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: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.1 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.211 |
Dual form | 630.2.j.h.421.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||
\(3\) | −0.724745 | + | 1.57313i | −0.418432 | + | 0.908248i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | −1.72474 | + | 0.158919i | −0.704124 | + | 0.0648783i | ||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.94949 | − | 2.28024i | −0.649830 | − | 0.760080i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0.275255 | + | 0.476756i | 0.0829925 | + | 0.143747i | 0.904534 | − | 0.426401i | \(-0.140219\pi\) |
−0.821541 | + | 0.570149i | \(0.806886\pi\) | |||||||
\(12\) | −1.00000 | − | 1.41421i | −0.288675 | − | 0.408248i | ||||
\(13\) | −2.22474 | + | 3.85337i | −0.617033 | + | 1.06873i | 0.372991 | + | 0.927835i | \(0.378332\pi\) |
−0.990024 | + | 0.140898i | \(0.955001\pi\) | |||||||
\(14\) | 0.500000 | − | 0.866025i | 0.133631 | − | 0.231455i | ||||
\(15\) | −1.00000 | − | 1.41421i | −0.258199 | − | 0.365148i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | 1.00000 | − | 2.82843i | 0.235702 | − | 0.666667i | ||||
\(19\) | −5.89898 | −1.35332 | −0.676659 | − | 0.736296i | \(-0.736573\pi\) | ||||
−0.676659 | + | 0.736296i | \(0.736573\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | 1.72474 | − | 0.158919i | 0.376370 | − | 0.0346789i | ||||
\(22\) | −0.275255 | + | 0.476756i | −0.0586846 | + | 0.101645i | ||||
\(23\) | 1.22474 | − | 2.12132i | 0.255377 | − | 0.442326i | −0.709621 | − | 0.704584i | \(-0.751134\pi\) |
0.964998 | + | 0.262258i | \(0.0844671\pi\) | |||||||
\(24\) | 0.724745 | − | 1.57313i | 0.147938 | − | 0.321114i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −4.44949 | −0.872617 | ||||||||
\(27\) | 5.00000 | − | 1.41421i | 0.962250 | − | 0.272166i | ||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −1.22474 | − | 2.12132i | −0.227429 | − | 0.393919i | 0.729616 | − | 0.683857i | \(-0.239699\pi\) |
−0.957046 | + | 0.289938i | \(0.906365\pi\) | |||||||
\(30\) | 0.724745 | − | 1.57313i | 0.132320 | − | 0.287213i | ||||
\(31\) | −1.00000 | + | 1.73205i | −0.179605 | + | 0.311086i | −0.941745 | − | 0.336327i | \(-0.890815\pi\) |
0.762140 | + | 0.647412i | \(0.224149\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −0.949490 | + | 0.0874863i | −0.165285 | + | 0.0152294i | ||||
\(34\) | −1.50000 | − | 2.59808i | −0.257248 | − | 0.445566i | ||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 2.94949 | − | 0.548188i | 0.491582 | − | 0.0913647i | ||||
\(37\) | −1.55051 | −0.254902 | −0.127451 | − | 0.991845i | \(-0.540680\pi\) | ||||
−0.127451 | + | 0.991845i | \(0.540680\pi\) | |||||||
\(38\) | −2.94949 | − | 5.10867i | −0.478470 | − | 0.828735i | ||||
\(39\) | −4.44949 | − | 6.29253i | −0.712489 | − | 1.00761i | ||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | 5.72474 | − | 9.91555i | 0.894055 | − | 1.54855i | 0.0590851 | − | 0.998253i | \(-0.481182\pi\) |
0.834970 | − | 0.550296i | \(-0.185485\pi\) | |||||||
\(42\) | 1.00000 | + | 1.41421i | 0.154303 | + | 0.218218i | ||||
\(43\) | 2.94949 | + | 5.10867i | 0.449793 | + | 0.779064i | 0.998372 | − | 0.0570343i | \(-0.0181644\pi\) |
−0.548579 | + | 0.836099i | \(0.684831\pi\) | |||||||
\(44\) | −0.550510 | −0.0829925 | ||||||||
\(45\) | 2.94949 | − | 0.548188i | 0.439684 | − | 0.0817191i | ||||
\(46\) | 2.44949 | 0.361158 | ||||||||
\(47\) | 4.89898 | + | 8.48528i | 0.714590 | + | 1.23771i | 0.963118 | + | 0.269081i | \(0.0867199\pi\) |
−0.248528 | + | 0.968625i | \(0.579947\pi\) | |||||||
\(48\) | 1.72474 | − | 0.158919i | 0.248945 | − | 0.0229379i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0.500000 | − | 0.866025i | 0.0707107 | − | 0.122474i | ||||
\(51\) | 2.17423 | − | 4.71940i | 0.304454 | − | 0.660848i | ||||
\(52\) | −2.22474 | − | 3.85337i | −0.308517 | − | 0.534366i | ||||
\(53\) | −1.34847 | −0.185226 | −0.0926132 | − | 0.995702i | \(-0.529522\pi\) | ||||
−0.0926132 | + | 0.995702i | \(0.529522\pi\) | |||||||
\(54\) | 3.72474 | + | 3.62302i | 0.506874 | + | 0.493031i | ||||
\(55\) | −0.550510 | −0.0742308 | ||||||||
\(56\) | 0.500000 | + | 0.866025i | 0.0668153 | + | 0.115728i | ||||
\(57\) | 4.27526 | − | 9.27987i | 0.566271 | − | 1.22915i | ||||
\(58\) | 1.22474 | − | 2.12132i | 0.160817 | − | 0.278543i | ||||
\(59\) | −3.94949 | + | 6.84072i | −0.514180 | + | 0.890585i | 0.485685 | + | 0.874134i | \(0.338570\pi\) |
−0.999865 | + | 0.0164515i | \(0.994763\pi\) | |||||||
\(60\) | 1.72474 | − | 0.158919i | 0.222664 | − | 0.0205163i | ||||
\(61\) | 2.67423 | + | 4.63191i | 0.342401 | + | 0.593055i | 0.984878 | − | 0.173249i | \(-0.0554267\pi\) |
−0.642477 | + | 0.766305i | \(0.722093\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | −1.00000 | + | 2.82843i | −0.125988 | + | 0.356348i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.22474 | − | 3.85337i | −0.275946 | − | 0.477952i | ||||
\(66\) | −0.550510 | − | 0.778539i | −0.0677631 | − | 0.0958315i | ||||
\(67\) | −6.84847 | + | 11.8619i | −0.836674 | + | 1.44916i | 0.0559867 | + | 0.998432i | \(0.482170\pi\) |
−0.892660 | + | 0.450730i | \(0.851164\pi\) | |||||||
\(68\) | 1.50000 | − | 2.59808i | 0.181902 | − | 0.315063i | ||||
\(69\) | 2.44949 | + | 3.46410i | 0.294884 | + | 0.417029i | ||||
\(70\) | 0.500000 | + | 0.866025i | 0.0597614 | + | 0.103510i | ||||
\(71\) | −8.44949 | −1.00277 | −0.501385 | − | 0.865224i | \(-0.667176\pi\) | ||||
−0.501385 | + | 0.865224i | \(0.667176\pi\) | |||||||
\(72\) | 1.94949 | + | 2.28024i | 0.229750 | + | 0.268729i | ||||
\(73\) | −11.8990 | −1.39267 | −0.696335 | − | 0.717717i | \(-0.745187\pi\) | ||||
−0.696335 | + | 0.717717i | \(0.745187\pi\) | |||||||
\(74\) | −0.775255 | − | 1.34278i | −0.0901216 | − | 0.156095i | ||||
\(75\) | 1.72474 | − | 0.158919i | 0.199156 | − | 0.0183503i | ||||
\(76\) | 2.94949 | − | 5.10867i | 0.338330 | − | 0.586004i | ||||
\(77\) | 0.275255 | − | 0.476756i | 0.0313682 | − | 0.0543314i | ||||
\(78\) | 3.22474 | − | 6.99964i | 0.365130 | − | 0.792553i | ||||
\(79\) | −1.00000 | − | 1.73205i | −0.112509 | − | 0.194871i | 0.804272 | − | 0.594261i | \(-0.202555\pi\) |
−0.916781 | + | 0.399390i | \(0.869222\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −1.39898 | + | 8.89060i | −0.155442 | + | 0.987845i | ||||
\(82\) | 11.4495 | 1.26438 | ||||||||
\(83\) | 3.55051 | + | 6.14966i | 0.389719 | + | 0.675013i | 0.992412 | − | 0.122960i | \(-0.0392388\pi\) |
−0.602692 | + | 0.797974i | \(0.705905\pi\) | |||||||
\(84\) | −0.724745 | + | 1.57313i | −0.0790761 | + | 0.171643i | ||||
\(85\) | 1.50000 | − | 2.59808i | 0.162698 | − | 0.281801i | ||||
\(86\) | −2.94949 | + | 5.10867i | −0.318052 | + | 0.550882i | ||||
\(87\) | 4.22474 | − | 0.389270i | 0.452940 | − | 0.0417341i | ||||
\(88\) | −0.275255 | − | 0.476756i | −0.0293423 | − | 0.0508223i | ||||
\(89\) | −10.8990 | −1.15529 | −0.577645 | − | 0.816288i | \(-0.696028\pi\) | ||||
−0.577645 | + | 0.816288i | \(0.696028\pi\) | |||||||
\(90\) | 1.94949 | + | 2.28024i | 0.205494 | + | 0.240358i | ||||
\(91\) | 4.44949 | 0.466433 | ||||||||
\(92\) | 1.22474 | + | 2.12132i | 0.127688 | + | 0.221163i | ||||
\(93\) | −2.00000 | − | 2.82843i | −0.207390 | − | 0.293294i | ||||
\(94\) | −4.89898 | + | 8.48528i | −0.505291 | + | 0.875190i | ||||
\(95\) | 2.94949 | − | 5.10867i | 0.302611 | − | 0.524138i | ||||
\(96\) | 1.00000 | + | 1.41421i | 0.102062 | + | 0.144338i | ||||
\(97\) | 7.84847 | + | 13.5939i | 0.796891 | + | 1.38026i | 0.921631 | + | 0.388067i | \(0.126857\pi\) |
−0.124740 | + | 0.992189i | \(0.539810\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0.550510 | − | 1.55708i | 0.0553284 | − | 0.156492i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −2.44949 | − | 4.24264i | −0.243733 | − | 0.422159i | 0.718041 | − | 0.696000i | \(-0.245039\pi\) |
−0.961775 | + | 0.273842i | \(0.911706\pi\) | |||||||
\(102\) | 5.17423 | − | 0.476756i | 0.512326 | − | 0.0472059i | ||||
\(103\) | −10.1237 | + | 17.5348i | −0.997520 | + | 1.72776i | −0.437809 | + | 0.899068i | \(0.644245\pi\) |
−0.559712 | + | 0.828687i | \(0.689088\pi\) | |||||||
\(104\) | 2.22474 | − | 3.85337i | 0.218154 | − | 0.377854i | ||||
\(105\) | −0.724745 | + | 1.57313i | −0.0707279 | + | 0.153522i | ||||
\(106\) | −0.674235 | − | 1.16781i | −0.0654875 | − | 0.113428i | ||||
\(107\) | 6.79796 | 0.657183 | 0.328592 | − | 0.944472i | \(-0.393426\pi\) | ||||
0.328592 | + | 0.944472i | \(0.393426\pi\) | |||||||
\(108\) | −1.27526 | + | 5.03723i | −0.122711 | + | 0.484708i | ||||
\(109\) | −12.4495 | −1.19244 | −0.596222 | − | 0.802819i | \(-0.703332\pi\) | ||||
−0.596222 | + | 0.802819i | \(0.703332\pi\) | |||||||
\(110\) | −0.275255 | − | 0.476756i | −0.0262445 | − | 0.0454569i | ||||
\(111\) | 1.12372 | − | 2.43916i | 0.106659 | − | 0.231515i | ||||
\(112\) | −0.500000 | + | 0.866025i | −0.0472456 | + | 0.0818317i | ||||
\(113\) | 8.44949 | − | 14.6349i | 0.794861 | − | 1.37674i | −0.128066 | − | 0.991766i | \(-0.540877\pi\) |
0.922927 | − | 0.384974i | \(-0.125790\pi\) | |||||||
\(114\) | 10.1742 | − | 0.937458i | 0.952904 | − | 0.0878010i | ||||
\(115\) | 1.22474 | + | 2.12132i | 0.114208 | + | 0.197814i | ||||
\(116\) | 2.44949 | 0.227429 | ||||||||
\(117\) | 13.1237 | − | 2.43916i | 1.21329 | − | 0.225500i | ||||
\(118\) | −7.89898 | −0.727160 | ||||||||
\(119\) | 1.50000 | + | 2.59808i | 0.137505 | + | 0.238165i | ||||
\(120\) | 1.00000 | + | 1.41421i | 0.0912871 | + | 0.129099i | ||||
\(121\) | 5.34847 | − | 9.26382i | 0.486224 | − | 0.842165i | ||||
\(122\) | −2.67423 | + | 4.63191i | −0.242114 | + | 0.419353i | ||||
\(123\) | 11.4495 | + | 16.1920i | 1.03237 | + | 1.45999i | ||||
