Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [19,3,Mod(8,19)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(19, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("19.8");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 19.d (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: | \(0.517712502285\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 6.0.6967728.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 8.2 | ||
Root | \(-1.13654 + 1.96854i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 19.8 |
Dual form | 19.3.d.a.12.2 |
$q$-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 \(\left(\mathbb{Z}/19\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.583430 | − | 0.336844i | −0.291715 | − | 0.168422i | 0.347000 | − | 0.937865i | \(-0.387200\pi\) |
−0.638715 | + | 0.769443i | \(0.720534\pi\) | |||||||
\(3\) | 2.49304 | + | 1.43936i | 0.831013 | + | 0.479786i | 0.854199 | − | 0.519946i | \(-0.174048\pi\) |
−0.0231863 | + | 0.999731i | \(0.507381\pi\) | |||||||
\(4\) | −1.77307 | − | 3.07105i | −0.443268 | − | 0.767763i | ||||
\(5\) | −1.55311 | + | 2.69006i | −0.310621 | + | 0.538012i | −0.978497 | − | 0.206261i | \(-0.933870\pi\) |
0.667876 | + | 0.744273i | \(0.267204\pi\) | |||||||
\(6\) | −0.969676 | − | 1.67953i | −0.161613 | − | 0.279921i | ||||
\(7\) | −8.15294 | −1.16471 | −0.582353 | − | 0.812936i | \(-0.697868\pi\) | ||||
−0.582353 | + | 0.812936i | \(0.697868\pi\) | |||||||
\(8\) | 5.08374i | 0.635468i | ||||||||
\(9\) | −0.356503 | − | 0.617481i | −0.0396114 | − | 0.0686090i | ||||
\(10\) | 1.81226 | − | 1.04631i | 0.181226 | − | 0.104631i | ||||
\(11\) | 17.6991 | 1.60901 | 0.804504 | − | 0.593947i | \(-0.202431\pi\) | ||||
0.804504 | + | 0.593947i | \(0.202431\pi\) | |||||||
\(12\) | − | 10.2083i | − | 0.850695i | ||||||
\(13\) | 5.33372 | − | 3.07942i | 0.410286 | − | 0.236879i | −0.280627 | − | 0.959817i | \(-0.590542\pi\) |
0.690913 | + | 0.722938i | \(0.257209\pi\) | |||||||
\(14\) | 4.75667 | + | 2.74626i | 0.339762 | + | 0.196162i | ||||
\(15\) | −7.74391 | + | 4.47095i | −0.516261 | + | 0.298063i | ||||
\(16\) | −5.37987 | + | 9.31820i | −0.336242 | + | 0.582388i | ||||
\(17\) | −6.91657 | + | 11.9799i | −0.406857 | + | 0.704697i | −0.994536 | − | 0.104397i | \(-0.966709\pi\) |
0.587679 | + | 0.809094i | \(0.300042\pi\) | |||||||
\(18\) | 0.480343i | 0.0266857i | ||||||||
\(19\) | 3.11375 | − | 18.7431i | 0.163882 | − | 0.986480i | ||||
\(20\) | 11.0151 | 0.550754 | ||||||||
\(21\) | −20.3256 | − | 11.7350i | −0.967886 | − | 0.558809i | ||||
\(22\) | −10.3262 | − | 5.96182i | −0.469372 | − | 0.270992i | ||||
\(23\) | 2.46968 | + | 4.27760i | 0.107377 | + | 0.185983i | 0.914707 | − | 0.404118i | \(-0.132421\pi\) |
−0.807330 | + | 0.590101i | \(0.799088\pi\) | |||||||
\(24\) | −7.31732 | + | 12.6740i | −0.304888 | + | 0.528082i | ||||
\(25\) | 7.67572 | + | 13.2947i | 0.307029 | + | 0.531790i | ||||
\(26\) | −4.14914 | −0.159582 | ||||||||
\(27\) | − | 27.9610i | − | 1.03559i | ||||||
\(28\) | 14.4558 | + | 25.0381i | 0.516277 | + | 0.894218i | ||||
\(29\) | −38.2711 | + | 22.0958i | −1.31969 | + | 0.761925i | −0.983679 | − | 0.179933i | \(-0.942412\pi\) |
−0.336013 | + | 0.941857i | \(0.609079\pi\) | |||||||
\(30\) | 6.02404 | 0.200801 | ||||||||
\(31\) | − | 43.0049i | − | 1.38725i | −0.720334 | − | 0.693627i | \(-0.756011\pi\) | ||
0.720334 | − | 0.693627i | \(-0.243989\pi\) | |||||||
\(32\) | 23.8881 | − | 13.7918i | 0.746505 | − | 0.430995i | ||||
\(33\) | 44.1245 | + | 25.4753i | 1.33711 | + | 0.771979i | ||||
\(34\) | 8.07067 | − | 4.65960i | 0.237373 | − | 0.137047i | ||||
\(35\) | 12.6624 | − | 21.9319i | 0.361782 | − | 0.626625i | ||||
\(36\) | −1.26421 | + | 2.18968i | −0.0351170 | + | 0.0608244i | ||||
\(37\) | 30.7849i | 0.832024i | 0.909359 | + | 0.416012i | \(0.136572\pi\) | ||||
−0.909359 | + | 0.416012i | \(0.863428\pi\) | |||||||
\(38\) | −8.13016 | + | 9.88645i | −0.213951 | + | 0.260170i | ||||
\(39\) | 17.7296 | 0.454604 | ||||||||
\(40\) | −13.6756 | − | 7.89559i | −0.341889 | − | 0.197390i | ||||
\(41\) | −28.6795 | − | 16.5581i | −0.699501 | − | 0.403857i | 0.107661 | − | 0.994188i | \(-0.465664\pi\) |
−0.807161 | + | 0.590331i | \(0.798997\pi\) | |||||||
\(42\) | 7.90571 | + | 13.6931i | 0.188231 | + | 0.326026i | ||||
\(43\) | −15.7586 | + | 27.2946i | −0.366478 | + | 0.634759i | −0.989012 | − | 0.147834i | \(-0.952770\pi\) |
0.622534 | + | 0.782593i | \(0.286103\pi\) | |||||||
\(44\) | −31.3818 | − | 54.3548i | −0.713222 | − | 1.23534i | ||||
\(45\) | 2.21475 | 0.0492166 | ||||||||
\(46\) | − | 3.32758i | − | 0.0723386i | ||||||
\(47\) | 8.86404 | + | 15.3530i | 0.188597 | + | 0.326659i | 0.944783 | − | 0.327698i | \(-0.106273\pi\) |
−0.756186 | + | 0.654357i | \(0.772939\pi\) | |||||||
\(48\) | −26.8244 | + | 15.4871i | −0.558842 | + | 0.322648i | ||||
\(49\) | 17.4704 | 0.356539 | ||||||||
\(50\) | − | 10.3421i | − | 0.206841i | ||||||
\(51\) | −34.4866 | + | 19.9108i | −0.676207 | + | 0.390408i | ||||
\(52\) | −18.9142 | − | 10.9201i | −0.363734 | − | 0.210002i | ||||
\(53\) | 14.6396 | − | 8.45218i | 0.276219 | − | 0.159475i | −0.355492 | − | 0.934679i | \(-0.615687\pi\) |
0.631710 | + | 0.775204i | \(0.282353\pi\) | |||||||
\(54\) | −9.41847 | + | 16.3133i | −0.174416 | + | 0.302098i | ||||
\(55\) | −27.4886 | + | 47.6116i | −0.499792 | + | 0.865665i | ||||
\(56\) | − | 41.4474i | − | 0.740133i | ||||||
\(57\) | 34.7408 | − | 42.2455i | 0.609487 | − | 0.741150i | ||||
\(58\) | 29.7713 | 0.513299 | ||||||||
\(59\) | 20.3412 | + | 11.7440i | 0.344766 | + | 0.199050i | 0.662377 | − | 0.749170i | \(-0.269548\pi\) |
−0.317612 | + | 0.948221i | \(0.602881\pi\) | |||||||
\(60\) | 27.4610 | + | 15.8546i | 0.457684 | + | 0.264244i | ||||
\(61\) | −8.52643 | − | 14.7682i | −0.139777 | − | 0.242102i | 0.787635 | − | 0.616142i | \(-0.211305\pi\) |
−0.927412 | + | 0.374041i | \(0.877972\pi\) | |||||||
\(62\) | −14.4859 | + | 25.0903i | −0.233644 | + | 0.404683i | ||||
\(63\) | 2.90655 | + | 5.03429i | 0.0461357 | + | 0.0799093i | ||||
\(64\) | 24.4562 | 0.382128 | ||||||||
\(65\) | 19.1307i | 0.294318i | ||||||||
\(66\) | −17.1624 | − | 29.7261i | −0.260036 | − | 0.450396i | ||||
\(67\) | 84.9924 | − | 49.0704i | 1.26854 | − | 0.732393i | 0.293831 | − | 0.955858i | \(-0.405070\pi\) |
0.974712 | + | 0.223464i | \(0.0717365\pi\) | |||||||
\(68\) | 49.0543 | 0.721387 | ||||||||
\(69\) | 14.2190i | 0.206072i | ||||||||
\(70\) | −14.7752 | + | 8.53048i | −0.211075 | + | 0.121864i | ||||
\(71\) | −1.36156 | − | 0.786099i | −0.0191769 | − | 0.0110718i | 0.490381 | − | 0.871508i | \(-0.336858\pi\) |
−0.509558 | + | 0.860436i | \(0.670191\pi\) | |||||||
\(72\) | 3.13911 | − | 1.81237i | 0.0435988 | − | 0.0251718i | ||||
\(73\) | 2.85534 | − | 4.94560i | 0.0391143 | − | 0.0677479i | −0.845806 | − | 0.533491i | \(-0.820880\pi\) |
0.884920 | + | 0.465743i | \(0.154213\pi\) | |||||||
\(74\) | 10.3697 | − | 17.9608i | 0.140131 | − | 0.242714i | ||||
\(75\) | 44.1924i | 0.589232i | ||||||||
\(76\) | −63.0820 | + | 23.6704i | −0.830026 | + | 0.311453i | ||||
\(77\) | −144.300 | −1.87402 | ||||||||
\(78\) | −10.3440 | − | 5.97209i | −0.132615 | − | 0.0765653i | ||||
\(79\) | 41.9327 | + | 24.2099i | 0.530794 | + | 0.306454i | 0.741340 | − | 0.671130i | \(-0.234191\pi\) |
−0.210546 | + | 0.977584i | \(0.567524\pi\) | |||||||
\(80\) | −16.7110 | − | 28.9443i | −0.208888 | − | 0.361804i | ||||
\(81\) | 37.0373 | − | 64.1505i | 0.457250 | − | 0.791981i | ||||
\(82\) | 11.1550 | + | 19.3210i | 0.136037 | + | 0.235622i | ||||
\(83\) | −74.2729 | −0.894854 | −0.447427 | − | 0.894320i | \(-0.647660\pi\) | ||||
−0.447427 | + | 0.894320i | \(0.647660\pi\) | |||||||
\(84\) | 83.2280i | 0.990809i | ||||||||
\(85\) | −21.4843 | − | 37.2120i | −0.252757 | − | 0.437788i | ||||
\(86\) | 18.3880 | − | 10.6163i | 0.213815 | − | 0.123446i | ||||
\(87\) | −127.215 | −1.46224 | ||||||||
\(88\) | 89.9776i | 1.02247i | ||||||||
\(89\) | 81.0798 | − | 46.8114i | 0.911008 | − | 0.525971i | 0.0302530 | − | 0.999542i | \(-0.490369\pi\) |
0.880755 | + | 0.473571i | \(0.157035\pi\) | |||||||
\(90\) | −1.29215 | − | 0.746024i | −0.0143572 | − | 0.00828915i | ||||
\(91\) | −43.4855 | + | 25.1064i | −0.477863 | + | 0.275894i | ||||
\(92\) | 8.75783 | − | 15.1690i | 0.0951938 | − | 0.164881i | ||||
\(93\) | 61.8994 | − | 107.213i | 0.665585 | − | 1.15283i | ||||
\(94\) | − | 11.9432i | − | 0.127055i | ||||||
\(95\) | 45.5841 | + | 37.4862i | 0.479833 | + | 0.394592i | ||||
\(96\) | 79.4055 | 0.827140 | ||||||||
\(97\) | −8.15700 | − | 4.70945i | −0.0840928 | − | 0.0485510i | 0.457364 | − | 0.889280i | \(-0.348794\pi\) |
−0.541457 | + | 0.840729i | \(0.682127\pi\) | |||||||
\(98\) | −10.1928 | − | 5.88480i | −0.104008 | − | 0.0600489i | ||||
\(99\) | −6.30978 | − | 10.9289i | −0.0637351 | − | 0.110392i | ||||
\(100\) | 27.2192 | − | 47.1451i | 0.272192 | − | 0.471451i | ||||
\(101\) | 66.5604 | + | 115.286i | 0.659014 | + | 1.14145i | 0.980871 | + | 0.194657i | \(0.0623595\pi\) |
−0.321858 | + | 0.946788i | \(0.604307\pi\) | |||||||
\(102\) | 26.8273 | 0.263013 | ||||||||
\(103\) | − | 92.7893i | − | 0.900867i | −0.892810 | − | 0.450433i | \(-0.851269\pi\) | ||
0.892810 | − | 0.450433i | \(-0.148731\pi\) | |||||||
\(104\) | 15.6550 | + | 27.1153i | 0.150529 | + | 0.260724i | ||||
\(105\) | 63.1356 | − | 36.4514i | 0.601292 | − | 0.347156i | ||||
\(106\) | −11.3882 | −0.107436 | ||||||||
\(107\) | 139.410i | 1.30289i | 0.758695 | + | 0.651446i | \(0.225837\pi\) | ||||
−0.758695 | + | 0.651446i | \(0.774163\pi\) | |||||||
\(108\) | −85.8696 | + | 49.5768i | −0.795089 | + | 0.459045i | ||||
\(109\) | −112.823 | − | 65.1381i | −1.03507 | − | 0.597597i | −0.116636 | − | 0.993175i | \(-0.537211\pi\) |
−0.918433 | + | 0.395577i | \(0.870545\pi\) | |||||||
\(110\) | 32.0753 | − | 18.5187i | 0.291594 | − | 0.168352i | ||||
