Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.13140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 81.2 | ||
Root | \(-0.386111 + 0.280526i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.81 |
Dual form | 605.2.g.e.366.2 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.386111 | + | 0.280526i | 0.273022 | + | 0.198362i | 0.715868 | − | 0.698236i | \(-0.246031\pi\) |
−0.442846 | + | 0.896598i | \(0.646031\pi\) | |||||||
\(3\) | 0.0998345 | − | 0.307259i | 0.0576395 | − | 0.177396i | −0.918092 | − | 0.396368i | \(-0.870270\pi\) |
0.975731 | + | 0.218972i | \(0.0702704\pi\) | |||||||
\(4\) | −0.547647 | − | 1.68548i | −0.273823 | − | 0.842742i | ||||
\(5\) | 0.809017 | − | 0.587785i | 0.361803 | − | 0.262866i | ||||
\(6\) | 0.124741 | − | 0.0906300i | 0.0509255 | − | 0.0369995i | ||||
\(7\) | −0.829779 | − | 2.55380i | −0.313627 | − | 0.965244i | −0.976316 | − | 0.216350i | \(-0.930585\pi\) |
0.662689 | − | 0.748895i | \(-0.269415\pi\) | |||||||
\(8\) | 0.556333 | − | 1.71222i | 0.196693 | − | 0.605360i | ||||
\(9\) | 2.34261 | + | 1.70201i | 0.780870 | + | 0.567335i | ||||
\(10\) | 0.477260 | 0.150923 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.572554 | −0.165282 | ||||||||
\(13\) | −3.77637 | − | 2.74369i | −1.04738 | − | 0.760963i | −0.0756644 | − | 0.997133i | \(-0.524108\pi\) |
−0.971712 | + | 0.236170i | \(0.924108\pi\) | |||||||
\(14\) | 0.396020 | − | 1.21882i | 0.105841 | − | 0.325745i | ||||
\(15\) | −0.0998345 | − | 0.307259i | −0.0257771 | − | 0.0793339i | ||||
\(16\) | −2.17239 | + | 1.57833i | −0.543097 | + | 0.394583i | ||||
\(17\) | −3.74278 | + | 2.71929i | −0.907756 | + | 0.659524i | −0.940446 | − | 0.339942i | \(-0.889593\pi\) |
0.0326901 | + | 0.999466i | \(0.489593\pi\) | |||||||
\(18\) | 0.427051 | + | 1.31433i | 0.100657 | + | 0.309790i | ||||
\(19\) | 1.34127 | − | 4.12801i | 0.307709 | − | 0.947030i | −0.670944 | − | 0.741508i | \(-0.734111\pi\) |
0.978653 | − | 0.205522i | \(-0.0658891\pi\) | |||||||
\(20\) | −1.43376 | − | 1.04169i | −0.320598 | − | 0.232928i | ||||
\(21\) | −0.867517 | −0.189308 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.77222 | 0.578048 | 0.289024 | − | 0.957322i | \(-0.406669\pi\) | ||||
0.289024 | + | 0.957322i | \(0.406669\pi\) | |||||||
\(24\) | −0.470553 | − | 0.341876i | −0.0960511 | − | 0.0697852i | ||||
\(25\) | 0.309017 | − | 0.951057i | 0.0618034 | − | 0.190211i | ||||
\(26\) | −0.688421 | − | 2.11874i | −0.135010 | − | 0.415519i | ||||
\(27\) | 1.54094 | − | 1.11956i | 0.296554 | − | 0.215459i | ||||
\(28\) | −3.84996 | + | 2.79716i | −0.727573 | + | 0.528613i | ||||
\(29\) | 0.931196 | + | 2.86593i | 0.172919 | + | 0.532189i | 0.999532 | − | 0.0305806i | \(-0.00973564\pi\) |
−0.826613 | + | 0.562770i | \(0.809736\pi\) | |||||||
\(30\) | 0.0476470 | − | 0.146642i | 0.00869911 | − | 0.0267731i | ||||
\(31\) | −1.93056 | − | 1.40263i | −0.346738 | − | 0.251920i | 0.400761 | − | 0.916183i | \(-0.368746\pi\) |
−0.747499 | + | 0.664262i | \(0.768746\pi\) | |||||||
\(32\) | −4.88221 | −0.863061 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.20796 | −0.378662 | ||||||||
\(35\) | −2.17239 | − | 1.57833i | −0.367201 | − | 0.266787i | ||||
\(36\) | 1.58578 | − | 4.88053i | 0.264297 | − | 0.813422i | ||||
\(37\) | −3.28884 | − | 10.1220i | −0.540682 | − | 1.66405i | −0.731041 | − | 0.682333i | \(-0.760965\pi\) |
0.190360 | − | 0.981714i | \(-0.439035\pi\) | |||||||
\(38\) | 1.67589 | − | 1.21761i | 0.271866 | − | 0.197522i | ||||
\(39\) | −1.22004 | + | 0.886408i | −0.195362 | + | 0.141939i | ||||
\(40\) | −0.556333 | − | 1.71222i | −0.0879640 | − | 0.270725i | ||||
\(41\) | 0.683053 | − | 2.10222i | 0.106675 | − | 0.328312i | −0.883445 | − | 0.468535i | \(-0.844782\pi\) |
0.990120 | + | 0.140223i | \(0.0447820\pi\) | |||||||
\(42\) | −0.334958 | − | 0.243361i | −0.0516852 | − | 0.0375515i | ||||
\(43\) | 7.06719 | 1.07774 | 0.538868 | − | 0.842390i | \(-0.318852\pi\) | ||||
0.538868 | + | 0.842390i | \(0.318852\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.89563 | 0.431654 | ||||||||
\(46\) | 1.07039 | + | 0.777682i | 0.157820 | + | 0.114663i | ||||
\(47\) | 1.34798 | − | 4.14865i | 0.196623 | − | 0.605143i | −0.803331 | − | 0.595533i | \(-0.796941\pi\) |
0.999954 | − | 0.00961001i | \(-0.00305901\pi\) | |||||||
\(48\) | 0.268077 | + | 0.825058i | 0.0386936 | + | 0.119087i | ||||
\(49\) | −0.170221 | + | 0.123673i | −0.0243174 | + | 0.0176676i | ||||
\(50\) | 0.386111 | − | 0.280526i | 0.0546044 | − | 0.0396724i | ||||
\(51\) | 0.461867 | + | 1.42148i | 0.0646743 | + | 0.199047i | ||||
\(52\) | −2.55633 | + | 7.86758i | −0.354500 | + | 1.09104i | ||||
\(53\) | 5.12435 | + | 3.72306i | 0.703883 | + | 0.511401i | 0.881195 | − | 0.472754i | \(-0.156740\pi\) |
−0.177311 | + | 0.984155i | \(0.556740\pi\) | |||||||
\(54\) | 0.909040 | 0.123705 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.83428 | −0.646008 | ||||||||
\(57\) | −1.13446 | − | 0.824235i | −0.150263 | − | 0.109173i | ||||
\(58\) | −0.444423 | + | 1.36779i | −0.0583556 | + | 0.179600i | ||||
\(59\) | 3.63011 | + | 11.1723i | 0.472600 | + | 1.45451i | 0.849167 | + | 0.528124i | \(0.177104\pi\) |
−0.376567 | + | 0.926389i | \(0.622896\pi\) | |||||||
\(60\) | −0.463206 | + | 0.336539i | −0.0597996 | + | 0.0434470i | ||||
\(61\) | −3.22201 | + | 2.34093i | −0.412537 | + | 0.299725i | −0.774628 | − | 0.632417i | \(-0.782063\pi\) |
0.362091 | + | 0.932143i | \(0.382063\pi\) | |||||||
\(62\) | −0.351935 | − | 1.08314i | −0.0446958 | − | 0.137559i | ||||
\(63\) | 2.40273 | − | 7.39484i | 0.302715 | − | 0.931662i | ||||
\(64\) | 2.45970 | + | 1.78708i | 0.307462 | + | 0.223385i | ||||
\(65\) | −4.66785 | −0.578975 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.31984 | 0.894260 | 0.447130 | − | 0.894469i | \(-0.352446\pi\) | ||||
0.447130 | + | 0.894469i | \(0.352446\pi\) | |||||||
\(68\) | 6.63303 | + | 4.81918i | 0.804373 | + | 0.584411i | ||||
\(69\) | 0.276763 | − | 0.851790i | 0.0333184 | − | 0.102543i | ||||
\(70\) | −0.396020 | − | 1.21882i | −0.0473335 | − | 0.145677i | ||||
\(71\) | −0.967351 | + | 0.702822i | −0.114803 | + | 0.0834096i | −0.643706 | − | 0.765273i | \(-0.722604\pi\) |
0.528902 | + | 0.848683i | \(0.322604\pi\) | |||||||
\(72\) | 4.21747 | − | 3.06417i | 0.497034 | − | 0.361116i | ||||
\(73\) | −0.315724 | − | 0.971700i | −0.0369528 | − | 0.113729i | 0.930879 | − | 0.365329i | \(-0.119043\pi\) |
−0.967831 | + | 0.251600i | \(0.919043\pi\) | |||||||
\(74\) | 1.56963 | − | 4.83083i | 0.182466 | − | 0.561572i | ||||
\(75\) | −0.261370 | − | 0.189896i | −0.0301804 | − | 0.0219274i | ||||
\(76\) | −7.69223 | −0.882360 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.719730 | −0.0814934 | ||||||||
\(79\) | 2.83328 | + | 2.05850i | 0.318769 | + | 0.231600i | 0.735650 | − | 0.677362i | \(-0.236877\pi\) |
−0.416881 | + | 0.908961i | \(0.636877\pi\) | |||||||
\(80\) | −0.829779 | + | 2.55380i | −0.0927721 | + | 0.285523i | ||||
\(81\) | 2.49424 | + | 7.67647i | 0.277137 | + | 0.852941i | ||||
\(82\) | 0.853463 | − | 0.620077i | 0.0942492 | − | 0.0684761i | ||||
\(83\) | 8.99290 | − | 6.53372i | 0.987099 | − | 0.717169i | 0.0278149 | − | 0.999613i | \(-0.491145\pi\) |
0.959284 | + | 0.282444i | \(0.0911451\pi\) | |||||||
\(84\) | 0.475093 | + | 1.46219i | 0.0518369 | + | 0.159538i | ||||
\(85\) | −1.42961 | + | 4.39990i | −0.155063 | + | 0.477236i | ||||
\(86\) | 2.72872 | + | 1.98253i | 0.294246 | + | 0.213782i | ||||
\(87\) | 0.973547 | 0.104375 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.76978 | 0.293596 | 0.146798 | − | 0.989167i | \(-0.453103\pi\) | ||||
0.146798 | + | 0.989167i | \(0.453103\pi\) | |||||||
\(90\) | 1.11803 | + | 0.812299i | 0.117851 | + | 0.0856239i | ||||
\(91\) | −3.87328 | + | 11.9207i | −0.406030 | + | 1.24963i | ||||
\(92\) | −1.51820 | − | 4.67254i | −0.158283 | − | 0.487146i | ||||
\(93\) | −0.623707 | + | 0.453150i | −0.0646754 | + | 0.0469894i | ||||
\(94\) | 1.68428 | − | 1.22370i | 0.173720 | − | 0.126215i | ||||
\(95\) | −1.34127 | − | 4.12801i | −0.137611 | − | 0.423525i | ||||
\(96\) | −0.487413 | + | 1.50010i | −0.0497464 | + | 0.153104i | ||||
\(97\) | −14.9945 | − | 10.8941i | −1.52246 | − | 1.10613i | −0.960252 | − | 0.279134i | \(-0.909952\pi\) |
−0.562207 | − | 0.826997i | \(-0.690048\pi\) | |||||||
\(98\) | −0.100418 | −0.0101438 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.77222 | −0.177222 | ||||||||
\(101\) | −5.75580 | − | 4.18183i | −0.572723 | − | 0.416108i | 0.263370 | − | 0.964695i | \(-0.415166\pi\) |
−0.836093 | + | 0.548587i | \(0.815166\pi\) | |||||||
\(102\) | −0.220430 | + | 0.678415i | −0.0218259 | + | 0.0671731i | ||||
\(103\) | 2.32639 | + | 7.15989i | 0.229226 | + | 0.705485i | 0.997835 | + | 0.0657661i | \(0.0209491\pi\) |
−0.768609 | + | 0.639719i | \(0.779051\pi\) | |||||||
\(104\) | −6.79871 | + | 4.93955i | −0.666669 | + | 0.484363i | ||||
\(105\) | −0.701836 | + | 0.509914i | −0.0684922 | + | 0.0497625i | ||||
\(106\) | 0.934153 | + | 2.87503i | 0.0907330 | + | 0.279247i | ||||
\(107\) | −5.57133 | + | 17.1468i | −0.538601 | + | 1.65764i | 0.197136 | + | 0.980376i | \(0.436836\pi\) |
−0.735737 | + | 0.677267i | \(0.763164\pi\) | |||||||
\(108\) | −2.73089 | − | 1.98411i | −0.262780 | − | 0.190921i | ||||
\(109\) | 16.3653 | 1.56751 | 0.783756 | − | 0.621068i | \(-0.213301\pi\) | ||||
0.783756 | + | 0.621068i | \(0.213301\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.43842 | −0.326360 | ||||||||
\(112\) | 5.83334 | + | 4.23817i | 0.551199 | + | 0.400469i | ||||
\(113\) | −0.634650 | + | 1.95325i | −0.0597029 | + | 0.183747i | −0.976460 | − | 0.215699i | \(-0.930797\pi\) |
0.916757 | + | 0.399445i | \(0.130797\pi\) | |||||||
\(114\) | −0.206809 | − | 0.636493i | −0.0193694 | − | 0.0596130i | ||||
\(115\) | 2.24278 | − | 1.62947i | 0.209140 | − | 0.151949i | ||||
\(116\) | 4.32051 | − | 3.13903i | 0.401149 | − | 0.291452i | ||||
