\) | −1.21910 | − | 2.11155i | −0.107336 | − | 0.185911i | ||||
\(130\) | −1.26131 | − | 6.68560i | −0.110624 | − | 0.586366i | ||||
\(131\) | −0.931640 | + | 1.61365i | −0.0813978 | + | 0.140985i | −0.903851 | − | 0.427848i | \(-0.859272\pi\) |
0.822453 | + | 0.568833i | \(0.192605\pi\) | |||||||
\(132\) | 0.377207 | + | 0.217781i | 0.0328317 | + | 0.0189554i | ||||
\(133\) | −2.56726 | − | 1.48221i | −0.222610 | − | 0.128524i | ||||
\(134\) | −14.8138 | −1.27972 | ||||||||
\(135\) | −2.19731 | + | 0.414545i | −0.189114 | + | 0.0356783i | ||||
\(136\) | 1.74471 | − | 3.02193i | 0.149608 | − | 0.259128i | ||||
\(137\) | − | 12.0562i | − | 1.03003i | −0.857181 | − | 0.515016i | \(-0.827786\pi\) | ||
0.857181 | − | 0.515016i | \(-0.172214\pi\) | |||||||
\(138\) | 12.9633i | 1.10351i | ||||||||
\(139\) | −0.0613544 | + | 0.106269i | −0.00520402 | + | 0.00901362i | −0.868616 | − | 0.495486i | \(-0.834990\pi\) |
0.863412 | + | 0.504500i | \(0.168323\pi\) | |||||||
\(140\) | −4.60844 | + | 13.1478i | −0.389484 | + | 1.11119i | ||||
\(141\) | 2.46483 | + | 4.26921i | 0.207576 | + | 0.359532i | ||||
\(142\) | − | 16.7190i | − | 1.40303i | ||||||
\(143\) | −0.161813 | + | 0.0934226i | −0.0135315 | + | 0.00781239i | ||||
\(144\) | −0.229029 | − | 0.396689i | −0.0190857 | − | 0.0330574i | ||||
\(145\) | −1.51210 | − | 8.01494i | −0.125573 | − | 0.665605i | ||||
\(146\) | 9.02236 | − | 15.6272i | 0.746696 | − | 1.29332i | ||||
\(147\) | − | 3.04048i | − | 0.250775i | ||||||
\(148\) | −5.67321 | + | 18.1817i | −0.466335 | + | 1.49453i | ||||
\(149\) | 21.3770 | 1.75127 | 0.875634 | − | 0.482975i | \(-0.160444\pi\) | ||||
0.875634 | + | 0.482975i | \(0.160444\pi\) | |||||||
\(150\) | −10.5475 | + | 4.12668i | −0.861201 | + | 0.336942i | ||||
\(151\) | −3.88553 | − | 6.72993i | −0.316200 | − | 0.547674i | 0.663492 | − | 0.748183i | \(-0.269074\pi\) |
−0.979692 | + | 0.200509i | \(0.935740\pi\) | |||||||
\(152\) | −3.30591 | + | 1.90867i | −0.268145 | + | 0.154813i | ||||
\(153\) | 1.17935 | − | 0.680898i | 0.0953447 | − | 0.0550473i | ||||
\(154\) | 0.627004 | 0.0505254 | ||||||||
\(155\) | 2.98896 | + | 15.8431i | 0.240079 | + | 1.27255i | ||||
\(156\) | −4.20581 | −0.336734 | ||||||||
\(157\) | 9.27102 | + | 5.35263i | 0.739908 | + | 0.427186i | 0.822036 | − | 0.569436i | \(-0.192838\pi\) |
−0.0821279 | + | 0.996622i | \(0.526172\pi\) | |||||||
\(158\) | − | 16.1860i | − | 1.28769i | ||||||
\(159\) | −8.46206 | −0.671085 | ||||||||
\(160\) | −8.98259 | − | 10.4492i | −0.710136 | − | 0.826079i | ||||
\(161\) | 5.69376 | + | 9.86188i | 0.448731 | + | 0.777225i | ||||
\(162\) | 2.26521i | 0.177972i | ||||||||
\(163\) | −12.1261 | − | 7.00099i | −0.949787 | − | 0.548360i | −0.0567722 | − | 0.998387i | \(-0.518081\pi\) |
−0.893015 | + | 0.450027i | \(0.851414\pi\) | |||||||
\(164\) | −4.83216 | + | 8.36955i | −0.377328 | + | 0.653552i | ||||
\(165\) | 0.202767 | + | 0.235872i | 0.0157854 | + | 0.0183626i | ||||
\(166\) | 6.78072 | + | 11.7446i | 0.526286 | + | 0.911555i | ||||
\(167\) | 6.07830 | − | 3.50931i | 0.470353 | − | 0.271558i | −0.246035 | − | 0.969261i | \(-0.579128\pi\) |
0.716387 | + | 0.697703i | \(0.245794\pi\) | |||||||
\(168\) | 4.41564 | + | 2.54937i | 0.340674 | + | 0.196688i | ||||
\(169\) | −5.59790 | + | 9.69585i | −0.430608 | + | 0.745835i | ||||
\(170\) | 5.23066 | − | 4.49652i | 0.401174 | − | 0.344867i | ||||
\(171\) | −1.48977 | −0.113925 | ||||||||
\(172\) | −6.61164 | + | 3.81723i | −0.504133 | + | 0.291061i | ||||
\(173\) | −19.4871 | − | 11.2509i | −1.48157 | − | 0.855387i | −0.481793 | − | 0.876285i | \(-0.660014\pi\) |
−0.999782 | + | 0.0208979i | \(0.993347\pi\) | |||||||
\(174\) | −8.26264 | −0.626389 | ||||||||
\(175\) | −6.21152 | + | 7.77206i | −0.469547 | + | 0.587513i | ||||
\(176\) | −0.0318589 | + | 0.0551812i | −0.00240145 | + | 0.00415944i | ||||
\(177\) | 5.06376i | 0.380615i | ||||||||
\(178\) | 29.7766 | − | 17.1915i | 2.23185 | − | 1.28856i | ||||
\(179\) | 14.8705 | 1.11148 | 0.555738 | − | 0.831358i | \(-0.312436\pi\) | ||||
0.555738 | + | 0.831358i | \(0.312436\pi\) | |||||||
\(180\) | 1.29802 | + | 6.88017i | 0.0967484 | + | 0.512817i | ||||
\(181\) | −10.8613 | − | 18.8122i | −0.807310 | − | 1.39830i | −0.914720 | − | 0.404088i | \(-0.867589\pi\) |
0.107410 | − | 0.994215i | \(-0.465744\pi\) | |||||||
\(182\) | −5.24326 | + | 3.02720i | −0.388657 | + | 0.224391i | ||||
\(183\) | 1.15301 | + | 0.665693i | 0.0852333 | + | 0.0492095i | ||||
\(184\) | 14.6639 | 1.08104 | ||||||||
\(185\) | −8.11821 | + | 10.9131i | −0.596863 | + | 0.802343i | ||||
\(186\) | 16.3327 | 1.19757 | ||||||||
\(187\) | −0.164053 | − | 0.0947158i | −0.0119967 | − | 0.00692631i | ||||
\(188\) | 13.3677 | − | 7.71783i | 0.974937 | − | 0.562880i | ||||
\(189\) | 0.994927 | + | 1.72326i | 0.0723703 | + | 0.125349i | ||||
\(190\) | −7.41511 | + | 1.39894i | −0.537949 | + | 0.101490i | ||||
\(191\) | 8.91725 | 0.645230 | 0.322615 | − | 0.946530i | \(-0.395438\pi\) | ||||
0.322615 | + | 0.946530i | \(0.395438\pi\) | |||||||
\(192\) | −11.2955 | + | 6.52144i | −0.815180 | + | 0.470644i | ||||
\(193\) | − | 10.5019i | − | 0.755947i | −0.925816 | − | 0.377973i | \(-0.876621\pi\) | ||
0.925816 | − | 0.377973i | \(-0.123379\pi\) | |||||||
\(194\) | 11.6469 | − | 20.1731i | 0.836200 | − | 1.44834i | ||||
\(195\) | −2.83442 | − | 0.993495i | −0.202977 | − | 0.0711456i | ||||
\(196\) | −9.52031 | −0.680022 | ||||||||
\(197\) | −13.6453 | − | 7.87814i | −0.972190 | − | 0.561294i | −0.0722866 | − | 0.997384i | \(-0.523030\pi\) |
−0.899903 | + | 0.436090i | \(0.856363\pi\) | |||||||
\(198\) | 0.272885 | − | 0.157550i | 0.0193931 | − | 0.0111966i | ||||
\(199\) | 27.6222 | 1.95809 | 0.979043 | − | 0.203654i | \(-0.0652817\pi\) | ||||
0.979043 | + | 0.203654i | \(0.0652817\pi\) | |||||||
\(200\) | 4.66803 | + | 11.9312i | 0.330080 | + | 0.843662i | ||||
\(201\) | −3.26985 | + | 5.66355i | −0.230638 | + | 0.399476i | ||||
\(202\) | 8.77051 | + | 5.06366i | 0.617091 | + | 0.356278i | ||||
\(203\) | −6.28582 | + | 3.62912i | −0.441178 | + | 0.254714i | ||||
\(204\) | −2.13202 | − | 3.69276i | −0.149271 | − | 0.258545i | ||||
\(205\) | −5.23358 | + | 4.49903i | −0.365529 | + | 0.314226i | ||||
\(206\) | 19.2970 | − | 33.4234i | 1.34449 | − | 2.32872i | ||||
\(207\) | 4.95608 | + | 2.86140i | 0.344472 | + | 0.198881i | ||||
\(208\) | − | 0.615263i | − | 0.0426608i | ||||||
\(209\) | 0.103617 | + | 0.179469i | 0.00716731 | + | 0.0124141i | ||||
\(210\) | 6.57031 | + | 7.64304i | 0.453394 | + | 0.527420i | ||||
\(211\) | −19.3433 | −1.33165 | −0.665824 | − | 0.746109i | \(-0.731920\pi\) | ||||
−0.665824 | + | 0.746109i | \(0.731920\pi\) | |||||||
\(212\) | 26.4963i | 1.81977i | ||||||||
\(213\) | −6.39193 | − | 3.69038i | −0.437968 | − | 0.252861i | ||||
\(214\) | −20.4464 | −1.39769 | ||||||||
\(215\) | −5.35748 | + | 1.01075i | −0.365377 | + | 0.0689323i | ||||
\(216\) | 2.56237 | 0.174347 | ||||||||
\(217\) | 12.4251 | − | 7.17365i | 0.843473 | − | 0.486979i | ||||
\(218\) | 9.09421 | − | 5.25054i | 0.615937 | − | 0.355612i | ||||
\(219\) | −3.98301 | − | 6.89878i | −0.269147 | − | 0.466176i | ||||
\(220\) | 0.738559 | − | 0.634900i | 0.0497937 | − | 0.0428049i | ||||
\(221\) | 1.82917 | 0.123043 | ||||||||
\(222\) | 9.33899 | + | 10.1310i | 0.626792 | + | 0.679948i | ||||
\(223\) | − | 5.21380i | − | 0.349142i | −0.984645 | − | 0.174571i | \(-0.944146\pi\) | ||
0.984645 | − | 0.174571i | \(-0.0558539\pi\) | |||||||
\(224\) | −6.13107 | + | 10.6193i | −0.409650 | + | 0.709534i | ||||
\(225\) | −0.750459 | + | 4.94336i | −0.0500306 | + | 0.329557i | ||||
\(226\) | −4.95872 | − | 8.58875i | −0.329849 | − | 0.571315i | ||||
\(227\) | 13.7651 | − | 7.94726i | 0.913619 | − | 0.527478i | 0.0320249 | − | 0.999487i | \(-0.489804\pi\) |
0.881594 | + | 0.472009i | \(0.156471\pi\) | |||||||
\(228\) | 4.66473i | 0.308930i | ||||||||
\(229\) | 8.81122 | + | 15.2615i | 0.582261 | + | 1.00851i | 0.995211 | + | 0.0977525i | \(0.0311653\pi\) |
−0.412949 | + | 0.910754i | \(0.635501\pi\) | |||||||
\(230\) | 27.3552 | + | 9.58829i | 1.80375 | + | 0.632233i | ||||
\(231\) | 0.138399 | − | 0.239713i | 0.00910596 | − | 0.0157720i | ||||
\(232\) | 9.34656i | 0.613632i | ||||||||
\(233\) | − | 22.9559i | − | 1.50389i | −0.659225 | − | 0.751946i | \(-0.729115\pi\) | ||
0.659225 | − | 0.751946i | \(-0.270885\pi\) | |||||||
\(234\) | −1.52132 | + | 2.63500i | −0.0994517 | + | 0.172255i | ||||
