Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,3,Mod(127,630)]
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, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.o (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: | \(17.1662566547\) |
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: | \( x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + \cdots + 2560000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 127.6 | ||
Root | \(3.76660 + 3.76660i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.127 |
Dual form | 630.3.o.f.253.6 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 4.16484 | + | 2.76660i | 0.832968 | + | 0.553321i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.87083 | − | 1.87083i | −0.267261 | − | 0.267261i | ||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.39824 | + | 6.93144i | 0.139824 | + | 0.693144i | ||||
\(11\) | −17.6826 | −1.60751 | −0.803757 | − | 0.594958i | \(-0.797169\pi\) | ||||
−0.803757 | + | 0.594958i | \(0.797169\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.3956 | + | 12.3956i | −0.953508 | + | 0.953508i | −0.998966 | − | 0.0454585i | \(-0.985525\pi\) |
0.0454585 | + | 0.998966i | \(0.485525\pi\) | |||||||
\(14\) | − | 3.74166i | − | 0.267261i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −18.7246 | − | 18.7246i | −1.10145 | − | 1.10145i | −0.994236 | − | 0.107210i | \(-0.965808\pi\) |
−0.107210 | − | 0.994236i | \(-0.534192\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.5476i | 1.34461i | 0.740273 | + | 0.672306i | \(0.234696\pi\) | ||||
−0.740273 | + | 0.672306i | \(0.765304\pi\) | |||||||
\(20\) | −5.53321 | + | 8.32968i | −0.276660 | + | 0.416484i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −17.6826 | − | 17.6826i | −0.803757 | − | 0.803757i | ||||
\(23\) | 5.90052 | − | 5.90052i | 0.256545 | − | 0.256545i | −0.567103 | − | 0.823647i | \(-0.691936\pi\) |
0.823647 | + | 0.567103i | \(0.191936\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.69181 | + | 23.0449i | 0.387673 | + | 0.921797i | ||||
\(26\) | −24.7912 | −0.953508 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.74166 | − | 3.74166i | 0.133631 | − | 0.133631i | ||||
\(29\) | 15.3647i | 0.529816i | 0.964274 | + | 0.264908i | \(0.0853416\pi\) | ||||
−0.964274 | + | 0.264908i | \(0.914658\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 11.3491 | 0.366102 | 0.183051 | − | 0.983103i | \(-0.441403\pi\) | ||||
0.183051 | + | 0.983103i | \(0.441403\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 37.4492i | − | 1.10145i | ||||||
\(35\) | −2.61586 | − | 12.9675i | −0.0747390 | − | 0.370501i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 25.5981 | + | 25.5981i | 0.691842 | + | 0.691842i | 0.962637 | − | 0.270795i | \(-0.0872866\pi\) |
−0.270795 | + | 0.962637i | \(0.587287\pi\) | |||||||
\(38\) | −25.5476 | + | 25.5476i | −0.672306 | + | 0.672306i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −13.8629 | + | 2.79648i | −0.346572 | + | 0.0699119i | ||||
\(41\) | −58.8283 | −1.43484 | −0.717418 | − | 0.696643i | \(-0.754676\pi\) | ||||
−0.717418 | + | 0.696643i | \(0.754676\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.282745 | − | 0.282745i | 0.00657546 | − | 0.00657546i | −0.703811 | − | 0.710387i | \(-0.748520\pi\) |
0.710387 | + | 0.703811i | \(0.248520\pi\) | |||||||
\(44\) | − | 35.3653i | − | 0.803757i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.8010 | 0.256545 | ||||||||
\(47\) | 48.6505 | + | 48.6505i | 1.03512 | + | 1.03512i | 0.999361 | + | 0.0357569i | \(0.0113842\pi\) |
0.0357569 | + | 0.999361i | \(0.488616\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000i | 0.142857i | ||||||||
\(50\) | −13.3531 | + | 32.7367i | −0.267062 | + | 0.654735i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −24.7912 | − | 24.7912i | −0.476754 | − | 0.476754i | ||||
\(53\) | −3.93909 | + | 3.93909i | −0.0743224 | + | 0.0743224i | −0.743291 | − | 0.668968i | \(-0.766736\pi\) |
0.668968 | + | 0.743291i | \(0.266736\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −73.6454 | − | 48.9209i | −1.33901 | − | 0.889470i | ||||
\(56\) | 7.48331 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −15.3647 | + | 15.3647i | −0.264908 | + | 0.264908i | ||||
\(59\) | − | 86.2636i | − | 1.46210i | −0.682326 | − | 0.731048i | \(-0.739032\pi\) | ||
0.682326 | − | 0.731048i | \(-0.260968\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 29.2079 | 0.478818 | 0.239409 | − | 0.970919i | \(-0.423046\pi\) | ||||
0.239409 | + | 0.970919i | \(0.423046\pi\) | |||||||
\(62\) | 11.3491 | + | 11.3491i | 0.183051 | + | 0.183051i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | −85.9194 | + | 17.3320i | −1.32184 | + | 0.266646i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −65.7277 | − | 65.7277i | −0.981010 | − | 0.981010i | 0.0188133 | − | 0.999823i | \(-0.494011\pi\) |
−0.999823 | + | 0.0188133i | \(0.994011\pi\) | |||||||
\(68\) | 37.4492 | − | 37.4492i | 0.550723 | − | 0.550723i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 10.3517 | − | 15.5834i | 0.147881 | − | 0.222620i | ||||
\(71\) | −1.19194 | −0.0167879 | −0.00839397 | − | 0.999965i | \(-0.502672\pi\) | ||||
−0.00839397 | + | 0.999965i | \(0.502672\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −87.0749 | + | 87.0749i | −1.19281 | + | 1.19281i | −0.216531 | + | 0.976276i | \(0.569474\pi\) |
−0.976276 | + | 0.216531i | \(0.930526\pi\) | |||||||
\(74\) | 51.1963i | 0.691842i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −51.0953 | −0.672306 | ||||||||
\(77\) | 33.0812 | + | 33.0812i | 0.429626 | + | 0.429626i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 55.0959i | 0.697417i | 0.937231 | + | 0.348708i | \(0.113380\pi\) | ||||
−0.937231 | + | 0.348708i | \(0.886620\pi\) | |||||||
\(80\) | −16.6594 | − | 11.0664i | −0.208242 | − | 0.138330i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −58.8283 | − | 58.8283i | −0.717418 | − | 0.717418i | ||||
\(83\) | 91.8012 | − | 91.8012i | 1.10604 | − | 1.10604i | 0.112372 | − | 0.993666i | \(-0.464155\pi\) |
0.993666 | − | 0.112372i | \(-0.0358448\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −26.1814 | − | 129.788i | −0.308017 | − | 1.52692i | ||||
\(86\) | 0.565490 | 0.00657546 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 35.3653 | − | 35.3653i | 0.401878 | − | 0.401878i | ||||
\(89\) | 103.966i | 1.16815i | 0.811699 | + | 0.584076i | \(0.198543\pi\) | ||||
−0.811699 | + | 0.584076i | \(0.801457\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 46.3801 | 0.509671 | ||||||||
\(92\) | 11.8010 | + | 11.8010i | 0.128272 | + | 0.128272i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 97.3010i | 1.03512i | ||||||||
\(95\) | −70.6802 | + | 106.402i | −0.744002 | + | 1.12002i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 87.4734 | + | 87.4734i | 0.901788 | + | 0.901788i | 0.995591 | − | 0.0938032i | \(-0.0299024\pi\) |
−0.0938032 | + | 0.995591i | \(0.529902\pi\) | |||||||
\(98\) | −7.00000 | + | 7.00000i | −0.0714286 | + | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −46.0899 | + | 19.3836i | −0.460899 | + | 0.193836i | ||||
\(101\) | −5.82092 | −0.0576329 | −0.0288164 | − | 0.999585i | \(-0.509174\pi\) | ||||
−0.0288164 | + | 0.999585i | \(0.509174\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 60.7804 | − | 60.7804i | 0.590101 | − | 0.590101i | −0.347558 | − | 0.937659i | \(-0.612989\pi\) |
0.937659 | + | 0.347558i | \(0.112989\pi\) | |||||||
\(104\) | − | 49.5824i | − | 0.476754i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.87818 | −0.0743224 | ||||||||
\(107\) | −80.6808 | − | 80.6808i | −0.754026 | − | 0.754026i | 0.221202 | − | 0.975228i | \(-0.429002\pi\) |
−0.975228 | + | 0.221202i | \(0.929002\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 64.4450i | 0.591238i | 0.955306 | + | 0.295619i | \(0.0955259\pi\) | ||||
−0.955306 | + | 0.295619i | \(0.904474\pi\) | |||||||
\(110\) | −24.7246 | − | 122.566i | −0.224769 | − | 1.11424i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.48331 | + | 7.48331i | 0.0668153 | + | 0.0668153i | ||||
\(113\) | −80.8773 | + | 80.8773i | −0.715729 | + | 0.715729i | −0.967728 | − | 0.251999i | \(-0.918912\pi\) |
