Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(307,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.307");
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.p (of order \(4\), 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: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 44 x^{14} - 160 x^{13} + 468 x^{12} - 1060 x^{11} + 2038 x^{10} - 3208 x^{9} + \cdots + 2468 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 433.2 | ||
Root | \(0.131441 - 2.64318i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.433 |
Dual form | 630.2.p.d.307.2 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −1.28422 | + | 1.83051i | −0.574320 | + | 0.818631i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0564123 | − | 2.64515i | 0.0213218 | − | 0.999773i | ||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.386289 | − | 2.20245i | −0.122155 | − | 0.696475i | ||||
\(11\) | −1.41421 | −0.426401 | −0.213201 | − | 0.977008i | \(-0.568389\pi\) | ||||
−0.213201 | + | 0.977008i | \(0.568389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.772577 | + | 0.772577i | −0.214274 | + | 0.214274i | −0.806080 | − | 0.591806i | \(-0.798415\pi\) |
0.591806 | + | 0.806080i | \(0.298415\pi\) | |||||||
\(14\) | 1.83051 | + | 1.91029i | 0.489225 | + | 0.510547i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0.546295 | + | 0.546295i | 0.132496 | + | 0.132496i | 0.770245 | − | 0.637749i | \(-0.220134\pi\) |
−0.637749 | + | 0.770245i | \(0.720134\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.95005 | −1.36504 | −0.682518 | − | 0.730869i | \(-0.739115\pi\) | ||||
−0.682518 | + | 0.730869i | \(0.739115\pi\) | |||||||
\(20\) | 1.83051 | + | 1.28422i | 0.409315 | + | 0.287160i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | − | 1.00000i | 0.213201 | − | 0.213201i | ||||
\(23\) | −5.23480 | − | 5.23480i | −1.09153 | − | 1.09153i | −0.995365 | − | 0.0961658i | \(-0.969342\pi\) |
−0.0961658 | − | 0.995365i | \(-0.530658\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.70156 | − | 4.70156i | −0.340312 | − | 0.940312i | ||||
\(26\) | − | 1.09259i | − | 0.214274i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.64515 | − | 0.0564123i | −0.499886 | − | 0.0106609i | ||||
\(29\) | 0.992159i | 0.184239i | 0.995748 | + | 0.0921196i | \(0.0293642\pi\) | ||||
−0.995748 | + | 0.0921196i | \(0.970636\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.85974i | − | 0.513625i | −0.966461 | − | 0.256813i | \(-0.917328\pi\) | ||
0.966461 | − | 0.256813i | \(-0.0826723\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.772577 | −0.132496 | ||||||||
\(35\) | 4.76954 | + | 3.50022i | 0.806199 | + | 0.591644i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.70156 | − | 5.70156i | 0.937331 | − | 0.937331i | −0.0608178 | − | 0.998149i | \(-0.519371\pi\) |
0.998149 | + | 0.0608178i | \(0.0193709\pi\) | |||||||
\(38\) | 4.20732 | − | 4.20732i | 0.682518 | − | 0.682518i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.20245 | + | 0.386289i | −0.348238 | + | 0.0610776i | ||||
\(41\) | 2.18518i | 0.341268i | 0.985335 | + | 0.170634i | \(0.0545815\pi\) | ||||
−0.985335 | + | 0.170634i | \(0.945418\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | − | 2.00000i | −0.304997 | − | 0.304997i | 0.537968 | − | 0.842965i | \(-0.319192\pi\) |
−0.842965 | + | 0.537968i | \(0.819192\pi\) | |||||||
\(44\) | 1.41421i | 0.213201i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.40312 | 1.09153 | ||||||||
\(47\) | −7.32206 | − | 7.32206i | −1.06803 | − | 1.06803i | −0.997510 | − | 0.0705213i | \(-0.977534\pi\) |
−0.0705213 | − | 0.997510i | \(-0.522466\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99364 | − | 0.298438i | −0.999091 | − | 0.0426340i | ||||
\(50\) | 4.52769 | + | 2.12132i | 0.640312 | + | 0.300000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.772577 | + | 0.772577i | 0.107137 | + | 0.107137i | ||||
\(53\) | −2.40637 | − | 2.40637i | −0.330541 | − | 0.330541i | 0.522251 | − | 0.852792i | \(-0.325092\pi\) |
−0.852792 | + | 0.522251i | \(0.825092\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.81616 | − | 2.58874i | 0.244891 | − | 0.349065i | ||||
\(56\) | 1.91029 | − | 1.83051i | 0.255274 | − | 0.244613i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.701562 | − | 0.701562i | −0.0921196 | − | 0.0921196i | ||||
\(59\) | −12.0757 | −1.57212 | −0.786059 | − | 0.618151i | \(-0.787882\pi\) | ||||
−0.786059 | + | 0.618151i | \(0.787882\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.63232i | 0.465071i | 0.972588 | + | 0.232535i | \(0.0747022\pi\) | ||||
−0.972588 | + | 0.232535i | \(0.925298\pi\) | |||||||
\(62\) | 2.02214 | + | 2.02214i | 0.256813 | + | 0.256813i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −0.422055 | − | 2.40637i | −0.0523495 | − | 0.298474i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | + | 4.00000i | −0.488678 | + | 0.488678i | −0.907889 | − | 0.419211i | \(-0.862307\pi\) |
0.419211 | + | 0.907889i | \(0.362307\pi\) | |||||||
\(68\) | 0.546295 | − | 0.546295i | 0.0662480 | − | 0.0662480i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.84760 | + | 0.897546i | −0.698922 | + | 0.107277i | ||||
\(71\) | 8.06323 | 0.956929 | 0.478464 | − | 0.878107i | \(-0.341194\pi\) | ||||
0.478464 | + | 0.878107i | \(0.341194\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.3985 | − | 11.3985i | 1.33410 | − | 1.33410i | 0.432430 | − | 0.901668i | \(-0.357656\pi\) |
0.901668 | − | 0.432430i | \(-0.142344\pi\) | |||||||
\(74\) | 8.06323i | 0.937331i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.95005i | 0.682518i | ||||||||
\(77\) | −0.0797790 | + | 3.74081i | −0.00909166 | + | 0.426304i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.40312i | 0.607899i | 0.952688 | + | 0.303949i | \(0.0983054\pi\) | ||||
−0.952688 | + | 0.303949i | \(0.901695\pi\) | |||||||
\(80\) | 1.28422 | − | 1.83051i | 0.143580 | − | 0.204658i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.54515 | − | 1.54515i | −0.170634 | − | 0.170634i | ||||
\(83\) | 8.79790 | − | 8.79790i | 0.965695 | − | 0.965695i | −0.0337353 | − | 0.999431i | \(-0.510740\pi\) |
0.999431 | + | 0.0337353i | \(0.0107403\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.70156 | + | 0.298438i | −0.184560 | + | 0.0323701i | ||||
\(86\) | 2.82843 | 0.304997 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | − | 1.00000i | −0.106600 | − | 0.106600i | ||||
\(89\) | −11.3663 | −1.20483 | −0.602415 | − | 0.798183i | \(-0.705795\pi\) | ||||
−0.602415 | + | 0.798183i | \(0.705795\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | + | 2.08717i | 0.209657 | + | 0.218794i | ||||
\(92\) | −5.23480 | + | 5.23480i | −0.545766 | + | 0.545766i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.3550 | 1.06803 | ||||||||
\(95\) | 7.64117 | − | 10.8917i | 0.783968 | − | 1.11746i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.76621 | + | 7.76621i | 0.788539 | + | 0.788539i | 0.981255 | − | 0.192715i | \(-0.0617294\pi\) |
−0.192715 | + | 0.981255i | \(0.561729\pi\) | |||||||
\(98\) | 5.15627 | − | 4.73422i | 0.520862 | − | 0.478228i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.70156 | + | 1.70156i | −0.470156 | + | 0.170156i | ||||
\(101\) | 8.79790i | 0.875424i | 0.899115 | + | 0.437712i | \(0.144211\pi\) | ||||
−0.899115 | + | 0.437712i | \(0.855789\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.85338 | + | 9.85338i | −0.970882 | + | 0.970882i | −0.999588 | − | 0.0287057i | \(-0.990861\pi\) |
0.0287057 | + | 0.999588i | \(0.490861\pi\) | |||||||
\(104\) | −1.09259 | −0.107137 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.40312 | 0.330541 | ||||||||
\(107\) | 0.422055 | − | 0.422055i | 0.0408016 | − | 0.0408016i | −0.686412 | − | 0.727213i | \(-0.740815\pi\) |
0.727213 | + | 0.686412i | \(0.240815\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.4031i | 1.28379i | 0.766794 | + | 0.641893i | \(0.221851\pi\) | ||||
−0.766794 | + | 0.641893i | \(0.778149\pi\) | |||||||
\(110\) | 0.546295 | + | 3.11473i | 0.0520872 | + | 0.296978i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.0564123 | + | 2.64515i | −0.00533046 | + | 0.249943i | ||||
\(113\) | −11.8838 | − | 11.8838i | −1.11794 | − | 1.11794i | −0.992044 | − | 0.125891i | \(-0.959821\pi\) |