\(111\) | −44.3104 | + | 76.7479i | −0.399193 | + | 0.691422i | ||||
\(112\) | 43.8617 | − | 75.9707i | 0.391623 | − | 0.678310i | ||||
\(113\) | − | 19.1195i | − | 0.169199i | −0.996415 | − | 0.0845997i | \(-0.973039\pi\) | ||
0.996415 | − | 0.0845997i | \(-0.0269612\pi\) | |||||||
\(114\) | −34.4989 | + | 12.9451i | −0.302622 | + | 0.113554i | ||||
\(115\) | −15.3427 | −0.133415 | ||||||||
\(116\) | 135.715 | + | 78.3550i | 1.16996 | + | 0.675474i | ||||
\(117\) | −3.80297 | − | 2.19565i | −0.0325041 | − | 0.0187662i | ||||
\(118\) | −7.91177 | − | 13.7036i | −0.0670489 | − | 0.116132i | ||||
\(119\) | 56.3904 | − | 97.6710i | 0.473869 | − | 0.820765i | ||||
\(120\) | −22.7291 | − | 39.3680i | −0.189410 | − | 0.328067i | ||||
\(121\) | 192.258 | 1.58891 | ||||||||
\(122\) | 11.4883i | 0.0941663i | ||||||||
\(123\) | −47.6661 | − | 82.5601i | −0.387529 | − | 0.671221i | ||||
\(124\) | −132.070 | + | 76.2508i | −1.06508 | + | 0.614926i | ||||
\(125\) | −125.340 | −1.00272 | ||||||||
\(126\) | − | 3.91621i | − | 0.0310810i | ||||||
\(127\) | −21.1332 | + | 12.2013i | −0.166403 | + | 0.0960730i | −0.580889 | − | 0.813983i | \(-0.697295\pi\) |
0.414486 | + | 0.910056i | \(0.363962\pi\) | |||||||
\(128\) | −109.821 | − | 63.4052i | −0.857977 | − | 0.495353i | ||||
\(129\) | −78.5735 | + | 45.3644i | −0.609097 | + | 0.351662i | ||||
\(130\) | 6.44405 | − | 11.1614i | 0.0495696 | − | 0.0858571i | ||||
\(131\) | −38.0958 | + | 65.9839i | −0.290808 | + | 0.503694i | −0.974001 | − | 0.226544i | \(-0.927257\pi\) |
0.683193 | + | 0.730238i | \(0.260591\pi\) | |||||||
\(132\) | − | 180.678i | − | 1.36877i | ||||||
\(133\) | −25.3862 | + | 152.812i | −0.190874 | + | 1.14896i | ||||
\(134\) | −66.1161 | −0.493404 | ||||||||
\(135\) | 75.2166 | + | 43.4264i | 0.557160 | + | 0.321677i | ||||
\(136\) | −60.9025 | − | 35.1620i | −0.447812 | − | 0.258544i | ||||
\(137\) | 118.616 | + | 205.449i | 0.865811 | + | 1.49963i | 0.866239 | + | 0.499629i | \(0.166530\pi\) |
−0.000428189 | 1.00000i | \(0.500136\pi\) | ||||||||
\(138\) | 4.78957 | − | 8.29578i | 0.0347070 | − | 0.0601144i | ||||
\(139\) | −10.0402 | − | 17.3902i | −0.0722320 | − | 0.125110i | 0.827647 | − | 0.561249i | \(-0.189679\pi\) |
−0.899879 | + | 0.436139i | \(0.856346\pi\) | |||||||
\(140\) | −89.8053 | −0.641466 | ||||||||
\(141\) | 51.0341i | 0.361944i | ||||||||
\(142\) | 0.529585 | + | 0.917267i | 0.00372947 | + | 0.00645963i | ||||
\(143\) | 94.4020 | − | 54.5030i | 0.660154 | − | 0.381140i | ||||
\(144\) | 7.67175 | 0.0532761 | ||||||||
\(145\) | − | 137.269i | − | 0.946680i | ||||||
\(146\) | −3.33178 | + | 1.92361i | −0.0228204 | + | 0.0131754i | ||||
\(147\) | 43.5544 | + | 25.1462i | 0.296289 | + | 0.171062i | ||||
\(148\) | 94.5419 | − | 54.5838i | 0.638797 | − | 0.368810i | ||||
\(149\) | 77.8489 | − | 134.838i | 0.522476 | − | 0.904954i | −0.477182 | − | 0.878804i | \(-0.658342\pi\) |
0.999658 | − | 0.0261500i | \(-0.00832476\pi\) | |||||||
\(150\) | 14.8859 | − | 25.7832i | 0.0992395 | − | 0.171888i | ||||
\(151\) | 41.4678i | 0.274621i | 0.990528 | + | 0.137310i | \(0.0438458\pi\) | ||||
−0.990528 | + | 0.137310i | \(0.956154\pi\) | |||||||
\(152\) | 95.2852 | + | 15.8295i | 0.626876 | + | 0.104142i | ||||
\(153\) | 9.86311 | 0.0644648 | ||||||||
\(154\) | 84.1887 | + | 48.6064i | 0.546680 | + | 0.315626i | ||||
\(155\) | 115.686 | + | 66.7912i | 0.746359 | + | 0.430911i | ||||
\(156\) | −31.4358 | − | 54.4484i | −0.201512 | − | 0.349028i | ||||
\(157\) | 39.5539 | − | 68.5094i | 0.251936 | − | 0.436366i | −0.712123 | − | 0.702055i | \(-0.752266\pi\) |
0.964059 | + | 0.265689i | \(0.0855994\pi\) | |||||||
\(158\) | −16.3099 | − | 28.2495i | −0.103227 | − | 0.178794i | ||||
\(159\) | 48.6628 | 0.306055 | ||||||||
\(160\) | 85.6807i | 0.535504i | ||||||||
\(161\) | −20.1351 | − | 34.8751i | −0.125063 | − | 0.216615i | ||||
\(162\) | −43.2173 | + | 24.9515i | −0.266774 | + | 0.154022i | ||||
\(163\) | −135.441 | −0.830926 | −0.415463 | − | 0.909610i | \(-0.636380\pi\) | ||||
−0.415463 | + | 0.909610i | \(0.636380\pi\) | |||||||
\(164\) | 117.435i | 0.716068i | ||||||||
\(165\) | −137.060 | + | 79.1317i | −0.830667 | + | 0.479586i | ||||
\(166\) | 43.3330 | + | 25.0183i | 0.261042 | + | 0.150713i | ||||
\(167\) | 54.3880 | − | 31.4010i | 0.325677 | − | 0.188030i | −0.328243 | − | 0.944593i | \(-0.606457\pi\) |
0.653920 | + | 0.756564i | \(0.273123\pi\) | |||||||
\(168\) | 59.6576 | − | 103.330i | 0.355105 | − | 0.615060i | ||||
\(169\) | −65.5343 | + | 113.509i | −0.387777 | + | 0.671649i | ||||
\(170\) | 28.9474i | 0.170279i | ||||||||
\(171\) | −12.6836 | + | 4.75929i | −0.0741730 | + | 0.0278321i | ||||
\(172\) | 111.764 | 0.649793 | ||||||||
\(173\) | −282.606 | − | 163.162i | −1.63356 | − | 0.943135i | −0.982984 | − | 0.183693i | \(-0.941195\pi\) |
−0.650574 | − | 0.759442i | \(-0.725472\pi\) | |||||||
\(174\) | 74.2211 | + | 42.8516i | 0.426558 | + | 0.246273i | ||||
\(175\) | −62.5797 | − | 108.391i | −0.357598 | − | 0.619378i | ||||
\(176\) | −95.2187 | + | 164.924i | −0.541015 | + | 0.937066i | ||||
\(177\) | 33.8076 | + | 58.5564i | 0.191003 | + | 0.330827i | ||||
\(178\) | −63.0725 | −0.354340 | ||||||||
\(179\) | − | 266.546i | − | 1.48909i | −0.667575 | − | 0.744543i | \(-0.732668\pi\) | ||
0.667575 | − | 0.744543i | \(-0.267332\pi\) | |||||||
\(180\) | −3.92691 | − | 6.80161i | −0.0218162 | − | 0.0377867i | ||||
\(181\) | 129.999 | − | 75.0548i | 0.718225 | − | 0.414667i | −0.0958743 | − | 0.995393i | \(-0.530565\pi\) |
0.814099 | + | 0.580726i | \(0.197231\pi\) | |||||||
\(182\) | 33.8277 | 0.185866 | ||||||||
\(183\) | − | 49.0903i | − | 0.268253i | ||||||
\(184\) | −21.7462 | + | 12.5552i | −0.118186 | + | 0.0682347i | ||||
\(185\) | −82.8131 | − | 47.8122i | −0.447638 | − | 0.258444i | ||||
\(186\) | −72.2279 | + | 41.7008i | −0.388322 | + | 0.224198i | ||||
\(187\) | −122.417 | + | 212.032i | −0.654636 | + | 1.13386i | ||||
\(188\) | 31.4332 | − | 54.4439i | 0.167198 | − | 0.289595i | ||||
\(189\) | 227.964i | 1.20616i | ||||||||
\(190\) | −13.9681 | − | 37.2253i | −0.0735165 | − | 0.195923i | ||||
\(191\) | −99.5798 | −0.521360 | −0.260680 | − | 0.965425i | \(-0.583947\pi\) | ||||
−0.260680 | + | 0.965425i | \(0.583947\pi\) | |||||||
\(192\) | 60.9702 | + | 35.2012i | 0.317553 | + | 0.183339i | ||||
\(193\) | −42.4195 | − | 24.4909i | −0.219790 | − | 0.126896i | 0.386063 | − | 0.922472i | \(-0.373835\pi\) |
−0.605853 | + | 0.795577i | \(0.707168\pi\) | |||||||
\(194\) | 3.17269 | + | 5.49527i | 0.0163541 | + | 0.0283261i | ||||
\(195\) | −27.5359 | + | 47.6936i | −0.141210 | + | 0.244582i | ||||
\(196\) | −30.9763 | − | 53.6526i | −0.158042 | − | 0.273738i | ||||
\(197\) | −167.819 | −0.851875 | −0.425938 | − | 0.904753i | \(-0.640056\pi\) | ||||
−0.425938 | + | 0.904753i | \(0.640056\pi\) | |||||||
\(198\) | 8.50163i | 0.0429375i | ||||||||
\(199\) | 46.2601 | + | 80.1249i | 0.232463 | + | 0.402638i | 0.958532 | − | 0.284984i | \(-0.0919882\pi\) |
−0.726069 | + | 0.687621i | \(0.758655\pi\) | |||||||
\(200\) | −67.5870 | + | 39.0214i | −0.337935 | + | 0.195107i | ||||
\(201\) | 282.519 | 1.40557 | ||||||||
\(202\) | − | 89.6818i | − | 0.443969i | ||||||
\(203\) | 312.022 | − | 180.146i | 1.53705 | − | 0.887418i | ||||
\(204\) | 122.294 | + | 70.6067i | 0.599482 | + | 0.346111i | ||||
\(205\) | 89.0847 | − | 51.4331i | 0.434559 | − | 0.250893i | ||||
\(206\) | −31.2555 | + | 54.1361i | −0.151726 | + | 0.262796i | ||||
\(207\) | 1.76089 | − | 3.04996i | 0.00850673 | − | 0.0147341i | ||||
\(208\) | 66.2676i | 0.318594i | ||||||||
\(209\) | 55.1106 | − | 331.736i | 0.263687 | − | 1.58725i | ||||
\(210\) | −49.1136 | −0.233874 | ||||||||
\(211\) | −54.4067 | − | 31.4117i | −0.257852 | − | 0.148871i | 0.365502 | − | 0.930810i | \(-0.380897\pi\) |
−0.623354 | + | 0.781940i | \(0.714231\pi\) | |||||||
\(212\) | −51.9142 | − | 29.9726i | −0.244878 | − | 0.141380i | ||||
\(213\) | −2.26295 | − | 3.91955i | −0.0106242 | − | 0.0184016i | ||||
\(214\) | 46.9592 | − | 81.3357i | 0.219436 | − | 0.380073i | ||||
\(215\) | −48.9495 | − | 84.7830i | −0.227672 | − | 0.394339i | ||||
\(216\) | 142.146 | 0.658085 | ||||||||
\(217\) | 350.616i | 1.61574i | ||||||||
\(218\) | 43.8827 | + | 76.0071i | 0.201297 | + | 0.348656i | ||||
\(219\) | 14.2370 | − | 8.21971i | 0.0650089 | − | 0.0375329i | ||||
\(220\) | 194.957 | 0.886168 | ||||||||
\(221\) | 85.1962i | 0.385503i | ||||||||
\(222\) | 51.7041 | − | 29.8514i | 0.232901 | − | 0.134466i | ||||
\(223\) | 371.890 | + | 214.711i | 1.66767 | + | 0.962830i | 0.968889 | + | 0.247494i | \(0.0796071\pi\) |
0.698781 | + | 0.715336i | \(0.253726\pi\) | |||||||
\(224\) | −194.759 | + | 112.444i | −0.869458 | + | 0.501982i | ||||
\(225\) | 5.47284 | − | 9.47923i | 0.0243237 | − | 0.0421299i | ||||
\(226\) | −6.44029 | + | 11.1549i | −0.0284969 | + | 0.0493580i | ||||
\(227\) | − | 246.184i | − | 1.08451i | −0.840213 | − | 0.542256i | \(-0.817570\pi\) | ||
0.840213 | − | 0.542256i | \(-0.182430\pi\) | |||||||
\(228\) | −191.336 | − | 31.7863i | −0.839194 | − | 0.139413i | ||||
\(229\) | −31.8783 | −0.139207 | −0.0696033 | − | 0.997575i | \(-0.522173\pi\) | ||||
−0.0696033 | + | 0.997575i | \(0.522173\pi\) | |||||||
\(230\) | 8.95138 | + | 5.16808i | 0.0389190 | + | 0.0224699i | ||||
\(231\) | −359.744 | − | 207.699i | −1.55734 | − | 0.899128i | ||||
\(232\) | −112.329 | − | 194.560i | −0.484178 | − | 0.838622i | ||||
\(233\) | −184.933 | + | 320.313i | −0.793704 | + | 1.37474i | 0.129955 | + | 0.991520i | \(0.458517\pi\) |
−0.923659 | + | 0.383216i | \(0.874817\pi\) | |||||||
\(234\) | 1.47918 | + | 2.56201i | 0.00632128 | + | 0.0109488i | ||||
\(235\) | −55.0672 | −0.234329 | ||||||||
\(236\) | − | 83.2917i | − | 0.352931i | ||||||
\(237\) | 69.6933 | + | 120.712i | 0.294064 | + | 0.509335i | ||||
\(238\) | −65.7997 | + | 37.9895i | −0.276469 | + | 0.159620i | ||||
