Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,4,Mod(2,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.2");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.e (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.885028650086\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.28356903014400.8 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 209x^{4} + 1600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2.1 | ||
Root | \(-2.66260 - 2.66260i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.2 |
Dual form | 15.4.e.a.8.1 |
$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.66260 | + | 2.66260i | −0.941372 | + | 0.941372i | −0.998374 | − | 0.0570018i | \(-0.981846\pi\) |
0.0570018 | + | 0.998374i | \(0.481846\pi\) | |||||||
\(3\) | −4.37420 | + | 2.80471i | −0.841814 | + | 0.539767i | ||||
\(4\) | − | 6.17891i | − | 0.772364i | ||||||
\(5\) | 9.55729 | + | 5.80157i | 0.854830 | + | 0.518908i | ||||
\(6\) | 4.17891 | − | 19.1146i | 0.284339 | − | 1.30058i | ||||
\(7\) | 9.35782 | + | 9.35782i | 0.505275 | + | 0.505275i | 0.913072 | − | 0.407798i | \(-0.133703\pi\) |
−0.407798 | + | 0.913072i | \(0.633703\pi\) | |||||||
\(8\) | −4.84884 | − | 4.84884i | −0.214291 | − | 0.214291i | ||||
\(9\) | 11.2672 | − | 24.5367i | 0.417303 | − | 0.908768i | ||||
\(10\) | −40.8945 | + | 10.0000i | −1.29320 | + | 0.316228i | ||||
\(11\) | 34.1375i | 0.935712i | 0.883805 | + | 0.467856i | \(0.154973\pi\) | ||||
−0.883805 | + | 0.467856i | \(0.845027\pi\) | |||||||
\(12\) | 17.3301 | + | 27.0278i | 0.416897 | + | 0.650187i | ||||
\(13\) | 2.82109 | − | 2.82109i | 0.0601869 | − | 0.0601869i | −0.676373 | − | 0.736560i | \(-0.736449\pi\) |
0.736560 | + | 0.676373i | \(0.236449\pi\) | |||||||
\(14\) | −49.8323 | −0.951303 | ||||||||
\(15\) | −58.0772 | + | 1.42827i | −0.999698 | + | 0.0245851i | ||||
\(16\) | 75.2524 | 1.17582 | ||||||||
\(17\) | 64.2384 | − | 64.2384i | 0.916477 | − | 0.916477i | −0.0802942 | − | 0.996771i | \(-0.525586\pi\) |
0.996771 | + | 0.0802942i | \(0.0255860\pi\) | |||||||
\(18\) | 35.3316 | + | 95.3316i | 0.462652 | + | 1.24833i | ||||
\(19\) | − | 19.0735i | − | 0.230303i | −0.993348 | − | 0.115151i | \(-0.963265\pi\) | ||
0.993348 | − | 0.115151i | \(-0.0367353\pi\) | |||||||
\(20\) | 35.8474 | − | 59.0536i | 0.400786 | − | 0.660240i | ||||
\(21\) | −67.1789 | − | 14.6869i | −0.698078 | − | 0.152617i | ||||
\(22\) | −90.8945 | − | 90.8945i | −0.880854 | − | 0.880854i | ||||
\(23\) | −51.4018 | − | 51.4018i | −0.466001 | − | 0.466001i | 0.434616 | − | 0.900616i | \(-0.356884\pi\) |
−0.900616 | + | 0.434616i | \(0.856884\pi\) | |||||||
\(24\) | 34.8094 | + | 7.61018i | 0.296060 | + | 0.0647259i | ||||
\(25\) | 57.6836 | + | 110.895i | 0.461469 | + | 0.887156i | ||||
\(26\) | 15.0229i | 0.113317i | ||||||||
\(27\) | 19.5337 | + | 138.930i | 0.139232 | + | 0.990260i | ||||
\(28\) | 57.8211 | − | 57.8211i | 0.390256 | − | 0.390256i | ||||
\(29\) | 50.5042 | 0.323393 | 0.161697 | − | 0.986841i | \(-0.448303\pi\) | ||||
0.161697 | + | 0.986841i | \(0.448303\pi\) | |||||||
\(30\) | 150.834 | − | 158.439i | 0.917944 | − | 0.964232i | ||||
\(31\) | −93.3673 | −0.540944 | −0.270472 | − | 0.962728i | \(-0.587180\pi\) | ||||
−0.270472 | + | 0.962728i | \(0.587180\pi\) | |||||||
\(32\) | −161.576 | + | 161.576i | −0.892592 | + | 0.892592i | ||||
\(33\) | −95.7458 | − | 149.324i | −0.505067 | − | 0.787696i | ||||
\(34\) | 342.083i | 1.72549i | ||||||||
\(35\) | 35.1454 | + | 143.725i | 0.169733 | + | 0.694115i | ||||
\(36\) | −151.610 | − | 69.6188i | −0.701899 | − | 0.322309i | ||||
\(37\) | −161.537 | − | 161.537i | −0.717743 | − | 0.717743i | 0.250400 | − | 0.968142i | \(-0.419438\pi\) |
−0.968142 | + | 0.250400i | \(0.919438\pi\) | |||||||
\(38\) | 50.7850 | + | 50.7850i | 0.216800 | + | 0.216800i | ||||
\(39\) | −4.42765 | + | 20.2524i | −0.0181793 | + | 0.0831531i | ||||
\(40\) | −18.2109 | − | 74.4727i | −0.0719850 | − | 0.294379i | ||||
\(41\) | − | 88.7935i | − | 0.338225i | −0.985597 | − | 0.169112i | \(-0.945910\pi\) | ||
0.985597 | − | 0.169112i | \(-0.0540901\pi\) | |||||||
\(42\) | 217.976 | − | 139.765i | 0.800820 | − | 0.513482i | ||||
\(43\) | 176.399 | − | 176.399i | 0.625596 | − | 0.625596i | −0.321361 | − | 0.946957i | \(-0.604140\pi\) |
0.946957 | + | 0.321361i | \(0.104140\pi\) | |||||||
\(44\) | 210.932 | 0.722710 | ||||||||
\(45\) | 250.035 | − | 169.137i | 0.828290 | − | 0.560300i | ||||
\(46\) | 273.725 | 0.877360 | ||||||||
\(47\) | 38.2843 | − | 38.2843i | 0.118816 | − | 0.118816i | −0.645199 | − | 0.764015i | \(-0.723225\pi\) |
0.764015 | + | 0.645199i | \(0.223225\pi\) | |||||||
\(48\) | −329.169 | + | 211.061i | −0.989820 | + | 0.634668i | ||||
\(49\) | − | 167.863i | − | 0.489395i | ||||||
\(50\) | −448.857 | − | 141.680i | −1.26956 | − | 0.400730i | ||||
\(51\) | −100.821 | + | 461.162i | −0.276819 | + | 1.26619i | ||||
\(52\) | −17.4313 | − | 17.4313i | −0.0464862 | − | 0.0464862i | ||||
\(53\) | 344.569 | + | 344.569i | 0.893022 | + | 0.893022i | 0.994806 | − | 0.101784i | \(-0.0324551\pi\) |
−0.101784 | + | 0.994806i | \(0.532455\pi\) | |||||||
\(54\) | −421.925 | − | 317.904i | −1.06327 | − | 0.801134i | ||||
\(55\) | −198.051 | + | 326.262i | −0.485549 | + | 0.799875i | ||||
\(56\) | − | 90.7492i | − | 0.216551i | ||||||
\(57\) | 53.4956 | + | 83.4310i | 0.124310 | + | 0.193872i | ||||
\(58\) | −134.473 | + | 134.473i | −0.304433 | + | 0.304433i | ||||
\(59\) | −421.133 | −0.929268 | −0.464634 | − | 0.885503i | \(-0.653814\pi\) | ||||
−0.464634 | + | 0.885503i | \(0.653814\pi\) | |||||||
\(60\) | 8.82514 | + | 358.854i | 0.0189887 | + | 0.772130i | ||||
\(61\) | 2.00000 | 0.00419793 | 0.00209897 | − | 0.999998i | \(-0.499332\pi\) | ||||
0.00209897 | + | 0.999998i | \(0.499332\pi\) | |||||||
\(62\) | 248.600 | − | 248.600i | 0.509229 | − | 0.509229i | ||||
\(63\) | 335.046 | − | 124.174i | 0.670030 | − | 0.248325i | ||||
\(64\) | − | 258.409i | − | 0.504704i | ||||||
\(65\) | 43.3287 | − | 10.5952i | 0.0826811 | − | 0.0202181i | ||||
\(66\) | 652.524 | + | 142.657i | 1.21697 | + | 0.266059i | ||||
\(67\) | 430.987 | + | 430.987i | 0.785872 | + | 0.785872i | 0.980815 | − | 0.194943i | \(-0.0624521\pi\) |
−0.194943 | + | 0.980815i | \(0.562452\pi\) | |||||||
\(68\) | −396.923 | − | 396.923i | −0.707853 | − | 0.707853i | ||||
\(69\) | 369.009 | + | 80.6742i | 0.643818 | + | 0.140754i | ||||
\(70\) | −476.262 | − | 289.105i | −0.813202 | − | 0.493639i | ||||
\(71\) | − | 733.866i | − | 1.22667i | −0.789822 | − | 0.613337i | \(-0.789827\pi\) | ||
0.789822 | − | 0.613337i | \(-0.210173\pi\) | |||||||
\(72\) | −173.607 | + | 64.3420i | −0.284164 | + | 0.105316i | ||||
\(73\) | −348.073 | + | 348.073i | −0.558067 | + | 0.558067i | −0.928757 | − | 0.370690i | \(-0.879121\pi\) |
0.370690 | + | 0.928757i | \(0.379121\pi\) | |||||||
\(74\) | 860.216 | 1.35133 | ||||||||
\(75\) | −563.347 | − | 323.288i | −0.867329 | − | 0.497735i | ||||
\(76\) | −117.853 | −0.177877 | ||||||||
\(77\) | −319.452 | + | 319.452i | −0.472792 | + | 0.472792i | ||||
\(78\) | −42.1349 | − | 65.7131i | −0.0611646 | − | 0.0953915i | ||||
\(79\) | − | 588.019i | − | 0.837434i | −0.908117 | − | 0.418717i | \(-0.862480\pi\) | ||
0.908117 | − | 0.418717i | \(-0.137520\pi\) | |||||||
\(80\) | 719.209 | + | 436.582i | 1.00512 | + | 0.610141i | ||||
\(81\) | −475.102 | − | 552.919i | −0.651717 | − | 0.758462i | ||||
\(82\) | 236.422 | + | 236.422i | 0.318395 | + | 0.318395i | ||||
\(83\) | −217.997 | − | 217.997i | −0.288293 | − | 0.288293i | 0.548112 | − | 0.836405i | \(-0.315347\pi\) |
−0.836405 | + | 0.548112i | \(0.815347\pi\) | |||||||
\(84\) | −90.7492 | + | 415.092i | −0.117876 | + | 0.539170i | ||||
\(85\) | 986.629 | − | 241.262i | 1.25900 | − | 0.307865i | ||||
\(86\) | 939.362i | 1.17784i | ||||||||
\(87\) | −220.915 | + | 141.650i | −0.272237 | + | 0.174557i | ||||
\(88\) | 165.527 | − | 165.527i | 0.200514 | − | 0.200514i | ||||
\(89\) | −1272.00 | −1.51497 | −0.757483 | − | 0.652855i | \(-0.773571\pi\) | ||||
−0.757483 | + | 0.652855i | \(0.773571\pi\) | |||||||
\(90\) | −215.399 | + | 1116.09i | −0.252278 | + | 1.30718i | ||||
\(91\) | 52.7985 | 0.0608219 | ||||||||
\(92\) | −317.607 | + | 317.607i | −0.359922 | + | 0.359922i | ||||
\(93\) | 408.407 | − | 261.868i | 0.455374 | − | 0.291984i | ||||
\(94\) | 203.872i | 0.223700i | ||||||||
\(95\) | 110.656 | − | 182.291i | 0.119506 | − | 0.196870i | ||||
\(96\) | 253.591 | − | 1159.94i | 0.269605 | − | 1.23319i | ||||
\(97\) | −432.111 | − | 432.111i | −0.452312 | − | 0.452312i | 0.443809 | − | 0.896121i | \(-0.353627\pi\) |
−0.896121 | + | 0.443809i | \(0.853627\pi\) | |||||||
\(98\) | 446.951 | + | 446.951i | 0.460703 | + | 0.460703i | ||||
\(99\) | 837.622 | + | 384.633i | 0.850345 | + | 0.390475i | ||||
\(100\) | 685.207 | − | 356.422i | 0.685207 | − | 0.356422i | ||||
\(101\) | 1662.30i | 1.63767i | 0.574029 | + | 0.818835i | \(0.305380\pi\) | ||||
−0.574029 | + | 0.818835i | \(0.694620\pi\) | |||||||
\(102\) | −959.444 | − | 1496.34i | −0.931364 | − | 1.45254i | ||||
\(103\) | −774.495 | + | 774.495i | −0.740906 | + | 0.740906i | −0.972752 | − | 0.231847i | \(-0.925523\pi\) |
0.231847 | + | 0.972752i | \(0.425523\pi\) | |||||||
\(104\) | −27.3581 | −0.0257950 | ||||||||
\(105\) | −556.841 | − | 530.110i | −0.517544 | − | 0.492700i | ||||
\(106\) | −1834.90 | −1.68133 | ||||||||
\(107\) | 1170.26 | − | 1170.26i | 1.05732 | − | 1.05732i | 0.0590633 | − | 0.998254i | \(-0.481189\pi\) |
0.998254 | − | 0.0590633i | \(-0.0188114\pi\) | |||||||
\(108\) | 858.433 | − | 120.697i | 0.764841 | − | 0.107537i | ||||
\(109\) | 1264.60i | 1.11125i | 0.831432 | + | 0.555627i | \(0.187522\pi\) | ||||
−0.831432 | + | 0.555627i | \(0.812478\pi\) | |||||||
\(110\) | −341.375 | − | 1396.04i | −0.295898 | − | 1.21006i | ||||
\(111\) | 1159.66 | + | 253.529i | 0.991620 | + | 0.216792i | ||||
