Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,4,Mod(4,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("39.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.j (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: | \(2.30107449022\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 17x^{2} + 289 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 10.2 | ||
Root | \(3.57071 - 2.06155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.10 |
Dual form | 39.4.j.b.4.2 |
$q$-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 \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).
\(n\) | \(14\) | \(28\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.57071 | − | 2.06155i | 1.26244 | − | 0.728869i | 0.288892 | − | 0.957362i | \(-0.406713\pi\) |
0.973546 | + | 0.228493i | \(0.0733797\pi\) | |||||||
\(3\) | 1.50000 | + | 2.59808i | 0.288675 | + | 0.500000i | ||||
\(4\) | 4.50000 | − | 7.79423i | 0.562500 | − | 0.974279i | ||||
\(5\) | − | 3.05006i | − | 0.272806i | −0.990653 | − | 0.136403i | \(-0.956446\pi\) | ||
0.990653 | − | 0.136403i | \(-0.0435541\pi\) | |||||||
\(6\) | 10.7121 | + | 6.18466i | 0.728869 | + | 0.420813i | ||||
\(7\) | −5.78786 | − | 3.34162i | −0.312515 | − | 0.180431i | 0.335536 | − | 0.942027i | \(-0.391082\pi\) |
−0.648051 | + | 0.761597i | \(0.724416\pi\) | |||||||
\(8\) | − | 4.12311i | − | 0.182217i | ||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | −6.28786 | − | 10.8909i | −0.198840 | − | 0.344400i | ||||
\(11\) | −27.9293 | + | 16.1250i | −0.765545 | + | 0.441988i | −0.831283 | − | 0.555849i | \(-0.812393\pi\) |
0.0657380 | + | 0.997837i | \(0.479060\pi\) | |||||||
\(12\) | 27.0000 | 0.649519 | ||||||||
\(13\) | −22.1364 | − | 41.3156i | −0.472272 | − | 0.881453i | ||||
\(14\) | −27.5557 | −0.526041 | ||||||||
\(15\) | 7.92429 | − | 4.57509i | 0.136403 | − | 0.0787522i | ||||
\(16\) | 27.5000 | + | 47.6314i | 0.429688 | + | 0.744241i | ||||
\(17\) | −14.4293 | + | 24.9923i | −0.205860 | + | 0.356560i | −0.950406 | − | 0.311011i | \(-0.899332\pi\) |
0.744547 | + | 0.667571i | \(0.232666\pi\) | |||||||
\(18\) | 37.1080i | 0.485913i | ||||||||
\(19\) | 87.6364 | + | 50.5969i | 1.05817 | + | 0.610933i | 0.924925 | − | 0.380150i | \(-0.124128\pi\) |
0.133242 | + | 0.991083i | \(0.457461\pi\) | |||||||
\(20\) | −23.7729 | − | 13.7253i | −0.265789 | − | 0.153453i | ||||
\(21\) | − | 20.0497i | − | 0.208343i | ||||||
\(22\) | −66.4850 | + | 115.155i | −0.644302 | + | 1.11596i | ||||
\(23\) | −59.4950 | − | 103.048i | −0.539372 | − | 0.934220i | −0.998938 | − | 0.0460765i | \(-0.985328\pi\) |
0.459566 | − | 0.888144i | \(-0.348005\pi\) | |||||||
\(24\) | 10.7121 | − | 6.18466i | 0.0911086 | − | 0.0526016i | ||||
\(25\) | 115.697 | 0.925577 | ||||||||
\(26\) | −164.217 | − | 101.891i | −1.23868 | − | 0.768555i | ||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −52.0907 | + | 30.0746i | −0.351579 | + | 0.202984i | ||||
\(29\) | −80.0557 | − | 138.661i | −0.512620 | − | 0.887883i | −0.999893 | − | 0.0146339i | \(-0.995342\pi\) |
0.487273 | − | 0.873250i | \(-0.337992\pi\) | |||||||
\(30\) | 18.8636 | − | 32.6727i | 0.114800 | − | 0.198840i | ||||
\(31\) | − | 38.0705i | − | 0.220570i | −0.993900 | − | 0.110285i | \(-0.964824\pi\) | ||
0.993900 | − | 0.110285i | \(-0.0351763\pi\) | |||||||
\(32\) | 224.955 | + | 129.878i | 1.24271 | + | 0.717480i | ||||
\(33\) | −83.7879 | − | 48.3749i | −0.441988 | − | 0.255182i | ||||
\(34\) | 118.987i | 0.600179i | ||||||||
\(35\) | −10.1921 | + | 17.6533i | −0.0492225 | + | 0.0852558i | ||||
\(36\) | 40.5000 | + | 70.1481i | 0.187500 | + | 0.324760i | ||||
\(37\) | 283.682 | − | 163.784i | 1.26046 | − | 0.727727i | 0.287297 | − | 0.957841i | \(-0.407243\pi\) |
0.973164 | + | 0.230114i | \(0.0739099\pi\) | |||||||
\(38\) | 417.233 | 1.78116 | ||||||||
\(39\) | 74.1364 | − | 119.486i | 0.304393 | − | 0.490590i | ||||
\(40\) | −12.5757 | −0.0497099 | ||||||||
\(41\) | 48.5707 | − | 28.0423i | 0.185011 | − | 0.106816i | −0.404634 | − | 0.914479i | \(-0.632601\pi\) |
0.589645 | + | 0.807662i | \(0.299268\pi\) | |||||||
\(42\) | −41.3336 | − | 71.5918i | −0.151855 | − | 0.263021i | ||||
\(43\) | 63.9393 | − | 110.746i | 0.226759 | − | 0.392759i | −0.730087 | − | 0.683355i | \(-0.760520\pi\) |
0.956846 | + | 0.290596i | \(0.0938536\pi\) | |||||||
\(44\) | 290.250i | 0.994472i | ||||||||
\(45\) | 23.7729 | + | 13.7253i | 0.0787522 | + | 0.0454676i | ||||
\(46\) | −424.879 | − | 245.304i | −1.36185 | − | 0.786264i | ||||
\(47\) | 517.983i | 1.60757i | 0.594923 | + | 0.803783i | \(0.297183\pi\) | ||||
−0.594923 | + | 0.803783i | \(0.702817\pi\) | |||||||
\(48\) | −82.5000 | + | 142.894i | −0.248080 | + | 0.429688i | ||||
\(49\) | −149.167 | − | 258.365i | −0.434890 | − | 0.753251i | ||||
\(50\) | 413.121 | − | 238.516i | 1.16848 | − | 0.674624i | ||||
\(51\) | −86.5757 | −0.237706 | ||||||||
\(52\) | −421.637 | − | 13.3838i | −1.12443 | − | 0.0356923i | ||||
\(53\) | −695.546 | −1.80265 | −0.901326 | − | 0.433141i | \(-0.857405\pi\) | ||||
−0.901326 | + | 0.433141i | \(0.857405\pi\) | |||||||
\(54\) | −96.4093 | + | 55.6619i | −0.242956 | + | 0.140271i | ||||
\(55\) | 49.1821 | + | 85.1860i | 0.120577 | + | 0.208845i | ||||
\(56\) | −13.7779 | + | 23.8639i | −0.0328776 | + | 0.0569456i | ||||
\(57\) | 303.581i | 0.705445i | ||||||||
\(58\) | −571.712 | − | 330.078i | −1.29430 | − | 0.747265i | ||||
\(59\) | 568.566 | + | 328.262i | 1.25459 | + | 0.724339i | 0.972018 | − | 0.234906i | \(-0.0754783\pi\) |
0.282574 | + | 0.959245i | \(0.408812\pi\) | |||||||
\(60\) | − | 82.3516i | − | 0.177192i | ||||||
\(61\) | −350.652 | + | 607.347i | −0.736007 | + | 1.27480i | 0.218274 | + | 0.975888i | \(0.429957\pi\) |
−0.954280 | + | 0.298913i | \(0.903376\pi\) | |||||||
\(62\) | −78.4843 | − | 135.939i | −0.160766 | − | 0.278456i | ||||
\(63\) | 52.0907 | − | 30.0746i | 0.104172 | − | 0.0601435i | ||||
\(64\) | 631.000 | 1.23242 | ||||||||
\(65\) | −126.015 | + | 67.5174i | −0.240465 | + | 0.128839i | ||||
\(66\) | −398.910 | −0.743976 | ||||||||
\(67\) | −49.5150 | + | 28.5875i | −0.0902869 | + | 0.0521271i | −0.544464 | − | 0.838784i | \(-0.683267\pi\) |
0.454177 | + | 0.890912i | \(0.349933\pi\) | |||||||
\(68\) | 129.864 | + | 224.930i | 0.231592 | + | 0.401130i | ||||
\(69\) | 178.485 | − | 309.145i | 0.311407 | − | 0.539372i | ||||
\(70\) | 84.0465i | 0.143507i | ||||||||
\(71\) | −267.798 | − | 154.613i | −0.447630 | − | 0.258440i | 0.259199 | − | 0.965824i | \(-0.416542\pi\) |
−0.706829 | + | 0.707385i | \(0.749875\pi\) | |||||||
\(72\) | 32.1364 | + | 18.5540i | 0.0526016 | + | 0.0303695i | ||||
\(73\) | 389.711i | 0.624826i | 0.949946 | + | 0.312413i | \(0.101137\pi\) | ||||
−0.949946 | + | 0.312413i | \(0.898863\pi\) | |||||||
\(74\) | 675.299 | − | 1169.65i | 1.06084 | − | 1.83742i | ||||
\(75\) | 173.546 | + | 300.590i | 0.267191 | + | 0.462789i | ||||
\(76\) | 788.728 | − | 455.372i | 1.19044 | − | 0.687300i | ||||
\(77\) | 215.534 | 0.318992 | ||||||||
\(78\) | 18.3943 | − | 579.485i | 0.0267018 | − | 0.841202i | ||||
\(79\) | 901.820 | 1.28434 | 0.642169 | − | 0.766563i | \(-0.278035\pi\) | ||||
0.642169 | + | 0.766563i | \(0.278035\pi\) | |||||||
\(80\) | 145.279 | − | 83.8766i | 0.203033 | − | 0.117221i | ||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 115.621 | − | 200.262i | 0.155710 | − | 0.269698i | ||||
\(83\) | 687.095i | 0.908657i | 0.890834 | + | 0.454328i | \(0.150121\pi\) | ||||
−0.890834 | + | 0.454328i | \(0.849879\pi\) | |||||||
\(84\) | −156.272 | − | 90.2238i | −0.202984 | − | 0.117193i | ||||
\(85\) | 76.2279 | + | 44.0102i | 0.0972714 | + | 0.0561597i | ||||
\(86\) | − | 527.257i | − | 0.661111i | ||||||
\(87\) | 240.167 | − | 415.982i | 0.295961 | − | 0.512620i | ||||
\(88\) | 66.4850 | + | 115.155i | 0.0805378 | + | 0.139496i | ||||
\(89\) | −927.113 | + | 535.269i | −1.10420 | + | 0.637510i | −0.937321 | − | 0.348467i | \(-0.886702\pi\) |
−0.166879 | + | 0.985977i | \(0.553369\pi\) | |||||||
\(90\) | 113.181 | 0.132560 | ||||||||
\(91\) | −9.93858 | + | 313.100i | −0.0114489 | + | 0.360679i | ||||
\(92\) | −1070.91 | −1.21359 | ||||||||
\(93\) | 98.9100 | − | 57.1057i | 0.110285 | − | 0.0636730i | ||||
\(94\) | 1067.85 | + | 1849.57i | 1.17170 | + | 2.02945i | ||||
\(95\) | 154.324 | − | 267.296i | 0.166666 | − | 0.288674i | ||||
\(96\) | 779.267i | 0.828475i | ||||||||
\(97\) | −1519.43 | − | 877.242i | −1.59046 | − | 0.918251i | −0.993228 | − | 0.116182i | \(-0.962935\pi\) |
−0.597230 | − | 0.802070i | \(-0.703732\pi\) | |||||||
\(98\) | −1065.27 | − | 615.032i | −1.09804 | − | 0.633955i | ||||
\(99\) | − | 290.250i | − | 0.294658i | ||||||
\(100\) | 520.637 | − | 901.770i | 0.520637 | − | 0.901770i | ||||
\(101\) | −320.420 | − | 554.984i | −0.315673 | − | 0.546762i | 0.663907 | − | 0.747815i | \(-0.268897\pi\) |
−0.979580 | + | 0.201053i | \(0.935564\pi\) | |||||||
\(102\) | −309.137 | + | 178.480i | −0.300090 | + | 0.173257i | ||||
\(103\) | 693.153 | 0.663091 | 0.331546 | − | 0.943439i | \(-0.392430\pi\) | ||||
0.331546 | + | 0.943439i | \(0.392430\pi\) | |||||||
\(104\) | −170.349 | + | 91.2708i | −0.160616 | + | 0.0860562i | ||||
\(105\) | −61.1528 | −0.0568372 | ||||||||
\(106\) | −2483.59 | + | 1433.90i | −2.27574 | + | 1.31390i | ||||
\(107\) | 202.838 | + | 351.325i | 0.183262 | + | 0.317420i | 0.942990 | − | 0.332822i | \(-0.108001\pi\) |
−0.759727 | + | 0.650242i | \(0.774668\pi\) | |||||||
\(108\) | −121.500 | + | 210.444i | −0.108253 | + | 0.187500i | ||||
\(109\) | − | 479.516i | − | 0.421370i | −0.977554 | − | 0.210685i | \(-0.932431\pi\) | ||
0.977554 | − | 0.210685i | \(-0.0675694\pi\) | |||||||
\(110\) | 351.231 | + | 202.783i | 0.304441 | + | 0.175769i | ||||
\(111\) | 851.046 | + | 491.352i | 0.727727 | + | 0.420154i | ||||