\(239\) | 106.567 | 0.445887 | 0.222944 | − | 0.974831i | \(-0.428433\pi\) | ||||
0.222944 | + | 0.974831i | \(0.428433\pi\) | |||||||
\(240\) | − | 96.2124i | − | 0.400885i | ||||||
\(241\) | −11.9695 | + | 6.91062i | −0.0496662 | + | 0.0286748i | −0.524627 | − | 0.851332i | \(-0.675795\pi\) |
0.474961 | + | 0.880007i | \(0.342462\pi\) | |||||||
\(242\) | −112.169 | − | 64.7607i | −0.463508 | − | 0.267606i | ||||
\(243\) | −33.2633 | + | 19.2046i | −0.136886 | + | 0.0790313i | ||||
\(244\) | −30.2359 | + | 52.3702i | −0.123918 | + | 0.214632i | ||||
\(245\) | −27.1334 | + | 46.9964i | −0.110749 | + | 0.191822i | ||||
\(246\) | 64.2241i | 0.261074i | ||||||||
\(247\) | −41.1101 | − | 109.559i | −0.166438 | − | 0.443559i | ||||
\(248\) | 218.626 | 0.881555 | ||||||||
\(249\) | −185.165 | − | 106.905i | −0.743635 | − | 0.429338i | ||||
\(250\) | 73.1272 | + | 42.2200i | 0.292509 | + | 0.168880i | ||||
\(251\) | 61.3921 | + | 106.334i | 0.244590 | + | 0.423642i | 0.962016 | − | 0.272992i | \(-0.0880133\pi\) |
−0.717426 | + | 0.696635i | \(0.754680\pi\) | |||||||
\(252\) | 10.3070 | − | 17.8523i | 0.0409010 | − | 0.0708425i | ||||
\(253\) | 43.7110 | + | 75.7097i | 0.172771 | + | 0.299248i | ||||
\(254\) | 16.4397 | 0.0647231 | ||||||||
\(255\) | − | 123.695i | − | 0.485077i | ||||||
\(256\) | −6.19708 | − | 10.7337i | −0.0242073 | − | 0.0419283i | ||||
\(257\) | −343.131 | + | 198.107i | −1.33514 | + | 0.770843i | −0.986082 | − | 0.166258i | \(-0.946832\pi\) |
−0.349058 | + | 0.937101i | \(0.613498\pi\) | |||||||
\(258\) | 61.1228 | 0.236910 | ||||||||
\(259\) | − | 250.987i | − | 0.969062i | ||||||
\(260\) | 58.7514 | − | 33.9201i | 0.225967 | − | 0.130462i | ||||
\(261\) | 27.2875 | + | 15.7544i | 0.104550 | + | 0.0603619i | ||||
\(262\) | 44.4525 | − | 25.6647i | 0.169666 | − | 0.0979568i | ||||
\(263\) | 26.7480 | − | 46.3289i | 0.101704 | − | 0.176156i | −0.810683 | − | 0.585485i | \(-0.800904\pi\) |
0.912387 | + | 0.409330i | \(0.134237\pi\) | |||||||
\(264\) | −129.510 | + | 224.318i | −0.490568 | + | 0.849688i | ||||
\(265\) | 52.5085i | 0.198145i | ||||||||
\(266\) | 66.2847 | − | 80.6036i | 0.249190 | − | 0.303021i | ||||
\(267\) | 269.513 | 1.00941 | ||||||||
\(268\) | −301.395 | − | 174.011i | −1.12461 | − | 0.649293i | ||||
\(269\) | 316.357 | + | 182.649i | 1.17605 | + | 0.678993i | 0.955098 | − | 0.296292i | \(-0.0957500\pi\) |
0.220953 | + | 0.975285i | \(0.429083\pi\) | |||||||
\(270\) | −29.2558 | − | 50.6725i | −0.108355 | − | 0.187676i | ||||
\(271\) | −87.1835 | + | 151.006i | −0.321710 | + | 0.557219i | −0.980841 | − | 0.194810i | \(-0.937591\pi\) |
0.659131 | + | 0.752028i | \(0.270924\pi\) | |||||||
\(272\) | −74.4204 | − | 128.900i | −0.273605 | − | 0.473897i | ||||
\(273\) | −144.548 | −0.529480 | ||||||||
\(274\) | − | 159.820i | − | 0.583286i | ||||||
\(275\) | 135.853 | + | 235.305i | 0.494012 | + | 0.855654i | ||||
\(276\) | 43.6672 | − | 25.2113i | 0.158215 | − | 0.0913453i | ||||
\(277\) | 93.2815 | 0.336756 | 0.168378 | − | 0.985722i | \(-0.446147\pi\) | ||||
0.168378 | + | 0.985722i | \(0.446147\pi\) | |||||||
\(278\) | 13.5280i | 0.0486618i | ||||||||
\(279\) | −26.5547 | + | 15.3314i | −0.0951782 | + | 0.0549512i | ||||
\(280\) | 111.496 | + | 64.3723i | 0.398200 | + | 0.229901i | ||||
\(281\) | 325.337 | − | 187.834i | 1.15778 | − | 0.668447i | 0.207013 | − | 0.978338i | \(-0.433626\pi\) |
0.950772 | + | 0.309891i | \(0.100293\pi\) | |||||||
\(282\) | 17.1905 | − | 29.7748i | 0.0609592 | − | 0.105584i | ||||
\(283\) | 32.0728 | − | 55.5518i | 0.113332 | − | 0.196296i | −0.803780 | − | 0.594927i | \(-0.797181\pi\) |
0.917112 | + | 0.398631i | \(0.130514\pi\) | |||||||
\(284\) | 5.57524i | 0.0196311i | ||||||||
\(285\) | 59.6869 | + | 159.066i | 0.209428 | + | 0.558128i | ||||
\(286\) | −73.4359 | −0.256769 | ||||||||
\(287\) | 233.822 | + | 134.997i | 0.814712 | + | 0.470374i | ||||
\(288\) | −17.0324 | − | 9.83366i | −0.0591402 | − | 0.0341446i | ||||
\(289\) | 48.8221 | + | 84.5624i | 0.168935 | + | 0.292603i | ||||
\(290\) | −46.2380 | + | 80.0866i | −0.159442 | + | 0.276161i | ||||
\(291\) | −13.5572 | − | 23.4817i | −0.0465882 | − | 0.0806931i | ||||
\(292\) | −20.2509 | −0.0693524 | ||||||||
\(293\) | − | 111.814i | − | 0.381618i | −0.981627 | − | 0.190809i | \(-0.938889\pi\) | ||
0.981627 | − | 0.190809i | \(-0.0611112\pi\) | |||||||
\(294\) | −16.9406 | − | 29.3421i | −0.0576212 | − | 0.0998029i | ||||
\(295\) | −63.1840 | + | 36.4793i | −0.214183 | + | 0.123659i | ||||
\(296\) | −156.502 | −0.528724 | ||||||||
\(297\) | − | 494.884i | − | 1.66627i | ||||||
\(298\) | −90.8387 | + | 52.4458i | −0.304828 | + | 0.175993i | ||||
\(299\) | 26.3451 | + | 15.2104i | 0.0881108 | + | 0.0508708i | ||||
\(300\) | 135.717 | − | 78.3564i | 0.452391 | − | 0.261188i | ||||
\(301\) | 128.479 | − | 222.532i | 0.426839 | − | 0.739308i | ||||
\(302\) | 13.9681 | − | 24.1935i | 0.0462521 | − | 0.0801110i | ||||
\(303\) | 383.217i | 1.26474i | ||||||||
\(304\) | 157.901 | + | 129.850i | 0.519410 | + | 0.427138i | ||||
\(305\) | 52.9698 | 0.173671 | ||||||||
\(306\) | −5.75444 | − | 3.32233i | −0.0188053 | − | 0.0108573i | ||||
\(307\) | −297.331 | − | 171.664i | −0.968503 | − | 0.559166i | −0.0697237 | − | 0.997566i | \(-0.522212\pi\) |
−0.898780 | + | 0.438401i | \(0.855545\pi\) | |||||||
\(308\) | 255.854 | + | 443.151i | 0.830694 | + | 1.43880i | ||||
\(309\) | 133.557 | − | 231.327i | 0.432223 | − | 0.748632i | ||||
\(310\) | −44.9963 | − | 77.9360i | −0.145150 | − | 0.251406i | ||||
\(311\) | −251.722 | −0.809397 | −0.404698 | − | 0.914450i | \(-0.632624\pi\) | ||||
−0.404698 | + | 0.914450i | \(0.632624\pi\) | |||||||
\(312\) | 90.1325i | 0.288886i | ||||||||
\(313\) | −243.143 | − | 421.136i | −0.776814 | − | 1.34548i | −0.933769 | − | 0.357876i | \(-0.883501\pi\) |
0.156955 | − | 0.987606i | \(-0.449832\pi\) | |||||||
\(314\) | −46.1539 | + | 26.6470i | −0.146987 | + | 0.0848630i | ||||
\(315\) | −18.0567 | −0.0573229 | ||||||||
\(316\) | − | 171.703i | − | 0.543365i | ||||||
\(317\) | −240.229 | + | 138.696i | −0.757819 | + | 0.437527i | −0.828512 | − | 0.559971i | \(-0.810812\pi\) |
0.0706929 | + | 0.997498i | \(0.477479\pi\) | |||||||
\(318\) | −28.3913 | − | 16.3917i | −0.0892809 | − | 0.0515464i | ||||
\(319\) | −677.363 | + | 391.076i | −2.12340 | + | 1.22594i | ||||
\(320\) | −37.9830 | + | 65.7886i | −0.118697 | + | 0.205589i | ||||
\(321\) | −200.660 | + | 347.553i | −0.625109 | + | 1.08272i | ||||
\(322\) | 27.1295i | 0.0842532i | ||||||||
\(323\) | 203.003 | + | 166.940i | 0.628493 | + | 0.516843i | ||||
\(324\) | −262.679 | −0.810738 | ||||||||
\(325\) | 81.8803 | + | 47.2736i | 0.251939 | + | 0.145457i | ||||
\(326\) | 79.0203 | + | 45.6224i | 0.242394 | + | 0.139946i | ||||
\(327\) | −187.514 | − | 324.784i | −0.573437 | − | 0.993222i | ||||
\(328\) | 84.1772 | − | 145.799i | 0.256638 | − | 0.444510i | ||||
\(329\) | −72.2680 | − | 125.172i | −0.219660 | − | 0.380462i | ||||
\(330\) | 106.620 | 0.323091 | ||||||||
\(331\) | − | 110.480i | − | 0.333776i | −0.985976 | − | 0.166888i | \(-0.946628\pi\) | ||
0.985976 | − | 0.166888i | \(-0.0533719\pi\) | |||||||
\(332\) | 131.691 | + | 228.096i | 0.396660 | + | 0.687036i | ||||
\(333\) | 19.0091 | − | 10.9749i | 0.0570843 | − | 0.0329577i | ||||
\(334\) | −42.3088 | −0.126673 | ||||||||
\(335\) | 304.846i | 0.909988i | ||||||||
\(336\) | 218.698 | − | 126.265i | 0.650887 | − | 0.375790i | ||||
\(337\) | 23.9735 | + | 13.8411i | 0.0711380 | + | 0.0410716i | 0.535147 | − | 0.844759i | \(-0.320256\pi\) |
−0.464009 | + | 0.885830i | \(0.653590\pi\) | |||||||
\(338\) | 76.4694 | − | 44.1496i | 0.226241 | − | 0.130620i | ||||
\(339\) | 27.5198 | − | 47.6658i | 0.0811795 | − | 0.140607i | ||||
\(340\) | −76.1866 | + | 131.959i | −0.224078 | + | 0.388115i | ||||
\(341\) | − | 761.147i | − | 2.23210i | ||||||
\(342\) | 9.00312 | + | 1.49567i | 0.0263249 | + | 0.00437330i | ||||
\(343\) | 257.059 | 0.749443 | ||||||||
\(344\) | −138.759 | − | 80.1125i | −0.403369 | − | 0.232885i | ||||
\(345\) | −38.2499 | − | 22.0836i | −0.110869 | − | 0.0640104i | ||||
\(346\) | 109.920 | + | 190.388i | 0.317689 | + | 0.550254i | ||||
\(347\) | −129.243 | + | 223.856i | −0.372459 | + | 0.645118i | −0.989943 | − | 0.141465i | \(-0.954819\pi\) |
0.617484 | + | 0.786583i | \(0.288152\pi\) | |||||||
\(348\) | 225.562 | + | 390.684i | 0.648165 | + | 1.12266i | ||||
\(349\) | 502.852 | 1.44084 | 0.720419 | − | 0.693539i | \(-0.243950\pi\) | ||||
0.720419 | + | 0.693539i | \(0.243950\pi\) | |||||||
\(350\) | 84.3183i | 0.240909i | ||||||||
\(351\) | −86.1037 | − | 149.136i | −0.245310 | − | 0.424889i | ||||
\(352\) | 422.798 | − | 244.103i | 1.20113 | − | 0.693474i | ||||
\(353\) | 54.1066 | 0.153277 | 0.0766383 | − | 0.997059i | \(-0.475581\pi\) | ||||
0.0766383 | + | 0.997059i | \(0.475581\pi\) | |||||||
\(354\) | − | 45.5514i | − | 0.128676i | ||||||
\(355\) | 4.22930 | − | 2.44179i | 0.0119135 | − | 0.00687828i | ||||
\(356\) | −287.521 | − | 166.000i | −0.807642 | − | 0.466292i | ||||
\(357\) | 281.167 | − | 162.332i | 0.787582 | − | 0.454711i | ||||
\(358\) | −89.7844 | + | 155.511i | −0.250794 | + | 0.434389i | ||||
\(359\) | 218.686 | − | 378.775i | 0.609152 | − | 1.05508i | −0.382228 | − | 0.924068i | \(-0.624843\pi\) |
0.991380 | − | 0.131015i | \(-0.0418236\pi\) | |||||||
\(360\) | 11.2592i | 0.0312756i | ||||||||
\(361\) | −341.609 | − | 116.723i | −0.946286 | − | 0.323332i | ||||
\(362\) | −101.127 | −0.279356 | ||||||||
\(363\) | 479.306 | + | 276.727i | 1.32040 | + | 0.762334i | ||||
\(364\) | 154.206 | + | 89.0308i | 0.423643 | + | 0.244590i | ||||
\(365\) | 8.86930 | + | 15.3621i | 0.0242994 | + | 0.0420879i | ||||
\(366\) | −16.5357 | + | 28.6407i | −0.0451796 | + | 0.0782534i | ||||
\(367\) | 48.1329 | + | 83.3687i | 0.131152 | + | 0.227163i | 0.924121 | − | 0.382100i | \(-0.124799\pi\) |
−0.792969 | + | 0.609262i | \(0.791466\pi\) | |||||||