\(112\) | 704.198 | + | 704.198i | 0.594111 | + | 0.594111i | ||||
\(113\) | −381.173 | − | 381.173i | −0.317325 | − | 0.317325i | 0.530414 | − | 0.847739i | \(-0.322037\pi\) |
−0.847739 | + | 0.530414i | \(0.822037\pi\) | |||||||
\(114\) | −364.581 | − | 79.7062i | −0.299528 | − | 0.0654839i | ||||
\(115\) | −193.051 | − | 789.473i | −0.156540 | − | 0.640163i | ||||
\(116\) | − | 312.061i | − | 0.249777i | ||||||
\(117\) | −37.4346 | − | 101.006i | −0.0295798 | − | 0.0798121i | ||||
\(118\) | 1121.31 | − | 1121.31i | 0.874787 | − | 0.874787i | ||||
\(119\) | 1202.26 | 0.926145 | ||||||||
\(120\) | 288.533 | + | 274.682i | 0.219494 | + | 0.208958i | ||||
\(121\) | 165.633 | 0.124442 | ||||||||
\(122\) | −5.32521 | + | 5.32521i | −0.00395182 | + | 0.00395182i | ||||
\(123\) | 249.040 | + | 388.400i | 0.182563 | + | 0.284722i | ||||
\(124\) | 576.908i | 0.417805i | ||||||||
\(125\) | −92.0630 | + | 1394.51i | −0.0658749 | + | 0.997828i | ||||
\(126\) | −561.469 | + | 1222.72i | −0.396981 | + | 0.864513i | ||||
\(127\) | −439.588 | − | 439.588i | −0.307142 | − | 0.307142i | 0.536658 | − | 0.843800i | \(-0.319687\pi\) |
−0.843800 | + | 0.536658i | \(0.819687\pi\) | |||||||
\(128\) | −604.571 | − | 604.571i | −0.417477 | − | 0.417477i | ||||
\(129\) | −276.856 | + | 1266.35i | −0.188959 | + | 0.864312i | ||||
\(130\) | −87.1563 | + | 143.578i | −0.0588009 | + | 0.0968664i | ||||
\(131\) | − | 1399.28i | − | 0.933247i | −0.884456 | − | 0.466623i | \(-0.845470\pi\) | ||
0.884456 | − | 0.466623i | \(-0.154530\pi\) | |||||||
\(132\) | −922.659 | + | 591.605i | −0.608388 | + | 0.390095i | ||||
\(133\) | 178.486 | − | 178.486i | 0.116366 | − | 0.116366i | ||||
\(134\) | −2295.09 | −1.47960 | ||||||||
\(135\) | −619.321 | + | 1441.12i | −0.394834 | + | 0.918752i | ||||
\(136\) | −622.964 | −0.392785 | ||||||||
\(137\) | −1092.28 | + | 1092.28i | −0.681169 | + | 0.681169i | −0.960264 | − | 0.279095i | \(-0.909966\pi\) |
0.279095 | + | 0.960264i | \(0.409966\pi\) | |||||||
\(138\) | −1197.33 | + | 767.720i | −0.738574 | + | 0.473570i | ||||
\(139\) | − | 2498.43i | − | 1.52456i | −0.647245 | − | 0.762282i | \(-0.724079\pi\) | ||
0.647245 | − | 0.762282i | \(-0.275921\pi\) | |||||||
\(140\) | 888.066 | − | 217.160i | 0.536109 | − | 0.131096i | ||||
\(141\) | −60.0866 | + | 274.840i | −0.0358880 | + | 0.164154i | ||||
\(142\) | 1953.99 | + | 1953.99i | 1.15476 | + | 1.15476i | ||||
\(143\) | 96.3049 | + | 96.3049i | 0.0563177 | + | 0.0563177i | ||||
\(144\) | 847.881 | − | 1846.45i | 0.490672 | − | 1.06855i | ||||
\(145\) | 482.684 | + | 293.004i | 0.276446 | + | 0.167811i | ||||
\(146\) | − | 1853.56i | − | 1.05070i | ||||||
\(147\) | 470.806 | + | 734.264i | 0.264159 | + | 0.411980i | ||||
\(148\) | −998.121 | + | 998.121i | −0.554358 | + | 0.554358i | ||||
\(149\) | 3570.40 | 1.96308 | 0.981538 | − | 0.191270i | \(-0.0612605\pi\) | ||||
0.981538 | + | 0.191270i | \(0.0612605\pi\) | |||||||
\(150\) | 2360.76 | − | 639.180i | 1.28503 | − | 0.347926i | ||||
\(151\) | 2687.14 | 1.44819 | 0.724094 | − | 0.689701i | \(-0.242258\pi\) | ||||
0.724094 | + | 0.689701i | \(0.242258\pi\) | |||||||
\(152\) | −92.4842 | + | 92.4842i | −0.0493517 | + | 0.0493517i | ||||
\(153\) | −852.415 | − | 2299.99i | −0.450416 | − | 1.21531i | ||||
\(154\) | − | 1701.15i | − | 0.890146i | ||||||
\(155\) | −892.338 | − | 541.676i | −0.462415 | − | 0.280700i | ||||
\(156\) | 125.137 | + | 27.3581i | 0.0642245 | + | 0.0140410i | ||||
\(157\) | −1810.48 | − | 1810.48i | −0.920333 | − | 0.920333i | 0.0767201 | − | 0.997053i | \(-0.475555\pi\) |
−0.997053 | + | 0.0767201i | \(0.975555\pi\) | |||||||
\(158\) | 1565.66 | + | 1565.66i | 0.788337 | + | 0.788337i | ||||
\(159\) | −2473.63 | − | 540.795i | −1.23378 | − | 0.269735i | ||||
\(160\) | −2481.63 | + | 606.836i | −1.22619 | + | 0.299841i | ||||
\(161\) | − | 962.017i | − | 0.470916i | ||||||
\(162\) | 2737.21 | + | 207.196i | 1.32750 | + | 0.100487i | ||||
\(163\) | −2679.06 | + | 2679.06i | −1.28736 | + | 1.28736i | −0.350982 | + | 0.936382i | \(0.614152\pi\) |
−0.936382 | + | 0.350982i | \(0.885848\pi\) | |||||||
\(164\) | −548.647 | −0.261232 | ||||||||
\(165\) | −48.7575 | − | 1982.61i | −0.0230046 | − | 0.935430i | ||||
\(166\) | 1160.88 | 0.542782 | ||||||||
\(167\) | −139.543 | + | 139.543i | −0.0646597 | + | 0.0646597i | −0.738697 | − | 0.674037i | \(-0.764559\pi\) |
0.674037 | + | 0.738697i | \(0.264559\pi\) | |||||||
\(168\) | 254.525 | + | 396.955i | 0.116887 | + | 0.182296i | ||||
\(169\) | 2181.08i | 0.992755i | ||||||||
\(170\) | −1984.62 | + | 3269.39i | −0.895372 | + | 1.47500i | ||||
\(171\) | −468.000 | − | 214.904i | −0.209292 | − | 0.0961059i | ||||
\(172\) | −1089.95 | − | 1089.95i | −0.483188 | − | 0.483188i | ||||
\(173\) | 881.613 | + | 881.613i | 0.387444 | + | 0.387444i | 0.873775 | − | 0.486331i | \(-0.161665\pi\) |
−0.486331 | + | 0.873775i | \(0.661665\pi\) | |||||||
\(174\) | 211.053 | − | 965.367i | 0.0919532 | − | 0.420599i | ||||
\(175\) | −497.938 | + | 1577.52i | −0.215089 | + | 0.681426i | ||||
\(176\) | 2568.93i | 1.10023i | ||||||||
\(177\) | 1842.12 | − | 1181.16i | 0.782271 | − | 0.501588i | ||||
\(178\) | 3386.84 | − | 3386.84i | 1.42615 | − | 1.42615i | ||||
\(179\) | −2512.87 | −1.04928 | −0.524638 | − | 0.851325i | \(-0.675799\pi\) | ||||
−0.524638 | + | 0.851325i | \(0.675799\pi\) | |||||||
\(180\) | −1045.08 | − | 1544.94i | −0.432755 | − | 0.639741i | ||||
\(181\) | 269.796 | 0.110795 | 0.0553973 | − | 0.998464i | \(-0.482357\pi\) | ||||
0.0553973 | + | 0.998464i | \(0.482357\pi\) | |||||||
\(182\) | −140.581 | + | 140.581i | −0.0572560 | + | 0.0572560i | ||||
\(183\) | −8.74839 | + | 5.60943i | −0.00353388 | + | 0.00226591i | ||||
\(184\) | 498.478i | 0.199719i | ||||||||
\(185\) | −606.687 | − | 2481.02i | −0.241106 | − | 0.985990i | ||||
\(186\) | −390.173 | + | 1784.68i | −0.153811 | + | 0.703542i | ||||
\(187\) | 2192.94 | + | 2192.94i | 0.857559 | + | 0.857559i | ||||
\(188\) | −236.555 | − | 236.555i | −0.0917690 | − | 0.0917690i | ||||
\(189\) | −1117.29 | + | 1482.87i | −0.430003 | + | 0.570703i | ||||
\(190\) | 190.735 | + | 780.000i | 0.0728281 | + | 0.297827i | ||||
\(191\) | 2420.22i | 0.916864i | 0.888729 | + | 0.458432i | \(0.151589\pi\) | ||||
−0.888729 | + | 0.458432i | \(0.848411\pi\) | |||||||
\(192\) | 724.762 | + | 1130.33i | 0.272423 | + | 0.424867i | ||||
\(193\) | 1965.28 | − | 1965.28i | 0.732973 | − | 0.732973i | −0.238234 | − | 0.971208i | \(-0.576569\pi\) |
0.971208 | + | 0.238234i | \(0.0765686\pi\) | |||||||
\(194\) | 2301.08 | 0.851588 | ||||||||
\(195\) | −159.812 | + | 167.870i | −0.0586890 | + | 0.0616484i | ||||
\(196\) | −1037.21 | −0.377991 | ||||||||
\(197\) | 832.602 | − | 832.602i | 0.301119 | − | 0.301119i | −0.540333 | − | 0.841452i | \(-0.681702\pi\) |
0.841452 | + | 0.540333i | \(0.181702\pi\) | |||||||
\(198\) | −3254.38 | + | 1206.13i | −1.16807 | + | 0.432909i | ||||
\(199\) | − | 1540.54i | − | 0.548775i | −0.961619 | − | 0.274387i | \(-0.911525\pi\) | ||
0.961619 | − | 0.274387i | \(-0.0884750\pi\) | |||||||
\(200\) | 258.011 | − | 817.409i | 0.0912208 | − | 0.288998i | ||||
\(201\) | −3094.02 | − | 676.426i | −1.08575 | − | 0.237370i | ||||
\(202\) | −4426.04 | − | 4426.04i | −1.54166 | − | 1.54166i | ||||
\(203\) | 472.609 | + | 472.609i | 0.163402 | + | 0.163402i | ||||
\(204\) | 2849.48 | + | 622.964i | 0.977957 | + | 0.213805i | ||||
\(205\) | 515.142 | − | 848.625i | 0.175508 | − | 0.289125i | ||||
\(206\) | − | 4124.35i | − | 1.39494i | ||||||
\(207\) | −1840.38 | + | 682.079i | −0.617949 | + | 0.229023i | ||||
\(208\) | 212.294 | − | 212.294i | 0.0707689 | − | 0.0707689i | ||||
\(209\) | 651.119 | 0.215497 | ||||||||
\(210\) | 2894.12 | − | 71.1739i | 0.951015 | − | 0.0233879i | ||||
\(211\) | −10.9380 | −0.00356874 | −0.00178437 | − | 0.999998i | \(-0.500568\pi\) | ||||
−0.00178437 | + | 0.999998i | \(0.500568\pi\) | |||||||
\(212\) | 2129.06 | − | 2129.06i | 0.689738 | − | 0.689738i | ||||
\(213\) | 2058.28 | + | 3210.07i | 0.662118 | + | 1.03263i | ||||
\(214\) | 6231.86i | 1.99066i | ||||||||
\(215\) | 2709.29 | − | 662.507i | 0.859405 | − | 0.210152i | ||||
\(216\) | 578.932 | − | 768.364i | 0.182367 | − | 0.242039i | ||||
\(217\) | −873.714 | − | 873.714i | −0.273325 | − | 0.273325i | ||||
\(218\) | −3367.13 | − | 3367.13i | −1.04610 | − | 1.04610i | ||||
\(219\) | 546.295 | − | 2498.79i | 0.168563 | − | 0.771016i | ||||
\(220\) | 2015.94 | + | 1223.74i | 0.617794 | + | 0.375020i | ||||
\(221\) | − | 362.445i | − | 0.110320i | ||||||
\(222\) | −3762.75 | + | 2412.66i | −1.13757 | + | 0.729401i | ||||
\(223\) | 831.512 | − | 831.512i | 0.249696 | − | 0.249696i | −0.571150 | − | 0.820846i | \(-0.693503\pi\) |
0.820846 | + | 0.571150i | \(0.193503\pi\) | |||||||
\(224\) | −3024.00 | −0.902008 | ||||||||
\(225\) | 3370.92 | − | 165.900i | 0.998791 | − | 0.0491554i | ||||
\(226\) | 2029.83 | 0.597443 | ||||||||
\(227\) | −3441.18 | + | 3441.18i | −1.00616 | + | 1.00616i | −0.00618314 | + | 0.999981i | \(0.501968\pi\) |
−0.999981 | + | 0.00618314i | \(0.998032\pi\) | |||||||
\(228\) | 515.512 | − | 330.544i | 0.149740 | − | 0.0960124i | ||||
\(229\) | 1680.38i | 0.484903i | 0.970164 | + | 0.242451i | \(0.0779515\pi\) | ||||
−0.970164 | + | 0.242451i | \(0.922049\pi\) | |||||||
\(230\) | 2616.07 | + | 1588.03i | 0.749994 | + | 0.455269i | ||||
\(231\) | 501.375 | − | 2293.32i | 0.142805 | − | 0.653200i | ||||
\(232\) | −244.887 | − | 244.887i | −0.0693001 | − | 0.0693001i | ||||
\(233\) | −2106.74 | − | 2106.74i | −0.592348 | − | 0.592348i | 0.345917 | − | 0.938265i | \(-0.387568\pi\) |
−0.938265 | + | 0.345917i | \(0.887568\pi\) | |||||||
\(234\) | 368.613 | + | 169.265i | 0.102978 | + | 0.0472873i | ||||
\(235\) | 588.004 | − | 143.785i | 0.163222 | − | 0.0399129i | ||||
\(236\) | 2602.14i | 0.717733i | ||||||||
\(237\) | 1649.22 | + | 2572.11i | 0.452019 | + | 0.704964i | ||||
