Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [121,4,Mod(3,121)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(121, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("121.3");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 121 = 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 121.c (of order \(5\), degree \(4\), 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: | \(7.13923111069\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.324000000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 3.2 | ||
Root | \(0.535233 + 1.64728i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 121.3 |
Dual form | 121.4.c.d.81.2 |
$q$-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 \(\left(\mathbb{Z}/121\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.99350 | − | 1.44836i | 0.704809 | − | 0.512074i | −0.176686 | − | 0.984267i | \(-0.556538\pi\) |
0.881495 | + | 0.472194i | \(0.156538\pi\) | |||||||
\(3\) | −0.165602 | − | 0.509670i | −0.0318701 | − | 0.0980860i | 0.933856 | − | 0.357649i | \(-0.116422\pi\) |
−0.965726 | + | 0.259563i | \(0.916422\pi\) | |||||||
\(4\) | −0.595848 | + | 1.83383i | −0.0744809 | + | 0.229229i | ||||
\(5\) | 1.24257 | + | 0.902778i | 0.111139 | + | 0.0807470i | 0.641966 | − | 0.766733i | \(-0.278119\pi\) |
−0.530828 | + | 0.847480i | \(0.678119\pi\) | |||||||
\(6\) | −1.06831 | − | 0.776175i | −0.0726895 | − | 0.0528120i | ||||
\(7\) | 8.72933 | − | 26.8661i | 0.471340 | − | 1.45063i | −0.379492 | − | 0.925195i | \(-0.623901\pi\) |
0.850831 | − | 0.525439i | \(-0.176099\pi\) | |||||||
\(8\) | 7.55982 | + | 23.2667i | 0.334100 | + | 1.02825i | ||||
\(9\) | 21.6111 | − | 15.7014i | 0.800412 | − | 0.581533i | ||||
\(10\) | 3.78461 | 0.119680 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.03332 | 0.0248578 | ||||||||
\(13\) | 55.3886 | − | 40.2422i | 1.18170 | − | 0.858552i | 0.189333 | − | 0.981913i | \(-0.439367\pi\) |
0.992362 | + | 0.123361i | \(0.0393673\pi\) | |||||||
\(14\) | −21.5100 | − | 66.2009i | −0.410627 | − | 1.26378i | ||||
\(15\) | 0.254347 | − | 0.782801i | 0.00437815 | − | 0.0134746i | ||||
\(16\) | 36.2896 | + | 26.3659i | 0.567025 | + | 0.411968i | ||||
\(17\) | 44.7822 | + | 32.5362i | 0.638899 | + | 0.464187i | 0.859472 | − | 0.511183i | \(-0.170793\pi\) |
−0.220573 | + | 0.975370i | \(0.570793\pi\) | |||||||
\(18\) | 20.3405 | − | 62.6015i | 0.266349 | − | 0.819739i | ||||
\(19\) | 17.0506 | + | 52.4764i | 0.205878 | + | 0.633627i | 0.999676 | + | 0.0254456i | \(0.00810047\pi\) |
−0.793798 | + | 0.608181i | \(0.791900\pi\) | |||||||
\(20\) | −2.39592 | + | 1.74074i | −0.0267872 | + | 0.0194621i | ||||
\(21\) | −15.1384 | −0.157308 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −178.315 | −1.61658 | −0.808290 | − | 0.588785i | \(-0.799606\pi\) | ||||
−0.808290 | + | 0.588785i | \(0.799606\pi\) | |||||||
\(24\) | 10.6064 | − | 7.70602i | 0.0902095 | − | 0.0655411i | ||||
\(25\) | −37.8982 | − | 116.639i | −0.303185 | − | 0.933108i | ||||
\(26\) | 52.1319 | − | 160.446i | 0.393227 | − | 1.21023i | ||||
\(27\) | −23.2872 | − | 16.9192i | −0.165986 | − | 0.120596i | ||||
\(28\) | 44.0666 | + | 32.0162i | 0.297421 | + | 0.216089i | ||||
\(29\) | −34.9720 | + | 107.633i | −0.223936 | + | 0.689203i | 0.774462 | + | 0.632620i | \(0.218021\pi\) |
−0.998398 | + | 0.0565831i | \(0.981979\pi\) | |||||||
\(30\) | −0.626738 | − | 1.92890i | −0.00381420 | − | 0.0117389i | ||||
\(31\) | −57.2887 | + | 41.6227i | −0.331915 | + | 0.241150i | −0.741243 | − | 0.671237i | \(-0.765763\pi\) |
0.409328 | + | 0.912387i | \(0.365763\pi\) | |||||||
\(32\) | −85.1821 | −0.470569 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 136.397 | 0.687999 | ||||||||
\(35\) | 35.1009 | − | 25.5023i | 0.169518 | − | 0.123162i | ||||
\(36\) | 15.9168 | + | 48.9868i | 0.0736887 | + | 0.226791i | ||||
\(37\) | −65.0988 | + | 200.353i | −0.289248 | + | 0.890213i | 0.695845 | + | 0.718192i | \(0.255030\pi\) |
−0.985093 | + | 0.172022i | \(0.944970\pi\) | |||||||
\(38\) | 109.995 | + | 79.9162i | 0.469568 | + | 0.341161i | ||||
\(39\) | −29.6827 | − | 21.5657i | −0.121873 | − | 0.0885456i | ||||
\(40\) | −11.6111 | + | 35.7354i | −0.0458970 | + | 0.141256i | ||||
\(41\) | −59.3091 | − | 182.535i | −0.225915 | − | 0.695295i | −0.998197 | − | 0.0600158i | \(-0.980885\pi\) |
0.772282 | − | 0.635280i | \(-0.219115\pi\) | |||||||
\(42\) | −30.1785 | + | 21.9259i | −0.110872 | + | 0.0805535i | ||||
\(43\) | 208.210 | 0.738413 | 0.369207 | − | 0.929347i | \(-0.379629\pi\) | ||||
0.369207 | + | 0.929347i | \(0.379629\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 41.0282 | 0.135914 | ||||||||
\(46\) | −355.472 | + | 258.265i | −1.13938 | + | 0.827807i | ||||
\(47\) | 158.376 | + | 487.431i | 0.491521 | + | 1.51275i | 0.822309 | + | 0.569042i | \(0.192686\pi\) |
−0.330787 | + | 0.943705i | \(0.607314\pi\) | |||||||
\(48\) | 7.42830 | − | 22.8619i | 0.0223371 | − | 0.0687466i | ||||
\(49\) | −368.094 | − | 267.436i | −1.07316 | − | 0.779697i | ||||
\(50\) | −244.485 | − | 177.629i | −0.691508 | − | 0.502410i | ||||
\(51\) | 9.16669 | − | 28.2122i | 0.0251685 | − | 0.0774607i | ||||
\(52\) | 40.7942 | + | 125.552i | 0.108791 | + | 0.334824i | ||||
\(53\) | 303.744 | − | 220.683i | 0.787217 | − | 0.571947i | −0.119919 | − | 0.992784i | \(-0.538264\pi\) |
0.907136 | + | 0.420837i | \(0.138264\pi\) | |||||||
\(54\) | −70.9282 | −0.178743 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 691.079 | 1.64910 | ||||||||
\(57\) | 23.9220 | − | 17.3804i | 0.0555885 | − | 0.0403874i | ||||
\(58\) | 86.1746 | + | 265.218i | 0.195091 | + | 0.600428i | ||||
\(59\) | −156.519 | + | 481.717i | −0.345375 | + | 1.06295i | 0.616008 | + | 0.787740i | \(0.288749\pi\) |
−0.961383 | + | 0.275214i | \(0.911251\pi\) | |||||||
\(60\) | 1.28397 | + | 0.932860i | 0.00276267 | + | 0.00200719i | ||||
\(61\) | −379.184 | − | 275.493i | −0.795894 | − | 0.578251i | 0.113812 | − | 0.993502i | \(-0.463694\pi\) |
−0.909707 | + | 0.415251i | \(0.863694\pi\) | |||||||
\(62\) | −53.9203 | + | 165.950i | −0.110450 | + | 0.339930i | ||||
\(63\) | −233.185 | − | 717.670i | −0.466326 | − | 1.43520i | ||||
\(64\) | −460.127 | + | 334.302i | −0.898686 | + | 0.652934i | ||||
\(65\) | 105.154 | 0.200657 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −289.895 | −0.528601 | −0.264301 | − | 0.964440i | \(-0.585141\pi\) | ||||
−0.264301 | + | 0.964440i | \(0.585141\pi\) | |||||||
\(68\) | −86.3492 | + | 62.7363i | −0.153991 | + | 0.111881i | ||||
\(69\) | 29.5293 | + | 90.8819i | 0.0515205 | + | 0.158564i | ||||
\(70\) | 33.0371 | − | 101.678i | 0.0564099 | − | 0.173612i | ||||
\(71\) | 318.761 | + | 231.593i | 0.532817 | + | 0.387114i | 0.821410 | − | 0.570338i | \(-0.193188\pi\) |
−0.288594 | + | 0.957452i | \(0.593188\pi\) | |||||||
\(72\) | 528.697 | + | 384.121i | 0.865382 | + | 0.628737i | ||||
\(73\) | −89.4723 | + | 275.367i | −0.143451 | + | 0.441497i | −0.996809 | − | 0.0798290i | \(-0.974563\pi\) |
0.853357 | + | 0.521326i | \(0.174563\pi\) | |||||||
\(74\) | 160.410 | + | 493.691i | 0.251990 | + | 0.775546i | ||||
\(75\) | −53.1711 | + | 38.6311i | −0.0818623 | + | 0.0594764i | ||||
\(76\) | −106.392 | −0.160579 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −90.4074 | −0.131239 | ||||||||
\(79\) | −137.199 | + | 99.6808i | −0.195393 | + | 0.141962i | −0.681180 | − | 0.732116i | \(-0.738533\pi\) |
0.485787 | + | 0.874077i | \(0.338533\pi\) | |||||||
\(80\) | 21.2897 | + | 65.5229i | 0.0297532 | + | 0.0915711i | ||||
\(81\) | 218.110 | − | 671.275i | 0.299191 | − | 0.920816i | ||||
\(82\) | −382.609 | − | 277.982i | −0.515269 | − | 0.374365i | ||||
\(83\) | −245.400 | − | 178.293i | −0.324532 | − | 0.235786i | 0.413575 | − | 0.910470i | \(-0.364280\pi\) |
−0.738107 | + | 0.674684i | \(0.764280\pi\) | |||||||
\(84\) | 9.02020 | − | 27.7613i | 0.0117165 | − | 0.0360596i | ||||
\(85\) | 26.2720 | + | 80.8568i | 0.0335246 | + | 0.103178i | ||||
\(86\) | 415.067 | − | 301.564i | 0.520440 | − | 0.378122i | ||||
\(87\) | 60.6486 | 0.0747380 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1146.68 | −1.36571 | −0.682854 | − | 0.730555i | \(-0.739262\pi\) | ||||
−0.682854 | + | 0.730555i | \(0.739262\pi\) | |||||||
\(90\) | 81.7897 | − | 59.4237i | 0.0957932 | − | 0.0695978i | ||||
\(91\) | −597.646 | − | 1839.36i | −0.688465 | − | 2.11888i | ||||
\(92\) | 106.249 | − | 327.000i | 0.120404 | − | 0.370566i | ||||
\(93\) | 30.7009 | + | 22.3055i | 0.0342316 | + | 0.0248707i | ||||
\(94\) | 1021.70 | + | 742.308i | 1.12107 | + | 0.814502i | ||||
\(95\) | −26.1880 | + | 80.5984i | −0.0282824 | + | 0.0870444i | ||||
\(96\) | 14.1063 | + | 43.4147i | 0.0149971 | + | 0.0461562i | ||||
\(97\) | −519.065 | + | 377.123i | −0.543331 | + | 0.394753i | −0.825321 | − | 0.564665i | \(-0.809006\pi\) |
0.281990 | + | 0.959417i | \(0.409006\pi\) | |||||||
\(98\) | −1121.14 | −1.15564 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 236.477 | 0.236477 | ||||||||
\(101\) | 896.042 | − | 651.013i | 0.882768 | − | 0.641368i | −0.0512145 | − | 0.998688i | \(-0.516309\pi\) |
0.933982 | + | 0.357319i | \(0.116309\pi\) | |||||||
\(102\) | −22.5877 | − | 69.5176i | −0.0219266 | − | 0.0674831i | ||||
\(103\) | −92.1790 | + | 283.698i | −0.0881812 | + | 0.271394i | −0.985417 | − | 0.170158i | \(-0.945572\pi\) |
0.897235 | + | 0.441552i | \(0.145572\pi\) | |||||||
\(104\) | 1355.03 | + | 984.489i | 1.27761 | + | 0.928241i | ||||
\(105\) | −18.8105 | − | 13.6667i | −0.0174831 | − | 0.0127022i | ||||
\(106\) | 285.885 | − | 879.864i | 0.261959 | − | 0.806226i | ||||
\(107\) | 184.831 | + | 568.851i | 0.166993 | + | 0.513953i | 0.999178 | − | 0.0405464i | \(-0.0129099\pi\) |
−0.832184 | + | 0.554499i | \(0.812910\pi\) | |||||||
\(108\) | 44.9025 | − | 32.6236i | 0.0400069 | − | 0.0290667i | ||||
