Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(117,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.117");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.j (of order \(6\), degree \(2\), 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: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 117.6 | ||
Character | \(\chi\) | \(=\) | 392.117 |
Dual form | 392.3.j.e.325.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.215431 | + | 1.98836i | −0.107716 | + | 0.994182i | ||||
\(3\) | −0.455431 | − | 0.788830i | −0.151810 | − | 0.262943i | 0.780083 | − | 0.625677i | \(-0.215177\pi\) |
−0.931893 | + | 0.362733i | \(0.881844\pi\) | |||||||
\(4\) | −3.90718 | − | 0.856711i | −0.976795 | − | 0.214178i | ||||
\(5\) | 3.17251 | − | 5.49495i | 0.634503 | − | 1.09899i | −0.352118 | − | 0.935956i | \(-0.614538\pi\) |
0.986620 | − | 0.163035i | \(-0.0521283\pi\) | |||||||
\(6\) | 1.66660 | − | 0.735624i | 0.277766 | − | 0.122604i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.54518 | − | 7.58433i | 0.318148 | − | 0.948041i | ||||
\(9\) | 4.08516 | − | 7.07571i | 0.453907 | − | 0.786190i | ||||
\(10\) | 10.2425 | + | 7.49189i | 1.02425 | + | 0.749189i | ||||
\(11\) | −11.4442 | + | 6.60732i | −1.04038 | + | 0.600666i | −0.919942 | − | 0.392054i | \(-0.871764\pi\) |
−0.120442 | + | 0.992720i | \(0.538431\pi\) | |||||||
\(12\) | 1.10365 | + | 3.47227i | 0.0919710 | + | 0.289356i | ||||
\(13\) | −19.4243 | −1.49418 | −0.747090 | − | 0.664723i | \(-0.768550\pi\) | ||||
−0.747090 | + | 0.664723i | \(0.768550\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.77945 | −0.385296 | ||||||||
\(16\) | 14.5321 | + | 6.69465i | 0.908256 | + | 0.418415i | ||||
\(17\) | −13.7930 | + | 7.96338i | −0.811352 | + | 0.468434i | −0.847425 | − | 0.530915i | \(-0.821848\pi\) |
0.0360732 | + | 0.999349i | \(0.488515\pi\) | |||||||
\(18\) | 13.1890 | + | 9.64712i | 0.732723 | + | 0.535951i | ||||
\(19\) | −8.22725 | + | 14.2500i | −0.433013 | + | 0.750001i | −0.997131 | − | 0.0756934i | \(-0.975883\pi\) |
0.564118 | + | 0.825694i | \(0.309216\pi\) | |||||||
\(20\) | −17.1032 | + | 18.7518i | −0.855158 | + | 0.937592i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10.6723 | − | 24.1787i | −0.485105 | − | 1.09903i | ||||
\(23\) | −11.9607 | + | 20.7166i | −0.520032 | + | 0.900721i | 0.479697 | + | 0.877434i | \(0.340746\pi\) |
−0.999729 | + | 0.0232870i | \(0.992587\pi\) | |||||||
\(24\) | −7.14190 | + | 1.44643i | −0.297579 | + | 0.0602677i | ||||
\(25\) | −7.62967 | − | 13.2150i | −0.305187 | − | 0.528599i | ||||
\(26\) | 4.18461 | − | 38.6227i | 0.160947 | − | 1.48549i | ||||
\(27\) | −15.6398 | −0.579252 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 16.6618i | − | 0.574544i | −0.957849 | − | 0.287272i | \(-0.907252\pi\) | ||
0.957849 | − | 0.287272i | \(-0.0927483\pi\) | |||||||
\(30\) | 1.24507 | − | 11.4916i | 0.0415024 | − | 0.383055i | ||||
\(31\) | 11.1360 | − | 6.42939i | 0.359227 | − | 0.207400i | −0.309515 | − | 0.950895i | \(-0.600167\pi\) |
0.668741 | + | 0.743495i | \(0.266833\pi\) | |||||||
\(32\) | −16.4421 | + | 27.4528i | −0.513814 | + | 0.857901i | ||||
\(33\) | 10.4241 | + | 6.01837i | 0.315882 | + | 0.182375i | ||||
\(34\) | −12.8627 | − | 29.1410i | −0.378314 | − | 0.857089i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −22.0233 | + | 24.1463i | −0.611759 | + | 0.670730i | ||||
\(37\) | −41.1844 | − | 23.7778i | −1.11309 | − | 0.642644i | −0.173463 | − | 0.984840i | \(-0.555496\pi\) |
−0.939628 | + | 0.342196i | \(0.888829\pi\) | |||||||
\(38\) | −26.5618 | − | 19.4287i | −0.698995 | − | 0.511281i | ||||
\(39\) | 8.84646 | + | 15.3225i | 0.226832 | + | 0.392885i | ||||
\(40\) | −33.6009 | − | 38.0470i | −0.840023 | − | 0.951176i | ||||
\(41\) | 6.49499i | 0.158415i | 0.996858 | + | 0.0792073i | \(0.0252389\pi\) | ||||
−0.996858 | + | 0.0792073i | \(0.974761\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 33.2928i | − | 0.774252i | −0.922027 | − | 0.387126i | \(-0.873468\pi\) | ||
0.922027 | − | 0.387126i | \(-0.126532\pi\) | |||||||
\(44\) | 50.3752 | − | 16.0116i | 1.14489 | − | 0.363900i | ||||
\(45\) | −25.9205 | − | 44.8956i | −0.576010 | − | 0.997679i | ||||
\(46\) | −38.6154 | − | 28.2453i | −0.839465 | − | 0.614028i | ||||
\(47\) | 18.9713 | + | 10.9531i | 0.403645 | + | 0.233045i | 0.688056 | − | 0.725658i | \(-0.258465\pi\) |
−0.284411 | + | 0.958703i | \(0.591798\pi\) | |||||||
\(48\) | −1.33743 | − | 14.5123i | −0.0278631 | − | 0.302340i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 27.9198 | − | 12.3236i | 0.558397 | − | 0.246473i | ||||
\(51\) | 12.5635 | + | 7.25355i | 0.246343 | + | 0.142226i | ||||
\(52\) | 75.8944 | + | 16.6411i | 1.45951 | + | 0.320020i | ||||
\(53\) | 32.2028 | − | 18.5923i | 0.607601 | − | 0.350798i | −0.164425 | − | 0.986390i | \(-0.552577\pi\) |
0.772026 | + | 0.635591i | \(0.219244\pi\) | |||||||
\(54\) | 3.36930 | − | 31.0976i | 0.0623945 | − | 0.575882i | ||||
\(55\) | 83.8473i | 1.52450i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.9878 | 0.262944 | ||||||||
\(58\) | 33.1296 | + | 3.58946i | 0.571201 | + | 0.0618873i | ||||
\(59\) | −27.3428 | − | 47.3591i | −0.463437 | − | 0.802696i | 0.535693 | − | 0.844413i | \(-0.320051\pi\) |
−0.999129 | + | 0.0417169i | \(0.986717\pi\) | |||||||
\(60\) | 22.5813 | + | 4.95132i | 0.376356 | + | 0.0825219i | ||||
\(61\) | −5.12340 | + | 8.87399i | −0.0839902 | + | 0.145475i | −0.904960 | − | 0.425496i | \(-0.860100\pi\) |
0.820970 | + | 0.570971i | \(0.193433\pi\) | |||||||
\(62\) | 10.3849 | + | 23.5276i | 0.167499 | + | 0.379477i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −51.0441 | − | 38.6070i | −0.797564 | − | 0.603234i | ||||
\(65\) | −61.6240 | + | 106.736i | −0.948061 | + | 1.64209i | ||||
\(66\) | −14.2124 | + | 19.4304i | −0.215339 | + | 0.294400i | ||||
\(67\) | 14.8386 | − | 8.56706i | 0.221471 | − | 0.127867i | −0.385160 | − | 0.922850i | \(-0.625854\pi\) |
0.606631 | + | 0.794983i | \(0.292520\pi\) | |||||||
\(68\) | 60.7140 | − | 19.2978i | 0.892853 | − | 0.283791i | ||||
\(69\) | 21.7892 | 0.315785 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 32.0568 | 0.451505 | 0.225752 | − | 0.974185i | \(-0.427516\pi\) | ||||
0.225752 | + | 0.974185i | \(0.427516\pi\) | |||||||
\(72\) | −43.2670 | − | 48.9922i | −0.600931 | − | 0.680447i | ||||
\(73\) | −92.8082 | + | 53.5828i | −1.27135 | + | 0.734011i | −0.975241 | − | 0.221144i | \(-0.929021\pi\) |
−0.296104 | + | 0.955156i | \(0.595687\pi\) | |||||||
\(74\) | 56.1514 | − | 76.7671i | 0.758802 | − | 1.03739i | ||||
\(75\) | −6.94958 | + | 12.0370i | −0.0926611 | + | 0.160494i | ||||
\(76\) | 44.3535 | − | 48.6290i | 0.583598 | − | 0.639855i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −32.3725 | + | 14.2890i | −0.415032 | + | 0.183193i | ||||
\(79\) | 29.1542 | − | 50.4965i | 0.369040 | − | 0.639196i | −0.620376 | − | 0.784305i | \(-0.713020\pi\) |
0.989416 | + | 0.145109i | \(0.0463532\pi\) | |||||||
\(80\) | 82.8900 | − | 58.6143i | 1.03613 | − | 0.732679i | ||||
\(81\) | −29.6436 | − | 51.3443i | −0.365971 | − | 0.633880i | ||||
\(82\) | −12.9144 | − | 1.39922i | −0.157493 | − | 0.0170637i | ||||
\(83\) | −36.3441 | −0.437880 | −0.218940 | − | 0.975738i | \(-0.570260\pi\) | ||||
−0.218940 | + | 0.975738i | \(0.570260\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 101.056i | 1.18889i | ||||||||
\(86\) | 66.1983 | + | 7.17232i | 0.769747 | + | 0.0833990i | ||||
\(87\) | −13.1433 | + | 7.58829i | −0.151072 | + | 0.0872217i | ||||
\(88\) | 20.9845 | + | 103.614i | 0.238460 | + | 1.17743i | ||||
\(89\) | −0.929882 | − | 0.536867i | −0.0104481 | − | 0.00603222i | 0.494767 | − | 0.869026i | \(-0.335253\pi\) |
−0.505215 | + | 0.862994i | \(0.668587\pi\) | |||||||
\(90\) | 94.8528 | − | 41.8674i | 1.05392 | − | 0.465193i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 64.4808 | − | 70.6965i | 0.700878 | − | 0.768440i | ||||
\(93\) | −10.1434 | − | 5.85629i | −0.109069 | − | 0.0629709i | ||||
\(94\) | −25.8657 | + | 35.3622i | −0.275167 | + | 0.376194i | ||||
\(95\) | 52.2021 | + | 90.4167i | 0.549496 | + | 0.951755i | ||||
\(96\) | 29.1439 | + | 0.467106i | 0.303582 | + | 0.00486569i | ||||
\(97\) | − | 169.517i | − | 1.74760i | −0.486286 | − | 0.873799i | \(-0.661649\pi\) | ||
0.486286 | − | 0.873799i | \(-0.338351\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 107.968i | 1.09059i | ||||||||
\(100\) | 18.4891 | + | 58.1697i | 0.184891 | + | 0.581697i | ||||
\(101\) | −14.0630 | − | 24.3579i | −0.139238 | − | 0.241167i | 0.787971 | − | 0.615713i | \(-0.211132\pi\) |
−0.927208 | + | 0.374546i | \(0.877799\pi\) | |||||||
\(102\) | −17.1293 | + | 23.4182i | −0.167934 | + | 0.229590i | ||||
\(103\) | 144.029 | + | 83.1551i | 1.39834 | + | 0.807331i | 0.994219 | − | 0.107374i | \(-0.0342444\pi\) |
0.404120 | + | 0.914706i | \(0.367578\pi\) | |||||||
\(104\) | −49.4385 | + | 147.321i | −0.475370 | + | 1.41654i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 30.0308 | + | 68.0363i | 0.283309 | + | 0.641852i | ||||
\(107\) | −171.112 | − | 98.7918i | −1.59918 | − | 0.923288i | −0.991645 | − | 0.128996i | \(-0.958825\pi\) |
−0.607536 | − | 0.794292i | \(-0.707842\pi\) | |||||||
\(108\) | 61.1075 | + | 13.3988i | 0.565811 | + | 0.124063i | ||||
\(109\) | −9.97643 | + | 5.75990i | −0.0915269 | + | 0.0528431i | −0.545065 | − | 0.838394i | \(-0.683495\pi\) |
0.453538 | + | 0.891237i | \(0.350162\pi\) | |||||||
\(110\) | −166.719 | − | 18.0633i | −1.51563 | − | 0.164212i | ||||
\(111\) | 43.3167i | 0.390240i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.7908 | −0.130892 | −0.0654460 | − | 0.997856i | \(-0.520847\pi\) | ||||
−0.0654460 | + | 0.997856i | \(0.520847\pi\) | |||||||