\(238\) | −3201.15 | + | 3201.15i | −0.871847 | + | 0.871847i | ||||
\(239\) | 261.125 | 0.0706728 | 0.0353364 | − | 0.999375i | \(-0.488750\pi\) | ||||
0.0353364 | + | 0.999375i | \(0.488750\pi\) | |||||||
\(240\) | −4370.45 | + | 107.481i | −1.17546 | + | 0.0289077i | ||||
\(241\) | −6001.45 | −1.60410 | −0.802048 | − | 0.597259i | \(-0.796256\pi\) | ||||
−0.802048 | + | 0.597259i | \(0.796256\pi\) | |||||||
\(242\) | −441.014 | + | 441.014i | −0.117147 | + | 0.117147i | ||||
\(243\) | 3628.97 | + | 1086.05i | 0.958018 | + | 0.286709i | ||||
\(244\) | − | 12.3578i | − | 0.00324233i | ||||||
\(245\) | 973.866 | − | 1604.31i | 0.253951 | − | 0.418350i | ||||
\(246\) | −1697.25 | − | 371.060i | −0.439889 | − | 0.0961704i | ||||
\(247\) | −53.8080 | − | 53.8080i | −0.0138612 | − | 0.0138612i | ||||
\(248\) | 452.723 | + | 452.723i | 0.115919 | + | 0.115919i | ||||
\(249\) | 1564.98 | + | 342.143i | 0.398300 | + | 0.0870781i | ||||
\(250\) | −3467.89 | − | 3958.15i | −0.877315 | − | 1.00134i | ||||
\(251\) | 3044.59i | 0.765630i | 0.923825 | + | 0.382815i | \(0.125045\pi\) | ||||
−0.923825 | + | 0.382815i | \(0.874955\pi\) | |||||||
\(252\) | −767.260 | − | 2070.22i | −0.191797 | − | 0.517506i | ||||
\(253\) | 1754.73 | − | 1754.73i | 0.436042 | − | 0.436042i | ||||
\(254\) | 2340.89 | 0.578271 | ||||||||
\(255\) | −3639.04 | + | 3822.54i | −0.893668 | + | 0.938732i | ||||
\(256\) | 5286.74 | 1.29071 | ||||||||
\(257\) | 946.317 | − | 946.317i | 0.229687 | − | 0.229687i | −0.582875 | − | 0.812562i | \(-0.698072\pi\) |
0.812562 | + | 0.582875i | \(0.198072\pi\) | |||||||
\(258\) | −2634.64 | − | 4108.95i | −0.635758 | − | 0.991521i | ||||
\(259\) | − | 3023.26i | − | 0.725314i | ||||||
\(260\) | −65.4670 | − | 267.724i | −0.0156157 | − | 0.0638598i | ||||
\(261\) | 569.040 | − | 1239.21i | 0.134953 | − | 0.293889i | ||||
\(262\) | 3725.72 | + | 3725.72i | 0.878532 | + | 0.878532i | ||||
\(263\) | −67.0257 | − | 67.0257i | −0.0157148 | − | 0.0157148i | 0.699206 | − | 0.714921i | \(-0.253537\pi\) |
−0.714921 | + | 0.699206i | \(0.753537\pi\) | |||||||
\(264\) | −259.792 | + | 1188.31i | −0.0605648 | + | 0.277027i | ||||
\(265\) | 1294.11 | + | 5292.18i | 0.299986 | + | 1.22678i | ||||
\(266\) | 950.474i | 0.219088i | ||||||||
\(267\) | 5563.99 | − | 3567.60i | 1.27532 | − | 0.817729i | ||||
\(268\) | 2663.03 | − | 2663.03i | 0.606979 | − | 0.606979i | ||||
\(269\) | −2658.15 | −0.602492 | −0.301246 | − | 0.953546i | \(-0.597403\pi\) | ||||
−0.301246 | + | 0.953546i | \(0.597403\pi\) | |||||||
\(270\) | −2188.12 | − | 5486.13i | −0.493202 | − | 1.23657i | ||||
\(271\) | 145.673 | 0.0326530 | 0.0163265 | − | 0.999867i | \(-0.494803\pi\) | ||||
0.0163265 | + | 0.999867i | \(0.494803\pi\) | |||||||
\(272\) | 4834.09 | − | 4834.09i | 1.07761 | − | 1.07761i | ||||
\(273\) | −230.951 | + | 148.085i | −0.0512007 | + | 0.0328296i | ||||
\(274\) | − | 5816.64i | − | 1.28247i | ||||||
\(275\) | −3785.66 | + | 1969.17i | −0.830123 | + | 0.431802i | ||||
\(276\) | 498.478 | − | 2280.07i | 0.108713 | − | 0.497261i | ||||
\(277\) | −1074.57 | − | 1074.57i | −0.233085 | − | 0.233085i | 0.580894 | − | 0.813979i | \(-0.302703\pi\) |
−0.813979 | + | 0.580894i | \(0.802703\pi\) | |||||||
\(278\) | 6652.34 | + | 6652.34i | 1.43518 | + | 1.43518i | ||||
\(279\) | −1051.98 | + | 2290.93i | −0.225737 | + | 0.491592i | ||||
\(280\) | 526.488 | − | 867.316i | 0.112370 | − | 0.185115i | ||||
\(281\) | 2020.29i | 0.428898i | 0.976735 | + | 0.214449i | \(0.0687956\pi\) | ||||
−0.976735 | + | 0.214449i | \(0.931204\pi\) | |||||||
\(282\) | −571.802 | − | 891.776i | −0.120746 | − | 0.188314i | ||||
\(283\) | −2400.34 | + | 2400.34i | −0.504189 | + | 0.504189i | −0.912737 | − | 0.408548i | \(-0.866035\pi\) |
0.408548 | + | 0.912737i | \(0.366035\pi\) | |||||||
\(284\) | −4534.49 | −0.947438 | ||||||||
\(285\) | 27.2420 | + | 1107.73i | 0.00566202 | + | 0.230233i | ||||
\(286\) | −512.844 | −0.106032 | ||||||||
\(287\) | 830.913 | − | 830.913i | 0.170896 | − | 0.170896i | ||||
\(288\) | 2144.05 | + | 5785.06i | 0.438678 | + | 1.18364i | ||||
\(289\) | − | 3340.15i | − | 0.679860i | ||||||
\(290\) | −2065.35 | + | 505.042i | −0.418212 | + | 0.102266i | ||||
\(291\) | 3102.09 | + | 678.191i | 0.624906 | + | 0.136619i | ||||
\(292\) | 2150.71 | + | 2150.71i | 0.431031 | + | 0.431031i | ||||
\(293\) | −2533.13 | − | 2533.13i | −0.505075 | − | 0.505075i | 0.407936 | − | 0.913011i | \(-0.366249\pi\) |
−0.913011 | + | 0.407936i | \(0.866249\pi\) | |||||||
\(294\) | −3208.62 | − | 701.482i | −0.636499 | − | 0.139154i | ||||
\(295\) | −4024.89 | − | 2443.23i | −0.794366 | − | 0.482204i | ||||
\(296\) | 1566.53i | 0.307611i | ||||||||
\(297\) | −4742.71 | + | 666.830i | −0.926598 | + | 0.130281i | ||||
\(298\) | −9506.54 | + | 9506.54i | −1.84798 | + | 1.84798i | ||||
\(299\) | −290.018 | −0.0560943 | ||||||||
\(300\) | −1997.57 | + | 3480.87i | −0.384432 | + | 0.669893i | ||||
\(301\) | 3301.42 | 0.632196 | ||||||||
\(302\) | −7154.79 | + | 7154.79i | −1.36328 | + | 1.36328i | ||||
\(303\) | −4662.27 | − | 7271.21i | −0.883961 | − | 1.37861i | ||||
\(304\) | − | 1435.32i | − | 0.270794i | ||||||
\(305\) | 19.1146 | + | 11.6031i | 0.00358852 | + | 0.00217834i | ||||
\(306\) | 8393.59 | + | 3854.31i | 1.56807 | + | 0.720052i | ||||
\(307\) | 3159.93 | + | 3159.93i | 0.587449 | + | 0.587449i | 0.936940 | − | 0.349491i | \(-0.113645\pi\) |
−0.349491 | + | 0.936940i | \(0.613645\pi\) | |||||||
\(308\) | 1973.87 | + | 1973.87i | 0.365167 | + | 0.365167i | ||||
\(309\) | 1215.56 | − | 5560.03i | 0.223788 | − | 1.02362i | ||||
\(310\) | 3818.21 | − | 933.673i | 0.699548 | − | 0.171061i | ||||
\(311\) | − | 7206.19i | − | 1.31391i | −0.753931 | − | 0.656954i | \(-0.771845\pi\) | ||
0.753931 | − | 0.656954i | \(-0.228155\pi\) | |||||||
\(312\) | 119.670 | − | 76.7315i | 0.0217146 | − | 0.0139233i | ||||
\(313\) | 2029.31 | − | 2029.31i | 0.366464 | − | 0.366464i | −0.499722 | − | 0.866186i | \(-0.666564\pi\) |
0.866186 | + | 0.499722i | \(0.166564\pi\) | |||||||
\(314\) | 9641.19 | 1.73275 | ||||||||
\(315\) | 3922.54 | + | 757.026i | 0.701619 | + | 0.135408i | ||||
\(316\) | −3633.31 | −0.646804 | ||||||||
\(317\) | 689.223 | − | 689.223i | 0.122116 | − | 0.122116i | −0.643408 | − | 0.765524i | \(-0.722480\pi\) |
0.765524 | + | 0.643408i | \(0.222480\pi\) | |||||||
\(318\) | 8026.21 | − | 5146.37i | 1.41537 | − | 0.907528i | ||||
\(319\) | 1724.09i | 0.302603i | ||||||||
\(320\) | 1499.18 | − | 2469.69i | 0.261895 | − | 0.431437i | ||||
\(321\) | −1836.70 | + | 8401.16i | −0.319360 | + | 1.46077i | ||||
\(322\) | 2561.47 | + | 2561.47i | 0.443308 | + | 0.443308i | ||||
\(323\) | −1225.25 | − | 1225.25i | −0.211067 | − | 0.211067i | ||||
\(324\) | −3416.44 | + | 2935.61i | −0.585809 | + | 0.503363i | ||||
\(325\) | 475.574 | + | 150.113i | 0.0811696 | + | 0.0256208i | ||||
\(326\) | − | 14266.6i | − | 2.42378i | ||||||
\(327\) | −3546.84 | − | 5531.60i | −0.599818 | − | 0.935469i | ||||
\(328\) | −430.546 | + | 430.546i | −0.0724784 | + | 0.0724784i | ||||
\(329\) | 716.516 | 0.120069 | ||||||||
\(330\) | 5408.72 | + | 5149.08i | 0.902243 | + | 0.858932i | ||||
\(331\) | −8226.53 | −1.36608 | −0.683038 | − | 0.730383i | \(-0.739342\pi\) | ||||
−0.683038 | + | 0.730383i | \(0.739342\pi\) | |||||||
\(332\) | −1346.99 | + | 1346.99i | −0.222667 | + | 0.222667i | ||||
\(333\) | −5783.64 | + | 2143.52i | −0.951777 | + | 0.352745i | ||||
\(334\) | − | 743.096i | − | 0.121738i | ||||||
\(335\) | 1618.67 | + | 6619.47i | 0.263992 | + | 1.07958i | ||||
\(336\) | −5055.37 | − | 1105.23i | −0.820813 | − | 0.179449i | ||||
\(337\) | 1777.34 | + | 1777.34i | 0.287294 | + | 0.287294i | 0.836009 | − | 0.548715i | \(-0.184883\pi\) |
−0.548715 | + | 0.836009i | \(0.684883\pi\) | |||||||
\(338\) | −5807.36 | − | 5807.36i | −0.934552 | − | 0.934552i | ||||
\(339\) | 2736.41 | + | 598.245i | 0.438411 | + | 0.0958472i | ||||
\(340\) | −1490.73 | − | 6096.29i | −0.237784 | − | 0.972405i | ||||
\(341\) | − | 3187.32i | − | 0.506168i | ||||||
\(342\) | 1818.30 | − | 673.895i | 0.287493 | − | 0.106550i | ||||
\(343\) | 4780.56 | − | 4780.56i | 0.752554 | − | 0.752554i | ||||
\(344\) | −1710.66 | −0.268119 | ||||||||
\(345\) | 3058.69 | + | 2911.86i | 0.477316 | + | 0.454403i | ||||
\(346\) | −4694.77 | −0.729458 | ||||||||
\(347\) | 1715.22 | − | 1715.22i | 0.265354 | − | 0.265354i | −0.561871 | − | 0.827225i | \(-0.689918\pi\) |
0.827225 | + | 0.561871i | \(0.189918\pi\) | |||||||
\(348\) | 875.242 | + | 1365.02i | 0.134821 | + | 0.210266i | ||||
\(349\) | 8603.96i | 1.31965i | 0.751417 | + | 0.659827i | \(0.229371\pi\) | ||||
−0.751417 | + | 0.659827i | \(0.770629\pi\) | |||||||
\(350\) | −2874.51 | − | 5526.13i | −0.438997 | − | 0.843954i | ||||
\(351\) | 447.039 | + | 336.827i | 0.0679806 | + | 0.0512208i | ||||
\(352\) | −5515.81 | − | 5515.81i | −0.835209 | − | 0.835209i | ||||
\(353\) | 5425.13 | + | 5425.13i | 0.817990 | + | 0.817990i | 0.985816 | − | 0.167827i | \(-0.0536750\pi\) |
−0.167827 | + | 0.985816i | \(0.553675\pi\) | |||||||
\(354\) | −1759.87 | + | 8049.77i | −0.264227 | + | 1.20859i | ||||
\(355\) | 4257.57 | − | 7013.77i | 0.636531 | − | 1.04860i | ||||
\(356\) | 7859.58i | 1.17010i | ||||||||
\(357\) | −5258.93 | + | 3372.00i | −0.779642 | + | 0.499903i | ||||
\(358\) | 6690.76 | − | 6690.76i | 0.987759 | − | 0.987759i | ||||
\(359\) | 11418.9 | 1.67874 | 0.839370 | − | 0.543560i | \(-0.182924\pi\) | ||||
0.839370 | + | 0.543560i | \(0.182924\pi\) | |||||||
\(360\) | −2032.50 | − | 392.260i | −0.297562 | − | 0.0574276i | ||||
\(361\) | 6495.20 | 0.946961 | ||||||||
\(362\) | −718.361 | + | 718.361i | −0.104299 | + | 0.104299i | ||||
\(363\) | −724.510 | + | 464.552i | −0.104757 | + | 0.0671699i | ||||
\(364\) | − | 326.237i | − | 0.0469766i | ||||||
\(365\) | −5346.01 | + | 1307.27i | −0.766638 | + | 0.187467i | ||||
\(366\) | 8.35782 | − | 38.2292i | 0.00119363 | − | 0.00545976i | ||||
