Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,3,Mod(19,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 16]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.j (of order \(18\), degree \(6\), not 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: | \(8.82836056527\) |
Analytic rank: | \(0\) |
Dimension: | \(204\) |
Relative dimension: | \(34\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 199.17 | ||
Character | \(\chi\) | \(=\) | 324.199 |
Dual form | 324.3.j.a.127.17 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.00794476 | − | 1.99998i | 0.00397238 | − | 0.999992i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.99987 | − | 0.0317788i | −0.999968 | − | 0.00794470i | ||||
\(5\) | −7.18780 | + | 2.61614i | −1.43756 | + | 0.523229i | −0.939088 | − | 0.343677i | \(-0.888327\pi\) |
−0.498471 | + | 0.866906i | \(0.666105\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.65258 | − | 0.996703i | 0.807512 | − | 0.142386i | 0.245373 | − | 0.969429i | \(-0.421090\pi\) |
0.562139 | + | 0.827043i | \(0.309979\pi\) | |||||||
\(8\) | −0.0953352 | + | 7.99943i | −0.0119169 | + | 0.999929i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.17514 | + | 14.3963i | 0.517514 | + | 1.43963i | ||||
\(11\) | 2.01574 | − | 5.53819i | 0.183249 | − | 0.503472i | −0.813722 | − | 0.581255i | \(-0.802562\pi\) |
0.996970 | + | 0.0777831i | \(0.0247842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.25839 | + | 6.92961i | 0.635261 | + | 0.533047i | 0.902559 | − | 0.430567i | \(-0.141686\pi\) |
−0.267298 | + | 0.963614i | \(0.586131\pi\) | |||||||
\(14\) | −1.94848 | − | 11.3130i | −0.139177 | − | 0.808071i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.9980 | + | 0.254222i | 0.999874 | + | 0.0158889i | ||||
\(17\) | −10.4844 | + | 18.1596i | −0.616731 | + | 1.06821i | 0.373347 | + | 0.927692i | \(0.378210\pi\) |
−0.990078 | + | 0.140518i | \(0.955123\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 21.5373 | − | 12.4346i | 1.13354 | − | 0.654450i | 0.188718 | − | 0.982031i | \(-0.439567\pi\) |
0.944823 | + | 0.327581i | \(0.106233\pi\) | |||||||
\(20\) | 28.8334 | − | 10.2358i | 1.44167 | − | 0.511791i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −11.0603 | − | 4.07544i | −0.502740 | − | 0.185247i | ||||
\(23\) | 20.5338 | + | 3.62067i | 0.892776 | + | 0.157420i | 0.601173 | − | 0.799119i | \(-0.294700\pi\) |
0.291603 | + | 0.956539i | \(0.405811\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.6691 | − | 21.5389i | 1.02676 | − | 0.861557i | ||||
\(26\) | 13.9247 | − | 16.4616i | 0.535566 | − | 0.633138i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −22.6413 | + | 3.80705i | −0.808617 | + | 0.135966i | ||||
\(29\) | 30.1767 | − | 25.3212i | 1.04058 | − | 0.873146i | 0.0485038 | − | 0.998823i | \(-0.484555\pi\) |
0.992071 | + | 0.125677i | \(0.0401102\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.3697 | + | 1.82845i | 0.334505 | + | 0.0589823i | 0.338378 | − | 0.941010i | \(-0.390122\pi\) |
−0.00387293 | + | 0.999993i | \(0.501233\pi\) | |||||||
\(32\) | 0.635541 | − | 31.9937i | 0.0198607 | − | 0.999803i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 36.2355 | + | 21.1130i | 1.06575 | + | 0.620969i | ||||
\(35\) | −38.0221 | + | 21.9521i | −1.08635 | + | 0.627202i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.83871 | + | 3.18474i | −0.0496950 | + | 0.0860742i | −0.889803 | − | 0.456345i | \(-0.849158\pi\) |
0.840108 | + | 0.542419i | \(0.182492\pi\) | |||||||
\(38\) | −24.6978 | − | 43.1730i | −0.649942 | − | 1.13613i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −20.2424 | − | 57.7477i | −0.506060 | − | 1.44369i | ||||
\(41\) | 51.1323 | + | 42.9051i | 1.24713 | + | 1.04647i | 0.996932 | + | 0.0782699i | \(0.0249396\pi\) |
0.250196 | + | 0.968195i | \(0.419505\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −28.3547 | + | 77.9040i | −0.659412 | + | 1.81172i | −0.0798268 | + | 0.996809i | \(0.525437\pi\) |
−0.579585 | + | 0.814912i | \(0.696785\pi\) | |||||||
\(44\) | −8.23869 | + | 22.0880i | −0.187243 | + | 0.502000i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.40442 | − | 41.0386i | 0.160966 | − | 0.892143i | ||||
\(47\) | −33.3947 | + | 5.88839i | −0.710526 | + | 0.125285i | −0.517219 | − | 0.855853i | \(-0.673033\pi\) |
−0.193308 | + | 0.981138i | \(0.561922\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.0867 | + | 5.49110i | −0.307891 | + | 0.112063i | ||||
\(50\) | −42.8736 | − | 51.5089i | −0.857471 | − | 1.03018i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −32.8123 | − | 27.9800i | −0.631006 | − | 0.538077i | ||||
\(53\) | 43.9772 | 0.829758 | 0.414879 | − | 0.909877i | \(-0.363824\pi\) | ||||
0.414879 | + | 0.909877i | \(0.363824\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 45.0808i | 0.819651i | ||||||||
\(56\) | 7.43417 | + | 45.3125i | 0.132753 | + | 0.809151i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −50.4023 | − | 60.5540i | −0.869006 | − | 1.04404i | ||||
\(59\) | −9.37752 | − | 25.7645i | −0.158941 | − | 0.436687i | 0.834503 | − | 0.551003i | \(-0.185755\pi\) |
−0.993444 | + | 0.114316i | \(0.963532\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.47945 | − | 8.39040i | −0.0242533 | − | 0.137548i | 0.970277 | − | 0.241998i | \(-0.0778028\pi\) |
−0.994530 | + | 0.104450i | \(0.966692\pi\) | |||||||
\(62\) | 3.73926 | − | 20.7246i | 0.0603106 | − | 0.334268i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −63.9818 | − | 1.52525i | −0.999716 | − | 0.0238321i | ||||
\(65\) | −77.4885 | − | 28.2035i | −1.19213 | − | 0.433900i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 31.0935 | − | 37.0558i | 0.464083 | − | 0.553072i | −0.482348 | − | 0.875980i | \(-0.660216\pi\) |
0.946431 | + | 0.322908i | \(0.104660\pi\) | |||||||
\(68\) | 42.5135 | − | 72.3028i | 0.625198 | − | 1.06328i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 43.6017 | + | 76.2180i | 0.622881 | + | 1.08883i | ||||
\(71\) | 24.2168 | + | 13.9816i | 0.341082 | + | 0.196924i | 0.660751 | − | 0.750606i | \(-0.270238\pi\) |
−0.319668 | + | 0.947530i | \(0.603571\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 43.5064 | + | 75.3554i | 0.595979 | + | 1.03227i | 0.993408 | + | 0.114633i | \(0.0365691\pi\) |
−0.397429 | + | 0.917633i | \(0.630098\pi\) | |||||||
\(74\) | 6.35483 | + | 3.70270i | 0.0858761 | + | 0.0500365i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −86.5416 | + | 49.0522i | −1.13870 | + | 0.645424i | ||||
\(77\) | 5.87418 | − | 33.3142i | 0.0762881 | − | 0.432651i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.6931 | + | 13.9353i | 0.148014 | + | 0.176396i | 0.834957 | − | 0.550315i | \(-0.185492\pi\) |
−0.686943 | + | 0.726711i | \(0.741048\pi\) | |||||||
\(80\) | −115.655 | + | 40.0257i | −1.44569 | + | 0.500321i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 86.2157 | − | 101.923i | 1.05141 | − | 1.24296i | ||||
\(83\) | 8.95501 | + | 10.6722i | 0.107892 | + | 0.128580i | 0.817288 | − | 0.576230i | \(-0.195477\pi\) |
−0.709396 | + | 0.704810i | \(0.751032\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 27.8519 | − | 157.956i | 0.327669 | − | 1.85831i | ||||
\(86\) | 155.581 | + | 57.3279i | 1.80909 | + | 0.666604i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 44.1102 | + | 16.6527i | 0.501252 | + | 0.189236i | ||||
\(89\) | 81.2903 | + | 140.799i | 0.913374 | + | 1.58201i | 0.809264 | + | 0.587445i | \(0.199866\pi\) |
0.104110 | + | 0.994566i | \(0.466801\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 53.5880 | + | 30.9390i | 0.588879 | + | 0.339989i | ||||
\(92\) | −82.0177 | − | 15.1348i | −0.891497 | − | 0.164508i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.5114 | + | 66.8357i | 0.122462 | + | 0.711019i | ||||
\(95\) | −122.275 | + | 145.722i | −1.28711 | + | 1.53391i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 39.6511 | + | 14.4318i | 0.408775 | + | 0.148782i | 0.538219 | − | 0.842805i | \(-0.319097\pi\) |
−0.129445 | + | 0.991587i | \(0.541319\pi\) | |||||||
\(98\) | 10.8623 | + | 30.2167i | 0.110839 | + | 0.308334i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −103.358 | + | 85.3372i | −1.03358 | + | 0.853372i | ||||
\(101\) | −19.0016 | − | 107.763i | −0.188134 | − | 1.06696i | −0.921862 | − | 0.387519i | \(-0.873332\pi\) |
0.733728 | − | 0.679444i | \(-0.237779\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.336017 | + | 0.923198i | 0.00326230 | + | 0.00896309i | 0.941313 | − | 0.337535i | \(-0.109593\pi\) |
−0.938051 | + | 0.346498i | \(0.887371\pi\) | |||||||
\(104\) | −56.2203 | + | 65.4018i | −0.540579 | + | 0.628863i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.349388 | − | 87.9536i | 0.00329612 | − | 0.829751i | ||||
\(107\) | − | 129.179i | − | 1.20728i | −0.797258 | − | 0.603639i | \(-0.793717\pi\) | ||
0.797258 | − | 0.603639i | \(-0.206283\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −160.479 | −1.47229 | −0.736144 | − | 0.676825i | \(-0.763355\pi\) | ||||
−0.736144 | + | 0.676825i | \(0.763355\pi\) | |||||||