−0.125891 | − | 0.992044i | \(-0.540179\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.3050 | − | 2.85974i | 1.52045 | − | 0.266672i | ||||
\(116\) | 0.992159 | 0.0921196 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.53879 | − | 8.53879i | 0.786059 | − | 0.786059i | ||||
\(119\) | 1.47585 | − | 1.41421i | 0.135291 | − | 0.129641i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | −2.56844 | − | 2.56844i | −0.232535 | − | 0.232535i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.85974 | −0.256813 | ||||||||
\(125\) | 10.7915 | + | 2.92310i | 0.965217 | + | 0.261450i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.701562 | − | 0.701562i | 0.0622536 | − | 0.0622536i | −0.675295 | − | 0.737548i | \(-0.735983\pi\) |
0.737548 | + | 0.675295i | \(0.235983\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | + | 1.40312i | 0.175412 | + | 0.123062i | ||||
\(131\) | − | 2.56844i | − | 0.224406i | −0.993685 | − | 0.112203i | \(-0.964209\pi\) | ||
0.993685 | − | 0.112203i | \(-0.0357906\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.335656 | + | 15.7388i | −0.0291051 | + | 1.36473i | ||||
\(134\) | − | 5.65685i | − | 0.488678i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.772577i | 0.0662480i | ||||||||
\(137\) | −6.22696 | + | 6.22696i | −0.532005 | + | 0.532005i | −0.921169 | − | 0.389164i | \(-0.872764\pi\) |
0.389164 | + | 0.921169i | \(0.372764\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.49521 | 0.635735 | 0.317868 | − | 0.948135i | \(-0.397033\pi\) | ||||
0.317868 | + | 0.948135i | \(0.397033\pi\) | |||||||
\(140\) | 3.50022 | − | 4.76954i | 0.295822 | − | 0.403100i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.70156 | + | 5.70156i | −0.478464 | + | 0.478464i | ||||
\(143\) | 1.09259 | − | 1.09259i | 0.0913669 | − | 0.0913669i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.81616 | − | 1.27415i | −0.150824 | − | 0.105812i | ||||
\(146\) | 16.1200i | 1.33410i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.70156 | − | 5.70156i | −0.468666 | − | 0.468666i | ||||
\(149\) | 17.1186i | 1.40241i | 0.712959 | + | 0.701206i | \(0.247355\pi\) | ||||
−0.712959 | + | 0.701206i | \(0.752645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.80625 | −0.553885 | −0.276942 | − | 0.960887i | \(-0.589321\pi\) | ||||
−0.276942 | + | 0.960887i | \(0.589321\pi\) | |||||||
\(152\) | −4.20732 | − | 4.20732i | −0.341259 | − | 0.341259i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.58874 | − | 2.70156i | −0.208606 | − | 0.217698i | ||||
\(155\) | 5.23480 | + | 3.67254i | 0.420469 | + | 0.294985i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.6727 | + | 12.6727i | 1.01139 | + | 1.01139i | 0.999934 | + | 0.0114558i | \(0.00364656\pi\) |
0.0114558 | + | 0.999934i | \(0.496353\pi\) | |||||||
\(158\) | −3.82059 | − | 3.82059i | −0.303949 | − | 0.303949i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.386289 | + | 2.20245i | 0.0305388 | + | 0.174119i | ||||
\(161\) | −14.1421 | + | 13.5515i | −1.11456 | + | 1.06801i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.4031 | + | 11.4031i | 0.893162 | + | 0.893162i | 0.994819 | − | 0.101658i | \(-0.0324147\pi\) |
−0.101658 | + | 0.994819i | \(0.532415\pi\) | |||||||
\(164\) | 2.18518 | 0.170634 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.4421i | 0.965695i | ||||||||
\(167\) | −6.22947 | − | 6.22947i | −0.482051 | − | 0.482051i | 0.423735 | − | 0.905786i | \(-0.360719\pi\) |
−0.905786 | + | 0.423735i | \(0.860719\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8062i | 0.908173i | ||||||||
\(170\) | 0.992159 | − | 1.41421i | 0.0760951 | − | 0.108465i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.00000 | + | 2.00000i | −0.152499 | + | 0.152499i | ||||
\(173\) | 6.39250 | − | 6.39250i | 0.486013 | − | 0.486013i | −0.421033 | − | 0.907045i | \(-0.638332\pi\) |
0.907045 | + | 0.421033i | \(0.138332\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.5323 | + | 4.23566i | −0.947355 | + | 0.320186i | ||||
\(176\) | 1.41421 | 0.106600 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.03722 | − | 8.03722i | 0.602415 | − | 0.602415i | ||||
\(179\) | 14.7122i | 1.09964i | 0.835282 | + | 0.549822i | \(0.185305\pi\) | ||||
−0.835282 | + | 0.549822i | \(0.814695\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.5324i | − | 1.15452i | −0.816562 | − | 0.577258i | \(-0.804123\pi\) | ||
0.816562 | − | 0.577258i | \(-0.195877\pi\) | |||||||
\(182\) | −2.89006 | − | 0.0616355i | −0.214226 | − | 0.00456872i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 7.40312i | − | 0.545766i | ||||||
\(185\) | 3.11473 | + | 17.7588i | 0.229000 | + | 1.30566i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.772577 | − | 0.772577i | −0.0564965 | − | 0.0564965i | ||||
\(188\) | −7.32206 | + | 7.32206i | −0.534016 | + | 0.534016i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.29844 | + | 13.1047i | 0.166746 | + | 0.950714i | ||||
\(191\) | 24.1897 | 1.75030 | 0.875152 | − | 0.483848i | \(-0.160761\pi\) | ||||
0.875152 | + | 0.483848i | \(0.160761\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.0000 | − | 11.0000i | −0.791797 | − | 0.791797i | 0.189989 | − | 0.981786i | \(-0.439155\pi\) |
−0.981786 | + | 0.189989i | \(0.939155\pi\) | |||||||
\(194\) | −10.9831 | −0.788539 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.298438 | + | 6.99364i | −0.0213170 | + | 0.499545i | ||||
\(197\) | −16.5485 | + | 16.5485i | −1.17903 | + | 1.17903i | −0.199041 | + | 0.979991i | \(0.563783\pi\) |
−0.979991 | + | 0.199041i | \(0.936217\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 27.2020 | 1.92830 | 0.964148 | − | 0.265365i | \(-0.0854924\pi\) | ||||
0.964148 | + | 0.265365i | \(0.0854924\pi\) | |||||||
\(200\) | 2.12132 | − | 4.52769i | 0.150000 | − | 0.320156i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.22106 | − | 6.22106i | −0.437712 | − | 0.437712i | ||||
\(203\) | 2.62441 | + | 0.0559699i | 0.184197 | + | 0.00392832i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.00000 | − | 2.80625i | −0.279372 | − | 0.195997i | ||||
\(206\) | − | 13.9348i | − | 0.970882i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.772577 | − | 0.772577i | 0.0535686 | − | 0.0535686i | ||||
\(209\) | 8.41464 | 0.582053 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.8062 | −0.743933 | −0.371966 | − | 0.928246i | \(-0.621316\pi\) | ||||
−0.371966 | + | 0.928246i | \(0.621316\pi\) | |||||||
\(212\) | −2.40637 | + | 2.40637i | −0.165270 | + | 0.165270i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.596876i | 0.0408016i | ||||||||
\(215\) | 6.22947 | − | 1.09259i | 0.424846 | − | 0.0745140i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.56445 | − | 0.161325i | −0.513508 | − | 0.0109514i | ||||
\(218\) | −9.47744 | − | 9.47744i | −0.641893 | − | 0.641893i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.58874 | − | 1.81616i | −0.174533 | − | 0.122445i | ||||
\(221\) | −0.844110 | −0.0567810 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.36131 | + | 3.36131i | −0.225090 | + | 0.225090i | −0.810638 | − | 0.585548i | \(-0.800879\pi\) |
0.585548 | + | 0.810638i | \(0.300879\pi\) | |||||||
\(224\) | −1.83051 | − | 1.91029i | −0.122306 | − | 0.127637i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.8062 | 1.11794 | ||||||||
\(227\) | −10.5998 | − | 10.5998i | −0.703535 | − | 0.703535i | 0.261633 | − | 0.965168i | \(-0.415739\pi\) |
−0.965168 | + | 0.261633i | \(0.915739\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.3422 | −1.60858 | −0.804290 | − | 0.594238i | \(-0.797454\pi\) | ||||
−0.804290 | + | 0.594238i | \(0.797454\pi\) | |||||||
\(230\) | −9.50723 | + | 13.5515i | −0.626888 | + | 0.893561i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.701562 | + | 0.701562i | −0.0460598 | + | 0.0460598i | ||||
\(233\) | −4.24264 | − | 4.24264i | −0.277945 | − | 0.277945i | 0.554343 | − | 0.832288i | \(-0.312969\pi\) |
−0.832288 | + | 0.554343i | \(0.812969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.8062 | − | 4.00000i | 1.48772 | − | 0.260931i | ||||
\(236\) | 12.0757i | 0.786059i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.0435829 | + | 2.04358i | −0.00282506 | + | 0.132466i | ||||
\(239\) | − | 14.5642i | − | 0.942079i | −0.882112 | − | 0.471040i | \(-0.843879\pi\) | ||
0.882112 | − | 0.471040i | \(-0.156121\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 19.7068i | − | 1.26942i | −0.772749 | − | 0.634712i | \(-0.781119\pi\) | ||