\(124\) | −1.00000 | − | 1.73205i | −0.0898027 | − | 0.155543i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −2.94949 | + | 0.548188i | −0.262761 | + | 0.0488365i | ||||
\(127\) | 13.1464 | 1.16656 | 0.583278 | − | 0.812272i | \(-0.301770\pi\) | ||||
0.583278 | + | 0.812272i | \(0.301770\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −10.1742 | + | 0.937458i | −0.895791 | + | 0.0825385i | ||||
\(130\) | 2.22474 | − | 3.85337i | 0.195123 | − | 0.337963i | ||||
\(131\) | −4.34847 | + | 7.53177i | −0.379928 | + | 0.658054i | −0.991051 | − | 0.133481i | \(-0.957384\pi\) |
0.611124 | + | 0.791535i | \(0.290718\pi\) | |||||||
\(132\) | 0.398979 | − | 0.866025i | 0.0347267 | − | 0.0753778i | ||||
\(133\) | 2.94949 | + | 5.10867i | 0.255753 | + | 0.442978i | ||||
\(134\) | −13.6969 | −1.18324 | ||||||||
\(135\) | −1.27526 | + | 5.03723i | −0.109756 | + | 0.433536i | ||||
\(136\) | 3.00000 | 0.257248 | ||||||||
\(137\) | −1.62372 | − | 2.81237i | −0.138724 | − | 0.240277i | 0.788290 | − | 0.615304i | \(-0.210967\pi\) |
−0.927014 | + | 0.375027i | \(0.877633\pi\) | |||||||
\(138\) | −1.77526 | + | 3.85337i | −0.151120 | + | 0.328021i | ||||
\(139\) | −4.39898 | + | 7.61926i | −0.373117 | + | 0.646257i | −0.990043 | − | 0.140764i | \(-0.955044\pi\) |
0.616927 | + | 0.787021i | \(0.288378\pi\) | |||||||
\(140\) | −0.500000 | + | 0.866025i | −0.0422577 | + | 0.0731925i | ||||
\(141\) | −16.8990 | + | 1.55708i | −1.42315 | + | 0.131130i | ||||
\(142\) | −4.22474 | − | 7.31747i | −0.354533 | − | 0.614069i | ||||
\(143\) | −2.44949 | −0.204837 | ||||||||
\(144\) | −1.00000 | + | 2.82843i | −0.0833333 | + | 0.235702i | ||||
\(145\) | 2.44949 | 0.203419 | ||||||||
\(146\) | −5.94949 | − | 10.3048i | −0.492383 | − | 0.852833i | ||||
\(147\) | −1.00000 | − | 1.41421i | −0.0824786 | − | 0.116642i | ||||
\(148\) | 0.775255 | − | 1.34278i | 0.0637256 | − | 0.110376i | ||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 1.00000 | + | 1.41421i | 0.0816497 | + | 0.115470i | ||||
\(151\) | 5.00000 | + | 8.66025i | 0.406894 | + | 0.704761i | 0.994540 | − | 0.104357i | \(-0.0332784\pi\) |
−0.587646 | + | 0.809118i | \(0.699945\pi\) | |||||||
\(152\) | 5.89898 | 0.478470 | ||||||||
\(153\) | 5.84847 | + | 6.84072i | 0.472821 | + | 0.553039i | ||||
\(154\) | 0.550510 | 0.0443614 | ||||||||
\(155\) | −1.00000 | − | 1.73205i | −0.0803219 | − | 0.139122i | ||||
\(156\) | 7.67423 | − | 0.707107i | 0.614431 | − | 0.0566139i | ||||
\(157\) | −4.67423 | + | 8.09601i | −0.373045 | + | 0.646132i | −0.990032 | − | 0.140841i | \(-0.955019\pi\) |
0.616988 | + | 0.786973i | \(0.288353\pi\) | |||||||
\(158\) | 1.00000 | − | 1.73205i | 0.0795557 | − | 0.137795i | ||||
\(159\) | 0.977296 | − | 2.12132i | 0.0775046 | − | 0.168232i | ||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | −2.44949 | −0.193047 | ||||||||
\(162\) | −8.39898 | + | 3.23375i | −0.659886 | + | 0.254067i | ||||
\(163\) | 2.00000 | 0.156652 | 0.0783260 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783260 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(164\) | 5.72474 | + | 9.91555i | 0.447027 | + | 0.774274i | ||||
\(165\) | 0.398979 | − | 0.866025i | 0.0310605 | − | 0.0674200i | ||||
\(166\) | −3.55051 | + | 6.14966i | −0.275573 | + | 0.477307i | ||||
\(167\) | 12.6742 | − | 21.9524i | 0.980762 | − | 1.69873i | 0.321325 | − | 0.946969i | \(-0.395872\pi\) |
0.659437 | − | 0.751760i | \(-0.270795\pi\) | |||||||
\(168\) | −1.72474 | + | 0.158919i | −0.133067 | + | 0.0122608i | ||||
\(169\) | −3.39898 | − | 5.88721i | −0.261460 | − | 0.452862i | ||||
\(170\) | 3.00000 | 0.230089 | ||||||||
\(171\) | 11.5000 | + | 13.4511i | 0.879427 | + | 1.02863i | ||||
\(172\) | −5.89898 | −0.449793 | ||||||||
\(173\) | 3.00000 | + | 5.19615i | 0.228086 | + | 0.395056i | 0.957241 | − | 0.289292i | \(-0.0934200\pi\) |
−0.729155 | + | 0.684349i | \(0.760087\pi\) | |||||||
\(174\) | 2.44949 | + | 3.46410i | 0.185695 | + | 0.262613i | ||||
\(175\) | −0.500000 | + | 0.866025i | −0.0377964 | + | 0.0654654i | ||||
\(176\) | 0.275255 | − | 0.476756i | 0.0207481 | − | 0.0359368i | ||||
\(177\) | −7.89898 | − | 11.1708i | −0.593724 | − | 0.839652i | ||||
\(178\) | −5.44949 | − | 9.43879i | −0.408457 | − | 0.707467i | ||||
\(179\) | 6.00000 | 0.448461 | 0.224231 | − | 0.974536i | \(-0.428013\pi\) | ||||
0.224231 | + | 0.974536i | \(0.428013\pi\) | |||||||
\(180\) | −1.00000 | + | 2.82843i | −0.0745356 | + | 0.210819i | ||||
\(181\) | 17.7980 | 1.32291 | 0.661456 | − | 0.749984i | \(-0.269939\pi\) | ||||
0.661456 | + | 0.749984i | \(0.269939\pi\) | |||||||
\(182\) | 2.22474 | + | 3.85337i | 0.164909 | + | 0.285631i | ||||
\(183\) | −9.22474 | + | 0.849971i | −0.681913 | + | 0.0628317i | ||||
\(184\) | −1.22474 | + | 2.12132i | −0.0902894 | + | 0.156386i | ||||
\(185\) | 0.775255 | − | 1.34278i | 0.0569979 | − | 0.0987232i | ||||
\(186\) | 1.44949 | − | 3.14626i | 0.106282 | − | 0.230695i | ||||
\(187\) | −0.825765 | − | 1.43027i | −0.0603859 | − | 0.104592i | ||||
\(188\) | −9.79796 | −0.714590 | ||||||||
\(189\) | −3.72474 | − | 3.62302i | −0.270935 | − | 0.263536i | ||||
\(190\) | 5.89898 | 0.427957 | ||||||||
\(191\) | −3.55051 | − | 6.14966i | −0.256906 | − | 0.444974i | 0.708506 | − | 0.705705i | \(-0.249370\pi\) |
−0.965411 | + | 0.260731i | \(0.916036\pi\) | |||||||
\(192\) | −0.724745 | + | 1.57313i | −0.0523040 | + | 0.113531i | ||||
\(193\) | −0.724745 | + | 1.25529i | −0.0521683 | + | 0.0903581i | −0.890930 | − | 0.454140i | \(-0.849947\pi\) |
0.838762 | + | 0.544498i | \(0.183280\pi\) | |||||||
\(194\) | −7.84847 | + | 13.5939i | −0.563487 | + | 0.975989i | ||||
\(195\) | 7.67423 | − | 0.707107i | 0.549563 | − | 0.0506370i | ||||
\(196\) | −0.500000 | − | 0.866025i | −0.0357143 | − | 0.0618590i | ||||
\(197\) | 7.34847 | 0.523557 | 0.261778 | − | 0.965128i | \(-0.415691\pi\) | ||||
0.261778 | + | 0.965128i | \(0.415691\pi\) | |||||||
\(198\) | 1.62372 | − | 0.301783i | 0.115393 | − | 0.0214468i | ||||
\(199\) | 6.65153 | 0.471515 | 0.235757 | − | 0.971812i | \(-0.424243\pi\) | ||||
0.235757 | + | 0.971812i | \(0.424243\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | −13.6969 | − | 19.3704i | −0.966108 | − | 1.36628i | ||||
\(202\) | 2.44949 | − | 4.24264i | 0.172345 | − | 0.298511i | ||||
\(203\) | −1.22474 | + | 2.12132i | −0.0859602 | + | 0.148888i | ||||
\(204\) | 3.00000 | + | 4.24264i | 0.210042 | + | 0.297044i | ||||
\(205\) | 5.72474 | + | 9.91555i | 0.399834 | + | 0.692532i | ||||
\(206\) | −20.2474 | −1.41071 | ||||||||
\(207\) | −7.22474 | + | 1.34278i | −0.502154 | + | 0.0933298i | ||||
\(208\) | 4.44949 | 0.308517 | ||||||||
\(209\) | −1.62372 | − | 2.81237i | −0.112315 | − | 0.194536i | ||||
\(210\) | −1.72474 | + | 0.158919i | −0.119019 | + | 0.0109664i | ||||
\(211\) | 3.34847 | − | 5.79972i | 0.230518 | − | 0.399269i | −0.727443 | − | 0.686169i | \(-0.759291\pi\) |
0.957961 | + | 0.286899i | \(0.0926246\pi\) | |||||||
\(212\) | 0.674235 | − | 1.16781i | 0.0463066 | − | 0.0802054i | ||||
\(213\) | 6.12372 | − | 13.2922i | 0.419591 | − | 0.910764i | ||||
\(214\) | 3.39898 | + | 5.88721i | 0.232349 | + | 0.402441i | ||||
\(215\) | −5.89898 | −0.402307 | ||||||||
\(216\) | −5.00000 | + | 1.41421i | −0.340207 | + | 0.0962250i | ||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | −6.22474 | − | 10.7816i | −0.421593 | − | 0.730220i | ||||
\(219\) | 8.62372 | − | 18.7187i | 0.582737 | − | 1.26489i | ||||
\(220\) | 0.275255 | − | 0.476756i | 0.0185577 | − | 0.0321429i | ||||
\(221\) | 6.67423 | − | 11.5601i | 0.448958 | − | 0.777617i | ||||
\(222\) | 2.67423 | − | 0.246405i | 0.179483 | − | 0.0165376i | ||||
\(223\) | −3.32577 | − | 5.76039i | −0.222710 | − | 0.385745i | 0.732920 | − | 0.680315i | \(-0.238157\pi\) |
−0.955630 | + | 0.294570i | \(0.904824\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −1.00000 | + | 2.82843i | −0.0666667 | + | 0.188562i | ||||
\(226\) | 16.8990 | 1.12410 | ||||||||
\(227\) | 12.5227 | + | 21.6900i | 0.831161 | + | 1.43961i | 0.897118 | + | 0.441791i | \(0.145657\pi\) |
−0.0659571 | + | 0.997822i | \(0.521010\pi\) | |||||||
\(228\) | 5.89898 | + | 8.34242i | 0.390669 | + | 0.552490i | ||||
\(229\) | −0.325765 | + | 0.564242i | −0.0215272 | + | 0.0372862i | −0.876588 | − | 0.481241i | \(-0.840186\pi\) |
0.855061 | + | 0.518527i | \(0.173520\pi\) | |||||||
\(230\) | −1.22474 | + | 2.12132i | −0.0807573 | + | 0.139876i | ||||
\(231\) | 0.550510 | + | 0.778539i | 0.0362209 | + | 0.0512241i | ||||
\(232\) | 1.22474 | + | 2.12132i | 0.0804084 | + | 0.139272i | ||||
\(233\) | −18.5505 | −1.21528 | −0.607642 | − | 0.794211i | \(-0.707885\pi\) | ||||
−0.607642 | + | 0.794211i | \(0.707885\pi\) | |||||||
\(234\) | 8.67423 | + | 10.1459i | 0.567052 | + | 0.663258i | ||||
\(235\) | −9.79796 | −0.639148 | ||||||||
\(236\) | −3.94949 | − | 6.84072i | −0.257090 | − | 0.445293i | ||||
\(237\) | 3.44949 | − | 0.317837i | 0.224068 | − | 0.0206457i | ||||
\(238\) | −1.50000 | + | 2.59808i | −0.0972306 | + | 0.168408i | ||||
\(239\) | −6.55051 | + | 11.3458i | −0.423717 | + | 0.733900i | −0.996300 | − | 0.0859473i | \(-0.972608\pi\) |
0.572582 | + | 0.819847i | \(0.305942\pi\) | |||||||
\(240\) | −0.724745 | + | 1.57313i | −0.0467821 | + | 0.101545i | ||||
\(241\) | −6.17423 | − | 10.6941i | −0.397717 | − | 0.688867i | 0.595726 | − | 0.803187i | \(-0.296864\pi\) |
−0.993444 | + | 0.114321i | \(0.963531\pi\) | |||||||
\(242\) | 10.6969 | 0.687625 | ||||||||
\(243\) | −12.9722 | − | 8.64420i | −0.832167 | − | 0.554526i | ||||
\(244\) | −5.34847 | −0.342401 | ||||||||
\(245\) | −0.500000 | − | 0.866025i | −0.0319438 | − | 0.0553283i | ||||
\(246\) | −8.29796 | + | 18.0116i | −0.529059 | + | 1.14838i | ||||
\(247\) | 13.1237 | − | 22.7310i | 0.835043 | − | 1.44634i | ||||
