Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,3,Mod(7,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([8, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.k (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: | \(1.22616118962\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 43.9 | ||
Character | \(\chi\) | \(=\) | 45.43 |
Dual form | 45.3.k.a.22.9 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.863931 | + | 3.22423i | 0.431965 | + | 1.61212i | 0.748226 | + | 0.663444i | \(0.230906\pi\) |
−0.316261 | + | 0.948672i | \(0.602427\pi\) | |||||||
\(3\) | −2.79645 | + | 1.08621i | −0.932151 | + | 0.362071i | ||||
\(4\) | −6.18520 | + | 3.57103i | −1.54630 | + | 0.892757i | ||||
\(5\) | 3.34831 | − | 3.71333i | 0.669661 | − | 0.742667i | ||||
\(6\) | −5.91814 | − | 8.07800i | −0.986357 | − | 1.34633i | ||||
\(7\) | 2.35787 | + | 8.79970i | 0.336839 | + | 1.25710i | 0.901862 | + | 0.432024i | \(0.142201\pi\) |
−0.565023 | + | 0.825075i | \(0.691133\pi\) | |||||||
\(8\) | −7.41620 | − | 7.41620i | −0.927025 | − | 0.927025i | ||||
\(9\) | 6.64028 | − | 6.07508i | 0.737809 | − | 0.675009i | ||||
\(10\) | 14.8654 | + | 7.58766i | 1.48654 | + | 0.758766i | ||||
\(11\) | 1.02371 | − | 1.77311i | 0.0930642 | − | 0.161192i | −0.815735 | − | 0.578426i | \(-0.803667\pi\) |
0.908799 | + | 0.417234i | \(0.137000\pi\) | |||||||
\(12\) | 13.4177 | − | 16.7046i | 1.11814 | − | 1.39205i | ||||
\(13\) | −1.12075 | + | 4.18269i | −0.0862115 | + | 0.321746i | −0.995541 | − | 0.0943314i | \(-0.969929\pi\) |
0.909329 | + | 0.416077i | \(0.136595\pi\) | |||||||
\(14\) | −26.3352 | + | 15.2047i | −1.88109 | + | 1.08605i | ||||
\(15\) | −5.32991 | + | 14.0211i | −0.355327 | + | 0.934742i | ||||
\(16\) | 3.22036 | − | 5.57783i | 0.201273 | − | 0.348615i | ||||
\(17\) | 17.1585 | − | 17.1585i | 1.00932 | − | 1.00932i | 0.00936716 | − | 0.999956i | \(-0.497018\pi\) |
0.999956 | − | 0.00936716i | \(-0.00298170\pi\) | |||||||
\(18\) | 25.3242 | + | 16.1614i | 1.40690 | + | 0.897854i | ||||
\(19\) | − | 18.6363i | − | 0.980857i | −0.871481 | − | 0.490428i | \(-0.836840\pi\) | ||
0.871481 | − | 0.490428i | \(-0.163160\pi\) | |||||||
\(20\) | −7.44954 | + | 34.9246i | −0.372477 | + | 1.74623i | ||||
\(21\) | −16.1520 | − | 22.0468i | −0.769143 | − | 1.04985i | ||||
\(22\) | 6.60133 | + | 1.76882i | 0.300061 | + | 0.0804010i | ||||
\(23\) | 3.08350 | − | 11.5078i | 0.134065 | − | 0.500338i | −0.865935 | − | 0.500157i | \(-0.833276\pi\) |
1.00000 | 0.000180980i | \(-5.76078e-5\pi\) | ||||||||
\(24\) | 28.7946 | + | 12.6835i | 1.19978 | + | 0.528478i | ||||
\(25\) | −2.57768 | − | 24.8668i | −0.103107 | − | 0.994670i | ||||
\(26\) | −14.4542 | −0.555932 | ||||||||
\(27\) | −11.9704 | + | 24.2014i | −0.443348 | + | 0.896349i | ||||
\(28\) | −46.0079 | − | 46.0079i | −1.64314 | − | 1.64314i | ||||
\(29\) | −19.4918 | − | 11.2536i | −0.672131 | − | 0.388055i | 0.124753 | − | 0.992188i | \(-0.460186\pi\) |
−0.796883 | + | 0.604133i | \(0.793520\pi\) | |||||||
\(30\) | −49.8121 | − | 5.07159i | −1.66040 | − | 0.169053i | ||||
\(31\) | 11.9368 | + | 20.6752i | 0.385059 | + | 0.666941i | 0.991777 | − | 0.127975i | \(-0.0408478\pi\) |
−0.606719 | + | 0.794917i | \(0.707514\pi\) | |||||||
\(32\) | −19.7565 | − | 5.29373i | −0.617389 | − | 0.165429i | ||||
\(33\) | −0.936770 | + | 6.07038i | −0.0283870 | + | 0.183951i | ||||
\(34\) | 70.1467 | + | 40.4992i | 2.06314 | + | 1.19115i | ||||
\(35\) | 40.5711 | + | 20.7085i | 1.15917 | + | 0.591672i | ||||
\(36\) | −19.3772 | + | 61.2882i | −0.538256 | + | 1.70245i | ||||
\(37\) | −33.2840 | + | 33.2840i | −0.899568 | + | 0.899568i | −0.995398 | − | 0.0958294i | \(-0.969450\pi\) |
0.0958294 | + | 0.995398i | \(0.469450\pi\) | |||||||
\(38\) | 60.0877 | − | 16.1005i | 1.58126 | − | 0.423696i | ||||
\(39\) | −1.40917 | − | 12.9141i | −0.0361326 | − | 0.331130i | ||||
\(40\) | −52.3705 | + | 2.70711i | −1.30926 | + | 0.0676777i | ||||
\(41\) | 2.15756 | + | 3.73700i | 0.0526234 | + | 0.0911464i | 0.891137 | − | 0.453734i | \(-0.149908\pi\) |
−0.838514 | + | 0.544880i | \(0.816575\pi\) | |||||||
\(42\) | 57.1297 | − | 71.1247i | 1.36023 | − | 1.69345i | ||||
\(43\) | −30.4181 | + | 8.15051i | −0.707398 | + | 0.189547i | −0.594542 | − | 0.804065i | \(-0.702667\pi\) |
−0.112856 | + | 0.993611i | \(0.536000\pi\) | |||||||
\(44\) | 14.6227i | 0.332335i | ||||||||
\(45\) | −0.325090 | − | 44.9988i | −0.00722421 | − | 0.999974i | ||||
\(46\) | 39.7677 | 0.864514 | ||||||||
\(47\) | 0.224807 | + | 0.838990i | 0.00478312 | + | 0.0178509i | 0.968276 | − | 0.249883i | \(-0.0803920\pi\) |
−0.963493 | + | 0.267733i | \(0.913725\pi\) | |||||||
\(48\) | −2.94688 | + | 19.0961i | −0.0613933 | + | 0.397836i | ||||
\(49\) | −29.4398 | + | 16.9971i | −0.600813 | + | 0.346880i | ||||
\(50\) | 77.9493 | − | 29.7942i | 1.55899 | − | 0.595884i | ||||
\(51\) | −29.3451 | + | 66.6207i | −0.575395 | + | 1.30629i | ||||
\(52\) | −8.00445 | − | 29.8730i | −0.153932 | − | 0.574481i | ||||
\(53\) | −3.33316 | − | 3.33316i | −0.0628899 | − | 0.0628899i | 0.674962 | − | 0.737852i | \(-0.264160\pi\) |
−0.737852 | + | 0.674962i | \(0.764160\pi\) | |||||||
\(54\) | −88.3727 | − | 17.6870i | −1.63653 | − | 0.327537i | ||||
\(55\) | −3.15647 | − | 9.73828i | −0.0573904 | − | 0.177060i | ||||
\(56\) | 47.7739 | − | 82.7467i | 0.853105 | − | 1.47762i | ||||
\(57\) | 20.2430 | + | 52.1155i | 0.355140 | + | 0.914306i | ||||
\(58\) | 19.4446 | − | 72.5684i | 0.335252 | − | 1.25118i | ||||
\(59\) | 66.3254 | − | 38.2930i | 1.12416 | − | 0.649033i | 0.181699 | − | 0.983354i | \(-0.441840\pi\) |
0.942459 | + | 0.334321i | \(0.108507\pi\) | |||||||
\(60\) | −17.1033 | − | 105.757i | −0.285055 | − | 1.76261i | ||||
\(61\) | 35.3623 | − | 61.2493i | 0.579710 | − | 1.00409i | −0.415802 | − | 0.909455i | \(-0.636499\pi\) |
0.995512 | − | 0.0946322i | \(-0.0301675\pi\) | |||||||
\(62\) | −56.3490 | + | 56.3490i | −0.908855 | + | 0.908855i | ||||
\(63\) | 69.1158 | + | 44.1082i | 1.09708 | + | 0.700131i | ||||
\(64\) | − | 94.0358i | − | 1.46931i | ||||||
\(65\) | 11.7791 | + | 18.1667i | 0.181217 | + | 0.279487i | ||||
\(66\) | −20.3816 | + | 2.22403i | −0.308813 | + | 0.0336974i | ||||
\(67\) | −20.8965 | − | 5.59919i | −0.311888 | − | 0.0835700i | 0.0994800 | − | 0.995040i | \(-0.468282\pi\) |
−0.411368 | + | 0.911470i | \(0.634949\pi\) | |||||||
\(68\) | −44.8553 | + | 167.402i | −0.659637 | + | 2.46180i | ||||
\(69\) | 3.87703 | + | 35.5302i | 0.0561888 | + | 0.514931i | ||||
\(70\) | −31.7185 | + | 148.701i | −0.453121 | + | 2.12430i | ||||
\(71\) | −28.6105 | −0.402965 | −0.201483 | − | 0.979492i | \(-0.564576\pi\) | ||||
−0.201483 | + | 0.979492i | \(0.564576\pi\) | |||||||
\(72\) | −94.2997 | − | 4.19166i | −1.30972 | − | 0.0582175i | ||||
\(73\) | 48.1316 | + | 48.1316i | 0.659336 | + | 0.659336i | 0.955223 | − | 0.295887i | \(-0.0956151\pi\) |
−0.295887 | + | 0.955223i | \(0.595615\pi\) | |||||||
\(74\) | −136.071 | − | 78.5604i | −1.83879 | − | 1.06163i | ||||
\(75\) | 34.2189 | + | 66.7388i | 0.456253 | + | 0.889850i | ||||
\(76\) | 66.5507 | + | 115.269i | 0.875667 | + | 1.51670i | ||||
\(77\) | 18.0166 | + | 4.82753i | 0.233982 | + | 0.0626953i | ||||
\(78\) | 40.4205 | − | 15.7004i | 0.518212 | − | 0.201287i | ||||
\(79\) | 0.201686 | + | 0.116444i | 0.00255299 | + | 0.00147397i | 0.501276 | − | 0.865287i | \(-0.332864\pi\) |
−0.498723 | + | 0.866761i | \(0.666197\pi\) | |||||||
\(80\) | −9.92959 | − | 30.6346i | −0.124120 | − | 0.382932i | ||||
\(81\) | 7.18677 | − | 80.6805i | 0.0887255 | − | 0.996056i | ||||
\(82\) | −10.1850 | + | 10.1850i | −0.124207 | + | 0.124207i | ||||
\(83\) | −153.477 | + | 41.1240i | −1.84912 | + | 0.495470i | −0.999491 | − | 0.0319094i | \(-0.989841\pi\) |
−0.849630 | + | 0.527380i | \(0.823175\pi\) | |||||||
\(84\) | 178.633 | + | 78.6845i | 2.12658 | + | 0.936720i | ||||
\(85\) | −6.26330 | − | 121.167i | −0.0736859 | − | 1.42550i | ||||
\(86\) | −52.5583 | − | 91.0337i | −0.611143 | − | 1.05853i | ||||
\(87\) | 66.7316 | + | 10.2979i | 0.767030 | + | 0.118367i | ||||
\(88\) | −20.7418 | + | 5.55774i | −0.235702 | + | 0.0631561i | ||||
\(89\) | 103.385i | 1.16163i | 0.814035 | + | 0.580816i | \(0.197266\pi\) | ||||
−0.814035 | + | 0.580816i | \(0.802734\pi\) | |||||||
\(90\) | 144.806 | − | 39.9240i | 1.60895 | − | 0.443600i | ||||
\(91\) | −39.4490 | −0.433506 | ||||||||
\(92\) | 22.0225 | + | 82.1891i | 0.239375 | + | 0.893360i | ||||
\(93\) | −55.8384 | − | 44.8512i | −0.600413 | − | 0.482271i | ||||
\(94\) | −2.51088 | + | 1.44966i | −0.0267115 | + | 0.0154219i | ||||
\(95\) | −69.2027 | − | 62.4000i | −0.728450 | − | 0.656842i | ||||
\(96\) | 60.9981 | − | 6.65606i | 0.635397 | − | 0.0693340i | ||||
\(97\) | −18.6837 | − | 69.7287i | −0.192616 | − | 0.718852i | −0.992871 | − | 0.119193i | \(-0.961969\pi\) |
0.800255 | − | 0.599660i | \(-0.204697\pi\) | |||||||
\(98\) | −80.2366 | − | 80.2366i | −0.818741 | − | 0.818741i | ||||
\(99\) | −3.97409 | − | 17.9931i | −0.0401424 | − | 0.181748i | ||||
\(100\) | 104.743 | + | 144.601i | 1.04743 | + | 1.44601i | ||||
\(101\) | −31.0086 | + | 53.7085i | −0.307016 | + | 0.531767i | −0.977708 | − | 0.209969i | \(-0.932664\pi\) |
0.670692 | + | 0.741736i | \(0.265997\pi\) | |||||||
\(102\) | −240.153 | − | 37.0599i | −2.35444 | − | 0.363332i | ||||
\(103\) | −13.6798 | + | 51.0537i | −0.132813 | + | 0.495667i | −0.999997 | − | 0.00232157i | \(-0.999261\pi\) |
0.867184 | + | 0.497988i | \(0.165928\pi\) | |||||||
\(104\) | 39.3314 | − | 22.7080i | 0.378186 | − | 0.218346i | ||||
\(105\) | −135.949 | − | 13.8416i | −1.29475 | − | 0.131824i | ||||
\(106\) | 7.86727 | − | 13.6265i | 0.0742195 | − | 0.128552i | ||||
\(107\) | 84.3909 | − | 84.3909i | 0.788700 | − | 0.788700i | −0.192581 | − | 0.981281i | \(-0.561686\pi\) |
0.981281 | + | 0.192581i | \(0.0616859\pi\) | |||||||
\(108\) | −12.3846 | − | 192.437i | −0.114672 | − | 1.78183i | ||||
\(109\) | − | 102.481i | − | 0.940190i | −0.882616 | − | 0.470095i | \(-0.844220\pi\) | ||
0.882616 | − | 0.470095i | \(-0.155780\pi\) | |||||||
\(110\) | 28.6715 | − | 18.5904i | 0.260650 | − | 0.169004i | ||||
\(111\) | 56.9237 | − | 129.231i | 0.512826 | − | 1.16424i | ||||
\(112\) | 56.6764 | + | 15.1864i | 0.506040 | + | 0.135593i | ||||
\(113\) | −10.5178 | + | 39.2529i | −0.0930777 | + | 0.347371i | −0.996721 | − | 0.0809152i | \(-0.974216\pi\) |
0.903643 | + | 0.428286i | \(0.140882\pi\) | |||||||
