Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(37,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.v (of order \(12\), degree \(4\), 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: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 88.8 | ||
Character | \(\chi\) | \(=\) | 105.88 |
Dual form | 105.3.v.a.37.8 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.435396 | − | 0.116664i | −0.217698 | − | 0.0583319i | 0.148322 | − | 0.988939i | \(-0.452613\pi\) |
−0.366019 | + | 0.930607i | \(0.619280\pi\) | |||||||
\(3\) | 1.67303 | − | 0.448288i | 0.557678 | − | 0.149429i | ||||
\(4\) | −3.28814 | − | 1.89841i | −0.822036 | − | 0.474603i | ||||
\(5\) | 3.62365 | + | 3.44517i | 0.724729 | + | 0.689034i | ||||
\(6\) | −0.780730 | −0.130122 | ||||||||
\(7\) | 6.87993 | − | 1.29096i | 0.982847 | − | 0.184423i | ||||
\(8\) | 2.48509 | + | 2.48509i | 0.310637 | + | 0.310637i | ||||
\(9\) | 2.59808 | − | 1.50000i | 0.288675 | − | 0.166667i | ||||
\(10\) | −1.17579 | − | 1.92276i | −0.117579 | − | 0.192276i | ||||
\(11\) | 10.0112 | − | 17.3398i | 0.910106 | − | 1.57635i | 0.0961926 | − | 0.995363i | \(-0.469334\pi\) |
0.813913 | − | 0.580987i | \(-0.197333\pi\) | |||||||
\(12\) | −6.35220 | − | 1.70207i | −0.529350 | − | 0.141839i | ||||
\(13\) | −2.67217 | − | 2.67217i | −0.205552 | − | 0.205552i | 0.596822 | − | 0.802374i | \(-0.296430\pi\) |
−0.802374 | + | 0.596822i | \(0.796430\pi\) | |||||||
\(14\) | −3.14610 | − | 0.240560i | −0.224721 | − | 0.0171828i | ||||
\(15\) | 7.60691 | + | 4.13944i | 0.507127 | + | 0.275963i | ||||
\(16\) | 6.80156 | + | 11.7807i | 0.425098 | + | 0.736291i | ||||
\(17\) | 3.22785 | + | 12.0465i | 0.189874 | + | 0.708618i | 0.993535 | + | 0.113530i | \(0.0362159\pi\) |
−0.803661 | + | 0.595087i | \(0.797117\pi\) | |||||||
\(18\) | −1.30619 | + | 0.349992i | −0.0725659 | + | 0.0194440i | ||||
\(19\) | −18.7697 | + | 10.8367i | −0.987878 | + | 0.570352i | −0.904639 | − | 0.426178i | \(-0.859860\pi\) |
−0.0832385 | + | 0.996530i | \(0.526526\pi\) | |||||||
\(20\) | −5.37472 | − | 18.2074i | −0.268736 | − | 0.910369i | ||||
\(21\) | 10.9316 | − | 5.24401i | 0.520553 | − | 0.249715i | ||||
\(22\) | −6.38175 | + | 6.38175i | −0.290080 | + | 0.290080i | ||||
\(23\) | 7.07907 | − | 26.4195i | 0.307786 | − | 1.14867i | −0.622735 | − | 0.782433i | \(-0.713979\pi\) |
0.930521 | − | 0.366239i | \(-0.119355\pi\) | |||||||
\(24\) | 5.27168 | + | 3.04361i | 0.219653 | + | 0.126817i | ||||
\(25\) | 1.26162 | + | 24.9681i | 0.0504649 | + | 0.998726i | ||||
\(26\) | 0.851706 | + | 1.47520i | 0.0327579 | + | 0.0567384i | ||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | −25.0730 | − | 8.81606i | −0.895463 | − | 0.314859i | ||||
\(29\) | 29.0697i | 1.00240i | 0.865330 | + | 0.501202i | \(0.167109\pi\) | ||||
−0.865330 | + | 0.501202i | \(0.832891\pi\) | |||||||
\(30\) | −2.82909 | − | 2.68975i | −0.0943030 | − | 0.0896582i | ||||
\(31\) | −22.1260 | + | 38.3234i | −0.713742 | + | 1.23624i | 0.249701 | + | 0.968323i | \(0.419668\pi\) |
−0.963443 | + | 0.267915i | \(0.913666\pi\) | |||||||
\(32\) | −5.22542 | − | 19.5015i | −0.163294 | − | 0.609423i | ||||
\(33\) | 8.97576 | − | 33.4980i | 0.271993 | − | 1.01509i | ||||
\(34\) | − | 5.62157i | − | 0.165340i | ||||||
\(35\) | 29.3780 | + | 19.0245i | 0.839372 | + | 0.543558i | ||||
\(36\) | −11.3905 | −0.316402 | ||||||||
\(37\) | −59.0392 | − | 15.8195i | −1.59565 | − | 0.427554i | −0.651928 | − | 0.758281i | \(-0.726040\pi\) |
−0.943727 | + | 0.330727i | \(0.892706\pi\) | |||||||
\(38\) | 9.43648 | − | 2.52850i | 0.248329 | − | 0.0665394i | ||||
\(39\) | −5.66854 | − | 3.27273i | −0.145347 | − | 0.0839162i | ||||
\(40\) | 0.443533 | + | 17.5667i | 0.0110883 | + | 0.439167i | ||||
\(41\) | −19.8782 | −0.484834 | −0.242417 | − | 0.970172i | \(-0.577940\pi\) | ||||
−0.242417 | + | 0.970172i | \(0.577940\pi\) | |||||||
\(42\) | −5.37137 | + | 1.00789i | −0.127890 | + | 0.0239975i | ||||
\(43\) | −14.0418 | − | 14.0418i | −0.326555 | − | 0.326555i | 0.524720 | − | 0.851275i | \(-0.324170\pi\) |
−0.851275 | + | 0.524720i | \(0.824170\pi\) | |||||||
\(44\) | −65.8363 | + | 38.0106i | −1.49628 | + | 0.863877i | ||||
\(45\) | 14.5823 | + | 3.51534i | 0.324050 | + | 0.0781187i | ||||
\(46\) | −6.16439 | + | 10.6770i | −0.134009 | + | 0.232110i | ||||
\(47\) | −10.8275 | − | 2.90122i | −0.230372 | − | 0.0617280i | 0.141786 | − | 0.989897i | \(-0.454715\pi\) |
−0.372158 | + | 0.928169i | \(0.621382\pi\) | |||||||
\(48\) | 16.6604 | + | 16.6604i | 0.347091 | + | 0.347091i | ||||
\(49\) | 45.6668 | − | 17.7635i | 0.931976 | − | 0.362520i | ||||
\(50\) | 2.36358 | − | 11.0182i | 0.0472715 | − | 0.220364i | ||||
\(51\) | 10.8006 | + | 18.7072i | 0.211776 | + | 0.366808i | ||||
\(52\) | 3.71361 | + | 13.8594i | 0.0714155 | + | 0.266526i | ||||
\(53\) | −31.2612 | + | 8.37642i | −0.589834 | + | 0.158046i | −0.541377 | − | 0.840780i | \(-0.682097\pi\) |
−0.0484568 | + | 0.998825i | \(0.515430\pi\) | |||||||
\(54\) | −2.02840 | + | 1.17109i | −0.0375629 | + | 0.0216869i | ||||
\(55\) | 96.0156 | − | 28.3433i | 1.74574 | − | 0.515333i | ||||
\(56\) | 20.3054 | + | 13.8891i | 0.362597 | + | 0.248020i | ||||
\(57\) | −26.5443 | + | 26.5443i | −0.465690 | + | 0.465690i | ||||
\(58\) | 3.39139 | − | 12.6568i | 0.0584722 | − | 0.218221i | ||||
\(59\) | 49.6246 | + | 28.6507i | 0.841094 | + | 0.485606i | 0.857636 | − | 0.514257i | \(-0.171932\pi\) |
−0.0165419 | + | 0.999863i | \(0.505266\pi\) | |||||||
\(60\) | −17.1542 | − | 28.0521i | −0.285904 | − | 0.467535i | ||||
\(61\) | −9.82028 | − | 17.0092i | −0.160988 | − | 0.278840i | 0.774235 | − | 0.632898i | \(-0.218135\pi\) |
−0.935223 | + | 0.354058i | \(0.884801\pi\) | |||||||
\(62\) | 14.1045 | − | 14.1045i | 0.227492 | − | 0.227492i | ||||
\(63\) | 15.9381 | − | 13.6739i | 0.252986 | − | 0.217046i | ||||
\(64\) | − | 45.3120i | − | 0.708000i | ||||||
\(65\) | −0.476922 | − | 18.8891i | −0.00733727 | − | 0.290602i | ||||
\(66\) | −7.81601 | + | 13.5377i | −0.118424 | + | 0.205117i | ||||
\(67\) | −3.54467 | − | 13.2289i | −0.0529055 | − | 0.197446i | 0.934415 | − | 0.356187i | \(-0.115923\pi\) |
−0.987320 | + | 0.158741i | \(0.949257\pi\) | |||||||
\(68\) | 12.2556 | − | 45.7384i | 0.180229 | − | 0.672624i | ||||
\(69\) | − | 47.3741i | − | 0.686581i | ||||||
\(70\) | −10.5716 | − | 11.7105i | −0.151023 | − | 0.167294i | ||||
\(71\) | 71.1638 | 1.00231 | 0.501153 | − | 0.865358i | \(-0.332909\pi\) | ||||
0.501153 | + | 0.865358i | \(0.332909\pi\) | |||||||
\(72\) | 10.1841 | + | 2.72882i | 0.141446 | + | 0.0379003i | ||||
\(73\) | 90.0261 | − | 24.1224i | 1.23323 | − | 0.330444i | 0.417396 | − | 0.908725i | \(-0.362943\pi\) |
0.815838 | + | 0.578281i | \(0.196276\pi\) | |||||||
\(74\) | 23.8598 | + | 13.7755i | 0.322430 | + | 0.186155i | ||||
\(75\) | 13.3037 | + | 41.2070i | 0.177382 | + | 0.549426i | ||||
\(76\) | 82.2898 | 1.08276 | ||||||||
\(77\) | 46.4910 | − | 132.221i | 0.603779 | − | 1.71715i | ||||
\(78\) | 2.08625 | + | 2.08625i | 0.0267467 | + | 0.0267467i | ||||
\(79\) | −112.260 | + | 64.8134i | −1.42101 | + | 0.820423i | −0.996386 | − | 0.0849448i | \(-0.972929\pi\) |
−0.424629 | + | 0.905368i | \(0.639595\pi\) | |||||||
\(80\) | −15.9399 | + | 66.1214i | −0.199248 | + | 0.826518i | ||||
\(81\) | 4.50000 | − | 7.79423i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | 8.65488 | + | 2.31907i | 0.105547 | + | 0.0282813i | ||||
\(83\) | −20.5661 | − | 20.5661i | −0.247785 | − | 0.247785i | 0.572276 | − | 0.820061i | \(-0.306061\pi\) |
−0.820061 | + | 0.572276i | \(0.806061\pi\) | |||||||
\(84\) | −45.9000 | − | 3.50965i | −0.546429 | − | 0.0417815i | ||||
\(85\) | −29.8056 | + | 54.7727i | −0.350655 | + | 0.644385i | ||||
\(86\) | 4.47558 | + | 7.75193i | 0.0520416 | + | 0.0901388i | ||||
\(87\) | 13.0316 | + | 48.6346i | 0.149788 | + | 0.559018i | ||||
\(88\) | 67.9698 | − | 18.2125i | 0.772384 | − | 0.206960i | ||||
\(89\) | −29.0452 | + | 16.7692i | −0.326350 | + | 0.188418i | −0.654219 | − | 0.756305i | \(-0.727003\pi\) |
0.327869 | + | 0.944723i | \(0.393669\pi\) | |||||||
\(90\) | −5.93894 | − | 3.23179i | −0.0659882 | − | 0.0359088i | ||||
\(91\) | −21.8340 | − | 14.9347i | −0.239935 | − | 0.164117i | ||||
\(92\) | −73.4319 | + | 73.4319i | −0.798173 | + | 0.798173i | ||||
\(93\) | −19.8376 | + | 74.0351i | −0.213308 | + | 0.796076i | ||||
\(94\) | 4.37578 | + | 2.52635i | 0.0465508 | + | 0.0268761i | ||||
\(95\) | −105.349 | − | 25.3964i | −1.10894 | − | 0.267331i | ||||
\(96\) | −17.4846 | − | 30.2842i | −0.182131 | − | 0.315461i | ||||
\(97\) | −36.1403 | + | 36.1403i | −0.372580 | + | 0.372580i | −0.868416 | − | 0.495836i | \(-0.834862\pi\) |
0.495836 | + | 0.868416i | \(0.334862\pi\) | |||||||
\(98\) | −21.9555 | + | 2.40646i | −0.224036 | + | 0.0245557i | ||||
\(99\) | − | 60.0670i | − | 0.606737i | ||||||
\(100\) | 43.2514 | − | 84.4939i | 0.432514 | − | 0.844939i | ||||
\(101\) | −40.1000 | + | 69.4552i | −0.397030 | + | 0.687676i | −0.993358 | − | 0.115065i | \(-0.963292\pi\) |
0.596328 | + | 0.802741i | \(0.296626\pi\) | |||||||
\(102\) | −2.52008 | − | 9.40506i | −0.0247067 | − | 0.0922065i | ||||
\(103\) | −8.04297 | + | 30.0168i | −0.0780871 | + | 0.291425i | −0.993916 | − | 0.110145i | \(-0.964869\pi\) |
0.915828 | + | 0.401570i | \(0.131535\pi\) | |||||||
\(104\) | − | 13.2812i | − | 0.127704i | ||||||
\(105\) | 57.6788 | + | 18.6588i | 0.549322 | + | 0.177703i | ||||
\(106\) | 14.5882 | 0.137625 | ||||||||
\(107\) | 101.272 | + | 27.1358i | 0.946469 | + | 0.253606i | 0.698863 | − | 0.715255i | \(-0.253689\pi\) |
0.247606 | + | 0.968861i | \(0.420356\pi\) | |||||||
\(108\) | −19.0566 | + | 5.10620i | −0.176450 | + | 0.0472797i | ||||
\(109\) | 11.9781 | + | 6.91555i | 0.109891 | + | 0.0634454i | 0.553938 | − | 0.832558i | \(-0.313124\pi\) |
−0.444047 | + | 0.896003i | \(0.646458\pi\) | |||||||
\(110\) | −45.1114 | + | 1.13900i | −0.410104 | + | 0.0103545i | ||||
\(111\) | −105.866 | −0.953750 | ||||||||
\(112\) | 62.0026 | + | 72.2695i | 0.553595 | + | 0.645263i | ||||
\(113\) | −67.9147 | − | 67.9147i | −0.601015 | − | 0.601015i | 0.339567 | − | 0.940582i | \(-0.389720\pi\) |
−0.940582 | + | 0.339567i | \(0.889720\pi\) | |||||||
\(114\) | 14.6540 | − | 8.46052i | 0.128544 | − | 0.0742151i | ||||
\(115\) | 116.672 | − | 71.3461i | 1.01453 | − | 0.620401i | ||||