\(112\) | − | 367.578i | − | 0.310115i | ||||||
\(113\) | 773.602 | − | 1339.92i | 0.644021 | − | 1.11548i | −0.340506 | − | 0.940242i | \(-0.610598\pi\) |
0.984527 | − | 0.175235i | \(-0.0560684\pi\) | |||||||
\(114\) | 625.849 | + | 1084.00i | 0.514177 | + | 0.890580i | ||||
\(115\) | −314.304 | + | 181.463i | −0.254861 | + | 0.147144i | ||||
\(116\) | −1441.00 | −1.15339 | ||||||||
\(117\) | 421.637 | + | 13.3838i | 0.333166 | + | 0.0105755i | ||||
\(118\) | 2706.91 | 2.11179 | ||||||||
\(119\) | 167.029 | − | 96.4344i | 0.128668 | − | 0.0742868i | ||||
\(120\) | −18.8636 | − | 32.6727i | −0.0143500 | − | 0.0248549i | ||||
\(121\) | −145.470 | + | 251.961i | −0.109294 | + | 0.189302i | ||||
\(122\) | 2891.55i | 2.14581i | ||||||||
\(123\) | 145.712 | + | 84.1269i | 0.106816 | + | 0.0616705i | ||||
\(124\) | −296.730 | − | 171.317i | −0.214896 | − | 0.124070i | ||||
\(125\) | − | 734.140i | − | 0.525308i | ||||||
\(126\) | 124.001 | − | 214.776i | 0.0876735 | − | 0.151855i | ||||
\(127\) | −1247.58 | − | 2160.87i | −0.871690 | − | 1.50981i | −0.860248 | − | 0.509876i | \(-0.829691\pi\) |
−0.0114416 | − | 0.999935i | \(-0.503642\pi\) | |||||||
\(128\) | 453.481 | − | 261.817i | 0.313144 | − | 0.180794i | ||||
\(129\) | 383.636 | 0.261839 | ||||||||
\(130\) | −310.773 | + | 500.872i | −0.209666 | + | 0.337918i | ||||
\(131\) | 43.7571 | 0.0291838 | 0.0145919 | − | 0.999894i | \(-0.495355\pi\) | ||||
0.0145919 | + | 0.999894i | \(0.495355\pi\) | |||||||
\(132\) | −754.091 | + | 435.374i | −0.497236 | + | 0.287079i | ||||
\(133\) | −338.151 | − | 585.695i | −0.220462 | − | 0.381851i | ||||
\(134\) | −117.869 | + | 204.156i | −0.0759877 | + | 0.131615i | ||||
\(135\) | 82.3516i | 0.0525015i | ||||||||
\(136\) | 103.046 | + | 59.4935i | 0.0649713 | + | 0.0375112i | ||||
\(137\) | −178.569 | − | 103.097i | −0.111359 | − | 0.0642932i | 0.443286 | − | 0.896380i | \(-0.353813\pi\) |
−0.554645 | + | 0.832087i | \(0.687146\pi\) | |||||||
\(138\) | − | 1471.83i | − | 0.907899i | ||||||
\(139\) | 50.0000 | − | 86.6025i | 0.0305104 | − | 0.0528456i | −0.850367 | − | 0.526190i | \(-0.823620\pi\) |
0.880877 | + | 0.473344i | \(0.156953\pi\) | |||||||
\(140\) | 91.7293 | + | 158.880i | 0.0553753 | + | 0.0959128i | ||||
\(141\) | −1345.76 | + | 776.974i | −0.803783 | + | 0.464064i | ||||
\(142\) | −1274.97 | −0.753474 | ||||||||
\(143\) | 1284.47 | + | 796.966i | 0.751137 | + | 0.466053i | ||||
\(144\) | −495.000 | −0.286458 | ||||||||
\(145\) | −422.923 | + | 244.175i | −0.242220 | + | 0.139846i | ||||
\(146\) | 803.411 | + | 1391.55i | 0.455416 | + | 0.788804i | ||||
\(147\) | 447.501 | − | 775.095i | 0.251084 | − | 0.434890i | ||||
\(148\) | − | 2948.11i | − | 1.63739i | ||||||
\(149\) | −329.480 | − | 190.225i | −0.181155 | − | 0.104590i | 0.406680 | − | 0.913571i | \(-0.366686\pi\) |
−0.587835 | + | 0.808981i | \(0.700020\pi\) | |||||||
\(150\) | 1239.36 | + | 715.547i | 0.674624 | + | 0.389495i | ||||
\(151\) | 1517.45i | 0.817805i | 0.912578 | + | 0.408902i | \(0.134088\pi\) | ||||
−0.912578 | + | 0.408902i | \(0.865912\pi\) | |||||||
\(152\) | 208.616 | − | 361.334i | 0.111323 | − | 0.192816i | ||||
\(153\) | −129.864 | − | 224.930i | −0.0686199 | − | 0.118853i | ||||
\(154\) | 769.611 | − | 444.335i | 0.402708 | − | 0.232504i | ||||
\(155\) | −116.117 | −0.0601726 | ||||||||
\(156\) | −597.684 | − | 1115.52i | −0.306750 | − | 0.572520i | ||||
\(157\) | 1450.16 | 0.737166 | 0.368583 | − | 0.929595i | \(-0.379843\pi\) | ||||
0.368583 | + | 0.929595i | \(0.379843\pi\) | |||||||
\(158\) | 3220.14 | − | 1859.15i | 1.62140 | − | 0.936114i | ||||
\(159\) | −1043.32 | − | 1807.08i | −0.520381 | − | 0.901326i | ||||
\(160\) | 396.135 | − | 686.126i | 0.195733 | − | 0.339019i | ||||
\(161\) | 795.239i | 0.389277i | ||||||||
\(162\) | −289.228 | − | 166.986i | −0.140271 | − | 0.0809854i | ||||
\(163\) | 2028.54 | + | 1171.18i | 0.974772 | + | 0.562785i | 0.900688 | − | 0.434467i | \(-0.143063\pi\) |
0.0740844 | + | 0.997252i | \(0.476397\pi\) | |||||||
\(164\) | − | 504.762i | − | 0.240337i | ||||||
\(165\) | −147.546 | + | 255.558i | −0.0696150 | + | 0.120577i | ||||
\(166\) | 1416.48 | + | 2453.42i | 0.662292 | + | 1.14712i | ||||
\(167\) | 34.7043 | − | 20.0365i | 0.0160808 | − | 0.00928428i | −0.491938 | − | 0.870630i | \(-0.663711\pi\) |
0.508019 | + | 0.861346i | \(0.330378\pi\) | |||||||
\(168\) | −82.6671 | −0.0379637 | ||||||||
\(169\) | −1216.96 | + | 1829.16i | −0.553918 | + | 0.832571i | ||||
\(170\) | 362.917 | 0.163732 | ||||||||
\(171\) | −788.728 | + | 455.372i | −0.352722 | + | 0.203644i | ||||
\(172\) | −575.454 | − | 996.715i | −0.255104 | − | 0.441853i | ||||
\(173\) | 954.770 | − | 1653.71i | 0.419594 | − | 0.726759i | −0.576304 | − | 0.817235i | \(-0.695506\pi\) |
0.995899 | + | 0.0904765i | \(0.0288390\pi\) | |||||||
\(174\) | − | 1980.47i | − | 0.862868i | ||||||
\(175\) | −669.639 | − | 386.616i | −0.289257 | − | 0.167002i | ||||
\(176\) | −1536.11 | − | 886.874i | −0.657890 | − | 0.379833i | ||||
\(177\) | 1969.57i | 0.836395i | ||||||||
\(178\) | −2206.97 | + | 3822.58i | −0.929322 | + | 1.60963i | ||||
\(179\) | −254.979 | − | 441.637i | −0.106470 | − | 0.184411i | 0.807868 | − | 0.589363i | \(-0.200621\pi\) |
−0.914338 | + | 0.404953i | \(0.867288\pi\) | |||||||
\(180\) | 213.956 | − | 123.527i | 0.0885962 | − | 0.0511510i | ||||
\(181\) | 2136.88 | 0.877531 | 0.438766 | − | 0.898602i | \(-0.355416\pi\) | ||||
0.438766 | + | 0.898602i | \(0.355416\pi\) | |||||||
\(182\) | 609.985 | + | 1138.48i | 0.248435 | + | 0.463680i | ||||
\(183\) | −2103.91 | −0.849867 | ||||||||
\(184\) | −424.879 | + | 245.304i | −0.170231 | + | 0.0982830i | ||||
\(185\) | −499.551 | − | 865.247i | −0.198528 | − | 0.343861i | ||||
\(186\) | 235.453 | − | 407.816i | 0.0928185 | − | 0.160766i | ||||
\(187\) | − | 930.688i | − | 0.363950i | ||||||
\(188\) | 4037.28 | + | 2330.92i | 1.56622 | + | 0.904256i | ||||
\(189\) | 156.272 | + | 90.2238i | 0.0601435 | + | 0.0347239i | ||||
\(190\) | − | 1272.58i | − | 0.485911i | ||||||
\(191\) | −2028.87 | + | 3514.11i | −0.768607 | + | 1.33127i | 0.169711 | + | 0.985494i | \(0.445717\pi\) |
−0.938318 | + | 0.345773i | \(0.887617\pi\) | |||||||
\(192\) | 946.500 | + | 1639.39i | 0.355770 | + | 0.616211i | ||||
\(193\) | −756.381 | + | 436.697i | −0.282101 | + | 0.162871i | −0.634374 | − | 0.773026i | \(-0.718742\pi\) |
0.352273 | + | 0.935897i | \(0.385409\pi\) | |||||||
\(194\) | −7233.92 | −2.67714 | ||||||||
\(195\) | −364.438 | − | 226.120i | −0.133836 | − | 0.0830401i | ||||
\(196\) | −2685.01 | −0.978502 | ||||||||
\(197\) | 3591.62 | − | 2073.62i | 1.29895 | − | 0.749947i | 0.318724 | − | 0.947848i | \(-0.396746\pi\) |
0.980222 | + | 0.197901i | \(0.0634124\pi\) | |||||||
\(198\) | −598.365 | − | 1036.40i | −0.214767 | − | 0.371988i | ||||
\(199\) | −1202.03 | + | 2081.98i | −0.428189 | + | 0.741646i | −0.996712 | − | 0.0810216i | \(-0.974182\pi\) |
0.568523 | + | 0.822667i | \(0.307515\pi\) | |||||||
\(200\) | − | 477.032i | − | 0.168656i | ||||||
\(201\) | −148.545 | − | 85.7625i | −0.0521271 | − | 0.0300956i | ||||
\(202\) | −2288.26 | − | 1321.13i | −0.797035 | − | 0.460169i | ||||
\(203\) | 1070.06i | 0.369969i | ||||||||
\(204\) | −389.591 | + | 674.791i | −0.133710 | + | 0.231592i | ||||
\(205\) | −85.5307 | − | 148.144i | −0.0291401 | − | 0.0504722i | ||||
\(206\) | 2475.05 | − | 1428.97i | 0.837111 | − | 0.483307i | ||||
\(207\) | 1070.91 | 0.359582 | ||||||||
\(208\) | 1359.17 | − | 2190.57i | 0.453083 | − | 0.730233i | ||||
\(209\) | −3263.50 | −1.08010 | ||||||||
\(210\) | −218.359 | + | 126.070i | −0.0717535 | + | 0.0414269i | ||||
\(211\) | −1934.43 | − | 3350.53i | −0.631144 | − | 1.09317i | −0.987318 | − | 0.158754i | \(-0.949252\pi\) |
0.356174 | − | 0.934420i | \(-0.384081\pi\) | |||||||
\(212\) | −3129.96 | + | 5421.24i | −1.01399 | + | 1.75629i | ||||
\(213\) | − | 927.679i | − | 0.298420i | ||||||
\(214\) | 1448.55 | + | 836.322i | 0.462715 | + | 0.267149i | ||||
\(215\) | −337.782 | − | 195.019i | −0.107147 | − | 0.0618612i | ||||
\(216\) | 111.324i | 0.0350677i | ||||||||
\(217\) | −127.217 | + | 220.346i | −0.0397975 | + | 0.0689313i | ||||
\(218\) | −988.547 | − | 1712.21i | −0.307123 | − | 0.531953i | ||||
\(219\) | −1012.50 | + | 584.567i | −0.312413 | + | 0.180372i | ||||
\(220\) | 885.279 | 0.271298 | ||||||||
\(221\) | 1351.98 | + | 42.9153i | 0.411512 | + | 0.0130624i | ||||
\(222\) | 4051.79 | 1.22495 | ||||||||
\(223\) | 2436.61 | − | 1406.78i | 0.731692 | − | 0.422443i | −0.0873487 | − | 0.996178i | \(-0.527839\pi\) |
0.819041 | + | 0.573735i | \(0.194506\pi\) | |||||||
\(224\) | −868.005 | − | 1503.43i | −0.258911 | − | 0.448447i | ||||
\(225\) | −520.637 | + | 901.770i | −0.154263 | + | 0.267191i | ||||
\(226\) | − | 6379.29i | − | 1.87763i | ||||||
\(227\) | 3913.02 | + | 2259.19i | 1.14413 | + | 0.660561i | 0.947449 | − | 0.319907i | \(-0.103652\pi\) |
0.196677 | + | 0.980468i | \(0.436985\pi\) | |||||||
\(228\) | 2366.18 | + | 1366.12i | 0.687300 | + | 0.396813i | ||||
\(229\) | 1305.27i | 0.376658i | 0.982106 | + | 0.188329i | \(0.0603070\pi\) | ||||
−0.982106 | + | 0.188329i | \(0.939693\pi\) | |||||||
\(230\) | −748.192 | + | 1295.91i | −0.214497 | + | 0.371520i | ||||
\(231\) | 323.301 | + | 559.975i | 0.0920852 | + | 0.159496i | ||||
\(232\) | −571.712 | + | 330.078i | −0.161788 | + | 0.0934082i | ||||
\(233\) | 3360.55 | 0.944879 | 0.472440 | − | 0.881363i | \(-0.343373\pi\) | ||||
0.472440 | + | 0.881363i | \(0.343373\pi\) | |||||||
\(234\) | 1533.14 | − | 821.437i | 0.428309 | − | 0.229483i | ||||
\(235\) | 1579.88 | 0.438553 | ||||||||
\(236\) | 5117.09 | − | 2954.35i | 1.41142 | − | 0.814882i | ||||
\(237\) | 1352.73 | + | 2343.00i | 0.370756 | + | 0.642169i | ||||