\(368\) | −53.1461 | −0.144419 | ||||||||
\(369\) | 23.6121i | 0.0639894i | ||||||||
\(370\) | 32.2104 | + | 55.7901i | 0.0870553 | + | 0.150784i | ||||
\(371\) | −119.356 | + | 68.9101i | −0.321714 | + | 0.185741i | ||||
\(372\) | −439.009 | −1.18013 | ||||||||
\(373\) | 598.561i | 1.60472i | 0.596840 | + | 0.802360i | \(0.296423\pi\) | ||||
−0.596840 | + | 0.802360i | \(0.703577\pi\) | |||||||
\(374\) | 142.843 | − | 82.4707i | 0.381934 | − | 0.220510i | ||||
\(375\) | −312.478 | − | 180.409i | −0.833275 | − | 0.481091i | ||||
\(376\) | −78.0505 | + | 45.0625i | −0.207581 | + | 0.119847i | ||||
\(377\) | −136.085 | + | 235.706i | −0.360968 | + | 0.625214i | ||||
\(378\) | 76.7882 | − | 133.001i | 0.203143 | − | 0.351855i | ||||
\(379\) | 161.020i | 0.424855i | 0.977177 | + | 0.212427i | \(0.0681369\pi\) | ||||
−0.977177 | + | 0.212427i | \(0.931863\pi\) | |||||||
\(380\) | 34.2983 | − | 206.457i | 0.0902586 | − | 0.543308i | ||||
\(381\) | −70.2479 | −0.184378 | ||||||||
\(382\) | 58.0979 | + | 33.5428i | 0.152089 | + | 0.0878084i | ||||
\(383\) | 200.487 | + | 115.751i | 0.523464 | + | 0.302222i | 0.738351 | − | 0.674417i | \(-0.235605\pi\) |
−0.214887 | + | 0.976639i | \(0.568938\pi\) | |||||||
\(384\) | −182.525 | − | 316.143i | −0.475327 | − | 0.823290i | ||||
\(385\) | 224.113 | − | 388.174i | 0.582111 | − | 1.00825i | ||||
\(386\) | 16.4992 | + | 28.5775i | 0.0427440 | + | 0.0740348i | ||||
\(387\) | 22.4719 | 0.0580670 | ||||||||
\(388\) | 33.4008i | 0.0860845i | ||||||||
\(389\) | −40.5074 | − | 70.1609i | −0.104132 | − | 0.180362i | 0.809251 | − | 0.587463i | \(-0.199873\pi\) |
−0.913383 | + | 0.407101i | \(0.866540\pi\) | |||||||
\(390\) | 32.1306 | − | 18.5506i | 0.0823860 | − | 0.0475656i | ||||
\(391\) | −68.3268 | −0.174749 | ||||||||
\(392\) | 88.8151i | 0.226569i | ||||||||
\(393\) | −189.949 | + | 109.667i | −0.483330 | + | 0.279051i | ||||
\(394\) | 97.9109 | + | 56.5289i | 0.248505 | + | 0.143474i | ||||
\(395\) | −130.252 | + | 75.2010i | −0.329752 | + | 0.190382i | ||||
\(396\) | −22.3754 | + | 38.7553i | −0.0565035 | + | 0.0978669i | ||||
\(397\) | 341.051 | − | 590.718i | 0.859071 | − | 1.48796i | −0.0137446 | − | 0.999906i | \(-0.504375\pi\) |
0.872816 | − | 0.488050i | \(-0.162291\pi\) | |||||||
\(398\) | − | 62.3297i | − | 0.156607i | ||||||
\(399\) | −283.239 | + | 344.425i | −0.709873 | + | 0.863221i | ||||
\(400\) | −165.177 | −0.412944 | ||||||||
\(401\) | −82.6912 | − | 47.7418i | −0.206213 | − | 0.119057i | 0.393337 | − | 0.919394i | \(-0.371320\pi\) |
−0.599550 | + | 0.800337i | \(0.704654\pi\) | |||||||
\(402\) | −164.830 | − | 95.1647i | −0.410025 | − | 0.236728i | ||||
\(403\) | −132.430 | − | 229.376i | −0.328611 | − | 0.569171i | ||||
\(404\) | 236.033 | − | 408.821i | 0.584240 | − | 1.01193i | ||||
\(405\) | 115.046 | + | 199.265i | 0.284063 | + | 0.492012i | ||||
\(406\) | −242.724 | −0.597842 | ||||||||
\(407\) | 544.864i | 1.33873i | ||||||||
\(408\) | −101.221 | − | 175.321i | −0.248092 | − | 0.429708i | ||||
\(409\) | −169.330 | + | 97.7625i | −0.414009 | + | 0.239028i | −0.692511 | − | 0.721408i | \(-0.743495\pi\) |
0.278502 | + | 0.960436i | \(0.410162\pi\) | |||||||
\(410\) | −69.2996 | −0.169023 | ||||||||
\(411\) | 682.924i | 1.66162i | ||||||||
\(412\) | −284.961 | + | 164.522i | −0.691652 | + | 0.399326i | ||||
\(413\) | −165.840 | − | 95.7479i | −0.401550 | − | 0.231835i | ||||
\(414\) | −2.05472 | + | 1.18629i | −0.00496308 | + | 0.00286544i | ||||
\(415\) | 115.354 | − | 199.798i | 0.277961 | − | 0.481442i | ||||
\(416\) | 84.9418 | − | 147.124i | 0.204187 | − | 0.353662i | ||||
\(417\) | − | 57.8060i | − | 0.138624i | ||||||
\(418\) | −143.896 | + | 174.981i | −0.344250 | + | 0.418615i | ||||
\(419\) | −388.318 | −0.926773 | −0.463387 | − | 0.886156i | \(-0.653366\pi\) | ||||
−0.463387 | + | 0.886156i | \(0.653366\pi\) | |||||||
\(420\) | −223.888 | − | 129.262i | −0.533067 | − | 0.307766i | ||||
\(421\) | 225.968 | + | 130.463i | 0.536742 | + | 0.309888i | 0.743758 | − | 0.668449i | \(-0.233042\pi\) |
−0.207015 | + | 0.978338i | \(0.566375\pi\) | |||||||
\(422\) | 21.1617 | + | 36.6531i | 0.0501462 | + | 0.0868557i | ||||
\(423\) | 6.32012 | − | 10.9468i | 0.0149412 | − | 0.0258789i | ||||
\(424\) | 42.9687 | + | 74.4239i | 0.101341 | + | 0.175528i | ||||
\(425\) | −212.359 | −0.499667 | ||||||||
\(426\) | 3.04904i | 0.00715738i | ||||||||
\(427\) | 69.5154 | + | 120.404i | 0.162800 | + | 0.281977i | ||||
\(428\) | 428.134 | − | 247.183i | 1.00031 | − | 0.577531i | ||||
\(429\) | 313.797 | 0.731462 | ||||||||
\(430\) | 65.9533i | 0.153380i | ||||||||
\(431\) | 496.682 | − | 286.760i | 1.15239 | − | 0.665335i | 0.202925 | − | 0.979194i | \(-0.434955\pi\) |
0.949470 | + | 0.313859i | \(0.101622\pi\) | |||||||
\(432\) | 260.546 | + | 150.426i | 0.603116 | + | 0.348209i | ||||
\(433\) | 216.750 | − | 125.141i | 0.500578 | − | 0.289009i | −0.228374 | − | 0.973573i | \(-0.573341\pi\) |
0.728952 | + | 0.684565i | \(0.240008\pi\) | |||||||
\(434\) | 118.103 | − | 204.560i | 0.272126 | − | 0.471337i | ||||
\(435\) | 197.579 | − | 342.216i | 0.454203 | − | 0.786704i | ||||
\(436\) | 461.978i | 1.05958i | ||||||||
\(437\) | 87.8656 | − | 32.9700i | 0.201065 | − | 0.0754463i | ||||
\(438\) | −11.0750 | −0.0252854 | ||||||||
\(439\) | 406.897 | + | 234.922i | 0.926872 | + | 0.535130i | 0.885821 | − | 0.464027i | \(-0.153596\pi\) |
0.0410511 | + | 0.999157i | \(0.486929\pi\) | |||||||
\(440\) | −242.045 | − | 139.745i | −0.550102 | − | 0.317602i | ||||
\(441\) | −6.22826 | − | 10.7877i | −0.0141230 | − | 0.0244618i | ||||
\(442\) | 28.6978 | − | 49.7060i | 0.0649271 | − | 0.112457i | ||||
\(443\) | −360.119 | − | 623.744i | −0.812909 | − | 1.40800i | −0.910819 | − | 0.412805i | \(-0.864549\pi\) |
0.0979100 | − | 0.995195i | \(-0.468784\pi\) | |||||||
\(444\) | 314.262 | 0.707798 | ||||||||
\(445\) | 290.812i | 0.653511i | ||||||||
\(446\) | −144.648 | − | 250.538i | −0.324323 | − | 0.561744i | ||||
\(447\) | 388.161 | − | 224.105i | 0.868368 | − | 0.501353i | ||||
\(448\) | −199.390 | −0.445066 | ||||||||
\(449\) | 726.910i | 1.61895i | 0.587151 | + | 0.809477i | \(0.300249\pi\) | ||||
−0.587151 | + | 0.809477i | \(0.699751\pi\) | |||||||
\(450\) | −6.38603 | + | 3.68698i | −0.0141912 | + | 0.00819329i | ||||
\(451\) | −507.601 | − | 293.064i | −1.12550 | − | 0.649809i | ||||
\(452\) | −58.7171 | + | 33.9003i | −0.129905 | + | 0.0750007i | ||||
\(453\) | −59.6869 | + | 103.381i | −0.131759 | + | 0.228214i | ||||
\(454\) | −82.9256 | + | 143.631i | −0.182655 | + | 0.316369i | ||||
\(455\) | − | 155.971i | − | 0.342794i | ||||||
\(456\) | 214.765 | + | 176.613i | 0.470977 | + | 0.387309i | ||||
\(457\) | 114.104 | 0.249681 | 0.124841 | − | 0.992177i | \(-0.460158\pi\) | ||||
0.124841 | + | 0.992177i | \(0.460158\pi\) | |||||||
\(458\) | 18.5988 | + | 10.7380i | 0.0406087 | + | 0.0234454i | ||||
\(459\) | 334.968 | + | 193.394i | 0.729778 | + | 0.421338i | ||||
\(460\) | 27.2037 | + | 47.1182i | 0.0591385 | + | 0.102431i | ||||
\(461\) | 157.029 | − | 271.982i | 0.340626 | − | 0.589982i | −0.643923 | − | 0.765090i | \(-0.722694\pi\) |
0.984549 | + | 0.175108i | \(0.0560276\pi\) | |||||||
\(462\) | 139.924 | + | 242.355i | 0.302865 | + | 0.524578i | ||||
\(463\) | 402.830 | 0.870044 | 0.435022 | − | 0.900420i | \(-0.356741\pi\) | ||||
0.435022 | + | 0.900420i | \(0.356741\pi\) | |||||||
\(464\) | − | 475.490i | − | 1.02476i | ||||||
\(465\) | 192.273 | + | 333.026i | 0.413490 | + | 0.716185i | ||||
\(466\) | 215.791 | − | 124.587i | 0.463071 | − | 0.267354i | ||||
\(467\) | −759.715 | −1.62680 | −0.813399 | − | 0.581706i | \(-0.802386\pi\) | ||||
−0.813399 | + | 0.581706i | \(0.802386\pi\) | |||||||
\(468\) | 15.5722i | 0.0332739i | ||||||||
\(469\) | −692.938 | + | 400.068i | −1.47748 | + | 0.853023i | ||||
\(470\) | 32.1279 | + | 18.5490i | 0.0683572 | + | 0.0394660i | ||||
\(471\) | 197.219 | − | 113.864i | 0.418724 | − | 0.241751i | ||||
\(472\) | −59.7033 | + | 103.409i | −0.126490 | + | 0.219087i | ||||
\(473\) | −278.912 | + | 483.090i | −0.589667 | + | 1.02133i | ||||
\(474\) | − | 93.9029i | − | 0.198107i | ||||||
\(475\) | 273.085 | − | 102.470i | 0.574916 | − | 0.215727i | ||||
\(476\) | −399.937 | −0.840204 | ||||||||
\(477\) | −10.4381 | − | 6.02645i | −0.0218829 | − | 0.0126341i | ||||
\(478\) | −62.1744 | − | 35.8964i | −0.130072 | − | 0.0750971i | ||||
\(479\) | 14.1426 | + | 24.4957i | 0.0295253 | + | 0.0511393i | 0.880411 | − | 0.474212i | \(-0.157267\pi\) |
−0.850885 | + | 0.525352i | \(0.823934\pi\) | |||||||
\(480\) | −123.325 | + | 213.605i | −0.256927 | + | 0.445011i | ||||
\(481\) | 94.7997 | + | 164.198i | 0.197089 | + | 0.341368i | ||||
\(482\) | 9.31119 | 0.0193178 | ||||||||
\(483\) | − | 115.926i | − | 0.240013i | ||||||
\(484\) | −340.887 | − | 590.433i | −0.704311 | − | 1.21990i | ||||
\(485\) | 25.3374 | − | 14.6285i | 0.0522420 | − | 0.0301620i | ||||
\(486\) | 25.8758 | 0.0532423 | ||||||||
\(487\) | − | 918.051i | − | 1.88511i | −0.334045 | − | 0.942557i | \(-0.608414\pi\) | ||
0.334045 | − | 0.942557i | \(-0.391586\pi\) | |||||||
\(488\) | 75.0777 | − | 43.3461i | 0.153848 | − | 0.0888241i | ||||
\(489\) | −337.660 | − | 194.948i | −0.690510 | − | 0.398666i | ||||
\(490\) | 31.6609 | − | 18.2794i | 0.0646141 | − | 0.0373050i | ||||
\(491\) | −20.5361 | + | 35.5696i | −0.0418250 | + | 0.0724431i | −0.886180 | − | 0.463341i | \(-0.846651\pi\) |
0.844355 | + | 0.535784i | \(0.179984\pi\) | |||||||
\(492\) | −169.031 | + | 292.770i | −0.343559 | + | 0.595062i | ||||
\(493\) | − | 611.309i | − | 1.23998i | ||||||
\(494\) | −12.9194 | + | 77.7678i | −0.0261526 | + | 0.157425i | ||||
\(495\) | 39.1990 | 0.0791899 | ||||||||
\(496\) | 400.728 | + | 231.361i | 0.807920 | + | 0.466453i | ||||
\(497\) | 11.1007 | + | 6.40901i | 0.0223355 | + | 0.0128954i | ||||
