Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,3,Mod(97,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.h (of order \(6\), 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: | \(5.47685331364\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 172.6 | ||
Character | \(\chi\) | \(=\) | 201.172 |
Dual form | 201.3.h.a.97.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0720773 | + | 0.0416138i | 0.0360386 | + | 0.0208069i | 0.517911 | − | 0.855434i | \(-0.326710\pi\) |
−0.481872 | + | 0.876241i | \(0.660043\pi\) | |||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | −1.99654 | − | 3.45810i | −0.499134 | − | 0.864526i | ||||
\(5\) | 1.32016i | 0.264031i | 0.991248 | + | 0.132016i | \(0.0421449\pi\) | ||||
−0.991248 | + | 0.132016i | \(0.957855\pi\) | |||||||
\(6\) | −0.0720773 | + | 0.124841i | −0.0120129 | + | 0.0208069i | ||||
\(7\) | 1.88003 | − | 1.08543i | 0.268575 | − | 0.155062i | −0.359665 | − | 0.933082i | \(-0.617109\pi\) |
0.628240 | + | 0.778020i | \(0.283776\pi\) | |||||||
\(8\) | − | 0.665245i | − | 0.0831556i | ||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | −0.0549368 | + | 0.0951533i | −0.00549368 | + | 0.00951533i | ||||
\(11\) | 18.4349 | − | 10.6434i | 1.67590 | − | 0.967582i | 0.711673 | − | 0.702511i | \(-0.247938\pi\) |
0.964229 | − | 0.265071i | \(-0.0853955\pi\) | |||||||
\(12\) | 5.98961 | − | 3.45810i | 0.499134 | − | 0.288175i | ||||
\(13\) | 6.76145 | + | 3.90372i | 0.520111 | + | 0.300286i | 0.736980 | − | 0.675914i | \(-0.236251\pi\) |
−0.216869 | + | 0.976201i | \(0.569584\pi\) | |||||||
\(14\) | 0.180676 | 0.0129054 | ||||||||
\(15\) | −2.28658 | −0.152439 | ||||||||
\(16\) | −7.95846 | + | 13.7845i | −0.497404 | + | 0.861529i | ||||
\(17\) | 13.7876 | − | 23.8809i | 0.811038 | − | 1.40476i | −0.101101 | − | 0.994876i | \(-0.532237\pi\) |
0.912139 | − | 0.409882i | \(-0.134430\pi\) | |||||||
\(18\) | −0.216232 | − | 0.124841i | −0.0120129 | − | 0.00693564i | ||||
\(19\) | 3.95745 | − | 6.85451i | 0.208287 | − | 0.360764i | −0.742888 | − | 0.669416i | \(-0.766545\pi\) |
0.951175 | + | 0.308652i | \(0.0998779\pi\) | |||||||
\(20\) | 4.56524 | − | 2.63574i | 0.228262 | − | 0.131787i | ||||
\(21\) | 1.88003 | + | 3.25630i | 0.0895251 | + | 0.155062i | ||||
\(22\) | 1.77165 | 0.0805296 | ||||||||
\(23\) | −11.7884 | + | 20.4181i | −0.512538 | + | 0.887742i | 0.487356 | + | 0.873203i | \(0.337961\pi\) |
−0.999894 | + | 0.0145390i | \(0.995372\pi\) | |||||||
\(24\) | 1.15224 | 0.0480099 | ||||||||
\(25\) | 23.2572 | 0.930287 | ||||||||
\(26\) | 0.324898 | + | 0.562739i | 0.0124961 | + | 0.0216438i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | −7.50708 | − | 4.33422i | −0.268110 | − | 0.154793i | ||||
\(29\) | −10.4969 | − | 18.1811i | −0.361961 | − | 0.626935i | 0.626322 | − | 0.779564i | \(-0.284559\pi\) |
−0.988284 | + | 0.152629i | \(0.951226\pi\) | |||||||
\(30\) | −0.164810 | − | 0.0951533i | −0.00549368 | − | 0.00317178i | ||||
\(31\) | 34.8799 | − | 20.1379i | 1.12516 | − | 0.649611i | 0.182446 | − | 0.983216i | \(-0.441599\pi\) |
0.942713 | + | 0.333605i | \(0.108265\pi\) | |||||||
\(32\) | −3.45172 | + | 1.99285i | −0.107866 | + | 0.0622767i | ||||
\(33\) | 18.4349 | + | 31.9302i | 0.558634 | + | 0.967582i | ||||
\(34\) | 1.98755 | − | 1.14751i | 0.0584574 | − | 0.0337504i | ||||
\(35\) | 1.43294 | + | 2.48193i | 0.0409412 | + | 0.0709123i | ||||
\(36\) | 5.98961 | + | 10.3743i | 0.166378 | + | 0.288175i | ||||
\(37\) | −26.1129 | + | 45.2288i | −0.705754 | + | 1.22240i | 0.260665 | + | 0.965429i | \(0.416058\pi\) |
−0.966419 | + | 0.256972i | \(0.917275\pi\) | |||||||
\(38\) | 0.570485 | − | 0.329369i | 0.0150128 | − | 0.00866762i | ||||
\(39\) | −6.76145 | + | 11.7112i | −0.173370 | + | 0.300286i | ||||
\(40\) | 0.878227 | 0.0219557 | ||||||||
\(41\) | −8.87200 | + | 5.12225i | −0.216390 | + | 0.124933i | −0.604278 | − | 0.796774i | \(-0.706538\pi\) |
0.387888 | + | 0.921707i | \(0.373205\pi\) | |||||||
\(42\) | 0.312940i | 0.00745096i | ||||||||
\(43\) | − | 3.99024i | − | 0.0927963i | −0.998923 | − | 0.0463982i | \(-0.985226\pi\) | ||
0.998923 | − | 0.0463982i | \(-0.0147743\pi\) | |||||||
\(44\) | −73.6120 | − | 42.4999i | −1.67300 | − | 0.965907i | ||||
\(45\) | − | 3.96047i | − | 0.0880105i | ||||||
\(46\) | −1.69935 | + | 0.981119i | −0.0369424 | + | 0.0213287i | ||||
\(47\) | −27.2153 | − | 47.1383i | −0.579049 | − | 1.00294i | −0.995589 | − | 0.0938247i | \(-0.970091\pi\) |
0.416540 | − | 0.909118i | \(-0.363243\pi\) | |||||||
\(48\) | −23.8754 | − | 13.7845i | −0.497404 | − | 0.287176i | ||||
\(49\) | −22.1437 | + | 38.3540i | −0.451912 | + | 0.782734i | ||||
\(50\) | 1.67631 | + | 0.967820i | 0.0335263 | + | 0.0193564i | ||||
\(51\) | 41.3629 | + | 23.8809i | 0.811038 | + | 0.468253i | ||||
\(52\) | − | 31.1757i | − | 0.599533i | ||||||
\(53\) | − | 18.5232i | − | 0.349494i | −0.984613 | − | 0.174747i | \(-0.944089\pi\) | ||
0.984613 | − | 0.174747i | \(-0.0559108\pi\) | |||||||
\(54\) | 0.216232 | − | 0.374524i | 0.00400429 | − | 0.00693564i | ||||
\(55\) | 14.0510 | + | 24.3370i | 0.255472 | + | 0.442491i | ||||
\(56\) | −0.722079 | − | 1.25068i | −0.0128943 | − | 0.0223335i | ||||
\(57\) | 11.8724 | + | 6.85451i | 0.208287 | + | 0.120255i | ||||
\(58\) | − | 1.74726i | − | 0.0301252i | ||||||
\(59\) | 18.6108 | 0.315437 | 0.157719 | − | 0.987484i | \(-0.449586\pi\) | ||||
0.157719 | + | 0.987484i | \(0.449586\pi\) | |||||||
\(60\) | 4.56524 | + | 7.90722i | 0.0760873 | + | 0.131787i | ||||
\(61\) | −41.8398 | − | 24.1562i | −0.685898 | − | 0.396003i | 0.116175 | − | 0.993229i | \(-0.462937\pi\) |
−0.802074 | + | 0.597225i | \(0.796270\pi\) | |||||||
\(62\) | 3.35207 | 0.0540656 | ||||||||
\(63\) | −5.64008 | + | 3.25630i | −0.0895251 | + | 0.0516873i | ||||
\(64\) | 63.3360 | 0.989625 | ||||||||
\(65\) | −5.15353 | + | 8.92617i | −0.0792850 | + | 0.137326i | ||||
\(66\) | 3.06859i | 0.0464938i | ||||||||
\(67\) | 27.8247 | + | 60.9491i | 0.415294 | + | 0.909687i | ||||
\(68\) | −110.110 | −1.61927 | ||||||||
\(69\) | −35.3651 | − | 20.4181i | −0.512538 | − | 0.295914i | ||||
\(70\) | 0.238521i | 0.00340744i | ||||||||
\(71\) | −43.8165 | − | 75.8924i | −0.617133 | − | 1.06891i | −0.990006 | − | 0.141024i | \(-0.954961\pi\) |
0.372873 | − | 0.927882i | \(-0.378373\pi\) | |||||||
\(72\) | 1.99573i | 0.0277185i | ||||||||
\(73\) | −22.6415 | + | 39.2163i | −0.310158 | + | 0.537210i | −0.978396 | − | 0.206738i | \(-0.933715\pi\) |
0.668238 | + | 0.743947i | \(0.267049\pi\) | |||||||
\(74\) | −3.76429 | + | 2.17331i | −0.0508688 | + | 0.0293691i | ||||
\(75\) | 40.2826i | 0.537102i | ||||||||
\(76\) | −31.6048 | −0.415853 | ||||||||
\(77\) | 23.1054 | − | 40.0198i | 0.300071 | − | 0.519737i | ||||
\(78\) | −0.974693 | + | 0.562739i | −0.0124961 | + | 0.00721461i | ||||
\(79\) | −129.424 | + | 74.7227i | −1.63827 | + | 0.945857i | −0.656844 | + | 0.754026i | \(0.728109\pi\) |
−0.981428 | + | 0.191831i | \(0.938558\pi\) | |||||||
\(80\) | −18.1977 | − | 10.5064i | −0.227471 | − | 0.131330i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −0.852626 | −0.0103979 | ||||||||
\(83\) | −72.7315 | + | 125.975i | −0.876283 | + | 1.51777i | −0.0208927 | + | 0.999782i | \(0.506651\pi\) |
−0.855390 | + | 0.517984i | \(0.826682\pi\) | |||||||
\(84\) | 7.50708 | − | 13.0027i | 0.0893701 | − | 0.154793i | ||||
\(85\) | 31.5265 | + | 18.2018i | 0.370900 | + | 0.214139i | ||||
\(86\) | 0.166049 | − | 0.287606i | 0.00193081 | − | 0.00334425i | ||||
\(87\) | 31.4906 | − | 18.1811i | 0.361961 | − | 0.208978i | ||||
\(88\) | −7.08047 | − | 12.2637i | −0.0804599 | − | 0.139361i | ||||
\(89\) | 139.378 | 1.56604 | 0.783020 | − | 0.621997i | \(-0.213678\pi\) | ||||
0.783020 | + | 0.621997i | \(0.213678\pi\) | |||||||
\(90\) | 0.164810 | − | 0.285460i | 0.00183123 | − | 0.00317178i | ||||
\(91\) | 16.9489 | 0.186252 | ||||||||
\(92\) | 94.1437 | 1.02330 | ||||||||
\(93\) | 34.8799 | + | 60.4138i | 0.375053 | + | 0.649611i | ||||
\(94\) | − | 4.53013i | − | 0.0481929i | ||||||
\(95\) | 9.04903 | + | 5.22446i | 0.0952529 | + | 0.0549943i | ||||
\(96\) | −3.45172 | − | 5.97856i | −0.0359555 | − | 0.0622767i | ||||
\(97\) | 25.9025 | + | 14.9548i | 0.267036 | + | 0.154173i | 0.627540 | − | 0.778584i | \(-0.284062\pi\) |
−0.360504 | + | 0.932758i | \(0.617395\pi\) | |||||||
\(98\) | −3.19211 | + | 1.84297i | −0.0325725 | + | 0.0188058i | ||||
\(99\) | −55.3048 | + | 31.9302i | −0.558634 | + | 0.322527i | ||||
\(100\) | −46.4338 | − | 80.4257i | −0.464338 | − | 0.804257i | ||||
\(101\) | −14.6542 | + | 8.46060i | −0.145091 | + | 0.0837683i | −0.570788 | − | 0.821097i | \(-0.693362\pi\) |
0.425697 | + | 0.904866i | \(0.360029\pi\) | |||||||
\(102\) | 1.98755 | + | 3.44254i | 0.0194858 | + | 0.0337504i | ||||
\(103\) | 53.1047 | + | 91.9800i | 0.515579 | + | 0.893009i | 0.999836 | + | 0.0180837i | \(0.00575652\pi\) |
−0.484257 | + | 0.874926i | \(0.660910\pi\) | |||||||
\(104\) | 2.59693 | − | 4.49802i | 0.0249705 | − | 0.0432502i | ||||
\(105\) | −4.29883 | + | 2.48193i | −0.0409412 | + | 0.0236374i | ||||
\(106\) | 0.770821 | − | 1.33510i | 0.00727190 | − | 0.0125953i | ||||
\(107\) | 27.2236 | 0.254427 | 0.127213 | − | 0.991875i | \(-0.459397\pi\) | ||||
0.127213 | + | 0.991875i | \(0.459397\pi\) | |||||||
\(108\) | −17.9688 | + | 10.3743i | −0.166378 | + | 0.0960584i | ||||
\(109\) | − | 153.905i | − | 1.41198i | −0.708223 | − | 0.705988i | \(-0.750503\pi\) | ||
0.708223 | − | 0.705988i | \(-0.249497\pi\) | |||||||
\(110\) | 2.33886i | 0.0212623i | ||||||||
\(111\) | −78.3386 | − | 45.2288i | −0.705754 | − | 0.407467i | ||||
\(112\) | 34.5535i | 0.308514i | ||||||||
