Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,4,Mod(16,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.16");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.g (of order \(5\), degree \(4\), 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: | \(4.42514325043\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 16.7 | ||
Character | \(\chi\) | \(=\) | 75.16 |
Dual form | 75.4.g.b.61.7 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.87763 | + | 2.81726i | 1.37095 | + | 0.996053i | 0.997662 | + | 0.0683371i | \(0.0217693\pi\) |
0.373287 | + | 0.927716i | \(0.378231\pi\) | |||||||
\(3\) | 0.927051 | + | 2.85317i | 0.178411 | + | 0.549093i | ||||
\(4\) | 4.62691 | + | 14.2402i | 0.578364 | + | 1.78002i | ||||
\(5\) | 7.51887 | − | 8.27445i | 0.672509 | − | 0.740089i | ||||
\(6\) | −4.44337 | + | 13.6753i | −0.302333 | + | 0.930485i | ||||
\(7\) | 0.140520 | 0.00758737 | 0.00379368 | − | 0.999993i | \(-0.498792\pi\) | ||||
0.00379368 | + | 0.999993i | \(0.498792\pi\) | |||||||
\(8\) | −10.3279 | + | 31.7859i | −0.456431 | + | 1.40475i | ||||
\(9\) | −7.28115 | + | 5.29007i | −0.269672 | + | 0.195928i | ||||
\(10\) | 52.4667 | − | 10.9026i | 1.65914 | − | 0.344771i | ||||
\(11\) | −38.3073 | − | 27.8319i | −1.05001 | − | 0.762875i | −0.0777938 | − | 0.996969i | \(-0.524788\pi\) |
−0.972214 | + | 0.234094i | \(0.924788\pi\) | |||||||
\(12\) | −36.3402 | + | 26.4027i | −0.874210 | + | 0.635150i | ||||
\(13\) | −27.7836 | + | 20.1859i | −0.592752 | + | 0.430660i | −0.843299 | − | 0.537445i | \(-0.819390\pi\) |
0.250547 | + | 0.968104i | \(0.419390\pi\) | |||||||
\(14\) | 0.544885 | + | 0.395882i | 0.0104019 | + | 0.00755742i | ||||
\(15\) | 30.5788 | + | 13.7818i | 0.526361 | + | 0.237229i | ||||
\(16\) | −32.6895 | + | 23.7503i | −0.510774 | + | 0.371099i | ||||
\(17\) | 5.10385 | − | 15.7080i | 0.0728156 | − | 0.224103i | −0.908025 | − | 0.418916i | \(-0.862410\pi\) |
0.980840 | + | 0.194813i | \(0.0624100\pi\) | |||||||
\(18\) | −43.1371 | −0.564862 | ||||||||
\(19\) | 28.1212 | − | 86.5481i | 0.339549 | − | 1.04503i | −0.624888 | − | 0.780714i | \(-0.714855\pi\) |
0.964437 | − | 0.264311i | \(-0.0851446\pi\) | |||||||
\(20\) | 152.619 | + | 68.7848i | 1.70633 | + | 0.769038i | ||||
\(21\) | 0.130269 | + | 0.400927i | 0.00135367 | + | 0.00416617i | ||||
\(22\) | −70.1318 | − | 215.843i | −0.679643 | − | 2.09173i | ||||
\(23\) | 130.722 | + | 94.9752i | 1.18511 | + | 0.861031i | 0.992739 | − | 0.120292i | \(-0.0383831\pi\) |
0.192368 | + | 0.981323i | \(0.438383\pi\) | |||||||
\(24\) | −100.265 | −0.852771 | ||||||||
\(25\) | −11.9331 | − | 124.429i | −0.0954645 | − | 0.995433i | ||||
\(26\) | −164.604 | −1.24159 | ||||||||
\(27\) | −21.8435 | − | 15.8702i | −0.155695 | − | 0.113119i | ||||
\(28\) | 0.650173 | + | 2.00103i | 0.00438826 | + | 0.0135057i | ||||
\(29\) | −3.81101 | − | 11.7291i | −0.0244030 | − | 0.0751048i | 0.938113 | − | 0.346328i | \(-0.112572\pi\) |
−0.962516 | + | 0.271224i | \(0.912572\pi\) | |||||||
\(30\) | 79.7463 | + | 139.589i | 0.485321 | + | 0.849513i | ||||
\(31\) | −102.914 | + | 316.738i | −0.596257 | + | 1.83509i | −0.0478915 | + | 0.998853i | \(0.515250\pi\) |
−0.548366 | + | 0.836239i | \(0.684750\pi\) | |||||||
\(32\) | 73.7042 | 0.407162 | ||||||||
\(33\) | 43.8963 | − | 135.099i | 0.231556 | − | 0.712657i | ||||
\(34\) | 64.0445 | − | 46.5310i | 0.323045 | − | 0.234706i | ||||
\(35\) | 1.05655 | − | 1.16273i | 0.00510257 | − | 0.00561533i | ||||
\(36\) | −109.021 | − | 79.2081i | −0.504725 | − | 0.366704i | ||||
\(37\) | 227.659 | − | 165.404i | 1.01154 | − | 0.734926i | 0.0470077 | − | 0.998895i | \(-0.485031\pi\) |
0.964531 | + | 0.263968i | \(0.0850315\pi\) | |||||||
\(38\) | 352.872 | − | 256.377i | 1.50641 | − | 1.09447i | ||||
\(39\) | −83.3507 | − | 60.5578i | −0.342226 | − | 0.248641i | ||||
\(40\) | 185.357 | + | 324.451i | 0.732687 | + | 1.28251i | ||||
\(41\) | −101.620 | + | 73.8315i | −0.387084 | + | 0.281233i | −0.764259 | − | 0.644909i | \(-0.776895\pi\) |
0.377176 | + | 0.926142i | \(0.376895\pi\) | |||||||
\(42\) | −0.624382 | + | 1.92165i | −0.00229391 | + | 0.00705993i | ||||
\(43\) | −529.821 | −1.87900 | −0.939500 | − | 0.342549i | \(-0.888710\pi\) | ||||
−0.939500 | + | 0.342549i | \(0.888710\pi\) | |||||||
\(44\) | 219.086 | − | 674.278i | 0.750647 | − | 2.31025i | ||||
\(45\) | −10.9737 | + | 100.023i | −0.0363524 | + | 0.331345i | ||||
\(46\) | 239.322 | + | 736.558i | 0.767090 | + | 2.36086i | ||||
\(47\) | 23.1983 | + | 71.3970i | 0.0719962 | + | 0.221581i | 0.980579 | − | 0.196122i | \(-0.0628350\pi\) |
−0.908583 | + | 0.417704i | \(0.862835\pi\) | |||||||
\(48\) | −98.0686 | − | 71.2510i | −0.294896 | − | 0.214254i | ||||
\(49\) | −342.980 | −0.999942 | ||||||||
\(50\) | 304.278 | − | 516.109i | 0.860627 | − | 1.45978i | ||||
\(51\) | 49.5492 | 0.136045 | ||||||||
\(52\) | −416.003 | − | 302.244i | −1.10941 | − | 0.806033i | ||||
\(53\) | −77.0767 | − | 237.218i | −0.199760 | − | 0.614799i | −0.999888 | − | 0.0149695i | \(-0.995235\pi\) |
0.800127 | − | 0.599830i | \(-0.204765\pi\) | |||||||
\(54\) | −39.9903 | − | 123.078i | −0.100778 | − | 0.310162i | ||||
\(55\) | −518.321 | + | 107.707i | −1.27074 | + | 0.264059i | ||||
\(56\) | −1.45127 | + | 4.46655i | −0.00346311 | + | 0.0106584i | ||||
\(57\) | 273.006 | 0.634395 | ||||||||
\(58\) | 18.2662 | − | 56.2177i | 0.0413530 | − | 0.127272i | ||||
\(59\) | 217.273 | − | 157.858i | 0.479432 | − | 0.348328i | −0.321674 | − | 0.946851i | \(-0.604245\pi\) |
0.801106 | + | 0.598523i | \(0.204245\pi\) | |||||||
\(60\) | −54.7696 | + | 499.214i | −0.117845 | + | 1.07414i | ||||
\(61\) | −299.213 | − | 217.391i | −0.628038 | − | 0.456296i | 0.227682 | − | 0.973736i | \(-0.426885\pi\) |
−0.855720 | + | 0.517439i | \(0.826885\pi\) | |||||||
\(62\) | −1291.40 | + | 938.256i | −2.64529 | + | 1.92191i | ||||
\(63\) | −1.02315 | + | 0.743360i | −0.00204610 | + | 0.00148658i | ||||
\(64\) | 547.314 | + | 397.647i | 1.06897 | + | 0.776654i | ||||
\(65\) | −41.8736 | + | 381.669i | −0.0799042 | + | 0.728312i | ||||
\(66\) | 550.822 | − | 400.196i | 1.02730 | − | 0.746374i | ||||
\(67\) | −54.5434 | + | 167.867i | −0.0994558 | + | 0.306094i | −0.988389 | − | 0.151943i | \(-0.951447\pi\) |
0.888933 | + | 0.458036i | \(0.151447\pi\) | |||||||
\(68\) | 247.300 | 0.441022 | ||||||||
\(69\) | −149.794 | + | 461.019i | −0.261349 | + | 0.804351i | ||||
\(70\) | 7.37262 | − | 1.53204i | 0.0125885 | − | 0.00261590i | ||||
\(71\) | 223.142 | + | 686.762i | 0.372988 | + | 1.14794i | 0.944826 | + | 0.327572i | \(0.106230\pi\) |
−0.571839 | + | 0.820366i | \(0.693770\pi\) | |||||||
\(72\) | −92.9507 | − | 286.073i | −0.152144 | − | 0.468250i | ||||
\(73\) | 1.97619 | + | 1.43579i | 0.00316844 | + | 0.00230201i | 0.589368 | − | 0.807864i | \(-0.299377\pi\) |
−0.586200 | + | 0.810166i | \(0.699377\pi\) | |||||||
\(74\) | 1348.77 | 2.11879 | ||||||||
\(75\) | 343.955 | − | 149.399i | 0.529553 | − | 0.230015i | ||||
\(76\) | 1362.57 | 2.05655 | ||||||||
\(77\) | −5.38294 | − | 3.91094i | −0.00796679 | − | 0.00578822i | ||||
\(78\) | −152.596 | − | 469.642i | −0.221514 | − | 0.681749i | ||||
\(79\) | 187.778 | + | 577.921i | 0.267426 | + | 0.823053i | 0.991125 | + | 0.132937i | \(0.0424407\pi\) |
−0.723698 | + | 0.690116i | \(0.757559\pi\) | |||||||
\(80\) | −49.2675 | + | 449.064i | −0.0688535 | + | 0.627586i | ||||
\(81\) | 25.0304 | − | 77.0356i | 0.0343352 | − | 0.105673i | ||||
\(82\) | −602.049 | −0.810795 | ||||||||
\(83\) | −392.005 | + | 1206.47i | −0.518411 | + | 1.59551i | 0.258577 | + | 0.965991i | \(0.416747\pi\) |
−0.776988 | + | 0.629515i | \(0.783253\pi\) | |||||||
\(84\) | −5.10653 | + | 3.71011i | −0.00663295 | + | 0.00481912i | ||||
\(85\) | −91.6001 | − | 160.338i | −0.116887 | − | 0.204601i | ||||
\(86\) | −2054.45 | − | 1492.65i | −2.57601 | − | 1.87158i | ||||
\(87\) | 29.9321 | − | 21.7469i | 0.0368857 | − | 0.0267990i | ||||
\(88\) | 1280.29 | − | 930.187i | 1.55091 | − | 1.12680i | ||||
\(89\) | 1082.09 | + | 786.182i | 1.28878 | + | 0.936350i | 0.999780 | − | 0.0209802i | \(-0.00667870\pi\) |
0.288996 | + | 0.957330i | \(0.406679\pi\) | |||||||
\(90\) | −324.343 | + | 356.936i | −0.379875 | + | 0.418049i | ||||
\(91\) | −3.90415 | + | 2.83653i | −0.00449743 | + | 0.00326757i | ||||
\(92\) | −747.623 | + | 2300.95i | −0.847229 | + | 2.60750i | ||||
\(93\) | −999.114 | −1.11401 | ||||||||
\(94\) | −111.190 | + | 342.207i | −0.122004 | + | 0.375489i | ||||
\(95\) | −504.698 | − | 883.431i | −0.545063 | − | 0.954086i | ||||
\(96\) | 68.3275 | + | 210.291i | 0.0726422 | + | 0.223570i | ||||
\(97\) | −442.269 | − | 1361.16i | −0.462944 | − | 1.42480i | −0.861550 | − | 0.507673i | \(-0.830506\pi\) |
0.398605 | − | 0.917122i | \(-0.369494\pi\) | |||||||
\(98\) | −1329.95 | − | 966.266i | −1.37087 | − | 0.995996i | ||||
\(99\) | 426.154 | 0.432627 | ||||||||
\(100\) | 1716.68 | − | 745.651i | 1.71668 | − | 0.745651i | ||||
\(101\) | −374.102 | −0.368559 | −0.184280 | − | 0.982874i | \(-0.558995\pi\) | ||||
−0.184280 | + | 0.982874i | \(0.558995\pi\) | |||||||
\(102\) | 192.133 | + | 139.593i | 0.186510 | + | 0.135508i | ||||
\(103\) | −623.556 | − | 1919.11i | −0.596512 | − | 1.83588i | −0.547050 | − | 0.837100i | \(-0.684249\pi\) |
−0.0494621 | − | 0.998776i | \(-0.515751\pi\) | |||||||