0.251999 | + | 0.967728i | \(0.418912\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 40.8992 | − | 8.25034i | 0.355645 | − | 0.0717421i | ||||
\(116\) | −30.7293 | −0.264908 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 86.2636 | − | 86.2636i | 0.731048 | − | 0.731048i | ||||
\(119\) | 70.0610i | 0.588748i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 191.676 | 1.58410 | ||||||||
\(122\) | 29.2079 | + | 29.2079i | 0.239409 | + | 0.239409i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 22.6983i | 0.183051i | ||||||||
\(125\) | −23.3913 | + | 122.792i | −0.187130 | + | 0.982335i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 55.3737 | + | 55.3737i | 0.436014 | + | 0.436014i | 0.890668 | − | 0.454654i | \(-0.150237\pi\) |
−0.454654 | + | 0.890668i | \(0.650237\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −103.251 | − | 68.5874i | −0.794242 | − | 0.527596i | ||||
\(131\) | 69.2950 | 0.528969 | 0.264485 | − | 0.964390i | \(-0.414798\pi\) | ||||
0.264485 | + | 0.964390i | \(0.414798\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 47.7953 | − | 47.7953i | 0.359363 | − | 0.359363i | ||||
\(134\) | − | 131.455i | − | 0.981010i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 74.8984 | 0.550723 | ||||||||
\(137\) | 29.0370 | + | 29.0370i | 0.211949 | + | 0.211949i | 0.805095 | − | 0.593146i | \(-0.202114\pi\) |
−0.593146 | + | 0.805095i | \(0.702114\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 80.1068i | − | 0.576308i | −0.957584 | − | 0.288154i | \(-0.906958\pi\) | ||
0.957584 | − | 0.288154i | \(-0.0930415\pi\) | |||||||
\(140\) | 25.9351 | − | 5.23173i | 0.185251 | − | 0.0373695i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.19194 | − | 1.19194i | −0.00839397 | − | 0.00839397i | ||||
\(143\) | 219.187 | − | 219.187i | 1.53278 | − | 1.53278i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −42.5079 | + | 63.9914i | −0.293158 | + | 0.441320i | ||||
\(146\) | −174.150 | −1.19281 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −51.1963 | + | 51.1963i | −0.345921 | + | 0.345921i | ||||
\(149\) | − | 216.650i | − | 1.45403i | −0.686624 | − | 0.727013i | \(-0.740908\pi\) | ||
0.686624 | − | 0.727013i | \(-0.259092\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −170.036 | −1.12607 | −0.563033 | − | 0.826434i | \(-0.690366\pi\) | ||||
−0.563033 | + | 0.826434i | \(0.690366\pi\) | |||||||
\(152\) | −51.0953 | − | 51.0953i | −0.336153 | − | 0.336153i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 66.1624i | 0.429626i | ||||||||
\(155\) | 47.2674 | + | 31.3986i | 0.304951 | + | 0.202572i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 164.649 | + | 164.649i | 1.04872 | + | 1.04872i | 0.998751 | + | 0.0499682i | \(0.0159120\pi\) |
0.0499682 | + | 0.998751i | \(0.484088\pi\) | |||||||
\(158\) | −55.0959 | + | 55.0959i | −0.348708 | + | 0.348708i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.59295 | − | 27.7258i | −0.0349560 | − | 0.173286i | ||||
\(161\) | −22.0777 | −0.137129 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 104.632 | − | 104.632i | 0.641912 | − | 0.641912i | −0.309113 | − | 0.951025i | \(-0.600032\pi\) |
0.951025 | + | 0.309113i | \(0.100032\pi\) | |||||||
\(164\) | − | 117.657i | − | 0.717418i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 183.602 | 1.10604 | ||||||||
\(167\) | 215.324 | + | 215.324i | 1.28937 | + | 1.28937i | 0.935171 | + | 0.354196i | \(0.115246\pi\) |
0.354196 | + | 0.935171i | \(0.384754\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 138.302i | − | 0.818354i | ||||||
\(170\) | 103.607 | − | 155.970i | 0.609453 | − | 0.917470i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.565490 | + | 0.565490i | 0.00328773 | + | 0.00328773i | ||||
\(173\) | 50.4009 | − | 50.4009i | 0.291334 | − | 0.291334i | −0.546273 | − | 0.837607i | \(-0.683954\pi\) |
0.837607 | + | 0.546273i | \(0.183954\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 24.9814 | − | 61.2448i | 0.142751 | − | 0.349970i | ||||
\(176\) | 70.7306 | 0.401878 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −103.966 | + | 103.966i | −0.584076 | + | 0.584076i | ||||
\(179\) | 21.2898i | 0.118937i | 0.998230 | + | 0.0594687i | \(0.0189406\pi\) | ||||
−0.998230 | + | 0.0594687i | \(0.981059\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.7581 | −0.125736 | −0.0628678 | − | 0.998022i | \(-0.520025\pi\) | ||||
−0.0628678 | + | 0.998022i | \(0.520025\pi\) | |||||||
\(182\) | 46.3801 | + | 46.3801i | 0.254836 | + | 0.254836i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 23.6021i | 0.128272i | ||||||||
\(185\) | 35.7923 | + | 177.432i | 0.193472 | + | 0.959093i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 331.100 | + | 331.100i | 1.77059 | + | 1.77059i | ||||
\(188\) | −97.3010 | + | 97.3010i | −0.517559 | + | 0.517559i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −177.082 | + | 35.7217i | −0.932011 | + | 0.188009i | ||||
\(191\) | 113.711 | 0.595344 | 0.297672 | − | 0.954668i | \(-0.403790\pi\) | ||||
0.297672 | + | 0.954668i | \(0.403790\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 109.936 | − | 109.936i | 0.569616 | − | 0.569616i | −0.362405 | − | 0.932021i | \(-0.618044\pi\) |
0.932021 | + | 0.362405i | \(0.118044\pi\) | |||||||
\(194\) | 174.947i | 0.901788i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | −82.2107 | − | 82.2107i | −0.417313 | − | 0.417313i | 0.466963 | − | 0.884277i | \(-0.345348\pi\) |
−0.884277 | + | 0.466963i | \(0.845348\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 232.689i | 1.16929i | 0.811289 | + | 0.584646i | \(0.198766\pi\) | ||||
−0.811289 | + | 0.584646i | \(0.801234\pi\) | |||||||
\(200\) | −65.4735 | − | 26.7062i | −0.327367 | − | 0.133531i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.82092 | − | 5.82092i | −0.0288164 | − | 0.0288164i | ||||
\(203\) | 28.7447 | − | 28.7447i | 0.141599 | − | 0.141599i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −245.011 | − | 162.755i | −1.19517 | − | 0.793925i | ||||
\(206\) | 121.561 | 0.590101 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 49.5824 | − | 49.5824i | 0.238377 | − | 0.238377i | ||||
\(209\) | − | 451.750i | − | 2.16148i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −341.021 | −1.61621 | −0.808107 | − | 0.589035i | \(-0.799508\pi\) | ||||
−0.808107 | + | 0.589035i | \(0.799508\pi\) | |||||||
\(212\) | −7.87818 | − | 7.87818i | −0.0371612 | − | 0.0371612i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 161.362i | − | 0.754026i | ||||||
\(215\) | 1.95983 | − | 0.395345i | 0.00911549 | − | 0.00183881i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.2323 | − | 21.2323i | −0.0978447 | − | 0.0978447i | ||||
\(218\) | −64.4450 | + | 64.4450i | −0.295619 | + | 0.295619i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 97.8417 | − | 147.291i | 0.444735 | − | 0.669504i | ||||
\(221\) | 464.205 | 2.10048 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 118.521 | − | 118.521i | 0.531482 | − | 0.531482i | −0.389531 | − | 0.921013i | \(-0.627363\pi\) |
0.921013 | + | 0.389531i | \(0.127363\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −161.755 | −0.715729 | ||||||||
\(227\) | 1.59958 | + | 1.59958i | 0.00704662 | + | 0.00704662i | 0.710621 | − | 0.703575i | \(-0.248414\pi\) |
−0.703575 | + | 0.710621i | \(0.748414\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 59.2261i | 0.258629i | 0.991604 | + | 0.129315i | \(0.0412777\pi\) | ||||
−0.991604 | + | 0.129315i | \(0.958722\pi\) | |||||||
\(230\) | 49.1495 | + | 32.6488i | 0.213693 | + | 0.141951i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −30.7293 | − | 30.7293i | −0.132454 | − | 0.132454i | ||||
\(233\) | −266.052 | + | 266.052i | −1.14185 | + | 1.14185i | −0.153743 | + | 0.988111i | \(0.549133\pi\) |
−0.988111 | + | 0.153743i | \(0.950867\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 68.0250 | + | 337.218i | 0.289468 | + | 1.43497i | ||||
\(236\) | 172.527 | 0.731048 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −70.0610 | + | 70.0610i | −0.294374 | + | 0.294374i | ||||
\(239\) | 420.919i | 1.76117i | 0.473890 | + | 0.880584i | \(0.342849\pi\) | ||||