\(235\) | 10.8320 | − | 2.04356i | 0.706599 | − | 0.133307i | ||||
\(236\) | 15.8556 | 1.03211 | ||||||||
\(237\) | −6.18814 | − | 3.57273i | −0.401963 | − | 0.232074i | ||||
\(238\) | −5.31584 | − | 3.06910i | −0.344575 | − | 0.198940i | ||||
\(239\) | −0.483112 | + | 0.836775i | −0.0312499 | + | 0.0541265i | −0.881227 | − | 0.472693i | \(-0.843282\pi\) |
0.849977 | + | 0.526819i | \(0.176615\pi\) | |||||||
\(240\) | −1.00649 | + | 0.189885i | −0.0649688 | + | 0.0122570i | ||||
\(241\) | 0.272240 | + | 0.471533i | 0.0175365 | + | 0.0303741i | 0.874660 | − | 0.484736i | \(-0.161084\pi\) |
−0.857124 | + | 0.515110i | \(0.827751\pi\) | |||||||
\(242\) | 21.5411 | + | 12.4367i | 1.38471 | + | 0.799464i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 2.08441 | − | 3.61030i | 0.133441 | − | 0.231126i | ||||
\(245\) | −6.41601 | − | 2.24888i | −0.409904 | − | 0.143676i | ||||
\(246\) | 3.49576 | + | 6.05484i | 0.222882 | + | 0.386042i | ||||
\(247\) | −1.73297 | − | 1.00053i | −0.110266 | − | 0.0636622i | ||||
\(248\) | − | 18.4753i | − | 1.17318i | ||||||
\(249\) | 5.98684 | 0.379400 | ||||||||
\(250\) | 0.906665 | + | 25.3096i | 0.0573425 | + | 1.60072i | ||||
\(251\) | 9.15687 | 0.577976 | 0.288988 | − | 0.957333i | \(-0.406681\pi\) | ||||
0.288988 | + | 0.957333i | \(0.406681\pi\) | |||||||
\(252\) | 5.39585 | − | 3.11530i | 0.339907 | − | 0.196245i | ||||
\(253\) | − | 0.796065i | − | 0.0500482i | ||||||
\(254\) | 6.10381 | + | 10.5721i | 0.382987 | + | 0.663353i | ||||
\(255\) | −0.564525 | − | 2.99228i | −0.0353519 | − | 0.187384i | ||||
\(256\) | 6.46083 | + | 11.1905i | 0.403802 | + | 0.699405i | ||||
\(257\) | 14.1361 | + | 8.16146i | 0.881783 | + | 0.509098i | 0.871246 | − | 0.490847i | \(-0.163312\pi\) |
0.0105373 | + | 0.999944i | \(0.496646\pi\) | |||||||
\(258\) | 5.52305i | 0.343850i | ||||||||
\(259\) | 11.5544 | + | 3.60530i | 0.717955 | + | 0.224022i | ||||
\(260\) | −3.11081 | + | 8.87508i | −0.192925 | + | 0.550409i | ||||
\(261\) | −1.82381 | + | 3.15893i | −0.112891 | + | 0.195533i | ||||
\(262\) | 3.65526 | − | 2.11036i | 0.225822 | − | 0.130379i | ||||
\(263\) | 15.0422 | − | 8.68461i | 0.927541 | − | 0.535516i | 0.0415080 | − | 0.999138i | \(-0.486784\pi\) |
0.886033 | + | 0.463622i | \(0.153450\pi\) | |||||||
\(264\) | −0.178218 | − | 0.308683i | −0.0109686 | − | 0.0189981i | ||||
\(265\) | −6.25894 | + | 17.8566i | −0.384483 | + | 1.09692i | ||||
\(266\) | 3.35752 | + | 5.81539i | 0.205863 | + | 0.356564i | ||||
\(267\) | − | 15.1787i | − | 0.928924i | ||||||
\(268\) | 17.7336 | + | 10.2385i | 1.08325 | + | 0.625416i | ||||
\(269\) | −20.7235 | −1.26353 | −0.631767 | − | 0.775158i | \(-0.717670\pi\) | ||||
−0.631767 | + | 0.775158i | \(0.717670\pi\) | |||||||
\(270\) | 4.78004 | + | 1.67546i | 0.290904 | + | 0.101965i | ||||
\(271\) | 10.7704 | − | 18.6549i | 0.654257 | − | 1.13321i | −0.327823 | − | 0.944739i | \(-0.606315\pi\) |
0.982080 | − | 0.188467i | \(-0.0603517\pi\) | |||||||
\(272\) | 0.540209 | − | 0.311890i | 0.0327550 | − | 0.0189111i | ||||
\(273\) | 2.67277i | 0.161764i | ||||||||
\(274\) | −13.6549 | + | 23.6510i | −0.824925 | + | 1.42881i | ||||
\(275\) | 0.647712 | − | 0.253415i | 0.0390585 | − | 0.0152815i | ||||
\(276\) | 8.95956 | − | 15.5184i | 0.539302 | − | 0.934098i | ||||
\(277\) | 9.66521 | − | 5.58021i | 0.580726 | − | 0.335282i | −0.180696 | − | 0.983539i | \(-0.557835\pi\) |
0.761422 | + | 0.648257i | \(0.224502\pi\) | |||||||
\(278\) | 0.240722 | − | 0.138981i | 0.0144375 | − | 0.00833551i | ||||
\(279\) | 3.60512 | − | 6.24424i | 0.215833 | − | 0.373833i | ||||
\(280\) | 8.64568 | − | 7.43223i | 0.516678 | − | 0.444160i | ||||
\(281\) | −14.1081 | + | 24.4360i | −0.841619 | + | 1.45773i | 0.0469055 | + | 0.998899i | \(0.485064\pi\) |
−0.888525 | + | 0.458828i | \(0.848269\pi\) | |||||||
\(282\) | − | 11.1667i | − | 0.664968i | ||||||
\(283\) | 21.9041 | − | 12.6463i | 1.30206 | − | 0.751745i | 0.321304 | − | 0.946976i | \(-0.395879\pi\) |
0.980757 | + | 0.195231i | \(0.0625457\pi\) | |||||||
\(284\) | −11.5553 | + | 20.0143i | −0.685679 | + | 1.18763i | ||||
\(285\) | −1.10190 | + | 3.14370i | −0.0652710 | + | 0.186217i | ||||
\(286\) | 0.423244 | 0.0250269 | ||||||||
\(287\) | 5.31881 | + | 3.07082i | 0.313960 | + | 0.181265i | ||||
\(288\) | 6.16234i | 0.363119i | ||||||||
\(289\) | −7.57276 | − | 13.1164i | −0.445456 | − | 0.771553i | ||||
\(290\) | −6.11143 | + | 17.4358i | −0.358876 | + | 1.02386i | ||||
\(291\) | −5.14165 | − | 8.90560i | −0.301409 | − | 0.522055i | ||||
\(292\) | −21.6013 | + | 12.4715i | −1.26412 | + | 0.729842i | ||||
\(293\) | −7.98837 | + | 4.61209i | −0.466685 | + | 0.269441i | −0.714851 | − | 0.699277i | \(-0.753506\pi\) |
0.248166 | + | 0.968718i | \(0.420172\pi\) | |||||||
\(294\) | −3.44367 | + | 5.96461i | −0.200839 | + | 0.347863i | ||||
\(295\) | 10.6855 | + | 3.74539i | 0.622135 | + | 0.218065i | ||||
\(296\) | 11.4600 | − | 10.5641i | 0.666100 | − | 0.614026i | ||||
\(297\) | − | 0.139104i | − | 0.00807165i | ||||||
\(298\) | −41.9358 | − | 24.2117i | −2.42928 | − | 1.40254i | ||||
\(299\) | 3.84343 | + | 6.65702i | 0.222271 | + | 0.384985i | ||||
\(300\) | 15.4786 | + | 2.34983i | 0.893656 | + | 0.135667i | ||||
\(301\) | 2.42584 | + | 4.20167i | 0.139823 | + | 0.242180i | ||||
\(302\) | 17.6031i | 1.01294i | ||||||||
\(303\) | 3.87183 | − | 2.23540i | 0.222431 | − | 0.128420i | ||||
\(304\) | −0.682399 | −0.0391382 | ||||||||
\(305\) | 2.25757 | − | 1.94071i | 0.129268 | − | 0.111125i | ||||
\(306\) | −3.08475 | −0.176344 | ||||||||
\(307\) | − | 6.43870i | − | 0.367476i | −0.982975 | − | 0.183738i | \(-0.941180\pi\) | ||
0.982975 | − | 0.183738i | \(-0.0588198\pi\) | |||||||
\(308\) | −0.750587 | − | 0.433351i | −0.0427686 | − | 0.0246925i | ||||
\(309\) | −8.51887 | − | 14.7551i | −0.484621 | − | 0.839389i | ||||
\(310\) | 12.0804 | − | 34.4652i | 0.686122 | − | 1.95749i | ||||
\(311\) | 0.829152 | − | 1.43613i | 0.0470169 | − | 0.0814356i | −0.841559 | − | 0.540165i | \(-0.818362\pi\) |
0.888576 | + | 0.458729i | \(0.151695\pi\) | |||||||
\(312\) | 2.98067 | + | 1.72089i | 0.168747 | + | 0.0974262i | ||||
\(313\) | −6.97020 | − | 4.02425i | −0.393979 | − | 0.227464i | 0.289904 | − | 0.957056i | \(-0.406377\pi\) |
−0.683883 | + | 0.729592i | \(0.739710\pi\) | |||||||
\(314\) | −12.1248 | − | 21.0008i | −0.684244 | − | 1.18514i | ||||
\(315\) | 4.37232 | − | 0.824883i | 0.246352 | − | 0.0464769i | ||||
\(316\) | −11.1869 | + | 19.3762i | −0.629310 | + | 1.09000i | ||||
\(317\) | 7.55926 | + | 4.36434i | 0.424570 | + | 0.245126i | 0.697031 | − | 0.717041i | \(-0.254504\pi\) |
−0.272461 | + | 0.962167i | \(0.587837\pi\) | |||||||
\(318\) | 16.6003 | + | 9.58418i | 0.930898 | + | 0.537454i | ||||
\(319\) | 0.507400 | 0.0284090 | ||||||||
\(320\) | 5.40686 | + | 28.6592i | 0.302253 | + | 1.60210i | ||||
\(321\) | −4.51314 | + | 7.81698i | −0.251899 | + | 0.436301i | ||||
\(322\) | − | 25.7951i | − | 1.43751i | ||||||
\(323\) | − | 2.02876i | − | 0.112883i | ||||||
\(324\) | 1.56559 | − | 2.71168i | 0.0869773 | − | 0.150649i | ||||
\(325\) | −4.19294 | + | 5.24634i | −0.232582 | + | 0.291015i | ||||
\(326\) | 15.8587 | + | 27.4681i | 0.878333 | + | 1.52132i | ||||
\(327\) | − | 4.63581i | − | 0.256361i | ||||||
\(328\) | 6.84913 | − | 3.95435i | 0.378180 | − | 0.218342i | ||||
\(329\) | −4.90464 | − | 8.49509i | −0.270402 | − | 0.468350i | ||||
\(330\) | −0.130623 | − | 0.692373i | −0.00719058 | − | 0.0381139i | ||||
\(331\) | 0.388850 | − | 0.673509i | 0.0213732 | − | 0.0370194i | −0.855141 | − | 0.518395i | \(-0.826530\pi\) |
0.876514 | + | 0.481376i | \(0.159863\pi\) | |||||||
\(332\) | − | 18.7459i | − | 1.02881i | ||||||
\(333\) | 5.93463 | − | 1.33423i | 0.325216 | − | 0.0731152i | ||||
\(334\) | −15.8986 | −0.869935 | ||||||||
\(335\) | 9.53266 | + | 11.0891i | 0.520825 | + | 0.605860i | ||||
\(336\) | 0.455733 | + | 0.789353i | 0.0248623 | + | 0.0430628i | ||||
\(337\) | −18.4108 | + | 10.6295i | −1.00290 | + | 0.579026i | −0.909106 | − | 0.416565i | \(-0.863234\pi\) |
−0.0937967 | + | 0.995591i | \(0.529900\pi\) | |||||||
\(338\) | 21.9632 | − | 12.6804i | 1.19464 | − | 0.689725i | ||||
\(339\) | −4.37815 | −0.237788 | ||||||||
\(340\) | −9.36938 | + | 1.76763i | −0.508126 | + | 0.0958633i | ||||
\(341\) | −1.00297 | −0.0543141 | ||||||||
\(342\) | 2.92252 | + | 1.68732i | 0.158032 | + | 0.0912398i | ||||
\(343\) | 19.9791i | 1.07877i | ||||||||
\(344\) | 6.24758 | 0.336847 | ||||||||