\(104\) | −354.683 | − | 1091.60i | −0.334419 | − | 1.02923i | ||||
\(105\) | 4.29693 | + | 1.93662i | 0.00399369 | + | 0.00179995i | ||||
\(106\) | 369.430 | − | 1136.99i | 0.338511 | − | 1.04183i | ||||
\(107\) | 1679.71 | 1.51761 | 0.758804 | − | 0.651319i | \(-0.225784\pi\) | ||||
0.758804 | + | 0.651319i | \(0.225784\pi\) | |||||||
\(108\) | 124.927 | − | 384.484i | 0.111306 | − | 0.342565i | ||||
\(109\) | −16.3651 | + | 11.8899i | −0.0143806 | + | 0.0104481i | −0.594952 | − | 0.803761i | \(-0.702829\pi\) |
0.580572 | + | 0.814209i | \(0.302829\pi\) | |||||||
\(110\) | −2313.30 | − | 1042.60i | −2.00513 | − | 0.903707i | ||||
\(111\) | 682.978 | + | 496.212i | 0.584012 | + | 0.424310i | ||||
\(112\) | −4.59354 | + | 3.33740i | −0.00387543 | + | 0.00281567i | ||||
\(113\) | 519.810 | − | 377.664i | 0.432740 | − | 0.314404i | −0.350004 | − | 0.936748i | \(-0.613820\pi\) |
0.782744 | + | 0.622344i | \(0.213820\pi\) | |||||||
\(114\) | 1058.62 | + | 769.130i | 0.869724 | + | 0.631891i | ||||
\(115\) | 1768.75 | − | 367.548i | 1.43423 | − | 0.298035i | ||||
\(116\) | 149.391 | − | 108.539i | 0.119574 | − | 0.0868757i | ||||
\(117\) | 95.5114 | − | 293.954i | 0.0754704 | − | 0.232274i | ||||
\(118\) | 1287.23 | 1.00423 | ||||||||
\(119\) | 0.717193 | − | 2.20729i | 0.000552479 | − | 0.00170035i | ||||
\(120\) | −753.879 | + | 829.637i | −0.573495 | + | 0.631126i | ||||
\(121\) | 281.534 | + | 866.472i | 0.211521 | + | 0.650993i | ||||
\(122\) | −547.790 | − | 1685.92i | −0.406513 | − | 1.25112i | ||||
\(123\) | −304.861 | − | 221.494i | −0.223483 | − | 0.162370i | ||||
\(124\) | −4986.58 | −3.61135 | ||||||||
\(125\) | −1119.31 | − | 836.827i | −0.800910 | − | 0.598785i | ||||
\(126\) | −6.06163 | −0.00428582 | ||||||||
\(127\) | 959.422 | + | 697.061i | 0.670354 | + | 0.487041i | 0.870144 | − | 0.492798i | \(-0.164026\pi\) |
−0.199790 | + | 0.979839i | \(0.564026\pi\) | |||||||
\(128\) | 819.798 | + | 2523.08i | 0.566099 | + | 1.74227i | ||||
\(129\) | −491.171 | − | 1511.67i | −0.335234 | − | 1.03175i | ||||
\(130\) | −1237.63 | + | 1362.00i | −0.834982 | + | 0.918889i | ||||
\(131\) | −68.9399 | + | 212.175i | −0.0459794 | + | 0.141510i | −0.971411 | − | 0.237406i | \(-0.923703\pi\) |
0.925431 | + | 0.378916i | \(0.123703\pi\) | |||||||
\(132\) | 2126.93 | 1.40247 | ||||||||
\(133\) | 3.95159 | − | 12.1617i | 0.00257629 | − | 0.00792900i | ||||
\(134\) | −684.426 | + | 497.265i | −0.441234 | + | 0.320575i | ||||
\(135\) | −295.555 | + | 61.4166i | −0.188425 | + | 0.0391548i | ||||
\(136\) | 446.582 | + | 324.461i | 0.281574 | + | 0.204575i | ||||
\(137\) | 1277.88 | − | 928.434i | 0.796910 | − | 0.578989i | −0.113096 | − | 0.993584i | \(-0.536077\pi\) |
0.910006 | + | 0.414595i | \(0.136077\pi\) | |||||||
\(138\) | −1879.66 | + | 1365.65i | −1.15947 | + | 0.842407i | ||||
\(139\) | −1266.31 | − | 920.031i | −0.772715 | − | 0.561410i | 0.130069 | − | 0.991505i | \(-0.458480\pi\) |
−0.902784 | + | 0.430095i | \(0.858480\pi\) | |||||||
\(140\) | 21.4460 | + | 9.66565i | 0.0129465 | + | 0.00583497i | ||||
\(141\) | −182.202 | + | 132.377i | −0.108824 | + | 0.0790652i | ||||
\(142\) | −1069.52 | + | 3291.66i | −0.632060 | + | 1.94528i | ||||
\(143\) | 1626.13 | 0.950934 | ||||||||
\(144\) | 112.377 | − | 345.860i | 0.0650328 | − | 0.200150i | ||||
\(145\) | −125.706 | − | 56.6556i | −0.0719955 | − | 0.0324482i | ||||
\(146\) | 3.61796 | + | 11.1349i | 0.00205085 | + | 0.00631187i | ||||
\(147\) | −317.960 | − | 978.581i | −0.178401 | − | 0.549061i | ||||
\(148\) | 3408.74 | + | 2476.59i | 1.89322 | + | 1.37551i | ||||
\(149\) | 192.635 | 0.105915 | 0.0529574 | − | 0.998597i | \(-0.483135\pi\) | ||||
0.0529574 | + | 0.998597i | \(0.483135\pi\) | |||||||
\(150\) | 1754.63 | + | 389.696i | 0.955098 | + | 0.212124i | ||||
\(151\) | 1052.83 | 0.567406 | 0.283703 | − | 0.958912i | \(-0.408437\pi\) | ||||
0.283703 | + | 0.958912i | \(0.408437\pi\) | |||||||
\(152\) | 2460.57 | + | 1787.71i | 1.31302 | + | 0.953964i | ||||
\(153\) | 45.9346 | + | 141.372i | 0.0242719 | + | 0.0747011i | ||||
\(154\) | −9.85492 | − | 30.3303i | −0.00515670 | − | 0.0158707i | ||||
\(155\) | 1847.03 | + | 3233.07i | 0.957143 | + | 1.67540i | ||||
\(156\) | 476.697 | − | 1467.12i | 0.244656 | − | 0.752973i | ||||
\(157\) | 2045.26 | 1.03968 | 0.519838 | − | 0.854265i | \(-0.325992\pi\) | ||||
0.519838 | + | 0.854265i | \(0.325992\pi\) | |||||||
\(158\) | −900.022 | + | 2769.98i | −0.453177 | + | 1.39473i | ||||
\(159\) | 605.369 | − | 439.826i | 0.301942 | − | 0.219374i | ||||
\(160\) | 554.172 | − | 609.862i | 0.273820 | − | 0.301336i | ||||
\(161\) | 18.3691 | + | 13.3459i | 0.00899184 | + | 0.00653296i | ||||
\(162\) | 314.088 | − | 228.198i | 0.152328 | − | 0.110673i | ||||
\(163\) | −686.057 | + | 498.449i | −0.329669 | + | 0.239519i | −0.740290 | − | 0.672287i | \(-0.765312\pi\) |
0.410621 | + | 0.911806i | \(0.365312\pi\) | |||||||
\(164\) | −1521.56 | − | 1105.48i | −0.724475 | − | 0.526362i | ||||
\(165\) | −787.818 | − | 1379.01i | −0.371706 | − | 0.650640i | ||||
\(166\) | −4918.99 | + | 3573.85i | −2.29992 | + | 1.67099i | ||||
\(167\) | 609.520 | − | 1875.91i | 0.282432 | − | 0.869235i | −0.704725 | − | 0.709480i | \(-0.748930\pi\) |
0.987157 | − | 0.159755i | \(-0.0510703\pi\) | |||||||
\(168\) | −14.0892 | −0.00647028 | ||||||||
\(169\) | −314.456 | + | 967.796i | −0.143130 | + | 0.440508i | ||||
\(170\) | 96.5236 | − | 879.794i | 0.0435472 | − | 0.396924i | ||||
\(171\) | 253.091 | + | 778.933i | 0.113183 | + | 0.348342i | ||||
\(172\) | −2451.44 | − | 7544.74i | −1.08675 | − | 3.34466i | ||||
\(173\) | −2190.53 | − | 1591.51i | −0.962676 | − | 0.699425i | −0.00890552 | − | 0.999960i | \(-0.502835\pi\) |
−0.953771 | + | 0.300535i | \(0.902835\pi\) | |||||||
\(174\) | 177.332 | 0.0772617 | ||||||||
\(175\) | −1.67683 | − | 17.4848i | −0.000724324 | − | 0.00755272i | ||||
\(176\) | 1913.26 | 0.819419 | ||||||||
\(177\) | 651.818 | + | 473.574i | 0.276800 | + | 0.201107i | ||||
\(178\) | 1981.05 | + | 6097.05i | 0.834191 | + | 2.56738i | ||||
\(179\) | 967.918 | + | 2978.95i | 0.404165 | + | 1.24389i | 0.921590 | + | 0.388164i | \(0.126891\pi\) |
−0.517425 | + | 0.855729i | \(0.673109\pi\) | |||||||
\(180\) | −1475.12 | + | 306.530i | −0.610826 | + | 0.126930i | ||||
\(181\) | 97.9741 | − | 301.533i | 0.0402340 | − | 0.123828i | −0.928922 | − | 0.370275i | \(-0.879263\pi\) |
0.969156 | + | 0.246448i | \(0.0792634\pi\) | |||||||
\(182\) | −23.1301 | −0.00942042 | ||||||||
\(183\) | 342.868 | − | 1055.24i | 0.138500 | − | 0.426259i | ||||
\(184\) | −4368.95 | + | 3174.23i | −1.75045 | + | 1.27178i | ||||
\(185\) | 343.113 | − | 3127.41i | 0.136358 | − | 1.24287i | ||||
\(186\) | −3874.20 | − | 2814.77i | −1.52726 | − | 1.10962i | ||||
\(187\) | −632.699 | + | 459.682i | −0.247420 | + | 0.179761i | ||||
\(188\) | −909.369 | + | 660.695i | −0.352779 | + | 0.256309i | ||||
\(189\) | −3.06944 | − | 2.23008i | −0.00118132 | − | 0.000858278i | ||||
\(190\) | 531.826 | − | 4847.49i | 0.203067 | − | 1.85091i | ||||
\(191\) | −1358.71 | + | 987.161i | −0.514727 | + | 0.373971i | −0.814614 | − | 0.580004i | \(-0.803051\pi\) |
0.299887 | + | 0.953975i | \(0.403051\pi\) | |||||||
\(192\) | −627.166 | + | 1930.22i | −0.235739 | + | 0.725529i | ||||
\(193\) | −1449.62 | −0.540653 | −0.270326 | − | 0.962769i | \(-0.587132\pi\) | ||||
−0.270326 | + | 0.962769i | \(0.587132\pi\) | |||||||
\(194\) | 2119.80 | − | 6524.08i | 0.784499 | − | 2.41444i | ||||
\(195\) | −1127.79 | + | 234.355i | −0.414166 | + | 0.0860640i | ||||
\(196\) | −1586.94 | − | 4884.09i | −0.578330 | − | 1.77992i | ||||
\(197\) | −327.751 | − | 1008.71i | −0.118535 | − | 0.364812i | 0.874133 | − | 0.485686i | \(-0.161430\pi\) |
−0.992668 | + | 0.120874i | \(0.961430\pi\) | |||||||
\(198\) | 1652.47 | + | 1200.59i | 0.593110 | + | 0.430919i | ||||
\(199\) | −183.077 | −0.0652159 | −0.0326080 | − | 0.999468i | \(-0.510381\pi\) | ||||
−0.0326080 | + | 0.999468i | \(0.510381\pi\) | |||||||
\(200\) | 4078.33 | + | 905.783i | 1.44191 | + | 0.320243i | ||||
\(201\) | −529.519 | −0.185818 | ||||||||
\(202\) | −1450.63 | − | 1053.94i | −0.505276 | − | 0.367105i | ||||
\(203\) | −0.535524 | − | 1.64817i | −0.000185155 | − | 0.000569848i | ||||
\(204\) | 229.260 | + | 705.589i | 0.0786833 | + | 0.242162i | ||||
\(205\) | −153.155 | + | 1395.98i | −0.0521797 | + | 0.475608i | ||||
\(206\) | 2988.71 | − | 9198.31i | 1.01084 | − | 3.11105i | ||||
\(207\) | −1454.23 | −0.488291 | ||||||||
\(208\) | 428.809 | − | 1319.74i | 0.142945 | − | 0.439940i | ||||
\(209\) | −3486.04 | + | 2532.76i | −1.15375 | + | 0.838251i | ||||
\(210\) | 11.2060 | + | 19.6151i | 0.00368231 | + | 0.00644557i | ||||
\(211\) | 3968.01 | + | 2882.93i | 1.29464 | + | 0.940611i | 0.999888 | − | 0.0149634i | \(-0.00476319\pi\) |
0.294751 | + | 0.955574i | \(0.404763\pi\) | |||||||
\(212\) | 3021.39 | − | 2195.17i | 0.978821 | − | 0.711155i | ||||
\(213\) | −1752.58 | + | 1273.33i | −0.563779 | + | 0.409610i | ||||
\(214\) | 6513.31 | + | 4732.20i | 2.08056 | + | 1.51162i | ||||
\(215\) | −3983.66 | + | 4383.98i | −1.26364 | + | 1.39063i | ||||
\(216\) | 730.044 | − | 530.408i | 0.229969 | − | 0.167082i | ||||
\(217\) | −14.4615 | + | 44.5080i | −0.00452402 | + | 0.0139235i | ||||
\(218\) | −96.9547 | −0.0301220 | ||||||||