\(248\) | 1.00000 | − | 1.73205i | 0.0635001 | − | 0.109985i | ||||
\(249\) | −12.2474 | + | 1.12848i | −0.776151 | + | 0.0715148i | ||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | −13.8990 | −0.877296 | −0.438648 | − | 0.898659i | \(-0.644542\pi\) | ||||
−0.438648 | + | 0.898659i | \(0.644542\pi\) | |||||||
\(252\) | −1.94949 | − | 2.28024i | −0.122806 | − | 0.143642i | ||||
\(253\) | 1.34847 | 0.0847775 | ||||||||
\(254\) | 6.57321 | + | 11.3851i | 0.412440 | + | 0.714367i | ||||
\(255\) | 3.00000 | + | 4.24264i | 0.187867 | + | 0.265684i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 2.84847 | − | 4.93369i | 0.177683 | − | 0.307755i | −0.763404 | − | 0.645922i | \(-0.776473\pi\) |
0.941086 | + | 0.338166i | \(0.109807\pi\) | |||||||
\(258\) | −5.89898 | − | 8.34242i | −0.367254 | − | 0.519376i | ||||
\(259\) | 0.775255 | + | 1.34278i | 0.0481720 | + | 0.0834364i | ||||
\(260\) | 4.44949 | 0.275946 | ||||||||
\(261\) | −2.44949 | + | 6.92820i | −0.151620 | + | 0.428845i | ||||
\(262\) | −8.69694 | −0.537299 | ||||||||
\(263\) | 0.674235 | + | 1.16781i | 0.0415751 | + | 0.0720102i | 0.886064 | − | 0.463563i | \(-0.153429\pi\) |
−0.844489 | + | 0.535573i | \(0.820096\pi\) | |||||||
\(264\) | 0.949490 | − | 0.0874863i | 0.0584371 | − | 0.00538441i | ||||
\(265\) | 0.674235 | − | 1.16781i | 0.0414179 | − | 0.0717379i | ||||
\(266\) | −2.94949 | + | 5.10867i | −0.180845 | + | 0.313232i | ||||
\(267\) | 7.89898 | − | 17.1455i | 0.483410 | − | 1.04929i | ||||
\(268\) | −6.84847 | − | 11.8619i | −0.418337 | − | 0.724581i | ||||
\(269\) | 23.1464 | 1.41126 | 0.705631 | − | 0.708579i | \(-0.250664\pi\) | ||||
0.705631 | + | 0.708579i | \(0.250664\pi\) | |||||||
\(270\) | −5.00000 | + | 1.41421i | −0.304290 | + | 0.0860663i | ||||
\(271\) | 21.3485 | 1.29683 | 0.648414 | − | 0.761288i | \(-0.275433\pi\) | ||||
0.648414 | + | 0.761288i | \(0.275433\pi\) | |||||||
\(272\) | 1.50000 | + | 2.59808i | 0.0909509 | + | 0.157532i | ||||
\(273\) | −3.22474 | + | 6.99964i | −0.195170 | + | 0.423637i | ||||
\(274\) | 1.62372 | − | 2.81237i | 0.0980928 | − | 0.169902i | ||||
\(275\) | 0.275255 | − | 0.476756i | 0.0165985 | − | 0.0287495i | ||||
\(276\) | −4.22474 | + | 0.389270i | −0.254300 | + | 0.0234313i | ||||
\(277\) | −1.00000 | − | 1.73205i | −0.0600842 | − | 0.104069i | 0.834419 | − | 0.551131i | \(-0.185804\pi\) |
−0.894503 | + | 0.447062i | \(0.852470\pi\) | |||||||
\(278\) | −8.79796 | −0.527667 | ||||||||
\(279\) | 5.89898 | − | 1.09638i | 0.353163 | − | 0.0656383i | ||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 12.0000 | + | 20.7846i | 0.715860 | + | 1.23991i | 0.962627 | + | 0.270831i | \(0.0872985\pi\) |
−0.246767 | + | 0.969075i | \(0.579368\pi\) | |||||||
\(282\) | −9.79796 | − | 13.8564i | −0.583460 | − | 0.825137i | ||||
\(283\) | 8.00000 | − | 13.8564i | 0.475551 | − | 0.823678i | −0.524057 | − | 0.851683i | \(-0.675582\pi\) |
0.999608 | + | 0.0280052i | \(0.00891551\pi\) | |||||||
\(284\) | 4.22474 | − | 7.31747i | 0.250692 | − | 0.434212i | ||||
\(285\) | 5.89898 | + | 8.34242i | 0.349425 | + | 0.494162i | ||||
\(286\) | −1.22474 | − | 2.12132i | −0.0724207 | − | 0.125436i | ||||
\(287\) | −11.4495 | −0.675842 | ||||||||
\(288\) | −2.94949 | + | 0.548188i | −0.173800 | + | 0.0323023i | ||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 1.22474 | + | 2.12132i | 0.0719195 | + | 0.124568i | ||||
\(291\) | −27.0732 | + | 2.49454i | −1.58706 | + | 0.146232i | ||||
\(292\) | 5.94949 | − | 10.3048i | 0.348168 | − | 0.603044i | ||||
\(293\) | 14.5732 | − | 25.2415i | 0.851376 | − | 1.47463i | −0.0285903 | − | 0.999591i | \(-0.509102\pi\) |
0.879967 | − | 0.475036i | \(-0.157565\pi\) | |||||||
\(294\) | 0.724745 | − | 1.57313i | 0.0422680 | − | 0.0917469i | ||||
\(295\) | −3.94949 | − | 6.84072i | −0.229948 | − | 0.398282i | ||||
\(296\) | 1.55051 | 0.0901216 | ||||||||
\(297\) | 2.05051 | + | 1.99451i | 0.118983 | + | 0.115733i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.44949 | + | 9.43879i | 0.315152 | + | 0.545859i | ||||
\(300\) | −0.724745 | + | 1.57313i | −0.0418432 | + | 0.0908248i | ||||
\(301\) | 2.94949 | − | 5.10867i | 0.170006 | − | 0.294459i | ||||
\(302\) | −5.00000 | + | 8.66025i | −0.287718 | + | 0.498342i | ||||
\(303\) | 8.44949 | − | 0.778539i | 0.485411 | − | 0.0447259i | ||||
\(304\) | 2.94949 | + | 5.10867i | 0.169165 | + | 0.293002i | ||||
\(305\) | −5.34847 | −0.306252 | ||||||||
\(306\) | −3.00000 | + | 8.48528i | −0.171499 | + | 0.485071i | ||||
\(307\) | −27.4495 | −1.56663 | −0.783313 | − | 0.621628i | \(-0.786472\pi\) | ||||
−0.783313 | + | 0.621628i | \(0.786472\pi\) | |||||||
\(308\) | 0.275255 | + | 0.476756i | 0.0156841 | + | 0.0271657i | ||||
\(309\) | −20.2474 | − | 28.6342i | −1.15184 | − | 1.62894i | ||||
\(310\) | 1.00000 | − | 1.73205i | 0.0567962 | − | 0.0983739i | ||||
\(311\) | 0.550510 | − | 0.953512i | 0.0312166 | − | 0.0540687i | −0.849995 | − | 0.526791i | \(-0.823395\pi\) |
0.881212 | + | 0.472722i | \(0.156729\pi\) | |||||||
\(312\) | 4.44949 | + | 6.29253i | 0.251903 | + | 0.356244i | ||||
\(313\) | 4.60102 | + | 7.96920i | 0.260065 | + | 0.450446i | 0.966259 | − | 0.257573i | \(-0.0829227\pi\) |
−0.706194 | + | 0.708018i | \(0.749589\pi\) | |||||||
\(314\) | −9.34847 | −0.527565 | ||||||||
\(315\) | −1.94949 | − | 2.28024i | −0.109841 | − | 0.128477i | ||||
\(316\) | 2.00000 | 0.112509 | ||||||||
\(317\) | −0.123724 | − | 0.214297i | −0.00694905 | − | 0.0120361i | 0.862530 | − | 0.506006i | \(-0.168879\pi\) |
−0.869479 | + | 0.493970i | \(0.835545\pi\) | |||||||
\(318\) | 2.32577 | − | 0.214297i | 0.130422 | − | 0.0120172i | ||||
\(319\) | 0.674235 | − | 1.16781i | 0.0377499 | − | 0.0653847i | ||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | −4.92679 | + | 10.6941i | −0.274986 | + | 0.596886i | ||||
\(322\) | −1.22474 | − | 2.12132i | −0.0682524 | − | 0.118217i | ||||
\(323\) | 17.6969 | 0.984684 | ||||||||
\(324\) | −7.00000 | − | 5.65685i | −0.388889 | − | 0.314270i | ||||
\(325\) | 4.44949 | 0.246813 | ||||||||
\(326\) | 1.00000 | + | 1.73205i | 0.0553849 | + | 0.0959294i | ||||
\(327\) | 9.02270 | − | 19.5847i | 0.498957 | − | 1.08304i | ||||
\(328\) | −5.72474 | + | 9.91555i | −0.316096 | + | 0.547495i | ||||
\(329\) | 4.89898 | − | 8.48528i | 0.270089 | − | 0.467809i | ||||
\(330\) | 0.949490 | − | 0.0874863i | 0.0522677 | − | 0.00481596i | ||||
\(331\) | −5.34847 | − | 9.26382i | −0.293978 | − | 0.509186i | 0.680768 | − | 0.732499i | \(-0.261646\pi\) |
−0.974747 | + | 0.223313i | \(0.928313\pi\) | |||||||
\(332\) | −7.10102 | −0.389719 | ||||||||
\(333\) | 3.02270 | + | 3.53553i | 0.165643 | + | 0.193746i | ||||
\(334\) | 25.3485 | 1.38701 | ||||||||
\(335\) | −6.84847 | − | 11.8619i | −0.374172 | − | 0.648085i | ||||
\(336\) | −1.00000 | − | 1.41421i | −0.0545545 | − | 0.0771517i | ||||
\(337\) | −9.72474 | + | 16.8438i | −0.529741 | + | 0.917538i | 0.469658 | + | 0.882849i | \(0.344377\pi\) |
−0.999398 | + | 0.0346890i | \(0.988956\pi\) | |||||||
\(338\) | 3.39898 | − | 5.88721i | 0.184880 | − | 0.320222i | ||||
\(339\) | 16.8990 | + | 23.8988i | 0.917827 | + | 1.29800i | ||||
\(340\) | 1.50000 | + | 2.59808i | 0.0813489 | + | 0.140900i | ||||
\(341\) | −1.10102 | −0.0596236 | ||||||||
\(342\) | −5.89898 | + | 16.6848i | −0.318980 | + | 0.902212i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −2.94949 | − | 5.10867i | −0.159026 | − | 0.275441i | ||||
\(345\) | −4.22474 | + | 0.389270i | −0.227453 | + | 0.0209576i | ||||
\(346\) | −3.00000 | + | 5.19615i | −0.161281 | + | 0.279347i | ||||
\(347\) | −9.94949 | + | 17.2330i | −0.534117 | + | 0.925117i | 0.465089 | + | 0.885264i | \(0.346022\pi\) |
−0.999206 | + | 0.0398531i | \(0.987311\pi\) | |||||||
\(348\) | −1.77526 | + | 3.85337i | −0.0951637 | + | 0.206562i | ||||
\(349\) | −15.0227 | − | 26.0201i | −0.804147 | − | 1.39282i | −0.916865 | − | 0.399196i | \(-0.869289\pi\) |
0.112719 | − | 0.993627i | \(-0.464044\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −5.67423 | + | 22.4131i | −0.302868 | + | 1.19632i | ||||
\(352\) | 0.550510 | 0.0293423 | ||||||||
\(353\) | −5.84847 | − | 10.1298i | −0.311283 | − | 0.539157i | 0.667358 | − | 0.744737i | \(-0.267425\pi\) |
−0.978640 | + | 0.205580i | \(0.934092\pi\) | |||||||
\(354\) | 5.72474 | − | 12.4261i | 0.304267 | − | 0.660442i | ||||
\(355\) | 4.22474 | − | 7.31747i | 0.224226 | − | 0.388371i | ||||
\(356\) | 5.44949 | − | 9.43879i | 0.288822 | − | 0.500255i | ||||
\(357\) | −5.17423 | + | 0.476756i | −0.273850 | + | 0.0252326i | ||||
\(358\) | 3.00000 | + | 5.19615i | 0.158555 | + | 0.274625i | ||||
\(359\) | 22.0454 | 1.16351 | 0.581756 | − | 0.813363i | \(-0.302366\pi\) | ||||
0.581756 | + | 0.813363i | \(0.302366\pi\) | |||||||
\(360\) | −2.94949 | + | 0.548188i | −0.155452 | + | 0.0288921i | ||||
\(361\) | 15.7980 | 0.831472 | ||||||||
\(362\) | 8.89898 | + | 15.4135i | 0.467720 | + | 0.810115i | ||||
\(363\) | 10.6969 | + | 15.1278i | 0.561444 | + | 0.794001i | ||||
\(364\) | −2.22474 | + | 3.85337i | −0.116608 | + | 0.201972i | ||||
\(365\) | 5.94949 | − | 10.3048i | 0.311411 | − | 0.539379i | ||||
\(366\) | −5.34847 | − | 7.56388i | −0.279569 | − | 0.395370i | ||||
\(367\) | −7.67423 | − | 13.2922i | −0.400592 | − | 0.693845i | 0.593206 | − | 0.805051i | \(-0.297862\pi\) |
−0.993797 | + | 0.111206i | \(0.964529\pi\) | |||||||
\(368\) | −2.44949 | −0.127688 | ||||||||
\(369\) | −33.7702 | + | 6.27647i | −1.75800 | + | 0.326740i | ||||
\(370\) | 1.55051 | 0.0806072 | ||||||||
\(371\) | 0.674235 | + | 1.16781i | 0.0350045 | + | 0.0606296i | ||||
\(372\) | 3.44949 | − | 0.317837i | 0.178848 | − | 0.0164791i | ||||
\(373\) | 13.4495 | − | 23.2952i | 0.696388 | − | 1.20618i | −0.273322 | − | 0.961923i | \(-0.588123\pi\) |