−0.473890 | + | 0.880584i | \(0.657151\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −347.574 | −1.44222 | −0.721108 | − | 0.692823i | \(-0.756367\pi\) | ||||
−0.721108 | + | 0.692823i | \(0.756367\pi\) | |||||||
\(242\) | 191.676 | + | 191.676i | 0.792049 | + | 0.792049i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 58.4157i | 0.239409i | ||||||||
\(245\) | −19.3662 | + | 29.1539i | −0.0790458 | + | 0.118995i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −316.678 | − | 316.678i | −1.28210 | − | 1.28210i | ||||
\(248\) | −22.6983 | + | 22.6983i | −0.0915254 | + | 0.0915254i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −146.183 | + | 99.4006i | −0.584733 | + | 0.397602i | ||||
\(251\) | −175.106 | −0.697632 | −0.348816 | − | 0.937191i | \(-0.613416\pi\) | ||||
−0.348816 | + | 0.937191i | \(0.613416\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −104.337 | + | 104.337i | −0.412399 | + | 0.412399i | ||||
\(254\) | 110.747i | 0.436014i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 227.773 | + | 227.773i | 0.886275 | + | 0.886275i | 0.994163 | − | 0.107888i | \(-0.0344089\pi\) |
−0.107888 | + | 0.994163i | \(0.534409\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 95.7795i | − | 0.369805i | ||||||
\(260\) | −34.6640 | − | 171.839i | −0.133323 | − | 0.660919i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 69.2950 | + | 69.2950i | 0.264485 | + | 0.264485i | ||||
\(263\) | 37.9825 | − | 37.9825i | 0.144420 | − | 0.144420i | −0.631200 | − | 0.775620i | \(-0.717437\pi\) |
0.775620 | + | 0.631200i | \(0.217437\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −27.3036 | + | 5.50778i | −0.103032 | + | 0.0207841i | ||||
\(266\) | 95.5905 | 0.359363 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 131.455 | − | 131.455i | 0.490505 | − | 0.490505i | ||||
\(269\) | 236.114i | 0.877748i | 0.898549 | + | 0.438874i | \(0.144623\pi\) | ||||
−0.898549 | + | 0.438874i | \(0.855377\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 167.587 | 0.618404 | 0.309202 | − | 0.950996i | \(-0.399938\pi\) | ||||
0.309202 | + | 0.950996i | \(0.399938\pi\) | |||||||
\(272\) | 74.8984 | + | 74.8984i | 0.275362 | + | 0.275362i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 58.0741i | 0.211949i | ||||||||
\(275\) | −171.377 | − | 407.495i | −0.623189 | − | 1.48180i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 354.986 | + | 354.986i | 1.28154 | + | 1.28154i | 0.939793 | + | 0.341743i | \(0.111017\pi\) |
0.341743 | + | 0.939793i | \(0.388983\pi\) | |||||||
\(278\) | 80.1068 | − | 80.1068i | 0.288154 | − | 0.288154i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 31.1668 | + | 20.7034i | 0.111310 | + | 0.0739406i | ||||
\(281\) | −396.987 | −1.41277 | −0.706383 | − | 0.707829i | \(-0.749674\pi\) | ||||
−0.706383 | + | 0.707829i | \(0.749674\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 204.927 | − | 204.927i | 0.724124 | − | 0.724124i | −0.245319 | − | 0.969442i | \(-0.578893\pi\) |
0.969442 | + | 0.245319i | \(0.0788926\pi\) | |||||||
\(284\) | − | 2.38389i | − | 0.00839397i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 438.374 | 1.53278 | ||||||||
\(287\) | 110.058 | + | 110.058i | 0.383476 | + | 0.383476i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 412.221i | 1.42637i | ||||||||
\(290\) | −106.499 | + | 21.4835i | −0.367239 | + | 0.0740809i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −174.150 | − | 174.150i | −0.596404 | − | 0.596404i | ||||
\(293\) | 320.724 | − | 320.724i | 1.09462 | − | 1.09462i | 0.0995946 | − | 0.995028i | \(-0.468245\pi\) |
0.995028 | − | 0.0995946i | \(-0.0317546\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 238.657 | − | 359.274i | 0.809008 | − | 1.21788i | ||||
\(296\) | −102.393 | −0.345921 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 216.650 | − | 216.650i | 0.727013 | − | 0.727013i | ||||
\(299\) | 146.281i | 0.489234i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.05793 | −0.00351473 | ||||||||
\(302\) | −170.036 | − | 170.036i | −0.563033 | − | 0.563033i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 102.191i | − | 0.336153i | ||||||
\(305\) | 121.646 | + | 80.8066i | 0.398840 | + | 0.264940i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33.1738 | + | 33.1738i | 0.108058 | + | 0.108058i | 0.759069 | − | 0.651011i | \(-0.225655\pi\) |
−0.651011 | + | 0.759069i | \(0.725655\pi\) | |||||||
\(308\) | −66.1624 | + | 66.1624i | −0.214813 | + | 0.214813i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15.8688 | + | 78.6660i | 0.0511897 | + | 0.253761i | ||||
\(311\) | 31.4965 | 0.101275 | 0.0506375 | − | 0.998717i | \(-0.483875\pi\) | ||||
0.0506375 | + | 0.998717i | \(0.483875\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 117.156 | − | 117.156i | 0.374299 | − | 0.374299i | −0.494741 | − | 0.869040i | \(-0.664737\pi\) |
0.869040 | + | 0.494741i | \(0.164737\pi\) | |||||||
\(314\) | 329.298i | 1.04872i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −110.192 | −0.348708 | ||||||||
\(317\) | −256.649 | − | 256.649i | −0.809619 | − | 0.809619i | 0.174957 | − | 0.984576i | \(-0.444021\pi\) |
−0.984576 | + | 0.174957i | \(0.944021\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 271.688i | − | 0.851686i | ||||||
\(320\) | 22.1328 | − | 33.3187i | 0.0691651 | − | 0.104121i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −22.0777 | − | 22.0777i | −0.0685644 | − | 0.0685644i | ||||
\(323\) | 478.369 | − | 478.369i | 1.48102 | − | 1.48102i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −405.792 | − | 165.520i | −1.24859 | − | 0.509292i | ||||
\(326\) | 209.263 | 0.641912 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 117.657 | − | 117.657i | 0.358709 | − | 0.358709i | ||||
\(329\) | − | 182.034i | − | 0.553294i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −536.093 | −1.61962 | −0.809809 | − | 0.586694i | \(-0.800429\pi\) | ||||
−0.809809 | + | 0.586694i | \(0.800429\pi\) | |||||||
\(332\) | 183.602 | + | 183.602i | 0.553019 | + | 0.553019i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 430.649i | 1.28937i | ||||||||
\(335\) | −91.9029 | − | 455.588i | −0.274337 | − | 1.35996i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 147.571 | + | 147.571i | 0.437896 | + | 0.437896i | 0.891304 | − | 0.453407i | \(-0.149792\pi\) |
−0.453407 | + | 0.891304i | \(0.649792\pi\) | |||||||
\(338\) | 138.302 | − | 138.302i | 0.409177 | − | 0.409177i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 259.577 | − | 52.3629i | 0.763462 | − | 0.154008i | ||||
\(341\) | −200.683 | −0.588513 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0958 | − | 13.0958i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | 1.13098i | 0.00328773i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 100.802 | 0.291334 | ||||||||
\(347\) | −53.7981 | − | 53.7981i | −0.155038 | − | 0.155038i | 0.625326 | − | 0.780364i | \(-0.284966\pi\) |
−0.780364 | + | 0.625326i | \(0.784966\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 71.8031i | 0.205740i | 0.994695 | + | 0.102870i | \(0.0328025\pi\) | ||||
−0.994695 | + | 0.102870i | \(0.967197\pi\) | |||||||
\(350\) | 86.2262 | − | 36.2634i | 0.246361 | − | 0.103610i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 70.7306 | + | 70.7306i | 0.200939 | + | 0.200939i | ||||
\(353\) | −114.588 | + | 114.588i | −0.324612 | + | 0.324612i | −0.850533 | − | 0.525921i | \(-0.823721\pi\) |
0.525921 | + | 0.850533i | \(0.323721\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.96426 | − | 3.29764i | −0.0139838 | − | 0.00928912i | ||||
\(356\) | −207.931 | −0.584076 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.2898 | + | 21.2898i | −0.0594687 | + | 0.0594687i | ||||
\(359\) | − | 60.5664i | − | 0.168709i | −0.996436 | − | 0.0843543i | \(-0.973117\pi\) | ||
0.996436 | − | 0.0843543i | \(-0.0268828\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −291.682 | −0.807983 | ||||||||
\(362\) | −22.7581 | − | 22.7581i | −0.0628678 | − | 0.0628678i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 92.7602i | 0.254836i | ||||||||
\(365\) | −603.555 | + | 121.751i | −1.65358 | + | 0.333566i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.4536 | − | 18.4536i | −0.0502824 | − | 0.0502824i | 0.681519 | − | 0.731801i | \(-0.261320\pi\) |