0.772749 | − | 0.634712i | \(-0.218881\pi\) | |||||||
\(242\) | 6.36396 | − | 6.36396i | 0.409091 | − | 0.409091i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.63232 | 0.232535 | ||||||||
\(245\) | 9.52766 | − | 12.4187i | 0.608700 | − | 0.793401i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.59688 | − | 4.59688i | 0.292492 | − | 0.292492i | ||||
\(248\) | 2.02214 | − | 2.02214i | 0.128406 | − | 0.128406i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.69766 | + | 5.56376i | −0.613334 | + | 0.351883i | ||||
\(251\) | − | 24.5346i | − | 1.54861i | −0.632812 | − | 0.774305i | \(-0.718100\pi\) | ||
0.632812 | − | 0.774305i | \(-0.281900\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.40312 | + | 7.40312i | 0.465430 | + | 0.465430i | ||||
\(254\) | 0.992159i | 0.0622536i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.63888 | + | 1.63888i | 0.102231 | + | 0.102231i | 0.756372 | − | 0.654141i | \(-0.226970\pi\) |
−0.654141 | + | 0.756372i | \(0.726970\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.7598 | − | 15.4031i | −0.917132 | − | 0.957104i | ||||
\(260\) | −2.40637 | + | 0.422055i | −0.149237 | + | 0.0261747i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.81616 | + | 1.81616i | 0.112203 | + | 0.112203i | ||||
\(263\) | 11.3137 | + | 11.3137i | 0.697633 | + | 0.697633i | 0.963899 | − | 0.266266i | \(-0.0857901\pi\) |
−0.266266 | + | 0.963899i | \(0.585790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.49521 | − | 1.31459i | 0.460427 | − | 0.0807545i | ||||
\(266\) | −10.8917 | − | 11.3663i | −0.667810 | − | 0.696915i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.00000 | + | 4.00000i | 0.244339 | + | 0.244339i | ||||
\(269\) | 18.3051 | 1.11608 | 0.558042 | − | 0.829813i | \(-0.311553\pi\) | ||||
0.558042 | + | 0.829813i | \(0.311553\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 12.6727i | − | 0.769811i | −0.922956 | − | 0.384905i | \(-0.874234\pi\) | ||
0.922956 | − | 0.384905i | \(-0.125766\pi\) | |||||||
\(272\) | −0.546295 | − | 0.546295i | −0.0331240 | − | 0.0331240i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 8.80625i | − | 0.532005i | ||||||
\(275\) | 2.40637 | + | 6.64901i | 0.145110 | + | 0.400951i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.10469 | − | 5.10469i | 0.306711 | − | 0.306711i | −0.536921 | − | 0.843632i | \(-0.680413\pi\) |
0.843632 | + | 0.536921i | \(0.180413\pi\) | |||||||
\(278\) | −5.29991 | + | 5.29991i | −0.317868 | + | 0.317868i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.897546 | + | 5.84760i | 0.0536386 | + | 0.349461i | ||||
\(281\) | 19.7990 | 1.18111 | 0.590554 | − | 0.806998i | \(-0.298909\pi\) | ||||
0.590554 | + | 0.806998i | \(0.298909\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.542011 | − | 0.542011i | 0.0322192 | − | 0.0322192i | −0.690814 | − | 0.723033i | \(-0.742748\pi\) |
0.723033 | + | 0.690814i | \(0.242748\pi\) | |||||||
\(284\) | − | 8.06323i | − | 0.478464i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.54515i | 0.0913669i | ||||||||
\(287\) | 5.78013 | + | 0.123271i | 0.341190 | + | 0.00727645i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 16.4031i | − | 0.964890i | ||||||
\(290\) | 2.18518 | − | 0.383260i | 0.128318 | − | 0.0225058i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.3985 | − | 11.3985i | −0.667049 | − | 0.667049i | ||||
\(293\) | 17.3756 | − | 17.3756i | 1.01509 | − | 1.01509i | 0.0152081 | − | 0.999884i | \(-0.495159\pi\) |
0.999884 | − | 0.0152081i | \(-0.00484109\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.5078 | − | 22.1047i | 0.902900 | − | 1.28698i | ||||
\(296\) | 8.06323 | 0.468666 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.1047 | − | 12.1047i | −0.701206 | − | 0.701206i | ||||
\(299\) | 8.08857 | 0.467774 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.40312 | + | 5.17748i | −0.311431 | + | 0.298425i | ||||
\(302\) | 4.81274 | − | 4.81274i | 0.276942 | − | 0.276942i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.95005 | 0.341259 | ||||||||
\(305\) | −6.64901 | − | 4.66470i | −0.380721 | − | 0.267100i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.7598 | − | 14.7598i | −0.842389 | − | 0.842389i | 0.146780 | − | 0.989169i | \(-0.453109\pi\) |
−0.989169 | + | 0.146780i | \(0.953109\pi\) | |||||||
\(308\) | 3.74081 | + | 0.0797790i | 0.213152 | + | 0.00454583i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.29844 | + | 1.10469i | −0.357727 | + | 0.0627420i | ||||
\(311\) | 2.95170i | 0.167375i | 0.996492 | + | 0.0836877i | \(0.0266698\pi\) | ||||
−0.996492 | + | 0.0836877i | \(0.973330\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.4888 | + | 14.4888i | −0.818958 | + | 0.818958i | −0.985957 | − | 0.166999i | \(-0.946592\pi\) |
0.166999 | + | 0.985957i | \(0.446592\pi\) | |||||||
\(314\) | −17.9219 | −1.01139 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.40312 | 0.303949 | ||||||||
\(317\) | 1.41421 | − | 1.41421i | 0.0794301 | − | 0.0794301i | −0.666276 | − | 0.745706i | \(-0.732113\pi\) |
0.745706 | + | 0.666276i | \(0.232113\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.40312i | − | 0.0785599i | ||||||
\(320\) | −1.83051 | − | 1.28422i | −0.102329 | − | 0.0717900i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.417627 | − | 19.5824i | 0.0232735 | − | 1.09128i | ||||
\(323\) | −3.25048 | − | 3.25048i | −0.180862 | − | 0.180862i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.94691 | + | 2.31773i | 0.274405 | + | 0.128565i | ||||
\(326\) | −16.1265 | −0.893162 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.54515 | + | 1.54515i | −0.0853169 | + | 0.0853169i | ||||
\(329\) | −19.7810 | + | 18.9549i | −1.09056 | + | 1.04502i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.6125 | −1.40779 | −0.703895 | − | 0.710304i | \(-0.748557\pi\) | ||||
−0.703895 | + | 0.710304i | \(0.748557\pi\) | |||||||
\(332\) | −8.79790 | − | 8.79790i | −0.482848 | − | 0.482848i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.80980 | 0.482051 | ||||||||
\(335\) | −2.18518 | − | 12.4589i | −0.119389 | − | 0.680704i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.00000 | + | 1.00000i | −0.0544735 | + | 0.0544735i | −0.733819 | − | 0.679345i | \(-0.762264\pi\) |
0.679345 | + | 0.733819i | \(0.262264\pi\) | |||||||
\(338\) | −8.34828 | − | 8.34828i | −0.454086 | − | 0.454086i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.298438 | + | 1.70156i | 0.0161851 | + | 0.0922802i | ||||
\(341\) | 4.04429i | 0.219010i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.18394 | + | 18.4824i | −0.0639267 | + | 0.997955i | ||||
\(344\) | − | 2.82843i | − | 0.152499i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.04036i | 0.486013i | ||||||||
\(347\) | 17.1186 | − | 17.1186i | 0.918975 | − | 0.918975i | −0.0779797 | − | 0.996955i | \(-0.524847\pi\) |
0.996955 | + | 0.0779797i | \(0.0248469\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.81294 | −0.525275 | −0.262637 | − | 0.964895i | \(-0.584592\pi\) | ||||
−0.262637 | + | 0.964895i | \(0.584592\pi\) | |||||||
\(350\) | 5.86663 | − | 11.8568i | 0.313584 | − | 0.633770i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | + | 1.00000i | −0.0533002 | + | 0.0533002i | ||||
\(353\) | −10.0535 | + | 10.0535i | −0.535095 | + | 0.535095i | −0.922084 | − | 0.386989i | \(-0.873515\pi\) |
0.386989 | + | 0.922084i | \(0.373515\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.3550 | + | 14.7598i | −0.549584 | + | 0.783371i | ||||
\(356\) | 11.3663i | 0.602415i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.4031 | − | 10.4031i | −0.549822 | − | 0.549822i | ||||
\(359\) | 1.26616i | 0.0668256i | 0.999442 | + | 0.0334128i | \(0.0106376\pi\) | ||||
−0.999442 | + | 0.0334128i | \(0.989362\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.4031 | 0.863322 | ||||||||
\(362\) | 10.9831 | + | 10.9831i | 0.577258 | + | 0.577258i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.08717 | − | 2.00000i | 0.109397 | − | 0.104828i | ||||
\(365\) | 6.22696 | + | 35.5034i | 0.325934 | + | 1.85833i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.6260 | − | 10.6260i | −0.554670 | − | 0.554670i | 0.373115 | − | 0.927785i | \(-0.378290\pi\) |
−0.927785 | + | 0.373115i | \(0.878290\pi\) | |||||||