\(114\) | −3.22884 | + | 29.8012i | −0.0283231 | + | 0.261414i | ||||
\(115\) | 75.8911 | + | 131.447i | 0.659923 | + | 1.14302i | ||||
\(116\) | −14.2743 | + | 65.1005i | −0.123054 | + | 0.561211i | ||||
\(117\) | −79.3516 | + | 137.441i | −0.678219 | + | 1.17471i | ||||
\(118\) | 100.058 | − | 44.1648i | 0.847945 | − | 0.374278i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −14.7097 | + | 43.8332i | −0.122581 | + | 0.365277i | ||||
\(121\) | 26.8135 | − | 46.4423i | 0.221599 | − | 0.383821i | ||||
\(122\) | −16.5410 | − | 12.0989i | −0.135582 | − | 0.0991715i | ||||
\(123\) | 5.12345 | − | 2.95802i | 0.0416541 | − | 0.0240490i | ||||
\(124\) | −49.0186 | + | 15.5804i | −0.395311 | + | 0.125648i | ||||
\(125\) | 61.8047 | 0.494438 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −70.2656 | −0.553272 | −0.276636 | − | 0.960975i | \(-0.589220\pi\) | ||||
−0.276636 | + | 0.960975i | \(0.589220\pi\) | |||||||
\(128\) | 87.7612 | − | 93.1771i | 0.685635 | − | 0.727946i | ||||
\(129\) | −26.2624 | + | 15.1626i | −0.203584 | + | 0.117540i | ||||
\(130\) | −198.954 | − | 145.525i | −1.53041 | − | 1.11942i | ||||
\(131\) | −71.0646 | + | 123.088i | −0.542478 | + | 0.939600i | 0.456283 | + | 0.889835i | \(0.349181\pi\) |
−0.998761 | + | 0.0497649i | \(0.984153\pi\) | |||||||
\(132\) | −35.5729 | − | 32.4453i | −0.269492 | − | 0.245798i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.8377 | + | 31.3501i | 0.103267 | + | 0.233956i | ||||
\(135\) | −49.6175 | + | 85.9400i | −0.367537 | + | 0.636593i | ||||
\(136\) | 25.2913 | + | 124.879i | 0.185965 | + | 0.918226i | ||||
\(137\) | −126.537 | − | 219.168i | −0.923626 | − | 1.59977i | −0.793756 | − | 0.608236i | \(-0.791877\pi\) |
−0.129870 | − | 0.991531i | \(-0.541456\pi\) | |||||||
\(138\) | −4.69407 | + | 43.3248i | −0.0340150 | + | 0.313948i | ||||
\(139\) | −49.1909 | −0.353892 | −0.176946 | − | 0.984221i | \(-0.556622\pi\) | ||||
−0.176946 | + | 0.984221i | \(0.556622\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 19.9535i | − | 0.141514i | ||||||
\(142\) | −6.90605 | + | 63.7407i | −0.0486341 | + | 0.448878i | ||||
\(143\) | 222.296 | − | 128.343i | 1.55452 | − | 0.897503i | ||||
\(144\) | 106.735 | − | 75.4762i | 0.741218 | − | 0.524140i | ||||
\(145\) | −91.5556 | − | 52.8597i | −0.631418 | − | 0.364549i | ||||
\(146\) | −86.5484 | − | 196.080i | −0.592797 | − | 1.34301i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 140.544 | + | 128.187i | 0.949622 | + | 0.866131i | ||||
\(149\) | 36.1077 | + | 20.8468i | 0.242334 | + | 0.139911i | 0.616249 | − | 0.787551i | \(-0.288652\pi\) |
−0.373915 | + | 0.927463i | \(0.621985\pi\) | |||||||
\(150\) | −22.4368 | − | 16.4115i | −0.149579 | − | 0.109410i | ||||
\(151\) | 48.8145 | + | 84.5492i | 0.323275 | + | 0.559928i | 0.981162 | − | 0.193188i | \(-0.0618829\pi\) |
−0.657887 | + | 0.753117i | \(0.728550\pi\) | |||||||
\(152\) | 87.1370 | + | 98.6670i | 0.573269 | + | 0.649125i | ||||
\(153\) | 130.127i | 0.850503i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 81.5892i | − | 0.526382i | ||||||
\(156\) | −21.4377 | − | 67.4466i | −0.137421 | − | 0.432350i | ||||
\(157\) | −14.0827 | − | 24.3919i | −0.0896986 | − | 0.155363i | 0.817685 | − | 0.575666i | \(-0.195257\pi\) |
−0.907384 | + | 0.420303i | \(0.861924\pi\) | |||||||
\(158\) | 94.1246 | + | 68.8476i | 0.595726 | + | 0.435744i | ||||
\(159\) | −29.3324 | − | 16.9350i | −0.184480 | − | 0.106510i | ||||
\(160\) | 98.6895 | + | 177.443i | 0.616809 | + | 1.10902i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 108.477 | − | 47.8811i | 0.669612 | − | 0.295563i | ||||
\(163\) | 209.952 | + | 121.216i | 1.28805 | + | 0.743655i | 0.978306 | − | 0.207165i | \(-0.0664237\pi\) |
0.309743 | + | 0.950820i | \(0.399757\pi\) | |||||||
\(164\) | 5.56433 | − | 25.3771i | 0.0339289 | − | 0.154738i | ||||
\(165\) | 66.1413 | − | 38.1867i | 0.400856 | − | 0.231434i | ||||
\(166\) | 7.82965 | − | 72.2652i | 0.0471665 | − | 0.435333i | ||||
\(167\) | − | 60.1108i | − | 0.359945i | −0.983672 | − | 0.179972i | \(-0.942399\pi\) | ||
0.983672 | − | 0.179972i | \(-0.0576008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 208.305 | 1.23257 | ||||||||
\(170\) | −200.936 | − | 21.7706i | −1.18197 | − | 0.128062i | ||||
\(171\) | 67.2193 | + | 116.427i | 0.393096 | + | 0.680861i | ||||
\(172\) | −28.5223 | + | 130.081i | −0.165828 | + | 0.756285i | ||||
\(173\) | 69.6820 | − | 120.693i | 0.402786 | − | 0.697646i | −0.591275 | − | 0.806470i | \(-0.701375\pi\) |
0.994061 | + | 0.108824i | \(0.0347085\pi\) | |||||||
\(174\) | −12.2568 | − | 27.7684i | −0.0704414 | − | 0.159589i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −210.542 | + | 19.4032i | −1.19626 | + | 0.110246i | ||||
\(177\) | −24.9055 | + | 43.1376i | −0.140709 | + | 0.243715i | ||||
\(178\) | 1.26781 | − | 1.73328i | 0.00712255 | − | 0.00973755i | ||||
\(179\) | −252.643 | + | 145.863i | −1.41141 | + | 0.814879i | −0.995522 | − | 0.0945354i | \(-0.969863\pi\) |
−0.415891 | + | 0.909415i | \(0.636530\pi\) | |||||||
\(180\) | 62.8134 | + | 197.621i | 0.348963 | + | 1.09790i | ||||
\(181\) | 166.844 | 0.921791 | 0.460895 | − | 0.887455i | \(-0.347528\pi\) | ||||
0.460895 | + | 0.887455i | \(0.347528\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.33343 | 0.0510024 | ||||||||
\(184\) | 126.679 | + | 143.442i | 0.688474 | + | 0.779574i | ||||
\(185\) | −261.316 | + | 150.871i | −1.41252 | + | 0.815518i | ||||
\(186\) | 13.8296 | − | 18.9071i | 0.0743529 | − | 0.101651i | ||||
\(187\) | 105.233 | − | 182.269i | 0.562745 | − | 0.974703i | ||||
\(188\) | −64.7407 | − | 59.0486i | −0.344365 | − | 0.314088i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −191.027 | + | 84.3182i | −1.00541 | + | 0.443780i | ||||
\(191\) | 65.6781 | − | 113.758i | 0.343864 | − | 0.595590i | −0.641283 | − | 0.767305i | \(-0.721597\pi\) |
0.985147 | + | 0.171715i | \(0.0549307\pi\) | |||||||
\(192\) | −7.20727 | + | 57.8480i | −0.0375379 | + | 0.301292i | ||||
\(193\) | 40.7196 | + | 70.5284i | 0.210982 | + | 0.365432i | 0.952022 | − | 0.306029i | \(-0.0990004\pi\) |
−0.741040 | + | 0.671461i | \(0.765667\pi\) | |||||||
\(194\) | 337.062 | + | 36.5193i | 1.73743 | + | 0.188244i | ||||
\(195\) | 112.262 | 0.575702 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.09549i | − | 0.0106370i | −0.999986 | − | 0.00531851i | \(-0.998307\pi\) | ||
0.999986 | − | 0.00531851i | \(-0.00169294\pi\) | |||||||
\(198\) | −214.680 | − | 23.2597i | −1.08424 | − | 0.117473i | ||||
\(199\) | 109.937 | − | 63.4721i | 0.552447 | − | 0.318955i | −0.197662 | − | 0.980270i | \(-0.563335\pi\) |
0.750108 | + | 0.661315i | \(0.230001\pi\) | |||||||
\(200\) | −119.646 | + | 24.2314i | −0.598228 | + | 0.121157i | ||||
\(201\) | −13.5159 | − | 7.80341i | −0.0672433 | − | 0.0388230i | ||||
\(202\) | 51.4619 | − | 22.7149i | 0.254762 | − | 0.112450i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −42.8737 | − | 39.1042i | −0.210165 | − | 0.191687i | ||||
\(205\) | 35.6897 | + | 20.6055i | 0.174096 | + | 0.100514i | ||||
\(206\) | −196.371 | + | 268.468i | −0.953257 | + | 1.30324i | ||||
\(207\) | 97.7231 | + | 169.261i | 0.472092 | + | 0.817687i | ||||
\(208\) | −282.276 | − | 130.039i | −1.35710 | − | 0.625188i | ||||
\(209\) | − | 217.440i | − | 1.04038i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.16822i | 0.0339726i | 0.999856 | + | 0.0169863i | \(0.00540717\pi\) | ||||
−0.999856 | + | 0.0169863i | \(0.994593\pi\) | |||||||
\(212\) | −141.750 | + | 45.0550i | −0.668634 | + | 0.212523i | ||||
\(213\) | −14.5997 | − | 25.2874i | −0.0685432 | − | 0.118720i | ||||
\(214\) | 233.297 | − | 318.951i | 1.09017 | − | 1.49042i | ||||
\(215\) | −182.943 | − | 105.622i | −0.850896 | − | 0.491265i | ||||
\(216\) | −39.8062 | + | 118.617i | −0.184288 | + | 0.549155i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.30353 | − | 21.0776i | −0.0426768 | − | 0.0966864i | ||||
\(219\) | 84.5355 | + | 48.8066i | 0.386007 | + | 0.222861i | ||||
\(220\) | 71.8329 | − | 327.606i | 0.326513 | − | 1.48912i | ||||
\(221\) | 267.920 | − | 154.683i | 1.21231 | − | 0.699925i | ||||
\(222\) | −86.1293 | − | 9.33176i | −0.387970 | − | 0.0420350i | ||||
\(223\) | 279.720i | 1.25435i | 0.778878 | + | 0.627175i | \(0.215789\pi\) | ||||
−0.778878 | + | 0.627175i | \(0.784211\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −124.674 | −0.554106 | ||||||||
\(226\) | 3.18640 | − | 29.4095i | 0.0140991 | − | 0.130130i | ||||
\(227\) | −152.392 | − | 263.950i | −0.671330 | − | 1.16278i | −0.977527 | − | 0.210809i | \(-0.932390\pi\) |
0.306198 | − | 0.951968i | \(-0.400943\pi\) | |||||||
\(228\) | −58.5600 | − | 12.8402i | −0.256842 | − | 0.0563167i | ||||
\(229\) | 207.344 | − | 359.130i | 0.905433 | − | 1.56826i | 0.0850971 | − | 0.996373i | \(-0.472880\pi\) |
0.820335 | − | 0.571883i | \(-0.193787\pi\) | |||||||
\(230\) | −277.714 | + | 122.581i | −1.20745 | + | 0.532962i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −126.368 | − | 42.4072i | −0.544691 | − | 0.182790i | ||||
\(233\) | 82.4628 | − | 142.830i | 0.353918 | − | 0.613004i | −0.633014 | − | 0.774140i | \(-0.718183\pi\) |
0.986932 | + | 0.161136i | \(0.0515159\pi\) | |||||||
\(234\) | −256.188 | − | 187.389i | −1.09482 | − | 0.800808i | ||||
\(235\) | 120.373 | − | 69.4976i | 0.512227 | − | 0.295735i | ||||
\(236\) | 66.2601 | + | 208.465i | 0.280763 | + | 0.883327i | ||||
\(237\) | −53.1109 | −0.224097 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.1182 | −0.0799926 | −0.0399963 | − | 0.999200i | \(-0.512735\pi\) | ||||
−0.0399963 | + | 0.999200i | \(0.512735\pi\) | |||||||
\(240\) | −83.9875 | − | 38.6914i | −0.349948 | − | 0.161214i | ||||