\(114\) | −150.544 | + | 110.292i | −1.32056 | + | 0.967475i | ||||
\(115\) | −32.4077 | − | 49.9816i | −0.281806 | − | 0.434622i | ||||
\(116\) | 160.747 | 1.38575 | ||||||||
\(117\) | 17.9681 | + | 34.5829i | 0.153574 | + | 0.295580i | ||||
\(118\) | 180.766 | + | 180.766i | 1.53192 | + | 1.53192i | ||||
\(119\) | 191.447 | + | 110.532i | 1.60880 | + | 0.928840i | ||||
\(120\) | 143.511 | − | 64.4558i | 1.19593 | − | 0.537132i | ||||
\(121\) | 58.4041 | + | 101.159i | 0.482678 | + | 0.836023i | ||||
\(122\) | 228.033 | + | 61.1012i | 1.86912 | + | 0.500829i | ||||
\(123\) | −10.0927 | − | 8.10678i | −0.0820544 | − | 0.0659088i | ||||
\(124\) | −147.663 | − | 85.2534i | −1.19083 | − | 0.687528i | ||||
\(125\) | −100.969 | − | 73.6897i | −0.807755 | − | 0.589518i | ||||
\(126\) | −82.5039 | + | 260.952i | −0.654793 | + | 2.07105i | ||||
\(127\) | −81.3527 | + | 81.3527i | −0.640572 | + | 0.640572i | −0.950696 | − | 0.310124i | \(-0.899630\pi\) |
0.310124 | + | 0.950696i | \(0.399630\pi\) | |||||||
\(128\) | 224.167 | − | 60.0655i | 1.75131 | − | 0.469261i | ||||
\(129\) | 76.2096 | − | 55.8331i | 0.590772 | − | 0.432814i | ||||
\(130\) | −48.3972 | + | 53.6734i | −0.372286 | + | 0.412872i | ||||
\(131\) | −41.3420 | − | 71.6064i | −0.315588 | − | 0.546614i | 0.663975 | − | 0.747755i | \(-0.268868\pi\) |
−0.979562 | + | 0.201141i | \(0.935535\pi\) | |||||||
\(132\) | −15.8834 | − | 40.8918i | −0.120329 | − | 0.309786i | ||||
\(133\) | 163.994 | − | 43.9420i | 1.23303 | − | 0.330391i | ||||
\(134\) | − | 72.2124i | − | 0.538899i | ||||||
\(135\) | 49.7874 | + | 125.484i | 0.368795 | + | 0.929511i | ||||
\(136\) | −254.502 | −1.87134 | ||||||||
\(137\) | −40.3630 | − | 150.637i | −0.294621 | − | 1.09954i | −0.941518 | − | 0.336962i | \(-0.890601\pi\) |
0.646898 | − | 0.762577i | \(-0.276066\pi\) | |||||||
\(138\) | −111.208 | + | 43.1961i | −0.805857 | + | 0.313015i | ||||
\(139\) | −1.35272 | + | 0.780993i | −0.00973180 | + | 0.00561866i | −0.504858 | − | 0.863202i | \(-0.668455\pi\) |
0.495126 | + | 0.868821i | \(0.335122\pi\) | |||||||
\(140\) | −324.891 | + | 16.7941i | −2.32065 | + | 0.119958i | ||||
\(141\) | −1.53998 | − | 2.10201i | −0.0109219 | − | 0.0149079i | ||||
\(142\) | −24.7175 | − | 92.2470i | −0.174067 | − | 0.649627i | ||||
\(143\) | 6.26906 | + | 6.26906i | 0.0438396 | + | 0.0438396i | ||||
\(144\) | −12.5017 | − | 56.6024i | −0.0868171 | − | 0.393072i | ||||
\(145\) | −107.053 | + | 34.6990i | −0.738295 | + | 0.239304i | ||||
\(146\) | −113.605 | + | 196.770i | −0.778117 | + | 1.34774i | ||||
\(147\) | 63.8646 | − | 79.5095i | 0.434453 | − | 0.540881i | ||||
\(148\) | 87.0102 | − | 324.727i | 0.587907 | − | 2.19410i | ||||
\(149\) | −87.4092 | + | 50.4657i | −0.586639 | + | 0.338696i | −0.763767 | − | 0.645492i | \(-0.776653\pi\) |
0.177128 | + | 0.984188i | \(0.443319\pi\) | |||||||
\(150\) | −185.619 | + | 167.988i | −1.23746 | + | 1.11992i | ||||
\(151\) | −109.094 | + | 188.956i | −0.722477 | + | 1.25137i | 0.237527 | + | 0.971381i | \(0.423663\pi\) |
−0.960004 | + | 0.279986i | \(0.909670\pi\) | |||||||
\(152\) | −138.210 | + | 138.210i | −0.909279 | + | 0.909279i | ||||
\(153\) | 9.69804 | − | 218.177i | 0.0633859 | − | 1.42599i | ||||
\(154\) | 62.2604i | 0.404288i | ||||||||
\(155\) | 116.742 | + | 24.9015i | 0.753174 | + | 0.160655i | ||||
\(156\) | 54.8325 | + | 74.8439i | 0.351490 | + | 0.479769i | ||||
\(157\) | 256.443 | + | 68.7136i | 1.63339 | + | 0.437666i | 0.954897 | − | 0.296937i | \(-0.0959653\pi\) |
0.678496 | + | 0.734604i | \(0.262632\pi\) | |||||||
\(158\) | −0.201198 | + | 0.750883i | −0.00127341 | + | 0.00475242i | ||||
\(159\) | 12.9416 | + | 5.70051i | 0.0813934 | + | 0.0358522i | ||||
\(160\) | −85.8081 | + | 55.6373i | −0.536300 | + | 0.347733i | ||||
\(161\) | 108.535 | 0.674133 | ||||||||
\(162\) | 266.342 | − | 46.5306i | 1.64408 | − | 0.287226i | ||||
\(163\) | −161.076 | − | 161.076i | −0.988199 | − | 0.988199i | 0.0117324 | − | 0.999931i | \(-0.496265\pi\) |
−0.999931 | + | 0.0117324i | \(0.996265\pi\) | |||||||
\(164\) | −26.6899 | − | 15.4094i | −0.162743 | − | 0.0939598i | ||||
\(165\) | 19.4048 | + | 23.8040i | 0.117605 | + | 0.144267i | ||||
\(166\) | −265.187 | − | 459.317i | −1.59751 | − | 2.76697i | ||||
\(167\) | −57.6223 | − | 15.4399i | −0.345044 | − | 0.0924542i | 0.0821354 | − | 0.996621i | \(-0.473826\pi\) |
−0.427179 | + | 0.904167i | \(0.640493\pi\) | |||||||
\(168\) | −43.7167 | + | 283.290i | −0.260219 | + | 1.68625i | ||||
\(169\) | 130.119 | + | 75.1245i | 0.769938 | + | 0.444524i | ||||
\(170\) | 385.260 | − | 124.874i | 2.26624 | − | 0.734555i | ||||
\(171\) | −113.217 | − | 123.750i | −0.662087 | − | 0.723685i | ||||
\(172\) | 159.037 | − | 159.037i | 0.924631 | − | 0.924631i | ||||
\(173\) | −93.6378 | + | 25.0902i | −0.541259 | + | 0.145030i | −0.519083 | − | 0.854724i | \(-0.673726\pi\) |
−0.0221766 | + | 0.999754i | \(0.507060\pi\) | |||||||
\(174\) | 24.4487 | + | 224.055i | 0.140510 | + | 1.28767i | ||||
\(175\) | 212.742 | − | 81.3154i | 1.21567 | − | 0.464660i | ||||
\(176\) | −6.59341 | − | 11.4201i | −0.0374626 | − | 0.0648871i | ||||
\(177\) | −143.881 | + | 179.128i | −0.812889 | + | 1.01202i | ||||
\(178\) | −333.338 | + | 89.3176i | −1.87269 | + | 0.501784i | ||||
\(179\) | 89.4315i | 0.499617i | 0.968295 | + | 0.249809i | \(0.0803677\pi\) | ||||
−0.968295 | + | 0.249809i | \(0.919632\pi\) | |||||||
\(180\) | 162.703 | + | 277.166i | 0.903904 | + | 1.53981i | ||||
\(181\) | 307.336 | 1.69799 | 0.848995 | − | 0.528401i | \(-0.177208\pi\) | ||||
0.848995 | + | 0.528401i | \(0.177208\pi\) | |||||||
\(182\) | −34.0812 | − | 127.193i | −0.187259 | − | 0.698861i | ||||
\(183\) | −32.3592 | + | 209.692i | −0.176826 | + | 1.14586i | ||||
\(184\) | −108.212 | + | 62.4761i | −0.588107 | + | 0.339544i | ||||
\(185\) | 12.1495 | + | 235.040i | 0.0656732 | + | 1.27049i | ||||
\(186\) | 96.3703 | − | 218.784i | 0.518120 | − | 1.17626i | ||||
\(187\) | −12.8587 | − | 47.9892i | −0.0687629 | − | 0.256627i | ||||
\(188\) | −4.38653 | − | 4.38653i | −0.0233326 | − | 0.0233326i | ||||
\(189\) | −241.190 | − | 48.2721i | −1.27614 | − | 0.255408i | ||||
\(190\) | 141.406 | − | 277.035i | 0.744241 | − | 1.45808i | ||||
\(191\) | 81.7990 | − | 141.680i | 0.428267 | − | 0.741780i | −0.568452 | − | 0.822716i | \(-0.692458\pi\) |
0.996719 | + | 0.0809360i | \(0.0257910\pi\) | |||||||
\(192\) | 102.143 | + | 262.966i | 0.531994 | + | 1.36962i | ||||
\(193\) | −65.7869 | + | 245.520i | −0.340865 | + | 1.27212i | 0.556504 | + | 0.830845i | \(0.312142\pi\) |
−0.897369 | + | 0.441280i | \(0.854524\pi\) | |||||||
\(194\) | 208.680 | − | 120.481i | 1.07567 | − | 0.621039i | ||||
\(195\) | −52.6726 | − | 38.0075i | −0.270116 | − | 0.194910i | ||||
\(196\) | 121.394 | − | 210.261i | 0.619358 | − | 1.07276i | ||||
\(197\) | −83.9878 | + | 83.9878i | −0.426334 | + | 0.426334i | −0.887377 | − | 0.461044i | \(-0.847475\pi\) |
0.461044 | + | 0.887377i | \(0.347475\pi\) | |||||||
\(198\) | 54.5805 | − | 28.3582i | 0.275659 | − | 0.143223i | ||||
\(199\) | 165.065i | 0.829471i | 0.909942 | + | 0.414736i | \(0.136126\pi\) | ||||
−0.909942 | + | 0.414736i | \(0.863874\pi\) | |||||||
\(200\) | −165.300 | + | 203.533i | −0.826501 | + | 1.01767i | ||||
\(201\) | 64.5179 | − | 7.04014i | 0.320985 | − | 0.0350256i | ||||
\(202\) | −199.958 | − | 53.5786i | −0.989891 | − | 0.265240i | ||||
\(203\) | 53.0690 | − | 198.056i | 0.261424 | − | 0.975647i | ||||
\(204\) | −56.3987 | − | 516.855i | −0.276464 | − | 2.53360i | ||||
\(205\) | 21.1009 | + | 4.50089i | 0.102931 | + | 0.0219556i | ||||
\(206\) | −176.427 | −0.856443 | ||||||||
\(207\) | −49.4353 | − | 95.1473i | −0.238818 | − | 0.459649i | ||||
\(208\) | 19.7211 | + | 19.7211i | 0.0948132 | + | 0.0948132i | ||||
\(209\) | −33.0442 | − | 19.0781i | −0.158106 | − | 0.0912827i | ||||
\(210\) | −72.8220 | − | 450.289i | −0.346771 | − | 2.14423i | ||||
\(211\) | 5.87275 | + | 10.1719i | 0.0278329 | + | 0.0482081i | 0.879606 | − | 0.475702i | \(-0.157806\pi\) |
−0.851773 | + | 0.523910i | \(0.824473\pi\) | |||||||
\(212\) | 32.5191 | + | 8.71347i | 0.153392 | + | 0.0411013i | ||||
\(213\) | 80.0080 | − | 31.0771i | 0.375624 | − | 0.145902i | ||||
\(214\) | 345.004 | + | 199.188i | 1.61217 | + | 0.930785i | ||||
\(215\) | −71.5837 | + | 140.243i | −0.332947 | + | 0.652293i | ||||
\(216\) | 268.258 | − | 90.7077i | 1.24193 | − | 0.419943i | ||||
\(217\) | −153.790 | + | 153.790i | −0.708709 | + | 0.708709i | ||||
\(218\) | 330.422 | − | 88.5362i | 1.51570 | − | 0.406129i | ||||
\(219\) | −186.879 | − | 82.3165i | −0.853327 | − | 0.375874i | ||||
\(220\) | 54.2991 | + | 48.9614i | 0.246814 | + | 0.222552i | ||||
\(221\) | 52.5383 | + | 90.9991i | 0.237730 | + | 0.411761i | ||||
\(222\) | 465.848 | + | 71.8888i | 2.09841 | + | 0.323823i | ||||
\(223\) | 12.3702 | − | 3.31460i | 0.0554720 | − | 0.0148637i | −0.230976 | − | 0.972959i | \(-0.574192\pi\) |
0.286448 | + | 0.958096i | \(0.407525\pi\) | |||||||
\(224\) | − | 186.333i | − | 0.831843i | ||||||
\(225\) | −168.184 | − | 149.463i | −0.747485 | − | 0.664279i | ||||
\(226\) | −135.647 | −0.600208 | ||||||||
\(227\) | −114.563 | − | 427.557i | −0.504685 | − | 1.88351i | −0.467076 | − | 0.884217i | \(-0.654692\pi\) |
−0.0376093 | − | 0.999293i | \(-0.511974\pi\) | |||||||
\(228\) | −311.313 | − | 250.056i | −1.36541 | − | 1.09674i | ||||
\(229\) | −164.262 | + | 94.8369i | −0.717303 | + | 0.414135i | −0.813759 | − | 0.581202i | \(-0.802583\pi\) |
0.0964562 | + | 0.995337i | \(0.469249\pi\) | |||||||
\(230\) | 133.154 | − | 147.671i | 0.578932 | − | 0.642046i | ||||
\(231\) | −55.6263 | + | 6.06989i | −0.240806 | + | 0.0262766i | ||||
\(232\) | 61.0961 | + | 228.014i | 0.263345 | + | 0.982818i | ||||
\(233\) | −62.7917 | − | 62.7917i | −0.269492 | − | 0.269492i | 0.559403 | − | 0.828896i | \(-0.311030\pi\) |
−0.828896 | + | 0.559403i | \(0.811030\pi\) | |||||||
\(234\) | −95.9802 | + | 87.8106i | −0.410172 | + | 0.375259i | ||||
\(235\) | 3.86817 | + | 1.97441i | 0.0164603 | + | 0.00840176i | ||||
\(236\) | −273.491 | + | 473.699i | −1.15886 | + | 2.00720i | ||||
\(237\) | −0.690489 | − | 0.106555i | −0.00291345 | − | 0.000449599i | ||||
\(238\) | −190.984 | + | 712.762i | −0.802454 | + | 2.99480i | ||||
\(239\) | −57.9140 | + | 33.4367i | −0.242318 | + | 0.139902i | −0.616242 | − | 0.787557i | \(-0.711346\pi\) |
0.373924 | + | 0.927460i | \(0.378012\pi\) | |||||||
\(240\) | 61.0433 | + | 74.8825i | 0.254347 | + | 0.312010i | ||||