0.969710 | − | 0.244257i | \(-0.0785441\pi\) | |||||||
\(374\) | 0.825765 | − | 1.43027i | 0.0426993 | − | 0.0739574i | ||||
\(375\) | −0.724745 | + | 1.57313i | −0.0374257 | + | 0.0812362i | ||||
\(376\) | −4.89898 | − | 8.48528i | −0.252646 | − | 0.437595i | ||||
\(377\) | 10.8990 | 0.561326 | ||||||||
\(378\) | 1.27526 | − | 5.03723i | 0.0655920 | − | 0.259087i | ||||
\(379\) | 2.55051 | 0.131011 | 0.0655055 | − | 0.997852i | \(-0.479134\pi\) | ||||
0.0655055 | + | 0.997852i | \(0.479134\pi\) | |||||||
\(380\) | 2.94949 | + | 5.10867i | 0.151306 | + | 0.262069i | ||||
\(381\) | −9.52781 | + | 20.6811i | −0.488124 | + | 1.05952i | ||||
\(382\) | 3.55051 | − | 6.14966i | 0.181660 | − | 0.314644i | ||||
\(383\) | −13.3485 | + | 23.1202i | −0.682075 | + | 1.18139i | 0.292272 | + | 0.956335i | \(0.405589\pi\) |
−0.974347 | + | 0.225053i | \(0.927744\pi\) | |||||||
\(384\) | −1.72474 | + | 0.158919i | −0.0880155 | + | 0.00810978i | ||||
\(385\) | 0.275255 | + | 0.476756i | 0.0140283 | + | 0.0242977i | ||||
\(386\) | −1.44949 | −0.0737771 | ||||||||
\(387\) | 5.89898 | − | 16.6848i | 0.299862 | − | 0.848138i | ||||
\(388\) | −15.6969 | −0.796891 | ||||||||
\(389\) | −15.7980 | − | 27.3629i | −0.800988 | − | 1.38735i | −0.918966 | − | 0.394336i | \(-0.870975\pi\) |
0.117978 | − | 0.993016i | \(-0.462359\pi\) | |||||||
\(390\) | 4.44949 | + | 6.29253i | 0.225309 | + | 0.318635i | ||||
\(391\) | −3.67423 | + | 6.36396i | −0.185814 | + | 0.321839i | ||||
\(392\) | 0.500000 | − | 0.866025i | 0.0252538 | − | 0.0437409i | ||||
\(393\) | −8.69694 | − | 12.2993i | −0.438703 | − | 0.620419i | ||||
\(394\) | 3.67423 | + | 6.36396i | 0.185105 | + | 0.320612i | ||||
\(395\) | 2.00000 | 0.100631 | ||||||||
\(396\) | 1.07321 | + | 1.25529i | 0.0539310 | + | 0.0630809i | ||||
\(397\) | −32.0454 | −1.60831 | −0.804156 | − | 0.594418i | \(-0.797383\pi\) | ||||
−0.804156 | + | 0.594418i | \(0.797383\pi\) | |||||||
\(398\) | 3.32577 | + | 5.76039i | 0.166706 | + | 0.288742i | ||||
\(399\) | −10.1742 | + | 0.937458i | −0.509349 | + | 0.0469316i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | −4.50000 | + | 7.79423i | −0.224719 | + | 0.389225i | −0.956235 | − | 0.292599i | \(-0.905480\pi\) |
0.731516 | + | 0.681824i | \(0.238813\pi\) | |||||||
\(402\) | 9.92679 | − | 21.5471i | 0.495103 | − | 1.07467i | ||||
\(403\) | −4.44949 | − | 7.70674i | −0.221645 | − | 0.383900i | ||||
\(404\) | 4.89898 | 0.243733 | ||||||||
\(405\) | −7.00000 | − | 5.65685i | −0.347833 | − | 0.281091i | ||||
\(406\) | −2.44949 | −0.121566 | ||||||||
\(407\) | −0.426786 | − | 0.739215i | −0.0211550 | − | 0.0366415i | ||||
\(408\) | −2.17423 | + | 4.71940i | −0.107641 | + | 0.233645i | ||||
\(409\) | 0.376276 | − | 0.651729i | 0.0186056 | − | 0.0322259i | −0.856573 | − | 0.516026i | \(-0.827411\pi\) |
0.875178 | + | 0.483800i | \(0.160744\pi\) | |||||||
\(410\) | −5.72474 | + | 9.91555i | −0.282725 | + | 0.489694i | ||||
\(411\) | 5.60102 | − | 0.516080i | 0.276278 | − | 0.0254564i | ||||
\(412\) | −10.1237 | − | 17.5348i | −0.498760 | − | 0.863878i | ||||
\(413\) | 7.89898 | 0.388683 | ||||||||
\(414\) | −4.77526 | − | 5.58542i | −0.234691 | − | 0.274509i | ||||
\(415\) | −7.10102 | −0.348575 | ||||||||
\(416\) | 2.22474 | + | 3.85337i | 0.109077 | + | 0.188927i | ||||
\(417\) | −8.79796 | − | 12.4422i | −0.430838 | − | 0.609297i | ||||
\(418\) | 1.62372 | − | 2.81237i | 0.0794190 | − | 0.137558i | ||||
\(419\) | 6.79796 | − | 11.7744i | 0.332102 | − | 0.575218i | −0.650822 | − | 0.759231i | \(-0.725576\pi\) |
0.982924 | + | 0.184013i | \(0.0589088\pi\) | |||||||
\(420\) | −1.00000 | − | 1.41421i | −0.0487950 | − | 0.0690066i | ||||
\(421\) | 9.22474 | + | 15.9777i | 0.449587 | + | 0.778707i | 0.998359 | − | 0.0572650i | \(-0.0182380\pi\) |
−0.548772 | + | 0.835972i | \(0.684905\pi\) | |||||||
\(422\) | 6.69694 | 0.326002 | ||||||||
\(423\) | 9.79796 | − | 27.7128i | 0.476393 | − | 1.34744i | ||||
\(424\) | 1.34847 | 0.0654875 | ||||||||
\(425\) | 1.50000 | + | 2.59808i | 0.0727607 | + | 0.126025i | ||||
\(426\) | 14.5732 | − | 1.34278i | 0.706075 | − | 0.0650580i | ||||
\(427\) | 2.67423 | − | 4.63191i | 0.129415 | − | 0.224154i | ||||
\(428\) | −3.39898 | + | 5.88721i | −0.164296 | + | 0.284569i | ||||
\(429\) | 1.77526 | − | 3.85337i | 0.0857101 | − | 0.186043i | ||||
\(430\) | −2.94949 | − | 5.10867i | −0.142237 | − | 0.246362i | ||||
\(431\) | −12.4949 | −0.601858 | −0.300929 | − | 0.953647i | \(-0.597297\pi\) | ||||
−0.300929 | + | 0.953647i | \(0.597297\pi\) | |||||||
\(432\) | −3.72474 | − | 3.62302i | −0.179207 | − | 0.174313i | ||||
\(433\) | −32.5959 | −1.56646 | −0.783230 | − | 0.621732i | \(-0.786429\pi\) | ||||
−0.783230 | + | 0.621732i | \(0.786429\pi\) | |||||||
\(434\) | 1.00000 | + | 1.73205i | 0.0480015 | + | 0.0831411i | ||||
\(435\) | −1.77526 | + | 3.85337i | −0.0851170 | + | 0.184755i | ||||
\(436\) | 6.22474 | − | 10.7816i | 0.298111 | − | 0.516344i | ||||
\(437\) | −7.22474 | + | 12.5136i | −0.345606 | + | 0.598608i | ||||
\(438\) | 20.5227 | − | 1.89097i | 0.980613 | − | 0.0903540i | ||||
\(439\) | −13.6742 | − | 23.6845i | −0.652636 | − | 1.13040i | −0.982481 | − | 0.186363i | \(-0.940330\pi\) |
0.329845 | − | 0.944035i | \(-0.393003\pi\) | |||||||
\(440\) | 0.550510 | 0.0262445 | ||||||||
\(441\) | 2.94949 | − | 0.548188i | 0.140452 | − | 0.0261042i | ||||
\(442\) | 13.3485 | 0.634922 | ||||||||
\(443\) | 17.8485 | + | 30.9145i | 0.848006 | + | 1.46879i | 0.882985 | + | 0.469402i | \(0.155530\pi\) |
−0.0349782 | + | 0.999388i | \(0.511136\pi\) | |||||||
\(444\) | 1.55051 | + | 2.19275i | 0.0735840 | + | 0.104063i | ||||
\(445\) | 5.44949 | − | 9.43879i | 0.258331 | − | 0.447442i | ||||
\(446\) | 3.32577 | − | 5.76039i | 0.157480 | − | 0.272763i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.500000 | − | 0.866025i | −0.0236228 | − | 0.0409159i | ||||
\(449\) | −6.30306 | −0.297460 | −0.148730 | − | 0.988878i | \(-0.547519\pi\) | ||||
−0.148730 | + | 0.988878i | \(0.547519\pi\) | |||||||
\(450\) | −2.94949 | + | 0.548188i | −0.139040 | + | 0.0258418i | ||||
\(451\) | 6.30306 | 0.296800 | ||||||||
\(452\) | 8.44949 | + | 14.6349i | 0.397431 | + | 0.688370i | ||||
\(453\) | −17.2474 | + | 1.58919i | −0.810356 | + | 0.0746665i | ||||
\(454\) | −12.5227 | + | 21.6900i | −0.587720 | + | 1.01796i | ||||
\(455\) | −2.22474 | + | 3.85337i | −0.104298 | + | 0.180649i | ||||
\(456\) | −4.27526 | + | 9.27987i | −0.200207 | + | 0.434570i | ||||
\(457\) | 16.7247 | + | 28.9681i | 0.782351 | + | 1.35507i | 0.930569 | + | 0.366116i | \(0.119313\pi\) |
−0.148219 | + | 0.988955i | \(0.547354\pi\) | |||||||
\(458\) | −0.651531 | −0.0304440 | ||||||||
\(459\) | −15.0000 | + | 4.24264i | −0.700140 | + | 0.198030i | ||||
\(460\) | −2.44949 | −0.114208 | ||||||||
\(461\) | −3.67423 | − | 6.36396i | −0.171126 | − | 0.296399i | 0.767688 | − | 0.640824i | \(-0.221407\pi\) |
−0.938814 | + | 0.344425i | \(0.888074\pi\) | |||||||
\(462\) | −0.398979 | + | 0.866025i | −0.0185622 | + | 0.0402911i | ||||
\(463\) | 14.0000 | − | 24.2487i | 0.650635 | − | 1.12693i | −0.332334 | − | 0.943162i | \(-0.607836\pi\) |
0.982969 | − | 0.183771i | \(-0.0588306\pi\) | |||||||
\(464\) | −1.22474 | + | 2.12132i | −0.0568574 | + | 0.0984798i | ||||
\(465\) | 3.44949 | − | 0.317837i | 0.159966 | − | 0.0147393i | ||||
\(466\) | −9.27526 | − | 16.0652i | −0.429668 | − | 0.744207i | ||||
\(467\) | 23.9444 | 1.10801 | 0.554007 | − | 0.832512i | \(-0.313098\pi\) | ||||
0.554007 | + | 0.832512i | \(0.313098\pi\) | |||||||
\(468\) | −4.44949 | + | 12.5851i | −0.205678 | + | 0.581744i | ||||
\(469\) | 13.6969 | 0.632466 | ||||||||
\(470\) | −4.89898 | − | 8.48528i | −0.225973 | − | 0.391397i | ||||
\(471\) | −9.34847 | − | 13.2207i | −0.430755 | − | 0.609179i | ||||
\(472\) | 3.94949 | − | 6.84072i | 0.181790 | − | 0.314870i | ||||
\(473\) | −1.62372 | + | 2.81237i | −0.0746589 | + | 0.129313i | ||||
\(474\) | 2.00000 | + | 2.82843i | 0.0918630 | + | 0.129914i | ||||
\(475\) | 2.94949 | + | 5.10867i | 0.135332 | + | 0.234402i | ||||
\(476\) | −3.00000 | −0.137505 | ||||||||
\(477\) | 2.62883 | + | 3.07483i | 0.120366 | + | 0.140787i | ||||
\(478\) | −13.1010 | −0.599227 | ||||||||
\(479\) | 13.4722 | + | 23.3345i | 0.615560 | + | 1.06618i | 0.990286 | + | 0.139046i | \(0.0444036\pi\) |
−0.374726 | + | 0.927136i | \(0.622263\pi\) | |||||||
\(480\) | −1.72474 | + | 0.158919i | −0.0787235 | + | 0.00725361i | ||||
\(481\) | 3.44949 | − | 5.97469i | 0.157283 | − | 0.272422i | ||||
\(482\) | 6.17423 | − | 10.6941i | 0.281229 | − | 0.487102i | ||||
\(483\) | 1.77526 | − | 3.85337i | 0.0807769 | − | 0.175334i | ||||
\(484\) | 5.34847 | + | 9.26382i | 0.243112 | + | 0.421083i | ||||
\(485\) | −15.6969 | −0.712761 | ||||||||
\(486\) | 1.00000 | − | 15.5563i | 0.0453609 | − | 0.705650i | ||||
\(487\) | −22.4949 | −1.01934 | −0.509671 | − | 0.860370i | \(-0.670233\pi\) | ||||
−0.509671 | + | 0.860370i | \(0.670233\pi\) | |||||||
\(488\) | −2.67423 | − | 4.63191i | −0.121057 | − | 0.209677i | ||||
\(489\) | −1.44949 | + | 3.14626i | −0.0655482 | + | 0.142279i | ||||
\(490\) | 0.500000 | − | 0.866025i | 0.0225877 | − | 0.0391230i | ||||
\(491\) | −5.17423 | + | 8.96204i | −0.233510 | + | 0.404451i | −0.958839 | − | 0.283952i | \(-0.908354\pi\) |
0.725329 | + | 0.688403i | \(0.241688\pi\) | |||||||
\(492\) | −19.7474 | + | 1.81954i | −0.890284 | + | 0.0820311i | ||||
\(493\) | 3.67423 | + | 6.36396i | 0.165479 | + | 0.286618i | ||||
\(494\) | 26.2474 | 1.18093 | ||||||||
\(495\) | 1.07321 | + | 1.25529i | 0.0482374 | + | 0.0564213i | ||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 4.22474 | + | 7.31747i | 0.189506 | + | 0.328234i | ||||
\(498\) | −7.10102 | − | 10.0424i | −0.318204 | − | 0.450009i | ||||