\(238\) | 397.609 | − | 688.679i | 0.108291 | − | 0.187565i | ||||
\(239\) | − | 4737.17i | − | 1.28210i | −0.767499 | − | 0.641050i | \(-0.778499\pi\) | ||
0.767499 | − | 0.641050i | \(-0.221501\pi\) | |||||||
\(240\) | 435.836 | + | 251.630i | 0.117221 | + | 0.0676777i | ||||
\(241\) | 4144.17 | + | 2392.64i | 1.10767 | + | 0.639516i | 0.938226 | − | 0.346023i | \(-0.112468\pi\) |
0.169448 | + | 0.985539i | \(0.445801\pi\) | |||||||
\(242\) | 1199.58i | 0.318643i | ||||||||
\(243\) | 121.500 | − | 210.444i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 3155.87 | + | 5466.13i | 0.828007 | + | 1.43415i | ||||
\(245\) | −788.029 | + | 454.969i | −0.205491 | + | 0.118640i | ||||
\(246\) | 693.729 | 0.179799 | ||||||||
\(247\) | 150.484 | − | 4740.79i | 0.0387655 | − | 1.22125i | ||||
\(248\) | −156.969 | −0.0401916 | ||||||||
\(249\) | −1785.13 | + | 1030.64i | −0.454328 | + | 0.262307i | ||||
\(250\) | −1513.47 | − | 2621.41i | −0.382881 | − | 0.663169i | ||||
\(251\) | −1636.93 | + | 2835.25i | −0.411642 | + | 0.712985i | −0.995069 | − | 0.0991805i | \(-0.968378\pi\) |
0.583428 | + | 0.812165i | \(0.301711\pi\) | |||||||
\(252\) | − | 541.343i | − | 0.135323i | ||||||
\(253\) | 3323.31 | + | 1918.71i | 0.825828 | + | 0.476792i | ||||
\(254\) | −8909.48 | − | 5143.89i | −2.20091 | − | 1.27069i | ||||
\(255\) | 264.061i | 0.0648476i | ||||||||
\(256\) | −1444.50 | + | 2501.95i | −0.352661 | + | 0.610827i | ||||
\(257\) | −3272.91 | − | 5668.84i | −0.794390 | − | 1.37592i | −0.923226 | − | 0.384258i | \(-0.874457\pi\) |
0.128835 | − | 0.991666i | \(-0.458876\pi\) | |||||||
\(258\) | 1369.85 | − | 790.885i | 0.330556 | − | 0.190846i | ||||
\(259\) | −2189.22 | −0.525217 | ||||||||
\(260\) | −40.8214 | + | 1286.02i | −0.00973706 | + | 0.306752i | ||||
\(261\) | 1441.00 | 0.341746 | ||||||||
\(262\) | 156.244 | − | 90.2077i | 0.0368428 | − | 0.0212712i | ||||
\(263\) | −44.1007 | − | 76.3847i | −0.0103398 | − | 0.0179091i | 0.860809 | − | 0.508928i | \(-0.169958\pi\) |
−0.871149 | + | 0.491019i | \(0.836625\pi\) | |||||||
\(264\) | −199.455 | + | 345.466i | −0.0464985 | + | 0.0805378i | ||||
\(265\) | 2121.46i | 0.491773i | ||||||||
\(266\) | −2414.88 | − | 1394.23i | −0.556639 | − | 0.321376i | ||||
\(267\) | −2781.34 | − | 1605.81i | −0.637510 | − | 0.368067i | ||||
\(268\) | 514.575i | 0.117286i | ||||||||
\(269\) | 2263.80 | − | 3921.01i | 0.513109 | − | 0.888730i | −0.486776 | − | 0.873527i | \(-0.661827\pi\) |
0.999884 | − | 0.0152033i | \(-0.00483956\pi\) | |||||||
\(270\) | 169.772 | + | 294.054i | 0.0382667 | + | 0.0662798i | ||||
\(271\) | −7206.91 | + | 4160.91i | −1.61546 | + | 0.932684i | −0.627380 | + | 0.778713i | \(0.715873\pi\) |
−0.988075 | + | 0.153971i | \(0.950794\pi\) | |||||||
\(272\) | −1587.22 | −0.353821 | ||||||||
\(273\) | −828.366 | + | 443.829i | −0.183645 | + | 0.0983948i | ||||
\(274\) | −850.160 | −0.187445 | ||||||||
\(275\) | −3231.34 | + | 1865.61i | −0.708571 | + | 0.409094i | ||||
\(276\) | −1606.36 | − | 2782.31i | −0.350333 | − | 0.606794i | ||||
\(277\) | −1440.65 | + | 2495.29i | −0.312493 | + | 0.541254i | −0.978901 | − | 0.204333i | \(-0.934497\pi\) |
0.666408 | + | 0.745587i | \(0.267831\pi\) | |||||||
\(278\) | − | 412.311i | − | 0.0889523i | ||||||
\(279\) | 296.730 | + | 171.317i | 0.0636730 | + | 0.0367616i | ||||
\(280\) | 72.7864 | + | 42.0233i | 0.0155351 | + | 0.00896918i | ||||
\(281\) | 2817.99i | 0.598247i | 0.954214 | + | 0.299123i | \(0.0966942\pi\) | ||||
−0.954214 | + | 0.299123i | \(0.903306\pi\) | |||||||
\(282\) | −3203.55 | + | 5548.71i | −0.676484 | + | 1.17170i | ||||
\(283\) | 132.301 | + | 229.152i | 0.0277896 | + | 0.0481330i | 0.879586 | − | 0.475740i | \(-0.157820\pi\) |
−0.851796 | + | 0.523873i | \(0.824486\pi\) | |||||||
\(284\) | −2410.18 | + | 1391.52i | −0.503584 | + | 0.290744i | ||||
\(285\) | 925.941 | 0.192449 | ||||||||
\(286\) | 6229.45 | + | 197.738i | 1.28796 | + | 0.0408829i | ||||
\(287\) | −374.827 | −0.0770918 | ||||||||
\(288\) | −2024.59 | + | 1168.90i | −0.414238 | + | 0.239160i | ||||
\(289\) | 2040.09 | + | 3533.54i | 0.415244 | + | 0.719223i | ||||
\(290\) | −1006.76 | + | 1743.76i | −0.203858 | + | 0.353093i | ||||
\(291\) | − | 5263.45i | − | 1.06031i | ||||||
\(292\) | 3037.50 | + | 1753.70i | 0.608754 | + | 0.351464i | ||||
\(293\) | 3717.43 | + | 2146.26i | 0.741211 | + | 0.427938i | 0.822509 | − | 0.568751i | \(-0.192573\pi\) |
−0.0812984 | + | 0.996690i | \(0.525907\pi\) | |||||||
\(294\) | − | 3690.19i | − | 0.732028i | ||||||
\(295\) | 1001.22 | − | 1734.16i | 0.197604 | − | 0.342260i | ||||
\(296\) | −675.299 | − | 1169.65i | −0.132604 | − | 0.229678i | ||||
\(297\) | 754.091 | − | 435.374i | 0.147329 | − | 0.0850606i | ||||
\(298\) | −1568.64 | −0.304929 | ||||||||
\(299\) | −2940.50 | + | 4739.19i | −0.568740 | + | 0.916638i | ||||
\(300\) | 3123.82 | 0.601180 | ||||||||
\(301\) | −740.143 | + | 427.322i | −0.141731 | + | 0.0818286i | ||||
\(302\) | 3128.31 | + | 5418.39i | 0.596072 | + | 1.03243i | ||||
\(303\) | 961.260 | − | 1664.95i | 0.182254 | − | 0.315673i | ||||
\(304\) | 5565.66i | 1.05004i | ||||||||
\(305\) | 1852.45 | + | 1069.51i | 0.347773 | + | 0.200787i | ||||
\(306\) | −927.411 | − | 535.441i | −0.173257 | − | 0.100030i | ||||
\(307\) | − | 7026.26i | − | 1.30622i | −0.757263 | − | 0.653110i | \(-0.773464\pi\) | ||
0.757263 | − | 0.653110i | \(-0.226536\pi\) | |||||||
\(308\) | 969.904 | − | 1679.92i | 0.179433 | − | 0.310787i | ||||
\(309\) | 1039.73 | + | 1800.86i | 0.191418 | + | 0.331546i | ||||
\(310\) | −414.621 | + | 239.382i | −0.0759642 | + | 0.0438580i | ||||
\(311\) | 1133.21 | 0.206618 | 0.103309 | − | 0.994649i | \(-0.467057\pi\) | ||||
0.103309 | + | 0.994649i | \(0.467057\pi\) | |||||||
\(312\) | −492.651 | − | 305.672i | −0.0893939 | − | 0.0554657i | ||||
\(313\) | −5285.95 | −0.954566 | −0.477283 | − | 0.878750i | \(-0.658378\pi\) | ||||
−0.477283 | + | 0.878750i | \(0.658378\pi\) | |||||||
\(314\) | 5178.09 | − | 2989.57i | 0.930626 | − | 0.537297i | ||||
\(315\) | −91.7293 | − | 158.880i | −0.0164075 | − | 0.0284186i | ||||
\(316\) | 4058.19 | − | 7028.99i | 0.722440 | − | 1.25130i | ||||
\(317\) | − | 4782.16i | − | 0.847296i | −0.905827 | − | 0.423648i | \(-0.860749\pi\) | ||
0.905827 | − | 0.423648i | \(-0.139251\pi\) | |||||||
\(318\) | −7450.78 | − | 4301.71i | −1.31390 | − | 0.758579i | ||||
\(319\) | 4471.80 | + | 2581.79i | 0.784867 | + | 0.453143i | ||||
\(320\) | − | 1924.59i | − | 0.336212i | ||||||
\(321\) | −608.514 | + | 1053.98i | −0.105807 | + | 0.183262i | ||||
\(322\) | 1639.43 | + | 2839.57i | 0.283732 | + | 0.491438i | ||||
\(323\) | −2529.06 | + | 1460.15i | −0.435668 | + | 0.251533i | ||||
\(324\) | −729.000 | −0.125000 | ||||||||
\(325\) | −2561.12 | − | 4780.10i | −0.437124 | − | 0.815852i | ||||
\(326\) | 9657.80 | 1.64079 | ||||||||
\(327\) | 1245.82 | − | 719.274i | 0.210685 | − | 0.121639i | ||||
\(328\) | −115.621 | − | 200.262i | −0.0194638 | − | 0.0337123i | ||||
\(329\) | 1730.90 | − | 2998.01i | 0.290054 | − | 0.502388i | ||||
\(330\) | 1216.70i | 0.202961i | ||||||||
\(331\) | −7508.43 | − | 4334.99i | −1.24683 | − | 0.719857i | −0.276353 | − | 0.961056i | \(-0.589126\pi\) |
−0.970476 | + | 0.241199i | \(0.922459\pi\) | |||||||
\(332\) | 5355.38 | + | 3091.93i | 0.885285 | + | 0.511120i | ||||
\(333\) | 2948.11i | 0.485152i | ||||||||
\(334\) | 82.6128 | − | 143.090i | 0.0135340 | − | 0.0234417i | ||||
\(335\) | 87.1936 | + | 151.024i | 0.0142206 | + | 0.0246308i | ||||
\(336\) | 954.996 | − | 551.367i | 0.155058 | − | 0.0895225i | ||||
\(337\) | −8526.59 | −1.37826 | −0.689129 | − | 0.724639i | \(-0.742007\pi\) | ||||
−0.689129 | + | 0.724639i | \(0.742007\pi\) | |||||||
\(338\) | −574.497 | + | 9040.23i | −0.0924513 | + | 1.45480i | ||||
\(339\) | 4641.61 | 0.743651 | ||||||||
\(340\) | 686.051 | − | 396.092i | 0.109430 | − | 0.0631796i | ||||
\(341\) | 613.886 | + | 1063.28i | 0.0974891 | + | 0.168856i | ||||
\(342\) | −1877.55 | + | 3252.01i | −0.296860 | + | 0.514177i | ||||
\(343\) | 4286.19i | 0.674731i | ||||||||
\(344\) | −456.618 | − | 263.628i | −0.0715674 | − | 0.0413195i | ||||
\(345\) | −942.911 | − | 544.390i | −0.147144 | − | 0.0849535i | ||||
\(346\) | − | 7873.23i | − | 1.22332i | ||||||
\(347\) | 6290.74 | − | 10895.9i | 0.973213 | − | 1.68565i | 0.287501 | − | 0.957780i | \(-0.407175\pi\) |
0.685711 | − | 0.727874i | \(-0.259491\pi\) | |||||||
\(348\) | −2161.50 | − | 3743.84i | −0.332956 | − | 0.576697i | ||||
\(349\) | 7760.61 | − | 4480.59i | 1.19030 | − | 0.687222i | 0.231928 | − | 0.972733i | \(-0.425497\pi\) |
0.958375 | + | 0.285511i | \(0.0921633\pi\) | |||||||
\(350\) | −3188.12 | −0.486892 | ||||||||
\(351\) | 597.684 | + | 1115.52i | 0.0908889 | + | 0.169636i | ||||
\(352\) | −8377.11 | −1.26847 | ||||||||
\(353\) | −4640.16 | + | 2679.00i | −0.699634 | + | 0.403934i | −0.807211 | − | 0.590263i | \(-0.799024\pi\) |
0.107577 | + | 0.994197i | \(0.465691\pi\) | |||||||
\(354\) | 4060.37 | + | 7032.77i | 0.609622 | + | 1.05590i | ||||
\(355\) | −471.579 | + | 816.799i | −0.0705037 | + | 0.122116i | ||||
\(356\) | 9634.84i | 1.43440i | ||||||||
\(357\) | 501.088 | + | 289.303i | 0.0742868 | + | 0.0428895i | ||||
\(358\) | −1820.92 | − | 1051.31i | −0.268822 | − | 0.155205i | ||||
\(359\) | 2705.40i | 0.397731i | 0.980027 | + | 0.198866i | \(0.0637257\pi\) | ||||
−0.980027 | + | 0.198866i | \(0.936274\pi\) | |||||||
\(360\) | 56.5907 | − | 98.0180i | 0.00828498 | − | 0.0143500i | ||||
\(361\) | 1690.60 | + | 2928.20i | 0.246478 | + | 0.426913i | ||||
\(362\) | 7630.19 | − | 4405.29i | 1.10783 | − | 0.639605i | ||||
\(363\) | −872.820 | −0.126202 | ||||||||
\(364\) | 2395.65 | + | 1486.42i | 0.344962 | + | 0.214037i | ||||
\(365\) | 1188.64 | 0.170456 | ||||||||