\(241\) | 303.376 | − | 175.154i | 1.25882 | − | 0.726780i | 0.285975 | − | 0.958237i | \(-0.407683\pi\) |
0.972845 | + | 0.231457i | \(0.0743492\pi\) | |||||||
\(242\) | 86.5677 | + | 63.3201i | 0.357718 | + | 0.261653i | ||||
\(243\) | −97.3804 | + | 168.668i | −0.400743 | + | 0.694106i | ||||
\(244\) | 27.6205 | − | 30.2830i | 0.113199 | − | 0.124111i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.77788 | + | 10.8245i | 0.0194223 | + | 0.0440022i | ||||
\(247\) | 159.809 | − | 276.797i | 0.647000 | − | 1.12064i | ||||
\(248\) | −20.4194 | − | 100.823i | −0.0823362 | − | 0.406545i | ||||
\(249\) | 16.5522 | + | 28.6693i | 0.0664748 | + | 0.115138i | ||||
\(250\) | −13.3147 | + | 122.890i | −0.0532587 | + | 0.491561i | ||||
\(251\) | −88.3204 | −0.351874 | −0.175937 | − | 0.984401i | \(-0.556296\pi\) | ||||
−0.175937 | + | 0.984401i | \(0.556296\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 316.114i | − | 1.24946i | ||||||
\(254\) | 15.1374 | − | 139.714i | 0.0595961 | − | 0.550053i | ||||
\(255\) | 79.7158 | − | 46.0240i | 0.312611 | − | 0.180486i | ||||
\(256\) | 166.363 | + | 194.574i | 0.649857 | + | 0.760056i | ||||
\(257\) | −74.5499 | − | 43.0414i | −0.290077 | − | 0.167476i | 0.347899 | − | 0.937532i | \(-0.386895\pi\) |
−0.637977 | + | 0.770056i | \(0.720228\pi\) | |||||||
\(258\) | −24.4910 | − | 55.4857i | −0.0949265 | − | 0.215061i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 332.218 | − | 364.242i | 1.27776 | − | 1.40093i | ||||
\(261\) | −117.894 | − | 68.0661i | −0.451701 | − | 0.260789i | ||||
\(262\) | −229.433 | − | 167.819i | −0.875699 | − | 0.640531i | ||||
\(263\) | −159.605 | − | 276.444i | −0.606863 | − | 1.05112i | −0.991754 | − | 0.128156i | \(-0.959094\pi\) |
0.384891 | − | 0.922962i | \(-0.374239\pi\) | |||||||
\(264\) | 72.1765 | − | 63.7421i | 0.273396 | − | 0.241447i | ||||
\(265\) | − | 235.937i | − | 0.890330i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.978025i | 0.00366302i | ||||||||
\(268\) | −65.3165 | + | 20.7607i | −0.243718 | + | 0.0774651i | ||||
\(269\) | 28.7340 | + | 49.7687i | 0.106818 | + | 0.185014i | 0.914479 | − | 0.404632i | \(-0.132601\pi\) |
−0.807662 | + | 0.589646i | \(0.799267\pi\) | |||||||
\(270\) | −160.191 | − | 117.172i | −0.593300 | − | 0.433970i | ||||
\(271\) | −26.7398 | − | 15.4382i | −0.0986709 | − | 0.0569677i | 0.449853 | − | 0.893103i | \(-0.351477\pi\) |
−0.548523 | + | 0.836135i | \(0.684810\pi\) | |||||||
\(272\) | −253.753 | + | 23.3855i | −0.932915 | + | 0.0859759i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 463.046 | − | 204.385i | 1.68995 | − | 0.745932i | ||||
\(275\) | 174.631 | + | 100.823i | 0.635023 | + | 0.366631i | ||||
\(276\) | −85.1341 | − | 18.6670i | −0.308457 | − | 0.0676341i | ||||
\(277\) | −308.465 | + | 178.092i | −1.11359 | + | 0.642933i | −0.939757 | − | 0.341842i | \(-0.888949\pi\) |
−0.173834 | + | 0.984775i | \(0.555616\pi\) | |||||||
\(278\) | 10.5973 | − | 97.8095i | 0.0381197 | − | 0.351833i | ||||
\(279\) | − | 105.060i | − | 0.376561i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −294.160 | −1.04683 | −0.523416 | − | 0.852077i | \(-0.675343\pi\) | ||||
−0.523416 | + | 0.852077i | \(0.675343\pi\) | |||||||
\(282\) | 39.6749 | + | 4.29861i | 0.140691 | + | 0.0152433i | ||||
\(283\) | 207.501 | + | 359.402i | 0.733219 | + | 1.26997i | 0.955501 | + | 0.294989i | \(0.0953161\pi\) |
−0.222282 | + | 0.974982i | \(0.571351\pi\) | |||||||
\(284\) | −125.252 | − | 27.4635i | −0.441028 | − | 0.0967023i | ||||
\(285\) | 47.5490 | − | 82.3572i | 0.166838 | − | 0.288973i | ||||
\(286\) | 207.303 | + | 469.655i | 0.724835 | + | 1.64215i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 127.080 | + | 228.489i | 0.441250 | + | 0.793363i | ||||
\(289\) | −17.6691 | + | 30.6037i | −0.0611386 | + | 0.105895i | ||||
\(290\) | 124.828 | − | 170.658i | 0.430442 | − | 0.588477i | ||||
\(291\) | −133.720 | + | 77.2034i | −0.459520 | + | 0.265304i | ||||
\(292\) | 408.523 | − | 129.848i | 1.39905 | − | 0.444685i | ||||
\(293\) | −370.564 | −1.26472 | −0.632362 | − | 0.774673i | \(-0.717915\pi\) | ||||
−0.632362 | + | 0.774673i | \(0.717915\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −346.981 | −1.17621 | ||||||||
\(296\) | −285.161 | + | 251.837i | −0.963380 | + | 0.850801i | ||||
\(297\) | 178.986 | − | 103.337i | 0.602645 | − | 0.347937i | ||||
\(298\) | −49.2298 | + | 67.3042i | −0.165201 | + | 0.225853i | ||||
\(299\) | 232.329 | − | 402.406i | 0.777021 | − | 1.34584i | ||||
\(300\) | 37.4655 | − | 41.0770i | 0.124885 | − | 0.136923i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −178.631 | + | 78.8464i | −0.591492 | + | 0.261081i | ||||
\(303\) | −12.8095 | + | 22.1867i | −0.0422755 | + | 0.0732233i | ||||
\(304\) | −214.958 | + | 152.004i | −0.707099 | + | 0.500013i | ||||
\(305\) | 32.5081 | + | 56.3057i | 0.106584 | + | 0.184609i | ||||
\(306\) | −258.740 | − | 28.0334i | −0.845554 | − | 0.0916124i | ||||
\(307\) | −160.327 | −0.522239 | −0.261120 | − | 0.965306i | \(-0.584092\pi\) | ||||
−0.261120 | + | 0.965306i | \(0.584092\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 151.486i | − | 0.490245i | ||||||
\(310\) | 162.229 | + | 17.5769i | 0.523320 | + | 0.0566996i | ||||
\(311\) | −409.490 | + | 236.419i | −1.31669 | + | 0.760191i | −0.983195 | − | 0.182561i | \(-0.941561\pi\) |
−0.333495 | + | 0.942752i | \(0.608228\pi\) | |||||||
\(312\) | 138.727 | − | 28.0959i | 0.444637 | − | 0.0900508i | ||||
\(313\) | −200.063 | − | 115.506i | −0.639179 | − | 0.369030i | 0.145119 | − | 0.989414i | \(-0.453643\pi\) |
−0.784298 | + | 0.620384i | \(0.786977\pi\) | |||||||
\(314\) | 51.5339 | − | 22.7467i | 0.164121 | − | 0.0724418i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −157.171 | + | 172.322i | −0.497378 | + | 0.545323i | ||||
\(317\) | 195.132 | + | 112.659i | 0.615557 | + | 0.355392i | 0.775137 | − | 0.631793i | \(-0.217681\pi\) |
−0.159580 | + | 0.987185i | \(0.551014\pi\) | |||||||
\(318\) | 39.9921 | − | 54.6751i | 0.125761 | − | 0.171934i | ||||
\(319\) | 110.090 | + | 190.681i | 0.345109 | + | 0.597746i | ||||
\(320\) | −374.082 | + | 158.004i | −1.16901 | + | 0.493762i | ||||
\(321\) | 179.972i | 0.560659i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 262.067i | − | 0.811353i | ||||||
\(324\) | 71.8357 | + | 226.007i | 0.221715 | + | 0.697553i | ||||
\(325\) | 148.201 | + | 256.692i | 0.456004 | + | 0.789822i | ||||
\(326\) | −286.251 | + | 391.347i | −0.878072 | + | 1.20045i | ||||
\(327\) | 9.08716 | + | 5.24648i | 0.0277895 | + | 0.0160443i | ||||
\(328\) | 49.2602 | + | 16.5309i | 0.150183 | + | 0.0503992i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 61.6801 | + | 139.740i | 0.186909 | + | 0.423453i | ||||
\(331\) | −17.9257 | − | 10.3494i | −0.0541561 | − | 0.0312671i | 0.472677 | − | 0.881236i | \(-0.343288\pi\) |
−0.526834 | + | 0.849968i | \(0.676621\pi\) | |||||||
\(332\) | 142.003 | + | 31.1364i | 0.427719 | + | 0.0937842i | ||||
\(333\) | −336.490 | + | 194.273i | −1.01048 | + | 0.583401i | ||||
\(334\) | 119.522 | + | 12.9497i | 0.357851 | + | 0.0387717i | ||||
\(335\) | − | 108.716i | − | 0.324527i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.9645 | 0.103752 | 0.0518762 | − | 0.998654i | \(-0.483480\pi\) | ||||
0.0518762 | + | 0.998654i | \(0.483480\pi\) | |||||||
\(338\) | −44.8754 | + | 414.186i | −0.132768 | + | 1.22540i | ||||
\(339\) | 6.73619 | + | 11.6674i | 0.0198708 | + | 0.0344172i | ||||
\(340\) | 86.5756 | − | 394.843i | 0.254634 | − | 1.16130i | ||||
\(341\) | −84.9621 | + | 147.159i | −0.249156 | + | 0.431550i | ||||
\(342\) | −245.981 | + | 108.574i | −0.719243 | + | 0.317469i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −252.504 | − | 84.7363i | −0.734023 | − | 0.246326i | ||||
\(345\) | 69.1264 | − | 119.730i | 0.200366 | − | 0.347045i | ||||
\(346\) | 224.969 | + | 164.554i | 0.650201 | + | 0.475590i | ||||
\(347\) | 379.958 | − | 219.369i | 1.09498 | − | 0.632188i | 0.160083 | − | 0.987104i | \(-0.448824\pi\) |
0.934898 | + | 0.354916i | \(0.115491\pi\) | |||||||
\(348\) | 57.8542 | − | 18.3888i | 0.166248 | − | 0.0528414i | ||||
\(349\) | 435.121 | 1.24677 | 0.623383 | − | 0.781917i | \(-0.285758\pi\) | ||||
0.623383 | + | 0.781917i | \(0.285758\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 303.793 | 0.865507 | ||||||||
\(352\) | 6.77670 | − | 422.814i | 0.0192520 | − | 1.20118i | ||||
\(353\) | −243.447 | + | 140.554i | −0.689653 | + | 0.398171i | −0.803482 | − | 0.595329i | \(-0.797022\pi\) |
0.113829 | + | 0.993500i | \(0.463688\pi\) | |||||||
\(354\) | −80.4078 | − | 58.8144i | −0.227141 | − | 0.166142i | ||||
\(355\) | 101.701 | − | 176.151i | 0.286481 | − | 0.496200i | ||||
\(356\) | 3.17327 | + | 2.89428i | 0.00891369 | + | 0.00812999i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −235.602 | − | 533.769i | −0.658107 | − | 1.49098i | ||||
\(359\) | −131.965 | + | 228.570i | −0.367590 | + | 0.636685i | −0.989188 | − | 0.146652i | \(-0.953150\pi\) |
0.621598 | + | 0.783336i | \(0.286484\pi\) | |||||||
\(360\) | −406.475 | + | 82.3220i | −1.12910 | + | 0.228672i | ||||
\(361\) | 45.1247 | + | 78.1583i | 0.124999 | + | 0.216505i | ||||
\(362\) | −35.9434 | + | 331.747i | −0.0992912 | + | 0.916427i | ||||
\(363\) | −48.8468 | −0.134564 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 679.969i | 1.86293i | ||||||||
\(366\) | −2.01071 | + | 18.5583i | −0.00549375 | + | 0.0507056i | ||||
\(367\) | 134.181 | − | 77.4694i | 0.365615 | − | 0.211088i | −0.305926 | − | 0.952055i | \(-0.598966\pi\) |
0.671541 | + | 0.740967i | \(0.265633\pi\) | |||||||
\(368\) | −312.505 | + | 220.982i | −0.849197 | + | 0.600496i | ||||
\(369\) | 45.9567 | + | 26.5331i | 0.124544 | + | 0.0719055i | ||||
