Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(211,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.j (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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.856615824.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.4 | ||
Root | \(1.07834i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.211 |
Dual form | 630.2.j.l.421.4 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 1.66483 | − | 0.477841i | 0.961192 | − | 0.275882i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | −1.24624 | − | 1.20287i | −0.508775 | − | 0.491068i | ||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.54334 | − | 1.59105i | 0.847779 | − | 0.530350i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 3.08343 | + | 5.34065i | 0.929688 | + | 1.61027i | 0.783843 | + | 0.620960i | \(0.213257\pi\) |
0.145845 | + | 0.989307i | \(0.453410\pi\) | |||||||
\(12\) | −0.418594 | + | 1.68071i | −0.120838 | + | 0.485179i | ||||
\(13\) | 0.933868 | − | 1.61751i | 0.259008 | − | 0.448616i | −0.706968 | − | 0.707245i | \(-0.749938\pi\) |
0.965977 | + | 0.258630i | \(0.0832709\pi\) | |||||||
\(14\) | 0.500000 | − | 0.866025i | 0.133631 | − | 0.231455i | ||||
\(15\) | 0.418594 | − | 1.68071i | 0.108080 | − | 0.433957i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.52303 | −0.369388 | −0.184694 | − | 0.982796i | \(-0.559129\pi\) | ||||
−0.184694 | + | 0.982796i | \(0.559129\pi\) | |||||||
\(18\) | −2.64956 | − | 1.40707i | −0.624507 | − | 0.331649i | ||||
\(19\) | 5.08667 | 1.16696 | 0.583481 | − | 0.812127i | \(-0.301690\pi\) | ||||
0.583481 | + | 0.812127i | \(0.301690\pi\) | |||||||
\(20\) | 0.500000 | + | 0.866025i | 0.111803 | + | 0.193649i | ||||
\(21\) | 1.24624 | + | 1.20287i | 0.271952 | + | 0.262487i | ||||
\(22\) | 3.08343 | − | 5.34065i | 0.657389 | − | 1.13863i | ||||
\(23\) | −3.58343 | + | 6.20668i | −0.747196 | + | 1.29418i | 0.201966 | + | 0.979393i | \(0.435267\pi\) |
−0.949162 | + | 0.314789i | \(0.898066\pi\) | |||||||
\(24\) | 1.66483 | − | 0.477841i | 0.339833 | − | 0.0975389i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −1.86774 | −0.366293 | ||||||||
\(27\) | 3.47396 | − | 3.86414i | 0.668564 | − | 0.743655i | ||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −5.23872 | − | 9.07372i | −0.972805 | − | 1.68495i | −0.686995 | − | 0.726662i | \(-0.741071\pi\) |
−0.285810 | − | 0.958286i | \(-0.592263\pi\) | |||||||
\(30\) | −1.66483 | + | 0.477841i | −0.303955 | + | 0.0872415i | ||||
\(31\) | 4.08667 | − | 7.07832i | 0.733988 | − | 1.27130i | −0.221178 | − | 0.975233i | \(-0.570990\pi\) |
0.955166 | − | 0.296071i | \(-0.0956764\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 7.68537 | + | 7.41790i | 1.33785 | + | 1.29129i | ||||
\(34\) | 0.761513 | + | 1.31898i | 0.130598 | + | 0.226203i | ||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0.106223 | + | 2.99812i | 0.0177038 | + | 0.499686i | ||||
\(37\) | −4.21894 | −0.693589 | −0.346794 | − | 0.937941i | \(-0.612730\pi\) | ||||
−0.346794 | + | 0.937941i | \(0.612730\pi\) | |||||||
\(38\) | −2.54334 | − | 4.40519i | −0.412584 | − | 0.714616i | ||||
\(39\) | 0.781823 | − | 3.13912i | 0.125192 | − | 0.502661i | ||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −0.433868 | + | 0.751481i | −0.0677588 | + | 0.117362i | −0.897914 | − | 0.440170i | \(-0.854918\pi\) |
0.830156 | + | 0.557532i | \(0.188251\pi\) | |||||||
\(42\) | 0.418594 | − | 1.68071i | 0.0645904 | − | 0.259339i | ||||
\(43\) | 4.01729 | + | 6.95816i | 0.612632 | + | 1.06111i | 0.990795 | + | 0.135370i | \(0.0432224\pi\) |
−0.378163 | + | 0.925739i | \(0.623444\pi\) | |||||||
\(44\) | −6.16685 | −0.929688 | ||||||||
\(45\) | −0.106223 | − | 2.99812i | −0.0158348 | − | 0.446933i | ||||
\(46\) | 7.16685 | 1.05669 | ||||||||
\(47\) | −3.43711 | − | 5.95325i | −0.501354 | − | 0.868371i | −0.999999 | − | 0.00156468i | \(-0.999502\pi\) |
0.498644 | − | 0.866807i | \(-0.333831\pi\) | |||||||
\(48\) | −1.24624 | − | 1.20287i | −0.179879 | − | 0.173619i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | −2.53558 | + | 0.727765i | −0.355053 | + | 0.101907i | ||||
\(52\) | 0.933868 | + | 1.61751i | 0.129504 | + | 0.224308i | ||||
\(53\) | 0.0455927 | 0.00626264 | 0.00313132 | − | 0.999995i | \(-0.499003\pi\) | ||||
0.00313132 | + | 0.999995i | \(0.499003\pi\) | |||||||
\(54\) | −5.08343 | − | 1.07646i | −0.691767 | − | 0.146488i | ||||
\(55\) | 6.16685 | 0.831538 | ||||||||
\(56\) | 0.500000 | + | 0.866025i | 0.0668153 | + | 0.115728i | ||||
\(57\) | 8.46846 | − | 2.43062i | 1.12167 | − | 0.321944i | ||||
\(58\) | −5.23872 | + | 9.07372i | −0.687877 | + | 1.19144i | ||||
\(59\) | −3.62352 | + | 6.27612i | −0.471742 | + | 0.817081i | −0.999477 | − | 0.0323280i | \(-0.989708\pi\) |
0.527736 | + | 0.849409i | \(0.323041\pi\) | |||||||
\(60\) | 1.24624 | + | 1.20287i | 0.160889 | + | 0.155289i | ||||
\(61\) | 1.32191 | + | 2.28962i | 0.169254 | + | 0.293156i | 0.938158 | − | 0.346208i | \(-0.112531\pi\) |
−0.768904 | + | 0.639364i | \(0.779198\pi\) | |||||||
\(62\) | −8.17334 | −1.03802 | ||||||||
\(63\) | 2.64956 | + | 1.40707i | 0.333813 | + | 0.177274i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.933868 | − | 1.61751i | −0.115832 | − | 0.200627i | ||||
\(66\) | 2.58141 | − | 10.3647i | 0.317749 | − | 1.27580i | ||||
\(67\) | −0.244219 | + | 0.422999i | −0.0298361 | + | 0.0516776i | −0.880558 | − | 0.473939i | \(-0.842832\pi\) |
0.850722 | + | 0.525616i | \(0.176165\pi\) | |||||||
\(68\) | 0.761513 | − | 1.31898i | 0.0923470 | − | 0.159950i | ||||
\(69\) | −3.00000 | + | 12.0454i | −0.361158 | + | 1.45009i | ||||
\(70\) | −0.500000 | − | 0.866025i | −0.0597614 | − | 0.103510i | ||||
\(71\) | 3.34471 | 0.396944 | 0.198472 | − | 0.980107i | \(-0.436402\pi\) | ||||
0.198472 | + | 0.980107i | \(0.436402\pi\) | |||||||
\(72\) | 2.54334 | − | 1.59105i | 0.299735 | − | 0.187507i | ||||
\(73\) | −4.73547 | −0.554245 | −0.277123 | − | 0.960835i | \(-0.589381\pi\) | ||||
−0.277123 | + | 0.960835i | \(0.589381\pi\) | |||||||
\(74\) | 2.10947 | + | 3.65371i | 0.245221 | + | 0.424735i | ||||
\(75\) | −1.24624 | − | 1.20287i | −0.143903 | − | 0.138895i | ||||
\(76\) | −2.54334 | + | 4.40519i | −0.291741 | + | 0.505310i | ||||
\(77\) | −3.08343 | + | 5.34065i | −0.351389 | + | 0.608624i | ||||
\(78\) | −3.10947 | + | 0.892481i | −0.352078 | + | 0.101054i | ||||
\(79\) | −6.51729 | − | 11.2883i | −0.733253 | − | 1.27003i | −0.955486 | − | 0.295038i | \(-0.904668\pi\) |
0.222233 | − | 0.974994i | \(-0.428666\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 3.93711 | − | 8.09315i | 0.437457 | − | 0.899239i | ||||
\(82\) | 0.867736 | 0.0958254 | ||||||||
\(83\) | −7.38503 | − | 12.7912i | −0.810612 | − | 1.40402i | −0.912436 | − | 0.409219i | \(-0.865801\pi\) |
0.101824 | − | 0.994802i | \(-0.467532\pi\) | |||||||
\(84\) | −1.66483 | + | 0.477841i | −0.181648 | + | 0.0521367i | ||||
\(85\) | −0.761513 | + | 1.31898i | −0.0825977 | + | 0.143063i | ||||
\(86\) | 4.01729 | − | 6.95816i | 0.433196 | − | 0.750317i | ||||
\(87\) | −13.0574 | − | 12.6030i | −1.39990 | − | 1.35118i | ||||
\(88\) | 3.08343 | + | 5.34065i | 0.328694 | + | 0.569315i | ||||
\(89\) | 3.57511 | 0.378961 | 0.189480 | − | 0.981885i | \(-0.439320\pi\) | ||||
0.189480 | + | 0.981885i | \(0.439320\pi\) | |||||||
\(90\) | −2.54334 | + | 1.59105i | −0.268091 | + | 0.167712i | ||||
\(91\) | 1.86774 | 0.195792 | ||||||||
\(92\) | −3.58343 | − | 6.20668i | −0.373598 | − | 0.647091i | ||||
\(93\) | 3.42131 | − | 13.7370i | 0.354773 | − | 1.42446i | ||||
\(94\) | −3.43711 | + | 5.95325i | −0.354511 | + | 0.614031i | ||||
\(95\) | 2.54334 | − | 4.40519i | 0.260941 | − | 0.451963i | ||||
\(96\) | −0.418594 | + | 1.68071i | −0.0427225 | + | 0.171537i | ||||
\(97\) | −5.01156 | − | 8.68028i | −0.508847 | − | 0.881349i | −0.999948 | − | 0.0102460i | \(-0.996739\pi\) |
0.491100 | − | 0.871103i | \(-0.336595\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 16.3394 | + | 8.67718i | 1.64218 | + | 0.872089i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 8.12126 | + | 14.0664i | 0.808096 | + | 1.39966i | 0.914181 | + | 0.405306i | \(0.132835\pi\) |
−0.106086 | + | 0.994357i | \(0.533832\pi\) | |||||||
\(102\) | 1.89805 | + | 1.83200i | 0.187935 | + | 0.181395i | ||||
\(103\) | −5.14406 | + | 8.90977i | −0.506859 | + | 0.877905i | 0.493110 | + | 0.869967i | \(0.335860\pi\) |
−0.999968 | + | 0.00793823i | \(0.997473\pi\) | |||||||
\(104\) | 0.933868 | − | 1.61751i | 0.0915733 | − | 0.158610i | ||||
\(105\) | 1.66483 | − | 0.477841i | 0.162471 | − | 0.0466325i | ||||
\(106\) | −0.0227964 | − | 0.0394845i | −0.00221418 | − | 0.00383507i | ||||
\(107\) | −10.7310 | −1.03740 | −0.518700 | − | 0.854956i | \(-0.673584\pi\) | ||||
−0.518700 | + | 0.854956i | \(0.673584\pi\) | |||||||
\(108\) | 1.60947 | + | 4.94061i | 0.154871 | + | 0.475410i | ||||
\(109\) | 15.7766 | 1.51112 | 0.755560 | − | 0.655080i | \(-0.227365\pi\) | ||||
0.755560 | + | 0.655080i | \(0.227365\pi\) | |||||||
\(110\) | −3.08343 | − | 5.34065i | −0.293993 | − | 0.509211i | ||||
\(111\) | −7.02382 | + | 2.01598i | −0.666672 | + | 0.191348i | ||||
\(112\) | 0.500000 | − | 0.866025i | 0.0472456 | − | 0.0818317i | ||||
\(113\) | −7.90534 | + | 13.6925i | −0.743672 | + | 1.28808i | 0.207141 | + | 0.978311i | \(0.433584\pi\) |
−0.950813 | + | 0.309766i | \(0.899749\pi\) | |||||||
\(114\) | −6.33921 | − | 6.11859i | −0.593721 | − | 0.573058i | ||||
\(115\) | 3.58343 | + | 6.20668i | 0.334156 | + | 0.578776i | ||||
\(116\) | 10.4774 | 0.972805 | ||||||||
\(117\) | −0.198396 | − | 5.59969i | −0.0183417 | − | 0.517692i | ||||
\(118\) | 7.24703 | 0.667144 | ||||||||
\(119\) | −0.761513 | − | 1.31898i | −0.0698078 | − | 0.120911i | ||||
\(120\) | 0.418594 | − | 1.68071i | 0.0382122 | − | 0.153427i | ||||