\(109\) | 1530.16 | 1.34461 | 0.672305 | − | 0.740275i | \(-0.265305\pi\) | ||||
0.672305 | + | 0.740275i | \(0.265305\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 112.895 | 0.0965358 | ||||||||
\(112\) | 1025.13 | − | 744.804i | 0.864876 | − | 0.628369i | ||||
\(113\) | −46.6648 | − | 143.619i | −0.0388482 | − | 0.119563i | 0.929752 | − | 0.368187i | \(-0.120021\pi\) |
−0.968600 | + | 0.248625i | \(0.920021\pi\) | |||||||
\(114\) | 22.5155 | − | 69.2955i | 0.0184979 | − | 0.0569308i | ||||
\(115\) | −221.569 | − | 160.979i | −0.179664 | − | 0.130534i | ||||
\(116\) | −176.542 | − | 128.265i | −0.141306 | − | 0.102665i | ||||
\(117\) | 565.152 | − | 1739.36i | 0.446566 | − | 1.37439i | ||||
\(118\) | 385.680 | + | 1187.00i | 0.300887 | + | 0.926036i | ||||
\(119\) | 1265.04 | − | 919.105i | 0.974504 | − | 0.708018i | ||||
\(120\) | 20.1360 | 0.0153180 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1154.92 | −0.857060 | ||||||||
\(123\) | −83.2106 | + | 60.4561i | −0.0609988 | + | 0.0443182i | ||||
\(124\) | −42.1936 | − | 129.859i | −0.0305572 | − | 0.0940455i | ||||
\(125\) | 117.535 | − | 361.736i | 0.0841012 | − | 0.258837i | ||||
\(126\) | −1504.30 | − | 1092.94i | −1.06360 | − | 0.772751i | ||||
\(127\) | −562.872 | − | 408.951i | −0.393282 | − | 0.285736i | 0.373517 | − | 0.927623i | \(-0.378152\pi\) |
−0.766799 | + | 0.641887i | \(0.778152\pi\) | |||||||
\(128\) | −222.491 | + | 684.758i | −0.153638 | + | 0.472849i | ||||
\(129\) | −34.4800 | − | 106.118i | −0.0235333 | − | 0.0724280i | ||||
\(130\) | 209.624 | − | 152.301i | 0.141425 | − | 0.102751i | ||||
\(131\) | −1665.68 | −1.11093 | −0.555463 | − | 0.831541i | \(-0.687459\pi\) | ||||
−0.555463 | + | 0.831541i | \(0.687459\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1558.68 | 1.01620 | ||||||||
\(134\) | −577.905 | + | 419.873i | −0.372563 | + | 0.270683i | ||||
\(135\) | −13.6617 | − | 42.0464i | −0.00870973 | − | 0.0268058i | ||||
\(136\) | −418.465 | + | 1287.90i | −0.263846 | + | 0.812035i | ||||
\(137\) | 1298.86 | + | 943.675i | 0.809992 | + | 0.588494i | 0.913828 | − | 0.406101i | \(-0.133112\pi\) |
−0.103836 | + | 0.994594i | \(0.533112\pi\) | |||||||
\(138\) | 190.497 | + | 138.404i | 0.117508 | + | 0.0853748i | ||||
\(139\) | 330.432 | − | 1016.96i | 0.201632 | − | 0.620560i | −0.798203 | − | 0.602389i | \(-0.794216\pi\) |
0.999835 | − | 0.0181710i | \(-0.00578432\pi\) | |||||||
\(140\) | 25.8521 | + | 79.5647i | 0.0156065 | + | 0.0480317i | ||||
\(141\) | 222.201 | − | 161.439i | 0.132714 | − | 0.0964227i | ||||
\(142\) | 970.881 | 0.573765 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1198.24 | 0.693426 | ||||||||
\(145\) | −140.624 | + | 102.169i | −0.0805390 | + | 0.0585150i | ||||
\(146\) | 220.469 | + | 678.533i | 0.124973 | + | 0.384629i | ||||
\(147\) | −75.3471 | + | 231.894i | −0.0422757 | + | 0.130111i | ||||
\(148\) | −328.625 | − | 238.760i | −0.182519 | − | 0.132608i | ||||
\(149\) | −287.340 | − | 208.765i | −0.157985 | − | 0.114783i | 0.505984 | − | 0.862543i | \(-0.331129\pi\) |
−0.663969 | + | 0.747760i | \(0.731129\pi\) | |||||||
\(150\) | −50.0448 | + | 154.022i | −0.0272410 | + | 0.0838390i | ||||
\(151\) | −580.814 | − | 1787.56i | −0.313020 | − | 0.963375i | −0.976562 | − | 0.215237i | \(-0.930948\pi\) |
0.663542 | − | 0.748139i | \(-0.269052\pi\) | |||||||
\(152\) | −1092.05 | + | 793.424i | −0.582746 | + | 0.423389i | ||||
\(153\) | 1478.66 | 0.781322 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −108.761 | −0.0563607 | ||||||||
\(156\) | 57.2342 | − | 41.5831i | 0.0293744 | − | 0.0213417i | ||||
\(157\) | 772.539 | + | 2377.63i | 0.392709 | + | 1.20863i | 0.930731 | + | 0.365704i | \(0.119172\pi\) |
−0.538022 | + | 0.842931i | \(0.680828\pi\) | |||||||
\(158\) | −129.132 | + | 397.427i | −0.0650202 | + | 0.200112i | ||||
\(159\) | −162.776 | − | 118.264i | −0.0811886 | − | 0.0589870i | ||||
\(160\) | −105.845 | − | 76.9005i | −0.0522984 | − | 0.0379970i | ||||
\(161\) | −1556.57 | + | 4790.64i | −0.761958 | + | 2.34507i | ||||
\(162\) | −537.446 | − | 1654.09i | −0.260653 | − | 0.802207i | ||||
\(163\) | −1507.22 | + | 1095.06i | −0.724260 | + | 0.526206i | −0.887742 | − | 0.460341i | \(-0.847727\pi\) |
0.163482 | + | 0.986546i | \(0.447727\pi\) | |||||||
\(164\) | 370.077 | 0.176208 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −747.438 | −0.349473 | ||||||||
\(167\) | −2141.68 | + | 1556.02i | −0.992386 | + | 0.721011i | −0.960442 | − | 0.278479i | \(-0.910170\pi\) |
−0.0319436 | + | 0.999490i | \(0.510170\pi\) | |||||||
\(168\) | −114.444 | − | 352.222i | −0.0525568 | − | 0.161753i | ||||
\(169\) | 769.555 | − | 2368.45i | 0.350276 | − | 1.07804i | ||||
\(170\) | 169.483 | + | 123.137i | 0.0764633 | + | 0.0555538i | ||||
\(171\) | 1192.43 | + | 866.355i | 0.533262 | + | 0.387437i | ||||
\(172\) | −124.062 | + | 381.822i | −0.0549977 | + | 0.169266i | ||||
\(173\) | 651.836 | + | 2006.14i | 0.286463 | + | 0.881643i | 0.985956 | + | 0.167004i | \(0.0534092\pi\) |
−0.699493 | + | 0.714639i | \(0.746591\pi\) | |||||||
\(174\) | 120.903 | − | 87.8411i | 0.0526760 | − | 0.0382714i | ||||
\(175\) | −3464.45 | −1.49650 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 271.437 | 0.115268 | ||||||||
\(178\) | −2285.91 | + | 1660.81i | −0.962563 | + | 0.699343i | ||||
\(179\) | 429.919 | + | 1323.15i | 0.179517 | + | 0.552498i | 0.999811 | − | 0.0194450i | \(-0.00618992\pi\) |
−0.820294 | + | 0.571943i | \(0.806190\pi\) | |||||||
\(180\) | −24.4465 | + | 75.2387i | −0.0101230 | + | 0.0311553i | ||||
\(181\) | −2994.50 | − | 2175.63i | −1.22972 | − | 0.893443i | −0.232850 | − | 0.972513i | \(-0.574805\pi\) |
−0.996869 | + | 0.0790692i | \(0.974805\pi\) | |||||||
\(182\) | −3855.47 | − | 2801.17i | −1.57026 | − | 1.14086i | ||||
\(183\) | −77.6171 | + | 238.881i | −0.0313531 | + | 0.0964950i | ||||
\(184\) | −1348.03 | − | 4148.82i | −0.540099 | − | 1.66225i | ||||
\(185\) | −261.764 | + | 190.183i | −0.104029 | + | 0.0755812i | ||||
\(186\) | 93.5088 | 0.0368624 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −988.234 | −0.383374 | ||||||||
\(189\) | −657.834 | + | 477.945i | −0.253177 | + | 0.183944i | ||||
\(190\) | 64.5299 | + | 198.603i | 0.0246394 | + | 0.0758323i | ||||
\(191\) | −1091.77 | + | 3360.11i | −0.413599 | + | 1.27293i | 0.499899 | + | 0.866084i | \(0.333371\pi\) |
−0.913498 | + | 0.406844i | \(0.866629\pi\) | |||||||
\(192\) | 246.581 | + | 179.152i | 0.0926848 | + | 0.0673395i | ||||
\(193\) | 2108.02 | + | 1531.57i | 0.786212 | + | 0.571216i | 0.906837 | − | 0.421482i | \(-0.138490\pi\) |
−0.120625 | + | 0.992698i | \(0.538490\pi\) | |||||||
\(194\) | −488.546 | + | 1503.59i | −0.180802 | + | 0.556451i | ||||
\(195\) | −17.4137 | − | 53.5938i | −0.00639497 | − | 0.0196817i | ||||
\(196\) | 709.761 | − | 515.671i | 0.258659 | − | 0.187927i | ||||
\(197\) | 719.202 | 0.260107 | 0.130053 | − | 0.991507i | \(-0.458485\pi\) | ||||
0.130053 | + | 0.991507i | \(0.458485\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1035.15 | 0.368744 | 0.184372 | − | 0.982857i | \(-0.440975\pi\) | ||||
0.184372 | + | 0.982857i | \(0.440975\pi\) | |||||||
\(200\) | 2427.30 | − | 1763.53i | 0.858179 | − | 0.623503i | ||||
\(201\) | 48.0071 | + | 147.751i | 0.0168466 | + | 0.0518484i | ||||
\(202\) | 843.358 | − | 2595.59i | 0.293755 | − | 0.904084i | ||||
\(203\) | 2586.39 | + | 1879.12i | 0.894232 | + | 0.649698i | ||||
\(204\) | 46.2744 | + | 33.6203i | 0.0158816 | + | 0.0115387i | ||||
\(205\) | 91.0927 | − | 280.355i | 0.0310351 | − | 0.0955162i | ||||
\(206\) | 227.138 | + | 699.060i | 0.0768227 | + | 0.236436i | ||||
\(207\) | −3853.59 | + | 2799.80i | −1.29393 | + | 0.940095i | ||||
\(208\) | 3071.05 | 1.02375 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −57.2931 | −0.0188267 | ||||||||
\(211\) | 288.250 | − | 209.426i | 0.0940472 | − | 0.0683293i | −0.539768 | − | 0.841814i | \(-0.681488\pi\) |
0.633815 | + | 0.773485i | \(0.281488\pi\) | |||||||
\(212\) | 223.710 | + | 688.509i | 0.0724739 | + | 0.223052i | ||||
\(213\) | 65.2488 | − | 200.815i | 0.0209895 | − | 0.0645992i | ||||
\(214\) | 1192.36 | + | 866.303i | 0.380880 | + | 0.276725i | ||||
\(215\) | 258.715 | + | 187.968i | 0.0820662 | + | 0.0596246i | ||||
\(216\) | 217.607 | − | 669.724i | 0.0685475 | − | 0.210967i | ||||
\(217\) | 618.148 | + | 1902.46i | 0.193376 | + | 0.595151i | ||||
\(218\) | 3050.37 | − | 2216.22i | 0.947692 | − | 0.688539i | ||||
\(219\) | 155.163 | 0.0478765 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3789.75 | 1.15351 | ||||||||
\(222\) | 225.055 | − | 163.512i | 0.0680393 | − | 0.0494334i | ||||
\(223\) | −90.4011 | − | 278.226i | −0.0271467 | − | 0.0835489i | 0.936565 | − | 0.350493i | \(-0.113986\pi\) |
−0.963712 | + | 0.266944i | \(0.913986\pi\) | |||||||
\(224\) | −743.583 | + | 2288.51i | −0.221798 | + | 0.682623i | ||||
\(225\) | −2650.41 | − | 1925.64i | −0.785307 | − | 0.570559i | ||||
\(226\) | −301.039 | − | 218.718i | −0.0886054 | − | 0.0643756i | ||||
\(227\) | 1731.74 | − | 5329.75i | 0.506343 | − | 1.55836i | −0.292159 | − | 0.956370i | \(-0.594374\pi\) |
0.798502 | − | 0.601993i | \(-0.205626\pi\) | |||||||
\(228\) | 17.6187 | + | 54.2249i | 0.00511768 | + | 0.0157506i | ||||
\(229\) | 4574.49 | − | 3323.56i | 1.32005 | − | 0.959070i | 0.320114 | − | 0.947379i | \(-0.396279\pi\) |
0.999932 | − | 0.0116906i | \(-0.00372132\pi\) | |||||||
\(230\) | −674.854 | −0.193472 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2768.65 | −0.783493 | ||||||||
\(233\) | 2065.49 | − | 1500.66i | 0.580749 | − | 0.421939i | −0.258245 | − | 0.966079i | \(-0.583144\pi\) |
0.838994 | + | 0.544141i | \(0.183144\pi\) | |||||||
\(234\) | −1392.59 | − | 4285.95i | −0.389045 | − | 1.19736i | ||||
\(235\) | −243.249 | + | 748.644i | −0.0675227 | + | 0.207814i | ||||