\(241\) | 29.6700 | − | 51.3900i | 0.123112 | − | 0.213236i | −0.797881 | − | 0.602815i | \(-0.794046\pi\) |
0.920993 | + | 0.389578i | \(0.127379\pi\) | |||||||
\(242\) | −275.702 | + | 275.702i | −1.13927 | + | 1.13927i | ||||
\(243\) | 67.5388 | + | 233.426i | 0.277937 | + | 0.960599i | ||||
\(244\) | 505.119i | 2.07016i | ||||||||
\(245\) | −35.4577 | + | 166.231i | −0.144725 | + | 0.678496i | ||||
\(246\) | 17.4188 | − | 39.5449i | 0.0708080 | − | 0.160751i | ||||
\(247\) | 77.9498 | + | 20.8866i | 0.315586 | + | 0.0845611i | ||||
\(248\) | 64.8054 | − | 241.857i | 0.261312 | − | 0.975230i | ||||
\(249\) | 384.522 | − | 281.710i | 1.54426 | − | 1.13137i | ||||
\(250\) | 150.362 | − | 389.212i | 0.601449 | − | 1.55685i | ||||
\(251\) | −88.5781 | −0.352901 | −0.176450 | − | 0.984310i | \(-0.556461\pi\) | ||||
−0.176450 | + | 0.984310i | \(0.556461\pi\) | |||||||
\(252\) | −585.007 | − | 26.0038i | −2.32146 | − | 0.103190i | ||||
\(253\) | −17.2480 | − | 17.2480i | −0.0681737 | − | 0.0681737i | ||||
\(254\) | −332.583 | − | 192.017i | −1.30938 | − | 0.755972i | ||||
\(255\) | 149.128 | + | 332.035i | 0.584817 | + | 1.30210i | ||||
\(256\) | 199.259 | + | 345.126i | 0.778354 | + | 1.34815i | ||||
\(257\) | 151.819 | + | 40.6797i | 0.590734 | + | 0.158287i | 0.541789 | − | 0.840515i | \(-0.317747\pi\) |
0.0489452 | + | 0.998801i | \(0.484414\pi\) | |||||||
\(258\) | 245.859 | + | 197.482i | 0.952940 | + | 0.765433i | ||||
\(259\) | −371.369 | − | 214.410i | −1.43386 | − | 0.827837i | ||||
\(260\) | −137.730 | − | 70.3008i | −0.529730 | − | 0.270388i | ||||
\(261\) | −197.797 | + | 43.6872i | −0.757845 | + | 0.167384i | ||||
\(262\) | 195.159 | − | 195.159i | 0.744882 | − | 0.744882i | ||||
\(263\) | 339.020 | − | 90.8401i | 1.28905 | − | 0.345400i | 0.451750 | − | 0.892145i | \(-0.350800\pi\) |
0.837299 | + | 0.546745i | \(0.184133\pi\) | |||||||
\(264\) | 51.9664 | − | 38.0719i | 0.196843 | − | 0.144212i | ||||
\(265\) | −23.5376 | + | 1.21669i | −0.0888211 | + | 0.00459129i | ||||
\(266\) | 283.358 | + | 490.791i | 1.06526 | + | 1.84508i | ||||
\(267\) | −112.298 | − | 289.112i | −0.420593 | − | 1.08282i | ||||
\(268\) | 149.244 | − | 39.9897i | 0.556880 | − | 0.149215i | ||||
\(269\) | 81.1798i | 0.301784i | 0.988550 | + | 0.150892i | \(0.0482145\pi\) | ||||
−0.988550 | + | 0.150892i | \(0.951785\pi\) | |||||||
\(270\) | −361.577 | + | 268.936i | −1.33917 | + | 0.996058i | ||||
\(271\) | −96.4105 | −0.355758 | −0.177879 | − | 0.984052i | \(-0.556924\pi\) | ||||
−0.177879 | + | 0.984052i | \(0.556924\pi\) | |||||||
\(272\) | −40.4506 | − | 150.964i | −0.148716 | − | 0.555014i | ||||
\(273\) | 110.317 | − | 42.8500i | 0.404092 | − | 0.156960i | ||||
\(274\) | 450.817 | − | 260.280i | 1.64532 | − | 0.949925i | ||||
\(275\) | −46.7303 | − | 20.8857i | −0.169928 | − | 0.0759481i | ||||
\(276\) | −150.860 | − | 205.917i | −0.546593 | − | 0.746075i | ||||
\(277\) | 113.398 | + | 423.206i | 0.409378 | + | 1.52782i | 0.795836 | + | 0.605512i | \(0.207032\pi\) |
−0.386458 | + | 0.922307i | \(0.626302\pi\) | |||||||
\(278\) | −3.68676 | − | 3.68676i | −0.0132617 | − | 0.0132617i | ||||
\(279\) | 204.867 | + | 64.7719i | 0.734292 | + | 0.232157i | ||||
\(280\) | −147.305 | − | 454.462i | −0.526088 | − | 1.62308i | ||||
\(281\) | −95.5531 | + | 165.503i | −0.340047 | + | 0.588978i | −0.984441 | − | 0.175715i | \(-0.943776\pi\) |
0.644394 | + | 0.764693i | \(0.277110\pi\) | |||||||
\(282\) | 5.44693 | − | 6.78125i | 0.0193153 | − | 0.0240470i | ||||
\(283\) | 89.6088 | − | 334.424i | 0.316639 | − | 1.18171i | −0.605815 | − | 0.795605i | \(-0.707153\pi\) |
0.922454 | − | 0.386107i | \(-0.126180\pi\) | |||||||
\(284\) | 176.962 | − | 102.169i | 0.623105 | − | 0.359750i | ||||
\(285\) | 261.302 | + | 99.3297i | 0.916848 | + | 0.348525i | ||||
\(286\) | −14.7969 | + | 25.6289i | −0.0517373 | + | 0.0896117i | ||||
\(287\) | −27.7972 | + | 27.7972i | −0.0968545 | + | 0.0968545i | ||||
\(288\) | −163.348 | + | 84.8702i | −0.567182 | + | 0.294688i | ||||
\(289\) | − | 299.828i | − | 1.03747i | ||||||
\(290\) | −204.364 | − | 315.186i | −0.704703 | − | 1.08685i | ||||
\(291\) | 127.988 | + | 174.698i | 0.439822 | + | 0.600338i | ||||
\(292\) | −469.582 | − | 125.824i | −1.60816 | − | 0.430905i | ||||
\(293\) | −77.5588 | + | 289.453i | −0.264706 | + | 0.987895i | 0.697725 | + | 0.716366i | \(0.254196\pi\) |
−0.962430 | + | 0.271529i | \(0.912471\pi\) | |||||||
\(294\) | 311.532 | + | 137.224i | 1.05963 | + | 0.466748i | ||||
\(295\) | 79.8831 | − | 374.505i | 0.270790 | − | 1.26951i | ||||
\(296\) | 493.682 | 1.66784 | ||||||||
\(297\) | 30.6576 | + | 46.0000i | 0.103224 | + | 0.154882i | ||||
\(298\) | −238.229 | − | 238.229i | −0.799426 | − | 0.799426i | ||||
\(299\) | 44.6776 | + | 25.7946i | 0.149423 | + | 0.0862697i | ||||
\(300\) | −449.977 | − | 290.596i | −1.49992 | − | 0.968653i | ||||
\(301\) | −143.444 | − | 248.452i | −0.476558 | − | 0.825423i | ||||
\(302\) | −703.489 | − | 188.499i | −2.32944 | − | 0.624170i | ||||
\(303\) | 28.3753 | − | 183.875i | 0.0936477 | − | 0.606849i | ||||
\(304\) | −103.950 | − | 60.0156i | −0.341941 | − | 0.197420i | ||||
\(305\) | −109.035 | − | 336.394i | −0.357493 | − | 1.10293i | ||||
\(306\) | 711.831 | − | 157.221i | 2.32624 | − | 0.513793i | ||||
\(307\) | 138.397 | − | 138.397i | 0.450805 | − | 0.450805i | −0.444817 | − | 0.895622i | \(-0.646731\pi\) |
0.895622 | + | 0.444817i | \(0.146731\pi\) | |||||||
\(308\) | −128.676 | + | 34.4785i | −0.417778 | + | 0.111943i | ||||
\(309\) | −17.2003 | − | 157.628i | −0.0556643 | − | 0.510124i | ||||
\(310\) | 20.5689 | + | 397.917i | 0.0663512 | + | 1.28360i | ||||
\(311\) | 53.6367 | + | 92.9015i | 0.172465 | + | 0.298719i | 0.939281 | − | 0.343148i | \(-0.111493\pi\) |
−0.766816 | + | 0.641867i | \(0.778160\pi\) | |||||||
\(312\) | −85.3226 | + | 106.224i | −0.273470 | + | 0.340462i | ||||
\(313\) | 528.306 | − | 141.559i | 1.68788 | − | 0.452266i | 0.718038 | − | 0.696004i | \(-0.245040\pi\) |
0.969841 | + | 0.243738i | \(0.0783736\pi\) | |||||||
\(314\) | 886.195i | 2.82228i | ||||||||
\(315\) | 395.209 | − | 108.962i | 1.25463 | − | 0.345912i | ||||
\(316\) | −1.66329 | −0.00526359 | ||||||||
\(317\) | 112.931 | + | 421.463i | 0.356248 | + | 1.32954i | 0.878906 | + | 0.476994i | \(0.158274\pi\) |
−0.522658 | + | 0.852542i | \(0.675059\pi\) | |||||||
\(318\) | −7.19916 | + | 46.6514i | −0.0226389 | + | 0.146703i | ||||
\(319\) | −39.9077 | + | 23.0407i | −0.125103 | + | 0.0722280i | ||||
\(320\) | −349.186 | − | 314.861i | −1.09121 | − | 0.983939i | ||||
\(321\) | −144.329 | + | 327.661i | −0.449622 | + | 1.02075i | ||||
\(322\) | 93.7670 | + | 349.943i | 0.291202 | + | 1.08678i | ||||
\(323\) | −319.771 | − | 319.771i | −0.990002 | − | 0.990002i | ||||
\(324\) | 243.661 | + | 524.690i | 0.752040 | + | 1.61941i | ||||
\(325\) | 106.899 | + | 17.0877i | 0.328920 | + | 0.0525777i | ||||
\(326\) | 380.189 | − | 658.507i | 1.16622 | − | 2.01996i | ||||
\(327\) | 111.316 | + | 286.582i | 0.340415 | + | 0.876398i | ||||
\(328\) | 11.7135 | − | 43.7152i | 0.0357118 | − | 0.133278i | ||||
\(329\) | −6.85279 | + | 3.95646i | −0.0208292 | + | 0.0120257i | ||||
\(330\) | −59.9854 | + | 83.1305i | −0.181774 | + | 0.251911i | ||||
\(331\) | −293.152 | + | 507.754i | −0.885655 | + | 1.53400i | −0.0406933 | + | 0.999172i | \(0.512957\pi\) |
−0.844961 | + | 0.534827i | \(0.820377\pi\) | |||||||
\(332\) | 802.431 | − | 802.431i | 2.41696 | − | 2.41696i | ||||
\(333\) | −18.8122 | + | 423.219i | −0.0564932 | + | 1.27093i | ||||
\(334\) | − | 199.127i | − | 0.596188i | ||||||
\(335\) | −90.7595 | + | 58.8477i | −0.270924 | + | 0.175665i | ||||
\(336\) | −174.989 | + | 19.0946i | −0.520799 | + | 0.0568292i | ||||
\(337\) | −459.691 | − | 123.174i | −1.36407 | − | 0.365501i | −0.498760 | − | 0.866740i | \(-0.666211\pi\) |
−0.865309 | + | 0.501239i | \(0.832878\pi\) | |||||||
\(338\) | −129.805 | + | 484.438i | −0.384038 | + | 1.43325i | ||||
\(339\) | −13.2245 | − | 121.193i | −0.0390104 | − | 0.357502i | ||||
\(340\) | 471.431 | + | 727.077i | 1.38656 | + | 2.13846i | ||||
\(341\) | 48.8792 | 0.143341 | ||||||||
\(342\) | 301.188 | − | 471.949i | 0.880667 | − | 1.37997i | ||||
\(343\) | 96.6647 | + | 96.6647i | 0.281821 | + | 0.281821i | ||||
\(344\) | 286.033 | + | 165.141i | 0.831490 | + | 0.480061i | ||||
\(345\) | 144.917 | + | 104.569i | 0.420050 | + | 0.303100i | ||||
\(346\) | −161.793 | − | 280.234i | −0.467610 | − | 0.809925i | ||||
\(347\) | 169.638 | + | 45.4544i | 0.488870 | + | 0.130992i | 0.494830 | − | 0.868990i | \(-0.335230\pi\) |
−0.00595969 | + | 0.999982i | \(0.501897\pi\) | |||||||
\(348\) | −449.523 | + | 174.606i | −1.29173 | + | 0.501741i | ||||
\(349\) | −298.148 | − | 172.136i | −0.854292 | − | 0.493226i | 0.00780468 | − | 0.999970i | \(-0.497516\pi\) |
−0.862097 | + | 0.506744i | \(0.830849\pi\) | |||||||
\(350\) | 445.974 | + | 615.679i | 1.27421 | + | 1.75908i | ||||
\(351\) | −87.8113 | − | 77.1923i | −0.250175 | − | 0.219921i | ||||
\(352\) | −29.6112 | + | 29.6112i | −0.0841227 | + | 0.0841227i | ||||
\(353\) | 260.440 | − | 69.7848i | 0.737792 | − | 0.197691i | 0.129695 | − | 0.991554i | \(-0.458600\pi\) |
0.608096 | + | 0.793863i | \(0.291933\pi\) | |||||||
\(354\) | −701.854 | − | 309.153i | −1.98264 | − | 0.873314i | ||||
\(355\) | −95.7968 | + | 106.240i | −0.269850 | + | 0.299269i | ||||
\(356\) | −369.191 | − | 639.458i | −1.03705 | − | 1.79623i | ||||
\(357\) | −655.434 | − | 101.145i | −1.83595 | − | 0.283320i | ||||
\(358\) | −288.348 | + | 77.2626i | −0.805441 | + | 0.215817i | ||||
\(359\) | − | 411.438i | − | 1.14607i | −0.819532 | − | 0.573033i | \(-0.805767\pi\) | ||
0.819532 | − | 0.573033i | \(-0.194233\pi\) | |||||||
\(360\) | −331.309 | + | 336.131i | −0.920304 | + | 0.933698i | ||||
\(361\) | 13.6890 | 0.0379198 | ||||||||
\(362\) | 265.517 | + | 990.923i | 0.733473 | + | 2.73736i | ||||
\(363\) | −273.204 | − | 219.446i | −0.752628 | − | 0.604536i | ||||
\(364\) | 244.000 | − | 140.873i | 0.670330 | − | 0.387015i | ||||
\(365\) | 339.888 | − | 17.5693i | 0.931199 | − | 0.0481350i | ||||
\(366\) | −704.051 | + | 76.8255i | −1.92364 | + | 0.209906i | ||||
\(367\) | −167.988 | − | 626.938i | −0.457732 | − | 1.70828i | −0.679930 | − | 0.733277i | \(-0.737990\pi\) |
0.222199 | − | 0.975001i | \(-0.428677\pi\) | |||||||
\(368\) | −54.2584 | − | 54.2584i | −0.147441 | − | 0.147441i | ||||