\(121\) | −13.5150 | + | 23.4087i | −1.22864 | + | 2.12807i | ||||
\(122\) | 1.32191 | − | 2.28962i | 0.119680 | − | 0.207293i | ||||
\(123\) | −0.363229 | + | 1.45841i | −0.0327512 | + | 0.131500i | ||||
\(124\) | 4.08667 | + | 7.07832i | 0.366994 | + | 0.635652i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.106223 | − | 2.99812i | −0.00946308 | − | 0.267094i | ||||
\(127\) | 5.16685 | 0.458484 | 0.229242 | − | 0.973369i | \(-0.426375\pi\) | ||||
0.229242 | + | 0.973369i | \(0.426375\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 10.0130 | + | 9.66454i | 0.881597 | + | 0.850915i | ||||
\(130\) | −0.933868 | + | 1.61751i | −0.0819056 | + | 0.141865i | ||||
\(131\) | −5.39378 | + | 9.34230i | −0.471257 | + | 0.816240i | −0.999459 | − | 0.0328780i | \(-0.989533\pi\) |
0.528203 | + | 0.849118i | \(0.322866\pi\) | |||||||
\(132\) | −10.2668 | + | 2.94678i | −0.893608 | + | 0.256484i | ||||
\(133\) | 2.54334 | + | 4.40519i | 0.220535 | + | 0.381978i | ||||
\(134\) | 0.488437 | 0.0421946 | ||||||||
\(135\) | −1.60947 | − | 4.94061i | −0.138521 | − | 0.425220i | ||||
\(136\) | −1.52303 | −0.130598 | ||||||||
\(137\) | −6.82765 | − | 11.8258i | −0.583325 | − | 1.01035i | −0.995082 | − | 0.0990550i | \(-0.968418\pi\) |
0.411757 | − | 0.911294i | \(-0.364915\pi\) | |||||||
\(138\) | 11.9316 | − | 3.42462i | 1.01569 | − | 0.291523i | ||||
\(139\) | −0.327415 | + | 0.567100i | −0.0277710 | + | 0.0481008i | −0.879577 | − | 0.475757i | \(-0.842174\pi\) |
0.851806 | + | 0.523858i | \(0.175508\pi\) | |||||||
\(140\) | −0.500000 | + | 0.866025i | −0.0422577 | + | 0.0731925i | ||||
\(141\) | −8.56693 | − | 8.26878i | −0.721465 | − | 0.696357i | ||||
\(142\) | −1.67235 | − | 2.89660i | −0.140341 | − | 0.243078i | ||||
\(143\) | 11.5181 | 0.963188 | ||||||||
\(144\) | −2.64956 | − | 1.40707i | −0.220797 | − | 0.117256i | ||||
\(145\) | −10.4774 | −0.870103 | ||||||||
\(146\) | 2.36774 | + | 4.10104i | 0.195955 | + | 0.339404i | ||||
\(147\) | −0.418594 | + | 1.68071i | −0.0345250 | + | 0.138622i | ||||
\(148\) | 2.10947 | − | 3.65371i | 0.173397 | − | 0.300333i | ||||
\(149\) | −9.39152 | + | 16.2666i | −0.769383 | + | 1.33261i | 0.168514 | + | 0.985699i | \(0.446103\pi\) |
−0.937898 | + | 0.346912i | \(0.887230\pi\) | |||||||
\(150\) | −0.418594 | + | 1.68071i | −0.0341780 | + | 0.137229i | ||||
\(151\) | 2.17258 | + | 3.76303i | 0.176802 | + | 0.306231i | 0.940784 | − | 0.339008i | \(-0.110091\pi\) |
−0.763981 | + | 0.645239i | \(0.776758\pi\) | |||||||
\(152\) | 5.08667 | 0.412584 | ||||||||
\(153\) | −3.87357 | + | 2.42321i | −0.313159 | + | 0.195905i | ||||
\(154\) | 6.16685 | 0.496939 | ||||||||
\(155\) | −4.08667 | − | 7.07832i | −0.328249 | − | 0.568545i | ||||
\(156\) | 2.32765 | + | 2.24664i | 0.186361 | + | 0.179875i | ||||
\(157\) | 6.58916 | − | 11.4128i | 0.525872 | − | 0.910837i | −0.473674 | − | 0.880700i | \(-0.657072\pi\) |
0.999546 | − | 0.0301367i | \(-0.00959427\pi\) | |||||||
\(158\) | −6.51729 | + | 11.2883i | −0.518488 | + | 0.898048i | ||||
\(159\) | 0.0759043 | − | 0.0217861i | 0.00601960 | − | 0.00172775i | ||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | −7.16685 | −0.564827 | ||||||||
\(162\) | −8.97743 | + | 0.636937i | −0.705334 | + | 0.0500425i | ||||
\(163\) | 1.47697 | 0.115686 | 0.0578428 | − | 0.998326i | \(-0.481578\pi\) | ||||
0.0578428 | + | 0.998326i | \(0.481578\pi\) | |||||||
\(164\) | −0.433868 | − | 0.751481i | −0.0338794 | − | 0.0586808i | ||||
\(165\) | 10.2668 | − | 2.94678i | 0.799268 | − | 0.229406i | ||||
\(166\) | −7.38503 | + | 12.7912i | −0.573190 | + | 0.992793i | ||||
\(167\) | −11.5812 | + | 20.0592i | −0.896178 | + | 1.55223i | −0.0638377 | + | 0.997960i | \(0.520334\pi\) |
−0.832340 | + | 0.554265i | \(0.812999\pi\) | |||||||
\(168\) | 1.24624 | + | 1.20287i | 0.0961494 | + | 0.0928032i | ||||
\(169\) | 4.75578 | + | 8.23725i | 0.365829 | + | 0.633635i | ||||
\(170\) | 1.52303 | 0.116811 | ||||||||
\(171\) | 12.9371 | − | 8.09315i | 0.989326 | − | 0.618899i | ||||
\(172\) | −8.03459 | −0.612632 | ||||||||
\(173\) | 4.08667 | + | 7.07832i | 0.310704 | + | 0.538155i | 0.978515 | − | 0.206176i | \(-0.0661019\pi\) |
−0.667811 | + | 0.744331i | \(0.732769\pi\) | |||||||
\(174\) | −4.38579 | + | 17.6095i | −0.332486 | + | 1.33497i | ||||
\(175\) | 0.500000 | − | 0.866025i | 0.0377964 | − | 0.0654654i | ||||
\(176\) | 3.08343 | − | 5.34065i | 0.232422 | − | 0.402567i | ||||
\(177\) | −3.03356 | + | 12.1801i | −0.228017 | + | 0.915516i | ||||
\(178\) | −1.78755 | − | 3.09613i | −0.133983 | − | 0.232065i | ||||
\(179\) | −9.13272 | −0.682612 | −0.341306 | − | 0.939952i | \(-0.610869\pi\) | ||||
−0.341306 | + | 0.939952i | \(0.610869\pi\) | |||||||
\(180\) | 2.64956 | + | 1.40707i | 0.197486 | + | 0.104877i | ||||
\(181\) | −10.7586 | −0.799680 | −0.399840 | − | 0.916585i | \(-0.630934\pi\) | ||||
−0.399840 | + | 0.916585i | \(0.630934\pi\) | |||||||
\(182\) | −0.933868 | − | 1.61751i | −0.0692229 | − | 0.119898i | ||||
\(183\) | 3.29484 | + | 3.18017i | 0.243562 | + | 0.235085i | ||||
\(184\) | −3.58343 | + | 6.20668i | −0.264174 | + | 0.457562i | ||||
\(185\) | −2.10947 | + | 3.65371i | −0.155091 | + | 0.268626i | ||||
\(186\) | −13.6072 | + | 3.90556i | −0.997732 | + | 0.286370i | ||||
\(187\) | −4.69614 | − | 8.13395i | −0.343416 | − | 0.594813i | ||||
\(188\) | 6.87423 | 0.501354 | ||||||||
\(189\) | 5.08343 | + | 1.07646i | 0.369765 | + | 0.0783013i | ||||
\(190\) | −5.08667 | −0.369026 | ||||||||
\(191\) | −7.77609 | − | 13.4686i | −0.562658 | − | 0.974553i | −0.997263 | − | 0.0739315i | \(-0.976445\pi\) |
0.434605 | − | 0.900621i | \(-0.356888\pi\) | |||||||
\(192\) | 1.66483 | − | 0.477841i | 0.120149 | − | 0.0344852i | ||||
\(193\) | 1.69538 | − | 2.93649i | 0.122036 | − | 0.211373i | −0.798534 | − | 0.601949i | \(-0.794391\pi\) |
0.920571 | + | 0.390576i | \(0.127724\pi\) | |||||||
\(194\) | −5.01156 | + | 8.68028i | −0.359809 | + | 0.623208i | ||||
\(195\) | −2.32765 | − | 2.24664i | −0.166686 | − | 0.160885i | ||||
\(196\) | −0.500000 | − | 0.866025i | −0.0357143 | − | 0.0618590i | ||||
\(197\) | −6.55264 | −0.466856 | −0.233428 | − | 0.972374i | \(-0.574994\pi\) | ||||
−0.233428 | + | 0.972374i | \(0.574994\pi\) | |||||||
\(198\) | −0.655060 | − | 18.4890i | −0.0465531 | − | 1.31395i | ||||
\(199\) | −1.85627 | −0.131588 | −0.0657938 | − | 0.997833i | \(-0.520958\pi\) | ||||
−0.0657938 | + | 0.997833i | \(0.520958\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | −0.204457 | + | 0.820921i | −0.0144213 | + | 0.0579033i | ||||
\(202\) | 8.12126 | − | 14.0664i | 0.571410 | − | 0.989711i | ||||
\(203\) | 5.23872 | − | 9.07372i | 0.367686 | − | 0.636851i | ||||
\(204\) | 0.637529 | − | 2.55976i | 0.0446360 | − | 0.179219i | ||||
\(205\) | 0.433868 | + | 0.751481i | 0.0303027 | + | 0.0524857i | ||||
\(206\) | 10.2881 | 0.716807 | ||||||||
\(207\) | 0.761283 | + | 21.4871i | 0.0529128 | + | 1.49346i | ||||
\(208\) | −1.86774 | −0.129504 | ||||||||
\(209\) | 15.6844 | + | 27.1661i | 1.08491 | + | 1.87912i | ||||
\(210\) | −1.24624 | − | 1.20287i | −0.0859987 | − | 0.0830057i | ||||
\(211\) | 0.643069 | − | 1.11383i | 0.0442707 | − | 0.0766791i | −0.843041 | − | 0.537849i | \(-0.819237\pi\) |
0.887312 | + | 0.461170i | \(0.152570\pi\) | |||||||
\(212\) | −0.0227964 | + | 0.0394845i | −0.00156566 | + | 0.00271180i | ||||
\(213\) | 5.56838 | − | 1.59824i | 0.381539 | − | 0.109510i | ||||
\(214\) | 5.36548 | + | 9.29328i | 0.366777 | + | 0.635276i | ||||
\(215\) | 8.03459 | 0.547954 | ||||||||
\(216\) | 3.47396 | − | 3.86414i | 0.236373 | − | 0.262922i | ||||
\(217\) | 8.17334 | 0.554843 | ||||||||
\(218\) | −7.88828 | − | 13.6629i | −0.534261 | − | 0.925368i | ||||
\(219\) | −7.88377 | + | 2.26280i | −0.532736 | + | 0.152906i | ||||
\(220\) | −3.08343 | + | 5.34065i | −0.207885 | + | 0.360067i | ||||
\(221\) | −1.42231 | + | 2.46351i | −0.0956746 | + | 0.165713i | ||||
\(222\) | 5.25780 | + | 5.07482i | 0.352881 | + | 0.340599i | ||||
\(223\) | −0.620272 | − | 1.07434i | −0.0415365 | − | 0.0719433i | 0.844510 | − | 0.535540i | \(-0.179892\pi\) |
−0.886046 | + | 0.463597i | \(0.846559\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −2.64956 | − | 1.40707i | −0.176637 | − | 0.0938045i | ||||
\(226\) | 15.8107 | 1.05171 | ||||||||
\(227\) | 9.85650 | + | 17.0720i | 0.654199 | + | 1.13311i | 0.982094 | + | 0.188392i | \(0.0603275\pi\) |
−0.327895 | + | 0.944714i | \(0.606339\pi\) | |||||||
\(228\) | −2.12925 | + | 8.54921i | −0.141013 | + | 0.566185i | ||||
\(229\) | −3.05739 | + | 5.29555i | −0.202038 | + | 0.349940i | −0.949185 | − | 0.314719i | \(-0.898090\pi\) |
0.747147 | + | 0.664659i | \(0.231423\pi\) | |||||||
\(230\) | 3.58343 | − | 6.20668i | 0.236284 | − | 0.409256i | ||||
\(231\) | −2.58141 | + | 10.3647i | −0.169844 | + | 0.681946i | ||||
\(232\) | −5.23872 | − | 9.07372i | −0.343939 | − | 0.595719i | ||||
\(233\) | −5.30561 | −0.347582 | −0.173791 | − | 0.984783i | \(-0.555602\pi\) | ||||
−0.173791 | + | 0.984783i | \(0.555602\pi\) | |||||||
\(234\) | −4.75028 | + | 2.97166i | −0.310535 | + | 0.194264i | ||||
\(235\) | −6.87423 | −0.448425 | ||||||||
\(236\) | −3.62352 | − | 6.27612i | −0.235871 | − | 0.408540i | ||||
\(237\) | −16.2442 | − | 15.6789i | −1.05517 | − | 1.01845i | ||||
\(238\) | −0.761513 | + | 1.31898i | −0.0493616 | + | 0.0854967i | ||||
\(239\) | 11.9088 | − | 20.6267i | 0.770317 | − | 1.33423i | −0.167072 | − | 0.985945i | \(-0.553431\pi\) |
0.937389 | − | 0.348284i | \(-0.113235\pi\) | |||||||
\(240\) | −1.66483 | + | 0.477841i | −0.107464 | + | 0.0308445i | ||||
\(241\) | 4.73600 | + | 8.20299i | 0.305073 | + | 0.528401i | 0.977277 | − | 0.211964i | \(-0.0679859\pi\) |
−0.672205 | + | 0.740365i | \(0.734653\pi\) | |||||||
\(242\) | 27.0301 | 1.73756 | ||||||||
\(243\) | 2.68739 | − | 15.3551i | 0.172396 | − | 0.985028i | ||||