\(366\) | −7512.47 | + | 4337.33i | −1.07290 | + | 0.619442i | ||||
\(367\) | −5236.88 | − | 9070.54i | −0.744858 | − | 1.29013i | −0.950261 | − | 0.311455i | \(-0.899184\pi\) |
0.205403 | − | 0.978678i | \(-0.434150\pi\) | |||||||
\(368\) | 3272.22 | − | 5667.66i | 0.463523 | − | 0.802846i | ||||
\(369\) | 504.762i | 0.0712110i | ||||||||
\(370\) | −3567.51 | − | 2059.70i | −0.501259 | − | 0.289402i | ||||
\(371\) | 4025.72 | + | 2324.25i | 0.563356 | + | 0.325254i | ||||
\(372\) | − | 1027.90i | − | 0.143264i | ||||||
\(373\) | 6381.51 | − | 11053.1i | 0.885850 | − | 1.53434i | 0.0411127 | − | 0.999155i | \(-0.486910\pi\) |
0.844737 | − | 0.535182i | \(-0.179757\pi\) | |||||||
\(374\) | −1918.66 | − | 3323.22i | −0.265272 | − | 0.459464i | ||||
\(375\) | 1907.35 | − | 1101.21i | 0.262654 | − | 0.151643i | ||||
\(376\) | 2135.70 | 0.292926 | ||||||||
\(377\) | −3956.70 | + | 6377.00i | −0.540531 | + | 0.871173i | ||||
\(378\) | 744.004 | 0.101237 | ||||||||
\(379\) | −2007.47 | + | 1159.01i | −0.272076 | + | 0.157083i | −0.629831 | − | 0.776733i | \(-0.716876\pi\) |
0.357755 | + | 0.933816i | \(0.383542\pi\) | |||||||
\(380\) | −1388.91 | − | 2405.67i | −0.187499 | − | 0.324758i | ||||
\(381\) | 3742.73 | − | 6482.60i | 0.503270 | − | 0.871690i | ||||
\(382\) | 16730.5i | 2.24086i | ||||||||
\(383\) | −1717.63 | − | 991.672i | −0.229156 | − | 0.132303i | 0.381027 | − | 0.924564i | \(-0.375571\pi\) |
−0.610183 | + | 0.792261i | \(0.708904\pi\) | |||||||
\(384\) | 1360.44 | + | 785.452i | 0.180794 | + | 0.104381i | ||||
\(385\) | − | 657.392i | − | 0.0870229i | ||||||
\(386\) | −1800.55 | + | 3118.64i | −0.237424 | + | 0.411230i | ||||
\(387\) | 575.454 | + | 996.715i | 0.0755864 | + | 0.130920i | ||||
\(388\) | −13674.8 | + | 7895.17i | −1.78927 | + | 1.03303i | ||||
\(389\) | 3244.51 | 0.422887 | 0.211444 | − | 0.977390i | \(-0.432184\pi\) | ||||
0.211444 | + | 0.977390i | \(0.432184\pi\) | |||||||
\(390\) | −1767.46 | − | 56.1036i | −0.229485 | − | 0.00728441i | ||||
\(391\) | 3433.88 | 0.444140 | ||||||||
\(392\) | −1065.27 | + | 615.032i | −0.137255 | + | 0.0792444i | ||||
\(393\) | 65.6357 | + | 113.684i | 0.00842464 | + | 0.0145919i | ||||
\(394\) | 8549.77 | − | 14808.6i | 1.09323 | − | 1.89352i | ||||
\(395\) | − | 2750.60i | − | 0.350374i | ||||||
\(396\) | −2262.27 | − | 1306.12i | −0.287079 | − | 0.165745i | ||||
\(397\) | 3256.02 | + | 1879.86i | 0.411624 | + | 0.237651i | 0.691487 | − | 0.722389i | \(-0.256956\pi\) |
−0.279863 | + | 0.960040i | \(0.590289\pi\) | |||||||
\(398\) | 9912.20i | 1.24838i | ||||||||
\(399\) | 1014.45 | − | 1757.09i | 0.127284 | − | 0.220462i | ||||
\(400\) | 3181.67 | + | 5510.82i | 0.397709 | + | 0.688852i | ||||
\(401\) | 1729.93 | − | 998.773i | 0.215432 | − | 0.124380i | −0.388401 | − | 0.921490i | \(-0.626973\pi\) |
0.603833 | + | 0.797110i | \(0.293639\pi\) | |||||||
\(402\) | −707.216 | −0.0877431 | ||||||||
\(403\) | −1572.90 | + | 842.744i | −0.194422 | + | 0.104169i | ||||
\(404\) | −5767.56 | −0.710264 | ||||||||
\(405\) | −213.956 | + | 123.527i | −0.0262507 | + | 0.0151559i | ||||
\(406\) | 2205.99 | + | 3820.89i | 0.269659 | + | 0.467063i | ||||
\(407\) | −5282.03 | + | 9148.74i | −0.643293 | + | 1.11422i | ||||
\(408\) | 356.961i | 0.0433142i | ||||||||
\(409\) | 4499.20 | + | 2597.62i | 0.543940 | + | 0.314044i | 0.746674 | − | 0.665190i | \(-0.231650\pi\) |
−0.202735 | + | 0.979234i | \(0.564983\pi\) | |||||||
\(410\) | −610.811 | − | 352.652i | −0.0735752 | − | 0.0424787i | ||||
\(411\) | − | 618.582i | − | 0.0742394i | ||||||
\(412\) | 3119.19 | − | 5402.59i | 0.372989 | − | 0.646035i | ||||
\(413\) | −2193.85 | − | 3799.86i | −0.261386 | − | 0.452734i | ||||
\(414\) | 3823.91 | − | 2207.74i | 0.453950 | − | 0.262088i | ||||
\(415\) | 2095.68 | 0.247887 | ||||||||
\(416\) | 386.280 | − | 12169.2i | 0.0455263 | − | 1.43424i | ||||
\(417\) | 300.000 | 0.0352304 | ||||||||
\(418\) | −11653.0 | + | 6727.87i | −1.36356 | + | 0.787251i | ||||
\(419\) | 3411.05 | + | 5908.12i | 0.397711 | + | 0.688855i | 0.993443 | − | 0.114328i | \(-0.0364714\pi\) |
−0.595732 | + | 0.803183i | \(0.703138\pi\) | |||||||
\(420\) | −275.188 | + | 476.639i | −0.0319709 | + | 0.0553753i | ||||
\(421\) | 7537.70i | 0.872601i | 0.899801 | + | 0.436300i | \(0.143712\pi\) | ||||
−0.899801 | + | 0.436300i | \(0.856288\pi\) | |||||||
\(422\) | −13814.6 | − | 7975.85i | −1.59356 | − | 0.920043i | ||||
\(423\) | −4037.28 | − | 2330.92i | −0.464064 | − | 0.267928i | ||||
\(424\) | 2867.81i | 0.328474i | ||||||||
\(425\) | −1669.43 | + | 2891.53i | −0.190539 | + | 0.330023i | ||||
\(426\) | −1912.46 | − | 3312.48i | −0.217509 | − | 0.376737i | ||||
\(427\) | 4059.05 | − | 2343.49i | 0.460026 | − | 0.265596i | ||||
\(428\) | 3651.08 | 0.412340 | ||||||||
\(429\) | −143.876 | + | 4532.59i | −0.0161920 | + | 0.510107i | ||||
\(430\) | −1608.16 | −0.180355 | ||||||||
\(431\) | −11608.4 | + | 6702.10i | −1.29735 | + | 0.749023i | −0.979945 | − | 0.199268i | \(-0.936143\pi\) |
−0.317401 | + | 0.948291i | \(0.602810\pi\) | |||||||
\(432\) | −742.500 | − | 1286.05i | −0.0826934 | − | 0.143229i | ||||
\(433\) | −8857.97 | + | 15342.5i | −0.983110 | + | 1.70280i | −0.333061 | + | 0.942905i | \(0.608081\pi\) |
−0.650050 | + | 0.759892i | \(0.725252\pi\) | |||||||
\(434\) | 1049.06i | 0.116029i | ||||||||
\(435\) | −1268.77 | − | 732.524i | −0.139846 | − | 0.0807398i | ||||
\(436\) | −3737.46 | − | 2157.82i | −0.410531 | − | 0.237020i | ||||
\(437\) | − | 12041.1i | − | 1.31808i | ||||||
\(438\) | −2410.23 | + | 4174.64i | −0.262935 | + | 0.455416i | ||||
\(439\) | 3581.73 | + | 6203.75i | 0.389401 | + | 0.674462i | 0.992369 | − | 0.123303i | \(-0.0393488\pi\) |
−0.602968 | + | 0.797765i | \(0.706015\pi\) | |||||||
\(440\) | 351.231 | − | 202.783i | 0.0380552 | − | 0.0219712i | ||||
\(441\) | 2685.01 | 0.289926 | ||||||||
\(442\) | 4916.02 | − | 2633.95i | 0.529030 | − | 0.283448i | ||||
\(443\) | −10169.2 | −1.09064 | −0.545321 | − | 0.838227i | \(-0.683592\pi\) | ||||
−0.545321 | + | 0.838227i | \(0.683592\pi\) | |||||||
\(444\) | 7659.42 | − | 4422.17i | 0.818693 | − | 0.472673i | ||||
\(445\) | 1632.60 | + | 2827.75i | 0.173916 | + | 0.301232i | ||||
\(446\) | 5800.29 | − | 10046.4i | 0.615811 | − | 1.06662i | ||||
\(447\) | − | 1141.35i | − | 0.120770i | ||||||
\(448\) | −3652.14 | − | 2108.56i | −0.385150 | − | 0.222367i | ||||
\(449\) | −14845.8 | − | 8571.24i | −1.56040 | − | 0.900895i | −0.997217 | − | 0.0745603i | \(-0.976245\pi\) |
−0.563179 | − | 0.826335i | \(-0.690422\pi\) | |||||||
\(450\) | 4293.28i | 0.449750i | ||||||||
\(451\) | −904.364 | + | 1566.40i | −0.0944231 | + | 0.163546i | ||||
\(452\) | −6962.42 | − | 12059.3i | −0.724524 | − | 1.25491i | ||||
\(453\) | −3942.46 | + | 2276.18i | −0.408902 | + | 0.236080i | ||||
\(454\) | 18629.7 | 1.92585 | ||||||||
\(455\) | 954.974 | + | 30.3133i | 0.0983954 | + | 0.00312331i | ||||
\(456\) | 1251.70 | 0.128544 | ||||||||
\(457\) | 12203.3 | − | 7045.57i | 1.24912 | − | 0.721177i | 0.278183 | − | 0.960528i | \(-0.410268\pi\) |
0.970933 | + | 0.239351i | \(0.0769346\pi\) | |||||||
\(458\) | 2690.88 | + | 4660.74i | 0.274534 | + | 0.475507i | ||||
\(459\) | 389.591 | − | 674.791i | 0.0396177 | − | 0.0686199i | ||||
\(460\) | 3266.34i | 0.331074i | ||||||||
\(461\) | 2530.72 | + | 1461.11i | 0.255678 | + | 0.147616i | 0.622361 | − | 0.782730i | \(-0.286174\pi\) |
−0.366684 | + | 0.930346i | \(0.619507\pi\) | |||||||
\(462\) | 2308.83 | + | 1333.01i | 0.232504 | + | 0.134236i | ||||
\(463\) | 2072.61i | 0.208040i | 0.994575 | + | 0.104020i | \(0.0331706\pi\) | ||||
−0.994575 | + | 0.104020i | \(0.966829\pi\) | |||||||
\(464\) | 4403.06 | − | 7626.33i | 0.440533 | − | 0.763025i | ||||
\(465\) | −174.176 | − | 301.681i | −0.0173703 | − | 0.0300863i | ||||
\(466\) | 11999.6 | − | 6927.95i | 1.19285 | − | 0.688693i | ||||
\(467\) | 2664.19 | 0.263992 | 0.131996 | − | 0.991250i | \(-0.457861\pi\) | ||||
0.131996 | + | 0.991250i | \(0.457861\pi\) | |||||||
\(468\) | 2001.68 | − | 3226.11i | 0.197709 | − | 0.318647i | ||||
\(469\) | 382.114 | 0.0376213 | ||||||||
\(470\) | 5641.29 | − | 3257.00i | 0.553646 | − | 0.319648i | ||||
\(471\) | 2175.23 | + | 3767.61i | 0.212801 | + | 0.368583i | ||||
\(472\) | 1353.46 | − | 2344.26i | 0.131987 | − | 0.228608i | ||||
\(473\) | 4124.08i | 0.400899i | ||||||||
\(474\) | 9660.42 | + | 5577.45i | 0.936114 | + | 0.540466i | ||||
\(475\) | 10139.3 | + | 5853.92i | 0.979415 | + | 0.565466i | ||||
\(476\) | − | 1735.82i | − | 0.167145i | ||||||
\(477\) | 3129.96 | − | 5421.24i | 0.300442 | − | 0.520381i | ||||
\(478\) | −9765.92 | − | 16915.1i | −0.934483 | − | 1.61857i | ||||
\(479\) | 4521.26 | − | 2610.35i | 0.431277 | − | 0.248998i | −0.268614 | − | 0.963248i | \(-0.586566\pi\) |
0.699890 | + | 0.714250i | \(0.253232\pi\) | |||||||
\(480\) | 2376.81 | 0.226013 | ||||||||
\(481\) | −13046.5 | − | 8094.91i | −1.23674 | − | 0.767351i | ||||
\(482\) | 19730.2 | 1.86449 | ||||||||
\(483\) | −2066.09 | + | 1192.86i | −0.194639 | + | 0.112375i | ||||
\(484\) | 1309.23 | + | 2267.65i | 0.122955 | + | 0.212965i | ||||
\(485\) | −2675.64 | + | 4634.34i | −0.250504 | + | 0.433886i | ||||
\(486\) | − | 1001.91i | − | 0.0935139i | ||||||
\(487\) | 10586.8 | + | 6112.30i | 0.985081 | + | 0.568737i | 0.903800 | − | 0.427954i | \(-0.140766\pi\) |
0.0812808 | + | 0.996691i | \(0.474099\pi\) | |||||||
\(488\) | 2504.16 | + | 1445.78i | 0.232291 | + | 0.134113i | ||||
\(489\) | 7027.08i | 0.649848i | ||||||||
\(490\) | −1875.88 | + | 3249.13i | −0.172946 | + | 0.299552i | ||||
\(491\) | 9826.61 | + | 17020.2i | 0.903195 | + | 1.56438i | 0.823323 | + | 0.567574i | \(0.192118\pi\) |
0.0798720 | + | 0.996805i | \(0.474549\pi\) | |||||||
