Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [322,2,Mod(93,322)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(322, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("322.93");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.57118294509\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.6498455769.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 6x^{6} + 3x^{5} + 25x^{4} - 3x^{3} + 6x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 93.1 | ||
Root | \(1.33821 + 2.31784i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 322.93 |
Dual form | 322.2.e.d.277.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).
\(n\) | \(185\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | −1.33821 | − | 2.31784i | −0.772613 | − | 1.33821i | −0.936126 | − | 0.351664i | \(-0.885616\pi\) |
0.163513 | − | 0.986541i | \(-0.447717\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.93020 | − | 3.34320i | 0.863211 | − | 1.49513i | −0.00560159 | − | 0.999984i | \(-0.501783\pi\) |
0.868813 | − | 0.495141i | \(-0.164884\pi\) | |||||||
\(6\) | −2.67641 | −1.09264 | ||||||||
\(7\) | −2.21184 | − | 1.45181i | −0.835997 | − | 0.548734i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.08159 | + | 3.60541i | −0.693862 | + | 1.20180i | ||||
\(10\) | −1.93020 | − | 3.34320i | −0.610382 | − | 1.05721i | ||||
\(11\) | 3.04616 | + | 5.27610i | 0.918451 | + | 1.59080i | 0.801769 | + | 0.597634i | \(0.203892\pi\) |
0.116682 | + | 0.993169i | \(0.462774\pi\) | |||||||
\(12\) | −1.33821 | + | 2.31784i | −0.386307 | + | 0.669103i | ||||
\(13\) | 5.97919 | 1.65833 | 0.829164 | − | 0.559006i | \(-0.188817\pi\) | ||||
0.829164 | + | 0.559006i | \(0.188817\pi\) | |||||||
\(14\) | −2.36323 | + | 1.18960i | −0.631599 | + | 0.317935i | ||||
\(15\) | −10.3320 | −2.66771 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.430199 | − | 0.745126i | −0.104338 | − | 0.180720i | 0.809129 | − | 0.587631i | \(-0.199939\pi\) |
−0.913468 | + | 0.406911i | \(0.866606\pi\) | |||||||
\(18\) | 2.08159 | + | 3.60541i | 0.490635 | + | 0.849804i | ||||
\(19\) | −0.556564 | + | 0.963997i | −0.127684 | + | 0.221156i | −0.922779 | − | 0.385329i | \(-0.874088\pi\) |
0.795095 | + | 0.606485i | \(0.207421\pi\) | |||||||
\(20\) | −3.86040 | −0.863211 | ||||||||
\(21\) | −0.405176 | + | 7.06951i | −0.0884166 | + | 1.54269i | ||||
\(22\) | 6.09231 | 1.29889 | ||||||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | ||||
\(24\) | 1.33821 | + | 2.31784i | 0.273160 | + | 0.473127i | ||||
\(25\) | −4.95133 | − | 8.57596i | −0.990267 | − | 1.71519i | ||||
\(26\) | 2.98959 | − | 5.17813i | 0.586307 | − | 1.01551i | ||||
\(27\) | 3.11313 | 0.599122 | ||||||||
\(28\) | −0.151388 | + | 2.64142i | −0.0286096 | + | 0.499181i | ||||
\(29\) | 0.670749 | 0.124555 | 0.0622775 | − | 0.998059i | \(-0.480164\pi\) | ||||
0.0622775 | + | 0.998059i | \(0.480164\pi\) | |||||||
\(30\) | −5.16600 | + | 8.94778i | −0.943179 | + | 1.63363i | ||||
\(31\) | 2.11702 | + | 3.66678i | 0.380227 | + | 0.658573i | 0.991095 | − | 0.133160i | \(-0.0425124\pi\) |
−0.610867 | + | 0.791733i | \(0.709179\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 8.15277 | − | 14.1210i | 1.41921 | − | 2.45815i | ||||
\(34\) | −0.860397 | −0.147557 | ||||||||
\(35\) | −9.12300 | + | 4.59234i | −1.54207 | + | 0.776247i | ||||
\(36\) | 4.16317 | 0.693862 | ||||||||
\(37\) | 1.71078 | − | 2.96316i | 0.281251 | − | 0.487141i | −0.690442 | − | 0.723388i | \(-0.742584\pi\) |
0.971693 | + | 0.236247i | \(0.0759174\pi\) | |||||||
\(38\) | 0.556564 | + | 0.963997i | 0.0902866 | + | 0.156381i | ||||
\(39\) | −8.00138 | − | 13.8588i | −1.28125 | − | 2.21918i | ||||
\(40\) | −1.93020 | + | 3.34320i | −0.305191 | + | 0.528607i | ||||
\(41\) | −9.45817 | −1.47712 | −0.738559 | − | 0.674189i | \(-0.764493\pi\) | ||||
−0.738559 | + | 0.674189i | \(0.764493\pi\) | |||||||
\(42\) | 5.91979 | + | 3.88565i | 0.913444 | + | 0.599569i | ||||
\(43\) | −3.73949 | −0.570267 | −0.285134 | − | 0.958488i | \(-0.592038\pi\) | ||||
−0.285134 | + | 0.958488i | \(0.592038\pi\) | |||||||
\(44\) | 3.04616 | − | 5.27610i | 0.459225 | − | 0.795402i | ||||
\(45\) | 8.03575 | + | 13.9183i | 1.19790 | + | 2.07482i | ||||
\(46\) | −0.500000 | − | 0.866025i | −0.0737210 | − | 0.127688i | ||||
\(47\) | 2.00283 | − | 3.46900i | 0.292143 | − | 0.506006i | −0.682173 | − | 0.731191i | \(-0.738965\pi\) |
0.974316 | + | 0.225184i | \(0.0722984\pi\) | |||||||
\(48\) | 2.67641 | 0.386307 | ||||||||
\(49\) | 2.78447 | + | 6.42236i | 0.397782 | + | 0.917480i | ||||
\(50\) | −9.90267 | −1.40045 | ||||||||
\(51\) | −1.15139 | + | 1.99426i | −0.161227 | + | 0.279253i | ||||
\(52\) | −2.98959 | − | 5.17813i | −0.414582 | − | 0.718077i | ||||
\(53\) | 1.01462 | + | 1.75737i | 0.139368 | + | 0.241393i | 0.927258 | − | 0.374424i | \(-0.122160\pi\) |
−0.787889 | + | 0.615817i | \(0.788826\pi\) | |||||||
\(54\) | 1.55656 | − | 2.69605i | 0.211821 | − | 0.366886i | ||||
\(55\) | 23.5187 | 3.17127 | ||||||||
\(56\) | 2.21184 | + | 1.45181i | 0.295570 | + | 0.194007i | ||||
\(57\) | 2.97919 | 0.394603 | ||||||||
\(58\) | 0.335374 | − | 0.580886i | 0.0440368 | − | 0.0762740i | ||||
\(59\) | 0.580208 | + | 1.00495i | 0.0755367 | + | 0.130833i | 0.901320 | − | 0.433155i | \(-0.142600\pi\) |
−0.825783 | + | 0.563988i | \(0.809266\pi\) | |||||||
\(60\) | 5.16600 | + | 8.94778i | 0.666928 | + | 1.15515i | ||||
\(61\) | 4.10661 | − | 7.11286i | 0.525797 | − | 0.910708i | −0.473751 | − | 0.880659i | \(-0.657100\pi\) |
0.999548 | − | 0.0300490i | \(-0.00956633\pi\) | |||||||
\(62\) | 4.23403 | 0.537723 | ||||||||
\(63\) | 9.83853 | − | 4.95252i | 1.23954 | − | 0.623959i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 11.5410 | − | 19.9896i | 1.43149 | − | 2.47941i | ||||
\(66\) | −8.15277 | − | 14.1210i | −1.00354 | − | 1.73818i | ||||
\(67\) | 0.0278533 | + | 0.0482434i | 0.00340283 | + | 0.00589387i | 0.867722 | − | 0.497050i | \(-0.165584\pi\) |
−0.864319 | + | 0.502944i | \(0.832250\pi\) | |||||||
\(68\) | −0.430199 | + | 0.745126i | −0.0521692 | + | 0.0903598i | ||||
\(69\) | −2.67641 | −0.322202 | ||||||||
\(70\) | −0.584417 | + | 10.1969i | −0.0698512 | + | 1.21876i | ||||
\(71\) | 0.863943 | 0.102531 | 0.0512656 | − | 0.998685i | \(-0.483674\pi\) | ||||
0.0512656 | + | 0.998685i | \(0.483674\pi\) | |||||||
\(72\) | 2.08159 | − | 3.60541i | 0.245317 | − | 0.424902i | ||||
\(73\) | 8.46984 | + | 14.6702i | 0.991319 | + | 1.71702i | 0.609521 | + | 0.792770i | \(0.291362\pi\) |
0.381799 | + | 0.924246i | \(0.375305\pi\) | |||||||
\(74\) | −1.71078 | − | 2.96316i | −0.198874 | − | 0.344461i | ||||
\(75\) | −13.2518 | + | 22.9528i | −1.53019 | + | 2.65036i | ||||
\(76\) | 1.11313 | 0.127684 | ||||||||
\(77\) | 0.922302 | − | 16.0923i | 0.105106 | − | 1.83389i | ||||
\(78\) | −16.0028 | −1.81196 | ||||||||
\(79\) | −1.24055 | + | 2.14870i | −0.139573 | + | 0.241747i | −0.927335 | − | 0.374232i | \(-0.877906\pi\) |
0.787762 | + | 0.615980i | \(0.211240\pi\) | |||||||
\(80\) | 1.93020 | + | 3.34320i | 0.215803 | + | 0.373781i | ||||
\(81\) | 2.07876 | + | 3.60051i | 0.230973 | + | 0.400057i | ||||
\(82\) | −4.72909 | + | 8.19102i | −0.522240 | + | 0.904546i | ||||
\(83\) | −1.05005 | −0.115257 | −0.0576287 | − | 0.998338i | \(-0.518354\pi\) | ||||
−0.0576287 | + | 0.998338i | \(0.518354\pi\) | |||||||
\(84\) | 6.32497 | − | 3.18386i | 0.690111 | − | 0.347388i | ||||
\(85\) | −3.32147 | −0.360264 | ||||||||
\(86\) | −1.86975 | + | 3.23850i | −0.201620 | + | 0.349216i | ||||
\(87\) | −0.897600 | − | 1.55469i | −0.0962328 | − | 0.166680i | ||||
\(88\) | −3.04616 | − | 5.27610i | −0.324721 | − | 0.562434i | ||||
\(89\) | 3.44344 | − | 5.96421i | 0.365004 | − | 0.632205i | −0.623773 | − | 0.781605i | \(-0.714401\pi\) |
0.988777 | + | 0.149401i | \(0.0477345\pi\) | |||||||
\(90\) | 16.0715 | 1.69408 | ||||||||
\(91\) | −13.2250 | − | 8.68067i | −1.38636 | − | 0.909981i | ||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 5.66600 | − | 9.81381i | 0.587537 | − | 1.01764i | ||||
\(94\) | −2.00283 | − | 3.46900i | −0.206576 | − | 0.357801i | ||||
\(95\) | 2.14856 | + | 3.72141i | 0.220437 | + | 0.381809i | ||||
\(96\) | 1.33821 | − | 2.31784i | 0.136580 | − | 0.236563i | ||||
\(97\) | −12.8932 | −1.30910 | −0.654552 | − | 0.756017i | \(-0.727143\pi\) | ||||
−0.654552 | + | 0.756017i | \(0.727143\pi\) | |||||||
\(98\) | 6.95416 | + | 0.799757i | 0.702477 | + | 0.0807876i | ||||
\(99\) | −25.3634 | −2.54911 | ||||||||
\(100\) | −4.95133 | + | 8.57596i | −0.495133 | + | 0.857596i | ||||
\(101\) | −1.57012 | − | 2.71953i | −0.156233 | − | 0.270603i | 0.777274 | − | 0.629162i | \(-0.216602\pi\) |
−0.933507 | + | 0.358558i | \(0.883268\pi\) | |||||||
\(102\) | 1.15139 | + | 1.99426i | 0.114004 | + | 0.197461i | ||||
\(103\) | 1.60924 | − | 2.78728i | 0.158563 | − | 0.274639i | −0.775788 | − | 0.630994i | \(-0.782647\pi\) |
0.934351 | + | 0.356355i | \(0.115981\pi\) | |||||||
\(104\) | −5.97919 | −0.586307 | ||||||||
\(105\) | 22.8527 | + | 15.0002i | 2.23020 | + | 1.46386i | ||||
\(106\) | 2.02923 | 0.197096 | ||||||||
\(107\) | 0.477093 | − | 0.826349i | 0.0461223 | − | 0.0798862i | −0.842043 | − | 0.539411i | \(-0.818647\pi\) |
0.888165 | + | 0.459525i | \(0.151980\pi\) | |||||||
\(108\) | −1.55656 | − | 2.69605i | −0.149780 | − | 0.259427i | ||||
\(109\) | 6.40267 | + | 11.0897i | 0.613264 | + | 1.06220i | 0.990686 | + | 0.136163i | \(0.0434772\pi\) |
−0.377422 | + | 0.926041i | \(0.623189\pi\) | |||||||
\(110\) | 11.7594 | − | 20.3678i | 1.12121 | − | 1.94200i | ||||
\(111\) | −9.15751 | −0.869192 | ||||||||
\(112\) | 2.36323 | − | 1.18960i | 0.223304 | − | 0.112407i | ||||
