Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(529,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.e (of order \(3\), degree \(2\), not 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: | \(8.09683076496\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.64827.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 991.3 | ||
Root | \(0.900969 + 1.56052i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.991 |
Dual form | 1014.2.e.l.529.3 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 3.15883 | 1.41267 | 0.706337 | − | 0.707876i | \(-0.250346\pi\) | ||||
0.706337 | + | 0.707876i | \(0.250346\pi\) | |||||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | −2.34601 | + | 4.06341i | −0.886709 | + | 1.53582i | −0.0429661 | + | 0.999077i | \(0.513681\pi\) |
−0.843743 | + | 0.536748i | \(0.819653\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −1.57942 | − | 2.73563i | −0.499455 | − | 0.865082i | ||||
\(11\) | 0.0685317 | + | 0.118700i | 0.0206631 | + | 0.0357895i | 0.876172 | − | 0.481998i | \(-0.160089\pi\) |
−0.855509 | + | 0.517788i | \(0.826756\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.69202 | 1.25400 | ||||||||
\(15\) | 1.57942 | + | 2.73563i | 0.407804 | + | 0.706337i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.80194 | − | 4.85310i | 0.679570 | − | 1.17705i | −0.295541 | − | 0.955330i | \(-0.595500\pi\) |
0.975111 | − | 0.221719i | \(-0.0711668\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −2.49396 | + | 4.31966i | −0.572153 | + | 0.990999i | 0.424191 | + | 0.905573i | \(0.360559\pi\) |
−0.996345 | + | 0.0854262i | \(0.972775\pi\) | |||||||
\(20\) | −1.57942 | + | 2.73563i | −0.353168 | + | 0.611705i | ||||
\(21\) | −4.69202 | −1.02388 | ||||||||
\(22\) | 0.0685317 | − | 0.118700i | 0.0146110 | − | 0.0253070i | ||||
\(23\) | 3.04892 | + | 5.28088i | 0.635743 | + | 1.10114i | 0.986357 | + | 0.164619i | \(0.0526396\pi\) |
−0.350614 | + | 0.936520i | \(0.614027\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 4.97823 | 0.995646 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.34601 | − | 4.06341i | −0.443354 | − | 0.767912i | ||||
\(29\) | 0.425428 | + | 0.736862i | 0.0789999 | + | 0.136832i | 0.902819 | − | 0.430021i | \(-0.141494\pi\) |
−0.823819 | + | 0.566853i | \(0.808161\pi\) | |||||||
\(30\) | 1.57942 | − | 2.73563i | 0.288361 | − | 0.499455i | ||||
\(31\) | −6.23490 | −1.11982 | −0.559910 | − | 0.828553i | \(-0.689164\pi\) | ||||
−0.559910 | + | 0.828553i | \(0.689164\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −0.0685317 | + | 0.118700i | −0.0119298 | + | 0.0206631i | ||||
\(34\) | −5.60388 | −0.961057 | ||||||||
\(35\) | −7.41066 | + | 12.8356i | −1.25263 | + | 2.16962i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 5.85086 | + | 10.1340i | 0.961875 | + | 1.66602i | 0.717787 | + | 0.696263i | \(0.245155\pi\) |
0.244087 | + | 0.969753i | \(0.421512\pi\) | |||||||
\(38\) | 4.98792 | 0.809147 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.15883 | 0.499455 | ||||||||
\(41\) | −2.13706 | − | 3.70150i | −0.333753 | − | 0.578078i | 0.649491 | − | 0.760369i | \(-0.274982\pi\) |
−0.983245 | + | 0.182291i | \(0.941649\pi\) | |||||||
\(42\) | 2.34601 | + | 4.06341i | 0.361997 | + | 0.626998i | ||||
\(43\) | 1.04892 | − | 1.81678i | 0.159958 | − | 0.277056i | −0.774895 | − | 0.632090i | \(-0.782197\pi\) |
0.934853 | + | 0.355034i | \(0.115531\pi\) | |||||||
\(44\) | −0.137063 | −0.0206631 | ||||||||
\(45\) | −1.57942 | + | 2.73563i | −0.235446 | + | 0.407804i | ||||
\(46\) | 3.04892 | − | 5.28088i | 0.449538 | − | 0.778623i | ||||
\(47\) | −4.98792 | −0.727563 | −0.363781 | − | 0.931484i | \(-0.618514\pi\) | ||||
−0.363781 | + | 0.931484i | \(0.618514\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −7.50753 | − | 13.0034i | −1.07250 | − | 1.85763i | ||||
\(50\) | −2.48911 | − | 4.31127i | −0.352014 | − | 0.609706i | ||||
\(51\) | 5.60388 | 0.784700 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.82908 | −0.251244 | −0.125622 | − | 0.992078i | \(-0.540093\pi\) | ||||
−0.125622 | + | 0.992078i | \(0.540093\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 0.216480 | + | 0.374955i | 0.0291902 | + | 0.0505589i | ||||
\(56\) | −2.34601 | + | 4.06341i | −0.313499 | + | 0.542996i | ||||
\(57\) | −4.98792 | −0.660666 | ||||||||
\(58\) | 0.425428 | − | 0.736862i | 0.0558614 | − | 0.0967547i | ||||
\(59\) | −2.94989 | + | 5.10935i | −0.384042 | + | 0.665181i | −0.991636 | − | 0.129067i | \(-0.958802\pi\) |
0.607593 | + | 0.794248i | \(0.292135\pi\) | |||||||
\(60\) | −3.15883 | −0.407804 | ||||||||
\(61\) | −2.19806 | + | 3.80716i | −0.281433 | + | 0.487456i | −0.971738 | − | 0.236062i | \(-0.924143\pi\) |
0.690305 | + | 0.723519i | \(0.257476\pi\) | |||||||
\(62\) | 3.11745 | + | 5.39958i | 0.395916 | + | 0.685747i | ||||
\(63\) | −2.34601 | − | 4.06341i | −0.295570 | − | 0.511942i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.137063 | 0.0168713 | ||||||||
\(67\) | −2.35690 | − | 4.08226i | −0.287941 | − | 0.498728i | 0.685377 | − | 0.728188i | \(-0.259637\pi\) |
−0.973318 | + | 0.229460i | \(0.926304\pi\) | |||||||
\(68\) | 2.80194 | + | 4.85310i | 0.339785 | + | 0.588525i | ||||
\(69\) | −3.04892 | + | 5.28088i | −0.367047 | + | 0.635743i | ||||
\(70\) | 14.8213 | 1.77149 | ||||||||
\(71\) | −0.0489173 | + | 0.0847273i | −0.00580542 | + | 0.0100553i | −0.868914 | − | 0.494964i | \(-0.835181\pi\) |
0.863108 | + | 0.505019i | \(0.168515\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 2.32304 | 0.271892 | 0.135946 | − | 0.990716i | \(-0.456593\pi\) | ||||
0.135946 | + | 0.990716i | \(0.456593\pi\) | |||||||
\(74\) | 5.85086 | − | 10.1340i | 0.680148 | − | 1.17805i | ||||
\(75\) | 2.48911 | + | 4.31127i | 0.287418 | + | 0.497823i | ||||
\(76\) | −2.49396 | − | 4.31966i | −0.286077 | − | 0.495499i | ||||
\(77\) | −0.643104 | −0.0732885 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.5157 | 1.63315 | 0.816574 | − | 0.577241i | \(-0.195871\pi\) | ||||
0.816574 | + | 0.577241i | \(0.195871\pi\) | |||||||
\(80\) | −1.57942 | − | 2.73563i | −0.176584 | − | 0.305853i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.13706 | + | 3.70150i | −0.235999 | + | 0.408763i | ||||
\(83\) | 9.85623 | 1.08186 | 0.540931 | − | 0.841067i | \(-0.318072\pi\) | ||||
0.540931 | + | 0.841067i | \(0.318072\pi\) | |||||||
\(84\) | 2.34601 | − | 4.06341i | 0.255971 | − | 0.443354i | ||||
\(85\) | 8.85086 | − | 15.3301i | 0.960010 | − | 1.66279i | ||||
\(86\) | −2.09783 | −0.226215 | ||||||||
\(87\) | −0.425428 | + | 0.736862i | −0.0456106 | + | 0.0789999i | ||||
\(88\) | 0.0685317 | + | 0.118700i | 0.00730550 | + | 0.0126535i | ||||
\(89\) | 8.54288 | + | 14.7967i | 0.905543 | + | 1.56845i | 0.820187 | + | 0.572096i | \(0.193870\pi\) |
0.0853566 | + | 0.996350i | \(0.472797\pi\) | |||||||
\(90\) | 3.15883 | 0.332970 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.09783 | −0.635743 | ||||||||
\(93\) | −3.11745 | − | 5.39958i | −0.323264 | − | 0.559910i | ||||
\(94\) | 2.49396 | + | 4.31966i | 0.257232 | + | 0.445539i | ||||
\(95\) | −7.87800 | + | 13.6451i | −0.808266 | + | 1.39996i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 1.06369 | − | 1.84236i | 0.108001 | − | 0.187063i | −0.806959 | − | 0.590607i | \(-0.798888\pi\) |
0.914960 | + | 0.403544i | \(0.132222\pi\) | |||||||
\(98\) | −7.50753 | + | 13.0034i | −0.758375 | + | 1.31354i | ||||
\(99\) | −0.137063 | −0.0137754 | ||||||||
\(100\) | −2.48911 | + | 4.31127i | −0.248911 | + | 0.431127i | ||||
\(101\) | 4.59299 | + | 7.95529i | 0.457020 | + | 0.791581i | 0.998802 | − | 0.0489377i | \(-0.0155836\pi\) |
−0.541782 | + | 0.840519i | \(0.682250\pi\) | |||||||
\(102\) | −2.80194 | − | 4.85310i | −0.277433 | − | 0.480528i | ||||
\(103\) | 0.225209 | 0.0221905 | 0.0110953 | − | 0.999938i | \(-0.496468\pi\) | ||||
0.0110953 | + | 0.999938i | \(0.496468\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14.8213 | −1.44641 | ||||||||
\(106\) | 0.914542 | + | 1.58403i | 0.0888282 | + | 0.153855i | ||||
\(107\) | −5.64191 | − | 9.77207i | −0.545424 | − | 0.944702i | −0.998580 | − | 0.0532707i | \(-0.983035\pi\) |
0.453156 | − | 0.891431i | \(-0.350298\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 0.195669 | 0.0187417 | 0.00937086 | − | 0.999956i | \(-0.497017\pi\) | ||||
0.00937086 | + | 0.999956i | \(0.497017\pi\) | |||||||
\(110\) | 0.216480 | − | 0.374955i | 0.0206406 | − | 0.0357505i | ||||
\(111\) | −5.85086 | + | 10.1340i | −0.555339 | + | 0.961875i | ||||
\(112\) | 4.69202 | 0.443354 | ||||||||
\(113\) | 0.219833 | − | 0.380761i | 0.0206801 | − | 0.0358190i | −0.855500 | − | 0.517803i | \(-0.826750\pi\) |
0.876180 | + | 0.481984i | \(0.160084\pi\) | |||||||
\(114\) | 2.49396 | + | 4.31966i | 0.233581 | + | 0.404574i | ||||
\(115\) | 9.63102 | + | 16.6814i | 0.898097 | + | 1.55555i | ||||
\(116\) | −0.850855 | −0.0789999 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.89977 | 0.543118 | ||||||||
\(119\) | 13.1468 | + | 22.7708i | 1.20516 | + | 2.08740i | ||||
\(120\) | 1.57942 | + | 2.73563i | 0.144180 | + | 0.249728i | ||||
\(121\) | 5.49061 | − | 9.51001i | 0.499146 | − | 0.864546i | ||||
\(122\) | 4.39612 | 0.398006 | ||||||||
\(123\) | 2.13706 | − | 3.70150i | 0.192693 | − | 0.333753i | ||||