\(370\) | −243.691 | − | 552.094i | −0.658623 | − | 1.49214i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 34.6149 | + | 31.5715i | 0.0930508 | + | 0.0848697i | ||||
\(373\) | 506.505 | + | 292.431i | 1.35792 | + | 0.783997i | 0.989344 | − | 0.145600i | \(-0.0465112\pi\) |
0.368579 | + | 0.929597i | \(0.379845\pi\) | |||||||
\(374\) | 339.747 | + | 248.509i | 0.908415 | + | 0.664462i | ||||
\(375\) | −28.1478 | − | 48.7534i | −0.0750608 | − | 0.130009i | ||||
\(376\) | 131.357 | − | 116.007i | 0.349355 | − | 0.308529i | ||||
\(377\) | 323.644i | 0.858472i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 128.176i | − | 0.338195i | −0.985599 | − | 0.169098i | \(-0.945915\pi\) | ||
0.985599 | − | 0.169098i | \(-0.0540853\pi\) | |||||||
\(380\) | −126.502 | − | 397.996i | −0.332900 | − | 1.04736i | ||||
\(381\) | 32.0011 | + | 55.4276i | 0.0839925 | + | 0.145479i | ||||
\(382\) | 212.043 | + | 155.099i | 0.555085 | + | 0.406018i | ||||
\(383\) | 216.437 | + | 124.960i | 0.565110 | + | 0.326266i | 0.755194 | − | 0.655502i | \(-0.227543\pi\) |
−0.190084 | + | 0.981768i | \(0.560876\pi\) | |||||||
\(384\) | −113.470 | − | 26.7929i | −0.295495 | − | 0.0697733i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −149.008 | + | 65.7713i | −0.386032 | + | 0.170392i | ||||
\(387\) | −235.571 | − | 136.007i | −0.608709 | − | 0.351439i | ||||
\(388\) | −145.227 | + | 662.334i | −0.374297 | + | 1.70705i | ||||
\(389\) | 187.428 | − | 108.212i | 0.481821 | − | 0.278179i | −0.239354 | − | 0.970932i | \(-0.576936\pi\) |
0.721175 | + | 0.692753i | \(0.243602\pi\) | |||||||
\(390\) | −24.1847 | + | 223.218i | −0.0620121 | + | 0.572353i | ||||
\(391\) | − | 380.991i | − | 0.974402i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 129.460 | 0.329415 | ||||||||
\(394\) | 4.16660 | + | 0.451434i | 0.0105751 | + | 0.00114577i | ||||
\(395\) | −184.984 | − | 320.401i | −0.468314 | − | 0.811143i | ||||
\(396\) | 92.4974 | − | 421.850i | 0.233579 | − | 1.06528i | ||||
\(397\) | −349.941 | + | 606.116i | −0.881463 | + | 1.52674i | −0.0317493 | + | 0.999496i | \(0.510108\pi\) |
−0.849714 | + | 0.527244i | \(0.823226\pi\) | |||||||
\(398\) | 102.522 | + | 232.268i | 0.257592 | + | 0.583589i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −22.4055 | − | 243.119i | −0.0560137 | − | 0.607798i | ||||
\(401\) | 90.4903 | − | 156.734i | 0.225662 | − | 0.390858i | −0.730856 | − | 0.682532i | \(-0.760879\pi\) |
0.956518 | + | 0.291674i | \(0.0942123\pi\) | |||||||
\(402\) | 18.4278 | − | 25.1934i | 0.0458402 | − | 0.0626703i | ||||
\(403\) | −216.310 | + | 124.887i | −0.536749 | + | 0.309892i | ||||
\(404\) | 34.0791 | + | 107.218i | 0.0843541 | + | 0.265392i | ||||
\(405\) | −376.179 | −0.928837 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 628.431 | 1.54406 | ||||||||
\(408\) | 86.9897 | − | 76.8242i | 0.213210 | − | 0.188295i | ||||
\(409\) | 310.767 | − | 179.421i | 0.759821 | − | 0.438683i | −0.0694104 | − | 0.997588i | \(-0.522112\pi\) |
0.829232 | + | 0.558905i | \(0.188778\pi\) | |||||||
\(410\) | −48.6598 | + | 66.5250i | −0.118682 | + | 0.162256i | ||||
\(411\) | −115.258 | + | 199.632i | −0.280432 | + | 0.485723i | ||||
\(412\) | −491.507 | − | 448.293i | −1.19298 | − | 1.08809i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −357.606 | + | 157.845i | −0.863782 | + | 0.381268i | ||||
\(415\) | −115.302 | + | 199.709i | −0.277836 | + | 0.481226i | ||||
\(416\) | 319.376 | − | 533.253i | 0.767731 | − | 1.28186i | ||||
\(417\) | 22.4031 | + | 38.8033i | 0.0537245 | + | 0.0930535i | ||||
\(418\) | 432.351 | + | 46.8435i | 1.03433 | + | 0.112066i | ||||
\(419\) | 780.890 | 1.86370 | 0.931849 | − | 0.362846i | \(-0.118195\pi\) | ||||
0.931849 | + | 0.362846i | \(0.118195\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 114.961i | 0.273068i | 0.990635 | + | 0.136534i | \(0.0435962\pi\) | ||||
−0.990635 | + | 0.136534i | \(0.956404\pi\) | |||||||
\(422\) | −14.2530 | − | 1.54426i | −0.0337749 | − | 0.00365938i | ||||
\(423\) | 155.002 | − | 89.4904i | 0.366435 | − | 0.211561i | ||||
\(424\) | −59.0482 | − | 291.558i | −0.139265 | − | 0.687636i | ||||
\(425\) | 210.472 | + | 121.516i | 0.495228 | + | 0.285920i | ||||
\(426\) | 53.4258 | − | 23.5818i | 0.125413 | − | 0.0553563i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 583.931 | + | 532.591i | 1.36432 | + | 1.24437i | ||||
\(429\) | −202.482 | − | 116.903i | −0.471985 | − | 0.272501i | ||||
\(430\) | 249.426 | − | 341.002i | 0.580061 | − | 0.793028i | ||||
\(431\) | −154.856 | − | 268.219i | −0.359295 | − | 0.622317i | 0.628548 | − | 0.777771i | \(-0.283649\pi\) |
−0.987843 | + | 0.155453i | \(0.950316\pi\) | |||||||
\(432\) | −227.279 | − | 104.703i | −0.526109 | − | 0.242368i | ||||
\(433\) | 595.775i | 1.37592i | 0.725747 | + | 0.687962i | \(0.241494\pi\) | ||||
−0.725747 | + | 0.687962i | \(0.758506\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 96.2958i | 0.221370i | ||||||||
\(436\) | 43.9143 | − | 13.9580i | 0.100721 | − | 0.0320138i | ||||
\(437\) | −196.808 | − | 340.881i | −0.450361 | − | 0.780048i | ||||
\(438\) | −115.257 | + | 157.573i | −0.263144 | + | 0.359755i | ||||
\(439\) | −698.796 | − | 403.450i | −1.59179 | − | 0.919020i | −0.993000 | − | 0.118113i | \(-0.962315\pi\) |
−0.598789 | − | 0.800907i | \(-0.704351\pi\) | |||||||
\(440\) | 635.925 | + | 213.407i | 1.44529 | + | 0.485015i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 249.849 | + | 566.045i | 0.565269 | + | 1.28065i | ||||
\(443\) | −385.214 | − | 222.403i | −0.869557 | − | 0.502039i | −0.00235617 | − | 0.999997i | \(-0.500750\pi\) |
−0.867201 | + | 0.497958i | \(0.834083\pi\) | |||||||
\(444\) | 37.1099 | − | 169.246i | 0.0835808 | − | 0.381185i | ||||
\(445\) | −5.90012 | + | 3.40644i | −0.0132587 | + | 0.00765491i | ||||
\(446\) | −556.185 | − | 60.2605i | −1.24705 | − | 0.135113i | ||||
\(447\) | − | 37.9772i | − | 0.0849601i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 262.420 | 0.584455 | 0.292228 | − | 0.956349i | \(-0.405604\pi\) | ||||
0.292228 | + | 0.956349i | \(0.405604\pi\) | |||||||
\(450\) | 26.8586 | − | 247.897i | 0.0596859 | − | 0.550882i | ||||
\(451\) | −42.9145 | − | 74.3302i | −0.0951542 | − | 0.164812i | ||||
\(452\) | 57.7903 | + | 12.6714i | 0.127855 | + | 0.0280342i | ||||
\(453\) | 44.4633 | − | 77.0127i | 0.0981530 | − | 0.170006i | ||||
\(454\) | 557.659 | − | 246.147i | 1.22832 | − | 0.542174i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 38.1466 | − | 113.672i | 0.0836549 | − | 0.249281i | ||||
\(457\) | −194.738 | + | 337.296i | −0.426122 | + | 0.738065i | −0.996524 | − | 0.0833004i | \(-0.973454\pi\) |
0.570403 | + | 0.821365i | \(0.306787\pi\) | |||||||
\(458\) | 669.413 | + | 489.643i | 1.46160 | + | 1.06909i | ||||
\(459\) | 215.720 | − | 124.546i | 0.469978 | − | 0.271342i | ||||
\(460\) | −183.908 | − | 578.605i | −0.399800 | − | 1.25784i | ||||
\(461\) | 158.714 | 0.344283 | 0.172141 | − | 0.985072i | \(-0.444931\pi\) | ||||
0.172141 | + | 0.985072i | \(0.444931\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −528.844 | −1.14221 | −0.571106 | − | 0.820877i | \(-0.693485\pi\) | ||||
−0.571106 | + | 0.820877i | \(0.693485\pi\) | |||||||
\(464\) | 111.545 | − | 242.130i | 0.240398 | − | 0.521833i | ||||
\(465\) | −64.3601 | + | 37.1583i | −0.138409 | + | 0.0799103i | ||||
\(466\) | 266.233 | + | 194.736i | 0.571314 | + | 0.417889i | ||||
\(467\) | −218.449 | + | 378.365i | −0.467771 | + | 0.810203i | −0.999322 | − | 0.0368236i | \(-0.988276\pi\) |
0.531551 | + | 0.847026i | \(0.321609\pi\) | |||||||
\(468\) | 427.788 | − | 469.025i | 0.914078 | − | 1.00219i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 112.254 | + | 254.318i | 0.238839 | + | 0.541102i | ||||
\(471\) | −12.8274 | + | 22.2177i | −0.0272344 | + | 0.0471713i | ||||
\(472\) | −428.779 | + | 86.8392i | −0.908430 | + | 0.183981i | ||||
\(473\) | 219.977 | + | 381.011i | 0.465067 | + | 0.805519i | ||||
\(474\) | 11.4417 | − | 105.604i | 0.0241387 | − | 0.222793i | ||||
\(475\) | 251.085 | 0.528600 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 303.811i | − | 0.636920i | ||||||
\(478\) | 4.11866 | − | 38.0140i | 0.00861645 | − | 0.0795272i | ||||
\(479\) | −472.737 | + | 272.935i | −0.986925 | + | 0.569802i | −0.904354 | − | 0.426783i | \(-0.859647\pi\) |
−0.0825716 | + | 0.996585i | \(0.526313\pi\) | |||||||
\(480\) | 95.0260 | − | 158.662i | 0.197971 | − | 0.330546i | ||||
\(481\) | 799.980 | + | 461.869i | 1.66316 | + | 0.960226i | ||||
\(482\) | 282.913 | + | 640.955i | 0.586957 | + | 1.32978i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −144.553 | + | 158.487i | −0.298663 | + | 0.327453i | ||||
\(485\) | −931.488 | − | 537.795i | −1.92059 | − | 1.10886i | ||||
\(486\) | −314.394 | − | 229.964i | −0.646902 | − | 0.473177i | ||||
\(487\) | −324.115 | − | 561.384i | −0.665534 | − | 1.15274i | −0.979140 | − | 0.203185i | \(-0.934871\pi\) |
0.313606 | − | 0.949553i | \(-0.398463\pi\) | |||||||
\(488\) | 54.2633 | + | 61.4435i | 0.111195 | + | 0.125909i | ||||
\(489\) | − | 220.822i | − | 0.451579i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 732.074i | 1.49098i | 0.666514 | + | 0.745492i | \(0.267786\pi\) | ||||
−0.666514 | + | 0.745492i | \(0.732214\pi\) | |||||||
\(492\) | −22.5524 | + | 7.16822i | −0.0458382 | + | 0.0145695i | ||||
\(493\) | 132.684 | + | 229.815i | 0.269136 | + | 0.466157i | ||||
\(494\) | 515.946 | + | 377.389i | 1.04442 | + | 0.763945i | ||||
\(495\) | 593.279 | + | 342.530i | 1.19854 | + | 0.691980i | ||||
\(496\) | 204.872 | − | 18.8807i | 0.413049 | − | 0.0380659i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −60.5709 | + | 26.7356i | −0.121628 | + | 0.0536859i | ||||
\(499\) | −23.1264 | − | 13.3520i | −0.0463454 | − | 0.0267575i | 0.476648 | − | 0.879094i | \(-0.341852\pi\) |