\(113\) | 2.53681 | 0.238643 | 0.119321 | − | 0.992856i | \(-0.461928\pi\) | ||||
0.119321 | + | 0.992856i | \(0.461928\pi\) | |||||||
\(114\) | 1.48959 | − | 2.58005i | 0.139513 | − | 0.241644i | ||||
\(115\) | −1.93020 | − | 3.34320i | −0.179992 | − | 0.311755i | ||||
\(116\) | −0.335374 | − | 0.580886i | −0.0311387 | − | 0.0539339i | ||||
\(117\) | −12.4462 | + | 21.5574i | −1.15065 | + | 1.99299i | ||||
\(118\) | 1.16042 | 0.106825 | ||||||||
\(119\) | −0.130254 | + | 2.27267i | −0.0119403 | + | 0.208335i | ||||
\(120\) | 10.3320 | 0.943179 | ||||||||
\(121\) | −13.0581 | + | 22.6174i | −1.18710 | + | 2.05612i | ||||
\(122\) | −4.10661 | − | 7.11286i | −0.371795 | − | 0.643968i | ||||
\(123\) | 12.6570 | + | 21.9225i | 1.14124 | + | 1.97669i | ||||
\(124\) | 2.11702 | − | 3.66678i | 0.190114 | − | 0.329286i | ||||
\(125\) | −18.9262 | −1.69281 | ||||||||
\(126\) | 0.630254 | − | 10.9967i | 0.0561475 | − | 0.979662i | ||||
\(127\) | −13.1237 | −1.16454 | −0.582268 | − | 0.812997i | \(-0.697835\pi\) | ||||
−0.582268 | + | 0.812997i | \(0.697835\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 5.00421 | + | 8.66754i | 0.440596 | + | 0.763135i | ||||
\(130\) | −11.5410 | − | 19.9896i | −1.01221 | − | 1.75321i | ||||
\(131\) | 6.57790 | − | 11.3933i | 0.574714 | − | 0.995433i | −0.421359 | − | 0.906894i | \(-0.638447\pi\) |
0.996073 | − | 0.0885393i | \(-0.0282199\pi\) | |||||||
\(132\) | −16.3055 | −1.41921 | ||||||||
\(133\) | 2.63057 | − | 1.32418i | 0.228100 | − | 0.114821i | ||||
\(134\) | 0.0557067 | 0.00481232 | ||||||||
\(135\) | 6.00895 | − | 10.4078i | 0.517168 | − | 0.895762i | ||||
\(136\) | 0.430199 | + | 0.745126i | 0.0368892 | + | 0.0638940i | ||||
\(137\) | −5.57401 | − | 9.65447i | −0.476220 | − | 0.824837i | 0.523409 | − | 0.852082i | \(-0.324660\pi\) |
−0.999629 | + | 0.0272447i | \(0.991327\pi\) | |||||||
\(138\) | −1.33821 | + | 2.31784i | −0.113916 | + | 0.197308i | ||||
\(139\) | −1.20309 | −0.102044 | −0.0510222 | − | 0.998698i | \(-0.516248\pi\) | ||||
−0.0510222 | + | 0.998698i | \(0.516248\pi\) | |||||||
\(140\) | 8.53858 | + | 5.60458i | 0.721642 | + | 0.473673i | ||||
\(141\) | −10.7208 | −0.902854 | ||||||||
\(142\) | 0.431972 | − | 0.748197i | 0.0362503 | − | 0.0627873i | ||||
\(143\) | 18.2135 | + | 31.5468i | 1.52309 | + | 2.63807i | ||||
\(144\) | −2.08159 | − | 3.60541i | −0.173466 | − | 0.300451i | ||||
\(145\) | 1.29468 | − | 2.24245i | 0.107517 | − | 0.186225i | ||||
\(146\) | 16.9397 | 1.40194 | ||||||||
\(147\) | 11.1598 | − | 15.0484i | 0.920445 | − | 1.24117i | ||||
\(148\) | −3.42156 | −0.281251 | ||||||||
\(149\) | −7.33201 | + | 12.6994i | −0.600661 | + | 1.04038i | 0.392060 | + | 0.919940i | \(0.371763\pi\) |
−0.992721 | + | 0.120436i | \(0.961571\pi\) | |||||||
\(150\) | 13.2518 | + | 22.9528i | 1.08200 | + | 1.87409i | ||||
\(151\) | −3.05551 | − | 5.29229i | −0.248654 | − | 0.430681i | 0.714499 | − | 0.699637i | \(-0.246655\pi\) |
−0.963152 | + | 0.268956i | \(0.913321\pi\) | |||||||
\(152\) | 0.556564 | − | 0.963997i | 0.0451433 | − | 0.0781905i | ||||
\(153\) | 3.58198 | 0.289586 | ||||||||
\(154\) | −13.4752 | − | 8.84491i | −1.08586 | − | 0.712743i | ||||
\(155\) | 16.3450 | 1.31287 | ||||||||
\(156\) | −8.00138 | + | 13.8588i | −0.640623 | + | 1.10959i | ||||
\(157\) | −0.832544 | − | 1.44201i | −0.0664442 | − | 0.115085i | 0.830889 | − | 0.556437i | \(-0.187832\pi\) |
−0.897334 | + | 0.441353i | \(0.854499\pi\) | |||||||
\(158\) | 1.24055 | + | 2.14870i | 0.0986929 | + | 0.170941i | ||||
\(159\) | 2.71553 | − | 4.70343i | 0.215355 | − | 0.373006i | ||||
\(160\) | 3.86040 | 0.305191 | ||||||||
\(161\) | −2.36323 | + | 1.18960i | −0.186248 | + | 0.0937538i | ||||
\(162\) | 4.15751 | 0.326645 | ||||||||
\(163\) | −3.83452 | + | 6.64158i | −0.300343 | + | 0.520209i | −0.976214 | − | 0.216811i | \(-0.930434\pi\) |
0.675871 | + | 0.737020i | \(0.263768\pi\) | |||||||
\(164\) | 4.72909 | + | 8.19102i | 0.369280 | + | 0.639611i | ||||
\(165\) | −31.4729 | − | 54.5127i | −2.45016 | − | 4.24381i | ||||
\(166\) | −0.525023 | + | 0.909366i | −0.0407497 | + | 0.0705805i | ||||
\(167\) | 24.7486 | 1.91510 | 0.957550 | − | 0.288267i | \(-0.0930790\pi\) | ||||
0.957550 | + | 0.288267i | \(0.0930790\pi\) | |||||||
\(168\) | 0.405176 | − | 7.06951i | 0.0312600 | − | 0.545425i | ||||
\(169\) | 22.7507 | 1.75005 | ||||||||
\(170\) | −1.66074 | + | 2.87648i | −0.127373 | + | 0.220616i | ||||
\(171\) | −2.31707 | − | 4.01328i | −0.177191 | − | 0.306904i | ||||
\(172\) | 1.86975 | + | 3.23850i | 0.142567 | + | 0.246933i | ||||
\(173\) | 0.910837 | − | 1.57762i | 0.0692497 | − | 0.119944i | −0.829322 | − | 0.558772i | \(-0.811273\pi\) |
0.898571 | + | 0.438828i | \(0.144606\pi\) | |||||||
\(174\) | −1.79520 | −0.136094 | ||||||||
\(175\) | −1.49914 | + | 26.1571i | −0.113325 | + | 1.97729i | ||||
\(176\) | −6.09231 | −0.459225 | ||||||||
\(177\) | 1.55288 | − | 2.68966i | 0.116721 | − | 0.202167i | ||||
\(178\) | −3.44344 | − | 5.96421i | −0.258096 | − | 0.447036i | ||||
\(179\) | −5.70249 | − | 9.87700i | −0.426224 | − | 0.738242i | 0.570310 | − | 0.821430i | \(-0.306823\pi\) |
−0.996534 | + | 0.0831878i | \(0.973490\pi\) | |||||||
\(180\) | 8.03575 | − | 13.9183i | 0.598949 | − | 1.03741i | ||||
\(181\) | 0.627006 | 0.0466050 | 0.0233025 | − | 0.999728i | \(-0.492582\pi\) | ||||
0.0233025 | + | 0.999728i | \(0.492582\pi\) | |||||||
\(182\) | −14.1302 | + | 7.11286i | −1.04740 | + | 0.527240i | ||||
\(183\) | −21.9819 | −1.62495 | ||||||||
\(184\) | −0.500000 | + | 0.866025i | −0.0368605 | + | 0.0638442i | ||||
\(185\) | −6.60430 | − | 11.4390i | −0.485558 | − | 0.841011i | ||||
\(186\) | −5.66600 | − | 9.81381i | −0.415452 | − | 0.719583i | ||||
\(187\) | 2.62090 | − | 4.53954i | 0.191660 | − | 0.331964i | ||||
\(188\) | −4.00566 | −0.292143 | ||||||||
\(189\) | −6.88574 | − | 4.51968i | −0.500864 | − | 0.328758i | ||||
\(190\) | 4.29711 | 0.311745 | ||||||||
\(191\) | −3.54070 | + | 6.13267i | −0.256196 | + | 0.443744i | −0.965220 | − | 0.261440i | \(-0.915803\pi\) |
0.709024 | + | 0.705184i | \(0.249136\pi\) | |||||||
\(192\) | −1.33821 | − | 2.31784i | −0.0965766 | − | 0.167276i | ||||
\(193\) | 10.5081 | + | 18.2006i | 0.756389 | + | 1.31010i | 0.944681 | + | 0.327992i | \(0.106372\pi\) |
−0.188291 | + | 0.982113i | \(0.560295\pi\) | |||||||
\(194\) | −6.44659 | + | 11.1658i | −0.462838 | + | 0.801659i | ||||
\(195\) | −61.7770 | −4.42394 | ||||||||
\(196\) | 4.16969 | − | 5.62260i | 0.297835 | − | 0.401615i | ||||
\(197\) | −0.806121 | −0.0574338 | −0.0287169 | − | 0.999588i | \(-0.509142\pi\) | ||||
−0.0287169 | + | 0.999588i | \(0.509142\pi\) | |||||||
\(198\) | −12.6817 | + | 21.9653i | −0.901248 | + | 1.56101i | ||||
\(199\) | −7.25800 | − | 12.5712i | −0.514506 | − | 0.891150i | −0.999858 | − | 0.0168316i | \(-0.994642\pi\) |
0.485353 | − | 0.874319i | \(-0.338691\pi\) | |||||||
\(200\) | 4.95133 | + | 8.57596i | 0.350112 | + | 0.606412i | ||||
\(201\) | 0.0745470 | − | 0.129119i | 0.00525814 | − | 0.00910736i | ||||
\(202\) | −3.14024 | −0.220947 | ||||||||
\(203\) | −1.48359 | − | 0.973803i | −0.104128 | − | 0.0683475i | ||||
\(204\) | 2.30278 | 0.161227 | ||||||||
\(205\) | −18.2561 | + | 31.6206i | −1.27506 | + | 2.20848i | ||||
\(206\) | −1.60924 | − | 2.78728i | −0.112121 | − | 0.194199i | ||||
\(207\) | 2.08159 | + | 3.60541i | 0.144680 | + | 0.250594i | ||||
\(208\) | −2.98959 | + | 5.17813i | −0.207291 | + | 0.359039i | ||||
\(209\) | −6.78152 | −0.469088 | ||||||||
\(210\) | 24.4169 | − | 12.2910i | 1.68493 | − | 0.848158i | ||||
\(211\) | 24.1903 | 1.66533 | 0.832664 | − | 0.553778i | \(-0.186815\pi\) | ||||
0.832664 | + | 0.553778i | \(0.186815\pi\) | |||||||
\(212\) | 1.01462 | − | 1.75737i | 0.0696841 | − | 0.120696i | ||||
\(213\) | −1.15613 | − | 2.00248i | −0.0792169 | − | 0.137208i | ||||
\(214\) | −0.477093 | − | 0.826349i | −0.0326134 | − | 0.0564880i | ||||
\(215\) | −7.21796 | + | 12.5019i | −0.492261 | + | 0.852621i | ||||
\(216\) | −3.11313 | −0.211821 | ||||||||
\(217\) | 0.640981 | − | 11.1838i | 0.0435126 | − | 0.759209i | ||||
\(218\) | 12.8053 | 0.867286 | ||||||||
\(219\) | 22.6688 | − | 39.2634i | 1.53181 | − | 2.65318i | ||||
\(220\) | −11.7594 | − | 20.3678i | −0.792817 | − | 1.37320i | ||||
\(221\) | −2.57224 | − | 4.45525i | −0.173027 | − | 0.299692i | ||||
\(222\) | −4.57876 | + | 7.93064i | −0.307306 | + | 0.532270i | ||||
\(223\) | 10.9260 | 0.731659 | 0.365829 | − | 0.930682i | \(-0.380785\pi\) | ||||
0.365829 | + | 0.930682i | \(0.380785\pi\) | |||||||
\(224\) | 0.151388 | − | 2.64142i | 0.0101150 | − | 0.176487i | ||||
\(225\) | 41.2265 | 2.74843 | ||||||||
\(226\) | 1.26840 | − | 2.19694i | 0.0843730 | − | 0.146138i | ||||
\(227\) | −12.8334 | − | 22.2281i | −0.851782 | − | 1.47533i | −0.879599 | − | 0.475716i | \(-0.842189\pi\) |
0.0278172 | − | 0.999613i | \(-0.491144\pi\) | |||||||
\(228\) | −1.48959 | − | 2.58005i | −0.0986507 | − | 0.170868i | ||||
\(229\) | −11.2966 | + | 19.5662i | −0.746499 | + | 1.29297i | 0.202992 | + | 0.979180i | \(0.434933\pi\) |
−0.949491 | + | 0.313794i | \(0.898400\pi\) | |||||||
\(230\) | −3.86040 | −0.254547 | ||||||||
\(231\) | −38.5337 | + | 19.3971i | −2.53533 | + | 1.27624i | ||||
\(232\) | −0.670749 | −0.0440368 | ||||||||
\(233\) | 1.75622 | − | 3.04187i | 0.115054 | − | 0.199279i | −0.802747 | − | 0.596319i | \(-0.796629\pi\) |
0.917801 | + | 0.397040i | \(0.129963\pi\) | |||||||
\(234\) | 12.4462 | + | 21.5574i | 0.813633 | + | 1.40925i | ||||
\(235\) | −7.73172 | − | 13.3917i | −0.504362 | − | 0.873580i | ||||
\(236\) | 0.580208 | − | 1.00495i | 0.0377684 | − | 0.0654167i | ||||
\(237\) | 6.64044 | 0.431343 | ||||||||