\(498\) | 72.0206 | + | 124.743i | 0.144620 | + | 0.250489i | ||||
\(499\) | −324.374 | + | 561.832i | −0.650047 | + | 1.12592i | 0.333063 | + | 0.942904i | \(0.391918\pi\) |
−0.983111 | + | 0.183011i | \(0.941416\pi\) | |||||||
\(500\) | 222.237 | + | 384.926i | 0.444474 | + | 0.769852i | ||||
\(501\) | 180.789 | 0.360856 | ||||||||
\(502\) | − | 82.7181i | − | 0.164777i | ||||||
\(503\) | −205.525 | − | 355.979i | −0.408598 | − | 0.707712i | 0.586135 | − | 0.810213i | \(-0.300649\pi\) |
−0.994733 | + | 0.102501i | \(0.967315\pi\) | |||||||
\(504\) | −25.5930 | + | 14.7761i | −0.0507798 | + | 0.0293177i | ||||
\(505\) | −413.501 | −0.818815 | ||||||||
\(506\) | − | 58.8951i | − | 0.116393i | ||||||
\(507\) | −326.759 | + | 188.654i | −0.644495 | + | 0.372100i | ||||
\(508\) | 74.9414 | + | 43.2675i | 0.147523 | + | 0.0851722i | ||||
\(509\) | −19.2779 | + | 11.1301i | −0.0378740 | + | 0.0218666i | −0.518817 | − | 0.854885i | \(-0.673628\pi\) |
0.480943 | + | 0.876752i | \(0.340294\pi\) | |||||||
\(510\) | −41.6657 | + | 72.1671i | −0.0816974 | + | 0.141504i | ||||
\(511\) | −23.2794 | + | 40.3211i | −0.0455566 | + | 0.0789064i | ||||
\(512\) | 515.592i | 1.00701i | ||||||||
\(513\) | −524.076 | − | 87.0636i | −1.02159 | − | 0.169715i | ||||
\(514\) | 266.924 | 0.519307 | ||||||||
\(515\) | 249.609 | + | 144.112i | 0.484677 | + | 0.279828i | ||||
\(516\) | 278.633 | + | 160.869i | 0.539986 | + | 0.311761i | ||||
\(517\) | 156.885 | + | 271.734i | 0.303454 | + | 0.525597i | ||||
\(518\) | −84.5434 | + | 146.433i | −0.163211 | + | 0.282690i | ||||
\(519\) | −469.698 | − | 813.541i | −0.905006 | − | 1.56752i | ||||
\(520\) | −97.2555 | −0.187030 | ||||||||
\(521\) | 87.1316i | 0.167239i | 0.996498 | + | 0.0836196i | \(0.0266481\pi\) | ||||
−0.996498 | + | 0.0836196i | \(0.973352\pi\) | |||||||
\(522\) | −10.6136 | − | 18.3832i | −0.0203325 | − | 0.0352169i | ||||
\(523\) | −342.658 | + | 197.833i | −0.655177 | + | 0.378267i | −0.790437 | − | 0.612544i | \(-0.790146\pi\) |
0.135260 | + | 0.990810i | \(0.456813\pi\) | |||||||
\(524\) | 270.187 | 0.515624 | ||||||||
\(525\) | − | 360.298i | − | 0.686282i | ||||||
\(526\) | −31.2112 | + | 18.0198i | −0.0593369 | + | 0.0342582i | ||||
\(527\) | 515.192 | + | 297.446i | 0.977594 | + | 0.564414i | ||||
\(528\) | −474.768 | + | 274.107i | −0.899182 | + | 0.519143i | ||||
\(529\) | 252.301 | − | 436.999i | 0.476940 | − | 0.826085i | ||||
\(530\) | 17.6872 | − | 30.6350i | 0.0333720 | − | 0.0578020i | ||||
\(531\) | − | 16.7471i | − | 0.0315387i | ||||||
\(532\) | 514.304 | − | 192.983i | 0.966736 | − | 0.362751i | ||||
\(533\) | −203.958 | −0.382661 | ||||||||
\(534\) | −157.242 | − | 90.7838i | −0.294461 | − | 0.170007i | ||||
\(535\) | −375.020 | − | 216.518i | −0.700972 | − | 0.404706i | ||||
\(536\) | 249.461 | + | 432.079i | 0.465412 | + | 0.806118i | ||||
\(537\) | 383.655 | − | 664.510i | 0.714442 | − | 1.23745i | ||||
\(538\) | −123.048 | − | 213.126i | −0.228714 | − | 0.396145i | ||||
\(539\) | 309.210 | 0.573674 | ||||||||
\(540\) | − | 307.992i | − | 0.570356i | ||||||
\(541\) | 509.586 | + | 882.629i | 0.941933 | + | 1.63148i | 0.761778 | + | 0.647838i | \(0.224327\pi\) |
0.180155 | + | 0.983638i | \(0.442340\pi\) | |||||||
\(542\) | 101.731 | − | 58.7344i | 0.187696 | − | 0.108366i | ||||
\(543\) | 432.122 | 0.795805 | ||||||||
\(544\) | 381.569i | 0.701413i | ||||||||
\(545\) | 350.451 | − | 202.333i | 0.643029 | − | 0.371253i | ||||
\(546\) | 84.3337 | + | 48.6901i | 0.154457 | + | 0.0891760i | ||||
\(547\) | 582.402 | − | 336.250i | 1.06472 | − | 0.614717i | 0.137986 | − | 0.990434i | \(-0.455937\pi\) |
0.926734 | + | 0.375717i | \(0.122604\pi\) | |||||||
\(548\) | 420.630 | − | 728.553i | 0.767573 | − | 1.32948i | ||||
\(549\) | −6.07939 | + | 10.5298i | −0.0110736 | + | 0.0191800i | ||||
\(550\) | − | 183.045i | − | 0.332809i | ||||||
\(551\) | 294.978 | + | 786.120i | 0.535350 | + | 1.42672i | ||||
\(552\) | −72.2856 | −0.130952 | ||||||||
\(553\) | −341.875 | − | 197.382i | −0.618219 | − | 0.356929i | ||||
\(554\) | −54.4232 | − | 31.4213i | −0.0982369 | − | 0.0567171i | ||||
\(555\) | −137.638 | − | 238.395i | −0.247996 | − | 0.429541i | ||||
\(556\) | −35.6042 | + | 61.6683i | −0.0640363 | + | 0.110914i | ||||
\(557\) | 108.576 | + | 188.060i | 0.194931 | + | 0.337630i | 0.946878 | − | 0.321594i | \(-0.104219\pi\) |
−0.751947 | + | 0.659223i | \(0.770885\pi\) | |||||||
\(558\) | 20.6571 | 0.0370199 | ||||||||
\(559\) | 194.109i | 0.347244i | ||||||||
\(560\) | 136.244 | + | 235.981i | 0.243293 | + | 0.421395i | ||||
\(561\) | −610.381 | + | 352.403i | −1.08802 | + | 0.628170i | ||||
\(562\) | −253.082 | −0.450324 | ||||||||
\(563\) | − | 571.551i | − | 1.01519i | −0.861596 | − | 0.507594i | \(-0.830535\pi\) | ||
0.861596 | − | 0.507594i | \(-0.169465\pi\) | |||||||
\(564\) | 156.728 | − | 90.4872i | 0.277887 | − | 0.160438i | ||||
\(565\) | 51.4327 | + | 29.6947i | 0.0910313 | + | 0.0525570i | ||||
\(566\) | −37.4245 | + | 21.6071i | −0.0661211 | + | 0.0381750i | ||||
\(567\) | −301.963 | + | 523.015i | −0.532562 | + | 0.922425i | ||||
\(568\) | 3.99632 | − | 6.92183i | 0.00703578 | − | 0.0121863i | ||||
\(569\) | 411.891i | 0.723886i | 0.932200 | + | 0.361943i | \(0.117886\pi\) | ||||
−0.932200 | + | 0.361943i | \(0.882114\pi\) | |||||||
\(570\) | 18.7574 | − | 112.909i | 0.0329077 | − | 0.198087i | ||||
\(571\) | 746.121 | 1.30669 | 0.653346 | − | 0.757060i | \(-0.273365\pi\) | ||||
0.653346 | + | 0.757060i | \(0.273365\pi\) | |||||||
\(572\) | −334.763 | − | 193.276i | −0.585250 | − | 0.337894i | ||||
\(573\) | −248.256 | − | 143.331i | −0.433257 | − | 0.250141i | ||||
\(574\) | −90.9460 | − | 157.523i | −0.158443 | − | 0.274431i | ||||
\(575\) | −37.9131 | + | 65.6674i | −0.0659358 | + | 0.114204i | ||||
\(576\) | −8.71870 | − | 15.1012i | −0.0151366 | − | 0.0262174i | ||||
\(577\) | −877.551 | −1.52089 | −0.760443 | − | 0.649405i | \(-0.775018\pi\) | ||||
−0.760443 | + | 0.649405i | \(0.775018\pi\) | |||||||
\(578\) | − | 65.7817i | − | 0.113809i | ||||||
\(579\) | −70.5023 | − | 122.114i | −0.121766 | − | 0.210904i | ||||
\(580\) | −421.559 | + | 243.387i | −0.726826 | + | 0.419633i | ||||
\(581\) | 605.542 | 1.04224 | ||||||||
\(582\) | 18.2666i | 0.0313858i | ||||||||
\(583\) | 259.107 | − | 149.596i | 0.444438 | − | 0.256597i | ||||
\(584\) | 25.1421 | + | 14.5158i | 0.0430516 | + | 0.0248558i | ||||
\(585\) | 11.8128 | − | 6.82015i | 0.0201929 | − | 0.0116584i | ||||
\(586\) | −37.6639 | + | 65.2358i | −0.0642728 | + | 0.111324i | ||||
\(587\) | −0.899138 | + | 1.55735i | −0.00153175 | + | 0.00265307i | −0.866790 | − | 0.498673i | \(-0.833821\pi\) |
0.865259 | + | 0.501326i | \(0.167154\pi\) | |||||||
\(588\) | − | 178.344i | − | 0.303306i | ||||||
\(589\) | −806.046 | − | 133.907i | −1.36850 | − | 0.227346i | ||||
\(590\) | 49.1513 | 0.0833072 | ||||||||
\(591\) | −418.380 | − | 241.552i | −0.707919 | − | 0.408717i | ||||
\(592\) | −286.860 | − | 165.618i | −0.484560 | − | 0.279761i | ||||
\(593\) | −5.61476 | − | 9.72504i | −0.00946839 | − | 0.0163997i | 0.861252 | − | 0.508177i | \(-0.169681\pi\) |
−0.870721 | + | 0.491778i | \(0.836347\pi\) | |||||||
\(594\) | −166.698 | + | 288.730i | −0.280637 | + | 0.486077i | ||||
\(595\) | 175.160 | + | 303.387i | 0.294387 | + | 0.509894i | ||||
\(596\) | −552.127 | −0.926387 | ||||||||
\(597\) | 266.339i | 0.446129i | ||||||||
\(598\) | −10.2470 | − | 17.7484i | −0.0171355 | − | 0.0296795i | ||||
\(599\) | −391.707 | + | 226.152i | −0.653934 | + | 0.377549i | −0.789962 | − | 0.613156i | \(-0.789900\pi\) |
0.136028 | + | 0.990705i | \(0.456566\pi\) | |||||||
\(600\) | −224.663 | −0.374438 | ||||||||
\(601\) | − | 32.0350i | − | 0.0533029i | −0.999645 | − | 0.0266514i | \(-0.991516\pi\) | ||
0.999645 | − | 0.0266514i | \(-0.00848442\pi\) | |||||||
\(602\) | −149.917 | + | 86.5544i | −0.249031 | + | 0.143778i | ||||
\(603\) | −60.6001 | − | 34.9875i | −0.100498 | − | 0.0580223i | ||||
\(604\) | 127.350 | − | 73.5253i | 0.210844 | − | 0.121731i | ||||
\(605\) | −298.596 | + | 517.184i | −0.493548 | + | 0.854850i | ||||
\(606\) | 129.084 | − | 223.580i | 0.213010 | − | 0.368944i | ||||
\(607\) | 161.891i | 0.266706i | 0.991069 | + | 0.133353i | \(0.0425745\pi\) | ||||
−0.991069 | + | 0.133353i | \(0.957426\pi\) | |||||||
\(608\) | −184.120 | − | 490.683i | −0.302829 | − | 0.807044i | ||||
\(609\) | 1037.18 | 1.70308 | ||||||||
\(610\) | −30.9042 | − | 17.8425i | −0.0506626 | − | 0.0292500i | ||||
\(611\) | 94.5567 | + | 54.5923i | 0.154757 | + | 0.0893491i | ||||
\(612\) | −17.4880 | − | 30.2901i | −0.0285752 | − | 0.0494937i | ||||
\(613\) | −9.10873 | + | 15.7768i | −0.0148593 | + | 0.0257370i | −0.873359 | − | 0.487076i | \(-0.838063\pi\) |
0.858500 | + | 0.512813i | \(0.171397\pi\) | |||||||
\(614\) | 115.648 | + | 200.308i | 0.188351 | + | 0.326234i | ||||
\(615\) | 296.122 | 0.481500 | ||||||||
\(616\) | − | 733.582i | − | 1.19088i | ||||||
\(617\) | 355.912 | + | 616.457i | 0.576842 | + | 0.999120i | 0.995839 | + | 0.0911323i | \(0.0290486\pi\) |
−0.418997 | + | 0.907988i | \(0.637618\pi\) | |||||||
\(618\) | −155.842 | + | 89.9756i | −0.252172 | + | 0.145592i | ||||
\(619\) | 1039.82 | 1.67984 | 0.839918 | − | 0.542713i | \(-0.182603\pi\) | ||||
0.839918 | + | 0.542713i | \(0.182603\pi\) | |||||||
\(620\) | − | 473.702i | − | 0.764036i | ||||||
\(621\) | 119.606 | − | 69.0545i | 0.192602 | − | 0.111199i | ||||
\(622\) | 146.862 | + | 84.7911i | 0.236113 | + | 0.136320i | ||||
\(623\) | −661.038 | + | 381.651i | −1.06106 | + | 0.612601i | ||||
\(624\) | −95.3827 | + | 165.208i | −0.152857 | + | 0.264756i | ||||
\(625\) | 2.77356 | − | 4.80394i | 0.00443769 | − | 0.00768631i | ||||
\(626\) | 327.604i | 0.523330i | ||||||||
\(627\) | 614.880 | − | 747.707i | 0.980669 | − | 1.19252i | ||||
\(628\) | −280.528 | −0.446701 | ||||||||
\(629\) | −368.798 | − | 212.926i | −0.586325 | − | 0.338515i | ||||