\(499\) | 18.6237 | − | 32.2572i | 0.833712 | − | 1.44403i | −0.0613621 | − | 0.998116i | \(-0.519544\pi\) |
0.895074 | − | 0.445917i | \(-0.147122\pi\) | |||||||
\(500\) | −0.500000 | + | 0.866025i | −0.0223607 | + | 0.0387298i | ||||
\(501\) | 25.3485 | + | 35.8481i | 1.13249 | + | 1.60158i | ||||
\(502\) | −6.94949 | − | 12.0369i | −0.310171 | − | 0.537232i | ||||
\(503\) | 23.3939 | 1.04308 | 0.521541 | − | 0.853226i | \(-0.325357\pi\) | ||||
0.521541 | + | 0.853226i | \(0.325357\pi\) | |||||||
\(504\) | 1.00000 | − | 2.82843i | 0.0445435 | − | 0.125988i | ||||
\(505\) | 4.89898 | 0.218002 | ||||||||
\(506\) | 0.674235 | + | 1.16781i | 0.0299734 | + | 0.0519154i | ||||
\(507\) | 11.7247 | − | 1.08032i | 0.520714 | − | 0.0479788i | ||||
\(508\) | −6.57321 | + | 11.3851i | −0.291639 | + | 0.505134i | ||||
\(509\) | −5.87628 | + | 10.1780i | −0.260461 | + | 0.451132i | −0.966365 | − | 0.257176i | \(-0.917208\pi\) |
0.705903 | + | 0.708308i | \(0.250541\pi\) | |||||||
\(510\) | −2.17423 | + | 4.71940i | −0.0962767 | + | 0.208978i | ||||
\(511\) | 5.94949 | + | 10.3048i | 0.263190 | + | 0.455858i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −29.4949 | + | 8.34242i | −1.30223 | + | 0.368327i | ||||
\(514\) | 5.69694 | 0.251281 | ||||||||
\(515\) | −10.1237 | − | 17.5348i | −0.446105 | − | 0.772676i | ||||
\(516\) | 4.27526 | − | 9.27987i | 0.188208 | − | 0.408524i | ||||
\(517\) | −2.69694 | + | 4.67123i | −0.118611 | + | 0.205441i | ||||
\(518\) | −0.775255 | + | 1.34278i | −0.0340628 | + | 0.0589984i | ||||
\(519\) | −10.3485 | + | 0.953512i | −0.454247 | + | 0.0418545i | ||||
\(520\) | 2.22474 | + | 3.85337i | 0.0975615 | + | 0.168982i | ||||
\(521\) | 1.65153 | 0.0723549 | 0.0361774 | − | 0.999345i | \(-0.488482\pi\) | ||||
0.0361774 | + | 0.999345i | \(0.488482\pi\) | |||||||
\(522\) | −7.22474 | + | 1.34278i | −0.316218 | + | 0.0587719i | ||||
\(523\) | −29.5959 | −1.29414 | −0.647070 | − | 0.762431i | \(-0.724006\pi\) | ||||
−0.647070 | + | 0.762431i | \(0.724006\pi\) | |||||||
\(524\) | −4.34847 | − | 7.53177i | −0.189964 | − | 0.329027i | ||||
\(525\) | −1.00000 | − | 1.41421i | −0.0436436 | − | 0.0617213i | ||||
\(526\) | −0.674235 | + | 1.16781i | −0.0293980 | + | 0.0509189i | ||||
\(527\) | 3.00000 | − | 5.19615i | 0.130682 | − | 0.226348i | ||||
\(528\) | 0.550510 | + | 0.778539i | 0.0239579 | + | 0.0338816i | ||||
\(529\) | 8.50000 | + | 14.7224i | 0.369565 | + | 0.640106i | ||||
\(530\) | 1.34847 | 0.0585738 | ||||||||
\(531\) | 23.2980 | − | 4.33013i | 1.01105 | − | 0.187912i | ||||
\(532\) | −5.89898 | −0.255753 | ||||||||
\(533\) | 25.4722 | + | 44.1191i | 1.10332 | + | 1.91101i | ||||
\(534\) | 18.7980 | − | 1.73205i | 0.813467 | − | 0.0749532i | ||||
\(535\) | −3.39898 | + | 5.88721i | −0.146951 | + | 0.254526i | ||||
\(536\) | 6.84847 | − | 11.8619i | 0.295809 | − | 0.512356i | ||||
\(537\) | −4.34847 | + | 9.43879i | −0.187650 | + | 0.407314i | ||||
\(538\) | 11.5732 | + | 20.0454i | 0.498957 | + | 0.864218i | ||||
\(539\) | −0.550510 | −0.0237122 | ||||||||
\(540\) | −3.72474 | − | 3.62302i | −0.160287 | − | 0.155910i | ||||
\(541\) | 10.6969 | 0.459897 | 0.229949 | − | 0.973203i | \(-0.426144\pi\) | ||||
0.229949 | + | 0.973203i | \(0.426144\pi\) | |||||||
\(542\) | 10.6742 | + | 18.4883i | 0.458498 | + | 0.794141i | ||||
\(543\) | −12.8990 | + | 27.9985i | −0.553548 | + | 1.20153i | ||||
\(544\) | −1.50000 | + | 2.59808i | −0.0643120 | + | 0.111392i | ||||
\(545\) | 6.22474 | − | 10.7816i | 0.266639 | − | 0.461832i | ||||
\(546\) | −7.67423 | + | 0.707107i | −0.328427 | + | 0.0302614i | ||||
\(547\) | 7.84847 | + | 13.5939i | 0.335576 | + | 0.581235i | 0.983595 | − | 0.180389i | \(-0.0577356\pi\) |
−0.648019 | + | 0.761624i | \(0.724402\pi\) | |||||||
\(548\) | 3.24745 | 0.138724 | ||||||||
\(549\) | 5.34847 | − | 15.1278i | 0.228267 | − | 0.645637i | ||||
\(550\) | 0.550510 | 0.0234738 | ||||||||
\(551\) | 7.22474 | + | 12.5136i | 0.307784 | + | 0.533098i | ||||
\(552\) | −2.44949 | − | 3.46410i | −0.104257 | − | 0.147442i | ||||
\(553\) | −1.00000 | + | 1.73205i | −0.0425243 | + | 0.0736543i | ||||
\(554\) | 1.00000 | − | 1.73205i | 0.0424859 | − | 0.0735878i | ||||
\(555\) | 1.55051 | + | 2.19275i | 0.0658155 | + | 0.0930772i | ||||
\(556\) | −4.39898 | − | 7.61926i | −0.186558 | − | 0.323128i | ||||
\(557\) | −7.59592 | −0.321849 | −0.160925 | − | 0.986967i | \(-0.551448\pi\) | ||||
−0.160925 | + | 0.986967i | \(0.551448\pi\) | |||||||
\(558\) | 3.89898 | + | 4.56048i | 0.165057 | + | 0.193060i | ||||
\(559\) | −26.2474 | −1.11015 | ||||||||
\(560\) | −0.500000 | − | 0.866025i | −0.0211289 | − | 0.0365963i | ||||
\(561\) | 2.84847 | − | 0.262459i | 0.120262 | − | 0.0110810i | ||||
\(562\) | −12.0000 | + | 20.7846i | −0.506189 | + | 0.876746i | ||||
\(563\) | 17.9722 | − | 31.1288i | 0.757438 | − | 1.31192i | −0.186716 | − | 0.982414i | \(-0.559784\pi\) |
0.944153 | − | 0.329506i | \(-0.106882\pi\) | |||||||
\(564\) | 7.10102 | − | 15.4135i | 0.299007 | − | 0.649025i | ||||
\(565\) | 8.44949 | + | 14.6349i | 0.355473 | + | 0.615697i | ||||
\(566\) | 16.0000 | 0.672530 | ||||||||
\(567\) | 8.39898 | − | 3.23375i | 0.352724 | − | 0.135805i | ||||
\(568\) | 8.44949 | 0.354533 | ||||||||
\(569\) | 15.6464 | + | 27.1004i | 0.655932 | + | 1.13611i | 0.981659 | + | 0.190644i | \(0.0610577\pi\) |
−0.325727 | + | 0.945464i | \(0.605609\pi\) | |||||||
\(570\) | −4.27526 | + | 9.27987i | −0.179071 | + | 0.388691i | ||||
\(571\) | −12.1742 | + | 21.0864i | −0.509476 | + | 0.882438i | 0.490464 | + | 0.871462i | \(0.336827\pi\) |
−0.999940 | + | 0.0109766i | \(0.996506\pi\) | |||||||
\(572\) | 1.22474 | − | 2.12132i | 0.0512092 | − | 0.0886969i | ||||
\(573\) | 12.2474 | − | 1.12848i | 0.511645 | − | 0.0471431i | ||||
\(574\) | −5.72474 | − | 9.91555i | −0.238946 | − | 0.413867i | ||||
\(575\) | −2.44949 | −0.102151 | ||||||||
\(576\) | −1.94949 | − | 2.28024i | −0.0812287 | − | 0.0950100i | ||||
\(577\) | −29.8990 | −1.24471 | −0.622355 | − | 0.782735i | \(-0.713824\pi\) | ||||
−0.622355 | + | 0.782735i | \(0.713824\pi\) | |||||||
\(578\) | −4.00000 | − | 6.92820i | −0.166378 | − | 0.288175i | ||||
\(579\) | −1.44949 | − | 2.04989i | −0.0602387 | − | 0.0851904i | ||||
\(580\) | −1.22474 | + | 2.12132i | −0.0508548 | + | 0.0880830i | ||||
\(581\) | 3.55051 | − | 6.14966i | 0.147300 | − | 0.255131i | ||||
\(582\) | −15.6969 | − | 22.1988i | −0.650659 | − | 0.920171i | ||||
\(583\) | −0.371173 | − | 0.642891i | −0.0153724 | − | 0.0266258i | ||||
\(584\) | 11.8990 | 0.492383 | ||||||||
\(585\) | −4.44949 | + | 12.5851i | −0.183964 | + | 0.520328i | ||||
\(586\) | 29.1464 | 1.20403 | ||||||||
\(587\) | 7.37628 | + | 12.7761i | 0.304451 | + | 0.527325i | 0.977139 | − | 0.212601i | \(-0.0681935\pi\) |
−0.672688 | + | 0.739927i | \(0.734860\pi\) | |||||||
\(588\) | 1.72474 | − | 0.158919i | 0.0711273 | − | 0.00655369i | ||||
\(589\) | 5.89898 | − | 10.2173i | 0.243063 | − | 0.420998i | ||||
\(590\) | 3.94949 | − | 6.84072i | 0.162598 | − | 0.281628i | ||||
\(591\) | −5.32577 | + | 11.5601i | −0.219073 | + | 0.475520i | ||||
\(592\) | 0.775255 | + | 1.34278i | 0.0318628 | + | 0.0551880i | ||||
\(593\) | −2.20204 | −0.0904270 | −0.0452135 | − | 0.998977i | \(-0.514397\pi\) | ||||
−0.0452135 | + | 0.998977i | \(0.514397\pi\) | |||||||
\(594\) | −0.702041 | + | 2.77305i | −0.0288051 | + | 0.113780i | ||||
\(595\) | −3.00000 | −0.122988 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.82066 | + | 10.4637i | −0.197297 | + | 0.428252i | ||||
\(598\) | −5.44949 | + | 9.43879i | −0.222846 | + | 0.385981i | ||||
\(599\) | 3.79796 | − | 6.57826i | 0.155180 | − | 0.268780i | −0.777944 | − | 0.628333i | \(-0.783737\pi\) |
0.933125 | + | 0.359553i | \(0.117071\pi\) | |||||||
\(600\) | −1.72474 | + | 0.158919i | −0.0704124 | + | 0.00648783i | ||||
\(601\) | −7.27526 | − | 12.6011i | −0.296764 | − | 0.514010i | 0.678630 | − | 0.734480i | \(-0.262574\pi\) |
−0.975394 | + | 0.220470i | \(0.929241\pi\) | |||||||
\(602\) | 5.89898 | 0.240424 | ||||||||
\(603\) | 40.3990 | − | 7.50850i | 1.64517 | − | 0.305770i | ||||
\(604\) | −10.0000 | −0.406894 | ||||||||
\(605\) | 5.34847 | + | 9.26382i | 0.217446 | + | 0.376628i | ||||
\(606\) | 4.89898 | + | 6.92820i | 0.199007 | + | 0.281439i | ||||
\(607\) | −1.79796 | + | 3.11416i | −0.0729769 | + | 0.126400i | −0.900205 | − | 0.435467i | \(-0.856583\pi\) |
0.827228 | + | 0.561867i | \(0.189917\pi\) | |||||||
\(608\) | −2.94949 | + | 5.10867i | −0.119618 | + | 0.207184i | ||||
\(609\) | −2.44949 | − | 3.46410i | −0.0992583 | − | 0.140372i | ||||
\(610\) | −2.67423 | − | 4.63191i | −0.108277 | − | 0.187541i | ||||
\(611\) | −43.5959 | −1.76370 | ||||||||
\(612\) | −8.84847 | + | 1.64456i | −0.357678 | + | 0.0664776i | ||||
\(613\) | 31.3939 | 1.26799 | 0.633993 | − | 0.773338i | \(-0.281415\pi\) | ||||
0.633993 | + | 0.773338i | \(0.281415\pi\) | |||||||
\(614\) | −13.7247 | − | 23.7720i | −0.553886 | − | 0.959358i | ||||
\(615\) | −19.7474 | + | 1.81954i | −0.796294 | + | 0.0733708i | ||||
\(616\) | −0.275255 | + | 0.476756i | −0.0110903 | + | 0.0192090i | ||||
\(617\) | −15.5227 | + | 26.8861i | −0.624921 | + | 1.08239i | 0.363636 | + | 0.931541i | \(0.381535\pi\) |
−0.988556 | + | 0.150853i | \(0.951798\pi\) | |||||||
\(618\) | 14.6742 | − | 31.8519i | 0.590284 | − | 1.28127i | ||||
\(619\) | 14.6464 | + | 25.3684i | 0.588690 | + | 1.01964i | 0.994404 | + | 0.105641i | \(0.0336893\pi\) |
−0.405715 | + | 0.914000i | \(0.632977\pi\) | |||||||
\(620\) | 2.00000 | 0.0803219 | ||||||||
\(621\) | 3.12372 | − | 12.3387i | 0.125351 | − | 0.495133i | ||||
\(622\) | 1.10102 | 0.0441469 | ||||||||
\(623\) | 5.44949 | + | 9.43879i | 0.218329 | + | 0.378157i | ||||