\(117\) | −4.17678 | − | 12.8548i | −0.386143 | − | 1.18843i | ||||
\(118\) | −1.73251 | + | 5.33211i | −0.159490 | + | 0.490860i | ||||
\(119\) | 10.0502 | + | 7.30188i | 0.921298 | + | 0.669362i | ||||
\(120\) | −0.581635 | −0.0530958 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.90075 | −0.172086 | ||||||||
\(123\) | −0.577734 | − | 0.419748i | −0.0520925 | − | 0.0378474i | ||||
\(124\) | −1.30685 | + | 4.02207i | −0.117359 | + | 0.361193i | ||||
\(125\) | −0.309017 | − | 0.951057i | −0.0276393 | − | 0.0850651i | ||||
\(126\) | 3.00217 | − | 2.18120i | 0.267454 | − | 0.194317i | ||||
\(127\) | −0.0617011 | + | 0.0448285i | −0.00547509 | + | 0.00397788i | −0.590519 | − | 0.807023i | \(-0.701077\pi\) |
0.585044 | + | 0.811001i | \(0.301077\pi\) | |||||||
\(128\) | 3.46577 | + | 10.6665i | 0.306333 | + | 0.942798i | ||||
\(129\) | 0.705549 | − | 2.17146i | 0.0621201 | − | 0.191186i | ||||
\(130\) | −1.80231 | − | 1.30945i | −0.158073 | − | 0.114847i | ||||
\(131\) | 11.4831 | 1.00328 | 0.501642 | − | 0.865075i | \(-0.332730\pi\) | ||||
0.501642 | + | 0.865075i | \(0.332730\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.6550 | −1.01062 | ||||||||
\(134\) | 2.82627 | + | 2.05341i | 0.244153 | + | 0.177387i | ||||
\(135\) | 0.588587 | − | 1.81148i | 0.0506575 | − | 0.155908i | ||||
\(136\) | 2.57378 | + | 7.92127i | 0.220700 | + | 0.679243i | ||||
\(137\) | 14.8287 | − | 10.7737i | 1.26690 | − | 0.920458i | 0.267827 | − | 0.963467i | \(-0.413694\pi\) |
0.999075 | + | 0.0430086i | \(0.0136943\pi\) | |||||||
\(138\) | 0.345811 | − | 0.251246i | 0.0294374 | − | 0.0213875i | ||||
\(139\) | 7.16529 | + | 22.0525i | 0.607752 | + | 1.87047i | 0.476638 | + | 0.879100i | \(0.341855\pi\) |
0.131114 | + | 0.991367i | \(0.458145\pi\) | |||||||
\(140\) | −1.47055 | + | 4.52590i | −0.124284 | + | 0.382508i | ||||
\(141\) | −1.14013 | − | 0.828356i | −0.0960167 | − | 0.0697602i | ||||
\(142\) | −0.570666 | −0.0478892 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −7.77539 | −0.647949 | ||||||||
\(145\) | 2.43790 | + | 1.77124i | 0.202457 | + | 0.147094i | ||||
\(146\) | 0.150683 | − | 0.463754i | 0.0124706 | − | 0.0383805i | ||||
\(147\) | 0.0210057 | + | 0.0646489i | 0.00173252 | + | 0.00533215i | ||||
\(148\) | −15.2594 | + | 11.0866i | −1.25431 | + | 0.911311i | ||||
\(149\) | 11.8639 | − | 8.61964i | 0.971930 | − | 0.706149i | 0.0160396 | − | 0.999871i | \(-0.494894\pi\) |
0.955891 | + | 0.293723i | \(0.0948942\pi\) | |||||||
\(150\) | −0.0476470 | − | 0.146642i | −0.00389036 | − | 0.0119733i | ||||
\(151\) | 2.32350 | − | 7.15101i | 0.189084 | − | 0.581941i | −0.810911 | − | 0.585170i | \(-0.801028\pi\) |
0.999995 | + | 0.00322899i | \(0.00102782\pi\) | |||||||
\(152\) | −6.32185 | − | 4.59309i | −0.512770 | − | 0.372549i | ||||
\(153\) | −13.3961 | −1.08301 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.38630 | −0.191672 | ||||||||
\(156\) | 2.16217 | + | 1.57091i | 0.173113 | + | 0.125774i | ||||
\(157\) | −4.13523 | + | 12.7269i | −0.330028 | + | 1.01572i | 0.639092 | + | 0.769130i | \(0.279310\pi\) |
−0.969120 | + | 0.246590i | \(0.920690\pi\) | |||||||
\(158\) | 0.516500 | + | 1.58962i | 0.0410905 | + | 0.126464i | ||||
\(159\) | 1.65553 | − | 1.20281i | 0.131292 | − | 0.0953892i | ||||
\(160\) | −3.94979 | + | 2.86969i | −0.312258 | + | 0.226869i | ||||
\(161\) | −2.30033 | − | 7.07969i | −0.181291 | − | 0.557958i | ||||
\(162\) | −1.19040 | + | 3.66367i | −0.0935266 | + | 0.287845i | ||||
\(163\) | 0.624553 | + | 0.453764i | 0.0489188 | + | 0.0355416i | 0.611976 | − | 0.790876i | \(-0.290375\pi\) |
−0.563057 | + | 0.826418i | \(0.690375\pi\) | |||||||
\(164\) | −3.91733 | −0.305892 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.30514 | 0.411759 | ||||||||
\(167\) | −6.86234 | − | 4.98578i | −0.531024 | − | 0.385811i | 0.289717 | − | 0.957112i | \(-0.406439\pi\) |
−0.820741 | + | 0.571301i | \(0.806439\pi\) | |||||||
\(168\) | −0.482628 | + | 1.48538i | −0.0372356 | + | 0.114599i | ||||
\(169\) | 2.71589 | + | 8.35865i | 0.208915 | + | 0.642973i | ||||
\(170\) | −1.78628 | + | 1.29781i | −0.137001 | + | 0.0995372i | ||||
\(171\) | 10.1680 | − | 7.38746i | 0.777564 | − | 0.564933i | ||||
\(172\) | −3.87032 | − | 11.9116i | −0.295109 | − | 0.908253i | ||||
\(173\) | −1.56941 | + | 4.83014i | −0.119320 | + | 0.367229i | −0.992824 | − | 0.119589i | \(-0.961842\pi\) |
0.873504 | + | 0.486818i | \(0.161842\pi\) | |||||||
\(174\) | 0.375898 | + | 0.273106i | 0.0284967 | + | 0.0207041i | ||||
\(175\) | −2.68522 | −0.202984 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.79521 | 0.285265 | ||||||||
\(178\) | 1.06944 | + | 0.776996i | 0.0801581 | + | 0.0582383i | ||||
\(179\) | −3.49716 | + | 10.7632i | −0.261390 | + | 0.804476i | 0.731113 | + | 0.682256i | \(0.239001\pi\) |
−0.992503 | + | 0.122219i | \(0.960999\pi\) | |||||||
\(180\) | −1.58578 | − | 4.88053i | −0.118197 | − | 0.363773i | ||||
\(181\) | −5.98677 | + | 4.34965i | −0.444993 | + | 0.323307i | −0.787616 | − | 0.616167i | \(-0.788685\pi\) |
0.342623 | + | 0.939473i | \(0.388685\pi\) | |||||||
\(182\) | −4.83960 | + | 3.51617i | −0.358735 | + | 0.260636i | ||||
\(183\) | 0.397604 | + | 1.22370i | 0.0293917 | + | 0.0904583i | ||||
\(184\) | 1.54228 | − | 4.74665i | 0.113698 | − | 0.349927i | ||||
\(185\) | −8.61029 | − | 6.25574i | −0.633041 | − | 0.459931i | ||||
\(186\) | −0.367941 | −0.0269787 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −7.73070 | −0.563819 | ||||||||
\(189\) | −4.13776 | − | 3.00626i | −0.300978 | − | 0.218673i | ||||
\(190\) | 0.640135 | − | 1.97013i | 0.0464403 | − | 0.142928i | ||||
\(191\) | −1.59332 | − | 4.90372i | −0.115288 | − | 0.354821i | 0.876719 | − | 0.481003i | \(-0.159728\pi\) |
−0.992007 | + | 0.126183i | \(0.959728\pi\) | |||||||
\(192\) | 0.794658 | − | 0.577353i | 0.0573495 | − | 0.0416668i | ||||
\(193\) | −3.26220 | + | 2.37013i | −0.234818 | + | 0.170605i | −0.698972 | − | 0.715149i | \(-0.746359\pi\) |
0.464153 | + | 0.885755i | \(0.346359\pi\) | |||||||
\(194\) | −2.73345 | − | 8.41270i | −0.196250 | − | 0.603996i | ||||
\(195\) | −0.466012 | + | 1.43424i | −0.0333718 | + | 0.102708i | ||||
\(196\) | 0.301670 | + | 0.219176i | 0.0215479 | + | 0.0156555i | ||||
\(197\) | −11.4176 | −0.813469 | −0.406734 | − | 0.913547i | \(-0.633333\pi\) | ||||
−0.406734 | + | 0.913547i | \(0.633333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.16644 | −0.508015 | −0.254008 | − | 0.967202i | \(-0.581749\pi\) | ||||
−0.254008 | + | 0.967202i | \(0.581749\pi\) | |||||||
\(200\) | −1.45650 | − | 1.05821i | −0.102990 | − | 0.0748266i | ||||
\(201\) | 0.730772 | − | 2.24908i | 0.0515447 | − | 0.158638i | ||||
\(202\) | −1.04926 | − | 3.22930i | −0.0738260 | − | 0.227213i | ||||
\(203\) | 6.54631 | − | 4.75617i | 0.459461 | − | 0.333818i | ||||
\(204\) | 2.14294 | − | 1.55694i | 0.150036 | − | 0.109007i | ||||
\(205\) | −0.683053 | − | 2.10222i | −0.0477065 | − | 0.146825i | ||||
\(206\) | −1.11029 | + | 3.41713i | −0.0773577 | + | 0.238083i | ||||
\(207\) | 6.49424 | + | 4.71834i | 0.451381 | + | 0.327947i | ||||
\(208\) | 12.5342 | 0.869090 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.414031 | −0.0285709 | ||||||||
\(211\) | 2.81829 | + | 2.04760i | 0.194019 | + | 0.140963i | 0.680554 | − | 0.732698i | \(-0.261739\pi\) |
−0.486535 | + | 0.873661i | \(0.661739\pi\) | |||||||
\(212\) | 3.46882 | − | 10.6759i | 0.238239 | − | 0.733226i | ||||
\(213\) | 0.119373 | + | 0.367393i | 0.00817932 | + | 0.0251734i | ||||
\(214\) | −6.96128 | + | 5.05767i | −0.475864 | + | 0.345735i | ||||
\(215\) | 5.71747 | − | 4.15399i | 0.389928 | − | 0.283300i | ||||
\(216\) | −1.05965 | − | 3.26127i | −0.0721001 | − | 0.221901i | ||||
\(217\) | −1.98010 | + | 6.09412i | −0.134418 | + | 0.413696i | ||||
\(218\) | 6.31884 | + | 4.59090i | 0.427966 | + | 0.310935i | ||||
\(219\) | −0.330084 | −0.0223050 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.5950 | 1.45264 | ||||||||
\(222\) | −1.32761 | − | 0.964566i | −0.0891035 | − | 0.0647374i | ||||
\(223\) | 3.25856 | − | 10.0288i | 0.218210 | − | 0.671580i | −0.780701 | − | 0.624905i | \(-0.785138\pi\) |
0.998910 | − | 0.0466747i | \(-0.0148624\pi\) | |||||||
\(224\) | 4.05115 | + | 12.4682i | 0.270679 | + | 0.833064i | ||||
\(225\) | 2.34261 | − | 1.70201i | 0.156174 | − | 0.113467i | ||||
\(226\) | −0.792984 | + | 0.576137i | −0.0527485 | + | 0.0383241i | ||||
\(227\) | −0.0667531 | − | 0.205445i | −0.00443056 | − | 0.0136359i | 0.948817 | − | 0.315827i | \(-0.102282\pi\) |
−0.953247 | + | 0.302191i | \(0.902282\pi\) | |||||||
\(228\) | −0.767950 | + | 2.36351i | −0.0508587 | + | 0.156527i | ||||
\(229\) | 0.0612504 | + | 0.0445011i | 0.00404754 | + | 0.00294071i | 0.589807 | − | 0.807544i | \(-0.299204\pi\) |
−0.585760 | + | 0.810485i | \(0.699204\pi\) | |||||||
\(230\) | 1.32307 | 0.0872407 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.42514 | 0.356178 | ||||||||
\(233\) | 12.2324 | + | 8.88735i | 0.801370 | + | 0.582229i | 0.911316 | − | 0.411708i | \(-0.135068\pi\) |
−0.109946 | + | 0.993938i | \(0.535068\pi\) | |||||||
\(234\) | 1.99341 | − | 6.13508i | 0.130313 | − | 0.401063i | ||||
\(235\) | −1.34798 | − | 4.14865i | −0.0879324 | − | 0.270628i | ||||
\(236\) | 16.8428 | − | 12.2370i | 1.09637 | − | 0.796560i | ||||
\(237\) | 0.915352 | − | 0.665042i | 0.0594585 | − | 0.0431991i | ||||
\(238\) | 1.83212 | + | 5.63868i | 0.118759 | + | 0.365501i | ||||
\(239\) | 7.15826 | − | 22.0309i | 0.463029 | − | 1.42506i | −0.398414 | − | 0.917206i | \(-0.630439\pi\) |
0.861444 | − | 0.507853i | \(-0.169561\pi\) | |||||||
\(240\) | 0.701836 | + | 0.509914i | 0.0453033 | + | 0.0329148i | ||||
\(241\) | 21.3349 | 1.37430 | 0.687151 | − | 0.726515i | \(-0.258861\pi\) | ||||
0.687151 | + | 0.726515i | \(0.258861\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.32179 | 0.533843 | ||||||||