\(492\) | 1311.41 | − | 757.143i | 0.120168 | − | 0.0693793i | ||||
\(493\) | 4620.59 | 0.422111 | ||||||||
\(494\) | −9236.04 | − | 17238.2i | −0.841193 | − | 1.57001i | ||||
\(495\) | −885.279 | −0.0803845 | ||||||||
\(496\) | 1813.35 | − | 1046.94i | 0.164157 | − | 0.0947760i | ||||
\(497\) | 1033.32 | + | 1789.76i | 0.0932608 | + | 0.161532i | ||||
\(498\) | −4249.45 | + | 7360.26i | −0.382374 | + | 0.662292i | ||||
\(499\) | − | 11713.6i | − | 1.05084i | −0.850842 | − | 0.525422i | \(-0.823907\pi\) | ||
0.850842 | − | 0.525422i | \(-0.176093\pi\) | |||||||
\(500\) | −5722.06 | − | 3303.63i | −0.511796 | − | 0.295486i | ||||
\(501\) | 104.113 | + | 60.1096i | 0.00928428 | + | 0.00536028i | ||||
\(502\) | 13498.5i | 1.20013i | ||||||||
\(503\) | −6501.67 | + | 11261.2i | −0.576332 | + | 0.998236i | 0.419563 | + | 0.907726i | \(0.362183\pi\) |
−0.995896 | + | 0.0905104i | \(0.971150\pi\) | |||||||
\(504\) | −124.001 | − | 214.776i | −0.0109592 | − | 0.0189819i | ||||
\(505\) | −1692.73 | + | 977.300i | −0.149160 | + | 0.0861174i | ||||
\(506\) | 15822.1 | 1.39008 | ||||||||
\(507\) | −6577.73 | − | 418.008i | −0.576188 | − | 0.0366162i | ||||
\(508\) | −22456.4 | −1.96130 | ||||||||
\(509\) | −4614.99 | + | 2664.47i | −0.401878 | + | 0.232024i | −0.687294 | − | 0.726379i | \(-0.741202\pi\) |
0.285416 | + | 0.958404i | \(0.407868\pi\) | |||||||
\(510\) | 544.376 | + | 942.886i | 0.0472654 | + | 0.0818661i | ||||
\(511\) | 1302.27 | − | 2255.59i | 0.112738 | − | 0.195267i | ||||
\(512\) | 16100.7i | 1.38976i | ||||||||
\(513\) | −2366.18 | − | 1366.12i | −0.203644 | − | 0.117574i | ||||
\(514\) | −23373.2 | − | 13494.5i | −2.00574 | − | 1.15801i | ||||
\(515\) | − | 2114.16i | − | 0.180895i | ||||||
\(516\) | 1726.36 | − | 2990.14i | 0.147284 | − | 0.255104i | ||||
\(517\) | −8352.47 | − | 14466.9i | −0.710524 | − | 1.23066i | ||||
\(518\) | −7817.06 | + | 4513.18i | −0.663054 | + | 0.382814i | ||||
\(519\) | 5728.62 | 0.484506 | ||||||||
\(520\) | 278.381 | + | 519.573i | 0.0234766 | + | 0.0438169i | ||||
\(521\) | −11700.3 | −0.983876 | −0.491938 | − | 0.870630i | \(-0.663711\pi\) | ||||
−0.491938 | + | 0.870630i | \(0.663711\pi\) | |||||||
\(522\) | 5145.41 | − | 2970.70i | 0.431434 | − | 0.249088i | ||||
\(523\) | 2267.52 | + | 3927.46i | 0.189583 | + | 0.328367i | 0.945111 | − | 0.326749i | \(-0.105953\pi\) |
−0.755528 | + | 0.655116i | \(0.772620\pi\) | |||||||
\(524\) | 196.907 | − | 341.053i | 0.0164159 | − | 0.0284332i | ||||
\(525\) | − | 2319.70i | − | 0.192838i | ||||||
\(526\) | −314.942 | − | 181.832i | −0.0261067 | − | 0.0150727i | ||||
\(527\) | 951.467 | + | 549.330i | 0.0786462 | + | 0.0454064i | ||||
\(528\) | − | 5321.24i | − | 0.438594i | ||||||
\(529\) | −995.810 | + | 1724.79i | −0.0818451 | + | 0.141760i | ||||
\(530\) | 4373.49 | + | 7575.11i | 0.358438 | + | 0.620834i | ||||
\(531\) | −5117.09 | + | 2954.35i | −0.418197 | + | 0.241446i | ||||
\(532\) | −6086.73 | −0.496040 | ||||||||
\(533\) | −2233.77 | − | 1385.97i | −0.181529 | − | 0.112632i | ||||
\(534\) | −13241.8 | −1.07309 | ||||||||
\(535\) | 1071.56 | − | 618.667i | 0.0865939 | − | 0.0499950i | ||||
\(536\) | 117.869 | + | 204.156i | 0.00949847 | + | 0.0164518i | ||||
\(537\) | 764.938 | − | 1324.91i | 0.0614702 | − | 0.106470i | ||||
\(538\) | − | 18667.8i | − | 1.49596i | ||||||
\(539\) | 8332.26 | + | 4810.63i | 0.665855 | + | 0.384432i | ||||
\(540\) | 641.867 | + | 370.582i | 0.0511510 | + | 0.0295321i | ||||
\(541\) | 5184.89i | 0.412044i | 0.978547 | + | 0.206022i | \(0.0660519\pi\) | ||||
−0.978547 | + | 0.206022i | \(0.933948\pi\) | |||||||
\(542\) | −17155.9 | + | 29714.8i | −1.35961 | + | 2.35491i | ||||
\(543\) | 3205.32 | + | 5551.78i | 0.253321 | + | 0.438766i | ||||
\(544\) | −6491.88 | + | 3748.09i | −0.511649 | + | 0.295401i | ||||
\(545\) | −1462.55 | −0.114952 | ||||||||
\(546\) | −2042.88 | + | 3292.51i | −0.160123 | + | 0.258070i | ||||
\(547\) | 5609.12 | 0.438443 | 0.219222 | − | 0.975675i | \(-0.429648\pi\) | ||||
0.219222 | + | 0.975675i | \(0.429648\pi\) | |||||||
\(548\) | −1607.12 | + | 927.873i | −0.125279 | + | 0.0723299i | ||||
\(549\) | −3155.87 | − | 5466.13i | −0.245336 | − | 0.424934i | ||||
\(550\) | −7692.12 | + | 13323.2i | −0.596351 | + | 1.03291i | ||||
\(551\) | − | 16202.3i | − | 1.25271i | ||||||
\(552\) | −1274.64 | − | 735.913i | −0.0982830 | − | 0.0567437i | ||||
\(553\) | −5219.61 | − | 3013.54i | −0.401375 | − | 0.231734i | ||||
\(554\) | 11879.9i | 0.911066i | ||||||||
\(555\) | 1498.65 | − | 2595.74i | 0.114620 | − | 0.198528i | ||||
\(556\) | −450.000 | − | 779.423i | −0.0343242 | − | 0.0594512i | ||||
\(557\) | 17450.9 | − | 10075.3i | 1.32750 | − | 0.766432i | 0.342586 | − | 0.939486i | \(-0.388697\pi\) |
0.984912 | + | 0.173055i | \(0.0553637\pi\) | |||||||
\(558\) | 1412.72 | 0.107178 | ||||||||
\(559\) | −5990.93 | − | 190.167i | −0.453290 | − | 0.0143886i | ||||
\(560\) | −1121.14 | −0.0846011 | ||||||||
\(561\) | 2418.00 | − | 1396.03i | 0.181975 | − | 0.105063i | ||||
\(562\) | 5809.44 | + | 10062.2i | 0.436044 | + | 0.755250i | ||||
\(563\) | 8146.10 | − | 14109.5i | 0.609800 | − | 1.05620i | −0.381474 | − | 0.924380i | \(-0.624583\pi\) |
0.991273 | − | 0.131824i | \(-0.0420834\pi\) | |||||||
\(564\) | 13985.5i | 1.04414i | ||||||||
\(565\) | −4086.83 | − | 2359.53i | −0.304308 | − | 0.175692i | ||||
\(566\) | 944.816 | + | 545.490i | 0.0701654 | + | 0.0405100i | ||||
\(567\) | 541.343i | 0.0400957i | ||||||||
\(568\) | −637.486 | + | 1104.16i | −0.0470921 | + | 0.0815660i | ||||
\(569\) | 5230.27 | + | 9059.09i | 0.385350 | + | 0.667446i | 0.991818 | − | 0.127662i | \(-0.0407474\pi\) |
−0.606468 | + | 0.795108i | \(0.707414\pi\) | |||||||
\(570\) | 3306.27 | − | 1908.88i | 0.242955 | − | 0.140270i | ||||
\(571\) | −2225.96 | −0.163141 | −0.0815705 | − | 0.996668i | \(-0.525994\pi\) | ||||
−0.0815705 | + | 0.996668i | \(0.525994\pi\) | |||||||
\(572\) | 11991.8 | − | 6425.09i | 0.876580 | − | 0.469662i | ||||
\(573\) | −12173.2 | −0.887511 | ||||||||
\(574\) | −1338.40 | + | 772.726i | −0.0973236 | + | 0.0561898i | ||||
\(575\) | −6883.40 | − | 11922.4i | −0.499231 | − | 0.864693i | ||||
\(576\) | −2839.50 | + | 4918.16i | −0.205404 | + | 0.355770i | ||||
\(577\) | 4686.23i | 0.338112i | 0.985606 | + | 0.169056i | \(0.0540718\pi\) | ||||
−0.985606 | + | 0.169056i | \(0.945928\pi\) | |||||||
\(578\) | 14569.2 | + | 8411.51i | 1.04844 | + | 0.605316i | ||||
\(579\) | −2269.14 | − | 1310.09i | −0.162871 | − | 0.0940337i | ||||
\(580\) | 4395.14i | 0.314652i | ||||||||
\(581\) | 2296.01 | − | 3976.81i | 0.163949 | − | 0.283969i | ||||
\(582\) | −10850.9 | − | 18794.3i | −0.772824 | − | 1.33857i | ||||
\(583\) | 19426.1 | − | 11215.7i | 1.38001 | − | 0.796750i | ||||
\(584\) | 1606.82 | 0.113854 | ||||||||
\(585\) | 40.8214 | − | 1286.02i | 0.00288505 | − | 0.0908894i | ||||
\(586\) | 17698.5 | 1.24764 | ||||||||
\(587\) | 10470.7 | − | 6045.28i | 0.736241 | − | 0.425069i | −0.0844601 | − | 0.996427i | \(-0.526917\pi\) |
0.820701 | + | 0.571358i | \(0.193583\pi\) | |||||||
\(588\) | −4027.51 | − | 6975.86i | −0.282469 | − | 0.489251i | ||||
\(589\) | 1926.25 | − | 3336.36i | 0.134753 | − | 0.233400i | ||||
\(590\) | − | 8256.25i | − | 0.576109i | ||||||
\(591\) | 10774.9 | + | 6220.87i | 0.749947 | + | 0.432982i | ||||
\(592\) | 15602.5 | + | 9008.12i | 1.08321 | + | 0.625391i | ||||
\(593\) | − | 6135.97i | − | 0.424914i | −0.977170 | − | 0.212457i | \(-0.931853\pi\) | ||
0.977170 | − | 0.212457i | \(-0.0681466\pi\) | |||||||
\(594\) | 1795.09 | − | 3109.20i | 0.123996 | − | 0.214767i | ||||
\(595\) | −294.131 | − | 509.449i | −0.0202658 | − | 0.0351015i | ||||
\(596\) | −2965.32 | + | 1712.03i | −0.203799 | + | 0.117663i | ||||
\(597\) | −7212.18 | −0.494431 | ||||||||
\(598\) | −729.579 | + | 22984.3i | −0.0498908 | + | 1.57174i | ||||
\(599\) | −6198.80 | −0.422831 | −0.211416 | − | 0.977396i | \(-0.567807\pi\) | ||||
−0.211416 | + | 0.977396i | \(0.567807\pi\) | |||||||
\(600\) | 1239.36 | − | 715.547i | 0.0843281 | − | 0.0486868i | ||||
\(601\) | −9172.69 | − | 15887.6i | −0.622565 | − | 1.07831i | −0.989006 | − | 0.147873i | \(-0.952757\pi\) |
0.366441 | − | 0.930441i | \(-0.380576\pi\) | |||||||
\(602\) | −1761.89 | + | 3051.69i | −0.119285 | + | 0.206607i | ||||
\(603\) | − | 514.575i | − | 0.0347514i | ||||||
\(604\) | 11827.4 | + | 6828.53i | 0.796770 | + | 0.460015i | ||||
\(605\) | 768.497 | + | 443.692i | 0.0516427 | + | 0.0298159i | ||||
\(606\) | − | 7926.75i | − | 0.531357i | ||||||
\(607\) | −5194.06 | + | 8996.38i | −0.347315 | + | 0.601568i | −0.985772 | − | 0.168090i | \(-0.946240\pi\) |
0.638456 | + | 0.769658i | \(0.279573\pi\) | |||||||
\(608\) | 13142.8 | + | 22764.1i | 0.876665 | + | 1.51843i | ||||
\(609\) | −2780.11 | + | 1605.10i | −0.184985 | + | 0.106801i | ||||
\(610\) | 8819.40 | 0.585389 | ||||||||
\(611\) | 21400.8 | − | 11466.3i | 1.41699 | − | 0.759209i | ||||
\(612\) | −2337.54 | −0.154395 | ||||||||
\(613\) | −696.701 | + | 402.240i | −0.0459045 | + | 0.0265030i | −0.522777 | − | 0.852470i | \(-0.675104\pi\) |
0.476872 | + | 0.878973i | \(0.341770\pi\) | |||||||
\(614\) | −14485.0 | − | 25088.8i | −0.952064 | − | 1.64902i | ||||
\(615\) | 256.592 | − | 444.431i | 0.0168241 | − | 0.0291401i | ||||
\(616\) | − | 888.671i | − | 0.0581259i | ||||||
\(617\) | −13179.4 | − | 7609.13i | −0.859940 | − | 0.496486i | 0.00405239 | − | 0.999992i | \(-0.498710\pi\) |
−0.863992 | + | 0.503505i | \(0.832043\pi\) | |||||||
\(618\) | 7425.15 | + | 4286.91i | 0.483307 | + | 0.279037i | ||||
\(619\) | 11462.5i | 0.744291i | 0.928174 | + | 0.372145i | \(0.121378\pi\) | ||||
−0.928174 | + | 0.372145i | \(0.878622\pi\) | |||||||
\(620\) | −522.527 | + | 905.044i | −0.0338471 | + | 0.0586249i | ||||