\(238\) | 1.90306 | + | 1.24914i | 0.123357 | + | 0.0809695i | ||||
\(239\) | 2.35218 | 0.152150 | 0.0760749 | − | 0.997102i | \(-0.475761\pi\) | ||||
0.0760749 | + | 0.997102i | \(0.475761\pi\) | |||||||
\(240\) | 5.16600 | − | 8.94778i | 0.333464 | − | 0.577577i | ||||
\(241\) | 11.1517 | + | 19.3153i | 0.718345 | + | 1.24421i | 0.961655 | + | 0.274261i | \(0.0884332\pi\) |
−0.243311 | + | 0.969948i | \(0.578233\pi\) | |||||||
\(242\) | 13.0581 | + | 22.6174i | 0.839409 | + | 1.45390i | ||||
\(243\) | 10.2333 | − | 17.7246i | 0.656466 | − | 1.13703i | ||||
\(244\) | −8.21322 | −0.525797 | ||||||||
\(245\) | 26.8458 | + | 3.08738i | 1.71512 | + | 0.197245i | ||||
\(246\) | 25.3139 | 1.61396 | ||||||||
\(247\) | −3.32780 | + | 5.76392i | −0.211743 | + | 0.366749i | ||||
\(248\) | −2.11702 | − | 3.66678i | −0.134431 | − | 0.232841i | ||||
\(249\) | 1.40518 | + | 2.43384i | 0.0890494 | + | 0.154238i | ||||
\(250\) | −9.46312 | + | 16.3906i | −0.598500 | + | 1.03663i | ||||
\(251\) | −13.7643 | −0.868792 | −0.434396 | − | 0.900722i | \(-0.643038\pi\) | ||||
−0.434396 | + | 0.900722i | \(0.643038\pi\) | |||||||
\(252\) | −9.20827 | − | 6.04415i | −0.580067 | − | 0.380746i | ||||
\(253\) | 6.09231 | 0.383020 | ||||||||
\(254\) | −6.56183 | + | 11.3654i | −0.411726 | + | 0.713130i | ||||
\(255\) | 4.44481 | + | 7.69864i | 0.278345 | + | 0.482108i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 5.12954 | − | 8.88462i | 0.319972 | − | 0.554207i | −0.660510 | − | 0.750817i | \(-0.729660\pi\) |
0.980482 | + | 0.196610i | \(0.0629932\pi\) | |||||||
\(258\) | 10.0084 | 0.623097 | ||||||||
\(259\) | −8.08594 | + | 4.07030i | −0.502436 | + | 0.252916i | ||||
\(260\) | −23.0820 | −1.43149 | ||||||||
\(261\) | −1.39622 | + | 2.41833i | −0.0864240 | + | 0.149691i | ||||
\(262\) | −6.57790 | − | 11.3933i | −0.406384 | − | 0.703878i | ||||
\(263\) | −7.35400 | − | 12.7375i | −0.453467 | − | 0.785428i | 0.545132 | − | 0.838350i | \(-0.316480\pi\) |
−0.998599 | + | 0.0529226i | \(0.983146\pi\) | |||||||
\(264\) | −8.15277 | + | 14.1210i | −0.501768 | + | 0.869088i | ||||
\(265\) | 7.83364 | 0.481217 | ||||||||
\(266\) | 0.168514 | − | 2.94023i | 0.0103323 | − | 0.180277i | ||||
\(267\) | −18.4321 | −1.12803 | ||||||||
\(268\) | 0.0278533 | − | 0.0482434i | 0.00170141 | − | 0.00294693i | ||||
\(269\) | −2.94902 | − | 5.10786i | −0.179805 | − | 0.311432i | 0.762009 | − | 0.647567i | \(-0.224213\pi\) |
−0.941814 | + | 0.336135i | \(0.890880\pi\) | |||||||
\(270\) | −6.00895 | − | 10.4078i | −0.365693 | − | 0.633399i | ||||
\(271\) | 6.91465 | − | 11.9765i | 0.420035 | − | 0.727522i | −0.575907 | − | 0.817515i | \(-0.695351\pi\) |
0.995942 | + | 0.0899928i | \(0.0286844\pi\) | |||||||
\(272\) | 0.860397 | 0.0521692 | ||||||||
\(273\) | −2.42262 | + | 42.2699i | −0.146624 | + | 2.55829i | ||||
\(274\) | −11.1480 | −0.673477 | ||||||||
\(275\) | 30.1651 | − | 52.2474i | 1.81902 | − | 3.15064i | ||||
\(276\) | 1.33821 | + | 2.31784i | 0.0805505 | + | 0.139518i | ||||
\(277\) | 11.7937 | + | 20.4274i | 0.708618 | + | 1.22736i | 0.965370 | + | 0.260884i | \(0.0840141\pi\) |
−0.256752 | + | 0.966477i | \(0.582653\pi\) | |||||||
\(278\) | −0.601543 | + | 1.04190i | −0.0360782 | + | 0.0624892i | ||||
\(279\) | −17.6270 | −1.05530 | ||||||||
\(280\) | 9.12300 | − | 4.59234i | 0.545203 | − | 0.274445i | ||||
\(281\) | 23.2982 | 1.38985 | 0.694926 | − | 0.719082i | \(-0.255437\pi\) | ||||
0.694926 | + | 0.719082i | \(0.255437\pi\) | |||||||
\(282\) | −5.36040 | + | 9.28448i | −0.319207 | + | 0.552883i | ||||
\(283\) | 15.9014 | + | 27.5421i | 0.945241 | + | 1.63721i | 0.755268 | + | 0.655416i | \(0.227507\pi\) |
0.189973 | + | 0.981789i | \(0.439160\pi\) | |||||||
\(284\) | −0.431972 | − | 0.748197i | −0.0256328 | − | 0.0443973i | ||||
\(285\) | 5.75042 | − | 9.96002i | 0.340626 | − | 0.589981i | ||||
\(286\) | 36.4271 | 2.15398 | ||||||||
\(287\) | 20.9200 | + | 13.7315i | 1.23487 | + | 0.810545i | ||||
\(288\) | −4.16317 | −0.245317 | ||||||||
\(289\) | 8.12986 | − | 14.0813i | 0.478227 | − | 0.828313i | ||||
\(290\) | −1.29468 | − | 2.24245i | −0.0760261 | − | 0.131681i | ||||
\(291\) | 17.2537 | + | 29.8843i | 1.01143 | + | 1.75185i | ||||
\(292\) | 8.46984 | − | 14.6702i | 0.495660 | − | 0.858508i | ||||
\(293\) | −17.6327 | −1.03011 | −0.515056 | − | 0.857157i | \(-0.672229\pi\) | ||||
−0.515056 | + | 0.857157i | \(0.672229\pi\) | |||||||
\(294\) | −7.45239 | − | 17.1889i | −0.434632 | − | 1.00248i | ||||
\(295\) | 4.47967 | 0.260816 | ||||||||
\(296\) | −1.71078 | + | 2.96316i | −0.0994372 | + | 0.172230i | ||||
\(297\) | 9.48307 | + | 16.4252i | 0.550264 | + | 0.953085i | ||||
\(298\) | 7.33201 | + | 12.6994i | 0.424732 | + | 0.735657i | ||||
\(299\) | 2.98959 | − | 5.17813i | 0.172893 | − | 0.299459i | ||||
\(300\) | 26.5036 | 1.53019 | ||||||||
\(301\) | 8.27116 | + | 5.42905i | 0.476742 | + | 0.312925i | ||||
\(302\) | −6.11101 | −0.351649 | ||||||||
\(303\) | −4.20229 | + | 7.27858i | −0.241415 | + | 0.418143i | ||||
\(304\) | −0.556564 | − | 0.963997i | −0.0319211 | − | 0.0552890i | ||||
\(305\) | −15.8531 | − | 27.4584i | −0.907748 | − | 1.57227i | ||||
\(306\) | 1.79099 | − | 3.10209i | 0.102384 | − | 0.177335i | ||||
\(307\) | −12.2618 | −0.699817 | −0.349909 | − | 0.936784i | \(-0.613787\pi\) | ||||
−0.349909 | + | 0.936784i | \(0.613787\pi\) | |||||||
\(308\) | −14.3975 | + | 7.24743i | −0.820375 | + | 0.412961i | ||||
\(309\) | −8.61397 | −0.490032 | ||||||||
\(310\) | 8.17252 | − | 14.1552i | 0.464168 | − | 0.803963i | ||||
\(311\) | −1.61030 | − | 2.78912i | −0.0913116 | − | 0.158156i | 0.816752 | − | 0.576989i | \(-0.195773\pi\) |
−0.908063 | + | 0.418833i | \(0.862439\pi\) | |||||||
\(312\) | 8.00138 | + | 13.8588i | 0.452989 | + | 0.784600i | ||||
\(313\) | 10.6596 | − | 18.4630i | 0.602516 | − | 1.04359i | −0.389922 | − | 0.920848i | \(-0.627498\pi\) |
0.992439 | − | 0.122741i | \(-0.0391686\pi\) | |||||||
\(314\) | −1.66509 | −0.0939663 | ||||||||
\(315\) | 2.43303 | − | 42.4515i | 0.137086 | − | 2.39187i | ||||
\(316\) | 2.48110 | 0.139573 | ||||||||
\(317\) | −8.40227 | + | 14.5532i | −0.471919 | + | 0.817387i | −0.999484 | − | 0.0321277i | \(-0.989772\pi\) |
0.527565 | + | 0.849515i | \(0.323105\pi\) | |||||||
\(318\) | −2.71553 | − | 4.70343i | −0.152279 | − | 0.263755i | ||||
\(319\) | 2.04321 | + | 3.53894i | 0.114398 | + | 0.198142i | ||||
\(320\) | 1.93020 | − | 3.34320i | 0.107901 | − | 0.186891i | ||||
\(321\) | −2.55379 | −0.142539 | ||||||||
\(322\) | −0.151388 | + | 2.64142i | −0.00843651 | + | 0.147200i | ||||
\(323\) | 0.957732 | 0.0532896 | ||||||||
\(324\) | 2.07876 | − | 3.60051i | 0.115486 | − | 0.200028i | ||||
\(325\) | −29.6049 | − | 51.2773i | −1.64219 | − | 2.84435i | ||||
\(326\) | 3.83452 | + | 6.64158i | 0.212374 | + | 0.367843i | ||||
\(327\) | 17.1362 | − | 29.6807i | 0.947632 | − | 1.64135i | ||||
\(328\) | 9.45817 | 0.522240 | ||||||||
\(329\) | −9.46629 | + | 4.76515i | −0.521893 | + | 0.262711i | ||||
\(330\) | −62.9458 | −3.46505 | ||||||||
\(331\) | −4.79448 | + | 8.30429i | −0.263529 | + | 0.456445i | −0.967177 | − | 0.254103i | \(-0.918220\pi\) |
0.703648 | + | 0.710548i | \(0.251553\pi\) | |||||||
\(332\) | 0.525023 | + | 0.909366i | 0.0288144 | + | 0.0499079i | ||||
\(333\) | 7.12228 | + | 12.3362i | 0.390299 | + | 0.676017i | ||||
\(334\) | 12.3743 | − | 21.4329i | 0.677090 | − | 1.17275i | ||||
\(335\) | 0.215050 | 0.0117494 | ||||||||
\(336\) | −5.91979 | − | 3.88565i | −0.322951 | − | 0.211980i | ||||
\(337\) | −7.98011 | −0.434704 | −0.217352 | − | 0.976093i | \(-0.569742\pi\) | ||||
−0.217352 | + | 0.976093i | \(0.569742\pi\) | |||||||
\(338\) | 11.3753 | − | 19.7027i | 0.618737 | − | 1.07168i | ||||
\(339\) | −3.39477 | − | 5.87991i | −0.184379 | − | 0.319353i | ||||
\(340\) | 1.66074 | + | 2.87648i | 0.0900661 | + | 0.155999i | ||||
\(341\) | −12.8975 | + | 22.3392i | −0.698440 | + | 1.20973i | ||||
\(342\) | −4.63414 | −0.250586 | ||||||||
\(343\) | 3.16527 | − | 18.2478i | 0.170908 | − | 0.985287i | ||||
\(344\) | 3.73949 | 0.201620 | ||||||||
\(345\) | −5.16600 | + | 8.94778i | −0.278128 | + | 0.481732i | ||||
\(346\) | −0.910837 | − | 1.57762i | −0.0489669 | − | 0.0848132i | ||||
\(347\) | 10.9079 | + | 18.8931i | 0.585568 | + | 1.01423i | 0.994804 | + | 0.101806i | \(0.0324620\pi\) |
−0.409236 | + | 0.912429i | \(0.634205\pi\) | |||||||
\(348\) | −0.897600 | + | 1.55469i | −0.0481164 | + | 0.0833400i | ||||
\(349\) | 11.6542 | 0.623833 | 0.311917 | − | 0.950109i | \(-0.399029\pi\) | ||||
0.311917 | + | 0.950109i | \(0.399029\pi\) | |||||||
\(350\) | 21.9031 | + | 14.3768i | 1.17077 | + | 0.768474i | ||||
\(351\) | 18.6140 | 0.993540 | ||||||||
\(352\) | −3.04616 | + | 5.27610i | −0.162361 | + | 0.281217i | ||||
\(353\) | −1.85690 | − | 3.21625i | −0.0988330 | − | 0.171184i | 0.812369 | − | 0.583144i | \(-0.198178\pi\) |
−0.911202 | + | 0.411960i | \(0.864844\pi\) | |||||||
\(354\) | −1.55288 | − | 2.68966i | −0.0825344 | − | 0.142954i | ||||
\(355\) | 1.66758 | − | 2.88834i | 0.0885061 | − | 0.153297i | ||||
\(356\) | −6.88687 | −0.365004 | ||||||||
\(357\) | 5.44198 | − | 2.73939i | 0.288020 | − | 0.144984i | ||||
\(358\) | −11.4050 | −0.602772 | ||||||||
\(359\) | −5.79909 | + | 10.0443i | −0.306064 | + | 0.530119i | −0.977498 | − | 0.210946i | \(-0.932346\pi\) |
0.671434 | + | 0.741065i | \(0.265679\pi\) | |||||||
\(360\) | −8.03575 | − | 13.9183i | −0.423521 | − | 0.733560i | ||||
\(361\) | 8.88047 | + | 15.3814i | 0.467393 | + | 0.809549i | ||||
\(362\) | 0.313503 | − | 0.543003i | 0.0164773 | − | 0.0285396i | ||||
\(363\) | 69.8979 | 3.66869 | ||||||||
\(364\) | −0.905176 | + | 15.7935i | −0.0474441 | + | 0.827805i | ||||