\(244\) | −2.64383 | −0.169254 | ||||||||
\(245\) | 0.500000 | + | 0.866025i | 0.0319438 | + | 0.0553283i | ||||
\(246\) | 1.44464 | − | 0.414640i | 0.0921066 | − | 0.0264365i | ||||
\(247\) | 4.75028 | − | 8.22773i | 0.302253 | − | 0.523518i | ||||
\(248\) | 4.08667 | − | 7.07832i | 0.259504 | − | 0.449474i | ||||
\(249\) | −18.4070 | − | 17.7664i | −1.16650 | − | 1.12590i | ||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | 22.2771 | 1.40612 | 0.703059 | − | 0.711131i | \(-0.251817\pi\) | ||||
0.703059 | + | 0.711131i | \(0.251817\pi\) | |||||||
\(252\) | −2.54334 | + | 1.59105i | −0.160215 | + | 0.100227i | ||||
\(253\) | −44.1969 | −2.77864 | ||||||||
\(254\) | −2.58343 | − | 4.47463i | −0.162099 | − | 0.280763i | ||||
\(255\) | −0.637529 | + | 2.55976i | −0.0399236 | + | 0.160299i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 11.0982 | − | 19.2227i | 0.692289 | − | 1.19908i | −0.278797 | − | 0.960350i | \(-0.589936\pi\) |
0.971086 | − | 0.238729i | \(-0.0767309\pi\) | |||||||
\(258\) | 3.36323 | − | 13.5038i | 0.209385 | − | 0.840710i | ||||
\(259\) | −2.10947 | − | 3.65371i | −0.131076 | − | 0.227030i | ||||
\(260\) | 1.86774 | 0.115832 | ||||||||
\(261\) | −27.7606 | − | 14.7425i | −1.71834 | − | 0.912535i | ||||
\(262\) | 10.7876 | 0.666457 | ||||||||
\(263\) | −5.71569 | − | 9.89987i | −0.352445 | − | 0.610452i | 0.634233 | − | 0.773142i | \(-0.281316\pi\) |
−0.986677 | + | 0.162690i | \(0.947983\pi\) | |||||||
\(264\) | 7.68537 | + | 7.41790i | 0.473002 | + | 0.456540i | ||||
\(265\) | 0.0227964 | − | 0.0394845i | 0.00140037 | − | 0.00242551i | ||||
\(266\) | 2.54334 | − | 4.40519i | 0.155942 | − | 0.270099i | ||||
\(267\) | 5.95196 | − | 1.70833i | 0.364254 | − | 0.104548i | ||||
\(268\) | −0.244219 | − | 0.422999i | −0.0149180 | − | 0.0258388i | ||||
\(269\) | 4.37930 | 0.267011 | 0.133505 | − | 0.991048i | \(-0.457377\pi\) | ||||
0.133505 | + | 0.991048i | \(0.457377\pi\) | |||||||
\(270\) | −3.47396 | + | 3.86414i | −0.211418 | + | 0.235164i | ||||
\(271\) | −17.9614 | −1.09107 | −0.545537 | − | 0.838087i | \(-0.683674\pi\) | ||||
−0.545537 | + | 0.838087i | \(0.683674\pi\) | |||||||
\(272\) | 0.761513 | + | 1.31898i | 0.0461735 | + | 0.0799749i | ||||
\(273\) | 3.10947 | − | 0.892481i | 0.188194 | − | 0.0540154i | ||||
\(274\) | −6.82765 | + | 11.8258i | −0.412473 | + | 0.714424i | ||||
\(275\) | 3.08343 | − | 5.34065i | 0.185938 | − | 0.322053i | ||||
\(276\) | −8.93161 | − | 8.62077i | −0.537620 | − | 0.518909i | ||||
\(277\) | −8.12126 | − | 14.0664i | −0.487959 | − | 0.845170i | 0.511945 | − | 0.859018i | \(-0.328925\pi\) |
−0.999904 | + | 0.0138481i | \(0.995592\pi\) | |||||||
\(278\) | 0.654831 | 0.0392741 | ||||||||
\(279\) | −0.868195 | − | 24.5047i | −0.0519775 | − | 1.46706i | ||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | −0.381556 | − | 0.660874i | −0.0227617 | − | 0.0394244i | 0.854420 | − | 0.519583i | \(-0.173913\pi\) |
−0.877182 | + | 0.480158i | \(0.840579\pi\) | |||||||
\(282\) | −2.87751 | + | 11.5536i | −0.171353 | + | 0.688005i | ||||
\(283\) | 4.43711 | − | 7.68530i | 0.263759 | − | 0.456844i | −0.703479 | − | 0.710716i | \(-0.748371\pi\) |
0.967238 | + | 0.253872i | \(0.0817043\pi\) | |||||||
\(284\) | −1.67235 | + | 2.89660i | −0.0992360 | + | 0.171882i | ||||
\(285\) | 2.12925 | − | 8.54921i | 0.126126 | − | 0.506411i | ||||
\(286\) | −5.75903 | − | 9.97493i | −0.340538 | − | 0.589830i | ||||
\(287\) | −0.867736 | −0.0512208 | ||||||||
\(288\) | 0.106223 | + | 2.99812i | 0.00625924 | + | 0.176666i | ||||
\(289\) | −14.6804 | −0.863552 | ||||||||
\(290\) | 5.23872 | + | 9.07372i | 0.307628 | + | 0.532827i | ||||
\(291\) | −12.4912 | − | 12.0565i | −0.732248 | − | 0.706764i | ||||
\(292\) | 2.36774 | − | 4.10104i | 0.138561 | − | 0.239995i | ||||
\(293\) | −5.68156 | + | 9.84075i | −0.331920 | + | 0.574903i | −0.982888 | − | 0.184202i | \(-0.941030\pi\) |
0.650968 | + | 0.759105i | \(0.274363\pi\) | |||||||
\(294\) | 1.66483 | − | 0.477841i | 0.0970950 | − | 0.0278683i | ||||
\(295\) | 3.62352 | + | 6.27612i | 0.210969 | + | 0.365410i | ||||
\(296\) | −4.21894 | −0.245221 | ||||||||
\(297\) | 31.3487 | + | 6.63840i | 1.81904 | + | 0.385199i | ||||
\(298\) | 18.7830 | 1.08807 | ||||||||
\(299\) | 6.69289 | + | 11.5924i | 0.387060 | + | 0.670408i | ||||
\(300\) | 1.66483 | − | 0.477841i | 0.0961192 | − | 0.0275882i | ||||
\(301\) | −4.01729 | + | 6.95816i | −0.231553 | + | 0.401062i | ||||
\(302\) | 2.17258 | − | 3.76303i | 0.125018 | − | 0.216538i | ||||
\(303\) | 20.2421 | + | 19.5376i | 1.16288 | + | 1.12241i | ||||
\(304\) | −2.54334 | − | 4.40519i | −0.145870 | − | 0.252655i | ||||
\(305\) | 2.64383 | 0.151385 | ||||||||
\(306\) | 4.03535 | + | 2.14300i | 0.230685 | + | 0.122507i | ||||
\(307\) | 30.1678 | 1.72177 | 0.860883 | − | 0.508803i | \(-0.169912\pi\) | ||||
0.860883 | + | 0.508803i | \(0.169912\pi\) | |||||||
\(308\) | −3.08343 | − | 5.34065i | −0.175695 | − | 0.304312i | ||||
\(309\) | −4.30654 | + | 17.2913i | −0.244991 | + | 0.983668i | ||||
\(310\) | −4.08667 | + | 7.07832i | −0.232107 | + | 0.402022i | ||||
\(311\) | 3.85627 | − | 6.67926i | 0.218669 | − | 0.378746i | −0.735732 | − | 0.677273i | \(-0.763162\pi\) |
0.954401 | + | 0.298526i | \(0.0964951\pi\) | |||||||
\(312\) | 0.781823 | − | 3.13912i | 0.0442620 | − | 0.177718i | ||||
\(313\) | 1.23276 | + | 2.13519i | 0.0696794 | + | 0.120688i | 0.898760 | − | 0.438441i | \(-0.144469\pi\) |
−0.829081 | + | 0.559129i | \(0.811136\pi\) | |||||||
\(314\) | −13.1783 | −0.743695 | ||||||||
\(315\) | 2.54334 | − | 1.59105i | 0.143301 | − | 0.0896456i | ||||
\(316\) | 13.0346 | 0.733253 | ||||||||
\(317\) | −9.79935 | − | 16.9730i | −0.550386 | − | 0.953297i | −0.998247 | − | 0.0591933i | \(-0.981147\pi\) |
0.447860 | − | 0.894104i | \(-0.352186\pi\) | |||||||
\(318\) | −0.0568194 | − | 0.0548420i | −0.00318628 | − | 0.00307539i | ||||
\(319\) | 32.3064 | − | 55.9563i | 1.80881 | − | 3.13295i | ||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | −17.8652 | + | 5.12769i | −0.997141 | + | 0.286200i | ||||
\(322\) | 3.58343 | + | 6.20668i | 0.199697 | + | 0.345885i | ||||
\(323\) | −7.74713 | −0.431062 | ||||||||
\(324\) | 5.04032 | + | 7.45622i | 0.280018 | + | 0.414234i | ||||
\(325\) | −1.86774 | −0.103603 | ||||||||
\(326\) | −0.738487 | − | 1.27910i | −0.0409010 | − | 0.0708426i | ||||
\(327\) | 26.2653 | − | 7.53868i | 1.45248 | − | 0.416890i | ||||
\(328\) | −0.433868 | + | 0.751481i | −0.0239563 | + | 0.0414936i | ||||
\(329\) | 3.43711 | − | 5.95325i | 0.189494 | − | 0.328214i | ||||
\(330\) | −7.68537 | − | 7.41790i | −0.423066 | − | 0.408342i | ||||
\(331\) | −12.5238 | − | 21.6918i | −0.688369 | − | 1.19229i | −0.972365 | − | 0.233465i | \(-0.924993\pi\) |
0.283996 | − | 0.958826i | \(-0.408340\pi\) | |||||||
\(332\) | 14.7701 | 0.810612 | ||||||||
\(333\) | −10.7302 | + | 6.71254i | −0.588010 | + | 0.367845i | ||||
\(334\) | 23.1623 | 1.26739 | ||||||||
\(335\) | 0.244219 | + | 0.422999i | 0.0133431 | + | 0.0231109i | ||||
\(336\) | 0.418594 | − | 1.68071i | 0.0228362 | − | 0.0916901i | ||||
\(337\) | 1.09217 | − | 1.89170i | 0.0594945 | − | 0.103047i | −0.834744 | − | 0.550638i | \(-0.814384\pi\) |
0.894239 | + | 0.447591i | \(0.147718\pi\) | |||||||
\(338\) | 4.75578 | − | 8.23725i | 0.258680 | − | 0.448048i | ||||
\(339\) | −6.61825 | + | 26.5731i | −0.359454 | + | 1.44325i | ||||
\(340\) | −0.761513 | − | 1.31898i | −0.0412988 | − | 0.0715317i | ||||
\(341\) | 50.4038 | 2.72952 | ||||||||
\(342\) | −13.4774 | − | 7.15729i | −0.728776 | − | 0.387022i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 4.01729 | + | 6.95816i | 0.216598 | + | 0.375159i | ||||
\(345\) | 8.93161 | + | 8.62077i | 0.480862 | + | 0.464127i | ||||
\(346\) | 4.08667 | − | 7.07832i | 0.219701 | − | 0.380533i | ||||
\(347\) | −1.96823 | + | 3.40907i | −0.105660 | + | 0.183008i | −0.914008 | − | 0.405697i | \(-0.867029\pi\) |
0.808348 | + | 0.588705i | \(0.200362\pi\) | |||||||
\(348\) | 17.4432 | − | 5.00655i | 0.935052 | − | 0.268379i | ||||
\(349\) | −17.9206 | − | 31.0394i | −0.959268 | − | 1.66150i | −0.724284 | − | 0.689502i | \(-0.757829\pi\) |
−0.234984 | − | 0.971999i | \(-0.575504\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −3.00606 | − | 9.22775i | −0.160452 | − | 0.492541i | ||||
\(352\) | −6.16685 | −0.328694 | ||||||||
\(353\) | 3.75277 | + | 6.49998i | 0.199740 | + | 0.345959i | 0.948444 | − | 0.316945i | \(-0.102657\pi\) |
−0.748704 | + | 0.662904i | \(0.769324\pi\) | |||||||
\(354\) | 12.0651 | − | 3.46293i | 0.641253 | − | 0.184053i | ||||
\(355\) | 1.67235 | − | 2.89660i | 0.0887594 | − | 0.153736i | ||||
\(356\) | −1.78755 | + | 3.09613i | −0.0947402 | + | 0.164095i | ||||
\(357\) | −1.89805 | − | 1.83200i | −0.100456 | − | 0.0969596i | ||||
\(358\) | 4.56636 | + | 7.90917i | 0.241340 | + | 0.418013i | ||||
\(359\) | 28.6218 | 1.51060 | 0.755301 | − | 0.655378i | \(-0.227491\pi\) | ||||
0.755301 | + | 0.655378i | \(0.227491\pi\) | |||||||
\(360\) | −0.106223 | − | 2.99812i | −0.00559843 | − | 0.158015i | ||||
\(361\) | 6.87423 | 0.361801 | ||||||||
\(362\) | 5.37930 | + | 9.31722i | 0.282730 | + | 0.489702i | ||||
\(363\) | −11.3146 | + | 45.4297i | −0.593864 | + | 2.38444i | ||||
\(364\) | −0.933868 | + | 1.61751i | −0.0489480 | + | 0.0847804i | ||||
\(365\) | −2.36774 | + | 4.10104i | −0.123933 | + | 0.214658i | ||||
\(366\) | 1.10669 | − | 4.44350i | 0.0578476 | − | 0.232266i | ||||
\(367\) | −3.93085 | − | 6.80844i | −0.205189 | − | 0.355398i | 0.745004 | − | 0.667060i | \(-0.232448\pi\) |
−0.950193 | + | 0.311662i | \(0.899114\pi\) | |||||||
\(368\) | 7.16685 | 0.373598 | ||||||||
\(369\) | 0.0921733 | + | 2.60158i | 0.00479835 | + | 0.135433i | ||||
\(370\) | 4.21894 | 0.219332 | ||||||||
\(371\) | 0.0227964 | + | 0.0394845i | 0.00118353 | + | 0.00204993i | ||||