−0.522994 | + | 0.852337i | \(0.675185\pi\) | |||||||
\(500\) | −241.482 | − | 52.9488i | −0.482964 | − | 0.105898i | ||||
\(501\) | −47.4172 | + | 27.3763i | −0.0946451 | + | 0.0546434i | ||||
\(502\) | 19.0270 | − | 175.613i | 0.0379023 | − | 0.349827i | ||||
\(503\) | − | 616.414i | − | 1.22548i | −0.790286 | − | 0.612738i | \(-0.790068\pi\) | ||
0.790286 | − | 0.612738i | \(-0.209932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −178.460 | −0.353387 | ||||||||
\(506\) | 628.549 | + | 68.1007i | 1.24219 | + | 0.134586i | ||||
\(507\) | −94.8687 | − | 164.317i | −0.187118 | − | 0.324097i | ||||
\(508\) | 274.540 | + | 60.1973i | 0.540433 | + | 0.118499i | ||||
\(509\) | −66.3763 | + | 114.967i | −0.130405 | + | 0.225869i | −0.923833 | − | 0.382796i | \(-0.874961\pi\) |
0.793428 | + | 0.608665i | \(0.208295\pi\) | |||||||
\(510\) | 74.3391 | + | 168.419i | 0.145763 | + | 0.330233i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −422.725 | + | 288.874i | −0.825634 | + | 0.564206i | ||||
\(513\) | 128.673 | − | 222.868i | 0.250824 | − | 0.434440i | ||||
\(514\) | 101.642 | − | 138.960i | 0.197748 | − | 0.270350i | ||||
\(515\) | 913.867 | − | 527.621i | 1.77450 | − | 1.02451i | ||||
\(516\) | 115.602 | − | 36.7437i | 0.224035 | − | 0.0712087i | ||||
\(517\) | −289.483 | −0.559928 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −126.942 | −0.244589 | ||||||||
\(520\) | 652.676 | + | 739.039i | 1.25515 | + | 1.42123i | ||||
\(521\) | 585.480 | − | 338.027i | 1.12376 | − | 0.648804i | 0.181403 | − | 0.983409i | \(-0.441936\pi\) |
0.942359 | + | 0.334605i | \(0.108603\pi\) | |||||||
\(522\) | 160.738 | − | 219.752i | 0.307927 | − | 0.420981i | ||||
\(523\) | −186.224 | + | 322.550i | −0.356069 | + | 0.616730i | −0.987300 | − | 0.158865i | \(-0.949217\pi\) |
0.631231 | + | 0.775595i | \(0.282550\pi\) | |||||||
\(524\) | 383.113 | − | 420.043i | 0.731131 | − | 0.801609i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 584.055 | − | 257.798i | 1.11037 | − | 0.490110i | ||||
\(527\) | −102.399 | + | 177.361i | −0.194306 | + | 0.336548i | ||||
\(528\) | 111.193 | + | 157.245i | 0.210594 | + | 0.297813i | ||||
\(529\) | −21.6179 | − | 37.4433i | −0.0408656 | − | 0.0707813i | ||||
\(530\) | 469.129 | + | 50.8283i | 0.885150 | + | 0.0959024i | ||||
\(531\) | −446.799 | −0.841429 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 126.161i | − | 0.236700i | ||||||
\(534\) | −1.94467 | − | 0.210697i | −0.00364170 | − | 0.000394564i | ||||
\(535\) | −1085.71 | + | 626.836i | −2.02937 | + | 1.17166i | ||||
\(536\) | −27.2085 | − | 134.345i | −0.0507622 | − | 0.250644i | ||||
\(537\) | 230.123 | + | 132.862i | 0.428534 | + | 0.247414i | ||||
\(538\) | −105.148 | + | 46.4119i | −0.195443 | + | 0.0862674i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 267.490 | − | 293.275i | 0.495352 | − | 0.543102i | ||||
\(541\) | 60.3373 | + | 34.8357i | 0.111529 | + | 0.0643914i | 0.554727 | − | 0.832032i | \(-0.312823\pi\) |
−0.443198 | + | 0.896424i | \(0.646156\pi\) | |||||||
\(542\) | 36.4574 | − | 49.8426i | 0.0672646 | − | 0.0919605i | ||||
\(543\) | −75.9860 | − | 131.612i | −0.139937 | − | 0.242379i | ||||
\(544\) | 8.16752 | − | 509.591i | 0.0150138 | − | 0.936748i | ||||
\(545\) | 73.0934i | 0.134116i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 466.463i | 0.852765i | 0.904543 | + | 0.426383i | \(0.140212\pi\) | ||||
−0.904543 | + | 0.426383i | \(0.859788\pi\) | |||||||
\(548\) | 306.638 | + | 964.734i | 0.559558 | + | 1.76046i | ||||
\(549\) | 41.8599 | + | 72.5034i | 0.0762475 | + | 0.132065i | ||||
\(550\) | −238.095 | + | 325.510i | −0.432899 | + | 0.591836i | ||||
\(551\) | 237.430 | + | 137.081i | 0.430908 | + | 0.248785i | ||||
\(552\) | 55.4574 | − | 165.256i | 0.100466 | − | 0.299377i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −287.659 | − | 651.707i | −0.519241 | − | 1.17637i | ||||
\(555\) | 238.023 | + | 137.423i | 0.428870 | + | 0.247608i | ||||
\(556\) | 192.198 | + | 42.1424i | 0.345679 | + | 0.0757957i | ||||
\(557\) | 118.835 | − | 68.6094i | 0.213348 | − | 0.123177i | −0.389518 | − | 0.921019i | \(-0.627358\pi\) |
0.602866 | + | 0.797842i | \(0.294025\pi\) | |||||||
\(558\) | 208.898 | + | 22.6333i | 0.374370 | + | 0.0405615i | ||||
\(559\) | 646.692i | 1.15687i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −191.706 | −0.341722 | ||||||||
\(562\) | 63.3712 | − | 584.897i | 0.112760 | − | 1.04074i | ||||
\(563\) | −84.5632 | − | 146.468i | −0.150201 | − | 0.260156i | 0.781100 | − | 0.624406i | \(-0.214659\pi\) |
−0.931301 | + | 0.364250i | \(0.881325\pi\) | |||||||
\(564\) | −17.0944 | + | 77.9620i | −0.0303092 | + | 0.138231i | ||||
\(565\) | −46.9240 | + | 81.2747i | −0.0830513 | + | 0.143849i | ||||
\(566\) | −759.324 | + | 335.161i | −1.34156 | + | 0.592157i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 81.5905 | − | 243.130i | 0.143645 | − | 0.428045i | ||||
\(569\) | −372.466 | + | 645.129i | −0.654597 | + | 1.13379i | 0.327398 | + | 0.944887i | \(0.393828\pi\) |
−0.981995 | + | 0.188908i | \(0.939505\pi\) | |||||||
\(570\) | 153.513 | + | 112.287i | 0.269320 | + | 0.196995i | ||||
\(571\) | −767.828 | + | 443.306i | −1.34471 | + | 0.776367i | −0.987494 | − | 0.157655i | \(-0.949606\pi\) |
−0.357213 | + | 0.934023i | \(0.616273\pi\) | |||||||
\(572\) | −978.505 | + | 311.015i | −1.71067 | + | 0.543732i | ||||
\(573\) | −119.647 | −0.208809 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 365.026 | 0.634827 | ||||||||
\(576\) | −481.696 | + | 203.458i | −0.836277 | + | 0.353225i | ||||
\(577\) | 207.900 | − | 120.031i | 0.360311 | − | 0.208026i | −0.308906 | − | 0.951093i | \(-0.599963\pi\) |
0.669217 | + | 0.743067i | \(0.266630\pi\) | |||||||
\(578\) | −57.0448 | − | 41.7255i | −0.0986935 | − | 0.0721894i | ||||
\(579\) | 37.0900 | − | 64.2417i | 0.0640586 | − | 0.110953i | ||||
\(580\) | 312.439 | + | 284.969i | 0.538687 | + | 0.491326i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −124.701 | − | 282.516i | −0.214263 | − | 0.485423i | ||||
\(583\) | −245.691 | + | 425.549i | −0.421425 | + | 0.729930i | ||||
\(584\) | 170.176 | + | 840.266i | 0.291398 | + | 1.43881i | ||||
\(585\) | 503.488 | + | 872.067i | 0.860663 | + | 1.49071i | ||||
\(586\) | 79.8311 | − | 736.817i | 0.136231 | − | 1.25737i | ||||
\(587\) | 190.873 | 0.325168 | 0.162584 | − | 0.986695i | \(-0.448017\pi\) | ||||
0.162584 | + | 0.986695i | \(0.448017\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 211.585i | 0.359227i | ||||||||
\(590\) | 74.7506 | − | 689.925i | 0.126696 | − | 1.16936i | ||||
\(591\) | −1.65299 | + | 0.954353i | −0.00279693 | + | 0.00161481i | ||||
\(592\) | −439.311 | − | 621.256i | −0.742080 | − | 1.04942i | ||||
\(593\) | −637.548 | − | 368.089i | −1.07512 | − | 0.620723i | −0.145547 | − | 0.989351i | \(-0.546494\pi\) |
−0.929577 | + | 0.368629i | \(0.879827\pi\) | |||||||
\(594\) | 166.913 | + | 378.150i | 0.280998 | + | 0.636617i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −123.220 | − | 112.386i | −0.206744 | − | 0.188567i | ||||
\(597\) | −100.137 | − | 57.8144i | −0.167734 | − | 0.0968415i | ||||
\(598\) | 750.078 | + | 548.646i | 1.25431 | + | 0.917468i | ||||
\(599\) | −558.330 | − | 967.057i | −0.932104 | − | 1.61445i | −0.779718 | − | 0.626131i | \(-0.784638\pi\) |
−0.152386 | − | 0.988321i | \(-0.548696\pi\) | |||||||
\(600\) | 73.6049 | + | 83.3444i | 0.122675 | + | 0.138907i | ||||
\(601\) | − | 183.100i | − | 0.304659i | −0.988330 | − | 0.152329i | \(-0.951323\pi\) | ||
0.988330 | − | 0.152329i | \(-0.0486774\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 139.991i | − | 0.232158i | ||||||
\(604\) | −118.293 | − | 372.169i | −0.195849 | − | 0.616173i | ||||
\(605\) | −170.132 | − | 294.678i | −0.281210 | − | 0.487071i | ||||
\(606\) | −41.3556 | − | 30.2496i | −0.0682436 | − | 0.0499168i | ||||
\(607\) | −394.026 | − | 227.491i | −0.649136 | − | 0.374779i | 0.138989 | − | 0.990294i | \(-0.455615\pi\) |
−0.788125 | + | 0.615515i | \(0.788948\pi\) | |||||||
\(608\) | −255.931 | − | 460.161i | −0.420938 | − | 0.756844i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −118.959 | + | 52.5079i | −0.195015 | + | 0.0860786i | ||||
\(611\) | −368.505 | − | 212.757i | −0.603118 | − | 0.348211i | ||||
\(612\) | 111.481 | − | 508.429i | 0.182159 | − | 0.830767i | ||||
\(613\) | −232.853 | + | 134.438i | −0.379859 | + | 0.219312i | −0.677757 | − | 0.735286i | \(-0.737048\pi\) |
0.297898 | + | 0.954598i | \(0.403714\pi\) | |||||||
\(614\) | 34.5395 | − | 318.789i | 0.0562533 | − | 0.519201i | ||||
\(615\) | − | 37.5375i | − | 0.0610366i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −184.934 | −0.299731 | −0.149866 | − | 0.988706i | \(-0.547884\pi\) | ||||
−0.149866 | + | 0.988706i | \(0.547884\pi\) | |||||||
\(618\) | 301.209 | + | 32.6348i | 0.487393 | + | 0.0528071i | ||||
\(619\) | −496.809 | − | 860.498i | −0.802599 | − | 1.39014i | −0.917900 | − | 0.396812i | \(-0.870116\pi\) |
0.115301 | − | 0.993331i | \(-0.463217\pi\) | |||||||
\(620\) | −69.8984 | + | 318.784i | −0.112739 | + | 0.514167i | ||||
\(621\) | 187.064 | − | 324.004i | 0.301229 | − | 0.521745i | ||||
\(622\) | −381.871 | − | 865.148i | −0.613940 | − | 1.39091i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 25.9787 | + | 281.892i | 0.0416325 | + | 0.451750i | ||||
\(625\) | 386.818 | − | 669.988i | 0.618909 | − | 1.07198i | ||||
\(626\) | 272.769 | − | 372.914i | 0.435732 | − | 0.595710i | ||||
\(627\) | −171.524 | + | 99.0292i | −0.273562 | + | 0.157941i | ||||
\(628\) | 34.1267 | + | 107.368i | 0.0543419 | + | 0.170969i | ||||