\(369\) | 37.0294 | + | 11.7074i | 0.100351 | + | 0.0317274i | ||||
\(370\) | −747.327 | + | 242.231i | −2.01980 | + | 0.654679i | ||||
\(371\) | 21.4716 | − | 37.1900i | 0.0578751 | − | 0.100243i | ||||
\(372\) | 505.537 | + | 78.0134i | 1.35897 | + | 0.209714i | ||||
\(373\) | 28.7295 | − | 107.220i | 0.0770229 | − | 0.287453i | −0.916662 | − | 0.399664i | \(-0.869127\pi\) |
0.993684 | + | 0.112211i | \(0.0357933\pi\) | |||||||
\(374\) | 143.619 | − | 82.9186i | 0.384009 | − | 0.221708i | ||||
\(375\) | 362.399 | + | 96.3955i | 0.966397 | + | 0.257055i | ||||
\(376\) | 4.55491 | − | 7.88933i | 0.0121141 | − | 0.0209823i | ||||
\(377\) | 68.9157 | − | 68.9157i | 0.182800 | − | 0.182800i | ||||
\(378\) | −52.7309 | − | 819.356i | −0.139500 | − | 2.16761i | ||||
\(379\) | 317.077i | 0.836614i | 0.908306 | + | 0.418307i | \(0.137376\pi\) | ||||
−0.908306 | + | 0.418307i | \(0.862624\pi\) | |||||||
\(380\) | 650.865 | + | 138.832i | 1.71280 | + | 0.365346i | ||||
\(381\) | 139.133 | − | 315.865i | 0.365177 | − | 0.829043i | ||||
\(382\) | 527.478 | + | 141.337i | 1.38083 | + | 0.369993i | ||||
\(383\) | 23.0644 | − | 86.0774i | 0.0602203 | − | 0.224745i | −0.929257 | − | 0.369434i | \(-0.879552\pi\) |
0.989477 | + | 0.144689i | \(0.0462182\pi\) | |||||||
\(384\) | −561.629 | + | 411.464i | −1.46258 | + | 1.07152i | ||||
\(385\) | 78.2514 | − | 50.7376i | 0.203250 | − | 0.131786i | ||||
\(386\) | −848.449 | −2.19806 | ||||||||
\(387\) | −152.470 | + | 238.914i | −0.393979 | + | 0.617350i | ||||
\(388\) | 364.566 | + | 364.566i | 0.939602 | + | 0.939602i | ||||
\(389\) | 64.0677 | + | 36.9895i | 0.164698 | + | 0.0950887i | 0.580084 | − | 0.814557i | \(-0.303020\pi\) |
−0.415385 | + | 0.909646i | \(0.636353\pi\) | |||||||
\(390\) | 77.0397 | − | 202.665i | 0.197538 | − | 0.519653i | ||||
\(391\) | −144.548 | − | 250.364i | −0.369687 | − | 0.640318i | ||||
\(392\) | 344.386 | + | 92.2778i | 0.878535 | + | 0.235403i | ||||
\(393\) | 193.391 | + | 155.338i | 0.492088 | + | 0.395261i | ||||
\(394\) | −343.356 | − | 198.237i | −0.871461 | − | 0.503138i | ||||
\(395\) | 1.10770 | − | 0.359039i | 0.00280431 | − | 0.000908961i | ||||
\(396\) | 88.8343 | + | 97.0991i | 0.224329 | + | 0.245200i | ||||
\(397\) | 331.663 | − | 331.663i | 0.835422 | − | 0.835422i | −0.152830 | − | 0.988252i | \(-0.548839\pi\) |
0.988252 | + | 0.152830i | \(0.0488387\pi\) | |||||||
\(398\) | −532.207 | + | 142.605i | −1.33720 | + | 0.358303i | ||||
\(399\) | −410.870 | + | 301.013i | −1.02975 | + | 0.754420i | ||||
\(400\) | −147.004 | − | 65.7021i | −0.367509 | − | 0.164255i | ||||
\(401\) | −324.360 | − | 561.808i | −0.808877 | − | 1.40102i | −0.913642 | − | 0.406520i | \(-0.866742\pi\) |
0.104765 | − | 0.994497i | \(-0.466591\pi\) | |||||||
\(402\) | 78.4380 | + | 201.939i | 0.195119 | + | 0.502335i | ||||
\(403\) | −99.8561 | + | 26.7564i | −0.247782 | + | 0.0663930i | ||||
\(404\) | − | 442.930i | − | 1.09636i | ||||||
\(405\) | −275.530 | − | 296.830i | −0.680322 | − | 0.732914i | ||||
\(406\) | 684.428 | 1.68578 | ||||||||
\(407\) | 24.9432 | + | 93.0893i | 0.0612855 | + | 0.228721i | ||||
\(408\) | 711.702 | − | 276.443i | 1.74437 | − | 0.677556i | ||||
\(409\) | −545.487 | + | 314.937i | −1.33371 | + | 0.770017i | −0.985866 | − | 0.167536i | \(-0.946419\pi\) |
−0.347842 | + | 0.937553i | \(0.613086\pi\) | |||||||
\(410\) | 3.71779 | + | 71.9227i | 0.00906777 | + | 0.175421i | ||||
\(411\) | 276.497 | + | 377.406i | 0.672742 | + | 0.918262i | ||||
\(412\) | −97.7018 | − | 364.628i | −0.237140 | − | 0.885019i | ||||
\(413\) | 493.353 | + | 493.353i | 1.19456 | + | 1.19456i | ||||
\(414\) | 264.069 | − | 241.592i | 0.637847 | − | 0.583555i | ||||
\(415\) | −361.181 | + | 707.607i | −0.870315 | + | 1.70508i | ||||
\(416\) | 44.2841 | − | 76.7023i | 0.106452 | − | 0.184380i | ||||
\(417\) | 2.93449 | − | 3.65335i | 0.00703715 | − | 0.00876103i | ||||
\(418\) | 32.9643 | − | 123.024i | 0.0788619 | − | 0.294317i | ||||
\(419\) | −153.113 | + | 88.3997i | −0.365424 | + | 0.210978i | −0.671457 | − | 0.741043i | \(-0.734331\pi\) |
0.306033 | + | 0.952021i | \(0.400998\pi\) | |||||||
\(420\) | 890.300 | − | 399.864i | 2.11976 | − | 0.952058i | ||||
\(421\) | 44.6779 | − | 77.3843i | 0.106123 | − | 0.183811i | −0.808073 | − | 0.589082i | \(-0.799490\pi\) |
0.914197 | + | 0.405271i | \(0.132823\pi\) | |||||||
\(422\) | −27.7229 | + | 27.7229i | −0.0656941 | + | 0.0656941i | ||||
\(423\) | 6.58972 | + | 4.20542i | 0.0155785 | + | 0.00994188i | ||||
\(424\) | 49.4388i | 0.116601i | ||||||||
\(425\) | −470.905 | − | 382.447i | −1.10801 | − | 0.899875i | ||||
\(426\) | 169.321 | + | 231.116i | 0.397468 | + | 0.542526i | ||||
\(427\) | 622.355 | + | 166.760i | 1.45751 | + | 0.390538i | ||||
\(428\) | −220.612 | + | 823.337i | −0.515449 | + | 1.92368i | ||||
\(429\) | −24.3407 | − | 10.7216i | −0.0567381 | − | 0.0249921i | ||||
\(430\) | −514.020 | − | 109.642i | −1.19539 | − | 0.254982i | ||||
\(431\) | 648.364 | 1.50433 | 0.752163 | − | 0.658977i | \(-0.229011\pi\) | ||||
0.752163 | + | 0.658977i | \(0.229011\pi\) | |||||||
\(432\) | 96.4425 | + | 144.706i | 0.223247 | + | 0.334968i | ||||
\(433\) | −481.270 | − | 481.270i | −1.11148 | − | 1.11148i | −0.992951 | − | 0.118526i | \(-0.962183\pi\) |
−0.118526 | − | 0.992951i | \(-0.537817\pi\) | |||||||
\(434\) | −628.718 | − | 362.991i | −1.44866 | − | 0.836384i | ||||
\(435\) | 261.677 | − | 213.316i | 0.601557 | − | 0.490382i | ||||
\(436\) | 365.961 | + | 633.864i | 0.839361 | + | 1.45382i | ||||
\(437\) | −214.462 | − | 57.4649i | −0.490760 | − | 0.131499i | ||||
\(438\) | 103.957 | − | 673.656i | 0.237345 | − | 1.53803i | ||||
\(439\) | 543.519 | + | 313.801i | 1.23808 | + | 0.714809i | 0.968702 | − | 0.248225i | \(-0.0798471\pi\) |
0.269382 | + | 0.963033i | \(0.413180\pi\) | |||||||
\(440\) | −48.8120 | + | 95.6301i | −0.110936 | + | 0.217341i | ||||
\(441\) | −92.2302 | + | 291.715i | −0.209139 | + | 0.661485i | ||||
\(442\) | −248.013 | + | 248.013i | −0.561115 | + | 0.561115i | ||||
\(443\) | −519.441 | + | 139.184i | −1.17255 | + | 0.314185i | −0.791969 | − | 0.610562i | \(-0.790944\pi\) |
−0.380584 | + | 0.924746i | \(0.624277\pi\) | |||||||
\(444\) | 109.402 | + | 1002.59i | 0.246401 | + | 2.25809i | ||||
\(445\) | 383.904 | + | 346.165i | 0.862705 | + | 0.777900i | ||||
\(446\) | 21.3741 | + | 37.0210i | 0.0479239 | + | 0.0830067i | ||||
\(447\) | 189.619 | − | 236.070i | 0.424204 | − | 0.528121i | ||||
\(448\) | 827.486 | − | 221.724i | 1.84707 | − | 0.494920i | ||||
\(449\) | − | 252.073i | − | 0.561410i | −0.959794 | − | 0.280705i | \(-0.909432\pi\) | ||
0.959794 | − | 0.280705i | \(-0.0905683\pi\) | |||||||
\(450\) | 336.603 | − | 671.390i | 0.748007 | − | 1.49198i | ||||
\(451\) | 8.83482 | 0.0195894 | ||||||||
\(452\) | −75.1186 | − | 280.346i | −0.166191 | − | 0.620235i | ||||
\(453\) | 99.8294 | − | 646.907i | 0.220374 | − | 1.42805i | ||||
\(454\) | 1279.57 | − | 738.759i | 2.81843 | − | 1.62722i | ||||
\(455\) | −132.087 | + | 146.487i | −0.290302 | + | 0.321950i | ||||
\(456\) | 236.373 | − | 536.624i | 0.518361 | − | 1.17681i | ||||
\(457\) | 76.3993 | + | 285.126i | 0.167176 | + | 0.623908i | 0.997753 | + | 0.0670042i | \(0.0213441\pi\) |
−0.830577 | + | 0.556904i | \(0.811989\pi\) | |||||||
\(458\) | −447.688 | − | 447.688i | −0.977484 | − | 0.977484i | ||||
\(459\) | 209.866 | + | 620.654i | 0.457224 | + | 1.35219i | ||||
\(460\) | 378.934 | + | 193.417i | 0.823769 | + | 0.420473i | ||||
\(461\) | 254.881 | − | 441.467i | 0.552887 | − | 0.957629i | −0.445177 | − | 0.895443i | \(-0.646859\pi\) |
0.998065 | − | 0.0621865i | \(-0.0198074\pi\) | |||||||
\(462\) | −67.6280 | − | 174.108i | −0.146381 | − | 0.376858i | ||||
\(463\) | −76.4168 | + | 285.192i | −0.165047 | + | 0.615964i | 0.832987 | + | 0.553293i | \(0.186629\pi\) |
−0.998034 | + | 0.0626719i | \(0.980038\pi\) | |||||||
\(464\) | −125.541 | + | 72.4813i | −0.270563 | + | 0.156210i | ||||
\(465\) | −353.512 | + | 57.1709i | −0.760240 | + | 0.122948i | ||||
\(466\) | 148.208 | − | 256.703i | 0.318042 | − | 0.550865i | ||||
\(467\) | −375.745 | + | 375.745i | −0.804593 | + | 0.804593i | −0.983810 | − | 0.179217i | \(-0.942644\pi\) |
0.179217 | + | 0.983810i | \(0.442644\pi\) | |||||||
\(468\) | −234.633 | − | 149.738i | −0.501352 | − | 0.319952i | ||||
\(469\) | − | 197.085i | − | 0.420223i | ||||||
\(470\) | −3.02414 | + | 14.1776i | −0.00643434 | + | 0.0301652i | ||||
\(471\) | −791.767 | + | 86.3970i | −1.68103 | + | 0.183433i | ||||
\(472\) | −775.871 | − | 207.894i | −1.64379 | − | 0.440453i | ||||
\(473\) | −16.6875 | + | 62.2784i | −0.0352800 | + | 0.131667i | ||||
\(474\) | −0.252977 | − | 2.31835i | −0.000533706 | − | 0.00489104i | ||||
\(475\) | −463.424 | + | 48.0384i | −0.975629 | + | 0.101134i | ||||
\(476\) | −1578.85 | −3.31691 | ||||||||
\(477\) | −42.3824 | − | 1.88391i | −0.0888520 | − | 0.00394951i | ||||
\(478\) | −157.841 | − | 157.841i | −0.330212 | − | 0.330212i | ||||
\(479\) | 375.237 | + | 216.643i | 0.783376 | + | 0.452282i | 0.837625 | − | 0.546245i | \(-0.183943\pi\) |
−0.0542492 | + | 0.998527i | \(0.517277\pi\) | |||||||
\(480\) | 179.524 | − | 248.793i | 0.374009 | − | 0.518318i | ||||
\(481\) | −101.914 | − | 176.520i | −0.211879 | − | 0.366985i | ||||
\(482\) | 191.326 | + | 51.2656i | 0.396942 | + | 0.106360i | ||||
\(483\) | −303.514 | + | 117.892i | −0.628393 | + | 0.244084i | ||||
\(484\) | −722.482 | − | 417.125i | −1.49273 | − | 0.861828i | ||||
\(485\) | −321.485 | − | 164.094i | −0.662855 | − | 0.338338i | ||||
\(486\) | −694.270 | + | 419.424i | −1.42854 | + | 0.863013i | ||||
\(487\) | 417.712 | − | 417.712i | 0.857725 | − | 0.857725i | −0.133345 | − | 0.991070i | \(-0.542572\pi\) |
0.991070 | + | 0.133345i | \(0.0425719\pi\) | |||||||
\(488\) | −716.491 | + | 191.983i | −1.46822 | + | 0.393408i | ||||
\(489\) | 625.406 | + | 275.479i | 1.27895 | + | 0.563352i | ||||
\(490\) | −566.602 | + | 29.2885i | −1.15633 | + | 0.0597724i | ||||
\(491\) | 385.003 | + | 666.845i | 0.784121 | + | 1.35814i | 0.929523 | + | 0.368765i | \(0.120219\pi\) |
−0.145402 | + | 0.989373i | \(0.546447\pi\) | |||||||
\(492\) | 91.3748 | + | 14.1008i | 0.185721 | + | 0.0286601i | ||||
\(493\) | −527.544 | + | 141.355i | −1.07007 | + | 0.286724i | ||||
\(494\) | 269.373i | 0.545289i | ||||||||
\(495\) | −80.1207 | − | 45.4892i | −0.161860 | − | 0.0918973i | ||||
\(496\) | 153.764 | 0.310007 | ||||||||