\(368\) | 5.23480 | + | 5.23480i | 0.272883 | + | 0.272883i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −14.7598 | − | 10.3550i | −0.767328 | − | 0.538328i | ||||
\(371\) | −6.50096 | + | 6.22947i | −0.337513 | + | 0.323418i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.70156 | − | 3.70156i | −0.191660 | − | 0.191660i | 0.604753 | − | 0.796413i | \(-0.293272\pi\) |
−0.796413 | + | 0.604753i | \(0.793272\pi\) | |||||||
\(374\) | 1.09259 | 0.0564965 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 10.3550i | − | 0.534016i | ||||||
\(377\) | −0.766519 | − | 0.766519i | −0.0394778 | − | 0.0394778i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 17.6125i | − | 0.904693i | −0.891842 | − | 0.452347i | \(-0.850587\pi\) | ||
0.891842 | − | 0.452347i | \(-0.149413\pi\) | |||||||
\(380\) | −10.8917 | − | 7.64117i | −0.558730 | − | 0.391984i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.1047 | + | 17.1047i | −0.875152 | + | 0.875152i | ||||
\(383\) | 16.5032 | − | 16.5032i | 0.843275 | − | 0.843275i | −0.146008 | − | 0.989283i | \(-0.546643\pi\) |
0.989283 | + | 0.146008i | \(0.0466426\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.74514 | − | 4.95005i | −0.343764 | − | 0.252278i | ||||
\(386\) | 15.5563 | 0.791797 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.76621 | − | 7.76621i | 0.394270 | − | 0.394270i | ||||
\(389\) | 13.1500i | 0.666730i | 0.942798 | + | 0.333365i | \(0.108184\pi\) | ||||
−0.942798 | + | 0.333365i | \(0.891816\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.71949i | − | 0.289247i | ||||||
\(392\) | −4.73422 | − | 5.15627i | −0.239114 | − | 0.260431i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 23.4031i | − | 1.17903i | ||||||
\(395\) | −9.89049 | − | 6.93880i | −0.497645 | − | 0.349129i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.95005 | − | 5.95005i | −0.298625 | − | 0.298625i | 0.541850 | − | 0.840475i | \(-0.317724\pi\) |
−0.840475 | + | 0.541850i | \(0.817724\pi\) | |||||||
\(398\) | −19.2347 | + | 19.2347i | −0.964148 | + | 0.964148i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.70156 | + | 4.70156i | 0.0850781 | + | 0.235078i | ||||
\(401\) | −22.9235 | −1.14475 | −0.572373 | − | 0.819993i | \(-0.693977\pi\) | ||||
−0.572373 | + | 0.819993i | \(0.693977\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.20937 | + | 2.20937i | 0.110057 | + | 0.110057i | ||||
\(404\) | 8.79790 | 0.437712 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.89531 | + | 1.81616i | −0.0940628 | + | 0.0901345i | ||||
\(407\) | −8.06323 | + | 8.06323i | −0.399679 | + | 0.399679i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.63232 | −0.179607 | −0.0898033 | − | 0.995960i | \(-0.528624\pi\) | ||||
−0.0898033 | + | 0.995960i | \(0.528624\pi\) | |||||||
\(410\) | 4.81274 | − | 0.844110i | 0.237685 | − | 0.0416876i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.85338 | + | 9.85338i | 0.485441 | + | 0.485441i | ||||
\(413\) | −0.681216 | + | 31.9420i | −0.0335205 | + | 1.57176i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.80625 | + | 27.4031i | 0.235929 | + | 1.34517i | ||||
\(416\) | 1.09259i | 0.0535686i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.95005 | + | 5.95005i | −0.291027 | + | 0.291027i | ||||
\(419\) | −5.52014 | −0.269676 | −0.134838 | − | 0.990868i | \(-0.543051\pi\) | ||||
−0.134838 | + | 0.990868i | \(0.543051\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.59688 | 0.321512 | 0.160756 | − | 0.986994i | \(-0.448607\pi\) | ||||
0.160756 | + | 0.986994i | \(0.448607\pi\) | |||||||
\(422\) | 7.64117 | − | 7.64117i | 0.371966 | − | 0.371966i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 3.40312i | − | 0.165270i | ||||||
\(425\) | 1.63888 | − | 3.49799i | 0.0794976 | − | 0.169678i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.60803 | + | 0.204907i | 0.464965 | + | 0.00991617i | ||||
\(428\) | −0.422055 | − | 0.422055i | −0.0204008 | − | 0.0204008i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.63232 | + | 5.17748i | −0.175166 | + | 0.249680i | ||||
\(431\) | −27.0181 | −1.30142 | −0.650708 | − | 0.759328i | \(-0.725528\pi\) | ||||
−0.650708 | + | 0.759328i | \(0.725528\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.31137 | − | 9.31137i | 0.447476 | − | 0.447476i | −0.447039 | − | 0.894515i | \(-0.647521\pi\) |
0.894515 | + | 0.447039i | \(0.147521\pi\) | |||||||
\(434\) | 5.46295 | − | 5.23480i | 0.262230 | − | 0.251278i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.4031 | 0.641893 | ||||||||
\(437\) | 31.1473 | + | 31.1473i | 1.48998 | + | 1.48998i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.58237 | 0.457342 | 0.228671 | − | 0.973504i | \(-0.426562\pi\) | ||||
0.228671 | + | 0.973504i | \(0.426562\pi\) | |||||||
\(440\) | 3.11473 | − | 0.546295i | 0.148489 | − | 0.0260436i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.596876 | − | 0.596876i | 0.0283905 | − | 0.0283905i | ||||
\(443\) | −7.49312 | − | 7.49312i | −0.356009 | − | 0.356009i | 0.506331 | − | 0.862340i | \(-0.331002\pi\) |
−0.862340 | + | 0.506331i | \(0.831002\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.5969 | − | 20.8062i | 0.691958 | − | 0.986311i | ||||
\(446\) | − | 4.75362i | − | 0.225090i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.64515 | + | 0.0564123i | 0.124972 | + | 0.00266523i | ||||
\(449\) | − | 35.9254i | − | 1.69543i | −0.530455 | − | 0.847713i | \(-0.677979\pi\) | ||
0.530455 | − | 0.847713i | \(-0.322021\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 3.09031i | − | 0.145517i | ||||||
\(452\) | −11.8838 | + | 11.8838i | −0.558968 | + | 0.558968i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.9904 | 0.703535 | ||||||||
\(455\) | −6.38902 | + | 0.980649i | −0.299522 | + | 0.0459736i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.8062 | − | 19.8062i | 0.926497 | − | 0.926497i | −0.0709805 | − | 0.997478i | \(-0.522613\pi\) |
0.997478 | + | 0.0709805i | \(0.0226128\pi\) | |||||||
\(458\) | 17.2125 | − | 17.2125i | 0.804290 | − | 0.804290i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.85974 | − | 16.3050i | −0.133336 | − | 0.760225i | ||||
\(461\) | − | 17.2125i | − | 0.801668i | −0.916151 | − | 0.400834i | \(-0.868720\pi\) | ||
0.916151 | − | 0.400834i | \(-0.131280\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.10469 | + | 6.10469i | 0.283709 | + | 0.283709i | 0.834586 | − | 0.550877i | \(-0.185707\pi\) |
−0.550877 | + | 0.834586i | \(0.685707\pi\) | |||||||
\(464\) | − | 0.992159i | − | 0.0460598i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.00000 | 0.277945 | ||||||||
\(467\) | 25.6272 | + | 25.6272i | 1.18589 | + | 1.18589i | 0.978195 | + | 0.207691i | \(0.0665947\pi\) |
0.207691 | + | 0.978195i | \(0.433405\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.3550 | + | 10.8062i | 0.478147 | + | 0.498986i | ||||
\(470\) | −13.2980 | + | 18.9549i | −0.613392 | + | 0.874323i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.53879 | − | 8.53879i | −0.393030 | − | 0.393030i | ||||
\(473\) | 2.82843 | + | 2.82843i | 0.130051 | + | 0.130051i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.1244 | + | 27.9745i | 0.464539 | + | 1.28356i | ||||
\(476\) | −1.41421 | − | 1.47585i | −0.0648204 | − | 0.0676454i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.2984 | + | 10.2984i | 0.471040 | + | 0.471040i | ||||
\(479\) | −21.9662 | −1.00366 | −0.501830 | − | 0.864966i | \(-0.667340\pi\) | ||||
−0.501830 | + | 0.864966i | \(0.667340\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.80980i | 0.401692i | ||||||||
\(482\) | 13.9348 | + | 13.9348i | 0.634712 | + | 0.634712i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.00000i | 0.409091i | ||||||||
\(485\) | −24.1897 | + | 4.24264i | −1.09840 | + | 0.192648i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.5078 | + | 15.5078i | −0.702726 | + | 0.702726i | −0.964995 | − | 0.262269i | \(-0.915529\pi\) |
0.262269 | + | 0.964995i | \(0.415529\pi\) | |||||||
\(488\) | −2.56844 | + | 2.56844i | −0.116268 | + | 0.116268i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.04427 | + | 15.5184i | 0.0923506 | + | 0.701050i | ||||
\(491\) | 22.0573 | 0.995433 | 0.497716 | − | 0.867340i | \(-0.334172\pi\) | ||||
0.497716 | + | 0.867340i | \(0.334172\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.542011 | + | 0.542011i | −0.0244109 | + | 0.0244109i | ||||