\(124\) | 3.11745 | − | 5.39958i | 0.279955 | − | 0.484897i | ||||
\(125\) | −0.0687686 | −0.00615085 | ||||||||
\(126\) | −2.34601 | + | 4.06341i | −0.208999 | + | 0.361997i | ||||
\(127\) | 3.93631 | + | 6.81789i | 0.349291 | + | 0.604990i | 0.986124 | − | 0.166012i | \(-0.0530890\pi\) |
−0.636832 | + | 0.771002i | \(0.719756\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 2.09783 | 0.184704 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.621334 | −0.0542862 | −0.0271431 | − | 0.999632i | \(-0.508641\pi\) | ||||
−0.0271431 | + | 0.999632i | \(0.508641\pi\) | |||||||
\(132\) | −0.0685317 | − | 0.118700i | −0.00596492 | − | 0.0103315i | ||||
\(133\) | −11.7017 | − | 20.2680i | −1.01467 | − | 1.75745i | ||||
\(134\) | −2.35690 | + | 4.08226i | −0.203605 | + | 0.352654i | ||||
\(135\) | −3.15883 | −0.271869 | ||||||||
\(136\) | 2.80194 | − | 4.85310i | 0.240264 | − | 0.416150i | ||||
\(137\) | 2.00000 | − | 3.46410i | 0.170872 | − | 0.295958i | −0.767853 | − | 0.640626i | \(-0.778675\pi\) |
0.938725 | + | 0.344668i | \(0.112008\pi\) | |||||||
\(138\) | 6.09783 | 0.519082 | ||||||||
\(139\) | 6.82908 | − | 11.8283i | 0.579235 | − | 1.00327i | −0.416332 | − | 0.909213i | \(-0.636685\pi\) |
0.995567 | − | 0.0940524i | \(-0.0299821\pi\) | |||||||
\(140\) | −7.41066 | − | 12.8356i | −0.626315 | − | 1.08481i | ||||
\(141\) | −2.49396 | − | 4.31966i | −0.210029 | − | 0.363781i | ||||
\(142\) | 0.0978347 | 0.00821010 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 1.34385 | + | 2.32762i | 0.111601 | + | 0.193299i | ||||
\(146\) | −1.16152 | − | 2.01182i | −0.0961282 | − | 0.166499i | ||||
\(147\) | 7.50753 | − | 13.0034i | 0.619211 | − | 1.07250i | ||||
\(148\) | −11.7017 | −0.961875 | ||||||||
\(149\) | 8.02930 | − | 13.9072i | 0.657786 | − | 1.13932i | −0.323401 | − | 0.946262i | \(-0.604826\pi\) |
0.981188 | − | 0.193057i | \(-0.0618403\pi\) | |||||||
\(150\) | 2.48911 | − | 4.31127i | 0.203235 | − | 0.352014i | ||||
\(151\) | 21.8823 | 1.78076 | 0.890379 | − | 0.455221i | \(-0.150440\pi\) | ||||
0.890379 | + | 0.455221i | \(0.150440\pi\) | |||||||
\(152\) | −2.49396 | + | 4.31966i | −0.202287 | + | 0.350371i | ||||
\(153\) | 2.80194 | + | 4.85310i | 0.226523 | + | 0.392350i | ||||
\(154\) | 0.321552 | + | 0.556945i | 0.0259114 | + | 0.0448799i | ||||
\(155\) | −19.6950 | −1.58194 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.90217 | −0.630661 | −0.315331 | − | 0.948982i | \(-0.602115\pi\) | ||||
−0.315331 | + | 0.948982i | \(0.602115\pi\) | |||||||
\(158\) | −7.25786 | − | 12.5710i | −0.577405 | − | 1.00009i | ||||
\(159\) | −0.914542 | − | 1.58403i | −0.0725279 | − | 0.125622i | ||||
\(160\) | −1.57942 | + | 2.73563i | −0.124864 | + | 0.216271i | ||||
\(161\) | −28.6112 | −2.25488 | ||||||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | 4.00969 | − | 6.94498i | 0.314063 | − | 0.543973i | −0.665175 | − | 0.746688i | \(-0.731643\pi\) |
0.979238 | + | 0.202714i | \(0.0649763\pi\) | |||||||
\(164\) | 4.27413 | 0.333753 | ||||||||
\(165\) | −0.216480 | + | 0.374955i | −0.0168530 | + | 0.0291902i | ||||
\(166\) | −4.92812 | − | 8.53575i | −0.382496 | − | 0.662502i | ||||
\(167\) | −8.54288 | − | 14.7967i | −0.661068 | − | 1.14500i | −0.980335 | − | 0.197338i | \(-0.936770\pi\) |
0.319268 | − | 0.947665i | \(-0.396563\pi\) | |||||||
\(168\) | −4.69202 | −0.361997 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −17.7017 | −1.35766 | ||||||||
\(171\) | −2.49396 | − | 4.31966i | −0.190718 | − | 0.330333i | ||||
\(172\) | 1.04892 | + | 1.81678i | 0.0799792 | + | 0.138528i | ||||
\(173\) | 7.67241 | − | 13.2890i | 0.583322 | − | 1.01034i | −0.411760 | − | 0.911292i | \(-0.635086\pi\) |
0.995082 | − | 0.0990516i | \(-0.0315809\pi\) | |||||||
\(174\) | 0.850855 | 0.0645032 | ||||||||
\(175\) | −11.6790 | + | 20.2286i | −0.882848 | + | 1.52914i | ||||
\(176\) | 0.0685317 | − | 0.118700i | 0.00516577 | − | 0.00894737i | ||||
\(177\) | −5.89977 | −0.443454 | ||||||||
\(178\) | 8.54288 | − | 14.7967i | 0.640316 | − | 1.10906i | ||||
\(179\) | −0.261750 | − | 0.453364i | −0.0195641 | − | 0.0338860i | 0.856078 | − | 0.516847i | \(-0.172895\pi\) |
−0.875642 | + | 0.482961i | \(0.839561\pi\) | |||||||
\(180\) | −1.57942 | − | 2.73563i | −0.117723 | − | 0.203902i | ||||
\(181\) | 8.89008 | 0.660795 | 0.330397 | − | 0.943842i | \(-0.392817\pi\) | ||||
0.330397 | + | 0.943842i | \(0.392817\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.39612 | −0.324971 | ||||||||
\(184\) | 3.04892 | + | 5.28088i | 0.224769 | + | 0.389312i | ||||
\(185\) | 18.4819 | + | 32.0116i | 1.35881 | + | 2.35354i | ||||
\(186\) | −3.11745 | + | 5.39958i | −0.228582 | + | 0.395916i | ||||
\(187\) | 0.768086 | 0.0561680 | ||||||||
\(188\) | 2.49396 | − | 4.31966i | 0.181891 | − | 0.315044i | ||||
\(189\) | 2.34601 | − | 4.06341i | 0.170647 | − | 0.295570i | ||||
\(190\) | 15.7560 | 1.14306 | ||||||||
\(191\) | 3.51573 | − | 6.08942i | 0.254389 | − | 0.440615i | −0.710340 | − | 0.703859i | \(-0.751459\pi\) |
0.964729 | + | 0.263243i | \(0.0847922\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −8.87800 | − | 15.3772i | −0.639053 | − | 1.10687i | −0.985641 | − | 0.168854i | \(-0.945993\pi\) |
0.346588 | − | 0.938017i | \(-0.387340\pi\) | |||||||
\(194\) | −2.12737 | −0.152737 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.0151 | 1.07250 | ||||||||
\(197\) | 9.32855 | + | 16.1575i | 0.664632 | + | 1.15118i | 0.979385 | + | 0.202003i | \(0.0647449\pi\) |
−0.314753 | + | 0.949174i | \(0.601922\pi\) | |||||||
\(198\) | 0.0685317 | + | 0.118700i | 0.00487033 | + | 0.00843567i | ||||
\(199\) | −3.83124 | + | 6.63590i | −0.271589 | + | 0.470407i | −0.969269 | − | 0.246003i | \(-0.920883\pi\) |
0.697680 | + | 0.716410i | \(0.254216\pi\) | |||||||
\(200\) | 4.97823 | 0.352014 | ||||||||
\(201\) | 2.35690 | − | 4.08226i | 0.166243 | − | 0.287941i | ||||
\(202\) | 4.59299 | − | 7.95529i | 0.323162 | − | 0.559732i | ||||
\(203\) | −3.99223 | −0.280200 | ||||||||
\(204\) | −2.80194 | + | 4.85310i | −0.196175 | + | 0.339785i | ||||
\(205\) | −6.75063 | − | 11.6924i | −0.471484 | − | 0.816635i | ||||
\(206\) | −0.112605 | − | 0.195037i | −0.00784554 | − | 0.0135889i | ||||
\(207\) | −6.09783 | −0.423829 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.683661 | −0.0472898 | ||||||||
\(210\) | 7.41066 | + | 12.8356i | 0.511384 | + | 0.885743i | ||||
\(211\) | −5.58211 | − | 9.66849i | −0.384288 | − | 0.665606i | 0.607382 | − | 0.794410i | \(-0.292220\pi\) |
−0.991670 | + | 0.128803i | \(0.958886\pi\) | |||||||
\(212\) | 0.914542 | − | 1.58403i | 0.0628110 | − | 0.108792i | ||||
\(213\) | −0.0978347 | −0.00670352 | ||||||||
\(214\) | −5.64191 | + | 9.77207i | −0.385673 | + | 0.668005i | ||||
\(215\) | 3.31336 | − | 5.73890i | 0.225969 | − | 0.391390i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 14.6271 | − | 25.3349i | 0.992955 | − | 1.71985i | ||||
\(218\) | −0.0978347 | − | 0.169455i | −0.00662620 | − | 0.0114769i | ||||
\(219\) | 1.16152 | + | 2.01182i | 0.0784884 | + | 0.135946i | ||||
\(220\) | −0.432960 | −0.0291902 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 11.7017 | 0.785367 | ||||||||
\(223\) | −12.3177 | − | 21.3348i | −0.824852 | − | 1.42869i | −0.902032 | − | 0.431668i | \(-0.857925\pi\) |
0.0771803 | − | 0.997017i | \(-0.475408\pi\) | |||||||
\(224\) | −2.34601 | − | 4.06341i | −0.156749 | − | 0.271498i | ||||
\(225\) | −2.48911 | + | 4.31127i | −0.165941 | + | 0.287418i | ||||
\(226\) | −0.439665 | −0.0292461 | ||||||||
\(227\) | 3.73825 | − | 6.47484i | 0.248116 | − | 0.429750i | −0.714887 | − | 0.699240i | \(-0.753522\pi\) |
0.963003 | + | 0.269490i | \(0.0868551\pi\) | |||||||
\(228\) | 2.49396 | − | 4.31966i | 0.165166 | − | 0.286077i | ||||
\(229\) | −19.2271 | −1.27056 | −0.635282 | − | 0.772280i | \(-0.719116\pi\) | ||||
−0.635282 | + | 0.772280i | \(0.719116\pi\) | |||||||
\(230\) | 9.63102 | − | 16.6814i | 0.635051 | − | 1.09994i | ||||
\(231\) | −0.321552 | − | 0.556945i | −0.0211566 | − | 0.0366443i | ||||
\(232\) | 0.425428 | + | 0.736862i | 0.0279307 | + | 0.0483774i | ||||
\(233\) | 3.70171 | 0.242507 | 0.121254 | − | 0.992622i | \(-0.461309\pi\) | ||||
0.121254 | + | 0.992622i | \(0.461309\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.7560 | −1.02781 | ||||||||
\(236\) | −2.94989 | − | 5.10935i | −0.192021 | − | 0.332591i | ||||
\(237\) | 7.25786 | + | 12.5710i | 0.471449 | + | 0.816574i | ||||
\(238\) | 13.1468 | − | 22.7708i | 0.852177 | − | 1.47601i | ||||
\(239\) | 8.51334 | 0.550682 | 0.275341 | − | 0.961347i | \(-0.411209\pi\) | ||||
0.275341 | + | 0.961347i | \(0.411209\pi\) | |||||||
\(240\) | 1.57942 | − | 2.73563i | 0.101951 | − | 0.176584i | ||||
\(241\) | −8.71648 | + | 15.0974i | −0.561478 | + | 0.972508i | 0.435890 | + | 0.900000i | \(0.356434\pi\) |
−0.997368 | + | 0.0725082i | \(0.976900\pi\) | |||||||
\(242\) | −10.9812 | −0.705899 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −2.19806 | − | 3.80716i | −0.140717 | − | 0.243728i | ||||
\(245\) | −23.7150 | − | 41.0757i | −1.51510 | − | 2.62423i | ||||
\(246\) | −4.27413 | −0.272508 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.23490 | −0.395916 | ||||||||
\(249\) | 4.92812 | + | 8.53575i | 0.312307 | + | 0.540931i | ||||