\(236\) | −790.126 | − | 574.060i | −0.217936 | − | 0.158340i | ||||
\(237\) | 73.5246 | + | 53.4188i | 0.0201516 | + | 0.0146410i | ||||
\(238\) | 1190.66 | − | 3664.47i | 0.324281 | − | 0.998035i | ||||
\(239\) | 1636.95 | + | 5038.00i | 0.443034 | + | 1.36352i | 0.884625 | + | 0.466303i | \(0.154414\pi\) |
−0.441591 | + | 0.897217i | \(0.645586\pi\) | |||||||
\(240\) | 29.8694 | − | 21.7014i | 0.00803360 | − | 0.00583675i | ||||
\(241\) | −4145.14 | −1.10793 | −0.553966 | − | 0.832539i | \(-0.686886\pi\) | ||||
−0.553966 | + | 0.832539i | \(0.686886\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1155.43 | −0.305025 | ||||||||
\(244\) | 731.144 | − | 531.207i | 0.191831 | − | 0.139373i | ||||
\(245\) | −215.947 | − | 664.615i | −0.0563115 | − | 0.173309i | ||||
\(246\) | −78.3181 | + | 241.038i | −0.0202983 | + | 0.0624717i | ||||
\(247\) | 3056.17 | + | 2220.44i | 0.787286 | + | 0.571997i | ||||
\(248\) | −1401.52 | − | 1018.26i | −0.358857 | − | 0.260725i | ||||
\(249\) | −50.2321 | + | 154.599i | −0.0127845 | + | 0.0393465i | ||||
\(250\) | −289.618 | − | 891.354i | −0.0732683 | − | 0.225497i | ||||
\(251\) | 1446.63 | − | 1051.04i | 0.363786 | − | 0.264306i | −0.390843 | − | 0.920457i | \(-0.627817\pi\) |
0.754630 | + | 0.656151i | \(0.227817\pi\) | |||||||
\(252\) | 1455.03 | 0.363723 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1714.40 | −0.423507 | ||||||||
\(255\) | 36.8596 | − | 26.7800i | 0.00905190 | − | 0.00657659i | ||||
\(256\) | −857.782 | − | 2639.98i | −0.209419 | − | 0.644527i | ||||
\(257\) | 1596.69 | − | 4914.12i | 0.387545 | − | 1.19274i | −0.547072 | − | 0.837085i | \(-0.684258\pi\) |
0.934617 | − | 0.355655i | \(-0.115742\pi\) | |||||||
\(258\) | −222.434 | − | 161.608i | −0.0536749 | − | 0.0389971i | ||||
\(259\) | 4814.45 | + | 3497.90i | 1.15504 | + | 0.839186i | ||||
\(260\) | −62.6557 | + | 192.834i | −0.0149452 | + | 0.0459965i | ||||
\(261\) | 934.200 | + | 2875.17i | 0.221554 | + | 0.681873i | ||||
\(262\) | −3320.54 | + | 2412.51i | −0.782990 | + | 0.568876i | ||||
\(263\) | 57.6791 | 0.0135234 | 0.00676169 | − | 0.999977i | \(-0.497848\pi\) | ||||
0.00676169 | + | 0.999977i | \(0.497848\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 576.651 | 0.133673 | ||||||||
\(266\) | 3107.22 | − | 2257.53i | 0.716226 | − | 0.520368i | ||||
\(267\) | 189.892 | + | 584.429i | 0.0435252 | + | 0.133957i | ||||
\(268\) | 172.733 | − | 531.618i | 0.0393707 | − | 0.121171i | ||||
\(269\) | 2449.75 | + | 1779.85i | 0.555256 | + | 0.403417i | 0.829720 | − | 0.558180i | \(-0.188500\pi\) |
−0.274463 | + | 0.961598i | \(0.588500\pi\) | |||||||
\(270\) | −88.1331 | − | 64.0325i | −0.0198652 | − | 0.0144329i | ||||
\(271\) | 459.767 | − | 1415.02i | 0.103058 | − | 0.317181i | −0.886211 | − | 0.463281i | \(-0.846672\pi\) |
0.989270 | + | 0.146100i | \(0.0466720\pi\) | |||||||
\(272\) | 767.281 | + | 2361.45i | 0.171041 | + | 0.526411i | ||||
\(273\) | −838.497 | + | 609.204i | −0.185891 | + | 0.135058i | ||||
\(274\) | 3956.06 | 0.872241 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −184.257 | −0.0401847 | ||||||||
\(277\) | 6035.64 | − | 4385.15i | 1.30919 | − | 0.951185i | 0.309194 | − | 0.950999i | \(-0.399941\pi\) |
1.00000 | 0.000185599i | \(-5.90779e-5\pi\) | ||||||||
\(278\) | −814.218 | − | 2505.90i | −0.175660 | − | 0.540626i | ||||
\(279\) | −584.539 | + | 1799.03i | −0.125432 | + | 0.386039i | ||||
\(280\) | 858.713 | + | 623.892i | 0.183278 | + | 0.133159i | ||||
\(281\) | 728.240 | + | 529.098i | 0.154602 | + | 0.112325i | 0.662397 | − | 0.749153i | \(-0.269539\pi\) |
−0.507795 | + | 0.861478i | \(0.669539\pi\) | |||||||
\(282\) | 209.137 | − | 643.657i | 0.0441628 | − | 0.135919i | ||||
\(283\) | −2004.57 | − | 6169.42i | −0.421057 | − | 1.29588i | −0.906720 | − | 0.421734i | \(-0.861422\pi\) |
0.485662 | − | 0.874146i | \(-0.338578\pi\) | |||||||
\(284\) | −614.636 | + | 446.559i | −0.128422 | + | 0.0933043i | ||||
\(285\) | 45.4153 | 0.00943920 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5421.72 | −1.11510 | ||||||||
\(288\) | −1840.88 | + | 1337.48i | −0.376649 | + | 0.273651i | ||||
\(289\) | −571.358 | − | 1758.46i | −0.116295 | − | 0.357920i | ||||
\(290\) | −132.355 | + | 407.348i | −0.0268006 | + | 0.0824838i | ||||
\(291\) | 278.166 | + | 202.100i | 0.0560357 | + | 0.0407123i | ||||
\(292\) | −451.665 | − | 328.154i | −0.0905195 | − | 0.0657663i | ||||
\(293\) | −1894.08 | + | 5829.39i | −0.377657 | + | 1.16231i | 0.564011 | + | 0.825767i | \(0.309257\pi\) |
−0.941668 | + | 0.336542i | \(0.890743\pi\) | |||||||
\(294\) | 185.663 | + | 571.411i | 0.0368302 | + | 0.113352i | ||||
\(295\) | −629.370 | + | 457.264i | −0.124215 | + | 0.0902473i | ||||
\(296\) | −5153.71 | −1.01200 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −875.179 | −0.170127 | ||||||||
\(299\) | −9876.64 | + | 7175.80i | −1.91030 | + | 1.38792i | ||||
\(300\) | −39.1610 | − | 120.525i | −0.00753653 | − | 0.0231951i | ||||
\(301\) | 1817.54 | − | 5593.80i | 0.348043 | − | 1.07117i | ||||
\(302\) | −3746.89 | − | 2722.27i | −0.713938 | − | 0.518706i | ||||
\(303\) | −480.188 | − | 348.877i | −0.0910431 | − | 0.0661467i | ||||
\(304\) | −764.829 | + | 2353.90i | −0.144296 | + | 0.444097i | ||||
\(305\) | −222.453 | − | 684.638i | −0.0417626 | − | 0.128532i | ||||
\(306\) | 2947.70 | − | 2141.63i | 0.550683 | − | 0.400094i | ||||
\(307\) | −5377.67 | −0.999740 | −0.499870 | − | 0.866101i | \(-0.666619\pi\) | ||||
−0.499870 | + | 0.866101i | \(0.666619\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 159.857 | 0.0294303 | ||||||||
\(310\) | −216.816 | + | 157.526i | −0.0397235 | + | 0.0288608i | ||||
\(311\) | −1874.63 | − | 5769.50i | −0.341801 | − | 1.05196i | −0.963274 | − | 0.268521i | \(-0.913465\pi\) |
0.621473 | − | 0.783436i | \(-0.286535\pi\) | |||||||
\(312\) | 277.368 | − | 853.652i | 0.0503298 | − | 0.154899i | ||||
\(313\) | −2622.17 | − | 1905.12i | −0.473526 | − | 0.344037i | 0.325288 | − | 0.945615i | \(-0.394539\pi\) |
−0.798814 | + | 0.601578i | \(0.794539\pi\) | |||||||
\(314\) | 4983.73 | + | 3620.89i | 0.895695 | + | 0.650760i | ||||
\(315\) | 358.148 | − | 1102.27i | 0.0640615 | − | 0.197161i | ||||
\(316\) | −101.048 | − | 310.994i | −0.0179886 | − | 0.0553632i | ||||
\(317\) | −5274.24 | + | 3831.96i | −0.934482 | + | 0.678941i | −0.947086 | − | 0.320979i | \(-0.895988\pi\) |
0.0126037 | + | 0.999921i | \(0.495988\pi\) | |||||||
\(318\) | −495.783 | −0.0874281 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −873.540 | −0.152601 | ||||||||
\(321\) | 259.318 | − | 188.406i | 0.0450895 | − | 0.0327594i | ||||
\(322\) | 3835.56 | + | 11804.6i | 0.663811 | + | 2.04300i | ||||
\(323\) | −943.816 | + | 2904.77i | −0.162586 | + | 0.500389i | ||||
\(324\) | 1101.04 | + | 799.955i | 0.188794 | + | 0.137167i | ||||
\(325\) | −6792.92 | − | 4935.34i | −1.15939 | − | 0.842349i | ||||
\(326\) | −1418.60 | + | 4365.99i | −0.241009 | + | 0.741749i | ||||
\(327\) | −253.396 | − | 779.874i | −0.0428528 | − | 0.131887i | ||||
\(328\) | 3798.62 | − | 2759.86i | 0.639462 | − | 0.464597i | ||||
\(329\) | 14477.9 | 2.42612 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5879.55 | 0.976343 | 0.488171 | − | 0.872748i | \(-0.337664\pi\) | ||||
0.488171 | + | 0.872748i | \(0.337664\pi\) | |||||||
\(332\) | 473.181 | − | 343.786i | 0.0782204 | − | 0.0568304i | ||||
\(333\) | 1738.97 | + | 5352.00i | 0.286171 | + | 0.880745i | ||||
\(334\) | −2015.76 | + | 6203.87i | −0.330232 | + | 1.01635i | ||||
\(335\) | −360.214 | − | 261.711i | −0.0587481 | − | 0.0426830i | ||||
\(336\) | −549.368 | − | 399.139i | −0.0891978 | − | 0.0648060i | ||||
\(337\) | −414.906 | + | 1276.95i | −0.0670663 | + | 0.206409i | −0.978973 | − | 0.203988i | \(-0.934610\pi\) |
0.911907 | + | 0.410397i | \(0.134610\pi\) | |||||||
\(338\) | −1896.26 | − | 5836.10i | −0.305157 | − | 0.939177i | ||||
\(339\) | −65.4707 | + | 47.5672i | −0.0104893 | + | 0.00762093i | ||||
\(340\) | −163.932 | −0.0261484 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 3631.91 | 0.574244 | ||||||||
\(343\) | −2559.38 | + | 1859.50i | −0.402896 | + | 0.292721i | ||||
\(344\) | 1574.03 | + | 4844.37i | 0.246704 | + | 0.759277i | ||||
\(345\) | −45.3540 | + | 139.585i | −0.00707762 | + | 0.0217827i | ||||
\(346\) | 4205.06 | + | 3055.15i | 0.653368 | + | 0.474700i | ||||
\(347\) | −4570.97 | − | 3321.01i | −0.707155 | − | 0.513778i | 0.175100 | − | 0.984551i | \(-0.443975\pi\) |
−0.882255 | + | 0.470773i | \(0.843975\pi\) | |||||||
\(348\) | −36.1373 | + | 111.219i | −0.00556656 | + | 0.0171321i | ||||
\(349\) | 386.133 | + | 1188.39i | 0.0592241 | + | 0.182273i | 0.976292 | − | 0.216458i | \(-0.0694506\pi\) |
−0.917068 | + | 0.398731i | \(0.869451\pi\) | |||||||
\(350\) | −6906.38 | + | 5017.78i | −1.05475 | + | 0.766319i | ||||
\(351\) | −1970.71 | −0.299683 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5984.25 | 0.902293 | 0.451147 | − | 0.892450i | \(-0.351015\pi\) | ||||
0.451147 | + | 0.892450i | \(0.351015\pi\) | |||||||
\(354\) | 541.109 | − | 393.139i | 0.0812419 | − | 0.0590257i | ||||
\(355\) | 187.005 | + | 575.541i | 0.0279582 | + | 0.0860466i | ||||
\(356\) | 683.248 | − | 2102.82i | 0.101719 | − | 0.313060i | ||||
\(357\) | −677.932 | − | 492.547i | −0.100504 | − | 0.0730206i | ||||
\(358\) | 2773.45 | + | 2015.03i | 0.409445 | + | 0.297479i | ||||
\(359\) | 672.424 | − | 2069.51i | 0.0988557 | − | 0.304247i | −0.889384 | − | 0.457162i | \(-0.848866\pi\) |
0.988239 | + | 0.152915i | \(0.0488661\pi\) | |||||||
\(360\) | 310.166 | + | 954.592i | 0.0454088 | + | 0.139754i | ||||
\(361\) | 3086.00 | − | 2242.11i | 0.449920 | − | 0.326886i | ||||
\(362\) | −9120.63 | −1.32423 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3729.19 | 0.536985 | ||||||||