\(116\) | 55.1862 | − | 95.5854i | 0.475743 | − | 0.824012i | ||||
\(117\) | −10.9508 | − | 2.93425i | −0.0935963 | − | 0.0250791i | ||||
\(118\) | −18.2638 | − | 18.2638i | −0.154778 | − | 0.154778i | ||||
\(119\) | 37.7590 | + | 78.7120i | 0.317302 | + | 0.661446i | ||||
\(120\) | 8.61697 | + | 29.1908i | 0.0718080 | + | 0.243256i | ||||
\(121\) | −139.947 | − | 242.395i | −1.15658 | − | 2.00326i | ||||
\(122\) | 2.29134 | + | 8.55141i | 0.0187815 | + | 0.0700936i | ||||
\(123\) | −33.2569 | + | 8.91115i | −0.270381 | + | 0.0724484i | ||||
\(124\) | 145.507 | − | 84.0085i | 1.17344 | − | 0.677488i | ||||
\(125\) | −81.4478 | + | 94.8222i | −0.651582 | + | 0.758578i | ||||
\(126\) | −8.53464 | + | 4.09416i | −0.0677353 | + | 0.0324933i | ||||
\(127\) | −1.81108 | + | 1.81108i | −0.0142604 | + | 0.0142604i | −0.714201 | − | 0.699941i | \(-0.753210\pi\) |
0.699941 | + | 0.714201i | \(0.253210\pi\) | |||||||
\(128\) | −26.1880 | + | 97.7348i | −0.204593 | + | 0.763553i | ||||
\(129\) | −29.7872 | − | 17.1977i | −0.230909 | − | 0.133315i | ||||
\(130\) | −1.99603 | + | 8.27987i | −0.0153540 | + | 0.0636913i | ||||
\(131\) | 66.0246 | + | 114.358i | 0.504005 | + | 0.872961i | 0.999989 | + | 0.00463021i | \(0.00147385\pi\) |
−0.495985 | + | 0.868331i | \(0.665193\pi\) | |||||||
\(132\) | −93.1065 | + | 93.1065i | −0.705353 | + | 0.705353i | ||||
\(133\) | −115.144 | + | 98.7865i | −0.865747 | + | 0.742756i | ||||
\(134\) | 6.17334i | 0.0460697i | ||||||||
\(135\) | 25.9725 | − | 0.655768i | 0.192389 | − | 0.00485754i | ||||
\(136\) | −21.9152 | + | 37.9582i | −0.161141 | + | 0.279104i | ||||
\(137\) | 11.7173 | + | 43.7294i | 0.0855275 | + | 0.319193i | 0.995414 | − | 0.0956653i | \(-0.0304979\pi\) |
−0.909886 | + | 0.414858i | \(0.863831\pi\) | |||||||
\(138\) | −5.52684 | + | 20.6265i | −0.0400496 | + | 0.149467i | ||||
\(139\) | − | 104.614i | − | 0.752620i | −0.926494 | − | 0.376310i | \(-0.877193\pi\) | ||
0.926494 | − | 0.376310i | \(-0.122807\pi\) | |||||||
\(140\) | −60.4827 | − | 118.327i | −0.432020 | − | 0.845192i | ||||
\(141\) | −19.4153 | −0.137697 | ||||||||
\(142\) | −30.9844 | − | 8.30224i | −0.218200 | − | 0.0584665i | ||||
\(143\) | −73.0866 | + | 19.5835i | −0.511095 | + | 0.136948i | ||||
\(144\) | 35.3420 | + | 20.4047i | 0.245430 | + | 0.141699i | ||||
\(145\) | −100.150 | + | 105.338i | −0.690690 | + | 0.726471i | ||||
\(146\) | −42.0112 | −0.287748 | ||||||||
\(147\) | 68.4390 | − | 50.1907i | 0.465571 | − | 0.341434i | ||||
\(148\) | 164.097 | + | 164.097i | 1.10877 | + | 1.10877i | ||||
\(149\) | 39.0472 | − | 22.5439i | 0.262061 | − | 0.151301i | −0.363213 | − | 0.931706i | \(-0.618320\pi\) |
0.625275 | + | 0.780405i | \(0.284987\pi\) | |||||||
\(150\) | −0.984987 | − | 19.4934i | −0.00656658 | − | 0.129956i | ||||
\(151\) | −84.2120 | + | 145.859i | −0.557695 | + | 0.965956i | 0.439993 | + | 0.898001i | \(0.354981\pi\) |
−0.997688 | + | 0.0679552i | \(0.978353\pi\) | |||||||
\(152\) | −73.5746 | − | 19.7142i | −0.484043 | − | 0.129699i | ||||
\(153\) | 26.4560 | + | 26.4560i | 0.172915 | + | 0.172915i | ||||
\(154\) | −35.6674 | + | 52.1446i | −0.231606 | + | 0.338601i | ||||
\(155\) | −212.207 | + | 62.6425i | −1.36908 | + | 0.404145i | ||||
\(156\) | 12.4260 | + | 21.5224i | 0.0796537 | + | 0.137964i | ||||
\(157\) | −61.9280 | − | 231.119i | −0.394446 | − | 1.47209i | −0.822722 | − | 0.568444i | \(-0.807545\pi\) |
0.428276 | − | 0.903648i | \(-0.359121\pi\) | |||||||
\(158\) | 56.4389 | − | 15.1228i | 0.357208 | − | 0.0957137i | ||||
\(159\) | −48.5460 | + | 28.0280i | −0.305321 | + | 0.176277i | ||||
\(160\) | 48.2510 | − | 88.6692i | 0.301569 | − | 0.554182i | ||||
\(161\) | 14.5970 | − | 190.903i | 0.0906645 | − | 1.18573i | ||||
\(162\) | −2.86858 | + | 2.86858i | −0.0177073 | + | 0.0177073i | ||||
\(163\) | −7.78599 | + | 29.0577i | −0.0477668 | + | 0.178268i | −0.985688 | − | 0.168581i | \(-0.946082\pi\) |
0.937921 | + | 0.346849i | \(0.112748\pi\) | |||||||
\(164\) | 65.3624 | + | 37.7370i | 0.398551 | + | 0.230103i | ||||
\(165\) | 147.931 | − | 90.4619i | 0.896553 | − | 0.548254i | ||||
\(166\) | 6.55508 | + | 11.3537i | 0.0394884 | + | 0.0683959i | ||||
\(167\) | 205.571 | − | 205.571i | 1.23096 | − | 1.23096i | 0.267371 | − | 0.963594i | \(-0.413845\pi\) |
0.963594 | − | 0.267371i | \(-0.0861549\pi\) | |||||||
\(168\) | 40.1980 | + | 14.1342i | 0.239274 | + | 0.0841324i | ||||
\(169\) | − | 154.719i | − | 0.915497i | ||||||
\(170\) | 19.3672 | − | 20.3706i | 0.113925 | − | 0.119827i | ||||
\(171\) | −32.5100 | + | 56.3090i | −0.190117 | + | 0.329293i | ||||
\(172\) | 19.5144 | + | 72.8288i | 0.113456 | + | 0.423423i | ||||
\(173\) | 12.9989 | − | 48.5124i | 0.0751379 | − | 0.280418i | −0.918127 | − | 0.396287i | \(-0.870299\pi\) |
0.993265 | + | 0.115869i | \(0.0369652\pi\) | |||||||
\(174\) | − | 22.6956i | − | 0.130434i | ||||||
\(175\) | 40.9128 | + | 170.150i | 0.233788 | + | 0.972288i | ||||
\(176\) | 272.366 | 1.54754 | ||||||||
\(177\) | 95.8673 | + | 25.6876i | 0.541623 | + | 0.145127i | ||||
\(178\) | 14.6025 | − | 3.91273i | 0.0820365 | − | 0.0219816i | ||||
\(179\) | 100.688 | + | 58.1320i | 0.562500 | + | 0.324760i | 0.754148 | − | 0.656704i | \(-0.228050\pi\) |
−0.191648 | + | 0.981464i | \(0.561383\pi\) | |||||||
\(180\) | −41.2750 | − | 39.2421i | −0.229306 | − | 0.218011i | ||||
\(181\) | 43.1119 | 0.238187 | 0.119094 | − | 0.992883i | \(-0.462001\pi\) | ||||
0.119094 | + | 0.992883i | \(0.462001\pi\) | |||||||
\(182\) | 7.76411 | + | 9.04974i | 0.0426599 | + | 0.0497239i | ||||
\(183\) | −24.0547 | − | 24.0547i | −0.131446 | − | 0.131446i | ||||
\(184\) | 83.2470 | − | 48.0627i | 0.452429 | − | 0.261210i | ||||
\(185\) | −159.436 | − | 260.724i | −0.861818 | − | 1.40932i | ||||
\(186\) | 17.2744 | − | 29.9202i | 0.0928733 | − | 0.160861i | ||||
\(187\) | 241.199 | + | 64.6291i | 1.28983 | + | 0.345610i | ||||
\(188\) | 30.0946 | + | 30.0946i | 0.160078 | + | 0.160078i | ||||
\(189\) | 20.5352 | − | 30.0218i | 0.108652 | − | 0.158845i | ||||
\(190\) | 42.9056 | + | 23.3479i | 0.225819 | + | 0.122884i | ||||
\(191\) | 65.1517 | + | 112.846i | 0.341109 | + | 0.590817i | 0.984639 | − | 0.174603i | \(-0.0558643\pi\) |
−0.643530 | + | 0.765421i | \(0.722531\pi\) | |||||||
\(192\) | −20.3128 | − | 75.8084i | −0.105796 | − | 0.394836i | ||||
\(193\) | −327.789 | + | 87.8309i | −1.69839 | + | 0.455082i | −0.972533 | − | 0.232763i | \(-0.925223\pi\) |
−0.725857 | + | 0.687846i | \(0.758557\pi\) | |||||||
\(194\) | 19.9516 | − | 11.5191i | 0.102843 | − | 0.0593766i | ||||
\(195\) | −9.26566 | − | 31.3883i | −0.0475162 | − | 0.160966i | ||||
\(196\) | −183.881 | − | 28.2856i | −0.938170 | − | 0.144314i | ||||
\(197\) | 90.1542 | − | 90.1542i | 0.457636 | − | 0.457636i | −0.440243 | − | 0.897879i | \(-0.645108\pi\) |
0.897879 | + | 0.440243i | \(0.145108\pi\) | |||||||
\(198\) | −7.00765 | + | 26.1529i | −0.0353922 | + | 0.132085i | ||||
\(199\) | 25.6088 | + | 14.7853i | 0.128688 | + | 0.0742979i | 0.562962 | − | 0.826483i | \(-0.309662\pi\) |
−0.434274 | + | 0.900781i | \(0.642995\pi\) | |||||||
\(200\) | −58.9129 | + | 65.1834i | −0.294565 | + | 0.325917i | ||||
\(201\) | −11.8607 | − | 20.5433i | −0.0590085 | − | 0.102206i | ||||
\(202\) | 25.5623 | − | 25.5623i | 0.126546 | − | 0.126546i | ||||
\(203\) | 37.5279 | + | 199.998i | 0.184867 | + | 0.985210i | ||||
\(204\) | − | 82.0159i | − | 0.402038i | ||||||
\(205\) | −72.0316 | − | 68.4837i | −0.351373 | − | 0.334067i | ||||
\(206\) | 7.00375 | − | 12.1308i | 0.0339988 | − | 0.0588876i | ||||
\(207\) | −21.2372 | − | 79.2584i | −0.102595 | − | 0.382891i | ||||
\(208\) | 13.3050 | − | 49.6549i | 0.0639663 | − | 0.238726i | ||||
\(209\) | 433.951i | 2.07632i | ||||||||
\(210\) | −22.9363 | − | 14.8530i | −0.109220 | − | 0.0707286i | ||||
\(211\) | 116.220 | 0.550808 | 0.275404 | − | 0.961329i | \(-0.411188\pi\) | ||||
0.275404 | + | 0.961329i | \(0.411188\pi\) | |||||||
\(212\) | 118.693 | + | 31.8038i | 0.559874 | + | 0.150018i | ||||
\(213\) | 119.059 | − | 31.9018i | 0.558964 | − | 0.149774i | ||||
\(214\) | −40.9277 | − | 23.6296i | −0.191251 | − | 0.110419i | ||||
\(215\) | −2.50615 | − | 99.2592i | −0.0116565 | − | 0.461671i | ||||
\(216\) | 18.2616 | 0.0845446 | ||||||||
\(217\) | −102.751 | + | 292.226i | −0.473508 | + | 1.34666i | ||||
\(218\) | −4.40841 | − | 4.40841i | −0.0202221 | − | 0.0202221i | ||||
\(219\) | 139.803 | − | 80.7152i | 0.638369 | − | 0.368562i | ||||
\(220\) | −369.520 | − | 89.0801i | −1.67964 | − | 0.404910i | ||||
\(221\) | 23.5650 | − | 40.8157i | 0.106629 | − | 0.184687i | ||||
\(222\) | 46.0937 | + | 12.3508i | 0.207629 | + | 0.0556341i | ||||
\(223\) | 268.713 | + | 268.713i | 1.20499 | + | 1.20499i | 0.972629 | + | 0.232363i | \(0.0746456\pi\) |
0.232363 | + | 0.972629i | \(0.425354\pi\) | |||||||
\(224\) | −61.1263 | − | 127.423i | −0.272885 | − | 0.568854i | ||||
\(225\) | 40.7300 | + | 62.9767i | 0.181022 | + | 0.279896i | ||||
\(226\) | 21.6466 | + | 37.4930i | 0.0957813 | + | 0.165898i | ||||
\(227\) | −48.3424 | − | 180.416i | −0.212962 | − | 0.794785i | −0.986874 | − | 0.161492i | \(-0.948369\pi\) |
0.773912 | − | 0.633293i | \(-0.218297\pi\) | |||||||
\(228\) | 137.674 | − | 36.8895i | 0.603832 | − | 0.161796i | ||||
\(229\) | 8.99125 | − | 5.19110i | 0.0392631 | − | 0.0226686i | −0.480240 | − | 0.877137i | \(-0.659450\pi\) |
0.519503 | + | 0.854469i | \(0.326117\pi\) | |||||||
\(230\) | −59.1218 | + | 17.4524i | −0.257051 | + | 0.0758802i | ||||
\(231\) | 18.5079 | − | 242.051i | 0.0801210 | − | 1.04784i | ||||
\(232\) | −72.2410 | + | 72.2410i | −0.311383 | + | 0.311383i | ||||
\(233\) | 28.9305 | − | 107.970i | 0.124165 | − | 0.463391i | −0.875643 | − | 0.482959i | \(-0.839562\pi\) |
0.999809 | + | 0.0195672i | \(0.00622883\pi\) | |||||||
\(234\) | 4.42560 | + | 2.55512i | 0.0189128 | + | 0.0109193i | ||||
\(235\) | −29.2398 | − | 47.8155i | −0.124425 | − | 0.203470i | ||||
\(236\) | −108.782 | − | 188.416i | −0.460940 | − | 0.798371i | ||||
\(237\) | −158.760 | + | 158.760i | −0.669873 | + | 0.669873i | ||||
\(238\) | −7.25723 | − | 38.6760i | −0.0304926 | − | 0.162504i | ||||
\(239\) | − | 196.209i | − | 0.820956i | −0.911870 | − | 0.410478i | \(-0.865362\pi\) | ||
0.911870 | − | 0.410478i | \(-0.134638\pi\) | |||||||
\(240\) | 2.97350 | + | 117.769i | 0.0123896 | + | 0.490704i | ||||