\(624\) | −3.22474 | + | 6.99964i | −0.129093 | + | 0.280210i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −4.60102 | + | 7.96920i | −0.183894 | + | 0.318513i | ||||
\(627\) | 5.60102 | − | 0.516080i | 0.223683 | − | 0.0206103i | ||||
\(628\) | −4.67423 | − | 8.09601i | −0.186522 | − | 0.323066i | ||||
\(629\) | 4.65153 | 0.185469 | ||||||||
\(630\) | 1.00000 | − | 2.82843i | 0.0398410 | − | 0.112687i | ||||
\(631\) | 18.6515 | 0.742506 | 0.371253 | − | 0.928532i | \(-0.378928\pi\) | ||||
0.371253 | + | 0.928532i | \(0.378928\pi\) | |||||||
\(632\) | 1.00000 | + | 1.73205i | 0.0397779 | + | 0.0688973i | ||||
\(633\) | 6.69694 | + | 9.47090i | 0.266179 | + | 0.376435i | ||||
\(634\) | 0.123724 | − | 0.214297i | 0.00491372 | − | 0.00851082i | ||||
\(635\) | −6.57321 | + | 11.3851i | −0.260850 | + | 0.451806i | ||||
\(636\) | 1.34847 | + | 1.90702i | 0.0534703 | + | 0.0756184i | ||||
\(637\) | −2.22474 | − | 3.85337i | −0.0881476 | − | 0.152676i | ||||
\(638\) | 1.34847 | 0.0533864 | ||||||||
\(639\) | 16.4722 | + | 19.2669i | 0.651630 | + | 0.762185i | ||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −9.94949 | − | 17.2330i | −0.392981 | − | 0.680663i | 0.599860 | − | 0.800105i | \(-0.295223\pi\) |
−0.992841 | + | 0.119442i | \(0.961890\pi\) | |||||||
\(642\) | −11.7247 | + | 1.08032i | −0.462739 | + | 0.0426369i | ||||
\(643\) | 1.47730 | − | 2.55875i | 0.0582589 | − | 0.100907i | −0.835425 | − | 0.549604i | \(-0.814778\pi\) |
0.893684 | + | 0.448697i | \(0.148112\pi\) | |||||||
\(644\) | 1.22474 | − | 2.12132i | 0.0482617 | − | 0.0835917i | ||||
\(645\) | 4.27526 | − | 9.27987i | 0.168338 | − | 0.365395i | ||||
\(646\) | 8.84847 | + | 15.3260i | 0.348138 | + | 0.602993i | ||||
\(647\) | −44.9444 | −1.76695 | −0.883473 | − | 0.468482i | \(-0.844801\pi\) | ||||
−0.883473 | + | 0.468482i | \(0.844801\pi\) | |||||||
\(648\) | 1.39898 | − | 8.89060i | 0.0549571 | − | 0.349256i | ||||
\(649\) | −4.34847 | −0.170692 | ||||||||
\(650\) | 2.22474 | + | 3.85337i | 0.0872617 | + | 0.151142i | ||||
\(651\) | −1.44949 | + | 3.14626i | −0.0568100 | + | 0.123312i | ||||
\(652\) | −1.00000 | + | 1.73205i | −0.0391630 | + | 0.0678323i | ||||
\(653\) | −16.5959 | + | 28.7450i | −0.649448 | + | 1.12488i | 0.333806 | + | 0.942642i | \(0.391667\pi\) |
−0.983255 | + | 0.182236i | \(0.941666\pi\) | |||||||
\(654\) | 21.4722 | − | 1.97846i | 0.839629 | − | 0.0773637i | ||||
\(655\) | −4.34847 | − | 7.53177i | −0.169909 | − | 0.294291i | ||||
\(656\) | −11.4495 | −0.447027 | ||||||||
\(657\) | 23.1969 | + | 27.1325i | 0.904999 | + | 1.05854i | ||||
\(658\) | 9.79796 | 0.381964 | ||||||||
\(659\) | 6.24745 | + | 10.8209i | 0.243366 | + | 0.421522i | 0.961671 | − | 0.274206i | \(-0.0884150\pi\) |
−0.718305 | + | 0.695728i | \(0.755082\pi\) | |||||||
\(660\) | 0.550510 | + | 0.778539i | 0.0214286 | + | 0.0303046i | ||||
\(661\) | 13.1464 | − | 22.7703i | 0.511337 | − | 0.885661i | −0.488577 | − | 0.872521i | \(-0.662484\pi\) |
0.999914 | − | 0.0131405i | \(-0.00418286\pi\) | |||||||
\(662\) | 5.34847 | − | 9.26382i | 0.207874 | − | 0.360049i | ||||
\(663\) | 13.3485 | + | 18.8776i | 0.518412 | + | 0.733145i | ||||
\(664\) | −3.55051 | − | 6.14966i | −0.137787 | − | 0.238653i | ||||
\(665\) | −5.89898 | −0.228753 | ||||||||
\(666\) | −1.55051 | + | 4.38551i | −0.0600811 | + | 0.169935i | ||||
\(667\) | −6.00000 | −0.232321 | ||||||||
\(668\) | 12.6742 | + | 21.9524i | 0.490381 | + | 0.849365i | ||||
\(669\) | 11.4722 | − | 1.05705i | 0.443541 | − | 0.0408680i | ||||
\(670\) | 6.84847 | − | 11.8619i | 0.264579 | − | 0.458265i | ||||
\(671\) | −1.47219 | + | 2.54991i | −0.0568334 | + | 0.0984383i | ||||
\(672\) | 0.724745 | − | 1.57313i | 0.0279576 | − | 0.0606849i | ||||
\(673\) | 19.6969 | + | 34.1161i | 0.759261 | + | 1.31508i | 0.943228 | + | 0.332146i | \(0.107773\pi\) |
−0.183967 | + | 0.982932i | \(0.558894\pi\) | |||||||
\(674\) | −19.4495 | −0.749166 | ||||||||
\(675\) | −3.72474 | − | 3.62302i | −0.143365 | − | 0.139450i | ||||
\(676\) | 6.79796 | 0.261460 | ||||||||
\(677\) | −6.42679 | − | 11.1315i | −0.247001 | − | 0.427819i | 0.715691 | − | 0.698417i | \(-0.246112\pi\) |
−0.962692 | + | 0.270598i | \(0.912779\pi\) | |||||||
\(678\) | −12.2474 | + | 26.5843i | −0.470360 | + | 1.02096i | ||||
\(679\) | 7.84847 | − | 13.5939i | 0.301197 | − | 0.521688i | ||||
\(680\) | −1.50000 | + | 2.59808i | −0.0575224 | + | 0.0996317i | ||||
\(681\) | −43.1969 | + | 3.98018i | −1.65531 | + | 0.152521i | ||||
\(682\) | −0.550510 | − | 0.953512i | −0.0210801 | − | 0.0365119i | ||||
\(683\) | 18.7980 | 0.719284 | 0.359642 | − | 0.933090i | \(-0.382899\pi\) | ||||
0.359642 | + | 0.933090i | \(0.382899\pi\) | |||||||
\(684\) | −17.3990 | + | 3.23375i | −0.665267 | + | 0.123646i | ||||
\(685\) | 3.24745 | 0.124079 | ||||||||
\(686\) | 0.500000 | + | 0.866025i | 0.0190901 | + | 0.0330650i | ||||
\(687\) | −0.651531 | − | 0.921404i | −0.0248574 | − | 0.0351537i | ||||
\(688\) | 2.94949 | − | 5.10867i | 0.112448 | − | 0.194766i | ||||
\(689\) | 3.00000 | − | 5.19615i | 0.114291 | − | 0.197958i | ||||
\(690\) | −2.44949 | − | 3.46410i | −0.0932505 | − | 0.131876i | ||||
\(691\) | −1.79796 | − | 3.11416i | −0.0683976 | − | 0.118468i | 0.829799 | − | 0.558063i | \(-0.188455\pi\) |
−0.898196 | + | 0.439595i | \(0.855122\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | −1.62372 | + | 0.301783i | −0.0616802 | + | 0.0114638i | ||||
\(694\) | −19.8990 | −0.755355 | ||||||||
\(695\) | −4.39898 | − | 7.61926i | −0.166863 | − | 0.289015i | ||||
\(696\) | −4.22474 | + | 0.389270i | −0.160139 | + | 0.0147552i | ||||
\(697\) | −17.1742 | + | 29.7466i | −0.650521 | + | 1.12673i | ||||
\(698\) | 15.0227 | − | 26.0201i | 0.568618 | − | 0.984875i | ||||
\(699\) | 13.4444 | − | 29.1824i | 0.508513 | − | 1.10378i | ||||
\(700\) | −0.500000 | − | 0.866025i | −0.0188982 | − | 0.0327327i | ||||
\(701\) | 31.8434 | 1.20271 | 0.601354 | − | 0.798983i | \(-0.294628\pi\) | ||||
0.601354 | + | 0.798983i | \(0.294628\pi\) | |||||||
\(702\) | −22.2474 | + | 6.29253i | −0.839676 | + | 0.237496i | ||||
\(703\) | 9.14643 | 0.344964 | ||||||||
\(704\) | 0.275255 | + | 0.476756i | 0.0103741 | + | 0.0179684i | ||||
\(705\) | 7.10102 | − | 15.4135i | 0.267440 | − | 0.580505i | ||||
\(706\) | 5.84847 | − | 10.1298i | 0.220110 | − | 0.381242i | ||||
\(707\) | −2.44949 | + | 4.24264i | −0.0921225 | + | 0.159561i | ||||
\(708\) | 13.6237 | − | 1.25529i | 0.512011 | − | 0.0471769i | ||||
\(709\) | 11.6742 | + | 20.2204i | 0.438435 | + | 0.759392i | 0.997569 | − | 0.0696855i | \(-0.0221996\pi\) |
−0.559134 | + | 0.829077i | \(0.688866\pi\) | |||||||
\(710\) | 8.44949 | 0.317104 | ||||||||
\(711\) | −2.00000 | + | 5.65685i | −0.0750059 | + | 0.212149i | ||||
\(712\) | 10.8990 | 0.408457 | ||||||||
\(713\) | 2.44949 | + | 4.24264i | 0.0917341 | + | 0.158888i | ||||
\(714\) | −3.00000 | − | 4.24264i | −0.112272 | − | 0.158777i | ||||
\(715\) | 1.22474 | − | 2.12132i | 0.0458029 | − | 0.0793329i | ||||
\(716\) | −3.00000 | + | 5.19615i | −0.112115 | + | 0.194189i | ||||
\(717\) | −13.1010 | − | 18.5276i | −0.489267 | − | 0.691927i | ||||
\(718\) | 11.0227 | + | 19.0919i | 0.411364 | + | 0.712503i | ||||
\(719\) | 44.4495 | 1.65769 | 0.828843 | − | 0.559481i | \(-0.189000\pi\) | ||||
0.828843 | + | 0.559481i | \(0.189000\pi\) | |||||||
\(720\) | −1.94949 | − | 2.28024i | −0.0726532 | − | 0.0849795i | ||||
\(721\) | 20.2474 | 0.754054 | ||||||||
\(722\) | 7.89898 | + | 13.6814i | 0.293970 | + | 0.509170i | ||||
\(723\) | 21.2980 | − | 1.96240i | 0.792080 | − | 0.0729825i | ||||
\(724\) | −8.89898 | + | 15.4135i | −0.330728 | + | 0.572838i | ||||
\(725\) | −1.22474 | + | 2.12132i | −0.0454859 | + | 0.0787839i | ||||
\(726\) | −7.75255 | + | 16.8277i | −0.287724 | + | 0.624534i | ||||
\(727\) | 8.12372 | + | 14.0707i | 0.301292 | + | 0.521854i | 0.976429 | − | 0.215839i | \(-0.0692487\pi\) |
−0.675137 | + | 0.737693i | \(0.735915\pi\) | |||||||
\(728\) | −4.44949 | −0.164909 | ||||||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | 11.8990 | 0.440401 | ||||||||
\(731\) | −8.84847 | − | 15.3260i | −0.327272 | − | 0.566853i | ||||
\(732\) | 3.87628 | − | 8.41385i | 0.143271 | − | 0.310985i | ||||
\(733\) | 23.1237 | − | 40.0515i | 0.854094 | − | 1.47933i | −0.0233885 | − | 0.999726i | \(-0.507445\pi\) |
0.877483 | − | 0.479608i | \(-0.159221\pi\) | |||||||
\(734\) | 7.67423 | − | 13.2922i | 0.283261 | − | 0.490623i | ||||
\(735\) | 1.72474 | − | 0.158919i | 0.0636182 | − | 0.00586180i | ||||
\(736\) | −1.22474 | − | 2.12132i | −0.0451447 | − | 0.0781929i | ||||
\(737\) | −7.54031 | −0.277751 | ||||||||
\(738\) | −22.3207 | − | 26.1076i | −0.821635 | − | 0.961033i | ||||
\(739\) | −13.2474 | −0.487315 | −0.243658 | − | 0.969861i | \(-0.578347\pi\) | ||||
−0.243658 | + | 0.969861i | \(0.578347\pi\) | |||||||
\(740\) | 0.775255 | + | 1.34278i | 0.0284989 | + | 0.0493616i | ||||
\(741\) | 26.2474 | + | 37.1195i | 0.964224 | + | 1.36362i | ||||
\(742\) | −0.674235 | + | 1.16781i | −0.0247519 | + | 0.0428716i | ||||
\(743\) | −12.7980 | + | 22.1667i | −0.469512 | + | 0.813218i | −0.999392 | − | 0.0348542i | \(-0.988903\pi\) |
0.529881 | + | 0.848072i | \(0.322237\pi\) | |||||||
\(744\) | 2.00000 | + | 2.82843i | 0.0733236 | + | 0.103695i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 26.8990 | 0.984842 | ||||||||
\(747\) | 7.10102 | − | 20.0847i | 0.259813 | − | 0.734861i | ||||
\(748\) | 1.65153 | 0.0603859 | ||||||||
\(749\) | −3.39898 | − | 5.88721i | −0.124196 | − | 0.215114i | ||||
\(750\) | −1.72474 | + | 0.158919i | −0.0629788 | + | 0.00580289i | ||||
\(751\) | 4.57321 | − | 7.92104i | 0.166879 | − | 0.289043i | −0.770442 | − | 0.637510i | \(-0.779964\pi\) |
0.937321 | + | 0.348467i | \(0.113298\pi\) | |||||||