\(630\) | 10.5348 | + | 6.08228i | 0.0167219 | + | 0.00965442i | ||||
\(631\) | −417.964 | − | 723.935i | −0.662383 | − | 1.14728i | −0.979988 | − | 0.199058i | \(-0.936212\pi\) |
0.317604 | − | 0.948223i | \(-0.397122\pi\) | |||||||
\(632\) | −123.077 | + | 213.175i | −0.194742 | + | 0.337302i | ||||
\(633\) | −90.4254 | − | 156.621i | −0.142852 | − | 0.247427i | ||||
\(634\) | 186.876 | 0.294756 | ||||||||
\(635\) | − | 75.7994i | − | 0.119369i | ||||||
\(636\) | −86.2827 | − | 149.446i | −0.135665 | − | 0.234978i | ||||
\(637\) | 93.1823 | − | 53.7988i | 0.146283 | − | 0.0844566i | ||||
\(638\) | 526.925 | 0.825902 | ||||||||
\(639\) | 1.12099i | 0.00175428i | ||||||||
\(640\) | 341.128 | − | 196.950i | 0.533012 | − | 0.307735i | ||||
\(641\) | 504.690 | + | 291.383i | 0.787347 | + | 0.454575i | 0.839028 | − | 0.544089i | \(-0.183124\pi\) |
−0.0516806 | + | 0.998664i | \(0.516458\pi\) | |||||||
\(642\) | 234.142 | − | 135.182i | 0.364708 | − | 0.210564i | ||||
\(643\) | −238.122 | + | 412.439i | −0.370330 | + | 0.641430i | −0.989616 | − | 0.143735i | \(-0.954089\pi\) |
0.619286 | + | 0.785165i | \(0.287422\pi\) | |||||||
\(644\) | −71.4021 | + | 123.672i | −0.110873 | + | 0.192037i | ||||
\(645\) | − | 281.823i | − | 0.436935i | ||||||
\(646\) | −62.2054 | − | 165.778i | −0.0962932 | − | 0.256623i | ||||
\(647\) | −304.985 | −0.471383 | −0.235691 | − | 0.971828i | \(-0.575735\pi\) | ||||
−0.235691 | + | 0.971828i | \(0.575735\pi\) | |||||||
\(648\) | 326.124 | + | 188.288i | 0.503278 | + | 0.290568i | ||||
\(649\) | 360.020 | + | 207.858i | 0.554730 | + | 0.320274i | ||||
\(650\) | −31.8476 | − | 55.1617i | −0.0489963 | − | 0.0848642i | ||||
\(651\) | −504.662 | + | 874.100i | −0.775210 | + | 1.34270i | ||||
\(652\) | 240.147 | + | 415.946i | 0.368323 | + | 0.637954i | ||||
\(653\) | 123.278 | 0.188787 | 0.0943937 | − | 0.995535i | \(-0.469909\pi\) | ||||
0.0943937 | + | 0.995535i | \(0.469909\pi\) | |||||||
\(654\) | 252.651i | 0.386317i | ||||||||
\(655\) | −118.334 | − | 204.960i | −0.180662 | − | 0.312916i | ||||
\(656\) | 308.584 | − | 178.161i | 0.470402 | − | 0.271587i | ||||
\(657\) | −4.07175 | −0.00619749 | ||||||||
\(658\) | 97.3721i | 0.147982i | ||||||||
\(659\) | 749.625 | − | 432.796i | 1.13752 | − | 0.656747i | 0.191704 | − | 0.981453i | \(-0.438599\pi\) |
0.945815 | + | 0.324706i | \(0.105265\pi\) | |||||||
\(660\) | 486.035 | + | 280.613i | 0.736417 | + | 0.425171i | ||||
\(661\) | −572.988 | + | 330.815i | −0.866850 | + | 0.500476i | −0.866300 | − | 0.499524i | \(-0.833508\pi\) |
−0.000549974 | 1.00000i | \(0.500175\pi\) | ||||||||
\(662\) | −37.2145 | + | 64.4573i | −0.0562152 | + | 0.0973676i | ||||
\(663\) | −122.628 | + | 212.398i | −0.184959 | + | 0.320358i | ||||
\(664\) | − | 377.584i | − | 0.568651i | ||||||
\(665\) | −371.644 | − | 305.623i | −0.558864 | − | 0.459583i | ||||
\(666\) | −14.7873 | −0.0222031 | ||||||||
\(667\) | −189.034 | − | 109.139i | −0.283410 | − | 0.163627i | ||||
\(668\) | −192.868 | − | 111.352i | −0.288724 | − | 0.166695i | ||||
\(669\) | 618.092 | + | 1070.57i | 0.923904 | + | 1.60025i | ||||
\(670\) | 102.685 | − | 177.856i | 0.153262 | − | 0.265457i | ||||
\(671\) | −150.910 | − | 261.384i | −0.224903 | − | 0.389543i | ||||
\(672\) | −647.388 | −0.963375 | ||||||||
\(673\) | − | 104.231i | − | 0.154875i | −0.996997 | − | 0.0774373i | \(-0.975326\pi\) | ||
0.996997 | − | 0.0774373i | \(-0.0246737\pi\) | |||||||
\(674\) | −9.32458 | − | 16.1506i | −0.0138347 | − | 0.0239624i | ||||
\(675\) | 371.734 | − | 214.621i | 0.550717 | − | 0.317956i | ||||
\(676\) | 464.788 | 0.687557 | ||||||||
\(677\) | − | 863.985i | − | 1.27620i | −0.769955 | − | 0.638099i | \(-0.779721\pi\) | ||
0.769955 | − | 0.638099i | \(-0.220279\pi\) | |||||||
\(678\) | −32.1118 | + | 18.5398i | −0.0473626 | + | 0.0273448i | ||||
\(679\) | 66.5036 | + | 38.3958i | 0.0979434 | + | 0.0565476i | ||||
\(680\) | 189.176 | − | 109.221i | 0.278200 | − | 0.160619i | ||||
\(681\) | 354.347 | − | 613.747i | 0.520333 | − | 0.901244i | ||||
\(682\) | −256.388 | + | 444.076i | −0.375935 | + | 0.651138i | ||||
\(683\) | − | 34.9808i | − | 0.0512165i | −0.999672 | − | 0.0256082i | \(-0.991848\pi\) | ||
0.999672 | − | 0.0256082i | \(-0.00815224\pi\) | |||||||
\(684\) | 37.1050 | + | 30.5134i | 0.0542470 | + | 0.0446102i | ||||
\(685\) | −736.894 | −1.07576 | ||||||||
\(686\) | −149.976 | − | 86.5886i | −0.218624 | − | 0.126222i | ||||
\(687\) | −79.4739 | − | 45.8843i | −0.115683 | − | 0.0667893i | ||||
\(688\) | −169.558 | − | 293.683i | −0.246451 | − | 0.426865i | ||||
\(689\) | 52.0557 | − | 90.1631i | 0.0755525 | − | 0.130861i | ||||
\(690\) | 14.8774 | + | 25.7685i | 0.0215615 | + | 0.0373456i | ||||
\(691\) | −346.797 | −0.501876 | −0.250938 | − | 0.968003i | \(-0.580739\pi\) | ||||
−0.250938 | + | 0.968003i | \(0.580739\pi\) | |||||||
\(692\) | 1157.20i | 1.67225i | ||||||||
\(693\) | 51.4432 | + | 89.1023i | 0.0742326 | + | 0.128575i | ||||
\(694\) | 150.809 | − | 87.0696i | 0.217304 | − | 0.125461i | ||||
\(695\) | 62.3743 | 0.0897472 | ||||||||
\(696\) | − | 646.728i | − | 0.929208i | ||||||
\(697\) | 396.728 | − | 229.051i | 0.569193 | − | 0.328624i | ||||
\(698\) | −293.379 | − | 169.383i | −0.420314 | − | 0.242668i | ||||
\(699\) | −922.091 | + | 532.369i | −1.31916 | + | 0.761615i | ||||
\(700\) | −221.917 | + | 384.371i | −0.317024 | + | 0.549101i | ||||
\(701\) | −320.881 | + | 555.783i | −0.457748 | + | 0.792843i | −0.998842 | − | 0.0481197i | \(-0.984677\pi\) |
0.541094 | + | 0.840962i | \(0.318010\pi\) | |||||||
\(702\) | 116.014i | 0.165262i | ||||||||
\(703\) | 577.005 | + | 95.8565i | 0.820775 | + | 0.136354i | ||||
\(704\) | 432.852 | 0.614847 | ||||||||
\(705\) | −137.285 | − | 79.2614i | −0.194730 | − | 0.112427i | ||||
\(706\) | −31.5674 | − | 18.2255i | −0.0447131 | − | 0.0258151i | ||||
\(707\) | −542.663 | − | 939.920i | −0.767557 | − | 1.32945i | ||||
\(708\) | 119.887 | − | 207.650i | 0.169331 | − | 0.293290i | ||||
\(709\) | −277.968 | − | 481.454i | −0.392056 | − | 0.679061i | 0.600665 | − | 0.799501i | \(-0.294903\pi\) |
−0.992721 | + | 0.120440i | \(0.961569\pi\) | |||||||
\(710\) | −3.29000 | −0.00463381 | ||||||||
\(711\) | − | 34.5236i | − | 0.0485563i | ||||||
\(712\) | 237.977 | + | 412.188i | 0.334238 | + | 0.578916i | ||||
\(713\) | 183.958 | − | 106.208i | 0.258006 | − | 0.148960i | ||||
\(714\) | −218.722 | −0.306333 | ||||||||
\(715\) | 338.596i | 0.473561i | ||||||||
\(716\) | −818.578 | + | 472.606i | −1.14326 | + | 0.660064i | ||||
\(717\) | 265.676 | + | 153.388i | 0.370538 | + | 0.213930i | ||||
\(718\) | −255.176 | + | 147.326i | −0.355398 | + | 0.205189i | ||||
\(719\) | 120.548 | − | 208.795i | 0.167661 | − | 0.290397i | −0.769936 | − | 0.638121i | \(-0.779712\pi\) |
0.937597 | + | 0.347724i | \(0.113045\pi\) | |||||||
\(720\) | −11.9150 | + | 20.6375i | −0.0165487 | + | 0.0286632i | ||||
\(721\) | 756.505i | 1.04924i | ||||||||
\(722\) | 159.988 | + | 183.168i | 0.221590 | + | 0.253696i | ||||
\(723\) | −39.7874 | −0.0550310 | ||||||||
\(724\) | −460.994 | − | 266.155i | −0.636732 | − | 0.367618i | ||||
\(725\) | −587.516 | − | 339.203i | −0.810367 | − | 0.467866i | ||||
\(726\) | −186.428 | − | 322.902i | −0.256787 | − | 0.444769i | ||||
\(727\) | −495.032 | + | 857.420i | −0.680924 | + | 1.17939i | 0.293776 | + | 0.955874i | \(0.405088\pi\) |
−0.974699 | + | 0.223520i | \(0.928245\pi\) | |||||||
\(728\) | −127.634 | − | 221.069i | −0.175322 | − | 0.303666i | ||||
\(729\) | −777.240 | −1.06617 | ||||||||
\(730\) | − | 11.9503i | − | 0.0163702i | ||||||
\(731\) | −217.991 | − | 377.571i | −0.298209 | − | 0.516513i | ||||
\(732\) | −150.759 | + | 87.0406i | −0.205955 | + | 0.118908i | ||||
\(733\) | 748.994 | 1.02182 | 0.510910 | − | 0.859634i | \(-0.329309\pi\) | ||||
0.510910 | + | 0.859634i | \(0.329309\pi\) | |||||||
\(734\) | − | 64.8531i | − | 0.0883557i | ||||||
\(735\) | −135.289 | + | 78.1093i | −0.184067 | + | 0.106271i | ||||
\(736\) | 117.992 | + | 68.1227i | 0.160315 | + | 0.0925580i | ||||
\(737\) | 1504.29 | − | 868.501i | 2.04110 | − | 1.17843i | ||||
\(738\) | 7.95358 | − | 13.7760i | 0.0107772 | − | 0.0186667i | ||||
\(739\) | −123.521 | + | 213.945i | −0.167147 | + | 0.289506i | −0.937415 | − | 0.348213i | \(-0.886789\pi\) |
0.770269 | + | 0.637719i | \(0.220122\pi\) | |||||||
\(740\) | 339.098i | 0.458240i | ||||||||
\(741\) | 55.2055 | − | 332.307i | 0.0745014 | − | 0.448458i | ||||
\(742\) | 92.8477 | 0.125132 | ||||||||
\(743\) | 278.718 | + | 160.918i | 0.375126 | + | 0.216579i | 0.675695 | − | 0.737181i | \(-0.263843\pi\) |
−0.300570 | + | 0.953760i | \(0.597177\pi\) | |||||||
\(744\) | 545.043 | + | 314.680i | 0.732584 | + | 0.422958i | ||||
\(745\) | 241.815 | + | 418.836i | 0.324584 | + | 0.562196i | ||||
\(746\) | 201.621 | − | 349.218i | 0.270270 | − | 0.468121i | ||||
\(747\) | 26.4785 | + | 45.8621i | 0.0354465 | + | 0.0613951i | ||||
\(748\) | 868.217 | 1.16072 | ||||||||
\(749\) | − | 1136.60i | − | 1.51749i | ||||||
\(750\) | 121.539 | + | 210.512i | 0.162052 | + | 0.280683i | ||||
\(751\) | −165.099 | + | 95.3199i | −0.219839 | + | 0.126924i | −0.605876 | − | 0.795559i | \(-0.707177\pi\) |
0.386037 | + | 0.922483i | \(0.373844\pi\) | |||||||
\(752\) | −190.749 | −0.253656 | ||||||||
\(753\) | 353.461i | 0.469403i | ||||||||
\(754\) | 158.792 | − | 91.6786i | 0.210599 | − | 0.121590i | ||||
\(755\) | −111.551 | − | 64.4038i | −0.147749 | − | 0.0853031i | ||||
\(756\) | 700.090 | − | 404.197i | 0.926044 | − | 0.534652i | ||||
\(757\) | 292.845 | − | 507.222i | 0.386849 | − | 0.670042i | −0.605175 | − | 0.796093i | \(-0.706897\pi\) |
0.992024 | + | 0.126050i | \(0.0402301\pi\) | |||||||
\(758\) | 54.2385 | − | 93.9439i | 0.0715548 | − | 0.123936i | ||||
\(759\) | 251.663i | 0.331572i | ||||||||
\(760\) | −190.570 | + | 231.738i | −0.250750 | + | 0.304918i | ||||