\(372\) | 10.1859 | + | 9.83144i | 0.528116 | + | 0.509737i | ||||
\(373\) | 8.00000 | − | 13.8564i | 0.414224 | − | 0.717458i | −0.581122 | − | 0.813816i | \(-0.697386\pi\) |
0.995347 | + | 0.0963587i | \(0.0307196\pi\) | |||||||
\(374\) | −4.69614 | + | 8.13395i | −0.242832 | + | 0.420597i | ||||
\(375\) | −1.66483 | + | 0.477841i | −0.0859716 | + | 0.0246756i | ||||
\(376\) | −3.43711 | − | 5.95325i | −0.177256 | − | 0.307016i | ||||
\(377\) | −19.5691 | −1.00786 | ||||||||
\(378\) | −1.60947 | − | 4.94061i | −0.0827821 | − | 0.254117i | ||||
\(379\) | −4.25201 | −0.218411 | −0.109205 | − | 0.994019i | \(-0.534831\pi\) | ||||
−0.109205 | + | 0.994019i | \(0.534831\pi\) | |||||||
\(380\) | 2.54334 | + | 4.40519i | 0.130470 | + | 0.225981i | ||||
\(381\) | 8.60195 | − | 2.46893i | 0.440691 | − | 0.126487i | ||||
\(382\) | −7.77609 | + | 13.4686i | −0.397859 | + | 0.689113i | ||||
\(383\) | 7.12699 | − | 12.3443i | 0.364172 | − | 0.630765i | −0.624471 | − | 0.781048i | \(-0.714685\pi\) |
0.988643 | + | 0.150283i | \(0.0480186\pi\) | |||||||
\(384\) | −1.24624 | − | 1.20287i | −0.0635969 | − | 0.0613835i | ||||
\(385\) | 3.08343 | + | 5.34065i | 0.157146 | + | 0.272185i | ||||
\(386\) | −3.39076 | −0.172585 | ||||||||
\(387\) | 21.2881 | + | 11.3052i | 1.08214 | + | 0.574676i | ||||
\(388\) | 10.0231 | 0.508847 | ||||||||
\(389\) | −6.65605 | − | 11.5286i | −0.337475 | − | 0.584524i | 0.646482 | − | 0.762929i | \(-0.276240\pi\) |
−0.983957 | + | 0.178405i | \(0.942906\pi\) | |||||||
\(390\) | −0.781823 | + | 3.13912i | −0.0395891 | + | 0.158955i | ||||
\(391\) | 5.45765 | − | 9.45293i | 0.276005 | − | 0.478055i | ||||
\(392\) | −0.500000 | + | 0.866025i | −0.0252538 | + | 0.0437409i | ||||
\(393\) | −4.51560 | + | 18.1307i | −0.227782 | + | 0.914574i | ||||
\(394\) | 3.27632 | + | 5.67475i | 0.165059 | + | 0.285890i | ||||
\(395\) | −13.0346 | −0.655841 | ||||||||
\(396\) | −15.6844 | + | 9.81178i | −0.788170 | + | 0.493060i | ||||
\(397\) | −21.7880 | −1.09351 | −0.546755 | − | 0.837293i | \(-0.684137\pi\) | ||||
−0.546755 | + | 0.837293i | \(0.684137\pi\) | |||||||
\(398\) | 0.928136 | + | 1.60758i | 0.0465233 | + | 0.0805807i | ||||
\(399\) | 6.33921 | + | 6.11859i | 0.317357 | + | 0.306313i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 0.839438 | − | 1.45395i | 0.0419195 | − | 0.0726067i | −0.844304 | − | 0.535864i | \(-0.819986\pi\) |
0.886224 | + | 0.463257i | \(0.153319\pi\) | |||||||
\(402\) | 0.813166 | − | 0.233395i | 0.0405571 | − | 0.0116407i | ||||
\(403\) | −7.63282 | − | 13.2204i | −0.380218 | − | 0.658557i | ||||
\(404\) | −16.2425 | −0.808096 | ||||||||
\(405\) | −5.04032 | − | 7.45622i | −0.250456 | − | 0.370502i | ||||
\(406\) | −10.4774 | −0.519986 | ||||||||
\(407\) | −13.0088 | − | 22.5319i | −0.644821 | − | 1.11686i | ||||
\(408\) | −2.53558 | + | 0.727765i | −0.125530 | + | 0.0360297i | ||||
\(409\) | −9.29663 | + | 16.1022i | −0.459689 | + | 0.796204i | −0.998944 | − | 0.0459379i | \(-0.985372\pi\) |
0.539256 | + | 0.842142i | \(0.318706\pi\) | |||||||
\(410\) | 0.433868 | − | 0.751481i | 0.0214272 | − | 0.0371130i | ||||
\(411\) | −17.0178 | − | 16.4255i | −0.839424 | − | 0.810210i | ||||
\(412\) | −5.14406 | − | 8.90977i | −0.253429 | − | 0.438953i | ||||
\(413\) | −7.24703 | −0.356603 | ||||||||
\(414\) | 18.2277 | − | 11.4028i | 0.895843 | − | 0.560418i | ||||
\(415\) | −14.7701 | −0.725034 | ||||||||
\(416\) | 0.933868 | + | 1.61751i | 0.0457866 | + | 0.0793048i | ||||
\(417\) | −0.274108 | + | 1.10058i | −0.0134231 | + | 0.0538956i | ||||
\(418\) | 15.6844 | − | 27.1661i | 0.767148 | − | 1.32874i | ||||
\(419\) | 17.9920 | − | 31.1631i | 0.878967 | − | 1.52242i | 0.0264916 | − | 0.999649i | \(-0.491566\pi\) |
0.852476 | − | 0.522767i | \(-0.175100\pi\) | |||||||
\(420\) | −0.418594 | + | 1.68071i | −0.0204253 | + | 0.0820102i | ||||
\(421\) | 2.54357 | + | 4.40558i | 0.123966 | + | 0.214715i | 0.921328 | − | 0.388786i | \(-0.127105\pi\) |
−0.797362 | + | 0.603501i | \(0.793772\pi\) | |||||||
\(422\) | −1.28614 | −0.0626082 | ||||||||
\(423\) | −18.2137 | − | 9.67250i | −0.885579 | − | 0.470293i | ||||
\(424\) | 0.0455927 | 0.00221418 | ||||||||
\(425\) | 0.761513 | + | 1.31898i | 0.0369388 | + | 0.0639799i | ||||
\(426\) | −4.16831 | − | 4.02324i | −0.201955 | − | 0.194927i | ||||
\(427\) | −1.32191 | + | 2.28962i | −0.0639719 | + | 0.110803i | ||||
\(428\) | 5.36548 | − | 9.29328i | 0.259350 | − | 0.449208i | ||||
\(429\) | 19.1756 | − | 5.50380i | 0.925808 | − | 0.265726i | ||||
\(430\) | −4.01729 | − | 6.95816i | −0.193731 | − | 0.335552i | ||||
\(431\) | 24.3452 | 1.17267 | 0.586333 | − | 0.810070i | \(-0.300571\pi\) | ||||
0.586333 | + | 0.810070i | \(0.300571\pi\) | |||||||
\(432\) | −5.08343 | − | 1.07646i | −0.244576 | − | 0.0517914i | ||||
\(433\) | −4.20701 | −0.202176 | −0.101088 | − | 0.994877i | \(-0.532232\pi\) | ||||
−0.101088 | + | 0.994877i | \(0.532232\pi\) | |||||||
\(434\) | −4.08667 | − | 7.07832i | −0.196167 | − | 0.339770i | ||||
\(435\) | −17.4432 | + | 5.00655i | −0.836336 | + | 0.240046i | ||||
\(436\) | −7.88828 | + | 13.6629i | −0.377780 | + | 0.654334i | ||||
\(437\) | −18.2277 | + | 31.5713i | −0.871950 | + | 1.51026i | ||||
\(438\) | 5.90153 | + | 5.69614i | 0.281986 | + | 0.272172i | ||||
\(439\) | 12.4577 | + | 21.5773i | 0.594571 | + | 1.02983i | 0.993607 | + | 0.112892i | \(0.0360115\pi\) |
−0.399036 | + | 0.916935i | \(0.630655\pi\) | |||||||
\(440\) | 6.16685 | 0.293993 | ||||||||
\(441\) | 0.106223 | + | 2.99812i | 0.00505823 | + | 0.142768i | ||||
\(442\) | 2.84461 | 0.135304 | ||||||||
\(443\) | −14.1500 | − | 24.5086i | −0.672288 | − | 1.16444i | −0.977254 | − | 0.212073i | \(-0.931978\pi\) |
0.304966 | − | 0.952363i | \(-0.401355\pi\) | |||||||
\(444\) | 1.76602 | − | 7.09080i | 0.0838116 | − | 0.336514i | ||||
\(445\) | 1.78755 | − | 3.09613i | 0.0847382 | − | 0.146771i | ||||
\(446\) | −0.620272 | + | 1.07434i | −0.0293707 | + | 0.0508716i | ||||
\(447\) | −7.86246 | + | 31.5688i | −0.371882 | + | 1.49315i | ||||
\(448\) | 0.500000 | + | 0.866025i | 0.0236228 | + | 0.0409159i | ||||
\(449\) | −3.60275 | −0.170024 | −0.0850121 | − | 0.996380i | \(-0.527093\pi\) | ||||
−0.0850121 | + | 0.996380i | \(0.527093\pi\) | |||||||
\(450\) | 0.106223 | + | 2.99812i | 0.00500739 | + | 0.141333i | ||||
\(451\) | −5.35120 | −0.251978 | ||||||||
\(452\) | −7.90534 | − | 13.6925i | −0.371836 | − | 0.644039i | ||||
\(453\) | 5.41512 | + | 5.22666i | 0.254424 | + | 0.245570i | ||||
\(454\) | 9.85650 | − | 17.0720i | 0.462589 | − | 0.801227i | ||||
\(455\) | 0.933868 | − | 1.61751i | 0.0437804 | − | 0.0758299i | ||||
\(456\) | 8.46846 | − | 2.43062i | 0.396572 | − | 0.113824i | ||||
\(457\) | 14.1302 | + | 24.4743i | 0.660985 | + | 1.14486i | 0.980357 | + | 0.197230i | \(0.0631945\pi\) |
−0.319373 | + | 0.947629i | \(0.603472\pi\) | |||||||
\(458\) | 6.11477 | 0.285724 | ||||||||
\(459\) | −5.29093 | + | 5.88519i | −0.246959 | + | 0.274697i | ||||
\(460\) | −7.16685 | −0.334156 | ||||||||
\(461\) | 16.2768 | + | 28.1922i | 0.758085 | + | 1.31304i | 0.943826 | + | 0.330443i | \(0.107198\pi\) |
−0.185741 | + | 0.982599i | \(0.559468\pi\) | |||||||
\(462\) | 10.2668 | − | 2.94678i | 0.477654 | − | 0.137096i | ||||
\(463\) | −17.4204 | + | 30.1730i | −0.809594 | + | 1.40226i | 0.103552 | + | 0.994624i | \(0.466979\pi\) |
−0.913146 | + | 0.407633i | \(0.866354\pi\) | |||||||
\(464\) | −5.23872 | + | 9.07372i | −0.243201 | + | 0.421237i | ||||
\(465\) | −10.1859 | − | 9.83144i | −0.472362 | − | 0.455922i | ||||
\(466\) | 2.65280 | + | 4.59479i | 0.122889 | + | 0.212850i | ||||
\(467\) | −42.1518 | −1.95055 | −0.975276 | − | 0.220989i | \(-0.929071\pi\) | ||||
−0.975276 | + | 0.220989i | \(0.929071\pi\) | |||||||
\(468\) | 4.94868 | + | 2.62803i | 0.228753 | + | 0.121481i | ||||
\(469\) | −0.488437 | −0.0225539 | ||||||||
\(470\) | 3.43711 | + | 5.95325i | 0.158542 | + | 0.274603i | ||||
\(471\) | 5.51636 | − | 22.1489i | 0.254181 | − | 1.02057i | ||||
\(472\) | −3.62352 | + | 6.27612i | −0.166786 | + | 0.288882i | ||||
\(473\) | −24.7741 | + | 42.9099i | −1.13911 | + | 1.97300i | ||||
\(474\) | −5.45620 | + | 21.9073i | −0.250611 | + | 1.00624i | ||||
\(475\) | −2.54334 | − | 4.40519i | −0.116696 | − | 0.202124i | ||||
\(476\) | 1.52303 | 0.0698078 | ||||||||
\(477\) | 0.115958 | − | 0.0725404i | 0.00530933 | − | 0.00332139i | ||||
\(478\) | −23.8176 | −1.08939 | ||||||||
\(479\) | −7.74379 | − | 13.4126i | −0.353823 | − | 0.612839i | 0.633093 | − | 0.774076i | \(-0.281785\pi\) |
−0.986916 | + | 0.161237i | \(0.948452\pi\) | |||||||
\(480\) | 1.24624 | + | 1.20287i | 0.0568828 | + | 0.0549031i | ||||
\(481\) | −3.93993 | + | 6.82416i | −0.179645 | + | 0.311155i | ||||
\(482\) | 4.73600 | − | 8.20299i | 0.215719 | − | 0.373636i | ||||
\(483\) | −11.9316 | + | 3.42462i | −0.542907 | + | 0.155825i | ||||
\(484\) | −13.5150 | − | 23.4087i | −0.614320 | − | 1.06403i | ||||
\(485\) | −10.0231 | −0.455127 | ||||||||
\(486\) | −14.6416 | + | 5.35018i | −0.664155 | + | 0.242689i | ||||
\(487\) | 12.0009 | 0.543814 | 0.271907 | − | 0.962324i | \(-0.412346\pi\) | ||||
0.271907 | + | 0.962324i | \(0.412346\pi\) | |||||||
\(488\) | 1.32191 | + | 2.28962i | 0.0598402 | + | 0.103646i | ||||
\(489\) | 2.45891 | − | 0.705759i | 0.111196 | − | 0.0319155i | ||||
\(490\) | 0.500000 | − | 0.866025i | 0.0225877 | − | 0.0391230i | ||||
\(491\) | −11.9953 | + | 20.7764i | −0.541338 | + | 0.937625i | 0.457489 | + | 0.889215i | \(0.348749\pi\) |
−0.998828 | + | 0.0484103i | \(0.984584\pi\) | |||||||
\(492\) | −1.08141 | − | 1.04377i | −0.0487536 | − | 0.0470568i | ||||
\(493\) | 7.97870 | + | 13.8195i | 0.359343 | + | 0.622400i | ||||
\(494\) | −9.50056 | −0.427450 | ||||||||
\(495\) | 15.6844 | − | 9.81178i | 0.704960 | − | 0.441007i | ||||