\(241\) | −20.5135 | + | 35.5305i | −0.0851183 | + | 0.147429i | −0.905442 | − | 0.424471i | \(-0.860460\pi\) |
0.820323 | + | 0.571900i | \(0.193794\pi\) | |||||||
\(242\) | 32.6535 | + | 121.864i | 0.134932 | + | 0.503572i | ||||
\(243\) | 4.03459 | − | 15.0573i | 0.0166032 | − | 0.0619642i | ||||
\(244\) | 74.5717i | 0.305622i | ||||||||
\(245\) | 226.679 | + | 92.9615i | 0.925219 | + | 0.379435i | ||||
\(246\) | 15.5195 | 0.0630874 | ||||||||
\(247\) | 79.1133 | + | 21.1984i | 0.320297 | + | 0.0858233i | ||||
\(248\) | −150.222 | + | 40.2520i | −0.605735 | + | 0.162306i | ||||
\(249\) | −43.6273 | − | 25.1883i | −0.175210 | − | 0.101158i | ||||
\(250\) | 46.5243 | − | 31.7832i | 0.186097 | − | 0.127133i | ||||
\(251\) | −495.319 | −1.97338 | −0.986692 | − | 0.162600i | \(-0.948012\pi\) | ||||
−0.986692 | + | 0.162600i | \(0.948012\pi\) | |||||||
\(252\) | −78.3656 | + | 14.7047i | −0.310974 | + | 0.0583518i | ||||
\(253\) | −387.239 | − | 387.239i | −1.53059 | − | 1.53059i | ||||
\(254\) | 0.999822 | − | 0.577247i | 0.00393631 | − | 0.00227263i | ||||
\(255\) | −25.3119 | + | 104.998i | −0.0992622 | + | 0.411757i | ||||
\(256\) | −67.8197 | + | 117.467i | −0.264921 | + | 0.458856i | ||||
\(257\) | −55.3682 | − | 14.8359i | −0.215440 | − | 0.0577271i | 0.149484 | − | 0.988764i | \(-0.452239\pi\) |
−0.364925 | + | 0.931037i | \(0.618905\pi\) | |||||||
\(258\) | 10.9629 | + | 10.9629i | 0.0424918 | + | 0.0424918i | ||||
\(259\) | −426.608 | − | 32.6197i | −1.64713 | − | 0.125945i | ||||
\(260\) | −34.2911 | + | 63.0155i | −0.131889 | + | 0.242367i | ||||
\(261\) | 43.6046 | + | 75.5253i | 0.167067 | + | 0.289369i | ||||
\(262\) | −15.4054 | − | 57.4936i | −0.0587991 | − | 0.219441i | ||||
\(263\) | 299.121 | − | 80.1492i | 1.13734 | − | 0.304750i | 0.359460 | − | 0.933160i | \(-0.382961\pi\) |
0.777882 | + | 0.628410i | \(0.216294\pi\) | |||||||
\(264\) | 105.551 | − | 60.9401i | 0.399815 | − | 0.230834i | ||||
\(265\) | −142.138 | − | 77.3470i | −0.536369 | − | 0.291875i | ||||
\(266\) | 61.6581 | − | 29.5780i | 0.231797 | − | 0.111196i | ||||
\(267\) | −41.0760 | + | 41.0760i | −0.153843 | + | 0.153843i | ||||
\(268\) | −13.4585 | + | 50.2277i | −0.0502182 | + | 0.187417i | ||||
\(269\) | 231.086 | + | 133.418i | 0.859056 | + | 0.495976i | 0.863696 | − | 0.504013i | \(-0.168144\pi\) |
−0.00464016 | + | 0.999989i | \(0.501477\pi\) | |||||||
\(270\) | −11.3848 | − | 2.74453i | −0.0421660 | − | 0.0101649i | ||||
\(271\) | 135.488 | + | 234.673i | 0.499957 | + | 0.865951i | 1.00000 | 4.97359e-5i | \(-1.58314e-5\pi\) | |
−0.500043 | + | 0.866001i | \(0.666682\pi\) | |||||||
\(272\) | −119.961 | + | 119.961i | −0.441034 | + | 0.441034i | ||||
\(273\) | −43.2241 | − | 15.1983i | −0.158330 | − | 0.0556714i | ||||
\(274\) | − | 20.4066i | − | 0.0744766i | ||||||
\(275\) | 445.574 | + | 228.084i | 1.62027 | + | 0.829396i | ||||
\(276\) | −89.9354 | + | 155.773i | −0.325853 | + | 0.564394i | ||||
\(277\) | 68.0999 | + | 254.152i | 0.245848 | + | 0.917517i | 0.972955 | + | 0.230994i | \(0.0741976\pi\) |
−0.727107 | + | 0.686524i | \(0.759136\pi\) | |||||||
\(278\) | −12.2047 | + | 45.5486i | −0.0439018 | + | 0.163844i | ||||
\(279\) | 132.756i | 0.475828i | ||||||||
\(280\) | 25.7294 | + | 120.285i | 0.0918906 | + | 0.429589i | ||||
\(281\) | −4.50255 | −0.0160233 | −0.00801165 | − | 0.999968i | \(-0.502550\pi\) | ||||
−0.00801165 | + | 0.999968i | \(0.502550\pi\) | |||||||
\(282\) | 8.45335 | + | 2.26507i | 0.0299764 | + | 0.00803216i | ||||
\(283\) | 352.367 | − | 94.4165i | 1.24511 | − | 0.333627i | 0.424667 | − | 0.905350i | \(-0.360391\pi\) |
0.820447 | + | 0.571722i | \(0.193725\pi\) | |||||||
\(284\) | −233.997 | − | 135.098i | −0.823932 | − | 0.475697i | ||||
\(285\) | −187.637 | + | 4.73756i | −0.658375 | + | 0.0166230i | ||||
\(286\) | 34.1063 | 0.119253 | ||||||||
\(287\) | −136.761 | + | 25.6620i | −0.476518 | + | 0.0894147i | ||||
\(288\) | −42.8284 | − | 42.8284i | −0.148710 | − | 0.148710i | ||||
\(289\) | 115.582 | − | 66.7314i | 0.399938 | − | 0.230905i | ||||
\(290\) | 55.8941 | − | 34.1800i | 0.192738 | − | 0.117862i | ||||
\(291\) | −44.2627 | + | 76.6652i | −0.152105 | + | 0.263454i | ||||
\(292\) | −341.813 | − | 91.5885i | −1.17059 | − | 0.313659i | ||||
\(293\) | −159.329 | − | 159.329i | −0.543786 | − | 0.543786i | 0.380851 | − | 0.924637i | \(-0.375631\pi\) |
−0.924637 | + | 0.380851i | \(0.875631\pi\) | |||||||
\(294\) | −35.6535 | + | 13.8685i | −0.121270 | + | 0.0471716i | ||||
\(295\) | 81.1152 | + | 274.785i | 0.274967 | + | 0.931475i | ||||
\(296\) | −107.405 | − | 186.031i | −0.362855 | − | 0.628483i | ||||
\(297\) | −26.9273 | − | 100.494i | −0.0906643 | − | 0.338364i | ||||
\(298\) | −19.6310 | + | 5.26011i | −0.0658759 | + | 0.0176514i | ||||
\(299\) | −89.5139 | + | 51.6809i | −0.299378 | + | 0.172846i | ||||
\(300\) | 34.4834 | − | 160.750i | 0.114945 | − | 0.535834i | ||||
\(301\) | −114.734 | − | 78.4794i | −0.381177 | − | 0.260729i | ||||
\(302\) | 53.6820 | − | 53.6820i | 0.177755 | − | 0.177755i | ||||
\(303\) | −35.9527 | + | 134.177i | −0.118656 | + | 0.442829i | ||||
\(304\) | −255.326 | − | 147.413i | −0.839889 | − | 0.484910i | ||||
\(305\) | 23.0144 | − | 95.4680i | 0.0754572 | − | 0.313010i | ||||
\(306\) | −8.43235 | − | 14.6053i | −0.0275567 | − | 0.0477296i | ||||
\(307\) | 170.687 | − | 170.687i | 0.555983 | − | 0.555983i | −0.372179 | − | 0.928161i | \(-0.621389\pi\) |
0.928161 | + | 0.372179i | \(0.121389\pi\) | |||||||
\(308\) | −403.879 | + | 346.502i | −1.31129 | + | 1.12501i | ||||
\(309\) | 53.8246i | 0.174190i | ||||||||
\(310\) | 99.7022 | − | 2.51734i | 0.321620 | − | 0.00812044i | ||||
\(311\) | 21.6690 | − | 37.5319i | 0.0696754 | − | 0.120681i | −0.829083 | − | 0.559126i | \(-0.811137\pi\) |
0.898758 | + | 0.438444i | \(0.144470\pi\) | |||||||
\(312\) | −5.95380 | − | 22.2199i | −0.0190827 | − | 0.0712176i | ||||
\(313\) | 49.7049 | − | 185.501i | 0.158802 | − | 0.592656i | −0.839948 | − | 0.542667i | \(-0.817415\pi\) |
0.998750 | − | 0.0499891i | \(-0.0159186\pi\) | |||||||
\(314\) | 107.853i | 0.343480i | ||||||||
\(315\) | 104.863 | + | 5.36015i | 0.332899 | + | 0.0170163i | ||||
\(316\) | 492.170 | 1.55750 | ||||||||
\(317\) | 15.9228 | + | 4.26650i | 0.0502296 | + | 0.0134590i | 0.283846 | − | 0.958870i | \(-0.408389\pi\) |
−0.233617 | + | 0.972329i | \(0.575056\pi\) | |||||||
\(318\) | 24.4066 | − | 6.53972i | 0.0767502 | − | 0.0205652i | ||||
\(319\) | 504.064 | + | 291.022i | 1.58014 | + | 0.912294i | ||||
\(320\) | 156.107 | − | 164.195i | 0.487836 | − | 0.513108i | ||||
\(321\) | 181.596 | 0.565721 | ||||||||
\(322\) | −28.6269 | + | 81.4153i | −0.0889035 | + | 0.252842i | ||||
\(323\) | −191.130 | − | 191.130i | −0.591733 | − | 0.591733i | ||||
\(324\) | −29.5933 | + | 17.0857i | −0.0913373 | + | 0.0527336i | ||||
\(325\) | 63.3480 | − | 70.0905i | 0.194917 | − | 0.215663i | ||||
\(326\) | 6.77997 | − | 11.7432i | 0.0207974 | − | 0.0360222i | ||||
\(327\) | 23.1399 | + | 6.20031i | 0.0707641 | + | 0.0189612i | ||||
\(328\) | −49.3992 | − | 49.3992i | −0.150607 | − | 0.150607i | ||||
\(329\) | −78.2377 | − | 5.98229i | −0.237805 | − | 0.0181832i | ||||
\(330\) | −74.9623 | + | 22.1285i | −0.227158 | + | 0.0670560i | ||||
\(331\) | −270.891 | − | 469.197i | −0.818402 | − | 1.41751i | −0.906859 | − | 0.421434i | \(-0.861527\pi\) |
0.0884570 | − | 0.996080i | \(-0.471806\pi\) | |||||||
\(332\) | 28.5814 | + | 106.667i | 0.0860886 | + | 0.321287i | ||||
\(333\) | −177.118 | + | 47.4585i | −0.531885 | + | 0.142518i | ||||
\(334\) | −113.487 | + | 65.5220i | −0.339783 | + | 0.196174i | ||||
\(335\) | 32.7311 | − | 60.1488i | 0.0977049 | − | 0.179549i | ||||
\(336\) | 136.130 | + | 93.1142i | 0.405149 | + | 0.277126i | ||||
\(337\) | 182.640 | − | 182.640i | 0.541959 | − | 0.541959i | −0.382144 | − | 0.924103i | \(-0.624814\pi\) |
0.924103 | + | 0.382144i | \(0.124814\pi\) | |||||||
\(338\) | −18.0501 | + | 67.3640i | −0.0534027 | + | 0.199302i | ||||
\(339\) | −144.069 | − | 83.1782i | −0.424982 | − | 0.245363i | ||||
\(340\) | 201.986 | − | 123.517i | 0.594077 | − | 0.363286i | ||||
\(341\) | 443.014 | + | 767.323i | 1.29916 | + | 2.25021i | ||||
\(342\) | 20.7240 | − | 20.7240i | 0.0605964 | − | 0.0605964i | ||||
\(343\) | 291.253 | − | 181.165i | 0.849133 | − | 0.528179i | ||||
\(344\) | − | 69.7906i | − | 0.202880i | ||||||
\(345\) | 163.212 | − | 171.667i | 0.473077 | − | 0.497585i | ||||
\(346\) | −11.3193 | + | 19.6056i | −0.0327147 | + | 0.0566635i | ||||
\(347\) | −110.100 | − | 410.897i | −0.317290 | − | 1.18414i | −0.921839 | − | 0.387573i | \(-0.873313\pi\) |
0.604549 | − | 0.796568i | \(-0.293353\pi\) | |||||||
\(348\) | 49.4786 | − | 184.657i | 0.142180 | − | 0.530623i | ||||
\(349\) | 205.632i | 0.589202i | 0.955620 | + | 0.294601i | \(0.0951868\pi\) | ||||
−0.955620 | + | 0.294601i | \(0.904813\pi\) | |||||||
\(350\) | 2.03714 | − | 78.8558i | 0.00582041 | − | 0.225302i | ||||
\(351\) | −19.6364 | −0.0559441 | ||||||||
\(352\) | −390.466 | − | 104.625i | −1.10928 | − | 0.297230i | ||||
\(353\) | 302.605 | − | 81.0827i | 0.857237 | − | 0.229696i | 0.196676 | − | 0.980468i | \(-0.436985\pi\) |
0.660561 | + | 0.750772i | \(0.270319\pi\) | |||||||
\(354\) | −38.7434 | − | 22.3685i | −0.109445 | − | 0.0631878i | ||||
\(355\) | 257.872 | + | 245.171i | 0.726401 | + | 0.690623i | ||||
\(356\) | 127.339 | 0.357695 | ||||||||
\(357\) | 98.4576 | + | 114.761i | 0.275792 | + | 0.321459i | ||||
\(358\) | −37.0570 | − | 37.0570i | −0.103511 | − | 0.103511i | ||||
\(359\) | −327.820 | + | 189.267i | −0.913149 | + | 0.527207i | −0.881443 | − | 0.472291i | \(-0.843427\pi\) |
−0.0317058 | + | 0.999497i | \(0.510094\pi\) | |||||||
\(360\) | 27.5023 | + | 44.9742i | 0.0763954 | + | 0.124928i | ||||
\(361\) | 54.3672 | − | 94.1668i | 0.150602 | − | 0.260850i | ||||
\(362\) | −18.7707 | − | 5.02960i | −0.0518528 | − | 0.0138939i | ||||
\(363\) | −342.798 | − | 342.798i | −0.944348 | − | 0.944348i | ||||
\(364\) | 43.4413 | + | 90.5574i | 0.119344 | + | 0.248784i | ||||
\(365\) | 409.328 | + | 222.744i | 1.12145 | + | 0.610257i | ||||
\(366\) | 7.66699 | + | 13.2796i | 0.0209481 | + | 0.0362831i | ||||
\(367\) | −57.1272 | − | 213.202i | −0.155660 | − | 0.580931i | −0.999048 | − | 0.0436259i | \(-0.986109\pi\) |