\(365\) | 65.3939 | 3.42287 | ||||||||
\(366\) | −10.9910 | + | 19.0369i | −0.574507 | + | 0.995076i | ||||
\(367\) | 1.82780 | + | 3.16584i | 0.0954103 | + | 0.165255i | 0.909780 | − | 0.415091i | \(-0.136250\pi\) |
−0.814369 | + | 0.580347i | \(0.802917\pi\) | |||||||
\(368\) | 0.500000 | + | 0.866025i | 0.0260643 | + | 0.0451447i | ||||
\(369\) | 19.6880 | − | 34.1006i | 1.02492 | − | 1.77521i | ||||
\(370\) | −13.2086 | −0.686682 | ||||||||
\(371\) | 0.307201 | − | 5.36005i | 0.0159491 | − | 0.278280i | ||||
\(372\) | −11.3320 | −0.587537 | ||||||||
\(373\) | −1.91307 | + | 3.31354i | −0.0990551 | + | 0.171569i | −0.911294 | − | 0.411757i | \(-0.864915\pi\) |
0.812239 | + | 0.583325i | \(0.198249\pi\) | |||||||
\(374\) | −2.62090 | − | 4.53954i | −0.135524 | − | 0.234734i | ||||
\(375\) | 25.3272 | + | 43.8680i | 1.30789 | + | 2.26533i | ||||
\(376\) | −2.00283 | + | 3.46900i | −0.103288 | + | 0.178900i | ||||
\(377\) | 4.01053 | 0.206553 | ||||||||
\(378\) | −7.35703 | + | 3.70338i | −0.378405 | + | 0.190482i | ||||
\(379\) | −7.57829 | −0.389270 | −0.194635 | − | 0.980876i | \(-0.562352\pi\) | ||||
−0.194635 | + | 0.980876i | \(0.562352\pi\) | |||||||
\(380\) | 2.14856 | − | 3.72141i | 0.110219 | − | 0.190904i | ||||
\(381\) | 17.5622 | + | 30.4185i | 0.899736 | + | 1.55839i | ||||
\(382\) | 3.54070 | + | 6.13267i | 0.181158 | + | 0.313774i | ||||
\(383\) | −3.22264 | + | 5.58178i | −0.164669 | + | 0.285216i | −0.936538 | − | 0.350567i | \(-0.885989\pi\) |
0.771868 | + | 0.635782i | \(0.219322\pi\) | |||||||
\(384\) | −2.67641 | −0.136580 | ||||||||
\(385\) | −52.0197 | − | 34.1448i | −2.65117 | − | 1.74018i | ||||
\(386\) | 21.0162 | 1.06970 | ||||||||
\(387\) | 7.78408 | − | 13.4824i | 0.395687 | − | 0.685350i | ||||
\(388\) | 6.44659 | + | 11.1658i | 0.327276 | + | 0.566858i | ||||
\(389\) | −6.92948 | − | 12.0022i | −0.351339 | − | 0.608537i | 0.635146 | − | 0.772392i | \(-0.280940\pi\) |
−0.986484 | + | 0.163856i | \(0.947607\pi\) | |||||||
\(390\) | −30.8885 | + | 53.5004i | −1.56410 | + | 2.70910i | ||||
\(391\) | −0.860397 | −0.0435121 | ||||||||
\(392\) | −2.78447 | − | 6.42236i | −0.140637 | − | 0.324378i | ||||
\(393\) | −35.2103 | −1.77613 | ||||||||
\(394\) | −0.403061 | + | 0.698121i | −0.0203059 | + | 0.0351709i | ||||
\(395\) | 4.78902 | + | 8.29482i | 0.240962 | + | 0.417358i | ||||
\(396\) | 12.6817 | + | 21.9653i | 0.637278 | + | 1.10380i | ||||
\(397\) | −13.7830 | + | 23.8729i | −0.691750 | + | 1.19815i | 0.279514 | + | 0.960142i | \(0.409827\pi\) |
−0.971264 | + | 0.238004i | \(0.923507\pi\) | |||||||
\(398\) | −14.5160 | −0.727621 | ||||||||
\(399\) | −6.58948 | − | 4.32522i | −0.329887 | − | 0.216532i | ||||
\(400\) | 9.90267 | 0.495133 | ||||||||
\(401\) | −16.9164 | + | 29.3001i | −0.844766 | + | 1.46318i | 0.0410584 | + | 0.999157i | \(0.486927\pi\) |
−0.885824 | + | 0.464021i | \(0.846406\pi\) | |||||||
\(402\) | −0.0745470 | − | 0.129119i | −0.00371806 | − | 0.00643988i | ||||
\(403\) | 12.6580 | + | 21.9244i | 0.630541 | + | 1.09213i | ||||
\(404\) | −1.57012 | + | 2.71953i | −0.0781165 | + | 0.135302i | ||||
\(405\) | 16.0496 | 0.797513 | ||||||||
\(406\) | −1.58513 | + | 0.797925i | −0.0786688 | + | 0.0396003i | ||||
\(407\) | 20.8452 | 1.03326 | ||||||||
\(408\) | 1.15139 | − | 1.99426i | 0.0570022 | − | 0.0987307i | ||||
\(409\) | −9.43072 | − | 16.3345i | −0.466319 | − | 0.807688i | 0.532941 | − | 0.846152i | \(-0.321087\pi\) |
−0.999260 | + | 0.0384641i | \(0.987753\pi\) | |||||||
\(410\) | 18.2561 | + | 31.6206i | 0.901607 | + | 1.56163i | ||||
\(411\) | −14.9183 | + | 25.8393i | −0.735867 | + | 1.27456i | ||||
\(412\) | −3.21848 | −0.158563 | ||||||||
\(413\) | 0.175673 | − | 3.06514i | 0.00864430 | − | 0.150826i | ||||
\(414\) | 4.16317 | 0.204609 | ||||||||
\(415\) | −2.02680 | + | 3.51051i | −0.0994915 | + | 0.172324i | ||||
\(416\) | 2.98959 | + | 5.17813i | 0.146577 | + | 0.253879i | ||||
\(417\) | 1.60998 | + | 2.78856i | 0.0788409 | + | 0.136556i | ||||
\(418\) | −3.39076 | + | 5.87297i | −0.165848 | + | 0.287256i | ||||
\(419\) | −35.1574 | −1.71755 | −0.858775 | − | 0.512353i | \(-0.828774\pi\) | ||||
−0.858775 | + | 0.512353i | \(0.828774\pi\) | |||||||
\(420\) | 1.56414 | − | 27.2911i | 0.0763222 | − | 1.33167i | ||||
\(421\) | −28.1241 | −1.37068 | −0.685341 | − | 0.728222i | \(-0.740347\pi\) | ||||
−0.685341 | + | 0.728222i | \(0.740347\pi\) | |||||||
\(422\) | 12.0951 | − | 20.9494i | 0.588782 | − | 1.01980i | ||||
\(423\) | 8.33813 | + | 14.4421i | 0.405414 | + | 0.702197i | ||||
\(424\) | −1.01462 | − | 1.75737i | −0.0492741 | − | 0.0853452i | ||||
\(425\) | −4.26011 | + | 7.37873i | −0.206646 | + | 0.357921i | ||||
\(426\) | −2.31227 | −0.112030 | ||||||||
\(427\) | −19.4097 | + | 9.77047i | −0.939301 | + | 0.472826i | ||||
\(428\) | −0.954185 | −0.0461223 | ||||||||
\(429\) | 48.7469 | − | 84.4321i | 2.35352 | − | 4.07642i | ||||
\(430\) | 7.21796 | + | 12.5019i | 0.348081 | + | 0.602894i | ||||
\(431\) | 2.88793 | + | 5.00204i | 0.139107 | + | 0.240940i | 0.927159 | − | 0.374669i | \(-0.122244\pi\) |
−0.788052 | + | 0.615609i | \(0.788910\pi\) | |||||||
\(432\) | −1.55656 | + | 2.69605i | −0.0748902 | + | 0.129714i | ||||
\(433\) | −28.9576 | −1.39161 | −0.695806 | − | 0.718229i | \(-0.744953\pi\) | ||||
−0.695806 | + | 0.718229i | \(0.744953\pi\) | |||||||
\(434\) | −9.36500 | − | 6.14703i | −0.449534 | − | 0.295067i | ||||
\(435\) | −6.93018 | −0.332277 | ||||||||
\(436\) | 6.40267 | − | 11.0897i | 0.306632 | − | 0.531102i | ||||
\(437\) | 0.556564 | + | 0.963997i | 0.0266241 | + | 0.0461142i | ||||
\(438\) | −22.6688 | − | 39.2634i | −1.08316 | − | 1.87608i | ||||
\(439\) | −8.40340 | + | 14.5551i | −0.401073 | + | 0.694678i | −0.993856 | − | 0.110684i | \(-0.964696\pi\) |
0.592783 | + | 0.805362i | \(0.298029\pi\) | |||||||
\(440\) | −23.5187 | −1.12121 | ||||||||
\(441\) | −28.9514 | − | 3.32952i | −1.37864 | − | 0.158549i | ||||
\(442\) | −5.14447 | −0.244698 | ||||||||
\(443\) | −5.00824 | + | 8.67452i | −0.237949 | + | 0.412139i | −0.960126 | − | 0.279569i | \(-0.909808\pi\) |
0.722177 | + | 0.691708i | \(0.243142\pi\) | |||||||
\(444\) | 4.57876 | + | 7.93064i | 0.217298 | + | 0.376371i | ||||
\(445\) | −13.2930 | − | 23.0242i | −0.630150 | − | 1.09145i | ||||
\(446\) | 5.46300 | − | 9.46219i | 0.258680 | − | 0.448048i | ||||
\(447\) | 39.2469 | 1.85632 | ||||||||
\(448\) | −2.21184 | − | 1.45181i | −0.104500 | − | 0.0685918i | ||||
\(449\) | −36.6615 | −1.73016 | −0.865082 | − | 0.501631i | \(-0.832734\pi\) | ||||
−0.865082 | + | 0.501631i | \(0.832734\pi\) | |||||||
\(450\) | 20.6133 | − | 35.7032i | 0.971718 | − | 1.68307i | ||||
\(451\) | −28.8111 | − | 49.9022i | −1.35666 | − | 2.34980i | ||||
\(452\) | −1.26840 | − | 2.19694i | −0.0596607 | − | 0.103335i | ||||
\(453\) | −8.17779 | + | 14.1643i | −0.384226 | + | 0.665499i | ||||
\(454\) | −25.6668 | −1.20460 | ||||||||
\(455\) | −54.5481 | + | 27.4584i | −2.55725 | + | 1.28727i | ||||
\(456\) | −2.97919 | −0.139513 | ||||||||
\(457\) | 13.6998 | − | 23.7287i | 0.640849 | − | 1.10998i | −0.344395 | − | 0.938825i | \(-0.611916\pi\) |
0.985244 | − | 0.171158i | \(-0.0547507\pi\) | |||||||
\(458\) | 11.2966 | + | 19.5662i | 0.527854 | + | 0.914271i | ||||
\(459\) | −1.33926 | − | 2.31967i | −0.0625114 | − | 0.108273i | ||||
\(460\) | −1.93020 | + | 3.34320i | −0.0899960 | + | 0.155878i | ||||
\(461\) | −21.7137 | −1.01131 | −0.505653 | − | 0.862737i | \(-0.668748\pi\) | ||||
−0.505653 | + | 0.862737i | \(0.668748\pi\) | |||||||
\(462\) | −2.46846 | + | 43.0697i | −0.114843 | + | 2.00378i | ||||
\(463\) | 39.3093 | 1.82686 | 0.913430 | − | 0.406996i | \(-0.133424\pi\) | ||||
0.913430 | + | 0.406996i | \(0.133424\pi\) | |||||||
\(464\) | −0.335374 | + | 0.580886i | −0.0155694 | + | 0.0269669i | ||||
\(465\) | −21.8730 | − | 37.8852i | −1.01434 | − | 1.75688i | ||||
\(466\) | −1.75622 | − | 3.04187i | −0.0813555 | − | 0.140912i | ||||
\(467\) | 11.0602 | − | 19.1568i | 0.511804 | − | 0.886470i | −0.488102 | − | 0.872786i | \(-0.662311\pi\) |
0.999906 | − | 0.0136841i | \(-0.00435591\pi\) | |||||||
\(468\) | 24.8924 | 1.15065 | ||||||||
\(469\) | 0.00843331 | − | 0.147145i | 0.000389414 | − | 0.00679450i | ||||
\(470\) | −15.4634 | −0.713275 | ||||||||
\(471\) | −2.22823 | + | 3.85941i | −0.102671 | + | 0.177832i | ||||
\(472\) | −0.580208 | − | 1.00495i | −0.0267063 | − | 0.0462566i | ||||
\(473\) | −11.3911 | − | 19.7299i | −0.523762 | − | 0.907183i | ||||
\(474\) | 3.32022 | − | 5.75079i | 0.152503 | − | 0.264143i | ||||
\(475\) | 11.0229 | 0.505767 | ||||||||
\(476\) | 2.03331 | − | 1.02353i | 0.0931968 | − | 0.0469134i | ||||
\(477\) | −8.44804 | −0.386809 | ||||||||
\(478\) | 1.17609 | − | 2.03705i | 0.0537931 | − | 0.0931724i | ||||
\(479\) | −2.27229 | − | 3.93573i | −0.103824 | − | 0.179828i | 0.809433 | − | 0.587212i | \(-0.199774\pi\) |
−0.913257 | + | 0.407384i | \(0.866441\pi\) | |||||||
\(480\) | −5.16600 | − | 8.94778i | −0.235795 | − | 0.408408i | ||||
\(481\) | 10.2291 | − | 17.7173i | 0.466406 | − | 0.807839i | ||||
\(482\) | 22.3034 | 1.01589 | ||||||||
\(483\) | 5.91979 | + | 3.88565i | 0.269360 | + | 0.176803i | ||||
\(484\) | 26.1163 | 1.18710 | ||||||||
\(485\) | −24.8864 | + | 43.1045i | −1.13003 | + | 1.95727i | ||||
\(486\) | −10.2333 | − | 17.7246i | −0.464192 | − | 0.804004i | ||||
\(487\) | 13.4897 | + | 23.3649i | 0.611277 | + | 1.05876i | 0.991025 | + | 0.133673i | \(0.0426773\pi\) |
−0.379748 | + | 0.925090i | \(0.623989\pi\) | |||||||
\(488\) | −4.10661 | + | 7.11286i | −0.185897 | + | 0.321984i | ||||
\(489\) | 20.5255 | 0.928194 | ||||||||