\(113\) | 120.926 | − | 69.8168i | 1.07014 | − | 0.617848i | 0.141923 | − | 0.989878i | \(-0.454672\pi\) |
0.928221 | + | 0.372030i | \(0.121338\pi\) | |||||||
\(114\) | 0.570485 | + | 0.988108i | 0.00500425 | + | 0.00866762i | ||||
\(115\) | −26.9551 | − | 15.5625i | −0.234392 | − | 0.135326i | ||||
\(116\) | −41.9148 | + | 72.5985i | −0.361334 | + | 0.625849i | ||||
\(117\) | −20.2843 | − | 11.7112i | −0.173370 | − | 0.100095i | ||||
\(118\) | 1.34142 | + | 0.774466i | 0.0113679 | + | 0.00656327i | ||||
\(119\) | − | 59.8623i | − | 0.503044i | ||||||
\(120\) | 1.52113i | 0.0126761i | ||||||||
\(121\) | 166.064 | − | 287.632i | 1.37243 | − | 2.37712i | ||||
\(122\) | −2.01046 | − | 3.48223i | −0.0164792 | − | 0.0285428i | ||||
\(123\) | −8.87200 | − | 15.3667i | −0.0721300 | − | 0.124933i | ||||
\(124\) | −139.278 | − | 80.4122i | −1.12321 | − | 0.648486i | ||||
\(125\) | 63.7071i | 0.509656i | ||||||||
\(126\) | −0.542029 | −0.00430182 | ||||||||
\(127\) | 89.6263 | + | 155.237i | 0.705719 | + | 1.22234i | 0.966432 | + | 0.256924i | \(0.0827091\pi\) |
−0.260713 | + | 0.965416i | \(0.583958\pi\) | |||||||
\(128\) | 18.3720 | + | 10.6071i | 0.143531 | + | 0.0828677i | ||||
\(129\) | 6.91130 | 0.0535760 | ||||||||
\(130\) | −0.742904 | + | 0.428916i | −0.00571465 | + | 0.00329935i | ||||
\(131\) | −52.2049 | −0.398511 | −0.199255 | − | 0.979948i | \(-0.563852\pi\) | ||||
−0.199255 | + | 0.979948i | \(0.563852\pi\) | |||||||
\(132\) | 73.6120 | − | 127.500i | 0.557667 | − | 0.965907i | ||||
\(133\) | − | 17.1822i | − | 0.129190i | ||||||
\(134\) | −0.530797 | + | 5.55093i | −0.00396117 | + | 0.0414249i | ||||
\(135\) | 6.85974 | 0.0508129 | ||||||||
\(136\) | −15.8866 | − | 9.17215i | −0.116814 | − | 0.0674423i | ||||
\(137\) | − | 133.362i | − | 0.973443i | −0.873557 | − | 0.486722i | \(-0.838193\pi\) | ||
0.873557 | − | 0.486722i | \(-0.161807\pi\) | |||||||
\(138\) | −1.69935 | − | 2.94336i | −0.0123141 | − | 0.0213287i | ||||
\(139\) | 119.427i | 0.859184i | 0.903023 | + | 0.429592i | \(0.141343\pi\) | ||||
−0.903023 | + | 0.429592i | \(0.858657\pi\) | |||||||
\(140\) | 5.72185 | − | 9.91053i | 0.0408703 | − | 0.0707895i | ||||
\(141\) | 81.6459 | − | 47.1383i | 0.579049 | − | 0.334314i | ||||
\(142\) | − | 7.29348i | − | 0.0513626i | ||||||
\(143\) | 166.196 | 1.16221 | ||||||||
\(144\) | 23.8754 | − | 41.3534i | 0.165801 | − | 0.287176i | ||||
\(145\) | 24.0019 | − | 13.8575i | 0.165531 | − | 0.0955691i | ||||
\(146\) | −3.26388 | + | 1.88440i | −0.0223554 | + | 0.0129069i | ||||
\(147\) | −66.4310 | − | 38.3540i | −0.451912 | − | 0.260911i | ||||
\(148\) | 208.541 | 1.40906 | ||||||||
\(149\) | 107.903 | 0.724183 | 0.362091 | − | 0.932143i | \(-0.382063\pi\) | ||||
0.362091 | + | 0.932143i | \(0.382063\pi\) | |||||||
\(150\) | −1.67631 | + | 2.90346i | −0.0111754 | + | 0.0193564i | ||||
\(151\) | 0.0602967 | − | 0.104437i | 0.000399316 | − | 0.000691635i | −0.865826 | − | 0.500346i | \(-0.833206\pi\) |
0.866225 | + | 0.499654i | \(0.166540\pi\) | |||||||
\(152\) | −4.55993 | − | 2.63267i | −0.0299995 | − | 0.0173202i | ||||
\(153\) | −41.3629 | + | 71.6427i | −0.270346 | + | 0.468253i | ||||
\(154\) | 3.33075 | − | 1.92301i | 0.0216283 | − | 0.0124871i | ||||
\(155\) | 26.5852 | + | 46.0470i | 0.171518 | + | 0.297077i | ||||
\(156\) | 53.9979 | 0.346140 | ||||||||
\(157\) | −82.5294 | + | 142.945i | −0.525665 | + | 0.910478i | 0.473888 | + | 0.880585i | \(0.342850\pi\) |
−0.999553 | + | 0.0298931i | \(0.990483\pi\) | |||||||
\(158\) | −12.4380 | −0.0787215 | ||||||||
\(159\) | 32.0831 | 0.201781 | ||||||||
\(160\) | −2.63088 | − | 4.55682i | −0.0164430 | − | 0.0284801i | ||||
\(161\) | 51.1820i | 0.317901i | ||||||||
\(162\) | 0.648695 | + | 0.374524i | 0.00400429 | + | 0.00231188i | ||||
\(163\) | 63.5218 | + | 110.023i | 0.389704 | + | 0.674988i | 0.992410 | − | 0.122976i | \(-0.0392439\pi\) |
−0.602705 | + | 0.797964i | \(0.705911\pi\) | |||||||
\(164\) | 35.4265 | + | 20.4535i | 0.216015 | + | 0.124717i | ||||
\(165\) | −42.1529 | + | 24.3370i | −0.255472 | + | 0.147497i | ||||
\(166\) | −10.4846 | + | 6.05327i | −0.0631601 | + | 0.0364655i | ||||
\(167\) | −94.2251 | − | 163.203i | −0.564222 | − | 0.977261i | −0.997122 | − | 0.0758191i | \(-0.975843\pi\) |
0.432900 | − | 0.901442i | \(-0.357490\pi\) | |||||||
\(168\) | 2.16624 | − | 1.25068i | 0.0128943 | − | 0.00744451i | ||||
\(169\) | −54.0219 | − | 93.5686i | −0.319656 | − | 0.553661i | ||||
\(170\) | 1.51490 | + | 2.62388i | 0.00891116 | + | 0.0154346i | ||||
\(171\) | −11.8724 | + | 20.5635i | −0.0694290 | + | 0.120255i | ||||
\(172\) | −13.7987 | + | 7.96666i | −0.0802248 | + | 0.0463178i | ||||
\(173\) | −25.1820 | + | 43.6164i | −0.145560 | + | 0.252118i | −0.929582 | − | 0.368616i | \(-0.879832\pi\) |
0.784021 | + | 0.620734i | \(0.213165\pi\) | |||||||
\(174\) | 3.02634 | 0.0173928 | ||||||||
\(175\) | 43.7241 | − | 25.2441i | 0.249852 | − | 0.144252i | ||||
\(176\) | 338.821i | 1.92512i | ||||||||
\(177\) | 32.2348i | 0.182118i | ||||||||
\(178\) | 10.0460 | + | 5.80003i | 0.0564379 | + | 0.0325845i | ||||
\(179\) | 252.236i | 1.40914i | 0.709634 | + | 0.704571i | \(0.248860\pi\) | ||||
−0.709634 | + | 0.704571i | \(0.751140\pi\) | |||||||
\(180\) | −13.6957 | + | 7.90722i | −0.0760873 | + | 0.0439290i | ||||
\(181\) | −50.0517 | − | 86.6921i | −0.276529 | − | 0.478962i | 0.693991 | − | 0.719984i | \(-0.255851\pi\) |
−0.970520 | + | 0.241022i | \(0.922517\pi\) | |||||||
\(182\) | 1.22163 | + | 0.705310i | 0.00671227 | + | 0.00387533i | ||||
\(183\) | 41.8398 | − | 72.4686i | 0.228633 | − | 0.396003i | ||||
\(184\) | 13.5830 | + | 7.84216i | 0.0738207 | + | 0.0426204i | ||||
\(185\) | −59.7092 | − | 34.4731i | −0.322752 | − | 0.186341i | ||||
\(186\) | 5.80595i | 0.0312148i | ||||||||
\(187\) | − | 586.990i | − | 3.13898i | ||||||
\(188\) | −108.673 | + | 188.227i | −0.578046 | + | 1.00121i | ||||
\(189\) | −5.64008 | − | 9.76891i | −0.0298417 | − | 0.0516873i | ||||
\(190\) | 0.434819 | + | 0.753129i | 0.00228852 | + | 0.00396384i | ||||
\(191\) | 123.690 | + | 71.4122i | 0.647590 | + | 0.373886i | 0.787532 | − | 0.616274i | \(-0.211358\pi\) |
−0.139942 | + | 0.990160i | \(0.544692\pi\) | |||||||
\(192\) | 109.701i | 0.571360i | ||||||||
\(193\) | −29.9393 | −0.155126 | −0.0775629 | − | 0.996987i | \(-0.524714\pi\) | ||||
−0.0775629 | + | 0.996987i | \(0.524714\pi\) | |||||||
\(194\) | 1.24465 | + | 2.15580i | 0.00641574 | + | 0.0111124i | ||||
\(195\) | −15.4606 | − | 8.92617i | −0.0792850 | − | 0.0457752i | ||||
\(196\) | 176.843 | 0.902258 | ||||||||
\(197\) | −113.500 | + | 65.5295i | −0.576144 | + | 0.332637i | −0.759600 | − | 0.650391i | \(-0.774605\pi\) |
0.183455 | + | 0.983028i | \(0.441272\pi\) | |||||||
\(198\) | −5.31495 | −0.0268432 | ||||||||
\(199\) | −127.781 | + | 221.323i | −0.642115 | + | 1.11218i | 0.342844 | + | 0.939392i | \(0.388610\pi\) |
−0.984960 | + | 0.172784i | \(0.944724\pi\) | |||||||
\(200\) | − | 15.4717i | − | 0.0773586i | ||||||
\(201\) | −105.567 | + | 48.1938i | −0.525208 | + | 0.239770i | ||||
\(202\) | −1.40831 | −0.00697184 | ||||||||
\(203\) | −39.4688 | − | 22.7873i | −0.194428 | − | 0.112253i | ||||
\(204\) | − | 190.716i | − | 0.934884i | ||||||
\(205\) | −6.76217 | − | 11.7124i | −0.0329862 | − | 0.0571338i | ||||
\(206\) | 8.83955i | 0.0429104i | ||||||||
\(207\) | 35.3651 | − | 61.2542i | 0.170846 | − | 0.295914i | ||||
\(208\) | −107.621 | + | 62.1353i | −0.517411 | + | 0.298727i | ||||
\(209\) | − | 168.483i | − | 0.806139i | ||||||
\(210\) | −0.413130 | −0.00196729 | ||||||||
\(211\) | −32.0595 | + | 55.5286i | −0.151941 | + | 0.263169i | −0.931941 | − | 0.362610i | \(-0.881886\pi\) |
0.780000 | + | 0.625779i | \(0.215219\pi\) | |||||||
\(212\) | −64.0551 | + | 36.9823i | −0.302147 | + | 0.174445i | ||||
\(213\) | 131.449 | − | 75.8924i | 0.617133 | − | 0.356302i | ||||
\(214\) | 1.96221 | + | 1.13288i | 0.00916919 | + | 0.00529383i | ||||
\(215\) | 5.26775 | 0.0245011 | ||||||||
\(216\) | −3.45671 | −0.0160033 | ||||||||
\(217\) | 43.7168 | − | 75.7197i | 0.201460 | − | 0.348939i | ||||
\(218\) | 6.40460 | − | 11.0931i | 0.0293789 | − | 0.0508857i | ||||
\(219\) | −67.9246 | − | 39.2163i | −0.310158 | − | 0.179070i | ||||
\(220\) | 56.1065 | − | 97.1794i | 0.255030 | − | 0.441724i | ||||
\(221\) | 186.449 | − | 107.646i | 0.843660 | − | 0.487087i | ||||
\(222\) | −3.76429 | − | 6.51994i | −0.0169563 | − | 0.0293691i | ||||
\(223\) | −421.085 | −1.88827 | −0.944137 | − | 0.329554i | \(-0.893102\pi\) | ||||
−0.944137 | + | 0.329554i | \(0.893102\pi\) | |||||||
\(224\) | −4.32622 | + | 7.49324i | −0.0193135 | + | 0.0334519i | ||||
\(225\) | −69.7716 | −0.310096 | ||||||||
\(226\) | 11.6214 | 0.0514220 | ||||||||
\(227\) | 135.759 | + | 235.142i | 0.598058 | + | 1.03587i | 0.993107 | + | 0.117207i | \(0.0373942\pi\) |
−0.395049 | + | 0.918660i | \(0.629272\pi\) | |||||||
\(228\) | − | 54.7411i | − | 0.240093i | ||||||
\(229\) | −125.753 | − | 72.6038i | −0.549142 | − | 0.317047i | 0.199634 | − | 0.979871i | \(-0.436025\pi\) |
−0.748776 | + | 0.662823i | \(0.769358\pi\) | |||||||
\(230\) | −1.29523 | − | 2.24341i | −0.00563144 | − | 0.00975394i | ||||
\(231\) | 69.3163 | + | 40.0198i | 0.300071 | + | 0.173246i | ||||
\(232\) | −12.0949 | + | 6.98299i | −0.0521331 | + | 0.0300991i | ||||
\(233\) | −111.144 | + | 64.1693i | −0.477015 | + | 0.275405i | −0.719172 | − | 0.694832i | \(-0.755479\pi\) |
0.242157 | + | 0.970237i | \(0.422145\pi\) | |||||||
\(234\) | −0.974693 | − | 1.68822i | −0.00416536 | − | 0.00721461i | ||||
\(235\) | 62.2299 | − | 35.9285i | 0.264808 | − | 0.152887i | ||||
\(236\) | −37.1571 | − | 64.3580i | −0.157445 | − | 0.272704i | ||||