\(250\) | 0.0343843 | + | 0.0595554i | 0.00217466 | + | 0.00376661i | ||||
\(251\) | 1.74214 | − | 3.01747i | 0.109963 | − | 0.190461i | −0.805792 | − | 0.592198i | \(-0.798260\pi\) |
0.915755 | + | 0.401737i | \(0.131594\pi\) | |||||||
\(252\) | 4.69202 | 0.295570 | ||||||||
\(253\) | −0.417895 | + | 0.723815i | −0.0262728 | + | 0.0455059i | ||||
\(254\) | 3.93631 | − | 6.81789i | 0.246986 | − | 0.427793i | ||||
\(255\) | 17.7017 | 1.10852 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 6.80194 | + | 11.7813i | 0.424293 | + | 0.734897i | 0.996354 | − | 0.0853137i | \(-0.0271893\pi\) |
−0.572061 | + | 0.820211i | \(0.693856\pi\) | |||||||
\(258\) | −1.04892 | − | 1.81678i | −0.0653027 | − | 0.113108i | ||||
\(259\) | −54.9047 | −3.41161 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.850855 | −0.0526666 | ||||||||
\(262\) | 0.310667 | + | 0.538091i | 0.0191931 | + | 0.0332434i | ||||
\(263\) | −5.72886 | − | 9.92267i | −0.353256 | − | 0.611858i | 0.633561 | − | 0.773692i | \(-0.281592\pi\) |
−0.986818 | + | 0.161834i | \(0.948259\pi\) | |||||||
\(264\) | −0.0685317 | + | 0.118700i | −0.00421783 | + | 0.00730550i | ||||
\(265\) | −5.77777 | −0.354926 | ||||||||
\(266\) | −11.7017 | + | 20.2680i | −0.717478 | + | 1.24271i | ||||
\(267\) | −8.54288 | + | 14.7967i | −0.522816 | + | 0.905543i | ||||
\(268\) | 4.71379 | 0.287941 | ||||||||
\(269\) | −11.1833 | + | 19.3700i | −0.681857 | + | 1.18101i | 0.292556 | + | 0.956248i | \(0.405494\pi\) |
−0.974413 | + | 0.224763i | \(0.927839\pi\) | |||||||
\(270\) | 1.57942 | + | 2.73563i | 0.0961202 | + | 0.166485i | ||||
\(271\) | 1.93631 | + | 3.35379i | 0.117623 | + | 0.203728i | 0.918825 | − | 0.394665i | \(-0.129139\pi\) |
−0.801202 | + | 0.598393i | \(0.795806\pi\) | |||||||
\(272\) | −5.60388 | −0.339785 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.00000 | −0.241649 | ||||||||
\(275\) | 0.341166 | + | 0.590918i | 0.0205731 | + | 0.0356337i | ||||
\(276\) | −3.04892 | − | 5.28088i | −0.183523 | − | 0.317872i | ||||
\(277\) | −14.3545 | + | 24.8627i | −0.862478 | + | 1.49386i | 0.00705077 | + | 0.999975i | \(0.497756\pi\) |
−0.869529 | + | 0.493881i | \(0.835578\pi\) | |||||||
\(278\) | −13.6582 | −0.819163 | ||||||||
\(279\) | 3.11745 | − | 5.39958i | 0.186637 | − | 0.323264i | ||||
\(280\) | −7.41066 | + | 12.8356i | −0.442871 | + | 0.767076i | ||||
\(281\) | 29.0858 | 1.73511 | 0.867555 | − | 0.497341i | \(-0.165690\pi\) | ||||
0.867555 | + | 0.497341i | \(0.165690\pi\) | |||||||
\(282\) | −2.49396 | + | 4.31966i | −0.148513 | + | 0.257232i | ||||
\(283\) | −6.87800 | − | 11.9130i | −0.408855 | − | 0.708157i | 0.585907 | − | 0.810378i | \(-0.300738\pi\) |
−0.994762 | + | 0.102221i | \(0.967405\pi\) | |||||||
\(284\) | −0.0489173 | − | 0.0847273i | −0.00290271 | − | 0.00502764i | ||||
\(285\) | −15.7560 | −0.933305 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.0543 | 1.18377 | ||||||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | −7.20171 | − | 12.4737i | −0.423630 | − | 0.733749i | ||||
\(290\) | 1.34385 | − | 2.32762i | 0.0789139 | − | 0.136683i | ||||
\(291\) | 2.12737 | 0.124709 | ||||||||
\(292\) | −1.16152 | + | 2.01182i | −0.0679729 | + | 0.117733i | ||||
\(293\) | 13.8681 | − | 24.0202i | 0.810182 | − | 1.40328i | −0.102555 | − | 0.994727i | \(-0.532702\pi\) |
0.912737 | − | 0.408548i | \(-0.133965\pi\) | |||||||
\(294\) | −15.0151 | −0.875696 | ||||||||
\(295\) | −9.31820 | + | 16.1396i | −0.542527 | + | 0.939684i | ||||
\(296\) | 5.85086 | + | 10.1340i | 0.340074 | + | 0.589026i | ||||
\(297\) | −0.0685317 | − | 0.118700i | −0.00397661 | − | 0.00688769i | ||||
\(298\) | −16.0586 | −0.930250 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.97823 | −0.287418 | ||||||||
\(301\) | 4.92154 | + | 8.52436i | 0.283673 | + | 0.491336i | ||||
\(302\) | −10.9412 | − | 18.9506i | −0.629593 | − | 1.09049i | ||||
\(303\) | −4.59299 | + | 7.95529i | −0.263860 | + | 0.457020i | ||||
\(304\) | 4.98792 | 0.286077 | ||||||||
\(305\) | −6.94331 | + | 12.0262i | −0.397573 | + | 0.688617i | ||||
\(306\) | 2.80194 | − | 4.85310i | 0.160176 | − | 0.277433i | ||||
\(307\) | 12.4590 | 0.711075 | 0.355538 | − | 0.934662i | \(-0.384298\pi\) | ||||
0.355538 | + | 0.934662i | \(0.384298\pi\) | |||||||
\(308\) | 0.321552 | − | 0.556945i | 0.0183221 | − | 0.0317349i | ||||
\(309\) | 0.112605 | + | 0.195037i | 0.00640586 | + | 0.0110953i | ||||
\(310\) | 9.84750 | + | 17.0564i | 0.559301 | + | 0.968737i | ||||
\(311\) | −6.09783 | −0.345776 | −0.172888 | − | 0.984941i | \(-0.555310\pi\) | ||||
−0.172888 | + | 0.984941i | \(0.555310\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.7385 | −0.720025 | −0.360013 | − | 0.932947i | \(-0.617228\pi\) | ||||
−0.360013 | + | 0.932947i | \(0.617228\pi\) | |||||||
\(314\) | 3.95108 | + | 6.84348i | 0.222972 | + | 0.386200i | ||||
\(315\) | −7.41066 | − | 12.8356i | −0.417543 | − | 0.723206i | ||||
\(316\) | −7.25786 | + | 12.5710i | −0.408287 | + | 0.707173i | ||||
\(317\) | −14.8140 | −0.832038 | −0.416019 | − | 0.909356i | \(-0.636575\pi\) | ||||
−0.416019 | + | 0.909356i | \(0.636575\pi\) | |||||||
\(318\) | −0.914542 | + | 1.58403i | −0.0512850 | + | 0.0888282i | ||||
\(319\) | −0.0583105 | + | 0.100997i | −0.00326476 | + | 0.00565473i | ||||
\(320\) | 3.15883 | 0.176584 | ||||||||
\(321\) | 5.64191 | − | 9.77207i | 0.314901 | − | 0.545424i | ||||
\(322\) | 14.3056 | + | 24.7780i | 0.797219 | + | 1.38082i | ||||
\(323\) | 13.9758 | + | 24.2069i | 0.777636 | + | 1.34691i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.01938 | −0.444152 | ||||||||
\(327\) | 0.0978347 | + | 0.169455i | 0.00541027 | + | 0.00937086i | ||||
\(328\) | −2.13706 | − | 3.70150i | −0.118000 | − | 0.204381i | ||||
\(329\) | 11.7017 | − | 20.2680i | 0.645136 | − | 1.11741i | ||||
\(330\) | 0.432960 | 0.0238337 | ||||||||
\(331\) | 3.85086 | − | 6.66988i | 0.211662 | − | 0.366610i | −0.740573 | − | 0.671976i | \(-0.765446\pi\) |
0.952235 | + | 0.305367i | \(0.0987790\pi\) | |||||||
\(332\) | −4.92812 | + | 8.53575i | −0.270465 | + | 0.468460i | ||||
\(333\) | −11.7017 | −0.641250 | ||||||||
\(334\) | −8.54288 | + | 14.7967i | −0.467445 | + | 0.809639i | ||||
\(335\) | −7.44504 | − | 12.8952i | −0.406766 | − | 0.704540i | ||||
\(336\) | 2.34601 | + | 4.06341i | 0.127985 | + | 0.221677i | ||||
\(337\) | 26.5961 | 1.44878 | 0.724391 | − | 0.689389i | \(-0.242121\pi\) | ||||
0.724391 | + | 0.689389i | \(0.242121\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.439665 | 0.0238793 | ||||||||
\(340\) | 8.85086 | + | 15.3301i | 0.480005 | + | 0.831393i | ||||
\(341\) | −0.427288 | − | 0.740084i | −0.0231389 | − | 0.0400778i | ||||
\(342\) | −2.49396 | + | 4.31966i | −0.134858 | + | 0.233581i | ||||
\(343\) | 37.6069 | 2.03058 | ||||||||
\(344\) | 1.04892 | − | 1.81678i | 0.0565538 | − | 0.0979541i | ||||
\(345\) | −9.63102 | + | 16.6814i | −0.518517 | + | 0.898097i | ||||
\(346\) | −15.3448 | −0.824942 | ||||||||
\(347\) | −0.455927 | + | 0.789689i | −0.0244754 | + | 0.0423927i | −0.878004 | − | 0.478654i | \(-0.841125\pi\) |
0.853528 | + | 0.521047i | \(0.174458\pi\) | |||||||
\(348\) | −0.425428 | − | 0.736862i | −0.0228053 | − | 0.0395000i | ||||
\(349\) | −8.86054 | − | 15.3469i | −0.474294 | − | 0.821501i | 0.525273 | − | 0.850934i | \(-0.323963\pi\) |
−0.999567 | + | 0.0294326i | \(0.990630\pi\) | |||||||
\(350\) | 23.3580 | 1.24854 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.137063 | −0.00730550 | ||||||||
\(353\) | −13.2174 | − | 22.8933i | −0.703493 | − | 1.21849i | −0.967233 | − | 0.253892i | \(-0.918289\pi\) |
0.263739 | − | 0.964594i | \(-0.415044\pi\) | |||||||
\(354\) | 2.94989 | + | 5.10935i | 0.156785 | + | 0.271559i | ||||
\(355\) | −0.154522 | + | 0.267639i | −0.00820116 | + | 0.0142048i | ||||
\(356\) | −17.0858 | −0.905543 | ||||||||
\(357\) | −13.1468 | + | 22.7708i | −0.695800 | + | 1.20516i | ||||
\(358\) | −0.261750 | + | 0.453364i | −0.0138339 | + | 0.0239610i | ||||
\(359\) | −7.76941 | −0.410054 | −0.205027 | − | 0.978756i | \(-0.565728\pi\) | ||||
−0.205027 | + | 0.978756i | \(0.565728\pi\) | |||||||
\(360\) | −1.57942 | + | 2.73563i | −0.0832426 | + | 0.144180i | ||||
\(361\) | −2.93967 | − | 5.09165i | −0.154719 | − | 0.267982i | ||||
\(362\) | −4.44504 | − | 7.69904i | −0.233626 | − | 0.404652i | ||||
\(363\) | 10.9812 | 0.576364 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.33811 | 0.384094 | ||||||||
\(366\) | 2.19806 | + | 3.80716i | 0.114895 | + | 0.199003i | ||||
\(367\) | 6.66368 | + | 11.5418i | 0.347841 | + | 0.602479i | 0.985866 | − | 0.167537i | \(-0.0535815\pi\) |
−0.638025 | + | 0.770016i | \(0.720248\pi\) | |||||||
\(368\) | 3.04892 | − | 5.28088i | 0.158936 | − | 0.275285i | ||||
\(369\) | 4.27413 | 0.222502 | ||||||||
\(370\) | 18.4819 | − | 32.0116i | 0.960827 | − | 1.66420i | ||||
\(371\) | 4.29105 | − | 7.43232i | 0.222780 | − | 0.385867i | ||||
\(372\) | 6.23490 | 0.323264 | ||||||||
\(373\) | −3.35152 | + | 5.80500i | −0.173535 | + | 0.300572i | −0.939653 | − | 0.342128i | \(-0.888852\pi\) |
0.766118 | + | 0.642700i | \(0.222186\pi\) | |||||||
\(374\) | −0.384043 | − | 0.665182i | −0.0198584 | − | 0.0343957i | ||||
\(375\) | −0.0343843 | − | 0.0595554i | −0.00177560 | − | 0.00307543i | ||||