−0.731801 | + | 0.681519i | \(0.761320\pi\) | |||||||
\(368\) | −23.6021 | + | 23.6021i | −0.0641361 | + | 0.0641361i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −141.640 | + | 213.224i | −0.382810 | + | 0.576282i | ||||
\(371\) | 14.7387 | 0.0397270 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 269.454 | − | 269.454i | 0.722397 | − | 0.722397i | −0.246696 | − | 0.969093i | \(-0.579345\pi\) |
0.969093 | + | 0.246696i | \(0.0793448\pi\) | |||||||
\(374\) | 662.201i | 1.77059i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −194.602 | −0.517559 | ||||||||
\(377\) | −190.454 | − | 190.454i | −0.505184 | − | 0.505184i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.4860i | 0.0276676i | 0.999904 | + | 0.0138338i | \(0.00440357\pi\) | ||||
−0.999904 | + | 0.0138338i | \(0.995596\pi\) | |||||||
\(380\) | −212.804 | − | 141.360i | −0.560010 | − | 0.372001i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 113.711 | + | 113.711i | 0.297672 | + | 0.297672i | ||||
\(383\) | −93.8346 | + | 93.8346i | −0.244999 | + | 0.244999i | −0.818915 | − | 0.573916i | \(-0.805424\pi\) |
0.573916 | + | 0.818915i | \(0.305424\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 46.2554 | + | 229.301i | 0.120144 | + | 0.595586i | ||||
\(386\) | 219.872 | 0.569616 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −174.947 | + | 174.947i | −0.450894 | + | 0.450894i | ||||
\(389\) | 130.485i | 0.335437i | 0.985835 | + | 0.167718i | \(0.0536399\pi\) | ||||
−0.985835 | + | 0.167718i | \(0.946360\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −220.970 | −0.565140 | ||||||||
\(392\) | −14.0000 | − | 14.0000i | −0.0357143 | − | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 164.421i | − | 0.417313i | ||||||
\(395\) | −152.429 | + | 229.466i | −0.385895 | + | 0.580926i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 44.8845 | + | 44.8845i | 0.113059 | + | 0.113059i | 0.761373 | − | 0.648314i | \(-0.224526\pi\) |
−0.648314 | + | 0.761373i | \(0.724526\pi\) | |||||||
\(398\) | −232.689 | + | 232.689i | −0.584646 | + | 0.584646i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −38.7673 | − | 92.1797i | −0.0969181 | − | 0.230449i | ||||
\(401\) | −329.486 | −0.821660 | −0.410830 | − | 0.911712i | \(-0.634761\pi\) | ||||
−0.410830 | + | 0.911712i | \(0.634761\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −140.679 | + | 140.679i | −0.349081 | + | 0.349081i | ||||
\(404\) | − | 11.6418i | − | 0.0288164i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 57.4893 | 0.141599 | ||||||||
\(407\) | −452.643 | − | 452.643i | −1.11214 | − | 1.11214i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 388.439i | − | 0.949730i | −0.880059 | − | 0.474865i | \(-0.842497\pi\) | ||
0.880059 | − | 0.474865i | \(-0.157503\pi\) | |||||||
\(410\) | −82.2560 | − | 407.765i | −0.200624 | − | 0.994549i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 121.561 | + | 121.561i | 0.295051 | + | 0.295051i | ||||
\(413\) | −161.384 | + | 161.384i | −0.390761 | + | 0.390761i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 636.315 | − | 128.360i | 1.53329 | − | 0.309301i | ||||
\(416\) | 99.1648 | 0.238377 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 451.750 | − | 451.750i | 1.08074 | − | 1.08074i | ||||
\(419\) | − | 268.553i | − | 0.640937i | −0.947259 | − | 0.320469i | \(-0.896160\pi\) | ||
0.947259 | − | 0.320469i | \(-0.103840\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −680.092 | −1.61542 | −0.807710 | − | 0.589580i | \(-0.799293\pi\) | ||||
−0.807710 | + | 0.589580i | \(0.799293\pi\) | |||||||
\(422\) | −341.021 | − | 341.021i | −0.808107 | − | 0.808107i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 15.7564i | − | 0.0371612i | ||||||
\(425\) | 250.032 | − | 612.982i | 0.588310 | − | 1.44231i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −54.6429 | − | 54.6429i | −0.127969 | − | 0.127969i | ||||
\(428\) | 161.362 | − | 161.362i | 0.377013 | − | 0.377013i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.35518 | + | 1.56449i | 0.00547715 | + | 0.00363834i | ||||
\(431\) | −451.123 | −1.04669 | −0.523344 | − | 0.852121i | \(-0.675316\pi\) | ||||
−0.523344 | + | 0.852121i | \(0.675316\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −223.798 | + | 223.798i | −0.516855 | + | 0.516855i | −0.916618 | − | 0.399763i | \(-0.869092\pi\) |
0.399763 | + | 0.916618i | \(0.369092\pi\) | |||||||
\(434\) | − | 42.4646i | − | 0.0978447i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −128.890 | −0.295619 | ||||||||
\(437\) | 150.744 | + | 150.744i | 0.344953 | + | 0.344953i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 599.647i | − | 1.36594i | −0.730447 | − | 0.682969i | \(-0.760688\pi\) | ||
0.730447 | − | 0.682969i | \(-0.239312\pi\) | |||||||
\(440\) | 245.133 | − | 49.4491i | 0.557119 | − | 0.112384i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 464.205 | + | 464.205i | 1.05024 | + | 1.05024i | ||||
\(443\) | −212.227 | + | 212.227i | −0.479068 | + | 0.479068i | −0.904834 | − | 0.425765i | \(-0.860005\pi\) |
0.425765 | + | 0.904834i | \(0.360005\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −287.631 | + | 433.000i | −0.646362 | + | 0.973033i | ||||
\(446\) | 237.041 | 0.531482 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −14.9666 | + | 14.9666i | −0.0334077 | + | 0.0334077i | ||||
\(449\) | 69.3409i | 0.154434i | 0.997014 | + | 0.0772170i | \(0.0246034\pi\) | ||||
−0.997014 | + | 0.0772170i | \(0.975397\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1040.24 | 2.30652 | ||||||||
\(452\) | −161.755 | − | 161.755i | −0.357864 | − | 0.357864i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.19917i | 0.00704662i | ||||||||
\(455\) | 193.166 | + | 128.315i | 0.424540 | + | 0.282012i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −399.145 | − | 399.145i | −0.873404 | − | 0.873404i | 0.119438 | − | 0.992842i | \(-0.461891\pi\) |
−0.992842 | + | 0.119438i | \(0.961891\pi\) | |||||||
\(458\) | −59.2261 | + | 59.2261i | −0.129315 | + | 0.129315i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 16.5007 | + | 81.7983i | 0.0358710 | + | 0.177822i | ||||
\(461\) | −357.157 | −0.774743 | −0.387372 | − | 0.921924i | \(-0.626617\pi\) | ||||
−0.387372 | + | 0.921924i | \(0.626617\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 139.822 | − | 139.822i | 0.301991 | − | 0.301991i | −0.539801 | − | 0.841793i | \(-0.681501\pi\) |
0.841793 | + | 0.539801i | \(0.181501\pi\) | |||||||
\(464\) | − | 61.4587i | − | 0.132454i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −532.104 | −1.14185 | ||||||||
\(467\) | 429.131 | + | 429.131i | 0.918909 | + | 0.918909i | 0.996950 | − | 0.0780407i | \(-0.0248664\pi\) |
−0.0780407 | + | 0.996950i | \(0.524866\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 245.930i | 0.524372i | ||||||||
\(470\) | −269.193 | + | 405.243i | −0.572752 | + | 0.862220i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 172.527 | + | 172.527i | 0.365524 | + | 0.365524i | ||||
\(473\) | −4.99968 | + | 4.99968i | −0.0105701 | + | 0.0105701i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −588.743 | + | 247.603i | −1.23946 | + | 0.521269i | ||||
\(476\) | −140.122 | −0.294374 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −420.919 | + | 420.919i | −0.880584 | + | 0.880584i | ||||
\(479\) | 524.078i | 1.09411i | 0.837097 | + | 0.547054i | \(0.184251\pi\) | ||||
−0.837097 | + | 0.547054i | \(0.815749\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −634.609 | −1.31935 | ||||||||
\(482\) | −347.574 | − | 347.574i | −0.721108 | − | 0.721108i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 383.352i | 0.792049i | ||||||||
\(485\) | 122.309 | + | 606.317i | 0.252183 | + | 1.25014i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 234.249 | + | 234.249i | 0.481005 | + | 0.481005i | 0.905453 | − | 0.424447i | \(-0.139532\pi\) |
−0.424447 | + | 0.905453i | \(0.639532\pi\) | |||||||
\(488\) | −58.4157 | + | 58.4157i | −0.119704 | + | 0.119704i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −48.5201 | + | 9.78767i | −0.0990206 | + | 0.0199748i | ||||
\(491\) | −171.731 | −0.349758 | −0.174879 | − | 0.984590i | \(-0.555954\pi\) | ||||