\(237\) | −129.424 | − | 224.168i | −0.546091 | − | 0.945857i | ||||
\(238\) | 2.49110 | − | 4.31471i | 0.0104668 | − | 0.0181290i | ||||
\(239\) | −100.961 | + | 58.2896i | −0.422429 | + | 0.243890i | −0.696116 | − | 0.717929i | \(-0.745090\pi\) |
0.273687 | + | 0.961819i | \(0.411757\pi\) | |||||||
\(240\) | 18.1977 | − | 31.5193i | 0.0758236 | − | 0.131330i | ||||
\(241\) | −391.536 | −1.62463 | −0.812316 | − | 0.583218i | \(-0.801793\pi\) | ||||
−0.812316 | + | 0.583218i | \(0.801793\pi\) | |||||||
\(242\) | 23.9389 | − | 13.8211i | 0.0989211 | − | 0.0571121i | ||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 192.915i | 0.790635i | ||||||||
\(245\) | −50.6332 | − | 29.2331i | −0.206666 | − | 0.119319i | ||||
\(246\) | − | 1.47679i | − | 0.00600321i | ||||||
\(247\) | 53.5162 | − | 30.8976i | 0.216665 | − | 0.125091i | ||||
\(248\) | −13.3967 | − | 23.2037i | −0.0540188 | − | 0.0935633i | ||||
\(249\) | −218.194 | − | 125.975i | −0.876283 | − | 0.505922i | ||||
\(250\) | −2.65109 | + | 4.59183i | −0.0106044 | + | 0.0183673i | ||||
\(251\) | −311.684 | − | 179.951i | −1.24177 | − | 0.716935i | −0.272314 | − | 0.962208i | \(-0.587789\pi\) |
−0.969454 | + | 0.245273i | \(0.921122\pi\) | |||||||
\(252\) | 22.5213 | + | 13.0027i | 0.0893701 | + | 0.0515978i | ||||
\(253\) | 501.874i | 1.98369i | ||||||||
\(254\) | 14.9188i | 0.0587353i | ||||||||
\(255\) | −31.5265 | + | 54.6055i | −0.123633 | + | 0.214139i | ||||
\(256\) | −125.789 | − | 217.873i | −0.491364 | − | 0.851067i | ||||
\(257\) | 133.193 | + | 230.697i | 0.518260 | + | 0.897652i | 0.999775 | + | 0.0212144i | \(0.00675326\pi\) |
−0.481515 | + | 0.876438i | \(0.659913\pi\) | |||||||
\(258\) | 0.498148 | + | 0.287606i | 0.00193081 | + | 0.00111475i | ||||
\(259\) | 113.375i | 0.437742i | ||||||||
\(260\) | 41.1568 | 0.158295 | ||||||||
\(261\) | 31.4906 | + | 54.5433i | 0.120654 | + | 0.208978i | ||||
\(262\) | −3.76279 | − | 2.17245i | −0.0143618 | − | 0.00829178i | ||||
\(263\) | 23.9607 | 0.0911055 | 0.0455527 | − | 0.998962i | \(-0.485495\pi\) | ||||
0.0455527 | + | 0.998962i | \(0.485495\pi\) | |||||||
\(264\) | 21.2414 | − | 12.2637i | 0.0804599 | − | 0.0464535i | ||||
\(265\) | 24.4535 | 0.0922775 | ||||||||
\(266\) | 0.715018 | − | 1.23845i | 0.00268804 | − | 0.00465582i | ||||
\(267\) | 241.409i | 0.904154i | ||||||||
\(268\) | 155.215 | − | 217.908i | 0.579161 | − | 0.813088i | ||||
\(269\) | 260.612 | 0.968818 | 0.484409 | − | 0.874842i | \(-0.339035\pi\) | ||||
0.484409 | + | 0.874842i | \(0.339035\pi\) | |||||||
\(270\) | 0.494431 | + | 0.285460i | 0.00183123 | + | 0.00105726i | ||||
\(271\) | 433.854i | 1.60094i | 0.599375 | + | 0.800469i | \(0.295416\pi\) | ||||
−0.599375 | + | 0.800469i | \(0.704584\pi\) | |||||||
\(272\) | 219.457 | + | 380.110i | 0.806827 | + | 1.39746i | ||||
\(273\) | 29.3564i | 0.107533i | ||||||||
\(274\) | 5.54969 | − | 9.61235i | 0.0202544 | − | 0.0350816i | ||||
\(275\) | 428.744 | − | 247.536i | 1.55907 | − | 0.900130i | ||||
\(276\) | 163.062i | 0.590803i | ||||||||
\(277\) | 244.786 | 0.883703 | 0.441852 | − | 0.897088i | \(-0.354322\pi\) | ||||
0.441852 | + | 0.897088i | \(0.354322\pi\) | |||||||
\(278\) | −4.96980 | + | 8.60794i | −0.0178770 | + | 0.0309638i | ||||
\(279\) | −104.640 | + | 60.4138i | −0.375053 | + | 0.216537i | ||||
\(280\) | 1.65109 | − | 0.953258i | 0.00589675 | − | 0.00340449i | ||||
\(281\) | −279.252 | − | 161.226i | −0.993778 | − | 0.573758i | −0.0873763 | − | 0.996175i | \(-0.527848\pi\) |
−0.906401 | + | 0.422418i | \(0.861182\pi\) | |||||||
\(282\) | 7.84642 | 0.0278242 | ||||||||
\(283\) | −273.577 | −0.966702 | −0.483351 | − | 0.875427i | \(-0.660581\pi\) | ||||
−0.483351 | + | 0.875427i | \(0.660581\pi\) | |||||||
\(284\) | −174.962 | + | 303.044i | −0.616065 | + | 1.06706i | ||||
\(285\) | −9.04903 | + | 15.6734i | −0.0317510 | + | 0.0549943i | ||||
\(286\) | 11.9789 | + | 6.91604i | 0.0418844 | + | 0.0241819i | ||||
\(287\) | −11.1197 | + | 19.2599i | −0.0387447 | + | 0.0671078i | ||||
\(288\) | 10.3552 | − | 5.97856i | 0.0359555 | − | 0.0207589i | ||||
\(289\) | −235.698 | − | 408.241i | −0.815564 | − | 1.41260i | ||||
\(290\) | 2.30666 | 0.00795399 | ||||||||
\(291\) | −25.9025 | + | 44.8644i | −0.0890119 | + | 0.154173i | ||||
\(292\) | 180.819 | 0.619242 | ||||||||
\(293\) | −19.6953 | −0.0672193 | −0.0336096 | − | 0.999435i | \(-0.510700\pi\) | ||||
−0.0336096 | + | 0.999435i | \(0.510700\pi\) | |||||||
\(294\) | −3.19211 | − | 5.52890i | −0.0108575 | − | 0.0188058i | ||||
\(295\) | 24.5692i | 0.0832853i | ||||||||
\(296\) | 30.0882 | + | 17.3715i | 0.101649 | + | 0.0586874i | ||||
\(297\) | −55.3048 | − | 95.7907i | −0.186211 | − | 0.322527i | ||||
\(298\) | 7.77737 | + | 4.49027i | 0.0260986 | + | 0.0150680i | ||||
\(299\) | −159.413 | + | 92.0372i | −0.533154 | + | 0.307817i | ||||
\(300\) | 139.301 | − | 80.4257i | 0.464338 | − | 0.268086i | ||||
\(301\) | −4.33114 | − | 7.50176i | −0.0143892 | − | 0.0249228i | ||||
\(302\) | 0.00869204 | − | 0.00501835i | 2.87816e−5 | − | 1.66171e-5i | ||||
\(303\) | −14.6542 | − | 25.3818i | −0.0483637 | − | 0.0837683i | ||||
\(304\) | 62.9905 | + | 109.103i | 0.207206 | + | 0.358890i | ||||
\(305\) | 31.8900 | − | 55.2351i | 0.104557 | − | 0.181099i | ||||
\(306\) | −5.96265 | + | 3.44254i | −0.0194858 | + | 0.0112501i | ||||
\(307\) | 210.303 | − | 364.255i | 0.685025 | − | 1.18650i | −0.288405 | − | 0.957509i | \(-0.593125\pi\) |
0.973429 | − | 0.228989i | \(-0.0735419\pi\) | |||||||
\(308\) | −184.523 | −0.599102 | ||||||||
\(309\) | −159.314 | + | 91.9800i | −0.515579 | + | 0.297670i | ||||
\(310\) | 4.42525i | 0.0142750i | ||||||||
\(311\) | 289.143i | 0.929719i | 0.885385 | + | 0.464859i | \(0.153895\pi\) | ||||
−0.885385 | + | 0.464859i | \(0.846105\pi\) | |||||||
\(312\) | 7.79079 | + | 4.49802i | 0.0249705 | + | 0.0144167i | ||||
\(313\) | − | 388.890i | − | 1.24246i | −0.783628 | − | 0.621231i | \(-0.786633\pi\) | ||
0.783628 | − | 0.621231i | \(-0.213367\pi\) | |||||||
\(314\) | −11.8970 | + | 6.86873i | −0.0378885 | + | 0.0218749i | ||||
\(315\) | −4.29883 | − | 7.44579i | −0.0136471 | − | 0.0236374i | ||||
\(316\) | 516.798 | + | 298.373i | 1.63544 | + | 0.944219i | ||||
\(317\) | 127.371 | − | 220.613i | 0.401801 | − | 0.695939i | −0.592143 | − | 0.805833i | \(-0.701718\pi\) |
0.993943 | + | 0.109894i | \(0.0350511\pi\) | |||||||
\(318\) | 2.31246 | + | 1.33510i | 0.00727190 | + | 0.00419843i | ||||
\(319\) | −387.018 | − | 223.445i | −1.21322 | − | 0.700454i | ||||
\(320\) | 83.6134i | 0.261292i | ||||||||
\(321\) | 47.1527i | 0.146893i | ||||||||
\(322\) | −2.12988 | + | 3.68906i | −0.00661454 | + | 0.0114567i | ||||
\(323\) | −109.128 | − | 189.015i | −0.337857 | − | 0.585186i | ||||
\(324\) | −17.9688 | − | 31.1229i | −0.0554593 | − | 0.0960584i | ||||
\(325\) | 157.252 | + | 90.7896i | 0.483853 | + | 0.279353i | ||||
\(326\) | 10.5735i | 0.0324342i | ||||||||
\(327\) | 266.572 | 0.815205 | ||||||||
\(328\) | 3.40755 | + | 5.90205i | 0.0103889 | + | 0.0179941i | ||||
\(329\) | −102.331 | − | 59.0808i | −0.311036 | − | 0.179577i | ||||
\(330\) | −4.05102 | −0.0122758 | ||||||||
\(331\) | −55.9600 | + | 32.3085i | −0.169063 | + | 0.0976088i | −0.582144 | − | 0.813086i | \(-0.697786\pi\) |
0.413081 | + | 0.910694i | \(0.364453\pi\) | |||||||
\(332\) | 580.844 | 1.74953 | ||||||||
\(333\) | 78.3386 | − | 135.687i | 0.235251 | − | 0.407467i | ||||
\(334\) | − | 15.6843i | − | 0.0469589i | ||||||
\(335\) | −80.4623 | + | 36.7329i | −0.240186 | + | 0.109651i | ||||
\(336\) | −59.8485 | −0.178121 | ||||||||
\(337\) | 323.719 | + | 186.900i | 0.960592 | + | 0.554598i | 0.896355 | − | 0.443337i | \(-0.146205\pi\) |
0.0642367 | + | 0.997935i | \(0.479539\pi\) | |||||||
\(338\) | − | 8.99223i | − | 0.0266042i | ||||||
\(339\) | 120.926 | + | 209.450i | 0.356714 | + | 0.617848i | ||||
\(340\) | − | 145.363i | − | 0.427537i | ||||||
\(341\) | 428.672 | − | 742.482i | 1.25710 | − | 2.17737i | ||||
\(342\) | −1.71145 | + | 0.988108i | −0.00500425 | + | 0.00288921i | ||||
\(343\) | 202.514i | 0.590421i | ||||||||
\(344\) | −2.65449 | −0.00771653 | ||||||||
\(345\) | 26.9551 | − | 46.6875i | 0.0781306 | − | 0.135326i | ||||
\(346\) | −3.63009 | + | 2.09584i | −0.0104916 | + | 0.00605733i | ||||
\(347\) | 410.827 | − | 237.191i | 1.18394 | − | 0.683547i | 0.227016 | − | 0.973891i | \(-0.427103\pi\) |
0.956922 | + | 0.290344i | \(0.0937696\pi\) | |||||||
\(348\) | −125.744 | − | 72.5985i | −0.361334 | − | 0.208616i | ||||
\(349\) | −19.6065 | −0.0561789 | −0.0280895 | − | 0.999605i | \(-0.508942\pi\) | ||||
−0.0280895 | + | 0.999605i | \(0.508942\pi\) | |||||||
\(350\) | 4.20202 | 0.0120058 | ||||||||
\(351\) | 20.2843 | − | 35.1335i | 0.0577902 | − | 0.100095i | ||||
\(352\) | −42.4215 | + | 73.4762i | −0.120516 | + | 0.208739i | ||||
\(353\) | −274.593 | − | 158.536i | −0.777884 | − | 0.449111i | 0.0577960 | − | 0.998328i | \(-0.481593\pi\) |
−0.835680 | + | 0.549217i | \(0.814926\pi\) | |||||||
\(354\) | −1.34142 | + | 2.32340i | −0.00378931 | + | 0.00656327i | ||||
\(355\) | 100.190 | − | 57.8446i | 0.282225 | − | 0.162943i | ||||
\(356\) | −278.272 | − | 481.982i | −0.781664 | − | 1.35388i | ||||
\(357\) | 103.685 | 0.290433 | ||||||||
\(358\) | −10.4965 | + | 18.1805i | −0.0293199 | + | 0.0507835i | ||||
\(359\) | −372.386 | −1.03729 | −0.518643 | − | 0.854991i | \(-0.673563\pi\) | ||||
−0.518643 | + | 0.854991i | \(0.673563\pi\) | |||||||
\(360\) | −2.63468 | −0.00731856 | ||||||||
\(361\) | 149.177 | + | 258.382i | 0.413233 | + | 0.715741i | ||||
\(362\) | − | 8.33138i | − | 0.0230148i | ||||||
\(363\) | 498.193 | + | 287.632i | 1.37243 | + | 0.792373i | ||||