\(244\) | 5.71013 | + | 4.14865i | 0.365553 | + | 0.265590i | ||||
\(245\) | −0.0650188 | + | 0.200107i | −0.00415390 | + | 0.0127844i | ||||
\(246\) | −0.105319 | − | 0.324139i | −0.00671490 | − | 0.0206664i | ||||
\(247\) | −16.3911 | + | 11.9088i | −1.04294 | + | 0.757741i | ||||
\(248\) | −3.47564 | + | 2.52520i | −0.220704 | + | 0.160350i | ||||
\(249\) | −1.10974 | − | 3.41544i | −0.0703271 | − | 0.216445i | ||||
\(250\) | 0.147481 | − | 0.453901i | 0.00932755 | − | 0.0287072i | ||||
\(251\) | 5.03359 | + | 3.65712i | 0.317718 | + | 0.230835i | 0.735201 | − | 0.677849i | \(-0.237088\pi\) |
−0.417483 | + | 0.908685i | \(0.637088\pi\) | |||||||
\(252\) | −13.7797 | −0.868041 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.0363991 | −0.00228388 | ||||||||
\(255\) | 1.20918 | + | 0.878523i | 0.0757219 | + | 0.0550152i | ||||
\(256\) | 0.224971 | − | 0.692389i | 0.0140607 | − | 0.0432743i | ||||
\(257\) | −4.41595 | − | 13.5909i | −0.275460 | − | 0.847778i | −0.989097 | − | 0.147263i | \(-0.952954\pi\) |
0.713638 | − | 0.700515i | \(-0.247046\pi\) | |||||||
\(258\) | 0.881571 | − | 0.640499i | 0.0548842 | − | 0.0398757i | ||||
\(259\) | −23.1205 | + | 16.7980i | −1.43664 | + | 1.04378i | ||||
\(260\) | 2.55633 | + | 7.86758i | 0.158537 | + | 0.487927i | ||||
\(261\) | −2.69640 | + | 8.29865i | −0.166903 | + | 0.513674i | ||||
\(262\) | 4.43376 | + | 3.22131i | 0.273919 | + | 0.199013i | ||||
\(263\) | −4.13132 | −0.254748 | −0.127374 | − | 0.991855i | \(-0.540655\pi\) | ||||
−0.127374 | + | 0.991855i | \(0.540655\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.33404 | 0.389097 | ||||||||
\(266\) | −4.50015 | − | 3.26955i | −0.275922 | − | 0.200469i | ||||
\(267\) | 0.276519 | − | 0.851039i | 0.0169227 | − | 0.0520827i | ||||
\(268\) | −4.00869 | − | 12.3375i | −0.244869 | − | 0.753631i | ||||
\(269\) | 1.36234 | − | 0.989796i | 0.0830632 | − | 0.0603489i | −0.545479 | − | 0.838125i | \(-0.683652\pi\) |
0.628542 | + | 0.777776i | \(0.283652\pi\) | |||||||
\(270\) | 0.735429 | − | 0.534320i | 0.0447568 | − | 0.0325177i | ||||
\(271\) | 5.69549 | + | 17.5289i | 0.345976 | + | 1.06481i | 0.961059 | + | 0.276343i | \(0.0891226\pi\) |
−0.615083 | + | 0.788463i | \(0.710877\pi\) | |||||||
\(272\) | 3.83883 | − | 11.8147i | 0.232763 | − | 0.716371i | ||||
\(273\) | 3.27606 | + | 2.38020i | 0.198276 | + | 0.144056i | ||||
\(274\) | 8.74784 | 0.528476 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.58725 | −0.0955411 | ||||||||
\(277\) | −2.77286 | − | 2.01460i | −0.166605 | − | 0.121046i | 0.501358 | − | 0.865240i | \(-0.332834\pi\) |
−0.667964 | + | 0.744194i | \(0.732834\pi\) | |||||||
\(278\) | −3.41970 | + | 10.5248i | −0.205100 | + | 0.631234i | ||||
\(279\) | −2.13525 | − | 6.57164i | −0.127834 | − | 0.393434i | ||||
\(280\) | −3.91102 | + | 2.84152i | −0.233728 | + | 0.169813i | ||||
\(281\) | −18.4632 | + | 13.4143i | −1.10142 | + | 0.800229i | −0.981291 | − | 0.192529i | \(-0.938331\pi\) |
−0.120129 | + | 0.992758i | \(0.538331\pi\) | |||||||
\(282\) | −0.207843 | − | 0.639676i | −0.0123769 | − | 0.0380921i | ||||
\(283\) | 8.99211 | − | 27.6749i | 0.534525 | − | 1.64510i | −0.210147 | − | 0.977670i | \(-0.567394\pi\) |
0.744673 | − | 0.667430i | \(-0.232606\pi\) | |||||||
\(284\) | 1.71436 | + | 1.24556i | 0.101729 | + | 0.0739102i | ||||
\(285\) | −1.40227 | −0.0830634 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.93542 | −0.350357 | ||||||||
\(288\) | −11.4371 | − | 8.30955i | −0.673938 | − | 0.489645i | ||||
\(289\) | 1.36057 | − | 4.18739i | 0.0800333 | − | 0.246317i | ||||
\(290\) | 0.444423 | + | 1.36779i | 0.0260974 | + | 0.0803196i | ||||
\(291\) | −4.84428 | + | 3.51958i | −0.283977 | + | 0.206321i | ||||
\(292\) | −1.46488 | + | 1.06430i | −0.0857256 | + | 0.0622833i | ||||
\(293\) | −6.55535 | − | 20.1753i | −0.382968 | − | 1.17865i | −0.937944 | − | 0.346787i | \(-0.887273\pi\) |
0.554976 | − | 0.831866i | \(-0.312727\pi\) | |||||||
\(294\) | −0.0100252 | + | 0.0308543i | −0.000584680 | + | 0.00179946i | ||||
\(295\) | 9.50375 | + | 6.90488i | 0.553330 | + | 0.402018i | ||||
\(296\) | −19.1608 | −1.11370 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.99883 | 0.405432 | ||||||||
\(299\) | −10.4689 | − | 7.60613i | −0.605434 | − | 0.439874i | ||||
\(300\) | −0.176929 | + | 0.544531i | −0.0102150 | + | 0.0314385i | ||||
\(301\) | −5.86420 | − | 18.0481i | −0.338007 | − | 1.04028i | ||||
\(302\) | 2.90318 | − | 2.10928i | 0.167059 | − | 0.121376i | ||||
\(303\) | −1.85953 | + | 1.35103i | −0.106827 | + | 0.0776146i | ||||
\(304\) | 3.60161 | + | 11.0846i | 0.206566 | + | 0.635746i | ||||
\(305\) | −1.23070 | + | 3.78770i | −0.0704697 | + | 0.216883i | ||||
\(306\) | −5.17239 | − | 3.75796i | −0.295686 | − | 0.214828i | ||||
\(307\) | 6.87520 | 0.392388 | 0.196194 | − | 0.980565i | \(-0.437142\pi\) | ||||
0.196194 | + | 0.980565i | \(0.437142\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.43219 | 0.138363 | ||||||||
\(310\) | −0.921378 | − | 0.669420i | −0.0523307 | − | 0.0380205i | ||||
\(311\) | 7.77415 | − | 23.9264i | 0.440831 | − | 1.35674i | −0.446160 | − | 0.894953i | \(-0.647209\pi\) |
0.886991 | − | 0.461786i | \(-0.152791\pi\) | |||||||
\(312\) | 0.838976 | + | 2.58210i | 0.0474977 | + | 0.146183i | ||||
\(313\) | 9.36788 | − | 6.80616i | 0.529504 | − | 0.384707i | −0.290668 | − | 0.956824i | \(-0.593878\pi\) |
0.820172 | + | 0.572117i | \(0.193878\pi\) | |||||||
\(314\) | −5.16690 | + | 3.75398i | −0.291585 | + | 0.211849i | ||||
\(315\) | −2.40273 | − | 7.39484i | −0.135378 | − | 0.416652i | ||||
\(316\) | 1.91793 | − | 5.90279i | 0.107892 | − | 0.332058i | ||||
\(317\) | −16.7800 | − | 12.1914i | −0.942460 | − | 0.684737i | 0.00655133 | − | 0.999979i | \(-0.497915\pi\) |
−0.949012 | + | 0.315241i | \(0.897915\pi\) | |||||||
\(318\) | 0.976639 | 0.0547672 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.04036 | 0.169961 | ||||||||
\(321\) | 4.71229 | + | 3.42368i | 0.263015 | + | 0.191091i | ||||
\(322\) | 1.09786 | − | 3.37885i | 0.0611811 | − | 0.188296i | ||||
\(323\) | 6.20515 | + | 19.0975i | 0.345264 | + | 1.06261i | ||||
\(324\) | 11.5726 | − | 8.40799i | 0.642923 | − | 0.467111i | ||||
\(325\) | −3.77637 | + | 2.74369i | −0.209475 | + | 0.152193i | ||||
\(326\) | 0.113854 | + | 0.350407i | 0.00630580 | + | 0.0194073i | ||||
\(327\) | 1.63382 | − | 5.02839i | 0.0903506 | − | 0.278071i | ||||
\(328\) | −3.21945 | − | 2.33907i | −0.177764 | − | 0.129153i | ||||
\(329\) | −11.7133 | −0.645777 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.1415 | −1.76665 | −0.883327 | − | 0.468757i | \(-0.844702\pi\) | ||||
−0.883327 | + | 0.468757i | \(0.844702\pi\) | |||||||
\(332\) | −15.9374 | − | 11.5792i | −0.874679 | − | 0.635492i | ||||
\(333\) | 9.52324 | − | 29.3095i | 0.521871 | − | 1.60615i | ||||
\(334\) | −1.25098 | − | 3.85013i | −0.0684508 | − | 0.210670i | ||||
\(335\) | 5.92187 | − | 4.30249i | 0.323546 | − | 0.235070i | ||||
\(336\) | 1.88458 | − | 1.36923i | 0.102812 | − | 0.0746976i | ||||
\(337\) | 5.56119 | + | 17.1156i | 0.302937 | + | 0.932345i | 0.980439 | + | 0.196824i | \(0.0630627\pi\) |
−0.677502 | + | 0.735521i | \(0.736937\pi\) | |||||||
\(338\) | −1.29619 | + | 3.98925i | −0.0705032 | + | 0.216987i | ||||
\(339\) | 0.536794 | + | 0.390004i | 0.0291547 | + | 0.0211821i | ||||
\(340\) | 8.19888 | 0.444647 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 5.99834 | 0.324353 | ||||||||
\(343\) | −14.7496 | − | 10.7162i | −0.796406 | − | 0.578622i | ||||
\(344\) | 3.93171 | − | 12.1006i | 0.211983 | − | 0.652418i | ||||
\(345\) | −0.276763 | − | 0.851790i | −0.0149004 | − | 0.0458588i | ||||
\(346\) | −1.96095 | + | 1.42471i | −0.105421 | + | 0.0765930i | ||||
\(347\) | −6.51244 | + | 4.73156i | −0.349606 | + | 0.254004i | −0.748704 | − | 0.662905i | \(-0.769323\pi\) |
0.399098 | + | 0.916908i | \(0.369323\pi\) | |||||||
\(348\) | −0.533160 | − | 1.64090i | −0.0285804 | − | 0.0879614i | ||||
\(349\) | −5.94220 | + | 18.2882i | −0.318079 | + | 0.978946i | 0.656390 | + | 0.754422i | \(0.272083\pi\) |
−0.974469 | + | 0.224524i | \(0.927917\pi\) | |||||||
\(350\) | −1.03679 | − | 0.753275i | −0.0554190 | − | 0.0402642i | ||||
\(351\) | −8.89088 | −0.474560 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.8497 | 0.790371 | 0.395186 | − | 0.918601i | \(-0.370680\pi\) | ||||
0.395186 | + | 0.918601i | \(0.370680\pi\) | |||||||
\(354\) | 1.46537 | + | 1.06466i | 0.0778837 | + | 0.0565858i | ||||
\(355\) | −0.369495 | + | 1.13719i | −0.0196108 | + | 0.0603558i | ||||
\(356\) | −1.51686 | − | 4.66842i | −0.0803934 | − | 0.247426i | ||||
\(357\) | 3.24692 | − | 2.35903i | 0.171845 | − | 0.124853i | ||||
\(358\) | −4.36964 | + | 3.17473i | −0.230943 | + | 0.167790i | ||||
\(359\) | −3.15916 | − | 9.72290i | −0.166734 | − | 0.513155i | 0.832426 | − | 0.554137i | \(-0.186952\pi\) |
−0.999160 | + | 0.0409816i | \(0.986952\pi\) | |||||||
\(360\) | 1.61093 | − | 4.95794i | 0.0849035 | − | 0.261306i | ||||
\(361\) | 0.129892 | + | 0.0943721i | 0.00683642 | + | 0.00496695i | ||||
\(362\) | −3.53175 | −0.185625 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 22.2134 | 1.16430 | ||||||||
\(365\) | −0.826577 | − | 0.600544i | −0.0432650 | − | 0.0314339i | ||||
\(366\) | −0.189760 | + | 0.584022i | −0.00991893 | + | 0.0305273i | ||||
\(367\) | 4.37055 | + | 13.4512i | 0.228141 | + | 0.702145i | 0.997958 | + | 0.0638800i | \(0.0203475\pi\) |
−0.769817 | + | 0.638265i | \(0.779653\pi\) | |||||||
\(368\) | −6.02234 | + | 4.37549i | −0.313936 | + | 0.228088i | ||||
\(369\) | 5.17812 | − | 3.76212i | 0.269562 | − | 0.195848i | ||||
\(370\) | −1.56963 | − | 4.83083i | −0.0816012 | − | 0.251143i | ||||
\(371\) | 5.25585 | − | 16.1758i | 0.272870 | − | 0.839808i | ||||
\(372\) | 1.10535 | + | 0.803083i | 0.0573096 | + | 0.0416379i | ||||
\(373\) | −12.4600 | −0.645154 | −0.322577 | − | 0.946543i | \(-0.604549\pi\) | ||||