−0.174879 | + | 0.984590i | \(0.555954\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 287.697 | − | 287.697i | 0.583564 | − | 0.583564i | ||||
\(494\) | − | 633.357i | − | 1.28210i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −45.3966 | −0.0915254 | ||||||||
\(497\) | 2.22992 | + | 2.22992i | 0.00448677 | + | 0.00448677i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 507.901i | − | 1.01784i | −0.860814 | − | 0.508919i | \(-0.830045\pi\) | ||
0.860814 | − | 0.508919i | \(-0.169955\pi\) | |||||||
\(500\) | −245.584 | − | 46.7826i | −0.491168 | − | 0.0935652i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −175.106 | − | 175.106i | −0.348816 | − | 0.348816i | ||||
\(503\) | −409.302 | + | 409.302i | −0.813722 | + | 0.813722i | −0.985190 | − | 0.171468i | \(-0.945149\pi\) |
0.171468 | + | 0.985190i | \(0.445149\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.2432 | − | 16.1042i | −0.0480064 | − | 0.0318895i | ||||
\(506\) | −208.674 | −0.412399 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −110.747 | + | 110.747i | −0.218007 | + | 0.218007i | ||||
\(509\) | 762.148i | 1.49734i | 0.662941 | + | 0.748671i | \(0.269308\pi\) | ||||
−0.662941 | + | 0.748671i | \(0.730692\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 325.805 | 0.637582 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 455.545i | 0.886275i | ||||||||
\(515\) | 421.296 | − | 84.9855i | 0.818051 | − | 0.165020i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −860.270 | − | 860.270i | −1.66396 | − | 1.66396i | ||||
\(518\) | 95.7795 | − | 95.7795i | 0.184903 | − | 0.184903i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 137.175 | − | 206.503i | 0.263798 | − | 0.397121i | ||||
\(521\) | 870.243 | 1.67033 | 0.835166 | − | 0.549999i | \(-0.185372\pi\) | ||||
0.835166 | + | 0.549999i | \(0.185372\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 94.5185 | − | 94.5185i | 0.180724 | − | 0.180724i | −0.610947 | − | 0.791671i | \(-0.709211\pi\) |
0.791671 | + | 0.610947i | \(0.209211\pi\) | |||||||
\(524\) | 138.590i | 0.264485i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 75.9650 | 0.144420 | ||||||||
\(527\) | −212.508 | − | 212.508i | −0.403241 | − | 0.403241i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 459.368i | 0.868370i | ||||||||
\(530\) | −32.8114 | − | 21.7958i | −0.0619082 | − | 0.0411241i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 95.5905 | + | 95.5905i | 0.179681 | + | 0.179681i | ||||
\(533\) | 729.212 | − | 729.212i | 1.36813 | − | 1.36813i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −112.811 | − | 559.234i | −0.210862 | − | 1.04530i | ||||
\(536\) | 262.911 | 0.490505 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −236.114 | + | 236.114i | −0.438874 | + | 0.438874i | ||||
\(539\) | − | 123.779i | − | 0.229645i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −211.503 | −0.390948 | −0.195474 | − | 0.980709i | \(-0.562624\pi\) | ||||
−0.195474 | + | 0.980709i | \(0.562624\pi\) | |||||||
\(542\) | 167.587 | + | 167.587i | 0.309202 | + | 0.309202i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 149.797i | 0.275362i | ||||||||
\(545\) | −178.294 | + | 268.403i | −0.327144 | + | 0.492483i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 76.5236 | + | 76.5236i | 0.139897 | + | 0.139897i | 0.773587 | − | 0.633690i | \(-0.218461\pi\) |
−0.633690 | + | 0.773587i | \(0.718461\pi\) | |||||||
\(548\) | −58.0741 | + | 58.0741i | −0.105975 | + | 0.105975i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 236.118 | − | 578.872i | 0.429306 | − | 1.05249i | ||||
\(551\) | −392.531 | −0.712397 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 103.075 | − | 103.075i | 0.186392 | − | 0.186392i | ||||
\(554\) | 709.971i | 1.28154i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 160.214 | 0.288154 | ||||||||
\(557\) | −251.466 | − | 251.466i | −0.451465 | − | 0.451465i | 0.444376 | − | 0.895841i | \(-0.353426\pi\) |
−0.895841 | + | 0.444376i | \(0.853426\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.00959i | 0.0125395i | ||||||||
\(560\) | 10.4635 | + | 51.8702i | 0.0186847 | + | 0.0926253i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −396.987 | − | 396.987i | −0.706383 | − | 0.706383i | ||||
\(563\) | 89.8908 | − | 89.8908i | 0.159664 | − | 0.159664i | −0.622754 | − | 0.782418i | \(-0.713986\pi\) |
0.782418 | + | 0.622754i | \(0.213986\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −560.597 | + | 113.086i | −0.992207 | + | 0.200152i | ||||
\(566\) | 409.854 | 0.724124 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.38389 | − | 2.38389i | 0.00419699 | − | 0.00419699i | ||||
\(569\) | − | 404.950i | − | 0.711687i | −0.934545 | − | 0.355844i | \(-0.884194\pi\) | ||
0.934545 | − | 0.355844i | \(-0.115806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 186.774 | 0.327099 | 0.163550 | − | 0.986535i | \(-0.447706\pi\) | ||||
0.163550 | + | 0.986535i | \(0.447706\pi\) | |||||||
\(572\) | 438.374 | + | 438.374i | 0.766388 | + | 0.766388i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 220.115i | 0.383476i | ||||||||
\(575\) | 193.164 | + | 78.7904i | 0.335937 | + | 0.137027i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −428.779 | − | 428.779i | −0.743117 | − | 0.743117i | 0.230059 | − | 0.973177i | \(-0.426108\pi\) |
−0.973177 | + | 0.230059i | \(0.926108\pi\) | |||||||
\(578\) | −412.221 | + | 412.221i | −0.713184 | + | 0.713184i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −127.983 | − | 85.0159i | −0.220660 | − | 0.146579i | ||||
\(581\) | −343.489 | −0.591202 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 69.6535 | − | 69.6535i | 0.119474 | − | 0.119474i | ||||
\(584\) | − | 348.300i | − | 0.596404i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 641.449 | 1.09462 | ||||||||
\(587\) | 278.861 | + | 278.861i | 0.475061 | + | 0.475061i | 0.903548 | − | 0.428487i | \(-0.140953\pi\) |
−0.428487 | + | 0.903548i | \(0.640953\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 289.944i | 0.492265i | ||||||||
\(590\) | 597.932 | − | 120.617i | 1.01344 | − | 0.204436i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −102.393 | − | 102.393i | −0.172960 | − | 0.172960i | ||||
\(593\) | −439.594 | + | 439.594i | −0.741306 | + | 0.741306i | −0.972829 | − | 0.231523i | \(-0.925629\pi\) |
0.231523 | + | 0.972829i | \(0.425629\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −193.831 | + | 291.793i | −0.325766 | + | 0.490408i | ||||
\(596\) | 433.300 | 0.727013 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −146.281 | + | 146.281i | −0.244617 | + | 0.244617i | ||||
\(599\) | 782.181i | 1.30581i | 0.757439 | + | 0.652906i | \(0.226450\pi\) | ||||
−0.757439 | + | 0.652906i | \(0.773550\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 589.687 | 0.981177 | 0.490589 | − | 0.871391i | \(-0.336782\pi\) | ||||
0.490589 | + | 0.871391i | \(0.336782\pi\) | |||||||
\(602\) | −1.05793 | − | 1.05793i | −0.00175737 | − | 0.00175737i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 340.072i | − | 0.563033i | ||||||
\(605\) | 798.300 | + | 530.291i | 1.31950 | + | 0.876514i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −167.200 | − | 167.200i | −0.275453 | − | 0.275453i | 0.555838 | − | 0.831291i | \(-0.312398\pi\) |
−0.831291 | + | 0.555838i | \(0.812398\pi\) | |||||||
\(608\) | 102.191 | − | 102.191i | 0.168077 | − | 0.168077i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 40.8396 | + | 202.453i | 0.0669501 | + | 0.331890i | ||||
\(611\) | −1206.10 | −1.97398 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −334.599 | + | 334.599i | −0.545838 | + | 0.545838i | −0.925234 | − | 0.379396i | \(-0.876132\pi\) |
0.379396 | + | 0.925234i | \(0.376132\pi\) | |||||||
\(614\) | 66.3477i | 0.108058i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −132.325 | −0.214813 | ||||||||
\(617\) | 79.8866 | + | 79.8866i | 0.129476 | + | 0.129476i | 0.768875 | − | 0.639399i | \(-0.220817\pi\) |
−0.639399 | + | 0.768875i | \(0.720817\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 415.380i | 0.671050i | 0.942031 | + | 0.335525i | \(0.108914\pi\) | ||||
−0.942031 | + | 0.335525i | \(0.891086\pi\) | |||||||