\(110\) | 90.1609 | + | 0.358157i | 0.819645 | + | 0.00325597i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 90.6833 | − | 14.5082i | 0.809672 | − | 0.129538i | ||||
\(113\) | −61.3383 | + | 22.3253i | −0.542817 | + | 0.197569i | −0.598852 | − | 0.800860i | \(-0.704376\pi\) |
0.0560354 | + | 0.998429i | \(0.482154\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −157.065 | + | 27.6948i | −1.36578 | + | 0.240825i | ||||
\(116\) | −121.508 | + | 100.323i | −1.04748 | + | 0.864852i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −51.6031 | + | 18.5502i | −0.437315 | + | 0.157205i | ||||
\(119\) | −41.1644 | + | 113.098i | −0.345919 | + | 0.950405i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 66.0830 | + | 55.4502i | 0.546141 | + | 0.458267i | ||||
\(122\) | −16.7924 | + | 2.89223i | −0.137643 | + | 0.0237068i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −41.4192 | − | 7.64311i | −0.334026 | − | 0.0616380i | ||||
\(125\) | −32.5416 | + | 56.3637i | −0.260333 | + | 0.450909i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −42.9918 | + | 24.8213i | −0.338518 | + | 0.195443i | −0.659616 | − | 0.751602i | \(-0.729281\pi\) |
0.321099 | + | 0.947046i | \(0.395948\pi\) | |||||||
\(128\) | −3.55880 | + | 127.951i | −0.0278032 | + | 0.999613i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −57.0222 | + | 154.752i | −0.438632 | + | 1.19040i | ||||
\(131\) | 170.857 | + | 30.1266i | 1.30425 | + | 0.229974i | 0.782246 | − | 0.622970i | \(-0.214074\pi\) |
0.522002 | + | 0.852944i | \(0.325185\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 109.348 | − | 91.7536i | 0.822163 | − | 0.689877i | ||||
\(134\) | −73.8641 | − | 62.4810i | −0.551224 | − | 0.466276i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −144.267 | − | 85.6007i | −1.06078 | − | 0.629417i | ||||
\(137\) | −38.4087 | + | 32.2287i | −0.280356 | + | 0.235246i | −0.772112 | − | 0.635487i | \(-0.780800\pi\) |
0.491756 | + | 0.870733i | \(0.336355\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −183.877 | − | 32.4224i | −1.32285 | − | 0.233255i | −0.532773 | − | 0.846258i | \(-0.678850\pi\) |
−0.790081 | + | 0.613003i | \(0.789961\pi\) | |||||||
\(140\) | 152.781 | − | 86.5972i | 1.09129 | − | 0.618551i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 28.1554 | − | 48.3222i | 0.198277 | − | 0.340297i | ||||
\(143\) | 55.0242 | − | 31.7682i | 0.384785 | − | 0.222156i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −150.660 | + | 260.950i | −1.03903 | + | 1.79966i | ||||
\(146\) | 151.055 | − | 86.4135i | 1.03462 | − | 0.591873i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.45583 | − | 12.6801i | 0.0503772 | − | 0.0856767i | ||||
\(149\) | −29.7807 | − | 24.9890i | −0.199871 | − | 0.167711i | 0.537359 | − | 0.843354i | \(-0.319422\pi\) |
−0.737230 | + | 0.675642i | \(0.763866\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 97.1070 | − | 266.799i | 0.643093 | − | 1.76688i | 0.00130597 | − | 0.999999i | \(-0.499584\pi\) |
0.641787 | − | 0.766883i | \(-0.278193\pi\) | |||||||
\(152\) | 97.4161 | + | 173.471i | 0.640896 | + | 1.14126i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −66.5811 | − | 12.0129i | −0.432345 | − | 0.0780062i | ||||
\(155\) | −79.3185 | + | 13.9860i | −0.511732 | + | 0.0902322i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 137.397 | − | 50.0085i | 0.875141 | − | 0.318525i | 0.134894 | − | 0.990860i | \(-0.456931\pi\) |
0.740247 | + | 0.672335i | \(0.234708\pi\) | |||||||
\(158\) | 27.9632 | − | 23.2753i | 0.176982 | − | 0.147312i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 79.1319 | + | 231.627i | 0.494575 | + | 1.44767i | ||||
\(161\) | 119.678 | 0.743341 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 55.1271i | 0.338203i | 0.985599 | + | 0.169102i | \(0.0540866\pi\) | ||||
−0.985599 | + | 0.169102i | \(0.945913\pi\) | |||||||
\(164\) | −203.159 | − | 173.240i | −1.23878 | − | 1.05634i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 21.4153 | − | 17.8251i | 0.129008 | − | 0.107380i | ||||
\(167\) | 58.1117 | + | 159.661i | 0.347974 | + | 0.956051i | 0.983007 | + | 0.183566i | \(0.0587642\pi\) |
−0.635033 | + | 0.772485i | \(0.719014\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.16507 | − | 51.9777i | −0.0542312 | − | 0.307560i | ||||
\(170\) | −315.688 | − | 56.9583i | −1.85699 | − | 0.335049i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 115.891 | − | 310.705i | 0.673785 | − | 1.80642i | ||||
\(173\) | −87.8563 | − | 31.9771i | −0.507840 | − | 0.184839i | 0.0753771 | − | 0.997155i | \(-0.475984\pi\) |
−0.583217 | + | 0.812317i | \(0.698206\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 123.629 | − | 147.335i | 0.706450 | − | 0.841914i | ||||
\(176\) | 33.6556 | − | 88.0874i | 0.191225 | − | 0.500497i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 282.241 | − | 161.461i | 1.58563 | − | 0.907083i | ||||
\(179\) | 130.749 | + | 75.4882i | 0.730444 | + | 0.421722i | 0.818585 | − | 0.574386i | \(-0.194759\pi\) |
−0.0881407 | + | 0.996108i | \(0.528092\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.82485 | + | 17.0171i | 0.0542809 | + | 0.0940173i | 0.891889 | − | 0.452254i | \(-0.149380\pi\) |
−0.837608 | + | 0.546272i | \(0.816047\pi\) | |||||||
\(182\) | 62.3033 | − | 106.929i | 0.342326 | − | 0.587524i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −30.9209 | + | 163.914i | −0.168048 | + | 0.890836i | ||||
\(185\) | 4.88455 | − | 27.7016i | 0.0264029 | − | 0.149739i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 79.4372 | + | 94.6696i | 0.424798 | + | 0.506255i | ||||
\(188\) | 133.762 | − | 22.4916i | 0.711499 | − | 0.119636i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 290.470 | + | 245.706i | 1.52879 | + | 1.29319i | ||||
\(191\) | −161.522 | − | 192.495i | −0.845667 | − | 1.00783i | −0.999804 | − | 0.0197775i | \(-0.993704\pi\) |
0.154137 | − | 0.988049i | \(-0.450740\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.54996 | − | 14.4615i | 0.0132122 | − | 0.0749303i | −0.977489 | − | 0.210988i | \(-0.932332\pi\) |
0.990701 | + | 0.136057i | \(0.0434431\pi\) | |||||||
\(194\) | 29.1785 | − | 79.1870i | 0.150404 | − | 0.408180i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 60.5193 | − | 21.4843i | 0.308772 | − | 0.109614i | ||||
\(197\) | −104.711 | − | 181.365i | −0.531528 | − | 0.920634i | −0.999323 | − | 0.0367968i | \(-0.988285\pi\) |
0.467794 | − | 0.883837i | \(-0.345049\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.56353 | − | 2.63476i | −0.0229323 | − | 0.0132400i | 0.488490 | − | 0.872569i | \(-0.337548\pi\) |
−0.511422 | + | 0.859330i | \(0.670881\pi\) | |||||||
\(200\) | 169.852 | + | 207.392i | 0.849260 | + | 1.03696i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −215.676 | + | 37.1467i | −1.06770 | + | 0.183894i | ||||
\(203\) | 145.338 | − | 173.208i | 0.715953 | − | 0.853239i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −479.774 | − | 174.623i | −2.34036 | − | 0.851822i | ||||
\(206\) | 1.84905 | − | 0.664693i | 0.00897598 | − | 0.00322667i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 130.356 | + | 112.959i | 0.626711 | + | 0.543073i | ||||
\(209\) | −25.4514 | − | 144.342i | −0.121777 | − | 0.690633i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −30.7845 | − | 84.5797i | −0.145898 | − | 0.400852i | 0.845120 | − | 0.534576i | \(-0.179529\pi\) |
−0.991019 | + | 0.133724i | \(0.957306\pi\) | |||||||
\(212\) | −175.903 | − | 1.39754i | −0.829732 | − | 0.00659218i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −258.355 | − | 1.02629i | −1.20727 | − | 0.00479577i | ||||
\(215\) | − | 634.138i | − | 2.94948i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 60.4378 | 0.278515 | ||||||||
\(218\) | −1.27497 | + | 320.956i | −0.00584849 | + | 1.47228i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.43261 | − | 180.318i | 0.00651189 | − | 0.819625i | ||||
\(221\) | −212.423 | + | 77.3157i | −0.961191 | + | 0.349845i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −233.603 | + | 41.1905i | −1.04755 | + | 0.184711i | −0.670825 | − | 0.741616i | \(-0.734060\pi\) |
−0.376722 | + | 0.926326i | \(0.622949\pi\) | |||||||
\(224\) | −28.2957 | − | 181.480i | −0.126320 | − | 0.810180i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 44.1629 | + | 122.853i | 0.195411 | + | 0.543597i | ||||
\(227\) | 92.2846 | − | 253.550i | 0.406540 | − | 1.11696i | −0.552456 | − | 0.833542i | \(-0.686309\pi\) |
0.958996 | − | 0.283418i | \(-0.0914684\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 132.829 | + | 111.457i | 0.580039 | + | 0.486710i | 0.884960 | − | 0.465667i | \(-0.154186\pi\) |
−0.304921 | + | 0.952378i | \(0.598630\pi\) | |||||||
\(230\) | 54.1414 | + | 314.348i | 0.235397 | + | 1.36673i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 199.679 | + | 243.810i | 0.860684 | + | 1.05091i | ||||
\(233\) | 85.3765 | − | 147.877i | 0.366423 | − | 0.634663i | −0.622580 | − | 0.782556i | \(-0.713916\pi\) |
0.989003 | + | 0.147893i | \(0.0472490\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 224.630 | − | 129.690i | 0.955871 | − | 0.551872i | ||||