\(621\) | 1606.36 | + | 2782.31i | 0.103802 | + | 0.179791i | ||||
\(622\) | 4046.36 | − | 2336.17i | 0.260843 | − | 0.150598i | ||||
\(623\) | 7154.66 | 0.460105 | ||||||||
\(624\) | 7730.01 | + | 245.370i | 0.495911 | + | 0.0157414i | ||||
\(625\) | 12223.0 | 0.782270 | ||||||||
\(626\) | −18874.6 | + | 10897.3i | −1.20508 | + | 0.695754i | ||||
\(627\) | −4895.25 | − | 8478.81i | −0.311798 | − | 0.540050i | ||||
\(628\) | 6525.70 | − | 11302.8i | 0.414656 | − | 0.718205i | ||||
\(629\) | 9453.14i | 0.599239i | ||||||||
\(630\) | −655.078 | − | 378.209i | −0.0414269 | − | 0.0239178i | ||||
\(631\) | −3869.99 | − | 2234.34i | −0.244155 | − | 0.140963i | 0.372930 | − | 0.927860i | \(-0.378353\pi\) |
−0.617085 | + | 0.786896i | \(0.711687\pi\) | |||||||
\(632\) | − | 3718.30i | − | 0.234028i | ||||||
\(633\) | 5803.28 | − | 10051.6i | 0.364391 | − | 0.631144i | ||||
\(634\) | −9858.67 | − | 17075.7i | −0.617568 | − | 1.06966i | ||||
\(635\) | −6590.77 | + | 3805.18i | −0.411885 | + | 0.237802i | ||||
\(636\) | −18779.7 | −1.17086 | ||||||||
\(637\) | −7372.48 | + | 11882.2i | −0.458569 | + | 0.739074i | ||||
\(638\) | 21290.0 | 1.32113 | ||||||||
\(639\) | 2410.18 | − | 1391.52i | 0.149210 | − | 0.0861465i | ||||
\(640\) | −798.558 | − | 1383.14i | −0.0493215 | − | 0.0854274i | ||||
\(641\) | 3071.18 | − | 5319.44i | 0.189242 | − | 0.327777i | −0.755756 | − | 0.654854i | \(-0.772730\pi\) |
0.944998 | + | 0.327077i | \(0.106064\pi\) | |||||||
\(642\) | 5017.93i | 0.308477i | ||||||||
\(643\) | −17959.8 | − | 10369.1i | −1.10150 | − | 0.635951i | −0.164886 | − | 0.986313i | \(-0.552726\pi\) |
−0.936615 | + | 0.350361i | \(0.886059\pi\) | |||||||
\(644\) | 6198.27 | + | 3578.58i | 0.379264 | + | 0.218968i | ||||
\(645\) | − | 1170.11i | − | 0.0714312i | ||||||
\(646\) | −6020.37 | + | 10427.6i | −0.366669 | + | 0.635090i | ||||
\(647\) | 426.379 | + | 738.509i | 0.0259083 | + | 0.0448745i | 0.878689 | − | 0.477395i | \(-0.158419\pi\) |
−0.852781 | + | 0.522269i | \(0.825086\pi\) | |||||||
\(648\) | −289.228 | + | 166.986i | −0.0175339 | + | 0.0101232i | ||||
\(649\) | −21172.8 | −1.28060 | ||||||||
\(650\) | −18999.5 | − | 11788.5i | −1.14649 | − | 0.711357i | ||||
\(651\) | −763.303 | −0.0459542 | ||||||||
\(652\) | 18256.9 | − | 10540.6i | 1.09662 | − | 0.633133i | ||||
\(653\) | 3672.88 | + | 6361.61i | 0.220108 | + | 0.381239i | 0.954841 | − | 0.297118i | \(-0.0960256\pi\) |
−0.734732 | + | 0.678357i | \(0.762692\pi\) | |||||||
\(654\) | 2965.64 | − | 5136.64i | 0.177318 | − | 0.307123i | ||||
\(655\) | − | 133.462i | − | 0.00796151i | ||||||
\(656\) | 2671.39 | + | 1542.33i | 0.158994 | + | 0.0917954i | ||||
\(657\) | −3037.50 | − | 1753.70i | −0.180372 | − | 0.104138i | ||||
\(658\) | − | 14273.4i | − | 0.845645i | ||||||
\(659\) | −6270.33 | + | 10860.5i | −0.370648 | + | 0.641982i | −0.989665 | − | 0.143396i | \(-0.954198\pi\) |
0.619017 | + | 0.785378i | \(0.287531\pi\) | |||||||
\(660\) | 1327.92 | + | 2300.02i | 0.0783169 | + | 0.135649i | ||||
\(661\) | 1942.45 | − | 1121.48i | 0.114301 | − | 0.0659915i | −0.441760 | − | 0.897133i | \(-0.645646\pi\) |
0.556060 | + | 0.831142i | \(0.312312\pi\) | |||||||
\(662\) | −35747.3 | −2.09873 | ||||||||
\(663\) | 1916.48 | + | 3576.93i | 0.112262 | + | 0.209527i | ||||
\(664\) | 2832.97 | 0.165573 | ||||||||
\(665\) | −1786.41 | + | 1031.38i | −0.104171 | + | 0.0601433i | ||||
\(666\) | 6077.69 | + | 10526.9i | 0.353612 | + | 0.612474i | ||||
\(667\) | −9525.83 | + | 16499.2i | −0.552986 | + | 0.957800i | ||||
\(668\) | − | 360.658i | − | 0.0208896i | ||||||
\(669\) | 7309.83 | + | 4220.33i | 0.422443 | + | 0.243897i | ||||
\(670\) | 622.687 | + | 359.508i | 0.0359052 | + | 0.0207299i | ||||
\(671\) | − | 22617.0i | − | 1.30122i | ||||||
\(672\) | 2604.01 | − | 4510.29i | 0.149482 | − | 0.258911i | ||||
\(673\) | −2388.23 | − | 4136.53i | −0.136790 | − | 0.236927i | 0.789490 | − | 0.613763i | \(-0.210345\pi\) |
−0.926280 | + | 0.376837i | \(0.877012\pi\) | |||||||
\(674\) | −30446.0 | + | 17578.0i | −1.73997 | + | 1.00457i | ||||
\(675\) | −3123.82 | −0.178127 | ||||||||
\(676\) | 8780.58 | + | 17716.5i | 0.499578 | + | 1.00799i | ||||
\(677\) | −7933.57 | −0.450387 | −0.225193 | − | 0.974314i | \(-0.572301\pi\) | ||||
−0.225193 | + | 0.974314i | \(0.572301\pi\) | |||||||
\(678\) | 16573.9 | − | 9568.93i | 0.938814 | − | 0.542024i | ||||
\(679\) | 5862.82 | + | 10154.7i | 0.331361 | + | 0.573935i | ||||
\(680\) | 181.459 | − | 314.295i | 0.0102333 | − | 0.0177245i | ||||
\(681\) | 13555.1i | 0.762750i | ||||||||
\(682\) | 4384.02 | + | 2531.12i | 0.246148 | + | 0.142114i | ||||
\(683\) | 20415.5 | + | 11786.9i | 1.14374 | + | 0.660340i | 0.947355 | − | 0.320186i | \(-0.103745\pi\) |
0.196388 | + | 0.980526i | \(0.437079\pi\) | |||||||
\(684\) | 8196.70i | 0.458200i | ||||||||
\(685\) | −314.452 | + | 544.647i | −0.0175396 | + | 0.0303794i | ||||
\(686\) | 8836.21 | + | 15304.8i | 0.491790 | + | 0.851806i | ||||
\(687\) | −3391.19 | + | 1957.90i | −0.188329 | + | 0.108732i | ||||
\(688\) | 7033.32 | 0.389743 | ||||||||
\(689\) | 15396.9 | + | 28736.9i | 0.851343 | + | 1.58895i | ||||
\(690\) | −4489.15 | −0.247680 | ||||||||
\(691\) | −10863.2 | + | 6271.89i | −0.598056 | + | 0.345288i | −0.768276 | − | 0.640118i | \(-0.778885\pi\) |
0.170221 | + | 0.985406i | \(0.445552\pi\) | |||||||
\(692\) | −8592.93 | − | 14883.4i | −0.472044 | − | 0.817604i | ||||
\(693\) | −969.904 | + | 1679.92i | −0.0531654 | + | 0.0920852i | ||||
\(694\) | − | 51874.8i | − | 2.83738i | ||||||
\(695\) | −264.143 | − | 152.503i | −0.0144166 | − | 0.00832340i | ||||
\(696\) | −1715.14 | − | 990.234i | −0.0934082 | − | 0.0539292i | ||||
\(697\) | 1618.52i | 0.0879568i | ||||||||
\(698\) | 18473.9 | − | 31997.8i | 1.00179 | − | 1.73515i | ||||
\(699\) | 5040.82 | + | 8730.96i | 0.272763 | + | 0.472440i | ||||
\(700\) | −6026.75 | + | 3479.54i | −0.325414 | + | 0.187878i | ||||
\(701\) | 581.786 | 0.0313463 | 0.0156731 | − | 0.999877i | \(-0.495011\pi\) | ||||
0.0156731 | + | 0.999877i | \(0.495011\pi\) | |||||||
\(702\) | 4433.86 | + | 2751.05i | 0.238384 | + | 0.147908i | ||||
\(703\) | 33147.9 | 1.77837 | ||||||||
\(704\) | −17623.4 | + | 10174.9i | −0.943475 | + | 0.544715i | ||||
\(705\) | 2369.82 | + | 4104.64i | 0.126599 | + | 0.219276i | ||||
\(706\) | −11045.8 | + | 19131.9i | −0.588830 | + | 1.01988i | ||||
\(707\) | 4282.89i | 0.227828i | ||||||||
\(708\) | 15351.3 | + | 8863.06i | 0.814882 | + | 0.470472i | ||||
\(709\) | −17963.1 | − | 10371.0i | −0.951507 | − | 0.549353i | −0.0579583 | − | 0.998319i | \(-0.518459\pi\) |
−0.893549 | + | 0.448966i | \(0.851792\pi\) | |||||||
\(710\) | 3888.74i | 0.205552i | ||||||||
\(711\) | −4058.19 | + | 7028.99i | −0.214056 | + | 0.370756i | ||||
\(712\) | 2206.97 | + | 3822.58i | 0.116165 | + | 0.201204i | ||||
\(713\) | −3923.10 | + | 2265.00i | −0.206061 | + | 0.118969i | ||||
\(714\) | 2385.66 | 0.125043 | ||||||||
\(715\) | 2430.79 | − | 3917.70i | 0.127142 | − | 0.204914i | ||||
\(716\) | −4589.63 | −0.239556 | ||||||||
\(717\) | 12307.5 | − | 7105.75i | 0.641050 | − | 0.370110i | ||||
\(718\) | 5577.32 | + | 9660.21i | 0.289894 | + | 0.502111i | ||||
\(719\) | 12675.1 | − | 21953.9i | 0.657443 | − | 1.13872i | −0.323832 | − | 0.946114i | \(-0.604971\pi\) |
0.981275 | − | 0.192610i | \(-0.0616953\pi\) | |||||||
\(720\) | 1509.78i | 0.0781474i | ||||||||
\(721\) | −4011.87 | − | 2316.25i | −0.207226 | − | 0.119642i | ||||
\(722\) | 12073.3 | + | 6970.50i | 0.622328 | + | 0.359301i | ||||
\(723\) | 14355.8i | 0.738449i | ||||||||
\(724\) | 9615.97 | − | 16655.3i | 0.493611 | − | 0.854960i | ||||
\(725\) | −9262.22 | − | 16042.6i | −0.474469 | − | 0.821805i | ||||
\(726\) | −3116.59 | + | 1799.36i | −0.159322 | + | 0.0919844i | ||||
\(727\) | −33428.2 | −1.70534 | −0.852672 | − | 0.522447i | \(-0.825019\pi\) | ||||
−0.852672 | + | 0.522447i | \(0.825019\pi\) | |||||||
\(728\) | 1290.95 | + | 40.9778i | 0.0657220 | + | 0.00208618i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 4244.30 | − | 2450.45i | 0.215190 | − | 0.124240i | ||||
\(731\) | 1845.20 | + | 3195.97i | 0.0933612 | + | 0.161706i | ||||
\(732\) | −9467.61 | + | 16398.4i | −0.478050 | + | 0.828007i | ||||
\(733\) | − | 3842.67i | − | 0.193632i | −0.995302 | − | 0.0968160i | \(-0.969134\pi\) | ||
0.995302 | − | 0.0968160i | \(-0.0308658\pi\) | |||||||
\(734\) | −37398.8 | − | 21592.2i | −1.88067 | − | 1.08581i | ||||
\(735\) | −2364.09 | − | 1364.91i | −0.118640 | − | 0.0684970i | ||||
\(736\) | − | 30908.3i | − | 1.54796i | ||||||
\(737\) | 921.946 | − | 1596.86i | 0.0460791 | − | 0.0798114i | ||||
\(738\) | 1040.59 | + | 1802.36i | 0.0519035 | + | 0.0898994i | ||||
\(739\) | −25140.4 | + | 14514.8i | −1.25143 | + | 0.722511i | −0.971393 | − | 0.237479i | \(-0.923679\pi\) |
−0.280034 | + | 0.959990i | \(0.590346\pi\) | |||||||
\(740\) | −8991.91 | −0.446688 | ||||||||
\(741\) | 12542.7 | − | 6720.21i | 0.621816 | − | 0.333162i | ||||
\(742\) | 19166.3 | 0.948269 | ||||||||
\(743\) | −30308.0 | + | 17498.3i | −1.49649 | + | 0.864000i | −0.999992 | − | 0.00403656i | \(-0.998715\pi\) |
−0.496500 | + | 0.868037i | \(0.665382\pi\) | |||||||
\(744\) | −235.453 | − | 407.816i | −0.0116023 | − | 0.0200958i | ||||
\(745\) | −580.199 | + | 1004.93i | −0.0285327 | + | 0.0494200i | ||||
\(746\) | − | 52623.2i | − | 2.58267i | ||||||
\(747\) | −5355.38 | − | 3091.93i | −0.262307 | − | 0.151443i | ||||
\(748\) | −7253.99 | − | 4188.10i | −0.354589 | − | 0.204722i | ||||
\(749\) | − | 2711.23i | − | 0.132265i | ||||||
\(750\) | 4540.41 | − | 7864.22i | 0.221056 | − | 0.382881i | ||||
\(751\) | 5227.06 | + | 9053.52i | 0.253979 | + | 0.439904i | 0.964618 | − | 0.263653i | \(-0.0849274\pi\) |
−0.710639 | + | 0.703557i | \(0.751594\pi\) | |||||||