\(620\) | −62.7972 | + | 94.5348i | −0.101286 | + | 0.152475i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 31.4965 | + | 31.4965i | 0.0506375 | + | 0.0506375i | ||||
\(623\) | 194.502 | − | 194.502i | 0.312202 | − | 0.312202i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −437.138 | + | 446.694i | −0.699420 | + | 0.714711i | ||||
\(626\) | 234.311 | 0.374299 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −329.298 | + | 329.298i | −0.524360 | + | 0.524360i | ||||
\(629\) | − | 958.630i | − | 1.52405i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −452.429 | −0.717002 | −0.358501 | − | 0.933529i | \(-0.616712\pi\) | ||||
−0.358501 | + | 0.933529i | \(0.616712\pi\) | |||||||
\(632\) | −110.192 | − | 110.192i | −0.174354 | − | 0.174354i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 513.298i | − | 0.809619i | ||||||
\(635\) | 77.4257 | + | 383.820i | 0.121930 | + | 0.604441i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −86.7692 | − | 86.7692i | −0.136215 | − | 0.136215i | ||||
\(638\) | 271.688 | − | 271.688i | 0.425843 | − | 0.425843i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 55.4516 | − | 11.1859i | 0.0866431 | − | 0.0174780i | ||||
\(641\) | 333.271 | 0.519924 | 0.259962 | − | 0.965619i | \(-0.416290\pi\) | ||||
0.259962 | + | 0.965619i | \(0.416290\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 614.442 | − | 614.442i | 0.955587 | − | 0.955587i | −0.0434678 | − | 0.999055i | \(-0.513841\pi\) |
0.999055 | + | 0.0434678i | \(0.0138406\pi\) | |||||||
\(644\) | − | 44.1555i | − | 0.0685644i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 956.738 | 1.48102 | ||||||||
\(647\) | −800.292 | − | 800.292i | −1.23693 | − | 1.23693i | −0.961250 | − | 0.275678i | \(-0.911098\pi\) |
−0.275678 | − | 0.961250i | \(-0.588902\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1525.37i | 2.35034i | ||||||||
\(650\) | −240.272 | − | 571.311i | −0.369649 | − | 0.878941i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 209.263 | + | 209.263i | 0.320956 | + | 0.320956i | ||||
\(653\) | 327.250 | − | 327.250i | 0.501148 | − | 0.501148i | −0.410647 | − | 0.911795i | \(-0.634697\pi\) |
0.911795 | + | 0.410647i | \(0.134697\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 288.603 | + | 191.712i | 0.440615 | + | 0.292690i | ||||
\(656\) | 235.313 | 0.358709 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 182.034 | − | 182.034i | 0.276647 | − | 0.276647i | ||||
\(659\) | − | 1113.68i | − | 1.68995i | −0.534802 | − | 0.844977i | \(-0.679614\pi\) | ||
0.534802 | − | 0.844977i | \(-0.320386\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −58.5883 | −0.0886359 | −0.0443179 | − | 0.999017i | \(-0.514111\pi\) | ||||
−0.0443179 | + | 0.999017i | \(0.514111\pi\) | |||||||
\(662\) | −536.093 | − | 536.093i | −0.809809 | − | 0.809809i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 367.205i | 0.553019i | ||||||||
\(665\) | 331.290 | − | 66.8292i | 0.498181 | − | 0.100495i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 90.6596 | + | 90.6596i | 0.135921 | + | 0.135921i | ||||
\(668\) | −430.649 | + | 430.649i | −0.644684 | + | 0.644684i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 363.685 | − | 547.491i | 0.542813 | − | 0.817150i | ||||
\(671\) | −516.472 | −0.769706 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 544.810 | − | 544.810i | 0.809524 | − | 0.809524i | −0.175038 | − | 0.984562i | \(-0.556005\pi\) |
0.984562 | + | 0.175038i | \(0.0560048\pi\) | |||||||
\(674\) | 295.142i | 0.437896i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 276.604 | 0.409177 | ||||||||
\(677\) | 654.528 | + | 654.528i | 0.966807 | + | 0.966807i | 0.999467 | − | 0.0326593i | \(-0.0103976\pi\) |
−0.0326593 | + | 0.999467i | \(0.510398\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 327.295i | − | 0.482026i | ||||||
\(680\) | 311.940 | + | 207.214i | 0.458735 | + | 0.304727i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −200.683 | − | 200.683i | −0.294257 | − | 0.294257i | ||||
\(683\) | 378.585 | − | 378.585i | 0.554298 | − | 0.554298i | −0.373381 | − | 0.927678i | \(-0.621801\pi\) |
0.927678 | + | 0.373381i | \(0.121801\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.6007 | + | 201.269i | 0.0592711 | + | 0.293823i | ||||
\(686\) | 26.1916 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.13098 | + | 1.13098i | −0.00164387 | + | 0.00164387i | ||||
\(689\) | − | 97.6547i | − | 0.141734i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 612.032 | 0.885719 | 0.442859 | − | 0.896591i | \(-0.353964\pi\) | ||||
0.442859 | + | 0.896591i | \(0.353964\pi\) | |||||||
\(692\) | 100.802 | + | 100.802i | 0.145667 | + | 0.145667i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 107.596i | − | 0.155038i | ||||||
\(695\) | 221.624 | − | 333.632i | 0.318883 | − | 0.480046i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1101.54 | + | 1101.54i | 1.58040 | + | 1.58040i | ||||
\(698\) | −71.8031 | + | 71.8031i | −0.102870 | + | 0.102870i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 122.490 | + | 49.9628i | 0.174985 | + | 0.0713754i | ||||
\(701\) | −351.130 | −0.500899 | −0.250450 | − | 0.968130i | \(-0.580578\pi\) | ||||
−0.250450 | + | 0.968130i | \(0.580578\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −653.972 | + | 653.972i | −0.930259 | + | 0.930259i | ||||
\(704\) | 141.461i | 0.200939i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −229.176 | −0.324612 | ||||||||
\(707\) | 10.8899 | + | 10.8899i | 0.0154030 | + | 0.0154030i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 652.326i | 0.920065i | 0.887902 | + | 0.460033i | \(0.152162\pi\) | ||||
−0.887902 | + | 0.460033i | \(0.847838\pi\) | |||||||
\(710\) | −1.66662 | − | 8.26189i | −0.00234735 | − | 0.0116365i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −207.931 | − | 207.931i | −0.292038 | − | 0.292038i | ||||
\(713\) | 66.9659 | − | 66.9659i | 0.0939213 | − | 0.0939213i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1519.28 | − | 306.476i | 2.12487 | − | 0.428637i | ||||
\(716\) | −42.5796 | −0.0594687 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 60.5664 | − | 60.5664i | 0.0843543 | − | 0.0843543i | ||||
\(719\) | − | 823.559i | − | 1.14542i | −0.819757 | − | 0.572711i | \(-0.805892\pi\) | ||
0.819757 | − | 0.572711i | \(-0.194108\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −227.419 | −0.315422 | ||||||||
\(722\) | −291.682 | − | 291.682i | −0.403991 | − | 0.403991i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 45.5163i | − | 0.0628678i | ||||||
\(725\) | −354.078 | + | 148.911i | −0.488383 | + | 0.205395i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −724.914 | − | 724.914i | −0.997131 | − | 0.997131i | 0.00286477 | − | 0.999996i | \(-0.499088\pi\) |
−0.999996 | + | 0.00286477i | \(0.999088\pi\) | |||||||
\(728\) | −92.7602 | + | 92.7602i | −0.127418 | + | 0.127418i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −725.306 | − | 481.804i | −0.993571 | − | 0.660005i | ||||
\(731\) | −10.5886 | −0.0144850 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.2582 | − | 49.2582i | 0.0672008 | − | 0.0672008i | −0.672708 | − | 0.739908i | \(-0.734869\pi\) |
0.739908 | + | 0.672708i | \(0.234869\pi\) | |||||||
\(734\) | − | 36.9073i | − | 0.0502824i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −47.2042 | −0.0641361 | ||||||||
\(737\) | 1162.24 | + | 1162.24i | 1.57699 | + | 1.57699i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 417.024i | 0.564309i | 0.959369 | + | 0.282154i | \(0.0910490\pi\) | ||||
−0.959369 | + | 0.282154i | \(0.908951\pi\) | |||||||
\(740\) | −354.864 | + | 71.5846i | −0.479546 | + | 0.0967360i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.7387 | + | 14.7387i | 0.0198635 | + | 0.0198635i | ||||
\(743\) | 736.124 | − | 736.124i | 0.990746 | − | 0.990746i | −0.00921142 | − | 0.999958i | \(-0.502932\pi\) |
0.999958 | + | 0.00921142i | \(0.00293213\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 599.384 | − | 902.313i | 0.804543 | − | 1.21116i | ||||
\(746\) | 538.908 | 0.722397 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −662.201 | + | 662.201i | −0.885295 | + | 0.885295i | ||||
