Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(277,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.i (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: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 8 x^{10} - 3 x^{9} + 42 x^{8} - 15 x^{7} + 101 x^{6} + 6 x^{5} + 150 x^{4} - 28 x^{3} + 40 x^{2} + 8 x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 415.4 | ||
Root | \(0.296764 + 0.514011i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.415 |
Dual form | 483.2.i.f.277.4 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.296764 | − | 0.514011i | 0.209844 | − | 0.363460i | −0.741821 | − | 0.670598i | \(-0.766038\pi\) |
0.951665 | + | 0.307137i | \(0.0993711\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0.823862 | + | 1.42697i | 0.411931 | + | 0.713485i | ||||
\(5\) | 1.57560 | − | 2.72902i | 0.704631 | − | 1.22046i | −0.262194 | − | 0.965015i | \(-0.584446\pi\) |
0.966825 | − | 0.255441i | \(-0.0822206\pi\) | |||||||
\(6\) | 0.593528 | 0.242307 | ||||||||
\(7\) | −1.69175 | + | 2.03420i | −0.639422 | + | 0.768856i | ||||
\(8\) | 2.16503 | 0.765453 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.935165 | − | 1.61975i | −0.295725 | − | 0.512211i | ||||
\(11\) | 3.27267 | + | 5.66843i | 0.986747 | + | 1.70910i | 0.633900 | + | 0.773415i | \(0.281453\pi\) |
0.352847 | + | 0.935681i | \(0.385214\pi\) | |||||||
\(12\) | −0.823862 | + | 1.42697i | −0.237828 | + | 0.411931i | ||||
\(13\) | −0.692965 | −0.192194 | −0.0960970 | − | 0.995372i | \(-0.530636\pi\) | ||||
−0.0960970 | + | 0.995372i | \(0.530636\pi\) | |||||||
\(14\) | 0.543550 | + | 1.47326i | 0.145270 | + | 0.393744i | ||||
\(15\) | 3.15120 | 0.813637 | ||||||||
\(16\) | −1.00522 | + | 1.74109i | −0.251305 | + | 0.435273i | ||||
\(17\) | −3.42208 | − | 5.92722i | −0.829977 | − | 1.43756i | −0.898055 | − | 0.439883i | \(-0.855020\pi\) |
0.0680776 | − | 0.997680i | \(-0.478313\pi\) | |||||||
\(18\) | 0.296764 | + | 0.514011i | 0.0699480 | + | 0.121153i | ||||
\(19\) | 1.45831 | − | 2.52587i | 0.334560 | − | 0.579475i | −0.648840 | − | 0.760925i | \(-0.724746\pi\) |
0.983400 | + | 0.181450i | \(0.0580791\pi\) | |||||||
\(20\) | 5.19231 | 1.16104 | ||||||||
\(21\) | −2.60755 | − | 0.447998i | −0.569013 | − | 0.0977613i | ||||
\(22\) | 3.88485 | 0.828252 | ||||||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | ||||
\(24\) | 1.08251 | + | 1.87497i | 0.220967 | + | 0.382726i | ||||
\(25\) | −2.46504 | − | 4.26958i | −0.493009 | − | 0.853916i | ||||
\(26\) | −0.205647 | + | 0.356192i | −0.0403308 | + | 0.0698549i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.29652 | − | 0.738178i | −0.811965 | − | 0.139502i | ||||
\(29\) | 2.94619 | 0.547094 | 0.273547 | − | 0.961859i | \(-0.411803\pi\) | ||||
0.273547 | + | 0.961859i | \(0.411803\pi\) | |||||||
\(30\) | 0.935165 | − | 1.61975i | 0.170737 | − | 0.295725i | ||||
\(31\) | 0.269666 | + | 0.467076i | 0.0484335 | + | 0.0838893i | 0.889226 | − | 0.457469i | \(-0.151244\pi\) |
−0.840792 | + | 0.541358i | \(0.817910\pi\) | |||||||
\(32\) | 2.76166 | + | 4.78333i | 0.488196 | + | 0.845581i | ||||
\(33\) | −3.27267 | + | 5.66843i | −0.569699 | + | 0.986747i | ||||
\(34\) | −4.06221 | −0.696663 | ||||||||
\(35\) | 2.88586 | + | 7.82192i | 0.487799 | + | 1.32215i | ||||
\(36\) | −1.64772 | −0.274621 | ||||||||
\(37\) | 1.44806 | − | 2.50812i | 0.238060 | − | 0.412332i | −0.722097 | − | 0.691791i | \(-0.756822\pi\) |
0.960158 | + | 0.279459i | \(0.0901551\pi\) | |||||||
\(38\) | −0.865550 | − | 1.49918i | −0.140411 | − | 0.243198i | ||||
\(39\) | −0.346483 | − | 0.600126i | −0.0554816 | − | 0.0960970i | ||||
\(40\) | 3.41122 | − | 5.90841i | 0.539362 | − | 0.934202i | ||||
\(41\) | 9.26871 | 1.44753 | 0.723765 | − | 0.690047i | \(-0.242410\pi\) | ||||
0.723765 | + | 0.690047i | \(0.242410\pi\) | |||||||
\(42\) | −1.00410 | + | 1.20736i | −0.154936 | + | 0.186299i | ||||
\(43\) | −4.27043 | −0.651235 | −0.325617 | − | 0.945502i | \(-0.605572\pi\) | ||||
−0.325617 | + | 0.945502i | \(0.605572\pi\) | |||||||
\(44\) | −5.39246 | + | 9.34001i | −0.812943 | + | 1.40806i | ||||
\(45\) | 1.57560 | + | 2.72902i | 0.234877 | + | 0.406819i | ||||
\(46\) | −0.296764 | − | 0.514011i | −0.0437555 | − | 0.0757867i | ||||
\(47\) | −5.23372 | + | 9.06507i | −0.763416 | + | 1.32228i | 0.177664 | + | 0.984091i | \(0.443146\pi\) |
−0.941080 | + | 0.338184i | \(0.890187\pi\) | |||||||
\(48\) | −2.01044 | −0.290182 | ||||||||
\(49\) | −1.27596 | − | 6.88273i | −0.182279 | − | 0.983247i | ||||
\(50\) | −2.92615 | −0.413820 | ||||||||
\(51\) | 3.42208 | − | 5.92722i | 0.479188 | − | 0.829977i | ||||
\(52\) | −0.570908 | − | 0.988841i | −0.0791707 | − | 0.137128i | ||||
\(53\) | −6.28744 | − | 10.8902i | −0.863647 | − | 1.49588i | −0.868385 | − | 0.495891i | \(-0.834841\pi\) |
0.00473784 | − | 0.999989i | \(-0.498492\pi\) | |||||||
\(54\) | −0.296764 | + | 0.514011i | −0.0403845 | + | 0.0699480i | ||||
\(55\) | 20.6257 | 2.78117 | ||||||||
\(56\) | −3.66269 | + | 4.40410i | −0.489447 | + | 0.588523i | ||||
\(57\) | 2.91662 | 0.386316 | ||||||||
\(58\) | 0.874324 | − | 1.51437i | 0.114804 | − | 0.198847i | ||||
\(59\) | −3.35163 | − | 5.80519i | −0.436345 | − | 0.755772i | 0.561059 | − | 0.827776i | \(-0.310394\pi\) |
−0.997404 | + | 0.0720038i | \(0.977061\pi\) | |||||||
\(60\) | 2.59616 | + | 4.49668i | 0.335162 | + | 0.580518i | ||||
\(61\) | −2.65091 | + | 4.59152i | −0.339415 | + | 0.587884i | −0.984323 | − | 0.176377i | \(-0.943562\pi\) |
0.644908 | + | 0.764260i | \(0.276896\pi\) | |||||||
\(62\) | 0.320109 | 0.0406539 | ||||||||
\(63\) | −0.915795 | − | 2.48220i | −0.115379 | − | 0.312728i | ||||
\(64\) | −0.742642 | −0.0928303 | ||||||||
\(65\) | −1.09184 | + | 1.89112i | −0.135426 | + | 0.234564i | ||||
\(66\) | 1.94242 | + | 3.36437i | 0.239096 | + | 0.414126i | ||||
\(67\) | 1.36814 | + | 2.36969i | 0.167145 | + | 0.289504i | 0.937415 | − | 0.348214i | \(-0.113212\pi\) |
−0.770270 | + | 0.637718i | \(0.779878\pi\) | |||||||
\(68\) | 5.63865 | − | 9.76643i | 0.683787 | − | 1.18435i | ||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 4.87697 | + | 0.837905i | 0.582909 | + | 0.100149i | ||||
\(71\) | −0.587217 | −0.0696899 | −0.0348449 | − | 0.999393i | \(-0.511094\pi\) | ||||
−0.0348449 | + | 0.999393i | \(0.511094\pi\) | |||||||
\(72\) | −1.08251 | + | 1.87497i | −0.127575 | + | 0.220967i | ||||
\(73\) | −5.26330 | − | 9.11630i | −0.616023 | − | 1.06698i | −0.990204 | − | 0.139627i | \(-0.955410\pi\) |
0.374181 | − | 0.927356i | \(-0.377924\pi\) | |||||||
\(74\) | −0.859467 | − | 1.48864i | −0.0999110 | − | 0.173051i | ||||
\(75\) | 2.46504 | − | 4.26958i | 0.284639 | − | 0.493009i | ||||
\(76\) | 4.80579 | 0.551262 | ||||||||
\(77\) | −17.0673 | − | 2.93230i | −1.94500 | − | 0.334167i | ||||
\(78\) | −0.411295 | −0.0465699 | ||||||||
\(79\) | 6.69351 | − | 11.5935i | 0.753078 | − | 1.30437i | −0.193246 | − | 0.981150i | \(-0.561902\pi\) |
0.946324 | − | 0.323219i | \(-0.104765\pi\) | |||||||
\(80\) | 3.16766 | + | 5.48654i | 0.354155 | + | 0.613414i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 2.75062 | − | 4.76422i | 0.303755 | − | 0.526120i | ||||
\(83\) | −9.77501 | −1.07295 | −0.536473 | − | 0.843917i | \(-0.680244\pi\) | ||||
−0.536473 | + | 0.843917i | \(0.680244\pi\) | |||||||
\(84\) | −1.50898 | − | 4.08998i | −0.164643 | − | 0.446254i | ||||
\(85\) | −21.5674 | −2.33931 | ||||||||
\(86\) | −1.26731 | + | 2.19505i | −0.136658 | + | 0.236698i | ||||
\(87\) | 1.47310 | + | 2.55148i | 0.157932 | + | 0.273547i | ||||
\(88\) | 7.08542 | + | 12.2723i | 0.755308 | + | 1.30823i | ||||
\(89\) | −1.46470 | + | 2.53693i | −0.155258 | + | 0.268914i | −0.933153 | − | 0.359480i | \(-0.882954\pi\) |
0.777895 | + | 0.628394i | \(0.216287\pi\) | |||||||
\(90\) | 1.87033 | 0.197150 | ||||||||
\(91\) | 1.17232 | − | 1.40963i | 0.122893 | − | 0.147770i | ||||
\(92\) | 1.64772 | 0.171787 | ||||||||
\(93\) | −0.269666 | + | 0.467076i | −0.0279631 | + | 0.0484335i | ||||
\(94\) | 3.10636 | + | 5.38037i | 0.320397 | + | 0.554943i | ||||
\(95\) | −4.59544 | − | 7.95953i | −0.471482 | − | 0.816631i | ||||
\(96\) | −2.76166 | + | 4.78333i | −0.281860 | + | 0.488196i | ||||
\(97\) | −8.14170 | −0.826664 | −0.413332 | − | 0.910580i | \(-0.635635\pi\) | ||||
−0.413332 | + | 0.910580i | \(0.635635\pi\) | |||||||
\(98\) | −3.91645 | − | 1.38669i | −0.395622 | − | 0.140077i | ||||
\(99\) | −6.54534 | −0.657831 | ||||||||
\(100\) | 4.06171 | − | 7.03509i | 0.406171 | − | 0.703509i | ||||
\(101\) | 0.0666245 | + | 0.115397i | 0.00662939 | + | 0.0114824i | 0.869321 | − | 0.494248i | \(-0.164556\pi\) |
−0.862692 | + | 0.505730i | \(0.831223\pi\) | |||||||
\(102\) | −2.03110 | − | 3.51798i | −0.201109 | − | 0.348332i | ||||
\(103\) | 5.50533 | − | 9.53551i | 0.542456 | − | 0.939562i | −0.456306 | − | 0.889823i | \(-0.650828\pi\) |
0.998762 | − | 0.0497387i | \(-0.0158389\pi\) | |||||||
\(104\) | −1.50029 | −0.147115 | ||||||||
\(105\) | −5.33105 | + | 6.41019i | −0.520258 | + | 0.625570i | ||||
\(106\) | −7.46355 | −0.724924 | ||||||||
\(107\) | 4.28755 | − | 7.42625i | 0.414493 | − | 0.717923i | −0.580882 | − | 0.813988i | \(-0.697292\pi\) |
0.995375 | + | 0.0960649i | \(0.0306256\pi\) | |||||||
\(108\) | −0.823862 | − | 1.42697i | −0.0792762 | − | 0.137310i | ||||
\(109\) | −5.64113 | − | 9.77072i | −0.540322 | − | 0.935865i | −0.998885 | − | 0.0472034i | \(-0.984969\pi\) |
0.458563 | − | 0.888662i | \(-0.348364\pi\) | |||||||
\(110\) | 6.12097 | − | 10.6018i | 0.583612 | − | 1.01084i | ||||
\(111\) | 2.89613 | 0.274888 | ||||||||
\(112\) | −1.84115 | − | 4.99032i | −0.173973 | − | 0.471541i | ||||
\(113\) | 3.14165 | 0.295541 | 0.147771 | − | 0.989022i | \(-0.452790\pi\) | ||||