0.843388 | − | 0.537305i | \(-0.180558\pi\) | |||||||
\(368\) | 359.387 | − | 96.2975i | 0.976595 | − | 0.261678i | ||||
\(369\) | −51.6451 | + | 29.8173i | −0.139960 | + | 0.0808057i | ||||
\(370\) | 39.0008 | + | 132.119i | 0.105407 | + | 0.357078i | ||||
\(371\) | −204.261 | + | 97.9862i | −0.550570 | + | 0.264114i | ||||
\(372\) | 205.778 | − | 205.778i | 0.553166 | − | 0.553166i | ||||
\(373\) | −63.4330 | + | 236.735i | −0.170062 | + | 0.634679i | 0.827279 | + | 0.561792i | \(0.189888\pi\) |
−0.997340 | + | 0.0728868i | \(0.976779\pi\) | |||||||
\(374\) | −97.4771 | − | 56.2784i | −0.260634 | − | 0.150477i | ||||
\(375\) | −93.7572 | + | 195.153i | −0.250019 | + | 0.520407i | ||||
\(376\) | −19.6975 | − | 34.1171i | −0.0523871 | − | 0.0907371i | ||||
\(377\) | 77.6793 | − | 77.6793i | 0.206046 | − | 0.206046i | ||||
\(378\) | −12.4434 | + | 10.6756i | −0.0329190 | + | 0.0282424i | ||||
\(379\) | − | 238.727i | − | 0.629888i | −0.949110 | − | 0.314944i | \(-0.898014\pi\) | ||
0.949110 | − | 0.314944i | \(-0.101986\pi\) | |||||||
\(380\) | 298.189 | + | 283.502i | 0.784709 | + | 0.746059i | ||||
\(381\) | −2.21811 | + | 3.84187i | −0.00582180 | + | 0.0100837i | ||||
\(382\) | −15.2017 | − | 56.7335i | −0.0397950 | − | 0.148517i | ||||
\(383\) | 54.5095 | − | 203.432i | 0.142322 | − | 0.531154i | −0.857538 | − | 0.514421i | \(-0.828007\pi\) |
0.999860 | − | 0.0167331i | \(-0.00532656\pi\) | |||||||
\(384\) | 175.253i | 0.456389i | ||||||||
\(385\) | 623.990 | − | 318.952i | 1.62075 | − | 0.828448i | ||||
\(386\) | 152.965 | 0.396282 | ||||||||
\(387\) | −57.5445 | − | 15.4190i | −0.148694 | − | 0.0398424i | ||||
\(388\) | 187.444 | − | 50.2254i | 0.483102 | − | 0.129447i | ||||
\(389\) | −322.620 | − | 186.264i | −0.829356 | − | 0.478829i | 0.0242760 | − | 0.999705i | \(-0.492272\pi\) |
−0.853632 | + | 0.520876i | \(0.825605\pi\) | |||||||
\(390\) | 0.372348 | + | 14.7473i | 0.000954738 | + | 0.0378136i | ||||
\(391\) | 341.112 | 0.872409 | ||||||||
\(392\) | 157.630 | + | 69.3425i | 0.402118 | + | 0.176894i | ||||
\(393\) | 161.727 | + | 161.727i | 0.411518 | + | 0.411518i | ||||
\(394\) | −49.7705 | + | 28.7350i | −0.126321 | + | 0.0729315i | ||||
\(395\) | −630.084 | − | 151.894i | −1.59515 | − | 0.384542i | ||||
\(396\) | −114.032 | + | 197.509i | −0.287959 | + | 0.498760i | ||||
\(397\) | −209.470 | − | 56.1274i | −0.527633 | − | 0.141379i | −0.0148382 | − | 0.999890i | \(-0.504723\pi\) |
−0.512795 | + | 0.858511i | \(0.671390\pi\) | |||||||
\(398\) | −9.42507 | − | 9.42507i | −0.0236811 | − | 0.0236811i | ||||
\(399\) | −148.355 | + | 216.891i | −0.371818 | + | 0.543586i | ||||
\(400\) | −285.560 | + | 184.685i | −0.713900 | + | 0.461713i | ||||
\(401\) | −207.883 | − | 360.064i | −0.518412 | − | 0.897915i | −0.999771 | − | 0.0213919i | \(-0.993190\pi\) |
0.481360 | − | 0.876523i | \(-0.340143\pi\) | |||||||
\(402\) | 2.76743 | + | 10.3282i | 0.00688416 | + | 0.0256920i | ||||
\(403\) | 161.531 | − | 43.2822i | 0.400822 | − | 0.107400i | ||||
\(404\) | 263.709 | − | 152.252i | 0.652745 | − | 0.376863i | ||||
\(405\) | 43.1588 | − | 12.7403i | 0.106565 | − | 0.0314574i | ||||
\(406\) | 6.99301 | − | 91.4562i | 0.0172242 | − | 0.225262i | ||||
\(407\) | −865.359 | + | 865.359i | −2.12619 | + | 2.12619i | ||||
\(408\) | −19.6486 | + | 73.3296i | −0.0481583 | + | 0.179729i | ||||
\(409\) | 360.314 | + | 208.027i | 0.880963 | + | 0.508624i | 0.870976 | − | 0.491326i | \(-0.163488\pi\) |
0.00998686 | + | 0.999950i | \(0.496821\pi\) | |||||||
\(410\) | 23.3726 | + | 38.2210i | 0.0570064 | + | 0.0932220i | ||||
\(411\) | 39.2067 | + | 67.9080i | 0.0953935 | + | 0.165226i | ||||
\(412\) | 83.4306 | − | 83.4306i | 0.202501 | − | 0.202501i | ||||
\(413\) | 378.400 | + | 133.052i | 0.916224 | + | 0.322159i | ||||
\(414\) | 36.9863i | 0.0893390i | ||||||||
\(415\) | −3.67059 | − | 145.378i | −0.00884479 | − | 0.350309i | ||||
\(416\) | −38.1483 | + | 66.0748i | −0.0917026 | + | 0.158834i | ||||
\(417\) | −46.8973 | − | 175.023i | −0.112463 | − | 0.419719i | ||||
\(418\) | 50.6264 | − | 188.940i | 0.121116 | − | 0.452010i | ||||
\(419\) | − | 655.999i | − | 1.56563i | −0.622254 | − | 0.782815i | \(-0.713783\pi\) | ||
0.622254 | − | 0.782815i | \(-0.286217\pi\) | |||||||
\(420\) | −154.234 | − | 170.851i | −0.367224 | − | 0.406788i | ||||
\(421\) | 65.9825 | 0.156728 | 0.0783641 | − | 0.996925i | \(-0.475030\pi\) | ||||
0.0783641 | + | 0.996925i | \(0.475030\pi\) | |||||||
\(422\) | −50.6019 | − | 13.5587i | −0.119910 | − | 0.0321297i | ||||
\(423\) | −32.4825 | + | 8.70365i | −0.0767907 | + | 0.0205760i | ||||
\(424\) | −98.5032 | − | 56.8709i | −0.232319 | − | 0.134129i | ||||
\(425\) | −296.706 | + | 95.7916i | −0.698133 | + | 0.225392i | ||||
\(426\) | −55.5597 | −0.130422 | ||||||||
\(427\) | −89.5211 | − | 104.345i | −0.209651 | − | 0.244367i | ||||
\(428\) | −281.483 | − | 281.483i | −0.657670 | − | 0.657670i | ||||
\(429\) | −113.497 | + | 65.5277i | −0.264562 | + | 0.152745i | ||||
\(430\) | −10.4888 | + | 43.5094i | −0.0243926 | + | 0.101185i | ||||
\(431\) | −355.868 | + | 616.382i | −0.825681 | + | 1.43012i | 0.0757171 | + | 0.997129i | \(0.475875\pi\) |
−0.901398 | + | 0.432992i | \(0.857458\pi\) | |||||||
\(432\) | 68.2754 | + | 18.2943i | 0.158045 | + | 0.0423480i | ||||
\(433\) | −8.06832 | − | 8.06832i | −0.0186335 | − | 0.0186335i | 0.697729 | − | 0.716362i | \(-0.254194\pi\) |
−0.716362 | + | 0.697729i | \(0.754194\pi\) | |||||||
\(434\) | 78.8297 | − | 115.246i | 0.181635 | − | 0.265545i | ||||
\(435\) | −120.332 | + | 221.131i | −0.276626 | + | 0.508346i | ||||
\(436\) | −26.2571 | − | 45.4786i | −0.0602227 | − | 0.104309i | ||||
\(437\) | 153.427 | + | 572.598i | 0.351092 | + | 1.31029i | ||||
\(438\) | −70.2860 | + | 18.8331i | −0.160470 | + | 0.0429979i | ||||
\(439\) | −103.783 | + | 59.9191i | −0.236408 | + | 0.136490i | −0.613525 | − | 0.789676i | \(-0.710249\pi\) |
0.377117 | + | 0.926166i | \(0.376915\pi\) | |||||||
\(440\) | 309.044 | + | 168.172i | 0.702372 | + | 0.382209i | ||||
\(441\) | 92.0007 | − | 114.651i | 0.208618 | − | 0.259980i | ||||
\(442\) | −15.0218 | + | 15.0218i | −0.0339860 | + | 0.0339860i | ||||
\(443\) | 86.6536 | − | 323.396i | 0.195606 | − | 0.730012i | −0.796503 | − | 0.604635i | \(-0.793319\pi\) |
0.992109 | − | 0.125378i | \(-0.0400143\pi\) | |||||||
\(444\) | 348.103 | + | 200.978i | 0.784016 | + | 0.452652i | ||||
\(445\) | −163.022 | − | 39.2997i | −0.366342 | − | 0.0883140i | ||||
\(446\) | −85.6474 | − | 148.346i | −0.192035 | − | 0.332614i | ||||
\(447\) | 55.2210 | − | 55.2210i | 0.123537 | − | 0.123537i | ||||
\(448\) | −58.4961 | − | 311.743i | −0.130572 | − | 0.695856i | ||||
\(449\) | − | 63.6098i | − | 0.141670i | −0.997488 | − | 0.0708349i | \(-0.977434\pi\) | ||
0.997488 | − | 0.0708349i | \(-0.0225664\pi\) | |||||||
\(450\) | −10.3866 | − | 32.1715i | −0.0230812 | − | 0.0714922i | ||||
\(451\) | −199.004 | + | 344.685i | −0.441250 | + | 0.764268i | ||||
\(452\) | 94.3833 | + | 352.243i | 0.208813 | + | 0.779299i | ||||
\(453\) | −75.5024 | + | 281.779i | −0.166672 | + | 0.622028i | ||||
\(454\) | 84.1922i | 0.185445i | ||||||||
\(455\) | −27.6663 | − | 129.340i | −0.0608051 | − | 0.284264i | ||||
\(456\) | −131.930 | −0.289321 | ||||||||
\(457\) | 644.842 | + | 172.785i | 1.41103 | + | 0.378085i | 0.882294 | − | 0.470699i | \(-0.155998\pi\) |
0.528739 | + | 0.848784i | \(0.322665\pi\) | |||||||
\(458\) | −4.52036 | + | 1.21123i | −0.00986979 | + | 0.00264460i | ||||
\(459\) | 56.1215 | + | 32.4018i | 0.122269 | + | 0.0705921i | ||||
\(460\) | −519.077 | + | 13.1059i | −1.12843 | + | 0.0284912i | ||||
\(461\) | −3.62806 | −0.00786997 | −0.00393499 | − | 0.999992i | \(-0.501253\pi\) | ||||
−0.00393499 | + | 0.999992i | \(0.501253\pi\) | |||||||
\(462\) | −36.2969 | + | 103.229i | −0.0785647 | + | 0.223439i | ||||
\(463\) | −283.246 | − | 283.246i | −0.611763 | − | 0.611763i | 0.331642 | − | 0.943405i | \(-0.392397\pi\) |
−0.943405 | + | 0.331642i | \(0.892397\pi\) | |||||||
\(464\) | −342.460 | + | 197.719i | −0.738061 | + | 0.426120i | ||||
\(465\) | −326.948 | + | 199.933i | −0.703114 | + | 0.429963i | ||||
\(466\) | −25.1924 | + | 43.6346i | −0.0540610 | + | 0.0936365i | ||||
\(467\) | −791.002 | − | 211.948i | −1.69379 | − | 0.453851i | −0.722430 | − | 0.691444i | \(-0.756975\pi\) |
−0.971365 | + | 0.237593i | \(0.923642\pi\) | |||||||
\(468\) | 30.4373 | + | 30.4373i | 0.0650369 | + | 0.0650369i | ||||
\(469\) | −41.4651 | − | 86.4378i | −0.0884117 | − | 0.184302i | ||||
\(470\) | 7.15254 | + | 24.2299i | 0.0152182 | + | 0.0515530i | ||||
\(471\) | −207.215 | − | 358.907i | −0.439947 | − | 0.762011i | ||||
\(472\) | 52.1219 | + | 194.521i | 0.110428 | + | 0.412122i | ||||
\(473\) | −384.059 | + | 102.908i | −0.811963 | + | 0.217565i | ||||
\(474\) | 87.6448 | − | 50.6018i | 0.184905 | − | 0.106755i | ||||
\(475\) | −294.252 | − | 454.972i | −0.619478 | − | 0.957836i | ||||
\(476\) | 25.2709 | − | 330.498i | 0.0530901 | − | 0.694324i | ||||
\(477\) | −68.6544 | + | 68.6544i | −0.143930 | + | 0.143930i | ||||
\(478\) | −22.8905 | + | 85.4283i | −0.0478880 | + | 0.178720i | ||||
\(479\) | 464.561 | + | 268.214i | 0.969856 | + | 0.559947i | 0.899192 | − | 0.437554i | \(-0.144155\pi\) |
0.0706637 | + | 0.997500i | \(0.477488\pi\) | |||||||
\(480\) | 40.9762 | − | 169.977i | 0.0853672 | − | 0.354118i | ||||
\(481\) | 115.491 | + | 200.036i | 0.240105 | + | 0.415874i | ||||
\(482\) | 13.0766 | − | 13.0766i | 0.0271299 | − | 0.0271299i | ||||
\(483\) | −61.1581 | − | 325.930i | −0.126621 | − | 0.674804i | ||||
\(484\) | 1062.71i | 2.19567i | ||||||||
\(485\) | −255.469 | + | 6.45023i | −0.526741 | + | 0.0132994i | ||||
\(486\) | −3.51328 | + | 6.08519i | −0.00722898 | + | 0.0125210i | ||||
\(487\) | −97.5549 | − | 364.080i | −0.200318 | − | 0.747597i | −0.990826 | − | 0.135145i | \(-0.956850\pi\) |
0.790508 | − | 0.612452i | \(-0.209817\pi\) | |||||||
\(488\) | 17.8652 | − | 66.6738i | 0.0366090 | − | 0.136627i | ||||
\(489\) | 52.1048i | 0.106554i | ||||||||
\(490\) | −87.8496 | − | 66.9202i | −0.179285 | − | 0.136572i | ||||
\(491\) | 142.980 | 0.291202 | 0.145601 | − | 0.989343i | \(-0.453488\pi\) | ||||
0.145601 | + | 0.989343i | \(0.453488\pi\) | |||||||
\(492\) | 126.270 | + | 33.8340i | 0.256647 | + | 0.0687684i | ||||
\(493\) | −350.188 | + | 93.8327i | −0.710321 | + | 0.190330i | ||||