\(496\) | −8.17334 | −0.366994 | ||||||||
\(497\) | 1.67235 | + | 2.89660i | 0.0750154 | + | 0.129930i | ||||
\(498\) | −6.18266 | + | 24.8242i | −0.277051 | + | 1.11240i | ||||
\(499\) | −11.7273 | + | 20.3122i | −0.524984 | + | 0.909299i | 0.474593 | + | 0.880206i | \(0.342595\pi\) |
−0.999577 | + | 0.0290934i | \(0.990738\pi\) | |||||||
\(500\) | 0.500000 | − | 0.866025i | 0.0223607 | − | 0.0387298i | ||||
\(501\) | −9.69561 | + | 38.9291i | −0.433168 | + | 1.73923i | ||||
\(502\) | −11.1386 | − | 19.2925i | −0.497138 | − | 0.861068i | ||||
\(503\) | 23.8968 | 1.06550 | 0.532752 | − | 0.846272i | \(-0.321158\pi\) | ||||
0.532752 | + | 0.846272i | \(0.321158\pi\) | |||||||
\(504\) | 2.64956 | + | 1.40707i | 0.118021 | + | 0.0626758i | ||||
\(505\) | 16.2425 | 0.722783 | ||||||||
\(506\) | 22.0985 | + | 38.2757i | 0.982397 | + | 1.70156i | ||||
\(507\) | 11.8537 | + | 11.4411i | 0.526440 | + | 0.508119i | ||||
\(508\) | −2.58343 | + | 4.47463i | −0.114621 | + | 0.198529i | ||||
\(509\) | 1.32191 | − | 2.28962i | 0.0585928 | − | 0.101486i | −0.835241 | − | 0.549884i | \(-0.814672\pi\) |
0.893834 | + | 0.448398i | \(0.148005\pi\) | |||||||
\(510\) | 2.53558 | − | 0.727765i | 0.112278 | − | 0.0322260i | ||||
\(511\) | −2.36774 | − | 4.10104i | −0.104742 | − | 0.181419i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 17.6709 | − | 19.6556i | 0.780189 | − | 0.867817i | ||||
\(514\) | −22.1965 | −0.979044 | ||||||||
\(515\) | 5.14406 | + | 8.90977i | 0.226674 | + | 0.392611i | ||||
\(516\) | −13.3762 | + | 3.83926i | −0.588856 | + | 0.169014i | ||||
\(517\) | 21.1962 | − | 36.7128i | 0.932206 | − | 1.61463i | ||||
\(518\) | −2.10947 | + | 3.65371i | −0.0926847 | + | 0.160535i | ||||
\(519\) | 10.1859 | + | 9.83144i | 0.447113 | + | 0.431552i | ||||
\(520\) | −0.933868 | − | 1.61751i | −0.0409528 | − | 0.0709324i | ||||
\(521\) | 38.3227 | 1.67895 | 0.839474 | − | 0.543400i | \(-0.182863\pi\) | ||||
0.839474 | + | 0.543400i | \(0.182863\pi\) | |||||||
\(522\) | 1.11294 | + | 31.4126i | 0.0487122 | + | 1.37489i | ||||
\(523\) | 27.9043 | 1.22017 | 0.610085 | − | 0.792336i | \(-0.291135\pi\) | ||||
0.610085 | + | 0.792336i | \(0.291135\pi\) | |||||||
\(524\) | −5.39378 | − | 9.34230i | −0.235628 | − | 0.408120i | ||||
\(525\) | 0.418594 | − | 1.68071i | 0.0182689 | − | 0.0733521i | ||||
\(526\) | −5.71569 | + | 9.89987i | −0.249216 | + | 0.431655i | ||||
\(527\) | −6.22411 | + | 10.7805i | −0.271126 | + | 0.469605i | ||||
\(528\) | 2.58141 | − | 10.3647i | 0.112341 | − | 0.451065i | ||||
\(529\) | −14.1819 | − | 24.5638i | −0.616604 | − | 1.06799i | ||||
\(530\) | −0.0455927 | −0.00198042 | ||||||||
\(531\) | 0.769800 | + | 21.7275i | 0.0334065 | + | 0.942892i | ||||
\(532\) | −5.08667 | −0.220535 | ||||||||
\(533\) | 0.810351 | + | 1.40357i | 0.0351002 | + | 0.0607953i | ||||
\(534\) | −4.45544 | − | 4.30038i | −0.192806 | − | 0.186096i | ||||
\(535\) | −5.36548 | + | 9.29328i | −0.231970 | + | 0.401784i | ||||
\(536\) | −0.244219 | + | 0.422999i | −0.0105486 | + | 0.0182708i | ||||
\(537\) | −15.2045 | + | 4.36399i | −0.656121 | + | 0.188320i | ||||
\(538\) | −2.18965 | − | 3.79258i | −0.0944025 | − | 0.163510i | ||||
\(539\) | −6.16685 | −0.265625 | ||||||||
\(540\) | 5.08343 | + | 1.07646i | 0.218756 | + | 0.0463237i | ||||
\(541\) | −19.0355 | −0.818400 | −0.409200 | − | 0.912445i | \(-0.634192\pi\) | ||||
−0.409200 | + | 0.912445i | \(0.634192\pi\) | |||||||
\(542\) | 8.98068 | + | 15.5550i | 0.385753 | + | 0.668144i | ||||
\(543\) | −17.9113 | + | 5.14090i | −0.768646 | + | 0.220617i | ||||
\(544\) | 0.761513 | − | 1.31898i | 0.0326496 | − | 0.0565508i | ||||
\(545\) | 7.88828 | − | 13.6629i | 0.337897 | − | 0.585254i | ||||
\(546\) | −2.32765 | − | 2.24664i | −0.0996140 | − | 0.0961472i | ||||
\(547\) | 11.8113 | + | 20.4578i | 0.505016 | + | 0.874714i | 0.999983 | + | 0.00580213i | \(0.00184688\pi\) |
−0.494967 | + | 0.868912i | \(0.664820\pi\) | |||||||
\(548\) | 13.6553 | 0.583325 | ||||||||
\(549\) | 7.00497 | + | 3.72004i | 0.298965 | + | 0.158768i | ||||
\(550\) | −6.16685 | −0.262955 | ||||||||
\(551\) | −26.6476 | − | 46.1550i | −1.13523 | − | 1.96627i | ||||
\(552\) | −3.00000 | + | 12.0454i | −0.127688 | + | 0.512686i | ||||
\(553\) | 6.51729 | − | 11.2883i | 0.277144 | − | 0.480027i | ||||
\(554\) | −8.12126 | + | 14.0664i | −0.345039 | + | 0.597626i | ||||
\(555\) | −1.76602 | + | 7.09080i | −0.0749634 | + | 0.300988i | ||||
\(556\) | −0.327415 | − | 0.567100i | −0.0138855 | − | 0.0240504i | ||||
\(557\) | 16.8628 | 0.714498 | 0.357249 | − | 0.934009i | \(-0.383715\pi\) | ||||
0.357249 | + | 0.934009i | \(0.383715\pi\) | |||||||
\(558\) | −20.7876 | + | 13.0042i | −0.880007 | + | 0.550512i | ||||
\(559\) | 15.0065 | 0.634707 | ||||||||
\(560\) | −0.500000 | − | 0.866025i | −0.0211289 | − | 0.0365963i | ||||
\(561\) | −11.7050 | − | 11.2977i | −0.494186 | − | 0.476988i | ||||
\(562\) | −0.381556 | + | 0.660874i | −0.0160950 | + | 0.0278773i | ||||
\(563\) | 8.99224 | − | 15.5750i | 0.378978 | − | 0.656409i | −0.611936 | − | 0.790907i | \(-0.709609\pi\) |
0.990914 | + | 0.134499i | \(0.0429423\pi\) | |||||||
\(564\) | 11.4444 | − | 3.28479i | 0.481898 | − | 0.138315i | ||||
\(565\) | 7.90534 | + | 13.6925i | 0.332580 | + | 0.576046i | ||||
\(566\) | −8.87423 | −0.373012 | ||||||||
\(567\) | 8.97743 | − | 0.636937i | 0.377017 | − | 0.0267489i | ||||
\(568\) | 3.34471 | 0.140341 | ||||||||
\(569\) | −3.75005 | − | 6.49528i | −0.157210 | − | 0.272296i | 0.776651 | − | 0.629931i | \(-0.216917\pi\) |
−0.933862 | + | 0.357635i | \(0.883583\pi\) | |||||||
\(570\) | −8.46846 | + | 2.43062i | −0.354705 | + | 0.101808i | ||||
\(571\) | −0.0177236 | + | 0.0306981i | −0.000741709 | + | 0.00128468i | −0.866396 | − | 0.499358i | \(-0.833569\pi\) |
0.865654 | + | 0.500642i | \(0.166903\pi\) | |||||||
\(572\) | −5.75903 | + | 9.97493i | −0.240797 | + | 0.417073i | ||||
\(573\) | −19.3817 | − | 18.7072i | −0.809684 | − | 0.781505i | ||||
\(574\) | 0.433868 | + | 0.751481i | 0.0181093 | + | 0.0313662i | ||||
\(575\) | 7.16685 | 0.298878 | ||||||||
\(576\) | 2.54334 | − | 1.59105i | 0.105972 | − | 0.0662938i | ||||
\(577\) | −29.0402 | −1.20896 | −0.604480 | − | 0.796620i | \(-0.706619\pi\) | ||||
−0.604480 | + | 0.796620i | \(0.706619\pi\) | |||||||
\(578\) | 7.34020 | + | 12.7136i | 0.305312 | + | 0.528816i | ||||
\(579\) | 1.41935 | − | 5.69888i | 0.0589863 | − | 0.236837i | ||||
\(580\) | 5.23872 | − | 9.07372i | 0.217526 | − | 0.376766i | ||||
\(581\) | 7.38503 | − | 12.7912i | 0.306383 | − | 0.530670i | ||||
\(582\) | −4.19562 | + | 16.8459i | −0.173914 | + | 0.698287i | ||||
\(583\) | 0.140582 | + | 0.243495i | 0.00582230 | + | 0.0100845i | ||||
\(584\) | −4.73547 | −0.195955 | ||||||||
\(585\) | −4.94868 | − | 2.62803i | −0.204603 | − | 0.108656i | ||||
\(586\) | 11.3631 | 0.469406 | ||||||||
\(587\) | 18.2445 | + | 31.6005i | 0.753033 | + | 1.30429i | 0.946346 | + | 0.323154i | \(0.104743\pi\) |
−0.193313 | + | 0.981137i | \(0.561923\pi\) | |||||||
\(588\) | −1.24624 | − | 1.20287i | −0.0513940 | − | 0.0496054i | ||||
\(589\) | 20.7876 | − | 36.0051i | 0.856536 | − | 1.48356i | ||||
\(590\) | 3.62352 | − | 6.27612i | 0.149178 | − | 0.258384i | ||||
\(591\) | −10.9091 | + | 3.13112i | −0.448738 | + | 0.128797i | ||||
\(592\) | 2.10947 | + | 3.65371i | 0.0866986 | + | 0.150166i | ||||
\(593\) | 2.60426 | 0.106944 | 0.0534722 | − | 0.998569i | \(-0.482971\pi\) | ||||
0.0534722 | + | 0.998569i | \(0.482971\pi\) | |||||||
\(594\) | −9.92535 | − | 30.4680i | −0.407242 | − | 1.25012i | ||||
\(595\) | −1.52303 | −0.0624380 | ||||||||
\(596\) | −9.39152 | − | 16.2666i | −0.384692 | − | 0.666305i | ||||
\(597\) | −3.09038 | + | 0.887003i | −0.126481 | + | 0.0363026i | ||||
\(598\) | 6.69289 | − | 11.5924i | 0.273693 | − | 0.474050i | ||||
\(599\) | −1.79329 | + | 3.10606i | −0.0732717 | + | 0.126910i | −0.900333 | − | 0.435201i | \(-0.856677\pi\) |
0.827062 | + | 0.562111i | \(0.190011\pi\) | |||||||
\(600\) | −1.24624 | − | 1.20287i | −0.0508775 | − | 0.0491068i | ||||
\(601\) | 8.55467 | + | 14.8171i | 0.348952 | + | 0.604403i | 0.986064 | − | 0.166369i | \(-0.0532042\pi\) |
−0.637111 | + | 0.770772i | \(0.719871\pi\) | |||||||
\(602\) | 8.03459 | 0.327465 | ||||||||
\(603\) | 0.0518832 | + | 1.46439i | 0.00211285 | + | 0.0596347i | ||||
\(604\) | −4.34517 | −0.176802 | ||||||||
\(605\) | 13.5150 | + | 23.4087i | 0.549464 | + | 0.951700i | ||||
\(606\) | 6.79902 | − | 27.2989i | 0.276191 | − | 1.10894i | ||||
\(607\) | 0.689419 | − | 1.19411i | 0.0279827 | − | 0.0484674i | −0.851695 | − | 0.524038i | \(-0.824425\pi\) |
0.879678 | + | 0.475570i | \(0.157758\pi\) | |||||||
\(608\) | −2.54334 | + | 4.40519i | −0.103146 | + | 0.178654i | ||||
\(609\) | 4.38579 | − | 17.6095i | 0.177721 | − | 0.713573i | ||||
\(610\) | −1.32191 | − | 2.28962i | −0.0535227 | − | 0.0927040i | ||||
\(611\) | −12.8392 | −0.519420 | ||||||||
\(612\) | −0.161780 | − | 4.56621i | −0.00653957 | − | 0.184578i | ||||
\(613\) | −35.8859 | −1.44942 | −0.724709 | − | 0.689055i | \(-0.758026\pi\) | ||||
−0.724709 | + | 0.689055i | \(0.758026\pi\) | |||||||
\(614\) | −15.0839 | − | 26.1261i | −0.608736 | − | 1.05436i | ||||
\(615\) | 1.08141 | + | 1.04377i | 0.0436065 | + | 0.0420889i | ||||
\(616\) | −3.08343 | + | 5.34065i | −0.124235 | + | 0.215181i | ||||
\(617\) | 5.21841 | − | 9.03855i | 0.210085 | − | 0.363878i | −0.741656 | − | 0.670781i | \(-0.765959\pi\) |
0.951741 | + | 0.306902i | \(0.0992925\pi\) | |||||||
\(618\) | 17.1280 | − | 4.91608i | 0.688989 | − | 0.197754i | ||||
\(619\) | −13.9082 | − | 24.0896i | −0.559016 | − | 0.968244i | −0.997579 | − | 0.0695436i | \(-0.977846\pi\) |
0.438563 | − | 0.898700i | \(-0.355488\pi\) | |||||||
\(620\) | 8.17334 | 0.328249 | ||||||||
\(621\) | 11.5348 | + | 35.4086i | 0.462876 | + | 1.42090i | ||||