0.147771 | + | 0.989022i | \(0.452790\pi\) | |||||||
\(114\) | 0.865550 | − | 1.49918i | 0.0810662 | − | 0.140411i | ||||
\(115\) | −1.57560 | − | 2.72902i | −0.146926 | − | 0.254483i | ||||
\(116\) | 2.42726 | + | 4.20413i | 0.225365 | + | 0.390344i | ||||
\(117\) | 0.346483 | − | 0.600126i | 0.0320323 | − | 0.0554816i | ||||
\(118\) | −3.97858 | −0.366258 | ||||||||
\(119\) | 17.8465 | + | 3.06618i | 1.63598 | + | 0.281076i | ||||
\(120\) | 6.82244 | 0.622801 | ||||||||
\(121\) | −15.9207 | + | 27.5755i | −1.44734 | + | 2.50687i | ||||
\(122\) | 1.57339 | + | 2.72520i | 0.142448 | + | 0.246728i | ||||
\(123\) | 4.63435 | + | 8.02694i | 0.417866 | + | 0.723765i | ||||
\(124\) | −0.444336 | + | 0.769612i | −0.0399025 | + | 0.0691132i | ||||
\(125\) | 0.220311 | 0.0197052 | ||||||||
\(126\) | −1.54765 | − | 0.265900i | −0.137876 | − | 0.0236882i | ||||
\(127\) | −12.9337 | −1.14768 | −0.573841 | − | 0.818967i | \(-0.694547\pi\) | ||||
−0.573841 | + | 0.818967i | \(0.694547\pi\) | |||||||
\(128\) | −5.74370 | + | 9.94838i | −0.507676 | + | 0.879321i | ||||
\(129\) | −2.13522 | − | 3.69830i | −0.187995 | − | 0.325617i | ||||
\(130\) | 0.648037 | + | 1.12243i | 0.0568366 | + | 0.0984438i | ||||
\(131\) | −3.07333 | + | 5.32317i | −0.268518 | + | 0.465088i | −0.968479 | − | 0.249094i | \(-0.919867\pi\) |
0.699961 | + | 0.714181i | \(0.253201\pi\) | |||||||
\(132\) | −10.7849 | −0.938706 | ||||||||
\(133\) | 2.67103 | + | 7.23965i | 0.231608 | + | 0.627757i | ||||
\(134\) | 1.62406 | 0.140298 | ||||||||
\(135\) | −1.57560 | + | 2.72902i | −0.135606 | + | 0.234877i | ||||
\(136\) | −7.40891 | − | 12.8326i | −0.635309 | − | 1.10039i | ||||
\(137\) | 9.80611 | + | 16.9847i | 0.837792 | + | 1.45110i | 0.891737 | + | 0.452555i | \(0.149487\pi\) |
−0.0539443 | + | 0.998544i | \(0.517179\pi\) | |||||||
\(138\) | 0.296764 | − | 0.514011i | 0.0252622 | − | 0.0437555i | ||||
\(139\) | −11.8453 | −1.00470 | −0.502352 | − | 0.864663i | \(-0.667532\pi\) | ||||
−0.502352 | + | 0.864663i | \(0.667532\pi\) | |||||||
\(140\) | −8.78410 | + | 10.5622i | −0.742392 | + | 0.892670i | ||||
\(141\) | −10.4674 | −0.881517 | ||||||||
\(142\) | −0.174265 | + | 0.301836i | −0.0146240 | + | 0.0253295i | ||||
\(143\) | −2.26785 | − | 3.92803i | −0.189647 | − | 0.328478i | ||||
\(144\) | −1.00522 | − | 1.74109i | −0.0837684 | − | 0.145091i | ||||
\(145\) | 4.64203 | − | 8.04023i | 0.385499 | − | 0.667704i | ||||
\(146\) | −6.24784 | −0.517075 | ||||||||
\(147\) | 5.32264 | − | 4.54637i | 0.439004 | − | 0.374979i | ||||
\(148\) | 4.77202 | 0.392258 | ||||||||
\(149\) | 2.58687 | − | 4.48059i | 0.211925 | − | 0.367064i | −0.740392 | − | 0.672175i | \(-0.765360\pi\) |
0.952317 | + | 0.305111i | \(0.0986935\pi\) | |||||||
\(150\) | −1.46307 | − | 2.53412i | −0.119459 | − | 0.206910i | ||||
\(151\) | 2.52507 | + | 4.37355i | 0.205487 | + | 0.355914i | 0.950288 | − | 0.311373i | \(-0.100789\pi\) |
−0.744801 | + | 0.667287i | \(0.767455\pi\) | |||||||
\(152\) | 3.15729 | − | 5.46858i | 0.256090 | − | 0.443560i | ||||
\(153\) | 6.84417 | 0.553318 | ||||||||
\(154\) | −6.57219 | + | 7.90256i | −0.529602 | + | 0.636806i | ||||
\(155\) | 1.69955 | 0.136511 | ||||||||
\(156\) | 0.570908 | − | 0.988841i | 0.0457092 | − | 0.0791707i | ||||
\(157\) | 4.82407 | + | 8.35553i | 0.385003 | + | 0.666844i | 0.991770 | − | 0.128036i | \(-0.0408672\pi\) |
−0.606767 | + | 0.794880i | \(0.707534\pi\) | |||||||
\(158\) | −3.97279 | − | 6.88107i | −0.316058 | − | 0.547428i | ||||
\(159\) | 6.28744 | − | 10.8902i | 0.498627 | − | 0.863647i | ||||
\(160\) | 17.4051 | 1.37599 | ||||||||
\(161\) | 0.915795 | + | 2.48220i | 0.0721748 | + | 0.195625i | ||||
\(162\) | −0.593528 | −0.0466320 | ||||||||
\(163\) | −11.9663 | + | 20.7262i | −0.937271 | + | 1.62340i | −0.166737 | + | 0.986001i | \(0.553323\pi\) |
−0.770534 | + | 0.637399i | \(0.780010\pi\) | |||||||
\(164\) | 7.63614 | + | 13.2262i | 0.596282 | + | 1.03279i | ||||
\(165\) | 10.3129 | + | 17.8624i | 0.802854 | + | 1.39058i | ||||
\(166\) | −2.90087 | + | 5.02446i | −0.225151 | + | 0.389974i | ||||
\(167\) | 12.0368 | 0.931435 | 0.465718 | − | 0.884933i | \(-0.345796\pi\) | ||||
0.465718 | + | 0.884933i | \(0.345796\pi\) | |||||||
\(168\) | −5.64541 | − | 0.969929i | −0.435553 | − | 0.0748317i | ||||
\(169\) | −12.5198 | −0.963061 | ||||||||
\(170\) | −6.40043 | + | 11.0859i | −0.490890 | + | 0.850247i | ||||
\(171\) | 1.45831 | + | 2.52587i | 0.111520 | + | 0.193158i | ||||
\(172\) | −3.51825 | − | 6.09378i | −0.268264 | − | 0.464647i | ||||
\(173\) | 8.30191 | − | 14.3793i | 0.631182 | − | 1.09324i | −0.356128 | − | 0.934437i | \(-0.615903\pi\) |
0.987310 | − | 0.158803i | \(-0.0507634\pi\) | |||||||
\(174\) | 1.74865 | 0.132565 | ||||||||
\(175\) | 12.8554 | + | 2.20867i | 0.971779 | + | 0.166960i | ||||
\(176\) | −13.1590 | −0.991899 | ||||||||
\(177\) | 3.35163 | − | 5.80519i | 0.251924 | − | 0.436345i | ||||
\(178\) | 0.869340 | + | 1.50574i | 0.0651598 | + | 0.112860i | ||||
\(179\) | −1.62269 | − | 2.81058i | −0.121285 | − | 0.210073i | 0.798989 | − | 0.601345i | \(-0.205368\pi\) |
−0.920275 | + | 0.391273i | \(0.872035\pi\) | |||||||
\(180\) | −2.59616 | + | 4.49668i | −0.193506 | + | 0.335162i | ||||
\(181\) | 14.3797 | 1.06883 | 0.534417 | − | 0.845221i | \(-0.320531\pi\) | ||||
0.534417 | + | 0.845221i | \(0.320531\pi\) | |||||||
\(182\) | −0.376662 | − | 1.02092i | −0.0279200 | − | 0.0756753i | ||||
\(183\) | −5.30183 | −0.391923 | ||||||||
\(184\) | 1.08251 | − | 1.87497i | 0.0798040 | − | 0.138225i | ||||
\(185\) | −4.56314 | − | 7.90360i | −0.335489 | − | 0.581084i | ||||
\(186\) | 0.160055 | + | 0.277223i | 0.0117358 | + | 0.0203270i | ||||
\(187\) | 22.3987 | − | 38.7957i | 1.63796 | − | 2.83702i | ||||
\(188\) | −17.2474 | −1.25790 | ||||||||
\(189\) | 1.69175 | − | 2.03420i | 0.123057 | − | 0.147966i | ||||
\(190\) | −5.45505 | −0.395751 | ||||||||
\(191\) | 4.94456 | − | 8.56423i | 0.357776 | − | 0.619686i | −0.629813 | − | 0.776747i | \(-0.716869\pi\) |
0.987589 | + | 0.157061i | \(0.0502019\pi\) | |||||||
\(192\) | −0.371321 | − | 0.643147i | −0.0267978 | − | 0.0464151i | ||||
\(193\) | 1.79525 | + | 3.10947i | 0.129225 | + | 0.223825i | 0.923377 | − | 0.383895i | \(-0.125418\pi\) |
−0.794151 | + | 0.607720i | \(0.792084\pi\) | |||||||
\(194\) | −2.41616 | + | 4.18492i | −0.173471 | + | 0.300460i | ||||
\(195\) | −2.18368 | −0.156376 | ||||||||
\(196\) | 8.77024 | − | 7.49117i | 0.626446 | − | 0.535084i | ||||
\(197\) | 8.21279 | 0.585137 | 0.292569 | − | 0.956245i | \(-0.405490\pi\) | ||||
0.292569 | + | 0.956245i | \(0.405490\pi\) | |||||||
\(198\) | −1.94242 | + | 3.36437i | −0.138042 | + | 0.239096i | ||||
\(199\) | −1.12253 | − | 1.94429i | −0.0795743 | − | 0.137827i | 0.823492 | − | 0.567328i | \(-0.192023\pi\) |
−0.903066 | + | 0.429501i | \(0.858689\pi\) | |||||||
\(200\) | −5.33689 | − | 9.24376i | −0.377375 | − | 0.653633i | ||||
\(201\) | −1.36814 | + | 2.36969i | −0.0965013 | + | 0.167145i | ||||
\(202\) | 0.0790871 | 0.00556455 | ||||||||
\(203\) | −4.98422 | + | 5.99315i | −0.349824 | + | 0.420637i | ||||
\(204\) | 11.2773 | 0.789569 | ||||||||
\(205\) | 14.6038 | − | 25.2945i | 1.01997 | − | 1.76665i | ||||
\(206\) | −3.26757 | − | 5.65960i | −0.227662 | − | 0.394323i | ||||
\(207\) | 0.500000 | + | 0.866025i | 0.0347524 | + | 0.0601929i | ||||
\(208\) | 0.696583 | − | 1.20652i | 0.0482994 | − | 0.0836570i | ||||
\(209\) | 19.0903 | 1.32050 | ||||||||
\(210\) | 1.71284 | + | 4.64253i | 0.118197 | + | 0.320365i | ||||
\(211\) | −23.0784 | −1.58878 | −0.794392 | − | 0.607406i | \(-0.792210\pi\) | ||||
−0.794392 | + | 0.607406i | \(0.792210\pi\) | |||||||
\(212\) | 10.3600 | − | 17.9440i | 0.711526 | − | 1.23240i | ||||
\(213\) | −0.293609 | − | 0.508545i | −0.0201177 | − | 0.0348449i | ||||
\(214\) | −2.54478 | − | 4.40769i | −0.173958 | − | 0.301304i | ||||
\(215\) | −6.72850 | + | 11.6541i | −0.458880 | + | 0.794804i | ||||
\(216\) | −2.16503 | −0.147311 | ||||||||
\(217\) | −1.40634 | − | 0.241620i | −0.0954683 | − | 0.0164023i | ||||
\(218\) | −6.69634 | −0.453533 | ||||||||
\(219\) | 5.26330 | − | 9.11630i | 0.355661 | − | 0.616023i | ||||
\(220\) | 16.9927 | + | 29.4323i | 1.14565 | + | 1.98432i | ||||
\(221\) | 2.37139 | + | 4.10736i | 0.159517 | + | 0.276291i | ||||
\(222\) | 0.859467 | − | 1.48864i | 0.0576837 | − | 0.0999110i | ||||
\(223\) | 4.28573 | 0.286993 | 0.143497 | − | 0.989651i | \(-0.454165\pi\) | ||||
0.143497 | + | 0.989651i | \(0.454165\pi\) | |||||||
\(224\) | −14.4023 | − | 2.47443i | −0.962293 | − | 0.165330i | ||||
\(225\) | 4.93009 | 0.328672 | ||||||||
\(226\) | 0.932328 | − | 1.61484i | 0.0620175 | − | 0.107418i | ||||
\(227\) | −5.46669 | − | 9.46858i | −0.362837 | − | 0.628452i | 0.625590 | − | 0.780152i | \(-0.284858\pi\) |
−0.988427 | + | 0.151701i | \(0.951525\pi\) | |||||||
\(228\) | 2.40290 | + | 4.16194i | 0.159136 | + | 0.275631i | ||||
\(229\) | −2.78875 | + | 4.83026i | −0.184286 | + | 0.319193i | −0.943336 | − | 0.331840i | \(-0.892331\pi\) |
0.759050 | + | 0.651033i | \(0.225664\pi\) | |||||||
\(230\) | −1.87033 | −0.123326 | ||||||||
\(231\) | −5.99419 | − | 16.2468i | −0.394389 | − | 1.06896i | ||||
\(232\) | 6.37859 | 0.418775 | ||||||||
\(233\) | 11.1353 | − | 19.2869i | 0.729497 | − | 1.26353i | −0.227598 | − | 0.973755i | \(-0.573087\pi\) |
0.957096 | − | 0.289772i | \(-0.0935793\pi\) | |||||||
\(234\) | −0.205647 | − | 0.356192i | −0.0134436 | − | 0.0232850i | ||||
\(235\) | 16.4925 | + | 28.5659i | 1.07585 | + | 1.86343i | ||||
\(236\) | 5.52256 | − | 9.56536i | 0.359488 | − | 0.622652i | ||||
\(237\) | 13.3870 | 0.869580 | ||||||||