\(494\) | −31.9725 | − | 18.4593i | −0.0647217 | − | 0.0373671i | ||||
\(495\) | 206.941 | − | 217.661i | 0.418062 | − | 0.439720i | ||||
\(496\) | −601.966 | −1.21364 | ||||||||
\(497\) | 489.602 | − | 91.8698i | 0.985114 | − | 0.184849i | ||||
\(498\) | 16.0566 | + | 16.0566i | 0.0322422 | + | 0.0322422i | ||||
\(499\) | −536.150 | + | 309.546i | −1.07445 | + | 0.620334i | −0.929394 | − | 0.369090i | \(-0.879669\pi\) |
−0.145056 | + | 0.989424i | \(0.546336\pi\) | |||||||
\(500\) | 447.823 | − | 157.168i | 0.895647 | − | 0.314335i | ||||
\(501\) | 251.772 | − | 436.082i | 0.502539 | − | 0.870423i | ||||
\(502\) | 215.660 | + | 57.7859i | 0.429601 | + | 0.115111i | ||||
\(503\) | 661.069 | + | 661.069i | 1.31425 | + | 1.31425i | 0.918249 | + | 0.396004i | \(0.129603\pi\) |
0.396004 | + | 0.918249i | \(0.370397\pi\) | |||||||
\(504\) | 73.5887 | + | 5.62681i | 0.146009 | + | 0.0111643i | ||||
\(505\) | −384.593 | + | 113.530i | −0.761571 | + | 0.224812i | ||||
\(506\) | 123.425 | + | 213.779i | 0.243924 | + | 0.422488i | ||||
\(507\) | −69.3586 | − | 258.850i | −0.136802 | − | 0.510552i | ||||
\(508\) | 9.39324 | − | 2.51691i | 0.0184906 | − | 0.00495455i | ||||
\(509\) | 416.656 | − | 240.557i | 0.818578 | − | 0.472606i | −0.0313476 | − | 0.999509i | \(-0.509980\pi\) |
0.849926 | + | 0.526902i | \(0.176647\pi\) | |||||||
\(510\) | 23.2702 | − | 42.7627i | 0.0456278 | − | 0.0838485i | ||||
\(511\) | 588.232 | − | 282.181i | 1.15114 | − | 0.552213i | ||||
\(512\) | 329.420 | − | 329.420i | 0.643398 | − | 0.643398i | ||||
\(513\) | −29.1477 | + | 108.781i | −0.0568181 | + | 0.212048i | ||||
\(514\) | 22.3762 | + | 12.9189i | 0.0435336 | + | 0.0251341i | ||||
\(515\) | −132.558 | + | 81.0608i | −0.257394 | + | 0.157400i | ||||
\(516\) | 65.2965 | + | 113.097i | 0.126544 | + | 0.219180i | ||||
\(517\) | −158.702 | + | 158.702i | −0.306968 | + | 0.306968i | ||||
\(518\) | 181.938 | + | 63.9722i | 0.351231 | + | 0.123498i | ||||
\(519\) | − | 86.9900i | − | 0.167611i | ||||||
\(520\) | 45.7560 | − | 48.1264i | 0.0879923 | − | 0.0925507i | ||||
\(521\) | −164.031 | + | 284.110i | −0.314839 | + | 0.545318i | −0.979403 | − | 0.201914i | \(-0.935284\pi\) |
0.664564 | + | 0.747231i | \(0.268617\pi\) | |||||||
\(522\) | −10.1742 | − | 37.9705i | −0.0194907 | − | 0.0727404i | ||||
\(523\) | −88.9020 | + | 331.787i | −0.169985 | + | 0.634391i | 0.827367 | + | 0.561662i | \(0.189838\pi\) |
−0.997352 | + | 0.0727298i | \(0.976829\pi\) | |||||||
\(524\) | − | 501.367i | − | 0.956807i | ||||||
\(525\) | 144.725 | + | 266.326i | 0.275666 | + | 0.507288i | ||||
\(526\) | −139.586 | −0.265374 | ||||||||
\(527\) | −533.082 | − | 142.839i | −1.01154 | − | 0.271041i | ||||
\(528\) | 455.678 | − | 122.098i | 0.863026 | − | 0.231247i | ||||
\(529\) | −189.747 | − | 109.550i | −0.358689 | − | 0.207089i | ||||
\(530\) | 52.8625 | + | 50.2589i | 0.0997407 | + | 0.0948281i | ||||
\(531\) | 171.904 | 0.323737 | ||||||||
\(532\) | 566.148 | − | 106.233i | 1.06419 | − | 0.199686i | ||||
\(533\) | 53.1180 | + | 53.1180i | 0.0996585 | + | 0.0996585i | ||||
\(534\) | 22.6764 | − | 13.0922i | 0.0424652 | − | 0.0245173i | ||||
\(535\) | 273.487 | + | 447.231i | 0.511191 | + | 0.835945i | ||||
\(536\) | 24.0662 | − | 41.6839i | 0.0448996 | − | 0.0777684i | ||||
\(537\) | 194.513 | + | 52.1197i | 0.362222 | + | 0.0970572i | ||||
\(538\) | −85.0488 | − | 85.0488i | −0.158083 | − | 0.158083i | ||||
\(539\) | 149.163 | − | 969.689i | 0.276739 | − | 1.79905i | ||||
\(540\) | −86.6462 | − | 47.1502i | −0.160456 | − | 0.0873151i | ||||
\(541\) | 253.542 | + | 439.148i | 0.468655 | + | 0.811735i | 0.999358 | − | 0.0358232i | \(-0.0114053\pi\) |
−0.530703 | + | 0.847558i | \(0.678072\pi\) | |||||||
\(542\) | −31.6132 | − | 117.982i | −0.0583269 | − | 0.217679i | ||||
\(543\) | 72.1276 | − | 19.3265i | 0.132832 | − | 0.0355921i | ||||
\(544\) | 218.058 | − | 125.896i | 0.400843 | − | 0.231427i | ||||
\(545\) | 19.5791 | + | 66.3260i | 0.0359249 | + | 0.121699i | ||||
\(546\) | 17.0465 | + | 11.6600i | 0.0312207 | + | 0.0213552i | ||||
\(547\) | −24.1757 | + | 24.1757i | −0.0441969 | + | 0.0441969i | −0.728860 | − | 0.684663i | \(-0.759949\pi\) |
0.684663 | + | 0.728860i | \(0.259949\pi\) | |||||||
\(548\) | 44.4883 | − | 166.033i | 0.0811831 | − | 0.302979i | ||||
\(549\) | −51.0277 | − | 29.4608i | −0.0929466 | − | 0.0536627i | ||||
\(550\) | −167.392 | − | 151.289i | −0.304349 | − | 0.275071i | ||||
\(551\) | −315.019 | − | 545.629i | −0.571723 | − | 0.990253i | ||||
\(552\) | 117.729 | − | 117.729i | 0.213277 | − | 0.213277i | ||||
\(553\) | −688.670 | + | 590.835i | −1.24533 | + | 1.06842i | ||||
\(554\) | − | 118.602i | − | 0.214082i | ||||||
\(555\) | −383.622 | − | 364.727i | −0.691210 | − | 0.657166i | ||||
\(556\) | −198.601 | + | 343.986i | −0.357195 | + | 0.618681i | ||||
\(557\) | −31.2217 | − | 116.521i | −0.0560533 | − | 0.209194i | 0.932219 | − | 0.361894i | \(-0.117870\pi\) |
−0.988273 | + | 0.152700i | \(0.951203\pi\) | |||||||
\(558\) | 15.4878 | − | 57.8014i | 0.0277560 | − | 0.103587i | ||||
\(559\) | 75.0445i | 0.134248i | ||||||||
\(560\) | −24.3049 | + | 475.489i | −0.0434016 | + | 0.849087i | ||||
\(561\) | 432.506 | 0.770956 | ||||||||
\(562\) | 1.96039 | + | 0.525284i | 0.00348824 | + | 0.000934670i | ||||
\(563\) | 89.6915 | − | 24.0328i | 0.159310 | − | 0.0426870i | −0.178283 | − | 0.983979i | \(-0.557054\pi\) |
0.337592 | + | 0.941292i | \(0.390387\pi\) | |||||||
\(564\) | 63.8404 | + | 36.8583i | 0.113192 | + | 0.0653515i | ||||
\(565\) | −12.1212 | − | 480.077i | −0.0214535 | − | 0.849693i | ||||
\(566\) | −164.434 | −0.290520 | ||||||||
\(567\) | 20.8976 | − | 59.4331i | 0.0368565 | − | 0.104820i | ||||
\(568\) | 176.849 | + | 176.849i | 0.311353 | + | 0.311353i | ||||
\(569\) | −123.242 | + | 71.1541i | −0.216595 | + | 0.125051i | −0.604373 | − | 0.796702i | \(-0.706576\pi\) |
0.387778 | + | 0.921753i | \(0.373243\pi\) | |||||||
\(570\) | 82.2490 | + | 19.8277i | 0.144297 | + | 0.0347855i | ||||
\(571\) | 288.489 | − | 499.678i | 0.505235 | − | 0.875092i | −0.494747 | − | 0.869037i | \(-0.664739\pi\) |
0.999982 | − | 0.00605499i | \(-0.00192738\pi\) | |||||||
\(572\) | 277.497 | + | 74.3551i | 0.485134 | + | 0.129991i | ||||
\(573\) | 159.588 | + | 159.588i | 0.278514 | + | 0.278514i | ||||
\(574\) | 62.5388 | + | 4.78190i | 0.108953 | + | 0.00833083i | ||||
\(575\) | 668.576 | + | 143.420i | 1.16274 | + | 0.249426i | ||||
\(576\) | −67.9680 | − | 117.724i | −0.118000 | − | 0.204382i | ||||
\(577\) | 164.767 | + | 614.920i | 0.285559 | + | 1.06572i | 0.948430 | + | 0.316986i | \(0.102671\pi\) |
−0.662871 | + | 0.748733i | \(0.730662\pi\) | |||||||
\(578\) | −58.1091 | + | 15.5703i | −0.100535 | + | 0.0269382i | ||||
\(579\) | −509.029 | + | 293.888i | −0.879152 | + | 0.507578i | ||||
\(580\) | 529.283 | − | 156.242i | 0.912557 | − | 0.269382i | ||||
\(581\) | −168.044 | − | 114.943i | −0.289232 | − | 0.197837i | ||||
\(582\) | 28.2158 | − | 28.2158i | 0.0484808 | − | 0.0484808i | ||||
\(583\) | −167.715 | + | 625.922i | −0.287676 | + | 1.07362i | ||||
\(584\) | 283.670 | + | 163.777i | 0.485736 | + | 0.280440i | ||||
\(585\) | −29.5727 | − | 48.3599i | −0.0505517 | − | 0.0826666i | ||||
\(586\) | 50.7833 | + | 87.9592i | 0.0866609 | + | 0.150101i | ||||
\(587\) | 584.066 | − | 584.066i | 0.995002 | − | 0.995002i | −0.00498534 | − | 0.999988i | \(-0.501587\pi\) |
0.999988 | + | 0.00498534i | \(0.00158689\pi\) | |||||||
\(588\) | −320.320 | + | 35.1091i | −0.544761 | + | 0.0597093i | ||||
\(589\) | − | 959.090i | − | 1.62834i | ||||||
\(590\) | −3.25967 | − | 129.103i | −0.00552487 | − | 0.218819i | ||||
\(591\) | 110.416 | − | 191.246i | 0.186829 | − | 0.323597i | ||||
\(592\) | −215.195 | − | 803.118i | −0.363505 | − | 1.35662i | ||||
\(593\) | −197.236 | + | 736.094i | −0.332607 | + | 1.24131i | 0.573833 | + | 0.818972i | \(0.305456\pi\) |
−0.906440 | + | 0.422334i | \(0.861211\pi\) | |||||||
\(594\) | 46.8961i | 0.0789496i | ||||||||
\(595\) | −134.351 | + | 415.311i | −0.225800 | + | 0.698001i | ||||
\(596\) | −171.190 | −0.287232 | ||||||||
\(597\) | 49.4725 | + | 13.2561i | 0.0828685 | + | 0.0222045i | ||||
\(598\) | 45.0032 | − | 12.0586i | 0.0752562 | − | 0.0201648i | ||||
\(599\) | 385.326 | + | 222.468i | 0.643282 | + | 0.371399i | 0.785878 | − | 0.618382i | \(-0.212212\pi\) |
−0.142596 | + | 0.989781i | \(0.545545\pi\) | |||||||
\(600\) | −69.3423 | + | 135.464i | −0.115571 | + | 0.225773i | ||||
\(601\) | −618.650 | −1.02937 | −0.514684 | − | 0.857380i | \(-0.672091\pi\) | ||||
−0.514684 | + | 0.857380i | \(0.672091\pi\) | |||||||
\(602\) | 40.7991 | + | 47.5549i | 0.0677726 | + | 0.0789949i | ||||
\(603\) | −29.0527 | − | 29.0527i | −0.0481802 | − | 0.0481802i | ||||
\(604\) | 553.802 | − | 319.738i | 0.916891 | − | 0.529367i | ||||
\(605\) | 327.974 | − | 1360.49i | 0.542105 | − | 2.24875i | ||||
\(606\) | 31.3073 | − | 54.2258i | 0.0516622 | − | 0.0894815i | ||||
\(607\) | −203.819 | − | 54.6130i | −0.335780 | − | 0.0899721i | 0.0869894 | − | 0.996209i | \(-0.472275\pi\) |
−0.422770 | + | 0.906237i | \(0.638942\pi\) | |||||||
\(608\) | 309.411 | + | 309.411i | 0.508900 | + | 0.508900i | ||||
\(609\) | 152.442 | + | 317.779i | 0.250315 | + | 0.521805i | ||||
\(610\) | −21.1580 | + | 38.8814i | −0.0346853 | + | 0.0637399i | ||||
\(611\) | 21.1804 | + | 36.6855i | 0.0346651 | + | 0.0600417i | ||||
\(612\) | −36.7667 | − | 137.215i | −0.0600763 | − | 0.224208i | ||||
\(613\) | −238.755 | + | 63.9742i | −0.389486 | + | 0.104362i | −0.448247 | − | 0.893910i | \(-0.647952\pi\) |
0.0587613 | + | 0.998272i | \(0.481285\pi\) | |||||||
\(614\) | −94.2292 | + | 54.4032i | −0.153468 | + | 0.0886046i | ||||
\(615\) | −151.212 | − | 82.2847i | −0.245872 | − | 0.133796i | ||||
\(616\) | 444.116 | − | 213.047i | 0.720967 | − | 0.345855i | ||||
\(617\) | −396.280 | + | 396.280i | −0.642268 | + | 0.642268i | −0.951113 | − | 0.308844i | \(-0.900058\pi\) |
0.308844 | + | 0.951113i | \(0.400058\pi\) | |||||||
\(618\) | 6.27939 | − | 23.4350i | 0.0101608 | − | 0.0379207i | ||||
\(619\) | −93.8294 | − | 54.1724i | −0.151582 | − | 0.0875160i | 0.422290 | − | 0.906461i | \(-0.361226\pi\) |
−0.573873 | + | 0.818945i | \(0.694560\pi\) | |||||||
\(620\) | 816.689 | + | 196.879i | 1.31724 | + | 0.317547i | ||||