\(236\) | 36.6901 | + | 103.353i | 0.155467 | + | 0.437936i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 225.868 | + | 83.2267i | 0.949024 | + | 0.349692i | ||||
\(239\) | 126.129 | + | 22.2400i | 0.527738 | + | 0.0930544i | 0.431168 | − | 0.902272i | \(-0.358102\pi\) |
0.0965700 | + | 0.995326i | \(0.469213\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −126.565 | + | 106.201i | −0.525167 | + | 0.440668i | −0.866429 | − | 0.499301i | \(-0.833590\pi\) |
0.341261 | + | 0.939968i | \(0.389146\pi\) | |||||||
\(242\) | 111.425 | − | 131.724i | 0.460432 | − | 0.544316i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.65099 | + | 33.6076i | 0.0231598 | + | 0.137736i | ||||
\(245\) | 94.0744 | − | 78.9378i | 0.383977 | − | 0.322195i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 264.030 | + | 46.5556i | 1.06895 | + | 0.188484i | ||||
\(248\) | −15.6152 | + | 82.7771i | −0.0629644 | + | 0.333779i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 112.468 | + | 65.5304i | 0.449872 | + | 0.262122i | ||||
\(251\) | −114.384 | + | 66.0395i | −0.455712 | + | 0.263106i | −0.710240 | − | 0.703960i | \(-0.751413\pi\) |
0.254527 | + | 0.967066i | \(0.418080\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 61.4428 | − | 106.422i | 0.242857 | − | 0.420640i | ||||
\(254\) | 49.3007 | + | 86.1801i | 0.194097 | + | 0.339292i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 255.871 | + | 8.13409i | 0.999495 | + | 0.0317738i | ||||
\(257\) | −7.69515 | − | 6.45700i | −0.0299422 | − | 0.0251245i | 0.627694 | − | 0.778460i | \(-0.283999\pi\) |
−0.657636 | + | 0.753336i | \(0.728443\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.21923 | + | 19.8347i | −0.0278735 | + | 0.0765818i | ||||
\(260\) | 309.048 | + | 115.273i | 1.18865 | + | 0.443357i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 61.6102 | − | 341.471i | 0.235153 | − | 1.30332i | ||||
\(263\) | −97.1175 | + | 17.1244i | −0.369268 | + | 0.0651119i | −0.355203 | − | 0.934789i | \(-0.615588\pi\) |
−0.0140650 | + | 0.999901i | \(0.504477\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −316.099 | + | 115.051i | −1.19283 | + | 0.434153i | ||||
\(266\) | −182.637 | − | 219.423i | −0.686605 | − | 0.824897i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −125.548 | + | 147.231i | −0.468462 | + | 0.549368i | ||||
\(269\) | −39.0655 | −0.145225 | −0.0726125 | − | 0.997360i | \(-0.523134\pi\) | ||||
−0.0726125 | + | 0.997360i | \(0.523134\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 286.162i | − | 1.05595i | −0.849260 | − | 0.527975i | \(-0.822951\pi\) | ||
0.849260 | − | 0.527975i | \(-0.177049\pi\) | |||||||
\(272\) | −172.346 | + | 287.851i | −0.633626 | + | 1.05828i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 64.1518 | + | 77.0729i | 0.234131 | + | 0.281288i | ||||
\(275\) | −67.5445 | − | 185.577i | −0.245616 | − | 0.674826i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.2278 | + | 63.6758i | 0.0405334 | + | 0.229877i | 0.998344 | − | 0.0575231i | \(-0.0183203\pi\) |
−0.957811 | + | 0.287400i | \(0.907209\pi\) | |||||||
\(278\) | −66.3052 | + | 367.493i | −0.238508 | + | 1.32192i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −171.979 | − | 306.248i | −0.614211 | − | 1.09374i | ||||
\(281\) | 370.748 | + | 134.941i | 1.31939 | + | 0.480219i | 0.903263 | − | 0.429088i | \(-0.141165\pi\) |
0.416127 | + | 0.909307i | \(0.363387\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.3644 | − | 37.3786i | 0.110828 | − | 0.132080i | −0.707778 | − | 0.706435i | \(-0.750302\pi\) |
0.818607 | + | 0.574355i | \(0.194747\pi\) | |||||||
\(284\) | −96.4200 | − | 56.6942i | −0.339507 | − | 0.199628i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −63.0988 | − | 110.300i | −0.220625 | − | 0.385664i | ||||
\(287\) | 331.793 | + | 191.561i | 1.15607 | + | 0.667459i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −75.3464 | − | 130.504i | −0.260714 | − | 0.451570i | ||||
\(290\) | 520.700 | + | 303.390i | 1.79552 | + | 1.04617i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −171.626 | − | 302.795i | −0.587759 | − | 1.03697i | ||||
\(293\) | −95.7393 | + | 542.964i | −0.326755 | + | 1.85312i | 0.170287 | + | 0.985395i | \(0.445531\pi\) |
−0.497042 | + | 0.867727i | \(0.665580\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 134.807 | + | 160.657i | 0.456974 | + | 0.544600i | ||||
\(296\) | −25.3009 | − | 15.0123i | −0.0854759 | − | 0.0507172i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −50.2142 | + | 59.3625i | −0.168504 | + | 0.199203i | ||||
\(299\) | 144.487 | + | 172.192i | 0.483233 | + | 0.575894i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −82.6303 | + | 468.620i | −0.274519 | + | 1.55688i | ||||
\(302\) | −532.823 | − | 196.332i | −1.76431 | − | 0.650106i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 347.714 | − | 193.453i | 1.14380 | − | 0.636357i | ||||
\(305\) | 32.5845 | + | 56.4380i | 0.106834 | + | 0.185043i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 256.843 | + | 148.288i | 0.836622 | + | 0.483024i | 0.856115 | − | 0.516786i | \(-0.172872\pi\) |
−0.0194923 | + | 0.999810i | \(0.506205\pi\) | |||||||
\(308\) | −24.5547 | + | 133.066i | −0.0797230 | + | 0.432032i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 27.3416 | + | 158.747i | 0.0881987 | + | 0.512087i | ||||
\(311\) | 96.9784 | − | 115.574i | 0.311828 | − | 0.371622i | −0.587254 | − | 0.809403i | \(-0.699791\pi\) |
0.899082 | + | 0.437781i | \(0.144235\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −290.511 | − | 105.737i | −0.928150 | − | 0.337819i | −0.166674 | − | 0.986012i | \(-0.553303\pi\) |
−0.761476 | + | 0.648193i | \(0.775525\pi\) | |||||||
\(314\) | −98.9246 | − | 275.189i | −0.315046 | − | 0.876399i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −46.3280 | − | 56.1109i | −0.146608 | − | 0.177566i | ||||
\(317\) | −26.3539 | − | 149.461i | −0.0831355 | − | 0.471485i | −0.997743 | − | 0.0671428i | \(-0.978612\pi\) |
0.914608 | − | 0.404342i | \(-0.132499\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −79.4056 | − | 218.165i | −0.248920 | − | 0.683903i | ||||
\(320\) | 463.879 | − | 156.422i | 1.44962 | − | 0.488820i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.950813 | − | 239.354i | 0.00295284 | − | 0.743335i | ||||
\(323\) | 521.477i | 1.61448i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 361.242 | 1.11151 | ||||||||
\(326\) | 110.253 | + | 0.437972i | 0.338201 | + | 0.00134347i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −348.091 | + | 404.939i | −1.06125 | + | 1.23457i | ||||
\(329\) | −182.898 | + | 66.5693i | −0.555920 | + | 0.202338i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −569.180 | + | 100.362i | −1.71958 | + | 0.303208i | −0.944464 | − | 0.328614i | \(-0.893419\pi\) |
−0.775114 | + | 0.631822i | \(0.782308\pi\) | |||||||
\(332\) | −35.4798 | − | 42.9719i | −0.106867 | − | 0.129433i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 319.780 | − | 114.954i | 0.957426 | − | 0.344174i | ||||
\(335\) | −126.551 | + | 347.695i | −0.377763 | + | 1.03790i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 340.126 | + | 285.400i | 1.00928 | + | 0.846883i | 0.988242 | − | 0.152896i | \(-0.0488599\pi\) |
0.0210336 | + | 0.999779i | \(0.493304\pi\) | |||||||
\(338\) | −104.027 | + | 17.9170i | −0.307773 | + | 0.0530090i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −116.424 | + | 630.919i | −0.342423 | + | 1.85564i | ||||
\(341\) | 31.0288 | − | 53.7435i | 0.0909936 | − | 0.157606i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −323.375 | + | 186.700i | −0.942783 | + | 0.544316i | ||||
\(344\) | −620.484 | − | 234.249i | −1.80373 | − | 0.680956i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −64.6516 | + | 175.457i | −0.186854 | + | 0.507101i | ||||
\(347\) | −539.222 | − | 95.0793i | −1.55395 | − | 0.274004i | −0.670280 | − | 0.742108i | \(-0.733826\pi\) |
−0.883673 | + | 0.468105i | \(0.844937\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 308.273 | − | 258.672i | 0.883305 | − | 0.741181i | −0.0835512 | − | 0.996503i | \(-0.526626\pi\) |
0.966856 | + | 0.255323i | \(0.0821818\pi\) | |||||||
\(350\) | −293.685 | − | 248.426i | −0.839101 | − | 0.709789i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −175.906 | − | 68.0106i | −0.499733 | − | 0.193212i | ||||
\(353\) | 87.4208 | − | 73.3547i | 0.247651 | − | 0.207804i | −0.510509 | − | 0.859872i | \(-0.670543\pi\) |
0.758160 | + | 0.652069i | \(0.226099\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −210.644 | − | 37.1421i | −0.593362 | − | 0.104626i | ||||
\(356\) | −320.677 | − | 565.761i | −0.900777 | − | 1.58922i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 152.014 | − | 260.897i | 0.424620 | − | 0.728763i | ||||
\(359\) | −441.999 | + | 255.188i | −1.23120 | + | 0.710831i | −0.967279 | − | 0.253715i | \(-0.918348\pi\) |
−0.263916 | + | 0.964546i | \(0.585014\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 128.736 | − | 222.978i | 0.356610 | − | 0.617667i | ||||
\(362\) | 34.1120 | − | 19.5143i | 0.0942322 | − | 0.0539070i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −213.362 | − | 125.455i | −0.586159 | − | 0.344657i | ||||