\(749\) | 301.880i | 0.403044i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1083.70 | 1.44301 | 0.721506 | − | 0.692409i | \(-0.243450\pi\) | ||||
0.721506 | + | 0.692409i | \(0.243450\pi\) | |||||||
\(752\) | −194.602 | − | 194.602i | −0.258779 | − | 0.258779i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 380.909i | − | 0.505184i | ||||||
\(755\) | −708.173 | − | 470.422i | −0.937978 | − | 0.623076i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1002.25 | + | 1002.25i | 1.32397 | + | 1.32397i | 0.910532 | + | 0.413439i | \(0.135672\pi\) |
0.413439 | + | 0.910532i | \(0.364328\pi\) | |||||||
\(758\) | −10.4860 | + | 10.4860i | −0.0138338 | + | 0.0138338i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −71.4434 | − | 354.164i | −0.0940044 | − | 0.466005i | ||||
\(761\) | −1104.17 | −1.45095 | −0.725474 | − | 0.688250i | \(-0.758379\pi\) | ||||
−0.725474 | + | 0.688250i | \(0.758379\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 120.566 | − | 120.566i | 0.158015 | − | 0.158015i | ||||
\(764\) | 227.421i | 0.297672i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −187.669 | −0.244999 | ||||||||
\(767\) | 1069.29 | + | 1069.29i | 1.39412 | + | 1.39412i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 198.908i | − | 0.258658i | −0.991602 | − | 0.129329i | \(-0.958718\pi\) | ||
0.991602 | − | 0.129329i | \(-0.0412823\pi\) | |||||||
\(770\) | −183.045 | + | 275.556i | −0.237721 | + | 0.357865i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 219.872 | + | 219.872i | 0.284808 | + | 0.284808i | ||||
\(773\) | −326.316 | + | 326.316i | −0.422142 | + | 0.422142i | −0.885941 | − | 0.463798i | \(-0.846486\pi\) |
0.463798 | + | 0.885941i | \(0.346486\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 109.994 | + | 261.540i | 0.141927 | + | 0.337471i | ||||
\(776\) | −349.894 | −0.450894 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −130.485 | + | 130.485i | −0.167718 | + | 0.167718i | ||||
\(779\) | − | 1502.92i | − | 1.92930i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.0767 | 0.0269868 | ||||||||
\(782\) | −220.970 | − | 220.970i | −0.282570 | − | 0.282570i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 28.0000i | − | 0.0357143i | ||||||
\(785\) | 230.218 | + | 1141.25i | 0.293272 | + | 1.45383i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 337.521 | + | 337.521i | 0.428870 | + | 0.428870i | 0.888243 | − | 0.459373i | \(-0.151926\pi\) |
−0.459373 | + | 0.888243i | \(0.651926\pi\) | |||||||
\(788\) | 164.421 | − | 164.421i | 0.208657 | − | 0.208657i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −381.894 | + | 77.0372i | −0.483411 | + | 0.0975155i | ||||
\(791\) | 302.615 | 0.382573 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −362.049 | + | 362.049i | −0.456556 | + | 0.456556i | ||||
\(794\) | 89.7690i | 0.113059i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −465.378 | −0.584646 | ||||||||
\(797\) | −111.780 | − | 111.780i | −0.140250 | − | 0.140250i | 0.633496 | − | 0.773746i | \(-0.281619\pi\) |
−0.773746 | + | 0.633496i | \(0.781619\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1821.92i | − | 2.28025i | ||||||
\(800\) | 53.4125 | − | 130.947i | 0.0667656 | − | 0.163684i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −329.486 | − | 329.486i | −0.410830 | − | 0.410830i | ||||
\(803\) | 1539.71 | − | 1539.71i | 1.91745 | − | 1.91745i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −91.9503 | − | 61.0803i | −0.114224 | − | 0.0758762i | ||||
\(806\) | −281.359 | −0.349081 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.6418 | − | 11.6418i | 0.0144082 | − | 0.0144082i | ||||
\(809\) | − | 30.4788i | − | 0.0376746i | −0.999823 | − | 0.0188373i | \(-0.994004\pi\) | ||
0.999823 | − | 0.0188373i | \(-0.00599646\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 71.2377 | 0.0878393 | 0.0439197 | − | 0.999035i | \(-0.486015\pi\) | ||||
0.0439197 | + | 0.999035i | \(0.486015\pi\) | |||||||
\(812\) | 57.4893 | + | 57.4893i | 0.0707996 | + | 0.0707996i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 905.286i | − | 1.11214i | ||||||
\(815\) | 725.248 | − | 146.300i | 0.889875 | − | 0.179509i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.22346 | + | 7.22346i | 0.00884145 | + | 0.00884145i | ||||
\(818\) | 388.439 | − | 388.439i | 0.474865 | − | 0.474865i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 325.509 | − | 490.021i | 0.396962 | − | 0.597587i | ||||
\(821\) | 232.520 | 0.283216 | 0.141608 | − | 0.989923i | \(-0.454773\pi\) | ||||
0.141608 | + | 0.989923i | \(0.454773\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −157.877 | + | 157.877i | −0.191832 | + | 0.191832i | −0.796487 | − | 0.604656i | \(-0.793311\pi\) |
0.604656 | + | 0.796487i | \(0.293311\pi\) | |||||||
\(824\) | 243.122i | 0.295051i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −322.769 | −0.390761 | ||||||||
\(827\) | 654.653 | + | 654.653i | 0.791600 | + | 0.791600i | 0.981754 | − | 0.190154i | \(-0.0608987\pi\) |
−0.190154 | + | 0.981754i | \(0.560899\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 863.280i | − | 1.04135i | −0.853755 | − | 0.520675i | \(-0.825680\pi\) | ||
0.853755 | − | 0.520675i | \(-0.174320\pi\) | |||||||
\(830\) | 764.675 | + | 507.955i | 0.921295 | + | 0.611994i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 99.1648 | + | 99.1648i | 0.119188 | + | 0.119188i | ||||
\(833\) | 131.072 | − | 131.072i | 0.157349 | − | 0.157349i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 301.075 | + | 1492.51i | 0.360569 | + | 1.78744i | ||||
\(836\) | 903.500 | 1.08074 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 268.553 | − | 268.553i | 0.320469 | − | 0.320469i | ||||
\(839\) | 1114.46i | 1.32832i | 0.747593 | + | 0.664158i | \(0.231210\pi\) | ||||
−0.747593 | + | 0.664158i | \(0.768790\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 604.927 | 0.719295 | ||||||||
\(842\) | −680.092 | − | 680.092i | −0.807710 | − | 0.807710i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 682.043i | − | 0.808107i | ||||||
\(845\) | 382.626 | − | 576.005i | 0.452812 | − | 0.681663i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −358.593 | − | 358.593i | −0.423368 | − | 0.423368i | ||||
\(848\) | 15.7564 | − | 15.7564i | 0.0185806 | − | 0.0185806i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 863.014 | − | 362.950i | 1.01531 | − | 0.427001i | ||||
\(851\) | 302.085 | 0.354976 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 981.738 | − | 981.738i | 1.15092 | − | 1.15092i | 0.164556 | − | 0.986368i | \(-0.447381\pi\) |
0.986368 | − | 0.164556i | \(-0.0526190\pi\) | |||||||
\(854\) | − | 109.286i | − | 0.127969i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 322.723 | 0.377013 | ||||||||
\(857\) | −52.3297 | − | 52.3297i | −0.0610615 | − | 0.0610615i | 0.675917 | − | 0.736978i | \(-0.263748\pi\) |
−0.736978 | + | 0.675917i | \(0.763748\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1321.03i | 1.53787i | 0.639328 | + | 0.768934i | \(0.279212\pi\) | ||||
−0.639328 | + | 0.768934i | \(0.720788\pi\) | |||||||
\(860\) | 0.790689 | + | 3.91966i | 0.000919406 | + | 0.00455775i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −451.123 | − | 451.123i | −0.523344 | − | 0.523344i | ||||
\(863\) | −610.077 | + | 610.077i | −0.706926 | + | 0.706926i | −0.965888 | − | 0.258962i | \(-0.916620\pi\) |
0.258962 | + | 0.965888i | \(0.416620\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 349.351 | − | 70.4724i | 0.403874 | − | 0.0814710i | ||||
\(866\) | −447.596 | −0.516855 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 42.4646 | − | 42.4646i | 0.0489224 | − | 0.0489224i | ||||
\(869\) | − | 974.242i | − | 1.12111i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1629.47 | 1.87080 | ||||||||
\(872\) | −128.890 | − | 128.890i | −0.147810 | − | 0.147810i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 301.489i | 0.344953i | ||||||||
\(875\) | 273.484 | − | 185.961i | 0.312553 | − | 0.212527i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −866.286 | − | 866.286i | −0.987783 | − | 0.987783i | 0.0121430 | − | 0.999926i | \(-0.496135\pi\) |
−0.999926 | + | 0.0121430i | \(0.996135\pi\) | |||||||
\(878\) | 599.647 | − | 599.647i | 0.682969 | − | 0.682969i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 294.582 | + | 195.683i | 0.334752 | + | 0.222368i | ||||