\(376\) | −4.98792 | −0.257232 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −4.69202 | −0.241332 | ||||||||
\(379\) | 1.20775 | + | 2.09189i | 0.0620380 | + | 0.107453i | 0.895376 | − | 0.445310i | \(-0.146907\pi\) |
−0.833338 | + | 0.552763i | \(0.813573\pi\) | |||||||
\(380\) | −7.87800 | − | 13.6451i | −0.404133 | − | 0.699979i | ||||
\(381\) | −3.93631 | + | 6.81789i | −0.201663 | + | 0.349291i | ||||
\(382\) | −7.03146 | −0.359761 | ||||||||
\(383\) | 5.04892 | − | 8.74498i | 0.257988 | − | 0.446848i | −0.707715 | − | 0.706498i | \(-0.750274\pi\) |
0.965703 | + | 0.259650i | \(0.0836073\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | −2.03146 | −0.103533 | ||||||||
\(386\) | −8.87800 | + | 15.3772i | −0.451878 | + | 0.782676i | ||||
\(387\) | 1.04892 | + | 1.81678i | 0.0533195 | + | 0.0923520i | ||||
\(388\) | 1.06369 | + | 1.84236i | 0.0540005 | + | 0.0935317i | ||||
\(389\) | 25.1336 | 1.27432 | 0.637162 | − | 0.770730i | \(-0.280108\pi\) | ||||
0.637162 | + | 0.770730i | \(0.280108\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 34.1715 | 1.72813 | ||||||||
\(392\) | −7.50753 | − | 13.0034i | −0.379188 | − | 0.656772i | ||||
\(393\) | −0.310667 | − | 0.538091i | −0.0156711 | − | 0.0271431i | ||||
\(394\) | 9.32855 | − | 16.1575i | 0.469966 | − | 0.814004i | ||||
\(395\) | 45.8528 | 2.30710 | ||||||||
\(396\) | 0.0685317 | − | 0.118700i | 0.00344385 | − | 0.00596492i | ||||
\(397\) | 10.4179 | − | 18.0443i | 0.522859 | − | 0.905619i | −0.476787 | − | 0.879019i | \(-0.658199\pi\) |
0.999646 | − | 0.0265998i | \(-0.00846797\pi\) | |||||||
\(398\) | 7.66248 | 0.384085 | ||||||||
\(399\) | 11.7017 | − | 20.2680i | 0.585818 | − | 1.01467i | ||||
\(400\) | −2.48911 | − | 4.31127i | −0.124456 | − | 0.215564i | ||||
\(401\) | −2.97823 | − | 5.15845i | −0.148726 | − | 0.257600i | 0.782031 | − | 0.623239i | \(-0.214184\pi\) |
−0.930757 | + | 0.365639i | \(0.880850\pi\) | |||||||
\(402\) | −4.71379 | −0.235103 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −9.18598 | −0.457020 | ||||||||
\(405\) | −1.57942 | − | 2.73563i | −0.0784819 | − | 0.135935i | ||||
\(406\) | 1.99612 | + | 3.45737i | 0.0990655 | + | 0.171587i | ||||
\(407\) | −0.801938 | + | 1.38900i | −0.0397506 | + | 0.0688500i | ||||
\(408\) | 5.60388 | 0.277433 | ||||||||
\(409\) | −0.900969 | + | 1.56052i | −0.0445500 | + | 0.0771629i | −0.887441 | − | 0.460922i | \(-0.847519\pi\) |
0.842891 | + | 0.538085i | \(0.180852\pi\) | |||||||
\(410\) | −6.75063 | + | 11.6924i | −0.333390 | + | 0.577448i | ||||
\(411\) | 4.00000 | 0.197305 | ||||||||
\(412\) | −0.112605 | + | 0.195037i | −0.00554763 | + | 0.00960878i | ||||
\(413\) | −13.8409 | − | 23.9732i | −0.681068 | − | 1.17964i | ||||
\(414\) | 3.04892 | + | 5.28088i | 0.149846 | + | 0.259541i | ||||
\(415\) | 31.1342 | 1.52832 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.6582 | 0.668843 | ||||||||
\(418\) | 0.341830 | + | 0.592068i | 0.0167195 | + | 0.0289590i | ||||
\(419\) | 14.2250 | + | 24.6384i | 0.694935 | + | 1.20366i | 0.970202 | + | 0.242296i | \(0.0779004\pi\) |
−0.275267 | + | 0.961368i | \(0.588766\pi\) | |||||||
\(420\) | 7.41066 | − | 12.8356i | 0.361603 | − | 0.626315i | ||||
\(421\) | −13.9323 | −0.679019 | −0.339509 | − | 0.940603i | \(-0.610261\pi\) | ||||
−0.339509 | + | 0.940603i | \(0.610261\pi\) | |||||||
\(422\) | −5.58211 | + | 9.66849i | −0.271733 | + | 0.470655i | ||||
\(423\) | 2.49396 | − | 4.31966i | 0.121260 | − | 0.210029i | ||||
\(424\) | −1.82908 | −0.0888282 | ||||||||
\(425\) | 13.9487 | − | 24.1598i | 0.676611 | − | 1.17192i | ||||
\(426\) | 0.0489173 | + | 0.0847273i | 0.00237005 | + | 0.00410505i | ||||
\(427\) | −10.3134 | − | 17.8633i | −0.499098 | − | 0.864464i | ||||
\(428\) | 11.2838 | 0.545424 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.62671 | −0.319568 | ||||||||
\(431\) | −7.95108 | − | 13.7717i | −0.382990 | − | 0.663358i | 0.608498 | − | 0.793555i | \(-0.291772\pi\) |
−0.991488 | + | 0.130197i | \(0.958439\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −2.38859 | + | 4.13716i | −0.114788 | + | 0.198819i | −0.917695 | − | 0.397285i | \(-0.869952\pi\) |
0.802907 | + | 0.596105i | \(0.203286\pi\) | |||||||
\(434\) | −29.2543 | −1.40425 | ||||||||
\(435\) | −1.34385 | + | 2.32762i | −0.0644329 | + | 0.111601i | ||||
\(436\) | −0.0978347 | + | 0.169455i | −0.00468543 | + | 0.00811541i | ||||
\(437\) | −30.4155 | −1.45497 | ||||||||
\(438\) | 1.16152 | − | 2.01182i | 0.0554997 | − | 0.0961282i | ||||
\(439\) | 16.8158 | + | 29.1258i | 0.802575 | + | 1.39010i | 0.917916 | + | 0.396774i | \(0.129870\pi\) |
−0.115342 | + | 0.993326i | \(0.536796\pi\) | |||||||
\(440\) | 0.216480 | + | 0.374955i | 0.0103203 | + | 0.0178753i | ||||
\(441\) | 15.0151 | 0.715003 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −35.3749 | −1.68071 | −0.840357 | − | 0.542033i | \(-0.817655\pi\) | ||||
−0.840357 | + | 0.542033i | \(0.817655\pi\) | |||||||
\(444\) | −5.85086 | − | 10.1340i | −0.277669 | − | 0.480937i | ||||
\(445\) | 26.9855 | + | 46.7403i | 1.27924 | + | 2.21570i | ||||
\(446\) | −12.3177 | + | 21.3348i | −0.583258 | + | 1.01023i | ||||
\(447\) | 16.0586 | 0.759546 | ||||||||
\(448\) | −2.34601 | + | 4.06341i | −0.110839 | + | 0.191978i | ||||
\(449\) | 9.03146 | − | 15.6429i | 0.426221 | − | 0.738236i | −0.570313 | − | 0.821428i | \(-0.693178\pi\) |
0.996534 | + | 0.0831914i | \(0.0265113\pi\) | |||||||
\(450\) | 4.97823 | 0.234676 | ||||||||
\(451\) | 0.292913 | − | 0.507340i | 0.0137927 | − | 0.0238897i | ||||
\(452\) | 0.219833 | + | 0.380761i | 0.0103401 | + | 0.0179095i | ||||
\(453\) | 10.9412 | + | 18.9506i | 0.514060 | + | 0.890379i | ||||
\(454\) | −7.47650 | −0.350890 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.98792 | −0.233581 | ||||||||
\(457\) | 7.73341 | + | 13.3947i | 0.361753 | + | 0.626575i | 0.988250 | − | 0.152849i | \(-0.0488449\pi\) |
−0.626496 | + | 0.779425i | \(0.715512\pi\) | |||||||
\(458\) | 9.61356 | + | 16.6512i | 0.449212 | + | 0.778059i | ||||
\(459\) | −2.80194 | + | 4.85310i | −0.130783 | + | 0.226523i | ||||
\(460\) | −19.2620 | −0.898097 | ||||||||
\(461\) | 9.40462 | − | 16.2893i | 0.438017 | − | 0.758667i | −0.559520 | − | 0.828817i | \(-0.689014\pi\) |
0.997536 | + | 0.0701499i | \(0.0223477\pi\) | |||||||
\(462\) | −0.321552 | + | 0.556945i | −0.0149600 | + | 0.0259114i | ||||
\(463\) | −15.8431 | −0.736291 | −0.368145 | − | 0.929768i | \(-0.620007\pi\) | ||||
−0.368145 | + | 0.929768i | \(0.620007\pi\) | |||||||
\(464\) | 0.425428 | − | 0.736862i | 0.0197500 | − | 0.0342080i | ||||
\(465\) | −9.84750 | − | 17.0564i | −0.456667 | − | 0.790970i | ||||
\(466\) | −1.85086 | − | 3.20578i | −0.0857392 | − | 0.148505i | ||||
\(467\) | 22.0006 | 1.01807 | 0.509033 | − | 0.860747i | \(-0.330003\pi\) | ||||
0.509033 | + | 0.860747i | \(0.330003\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.1172 | 1.02128 | ||||||||
\(470\) | 7.87800 | + | 13.6451i | 0.363385 | + | 0.629402i | ||||
\(471\) | −3.95108 | − | 6.84348i | −0.182056 | − | 0.315331i | ||||
\(472\) | −2.94989 | + | 5.10935i | −0.135780 | + | 0.235177i | ||||
\(473\) | 0.287536 | 0.0132209 | ||||||||
\(474\) | 7.25786 | − | 12.5710i | 0.333365 | − | 0.577405i | ||||
\(475\) | −12.4155 | + | 21.5043i | −0.569662 | + | 0.986684i | ||||
\(476\) | −26.2935 | −1.20516 | ||||||||
\(477\) | 0.914542 | − | 1.58403i | 0.0418740 | − | 0.0725279i | ||||
\(478\) | −4.25667 | − | 7.37277i | −0.194695 | − | 0.337222i | ||||
\(479\) | 10.6746 | + | 18.4889i | 0.487733 | + | 0.844779i | 0.999900 | − | 0.0141070i | \(-0.00449054\pi\) |
−0.512167 | + | 0.858886i | \(0.671157\pi\) | |||||||
\(480\) | −3.15883 | −0.144180 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 17.4330 | 0.794050 | ||||||||
\(483\) | −14.3056 | − | 24.7780i | −0.650927 | − | 1.12744i | ||||
\(484\) | 5.49061 | + | 9.51001i | 0.249573 | + | 0.432273i | ||||
\(485\) | 3.36001 | − | 5.81971i | 0.152570 | − | 0.264259i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 15.8197 | − | 27.4005i | 0.716859 | − | 1.24164i | −0.245380 | − | 0.969427i | \(-0.578913\pi\) |
0.962238 | − | 0.272209i | \(-0.0877541\pi\) | |||||||
\(488\) | −2.19806 | + | 3.80716i | −0.0995016 | + | 0.172342i | ||||
\(489\) | 8.01938 | 0.362649 | ||||||||
\(490\) | −23.7150 | + | 41.0757i | −1.07134 | + | 1.85561i | ||||
\(491\) | 0.699554 | + | 1.21166i | 0.0315704 | + | 0.0546816i | 0.881379 | − | 0.472410i | \(-0.156616\pi\) |
−0.849808 | + | 0.527092i | \(0.823282\pi\) | |||||||
\(492\) | 2.13706 | + | 3.70150i | 0.0963463 | + | 0.166877i | ||||
\(493\) | 4.76809 | 0.214744 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.432960 | −0.0194601 | ||||||||
\(496\) | 3.11745 | + | 5.39958i | 0.139978 | + | 0.242448i | ||||
\(497\) | −0.229521 | − | 0.397542i | −0.0102954 | − | 0.0178322i | ||||
\(498\) | 4.92812 | − | 8.53575i | 0.220834 | − | 0.382496i | ||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 0.0343843 | − | 0.0595554i | 0.00153771 | − | 0.00266340i | ||||
\(501\) | 8.54288 | − | 14.7967i | 0.381668 | − | 0.661068i | ||||
\(502\) | −3.48427 | −0.155511 | ||||||||
\(503\) | 9.19136 | − | 15.9199i | 0.409822 | − | 0.709833i | −0.585047 | − | 0.810999i | \(-0.698924\pi\) |