\(238\) | 6.87225 | − | 8.26335i | 0.445462 | − | 0.535634i | ||||
\(239\) | 13.3901 | 0.866134 | 0.433067 | − | 0.901362i | \(-0.357431\pi\) | ||||
0.433067 | + | 0.901362i | \(0.357431\pi\) | |||||||
\(240\) | −3.16766 | + | 5.48654i | −0.204471 | + | 0.354155i | ||||
\(241\) | 1.64322 | + | 2.84615i | 0.105849 | + | 0.183336i | 0.914085 | − | 0.405523i | \(-0.132911\pi\) |
−0.808236 | + | 0.588859i | \(0.799577\pi\) | |||||||
\(242\) | 9.44941 | + | 16.3669i | 0.607431 | + | 1.05210i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −8.73595 | −0.559262 | ||||||||
\(245\) | −20.7935 | − | 7.36233i | −1.32845 | − | 0.470362i | ||||
\(246\) | 5.50124 | 0.350746 | ||||||||
\(247\) | −1.01056 | + | 1.75034i | −0.0643004 | + | 0.111372i | ||||
\(248\) | 0.583835 | + | 1.01123i | 0.0370736 | + | 0.0642133i | ||||
\(249\) | −4.88750 | − | 8.46540i | −0.309733 | − | 0.536473i | ||||
\(250\) | 0.0653804 | − | 0.113242i | 0.00413502 | − | 0.00716207i | ||||
\(251\) | 10.2769 | 0.648672 | 0.324336 | − | 0.945942i | \(-0.394859\pi\) | ||||
0.324336 | + | 0.945942i | \(0.394859\pi\) | |||||||
\(252\) | 2.78754 | − | 3.35180i | 0.175598 | − | 0.211144i | ||||
\(253\) | 6.54534 | 0.411502 | ||||||||
\(254\) | −3.83827 | + | 6.64807i | −0.240834 | + | 0.417137i | ||||
\(255\) | −10.7837 | − | 18.6779i | −0.675301 | − | 1.16966i | ||||
\(256\) | 2.66641 | + | 4.61835i | 0.166650 | + | 0.288647i | ||||
\(257\) | −11.7035 | + | 20.2711i | −0.730046 | + | 1.26448i | 0.226817 | + | 0.973937i | \(0.427168\pi\) |
−0.956863 | + | 0.290539i | \(0.906165\pi\) | |||||||
\(258\) | −2.53462 | −0.157799 | ||||||||
\(259\) | 2.65226 | + | 7.18877i | 0.164803 | + | 0.446688i | ||||
\(260\) | −3.59809 | −0.223144 | ||||||||
\(261\) | −1.47310 | + | 2.55148i | −0.0911824 | + | 0.157932i | ||||
\(262\) | 1.82411 | + | 3.15945i | 0.112694 | + | 0.195192i | ||||
\(263\) | 13.6828 | + | 23.6993i | 0.843719 | + | 1.46136i | 0.886729 | + | 0.462289i | \(0.152972\pi\) |
−0.0430104 | + | 0.999075i | \(0.513695\pi\) | |||||||
\(264\) | −7.08542 | + | 12.2723i | −0.436078 | + | 0.755308i | ||||
\(265\) | −39.6260 | −2.43421 | ||||||||
\(266\) | 4.51392 | + | 0.775530i | 0.276766 | + | 0.0475508i | ||||
\(267\) | −2.92939 | −0.179276 | ||||||||
\(268\) | −2.25432 | + | 3.90460i | −0.137705 | + | 0.238511i | ||||
\(269\) | 13.1885 | + | 22.8432i | 0.804119 | + | 1.39277i | 0.916884 | + | 0.399153i | \(0.130696\pi\) |
−0.112765 | + | 0.993622i | \(0.535971\pi\) | |||||||
\(270\) | 0.935165 | + | 1.61975i | 0.0569123 | + | 0.0985750i | ||||
\(271\) | −2.15218 | + | 3.72768i | −0.130736 | + | 0.226441i | −0.923960 | − | 0.382488i | \(-0.875067\pi\) |
0.793225 | + | 0.608929i | \(0.208401\pi\) | |||||||
\(272\) | 13.7598 | 0.834311 | ||||||||
\(273\) | 1.80694 | + | 0.310447i | 0.109361 | + | 0.0187891i | ||||
\(274\) | 11.6404 | 0.703223 | ||||||||
\(275\) | 16.1345 | − | 27.9459i | 0.972950 | − | 1.68520i | ||||
\(276\) | 0.823862 | + | 1.42697i | 0.0495907 | + | 0.0858935i | ||||
\(277\) | 7.32466 | + | 12.6867i | 0.440096 | + | 0.762269i | 0.997696 | − | 0.0678408i | \(-0.0216110\pi\) |
−0.557600 | + | 0.830110i | \(0.688278\pi\) | |||||||
\(278\) | −3.51526 | + | 6.08861i | −0.210831 | + | 0.365171i | ||||
\(279\) | −0.539333 | −0.0322890 | ||||||||
\(280\) | 6.24796 | + | 16.9347i | 0.373387 | + | 1.01204i | ||||
\(281\) | 17.0380 | 1.01640 | 0.508202 | − | 0.861238i | \(-0.330310\pi\) | ||||
0.508202 | + | 0.861238i | \(0.330310\pi\) | |||||||
\(282\) | −3.10636 | + | 5.38037i | −0.184981 | + | 0.320397i | ||||
\(283\) | 8.95641 | + | 15.5130i | 0.532403 | + | 0.922150i | 0.999284 | + | 0.0378294i | \(0.0120443\pi\) |
−0.466881 | + | 0.884320i | \(0.654622\pi\) | |||||||
\(284\) | −0.483786 | − | 0.837942i | −0.0287074 | − | 0.0497227i | ||||
\(285\) | 4.59544 | − | 7.95953i | 0.272210 | − | 0.471482i | ||||
\(286\) | −2.69206 | −0.159185 | ||||||||
\(287\) | −15.6803 | + | 18.8544i | −0.925582 | + | 1.11294i | ||||
\(288\) | −5.52331 | −0.325464 | ||||||||
\(289\) | −14.9213 | + | 25.8445i | −0.877725 | + | 1.52026i | ||||
\(290\) | −2.75517 | − | 4.77210i | −0.161789 | − | 0.280228i | ||||
\(291\) | −4.07085 | − | 7.05092i | −0.238637 | − | 0.413332i | ||||
\(292\) | 8.67247 | − | 15.0212i | 0.507518 | − | 0.879047i | ||||
\(293\) | −18.7699 | −1.09655 | −0.548273 | − | 0.836299i | \(-0.684715\pi\) | ||||
−0.548273 | + | 0.836299i | \(0.684715\pi\) | |||||||
\(294\) | −0.757316 | − | 4.08509i | −0.0441676 | − | 0.238248i | ||||
\(295\) | −21.1233 | −1.22985 | ||||||||
\(296\) | 3.13510 | − | 5.43015i | 0.182224 | − | 0.315621i | ||||
\(297\) | −3.27267 | − | 5.66843i | −0.189900 | − | 0.328916i | ||||
\(298\) | −1.53538 | − | 2.65936i | −0.0889422 | − | 0.154052i | ||||
\(299\) | −0.346483 | + | 0.600126i | −0.0200376 | + | 0.0347062i | ||||
\(300\) | 8.12342 | 0.469006 | ||||||||
\(301\) | 7.22451 | − | 8.68692i | 0.416414 | − | 0.500706i | ||||
\(302\) | 2.99740 | 0.172481 | ||||||||
\(303\) | −0.0666245 | + | 0.115397i | −0.00382748 | + | 0.00662939i | ||||
\(304\) | 2.93185 | + | 5.07812i | 0.168153 | + | 0.291250i | ||||
\(305\) | 8.35357 | + | 14.4688i | 0.478324 | + | 0.828482i | ||||
\(306\) | 2.03110 | − | 3.51798i | 0.116111 | − | 0.201109i | ||||
\(307\) | −1.42373 | −0.0812566 | −0.0406283 | − | 0.999174i | \(-0.512936\pi\) | ||||
−0.0406283 | + | 0.999174i | \(0.512936\pi\) | |||||||
\(308\) | −9.87677 | − | 26.7703i | −0.562781 | − | 1.52538i | ||||
\(309\) | 11.0107 | 0.626374 | ||||||||
\(310\) | 0.504365 | − | 0.873586i | 0.0286460 | − | 0.0496164i | ||||
\(311\) | 2.21236 | + | 3.83191i | 0.125451 | + | 0.217288i | 0.921909 | − | 0.387406i | \(-0.126629\pi\) |
−0.796458 | + | 0.604694i | \(0.793295\pi\) | |||||||
\(312\) | −0.750145 | − | 1.29929i | −0.0424686 | − | 0.0735577i | ||||
\(313\) | −10.8433 | + | 18.7811i | −0.612898 | + | 1.06157i | 0.377852 | + | 0.925866i | \(0.376663\pi\) |
−0.990749 | + | 0.135704i | \(0.956670\pi\) | |||||||
\(314\) | 5.72644 | 0.323162 | ||||||||
\(315\) | −8.21691 | − | 1.41173i | −0.462970 | − | 0.0795422i | ||||
\(316\) | 22.0581 | 1.24086 | ||||||||
\(317\) | 5.81349 | − | 10.0693i | 0.326518 | − | 0.565546i | −0.655300 | − | 0.755369i | \(-0.727458\pi\) |
0.981818 | + | 0.189822i | \(0.0607912\pi\) | |||||||
\(318\) | −3.73178 | − | 6.46363i | −0.209268 | − | 0.362462i | ||||
\(319\) | 9.64191 | + | 16.7003i | 0.539844 | + | 0.935036i | ||||
\(320\) | −1.17011 | + | 2.02669i | −0.0654111 | + | 0.113295i | ||||
\(321\) | 8.57510 | 0.478615 | ||||||||
\(322\) | 1.54765 | + | 0.265900i | 0.0862473 | + | 0.0148180i | ||||
\(323\) | −19.9619 | −1.11071 | ||||||||
\(324\) | 0.823862 | − | 1.42697i | 0.0457701 | − | 0.0792762i | ||||
\(325\) | 1.70819 | + | 2.95867i | 0.0947533 | + | 0.164118i | ||||
\(326\) | 7.10232 | + | 12.3016i | 0.393361 | + | 0.681322i | ||||
\(327\) | 5.64113 | − | 9.77072i | 0.311955 | − | 0.540322i | ||||
\(328\) | 20.0670 | 1.10802 | ||||||||
\(329\) | −9.58603 | − | 25.9823i | −0.528495 | − | 1.43245i | ||||
\(330\) | 12.2419 | 0.673897 | ||||||||
\(331\) | −3.94742 | + | 6.83713i | −0.216970 | + | 0.375803i | −0.953880 | − | 0.300188i | \(-0.902951\pi\) |
0.736910 | + | 0.675991i | \(0.236284\pi\) | |||||||
\(332\) | −8.05326 | − | 13.9486i | −0.441980 | − | 0.765531i | ||||
\(333\) | 1.44806 | + | 2.50812i | 0.0793534 | + | 0.137444i | ||||
\(334\) | 3.57209 | − | 6.18704i | 0.195456 | − | 0.338540i | ||||
\(335\) | 8.62259 | 0.471102 | ||||||||
\(336\) | 3.40117 | − | 4.08965i | 0.185549 | − | 0.223108i | ||||
\(337\) | 12.1596 | 0.662378 | 0.331189 | − | 0.943565i | \(-0.392550\pi\) | ||||
0.331189 | + | 0.943565i | \(0.392550\pi\) | |||||||
\(338\) | −3.71543 | + | 6.43531i | −0.202093 | + | 0.350035i | ||||
\(339\) | 1.57082 | + | 2.72074i | 0.0853154 | + | 0.147771i | ||||
\(340\) | −17.7685 | − | 30.7760i | −0.963634 | − | 1.66906i | ||||
\(341\) | −1.76506 | + | 3.05717i | −0.0955833 | + | 0.165555i | ||||
\(342\) | 1.73110 | 0.0936071 | ||||||||
\(343\) | 16.1595 | + | 9.04831i | 0.872529 | + | 0.488563i | ||||
\(344\) | −9.24561 | −0.498490 | ||||||||
\(345\) | 1.57560 | − | 2.72902i | 0.0848276 | − | 0.146926i | ||||
\(346\) | −4.92742 | − | 8.53454i | −0.264900 | − | 0.458820i | ||||
\(347\) | −7.00958 | − | 12.1409i | −0.376294 | − | 0.651760i | 0.614226 | − | 0.789130i | \(-0.289468\pi\) |
−0.990520 | + | 0.137370i | \(0.956135\pi\) | |||||||
\(348\) | −2.42726 | + | 4.20413i | −0.130115 | + | 0.225365i | ||||
\(349\) | 2.94132 | 0.157445 | 0.0787226 | − | 0.996897i | \(-0.474916\pi\) | ||||
0.0787226 | + | 0.996897i | \(0.474916\pi\) | |||||||
\(350\) | 4.95031 | − | 5.95237i | 0.264605 | − | 0.318168i | ||||
\(351\) | 0.692965 | 0.0369878 | ||||||||
\(352\) | −18.0760 | + | 31.3085i | −0.963453 | + | 1.66875i | ||||
\(353\) | 5.03670 | + | 8.72382i | 0.268076 | + | 0.464322i | 0.968365 | − | 0.249538i | \(-0.0802787\pi\) |
−0.700289 | + | 0.713860i | \(0.746945\pi\) | |||||||
\(354\) | −1.98929 | − | 3.44555i | −0.105729 | − | 0.183129i | ||||
\(355\) | −0.925221 | + | 1.60253i | −0.0491056 | + | 0.0850534i | ||||
\(356\) | −4.82683 | −0.255822 | ||||||||
\(357\) | 6.26786 | + | 16.9886i | 0.331730 | + | 0.899132i | ||||
\(358\) | −1.92622 | −0.101804 | ||||||||
\(359\) | 16.2478 | − | 28.1420i | 0.857526 | − | 1.48528i | −0.0167563 | − | 0.999860i | \(-0.505334\pi\) |
0.874282 | − | 0.485418i | \(-0.161333\pi\) | |||||||
\(360\) | 3.41122 | + | 5.90841i | 0.179787 | + | 0.311401i | ||||
\(361\) | 5.24665 | + | 9.08747i | 0.276140 | + | 0.478288i | ||||
\(362\) | 4.26738 | − | 7.39132i | 0.224289 | − | 0.388479i | ||||
\(363\) | −31.8415 | −1.67124 | ||||||||
\(364\) | 2.97734 | + | 0.511532i | 0.156055 | + | 0.0268115i | ||||