\(345\) | 9.70385 | − | 8.34188i | 0.522438 | − | 0.449112i | ||||
\(346\) | 25.4856 | + | 44.1423i | 1.37011 | + | 2.37311i | ||||
\(347\) | − | 31.7474i | − | 1.70429i | −0.523307 | − | 0.852144i | \(-0.675302\pi\) | ||
0.523307 | − | 0.852144i | \(-0.324698\pi\) | |||||||
\(348\) | 9.89120 | + | 5.71069i | 0.530224 | + | 0.306125i | ||||
\(349\) | 13.3130 | − | 23.0587i | 0.712626 | − | 1.23430i | −0.251242 | − | 0.967924i | \(-0.580839\pi\) |
0.963868 | − | 0.266380i | \(-0.0858277\pi\) | |||||||
\(350\) | 20.9880 | − | 8.21149i | 1.12186 | − | 0.438922i | ||||
\(351\) | 0.671601 | + | 1.16325i | 0.0358474 | + | 0.0620895i | ||||
\(352\) | 0.742364 | − | 0.428604i | 0.0395681 | − | 0.0228447i | ||||
\(353\) | −15.2388 | − | 8.79810i | −0.811078 | − | 0.468276i | 0.0362524 | − | 0.999343i | \(-0.488458\pi\) |
−0.847330 | + | 0.531067i | \(0.821791\pi\) | |||||||
\(354\) | 5.73524 | − | 9.93373i | 0.304825 | − | 0.527972i | ||||
\(355\) | −12.5152 | + | 10.7586i | −0.664237 | + | 0.571009i | ||||
\(356\) | −47.5274 | −2.51895 | ||||||||
\(357\) | −2.34673 | + | 1.35489i | −0.124202 | + | 0.0717082i | ||||
\(358\) | −29.1720 | − | 16.8425i | −1.54179 | − | 0.890151i | ||||
\(359\) | −14.0849 | −0.743375 | −0.371688 | − | 0.928358i | \(-0.621221\pi\) | ||||
−0.371688 | + | 0.928358i | \(0.621221\pi\) | |||||||
\(360\) | 1.89525 | − | 5.40710i | 0.0998883 | − | 0.284979i | ||||
\(361\) | 8.39030 | − | 14.5324i | 0.441595 | − | 0.764864i | ||||
\(362\) | 49.2061i | 2.58621i | ||||||||
\(363\) | 9.50952 | − | 5.49032i | 0.499120 | − | 0.288167i | ||||
\(364\) | 8.36895 | 0.438652 | ||||||||
\(365\) | −17.5038 | + | 3.30227i | −0.916190 | + | 0.172849i | ||||
\(366\) | −1.50794 | − | 2.61182i | −0.0788211 | − | 0.136522i | ||||
\(367\) | −24.0112 | + | 13.8628i | −1.25337 | + | 0.723635i | −0.971778 | − | 0.235899i | \(-0.924197\pi\) |
−0.281594 | + | 0.959534i | \(0.590863\pi\) | |||||||
\(368\) | 2.27017 | + | 1.31068i | 0.118341 | + | 0.0683241i | ||||
\(369\) | 3.08648 | 0.160676 | ||||||||
\(370\) | 28.2859 | − | 12.2137i | 1.47052 | − | 0.634962i | ||||
\(371\) | 16.8383 | 0.874199 | ||||||||
\(372\) | −19.5519 | − | 11.2883i | −1.01372 | − | 0.585270i | ||||
\(373\) | −5.02514 | + | 2.90126i | −0.260192 | + | 0.150222i | −0.624422 | − | 0.781087i | \(-0.714665\pi\) |
0.364230 | + | 0.931309i | \(0.381332\pi\) | |||||||
\(374\) | 0.214551 | + | 0.371614i | 0.0110942 | + | 0.0192157i | ||||
\(375\) | 9.87638 | + | 5.23995i | 0.510014 | + | 0.270590i | ||||
\(376\) | −12.6316 | −0.651425 | ||||||||
\(377\) | −4.24309 | + | 2.44975i | −0.218530 | + | 0.126168i | ||||
\(378\) | − | 4.50744i | − | 0.231838i | ||||||
\(379\) | 9.64665 | − | 16.7085i | 0.495515 | − | 0.858257i | −0.504472 | − | 0.863428i | \(-0.668313\pi\) |
0.999987 | + | 0.00517107i | \(0.00164601\pi\) | |||||||
\(380\) | 9.84350 | + | 3.45025i | 0.504961 | + | 0.176994i | ||||
\(381\) | 5.38918 | 0.276096 | ||||||||
\(382\) | −17.4932 | − | 10.0997i | −0.895032 | − | 0.516747i | ||||
\(383\) | −11.1439 | + | 6.43392i | −0.569425 | + | 0.328758i | −0.756920 | − | 0.653508i | \(-0.773297\pi\) |
0.187494 | + | 0.982266i | \(0.439963\pi\) | |||||||
\(384\) | 17.2202 | 0.878765 | ||||||||
\(385\) | −0.403476 | − | 0.469351i | −0.0205630 | − | 0.0239204i | ||||
\(386\) | −11.8946 | + | 20.6020i | −0.605418 | + | 1.04861i | ||||
\(387\) | 2.11155 | + | 1.21910i | 0.107336 | + | 0.0619705i | ||||
\(388\) | −27.8851 | + | 16.0994i | −1.41565 | + | 0.817326i | ||||
\(389\) | −13.2314 | − | 22.9174i | −0.670857 | − | 1.16196i | −0.977662 | − | 0.210185i | \(-0.932593\pi\) |
0.306805 | − | 0.951772i | \(-0.400740\pi\) | |||||||
\(390\) | 4.43513 | + | 5.15925i | 0.224581 | + | 0.261249i | ||||
\(391\) | −3.89664 | + | 6.74917i | −0.197061 | + | 0.341320i | ||||
\(392\) | 6.74707 | + | 3.89542i | 0.340778 | + | 0.196749i | ||||
\(393\) | − | 1.86328i | − | 0.0939901i | ||||||
\(394\) | 17.8456 | + | 30.9096i | 0.899051 | + | 1.55720i | ||||
\(395\) | −12.1162 | + | 10.4156i | −0.609632 | + | 0.524068i | ||||
\(396\) | −0.435561 | −0.0218878 | ||||||||
\(397\) | − | 9.66789i | − | 0.485217i | −0.970124 | − | 0.242609i | \(-0.921997\pi\) | ||
0.970124 | − | 0.242609i | \(-0.0780031\pi\) | |||||||
\(398\) | −54.1873 | − | 31.2851i | −2.71617 | − | 1.56818i | ||||
\(399\) | 2.96442 | 0.148407 | ||||||||
\(400\) | −0.343753 | + | 2.26434i | −0.0171877 | + | 0.113217i | ||||
\(401\) | −31.0922 | −1.55267 | −0.776336 | − | 0.630319i | \(-0.782924\pi\) | ||||
−0.776336 | + | 0.630319i | \(0.782924\pi\) | |||||||
\(402\) | 12.8291 | − | 7.40691i | 0.639859 | − | 0.369423i | ||||
\(403\) | 8.38728 | − | 4.84240i | 0.417800 | − | 0.241217i | ||||
\(404\) | −6.99945 | − | 12.1234i | −0.348236 | − | 0.603162i | ||||
\(405\) | 1.69565 | − | 1.45766i | 0.0842575 | − | 0.0724317i | ||||
\(406\) | 16.4414 | 0.815975 | ||||||||
\(407\) | −0.573498 | − | 0.622134i | −0.0284272 | − | 0.0308380i | ||||
\(408\) | 3.48942i | 0.172752i | ||||||||
\(409\) | −6.25333 | + | 10.8311i | −0.309207 | + | 0.535563i | −0.978189 | − | 0.207716i | \(-0.933397\pi\) |
0.668982 | + | 0.743279i | \(0.266730\pi\) | |||||||
\(410\) | 15.3625 | − | 2.89830i | 0.758700 | − | 0.143137i | ||||
\(411\) | 6.02811 | + | 10.4410i | 0.297345 | + | 0.515016i | ||||
\(412\) | −46.2010 | + | 26.6741i | −2.27616 | + | 1.31414i | ||||
\(413\) | − | 10.0761i | − | 0.495814i | ||||||
\(414\) | −6.48167 | − | 11.2266i | −0.318557 | − | 0.551756i | ||||
\(415\) | 4.42814 | − | 12.6334i | 0.217369 | − | 0.620149i | ||||
\(416\) | −4.13863 | + | 7.16832i | −0.202913 | + | 0.351456i | ||||
\(417\) | − | 0.122709i | − | 0.00600908i | ||||||
\(418\) | − | 0.469427i | − | 0.0229604i | ||||||
\(419\) | 16.2092 | − | 28.0752i | 0.791872 | − | 1.37156i | −0.132934 | − | 0.991125i | \(-0.542440\pi\) |
0.924807 | − | 0.380438i | \(-0.124227\pi\) | |||||||
\(420\) | −2.58286 | − | 13.6905i | −0.126031 | − | 0.668029i | ||||
\(421\) | 37.4186 | 1.82367 | 0.911835 | − | 0.410558i | \(-0.134666\pi\) | ||||
0.911835 | + | 0.410558i | \(0.134666\pi\) | |||||||
\(422\) | 37.9463 | + | 21.9083i | 1.84720 | + | 1.06648i | ||||
\(423\) | −4.26921 | − | 2.46483i | −0.207576 | − | 0.119844i | ||||
\(424\) | 10.8415 | − | 18.7780i | 0.526508 | − | 0.911939i | ||||
\(425\) | −6.73184 | − | 1.02197i | −0.326542 | − | 0.0495729i | ||||
\(426\) | 8.35949 | + | 14.4791i | 0.405019 | + | 0.701513i | ||||
\(427\) | −2.29433 | − | 1.32463i | −0.111030 | − | 0.0641034i | ||||
\(428\) | 24.4764 | + | 14.1315i | 1.18311 | + | 0.683070i | ||||
\(429\) | 0.0934226 | − | 0.161813i | 0.00451049 | − | 0.00781239i | ||||
\(430\) | 11.6547 | + | 4.08510i | 0.562040 | + | 0.197001i | ||||
\(431\) | −10.0691 | − | 17.4401i | −0.485010 | − | 0.840062i | 0.514842 | − | 0.857285i | \(-0.327851\pi\) |
−0.999852 | + | 0.0172235i | \(0.994517\pi\) | |||||||
\(432\) | 0.396689 | + | 0.229029i | 0.0190857 | + | 0.0110191i | ||||
\(433\) | 25.4748i | 1.22424i | 0.790765 | + | 0.612120i | \(0.209683\pi\) | ||||
−0.790765 | + | 0.612120i | \(0.790317\pi\) | |||||||
\(434\) | −32.4997 | −1.56003 | ||||||||
\(435\) | 5.31699 | + | 6.18509i | 0.254930 | + | 0.296553i | ||||
\(436\) | −14.5156 | −0.695170 | ||||||||
\(437\) | 7.38341 | − | 4.26281i | 0.353196 | − | 0.203918i | ||||
\(438\) | 18.0447i | 0.862210i | ||||||||
\(439\) | 17.9509 | + | 31.0919i | 0.856749 | + | 1.48393i | 0.875013 | + | 0.484100i | \(0.160853\pi\) |
−0.0182633 | + | 0.999833i | \(0.505814\pi\) | |||||||
\(440\) | −0.783200 | + | 0.147759i | −0.0373376 | + | 0.00704413i | ||||
\(441\) | 1.52024 | + | 2.63314i | 0.0723925 | + | 0.125387i | ||||
\(442\) | −3.58833 | − | 2.07172i | −0.170680 | − | 0.0985419i | ||||
\(443\) | 1.13498i | 0.0539245i | 0.999636 | + | 0.0269622i | \(0.00858339\pi\) | ||||
−0.999636 | + | 0.0269622i | \(0.991417\pi\) | |||||||
\(444\) | −4.17771 | − | 18.5824i | −0.198265 | − | 0.881882i | ||||
\(445\) | −32.0301 | − | 11.2269i | −1.51837 | − | 0.532206i | ||||
\(446\) | −5.90518 | + | 10.2281i | −0.279618 | + | 0.484313i | ||||
\(447\) | −18.5130 | + | 10.6885i | −0.875634 | + | 0.505548i | ||||
\(448\) | 22.4763 | − | 12.9767i | 1.06191 | − | 0.613092i | ||||
\(449\) | 11.7119 | + | 20.2856i | 0.552718 | + | 0.957336i | 0.998077 | + | 0.0619838i | \(0.0197427\pi\) |
−0.445359 | + | 0.895352i | \(0.646924\pi\) | |||||||
\(450\) | 7.07108 | − | 8.84757i | 0.333334 | − | 0.417078i | ||||
\(451\) | −0.214671 | − | 0.371821i | −0.0101085 | − | 0.0175084i | ||||