\(219\) | −2.26452 | + | 6.96947i | −0.000698730 | + | 0.00215047i | ||||
\(220\) | −3932.00 | − | 6882.63i | −1.20498 | − | 2.10921i | ||||
\(221\) | 175.278 | + | 539.451i | 0.0533507 | + | 0.164196i | ||||
\(222\) | 1250.37 | + | 3848.26i | 0.378016 | + | 1.16341i | ||||
\(223\) | 3913.55 | + | 2843.36i | 1.17521 | + | 0.853837i | 0.991623 | − | 0.129167i | \(-0.0412303\pi\) |
0.183583 | + | 0.983004i | \(0.441230\pi\) | |||||||
\(224\) | 10.3569 | 0.00308929 | ||||||||
\(225\) | 745.125 | + | 842.861i | 0.220778 | + | 0.249736i | ||||
\(226\) | 3079.61 | 0.906428 | ||||||||
\(227\) | 36.2582 | + | 26.3431i | 0.0106015 | + | 0.00770244i | 0.593073 | − | 0.805148i | \(-0.297914\pi\) |
−0.582472 | + | 0.812851i | \(0.697914\pi\) | |||||||
\(228\) | 1263.17 | + | 3887.65i | 0.366911 | + | 1.12924i | ||||
\(229\) | −1285.44 | − | 3956.19i | −0.370937 | − | 1.14163i | −0.946179 | − | 0.323643i | \(-0.895092\pi\) |
0.575243 | − | 0.817983i | \(-0.304908\pi\) | |||||||
\(230\) | 7894.04 | + | 3557.83i | 2.26312 | + | 1.01998i | ||||
\(231\) | 6.16830 | − | 18.9841i | 0.00175690 | − | 0.00540719i | ||||
\(232\) | 412.179 | 0.116642 | ||||||||
\(233\) | 910.177 | − | 2801.24i | 0.255913 | − | 0.787619i | −0.737736 | − | 0.675090i | \(-0.764105\pi\) |
0.993648 | − | 0.112529i | \(-0.0358952\pi\) | |||||||
\(234\) | 1198.50 | − | 870.764i | 0.334823 | − | 0.243263i | ||||
\(235\) | 765.196 | + | 344.872i | 0.212408 | + | 0.0957318i | ||||
\(236\) | 3253.22 | + | 2363.61i | 0.897317 | + | 0.651939i | ||||
\(237\) | −1474.83 | + | 1071.52i | −0.404221 | + | 0.293684i | ||||
\(238\) | 8.99953 | − | 6.53854i | 0.00245106 | − | 0.00178080i | ||||
\(239\) | −1759.24 | − | 1278.16i | −0.476133 | − | 0.345931i | 0.323694 | − | 0.946162i | \(-0.395075\pi\) |
−0.799827 | + | 0.600231i | \(0.795075\pi\) | |||||||
\(240\) | −1326.93 | + | 275.737i | −0.356887 | + | 0.0741613i | ||||
\(241\) | −1861.30 | + | 1352.31i | −0.497496 | + | 0.361452i | −0.808060 | − | 0.589100i | \(-0.799482\pi\) |
0.310564 | + | 0.950553i | \(0.399482\pi\) | |||||||
\(242\) | −1349.40 | + | 4153.01i | −0.358440 | + | 1.10316i | ||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 1711.25 | − | 5266.69i | 0.448982 | − | 1.38182i | ||||
\(245\) | −2578.83 | + | 2837.97i | −0.672470 | + | 0.740047i | ||||
\(246\) | −558.130 | − | 1717.75i | −0.144655 | − | 0.445201i | ||||
\(247\) | 965.748 | + | 2972.27i | 0.248782 | + | 0.765671i | ||||
\(248\) | −9004.91 | − | 6542.45i | −2.30569 | − | 1.67519i | ||||
\(249\) | −3805.66 | −0.968571 | ||||||||
\(250\) | −1982.69 | − | 6398.29i | −0.501586 | − | 1.61865i | ||||
\(251\) | 3368.55 | 0.847096 | 0.423548 | − | 0.905874i | \(-0.360785\pi\) | ||||
0.423548 | + | 0.905874i | \(0.360785\pi\) | |||||||
\(252\) | −15.3196 | − | 11.1303i | −0.00382954 | − | 0.00278232i | ||||
\(253\) | −2364.27 | − | 7276.49i | −0.587513 | − | 1.80818i | ||||
\(254\) | 1756.48 | + | 5405.89i | 0.433903 | + | 1.33542i | ||||
\(255\) | 372.554 | − | 409.992i | 0.0914912 | − | 0.100685i | ||||
\(256\) | −2256.86 | + | 6945.91i | −0.550992 | + | 1.69578i | ||||
\(257\) | 404.905 | 0.0982772 | 0.0491386 | − | 0.998792i | \(-0.484352\pi\) | ||||
0.0491386 | + | 0.998792i | \(0.484352\pi\) | |||||||
\(258\) | 2354.19 | − | 7245.46i | 0.568084 | − | 1.74838i | ||||
\(259\) | 31.9907 | − | 23.2426i | 0.00767492 | − | 0.00557616i | ||||
\(260\) | −5628.78 | + | 1169.66i | −1.34262 | + | 0.278998i | ||||
\(261\) | 89.7963 | + | 65.2408i | 0.0212960 | + | 0.0154724i | ||||
\(262\) | −865.077 | + | 628.515i | −0.203987 | + | 0.148205i | ||||
\(263\) | 1225.42 | − | 890.319i | 0.287310 | − | 0.208743i | −0.434790 | − | 0.900532i | \(-0.643177\pi\) |
0.722100 | + | 0.691789i | \(0.243177\pi\) | |||||||
\(264\) | 3840.88 | + | 2790.56i | 0.895416 | + | 0.650558i | ||||
\(265\) | −2542.38 | − | 1145.84i | −0.589347 | − | 0.265617i | ||||
\(266\) | 49.5856 | − | 36.0261i | 0.0114297 | − | 0.00830413i | ||||
\(267\) | −1239.96 | + | 3816.21i | −0.284211 | + | 0.874712i | ||||
\(268\) | −2642.83 | −0.602374 | ||||||||
\(269\) | −584.624 | + | 1799.29i | −0.132510 | + | 0.407823i | −0.995194 | − | 0.0979190i | \(-0.968781\pi\) |
0.862685 | + | 0.505742i | \(0.168781\pi\) | |||||||
\(270\) | −1319.08 | − | 594.507i | −0.297321 | − | 0.134002i | ||||
\(271\) | −647.179 | − | 1991.81i | −0.145068 | − | 0.446472i | 0.851952 | − | 0.523620i | \(-0.175419\pi\) |
−0.997020 | + | 0.0771477i | \(0.975419\pi\) | |||||||
\(272\) | 206.229 | + | 634.707i | 0.0459722 | + | 0.141488i | ||||
\(273\) | −11.7124 | − | 8.50959i | −0.00259659 | − | 0.00188653i | ||||
\(274\) | 7570.79 | 1.66923 | ||||||||
\(275\) | −3005.97 | + | 5098.66i | −0.659153 | + | 1.11804i | ||||
\(276\) | −7258.08 | −1.58292 | ||||||||
\(277\) | 1207.64 | + | 877.405i | 0.261950 | + | 0.190318i | 0.711006 | − | 0.703185i | \(-0.248240\pi\) |
−0.449056 | + | 0.893504i | \(0.648240\pi\) | |||||||
\(278\) | −2318.33 | − | 7135.08i | −0.500159 | − | 1.53933i | ||||
\(279\) | −926.230 | − | 2850.64i | −0.198752 | − | 0.611697i | ||||
\(280\) | 26.0463 | + | 45.5919i | 0.00555917 | + | 0.00973085i | ||||
\(281\) | 639.509 | − | 1968.21i | 0.135765 | − | 0.417841i | −0.859943 | − | 0.510389i | \(-0.829501\pi\) |
0.995708 | + | 0.0925483i | \(0.0295013\pi\) | |||||||
\(282\) | −1079.45 | −0.227945 | ||||||||
\(283\) | 1050.32 | − | 3232.55i | 0.220618 | − | 0.678992i | −0.778089 | − | 0.628154i | \(-0.783811\pi\) |
0.998707 | − | 0.0508383i | \(-0.0161893\pi\) | |||||||
\(284\) | −8747.13 | + | 6355.17i | −1.82763 | + | 1.32785i | ||||
\(285\) | 2052.70 | − | 2258.98i | 0.426636 | − | 0.469509i | ||||
\(286\) | 6305.52 | + | 4581.23i | 1.30368 | + | 0.947180i | ||||
\(287\) | −14.2797 | + | 10.3748i | −0.00293695 | + | 0.00213382i | ||||
\(288\) | −536.651 | + | 389.900i | −0.109800 | + | 0.0797746i | ||||
\(289\) | 3754.01 | + | 2727.45i | 0.764097 | + | 0.555149i | ||||
\(290\) | −327.829 | − | 573.837i | −0.0663821 | − | 0.116196i | ||||
\(291\) | 3473.62 | − | 2523.74i | 0.699751 | − | 0.508399i | ||||
\(292\) | −11.3022 | + | 34.7846i | −0.00226511 | + | 0.00697128i | ||||
\(293\) | 7677.60 | 1.53082 | 0.765410 | − | 0.643543i | \(-0.222536\pi\) | ||||
0.765410 | + | 0.643543i | \(0.222536\pi\) | |||||||
\(294\) | 1523.99 | − | 4690.35i | 0.302316 | − | 0.930432i | ||||
\(295\) | 327.459 | − | 2984.73i | 0.0646285 | − | 0.589076i | ||||
\(296\) | 2906.28 | + | 8944.62i | 0.570690 | + | 1.75640i | ||||
\(297\) | 395.066 | + | 1215.89i | 0.0771854 | + | 0.237552i | ||||
\(298\) | 746.968 | + | 542.704i | 0.145204 | + | 0.105497i | ||||
\(299\) | −5549.09 | −1.07329 | ||||||||
\(300\) | 3718.92 | + | 4206.71i | 0.715706 | + | 0.809583i | ||||
\(301\) | −74.4505 | −0.0142567 | ||||||||
\(302\) | 4082.49 | + | 2966.11i | 0.777885 | + | 0.565166i | ||||
\(303\) | −346.811 | − | 1067.38i | −0.0657551 | − | 0.202373i | ||||
\(304\) | 1136.28 | + | 3497.10i | 0.214375 | + | 0.659779i | ||||
\(305\) | −4048.54 | + | 841.288i | −0.760061 | + | 0.157941i | ||||
\(306\) | −220.165 | + | 677.599i | −0.0411308 | + | 0.126588i | ||||
\(307\) | −4507.90 | −0.838043 | −0.419022 | − | 0.907976i | \(-0.637627\pi\) | ||||
−0.419022 | + | 0.907976i | \(0.637627\pi\) | |||||||
\(308\) | 30.7860 | − | 94.7495i | 0.00569543 | − | 0.0175287i | ||||
\(309\) | 4897.47 | − | 3558.22i | 0.901642 | − | 0.655081i | ||||
\(310\) | −1946.31 | + | 17740.2i | −0.356590 | + | 3.25025i | ||||
\(311\) | −5715.86 | − | 4152.81i | −1.04218 | − | 0.757185i | −0.0714665 | − | 0.997443i | \(-0.522768\pi\) |
−0.970709 | + | 0.240258i | \(0.922768\pi\) | |||||||
\(312\) | 2785.72 | − | 2023.94i | 0.505481 | − | 0.367254i | ||||
\(313\) | −1669.65 | + | 1213.07i | −0.301516 | + | 0.219064i | −0.728247 | − | 0.685314i | \(-0.759665\pi\) |
0.426732 | + | 0.904378i | \(0.359665\pi\) | |||||||
\(314\) | 7930.75 | + | 5762.02i | 1.42534 | + | 1.03557i | ||||
\(315\) | −1.54202 | + | 14.0552i | −0.000275819 | + | 0.00251404i | ||||
\(316\) | −7360.86 | + | 5347.97i | −1.31038 | + | 0.952048i | ||||
\(317\) | 2656.46 | − | 8175.75i | 0.470668 | − | 1.44857i | −0.381044 | − | 0.924557i | \(-0.624435\pi\) |
0.851712 | − | 0.524010i | \(-0.175565\pi\) | |||||||
\(318\) | 3586.50 | 0.632456 | ||||||||
\(319\) | −180.453 | + | 555.378i | −0.0316722 | + | 0.0974771i | ||||
\(320\) | 7405.49 | − | 1538.87i | 1.29369 | − | 0.268829i | ||||
\(321\) | 1557.18 | + | 4792.51i | 0.270758 | + | 0.833308i | ||||
\(322\) | 33.6295 | + | 103.501i | 0.00582019 | + | 0.0179127i | ||||
\(323\) | −1215.97 | − | 883.456i | −0.209469 | − | 0.152188i | ||||
\(324\) | 1212.81 | 0.207958 | ||||||||
\(325\) | 2843.26 | + | 3216.20i | 0.485279 | + | 0.548932i | ||||
\(326\) | −4064.54 | −0.690533 | ||||||||
\(327\) | −49.0952 | − | 35.6698i | −0.00830266 | − | 0.00603224i | ||||
\(328\) | −1297.28 | − | 3992.61i | −0.218385 | − | 0.672119i | ||||
\(329\) | 3.25983 | + | 10.0327i | 0.000546262 | + | 0.00168122i | ||||
\(330\) | 830.163 | − | 7566.77i | 0.138482 | − | 1.26223i | ||||
\(331\) | 80.2294 | − | 246.921i | 0.0133227 | − | 0.0410030i | −0.944174 | − | 0.329447i | \(-0.893138\pi\) |
0.957497 | + | 0.288444i | \(0.0931378\pi\) | |||||||
\(332\) | −18994.1 | −3.13986 | ||||||||
\(333\) | −782.623 | + | 2408.67i | −0.128791 | + | 0.396379i | ||||