\(752\) | 4.89898 | − | 8.48528i | 0.178647 | − | 0.309426i | ||||
\(753\) | 10.0732 | − | 21.8649i | 0.367088 | − | 0.796802i | ||||
\(754\) | 5.44949 | + | 9.43879i | 0.198459 | + | 0.343741i | ||||
\(755\) | −10.0000 | −0.363937 | ||||||||
\(756\) | 5.00000 | − | 1.41421i | 0.181848 | − | 0.0514344i | ||||
\(757\) | 33.3485 | 1.21207 | 0.606035 | − | 0.795438i | \(-0.292759\pi\) | ||||
0.606035 | + | 0.795438i | \(0.292759\pi\) | |||||||
\(758\) | 1.27526 | + | 2.20881i | 0.0463194 | + | 0.0802275i | ||||
\(759\) | −0.977296 | + | 2.12132i | −0.0354736 | + | 0.0769991i | ||||
\(760\) | −2.94949 | + | 5.10867i | −0.106989 | + | 0.185311i | ||||
\(761\) | 18.7980 | − | 32.5590i | 0.681425 | − | 1.18026i | −0.293120 | − | 0.956076i | \(-0.594694\pi\) |
0.974546 | − | 0.224188i | \(-0.0719730\pi\) | |||||||
\(762\) | −22.6742 | + | 2.08921i | −0.821401 | + | 0.0756842i | ||||
\(763\) | 6.22474 | + | 10.7816i | 0.225351 | + | 0.390319i | ||||
\(764\) | 7.10102 | 0.256906 | ||||||||
\(765\) | −8.84847 | + | 1.64456i | −0.319917 | + | 0.0594594i | ||||
\(766\) | −26.6969 | −0.964600 | ||||||||
\(767\) | −17.5732 | − | 30.4377i | −0.634532 | − | 1.09904i | ||||
\(768\) | −1.00000 | − | 1.41421i | −0.0360844 | − | 0.0510310i | ||||
\(769\) | 11.5505 | − | 20.0061i | 0.416522 | − | 0.721437i | −0.579065 | − | 0.815281i | \(-0.696582\pi\) |
0.995587 | + | 0.0938441i | \(0.0299155\pi\) | |||||||
\(770\) | −0.275255 | + | 0.476756i | −0.00991951 | + | 0.0171811i | ||||
\(771\) | 5.69694 | + | 8.05669i | 0.205170 | + | 0.290155i | ||||
\(772\) | −0.724745 | − | 1.25529i | −0.0260841 | − | 0.0451791i | ||||
\(773\) | −36.2474 | −1.30373 | −0.651865 | − | 0.758335i | \(-0.726013\pi\) | ||||
−0.651865 | + | 0.758335i | \(0.726013\pi\) | |||||||
\(774\) | 17.3990 | − | 3.23375i | 0.625393 | − | 0.116235i | ||||
\(775\) | 2.00000 | 0.0718421 | ||||||||
\(776\) | −7.84847 | − | 13.5939i | −0.281744 | − | 0.487994i | ||||
\(777\) | −2.67423 | + | 0.246405i | −0.0959376 | + | 0.00883973i | ||||
\(778\) | 15.7980 | − | 27.3629i | 0.566384 | − | 0.981006i | ||||
\(779\) | −33.7702 | + | 58.4916i | −1.20994 | + | 2.09568i | ||||
\(780\) | −3.22474 | + | 6.99964i | −0.115464 | + | 0.250627i | ||||
\(781\) | −2.32577 | − | 4.02834i | −0.0832224 | − | 0.144145i | ||||
\(782\) | −7.34847 | −0.262781 | ||||||||
\(783\) | −9.12372 | − | 8.87455i | −0.326055 | − | 0.317151i | ||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −4.67423 | − | 8.09601i | −0.166831 | − | 0.288959i | ||||
\(786\) | 6.30306 | − | 13.6814i | 0.224823 | − | 0.488001i | ||||
\(787\) | −18.6969 | + | 32.3840i | −0.666474 | + | 1.15437i | 0.312410 | + | 0.949948i | \(0.398864\pi\) |
−0.978883 | + | 0.204419i | \(0.934469\pi\) | |||||||
\(788\) | −3.67423 | + | 6.36396i | −0.130889 | + | 0.226707i | ||||
\(789\) | −2.32577 | + | 0.214297i | −0.0827994 | + | 0.00762917i | ||||
\(790\) | 1.00000 | + | 1.73205i | 0.0355784 | + | 0.0616236i | ||||
\(791\) | −16.8990 | −0.600859 | ||||||||
\(792\) | −0.550510 | + | 1.55708i | −0.0195615 | + | 0.0553284i | ||||
\(793\) | −23.7980 | −0.845090 | ||||||||
\(794\) | −16.0227 | − | 27.7521i | −0.568624 | − | 0.984886i | ||||
\(795\) | 1.34847 | + | 1.90702i | 0.0478253 | + | 0.0676352i | ||||
\(796\) | −3.32577 | + | 5.76039i | −0.117879 | + | 0.204172i | ||||
\(797\) | 10.8990 | − | 18.8776i | 0.386062 | − | 0.668678i | −0.605854 | − | 0.795576i | \(-0.707169\pi\) |
0.991916 | + | 0.126897i | \(0.0405019\pi\) | |||||||
\(798\) | −5.89898 | − | 8.34242i | −0.208822 | − | 0.295318i | ||||
\(799\) | −14.6969 | − | 25.4558i | −0.519940 | − | 0.900563i | ||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 21.2474 | + | 24.8523i | 0.750742 | + | 0.878112i | ||||
\(802\) | −9.00000 | −0.317801 | ||||||||
\(803\) | −3.27526 | − | 5.67291i | −0.115581 | − | 0.200193i | ||||
\(804\) | 23.6237 | − | 2.17670i | 0.833145 | − | 0.0767662i | ||||
\(805\) | 1.22474 | − | 2.12132i | 0.0431666 | − | 0.0747667i | ||||
\(806\) | 4.44949 | − | 7.70674i | 0.156727 | − | 0.271458i | ||||
\(807\) | −16.7753 | + | 36.4124i | −0.590517 | + | 1.28178i | ||||
\(808\) | 2.44949 | + | 4.24264i | 0.0861727 | + | 0.149256i | ||||
\(809\) | 17.2020 | 0.604792 | 0.302396 | − | 0.953182i | \(-0.402214\pi\) | ||||
0.302396 | + | 0.953182i | \(0.402214\pi\) | |||||||
\(810\) | 1.39898 | − | 8.89060i | 0.0491551 | − | 0.312384i | ||||
\(811\) | −33.6969 | −1.18326 | −0.591630 | − | 0.806210i | \(-0.701515\pi\) | ||||
−0.591630 | + | 0.806210i | \(0.701515\pi\) | |||||||
\(812\) | −1.22474 | − | 2.12132i | −0.0429801 | − | 0.0744438i | ||||
\(813\) | −15.4722 | + | 33.5840i | −0.542634 | + | 1.17784i | ||||
\(814\) | 0.426786 | − | 0.739215i | 0.0149588 | − | 0.0259095i | ||||
\(815\) | −1.00000 | + | 1.73205i | −0.0350285 | + | 0.0606711i | ||||
\(816\) | −5.17423 | + | 0.476756i | −0.181134 | + | 0.0166898i | ||||
\(817\) | −17.3990 | − | 30.1359i | −0.608713 | − | 1.05432i | ||||
\(818\) | 0.752551 | 0.0263123 | ||||||||
\(819\) | −8.67423 | − | 10.1459i | −0.303102 | − | 0.354526i | ||||
\(820\) | −11.4495 | −0.399834 | ||||||||
\(821\) | −7.77526 | − | 13.4671i | −0.271358 | − | 0.470006i | 0.697852 | − | 0.716242i | \(-0.254139\pi\) |
−0.969210 | + | 0.246236i | \(0.920806\pi\) | |||||||
\(822\) | 3.24745 | + | 4.59259i | 0.113268 | + | 0.160185i | ||||
\(823\) | 22.0227 | − | 38.1444i | 0.767663 | − | 1.32963i | −0.171164 | − | 0.985243i | \(-0.554753\pi\) |
0.938827 | − | 0.344389i | \(-0.111914\pi\) | |||||||
\(824\) | 10.1237 | − | 17.5348i | 0.352677 | − | 0.610854i | ||||
\(825\) | 0.550510 | + | 0.778539i | 0.0191663 | + | 0.0271053i | ||||
\(826\) | 3.94949 | + | 6.84072i | 0.137420 | + | 0.238019i | ||||
\(827\) | −20.6969 | −0.719703 | −0.359852 | − | 0.933010i | \(-0.617173\pi\) | ||||
−0.359852 | + | 0.933010i | \(0.617173\pi\) | |||||||
\(828\) | 2.44949 | − | 6.92820i | 0.0851257 | − | 0.240772i | ||||
\(829\) | 40.0908 | 1.39241 | 0.696206 | − | 0.717842i | \(-0.254870\pi\) | ||||
0.696206 | + | 0.717842i | \(0.254870\pi\) | |||||||
\(830\) | −3.55051 | − | 6.14966i | −0.123240 | − | 0.213458i | ||||
\(831\) | 3.44949 | − | 0.317837i | 0.119661 | − | 0.0110257i | ||||
\(832\) | −2.22474 | + | 3.85337i | −0.0771292 | + | 0.133592i | ||||
\(833\) | 1.50000 | − | 2.59808i | 0.0519719 | − | 0.0900180i | ||||
\(834\) | 6.37628 | − | 13.8404i | 0.220792 | − | 0.479252i | ||||
\(835\) | 12.6742 | + | 21.9524i | 0.438610 | + | 0.759695i | ||||
\(836\) | 3.24745 | 0.112315 | ||||||||
\(837\) | −2.55051 | + | 10.0745i | −0.0881585 | + | 0.348225i | ||||
\(838\) | 13.5959 | 0.469663 | ||||||||
\(839\) | −8.32577 | − | 14.4206i | −0.287437 | − | 0.497856i | 0.685760 | − | 0.727828i | \(-0.259470\pi\) |
−0.973197 | + | 0.229972i | \(0.926137\pi\) | |||||||
\(840\) | 0.724745 | − | 1.57313i | 0.0250061 | − | 0.0542782i | ||||
\(841\) | 11.5000 | − | 19.9186i | 0.396552 | − | 0.686848i | ||||
\(842\) | −9.22474 | + | 15.9777i | −0.317906 | + | 0.550629i | ||||
\(843\) | −41.3939 | + | 3.81405i | −1.42568 | + | 0.131363i | ||||
\(844\) | 3.34847 | + | 5.79972i | 0.115259 | + | 0.199635i | ||||
\(845\) | 6.79796 | 0.233857 | ||||||||
\(846\) | 28.8990 | − | 5.37113i | 0.993567 | − | 0.184663i | ||||
\(847\) | −10.6969 | −0.367551 | ||||||||
\(848\) | 0.674235 | + | 1.16781i | 0.0231533 | + | 0.0401027i | ||||
\(849\) | 16.0000 | + | 22.6274i | 0.549119 | + | 0.776571i | ||||
\(850\) | −1.50000 | + | 2.59808i | −0.0514496 | + | 0.0891133i | ||||
\(851\) | −1.89898 | + | 3.28913i | −0.0650962 | + | 0.112750i | ||||
\(852\) | 8.44949 | + | 11.9494i | 0.289475 | + | 0.409379i | ||||
\(853\) | 27.3485 | + | 47.3689i | 0.936394 | + | 1.62188i | 0.772130 | + | 0.635465i | \(0.219192\pi\) |
0.164264 | + | 0.986416i | \(0.447475\pi\) | |||||||
\(854\) | 5.34847 | 0.183021 | ||||||||
\(855\) | −17.3990 | + | 3.23375i | −0.595033 | + | 0.110592i | ||||
\(856\) | −6.79796 | −0.232349 | ||||||||
\(857\) | −28.0454 | − | 48.5761i | −0.958013 | − | 1.65933i | −0.727318 | − | 0.686301i | \(-0.759233\pi\) |
−0.230695 | − | 0.973026i | \(-0.574100\pi\) | |||||||
\(858\) | 4.22474 | − | 0.389270i | 0.144230 | − | 0.0132894i | ||||
\(859\) | −26.1969 | + | 45.3744i | −0.893828 | + | 1.54816i | −0.0585796 | + | 0.998283i | \(0.518657\pi\) |
−0.835248 | + | 0.549873i | \(0.814676\pi\) | |||||||
\(860\) | 2.94949 | − | 5.10867i | 0.100577 | − | 0.174204i | ||||
\(861\) | 8.29796 | − | 18.0116i | 0.282794 | − | 0.613832i | ||||
\(862\) | −6.24745 | − | 10.8209i | −0.212789 | − | 0.368561i | ||||
\(863\) | −34.8990 | −1.18798 | −0.593988 | − | 0.804474i | \(-0.702447\pi\) | ||||
−0.593988 | + | 0.804474i | \(0.702447\pi\) | |||||||
\(864\) | 1.27526 | − | 5.03723i | 0.0433851 | − | 0.171370i | ||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | −16.2980 | − | 28.2289i | −0.553827 | − | 0.959257i | ||||
\(867\) | 5.79796 | − | 12.5851i | 0.196909 | − | 0.427411i | ||||
\(868\) | −1.00000 | + | 1.73205i | −0.0339422 | + | 0.0587896i | ||||
\(869\) | 0.550510 | − | 0.953512i | 0.0186748 | − | 0.0323457i | ||||
\(870\) | −4.22474 | + | 0.389270i | −0.143232 | + | 0.0131975i | ||||
\(871\) | −30.4722 | − | 52.7794i | −1.03251 | − | 1.78836i | ||||
\(872\) | 12.4495 | 0.421593 | ||||||||
\(873\) | 15.6969 | − | 44.3976i | 0.531261 | − | 1.50263i | ||||
\(874\) | −14.4495 | −0.488761 | ||||||||
\(875\) | −0.500000 | − | 0.866025i | −0.0169031 | − | 0.0292770i | ||||
\(876\) | 11.8990 | + | 16.8277i | 0.402029 | + | 0.568555i | ||||
\(877\) | −18.0227 | + | 31.2162i | −0.608583 | + | 1.05410i | 0.382891 | + | 0.923794i | \(0.374929\pi\) |
−0.991474 | + | 0.130304i | \(0.958405\pi\) | |||||||
\(878\) | 13.6742 | − | 23.6845i | 0.461483 | − | 0.799312i | ||||
\(879\) | 29.1464 | + | 41.2193i | 0.983085 | + | 1.39029i | ||||