\(365\) | −509.856 | − | 427.820i | −1.39687 | − | 1.17211i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.6859 | + | 51.3391i | −0.0509152 | + | 0.139888i | −0.962544 | − | 0.271127i | \(-0.912604\pi\) |
0.911628 | + | 0.411016i | \(0.134826\pi\) | |||||||
\(368\) | 327.580 | + | 63.1436i | 0.890162 | + | 0.171586i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −55.3640 | − | 9.98910i | −0.149632 | − | 0.0269976i | ||||
\(371\) | 248.585 | − | 43.8322i | 0.670039 | − | 0.118146i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 620.992 | − | 226.023i | 1.66486 | − | 0.605959i | 0.673744 | − | 0.738965i | \(-0.264685\pi\) |
0.991115 | + | 0.133006i | \(0.0424629\pi\) | |||||||
\(374\) | 189.969 | − | 158.121i | 0.507938 | − | 0.422784i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −43.9201 | − | 267.700i | −0.116809 | − | 0.711969i | ||||
\(377\) | 424.677 | 1.12646 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 294.012i | 0.775757i | 0.921711 | + | 0.387878i | \(0.126792\pi\) | ||||
−0.921711 | + | 0.387878i | \(0.873208\pi\) | |||||||
\(380\) | 493.715 | − | 578.983i | 1.29925 | − | 1.52364i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −386.270 | + | 321.513i | −1.01118 | + | 0.841657i | ||||
\(383\) | 178.617 | + | 490.746i | 0.466362 | + | 1.28132i | 0.920624 | + | 0.390451i | \(0.127681\pi\) |
−0.454261 | + | 0.890869i | \(0.650097\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 44.9322 | + | 254.823i | 0.116707 | + | 0.661878i | ||||
\(386\) | −28.9026 | − | 5.21477i | −0.0748772 | − | 0.0135098i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −158.141 | − | 58.9856i | −0.407580 | − | 0.152025i | ||||
\(389\) | −101.361 | − | 36.8924i | −0.260568 | − | 0.0948391i | 0.208433 | − | 0.978037i | \(-0.433164\pi\) |
−0.469001 | + | 0.883198i | \(0.655386\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −281.035 | + | 334.925i | −0.718760 | + | 0.856585i | ||||
\(392\) | −42.4874 | − | 121.208i | −0.108386 | − | 0.309205i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −363.559 | + | 207.980i | −0.922738 | + | 0.527867i | ||||
\(395\) | −120.504 | − | 69.5731i | −0.305074 | − | 0.176134i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −197.478 | − | 342.043i | −0.497427 | − | 0.861568i | 0.502569 | − | 0.864537i | \(-0.332388\pi\) |
−0.999996 | + | 0.00296877i | \(0.999055\pi\) | |||||||
\(398\) | −5.30573 | + | 9.10606i | −0.0133310 | + | 0.0228796i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 416.129 | − | 338.054i | 1.04032 | − | 0.845134i | ||||
\(401\) | −5.45754 | + | 30.9512i | −0.0136098 | + | 0.0771851i | −0.990856 | − | 0.134922i | \(-0.956922\pi\) |
0.977246 | + | 0.212107i | \(0.0680326\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 72.9663 | + | 86.9578i | 0.181058 | + | 0.215776i | ||||
\(404\) | 72.5792 | + | 431.643i | 0.179652 | + | 1.06842i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −345.258 | − | 292.051i | −0.850388 | − | 0.719336i | ||||
\(407\) | 13.9314 | + | 16.6027i | 0.0342294 | + | 0.0407930i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 36.6237 | − | 207.703i | 0.0895445 | − | 0.507832i | −0.906739 | − | 0.421693i | \(-0.861436\pi\) |
0.996283 | − | 0.0861391i | \(-0.0274529\pi\) | |||||||
\(410\) | −353.056 | + | 958.153i | −0.861112 | + | 2.33696i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.31469 | − | 3.70335i | −0.00319099 | − | 0.00898872i | ||||
\(413\) | −78.6867 | − | 136.289i | −0.190525 | − | 0.329999i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −92.2867 | − | 53.2817i | −0.222378 | − | 0.128390i | ||||
\(416\) | 226.952 | − | 259.812i | 0.545559 | − | 0.624549i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −288.885 | + | 49.7557i | −0.691111 | + | 0.119033i | ||||
\(419\) | 26.3541 | − | 31.4075i | 0.0628975 | − | 0.0749583i | −0.733678 | − | 0.679497i | \(-0.762198\pi\) |
0.796576 | + | 0.604539i | \(0.206643\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 180.665 | + | 65.7568i | 0.429134 | + | 0.156192i | 0.547551 | − | 0.836772i | \(-0.315560\pi\) |
−0.118418 | + | 0.992964i | \(0.537782\pi\) | |||||||
\(422\) | −169.403 | + | 60.8966i | −0.401428 | + | 0.144305i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.19257 | + | 351.792i | −0.00988814 | + | 0.829699i | ||||
\(425\) | 122.012 | + | 691.962i | 0.287086 | + | 1.62815i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.7255 | − | 45.9529i | −0.0391697 | − | 0.107618i | ||||
\(428\) | −4.10515 | + | 516.699i | −0.00959146 | + | 1.20724i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1268.27 | − | 5.03808i | −2.94946 | − | 0.0117165i | ||||
\(431\) | − | 427.089i | − | 0.990927i | −0.868629 | − | 0.495463i | \(-0.834998\pi\) | ||
0.868629 | − | 0.495463i | \(-0.165002\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −265.388 | −0.612906 | −0.306453 | − | 0.951886i | \(-0.599142\pi\) | ||||
−0.306453 | + | 0.951886i | \(0.599142\pi\) | |||||||
\(434\) | 0.480164 | − | 120.875i | 0.00110637 | − | 0.278513i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 641.897 | + | 5.09984i | 1.47224 | + | 0.0116969i | ||||
\(437\) | 487.265 | − | 177.350i | 1.11502 | − | 0.405835i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 553.109 | − | 97.5280i | 1.25993 | − | 0.222159i | 0.496492 | − | 0.868041i | \(-0.334621\pi\) |
0.763437 | + | 0.645882i | \(0.223510\pi\) | |||||||
\(440\) | −360.621 | − | 4.29779i | −0.819593 | − | 0.00976770i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 152.943 | + | 425.457i | 0.346024 | + | 0.962573i | ||||
\(443\) | −111.741 | + | 307.006i | −0.252237 | + | 0.693016i | 0.747354 | + | 0.664426i | \(0.231324\pi\) |
−0.999591 | + | 0.0285901i | \(0.990898\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −952.648 | − | 799.367i | −2.14078 | − | 1.79633i | ||||
\(446\) | 80.5245 | + | 467.530i | 0.180548 | + | 1.04827i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −363.183 | + | 55.1492i | −0.810676 | + | 0.123101i | ||||
\(449\) | −97.3394 | + | 168.597i | −0.216791 | + | 0.375494i | −0.953825 | − | 0.300362i | \(-0.902892\pi\) |
0.737034 | + | 0.675856i | \(0.236226\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 340.686 | − | 196.695i | 0.755400 | − | 0.436131i | ||||
\(452\) | 246.055 | − | 87.3491i | 0.544369 | − | 0.193250i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −506.363 | − | 186.582i | −1.11534 | − | 0.410974i | ||||
\(455\) | −466.120 | − | 82.1896i | −1.02444 | − | 0.180636i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 237.405 | − | 199.206i | 0.519486 | − | 0.435900i | −0.344967 | − | 0.938615i | \(-0.612110\pi\) |
0.864452 | + | 0.502715i | \(0.167665\pi\) | |||||||
\(458\) | 223.967 | − | 264.770i | 0.489010 | − | 0.578101i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 629.121 | − | 105.785i | 1.36765 | − | 0.229966i | ||||
\(461\) | −308.002 | + | 258.445i | −0.668118 | + | 0.560617i | −0.912508 | − | 0.409060i | \(-0.865857\pi\) |
0.244390 | + | 0.969677i | \(0.421412\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −66.1231 | − | 11.6593i | −0.142814 | − | 0.0251820i | 0.101784 | − | 0.994807i | \(-0.467545\pi\) |
−0.244598 | + | 0.969624i | \(0.578656\pi\) | |||||||
\(464\) | 489.203 | − | 397.417i | 1.05432 | − | 0.856502i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −295.072 | − | 171.927i | −0.633203 | − | 0.368941i | ||||
\(467\) | −309.740 | + | 178.828i | −0.663254 | + | 0.382930i | −0.793516 | − | 0.608550i | \(-0.791752\pi\) |
0.130261 | + | 0.991480i | \(0.458418\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 138.825 | − | 240.452i | 0.296002 | − | 0.512691i | ||||
\(470\) | −257.593 | − | 450.286i | −0.548071 | − | 0.958056i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 206.995 | − | 72.5585i | 0.438550 | − | 0.153726i | ||||
\(473\) | 374.291 | + | 314.068i | 0.791313 | + | 0.663991i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 285.015 | − | 783.074i | 0.600033 | − | 1.64858i | ||||
\(476\) | 168.246 | − | 451.071i | 0.353459 | − | 0.947627i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 45.4817 | − | 252.080i | 0.0951501 | − | 0.527364i | ||||
\(479\) | 7.06355 | − | 1.24549i | 0.0147464 | − | 0.00260020i | −0.166270 | − | 0.986080i | \(-0.553172\pi\) |
0.181017 | + | 0.983480i | \(0.442061\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.2539 | + | 13.5593i | −0.0774508 | + | 0.0281898i | ||||
\(482\) | 211.395 | + | 253.972i | 0.438578 | + | 0.526914i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −262.562 | − | 223.894i | −0.542483 | − | 0.462591i | ||||
\(485\) | −322.760 | −0.665485 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 432.322i | 0.887725i | 0.896095 | + | 0.443862i | \(0.146392\pi\) | ||||
−0.896095 | + | 0.443862i | \(0.853608\pi\) | |||||||
\(488\) | 67.2595 | − | 11.0349i | 0.137827 | − | 0.0226125i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −157.127 | − | 188.775i | −0.320667 | − | 0.385254i | ||||