\(367\) | 6554.73 | + | 6554.73i | 0.932299 | + | 0.932299i | 0.997849 | − | 0.0655499i | \(-0.0208802\pi\) |
−0.0655499 | + | 0.997849i | \(0.520880\pi\) | |||||||
\(368\) | −3868.11 | − | 3868.11i | −0.547932 | − | 0.547932i | ||||
\(369\) | −2178.70 | − | 1000.45i | −0.307368 | − | 0.141142i | ||||
\(370\) | 8221.34 | + | 4990.60i | 1.15515 | + | 0.701214i | ||||
\(371\) | 6448.83i | 0.902443i | ||||||||
\(372\) | −1618.06 | − | 2523.51i | −0.225518 | − | 0.351714i | ||||
\(373\) | −5967.46 | + | 5967.46i | −0.828374 | + | 0.828374i | −0.987292 | − | 0.158918i | \(-0.949199\pi\) |
0.158918 | + | 0.987292i | \(0.449199\pi\) | |||||||
\(374\) | −11677.8 | −1.61456 | ||||||||
\(375\) | −3508.49 | − | 6358.06i | −0.483140 | − | 0.875543i | ||||
\(376\) | −371.270 | −0.0509222 | ||||||||
\(377\) | 142.477 | − | 142.477i | 0.0194640 | − | 0.0194640i | ||||
\(378\) | −973.408 | − | 6923.18i | −0.132452 | − | 0.942037i | ||||
\(379\) | 1680.48i | 0.227758i | 0.993495 | + | 0.113879i | \(0.0363276\pi\) | ||||
−0.993495 | + | 0.113879i | \(0.963672\pi\) | |||||||
\(380\) | −1126.36 | − | 683.733i | −0.152055 | − | 0.0923020i | ||||
\(381\) | 3155.76 | + | 689.925i | 0.424342 | + | 0.0927715i | ||||
\(382\) | −6444.09 | − | 6444.09i | −0.863110 | − | 0.863110i | ||||
\(383\) | 7493.42 | + | 7493.42i | 0.999728 | + | 0.999728i | 1.00000 | 0.000271480i | \(-8.64148e-5\pi\) | |
−0.000271480 | 1.00000i | \(0.500086\pi\) | ||||||||
\(384\) | 4340.16 | + | 948.864i | 0.576779 | + | 0.126098i | ||||
\(385\) | −4906.42 | + | 1199.77i | −0.649492 | + | 0.158821i | ||||
\(386\) | 10465.5i | 1.38000i | ||||||||
\(387\) | −2340.74 | − | 6315.78i | −0.307459 | − | 0.829584i | ||||
\(388\) | −2669.98 | + | 2669.98i | −0.349349 | + | 0.349349i | ||||
\(389\) | −7966.97 | −1.03841 | −0.519205 | − | 0.854650i | \(-0.673772\pi\) | ||||
−0.519205 | + | 0.854650i | \(0.673772\pi\) | |||||||
\(390\) | −21.4567 | − | 872.487i | −0.00278591 | − | 0.113282i | ||||
\(391\) | −6603.94 | −0.854158 | ||||||||
\(392\) | −813.939 | + | 813.939i | −0.104873 | + | 0.104873i | ||||
\(393\) | 3924.57 | + | 6120.71i | 0.503736 | + | 0.785620i | ||||
\(394\) | 4433.78i | 0.566930i | ||||||||
\(395\) | 3411.43 | − | 5619.87i | 0.434551 | − | 0.715864i | ||||
\(396\) | 2376.61 | − | 5175.59i | 0.301589 | − | 0.656776i | ||||
\(397\) | −8188.88 | − | 8188.88i | −1.03523 | − | 1.03523i | −0.999356 | − | 0.0358786i | \(-0.988577\pi\) |
−0.0358786 | − | 0.999356i | \(-0.511423\pi\) | |||||||
\(398\) | 4101.85 | + | 4101.85i | 0.516601 | + | 0.516601i | ||||
\(399\) | −280.130 | + | 1281.33i | −0.0351480 | + | 0.160769i | ||||
\(400\) | 4340.83 | + | 8345.08i | 0.542604 | + | 1.04313i | ||||
\(401\) | − | 5167.66i | − | 0.643542i | −0.946817 | − | 0.321771i | \(-0.895722\pi\) | ||
0.946817 | − | 0.321771i | \(-0.104278\pi\) | |||||||
\(402\) | 10039.2 | − | 6437.08i | 1.24555 | − | 0.798638i | ||||
\(403\) | −263.398 | + | 263.398i | −0.0325577 | + | 0.0325577i | ||||
\(404\) | 10271.2 | 1.26488 | ||||||||
\(405\) | −1332.89 | − | 8040.74i | −0.163535 | − | 0.986537i | ||||
\(406\) | −2516.74 | −0.307645 | ||||||||
\(407\) | 5514.46 | − | 5514.46i | 0.671601 | − | 0.671601i | ||||
\(408\) | 2724.97 | − | 1747.24i | 0.330652 | − | 0.212012i | ||||
\(409\) | − | 8514.82i | − | 1.02941i | −0.857366 | − | 0.514707i | \(-0.827901\pi\) | ||
0.857366 | − | 0.514707i | \(-0.172099\pi\) | |||||||
\(410\) | 887.935 | + | 3631.17i | 0.106956 | + | 0.437392i | ||||
\(411\) | 1714.32 | − | 7841.41i | 0.205745 | − | 0.941090i | ||||
\(412\) | 4785.54 | + | 4785.54i | 0.572249 | + | 0.572249i | ||||
\(413\) | −3940.88 | − | 3940.88i | −0.469535 | − | 0.469535i | ||||
\(414\) | 3084.11 | − | 6716.32i | 0.366125 | − | 0.797316i | ||||
\(415\) | −818.738 | − | 3348.19i | −0.0968440 | − | 0.396039i | ||||
\(416\) | 911.644i | 0.107445i | ||||||||
\(417\) | 7007.39 | + | 10928.6i | 0.822910 | + | 1.28340i | ||||
\(418\) | −1733.67 | + | 1733.67i | −0.202863 | + | 0.202863i | ||||
\(419\) | −11939.7 | −1.39211 | −0.696053 | − | 0.717990i | \(-0.745062\pi\) | ||||
−0.696053 | + | 0.717990i | \(0.745062\pi\) | |||||||
\(420\) | −3275.50 | + | 3440.67i | −0.380543 | + | 0.399732i | ||||
\(421\) | 10873.3 | 1.25875 | 0.629373 | − | 0.777103i | \(-0.283312\pi\) | ||||
0.629373 | + | 0.777103i | \(0.283312\pi\) | |||||||
\(422\) | 29.1236 | − | 29.1236i | 0.00335951 | − | 0.00335951i | ||||
\(423\) | −508.016 | − | 1370.73i | −0.0583938 | − | 0.157558i | ||||
\(424\) | − | 3341.52i | − | 0.382733i | ||||||
\(425\) | 10829.2 | + | 3418.19i | 1.23598 | + | 0.390133i | ||||
\(426\) | −14027.5 | − | 3066.76i | −1.59539 | − | 0.348791i | ||||
\(427\) | 18.7156 | + | 18.7156i | 0.00212111 | + | 0.00212111i | ||||
\(428\) | −7230.91 | − | 7230.91i | −0.816634 | − | 0.816634i | ||||
\(429\) | −691.364 | − | 151.149i | −0.0778074 | − | 0.0170106i | ||||
\(430\) | −5449.77 | + | 8977.76i | −0.611189 | + | 1.00685i | ||||
\(431\) | 7603.48i | 0.849760i | 0.905250 | + | 0.424880i | \(0.139684\pi\) | ||||
−0.905250 | + | 0.424880i | \(0.860316\pi\) | |||||||
\(432\) | 1469.95 | + | 10454.8i | 0.163711 | + | 1.16437i | ||||
\(433\) | 4681.19 | − | 4681.19i | 0.519547 | − | 0.519547i | −0.397887 | − | 0.917434i | \(-0.630257\pi\) |
0.917434 | + | 0.397887i | \(0.130257\pi\) | |||||||
\(434\) | 4652.70 | 0.514601 | ||||||||
\(435\) | −2933.14 | + | 72.1336i | −0.323295 | + | 0.00795067i | ||||
\(436\) | 7813.84 | 0.858292 | ||||||||
\(437\) | −980.409 | + | 980.409i | −0.107321 | + | 0.107321i | ||||
\(438\) | 5198.71 | + | 8107.85i | 0.567133 | + | 0.884493i | ||||
\(439\) | 8608.08i | 0.935857i | 0.883766 | + | 0.467929i | \(0.155000\pi\) | ||||
−0.883766 | + | 0.467929i | \(0.845000\pi\) | |||||||
\(440\) | 2542.31 | − | 621.675i | 0.275454 | − | 0.0673572i | ||||
\(441\) | −4118.80 | − | 1891.34i | −0.444746 | − | 0.204226i | ||||
\(442\) | 965.047 | + | 965.047i | 0.103852 | + | 0.103852i | ||||
\(443\) | −6466.81 | − | 6466.81i | −0.693561 | − | 0.693561i | 0.269453 | − | 0.963014i | \(-0.413157\pi\) |
−0.963014 | + | 0.269453i | \(0.913157\pi\) | |||||||
\(444\) | 1566.53 | − | 7165.42i | 0.167442 | − | 0.765891i | ||||
\(445\) | −12156.9 | − | 7379.61i | −1.29504 | − | 0.786128i | ||||
\(446\) | 4427.97i | 0.470113i | ||||||||
\(447\) | −15617.6 | + | 10013.9i | −1.65254 | + | 1.05960i | ||||
\(448\) | 2418.14 | − | 2418.14i | 0.255014 | − | 0.255014i | ||||
\(449\) | −356.370 | −0.0374569 | −0.0187284 | − | 0.999825i | \(-0.505962\pi\) | ||||
−0.0187284 | + | 0.999825i | \(0.505962\pi\) | |||||||
\(450\) | −8533.70 | + | 9417.15i | −0.893961 | + | 0.986508i | ||||
\(451\) | 3031.19 | 0.316481 | ||||||||
\(452\) | −2355.24 | + | 2355.24i | −0.245091 | + | 0.245091i | ||||
\(453\) | −11754.1 | + | 7536.66i | −1.21911 | + | 0.781685i | ||||
\(454\) | − | 18325.0i | − | 1.89435i | ||||||
\(455\) | 504.611 | + | 306.314i | 0.0519923 | + | 0.0315609i | ||||
\(456\) | 145.152 | − | 663.935i | 0.0149065 | − | 0.0681834i | ||||
\(457\) | 1512.80 | + | 1512.80i | 0.154849 | + | 0.154849i | 0.780280 | − | 0.625431i | \(-0.215077\pi\) |
−0.625431 | + | 0.780280i | \(0.715077\pi\) | |||||||
\(458\) | −4474.19 | − | 4474.19i | −0.456474 | − | 0.456474i | ||||
\(459\) | 10179.4 | + | 7669.81i | 1.03515 | + | 0.779948i | ||||
\(460\) | −4878.08 | + | 1192.84i | −0.494438 | + | 0.120906i | ||||
\(461\) | − | 13307.9i | − | 1.34449i | −0.740327 | − | 0.672246i | \(-0.765330\pi\) | ||
0.740327 | − | 0.672246i | \(-0.234670\pi\) | |||||||
\(462\) | 4771.23 | + | 7441.16i | 0.480472 | + | 0.749338i | ||||
\(463\) | −1237.43 | + | 1237.43i | −0.124208 | + | 0.124208i | −0.766478 | − | 0.642270i | \(-0.777993\pi\) |
0.642270 | + | 0.766478i | \(0.277993\pi\) | |||||||
\(464\) | 3800.56 | 0.380251 | ||||||||
\(465\) | 5422.51 | − | 133.353i | 0.540780 | − | 0.0132992i | ||||
\(466\) | 11218.8 | 1.11524 | ||||||||
\(467\) | −8201.87 | + | 8201.87i | −0.812713 | + | 0.812713i | −0.985040 | − | 0.172327i | \(-0.944872\pi\) |
0.172327 | + | 0.985040i | \(0.444872\pi\) | |||||||
\(468\) | −624.107 | + | 231.305i | −0.0616439 | + | 0.0228463i | ||||
\(469\) | 8066.19i | 0.794162i | ||||||||
\(470\) | −1182.78 | + | 1948.46i | −0.116080 | + | 0.191225i | ||||
\(471\) | 12997.3 | + | 2841.52i | 1.27151 | + | 0.277984i | ||||
\(472\) | 2042.01 | + | 2042.01i | 0.199133 | + | 0.199133i | ||||
\(473\) | 6021.83 | + | 6021.83i | 0.585378 | + | 0.585378i | ||||
\(474\) | −11239.7 | − | 2457.28i | −1.08915 | − | 0.238115i | ||||
\(475\) | 2115.14 | − | 1100.23i | 0.204314 | − | 0.106278i | ||||
\(476\) | − | 7428.67i | − | 0.715321i | ||||||
\(477\) | 12336.9 | − | 4572.28i | 1.18421 | − | 0.438889i | ||||
\(478\) | −695.273 | + | 695.273i | −0.0665294 | + | 0.0665294i | ||||
\(479\) | −11419.1 | −1.08926 | −0.544629 | − | 0.838677i | \(-0.683329\pi\) | ||||
−0.544629 | + | 0.838677i | \(0.683329\pi\) | |||||||
\(480\) | 9153.13 | − | 9614.68i | 0.870378 | − | 0.914267i | ||||
\(481\) | −911.420 | −0.0863974 | ||||||||
\(482\) | 15979.5 | − | 15979.5i | 1.51005 | − | 1.51005i | ||||
\(483\) | 2698.18 | + | 4208.05i | 0.254185 | + | 0.396424i | ||||
\(484\) | − | 1023.43i | − | 0.0961147i | ||||||
\(485\) | −1622.89 | − | 6636.73i | −0.151942 | − | 0.621358i | ||||
\(486\) | −12554.2 | + | 6770.77i | −1.17175 | + | 0.631952i | ||||
\(487\) | −6066.93 | − | 6066.93i | −0.564515 | − | 0.564515i | 0.366071 | − | 0.930587i | \(-0.380703\pi\) |
−0.930587 | + | 0.366071i | \(0.880703\pi\) | |||||||
\(488\) | −9.69769 | − | 9.69769i | −0.000899577 | − | 0.000899577i | ||||
\(489\) | 4204.74 | − | 19232.7i | 0.388845 | − | 1.77860i | ||||
\(490\) | 1678.63 | + | 6864.66i | 0.154760 | + | 0.632885i | ||||
\(491\) | − | 8978.88i | − | 0.825277i | −0.910895 | − | 0.412639i | \(-0.864607\pi\) | ||
0.910895 | − | 0.412639i | \(-0.135393\pi\) | |||||||