\(365\) | −359.771 | + | 261.389i | −0.0515925 | + | 0.0374842i | ||||
\(366\) | 191.256 | + | 588.627i | 0.0273146 | + | 0.0840656i | ||||
\(367\) | −2615.64 | + | 8050.11i | −0.372031 | + | 1.14499i | 0.573430 | + | 0.819255i | \(0.305613\pi\) |
−0.945460 | + | 0.325738i | \(0.894387\pi\) | |||||||
\(368\) | −6470.99 | − | 4701.45i | −0.916641 | − | 0.665978i | ||||
\(369\) | −4147.78 | − | 3013.54i | −0.585163 | − | 0.425145i | ||||
\(370\) | −246.373 | + | 758.259i | −0.0346171 | + | 0.106541i | ||||
\(371\) | −3277.42 | − | 10086.8i | −0.458639 | − | 1.41154i | ||||
\(372\) | −59.1977 | + | 43.0096i | −0.00825069 | + | 0.00599447i | ||||
\(373\) | 4248.93 | 0.589816 | 0.294908 | − | 0.955526i | \(-0.404711\pi\) | ||||
0.294908 | + | 0.955526i | \(0.404711\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −203.830 | −0.0280686 | ||||||||
\(376\) | −10143.6 | + | 7369.78i | −1.39127 | + | 1.01082i | ||||
\(377\) | 2394.33 | + | 7368.98i | 0.327093 | + | 1.00669i | ||||
\(378\) | −619.156 | + | 1905.57i | −0.0842485 | + | 0.259290i | ||||
\(379\) | −3926.11 | − | 2852.48i | −0.532112 | − | 0.386602i | 0.289035 | − | 0.957318i | \(-0.406666\pi\) |
−0.821147 | + | 0.570716i | \(0.806666\pi\) | |||||||
\(380\) | −132.200 | − | 96.0487i | −0.0178466 | − | 0.0129663i | ||||
\(381\) | −115.217 | + | 354.602i | −0.0154928 | + | 0.0476819i | ||||
\(382\) | 2690.22 | + | 8279.66i | 0.360324 | + | 1.10896i | ||||
\(383\) | 6619.22 | − | 4809.15i | 0.883098 | − | 0.641608i | −0.0509713 | − | 0.998700i | \(-0.516232\pi\) |
0.934069 | + | 0.357092i | \(0.116232\pi\) | |||||||
\(384\) | 385.846 | 0.0512763 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6420.61 | 0.846634 | ||||||||
\(387\) | 4499.66 | − | 3269.19i | 0.591035 | − | 0.429412i | ||||
\(388\) | −382.296 | − | 1176.59i | −0.0500209 | − | 0.153949i | ||||
\(389\) | 387.760 | − | 1193.40i | 0.0505404 | − | 0.155547i | −0.922601 | − | 0.385756i | \(-0.873941\pi\) |
0.973141 | + | 0.230208i | \(0.0739407\pi\) | |||||||
\(390\) | −112.337 | − | 81.6178i | −0.0145857 | − | 0.0105971i | ||||
\(391\) | −7985.35 | − | 5801.70i | −1.03283 | − | 0.750395i | ||||
\(392\) | 3439.64 | − | 10586.1i | 0.443184 | − | 1.36398i | ||||
\(393\) | 275.840 | + | 848.948i | 0.0354053 | + | 0.108966i | ||||
\(394\) | 1433.73 | − | 1041.67i | 0.183325 | − | 0.133194i | ||||
\(395\) | −260.469 | −0.0331787 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11519.3 | −1.45627 | −0.728133 | − | 0.685436i | \(-0.759612\pi\) | ||||
−0.728133 | + | 0.685436i | \(0.759612\pi\) | |||||||
\(398\) | 2063.58 | − | 1499.28i | 0.259894 | − | 0.188824i | ||||
\(399\) | −258.120 | − | 794.410i | −0.0323863 | − | 0.0996748i | ||||
\(400\) | 1699.98 | − | 5231.99i | 0.212497 | − | 0.653998i | ||||
\(401\) | 1214.06 | + | 882.069i | 0.151191 | + | 0.109846i | 0.660809 | − | 0.750554i | \(-0.270213\pi\) |
−0.509618 | + | 0.860401i | \(0.670213\pi\) | |||||||
\(402\) | 309.699 | + | 225.009i | 0.0384238 | + | 0.0279165i | ||||
\(403\) | −1498.16 | + | 4610.85i | −0.185182 | + | 0.569932i | ||||
\(404\) | 659.942 | + | 2031.09i | 0.0812707 | + | 0.250125i | ||||
\(405\) | 877.030 | − | 637.199i | 0.107605 | − | 0.0781795i | ||||
\(406\) | 7877.63 | 0.962956 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 725.704 | 0.0880581 | ||||||||
\(409\) | 73.9390 | − | 53.7198i | 0.00893899 | − | 0.00649456i | −0.583307 | − | 0.812252i | \(-0.698241\pi\) |
0.592246 | + | 0.805757i | \(0.298241\pi\) | |||||||
\(410\) | −224.462 | − | 690.822i | −0.0270375 | − | 0.0832129i | ||||
\(411\) | 265.870 | − | 818.263i | 0.0319085 | − | 0.0982042i | ||||
\(412\) | −465.329 | − | 338.081i | −0.0556435 | − | 0.0404274i | ||||
\(413\) | 11575.6 | + | 8410.14i | 1.37917 | + | 1.00202i | ||||
\(414\) | −3627.01 | + | 11162.8i | −0.430575 | + | 1.32517i | ||||
\(415\) | −143.966 | − | 443.083i | −0.0170290 | − | 0.0524099i | ||||
\(416\) | −4718.12 | + | 3427.91i | −0.556069 | + | 0.404008i | ||||
\(417\) | −573.036 | −0.0672942 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1880.83 | −0.219295 | −0.109648 | − | 0.993971i | \(-0.534972\pi\) | ||||
−0.109648 | + | 0.993971i | \(0.534972\pi\) | |||||||
\(420\) | 36.2705 | − | 26.3521i | 0.00421386 | − | 0.00306155i | ||||
\(421\) | −2249.59 | − | 6923.53i | −0.260424 | − | 0.801501i | −0.992712 | − | 0.120507i | \(-0.961548\pi\) |
0.732289 | − | 0.680994i | \(-0.238452\pi\) | |||||||
\(422\) | 271.302 | − | 834.981i | 0.0312957 | − | 0.0963181i | ||||
\(423\) | 11076.0 | + | 8047.21i | 1.27313 | + | 0.924985i | ||||
\(424\) | 7430.83 | + | 5398.82i | 0.851116 | + | 0.618372i | ||||
\(425\) | 2097.81 | − | 6456.39i | 0.239432 | − | 0.736896i | ||||
\(426\) | −160.780 | − | 494.829i | −0.0182859 | − | 0.0562782i | ||||
\(427\) | −10711.5 | + | 7782.33i | −1.21397 | + | 0.881999i | ||||
\(428\) | −1153.31 | −0.130251 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 787.994 | 0.0883732 | ||||||||
\(431\) | 5558.44 | − | 4038.44i | 0.621208 | − | 0.451334i | −0.232135 | − | 0.972684i | \(-0.574571\pi\) |
0.853343 | + | 0.521350i | \(0.174571\pi\) | |||||||
\(432\) | −398.995 | − | 1227.98i | −0.0444367 | − | 0.136762i | ||||
\(433\) | 346.508 | − | 1066.44i | 0.0384575 | − | 0.118360i | −0.929985 | − | 0.367598i | \(-0.880180\pi\) |
0.968442 | + | 0.249238i | \(0.0801802\pi\) | |||||||
\(434\) | 3987.74 | + | 2897.26i | 0.441054 | + | 0.320445i | ||||
\(435\) | 75.3600 | + | 54.7522i | 0.00830628 | + | 0.00603487i | ||||
\(436\) | −911.740 | + | 2806.05i | −0.100148 | + | 0.308223i | ||||
\(437\) | −3040.38 | − | 9357.34i | −0.332818 | − | 1.02431i | ||||
\(438\) | 309.318 | − | 224.732i | 0.0337438 | − | 0.0245163i | ||||
\(439\) | −7114.94 | −0.773525 | −0.386763 | − | 0.922179i | \(-0.626407\pi\) | ||||
−0.386763 | + | 0.922179i | \(0.626407\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12154.1 | −1.31239 | ||||||||
\(442\) | 7554.87 | − | 5488.93i | 0.813005 | − | 0.590683i | ||||
\(443\) | −4343.97 | − | 13369.4i | −0.465888 | − | 1.43385i | −0.857863 | − | 0.513879i | \(-0.828208\pi\) |
0.391975 | − | 0.919976i | \(-0.371792\pi\) | |||||||
\(444\) | −67.2679 | + | 207.029i | −0.00719008 | + | 0.0221288i | ||||
\(445\) | −1424.83 | − | 1035.20i | −0.151783 | − | 0.110277i | ||||
\(446\) | −583.187 | − | 423.710i | −0.0619164 | − | 0.0449849i | ||||
\(447\) | −58.8171 | + | 181.020i | −0.00622360 | + | 0.0191543i | ||||
\(448\) | 4964.79 | + | 15280.1i | 0.523581 | + | 1.61142i | ||||
\(449\) | 12397.3 | − | 9007.14i | 1.30304 | − | 0.946711i | 0.303055 | − | 0.952973i | \(-0.401993\pi\) |
0.999980 | + | 0.00626255i | \(0.00199345\pi\) | |||||||
\(450\) | −8072.61 | −0.845659 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 291.179 | 0.0303006 | ||||||||
\(453\) | −814.882 | + | 592.046i | −0.0845177 | + | 0.0614057i | ||||
\(454\) | −4267.19 | − | 13133.1i | −0.441121 | − | 1.35763i | ||||
\(455\) | 917.923 | − | 2825.08i | 0.0945778 | − | 0.291081i | ||||
\(456\) | 585.230 | + | 425.195i | 0.0601007 | + | 0.0436657i | ||||
\(457\) | −5834.80 | − | 4239.23i | −0.597243 | − | 0.433923i | 0.247656 | − | 0.968848i | \(-0.420340\pi\) |
−0.844899 | + | 0.534925i | \(0.820340\pi\) | |||||||
\(458\) | 4305.52 | − | 13251.0i | 0.439266 | − | 1.35192i | ||||
\(459\) | −492.369 | − | 1515.35i | −0.0500693 | − | 0.154097i | ||||
\(460\) | 427.230 | − | 310.401i | 0.0433037 | − | 0.0314620i | ||||
\(461\) | 10159.6 | 1.02642 | 0.513212 | − | 0.858262i | \(-0.328456\pi\) | ||||
0.513212 | + | 0.858262i | \(0.328456\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10292.0 | −1.03306 | −0.516532 | − | 0.856268i | \(-0.672777\pi\) | ||||
−0.516532 | + | 0.856268i | \(0.672777\pi\) | |||||||
\(464\) | −4106.96 | + | 2983.88i | −0.410907 | + | 0.298541i | ||||
\(465\) | 18.0110 | + | 55.4323i | 0.00179622 | + | 0.00552820i | ||||
\(466\) | 1944.04 | − | 5983.15i | 0.193253 | − | 0.594772i | ||||
\(467\) | −14580.9 | − | 10593.6i | −1.44480 | − | 1.04971i | −0.987011 | − | 0.160652i | \(-0.948640\pi\) |
−0.457792 | − | 0.889059i | \(-0.651360\pi\) | |||||||
\(468\) | 2852.94 | + | 2072.78i | 0.281789 | + | 0.204732i | ||||
\(469\) | −2530.59 | + | 7788.35i | −0.249151 | + | 0.766807i | ||||
\(470\) | 599.391 | + | 1844.74i | 0.0588252 | + | 0.181045i | ||||
\(471\) | 1083.87 | − | 787.480i | 0.106034 | − | 0.0770385i | ||||
\(472\) | −12391.3 | −1.20838 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 223.941 | 0.0217003 | ||||||||
\(475\) | 5474.58 | − | 3977.52i | 0.528823 | − | 0.384212i | ||||
\(476\) | 931.712 | + | 2867.51i | 0.0897162 | + | 0.276118i | ||||
\(477\) | 3099.22 | − | 9538.42i | 0.297492 | − | 0.915586i | ||||
\(478\) | 10560.1 | + | 7672.37i | 1.01048 | + | 0.734154i | ||||
\(479\) | 13821.1 | + | 10041.6i | 1.31837 | + | 0.957855i | 0.999951 | + | 0.00990707i | \(0.00315357\pi\) |
0.318424 | + | 0.947948i | \(0.396846\pi\) | |||||||
\(480\) | −21.6658 | + | 66.6806i | −0.00206022 | + | 0.00634071i | ||||
\(481\) | 4456.93 | + | 13717.0i | 0.422492 | + | 1.30030i | ||||
\(482\) | −8263.33 | + | 6003.66i | −0.780881 | + | 0.567343i | ||||
\(483\) | 2699.42 | 0.254302 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −985.432 | −0.0922601 | ||||||||
\(486\) | −2303.35 | + | 1673.49i | −0.214984 | + | 0.156195i | ||||
\(487\) | 142.705 | + | 439.202i | 0.0132784 | + | 0.0408668i | 0.957476 | − | 0.288512i | \(-0.0931606\pi\) |
−0.944198 | + | 0.329379i | \(0.893161\pi\) | |||||||
\(488\) | 3543.27 | − | 10905.1i | 0.328681 | − | 1.01158i | ||||
\(489\) | 807.715 | + | 586.840i | 0.0746956 | + | 0.0542695i | ||||
\(490\) | −1393.09 | − | 1012.14i | −0.128436 | − | 0.0933141i | ||||
\(491\) | 3875.92 | − | 11928.9i | 0.356248 | − | 1.09642i | −0.599034 | − | 0.800724i | \(-0.704448\pi\) |