−0.322577 | + | 0.946543i | \(0.604549\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.323071 | −0.0166833 | ||||||||
\(376\) | −6.35346 | − | 4.61606i | −0.327655 | − | 0.238055i | ||||
\(377\) | 4.34668 | − | 13.3777i | 0.223866 | − | 0.688987i | ||||
\(378\) | −0.754302 | − | 2.32150i | −0.0387971 | − | 0.119405i | ||||
\(379\) | −13.2169 | + | 9.60263i | −0.678906 | + | 0.493254i | −0.872995 | − | 0.487730i | \(-0.837825\pi\) |
0.194089 | + | 0.980984i | \(0.437825\pi\) | |||||||
\(380\) | −6.22315 | + | 4.52138i | −0.319241 | + | 0.231942i | ||||
\(381\) | 0.00761405 | + | 0.0234336i | 0.000390080 | + | 0.00120054i | ||||
\(382\) | 0.760426 | − | 2.34035i | 0.0389068 | − | 0.119743i | ||||
\(383\) | 0.657446 | + | 0.477662i | 0.0335939 | + | 0.0244074i | 0.604456 | − | 0.796639i | \(-0.293391\pi\) |
−0.570862 | + | 0.821046i | \(0.693391\pi\) | |||||||
\(384\) | 3.62339 | 0.184905 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.92445 | −0.0979522 | ||||||||
\(387\) | 16.5557 | + | 12.0284i | 0.841571 | + | 0.611437i | ||||
\(388\) | −10.1502 | + | 31.2391i | −0.515298 | + | 1.58592i | ||||
\(389\) | −9.39230 | − | 28.9065i | −0.476208 | − | 1.46562i | −0.844321 | − | 0.535837i | \(-0.819996\pi\) |
0.368113 | − | 0.929781i | \(-0.380004\pi\) | |||||||
\(390\) | −0.582274 | + | 0.423047i | −0.0294846 | + | 0.0214218i | ||||
\(391\) | −10.3758 | + | 7.53847i | −0.524727 | + | 0.381237i | ||||
\(392\) | 0.117055 | + | 0.360259i | 0.00591219 | + | 0.0181958i | ||||
\(393\) | 1.14641 | − | 3.52829i | 0.0578287 | − | 0.177978i | ||||
\(394\) | −4.40846 | − | 3.20293i | −0.222095 | − | 0.161361i | ||||
\(395\) | 3.50213 | 0.176211 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.8996 | −0.747789 | −0.373894 | − | 0.927471i | \(-0.621978\pi\) | ||||
−0.373894 | + | 0.927471i | \(0.621978\pi\) | |||||||
\(398\) | −2.76704 | − | 2.01037i | −0.138699 | − | 0.100771i | ||||
\(399\) | −1.16357 | + | 3.58112i | −0.0582516 | + | 0.179280i | ||||
\(400\) | 0.829779 | + | 2.55380i | 0.0414889 | + | 0.127690i | ||||
\(401\) | −9.84508 | + | 7.15287i | −0.491640 | + | 0.357197i | −0.805815 | − | 0.592168i | \(-0.798272\pi\) |
0.314175 | + | 0.949365i | \(0.398272\pi\) | |||||||
\(402\) | 0.913087 | − | 0.663396i | 0.0455406 | − | 0.0330872i | ||||
\(403\) | 3.44210 | + | 10.5937i | 0.171463 | + | 0.527710i | ||||
\(404\) | −3.89626 | + | 11.9915i | −0.193846 | + | 0.596598i | ||||
\(405\) | 6.53000 | + | 4.74432i | 0.324478 | + | 0.235747i | ||||
\(406\) | 3.86184 | 0.191660 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.69083 | 0.133216 | ||||||||
\(409\) | −0.212050 | − | 0.154063i | −0.0104852 | − | 0.00761793i | 0.582530 | − | 0.812809i | \(-0.302063\pi\) |
−0.593016 | + | 0.805191i | \(0.702063\pi\) | |||||||
\(410\) | 0.325994 | − | 1.00331i | 0.0160997 | − | 0.0495497i | ||||
\(411\) | −1.82990 | − | 5.63184i | −0.0902621 | − | 0.277798i | ||||
\(412\) | 10.7938 | − | 7.84218i | 0.531774 | − | 0.386357i | ||||
\(413\) | 25.5197 | − | 18.5411i | 1.25574 | − | 0.912349i | ||||
\(414\) | 1.18388 | + | 3.64361i | 0.0581846 | + | 0.179074i | ||||
\(415\) | 3.43498 | − | 10.5718i | 0.168617 | − | 0.518949i | ||||
\(416\) | 18.4370 | + | 13.3953i | 0.903949 | + | 0.656758i | ||||
\(417\) | 7.49116 | 0.366844 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.26916 | −0.0620023 | −0.0310012 | − | 0.999519i | \(-0.509870\pi\) | ||||
−0.0310012 | + | 0.999519i | \(0.509870\pi\) | |||||||
\(420\) | 1.24381 | + | 0.903681i | 0.0606917 | + | 0.0440951i | ||||
\(421\) | −9.16714 | + | 28.2135i | −0.446779 | + | 1.37504i | 0.433742 | + | 0.901037i | \(0.357193\pi\) |
−0.880521 | + | 0.474007i | \(0.842807\pi\) | |||||||
\(422\) | 0.513765 | + | 1.58121i | 0.0250097 | + | 0.0769720i | ||||
\(423\) | 10.2188 | − | 7.42440i | 0.496856 | − | 0.360987i | ||||
\(424\) | 9.22552 | − | 6.70273i | 0.448031 | − | 0.325513i | ||||
\(425\) | 1.42961 | + | 4.39990i | 0.0693464 | + | 0.213426i | ||||
\(426\) | −0.0569721 | + | 0.175342i | −0.00276031 | + | 0.00849535i | ||||
\(427\) | 8.65182 | + | 6.28591i | 0.418691 | + | 0.304197i | ||||
\(428\) | 31.9518 | 1.54445 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.37289 | 0.162655 | ||||||||
\(431\) | 25.3666 | + | 18.4299i | 1.22187 | + | 0.887739i | 0.996254 | − | 0.0864778i | \(-0.0275611\pi\) |
0.225614 | + | 0.974217i | \(0.427561\pi\) | |||||||
\(432\) | −1.58048 | + | 4.86423i | −0.0760411 | + | 0.234030i | ||||
\(433\) | −8.04449 | − | 24.7584i | −0.386594 | − | 1.18981i | −0.935318 | − | 0.353809i | \(-0.884886\pi\) |
0.548724 | − | 0.836003i | \(-0.315114\pi\) | |||||||
\(434\) | −2.47410 | + | 1.79754i | −0.118761 | + | 0.0862847i | ||||
\(435\) | 0.787616 | − | 0.572237i | 0.0377633 | − | 0.0274367i | ||||
\(436\) | −8.96242 | − | 27.5835i | −0.429222 | − | 1.32101i | ||||
\(437\) | 3.71830 | − | 11.4438i | 0.177870 | − | 0.547429i | ||||
\(438\) | −0.127449 | − | 0.0925972i | −0.00608975 | − | 0.00442446i | ||||
\(439\) | −14.4191 | −0.688185 | −0.344093 | − | 0.938936i | \(-0.611813\pi\) | ||||
−0.344093 | + | 0.938936i | \(0.611813\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.609255 | −0.0290121 | ||||||||
\(442\) | 8.33807 | + | 6.05796i | 0.396602 | + | 0.288148i | ||||
\(443\) | −0.102163 | + | 0.314427i | −0.00485393 | + | 0.0149389i | −0.953454 | − | 0.301538i | \(-0.902500\pi\) |
0.948600 | + | 0.316477i | \(0.102500\pi\) | |||||||
\(444\) | 1.88304 | + | 5.79539i | 0.0893650 | + | 0.275037i | ||||
\(445\) | 2.24080 | − | 1.62803i | 0.106224 | − | 0.0771762i | ||||
\(446\) | 4.07152 | − | 2.95813i | 0.192792 | − | 0.140072i | ||||
\(447\) | −1.46403 | − | 4.50583i | −0.0692464 | − | 0.213119i | ||||
\(448\) | 2.52282 | − | 7.76445i | 0.119192 | − | 0.366836i | ||||
\(449\) | −6.88334 | − | 5.00104i | −0.324845 | − | 0.236014i | 0.413395 | − | 0.910552i | \(-0.364343\pi\) |
−0.738240 | + | 0.674538i | \(0.764343\pi\) | |||||||
\(450\) | 1.38197 | 0.0651465 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 3.63974 | 0.171199 | ||||||||
\(453\) | −1.96525 | − | 1.42783i | −0.0923353 | − | 0.0670855i | ||||
\(454\) | 0.0318586 | − | 0.0980507i | 0.00149520 | − | 0.00460175i | ||||
\(455\) | 3.87328 | + | 11.9207i | 0.181582 | + | 0.558852i | ||||
\(456\) | −2.04241 | + | 1.48390i | −0.0956444 | + | 0.0694898i | ||||
\(457\) | 0.921044 | − | 0.669177i | 0.0430846 | − | 0.0313028i | −0.566035 | − | 0.824382i | \(-0.691523\pi\) |
0.609119 | + | 0.793079i | \(0.291523\pi\) | |||||||
\(458\) | 0.0111658 | + | 0.0343647i | 0.000521743 | + | 0.00160576i | ||||
\(459\) | −2.72299 | + | 8.38051i | −0.127098 | + | 0.391169i | ||||
\(460\) | −3.97470 | − | 2.88779i | −0.185321 | − | 0.134644i | ||||
\(461\) | −14.5073 | −0.675670 | −0.337835 | − | 0.941205i | \(-0.609695\pi\) | ||||
−0.337835 | + | 0.941205i | \(0.609695\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.89739 | −0.227601 | −0.113801 | − | 0.993504i | \(-0.536302\pi\) | ||||
−0.113801 | + | 0.993504i | \(0.536302\pi\) | |||||||
\(464\) | −6.54631 | − | 4.75617i | −0.303905 | − | 0.220800i | ||||
\(465\) | −0.238235 | + | 0.733212i | −0.0110479 | + | 0.0340019i | ||||
\(466\) | 2.22993 | + | 6.86301i | 0.103299 | + | 0.317923i | ||||
\(467\) | −26.2308 | + | 19.0578i | −1.21382 | + | 0.881889i | −0.995572 | − | 0.0940049i | \(-0.970033\pi\) |
−0.218245 | + | 0.975894i | \(0.570033\pi\) | |||||||
\(468\) | −19.3792 | + | 14.0798i | −0.895802 | + | 0.650838i | ||||
\(469\) | −6.07384 | − | 18.6934i | −0.280464 | − | 0.863179i | ||||
\(470\) | 0.643336 | − | 1.97998i | 0.0296749 | − | 0.0913299i | ||||
\(471\) | 3.49763 | + | 2.54117i | 0.161162 | + | 0.117091i | ||||
\(472\) | 21.1490 | 0.973461 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.539990 | 0.0248026 | ||||||||
\(475\) | −3.51149 | − | 2.55125i | −0.161118 | − | 0.117059i | ||||
\(476\) | 6.80325 | − | 20.9383i | 0.311827 | − | 0.959704i | ||||
\(477\) | 5.66768 | + | 17.4433i | 0.259505 | + | 0.798675i | ||||
\(478\) | 8.94413 | − | 6.49829i | 0.409095 | − | 0.297225i | ||||
\(479\) | 14.3482 | − | 10.4246i | 0.655588 | − | 0.476313i | −0.209582 | − | 0.977791i | \(-0.567210\pi\) |
0.865170 | + | 0.501478i | \(0.167210\pi\) | |||||||
\(480\) | 0.487413 | + | 1.50010i | 0.0222472 | + | 0.0684700i | ||||
\(481\) | −15.3518 | + | 47.2480i | −0.699982 | + | 2.15432i | ||||
\(482\) | 8.23765 | + | 5.98500i | 0.375215 | + | 0.272609i | ||||
\(483\) | −2.40495 | −0.109429 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.5342 | −0.841595 | ||||||||
\(486\) | 3.21314 | + | 2.33448i | 0.145751 | + | 0.105894i | ||||
\(487\) | −5.70454 | + | 17.5568i | −0.258497 | + | 0.795573i | 0.734623 | + | 0.678475i | \(0.237359\pi\) |
−0.993120 | + | 0.117097i | \(0.962641\pi\) | |||||||
\(488\) | 2.21567 | + | 6.81912i | 0.100299 | + | 0.308687i | ||||
\(489\) | 0.201775 | − | 0.146598i | 0.00912458 | − | 0.00662940i | ||||
\(490\) | −0.0812399 | + | 0.0590242i | −0.00367004 | + | 0.00266644i | ||||
\(491\) | 3.53325 | + | 10.8742i | 0.159453 | + | 0.490747i | 0.998585 | − | 0.0531814i | \(-0.0169362\pi\) |
−0.839131 | + | 0.543929i | \(0.816936\pi\) | |||||||
\(492\) | −0.391085 | + | 1.20363i | −0.0176315 | + | 0.0542640i | ||||
\(493\) | −11.2785 | − | 8.19434i | −0.507960 | − | 0.369054i | ||||
\(494\) | −9.66954 | −0.435053 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.40774 | 0.287716 | ||||||||
\(497\) | 2.59755 | + | 1.88723i | 0.116516 | + | 0.0846539i | ||||
\(498\) | 0.529636 | − | 1.63005i | 0.0237336 | − | 0.0730444i | ||||
\(499\) | 3.36258 | + | 10.3490i | 0.150530 | + | 0.463283i | 0.997681 | − | 0.0680695i | \(-0.0216839\pi\) |
−0.847151 | + | 0.531353i | \(0.821684\pi\) | |||||||
\(500\) | −1.43376 | + | 1.04169i | −0.0641196 | + | 0.0465856i | ||||
\(501\) | −2.21702 | + | 1.61076i | −0.0990493 | + | 0.0719635i | ||||
\(502\) | 0.917609 | + | 2.82411i | 0.0409549 | + | 0.126046i | ||||