\(492\) | 2399.89 | − | 1538.80i | 0.219909 | − | 0.141005i | ||||
\(493\) | 3244.31 | − | 3244.31i | 0.296382 | − | 0.296382i | ||||
\(494\) | 286.538 | 0.0260971 | ||||||||
\(495\) | 5773.92 | + | 8535.57i | 0.524280 | + | 0.775041i | ||||
\(496\) | −7026.11 | −0.636051 | ||||||||
\(497\) | 6867.38 | − | 6867.38i | 0.619807 | − | 0.619807i | ||||
\(498\) | −5077.92 | + | 3255.94i | −0.456922 | + | 0.292976i | ||||
\(499\) | 7674.34i | 0.688478i | 0.938882 | + | 0.344239i | \(0.111863\pi\) | ||||
−0.938882 | + | 0.344239i | \(0.888137\pi\) | |||||||
\(500\) | 8616.53 | + | 568.849i | 0.770686 | + | 0.0508794i | ||||
\(501\) | 219.010 | − | 1001.77i | 0.0195303 | − | 0.0893326i | ||||
\(502\) | −8106.54 | − | 8106.54i | −0.720743 | − | 0.720743i | ||||
\(503\) | 4044.23 | + | 4044.23i | 0.358496 | + | 0.358496i | 0.863258 | − | 0.504762i | \(-0.168420\pi\) |
−0.504762 | + | 0.863258i | \(0.668420\pi\) | |||||||
\(504\) | −2226.69 | − | 1022.49i | −0.196795 | − | 0.0903674i | ||||
\(505\) | −9643.93 | + | 15887.1i | −0.849800 | + | 1.39993i | ||||
\(506\) | 9344.28i | 0.820957i | ||||||||
\(507\) | −6117.31 | − | 9540.48i | −0.535857 | − | 0.835715i | ||||
\(508\) | −2716.17 | + | 2716.17i | −0.237226 | + | 0.237226i | ||||
\(509\) | 12532.5 | 1.09134 | 0.545672 | − | 0.837999i | \(-0.316275\pi\) | ||||
0.545672 | + | 0.837999i | \(0.316275\pi\) | |||||||
\(510\) | −488.586 | − | 19867.2i | −0.0424215 | − | 1.72497i | ||||
\(511\) | −6514.42 | −0.563955 | ||||||||
\(512\) | −9239.91 | + | 9239.91i | −0.797559 | + | 0.797559i | ||||
\(513\) | 2649.87 | − | 372.574i | 0.228059 | − | 0.0320654i | ||||
\(514\) | 5039.33i | 0.432443i | ||||||||
\(515\) | −11895.4 | + | 2908.79i | −1.01781 | + | 0.248887i | ||||
\(516\) | 7824.69 | + | 1710.66i | 0.667563 | + | 0.145945i | ||||
\(517\) | 1306.93 | + | 1306.93i | 0.111177 | + | 0.111177i | ||||
\(518\) | 8049.75 | + | 8049.75i | 0.682791 | + | 0.682791i | ||||
\(519\) | −6329.02 | − | 1383.68i | −0.535285 | − | 0.117026i | ||||
\(520\) | −261.469 | − | 158.720i | −0.0220503 | − | 0.0133852i | ||||
\(521\) | 19201.8i | 1.61468i | 0.590089 | + | 0.807338i | \(0.299093\pi\) | ||||
−0.590089 | + | 0.807338i | \(0.700907\pi\) | |||||||
\(522\) | 1784.39 | + | 4814.65i | 0.149618 | + | 0.403700i | ||||
\(523\) | 5472.69 | − | 5472.69i | 0.457560 | − | 0.457560i | −0.440294 | − | 0.897854i | \(-0.645126\pi\) |
0.897854 | + | 0.440294i | \(0.145126\pi\) | |||||||
\(524\) | −8646.00 | −0.720806 | ||||||||
\(525\) | −2246.42 | − | 8296.97i | −0.186747 | − | 0.689732i | ||||
\(526\) | 356.926 | 0.0295869 | ||||||||
\(527\) | −5997.77 | + | 5997.77i | −0.495762 | + | 0.495762i | ||||
\(528\) | −7205.10 | − | 11237.0i | −0.593867 | − | 0.926187i | ||||
\(529\) | − | 6882.71i | − | 0.565687i | ||||||
\(530\) | −17536.7 | − | 10645.3i | −1.43725 | − | 0.872457i | ||||
\(531\) | −4744.97 | + | 10333.2i | −0.387786 | + | 0.844488i | ||||
\(532\) | −1102.85 | − | 1102.85i | −0.0898769 | − | 0.0898769i | ||||
\(533\) | −250.495 | − | 250.495i | −0.0203567 | − | 0.0203567i | ||||
\(534\) | −5315.58 | + | 24313.8i | −0.430763 | + | 1.97034i | ||||
\(535\) | 17973.8 | − | 4395.16i | 1.45248 | − | 0.355176i | ||||
\(536\) | − | 4179.58i | − | 0.336810i | ||||||
\(537\) | 10991.8 | − | 7047.87i | 0.883295 | − | 0.566365i | ||||
\(538\) | 7077.60 | − | 7077.60i | 0.567169 | − | 0.567169i | ||||
\(539\) | 5730.40 | 0.457933 | ||||||||
\(540\) | 8904.53 | + | 3826.73i | 0.709611 | + | 0.304956i | ||||
\(541\) | 12778.2 | 1.01548 | 0.507741 | − | 0.861510i | \(-0.330481\pi\) | ||||
0.507741 | + | 0.861510i | \(0.330481\pi\) | |||||||
\(542\) | −387.868 | + | 387.868i | −0.0307387 | + | 0.0307387i | ||||
\(543\) | −1180.14 | + | 756.702i | −0.0932684 | + | 0.0598033i | ||||
\(544\) | 20758.8i | 1.63608i | ||||||||
\(545\) | −7336.66 | + | 12086.1i | −0.576638 | + | 0.949933i | ||||
\(546\) | 220.640 | − | 1009.22i | 0.0172940 | − | 0.0791038i | ||||
\(547\) | −2414.12 | − | 2414.12i | −0.188702 | − | 0.188702i | 0.606433 | − | 0.795135i | \(-0.292600\pi\) |
−0.795135 | + | 0.606433i | \(0.792600\pi\) | |||||||
\(548\) | 6749.12 | + | 6749.12i | 0.526110 | + | 0.526110i | ||||
\(549\) | 22.5343 | − | 49.0735i | 0.00175181 | − | 0.00381494i | ||||
\(550\) | 4836.58 | − | 15322.8i | 0.374968 | − | 1.18794i | ||||
\(551\) | − | 963.290i | − | 0.0744783i | ||||||
\(552\) | −1398.09 | − | 2180.44i | −0.107802 | − | 0.168126i | ||||
\(553\) | 5502.57 | − | 5502.57i | 0.423134 | − | 0.423134i | ||||
\(554\) | 5722.30 | 0.438840 | ||||||||
\(555\) | 9612.32 | + | 9150.88i | 0.735171 | + | 0.699880i | ||||
\(556\) | −15437.6 | −1.17752 | ||||||||
\(557\) | −5573.05 | + | 5573.05i | −0.423946 | + | 0.423946i | −0.886560 | − | 0.462614i | \(-0.846912\pi\) |
0.462614 | + | 0.886560i | \(0.346912\pi\) | |||||||
\(558\) | −3298.81 | − | 8900.85i | −0.250268 | − | 0.675274i | ||||
\(559\) | − | 995.277i | − | 0.0753054i | ||||||
\(560\) | 2644.77 | + | 10815.7i | 0.199575 | + | 0.816153i | ||||
\(561\) | −15742.9 | − | 3441.78i | −1.18479 | − | 0.259023i | ||||
\(562\) | −5379.23 | − | 5379.23i | −0.403753 | − | 0.403753i | ||||
\(563\) | −3488.75 | − | 3488.75i | −0.261160 | − | 0.261160i | 0.564365 | − | 0.825525i | \(-0.309121\pi\) |
−0.825525 | + | 0.564365i | \(0.809121\pi\) | |||||||
\(564\) | 1698.21 | + | 371.270i | 0.126786 | + | 0.0277186i | ||||
\(565\) | −1431.58 | − | 5854.39i | −0.106597 | − | 0.435922i | ||||
\(566\) | − | 12782.3i | − | 0.949260i | ||||||
\(567\) | 728.199 | − | 9620.03i | 0.0539356 | − | 0.712528i | ||||
\(568\) | −3558.40 | + | 3558.40i | −0.262865 | + | 0.262865i | ||||
\(569\) | 4924.15 | 0.362796 | 0.181398 | − | 0.983410i | \(-0.441938\pi\) | ||||
0.181398 | + | 0.983410i | \(0.441938\pi\) | |||||||
\(570\) | −3021.99 | − | 2876.92i | −0.222065 | − | 0.211405i | ||||
\(571\) | −5642.12 | −0.413512 | −0.206756 | − | 0.978393i | \(-0.566291\pi\) | ||||
−0.206756 | + | 0.978393i | \(0.566291\pi\) | |||||||
\(572\) | 595.059 | − | 595.059i | 0.0434977 | − | 0.0434977i | ||||
\(573\) | −6788.02 | − | 10586.5i | −0.494893 | − | 0.771829i | ||||
\(574\) | 4424.78i | 0.321754i | ||||||||
\(575\) | 2735.14 | − | 8665.22i | 0.198371 | − | 0.628460i | ||||
\(576\) | −6340.50 | − | 2911.53i | −0.458659 | − | 0.210614i | ||||
\(577\) | 8505.39 | + | 8505.39i | 0.613663 | + | 0.613663i | 0.943899 | − | 0.330235i | \(-0.107128\pi\) |
−0.330235 | + | 0.943899i | \(0.607128\pi\) | |||||||
\(578\) | 8893.50 | + | 8893.50i | 0.640002 | + | 0.640002i | ||||
\(579\) | −3084.47 | + | 14108.6i | −0.221392 | + | 1.01266i | ||||
\(580\) | 1810.44 | − | 2982.46i | 0.129611 | − | 0.213517i | ||||
\(581\) | − | 4079.96i | − | 0.291334i | ||||||
\(582\) | −10065.4 | + | 6453.87i | −0.716879 | + | 0.459659i | ||||
\(583\) | −11762.7 | + | 11762.7i | −0.835612 | + | 0.835612i | ||||
\(584\) | 3375.51 | 0.239177 | ||||||||
\(585\) | 228.220 | − | 1182.52i | 0.0161295 | − | 0.0835750i | ||||
\(586\) | 13489.4 | 0.950927 | ||||||||
\(587\) | 1464.72 | − | 1464.72i | 0.102990 | − | 0.102990i | −0.653734 | − | 0.756724i | \(-0.726798\pi\) |
0.756724 | + | 0.653734i | \(0.226798\pi\) | |||||||
\(588\) | 4536.95 | − | 2909.07i | 0.318198 | − | 0.204027i | ||||
\(589\) | 1780.84i | 0.124581i | ||||||||
\(590\) | 17222.0 | − | 4211.33i | 1.20173 | − | 0.293860i | ||||
\(591\) | −1306.75 | + | 5977.17i | −0.0909521 | + | 0.416020i | ||||
\(592\) | −12156.0 | − | 12156.0i | −0.843935 | − | 0.843935i | ||||
\(593\) | −18086.4 | − | 18086.4i | −1.25248 | − | 1.25248i | −0.954606 | − | 0.297871i | \(-0.903723\pi\) |
−0.297871 | − | 0.954606i | \(-0.596277\pi\) | |||||||
\(594\) | 10852.4 | − | 14403.4i | 0.749631 | − | 0.994917i | ||||
\(595\) | 11490.4 | + | 6975.01i | 0.791697 | + | 0.480584i | ||||
\(596\) | − | 22061.1i | − | 1.51621i | ||||||
\(597\) | 4320.78 | + | 6738.63i | 0.296211 | + | 0.461966i | ||||
\(598\) | 772.204 | − | 772.204i | 0.0528056 | − | 0.0528056i | ||||
\(599\) | 21899.3 | 1.49379 | 0.746897 | − | 0.664940i | \(-0.231543\pi\) | ||||
0.746897 | + | 0.664940i | \(0.231543\pi\) | |||||||
\(600\) | 1164.01 | + | 4299.16i | 0.0792006 | + | 0.292520i | ||||
\(601\) | −12431.8 | −0.843766 | −0.421883 | − | 0.906650i | \(-0.638631\pi\) | ||||
−0.421883 | + | 0.906650i | \(0.638631\pi\) | |||||||
\(602\) | −8790.38 | + | 8790.38i | −0.595132 | + | 0.595132i | ||||
\(603\) | 15431.0 | − | 5719.00i | 1.04212 | − | 0.386229i | ||||
\(604\) | − | 16603.6i | − | 1.11853i | ||||||
\(605\) | 1583.00 | + | 960.930i | 0.106377 | + | 0.0645741i | ||||
\(606\) | 31774.1 | + | 6946.59i | 2.12993 | + | 0.465653i | ||||
\(607\) | 8237.79 | + | 8237.79i | 0.550843 | + | 0.550843i | 0.926684 | − | 0.375841i | \(-0.122646\pi\) |
−0.375841 | + | 0.926684i | \(0.622646\pi\) | |||||||
\(608\) | 3081.82 | + | 3081.82i | 0.205566 | + | 0.205566i | ||||
\(609\) | −3392.82 | − | 741.752i | −0.225754 | − | 0.0493552i | ||||
\(610\) | −81.7891 | + | 20.0000i | −0.00542876 | + | 0.00132750i | ||||
\(611\) | − | 216.007i | − | 0.0143023i | ||||||
\(612\) | −14211.4 | + | 5267.00i | −0.938663 | + | 0.347885i | ||||
\(613\) | −8913.02 | + | 8913.02i | −0.587265 | + | 0.587265i | −0.936890 | − | 0.349625i | \(-0.886309\pi\) |
0.349625 | + | 0.936890i | \(0.386309\pi\) | |||||||
\(614\) | −16827.3 | −1.10602 | ||||||||
\(615\) | 126.821 | + | 5156.88i | 0.00831530 | + | 0.338123i | ||||
\(616\) | 3097.95 | 0.202630 | ||||||||
\(617\) | −1378.18 | + | 1378.18i | −0.0899244 | + | 0.0899244i | −0.750638 | − | 0.660714i | \(-0.770254\pi\) |
0.660714 | + | 0.750638i | \(0.270254\pi\) | |||||||
\(618\) | 11567.6 | + | 18040.7i | 0.752941 | + | 1.17428i | ||||
\(619\) | − | 18926.2i | − | 1.22893i | −0.788945 | − | 0.614464i | \(-0.789372\pi\) | ||
0.788945 | − | 0.614464i | \(-0.210628\pi\) | |||||||
\(620\) | −3346.97 | + | 5513.67i | −0.216802 | + | 0.357152i | ||||
\(621\) | 6137.16 | − | 8145.29i | 0.396580 | − | 0.526344i | ||||