\(364\) | −33.8392 | − | 58.6112i | −0.0929648 | − | 0.161020i | ||||
\(365\) | −51.7717 | − | 29.8904i | −0.141840 | − | 0.0818915i | ||||
\(366\) | 6.03139 | − | 3.48223i | 0.0164792 | − | 0.00951428i | ||||
\(367\) | 187.457 | − | 108.228i | 0.510781 | − | 0.294900i | −0.222374 | − | 0.974962i | \(-0.571380\pi\) |
0.733155 | + | 0.680062i | \(0.238047\pi\) | |||||||
\(368\) | −187.635 | − | 324.993i | −0.509877 | − | 0.883133i | ||||
\(369\) | 26.6160 | − | 15.3667i | 0.0721300 | − | 0.0416443i | ||||
\(370\) | −2.86912 | − | 4.96945i | −0.00775437 | − | 0.0134310i | ||||
\(371\) | −20.1057 | − | 34.8241i | −0.0541933 | − | 0.0938656i | ||||
\(372\) | 139.278 | − | 241.237i | 0.374403 | − | 0.648486i | ||||
\(373\) | −161.356 | + | 93.1588i | −0.432589 | + | 0.249756i | −0.700449 | − | 0.713702i | \(-0.747017\pi\) |
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(374\) | 24.4269 | − | 42.3086i | 0.0653125 | − | 0.113125i | ||||
\(375\) | −110.344 | −0.294250 | ||||||||
\(376\) | −31.3585 | + | 18.1048i | −0.0834003 | + | 0.0481512i | ||||
\(377\) | − | 163.908i | − | 0.434768i | ||||||
\(378\) | − | 0.938821i | − | 0.00248365i | ||||||
\(379\) | 207.017 | + | 119.521i | 0.546219 | + | 0.315360i | 0.747596 | − | 0.664154i | \(-0.231208\pi\) |
−0.201376 | + | 0.979514i | \(0.564541\pi\) | |||||||
\(380\) | − | 41.7233i | − | 0.109798i | ||||||
\(381\) | −268.879 | + | 155.237i | −0.705719 | + | 0.407447i | ||||
\(382\) | 5.94347 | + | 10.2944i | 0.0155588 | + | 0.0269487i | ||||
\(383\) | −307.739 | − | 177.673i | −0.803497 | − | 0.463899i | 0.0411955 | − | 0.999151i | \(-0.486883\pi\) |
−0.844693 | + | 0.535252i | \(0.820217\pi\) | |||||||
\(384\) | −18.3720 | + | 31.8212i | −0.0478437 | + | 0.0828677i | ||||
\(385\) | 52.8324 | + | 30.5028i | 0.137227 | + | 0.0792280i | ||||
\(386\) | −2.15794 | − | 1.24589i | −0.00559052 | − | 0.00322769i | ||||
\(387\) | 11.9707i | 0.0309321i | ||||||||
\(388\) | − | 119.431i | − | 0.307812i | ||||||
\(389\) | 36.5081 | − | 63.2339i | 0.0938512 | − | 0.162555i | −0.815277 | − | 0.579071i | \(-0.803416\pi\) |
0.909129 | + | 0.416516i | \(0.136749\pi\) | |||||||
\(390\) | −0.742904 | − | 1.28675i | −0.00190488 | − | 0.00329935i | ||||
\(391\) | 325.068 | + | 563.034i | 0.831376 | + | 1.43998i | ||||
\(392\) | 25.5148 | + | 14.7310i | 0.0650887 | + | 0.0375790i | ||||
\(393\) | − | 90.4216i | − | 0.230080i | ||||||
\(394\) | −10.9077 | −0.0276846 | ||||||||
\(395\) | −98.6457 | − | 170.859i | −0.249736 | − | 0.432555i | ||||
\(396\) | 220.836 | + | 127.500i | 0.557667 | + | 0.321969i | ||||
\(397\) | 104.627 | 0.263544 | 0.131772 | − | 0.991280i | \(-0.457933\pi\) | ||||
0.131772 | + | 0.991280i | \(0.457933\pi\) | |||||||
\(398\) | −18.4202 | + | 10.6349i | −0.0462819 | + | 0.0267209i | ||||
\(399\) | 29.7605 | 0.0745876 | ||||||||
\(400\) | −185.091 | + | 320.588i | −0.462729 | + | 0.801469i | ||||
\(401\) | 164.349i | 0.409848i | 0.978778 | + | 0.204924i | \(0.0656947\pi\) | ||||
−0.978778 | + | 0.204924i | \(0.934305\pi\) | |||||||
\(402\) | −9.61450 | − | 0.919367i | −0.0239167 | − | 0.00228698i | ||||
\(403\) | 314.452 | 0.780277 | ||||||||
\(404\) | 58.5153 | + | 33.7838i | 0.144840 | + | 0.0836233i | ||||
\(405\) | 11.8814i | 0.0293368i | ||||||||
\(406\) | −1.89654 | − | 3.28490i | −0.00467127 | − | 0.00809088i | ||||
\(407\) | 1111.72i | 2.73150i | ||||||||
\(408\) | 15.8866 | − | 27.5165i | 0.0389378 | − | 0.0674423i | ||||
\(409\) | −148.651 | + | 85.8238i | −0.363450 | + | 0.209838i | −0.670593 | − | 0.741825i | \(-0.733960\pi\) |
0.307143 | + | 0.951663i | \(0.400627\pi\) | |||||||
\(410\) | − | 1.12560i | − | 0.00274536i | ||||||
\(411\) | 230.989 | 0.562018 | ||||||||
\(412\) | 212.051 | − | 367.283i | 0.514686 | − | 0.891463i | ||||
\(413\) | 34.9888 | − | 20.2008i | 0.0847186 | − | 0.0489123i | ||||
\(414\) | 5.09805 | − | 2.94336i | 0.0123141 | − | 0.00710956i | ||||
\(415\) | −166.306 | − | 96.0169i | −0.400738 | − | 0.231366i | ||||
\(416\) | −31.1182 | −0.0748034 | ||||||||
\(417\) | −206.853 | −0.496050 | ||||||||
\(418\) | 7.01123 | − | 12.1438i | 0.0167733 | − | 0.0290522i | ||||
\(419\) | −327.986 | + | 568.088i | −0.782782 | + | 1.35582i | 0.147534 | + | 0.989057i | \(0.452867\pi\) |
−0.930315 | + | 0.366761i | \(0.880467\pi\) | |||||||
\(420\) | 17.1655 | + | 9.91053i | 0.0408703 | + | 0.0235965i | ||||
\(421\) | 306.271 | − | 530.478i | 0.727485 | − | 1.26004i | −0.230457 | − | 0.973082i | \(-0.574022\pi\) |
0.957943 | − | 0.286959i | \(-0.0926445\pi\) | |||||||
\(422\) | −4.62152 | + | 2.66823i | −0.0109515 | + | 0.00632283i | ||||
\(423\) | 81.6459 | + | 141.415i | 0.193016 | + | 0.334314i | ||||
\(424\) | −12.3225 | −0.0290624 | ||||||||
\(425\) | 320.662 | − | 555.402i | 0.754498 | − | 1.30683i | ||||
\(426\) | 12.6327 | 0.0296542 | ||||||||
\(427\) | −104.880 | −0.245620 | ||||||||
\(428\) | −54.3530 | − | 94.1422i | −0.126993 | − | 0.219958i | ||||
\(429\) | 287.859i | 0.671001i | ||||||||
\(430\) | 0.379685 | + | 0.219211i | 0.000882988 | + | 0.000509793i | ||||
\(431\) | −327.147 | − | 566.635i | −0.759041 | − | 1.31470i | −0.943340 | − | 0.331828i | \(-0.892335\pi\) |
0.184299 | − | 0.982870i | \(-0.440999\pi\) | |||||||
\(432\) | 71.6262 | + | 41.3534i | 0.165801 | + | 0.0957254i | ||||
\(433\) | 241.700 | − | 139.546i | 0.558200 | − | 0.322277i | −0.194223 | − | 0.980957i | \(-0.562219\pi\) |
0.752423 | + | 0.658681i | \(0.228885\pi\) | |||||||
\(434\) | 6.30197 | − | 3.63845i | 0.0145207 | − | 0.00838352i | ||||
\(435\) | 24.0019 | + | 41.5726i | 0.0551768 | + | 0.0955691i | ||||
\(436\) | −532.221 | + | 307.278i | −1.22069 | + | 0.704766i | ||||
\(437\) | 93.3039 | + | 161.607i | 0.213510 | + | 0.369810i | ||||
\(438\) | −3.26388 | − | 5.65321i | −0.00745178 | − | 0.0129069i | ||||
\(439\) | −76.1249 | + | 131.852i | −0.173405 | + | 0.300347i | −0.939608 | − | 0.342252i | \(-0.888810\pi\) |
0.766203 | + | 0.642599i | \(0.222144\pi\) | |||||||
\(440\) | 16.1901 | − | 9.34733i | 0.0367956 | − | 0.0212439i | ||||
\(441\) | 66.4310 | − | 115.062i | 0.150637 | − | 0.260911i | ||||
\(442\) | 17.9183 | 0.0405391 | ||||||||
\(443\) | 293.736 | − | 169.588i | 0.663061 | − | 0.382818i | −0.130381 | − | 0.991464i | \(-0.541620\pi\) |
0.793442 | + | 0.608646i | \(0.208287\pi\) | |||||||
\(444\) | 361.204i | 0.813523i | ||||||||
\(445\) | 184.000i | 0.413484i | ||||||||
\(446\) | −30.3507 | − | 17.5230i | −0.0680508 | − | 0.0392891i | ||||
\(447\) | 186.894i | 0.418107i | ||||||||
\(448\) | 119.073 | − | 68.7470i | 0.265789 | − | 0.153453i | ||||
\(449\) | 64.4246 | + | 111.587i | 0.143485 | + | 0.248523i | 0.928807 | − | 0.370565i | \(-0.120836\pi\) |
−0.785322 | + | 0.619088i | \(0.787503\pi\) | |||||||
\(450\) | −5.02894 | − | 2.90346i | −0.0111754 | − | 0.00645214i | ||||
\(451\) | −109.036 | + | 188.857i | −0.241766 | + | 0.418751i | ||||
\(452\) | −482.867 | − | 278.784i | −1.06829 | − | 0.616778i | ||||
\(453\) | 0.180890 | + | 0.104437i | 0.000399316 | + | 0.000230545i | ||||
\(454\) | 22.5978i | 0.0497750i | ||||||||
\(455\) | 22.3753i | 0.0491764i | ||||||||
\(456\) | 4.55993 | − | 7.89802i | 0.00999984 | − | 0.0173202i | ||||
\(457\) | −125.105 | − | 216.688i | −0.273752 | − | 0.474152i | 0.696067 | − | 0.717976i | \(-0.254931\pi\) |
−0.969820 | + | 0.243824i | \(0.921598\pi\) | |||||||
\(458\) | −6.04264 | − | 10.4662i | −0.0131935 | − | 0.0228519i | ||||
\(459\) | −124.089 | − | 71.6427i | −0.270346 | − | 0.156084i | ||||
\(460\) | 124.284i | 0.270184i | ||||||||
\(461\) | −248.045 | −0.538059 | −0.269029 | − | 0.963132i | \(-0.586703\pi\) | ||||
−0.269029 | + | 0.963132i | \(0.586703\pi\) | |||||||
\(462\) | 3.33075 | + | 5.76903i | 0.00720942 | + | 0.0124871i | ||||
\(463\) | −67.4470 | − | 38.9406i | −0.145674 | − | 0.0841049i | 0.425391 | − | 0.905009i | \(-0.360136\pi\) |
−0.571065 | + | 0.820905i | \(0.693470\pi\) | |||||||
\(464\) | 334.156 | 0.720163 | ||||||||
\(465\) | −79.7557 | + | 46.0470i | −0.171518 | + | 0.0990258i | ||||
\(466\) | −10.6813 | −0.0229213 | ||||||||
\(467\) | −36.2876 | + | 62.8520i | −0.0777037 | + | 0.134587i | −0.902259 | − | 0.431195i | \(-0.858092\pi\) |
0.824555 | + | 0.565782i | \(0.191425\pi\) | |||||||
\(468\) | 93.5271i | 0.199844i | ||||||||
\(469\) | 118.467 | + | 84.3840i | 0.252596 | + | 0.179923i | ||||
\(470\) | 5.98048 | 0.0127244 | ||||||||
\(471\) | −247.588 | − | 142.945i | −0.525665 | − | 0.303493i | ||||
\(472\) | − | 12.3807i | − | 0.0262304i | ||||||
\(473\) | −42.4698 | − | 73.5598i | −0.0897881 | − | 0.155518i | ||||
\(474\) | − | 21.5432i | − | 0.0454499i | ||||||
\(475\) | 92.0392 | − | 159.417i | 0.193767 | − | 0.335614i | ||||
\(476\) | −207.010 | + | 119.517i | −0.434895 | + | 0.251087i | ||||
\(477\) | 55.5696i | 0.116498i | ||||||||
\(478\) | −9.70262 | −0.0202984 | ||||||||
\(479\) | 398.024 | − | 689.398i | 0.830949 | − | 1.43925i | −0.0663382 | − | 0.997797i | \(-0.521132\pi\) |
0.897287 | − | 0.441448i | \(-0.145535\pi\) | |||||||
\(480\) | 7.89264 | − | 4.55682i | 0.0164430 | − | 0.00949337i | ||||
\(481\) | −353.122 | + | 203.875i | −0.734141 | + | 0.423856i | ||||
\(482\) | −28.2209 | − | 16.2933i | −0.0585495 | − | 0.0338036i | ||||
\(483\) | −88.6499 | −0.183540 | ||||||||
\(484\) | −1326.21 | −2.74011 | ||||||||
\(485\) | −19.7427 | + | 34.1953i | −0.0407066 | + | 0.0705058i | ||||
\(486\) | −0.648695 | + | 1.12357i | −0.00133476 | + | 0.00231188i | ||||
\(487\) | 402.257 | + | 232.243i | 0.825990 | + | 0.476885i | 0.852478 | − | 0.522764i | \(-0.175099\pi\) |
−0.0264879 | + | 0.999649i | \(0.508432\pi\) | |||||||
\(488\) | −16.0698 | + | 27.8337i | −0.0329299 | + | 0.0570363i | ||||