0.955282 | − | 0.295696i | \(-0.0955515\pi\) | |||||||
\(492\) | −61.2853 | − | 188.617i | −0.00561576 | − | 0.0172835i | ||||
\(493\) | −5068.08 | + | 3682.17i | −0.462991 | + | 0.336383i | ||||
\(494\) | 9308.48 | 0.847790 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3176.41 | −0.287550 | ||||||||
\(497\) | 9004.59 | − | 6542.22i | 0.812698 | − | 0.590460i | ||||
\(498\) | 123.777 | + | 380.946i | 0.0111377 | + | 0.0342783i | ||||
\(499\) | −5647.90 | + | 17382.4i | −0.506682 | + | 1.55941i | 0.291241 | + | 0.956650i | \(0.405932\pi\) |
−0.797924 | + | 0.602759i | \(0.794068\pi\) | |||||||
\(500\) | 593.329 | + | 431.079i | 0.0530690 | + | 0.0385569i | ||||
\(501\) | 1147.72 | + | 833.871i | 0.102348 | + | 0.0743605i | ||||
\(502\) | 1361.57 | − | 4190.48i | 0.121056 | − | 0.372571i | ||||
\(503\) | 820.496 | + | 2525.23i | 0.0727319 | + | 0.223846i | 0.980814 | − | 0.194947i | \(-0.0624534\pi\) |
−0.908082 | + | 0.418793i | \(0.862453\pi\) | |||||||
\(504\) | 14935.0 | − | 10850.9i | 1.31996 | − | 0.959004i | ||||
\(505\) | 1701.11 | 0.149898 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1334.57 | −0.116904 | ||||||||
\(508\) | 1085.33 | − | 788.540i | 0.0947910 | − | 0.0688697i | ||||
\(509\) | −1510.21 | − | 4647.96i | −0.131511 | − | 0.404749i | 0.863520 | − | 0.504315i | \(-0.168255\pi\) |
−0.995031 | + | 0.0995653i | \(0.968255\pi\) | |||||||
\(510\) | 34.6923 | − | 106.772i | 0.00301216 | − | 0.00927048i | ||||
\(511\) | 6617.02 | + | 4807.54i | 0.572837 | + | 0.416190i | ||||
\(512\) | −10193.6 | − | 7406.06i | −0.879875 | − | 0.639267i | ||||
\(513\) | 490.795 | − | 1510.51i | 0.0422400 | − | 0.130001i | ||||
\(514\) | −3934.42 | − | 12108.9i | −0.337626 | − | 1.03911i | ||||
\(515\) | −370.655 | + | 269.297i | −0.0317146 | + | 0.0230420i | ||||
\(516\) | 215.148 | 0.0183554 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 14663.8 | 1.24381 | ||||||||
\(519\) | 914.526 | − | 664.442i | 0.0773472 | − | 0.0561961i | ||||
\(520\) | 794.945 | + | 2446.59i | 0.0670397 | + | 0.206327i | ||||
\(521\) | −6780.17 | + | 20867.2i | −0.570144 | + | 1.75472i | 0.0820064 | + | 0.996632i | \(0.473867\pi\) |
−0.652150 | + | 0.758090i | \(0.726133\pi\) | |||||||
\(522\) | 6026.62 | + | 4378.60i | 0.505322 | + | 0.367138i | ||||
\(523\) | −4936.85 | − | 3586.83i | −0.412759 | − | 0.299887i | 0.361959 | − | 0.932194i | \(-0.382108\pi\) |
−0.774718 | + | 0.632307i | \(0.782108\pi\) | |||||||
\(524\) | 992.492 | − | 3054.58i | 0.0827428 | − | 0.254656i | ||||
\(525\) | 573.719 | + | 1765.73i | 0.0476936 | + | 0.146786i | ||||
\(526\) | 114.983 | − | 83.5403i | 0.00953139 | − | 0.00692496i | ||||
\(527\) | −3919.76 | −0.323999 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19629.4 | 1.61333 | ||||||||
\(530\) | 1149.55 | − | 835.200i | 0.0942140 | − | 0.0684505i | ||||
\(531\) | 4181.08 | + | 12868.0i | 0.341701 | + | 1.05165i | ||||
\(532\) | −928.734 | + | 2858.35i | −0.0756874 | + | 0.232942i | ||||
\(533\) | −10630.6 | − | 7723.61i | −0.863910 | − | 0.627667i | ||||
\(534\) | 1225.02 | + | 890.026i | 0.0992727 | + | 0.0721258i | ||||
\(535\) | −283.882 | + | 873.698i | −0.0229407 | + | 0.0706042i | ||||
\(536\) | −2191.55 | − | 6744.91i | −0.176606 | − | 0.543537i | ||||
\(537\) | 603.176 | − | 438.233i | 0.0484711 | − | 0.0352163i | ||||
\(538\) | 7461.44 | 0.597929 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 85.2463 | 0.00679337 | ||||||||
\(541\) | −1698.41 | + | 1233.97i | −0.134973 | + | 0.0980636i | −0.653223 | − | 0.757165i | \(-0.726584\pi\) |
0.518250 | + | 0.855229i | \(0.326584\pi\) | |||||||
\(542\) | −1132.91 | − | 3486.74i | −0.0897837 | − | 0.276326i | ||||
\(543\) | −612.958 | + | 1886.49i | −0.0484430 | + | 0.149092i | ||||
\(544\) | −3814.64 | − | 2771.50i | −0.300646 | − | 0.218432i | ||||
\(545\) | 1901.32 | + | 1381.39i | 0.149438 | + | 0.108573i | ||||
\(546\) | −789.196 | + | 2428.90i | −0.0618580 | + | 0.190379i | ||||
\(547\) | 2790.13 | + | 8587.15i | 0.218094 | + | 0.671225i | 0.998919 | + | 0.0464753i | \(0.0147989\pi\) |
−0.780825 | + | 0.624749i | \(0.785201\pi\) | |||||||
\(548\) | −2504.46 | + | 1819.60i | −0.195229 | + | 0.141842i | ||||
\(549\) | −12520.2 | −0.973315 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6244.47 | −0.482801 | ||||||||
\(552\) | −1891.29 | + | 1374.10i | −0.145831 | + | 0.105952i | ||||
\(553\) | 1480.38 | + | 4556.15i | 0.113838 | + | 0.350356i | ||||
\(554\) | 5680.76 | − | 17483.6i | 0.435654 | − | 1.34081i | ||||
\(555\) | 140.279 | + | 101.919i | 0.0107289 | + | 0.00779497i | ||||
\(556\) | 1668.05 | + | 1211.91i | 0.127232 | + | 0.0924398i | ||||
\(557\) | −2439.55 | + | 7508.15i | −0.185578 | + | 0.571150i | −0.999958 | − | 0.00918192i | \(-0.997077\pi\) |
0.814380 | + | 0.580332i | \(0.197077\pi\) | |||||||
\(558\) | 1440.36 | + | 4432.98i | 0.109275 | + | 0.336314i | ||||
\(559\) | 11532.5 | − | 8378.84i | 0.872579 | − | 0.633966i | ||||
\(560\) | 1946.19 | 0.146860 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2218.07 | 0.166484 | ||||||||
\(563\) | −18103.8 | + | 13153.2i | −1.35521 | + | 0.984621i | −0.356481 | + | 0.934303i | \(0.616024\pi\) |
−0.998733 | + | 0.0503183i | \(0.983976\pi\) | |||||||
\(564\) | 163.653 | + | 503.673i | 0.0122182 | + | 0.0376036i | ||||
\(565\) | 71.6723 | − | 220.585i | 0.00533677 | − | 0.0164249i | ||||
\(566\) | −12931.7 | − | 9395.41i | −0.960351 | − | 0.697736i | ||||
\(567\) | −16130.6 | − | 11719.6i | −1.19475 | − | 0.868034i | ||||
\(568\) | −2978.65 | + | 9167.34i | −0.220038 | + | 0.677206i | ||||
\(569\) | −5228.72 | − | 16092.4i | −0.385236 | − | 1.18564i | −0.936309 | − | 0.351178i | \(-0.885781\pi\) |
0.551072 | − | 0.834457i | \(-0.314219\pi\) | |||||||
\(570\) | 90.5354 | − | 65.7778i | 0.00665283 | − | 0.00483356i | ||||
\(571\) | 16320.0 | 1.19609 | 0.598047 | − | 0.801461i | \(-0.295944\pi\) | ||||
0.598047 | + | 0.801461i | \(0.295944\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1893.35 | 0.138038 | ||||||||
\(574\) | −10808.2 | + | 7852.62i | −0.785934 | + | 0.571014i | ||||
\(575\) | 6757.82 | + | 20798.4i | 0.490123 | + | 1.50844i | ||||
\(576\) | −4694.86 | + | 14449.3i | −0.339616 | + | 1.04523i | ||||
\(577\) | −671.696 | − | 488.016i | −0.0484629 | − | 0.0352103i | 0.563290 | − | 0.826259i | \(-0.309535\pi\) |
−0.611753 | + | 0.791049i | \(0.709535\pi\) | |||||||
\(578\) | −3685.89 | − | 2677.96i | −0.265247 | − | 0.192713i | ||||
\(579\) | 431.502 | − | 1328.03i | 0.0309717 | − | 0.0953211i | ||||
\(580\) | −103.570 | − | 318.757i | −0.00741470 | − | 0.0228201i | ||||
\(581\) | −6932.23 | + | 5036.56i | −0.495004 | + | 0.359641i | ||||
\(582\) | 847.238 | 0.0603422 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −7083.29 | −0.501899 | ||||||||
\(585\) | 2272.49 | − | 1651.06i | 0.160609 | − | 0.116689i | ||||
\(586\) | 4667.21 | + | 14364.2i | 0.329012 | + | 1.01259i | ||||
\(587\) | 6773.45 | − | 20846.5i | 0.476270 | − | 1.46581i | −0.367968 | − | 0.929839i | \(-0.619946\pi\) |
0.844238 | − | 0.535969i | \(-0.180054\pi\) | |||||||
\(588\) | −380.360 | − | 276.347i | −0.0266765 | − | 0.0193816i | ||||
\(589\) | −3161.02 | − | 2296.61i | −0.221133 | − | 0.160663i | ||||
\(590\) | −592.365 | + | 1823.11i | −0.0413344 | + | 0.127214i | ||||
\(591\) | −119.101 | − | 366.555i | −0.00828962 | − | 0.0255128i | ||||
\(592\) | −7644.91 | + | 5554.35i | −0.530750 | + | 0.385612i | ||||
\(593\) | −8236.51 | −0.570376 | −0.285188 | − | 0.958472i | \(-0.592056\pi\) | ||||
−0.285188 | + | 0.958472i | \(0.592056\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2401.64 | 0.165475 | ||||||||
\(596\) | 554.050 | − | 402.541i | 0.0380785 | − | 0.0276656i | ||||
\(597\) | −171.423 | − | 527.586i | −0.0117519 | − | 0.0361686i | ||||
\(598\) | −9295.93 | + | 28609.9i | −0.635683 | + | 1.95643i | ||||
\(599\) | 8836.08 | + | 6419.79i | 0.602725 | + | 0.437906i | 0.846845 | − | 0.531839i | \(-0.178499\pi\) |
−0.244120 | + | 0.969745i | \(0.578499\pi\) | |||||||
\(600\) | −1300.78 | − | 945.075i | −0.0885071 | − | 0.0643042i | ||||
\(601\) | −428.432 | + | 1318.58i | −0.0290784 | + | 0.0894941i | −0.964542 | − | 0.263928i | \(-0.914982\pi\) |
0.935464 | + | 0.353422i | \(0.114982\pi\) | |||||||
\(602\) | −4478.59 | − | 13783.7i | −0.303212 | − | 0.933192i | ||||
\(603\) | −6264.95 | + | 4551.75i | −0.423099 | + | 0.307399i | ||||
\(604\) | 3624.16 | 0.244147 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1462.55 | −0.0980399 | ||||||||
\(607\) | −1147.00 | + | 833.347i | −0.0766976 | + | 0.0557241i | −0.625473 | − | 0.780246i | \(-0.715094\pi\) |
0.548776 | + | 0.835970i | \(0.315094\pi\) | |||||||
\(608\) | −1452.41 | − | 4470.05i | −0.0968797 | − | 0.298165i | ||||
\(609\) | 529.421 | − | 1629.39i | 0.0352270 | − | 0.108418i | ||||
\(610\) | −1435.06 | − | 1042.63i | −0.0952525 | − | 0.0692050i | ||||
\(611\) | 28387.5 | + | 20624.7i | 1.87960 | + | 1.36561i | ||||
\(612\) | −881.054 | + | 2711.60i | −0.0581936 | + | 0.179102i | ||||
\(613\) | −4766.56 | − | 14670.0i | −0.314061 | − | 0.966582i | −0.976139 | − | 0.217146i | \(-0.930325\pi\) |
0.662078 | − | 0.749435i | \(-0.269675\pi\) | |||||||
\(614\) | −10720.4 | + | 7788.82i | −0.704625 | + | 0.511940i | ||||
\(615\) | −157.973 | −0.0103579 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15169.5 | 0.989793 | 0.494897 | − | 0.868952i | \(-0.335206\pi\) | ||||
0.494897 | + | 0.868952i | \(0.335206\pi\) | |||||||
\(618\) | 318.675 | − | 231.531i | 0.0207427 | − | 0.0150705i | ||||
\(619\) | −643.239 | − | 1979.69i | −0.0417673 | − | 0.128547i | 0.927999 | − | 0.372584i | \(-0.121528\pi\) |
−0.969766 | + | 0.244037i | \(0.921528\pi\) | |||||||
\(620\) | 64.8051 | − | 199.450i | 0.00419780 | − | 0.0129195i | ||||
\(621\) | 4152.47 | + | 3016.95i | 0.268330 | + | 0.194953i | ||||