\(752\) | −24672.3 | + | 14244.5i | −1.19642 | + | 0.690751i | ||||
\(753\) | −9821.58 | −0.475323 | ||||||||
\(754\) | −981.712 | + | 30927.4i | −0.0474162 | + | 1.49378i | ||||
\(755\) | 4628.32 | 0.223102 | ||||||||
\(756\) | 1406.45 | − | 812.014i | 0.0676615 | − | 0.0390644i | ||||
\(757\) | 14065.2 | + | 24361.6i | 0.675308 | + | 1.16967i | 0.976379 | + | 0.216065i | \(0.0693225\pi\) |
−0.301071 | + | 0.953602i | \(0.597344\pi\) | |||||||
\(758\) | −4778.73 | + | 8277.00i | −0.228986 | + | 0.396615i | ||||
\(759\) | 11512.3i | 0.550552i | ||||||||
\(760\) | −1102.09 | − | 636.292i | −0.0526014 | − | 0.0303694i | ||||
\(761\) | 18261.9 | + | 10543.5i | 0.869899 | + | 0.502236i | 0.867315 | − | 0.497761i | \(-0.165844\pi\) |
0.00258400 | + | 0.999997i | \(0.499177\pi\) | |||||||
\(762\) | − | 30863.4i | − | 1.46727i | ||||||
\(763\) | −1602.36 | + | 2775.37i | −0.0760280 | + | 0.131684i | ||||
\(764\) | 18259.8 | + | 31627.0i | 0.864683 | + | 1.49768i | ||||
\(765\) | −686.051 | + | 396.092i | −0.0324238 | + | 0.0187199i | ||||
\(766\) | −8177.54 | −0.385727 | ||||||||
\(767\) | 976.309 | − | 30757.2i | 0.0459615 | − | 1.44795i | ||||
\(768\) | −8667.00 | −0.407218 | ||||||||
\(769\) | 16911.7 | − | 9763.96i | 0.793044 | − | 0.457864i | −0.0479893 | − | 0.998848i | \(-0.515281\pi\) |
0.841033 | + | 0.540984i | \(0.181948\pi\) | |||||||
\(770\) | −1355.25 | − | 2347.36i | −0.0634283 | − | 0.109861i | ||||
\(771\) | 9818.72 | − | 17006.5i | 0.458641 | − | 0.794390i | ||||
\(772\) | 7860.55i | 0.366460i | ||||||||
\(773\) | 25419.6 | + | 14676.0i | 1.18277 | + | 0.682870i | 0.956653 | − | 0.291231i | \(-0.0940648\pi\) |
0.226113 | + | 0.974101i | \(0.427398\pi\) | |||||||
\(774\) | 4109.56 | + | 2372.66i | 0.190846 | + | 0.110185i | ||||
\(775\) | − | 4404.64i | − | 0.204154i | ||||||
\(776\) | −3616.96 | + | 6264.76i | −0.167321 | + | 0.289809i | ||||
\(777\) | −3283.82 | − | 5687.75i | −0.151617 | − | 0.262609i | ||||
\(778\) | 11585.2 | − | 6688.73i | 0.533869 | − | 0.308229i | ||||
\(779\) | 5675.42 | 0.261031 | ||||||||
\(780\) | −3402.41 | + | 1822.97i | −0.156187 | + | 0.0836831i | ||||
\(781\) | 9972.54 | 0.456908 | ||||||||
\(782\) | 12261.4 | − | 7079.13i | 0.560700 | − | 0.323720i | ||||
\(783\) | 2161.50 | + | 3743.84i | 0.0986537 | + | 0.170873i | ||||
\(784\) | 8204.19 | − | 14210.1i | 0.373733 | − | 0.647325i | ||||
\(785\) | − | 4423.06i | − | 0.201103i | ||||||
\(786\) | 468.733 | + | 270.623i | 0.0212712 | + | 0.0122809i | ||||
\(787\) | 3865.18 | + | 2231.56i | 0.175068 | + | 0.101076i | 0.584974 | − | 0.811052i | \(-0.301105\pi\) |
−0.409905 | + | 0.912128i | \(0.634438\pi\) | |||||||
\(788\) | − | 37325.2i | − | 1.68738i | ||||||
\(789\) | 132.302 | − | 229.154i | 0.00596968 | − | 0.0103398i | ||||
\(790\) | −5670.52 | − | 9821.62i | −0.255377 | − | 0.442326i | ||||
\(791\) | −8955.00 | + | 5170.17i | −0.402532 | + | 0.232402i | ||||
\(792\) | −1196.73 | −0.0536919 | ||||||||
\(793\) | 32855.1 | + | 1042.90i | 1.47127 | + | 0.0467018i | ||||
\(794\) | 15501.7 | 0.692866 | ||||||||
\(795\) | −5511.70 | + | 3182.18i | −0.245887 | + | 0.141963i | ||||
\(796\) | 10818.3 | + | 18737.8i | 0.481713 | + | 0.834352i | ||||
\(797\) | −17392.7 | + | 30125.1i | −0.773002 | + | 1.33888i | 0.162909 | + | 0.986641i | \(0.447912\pi\) |
−0.935911 | + | 0.352237i | \(0.885421\pi\) | |||||||
\(798\) | − | 8365.40i | − | 0.371093i | ||||||
\(799\) | −12945.6 | − | 7474.12i | −0.573193 | − | 0.330933i | ||||
\(800\) | 26026.6 | + | 15026.5i | 1.15023 | + | 0.664083i | ||||
\(801\) | − | 9634.84i | − | 0.425007i | ||||||
\(802\) | 4118.05 | − | 7132.66i | 0.181313 | − | 0.314044i | ||||
\(803\) | −6284.09 | − | 10884.4i | −0.276165 | − | 0.478332i | ||||
\(804\) | −1336.91 | + | 771.862i | −0.0586430 | + | 0.0338576i | ||||
\(805\) | 2425.53 | 0.106197 | ||||||||
\(806\) | −3879.03 | + | 6251.82i | −0.169520 | + | 0.273215i | ||||
\(807\) | 13582.8 | 0.592487 | ||||||||
\(808\) | −2288.26 | + | 1321.13i | −0.0996294 | + | 0.0575211i | ||||
\(809\) | 5309.98 | + | 9197.15i | 0.230765 | + | 0.399697i | 0.958033 | − | 0.286656i | \(-0.0925438\pi\) |
−0.727268 | + | 0.686353i | \(0.759210\pi\) | |||||||
\(810\) | −509.316 | + | 882.162i | −0.0220933 | + | 0.0382667i | ||||
\(811\) | 5497.87i | 0.238047i | 0.992891 | + | 0.119024i | \(0.0379764\pi\) | ||||
−0.992891 | + | 0.119024i | \(0.962024\pi\) | |||||||
\(812\) | 8340.32 | + | 4815.29i | 0.360453 | + | 0.208108i | ||||
\(813\) | −21620.7 | − | 12482.7i | −0.932684 | − | 0.538485i | ||||
\(814\) | 43556.7i | 1.87551i | ||||||||
\(815\) | 3572.17 | − | 6187.18i | 0.153531 | − | 0.265923i | ||||
\(816\) | −2380.83 | − | 4123.72i | −0.102139 | − | 0.176911i | ||||
\(817\) | 11206.8 | − | 6470.26i | 0.479898 | − | 0.277070i | ||||
\(818\) | 21420.5 | 0.915587 | ||||||||
\(819\) | −2395.65 | − | 1486.42i | −0.102211 | − | 0.0634182i | ||||
\(820\) | −1539.55 | −0.0655653 | ||||||||
\(821\) | 18451.0 | − | 10652.7i | 0.784340 | − | 0.452839i | −0.0536261 | − | 0.998561i | \(-0.517078\pi\) |
0.837966 | + | 0.545722i | \(0.183745\pi\) | |||||||
\(822\) | −1275.24 | − | 2208.78i | −0.0541108 | − | 0.0937227i | ||||
\(823\) | 8671.28 | − | 15019.1i | 0.367268 | − | 0.636127i | −0.621869 | − | 0.783121i | \(-0.713626\pi\) |
0.989137 | + | 0.146994i | \(0.0469597\pi\) | |||||||
\(824\) | − | 2857.94i | − | 0.120827i | ||||||
\(825\) | −9694.02 | − | 5596.84i | −0.409094 | − | 0.236190i | ||||
\(826\) | −15667.2 | − | 9045.48i | −0.659967 | − | 0.381032i | ||||
\(827\) | − | 5129.96i | − | 0.215703i | −0.994167 | − | 0.107851i | \(-0.965603\pi\) | ||
0.994167 | − | 0.107851i | \(-0.0343971\pi\) | |||||||
\(828\) | 4819.09 | − | 8346.92i | 0.202265 | − | 0.350333i | ||||
\(829\) | −4235.90 | − | 7336.80i | −0.177466 | − | 0.307380i | 0.763546 | − | 0.645753i | \(-0.223457\pi\) |
−0.941012 | + | 0.338374i | \(0.890123\pi\) | |||||||
\(830\) | 7483.08 | − | 4320.36i | 0.312942 | − | 0.180677i | ||||
\(831\) | −8643.93 | −0.360836 | ||||||||
\(832\) | −13968.1 | − | 26070.1i | −0.582039 | − | 1.08632i | ||||
\(833\) | 8609.50 | 0.358105 | ||||||||
\(834\) | 1071.21 | − | 618.466i | 0.0444762 | − | 0.0256783i | ||||
\(835\) | −61.1126 | − | 105.850i | −0.00253280 | − | 0.00438694i | ||||
\(836\) | −14685.7 | + | 25436.4i | −0.607556 | + | 1.05232i | ||||
\(837\) | 1027.90i | 0.0424486i | ||||||||
\(838\) | 24359.8 | + | 14064.1i | 1.00417 | + | 0.579758i | ||||
\(839\) | −16588.8 | − | 9577.52i | −0.682607 | − | 0.394103i | 0.118230 | − | 0.992986i | \(-0.462278\pi\) |
−0.800837 | + | 0.598883i | \(0.795611\pi\) | |||||||
\(840\) | 252.140i | 0.0103567i | ||||||||
\(841\) | −623.334 | + | 1079.65i | −0.0255580 | + | 0.0442678i | ||||
\(842\) | 15539.4 | + | 26915.0i | 0.636012 | + | 1.10160i | ||||
\(843\) | −7321.36 | + | 4226.99i | −0.299123 | + | 0.172699i | ||||
\(844\) | −34819.7 | −1.42007 | ||||||||
\(845\) | 5579.04 | + | 3711.79i | 0.227130 | + | 0.151112i | ||||
\(846\) | −19221.3 | −0.781136 | ||||||||
\(847\) | 1683.92 | − | 972.211i | 0.0683119 | − | 0.0394399i | ||||
\(848\) | −19127.5 | − | 33129.8i | −0.774577 | − | 1.34161i | ||||
\(849\) | −396.902 | + | 687.455i | −0.0160443 | + | 0.0277896i | ||||
\(850\) | 13766.4i | 0.555512i | ||||||||
\(851\) | −33755.3 | − | 19488.7i | −1.35972 | − | 0.785032i | ||||
\(852\) | −7230.54 | − | 4174.56i | −0.290744 | − | 0.167861i | ||||
\(853\) | 18075.1i | 0.725532i | 0.931880 | + | 0.362766i | \(0.118168\pi\) | ||||
−0.931880 | + | 0.362766i | \(0.881832\pi\) | |||||||
\(854\) | 9662.47 | − | 16735.9i | 0.387170 | − | 0.670598i | ||||
\(855\) | 1388.91 | + | 2405.67i | 0.0555553 | + | 0.0962246i | ||||
\(856\) | 1448.55 | − | 836.322i | 0.0578394 | − | 0.0333936i | ||||
\(857\) | 21054.6 | 0.839219 | 0.419609 | − | 0.907705i | \(-0.362167\pi\) | ||||
0.419609 | + | 0.907705i | \(0.362167\pi\) | |||||||
\(858\) | 8830.44 | + | 16481.2i | 0.351359 | + | 0.655780i | ||||
\(859\) | 920.322 | 0.0365553 | 0.0182776 | − | 0.999833i | \(-0.494182\pi\) | ||||
0.0182776 | + | 0.999833i | \(0.494182\pi\) | |||||||
\(860\) | −3040.04 | + | 1755.17i | −0.120540 | + | 0.0695938i | ||||
\(861\) | −562.241 | − | 973.830i | −0.0222545 | − | 0.0385459i | ||||
\(862\) | −27633.5 | + | 47862.6i | −1.09188 | + | 1.89119i | ||||
\(863\) | − | 19427.5i | − | 0.766304i | −0.923685 | − | 0.383152i | \(-0.874839\pi\) | ||
0.923685 | − | 0.383152i | \(-0.125161\pi\) | |||||||
\(864\) | −6073.78 | − | 3506.70i | −0.239160 | − | 0.138079i | ||||
\(865\) | −5043.91 | − | 2912.10i | −0.198264 | − | 0.114468i | ||||
\(866\) | 73044.7i | 2.86623i | ||||||||
\(867\) | −6120.27 | + | 10600.6i | −0.239741 | + | 0.415244i | ||||
\(868\) | 1144.95 | + | 1983.12i | 0.0447722 | + | 0.0775477i | ||||
\(869\) | −25187.2 | + | 14541.8i | −0.983218 | + | 0.567661i | ||||
\(870\) | −6040.55 | −0.235395 | ||||||||
\(871\) | 2277.19 | + | 1412.92i | 0.0885876 | + | 0.0549654i | ||||
\(872\) | −1977.09 | −0.0767808 | ||||||||
\(873\) | 13674.8 | − | 7895.17i | 0.530153 | − | 0.306084i | ||||
\(874\) | −24823.3 | − | 42995.2i | −0.960709 | − | 1.66400i | ||||
\(875\) | −2453.22 | + | 4249.10i | −0.0947816 | + | 0.164167i | ||||
\(876\) | 10522.2i | 0.405836i | ||||||||
\(877\) | −12879.7 | − | 7436.09i | −0.495914 | − | 0.286316i | 0.231111 | − | 0.972927i | \(-0.425764\pi\) |
−0.727024 | + | 0.686612i | \(0.759097\pi\) | |||||||
\(878\) | 25578.7 | + | 14767.9i | 0.983188 | + | 0.567644i | ||||
\(879\) | 12877.6i | 0.494141i | ||||||||
\(880\) | −2705.02 | + | 4685.23i | −0.103621 | + | 0.179476i | ||||
\(881\) | −6470.30 | − | 11206.9i | −0.247435 | − | 0.428570i | 0.715379 | − | 0.698737i | \(-0.246254\pi\) |
−0.962813 | + | 0.270167i | \(0.912921\pi\) | |||||||
\(882\) | 9587.40 | − | 5535.29i | 0.366014 | − | 0.211318i | ||||