\(497\) | −67.4600 | − | 251.764i | −0.135734 | − | 0.506567i | ||||
\(498\) | 1240.50 | + | 996.409i | 2.49096 | + | 2.00082i | ||||
\(499\) | −84.7687 | + | 48.9412i | −0.169877 | + | 0.0980786i | −0.582528 | − | 0.812811i | \(-0.697936\pi\) |
0.412651 | + | 0.910889i | \(0.364603\pi\) | |||||||
\(500\) | 887.664 | + | 95.2212i | 1.77533 | + | 0.190442i | ||||
\(501\) | 177.909 | − | 19.4133i | 0.355108 | − | 0.0387491i | ||||
\(502\) | −76.5253 | − | 285.596i | −0.152441 | − | 0.568917i | ||||
\(503\) | 350.849 | + | 350.849i | 0.697512 | + | 0.697512i | 0.963873 | − | 0.266361i | \(-0.0858213\pi\) |
−0.266361 | + | 0.963873i | \(0.585821\pi\) | |||||||
\(504\) | −185.461 | − | 839.692i | −0.367979 | − | 1.66606i | ||||
\(505\) | 95.6112 | + | 294.978i | 0.189329 | + | 0.584114i | ||||
\(506\) | 40.7104 | − | 70.5125i | 0.0804553 | − | 0.139353i | ||||
\(507\) | −445.474 | − | 68.7447i | −0.878647 | − | 0.135591i | ||||
\(508\) | 212.670 | − | 793.696i | 0.418642 | − | 1.56239i | ||||
\(509\) | 389.842 | − | 225.075i | 0.765897 | − | 0.442191i | −0.0655119 | − | 0.997852i | \(-0.520868\pi\) |
0.831409 | + | 0.555661i | \(0.187535\pi\) | |||||||
\(510\) | −941.721 | + | 767.679i | −1.84651 | + | 1.50525i | ||||
\(511\) | −310.055 | + | 537.031i | −0.606761 | + | 1.05094i | ||||
\(512\) | −284.213 | + | 284.213i | −0.555104 | + | 0.555104i | ||||
\(513\) | 451.025 | + | 223.084i | 0.879190 | + | 0.434861i | ||||
\(514\) | 524.643i | 1.02071i | ||||||||
\(515\) | 143.775 | + | 221.741i | 0.279175 | + | 0.430565i | ||||
\(516\) | −271.991 | + | 617.485i | −0.527113 | + | 1.19668i | ||||
\(517\) | 1.71776 | + | 0.460272i | 0.00332255 | + | 0.000890275i | ||||
\(518\) | 370.470 | − | 1382.61i | 0.715194 | − | 2.66914i | ||||
\(519\) | 234.600 | − | 171.874i | 0.452024 | − | 0.331164i | ||||
\(520\) | 47.3712 | − | 222.084i | 0.0910985 | − | 0.427084i | ||||
\(521\) | 749.947 | 1.43944 | 0.719718 | − | 0.694266i | \(-0.244271\pi\) | ||||
0.719718 | + | 0.694266i | \(0.244271\pi\) | |||||||
\(522\) | −311.741 | − | 600.002i | −0.597205 | − | 1.14943i | ||||
\(523\) | 377.284 | + | 377.284i | 0.721385 | + | 0.721385i | 0.968887 | − | 0.247502i | \(-0.0796098\pi\) |
−0.247502 | + | 0.968887i | \(0.579610\pi\) | |||||||
\(524\) | 511.417 | + | 295.267i | 0.975986 | + | 0.563486i | ||||
\(525\) | −506.597 | + | 458.478i | −0.964947 | + | 0.873291i | ||||
\(526\) | 585.779 | + | 1014.60i | 1.11365 | + | 1.92890i | ||||
\(527\) | 559.573 | + | 149.937i | 1.06181 | + | 0.284511i | ||||
\(528\) | 30.8428 | + | 24.7740i | 0.0584145 | + | 0.0469204i | ||||
\(529\) | 335.207 | + | 193.532i | 0.633661 | + | 0.365844i | ||||
\(530\) | −24.2577 | − | 74.8395i | −0.0457693 | − | 0.141207i | ||||
\(531\) | 207.786 | − | 657.208i | 0.391312 | − | 1.23768i | ||||
\(532\) | −857.415 | + | 857.415i | −1.61168 | + | 1.61168i | ||||
\(533\) | −18.0488 | + | 4.83616i | −0.0338627 | + | 0.00907348i | ||||
\(534\) | 835.146 | − | 611.848i | 1.56394 | − | 1.14578i | ||||
\(535\) | −30.8049 | − | 595.938i | −0.0575792 | − | 1.11390i | ||||
\(536\) | 113.448 | + | 196.497i | 0.211656 | + | 0.366599i | ||||
\(537\) | −97.1416 | − | 250.091i | −0.180897 | − | 0.465719i | ||||
\(538\) | −261.743 | + | 70.1337i | −0.486510 | + | 0.130360i | ||||
\(539\) | 69.6001i | 0.129128i | ||||||||
\(540\) | −756.052 | − | 598.351i | −1.40010 | − | 1.10806i | ||||
\(541\) | 861.919 | 1.59320 | 0.796598 | − | 0.604509i | \(-0.206631\pi\) | ||||
0.796598 | + | 0.604509i | \(0.206631\pi\) | |||||||
\(542\) | −83.2920 | − | 310.850i | −0.153675 | − | 0.573524i | ||||
\(543\) | −859.451 | + | 333.832i | −1.58278 | + | 0.614793i | ||||
\(544\) | −429.824 | + | 248.159i | −0.790117 | + | 0.456174i | ||||
\(545\) | −380.545 | − | 343.137i | −0.698248 | − | 0.629609i | ||||
\(546\) | 233.465 | + | 318.669i | 0.427591 | + | 0.583643i | ||||
\(547\) | 103.247 | + | 385.325i | 0.188752 | + | 0.704433i | 0.993796 | + | 0.111218i | \(0.0354750\pi\) |
−0.805044 | + | 0.593215i | \(0.797858\pi\) | |||||||
\(548\) | 787.582 | + | 787.582i | 1.43719 | + | 1.43719i | ||||
\(549\) | −137.279 | − | 621.542i | −0.250052 | − | 1.13213i | ||||
\(550\) | 26.9687 | − | 168.713i | 0.0490340 | − | 0.306751i | ||||
\(551\) | −209.725 | + | 363.254i | −0.380626 | + | 0.659264i | ||||
\(552\) | 234.747 | − | 292.252i | 0.425266 | − | 0.529442i | ||||
\(553\) | −0.549118 | + | 2.04934i | −0.000992981 | + | 0.00370585i | ||||
\(554\) | −1266.55 | + | 731.241i | −2.28619 | + | 1.31993i | ||||
\(555\) | −289.279 | − | 644.081i | −0.521223 | − | 1.16051i | ||||
\(556\) | 5.57790 | − | 9.66120i | 0.0100322 | − | 0.0173763i | ||||
\(557\) | −262.321 | + | 262.321i | −0.470954 | + | 0.470954i | −0.902223 | − | 0.431269i | \(-0.858066\pi\) |
0.431269 | + | 0.902223i | \(0.358066\pi\) | |||||||
\(558\) | −31.8487 | + | 716.499i | −0.0570765 | + | 1.28405i | ||||
\(559\) | − | 136.364i | − | 0.243943i | ||||||
\(560\) | 246.162 | − | 159.610i | 0.439576 | − | 0.285017i | ||||
\(561\) | 88.0851 | + | 120.232i | 0.157014 | + | 0.214318i | ||||
\(562\) | −616.171 | − | 165.102i | −1.09639 | − | 0.293777i | ||||
\(563\) | 235.225 | − | 877.872i | 0.417806 | − | 1.55928i | −0.361341 | − | 0.932434i | \(-0.617681\pi\) |
0.779147 | − | 0.626841i | \(-0.215653\pi\) | |||||||
\(564\) | 17.0314 | + | 7.50202i | 0.0301976 | + | 0.0133015i | ||||
\(565\) | 110.542 | + | 170.487i | 0.195650 | + | 0.301746i | ||||
\(566\) | 1155.68 | 2.04183 | ||||||||
\(567\) | 726.910 | − | 126.993i | 1.28203 | − | 0.223973i | ||||
\(568\) | 212.181 | + | 212.181i | 0.373559 | + | 0.373559i | ||||
\(569\) | −632.780 | − | 365.336i | −1.11209 | − | 0.642066i | −0.172721 | − | 0.984971i | \(-0.555256\pi\) |
−0.939370 | + | 0.342905i | \(0.888589\pi\) | |||||||
\(570\) | −94.5155 | + | 928.312i | −0.165817 | + | 1.62862i | ||||
\(571\) | −348.293 | − | 603.262i | −0.609971 | − | 1.05650i | −0.991245 | − | 0.132039i | \(-0.957848\pi\) |
0.381273 | − | 0.924462i | \(-0.375486\pi\) | |||||||
\(572\) | −61.1624 | − | 16.3884i | −0.106927 | − | 0.0286511i | ||||
\(573\) | −74.8523 | + | 485.052i | −0.130632 | + | 0.846514i | ||||
\(574\) | −113.640 | − | 65.6099i | −0.197978 | − | 0.114303i | ||||
\(575\) | −294.109 | − | 47.0132i | −0.511494 | − | 0.0817621i | ||||
\(576\) | −571.275 | − | 624.424i | −0.991797 | − | 1.08407i | ||||
\(577\) | −524.179 | + | 524.179i | −0.908455 | + | 0.908455i | −0.996148 | − | 0.0876926i | \(-0.972051\pi\) |
0.0876926 | + | 0.996148i | \(0.472051\pi\) | |||||||
\(578\) | 966.715 | − | 259.031i | 1.67252 | − | 0.448150i | ||||
\(579\) | −82.7171 | − | 758.044i | −0.142862 | − | 1.30923i | ||||
\(580\) | 538.232 | − | 596.909i | 0.927986 | − | 1.02915i | ||||
\(581\) | −723.758 | − | 1253.59i | −1.24571 | − | 2.15763i | ||||
\(582\) | −452.695 | + | 563.591i | −0.777827 | + | 0.968370i | ||||
\(583\) | −9.32225 | + | 2.49789i | −0.0159901 | + | 0.00428454i | ||||
\(584\) | − | 713.907i | − | 1.22244i | ||||||
\(585\) | 188.581 | + | 49.0726i | 0.322360 | + | 0.0838849i | ||||
\(586\) | −1000.27 | −1.70695 | ||||||||
\(587\) | −141.391 | − | 527.677i | −0.240870 | − | 0.898938i | −0.975415 | − | 0.220378i | \(-0.929271\pi\) |
0.734545 | − | 0.678560i | \(-0.237396\pi\) | |||||||
\(588\) | −111.085 | + | 719.845i | −0.188920 | + | 1.22423i | ||||
\(589\) | 385.309 | − | 222.458i | 0.654174 | − | 0.377688i | ||||
\(590\) | 1276.50 | − | 65.9843i | 2.16357 | − | 0.111838i | ||||
\(591\) | 143.639 | − | 326.096i | 0.243044 | − | 0.551770i | ||||
\(592\) | 78.4661 | + | 292.839i | 0.132544 | + | 0.494661i | ||||
\(593\) | −61.2676 | − | 61.2676i | −0.103318 | − | 0.103318i | 0.653558 | − | 0.756876i | \(-0.273275\pi\) |
−0.756876 | + | 0.653558i | \(0.773275\pi\) | |||||||
\(594\) | −121.829 | + | 138.588i | −0.205099 | + | 0.233314i | ||||
\(595\) | 1051.47 | − | 340.812i | 1.76717 | − | 0.572793i | ||||
\(596\) | 360.429 | − | 624.282i | 0.604747 | − | 1.04745i | ||||
\(597\) | −179.295 | − | 461.596i | −0.300327 | − | 0.773192i | ||||
\(598\) | −44.5696 | + | 166.336i | −0.0745310 | + | 0.278154i | ||||
\(599\) | −572.037 | + | 330.266i | −0.954987 | + | 0.551362i | −0.894626 | − | 0.446815i | \(-0.852558\pi\) |
−0.0603602 | + | 0.998177i | \(0.519225\pi\) | |||||||
\(600\) | 241.174 | − | 748.723i | 0.401956 | − | 1.24787i | ||||
\(601\) | 65.1748 | − | 112.886i | 0.108444 | − | 0.187830i | −0.806696 | − | 0.590966i | \(-0.798747\pi\) |
0.915140 | + | 0.403136i | \(0.132080\pi\) | |||||||
\(602\) | 677.143 | − | 677.143i | 1.12482 | − | 1.12482i | ||||
\(603\) | −172.774 | + | 89.7675i | −0.286524 | + | 0.148868i | ||||
\(604\) | − | 1558.31i | − | 2.57999i | ||||||
\(605\) | 571.191 | + | 121.837i | 0.944117 | + | 0.201383i | ||||
\(606\) | 617.371 | − | 67.3669i | 1.01876 | − | 0.111167i | ||||
\(607\) | 313.749 | + | 84.0689i | 0.516885 | + | 0.138499i | 0.507826 | − | 0.861460i | \(-0.330449\pi\) |
0.00905986 | + | 0.999959i | \(0.497116\pi\) | |||||||
\(608\) | −98.6554 | + | 368.187i | −0.162262 | + | 0.605571i | ||||
\(609\) | 66.7263 | + | 611.499i | 0.109567 | + | 1.00410i | ||||
\(610\) | 990.412 | − | 642.176i | 1.62363 | − | 1.05275i | ||||
\(611\) | −3.76119 | −0.00615580 | ||||||||
\(612\) | 719.130 | + | 1384.10i | 1.17505 | + | 2.26160i | ||||
\(613\) | −778.916 | − | 778.916i | −1.27066 | − | 1.27066i | −0.945741 | − | 0.324921i | \(-0.894662\pi\) |
−0.324921 | − | 0.945741i | \(-0.605338\pi\) | |||||||
\(614\) | 565.790 | + | 326.659i | 0.921482 | + | 0.532018i | ||||
\(615\) | −63.8966 | + | 10.3335i | −0.103897 | + | 0.0168025i | ||||
\(616\) | −97.8128 | − | 169.417i | −0.158787 | − | 0.275027i | ||||
\(617\) | 331.081 | + | 88.7130i | 0.536599 | + | 0.143781i | 0.516934 | − | 0.856025i | \(-0.327073\pi\) |
0.0196651 | + | 0.999807i | \(0.493740\pi\) | |||||||
\(618\) | 493.370 | − | 191.637i | 0.798334 | − | 0.310093i | ||||
\(619\) | 448.805 | + | 259.118i | 0.725049 | + | 0.418607i | 0.816608 | − | 0.577192i | \(-0.195852\pi\) |
−0.0915591 | + | 0.995800i | \(0.529185\pi\) | |||||||
\(620\) | −810.996 | + | 262.868i | −1.30806 | + | 0.423981i | ||||
\(621\) | 241.594 | + | 212.378i | 0.389040 | + | 0.341993i | ||||
\(622\) | −253.198 | + | 253.198i | −0.407070 | + | 0.407070i | ||||
\(623\) | −909.758 | + | 243.769i | −1.46029 | + | 0.391282i | ||||
\(624\) | −76.5706 | − | 33.7279i | −0.122709 | − | 0.0540511i | ||||
\(625\) | −611.711 | + | 128.197i | −0.978738 | + | 0.205116i | ||||