\(503\) | −13.8207 | + | 42.5357i | −0.616234 | + | 1.89657i | −0.235582 | + | 0.971855i | \(0.575699\pi\) |
−0.380652 | + | 0.924718i | \(0.624301\pi\) | |||||||
\(504\) | −11.3248 | − | 8.22798i | −0.504449 | − | 0.366503i | ||||
\(505\) | −7.11455 | −0.316594 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.83941 | 0.126103 | ||||||||
\(508\) | 0.109348 | + | 0.0794460i | 0.00485154 | + | 0.00352485i | ||||
\(509\) | −4.26732 | + | 13.1335i | −0.189146 | + | 0.582131i | −0.999995 | − | 0.00312421i | \(-0.999006\pi\) |
0.810849 | + | 0.585255i | \(0.199006\pi\) | |||||||
\(510\) | 0.220430 | + | 0.678415i | 0.00976083 | + | 0.0300407i | ||||
\(511\) | −2.21954 | + | 1.61259i | −0.0981868 | + | 0.0713368i | ||||
\(512\) | 18.4281 | − | 13.3888i | 0.814414 | − | 0.591707i | ||||
\(513\) | −2.55473 | − | 7.86264i | −0.112794 | − | 0.347144i | ||||
\(514\) | 2.10756 | − | 6.48640i | 0.0929604 | − | 0.286103i | ||||
\(515\) | 6.09056 | + | 4.42505i | 0.268382 | + | 0.194991i | ||||
\(516\) | −4.04635 | −0.178130 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −13.6394 | −0.599281 | ||||||||
\(519\) | 1.32742 | + | 0.964429i | 0.0582674 | + | 0.0423337i | ||||
\(520\) | −2.59688 | + | 7.99237i | −0.113881 | + | 0.350488i | ||||
\(521\) | −1.12783 | − | 3.47109i | −0.0494110 | − | 0.152071i | 0.923307 | − | 0.384063i | \(-0.125476\pi\) |
−0.972718 | + | 0.231992i | \(0.925476\pi\) | |||||||
\(522\) | −3.36910 | + | 2.44779i | −0.147462 | + | 0.107137i | ||||
\(523\) | −4.03463 | + | 2.93133i | −0.176422 | + | 0.128178i | −0.672492 | − | 0.740105i | \(-0.734776\pi\) |
0.496070 | + | 0.868283i | \(0.334776\pi\) | |||||||
\(524\) | −6.28869 | − | 19.3546i | −0.274723 | − | 0.845509i | ||||
\(525\) | −0.268077 | + | 0.825058i | −0.0116999 | + | 0.0360085i | ||||
\(526\) | −1.59515 | − | 1.15894i | −0.0695518 | − | 0.0505323i | ||||
\(527\) | 11.0398 | 0.480901 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.3148 | −0.665860 | ||||||||
\(530\) | 2.44565 | + | 1.77687i | 0.106232 | + | 0.0771821i | ||||
\(531\) | −10.5114 | + | 32.3509i | −0.456157 | + | 1.40391i | ||||
\(532\) | 6.38285 | + | 19.6444i | 0.276732 | + | 0.851692i | ||||
\(533\) | −8.34730 | + | 6.06467i | −0.361562 | + | 0.262690i | ||||
\(534\) | 0.345506 | − | 0.251025i | 0.0149515 | − | 0.0108629i | ||||
\(535\) | 5.57133 | + | 17.1468i | 0.240870 | + | 0.741321i | ||||
\(536\) | 4.07227 | − | 12.5331i | 0.175895 | − | 0.541349i | ||||
\(537\) | 2.95794 | + | 2.14907i | 0.127644 | + | 0.0927391i | ||||
\(538\) | 0.803678 | 0.0346490 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.37556 | −0.145261 | ||||||||
\(541\) | 0.200308 | + | 0.145532i | 0.00861192 | + | 0.00625692i | 0.592083 | − | 0.805877i | \(-0.298306\pi\) |
−0.583471 | + | 0.812134i | \(0.698306\pi\) | |||||||
\(542\) | −2.71823 | + | 8.36585i | −0.116758 | + | 0.359344i | ||||
\(543\) | 0.738781 | + | 2.27373i | 0.0317041 | + | 0.0975753i | ||||
\(544\) | 18.2730 | − | 13.2761i | 0.783449 | − | 0.569209i | ||||
\(545\) | 13.2398 | − | 9.61929i | 0.567132 | − | 0.412045i | ||||
\(546\) | 0.597217 | + | 1.83804i | 0.0255585 | + | 0.0786610i | ||||
\(547\) | 7.82185 | − | 24.0732i | 0.334438 | − | 1.02929i | −0.632560 | − | 0.774511i | \(-0.717996\pi\) |
0.966998 | − | 0.254783i | \(-0.0820041\pi\) | |||||||
\(548\) | −26.2798 | − | 19.0934i | −1.12262 | − | 0.815629i | ||||
\(549\) | −11.5322 | −0.492182 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.0796 | 0.557208 | ||||||||
\(552\) | −1.30448 | − | 0.947758i | −0.0555222 | − | 0.0403392i | ||||
\(553\) | 2.90599 | − | 8.94373i | 0.123575 | − | 0.380326i | ||||
\(554\) | −0.505485 | − | 1.55572i | −0.0214760 | − | 0.0660963i | ||||
\(555\) | −2.78174 | + | 2.02105i | −0.118078 | + | 0.0857888i | ||||
\(556\) | 33.2451 | − | 24.1540i | 1.40990 | − | 1.02436i | ||||
\(557\) | 11.9488 | + | 36.7746i | 0.506287 | + | 1.55819i | 0.798596 | + | 0.601867i | \(0.205576\pi\) |
−0.292309 | + | 0.956324i | \(0.594424\pi\) | |||||||
\(558\) | 1.01907 | − | 3.13638i | 0.0431407 | − | 0.132774i | ||||
\(559\) | −26.6883 | − | 19.3902i | −1.12879 | − | 0.820117i | ||||
\(560\) | 7.21041 | 0.304695 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.8919 | −0.459447 | ||||||||
\(563\) | 11.2746 | + | 8.19150i | 0.475169 | + | 0.345231i | 0.799452 | − | 0.600729i | \(-0.205123\pi\) |
−0.324283 | + | 0.945960i | \(0.605123\pi\) | |||||||
\(564\) | −0.771790 | + | 2.37533i | −0.0324982 | + | 0.100019i | ||||
\(565\) | 0.634650 | + | 1.95325i | 0.0266999 | + | 0.0821739i | ||||
\(566\) | 11.2355 | − | 8.16306i | 0.472263 | − | 0.343119i | ||||
\(567\) | 17.5345 | − | 12.7395i | 0.736379 | − | 0.535011i | ||||
\(568\) | 0.665214 | + | 2.04732i | 0.0279118 | + | 0.0859036i | ||||
\(569\) | −8.62543 | + | 26.5463i | −0.361597 | + | 1.11288i | 0.590488 | + | 0.807046i | \(0.298935\pi\) |
−0.952085 | + | 0.305834i | \(0.901065\pi\) | |||||||
\(570\) | −0.541433 | − | 0.393374i | −0.0226781 | − | 0.0164766i | ||||
\(571\) | 31.4113 | 1.31452 | 0.657261 | − | 0.753663i | \(-0.271715\pi\) | ||||
0.657261 | + | 0.753663i | \(0.271715\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.66578 | −0.0695889 | ||||||||
\(574\) | −2.29174 | − | 1.66504i | −0.0956552 | − | 0.0694976i | ||||
\(575\) | 0.856664 | − | 2.63654i | 0.0357254 | − | 0.109951i | ||||
\(576\) | 2.72050 | + | 8.37285i | 0.113354 | + | 0.348869i | ||||
\(577\) | −16.7749 | + | 12.1877i | −0.698348 | + | 0.507380i | −0.879394 | − | 0.476095i | \(-0.842052\pi\) |
0.181045 | + | 0.983475i | \(0.442052\pi\) | |||||||
\(578\) | 1.70000 | − | 1.23512i | 0.0707108 | − | 0.0513744i | ||||
\(579\) | 0.402562 | + | 1.23896i | 0.0167299 | + | 0.0514894i | ||||
\(580\) | 1.65029 | − | 5.07906i | 0.0685245 | − | 0.210897i | ||||
\(581\) | −24.1479 | − | 17.5445i | −1.00182 | − | 0.727868i | ||||
\(582\) | −2.85777 | −0.118458 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.83941 | −0.0761153 | ||||||||
\(585\) | −10.9349 | − | 7.94470i | −0.452104 | − | 0.328473i | ||||
\(586\) | 3.12861 | − | 9.62887i | 0.129242 | − | 0.397765i | ||||
\(587\) | 4.70840 | + | 14.4910i | 0.194336 | + | 0.598106i | 0.999984 | + | 0.00571050i | \(0.00181772\pi\) |
−0.805647 | + | 0.592396i | \(0.798182\pi\) | |||||||
\(588\) | 0.0974610 | − | 0.0708095i | 0.00401922 | − | 0.00292014i | ||||
\(589\) | −8.37947 | + | 6.08804i | −0.345270 | + | 0.250853i | ||||
\(590\) | 1.73251 | + | 5.33211i | 0.0713261 | + | 0.219519i | ||||
\(591\) | −1.13987 | + | 3.50815i | −0.0468879 | + | 0.144306i | ||||
\(592\) | 23.1205 | + | 16.7980i | 0.950248 | + | 0.690395i | ||||
\(593\) | −27.5413 | −1.13098 | −0.565492 | − | 0.824754i | \(-0.691314\pi\) | ||||
−0.565492 | + | 0.824754i | \(0.691314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.4227 | 0.509281 | ||||||||
\(596\) | −21.0255 | − | 15.2759i | −0.861239 | − | 0.625726i | ||||
\(597\) | −0.715457 | + | 2.20195i | −0.0292817 | + | 0.0901199i | ||||
\(598\) | −1.90846 | − | 5.87362i | −0.0780426 | − | 0.240190i | ||||
\(599\) | 21.6275 | − | 15.7133i | 0.883676 | − | 0.642028i | −0.0505453 | − | 0.998722i | \(-0.516096\pi\) |
0.934222 | + | 0.356693i | \(0.116096\pi\) | |||||||
\(600\) | −0.470553 | + | 0.341876i | −0.0192102 | + | 0.0139570i | ||||
\(601\) | −0.743741 | − | 2.28900i | −0.0303378 | − | 0.0933702i | 0.934741 | − | 0.355330i | \(-0.115631\pi\) |
−0.965079 | + | 0.261959i | \(0.915631\pi\) | |||||||
\(602\) | 2.79875 | − | 8.61366i | 0.114068 | − | 0.351067i | ||||
\(603\) | 17.1475 | + | 12.4584i | 0.698301 | + | 0.507345i | ||||
\(604\) | −13.3254 | −0.542202 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.09699 | −0.0445620 | ||||||||
\(607\) | 8.32710 | + | 6.04999i | 0.337987 | + | 0.245562i | 0.743812 | − | 0.668389i | \(-0.233016\pi\) |
−0.405825 | + | 0.913951i | \(0.633016\pi\) | |||||||
\(608\) | −6.54837 | + | 20.1538i | −0.265571 | + | 0.817344i | ||||
\(609\) | −0.807829 | − | 2.48624i | −0.0327349 | − | 0.100748i | ||||
\(610\) | −1.53774 | + | 1.11723i | −0.0622612 | + | 0.0452354i | ||||
\(611\) | −16.4731 | + | 11.9684i | −0.666429 | + | 0.484189i | ||||
\(612\) | 7.33634 | + | 22.5789i | 0.296554 | + | 0.912699i | ||||
\(613\) | −8.61404 | + | 26.5113i | −0.347918 | + | 1.07078i | 0.612085 | + | 0.790792i | \(0.290331\pi\) |
−0.960003 | + | 0.279989i | \(0.909669\pi\) | |||||||
\(614\) | 2.65459 | + | 1.92867i | 0.107131 | + | 0.0778350i | ||||
\(615\) | −0.714118 | −0.0287960 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.7216 | −1.15629 | −0.578143 | − | 0.815935i | \(-0.696222\pi\) | ||||
−0.578143 | + | 0.815935i | \(0.696222\pi\) | |||||||
\(618\) | 0.939098 | + | 0.682294i | 0.0377760 | + | 0.0274459i | ||||
\(619\) | 7.01370 | − | 21.5859i | 0.281904 | − | 0.867612i | −0.705405 | − | 0.708804i | \(-0.749235\pi\) |
0.987310 | − | 0.158808i | \(-0.0507650\pi\) | |||||||
\(620\) | 1.30685 | + | 4.02207i | 0.0524844 | + | 0.161530i | ||||
\(621\) | 4.27183 | − | 3.10366i | 0.171423 | − | 0.124546i | ||||
\(622\) | 9.71366 | − | 7.05739i | 0.389482 | − | 0.282976i | ||||
\(623\) | −2.29830 | − | 7.07345i | −0.0920795 | − | 0.283392i | ||||
\(624\) | 1.25134 | − | 3.85124i | 0.0500939 | − | 0.154173i | ||||
\(625\) | −0.809017 | − | 0.587785i | −0.0323607 | − | 0.0235114i | ||||
\(626\) | 5.52635 | 0.220877 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 23.7157 | 0.946360 | ||||||||
\(629\) | 39.8340 | + | 28.9411i | 1.58829 | + | 1.15396i | ||||
\(630\) | 1.14673 | − | 3.52926i | 0.0456866 | − | 0.140609i | ||||
\(631\) | 8.81823 | + | 27.1397i | 0.351048 | + | 1.08042i | 0.958266 | + | 0.285880i | \(0.0922857\pi\) |
−0.607217 | + | 0.794536i | \(0.707714\pi\) | |||||||
\(632\) | 5.10085 | − | 3.70598i | 0.202901 | − | 0.147416i | ||||
\(633\) | 0.910507 | − | 0.661522i | 0.0361894 | − | 0.0262931i | ||||
\(634\) | −3.05895 | − | 9.41448i | −0.121486 | − | 0.373897i | ||||