\(452\) | 13.7088i | 0.644807i | ||||||||
\(453\) | 6.72993 | + | 3.88553i | 0.316200 | + | 0.182558i | ||||
\(454\) | −36.0044 | −1.68977 | ||||||||
\(455\) | 5.64008 | + | 1.97691i | 0.264411 | + | 0.0926789i | ||||
\(456\) | 1.90867 | − | 3.30591i | 0.0893815 | − | 0.154813i | ||||
\(457\) | 5.77512 | − | 3.33427i | 0.270149 | − | 0.155970i | −0.358806 | − | 0.933412i | \(-0.616816\pi\) |
0.628955 | + | 0.777442i | \(0.283483\pi\) | |||||||
\(458\) | − | 39.9185i | − | 1.86527i | ||||||
\(459\) | −0.680898 | + | 1.17935i | −0.0317816 | + | 0.0550473i | ||||
\(460\) | −26.1200 | − | 30.3845i | −1.21785 | − | 1.41669i | ||||
\(461\) | 6.31363 | − | 10.9355i | 0.294055 | − | 0.509318i | −0.680710 | − | 0.732553i | \(-0.738328\pi\) |
0.974765 | + | 0.223235i | \(0.0716618\pi\) | |||||||
\(462\) | −0.543002 | + | 0.313502i | −0.0252627 | + | 0.0145854i | ||||
\(463\) | −17.0860 | + | 9.86458i | −0.794052 | + | 0.458446i | −0.841387 | − | 0.540433i | \(-0.818260\pi\) |
0.0473353 | + | 0.998879i | \(0.484927\pi\) | |||||||
\(464\) | −0.835410 | + | 1.44697i | −0.0387829 | + | 0.0671740i | ||||
\(465\) | −10.5101 | − | 12.2260i | −0.487392 | − | 0.566969i | ||||
\(466\) | −26.0000 | + | 45.0333i | −1.20443 | + | 2.08613i | ||||
\(467\) | 4.79533i | 0.221902i | 0.993826 | + | 0.110951i | \(0.0353896\pi\) | ||||
−0.993826 | + | 0.110951i | \(0.964610\pi\) | |||||||
\(468\) | 3.64234 | − | 2.10291i | 0.168367 | − | 0.0972069i | ||||
\(469\) | 6.50653 | − | 11.2696i | 0.300443 | − | 0.520383i | ||||
\(470\) | −23.5639 | − | 8.25942i | −1.08692 | − | 0.380979i | ||||
\(471\) | −10.7053 | −0.493272 | ||||||||
\(472\) | −11.2369 | − | 6.48761i | −0.517219 | − | 0.298617i | ||||
\(473\) | − | 0.339165i | − | 0.0155948i | ||||||
\(474\) | 8.09298 | + | 14.0175i | 0.371723 | + | 0.643843i | ||||
\(475\) | 5.81880 | + | 4.65045i | 0.266985 | + | 0.213377i | ||||
\(476\) | 4.24240 | + | 7.34805i | 0.194450 | + | 0.336797i | ||||
\(477\) | 7.32836 | − | 4.23103i | 0.335543 | − | 0.193726i | ||||
\(478\) | 1.89547 | − | 1.09435i | 0.0866969 | − | 0.0500545i | ||||
\(479\) | 9.44020 | − | 16.3509i | 0.431334 | − | 0.747092i | −0.565655 | − | 0.824642i | \(-0.691377\pi\) |
0.996988 | + | 0.0775503i | \(0.0247099\pi\) | |||||||
\(480\) | 13.0037 | + | 4.55795i | 0.593536 | + | 0.208041i | ||||
\(481\) | 7.79951 | + | 2.43367i | 0.355627 | + | 0.110966i | ||||
\(482\) | − | 1.23336i | − | 0.0561781i | ||||||
\(483\) | −9.86188 | − | 5.69376i | −0.448731 | − | 0.259075i | ||||
\(484\) | −17.1912 | − | 29.7761i | −0.781419 | − | 1.35346i | ||||
\(485\) | −22.5956 | + | 4.26289i | −1.02601 | + | 0.193568i | ||||
\(486\) | −1.13261 | − | 1.96173i | −0.0513760 | − | 0.0889859i | ||||
\(487\) | − | 0.945335i | − | 0.0428372i | −0.999771 | − | 0.0214186i | \(-0.993182\pi\) | ||
0.999771 | − | 0.0214186i | \(-0.00681827\pi\) | |||||||
\(488\) | −2.95445 | + | 1.70575i | −0.133742 | + | 0.0772158i | ||||
\(489\) | 14.0020 | 0.633191 | ||||||||
\(490\) | 10.0394 | + | 11.6785i | 0.453534 | + | 0.527582i | ||||
\(491\) | −34.5732 | −1.56027 | −0.780133 | − | 0.625613i | \(-0.784849\pi\) | ||||
−0.780133 | + | 0.625613i | \(0.784849\pi\) | |||||||
\(492\) | − | 9.66432i | − | 0.435701i | ||||||
\(493\) | −4.30182 | − | 2.48366i | −0.193744 | − | 0.111858i | ||||
\(494\) | 2.26641 | + | 3.92554i | 0.101971 | + | 0.176618i | ||||
\(495\) | −0.293537 | − | 0.102888i | −0.0131935 | − | 0.00462447i | ||||
\(496\) | 1.65135 | − | 2.86022i | 0.0741478 | − | 0.128428i | ||||
\(497\) | 12.7190 | + | 7.34332i | 0.570525 | + | 0.329393i | ||||
\(498\) | −11.7446 | − | 6.78072i | −0.526286 | − | 0.303852i | ||||
\(499\) | 1.74047 | + | 3.01458i | 0.0779142 | + | 0.134951i | 0.902350 | − | 0.431004i | \(-0.141841\pi\) |
−0.824436 | + | 0.565956i | \(0.808507\pi\) | |||||||
\(500\) | 16.4073 | − | 30.9248i | 0.733755 | − | 1.38300i | ||||
\(501\) | −3.50931 | + | 6.07830i | −0.156784 | + | 0.271558i | ||||
\(502\) | −17.9633 | − | 10.3711i | −0.801742 | − | 0.462886i | ||||
\(503\) | 6.13867 | + | 3.54416i | 0.273710 | + | 0.158026i | 0.630572 | − | 0.776131i | \(-0.282820\pi\) |
−0.356863 | + | 0.934157i | \(0.616154\pi\) | |||||||
\(504\) | −5.09874 | −0.227116 | ||||||||
\(505\) | −1.85335 | − | 9.82372i | −0.0824729 | − | 0.437150i | ||||
\(506\) | −0.901628 | + | 1.56167i | −0.0400823 | + | 0.0694245i | ||||
\(507\) | − | 11.1958i | − | 0.497223i | ||||||
\(508\) | − | 16.8745i | − | 0.748685i | ||||||
\(509\) | 7.83602 | − | 13.5724i | 0.347326 | − | 0.601585i | −0.638448 | − | 0.769665i | \(-0.720423\pi\) |
0.985773 | + | 0.168080i | \(0.0537566\pi\) | |||||||
\(510\) | −2.28163 | + | 6.50943i | −0.101032 | + | 0.288243i | ||||
\(511\) | 7.92561 | + | 13.7276i | 0.350608 | + | 0.607271i | ||||
\(512\) | 5.17013i | 0.228489i | ||||||||
\(513\) | 1.29018 | − | 0.744884i | 0.0569627 | − | 0.0328874i | ||||
\(514\) | −18.4874 | − | 32.0212i | −0.815446 | − | 1.41239i | ||||
\(515\) | −37.4371 | + | 7.06290i | −1.64968 | + | 0.311229i | ||||
\(516\) | 3.81723 | − | 6.61164i | 0.168044 | − | 0.291061i | ||||
\(517\) | 0.685736i | 0.0301586i | ||||||||
\(518\) | −18.5832 | − | 20.1592i | −0.816500 | − | 0.885744i | ||||
\(519\) | 22.5017 | 0.987716 | ||||||||
\(520\) | 5.83606 | − | 5.01694i | 0.255928 | − | 0.220007i | ||||
\(521\) | 3.04069 | + | 5.26664i | 0.133215 | + | 0.230736i | 0.924914 | − | 0.380176i | \(-0.124137\pi\) |
−0.791699 | + | 0.610911i | \(0.790803\pi\) | |||||||
\(522\) | 7.15566 | − | 4.13132i | 0.313195 | − | 0.180823i | ||||
\(523\) | −31.0251 | + | 17.9124i | −1.35663 | + | 0.783253i | −0.989169 | − | 0.146784i | \(-0.953108\pi\) |
−0.367466 | + | 0.930037i | \(0.619775\pi\) | |||||||
\(524\) | −5.83427 | −0.254871 | ||||||||
\(525\) | 1.49330 | − | 9.83656i | 0.0651731 | − | 0.429303i | ||||
\(526\) | −39.3450 | −1.71552 | ||||||||
\(527\) | 8.50338 | + | 4.90943i | 0.370413 | + | 0.213858i | ||||
\(528\) | − | 0.0637177i | − | 0.00277296i | ||||||
\(529\) | −9.75035 | −0.423928 | ||||||||
\(530\) | 32.5028 | − | 27.9409i | 1.41183 | − | 1.21368i | ||||
\(531\) | −2.53188 | − | 4.38534i | −0.109874 | − | 0.190308i | ||||
\(532\) | − | 9.28214i | − | 0.402432i | ||||||
\(533\) | 3.59033 | + | 2.07288i | 0.155515 | + | 0.0897864i | ||||
\(534\) | −17.1915 | + | 29.7766i | −0.743950 | + | 1.28856i | ||||
\(535\) | 13.1572 | + | 15.3054i | 0.568837 | + | 0.661710i | ||||
\(536\) | −8.37857 | − | 14.5121i | −0.361899 | − | 0.626828i | ||||
\(537\) | −12.8783 | + | 7.43527i | −0.555738 | + | 0.320855i | ||||
\(538\) | 40.6539 | + | 23.4716i | 1.75272 | + | 1.01193i | ||||
\(539\) | 0.211472 | − | 0.366281i | 0.00910875 | − | 0.0157768i | ||||
\(540\) | −4.56420 | − | 5.30939i | −0.196412 | − | 0.228480i | ||||
\(541\) | −35.3488 | −1.51976 | −0.759882 | − | 0.650061i | \(-0.774743\pi\) | ||||
−0.759882 | + | 0.650061i | \(0.774743\pi\) | |||||||
\(542\) | −42.2573 | + | 24.3973i | −1.81511 | + | 1.04795i | ||||
\(543\) | 18.8122 | + | 10.8613i | 0.807310 | + | 0.466101i | ||||
\(544\) | −8.39184 | −0.359797 | ||||||||
\(545\) | −9.78246 | − | 3.42886i | −0.419035 | − | 0.146876i | ||||
\(546\) | 3.02720 | − | 5.24326i | 0.129552 | − | 0.224391i | ||||
\(547\) | 9.47749i | 0.405228i | 0.979259 | + | 0.202614i | \(0.0649437\pi\) | ||||
−0.979259 | + | 0.202614i | \(0.935056\pi\) | |||||||
\(548\) | 32.6926 | − | 18.8751i | 1.39656 | − | 0.806305i | ||||
\(549\) | −1.33139 | −0.0568222 | ||||||||
\(550\) | −1.55766 | − | 0.236470i | −0.0664187 | − | 0.0100831i | ||||
\(551\) | 2.71706 | + | 4.70608i | 0.115750 | + | 0.200486i | ||||
\(552\) | −12.6993 | + | 7.33195i | −0.540519 | + | 0.312069i | ||||
\(553\) | 12.3135 | + | 7.10920i | 0.523623 | + | 0.302314i | ||||
\(554\) | −25.2807 | −1.07407 | ||||||||
\(555\) | 1.57405 | − | 13.5101i | 0.0668147 | − | 0.573471i | ||||
\(556\) | −0.384224 | −0.0162947 | ||||||||
\(557\) | 29.9805 | + | 17.3093i | 1.27032 | + | 0.733417i | 0.975047 | − | 0.221997i | \(-0.0712575\pi\) |
0.295269 | + | 0.955414i | \(0.404591\pi\) | |||||||
\(558\) | −14.1445 | + | 8.16635i | −0.598786 | + | 0.345709i | ||||
\(559\) | 1.63750 | + | 2.83623i | 0.0692589 | + | 0.119960i | ||||
\(560\) | 2.00277 | − | 0.377844i | 0.0846325 | − | 0.0159668i | ||||
\(561\) | 0.189432 | 0.00799781 | ||||||||
\(562\) | 55.3526 | − | 31.9579i | 2.33491 | − | 1.34806i | ||||
\(563\) | − | 9.69540i | − | 0.408613i | −0.978907 | − | 0.204306i | \(-0.934506\pi\) | ||
0.978907 | − | 0.204306i | \(-0.0654938\pi\) | |||||||