\(491\) | 61.1331 | + | 167.962i | 0.124507 | + | 0.342081i | 0.986249 | − | 0.165266i | \(-0.0528484\pi\) |
−0.861742 | + | 0.507347i | \(0.830626\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 143.437 | + | 813.474i | 0.290948 | + | 1.65005i | ||||
\(494\) | 95.2081 | − | 527.686i | 0.192729 | − | 1.06819i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 165.429 | + | 31.8877i | 0.333526 | + | 0.0642898i | ||||
\(497\) | 150.823 | + | 54.8951i | 0.303467 | + | 0.110453i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −413.773 | + | 493.116i | −0.829205 | + | 0.988208i | 0.170791 | + | 0.985307i | \(0.445368\pi\) |
−0.999996 | + | 0.00290072i | \(0.999077\pi\) | |||||||
\(500\) | 131.953 | − | 224.413i | 0.263907 | − | 0.448827i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 131.169 | + | 229.290i | 0.261293 | + | 0.456754i | ||||
\(503\) | 306.467 | + | 176.939i | 0.609279 | + | 0.351767i | 0.772683 | − | 0.634792i | \(-0.218914\pi\) |
−0.163404 | + | 0.986559i | \(0.552248\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 418.503 | + | 724.869i | 0.828719 | + | 1.43538i | ||||
\(506\) | −212.354 | − | 123.730i | −0.419672 | − | 0.244526i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 172.750 | − | 97.9159i | 0.340060 | − | 0.192748i | ||||
\(509\) | 94.0125 | − | 533.171i | 0.184700 | − | 1.04749i | −0.741639 | − | 0.670799i | \(-0.765951\pi\) |
0.926340 | − | 0.376689i | \(-0.122937\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 321.031 | + | 382.589i | 0.628240 | + | 0.748707i | ||||
\(512\) | 18.3009 | − | 511.673i | 0.0357439 | − | 0.999361i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.9750 | + | 15.3389i | −0.0252432 | + | 0.0298422i | ||||
\(515\) | −4.83044 | − | 5.75669i | −0.00937949 | − | 0.0111780i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.7039 | + | 196.816i | −0.0671256 | + | 0.380688i | ||||
\(518\) | 39.6117 | + | 14.5959i | 0.0764705 | + | 0.0281775i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 232.999 | − | 617.175i | 0.448076 | − | 1.18687i | ||||
\(521\) | −3.55297 | − | 6.15392i | −0.00681952 | − | 0.0118118i | 0.862596 | − | 0.505894i | \(-0.168837\pi\) |
−0.869415 | + | 0.494082i | \(0.835504\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.6849 | − | 15.4065i | −0.0510227 | − | 0.0294580i | 0.474272 | − | 0.880379i | \(-0.342711\pi\) |
−0.525294 | + | 0.850921i | \(0.676045\pi\) | |||||||
\(524\) | −682.447 | − | 125.932i | −1.30238 | − | 0.240329i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 33.4770 | + | 194.370i | 0.0636445 | + | 0.369524i | ||||
\(527\) | −141.924 | + | 169.138i | −0.269305 | + | 0.320945i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −88.5681 | − | 32.2361i | −0.167425 | − | 0.0609379i | ||||
\(530\) | 227.588 | + | 633.107i | 0.429411 | + | 1.19454i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −440.293 | + | 363.528i | −0.827618 | + | 0.683323i | ||||
\(533\) | 124.955 | + | 708.653i | 0.234437 | + | 1.32956i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 337.950 | + | 928.510i | 0.631682 | + | 1.73553i | ||||
\(536\) | 293.461 | + | 252.263i | 0.547503 | + | 0.470641i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.310366 | + | 78.1304i | −0.000576889 | + | 0.145224i | ||||
\(539\) | 94.6215i | 0.175550i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 74.8336 | 0.138325 | 0.0691623 | − | 0.997605i | \(-0.477967\pi\) | ||||
0.0691623 | + | 0.997605i | \(0.477967\pi\) | |||||||
\(542\) | −572.320 | − | 2.27349i | −1.05594 | − | 0.00419464i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 574.328 | + | 346.977i | 1.05575 | + | 0.637825i | ||||
\(545\) | 1153.49 | − | 419.837i | 2.11650 | − | 0.770343i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 290.555 | − | 51.2327i | 0.531179 | − | 0.0936612i | 0.0983754 | − | 0.995149i | \(-0.468635\pi\) |
0.432804 | + | 0.901488i | \(0.357524\pi\) | |||||||
\(548\) | 154.654 | − | 127.690i | 0.282216 | − | 0.233011i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −371.688 | + | 133.614i | −0.675796 | + | 0.242934i | ||||
\(551\) | 335.065 | − | 920.584i | 0.608104 | − | 1.67075i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 79.9854 | + | 67.1157i | 0.144639 | + | 0.121367i | ||||
\(554\) | 127.440 | − | 21.9495i | 0.230036 | − | 0.0396200i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 734.453 | + | 135.529i | 1.32096 | + | 0.243757i | ||||
\(557\) | 73.4754 | − | 127.263i | 0.131913 | − | 0.228480i | −0.792501 | − | 0.609870i | \(-0.791221\pi\) |
0.924414 | + | 0.381391i | \(0.124555\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −774.009 | + | 446.874i | −1.38463 | + | 0.799417i | ||||
\(560\) | −613.857 | + | 341.523i | −1.09617 | + | 0.609862i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 272.826 | − | 740.419i | 0.485456 | − | 1.31747i | ||||
\(563\) | 286.120 | + | 50.4507i | 0.508207 | + | 0.0896105i | 0.421871 | − | 0.906656i | \(-0.361373\pi\) |
0.0863350 | + | 0.996266i | \(0.472484\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 382.481 | − | 320.939i | 0.676957 | − | 0.568034i | ||||
\(566\) | −74.5075 | − | 63.0253i | −0.131639 | − | 0.111352i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −114.154 | + | 192.388i | −0.200975 | + | 0.338711i | ||||
\(569\) | 37.1059 | − | 31.1355i | 0.0652125 | − | 0.0547198i | −0.609599 | − | 0.792710i | \(-0.708669\pi\) |
0.674811 | + | 0.737990i | \(0.264225\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 860.734 | + | 151.771i | 1.50741 | + | 0.265798i | 0.865473 | − | 0.500956i | \(-0.167018\pi\) |
0.641941 | + | 0.766754i | \(0.278129\pi\) | |||||||
\(572\) | −221.099 | + | 125.320i | −0.386538 | + | 0.219092i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 385.754 | − | 662.059i | 0.672046 | − | 1.15341i | ||||
\(575\) | 605.070 | − | 349.337i | 1.05230 | − | 0.607543i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −92.1639 | + | 159.633i | −0.159730 | + | 0.276660i | −0.934771 | − | 0.355251i | \(-0.884396\pi\) |
0.775042 | + | 0.631910i | \(0.217729\pi\) | |||||||
\(578\) | −261.604 | + | 149.655i | −0.452602 | + | 0.258918i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 610.913 | − | 1038.98i | 1.05330 | − | 1.79135i | ||||
\(581\) | 61.2559 | + | 51.3998i | 0.105432 | + | 0.0884678i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 88.6464 | − | 243.554i | 0.152052 | − | 0.417760i | ||||
\(584\) | −606.948 | + | 340.843i | −1.03929 | + | 0.583635i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1085.16 | + | 195.791i | 1.85181 | + | 0.334114i | ||||
\(587\) | −624.158 | + | 110.056i | −1.06330 | + | 0.187489i | −0.677821 | − | 0.735227i | \(-0.737076\pi\) |
−0.385481 | + | 0.922716i | \(0.625965\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 246.070 | − | 89.5623i | 0.417777 | − | 0.152058i | ||||
\(590\) | 322.383 | − | 268.336i | 0.546411 | − | 0.454807i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −30.2253 | + | 50.4820i | −0.0510563 | + | 0.0852737i | ||||
\(593\) | −445.495 | −0.751256 | −0.375628 | − | 0.926771i | \(-0.622573\pi\) | ||||
−0.375628 | + | 0.926771i | \(0.622573\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 920.619i | − | 1.54726i | ||||||
\(596\) | 118.325 | + | 100.899i | 0.198532 | + | 0.169294i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 345.530 | − | 287.603i | 0.577809 | − | 0.480941i | ||||
\(599\) | −304.954 | − | 837.855i | −0.509105 | − | 1.39876i | −0.882162 | − | 0.470947i | \(-0.843912\pi\) |
0.373056 | − | 0.927809i | \(-0.378310\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 174.212 | + | 988.005i | 0.289870 | + | 1.64393i | 0.687352 | + | 0.726325i | \(0.258773\pi\) |
−0.397482 | + | 0.917610i | \(0.630116\pi\) | |||||||
\(602\) | 936.576 | + | 168.982i | 1.55577 | + | 0.280702i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −396.894 | + | 1064.08i | −0.657110 | + | 1.76172i | ||||
\(605\) | −620.057 | − | 225.682i | −1.02489 | − | 0.373029i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 522.302 | − | 622.455i | 0.860464 | − | 1.02546i | −0.138918 | − | 0.990304i | \(-0.544362\pi\) |
0.999382 | − | 0.0351573i | \(-0.0111932\pi\) | |||||||
\(608\) | −384.139 | − | 696.960i | −0.631808 | − | 1.14632i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 113.134 | − | 64.7201i | 0.185466 | − | 0.106099i | ||||
\(611\) | −316.591 | − | 182.784i | −0.518152 | − | 0.299155i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −176.799 | − | 306.225i | −0.288416 | − | 0.499551i | 0.685016 | − | 0.728528i | \(-0.259795\pi\) |
−0.973432 | + | 0.228977i | \(0.926462\pi\) | |||||||
\(614\) | 298.615 | − | 512.504i | 0.486344 | − | 0.834697i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 265.934 | + | 50.1661i | 0.431712 | + | 0.0814385i | ||||
\(617\) | −14.8981 | + | 84.4914i | −0.0241460 | + | 0.136939i | −0.994498 | − | 0.104758i | \(-0.966593\pi\) |
0.970352 | + | 0.241697i | \(0.0777042\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 409.962 | + | 488.574i | 0.662298 | + | 0.789296i | 0.987714 | − | 0.156275i | \(-0.0499487\pi\) |