\(622\) | 19187.2 | + | 19187.2i | 1.23688 | + | 1.23688i | ||||
\(623\) | −11903.2 | − | 11903.2i | −0.765474 | − | 0.765474i | ||||
\(624\) | −333.191 | + | 1524.04i | −0.0213755 | + | 0.0977730i | ||||
\(625\) | −8970.20 | + | 12793.6i | −0.574093 | + | 0.818790i | ||||
\(626\) | 10806.5i | 0.689959i | ||||||||
\(627\) | −2848.12 | + | 1826.20i | −0.181408 | + | 0.116318i | ||||
\(628\) | −11186.8 | + | 11186.8i | −0.710831 | + | 0.710831i | ||||
\(629\) | −20753.7 | −1.31559 | ||||||||
\(630\) | −12459.8 | + | 8428.50i | −0.787954 | + | 0.533015i | ||||
\(631\) | −26118.8 | −1.64782 | −0.823909 | − | 0.566723i | \(-0.808211\pi\) | ||||
−0.823909 | + | 0.566723i | \(0.808211\pi\) | |||||||
\(632\) | −2851.21 | + | 2851.21i | −0.179454 | + | 0.179454i | ||||
\(633\) | 47.8450 | − | 30.6780i | 0.00300421 | − | 0.00192629i | ||||
\(634\) | 3670.26i | 0.229912i | ||||||||
\(635\) | −1650.97 | − | 6751.56i | −0.103176 | − | 0.421933i | ||||
\(636\) | −3341.52 | + | 15284.3i | −0.208333 | + | 0.952929i | ||||
\(637\) | −473.556 | − | 473.556i | −0.0294552 | − | 0.0294552i | ||||
\(638\) | −4590.56 | − | 4590.56i | −0.284862 | − | 0.284862i | ||||
\(639\) | −18006.7 | − | 8268.59i | −1.11476 | − | 0.511894i | ||||
\(640\) | −2270.60 | − | 9285.53i | −0.140240 | − | 0.573504i | ||||
\(641\) | 15846.5i | 0.976442i | 0.872720 | + | 0.488221i | \(0.162354\pi\) | ||||
−0.872720 | + | 0.488221i | \(0.837646\pi\) | |||||||
\(642\) | −17478.6 | − | 27259.4i | −1.07449 | − | 1.67577i | ||||
\(643\) | 89.9404 | − | 89.9404i | 0.00551618 | − | 0.00551618i | −0.704343 | − | 0.709859i | \(-0.748758\pi\) |
0.709859 | + | 0.704343i | \(0.248758\pi\) | |||||||
\(644\) | −5944.21 | −0.363719 | ||||||||
\(645\) | −9992.83 | + | 10496.7i | −0.610027 | + | 0.640787i | ||||
\(646\) | 6524.70 | 0.397385 | ||||||||
\(647\) | 20057.0 | − | 20057.0i | 1.21874 | − | 1.21874i | 0.250665 | − | 0.968074i | \(-0.419351\pi\) |
0.968074 | − | 0.250665i | \(-0.0806492\pi\) | |||||||
\(648\) | −377.323 | + | 4984.71i | −0.0228745 | + | 0.302188i | ||||
\(649\) | − | 14376.4i | − | 0.869527i | ||||||
\(650\) | −1665.96 | + | 866.575i | −0.100530 | + | 0.0522921i | ||||
\(651\) | 6272.31 | + | 1371.28i | 0.377621 | + | 0.0825570i | ||||
\(652\) | 16553.7 | + | 16553.7i | 0.994313 | + | 0.994313i | ||||
\(653\) | 20478.4 | + | 20478.4i | 1.22723 | + | 1.22723i | 0.965007 | + | 0.262225i | \(0.0844562\pi\) |
0.262225 | + | 0.965007i | \(0.415544\pi\) | |||||||
\(654\) | 24172.3 | + | 5284.64i | 1.44528 | + | 0.315972i | ||||
\(655\) | 8117.99 | − | 13373.3i | 0.484269 | − | 0.797767i | ||||
\(656\) | − | 6681.92i | − | 0.397691i | ||||||
\(657\) | 4618.78 | + | 12462.4i | 0.274271 | + | 0.740036i | ||||
\(658\) | −1907.80 | + | 1907.80i | −0.113030 | + | 0.113030i | ||||
\(659\) | −1169.87 | −0.0691529 | −0.0345765 | − | 0.999402i | \(-0.511008\pi\) | ||||
−0.0345765 | + | 0.999402i | \(0.511008\pi\) | |||||||
\(660\) | −12250.4 | + | 301.268i | −0.722492 | + | 0.0177679i | ||||
\(661\) | 19622.6 | 1.15466 | 0.577329 | − | 0.816511i | \(-0.304095\pi\) | ||||
0.577329 | + | 0.816511i | \(0.304095\pi\) | |||||||
\(662\) | 21904.0 | − | 21904.0i | 1.28599 | − | 1.28599i | ||||
\(663\) | 1016.55 | + | 1585.41i | 0.0595471 | + | 0.0928688i | ||||
\(664\) | 2114.07i | 0.123557i | ||||||||
\(665\) | 2741.34 | − | 670.343i | 0.159856 | − | 0.0390899i | ||||
\(666\) | 9692.20 | − | 21106.9i | 0.563912 | − | 1.22804i | ||||
\(667\) | −2596.01 | − | 2596.01i | −0.150701 | − | 0.150701i | ||||
\(668\) | 862.224 | + | 862.224i | 0.0499408 | + | 0.0499408i | ||||
\(669\) | −1305.04 | + | 5969.35i | −0.0754199 | + | 0.344975i | ||||
\(670\) | −21934.9 | − | 13315.1i | −1.26480 | − | 0.767774i | ||||
\(671\) | 68.2750i | 0.00392806i | ||||||||
\(672\) | 13227.6 | − | 8481.46i | 0.759323 | − | 0.486874i | ||||
\(673\) | 15256.3 | − | 15256.3i | 0.873830 | − | 0.873830i | −0.119057 | − | 0.992887i | \(-0.537987\pi\) |
0.992887 | + | 0.119057i | \(0.0379872\pi\) | |||||||
\(674\) | −9464.72 | −0.540901 | ||||||||
\(675\) | −14279.8 | + | 10180.1i | −0.814264 | + | 0.580495i | ||||
\(676\) | 13476.7 | 0.766768 | ||||||||
\(677\) | 16.1429 | − | 16.1429i | 0.000916428 | − | 0.000916428i | −0.706648 | − | 0.707565i | \(-0.749794\pi\) |
0.707565 | + | 0.706648i | \(0.249794\pi\) | |||||||
\(678\) | −8878.86 | + | 5693.08i | −0.502936 | + | 0.322480i | ||||
\(679\) | − | 8087.23i | − | 0.457083i | ||||||
\(680\) | −5953.85 | − | 3614.17i | −0.335764 | − | 0.203819i | ||||
\(681\) | 5400.87 | − | 24703.9i | 0.303909 | − | 1.39010i | ||||
\(682\) | 8486.57 | + | 8486.57i | 0.476492 | + | 0.476492i | ||||
\(683\) | 3894.05 | + | 3894.05i | 0.218157 | + | 0.218157i | 0.807722 | − | 0.589564i | \(-0.200700\pi\) |
−0.589564 | + | 0.807722i | \(0.700700\pi\) | |||||||
\(684\) | −1327.87 | + | 2891.73i | −0.0742287 | + | 0.161649i | ||||
\(685\) | −16776.2 | + | 4102.32i | −0.935747 | + | 0.228820i | ||||
\(686\) | 25457.5i | 1.41687i | ||||||||
\(687\) | −4712.99 | − | 7350.31i | −0.261735 | − | 0.408198i | ||||
\(688\) | 13274.5 | − | 13274.5i | 0.735587 | − | 0.735587i | ||||
\(689\) | 1944.12 | 0.107497 | ||||||||
\(690\) | −15897.2 | + | 390.953i | −0.877095 | + | 0.0215700i | ||||
\(691\) | −1041.11 | −0.0573163 | −0.0286581 | − | 0.999589i | \(-0.509123\pi\) | ||||
−0.0286581 | + | 0.999589i | \(0.509123\pi\) | |||||||
\(692\) | 5447.40 | − | 5447.40i | 0.299247 | − | 0.299247i | ||||
\(693\) | 4238.99 | + | 11437.6i | 0.232361 | + | 0.626955i | ||||
\(694\) | 9133.91i | 0.499594i | ||||||||
\(695\) | 14494.8 | − | 23878.3i | 0.791108 | − | 1.30324i | ||||
\(696\) | 1758.02 | + | 384.346i | 0.0957438 | + | 0.0209319i | ||||
\(697\) | −5703.96 | − | 5703.96i | −0.309975 | − | 0.309975i | ||||
\(698\) | −22908.9 | − | 22908.9i | −1.24229 | − | 1.24229i | ||||
\(699\) | 15124.1 | + | 3306.49i | 0.818378 | + | 0.178917i | ||||
\(700\) | 9747.37 | + | 3076.71i | 0.526309 | + | 0.166127i | ||||
\(701\) | 29885.3i | 1.61020i | 0.593138 | + | 0.805101i | \(0.297889\pi\) | ||||
−0.593138 | + | 0.805101i | \(0.702111\pi\) | |||||||
\(702\) | −2087.12 | + | 293.452i | −0.112213 | + | 0.0157773i | ||||
\(703\) | −3081.06 | + | 3081.06i | −0.165298 | + | 0.165298i | ||||
\(704\) | 8821.42 | 0.472258 | ||||||||
\(705\) | −2168.77 | + | 2278.13i | −0.115859 | + | 0.121701i | ||||
\(706\) | −28889.9 | −1.54007 | ||||||||
\(707\) | −15555.5 | + | 15555.5i | −0.827473 | + | 0.827473i | ||||
\(708\) | −7298.26 | − | 11382.3i | −0.387409 | − | 0.604198i | ||||
\(709\) | − | 12115.0i | − | 0.641734i | −0.947124 | − | 0.320867i | \(-0.896026\pi\) | ||
0.947124 | − | 0.320867i | \(-0.103974\pi\) | |||||||
\(710\) | 7338.66 | + | 30011.1i | 0.387908 | + | 1.58633i | ||||
\(711\) | −14428.1 | − | 6625.31i | −0.761033 | − | 0.349463i | ||||
\(712\) | 6167.74 | + | 6167.74i | 0.324643 | + | 0.324643i | ||||
\(713\) | 4799.24 | + | 4799.24i | 0.252080 | + | 0.252080i | ||||
\(714\) | 5024.15 | − | 22980.8i | 0.263339 | − | 1.20453i | ||||
\(715\) | 361.695 | + | 1479.13i | 0.0189183 | + | 0.0773657i | ||||
\(716\) | 15526.8i | 0.810422i | ||||||||
\(717\) | −1142.21 | + | 732.381i | −0.0594933 | + | 0.0381468i | ||||
\(718\) | −30404.1 | + | 30404.1i | −1.58032 | + | 1.58032i | ||||
\(719\) | 6371.24 | 0.330469 | 0.165234 | − | 0.986254i | \(-0.447162\pi\) | ||||
0.165234 | + | 0.986254i | \(0.447162\pi\) | |||||||
\(720\) | 18815.7 | − | 12728.0i | 0.973918 | − | 0.658811i | ||||
\(721\) | −14495.2 | −0.748722 | ||||||||
\(722\) | −17294.1 | + | 17294.1i | −0.891443 | + | 0.891443i | ||||
\(723\) | 26251.5 | − | 16832.3i | 1.35035 | − | 0.865839i | ||||
\(724\) | − | 1667.05i | − | 0.0855737i | ||||||
\(725\) | 2913.27 | + | 5600.64i | 0.149236 | + | 0.286900i | ||||
\(726\) | 692.164 | − | 3166.00i | 0.0353838 | − | 0.161848i | ||||
\(727\) | 15771.9 | + | 15771.9i | 0.804604 | + | 0.804604i | 0.983811 | − | 0.179207i | \(-0.0573532\pi\) |
−0.179207 | + | 0.983811i | \(0.557353\pi\) | |||||||
\(728\) | −256.012 | − | 256.012i | −0.0130336 | − | 0.0130336i | ||||
\(729\) | −18919.9 | + | 5427.61i | −0.961229 | + | 0.275751i | ||||
\(730\) | 10753.6 | − | 17715.0i | 0.545216 | − | 0.898168i | ||||
\(731\) | − | 22663.2i | − | 1.14669i | ||||||
\(732\) | 34.6601 | + | 54.0555i | 0.00175010 | + | 0.00272944i | ||||
\(733\) | −5626.05 | + | 5626.05i | −0.283496 | + | 0.283496i | −0.834502 | − | 0.551005i | \(-0.814244\pi\) |
0.551005 | + | 0.834502i | \(0.314244\pi\) | |||||||
\(734\) | −34905.3 | −1.75528 | ||||||||
\(735\) | 239.753 | + | 9748.98i | 0.0120319 | + | 0.489247i | ||||
\(736\) | 16610.6 | 0.831897 | ||||||||
\(737\) | −14712.8 | + | 14712.8i | −0.735350 | + | 0.735350i | ||||
\(738\) | 8464.82 | − | 3137.21i | 0.422215 | − | 0.156480i | ||||
\(739\) | 30340.1i | 1.51026i | 0.655577 | + | 0.755129i | \(0.272426\pi\) | ||||
−0.655577 | + | 0.755129i | \(0.727574\pi\) | |||||||
\(740\) | −15330.0 | + | 3748.66i | −0.761543 | + | 0.186221i | ||||
\(741\) | 386.282 | + | 84.4506i | 0.0191504 | + | 0.00418674i | ||||
\(742\) | −17170.7 | − | 17170.7i | −0.849535 | − | 0.849535i | ||||
\(743\) | 2368.77 | + | 2368.77i | 0.116961 | + | 0.116961i | 0.763165 | − | 0.646204i | \(-0.223645\pi\) |
−0.646204 | + | 0.763165i | \(0.723645\pi\) | |||||||
\(744\) | −3250.06 | − | 710.541i | −0.160152 | − | 0.0350130i | ||||
\(745\) | 34123.3 | + | 20713.9i | 1.67810 | + | 1.01866i | ||||
\(746\) | − | 31778.0i | − | 1.55962i | ||||||
\(747\) | −7805.16 | + | 2892.73i | −0.382297 | + | 0.141686i | ||||
\(748\) | 13550.0 | − | 13550.0i | 0.662347 | − | 0.662347i | ||||
\(749\) | 21902.1 | 1.06847 | ||||||||
\(750\) | 26270.7 | + | 7587.26i | 1.27903 | + | 0.369397i | ||||
\(751\) | 10606.2 | 0.515346 | 0.257673 | − | 0.966232i | \(-0.417044\pi\) | ||||
0.257673 | + | 0.966232i | \(0.417044\pi\) | |||||||
\(752\) | 2880.99 | − | 2880.99i | 0.139706 | − | 0.139706i | ||||