\(494\) | 6.50096i | 0.292492i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.85974i | 0.128406i | ||||||||
\(497\) | 0.454865 | − | 21.3284i | 0.0204035 | − | 0.956711i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.00000i | 0.358129i | 0.983837 | + | 0.179065i | \(0.0573071\pi\) | ||||
−0.983837 | + | 0.179065i | \(0.942693\pi\) | |||||||
\(500\) | 2.92310 | − | 10.7915i | 0.130725 | − | 0.482608i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 17.3486 | + | 17.3486i | 0.774305 | + | 0.774305i | ||||
\(503\) | −4.04429 | + | 4.04429i | −0.180326 | + | 0.180326i | −0.791498 | − | 0.611172i | \(-0.790698\pi\) |
0.611172 | + | 0.791498i | \(0.290698\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.1047 | − | 11.2984i | −0.716649 | − | 0.502774i | ||||
\(506\) | −10.4696 | −0.465430 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.701562 | − | 0.701562i | −0.0311268 | − | 0.0311268i | ||||
\(509\) | 28.9050 | 1.28119 | 0.640595 | − | 0.767879i | \(-0.278688\pi\) | ||||
0.640595 | + | 0.767879i | \(0.278688\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.5078 | − | 30.7938i | −1.30535 | − | 1.36224i | ||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.31773 | −0.102231 | ||||||||
\(515\) | −5.38285 | − | 30.6906i | −0.237197 | − | 1.35239i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.3550 | + | 10.3550i | 0.455410 | + | 0.455410i | ||||
\(518\) | 21.3284 | + | 0.454865i | 0.937118 | + | 0.0199856i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.40312 | − | 2.00000i | 0.0615311 | − | 0.0877058i | ||||
\(521\) | 22.2922i | 0.976641i | 0.872664 | + | 0.488320i | \(0.162390\pi\) | ||||
−0.872664 | + | 0.488320i | \(0.837610\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.1275 | − | 11.1275i | 0.486573 | − | 0.486573i | −0.420650 | − | 0.907223i | \(-0.638198\pi\) |
0.907223 | + | 0.420650i | \(0.138198\pi\) | |||||||
\(524\) | −2.56844 | −0.112203 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.0000 | −0.697633 | ||||||||
\(527\) | 1.56226 | − | 1.56226i | 0.0680532 | − | 0.0680532i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31.8062i | 1.38288i | ||||||||
\(530\) | −4.37036 | + | 6.22947i | −0.189836 | + | 0.270591i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 15.7388 | + | 0.335656i | 0.682363 | + | 0.0145525i | ||||
\(533\) | −1.68822 | − | 1.68822i | −0.0731249 | − | 0.0731249i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.230566 | + | 1.31459i | 0.00996825 | + | 0.0568346i | ||||
\(536\) | −5.65685 | −0.244339 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.9437 | + | 12.9437i | −0.558042 | + | 0.558042i | ||||
\(539\) | 9.89049 | + | 0.422055i | 0.426014 | + | 0.0181792i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0000 | −0.773880 | −0.386940 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386940 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(542\) | 8.96094 | + | 8.96094i | 0.384905 | + | 0.384905i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.772577 | 0.0331240 | ||||||||
\(545\) | −24.5346 | − | 17.2125i | −1.05095 | − | 0.737305i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.4031 | + | 29.4031i | −1.25719 | + | 1.25719i | −0.304757 | + | 0.952430i | \(0.598575\pi\) |
−0.952430 | + | 0.304757i | \(0.901425\pi\) | |||||||
\(548\) | 6.22696 | + | 6.22696i | 0.266002 | + | 0.266002i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.40312 | − | 3.00000i | −0.273030 | − | 0.127920i | ||||
\(551\) | − | 5.90340i | − | 0.251493i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.2921 | + | 0.304803i | 0.607761 | + | 0.0129615i | ||||
\(554\) | 7.21912i | 0.306711i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 7.49521i | − | 0.317868i | ||||||
\(557\) | 10.8917 | − | 10.8917i | 0.461494 | − | 0.461494i | −0.437651 | − | 0.899145i | \(-0.644189\pi\) |
0.899145 | + | 0.437651i | \(0.144189\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.09031 | 0.130706 | ||||||||
\(560\) | −4.76954 | − | 3.50022i | −0.201550 | − | 0.147911i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.0000 | + | 14.0000i | −0.590554 | + | 0.590554i | ||||
\(563\) | −24.9179 | + | 24.9179i | −1.05016 | + | 1.05016i | −0.0514892 | + | 0.998674i | \(0.516397\pi\) |
−0.998674 | + | 0.0514892i | \(0.983603\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.0149 | − | 6.49206i | 1.55723 | − | 0.273123i | ||||
\(566\) | 0.766519i | 0.0322192i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.70156 | + | 5.70156i | 0.239232 | + | 0.239232i | ||||
\(569\) | − | 45.5509i | − | 1.90959i | −0.297258 | − | 0.954797i | \(-0.596072\pi\) | ||
0.297258 | − | 0.954797i | \(-0.403928\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | −1.09259 | − | 1.09259i | −0.0456835 | − | 0.0456835i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.17433 | + | 4.00000i | −0.174233 | + | 0.166957i | ||||
\(575\) | −15.7044 | + | 33.5191i | −0.654919 | + | 1.39784i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.0309 | + | 15.0309i | 0.625743 | + | 0.625743i | 0.946994 | − | 0.321251i | \(-0.104103\pi\) |
−0.321251 | + | 0.946994i | \(0.604103\pi\) | |||||||
\(578\) | 11.5988 | + | 11.5988i | 0.482445 | + | 0.482445i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.27415 | + | 1.81616i | −0.0529062 | + | 0.0754119i | ||||
\(581\) | −22.7755 | − | 23.7681i | −0.944886 | − | 0.986066i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.40312 | + | 3.40312i | 0.140943 | + | 0.140943i | ||||
\(584\) | 16.1200 | 0.667049 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.5728i | 1.01509i | ||||||||
\(587\) | −15.0274 | − | 15.0274i | −0.620246 | − | 0.620246i | 0.325348 | − | 0.945594i | \(-0.394518\pi\) |
−0.945594 | + | 0.325348i | \(0.894518\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.0156i | 0.701116i | ||||||||
\(590\) | 4.66470 | + | 26.5961i | 0.192042 | + | 1.09494i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.70156 | + | 5.70156i | −0.234333 | + | 0.234333i | ||||
\(593\) | −32.0197 | + | 32.0197i | −1.31489 | + | 1.31489i | −0.397128 | + | 0.917763i | \(0.629993\pi\) |
−0.917763 | + | 0.397128i | \(0.870007\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.693424 | + | 4.51772i | 0.0284276 | + | 0.185209i | ||||
\(596\) | 17.1186 | 0.701206 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.71949 | + | 5.71949i | −0.233887 | + | 0.233887i | ||||
\(599\) | 11.7358i | 0.479510i | 0.970833 | + | 0.239755i | \(0.0770672\pi\) | ||||
−0.970833 | + | 0.239755i | \(0.922933\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.6940i | 1.37441i | 0.726464 | + | 0.687204i | \(0.241162\pi\) | ||||
−0.726464 | + | 0.687204i | \(0.758838\pi\) | |||||||
\(602\) | 0.159558 | − | 7.48161i | 0.00650310 | − | 0.304928i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.80625i | 0.276942i | ||||||||
\(605\) | 11.5580 | − | 16.4746i | 0.469898 | − | 0.669789i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.99364 | + | 6.99364i | 0.283863 | + | 0.283863i | 0.834647 | − | 0.550785i | \(-0.185671\pi\) |
−0.550785 | + | 0.834647i | \(0.685671\pi\) | |||||||
\(608\) | −4.20732 | + | 4.20732i | −0.170629 | + | 0.170629i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.00000 | − | 1.40312i | 0.323911 | − | 0.0568108i | ||||
\(611\) | 11.3137 | 0.457704 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.7016 | − | 21.7016i | −0.876518 | − | 0.876518i | 0.116655 | − | 0.993173i | \(-0.462783\pi\) |
−0.993173 | + | 0.116655i | \(0.962783\pi\) | |||||||
\(614\) | 20.8736 | 0.842389 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.70156 | + | 2.58874i | −0.108849 | + | 0.104303i | ||||
\(617\) | 5.38285 | − | 5.38285i | 0.216705 | − | 0.216705i | −0.590403 | − | 0.807108i | \(-0.701031\pi\) |
0.807108 | + | 0.590403i | \(0.201031\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.3890 | −0.698924 | −0.349462 | − | 0.936951i | \(-0.613636\pi\) | ||||
−0.349462 | + | 0.936951i | \(0.613636\pi\) | |||||||
\(620\) | 3.67254 | − | 5.23480i | 0.147493 | − | 0.210235i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.08717 | − | 2.08717i | −0.0836877 | − | 0.0836877i | ||||
\(623\) | −0.641201 | + | 30.0657i | −0.0256892 | + | 1.20456i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.2094 | + | 16.0000i | −0.768375 | + | 0.640000i | ||||