\(564\) | −7.71783 | + | 13.3677i | −0.324979 | + | 0.562880i | ||||
\(565\) | −3.23828 | + | 9.23875i | −0.136236 | + | 0.388677i | ||||
\(566\) | −57.2931 | −2.40821 | ||||||||
\(567\) | −1.72326 | − | 0.994927i | −0.0723703 | − | 0.0417830i | ||||
\(568\) | 16.3785 | − | 9.45612i | 0.687226 | − | 0.396770i | ||||
\(569\) | 23.2169 | 0.973304 | 0.486652 | − | 0.873596i | \(-0.338218\pi\) | ||||
0.486652 | + | 0.873596i | \(0.338218\pi\) | |||||||
\(570\) | 5.72221 | − | 4.91907i | 0.239677 | − | 0.206037i | ||||
\(571\) | 18.3832 | − | 31.8406i | 0.769313 | − | 1.33249i | −0.168623 | − | 0.985681i | \(-0.553932\pi\) |
0.937936 | − | 0.346808i | \(-0.112735\pi\) | |||||||
\(572\) | −0.506665 | − | 0.292523i | −0.0211847 | − | 0.0122310i | ||||
\(573\) | −7.72257 | + | 4.45863i | −0.322615 | + | 0.186262i | ||||
\(574\) | −6.95605 | − | 12.0482i | −0.290340 | − | 0.502884i | ||||
\(575\) | −10.4256 | − | 26.6471i | −0.434776 | − | 1.11126i | ||||
\(576\) | 6.52144 | − | 11.2955i | 0.271727 | − | 0.470644i | ||||
\(577\) | 12.7911 | + | 7.38496i | 0.532502 | + | 0.307440i | 0.742035 | − | 0.670362i | \(-0.233861\pi\) |
−0.209533 | + | 0.977802i | \(0.567194\pi\) | |||||||
\(578\) | 34.3078i | 1.42702i | ||||||||
\(579\) | 5.25097 | + | 9.09495i | 0.218223 | + | 0.377973i | ||||
\(580\) | 19.3667 | − | 16.6485i | 0.804157 | − | 0.691290i | ||||
\(581\) | −11.9129 | −0.494231 | ||||||||
\(582\) | 23.2938i | 0.965561i | ||||||||
\(583\) | −1.01941 | − | 0.588555i | −0.0422195 | − | 0.0243754i | ||||
\(584\) | 20.4119 | 0.844650 | ||||||||
\(585\) | 2.95143 | − | 0.556817i | 0.122026 | − | 0.0230216i | ||||
\(586\) | 20.8947 | 0.863152 | ||||||||
\(587\) | 0.112600 | − | 0.0650099i | 0.00464752 | − | 0.00268325i | −0.497674 | − | 0.867364i | \(-0.665813\pi\) |
0.502322 | + | 0.864681i | \(0.332479\pi\) | |||||||
\(588\) | 8.24483 | − | 4.76016i | 0.340011 | − | 0.196306i | ||||
\(589\) | −5.37078 | − | 9.30247i | −0.221299 | − | 0.383302i | ||||
\(590\) | −16.7201 | − | 19.4499i | −0.688354 | − | 0.800741i | ||||
\(591\) | 15.7563 | 0.648126 | ||||||||
\(592\) | 2.71840 | − | 0.611152i | 0.111726 | − | 0.0251182i | ||||
\(593\) | 25.0529i | 1.02880i | 0.857551 | + | 0.514399i | \(0.171985\pi\) | ||||
−0.857551 | + | 0.514399i | \(0.828015\pi\) | |||||||
\(594\) | −0.157550 | + | 0.272885i | −0.00646437 | + | 0.0111966i | ||||
\(595\) | 1.12332 | + | 5.95420i | 0.0460517 | + | 0.244098i | ||||
\(596\) | 33.4676 | + | 57.9676i | 1.37089 | + | 2.37444i | ||||
\(597\) | −23.9215 | + | 13.8111i | −0.979043 | + | 0.565251i | ||||
\(598\) | − | 17.4124i | − | 0.712045i | ||||||
\(599\) | −8.03951 | − | 13.9248i | −0.328485 | − | 0.568953i | 0.653726 | − | 0.756731i | \(-0.273205\pi\) |
−0.982212 | + | 0.187778i | \(0.939872\pi\) | |||||||
\(600\) | −10.0082 | − | 7.99869i | −0.408584 | − | 0.326545i | ||||
\(601\) | 8.45821 | − | 14.6500i | 0.345017 | − | 0.597588i | −0.640339 | − | 0.768092i | \(-0.721206\pi\) |
0.985357 | + | 0.170504i | \(0.0545397\pi\) | |||||||
\(602\) | − | 10.9901i | − | 0.447921i | ||||||
\(603\) | − | 6.53970i | − | 0.266317i | ||||||
\(604\) | 12.1663 | − | 21.0726i | 0.495040 | − | 0.857434i | ||||
\(605\) | −4.55197 | − | 24.1278i | −0.185064 | − | 0.980936i | ||||
\(606\) | −10.1273 | −0.411394 | ||||||||
\(607\) | −1.22625 | − | 0.707974i | −0.0497718 | − | 0.0287358i | 0.474908 | − | 0.880036i | \(-0.342481\pi\) |
−0.524679 | + | 0.851300i | \(0.675815\pi\) | |||||||
\(608\) | 7.95050 | + | 4.59022i | 0.322435 | + | 0.186158i | ||||
\(609\) | 3.62912 | − | 6.28582i | 0.147059 | − | 0.254714i | ||||
\(610\) | −6.62679 | + | 1.25021i | −0.268311 | + | 0.0506197i | ||||
\(611\) | −3.31076 | − | 5.73441i | −0.133939 | − | 0.231989i | ||||
\(612\) | 3.69276 | + | 2.13202i | 0.149271 | + | 0.0861816i | ||||
\(613\) | 16.9668 | + | 9.79576i | 0.685281 | + | 0.395647i | 0.801842 | − | 0.597536i | \(-0.203854\pi\) |
−0.116561 | + | 0.993184i | \(0.537187\pi\) | |||||||
\(614\) | −7.29251 | + | 12.6310i | −0.294302 | + | 0.509745i | ||||
\(615\) | 2.28290 | − | 6.51307i | 0.0920555 | − | 0.262632i | ||||
\(616\) | 0.354628 | + | 0.614234i | 0.0142884 | + | 0.0247482i | ||||
\(617\) | −8.13849 | − | 4.69876i | −0.327643 | − | 0.189165i | 0.327151 | − | 0.944972i | \(-0.393911\pi\) |
−0.654794 | + | 0.755807i | \(0.727245\pi\) | |||||||
\(618\) | 38.5941i | 1.55248i | ||||||||
\(619\) | 38.5635 | 1.55000 | 0.775000 | − | 0.631961i | \(-0.217750\pi\) | ||||
0.775000 | + | 0.631961i | \(0.217750\pi\) | |||||||
\(620\) | −38.2819 | + | 32.9089i | −1.53744 | + | 1.32165i | ||||
\(621\) | −5.72279 | −0.229648 | ||||||||
\(622\) | −3.25315 | + | 1.87820i | −0.130439 | + | 0.0753091i | ||||
\(623\) | 30.2035i | 1.21008i | ||||||||
\(624\) | 0.307632 | + | 0.532834i | 0.0123151 | + | 0.0213304i | ||||
\(625\) | 18.3624 | − | 16.9654i | 0.734494 | − | 0.678615i | ||||
\(626\) | 9.11578 | + | 15.7890i | 0.364340 | + | 0.631055i | ||||
\(627\) | −0.179469 | − | 0.103617i | −0.00716731 | − | 0.00413805i | ||||
\(628\) | 33.5201i | 1.33760i | ||||||||
\(629\) | 1.81694 | + | 8.08175i | 0.0724463 | + | 0.322241i | ||||
\(630\) | −9.51157 | − | 3.33391i | −0.378950 | − | 0.132826i | ||||
\(631\) | 10.4190 | − | 18.0463i | 0.414776 | − | 0.718413i | −0.580629 | − | 0.814168i | \(-0.697193\pi\) |
0.995405 | + | 0.0957554i | \(0.0305267\pi\) | |||||||
\(632\) | 15.8563 | − | 9.15465i | 0.630730 | − | 0.364152i | ||||
\(633\) | 16.7518 | − | 9.67165i | 0.665824 | − | 0.384413i | ||||
\(634\) | −9.88615 | − | 17.1233i | −0.392629 | − | 0.680054i | ||||
\(635\) | 3.98609 | − | 11.3722i | 0.158183 | − | 0.451293i | ||||
\(636\) | −13.2481 | − | 22.9464i | −0.525323 | − | 0.909886i | ||||
\(637\) | 4.08398i | 0.161813i | ||||||||
\(638\) | −0.995383 | − | 0.574684i | −0.0394076 | − | 0.0227520i | ||||
\(639\) | 7.38076 | 0.291978 | ||||||||
\(640\) | 12.7369 | − | 36.3380i | 0.503469 | − | 1.43639i | ||||
\(641\) | 15.3203 | − | 26.5356i | 0.605116 | − | 1.04809i | −0.386917 | − | 0.922114i | \(-0.626460\pi\) |
0.992033 | − | 0.125977i | \(-0.0402066\pi\) | |||||||
\(642\) | 17.7071 | − | 10.2232i | 0.698844 | − | 0.403478i | ||||
\(643\) | 34.8708i | 1.37517i | 0.726104 | + | 0.687585i | \(0.241329\pi\) | ||||
−0.726104 | + | 0.687585i | \(0.758671\pi\) | |||||||
\(644\) | −17.8282 | + | 30.8793i | −0.702530 | + | 1.21682i | ||||
\(645\) | 4.13434 | − | 3.55407i | 0.162790 | − | 0.139941i | ||||
\(646\) | −2.29778 | + | 3.97988i | −0.0904051 | + | 0.156586i | ||||
\(647\) | 22.9615 | − | 13.2569i | 0.902711 | − | 0.521181i | 0.0246324 | − | 0.999697i | \(-0.492158\pi\) |
0.878079 | + | 0.478516i | \(0.158825\pi\) | |||||||
\(648\) | −2.21908 | + | 1.28118i | −0.0871736 | + | 0.0503297i | ||||
\(649\) | −0.352195 | + | 0.610020i | −0.0138249 | + | 0.0239454i | ||||
\(650\) | 14.1674 | − | 5.54296i | 0.555693 | − | 0.217413i | ||||
\(651\) | −7.17365 | + | 12.4251i | −0.281158 | + | 0.486979i | ||||
\(652\) | − | 43.8428i | − | 1.71702i | ||||||
\(653\) | 11.2002 | − | 6.46642i | 0.438296 | − | 0.253051i | −0.264578 | − | 0.964364i | \(-0.585233\pi\) |
0.702875 | + | 0.711314i | \(0.251899\pi\) | |||||||
\(654\) | −5.25054 | + | 9.09421i | −0.205312 | + | 0.355612i | ||||
\(655\) | −3.93189 | − | 1.37817i | −0.153631 | − | 0.0538495i | ||||
\(656\) | 1.41378 | 0.0551989 | ||||||||
\(657\) | 6.89878 | + | 3.98301i | 0.269147 | + | 0.155392i | ||||
\(658\) | 22.2201i | 0.866230i | ||||||||
\(659\) | 21.9111 | + | 37.9512i | 0.853536 | + | 1.47837i | 0.877996 | + | 0.478668i | \(0.158880\pi\) |
−0.0244598 | + | 0.999701i | \(0.507787\pi\) | |||||||
\(660\) | −0.322161 | + | 0.919119i | −0.0125401 | + | 0.0357767i | ||||
\(661\) | 1.61157 | + | 2.79132i | 0.0626829 | + | 0.108570i | 0.895664 | − | 0.444732i | \(-0.146701\pi\) |
−0.832981 | + | 0.553302i | \(0.813368\pi\) | |||||||
\(662\) | −1.52564 | + | 0.880829i | −0.0592957 | + | 0.0342344i | ||||
\(663\) | −1.58410 | + | 0.914583i | −0.0615215 | + | 0.0355195i | ||||
\(664\) | −7.67024 | + | 13.2853i | −0.297663 | + | 0.515568i | ||||
\(665\) | 2.19262 | − | 6.25550i | 0.0850262 | − | 0.242578i | ||||
\(666\) | −13.1533 | − | 4.10420i | −0.509680 | − | 0.159035i | ||||
\(667\) | − | 20.8746i | − | 0.808267i | ||||||
\(668\) | 19.0323 | + | 10.9883i | 0.736381 | + | 0.425150i | ||||
\(669\) | 2.60690 | + | 4.51528i | 0.100789 | + | 0.174571i | ||||
\(670\) | −6.14099 | − | 32.5505i | −0.237247 | − | 1.25753i | ||||