0.994870 | + | 0.101166i | \(0.0322573\pi\) | |||||||
\(504\) | −2.34601 | − | 4.06341i | −0.104500 | − | 0.180999i | ||||
\(505\) | 14.5085 | + | 25.1294i | 0.645619 | + | 1.11825i | ||||
\(506\) | 0.835790 | 0.0371554 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.87263 | −0.349291 | ||||||||
\(509\) | −0.0663757 | − | 0.114966i | −0.00294205 | − | 0.00509578i | 0.864551 | − | 0.502546i | \(-0.167603\pi\) |
−0.867493 | + | 0.497450i | \(0.834270\pi\) | |||||||
\(510\) | −8.85086 | − | 15.3301i | −0.391922 | − | 0.678830i | ||||
\(511\) | −5.44989 | + | 9.43948i | −0.241089 | + | 0.417578i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.49396 | − | 4.31966i | 0.110111 | − | 0.190718i | ||||
\(514\) | 6.80194 | − | 11.7813i | 0.300021 | − | 0.519651i | ||||
\(515\) | 0.711399 | 0.0313480 | ||||||||
\(516\) | −1.04892 | + | 1.81678i | −0.0461760 | + | 0.0799792i | ||||
\(517\) | −0.341830 | − | 0.592068i | −0.0150337 | − | 0.0260391i | ||||
\(518\) | 27.4523 | + | 47.5488i | 1.20619 | + | 2.08918i | ||||
\(519\) | 15.3448 | 0.673563 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.0508 | 1.62323 | 0.811613 | − | 0.584195i | \(-0.198590\pi\) | ||||
0.811613 | + | 0.584195i | \(0.198590\pi\) | |||||||
\(522\) | 0.425428 | + | 0.736862i | 0.0186205 | + | 0.0322516i | ||||
\(523\) | 1.57673 | + | 2.73097i | 0.0689455 | + | 0.119417i | 0.898437 | − | 0.439102i | \(-0.144703\pi\) |
−0.829492 | + | 0.558519i | \(0.811370\pi\) | |||||||
\(524\) | 0.310667 | − | 0.538091i | 0.0135715 | − | 0.0235066i | ||||
\(525\) | −23.3580 | −1.01942 | ||||||||
\(526\) | −5.72886 | + | 9.92267i | −0.249790 | + | 0.432649i | ||||
\(527\) | −17.4698 | + | 30.2586i | −0.760996 | + | 1.31808i | ||||
\(528\) | 0.137063 | 0.00596492 | ||||||||
\(529\) | −7.09179 | + | 12.2833i | −0.308339 | + | 0.534059i | ||||
\(530\) | 2.88889 | + | 5.00370i | 0.125485 | + | 0.217347i | ||||
\(531\) | −2.94989 | − | 5.10935i | −0.128014 | − | 0.221727i | ||||
\(532\) | 23.4034 | 1.01467 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 17.0858 | 0.739373 | ||||||||
\(535\) | −17.8218 | − | 30.8683i | −0.770506 | − | 1.33455i | ||||
\(536\) | −2.35690 | − | 4.08226i | −0.101802 | − | 0.176327i | ||||
\(537\) | 0.261750 | − | 0.453364i | 0.0112953 | − | 0.0195641i | ||||
\(538\) | 22.3666 | 0.964292 | ||||||||
\(539\) | 1.02901 | − | 1.78229i | 0.0443225 | − | 0.0767688i | ||||
\(540\) | 1.57942 | − | 2.73563i | 0.0679673 | − | 0.117723i | ||||
\(541\) | −4.07846 | −0.175347 | −0.0876733 | − | 0.996149i | \(-0.527943\pi\) | ||||
−0.0876733 | + | 0.996149i | \(0.527943\pi\) | |||||||
\(542\) | 1.93631 | − | 3.35379i | 0.0831718 | − | 0.144058i | ||||
\(543\) | 4.44504 | + | 7.69904i | 0.190755 | + | 0.330397i | ||||
\(544\) | 2.80194 | + | 4.85310i | 0.120132 | + | 0.208075i | ||||
\(545\) | 0.618087 | 0.0264759 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.0508 | −0.985583 | −0.492791 | − | 0.870148i | \(-0.664023\pi\) | ||||
−0.492791 | + | 0.870148i | \(0.664023\pi\) | |||||||
\(548\) | 2.00000 | + | 3.46410i | 0.0854358 | + | 0.147979i | ||||
\(549\) | −2.19806 | − | 3.80716i | −0.0938110 | − | 0.162485i | ||||
\(550\) | 0.341166 | − | 0.590918i | 0.0145474 | − | 0.0251968i | ||||
\(551\) | −4.24400 | −0.180800 | ||||||||
\(552\) | −3.04892 | + | 5.28088i | −0.129771 | + | 0.224769i | ||||
\(553\) | −34.0541 | + | 58.9834i | −1.44813 | + | 2.50823i | ||||
\(554\) | 28.7090 | 1.21973 | ||||||||
\(555\) | −18.4819 | + | 32.0116i | −0.784512 | + | 1.35881i | ||||
\(556\) | 6.82908 | + | 11.8283i | 0.289618 | + | 0.501633i | ||||
\(557\) | 10.2078 | + | 17.6803i | 0.432516 | + | 0.749140i | 0.997089 | − | 0.0762430i | \(-0.0242925\pi\) |
−0.564573 | + | 0.825383i | \(0.690959\pi\) | |||||||
\(558\) | −6.23490 | −0.263944 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 14.8213 | 0.626315 | ||||||||
\(561\) | 0.384043 | + | 0.665182i | 0.0162143 | + | 0.0280840i | ||||
\(562\) | −14.5429 | − | 25.1890i | −0.613454 | − | 1.06253i | ||||
\(563\) | −10.7805 | + | 18.6723i | −0.454342 | + | 0.786944i | −0.998650 | − | 0.0519416i | \(-0.983459\pi\) |
0.544308 | + | 0.838886i | \(0.316792\pi\) | |||||||
\(564\) | 4.98792 | 0.210029 | ||||||||
\(565\) | 0.694414 | − | 1.20276i | 0.0292142 | − | 0.0506005i | ||||
\(566\) | −6.87800 | + | 11.9130i | −0.289104 | + | 0.500743i | ||||
\(567\) | 4.69202 | 0.197046 | ||||||||
\(568\) | −0.0489173 | + | 0.0847273i | −0.00205253 | + | 0.00355508i | ||||
\(569\) | −4.49396 | − | 7.78377i | −0.188397 | − | 0.326312i | 0.756319 | − | 0.654203i | \(-0.226996\pi\) |
−0.944716 | + | 0.327890i | \(0.893662\pi\) | |||||||
\(570\) | 7.87800 | + | 13.6451i | 0.329973 | + | 0.571530i | ||||
\(571\) | 13.5603 | 0.567482 | 0.283741 | − | 0.958901i | \(-0.408424\pi\) | ||||
0.283741 | + | 0.958901i | \(0.408424\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.03146 | 0.293743 | ||||||||
\(574\) | −10.0271 | − | 17.3675i | −0.418525 | − | 0.724907i | ||||
\(575\) | 15.1782 | + | 26.2894i | 0.632975 | + | 1.09635i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −16.2825 | −0.677849 | −0.338924 | − | 0.940814i | \(-0.610063\pi\) | ||||
−0.338924 | + | 0.940814i | \(0.610063\pi\) | |||||||
\(578\) | −7.20171 | + | 12.4737i | −0.299552 | + | 0.518839i | ||||
\(579\) | 8.87800 | − | 15.3772i | 0.368957 | − | 0.639053i | ||||
\(580\) | −2.68771 | −0.111601 | ||||||||
\(581\) | −23.1228 | + | 40.0499i | −0.959296 | + | 1.66155i | ||||
\(582\) | −1.06369 | − | 1.84236i | −0.0440913 | − | 0.0763683i | ||||
\(583\) | −0.125350 | − | 0.217113i | −0.00519148 | − | 0.00899190i | ||||
\(584\) | 2.32304 | 0.0961282 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27.7362 | −1.14577 | ||||||||
\(587\) | 23.7853 | + | 41.1974i | 0.981725 | + | 1.70040i | 0.655673 | + | 0.755045i | \(0.272385\pi\) |
0.326052 | + | 0.945352i | \(0.394282\pi\) | |||||||
\(588\) | 7.50753 | + | 13.0034i | 0.309605 | + | 0.536252i | ||||
\(589\) | 15.5496 | − | 26.9327i | 0.640709 | − | 1.10974i | ||||
\(590\) | 18.6364 | 0.767248 | ||||||||
\(591\) | −9.32855 | + | 16.1575i | −0.383725 | + | 0.664632i | ||||
\(592\) | 5.85086 | − | 10.1340i | 0.240469 | − | 0.416504i | ||||
\(593\) | −31.0267 | −1.27411 | −0.637056 | − | 0.770817i | \(-0.719848\pi\) | ||||
−0.637056 | + | 0.770817i | \(0.719848\pi\) | |||||||
\(594\) | −0.0685317 | + | 0.118700i | −0.00281189 | + | 0.00487033i | ||||
\(595\) | 41.5284 | + | 71.9293i | 1.70250 | + | 2.94881i | ||||
\(596\) | 8.02930 | + | 13.9072i | 0.328893 | + | 0.569660i | ||||
\(597\) | −7.66248 | −0.313604 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.3263 | 0.912228 | 0.456114 | − | 0.889921i | \(-0.349241\pi\) | ||||
0.456114 | + | 0.889921i | \(0.349241\pi\) | |||||||
\(600\) | 2.48911 | + | 4.31127i | 0.101618 | + | 0.176007i | ||||
\(601\) | 4.09030 | + | 7.08461i | 0.166847 | + | 0.288987i | 0.937310 | − | 0.348498i | \(-0.113308\pi\) |
−0.770463 | + | 0.637485i | \(0.779975\pi\) | |||||||
\(602\) | 4.92154 | − | 8.52436i | 0.200587 | − | 0.347427i | ||||
\(603\) | 4.71379 | 0.191960 | ||||||||
\(604\) | −10.9412 | + | 18.9506i | −0.445189 | + | 0.771091i | ||||
\(605\) | 17.3439 | − | 30.0405i | 0.705130 | − | 1.22132i | ||||
\(606\) | 9.18598 | 0.373155 | ||||||||
\(607\) | −1.65399 | + | 2.86479i | −0.0671334 | + | 0.116278i | −0.897638 | − | 0.440733i | \(-0.854719\pi\) |
0.830505 | + | 0.557011i | \(0.188052\pi\) | |||||||
\(608\) | −2.49396 | − | 4.31966i | −0.101143 | − | 0.175186i | ||||
\(609\) | −1.99612 | − | 3.45737i | −0.0808867 | − | 0.140100i | ||||
\(610\) | 13.8866 | 0.562253 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −5.60388 | −0.226523 | ||||||||
\(613\) | −5.44265 | − | 9.42694i | −0.219827 | − | 0.380751i | 0.734928 | − | 0.678145i | \(-0.237216\pi\) |
−0.954755 | + | 0.297394i | \(0.903882\pi\) | |||||||
\(614\) | −6.22952 | − | 10.7898i | −0.251403 | − | 0.435443i | ||||
\(615\) | 6.75063 | − | 11.6924i | 0.272212 | − | 0.471484i | ||||
\(616\) | −0.643104 | −0.0259114 | ||||||||
\(617\) | −17.2838 | + | 29.9364i | −0.695820 | + | 1.20520i | 0.274083 | + | 0.961706i | \(0.411626\pi\) |
−0.969903 | + | 0.243490i | \(0.921708\pi\) | |||||||
\(618\) | 0.112605 | − | 0.195037i | 0.00452962 | − | 0.00784554i | ||||
\(619\) | −2.86592 | −0.115191 | −0.0575955 | − | 0.998340i | \(-0.518343\pi\) | ||||
−0.0575955 | + | 0.998340i | \(0.518343\pi\) | |||||||
\(620\) | 9.84750 | − | 17.0564i | 0.395485 | − | 0.685001i | ||||
\(621\) | −3.04892 | − | 5.28088i | −0.122349 | − | 0.211914i | ||||
\(622\) | 3.04892 | + | 5.28088i | 0.122250 | + | 0.211744i | ||||
\(623\) | −80.1667 | −3.21181 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.1084 | −1.00434 | ||||||||
\(626\) | 6.36927 | + | 11.0319i | 0.254567 | + | 0.440924i | ||||
\(627\) | −0.341830 | − | 0.592068i | −0.0136514 | − | 0.0236449i | ||||
\(628\) | 3.95108 | − | 6.84348i | 0.157665 | − | 0.273084i | ||||
\(629\) | 65.5749 | 2.61464 | ||||||||
\(630\) | −7.41066 | + | 12.8356i | −0.295248 | + | 0.511384i | ||||
\(631\) | −21.3315 | + | 36.9473i | −0.849195 | + | 1.47085i | 0.0327326 | + | 0.999464i | \(0.489579\pi\) |
−0.881928 | + | 0.471385i | \(0.843754\pi\) | |||||||
\(632\) | 14.5157 | 0.577405 | ||||||||