−0.325416 | + | 0.945571i | \(0.605504\pi\) | |||||||
\(620\) | 317.709 | − | 53.4216i | 0.512433 | − | 0.0861638i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −230.376 | − | 194.874i | −0.370380 | − | 0.313302i | ||||
\(623\) | 599.835 | + | 714.855i | 0.962817 | + | 1.14744i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −59.0210 | + | 334.725i | −0.0944335 | + | 0.535559i | ||||
\(626\) | −213.781 | + | 580.177i | −0.341503 | + | 0.926801i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −551.160 | + | 195.661i | −0.877644 | + | 0.311562i | ||||
\(629\) | −38.5557 | − | 66.7804i | −0.0612968 | − | 0.106169i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1010.86 | − | 583.618i | −1.60199 | − | 0.924909i | −0.991089 | − | 0.133203i | \(-0.957474\pi\) |
−0.610901 | − | 0.791707i | \(-0.709193\pi\) | |||||||
\(632\) | −112.589 | + | 92.2094i | −0.178147 | + | 0.145901i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −299.128 | + | 51.5201i | −0.471811 | + | 0.0812619i | ||||
\(635\) | 244.080 | − | 290.883i | 0.384378 | − | 0.458084i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −162.643 | − | 59.1971i | −0.255326 | − | 0.0929312i | ||||
\(638\) | −436.958 | + | 157.077i | −0.684886 | + | 0.246202i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −309.157 | − | 928.993i | −0.483058 | − | 1.45155i | ||||
\(641\) | −80.0762 | − | 454.134i | −0.124924 | − | 0.708478i | −0.981353 | − | 0.192214i | \(-0.938433\pi\) |
0.856429 | − | 0.516264i | \(-0.172678\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.9088 | + | 76.6788i | 0.0434040 | + | 0.119252i | 0.959501 | − | 0.281705i | \(-0.0909000\pi\) |
−0.916097 | + | 0.400957i | \(0.868678\pi\) | |||||||
\(644\) | −478.697 | − | 3.80322i | −0.743318 | − | 0.00590562i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1042.95 | + | 4.14301i | 1.61447 | + | 0.00641333i | ||||
\(647\) | 360.614i | 0.557363i | 0.960384 | + | 0.278682i | \(0.0898974\pi\) | ||||
−0.960384 | + | 0.278682i | \(0.910103\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −161.591 | −0.248985 | ||||||||
\(650\) | 2.86998 | − | 722.478i | 0.00441535 | − | 1.11150i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.75187 | − | 220.502i | 0.00268692 | − | 0.338193i | ||||
\(653\) | −114.976 | + | 41.8479i | −0.176074 | + | 0.0640857i | −0.428553 | − | 0.903517i | \(-0.640976\pi\) |
0.252479 | + | 0.967602i | \(0.418754\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1306.90 | + | 230.441i | −1.99526 | + | 0.351819i | ||||
\(656\) | 807.106 | + | 699.393i | 1.23034 | + | 1.06615i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 131.684 | + | 366.321i | 0.200128 | + | 0.556719i | ||||
\(659\) | 19.5137 | − | 53.6136i | 0.0296111 | − | 0.0813560i | −0.924006 | − | 0.382378i | \(-0.875105\pi\) |
0.953617 | + | 0.301022i | \(0.0973276\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −716.089 | − | 600.870i | −1.08334 | − | 0.909031i | −0.0871475 | − | 0.996195i | \(-0.527775\pi\) |
−0.996194 | + | 0.0871639i | \(0.972220\pi\) | |||||||
\(662\) | 196.200 | + | 1139.15i | 0.296375 | + | 1.72077i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −86.2250 | + | 70.6176i | −0.129857 | + | 0.106352i | ||||
\(665\) | −545.928 | + | 945.575i | −0.820945 | + | 1.42192i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 711.323 | − | 410.682i | 1.06645 | − | 0.615716i | ||||
\(668\) | −227.366 | − | 640.469i | −0.340368 | − | 0.958785i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 694.379 | + | 255.862i | 1.03639 | + | 0.381883i | ||||
\(671\) | −49.4498 | − | 8.71934i | −0.0736957 | − | 0.0129945i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.9893 | − | 41.1069i | 0.0727924 | − | 0.0610801i | −0.605666 | − | 0.795719i | \(-0.707093\pi\) |
0.678458 | + | 0.734639i | \(0.262649\pi\) | |||||||
\(674\) | 573.497 | − | 677.979i | 0.850886 | − | 1.00590i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 35.0073 | + | 208.195i | 0.0517860 | + | 0.307981i | ||||
\(677\) | 453.503 | − | 380.534i | 0.669872 | − | 0.562089i | −0.243156 | − | 0.969987i | \(-0.578183\pi\) |
0.913028 | + | 0.407898i | \(0.133738\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 238.516 | + | 42.0567i | 0.351275 | + | 0.0619392i | ||||
\(680\) | 1260.90 | + | 237.858i | 1.85427 | + | 0.349791i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −107.240 | − | 62.4841i | −0.157243 | − | 0.0916189i | ||||
\(683\) | 187.818 | − | 108.437i | 0.274990 | − | 0.158766i | −0.356163 | − | 0.934424i | \(-0.615915\pi\) |
0.631153 | + | 0.775658i | \(0.282582\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 191.759 | − | 332.136i | 0.279940 | − | 0.484870i | ||||
\(686\) | 370.829 | + | 648.228i | 0.540567 | + | 0.944938i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −473.423 | + | 1239.10i | −0.688115 | + | 1.80101i | ||||
\(689\) | 363.181 | + | 304.745i | 0.527112 | + | 0.442300i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 444.760 | − | 1221.97i | 0.643647 | − | 1.76841i | 0.00369336 | − | 0.999993i | \(-0.498824\pi\) |
0.639954 | − | 0.768413i | \(-0.278953\pi\) | |||||||
\(692\) | 350.398 | + | 130.696i | 0.506355 | + | 0.188867i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −194.441 | + | 1077.68i | −0.280175 | + | 1.55285i | ||||
\(695\) | 1406.49 | − | 248.002i | 2.02373 | − | 0.356838i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1315.23 | + | 478.704i | −1.88699 | + | 0.686807i | ||||
\(698\) | −514.891 | − | 618.597i | −0.737666 | − | 0.886242i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −499.181 | + | 585.392i | −0.713116 | + | 0.836275i | ||||
\(701\) | −937.091 | −1.33679 | −0.668396 | − | 0.743806i | \(-0.733019\pi\) | ||||
−0.668396 | + | 0.743806i | \(0.733019\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 91.4543i | 0.130092i | ||||||||
\(704\) | −137.418 | + | 351.269i | −0.195195 | + | 0.498962i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −146.014 | − | 175.423i | −0.206818 | − | 0.248474i | ||||
\(707\) | −214.816 | − | 590.201i | −0.303841 | − | 0.834797i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −223.970 | − | 1270.20i | −0.315896 | − | 1.79153i | −0.567152 | − | 0.823613i | \(-0.691955\pi\) |
0.251256 | − | 0.967921i | \(-0.419156\pi\) | |||||||
\(710\) | −75.9572 | + | 420.989i | −0.106982 | + | 0.592942i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1134.06 | + | 636.853i | −1.59278 | + | 0.894457i | ||||
\(713\) | 206.309 | + | 75.0903i | 0.289353 | + | 0.105316i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −312.393 | + | 372.295i | −0.436913 | + | 0.520692i | ||||
\(716\) | −520.582 | − | 306.098i | −0.727070 | − | 0.427512i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 506.861 | + | 886.019i | 0.705935 | + | 1.23401i | ||||
\(719\) | −843.005 | − | 486.709i | −1.17247 | − | 0.676925i | −0.218209 | − | 0.975902i | \(-0.570021\pi\) |
−0.954260 | + | 0.298977i | \(0.903355\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.81952 | + | 4.88354i | 0.00391056 | + | 0.00677329i | ||||
\(722\) | −444.930 | − | 259.242i | −0.616246 | − | 0.359061i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −38.7574 | − | 68.3786i | −0.0535323 | − | 0.0944456i | ||||
\(725\) | 229.216 | − | 1299.95i | 0.316159 | − | 1.79303i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 632.891 | + | 754.250i | 0.870551 | + | 1.03748i | 0.998952 | + | 0.0457605i | \(0.0145711\pi\) |
−0.128401 | + | 0.991722i | \(0.540984\pi\) | |||||||
\(728\) | −252.603 | + | 425.724i | −0.346983 | + | 0.584785i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −859.684 | + | 1016.30i | −1.17765 | + | 1.39220i | ||||
\(731\) | −1117.42 | − | 1331.69i | −1.52862 | − | 1.82173i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 102.753 | − | 582.739i | 0.140181 | − | 0.795006i | −0.830930 | − | 0.556377i | \(-0.812191\pi\) |
0.971111 | − | 0.238629i | \(-0.0766979\pi\) | |||||||
\(734\) | 102.529 | + | 37.7794i | 0.139685 | + | 0.0514705i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 128.889 | − | 654.652i | 0.175120 | − | 0.889473i | ||||
\(737\) | −142.546 | − | 246.897i | −0.193414 | − | 0.335002i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −722.804 | − | 417.311i | −0.978084 | − | 0.564697i | −0.0763932 | − | 0.997078i | \(-0.524340\pi\) |
−0.901691 | + | 0.432380i | \(0.857674\pi\) | |||||||
\(740\) | −20.4179 | + | 110.648i | −0.0275917 | + | 0.149524i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −85.6887 | − | 497.513i | −0.115483 | − | 0.670503i | ||||
\(743\) | −374.265 | + | 446.031i | −0.503721 | + | 0.600311i | −0.956652 | − | 0.291234i | \(-0.905934\pi\) |
0.452931 | + | 0.891546i | \(0.350378\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 279.433 | + | 101.705i | 0.375077 | + | 0.136517i | ||||
\(746\) | −447.108 | − | 1243.77i | −0.599341 | − | 1.66725i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −314.730 | − | 381.191i | −0.420763 | − | 0.509613i | ||||
\(749\) | −128.753 | − | 730.193i | −0.171900 | − | 0.974891i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −383.766 | − | 1054.39i | −0.511006 | − | 1.40398i | −0.880190 | − | 0.474622i | \(-0.842585\pi\) |