\(334\) | 7648.42 | − | 5556.90i | 1.25300 | − | 0.910360i | ||||
\(335\) | 978.905 | + | 1713.49i | 0.159652 | + | 0.279457i | ||||
\(336\) | −13.7806 | − | 10.0122i | −0.00223748 | − | 0.00162563i | ||||
\(337\) | −5437.56 | + | 3950.62i | −0.878940 | + | 0.638587i | −0.932971 | − | 0.359952i | \(-0.882793\pi\) |
0.0540310 | + | 0.998539i | \(0.482793\pi\) | |||||||
\(338\) | −3945.88 | + | 2866.85i | −0.634993 | + | 0.461349i | ||||
\(339\) | 1559.43 | + | 1132.99i | 0.249843 | + | 0.181521i | ||||
\(340\) | 1859.42 | − | 2046.27i | 0.296591 | − | 0.326396i | ||||
\(341\) | 12757.8 | − | 9269.08i | 2.02602 | − | 1.47199i | ||||
\(342\) | −1213.07 | + | 3733.44i | −0.191799 | + | 0.590296i | ||||
\(343\) | −96.3940 | −0.0151743 | ||||||||
\(344\) | 5471.92 | − | 16840.8i | 0.857634 | − | 2.63953i | ||||
\(345\) | 2688.40 | + | 4705.81i | 0.419532 | + | 0.734355i | ||||
\(346\) | −4010.36 | − | 12342.6i | −0.623116 | − | 1.91775i | ||||
\(347\) | −2206.24 | − | 6790.12i | −0.341318 | − | 1.05047i | −0.963525 | − | 0.267617i | \(-0.913764\pi\) |
0.622207 | − | 0.782853i | \(-0.286236\pi\) | |||||||
\(348\) | 448.173 | + | 325.617i | 0.0690362 | + | 0.0501577i | ||||
\(349\) | −11473.4 | −1.75976 | −0.879879 | − | 0.475198i | \(-0.842376\pi\) | ||||
−0.879879 | + | 0.475198i | \(0.842376\pi\) | |||||||
\(350\) | 42.7571 | − | 72.5236i | 0.00652989 | − | 0.0110759i | ||||
\(351\) | 927.244 | 0.141005 | ||||||||
\(352\) | −2823.41 | − | 2051.33i | −0.427523 | − | 0.310614i | ||||
\(353\) | 18.4180 | + | 56.6848i | 0.00277703 | + | 0.00854683i | 0.952435 | − | 0.304740i | \(-0.0985697\pi\) |
−0.949658 | + | 0.313287i | \(0.898570\pi\) | |||||||
\(354\) | 1193.33 | + | 3672.69i | 0.179166 | + | 0.551416i | ||||
\(355\) | 7360.35 | + | 3317.29i | 1.10041 | + | 0.495954i | ||||
\(356\) | −6188.64 | + | 19046.7i | −0.921341 | + | 2.83560i | ||||
\(357\) | 6.96265 | 0.00103222 | ||||||||
\(358\) | −4639.25 | + | 14278.1i | −0.684893 | + | 2.10788i | ||||
\(359\) | 6311.85 | − | 4585.83i | 0.927930 | − | 0.674180i | −0.0175554 | − | 0.999846i | \(-0.505588\pi\) |
0.945485 | + | 0.325666i | \(0.105588\pi\) | |||||||
\(360\) | −3065.98 | − | 1381.83i | −0.448865 | − | 0.202302i | ||||
\(361\) | −1150.72 | − | 836.048i | −0.167768 | − | 0.121891i | ||||
\(362\) | 1229.41 | − | 893.216i | 0.178498 | − | 0.129686i | ||||
\(363\) | −2211.20 | + | 1606.53i | −0.319718 | + | 0.232289i | ||||
\(364\) | −58.4568 | − | 42.4713i | −0.00841749 | − | 0.00611567i | ||||
\(365\) | 26.7391 | − | 5.55641i | 0.00383449 | − | 0.000796810i | ||||
\(366\) | 4302.40 | − | 3125.87i | 0.614453 | − | 0.446426i | ||||
\(367\) | −489.265 | + | 1505.80i | −0.0695897 | + | 0.214175i | −0.979803 | − | 0.199964i | \(-0.935917\pi\) |
0.910213 | + | 0.414139i | \(0.135917\pi\) | |||||||
\(368\) | −6528.94 | −0.924850 | ||||||||
\(369\) | 349.340 | − | 1075.16i | 0.0492842 | − | 0.151681i | ||||
\(370\) | 10141.2 | − | 11160.3i | 1.42491 | − | 1.56810i | ||||
\(371\) | −10.8308 | − | 33.3339i | −0.00151566 | − | 0.00466471i | ||||
\(372\) | −4622.81 | − | 14227.5i | −0.644305 | − | 1.98297i | ||||
\(373\) | 9045.77 | + | 6572.14i | 1.25569 | + | 0.912312i | 0.998538 | − | 0.0540593i | \(-0.0172160\pi\) |
0.257152 | + | 0.966371i | \(0.417216\pi\) | |||||||
\(374\) | −3748.42 | −0.518252 | ||||||||
\(375\) | 1349.96 | − | 3969.35i | 0.185897 | − | 0.546604i | ||||
\(376\) | −2509.01 | −0.344128 | ||||||||
\(377\) | 342.646 | + | 248.947i | 0.0468095 | + | 0.0340091i | ||||
\(378\) | −5.61944 | − | 17.2949i | −0.000764637 | − | 0.00235331i | ||||
\(379\) | −3622.62 | − | 11149.3i | −0.490980 | − | 1.51108i | −0.823129 | − | 0.567855i | \(-0.807773\pi\) |
0.332148 | − | 0.943227i | \(-0.392227\pi\) | |||||||
\(380\) | 10245.0 | − | 11274.5i | 1.38305 | − | 1.52203i | ||||
\(381\) | −1099.40 | + | 3383.61i | −0.147832 | + | 0.454980i | ||||
\(382\) | −8049.67 | −1.07816 | ||||||||
\(383\) | −2865.21 | + | 8818.21i | −0.382260 | + | 1.17647i | 0.556189 | + | 0.831056i | \(0.312263\pi\) |
−0.938449 | + | 0.345419i | \(0.887737\pi\) | |||||||
\(384\) | −6438.78 | + | 4678.05i | −0.855671 | + | 0.621681i | ||||
\(385\) | −72.8345 | + | 15.1351i | −0.00964153 | + | 0.00200352i | ||||
\(386\) | −5621.09 | − | 4083.96i | −0.741207 | − | 0.538519i | ||||
\(387\) | 3857.71 | − | 2802.79i | 0.506714 | − | 0.368150i | ||||
\(388\) | 17336.8 | − | 12596.0i | 2.26841 | − | 1.64810i | ||||
\(389\) | 1085.01 | + | 788.308i | 0.141420 | + | 0.102748i | 0.656246 | − | 0.754547i | \(-0.272143\pi\) |
−0.514826 | + | 0.857295i | \(0.672143\pi\) | |||||||
\(390\) | −5033.38 | − | 2268.53i | −0.653525 | − | 0.294542i | ||||
\(391\) | 2159.06 | − | 1568.65i | 0.279254 | − | 0.202890i | ||||
\(392\) | 3542.25 | − | 10901.9i | 0.456405 | − | 1.40467i | ||||
\(393\) | −669.283 | −0.0859054 | ||||||||
\(394\) | 1570.92 | − | 4834.78i | 0.200867 | − | 0.618205i | ||||
\(395\) | 6193.86 | + | 2791.56i | 0.788979 | + | 0.355591i | ||||
\(396\) | 1971.77 | + | 6068.50i | 0.250216 | + | 0.770085i | ||||
\(397\) | 3512.37 | + | 10810.0i | 0.444032 | + | 1.36659i | 0.883542 | + | 0.468353i | \(0.155152\pi\) |
−0.439510 | + | 0.898238i | \(0.644848\pi\) | |||||||
\(398\) | −709.904 | − | 515.775i | −0.0894077 | − | 0.0649585i | ||||
\(399\) | 38.3628 | 0.00481339 | ||||||||
\(400\) | 3345.32 | + | 3784.12i | 0.418165 | + | 0.473015i | ||||
\(401\) | −12421.7 | −1.54690 | −0.773451 | − | 0.633856i | \(-0.781471\pi\) | ||||
−0.773451 | + | 0.633856i | \(0.781471\pi\) | |||||||
\(402\) | −2053.28 | − | 1491.79i | −0.254747 | − | 0.185084i | ||||
\(403\) | −3534.33 | − | 10877.5i | −0.436867 | − | 1.34454i | ||||
\(404\) | −1730.93 | − | 5327.27i | −0.213161 | − | 0.656043i | ||||
\(405\) | −449.227 | − | 786.333i | −0.0551167 | − | 0.0964771i | ||||
\(406\) | 2.56677 | − | 7.89972i | 0.000313761 | − | 0.000965656i | ||||
\(407\) | −13324.5 | −1.62278 | ||||||||
\(408\) | −511.737 | + | 1574.96i | −0.0620950 | + | 0.191109i | ||||
\(409\) | −10450.7 | + | 7592.88i | −1.26346 | + | 0.917956i | −0.998922 | − | 0.0464199i | \(-0.985219\pi\) |
−0.264536 | + | 0.964376i | \(0.585219\pi\) | |||||||
\(410\) | −4526.73 | + | 4981.62i | −0.545266 | + | 0.600060i | ||||
\(411\) | 3833.64 | + | 2785.30i | 0.460096 | + | 0.334279i | ||||
\(412\) | 24443.3 | − | 17759.1i | 2.92289 | − | 2.12361i | ||||
\(413\) | 30.5312 | − | 22.1822i | 0.00363763 | − | 0.00264289i | ||||
\(414\) | −5638.98 | − | 4096.96i | −0.669422 | − | 0.486364i | ||||
\(415\) | 7035.42 | + | 12314.9i | 0.832181 | + | 1.45666i | ||||
\(416\) | −2047.77 | + | 1487.79i | −0.241346 | + | 0.175348i | ||||
\(417\) | 1451.07 | − | 4465.92i | 0.170405 | − | 0.524454i | ||||
\(418\) | −20653.0 | −2.41668 | ||||||||
\(419\) | −1286.38 | + | 3959.06i | −0.149985 | + | 0.461605i | −0.997618 | − | 0.0689767i | \(-0.978027\pi\) |
0.847634 | + | 0.530582i | \(0.178027\pi\) | |||||||
\(420\) | −7.69622 | + | 70.1495i | −0.000894136 | + | 0.00814987i | ||||
\(421\) | −4618.97 | − | 14215.7i | −0.534714 | − | 1.64568i | −0.744265 | − | 0.667884i | \(-0.767200\pi\) |
0.209551 | − | 0.977798i | \(-0.432800\pi\) | |||||||
\(422\) | 7264.50 | + | 22357.8i | 0.837987 | + | 2.57906i | ||||
\(423\) | −546.606 | − | 397.132i | −0.0628295 | − | 0.0456483i | ||||
\(424\) | 8336.21 | 0.954817 | ||||||||
\(425\) | −2015.44 | − | 447.622i | −0.230031 | − | 0.0510891i | ||||
\(426\) | −10383.2 | −1.18091 | ||||||||
\(427\) | −42.0454 | − | 30.5478i | −0.00476515 | − | 0.00346209i | ||||
\(428\) | 7771.89 | + | 23919.4i | 0.877730 | + | 2.70137i | ||||
\(429\) | 1507.50 | + | 4639.61i | 0.169657 | + | 0.522151i | ||||
\(430\) | −27798.0 | + | 5776.44i | −3.11753 | + | 0.647825i | ||||
\(431\) | −3943.96 | + | 12138.2i | −0.440774 | + | 1.35656i | 0.446278 | + | 0.894894i | \(0.352749\pi\) |
−0.887052 | + | 0.461669i | \(0.847251\pi\) | |||||||
\(432\) | 1090.98 | 0.121504 | ||||||||
\(433\) | 240.260 | − | 739.444i | 0.0266655 | − | 0.0820679i | −0.936838 | − | 0.349763i | \(-0.886262\pi\) |
0.963504 | + | 0.267695i | \(0.0862621\pi\) | |||||||
\(434\) | −181.467 | + | 131.844i | −0.0200708 | + | 0.0145823i | ||||
\(435\) | 45.1117 | − | 411.184i | 0.00497227 | − | 0.0453213i | ||||
\(436\) | −245.034 | − | 178.028i | −0.0269151 | − | 0.0195550i | ||||
\(437\) | 11896.0 | − | 8642.94i | 1.30220 | − | 0.946105i | ||||
\(438\) | −28.4158 | + | 20.6453i | −0.00309991 | + | 0.00225221i | ||||
\(439\) | −8038.76 | − | 5840.50i | −0.873961 | − | 0.634970i | 0.0576858 | − | 0.998335i | \(-0.481628\pi\) |
−0.931647 | + | 0.363365i | \(0.881628\pi\) | |||||||
\(440\) | 1929.57 | − | 17587.7i | 0.209065 | − | 1.90559i | ||||
\(441\) | 2497.29 | − | 1814.39i | 0.269657 | − | 0.195917i | ||||
\(442\) | −840.111 | + | 2585.60i | −0.0904073 | + | 0.278245i | ||||
\(443\) | 7139.86 | 0.765745 | 0.382873 | − | 0.923801i | \(-0.374935\pi\) | ||||
0.382873 | + | 0.923801i | \(0.374935\pi\) | |||||||
\(444\) | −3906.07 | + | 12021.6i | −0.417508 | + | 1.28496i | ||||
\(445\) | 14641.3 | − | 3042.47i | 1.55970 | − | 0.324106i | ||||
\(446\) | 7164.81 | + | 22051.0i | 0.760681 | + | 2.34114i | ||||
\(447\) | 178.583 | + | 549.621i | 0.0188964 | + | 0.0581570i | ||||
\(448\) | 76.9086 | + | 55.8773i | 0.00811069 | + | 0.00589276i | ||||
\(449\) | 10438.2 | 1.09712 | 0.548560 | − | 0.836111i | \(-0.315176\pi\) | ||||