\(671\) | 0.0926008 | + | 0.160389i | 0.00357482 | + | 0.00619176i | ||||
\(672\) | − | 12.2621i | − | 0.473023i | ||||||
\(673\) | 39.3576 | − | 22.7231i | 1.51712 | − | 0.875912i | 0.517326 | − | 0.855788i | \(-0.326927\pi\) |
0.999797 | − | 0.0201237i | \(-0.00640599\pi\) | |||||||
\(674\) | 48.1562 | 1.85491 | ||||||||
\(675\) | −1.82176 | − | 4.65631i | −0.0701197 | − | 0.179221i | ||||
\(676\) | −35.0561 | −1.34831 | ||||||||
\(677\) | 31.8762i | 1.22510i | 0.790431 | + | 0.612551i | \(0.209857\pi\) | ||||
−0.790431 | + | 0.612551i | \(0.790143\pi\) | |||||||
\(678\) | 8.58875 | + | 4.95872i | 0.329849 | + | 0.190438i | ||||
\(679\) | 10.2311 | + | 17.7208i | 0.392635 | + | 0.680063i | ||||
\(680\) | 7.36336 | + | 2.58094i | 0.282372 | + | 0.0989745i | ||||
\(681\) | −7.94726 | + | 13.7651i | −0.304540 | + | 0.527478i | ||||
\(682\) | 1.96757 | + | 1.13597i | 0.0753420 | + | 0.0434987i | ||||
\(683\) | −26.1641 | − | 15.1059i | −1.00114 | − | 0.578009i | −0.0925558 | − | 0.995708i | \(-0.529504\pi\) |
−0.908586 | + | 0.417698i | \(0.862837\pi\) | |||||||
\(684\) | −2.33237 | − | 4.03978i | −0.0891803 | − | 0.154465i | ||||
\(685\) | 26.4912 | − | 4.99784i | 1.01218 | − | 0.190958i | ||||
\(686\) | 22.6284 | − | 39.1936i | 0.863958 | − | 1.49642i | ||||
\(687\) | −15.2615 | − | 8.81122i | −0.582261 | − | 0.336169i | ||||
\(688\) | 0.967210 | + | 0.558419i | 0.0368745 | + | 0.0212895i | ||||
\(689\) | 11.3663 | 0.433020 | ||||||||
\(690\) | −28.4844 | + | 5.37388i | −1.08438 | + | 0.204580i | ||||
\(691\) | 12.6294 | − | 21.8748i | 0.480445 | − | 0.832156i | −0.519303 | − | 0.854590i | \(-0.673808\pi\) |
0.999748 | + | 0.0224344i | \(0.00714170\pi\) | |||||||
\(692\) | − | 70.4570i | − | 2.67837i | ||||||
\(693\) | 0.276797i | 0.0105147i | ||||||||
\(694\) | −35.9572 | + | 62.2798i | −1.36492 | + | 2.36411i | ||||
\(695\) | −0.258940 | − | 0.0907612i | −0.00982214 | − | 0.00344277i | ||||
\(696\) | −4.67328 | − | 8.09436i | −0.177140 | − | 0.306816i | ||||
\(697\) | 4.20315i | 0.159206i | ||||||||
\(698\) | −52.2329 | + | 30.1567i | −1.97704 | + | 1.14145i | ||||
\(699\) | 11.4780 | + | 19.8804i | 0.434136 | + | 0.751946i | ||||
\(700\) | −30.8001 | − | 4.67581i | −1.16413 | − | 0.176729i | ||||
\(701\) | −3.14432 | + | 5.44612i | −0.118759 | + | 0.205697i | −0.919276 | − | 0.393613i | \(-0.871225\pi\) |
0.800517 | + | 0.599310i | \(0.204558\pi\) | |||||||
\(702\) | − | 3.04264i | − | 0.114837i | ||||||
\(703\) | 2.69922 | − | 8.65056i | 0.101803 | − | 0.326262i | ||||
\(704\) | −1.81432 | −0.0683798 | ||||||||
\(705\) | −8.35897 | + | 7.18576i | −0.314817 | + | 0.270631i | ||||
\(706\) | 19.9296 | + | 34.5190i | 0.750059 | + | 1.29914i | ||||
\(707\) | −7.70437 | + | 4.44812i | −0.289753 | + | 0.167289i | ||||
\(708\) | −13.7313 | + | 7.92778i | −0.516054 | + | 0.297944i | ||||
\(709\) | −21.6686 | −0.813782 | −0.406891 | − | 0.913477i | \(-0.633387\pi\) | ||||
−0.406891 | + | 0.913477i | \(0.633387\pi\) | |||||||
\(710\) | 36.7367 | − | 6.93077i | 1.37870 | − | 0.260107i | ||||
\(711\) | 7.14545 | 0.267975 | ||||||||
\(712\) | 33.6828 | + | 19.4468i | 1.26232 | + | 0.728799i | ||||
\(713\) | 41.2627i | 1.54530i | ||||||||
\(714\) | 6.13821 | 0.229717 | ||||||||
\(715\) | −0.272357 | − | 0.316824i | −0.0101856 | − | 0.0118486i | ||||
\(716\) | 23.2812 | + | 40.3242i | 0.870059 | + | 1.50699i | ||||
\(717\) | − | 0.966225i | − | 0.0360843i | ||||||
\(718\) | 27.6309 | + | 15.9527i | 1.03118 | + | 0.595349i | ||||
\(719\) | 21.1134 | − | 36.5696i | 0.787399 | − | 1.36381i | −0.140157 | − | 0.990129i | \(-0.544761\pi\) |
0.927556 | − | 0.373685i | \(-0.121906\pi\) | |||||||
\(720\) | 0.776705 | − | 0.667691i | 0.0289461 | − | 0.0248834i | ||||
\(721\) | 16.9513 | + | 29.3605i | 0.631299 | + | 1.09344i | ||||
\(722\) | −32.9190 | + | 19.0058i | −1.22512 | + | 0.707323i | ||||
\(723\) | −0.471533 | − | 0.272240i | −0.0175365 | − | 0.0101247i | ||||
\(724\) | 34.0086 | − | 58.9046i | 1.26392 | − | 2.18917i | ||||
\(725\) | 16.9844 | − | 6.64511i | 0.630787 | − | 0.246793i | ||||
\(726\) | −24.8735 | −0.923142 | ||||||||
\(727\) | −25.9086 | + | 14.9583i | −0.960896 | + | 0.554774i | −0.896449 | − | 0.443148i | \(-0.853862\pi\) |
−0.0644473 | + | 0.997921i | \(0.520528\pi\) | |||||||
\(728\) | −5.93109 | − | 3.42432i | −0.219821 | − | 0.126914i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 38.0779 | + | 13.3467i | 1.40933 | + | 0.493984i | ||||
\(731\) | −1.66017 | + | 2.87550i | −0.0614035 | + | 0.106354i | ||||
\(732\) | 4.16882i | 0.154084i | ||||||||
\(733\) | 26.9123 | − | 15.5378i | 0.994029 | − | 0.573903i | 0.0875528 | − | 0.996160i | \(-0.472095\pi\) |
0.906476 | + | 0.422257i | \(0.138762\pi\) | |||||||
\(734\) | 62.8046 | 2.31816 | ||||||||
\(735\) | 6.68087 | − | 1.26042i | 0.246428 | − | 0.0464912i | ||||
\(736\) | −17.6329 | − | 30.5410i | −0.649957 | − | 1.12576i | ||||
\(737\) | −0.787824 | + | 0.454851i | −0.0290199 | + | 0.0167546i | ||||
\(738\) | −6.05484 | − | 3.49576i | −0.222882 | − | 0.128681i | ||||
\(739\) | −35.9209 | −1.32137 | −0.660686 | − | 0.750663i | \(-0.729734\pi\) | ||||
−0.660686 | + | 0.750663i | \(0.729734\pi\) | |||||||
\(740\) | −42.3026 | − | 4.92864i | −1.55507 | − | 0.181180i | ||||
\(741\) | 2.00106 | 0.0735107 | ||||||||
\(742\) | −33.0321 | − | 19.0711i | −1.21265 | − | 0.700123i | ||||
\(743\) | 40.0021 | − | 23.0952i | 1.46753 | − | 0.847281i | 0.468194 | − | 0.883626i | \(-0.344905\pi\) |
0.999339 | + | 0.0363450i | \(0.0115715\pi\) | |||||||
\(744\) | 9.23764 | + | 16.0001i | 0.338668 | + | 0.586591i | ||||
\(745\) | 8.86171 | + | 46.9717i | 0.324668 | + | 1.72091i | ||||
\(746\) | 13.1440 | 0.481234 | ||||||||
\(747\) | −5.18475 | + | 2.99342i | −0.189700 | + | 0.109523i | ||||
\(748\) | − | 0.593145i | − | 0.0216875i | ||||||
\(749\) | 8.98048 | − | 15.5546i | 0.328140 | − | 0.568354i | ||||
\(750\) | −13.4400 | − | 21.4654i | −0.490759 | − | 0.783806i | ||||
\(751\) | −47.4564 | −1.73171 | −0.865854 | − | 0.500296i | \(-0.833225\pi\) | ||||
−0.865854 | + | 0.500296i | \(0.833225\pi\) | |||||||
\(752\) | −1.95554 | − | 1.12903i | −0.0713112 | − | 0.0411716i | ||||
\(753\) | −7.93008 | + | 4.57843i | −0.288988 | + | 0.166847i | ||||
\(754\) | 11.0984 | 0.404180 | ||||||||
\(755\) | 13.1770 | − | 11.3275i | 0.479560 | − | 0.412252i | ||||
\(756\) | −3.11530 | + | 5.39585i | −0.113302 | + | 0.196245i | ||||
\(757\) | −13.4300 | − | 7.75380i | −0.488121 | − | 0.281817i | 0.235674 | − | 0.971832i | \(-0.424270\pi\) |
−0.723795 | + | 0.690016i | \(0.757604\pi\) | |||||||
\(758\) | −37.8483 | + | 21.8517i | −1.37471 | + | 0.793689i | ||||
\(759\) | 0.398033 | + | 0.689413i | 0.0144477 | + | 0.0250241i | ||||
\(760\) | −5.56437 | − | 6.47286i | −0.201841 | − | 0.234795i | ||||
\(761\) | −8.91886 | + | 15.4479i | −0.323308 | + | 0.559986i | −0.981169 | − | 0.193154i | \(-0.938128\pi\) |
0.657860 | + | 0.753140i | \(0.271462\pi\) | |||||||
\(762\) | −10.5721 | − | 6.10381i | −0.382987 | − | 0.221118i | ||||
\(763\) | 9.22458i | 0.333952i | ||||||||
\(764\) | 13.9608 | + | 24.1808i | 0.505083 | + | 0.874830i | ||||
\(765\) | 1.98503 | + | 2.30913i | 0.0717690 | + | 0.0834867i | ||||
\(766\) | 29.1484 | 1.05317 | ||||||||
\(767\) | − | 6.80165i | − | 0.245593i | ||||||
\(768\) | −11.1905 | − | 6.46083i | −0.403802 | − | 0.233135i | ||||
\(769\) | −21.2282 | −0.765510 | −0.382755 | − | 0.923850i | \(-0.625025\pi\) | ||||
−0.382755 | + | 0.923850i | \(0.625025\pi\) | |||||||
\(770\) | 0.259921 | + | 1.37772i | 0.00936692 | + | 0.0496496i | ||||
\(771\) | −16.3229 | −0.587856 | ||||||||
\(772\) | 28.4780 | − | 16.4418i | 1.02494 | − | 0.591752i | ||||
\(773\) | −33.6932 | + | 19.4528i | −1.21186 | + | 0.699668i | −0.963164 | − | 0.268913i | \(-0.913336\pi\) |
−0.248697 | + | 0.968581i | \(0.580002\pi\) | |||||||
\(774\) | −2.76153 | − | 4.78310i | −0.0992610 | − | 0.171925i | ||||
\(775\) | −33.5730 | + | 13.1353i | −1.20598 | + | 0.471835i | ||||
\(776\) | 26.3496 | 0.945896 | ||||||||
\(777\) | −11.8090 | + | 2.65492i | −0.423647 | + | 0.0952446i | ||||
\(778\) | 59.9437i | 2.14908i | ||||||||
\(779\) | 2.29907 | − | 3.98210i | 0.0823726 | − | 0.142673i | ||||
\(780\) | −1.74350 | − | 9.24145i | −0.0624272 | − | 0.330897i | ||||
\(781\) | −0.513348 | − | 0.889145i | −0.0183690 | − | 0.0318161i | ||||
\(782\) | 15.2883 | − | 8.82670i | 0.546708 | − | 0.315642i | ||||
\(783\) | − | 3.64762i | − | 0.130355i | ||||||