\(490\) | 16.0967 | − | 21.7055i | 0.727173 | − | 0.980554i | ||||
\(491\) | 33.2684 | 1.50138 | 0.750690 | − | 0.660654i | \(-0.229721\pi\) | ||||
0.750690 | + | 0.660654i | \(0.229721\pi\) | |||||||
\(492\) | 12.6570 | − | 21.9225i | 0.570620 | − | 0.988344i | ||||
\(493\) | −0.288555 | − | 0.499792i | −0.0129959 | − | 0.0225095i | ||||
\(494\) | 3.32780 | + | 5.76392i | 0.149725 | + | 0.259331i | ||||
\(495\) | −48.9563 | + | 84.7948i | −2.20042 | + | 3.81124i | ||||
\(496\) | −4.23403 | −0.190114 | ||||||||
\(497\) | −1.91090 | − | 1.25428i | −0.0857158 | − | 0.0562624i | ||||
\(498\) | 2.81035 | 0.125935 | ||||||||
\(499\) | −9.86704 | + | 17.0902i | −0.441709 | + | 0.765063i | −0.997816 | − | 0.0660478i | \(-0.978961\pi\) |
0.556107 | + | 0.831111i | \(0.312294\pi\) | |||||||
\(500\) | 9.46312 | + | 16.3906i | 0.423203 | + | 0.733010i | ||||
\(501\) | −33.1186 | − | 57.3632i | −1.47963 | − | 2.56280i | ||||
\(502\) | −6.88213 | + | 11.9202i | −0.307164 | + | 0.532024i | ||||
\(503\) | −20.8367 | −0.929062 | −0.464531 | − | 0.885557i | \(-0.653777\pi\) | ||||
−0.464531 | + | 0.885557i | \(0.653777\pi\) | |||||||
\(504\) | −9.83853 | + | 4.95252i | −0.438243 | + | 0.220603i | ||||
\(505\) | −12.1226 | −0.539448 | ||||||||
\(506\) | 3.04616 | − | 5.27610i | 0.135418 | − | 0.234551i | ||||
\(507\) | −30.4451 | − | 52.7324i | −1.35211 | − | 2.34193i | ||||
\(508\) | 6.56183 | + | 11.3654i | 0.291134 | + | 0.504259i | ||||
\(509\) | 8.24515 | − | 14.2810i | 0.365460 | − | 0.632995i | −0.623390 | − | 0.781911i | \(-0.714245\pi\) |
0.988850 | + | 0.148916i | \(0.0475784\pi\) | |||||||
\(510\) | 8.88963 | 0.393639 | ||||||||
\(511\) | 2.56446 | − | 44.7447i | 0.113445 | − | 1.97939i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.73265 | + | 3.00104i | −0.0764985 | + | 0.132499i | ||||
\(514\) | −5.12954 | − | 8.88462i | −0.226254 | − | 0.391884i | ||||
\(515\) | −6.21230 | − | 10.7600i | −0.273747 | − | 0.474143i | ||||
\(516\) | 5.00421 | − | 8.66754i | 0.220298 | − | 0.381567i | ||||
\(517\) | 24.4037 | 1.07328 | ||||||||
\(518\) | −0.517983 | + | 9.03778i | −0.0227589 | + | 0.397097i | ||||
\(519\) | −4.87555 | −0.214013 | ||||||||
\(520\) | −11.5410 | + | 19.9896i | −0.506107 | + | 0.876603i | ||||
\(521\) | 14.9196 | + | 25.8415i | 0.653638 | + | 1.13213i | 0.982233 | + | 0.187664i | \(0.0600916\pi\) |
−0.328595 | + | 0.944471i | \(0.606575\pi\) | |||||||
\(522\) | 1.39622 | + | 2.41833i | 0.0611110 | + | 0.105847i | ||||
\(523\) | −15.8845 | + | 27.5127i | −0.694580 | + | 1.20305i | 0.275742 | + | 0.961232i | \(0.411076\pi\) |
−0.970322 | + | 0.241816i | \(0.922257\pi\) | |||||||
\(524\) | −13.1558 | −0.574714 | ||||||||
\(525\) | 62.6340 | − | 31.5287i | 2.73357 | − | 1.37603i | ||||
\(526\) | −14.7080 | −0.641299 | ||||||||
\(527\) | 1.82147 | − | 3.15489i | 0.0793447 | − | 0.137429i | ||||
\(528\) | 8.15277 | + | 14.1210i | 0.354804 | + | 0.614538i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.0217391 | − | 0.0376533i | ||||
\(530\) | 3.91682 | − | 6.78413i | 0.170136 | − | 0.294684i | ||||
\(531\) | −4.83102 | −0.209648 | ||||||||
\(532\) | −2.46206 | − | 1.61605i | −0.106744 | − | 0.0700648i | ||||
\(533\) | −56.5522 | −2.44955 | ||||||||
\(534\) | −9.21605 | + | 15.9627i | −0.398817 | + | 0.690772i | ||||
\(535\) | −1.84177 | − | 3.19003i | −0.0796265 | − | 0.137917i | ||||
\(536\) | −0.0278533 | − | 0.0482434i | −0.00120308 | − | 0.00208380i | ||||
\(537\) | −15.2622 | + | 26.4349i | −0.658613 | + | 1.14075i | ||||
\(538\) | −5.89805 | −0.254283 | ||||||||
\(539\) | −25.4031 | + | 34.2547i | −1.09419 | + | 1.47545i | ||||
\(540\) | −12.0179 | −0.517168 | ||||||||
\(541\) | 8.47953 | − | 14.6870i | 0.364563 | − | 0.631442i | −0.624143 | − | 0.781310i | \(-0.714552\pi\) |
0.988706 | + | 0.149868i | \(0.0478849\pi\) | |||||||
\(542\) | −6.91465 | − | 11.9765i | −0.297010 | − | 0.514436i | ||||
\(543\) | −0.839062 | − | 1.45330i | −0.0360076 | − | 0.0623670i | ||||
\(544\) | 0.430199 | − | 0.745126i | 0.0184446 | − | 0.0319470i | ||||
\(545\) | 49.4337 | 2.11751 | ||||||||
\(546\) | 35.3955 | + | 23.2330i | 1.51479 | + | 0.994282i | ||||
\(547\) | 29.7635 | 1.27259 | 0.636297 | − | 0.771444i | \(-0.280465\pi\) | ||||
0.636297 | + | 0.771444i | \(0.280465\pi\) | |||||||
\(548\) | −5.57401 | + | 9.65447i | −0.238110 | + | 0.412418i | ||||
\(549\) | 17.0965 | + | 29.6120i | 0.729662 | + | 1.26381i | ||||
\(550\) | −30.1651 | − | 52.2474i | −1.28624 | − | 2.22784i | ||||
\(551\) | −0.373315 | + | 0.646600i | −0.0159037 | + | 0.0275461i | ||||
\(552\) | 2.67641 | 0.113916 | ||||||||
\(553\) | 5.86341 | − | 2.95152i | 0.249337 | − | 0.125512i | ||||
\(554\) | 23.5875 | 1.00214 | ||||||||
\(555\) | −17.6758 | + | 30.6154i | −0.750297 | + | 1.29955i | ||||
\(556\) | 0.601543 | + | 1.04190i | 0.0255111 | + | 0.0441865i | ||||
\(557\) | −23.1684 | − | 40.1289i | −0.981678 | − | 1.70032i | −0.655857 | − | 0.754885i | \(-0.727693\pi\) |
−0.325821 | − | 0.945431i | \(-0.605641\pi\) | |||||||
\(558\) | −8.81350 | + | 15.2654i | −0.373105 | + | 0.646237i | ||||
\(559\) | −22.3591 | −0.945690 | ||||||||
\(560\) | 0.584417 | − | 10.1969i | 0.0246961 | − | 0.430898i | ||||
\(561\) | −14.0292 | −0.592315 | ||||||||
\(562\) | 11.6491 | − | 20.1768i | 0.491387 | − | 0.851107i | ||||
\(563\) | −8.18799 | − | 14.1820i | −0.345083 | − | 0.597701i | 0.640286 | − | 0.768137i | \(-0.278816\pi\) |
−0.985369 | + | 0.170436i | \(0.945483\pi\) | |||||||
\(564\) | 5.36040 | + | 9.28448i | 0.225713 | + | 0.390947i | ||||
\(565\) | 4.89654 | − | 8.48106i | 0.205999 | − | 0.356801i | ||||
\(566\) | 31.8028 | 1.33677 | ||||||||
\(567\) | 0.629397 | − | 10.9817i | 0.0264322 | − | 0.461189i | ||||
\(568\) | −0.863943 | −0.0362503 | ||||||||
\(569\) | 11.7859 | − | 20.4137i | 0.494089 | − | 0.855786i | −0.505888 | − | 0.862599i | \(-0.668835\pi\) |
0.999977 | + | 0.00681257i | \(0.00216853\pi\) | |||||||
\(570\) | −5.75042 | − | 9.96002i | −0.240859 | − | 0.417179i | ||||
\(571\) | 5.81180 | + | 10.0663i | 0.243216 | + | 0.421263i | 0.961629 | − | 0.274354i | \(-0.0884641\pi\) |
−0.718412 | + | 0.695618i | \(0.755131\pi\) | |||||||
\(572\) | 18.2135 | − | 31.5468i | 0.761546 | − | 1.31904i | ||||
\(573\) | 18.9527 | 0.791761 | ||||||||
\(574\) | 22.3518 | − | 11.2515i | 0.932947 | − | 0.469627i | ||||
\(575\) | −9.90267 | −0.412970 | ||||||||
\(576\) | −2.08159 | + | 3.60541i | −0.0867328 | + | 0.150226i | ||||
\(577\) | −13.3214 | − | 23.0733i | −0.554577 | − | 0.960556i | −0.997936 | − | 0.0642117i | \(-0.979547\pi\) |
0.443359 | − | 0.896344i | \(-0.353787\pi\) | |||||||
\(578\) | −8.12986 | − | 14.0813i | −0.338158 | − | 0.585706i | ||||
\(579\) | 28.1240 | − | 48.7122i | 1.16879 | − | 2.02441i | ||||
\(580\) | −2.58936 | −0.107517 | ||||||||
\(581\) | 2.32253 | + | 1.52447i | 0.0963549 | + | 0.0632457i | ||||
\(582\) | 34.5074 | 1.43038 | ||||||||
\(583\) | −6.18136 | + | 10.7064i | −0.256006 | + | 0.443415i | ||||
\(584\) | −8.46984 | − | 14.6702i | −0.350484 | − | 0.607057i | ||||
\(585\) | 48.0472 | + | 83.2203i | 1.98651 | + | 3.44073i | ||||
\(586\) | −8.81633 | + | 15.2703i | −0.364199 | + | 0.630812i | ||||
\(587\) | −12.6846 | −0.523549 | −0.261774 | − | 0.965129i | \(-0.584308\pi\) | ||||
−0.261774 | + | 0.965129i | \(0.584308\pi\) | |||||||
\(588\) | −18.6122 | − | 2.14048i | −0.767554 | − | 0.0882718i | ||||
\(589\) | −4.71302 | −0.194196 | ||||||||
\(590\) | 2.23983 | − | 3.87951i | 0.0922125 | − | 0.159717i | ||||
\(591\) | 1.07876 | + | 1.86846i | 0.0443741 | + | 0.0768582i | ||||
\(592\) | 1.71078 | + | 2.96316i | 0.0703127 | + | 0.121785i | ||||
\(593\) | −4.84618 | + | 8.39382i | −0.199009 | + | 0.344693i | −0.948207 | − | 0.317652i | \(-0.897106\pi\) |
0.749199 | + | 0.662345i | \(0.230439\pi\) | |||||||
\(594\) | 18.9661 | 0.778191 | ||||||||
\(595\) | 7.34657 | + | 4.82216i | 0.301180 | + | 0.197689i | ||||
\(596\) | 14.6640 | 0.600661 | ||||||||
\(597\) | −19.4254 | + | 33.6457i | −0.795028 | + | 1.37703i | ||||
\(598\) | −2.98959 | − | 5.17813i | −0.122254 | − | 0.211749i | ||||
\(599\) | 5.41150 | + | 9.37299i | 0.221108 | + | 0.382970i | 0.955145 | − | 0.296140i | \(-0.0956994\pi\) |
−0.734037 | + | 0.679110i | \(0.762366\pi\) | |||||||
\(600\) | 13.2518 | − | 22.9528i | 0.541002 | − | 0.937044i | ||||
\(601\) | 28.6724 | 1.16957 | 0.584786 | − | 0.811187i | \(-0.301178\pi\) | ||||
0.584786 | + | 0.811187i | \(0.301178\pi\) | |||||||
\(602\) | 8.83727 | − | 4.44851i | 0.360180 | − | 0.181308i | ||||
\(603\) | −0.231917 | −0.00944437 | ||||||||
\(604\) | −3.05551 | + | 5.29229i | −0.124327 | + | 0.215340i | ||||
\(605\) | 50.4096 | + | 87.3120i | 2.04944 | + | 3.54974i | ||||
\(606\) | 4.20229 | + | 7.27858i | 0.170706 | + | 0.295672i | ||||
\(607\) | −7.91578 | + | 13.7105i | −0.321292 | + | 0.556494i | −0.980755 | − | 0.195243i | \(-0.937450\pi\) |
0.659463 | + | 0.751737i | \(0.270784\pi\) | |||||||
\(608\) | −1.11313 | −0.0451433 | ||||||||
\(609\) | −0.271771 | + | 4.74187i | −0.0110127 | + | 0.192150i | ||||
\(610\) | −31.7063 | −1.28375 | ||||||||
\(611\) | 11.9753 | − | 20.7418i | 0.484469 | − | 0.839124i | ||||
\(612\) | −1.79099 | − | 3.10209i | −0.0723965 | − | 0.125394i | ||||
\(613\) | −6.22222 | − | 10.7772i | −0.251313 | − | 0.435287i | 0.712574 | − | 0.701597i | \(-0.247529\pi\) |
−0.963888 | + | 0.266309i | \(0.914196\pi\) | |||||||
\(614\) | −6.13089 | + | 10.6190i | −0.247423 | + | 0.428549i | ||||
\(615\) | 97.7219 | 3.94053 | ||||||||
\(616\) | −0.922302 | + | 16.0923i | −0.0371606 | + | 0.648379i | ||||
\(617\) | −24.1914 | −0.973908 | −0.486954 | − | 0.873428i | \(-0.661892\pi\) | ||||
−0.486954 | + | 0.873428i | \(0.661892\pi\) | |||||||