\(621\) | −71.0611 | − | 123.081i | −0.114430 | − | 0.198199i | ||||
\(622\) | −13.8132 | + | 13.8132i | −0.0222078 | + | 0.0222078i | ||||
\(623\) | −178.180 | + | 152.867i | −0.286003 | + | 0.245373i | ||||
\(624\) | − | 89.0387i | − | 0.142690i | ||||||
\(625\) | −621.817 | + | 63.0008i | −0.994907 | + | 0.100801i | ||||
\(626\) | −43.2826 | + | 74.9676i | −0.0691415 | + | 0.119757i | ||||
\(627\) | 194.535 | + | 726.014i | 0.310263 | + | 1.15792i | ||||
\(628\) | −235.130 | + | 877.515i | −0.374410 | + | 1.39732i | ||||
\(629\) | − | 762.279i | − | 1.21189i | ||||||
\(630\) | −45.0316 | − | 14.5675i | −0.0714787 | − | 0.0231230i | ||||
\(631\) | 185.595 | 0.294129 | 0.147064 | − | 0.989127i | \(-0.453018\pi\) | ||||
0.147064 | + | 0.989127i | \(0.453018\pi\) | |||||||
\(632\) | −440.044 | − | 117.910i | −0.696273 | − | 0.186566i | ||||
\(633\) | 194.441 | − | 52.1002i | 0.307173 | − | 0.0823068i | ||||
\(634\) | −6.43497 | − | 3.71523i | −0.0101498 | − | 0.00585999i | ||||
\(635\) | −12.8022 | + | 0.323236i | −0.0201609 | + | 0.000509033i | ||||
\(636\) | 212.835 | 0.334646 | ||||||||
\(637\) | −169.497 | − | 74.5627i | −0.266086 | − | 0.117053i | ||||
\(638\) | −185.516 | − | 185.516i | −0.290777 | − | 0.290777i | ||||
\(639\) | 184.889 | − | 106.746i | 0.289341 | − | 0.167051i | ||||
\(640\) | −431.609 | + | 263.934i | −0.674389 | + | 0.412398i | ||||
\(641\) | 253.276 | − | 438.688i | 0.395127 | − | 0.684380i | −0.597990 | − | 0.801503i | \(-0.704034\pi\) |
0.993117 | + | 0.117123i | \(0.0373672\pi\) | |||||||
\(642\) | −79.0663 | − | 21.1857i | −0.123156 | − | 0.0329996i | ||||
\(643\) | −521.287 | − | 521.287i | −0.810711 | − | 0.810711i | 0.174030 | − | 0.984740i | \(-0.444321\pi\) |
−0.984740 | + | 0.174030i | \(0.944321\pi\) | |||||||
\(644\) | −410.409 | + | 600.004i | −0.637281 | + | 0.931684i | ||||
\(645\) | −48.6896 | − | 164.940i | −0.0754877 | − | 0.255722i | ||||
\(646\) | 60.9191 | + | 105.515i | 0.0943020 | + | 0.163336i | ||||
\(647\) | 235.372 | + | 878.419i | 0.363789 | + | 1.35768i | 0.869054 | + | 0.494717i | \(0.164728\pi\) |
−0.505265 | + | 0.862964i | \(0.668605\pi\) | |||||||
\(648\) | 30.5523 | − | 8.18647i | 0.0471486 | − | 0.0126334i | ||||
\(649\) | 993.599 | − | 573.655i | 1.53097 | − | 0.883905i | ||||
\(650\) | −35.7584 | + | 23.1267i | −0.0550130 | + | 0.0355795i | ||||
\(651\) | −40.9050 | + | 534.966i | −0.0628341 | + | 0.821760i | ||||
\(652\) | 80.7648 | − | 80.7648i | 0.123872 | − | 0.123872i | ||||
\(653\) | 42.2998 | − | 157.865i | 0.0647777 | − | 0.241754i | −0.925944 | − | 0.377661i | \(-0.876728\pi\) |
0.990722 | + | 0.135908i | \(0.0433951\pi\) | |||||||
\(654\) | −9.35164 | − | 5.39917i | −0.0142991 | − | 0.00825562i | ||||
\(655\) | −154.733 | + | 641.859i | −0.236233 | + | 0.979937i | ||||
\(656\) | −135.203 | − | 234.178i | −0.206102 | − | 0.356979i | ||||
\(657\) | 197.711 | − | 197.711i | 0.300930 | − | 0.300930i | ||||
\(658\) | 33.3664 | + | 11.7322i | 0.0507089 | + | 0.0178301i | ||||
\(659\) | − | 242.026i | − | 0.367262i | −0.982995 | − | 0.183631i | \(-0.941215\pi\) | ||
0.982995 | − | 0.183631i | \(-0.0587852\pi\) | |||||||
\(660\) | −658.153 | + | 16.6174i | −0.997201 | + | 0.0251779i | ||||
\(661\) | 9.69682 | − | 16.7954i | 0.0146699 | − | 0.0254090i | −0.858597 | − | 0.512651i | \(-0.828664\pi\) |
0.873267 | + | 0.487242i | \(0.161997\pi\) | |||||||
\(662\) | 63.2064 | + | 235.890i | 0.0954780 | + | 0.356329i | ||||
\(663\) | 21.1278 | − | 78.8499i | 0.0318669 | − | 0.118929i | ||||
\(664\) | − | 102.218i | − | 0.153942i | ||||||
\(665\) | −757.578 | − | 38.7241i | −1.13922 | − | 0.0582318i | ||||
\(666\) | 82.6529 | 0.124103 | ||||||||
\(667\) | 768.006 | + | 205.787i | 1.15143 | + | 0.308526i | ||||
\(668\) | −1066.21 | + | 285.689i | −1.59612 | + | 0.427678i | ||||
\(669\) | 570.027 | + | 329.105i | 0.852058 | + | 0.491936i | ||||
\(670\) | −21.2682 | + | 22.3700i | −0.0317436 | + | 0.0333880i | ||||
\(671\) | −393.250 | −0.586065 | ||||||||
\(672\) | −159.389 | − | 185.781i | −0.237185 | − | 0.276460i | ||||
\(673\) | 520.888 | + | 520.888i | 0.773980 | + | 0.773980i | 0.978800 | − | 0.204820i | \(-0.0656608\pi\) |
−0.204820 | + | 0.978800i | \(0.565661\pi\) | |||||||
\(674\) | −100.828 | + | 58.2132i | −0.149597 | + | 0.0863697i | ||||
\(675\) | 96.3743 | + | 87.1033i | 0.142777 | + | 0.129042i | ||||
\(676\) | −293.720 | + | 508.738i | −0.434497 | + | 0.752571i | ||||
\(677\) | 1141.49 | + | 305.862i | 1.68610 | + | 0.451790i | 0.969379 | − | 0.245568i | \(-0.0789746\pi\) |
0.716723 | + | 0.697358i | \(0.245641\pi\) | |||||||
\(678\) | 53.0230 | + | 53.0230i | 0.0782051 | + | 0.0782051i | ||||
\(679\) | −201.987 | + | 295.299i | −0.297477 | + | 0.434902i | ||||
\(680\) | −210.185 | + | 62.0456i | −0.309096 | + | 0.0912435i | ||||
\(681\) | −161.757 | − | 280.171i | −0.237528 | − | 0.411411i | ||||
\(682\) | −103.367 | − | 385.773i | −0.151565 | − | 0.565649i | ||||
\(683\) | 546.188 | − | 146.351i | 0.799689 | − | 0.214276i | 0.164242 | − | 0.986420i | \(-0.447482\pi\) |
0.635448 | + | 0.772144i | \(0.280816\pi\) | |||||||
\(684\) | 213.795 | − | 123.435i | 0.312566 | − | 0.180460i | ||||
\(685\) | −108.196 | + | 198.828i | −0.157950 | + | 0.290260i | ||||
\(686\) | −147.946 | + | 44.9000i | −0.215664 | + | 0.0654519i | ||||
\(687\) | 12.7155 | − | 12.7155i | 0.0185088 | − | 0.0185088i | ||||
\(688\) | 69.9156 | − | 260.929i | 0.101622 | − | 0.379257i | ||||
\(689\) | 105.919 | + | 61.1522i | 0.153728 | + | 0.0887550i | ||||
\(690\) | −91.0889 | + | 55.7021i | −0.132013 | + | 0.0807276i | ||||
\(691\) | −664.985 | − | 1151.79i | −0.962352 | − | 1.66684i | −0.716567 | − | 0.697518i | \(-0.754288\pi\) |
−0.245785 | − | 0.969324i | \(-0.579046\pi\) | |||||||
\(692\) | −134.838 | + | 134.838i | −0.194853 | + | 0.194853i | ||||
\(693\) | −77.5442 | − | 413.257i | −0.111896 | − | 0.596330i | ||||
\(694\) | 191.747i | 0.276293i | ||||||||
\(695\) | 360.414 | − | 379.085i | 0.518581 | − | 0.545446i | ||||
\(696\) | −88.4767 | + | 153.246i | −0.127122 | + | 0.220181i | ||||
\(697\) | −64.1638 | − | 239.463i | −0.0920572 | − | 0.343562i | ||||
\(698\) | 23.9898 | − | 89.5311i | 0.0343693 | − | 0.128268i | ||||
\(699\) | − | 193.607i | − | 0.276977i | ||||||
\(700\) | 188.488 | − | 637.148i | 0.269269 | − | 0.910211i | ||||
\(701\) | −316.598 | −0.451638 | −0.225819 | − | 0.974169i | \(-0.572506\pi\) | ||||
−0.225819 | + | 0.974169i | \(0.572506\pi\) | |||||||
\(702\) | 8.54960 | + | 2.29086i | 0.0121789 | + | 0.00326333i | ||||
\(703\) | 1279.58 | − | 342.862i | 1.82017 | − | 0.487712i | ||||
\(704\) | −785.703 | − | 453.626i | −1.11606 | − | 0.644355i | ||||
\(705\) | −70.3543 | − | 66.8891i | −0.0997933 | − | 0.0948781i | ||||
\(706\) | −141.212 | −0.200017 | ||||||||
\(707\) | −186.221 | + | 529.615i | −0.263396 | + | 0.749101i | ||||
\(708\) | −266.460 | − | 266.460i | −0.376356 | − | 0.376356i | ||||
\(709\) | −233.680 | + | 134.915i | −0.329591 | + | 0.190290i | −0.655660 | − | 0.755057i | \(-0.727609\pi\) |
0.326068 | + | 0.945346i | \(0.394276\pi\) | |||||||
\(710\) | −83.6738 | − | 136.831i | −0.117850 | − | 0.192720i | ||||
\(711\) | −194.440 | + | 336.780i | −0.273474 | + | 0.473671i | ||||
\(712\) | −113.853 | − | 30.5068i | −0.159906 | − | 0.0428467i | ||||
\(713\) | 855.851 | + | 855.851i | 1.20035 | + | 1.20035i | ||||
\(714\) | −29.4795 | − | 61.4528i | −0.0412879 | − | 0.0860684i | ||||
\(715\) | −332.309 | − | 180.832i | −0.464767 | − | 0.252912i | ||||
\(716\) | −220.717 | − | 382.293i | −0.308264 | − | 0.533928i | ||||
\(717\) | −87.9579 | − | 328.263i | −0.122675 | − | 0.457829i | ||||
\(718\) | 164.812 | − | 44.1613i | 0.229543 | − | 0.0615060i | ||||
\(719\) | −977.193 | + | 564.183i | −1.35910 | + | 0.784677i | −0.989503 | − | 0.144515i | \(-0.953838\pi\) |
−0.369598 | + | 0.929192i | \(0.620505\pi\) | |||||||
\(720\) | 57.7691 | + | 195.698i | 0.0802349 | + | 0.271803i | ||||
\(721\) | −16.5845 | + | 216.896i | −0.0230021 | + | 0.300827i | ||||
\(722\) | −34.6571 | + | 34.6571i | −0.0480015 | + | 0.0480015i | ||||
\(723\) | −18.3919 | + | 68.6396i | −0.0254383 | + | 0.0949372i | ||||
\(724\) | −141.758 | − | 81.8440i | −0.195798 | − | 0.113044i | ||||
\(725\) | −725.817 | + | 36.6750i | −1.00113 | + | 0.0505862i | ||||
\(726\) | 109.261 | + | 189.245i | 0.150497 | + | 0.260668i | ||||
\(727\) | −704.249 | + | 704.249i | −0.968705 | + | 0.968705i | −0.999525 | − | 0.0308196i | \(-0.990188\pi\) |
0.0308196 | + | 0.999525i | \(0.490188\pi\) | |||||||
\(728\) | −17.1455 | − | 91.3737i | −0.0235516 | − | 0.125513i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | −152.234 | − | 144.736i | −0.208539 | − | 0.198268i | ||||
\(731\) | 123.830 | − | 214.480i | 0.169398 | − | 0.293406i | ||||
\(732\) | 33.4296 | + | 124.761i | 0.0456688 | + | 0.170438i | ||||
\(733\) | 248.412 | − | 927.085i | 0.338897 | − | 1.26478i | −0.560684 | − | 0.828030i | \(-0.689462\pi\) |
0.899582 | − | 0.436753i | \(-0.143872\pi\) | |||||||
\(734\) | 99.4917i | 0.135547i | ||||||||
\(735\) | 420.914 | + | 53.9103i | 0.572672 | + | 0.0733474i | ||||
\(736\) | −552.211 | −0.750287 | ||||||||
\(737\) | −264.873 | − | 70.9726i | −0.359394 | − | 0.0962993i | ||||
\(738\) | 25.9646 | − | 6.95720i | 0.0351824 | − | 0.00942711i | ||||
\(739\) | 201.038 | + | 116.069i | 0.272040 | + | 0.157063i | 0.629815 | − | 0.776746i | \(-0.283131\pi\) |
−0.357774 | + | 0.933808i | \(0.616464\pi\) | |||||||
\(740\) | 29.2877 | + | 1159.97i | 0.0395779 | + | 1.56753i | ||||
\(741\) | 141.862 | 0.191447 | ||||||||
\(742\) | 100.366 | − | 18.8328i | 0.135264 | − | 0.0253812i | ||||
\(743\) | 678.958 | + | 678.958i | 0.913806 | + | 0.913806i | 0.996569 | − | 0.0827629i | \(-0.0263744\pi\) |
−0.0827629 | + | 0.996569i | \(0.526374\pi\) | |||||||
\(744\) | −233.282 | + | 134.686i | −0.313552 | + | 0.181029i | ||||
\(745\) | 219.161 | + | 52.8330i | 0.294175 | + | 0.0709168i | ||||
\(746\) | 55.2369 | − | 95.6731i | 0.0740441 | − | 0.128248i | ||||
\(747\) | −84.2816 | − | 22.5832i | −0.112827 | − | 0.0302318i | ||||
\(748\) | −670.404 | − | 670.404i | −0.896262 | − | 0.896262i | ||||
\(749\) | 731.777 | + | 55.9538i | 0.977005 | + | 0.0747047i | ||||
\(750\) | 63.5887 | − | 74.0306i | 0.0847850 | − | 0.0987074i | ||||
\(751\) | 617.773 | + | 1070.01i | 0.822601 | + | 1.42479i | 0.903739 | + | 0.428083i | \(0.140811\pi\) |