\(626\) | 912.840 | + | 1581.09i | 1.45821 | + | 2.52569i | ||||
\(627\) | 113.129 | + | 17.4579i | 0.180430 | + | 0.0278435i | ||||
\(628\) | −1831.53 | + | 490.756i | −2.91645 | + | 0.781459i | ||||
\(629\) | 1142.21i | 1.81591i | ||||||||
\(630\) | 692.753 | + | 1180.11i | 1.09961 | + | 1.87319i | ||||
\(631\) | −48.4016 | −0.0767062 | −0.0383531 | − | 0.999264i | \(-0.512211\pi\) | ||||
−0.0383531 | + | 0.999264i | \(0.512211\pi\) | |||||||
\(632\) | −0.632177 | − | 2.35932i | −0.00100028 | − | 0.00373309i | ||||
\(633\) | −27.4717 | − | 22.0662i | −0.0433992 | − | 0.0348597i | ||||
\(634\) | −1261.33 | + | 728.230i | −1.98948 | + | 1.14863i | ||||
\(635\) | 29.6959 | + | 574.483i | 0.0467651 | + | 0.904698i | ||||
\(636\) | −100.403 | + | 10.9559i | −0.157866 | + | 0.0172262i | ||||
\(637\) | −38.0990 | − | 142.187i | −0.0598100 | − | 0.223214i | ||||
\(638\) | −108.766 | − | 108.766i | −0.170480 | − | 0.170480i | ||||
\(639\) | −189.982 | + | 173.811i | −0.297312 | + | 0.272005i | ||||
\(640\) | 527.538 | − | 1033.53i | 0.824278 | − | 1.61488i | ||||
\(641\) | −313.217 | + | 542.507i | −0.488637 | + | 0.846345i | −0.999915 | − | 0.0130711i | \(-0.995839\pi\) |
0.511277 | + | 0.859416i | \(0.329173\pi\) | |||||||
\(642\) | −1181.15 | − | 182.272i | −1.83979 | − | 0.283913i | ||||
\(643\) | 125.261 | − | 467.479i | 0.194807 | − | 0.727028i | −0.797510 | − | 0.603305i | \(-0.793850\pi\) |
0.992317 | − | 0.123723i | \(-0.0394833\pi\) | |||||||
\(644\) | −671.313 | + | 387.583i | −1.04241 | + | 0.601836i | ||||
\(645\) | 47.8465 | − | 469.938i | 0.0741806 | − | 0.728586i | ||||
\(646\) | 754.755 | − | 1307.27i | 1.16835 | − | 2.02364i | ||||
\(647\) | −388.357 | + | 388.357i | −0.600242 | + | 0.600242i | −0.940377 | − | 0.340135i | \(-0.889527\pi\) |
0.340135 | + | 0.940377i | \(0.389527\pi\) | |||||||
\(648\) | −651.642 | + | 545.045i | −1.00562 | + | 0.841118i | ||||
\(649\) | − | 156.803i | − | 0.241607i | ||||||
\(650\) | 37.2584 | + | 359.430i | 0.0573206 | + | 0.552969i | ||||
\(651\) | 263.017 | − | 597.114i | 0.404021 | − | 0.917226i | ||||
\(652\) | 1571.50 | + | 421.082i | 2.41027 | + | 0.645831i | ||||
\(653\) | 51.2298 | − | 191.192i | 0.0784530 | − | 0.292791i | −0.915541 | − | 0.402225i | \(-0.868237\pi\) |
0.993994 | + | 0.109434i | \(0.0349038\pi\) | |||||||
\(654\) | −827.839 | + | 606.495i | −1.26581 | + | 0.927363i | ||||
\(655\) | −404.324 | − | 86.2437i | −0.617289 | − | 0.131670i | ||||
\(656\) | 27.7925 | 0.0423666 | ||||||||
\(657\) | 612.010 | + | 27.2041i | 0.931523 | + | 0.0414066i | ||||
\(658\) | −18.6769 | − | 18.6769i | −0.0283843 | − | 0.0283843i | ||||
\(659\) | −97.2838 | − | 56.1668i | −0.147623 | − | 0.0852304i | 0.424369 | − | 0.905489i | \(-0.360496\pi\) |
−0.571992 | + | 0.820259i | \(0.693829\pi\) | |||||||
\(660\) | −205.027 | − | 77.9378i | −0.310647 | − | 0.118088i | ||||
\(661\) | 55.4873 | + | 96.1067i | 0.0839444 | + | 0.145396i | 0.904941 | − | 0.425537i | \(-0.139915\pi\) |
−0.820997 | + | 0.570933i | \(0.806582\pi\) | |||||||
\(662\) | −1890.38 | − | 506.525i | −2.85556 | − | 0.765144i | ||||
\(663\) | −245.765 | − | 197.407i | −0.370687 | − | 0.297748i | ||||
\(664\) | 1443.20 | + | 833.232i | 2.17349 | + | 1.25487i | ||||
\(665\) | 385.930 | − | 756.094i | 0.580346 | − | 1.13698i | ||||
\(666\) | −1380.81 | + | 304.976i | −2.07329 | + | 0.457923i | ||||
\(667\) | −189.607 | + | 189.607i | −0.284268 | + | 0.284268i | ||||
\(668\) | 411.542 | − | 110.272i | 0.616081 | − | 0.165078i | ||||
\(669\) | −30.9924 | + | 22.7058i | −0.0463265 | + | 0.0339400i | ||||
\(670\) | −268.149 | − | 241.789i | −0.400222 | − | 0.360880i | ||||
\(671\) | −72.4012 | − | 125.403i | −0.107900 | − | 0.186889i | ||||
\(672\) | 202.397 | + | 521.071i | 0.301186 | + | 0.775403i | ||||
\(673\) | −202.929 | + | 54.3747i | −0.301529 | + | 0.0807945i | −0.406412 | − | 0.913690i | \(-0.633220\pi\) |
0.104882 | + | 0.994485i | \(0.466553\pi\) | |||||||
\(674\) | − | 1588.56i | − | 2.35692i | ||||||
\(675\) | 632.667 | + | 235.282i | 0.937285 | + | 0.348565i | ||||
\(676\) | −1073.09 | −1.58741 | ||||||||
\(677\) | 193.957 | + | 723.857i | 0.286495 | + | 1.06921i | 0.947740 | + | 0.319043i | \(0.103361\pi\) |
−0.661246 | + | 0.750169i | \(0.729972\pi\) | |||||||
\(678\) | 379.331 | − | 147.342i | 0.559485 | − | 0.217318i | ||||
\(679\) | 569.537 | − | 328.822i | 0.838788 | − | 0.484275i | ||||
\(680\) | −852.150 | + | 945.049i | −1.25316 | + | 1.38978i | ||||
\(681\) | 784.789 | + | 1071.20i | 1.15241 | + | 1.57298i | ||||
\(682\) | 42.2282 | + | 157.598i | 0.0619182 | + | 0.231082i | ||||
\(683\) | 441.268 | + | 441.268i | 0.646074 | + | 0.646074i | 0.952042 | − | 0.305968i | \(-0.0989800\pi\) |
−0.305968 | + | 0.952042i | \(0.598980\pi\) | |||||||
\(684\) | 1142.18 | + | 361.119i | 1.66986 | + | 0.527952i | ||||
\(685\) | −694.513 | − | 354.497i | −1.01389 | − | 0.517514i | ||||
\(686\) | −228.158 | + | 395.181i | −0.332592 | + | 0.576066i | ||||
\(687\) | 356.339 | − | 443.631i | 0.518688 | − | 0.645751i | ||||
\(688\) | −52.4952 | + | 195.915i | −0.0763012 | + | 0.284760i | ||||
\(689\) | 17.6772 | − | 10.2060i | 0.0256564 | − | 0.0148127i | ||||
\(690\) | −211.958 | + | 557.587i | −0.307185 | + | 0.808098i | ||||
\(691\) | 396.083 | − | 686.036i | 0.573202 | − | 0.992816i | −0.423032 | − | 0.906115i | \(-0.639034\pi\) |
0.996234 | − | 0.0867010i | \(-0.0276325\pi\) | |||||||
\(692\) | 489.571 | − | 489.571i | 0.707473 | − | 0.707473i | ||||
\(693\) | 148.963 | − | 77.3961i | 0.214954 | − | 0.111683i | ||||
\(694\) | 586.222i | 0.844700i | ||||||||
\(695\) | −1.62923 | + | 7.63810i | −0.00234422 | + | 0.0109901i | ||||
\(696\) | −418.524 | − | 571.266i | −0.601327 | − | 0.820785i | ||||
\(697\) | 101.142 | + | 27.1009i | 0.145110 | + | 0.0388822i | ||||
\(698\) | 297.427 | − | 1110.01i | 0.426113 | − | 1.59027i | ||||
\(699\) | 243.799 | + | 107.389i | 0.348783 | + | 0.153632i | ||||
\(700\) | −1025.47 | + | 1262.66i | −1.46496 | + | 1.80380i | ||||
\(701\) | −1185.25 | −1.69080 | −0.845401 | − | 0.534133i | \(-0.820638\pi\) | ||||
−0.845401 | + | 0.534133i | \(0.820638\pi\) | |||||||
\(702\) | 173.023 | − | 349.813i | 0.246471 | − | 0.498309i | ||||
\(703\) | 620.290 | + | 620.290i | 0.882348 | + | 0.882348i | ||||
\(704\) | −166.736 | − | 96.2650i | −0.236841 | − | 0.136740i | ||||
\(705\) | −12.9618 | − | 1.31970i | −0.0183855 | − | 0.00187191i | ||||
\(706\) | 450.005 | + | 779.431i | 0.637401 | + | 1.10401i | ||||
\(707\) | −545.733 | − | 146.229i | −0.771899 | − | 0.206830i | ||||
\(708\) | 250.265 | − | 1621.75i | 0.353481 | − | 2.29060i | ||||
\(709\) | 237.674 | + | 137.221i | 0.335224 | + | 0.193542i | 0.658158 | − | 0.752880i | \(-0.271336\pi\) |
−0.322934 | + | 0.946421i | \(0.604669\pi\) | |||||||
\(710\) | −425.306 | − | 217.087i | −0.599022 | − | 0.305756i | ||||
\(711\) | 2.04666 | − | 0.452042i | 0.00287856 | − | 0.000635783i | ||||
\(712\) | 766.725 | − | 766.725i | 1.07686 | − | 1.07686i | ||||
\(713\) | 274.732 | − | 73.6143i | 0.385319 | − | 0.103246i | ||||
\(714\) | −240.133 | − | 2200.65i | −0.336321 | − | 3.08215i | ||||
\(715\) | 44.2698 | − | 2.28837i | 0.0619159 | − | 0.00320052i | ||||
\(716\) | −319.362 | − | 553.152i | −0.446037 | − | 0.772558i | ||||
\(717\) | 125.634 | − | 156.411i | 0.175222 | − | 0.218146i | ||||
\(718\) | 1326.57 | − | 355.454i | 1.84759 | − | 0.495061i | ||||
\(719\) | − | 1409.12i | − | 1.95983i | −0.199416 | − | 0.979915i | \(-0.563904\pi\) | ||
0.199416 | − | 0.979915i | \(-0.436096\pi\) | |||||||
\(720\) | −252.043 | − | 143.099i | −0.350060 | − | 0.198749i | ||||
\(721\) | −481.512 | −0.667839 | ||||||||
\(722\) | 11.8264 | + | 44.1367i | 0.0163800 | + | 0.0611311i | ||||
\(723\) | −27.1503 | + | 175.937i | −0.0375523 | + | 0.243344i | ||||
\(724\) | −1900.94 | + | 1097.51i | −2.62560 | + | 1.51589i | ||||
\(725\) | −229.597 | + | 513.706i | −0.316685 | + | 0.708560i | ||||
\(726\) | 471.517 | − | 1070.46i | 0.649473 | − | 1.47446i | ||||
\(727\) | −184.607 | − | 688.962i | −0.253930 | − | 0.947678i | −0.968683 | − | 0.248302i | \(-0.920128\pi\) |
0.714753 | − | 0.699377i | \(-0.246539\pi\) | |||||||
\(728\) | 292.562 | + | 292.562i | 0.401870 | + | 0.401870i | ||||
\(729\) | −442.419 | − | 579.402i | −0.606884 | − | 0.794790i | ||||
\(730\) | 350.287 | + | 1080.70i | 0.479845 | + | 1.48041i | ||||
\(731\) | −382.079 | + | 661.780i | −0.522680 | + | 0.905308i | ||||
\(732\) | −548.667 | − | 1412.54i | −0.749545 | − | 1.92970i | ||||
\(733\) | −230.005 | + | 858.390i | −0.313786 | + | 1.17106i | 0.611329 | + | 0.791377i | \(0.290635\pi\) |
−0.925115 | + | 0.379688i | \(0.876031\pi\) | |||||||
\(734\) | 1876.26 | − | 1083.26i | 2.55622 | − | 1.47583i | ||||
\(735\) | −81.4068 | − | 503.373i | −0.110758 | − | 0.684861i | ||||
\(736\) | −121.838 | + | 211.030i | −0.165541 | + | 0.286725i | ||||
\(737\) | −31.3198 | + | 31.3198i | −0.0424964 | + | 0.0424964i | ||||
\(738\) | −5.75659 | + | 129.506i | −0.00780025 | + | 0.175482i | ||||
\(739\) | 719.160i | 0.973153i | 0.873638 | + | 0.486577i | \(0.161755\pi\) | ||||
−0.873638 | + | 0.486577i | \(0.838245\pi\) | |||||||
\(740\) | −914.481 | − | 1410.38i | −1.23579 | − | 1.90592i | ||||
\(741\) | −240.670 | + | 26.2617i | −0.324791 | + | 0.0354409i | ||||
\(742\) | 138.459 | + | 37.1000i | 0.186603 | + | 0.0500000i | ||||
\(743\) | −43.1096 | + | 160.887i | −0.0580210 | + | 0.216537i | −0.988849 | − | 0.148919i | \(-0.952421\pi\) |
0.930828 | + | 0.365457i | \(0.119087\pi\) | |||||||
\(744\) | 81.4830 | + | 746.734i | 0.109520 | + | 1.00368i | ||||
\(745\) | −105.277 | + | 493.554i | −0.141311 | + | 0.662489i | ||||
\(746\) | 370.523 | 0.496679 | ||||||||
\(747\) | −769.299 | + | 1205.46i | −1.02985 | + | 1.61374i | ||||
\(748\) | 250.904 | + | 250.904i | 0.335433 | + | 0.335433i | ||||
\(749\) | 941.597 | + | 543.631i | 1.25714 | + | 0.725809i | ||||
\(750\) | 2.28577 | + | 1251.74i | 0.00304770 | + | 1.66898i | ||||
\(751\) | 241.781 | + | 418.776i | 0.321945 | + | 0.557625i | 0.980889 | − | 0.194567i | \(-0.0623301\pi\) |
−0.658945 | + | 0.752192i | \(0.728997\pi\) | |||||||
\(752\) | 5.40371 | + | 1.44792i | 0.00718578 | + | 0.00192542i | ||||
\(753\) | 247.704 | − | 96.2146i | 0.328957 | − | 0.127775i | ||||
\(754\) | 281.739 | + | 162.662i | 0.373659 | + | 0.215732i | ||||
\(755\) | 336.378 | + | 1037.79i | 0.445534 | + | 1.37455i | ||||
\(756\) | 1664.19 | − | 562.723i | 2.20131 | − | 0.744343i | ||||