\(629\) | 757.408 | 1.20415 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 805.857 | 1.27711 | 0.638555 | − | 0.769576i | \(-0.279532\pi\) | ||||
0.638555 | + | 0.769576i | \(0.279532\pi\) | |||||||
\(632\) | −308.779 | − | 349.637i | −0.488575 | − | 0.553224i | ||||
\(633\) | 5.65451 | − | 3.26463i | 0.00893287 | − | 0.00515740i | ||||
\(634\) | −266.045 | + | 363.722i | −0.419629 | + | 0.573694i | ||||
\(635\) | −222.918 | + | 386.106i | −0.351053 | + | 0.608041i | ||||
\(636\) | 100.098 | + | 91.2976i | 0.157387 | + | 0.143550i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −402.860 | + | 177.820i | −0.631442 | + | 0.278714i | ||||
\(639\) | 130.957 | − | 226.825i | 0.204941 | − | 0.354969i | ||||
\(640\) | −233.580 | − | 777.849i | −0.364969 | − | 1.21539i | ||||
\(641\) | −2.75221 | − | 4.76696i | −0.00429361 | − | 0.00743676i | 0.863871 | − | 0.503714i | \(-0.168033\pi\) |
−0.868164 | + | 0.496277i | \(0.834700\pi\) | |||||||
\(642\) | −357.849 | − | 38.7715i | −0.557397 | − | 0.0603917i | ||||
\(643\) | −1024.08 | −1.59266 | −0.796331 | − | 0.604861i | \(-0.793229\pi\) | ||||
−0.796331 | + | 0.604861i | \(0.793229\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 192.414i | 0.298317i | ||||||||
\(646\) | 521.084 | + | 56.4574i | 0.806632 | + | 0.0873954i | ||||
\(647\) | −395.404 | + | 228.287i | −0.611134 | + | 0.352839i | −0.773409 | − | 0.633907i | \(-0.781450\pi\) |
0.162275 | + | 0.986746i | \(0.448117\pi\) | |||||||
\(648\) | −464.860 | + | 94.1465i | −0.717377 | + | 0.145288i | ||||
\(649\) | 625.834 | + | 361.325i | 0.964304 | + | 0.556741i | ||||
\(650\) | −542.325 | + | 239.379i | −0.834346 | + | 0.368275i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −716.473 | − | 653.480i | −1.09888 | − | 1.00227i | ||||
\(653\) | 24.4603 | + | 14.1222i | 0.0374584 | + | 0.0216266i | 0.518612 | − | 0.855010i | \(-0.326449\pi\) |
−0.481154 | + | 0.876636i | \(0.659782\pi\) | |||||||
\(654\) | −12.3896 | + | 16.9383i | −0.0189443 | + | 0.0258996i | ||||
\(655\) | 450.907 | + | 780.994i | 0.688407 | + | 1.19236i | ||||
\(656\) | −43.4817 | + | 94.3859i | −0.0662831 | + | 0.143881i | ||||
\(657\) | 875.579i | 1.33269i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 132.188i | − | 0.200589i | −0.994958 | − | 0.100295i | \(-0.968021\pi\) | ||
0.994958 | − | 0.100295i | \(-0.0319785\pi\) | |||||||
\(660\) | −291.141 | + | 92.5382i | −0.441122 | + | 0.140209i | ||||
\(661\) | 346.924 | + | 600.889i | 0.524847 | + | 0.909061i | 0.999581 | + | 0.0289321i | \(0.00921065\pi\) |
−0.474735 | + | 0.880129i | \(0.657456\pi\) | |||||||
\(662\) | 24.4401 | − | 33.4132i | 0.0369186 | − | 0.0504731i | ||||
\(663\) | −244.038 | − | 140.895i | −0.368082 | − | 0.212512i | ||||
\(664\) | −92.5022 | + | 275.645i | −0.139311 | + | 0.415129i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −313.794 | − | 710.917i | −0.471162 | − | 1.06744i | ||||
\(667\) | 345.175 | + | 199.287i | 0.517504 | + | 0.298781i | ||||
\(668\) | −51.4976 | + | 234.864i | −0.0770922 | + | 0.351592i | ||||
\(669\) | 220.652 | − | 127.393i | 0.329823 | − | 0.190424i | ||||
\(670\) | 216.168 | + | 23.4209i | 0.322638 | + | 0.0349566i | ||||
\(671\) | − | 135.408i | − | 0.201800i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 532.137 | 0.790694 | 0.395347 | − | 0.918532i | \(-0.370624\pi\) | ||||
0.395347 | + | 0.918532i | \(0.370624\pi\) | |||||||
\(674\) | −7.53246 | + | 69.5222i | −0.0111757 | + | 0.103149i | ||||
\(675\) | 119.327 | + | 206.680i | 0.176780 | + | 0.306192i | ||||
\(676\) | −813.885 | − | 178.457i | −1.20397 | − | 0.263990i | ||||
\(677\) | −143.115 | + | 247.883i | −0.211396 | + | 0.366149i | −0.952152 | − | 0.305626i | \(-0.901134\pi\) |
0.740756 | + | 0.671775i | \(0.234468\pi\) | |||||||
\(678\) | −24.6503 | + | 10.8805i | −0.0363573 | + | 0.0160479i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 766.440 | + | 257.205i | 1.12712 | + | 0.378243i | ||||
\(681\) | −138.808 | + | 240.423i | −0.203830 | + | 0.353043i | ||||
\(682\) | −274.301 | − | 200.638i | −0.402202 | − | 0.294191i | ||||
\(683\) | −387.838 | + | 223.918i | −0.567844 | + | 0.327845i | −0.756288 | − | 0.654239i | \(-0.772989\pi\) |
0.188443 | + | 0.982084i | \(0.439656\pi\) | |||||||
\(684\) | −162.893 | − | 512.490i | −0.238148 | − | 0.749254i | ||||
\(685\) | −1605.76 | −2.34417 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −377.724 | −0.549817 | ||||||||
\(688\) | 222.884 | − | 483.815i | 0.323959 | − | 0.703219i | ||||
\(689\) | −625.519 | + | 361.143i | −0.907865 | + | 0.524156i | ||||
\(690\) | 223.176 | + | 163.242i | 0.323443 | + | 0.236583i | ||||
\(691\) | 510.366 | − | 883.980i | 0.738591 | − | 1.27928i | −0.214539 | − | 0.976715i | \(-0.568825\pi\) |
0.953130 | − | 0.302561i | \(-0.0978417\pi\) | |||||||
\(692\) | −375.659 | + | 411.871i | −0.542860 | + | 0.595189i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 354.331 | + | 802.754i | 0.510563 | + | 1.15671i | ||||
\(695\) | −156.059 | + | 270.302i | −0.224545 | + | 0.388924i | ||||
\(696\) | 24.1000 | + | 118.997i | 0.0346264 | + | 0.170972i | ||||
\(697\) | −51.7221 | − | 89.5854i | −0.0742068 | − | 0.128530i | ||||
\(698\) | −93.7387 | + | 865.180i | −0.134296 | + | 1.23951i | ||||
\(699\) | −150.225 | −0.214914 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1311.02i | − | 1.87021i | −0.354369 | − | 0.935106i | \(-0.615304\pi\) | ||
0.354369 | − | 0.935106i | \(-0.384696\pi\) | |||||||
\(702\) | −65.4465 | + | 604.051i | −0.0932287 | + | 0.860472i | ||||
\(703\) | 677.669 | − | 391.252i | 0.963967 | − | 0.556546i | ||||
\(704\) | 839.249 | + | 104.562i | 1.19212 | + | 0.148526i | ||||
\(705\) | −109.644 | − | 63.3028i | −0.155523 | − | 0.0897912i | ||||
\(706\) | −227.027 | − | 514.342i | −0.321568 | − | 0.728530i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 134.267 | − | 147.210i | 0.189642 | − | 0.207923i | ||||
\(709\) | 465.495 | + | 268.754i | 0.656552 | + | 0.379061i | 0.790962 | − | 0.611865i | \(-0.209581\pi\) |
−0.134410 | + | 0.990926i | \(0.542914\pi\) | |||||||
\(710\) | 328.342 | + | 240.166i | 0.462454 | + | 0.338263i | ||||
\(711\) | −238.199 | − | 412.573i | −0.335020 | − | 0.580271i | ||||
\(712\) | −6.43850 | + | 5.68610i | −0.00904283 | + | 0.00798610i | ||||
\(713\) | 307.601i | 0.431417i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1628.68i | − | 2.27787i | ||||||
\(716\) | 1112.08 | − | 353.472i | 1.55319 | − | 0.493677i | ||||
\(717\) | 8.70704 | + | 15.0810i | 0.0121437 | + | 0.0210335i | ||||
\(718\) | −426.050 | − | 311.635i | −0.593385 | − | 0.434032i | ||||
\(719\) | 233.275 | + | 134.681i | 0.324443 | + | 0.187318i | 0.653371 | − | 0.757037i | \(-0.273354\pi\) |
−0.328928 | + | 0.944355i | \(0.606687\pi\) | |||||||
\(720\) | −76.1187 | − | 825.955i | −0.105720 | − | 1.14716i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −165.128 | + | 72.8866i | −0.228710 | + | 0.100951i | ||||
\(723\) | −276.334 | − | 159.541i | −0.382204 | − | 0.220666i | ||||
\(724\) | −651.890 | − | 142.937i | −0.900400 | − | 0.197427i | ||||
\(725\) | −220.185 | + | 127.124i | −0.303703 | + | 0.175343i | ||||
\(726\) | 10.5231 | − | 97.1252i | 0.0144947 | − | 0.133781i | ||||
\(727\) | − | 460.316i | − | 0.633172i | −0.948564 | − | 0.316586i | \(-0.897463\pi\) | ||
0.948564 | − | 0.316586i | \(-0.102537\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −356.185 | −0.488594 | ||||||||
\(730\) | −1352.03 | − | 146.487i | −1.85209 | − | 0.200666i | ||||
\(731\) | 265.124 | + | 459.208i | 0.362686 | + | 0.628191i | ||||
\(732\) | −36.4674 | − | 7.99605i | −0.0498188 | − | 0.0109236i | ||||
\(733\) | −33.3410 | + | 57.7484i | −0.0454857 | + | 0.0787836i | −0.887872 | − | 0.460091i | \(-0.847817\pi\) |
0.842386 | + | 0.538874i | \(0.181150\pi\) | |||||||
\(734\) | 125.130 | + | 283.490i | 0.170478 | + | 0.386226i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −372.070 | − | 668.979i | −0.505530 | − | 0.908939i | ||||
\(737\) | −113.211 | + | 196.087i | −0.153610 | + | 0.266061i | ||||
\(738\) | −62.6580 | + | 85.6626i | −0.0849024 | + | 0.116074i | ||||
\(739\) | 808.772 | − | 466.944i | 1.09441 | − | 0.631860i | 0.159665 | − | 0.987171i | \(-0.448958\pi\) |
0.934748 | + | 0.355311i | \(0.115625\pi\) | |||||||
\(740\) | 1150.26 | − | 365.607i | 1.55441 | − | 0.494064i | ||||
\(741\) | −291.128 | −0.392885 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1198.23 | −1.61269 | −0.806345 | − | 0.591446i | \(-0.798557\pi\) | ||||
−0.806345 | + | 0.591446i | \(0.798557\pi\) | |||||||
\(744\) | −70.2328 | + | 62.0255i | −0.0943989 | + | 0.0833676i | ||||
\(745\) | 229.104 | − | 132.273i | 0.307523 | − | 0.177548i | ||||
\(746\) | −690.576 | + | 944.117i | −0.925705 | + | 1.26557i | ||||
\(747\) | −148.471 | + | 257.160i | −0.198757 | + | 0.344257i | ||||
\(748\) | −567.318 | + | 622.005i | −0.758446 | + | 0.831557i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 103.003 | − | 45.4651i | 0.137338 | − | 0.0606201i | ||||
\(751\) | 84.2993 | − | 146.011i | 0.112249 | − | 0.194422i | −0.804427 | − | 0.594051i | \(-0.797528\pi\) |
0.916677 | + | 0.399629i | \(0.130861\pi\) | |||||||
\(752\) | 202.366 | + | 286.178i | 0.269103 | + | 0.380555i | ||||
\(753\) | 40.2239 | + | 69.6698i | 0.0534182 | + | 0.0925230i | ||||
\(754\) | −643.522 | − | 69.7230i | −0.853477 | − | 0.0924708i | ||||
\(755\) | 619.458 | 0.820474 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 209.207i | 0.276364i | 0.990407 | + | 0.138182i | \(0.0441259\pi\) | ||||
−0.990407 | + | 0.138182i | \(0.955874\pi\) | |||||||
\(758\) | 254.860 | + | 27.6131i | 0.336227 | + | 0.0364289i | ||||
\(759\) | −249.360 | + | 143.968i | −0.328538 | + | 0.189681i | ||||
\(760\) | 818.614 | − | 165.791i | 1.07712 | − | 0.218146i | ||||