\(489\) | −190.565 | + | 110.023i | −0.389704 | + | 0.224996i | ||||
\(490\) | −2.43300 | − | 4.21409i | −0.00496531 | − | 0.00860017i | ||||
\(491\) | −35.1415 | −0.0715713 | −0.0357857 | − | 0.999359i | \(-0.511393\pi\) | ||||
−0.0357857 | + | 0.999359i | \(0.511393\pi\) | |||||||
\(492\) | −35.4265 | + | 61.3605i | −0.0720051 | + | 0.124717i | ||||
\(493\) | −578.908 | −1.17426 | ||||||||
\(494\) | 5.14307 | 0.0104111 | ||||||||
\(495\) | −42.1529 | − | 73.0110i | −0.0851574 | − | 0.147497i | ||||
\(496\) | 641.068i | 1.29248i | ||||||||
\(497\) | −164.752 | − | 95.1198i | −0.331494 | − | 0.191388i | ||||
\(498\) | −10.4846 | − | 18.1598i | −0.0210534 | − | 0.0364655i | ||||
\(499\) | 841.000 | + | 485.552i | 1.68537 | + | 0.973049i | 0.957984 | + | 0.286822i | \(0.0925989\pi\) |
0.727387 | + | 0.686227i | \(0.240734\pi\) | |||||||
\(500\) | 220.306 | − | 127.193i | 0.440611 | − | 0.254387i | ||||
\(501\) | 282.675 | − | 163.203i | 0.564222 | − | 0.325754i | ||||
\(502\) | −14.9769 | − | 25.9407i | −0.0298344 | − | 0.0516747i | ||||
\(503\) | −235.153 | + | 135.766i | −0.467501 | + | 0.269912i | −0.715193 | − | 0.698927i | \(-0.753661\pi\) |
0.247692 | + | 0.968839i | \(0.420328\pi\) | |||||||
\(504\) | 2.16624 | + | 3.75203i | 0.00429809 | + | 0.00744451i | ||||
\(505\) | −11.1693 | − | 19.3458i | −0.0221175 | − | 0.0383086i | ||||
\(506\) | −20.8849 | + | 36.1737i | −0.0412745 | + | 0.0714895i | ||||
\(507\) | 162.066 | − | 93.5686i | 0.319656 | − | 0.184554i | ||||
\(508\) | 357.884 | − | 619.874i | 0.704497 | − | 1.22022i | ||||
\(509\) | −12.6359 | −0.0248250 | −0.0124125 | − | 0.999923i | \(-0.503951\pi\) | ||||
−0.0124125 | + | 0.999923i | \(0.503951\pi\) | |||||||
\(510\) | −4.54469 | + | 2.62388i | −0.00891116 | + | 0.00514486i | ||||
\(511\) | 98.3036i | 0.192375i | ||||||||
\(512\) | − | 105.795i | − | 0.206630i | ||||||
\(513\) | −35.6171 | − | 20.5635i | −0.0694290 | − | 0.0400848i | ||||
\(514\) | 22.1706i | 0.0431335i | ||||||||
\(515\) | −121.428 | + | 70.1065i | −0.235782 | + | 0.136129i | ||||
\(516\) | −13.7987 | − | 23.9000i | −0.0267416 | − | 0.0463178i | ||||
\(517\) | −1003.42 | − | 579.327i | −1.94086 | − | 1.12056i | ||||
\(518\) | −4.71798 | + | 8.17178i | −0.00910806 | + | 0.0157756i | ||||
\(519\) | −75.5459 | − | 43.6164i | −0.145560 | − | 0.0840394i | ||||
\(520\) | 5.93809 | + | 3.42836i | 0.0114194 | + | 0.00659299i | ||||
\(521\) | 474.496i | 0.910741i | 0.890302 | + | 0.455370i | \(0.150493\pi\) | ||||
−0.890302 | + | 0.455370i | \(0.849507\pi\) | |||||||
\(522\) | 5.24178i | 0.0100417i | ||||||||
\(523\) | 29.1150 | − | 50.4287i | 0.0556692 | − | 0.0964219i | −0.836848 | − | 0.547436i | \(-0.815604\pi\) |
0.892517 | + | 0.451014i | \(0.148937\pi\) | |||||||
\(524\) | 104.229 | + | 180.530i | 0.198910 | + | 0.344523i | ||||
\(525\) | 43.7241 | + | 75.7324i | 0.0832841 | + | 0.144252i | ||||
\(526\) | 1.72702 | + | 0.997098i | 0.00328332 | + | 0.00189562i | ||||
\(527\) | − | 1110.62i | − | 2.10744i | ||||||
\(528\) | −586.854 | −1.11147 | ||||||||
\(529\) | −13.4318 | − | 23.2646i | −0.0253910 | − | 0.0439785i | ||||
\(530\) | 1.76254 | + | 1.01761i | 0.00332555 | + | 0.00192001i | ||||
\(531\) | −55.8324 | −0.105146 | ||||||||
\(532\) | −59.4179 | + | 34.3049i | −0.111688 | + | 0.0644829i | ||||
\(533\) | −79.9834 | −0.150063 | ||||||||
\(534\) | −10.0460 | + | 17.4001i | −0.0188126 | + | 0.0325845i | ||||
\(535\) | 35.9395i | 0.0671766i | ||||||||
\(536\) | 40.5460 | − | 18.5102i | 0.0756456 | − | 0.0345340i | ||||
\(537\) | −436.886 | −0.813568 | ||||||||
\(538\) | 18.7842 | + | 10.8451i | 0.0349149 | + | 0.0201581i | ||||
\(539\) | 942.736i | 1.74905i | ||||||||
\(540\) | −13.6957 | − | 23.7217i | −0.0253624 | − | 0.0439290i | ||||
\(541\) | 747.280i | 1.38129i | 0.723192 | + | 0.690647i | \(0.242674\pi\) | ||||
−0.723192 | + | 0.690647i | \(0.757326\pi\) | |||||||
\(542\) | −18.0543 | + | 31.2710i | −0.0333106 | + | 0.0576956i | ||||
\(543\) | 150.155 | − | 86.6921i | 0.276529 | − | 0.159654i | ||||
\(544\) | 109.907i | 0.202035i | ||||||||
\(545\) | 203.179 | 0.372806 | ||||||||
\(546\) | −1.22163 | + | 2.11593i | −0.00223742 | + | 0.00387533i | ||||
\(547\) | 430.040 | − | 248.284i | 0.786179 | − | 0.453901i | −0.0524366 | − | 0.998624i | \(-0.516699\pi\) |
0.838616 | + | 0.544724i | \(0.183365\pi\) | |||||||
\(548\) | −461.179 | + | 266.262i | −0.841567 | + | 0.485879i | ||||
\(549\) | 125.519 | + | 72.4686i | 0.228633 | + | 0.132001i | ||||
\(550\) | 41.2036 | 0.0749157 | ||||||||
\(551\) | −166.163 | −0.301567 | ||||||||
\(552\) | −13.5830 | + | 23.5265i | −0.0246069 | + | 0.0426204i | ||||
\(553\) | −162.213 | + | 280.961i | −0.293333 | + | 0.508068i | ||||
\(554\) | 17.6435 | + | 10.1865i | 0.0318474 | + | 0.0183871i | ||||
\(555\) | 59.7092 | − | 103.419i | 0.107584 | − | 0.186341i | ||||
\(556\) | 412.989 | − | 238.439i | 0.742786 | − | 0.428848i | ||||
\(557\) | 348.722 | + | 604.004i | 0.626071 | + | 1.08439i | 0.988333 | + | 0.152310i | \(0.0486714\pi\) |
−0.362262 | + | 0.932076i | \(0.617995\pi\) | |||||||
\(558\) | −10.0562 | −0.0180219 | ||||||||
\(559\) | 15.5768 | − | 26.9798i | 0.0278655 | − | 0.0482644i | ||||
\(560\) | −45.6161 | −0.0814573 | ||||||||
\(561\) | 1016.70 | 1.81229 | ||||||||
\(562\) | −13.4185 | − | 23.2414i | −0.0238763 | − | 0.0413549i | ||||
\(563\) | − | 155.660i | − | 0.276484i | −0.990398 | − | 0.138242i | \(-0.955855\pi\) | ||
0.990398 | − | 0.138242i | \(-0.0441451\pi\) | |||||||
\(564\) | −326.018 | − | 188.227i | −0.578046 | − | 0.333735i | ||||
\(565\) | 92.1691 | + | 159.642i | 0.163131 | + | 0.282551i | ||||
\(566\) | −19.7187 | − | 11.3846i | −0.0348386 | − | 0.0201141i | ||||
\(567\) | 16.9202 | − | 9.76891i | 0.0298417 | − | 0.0172291i | ||||
\(568\) | −50.4870 | + | 29.1487i | −0.0888855 | + | 0.0513181i | ||||
\(569\) | −114.037 | − | 197.518i | −0.200416 | − | 0.347131i | 0.748246 | − | 0.663421i | \(-0.230896\pi\) |
−0.948663 | + | 0.316290i | \(0.897563\pi\) | |||||||
\(570\) | −1.30446 | + | 0.753129i | −0.00228852 | + | 0.00132128i | ||||
\(571\) | −85.4343 | − | 147.977i | −0.149622 | − | 0.259153i | 0.781466 | − | 0.623948i | \(-0.214472\pi\) |
−0.931088 | + | 0.364795i | \(0.881139\pi\) | |||||||
\(572\) | −331.816 | − | 574.722i | −0.580097 | − | 1.00476i | ||||
\(573\) | −123.690 | + | 214.237i | −0.215863 | + | 0.373886i | ||||
\(574\) | −1.60296 | + | 0.925469i | −0.00279261 | + | 0.00161231i | ||||
\(575\) | −274.165 | + | 474.867i | −0.476808 | + | 0.825856i | ||||
\(576\) | −190.008 | −0.329875 | ||||||||
\(577\) | −653.841 | + | 377.495i | −1.13317 | + | 0.654238i | −0.944731 | − | 0.327846i | \(-0.893677\pi\) |
−0.188442 | + | 0.982084i | \(0.560344\pi\) | |||||||
\(578\) | − | 39.2332i | − | 0.0678775i | ||||||
\(579\) | − | 51.8564i | − | 0.0895619i | ||||||
\(580\) | −95.8414 | − | 55.3341i | −0.165244 | − | 0.0954036i | ||||
\(581\) | 315.781i | 0.543513i | ||||||||
\(582\) | −3.73396 | + | 2.15580i | −0.00641574 | + | 0.00370413i | ||||
\(583\) | −197.150 | − | 341.474i | −0.338165 | − | 0.585718i | ||||
\(584\) | 26.0884 | + | 15.0622i | 0.0446720 | + | 0.0257914i | ||||
\(585\) | 15.4606 | − | 26.7785i | 0.0264283 | − | 0.0457752i | ||||
\(586\) | −1.41958 | − | 0.819595i | −0.00242249 | − | 0.00139863i | ||||
\(587\) | 661.144 | + | 381.712i | 1.12631 | + | 0.650276i | 0.943004 | − | 0.332780i | \(-0.107987\pi\) |
0.183306 | + | 0.983056i | \(0.441320\pi\) | |||||||
\(588\) | 306.300i | 0.520919i | ||||||||
\(589\) | − | 318.780i | − | 0.541222i | ||||||
\(590\) | −1.02242 | + | 1.77088i | −0.00173291 | + | 0.00300149i | ||||
\(591\) | −113.500 | − | 196.588i | −0.192048 | − | 0.332637i | ||||
\(592\) | −415.637 | − | 719.904i | −0.702089 | − | 1.21605i | ||||
\(593\) | 248.734 | + | 143.606i | 0.419449 | + | 0.242169i | 0.694842 | − | 0.719163i | \(-0.255474\pi\) |
−0.275392 | + | 0.961332i | \(0.588808\pi\) | |||||||
\(594\) | − | 9.20577i | − | 0.0154979i | ||||||
\(595\) | 79.0276 | 0.132820 | ||||||||
\(596\) | −215.433 | − | 373.140i | −0.361464 | − | 0.626075i | ||||
\(597\) | −383.343 | − | 221.323i | −0.642115 | − | 0.370725i | ||||
\(598\) | −15.3201 | −0.0256189 | ||||||||
\(599\) | −793.555 | + | 458.159i | −1.32480 | + | 0.764873i | −0.984490 | − | 0.175441i | \(-0.943865\pi\) |
−0.340309 | + | 0.940314i | \(0.610532\pi\) | |||||||
\(600\) | 26.7978 | 0.0446630 | ||||||||
\(601\) | 97.0535 | − | 168.102i | 0.161487 | − | 0.279703i | −0.773915 | − | 0.633289i | \(-0.781704\pi\) |
0.935402 | + | 0.353586i | \(0.115038\pi\) | |||||||
\(602\) | − | 0.720942i | − | 0.00119758i | ||||||
\(603\) | −83.4740 | − | 182.847i | −0.138431 | − | 0.303229i | ||||
\(604\) | −0.481538 | −0.000797248 | ||||||||
\(605\) | 379.719 | + | 219.231i | 0.627634 | + | 0.362365i | ||||
\(606\) | − | 2.43927i | − | 0.00402519i | ||||||
\(607\) | 52.7616 | + | 91.3858i | 0.0869220 | + | 0.150553i | 0.906209 | − | 0.422831i | \(-0.138964\pi\) |
−0.819287 | + | 0.573384i | \(0.805630\pi\) | |||||||
\(608\) | 31.5465i | 0.0518857i | ||||||||
\(609\) | 39.4688 | − | 68.3620i | 0.0648092 | − | 0.112253i | ||||
\(610\) | 4.59709 | − | 2.65413i | 0.00753621 | − | 0.00435103i | ||||
\(611\) | − | 424.964i | − | 0.695522i | ||||||
\(612\) | 330.330 | 0.539755 | ||||||||
\(613\) | 176.689 | − | 306.034i | 0.288236 | − | 0.499240i | −0.685153 | − | 0.728400i | \(-0.740265\pi\) |
0.973389 | + | 0.229160i | \(0.0735979\pi\) | |||||||
\(614\) | 30.3161 | − | 17.5030i | 0.0493747 | − | 0.0285065i | ||||
\(615\) | 20.2865 | − | 11.7124i | 0.0329862 | − | 0.0190446i | ||||
\(616\) | −26.6229 | − | 15.3708i | −0.0432191 | − | 0.0249525i | ||||