\(753\) | −8539.21 | − | 13317.6i | −0.413262 | − | 0.644518i | ||||
\(754\) | 758.720i | 0.0366458i | ||||||||
\(755\) | 25681.8 | + | 15589.6i | 1.23796 | + | 0.751477i | ||||
\(756\) | 9162.52 | + | 6903.60i | 0.440790 | + | 0.332119i | ||||
\(757\) | −18470.4 | − | 18470.4i | −0.886812 | − | 0.886812i | 0.107404 | − | 0.994215i | \(-0.465746\pi\) |
−0.994215 | + | 0.107404i | \(0.965746\pi\) | |||||||
\(758\) | −4474.44 | − | 4474.44i | −0.214405 | − | 0.214405i | ||||
\(759\) | −2754.01 | + | 12597.0i | −0.131705 | + | 0.602428i | ||||
\(760\) | −1420.45 | + | 347.345i | −0.0677963 | + | 0.0165783i | ||||
\(761\) | − | 13568.0i | − | 0.646307i | −0.946347 | − | 0.323153i | \(-0.895257\pi\) | ||
0.946347 | − | 0.323153i | \(-0.104743\pi\) | |||||||
\(762\) | −10239.5 | + | 6565.54i | −0.486797 | + | 0.312132i | ||||
\(763\) | −11833.9 | + | 11833.9i | −0.561488 | + | 0.561488i | ||||
\(764\) | 14954.3 | 0.708152 | ||||||||
\(765\) | 5196.74 | − | 26927.0i | 0.245606 | − | 1.27261i | ||||
\(766\) | −39904.0 | −1.88223 | ||||||||
\(767\) | −1188.05 | + | 1188.05i | −0.0559298 | + | 0.0559298i | ||||
\(768\) | −23125.2 | + | 14827.8i | −1.08654 | + | 0.696682i | ||||
\(769\) | 11029.1i | 0.517190i | 0.965986 | + | 0.258595i | \(0.0832594\pi\) | ||||
−0.965986 | + | 0.258595i | \(0.916741\pi\) | |||||||
\(770\) | 9869.33 | − | 16258.4i | 0.461904 | − | 0.760924i | ||||
\(771\) | −1485.23 | + | 6793.52i | −0.0693764 | + | 0.317332i | ||||
\(772\) | −12143.3 | − | 12143.3i | −0.566122 | − | 0.566122i | ||||
\(773\) | 7090.94 | + | 7090.94i | 0.329940 | + | 0.329940i | 0.852563 | − | 0.522624i | \(-0.175047\pi\) |
−0.522624 | + | 0.852563i | \(0.675047\pi\) | |||||||
\(774\) | 23048.9 | + | 10584.0i | 1.07038 | + | 0.491515i | ||||
\(775\) | −5385.76 | − | 10353.9i | −0.249629 | − | 0.479902i | ||||
\(776\) | 4190.48i | 0.193852i | ||||||||
\(777\) | 8479.38 | + | 13224.3i | 0.391501 | + | 0.610580i | ||||
\(778\) | 21212.9 | − | 21212.9i | 0.977530 | − | 0.977530i | ||||
\(779\) | −1693.60 | −0.0778940 | ||||||||
\(780\) | 1037.26 | + | 987.462i | 0.0476150 | + | 0.0453293i | ||||
\(781\) | 25052.3 | 1.14781 | ||||||||
\(782\) | 17583.7 | − | 17583.7i | 0.804080 | − | 0.804080i | ||||
\(783\) | 986.533 | + | 7016.53i | 0.0450266 | + | 0.320243i | ||||
\(784\) | − | 12632.1i | − | 0.575440i | ||||||
\(785\) | −6799.67 | − | 27806.9i | −0.309160 | − | 1.26430i | ||||
\(786\) | −26746.6 | − | 5847.45i | −1.21376 | − | 0.265358i | ||||
\(787\) | −17915.0 | − | 17915.0i | −0.811437 | − | 0.811437i | 0.173412 | − | 0.984849i | \(-0.444521\pi\) |
−0.984849 | + | 0.173412i | \(0.944521\pi\) | |||||||
\(788\) | −5144.57 | − | 5144.57i | −0.232573 | − | 0.232573i | ||||
\(789\) | 481.172 | + | 105.196i | 0.0217112 | + | 0.00474660i | ||||
\(790\) | 5880.19 | + | 24046.8i | 0.264820 | + | 1.08297i | ||||
\(791\) | − | 7133.90i | − | 0.320673i | ||||||
\(792\) | −2196.47 | − | 5926.52i | −0.0985458 | − | 0.265896i | ||||
\(793\) | 5.64218 | − | 5.64218i | 0.000252661 | − | 0.000252661i | ||||
\(794\) | 43607.5 | 1.94908 | ||||||||
\(795\) | −20503.7 | − | 19519.5i | −0.914707 | − | 0.870797i | ||||
\(796\) | −9518.87 | −0.423854 | ||||||||
\(797\) | −6043.79 | + | 6043.79i | −0.268610 | + | 0.268610i | −0.828540 | − | 0.559930i | \(-0.810828\pi\) |
0.559930 | + | 0.828540i | \(0.310828\pi\) | |||||||
\(798\) | −2665.81 | − | 4157.56i | −0.118256 | − | 0.184431i | ||||
\(799\) | − | 4918.65i | − | 0.217784i | ||||||
\(800\) | −27238.3 | − | 8597.63i | −1.20377 | − | 0.379965i | ||||
\(801\) | −14331.9 | + | 31210.8i | −0.632199 | + | 1.37675i | ||||
\(802\) | 13759.4 | + | 13759.4i | 0.605813 | + | 0.605813i | ||||
\(803\) | −11882.3 | − | 11882.3i | −0.522191 | − | 0.522191i | ||||
\(804\) | −4179.58 | + | 19117.6i | −0.183336 | + | 0.838591i | ||||
\(805\) | 5581.21 | − | 9194.28i | 0.244362 | − | 0.402554i | ||||
\(806\) | − | 1402.65i | − | 0.0612979i | ||||||
\(807\) | 11627.3 | − | 7455.35i | 0.507186 | − | 0.325205i | ||||
\(808\) | 8060.22 | − | 8060.22i | 0.350937 | − | 0.350937i | ||||
\(809\) | −35063.4 | −1.52381 | −0.761905 | − | 0.647689i | \(-0.775736\pi\) | ||||
−0.761905 | + | 0.647689i | \(0.775736\pi\) | |||||||
\(810\) | 24958.3 | + | 17860.3i | 1.08265 | + | 0.774751i | ||||
\(811\) | 24621.3 | 1.06605 | 0.533027 | − | 0.846098i | \(-0.321054\pi\) | ||||
0.533027 | + | 0.846098i | \(0.321054\pi\) | |||||||
\(812\) | 2920.21 | − | 2920.21i | 0.126206 | − | 0.126206i | ||||
\(813\) | −637.200 | + | 408.570i | −0.0274878 | + | 0.0176250i | ||||
\(814\) | 29365.6i | 1.26445i | ||||||||
\(815\) | −41147.3 | + | 10061.8i | −1.76850 | + | 0.432454i | ||||
\(816\) | −7587.02 | + | 34703.5i | −0.325489 | + | 1.48881i | ||||
\(817\) | −3364.54 | − | 3364.54i | −0.144076 | − | 0.144076i | ||||
\(818\) | 22671.6 | + | 22671.6i | 0.969063 | + | 0.969063i | ||||
\(819\) | 594.890 | − | 1295.50i | 0.0253811 | − | 0.0552729i | ||||
\(820\) | −5243.58 | − | 3183.01i | −0.223309 | − | 0.135556i | ||||
\(821\) | − | 14268.3i | − | 0.606538i | −0.952905 | − | 0.303269i | \(-0.901922\pi\) | ||
0.952905 | − | 0.303269i | \(-0.0980781\pi\) | |||||||
\(822\) | 16314.0 | + | 25443.1i | 0.692234 | + | 1.07960i | ||||
\(823\) | 13764.1 | − | 13764.1i | 0.582972 | − | 0.582972i | −0.352747 | − | 0.935719i | \(-0.614752\pi\) |
0.935719 | + | 0.352747i | \(0.114752\pi\) | |||||||
\(824\) | 7510.81 | 0.317538 | ||||||||
\(825\) | 11036.2 | − | 19231.2i | 0.465737 | − | 0.811571i | ||||
\(826\) | 20986.0 | 0.884015 | ||||||||
\(827\) | 27442.5 | − | 27442.5i | 1.15389 | − | 1.15389i | 0.168128 | − | 0.985765i | \(-0.446228\pi\) |
0.985765 | − | 0.168128i | \(-0.0537721\pi\) | |||||||
\(828\) | 4214.50 | + | 11371.6i | 0.176889 | + | 0.477282i | ||||
\(829\) | 12176.9i | 0.510159i | 0.966920 | + | 0.255080i | \(0.0821016\pi\) | ||||
−0.966920 | + | 0.255080i | \(0.917898\pi\) | |||||||
\(830\) | 11094.9 | + | 6734.93i | 0.463987 | + | 0.281654i | ||||
\(831\) | 7714.23 | + | 1686.52i | 0.322026 | + | 0.0704027i | ||||
\(832\) | −728.995 | − | 728.995i | −0.0303766 | − | 0.0303766i | ||||
\(833\) | −10783.2 | − | 10783.2i | −0.448519 | − | 0.448519i | ||||
\(834\) | −47756.5 | − | 10440.7i | −1.98282 | − | 0.433492i | ||||
\(835\) | −2143.22 | + | 524.085i | −0.0888255 | + | 0.0217206i | ||||
\(836\) | − | 4023.21i | − | 0.166442i | ||||||
\(837\) | −1823.80 | − | 12971.5i | −0.0753165 | − | 0.535675i | ||||
\(838\) | 31790.7 | − | 31790.7i | 1.31049 | − | 1.31049i | ||||
\(839\) | −13942.3 | −0.573710 | −0.286855 | − | 0.957974i | \(-0.592610\pi\) | ||||
−0.286855 | + | 0.957974i | \(0.592610\pi\) | |||||||
\(840\) | 129.614 | + | 5270.46i | 0.00532394 | + | 0.216486i | ||||
\(841\) | −21838.3 | −0.895417 | ||||||||
\(842\) | −28951.3 | + | 28951.3i | −1.18495 | + | 1.18495i | ||||
\(843\) | −5666.33 | − | 8837.14i | −0.231505 | − | 0.361053i | ||||
\(844\) | 67.5849i | 0.00275636i | ||||||||
\(845\) | −12653.7 | + | 20845.2i | −0.515149 | + | 0.848637i | ||||
\(846\) | 5002.35 | + | 2297.06i | 0.203291 | + | 0.0933505i | ||||
\(847\) | 1549.96 | + | 1549.96i | 0.0628776 | + | 0.0628776i | ||||
\(848\) | 25929.6 | + | 25929.6i | 1.05003 | + | 1.05003i | ||||
\(849\) | 3767.30 | − | 17231.8i | 0.152289 | − | 0.696579i | ||||
\(850\) | −37935.1 | + | 19732.6i | −1.53078 | + | 0.796261i | ||||
\(851\) | 16606.6i | 0.668937i | ||||||||
\(852\) | 19834.7 | − | 12717.9i | 0.797567 | − | 0.511396i | ||||
\(853\) | −32654.2 | + | 32654.2i | −1.31074 | + | 1.31074i | −0.389866 | + | 0.920871i | \(0.627479\pi\) |
−0.920871 | + | 0.389866i | \(0.872521\pi\) | |||||||
\(854\) | −99.6646 | −0.00399350 | ||||||||
\(855\) | −3226.03 | − | 4769.03i | −0.129039 | − | 0.190757i | ||||
\(856\) | −11348.8 | −0.453147 | ||||||||
\(857\) | 10358.9 | − | 10358.9i | 0.412898 | − | 0.412898i | −0.469849 | − | 0.882747i | \(-0.655692\pi\) |
0.882747 | + | 0.469849i | \(0.155692\pi\) | |||||||
\(858\) | 2243.28 | − | 1438.38i | 0.0892590 | − | 0.0572325i | ||||
\(859\) | − | 14100.5i | − | 0.560072i | −0.959990 | − | 0.280036i | \(-0.909654\pi\) | ||
0.959990 | − | 0.280036i | \(-0.0903464\pi\) | |||||||
\(860\) | −4093.57 | − | 16740.5i | −0.162313 | − | 0.663773i | ||||
\(861\) | −1304.10 | + | 5965.05i | −0.0516187 | + | 0.236107i | ||||
\(862\) | −20245.0 | − | 20245.0i | −0.799941 | − | 0.799941i | ||||
\(863\) | 16830.6 | + | 16830.6i | 0.663872 | + | 0.663872i | 0.956290 | − | 0.292419i | \(-0.0944601\pi\) |
−0.292419 | + | 0.956290i | \(0.594460\pi\) | |||||||
\(864\) | −25603.9 | − | 19291.6i | −1.00818 | − | 0.759621i | ||||
\(865\) | 3311.09 | + | 13540.6i | 0.130151 | + | 0.532246i | ||||
\(866\) | 24928.3i | 0.978174i | ||||||||
\(867\) | 9368.17 | + | 14610.5i | 0.366966 | + | 0.572316i | ||||
\(868\) | −5398.60 | + | 5398.60i | −0.211106 | + | 0.211106i | ||||
\(869\) | 20073.5 | 0.783597 | ||||||||
\(870\) | 7617.73 | − | 8001.86i | 0.296857 | − | 0.311826i | ||||
\(871\) | 2431.71 | 0.0945984 | ||||||||
\(872\) | 6131.84 | − | 6131.84i | 0.238131 | − | 0.238131i | ||||
\(873\) | −15471.3 | + | 5733.92i | −0.599797 | + | 0.222295i | ||||
\(874\) | − | 5220.88i | − | 0.202058i | ||||||
\(875\) | −13911.0 | + | 12188.0i | −0.537462 | + | 0.470892i | ||||
\(876\) | −15439.8 | − | 3375.51i | −0.595504 | − | 0.130192i | ||||
\(877\) | 9832.57 | + | 9832.57i | 0.378589 | + | 0.378589i | 0.870593 | − | 0.492004i | \(-0.163736\pi\) |
−0.492004 | + | 0.870593i | \(0.663736\pi\) | |||||||
\(878\) | −22919.9 | − | 22919.9i | −0.880990 | − | 0.880990i | ||||
\(879\) | 18185.1 | + | 3975.70i | 0.697802 | + | 0.152556i | ||||
\(880\) | −14903.8 | + | 24552.0i | −0.570917 | + | 0.940508i | ||||
\(881\) | − | 41729.4i | − | 1.59580i | −0.602789 | − | 0.797900i | \(-0.705944\pi\) | ||
0.602789 | − | 0.797900i | \(-0.294056\pi\) | |||||||
\(882\) | 16002.6 | − | 5930.84i | 0.610925 | − | 0.226419i | ||||