\(622\) | −12093.4 | − | 8786.37i | −0.779584 | − | 0.566401i | ||||
\(623\) | −10009.8 | + | 30806.9i | −0.643712 | + | 1.98114i | ||||
\(624\) | −508.572 | − | 1565.22i | −0.0326269 | − | 0.100415i | ||||
\(625\) | −11929.7 | + | 8667.45i | −0.763502 | + | 0.554717i | ||||
\(626\) | −7986.59 | −0.509918 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4820.49 | −0.306303 | ||||||||
\(629\) | −9434.00 | + | 6854.20i | −0.598026 | + | 0.434491i | ||||
\(630\) | −882.514 | − | 2716.10i | −0.0558099 | − | 0.171765i | ||||
\(631\) | 7802.57 | − | 24013.8i | 0.492259 | − | 1.51502i | −0.328926 | − | 0.944356i | \(-0.606687\pi\) |
0.821185 | − | 0.570662i | \(-0.193313\pi\) | |||||||
\(632\) | −3356.45 | − | 2438.60i | −0.211254 | − | 0.153485i | ||||
\(633\) | −154.473 | − | 112.231i | −0.00969943 | − | 0.00704705i | ||||
\(634\) | −4964.13 | + | 15278.0i | −0.310964 | + | 0.957047i | ||||
\(635\) | −330.215 | − | 1016.30i | −0.0206365 | − | 0.0635127i | ||||
\(636\) | 313.865 | − | 228.037i | 0.0195685 | − | 0.0142174i | ||||
\(637\) | −31150.5 | −1.93756 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10525.1 | 0.651592 | ||||||||
\(640\) | −894.646 | + | 649.998i | −0.0552562 | + | 0.0401460i | ||||
\(641\) | −811.656 | − | 2498.02i | −0.0500132 | − | 0.153925i | 0.922931 | − | 0.384966i | \(-0.125787\pi\) |
−0.972944 | + | 0.231041i | \(0.925787\pi\) | |||||||
\(642\) | 244.071 | − | 751.173i | 0.0150042 | − | 0.0461782i | ||||
\(643\) | −7466.91 | − | 5425.03i | −0.457957 | − | 0.332725i | 0.334772 | − | 0.942299i | \(-0.391341\pi\) |
−0.792729 | + | 0.609574i | \(0.791341\pi\) | |||||||
\(644\) | −7857.74 | − | 5708.98i | −0.480805 | − | 0.349325i | ||||
\(645\) | 52.9577 | − | 162.987i | 0.00323288 | − | 0.00994979i | ||||
\(646\) | 2325.66 | + | 7157.64i | 0.141644 | + | 0.435935i | ||||
\(647\) | −256.379 | + | 186.270i | −0.0155785 | + | 0.0113184i | −0.595547 | − | 0.803320i | \(-0.703065\pi\) |
0.579969 | + | 0.814639i | \(0.303065\pi\) | |||||||
\(648\) | 17267.3 | 1.04679 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −20689.8 | −1.24850 | ||||||||
\(651\) | 867.262 | − | 630.103i | 0.0522130 | − | 0.0379350i | ||||
\(652\) | −1110.08 | − | 3416.47i | −0.0666779 | − | 0.205214i | ||||
\(653\) | −1552.09 | + | 4776.83i | −0.0930136 | + | 0.286266i | −0.986731 | − | 0.162364i | \(-0.948088\pi\) |
0.893717 | + | 0.448631i | \(0.148088\pi\) | |||||||
\(654\) | −1634.69 | − | 1187.67i | −0.0977390 | − | 0.0710115i | ||||
\(655\) | −2069.72 | − | 1503.74i | −0.123467 | − | 0.0897039i | ||||
\(656\) | 2660.39 | − | 8187.84i | 0.158340 | − | 0.487320i | ||||
\(657\) | 2390.06 | + | 7355.83i | 0.141925 | + | 0.436801i | ||||
\(658\) | 28861.7 | − | 20969.2i | 1.70995 | − | 1.24235i | ||||
\(659\) | 24927.5 | 1.47350 | 0.736752 | − | 0.676163i | \(-0.236358\pi\) | ||||
0.736752 | + | 0.676163i | \(0.236358\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16440.5 | −0.967418 | −0.483709 | − | 0.875229i | \(-0.660711\pi\) | ||||
−0.483709 | + | 0.875229i | \(0.660711\pi\) | |||||||
\(662\) | 11720.9 | − | 8515.72i | 0.688135 | − | 0.499959i | ||||
\(663\) | −627.589 | − | 1931.52i | −0.0367625 | − | 0.113143i | ||||
\(664\) | 2293.13 | − | 7057.52i | 0.134022 | − | 0.412477i | ||||
\(665\) | 1936.76 | + | 1407.14i | 0.112939 | + | 0.0820549i | ||||
\(666\) | 11218.3 | + | 8150.56i | 0.652702 | + | 0.474216i | ||||
\(667\) | 6236.04 | − | 19192.6i | 0.362010 | − | 1.11415i | ||||
\(668\) | −1577.37 | − | 4854.64i | −0.0913625 | − | 0.281185i | ||||
\(669\) | −126.833 | + | 92.1494i | −0.00732980 | + | 0.00532541i | ||||
\(670\) | −1097.14 | −0.0632630 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1289.52 | 0.0740245 | ||||||||
\(673\) | −9528.14 | + | 6922.60i | −0.545740 | + | 0.396503i | −0.826212 | − | 0.563359i | \(-0.809509\pi\) |
0.280472 | + | 0.959862i | \(0.409509\pi\) | |||||||
\(674\) | 1022.37 | + | 3146.53i | 0.0584276 | + | 0.179822i | ||||
\(675\) | −1090.88 | + | 3357.39i | −0.0622046 | + | 0.191446i | ||||
\(676\) | 3884.79 | + | 2822.47i | 0.221028 | + | 0.160586i | ||||
\(677\) | −2280.21 | − | 1656.67i | −0.129447 | − | 0.0940486i | 0.521178 | − | 0.853448i | \(-0.325493\pi\) |
−0.650625 | + | 0.759400i | \(0.725493\pi\) | |||||||
\(678\) | −61.6212 | + | 189.650i | −0.00349048 | + | 0.0107426i | ||||
\(679\) | 5600.74 | + | 17237.3i | 0.316549 | + | 0.974237i | ||||
\(680\) | −1682.66 | + | 1222.53i | −0.0948929 | + | 0.0689437i | ||||
\(681\) | −3003.19 | −0.168991 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15803.2 | 0.885346 | 0.442673 | − | 0.896683i | \(-0.354030\pi\) | ||||
0.442673 | + | 0.896683i | \(0.354030\pi\) | |||||||
\(684\) | −2299.26 | + | 1670.51i | −0.128530 | + | 0.0933823i | ||||
\(685\) | 761.989 | + | 2345.16i | 0.0425023 | + | 0.130809i | ||||
\(686\) | −2408.89 | + | 7413.81i | −0.134070 | + | 0.412625i | ||||
\(687\) | −2451.46 | − | 1781.09i | −0.136141 | − | 0.0989124i | ||||
\(688\) | 7555.87 | + | 5489.66i | 0.418699 | + | 0.304202i | ||||
\(689\) | 7943.21 | − | 24446.7i | 0.439205 | − | 1.35173i | ||||
\(690\) | 111.757 | + | 343.953i | 0.00616596 | + | 0.0189769i | ||||
\(691\) | −2670.34 | + | 1940.12i | −0.147011 | + | 0.106810i | −0.658860 | − | 0.752266i | \(-0.728961\pi\) |
0.511849 | + | 0.859076i | \(0.328961\pi\) | |||||||
\(692\) | −4067.32 | −0.223434 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13922.3 | −0.761501 | ||||||||
\(695\) | 1328.68 | − | 965.341i | 0.0725174 | − | 0.0526870i | ||||
\(696\) | 458.492 | + | 1411.09i | 0.0249700 | + | 0.0768497i | ||||
\(697\) | 3282.98 | − | 10104.0i | 0.178410 | − | 0.549090i | ||||
\(698\) | 2490.98 | + | 1809.80i | 0.135079 | + | 0.0981405i | ||||
\(699\) | −1106.89 | − | 804.203i | −0.0598948 | − | 0.0435161i | ||||
\(700\) | 2064.28 | − | 6353.21i | 0.111461 | − | 0.343041i | ||||
\(701\) | 9200.43 | + | 28316.0i | 0.495714 | + | 1.52565i | 0.815841 | + | 0.578276i | \(0.196274\pi\) |
−0.320127 | + | 0.947375i | \(0.603726\pi\) | |||||||
\(702\) | −3928.62 | + | 2854.31i | −0.211219 | + | 0.153460i | ||||
\(703\) | −11623.8 | −0.623612 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 421.844 | 0.0225355 | ||||||||
\(706\) | 11929.6 | − | 8667.36i | 0.635944 | − | 0.462040i | ||||
\(707\) | −9668.34 | − | 29756.1i | −0.514307 | − | 1.58288i | ||||
\(708\) | −161.735 | + | 497.769i | −0.00858527 | + | 0.0264227i | ||||
\(709\) | 19418.4 | + | 14108.3i | 1.02860 | + | 0.747318i | 0.968027 | − | 0.250846i | \(-0.0807087\pi\) |
0.0605683 | + | 0.998164i | \(0.480709\pi\) | |||||||
\(710\) | 1206.39 | + | 876.491i | 0.0637674 | + | 0.0463297i | ||||
\(711\) | −1399.89 | + | 4308.43i | −0.0738398 | + | 0.227255i | ||||
\(712\) | −8668.71 | − | 26679.6i | −0.456283 | − | 1.40430i | ||||
\(713\) | 10215.5 | − | 7421.97i | 0.536567 | − | 0.389839i | ||||
\(714\) | −2064.84 | −0.108228 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2682.60 | −0.140019 | ||||||||
\(717\) | 2296.64 | − | 1668.60i | 0.119623 | − | 0.0869109i | ||||
\(718\) | −1656.92 | − | 5099.48i | −0.0861223 | − | 0.265057i | ||||
\(719\) | −6386.99 | + | 19657.1i | −0.331286 | + | 1.01959i | 0.637237 | + | 0.770668i | \(0.280077\pi\) |
−0.968523 | + | 0.248925i | \(0.919923\pi\) | |||||||
\(720\) | 1488.90 | + | 1081.75i | 0.0770665 | + | 0.0559921i | ||||
\(721\) | 6817.20 | + | 4952.98i | 0.352130 | + | 0.255837i | ||||
\(722\) | 2904.55 | − | 8939.30i | 0.149718 | − | 0.460784i | ||||
\(723\) | 686.442 | + | 2112.65i | 0.0353099 | + | 0.108673i | ||||
\(724\) | 5774.00 | − | 4195.06i | 0.296394 | − | 0.215343i | ||||
\(725\) | 13879.5 | 0.710995 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21928.9 | 1.11870 | 0.559351 | − | 0.828931i | \(-0.311050\pi\) | ||||
0.559351 | + | 0.828931i | \(0.311050\pi\) | |||||||
\(728\) | 38277.9 | − | 27810.5i | 1.94873 | − | 1.41583i | ||||
\(729\) | −5697.64 | − | 17535.5i | −0.289470 | − | 0.890898i | ||||
\(730\) | −338.618 | + | 1042.16i | −0.0171682 | + | 0.0528383i | ||||
\(731\) | 9324.11 | + | 6774.36i | 0.471771 | + | 0.342762i | ||||
\(732\) | −391.819 | − | 284.673i | −0.0197842 | − | 0.0143741i | ||||
\(733\) | 7763.76 | − | 23894.4i | 0.391215 | − | 1.20404i | −0.540655 | − | 0.841245i | \(-0.681823\pi\) |
0.931870 | − | 0.362792i | \(-0.118177\pi\) | |||||||
\(734\) | 6445.20 | + | 19836.3i | 0.324110 | + | 0.997508i | ||||
\(735\) | −302.973 | + | 220.123i | −0.0152045 | + | 0.0110467i | ||||
\(736\) | 15189.3 | 0.760712 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −12633.3 | −0.630133 | ||||||||
\(739\) | 29964.5 | − | 21770.5i | 1.49156 | − | 1.08368i | 0.517960 | − | 0.855405i | \(-0.326692\pi\) |
0.973597 | − | 0.228274i | \(-0.0733083\pi\) | |||||||
\(740\) | −192.792 | − | 593.351i | −0.00957724 | − | 0.0294757i | ||||
\(741\) | 625.583 | − | 1925.35i | 0.0310140 | − | 0.0954513i | ||||
\(742\) | −21142.9 | − | 15361.2i | −1.04607 | − | 0.760012i | ||||
\(743\) | −20062.0 | − | 14575.9i | −0.990582 | − | 0.719700i | −0.0305332 | − | 0.999534i | \(-0.509721\pi\) |
−0.960048 | + | 0.279834i | \(0.909721\pi\) | |||||||
\(744\) | −286.884 | + | 882.937i | −0.0141366 | + | 0.0435081i | ||||
\(745\) | −168.571 | − | 518.809i | −0.00828989 | − | 0.0255137i | ||||
\(746\) | 8470.25 | − | 6153.99i | 0.415707 | − | 0.302029i | ||||
\(747\) | −8102.82 | −0.396876 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16896.3 | 0.824268 | ||||||||
\(750\) | −406.335 | + | 295.219i | −0.0197830 | + | 0.0143732i | ||||
\(751\) | 4316.09 | + | 13283.6i | 0.209716 | + | 0.645439i | 0.999487 | + | 0.0320368i | \(0.0101994\pi\) |
−0.789771 | + | 0.613402i | \(0.789801\pi\) | |||||||
\(752\) | −7104.18 | + | 21864.4i | −0.344498 | + | 1.06026i | ||||
\(753\) | −775.246 | − | 563.249i | −0.0375186 | − | 0.0272589i | ||||