\(617\) | 928.398 | 1.50470 | 0.752349 | − | 0.658765i | \(-0.228921\pi\) | ||||
0.752349 | + | 0.658765i | \(0.228921\pi\) | |||||||
\(618\) | −15.3106 | −0.0247744 | ||||||||
\(619\) | 16.3011 | − | 28.2344i | 0.0263346 | − | 0.0456129i | −0.852558 | − | 0.522633i | \(-0.824950\pi\) |
0.878892 | + | 0.477020i | \(0.158283\pi\) | |||||||
\(620\) | 106.157 | − | 183.869i | 0.171221 | − | 0.296563i | ||||
\(621\) | 106.095 | + | 61.2542i | 0.170846 | + | 0.0986380i | ||||
\(622\) | −12.0323 | + | 20.8406i | −0.0193446 | + | 0.0335058i | ||||
\(623\) | 262.034 | − | 151.285i | 0.420600 | − | 0.242833i | ||||
\(624\) | −107.621 | − | 186.406i | −0.172470 | − | 0.298727i | ||||
\(625\) | 497.326 | 0.795722 | ||||||||
\(626\) | 16.1832 | − | 28.0301i | 0.0258518 | − | 0.0447766i | ||||
\(627\) | 291.821 | 0.465425 | ||||||||
\(628\) | 659.092 | 1.04951 | ||||||||
\(629\) | 720.070 | + | 1247.20i | 1.14479 | + | 1.98283i | ||||
\(630\) | − | 0.715563i | − | 0.00113581i | ||||||
\(631\) | 49.8363 | + | 28.7730i | 0.0789799 | + | 0.0455991i | 0.538970 | − | 0.842325i | \(-0.318814\pi\) |
−0.459990 | + | 0.887924i | \(0.652147\pi\) | |||||||
\(632\) | 49.7089 | + | 86.0983i | 0.0786533 | + | 0.136231i | ||||
\(633\) | −96.1784 | − | 55.5286i | −0.151941 | − | 0.0877230i | ||||
\(634\) | 18.3611 | − | 10.6008i | 0.0289607 | − | 0.0167205i | ||||
\(635\) | −204.938 | + | 118.321i | −0.322736 | + | 0.186332i | ||||
\(636\) | −64.0551 | − | 110.947i | −0.100716 | − | 0.174445i | ||||
\(637\) | −299.446 | + | 172.886i | −0.470089 | + | 0.271406i | ||||
\(638\) | −18.5968 | − | 32.2106i | −0.0291486 | − | 0.0504868i | ||||
\(639\) | 131.449 | + | 227.677i | 0.205711 | + | 0.356302i | ||||
\(640\) | −14.0030 | + | 24.2539i | −0.0218797 | + | 0.0378967i | ||||
\(641\) | 534.834 | − | 308.787i | 0.834375 | − | 0.481727i | −0.0209732 | − | 0.999780i | \(-0.506676\pi\) |
0.855348 | + | 0.518053i | \(0.173343\pi\) | |||||||
\(642\) | −1.96221 | + | 3.39864i | −0.00305640 | + | 0.00529383i | ||||
\(643\) | 127.673 | 0.198558 | 0.0992791 | − | 0.995060i | \(-0.468346\pi\) | ||||
0.0992791 | + | 0.995060i | \(0.468346\pi\) | |||||||
\(644\) | 176.993 | − | 102.187i | 0.274833 | − | 0.158675i | ||||
\(645\) | 9.12400i | 0.0141457i | ||||||||
\(646\) | − | 18.1649i | − | 0.0281191i | ||||||
\(647\) | −485.276 | − | 280.174i | −0.750041 | − | 0.433036i | 0.0756679 | − | 0.997133i | \(-0.475891\pi\) |
−0.825709 | + | 0.564097i | \(0.809224\pi\) | |||||||
\(648\) | − | 5.98720i | − | 0.00923951i | ||||||
\(649\) | 343.089 | − | 198.082i | 0.528642 | − | 0.305211i | ||||
\(650\) | 7.55621 | + | 13.0877i | 0.0116249 | + | 0.0201350i | ||||
\(651\) | 131.150 | + | 75.7197i | 0.201460 | + | 0.116313i | ||||
\(652\) | 253.647 | − | 439.330i | 0.389029 | − | 0.673819i | ||||
\(653\) | 523.760 | + | 302.393i | 0.802083 | + | 0.463083i | 0.844199 | − | 0.536030i | \(-0.180077\pi\) |
−0.0421163 | + | 0.999113i | \(0.513410\pi\) | |||||||
\(654\) | 19.2138 | + | 11.0931i | 0.0293789 | + | 0.0169619i | ||||
\(655\) | − | 68.9187i | − | 0.105219i | ||||||
\(656\) | − | 163.061i | − | 0.248568i | ||||||
\(657\) | 67.9246 | − | 117.649i | 0.103386 | − | 0.179070i | ||||
\(658\) | −4.91716 | − | 8.51677i | −0.00747289 | − | 0.0129434i | ||||
\(659\) | −144.030 | − | 249.468i | −0.218559 | − | 0.378555i | 0.735809 | − | 0.677189i | \(-0.236802\pi\) |
−0.954368 | + | 0.298634i | \(0.903469\pi\) | |||||||
\(660\) | 168.320 | + | 97.1794i | 0.255030 | + | 0.147241i | ||||
\(661\) | − | 227.874i | − | 0.344742i | −0.985032 | − | 0.172371i | \(-0.944857\pi\) | ||
0.985032 | − | 0.172371i | \(-0.0551428\pi\) | |||||||
\(662\) | −5.37792 | −0.00812375 | ||||||||
\(663\) | 186.449 | + | 322.939i | 0.281220 | + | 0.487087i | ||||
\(664\) | 83.8039 | + | 48.3842i | 0.126211 | + | 0.0728678i | ||||
\(665\) | 22.6832 | 0.0341101 | ||||||||
\(666\) | 11.2929 | − | 6.51994i | 0.0169563 | − | 0.00978970i | ||||
\(667\) | 494.964 | 0.742076 | ||||||||
\(668\) | −376.248 | + | 651.680i | −0.563245 | + | 0.975569i | ||||
\(669\) | − | 729.341i | − | 1.09020i | ||||||
\(670\) | −7.32810 | − | 0.700735i | −0.0109375 | − | 0.00104587i | ||||
\(671\) | −1028.42 | −1.53266 | ||||||||
\(672\) | −12.9787 | − | 7.49324i | −0.0193135 | − | 0.0111506i | ||||
\(673\) | − | 1134.40i | − | 1.68559i | −0.538232 | − | 0.842797i | \(-0.680908\pi\) | ||
0.538232 | − | 0.842797i | \(-0.319092\pi\) | |||||||
\(674\) | 15.5552 | + | 26.9424i | 0.0230789 | + | 0.0399739i | ||||
\(675\) | − | 120.848i | − | 0.179034i | ||||||
\(676\) | −215.713 | + | 373.626i | −0.319103 | + | 0.552702i | ||||
\(677\) | −442.248 | + | 255.332i | −0.653247 | + | 0.377153i | −0.789699 | − | 0.613494i | \(-0.789763\pi\) |
0.136452 | + | 0.990647i | \(0.456430\pi\) | |||||||
\(678\) | 20.1288i | 0.0296885i | ||||||||
\(679\) | 64.9298 | 0.0956256 | ||||||||
\(680\) | 12.1087 | − | 20.9729i | 0.0178069 | − | 0.0308424i | ||||
\(681\) | −407.278 | + | 235.142i | −0.598058 | + | 0.345289i | ||||
\(682\) | 61.7951 | − | 35.6774i | 0.0906086 | − | 0.0523129i | ||||
\(683\) | −397.948 | − | 229.756i | −0.582648 | − | 0.336392i | 0.179537 | − | 0.983751i | \(-0.442540\pi\) |
−0.762185 | + | 0.647359i | \(0.775873\pi\) | |||||||
\(684\) | 94.8144 | 0.138618 | ||||||||
\(685\) | 176.058 | 0.257020 | ||||||||
\(686\) | −8.42740 | + | 14.5967i | −0.0122848 | + | 0.0212780i | ||||
\(687\) | 125.753 | − | 217.811i | 0.183047 | − | 0.317047i | ||||
\(688\) | 55.0033 | + | 31.7562i | 0.0799467 | + | 0.0461573i | ||||
\(689\) | 72.3095 | − | 125.244i | 0.104948 | − | 0.181776i | ||||
\(690\) | 3.88569 | − | 2.24341i | 0.00563144 | − | 0.00325131i | ||||
\(691\) | −37.8371 | − | 65.5358i | −0.0547570 | − | 0.0948419i | 0.837348 | − | 0.546671i | \(-0.184105\pi\) |
−0.892105 | + | 0.451829i | \(0.850772\pi\) | |||||||
\(692\) | 201.107 | 0.290617 | ||||||||
\(693\) | −69.3163 | + | 120.059i | −0.100024 | + | 0.173246i | ||||
\(694\) | 39.4817 | 0.0568900 | ||||||||
\(695\) | −157.662 | −0.226851 | ||||||||
\(696\) | −12.0949 | − | 20.9490i | −0.0173777 | − | 0.0300991i | ||||
\(697\) | 282.495i | 0.405301i | ||||||||
\(698\) | −1.41318 | − | 0.815899i | −0.00202461 | − | 0.00116891i | ||||
\(699\) | −111.144 | − | 192.508i | −0.159005 | − | 0.275405i | ||||
\(700\) | −174.594 | − | 100.802i | −0.249420 | − | 0.144002i | ||||
\(701\) | 635.047 | − | 366.645i | 0.905916 | − | 0.523031i | 0.0268011 | − | 0.999641i | \(-0.491468\pi\) |
0.879115 | + | 0.476610i | \(0.158135\pi\) | |||||||
\(702\) | 2.92408 | − | 1.68822i | 0.00416536 | − | 0.00240487i | ||||
\(703\) | 206.681 | + | 357.982i | 0.293999 | + | 0.509220i | ||||
\(704\) | 1167.59 | − | 674.111i | 1.65851 | − | 0.957543i | ||||
\(705\) | 62.2299 | + | 107.785i | 0.0882694 | + | 0.152887i | ||||
\(706\) | −13.1946 | − | 22.8537i | −0.0186892 | − | 0.0323707i | ||||
\(707\) | −18.3669 | + | 31.8123i | −0.0259786 | + | 0.0449962i | ||||
\(708\) | 111.471 | − | 64.3580i | 0.157445 | − | 0.0909012i | ||||
\(709\) | −81.5736 | + | 141.290i | −0.115054 | + | 0.199280i | −0.917802 | − | 0.397040i | \(-0.870038\pi\) |
0.802747 | + | 0.596320i | \(0.203371\pi\) | |||||||
\(710\) | 9.62854 | 0.0135613 | ||||||||
\(711\) | 388.271 | − | 224.168i | 0.546091 | − | 0.315286i | ||||
\(712\) | − | 92.7202i | − | 0.130225i | ||||||
\(713\) | 949.575i | 1.33180i | ||||||||
\(714\) | 7.47330 | + | 4.31471i | 0.0104668 | + | 0.00604301i | ||||
\(715\) | 219.404i | 0.306859i | ||||||||
\(716\) | 872.259 | − | 503.599i | 1.21824 | − | 0.703351i | ||||
\(717\) | −100.961 | − | 174.869i | −0.140810 | − | 0.243890i | ||||
\(718\) | −26.8406 | − | 15.4964i | −0.0373824 | − | 0.0215827i | ||||
\(719\) | −339.980 | + | 588.863i | −0.472851 | + | 0.819003i | −0.999517 | − | 0.0310698i | \(-0.990109\pi\) |
0.526666 | + | 0.850072i | \(0.323442\pi\) | |||||||
\(720\) | 54.5930 | + | 31.5193i | 0.0758236 | + | 0.0437767i | ||||
\(721\) | 199.676 | + | 115.283i | 0.276944 | + | 0.159893i | ||||
\(722\) | 24.8313i | 0.0343924i | ||||||||
\(723\) | − | 678.160i | − | 0.937981i | ||||||
\(724\) | −199.860 | + | 346.168i | −0.276050 | + | 0.478133i | ||||
\(725\) | −244.128 | − | 422.842i | −0.336728 | − | 0.583230i | ||||
\(726\) | 23.9389 | + | 41.4634i | 0.0329737 | + | 0.0571121i | ||||
\(727\) | 696.345 | + | 402.035i | 0.957833 | + | 0.553005i | 0.895505 | − | 0.445051i | \(-0.146814\pi\) |
0.0623277 | + | 0.998056i | \(0.480148\pi\) | |||||||
\(728\) | − | 11.2752i | − | 0.0154879i | ||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −2.48771 | − | 4.30884i | −0.00340782 | − | 0.00590251i | ||||
\(731\) | −95.2905 | − | 55.0160i | −0.130356 | − | 0.0752613i | ||||
\(732\) | −334.139 | −0.456474 | ||||||||
\(733\) | 1098.27 | − | 634.089i | 1.49833 | − | 0.865060i | 0.498329 | − | 0.866988i | \(-0.333947\pi\) |
0.999998 | + | 0.00192791i | \(0.000613674\pi\) | |||||||
\(734\) | 18.0152 | 0.0245438 | ||||||||
\(735\) | 50.6332 | − | 87.6993i | 0.0688888 | − | 0.119319i | ||||
\(736\) | − | 93.9701i | − | 0.127677i | ||||||
\(737\) | 1161.65 | + | 827.442i | 1.57619 | + | 1.12272i | ||||
\(738\) | 2.55788 | 0.00346596 | ||||||||
\(739\) | −310.358 | − | 179.185i | −0.419970 | − | 0.242470i | 0.275094 | − | 0.961417i | \(-0.411291\pi\) |
−0.695065 | + | 0.718947i | \(0.744624\pi\) | |||||||
\(740\) | 275.307i | 0.372037i | ||||||||
\(741\) | 53.5162 | + | 92.6928i | 0.0722216 | + | 0.125091i | ||||
\(742\) | − | 3.34670i | − | 0.00451038i | ||||||
\(743\) | −610.173 | + | 1056.85i | −0.821229 | + | 1.42241i | 0.0835379 | + | 0.996505i | \(0.473378\pi\) |
−0.904767 | + | 0.425906i | \(0.859955\pi\) | |||||||
\(744\) | 40.1900 | − | 23.2037i | 0.0540188 | − | 0.0311878i | ||||