−0.0811386 | + | 0.996703i | \(0.525856\pi\) | |||||||
\(752\) | −39.4656 | − | 147.288i | −0.0524809 | − | 0.195861i | ||||
\(753\) | −828.686 | + | 222.046i | −1.10051 | + | 0.294881i | ||||
\(754\) | −42.8836 | + | 24.7589i | −0.0568748 | + | 0.0328367i | ||||
\(755\) | −807.665 | + | 238.418i | −1.06975 | + | 0.315786i | ||||
\(756\) | −124.516 | + | 59.7317i | −0.164704 | + | 0.0790102i | ||||
\(757\) | −256.783 | + | 256.783i | −0.339212 | + | 0.339212i | −0.856071 | − | 0.516859i | \(-0.827101\pi\) |
0.516859 | + | 0.856071i | \(0.327101\pi\) | |||||||
\(758\) | −27.8509 | + | 103.941i | −0.0367426 | + | 0.137125i | ||||
\(759\) | −821.459 | − | 474.269i | −1.08229 | − | 0.624861i | ||||
\(760\) | −198.689 | − | 324.914i | −0.261433 | − | 0.427519i | ||||
\(761\) | 486.625 | + | 842.859i | 0.639455 | + | 1.10757i | 0.985553 | + | 0.169369i | \(0.0541731\pi\) |
−0.346098 | + | 0.938198i | \(0.612494\pi\) | |||||||
\(762\) | 1.41396 | − | 1.41396i | 0.00185559 | − | 0.00185559i | ||||
\(763\) | 91.3360 | + | 32.1152i | 0.119706 | + | 0.0420907i | ||||
\(764\) | − | 494.739i | − | 0.647564i | ||||||
\(765\) | 4.72179 | + | 187.012i | 0.00617227 | + | 0.244460i | ||||
\(766\) | −47.4664 | + | 82.2142i | −0.0619665 | + | 0.107329i | ||||
\(767\) | −56.0457 | − | 209.165i | −0.0730713 | − | 0.272706i | ||||
\(768\) | −60.8055 | + | 226.929i | −0.0791739 | + | 0.295481i | ||||
\(769\) | 1319.36i | 1.71568i | 0.513917 | + | 0.857840i | \(0.328194\pi\) | ||||
−0.513917 | + | 0.857840i | \(0.671806\pi\) | |||||||
\(770\) | −308.893 | + | 66.0734i | −0.401160 | + | 0.0858095i | ||||
\(771\) | −99.2835 | −0.128772 | ||||||||
\(772\) | 1244.56 | + | 333.478i | 1.61212 | + | 0.431966i | ||||
\(773\) | −1379.80 | + | 369.715i | −1.78499 | + | 0.478286i | −0.991479 | − | 0.130270i | \(-0.958416\pi\) |
−0.793511 | + | 0.608557i | \(0.791749\pi\) | |||||||
\(774\) | 23.2558 | + | 13.4267i | 0.0300463 | + | 0.0173472i | ||||
\(775\) | −984.778 | − | 504.096i | −1.27068 | − | 0.650446i | ||||
\(776\) | −179.624 | −0.231474 | ||||||||
\(777\) | −728.352 | + | 136.669i | −0.937390 | + | 0.175894i | ||||
\(778\) | 118.737 | + | 118.737i | 0.152618 | + | 0.152618i | ||||
\(779\) | 373.107 | − | 215.414i | 0.478957 | − | 0.276526i | ||||
\(780\) | −29.1210 | + | 120.799i | −0.0373347 | + | 0.154871i | ||||
\(781\) | 712.432 | − | 1233.97i | 0.912205 | − | 1.57999i | ||||
\(782\) | −148.519 | − | 39.7955i | −0.189922 | − | 0.0508893i | ||||
\(783\) | 106.809 | + | 106.809i | 0.136410 | + | 0.136410i | ||||
\(784\) | 519.871 | + | 417.166i | 0.663101 | + | 0.532099i | ||||
\(785\) | 571.837 | − | 1050.84i | 0.728455 | − | 1.33866i | ||||
\(786\) | −51.5474 | − | 89.2827i | −0.0655819 | − | 0.113591i | ||||
\(787\) | −12.1345 | − | 45.2867i | −0.0154187 | − | 0.0575434i | 0.957788 | − | 0.287476i | \(-0.0928161\pi\) |
−0.973207 | + | 0.229932i | \(0.926149\pi\) | |||||||
\(788\) | −467.590 | + | 125.290i | −0.593388 | + | 0.158998i | ||||
\(789\) | 464.509 | − | 268.185i | 0.588732 | − | 0.339904i | ||||
\(790\) | 256.615 | + | 139.642i | 0.324829 | + | 0.176762i | ||||
\(791\) | −554.924 | − | 379.573i | −0.701547 | − | 0.479865i | ||||
\(792\) | 149.272 | − | 149.272i | 0.188475 | − | 0.188475i | ||||
\(793\) | −19.2101 | + | 71.6931i | −0.0242246 | + | 0.0904075i | ||||
\(794\) | 84.6545 | + | 48.8753i | 0.106618 | + | 0.0615558i | ||||
\(795\) | −272.475 | − | 65.6854i | −0.342736 | − | 0.0826232i | ||||
\(796\) | −56.1370 | − | 97.2322i | −0.0705239 | − | 0.122151i | ||||
\(797\) | −764.370 | + | 764.370i | −0.959059 | + | 0.959059i | −0.999194 | − | 0.0401348i | \(-0.987221\pi\) |
0.0401348 | + | 0.999194i | \(0.487221\pi\) | |||||||
\(798\) | 89.8966 | − | 77.1256i | 0.112652 | − | 0.0966486i | ||||
\(799\) | − | 139.798i | − | 0.174966i | ||||||
\(800\) | 480.325 | − | 155.073i | 0.600406 | − | 0.193841i | ||||
\(801\) | −50.3077 | + | 87.1355i | −0.0628061 | + | 0.108783i | ||||
\(802\) | 48.5049 | + | 181.023i | 0.0604799 | + | 0.225714i | ||||
\(803\) | 482.987 | − | 1802.53i | 0.601478 | − | 2.24475i | ||||
\(804\) | 90.0659i | 0.112022i | ||||||||
\(805\) | 710.586 | − | 641.475i | 0.882716 | − | 0.796863i | ||||
\(806\) | −75.3794 | −0.0935229 | ||||||||
\(807\) | 446.424 | + | 119.619i | 0.553189 | + | 0.148227i | ||||
\(808\) | −272.255 | + | 72.9505i | −0.336949 | + | 0.0902853i | ||||
\(809\) | 915.835 | + | 528.758i | 1.13206 | + | 0.653594i | 0.944452 | − | 0.328650i | \(-0.106594\pi\) |
0.187607 | + | 0.982244i | \(0.439927\pi\) | |||||||
\(810\) | −20.2775 | + | 0.511977i | −0.0250339 | + | 0.000632071i | ||||
\(811\) | 1365.86 | 1.68417 | 0.842083 | − | 0.539349i | \(-0.181330\pi\) | ||||
0.842083 | + | 0.539349i | \(0.181330\pi\) | |||||||
\(812\) | 256.280 | − | 728.864i | 0.315616 | − | 0.897616i | ||||
\(813\) | 331.877 | + | 331.877i | 0.408213 | + | 0.408213i | ||||
\(814\) | 477.730 | − | 275.817i | 0.586891 | − | 0.338842i | ||||
\(815\) | −128.322 | + | 78.4708i | −0.157451 | + | 0.0962831i | ||||
\(816\) | −146.922 | + | 254.476i | −0.180051 | + | 0.311858i | ||||
\(817\) | 415.728 | + | 111.394i | 0.508847 | + | 0.136345i | ||||
\(818\) | −132.610 | − | 132.610i | −0.162115 | − | 0.162115i | ||||
\(819\) | −79.1285 | − | 6.05040i | −0.0966160 | − | 0.00738754i | ||||
\(820\) | 106.840 | + | 361.930i | 0.130292 | + | 0.441378i | ||||
\(821\) | 460.776 | + | 798.087i | 0.561237 | + | 0.972091i | 0.997389 | + | 0.0722182i | \(0.0230078\pi\) |
−0.436152 | + | 0.899873i | \(0.643659\pi\) | |||||||
\(822\) | −9.14802 | − | 34.1409i | −0.0111290 | − | 0.0415339i | ||||
\(823\) | 969.882 | − | 259.879i | 1.17847 | − | 0.315770i | 0.384151 | − | 0.923270i | \(-0.374494\pi\) |
0.794320 | + | 0.607500i | \(0.207827\pi\) | |||||||
\(824\) | −94.5820 | + | 54.6070i | −0.114784 | + | 0.0662706i | ||||
\(825\) | 847.707 | + | 181.846i | 1.02752 | + | 0.220420i | ||||
\(826\) | −149.232 | − | 102.076i | −0.180668 | − | 0.123578i | ||||
\(827\) | 993.021 | − | 993.021i | 1.20075 | − | 1.20075i | 0.226813 | − | 0.973938i | \(-0.427169\pi\) |
0.973938 | − | 0.226813i | \(-0.0728305\pi\) | |||||||
\(828\) | −80.6339 | + | 300.930i | −0.0973839 | + | 0.363442i | ||||
\(829\) | −901.880 | − | 520.701i | −1.08791 | − | 0.628107i | −0.154893 | − | 0.987931i | \(-0.549503\pi\) |
−0.933020 | + | 0.359824i | \(0.882837\pi\) | |||||||
\(830\) | −15.3622 | + | 63.7252i | −0.0185087 | + | 0.0767774i | ||||
\(831\) | 227.867 | + | 394.677i | 0.274208 | + | 0.474942i | ||||
\(832\) | −121.082 | + | 121.082i | −0.145531 | + | 0.145531i | ||||
\(833\) | 361.393 | + | 492.788i | 0.433845 | + | 0.591582i | ||||
\(834\) | 81.6755i | 0.0979322i | ||||||||
\(835\) | 1453.14 | − | 36.6898i | 1.74029 | − | 0.0439399i | ||||
\(836\) | 823.817 | − | 1426.89i | 0.985427 | − | 1.70681i | ||||
\(837\) | 59.5129 | + | 222.105i | 0.0711026 | + | 0.265359i | ||||
\(838\) | −76.5314 | + | 285.619i | −0.0913262 | + | 0.340834i | ||||
\(839\) | − | 1063.92i | − | 1.26808i | −0.773300 | − | 0.634041i | \(-0.781395\pi\) | ||
0.773300 | − | 0.634041i | \(-0.218605\pi\) | |||||||
\(840\) | 96.9683 | + | 189.706i | 0.115438 | + | 0.225841i | ||||
\(841\) | −4.04821 | −0.00481357 | ||||||||
\(842\) | −28.7285 | − | 7.69778i | −0.0341194 | − | 0.00914226i | ||||
\(843\) | −7.53291 | + | 2.01844i | −0.00893583 | + | 0.00239435i | ||||
\(844\) | −382.149 | − | 220.634i | −0.452784 | − | 0.261415i | ||||
\(845\) | 533.033 | − | 560.647i | 0.630808 | − | 0.663487i | ||||
\(846\) | 15.1581 | 0.0179174 | ||||||||
\(847\) | −1275.75 | − | 1486.99i | −1.50619 | − | 1.75560i | ||||
\(848\) | −311.305 | − | 311.305i | −0.367105 | − | 0.367105i | ||||
\(849\) | 547.196 | − | 315.924i | 0.644518 | − | 0.372113i | ||||
\(850\) | 140.360 | − | 7.09230i | 0.165130 | − | 0.00834388i | ||||
\(851\) | −835.886 | + | 1447.80i | −0.982239 | + | 1.70129i | ||||
\(852\) | −452.047 | − | 121.126i | −0.530571 | − | 0.142166i | ||||
\(853\) | −94.3742 | − | 94.3742i | −0.110638 | − | 0.110638i | 0.649621 | − | 0.760259i | \(-0.274928\pi\) |
−0.760259 | + | 0.649621i | \(0.774928\pi\) | |||||||
\(854\) | 26.8038 | + | 55.8751i | 0.0313862 | + | 0.0654275i | ||||
\(855\) | −311.799 | + | 92.0415i | −0.364677 | + | 0.107651i | ||||
\(856\) | 184.236 | + | 319.106i | 0.215229 | + | 0.372787i | ||||
\(857\) | −263.085 | − | 981.846i | −0.306984 | − | 1.14568i | −0.931224 | − | 0.364446i | \(-0.881258\pi\) |
0.624241 | − | 0.781232i | \(-0.285408\pi\) | |||||||
\(858\) | 57.0609 | − | 15.2894i | 0.0665046 | − | 0.0178198i | ||||
\(859\) | −537.700 | + | 310.441i | −0.625961 | + | 0.361399i | −0.779186 | − | 0.626793i | \(-0.784367\pi\) |
0.153225 | + | 0.988191i | \(0.451034\pi\) | |||||||
\(860\) | −180.194 | + | 331.136i | −0.209528 | + | 0.385042i | ||||
\(861\) | −217.301 | + | 104.241i | −0.252382 | + | 0.121070i | ||||
\(862\) | 226.853 | − | 226.853i | 0.263171 | − | 0.263171i | ||||
\(863\) | 266.243 | − | 993.632i | 0.308509 | − | 1.15137i | −0.621374 | − | 0.783514i | \(-0.713425\pi\) |
0.929883 | − | 0.367856i | \(-0.119908\pi\) | |||||||
\(864\) | −90.8527 | − | 52.4538i | −0.105154 | − | 0.0607104i | ||||
\(865\) | 214.237 | − | 131.008i | 0.247672 | − | 0.151455i | ||||
\(866\) | 2.57163 | + | 4.45419i | 0.00296955 | + | 0.00514341i | ||||
\(867\) | 163.458 | − | 163.458i | 0.188533 | − | 0.188533i | ||||
\(868\) | 892.626 | − | 765.816i | 1.02837 | − | 0.882277i | ||||
\(869\) | 2595.43i | 2.98669i | ||||||||
\(870\) | 78.1902 | − | 82.2408i | 0.0898737 | − | 0.0945297i | ||||
\(871\) | −25.8779 | + | 44.8219i | −0.0297106 | + | 0.0514602i | ||||
\(872\) | 12.5809 | + | 46.9524i | 0.0144276 | + | 0.0538445i | ||||
\(873\) | −39.6848 | + | 148.106i | −0.0454580 | + | 0.169651i | ||||
\(874\) | − | 267.206i | − | 0.305728i | ||||||
\(875\) | −437.943 | + | 757.516i | −0.500506 | + | 0.865733i | ||||
\(876\) | −612.922 | −0.699683 | ||||||||
\(877\) | −330.191 | − | 88.4744i | −0.376501 | − | 0.100883i | 0.0656059 | − | 0.997846i | \(-0.479102\pi\) |
−0.442106 | + | 0.896963i | \(0.645769\pi\) | |||||||
\(878\) | 52.1770 | − | 13.9808i | 0.0594271 | − | 0.0159235i | ||||
\(879\) | −337.988 | − | 195.138i | −0.384515 | − | 0.222000i | ||||
\(880\) | 986.959 | + | 938.348i | 1.12154 | + | 1.06630i | ||||