\(365\) | −33.1715 | −1.73627 | ||||||||
\(366\) | −1.57339 | + | 2.72520i | −0.0822426 | + | 0.142448i | ||||
\(367\) | −12.1371 | − | 21.0221i | −0.633552 | − | 1.09734i | −0.986820 | − | 0.161821i | \(-0.948263\pi\) |
0.353269 | − | 0.935522i | \(-0.385070\pi\) | |||||||
\(368\) | 1.00522 | + | 1.74109i | 0.0524008 | + | 0.0907608i | ||||
\(369\) | −4.63435 | + | 8.02694i | −0.241255 | + | 0.417866i | ||||
\(370\) | −5.41671 | −0.281601 | ||||||||
\(371\) | 32.7896 | + | 5.63353i | 1.70235 | + | 0.292478i | ||||
\(372\) | −0.888672 | −0.0460755 | ||||||||
\(373\) | 11.0313 | − | 19.1069i | 0.571181 | − | 0.989315i | −0.425264 | − | 0.905070i | \(-0.639819\pi\) |
0.996445 | − | 0.0842458i | \(-0.0268481\pi\) | |||||||
\(374\) | −13.2943 | − | 23.0264i | −0.687430 | − | 1.19066i | ||||
\(375\) | 0.110155 | + | 0.190795i | 0.00568840 | + | 0.00985261i | ||||
\(376\) | −11.3311 | + | 19.6261i | −0.584359 | + | 1.01214i | ||||
\(377\) | −2.04161 | −0.105148 | ||||||||
\(378\) | −0.543550 | − | 1.47326i | −0.0279572 | − | 0.0757761i | ||||
\(379\) | 0.844591 | 0.0433837 | 0.0216919 | − | 0.999765i | \(-0.493095\pi\) | ||||
0.0216919 | + | 0.999765i | \(0.493095\pi\) | |||||||
\(380\) | 7.57202 | − | 13.1151i | 0.388436 | − | 0.672791i | ||||
\(381\) | −6.46686 | − | 11.2009i | −0.331307 | − | 0.573841i | ||||
\(382\) | −2.93474 | − | 5.08311i | −0.150154 | − | 0.260075i | ||||
\(383\) | −16.5176 | + | 28.6093i | −0.844009 | + | 1.46187i | 0.0424697 | + | 0.999098i | \(0.486477\pi\) |
−0.886479 | + | 0.462769i | \(0.846856\pi\) | |||||||
\(384\) | −11.4874 | −0.586214 | ||||||||
\(385\) | −34.8936 | + | 41.9568i | −1.77834 | + | 2.13832i | ||||
\(386\) | 2.13107 | 0.108469 | ||||||||
\(387\) | 2.13522 | − | 3.69830i | 0.108539 | − | 0.187995i | ||||
\(388\) | −6.70763 | − | 11.6180i | −0.340529 | − | 0.589813i | ||||
\(389\) | −0.386406 | − | 0.669275i | −0.0195916 | − | 0.0339336i | 0.856063 | − | 0.516871i | \(-0.172903\pi\) |
−0.875655 | + | 0.482937i | \(0.839570\pi\) | |||||||
\(390\) | −0.648037 | + | 1.12243i | −0.0328146 | + | 0.0568366i | ||||
\(391\) | −6.84417 | −0.346125 | ||||||||
\(392\) | −2.76248 | − | 14.9013i | −0.139526 | − | 0.752629i | ||||
\(393\) | −6.14667 | −0.310058 | ||||||||
\(394\) | 2.43726 | − | 4.22146i | 0.122788 | − | 0.212674i | ||||
\(395\) | −21.0926 | − | 36.5335i | −1.06128 | − | 1.83820i | ||||
\(396\) | −5.39246 | − | 9.34001i | −0.270981 | − | 0.469353i | ||||
\(397\) | 10.5690 | − | 18.3061i | 0.530444 | − | 0.918756i | −0.468925 | − | 0.883238i | \(-0.655359\pi\) |
0.999369 | − | 0.0355178i | \(-0.0113080\pi\) | |||||||
\(398\) | −1.33251 | −0.0667928 | ||||||||
\(399\) | −4.93420 | + | 5.93300i | −0.247019 | + | 0.297022i | ||||
\(400\) | 9.91165 | 0.495583 | ||||||||
\(401\) | −14.1572 | + | 24.5209i | −0.706975 | + | 1.22452i | 0.258999 | + | 0.965878i | \(0.416607\pi\) |
−0.965974 | + | 0.258639i | \(0.916726\pi\) | |||||||
\(402\) | 0.812031 | + | 1.40648i | 0.0405004 | + | 0.0701488i | ||||
\(403\) | −0.186870 | − | 0.323668i | −0.00930863 | − | 0.0161230i | ||||
\(404\) | −0.109779 | + | 0.190142i | −0.00546170 | + | 0.00945994i | ||||
\(405\) | −3.15120 | −0.156585 | ||||||||
\(406\) | 1.60140 | + | 4.34050i | 0.0794763 | + | 0.215415i | ||||
\(407\) | 18.9561 | 0.939621 | ||||||||
\(408\) | 7.40891 | − | 12.8326i | 0.366796 | − | 0.635309i | ||||
\(409\) | 11.1572 | + | 19.3248i | 0.551688 | + | 0.955551i | 0.998153 | + | 0.0607502i | \(0.0193493\pi\) |
−0.446465 | + | 0.894801i | \(0.647317\pi\) | |||||||
\(410\) | −8.66777 | − | 15.0130i | −0.428071 | − | 0.741440i | ||||
\(411\) | −9.80611 | + | 16.9847i | −0.483700 | + | 0.837792i | ||||
\(412\) | 18.1425 | 0.893818 | ||||||||
\(413\) | 17.4791 | + | 3.00305i | 0.860088 | + | 0.147770i | ||||
\(414\) | 0.593528 | 0.0291703 | ||||||||
\(415\) | −15.4015 | + | 26.6762i | −0.756031 | + | 1.30948i | ||||
\(416\) | −1.91373 | − | 3.31468i | −0.0938284 | − | 0.162516i | ||||
\(417\) | −5.92265 | − | 10.2583i | −0.290033 | − | 0.502352i | ||||
\(418\) | 5.66532 | − | 9.81262i | 0.277100 | − | 0.479951i | ||||
\(419\) | −5.99719 | −0.292982 | −0.146491 | − | 0.989212i | \(-0.546798\pi\) | ||||
−0.146491 | + | 0.989212i | \(0.546798\pi\) | |||||||
\(420\) | −13.5392 | − | 2.32615i | −0.660645 | − | 0.113504i | ||||
\(421\) | 12.4472 | 0.606638 | 0.303319 | − | 0.952889i | \(-0.401905\pi\) | ||||
0.303319 | + | 0.952889i | \(0.401905\pi\) | |||||||
\(422\) | −6.84885 | + | 11.8626i | −0.333397 | + | 0.577460i | ||||
\(423\) | −5.23372 | − | 9.06507i | −0.254472 | − | 0.440759i | ||||
\(424\) | −13.6125 | − | 23.5775i | −0.661081 | − | 1.14503i | ||||
\(425\) | −16.8712 | + | 29.2217i | −0.818372 | + | 1.41746i | ||||
\(426\) | −0.348530 | −0.0168863 | ||||||||
\(427\) | −4.85539 | − | 13.1602i | −0.234969 | − | 0.636867i | ||||
\(428\) | 14.1294 | 0.682970 | ||||||||
\(429\) | 2.26785 | − | 3.92803i | 0.109493 | − | 0.189647i | ||||
\(430\) | 3.99356 | + | 6.91704i | 0.192586 | + | 0.333570i | ||||
\(431\) | −2.69497 | − | 4.66783i | −0.129812 | − | 0.224842i | 0.793791 | − | 0.608190i | \(-0.208104\pi\) |
−0.923604 | + | 0.383349i | \(0.874771\pi\) | |||||||
\(432\) | 1.00522 | − | 1.74109i | 0.0483637 | − | 0.0837684i | ||||
\(433\) | −32.6738 | −1.57020 | −0.785102 | − | 0.619366i | \(-0.787390\pi\) | ||||
−0.785102 | + | 0.619366i | \(0.787390\pi\) | |||||||
\(434\) | −0.541546 | + | 0.651167i | −0.0259950 | + | 0.0312570i | ||||
\(435\) | 9.28405 | 0.445136 | ||||||||
\(436\) | 9.29502 | − | 16.0994i | 0.445151 | − | 0.771024i | ||||
\(437\) | −1.45831 | − | 2.52587i | −0.0697605 | − | 0.120829i | ||||
\(438\) | −3.12392 | − | 5.41079i | −0.149267 | − | 0.258537i | ||||
\(439\) | −0.0144158 | + | 0.0249690i | −0.000688030 | + | 0.00119170i | −0.866369 | − | 0.499404i | \(-0.833552\pi\) |
0.865681 | + | 0.500596i | \(0.166886\pi\) | |||||||
\(440\) | 44.6552 | 2.12885 | ||||||||
\(441\) | 6.59859 | + | 2.33635i | 0.314219 | + | 0.111255i | ||||
\(442\) | 2.81497 | 0.133894 | ||||||||
\(443\) | −8.46637 | + | 14.6642i | −0.402249 | + | 0.696716i | −0.993997 | − | 0.109407i | \(-0.965105\pi\) |
0.591748 | + | 0.806123i | \(0.298438\pi\) | |||||||
\(444\) | 2.38601 | + | 4.13269i | 0.113235 | + | 0.196129i | ||||
\(445\) | 4.61556 | + | 7.99438i | 0.218799 | + | 0.378970i | ||||
\(446\) | 1.27185 | − | 2.20291i | 0.0602239 | − | 0.104311i | ||||
\(447\) | 5.17374 | 0.244709 | ||||||||
\(448\) | 1.25637 | − | 1.51068i | 0.0593577 | − | 0.0713731i | ||||
\(449\) | 20.8257 | 0.982825 | 0.491412 | − | 0.870927i | \(-0.336481\pi\) | ||||
0.491412 | + | 0.870927i | \(0.336481\pi\) | |||||||
\(450\) | 1.46307 | − | 2.53412i | 0.0689699 | − | 0.119459i | ||||
\(451\) | 30.3334 | + | 52.5390i | 1.42835 | + | 2.47397i | ||||
\(452\) | 2.58828 | + | 4.48304i | 0.121743 | + | 0.210864i | ||||
\(453\) | −2.52507 | + | 4.37355i | −0.118638 | + | 0.205487i | ||||
\(454\) | −6.48927 | −0.304556 | ||||||||
\(455\) | −1.99980 | − | 5.42032i | −0.0937520 | − | 0.254108i | ||||
\(456\) | 6.31457 | 0.295707 | ||||||||
\(457\) | 7.17566 | − | 12.4286i | 0.335663 | − | 0.581386i | −0.647949 | − | 0.761684i | \(-0.724373\pi\) |
0.983612 | + | 0.180298i | \(0.0577063\pi\) | |||||||
\(458\) | 1.65520 | + | 2.86690i | 0.0773426 | + | 0.133961i | ||||
\(459\) | 3.42208 | + | 5.92722i | 0.159729 | + | 0.276659i | ||||
\(460\) | 2.59616 | − | 4.49668i | 0.121046 | − | 0.209659i | ||||
\(461\) | −3.54822 | −0.165257 | −0.0826286 | − | 0.996580i | \(-0.526332\pi\) | ||||
−0.0826286 | + | 0.996580i | \(0.526332\pi\) | |||||||
\(462\) | −10.1299 | − | 1.74040i | −0.471286 | − | 0.0809710i | ||||
\(463\) | 12.2267 | 0.568223 | 0.284111 | − | 0.958791i | \(-0.408301\pi\) | ||||
0.284111 | + | 0.958791i | \(0.408301\pi\) | |||||||
\(464\) | −2.96157 | + | 5.12960i | −0.137488 | + | 0.238136i | ||||
\(465\) | 0.849774 | + | 1.47185i | 0.0394073 | + | 0.0682555i | ||||
\(466\) | −6.60911 | − | 11.4473i | −0.306161 | − | 0.530287i | ||||
\(467\) | 14.2930 | − | 24.7562i | 0.661401 | − | 1.14558i | −0.318846 | − | 0.947806i | \(-0.603295\pi\) |
0.980248 | − | 0.197774i | \(-0.0633713\pi\) | |||||||
\(468\) | 1.14182 | 0.0527804 | ||||||||
\(469\) | −7.13499 | − | 1.22585i | −0.329463 | − | 0.0566045i | ||||
\(470\) | 19.5776 | 0.903045 | ||||||||
\(471\) | −4.82407 | + | 8.35553i | −0.222281 | + | 0.385003i | ||||
\(472\) | −7.25637 | − | 12.5684i | −0.334002 | − | 0.578508i | ||||
\(473\) | −13.9757 | − | 24.2066i | −0.642604 | − | 1.11302i | ||||
\(474\) | 3.97279 | − | 6.88107i | 0.182476 | − | 0.316058i | ||||
\(475\) | −14.3792 | −0.659763 | ||||||||
\(476\) | 10.3277 | + | 27.9925i | 0.473369 | + | 1.28304i | ||||
\(477\) | 12.5749 | 0.575765 | ||||||||
\(478\) | 3.97370 | − | 6.88266i | 0.181753 | − | 0.314805i | ||||
\(479\) | −15.1346 | − | 26.2138i | −0.691516 | − | 1.19774i | −0.971341 | − | 0.237690i | \(-0.923610\pi\) |
0.279825 | − | 0.960051i | \(-0.409724\pi\) | |||||||
\(480\) | 8.70254 | + | 15.0732i | 0.397215 | + | 0.687996i | ||||
\(481\) | −1.00346 | + | 1.73804i | −0.0457537 | + | 0.0792478i | ||||
\(482\) | 1.95060 | 0.0888474 | ||||||||
\(483\) | −1.69175 | + | 2.03420i | −0.0769773 | + | 0.0925594i | ||||
\(484\) | −52.4660 | −2.38482 | ||||||||
\(485\) | −12.8281 | + | 22.2189i | −0.582493 | + | 1.00891i | ||||
\(486\) | −0.296764 | − | 0.514011i | −0.0134615 | − | 0.0233160i | ||||
\(487\) | −14.4684 | − | 25.0601i | −0.655627 | − | 1.13558i | −0.981736 | − | 0.190247i | \(-0.939071\pi\) |
0.326109 | − | 0.945332i | \(-0.394262\pi\) | |||||||
\(488\) | −5.73930 | + | 9.94077i | −0.259806 | + | 0.449997i | ||||
\(489\) | −23.9325 | −1.08227 | ||||||||