\(745\) | 142.449i | 0.191207i | ||||||||
\(746\) | −15.5068 | −0.0207866 | ||||||||
\(747\) | 218.194 | − | 377.924i | 0.292094 | − | 0.505922i | ||||
\(748\) | −2029.87 | + | 1171.95i | −2.71373 | + | 1.56677i | ||||
\(749\) | 51.1812 | − | 29.5495i | 0.0683327 | − | 0.0394519i | ||||
\(750\) | −7.95328 | − | 4.59183i | −0.0106044 | − | 0.00612244i | ||||
\(751\) | −512.994 | −0.683081 | −0.341541 | − | 0.939867i | \(-0.610949\pi\) | ||||
−0.341541 | + | 0.939867i | \(0.610949\pi\) | |||||||
\(752\) | 866.368 | 1.15208 | ||||||||
\(753\) | 311.684 | − | 539.852i | 0.413923 | − | 0.716935i | ||||
\(754\) | 6.82082 | − | 11.8140i | 0.00904618 | − | 0.0156684i | ||||
\(755\) | 0.137873 | + | 0.0796011i | 0.000182613 | + | 0.000105432i | ||||
\(756\) | −22.5213 | + | 39.0080i | −0.0297900 | + | 0.0515978i | ||||
\(757\) | 937.541 | − | 541.290i | 1.23850 | − | 0.715046i | 0.269709 | − | 0.962942i | \(-0.413072\pi\) |
0.968787 | + | 0.247896i | \(0.0797391\pi\) | |||||||
\(758\) | 9.94748 | + | 17.2295i | 0.0131233 | + | 0.0227303i | ||||
\(759\) | −869.271 | −1.14529 | ||||||||
\(760\) | 3.47554 | − | 6.01982i | 0.00457308 | − | 0.00792081i | ||||
\(761\) | −689.803 | −0.906443 | −0.453221 | − | 0.891398i | \(-0.649725\pi\) | ||||
−0.453221 | + | 0.891398i | \(0.649725\pi\) | |||||||
\(762\) | −25.8401 | −0.0339109 | ||||||||
\(763\) | −167.054 | − | 289.346i | −0.218944 | − | 0.379222i | ||||
\(764\) | − | 570.309i | − | 0.746477i | ||||||
\(765\) | −94.5796 | − | 54.6055i | −0.123633 | − | 0.0713798i | ||||
\(766\) | −14.7873 | − | 25.6124i | −0.0193046 | − | 0.0334366i | ||||
\(767\) | 125.836 | + | 72.6514i | 0.164062 | + | 0.0947215i | ||||
\(768\) | 377.367 | − | 217.873i | 0.491364 | − | 0.283689i | ||||
\(769\) | −1062.06 | + | 613.178i | −1.38109 | + | 0.797370i | −0.992288 | − | 0.123953i | \(-0.960443\pi\) |
−0.388798 | + | 0.921323i | \(0.627110\pi\) | |||||||
\(770\) | 2.53868 | + | 4.39712i | 0.00329698 | + | 0.00571054i | ||||
\(771\) | −399.578 | + | 230.697i | −0.518260 | + | 0.299217i | ||||
\(772\) | 59.7749 | + | 103.533i | 0.0774286 | + | 0.134110i | ||||
\(773\) | −412.476 | − | 714.429i | −0.533604 | − | 0.924229i | −0.999230 | − | 0.0392476i | \(-0.987504\pi\) |
0.465625 | − | 0.884982i | \(-0.345829\pi\) | |||||||
\(774\) | −0.498148 | + | 0.862817i | −0.000643602 | + | 0.00111475i | ||||
\(775\) | 811.209 | − | 468.352i | 1.04672 | − | 0.604325i | ||||
\(776\) | 9.94860 | − | 17.2315i | 0.0128204 | − | 0.0222055i | ||||
\(777\) | −196.372 | −0.252731 | ||||||||
\(778\) | 5.26281 | − | 3.03848i | 0.00676454 | − | 0.00390551i | ||||
\(779\) | 81.0842i | 0.104088i | ||||||||
\(780\) | 71.2857i | 0.0913919i | ||||||||
\(781\) | −1615.51 | − | 932.713i | −2.06851 | − | 1.19425i | ||||
\(782\) | 54.1093i | 0.0691934i | ||||||||
\(783\) | −94.4718 | + | 54.5433i | −0.120654 | + | 0.0696594i | ||||
\(784\) | −352.459 | − | 610.477i | −0.449565 | − | 0.778670i | ||||
\(785\) | −188.710 | − | 108.952i | −0.240395 | − | 0.138792i | ||||
\(786\) | 3.76279 | − | 6.51734i | 0.00478726 | − | 0.00829178i | ||||
\(787\) | 175.898 | + | 101.555i | 0.223505 | + | 0.129041i | 0.607572 | − | 0.794265i | \(-0.292144\pi\) |
−0.384067 | + | 0.923305i | \(0.625477\pi\) | |||||||
\(788\) | 453.215 | + | 261.664i | 0.575146 | + | 0.332061i | ||||
\(789\) | 41.5012i | 0.0525998i | ||||||||
\(790\) | − | 16.4201i | − | 0.0207849i | ||||||
\(791\) | 151.563 | − | 262.515i | 0.191609 | − | 0.331877i | ||||
\(792\) | 21.2414 | + | 36.7912i | 0.0268200 | + | 0.0464535i | ||||
\(793\) | −188.598 | − | 326.662i | −0.237829 | − | 0.411932i | ||||
\(794\) | 7.54122 | + | 4.35392i | 0.00949776 | + | 0.00548353i | ||||
\(795\) | 42.3548i | 0.0532764i | ||||||||
\(796\) | 1020.48 | 1.28201 | ||||||||
\(797\) | 522.435 | + | 904.883i | 0.655501 | + | 1.13536i | 0.981768 | + | 0.190084i | \(0.0608760\pi\) |
−0.326266 | + | 0.945278i | \(0.605791\pi\) | |||||||
\(798\) | 2.14505 | + | 1.23845i | 0.00268804 | + | 0.00155194i | ||||
\(799\) | −1500.94 | −1.87852 | ||||||||
\(800\) | −80.2774 | + | 46.3482i | −0.100347 | + | 0.0579352i | ||||
\(801\) | −418.133 | −0.522013 | ||||||||
\(802\) | −6.83919 | + | 11.8458i | −0.00852767 | + | 0.0147704i | ||||
\(803\) | 963.933i | 1.20041i | ||||||||
\(804\) | 377.427 | + | 268.840i | 0.469437 | + | 0.334379i | ||||
\(805\) | −67.5683 | −0.0839358 | ||||||||
\(806\) | 22.6648 | + | 13.0855i | 0.0281201 | + | 0.0162352i | ||||
\(807\) | 451.393i | 0.559347i | ||||||||
\(808\) | 5.62837 | + | 9.74862i | 0.00696581 | + | 0.0120651i | ||||
\(809\) | − | 829.138i | − | 1.02489i | −0.858719 | − | 0.512447i | \(-0.828739\pi\) | ||
0.858719 | − | 0.512447i | \(-0.171261\pi\) | |||||||
\(810\) | −0.494431 | + | 0.856380i | −0.000610409 | + | 0.00105726i | ||||
\(811\) | 1073.72 | − | 619.912i | 1.32394 | − | 0.764379i | 0.339588 | − | 0.940574i | \(-0.389712\pi\) |
0.984355 | + | 0.176195i | \(0.0563789\pi\) | |||||||
\(812\) | 181.983i | 0.224117i | ||||||||
\(813\) | −751.457 | −0.924302 | ||||||||
\(814\) | −46.2629 | + | 80.1297i | −0.0568341 | + | 0.0984395i | ||||
\(815\) | −145.248 | + | 83.8587i | −0.178218 | + | 0.102894i | ||||
\(816\) | −658.370 | + | 380.110i | −0.806827 | + | 0.465822i | ||||
\(817\) | −27.3511 | − | 15.7912i | −0.0334775 | − | 0.0193283i | ||||
\(818\) | −14.2858 | −0.0174643 | ||||||||
\(819\) | −50.8468 | −0.0620840 | ||||||||
\(820\) | −27.0019 | + | 46.7686i | −0.0329291 | + | 0.0570349i | ||||
\(821\) | −498.817 | + | 863.976i | −0.607572 | + | 1.05235i | 0.384067 | + | 0.923305i | \(0.374523\pi\) |
−0.991639 | + | 0.129041i | \(0.958810\pi\) | |||||||
\(822\) | 16.6491 | + | 9.61235i | 0.0202544 | + | 0.0116939i | ||||
\(823\) | 236.793 | − | 410.137i | 0.287719 | − | 0.498343i | −0.685546 | − | 0.728029i | \(-0.740436\pi\) |
0.973265 | + | 0.229686i | \(0.0737698\pi\) | |||||||
\(824\) | 61.1892 | − | 35.3276i | 0.0742587 | − | 0.0428733i | ||||
\(825\) | 428.744 | + | 742.607i | 0.519690 | + | 0.900130i | ||||
\(826\) | 3.36253 | 0.00407086 | ||||||||
\(827\) | 334.190 | − | 578.834i | 0.404099 | − | 0.699920i | −0.590117 | − | 0.807318i | \(-0.700919\pi\) |
0.994216 | + | 0.107398i | \(0.0342519\pi\) | |||||||
\(828\) | −282.431 | −0.341100 | ||||||||
\(829\) | 611.395 | 0.737509 | 0.368754 | − | 0.929527i | \(-0.379784\pi\) | ||||
0.368754 | + | 0.929527i | \(0.379784\pi\) | |||||||
\(830\) | −7.99127 | − | 13.8413i | −0.00962803 | − | 0.0166762i | ||||
\(831\) | 423.981i | 0.510206i | ||||||||
\(832\) | 428.243 | + | 247.246i | 0.514715 | + | 0.297171i | ||||
\(833\) | 610.618 | + | 1057.62i | 0.733034 | + | 1.26965i | ||||
\(834\) | −14.9094 | − | 8.60794i | −0.0178770 | − | 0.0103213i | ||||
\(835\) | 215.453 | − | 124.392i | 0.258028 | − | 0.148972i | ||||
\(836\) | −582.632 | + | 336.383i | −0.696928 | + | 0.402372i | ||||
\(837\) | −104.640 | − | 181.241i | −0.125018 | − | 0.216537i | ||||
\(838\) | −47.2806 | + | 27.2975i | −0.0564208 | + | 0.0325745i | ||||
\(839\) | −41.7200 | − | 72.2612i | −0.0497259 | − | 0.0861278i | 0.840091 | − | 0.542445i | \(-0.182501\pi\) |
−0.889817 | + | 0.456318i | \(0.849168\pi\) | |||||||
\(840\) | 1.65109 | + | 2.85977i | 0.00196558 | + | 0.00340449i | ||||
\(841\) | 200.131 | − | 346.638i | 0.237968 | − | 0.412173i | ||||
\(842\) | 44.1504 | − | 25.4902i | 0.0524352 | − | 0.0302735i | ||||
\(843\) | 279.252 | − | 483.678i | 0.331259 | − | 0.573758i | ||||
\(844\) | 256.032 | 0.303355 | ||||||||
\(845\) | 123.525 | − | 71.3174i | 0.146184 | − | 0.0843992i | ||||
\(846\) | 13.5904i | 0.0160643i | ||||||||
\(847\) | − | 721.007i | − | 0.851248i | ||||||
\(848\) | 255.332 | + | 147.416i | 0.301100 | + | 0.173840i | ||||
\(849\) | − | 473.849i | − | 0.558126i | ||||||
\(850\) | 46.2248 | − | 26.6879i | 0.0543822 | − | 0.0313976i | ||||
\(851\) | −615.657 | − | 1066.35i | −0.723451 | − | 1.25305i | ||||
\(852\) | −524.887 | − | 303.044i | −0.616065 | − | 0.355685i | ||||
\(853\) | −351.581 | + | 608.956i | −0.412170 | + | 0.713899i | −0.995127 | − | 0.0986038i | \(-0.968562\pi\) |
0.582957 | + | 0.812503i | \(0.301896\pi\) | |||||||
\(854\) | −7.55946 | − | 4.36445i | −0.00885182 | − | 0.00511060i | ||||
\(855\) | −27.1471 | − | 15.6734i | −0.0317510 | − | 0.0183314i | ||||
\(856\) | − | 18.1104i | − | 0.0211570i | ||||||
\(857\) | − | 728.725i | − | 0.850321i | −0.905118 | − | 0.425161i | \(-0.860218\pi\) | ||
0.905118 | − | 0.425161i | \(-0.139782\pi\) | |||||||
\(858\) | −11.9789 | + | 20.7481i | −0.0139615 | + | 0.0241819i | ||||
\(859\) | −347.836 | − | 602.470i | −0.404931 | − | 0.701362i | 0.589382 | − | 0.807854i | \(-0.299371\pi\) |
−0.994313 | + | 0.106493i | \(0.966038\pi\) | |||||||
\(860\) | −10.5172 | − | 18.2164i | −0.0122294 | − | 0.0211819i | ||||
\(861\) | −33.3592 | − | 19.2599i | −0.0387447 | − | 0.0223693i | ||||
\(862\) | − | 54.4553i | − | 0.0631732i | ||||||
\(863\) | 1156.79 | 1.34043 | 0.670213 | − | 0.742169i | \(-0.266203\pi\) | ||||
0.670213 | + | 0.742169i | \(0.266203\pi\) | |||||||
\(864\) | 10.3552 | + | 17.9357i | 0.0119852 | + | 0.0207589i | ||||
\(865\) | −57.5805 | − | 33.2441i | −0.0665671 | − | 0.0384325i | ||||
\(866\) | 23.2281 | 0.0268223 | ||||||||
\(867\) | 707.094 | − | 408.241i | 0.815564 | − | 0.470866i | ||||
\(868\) | −349.129 | −0.402222 | ||||||||
\(869\) | −1590.61 | + | 2755.01i | −1.83039 | + | 3.17033i | ||||
\(870\) | 3.99525i | 0.00459224i | ||||||||
\(871\) | −49.7932 | + | 520.724i | −0.0571678 | + | 0.597846i | ||||
\(872\) | −102.385 | −0.117414 | ||||||||
\(873\) | −77.7074 | − | 44.8644i | −0.0890119 | − | 0.0513911i | ||||
\(874\) | 15.5309i | 0.0177699i | ||||||||
\(875\) | 69.1498 | + | 119.771i | 0.0790284 | + | 0.136881i | ||||