\(635\) | −0.0235677 | + | 0.0725340i | −0.000935256 | + | 0.00287842i | ||||
\(636\) | −2.93396 | − | 2.13165i | −0.116339 | − | 0.0845254i | ||||
\(637\) | 0.982140 | 0.0389138 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.46233 | −0.136968 | ||||||||
\(640\) | 9.07350 | + | 6.59228i | 0.358662 | + | 0.260583i | ||||
\(641\) | 0.733529 | − | 2.25757i | 0.0289727 | − | 0.0891687i | −0.935525 | − | 0.353262i | \(-0.885073\pi\) |
0.964497 | + | 0.264093i | \(0.0850726\pi\) | |||||||
\(642\) | 0.859037 | + | 2.64385i | 0.0339035 | + | 0.104344i | ||||
\(643\) | −9.19069 | + | 6.67742i | −0.362445 | + | 0.263332i | −0.754071 | − | 0.656793i | \(-0.771913\pi\) |
0.391626 | + | 0.920124i | \(0.371913\pi\) | |||||||
\(644\) | −10.6729 | + | 7.75434i | −0.420573 | + | 0.305564i | ||||
\(645\) | −0.705549 | − | 2.17146i | −0.0277810 | − | 0.0855010i | ||||
\(646\) | −2.96147 | + | 9.11447i | −0.116518 | + | 0.358604i | ||||
\(647\) | 39.1742 | + | 28.4617i | 1.54010 | + | 1.11895i | 0.950275 | + | 0.311411i | \(0.100802\pi\) |
0.589821 | + | 0.807534i | \(0.299198\pi\) | |||||||
\(648\) | 14.5314 | 0.570848 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.22778 | −0.0873806 | ||||||||
\(651\) | 1.67479 | + | 1.21681i | 0.0656402 | + | 0.0476904i | ||||
\(652\) | 0.422778 | − | 1.30118i | 0.0165573 | − | 0.0509580i | ||||
\(653\) | 9.19474 | + | 28.2985i | 0.359818 | + | 1.10741i | 0.953163 | + | 0.302458i | \(0.0978071\pi\) |
−0.593345 | + | 0.804949i | \(0.702193\pi\) | |||||||
\(654\) | 2.04143 | − | 1.48319i | 0.0798264 | − | 0.0579972i | ||||
\(655\) | 9.29003 | − | 6.74960i | 0.362991 | − | 0.263729i | ||||
\(656\) | 1.83415 | + | 5.64492i | 0.0716114 | + | 0.220397i | ||||
\(657\) | 0.914220 | − | 2.81368i | 0.0356671 | − | 0.109772i | ||||
\(658\) | −4.52265 | − | 3.28590i | −0.176311 | − | 0.128098i | ||||
\(659\) | 28.4931 | 1.10993 | 0.554966 | − | 0.831873i | \(-0.312731\pi\) | ||||
0.554966 | + | 0.831873i | \(0.312731\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.02875 | −0.0400139 | −0.0200070 | − | 0.999800i | \(-0.506369\pi\) | ||||
−0.0200070 | + | 0.999800i | \(0.506369\pi\) | |||||||
\(662\) | −12.4102 | − | 9.01653i | −0.482336 | − | 0.350437i | ||||
\(663\) | 2.15592 | − | 6.63525i | 0.0837291 | − | 0.257692i | ||||
\(664\) | −6.18410 | − | 19.0327i | −0.239990 | − | 0.738613i | ||||
\(665\) | −9.42913 | + | 6.85066i | −0.365646 | + | 0.265657i | ||||
\(666\) | 11.8991 | − | 8.64522i | 0.461082 | − | 0.334996i | ||||
\(667\) | 2.58148 | + | 7.94499i | 0.0999555 | + | 0.307631i | ||||
\(668\) | −4.64531 | + | 14.2968i | −0.179733 | + | 0.553160i | ||||
\(669\) | −2.75613 | − | 2.00245i | −0.106558 | − | 0.0774190i | ||||
\(670\) | 3.49346 | 0.134964 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 4.23540 | 0.163384 | ||||||||
\(673\) | 10.5471 | + | 7.66291i | 0.406560 | + | 0.295383i | 0.772208 | − | 0.635370i | \(-0.219152\pi\) |
−0.365647 | + | 0.930753i | \(0.619152\pi\) | |||||||
\(674\) | −2.65413 | + | 8.16858i | −0.102233 | + | 0.314642i | ||||
\(675\) | −0.588587 | − | 1.81148i | −0.0226547 | − | 0.0697240i | ||||
\(676\) | 12.6010 | − | 9.15518i | 0.484655 | − | 0.352122i | ||||
\(677\) | −30.0197 | + | 21.8106i | −1.15375 | + | 0.838250i | −0.988975 | − | 0.148081i | \(-0.952690\pi\) |
−0.164777 | + | 0.986331i | \(0.552690\pi\) | |||||||
\(678\) | 0.0978560 | + | 0.301170i | 0.00375814 | + | 0.0115664i | ||||
\(679\) | −15.3793 | + | 47.3326i | −0.590203 | + | 1.81646i | ||||
\(680\) | 6.73823 | + | 4.89561i | 0.258400 | + | 0.187738i | ||||
\(681\) | −0.0697890 | −0.00267432 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.8992 | −1.25885 | −0.629426 | − | 0.777061i | \(-0.716710\pi\) | ||||
−0.629426 | + | 0.777061i | \(0.716710\pi\) | |||||||
\(684\) | −18.0199 | − | 13.0922i | −0.689008 | − | 0.500594i | ||||
\(685\) | 5.66406 | − | 17.4322i | 0.216413 | − | 0.666050i | ||||
\(686\) | −2.68882 | − | 8.27532i | −0.102659 | − | 0.315953i | ||||
\(687\) | 0.0197882 | − | 0.0143770i | 0.000754969 | − | 0.000548517i | ||||
\(688\) | −15.3527 | + | 11.1544i | −0.585315 | + | 0.425256i | ||||
\(689\) | −9.13650 | − | 28.1193i | −0.348073 | − | 1.07126i | ||||
\(690\) | 0.132088 | − | 0.406525i | 0.00502851 | − | 0.0154762i | ||||
\(691\) | −29.6908 | − | 21.5716i | −1.12949 | − | 0.820623i | −0.143871 | − | 0.989597i | \(-0.545955\pi\) |
−0.985621 | + | 0.168973i | \(0.945955\pi\) | |||||||
\(692\) | 9.00061 | 0.342152 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.84185 | −0.145835 | ||||||||
\(695\) | 18.7590 | + | 13.6292i | 0.711568 | + | 0.516984i | ||||
\(696\) | 0.541616 | − | 1.66692i | 0.0205299 | − | 0.0631846i | ||||
\(697\) | 3.16002 | + | 9.72555i | 0.119694 | + | 0.368382i | ||||
\(698\) | −7.42468 | + | 5.39434i | −0.281028 | + | 0.204179i | ||||
\(699\) | 3.95193 | − | 2.87124i | 0.149476 | − | 0.108600i | ||||
\(700\) | 1.47055 | + | 4.52590i | 0.0555817 | + | 0.171063i | ||||
\(701\) | 11.2018 | − | 34.4755i | 0.423085 | − | 1.30212i | −0.481731 | − | 0.876319i | \(-0.659992\pi\) |
0.904816 | − | 0.425802i | \(-0.140008\pi\) | |||||||
\(702\) | −3.43287 | − | 2.49413i | −0.129565 | − | 0.0941347i | ||||
\(703\) | −46.1949 | −1.74227 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.40928 | −0.0530767 | ||||||||
\(706\) | 5.73365 | + | 4.16574i | 0.215789 | + | 0.156780i | ||||
\(707\) | −5.90350 | + | 18.1691i | −0.222024 | + | 0.683320i | ||||
\(708\) | −2.07843 | − | 6.39676i | −0.0781123 | − | 0.240405i | ||||
\(709\) | 15.0487 | − | 10.9336i | 0.565167 | − | 0.410618i | −0.268179 | − | 0.963369i | \(-0.586422\pi\) |
0.833347 | + | 0.552751i | \(0.186422\pi\) | |||||||
\(710\) | −0.461678 | + | 0.335429i | −0.0173265 | + | 0.0125884i | ||||
\(711\) | 3.13370 | + | 9.64453i | 0.117523 | + | 0.361698i | ||||
\(712\) | 1.54092 | − | 4.74246i | 0.0577484 | − | 0.177731i | ||||
\(713\) | −5.35193 | − | 3.88841i | −0.200432 | − | 0.145622i | ||||
\(714\) | 1.91544 | 0.0716836 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 20.0563 | 0.749540 | ||||||||
\(717\) | −6.05454 | − | 4.39888i | −0.226111 | − | 0.164279i | ||||
\(718\) | 1.50774 | − | 4.64035i | 0.0562684 | − | 0.173176i | ||||
\(719\) | −11.5659 | − | 35.5961i | −0.431335 | − | 1.32751i | −0.896796 | − | 0.442444i | \(-0.854112\pi\) |
0.465462 | − | 0.885068i | \(-0.345888\pi\) | |||||||
\(720\) | −6.29042 | + | 4.57026i | −0.234430 | + | 0.170324i | ||||
\(721\) | 16.3545 | − | 11.8822i | 0.609074 | − | 0.442518i | ||||
\(722\) | 0.0236789 | + | 0.0728763i | 0.000881239 | + | 0.00271217i | ||||
\(723\) | 2.12996 | − | 6.55534i | 0.0792140 | − | 0.243796i | ||||
\(724\) | 10.6099 | + | 7.70854i | 0.394314 | + | 0.286486i | ||||
\(725\) | 3.01341 | 0.111915 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.6011 | 0.541526 | 0.270763 | − | 0.962646i | \(-0.412724\pi\) | ||||
0.270763 | + | 0.962646i | \(0.412724\pi\) | |||||||
\(728\) | 18.2560 | + | 13.2638i | 0.676614 | + | 0.491589i | ||||
\(729\) | −6.65191 | + | 20.4725i | −0.246367 | + | 0.758240i | ||||
\(730\) | −0.150683 | − | 0.463754i | −0.00557702 | − | 0.0171643i | ||||
\(731\) | −26.4509 | + | 19.2177i | −0.978321 | + | 0.710792i | ||||
\(732\) | 1.84478 | − | 1.34031i | 0.0681849 | − | 0.0495392i | ||||
\(733\) | −12.9283 | − | 39.7893i | −0.477518 | − | 1.46965i | −0.842531 | − | 0.538647i | \(-0.818936\pi\) |
0.365013 | − | 0.931002i | \(-0.381064\pi\) | |||||||
\(734\) | −2.08589 | + | 6.41970i | −0.0769915 | + | 0.236955i | ||||
\(735\) | 0.0549936 | + | 0.0399552i | 0.00202847 | + | 0.00147377i | ||||
\(736\) | −13.5346 | −0.498891 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 3.05470 | 0.112445 | ||||||||
\(739\) | −9.65149 | − | 7.01222i | −0.355036 | − | 0.257949i | 0.395943 | − | 0.918275i | \(-0.370418\pi\) |
−0.750979 | + | 0.660327i | \(0.770418\pi\) | |||||||
\(740\) | −5.82856 | + | 17.9385i | −0.214262 | + | 0.659431i | ||||
\(741\) | 2.02270 | + | 6.22523i | 0.0743057 | + | 0.228689i | ||||
\(742\) | 6.56710 | − | 4.77127i | 0.241086 | − | 0.175159i | ||||
\(743\) | 37.7651 | − | 27.4380i | 1.38547 | − | 1.00660i | 0.389123 | − | 0.921186i | \(-0.372778\pi\) |
0.996345 | − | 0.0854162i | \(-0.0272220\pi\) | |||||||
\(744\) | 0.428902 | + | 1.32002i | 0.0157243 | + | 0.0483944i | ||||
\(745\) | 4.53161 | − | 13.9469i | 0.166026 | − | 0.510974i | ||||
\(746\) | −4.81095 | − | 3.49536i | −0.176141 | − | 0.127974i | ||||
\(747\) | 32.1873 | 1.17767 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48.4124 | 1.76895 | ||||||||
\(750\) | −0.124741 | − | 0.0906300i | −0.00455491 | − | 0.00330934i | ||||
\(751\) | 4.45106 | − | 13.6989i | 0.162421 | − | 0.499882i | −0.836416 | − | 0.548096i | \(-0.815353\pi\) |
0.998837 | + | 0.0482140i | \(0.0153529\pi\) | |||||||
\(752\) | 3.61962 | + | 11.1400i | 0.131994 | + | 0.406235i | ||||
\(753\) | 1.62621 | − | 1.18151i | 0.0592623 | − | 0.0430566i | ||||
\(754\) | 5.43111 | − | 3.94593i | 0.197789 | − | 0.143702i | ||||
\(755\) | −2.32350 | − | 7.15101i | −0.0845610 | − | 0.260252i | ||||
\(756\) | −2.80097 | + | 8.62050i | −0.101870 | + | 0.313525i | ||||
\(757\) | 12.9941 | + | 9.44076i | 0.472278 | + | 0.343130i | 0.798328 | − | 0.602222i | \(-0.205718\pi\) |
−0.326050 | + | 0.945352i | \(0.605718\pi\) | |||||||
\(758\) | −7.79698 | −0.283199 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.81423 | −0.283452 | ||||||||
\(761\) | −31.4578 | − | 22.8555i | −1.14035 | − | 0.828510i | −0.153178 | − | 0.988199i | \(-0.548951\pi\) |
−0.987167 | + | 0.159689i | \(0.948951\pi\) | |||||||
\(762\) | −0.00363388 | + | 0.0111839i | −0.000131642 | + | 0.000405151i | ||||
\(763\) | −13.5796 | − | 41.7937i | −0.491614 | − | 1.51303i | ||||
\(764\) | −7.39257 | + | 5.37102i | −0.267454 | + | 0.194317i | ||||
\(765\) | −10.8377 | + | 7.87403i | −0.391837 | + | 0.284686i | ||||