\(883\) | 25585.5 | 0.975108 | 0.487554 | − | 0.873093i | \(-0.337889\pi\) | ||||
0.487554 | + | 0.873093i | \(0.337889\pi\) | |||||||
\(884\) | 6418.41 | − | 10344.5i | 0.244202 | − | 0.393580i | ||||
\(885\) | 6007.30 | 0.228173 | ||||||||
\(886\) | −36311.4 | + | 20964.4i | −1.37687 | + | 0.794935i | ||||
\(887\) | −1858.23 | − | 3218.55i | −0.0703418 | − | 0.121836i | 0.828709 | − | 0.559679i | \(-0.189076\pi\) |
−0.899051 | + | 0.437844i | \(0.855742\pi\) | |||||||
\(888\) | 2025.90 | − | 3508.95i | 0.0765592 | − | 0.132604i | ||||
\(889\) | 16675.7i | 0.629118i | ||||||||
\(890\) | 11659.1 | + | 6731.39i | 0.439117 | + | 0.253524i | ||||
\(891\) | 2262.27 | + | 1306.12i | 0.0850606 | + | 0.0491097i | ||||
\(892\) | − | 25322.0i | − | 0.950496i | ||||||
\(893\) | −26208.3 | + | 45394.2i | −0.982115 | + | 1.70107i | ||||
\(894\) | −2352.96 | − | 4075.44i | −0.0880254 | − | 0.152464i | ||||
\(895\) | −1347.02 | + | 777.702i | −0.0503082 | + | 0.0290455i | ||||
\(896\) | −3499.58 | −0.130483 | ||||||||
\(897\) | −16723.5 | − | 530.846i | −0.622500 | − | 0.0197597i | ||||
\(898\) | −70680.3 | −2.62654 | ||||||||
\(899\) | −5278.87 | + | 3047.76i | −0.195840 | + | 0.113068i | ||||
\(900\) | 4685.73 | + | 8115.93i | 0.173546 | + | 0.300590i | ||||
\(901\) | 10036.2 | − | 17383.3i | 0.371093 | − | 0.642753i | ||||
\(902\) | 7457.57i | 0.275288i | ||||||||
\(903\) | −2220.43 | − | 1281.97i | −0.0818286 | − | 0.0472438i | ||||
\(904\) | −5524.62 | − | 3189.64i | −0.203259 | − | 0.117352i | ||||
\(905\) | − | 6517.61i | − | 0.239395i | ||||||
\(906\) | −9384.92 | + | 16255.2i | −0.344143 | + | 0.596072i | ||||
\(907\) | −6480.21 | − | 11224.0i | −0.237235 | − | 0.410902i | 0.722685 | − | 0.691177i | \(-0.242908\pi\) |
−0.959920 | + | 0.280275i | \(0.909574\pi\) | |||||||
\(908\) | 35217.2 | − | 20332.7i | 1.28714 | − | 0.743131i | ||||
\(909\) | 5767.56 | 0.210449 | ||||||||
\(910\) | 3472.43 | − | 1860.49i | 0.126495 | − | 0.0677743i | ||||
\(911\) | −36607.1 | −1.33134 | −0.665668 | − | 0.746248i | \(-0.731853\pi\) | ||||
−0.665668 | + | 0.746248i | \(0.731853\pi\) | |||||||
\(912\) | −14460.0 | + | 8348.49i | −0.525021 | + | 0.303121i | ||||
\(913\) | −11079.4 | − | 19190.1i | −0.401615 | − | 0.695618i | ||||
\(914\) | 29049.6 | − | 50315.5i | 1.05129 | − | 1.82088i | ||||
\(915\) | 6417.06i | 0.231849i | ||||||||
\(916\) | 10173.6 | + | 5873.71i | 0.366969 | + | 0.211870i | ||||
\(917\) | −253.260 | − | 146.220i | −0.00912038 | − | 0.00526565i | ||||
\(918\) | − | 3212.65i | − | 0.115505i | ||||||
\(919\) | −10178.1 | + | 17629.0i | −0.365338 | + | 0.632784i | −0.988830 | − | 0.149045i | \(-0.952380\pi\) |
0.623492 | + | 0.781830i | \(0.285713\pi\) | |||||||
\(920\) | 748.192 | + | 1295.91i | 0.0268121 | + | 0.0464400i | ||||
\(921\) | 18254.8 | − | 10539.4i | 0.653110 | − | 0.377073i | ||||
\(922\) | 12048.6 | 0.430370 | ||||||||
\(923\) | −459.847 | + | 14486.8i | −0.0163988 | + | 0.516619i | ||||
\(924\) | 5819.43 | 0.207192 | ||||||||
\(925\) | 32821.2 | − | 18949.3i | 1.16665 | − | 0.673568i | ||||
\(926\) | 4272.80 | + | 7400.71i | 0.151634 | + | 0.262638i | ||||
\(927\) | −3119.19 | + | 5402.59i | −0.110515 | + | 0.191418i | ||||
\(928\) | − | 41589.8i | − | 1.47118i | ||||||
\(929\) | 39031.5 | + | 22534.8i | 1.37845 | + | 0.795849i | 0.991973 | − | 0.126449i | \(-0.0403580\pi\) |
0.386478 | + | 0.922298i | \(0.373691\pi\) | |||||||
\(930\) | −1243.86 | − | 718.145i | −0.0438580 | − | 0.0253214i | ||||
\(931\) | − | 30189.6i | − | 1.06275i | ||||||
\(932\) | 15122.5 | − | 26192.9i | 0.531495 | − | 0.920576i | ||||
\(933\) | 1699.81 | + | 2944.16i | 0.0596456 | + | 0.103309i | ||||
\(934\) | 9513.07 | − | 5492.37i | 0.333273 | − | 0.192415i | ||||
\(935\) | −2838.65 | −0.0992876 | ||||||||
\(936\) | 55.1828 | − | 1738.45i | 0.00192704 | − | 0.0607085i | ||||
\(937\) | −6771.10 | −0.236075 | −0.118037 | − | 0.993009i | \(-0.537660\pi\) | ||||
−0.118037 | + | 0.993009i | \(0.537660\pi\) | |||||||
\(938\) | 1364.42 | − | 787.749i | 0.0474946 | − | 0.0274210i | ||||
\(939\) | −7928.92 | − | 13733.3i | −0.275560 | − | 0.477283i | ||||
\(940\) | 7109.45 | − | 12313.9i | 0.246686 | − | 0.427273i | ||||
\(941\) | 36690.7i | 1.27108i | 0.772070 | + | 0.635538i | \(0.219222\pi\) | ||||
−0.772070 | + | 0.635538i | \(0.780778\pi\) | |||||||
\(942\) | 15534.3 | + | 8968.72i | 0.537297 | + | 0.310209i | ||||
\(943\) | −5779.43 | − | 3336.76i | −0.199580 | − | 0.115228i | ||||
\(944\) | 36108.8i | 1.24496i | ||||||||
\(945\) | 275.188 | − | 476.639i | 0.00947287 | − | 0.0164075i | ||||
\(946\) | 8502.01 | + | 14725.9i | 0.292203 | + | 0.506111i | ||||
\(947\) | 44047.1 | − | 25430.6i | 1.51145 | − | 0.872634i | 0.511536 | − | 0.859262i | \(-0.329077\pi\) |
0.999911 | − | 0.0133718i | \(-0.00425649\pi\) | |||||||
\(948\) | 24349.1 | 0.834202 | ||||||||
\(949\) | 16101.2 | − | 8626.82i | 0.550754 | − | 0.295088i | ||||
\(950\) | 48272.6 | 1.64860 | ||||||||
\(951\) | 12424.4 | − | 7173.24i | 0.423648 | − | 0.244593i | ||||
\(952\) | −397.609 | − | 688.679i | −0.0135363 | − | 0.0234456i | ||||
\(953\) | 5927.79 | − | 10267.2i | 0.201490 | − | 0.348991i | −0.747519 | − | 0.664241i | \(-0.768755\pi\) |
0.949009 | + | 0.315250i | \(0.102088\pi\) | |||||||
\(954\) | − | 25810.3i | − | 0.875931i | ||||||
\(955\) | 10718.2 | + | 6188.18i | 0.363177 | + | 0.209680i | ||||
\(956\) | −36922.6 | − | 21317.3i | −1.24912 | − | 0.721181i | ||||
\(957\) | 15490.8i | 0.523245i | ||||||||
\(958\) | 10762.7 | − | 18641.6i | 0.362973 | − | 0.628688i | ||||
\(959\) | 689.022 | + | 1193.42i | 0.0232009 | + | 0.0401852i | ||||
\(960\) | 5000.22 | − | 2886.88i | 0.168106 | − | 0.0970559i | ||||
\(961\) | 28341.6 | 0.951349 | ||||||||
\(962\) | −63273.5 | − | 2008.46i | −2.12060 | − | 0.0673132i | ||||
\(963\) | −3651.08 | −0.122175 | ||||||||
\(964\) | 37297.5 | − | 21533.7i | 1.24613 | − | 0.719455i | ||||
\(965\) | 1331.95 | + | 2307.01i | 0.0444322 | + | 0.0769588i | ||||
\(966\) | −4918.28 | + | 8518.71i | −0.163813 | + | 0.283732i | ||||
\(967\) | 40661.7i | 1.35221i | 0.736803 | + | 0.676107i | \(0.236334\pi\) | ||||
−0.736803 | + | 0.676107i | \(0.763666\pi\) | |||||||
\(968\) | 1038.86 | + | 599.788i | 0.0344942 | + | 0.0199152i | ||||
\(969\) | −7587.19 | − | 4380.46i | −0.251533 | − | 0.145223i | ||||
\(970\) | 22063.9i | 0.730339i | ||||||||
\(971\) | −28659.1 | + | 49639.1i | −0.947184 | + | 1.64057i | −0.195866 | + | 0.980631i | \(0.562752\pi\) |
−0.751318 | + | 0.659940i | \(0.770582\pi\) | |||||||
\(972\) | −1093.50 | − | 1894.00i | −0.0360844 | − | 0.0625000i | ||||
\(973\) | −578.786 | + | 334.162i | −0.0190699 | + | 0.0110100i | ||||
\(974\) | 50403.3 | 1.65814 | ||||||||
\(975\) | 8577.37 | − | 13824.1i | 0.281739 | − | 0.454079i | ||||
\(976\) | −38571.7 | −1.26501 | ||||||||
\(977\) | −2621.23 | + | 1513.37i | −0.0858347 | + | 0.0495567i | −0.542303 | − | 0.840183i | \(-0.682448\pi\) |
0.456468 | + | 0.889740i | \(0.349114\pi\) | |||||||
\(978\) | 14486.7 | + | 25091.7i | 0.473654 | + | 0.820393i | ||||
\(979\) | 17262.4 | − | 29899.4i | 0.563543 | − | 0.976085i | ||||
\(980\) | 8189.43i | 0.266941i | ||||||||
\(981\) | 3737.46 | + | 2157.82i | 0.121639 | + | 0.0702283i | ||||
\(982\) | 70176.0 | + | 40516.1i | 2.28045 | + | 1.31662i | ||||
\(983\) | − | 33942.5i | − | 1.10132i | −0.834730 | − | 0.550659i | \(-0.814376\pi\) | ||
0.834730 | − | 0.550659i | \(-0.185624\pi\) | |||||||
\(984\) | 346.864 | − | 600.787i | 0.0112374 | − | 0.0194638i | ||||
\(985\) | −6324.67 | − | 10954.7i | −0.204590 | − | 0.354360i | ||||
\(986\) | 16498.8 | − | 9525.58i | 0.532889 | − | 0.307664i | ||||
\(987\) | 10385.4 | 0.334925 | ||||||||
\(988\) | −36273.6 | − | 22506.4i | −1.16803 | − | 0.724722i | ||||
\(989\) | −15216.3 | −0.489231 | ||||||||
\(990\) | −3161.08 | + | 1825.05i | −0.101480 | + | 0.0585897i | ||||
\(991\) | −10818.7 | − | 18738.6i | −0.346790 | − | 0.600658i | 0.638887 | − | 0.769300i | \(-0.279395\pi\) |
−0.985677 | + | 0.168642i | \(0.946062\pi\) | |||||||
\(992\) | 4944.51 | − | 8564.14i | 0.158254 | − | 0.274105i | ||||
\(993\) | − | 26009.9i | − | 0.831219i | ||||||
\(994\) | 7379.36 | + | 4260.48i | 0.235472 | + | 0.135950i | ||||
\(995\) | 6350.16 | + | 3666.26i | 0.202325 | + | 0.116812i | ||||
\(996\) | 18551.6i | 0.590190i | ||||||||
\(997\) | −9812.31 | + | 16995.4i | −0.311694 | + | 0.539870i | −0.978729 | − | 0.205156i | \(-0.934230\pi\) |
0.667035 | + | 0.745026i | \(0.267563\pi\) | |||||||
\(998\) | −24148.1 | − | 41825.8i | −0.765928 | − | 1.32663i | ||||
\(999\) | −7659.42 | + | 4422.17i | −0.242576 | + | 0.140051i |
(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 | 39.4.j.b.10.2 | yes | 4 | |
3.2 | odd | 2 | 117.4.q.d.10.1 | 4 | |||
4.3 | odd | 2 | 624.4.bv.c.49.1 | 4 | |||
13.2 | odd | 12 | 507.4.a.k.1.4 | 4 | |||
13.3 | even | 3 | 507.4.b.e.337.4 | 4 | |||
13.4 | even | 6 | inner | 39.4.j.b.4.2 | ✓ | 4 | |
13.10 | even | 6 | 507.4.b.e.337.1 | 4 | |||
13.11 | odd | 12 | 507.4.a.k.1.1 | 4 | |||
39.2 | even | 12 | 1521.4.a.z.1.1 | 4 | |||
39.11 | even | 12 | 1521.4.a.z.1.4 | 4 | |||
39.17 | odd | 6 | 117.4.q.d.82.1 | 4 | |||
52.43 | odd | 6 | 624.4.bv.c.433.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.b.4.2 | ✓ | 4 | 13.4 | even | 6 | inner | |
39.4.j.b.10.2 | yes | 4 | 1.1 | even | 1 | trivial | |
117.4.q.d.10.1 | 4 | 3.2 | odd | 2 | |||
117.4.q.d.82.1 | 4 | 39.17 | odd | 6 | |||
507.4.a.k.1.1 | 4 | 13.11 | odd | 12 | |||
507.4.a.k.1.4 | 4 | 13.2 | odd | 12 | |||
507.4.b.e.337.1 | 4 | 13.10 | even | 6 | |||
507.4.b.e.337.4 | 4 | 13.3 | even | 3 | |||
624.4.bv.c.49.1 | 4 | 4.3 | odd | 2 | |||
624.4.bv.c.433.2 | 4 | 52.43 | odd | 6 | |||
1521.4.a.z.1.1 | 4 | 39.2 | even | 12 | |||
1521.4.a.z.1.4 | 4 | 39.11 | even | 12 |