\(626\) | − | 20.4903i | − | 0.818958i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.6727 | − | 12.6727i | 0.505695 | − | 0.505695i | ||||
\(629\) | 6.22947 | 0.248385 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.4031 | 0.852045 | 0.426022 | − | 0.904713i | \(-0.359914\pi\) | ||||
0.426022 | + | 0.904713i | \(0.359914\pi\) | |||||||
\(632\) | −3.82059 | + | 3.82059i | −0.151975 | + | 0.151975i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.00000i | 0.0794301i | ||||||||
\(635\) | 0.383260 | + | 2.18518i | 0.0152092 | + | 0.0867162i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.63369 | − | 5.17256i | 0.223215 | − | 0.204944i | ||||
\(638\) | 0.992159 | + | 0.992159i | 0.0392799 | + | 0.0392799i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.20245 | − | 0.386289i | 0.0870594 | − | 0.0152694i | ||||
\(641\) | −29.1284 | −1.15050 | −0.575251 | − | 0.817977i | \(-0.695096\pi\) | ||||
−0.575251 | + | 0.817977i | \(0.695096\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.31773 | − | 2.31773i | 0.0914024 | − | 0.0914024i | −0.659927 | − | 0.751330i | \(-0.729413\pi\) |
0.751330 | + | 0.659927i | \(0.229413\pi\) | |||||||
\(644\) | 13.5515 | + | 14.1421i | 0.534005 | + | 0.557278i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.59688 | 0.180862 | ||||||||
\(647\) | −9.18116 | − | 9.18116i | −0.360949 | − | 0.360949i | 0.503213 | − | 0.864162i | \(-0.332151\pi\) |
−0.864162 | + | 0.503213i | \(0.832151\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.0776 | 0.670354 | ||||||||
\(650\) | −5.13688 | + | 1.85911i | −0.201485 | + | 0.0729202i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.4031 | − | 11.4031i | 0.446581 | − | 0.446581i | ||||
\(653\) | 17.5407 | + | 17.5407i | 0.686419 | + | 0.686419i | 0.961439 | − | 0.275019i | \(-0.0886843\pi\) |
−0.275019 | + | 0.961439i | \(0.588684\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.70156 | + | 3.29844i | 0.183705 | + | 0.128881i | ||||
\(656\) | − | 2.18518i | − | 0.0853169i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.584146 | − | 27.3904i | 0.0227724 | − | 1.06779i | ||||
\(659\) | − | 38.4799i | − | 1.49896i | −0.662025 | − | 0.749481i | \(-0.730303\pi\) | ||
0.662025 | − | 0.749481i | \(-0.269697\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.1616i | 0.706404i | 0.935547 | + | 0.353202i | \(0.114907\pi\) | ||||
−0.935547 | + | 0.353202i | \(0.885093\pi\) | |||||||
\(662\) | 18.1108 | − | 18.1108i | 0.703895 | − | 0.703895i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.4421 | 0.482848 | ||||||||
\(665\) | −28.3790 | − | 20.8265i | −1.10049 | − | 0.807616i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.19375 | − | 5.19375i | 0.201103 | − | 0.201103i | ||||
\(668\) | −6.22947 | + | 6.22947i | −0.241025 | + | 0.241025i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.3550 | + | 7.26464i | 0.400047 | + | 0.280658i | ||||
\(671\) | − | 5.13688i | − | 0.198307i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.19375 | + | 8.19375i | 0.315846 | + | 0.315846i | 0.847169 | − | 0.531323i | \(-0.178305\pi\) |
−0.531323 | + | 0.847169i | \(0.678305\pi\) | |||||||
\(674\) | − | 1.41421i | − | 0.0544735i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.8062 | 0.454086 | ||||||||
\(677\) | −28.3587 | − | 28.3587i | −1.08991 | − | 1.08991i | −0.995537 | − | 0.0943755i | \(-0.969915\pi\) |
−0.0943755 | − | 0.995537i | \(-0.530085\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.9809 | − | 20.1047i | 0.805173 | − | 0.771547i | ||||
\(680\) | −1.41421 | − | 0.992159i | −0.0542326 | − | 0.0380475i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.85974 | − | 2.85974i | −0.109505 | − | 0.109505i | ||||
\(683\) | 23.7676 | + | 23.7676i | 0.909443 | + | 0.909443i | 0.996227 | − | 0.0867843i | \(-0.0276591\pi\) |
−0.0867843 | + | 0.996227i | \(0.527659\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.40175 | − | 19.3953i | −0.129974 | − | 0.741057i | ||||
\(686\) | −12.2318 | − | 13.9062i | −0.467014 | − | 0.530941i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.00000 | + | 2.00000i | 0.0762493 | + | 0.0762493i | ||||
\(689\) | 3.71822 | 0.141653 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 10.1244i | − | 0.385150i | −0.981282 | − | 0.192575i | \(-0.938316\pi\) | ||
0.981282 | − | 0.192575i | \(-0.0616838\pi\) | |||||||
\(692\) | −6.39250 | − | 6.39250i | −0.243006 | − | 0.243006i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.2094i | 0.918975i | ||||||||
\(695\) | −9.62549 | + | 13.7201i | −0.365116 | + | 0.520432i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.19375 | + | 1.19375i | −0.0452166 | + | 0.0452166i | ||||
\(698\) | 6.93880 | − | 6.93880i | 0.262637 | − | 0.262637i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.23566 | + | 12.5323i | 0.160093 | + | 0.473677i | ||||
\(701\) | 25.3078 | 0.955862 | 0.477931 | − | 0.878397i | \(-0.341387\pi\) | ||||
0.477931 | + | 0.878397i | \(0.341387\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.9246 | + | 33.9246i | −1.27949 | + | 1.27949i | ||||
\(704\) | − | 1.41421i | − | 0.0533002i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 14.2178i | − | 0.535095i | ||||||
\(707\) | 23.2718 | + | 0.496310i | 0.875225 | + | 0.0186657i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.0156i | 0.864370i | 0.901785 | + | 0.432185i | \(0.142257\pi\) | ||||
−0.901785 | + | 0.432185i | \(0.857743\pi\) | |||||||
\(710\) | −3.11473 | − | 17.7588i | −0.116894 | − | 0.666478i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.03722 | − | 8.03722i | −0.301207 | − | 0.301207i | ||||
\(713\) | −14.9702 | + | 14.9702i | −0.560638 | + | 0.560638i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.596876 | + | 3.40312i | 0.0223219 | + | 0.127270i | ||||
\(716\) | 14.7122 | 0.549822 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.895314 | − | 0.895314i | −0.0334128 | − | 0.0334128i | ||||
\(719\) | 27.1030 | 1.01077 | 0.505386 | − | 0.862893i | \(-0.331350\pi\) | ||||
0.505386 | + | 0.862893i | \(0.331350\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.5078 | + | 26.6195i | 0.949961 | + | 0.991362i | ||||
\(722\) | −11.5988 | + | 11.5988i | −0.431661 | + | 0.431661i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −15.5324 | −0.577258 | ||||||||
\(725\) | 4.66470 | − | 1.68822i | 0.173242 | − | 0.0626989i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.8906 | + | 17.8906i | 0.663525 | + | 0.663525i | 0.956209 | − | 0.292684i | \(-0.0945483\pi\) |
−0.292684 | + | 0.956209i | \(0.594548\pi\) | |||||||
\(728\) | −0.0616355 | + | 2.89006i | −0.00228436 | + | 0.107113i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −29.5078 | − | 20.7016i | −1.09213 | − | 0.766199i | ||||
\(731\) | − | 2.18518i | − | 0.0808218i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.1148 | − | 25.1148i | 0.927636 | − | 0.927636i | −0.0699166 | − | 0.997553i | \(-0.522273\pi\) |
0.997553 | + | 0.0699166i | \(0.0222733\pi\) | |||||||
\(734\) | 15.0274 | 0.554670 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.40312 | −0.272883 | ||||||||
\(737\) | 5.65685 | − | 5.65685i | 0.208373 | − | 0.208373i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.19375i | 0.338198i | 0.985599 | + | 0.169099i | \(0.0540857\pi\) | ||||
−0.985599 | + | 0.169099i | \(0.945914\pi\) | |||||||
\(740\) | 17.7588 | − | 3.11473i | 0.652828 | − | 0.114500i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.191978 | − | 9.00177i | 0.00704773 | − | 0.330466i | ||||
\(743\) | −22.6274 | − | 22.6274i | −0.830119 | − | 0.830119i | 0.157413 | − | 0.987533i | \(-0.449684\pi\) |
−0.987533 | + | 0.157413i | \(0.949684\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31.3359 | − | 21.9840i | −1.14806 | − | 0.805433i | ||||
\(746\) | 5.23480 | 0.191660 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.772577 | + | 0.772577i | −0.0282482 | + | 0.0282482i | ||||
\(749\) | −1.09259 | − | 1.14021i | −0.0399223 | − | 0.0416623i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.20937 | 0.153602 | 0.0768011 | − | 0.997046i | \(-0.475529\pi\) | ||||
0.0768011 | + | 0.997046i | \(0.475529\pi\) | |||||||
\(752\) | 7.32206 | + | 7.32206i | 0.267008 | + | 0.267008i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.08402 | 0.0394778 | ||||||||