\(761\) | −479.127 | − | 276.624i | −0.629602 | − | 0.363501i | 0.150996 | − | 0.988534i | \(-0.451752\pi\) |
−0.780598 | + | 0.625033i | \(0.785085\pi\) | |||||||
\(762\) | −117.104 | + | 51.6891i | −0.153680 | + | 0.0678334i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −354.073 | + | 388.205i | −0.463447 | + | 0.508121i | ||||
\(765\) | 715.041 | + | 412.829i | 0.934695 | + | 0.539646i | ||||
\(766\) | −295.093 | + | 403.435i | −0.385239 | + | 0.526678i | ||||
\(767\) | 531.115 | + | 919.919i | 0.692458 | + | 1.19937i | ||||
\(768\) | 77.7191 | − | 219.848i | 0.101197 | − | 0.286260i | ||||
\(769\) | 219.524i | 0.285467i | 0.989761 | + | 0.142734i | \(0.0455892\pi\) | ||||
−0.989761 | + | 0.142734i | \(0.954411\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 78.4096i | 0.101699i | ||||||||
\(772\) | −98.6763 | − | 310.452i | −0.127819 | − | 0.402140i | ||||
\(773\) | −333.337 | − | 577.357i | −0.431225 | − | 0.746904i | 0.565754 | − | 0.824574i | \(-0.308585\pi\) |
−0.996979 | + | 0.0776701i | \(0.975252\pi\) | |||||||
\(774\) | 321.180 | − | 439.100i | 0.414961 | − | 0.567312i | ||||
\(775\) | −169.928 | − | 98.1082i | −0.219262 | − | 0.126591i | ||||
\(776\) | −1285.67 | − | 431.452i | −1.65680 | − | 0.555995i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 174.786 | + | 395.988i | 0.224661 | + | 0.508981i | ||||
\(779\) | −92.5538 | − | 53.4359i | −0.118811 | − | 0.0685956i | ||||
\(780\) | −438.628 | − | 96.1761i | −0.562343 | − | 0.123303i | ||||
\(781\) | −366.866 | + | 211.810i | −0.469738 | + | 0.271204i | ||||
\(782\) | 757.549 | + | 82.0774i | 0.968733 | + | 0.104958i | ||||
\(783\) | 260.587i | 0.332806i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −178.710 | −0.227656 | ||||||||
\(786\) | −27.8898 | + | 257.414i | −0.0354832 | + | 0.327499i | ||||
\(787\) | 459.932 | + | 796.626i | 0.584412 | + | 1.01223i | 0.994948 | + | 0.100387i | \(0.0320081\pi\) |
−0.410536 | + | 0.911844i | \(0.634659\pi\) | |||||||
\(788\) | −1.79523 | + | 8.18746i | −0.00227821 | + | 0.0103902i | ||||
\(789\) | −145.378 | + | 251.803i | −0.184256 | + | 0.319141i | ||||
\(790\) | 676.926 | − | 298.791i | 0.856868 | − | 0.378216i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 818.865 | + | 274.798i | 1.03392 | + | 0.346967i | ||||
\(793\) | 99.5187 | − | 172.371i | 0.125496 | − | 0.217366i | ||||
\(794\) | −1129.79 | − | 826.386i | −1.42291 | − | 1.04079i | ||||
\(795\) | −186.115 | + | 107.453i | −0.234106 | + | 0.135161i | ||||
\(796\) | −483.920 | + | 153.813i | −0.607940 | + | 0.193232i | ||||
\(797\) | 1016.13 | 1.27494 | 0.637470 | − | 0.770476i | \(-0.279981\pi\) | ||||
0.637470 | + | 0.770476i | \(0.279981\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −348.895 | −0.436664 | ||||||||
\(800\) | 488.236 | + | 7.82525i | 0.610295 | + | 0.00978156i | ||||
\(801\) | −7.59744 | + | 4.38638i | −0.00948494 | + | 0.00547613i | ||||
\(802\) | 292.149 | + | 213.693i | 0.364276 | + | 0.266450i | ||||
\(803\) | 708.078 | − | 1226.43i | 0.881791 | − | 1.52731i | ||||
\(804\) | 46.1238 | + | 42.0686i | 0.0573679 | + | 0.0523241i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −201.720 | − | 457.007i | −0.250273 | − | 0.567007i | ||||
\(807\) | 26.1727 | − | 45.3325i | 0.0324321 | − | 0.0561741i | ||||
\(808\) | −220.531 | + | 44.6634i | −0.272934 | + | 0.0552765i | ||||
\(809\) | −565.950 | − | 980.254i | −0.699567 | − | 1.21169i | −0.968617 | − | 0.248560i | \(-0.920043\pi\) |
0.269049 | − | 0.963126i | \(-0.413291\pi\) | |||||||
\(810\) | 81.0407 | − | 747.981i | 0.100050 | − | 0.923433i | ||||
\(811\) | 481.066 | 0.593176 | 0.296588 | − | 0.955006i | \(-0.404151\pi\) | ||||
0.296588 | + | 0.955006i | \(0.404151\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.1242i | 0.0345931i | ||||||||
\(814\) | −135.384 | + | 1249.55i | −0.166319 | + | 1.53507i | ||||
\(815\) | 1332.15 | − | 769.117i | 1.63454 | − | 0.943702i | ||||
\(816\) | 134.014 | + | 189.518i | 0.164233 | + | 0.232252i | ||||
\(817\) | 474.423 | + | 273.908i | 0.580690 | + | 0.335261i | ||||
\(818\) | 289.806 | + | 656.570i | 0.354286 | + | 0.802653i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −121.793 | − | 111.085i | −0.148528 | − | 0.135469i | ||||
\(821\) | 630.185 | + | 363.838i | 0.767582 | + | 0.443164i | 0.832011 | − | 0.554758i | \(-0.187189\pi\) |
−0.0644292 | + | 0.997922i | \(0.520523\pi\) | |||||||
\(822\) | −372.111 | − | 272.181i | −0.452690 | − | 0.331120i | ||||
\(823\) | 313.323 | + | 542.692i | 0.380709 | + | 0.659407i | 0.991164 | − | 0.132644i | \(-0.0423468\pi\) |
−0.610455 | + | 0.792051i | \(0.709013\pi\) | |||||||
\(824\) | 997.256 | − | 880.718i | 1.21026 | − | 1.06883i | ||||
\(825\) | − | 183.673i | − | 0.222633i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1468.52i | 1.77572i | 0.460116 | + | 0.887859i | \(0.347808\pi\) | ||||
−0.460116 | + | 0.887859i | \(0.652192\pi\) | |||||||
\(828\) | −236.813 | − | 745.055i | −0.286007 | − | 0.899824i | ||||
\(829\) | −409.352 | − | 709.019i | −0.493790 | − | 0.855270i | 0.506184 | − | 0.862425i | \(-0.331056\pi\) |
−0.999974 | + | 0.00715566i | \(0.997722\pi\) | |||||||
\(830\) | −372.254 | − | 272.286i | −0.448499 | − | 0.328055i | ||||
\(831\) | 280.969 | + | 162.218i | 0.338110 | + | 0.195208i | ||||
\(832\) | 991.498 | + | 749.915i | 1.19170 | + | 0.901341i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −81.9814 | + | 36.1861i | −0.0982990 | + | 0.0433886i | ||||
\(835\) | −330.306 | − | 190.702i | −0.395576 | − | 0.228386i | ||||
\(836\) | −186.284 | + | 849.579i | −0.222827 | + | 1.01624i | ||||
\(837\) | −174.165 | + | 100.554i | −0.208083 | + | 0.120137i | ||||
\(838\) | −168.228 | + | 1552.69i | −0.200749 | + | 1.85285i | ||||
\(839\) | − | 1108.84i | − | 1.32162i | −0.750555 | − | 0.660808i | \(-0.770214\pi\) | ||
0.750555 | − | 0.660808i | \(-0.229786\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 563.386 | 0.669900 | ||||||||
\(842\) | −228.585 | − | 24.7663i | −0.271479 | − | 0.0294136i | ||||
\(843\) | 133.970 | + | 232.042i | 0.158920 | + | 0.275258i | ||||
\(844\) | 6.14109 | − | 28.0075i | 0.00727618 | − | 0.0331843i | ||||
\(845\) | 660.850 | − | 1144.63i | 0.782072 | − | 1.35459i | ||||
\(846\) | 144.547 | + | 327.479i | 0.170860 | + | 0.387091i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 592.443 | − | 54.5986i | 0.698636 | − | 0.0643852i | ||||
\(849\) | 189.005 | − | 327.366i | 0.222621 | − | 0.385590i | ||||
\(850\) | −286.960 | + | 392.316i | −0.337600 | + | 0.461549i | ||||
\(851\) | 985.191 | − | 568.800i | 1.15769 | − | 0.668390i | ||||
\(852\) | 35.3796 | + | 111.310i | 0.0415254 | + | 0.130646i | ||||
\(853\) | 610.400 | 0.715592 | 0.357796 | − | 0.933800i | \(-0.383528\pi\) | ||||
0.357796 | + | 0.933800i | \(0.383528\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 853.017 | 0.997680 | ||||||||
\(856\) | −1184.78 | + | 1046.33i | −1.38409 | + | 1.22235i | ||||
\(857\) | −384.614 | + | 222.057i | −0.448791 | + | 0.259110i | −0.707319 | − | 0.706894i | \(-0.750096\pi\) |
0.258529 | + | 0.966004i | \(0.416762\pi\) | |||||||
\(858\) | 276.066 | − | 377.423i | 0.321755 | − | 0.439886i | ||||
\(859\) | 40.7547 | − | 70.5892i | 0.0474443 | − | 0.0821760i | −0.841328 | − | 0.540525i | \(-0.818226\pi\) |
0.888772 | + | 0.458349i | \(0.151559\pi\) | |||||||
\(860\) | 624.302 | + | 569.413i | 0.725932 | + | 0.662108i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 566.677 | − | 250.128i | 0.657398 | − | 0.290171i | ||||
\(863\) | 525.730 | − | 910.592i | 0.609189 | − | 1.05515i | −0.382185 | − | 0.924086i | \(-0.624828\pi\) |
0.991374 | − | 0.131061i | \(-0.0418384\pi\) | |||||||
\(864\) | 257.151 | − | 429.357i | 0.297628 | − | 0.496941i | ||||
\(865\) | −442.134 | − | 765.799i | −0.511138 | − | 0.885317i | ||||
\(866\) | −1184.62 | − | 128.349i | −1.36792 | − | 0.148208i | ||||
\(867\) | 32.1882 | 0.0371259 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 770.524i | 0.886679i | ||||||||
\(870\) | −191.471 | − | 20.7451i | −0.220082 | − | 0.0238450i | ||||
\(871\) | −288.230 | + | 166.409i | −0.330918 | + | 0.191056i | ||||
\(872\) | 18.2931 | + | 90.3245i | 0.0209784 | + | 0.103583i | ||||
\(873\) | −1199.45 | − | 692.505i | −1.37395 | − | 0.793248i | ||||
\(874\) | 720.194 | − | 317.889i | 0.824020 | − | 0.363717i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −288.482 | − | 263.119i | −0.329318 | − | 0.300364i | ||||
\(877\) | −1350.68 | − | 779.814i | −1.54011 | − | 0.889183i | −0.998831 | − | 0.0483410i | \(-0.984607\pi\) |
−0.541280 | − | 0.840842i | \(-0.682060\pi\) | |||||||
\(878\) | 952.747 | − | 1302.54i | 1.08513 | − | 1.48354i | ||||
\(879\) | 168.767 | + | 292.312i | 0.191998 | + | 0.332551i | ||||
\(880\) | −561.328 | + | 1218.48i | −0.637873 | + | 1.38463i | ||||
\(881\) | − | 1515.22i | − | 1.71989i | −0.510389 | − | 0.859944i | \(-0.670499\pi\) | ||
0.510389 | − | 0.859944i | \(-0.329501\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 763.828i | − | 0.865037i | −0.901625 | − | 0.432519i | \(-0.857625\pi\) | ||
0.901625 | − | 0.432519i | \(-0.142375\pi\) | |||||||
\(884\) | −1179.33 | + | 374.846i | −1.33408 | + | 0.424034i | ||||
\(885\) | 158.026 | + | 273.709i | 0.178561 | + | 0.309276i | ||||
\(886\) | 525.206 | − | 718.033i | 0.592783 | − | 0.810421i | ||||
\(887\) | −496.554 | − | 286.686i | −0.559813 | − | 0.323208i | 0.193258 | − | 0.981148i | \(-0.438095\pi\) |
−0.753070 | + | 0.657940i | \(0.771428\pi\) | |||||||
\(888\) | 328.528 | + | 110.249i | 0.369964 | + | 0.124154i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −5.50216 | − | 12.4654i | −0.00618221 | − | 0.0140061i | ||||
\(891\) | 678.496 | + | 391.730i | 0.761500 | + | 0.439652i | ||||