\(622\) | −7.71254 | −0.309245 | ||||||||
\(623\) | 1.78755 | + | 3.09613i | 0.0716169 | + | 0.124044i | ||||
\(624\) | −3.10947 | + | 0.892481i | −0.124478 | + | 0.0357278i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 1.23276 | − | 2.13519i | 0.0492708 | − | 0.0853395i | ||||
\(627\) | 39.0930 | + | 37.7324i | 1.56122 | + | 1.50689i | ||||
\(628\) | 6.58916 | + | 11.4128i | 0.262936 | + | 0.455419i | ||||
\(629\) | 6.42555 | 0.256203 | ||||||||
\(630\) | −2.64956 | − | 1.40707i | −0.105561 | − | 0.0560589i | ||||
\(631\) | 18.5412 | 0.738113 | 0.369056 | − | 0.929407i | \(-0.379681\pi\) | ||||
0.369056 | + | 0.929407i | \(0.379681\pi\) | |||||||
\(632\) | −6.51729 | − | 11.2883i | −0.259244 | − | 0.449024i | ||||
\(633\) | 0.538369 | − | 2.16162i | 0.0213982 | − | 0.0859167i | ||||
\(634\) | −9.79935 | + | 16.9730i | −0.389182 | + | 0.674083i | ||||
\(635\) | 2.58343 | − | 4.47463i | 0.102520 | − | 0.177570i | ||||
\(636\) | −0.0190848 | + | 0.0766281i | −0.000756763 | + | 0.00303850i | ||||
\(637\) | 0.933868 | + | 1.61751i | 0.0370012 | + | 0.0640880i | ||||
\(638\) | −64.6128 | −2.55804 | ||||||||
\(639\) | 8.50672 | − | 5.32160i | 0.336521 | − | 0.210519i | ||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −8.40458 | − | 14.5572i | −0.331961 | − | 0.574973i | 0.650935 | − | 0.759133i | \(-0.274377\pi\) |
−0.982896 | + | 0.184160i | \(0.941044\pi\) | |||||||
\(642\) | 13.3733 | + | 12.9079i | 0.527804 | + | 0.509435i | ||||
\(643\) | 8.85650 | − | 15.3399i | 0.349266 | − | 0.604947i | −0.636853 | − | 0.770985i | \(-0.719764\pi\) |
0.986119 | + | 0.166038i | \(0.0530975\pi\) | |||||||
\(644\) | 3.58343 | − | 6.20668i | 0.141207 | − | 0.244577i | ||||
\(645\) | 13.3762 | − | 3.83926i | 0.526689 | − | 0.151171i | ||||
\(646\) | 3.87357 | + | 6.70921i | 0.152403 | + | 0.263971i | ||||
\(647\) | −7.15990 | −0.281485 | −0.140742 | − | 0.990046i | \(-0.544949\pi\) | ||||
−0.140742 | + | 0.990046i | \(0.544949\pi\) | |||||||
\(648\) | 3.93711 | − | 8.09315i | 0.154664 | − | 0.317929i | ||||
\(649\) | −44.6914 | −1.75429 | ||||||||
\(650\) | 0.933868 | + | 1.61751i | 0.0366293 | + | 0.0634438i | ||||
\(651\) | 13.6072 | − | 3.90556i | 0.533310 | − | 0.153071i | ||||
\(652\) | −0.738487 | + | 1.27910i | −0.0289214 | + | 0.0500933i | ||||
\(653\) | 17.1619 | − | 29.7252i | 0.671596 | − | 1.16324i | −0.305855 | − | 0.952078i | \(-0.598942\pi\) |
0.977451 | − | 0.211161i | \(-0.0677243\pi\) | |||||||
\(654\) | −19.6614 | − | 18.9771i | −0.768820 | − | 0.742063i | ||||
\(655\) | 5.39378 | + | 9.34230i | 0.210752 | + | 0.365034i | ||||
\(656\) | 0.867736 | 0.0338794 | ||||||||
\(657\) | −12.0439 | + | 7.53438i | −0.469877 | + | 0.293944i | ||||
\(658\) | −6.87423 | −0.267985 | ||||||||
\(659\) | 9.43062 | + | 16.3343i | 0.367365 | + | 0.636295i | 0.989153 | − | 0.146891i | \(-0.0469267\pi\) |
−0.621788 | + | 0.783186i | \(0.713593\pi\) | |||||||
\(660\) | −2.58141 | + | 10.3647i | −0.100481 | + | 0.403445i | ||||
\(661\) | 1.69439 | − | 2.93477i | 0.0659043 | − | 0.114150i | −0.831190 | − | 0.555988i | \(-0.812340\pi\) |
0.897095 | + | 0.441838i | \(0.145673\pi\) | |||||||
\(662\) | −12.5238 | + | 21.6918i | −0.486751 | + | 0.843077i | ||||
\(663\) | −1.19074 | + | 4.78096i | −0.0462444 | + | 0.185677i | ||||
\(664\) | −7.38503 | − | 12.7912i | −0.286595 | − | 0.496397i | ||||
\(665\) | 5.08667 | 0.197253 | ||||||||
\(666\) | 11.1783 | + | 5.93633i | 0.433151 | + | 0.230028i | ||||
\(667\) | 75.0902 | 2.90751 | ||||||||
\(668\) | −11.5812 | − | 20.0592i | −0.448089 | − | 0.776113i | ||||
\(669\) | −1.54601 | − | 1.49221i | −0.0597724 | − | 0.0576922i | ||||
\(670\) | 0.244219 | − | 0.422999i | 0.00943499 | − | 0.0163419i | ||||
\(671\) | −8.15205 | + | 14.1198i | −0.314706 | + | 0.545087i | ||||
\(672\) | −1.66483 | + | 0.477841i | −0.0642223 | + | 0.0184331i | ||||
\(673\) | 16.2535 | + | 28.1519i | 0.626527 | + | 1.08518i | 0.988243 | + | 0.152889i | \(0.0488576\pi\) |
−0.361716 | + | 0.932288i | \(0.617809\pi\) | |||||||
\(674\) | −2.18435 | −0.0841379 | ||||||||
\(675\) | −5.08343 | − | 1.07646i | −0.195661 | − | 0.0414331i | ||||
\(676\) | −9.51156 | −0.365829 | ||||||||
\(677\) | 3.26757 | + | 5.65960i | 0.125583 | + | 0.217516i | 0.921961 | − | 0.387283i | \(-0.126587\pi\) |
−0.796378 | + | 0.604800i | \(0.793253\pi\) | |||||||
\(678\) | 26.3221 | − | 7.55499i | 1.01090 | − | 0.290148i | ||||
\(679\) | 5.01156 | − | 8.68028i | 0.192326 | − | 0.333119i | ||||
\(680\) | −0.761513 | + | 1.31898i | −0.0292027 | + | 0.0505805i | ||||
\(681\) | 24.5671 | + | 23.7121i | 0.941414 | + | 0.908650i | ||||
\(682\) | −25.2019 | − | 43.6510i | −0.965031 | − | 1.67148i | ||||
\(683\) | −15.6629 | −0.599324 | −0.299662 | − | 0.954045i | \(-0.596874\pi\) | ||||
−0.299662 | + | 0.954045i | \(0.596874\pi\) | |||||||
\(684\) | 0.540321 | + | 15.2504i | 0.0206597 | + | 0.583115i | ||||
\(685\) | −13.6553 | −0.521742 | ||||||||
\(686\) | 0.500000 | + | 0.866025i | 0.0190901 | + | 0.0330650i | ||||
\(687\) | −2.55960 | + | 10.2771i | −0.0976550 | + | 0.392097i | ||||
\(688\) | 4.01729 | − | 6.95816i | 0.153158 | − | 0.265277i | ||||
\(689\) | 0.0425776 | − | 0.0737465i | 0.00162208 | − | 0.00280952i | ||||
\(690\) | 3.00000 | − | 12.0454i | 0.114208 | − | 0.458560i | ||||
\(691\) | 12.6789 | + | 21.9605i | 0.482327 | + | 0.835415i | 0.999794 | − | 0.0202880i | \(-0.00645832\pi\) |
−0.517467 | + | 0.855703i | \(0.673125\pi\) | |||||||
\(692\) | −8.17334 | −0.310704 | ||||||||
\(693\) | 0.655060 | + | 18.4890i | 0.0248837 | + | 0.702337i | ||||
\(694\) | 3.93645 | 0.149426 | ||||||||
\(695\) | 0.327415 | + | 0.567100i | 0.0124196 | + | 0.0215113i | ||||
\(696\) | −13.0574 | − | 12.6030i | −0.494939 | − | 0.477714i | ||||
\(697\) | 0.660792 | − | 1.14453i | 0.0250293 | − | 0.0433520i | ||||
\(698\) | −17.9206 | + | 31.0394i | −0.678305 | + | 1.17486i | ||||
\(699\) | −8.83295 | + | 2.53524i | −0.334093 | + | 0.0958915i | ||||
\(700\) | 0.500000 | + | 0.866025i | 0.0188982 | + | 0.0327327i | ||||
\(701\) | 16.1103 | 0.608476 | 0.304238 | − | 0.952596i | \(-0.401598\pi\) | ||||
0.304238 | + | 0.952596i | \(0.401598\pi\) | |||||||
\(702\) | −6.48844 | + | 7.21720i | −0.244890 | + | 0.272396i | ||||
\(703\) | −21.4603 | −0.809392 | ||||||||
\(704\) | 3.08343 | + | 5.34065i | 0.116211 | + | 0.201283i | ||||
\(705\) | −11.4444 | + | 3.28479i | −0.431022 | + | 0.123712i | ||||
\(706\) | 3.75277 | − | 6.49998i | 0.141237 | − | 0.244630i | ||||
\(707\) | −8.12126 | + | 14.0664i | −0.305431 | + | 0.529023i | ||||
\(708\) | −9.03154 | − | 8.71722i | −0.339426 | − | 0.327613i | ||||
\(709\) | −12.8484 | − | 22.2541i | −0.482532 | − | 0.835771i | 0.517267 | − | 0.855824i | \(-0.326950\pi\) |
−0.999799 | + | 0.0200538i | \(0.993616\pi\) | |||||||
\(710\) | −3.34471 | −0.125525 | ||||||||
\(711\) | −34.5359 | − | 18.3405i | −1.29520 | − | 0.687824i | ||||
\(712\) | 3.57511 | 0.133983 | ||||||||
\(713\) | 29.2886 | + | 50.7293i | 1.09687 | + | 1.89983i | ||||
\(714\) | −0.637529 | + | 2.55976i | −0.0238589 | + | 0.0957967i | ||||
\(715\) | 5.75903 | − | 9.97493i | 0.215375 | − | 0.373041i | ||||
\(716\) | 4.56636 | − | 7.90917i | 0.170653 | − | 0.295580i | ||||
\(717\) | 9.96991 | − | 40.0305i | 0.372333 | − | 1.49497i | ||||
\(718\) | −14.3109 | − | 24.7872i | −0.534078 | − | 0.925051i | ||||
\(719\) | −32.4545 | −1.21035 | −0.605174 | − | 0.796093i | \(-0.706897\pi\) | ||||
−0.605174 | + | 0.796093i | \(0.706897\pi\) | |||||||
\(720\) | −2.54334 | + | 1.59105i | −0.0947845 | + | 0.0592950i | ||||
\(721\) | −10.2881 | −0.383149 | ||||||||
\(722\) | −3.43711 | − | 5.95325i | −0.127916 | − | 0.221557i | ||||
\(723\) | 11.8044 | + | 11.3936i | 0.439009 | + | 0.423731i | ||||
\(724\) | 5.37930 | − | 9.31722i | 0.199920 | − | 0.346272i | ||||
\(725\) | −5.23872 | + | 9.07372i | −0.194561 | + | 0.336990i | ||||
\(726\) | 45.0006 | − | 12.9161i | 1.67013 | − | 0.479361i | ||||
\(727\) | 25.6162 | + | 44.3686i | 0.950053 | + | 1.64554i | 0.745303 | + | 0.666726i | \(0.232305\pi\) |
0.204750 | + | 0.978814i | \(0.434362\pi\) | |||||||
\(728\) | 1.86774 | 0.0692229 | ||||||||
\(729\) | −2.86322 | − | 26.8478i | −0.106045 | − | 0.994361i | ||||
\(730\) | 4.73547 | 0.175268 | ||||||||
\(731\) | −6.11844 | − | 10.5975i | −0.226299 | − | 0.391961i | ||||
\(732\) | −4.40153 | + | 1.26333i | −0.162685 | + | 0.0466940i | ||||
\(733\) | 17.6586 | − | 30.5857i | 0.652237 | − | 1.12971i | −0.330342 | − | 0.943861i | \(-0.607164\pi\) |
0.982579 | − | 0.185846i | \(-0.0595024\pi\) | |||||||
\(734\) | −3.93085 | + | 6.80844i | −0.145090 | + | 0.251304i | ||||
\(735\) | 1.24624 | + | 1.20287i | 0.0459682 | + | 0.0443684i | ||||
\(736\) | −3.58343 | − | 6.20668i | −0.132087 | − | 0.228781i | ||||
\(737\) | −3.01212 | −0.110953 | ||||||||
\(738\) | 2.20694 | − | 1.38061i | 0.0812387 | − | 0.0508210i | ||||
\(739\) | 9.54509 | 0.351122 | 0.175561 | − | 0.984469i | \(-0.443826\pi\) | ||||
0.175561 | + | 0.984469i | \(0.443826\pi\) | |||||||
\(740\) | −2.10947 | − | 3.65371i | −0.0775456 | − | 0.134313i | ||||
\(741\) | 3.97687 | − | 15.9677i | 0.146094 | − | 0.586587i | ||||
\(742\) | 0.0227964 | − | 0.0394845i | 0.000836881 | − | 0.00144952i | ||||
\(743\) | 6.03459 | − | 10.4522i | 0.221388 | − | 0.383455i | −0.733842 | − | 0.679320i | \(-0.762275\pi\) |
0.955230 | + | 0.295866i | \(0.0956081\pi\) | |||||||
\(744\) | 3.42131 | − | 13.7370i | 0.125431 | − | 0.503623i | ||||
\(745\) | 9.39152 | + | 16.2666i | 0.344079 | + | 0.595962i | ||||
\(746\) | −16.0000 | −0.585802 | ||||||||
\(747\) | −39.1341 | − | 20.7825i | −1.43184 | − | 0.760391i | ||||
\(748\) | 9.39228 | 0.343416 | ||||||||
\(749\) | −5.36548 | − | 9.29328i | −0.196050 | − | 0.339569i | ||||
\(750\) | 1.24624 | + | 1.20287i | 0.0455062 | + | 0.0439225i | ||||