\(755\) | 8.74071 | − | 12.4589i | 0.318107 | − | 0.453427i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.507811 | − | 0.507811i | 0.0184567 | − | 0.0184567i | −0.697818 | − | 0.716275i | \(-0.745846\pi\) |
0.716275 | + | 0.697818i | \(0.245846\pi\) | |||||||
\(758\) | 12.4539 | + | 12.4539i | 0.452347 | + | 0.452347i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.1047 | − | 2.29844i | 0.475357 | − | 0.0833731i | ||||
\(761\) | − | 34.4251i | − | 1.24791i | −0.781461 | − | 0.623954i | \(-0.785525\pi\) | ||
0.781461 | − | 0.623954i | \(-0.214475\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35.4533 | + | 0.756101i | 1.28349 | + | 0.0273727i | ||||
\(764\) | − | 24.1897i | − | 0.875152i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.3391i | 0.843275i | ||||||||
\(767\) | 9.32939 | − | 9.32939i | 0.336865 | − | 0.336865i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.7003 | −1.28739 | −0.643693 | − | 0.765284i | \(-0.722599\pi\) | ||||
−0.643693 | + | 0.765284i | \(0.722599\pi\) | |||||||
\(770\) | 8.26975 | − | 1.26932i | 0.298021 | − | 0.0457432i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.0000 | + | 11.0000i | −0.395899 | + | 0.395899i | ||||
\(773\) | 14.4811 | − | 14.4811i | 0.520848 | − | 0.520848i | −0.396979 | − | 0.917828i | \(-0.629942\pi\) |
0.917828 | + | 0.396979i | \(0.129942\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.4453 | + | 4.86603i | −0.482968 | + | 0.174793i | ||||
\(776\) | 10.9831i | 0.394270i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.29844 | − | 9.29844i | −0.333365 | − | 0.333365i | ||||
\(779\) | − | 13.0019i | − | 0.465842i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.4031 | −0.408036 | ||||||||
\(782\) | 4.04429 | + | 4.04429i | 0.144623 | + | 0.144623i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.99364 | + | 0.298438i | 0.249773 | + | 0.0106585i | ||||
\(785\) | −39.4720 | + | 6.92302i | −1.40882 | + | 0.247093i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.3081 | − | 17.3081i | −0.616969 | − | 0.616969i | 0.327784 | − | 0.944753i | \(-0.393698\pi\) |
−0.944753 | + | 0.327784i | \(0.893698\pi\) | |||||||
\(788\) | 16.5485 | + | 16.5485i | 0.589516 | + | 0.589516i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.9001 | − | 2.08717i | 0.423387 | − | 0.0742580i | ||||
\(791\) | −32.1049 | + | 30.7641i | −1.14152 | + | 1.09384i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.80625 | − | 2.80625i | −0.0996528 | − | 0.0996528i | ||||
\(794\) | 8.41464 | 0.298625 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 27.2020i | − | 0.964148i | ||||||
\(797\) | 14.4811 | + | 14.4811i | 0.512946 | + | 0.512946i | 0.915428 | − | 0.402482i | \(-0.131852\pi\) |
−0.402482 | + | 0.915428i | \(0.631852\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 8.00000i | − | 0.283020i | ||||||
\(800\) | −4.52769 | − | 2.12132i | −0.160078 | − | 0.0750000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.2094 | − | 16.2094i | 0.572373 | − | 0.572373i | ||||
\(803\) | −16.1200 | + | 16.1200i | −0.568861 | + | 0.568861i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.64465 | − | 43.2905i | −0.234193 | − | 1.52579i | ||||
\(806\) | −3.12452 | −0.110057 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.22106 | + | 6.22106i | −0.218856 | + | 0.218856i | ||||
\(809\) | − | 20.0951i | − | 0.706506i | −0.935528 | − | 0.353253i | \(-0.885076\pi\) | ||
0.935528 | − | 0.353253i | \(-0.114924\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 10.1244i | − | 0.355515i | −0.984074 | − | 0.177758i | \(-0.943116\pi\) | ||
0.984074 | − | 0.177758i | \(-0.0568843\pi\) | |||||||
\(812\) | 0.0559699 | − | 2.62441i | 0.00196416 | − | 0.0920987i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 11.4031i | − | 0.399679i | ||||||
\(815\) | −35.5177 | + | 6.22947i | −1.24413 | + | 0.218209i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.9001 | + | 11.9001i | 0.416332 | + | 0.416332i | ||||
\(818\) | 2.56844 | − | 2.56844i | 0.0898033 | − | 0.0898033i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.80625 | + | 4.00000i | −0.0979984 | + | 0.139686i | ||||
\(821\) | 46.5431 | 1.62437 | 0.812183 | − | 0.583403i | \(-0.198279\pi\) | ||||
0.812183 | + | 0.583403i | \(0.198279\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.9109 | − | 16.9109i | −0.589478 | − | 0.589478i | 0.348012 | − | 0.937490i | \(-0.386857\pi\) |
−0.937490 | + | 0.348012i | \(0.886857\pi\) | |||||||
\(824\) | −13.9348 | −0.485441 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −22.1047 | − | 23.0681i | −0.769120 | − | 0.802641i | ||||
\(827\) | −7.91518 | + | 7.91518i | −0.275238 | + | 0.275238i | −0.831204 | − | 0.555967i | \(-0.812348\pi\) |
0.555967 | + | 0.831204i | \(0.312348\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −49.6876 | −1.72572 | −0.862861 | − | 0.505442i | \(-0.831329\pi\) | ||||
−0.862861 | + | 0.505442i | \(0.831329\pi\) | |||||||
\(830\) | −22.7755 | − | 15.9784i | −0.790548 | − | 0.554619i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.772577 | − | 0.772577i | −0.0267843 | − | 0.0267843i | ||||
\(833\) | −3.65755 | − | 3.98362i | −0.126727 | − | 0.138024i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.4031 | − | 3.40312i | 0.671473 | − | 0.117770i | ||||
\(836\) | − | 8.41464i | − | 0.291027i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.90333 | − | 3.90333i | 0.134838 | − | 0.134838i | ||||
\(839\) | 19.0145 | 0.656452 | 0.328226 | − | 0.944599i | \(-0.393549\pi\) | ||||
0.328226 | + | 0.944599i | \(0.393549\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.0156 | 0.966056 | ||||||||
\(842\) | −4.66470 | + | 4.66470i | −0.160756 | + | 0.160756i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.8062i | 0.371966i | ||||||||
\(845\) | −21.6115 | − | 15.1618i | −0.743458 | − | 0.521582i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.507711 | + | 23.8063i | −0.0174451 | + | 0.817996i | ||||
\(848\) | 2.40637 | + | 2.40637i | 0.0826352 | + | 0.0826352i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.31459 | + | 3.63232i | 0.0450900 | + | 0.124588i | ||||
\(851\) | −59.6931 | −2.04625 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.9405 | + | 20.9405i | −0.716988 | + | 0.716988i | −0.967987 | − | 0.250999i | \(-0.919241\pi\) |
0.250999 | + | 0.967987i | \(0.419241\pi\) | |||||||
\(854\) | −6.93880 | + | 6.64901i | −0.237441 | + | 0.227525i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.596876 | 0.0204008 | ||||||||
\(857\) | 7.86835 | + | 7.86835i | 0.268778 | + | 0.268778i | 0.828608 | − | 0.559830i | \(-0.189134\pi\) |
−0.559830 | + | 0.828608i | \(0.689134\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.6600 | 0.909626 | 0.454813 | − | 0.890587i | \(-0.349706\pi\) | ||||
0.454813 | + | 0.890587i | \(0.349706\pi\) | |||||||
\(860\) | −1.09259 | − | 6.22947i | −0.0372570 | − | 0.212423i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.1047 | − | 19.1047i | 0.650708 | − | 0.650708i | ||||
\(863\) | 1.56226 | + | 1.56226i | 0.0531800 | + | 0.0531800i | 0.733197 | − | 0.680017i | \(-0.238027\pi\) |
−0.680017 | + | 0.733197i | \(0.738027\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.49219 | + | 19.9109i | 0.118738 | + | 0.676992i | ||||
\(866\) | 13.1683i | 0.447476i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.161325 | + | 7.56445i | −0.00547571 | + | 0.256754i | ||||
\(869\) | − | 7.64117i | − | 0.259209i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 6.18062i | − | 0.209422i | ||||||
\(872\) | −9.47744 | + | 9.47744i | −0.320947 | + | 0.320947i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −44.0490 | −1.48998 | ||||||||
\(875\) | 8.34082 | − | 28.3801i | 0.281971 | − | 0.959423i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.5078 | − | 38.5078i | 1.30032 | − | 1.30032i | 0.372140 | − | 0.928177i | \(-0.378624\pi\) |
0.928177 | − | 0.372140i | \(-0.121376\pi\) | |||||||
\(878\) | −6.77576 | + | 6.77576i | −0.228671 | + | 0.228671i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.81616 | + | 2.58874i | −0.0612227 | + | 0.0872663i | ||||
\(881\) | − | 4.81081i | − | 0.162080i | −0.996711 | − | 0.0810401i | \(-0.974176\pi\) | ||
0.996711 | − | 0.0810401i | \(-0.0258242\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.8062 | − | 26.8062i | −0.902102 | − | 0.902102i | 0.0935157 | − | 0.995618i | \(-0.470189\pi\) |