\(490\) | −9.95509 | + | 8.50322i | −0.449725 | + | 0.384136i | ||||
\(491\) | −11.9185 | −0.537876 | −0.268938 | − | 0.963158i | \(-0.586673\pi\) | ||||
−0.268938 | + | 0.963158i | \(0.586673\pi\) | |||||||
\(492\) | −7.63614 | + | 13.2262i | −0.344264 | + | 0.596282i | ||||
\(493\) | −10.0821 | − | 17.4627i | −0.454076 | − | 0.786482i | ||||
\(494\) | 0.599796 | + | 1.03888i | 0.0269861 | + | 0.0467413i | ||||
\(495\) | −10.3129 | + | 17.8624i | −0.463528 | + | 0.802854i | ||||
\(496\) | −1.08430 | −0.0486864 | ||||||||
\(497\) | 0.993426 | − | 1.19452i | 0.0445612 | − | 0.0535815i | ||||
\(498\) | −5.80174 | −0.259982 | ||||||||
\(499\) | −5.18689 | + | 8.98396i | −0.232197 | + | 0.402177i | −0.958454 | − | 0.285246i | \(-0.907925\pi\) |
0.726257 | + | 0.687423i | \(0.241258\pi\) | |||||||
\(500\) | 0.181506 | + | 0.314377i | 0.00811719 | + | 0.0140594i | ||||
\(501\) | 6.01840 | + | 10.4242i | 0.268882 | + | 0.465718i | ||||
\(502\) | 3.04982 | − | 5.28243i | 0.136120 | − | 0.235767i | ||||
\(503\) | 22.4429 | 1.00068 | 0.500340 | − | 0.865829i | \(-0.333209\pi\) | ||||
0.500340 | + | 0.865829i | \(0.333209\pi\) | |||||||
\(504\) | −1.98272 | − | 5.37403i | −0.0883175 | − | 0.239378i | ||||
\(505\) | 0.419895 | 0.0186851 | ||||||||
\(506\) | 1.94242 | − | 3.36437i | 0.0863512 | − | 0.149565i | ||||
\(507\) | −6.25990 | − | 10.8425i | −0.278012 | − | 0.481531i | ||||
\(508\) | −10.6556 | − | 18.4560i | −0.472766 | − | 0.818855i | ||||
\(509\) | 2.98190 | − | 5.16481i | 0.132171 | − | 0.228926i | −0.792342 | − | 0.610077i | \(-0.791139\pi\) |
0.924513 | + | 0.381150i | \(0.124472\pi\) | |||||||
\(510\) | −12.8009 | −0.566831 | ||||||||
\(511\) | 27.4486 | + | 4.71590i | 1.21425 | + | 0.208619i | ||||
\(512\) | −19.8096 | −0.875470 | ||||||||
\(513\) | −1.45831 | + | 2.52587i | −0.0643861 | + | 0.111520i | ||||
\(514\) | 6.94637 | + | 12.0315i | 0.306391 | + | 0.530686i | ||||
\(515\) | −17.3484 | − | 30.0483i | −0.764462 | − | 1.32409i | ||||
\(516\) | 3.51825 | − | 6.09378i | 0.154882 | − | 0.268264i | ||||
\(517\) | −68.5129 | −3.01319 | ||||||||
\(518\) | 4.48220 | + | 0.770080i | 0.196937 | + | 0.0338354i | ||||
\(519\) | 16.6038 | 0.728827 | ||||||||
\(520\) | −2.36386 | + | 4.09432i | −0.103662 | + | 0.179548i | ||||
\(521\) | −0.510936 | − | 0.884968i | −0.0223845 | − | 0.0387711i | 0.854616 | − | 0.519260i | \(-0.173792\pi\) |
−0.877001 | + | 0.480489i | \(0.840459\pi\) | |||||||
\(522\) | 0.874324 | + | 1.51437i | 0.0382681 | + | 0.0662824i | ||||
\(523\) | −2.49185 | + | 4.31600i | −0.108961 | + | 0.188726i | −0.915350 | − | 0.402660i | \(-0.868086\pi\) |
0.806389 | + | 0.591386i | \(0.201419\pi\) | |||||||
\(524\) | −10.1280 | −0.442444 | ||||||||
\(525\) | 4.51495 | + | 12.2375i | 0.197049 | + | 0.534087i | ||||
\(526\) | 16.2423 | 0.708197 | ||||||||
\(527\) | 1.84564 | − | 3.19675i | 0.0803975 | − | 0.139253i | ||||
\(528\) | −6.57951 | − | 11.3961i | −0.286337 | − | 0.495949i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.0217391 | − | 0.0376533i | ||||
\(530\) | −11.7596 | + | 20.3682i | −0.510804 | + | 0.884738i | ||||
\(531\) | 6.70326 | 0.290897 | ||||||||
\(532\) | −8.13020 | + | 9.77595i | −0.352489 | + | 0.423841i | ||||
\(533\) | −6.42289 | −0.278206 | ||||||||
\(534\) | −0.869340 | + | 1.50574i | −0.0376200 | + | 0.0651598i | ||||
\(535\) | −13.5109 | − | 23.4016i | −0.584129 | − | 1.01174i | ||||
\(536\) | 2.96207 | + | 5.13045i | 0.127942 | + | 0.221602i | ||||
\(537\) | 1.62269 | − | 2.81058i | 0.0700242 | − | 0.121285i | ||||
\(538\) | 15.6555 | 0.674958 | ||||||||
\(539\) | 34.8385 | − | 29.7576i | 1.50060 | − | 1.28175i | ||||
\(540\) | −5.19231 | −0.223442 | ||||||||
\(541\) | −7.66700 | + | 13.2796i | −0.329630 | + | 0.570936i | −0.982438 | − | 0.186587i | \(-0.940257\pi\) |
0.652808 | + | 0.757523i | \(0.273591\pi\) | |||||||
\(542\) | 1.27738 | + | 2.21249i | 0.0548681 | + | 0.0950344i | ||||
\(543\) | 7.18985 | + | 12.4532i | 0.308546 | + | 0.534417i | ||||
\(544\) | 18.9012 | − | 32.7379i | 0.810384 | − | 1.40363i | ||||
\(545\) | −35.5527 | −1.52291 | ||||||||
\(546\) | 0.695808 | − | 0.836656i | 0.0297778 | − | 0.0358056i | ||||
\(547\) | −6.89796 | −0.294935 | −0.147468 | − | 0.989067i | \(-0.547112\pi\) | ||||
−0.147468 | + | 0.989067i | \(0.547112\pi\) | |||||||
\(548\) | −16.1578 | + | 27.9861i | −0.690225 | + | 1.19551i | ||||
\(549\) | −2.65091 | − | 4.59152i | −0.113138 | − | 0.195961i | ||||
\(550\) | −9.57631 | − | 16.5867i | −0.408335 | − | 0.707258i | ||||
\(551\) | 4.29647 | − | 7.44170i | 0.183036 | − | 0.317027i | ||||
\(552\) | 2.16503 | 0.0921497 | ||||||||
\(553\) | 12.2598 | + | 33.2292i | 0.521338 | + | 1.41305i | ||||
\(554\) | 8.69479 | 0.369406 | ||||||||
\(555\) | 4.56314 | − | 7.90360i | 0.193695 | − | 0.335489i | ||||
\(556\) | −9.75889 | − | 16.9029i | −0.413869 | − | 0.716842i | ||||
\(557\) | −14.7445 | − | 25.5382i | −0.624743 | − | 1.08209i | −0.988590 | − | 0.150628i | \(-0.951870\pi\) |
0.363847 | − | 0.931459i | \(-0.381463\pi\) | |||||||
\(558\) | −0.160055 | + | 0.277223i | −0.00677566 | + | 0.0117358i | ||||
\(559\) | 2.95926 | 0.125163 | ||||||||
\(560\) | −16.5196 | − | 2.83821i | −0.698081 | − | 0.119936i | ||||
\(561\) | 44.7974 | 1.89135 | ||||||||
\(562\) | 5.05628 | − | 8.75773i | 0.213286 | − | 0.369423i | ||||
\(563\) | 3.61211 | + | 6.25636i | 0.152232 | + | 0.263674i | 0.932048 | − | 0.362335i | \(-0.118020\pi\) |
−0.779815 | + | 0.626010i | \(0.784687\pi\) | |||||||
\(564\) | −8.62372 | − | 14.9367i | −0.363124 | − | 0.628950i | ||||
\(565\) | 4.94998 | − | 8.57362i | 0.208247 | − | 0.360695i | ||||
\(566\) | 10.6318 | 0.446887 | ||||||||
\(567\) | 2.60755 | + | 0.447998i | 0.109507 | + | 0.0188142i | ||||
\(568\) | −1.27134 | −0.0533443 | ||||||||
\(569\) | 1.80688 | − | 3.12960i | 0.0757482 | − | 0.131200i | −0.825663 | − | 0.564163i | \(-0.809199\pi\) |
0.901411 | + | 0.432964i | \(0.142532\pi\) | |||||||
\(570\) | −2.72752 | − | 4.72421i | −0.114243 | − | 0.197875i | ||||
\(571\) | 1.26695 | + | 2.19442i | 0.0530203 | + | 0.0918338i | 0.891317 | − | 0.453380i | \(-0.149782\pi\) |
−0.838297 | + | 0.545214i | \(0.816449\pi\) | |||||||
\(572\) | 3.73679 | − | 6.47230i | 0.156243 | − | 0.270621i | ||||
\(573\) | 9.88912 | 0.413124 | ||||||||
\(574\) | 5.03801 | + | 13.6552i | 0.210283 | + | 0.569957i | ||||
\(575\) | −4.93009 | −0.205599 | ||||||||
\(576\) | 0.371321 | − | 0.643147i | 0.0154717 | − | 0.0267978i | ||||
\(577\) | 1.05343 | + | 1.82459i | 0.0438548 | + | 0.0759588i | 0.887120 | − | 0.461540i | \(-0.152703\pi\) |
−0.843265 | + | 0.537498i | \(0.819369\pi\) | |||||||
\(578\) | 8.85623 | + | 15.3394i | 0.368371 | + | 0.638037i | ||||
\(579\) | −1.79525 | + | 3.10947i | −0.0746082 | + | 0.129225i | ||||
\(580\) | 15.2976 | 0.635196 | ||||||||
\(581\) | 16.5369 | − | 19.8843i | 0.686065 | − | 0.824941i | ||||
\(582\) | −4.83233 | −0.200306 | ||||||||
\(583\) | 41.1535 | − | 71.2799i | 1.70440 | − | 2.95211i | ||||
\(584\) | −11.3952 | − | 19.7371i | −0.471536 | − | 0.816725i | ||||
\(585\) | −1.09184 | − | 1.89112i | −0.0451419 | − | 0.0781881i | ||||
\(586\) | −5.57022 | + | 9.64791i | −0.230104 | + | 0.398551i | ||||
\(587\) | 3.01620 | 0.124492 | 0.0622460 | − | 0.998061i | \(-0.480174\pi\) | ||||
0.0622460 | + | 0.998061i | \(0.480174\pi\) | |||||||
\(588\) | 10.8727 | + | 3.84967i | 0.448381 | + | 0.158758i | ||||
\(589\) | 1.57303 | 0.0648156 | ||||||||
\(590\) | −6.26865 | + | 10.8576i | −0.258076 | + | 0.447001i | ||||
\(591\) | 4.10640 | + | 7.11249i | 0.168915 | + | 0.292569i | ||||
\(592\) | 2.91125 | + | 5.04243i | 0.119652 | + | 0.207243i | ||||
\(593\) | −5.22680 | + | 9.05308i | −0.214639 | + | 0.371765i | −0.953161 | − | 0.302464i | \(-0.902191\pi\) |
0.738522 | + | 0.674229i | \(0.235524\pi\) | |||||||
\(594\) | −3.88485 | −0.159397 | ||||||||
\(595\) | 36.4866 | − | 43.8724i | 1.49581 | − | 1.79859i | ||||
\(596\) | 8.52489 | 0.349193 | ||||||||
\(597\) | 1.12253 | − | 1.94429i | 0.0459423 | − | 0.0795743i | ||||
\(598\) | 0.205647 | + | 0.356192i | 0.00840954 | + | 0.0145658i | ||||
\(599\) | 0.885052 | + | 1.53296i | 0.0361623 | + | 0.0626349i | 0.883540 | − | 0.468356i | \(-0.155153\pi\) |
−0.847378 | + | 0.530990i | \(0.821820\pi\) | |||||||
\(600\) | 5.33689 | − | 9.24376i | 0.217878 | − | 0.377375i | ||||
\(601\) | −37.1024 | −1.51344 | −0.756720 | − | 0.653739i | \(-0.773199\pi\) | ||||
−0.756720 | + | 0.653739i | \(0.773199\pi\) | |||||||
\(602\) | −2.32120 | − | 6.29144i | −0.0946049 | − | 0.256420i | ||||
\(603\) | −2.73628 | −0.111430 | ||||||||
\(604\) | −4.16062 | + | 7.20640i | −0.169293 | + | 0.293224i | ||||
\(605\) | 50.1695 | + | 86.8961i | 2.03968 | + | 3.53283i | ||||
\(606\) | 0.0395435 | + | 0.0684914i | 0.00160635 | + | 0.00278227i | ||||
\(607\) | 4.95018 | − | 8.57397i | 0.200922 | − | 0.348007i | −0.747904 | − | 0.663807i | \(-0.768940\pi\) |
0.948826 | + | 0.315800i | \(0.102273\pi\) | |||||||
\(608\) | 16.1094 | 0.653323 | ||||||||
\(609\) | −7.68233 | − | 1.31989i | −0.311304 | − | 0.0534846i | ||||
\(610\) | 9.91617 | 0.401494 | ||||||||
\(611\) | 3.62679 | − | 6.28178i | 0.146724 | − | 0.254133i | ||||
\(612\) | 5.63865 | + | 9.76643i | 0.227929 | + | 0.394785i | ||||
\(613\) | 16.6981 | + | 28.9220i | 0.674430 | + | 1.16815i | 0.976635 | + | 0.214905i | \(0.0689441\pi\) |
−0.302205 | + | 0.953243i | \(0.597723\pi\) | |||||||
\(614\) | −0.422512 | + | 0.731813i | −0.0170512 | + | 0.0295336i | ||||
\(615\) | 29.2076 | 1.17776 | ||||||||
\(616\) | −36.9511 | − | 6.34852i | −1.48880 | − | 0.255789i | ||||
\(617\) | −19.5997 | −0.789054 | −0.394527 | − | 0.918884i | \(-0.629092\pi\) | ||||
−0.394527 | + | 0.918884i | \(0.629092\pi\) | |||||||