\(766\) | 0.119850 | + | 0.368862i | 0.00433037 | + | 0.0133275i | ||||
\(767\) | 16.9448 | − | 52.1507i | 0.611841 | − | 1.88305i | ||||
\(768\) | −0.190283 | − | 0.138249i | −0.00686624 | − | 0.00498862i | ||||
\(769\) | −43.0017 | −1.55068 | −0.775341 | − | 0.631543i | \(-0.782422\pi\) | ||||
−0.775341 | + | 0.631543i | \(0.782422\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.61679 | −0.166270 | ||||||||
\(772\) | 5.78134 | + | 4.20039i | 0.208075 | + | 0.151175i | ||||
\(773\) | −2.42721 | + | 7.47019i | −0.0873007 | + | 0.268684i | −0.985171 | − | 0.171576i | \(-0.945114\pi\) |
0.897870 | + | 0.440261i | \(0.145114\pi\) | |||||||
\(774\) | 3.01805 | + | 9.28860i | 0.108482 | + | 0.333872i | ||||
\(775\) | −1.93056 | + | 1.40263i | −0.0693477 | + | 0.0503840i | ||||
\(776\) | −26.9950 | + | 19.6130i | −0.969065 | + | 0.704067i | ||||
\(777\) | 2.85312 | + | 8.78101i | 0.102355 | + | 0.315017i | ||||
\(778\) | 4.48257 | − | 13.7959i | 0.160708 | − | 0.494608i | ||||
\(779\) | −7.76182 | − | 5.63929i | −0.278096 | − | 0.202049i | ||||
\(780\) | 2.67259 | 0.0956942 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −6.12096 | −0.218885 | ||||||||
\(783\) | 4.64349 | + | 3.37369i | 0.165945 | + | 0.120566i | ||||
\(784\) | 0.174590 | − | 0.537332i | 0.00623535 | − | 0.0191904i | ||||
\(785\) | 4.13523 | + | 12.7269i | 0.147593 | + | 0.454244i | ||||
\(786\) | 1.43242 | − | 1.04071i | 0.0510927 | − | 0.0371210i | ||||
\(787\) | −9.24293 | + | 6.71538i | −0.329475 | + | 0.239377i | −0.740208 | − | 0.672378i | \(-0.765273\pi\) |
0.410733 | + | 0.911756i | \(0.365273\pi\) | |||||||
\(788\) | 6.25280 | + | 19.2441i | 0.222747 | + | 0.685544i | ||||
\(789\) | −0.412448 | + | 1.26938i | −0.0146835 | + | 0.0451912i | ||||
\(790\) | 1.35221 | + | 0.982441i | 0.0481096 | + | 0.0349537i | ||||
\(791\) | 5.51483 | 0.196085 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.5903 | 0.660161 | ||||||||
\(794\) | −5.75290 | − | 4.17973i | −0.204163 | − | 0.148333i | ||||
\(795\) | 0.632355 | − | 1.94619i | 0.0224273 | − | 0.0690242i | ||||
\(796\) | 3.92468 | + | 12.0789i | 0.139107 | + | 0.428126i | ||||
\(797\) | 3.46665 | − | 2.51867i | 0.122795 | − | 0.0892159i | −0.524693 | − | 0.851292i | \(-0.675820\pi\) |
0.647488 | + | 0.762076i | \(0.275820\pi\) | |||||||
\(798\) | −1.45387 | + | 1.05630i | −0.0514663 | + | 0.0373925i | ||||
\(799\) | 6.23618 | + | 19.1930i | 0.220620 | + | 0.679000i | ||||
\(800\) | −1.50869 | + | 4.64326i | −0.0533401 | + | 0.164164i | ||||
\(801\) | 6.48851 | + | 4.71418i | 0.229260 | + | 0.166567i | ||||
\(802\) | −5.80787 | −0.205083 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −4.19100 | −0.147805 | ||||||||
\(805\) | −6.02234 | − | 4.37549i | −0.212260 | − | 0.154216i | ||||
\(806\) | −1.64278 | + | 5.05595i | −0.0578644 | + | 0.178088i | ||||
\(807\) | −0.168115 | − | 0.517406i | −0.00591794 | − | 0.0182136i | ||||
\(808\) | −10.3623 | + | 7.52868i | −0.364546 | + | 0.264858i | ||||
\(809\) | −16.0577 | + | 11.6666i | −0.564559 | + | 0.410176i | −0.833125 | − | 0.553085i | \(-0.813450\pi\) |
0.268566 | + | 0.963261i | \(0.413450\pi\) | |||||||
\(810\) | 1.19040 | + | 3.66367i | 0.0418264 | + | 0.128728i | ||||
\(811\) | 0.969807 | − | 2.98476i | 0.0340545 | − | 0.104809i | −0.932584 | − | 0.360952i | \(-0.882452\pi\) |
0.966639 | + | 0.256143i | \(0.0824518\pi\) | |||||||
\(812\) | −11.6015 | − | 8.42900i | −0.407133 | − | 0.295800i | ||||
\(813\) | 5.95452 | 0.208834 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.771990 | 0.0270416 | ||||||||
\(816\) | −3.24692 | − | 2.35903i | −0.113665 | − | 0.0825824i | ||||
\(817\) | 9.47901 | − | 29.1734i | 0.331629 | − | 1.02065i | ||||
\(818\) | −0.0386560 | − | 0.118971i | −0.00135158 | − | 0.00415972i | ||||
\(819\) | −29.3627 | + | 21.3333i | −1.02602 | + | 0.745445i | ||||
\(820\) | −3.16919 | + | 2.30255i | −0.110673 | + | 0.0804085i | ||||
\(821\) | −7.26186 | − | 22.3497i | −0.253441 | − | 0.780010i | −0.994133 | − | 0.108166i | \(-0.965502\pi\) |
0.740692 | − | 0.671845i | \(-0.234498\pi\) | |||||||
\(822\) | 0.873336 | − | 2.68785i | 0.0304611 | − | 0.0937496i | ||||
\(823\) | 10.2392 | + | 7.43922i | 0.356916 | + | 0.259315i | 0.751765 | − | 0.659431i | \(-0.229203\pi\) |
−0.394848 | + | 0.918746i | \(0.629203\pi\) | |||||||
\(824\) | 13.5535 | 0.472159 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.0547 | 0.523820 | ||||||||
\(827\) | 24.4514 | + | 17.7650i | 0.850258 | + | 0.617748i | 0.925217 | − | 0.379438i | \(-0.123883\pi\) |
−0.0749595 | + | 0.997187i | \(0.523883\pi\) | |||||||
\(828\) | 4.39614 | − | 13.5299i | 0.152776 | − | 0.470197i | ||||
\(829\) | 0.618546 | + | 1.90369i | 0.0214830 | + | 0.0661178i | 0.961223 | − | 0.275771i | \(-0.0889333\pi\) |
−0.939740 | + | 0.341889i | \(0.888933\pi\) | |||||||
\(830\) | 4.29195 | − | 3.11828i | 0.148976 | − | 0.108237i | ||||
\(831\) | −0.895832 | + | 0.650860i | −0.0310761 | + | 0.0225781i | ||||
\(832\) | −4.38554 | − | 13.4973i | −0.152041 | − | 0.467935i | ||||
\(833\) | 0.300798 | − | 0.925761i | 0.0104220 | − | 0.0320757i | ||||
\(834\) | 2.89242 | + | 2.10147i | 0.100156 | + | 0.0727679i | ||||
\(835\) | −8.48232 | −0.293543 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.54520 | −0.157105 | ||||||||
\(838\) | −0.490036 | − | 0.356032i | −0.0169280 | − | 0.0122989i | ||||
\(839\) | 10.9313 | − | 33.6430i | 0.377390 | − | 1.16149i | −0.564463 | − | 0.825459i | \(-0.690917\pi\) |
0.941852 | − | 0.336027i | \(-0.109083\pi\) | |||||||
\(840\) | 0.482628 | + | 1.48538i | 0.0166523 | + | 0.0512504i | ||||
\(841\) | 16.1151 | − | 11.7083i | 0.555692 | − | 0.403734i | ||||
\(842\) | −11.4542 | + | 8.32195i | −0.394737 | + | 0.286793i | ||||
\(843\) | 2.27840 | + | 7.01218i | 0.0784721 | + | 0.241512i | ||||
\(844\) | 1.90778 | − | 5.87154i | 0.0656685 | − | 0.202107i | ||||
\(845\) | 7.11029 | + | 5.16593i | 0.244601 | + | 0.177713i | ||||
\(846\) | 6.02834 | 0.207259 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −17.0083 | −0.584067 | ||||||||
\(849\) | −7.60562 | − | 5.52581i | −0.261024 | − | 0.189645i | ||||
\(850\) | −0.682297 | + | 2.09989i | −0.0234026 | + | 0.0720258i | ||||
\(851\) | −9.11739 | − | 28.0605i | −0.312540 | − | 0.961900i | ||||
\(852\) | 0.553861 | − | 0.402403i | 0.0189750 | − | 0.0137861i | ||||
\(853\) | −14.7268 | + | 10.6997i | −0.504237 | + | 0.366350i | −0.810633 | − | 0.585554i | \(-0.800877\pi\) |
0.306396 | + | 0.951904i | \(0.400877\pi\) | |||||||
\(854\) | 1.57720 | + | 4.85413i | 0.0539707 | + | 0.166105i | ||||
\(855\) | 3.88382 | − | 11.9532i | 0.132824 | − | 0.408789i | ||||
\(856\) | 26.2595 | + | 19.0787i | 0.897532 | + | 0.652095i | ||||
\(857\) | 29.2837 | 1.00031 | 0.500156 | − | 0.865935i | \(-0.333276\pi\) | ||||
0.500156 | + | 0.865935i | \(0.333276\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.44030 | 0.287979 | 0.143990 | − | 0.989579i | \(-0.454007\pi\) | ||||
0.143990 | + | 0.989579i | \(0.454007\pi\) | |||||||
\(860\) | −10.1326 | − | 7.36179i | −0.345520 | − | 0.251035i | ||||
\(861\) | −0.592560 | + | 1.82371i | −0.0201944 | + | 0.0621519i | ||||
\(862\) | 4.62426 | + | 14.2320i | 0.157503 | + | 0.484745i | ||||
\(863\) | 15.6534 | − | 11.3729i | 0.532848 | − | 0.387137i | −0.288574 | − | 0.957458i | \(-0.593181\pi\) |
0.821422 | + | 0.570321i | \(0.193181\pi\) | |||||||
\(864\) | −7.52319 | + | 5.46592i | −0.255944 | + | 0.185954i | ||||
\(865\) | 1.56941 | + | 4.83014i | 0.0533615 | + | 0.164230i | ||||
\(866\) | 3.83931 | − | 11.8162i | 0.130465 | − | 0.401531i | ||||
\(867\) | −1.15078 | − | 0.836091i | −0.0390826 | − | 0.0283952i | ||||
\(868\) | 11.3559 | 0.385446 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.464635 | 0.0157526 | ||||||||
\(871\) | −27.6424 | − | 20.0834i | −0.936627 | − | 0.680499i | ||||
\(872\) | 9.10456 | − | 28.0210i | 0.308319 | − | 0.948910i | ||||
\(873\) | −16.5844 | − | 51.0414i | −0.561295 | − | 1.72749i | ||||
\(874\) | 4.64595 | − | 3.37548i | 0.157152 | − | 0.114177i | ||||
\(875\) | −2.17239 | + | 1.57833i | −0.0734401 | + | 0.0533574i | ||||
\(876\) | 0.180769 | + | 0.556351i | 0.00610763 | + | 0.0187973i | ||||
\(877\) | −5.41211 | + | 16.6568i | −0.182754 | + | 0.562459i | −0.999902 | − | 0.0139682i | \(-0.995554\pi\) |
0.817148 | + | 0.576427i | \(0.195554\pi\) | |||||||
\(878\) | −5.56737 | − | 4.04493i | −0.187890 | − | 0.136510i | ||||
\(879\) | −6.85349 | −0.231163 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.0575 | −0.675754 | −0.337877 | − | 0.941190i | \(-0.609709\pi\) | ||||
−0.337877 | + | 0.941190i | \(0.609709\pi\) | |||||||
\(882\) | −0.235240 | − | 0.170912i | −0.00792095 | − | 0.00575491i | ||||
\(883\) | 8.31193 | − | 25.5815i | 0.279719 | − | 0.860886i | −0.708213 | − | 0.705998i | \(-0.750499\pi\) |
0.987932 | − | 0.154887i | \(-0.0495014\pi\) | |||||||
\(884\) | −11.8264 | − | 36.3980i | −0.397766 | − | 1.22420i | ||||
\(885\) | 3.07039 | − | 2.23077i | 0.103210 | − | 0.0749864i | ||||
\(886\) | −0.127651 | + | 0.0927442i | −0.00428853 | + | 0.00311580i | ||||
\(887\) | −2.10307 | − | 6.47258i | −0.0706142 | − | 0.217328i | 0.909521 | − | 0.415657i | \(-0.136448\pi\) |
−0.980135 | + | 0.198329i | \(0.936448\pi\) | |||||||
\(888\) | −1.91290 | + | 5.88731i | −0.0641928 | + | 0.197565i | ||||
\(889\) | 0.165681 | + | 0.120374i | 0.00555676 | + | 0.00403722i | ||||
\(890\) | 1.32190 | 0.0443103 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.6880 | −0.625720 | ||||||||
\(893\) | −15.3177 | − | 11.1289i | −0.512586 | − | 0.372415i | ||||
\(894\) | 0.698725 | − | 2.15045i | 0.0233688 | − | 0.0719219i | ||||
\(895\) | 3.49716 | + | 10.7632i | 0.116897 | + | 0.359772i | ||||
\(896\) | 24.3643 | − | 17.7017i | 0.813955 | − | 0.591373i | ||||
\(897\) | −3.38221 | + | 2.45732i | −0.112929 | + | 0.0820475i | ||||
\(898\) | −1.25481 | − | 3.86192i | −0.0418737 | − | 0.128874i | ||||