−0.995618 | + | 0.0935157i | \(0.970189\pi\) | |||||||
\(884\) | 0.844110i | 0.0283905i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.5969 | 0.356009 | ||||||||
\(887\) | 33.6586 | + | 33.6586i | 1.13014 | + | 1.13014i | 0.990153 | + | 0.139992i | \(0.0447076\pi\) |
0.139992 | + | 0.990153i | \(0.455292\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.81616 | − | 1.89531i | −0.0609121 | − | 0.0635668i | ||||
\(890\) | 4.39069 | + | 25.0338i | 0.147176 | + | 0.839135i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.36131 | + | 3.36131i | 0.112545 | + | 0.112545i | ||||
\(893\) | 43.5666 | + | 43.5666i | 1.45790 | + | 1.45790i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.9310 | − | 18.8937i | −0.900203 | − | 0.631548i | ||||
\(896\) | −1.91029 | + | 1.83051i | −0.0638184 | + | 0.0611532i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 25.4031 | + | 25.4031i | 0.847713 | + | 0.847713i | ||||
\(899\) | 2.83732 | 0.0946299 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2.62918i | − | 0.0875906i | ||||||
\(902\) | 2.18518 | + | 2.18518i | 0.0727585 | + | 0.0727585i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 16.8062i | − | 0.558968i | ||||||
\(905\) | 28.4323 | + | 19.9470i | 0.945122 | + | 0.663062i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.4031 | − | 29.4031i | 0.976315 | − | 0.976315i | −0.0234112 | − | 0.999726i | \(-0.507453\pi\) |
0.999726 | + | 0.0234112i | \(0.00745270\pi\) | |||||||
\(908\) | −10.5998 | + | 10.5998i | −0.351768 | + | 0.351768i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.82430 | − | 5.21115i | 0.126774 | − | 0.172748i | ||||
\(911\) | 39.1759 | 1.29796 | 0.648978 | − | 0.760807i | \(-0.275197\pi\) | ||||
0.648978 | + | 0.760807i | \(0.275197\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.4421 | + | 12.4421i | −0.411774 | + | 0.411774i | ||||
\(914\) | 28.0103i | 0.926497i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.3422i | 0.804290i | ||||||||
\(917\) | −6.79390 | − | 0.144891i | −0.224354 | − | 0.00478474i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 49.8219i | − | 1.64347i | −0.569868 | − | 0.821736i | \(-0.693006\pi\) | ||
0.569868 | − | 0.821736i | \(-0.306994\pi\) | |||||||
\(920\) | 13.5515 | + | 9.50723i | 0.446780 | + | 0.313444i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.1711 | + | 12.1711i | 0.400834 | + | 0.400834i | ||||
\(923\) | −6.22947 | + | 6.22947i | −0.205045 | + | 0.205045i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.5078 | − | 17.1047i | −1.20037 | − | 0.562399i | ||||
\(926\) | −8.63333 | −0.283709 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.701562 | + | 0.701562i | 0.0230299 | + | 0.0230299i | ||||
\(929\) | −59.3430 | −1.94698 | −0.973490 | − | 0.228731i | \(-0.926542\pi\) | ||||
−0.973490 | + | 0.228731i | \(0.926542\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 41.6125 | + | 1.77572i | 1.36379 | + | 0.0581969i | ||||
\(932\) | −4.24264 | + | 4.24264i | −0.138972 | + | 0.138972i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −36.2423 | −1.18589 | ||||||||
\(935\) | 2.40637 | − | 0.422055i | 0.0786968 | − | 0.0138027i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.7376 | − | 34.7376i | −1.13483 | − | 1.13483i | −0.989363 | − | 0.145465i | \(-0.953532\pi\) |
−0.145465 | − | 0.989363i | \(-0.546468\pi\) | |||||||
\(938\) | −14.9632 | − | 0.319116i | −0.488567 | − | 0.0104195i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.00000 | − | 22.8062i | −0.130466 | − | 0.743858i | ||||
\(941\) | − | 1.80192i | − | 0.0587409i | −0.999569 | − | 0.0293704i | \(-0.990650\pi\) | ||
0.999569 | − | 0.0293704i | \(-0.00935025\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.4390 | − | 11.4390i | 0.372504 | − | 0.372504i | ||||
\(944\) | 12.0757 | 0.393030 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.00000 | −0.130051 | ||||||||
\(947\) | −28.4323 | + | 28.4323i | −0.923926 | + | 0.923926i | −0.997304 | − | 0.0733779i | \(-0.976622\pi\) |
0.0733779 | + | 0.997304i | \(0.476622\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.6125i | 0.571726i | ||||||||
\(950\) | −26.9400 | − | 12.6220i | −0.874049 | − | 0.409511i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.04358 | + | 0.0435829i | 0.0662329 | + | 0.00141253i | ||||
\(953\) | −32.5269 | − | 32.5269i | −1.05365 | − | 1.05365i | −0.998477 | − | 0.0551732i | \(-0.982429\pi\) |
−0.0551732 | − | 0.998477i | \(-0.517571\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −31.0649 | + | 44.2795i | −1.00523 | + | 1.43285i | ||||
\(956\) | −14.5642 | −0.471040 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.5324 | − | 15.5324i | 0.501830 | − | 0.501830i | ||||
\(959\) | 16.1200 | + | 16.8225i | 0.520541 | + | 0.543227i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.8219 | 0.736189 | ||||||||
\(962\) | −6.22947 | − | 6.22947i | −0.200846 | − | 0.200846i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −19.7068 | −0.634712 | ||||||||
\(965\) | 34.2621 | − | 6.00924i | 1.10293 | − | 0.193444i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.10469 | + | 4.10469i | −0.131998 | + | 0.131998i | −0.770019 | − | 0.638021i | \(-0.779753\pi\) |
0.638021 | + | 0.770019i | \(0.279753\pi\) | |||||||
\(968\) | −6.36396 | − | 6.36396i | −0.204545 | − | 0.204545i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.1047 | − | 20.1047i | 0.452874 | − | 0.645523i | ||||
\(971\) | 45.0821i | 1.44675i | 0.690453 | + | 0.723377i | \(0.257411\pi\) | ||||
−0.690453 | + | 0.723377i | \(0.742589\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.422822 | − | 19.8259i | 0.0135550 | − | 0.635591i | ||||
\(974\) | − | 21.9314i | − | 0.702726i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 3.63232i | − | 0.116268i | ||||||
\(977\) | 28.0103 | − | 28.0103i | 0.896128 | − | 0.896128i | −0.0989633 | − | 0.995091i | \(-0.531553\pi\) |
0.995091 | + | 0.0989633i | \(0.0315526\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.0744 | 0.513741 | ||||||||
\(980\) | −12.4187 | − | 9.52766i | −0.396700 | − | 0.304350i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.5969 | + | 15.5969i | −0.497716 | + | 0.497716i | ||||
\(983\) | −20.5475 | + | 20.5475i | −0.655364 | + | 0.655364i | −0.954279 | − | 0.298916i | \(-0.903375\pi\) |
0.298916 | + | 0.954279i | \(0.403375\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.04036 | − | 51.5442i | −0.288050 | − | 1.64233i | ||||
\(986\) | − | 0.766519i | − | 0.0244109i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.59688 | − | 4.59688i | −0.146246 | − | 0.146246i | ||||
\(989\) | 20.9392i | 0.665828i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.8062 | −0.724464 | −0.362232 | − | 0.932088i | \(-0.617985\pi\) | ||||
−0.362232 | + | 0.932088i | \(0.617985\pi\) | |||||||
\(992\) | −2.02214 | − | 2.02214i | −0.0642031 | − | 0.0642031i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 14.7598 | + | 15.4031i | 0.468154 | + | 0.488557i | ||||
\(995\) | −34.9333 | + | 49.7936i | −1.10746 | + | 1.57856i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.0276 | − | 23.0276i | −0.729292 | − | 0.729292i | 0.241186 | − | 0.970479i | \(-0.422463\pi\) |
−0.970479 | + | 0.241186i | \(0.922463\pi\) | |||||||
\(998\) | −5.65685 | − | 5.65685i | −0.179065 | − | 0.179065i | ||||
\(999\) | 0 | 0 |
(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.p.d.433.2 | yes | 16 | |
3.2 | odd | 2 | inner | 630.2.p.d.433.7 | yes | 16 | |
5.2 | odd | 4 | inner | 630.2.p.d.307.3 | yes | 16 | |
7.6 | odd | 2 | inner | 630.2.p.d.433.3 | yes | 16 | |
15.2 | even | 4 | inner | 630.2.p.d.307.6 | yes | 16 | |
21.20 | even | 2 | inner | 630.2.p.d.433.6 | yes | 16 | |
35.27 | even | 4 | inner | 630.2.p.d.307.2 | ✓ | 16 | |
105.62 | odd | 4 | inner | 630.2.p.d.307.7 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.p.d.307.2 | ✓ | 16 | 35.27 | even | 4 | inner | |
630.2.p.d.307.3 | yes | 16 | 5.2 | odd | 4 | inner | |
630.2.p.d.307.6 | yes | 16 | 15.2 | even | 4 | inner | |
630.2.p.d.307.7 | yes | 16 | 105.62 | odd | 4 | inner | |
630.2.p.d.433.2 | yes | 16 | 1.1 | even | 1 | trivial | |
630.2.p.d.433.3 | yes | 16 | 7.6 | odd | 2 | inner | |
630.2.p.d.433.6 | yes | 16 | 21.20 | even | 2 | inner | |
630.2.p.d.433.7 | yes | 16 | 3.2 | odd | 2 | inner |