\(754\) | 15446.0 | + | 11222.2i | 0.746037 | + | 0.542027i | ||||
\(755\) | 892.071 | − | 2745.51i | 0.0430011 | − | 0.132344i | ||||
\(756\) | −484.500 | − | 1491.14i | −0.0233083 | − | 0.0717357i | ||||
\(757\) | 6889.14 | − | 5005.26i | 0.330766 | − | 0.240316i | −0.409989 | − | 0.912090i | \(-0.634468\pi\) |
0.740756 | + | 0.671774i | \(0.234468\pi\) | |||||||
\(758\) | −11958.1 | −0.573006 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2073.24 | −0.0989530 | ||||||||
\(761\) | −25611.8 | + | 18608.1i | −1.22001 | + | 0.886390i | −0.996101 | − | 0.0882195i | \(-0.971882\pi\) |
−0.223910 | + | 0.974610i | \(0.571882\pi\) | |||||||
\(762\) | 283.907 | + | 873.775i | 0.0134972 | + | 0.0415401i | ||||
\(763\) | 13357.2 | − | 41109.4i | 0.633768 | − | 1.95054i | ||||
\(764\) | −5511.35 | − | 4004.23i | −0.260986 | − | 0.189618i | ||||
\(765\) | 1837.33 | + | 1334.90i | 0.0868351 | + | 0.0630894i | ||||
\(766\) | 6230.03 | − | 19174.1i | 0.293865 | − | 0.904422i | ||||
\(767\) | 10716.0 | + | 32980.4i | 0.504473 | + | 1.55261i | ||||
\(768\) | −1203.47 | + | 874.371i | −0.0565448 | + | 0.0410822i | ||||
\(769\) | 606.519 | 0.0284416 | 0.0142208 | − | 0.999899i | \(-0.495473\pi\) | ||||
0.0142208 | + | 0.999899i | \(0.495473\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2768.99 | −0.129342 | ||||||||
\(772\) | −4064.70 | + | 2953.18i | −0.189497 | + | 0.137678i | ||||
\(773\) | −1452.31 | − | 4469.74i | −0.0675754 | − | 0.207976i | 0.911567 | − | 0.411152i | \(-0.134874\pi\) |
−0.979142 | + | 0.203176i | \(0.934874\pi\) | |||||||
\(774\) | 4235.09 | − | 13034.3i | 0.196676 | − | 0.605306i | ||||
\(775\) | 7025.95 | + | 5104.65i | 0.325651 | + | 0.236599i | ||||
\(776\) | −12698.5 | − | 9225.97i | −0.587433 | − | 0.426795i | ||||
\(777\) | 985.494 | − | 3033.04i | 0.0455011 | − | 0.140038i | ||||
\(778\) | −955.481 | − | 2940.67i | −0.0440304 | − | 0.135512i | ||||
\(779\) | 8567.49 | − | 6224.65i | 0.394047 | − | 0.286292i | ||||
\(780\) | 108.658 | 0.00498791 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −24321.8 | −1.11221 | ||||||||
\(783\) | 2635.46 | − | 1914.77i | 0.120286 | − | 0.0873926i | ||||
\(784\) | −6306.79 | − | 19410.3i | −0.287299 | − | 0.884216i | ||||
\(785\) | −1186.54 | + | 3651.80i | −0.0539484 | + | 0.166036i | ||||
\(786\) | 1779.47 | + | 1292.86i | 0.0807527 | + | 0.0586703i | ||||
\(787\) | 19479.6 | + | 14152.8i | 0.882303 | + | 0.641031i | 0.933860 | − | 0.357639i | \(-0.116418\pi\) |
−0.0515565 | + | 0.998670i | \(0.516418\pi\) | |||||||
\(788\) | −428.535 | + | 1318.89i | −0.0193730 | + | 0.0596239i | ||||
\(789\) | −9.55176 | − | 29.3973i | −0.000430991 | − | 0.00132645i | ||||
\(790\) | −519.244 | + | 377.253i | −0.0233846 | + | 0.0169899i | ||||
\(791\) | −4265.85 | −0.191752 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32088.9 | −1.43696 | ||||||||
\(794\) | −22963.8 | + | 16684.1i | −1.02639 | + | 0.745716i | ||||
\(795\) | −95.4944 | − | 293.901i | −0.00426017 | − | 0.0131115i | ||||
\(796\) | −616.794 | + | 1898.30i | −0.0274644 | + | 0.0845268i | ||||
\(797\) | 15353.3 | + | 11154.8i | 0.682360 | + | 0.495764i | 0.874140 | − | 0.485674i | \(-0.161426\pi\) |
−0.191780 | + | 0.981438i | \(0.561426\pi\) | |||||||
\(798\) | −1665.16 | − | 1209.81i | −0.0738670 | − | 0.0536675i | ||||
\(799\) | −8766.71 | + | 26981.2i | −0.388165 | + | 1.19465i | ||||
\(800\) | 3228.24 | + | 9935.51i | 0.142670 | + | 0.439092i | ||||
\(801\) | −24781.1 | + | 18004.5i | −1.09313 | + | 0.794205i | ||||
\(802\) | 3697.79 | 0.162810 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −299.554 | −0.0131399 | ||||||||
\(805\) | −6259.04 | + | 4547.46i | −0.274040 | + | 0.199102i | ||||
\(806\) | 3691.61 | + | 11361.6i | 0.161329 | + | 0.496520i | ||||
\(807\) | 501.452 | − | 1543.31i | 0.0218735 | − | 0.0673198i | ||||
\(808\) | 21920.9 | + | 15926.4i | 0.954423 | + | 0.693429i | ||||
\(809\) | 7378.80 | + | 5361.01i | 0.320674 | + | 0.232983i | 0.736463 | − | 0.676478i | \(-0.236495\pi\) |
−0.415789 | + | 0.909461i | \(0.636495\pi\) | |||||||
\(810\) | 825.463 | − | 2540.51i | 0.0358072 | − | 0.110203i | ||||
\(811\) | −12321.8 | − | 37922.6i | −0.533511 | − | 1.64198i | −0.746845 | − | 0.664999i | \(-0.768432\pi\) |
0.213334 | − | 0.976979i | \(-0.431568\pi\) | |||||||
\(812\) | −4987.09 | + | 3623.33i | −0.215533 | + | 0.156594i | ||||
\(813\) | −797.329 | −0.0343955 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2861.41 | −0.122983 | ||||||||
\(816\) | 1076.50 | − | 782.120i | 0.0461825 | − | 0.0335535i | ||||
\(817\) | 3550.11 | + | 10926.1i | 0.152023 | + | 0.467878i | ||||
\(818\) | 69.5916 | − | 214.181i | 0.00297459 | − | 0.00915484i | ||||
\(819\) | −41796.4 | − | 30366.9i | −1.78325 | − | 1.29561i | ||||
\(820\) | 459.845 | + | 334.097i | 0.0195835 | + | 0.0142283i | ||||
\(821\) | −1518.49 | + | 4673.43i | −0.0645501 | + | 0.198665i | −0.978130 | − | 0.207994i | \(-0.933306\pi\) |
0.913580 | + | 0.406659i | \(0.133306\pi\) | |||||||
\(822\) | −655.130 | − | 2016.28i | −0.0277984 | − | 0.0855546i | ||||
\(823\) | −2247.11 | + | 1632.62i | −0.0951752 | + | 0.0691488i | −0.634355 | − | 0.773042i | \(-0.718734\pi\) |
0.539180 | + | 0.842191i | \(0.318734\pi\) | |||||||
\(824\) | −7297.58 | −0.308523 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 35256.8 | 1.48516 | ||||||||
\(827\) | 16428.3 | − | 11935.9i | 0.690773 | − | 0.501876i | −0.186141 | − | 0.982523i | \(-0.559598\pi\) |
0.876914 | + | 0.480647i | \(0.159598\pi\) | |||||||
\(828\) | −2838.20 | − | 8735.09i | −0.119124 | − | 0.366625i | ||||
\(829\) | −10992.6 | + | 33831.7i | −0.460540 | + | 1.41740i | 0.403965 | + | 0.914774i | \(0.367632\pi\) |
−0.864506 | + | 0.502623i | \(0.832368\pi\) | |||||||
\(830\) | −928.742 | − | 674.771i | −0.0388399 | − | 0.0282188i | ||||
\(831\) | −3234.49 | − | 2350.00i | −0.135022 | − | 0.0980992i | ||||
\(832\) | −12032.8 | + | 37033.1i | −0.501396 | + | 1.54314i | ||||
\(833\) | −7782.72 | − | 23952.8i | −0.323716 | − | 0.996295i | ||||
\(834\) | −1142.35 | + | 829.964i | −0.0474296 | + | 0.0344596i | ||||
\(835\) | −4065.93 | −0.168512 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2038.32 | 0.0841751 | ||||||||
\(838\) | −3749.44 | + | 2724.13i | −0.154561 | + | 0.112295i | ||||
\(839\) | 2193.01 | + | 6749.38i | 0.0902396 | + | 0.277729i | 0.985984 | − | 0.166841i | \(-0.0533566\pi\) |
−0.895744 | + | 0.444570i | \(0.853357\pi\) | |||||||
\(840\) | 175.774 | − | 540.977i | 0.00721998 | − | 0.0222208i | ||||
\(841\) | 9369.35 | + | 6807.23i | 0.384163 | + | 0.279111i | ||||
\(842\) | −14512.3 | − | 10543.8i | −0.593976 | − | 0.431549i | ||||
\(843\) | 149.067 | − | 458.782i | 0.00609033 | − | 0.0187441i | ||||
\(844\) | 212.299 | + | 653.388i | 0.00865831 | + | 0.0266476i | ||||
\(845\) | 3094.41 | − | 2248.22i | 0.125977 | − | 0.0915279i | ||||
\(846\) | 33735.3 | 1.37097 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 16841.3 | 0.681995 | ||||||||
\(849\) | −2812.41 | + | 2043.33i | −0.113689 | + | 0.0825996i | ||||
\(850\) | −5169.21 | − | 15909.2i | −0.208591 | − | 0.641978i | ||||
\(851\) | 11608.1 | − | 35726.1i | 0.467592 | − | 1.43910i | ||||
\(852\) | 329.382 | + | 239.310i | 0.0132447 | + | 0.00962281i | ||||
\(853\) | 19543.9 | + | 14199.5i | 0.784490 | + | 0.569965i | 0.906323 | − | 0.422586i | \(-0.138877\pi\) |
−0.121834 | + | 0.992551i | \(0.538877\pi\) | |||||||
\(854\) | −10081.7 | + | 31028.2i | −0.403966 | + | 1.24328i | ||||
\(855\) | 699.555 | + | 2153.01i | 0.0279816 | + | 0.0861185i | ||||
\(856\) | −11838.0 | + | 8600.83i | −0.472682 | + | 0.343423i | ||||
\(857\) | −28806.8 | −1.14822 | −0.574108 | − | 0.818779i | \(-0.694651\pi\) | ||||
−0.574108 | + | 0.818779i | \(0.694651\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11244.4 | 0.446628 | 0.223314 | − | 0.974747i | \(-0.428312\pi\) | ||||
0.223314 | + | 0.974747i | \(0.428312\pi\) | |||||||
\(860\) | −498.856 | + | 362.440i | −0.0197800 | + | 0.0143710i | ||||
\(861\) | 897.847 | + | 2763.29i | 0.0355384 | + | 0.109376i | ||||
\(862\) | 5231.62 | − | 16101.3i | 0.206717 | − | 0.636208i | ||||
\(863\) | 1045.19 | + | 759.373i | 0.0412266 | + | 0.0299529i | 0.608208 | − | 0.793778i | \(-0.291889\pi\) |
−0.566981 | + | 0.823731i | \(0.691889\pi\) | |||||||
\(864\) | 1983.66 | + | 1441.21i | 0.0781080 | + | 0.0567488i | ||||
\(865\) | −1001.15 | + | 3081.23i | −0.0393529 | + | 0.121116i | ||||
\(866\) | −853.830 | − | 2627.82i | −0.0335038 | − | 0.103114i | ||||
\(867\) | −801.616 | + | 582.408i | −0.0314006 | + | 0.0228138i | ||||
\(868\) | −3857.12 | −0.150829 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 229.531 | 0.00894464 | ||||||||
\(871\) | −16056.9 | + | 11666.0i | −0.624646 | + | 0.453832i | ||||
\(872\) | 11567.7 | + | 35601.8i | 0.449234 | + | 1.38260i | ||||
\(873\) | −5296.22 | + | 16300.1i | −0.205326 | + | 0.631930i | ||||
\(874\) | −19613.8 | − | 14250.3i | −0.759093 | − | 0.551514i | ||||
\(875\) | −8692.43 | − | 6315.42i | −0.335838 | − | 0.244000i | ||||
\(876\) | −92.4536 | + | 284.543i | −0.00356589 | + | 0.0109747i | ||||
\(877\) | −8288.78 | − | 25510.3i | −0.319147 | − | 0.982235i | −0.974014 | − | 0.226490i | \(-0.927275\pi\) |
0.654866 | − | 0.755745i | \(-0.272725\pi\) | |||||||
\(878\) | −14183.6 | + | 10305.0i | −0.545187 | + | 0.396102i | ||||
\(879\) | 3284.73 | 0.126042 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28515.7 | −1.09049 | −0.545243 | − | 0.838278i | \(-0.683563\pi\) | ||||
−0.545243 | + | 0.838278i | \(0.683563\pi\) | |||||||
\(882\) | −24229.1 | + | 17603.5i | −0.924985 | + | 0.672041i | ||||
\(883\) | 12881.8 | + | 39646.1i | 0.490948 | + | 1.51098i | 0.823177 | + | 0.567784i | \(0.192199\pi\) |
−0.332229 | + | 0.943199i | \(0.607801\pi\) | |||||||