0.548560 | + | 0.836111i | \(0.315176\pi\) | |||||||
\(450\) | 514.758 | + | 5367.51i | 0.0539243 | + | 0.562282i | ||||
\(451\) | 5947.67 | 0.620986 | ||||||||
\(452\) | 7783.11 | + | 5654.76i | 0.809926 | + | 0.588446i | ||||
\(453\) | 976.029 | + | 3003.91i | 0.101231 | + | 0.311558i | ||||
\(454\) | 66.3804 | + | 204.298i | 0.00686208 | + | 0.0211193i | ||||
\(455\) | −5.88407 | + | 53.6322i | −0.000606263 | + | 0.00552597i | ||||
\(456\) | −2819.57 | + | 8677.74i | −0.289558 | + | 0.891167i | ||||
\(457\) | 5039.76 | 0.515864 | 0.257932 | − | 0.966163i | \(-0.416959\pi\) | ||||
0.257932 | + | 0.966163i | \(0.416959\pi\) | |||||||
\(458\) | 6161.15 | − | 18962.1i | 0.628584 | − | 1.93458i | ||||
\(459\) | −360.775 | + | 262.119i | −0.0366875 | + | 0.0266550i | ||||
\(460\) | 13417.8 | + | 23486.7i | 1.36002 | + | 2.38059i | ||||
\(461\) | −1482.67 | − | 1077.22i | −0.149794 | − | 0.108831i | 0.510364 | − | 0.859958i | \(-0.329511\pi\) |
−0.660158 | + | 0.751127i | \(0.729511\pi\) | |||||||
\(462\) | 77.4016 | − | 56.2355i | 0.00779447 | − | 0.00566302i | ||||
\(463\) | −1527.01 | + | 1109.44i | −0.153275 | + | 0.111361i | −0.661779 | − | 0.749699i | \(-0.730198\pi\) |
0.508505 | + | 0.861059i | \(0.330198\pi\) | |||||||
\(464\) | 403.150 | + | 292.906i | 0.0403358 | + | 0.0293056i | ||||
\(465\) | −7512.21 | + | 8267.12i | −0.749184 | + | 0.824470i | ||||
\(466\) | 11421.2 | − | 8297.96i | 1.13535 | − | 0.824883i | ||||
\(467\) | −1218.86 | + | 3751.27i | −0.120775 | + | 0.371708i | −0.993108 | − | 0.117205i | \(-0.962607\pi\) |
0.872332 | + | 0.488913i | \(0.162607\pi\) | |||||||
\(468\) | 4627.87 | 0.457101 | ||||||||
\(469\) | −7.66444 | + | 23.5887i | −0.000754608 | + | 0.00232244i | ||||
\(470\) | 1995.55 | + | 3493.05i | 0.195847 | + | 0.342813i | ||||
\(471\) | 1896.06 | + | 5835.46i | 0.185490 | + | 0.570879i | ||||
\(472\) | 2773.69 | + | 8536.54i | 0.270486 | + | 0.832470i | ||||
\(473\) | 20296.0 | + | 14745.9i | 1.97296 | + | 1.43344i | ||||
\(474\) | −8737.60 | −0.846690 | ||||||||
\(475\) | −11104.7 | − | 2466.31i | −1.07267 | − | 0.238236i | ||||
\(476\) | 34.7506 | 0.00334620 | ||||||||
\(477\) | 1816.11 | + | 1319.48i | 0.174327 | + | 0.126656i | ||||
\(478\) | −3220.76 | − | 9912.49i | −0.308189 | − | 0.948507i | ||||
\(479\) | −3324.76 | − | 10232.6i | −0.317144 | − | 0.976070i | −0.974863 | − | 0.222806i | \(-0.928478\pi\) |
0.657718 | − | 0.753264i | \(-0.271522\pi\) | |||||||
\(480\) | 2253.78 | + | 1015.78i | 0.214314 | + | 0.0965908i | ||||
\(481\) | −2986.35 | + | 9191.03i | −0.283089 | + | 0.871258i | ||||
\(482\) | −11027.2 | −1.04207 | ||||||||
\(483\) | −21.0491 | + | 64.7825i | −0.00198295 | + | 0.00610291i | ||||
\(484\) | −11036.1 | + | 8018.17i | −1.03645 | + | 0.753022i | ||||
\(485\) | −14588.2 | − | 6574.88i | −1.36581 | − | 0.615567i | ||||
\(486\) | 942.264 | + | 684.595i | 0.0879464 | + | 0.0638968i | ||||
\(487\) | −2581.85 | + | 1875.82i | −0.240236 | + | 0.174542i | −0.701388 | − | 0.712779i | \(-0.747436\pi\) |
0.461153 | + | 0.887321i | \(0.347436\pi\) | |||||||
\(488\) | 10000.2 | − | 7265.56i | 0.927638 | − | 0.673968i | ||||
\(489\) | −2058.17 | − | 1495.35i | −0.190335 | − | 0.138286i | ||||
\(490\) | −17995.0 | + | 3739.38i | −1.65905 | + | 0.344751i | ||||
\(491\) | −755.541 | + | 548.933i | −0.0694442 | + | 0.0504541i | −0.621966 | − | 0.783044i | \(-0.713666\pi\) |
0.552522 | + | 0.833499i | \(0.313666\pi\) | |||||||
\(492\) | 1743.55 | − | 5366.10i | 0.159767 | − | 0.491713i | ||||
\(493\) | −203.692 | −0.0186082 | ||||||||
\(494\) | −4628.84 | + | 14246.1i | −0.421582 | + | 1.29750i | ||||
\(495\) | 3204.20 | − | 3526.19i | 0.290945 | − | 0.320183i | ||||
\(496\) | −4158.41 | − | 12798.3i | −0.376448 | − | 1.15859i | ||||
\(497\) | 31.3560 | + | 96.5037i | 0.00282999 | + | 0.00870983i | ||||
\(498\) | −14757.0 | − | 10721.6i | −1.32786 | − | 0.964748i | ||||
\(499\) | 5499.10 | 0.493333 | 0.246667 | − | 0.969100i | \(-0.420665\pi\) | ||||
0.246667 | + | 0.969100i | \(0.420665\pi\) | |||||||
\(500\) | 6737.63 | − | 19811.0i | 0.602632 | − | 1.77195i | ||||
\(501\) | 5917.34 | 0.527679 | ||||||||
\(502\) | 13062.0 | + | 9490.09i | 1.16133 | + | 0.843752i | ||||
\(503\) | −3452.50 | − | 10625.7i | −0.306042 | − | 0.941901i | −0.979286 | − | 0.202481i | \(-0.935100\pi\) |
0.673244 | − | 0.739420i | \(-0.264900\pi\) | |||||||
\(504\) | −13.0614 | − | 40.1990i | −0.00115437 | − | 0.00355279i | ||||
\(505\) | −2812.82 | + | 3095.49i | −0.247859 | + | 0.272767i | ||||
\(506\) | 11332.0 | − | 34876.3i | 0.995591 | − | 3.06411i | ||||
\(507\) | −3052.80 | −0.267416 | ||||||||
\(508\) | −5487.10 | + | 16887.6i | −0.479234 | + | 1.47493i | ||||
\(509\) | 6938.79 | − | 5041.32i | 0.604236 | − | 0.439003i | −0.243144 | − | 0.969990i | \(-0.578179\pi\) |
0.847380 | + | 0.530987i | \(0.178179\pi\) | |||||||
\(510\) | 2599.68 | − | 540.216i | 0.225718 | − | 0.0469042i | ||||
\(511\) | 0.277695 | + | 0.201757i | 2.40401e−5 | + | 1.74662e-5i | ||||
\(512\) | −11149.7 | + | 8100.70i | −0.962403 | + | 0.699226i | ||||
\(513\) | −1987.80 | + | 1444.22i | −0.171079 | + | 0.124296i | ||||
\(514\) | 1570.07 | + | 1140.72i | 0.134733 | + | 0.0978893i | ||||
\(515\) | −20568.0 | − | 9269.94i | −1.75987 | − | 0.793170i | ||||
\(516\) | 19253.8 | − | 13988.7i | 1.64264 | − | 1.19345i | ||||
\(517\) | 1098.45 | − | 3380.68i | 0.0934425 | − | 0.287586i | ||||
\(518\) | 189.529 | 0.0160761 | ||||||||
\(519\) | 2510.13 | − | 7725.37i | 0.212297 | − | 0.653384i | ||||
\(520\) | −11699.2 | − | 5272.81i | −0.986625 | − | 0.444670i | ||||
\(521\) | −6097.64 | − | 18766.6i | −0.512750 | − | 1.57808i | −0.787339 | − | 0.616520i | \(-0.788542\pi\) |
0.274589 | − | 0.961562i | \(-0.411458\pi\) | |||||||
\(522\) | 164.396 | + | 505.960i | 0.0137843 | + | 0.0424239i | ||||
\(523\) | −13230.4 | − | 9612.48i | −1.10617 | − | 0.803680i | −0.124114 | − | 0.992268i | \(-0.539609\pi\) |
−0.982056 | + | 0.188588i | \(0.939609\pi\) | |||||||
\(524\) | −3340.39 | −0.278484 | ||||||||
\(525\) | 48.3325 | − | 20.9936i | 0.00401791 | − | 0.00174521i | ||||
\(526\) | 7259.98 | 0.601807 | ||||||||
\(527\) | 4450.07 | + | 3233.17i | 0.367833 | + | 0.267246i | ||||
\(528\) | 1773.69 | + | 5458.87i | 0.146193 | + | 0.449937i | ||||
\(529\) | 4308.19 | + | 13259.2i | 0.354088 | + | 1.08977i | ||||
\(530\) | −6630.26 | − | 11605.7i | −0.543396 | − | 0.951169i | ||||
\(531\) | −746.917 | + | 2298.78i | −0.0610423 | + | 0.187869i | ||||
\(532\) | 191.469 | 0.0156038 | ||||||||
\(533\) | 1333.02 | − | 4102.60i | 0.108329 | − | 0.333402i | ||||
\(534\) | −15559.4 | + | 11304.6i | −1.26090 | + | 0.916097i | ||||
\(535\) | 12629.6 | − | 13898.7i | 1.02060 | − | 1.12317i | ||||
\(536\) | −4772.49 | − | 3467.42i | −0.384590 | − | 0.279421i | ||||
\(537\) | −7602.13 | + | 5523.27i | −0.610905 | + | 0.443849i | ||||
\(538\) | −7336.02 | + | 5329.93i | −0.587878 | + | 0.427118i | ||||
\(539\) | 13138.6 | + | 9545.79i | 1.04995 | + | 0.762831i | ||||
\(540\) | −2242.09 | − | 3924.59i | −0.178674 | − | 0.312754i | ||||
\(541\) | −11519.4 | + | 8369.30i | −0.915445 | + | 0.665110i | −0.942386 | − | 0.334527i | \(-0.891423\pi\) |
0.0269410 | + | 0.999637i | \(0.491423\pi\) | |||||||
\(542\) | 3101.94 | − | 9546.78i | 0.245830 | − | 0.756585i | ||||
\(543\) | 951.153 | 0.0751710 | ||||||||
\(544\) | 376.175 | − | 1157.75i | 0.0296477 | − | 0.0912463i | ||||
\(545\) | −24.6644 | + | 224.811i | −0.00193854 | + | 0.0176694i | ||||
\(546\) | −21.4428 | − | 65.9941i | −0.00168071 | − | 0.00517268i | ||||
\(547\) | 2168.92 | + | 6675.24i | 0.169536 | + | 0.521778i | 0.999342 | − | 0.0362740i | \(-0.0115489\pi\) |
−0.829806 | + | 0.558052i | \(0.811549\pi\) | |||||||
\(548\) | 19133.7 | + | 13901.4i | 1.49152 | + | 1.08365i | ||||
\(549\) | 3328.63 | 0.258766 | ||||||||
\(550\) | −26020.3 | + | 11302.1i | −2.01729 | + | 0.876225i | ||||
\(551\) | −1122.30 | −0.0867725 | ||||||||
\(552\) | −13106.9 | − | 9522.68i | −1.01062 | − | 0.734262i | ||||
\(553\) | 26.3866 | + | 81.2095i | 0.00202906 | + | 0.00624481i | ||||
\(554\) | 2210.92 | + | 6804.50i | 0.169554 | + | 0.521833i | ||||
\(555\) | 9241.11 | − | 1920.31i | 0.706780 | − | 0.146869i | ||||
\(556\) | 7242.27 | − | 22289.4i | 0.552411 | − | 1.70015i | ||||
\(557\) | 6144.57 | 0.467421 | 0.233711 | − | 0.972306i | \(-0.424913\pi\) | ||||
0.233711 | + | 0.972306i | \(0.424913\pi\) | |||||||
\(558\) | 4439.43 | − | 13663.2i | 0.336803 | − | 1.03657i | ||||
\(559\) | 14720.3 | − | 10694.9i | 1.11378 | − | 0.809209i | ||||
\(560\) | −6.92307 | + | 63.1025i | −0.000522416 | + | 0.00476173i | ||||
\(561\) | −1898.10 | − | 1379.05i | −0.142848 | − | 0.103785i | ||||
\(562\) | 8024.74 | − | 5830.31i | 0.602319 | − | 0.437610i | ||||
\(563\) | −13890.4 | + | 10092.0i | −1.03981 | + | 0.755463i | −0.970248 | − | 0.242115i | \(-0.922159\pi\) |
−0.0695583 | + | 0.997578i | \(0.522159\pi\) | |||||||
\(564\) | −2728.11 | − | 1982.09i | −0.203677 | − | 0.147980i | ||||
\(565\) | 783.423 | − | 7140.75i | 0.0583343 | − | 0.531706i | ||||
\(566\) | 13179.7 | − | 9575.59i | 0.978769 | − | 0.711117i | ||||
\(567\) | 3.51727 | − | 10.8250i | 0.000260514 | − | 0.000801780i | ||||
\(568\) | −24133.9 | −1.78281 | ||||||||
\(569\) | −4813.01 | + | 14812.9i | −0.354608 | + | 1.09137i | 0.601629 | + | 0.798776i | \(0.294519\pi\) |