\(618\) | 3.26757 | − | 5.65960i | 0.131441 | − | 0.227662i | ||||
\(619\) | 10.2341 | + | 17.7259i | 0.411342 | + | 0.712466i | 0.995037 | − | 0.0995075i | \(-0.0317267\pi\) |
−0.583694 | + | 0.811973i | \(0.698393\pi\) | |||||||
\(620\) | 1.40019 | + | 2.42521i | 0.0562331 | + | 0.0973986i | ||||
\(621\) | −0.500000 | + | 0.866025i | −0.0200643 | + | 0.0347524i | ||||
\(622\) | 2.62619 | 0.105301 | ||||||||
\(623\) | −2.68273 | − | 7.27134i | −0.107481 | − | 0.291320i | ||||
\(624\) | 1.39317 | 0.0557713 | ||||||||
\(625\) | 12.6723 | − | 21.9491i | 0.506894 | − | 0.877965i | ||||
\(626\) | 6.43579 | + | 11.1471i | 0.257226 | + | 0.445528i | ||||
\(627\) | 9.54515 | + | 16.5327i | 0.381197 | + | 0.660252i | ||||
\(628\) | −7.94873 | + | 13.7676i | −0.317189 | + | 0.549387i | ||||
\(629\) | −19.8216 | −0.790338 | ||||||||
\(630\) | −3.16413 | + | 3.80463i | −0.126062 | + | 0.151580i | ||||
\(631\) | −16.9942 | −0.676529 | −0.338265 | − | 0.941051i | \(-0.609840\pi\) | ||||
−0.338265 | + | 0.941051i | \(0.609840\pi\) | |||||||
\(632\) | 14.4916 | − | 25.1002i | 0.576446 | − | 0.998434i | ||||
\(633\) | −11.5392 | − | 19.9865i | −0.458642 | − | 0.794392i | ||||
\(634\) | −3.45047 | − | 5.97640i | −0.137036 | − | 0.237353i | ||||
\(635\) | −20.3784 | + | 35.2964i | −0.808692 | + | 1.40070i | ||||
\(636\) | 20.7199 | 0.821599 | ||||||||
\(637\) | 0.884193 | + | 4.76949i | 0.0350330 | + | 0.188974i | ||||
\(638\) | 11.4455 | 0.453132 | ||||||||
\(639\) | 0.293609 | − | 0.508545i | 0.0116150 | − | 0.0201177i | ||||
\(640\) | 18.0996 | + | 31.3494i | 0.715448 | + | 1.23919i | ||||
\(641\) | −5.48164 | − | 9.49448i | −0.216512 | − | 0.375009i | 0.737227 | − | 0.675645i | \(-0.236135\pi\) |
−0.953739 | + | 0.300635i | \(0.902801\pi\) | |||||||
\(642\) | 2.54478 | − | 4.40769i | 0.100435 | − | 0.173958i | ||||
\(643\) | 11.7658 | 0.463996 | 0.231998 | − | 0.972716i | \(-0.425474\pi\) | ||||
0.231998 | + | 0.972716i | \(0.425474\pi\) | |||||||
\(644\) | −2.78754 | + | 3.35180i | −0.109844 | + | 0.132080i | ||||
\(645\) | −13.4570 | −0.529869 | ||||||||
\(646\) | −5.92397 | + | 10.2606i | −0.233075 | + | 0.403699i | ||||
\(647\) | −0.884701 | − | 1.53235i | −0.0347812 | − | 0.0602428i | 0.848111 | − | 0.529819i | \(-0.177740\pi\) |
−0.882892 | + | 0.469576i | \(0.844407\pi\) | |||||||
\(648\) | −1.08251 | − | 1.87497i | −0.0425252 | − | 0.0736557i | ||||
\(649\) | 21.9376 | − | 37.9970i | 0.861124 | − | 1.49151i | ||||
\(650\) | 2.02772 | 0.0795337 | ||||||||
\(651\) | −0.493918 | − | 1.33873i | −0.0193582 | − | 0.0524691i | ||||
\(652\) | −39.4342 | −1.54436 | ||||||||
\(653\) | −5.28392 | + | 9.15202i | −0.206776 | + | 0.358146i | −0.950697 | − | 0.310121i | \(-0.899630\pi\) |
0.743921 | + | 0.668267i | \(0.232964\pi\) | |||||||
\(654\) | −3.34817 | − | 5.79920i | −0.130924 | − | 0.226767i | ||||
\(655\) | 9.68470 | + | 16.7744i | 0.378413 | + | 0.655430i | ||||
\(656\) | −9.31710 | + | 16.1377i | −0.363772 | + | 0.630071i | ||||
\(657\) | 10.5266 | 0.410682 | ||||||||
\(658\) | −16.2000 | − | 2.78329i | −0.631540 | − | 0.108504i | ||||
\(659\) | −10.3840 | −0.404504 | −0.202252 | − | 0.979334i | \(-0.564826\pi\) | ||||
−0.202252 | + | 0.979334i | \(0.564826\pi\) | |||||||
\(660\) | −16.9927 | + | 29.4323i | −0.661441 | + | 1.14565i | ||||
\(661\) | 16.6734 | + | 28.8792i | 0.648521 | + | 1.12327i | 0.983476 | + | 0.181037i | \(0.0579455\pi\) |
−0.334955 | + | 0.942234i | \(0.608721\pi\) | |||||||
\(662\) | 2.34291 | + | 4.05803i | 0.0910596 | + | 0.157720i | ||||
\(663\) | −2.37139 | + | 4.10736i | −0.0920970 | + | 0.159517i | ||||
\(664\) | −21.1632 | −0.821290 | ||||||||
\(665\) | 23.9656 | + | 4.11750i | 0.929348 | + | 0.159670i | ||||
\(666\) | 1.71893 | 0.0666073 | ||||||||
\(667\) | 1.47310 | − | 2.55148i | 0.0570385 | − | 0.0987936i | ||||
\(668\) | 9.91666 | + | 17.1762i | 0.383687 | + | 0.664566i | ||||
\(669\) | 2.14286 | + | 3.71155i | 0.0828479 | + | 0.143497i | ||||
\(670\) | 2.55888 | − | 4.43210i | 0.0988580 | − | 0.171227i | ||||
\(671\) | −34.7023 | −1.33967 | ||||||||
\(672\) | −5.05822 | − | 13.7100i | −0.195125 | − | 0.528873i | ||||
\(673\) | 11.0030 | 0.424134 | 0.212067 | − | 0.977255i | \(-0.431980\pi\) | ||||
0.212067 | + | 0.977255i | \(0.431980\pi\) | |||||||
\(674\) | 3.60855 | − | 6.25018i | 0.138996 | − | 0.240748i | ||||
\(675\) | 2.46504 | + | 4.26958i | 0.0948796 | + | 0.164336i | ||||
\(676\) | −10.3146 | − | 17.8654i | −0.396715 | − | 0.687130i | ||||
\(677\) | −16.8484 | + | 29.1822i | −0.647536 | + | 1.12156i | 0.336174 | + | 0.941800i | \(0.390867\pi\) |
−0.983710 | + | 0.179765i | \(0.942466\pi\) | |||||||
\(678\) | 1.86466 | 0.0716117 | ||||||||
\(679\) | 13.7737 | − | 16.5619i | 0.528587 | − | 0.635586i | ||||
\(680\) | −46.6940 | −1.79063 | ||||||||
\(681\) | 5.46669 | − | 9.46858i | 0.209484 | − | 0.362837i | ||||
\(682\) | 1.04761 | + | 1.81452i | 0.0401152 | + | 0.0694815i | ||||
\(683\) | 23.5809 | + | 40.8433i | 0.902297 | + | 1.56282i | 0.824505 | + | 0.565854i | \(0.191454\pi\) |
0.0777918 | + | 0.996970i | \(0.475213\pi\) | |||||||
\(684\) | −2.40290 | + | 4.16194i | −0.0918770 | + | 0.159136i | ||||
\(685\) | 61.8021 | 2.36134 | ||||||||
\(686\) | 9.44648 | − | 5.62092i | 0.360668 | − | 0.214608i | ||||
\(687\) | −5.57751 | −0.212795 | ||||||||
\(688\) | 4.29273 | − | 7.43522i | 0.163659 | − | 0.283465i | ||||
\(689\) | 4.35698 | + | 7.54651i | 0.165988 | + | 0.287499i | ||||
\(690\) | −0.935165 | − | 1.61975i | −0.0356011 | − | 0.0616629i | ||||
\(691\) | −11.9250 | + | 20.6548i | −0.453650 | + | 0.785745i | −0.998609 | − | 0.0527174i | \(-0.983212\pi\) |
0.544959 | + | 0.838462i | \(0.316545\pi\) | |||||||
\(692\) | 27.3585 | 1.04001 | ||||||||
\(693\) | 11.0731 | − | 13.3145i | 0.420632 | − | 0.505778i | ||||
\(694\) | −8.32077 | −0.315852 | ||||||||
\(695\) | −18.6635 | + | 32.3261i | −0.707946 | + | 1.22620i | ||||
\(696\) | 3.18929 | + | 5.52402i | 0.120890 | + | 0.209387i | ||||
\(697\) | −31.7183 | − | 54.9377i | −1.20142 | − | 2.08091i | ||||
\(698\) | 0.872879 | − | 1.51187i | 0.0330390 | − | 0.0572251i | ||||
\(699\) | 22.2706 | 0.842351 | ||||||||
\(700\) | 7.43939 | + | 20.1640i | 0.281183 | + | 0.762126i | ||||
\(701\) | 6.20352 | 0.234304 | 0.117152 | − | 0.993114i | \(-0.462624\pi\) | ||||
0.117152 | + | 0.993114i | \(0.462624\pi\) | |||||||
\(702\) | 0.205647 | − | 0.356192i | 0.00776166 | − | 0.0134436i | ||||
\(703\) | −4.22346 | − | 7.31524i | −0.159291 | − | 0.275900i | ||||
\(704\) | −2.43042 | − | 4.20962i | −0.0916000 | − | 0.158656i | ||||
\(705\) | −16.4925 | + | 28.5659i | −0.621144 | + | 1.07585i | ||||
\(706\) | 5.97885 | 0.225017 | ||||||||
\(707\) | −0.347453 | − | 0.0596953i | −0.0130673 | − | 0.00224507i | ||||
\(708\) | 11.0451 | 0.415101 | ||||||||
\(709\) | −8.12457 | + | 14.0722i | −0.305124 | + | 0.528491i | −0.977289 | − | 0.211911i | \(-0.932031\pi\) |
0.672165 | + | 0.740402i | \(0.265365\pi\) | |||||||
\(710\) | 0.549145 | + | 0.951147i | 0.0206090 | + | 0.0356959i | ||||
\(711\) | 6.69351 | + | 11.5935i | 0.251026 | + | 0.434790i | ||||
\(712\) | −3.17111 | + | 5.49252i | −0.118842 | + | 0.205841i | ||||
\(713\) | 0.539333 | 0.0201982 | ||||||||
\(714\) | 10.5924 | + | 1.81986i | 0.396411 | + | 0.0681067i | ||||
\(715\) | −14.2929 | −0.534524 | ||||||||
\(716\) | 2.67374 | − | 4.63106i | 0.0999225 | − | 0.173071i | ||||
\(717\) | 6.69505 | + | 11.5962i | 0.250031 | + | 0.433067i | ||||
\(718\) | −9.64353 | − | 16.7031i | −0.359893 | − | 0.623353i | ||||
\(719\) | −20.0251 | + | 34.6845i | −0.746811 | + | 1.29351i | 0.202533 | + | 0.979275i | \(0.435083\pi\) |
−0.949344 | + | 0.314239i | \(0.898251\pi\) | |||||||
\(720\) | −6.33531 | −0.236103 | ||||||||
\(721\) | 10.0835 | + | 27.3307i | 0.375529 | + | 1.01785i | ||||
\(722\) | 6.22807 | 0.231785 | ||||||||
\(723\) | −1.64322 | + | 2.84615i | −0.0611121 | + | 0.105849i | ||||
\(724\) | 11.8469 | + | 20.5194i | 0.440286 | + | 0.762598i | ||||
\(725\) | −7.26249 | − | 12.5790i | −0.269722 | − | 0.467172i | ||||
\(726\) | −9.44941 | + | 16.3669i | −0.350700 | + | 0.607431i | ||||
\(727\) | 40.4544 | 1.50037 | 0.750185 | − | 0.661228i | \(-0.229964\pi\) | ||||
0.750185 | + | 0.661228i | \(0.229964\pi\) | |||||||
\(728\) | 2.53812 | − | 3.05189i | 0.0940688 | − | 0.113111i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −9.84411 | + | 17.0505i | −0.364347 | + | 0.631067i | ||||
\(731\) | 14.6138 | + | 25.3118i | 0.540510 | + | 0.936191i | ||||
\(732\) | −4.36798 | − | 7.56556i | −0.161445 | − | 0.279631i | ||||
\(733\) | 26.5084 | − | 45.9139i | 0.979110 | − | 1.69587i | 0.313464 | − | 0.949600i | \(-0.398510\pi\) |
0.665646 | − | 0.746268i | \(-0.268156\pi\) | |||||||
\(734\) | −14.4074 | −0.531788 | ||||||||
\(735\) | −4.02080 | − | 21.6889i | −0.148309 | − | 0.800006i | ||||
\(736\) | 5.52331 | 0.203592 | ||||||||
\(737\) | −8.95496 | + | 15.5104i | −0.329860 | + | 0.571334i | ||||
\(738\) | 2.75062 | + | 4.76422i | 0.101252 | + | 0.175373i | ||||
\(739\) | −15.2758 | − | 26.4585i | −0.561930 | − | 0.973292i | −0.997328 | − | 0.0730537i | \(-0.976726\pi\) |
0.435398 | − | 0.900238i | \(-0.356608\pi\) | |||||||
\(740\) | 7.51880 | − | 13.0229i | 0.276397 | − | 0.478733i | ||||
\(741\) | −2.02112 | −0.0742477 | ||||||||
\(742\) | 12.6265 | − | 15.1824i | 0.463532 | − | 0.557363i | ||||
\(743\) | −49.1733 | −1.80399 | −0.901997 | − | 0.431743i | \(-0.857899\pi\) | ||||
−0.901997 | + | 0.431743i | \(0.857899\pi\) | |||||||
\(744\) | −0.583835 | + | 1.01123i | −0.0214044 | + | 0.0370736i | ||||
\(745\) | −8.15175 | − | 14.1193i | −0.298657 | − | 0.517289i | ||||
\(746\) | −6.54742 | − | 11.3405i | −0.239718 | − | 0.415204i | ||||