\(618\) | −4.30698 | + | 7.45992i | −0.173252 | + | 0.300082i | ||||
\(619\) | 13.6142 | + | 23.5805i | 0.547200 | + | 0.947779i | 0.998465 | + | 0.0553885i | \(0.0176397\pi\) |
−0.451265 | + | 0.892390i | \(0.649027\pi\) | |||||||
\(620\) | −8.17252 | − | 14.1552i | −0.328216 | − | 0.568487i | ||||
\(621\) | 1.55656 | − | 2.69605i | 0.0624628 | − | 0.108189i | ||||
\(622\) | −3.22059 | −0.129134 | ||||||||
\(623\) | −16.2752 | + | 8.19264i | −0.652054 | + | 0.328231i | ||||
\(624\) | 16.0028 | 0.640623 | ||||||||
\(625\) | −11.7747 | + | 20.3944i | −0.470989 | + | 0.815777i | ||||
\(626\) | −10.6596 | − | 18.4630i | −0.426043 | − | 0.737929i | ||||
\(627\) | 9.07507 | + | 15.7185i | 0.362423 | + | 0.627736i | ||||
\(628\) | −0.832544 | + | 1.44201i | −0.0332221 | + | 0.0575424i | ||||
\(629\) | −2.94390 | −0.117381 | ||||||||
\(630\) | −35.5476 | − | 23.3328i | −1.41625 | − | 0.929602i | ||||
\(631\) | 17.2260 | 0.685757 | 0.342878 | − | 0.939380i | \(-0.388598\pi\) | ||||
0.342878 | + | 0.939380i | \(0.388598\pi\) | |||||||
\(632\) | 1.24055 | − | 2.14870i | 0.0493464 | − | 0.0854706i | ||||
\(633\) | −32.3716 | − | 56.0692i | −1.28665 | − | 2.22855i | ||||
\(634\) | 8.40227 | + | 14.5532i | 0.333697 | + | 0.577980i | ||||
\(635\) | −25.3313 | + | 43.8750i | −1.00524 | + | 1.74113i | ||||
\(636\) | −5.43106 | −0.215355 | ||||||||
\(637\) | 16.6489 | + | 38.4005i | 0.659653 | + | 1.52148i | ||||
\(638\) | 4.08641 | 0.161783 | ||||||||
\(639\) | −1.79837 | + | 3.11487i | −0.0711425 | + | 0.123222i | ||||
\(640\) | −1.93020 | − | 3.34320i | −0.0762978 | − | 0.132152i | ||||
\(641\) | 1.17161 | + | 2.02928i | 0.0462757 | + | 0.0801518i | 0.888235 | − | 0.459388i | \(-0.151931\pi\) |
−0.841960 | + | 0.539540i | \(0.818598\pi\) | |||||||
\(642\) | −1.27690 | + | 2.21165i | −0.0503951 | + | 0.0872868i | ||||
\(643\) | 33.8089 | 1.33329 | 0.666646 | − | 0.745374i | \(-0.267729\pi\) | ||||
0.666646 | + | 0.745374i | \(0.267729\pi\) | |||||||
\(644\) | 2.21184 | + | 1.45181i | 0.0871587 | + | 0.0572095i | ||||
\(645\) | 38.6365 | 1.52131 | ||||||||
\(646\) | 0.478866 | − | 0.829420i | 0.0188407 | − | 0.0326331i | ||||
\(647\) | 13.5918 | + | 23.5416i | 0.534348 | + | 0.925518i | 0.999195 | + | 0.0401265i | \(0.0127761\pi\) |
−0.464847 | + | 0.885391i | \(0.653891\pi\) | |||||||
\(648\) | −2.07876 | − | 3.60051i | −0.0816612 | − | 0.141441i | ||||
\(649\) | −3.53481 | + | 6.12247i | −0.138753 | + | 0.240328i | ||||
\(650\) | −59.2099 | −2.32240 | ||||||||
\(651\) | −26.7801 | + | 13.4806i | −1.04960 | + | 0.528346i | ||||
\(652\) | 7.66903 | 0.300343 | ||||||||
\(653\) | 10.8258 | − | 18.7509i | 0.423647 | − | 0.733777i | −0.572646 | − | 0.819803i | \(-0.694083\pi\) |
0.996293 | + | 0.0860250i | \(0.0274165\pi\) | |||||||
\(654\) | −17.1362 | − | 29.6807i | −0.670077 | − | 1.16061i | ||||
\(655\) | −25.3933 | − | 43.9825i | −0.992198 | − | 1.71854i | ||||
\(656\) | 4.72909 | − | 8.19102i | 0.184640 | − | 0.319805i | ||||
\(657\) | −70.5228 | −2.75136 | ||||||||
\(658\) | −0.606408 | + | 10.5806i | −0.0236403 | + | 0.412476i | ||||
\(659\) | 3.19097 | 0.124303 | 0.0621513 | − | 0.998067i | \(-0.480204\pi\) | ||||
0.0621513 | + | 0.998067i | \(0.480204\pi\) | |||||||
\(660\) | −31.4729 | + | 54.5127i | −1.22508 | + | 2.12190i | ||||
\(661\) | −7.52548 | − | 13.0345i | −0.292707 | − | 0.506984i | 0.681742 | − | 0.731593i | \(-0.261223\pi\) |
−0.974449 | + | 0.224609i | \(0.927890\pi\) | |||||||
\(662\) | 4.79448 | + | 8.30429i | 0.186343 | + | 0.322755i | ||||
\(663\) | −6.88436 | + | 11.9241i | −0.267366 | + | 0.463092i | ||||
\(664\) | 1.05005 | 0.0407497 | ||||||||
\(665\) | 0.650531 | − | 11.3505i | 0.0252265 | − | 0.440152i | ||||
\(666\) | 14.2446 | 0.551966 | ||||||||
\(667\) | 0.335374 | − | 0.580886i | 0.0129858 | − | 0.0224920i | ||||
\(668\) | −12.3743 | − | 21.4329i | −0.478775 | − | 0.829263i | ||||
\(669\) | −14.6212 | − | 25.3247i | −0.565289 | − | 0.979110i | ||||
\(670\) | 0.107525 | − | 0.186239i | 0.00415405 | − | 0.00719503i | ||||
\(671\) | 50.0375 | 1.93168 | ||||||||
\(672\) | −6.32497 | + | 3.18386i | −0.243991 | + | 0.122820i | ||||
\(673\) | −34.3972 | −1.32591 | −0.662957 | − | 0.748657i | \(-0.730699\pi\) | ||||
−0.662957 | + | 0.748657i | \(0.730699\pi\) | |||||||
\(674\) | −3.99005 | + | 6.91098i | −0.153691 | + | 0.266201i | ||||
\(675\) | −15.4141 | − | 26.6981i | −0.593290 | − | 1.02761i | ||||
\(676\) | −11.3753 | − | 19.7027i | −0.437513 | − | 0.757794i | ||||
\(677\) | −11.9979 | + | 20.7810i | −0.461116 | + | 0.798677i | −0.999017 | − | 0.0443313i | \(-0.985884\pi\) |
0.537900 | + | 0.843008i | \(0.319218\pi\) | |||||||
\(678\) | −6.78954 | −0.260751 | ||||||||
\(679\) | 28.5176 | + | 18.7185i | 1.09441 | + | 0.718350i | ||||
\(680\) | 3.32147 | 0.127373 | ||||||||
\(681\) | −34.3474 | + | 59.4914i | −1.31620 | + | 2.27972i | ||||
\(682\) | 12.8975 | + | 22.3392i | 0.493872 | + | 0.855411i | ||||
\(683\) | −22.5563 | − | 39.0687i | −0.863095 | − | 1.49492i | −0.868927 | − | 0.494941i | \(-0.835190\pi\) |
0.00583208 | − | 0.999983i | \(-0.498144\pi\) | |||||||
\(684\) | −2.31707 | + | 4.01328i | −0.0885954 | + | 0.153452i | ||||
\(685\) | −43.0358 | −1.64431 | ||||||||
\(686\) | −14.2204 | − | 11.8651i | −0.542937 | − | 0.453011i | ||||
\(687\) | 60.4686 | 2.30702 | ||||||||
\(688\) | 1.86975 | − | 3.23850i | 0.0712834 | − | 0.123466i | ||||
\(689\) | 6.06658 | + | 10.5076i | 0.231118 | + | 0.400308i | ||||
\(690\) | 5.16600 | + | 8.94778i | 0.196666 | + | 0.340636i | ||||
\(691\) | 9.34571 | − | 16.1872i | 0.355527 | − | 0.615792i | −0.631681 | − | 0.775229i | \(-0.717635\pi\) |
0.987208 | + | 0.159437i | \(0.0509679\pi\) | |||||||
\(692\) | −1.82167 | −0.0692497 | ||||||||
\(693\) | 56.0997 | + | 36.8229i | 2.13105 | + | 1.39879i | ||||
\(694\) | 21.8159 | 0.828119 | ||||||||
\(695\) | −2.32220 | + | 4.02216i | −0.0880859 | + | 0.152569i | ||||
\(696\) | 0.897600 | + | 1.55469i | 0.0340234 | + | 0.0589303i | ||||
\(697\) | 4.06889 | + | 7.04753i | 0.154120 | + | 0.266944i | ||||
\(698\) | 5.82708 | − | 10.0928i | 0.220558 | − | 0.382018i | ||||
\(699\) | −9.40075 | −0.355569 | ||||||||
\(700\) | 23.4023 | − | 11.7802i | 0.884522 | − | 0.445251i | ||||
\(701\) | 27.0349 | 1.02109 | 0.510547 | − | 0.859850i | \(-0.329443\pi\) | ||||
0.510547 | + | 0.859850i | \(0.329443\pi\) | |||||||
\(702\) | 9.30698 | − | 16.1202i | 0.351269 | − | 0.608417i | ||||
\(703\) | 1.90432 | + | 3.29838i | 0.0718227 | + | 0.124401i | ||||
\(704\) | 3.04616 | + | 5.27610i | 0.114806 | + | 0.198850i | ||||
\(705\) | −20.6933 | + | 35.8418i | −0.779353 | + | 1.34988i | ||||
\(706\) | −3.71381 | −0.139771 | ||||||||
\(707\) | −0.475395 | + | 8.29469i | −0.0178791 | + | 0.311954i | ||||
\(708\) | −3.10575 | −0.116721 | ||||||||
\(709\) | −4.74095 | + | 8.21156i | −0.178050 | + | 0.308392i | −0.941213 | − | 0.337815i | \(-0.890312\pi\) |
0.763163 | + | 0.646207i | \(0.223646\pi\) | |||||||
\(710\) | −1.66758 | − | 2.88834i | −0.0625832 | − | 0.108397i | ||||
\(711\) | −5.16463 | − | 8.94539i | −0.193689 | − | 0.335478i | ||||
\(712\) | −3.44344 | + | 5.96421i | −0.129048 | + | 0.223518i | ||||
\(713\) | 4.23403 | 0.158566 | ||||||||
\(714\) | 0.348612 | − | 6.08259i | 0.0130465 | − | 0.227635i | ||||
\(715\) | 140.623 | 5.25900 | ||||||||
\(716\) | −5.70249 | + | 9.87700i | −0.213112 | + | 0.369121i | ||||
\(717\) | −3.14770 | − | 5.45198i | −0.117553 | − | 0.203608i | ||||
\(718\) | 5.79909 | + | 10.0443i | 0.216420 | + | 0.374850i | ||||
\(719\) | 15.1886 | − | 26.3075i | 0.566441 | − | 0.981104i | −0.430474 | − | 0.902603i | \(-0.641653\pi\) |
0.996914 | − | 0.0785006i | \(-0.0250132\pi\) | |||||||
\(720\) | −16.0715 | −0.598949 | ||||||||
\(721\) | −7.60600 | + | 3.82871i | −0.283262 | + | 0.142589i | ||||
\(722\) | 17.7609 | 0.660994 | ||||||||
\(723\) | 29.8465 | − | 51.6957i | 1.11001 | − | 1.92259i | ||||
\(724\) | −0.313503 | − | 0.543003i | −0.0116512 | − | 0.0201805i | ||||
\(725\) | −3.32110 | − | 5.75232i | −0.123343 | − | 0.213636i | ||||
\(726\) | 34.9489 | − | 60.5334i | 1.29708 | − | 2.24660i | ||||
\(727\) | −36.5415 | −1.35525 | −0.677625 | − | 0.735407i | \(-0.736991\pi\) | ||||
−0.677625 | + | 0.735407i | \(0.736991\pi\) | |||||||
\(728\) | 13.2250 | + | 8.68067i | 0.490151 | + | 0.321727i | ||||
\(729\) | −42.3045 | −1.56683 | ||||||||
\(730\) | 32.6969 | − | 56.6327i | 1.21017 | − | 2.09607i | ||||
\(731\) | 1.60872 | + | 2.78639i | 0.0595008 | + | 0.103058i | ||||
\(732\) | 10.9910 | + | 19.0369i | 0.406238 | + | 0.703625i | ||||
\(733\) | −14.0285 | + | 24.2981i | −0.518155 | + | 0.897471i | 0.481622 | + | 0.876379i | \(0.340048\pi\) |
−0.999778 | + | 0.0210921i | \(0.993286\pi\) | |||||||
\(734\) | 3.65560 | 0.134931 | ||||||||
\(735\) | −28.7692 | − | 66.3559i | −1.06117 | − | 2.44757i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −0.169691 | + | 0.293914i | −0.00625066 | + | 0.0108265i | ||||
\(738\) | −19.6880 | − | 34.1006i | −0.724725 | − | 1.25526i | ||||
\(739\) | 0.950692 | + | 1.64665i | 0.0349718 | + | 0.0605729i | 0.882982 | − | 0.469408i | \(-0.155533\pi\) |
−0.848010 | + | 0.529981i | \(0.822199\pi\) | |||||||
\(740\) | −6.60430 | + | 11.4390i | −0.242779 | + | 0.420505i | ||||
\(741\) | 17.8131 | 0.654381 | ||||||||
\(742\) | −4.48833 | − | 2.94607i | −0.164772 | − | 0.108153i | ||||
\(743\) | −14.2220 | −0.521755 | −0.260878 | − | 0.965372i | \(-0.584012\pi\) | ||||
−0.260878 | + | 0.965372i | \(0.584012\pi\) | |||||||
\(744\) | −5.66600 | + | 9.81381i | −0.207726 | + | 0.359792i | ||||
\(745\) | 28.3045 | + | 49.0248i | 1.03700 | + | 1.79613i | ||||
\(746\) | 1.91307 | + | 3.31354i | 0.0700426 | + | 0.121317i | ||||