−0.956236 | + | 0.292595i | \(0.905481\pi\) | |||||||
\(570\) | 14323.7 | − | 2976.48i | 1.05255 | − | 0.218721i | ||||
\(571\) | −6553.52 | − | 20169.7i | −0.480309 | − | 1.47824i | −0.838662 | − | 0.544653i | \(-0.816661\pi\) |
0.358353 | − | 0.933586i | \(-0.383339\pi\) | |||||||
\(572\) | 7523.94 | + | 23156.3i | 0.549985 | + | 1.69268i | ||||
\(573\) | −4076.13 | − | 2961.48i | −0.297178 | − | 0.215912i | ||||
\(574\) | −84.5999 | −0.00615180 | ||||||||
\(575\) | 10257.8 | − | 17399.0i | 0.743963 | − | 1.26189i | ||||
\(576\) | −6088.65 | −0.440441 | ||||||||
\(577\) | 1675.68 | + | 1217.45i | 0.120900 | + | 0.0878392i | 0.646592 | − | 0.762836i | \(-0.276194\pi\) |
−0.525692 | + | 0.850675i | \(0.676194\pi\) | |||||||
\(578\) | 6872.72 | + | 21152.1i | 0.494580 | + | 1.52216i | ||||
\(579\) | −1343.87 | − | 4136.01i | −0.0964584 | − | 0.296868i | ||||
\(580\) | 225.152 | − | 2052.22i | 0.0161189 | − | 0.146920i | ||||
\(581\) | −55.0846 | + | 169.533i | −0.00393338 | + | 0.0121057i | ||||
\(582\) | 20579.5 | 1.46571 | ||||||||
\(583\) | −3649.62 | + | 11232.4i | −0.259265 | + | 0.797936i | ||||
\(584\) | −66.0477 | + | 47.9864i | −0.00467992 | + | 0.00340016i | ||||
\(585\) | −1714.17 | − | 3000.51i | −0.121149 | − | 0.212061i | ||||
\(586\) | 29770.9 | + | 21629.8i | 2.09868 | + | 1.52478i | ||||
\(587\) | −16771.4 | + | 12185.2i | −1.17927 | + | 0.856789i | −0.992089 | − | 0.125537i | \(-0.959935\pi\) |
−0.187180 | + | 0.982326i | \(0.559935\pi\) | |||||||
\(588\) | 12464.0 | − | 9055.61i | 0.874159 | − | 0.635114i | ||||
\(589\) | 24519.0 | + | 17814.1i | 1.71526 | + | 1.24621i | ||||
\(590\) | 9678.53 | − | 10651.1i | 0.675354 | − | 0.743220i | ||||
\(591\) | 2574.19 | − | 1870.26i | 0.179168 | − | 0.130173i | ||||
\(592\) | −3513.67 | + | 10814.0i | −0.243938 | + | 0.750763i | ||||
\(593\) | −1924.00 | −0.133236 | −0.0666182 | − | 0.997779i | \(-0.521221\pi\) | ||||
−0.0666182 | + | 0.997779i | \(0.521221\pi\) | |||||||
\(594\) | −1893.56 | + | 5827.77i | −0.130797 | + | 0.402553i | ||||
\(595\) | −12.8717 | − | 22.5307i | −0.000886868 | − | 0.00155239i | ||||
\(596\) | 891.306 | + | 2743.16i | 0.0612572 | + | 0.188530i | ||||
\(597\) | −169.721 | − | 522.349i | −0.0116352 | − | 0.0358096i | ||||
\(598\) | −21517.3 | − | 15633.3i | −1.47142 | − | 1.06905i | ||||
\(599\) | −8088.34 | −0.551720 | −0.275860 | − | 0.961198i | \(-0.588963\pi\) | ||||
−0.275860 | + | 0.961198i | \(0.588963\pi\) | |||||||
\(600\) | 1196.47 | + | 12475.9i | 0.0814093 | + | 0.848876i | ||||
\(601\) | 19953.8 | 1.35430 | 0.677149 | − | 0.735846i | \(-0.263215\pi\) | ||||
0.677149 | + | 0.735846i | \(0.263215\pi\) | |||||||
\(602\) | −288.692 | − | 209.747i | −0.0195452 | − | 0.0142004i | ||||
\(603\) | −490.891 | − | 1510.81i | −0.0331519 | − | 0.102031i | ||||
\(604\) | 4871.36 | + | 14992.5i | 0.328167 | + | 1.00999i | ||||
\(605\) | 9286.40 | + | 4185.36i | 0.624043 | + | 0.281254i | ||||
\(606\) | 1662.27 | − | 5115.95i | 0.111428 | − | 0.342939i | ||||
\(607\) | −3633.68 | −0.242976 | −0.121488 | − | 0.992593i | \(-0.538767\pi\) | ||||
−0.121488 | + | 0.992593i | \(0.538767\pi\) | |||||||
\(608\) | 2072.65 | − | 6378.95i | 0.138252 | − | 0.425495i | ||||
\(609\) | 4.20606 | − | 3.05588i | 0.000279866 | − | 0.000203334i | ||||
\(610\) | −18068.9 | − | 8143.59i | −1.19932 | − | 0.540532i | ||||
\(611\) | −2085.75 | − | 1515.38i | −0.138102 | − | 0.100337i | ||||
\(612\) | −1800.63 | + | 1308.23i | −0.118932 | + | 0.0864088i | ||||
\(613\) | 1279.79 | − | 929.823i | 0.0843235 | − | 0.0612646i | −0.544825 | − | 0.838550i | \(-0.683404\pi\) |
0.629148 | + | 0.777285i | \(0.283404\pi\) | |||||||
\(614\) | −17480.0 | − | 12699.9i | −1.14892 | − | 0.834736i | ||||
\(615\) | −4124.96 | + | 857.168i | −0.270462 | + | 0.0562022i | ||||
\(616\) | 179.907 | − | 130.710i | 0.0117673 | − | 0.00854944i | ||||
\(617\) | 1376.37 | − | 4236.04i | 0.0898065 | − | 0.276396i | −0.896059 | − | 0.443935i | \(-0.853582\pi\) |
0.985865 | + | 0.167539i | \(0.0535820\pi\) | |||||||
\(618\) | 29015.0 | 1.88860 | ||||||||
\(619\) | −812.796 | + | 2501.53i | −0.0527771 | + | 0.162431i | −0.973971 | − | 0.226673i | \(-0.927215\pi\) |
0.921194 | + | 0.389104i | \(0.127215\pi\) | |||||||
\(620\) | −37493.4 | + | 41261.2i | −2.42867 | + | 2.67272i | ||||
\(621\) | −1348.15 | − | 4149.18i | −0.0871165 | − | 0.268117i | ||||
\(622\) | −10464.4 | − | 32206.2i | −0.674574 | − | 2.07612i | ||||
\(623\) | 152.055 | + | 110.474i | 0.00977841 | + | 0.00710443i | ||||
\(624\) | 4162.97 | 0.267071 | ||||||||
\(625\) | −15340.2 | + | 2969.64i | −0.981773 | + | 0.190057i | ||||
\(626\) | −9891.85 | −0.631562 | ||||||||
\(627\) | −10458.1 | − | 7598.27i | −0.666120 | − | 0.483965i | ||||
\(628\) | 9463.21 | + | 29124.8i | 0.601311 | + | 1.85064i | ||||
\(629\) | −1436.23 | − | 4420.28i | −0.0910436 | − | 0.280203i | ||||
\(630\) | −45.5766 | + | 50.1567i | −0.00288225 | + | 0.00317189i | ||||
\(631\) | −5221.29 | + | 16069.5i | −0.329407 | + | 1.01381i | 0.640004 | + | 0.768371i | \(0.278933\pi\) |
−0.969412 | + | 0.245441i | \(0.921067\pi\) | |||||||
\(632\) | −20309.1 | −1.27825 | ||||||||
\(633\) | −4546.93 | + | 13994.0i | −0.285504 | + | 0.878692i | ||||
\(634\) | 33334.0 | − | 24218.6i | 2.08811 | − | 1.51710i | ||||
\(635\) | 12981.6 | − | 2697.58i | 0.811272 | − | 0.168583i | ||||
\(636\) | 9064.18 | + | 6585.51i | 0.565123 | + | 0.410586i | ||||
\(637\) | 9529.22 | − | 6923.38i | 0.592718 | − | 0.430635i | ||||
\(638\) | −2264.38 | + | 1645.17i | −0.140513 | + | 0.102089i | ||||
\(639\) | −5257.75 | − | 3819.98i | −0.325498 | − | 0.236488i | ||||
\(640\) | 27041.1 | + | 12187.3i | 1.67014 | + | 0.752730i | ||||
\(641\) | −23303.3 | + | 16930.8i | −1.43592 | + | 1.04326i | −0.447046 | + | 0.894511i | \(0.647524\pi\) |
−0.988875 | + | 0.148746i | \(0.952476\pi\) | |||||||
\(642\) | −7463.59 | + | 22970.6i | −0.458823 | + | 1.41211i | ||||
\(643\) | 10219.9 | 0.626801 | 0.313400 | − | 0.949621i | \(-0.398532\pi\) | ||||
0.313400 | + | 0.949621i | \(0.398532\pi\) | |||||||
\(644\) | −105.056 | + | 323.329i | −0.00642824 | + | 0.0197841i | ||||
\(645\) | −16201.3 | − | 7301.89i | −0.989032 | − | 0.445754i | ||||
\(646\) | −2226.17 | − | 6851.44i | −0.135584 | − | 0.417285i | ||||
\(647\) | −553.877 | − | 1704.66i | −0.0336555 | − | 0.103581i | 0.932818 | − | 0.360349i | \(-0.117342\pi\) |
−0.966473 | + | 0.256768i | \(0.917342\pi\) | |||||||
\(648\) | 2190.13 | + | 1591.22i | 0.132772 | + | 0.0964648i | ||||
\(649\) | −12716.6 | −0.769138 | ||||||||
\(650\) | 1964.22 | + | 20481.5i | 0.118528 | + | 1.23592i | ||||
\(651\) | −140.396 | −0.00845243 | ||||||||
\(652\) | −10272.3 | − | 7463.28i | −0.617017 | − | 0.448289i | ||||
\(653\) | −4142.49 | − | 12749.3i | −0.248252 | − | 0.764040i | −0.995085 | − | 0.0990282i | \(-0.968427\pi\) |
0.746833 | − | 0.665012i | \(-0.231573\pi\) | |||||||
\(654\) | −89.8820 | − | 276.628i | −0.00537410 | − | 0.0165398i | ||||
\(655\) | 1237.28 | + | 2165.76i | 0.0738086 | + | 0.129196i | ||||
\(656\) | 1568.40 | − | 4827.03i | 0.0933471 | − | 0.287293i | ||||
\(657\) | −21.9844 | −0.00130547 | ||||||||
\(658\) | −15.6244 | + | 48.0869i | −0.000925687 | + | 0.00284897i | ||||
\(659\) | 12492.5 | − | 9076.37i | 0.738453 | − | 0.536518i | −0.153773 | − | 0.988106i | \(-0.549142\pi\) |
0.892226 | + | 0.451589i | \(0.149142\pi\) | |||||||
\(660\) | 15992.1 | − | 17599.2i | 0.943171 | − | 1.03795i | ||||
\(661\) | −3524.55 | − | 2560.74i | −0.207397 | − | 0.150682i | 0.479238 | − | 0.877685i | \(-0.340913\pi\) |
−0.686635 | + | 0.727002i | \(0.740913\pi\) | |||||||
\(662\) | 1006.74 | − | 731.440i | 0.0591059 | − | 0.0429429i | ||||
\(663\) | −1376.65 | + | 1000.20i | −0.0806407 | + | 0.0585889i | ||||
\(664\) | −34300.0 | − | 24920.4i | −2.00467 | − | 1.45648i | ||||
\(665\) | −70.9202 | − | 124.140i | −0.00413559 | − | 0.00723900i | ||||
\(666\) | −9820.57 | + | 7135.06i | −0.571380 | + | 0.415132i | ||||
\(667\) | 615.790 | − | 1895.21i | 0.0357473 | − | 0.110019i | ||||
\(668\) | 29533.4 | 1.71060 | ||||||||
\(669\) | −4484.53 | + | 13802.0i | −0.259166 | + | 0.797631i | ||||
\(670\) | −1031.52 | + | 9402.12i | −0.0594793 | + | 0.542143i | ||||
\(671\) | 5411.64 | + | 16655.3i | 0.311347 | + | 0.958229i | ||||
\(672\) | 9.60139 | + | 29.5500i | 0.000551163 | + | 0.00169631i | ||||
\(673\) | 14252.6 | + | 10355.1i | 0.816341 | + | 0.593107i | 0.915662 | − | 0.401949i | \(-0.131667\pi\) |
−0.0993208 | + | 0.995055i | \(0.531667\pi\) | |||||||
\(674\) | −32214.8 | −1.84105 | ||||||||
\(675\) | −1714.06 | + | 2907.34i | −0.0977393 | + | 0.165783i | ||||
\(676\) | −15236.5 | −0.866894 | ||||||||
\(677\) | −2665.42 | − | 1936.54i | −0.151315 | − | 0.109937i | 0.509552 | − | 0.860440i | \(-0.329811\pi\) |
−0.660867 | + | 0.750503i | \(0.729811\pi\) | |||||||
\(678\) | 2854.96 | + | 8786.65i | 0.161717 | + | 0.497713i | ||||
\(679\) | −62.1476 | − | 191.271i | −0.00351253 | − | 0.0108104i | ||||
\(680\) | 6042.52 | − | 1255.64i | 0.340765 | − | 0.0708111i | ||||
\(681\) | −41.5482 | + | 127.872i | −0.00233793 | + | 0.00719541i | ||||
\(682\) | 75583.4 | 4.24375 | ||||||||
\(683\) | 1492.40 | − | 4593.13i | 0.0836091 | − | 0.257322i | −0.900509 | − | 0.434837i | \(-0.856806\pi\) |
0.984118 | + | 0.177515i | \(0.0568058\pi\) | |||||||