\(876\) | 313.187i | 0.357520i | ||||||||
\(877\) | 45.3347 | − | 78.5221i | 0.0516930 | − | 0.0895349i | −0.839021 | − | 0.544099i | \(-0.816872\pi\) |
0.890714 | + | 0.454564i | \(0.150205\pi\) | |||||||
\(878\) | −10.9737 | + | 6.33569i | −0.0124986 | + | 0.00721605i | ||||
\(879\) | − | 34.1132i | − | 0.0388091i | ||||||
\(880\) | −447.296 | −0.508291 | ||||||||
\(881\) | 243.251 | − | 421.323i | 0.276108 | − | 0.478233i | −0.694306 | − | 0.719680i | \(-0.744289\pi\) |
0.970414 | + | 0.241447i | \(0.0776219\pi\) | |||||||
\(882\) | 9.57633 | − | 5.52890i | 0.0108575 | − | 0.00626859i | ||||
\(883\) | −1351.19 | + | 780.108i | −1.53022 | + | 0.883475i | −0.530873 | + | 0.847452i | \(0.678136\pi\) |
−0.999351 | + | 0.0360235i | \(0.988531\pi\) | |||||||
\(884\) | −744.504 | − | 429.839i | −0.842199 | − | 0.486244i | ||||
\(885\) | −42.5551 | −0.0480848 | ||||||||
\(886\) | 28.2289 | 0.0318611 | ||||||||
\(887\) | −345.476 | + | 598.381i | −0.389488 | + | 0.674613i | −0.992381 | − | 0.123209i | \(-0.960681\pi\) |
0.602893 | + | 0.797822i | \(0.294015\pi\) | |||||||
\(888\) | −30.0882 | + | 52.1144i | −0.0338832 | + | 0.0586874i | ||||
\(889\) | 337.000 | + | 194.567i | 0.379077 | + | 0.218860i | ||||
\(890\) | −7.65695 | + | 13.2622i | −0.00860332 | + | 0.0149014i | ||||
\(891\) | 165.914 | − | 95.7907i | 0.186211 | − | 0.107509i | ||||
\(892\) | 840.712 | + | 1456.16i | 0.942502 | + | 1.63246i | ||||
\(893\) | −430.813 | −0.482433 | ||||||||
\(894\) | −7.77737 | + | 13.4708i | −0.00869952 | + | 0.0150680i | ||||
\(895\) | −332.992 | −0.372058 | ||||||||
\(896\) | 46.0531 | 0.0513985 | ||||||||
\(897\) | −159.413 | − | 276.111i | −0.177718 | − | 0.307817i | ||||
\(898\) | 10.7238i | 0.0119419i | ||||||||
\(899\) | −732.260 | − | 422.771i | −0.814527 | − | 0.470268i | ||||
\(900\) | 139.301 | + | 241.277i | 0.154779 | + | 0.268086i | ||||
\(901\) | −442.351 | − | 255.391i | −0.490955 | − | 0.283453i | ||||
\(902\) | −15.7181 | + | 9.07484i | −0.0174258 | + | 0.0100608i | ||||
\(903\) | 12.9934 | − | 7.50176i | 0.0143892 | − | 0.00830760i | ||||
\(904\) | −46.4452 | − | 80.4455i | −0.0513775 | − | 0.0889884i | ||||
\(905\) | 114.447 | − | 66.0761i | 0.126461 | − | 0.0730123i | ||||
\(906\) | 0.00869204 | + | 0.0150550i | 9.59386e−6 | + | 1.66171e-5i | ||||
\(907\) | −647.886 | − | 1122.17i | −0.714318 | − | 1.23723i | −0.963222 | − | 0.268707i | \(-0.913404\pi\) |
0.248904 | − | 0.968528i | \(-0.419930\pi\) | |||||||
\(908\) | 542.097 | − | 938.939i | 0.597023 | − | 1.03407i | ||||
\(909\) | 43.9626 | − | 25.3818i | 0.0483637 | − | 0.0279228i | ||||
\(910\) | −0.931120 | + | 1.61275i | −0.00102321 | + | 0.00177225i | ||||
\(911\) | 219.215 | 0.240631 | 0.120316 | − | 0.992736i | \(-0.461609\pi\) | ||||
0.120316 | + | 0.992736i | \(0.461609\pi\) | |||||||
\(912\) | −188.971 | + | 109.103i | −0.207206 | + | 0.119630i | ||||
\(913\) | 3096.44i | 3.39150i | ||||||||
\(914\) | − | 20.8243i | − | 0.0227837i | ||||||
\(915\) | 95.6700 | + | 55.2351i | 0.104557 | + | 0.0603662i | ||||
\(916\) | 579.824i | 0.632996i | ||||||||
\(917\) | −98.1466 | + | 56.6650i | −0.107030 | + | 0.0617939i | ||||
\(918\) | −5.96265 | − | 10.3276i | −0.00649526 | − | 0.0112501i | ||||
\(919\) | −1105.73 | − | 638.393i | −1.20319 | − | 0.694661i | −0.241925 | − | 0.970295i | \(-0.577779\pi\) |
−0.961263 | + | 0.275634i | \(0.911112\pi\) | |||||||
\(920\) | −10.3529 | + | 17.9317i | −0.0112531 | + | 0.0194910i | ||||
\(921\) | 630.908 | + | 364.255i | 0.685025 | + | 0.395499i | ||||
\(922\) | −17.8784 | − | 10.3221i | −0.0193909 | − | 0.0111953i | ||||
\(923\) | − | 684.190i | − | 0.741267i | ||||||
\(924\) | − | 319.604i | − | 0.345892i | ||||||
\(925\) | −607.312 | + | 1051.90i | −0.656554 | + | 1.13718i | ||||
\(926\) | −3.24093 | − | 5.61346i | −0.00349993 | − | 0.00606205i | ||||
\(927\) | −159.314 | − | 275.940i | −0.171860 | − | 0.297670i | ||||
\(928\) | 72.4646 | + | 41.8375i | 0.0780869 | + | 0.0450835i | ||||
\(929\) | − | 1104.12i | − | 1.18850i | −0.804280 | − | 0.594251i | \(-0.797449\pi\) | ||
0.804280 | − | 0.594251i | \(-0.202551\pi\) | |||||||
\(930\) | −7.66476 | −0.00824168 | ||||||||
\(931\) | 175.265 | + | 303.568i | 0.188255 | + | 0.326066i | ||||
\(932\) | 443.808 | + | 256.233i | 0.476189 | + | 0.274928i | ||||
\(933\) | −500.810 | −0.536773 | ||||||||
\(934\) | −5.23103 | + | 3.02014i | −0.00560067 | + | 0.00323355i | ||||
\(935\) | 774.919 | 0.828790 | ||||||||
\(936\) | −7.79079 | + | 13.4941i | −0.00832350 | + | 0.0144167i | ||||
\(937\) | 1371.16i | 1.46335i | 0.681655 | + | 0.731674i | \(0.261260\pi\) | ||||
−0.681655 | + | 0.731674i | \(0.738740\pi\) | |||||||
\(938\) | 5.02726 | + | 11.0120i | 0.00535955 | + | 0.0117399i | ||||
\(939\) | 673.578 | 0.717335 | ||||||||
\(940\) | −248.489 | − | 143.465i | −0.264350 | − | 0.152622i | ||||
\(941\) | − | 1180.46i | − | 1.25447i | −0.778828 | − | 0.627237i | \(-0.784186\pi\) | ||
0.778828 | − | 0.627237i | \(-0.215814\pi\) | |||||||
\(942\) | −11.8970 | − | 20.6062i | −0.0126295 | − | 0.0218749i | ||||
\(943\) | − | 241.532i | − | 0.256132i | ||||||
\(944\) | −148.113 | + | 256.540i | −0.156900 | + | 0.271758i | ||||
\(945\) | 12.8965 | − | 7.44579i | 0.0136471 | − | 0.00787914i | ||||
\(946\) | − | 7.06932i | − | 0.00747285i | ||||||
\(947\) | −1175.44 | −1.24123 | −0.620614 | − | 0.784116i | \(-0.713117\pi\) | ||||
−0.620614 | + | 0.784116i | \(0.713117\pi\) | |||||||
\(948\) | −516.798 | + | 895.120i | −0.545145 | + | 0.944219i | ||||
\(949\) | −306.179 | + | 176.773i | −0.322634 | + | 0.186273i | ||||
\(950\) | 13.2679 | − | 7.66021i | 0.0139662 | − | 0.00806338i | ||||
\(951\) | 382.112 | + | 220.613i | 0.401801 | + | 0.231980i | ||||
\(952\) | −39.8231 | −0.0418310 | ||||||||
\(953\) | −1533.59 | −1.60923 | −0.804614 | − | 0.593798i | \(-0.797628\pi\) | ||||
−0.804614 | + | 0.593798i | \(0.797628\pi\) | |||||||
\(954\) | −2.31246 | + | 4.00531i | −0.00242397 | + | 0.00419843i | ||||
\(955\) | −94.2754 | + | 163.290i | −0.0987177 | + | 0.170984i | ||||
\(956\) | 403.143 | + | 232.755i | 0.421698 | + | 0.243467i | ||||
\(957\) | 387.018 | − | 670.335i | 0.404407 | − | 0.700454i | ||||
\(958\) | 57.3770 | − | 33.1266i | 0.0598925 | − | 0.0345790i | ||||
\(959\) | −144.755 | − | 250.724i | −0.150944 | − | 0.261443i | ||||
\(960\) | −144.823 | −0.150857 | ||||||||
\(961\) | 330.573 | − | 572.569i | 0.343988 | − | 0.595805i | ||||
\(962\) | −33.9361 | −0.0352766 | ||||||||
\(963\) | −81.6709 | −0.0848089 | ||||||||
\(964\) | 781.716 | + | 1353.97i | 0.810909 | + | 1.40454i | ||||
\(965\) | − | 39.5246i | − | 0.0409581i | ||||||
\(966\) | −6.38964 | − | 3.68906i | −0.00661454 | − | 0.00381890i | ||||
\(967\) | −460.837 | − | 798.194i | −0.476564 | − | 0.825433i | 0.523075 | − | 0.852286i | \(-0.324785\pi\) |
−0.999639 | + | 0.0268534i | \(0.991451\pi\) | |||||||
\(968\) | −191.345 | − | 110.473i | −0.197671 | − | 0.114125i | ||||
\(969\) | 327.384 | − | 189.015i | 0.337857 | − | 0.195062i | ||||
\(970\) | −2.84600 | + | 1.64314i | −0.00293402 | + | 0.00169396i | ||||
\(971\) | −596.521 | − | 1033.20i | −0.614337 | − | 1.06406i | −0.990501 | − | 0.137509i | \(-0.956090\pi\) |
0.376164 | − | 0.926553i | \(-0.377243\pi\) | |||||||
\(972\) | 53.9065 | − | 31.1229i | 0.0554593 | − | 0.0320195i | ||||
\(973\) | 129.630 | + | 224.525i | 0.133227 | + | 0.230756i | ||||
\(974\) | 19.3291 | + | 33.4789i | 0.0198450 | + | 0.0343726i | ||||
\(975\) | −157.252 | + | 272.369i | −0.161284 | + | 0.279353i | ||||
\(976\) | 665.961 | − | 384.493i | 0.682337 | − | 0.393947i | ||||
\(977\) | 164.558 | − | 285.022i | 0.168432 | − | 0.291732i | −0.769437 | − | 0.638723i | \(-0.779463\pi\) |
0.937869 | + | 0.346990i | \(0.112796\pi\) | |||||||
\(978\) | −18.3139 | −0.0187259 | ||||||||
\(979\) | 2569.41 | − | 1483.45i | 2.62453 | − | 1.51527i | ||||
\(980\) | 233.460i | 0.238224i | ||||||||
\(981\) | 461.716i | 0.470659i | ||||||||
\(982\) | −2.53291 | − | 1.46237i | −0.00257933 | − | 0.00148918i | ||||
\(983\) | 715.983i | 0.728366i | 0.931328 | + | 0.364183i | \(0.118652\pi\) | ||||
−0.931328 | + | 0.364183i | \(0.881348\pi\) | |||||||
\(984\) | −10.2226 | + | 5.90205i | −0.0103889 | + | 0.00599802i | ||||
\(985\) | −86.5092 | − | 149.838i | −0.0878266 | − | 0.152120i | ||||
\(986\) | −41.7261 | − | 24.0906i | −0.0423186 | − | 0.0244326i | ||||
\(987\) | 102.331 | − | 177.242i | 0.103679 | − | 0.179577i | ||||
\(988\) | −213.694 | − | 123.376i | −0.216290 | − | 0.124875i | ||||
\(989\) | 81.4731 | + | 47.0385i | 0.0823792 | + | 0.0475617i | ||||
\(990\) | − | 7.01657i | − | 0.00708745i | ||||||
\(991\) | − | 246.871i | − | 0.249113i | −0.992213 | − | 0.124556i | \(-0.960249\pi\) | ||
0.992213 | − | 0.124556i | \(-0.0397508\pi\) | |||||||
\(992\) | −80.2639 | + | 139.021i | −0.0809112 | + | 0.140142i | ||||
\(993\) | −55.9600 | − | 96.9256i | −0.0563545 | − | 0.0976088i | ||||
\(994\) | −7.91660 | − | 13.7119i | −0.00796438 | − | 0.0137947i | ||||
\(995\) | −292.181 | − | 168.691i | −0.293649 | − | 0.169539i | ||||
\(996\) | 1006.05i | 1.01009i | ||||||||
\(997\) | −1407.00 | −1.41123 | −0.705617 | − | 0.708593i | \(-0.749330\pi\) | ||||
−0.705617 | + | 0.708593i | \(0.749330\pi\) | |||||||
\(998\) | 40.4113 | + | 69.9945i | 0.0404923 | + | 0.0701347i | ||||
\(999\) | 235.016 | + | 135.687i | 0.235251 | + | 0.135822i |
(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 | 201.3.h.a.172.6 | yes | 22 | |
67.30 | odd | 6 | inner | 201.3.h.a.97.6 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.3.h.a.97.6 | ✓ | 22 | 67.30 | odd | 6 | inner | |
201.3.h.a.172.6 | yes | 22 | 1.1 | even | 1 | trivial |