\(892\) | 239.639 | − | 1092.92i | 0.268654 | − | 1.22524i | ||||
\(893\) | −312.163 | + | 180.228i | −0.349567 | + | 0.201823i | ||||
\(894\) | 75.5124 | + | 8.18146i | 0.0844658 | + | 0.00915153i | ||||
\(895\) | 1851.01i | 2.06817i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −423.240 | −0.471840 | ||||||||
\(898\) | −56.5335 | + | 521.787i | −0.0629549 | + | 0.581055i | ||||
\(899\) | −107.125 | − | 185.546i | −0.119160 | − | 0.206391i | ||||
\(900\) | 487.123 | + | 106.809i | 0.541248 | + | 0.118677i | ||||
\(901\) | −296.115 | + | 512.887i | −0.328652 | + | 0.569242i | ||||
\(902\) | 157.041 | − | 69.3167i | 0.174103 | − | 0.0768477i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −37.6452 | + | 112.178i | −0.0416430 | + | 0.124091i | ||||
\(905\) | 529.315 | − | 916.800i | 0.584878 | − | 1.01304i | ||||
\(906\) | 143.550 | + | 105.000i | 0.158444 | + | 0.115894i | ||||
\(907\) | −885.036 | + | 510.976i | −0.975784 | + | 0.563369i | −0.900995 | − | 0.433830i | \(-0.857162\pi\) |
−0.0747894 | + | 0.997199i | \(0.523828\pi\) | |||||||
\(908\) | 369.293 | + | 1161.86i | 0.406710 | + | 1.27958i | ||||
\(909\) | −229.799 | −0.252804 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 630.111 | 0.691669 | 0.345835 | − | 0.938295i | \(-0.387596\pi\) | ||||
0.345835 | + | 0.938295i | \(0.387596\pi\) | |||||||
\(912\) | 217.804 | + | 100.338i | 0.238820 | + | 0.110020i | ||||
\(913\) | 415.930 | − | 240.137i | 0.455564 | − | 0.263020i | ||||
\(914\) | −628.714 | − | 459.873i | −0.687871 | − | 0.503144i | ||||
\(915\) | 29.6104 | − | 51.2868i | 0.0323611 | − | 0.0560511i | ||||
\(916\) | −1117.80 | + | 1225.55i | −1.22031 | + | 1.33794i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 201.170 | + | 455.760i | 0.219139 | + | 0.496471i | ||||
\(919\) | 421.489 | − | 730.041i | 0.458639 | − | 0.794386i | −0.540250 | − | 0.841504i | \(-0.681670\pi\) |
0.998889 | + | 0.0471182i | \(0.0150038\pi\) | |||||||
\(920\) | 1190.10 | − | 241.026i | 1.29358 | − | 0.261985i | ||||
\(921\) | 73.0182 | + | 126.471i | 0.0792814 | + | 0.137319i | ||||
\(922\) | −34.1920 | + | 315.582i | −0.0370846 | + | 0.342280i | ||||
\(923\) | −622.683 | −0.674630 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 725.668i | 0.784506i | ||||||||
\(926\) | 113.929 | − | 1051.53i | 0.123034 | − | 1.13557i | ||||
\(927\) | 1176.76 | − | 679.405i | 1.26943 | − | 0.732907i | ||||
\(928\) | 457.413 | + | 273.954i | 0.492902 | + | 0.295209i | ||||
\(929\) | −670.867 | − | 387.325i | −0.722139 | − | 0.416927i | 0.0934003 | − | 0.995629i | \(-0.470226\pi\) |
−0.815540 | + | 0.578701i | \(0.803560\pi\) | |||||||
\(930\) | −60.0190 | − | 135.976i | −0.0645366 | − | 0.146211i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −444.561 | + | 487.415i | −0.476997 | + | 0.522977i | ||||
\(933\) | 372.990 | + | 215.346i | 0.399774 | + | 0.230810i | ||||
\(934\) | −705.266 | − | 515.867i | −0.755103 | − | 0.552321i | ||||
\(935\) | −667.708 | − | 1156.50i | −0.714126 | − | 1.23690i | ||||
\(936\) | 840.434 | + | 951.641i | 0.897900 | + | 1.01671i | ||||
\(937\) | − | 1586.27i | − | 1.69293i | −0.532447 | − | 0.846463i | \(-0.678727\pi\) | ||
0.532447 | − | 0.846463i | \(-0.321273\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 210.421i | 0.224090i | ||||||||
\(940\) | −529.860 | + | 168.414i | −0.563681 | + | 0.179164i | ||||
\(941\) | 410.023 | + | 710.181i | 0.435731 | + | 0.754708i | 0.997355 | − | 0.0726842i | \(-0.0231565\pi\) |
−0.561624 | + | 0.827393i | \(0.689823\pi\) | |||||||
\(942\) | −41.4134 | − | 30.2919i | −0.0439633 | − | 0.0321570i | ||||
\(943\) | −134.554 | − | 77.6849i | −0.142687 | − | 0.0823805i | ||||
\(944\) | −80.2954 | − | 871.277i | −0.0850587 | − | 0.922963i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −804.977 | + | 355.312i | −0.850928 | + | 0.375594i | ||||
\(947\) | 551.949 | + | 318.668i | 0.582839 | + | 0.336502i | 0.762261 | − | 0.647270i | \(-0.224089\pi\) |
−0.179422 | + | 0.983772i | \(0.557423\pi\) | |||||||
\(948\) | 207.514 | + | 45.5007i | 0.218896 | + | 0.0479965i | ||||
\(949\) | 1802.74 | − | 1040.81i | 1.89962 | − | 1.09675i | ||||
\(950\) | −54.0915 | + | 499.248i | −0.0569384 | + | 0.525524i | ||||
\(951\) | − | 205.234i | − | 0.215809i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −350.626 | −0.367918 | −0.183959 | − | 0.982934i | \(-0.558891\pi\) | ||||
−0.183959 | + | 0.982934i | \(0.558891\pi\) | |||||||
\(954\) | 604.086 | + | 65.4503i | 0.633214 | + | 0.0686062i | ||||
\(955\) | −416.729 | − | 721.796i | −0.436365 | − | 0.755807i | ||||
\(956\) | 74.6983 | + | 16.3788i | 0.0781363 | + | 0.0171326i | ||||
\(957\) | 100.277 | − | 173.684i | 0.104782 | − | 0.181488i | ||||
\(958\) | −440.852 | − | 998.772i | −0.460179 | − | 1.04256i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 295.007 | + | 223.127i | 0.307299 | + | 0.232424i | ||||
\(961\) | −397.826 | + | 689.055i | −0.413971 | + | 0.717019i | ||||
\(962\) | −1090.70 | + | 1491.15i | −1.13379 | + | 1.55005i | ||||
\(963\) | −1398.04 | + | 807.161i | −1.45176 | + | 0.838174i | ||||
\(964\) | −1335.40 | + | 424.453i | −1.38527 | + | 0.440304i | ||||
\(965\) | 516.734 | 0.535475 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −649.816 | −0.671992 | −0.335996 | − | 0.941863i | \(-0.609073\pi\) | ||||
−0.335996 | + | 0.941863i | \(0.609073\pi\) | |||||||
\(968\) | −283.989 | − | 321.566i | −0.293377 | − | 0.332197i | ||||
\(969\) | −206.726 | + | 119.354i | −0.213340 | + | 0.123172i | ||||
\(970\) | 1270.00 | − | 1736.28i | 1.30928 | − | 1.78998i | ||||
\(971\) | −485.305 | + | 840.573i | −0.499799 | + | 0.865677i | −1.00000 | 0.000232071i | \(-0.999926\pi\) | |
0.500201 | + | 0.865909i | \(0.333259\pi\) | |||||||
\(972\) | 524.982 | − | 575.589i | 0.540105 | − | 0.592169i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1186.06 | − | 523.519i | 1.21772 | − | 0.537494i | ||||
\(975\) | 134.991 | − | 233.811i | 0.138452 | − | 0.239807i | ||||
\(976\) | −133.862 | + | 94.6583i | −0.137154 | + | 0.0969860i | ||||
\(977\) | 300.437 | + | 520.373i | 0.307510 | + | 0.532623i | 0.977817 | − | 0.209461i | \(-0.0671709\pi\) |
−0.670307 | + | 0.742084i | \(0.733838\pi\) | |||||||
\(978\) | 439.074 | + | 47.5719i | 0.448951 | + | 0.0486421i | ||||
\(979\) | 14.1890 | 0.0144934 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 94.1205i | 0.0959434i | ||||||||
\(982\) | −1455.63 | − | 157.712i | −1.48231 | − | 0.160602i | ||||
\(983\) | −1098.66 | + | 634.311i | −1.11766 | + | 0.645281i | −0.940802 | − | 0.338955i | \(-0.889926\pi\) |
−0.176857 | + | 0.984236i | \(0.556593\pi\) | |||||||
\(984\) | −9.39453 | − | 46.3866i | −0.00954728 | − | 0.0471409i | ||||
\(985\) | −11.5146 | − | 6.64797i | −0.0116900 | − | 0.00674921i | ||||
\(986\) | −485.541 | + | 214.315i | −0.492435 | + | 0.217358i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −861.537 | + | 944.586i | −0.872001 | + | 0.956059i | ||||
\(989\) | 689.714 | + | 398.207i | 0.697385 | + | 0.402636i | ||||
\(990\) | −808.885 | + | 1105.86i | −0.817055 | + | 1.11703i | ||||
\(991\) | 774.555 | + | 1341.57i | 0.781590 | + | 1.35375i | 0.931015 | + | 0.364980i | \(0.118924\pi\) |
−0.149426 | + | 0.988773i | \(0.547742\pi\) | |||||||
\(992\) | −6.59420 | + | 411.428i | −0.00664738 | + | 0.414746i | ||||
\(993\) | 18.8538i | 0.0189867i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 805.464i | − | 0.809512i | ||||||
\(996\) | −40.1112 | − | 126.197i | −0.0402723 | − | 0.126703i | ||||
\(997\) | 470.469 | + | 814.876i | 0.471885 | + | 0.817328i | 0.999483 | − | 0.0321661i | \(-0.0102406\pi\) |
−0.527598 | + | 0.849494i | \(0.676907\pi\) | |||||||
\(998\) | 31.5308 | − | 43.1072i | 0.0315940 | − | 0.0431936i | ||||
\(999\) | 644.116 | + | 371.881i | 0.644761 | + | 0.372253i |
(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 | 392.3.j.e.117.6 | 28 | ||
7.2 | even | 3 | 392.3.h.a.293.26 | 28 | |||
7.3 | odd | 6 | inner | 392.3.j.e.325.4 | 28 | ||
7.4 | even | 3 | 56.3.j.a.45.4 | yes | 28 | ||
7.5 | odd | 6 | 392.3.h.a.293.25 | 28 | |||
7.6 | odd | 2 | 56.3.j.a.5.6 | yes | 28 | ||
8.5 | even | 2 | inner | 392.3.j.e.117.4 | 28 | ||
28.11 | odd | 6 | 224.3.n.a.17.9 | 28 | |||
28.19 | even | 6 | 1568.3.h.a.881.17 | 28 | |||
28.23 | odd | 6 | 1568.3.h.a.881.11 | 28 | |||
28.27 | even | 2 | 224.3.n.a.145.6 | 28 | |||
56.5 | odd | 6 | 392.3.h.a.293.28 | 28 | |||
56.11 | odd | 6 | 224.3.n.a.17.6 | 28 | |||
56.13 | odd | 2 | 56.3.j.a.5.4 | ✓ | 28 | ||
56.19 | even | 6 | 1568.3.h.a.881.12 | 28 | |||
56.27 | even | 2 | 224.3.n.a.145.9 | 28 | |||
56.37 | even | 6 | 392.3.h.a.293.27 | 28 | |||
56.45 | odd | 6 | inner | 392.3.j.e.325.6 | 28 | ||
56.51 | odd | 6 | 1568.3.h.a.881.18 | 28 | |||
56.53 | even | 6 | 56.3.j.a.45.6 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.j.a.5.4 | ✓ | 28 | 56.13 | odd | 2 | ||
56.3.j.a.5.6 | yes | 28 | 7.6 | odd | 2 | ||
56.3.j.a.45.4 | yes | 28 | 7.4 | even | 3 | ||
56.3.j.a.45.6 | yes | 28 | 56.53 | even | 6 | ||
224.3.n.a.17.6 | 28 | 56.11 | odd | 6 | |||
224.3.n.a.17.9 | 28 | 28.11 | odd | 6 | |||
224.3.n.a.145.6 | 28 | 28.27 | even | 2 | |||
224.3.n.a.145.9 | 28 | 56.27 | even | 2 | |||
392.3.h.a.293.25 | 28 | 7.5 | odd | 6 | |||
392.3.h.a.293.26 | 28 | 7.2 | even | 3 | |||
392.3.h.a.293.27 | 28 | 56.37 | even | 6 | |||
392.3.h.a.293.28 | 28 | 56.5 | odd | 6 | |||
392.3.j.e.117.4 | 28 | 8.5 | even | 2 | inner | ||
392.3.j.e.117.6 | 28 | 1.1 | even | 1 | trivial | ||
392.3.j.e.325.4 | 28 | 7.3 | odd | 6 | inner | ||
392.3.j.e.325.6 | 28 | 56.45 | odd | 6 | inner | ||
1568.3.h.a.881.11 | 28 | 28.23 | odd | 6 | |||
1568.3.h.a.881.12 | 28 | 56.19 | even | 6 | |||
1568.3.h.a.881.17 | 28 | 28.19 | even | 6 | |||
1568.3.h.a.881.18 | 28 | 56.51 | odd | 6 |