\(684\) | −9921.10 | + | 7208.10i | −0.554595 | + | 0.402937i | ||||
\(685\) | 1925.94 | − | 17554.5i | 0.107425 | − | 0.979159i | ||||
\(686\) | −373.780 | − | 271.567i | −0.0208032 | − | 0.0151144i | ||||
\(687\) | 10096.0 | − | 7335.17i | 0.560679 | − | 0.407357i | ||||
\(688\) | 17319.6 | − | 12583.4i | 0.959745 | − | 0.697295i | ||||
\(689\) | 6929.93 | + | 5034.89i | 0.383178 | + | 0.278395i | ||||
\(690\) | −2832.90 | + | 25821.3i | −0.156299 | + | 1.42464i | ||||
\(691\) | −18874.8 | + | 13713.3i | −1.03912 | + | 0.754964i | −0.970113 | − | 0.242652i | \(-0.921983\pi\) |
−0.0690054 | + | 0.997616i | \(0.521983\pi\) | |||||||
\(692\) | 12528.0 | − | 38557.3i | 0.688214 | − | 2.11811i | ||||
\(693\) | 59.8831 | 0.00328250 | ||||||||
\(694\) | 10574.6 | − | 32545.2i | 0.578393 | − | 1.78011i | ||||
\(695\) | −17134.0 | + | 3560.46i | −0.935151 | + | 0.194325i | ||||
\(696\) | 382.111 | + | 1176.02i | 0.0208102 | + | 0.0640471i | ||||
\(697\) | 641.092 | + | 1973.08i | 0.0348395 | + | 0.107225i | ||||
\(698\) | −44489.5 | − | 32323.5i | −2.41254 | − | 1.75281i | ||||
\(699\) | 8836.19 | 0.478134 | ||||||||
\(700\) | 241.228 | − | 104.779i | 0.0130251 | − | 0.00565753i | ||||
\(701\) | 27619.7 | 1.48813 | 0.744066 | − | 0.668106i | \(-0.232895\pi\) | ||||
0.744066 | + | 0.668106i | \(0.232895\pi\) | |||||||
\(702\) | 3595.51 | + | 2612.29i | 0.193310 | + | 0.140448i | ||||
\(703\) | −7913.36 | − | 24354.8i | −0.424549 | − | 1.30663i | ||||
\(704\) | −9898.86 | − | 30465.6i | −0.529939 | − | 1.63099i | ||||
\(705\) | −274.603 | + | 2502.95i | −0.0146697 | + | 0.133711i | ||||
\(706\) | −88.2778 | + | 271.691i | −0.00470592 | + | 0.0144833i | ||||
\(707\) | −52.5688 | −0.00279640 | ||||||||
\(708\) | −3727.86 | + | 11473.2i | −0.197884 | + | 0.609023i | ||||
\(709\) | −20888.3 | + | 15176.2i | −1.10645 | + | 0.803886i | −0.982101 | − | 0.188353i | \(-0.939685\pi\) |
−0.124352 | + | 0.992238i | \(0.539685\pi\) | |||||||
\(710\) | 19195.0 | + | 33599.3i | 1.01462 | + | 1.77600i | ||||
\(711\) | −4424.48 | − | 3214.57i | −0.233377 | − | 0.169558i | ||||
\(712\) | −36165.1 | + | 26275.5i | −1.90358 | + | 1.38303i | ||||
\(713\) | −43535.5 | + | 31630.4i | −2.28670 | + | 1.66138i | ||||
\(714\) | 26.9986 | + | 19.6156i | 0.00141512 | + | 0.00102815i | ||||
\(715\) | 12226.6 | − | 13455.3i | 0.639511 | − | 0.703776i | ||||
\(716\) | −37942.2 | + | 27566.6i | −1.98040 | + | 1.43884i | ||||
\(717\) | 2015.91 | − | 6204.33i | 0.105001 | − | 0.323159i | ||||
\(718\) | 37394.5 | 1.94366 | ||||||||
\(719\) | −5049.02 | + | 15539.3i | −0.261887 | + | 0.806005i | 0.730507 | + | 0.682905i | \(0.239284\pi\) |
−0.992394 | + | 0.123100i | \(0.960716\pi\) | |||||||
\(720\) | −2016.85 | − | 3530.33i | −0.104394 | − | 0.182733i | ||||
\(721\) | −87.6220 | − | 269.673i | −0.00452596 | − | 0.0139295i | ||||
\(722\) | −2106.70 | − | 6483.77i | −0.108592 | − | 0.334212i | ||||
\(723\) | −5583.89 | − | 4056.93i | −0.287230 | − | 0.208684i | ||||
\(724\) | 4747.20 | 0.243685 | ||||||||
\(725\) | −1413.96 | + | 614.165i | −0.0724321 | + | 0.0314614i | ||||
\(726\) | −13100.2 | −0.669689 | ||||||||
\(727\) | 5895.72 | + | 4283.49i | 0.300771 | + | 0.218523i | 0.727926 | − | 0.685655i | \(-0.240484\pi\) |
−0.427156 | + | 0.904178i | \(0.640484\pi\) | |||||||
\(728\) | −49.8401 | − | 153.392i | −0.00253736 | − | 0.00780918i | ||||
\(729\) | 225.273 | + | 693.320i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | 119.338 | + | 53.7855i | 0.00605056 | + | 0.00272697i | ||||
\(731\) | −2704.13 | + | 8322.45i | −0.136821 | + | 0.421090i | ||||
\(732\) | 16613.2 | 0.838853 | ||||||||
\(733\) | −3717.51 | + | 11441.3i | −0.187325 | + | 0.576528i | −0.999981 | − | 0.00621681i | \(-0.998021\pi\) |
0.812656 | + | 0.582744i | \(0.198021\pi\) | |||||||
\(734\) | −6139.43 | + | 4460.56i | −0.308734 | + | 0.224308i | ||||
\(735\) | −10487.9 | − | 4726.88i | −0.526330 | − | 0.237216i | ||||
\(736\) | 9634.77 | + | 7000.07i | 0.482530 | + | 0.350579i | ||||
\(737\) | 6761.48 | − | 4912.50i | 0.337941 | − | 0.245528i | ||||
\(738\) | 4383.61 | − | 3184.88i | 0.218649 | − | 0.158858i | ||||
\(739\) | 12267.2 | + | 8912.61i | 0.610629 | + | 0.443648i | 0.849636 | − | 0.527370i | \(-0.176822\pi\) |
−0.239007 | + | 0.971018i | \(0.576822\pi\) | |||||||
\(740\) | 46122.3 | − | 9584.25i | 2.29120 | − | 0.476113i | ||||
\(741\) | −7585.08 | + | 5510.89i | −0.376039 | + | 0.273208i | ||||
\(742\) | 51.9123 | − | 159.770i | 0.00256841 | − | 0.00790475i | ||||
\(743\) | −22772.8 | −1.12443 | −0.562216 | − | 0.826991i | \(-0.690051\pi\) | ||||
−0.562216 | + | 0.826991i | \(0.690051\pi\) | |||||||
\(744\) | 10318.7 | − | 31757.7i | 0.508471 | − | 1.56491i | ||||
\(745\) | 1448.40 | − | 1593.95i | 0.0712286 | − | 0.0783864i | ||||
\(746\) | 16560.7 | + | 50968.6i | 0.812776 | + | 2.50147i | ||||
\(747\) | −3528.05 | − | 10858.2i | −0.172804 | − | 0.531835i | ||||
\(748\) | −9473.39 | − | 6882.82i | −0.463077 | − | 0.336445i | ||||
\(749\) | 236.034 | 0.0115147 | ||||||||
\(750\) | 16417.3 | − | 11588.5i | 0.799302 | − | 0.564202i | ||||
\(751\) | −27855.5 | −1.35348 | −0.676739 | − | 0.736223i | \(-0.736608\pi\) | ||||
−0.676739 | + | 0.736223i | \(0.736608\pi\) | |||||||
\(752\) | −2454.05 | − | 1782.97i | −0.119002 | − | 0.0864604i | ||||
\(753\) | 3122.82 | + | 9611.04i | 0.151131 | + | 0.465134i | ||||
\(754\) | 627.306 | + | 1930.65i | 0.0302986 | + | 0.0932495i | ||||
\(755\) | 7916.11 | − | 8711.61i | 0.381585 | − | 0.419931i | ||||
\(756\) | 17.5547 | − | 54.0277i | 0.000844520 | − | 0.00259917i | ||||
\(757\) | 302.235 | 0.0145111 | 0.00725557 | − | 0.999974i | \(-0.497690\pi\) | ||||
0.00725557 | + | 0.999974i | \(0.497690\pi\) | |||||||
\(758\) | 17363.3 | − | 53438.7i | 0.832009 | − | 2.56066i | ||||
\(759\) | 18569.3 | − | 13491.4i | 0.888038 | − | 0.645198i | ||||
\(760\) | 33293.1 | − | 6918.32i | 1.58904 | − | 0.330202i | ||||
\(761\) | 3638.31 | + | 2643.38i | 0.173309 | + | 0.125917i | 0.671058 | − | 0.741404i | \(-0.265840\pi\) |
−0.497749 | + | 0.867321i | \(0.665840\pi\) | |||||||
\(762\) | −13795.6 | + | 10023.1i | −0.655854 | + | 0.476506i | ||||
\(763\) | −2.29962 | + | 1.67077i | −0.000109111 | + | 7.92739e-5i | ||||
\(764\) | −20344.0 | − | 14780.7i | −0.963375 | − | 0.699933i | ||||
\(765\) | 1515.15 | + | 682.876i | 0.0716085 | + | 0.0322738i | ||||
\(766\) | −35953.5 | + | 26121.7i | −1.69589 | + | 1.23214i | ||||
\(767\) | −2850.10 | + | 8771.71i | −0.134174 | + | 0.412944i | ||||
\(768\) | −21910.1 | −1.02944 | ||||||||
\(769\) | 753.619 | − | 2319.40i | 0.0353397 | − | 0.108764i | −0.931831 | − | 0.362894i | \(-0.881789\pi\) |
0.967170 | + | 0.254129i | \(0.0817889\pi\) | |||||||
\(770\) | −325.065 | − | 146.506i | −0.0152137 | − | 0.00685676i | ||||
\(771\) | 375.367 | + | 1155.26i | 0.0175337 | + | 0.0539633i | ||||
\(772\) | −6707.26 | − | 20642.8i | −0.312694 | − | 0.962372i | ||||
\(773\) | 30309.4 | + | 22021.1i | 1.41029 | + | 1.02464i | 0.993280 | + | 0.115733i | \(0.0369218\pi\) |
0.417009 | + | 0.908902i | \(0.363078\pi\) | |||||||
\(774\) | 22855.0 | 1.06138 | ||||||||
\(775\) | 40639.5 | + | 9025.89i | 1.88363 | + | 0.418348i | ||||
\(776\) | 47833.4 | 2.21278 | ||||||||
\(777\) | 95.9720 | + | 69.7278i | 0.00443112 | + | 0.00321939i | ||||
\(778\) | 1986.41 | + | 6113.53i | 0.0915375 | + | 0.281723i | ||||
\(779\) | 3532.29 | + | 10871.3i | 0.162461 | + | 0.500005i | ||||
\(780\) | −8555.41 | − | 14975.5i | −0.392734 | − | 0.687448i | ||||
\(781\) | 10565.9 | − | 32518.4i | 0.484094 | − | 1.48989i | ||||
\(782\) | 12791.3 | 0.584932 | ||||||||
\(783\) | −102.897 | + | 316.686i | −0.00469636 | + | 0.0144539i | ||||
\(784\) | 11211.9 | − | 8145.90i | 0.510745 | − | 0.371078i | ||||
\(785\) | 15378.0 | − | 16923.4i | 0.699191 | − | 0.769453i | ||||
\(786\) | −2595.23 | − | 1885.55i | −0.117772 | − | 0.0855664i | ||||
\(787\) | −24527.6 | + | 17820.4i | −1.11095 | + | 0.807150i | −0.982812 | − | 0.184607i | \(-0.940899\pi\) |
−0.128134 | + | 0.991757i | \(0.540899\pi\) | |||||||
\(788\) | 12847.8 | − | 9334.46i | 0.580816 | − | 0.421988i | ||||
\(789\) | 3676.26 | + | 2670.96i | 0.165879 | + | 0.120518i | ||||
\(790\) | 16152.9 | + | 28274.3i | 0.727463 | + | 1.27336i | ||||
\(791\) | 73.0437 | − | 53.0694i | 0.00328336 | − | 0.00238550i | ||||
\(792\) | −4401.25 | + | 13545.7i | −0.197464 | + | 0.607733i | ||||
\(793\) | 12701.4 | 0.568779 | ||||||||
\(794\) | −16834.8 | + | 51812.3i | −0.752451 | + | 2.31581i | ||||
\(795\) | 912.371 | − | 8316.09i | 0.0407025 | − | 0.370995i | ||||
\(796\) | −847.079 | − | 2607.04i | −0.0377185 | − | 0.116086i | ||||
\(797\) | −7301.19 | − | 22470.7i | −0.324493 | − | 0.998688i | −0.971669 | − | 0.236347i | \(-0.924050\pi\) |
0.647175 | − | 0.762341i | \(-0.275950\pi\) | |||||||
\(798\) | 148.757 | + | 108.078i | 0.00659892 | + | 0.00479439i | ||||
\(799\) | 1239.91 | 0.0548996 | ||||||||
\(800\) | −879.517 | − | 9170.94i | −0.0388695 | − | 0.405302i | ||||
\(801\) | −12037.8 | −0.531005 | ||||||||
\(802\) | −48166.6 | − | 34995.1i | −2.12072 | − | 1.54080i | ||||
\(803\) | −35.7420 | − | 110.002i | −0.00157074 | − | 0.00483425i | ||||
\(804\) | −2450.03 | − | 7540.43i | −0.107470 | − | 0.330759i | ||||
\(805\) | 248.545 | − | 51.6478i | 0.0108821 | − | 0.00226130i | ||||