\(880\) | 0.275255 | + | 0.476756i | 0.00927885 | + | 0.0160714i | ||||
\(881\) | −46.2929 | −1.55965 | −0.779823 | − | 0.626000i | \(-0.784691\pi\) | ||||
−0.779823 | + | 0.626000i | \(0.784691\pi\) | |||||||
\(882\) | 1.94949 | + | 2.28024i | 0.0656427 | + | 0.0767796i | ||||
\(883\) | −44.5959 | −1.50077 | −0.750386 | − | 0.661000i | \(-0.770132\pi\) | ||||
−0.750386 | + | 0.661000i | \(0.770132\pi\) | |||||||
\(884\) | 6.67423 | + | 11.5601i | 0.224479 | + | 0.388809i | ||||
\(885\) | 13.6237 | − | 1.25529i | 0.457956 | − | 0.0421963i | ||||
\(886\) | −17.8485 | + | 30.9145i | −0.599631 | + | 1.03859i | ||||
\(887\) | −27.0000 | + | 46.7654i | −0.906571 | + | 1.57023i | −0.0877772 | + | 0.996140i | \(0.527976\pi\) |
−0.818794 | + | 0.574087i | \(0.805357\pi\) | |||||||
\(888\) | −1.12372 | + | 2.43916i | −0.0377097 | + | 0.0818528i | ||||
\(889\) | −6.57321 | − | 11.3851i | −0.220459 | − | 0.381845i | ||||
\(890\) | 10.8990 | 0.365335 | ||||||||
\(891\) | −4.62372 | + | 1.78021i | −0.154901 | + | 0.0596394i | ||||
\(892\) | 6.65153 | 0.222710 | ||||||||
\(893\) | −28.8990 | − | 50.0545i | −0.967067 | − | 1.67501i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.00000 | + | 5.19615i | −0.100279 | + | 0.173688i | ||||
\(896\) | 0.500000 | − | 0.866025i | 0.0167038 | − | 0.0289319i | ||||
\(897\) | −18.7980 | + | 1.73205i | −0.627646 | + | 0.0578315i | ||||
\(898\) | −3.15153 | − | 5.45861i | −0.105168 | − | 0.182156i | ||||
\(899\) | 4.89898 | 0.163390 | ||||||||
\(900\) | −1.94949 | − | 2.28024i | −0.0649830 | − | 0.0760080i | ||||
\(901\) | 4.04541 | 0.134772 | ||||||||
\(902\) | 3.15153 | + | 5.45861i | 0.104934 | + | 0.181752i | ||||
\(903\) | 5.89898 | + | 8.34242i | 0.196306 | + | 0.277618i | ||||
\(904\) | −8.44949 | + | 14.6349i | −0.281026 | + | 0.486751i | ||||
\(905\) | −8.89898 | + | 15.4135i | −0.295812 | + | 0.512362i | ||||
\(906\) | −10.0000 | − | 14.1421i | −0.332228 | − | 0.469841i | ||||
\(907\) | −10.1515 | − | 17.5830i | −0.337076 | − | 0.583833i | 0.646805 | − | 0.762655i | \(-0.276105\pi\) |
−0.983881 | + | 0.178822i | \(0.942771\pi\) | |||||||
\(908\) | −25.0454 | −0.831161 | ||||||||
\(909\) | −4.89898 | + | 13.8564i | −0.162489 | + | 0.459588i | ||||
\(910\) | −4.44949 | −0.147499 | ||||||||
\(911\) | −16.4722 | − | 28.5307i | −0.545748 | − | 0.945263i | −0.998559 | − | 0.0536571i | \(-0.982912\pi\) |
0.452811 | − | 0.891606i | \(-0.350421\pi\) | |||||||
\(912\) | −10.1742 | + | 0.937458i | −0.336903 | + | 0.0310423i | ||||
\(913\) | −1.95459 | + | 3.38545i | −0.0646876 | + | 0.112042i | ||||
\(914\) | −16.7247 | + | 28.9681i | −0.553205 | + | 0.958180i | ||||
\(915\) | 3.87628 | − | 8.41385i | 0.128146 | − | 0.278153i | ||||
\(916\) | −0.325765 | − | 0.564242i | −0.0107636 | − | 0.0186431i | ||||
\(917\) | 8.69694 | 0.287198 | ||||||||
\(918\) | −11.1742 | − | 10.8691i | −0.368805 | − | 0.358732i | ||||
\(919\) | 47.5505 | 1.56855 | 0.784273 | − | 0.620415i | \(-0.213036\pi\) | ||||
0.784273 | + | 0.620415i | \(0.213036\pi\) | |||||||
\(920\) | −1.22474 | − | 2.12132i | −0.0403786 | − | 0.0699379i | ||||
\(921\) | 19.8939 | − | 43.1817i | 0.655526 | − | 1.42288i | ||||
\(922\) | 3.67423 | − | 6.36396i | 0.121004 | − | 0.209586i | ||||
\(923\) | 18.7980 | − | 32.5590i | 0.618742 | − | 1.07169i | ||||
\(924\) | −0.949490 | + | 0.0874863i | −0.0312359 | + | 0.00287809i | ||||
\(925\) | 0.775255 | + | 1.34278i | 0.0254902 | + | 0.0441504i | ||||
\(926\) | 28.0000 | 0.920137 | ||||||||
\(927\) | 59.7196 | − | 11.0994i | 1.96145 | − | 0.364553i | ||||
\(928\) | −2.44949 | −0.0804084 | ||||||||
\(929\) | 9.00000 | + | 15.5885i | 0.295280 | + | 0.511441i | 0.975050 | − | 0.221985i | \(-0.0712536\pi\) |
−0.679770 | + | 0.733426i | \(0.737920\pi\) | |||||||
\(930\) | 2.00000 | + | 2.82843i | 0.0655826 | + | 0.0927478i | ||||
\(931\) | 2.94949 | − | 5.10867i | 0.0966656 | − | 0.167430i | ||||
\(932\) | 9.27526 | − | 16.0652i | 0.303821 | − | 0.526234i | ||||
\(933\) | 1.10102 | + | 1.55708i | 0.0360458 | + | 0.0509764i | ||||
\(934\) | 11.9722 | + | 20.7364i | 0.391742 | + | 0.678517i | ||||
\(935\) | 1.65153 | 0.0540108 | ||||||||
\(936\) | −13.1237 | + | 2.43916i | −0.428962 | + | 0.0797264i | ||||
\(937\) | −45.3939 | −1.48295 | −0.741477 | − | 0.670979i | \(-0.765874\pi\) | ||||
−0.741477 | + | 0.670979i | \(0.765874\pi\) | |||||||
\(938\) | 6.84847 | + | 11.8619i | 0.223610 | + | 0.387305i | ||||
\(939\) | −15.8712 | + | 1.46238i | −0.517936 | + | 0.0477228i | ||||
\(940\) | 4.89898 | − | 8.48528i | 0.159787 | − | 0.276759i | ||||
\(941\) | 29.1464 | − | 50.4831i | 0.950146 | − | 1.64570i | 0.205043 | − | 0.978753i | \(-0.434267\pi\) |
0.745103 | − | 0.666949i | \(-0.232400\pi\) | |||||||
\(942\) | 6.77526 | − | 14.7064i | 0.220750 | − | 0.479160i | ||||
\(943\) | −14.0227 | − | 24.2880i | −0.456642 | − | 0.790927i | ||||
\(944\) | 7.89898 | 0.257090 | ||||||||
\(945\) | 5.00000 | − | 1.41421i | 0.162650 | − | 0.0460044i | ||||
\(946\) | −3.24745 | −0.105584 | ||||||||
\(947\) | −29.2980 | − | 50.7456i | −0.952056 | − | 1.64901i | −0.740966 | − | 0.671542i | \(-0.765632\pi\) |
−0.211089 | − | 0.977467i | \(-0.567701\pi\) | |||||||
\(948\) | −1.44949 | + | 3.14626i | −0.0470772 | + | 0.102186i | ||||
\(949\) | 26.4722 | − | 45.8512i | 0.859324 | − | 1.48839i | ||||
\(950\) | −2.94949 | + | 5.10867i | −0.0956941 | + | 0.165747i | ||||
\(951\) | 0.426786 | − | 0.0393242i | 0.0138395 | − | 0.00127517i | ||||
\(952\) | −1.50000 | − | 2.59808i | −0.0486153 | − | 0.0842041i | ||||
\(953\) | −22.8434 | −0.739969 | −0.369985 | − | 0.929038i | \(-0.620637\pi\) | ||||
−0.369985 | + | 0.929038i | \(0.620637\pi\) | |||||||
\(954\) | −1.34847 | + | 3.81405i | −0.0436583 | + | 0.123484i | ||||
\(955\) | 7.10102 | 0.229784 | ||||||||
\(956\) | −6.55051 | − | 11.3458i | −0.211859 | − | 0.366950i | ||||
\(957\) | 1.34847 | + | 1.90702i | 0.0435898 | + | 0.0616453i | ||||
\(958\) | −13.4722 | + | 23.3345i | −0.435267 | + | 0.753904i | ||||
\(959\) | −1.62372 | + | 2.81237i | −0.0524328 | + | 0.0908163i | ||||
\(960\) | −1.00000 | − | 1.41421i | −0.0322749 | − | 0.0456435i | ||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | 6.89898 | 0.222432 | ||||||||
\(963\) | −13.2526 | − | 15.5010i | −0.427057 | − | 0.499512i | ||||
\(964\) | 12.3485 | 0.397717 | ||||||||
\(965\) | −0.724745 | − | 1.25529i | −0.0233304 | − | 0.0404094i | ||||
\(966\) | 4.22474 | − | 0.389270i | 0.135929 | − | 0.0125245i | ||||
\(967\) | −14.1010 | + | 24.4237i | −0.453458 | + | 0.785413i | −0.998598 | − | 0.0529324i | \(-0.983143\pi\) |
0.545140 | + | 0.838345i | \(0.316477\pi\) | |||||||
\(968\) | −5.34847 | + | 9.26382i | −0.171906 | + | 0.297750i | ||||
\(969\) | −12.8258 | + | 27.8396i | −0.412023 | + | 0.894338i | ||||
\(970\) | −7.84847 | − | 13.5939i | −0.251999 | − | 0.436475i | ||||
\(971\) | −45.7980 | −1.46973 | −0.734863 | − | 0.678215i | \(-0.762754\pi\) | ||||
−0.734863 | + | 0.678215i | \(0.762754\pi\) | |||||||
\(972\) | 13.9722 | − | 6.91215i | 0.448158 | − | 0.221707i | ||||
\(973\) | 8.79796 | 0.282050 | ||||||||
\(974\) | −11.2474 | − | 19.4812i | −0.360392 | − | 0.624216i | ||||
\(975\) | −3.22474 | + | 6.99964i | −0.103274 | + | 0.224168i | ||||
\(976\) | 2.67423 | − | 4.63191i | 0.0856002 | − | 0.148264i | ||||
\(977\) | −14.9722 | + | 25.9326i | −0.479003 | + | 0.829657i | −0.999710 | − | 0.0240780i | \(-0.992335\pi\) |
0.520707 | + | 0.853735i | \(0.325668\pi\) | |||||||
\(978\) | −3.44949 | + | 0.317837i | −0.110303 | + | 0.0101633i | ||||
\(979\) | −3.00000 | − | 5.19615i | −0.0958804 | − | 0.166070i | ||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 24.2702 | + | 28.3878i | 0.774886 | + | 0.906353i | ||||
\(982\) | −10.3485 | −0.330233 | ||||||||
\(983\) | −18.4949 | − | 32.0341i | −0.589896 | − | 1.02173i | −0.994246 | − | 0.107125i | \(-0.965836\pi\) |
0.404350 | − | 0.914604i | \(-0.367498\pi\) | |||||||
\(984\) | −11.4495 | − | 16.1920i | −0.364996 | − | 0.516183i | ||||
\(985\) | −3.67423 | + | 6.36396i | −0.117071 | + | 0.202773i | ||||
\(986\) | −3.67423 | + | 6.36396i | −0.117011 | + | 0.202670i | ||||
\(987\) | 9.79796 | + | 13.8564i | 0.311872 | + | 0.441054i | ||||
\(988\) | 13.1237 | + | 22.7310i | 0.417521 | + | 0.723168i | ||||
\(989\) | 14.4495 | 0.459467 | ||||||||
\(990\) | −0.550510 | + | 1.55708i | −0.0174964 | + | 0.0494872i | ||||
\(991\) | 3.10102 | 0.0985072 | 0.0492536 | − | 0.998786i | \(-0.484316\pi\) | ||||
0.0492536 | + | 0.998786i | \(0.484316\pi\) | |||||||
\(992\) | 1.00000 | + | 1.73205i | 0.0317500 | + | 0.0549927i | ||||
\(993\) | 18.4495 | − | 1.69994i | 0.585477 | − | 0.0539461i | ||||
\(994\) | −4.22474 | + | 7.31747i | −0.134001 | + | 0.232096i | ||||
\(995\) | −3.32577 | + | 5.76039i | −0.105434 | + | 0.182617i | ||||
\(996\) | 5.14643 | − | 11.1708i | 0.163071 | − | 0.353962i | ||||
\(997\) | −21.6969 | − | 37.5802i | −0.687149 | − | 1.19018i | −0.972756 | − | 0.231830i | \(-0.925529\pi\) |
0.285607 | − | 0.958347i | \(-0.407805\pi\) | |||||||
\(998\) | 37.2474 | 1.17905 | ||||||||
\(999\) | −7.75255 | + | 2.19275i | −0.245280 | + | 0.0693756i |
(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.h.211.1 | ✓ | 4 | |
3.2 | odd | 2 | 1890.2.j.g.631.2 | 4 | |||
9.2 | odd | 6 | 1890.2.j.g.1261.2 | 4 | |||
9.4 | even | 3 | 5670.2.a.ba.1.2 | 2 | |||
9.5 | odd | 6 | 5670.2.a.bi.1.1 | 2 | |||
9.7 | even | 3 | inner | 630.2.j.h.421.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.j.h.211.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
630.2.j.h.421.1 | yes | 4 | 9.7 | even | 3 | inner | |
1890.2.j.g.631.2 | 4 | 3.2 | odd | 2 | |||
1890.2.j.g.1261.2 | 4 | 9.2 | odd | 6 | |||
5670.2.a.ba.1.2 | 2 | 9.4 | even | 3 | |||
5670.2.a.bi.1.1 | 2 | 9.5 | odd | 6 |