\(881\) | 1215.34 | 1.37950 | 0.689749 | − | 0.724049i | \(-0.257721\pi\) | ||||
0.689749 | + | 0.724049i | \(0.257721\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −590.925 | + | 590.925i | −0.669224 | + | 0.669224i | −0.957536 | − | 0.288312i | \(-0.906906\pi\) |
0.288312 | + | 0.957536i | \(0.406906\pi\) | |||||||
\(884\) | 928.410i | 1.05024i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −424.454 | −0.479068 | ||||||||
\(887\) | −40.6073 | − | 40.6073i | −0.0457805 | − | 0.0457805i | 0.683846 | − | 0.729626i | \(-0.260306\pi\) |
−0.729626 | + | 0.683846i | \(0.760306\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 207.189i | − | 0.233059i | ||||||
\(890\) | −720.631 | + | 145.369i | −0.809698 | + | 0.163335i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 237.041 | + | 237.041i | 0.265741 | + | 0.265741i | ||||
\(893\) | −1242.91 | + | 1242.91i | −1.39183 | + | 1.39183i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −58.9004 | + | 88.6686i | −0.0658105 | + | 0.0990711i | ||||
\(896\) | −29.9333 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −69.3409 | + | 69.3409i | −0.0772170 | + | 0.0772170i | ||||
\(899\) | 174.376i | 0.193966i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 147.516 | 0.163724 | ||||||||
\(902\) | 1040.24 | + | 1040.24i | 1.15326 | + | 1.15326i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 323.509i | − | 0.357864i | ||||||
\(905\) | −94.7841 | − | 62.9628i | −0.104734 | − | 0.0695721i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −665.210 | − | 665.210i | −0.733417 | − | 0.733417i | 0.237878 | − | 0.971295i | \(-0.423548\pi\) |
−0.971295 | + | 0.237878i | \(0.923548\pi\) | |||||||
\(908\) | −3.19917 | + | 3.19917i | −0.00352331 | + | 0.00352331i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 64.8504 | + | 321.481i | 0.0712642 | + | 0.353276i | ||||
\(911\) | 1249.68 | 1.37177 | 0.685885 | − | 0.727710i | \(-0.259415\pi\) | ||||
0.685885 | + | 0.727710i | \(0.259415\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1623.29 | + | 1623.29i | −1.77797 | + | 1.77797i | ||||
\(914\) | − | 798.291i | − | 0.873404i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −118.452 | −0.129315 | ||||||||
\(917\) | −129.639 | − | 129.639i | −0.141373 | − | 0.141373i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 563.531i | 0.613200i | 0.951838 | + | 0.306600i | \(0.0991914\pi\) | ||||
−0.951838 | + | 0.306600i | \(0.900809\pi\) | |||||||
\(920\) | −65.2976 | + | 98.2990i | −0.0709757 | + | 0.106847i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −357.157 | − | 357.157i | −0.387372 | − | 0.387372i | ||||
\(923\) | 14.7749 | − | 14.7749i | 0.0160074 | − | 0.0160074i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −341.815 | + | 838.000i | −0.369530 | + | 0.905946i | ||||
\(926\) | 279.644 | 0.301991 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 61.4587 | − | 61.4587i | 0.0662270 | − | 0.0662270i | ||||
\(929\) | − | 599.537i | − | 0.645358i | −0.946509 | − | 0.322679i | \(-0.895417\pi\) | ||
0.946509 | − | 0.322679i | \(-0.104583\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −178.833 | −0.192087 | ||||||||
\(932\) | −532.104 | − | 532.104i | −0.570927 | − | 0.570927i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 858.261i | 0.918909i | ||||||||
\(935\) | 462.957 | + | 2295.00i | 0.495141 | + | 2.45455i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 630.405 | + | 630.405i | 0.672791 | + | 0.672791i | 0.958359 | − | 0.285568i | \(-0.0921821\pi\) |
−0.285568 | + | 0.958359i | \(0.592182\pi\) | |||||||
\(938\) | −245.930 | + | 245.930i | −0.262186 | + | 0.262186i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −674.437 | + | 136.050i | −0.717486 | + | 0.144734i | ||||
\(941\) | 734.091 | 0.780118 | 0.390059 | − | 0.920790i | \(-0.372455\pi\) | ||||
0.390059 | + | 0.920790i | \(0.372455\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −347.118 | + | 347.118i | −0.368099 | + | 0.368099i | ||||
\(944\) | 345.055i | 0.365524i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.99935 | −0.0105701 | ||||||||
\(947\) | 1025.55 | + | 1025.55i | 1.08294 | + | 1.08294i | 0.996234 | + | 0.0867100i | \(0.0276354\pi\) |
0.0867100 | + | 0.996234i | \(0.472365\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 2158.69i | − | 2.27470i | ||||||
\(950\) | −836.346 | − | 341.141i | −0.880365 | − | 0.359095i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −140.122 | − | 140.122i | −0.147187 | − | 0.147187i | ||||
\(953\) | −1070.88 | + | 1070.88i | −1.12370 | + | 1.12370i | −0.132515 | + | 0.991181i | \(0.542305\pi\) |
−0.991181 | + | 0.132515i | \(0.957695\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 473.587 | + | 314.592i | 0.495902 | + | 0.329416i | ||||
\(956\) | −841.838 | −0.880584 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −524.078 | + | 524.078i | −0.547054 | + | 0.547054i | ||||
\(959\) | − | 108.647i | − | 0.113292i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −832.197 | −0.865970 | ||||||||
\(962\) | −634.609 | − | 634.609i | −0.659677 | − | 0.659677i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 695.148i | − | 0.721108i | ||||||
\(965\) | 762.015 | − | 153.717i | 0.789653 | − | 0.159292i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −497.222 | − | 497.222i | −0.514191 | − | 0.514191i | 0.401617 | − | 0.915808i | \(-0.368448\pi\) |
−0.915808 | + | 0.401617i | \(0.868448\pi\) | |||||||
\(968\) | −383.352 | + | 383.352i | −0.396025 | + | 0.396025i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −484.008 | + | 728.626i | −0.498978 | + | 0.751161i | ||||
\(971\) | −978.176 | −1.00739 | −0.503695 | − | 0.863881i | \(-0.668027\pi\) | ||||
−0.503695 | + | 0.863881i | \(0.668027\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −149.866 | + | 149.866i | −0.154025 | + | 0.154025i | ||||
\(974\) | 468.499i | 0.481005i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −116.831 | −0.119704 | ||||||||
\(977\) | −964.006 | − | 964.006i | −0.986700 | − | 0.986700i | 0.0132130 | − | 0.999913i | \(-0.495794\pi\) |
−0.999913 | + | 0.0132130i | \(0.995794\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1838.39i | − | 1.87782i | ||||||
\(980\) | −58.3078 | − | 38.7324i | −0.0594977 | − | 0.0395229i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −171.731 | − | 171.731i | −0.174879 | − | 0.174879i | ||||
\(983\) | −93.2350 | + | 93.2350i | −0.0948474 | + | 0.0948474i | −0.752938 | − | 0.658091i | \(-0.771364\pi\) |
0.658091 | + | 0.752938i | \(0.271364\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −114.950 | − | 569.839i | −0.116701 | − | 0.578517i | ||||
\(986\) | 575.394 | 0.583564 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 633.357 | − | 633.357i | 0.641049 | − | 0.641049i | ||||
\(989\) | − | 3.33669i | − | 0.00337380i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 684.463 | 0.690679 | 0.345340 | − | 0.938478i | \(-0.387764\pi\) | ||||
0.345340 | + | 0.938478i | \(0.387764\pi\) | |||||||
\(992\) | −45.3966 | − | 45.3966i | −0.0457627 | − | 0.0457627i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.45985i | 0.00448677i | ||||||||
\(995\) | −643.758 | + | 969.113i | −0.646993 | + | 0.973982i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 426.193 | + | 426.193i | 0.427476 | + | 0.427476i | 0.887768 | − | 0.460292i | \(-0.152255\pi\) |
−0.460292 | + | 0.887768i | \(0.652255\pi\) | |||||||
\(998\) | 507.901 | − | 507.901i | 0.508919 | − | 0.508919i | ||||
\(999\) | 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 | 630.3.o.f.127.6 | 16 | ||
3.2 | odd | 2 | 210.3.l.b.127.2 | yes | 16 | ||
5.3 | odd | 4 | inner | 630.3.o.f.253.6 | 16 | ||
15.2 | even | 4 | 1050.3.l.h.43.8 | 16 | |||
15.8 | even | 4 | 210.3.l.b.43.2 | ✓ | 16 | ||
15.14 | odd | 2 | 1050.3.l.h.757.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.l.b.43.2 | ✓ | 16 | 15.8 | even | 4 | ||
210.3.l.b.127.2 | yes | 16 | 3.2 | odd | 2 | ||
630.3.o.f.127.6 | 16 | 1.1 | even | 1 | trivial | ||
630.3.o.f.253.6 | 16 | 5.3 | odd | 4 | inner | ||
1050.3.l.h.43.8 | 16 | 15.2 | even | 4 | |||
1050.3.l.h.757.8 | 16 | 15.14 | odd | 2 |