\(757\) | 144.792 | − | 144.792i | 0.191270 | − | 0.191270i | −0.604974 | − | 0.796245i | \(-0.706817\pi\) |
0.796245 | + | 0.604974i | \(0.206817\pi\) | |||||||
\(758\) | −1022.33 | + | 273.932i | −1.34872 | + | 0.361388i | ||||
\(759\) | 66.9680 | + | 29.4981i | 0.0882319 | + | 0.0388645i | ||||
\(760\) | 50.4504 | + | 975.992i | 0.0663821 | + | 1.28420i | ||||
\(761\) | 149.929 | + | 259.685i | 0.197016 | + | 0.341241i | 0.947559 | − | 0.319580i | \(-0.103542\pi\) |
−0.750544 | + | 0.660821i | \(0.770208\pi\) | |||||||
\(762\) | 1138.62 | + | 175.710i | 1.49426 | + | 0.230591i | ||||
\(763\) | 901.799 | − | 241.636i | 1.18191 | − | 0.316692i | ||||
\(764\) | 1168.43i | 1.52935i | ||||||||
\(765\) | −777.690 | − | 766.534i | −1.01659 | − | 1.00201i | ||||
\(766\) | 297.459 | 0.388328 | ||||||||
\(767\) | 85.8336 | + | 320.335i | 0.111908 | + | 0.417647i | ||||
\(768\) | −932.097 | − | 748.691i | −1.21367 | − | 0.974858i | ||||
\(769\) | −96.6554 | + | 55.8040i | −0.125690 | + | 0.0725670i | −0.561527 | − | 0.827459i | \(-0.689786\pi\) |
0.435837 | + | 0.900026i | \(0.356452\pi\) | |||||||
\(770\) | 231.194 | + | 208.467i | 0.300251 | + | 0.270736i | ||||
\(771\) | −468.740 | + | 51.1485i | −0.607964 | + | 0.0663405i | ||||
\(772\) | −469.854 | − | 1753.52i | −0.608619 | − | 2.27140i | ||||
\(773\) | −43.6287 | − | 43.6287i | −0.0564408 | − | 0.0564408i | 0.678323 | − | 0.734764i | \(-0.262707\pi\) |
−0.734764 | + | 0.678323i | \(0.762707\pi\) | |||||||
\(774\) | −902.039 | − | 285.193i | −1.16543 | − | 0.368467i | ||||
\(775\) | 483.355 | − | 350.124i | 0.623684 | − | 0.451773i | ||||
\(776\) | −378.559 | + | 655.684i | −0.487834 | + | 0.844954i | ||||
\(777\) | 1271.41 | + | 196.201i | 1.63631 | + | 0.252512i | ||||
\(778\) | −63.9127 | + | 238.526i | −0.0821500 | + | 0.306588i | ||||
\(779\) | 69.6438 | − | 40.2089i | 0.0894015 | − | 0.0516160i | ||||
\(780\) | 461.516 | + | 46.9891i | 0.591688 | + | 0.0602424i | ||||
\(781\) | −29.2888 | + | 50.7297i | −0.0375016 | + | 0.0649547i | ||||
\(782\) | 682.353 | − | 682.353i | 0.872574 | − | 0.872574i | ||||
\(783\) | 505.678 | − | 337.019i | 0.645821 | − | 0.430420i | ||||
\(784\) | 218.947i | 0.279270i | ||||||||
\(785\) | 1113.81 | − | 722.183i | 1.41886 | − | 0.919978i | ||||
\(786\) | −333.769 | + | 757.737i | −0.424642 | + | 0.964042i | ||||
\(787\) | −1190.57 | − | 319.011i | −1.51279 | − | 0.405351i | −0.595430 | − | 0.803407i | \(-0.703018\pi\) |
−0.917361 | + | 0.398056i | \(0.869685\pi\) | |||||||
\(788\) | 219.559 | − | 819.404i | 0.278628 | − | 1.03985i | ||||
\(789\) | −849.381 | + | 622.277i | −1.07653 | + | 0.788691i | ||||
\(790\) | 2.11460 | + | 3.26130i | 0.00267671 | + | 0.00412823i | ||||
\(791\) | −370.213 | −0.468032 | ||||||||
\(792\) | −103.967 | + | 162.913i | −0.131272 | + | 0.205698i | ||||
\(793\) | 216.555 | + | 216.555i | 0.273083 | + | 0.273083i | ||||
\(794\) | 1355.89 | + | 782.824i | 1.70767 | + | 0.985925i | ||||
\(795\) | 64.5002 | − | 28.9692i | 0.0811323 | − | 0.0364393i | ||||
\(796\) | −589.451 | − | 1020.96i | −0.740516 | − | 1.28261i | ||||
\(797\) | 735.470 | + | 197.069i | 0.922799 | + | 0.247263i | 0.688781 | − | 0.724969i | \(-0.258146\pi\) |
0.234017 | + | 0.972232i | \(0.424813\pi\) | |||||||
\(798\) | −1325.50 | − | 1064.69i | −1.66103 | − | 1.33419i | ||||
\(799\) | 18.2532 | + | 10.5385i | 0.0228450 | + | 0.0131896i | ||||
\(800\) | −80.7119 | + | 504.925i | −0.100890 | + | 0.631156i | ||||
\(801\) | 628.073 | + | 686.507i | 0.784112 | + | 0.857063i | ||||
\(802\) | 1531.17 | − | 1531.17i | 1.90920 | − | 1.90920i | ||||
\(803\) | 134.615 | − | 36.0700i | 0.167640 | − | 0.0449191i | ||||
\(804\) | −373.916 | + | 273.940i | −0.465069 | + | 0.340721i | ||||
\(805\) | 363.410 | − | 403.028i | 0.451441 | − | 0.500656i | ||||
\(806\) | −172.538 | − | 298.844i | −0.214066 | − | 0.370774i | ||||
\(807\) | −88.1785 | − | 227.015i | −0.109267 | − | 0.281308i | ||||
\(808\) | 628.279 | − | 168.347i | 0.777573 | − | 0.208350i | ||||
\(809\) | − | 225.758i | − | 0.279058i | −0.990218 | − | 0.139529i | \(-0.955441\pi\) | ||
0.990218 | − | 0.139529i | \(-0.0445589\pi\) | |||||||
\(810\) | 719.010 | − | 1144.81i | 0.887667 | − | 1.41335i | ||||
\(811\) | −149.469 | −0.184303 | −0.0921513 | − | 0.995745i | \(-0.529374\pi\) | ||||
−0.0921513 | + | 0.995745i | \(0.529374\pi\) | |||||||
\(812\) | 379.022 | + | 1414.53i | 0.466776 | + | 1.74203i | ||||
\(813\) | 269.607 | − | 104.722i | 0.331620 | − | 0.128810i | ||||
\(814\) | −278.593 | + | 160.845i | −0.342251 | + | 0.197599i | ||||
\(815\) | −1137.46 | + | 58.7971i | −1.39566 | + | 0.0721437i | ||||
\(816\) | 277.097 | + | 378.225i | 0.339580 | + | 0.463511i | ||||
\(817\) | 151.895 | + | 566.881i | 0.185918 | + | 0.693856i | ||||
\(818\) | −1486.69 | − | 1486.69i | −1.81747 | − | 1.81747i | ||||
\(819\) | −261.953 | + | 239.656i | −0.319844 | + | 0.292620i | ||||
\(820\) | −146.586 | + | 47.5130i | −0.178764 | + | 0.0579426i | ||||
\(821\) | 2.78890 | − | 4.83052i | 0.00339696 | − | 0.00588370i | −0.864322 | − | 0.502939i | \(-0.832252\pi\) |
0.867719 | + | 0.497055i | \(0.165585\pi\) | |||||||
\(822\) | −977.970 | + | 1217.54i | −1.18974 | + | 1.48120i | ||||
\(823\) | −167.604 | + | 625.506i | −0.203650 | + | 0.760032i | 0.786207 | + | 0.617963i | \(0.212042\pi\) |
−0.989857 | + | 0.142069i | \(0.954625\pi\) | |||||||
\(824\) | 480.076 | − | 277.172i | 0.582617 | − | 0.336374i | ||||
\(825\) | 153.365 | + | 7.64690i | 0.185897 | + | 0.00926897i | ||||
\(826\) | −1164.46 | + | 2016.91i | −1.40976 | + | 2.44178i | ||||
\(827\) | 230.120 | − | 230.120i | 0.278258 | − | 0.278258i | −0.554155 | − | 0.832413i | \(-0.686959\pi\) |
0.832413 | + | 0.554155i | \(0.186959\pi\) | |||||||
\(828\) | 645.541 | + | 411.971i | 0.779639 | + | 0.497549i | ||||
\(829\) | − | 1504.68i | − | 1.81505i | −0.419994 | − | 0.907527i | \(-0.637968\pi\) | ||
0.419994 | − | 0.907527i | \(-0.362032\pi\) | |||||||
\(830\) | −2593.53 | − | 553.208i | −3.12473 | − | 0.666515i | ||||
\(831\) | −776.803 | − | 1060.30i | −0.934781 | − | 1.27593i | ||||
\(832\) | 393.323 | + | 105.390i | 0.472744 | + | 0.126671i | ||||
\(833\) | −213.499 | + | 796.788i | −0.256301 | + | 0.956528i | ||||
\(834\) | 14.3145 | + | 6.30524i | 0.0171636 | + | 0.00756024i | ||||
\(835\) | −250.271 | + | 162.274i | −0.299725 | + | 0.194340i | ||||
\(836\) | 272.513 | 0.325973 | ||||||||
\(837\) | −643.258 | + | 41.3979i | −0.768528 | + | 0.0494598i | ||||
\(838\) | −417.300 | − | 417.300i | −0.497971 | − | 0.497971i | ||||
\(839\) | −915.370 | − | 528.489i | −1.09103 | − | 0.629904i | −0.157176 | − | 0.987571i | \(-0.550239\pi\) |
−0.933849 | + | 0.357667i | \(0.883572\pi\) | |||||||
\(840\) | 905.572 | + | 1110.88i | 1.07806 | + | 1.32247i | ||||
\(841\) | −167.214 | − | 289.622i | −0.198827 | − | 0.344378i | ||||
\(842\) | 288.104 | + | 77.1972i | 0.342166 | + | 0.0916831i | ||||
\(843\) | 87.4384 | − | 566.612i | 0.103723 | − | 0.672137i | ||||
\(844\) | −72.6483 | − | 41.9435i | −0.0860762 | − | 0.0496961i | ||||
\(845\) | 714.642 | − | 231.637i | 0.845730 | − | 0.274127i | ||||
\(846\) | −7.86618 | + | 24.8800i | −0.00929809 | + | 0.0294089i | ||||
\(847\) | −752.457 | + | 752.457i | −0.888379 | + | 0.888379i | ||||
\(848\) | −29.3258 | + | 7.85783i | −0.0345823 | + | 0.00926631i | ||||
\(849\) | 112.669 | + | 1032.54i | 0.132708 | + | 1.21618i | ||||
\(850\) | 826.269 | − | 1848.72i | 0.972081 | − | 2.17496i | ||||
\(851\) | 280.394 | + | 485.656i | 0.329487 | + | 0.570689i | ||||
\(852\) | −383.888 | + | 477.929i | −0.450573 | + | 0.560949i | ||||
\(853\) | −715.340 | + | 191.675i | −0.838617 | + | 0.224707i | −0.652469 | − | 0.757815i | \(-0.726267\pi\) |
−0.186148 | + | 0.982522i | \(0.559600\pi\) | |||||||
\(854\) | 2150.69i | 2.51837i | ||||||||
\(855\) | −838.611 | + | 6.05846i | −0.980831 | + | 0.00708592i | ||||
\(856\) | −1251.72 | −1.46229 | ||||||||
\(857\) | −326.446 | − | 1218.31i | −0.380918 | − | 1.42160i | −0.844503 | − | 0.535551i | \(-0.820104\pi\) |
0.463585 | − | 0.886052i | \(-0.346563\pi\) | |||||||
\(858\) | 13.5403 | − | 87.7427i | 0.0157812 | − | 0.102264i | ||||
\(859\) | 37.7603 | − | 21.8009i | 0.0439584 | − | 0.0253794i | −0.477860 | − | 0.878436i | \(-0.658587\pi\) |
0.521818 | + | 0.853057i | \(0.325254\pi\) | |||||||
\(860\) | −58.0525 | − | 1123.06i | −0.0675029 | − | 1.30588i | ||||
\(861\) | 47.5399 | − | 107.927i | 0.0552148 | − | 0.125351i | ||||
\(862\) | 560.142 | + | 2090.48i | 0.649817 | + | 2.42515i | ||||
\(863\) | −274.423 | − | 274.423i | −0.317988 | − | 0.317988i | 0.530006 | − | 0.847994i | \(-0.322190\pi\) |
−0.847994 | + | 0.530006i | \(0.822190\pi\) | |||||||
\(864\) | 364.609 | − | 414.767i | 0.422001 | − | 0.480054i | ||||
\(865\) | −220.360 | + | 431.718i | −0.254751 | + | 0.499096i | ||||
\(866\) | 1135.94 | − | 1967.51i | 1.31171 | − | 2.27195i | ||||
\(867\) | 325.677 | + | 838.454i | 0.375637 | + | 0.967075i | ||||
\(868\) | 402.033 | − | 1500.41i | 0.463172 | − | 1.72858i | ||||
\(869\) | 0.412935 | − | 0.238408i | 0.000475184 | − | 0.000274348i | ||||
\(870\) | 913.852 | + | 659.419i | 1.05041 | + | 0.757953i | ||||
\(871\) | 46.8394 | − | 81.1282i | 0.0537766 | − | 0.0931438i | ||||
\(872\) | −760.017 | + | 760.017i | −0.871579 | + | 0.871579i | ||||
\(873\) | −547.673 | − | 349.513i | −0.627346 | − | 0.400359i | ||||
\(874\) | − | 741.121i | − | 0.847965i | ||||||
\(875\) | 410.374 | − | 1062.25i | 0.468999 | − | 1.21400i | ||||
\(876\) | 1449.84 | − | 158.205i | 1.65506 | − | 0.180599i | ||||
\(877\) | 171.710 | + | 46.0094i | 0.195792 | + | 0.0524623i | 0.355382 | − | 0.934721i | \(-0.384351\pi\) |
−0.159590 | + | 0.987183i | \(0.551017\pi\) | |||||||
\(878\) | −542.205 | + | 2023.53i | −0.617545 | + | 2.30471i | ||||
\(879\) | −97.5184 | − | 893.687i | −0.110942 | − | 1.01671i | ||||
\(880\) | −64.4835 | − | 13.7545i | −0.0732767 | − | 0.0156302i | ||||
\(881\) | −1000.82 | −1.13600 | −0.568000 | − | 0.823029i | \(-0.692282\pi\) | ||||
−0.568000 | + | 0.823029i | \(0.692282\pi\) | |||||||
\(882\) | −1020.24 | − | 45.3500i | −1.15673 | − | 0.0514172i | ||||
\(883\) | 766.494 | + | 766.494i | 0.868057 | + | 0.868057i | 0.992257 | − | 0.124201i | \(-0.0396366\pi\) |
−0.124201 | + | 0.992257i | \(0.539637\pi\) | |||||||
\(884\) | −649.920 | − | 375.232i | −0.735204 | − | 0.424470i | ||||
\(885\) | 183.402 | + | 1134.05i | 0.207234 | + | 1.28142i | ||||
\(886\) | −897.522 | − | 1554.55i | −1.01300 | − | 1.75457i | ||||