\(761\) | 581.690 | 0.764376 | 0.382188 | − | 0.924085i | \(-0.375171\pi\) | ||||
0.382188 | + | 0.924085i | \(0.375171\pi\) | |||||||
\(762\) | 40.9847 | + | 23.6626i | 0.0537858 | + | 0.0310532i | ||||
\(763\) | 919.835 | + | 531.067i | 1.20555 | + | 0.696025i | ||||
\(764\) | 176.562 | + | 305.815i | 0.231102 | + | 0.400281i | ||||
\(765\) | −15.3185 | + | 26.5324i | −0.0200241 | + | 0.0346828i | ||||
\(766\) | −77.9799 | − | 135.065i | −0.101801 | − | 0.176325i | ||||
\(767\) | 144.659 | 0.188603 | ||||||||
\(768\) | − | 35.6792i | − | 0.0464573i | ||||||
\(769\) | −642.973 | − | 1113.66i | −0.836116 | − | 1.44820i | −0.893119 | − | 0.449821i | \(-0.851488\pi\) |
0.0570025 | − | 0.998374i | \(-0.481846\pi\) | |||||||
\(770\) | −261.508 | + | 150.982i | −0.339621 | + | 0.196080i | ||||
\(771\) | −1140.59 | −1.47936 | ||||||||
\(772\) | 173.697i | 0.224996i | ||||||||
\(773\) | −1069.34 | + | 617.384i | −1.38336 | + | 0.798686i | −0.992556 | − | 0.121786i | \(-0.961138\pi\) |
−0.390809 | + | 0.920472i | \(0.627805\pi\) | |||||||
\(774\) | −13.1108 | − | 7.56952i | −0.0169390 | − | 0.00977974i | ||||
\(775\) | 571.739 | − | 330.094i | 0.737728 | − | 0.425927i | ||||
\(776\) | 23.9416 | − | 41.4681i | 0.0308526 | − | 0.0534383i | ||||
\(777\) | 361.260 | − | 625.721i | 0.464942 | − | 0.805304i | ||||
\(778\) | 54.5786i | 0.0701525i | ||||||||
\(779\) | −399.652 | + | 485.986i | −0.513032 | + | 0.623859i | ||||
\(780\) | 195.293 | 0.250375 | ||||||||
\(781\) | −24.0984 | − | 13.9132i | −0.0308558 | − | 0.0178146i | ||||
\(782\) | 39.8639 | + | 23.0154i | 0.0509768 | + | 0.0294315i | ||||
\(783\) | 617.820 | + | 1070.10i | 0.789043 | + | 1.36666i | ||||
\(784\) | −93.9885 | + | 162.793i | −0.119883 | + | 0.207644i | ||||
\(785\) | 122.863 | + | 212.805i | 0.156513 | + | 0.271089i | ||||
\(786\) | 147.763 | 0.187993 | ||||||||
\(787\) | − | 543.258i | − | 0.690289i | −0.938550 | − | 0.345145i | \(-0.887830\pi\) | ||
0.938550 | − | 0.345145i | \(-0.112170\pi\) | |||||||
\(788\) | 297.556 | + | 515.382i | 0.377609 | + | 0.654038i | ||||
\(789\) | 133.368 | − | 76.9999i | 0.169034 | − | 0.0975918i | ||||
\(790\) | 101.324 | 0.128258 | ||||||||
\(791\) | 155.880i | 0.197068i | ||||||||
\(792\) | 55.5595 | − | 32.0773i | 0.0701508 | − | 0.0405016i | ||||
\(793\) | −90.9551 | − | 52.5130i | −0.114698 | − | 0.0662206i | ||||
\(794\) | −397.959 | + | 229.762i | −0.501208 | + | 0.289373i | ||||
\(795\) | −75.5785 | + | 130.906i | −0.0950673 | + | 0.164661i | ||||
\(796\) | 164.045 | − | 284.134i | 0.206087 | − | 0.356953i | ||||
\(797\) | − | 942.119i | − | 1.18208i | −0.806642 | − | 0.591041i | \(-0.798717\pi\) | ||
0.806642 | − | 0.591041i | \(-0.201283\pi\) | |||||||
\(798\) | 281.268 | − | 105.541i | 0.352466 | − | 0.132257i | ||||
\(799\) | −245.235 | −0.306928 | ||||||||
\(800\) | 366.718 | + | 211.724i | 0.458397 | + | 0.264656i | ||||
\(801\) | −57.8103 | − | 33.3768i | −0.0721727 | − | 0.0416689i | ||||
\(802\) | 32.1630 | + | 55.7080i | 0.0401035 | + | 0.0694614i | ||||
\(803\) | 50.5369 | − | 87.5325i | 0.0629352 | − | 0.109007i | ||||
\(804\) | −500.927 | − | 867.631i | −0.623043 | − | 1.07914i | ||||
\(805\) | 125.088 | 0.155389 | ||||||||
\(806\) | 178.433i | 0.221381i | ||||||||
\(807\) | 525.794 | + | 910.703i | 0.651542 | + | 1.12850i | ||||
\(808\) | −586.084 | + | 338.376i | −0.725352 | + | 0.418782i | ||||
\(809\) | −374.800 | −0.463288 | −0.231644 | − | 0.972801i | \(-0.574410\pi\) | ||||
−0.231644 | + | 0.972801i | \(0.574410\pi\) | |||||||
\(810\) | − | 155.010i | − | 0.191370i | ||||||
\(811\) | −145.337 | + | 83.9101i | −0.179207 | + | 0.103465i | −0.586920 | − | 0.809645i | \(-0.699660\pi\) |
0.407713 | + | 0.913110i | \(0.366326\pi\) | |||||||
\(812\) | −1106.47 | − | 638.823i | −1.36265 | − | 0.786728i | ||||
\(813\) | −434.704 | + | 250.976i | −0.534691 | + | 0.308704i | ||||
\(814\) | 183.534 | − | 317.890i | 0.225472 | − | 0.390528i | ||||
\(815\) | 210.354 | − | 364.344i | 0.258103 | − | 0.447048i | ||||
\(816\) | − | 428.470i | − | 0.525086i | ||||||
\(817\) | 462.518 | + | 380.354i | 0.566118 | + | 0.465549i | ||||
\(818\) | 131.723 | 0.161030 | ||||||||
\(819\) | 31.0054 | + | 17.9010i | 0.0378577 | + | 0.0218571i | ||||
\(820\) | −315.907 | − | 182.389i | −0.385253 | − | 0.222426i | ||||
\(821\) | −628.725 | − | 1088.98i | −0.765804 | − | 1.32641i | −0.939820 | − | 0.341669i | \(-0.889008\pi\) |
0.174016 | − | 0.984743i | \(-0.444325\pi\) | |||||||
\(822\) | 230.038 | − | 398.438i | 0.279852 | − | 0.484718i | ||||
\(823\) | 225.462 | + | 390.511i | 0.273951 | + | 0.474497i | 0.969870 | − | 0.243623i | \(-0.0783361\pi\) |
−0.695919 | + | 0.718120i | \(0.745003\pi\) | |||||||
\(824\) | 471.717 | 0.572472 | ||||||||
\(825\) | 782.165i | 0.948079i | ||||||||
\(826\) | 64.5041 | + | 111.724i | 0.0780922 | + | 0.135260i | ||||
\(827\) | −349.235 | + | 201.631i | −0.422292 | + | 0.243810i | −0.696057 | − | 0.717986i | \(-0.745064\pi\) |
0.273766 | + | 0.961796i | \(0.411731\pi\) | |||||||
\(828\) | −12.4888 | −0.0150831 | ||||||||
\(829\) | 676.543i | 0.816096i | 0.912961 | + | 0.408048i | \(0.133790\pi\) | ||||
−0.912961 | + | 0.408048i | \(0.866210\pi\) | |||||||
\(830\) | −134.602 | + | 77.7123i | −0.162171 | + | 0.0936293i | ||||
\(831\) | 232.554 | + | 134.265i | 0.279849 | + | 0.161571i | ||||
\(832\) | 130.442 | − | 75.3110i | 0.156782 | − | 0.0905180i | ||||
\(833\) | −120.835 | + | 209.293i | −0.145060 | + | 0.251252i | ||||
\(834\) | −19.4716 | + | 33.7258i | −0.0233472 | + | 0.0404386i | ||||
\(835\) | 195.076i | 0.233624i | ||||||||
\(836\) | −1116.49 | + | 418.945i | −1.33552 | + | 0.501130i | ||||
\(837\) | −1202.46 | −1.43663 | ||||||||
\(838\) | 226.556 | + | 130.802i | 0.270354 | + | 0.156089i | ||||
\(839\) | −1311.19 | − | 757.016i | −1.56280 | − | 0.902284i | −0.996972 | − | 0.0777621i | \(-0.975223\pi\) |
−0.565830 | − | 0.824522i | \(-0.691444\pi\) | |||||||
\(840\) | 185.309 | + | 320.965i | 0.220606 | + | 0.382101i | ||||
\(841\) | 555.950 | − | 962.934i | 0.661058 | − | 1.14499i | ||||
\(842\) | −87.8912 | − | 152.232i | −0.104384 | − | 0.180798i | ||||
\(843\) | 1081.44 | 1.28285 | ||||||||
\(844\) | 222.781i | 0.263959i | ||||||||
\(845\) | −203.563 | − | 352.582i | −0.240903 | − | 0.417257i | ||||
\(846\) | −7.37469 | + | 4.25778i | −0.00871713 | + | 0.00503284i | ||||
\(847\) | −1567.46 | −1.85061 | ||||||||
\(848\) | 181.886i | 0.214489i | ||||||||
\(849\) | 159.918 | − | 92.3285i | 0.188360 | − | 0.108750i | ||||
\(850\) | 123.896 | + | 71.5316i | 0.145761 | + | 0.0841549i | ||||
\(851\) | −131.686 | + | 76.0287i | −0.154742 | + | 0.0893404i | ||||
\(852\) | −8.02476 | + | 13.8993i | −0.00941873 | + | 0.0163137i | ||||
\(853\) | −533.457 | + | 923.975i | −0.625389 | + | 1.08321i | 0.363076 | + | 0.931760i | \(0.381727\pi\) |
−0.988465 | + | 0.151447i | \(0.951607\pi\) | |||||||
\(854\) | − | 93.6633i | − | 0.109676i | ||||||
\(855\) | 6.89618 | − | 41.5113i | 0.00806571 | − | 0.0485512i | ||||
\(856\) | −708.722 | −0.827946 | ||||||||
\(857\) | 1171.55 | + | 676.397i | 1.36704 | + | 0.789261i | 0.990549 | − | 0.137158i | \(-0.0437970\pi\) |
0.376492 | + | 0.926420i | \(0.377130\pi\) | |||||||
\(858\) | −183.079 | − | 105.701i | −0.213378 | − | 0.123194i | ||||
\(859\) | 419.232 | + | 726.131i | 0.488046 | + | 0.845321i | 0.999905 | − | 0.0137483i | \(-0.00437635\pi\) |
−0.511859 | + | 0.859069i | \(0.671043\pi\) | |||||||
\(860\) | −173.582 | + | 300.653i | −0.201839 | + | 0.349596i | ||||
\(861\) | 388.619 | + | 673.108i | 0.451358 | + | 0.781774i | ||||
\(862\) | −386.372 | −0.448228 | ||||||||
\(863\) | − | 61.7364i | − | 0.0715369i | −0.999360 | − | 0.0357685i | \(-0.988612\pi\) | ||
0.999360 | − | 0.0357685i | \(-0.0113879\pi\) | |||||||
\(864\) | −385.633 | − | 667.936i | −0.446334 | − | 0.773074i | ||||
\(865\) | 877.833 | − | 506.817i | 1.01484 | − | 0.585916i | ||||
\(866\) | −168.612 | −0.194702 | ||||||||
\(867\) | 281.090i | 0.324210i | ||||||||
\(868\) | 1076.76 | − | 621.668i | 1.24051 | − | 0.716208i | ||||
\(869\) | 742.171 | + | 428.492i | 0.854051 | + | 0.493087i | ||||
\(870\) | −230.547 | + | 133.106i | −0.264996 | + | 0.152996i | ||||
\(871\) | 302.217 | − | 523.455i | 0.346977 | − | 0.600982i | ||||
\(872\) | 331.145 | − | 573.560i | 0.379754 | − | 0.657753i | ||||
\(873\) | 6.71573i | 0.00769270i | ||||||||
\(874\) | −62.3692 | − | 10.3613i | −0.0713606 | − | 0.0118550i | ||||
\(875\) | 1021.89 | 1.16788 | ||||||||
\(876\) | −50.4863 | − | 29.1483i | −0.0576328 | − | 0.0332743i | ||||
\(877\) | −411.522 | − | 237.592i | −0.469239 | − | 0.270915i | 0.246682 | − | 0.969096i | \(-0.420660\pi\) |
−0.715921 | + | 0.698181i | \(0.753993\pi\) | |||||||
\(878\) | −158.264 | − | 274.121i | −0.180255 | − | 0.312211i | ||||
\(879\) | 160.940 | − | 278.757i | 0.183095 | − | 0.317130i | ||||
\(880\) | −295.770 | − | 512.288i | −0.336102 | − | 0.582145i | ||||
\(881\) | 1656.73 | 1.88051 | 0.940253 | − | 0.340477i | \(-0.110588\pi\) | ||||
0.940253 | + | 0.340477i | \(0.110588\pi\) | |||||||
\(882\) | 8.39179i | 0.00951450i | ||||||||
\(883\) | 3.24702 | + | 5.62400i | 0.00367726 | + | 0.00636920i | 0.867858 | − | 0.496812i | \(-0.165496\pi\) |
−0.864181 | + | 0.503181i | \(0.832163\pi\) | |||||||
\(884\) | 261.642 | − | 151.059i | 0.295975 | − | 0.170881i | ||||
\(885\) | −210.027 | −0.237319 | ||||||||
\(886\) | 485.215i | 0.547647i | ||||||||
\(887\) | −517.144 | + | 298.573i | −0.583026 | + | 0.336610i | −0.762335 | − | 0.647183i | \(-0.775947\pi\) |
0.179309 | + | 0.983793i | \(0.442614\pi\) | |||||||
\(888\) | −390.166 | − | 225.263i | −0.439377 | − | 0.253674i | ||||
\(889\) | 172.298 | − | 99.4762i | 0.193811 | − | 0.111897i | ||||
\(890\) | 97.9583 | − | 169.669i | 0.110065 | − | 0.190639i | ||||
\(891\) | 655.526 | − | 1135.40i | 0.735719 | − | 1.27430i | ||||
\(892\) | − | 1522.79i | − | 1.70717i | ||||||