\(881\) | 1000.15 | 1.13524 | 0.567621 | − | 0.823290i | \(-0.307864\pi\) | ||||
0.567621 | + | 0.823290i | \(0.307864\pi\) | |||||||
\(882\) | −53.4323 | + | 39.1854i | −0.0605809 | + | 0.0444279i | ||||
\(883\) | −141.373 | − | 141.373i | −0.160106 | − | 0.160106i | 0.622508 | − | 0.782614i | \(-0.286114\pi\) |
−0.782614 | + | 0.622508i | \(0.786114\pi\) | |||||||
\(884\) | −154.970 | + | 89.4719i | −0.175305 | + | 0.101213i | ||||
\(885\) | 258.891 | + | 423.362i | 0.292532 | + | 0.478375i | ||||
\(886\) | −75.4572 | + | 130.696i | −0.0851661 | + | 0.147512i | ||||
\(887\) | −291.915 | − | 78.2183i | −0.329104 | − | 0.0881830i | 0.0904840 | − | 0.995898i | \(-0.471159\pi\) |
−0.419588 | + | 0.907715i | \(0.637825\pi\) | |||||||
\(888\) | −263.087 | − | 263.087i | −0.296270 | − | 0.296270i | ||||
\(889\) | −10.1220 | + | 14.7981i | −0.0113859 | + | 0.0166458i | ||||
\(890\) | 66.3943 | + | 36.1297i | 0.0746003 | + | 0.0405952i | ||||
\(891\) | −90.1005 | − | 156.059i | −0.101123 | − | 0.175150i | ||||
\(892\) | −373.439 | − | 1393.70i | −0.418654 | − | 1.56244i | ||||
\(893\) | 234.668 | − | 62.8791i | 0.262786 | − | 0.0704134i | ||||
\(894\) | −30.4853 | + | 17.6007i | −0.0340999 | + | 0.0196876i | ||||
\(895\) | 164.582 | + | 557.535i | 0.183890 | + | 0.622945i | ||||
\(896\) | −53.9993 | + | 706.216i | −0.0602671 | + | 0.788188i | ||||
\(897\) | −126.592 | + | 126.592i | −0.141128 | + | 0.141128i | ||||
\(898\) | −7.42096 | + | 27.6954i | −0.00826388 | + | 0.0308412i | ||||
\(899\) | −1114.05 | − | 643.197i | −1.23921 | − | 0.715458i | ||||
\(900\) | −14.3705 | − | 284.399i | −0.0159672 | − | 0.315999i | ||||
\(901\) | −201.813 | − | 349.550i | −0.223988 | − | 0.387958i | ||||
\(902\) | 126.858 | − | 126.858i | 0.140640 | − | 0.140640i | ||||
\(903\) | −227.136 | − | 79.8646i | −0.251535 | − | 0.0884436i | ||||
\(904\) | − | 337.549i | − | 0.373395i | ||||||
\(905\) | 156.222 | + | 148.528i | 0.172621 | + | 0.164119i | ||||
\(906\) | 65.7468 | − | 113.877i | 0.0725682 | − | 0.125692i | ||||
\(907\) | 163.597 | + | 610.552i | 0.180371 | + | 0.673155i | 0.995574 | + | 0.0939796i | \(0.0299589\pi\) |
−0.815203 | + | 0.579176i | \(0.803374\pi\) | |||||||
\(908\) | −183.547 | + | 685.008i | −0.202145 | + | 0.754414i | ||||
\(909\) | 240.600i | 0.264686i | ||||||||
\(910\) | −3.04352 | + | 59.5417i | −0.00334452 | + | 0.0654305i | ||||
\(911\) | 1345.46 | 1.47691 | 0.738453 | − | 0.674305i | \(-0.235557\pi\) | ||||
0.738453 | + | 0.674305i | \(0.235557\pi\) | |||||||
\(912\) | −493.252 | − | 132.167i | −0.540847 | − | 0.144920i | ||||
\(913\) | −562.504 | + | 150.723i | −0.616105 | + | 0.165085i | ||||
\(914\) | −260.604 | − | 150.460i | −0.285124 | − | 0.164617i | ||||
\(915\) | −4.29322 | − | 170.038i | −0.00469204 | − | 0.185834i | ||||
\(916\) | −39.4194 | −0.0430342 | ||||||||
\(917\) | 601.876 | + | 701.539i | 0.656354 | + | 0.765037i | ||||
\(918\) | −20.6550 | − | 20.6550i | −0.0224999 | − | 0.0224999i | ||||
\(919\) | 236.556 | − | 136.575i | 0.257405 | − | 0.148613i | −0.365745 | − | 0.930715i | \(-0.619186\pi\) |
0.623150 | + | 0.782102i | \(0.285852\pi\) | |||||||
\(920\) | 467.241 | + | 112.638i | 0.507871 | + | 0.122432i | ||||
\(921\) | 209.048 | − | 362.081i | 0.226979 | − | 0.393139i | ||||
\(922\) | 1.57964 | + | 0.423263i | 0.00171328 | + | 0.000459071i | ||||
\(923\) | −190.162 | − | 190.162i | −0.206026 | − | 0.206026i | ||||
\(924\) | −520.369 | + | 760.763i | −0.563170 | + | 0.823337i | ||||
\(925\) | 320.499 | − | 1494.06i | 0.346485 | − | 1.61520i | ||||
\(926\) | 90.2795 | + | 156.369i | 0.0974941 | + | 0.168865i | ||||
\(927\) | 24.1289 | + | 90.0503i | 0.0260290 | + | 0.0971417i | ||||
\(928\) | 566.904 | − | 151.902i | 0.610888 | − | 0.163687i | ||||
\(929\) | −463.310 | + | 267.492i | −0.498719 | + | 0.287936i | −0.728184 | − | 0.685381i | \(-0.759636\pi\) |
0.229465 | + | 0.973317i | \(0.426302\pi\) | |||||||
\(930\) | 165.677 | − | 48.9069i | 0.178147 | − | 0.0525880i | ||||
\(931\) | −664.655 | + | 828.291i | −0.713915 | + | 0.889679i | ||||
\(932\) | −300.099 | + | 300.099i | −0.321995 | + | 0.321995i | ||||
\(933\) | 19.4279 | − | 72.5060i | 0.0208231 | − | 0.0777128i | ||||
\(934\) | 319.672 | + | 184.563i | 0.342261 | + | 0.197605i | ||||
\(935\) | 651.362 | + | 1065.16i | 0.696643 | + | 1.13921i | ||||
\(936\) | −19.9218 | − | 34.5056i | −0.0212840 | − | 0.0368649i | ||||
\(937\) | −993.941 | + | 993.941i | −1.06077 | + | 1.06077i | −0.0627391 | + | 0.998030i | \(0.519984\pi\) |
−0.998030 | + | 0.0627391i | \(0.980016\pi\) | |||||||
\(938\) | 7.96954 | + | 42.4721i | 0.00849632 | + | 0.0452794i | ||||
\(939\) | − | 332.632i | − | 0.354240i | ||||||
\(940\) | 5.37121 | + | 212.733i | 0.00571405 | + | 0.226312i | ||||
\(941\) | 411.864 | − | 713.369i | 0.437687 | − | 0.758097i | −0.559823 | − | 0.828612i | \(-0.689131\pi\) |
0.997511 | + | 0.0705152i | \(0.0224643\pi\) | |||||||
\(942\) | 48.3491 | + | 180.441i | 0.0513260 | + | 0.191551i | ||||
\(943\) | −140.719 | + | 525.171i | −0.149225 | + | 0.556915i | ||||
\(944\) | 779.479i | 0.825720i | ||||||||
\(945\) | 177.842 | − | 38.0411i | 0.188193 | − | 0.0402552i | ||||
\(946\) | 179.223 | 0.189454 | ||||||||
\(947\) | −789.991 | − | 211.678i | −0.834204 | − | 0.223524i | −0.183657 | − | 0.982990i | \(-0.558794\pi\) |
−0.650547 | + | 0.759466i | \(0.725460\pi\) | |||||||
\(948\) | 823.416 | − | 220.634i | 0.868582 | − | 0.232736i | ||||
\(949\) | −305.025 | − | 176.106i | −0.321417 | − | 0.185570i | ||||
\(950\) | 75.0372 | + | 232.421i | 0.0789865 | + | 0.244654i | ||||
\(951\) | 28.5520 | 0.0300231 | ||||||||
\(952\) | −101.772 | + | 289.441i | −0.106904 | + | 0.304035i | ||||
\(953\) | −1249.74 | − | 1249.74i | −1.31138 | − | 1.31138i | −0.920401 | − | 0.390975i | \(-0.872138\pi\) |
−0.390975 | − | 0.920401i | \(-0.627862\pi\) | |||||||
\(954\) | 37.9013 | − | 21.8823i | 0.0397288 | − | 0.0229375i | ||||
\(955\) | −152.687 | + | 633.373i | −0.159882 | + | 0.663218i | ||||
\(956\) | −372.484 | + | 645.162i | −0.389628 | + | 0.674855i | ||||
\(957\) | 973.777 | + | 260.923i | 1.01753 | + | 0.272647i | ||||
\(958\) | −170.977 | − | 170.977i | −0.178473 | − | 0.178473i | ||||
\(959\) | 137.067 | + | 285.729i | 0.142927 | + | 0.297944i | ||||
\(960\) | 187.566 | − | 344.684i | 0.195382 | − | 0.359046i | ||||
\(961\) | −498.620 | − | 863.636i | −0.518856 | − | 0.898684i | ||||
\(962\) | −26.9472 | − | 100.568i | −0.0280116 | − | 0.104541i | ||||
\(963\) | 303.817 | − | 81.4074i | 0.315490 | − | 0.0845352i | ||||
\(964\) | 134.903 | − | 77.8862i | 0.139941 | − | 0.0807948i | ||||
\(965\) | −1490.38 | − | 811.022i | −1.54444 | − | 0.840437i | ||||
\(966\) | −11.3963 | + | 149.043i | −0.0117974 | + | 0.154289i | ||||
\(967\) | −367.218 | + | 367.218i | −0.379750 | + | 0.379750i | −0.871012 | − | 0.491262i | \(-0.836536\pi\) |
0.491262 | + | 0.871012i | \(0.336536\pi\) | |||||||
\(968\) | 254.593 | − | 950.155i | 0.263010 | − | 0.981565i | ||||
\(969\) | −405.447 | − | 234.085i | −0.418418 | − | 0.241574i | ||||
\(970\) | 111.983 | + | 26.9956i | 0.115446 | + | 0.0278305i | ||||
\(971\) | 87.0711 | + | 150.812i | 0.0896716 | + | 0.155316i | 0.907372 | − | 0.420328i | \(-0.138085\pi\) |
−0.817701 | + | 0.575644i | \(0.804752\pi\) | |||||||
\(972\) | −41.8512 | + | 41.8512i | −0.0430568 | + | 0.0430568i | ||||
\(973\) | −135.053 | − | 719.738i | −0.138801 | − | 0.739711i | ||||
\(974\) | 169.900i | 0.174435i | ||||||||
\(975\) | 74.5625 | − | 145.662i | 0.0764743 | − | 0.149397i | ||||
\(976\) | 133.587 | − | 231.379i | 0.136871 | − | 0.237068i | ||||
\(977\) | −410.121 | − | 1530.59i | −0.419776 | − | 1.56662i | −0.775074 | − | 0.631871i | \(-0.782287\pi\) |
0.355298 | − | 0.934753i | \(-0.384379\pi\) | |||||||
\(978\) | 6.07875 | − | 22.6862i | 0.00621549 | − | 0.0231965i | ||||
\(979\) | 671.518i | 0.685922i | ||||||||
\(980\) | −568.872 | − | 735.999i | −0.580482 | − | 0.751020i | ||||
\(981\) | 41.4933 | 0.0422969 | ||||||||
\(982\) | −62.2529 | − | 16.6806i | −0.0633940 | − | 0.0169864i | ||||
\(983\) | −1496.43 | + | 400.967i | −1.52231 | + | 0.407901i | −0.920501 | − | 0.390741i | \(-0.872219\pi\) |
−0.601807 | + | 0.798642i | \(0.705552\pi\) | |||||||
\(984\) | −104.791 | − | 60.5014i | −0.106495 | − | 0.0614852i | ||||
\(985\) | 637.284 | − | 16.0905i | 0.646988 | − | 0.0163355i | ||||
\(986\) | 163.417 | 0.165738 | ||||||||
\(987\) | −133.576 | + | 25.0645i | −0.135335 | + | 0.0253946i | ||||
\(988\) | −219.893 | − | 219.893i | −0.222564 | − | 0.222564i | ||||
\(989\) | −470.381 | + | 271.575i | −0.475613 | + | 0.274595i | ||||
\(990\) | −115.494 | + | 70.6263i | −0.116661 | + | 0.0713397i | ||||
\(991\) | 311.136 | − | 538.904i | 0.313962 | − | 0.543798i | −0.665255 | − | 0.746617i | \(-0.731677\pi\) |
0.979216 | + | 0.202819i | \(0.0650103\pi\) | |||||||
\(992\) | 862.983 | + | 231.235i | 0.869942 | + | 0.233100i | ||||
\(993\) | −663.545 | − | 663.545i | −0.668223 | − | 0.668223i | ||||
\(994\) | −223.888 | − | 17.1191i | −0.225240 | − | 0.0172225i | ||||
\(995\) | 41.8596 | + | 141.803i | 0.0420700 | + | 0.142516i | ||||
\(996\) | 95.6353 | + | 165.645i | 0.0960194 | + | 0.166310i | ||||
\(997\) | 135.088 | + | 504.154i | 0.135494 | + | 0.505671i | 0.999995 | + | 0.00304053i | \(0.000967833\pi\) |
−0.864501 | + | 0.502631i | \(0.832366\pi\) | |||||||
\(998\) | 269.550 | − | 72.2258i | 0.270090 | − | 0.0723705i | ||||
\(999\) | −275.049 | + | 158.799i | −0.275324 | + | 0.158958i |
(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 | 105.3.v.a.88.8 | yes | 64 | |
3.2 | odd | 2 | 315.3.ca.b.298.9 | 64 | |||
5.2 | odd | 4 | inner | 105.3.v.a.67.9 | yes | 64 | |
7.2 | even | 3 | inner | 105.3.v.a.58.9 | yes | 64 | |
15.2 | even | 4 | 315.3.ca.b.172.8 | 64 | |||
21.2 | odd | 6 | 315.3.ca.b.163.8 | 64 | |||
35.2 | odd | 12 | inner | 105.3.v.a.37.8 | ✓ | 64 | |
105.2 | even | 12 | 315.3.ca.b.37.9 | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.v.a.37.8 | ✓ | 64 | 35.2 | odd | 12 | inner | |
105.3.v.a.58.9 | yes | 64 | 7.2 | even | 3 | inner | |
105.3.v.a.67.9 | yes | 64 | 5.2 | odd | 4 | inner | |
105.3.v.a.88.8 | yes | 64 | 1.1 | even | 1 | trivial | |
315.3.ca.b.37.9 | 64 | 105.2 | even | 12 | |||
315.3.ca.b.163.8 | 64 | 21.2 | odd | 6 | |||
315.3.ca.b.172.8 | 64 | 15.2 | even | 4 | |||
315.3.ca.b.298.9 | 64 | 3.2 | odd | 2 |