\(747\) | 4.88750 | − | 8.46540i | 0.178824 | − | 0.309733i | ||||
\(748\) | 73.8138 | 2.69890 | ||||||||
\(749\) | 7.85303 | + | 21.2851i | 0.286943 | + | 0.777741i | ||||
\(750\) | 0.130761 | 0.00477471 | ||||||||
\(751\) | −20.7611 | + | 35.9592i | −0.757582 | + | 1.31217i | 0.186498 | + | 0.982455i | \(0.440286\pi\) |
−0.944080 | + | 0.329715i | \(0.893047\pi\) | |||||||
\(752\) | −10.5221 | − | 18.2248i | −0.383701 | − | 0.664590i | ||||
\(753\) | 5.13845 | + | 8.90005i | 0.187255 | + | 0.324336i | ||||
\(754\) | −0.605877 | + | 1.04941i | −0.0220647 | + | 0.0382172i | ||||
\(755\) | 15.9140 | 0.579170 | ||||||||
\(756\) | 4.29652 | + | 0.738178i | 0.156263 | + | 0.0268473i | ||||
\(757\) | −26.7837 | −0.973470 | −0.486735 | − | 0.873550i | \(-0.661812\pi\) | ||||
−0.486735 | + | 0.873550i | \(0.661812\pi\) | |||||||
\(758\) | 0.250644 | − | 0.434129i | 0.00910381 | − | 0.0157683i | ||||
\(759\) | 3.27267 | + | 5.66843i | 0.118790 | + | 0.205751i | ||||
\(760\) | −9.94925 | − | 17.2326i | −0.360897 | − | 0.625093i | ||||
\(761\) | 11.8342 | − | 20.4974i | 0.428988 | − | 0.743029i | −0.567795 | − | 0.823170i | \(-0.692204\pi\) |
0.996784 | + | 0.0801405i | \(0.0255369\pi\) | |||||||
\(762\) | −7.67653 | −0.278091 | ||||||||
\(763\) | 29.4190 | + | 5.05443i | 1.06504 | + | 0.182983i | ||||
\(764\) | 16.2945 | 0.589516 | ||||||||
\(765\) | 10.7837 | − | 18.6779i | 0.389885 | − | 0.675301i | ||||
\(766\) | 9.80366 | + | 16.9804i | 0.354221 | + | 0.613528i | ||||
\(767\) | 2.32256 | + | 4.02280i | 0.0838629 | + | 0.145255i | ||||
\(768\) | −2.66641 | + | 4.61835i | −0.0962157 | + | 0.166650i | ||||
\(769\) | −16.2072 | −0.584448 | −0.292224 | − | 0.956350i | \(-0.594395\pi\) | ||||
−0.292224 | + | 0.956350i | \(0.594395\pi\) | |||||||
\(770\) | 11.2111 | + | 30.3870i | 0.404020 | + | 1.09507i | ||||
\(771\) | −23.4070 | −0.842984 | ||||||||
\(772\) | −2.95808 | + | 5.12355i | −0.106464 | + | 0.184401i | ||||
\(773\) | −21.9449 | − | 38.0098i | −0.789305 | − | 1.36712i | −0.926393 | − | 0.376557i | \(-0.877108\pi\) |
0.137089 | − | 0.990559i | \(-0.456225\pi\) | |||||||
\(774\) | −1.26731 | − | 2.19505i | −0.0455526 | − | 0.0788994i | ||||
\(775\) | 1.32948 | − | 2.30273i | 0.0477563 | − | 0.0827163i | ||||
\(776\) | −17.6270 | −0.632773 | ||||||||
\(777\) | −4.89953 | + | 5.89131i | −0.175770 | + | 0.211350i | ||||
\(778\) | −0.458686 | −0.0164447 | ||||||||
\(779\) | 13.5167 | − | 23.4116i | 0.484285 | − | 0.838806i | ||||
\(780\) | −1.79905 | − | 3.11604i | −0.0644162 | − | 0.111572i | ||||
\(781\) | −1.92177 | − | 3.32860i | −0.0687663 | − | 0.119107i | ||||
\(782\) | −2.03110 | + | 3.51798i | −0.0726322 | + | 0.125803i | ||||
\(783\) | −2.94619 | −0.105288 | ||||||||
\(784\) | 13.2661 | + | 4.69710i | 0.473789 | + | 0.167754i | ||||
\(785\) | 30.4033 | 1.08514 | ||||||||
\(786\) | −1.82411 | + | 3.15945i | −0.0650639 | + | 0.112694i | ||||
\(787\) | 12.8675 | + | 22.2871i | 0.458675 | + | 0.794449i | 0.998891 | − | 0.0470774i | \(-0.0149907\pi\) |
−0.540216 | + | 0.841527i | \(0.681657\pi\) | |||||||
\(788\) | 6.76621 | + | 11.7194i | 0.241036 | + | 0.417487i | ||||
\(789\) | −13.6828 | + | 23.6993i | −0.487121 | + | 0.843719i | ||||
\(790\) | −25.0381 | −0.890816 | ||||||||
\(791\) | −5.31488 | + | 6.39074i | −0.188975 | + | 0.227229i | ||||
\(792\) | −14.1708 | −0.503539 | ||||||||
\(793\) | 1.83699 | − | 3.18176i | 0.0652335 | − | 0.112988i | ||||
\(794\) | −6.27301 | − | 10.8652i | −0.222621 | − | 0.385591i | ||||
\(795\) | −19.8130 | − | 34.3172i | −0.702695 | − | 1.21710i | ||||
\(796\) | 1.84963 | − | 3.20365i | 0.0655583 | − | 0.113550i | ||||
\(797\) | −0.541418 | −0.0191780 | −0.00958901 | − | 0.999954i | \(-0.503052\pi\) | ||||
−0.00958901 | + | 0.999954i | \(0.503052\pi\) | |||||||
\(798\) | 1.58533 | + | 4.29694i | 0.0561202 | + | 0.152110i | ||||
\(799\) | 71.6409 | 2.53447 | ||||||||
\(800\) | 13.6152 | − | 23.5822i | 0.481370 | − | 0.833757i | ||||
\(801\) | −1.46470 | − | 2.53693i | −0.0517525 | − | 0.0896380i | ||||
\(802\) | 8.40268 | + | 14.5539i | 0.296709 | + | 0.513915i | ||||
\(803\) | 34.4501 | − | 59.6693i | 1.21572 | − | 2.10568i | ||||
\(804\) | −4.50864 | −0.159008 | ||||||||
\(805\) | 8.21691 | + | 1.41173i | 0.289608 | + | 0.0497571i | ||||
\(806\) | −0.221825 | −0.00781344 | ||||||||
\(807\) | −13.1885 | + | 22.8432i | −0.464258 | + | 0.804119i | ||||
\(808\) | 0.144244 | + | 0.249838i | 0.00507448 | + | 0.00878926i | ||||
\(809\) | 1.94860 | + | 3.37507i | 0.0685091 | + | 0.118661i | 0.898245 | − | 0.439495i | \(-0.144842\pi\) |
−0.829736 | + | 0.558156i | \(0.811509\pi\) | |||||||
\(810\) | −0.935165 | + | 1.61975i | −0.0328583 | + | 0.0569123i | ||||
\(811\) | 17.8242 | 0.625892 | 0.312946 | − | 0.949771i | \(-0.398684\pi\) | ||||
0.312946 | + | 0.949771i | \(0.398684\pi\) | |||||||
\(812\) | −12.6584 | − | 2.17481i | −0.444221 | − | 0.0763210i | ||||
\(813\) | −4.30436 | −0.150960 | ||||||||
\(814\) | 5.62550 | − | 9.74366i | 0.197174 | − | 0.341515i | ||||
\(815\) | 37.7082 | + | 65.3125i | 1.32086 | + | 2.28780i | ||||
\(816\) | 6.87990 | + | 11.9163i | 0.240845 | + | 0.417155i | ||||
\(817\) | −6.22762 | + | 10.7866i | −0.217877 | + | 0.377374i | ||||
\(818\) | 13.2442 | 0.463073 | ||||||||
\(819\) | 0.634614 | + | 1.72008i | 0.0221752 | + | 0.0601044i | ||||
\(820\) | 48.1261 | 1.68063 | ||||||||
\(821\) | 9.34489 | − | 16.1858i | 0.326139 | − | 0.564889i | −0.655603 | − | 0.755105i | \(-0.727586\pi\) |
0.981742 | + | 0.190217i | \(0.0609190\pi\) | |||||||
\(822\) | 5.82020 | + | 10.0809i | 0.203003 | + | 0.351611i | ||||
\(823\) | −1.72465 | − | 2.98717i | −0.0601174 | − | 0.104126i | 0.834400 | − | 0.551159i | \(-0.185814\pi\) |
−0.894518 | + | 0.447033i | \(0.852481\pi\) | |||||||
\(824\) | 11.9192 | − | 20.6446i | 0.415225 | − | 0.719190i | ||||
\(825\) | 32.2691 | 1.12347 | ||||||||
\(826\) | 6.73076 | − | 8.09323i | 0.234193 | − | 0.281599i | ||||
\(827\) | 55.4418 | 1.92790 | 0.963950 | − | 0.266085i | \(-0.0857301\pi\) | ||||
0.963950 | + | 0.266085i | \(0.0857301\pi\) | |||||||
\(828\) | −0.823862 | + | 1.42697i | −0.0286312 | + | 0.0495907i | ||||
\(829\) | −18.3829 | − | 31.8402i | −0.638465 | − | 1.10585i | −0.985770 | − | 0.168102i | \(-0.946236\pi\) |
0.347304 | − | 0.937752i | \(-0.387097\pi\) | |||||||
\(830\) | 9.14124 | + | 15.8331i | 0.317297 | + | 0.549575i | ||||
\(831\) | −7.32466 | + | 12.6867i | −0.254090 | + | 0.440096i | ||||
\(832\) | 0.514625 | 0.0178414 | ||||||||
\(833\) | −36.4290 | + | 31.1162i | −1.26219 | + | 1.07811i | ||||
\(834\) | −7.03052 | −0.243447 | ||||||||
\(835\) | 18.9652 | − | 32.8487i | 0.656318 | − | 1.13678i | ||||
\(836\) | 15.7278 | + | 27.2413i | 0.543956 | + | 0.942160i | ||||
\(837\) | −0.269666 | − | 0.467076i | −0.00932104 | − | 0.0161445i | ||||
\(838\) | −1.77975 | + | 3.08262i | −0.0614805 | + | 0.106487i | ||||
\(839\) | −25.3306 | −0.874508 | −0.437254 | − | 0.899338i | \(-0.644049\pi\) | ||||
−0.437254 | + | 0.899338i | \(0.644049\pi\) | |||||||
\(840\) | −11.5419 | + | 13.8782i | −0.398233 | + | 0.478844i | ||||
\(841\) | −20.3200 | −0.700688 | ||||||||
\(842\) | 3.69387 | − | 6.39798i | 0.127299 | − | 0.220489i | ||||
\(843\) | 8.51902 | + | 14.7554i | 0.293411 | + | 0.508202i | ||||
\(844\) | −19.0134 | − | 32.9322i | −0.654469 | − | 1.13357i | ||||
\(845\) | −19.7262 | + | 34.1668i | −0.678603 | + | 1.17537i | ||||
\(846\) | −6.21272 | −0.213598 | ||||||||
\(847\) | −29.1603 | − | 79.0369i | −1.00196 | − | 2.71574i | ||||
\(848\) | 25.2811 | 0.868156 | ||||||||
\(849\) | −8.95641 | + | 15.5130i | −0.307383 | + | 0.532403i | ||||
\(850\) | 10.0135 | + | 17.3439i | 0.343461 | + | 0.594892i | ||||
\(851\) | −1.44806 | − | 2.50812i | −0.0496390 | − | 0.0859772i | ||||
\(852\) | 0.483786 | − | 0.837942i | 0.0165742 | − | 0.0287074i | ||||
\(853\) | −51.3694 | −1.75885 | −0.879427 | − | 0.476034i | \(-0.842074\pi\) | ||||
−0.879427 | + | 0.476034i | \(0.842074\pi\) | |||||||
\(854\) | −8.20539 | − | 1.40976i | −0.280783 | − | 0.0482408i | ||||
\(855\) | 9.19088 | 0.314321 | ||||||||
\(856\) | 9.28266 | − | 16.0780i | 0.317275 | − | 0.549536i | ||||
\(857\) | −4.77766 | − | 8.27515i | −0.163202 | − | 0.282674i | 0.772814 | − | 0.634633i | \(-0.218849\pi\) |
−0.936015 | + | 0.351960i | \(0.885515\pi\) | |||||||
\(858\) | −1.34603 | − | 2.33140i | −0.0459528 | − | 0.0795925i | ||||
\(859\) | 1.81712 | − | 3.14735i | 0.0619994 | − | 0.107386i | −0.833360 | − | 0.552731i | \(-0.813586\pi\) |
0.895359 | + | 0.445345i | \(0.146919\pi\) | |||||||
\(860\) | −22.1734 | −0.756108 | ||||||||
\(861\) | −24.1686 | − | 4.15237i | −0.823663 | − | 0.141512i | ||||
\(862\) | −3.19909 | −0.108961 | ||||||||
\(863\) | −4.28894 | + | 7.42866i | −0.145997 | + | 0.252875i | −0.929745 | − | 0.368205i | \(-0.879972\pi\) |
0.783747 | + | 0.621080i | \(0.213306\pi\) | |||||||
\(864\) | −2.76166 | − | 4.78333i | −0.0939534 | − | 0.162732i | ||||
\(865\) | −26.1610 | − | 45.3122i | −0.889501 | − | 1.54066i | ||||
\(866\) | −9.69643 | + | 16.7947i | −0.329498 | + | 0.570707i | ||||
\(867\) | −29.8427 | −1.01351 | ||||||||
\(868\) | −0.813841 | − | 2.20586i | −0.0276236 | − | 0.0748718i | ||||
\(869\) | 87.6225 | 2.97239 | ||||||||
\(870\) | 2.75517 | − | 4.77210i | 0.0934092 | − | 0.161789i | ||||
\(871\) | −0.948075 | − | 1.64211i | −0.0321243 | − | 0.0556409i | ||||
\(872\) | −12.2132 | − | 21.1539i | −0.413591 | − | 0.716361i | ||||
\(873\) | 4.07085 | − | 7.05092i | 0.137777 | − | 0.238637i | ||||
\(874\) | −1.73110 | −0.0585553 | ||||||||
\(875\) | −0.372711 | + | 0.448157i | −0.0125999 | + | 0.0151505i | ||||
\(876\) | 17.3449 | 0.586031 | ||||||||