\(751\) | −15.5283 | + | 26.8959i | −0.566637 | + | 0.981444i | 0.430259 | + | 0.902706i | \(0.358422\pi\) |
−0.996895 | + | 0.0787380i | \(0.974911\pi\) | |||||||
\(752\) | −3.43711 | + | 5.95325i | −0.125339 | + | 0.217093i | ||||
\(753\) | 37.0877 | − | 10.6449i | 1.35155 | − | 0.387922i | ||||
\(754\) | 9.78454 | + | 16.9473i | 0.356332 | + | 0.617185i | ||||
\(755\) | 4.34517 | 0.158137 | ||||||||
\(756\) | −3.47396 | + | 3.86414i | −0.126347 | + | 0.140538i | ||||
\(757\) | −16.2548 | −0.590792 | −0.295396 | − | 0.955375i | \(-0.595452\pi\) | ||||
−0.295396 | + | 0.955375i | \(0.595452\pi\) | |||||||
\(758\) | 2.12600 | + | 3.68235i | 0.0772199 | + | 0.133749i | ||||
\(759\) | −73.5805 | + | 21.1191i | −2.67080 | + | 0.766575i | ||||
\(760\) | 2.54334 | − | 4.40519i | 0.0922565 | − | 0.159793i | ||||
\(761\) | 5.43184 | − | 9.40822i | 0.196904 | − | 0.341048i | −0.750619 | − | 0.660735i | \(-0.770245\pi\) |
0.947523 | + | 0.319687i | \(0.103578\pi\) | |||||||
\(762\) | −6.43913 | − | 6.21504i | −0.233265 | − | 0.225147i | ||||
\(763\) | 7.88828 | + | 13.6629i | 0.285575 | + | 0.494630i | ||||
\(764\) | 15.5522 | 0.562658 | ||||||||
\(765\) | 0.161780 | + | 4.56621i | 0.00584917 | + | 0.165092i | ||||
\(766\) | −14.2540 | −0.515017 | ||||||||
\(767\) | 6.76777 | + | 11.7221i | 0.244370 | + | 0.423261i | ||||
\(768\) | −0.418594 | + | 1.68071i | −0.0151047 | + | 0.0606473i | ||||
\(769\) | −2.25502 | + | 3.90581i | −0.0813182 | + | 0.140847i | −0.903816 | − | 0.427920i | \(-0.859246\pi\) |
0.822498 | + | 0.568768i | \(0.192580\pi\) | |||||||
\(770\) | 3.08343 | − | 5.34065i | 0.111119 | − | 0.192464i | ||||
\(771\) | 9.29130 | − | 37.3058i | 0.334618 | − | 1.34353i | ||||
\(772\) | 1.69538 | + | 2.93649i | 0.0610181 | + | 0.105686i | ||||
\(773\) | −4.25936 | −0.153198 | −0.0765992 | − | 0.997062i | \(-0.524406\pi\) | ||||
−0.0765992 | + | 0.997062i | \(0.524406\pi\) | |||||||
\(774\) | −0.853457 | − | 24.0887i | −0.0306769 | − | 0.865849i | ||||
\(775\) | −8.17334 | −0.293595 | ||||||||
\(776\) | −5.01156 | − | 8.68028i | −0.179905 | − | 0.311604i | ||||
\(777\) | −5.25780 | − | 5.07482i | −0.188623 | − | 0.182058i | ||||
\(778\) | −6.65605 | + | 11.5286i | −0.238631 | + | 0.413321i | ||||
\(779\) | −2.20694 | + | 3.82254i | −0.0790720 | + | 0.136957i | ||||
\(780\) | 3.10947 | − | 0.892481i | 0.111337 | − | 0.0319559i | ||||
\(781\) | 10.3132 | + | 17.8629i | 0.369034 | + | 0.639186i | ||||
\(782\) | −10.9153 | −0.390330 | ||||||||
\(783\) | −53.2613 | − | 11.2786i | −1.90340 | − | 0.403064i | ||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −6.58916 | − | 11.4128i | −0.235177 | − | 0.407339i | ||||
\(786\) | 17.9595 | − | 5.15474i | 0.640593 | − | 0.183863i | ||||
\(787\) | −9.29836 | + | 16.1052i | −0.331451 | + | 0.574089i | −0.982797 | − | 0.184692i | \(-0.940871\pi\) |
0.651346 | + | 0.758781i | \(0.274205\pi\) | |||||||
\(788\) | 3.27632 | − | 5.67475i | 0.116714 | − | 0.202155i | ||||
\(789\) | −14.2462 | − | 13.7504i | −0.507179 | − | 0.489528i | ||||
\(790\) | 6.51729 | + | 11.2883i | 0.231875 | + | 0.401619i | ||||
\(791\) | −15.8107 | −0.562163 | ||||||||
\(792\) | 16.3394 | + | 8.67718i | 0.580597 | + | 0.308330i | ||||
\(793\) | 4.93797 | 0.175352 | ||||||||
\(794\) | 10.8940 | + | 18.8690i | 0.386614 | + | 0.669635i | ||||
\(795\) | 0.0190848 | − | 0.0766281i | 0.000676869 | − | 0.00271772i | ||||
\(796\) | 0.928136 | − | 1.60758i | 0.0328969 | − | 0.0569791i | ||||
\(797\) | 8.18359 | − | 14.1744i | 0.289878 | − | 0.502083i | −0.683903 | − | 0.729573i | \(-0.739719\pi\) |
0.973780 | + | 0.227491i | \(0.0730521\pi\) | |||||||
\(798\) | 2.12925 | − | 8.54921i | 0.0753746 | − | 0.302639i | ||||
\(799\) | 5.23481 | + | 9.06696i | 0.185194 | + | 0.320766i | ||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 9.09270 | − | 5.68818i | 0.321275 | − | 0.200982i | ||||
\(802\) | −1.67888 | −0.0592831 | ||||||||
\(803\) | −14.6015 | − | 25.2905i | −0.515275 | − | 0.892482i | ||||
\(804\) | −0.608710 | − | 0.587525i | −0.0214675 | − | 0.0207204i | ||||
\(805\) | −3.58343 | + | 6.20668i | −0.126299 | + | 0.218757i | ||||
\(806\) | −7.63282 | + | 13.2204i | −0.268855 | + | 0.465670i | ||||
\(807\) | 7.29080 | − | 2.09261i | 0.256648 | − | 0.0736633i | ||||
\(808\) | 8.12126 | + | 14.0664i | 0.285705 | + | 0.494855i | ||||
\(809\) | 56.6845 | 1.99292 | 0.996461 | − | 0.0840616i | \(-0.0267892\pi\) | ||||
0.996461 | + | 0.0840616i | \(0.0267892\pi\) | |||||||
\(810\) | −3.93711 | + | 8.09315i | −0.138336 | + | 0.284364i | ||||
\(811\) | 21.4204 | 0.752171 | 0.376086 | − | 0.926585i | \(-0.377270\pi\) | ||||
0.376086 | + | 0.926585i | \(0.377270\pi\) | |||||||
\(812\) | 5.23872 | + | 9.07372i | 0.183843 | + | 0.318425i | ||||
\(813\) | −29.9027 | + | 8.58268i | −1.04873 | + | 0.301008i | ||||
\(814\) | −13.0088 | + | 22.5319i | −0.455957 | + | 0.789741i | ||||
\(815\) | 0.738487 | − | 1.27910i | 0.0258681 | − | 0.0448048i | ||||
\(816\) | 1.89805 | + | 1.83200i | 0.0664452 | + | 0.0641327i | ||||
\(817\) | 20.4347 | + | 35.3939i | 0.714918 | + | 1.23827i | ||||
\(818\) | 18.5933 | 0.650098 | ||||||||
\(819\) | 4.75028 | − | 2.97166i | 0.165988 | − | 0.103838i | ||||
\(820\) | −0.867736 | −0.0303027 | ||||||||
\(821\) | −15.7971 | − | 27.3614i | −0.551322 | − | 0.954918i | −0.998180 | − | 0.0603129i | \(-0.980790\pi\) |
0.446857 | − | 0.894605i | \(-0.352543\pi\) | |||||||
\(822\) | −5.71602 | + | 22.9506i | −0.199369 | + | 0.800493i | ||||
\(823\) | 14.1000 | − | 24.4219i | 0.491494 | − | 0.851292i | −0.508458 | − | 0.861087i | \(-0.669784\pi\) |
0.999952 | + | 0.00979442i | \(0.00311771\pi\) | |||||||
\(824\) | −5.14406 | + | 8.90977i | −0.179202 | + | 0.310386i | ||||
\(825\) | 2.58141 | − | 10.3647i | 0.0898730 | − | 0.360852i | ||||
\(826\) | 3.62352 | + | 6.27612i | 0.126078 | + | 0.218374i | ||||
\(827\) | −16.0402 | −0.557773 | −0.278887 | − | 0.960324i | \(-0.589965\pi\) | ||||
−0.278887 | + | 0.960324i | \(0.589965\pi\) | |||||||
\(828\) | −18.9890 | − | 10.0842i | −0.659913 | − | 0.350452i | ||||
\(829\) | 18.6804 | 0.648797 | 0.324398 | − | 0.945921i | \(-0.394838\pi\) | ||||
0.324398 | + | 0.945921i | \(0.394838\pi\) | |||||||
\(830\) | 7.38503 | + | 12.7912i | 0.256338 | + | 0.443991i | ||||
\(831\) | −20.2421 | − | 19.5376i | −0.702189 | − | 0.677751i | ||||
\(832\) | 0.933868 | − | 1.61751i | 0.0323760 | − | 0.0560770i | ||||
\(833\) | 0.761513 | − | 1.31898i | 0.0263849 | − | 0.0456999i | ||||
\(834\) | 1.09018 | − | 0.312905i | 0.0377500 | − | 0.0108350i | ||||
\(835\) | 11.5812 | + | 20.0592i | 0.400783 | + | 0.694176i | ||||
\(836\) | −31.3688 | −1.08491 | ||||||||
\(837\) | −13.1547 | − | 40.3813i | −0.454694 | − | 1.39578i | ||||
\(838\) | −35.9840 | −1.24305 | ||||||||
\(839\) | 18.5378 | + | 32.1085i | 0.639997 | + | 1.10851i | 0.985433 | + | 0.170065i | \(0.0543978\pi\) |
−0.345436 | + | 0.938442i | \(0.612269\pi\) | |||||||
\(840\) | 1.66483 | − | 0.477841i | 0.0574422 | − | 0.0164871i | ||||
\(841\) | −40.3883 | + | 69.9546i | −1.39270 | + | 2.41223i | ||||
\(842\) | 2.54357 | − | 4.40558i | 0.0876571 | − | 0.151826i | ||||
\(843\) | −0.951019 | − | 0.917921i | −0.0327548 | − | 0.0316149i | ||||
\(844\) | 0.643069 | + | 1.11383i | 0.0221353 | + | 0.0383395i | ||||
\(845\) | 9.51156 | 0.327208 | ||||||||
\(846\) | 0.730200 | + | 20.6097i | 0.0251048 | + | 0.708578i | ||||
\(847\) | −27.0301 | −0.928764 | ||||||||
\(848\) | −0.0227964 | − | 0.0394845i | −0.000782830 | − | 0.00135590i | ||||
\(849\) | 3.71470 | − | 14.9150i | 0.127488 | − | 0.511881i | ||||
\(850\) | 0.761513 | − | 1.31898i | 0.0261197 | − | 0.0452406i | ||||
\(851\) | 15.1182 | − | 26.1856i | 0.518247 | − | 0.897630i | ||||
\(852\) | −1.40007 | + | 5.62148i | −0.0479658 | + | 0.192589i | ||||
\(853\) | 3.44284 | + | 5.96318i | 0.117881 | + | 0.204175i | 0.918928 | − | 0.394426i | \(-0.129057\pi\) |
−0.801047 | + | 0.598602i | \(0.795723\pi\) | |||||||
\(854\) | 2.64383 | 0.0904699 | ||||||||
\(855\) | −0.540321 | − | 15.2504i | −0.0184786 | − | 0.521554i | ||||
\(856\) | −10.7310 | −0.366777 | ||||||||
\(857\) | −8.72672 | − | 15.1151i | −0.298099 | − | 0.516323i | 0.677602 | − | 0.735429i | \(-0.263019\pi\) |
−0.975701 | + | 0.219106i | \(0.929686\pi\) | |||||||
\(858\) | −14.3542 | − | 13.8547i | −0.490046 | − | 0.472991i | ||||
\(859\) | 8.26085 | − | 14.3082i | 0.281857 | − | 0.488190i | −0.689985 | − | 0.723823i | \(-0.742383\pi\) |
0.971842 | + | 0.235633i | \(0.0757164\pi\) | |||||||
\(860\) | −4.01729 | + | 6.95816i | −0.136989 | + | 0.237271i | ||||
\(861\) | −1.44464 | + | 0.414640i | −0.0492330 | + | 0.0141309i | ||||
\(862\) | −12.1726 | − | 21.0835i | −0.414600 | − | 0.718108i | ||||
\(863\) | 29.8077 | 1.01467 | 0.507333 | − | 0.861750i | \(-0.330632\pi\) | ||||
0.507333 | + | 0.861750i | \(0.330632\pi\) | |||||||
\(864\) | 1.60947 | + | 4.94061i | 0.0547552 | + | 0.168083i | ||||
\(865\) | 8.17334 | 0.277902 | ||||||||
\(866\) | 2.10351 | + | 3.64338i | 0.0714801 | + | 0.123807i | ||||
\(867\) | −24.4404 | + | 7.01489i | −0.830039 | + | 0.238238i | ||||
\(868\) | −4.08667 | + | 7.07832i | −0.138711 | + | 0.240254i | ||||
\(869\) | 40.1912 | − | 69.6132i | 1.36339 | − | 2.36147i | ||||
\(870\) | 13.0574 | + | 12.6030i | 0.442687 | + | 0.427280i | ||||
\(871\) | 0.456136 | + | 0.790051i | 0.0154556 | + | 0.0267698i | ||||
\(872\) | 15.7766 | 0.534261 | ||||||||
\(873\) | −26.5569 | − | 14.1032i | −0.898813 | − | 0.477322i | ||||
\(874\) | 36.4554 | 1.23312 | ||||||||
\(875\) | −0.500000 | − | 0.866025i | −0.0169031 | − | 0.0292770i | ||||
\(876\) | 1.98224 | − | 7.95895i | 0.0669736 | − | 0.268908i | ||||
\(877\) | −12.9952 | + | 22.5083i | −0.438815 | + | 0.760050i | −0.997598 | − | 0.0692635i | \(-0.977935\pi\) |
0.558783 | + | 0.829314i | \(0.311268\pi\) | |||||||
\(878\) | 12.4577 | − | 21.5773i | 0.420425 | − | 0.728198i | ||||