\(747\) | 2.18576 | − | 3.78585i | 0.0799728 | − | 0.138517i | ||||
\(748\) | −5.24181 | −0.191660 | ||||||||
\(749\) | −2.25496 | + | 1.13510i | −0.0823944 | + | 0.0414757i | ||||
\(750\) | 50.6544 | 1.84964 | ||||||||
\(751\) | −8.26840 | + | 14.3213i | −0.301718 | + | 0.522591i | −0.976525 | − | 0.215403i | \(-0.930894\pi\) |
0.674807 | + | 0.737994i | \(0.264227\pi\) | |||||||
\(752\) | 2.00283 | + | 3.46900i | 0.0730357 | + | 0.126502i | ||||
\(753\) | 18.4194 | + | 31.9033i | 0.671240 | + | 1.16262i | ||||
\(754\) | 2.00527 | − | 3.47322i | 0.0730275 | − | 0.126487i | ||||
\(755\) | −23.5909 | −0.858562 | ||||||||
\(756\) | −0.471290 | + | 8.22307i | −0.0171406 | + | 0.299070i | ||||
\(757\) | 12.5780 | 0.457155 | 0.228578 | − | 0.973526i | \(-0.426593\pi\) | ||||
0.228578 | + | 0.973526i | \(0.426593\pi\) | |||||||
\(758\) | −3.78914 | + | 6.56299i | −0.137628 | + | 0.238378i | ||||
\(759\) | −8.15277 | − | 14.1210i | −0.295927 | − | 0.512560i | ||||
\(760\) | −2.14856 | − | 3.72141i | −0.0779364 | − | 0.134990i | ||||
\(761\) | 14.2745 | − | 24.7242i | 0.517451 | − | 0.896252i | −0.482343 | − | 0.875982i | \(-0.660214\pi\) |
0.999795 | − | 0.0202695i | \(-0.00645243\pi\) | |||||||
\(762\) | 35.1243 | 1.27242 | ||||||||
\(763\) | 1.93857 | − | 33.8242i | 0.0701810 | − | 1.22452i | ||||
\(764\) | 7.08139 | 0.256196 | ||||||||
\(765\) | 6.91394 | − | 11.9753i | 0.249974 | − | 0.432967i | ||||
\(766\) | 3.22264 | + | 5.58178i | 0.116439 | + | 0.201678i | ||||
\(767\) | 3.46917 | + | 6.00879i | 0.125265 | + | 0.216965i | ||||
\(768\) | −1.33821 | + | 2.31784i | −0.0482883 | + | 0.0836378i | ||||
\(769\) | −2.48636 | −0.0896605 | −0.0448302 | − | 0.998995i | \(-0.514275\pi\) | ||||
−0.0448302 | + | 0.998995i | \(0.514275\pi\) | |||||||
\(770\) | −55.5802 | + | 27.9780i | −2.00297 | + | 1.00826i | ||||
\(771\) | −27.4575 | −0.988858 | ||||||||
\(772\) | 10.5081 | − | 18.2006i | 0.378195 | − | 0.655052i | ||||
\(773\) | −1.51521 | − | 2.62442i | −0.0544984 | − | 0.0943939i | 0.837489 | − | 0.546454i | \(-0.184023\pi\) |
−0.891988 | + | 0.452060i | \(0.850689\pi\) | |||||||
\(774\) | −7.78408 | − | 13.4824i | −0.279793 | − | 0.484615i | ||||
\(775\) | 20.9641 | − | 36.3109i | 0.753053 | − | 1.30433i | ||||
\(776\) | 12.8932 | 0.462838 | ||||||||
\(777\) | 20.2549 | + | 13.2950i | 0.726642 | + | 0.476956i | ||||
\(778\) | −13.8590 | −0.496868 | ||||||||
\(779\) | 5.26408 | − | 9.11765i | 0.188605 | − | 0.326674i | ||||
\(780\) | 30.8885 | + | 53.5004i | 1.10599 | + | 1.91562i | ||||
\(781\) | 2.63171 | + | 4.55825i | 0.0941699 | + | 0.163107i | ||||
\(782\) | −0.430199 | + | 0.745126i | −0.0153839 | + | 0.0266456i | ||||
\(783\) | 2.08813 | 0.0746236 | ||||||||
\(784\) | −6.95416 | − | 0.799757i | −0.248363 | − | 0.0285627i | ||||
\(785\) | −6.42790 | −0.229422 | ||||||||
\(786\) | −17.6052 | + | 30.4930i | −0.627955 | + | 1.08765i | ||||
\(787\) | −23.8794 | − | 41.3604i | −0.851209 | − | 1.47434i | −0.880117 | − | 0.474756i | \(-0.842536\pi\) |
0.0289080 | − | 0.999582i | \(-0.490797\pi\) | |||||||
\(788\) | 0.403061 | + | 0.698121i | 0.0143584 | + | 0.0248695i | ||||
\(789\) | −19.6823 | + | 34.0908i | −0.700709 | + | 1.21366i | ||||
\(790\) | 9.57803 | 0.340771 | ||||||||
\(791\) | −5.61101 | − | 3.68297i | −0.199505 | − | 0.130951i | ||||
\(792\) | 25.3634 | 0.901248 | ||||||||
\(793\) | 24.5542 | − | 42.5291i | 0.871944 | − | 1.51025i | ||||
\(794\) | 13.7830 | + | 23.8729i | 0.489141 | + | 0.847217i | ||||
\(795\) | −10.4830 | − | 18.1571i | −0.371794 | − | 0.643967i | ||||
\(796\) | −7.25800 | + | 12.5712i | −0.257253 | + | 0.445575i | ||||
\(797\) | −25.2116 | −0.893040 | −0.446520 | − | 0.894774i | \(-0.647337\pi\) | ||||
−0.446520 | + | 0.894774i | \(0.647337\pi\) | |||||||
\(798\) | −7.04050 | + | 3.54405i | −0.249231 | + | 0.125458i | ||||
\(799\) | −3.44646 | −0.121927 | ||||||||
\(800\) | 4.95133 | − | 8.57596i | 0.175056 | − | 0.303206i | ||||
\(801\) | 14.3356 | + | 24.8300i | 0.506524 | + | 0.877326i | ||||
\(802\) | 16.9164 | + | 29.3001i | 0.597340 | + | 1.03462i | ||||
\(803\) | −51.6009 | + | 89.3754i | −1.82096 | + | 3.15399i | ||||
\(804\) | −0.149094 | −0.00525814 | ||||||||
\(805\) | −0.584417 | + | 10.1969i | −0.0205980 | + | 0.359394i | ||||
\(806\) | 25.3161 | 0.891720 | ||||||||
\(807\) | −7.89280 | + | 13.6707i | −0.277840 | + | 0.481232i | ||||
\(808\) | 1.57012 | + | 2.71953i | 0.0552367 | + | 0.0956728i | ||||
\(809\) | −3.94272 | − | 6.82899i | −0.138619 | − | 0.240095i | 0.788355 | − | 0.615220i | \(-0.210933\pi\) |
−0.926974 | + | 0.375126i | \(0.877600\pi\) | |||||||
\(810\) | 8.02482 | − | 13.8994i | 0.281964 | − | 0.488375i | ||||
\(811\) | −4.28998 | −0.150641 | −0.0753207 | − | 0.997159i | \(-0.523998\pi\) | ||||
−0.0753207 | + | 0.997159i | \(0.523998\pi\) | |||||||
\(812\) | −0.101543 | + | 1.77173i | −0.00356347 | + | 0.0621754i | ||||
\(813\) | −37.0129 | −1.29810 | ||||||||
\(814\) | 10.4226 | − | 18.0525i | 0.365313 | − | 0.632740i | ||||
\(815\) | 14.8028 | + | 25.6391i | 0.518518 | + | 0.898100i | ||||
\(816\) | −1.15139 | − | 1.99426i | −0.0403066 | − | 0.0698131i | ||||
\(817\) | 2.08127 | − | 3.60486i | 0.0728143 | − | 0.126118i | ||||
\(818\) | −18.8614 | −0.659475 | ||||||||
\(819\) | 58.8264 | − | 29.6120i | 2.05556 | − | 1.03473i | ||||
\(820\) | 36.5123 | 1.27506 | ||||||||
\(821\) | −12.1131 | + | 20.9806i | −0.422751 | + | 0.732227i | −0.996207 | − | 0.0870095i | \(-0.972269\pi\) |
0.573456 | + | 0.819236i | \(0.305602\pi\) | |||||||
\(822\) | 14.9183 | + | 25.8393i | 0.520337 | + | 0.901250i | ||||
\(823\) | −0.876466 | − | 1.51808i | −0.0305517 | − | 0.0529170i | 0.850345 | − | 0.526225i | \(-0.176393\pi\) |
−0.880897 | + | 0.473308i | \(0.843060\pi\) | |||||||
\(824\) | −1.60924 | + | 2.78728i | −0.0560605 | + | 0.0970996i | ||||
\(825\) | −161.468 | −5.62160 | ||||||||
\(826\) | −2.56666 | − | 1.68471i | −0.0893054 | − | 0.0586185i | ||||
\(827\) | −32.8224 | −1.14135 | −0.570674 | − | 0.821177i | \(-0.693318\pi\) | ||||
−0.570674 | + | 0.821177i | \(0.693318\pi\) | |||||||
\(828\) | 2.08159 | − | 3.60541i | 0.0723401 | − | 0.125297i | ||||
\(829\) | −1.91748 | − | 3.32118i | −0.0665969 | − | 0.115349i | 0.830804 | − | 0.556565i | \(-0.187881\pi\) |
−0.897401 | + | 0.441215i | \(0.854547\pi\) | |||||||
\(830\) | 2.02680 | + | 3.51051i | 0.0703511 | + | 0.121852i | ||||
\(831\) | 31.5649 | − | 54.6720i | 1.09497 | − | 1.89655i | ||||
\(832\) | 5.97919 | 0.207291 | ||||||||
\(833\) | 3.58759 | − | 4.83767i | 0.124303 | − | 0.167615i | ||||
\(834\) | 3.21995 | 0.111498 | ||||||||
\(835\) | 47.7696 | − | 82.7394i | 1.65314 | − | 2.86332i | ||||
\(836\) | 3.39076 | + | 5.87297i | 0.117272 | + | 0.203121i | ||||
\(837\) | 6.59054 | + | 11.4152i | 0.227802 | + | 0.394565i | ||||
\(838\) | −17.5787 | + | 30.4472i | −0.607245 | + | 1.05178i | ||||
\(839\) | −9.38392 | −0.323969 | −0.161984 | − | 0.986793i | \(-0.551789\pi\) | ||||
−0.161984 | + | 0.986793i | \(0.551789\pi\) | |||||||
\(840\) | −22.8527 | − | 15.0002i | −0.788495 | − | 0.517554i | ||||
\(841\) | −28.5501 | −0.984486 | ||||||||
\(842\) | −14.0620 | + | 24.3562i | −0.484610 | + | 0.839368i | ||||
\(843\) | −31.1777 | − | 54.0014i | −1.07382 | − | 1.85991i | ||||
\(844\) | −12.0951 | − | 20.9494i | −0.416332 | − | 0.721108i | ||||
\(845\) | 43.9133 | − | 76.0601i | 1.51066 | − | 2.61655i | ||||
\(846\) | 16.6763 | 0.573342 | ||||||||
\(847\) | 61.7187 | − | 31.0680i | 2.12068 | − | 1.06751i | ||||
\(848\) | −2.02923 | −0.0696841 | ||||||||
\(849\) | 42.5587 | − | 73.7138i | 1.46061 | − | 2.52985i | ||||
\(850\) | 4.26011 | + | 7.37873i | 0.146121 | + | 0.253088i | ||||
\(851\) | −1.71078 | − | 2.96316i | −0.0586449 | − | 0.101576i | ||||
\(852\) | −1.15613 | + | 2.00248i | −0.0396085 | + | 0.0686039i | ||||
\(853\) | 47.5099 | 1.62671 | 0.813354 | − | 0.581769i | \(-0.197639\pi\) | ||||
0.813354 | + | 0.581769i | \(0.197639\pi\) | |||||||
\(854\) | −1.24338 | + | 21.6945i | −0.0425476 | + | 0.742372i | ||||
\(855\) | −17.8896 | −0.611812 | ||||||||
\(856\) | −0.477093 | + | 0.826349i | −0.0163067 | + | 0.0282440i | ||||
\(857\) | 4.30850 | + | 7.46255i | 0.147176 | + | 0.254916i | 0.930183 | − | 0.367097i | \(-0.119648\pi\) |
−0.783007 | + | 0.622013i | \(0.786315\pi\) | |||||||
\(858\) | −48.7469 | − | 84.4321i | −1.66419 | − | 2.88246i | ||||
\(859\) | 5.58665 | − | 9.67637i | 0.190614 | − | 0.330153i | −0.754840 | − | 0.655909i | \(-0.772285\pi\) |
0.945454 | + | 0.325756i | \(0.105619\pi\) | |||||||
\(860\) | 14.4359 | 0.492261 | ||||||||
\(861\) | 3.83222 | − | 66.8647i | 0.130602 | − | 2.27874i | ||||
\(862\) | 5.77586 | 0.196727 | ||||||||
\(863\) | 2.19553 | − | 3.80276i | 0.0747366 | − | 0.129448i | −0.826235 | − | 0.563325i | \(-0.809522\pi\) |
0.900972 | + | 0.433878i | \(0.142855\pi\) | |||||||
\(864\) | 1.55656 | + | 2.69605i | 0.0529554 | + | 0.0917214i | ||||
\(865\) | −3.51619 | − | 6.09023i | −0.119554 | − | 0.207074i | ||||
\(866\) | −14.4788 | + | 25.0780i | −0.492009 | + | 0.852185i | ||||
\(867\) | −43.5177 | −1.47794 | ||||||||
\(868\) | −10.0060 | + | 5.03682i | −0.339625 | + | 0.170961i | ||||
\(869\) | −15.1156 | −0.512763 | ||||||||
\(870\) | −3.46509 | + | 6.00171i | −0.117478 | + | 0.203477i | ||||
\(871\) | 0.166540 | + | 0.288456i | 0.00564300 | + | 0.00977397i | ||||
\(872\) | −6.40267 | − | 11.0897i | −0.216822 | − | 0.375546i | ||||
\(873\) | 26.8383 | − | 46.4852i | 0.908337 | − | 1.57329i | ||||
\(874\) | 1.11313 | 0.0376521 | ||||||||
\(875\) | 41.8618 | + | 27.4774i | 1.41519 | + | 0.928905i | ||||
\(876\) | −45.3375 | −1.53181 | ||||||||