0.369183 | − | 0.929357i | \(-0.379638\pi\) | |||||||
\(752\) | −535.745 | + | 85.7127i | −0.712427 | + | 0.113980i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.37396 | − | 849.347i | 0.00447475 | − | 1.12646i | ||||
\(755\) | 2171.74i | 2.87648i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 84.4056 | 0.111500 | 0.0557501 | − | 0.998445i | \(-0.482245\pi\) | ||||
0.0557501 | + | 0.998445i | \(0.482245\pi\) | |||||||
\(758\) | 588.019 | + | 2.33585i | 0.775750 | + | 0.00308160i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1154.03 | − | 992.023i | −1.51847 | − | 1.30529i | ||||
\(761\) | −1003.11 | + | 365.103i | −1.31815 | + | 0.479768i | −0.902865 | − | 0.429924i | \(-0.858540\pi\) |
−0.415285 | + | 0.909691i | \(0.636318\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −907.123 | + | 159.950i | −1.18889 | + | 0.209633i | ||||
\(764\) | 639.952 | + | 775.089i | 0.837634 | + | 1.01451i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 982.902 | − | 353.332i | 1.28316 | − | 0.461269i | ||||
\(767\) | 101.095 | − | 277.756i | 0.131806 | − | 0.362133i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 121.602 | + | 102.037i | 0.158131 | + | 0.132687i | 0.718420 | − | 0.695610i | \(-0.244866\pi\) |
−0.560289 | + | 0.828297i | \(0.689310\pi\) | |||||||
\(770\) | 509.999 | − | 87.8391i | 0.662336 | − | 0.114077i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.6591 | + | 57.7633i | −0.0138071 | + | 0.0748229i | ||||
\(773\) | 371.280 | − | 643.076i | 0.480310 | − | 0.831922i | −0.519434 | − | 0.854510i | \(-0.673857\pi\) |
0.999745 | + | 0.0225883i | \(0.00719069\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 305.563 | − | 176.417i | 0.394274 | − | 0.227634i | ||||
\(776\) | −119.227 | + | 315.811i | −0.153643 | + | 0.406973i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −74.5895 | + | 202.427i | −0.0958734 | + | 0.260190i | ||||
\(779\) | 1634.76 | + | 288.252i | 2.09853 | + | 0.370028i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 126.247 | − | 105.934i | 0.161649 | − | 0.135639i | ||||
\(782\) | 667.612 | + | 564.727i | 0.853723 | + | 0.722157i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −242.752 | + | 84.0112i | −0.309633 | + | 0.107157i | ||||
\(785\) | −856.753 | + | 718.901i | −1.09141 | + | 0.915798i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −754.529 | − | 133.044i | −0.958741 | − | 0.169052i | −0.327683 | − | 0.944788i | \(-0.606268\pi\) |
−0.631058 | + | 0.775736i | \(0.717379\pi\) | |||||||
\(788\) | 413.068 | + | 728.764i | 0.524197 | + | 0.924828i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −140.102 | + | 240.454i | −0.177345 | + | 0.304372i | ||||
\(791\) | −324.468 | + | 187.332i | −0.410200 | + | 0.236829i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45.9243 | − | 79.5432i | 0.0579121 | − | 0.100307i | ||||
\(794\) | −685.649 | + | 392.236i | −0.863538 | + | 0.494000i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.1698 | + | 10.6837i | 0.0228264 | + | 0.0134218i | ||||
\(797\) | 772.076 | + | 647.848i | 0.968727 | + | 0.812859i | 0.982351 | − | 0.187048i | \(-0.0598921\pi\) |
−0.0136233 | + | 0.999907i | \(0.504337\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 243.194 | − | 668.170i | 0.304373 | − | 0.836258i | ||||
\(800\) | −672.796 | − | 834.938i | −0.840995 | − | 1.04367i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 61.8586 | + | 11.1609i | 0.0771304 | + | 0.0139163i | ||||
\(803\) | 505.030 | − | 89.0504i | 0.628929 | − | 0.110897i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −860.221 | + | 313.095i | −1.06860 | + | 0.388937i | ||||
\(806\) | 174.494 | − | 145.240i | 0.216494 | − | 0.180199i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 863.856 | − | 141.728i | 1.06913 | − | 0.175406i | ||||
\(809\) | −909.106 | −1.12374 | −0.561870 | − | 0.827226i | \(-0.689918\pi\) | ||||
−0.561870 | + | 0.827226i | \(0.689918\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 241.760i | 0.298101i | 0.988830 | + | 0.149051i | \(0.0476217\pi\) | ||||
−0.988830 | + | 0.149051i | \(0.952378\pi\) | |||||||
\(812\) | −586.840 | + | 688.190i | −0.722709 | + | 0.847524i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 33.3159 | − | 27.7306i | 0.0409286 | − | 0.0340671i | ||||
\(815\) | −144.220 | − | 396.243i | −0.176958 | − | 0.486187i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 358.018 | + | 2030.42i | 0.438210 | + | 2.48521i | ||||
\(818\) | −415.112 | − | 74.8970i | −0.507472 | − | 0.0915611i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1913.49 | + | 713.719i | 2.33352 | + | 0.870388i | ||||
\(821\) | −381.889 | − | 138.996i | −0.465151 | − | 0.169301i | 0.0988038 | − | 0.995107i | \(-0.468498\pi\) |
−0.563954 | + | 0.825806i | \(0.690721\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.4525 | + | 36.2919i | −0.0370019 | + | 0.0440971i | −0.784228 | − | 0.620473i | \(-0.786941\pi\) |
0.747226 | + | 0.664570i | \(0.231385\pi\) | |||||||
\(824\) | −7.41709 | + | 2.59993i | −0.00900133 | + | 0.00315525i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −273.202 | + | 156.289i | −0.330753 | + | 0.189212i | ||||
\(827\) | 310.818 | + | 179.451i | 0.375839 | + | 0.216991i | 0.676006 | − | 0.736896i | \(-0.263709\pi\) |
−0.300168 | + | 0.953886i | \(0.597043\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 95.4686 | + | 165.356i | 0.115161 | + | 0.199465i | 0.917844 | − | 0.396941i | \(-0.129928\pi\) |
−0.802683 | + | 0.596406i | \(0.796595\pi\) | |||||||
\(830\) | −107.296 | + | 184.149i | −0.129272 | + | 0.221866i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −517.817 | − | 455.965i | −0.622377 | − | 0.548035i | ||||
\(833\) | 58.4592 | − | 331.538i | 0.0701791 | − | 0.398005i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −835.390 | − | 995.579i | −1.00047 | − | 1.19231i | ||||
\(836\) | 97.2155 | + | 578.160i | 0.116287 | + | 0.691579i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −62.6052 | − | 52.9572i | −0.0747079 | − | 0.0631948i | ||||
\(839\) | 826.157 | + | 984.575i | 0.984692 | + | 1.17351i | 0.984832 | + | 0.173511i | \(0.0555111\pi\) |
−0.000139714 | 1.00000i | \(0.500044\pi\) | ||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 123.429 | − | 699.998i | 0.146764 | − | 0.832340i | ||||
\(842\) | 132.948 | − | 360.805i | 0.157895 | − | 0.428510i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 120.446 | + | 339.287i | 0.142709 | + | 0.401998i | ||||
\(845\) | 201.858 | + | 349.628i | 0.238885 | + | 0.413761i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 428.807 | + | 247.572i | 0.506266 | + | 0.292293i | ||||
\(848\) | 703.546 | + | 11.1800i | 0.829653 | + | 0.0131839i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1384.88 | − | 238.524i | 1.62927 | − | 0.280616i | ||||
\(851\) | −49.2868 | + | 58.7377i | −0.0579163 | + | 0.0690219i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 508.554 | + | 185.098i | 0.596194 | + | 0.216997i | 0.622452 | − | 0.782658i | \(-0.286137\pi\) |
−0.0262574 | + | 0.999655i | \(0.508359\pi\) | |||||||
\(854\) | −92.0379 | + | 33.0856i | −0.107773 | + | 0.0387419i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1033.36 | + | 12.3153i | 1.20719 | + | 0.0143870i | ||||
\(857\) | −27.5580 | − | 156.289i | −0.0321563 | − | 0.182367i | 0.964499 | − | 0.264086i | \(-0.0850703\pi\) |
−0.996655 | + | 0.0817185i | \(0.973959\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 360.358 | + | 990.074i | 0.419508 | + | 1.15259i | 0.951985 | + | 0.306145i | \(0.0990392\pi\) |
−0.532477 | + | 0.846445i | \(0.678739\pi\) | |||||||
\(860\) | −20.1521 | + | 2536.47i | −0.0234327 | + | 2.94939i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −854.172 | − | 3.39313i | −0.990919 | − | 0.00393634i | ||||
\(863\) | − | 251.308i | − | 0.291203i | −0.989343 | − | 0.145601i | \(-0.953488\pi\) | ||
0.989343 | − | 0.145601i | \(-0.0465117\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 715.149 | 0.826762 | ||||||||
\(866\) | −2.10845 | + | 530.772i | −0.00243470 | + | 0.612901i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −241.744 | − | 1.92064i | −0.278506 | − | 0.00221272i | ||||
\(869\) | 100.746 | − | 36.6686i | 0.115934 | − | 0.0421964i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 513.565 | − | 90.5554i | 0.589627 | − | 0.103967i | ||||
\(872\) | 15.2993 | − | 1283.74i | 0.0175451 | − | 1.47218i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −350.826 | − | 975.930i | −0.401402 | − | 1.11663i | ||||
\(875\) | −127.766 | + | 351.035i | −0.146018 | + | 0.401182i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −153.816 | − | 129.067i | −0.175389 | − | 0.147168i | 0.550868 | − | 0.834593i | \(-0.314297\pi\) |
−0.726256 | + | 0.687424i | \(0.758741\pi\) | |||||||
\(878\) | −190.660 | − | 1106.98i | −0.217153 | − | 1.26080i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −11.4606 | + | 721.202i | −0.0130234 | + | 0.819548i | ||||