\(784\) | 0.696358 | + | 1.20613i | 0.0248699 | + | 0.0430760i | ||||
\(785\) | −7.91810 | + | 22.5902i | −0.282609 | + | 0.806278i | ||||
\(786\) | −2.11036 | + | 3.65526i | −0.0752741 | + | 0.130379i | ||||
\(787\) | 0.610223i | 0.0217521i | 0.999941 | + | 0.0108760i | \(0.00346202\pi\) | ||||
−0.999941 | + | 0.0108760i | \(0.996538\pi\) | |||||||
\(788\) | − | 49.3358i | − | 1.75751i | ||||||
\(789\) | −8.68461 | + | 15.0422i | −0.309180 | + | 0.535516i | ||||
\(790\) | 35.5655 | − | 6.70981i | 1.26536 | − | 0.238724i | ||||
\(791\) | 8.71187 | 0.309759 | ||||||||
\(792\) | 0.308683 | + | 0.178218i | 0.0109686 | + | 0.00633271i | ||||
\(793\) | −1.54873 | − | 0.894161i | −0.0549971 | − | 0.0317526i | ||||
\(794\) | −10.9499 | + | 18.9658i | −0.388598 | + | 0.673071i | ||||
\(795\) | −3.50790 | − | 18.5937i | −0.124413 | − | 0.659452i | ||||
\(796\) | 43.2451 | + | 74.9027i | 1.53278 | + | 2.65486i | ||||
\(797\) | −22.9411 | − | 13.2450i | −0.812615 | − | 0.469163i | 0.0352485 | − | 0.999379i | \(-0.488778\pi\) |
−0.847863 | + | 0.530215i | \(0.822111\pi\) | |||||||
\(798\) | −5.81539 | − | 3.35752i | −0.205863 | − | 0.118855i | ||||
\(799\) | 3.35659 | − | 5.81378i | 0.118748 | − | 0.205677i | ||||
\(800\) | 19.2363 | − | 24.0691i | 0.680107 | − | 0.850972i | ||||
\(801\) | 7.58937 | + | 13.1452i | 0.268157 | + | 0.464462i | ||||
\(802\) | 60.9946 | + | 35.2152i | 2.15379 | + | 1.24349i | ||||
\(803\) | − | 1.10811i | − | 0.0391043i | ||||||
\(804\) | −20.4770 | −0.722169 | ||||||||
\(805\) | −19.3092 | + | 16.5991i | −0.680561 | + | 0.585042i | ||||
\(806\) | −21.9381 | −0.772737 | ||||||||
\(807\) | 17.9471 | − | 10.3618i | 0.631767 | − | 0.364751i | ||||
\(808\) | 11.4559i | 0.403015i | ||||||||
\(809\) | 2.54245 | + | 4.40365i | 0.0893876 | + | 0.154824i | 0.907252 | − | 0.420587i | \(-0.138176\pi\) |
−0.817865 | + | 0.575410i | \(0.804842\pi\) | |||||||
\(810\) | −4.97736 | + | 0.939032i | −0.174887 | + | 0.0329942i | ||||
\(811\) | 15.8725 | + | 27.4920i | 0.557358 | + | 0.965373i | 0.997716 | + | 0.0675505i | \(0.0215184\pi\) |
−0.440357 | + | 0.897823i | \(0.645148\pi\) | |||||||
\(812\) | −19.6820 | − | 11.3634i | −0.690704 | − | 0.398778i | ||||
\(813\) | 21.5408i | 0.755471i | ||||||||
\(814\) | 0.420416 | + | 1.87001i | 0.0147356 | + | 0.0655437i | ||||
\(815\) | 10.3565 | − | 29.5469i | 0.362773 | − | 1.03498i | ||||
\(816\) | −0.311890 | + | 0.540209i | −0.0109183 | + | 0.0189111i | ||||
\(817\) | 3.14571 | − | 1.81618i | 0.110055 | − | 0.0635401i | ||||
\(818\) | 24.5347 | − | 14.1651i | 0.857836 | − | 0.495272i | ||||
\(819\) | −1.33639 | − | 2.31469i | −0.0466972 | − | 0.0808818i | ||||
\(820\) | −20.3936 | − | 7.14818i | −0.712176 | − | 0.249625i | ||||
\(821\) | −2.62563 | − | 4.54772i | −0.0916350 | − | 0.158716i | 0.816564 | − | 0.577255i | \(-0.195876\pi\) |
−0.908199 | + | 0.418538i | \(0.862543\pi\) | |||||||
\(822\) | − | 27.3099i | − | 0.952541i | ||||||
\(823\) | −31.9125 | − | 18.4247i | −1.11240 | − | 0.642244i | −0.172949 | − | 0.984931i | \(-0.555330\pi\) |
−0.939450 | + | 0.342687i | \(0.888663\pi\) | |||||||
\(824\) | 43.6570 | 1.52086 | ||||||||
\(825\) | −0.434228 | + | 0.543320i | −0.0151179 | + | 0.0189160i | ||||
\(826\) | −11.4123 | + | 19.7667i | −0.397084 | + | 0.687770i | ||||
\(827\) | −26.0304 | + | 15.0286i | −0.905165 | + | 0.522597i | −0.878872 | − | 0.477057i | \(-0.841703\pi\) |
−0.0262926 | + | 0.999654i | \(0.508370\pi\) | |||||||
\(828\) | 17.9191i | 0.622732i | ||||||||
\(829\) | 11.2631 | − | 19.5082i | 0.391182 | − | 0.677548i | −0.601423 | − | 0.798930i | \(-0.705400\pi\) |
0.992606 | + | 0.121383i | \(0.0387329\pi\) | |||||||
\(830\) | −22.9955 | + | 19.7680i | −0.798184 | + | 0.686156i | ||||
\(831\) | −5.58021 | + | 9.66521i | −0.193575 | + | 0.335282i | ||||
\(832\) | 15.1721 | − | 8.75961i | 0.525998 | − | 0.303685i | ||||
\(833\) | −3.58579 | + | 2.07026i | −0.124240 | + | 0.0717302i | ||||
\(834\) | −0.138981 | + | 0.240722i | −0.00481251 | + | 0.00833551i | ||||
\(835\) | 10.2307 | + | 11.9011i | 0.354050 | + | 0.411855i | ||||
\(836\) | −0.324442 | + | 0.561951i | −0.0112211 | + | 0.0194355i | ||||
\(837\) | 7.21023i | 0.249222i | ||||||||
\(838\) | −63.5962 | + | 36.7173i | −2.19690 | + | 1.26838i | ||||
\(839\) | −14.5451 | + | 25.1929i | −0.502153 | + | 0.869755i | 0.497844 | + | 0.867267i | \(0.334125\pi\) |
−0.999997 | + | 0.00248802i | \(0.999208\pi\) | |||||||
\(840\) | −3.77127 | + | 10.7593i | −0.130121 | + | 0.371232i | ||||
\(841\) | −15.6948 | −0.541201 | ||||||||
\(842\) | −73.4052 | − | 42.3805i | −2.52971 | − | 1.46053i | ||||
\(843\) | − | 28.2162i | − | 0.971818i | ||||||
\(844\) | −30.2837 | − | 52.4529i | −1.04241 | − | 1.80550i | ||||
\(845\) | −23.6253 | − | 8.28094i | −0.812736 | − | 0.284873i | ||||
\(846\) | 5.58335 | + | 9.67065i | 0.191960 | + | 0.332484i | ||||
\(847\) | −18.9226 | + | 10.9249i | −0.650187 | + | 0.375385i | ||||
\(848\) | 3.35681 | − | 1.93805i | 0.115273 | − | 0.0665531i | ||||
\(849\) | −12.6463 | + | 21.9041i | −0.434020 | + | 0.751745i | ||||
\(850\) | 12.0486 | + | 9.62936i | 0.413263 | + | 0.330284i | ||||
\(851\) | −25.5948 | + | 23.5939i | −0.877377 | + | 0.808787i | ||||
\(852\) | − | 23.1105i | − | 0.791753i | ||||||
\(853\) | −1.34282 | − | 0.775276i | −0.0459772 | − | 0.0265449i | 0.476835 | − | 0.878993i | \(-0.341784\pi\) |
−0.522812 | + | 0.852448i | \(0.675117\pi\) | |||||||
\(854\) | 3.00057 | + | 5.19714i | 0.102677 | + | 0.177843i | ||||
\(855\) | −0.617575 | − | 3.27347i | −0.0211206 | − | 0.111950i | ||||
\(856\) | −11.5643 | − | 20.0300i | −0.395260 | − | 0.684611i | ||||
\(857\) | − | 29.4919i | − | 1.00743i | −0.863871 | − | 0.503713i | \(-0.831967\pi\) | ||
0.863871 | − | 0.503713i | \(-0.168033\pi\) | |||||||
\(858\) | −0.366540 | + | 0.211622i | −0.0125135 | + | 0.00722465i | ||||
\(859\) | −34.7843 | −1.18683 | −0.593413 | − | 0.804898i | \(-0.702220\pi\) | ||||
−0.593413 | + | 0.804898i | \(0.702220\pi\) | |||||||
\(860\) | −11.1285 | − | 12.9454i | −0.379477 | − | 0.441434i | ||||
\(861\) | −6.14163 | −0.209306 | ||||||||
\(862\) | 45.6171i | 1.55373i | ||||||||
\(863\) | 5.54212 | + | 3.19974i | 0.188656 | + | 0.108920i | 0.591353 | − | 0.806413i | \(-0.298594\pi\) |
−0.402697 | + | 0.915333i | \(0.631927\pi\) | |||||||
\(864\) | −3.08117 | − | 5.33674i | −0.104823 | − | 0.181560i | ||||
\(865\) | 16.6433 | − | 47.4830i | 0.565890 | − | 1.61447i | ||||
\(866\) | 28.8529 | − | 49.9747i | 0.980461 | − | 1.69821i | ||||
\(867\) | 13.1164 | + | 7.57276i | 0.445456 | + | 0.257184i | ||||
\(868\) | 38.9054 | + | 22.4620i | 1.32053 | + | 0.762411i | ||||
\(869\) | −0.496982 | − | 0.860798i | −0.0168590 | − | 0.0292006i | ||||
\(870\) | −3.42523 | − | 18.1555i | −0.116126 | − | 0.615531i | ||||
\(871\) | 4.39207 | − | 7.60729i | 0.148820 | − | 0.257763i | ||||
\(872\) | 10.2872 | + | 5.93933i | 0.348369 | + | 0.201131i | ||||
\(873\) | 8.90560 | + | 5.14165i | 0.301409 | + | 0.174018i | ||||
\(874\) | −19.3124 | −0.653250 | ||||||||
\(875\) | −19.6525 | − | 10.4267i | −0.664377 | − | 0.352488i | ||||
\(876\) | 12.4715 | − | 21.6013i | 0.421374 | − | 0.729842i | ||||
\(877\) | 13.1412i | 0.443748i | 0.975075 | + | 0.221874i | \(0.0712174\pi\) | ||||
−0.975075 | + | 0.221874i | \(0.928783\pi\) | |||||||
\(878\) | − | 81.3251i | − | 2.74459i | ||||||
\(879\) | 4.61209 | − | 7.98837i | 0.155562 | − | 0.269441i | ||||
\(880\) | −0.134457 | − | 0.0471286i | −0.00453254 | − | 0.00158870i | ||||
\(881\) | 7.80597 | + | 13.5203i | 0.262990 | + | 0.455511i | 0.967035 | − | 0.254644i | \(-0.0819582\pi\) |
−0.704045 | + | 0.710155i | \(0.748625\pi\) | |||||||
\(882\) | − | 6.88734i | − | 0.231909i | ||||||
\(883\) | −19.8501 | + | 11.4605i | −0.668009 | + | 0.385675i | −0.795322 | − | 0.606188i | \(-0.792698\pi\) |
0.127313 | + | 0.991863i | \(0.459365\pi\) | |||||||
\(884\) | 2.86373 | + | 4.96012i | 0.0963176 | + | 0.166827i | ||||
\(885\) | −11.1266 | + | 2.09916i | −0.374017 | + | 0.0705623i | ||||
\(886\) | 1.28548 | − | 2.22652i | 0.0431867 | − | 0.0748015i | ||||
\(887\) | − | 36.4877i | − | 1.22514i | −0.790417 | − | 0.612569i | \(-0.790136\pi\) | ||
0.790417 | − | 0.612569i | \(-0.209864\pi\) | |||||||
\(888\) | −4.64261 | + | 14.8788i | −0.155796 | + | 0.499300i | ||||
\(889\) | −10.7237 | −0.359660 | ||||||||
\(890\) | 50.1188 | + | 58.3017i | 1.67999 | + | 1.95428i | ||||
\(891\) | 0.0695522 | + | 0.120468i | 0.00233009 | + | 0.00403583i | ||||