\(633\) | 5.58211 | − | 9.66849i | 0.221869 | − | 0.384288i | ||||
\(634\) | 7.40701 | + | 12.8293i | 0.294170 | + | 0.509517i | ||||
\(635\) | 12.4342 | + | 21.5366i | 0.493434 | + | 0.854654i | ||||
\(636\) | 1.82908 | 0.0725279 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.116621 | 0.00461707 | ||||||||
\(639\) | −0.0489173 | − | 0.0847273i | −0.00193514 | − | 0.00335176i | ||||
\(640\) | −1.57942 | − | 2.73563i | −0.0624319 | − | 0.108135i | ||||
\(641\) | −20.6963 | + | 35.8471i | −0.817456 | + | 1.41588i | 0.0900948 | + | 0.995933i | \(0.471283\pi\) |
−0.907551 | + | 0.419942i | \(0.862050\pi\) | |||||||
\(642\) | −11.2838 | −0.445337 | ||||||||
\(643\) | 6.85623 | − | 11.8753i | 0.270383 | − | 0.468318i | −0.698577 | − | 0.715535i | \(-0.746183\pi\) |
0.968960 | + | 0.247217i | \(0.0795162\pi\) | |||||||
\(644\) | 14.3056 | − | 24.7780i | 0.563719 | − | 0.976390i | ||||
\(645\) | 6.62671 | 0.260926 | ||||||||
\(646\) | 13.9758 | − | 24.2069i | 0.549872 | − | 0.952406i | ||||
\(647\) | −9.00431 | − | 15.5959i | −0.353996 | − | 0.613139i | 0.632950 | − | 0.774193i | \(-0.281844\pi\) |
−0.986946 | + | 0.161054i | \(0.948511\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −0.808643 | −0.0317420 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.2543 | 1.14657 | ||||||||
\(652\) | 4.00969 | + | 6.94498i | 0.157032 | + | 0.271987i | ||||
\(653\) | −23.2826 | − | 40.3267i | −0.911119 | − | 1.57810i | −0.812486 | − | 0.582981i | \(-0.801886\pi\) |
−0.0986335 | − | 0.995124i | \(-0.531447\pi\) | |||||||
\(654\) | 0.0978347 | − | 0.169455i | 0.00382564 | − | 0.00662620i | ||||
\(655\) | −1.96269 | −0.0766887 | ||||||||
\(656\) | −2.13706 | + | 3.70150i | −0.0834383 | + | 0.144519i | ||||
\(657\) | −1.16152 | + | 2.01182i | −0.0453153 | + | 0.0784884i | ||||
\(658\) | −23.4034 | −0.912360 | ||||||||
\(659\) | −6.92812 | + | 11.9998i | −0.269881 | + | 0.467448i | −0.968831 | − | 0.247723i | \(-0.920318\pi\) |
0.698950 | + | 0.715171i | \(0.253651\pi\) | |||||||
\(660\) | −0.216480 | − | 0.374955i | −0.00842648 | − | 0.0145951i | ||||
\(661\) | −21.5526 | − | 37.3301i | −0.838298 | − | 1.45197i | −0.891317 | − | 0.453381i | \(-0.850218\pi\) |
0.0530194 | − | 0.998593i | \(-0.483115\pi\) | |||||||
\(662\) | −7.70171 | −0.299335 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.85623 | 0.382496 | ||||||||
\(665\) | −36.9638 | − | 64.0231i | −1.43339 | − | 2.48271i | ||||
\(666\) | 5.85086 | + | 10.1340i | 0.226716 | + | 0.392684i | ||||
\(667\) | −2.59419 | + | 4.49326i | −0.100447 | + | 0.173980i | ||||
\(668\) | 17.0858 | 0.661068 | ||||||||
\(669\) | 12.3177 | − | 21.3348i | 0.476229 | − | 0.824852i | ||||
\(670\) | −7.44504 | + | 12.8952i | −0.287627 | + | 0.498185i | ||||
\(671\) | −0.602548 | −0.0232611 | ||||||||
\(672\) | 2.34601 | − | 4.06341i | 0.0904993 | − | 0.156749i | ||||
\(673\) | −15.3708 | − | 26.6229i | −0.592499 | − | 1.02624i | −0.993895 | − | 0.110334i | \(-0.964808\pi\) |
0.401395 | − | 0.915905i | \(-0.368525\pi\) | |||||||
\(674\) | −13.2981 | − | 23.0329i | −0.512222 | − | 0.887194i | ||||
\(675\) | −4.97823 | −0.191612 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.5894 | 0.637582 | 0.318791 | − | 0.947825i | \(-0.396723\pi\) | ||||
0.318791 | + | 0.947825i | \(0.396723\pi\) | |||||||
\(678\) | −0.219833 | − | 0.380761i | −0.00844262 | − | 0.0146230i | ||||
\(679\) | 4.99084 | + | 8.64440i | 0.191531 | + | 0.331741i | ||||
\(680\) | 8.85086 | − | 15.3301i | 0.339415 | − | 0.587884i | ||||
\(681\) | 7.47650 | 0.286500 | ||||||||
\(682\) | −0.427288 | + | 0.740084i | −0.0163617 | + | 0.0283393i | ||||
\(683\) | −17.4943 | + | 30.3009i | −0.669399 | + | 1.15943i | 0.308673 | + | 0.951168i | \(0.400115\pi\) |
−0.978072 | + | 0.208265i | \(0.933218\pi\) | |||||||
\(684\) | 4.98792 | 0.190718 | ||||||||
\(685\) | 6.31767 | − | 10.9425i | 0.241386 | − | 0.418092i | ||||
\(686\) | −18.8034 | − | 32.5685i | −0.717918 | − | 1.24347i | ||||
\(687\) | −9.61356 | − | 16.6512i | −0.366780 | − | 0.635282i | ||||
\(688\) | −2.09783 | −0.0799792 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 19.2620 | 0.733294 | ||||||||
\(691\) | 7.04354 | + | 12.1998i | 0.267949 | + | 0.464101i | 0.968332 | − | 0.249666i | \(-0.0803208\pi\) |
−0.700383 | + | 0.713767i | \(0.746987\pi\) | |||||||
\(692\) | 7.67241 | + | 13.2890i | 0.291661 | + | 0.505172i | ||||
\(693\) | 0.321552 | − | 0.556945i | 0.0122148 | − | 0.0211566i | ||||
\(694\) | 0.911854 | 0.0346135 | ||||||||
\(695\) | 21.5719 | − | 37.3637i | 0.818270 | − | 1.41729i | ||||
\(696\) | −0.425428 | + | 0.736862i | −0.0161258 | + | 0.0279307i | ||||
\(697\) | −23.9517 | −0.907234 | ||||||||
\(698\) | −8.86054 | + | 15.3469i | −0.335377 | + | 0.580889i | ||||
\(699\) | 1.85086 | + | 3.20578i | 0.0700058 | + | 0.121254i | ||||
\(700\) | −11.6790 | − | 20.2286i | −0.441424 | − | 0.764569i | ||||
\(701\) | 48.6112 | 1.83602 | 0.918009 | − | 0.396559i | \(-0.129796\pi\) | ||||
0.918009 | + | 0.396559i | \(0.129796\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −58.3672 | −2.20136 | ||||||||
\(704\) | 0.0685317 | + | 0.118700i | 0.00258288 | + | 0.00447369i | ||||
\(705\) | −7.87800 | − | 13.6451i | −0.296703 | − | 0.513904i | ||||
\(706\) | −13.2174 | + | 22.8933i | −0.497445 | + | 0.861600i | ||||
\(707\) | −43.1008 | −1.62097 | ||||||||
\(708\) | 2.94989 | − | 5.10935i | 0.110864 | − | 0.192021i | ||||
\(709\) | 8.64310 | − | 14.9703i | 0.324599 | − | 0.562221i | −0.656832 | − | 0.754037i | \(-0.728104\pi\) |
0.981431 | + | 0.191815i | \(0.0614375\pi\) | |||||||
\(710\) | 0.309043 | 0.0115982 | ||||||||
\(711\) | −7.25786 | + | 12.5710i | −0.272191 | + | 0.471449i | ||||
\(712\) | 8.54288 | + | 14.7967i | 0.320158 | + | 0.554530i | ||||
\(713\) | −19.0097 | − | 32.9257i | −0.711918 | − | 1.23308i | ||||
\(714\) | 26.2935 | 0.984010 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.523499 | 0.0195641 | ||||||||
\(717\) | 4.25667 | + | 7.37277i | 0.158968 | + | 0.275341i | ||||
\(718\) | 3.88471 | + | 6.72851i | 0.144976 | + | 0.251106i | ||||
\(719\) | −14.5603 | + | 25.2192i | −0.543009 | + | 0.940519i | 0.455720 | + | 0.890123i | \(0.349382\pi\) |
−0.998729 | + | 0.0503960i | \(0.983952\pi\) | |||||||
\(720\) | 3.15883 | 0.117723 | ||||||||
\(721\) | −0.528344 | + | 0.915118i | −0.0196765 | + | 0.0340808i | ||||
\(722\) | −2.93967 | + | 5.09165i | −0.109403 | + | 0.189492i | ||||
\(723\) | −17.4330 | −0.648339 | ||||||||
\(724\) | −4.44504 | + | 7.69904i | −0.165199 | + | 0.286133i | ||||
\(725\) | 2.11788 | + | 3.66827i | 0.0786559 | + | 0.136236i | ||||
\(726\) | −5.49061 | − | 9.51001i | −0.203776 | − | 0.352950i | ||||
\(727\) | 45.5666 | 1.68997 | 0.844985 | − | 0.534790i | \(-0.179609\pi\) | ||||
0.844985 | + | 0.534790i | \(0.179609\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −3.66905 | − | 6.35499i | −0.135798 | − | 0.235209i | ||||
\(731\) | −5.87800 | − | 10.1810i | −0.217406 | − | 0.376558i | ||||
\(732\) | 2.19806 | − | 3.80716i | 0.0812427 | − | 0.140717i | ||||
\(733\) | 21.7995 | 0.805185 | 0.402592 | − | 0.915379i | \(-0.368109\pi\) | ||||
0.402592 | + | 0.915379i | \(0.368109\pi\) | |||||||
\(734\) | 6.66368 | − | 11.5418i | 0.245961 | − | 0.426017i | ||||
\(735\) | 23.7150 | − | 41.0757i | 0.874743 | − | 1.51510i | ||||
\(736\) | −6.09783 | −0.224769 | ||||||||
\(737\) | 0.323044 | − | 0.559529i | 0.0118995 | − | 0.0206105i | ||||
\(738\) | −2.13706 | − | 3.70150i | −0.0786664 | − | 0.136254i | ||||
\(739\) | −20.7832 | − | 35.9975i | −0.764521 | − | 1.32419i | −0.940500 | − | 0.339795i | \(-0.889642\pi\) |
0.175979 | − | 0.984394i | \(-0.443691\pi\) | |||||||
\(740\) | −36.9638 | −1.35881 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.58211 | −0.315059 | ||||||||
\(743\) | 14.4112 | + | 24.9609i | 0.528695 | + | 0.915727i | 0.999440 | + | 0.0334577i | \(0.0106519\pi\) |
−0.470745 | + | 0.882269i | \(0.656015\pi\) | |||||||
\(744\) | −3.11745 | − | 5.39958i | −0.114291 | − | 0.197958i | ||||
\(745\) | 25.3632 | − | 43.9304i | 0.929237 | − | 1.60949i | ||||
\(746\) | 6.70304 | 0.245416 | ||||||||
\(747\) | −4.92812 | + | 8.53575i | −0.180310 | + | 0.312307i | ||||
\(748\) | −0.384043 | + | 0.665182i | −0.0140420 | + | 0.0243215i | ||||
\(749\) | 52.9439 | 1.93453 | ||||||||
\(750\) | −0.0343843 | + | 0.0595554i | −0.00125554 | + | 0.00217466i | ||||
\(751\) | −8.31013 | − | 14.3936i | −0.303241 | − | 0.525229i | 0.673627 | − | 0.739071i | \(-0.264735\pi\) |
−0.976868 | + | 0.213842i | \(0.931402\pi\) | |||||||
\(752\) | 2.49396 | + | 4.31966i | 0.0909453 | + | 0.157522i | ||||
\(753\) | 3.48427 | 0.126974 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 69.1226 | 2.51563 | ||||||||
\(756\) | 2.34601 | + | 4.06341i | 0.0853236 | + | 0.147785i | ||||
\(757\) | 20.1957 | + | 34.9799i | 0.734024 | + | 1.27137i | 0.955150 | + | 0.296122i | \(0.0956934\pi\) |
−0.221126 | + | 0.975245i | \(0.570973\pi\) | |||||||
\(758\) | 1.20775 | − | 2.09189i | 0.0438675 | − | 0.0759807i | ||||
\(759\) | −0.835790 | −0.0303372 | ||||||||
\(760\) | −7.87800 | + | 13.6451i | −0.285765 | + | 0.494960i | ||||
\(761\) | −1.64742 | + | 2.85341i | −0.0597188 | + | 0.103436i | −0.894339 | − | 0.447390i | \(-0.852354\pi\) |