\(879\) | −4.75653 | + | 19.0981i | −0.160434 | + | 0.644163i | ||||
\(880\) | −3.08343 | − | 5.34065i | −0.103942 | − | 0.180033i | ||||
\(881\) | 6.08819 | 0.205116 | 0.102558 | − | 0.994727i | \(-0.467297\pi\) | ||||
0.102558 | + | 0.994727i | \(0.467297\pi\) | |||||||
\(882\) | 2.54334 | − | 1.59105i | 0.0856386 | − | 0.0535735i | ||||
\(883\) | 17.1558 | 0.577340 | 0.288670 | − | 0.957429i | \(-0.406787\pi\) | ||||
0.288670 | + | 0.957429i | \(0.406787\pi\) | |||||||
\(884\) | −1.42231 | − | 2.46351i | −0.0478373 | − | 0.0828566i | ||||
\(885\) | 9.03154 | + | 8.71722i | 0.303592 | + | 0.293026i | ||||
\(886\) | −14.1500 | + | 24.5086i | −0.475379 | + | 0.823381i | ||||
\(887\) | −16.1327 | + | 27.9427i | −0.541684 | + | 0.938224i | 0.457124 | + | 0.889403i | \(0.348880\pi\) |
−0.998808 | + | 0.0488208i | \(0.984454\pi\) | |||||||
\(888\) | −7.02382 | + | 2.01598i | −0.235704 | + | 0.0676519i | ||||
\(889\) | 2.58343 | + | 4.47463i | 0.0866453 | + | 0.150074i | ||||
\(890\) | −3.57511 | −0.119838 | ||||||||
\(891\) | 55.3625 | − | 3.92790i | 1.85471 | − | 0.131590i | ||||
\(892\) | 1.24054 | 0.0415365 | ||||||||
\(893\) | −17.4835 | − | 30.2822i | −0.585062 | − | 1.01336i | ||||
\(894\) | 31.2706 | − | 8.97531i | 1.04585 | − | 0.300179i | ||||
\(895\) | −4.56636 | + | 7.90917i | −0.152637 | + | 0.264374i | ||||
\(896\) | 0.500000 | − | 0.866025i | 0.0167038 | − | 0.0289319i | ||||
\(897\) | 16.6819 | + | 16.1013i | 0.556992 | + | 0.537607i | ||||
\(898\) | 1.80137 | + | 3.12007i | 0.0601126 | + | 0.104118i | ||||
\(899\) | −85.6357 | −2.85611 | ||||||||
\(900\) | 2.54334 | − | 1.59105i | 0.0847779 | − | 0.0530350i | ||||
\(901\) | −0.0694389 | −0.00231335 | ||||||||
\(902\) | 2.67560 | + | 4.63427i | 0.0890877 | + | 0.154304i | ||||
\(903\) | −3.36323 | + | 13.5038i | −0.111921 | + | 0.449378i | ||||
\(904\) | −7.90534 | + | 13.6925i | −0.262928 | + | 0.455404i | ||||
\(905\) | −5.37930 | + | 9.31722i | −0.178814 | + | 0.309715i | ||||
\(906\) | 1.81886 | − | 7.30296i | 0.0604276 | − | 0.242625i | ||||
\(907\) | 2.71668 | + | 4.70543i | 0.0902058 | + | 0.156241i | 0.907598 | − | 0.419841i | \(-0.137914\pi\) |
−0.817392 | + | 0.576082i | \(0.804581\pi\) | |||||||
\(908\) | −19.7130 | −0.654199 | ||||||||
\(909\) | 43.0355 | + | 22.8543i | 1.42740 | + | 0.758030i | ||||
\(910\) | −1.86774 | −0.0619148 | ||||||||
\(911\) | 18.0406 | + | 31.2473i | 0.597713 | + | 1.03527i | 0.993158 | + | 0.116780i | \(0.0372573\pi\) |
−0.395444 | + | 0.918490i | \(0.629409\pi\) | |||||||
\(912\) | −6.33921 | − | 6.11859i | −0.209912 | − | 0.202607i | ||||
\(913\) | 45.5424 | − | 78.8817i | 1.50723 | − | 2.61060i | ||||
\(914\) | 14.1302 | − | 24.4743i | 0.467387 | − | 0.809538i | ||||
\(915\) | 4.40153 | − | 1.26333i | 0.145510 | − | 0.0417644i | ||||
\(916\) | −3.05739 | − | 5.29555i | −0.101019 | − | 0.174970i | ||||
\(917\) | −10.7876 | −0.356236 | ||||||||
\(918\) | 7.74219 | + | 1.63948i | 0.255530 | + | 0.0541110i | ||||
\(919\) | −15.4945 | −0.511117 | −0.255559 | − | 0.966794i | \(-0.582259\pi\) | ||||
−0.255559 | + | 0.966794i | \(0.582259\pi\) | |||||||
\(920\) | 3.58343 | + | 6.20668i | 0.118142 | + | 0.204628i | ||||
\(921\) | 50.2243 | − | 14.4154i | 1.65495 | − | 0.475004i | ||||
\(922\) | 16.2768 | − | 28.1922i | 0.536047 | − | 0.928461i | ||||
\(923\) | 3.12352 | − | 5.41009i | 0.102812 | − | 0.178075i | ||||
\(924\) | −7.68537 | − | 7.41790i | −0.252830 | − | 0.244031i | ||||
\(925\) | 2.10947 | + | 3.65371i | 0.0693589 | + | 0.120133i | ||||
\(926\) | 34.8408 | 1.14494 | ||||||||
\(927\) | 1.09283 | + | 30.8450i | 0.0358933 | + | 1.01308i | ||||
\(928\) | 10.4774 | 0.343939 | ||||||||
\(929\) | 16.9544 | + | 29.3659i | 0.556256 | + | 0.963464i | 0.997805 | + | 0.0662264i | \(0.0210960\pi\) |
−0.441549 | + | 0.897237i | \(0.645571\pi\) | |||||||
\(930\) | −3.42131 | + | 13.7370i | −0.112189 | + | 0.450454i | ||||
\(931\) | −2.54334 | + | 4.40519i | −0.0833545 | + | 0.144374i | ||||
\(932\) | 2.65280 | − | 4.59479i | 0.0868955 | − | 0.150507i | ||||
\(933\) | 3.22842 | − | 12.9625i | 0.105694 | − | 0.424374i | ||||
\(934\) | 21.0759 | + | 36.5045i | 0.689624 | + | 1.19446i | ||||
\(935\) | −9.39228 | −0.307160 | ||||||||
\(936\) | −0.198396 | − | 5.59969i | −0.00648478 | − | 0.183032i | ||||
\(937\) | 39.9726 | 1.30585 | 0.652923 | − | 0.757424i | \(-0.273542\pi\) | ||||
0.652923 | + | 0.757424i | \(0.273542\pi\) | |||||||
\(938\) | 0.244219 | + | 0.422999i | 0.00797402 | + | 0.0138114i | ||||
\(939\) | 3.07261 | + | 2.96568i | 0.100271 | + | 0.0967813i | ||||
\(940\) | 3.43711 | − | 5.95325i | 0.112106 | − | 0.194174i | ||||
\(941\) | −7.94143 | + | 13.7550i | −0.258883 | + | 0.448399i | −0.965943 | − | 0.258755i | \(-0.916688\pi\) |
0.707060 | + | 0.707154i | \(0.250021\pi\) | |||||||
\(942\) | −21.9397 | + | 6.29714i | −0.714834 | + | 0.205172i | ||||
\(943\) | −3.10947 | − | 5.38576i | −0.101258 | − | 0.175384i | ||||
\(944\) | 7.24703 | 0.235871 | ||||||||
\(945\) | 3.47396 | − | 3.86414i | 0.113008 | − | 0.125701i | ||||
\(946\) | 49.5481 | 1.61095 | ||||||||
\(947\) | −20.2307 | − | 35.0405i | −0.657408 | − | 1.13866i | −0.981284 | − | 0.192565i | \(-0.938319\pi\) |
0.323876 | − | 0.946099i | \(-0.395014\pi\) | |||||||
\(948\) | 21.7004 | − | 6.22846i | 0.704797 | − | 0.202291i | ||||
\(949\) | −4.42231 | + | 7.65966i | −0.143554 | + | 0.248643i | ||||
\(950\) | −2.54334 | + | 4.40519i | −0.0825167 | + | 0.142923i | ||||
\(951\) | −24.4247 | − | 23.5746i | −0.792024 | − | 0.764459i | ||||
\(952\) | −0.761513 | − | 1.31898i | −0.0246808 | − | 0.0427484i | ||||
\(953\) | 53.5261 | 1.73388 | 0.866941 | − | 0.498412i | \(-0.166083\pi\) | ||||
0.866941 | + | 0.498412i | \(0.166083\pi\) | |||||||
\(954\) | −0.120801 | − | 0.0641521i | −0.00391106 | − | 0.00207700i | ||||
\(955\) | −15.5522 | −0.503257 | ||||||||
\(956\) | 11.9088 | + | 20.6267i | 0.385159 | + | 0.667114i | ||||
\(957\) | 27.0465 | − | 108.595i | 0.874290 | − | 3.51039i | ||||
\(958\) | −7.74379 | + | 13.4126i | −0.250190 | + | 0.433343i | ||||
\(959\) | 6.82765 | − | 11.8258i | 0.220476 | − | 0.381876i | ||||
\(960\) | 0.418594 | − | 1.68071i | 0.0135101 | − | 0.0542446i | ||||
\(961\) | −17.9018 | − | 31.0068i | −0.577476 | − | 1.00022i | ||||
\(962\) | 7.87986 | 0.254057 | ||||||||
\(963\) | −27.2924 | + | 17.0735i | −0.879486 | + | 0.550186i | ||||
\(964\) | −9.47200 | −0.305073 | ||||||||
\(965\) | −1.69538 | − | 2.93649i | −0.0545762 | − | 0.0945288i | ||||
\(966\) | 8.93161 | + | 8.62077i | 0.287370 | + | 0.277369i | ||||
\(967\) | −24.0647 | + | 41.6812i | −0.773867 | + | 1.34038i | 0.161561 | + | 0.986863i | \(0.448347\pi\) |
−0.935429 | + | 0.353515i | \(0.884986\pi\) | |||||||
\(968\) | −13.5150 | + | 23.4087i | −0.434390 | + | 0.752385i | ||||
\(969\) | −12.8977 | + | 3.70190i | −0.414333 | + | 0.118922i | ||||
\(970\) | 5.01156 | + | 8.68028i | 0.160912 | + | 0.278707i | ||||
\(971\) | 34.5982 | 1.11031 | 0.555155 | − | 0.831747i | \(-0.312659\pi\) | ||||
0.555155 | + | 0.831747i | \(0.312659\pi\) | |||||||
\(972\) | 11.9542 | + | 10.0049i | 0.383430 | + | 0.320907i | ||||
\(973\) | −0.654831 | −0.0209929 | ||||||||
\(974\) | −6.00046 | − | 10.3931i | −0.192267 | − | 0.333016i | ||||
\(975\) | −3.10947 | + | 0.892481i | −0.0995827 | + | 0.0285823i | ||||
\(976\) | 1.32191 | − | 2.28962i | 0.0423134 | − | 0.0732890i | ||||
\(977\) | −20.7646 | + | 35.9653i | −0.664317 | + | 1.15063i | 0.315153 | + | 0.949041i | \(0.397944\pi\) |
−0.979470 | + | 0.201590i | \(0.935389\pi\) | |||||||
\(978\) | −1.84066 | − | 1.77660i | −0.0588579 | − | 0.0568095i | ||||
\(979\) | 11.0236 | + | 19.0934i | 0.352315 | + | 0.610228i | ||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 40.1251 | − | 25.1013i | 1.28109 | − | 0.801423i | ||||
\(982\) | 23.9905 | 0.765568 | ||||||||
\(983\) | −3.93767 | − | 6.82025i | −0.125592 | − | 0.217532i | 0.796372 | − | 0.604807i | \(-0.206750\pi\) |
−0.921964 | + | 0.387275i | \(0.873416\pi\) | |||||||
\(984\) | −0.363229 | + | 1.45841i | −0.0115793 | + | 0.0464924i | ||||
\(985\) | −3.27632 | + | 5.67475i | −0.104392 | + | 0.180813i | ||||
\(986\) | 7.97870 | − | 13.8195i | 0.254094 | − | 0.440103i | ||||
\(987\) | 2.87751 | − | 11.5536i | 0.0915921 | − | 0.367754i | ||||
\(988\) | 4.75028 | + | 8.22773i | 0.151127 | + | 0.261759i | ||||
\(989\) | −57.5827 | −1.83102 | ||||||||
\(990\) | −16.3394 | − | 8.67718i | −0.519301 | − | 0.275779i | ||||
\(991\) | 34.7251 | 1.10308 | 0.551540 | − | 0.834148i | \(-0.314040\pi\) | ||||
0.551540 | + | 0.834148i | \(0.314040\pi\) | |||||||
\(992\) | 4.08667 | + | 7.07832i | 0.129752 | + | 0.224737i | ||||
\(993\) | −31.2153 | − | 30.1289i | −0.990586 | − | 0.956111i | ||||
\(994\) | 1.67235 | − | 2.89660i | 0.0530439 | − | 0.0918747i | ||||
\(995\) | −0.928136 | + | 1.60758i | −0.0294239 | + | 0.0509637i | ||||
\(996\) | 24.5897 | − | 7.05774i | 0.779154 | − | 0.223633i | ||||
\(997\) | 12.4074 | + | 21.4902i | 0.392946 | + | 0.680603i | 0.992837 | − | 0.119479i | \(-0.0381225\pi\) |
−0.599890 | + | 0.800082i | \(0.704789\pi\) | |||||||
\(998\) | 23.4545 | 0.742439 | ||||||||
\(999\) | −14.6564 | + | 16.3026i | −0.463708 | + | 0.515791i |
(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 | 630.2.j.l.211.4 | ✓ | 8 | |
3.2 | odd | 2 | 1890.2.j.l.631.1 | 8 | |||
9.2 | odd | 6 | 1890.2.j.l.1261.1 | 8 | |||
9.4 | even | 3 | 5670.2.a.bw.1.1 | 4 | |||
9.5 | odd | 6 | 5670.2.a.bv.1.4 | 4 | |||
9.7 | even | 3 | inner | 630.2.j.l.421.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.j.l.211.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
630.2.j.l.421.4 | yes | 8 | 9.7 | even | 3 | inner | |
1890.2.j.l.631.1 | 8 | 3.2 | odd | 2 | |||
1890.2.j.l.1261.1 | 8 | 9.2 | odd | 6 | |||
5670.2.a.bv.1.4 | 4 | 9.5 | odd | 6 | |||
5670.2.a.bw.1.1 | 4 | 9.4 | even | 3 |