\(884\) | −2258.11 | + | 6949.76i | −0.0859147 | + | 0.264418i | ||||
\(885\) | 337.278 | + | 245.047i | 0.0128107 | + | 0.00930754i | ||||
\(886\) | −28023.4 | − | 20360.2i | −1.06260 | − | 0.772025i | ||||
\(887\) | −15197.2 | + | 46772.3i | −0.575280 | + | 1.77053i | 0.0599460 | + | 0.998202i | \(0.480907\pi\) |
−0.635226 | + | 0.772327i | \(0.719093\pi\) | |||||||
\(888\) | 853.463 | + | 2626.69i | 0.0322526 | + | 0.0992634i | ||||
\(889\) | −15900.4 | + | 11552.3i | −0.599868 | + | 0.435830i | ||||
\(890\) | −4339.74 | −0.163448 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 564.085 | 0.0211737 | ||||||||
\(893\) | −22878.2 | + | 16622.0i | −0.857323 | + | 0.622882i | ||||
\(894\) | 144.931 | + | 446.052i | 0.00542195 | + | 0.0166870i | ||||
\(895\) | −660.311 | + | 2032.23i | −0.0246612 | + | 0.0758993i | ||||
\(896\) | 16454.6 | + | 11955.0i | 0.613515 | + | 0.445745i | ||||
\(897\) | 5292.88 | + | 3845.50i | 0.197017 | + | 0.143141i | ||||
\(898\) | 11668.3 | − | 35911.5i | 0.433605 | − | 1.33450i | ||||
\(899\) | −2476.46 | − | 7621.77i | −0.0918740 | − | 0.282759i | ||||
\(900\) | 5110.53 | − | 3713.02i | 0.189279 | − | 0.137519i | ||||
\(901\) | 20782.5 | 0.768442 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3151.98 | −0.116159 | ||||||||
\(904\) | 2988.78 | − | 2171.47i | 0.109962 | − | 0.0798917i | ||||
\(905\) | −1756.75 | − | 5406.73i | −0.0645265 | − | 0.198592i | ||||
\(906\) | −766.969 | + | 2360.49i | −0.0281246 | + | 0.0865585i | ||||
\(907\) | −42859.9 | − | 31139.5i | −1.56906 | − | 1.13999i | −0.928047 | − | 0.372463i | \(-0.878513\pi\) |
−0.641016 | − | 0.767528i | \(-0.721487\pi\) | |||||||
\(908\) | 8742.01 | + | 6351.44i | 0.319509 | + | 0.232137i | ||||
\(909\) | 9142.67 | − | 28138.2i | 0.333601 | − | 1.02672i | ||||
\(910\) | −2261.86 | − | 6961.28i | −0.0823954 | − | 0.253587i | ||||
\(911\) | 25459.6 | − | 18497.5i | 0.925922 | − | 0.672722i | −0.0190689 | − | 0.999818i | \(-0.506070\pi\) |
0.944991 | + | 0.327096i | \(0.106070\pi\) | |||||||
\(912\) | 1326.37 | 0.0481584 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −17771.6 | −0.643143 | ||||||||
\(915\) | −312.101 | + | 226.755i | −0.0112762 | + | 0.00819265i | ||||
\(916\) | 3369.15 | + | 10369.2i | 0.121528 | + | 0.374025i | ||||
\(917\) | −14540.3 | + | 44750.4i | −0.523623 | + | 1.61155i | ||||
\(918\) | −3176.32 | − | 2307.73i | −0.114198 | − | 0.0829700i | ||||
\(919\) | −34675.2 | − | 25193.0i | −1.24465 | − | 0.904289i | −0.246748 | − | 0.969080i | \(-0.579362\pi\) |
−0.997899 | + | 0.0647909i | \(0.979362\pi\) | |||||||
\(920\) | 2070.44 | − | 6372.16i | 0.0741961 | − | 0.228352i | ||||
\(921\) | 890.552 | + | 2740.84i | 0.0318618 | + | 0.0980604i | ||||
\(922\) | 20253.2 | − | 14714.8i | 0.723432 | − | 0.525604i | ||||
\(923\) | 26975.6 | 0.961984 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25836.1 | 0.918361 | ||||||||
\(926\) | −20517.0 | + | 14906.5i | −0.728112 | + | 0.529004i | ||||
\(927\) | 2462.36 | + | 7578.37i | 0.0872433 | + | 0.268507i | ||||
\(928\) | 2978.99 | − | 9168.38i | 0.105377 | − | 0.324318i | ||||
\(929\) | 16963.7 | + | 12324.9i | 0.599097 | + | 0.435270i | 0.845558 | − | 0.533883i | \(-0.179268\pi\) |
−0.246461 | + | 0.969153i | \(0.579268\pi\) | |||||||
\(930\) | 116.191 | + | 84.4178i | 0.00409683 | + | 0.00297652i | ||||
\(931\) | 7757.85 | − | 23876.2i | 0.273097 | − | 0.840506i | ||||
\(932\) | 1521.25 | + | 4681.92i | 0.0534658 | + | 0.164551i | ||||
\(933\) | −2630.10 | + | 1910.88i | −0.0922889 | + | 0.0670518i | ||||
\(934\) | −44410.4 | −1.55584 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 44741.6 | 1.56242 | ||||||||
\(937\) | 13855.9 | − | 10066.9i | 0.483086 | − | 0.350982i | −0.319433 | − | 0.947609i | \(-0.603493\pi\) |
0.802519 | + | 0.596626i | \(0.203493\pi\) | |||||||
\(938\) | 6235.63 | + | 19191.3i | 0.217058 | + | 0.668036i | ||||
\(939\) | −536.745 | + | 1651.93i | −0.0186539 | + | 0.0574108i | ||||
\(940\) | −1227.95 | − | 892.156i | −0.0426077 | − | 0.0309563i | ||||
\(941\) | −35613.9 | − | 25875.0i | −1.23377 | − | 0.896387i | −0.236604 | − | 0.971606i | \(-0.576034\pi\) |
−0.997167 | + | 0.0752188i | \(0.976034\pi\) | |||||||
\(942\) | 1020.14 | − | 3139.68i | 0.0352846 | − | 0.108595i | ||||
\(943\) | 10575.7 | + | 32548.7i | 0.365210 | + | 1.12400i | ||||
\(944\) | −18381.0 | + | 13354.5i | −0.633739 | + | 0.460438i | ||||
\(945\) | −1248.88 | −0.0429906 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8692.03 | 0.298261 | 0.149130 | − | 0.988818i | \(-0.452353\pi\) | ||||
0.149130 | + | 0.988818i | \(0.452353\pi\) | |||||||
\(948\) | −141.770 | + | 103.002i | −0.00485706 | + | 0.00352886i | ||||
\(949\) | 6125.64 | + | 18852.8i | 0.209533 | + | 0.644876i | ||||
\(950\) | 5152.69 | − | 15858.4i | 0.175974 | − | 0.541593i | ||||
\(951\) | 2826.46 | + | 2053.54i | 0.0963766 | + | 0.0700217i | ||||
\(952\) | 30948.0 | + | 22485.1i | 1.05360 | + | 0.765489i | ||||
\(953\) | −17893.9 | + | 55071.8i | −0.608228 | + | 1.87193i | −0.135367 | + | 0.990796i | \(0.543221\pi\) |
−0.472861 | + | 0.881137i | \(0.656779\pi\) | |||||||
\(954\) | −7636.79 | − | 23503.6i | −0.259172 | − | 0.797650i | ||||
\(955\) | −4390.03 | + | 3189.54i | −0.148752 | + | 0.108075i | ||||
\(956\) | −10214.2 | −0.345556 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 42096.2 | 1.41969 | ||||||||
\(959\) | 36691.1 | − | 26657.6i | 1.23547 | − | 0.897622i | ||||
\(960\) | 144.660 | + | 445.217i | 0.00486341 | + | 0.0149680i | ||||
\(961\) | −7656.38 | + | 23563.9i | −0.257003 | + | 0.790974i | ||||
\(962\) | 28752.1 | + | 20889.6i | 0.963623 | + | 0.700113i | ||||
\(963\) | 12926.2 | + | 9391.41i | 0.432544 | + | 0.314262i | ||||
\(964\) | 2469.87 | − | 7601.48i | 0.0825199 | − | 0.253970i | ||||
\(965\) | 1236.70 | + | 3806.16i | 0.0412545 | + | 0.126968i | ||||
\(966\) | 5381.29 | − | 3909.73i | 0.179234 | − | 0.130221i | ||||
\(967\) | 56564.3 | 1.88106 | 0.940530 | − | 0.339711i | \(-0.110329\pi\) | ||||
0.940530 | + | 0.339711i | \(0.110329\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1636.77 | 0.0542628 | ||||||||
\(970\) | −1964.46 | + | 1427.26i | −0.0650257 | + | 0.0472440i | ||||
\(971\) | −9546.98 | − | 29382.6i | −0.315528 | − | 0.971094i | −0.975537 | − | 0.219836i | \(-0.929448\pi\) |
0.660009 | − | 0.751258i | \(-0.270552\pi\) | |||||||
\(972\) | 688.462 | − | 2118.87i | 0.0227185 | − | 0.0699205i | ||||
\(973\) | −24437.4 | − | 17754.8i | −0.805168 | − | 0.584989i | ||||
\(974\) | 920.607 | + | 668.860i | 0.0302856 | + | 0.0220038i | ||||
\(975\) | −1390.48 | + | 4279.44i | −0.0456727 | + | 0.140566i | ||||
\(976\) | −6496.80 | − | 19995.1i | −0.213071 | − | 0.655766i | ||||
\(977\) | 24269.6 | − | 17632.9i | 0.794732 | − | 0.577406i | −0.114632 | − | 0.993408i | \(-0.536569\pi\) |
0.909364 | + | 0.416002i | \(0.136569\pi\) | |||||||
\(978\) | 2460.14 | 0.0804361 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1347.46 | 0.0439216 | ||||||||
\(981\) | 33068.4 | − | 24025.6i | 1.07624 | − | 0.781935i | ||||
\(982\) | −9550.67 | − | 29393.9i | −0.310361 | − | 0.955192i | ||||
\(983\) | −7566.56 | + | 23287.5i | −0.245509 | + | 0.755600i | 0.750043 | + | 0.661389i | \(0.230033\pi\) |
−0.995552 | + | 0.0942108i | \(0.969967\pi\) | |||||||
\(984\) | −2035.67 | − | 1479.00i | −0.0659501 | − | 0.0479156i | ||||
\(985\) | 893.657 | + | 649.280i | 0.0289079 | + | 0.0210028i | ||||
\(986\) | −4770.09 | + | 14680.8i | −0.154068 | + | 0.474171i | ||||
\(987\) | −2397.56 | − | 7378.94i | −0.0773205 | − | 0.237968i | ||||
\(988\) | −5892.92 | + | 4281.46i | −0.189756 | + | 0.137866i | ||||
\(989\) | −37127.1 | −1.19370 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52661.1 | −1.68803 | −0.844014 | − | 0.536321i | \(-0.819814\pi\) | ||||
−0.844014 | + | 0.536321i | \(0.819814\pi\) | |||||||
\(992\) | 4879.97 | − | 3545.51i | 0.156189 | − | 0.113478i | ||||
\(993\) | −973.664 | − | 2996.63i | −0.0311161 | − | 0.0957655i | ||||
\(994\) | 8475.15 | − | 26083.8i | 0.270438 | − | 0.832322i | ||||
\(995\) | 1286.25 | + | 934.514i | 0.0409817 | + | 0.0297750i | ||||
\(996\) | −253.577 | − | 184.234i | −0.00806716 | − | 0.00586113i | ||||
\(997\) | 16918.2 | − | 52069.0i | 0.537418 | − | 1.65400i | −0.200947 | − | 0.979602i | \(-0.564402\pi\) |
0.738365 | − | 0.674401i | \(-0.235598\pi\) | |||||||
\(998\) | 13917.0 | + | 42832.1i | 0.441417 | + | 1.35854i | ||||
\(999\) | 4905.78 | − | 3564.26i | 0.155367 | − | 0.112881i |
(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 | 121.4.c.d.3.2 | 8 | ||
11.2 | odd | 10 | 121.4.a.b.1.2 | ✓ | 2 | ||
11.3 | even | 5 | inner | 121.4.c.d.27.1 | 8 | ||
11.4 | even | 5 | inner | 121.4.c.d.81.2 | 8 | ||
11.5 | even | 5 | inner | 121.4.c.d.9.1 | 8 | ||
11.6 | odd | 10 | 121.4.c.g.9.2 | 8 | |||
11.7 | odd | 10 | 121.4.c.g.81.1 | 8 | |||
11.8 | odd | 10 | 121.4.c.g.27.2 | 8 | |||
11.9 | even | 5 | 121.4.a.e.1.1 | yes | 2 | ||
11.10 | odd | 2 | 121.4.c.g.3.1 | 8 | |||
33.2 | even | 10 | 1089.4.a.x.1.1 | 2 | |||
33.20 | odd | 10 | 1089.4.a.k.1.2 | 2 | |||
44.31 | odd | 10 | 1936.4.a.y.1.1 | 2 | |||
44.35 | even | 10 | 1936.4.a.z.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
121.4.a.b.1.2 | ✓ | 2 | 11.2 | odd | 10 | ||
121.4.a.e.1.1 | yes | 2 | 11.9 | even | 5 | ||
121.4.c.d.3.2 | 8 | 1.1 | even | 1 | trivial | ||
121.4.c.d.9.1 | 8 | 11.5 | even | 5 | inner | ||
121.4.c.d.27.1 | 8 | 11.3 | even | 5 | inner | ||
121.4.c.d.81.2 | 8 | 11.4 | even | 5 | inner | ||
121.4.c.g.3.1 | 8 | 11.10 | odd | 2 | |||
121.4.c.g.9.2 | 8 | 11.6 | odd | 10 | |||
121.4.c.g.27.2 | 8 | 11.8 | odd | 10 | |||
121.4.c.g.81.1 | 8 | 11.7 | odd | 10 | |||
1089.4.a.k.1.2 | 2 | 33.20 | odd | 10 | |||
1089.4.a.x.1.1 | 2 | 33.2 | even | 10 | |||
1936.4.a.y.1.1 | 2 | 44.31 | odd | 10 | |||
1936.4.a.z.1.1 | 2 | 44.35 | even | 10 |