\(877\) | 7.68898 | − | 13.3177i | 0.259638 | − | 0.449707i | −0.706507 | − | 0.707706i | \(-0.749730\pi\) |
0.966145 | + | 0.258000i | \(0.0830633\pi\) | |||||||
\(878\) | 8.40340 | + | 14.5551i | 0.283601 | + | 0.491212i | ||||
\(879\) | 23.5961 | + | 40.8697i | 0.795878 | + | 1.37850i | ||||
\(880\) | −11.7594 | + | 20.3678i | −0.396408 | + | 0.686600i | ||||
\(881\) | 30.7005 | 1.03433 | 0.517163 | − | 0.855887i | \(-0.326988\pi\) | ||||
0.517163 | + | 0.855887i | \(0.326988\pi\) | |||||||
\(882\) | −17.3591 | + | 23.4079i | −0.584513 | + | 0.788184i | ||||
\(883\) | −14.0021 | −0.471209 | −0.235604 | − | 0.971849i | \(-0.575707\pi\) | ||||
−0.235604 | + | 0.971849i | \(0.575707\pi\) | |||||||
\(884\) | −2.57224 | + | 4.45525i | −0.0865137 | + | 0.149846i | ||||
\(885\) | −5.99472 | − | 10.3832i | −0.201510 | − | 0.349026i | ||||
\(886\) | 5.00824 | + | 8.67452i | 0.168255 | + | 0.291426i | ||||
\(887\) | −20.7021 | + | 35.8572i | −0.695110 | + | 1.20397i | 0.275034 | + | 0.961435i | \(0.411311\pi\) |
−0.970144 | + | 0.242531i | \(0.922022\pi\) | |||||||
\(888\) | 9.15751 | 0.307306 | ||||||||
\(889\) | 29.0274 | + | 19.0531i | 0.973549 | + | 0.639021i | ||||
\(890\) | −26.5861 | −0.891167 | ||||||||
\(891\) | −12.6644 | + | 21.9354i | −0.424274 | + | 0.734865i | ||||
\(892\) | −5.46300 | − | 9.46219i | −0.182915 | − | 0.316818i | ||||
\(893\) | 2.22941 | + | 3.86144i | 0.0746042 | + | 0.129218i | ||||
\(894\) | 19.6235 | − | 33.9888i | 0.656307 | − | 1.13676i | ||||
\(895\) | −44.0278 | −1.47169 | ||||||||
\(896\) | −2.36323 | + | 1.18960i | −0.0789499 | + | 0.0397418i | ||||
\(897\) | −16.0028 | −0.534316 | ||||||||
\(898\) | −18.3308 | + | 31.7498i | −0.611705 | + | 1.05950i | ||||
\(899\) | 1.41999 | + | 2.45949i | 0.0473592 | + | 0.0820285i | ||||
\(900\) | −20.6133 | − | 35.7032i | −0.687108 | − | 1.19011i | ||||
\(901\) | 0.872972 | − | 1.51203i | 0.0290829 | − | 0.0503731i | ||||
\(902\) | −57.6221 | −1.91861 | ||||||||
\(903\) | 1.51515 | − | 26.4364i | 0.0504211 | − | 0.879748i | ||||
\(904\) | −2.53681 | −0.0843730 | ||||||||
\(905\) | 1.21025 | − | 2.09621i | 0.0402299 | − | 0.0696803i | ||||
\(906\) | 8.17779 | + | 14.1643i | 0.271689 | + | 0.470579i | ||||
\(907\) | −24.4059 | − | 42.2723i | −0.810386 | − | 1.40363i | −0.912594 | − | 0.408867i | \(-0.865924\pi\) |
0.102208 | − | 0.994763i | \(-0.467409\pi\) | |||||||
\(908\) | −12.8334 | + | 22.2281i | −0.425891 | + | 0.737665i | ||||
\(909\) | 13.0734 | 0.433616 | ||||||||
\(910\) | −3.49434 | + | 60.9693i | −0.115836 | + | 2.02111i | ||||
\(911\) | 11.6605 | 0.386329 | 0.193164 | − | 0.981166i | \(-0.438125\pi\) | ||||
0.193164 | + | 0.981166i | \(0.438125\pi\) | |||||||
\(912\) | −1.48959 | + | 2.58005i | −0.0493254 | + | 0.0854340i | ||||
\(913\) | −3.19860 | − | 5.54014i | −0.105858 | − | 0.183352i | ||||
\(914\) | −13.6998 | − | 23.7287i | −0.453148 | − | 0.784876i | ||||
\(915\) | −42.4295 | + | 73.4901i | −1.40268 | + | 2.42951i | ||||
\(916\) | 22.5932 | 0.746499 | ||||||||
\(917\) | −31.0901 | + | 15.6502i | −1.02669 | + | 0.516814i | ||||
\(918\) | −2.67853 | −0.0884045 | ||||||||
\(919\) | −2.84767 | + | 4.93232i | −0.0939361 | + | 0.162702i | −0.909164 | − | 0.416438i | \(-0.863278\pi\) |
0.815228 | + | 0.579140i | \(0.196612\pi\) | |||||||
\(920\) | 1.93020 | + | 3.34320i | 0.0636368 | + | 0.110222i | ||||
\(921\) | 16.4088 | + | 28.4209i | 0.540688 | + | 0.936499i | ||||
\(922\) | −10.8568 | + | 18.8046i | −0.357551 | + | 0.619296i | ||||
\(923\) | 5.16568 | 0.170030 | ||||||||
\(924\) | 36.0652 | + | 23.6726i | 1.18646 | + | 0.778771i | ||||
\(925\) | −33.8826 | −1.11405 | ||||||||
\(926\) | 19.6547 | − | 34.0429i | 0.645892 | − | 1.11872i | ||||
\(927\) | 6.69954 | + | 11.6039i | 0.220042 | + | 0.381124i | ||||
\(928\) | 0.335374 | + | 0.580886i | 0.0110092 | + | 0.0190685i | ||||
\(929\) | 2.61603 | − | 4.53110i | 0.0858293 | − | 0.148661i | −0.819915 | − | 0.572485i | \(-0.805979\pi\) |
0.905744 | + | 0.423825i | \(0.139313\pi\) | |||||||
\(930\) | −43.7460 | −1.43449 | ||||||||
\(931\) | −7.74087 | − | 0.890231i | −0.253697 | − | 0.0291761i | ||||
\(932\) | −3.51245 | −0.115054 | ||||||||
\(933\) | −4.30982 | + | 7.46482i | −0.141097 | + | 0.244387i | ||||
\(934\) | −11.0602 | − | 19.1568i | −0.361900 | − | 0.626829i | ||||
\(935\) | −10.1177 | − | 17.5244i | −0.330885 | − | 0.573110i | ||||
\(936\) | 12.4462 | − | 21.5574i | 0.406817 | − | 0.704627i | ||||
\(937\) | −17.8841 | −0.584249 | −0.292124 | − | 0.956380i | \(-0.594362\pi\) | ||||
−0.292124 | + | 0.956380i | \(0.594362\pi\) | |||||||
\(938\) | −0.123214 | − | 0.0808757i | −0.00402309 | − | 0.00264069i | ||||
\(939\) | −57.0590 | −1.86205 | ||||||||
\(940\) | −7.73172 | + | 13.3917i | −0.252181 | + | 0.436790i | ||||
\(941\) | −12.3455 | − | 21.3830i | −0.402451 | − | 0.697066i | 0.591570 | − | 0.806254i | \(-0.298508\pi\) |
−0.994021 | + | 0.109187i | \(0.965175\pi\) | |||||||
\(942\) | 2.22823 | + | 3.85941i | 0.0725996 | + | 0.125746i | ||||
\(943\) | −4.72909 | + | 8.19102i | −0.154000 | + | 0.266736i | ||||
\(944\) | −1.16042 | −0.0377684 | ||||||||
\(945\) | −28.4011 | + | 14.2965i | −0.923886 | + | 0.465066i | ||||
\(946\) | −22.7822 | −0.740712 | ||||||||
\(947\) | −28.0570 | + | 48.5961i | −0.911730 | + | 1.57916i | −0.100109 | + | 0.994976i | \(0.531919\pi\) |
−0.811620 | + | 0.584186i | \(0.801414\pi\) | |||||||
\(948\) | −3.32022 | − | 5.75079i | −0.107836 | − | 0.186777i | ||||
\(949\) | 50.6427 | + | 87.7158i | 1.64393 | + | 2.84737i | ||||
\(950\) | 5.51146 | − | 9.54614i | 0.178816 | − | 0.309718i | ||||
\(951\) | 44.9758 | 1.45844 | ||||||||
\(952\) | 0.130254 | − | 2.27267i | 0.00422154 | − | 0.0736576i | ||||
\(953\) | −16.8019 | −0.544268 | −0.272134 | − | 0.962259i | \(-0.587729\pi\) | ||||
−0.272134 | + | 0.962259i | \(0.587729\pi\) | |||||||
\(954\) | −4.22402 | + | 7.31622i | −0.136758 | + | 0.236871i | ||||
\(955\) | 13.6685 | + | 23.6745i | 0.442302 | + | 0.766090i | ||||
\(956\) | −1.17609 | − | 2.03705i | −0.0380375 | − | 0.0658828i | ||||
\(957\) | 5.46846 | − | 9.47165i | 0.176770 | − | 0.306175i | ||||
\(958\) | −4.54458 | −0.146829 | ||||||||
\(959\) | −1.68767 | + | 29.4466i | −0.0544979 | + | 0.950879i | ||||
\(960\) | −10.3320 | −0.333464 | ||||||||
\(961\) | 6.53649 | − | 11.3215i | 0.210854 | − | 0.365211i | ||||
\(962\) | −10.2291 | − | 17.7173i | −0.329799 | − | 0.571229i | ||||
\(963\) | 1.98622 | + | 3.44023i | 0.0640050 | + | 0.110860i | ||||
\(964\) | 11.1517 | − | 19.3153i | 0.359172 | − | 0.622105i | ||||
\(965\) | 81.1309 | 2.61169 | ||||||||
\(966\) | 6.32497 | − | 3.18386i | 0.203502 | − | 0.102439i | ||||
\(967\) | −16.5124 | −0.531005 | −0.265502 | − | 0.964110i | \(-0.585538\pi\) | ||||
−0.265502 | + | 0.964110i | \(0.585538\pi\) | |||||||
\(968\) | 13.0581 | − | 22.6174i | 0.419705 | − | 0.726950i | ||||
\(969\) | −1.28164 | − | 2.21987i | −0.0411723 | − | 0.0713124i | ||||
\(970\) | 24.8864 | + | 43.1045i | 0.799054 | + | 1.38400i | ||||
\(971\) | −15.5960 | + | 27.0131i | −0.500500 | + | 0.866891i | 0.499500 | + | 0.866314i | \(0.333517\pi\) |
−1.00000 | 0.000577094i | \(0.999816\pi\) | ||||||||
\(972\) | −20.4666 | −0.656466 | ||||||||
\(973\) | 2.66103 | + | 1.74666i | 0.0853089 | + | 0.0559953i | ||||
\(974\) | 26.9794 | 0.864477 | ||||||||
\(975\) | −79.2350 | + | 137.239i | −2.53755 | + | 4.39517i | ||||
\(976\) | 4.10661 | + | 7.11286i | 0.131449 | + | 0.227677i | ||||
\(977\) | 2.74471 | + | 4.75398i | 0.0878112 | + | 0.152093i | 0.906586 | − | 0.422022i | \(-0.138679\pi\) |
−0.818774 | + | 0.574115i | \(0.805346\pi\) | |||||||
\(978\) | 10.2627 | − | 17.7756i | 0.328166 | − | 0.568401i | ||||
\(979\) | 41.9570 | 1.34095 | ||||||||
\(980\) | −10.7492 | − | 24.7929i | −0.343370 | − | 0.791979i | ||||
\(981\) | −53.3108 | −1.70208 | ||||||||
\(982\) | 16.6342 | − | 28.8113i | 0.530818 | − | 0.919404i | ||||
\(983\) | 9.35356 | + | 16.2008i | 0.298332 | + | 0.516726i | 0.975755 | − | 0.218868i | \(-0.0702363\pi\) |
−0.677422 | + | 0.735594i | \(0.736903\pi\) | |||||||
\(984\) | −12.6570 | − | 21.9225i | −0.403490 | − | 0.698864i | ||||
\(985\) | −1.55597 | + | 2.69503i | −0.0495775 | + | 0.0858707i | ||||
\(986\) | −0.577110 | −0.0183789 | ||||||||
\(987\) | 23.7127 | + | 15.5646i | 0.754783 | + | 0.495427i | ||||
\(988\) | 6.65560 | 0.211743 | ||||||||
\(989\) | −1.86975 | + | 3.23850i | −0.0594545 | + | 0.102978i | ||||
\(990\) | 48.9563 | + | 84.7948i | 1.55593 | + | 2.69496i | ||||
\(991\) | 16.4453 | + | 28.4841i | 0.522403 | + | 0.904829i | 0.999660 | + | 0.0260650i | \(0.00829769\pi\) |
−0.477257 | + | 0.878764i | \(0.658369\pi\) | |||||||
\(992\) | −2.11702 | + | 3.66678i | −0.0672153 | + | 0.116420i | ||||
\(993\) | 25.6640 | 0.814423 | ||||||||
\(994\) | −2.04169 | + | 1.02775i | −0.0647586 | + | 0.0325982i | ||||
\(995\) | −56.0375 | −1.77651 | ||||||||
\(996\) | 1.40518 | − | 2.43384i | 0.0445247 | − | 0.0771190i | ||||
\(997\) | 14.7515 | + | 25.5504i | 0.467185 | + | 0.809189i | 0.999297 | − | 0.0374852i | \(-0.0119347\pi\) |
−0.532112 | + | 0.846674i | \(0.678601\pi\) | |||||||
\(998\) | 9.86704 | + | 17.0902i | 0.312336 | + | 0.540981i | ||||
\(999\) | 5.32588 | − | 9.22470i | 0.168503 | − | 0.291857i |
(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 | 322.2.e.d.93.1 | ✓ | 8 | |
7.2 | even | 3 | 2254.2.a.u.1.4 | 4 | |||
7.4 | even | 3 | inner | 322.2.e.d.277.1 | yes | 8 | |
7.5 | odd | 6 | 2254.2.a.r.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.2.e.d.93.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
322.2.e.d.277.1 | yes | 8 | 7.4 | even | 3 | inner | |
2254.2.a.r.1.1 | 4 | 7.5 | odd | 6 | |||
2254.2.a.u.1.4 | 4 | 7.2 | even | 3 |