0.834620 | + | 0.550826i | \(0.185687\pi\) | |||||||
\(762\) | 7.87263 | 0.285195 | ||||||||
\(763\) | −0.459042 | + | 0.795085i | −0.0166185 | + | 0.0287840i | ||||
\(764\) | 3.51573 | + | 6.08942i | 0.127195 | + | 0.220308i | ||||
\(765\) | 8.85086 | + | 15.3301i | 0.320003 | + | 0.554262i | ||||
\(766\) | −10.0978 | −0.364850 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −1.17629 | − | 2.03740i | −0.0424182 | − | 0.0734704i | 0.844037 | − | 0.536285i | \(-0.180173\pi\) |
−0.886455 | + | 0.462815i | \(0.846840\pi\) | |||||||
\(770\) | 1.01573 | + | 1.75930i | 0.0366043 | + | 0.0634006i | ||||
\(771\) | −6.80194 | + | 11.7813i | −0.244966 | + | 0.424293i | ||||
\(772\) | 17.7560 | 0.639053 | ||||||||
\(773\) | −10.1969 | + | 17.6615i | −0.366756 | + | 0.635240i | −0.989056 | − | 0.147539i | \(-0.952865\pi\) |
0.622300 | + | 0.782778i | \(0.286198\pi\) | |||||||
\(774\) | 1.04892 | − | 1.81678i | 0.0377026 | − | 0.0653027i | ||||
\(775\) | −31.0388 | −1.11494 | ||||||||
\(776\) | 1.06369 | − | 1.84236i | 0.0381841 | − | 0.0661369i | ||||
\(777\) | −27.4523 | − | 47.5488i | −0.984847 | − | 1.70581i | ||||
\(778\) | −12.5668 | − | 21.7663i | −0.450542 | − | 0.780361i | ||||
\(779\) | 21.3190 | 0.763832 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0134095 | −0.000479831 | ||||||||
\(782\) | −17.0858 | − | 29.5934i | −0.610985 | − | 1.05826i | ||||
\(783\) | −0.425428 | − | 0.736862i | −0.0152035 | − | 0.0263333i | ||||
\(784\) | −7.50753 | + | 13.0034i | −0.268126 | + | 0.464408i | ||||
\(785\) | −24.9616 | −0.890919 | ||||||||
\(786\) | −0.310667 | + | 0.538091i | −0.0110811 | + | 0.0191931i | ||||
\(787\) | 9.83877 | − | 17.0413i | 0.350714 | − | 0.607455i | −0.635660 | − | 0.771969i | \(-0.719272\pi\) |
0.986375 | + | 0.164514i | \(0.0526055\pi\) | |||||||
\(788\) | −18.6571 | −0.664632 | ||||||||
\(789\) | 5.72886 | − | 9.92267i | 0.203953 | − | 0.353256i | ||||
\(790\) | −22.9264 | − | 39.7097i | −0.815684 | − | 1.41281i | ||||
\(791\) | 1.03146 | + | 1.78654i | 0.0366745 | + | 0.0635220i | ||||
\(792\) | −0.137063 | −0.00487033 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −20.8358 | −0.739435 | ||||||||
\(795\) | −2.88889 | − | 5.00370i | −0.102458 | − | 0.177463i | ||||
\(796\) | −3.83124 | − | 6.63590i | −0.135795 | − | 0.235203i | ||||
\(797\) | 22.9345 | − | 39.7236i | 0.812380 | − | 1.40708i | −0.0988140 | − | 0.995106i | \(-0.531505\pi\) |
0.911194 | − | 0.411977i | \(-0.135162\pi\) | |||||||
\(798\) | −23.4034 | −0.828472 | ||||||||
\(799\) | −13.9758 | + | 24.2069i | −0.494430 | + | 0.856377i | ||||
\(800\) | −2.48911 | + | 4.31127i | −0.0880035 | + | 0.152427i | ||||
\(801\) | −17.0858 | −0.603695 | ||||||||
\(802\) | −2.97823 | + | 5.15845i | −0.105165 | + | 0.182151i | ||||
\(803\) | 0.159202 | + | 0.275746i | 0.00561812 | + | 0.00973087i | ||||
\(804\) | 2.35690 | + | 4.08226i | 0.0831213 | + | 0.143970i | ||||
\(805\) | −90.3779 | −3.18540 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.3666 | −0.787341 | ||||||||
\(808\) | 4.59299 | + | 7.95529i | 0.161581 | + | 0.279866i | ||||
\(809\) | −19.0707 | − | 33.0314i | −0.670490 | − | 1.16132i | −0.977765 | − | 0.209702i | \(-0.932751\pi\) |
0.307276 | − | 0.951621i | \(-0.400583\pi\) | |||||||
\(810\) | −1.57942 | + | 2.73563i | −0.0554950 | + | 0.0961202i | ||||
\(811\) | −46.6983 | −1.63980 | −0.819899 | − | 0.572509i | \(-0.805970\pi\) | ||||
−0.819899 | + | 0.572509i | \(0.805970\pi\) | |||||||
\(812\) | 1.99612 | − | 3.45737i | 0.0700499 | − | 0.121330i | ||||
\(813\) | −1.93631 | + | 3.35379i | −0.0679095 | + | 0.117623i | ||||
\(814\) | 1.60388 | 0.0562158 | ||||||||
\(815\) | 12.6659 | − | 21.9381i | 0.443669 | − | 0.768456i | ||||
\(816\) | −2.80194 | − | 4.85310i | −0.0980874 | − | 0.169892i | ||||
\(817\) | 5.23191 | + | 9.06194i | 0.183042 | + | 0.317037i | ||||
\(818\) | 1.80194 | 0.0630033 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.5013 | 0.471484 | ||||||||
\(821\) | 16.3475 | + | 28.3147i | 0.570532 | + | 0.988190i | 0.996511 | + | 0.0834572i | \(0.0265962\pi\) |
−0.425980 | + | 0.904733i | \(0.640070\pi\) | |||||||
\(822\) | −2.00000 | − | 3.46410i | −0.0697580 | − | 0.120824i | ||||
\(823\) | 10.8400 | − | 18.7754i | 0.377858 | − | 0.654469i | −0.612893 | − | 0.790166i | \(-0.709994\pi\) |
0.990750 | + | 0.135698i | \(0.0433276\pi\) | |||||||
\(824\) | 0.225209 | 0.00784554 | ||||||||
\(825\) | −0.341166 | + | 0.590918i | −0.0118779 | + | 0.0205731i | ||||
\(826\) | −13.8409 | + | 23.9732i | −0.481588 | + | 0.834134i | ||||
\(827\) | 13.9172 | 0.483950 | 0.241975 | − | 0.970283i | \(-0.422205\pi\) | ||||
0.241975 | + | 0.970283i | \(0.422205\pi\) | |||||||
\(828\) | 3.04892 | − | 5.28088i | 0.105957 | − | 0.183523i | ||||
\(829\) | 8.20237 | + | 14.2069i | 0.284880 | + | 0.493427i | 0.972580 | − | 0.232568i | \(-0.0747128\pi\) |
−0.687700 | + | 0.725995i | \(0.741380\pi\) | |||||||
\(830\) | −15.5671 | − | 26.9630i | −0.540342 | − | 0.935900i | ||||
\(831\) | −28.7090 | −0.995904 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −84.1426 | −2.91537 | ||||||||
\(834\) | −6.82908 | − | 11.8283i | −0.236472 | − | 0.409581i | ||||
\(835\) | −26.9855 | − | 46.7403i | −0.933873 | − | 1.61751i | ||||
\(836\) | 0.341830 | − | 0.592068i | 0.0118225 | − | 0.0204771i | ||||
\(837\) | 6.23490 | 0.215510 | ||||||||
\(838\) | 14.2250 | − | 24.6384i | 0.491394 | − | 0.851119i | ||||
\(839\) | 5.80731 | − | 10.0586i | 0.200491 | − | 0.347260i | −0.748196 | − | 0.663478i | \(-0.769080\pi\) |
0.948687 | + | 0.316218i | \(0.102413\pi\) | |||||||
\(840\) | −14.8213 | −0.511384 | ||||||||
\(841\) | 14.1380 | − | 24.4878i | 0.487518 | − | 0.844406i | ||||
\(842\) | 6.96615 | + | 12.0657i | 0.240069 | + | 0.415812i | ||||
\(843\) | 14.5429 | + | 25.1890i | 0.500883 | + | 0.867555i | ||||
\(844\) | 11.1642 | 0.384288 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.98792 | −0.171488 | ||||||||
\(847\) | 25.7620 | + | 44.6212i | 0.885194 | + | 1.53320i | ||||
\(848\) | 0.914542 | + | 1.58403i | 0.0314055 | + | 0.0543959i | ||||
\(849\) | 6.87800 | − | 11.9130i | 0.236052 | − | 0.408855i | ||||
\(850\) | −27.8974 | −0.956872 | ||||||||
\(851\) | −35.6775 | + | 61.7953i | −1.22301 | + | 2.11832i | ||||
\(852\) | 0.0489173 | − | 0.0847273i | 0.00167588 | − | 0.00290271i | ||||
\(853\) | −26.2983 | −0.900436 | −0.450218 | − | 0.892919i | \(-0.648654\pi\) | ||||
−0.450218 | + | 0.892919i | \(0.648654\pi\) | |||||||
\(854\) | −10.3134 | + | 17.8633i | −0.352916 | + | 0.611268i | ||||
\(855\) | −7.87800 | − | 13.6451i | −0.269422 | − | 0.466653i | ||||
\(856\) | −5.64191 | − | 9.77207i | −0.192836 | − | 0.334003i | ||||
\(857\) | −48.6305 | −1.66119 | −0.830594 | − | 0.556879i | \(-0.811999\pi\) | ||||
−0.830594 | + | 0.556879i | \(0.811999\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.6185 | 1.14705 | 0.573524 | − | 0.819189i | \(-0.305576\pi\) | ||||
0.573524 | + | 0.819189i | \(0.305576\pi\) | |||||||
\(860\) | 3.31336 | + | 5.73890i | 0.112984 | + | 0.195695i | ||||
\(861\) | 10.0271 | + | 17.3675i | 0.341724 | + | 0.591884i | ||||
\(862\) | −7.95108 | + | 13.7717i | −0.270815 | + | 0.469065i | ||||
\(863\) | 5.78879 | 0.197053 | 0.0985264 | − | 0.995134i | \(-0.468587\pi\) | ||||
0.0985264 | + | 0.995134i | \(0.468587\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 24.2359 | − | 41.9777i | 0.824044 | − | 1.42729i | ||||
\(866\) | 4.77718 | 0.162335 | ||||||||
\(867\) | 7.20171 | − | 12.4737i | 0.244583 | − | 0.423630i | ||||
\(868\) | 14.6271 | + | 25.3349i | 0.496477 | + | 0.859924i | ||||
\(869\) | 0.994787 | + | 1.72302i | 0.0337458 | + | 0.0584495i | ||||
\(870\) | 2.68771 | 0.0911219 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.195669 | 0.00662620 | ||||||||
\(873\) | 1.06369 | + | 1.84236i | 0.0360004 | + | 0.0623545i | ||||
\(874\) | 15.2078 | + | 26.3406i | 0.514410 | + | 0.890984i | ||||
\(875\) | 0.161332 | − | 0.279435i | 0.00545402 | − | 0.00944663i | ||||
\(876\) | −2.32304 | −0.0784884 | ||||||||
\(877\) | 4.75302 | − | 8.23247i | 0.160498 | − | 0.277991i | −0.774549 | − | 0.632514i | \(-0.782023\pi\) |
0.935047 | + | 0.354523i | \(0.115357\pi\) | |||||||
\(878\) | 16.8158 | − | 29.1258i | 0.567506 | − | 0.982949i | ||||
\(879\) | 27.7362 | 0.935517 | ||||||||
\(880\) | 0.216480 | − | 0.374955i | 0.00729754 | − | 0.0126397i | ||||
\(881\) | 23.3937 | + | 40.5191i | 0.788155 | + | 1.36512i | 0.927096 | + | 0.374824i | \(0.122297\pi\) |
−0.138941 | + | 0.990301i | \(0.544370\pi\) | |||||||
\(882\) | −7.50753 | − | 13.0034i | −0.252792 | − | 0.437848i | ||||
\(883\) | 3.03146 | 0.102017 | 0.0510084 | − | 0.998698i | \(-0.483756\pi\) | ||||
0.0510084 | + | 0.998698i | \(0.483756\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.6364 | −0.626456 | ||||||||
\(886\) | 17.6875 | + | 30.6356i | 0.594222 | + | 1.02922i | ||||
\(887\) | −18.5090 | − | 32.0586i | −0.621472 | − | 1.07642i | −0.989212 | − | 0.146493i | \(-0.953202\pi\) |
0.367740 | − | 0.929929i | \(-0.380132\pi\) | |||||||
\(888\) | −5.85086 | + | 10.1340i | −0.196342 | + | 0.340074i | ||||
\(889\) | −36.9385 | −1.23888 | ||||||||
\(890\) | 26.9855 | − | 46.7403i | 0.904557 | − | 1.56674i | ||||
\(891\) | 0.0685317 | − | 0.118700i | 0.00229590 | − | 0.00397661i | ||||