\(877\) | −22.8156 | + | 39.5177i | −0.770427 | + | 1.33442i | 0.166902 | + | 0.985973i | \(0.446623\pi\) |
−0.937329 | + | 0.348445i | \(0.886710\pi\) | |||||||
\(878\) | 0.00855621 | + | 0.0148198i | 0.000288758 | + | 0.000500144i | ||||
\(879\) | −9.38493 | − | 16.2552i | −0.316546 | − | 0.548273i | ||||
\(880\) | −20.7334 | + | 35.9113i | −0.698922 | + | 1.21057i | ||||
\(881\) | −17.3176 | −0.583446 | −0.291723 | − | 0.956503i | \(-0.594229\pi\) | ||||
−0.291723 | + | 0.956503i | \(0.594229\pi\) | |||||||
\(882\) | 3.15914 | − | 2.69840i | 0.106374 | − | 0.0908599i | ||||
\(883\) | 14.3872 | 0.484166 | 0.242083 | − | 0.970256i | \(-0.422169\pi\) | ||||
0.242083 | + | 0.970256i | \(0.422169\pi\) | |||||||
\(884\) | −3.90739 | + | 6.76780i | −0.131420 | + | 0.227626i | ||||
\(885\) | −10.5617 | − | 18.2934i | −0.355027 | − | 0.614924i | ||||
\(886\) | 5.02503 | + | 8.70361i | 0.168819 | + | 0.292403i | ||||
\(887\) | −1.08599 | + | 1.88099i | −0.0364639 | + | 0.0631573i | −0.883681 | − | 0.468089i | \(-0.844943\pi\) |
0.847218 | + | 0.531246i | \(0.178276\pi\) | |||||||
\(888\) | 6.27020 | 0.210414 | ||||||||
\(889\) | 21.8806 | − | 26.3098i | 0.733853 | − | 0.882403i | ||||
\(890\) | 5.47893 | 0.183654 | ||||||||
\(891\) | 3.27267 | − | 5.66843i | 0.109639 | − | 0.189900i | ||||
\(892\) | 3.53085 | + | 6.11561i | 0.118222 | + | 0.204766i | ||||
\(893\) | 15.2648 | + | 26.4394i | 0.510817 | + | 0.884760i | ||||
\(894\) | 1.53538 | − | 2.65936i | 0.0513508 | − | 0.0889422i | ||||
\(895\) | −10.2268 | −0.341846 | ||||||||
\(896\) | −10.5201 | − | 28.5140i | −0.351452 | − | 0.952587i | ||||
\(897\) | −0.692965 | −0.0231374 | ||||||||
\(898\) | 6.18032 | − | 10.7046i | 0.206240 | − | 0.357218i | ||||
\(899\) | 0.794489 | + | 1.37610i | 0.0264977 | + | 0.0458954i | ||||
\(900\) | 4.06171 | + | 7.03509i | 0.135390 | + | 0.234503i | ||||
\(901\) | −43.0323 | + | 74.5342i | −1.43361 | + | 2.48309i | ||||
\(902\) | 36.0075 | 1.19892 | ||||||||
\(903\) | 11.1354 | + | 1.91315i | 0.370561 | + | 0.0636656i | ||||
\(904\) | 6.80175 | 0.226223 | ||||||||
\(905\) | 22.6567 | − | 39.2425i | 0.753134 | − | 1.30447i | ||||
\(906\) | 1.49870 | + | 2.59582i | 0.0497910 | + | 0.0862405i | ||||
\(907\) | 6.43433 | + | 11.1446i | 0.213648 | + | 0.370050i | 0.952854 | − | 0.303430i | \(-0.0981320\pi\) |
−0.739205 | + | 0.673480i | \(0.764799\pi\) | |||||||
\(908\) | 9.00759 | − | 15.6016i | 0.298927 | − | 0.517757i | ||||
\(909\) | −0.133249 | −0.00441959 | ||||||||
\(910\) | −3.37957 | − | 0.580639i | −0.112032 | − | 0.0192480i | ||||
\(911\) | −4.61820 | −0.153008 | −0.0765039 | − | 0.997069i | \(-0.524376\pi\) | ||||
−0.0765039 | + | 0.997069i | \(0.524376\pi\) | |||||||
\(912\) | −2.93185 | + | 5.07812i | −0.0970833 | + | 0.168153i | ||||
\(913\) | −31.9904 | − | 55.4089i | −1.05873 | − | 1.83377i | ||||
\(914\) | −4.25896 | − | 7.37673i | −0.140874 | − | 0.244001i | ||||
\(915\) | −8.35357 | + | 14.4688i | −0.276161 | + | 0.478324i | ||||
\(916\) | −9.19019 | −0.303652 | ||||||||
\(917\) | −5.62909 | − | 15.2573i | −0.185889 | − | 0.503839i | ||||
\(918\) | 4.06221 | 0.134073 | ||||||||
\(919\) | 0.197692 | − | 0.342412i | 0.00652124 | − | 0.0112951i | −0.862746 | − | 0.505637i | \(-0.831258\pi\) |
0.869268 | + | 0.494342i | \(0.164591\pi\) | |||||||
\(920\) | −3.41122 | − | 5.90841i | −0.112465 | − | 0.194795i | ||||
\(921\) | −0.711865 | − | 1.23299i | −0.0234568 | − | 0.0406283i | ||||
\(922\) | −1.05299 | + | 1.82382i | −0.0346782 | + | 0.0600644i | ||||
\(923\) | 0.406921 | 0.0133940 | ||||||||
\(924\) | 18.2454 | − | 21.9387i | 0.600229 | − | 0.721730i | ||||
\(925\) | −14.2782 | −0.469463 | ||||||||
\(926\) | 3.62845 | − | 6.28465i | 0.119238 | − | 0.206527i | ||||
\(927\) | 5.50533 | + | 9.53551i | 0.180819 | + | 0.313187i | ||||
\(928\) | 8.13637 | + | 14.0926i | 0.267089 | + | 0.462612i | ||||
\(929\) | 18.3243 | − | 31.7387i | 0.601202 | − | 1.04131i | −0.391438 | − | 0.920205i | \(-0.628022\pi\) |
0.992639 | − | 0.121107i | \(-0.0386445\pi\) | |||||||
\(930\) | 1.00873 | 0.0330776 | ||||||||
\(931\) | −19.2456 | − | 6.81427i | −0.630750 | − | 0.223329i | ||||
\(932\) | 36.6958 | 1.20201 | ||||||||
\(933\) | −2.21236 | + | 3.83191i | −0.0724293 | + | 0.125451i | ||||
\(934\) | −8.48330 | − | 14.6935i | −0.277582 | − | 0.480786i | ||||
\(935\) | −70.5829 | − | 122.253i | −2.30831 | − | 3.99811i | ||||
\(936\) | 0.750145 | − | 1.29929i | 0.0245192 | − | 0.0424686i | ||||
\(937\) | −37.1650 | −1.21413 | −0.607063 | − | 0.794654i | \(-0.707652\pi\) | ||||
−0.607063 | + | 0.794654i | \(0.707652\pi\) | |||||||
\(938\) | −2.74751 | + | 3.30367i | −0.0897094 | + | 0.107869i | ||||
\(939\) | −21.6865 | −0.707714 | ||||||||
\(940\) | −27.1751 | + | 47.0687i | −0.886354 | + | 1.53521i | ||||
\(941\) | −10.6874 | − | 18.5111i | −0.348398 | − | 0.603443i | 0.637567 | − | 0.770395i | \(-0.279941\pi\) |
−0.985965 | + | 0.166952i | \(0.946608\pi\) | |||||||
\(942\) | 2.86322 | + | 4.95925i | 0.0932888 | + | 0.161581i | ||||
\(943\) | 4.63435 | − | 8.02694i | 0.150915 | − | 0.261393i | ||||
\(944\) | 13.4765 | 0.438623 | ||||||||
\(945\) | −2.88586 | − | 7.82192i | −0.0938769 | − | 0.254447i | ||||
\(946\) | −16.5900 | −0.539386 | ||||||||
\(947\) | −29.0241 | + | 50.2713i | −0.943158 | + | 1.63360i | −0.183760 | + | 0.982971i | \(0.558827\pi\) |
−0.759398 | + | 0.650626i | \(0.774506\pi\) | |||||||
\(948\) | 11.0290 | + | 19.1029i | 0.358207 | + | 0.620432i | ||||
\(949\) | 3.64728 | + | 6.31728i | 0.118396 | + | 0.205068i | ||||
\(950\) | −4.26724 | + | 7.39107i | −0.138447 | + | 0.239798i | ||||
\(951\) | 11.6270 | 0.377031 | ||||||||
\(952\) | 38.6381 | + | 6.63836i | 1.25227 | + | 0.215150i | ||||
\(953\) | 0.853059 | 0.0276333 | 0.0138166 | − | 0.999905i | \(-0.495602\pi\) | ||||
0.0138166 | + | 0.999905i | \(0.495602\pi\) | |||||||
\(954\) | 3.73178 | − | 6.46363i | 0.120821 | − | 0.209268i | ||||
\(955\) | −15.5813 | − | 26.9876i | −0.504200 | − | 0.873299i | ||||
\(956\) | 11.0316 | + | 19.1073i | 0.356787 | + | 0.617974i | ||||
\(957\) | −9.64191 | + | 16.7003i | −0.311679 | + | 0.539844i | ||||
\(958\) | −17.9656 | −0.580442 | ||||||||
\(959\) | −51.1398 | − | 8.78624i | −1.65139 | − | 0.283723i | ||||
\(960\) | −2.34022 | −0.0755302 | ||||||||
\(961\) | 15.3546 | − | 26.5949i | 0.495308 | − | 0.857899i | ||||
\(962\) | 0.595581 | + | 1.03158i | 0.0192023 | + | 0.0332594i | ||||
\(963\) | 4.28755 | + | 7.42625i | 0.138164 | + | 0.239308i | ||||
\(964\) | −2.70758 | + | 4.68966i | −0.0872052 | + | 0.151044i | ||||
\(965\) | 11.3144 | 0.364224 | ||||||||
\(966\) | 0.543550 | + | 1.47326i | 0.0174884 | + | 0.0474013i | ||||
\(967\) | 38.6397 | 1.24257 | 0.621284 | − | 0.783585i | \(-0.286611\pi\) | ||||
0.621284 | + | 0.783585i | \(0.286611\pi\) | |||||||
\(968\) | −34.4688 | + | 59.7018i | −1.10787 | + | 1.91889i | ||||
\(969\) | −9.98094 | − | 17.2875i | −0.320634 | − | 0.555354i | ||||
\(970\) | 7.61383 | + | 13.1875i | 0.244465 | + | 0.423426i | ||||
\(971\) | 20.5682 | − | 35.6252i | 0.660066 | − | 1.14327i | −0.320532 | − | 0.947238i | \(-0.603862\pi\) |
0.980598 | − | 0.196030i | \(-0.0628050\pi\) | |||||||
\(972\) | 1.64772 | 0.0528508 | ||||||||
\(973\) | 20.0393 | − | 24.0957i | 0.642430 | − | 0.772473i | ||||
\(974\) | −17.1748 | −0.550318 | ||||||||
\(975\) | −1.70819 | + | 2.95867i | −0.0547058 | + | 0.0947533i | ||||
\(976\) | −5.32951 | − | 9.23098i | −0.170593 | − | 0.295477i | ||||
\(977\) | −3.79942 | − | 6.58079i | −0.121554 | − | 0.210538i | 0.798827 | − | 0.601561i | \(-0.205454\pi\) |
−0.920381 | + | 0.391023i | \(0.872121\pi\) | |||||||
\(978\) | −7.10232 | + | 12.3016i | −0.227107 | + | 0.393361i | ||||
\(979\) | −19.1739 | −0.612800 | ||||||||
\(980\) | −6.62517 | − | 35.7373i | −0.211633 | − | 1.14159i | ||||
\(981\) | 11.2823 | 0.360215 | ||||||||
\(982\) | −3.53699 | + | 6.12625i | −0.112870 | + | 0.195497i | ||||
\(983\) | −19.5315 | − | 33.8296i | −0.622959 | − | 1.07900i | −0.988932 | − | 0.148371i | \(-0.952597\pi\) |
0.365973 | − | 0.930626i | \(-0.380736\pi\) | |||||||
\(984\) | 10.0335 | + | 17.3785i | 0.319857 | + | 0.554008i | ||||
\(985\) | 12.9401 | − | 22.4129i | 0.412306 | − | 0.714134i | ||||
\(986\) | −11.9680 | −0.381140 | ||||||||
\(987\) | 17.7083 | − | 21.2929i | 0.563661 | − | 0.677760i | ||||
\(988\) | −3.33025 | −0.105949 | ||||||||
\(989\) | −2.13522 | + | 3.69830i | −0.0678959 | + | 0.117599i | ||||
\(990\) | 6.12097 | + | 10.6018i | 0.194537 | + | 0.336948i | ||||
\(991\) | −0.903144 | − | 1.56429i | −0.0286893 | − | 0.0496914i | 0.851324 | − | 0.524640i | \(-0.175800\pi\) |
−0.880014 | + | 0.474949i | \(0.842467\pi\) | |||||||
\(992\) | −1.48945 | + | 2.57981i | −0.0472901 | + | 0.0819089i | ||||
\(993\) | −7.89484 | −0.250535 | ||||||||
\(994\) | −0.319182 | − | 0.865122i | −0.0101238 | − | 0.0274400i | ||||
\(995\) | −7.07467 | −0.224282 | ||||||||
\(996\) | 8.05326 | − | 13.9486i | 0.255177 | − | 0.441980i | ||||
\(997\) | 19.7503 | + | 34.2086i | 0.625499 | + | 1.08340i | 0.988444 | + | 0.151586i | \(0.0484381\pi\) |
−0.362945 | + | 0.931811i | \(0.618229\pi\) | |||||||
\(998\) | 3.07857 | + | 5.33224i | 0.0974504 | + | 0.168789i | ||||
\(999\) | −1.44806 | + | 2.50812i | −0.0458147 | + | 0.0793534i |
(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 | 483.2.i.f.415.4 | yes | 12 | |
7.2 | even | 3 | 3381.2.a.bc.1.3 | 6 | |||
7.4 | even | 3 | inner | 483.2.i.f.277.4 | ✓ | 12 | |
7.5 | odd | 6 | 3381.2.a.bd.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.f.277.4 | ✓ | 12 | 7.4 | even | 3 | inner | |
483.2.i.f.415.4 | yes | 12 | 1.1 | even | 1 | trivial | |
3381.2.a.bc.1.3 | 6 | 7.2 | even | 3 | |||
3381.2.a.bd.1.3 | 6 | 7.5 | odd | 6 |