\(887\) | −621.429 | − | 166.511i | −0.700596 | − | 0.187724i | −0.109099 | − | 0.994031i | \(-0.534796\pi\) |
−0.591498 | + | 0.806307i | \(0.701463\pi\) | |||||||
\(888\) | −1380.56 | + | 536.244i | −1.55468 | + | 0.603878i | ||||
\(889\) | −907.698 | − | 524.060i | −1.02103 | − | 0.589494i | ||||
\(890\) | −784.452 | + | 1536.86i | −0.881406 | + | 1.72681i | ||||
\(891\) | −135.698 | − | 95.3361i | −0.152299 | − | 0.106999i | ||||
\(892\) | −64.6759 | + | 64.6759i | −0.0725067 | + | 0.0725067i | ||||
\(893\) | 15.6357 | − | 4.18956i | 0.0175091 | − | 0.00469156i | ||||
\(894\) | 924.963 | + | 407.428i | 1.03463 | + | 0.455736i | ||||
\(895\) | 332.089 | + | 299.444i | 0.371049 | + | 0.334574i | ||||
\(896\) | 1057.12 | + | 1830.98i | 1.17982 | + | 2.04350i | ||||
\(897\) | −152.957 | − | 23.6041i | −0.170521 | − | 0.0263145i | ||||
\(898\) | 812.743 | − | 217.774i | 0.905058 | − | 0.242510i | ||||
\(899\) | − | 537.328i | − | 0.597696i | ||||||
\(900\) | 1573.99 | + | 323.867i | 1.74888 | + | 0.359852i | ||||
\(901\) | −114.384 | −0.126952 | ||||||||
\(902\) | 7.63268 | + | 28.4855i | 0.00846195 | + | 0.0315804i | ||||
\(903\) | 671.006 | + | 538.974i | 0.743086 | + | 0.596871i | ||||
\(904\) | 369.109 | − | 213.105i | 0.408307 | − | 0.235736i | ||||
\(905\) | 1029.06 | − | 1141.24i | 1.13708 | − | 1.26104i | ||||
\(906\) | 2172.02 | − | 237.009i | 2.39738 | − | 0.261600i | ||||
\(907\) | −170.993 | − | 638.156i | −0.188526 | − | 0.703589i | −0.993848 | − | 0.110752i | \(-0.964674\pi\) |
0.805322 | − | 0.592838i | \(-0.201992\pi\) | |||||||
\(908\) | 2235.42 | + | 2235.42i | 2.46191 | + | 2.46191i | ||||
\(909\) | 120.377 | + | 545.019i | 0.132428 | + | 0.599581i | ||||
\(910\) | −586.423 | − | 299.326i | −0.644421 | − | 0.328929i | ||||
\(911\) | 536.476 | − | 929.204i | 0.588887 | − | 1.01998i | −0.405491 | − | 0.914099i | \(-0.632900\pi\) |
0.994379 | − | 0.105884i | \(-0.0337671\pi\) | |||||||
\(912\) | 355.881 | + | 54.9189i | 0.390221 | + | 0.0602181i | ||||
\(913\) | −84.1979 | + | 314.231i | −0.0922211 | + | 0.344174i | ||||
\(914\) | −853.309 | + | 492.658i | −0.933598 | + | 0.539013i | ||||
\(915\) | 670.307 | + | 822.273i | 0.732576 | + | 0.898659i | ||||
\(916\) | 677.331 | − | 1173.17i | 0.739444 | − | 1.28075i | ||||
\(917\) | 532.635 | − | 532.635i | 0.580846 | − | 0.580846i | ||||
\(918\) | −1819.82 | + | 1212.86i | −1.98238 | + | 1.32120i | ||||
\(919\) | − | 728.665i | − | 0.792889i | −0.918059 | − | 0.396444i | \(-0.870244\pi\) | ||
0.918059 | − | 0.396444i | \(-0.129756\pi\) | |||||||
\(920\) | −130.332 | + | 611.015i | −0.141665 | + | 0.664147i | ||||
\(921\) | −236.692 | + | 537.349i | −0.256995 | + | 0.583441i | ||||
\(922\) | 1643.59 | + | 440.399i | 1.78264 | + | 0.477656i | ||||
\(923\) | 32.0652 | − | 119.669i | 0.0347402 | − | 0.129652i | ||||
\(924\) | 322.384 | − | 236.187i | 0.348901 | − | 0.255613i | ||||
\(925\) | 913.461 | + | 741.870i | 0.987526 | + | 0.802022i | ||||
\(926\) | −985.543 | −1.06430 | ||||||||
\(927\) | 219.317 | + | 422.117i | 0.236588 | + | 0.455358i | ||||
\(928\) | 325.515 | + | 325.515i | 0.350771 | + | 0.350771i | ||||
\(929\) | −844.876 | − | 487.790i | −0.909447 | − | 0.525070i | −0.0291940 | − | 0.999574i | \(-0.509294\pi\) |
−0.880253 | + | 0.474504i | \(0.842627\pi\) | |||||||
\(930\) | −489.742 | − | 1090.41i | −0.526604 | − | 1.17249i | ||||
\(931\) | 316.763 | + | 548.649i | 0.340239 | + | 0.589312i | ||||
\(932\) | 612.611 | + | 164.149i | 0.657308 | + | 0.176125i | ||||
\(933\) | −250.903 | − | 201.534i | −0.268921 | − | 0.216006i | ||||
\(934\) | −1536.11 | − | 886.871i | −1.64465 | − | 0.949541i | ||||
\(935\) | −221.255 | − | 112.934i | −0.236636 | − | 0.120785i | ||||
\(936\) | 123.219 | − | 389.729i | 0.131644 | − | 0.416377i | ||||
\(937\) | −141.251 | + | 141.251i | −0.150749 | + | 0.150749i | −0.778452 | − | 0.627704i | \(-0.783995\pi\) |
0.627704 | + | 0.778452i | \(0.283995\pi\) | |||||||
\(938\) | 635.447 | − | 170.268i | 0.677449 | − | 0.181522i | ||||
\(939\) | −1323.62 | + | 969.716i | −1.40961 | + | 1.03271i | ||||
\(940\) | −30.9761 | + | 1.60120i | −0.0329533 | + | 0.00170340i | ||||
\(941\) | 557.909 | + | 966.326i | 0.592889 | + | 1.02691i | 0.993841 | + | 0.110815i | \(0.0353461\pi\) |
−0.400952 | + | 0.916099i | \(0.631321\pi\) | |||||||
\(942\) | −962.596 | − | 2478.20i | −1.02186 | − | 2.63079i | ||||
\(943\) | 49.6574 | − | 13.3057i | 0.0526589 | − | 0.0141099i | ||||
\(944\) | − | 493.269i | − | 0.522531i | ||||||
\(945\) | −986.828 | + | 733.989i | −1.04426 | + | 0.776708i | ||||
\(946\) | −215.217 | −0.227502 | ||||||||
\(947\) | 205.274 | + | 766.094i | 0.216763 | + | 0.808969i | 0.985539 | + | 0.169451i | \(0.0541994\pi\) |
−0.768776 | + | 0.639518i | \(0.779134\pi\) | |||||||
\(948\) | 4.65132 | − | 1.80669i | 0.00490646 | − | 0.00190579i | ||||
\(949\) | −255.263 | + | 147.376i | −0.268981 | + | 0.155296i | ||||
\(950\) | −555.253 | − | 1452.68i | −0.584477 | − | 1.52914i | ||||
\(951\) | −773.604 | − | 1055.93i | −0.813464 | − | 1.11034i | ||||
\(952\) | −600.082 | − | 2239.54i | −0.630338 | − | 2.35245i | ||||
\(953\) | −80.4623 | − | 80.4623i | −0.0844305 | − | 0.0844305i | 0.663630 | − | 0.748061i | \(-0.269015\pi\) |
−0.748061 | + | 0.663630i | \(0.769015\pi\) | |||||||
\(954\) | −30.5413 | − | 138.278i | −0.0320139 | − | 0.144946i | ||||
\(955\) | −252.217 | − | 778.135i | −0.264102 | − | 0.814801i | ||||
\(956\) | 238.807 | − | 413.625i | 0.249798 | − | 0.432662i | ||||
\(957\) | 86.5729 | − | 107.781i | 0.0904628 | − | 0.112623i | ||||
\(958\) | −374.330 | + | 1397.02i | −0.390741 | + | 1.45826i | ||||
\(959\) | 1230.39 | − | 710.365i | 1.28299 | − | 0.740735i | ||||
\(960\) | 1318.49 | + | 501.202i | 1.37342 | + | 0.522086i | ||||
\(961\) | 195.525 | − | 338.658i | 0.203459 | − | 0.352402i | ||||
\(962\) | 481.095 | − | 481.095i | 0.500099 | − | 0.500099i | ||||
\(963\) | 47.6980 | − | 1073.06i | 0.0495306 | − | 1.11429i | ||||
\(964\) | 423.810i | 0.439636i | ||||||||
\(965\) | 691.423 | + | 1066.37i | 0.716501 | + | 1.10504i | ||||
\(966\) | −642.328 | − | 876.748i | −0.664935 | − | 0.907607i | ||||
\(967\) | −328.164 | − | 87.9314i | −0.339363 | − | 0.0909322i | 0.0851126 | − | 0.996371i | \(-0.472875\pi\) |
−0.424476 | + | 0.905439i | \(0.639542\pi\) | |||||||
\(968\) | 317.078 | − | 1183.35i | 0.327560 | − | 1.22247i | ||||
\(969\) | 1241.56 | + | 546.884i | 1.28128 | + | 0.564380i | ||||
\(970\) | 251.337 | − | 1178.31i | 0.259110 | − | 1.21475i | ||||
\(971\) | 1786.19 | 1.83954 | 0.919769 | − | 0.392460i | \(-0.128376\pi\) | ||||
0.919769 | + | 0.392460i | \(0.128376\pi\) | |||||||
\(972\) | −1251.31 | − | 1202.60i | −1.28736 | − | 1.23724i | ||||
\(973\) | −10.0620 | − | 10.0620i | −0.0103413 | − | 0.0103413i | ||||
\(974\) | 1707.67 | + | 985.926i | 1.75326 | + | 1.01224i | ||||
\(975\) | −317.499 | + | 68.3299i | −0.325640 | + | 0.0700820i | ||||
\(976\) | −227.759 | − | 394.490i | −0.233360 | − | 0.404191i | ||||
\(977\) | 743.412 | + | 199.197i | 0.760913 | + | 0.203886i | 0.618353 | − | 0.785900i | \(-0.287800\pi\) |
0.142560 | + | 0.989786i | \(0.454467\pi\) | |||||||
\(978\) | −347.902 | + | 2254.45i | −0.355728 | + | 2.30516i | ||||
\(979\) | 183.313 | + | 105.836i | 0.187246 | + | 0.108106i | ||||
\(980\) | −374.304 | − | 1154.80i | −0.381943 | − | 1.17836i | ||||
\(981\) | −622.578 | − | 680.501i | −0.634637 | − | 0.693681i | ||||
\(982\) | −1817.45 | + | 1817.45i | −1.85076 | + | 1.85076i | ||||
\(983\) | 79.2948 | − | 21.2470i | 0.0806661 | − | 0.0216144i | −0.218260 | − | 0.975891i | \(-0.570038\pi\) |
0.298926 | + | 0.954276i | \(0.403371\pi\) | |||||||
\(984\) | 14.7279 | + | 134.971i | 0.0149674 | + | 0.137166i | ||||
\(985\) | 30.6577 | + | 593.091i | 0.0311246 | + | 0.602123i | ||||
\(986\) | −911.523 | − | 1578.80i | −0.924466 | − | 1.60122i | ||||
\(987\) | 14.8660 | − | 18.5076i | 0.0150618 | − | 0.0187514i | ||||
\(988\) | −556.722 | + | 149.173i | −0.563484 | + | 0.150985i | ||||
\(989\) | 375.177i | 0.379350i | ||||||||
\(990\) | 77.4489 | − | 297.627i | 0.0782312 | − | 0.300634i | ||||
\(991\) | −515.156 | −0.519835 | −0.259917 | − | 0.965631i | \(-0.583695\pi\) | ||||
−0.259917 | + | 0.965631i | \(0.583695\pi\) | |||||||
\(992\) | −126.381 | − | 471.659i | −0.127400 | − | 0.475462i | ||||
\(993\) | 268.256 | − | 1738.33i | 0.270147 | − | 1.75059i | ||||
\(994\) | 753.465 | − | 435.013i | 0.758013 | − | 0.437639i | ||||
\(995\) | 612.940 | + | 552.687i | 0.616021 | + | 0.555465i | ||||
\(996\) | −1372.35 | + | 3115.57i | −1.37786 | + | 3.12808i | ||||
\(997\) | −96.0965 | − | 358.637i | −0.0963856 | − | 0.359716i | 0.900840 | − | 0.434151i | \(-0.142951\pi\) |
−0.997226 | + | 0.0744346i | \(0.976285\pi\) | |||||||
\(998\) | −231.032 | − | 231.032i | −0.231495 | − | 0.231495i | ||||
\(999\) | −407.098 | − | 1203.94i | −0.407505 | − | 1.20515i |
(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 | 45.3.k.a.43.9 | yes | 40 | |
3.2 | odd | 2 | 135.3.l.a.73.2 | 40 | |||
5.2 | odd | 4 | inner | 45.3.k.a.7.2 | ✓ | 40 | |
5.3 | odd | 4 | 225.3.o.b.7.9 | 40 | |||
5.4 | even | 2 | 225.3.o.b.43.2 | 40 | |||
9.2 | odd | 6 | 405.3.g.g.163.2 | 20 | |||
9.4 | even | 3 | inner | 45.3.k.a.13.2 | yes | 40 | |
9.5 | odd | 6 | 135.3.l.a.118.9 | 40 | |||
9.7 | even | 3 | 405.3.g.h.163.9 | 20 | |||
15.2 | even | 4 | 135.3.l.a.127.9 | 40 | |||
45.2 | even | 12 | 405.3.g.g.82.2 | 20 | |||
45.4 | even | 6 | 225.3.o.b.193.9 | 40 | |||
45.7 | odd | 12 | 405.3.g.h.82.9 | 20 | |||
45.13 | odd | 12 | 225.3.o.b.157.2 | 40 | |||
45.22 | odd | 12 | inner | 45.3.k.a.22.9 | yes | 40 | |
45.32 | even | 12 | 135.3.l.a.37.2 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.3.k.a.7.2 | ✓ | 40 | 5.2 | odd | 4 | inner | |
45.3.k.a.13.2 | yes | 40 | 9.4 | even | 3 | inner | |
45.3.k.a.22.9 | yes | 40 | 45.22 | odd | 12 | inner | |
45.3.k.a.43.9 | yes | 40 | 1.1 | even | 1 | trivial | |
135.3.l.a.37.2 | 40 | 45.32 | even | 12 | |||
135.3.l.a.73.2 | 40 | 3.2 | odd | 2 | |||
135.3.l.a.118.9 | 40 | 9.5 | odd | 6 | |||
135.3.l.a.127.9 | 40 | 15.2 | even | 4 | |||
225.3.o.b.7.9 | 40 | 5.3 | odd | 4 | |||
225.3.o.b.43.2 | 40 | 5.4 | even | 2 | |||
225.3.o.b.157.2 | 40 | 45.13 | odd | 12 | |||
225.3.o.b.193.9 | 40 | 45.4 | even | 6 | |||
405.3.g.g.82.2 | 20 | 45.2 | even | 12 | |||
405.3.g.g.163.2 | 20 | 9.2 | odd | 6 | |||
405.3.g.h.82.9 | 20 | 45.7 | odd | 12 | |||
405.3.g.h.163.9 | 20 | 9.7 | even | 3 |