\(892\) | 24.6353 | 0.824852 | ||||||||
\(893\) | 12.4397 | − | 21.5461i | 0.416278 | − | 0.721014i | ||||
\(894\) | −8.02930 | − | 13.9072i | −0.268540 | − | 0.465125i | ||||
\(895\) | −0.826823 | − | 1.43210i | −0.0276377 | − | 0.0478698i | ||||
\(896\) | 4.69202 | 0.156749 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.0629 | −0.602767 | ||||||||
\(899\) | −2.65250 | − | 4.59426i | −0.0884657 | − | 0.153227i | ||||
\(900\) | −2.48911 | − | 4.31127i | −0.0829705 | − | 0.143709i | ||||
\(901\) | −5.12498 | + | 8.87673i | −0.170738 | + | 0.295727i | ||||
\(902\) | −0.585826 | −0.0195059 | ||||||||
\(903\) | −4.92154 | + | 8.52436i | −0.163779 | + | 0.283673i | ||||
\(904\) | 0.219833 | − | 0.380761i | 0.00731152 | − | 0.0126639i | ||||
\(905\) | 28.0823 | 0.933487 | ||||||||
\(906\) | 10.9412 | − | 18.9506i | 0.363496 | − | 0.629593i | ||||
\(907\) | −9.54825 | − | 16.5381i | −0.317045 | − | 0.549137i | 0.662825 | − | 0.748774i | \(-0.269357\pi\) |
−0.979870 | + | 0.199637i | \(0.936024\pi\) | |||||||
\(908\) | 3.73825 | + | 6.47484i | 0.124058 | + | 0.214875i | ||||
\(909\) | −9.18598 | −0.304680 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.3142 | −1.03749 | −0.518743 | − | 0.854930i | \(-0.673600\pi\) | ||||
−0.518743 | + | 0.854930i | \(0.673600\pi\) | |||||||
\(912\) | 2.49396 | + | 4.31966i | 0.0825832 | + | 0.143038i | ||||
\(913\) | 0.675464 | + | 1.16994i | 0.0223546 | + | 0.0387193i | ||||
\(914\) | 7.73341 | − | 13.3947i | 0.255798 | − | 0.443056i | ||||
\(915\) | −13.8866 | −0.459078 | ||||||||
\(916\) | 9.61356 | − | 16.6512i | 0.317641 | − | 0.550171i | ||||
\(917\) | 1.45766 | − | 2.52473i | 0.0481360 | − | 0.0833741i | ||||
\(918\) | 5.60388 | 0.184955 | ||||||||
\(919\) | −15.1984 | + | 26.3243i | −0.501348 | + | 0.868359i | 0.498651 | + | 0.866803i | \(0.333829\pi\) |
−0.999999 | + | 0.00155673i | \(0.999504\pi\) | |||||||
\(920\) | 9.63102 | + | 16.6814i | 0.317525 | + | 0.549970i | ||||
\(921\) | 6.22952 | + | 10.7898i | 0.205270 | + | 0.355538i | ||||
\(922\) | −18.8092 | −0.619449 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.643104 | 0.0211566 | ||||||||
\(925\) | 29.1269 | + | 50.4493i | 0.957687 | + | 1.65876i | ||||
\(926\) | 7.92154 | + | 13.7205i | 0.260318 | + | 0.450884i | ||||
\(927\) | −0.112605 | + | 0.195037i | −0.00369842 | + | 0.00640586i | ||||
\(928\) | −0.850855 | −0.0279307 | ||||||||
\(929\) | −20.2905 | + | 35.1442i | −0.665710 | + | 1.15304i | 0.313382 | + | 0.949627i | \(0.398538\pi\) |
−0.979092 | + | 0.203417i | \(0.934795\pi\) | |||||||
\(930\) | −9.84750 | + | 17.0564i | −0.322912 | + | 0.559301i | ||||
\(931\) | 74.8939 | 2.45455 | ||||||||
\(932\) | −1.85086 | + | 3.20578i | −0.0606268 | + | 0.105009i | ||||
\(933\) | −3.04892 | − | 5.28088i | −0.0998171 | − | 0.172888i | ||||
\(934\) | −11.0003 | − | 19.0531i | −0.359941 | − | 0.623436i | ||||
\(935\) | 2.42626 | 0.0793470 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.7047 | −0.611056 | −0.305528 | − | 0.952183i | \(-0.598833\pi\) | ||||
−0.305528 | + | 0.952183i | \(0.598833\pi\) | |||||||
\(938\) | −11.0586 | − | 19.1541i | −0.361076 | − | 0.625402i | ||||
\(939\) | −6.36927 | − | 11.0319i | −0.207853 | − | 0.360013i | ||||
\(940\) | 7.87800 | − | 13.6451i | 0.256952 | − | 0.445054i | ||||
\(941\) | 4.04998 | 0.132026 | 0.0660128 | − | 0.997819i | \(-0.478972\pi\) | ||||
0.0660128 | + | 0.997819i | \(0.478972\pi\) | |||||||
\(942\) | −3.95108 | + | 6.84348i | −0.128733 | + | 0.222972i | ||||
\(943\) | 13.0315 | − | 22.5711i | 0.424363 | − | 0.735018i | ||||
\(944\) | 5.89977 | 0.192021 | ||||||||
\(945\) | 7.41066 | − | 12.8356i | 0.241069 | − | 0.417543i | ||||
\(946\) | −0.143768 | − | 0.249014i | −0.00467430 | − | 0.00809613i | ||||
\(947\) | 5.76779 | + | 9.99011i | 0.187428 | + | 0.324635i | 0.944392 | − | 0.328822i | \(-0.106652\pi\) |
−0.756964 | + | 0.653457i | \(0.773318\pi\) | |||||||
\(948\) | −14.5157 | −0.471449 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 24.8310 | 0.805624 | ||||||||
\(951\) | −7.40701 | − | 12.8293i | −0.240189 | − | 0.416019i | ||||
\(952\) | 13.1468 | + | 22.7708i | 0.426089 | + | 0.738007i | ||||
\(953\) | 4.78554 | − | 8.28881i | 0.155019 | − | 0.268501i | −0.778047 | − | 0.628206i | \(-0.783789\pi\) |
0.933066 | + | 0.359705i | \(0.117123\pi\) | |||||||
\(954\) | −1.82908 | −0.0592188 | ||||||||
\(955\) | 11.1056 | − | 19.2355i | 0.359369 | − | 0.622445i | ||||
\(956\) | −4.25667 | + | 7.37277i | −0.137670 | + | 0.238452i | ||||
\(957\) | −0.116621 | −0.00376982 | ||||||||
\(958\) | 10.6746 | − | 18.4889i | 0.344879 | − | 0.597349i | ||||
\(959\) | 9.38404 | + | 16.2536i | 0.303027 | + | 0.524857i | ||||
\(960\) | 1.57942 | + | 2.73563i | 0.0509755 | + | 0.0882921i | ||||
\(961\) | 7.87395 | 0.253998 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.2838 | 0.363616 | ||||||||
\(964\) | −8.71648 | − | 15.0974i | −0.280739 | − | 0.486254i | ||||
\(965\) | −28.0441 | − | 48.5739i | −0.902773 | − | 1.56365i | ||||
\(966\) | −14.3056 | + | 24.7780i | −0.460275 | + | 0.797219i | ||||
\(967\) | 61.2073 | 1.96829 | 0.984147 | − | 0.177357i | \(-0.0567546\pi\) | ||||
0.984147 | + | 0.177357i | \(0.0567546\pi\) | |||||||
\(968\) | 5.49061 | − | 9.51001i | 0.176475 | − | 0.305663i | ||||
\(969\) | −13.9758 | + | 24.2069i | −0.448969 | + | 0.777636i | ||||
\(970\) | −6.72002 | −0.215767 | ||||||||
\(971\) | 14.4297 | − | 24.9930i | 0.463072 | − | 0.802065i | −0.536040 | − | 0.844193i | \(-0.680080\pi\) |
0.999112 | + | 0.0421278i | \(0.0134137\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | 32.0422 | + | 55.4987i | 1.02723 | + | 1.77921i | ||||
\(974\) | −31.6394 | −1.01379 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.39612 | 0.140717 | ||||||||
\(977\) | −23.3153 | − | 40.3832i | −0.745922 | − | 1.29197i | −0.949763 | − | 0.312970i | \(-0.898676\pi\) |
0.203841 | − | 0.979004i | \(-0.434657\pi\) | |||||||
\(978\) | −4.00969 | − | 6.94498i | −0.128216 | − | 0.222076i | ||||
\(979\) | −1.17092 | + | 2.02808i | −0.0374226 | + | 0.0648179i | ||||
\(980\) | 47.4301 | 1.51510 | ||||||||
\(981\) | −0.0978347 | + | 0.169455i | −0.00312362 | + | 0.00541027i | ||||
\(982\) | 0.699554 | − | 1.21166i | 0.0223237 | − | 0.0386657i | ||||
\(983\) | 55.6883 | 1.77618 | 0.888090 | − | 0.459669i | \(-0.152032\pi\) | ||||
0.888090 | + | 0.459669i | \(0.152032\pi\) | |||||||
\(984\) | 2.13706 | − | 3.70150i | 0.0681271 | − | 0.118000i | ||||
\(985\) | 29.4673 | + | 51.0389i | 0.938908 | + | 1.62624i | ||||
\(986\) | −2.38404 | − | 4.12928i | −0.0759234 | − | 0.131503i | ||||
\(987\) | 23.4034 | 0.744939 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.7922 | 0.406770 | ||||||||
\(990\) | 0.216480 | + | 0.374955i | 0.00688019 | + | 0.0119168i | ||||
\(991\) | 4.66086 | + | 8.07284i | 0.148057 | + | 0.256442i | 0.930509 | − | 0.366268i | \(-0.119365\pi\) |
−0.782452 | + | 0.622711i | \(0.786031\pi\) | |||||||
\(992\) | 3.11745 | − | 5.39958i | 0.0989791 | − | 0.171437i | ||||
\(993\) | 7.70171 | 0.244406 | ||||||||
\(994\) | −0.229521 | + | 0.397542i | −0.00727997 | + | 0.0126093i | ||||
\(995\) | −12.1023 | + | 20.9617i | −0.383667 | + | 0.664531i | ||||
\(996\) | −9.85623 | −0.312307 | ||||||||
\(997\) | −23.0127 | + | 39.8591i | −0.728819 | + | 1.26235i | 0.228564 | + | 0.973529i | \(0.426597\pi\) |
−0.957383 | + | 0.288822i | \(0.906736\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.85086 | − | 10.1340i | −0.185113 | − | 0.320625i |
(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 | 1014.2.e.l.991.3 | 6 | ||
13.2 | odd | 12 | 1014.2.b.f.337.1 | 6 | |||
13.3 | even | 3 | 1014.2.a.n.1.3 | yes | 3 | ||
13.4 | even | 6 | 1014.2.e.n.529.1 | 6 | |||
13.5 | odd | 4 | 1014.2.i.h.361.1 | 12 | |||
13.6 | odd | 12 | 1014.2.i.h.823.4 | 12 | |||
13.7 | odd | 12 | 1014.2.i.h.823.3 | 12 | |||
13.8 | odd | 4 | 1014.2.i.h.361.6 | 12 | |||
13.9 | even | 3 | inner | 1014.2.e.l.529.3 | 6 | ||
13.10 | even | 6 | 1014.2.a.l.1.1 | ✓ | 3 | ||
13.11 | odd | 12 | 1014.2.b.f.337.6 | 6 | |||
13.12 | even | 2 | 1014.2.e.n.991.1 | 6 | |||
39.2 | even | 12 | 3042.2.b.o.1351.6 | 6 | |||
39.11 | even | 12 | 3042.2.b.o.1351.1 | 6 | |||
39.23 | odd | 6 | 3042.2.a.bh.1.3 | 3 | |||
39.29 | odd | 6 | 3042.2.a.ba.1.1 | 3 | |||
52.3 | odd | 6 | 8112.2.a.cm.1.3 | 3 | |||
52.23 | odd | 6 | 8112.2.a.cj.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1014.2.a.l.1.1 | ✓ | 3 | 13.10 | even | 6 | ||
1014.2.a.n.1.3 | yes | 3 | 13.3 | even | 3 | ||
1014.2.b.f.337.1 | 6 | 13.2 | odd | 12 | |||
1014.2.b.f.337.6 | 6 | 13.11 | odd | 12 | |||
1014.2.e.l.529.3 | 6 | 13.9 | even | 3 | inner | ||
1014.2.e.l.991.3 | 6 | 1.1 | even | 1 | trivial | ||
1014.2.e.n.529.1 | 6 | 13.4 | even | 6 | |||
1014.2.e.n.991.1 | 6 | 13.12 | even | 2 | |||
1014.2.i.h.361.1 | 12 | 13.5 | odd | 4 | |||
1014.2.i.h.361.6 | 12 | 13.8 | odd | 4 | |||
1014.2.i.h.823.3 | 12 | 13.7 | odd | 12 | |||
1014.2.i.h.823.4 | 12 | 13.6 | odd | 12 | |||
3042.2.a.ba.1.1 | 3 | 39.29 | odd | 6 | |||
3042.2.a.bh.1.3 | 3 | 39.23 | odd | 6 | |||
3042.2.b.o.1351.1 | 6 | 39.11 | even | 12 | |||
3042.2.b.o.1351.6 | 6 | 39.2 | even | 12 | |||
8112.2.a.cj.1.1 | 3 | 52.23 | odd | 6 | |||
8112.2.a.cm.1.3 | 3 | 52.3 | odd | 6 |