\(893\) | 315.363 | − | 118.334i | 0.353150 | − | 0.132513i | ||||
\(894\) | −301.953 | −0.337755 | ||||||||
\(895\) | 717.025 | + | 413.975i | 0.801145 | + | 0.462542i | ||||
\(896\) | 895.364 | + | 516.939i | 0.999291 | + | 0.576941i | ||||
\(897\) | 43.7863 | + | 75.8401i | 0.0488141 | + | 0.0845486i | ||||
\(898\) | 244.855 | − | 424.101i | 0.272667 | − | 0.472273i | ||||
\(899\) | 950.228 | + | 1645.84i | 1.05698 | + | 1.83075i | ||||
\(900\) | −38.8149 | −0.0431277 | ||||||||
\(901\) | 233.840i | 0.259534i | ||||||||
\(902\) | 197.433 | + | 341.964i | 0.218884 | + | 0.379118i | ||||
\(903\) | 640.605 | − | 369.853i | 0.709418 | − | 0.409583i | ||||
\(904\) | 97.1988 | 0.107521 | ||||||||
\(905\) | 466.272i | 0.515218i | ||||||||
\(906\) | 69.6463 | − | 40.2103i | 0.0768723 | − | 0.0443822i | ||||
\(907\) | −1415.50 | − | 817.238i | −1.56064 | − | 0.901034i | −0.997192 | − | 0.0748809i | \(-0.976142\pi\) |
−0.563445 | − | 0.826154i | \(-0.690524\pi\) | |||||||
\(908\) | −756.045 | + | 436.503i | −0.832649 | + | 0.480730i | ||||
\(909\) | 47.4580 | − | 82.1996i | 0.0522090 | − | 0.0904286i | ||||
\(910\) | −52.5380 | + | 90.9984i | −0.0577340 | + | 0.0999983i | ||||
\(911\) | 1326.40i | 1.45598i | 0.685587 | + | 0.727991i | \(0.259546\pi\) | ||||
−0.685587 | + | 0.727991i | \(0.740454\pi\) | |||||||
\(912\) | 206.752 | + | 550.997i | 0.226702 | + | 0.604163i | ||||
\(913\) | −1314.56 | −1.43983 | ||||||||
\(914\) | −66.5719 | − | 38.4353i | −0.0728358 | − | 0.0420518i | ||||
\(915\) | 132.056 | + | 76.2424i | 0.144323 | + | 0.0833251i | ||||
\(916\) | 56.5226 | + | 97.9000i | 0.0617059 | + | 0.106878i | ||||
\(917\) | 310.593 | − | 537.963i | 0.338706 | − | 0.586655i | ||||
\(918\) | −130.287 | − | 225.664i | −0.141925 | − | 0.245821i | ||||
\(919\) | −1155.93 | −1.25782 | −0.628908 | − | 0.777479i | \(-0.716498\pi\) | ||||
−0.628908 | + | 0.777479i | \(0.716498\pi\) | |||||||
\(920\) | − | 77.9982i | − | 0.0847807i | ||||||
\(921\) | −494.171 | − | 855.930i | −0.536559 | − | 0.929348i | ||||
\(922\) | −183.231 | + | 105.788i | −0.198732 | + | 0.114738i | ||||
\(923\) | −9.68293 | −0.0104907 | ||||||||
\(924\) | 1473.06i | 1.59422i | ||||||||
\(925\) | −409.277 | + | 236.296i | −0.442461 | + | 0.255455i | ||||
\(926\) | −235.023 | − | 135.691i | −0.253805 | − | 0.146534i | ||||
\(927\) | −57.2957 | + | 33.0797i | −0.0618076 | + | 0.0356846i | ||||
\(928\) | −609.483 | + | 1055.66i | −0.656771 | + | 1.13756i | ||||
\(929\) | −24.9510 | + | 43.2164i | −0.0268579 | + | 0.0465192i | −0.879142 | − | 0.476560i | \(-0.841883\pi\) |
0.852284 | + | 0.523079i | \(0.175217\pi\) | |||||||
\(930\) | − | 259.063i | − | 0.278563i | ||||||
\(931\) | 54.3986 | − | 327.450i | 0.0584303 | − | 0.351719i | ||||
\(932\) | 1311.60 | 1.40729 | ||||||||
\(933\) | −627.554 | − | 362.318i | −0.672619 | − | 0.388337i | ||||
\(934\) | 443.241 | + | 255.905i | 0.474562 | + | 0.273988i | ||||
\(935\) | −380.253 | − | 658.618i | −0.406688 | − | 0.704404i | ||||
\(936\) | 11.1621 | − | 19.3333i | 0.0119253 | − | 0.0206553i | ||||
\(937\) | 261.663 | + | 453.214i | 0.279256 | + | 0.483686i | 0.971200 | − | 0.238265i | \(-0.0765788\pi\) |
−0.691944 | + | 0.721951i | \(0.743245\pi\) | |||||||
\(938\) | 539.041 | 0.574670 | ||||||||
\(939\) | − | 1399.88i | − | 1.49082i | ||||||
\(940\) | 97.6382 | + | 169.114i | 0.103870 | + | 0.179909i | ||||
\(941\) | 528.450 | − | 305.101i | 0.561583 | − | 0.324230i | −0.192197 | − | 0.981356i | \(-0.561561\pi\) |
0.753781 | + | 0.657126i | \(0.228228\pi\) | |||||||
\(942\) | −153.418 | −0.162864 | ||||||||
\(943\) | − | 163.573i | − | 0.173460i | ||||||
\(944\) | −218.865 | + | 126.362i | −0.231849 | + | 0.133858i | ||||
\(945\) | −613.237 | − | 354.052i | −0.648928 | − | 0.374659i | ||||
\(946\) | 325.452 | − | 187.900i | 0.344029 | − | 0.198625i | ||||
\(947\) | −727.100 | + | 1259.37i | −0.767794 | + | 1.32986i | 0.170963 | + | 0.985277i | \(0.445312\pi\) |
−0.938757 | + | 0.344580i | \(0.888021\pi\) | |||||||
\(948\) | 247.143 | − | 428.063i | 0.260699 | − | 0.451544i | ||||
\(949\) | − | 35.1712i | − | 0.0370614i | ||||||
\(950\) | −193.843 | − | 32.2027i | −0.204045 | − | 0.0338975i | ||||
\(951\) | −798.533 | −0.839677 | ||||||||
\(952\) | 496.534 | + | 286.674i | 0.521569 | + | 0.301128i | ||||
\(953\) | 1408.40 | + | 813.142i | 1.47786 | + | 0.853244i | 0.999687 | − | 0.0250198i | \(-0.00796489\pi\) |
0.478176 | + | 0.878264i | \(0.341298\pi\) | |||||||
\(954\) | 4.05994 | + | 7.03203i | 0.00425571 | + | 0.00737110i | ||||
\(955\) | 154.658 | − | 267.876i | 0.161946 | − | 0.280498i | ||||
\(956\) | −188.951 | − | 327.273i | −0.197648 | − | 0.342336i | ||||
\(957\) | −2251.59 | −2.35276 | ||||||||
\(958\) | − | 19.0554i | − | 0.0198908i | ||||||
\(959\) | −967.070 | − | 1675.01i | −1.00842 | − | 1.74663i | ||||
\(960\) | −189.386 | + | 109.342i | −0.197278 | + | 0.113898i | ||||
\(961\) | −888.421 | −0.924475 | ||||||||
\(962\) | − | 127.731i | − | 0.132776i | ||||||
\(963\) | 86.0828 | − | 49.6999i | 0.0893902 | − | 0.0516095i | ||||
\(964\) | 42.4457 | + | 24.5061i | 0.0440309 | + | 0.0254212i | ||||
\(965\) | 131.764 | − | 76.0739i | 0.136543 | − | 0.0788331i | ||||
\(966\) | −39.0491 | + | 67.6350i | −0.0404235 | + | 0.0700155i | ||||
\(967\) | 716.252 | − | 1240.59i | 0.740695 | − | 1.28292i | −0.211484 | − | 0.977381i | \(-0.567830\pi\) |
0.952179 | − | 0.305540i | \(-0.0988370\pi\) | |||||||
\(968\) | 977.388i | 1.00970i | ||||||||
\(969\) | 265.808 | + | 708.383i | 0.274312 | + | 0.731046i | ||||
\(970\) | −19.7101 | −0.0203197 | ||||||||
\(971\) | −870.744 | − | 502.724i | −0.896749 | − | 0.517738i | −0.0206051 | − | 0.999788i | \(-0.506559\pi\) |
−0.876144 | + | 0.482049i | \(0.839893\pi\) | |||||||
\(972\) | 117.957 | + | 68.1023i | 0.121355 | + | 0.0700641i | ||||
\(973\) | 81.8575 | + | 141.781i | 0.0841290 | + | 0.145716i | ||||
\(974\) | −309.239 | + | 535.618i | −0.317494 | + | 0.549916i | ||||
\(975\) | 136.087 | + | 235.710i | 0.139577 | + | 0.241754i | ||||
\(976\) | 183.484 | 0.187996 | ||||||||
\(977\) | 1459.45i | 1.49381i | 0.664931 | + | 0.746905i | \(0.268461\pi\) | ||||
−0.664931 | + | 0.746905i | \(0.731539\pi\) | |||||||
\(978\) | 131.334 | + | 227.477i | 0.134288 | + | 0.232594i | ||||
\(979\) | 1435.04 | − | 828.519i | 1.46582 | − | 0.846291i | ||||
\(980\) | 192.438 | 0.196365 | ||||||||
\(981\) | 92.8877i | 0.0946868i | ||||||||
\(982\) | 23.9628 | − | 13.8349i | 0.0244020 | − | 0.0140885i | ||||
\(983\) | 447.660 | + | 258.456i | 0.455401 | + | 0.262926i | 0.710109 | − | 0.704092i | \(-0.248646\pi\) |
−0.254707 | + | 0.967018i | \(0.581979\pi\) | |||||||
\(984\) | 419.714 | − | 242.322i | 0.426539 | − | 0.246262i | ||||
\(985\) | 260.641 | − | 451.444i | 0.264611 | − | 0.458319i | ||||
\(986\) | −205.915 | + | 356.656i | −0.208839 | + | 0.361720i | ||||
\(987\) | − | 416.078i | − | 0.421558i | ||||||
\(988\) | −263.571 | + | 320.508i | −0.266772 | + | 0.324401i | ||||
\(989\) | −155.674 | −0.157406 | ||||||||
\(990\) | −22.8699 | − | 13.2039i | −0.0231009 | − | 0.0133373i | ||||
\(991\) | −333.382 | − | 192.478i | −0.336410 | − | 0.194226i | 0.322274 | − | 0.946647i | \(-0.395553\pi\) |
−0.658683 | + | 0.752420i | \(0.728886\pi\) | |||||||
\(992\) | −593.116 | − | 1027.31i | −0.597899 | − | 1.03559i | ||||
\(993\) | 159.020 | − | 275.431i | 0.160141 | − | 0.277373i | ||||
\(994\) | −4.31767 | − | 7.47842i | −0.00434373 | − | 0.00752357i | ||||
\(995\) | −287.388 | −0.288832 | ||||||||
\(996\) | 758.203i | 0.761248i | ||||||||
\(997\) | 532.640 | + | 922.560i | 0.534243 | + | 0.925336i | 0.999200 | + | 0.0400025i | \(0.0127366\pi\) |
−0.464957 | + | 0.885333i | \(0.653930\pi\) | |||||||
\(998\) | 378.499 | − | 218.526i | 0.379257 | − | 0.218964i | ||||
\(999\) | 860.775 | 0.861636 |
(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 | 19.3.d.a.8.2 | ✓ | 6 | |
3.2 | odd | 2 | 171.3.p.d.46.2 | 6 | |||
4.3 | odd | 2 | 304.3.r.b.65.1 | 6 | |||
19.2 | odd | 18 | 361.3.f.i.127.2 | 18 | |||
19.3 | odd | 18 | 361.3.f.i.262.2 | 18 | |||
19.4 | even | 9 | 361.3.f.i.299.2 | 18 | |||
19.5 | even | 9 | 361.3.f.h.333.2 | 18 | |||
19.6 | even | 9 | 361.3.f.i.307.2 | 18 | |||
19.7 | even | 3 | 361.3.d.c.69.2 | 6 | |||
19.8 | odd | 6 | 361.3.b.b.360.3 | 6 | |||
19.9 | even | 9 | 361.3.f.i.116.2 | 18 | |||
19.10 | odd | 18 | 361.3.f.h.116.2 | 18 | |||
19.11 | even | 3 | 361.3.b.b.360.4 | 6 | |||
19.12 | odd | 6 | inner | 19.3.d.a.12.2 | yes | 6 | |
19.13 | odd | 18 | 361.3.f.h.307.2 | 18 | |||
19.14 | odd | 18 | 361.3.f.i.333.2 | 18 | |||
19.15 | odd | 18 | 361.3.f.h.299.2 | 18 | |||
19.16 | even | 9 | 361.3.f.h.262.2 | 18 | |||
19.17 | even | 9 | 361.3.f.h.127.2 | 18 | |||
19.18 | odd | 2 | 361.3.d.c.293.2 | 6 | |||
57.50 | even | 6 | 171.3.p.d.145.2 | 6 | |||
76.31 | even | 6 | 304.3.r.b.145.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
19.3.d.a.8.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
19.3.d.a.12.2 | yes | 6 | 19.12 | odd | 6 | inner | |
171.3.p.d.46.2 | 6 | 3.2 | odd | 2 | |||
171.3.p.d.145.2 | 6 | 57.50 | even | 6 | |||
304.3.r.b.65.1 | 6 | 4.3 | odd | 2 | |||
304.3.r.b.145.1 | 6 | 76.31 | even | 6 | |||
361.3.b.b.360.3 | 6 | 19.8 | odd | 6 | |||
361.3.b.b.360.4 | 6 | 19.11 | even | 3 | |||
361.3.d.c.69.2 | 6 | 19.7 | even | 3 | |||
361.3.d.c.293.2 | 6 | 19.18 | odd | 2 | |||
361.3.f.h.116.2 | 18 | 19.10 | odd | 18 | |||
361.3.f.h.127.2 | 18 | 19.17 | even | 9 | |||
361.3.f.h.262.2 | 18 | 19.16 | even | 9 | |||
361.3.f.h.299.2 | 18 | 19.15 | odd | 18 | |||
361.3.f.h.307.2 | 18 | 19.13 | odd | 18 | |||
361.3.f.h.333.2 | 18 | 19.5 | even | 9 | |||
361.3.f.i.116.2 | 18 | 19.9 | even | 9 | |||
361.3.f.i.127.2 | 18 | 19.2 | odd | 18 | |||
361.3.f.i.262.2 | 18 | 19.3 | odd | 18 | |||
361.3.f.i.299.2 | 18 | 19.4 | even | 9 | |||
361.3.f.i.307.2 | 18 | 19.6 | even | 9 | |||
361.3.f.i.333.2 | 18 | 19.14 | odd | 18 |