\(899\) | 2.22211 | − | 6.83896i | 0.0741117 | − | 0.228092i | ||||
\(900\) | −4.15163 | − | 3.01633i | −0.138388 | − | 0.100544i | ||||
\(901\) | −29.3033 | −0.976235 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.13090 | −0.204024 | ||||||||
\(904\) | 2.99131 | + | 2.17332i | 0.0994896 | + | 0.0722834i | ||||
\(905\) | −2.28674 | + | 7.03787i | −0.0760139 | + | 0.233947i | ||||
\(906\) | −0.358259 | − | 1.10261i | −0.0119023 | − | 0.0366316i | ||||
\(907\) | 17.2574 | − | 12.5382i | 0.573023 | − | 0.416325i | −0.263179 | − | 0.964747i | \(-0.584771\pi\) |
0.836202 | + | 0.548422i | \(0.184771\pi\) | |||||||
\(908\) | −0.309717 | + | 0.225023i | −0.0102783 | + | 0.00746764i | ||||
\(909\) | −6.36608 | − | 19.5928i | −0.211150 | − | 0.649852i | ||||
\(910\) | −1.84856 | + | 5.68929i | −0.0612792 | + | 0.188598i | ||||
\(911\) | 22.3198 | + | 16.2163i | 0.739489 | + | 0.537270i | 0.892551 | − | 0.450946i | \(-0.148913\pi\) |
−0.153062 | + | 0.988217i | \(0.548913\pi\) | |||||||
\(912\) | 3.76541 | 0.124685 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.543347 | 0.0179723 | ||||||||
\(915\) | 1.04094 | + | 0.756287i | 0.0344124 | + | 0.0250021i | ||||
\(916\) | 0.0414622 | − | 0.127608i | 0.00136995 | − | 0.00421627i | ||||
\(917\) | −9.52843 | − | 29.3255i | −0.314657 | − | 0.968414i | ||||
\(918\) | −3.40233 | + | 2.47194i | −0.112294 | + | 0.0815862i | ||||
\(919\) | −4.86129 | + | 3.53194i | −0.160359 | + | 0.116508i | −0.665071 | − | 0.746780i | \(-0.731599\pi\) |
0.504712 | + | 0.863288i | \(0.331599\pi\) | |||||||
\(920\) | −1.54228 | − | 4.74665i | −0.0508474 | − | 0.156492i | ||||
\(921\) | 0.686382 | − | 2.11247i | 0.0226170 | − | 0.0696081i | ||||
\(922\) | −5.60142 | − | 4.06967i | −0.184473 | − | 0.134027i | ||||
\(923\) | 5.58140 | 0.183714 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.6429 | −0.349937 | ||||||||
\(926\) | −1.89094 | − | 1.37385i | −0.0621401 | − | 0.0451474i | ||||
\(927\) | −6.73635 | + | 20.7324i | −0.221251 | + | 0.680940i | ||||
\(928\) | −4.54630 | − | 13.9921i | −0.149239 | − | 0.459312i | ||||
\(929\) | −7.76445 | + | 5.64121i | −0.254743 | + | 0.185082i | −0.707826 | − | 0.706386i | \(-0.750324\pi\) |
0.453083 | + | 0.891468i | \(0.350324\pi\) | |||||||
\(930\) | −0.297671 | + | 0.216270i | −0.00976100 | + | 0.00709178i | ||||
\(931\) | 0.282210 | + | 0.868554i | 0.00924907 | + | 0.0284657i | ||||
\(932\) | 8.28045 | − | 25.4846i | 0.271235 | − | 0.834776i | ||||
\(933\) | −6.57546 | − | 4.77735i | −0.215271 | − | 0.156403i | ||||
\(934\) | −15.4742 | −0.506332 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −24.3339 | −0.795378 | ||||||||
\(937\) | −31.2214 | − | 22.6837i | −1.01996 | − | 0.741043i | −0.0536837 | − | 0.998558i | \(-0.517096\pi\) |
−0.966274 | + | 0.257515i | \(0.917096\pi\) | |||||||
\(938\) | 2.89880 | − | 8.92160i | 0.0946492 | − | 0.291300i | ||||
\(939\) | −1.15602 | − | 3.55785i | −0.0377252 | − | 0.116106i | ||||
\(940\) | −6.25427 | + | 4.54399i | −0.203992 | + | 0.148209i | ||||
\(941\) | −23.6108 | + | 17.1543i | −0.769691 | + | 0.559213i | −0.901867 | − | 0.432013i | \(-0.857804\pi\) |
0.132176 | + | 0.991226i | \(0.457804\pi\) | |||||||
\(942\) | 0.637607 | + | 1.96235i | 0.0207744 | + | 0.0639369i | ||||
\(943\) | 1.89357 | − | 5.82782i | 0.0616633 | − | 0.189780i | ||||
\(944\) | −25.5197 | − | 18.5411i | −0.830594 | − | 0.603462i | ||||
\(945\) | −5.11455 | −0.166376 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.7623 | 1.51957 | 0.759785 | − | 0.650174i | \(-0.225304\pi\) | ||||
0.759785 | + | 0.650174i | \(0.225304\pi\) | |||||||
\(948\) | −1.62221 | − | 1.17860i | −0.0526869 | − | 0.0382793i | ||||
\(949\) | −1.47375 | + | 4.53575i | −0.0478401 | + | 0.147237i | ||||
\(950\) | −0.640135 | − | 1.97013i | −0.0207687 | − | 0.0639195i | ||||
\(951\) | −5.42114 | + | 3.93869i | −0.175793 | + | 0.127721i | ||||
\(952\) | 18.0936 | − | 13.1458i | 0.586418 | − | 0.426058i | ||||
\(953\) | 1.90119 | + | 5.85126i | 0.0615855 | + | 0.189541i | 0.977116 | − | 0.212709i | \(-0.0682285\pi\) |
−0.915530 | + | 0.402249i | \(0.868228\pi\) | |||||||
\(954\) | −2.70496 | + | 8.32501i | −0.0875763 | + | 0.269532i | ||||
\(955\) | −4.17135 | − | 3.03067i | −0.134982 | − | 0.0980701i | ||||
\(956\) | −41.0529 | −1.32774 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.46440 | 0.273472 | ||||||||
\(959\) | −39.8183 | − | 28.9297i | −1.28580 | − | 0.934189i | ||||
\(960\) | 0.303532 | − | 0.934176i | 0.00979646 | − | 0.0301504i | ||||
\(961\) | −7.81985 | − | 24.0670i | −0.252253 | − | 0.776356i | ||||
\(962\) | −19.1818 | + | 13.9364i | −0.618446 | + | 0.449328i | ||||
\(963\) | −42.2354 | + | 30.6858i | −1.36102 | + | 0.988836i | ||||
\(964\) | −11.6840 | − | 35.9596i | −0.376316 | − | 1.15818i | ||||
\(965\) | −1.24605 | + | 3.83494i | −0.0401117 | + | 0.123451i | ||||
\(966\) | −0.928579 | − | 0.674652i | −0.0298765 | − | 0.0217066i | ||||
\(967\) | −3.39625 | −0.109216 | −0.0546080 | − | 0.998508i | \(-0.517391\pi\) | ||||
−0.0546080 | + | 0.998508i | \(0.517391\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.48736 | 0.208404 | ||||||||
\(970\) | −7.15627 | − | 5.19933i | −0.229774 | − | 0.166940i | ||||
\(971\) | −2.90322 | + | 8.93518i | −0.0931686 | + | 0.286744i | −0.986772 | − | 0.162114i | \(-0.948169\pi\) |
0.893603 | + | 0.448857i | \(0.148169\pi\) | |||||||
\(972\) | −4.55740 | − | 14.0262i | −0.146179 | − | 0.449892i | ||||
\(973\) | 50.3719 | − | 36.5974i | 1.61485 | − | 1.17326i | ||||
\(974\) | −7.12772 | + | 5.17859i | −0.228387 | + | 0.165933i | ||||
\(975\) | 0.466012 | + | 1.43424i | 0.0149243 | + | 0.0459324i | ||||
\(976\) | 3.30470 | − | 10.1708i | 0.105781 | − | 0.325560i | ||||
\(977\) | 13.3935 | + | 9.73092i | 0.428495 | + | 0.311320i | 0.781047 | − | 0.624472i | \(-0.214686\pi\) |
−0.352552 | + | 0.935792i | \(0.614686\pi\) | |||||||
\(978\) | 0.119032 | 0.00380623 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.372885 | 0.0119114 | ||||||||
\(981\) | 38.3376 | + | 27.8539i | 1.22402 | + | 0.889305i | ||||
\(982\) | −1.68628 | + | 5.18984i | −0.0538114 | + | 0.165614i | ||||
\(983\) | 15.7036 | + | 48.3308i | 0.500868 | + | 1.54151i | 0.807608 | + | 0.589719i | \(0.200762\pi\) |
−0.306741 | + | 0.951793i | \(0.599238\pi\) | |||||||
\(984\) | −1.04011 | + | 0.755685i | −0.0331576 | + | 0.0240904i | ||||
\(985\) | −9.23701 | + | 6.71108i | −0.294316 | + | 0.213833i | ||||
\(986\) | −2.05604 | − | 6.32785i | −0.0654778 | − | 0.201520i | ||||
\(987\) | −1.16939 | + | 3.59902i | −0.0372222 | + | 0.114558i | ||||
\(988\) | 29.0487 | + | 21.1051i | 0.924162 | + | 0.671443i | ||||
\(989\) | 19.5918 | 0.622983 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.3642 | 0.360996 | 0.180498 | − | 0.983575i | \(-0.442229\pi\) | ||||
0.180498 | + | 0.983575i | \(0.442229\pi\) | |||||||
\(992\) | 9.42539 | + | 6.84794i | 0.299256 | + | 0.217422i | ||||
\(993\) | −3.20883 | + | 9.87575i | −0.101829 | + | 0.313397i | ||||
\(994\) | 0.473526 | + | 1.45736i | 0.0150193 | + | 0.0462248i | ||||
\(995\) | −5.79777 | + | 4.21233i | −0.183802 | + | 0.133540i | ||||
\(996\) | −5.14892 | + | 3.74091i | −0.163150 | + | 0.118535i | ||||
\(997\) | 9.01231 | + | 27.7370i | 0.285423 | + | 0.878441i | 0.986272 | + | 0.165131i | \(0.0528047\pi\) |
−0.700849 | + | 0.713310i | \(0.747195\pi\) | |||||||
\(998\) | −1.60483 | + | 4.93915i | −0.0507999 | + | 0.156346i | ||||
\(999\) | −16.4001 | − | 11.9154i | −0.518875 | − | 0.376985i |
(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 | 605.2.g.e.81.2 | 8 | ||
11.2 | odd | 10 | 55.2.g.b.16.2 | ✓ | 8 | ||
11.3 | even | 5 | inner | 605.2.g.e.366.2 | 8 | ||
11.4 | even | 5 | 605.2.g.k.251.1 | 8 | |||
11.5 | even | 5 | 605.2.a.k.1.2 | 4 | |||
11.6 | odd | 10 | 605.2.a.j.1.3 | 4 | |||
11.7 | odd | 10 | 55.2.g.b.31.2 | yes | 8 | ||
11.8 | odd | 10 | 605.2.g.m.366.1 | 8 | |||
11.9 | even | 5 | 605.2.g.k.511.1 | 8 | |||
11.10 | odd | 2 | 605.2.g.m.81.1 | 8 | |||
33.2 | even | 10 | 495.2.n.e.181.1 | 8 | |||
33.5 | odd | 10 | 5445.2.a.bi.1.3 | 4 | |||
33.17 | even | 10 | 5445.2.a.bp.1.2 | 4 | |||
33.29 | even | 10 | 495.2.n.e.361.1 | 8 | |||
44.7 | even | 10 | 880.2.bo.h.801.1 | 8 | |||
44.27 | odd | 10 | 9680.2.a.cm.1.3 | 4 | |||
44.35 | even | 10 | 880.2.bo.h.401.1 | 8 | |||
44.39 | even | 10 | 9680.2.a.cn.1.3 | 4 | |||
55.2 | even | 20 | 275.2.z.a.49.2 | 16 | |||
55.7 | even | 20 | 275.2.z.a.174.3 | 16 | |||
55.13 | even | 20 | 275.2.z.a.49.3 | 16 | |||
55.18 | even | 20 | 275.2.z.a.174.2 | 16 | |||
55.24 | odd | 10 | 275.2.h.a.126.1 | 8 | |||
55.29 | odd | 10 | 275.2.h.a.251.1 | 8 | |||
55.39 | odd | 10 | 3025.2.a.bd.1.2 | 4 | |||
55.49 | even | 10 | 3025.2.a.w.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.g.b.16.2 | ✓ | 8 | 11.2 | odd | 10 | ||
55.2.g.b.31.2 | yes | 8 | 11.7 | odd | 10 | ||
275.2.h.a.126.1 | 8 | 55.24 | odd | 10 | |||
275.2.h.a.251.1 | 8 | 55.29 | odd | 10 | |||
275.2.z.a.49.2 | 16 | 55.2 | even | 20 | |||
275.2.z.a.49.3 | 16 | 55.13 | even | 20 | |||
275.2.z.a.174.2 | 16 | 55.18 | even | 20 | |||
275.2.z.a.174.3 | 16 | 55.7 | even | 20 | |||
495.2.n.e.181.1 | 8 | 33.2 | even | 10 | |||
495.2.n.e.361.1 | 8 | 33.29 | even | 10 | |||
605.2.a.j.1.3 | 4 | 11.6 | odd | 10 | |||
605.2.a.k.1.2 | 4 | 11.5 | even | 5 | |||
605.2.g.e.81.2 | 8 | 1.1 | even | 1 | trivial | ||
605.2.g.e.366.2 | 8 | 11.3 | even | 5 | inner | ||
605.2.g.k.251.1 | 8 | 11.4 | even | 5 | |||
605.2.g.k.511.1 | 8 | 11.9 | even | 5 | |||
605.2.g.m.81.1 | 8 | 11.10 | odd | 2 | |||
605.2.g.m.366.1 | 8 | 11.8 | odd | 10 | |||
880.2.bo.h.401.1 | 8 | 44.35 | even | 10 | |||
880.2.bo.h.801.1 | 8 | 44.7 | even | 10 | |||
3025.2.a.w.1.3 | 4 | 55.49 | even | 10 | |||
3025.2.a.bd.1.2 | 4 | 55.39 | odd | 10 | |||
5445.2.a.bi.1.3 | 4 | 33.5 | odd | 10 | |||
5445.2.a.bp.1.2 | 4 | 33.17 | even | 10 | |||
9680.2.a.cm.1.3 | 4 | 44.27 | odd | 10 | |||
9680.2.a.cn.1.3 | 4 | 44.39 | even | 10 |