\(883\) | −11757.3 | + | 11757.3i | −0.448090 | + | 0.448090i | −0.894719 | − | 0.446629i | \(-0.852624\pi\) |
0.446629 | + | 0.894719i | \(0.352624\pi\) | |||||||
\(884\) | −2239.51 | −0.0852070 | ||||||||
\(885\) | 24458.2 | − | 601.490i | 0.928987 | − | 0.0228462i | ||||
\(886\) | 34437.1 | 1.30580 | ||||||||
\(887\) | −24303.5 | + | 24303.5i | −0.919989 | + | 0.919989i | −0.997028 | − | 0.0770388i | \(-0.975453\pi\) |
0.0770388 | + | 0.997028i | \(0.475453\pi\) | |||||||
\(888\) | −4393.67 | − | 6852.32i | −0.166038 | − | 0.258951i | ||||
\(889\) | − | 8227.16i | − | 0.310383i | ||||||
\(890\) | 52017.9 | − | 12720.0i | 1.95915 | − | 0.479074i | ||||
\(891\) | 18875.3 | − | 16218.8i | 0.709702 | − | 0.609820i | ||||
\(892\) | −5137.84 | − | 5137.84i | −0.192856 | − | 0.192856i | ||||
\(893\) | −730.214 | − | 730.214i | −0.0273636 | − | 0.0273636i | ||||
\(894\) | 14920.4 | − | 68246.6i | 0.558178 | − | 2.55314i | ||||
\(895\) | −24016.2 | − | 14578.6i | −0.896953 | − | 0.544478i | ||||
\(896\) | − | 11314.9i | − | 0.421881i | ||||||
\(897\) | 1268.60 | − | 813.418i | 0.0472210 | − | 0.0302779i | ||||
\(898\) | 948.871 | − | 948.871i | 0.0352609 | − | 0.0352609i | ||||
\(899\) | −4715.44 | −0.174937 | ||||||||
\(900\) | −1025.08 | − | 20828.6i | −0.0379659 | − | 0.771430i | ||||
\(901\) | 44269.1 | 1.63687 | ||||||||
\(902\) | −8070.84 | + | 8070.84i | −0.297927 | + | 0.297927i | ||||
\(903\) | −14441.1 | + | 9259.55i | −0.532191 | + | 0.341239i | ||||
\(904\) | 3696.50i | 0.136000i | ||||||||
\(905\) | 2578.52 | + | 1565.24i | 0.0947105 | + | 0.0574922i | ||||
\(906\) | 11229.3 | − | 51363.6i | 0.411776 | − | 1.88349i | ||||
\(907\) | 1017.75 | + | 1017.75i | 0.0372589 | + | 0.0372589i | 0.725491 | − | 0.688232i | \(-0.241613\pi\) |
−0.688232 | + | 0.725491i | \(0.741613\pi\) | |||||||
\(908\) | 21262.7 | + | 21262.7i | 0.777124 | + | 0.777124i | ||||
\(909\) | 40787.3 | + | 18729.4i | 1.48826 | + | 0.683404i | ||||
\(910\) | −2159.17 | + | 527.985i | −0.0786548 | + | 0.0192336i | ||||
\(911\) | 33165.2i | 1.20616i | 0.797681 | + | 0.603080i | \(0.206060\pi\) | ||||
−0.797681 | + | 0.603080i | \(0.793940\pi\) | |||||||
\(912\) | 4025.67 | + | 6278.38i | 0.146166 | + | 0.227958i | ||||
\(913\) | 7441.88 | − | 7441.88i | 0.269759 | − | 0.269759i | ||||
\(914\) | −8056.00 | −0.291541 | ||||||||
\(915\) | −116.154 | + | 2.85654i | −0.00419666 | + | 0.000103207i | ||||
\(916\) | 10382.9 | 0.374521 | ||||||||
\(917\) | 13094.2 | − | 13094.2i | 0.471546 | − | 0.471546i | ||||
\(918\) | −47525.4 | + | 6682.13i | −1.70869 | + | 0.240243i | ||||
\(919\) | − | 2162.18i | − | 0.0776103i | −0.999247 | − | 0.0388051i | \(-0.987645\pi\) | ||
0.999247 | − | 0.0388051i | \(-0.0123552\pi\) | |||||||
\(920\) | −2891.96 | + | 4764.10i | −0.103636 | + | 0.170726i | ||||
\(921\) | −22684.9 | − | 4959.46i | −0.811609 | − | 0.177437i | ||||
\(922\) | 35433.7 | + | 35433.7i | 1.26567 | + | 1.26567i | ||||
\(923\) | −2070.30 | − | 2070.30i | −0.0738297 | − | 0.0738297i | ||||
\(924\) | −14170.2 | − | 3097.95i | −0.504508 | − | 0.110298i | ||||
\(925\) | 8595.52 | − | 27231.6i | 0.305534 | − | 0.967966i | ||||
\(926\) | − | 6589.59i | − | 0.233852i | ||||||
\(927\) | 10277.2 | + | 27729.9i | 0.364129 | + | 0.982493i | ||||
\(928\) | −8160.29 | + | 8160.29i | −0.288658 | + | 0.288658i | ||||
\(929\) | 17695.1 | 0.624929 | 0.312464 | − | 0.949930i | \(-0.398846\pi\) | ||||
0.312464 | + | 0.949930i | \(0.398846\pi\) | |||||||
\(930\) | −14082.9 | + | 14793.1i | −0.496556 | + | 0.521595i | ||||
\(931\) | −3201.72 | −0.112709 | ||||||||
\(932\) | −13017.4 | + | 13017.4i | −0.457508 | + | 0.457508i | ||||
\(933\) | 20211.3 | + | 31521.3i | 0.709204 | + | 1.10607i | ||||
\(934\) | − | 43676.6i | − | 1.53013i | ||||||
\(935\) | 8236.07 | + | 33681.0i | 0.288073 | + | 1.17806i | ||||
\(936\) | −308.248 | + | 671.277i | −0.0107643 | + | 0.0234417i | ||||
\(937\) | −30208.0 | − | 30208.0i | −1.05320 | − | 1.05320i | −0.998503 | − | 0.0547017i | \(-0.982579\pi\) |
−0.0547017 | − | 0.998503i | \(-0.517421\pi\) | |||||||
\(938\) | −21477.1 | − | 21477.1i | −0.747602 | − | 0.747602i | ||||
\(939\) | −3184.96 | + | 14568.2i | −0.110689 | + | 0.506300i | ||||
\(940\) | −888.437 | − | 3633.22i | −0.0308272 | − | 0.126067i | ||||
\(941\) | 1499.59i | 0.0519503i | 0.999663 | + | 0.0259752i | \(0.00826908\pi\) | ||||
−0.999663 | + | 0.0259752i | \(0.991731\pi\) | |||||||
\(942\) | −42172.4 | + | 27040.8i | −1.45865 | + | 0.935282i | ||||
\(943\) | −4564.14 | + | 4564.14i | −0.157613 | + | 0.157613i | ||||
\(944\) | −31691.2 | −1.09265 | ||||||||
\(945\) | −19281.2 | + | 7690.22i | −0.663722 | + | 0.264722i | ||||
\(946\) | −32067.5 | −1.10212 | ||||||||
\(947\) | −13763.8 | + | 13763.8i | −0.472294 | + | 0.472294i | −0.902656 | − | 0.430362i | \(-0.858386\pi\) |
0.430362 | + | 0.902656i | \(0.358386\pi\) | |||||||
\(948\) | 15892.8 | − | 10190.4i | 0.544488 | − | 0.349123i | ||||
\(949\) | 1963.89i | 0.0671767i | ||||||||
\(950\) | −2702.32 | + | 8561.25i | −0.0922892 | + | 0.292383i | ||||
\(951\) | −1081.72 | + | 4947.87i | −0.0368847 | + | 0.168713i | ||||
\(952\) | −5829.59 | − | 5829.59i | −0.198464 | − | 0.198464i | ||||
\(953\) | −14570.7 | − | 14570.7i | −0.495268 | − | 0.495268i | 0.414693 | − | 0.909961i | \(-0.363889\pi\) |
−0.909961 | + | 0.414693i | \(0.863889\pi\) | |||||||
\(954\) | −20674.1 | + | 45022.4i | −0.701625 | + | 1.52794i | ||||
\(955\) | −14041.1 | + | 23130.8i | −0.475768 | + | 0.783763i | ||||
\(956\) | − | 1613.47i | − | 0.0545851i | ||||||
\(957\) | −4835.57 | − | 7541.49i | −0.163335 | − | 0.254735i | ||||
\(958\) | 30404.7 | − | 30404.7i | 1.02540 | − | 1.02540i | ||||
\(959\) | −20442.8 | −0.688355 | ||||||||
\(960\) | 369.077 | + | 15007.7i | 0.0124082 | + | 0.504552i | ||||
\(961\) | −21073.6 | −0.707380 | ||||||||
\(962\) | 2426.75 | − | 2426.75i | 0.0813322 | − | 0.0813322i | ||||
\(963\) | −15528.8 | − | 41899.7i | −0.519635 | − | 1.40208i | ||||
\(964\) | 37082.4i | 1.23895i | ||||||||
\(965\) | 30184.4 | − | 7381.04i | 1.00691 | − | 0.246222i | ||||
\(966\) | −18388.6 | − | 4020.18i | −0.612466 | − | 0.133900i | ||||
\(967\) | 28409.1 | + | 28409.1i | 0.944752 | + | 0.944752i | 0.998552 | − | 0.0538000i | \(-0.0171333\pi\) |
−0.0538000 | + | 0.998552i | \(0.517133\pi\) | |||||||
\(968\) | −803.127 | − | 803.127i | −0.0266668 | − | 0.0266668i | ||||
\(969\) | 8795.95 | + | 1923.01i | 0.291606 | + | 0.0637522i | ||||
\(970\) | 21992.1 | + | 13349.9i | 0.727963 | + | 0.441896i | ||||
\(971\) | 18059.4i | 0.596864i | 0.954431 | + | 0.298432i | \(0.0964637\pi\) | ||||
−0.954431 | + | 0.298432i | \(0.903536\pi\) | |||||||
\(972\) | 6710.61 | − | 22423.1i | 0.221443 | − | 0.739938i | ||||
\(973\) | 23379.9 | − | 23379.9i | 0.770323 | − | 0.770323i | ||||
\(974\) | 32307.7 | 1.06284 | ||||||||
\(975\) | −2501.28 | + | 677.227i | −0.0821590 | + | 0.0222447i | ||||
\(976\) | 150.505 | 0.00493600 | ||||||||
\(977\) | 31166.3 | − | 31166.3i | 1.02057 | − | 1.02057i | 0.0207872 | − | 0.999784i | \(-0.493383\pi\) |
0.999784 | − | 0.0207872i | \(-0.00661725\pi\) | |||||||
\(978\) | 40013.6 | + | 62404.7i | 1.30828 | + | 2.04037i | ||||
\(979\) | − | 43422.9i | − | 1.41757i | ||||||
\(980\) | −9912.89 | − | 6017.43i | −0.323118 | − | 0.196143i | ||||
\(981\) | 31029.1 | + | 14248.5i | 1.00987 | + | 0.463729i | ||||
\(982\) | 23907.2 | + | 23907.2i | 0.776893 | + | 0.776893i | ||||
\(983\) | −13839.4 | − | 13839.4i | −0.449042 | − | 0.449042i | 0.445994 | − | 0.895036i | \(-0.352850\pi\) |
−0.895036 | + | 0.445994i | \(0.852850\pi\) | |||||||
\(984\) | 675.734 | − | 3090.85i | 0.0218919 | − | 0.100135i | ||||
\(985\) | 12787.8 | − | 3127.02i | 0.413659 | − | 0.101153i | ||||
\(986\) | 17276.6i | 0.558012i | ||||||||
\(987\) | −3134.18 | + | 2009.62i | −0.101076 | + | 0.0648095i | ||||
\(988\) | −332.474 | + | 332.474i | −0.0107059 | + | 0.0107059i | ||||
\(989\) | −18134.5 | −0.583056 | ||||||||
\(990\) | −38100.5 | − | 7353.16i | −1.22314 | − | 0.236059i | ||||
\(991\) | 17820.9 | 0.571242 | 0.285621 | − | 0.958343i | \(-0.407800\pi\) | ||||
0.285621 | + | 0.958343i | \(0.407800\pi\) | |||||||
\(992\) | 15085.9 | − | 15085.9i | 0.482842 | − | 0.482842i | ||||
\(993\) | 35984.5 | − | 23073.1i | 1.14998 | − | 0.737363i | ||||
\(994\) | 36570.2i | 1.16694i | ||||||||
\(995\) | 8937.56 | − | 14723.4i | 0.284764 | − | 0.469109i | ||||
\(996\) | 2114.07 | − | 9669.89i | 0.0672559 | − | 0.307633i | ||||
\(997\) | −36985.0 | − | 36985.0i | −1.17485 | − | 1.17485i | −0.981038 | − | 0.193814i | \(-0.937914\pi\) |
−0.193814 | − | 0.981038i | \(-0.562086\pi\) | |||||||
\(998\) | −20433.7 | − | 20433.7i | −0.648114 | − | 0.648114i | ||||
\(999\) | 19286.8 | − | 25597.6i | 0.610819 | − | 0.810684i |
(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 | 15.4.e.a.2.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 15.4.e.a.2.4 | yes | 8 | |
4.3 | odd | 2 | 240.4.v.c.17.4 | 8 | |||
5.2 | odd | 4 | 75.4.e.c.68.1 | 8 | |||
5.3 | odd | 4 | inner | 15.4.e.a.8.4 | yes | 8 | |
5.4 | even | 2 | 75.4.e.c.32.4 | 8 | |||
12.11 | even | 2 | 240.4.v.c.17.3 | 8 | |||
15.2 | even | 4 | 75.4.e.c.68.4 | 8 | |||
15.8 | even | 4 | inner | 15.4.e.a.8.1 | yes | 8 | |
15.14 | odd | 2 | 75.4.e.c.32.1 | 8 | |||
20.3 | even | 4 | 240.4.v.c.113.3 | 8 | |||
60.23 | odd | 4 | 240.4.v.c.113.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.4.e.a.2.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
15.4.e.a.2.4 | yes | 8 | 3.2 | odd | 2 | inner | |
15.4.e.a.8.1 | yes | 8 | 15.8 | even | 4 | inner | |
15.4.e.a.8.4 | yes | 8 | 5.3 | odd | 4 | inner | |
75.4.e.c.32.1 | 8 | 15.14 | odd | 2 | |||
75.4.e.c.32.4 | 8 | 5.4 | even | 2 | |||
75.4.e.c.68.1 | 8 | 5.2 | odd | 4 | |||
75.4.e.c.68.4 | 8 | 15.2 | even | 4 | |||
240.4.v.c.17.3 | 8 | 12.11 | even | 2 | |||
240.4.v.c.17.4 | 8 | 4.3 | odd | 2 | |||
240.4.v.c.113.3 | 8 | 20.3 | even | 4 | |||
240.4.v.c.113.4 | 8 | 60.23 | odd | 4 |