\(892\) | 14.1382 | − | 8.16269i | 0.473381 | − | 0.273307i | ||||
\(893\) | −6.36012 | + | 3.67202i | −0.212833 | + | 0.122879i | ||||
\(894\) | 48.4233 | 1.61952 | ||||||||
\(895\) | 6.16450 | + | 32.6751i | 0.206057 | + | 1.09221i | ||||
\(896\) | −34.2657 | −1.14474 | ||||||||
\(897\) | −6.65702 | − | 3.84343i | −0.222271 | − | 0.128328i | ||||
\(898\) | − | 53.0598i | − | 1.77063i | ||||||
\(899\) | −26.3002 | −0.877161 | ||||||||
\(900\) | −14.5797 | + | 5.70428i | −0.485992 | + | 0.190143i | ||||
\(901\) | 5.76180 | + | 9.97973i | 0.191953 | + | 0.332473i | ||||
\(902\) | 0.972551i | 0.0323824i | ||||||||
\(903\) | −4.20167 | − | 2.42584i | −0.139823 | − | 0.0807267i | ||||
\(904\) | 5.60922 | − | 9.71545i | 0.186560 | − | 0.323131i | ||||
\(905\) | 36.8338 | − | 31.6640i | 1.22440 | − | 1.05255i | ||||
\(906\) | −8.80154 | − | 15.2447i | −0.292412 | − | 0.506472i | ||||
\(907\) | 13.8965 | − | 8.02316i | 0.461426 | − | 0.266405i | −0.251217 | − | 0.967931i | \(-0.580831\pi\) |
0.712644 | + | 0.701526i | \(0.247498\pi\) | |||||||
\(908\) | 43.1009 | + | 24.8843i | 1.43035 | + | 0.825815i | ||||
\(909\) | −2.23540 | + | 3.87183i | −0.0741436 | + | 0.128420i | ||||
\(910\) | −8.82525 | − | 10.2661i | −0.292554 | − | 0.340319i | ||||
\(911\) | −12.1034 | −0.401002 | −0.200501 | − | 0.979693i | \(-0.564257\pi\) | ||||
−0.200501 | + | 0.979693i | \(0.564257\pi\) | |||||||
\(912\) | 0.590975 | − | 0.341199i | 0.0195691 | − | 0.0112982i | ||||
\(913\) | 0.721221 | + | 0.416397i | 0.0238689 | + | 0.0137807i | ||||
\(914\) | −15.1056 | −0.499650 | ||||||||
\(915\) | −0.984755 | + | 2.80949i | −0.0325550 | + | 0.0928787i | ||||
\(916\) | −27.5895 | + | 47.7865i | −0.911584 | + | 1.57891i | ||||
\(917\) | 3.70766i | 0.122438i | ||||||||
\(918\) | 2.67148 | − | 1.54238i | 0.0881718 | − | 0.0509060i | ||||
\(919\) | 8.10690 | 0.267422 | 0.133711 | − | 0.991020i | \(-0.457311\pi\) | ||||
0.133711 | + | 0.991020i | \(0.457311\pi\) | |||||||
\(920\) | 6.07885 | + | 32.2211i | 0.200414 | + | 1.06230i | ||||
\(921\) | 3.21935 | + | 5.57608i | 0.106081 | + | 0.183738i | ||||
\(922\) | −24.7713 | + | 14.3017i | −0.815799 | + | 0.471002i | ||||
\(923\) | 8.58565 | + | 4.95693i | 0.282600 | + | 0.163159i | ||||
\(924\) | 0.866703 | 0.0285124 | ||||||||
\(925\) | −27.3447 | − | 13.3142i | −0.899087 | − | 0.437769i | ||||
\(926\) | 44.6907 | 1.46863 | ||||||||
\(927\) | 14.7551 | + | 8.51887i | 0.484621 | + | 0.279796i | ||||
\(928\) | 19.4664 | − | 11.2389i | 0.639016 | − | 0.368936i | ||||
\(929\) | 11.4317 | + | 19.8003i | 0.375063 | + | 0.649628i | 0.990336 | − | 0.138686i | \(-0.0442878\pi\) |
−0.615274 | + | 0.788314i | \(0.710954\pi\) | |||||||
\(930\) | 6.77064 | + | 35.8879i | 0.222018 | + | 1.17681i | ||||
\(931\) | 4.52961 | 0.148452 | ||||||||
\(932\) | 62.2492 | − | 35.9396i | 2.03904 | − | 1.17724i | ||||
\(933\) | 1.65830i | 0.0542904i | ||||||||
\(934\) | 5.43122 | − | 9.40716i | 0.177715 | − | 0.307812i | ||||
\(935\) | 0.140112 | − | 0.399738i | 0.00458217 | − | 0.0130728i | ||||
\(936\) | −3.44178 | −0.112498 | ||||||||
\(937\) | 36.1461 | + | 20.8689i | 1.18084 | + | 0.681758i | 0.956209 | − | 0.292685i | \(-0.0945489\pi\) |
0.224631 | + | 0.974444i | \(0.427882\pi\) | |||||||
\(938\) | −25.5281 | + | 14.7387i | −0.833522 | + | 0.481234i | ||||
\(939\) | 8.04850 | 0.262653 | ||||||||
\(940\) | 22.4999 | + | 26.1735i | 0.733866 | + | 0.853684i | ||||
\(941\) | −13.0833 | + | 22.6609i | −0.426502 | + | 0.738724i | −0.996559 | − | 0.0828812i | \(-0.973588\pi\) |
0.570057 | + | 0.821605i | \(0.306921\pi\) | |||||||
\(942\) | 21.0008 | + | 12.1248i | 0.684244 | + | 0.395048i | ||||
\(943\) | −15.2968 | + | 8.83163i | −0.498133 | + | 0.287597i | ||||
\(944\) | −1.15975 | − | 2.00874i | −0.0377465 | − | 0.0653789i | ||||
\(945\) | −3.37410 | + | 2.90053i | −0.109759 | + | 0.0943542i | ||||
\(946\) | −0.384140 | + | 0.665350i | −0.0124895 | + | 0.0216324i | ||||
\(947\) | −37.1492 | − | 21.4481i | −1.20719 | − | 0.696969i | −0.245042 | − | 0.969512i | \(-0.578802\pi\) |
−0.962143 | + | 0.272544i | \(0.912135\pi\) | |||||||
\(948\) | − | 22.3737i | − | 0.726665i | ||||||
\(949\) | 5.34999 | + | 9.26645i | 0.173668 | + | 0.300802i | ||||
\(950\) | −6.14779 | − | 15.7133i | −0.199461 | − | 0.509808i | ||||
\(951\) | −8.72868 | −0.283047 | ||||||||
\(952\) | − | 6.94344i | − | 0.225038i | ||||||
\(953\) | −28.0503 | − | 16.1949i | −0.908640 | − | 0.524604i | −0.0286466 | − | 0.999590i | \(-0.509120\pi\) |
−0.879993 | + | 0.474986i | \(0.842453\pi\) | |||||||
\(954\) | −19.1684 | −0.620599 | ||||||||
\(955\) | 3.69660 | + | 19.5939i | 0.119619 | + | 0.634045i | ||||
\(956\) | −3.02543 | −0.0978493 | ||||||||
\(957\) | −0.439422 | + | 0.253700i | −0.0142045 | + | 0.00820096i | ||||
\(958\) | −37.0383 | + | 21.3840i | −1.19665 | + | 0.690887i | ||||
\(959\) | −11.9950 | − | 20.7760i | −0.387340 | − | 0.670893i | ||||
\(960\) | −19.0121 | − | 22.1162i | −0.613612 | − | 0.713796i | ||||
\(961\) | 20.9874 | 0.677014 | ||||||||
\(962\) | −12.5442 | − | 13.6080i | −0.404440 | − | 0.438739i | ||||
\(963\) | − | 9.02627i | − | 0.290868i | ||||||
\(964\) | −0.852433 | + | 1.47646i | −0.0274550 | + | 0.0475535i | ||||
\(965\) | 23.0760 | − | 4.35353i | 0.742842 | − | 0.140145i | ||||
\(966\) | 12.8976 | + | 22.3392i | 0.414972 | + | 0.718753i | ||||
\(967\) | −14.8606 | + | 8.57978i | −0.477885 | + | 0.275907i | −0.719535 | − | 0.694456i | \(-0.755645\pi\) |
0.241649 | + | 0.970364i | \(0.422312\pi\) | |||||||
\(968\) | 28.1365i | 0.904341i | ||||||||
\(969\) | 1.01438 | + | 1.75696i | 0.0325865 | + | 0.0564416i | ||||
\(970\) | 49.1546 | + | 17.2292i | 1.57826 | + | 0.553197i | ||||
\(971\) | 15.7970 | − | 27.3612i | 0.506949 | − | 0.878061i | −0.493019 | − | 0.870019i | \(-0.664107\pi\) |
0.999968 | − | 0.00804267i | \(-0.00256009\pi\) | |||||||
\(972\) | 3.13118i | 0.100433i | ||||||||
\(973\) | 0.244173i | 0.00782782i | ||||||||
\(974\) | −1.07069 | + | 1.85449i | −0.0343072 | + | 0.0594218i | ||||
\(975\) | 1.00802 | − | 6.63993i | 0.0322824 | − | 0.212648i | ||||
\(976\) | −0.609851 | −0.0195209 | ||||||||
\(977\) | 25.9721 | + | 14.9950i | 0.830922 | + | 0.479733i | 0.854168 | − | 0.519997i | \(-0.174067\pi\) |
−0.0232466 | + | 0.999730i | \(0.507400\pi\) | |||||||
\(978\) | −27.4681 | − | 15.8587i | −0.878333 | − | 0.507106i | ||||
\(979\) | 1.05571 | − | 1.82855i | 0.0337408 | − | 0.0584408i | ||||
\(980\) | −3.94660 | − | 20.9190i | −0.126069 | − | 0.668234i | ||||
\(981\) | 2.31790 | + | 4.01473i | 0.0740050 | + | 0.128180i | ||||
\(982\) | 67.8233 | + | 39.1578i | 2.16433 | + | 1.24958i | ||||
\(983\) | 44.3450 | + | 25.6026i | 1.41439 | + | 0.816596i | 0.995798 | − | 0.0915810i | \(-0.0291920\pi\) |
0.418587 | + | 0.908177i | \(0.362525\pi\) | |||||||
\(984\) | −3.95435 | + | 6.84913i | −0.126060 | + | 0.218342i | ||||
\(985\) | 11.6541 | − | 33.2488i | 0.371330 | − | 1.05940i | ||||
\(986\) | 5.62601 | + | 9.74454i | 0.179169 | + | 0.310329i | ||||
\(987\) | 8.49509 | + | 4.90464i | 0.270402 | + | 0.156117i | ||||
\(988\) | − | 6.26568i | − | 0.199338i | ||||||
\(989\) | −13.9533 | −0.443690 | ||||||||
\(990\) | 0.459309 | + | 0.534301i | 0.0145978 | + | 0.0169812i | ||||
\(991\) | −16.7140 | −0.530939 | −0.265469 | − | 0.964119i | \(-0.585527\pi\) | ||||
−0.265469 | + | 0.964119i | \(0.585527\pi\) | |||||||
\(992\) | −38.4791 | + | 22.2159i | −1.22171 | + | 0.705357i | ||||
\(993\) | 0.777701i | 0.0246796i | ||||||||
\(994\) | −16.6342 | − | 28.8112i | −0.527604 | − | 0.913837i | ||||
\(995\) | 11.4506 | + | 60.6944i | 0.363010 | + | 1.92414i | ||||
\(996\) | 9.37294 | + | 16.2344i | 0.296993 | + | 0.514407i | ||||
\(997\) | −30.7507 | − | 17.7539i | −0.973886 | − | 0.562273i | −0.0734671 | − | 0.997298i | \(-0.523406\pi\) |
−0.900419 | + | 0.435024i | \(0.856740\pi\) | |||||||
\(998\) | − | 7.88507i | − | 0.249598i | ||||||
\(999\) | −4.47243 | + | 4.12279i | −0.141501 | + | 0.130439i |
(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 | 555.2.bb.a.454.5 | ✓ | 72 | |
5.4 | even | 2 | inner | 555.2.bb.a.454.32 | yes | 72 | |
37.26 | even | 3 | inner | 555.2.bb.a.544.32 | yes | 72 | |
185.174 | even | 6 | inner | 555.2.bb.a.544.5 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
555.2.bb.a.454.5 | ✓ | 72 | 1.1 | even | 1 | trivial | |
555.2.bb.a.454.32 | yes | 72 | 5.4 | even | 2 | inner | |
555.2.bb.a.544.5 | yes | 72 | 185.174 | even | 6 | inner | |
555.2.bb.a.544.32 | yes | 72 | 37.26 | even | 3 | inner |