\(881\) | 402.080 | − | 696.424i | 0.456391 | − | 0.790492i | −0.542376 | − | 0.840136i | \(-0.682475\pi\) |
0.998767 | + | 0.0496435i | \(0.0158085\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1490.79 | + | 860.707i | −1.68832 | + | 0.974753i | −0.732518 | + | 0.680747i | \(0.761655\pi\) |
−0.955804 | + | 0.294006i | \(0.905011\pi\) | |||||||
\(884\) | 852.123 | − | 302.502i | 0.963940 | − | 0.342197i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 613.120 | + | 225.920i | 0.692009 | + | 0.254988i | ||||
\(887\) | −1284.01 | − | 226.405i | −1.44759 | − | 0.255248i | −0.606040 | − | 0.795434i | \(-0.707243\pi\) |
−0.841546 | + | 0.540186i | \(0.818354\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −218.275 | + | 183.154i | −0.245529 | + | 0.206023i | ||||
\(890\) | −1606.29 | + | 1898.93i | −1.80482 | + | 2.13363i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 935.692 | − | 157.333i | 1.04898 | − | 0.176383i | ||||
\(893\) | −646.012 | + | 542.069i | −0.723418 | + | 0.607020i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1137.29 | − | 200.535i | −1.27071 | − | 0.224061i | ||||
\(896\) | 107.412 | + | 726.798i | 0.119880 | + | 0.811158i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 336.417 | + | 196.017i | 0.374630 | + | 0.218281i | ||||
\(899\) | 359.221 | − | 207.396i | 0.399578 | − | 0.230696i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −461.075 | + | 798.606i | −0.511737 | + | 0.886355i | ||||
\(902\) | −390.680 | − | 682.928i | −0.433126 | − | 0.757127i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −172.742 | − | 492.800i | −0.191086 | − | 0.545132i | ||||
\(905\) | −115.138 | − | 96.6125i | −0.127225 | − | 0.106754i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −329.124 | + | 904.260i | −0.362871 | + | 0.996979i | 0.615139 | + | 0.788419i | \(0.289100\pi\) |
−0.978010 | + | 0.208560i | \(0.933122\pi\) | |||||||
\(908\) | −377.184 | + | 1011.23i | −0.415401 | + | 1.11369i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −168.081 | + | 931.580i | −0.184705 | + | 1.02371i | ||||
\(911\) | 145.176 | − | 25.5984i | 0.159359 | − | 0.0280992i | −0.0933996 | − | 0.995629i | \(-0.529773\pi\) |
0.252758 | + | 0.967529i | \(0.418662\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 77.1554 | − | 28.0823i | 0.0845076 | − | 0.0307582i | ||||
\(914\) | −396.524 | − | 476.389i | −0.433833 | − | 0.521213i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −527.757 | − | 450.034i | −0.576153 | − | 0.491303i | ||||
\(917\) | 995.808 | 1.08594 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1373.16i | − | 1.49419i | −0.664720 | − | 0.747093i | \(-0.731449\pi\) | ||
0.664720 | − | 0.747093i | \(-0.268551\pi\) | |||||||
\(920\) | −206.569 | − | 1259.07i | −0.224532 | − | 1.36856i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 514.438 | + | 618.053i | 0.557959 | + | 0.670339i | ||||
\(923\) | 103.105 | + | 283.279i | 0.111706 | + | 0.306911i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.3979 | + | 121.353i | 0.0231328 | + | 0.131193i | ||||
\(926\) | −23.8437 | + | 132.153i | −0.0257492 | + | 0.142713i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −790.941 | − | 981.556i | −0.852307 | − | 1.05771i | ||||
\(929\) | 1478.64 | + | 538.182i | 1.59165 | + | 0.579313i | 0.977695 | − | 0.210029i | \(-0.0673557\pi\) |
0.613954 | + | 0.789342i | \(0.289578\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −256.647 | + | 305.860i | −0.275668 | + | 0.328528i | ||||
\(932\) | −346.195 | + | 588.774i | −0.371454 | + | 0.631732i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 355.193 | + | 620.895i | 0.380292 | + | 0.664770i | ||||
\(935\) | −818.648 | − | 472.647i | −0.875559 | − | 0.505504i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −829.427 | − | 1436.61i | −0.885195 | − | 1.53320i | −0.845491 | − | 0.533990i | \(-0.820692\pi\) |
−0.0397040 | − | 0.999211i | \(-0.512641\pi\) | |||||||
\(938\) | −479.798 | − | 279.558i | −0.511511 | − | 0.298037i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −902.612 | + | 511.605i | −0.960225 | + | 0.544261i | ||||
\(941\) | 48.3337 | − | 274.114i | 0.0513642 | − | 0.291301i | −0.948295 | − | 0.317389i | \(-0.897194\pi\) |
0.999660 | + | 0.0260881i | \(0.00830503\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 894.597 | + | 1066.14i | 0.948671 | + | 1.13058i | ||||
\(944\) | −143.471 | − | 414.564i | −0.151982 | − | 0.439157i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 631.104 | − | 746.081i | 0.667129 | − | 0.788670i | ||||
\(947\) | −84.4477 | − | 100.641i | −0.0891739 | − | 0.106273i | 0.719612 | − | 0.694376i | \(-0.244320\pi\) |
−0.808786 | + | 0.588103i | \(0.799875\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −162.890 | + | 923.797i | −0.171644 | + | 0.973442i | ||||
\(950\) | −1563.87 | − | 576.248i | −1.64618 | − | 0.606577i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −900.797 | − | 340.074i | −0.946216 | − | 0.357221i | ||||
\(953\) | −107.243 | − | 185.750i | −0.112532 | − | 0.194911i | 0.804258 | − | 0.594280i | \(-0.202563\pi\) |
−0.916791 | + | 0.399368i | \(0.869229\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1664.58 | + | 961.048i | 1.74302 | + | 1.00633i | ||||
\(956\) | −503.795 | − | 92.9655i | −0.526982 | − | 0.0972442i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.43485 | − | 14.1369i | −0.00254160 | − | 0.0147567i | ||||
\(959\) | −184.986 | + | 220.458i | −0.192895 | + | 0.229883i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −798.858 | − | 290.761i | −0.831278 | − | 0.302560i | ||||
\(962\) | 26.8224 | + | 74.6148i | 0.0278819 | + | 0.0775622i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 509.620 | − | 420.768i | 0.528652 | − | 0.436482i | ||||
\(965\) | 19.5049 | + | 110.618i | 0.0202123 | + | 0.114630i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −551.943 | − | 1516.45i | −0.570779 | − | 1.56820i | −0.803277 | − | 0.595605i | \(-0.796912\pi\) |
0.232499 | − | 0.972597i | \(-0.425310\pi\) | |||||||
\(968\) | −449.871 | + | 523.340i | −0.464742 | + | 0.540641i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.56425 | + | 645.515i | −0.00264356 | + | 0.665479i | ||||
\(971\) | − | 981.080i | − | 1.01038i | −0.863008 | − | 0.505190i | \(-0.831422\pi\) | ||
0.863008 | − | 0.505190i | \(-0.168578\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1071.69 | −1.10143 | ||||||||
\(974\) | 864.637 | + | 3.43470i | 0.887718 | + | 0.00352638i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −21.5353 | − | 134.606i | −0.0220648 | − | 0.137916i | ||||
\(977\) | −109.248 | + | 39.7629i | −0.111820 | + | 0.0406990i | −0.397324 | − | 0.917678i | \(-0.630061\pi\) |
0.285504 | + | 0.958377i | \(0.407839\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 943.631 | − | 166.388i | 0.963872 | − | 0.169957i | ||||
\(980\) | −378.794 | + | 312.752i | −0.386525 | + | 0.319134i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 336.406 | − | 120.931i | 0.342573 | − | 0.123147i | ||||
\(983\) | −318.542 | + | 875.187i | −0.324051 | + | 0.890322i | 0.665534 | + | 0.746368i | \(0.268204\pi\) |
−0.989584 | + | 0.143954i | \(0.954018\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1227.12 | + | 1029.67i | 1.24581 | + | 1.04536i | ||||
\(986\) | 1628.07 | − | 280.410i | 1.65119 | − | 0.284391i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1054.61 | − | 194.607i | −1.06742 | − | 0.196971i | ||||
\(989\) | −864.296 | + | 1497.00i | −0.873909 | + | 1.51365i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 509.689 | − | 294.269i | 0.514318 | − | 0.296941i | −0.220289 | − | 0.975435i | \(-0.570700\pi\) |
0.734607 | + | 0.678493i | \(0.237367\pi\) | |||||||
\(992\) | 65.0893 | − | 330.602i | 0.0656142 | − | 0.333268i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 110.988 | − | 301.208i | 0.111658 | − | 0.303026i | ||||
\(995\) | 39.6946 | + | 6.99924i | 0.0398941 | + | 0.00703441i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −89.4084 | + | 75.0226i | −0.0896774 | + | 0.0752483i | −0.686524 | − | 0.727107i | \(-0.740864\pi\) |
0.596847 | + | 0.802355i | \(0.296420\pi\) | |||||||
\(998\) | 982.937 | + | 831.458i | 0.984906 | + | 0.833124i | ||||
\(999\) | 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 | 324.3.j.a.199.17 | 204 | ||
3.2 | odd | 2 | 108.3.j.a.103.18 | yes | 204 | ||
4.3 | odd | 2 | inner | 324.3.j.a.199.33 | 204 | ||
12.11 | even | 2 | 108.3.j.a.103.2 | yes | 204 | ||
27.11 | odd | 18 | 108.3.j.a.43.2 | ✓ | 204 | ||
27.16 | even | 9 | inner | 324.3.j.a.127.33 | 204 | ||
108.11 | even | 18 | 108.3.j.a.43.18 | yes | 204 | ||
108.43 | odd | 18 | inner | 324.3.j.a.127.17 | 204 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.j.a.43.2 | ✓ | 204 | 27.11 | odd | 18 | ||
108.3.j.a.43.18 | yes | 204 | 108.11 | even | 18 | ||
108.3.j.a.103.2 | yes | 204 | 12.11 | even | 2 | ||
108.3.j.a.103.18 | yes | 204 | 3.2 | odd | 2 | ||
324.3.j.a.127.17 | 204 | 108.43 | odd | 18 | inner | ||
324.3.j.a.127.33 | 204 | 27.16 | even | 9 | inner | ||
324.3.j.a.199.17 | 204 | 1.1 | even | 1 | trivial | ||
324.3.j.a.199.33 | 204 | 4.3 | odd | 2 | inner |