\(806\) | 16940.1 | − | 52136.2i | 0.740309 | − | 2.27844i | ||||
\(807\) | −5675.65 | −0.247574 | ||||||||
\(808\) | 3863.67 | − | 11891.1i | 0.168222 | − | 0.517734i | ||||
\(809\) | 24729.0 | − | 17966.7i | 1.07469 | − | 0.780810i | 0.0979434 | − | 0.995192i | \(-0.468774\pi\) |
0.976750 | + | 0.214382i | \(0.0687736\pi\) | |||||||
\(810\) | 473.373 | − | 4314.70i | 0.0205341 | − | 0.187164i | ||||
\(811\) | −29914.5 | − | 21734.2i | −1.29524 | − | 0.941048i | −0.295345 | − | 0.955391i | \(-0.595435\pi\) |
−0.999897 | + | 0.0143423i | \(0.995435\pi\) | |||||||
\(812\) | 20.9924 | − | 15.2519i | 0.000907253 | − | 0.000659158i | ||||
\(813\) | 5083.01 | − | 3693.02i | 0.219273 | − | 0.159311i | ||||
\(814\) | −51667.6 | − | 37538.7i | −2.22475 | − | 1.61638i | ||||
\(815\) | −1033.98 | + | 9424.52i | −0.0444401 | + | 0.405063i | ||||
\(816\) | −1619.74 | + | 1176.81i | −0.0694881 | + | 0.0504860i | ||||
\(817\) | −14899.2 | + | 45855.0i | −0.638014 | + | 1.96360i | ||||
\(818\) | −61915.1 | −2.64647 | ||||||||
\(819\) | 13.4213 | − | 41.3064i | 0.000572621 | − | 0.00176235i | ||||
\(820\) | −20587.6 | + | 4278.12i | −0.876770 | + | 0.182193i | ||||
\(821\) | −2935.36 | − | 9034.11i | −0.124781 | − | 0.384035i | 0.869080 | − | 0.494671i | \(-0.164711\pi\) |
−0.993861 | + | 0.110636i | \(0.964711\pi\) | |||||||
\(822\) | 7018.51 | + | 21600.7i | 0.297808 | + | 0.916560i | ||||
\(823\) | 3845.46 | + | 2793.89i | 0.162873 | + | 0.118334i | 0.666236 | − | 0.745741i | \(-0.267904\pi\) |
−0.503363 | + | 0.864075i | \(0.667904\pi\) | |||||||
\(824\) | 67440.5 | 2.85121 | ||||||||
\(825\) | −17334.0 | − | 3849.83i | −0.731508 | − | 0.162465i | ||||
\(826\) | 180.882 | 0.00761947 | ||||||||
\(827\) | −10698.5 | − | 7772.89i | −0.449845 | − | 0.326832i | 0.339690 | − | 0.940538i | \(-0.389678\pi\) |
−0.789535 | + | 0.613706i | \(0.789678\pi\) | |||||||
\(828\) | −6728.61 | − | 20708.5i | −0.282410 | − | 0.869168i | ||||
\(829\) | −3155.27 | − | 9710.93i | −0.132192 | − | 0.406845i | 0.862951 | − | 0.505288i | \(-0.168614\pi\) |
−0.995143 | + | 0.0984431i | \(0.968614\pi\) | |||||||
\(830\) | −7413.57 | + | 67573.3i | −0.310035 | + | 2.82591i | ||||
\(831\) | −1383.84 | + | 4259.01i | −0.0577675 | + | 0.177790i | ||||
\(832\) | −23233.2 | −0.968109 | ||||||||
\(833\) | −1750.52 | + | 5387.54i | −0.0728114 | + | 0.224090i | ||||
\(834\) | 18208.4 | − | 13229.2i | 0.756001 | − | 0.549267i | ||||
\(835\) | −10939.2 | − | 19148.2i | −0.453374 | − | 0.793592i | ||||
\(836\) | −52196.5 | − | 37923.0i | −2.15939 | − | 1.56889i | ||||
\(837\) | 7274.70 | − | 5285.38i | 0.300419 | − | 0.218267i | ||||
\(838\) | −16141.8 | + | 11727.7i | −0.665405 | + | 0.483445i | ||||
\(839\) | 5438.55 | + | 3951.34i | 0.223790 | + | 0.162593i | 0.694031 | − | 0.719945i | \(-0.255833\pi\) |
−0.470241 | + | 0.882538i | \(0.655833\pi\) | |||||||
\(840\) | −105.935 | + | 116.581i | −0.00435132 | + | 0.00478859i | ||||
\(841\) | 19608.1 | − | 14246.1i | 0.803972 | − | 0.584120i | ||||
\(842\) | 22138.8 | − | 68136.2i | 0.906120 | − | 2.78875i | ||||
\(843\) | 6208.48 | 0.253655 | ||||||||
\(844\) | −22693.7 | + | 69844.1i | −0.925533 | + | 2.84850i | ||||
\(845\) | 5643.63 | + | 9878.69i | 0.229759 | + | 0.402174i | ||||
\(846\) | −1000.71 | − | 3079.86i | −0.0406679 | − | 0.125163i | ||||
\(847\) | 39.5611 | + | 121.757i | 0.00160488 | + | 0.00493933i | ||||
\(848\) | 8153.61 | + | 5923.94i | 0.330184 | + | 0.239893i | ||||
\(849\) | 10196.7 | 0.412191 | ||||||||
\(850\) | −6554.06 | − | 7413.74i | −0.264474 | − | 0.299164i | ||||
\(851\) | 45469.4 | 1.83158 | ||||||||
\(852\) | −26241.4 | − | 19065.5i | −1.05518 | − | 0.766635i | ||||
\(853\) | −1169.79 | − | 3600.24i | −0.0469552 | − | 0.144513i | 0.924830 | − | 0.380381i | \(-0.124207\pi\) |
−0.971785 | + | 0.235867i | \(0.924207\pi\) | |||||||
\(854\) | −76.9754 | − | 236.906i | −0.00308436 | − | 0.00949269i | ||||
\(855\) | 8348.20 | + | 3762.51i | 0.333921 | + | 0.150497i | ||||
\(856\) | −17347.9 | + | 53391.2i | −0.692684 | + | 2.13186i | ||||
\(857\) | 13421.7 | 0.534979 | 0.267489 | − | 0.963561i | \(-0.413806\pi\) | ||||
0.267489 | + | 0.963561i | \(0.413806\pi\) | |||||||
\(858\) | −7225.48 | + | 22237.7i | −0.287499 | + | 0.884830i | ||||
\(859\) | −398.008 | + | 289.170i | −0.0158089 | + | 0.0114859i | −0.595662 | − | 0.803235i | \(-0.703110\pi\) |
0.579853 | + | 0.814721i | \(0.303110\pi\) | |||||||
\(860\) | −80860.6 | − | 36443.7i | −3.20619 | − | 1.44502i | ||||
\(861\) | −42.8391 | − | 31.1244i | −0.00169565 | − | 0.00123196i | ||||
\(862\) | −49489.8 | + | 35956.5i | −1.95549 | + | 1.42075i | ||||
\(863\) | 6543.41 | − | 4754.07i | 0.258100 | − | 0.187521i | −0.451209 | − | 0.892418i | \(-0.649007\pi\) |
0.709309 | + | 0.704898i | \(0.249007\pi\) | |||||||
\(864\) | −1609.95 | − | 1169.70i | −0.0633932 | − | 0.0460579i | ||||
\(865\) | −29639.2 | + | 6159.05i | −1.16505 | + | 0.242097i | ||||
\(866\) | 3014.85 | − | 2190.41i | 0.118301 | − | 0.0859507i | ||||
\(867\) | −4301.71 | + | 13239.3i | −0.168505 | + | 0.518605i | ||||
\(868\) | −700.714 | −0.0274007 | ||||||||
\(869\) | 8891.36 | − | 27364.8i | 0.347087 | − | 1.06822i | ||||
\(870\) | 1333.34 | − | 1467.33i | 0.0519592 | − | 0.0571806i | ||||
\(871\) | −1873.15 | − | 5764.97i | −0.0728695 | − | 0.224269i | ||||
\(872\) | −208.915 | − | 642.975i | −0.00811326 | − | 0.0249701i | ||||
\(873\) | 10420.9 | + | 7571.21i | 0.404001 | + | 0.293524i | ||||
\(874\) | 70477.7 | 2.72762 | ||||||||
\(875\) | −157.285 | − | 117.591i | −0.00607680 | − | 0.00454320i | ||||
\(876\) | −109.724 | −0.00423200 | ||||||||
\(877\) | −9708.54 | − | 7053.67i | −0.373813 | − | 0.271591i | 0.384977 | − | 0.922926i | \(-0.374209\pi\) |
−0.758790 | + | 0.651335i | \(0.774209\pi\) | |||||||
\(878\) | −14717.1 | − | 45294.6i | −0.565693 | − | 1.74102i | ||||
\(879\) | 7117.53 | + | 21905.5i | 0.273115 | + | 0.840562i | ||||
\(880\) | 14385.6 | − | 15831.2i | 0.551066 | − | 0.606443i | ||||
\(881\) | −706.220 | + | 2173.52i | −0.0270070 | + | 0.0831190i | −0.963652 | − | 0.267162i | \(-0.913914\pi\) |
0.936645 | + | 0.350281i | \(0.113914\pi\) | |||||||
\(882\) | 14795.2 | 0.564830 | ||||||||
\(883\) | 5941.34 | − | 18285.6i | 0.226435 | − | 0.696895i | −0.771708 | − | 0.635977i | \(-0.780597\pi\) |
0.998143 | − | 0.0609179i | \(-0.0194028\pi\) | |||||||
\(884\) | −6870.87 | + | 4991.98i | −0.261417 | + | 0.189930i | ||||
\(885\) | 8819.50 | − | 1832.70i | 0.334988 | − | 0.0696107i | ||||
\(886\) | 27685.8 | + | 20114.9i | 1.04980 | + | 0.762723i | ||||
\(887\) | −12097.1 | + | 8789.05i | −0.457926 | + | 0.332703i | −0.792717 | − | 0.609589i | \(-0.791334\pi\) |
0.334791 | + | 0.942292i | \(0.391334\pi\) | |||||||
\(888\) | −22826.2 | + | 16584.2i | −0.862611 | + | 0.626723i | ||||
\(889\) | 134.818 | + | 97.9510i | 0.00508622 | + | 0.00369536i | ||||
\(890\) | 65345.0 | + | 29450.8i | 2.46109 | + | 1.10921i | ||||
\(891\) | −3102.89 | + | 2254.38i | −0.116668 | + | 0.0847639i | ||||
\(892\) | −22382.3 | + | 68885.6i | −0.840151 | + | 2.58572i | ||||
\(893\) | 6831.64 | 0.256005 | ||||||||
\(894\) | −855.950 | + | 2634.34i | −0.0320215 | + | 0.0985521i | ||||
\(895\) | 31926.8 | + | 14389.3i | 1.19240 | + | 0.537410i | ||||
\(896\) | 115.198 | + | 354.543i | 0.00429520 | + | 0.0132193i | ||||
\(897\) | −5144.29 | − | 15832.5i | −0.191486 | − | 0.589333i | ||||
\(898\) | 40475.3 | + | 29407.0i | 1.50410 | + | 1.09279i | ||||
\(899\) | 4107.26 | 0.152375 | ||||||||
\(900\) | −8554.85 | + | 14510.5i | −0.316846 | + | 0.537427i | ||||
\(901\) | −4119.61 | −0.152324 | ||||||||
\(902\) | 23062.9 | + | 16756.1i | 0.851340 | + | 0.618535i | ||||
\(903\) | −69.0194 | − | 212.420i | −0.00254355 | − | 0.00782823i | ||||
\(904\) | 6635.86 | + | 20423.1i | 0.244143 | + | 0.751395i | ||||
\(905\) | −1758.37 | − | 3077.87i | −0.0645857 | − | 0.113052i | ||||
\(906\) | −4678.12 | + | 14397.8i | −0.171545 | + | 0.527963i | ||||
\(907\) | 48744.8 | 1.78450 | 0.892251 | − | 0.451540i | \(-0.149125\pi\) | ||||
0.892251 | + | 0.451540i | \(0.149125\pi\) | |||||||
\(908\) | −207.367 | + | 638.210i | −0.00757898 | + | 0.0233257i | ||||
\(909\) | 2723.89 | − | 1979.02i | 0.0993903 | − | 0.0722113i | ||||
\(910\) | −173.912 | + | 191.389i | −0.00633531 | + | 0.00697195i | ||||
\(911\) | 28367.9 | + | 20610.5i | 1.03169 | + | 0.749568i | 0.968647 | − | 0.248442i | \(-0.0799186\pi\) |
0.0630456 | + | 0.998011i | \(0.479919\pi\) | |||||||
\(912\) | −8924.45 | + | 6483.99i | −0.324033 | + | 0.235424i | ||||
\(913\) | 48594.9 | − | 35306.3i | 1.76151 | − | 1.27981i | ||||
\(914\) | 19542.3 | + | 14198.3i | 0.707224 | + | 0.513828i | ||||
\(915\) | −6153.54 | − | 10771.2i | −0.222327 | − | 0.389165i | ||||
\(916\) | 50389.1 | − | 36609.8i | 1.81758 | − | 1.32055i | ||||
\(917\) | −9.68744 | + | 29.8149i | −0.000348863 | + | 0.00107369i | ||||
\(918\) | −2137.41 | −0.0768465 | ||||||||
\(919\) | −6229.66 | + | 19172.9i | −0.223610 | + | 0.688200i | 0.774820 | + | 0.632182i | \(0.217841\pi\) |
−0.998430 | + | 0.0560183i | \(0.982159\pi\) | |||||||
\(920\) | −6584.59 | + | 60017.3i | −0.235965 | + | 2.15077i | ||||
\(921\) | −4179.05 | − | 12861.8i | −0.149516 | − | 0.460164i | ||||
\(922\) | −2714.43 | − | 8354.15i | −0.0969576 | − | 0.298405i | ||||
\(923\) | −20062.6 | − | 14576.3i | −0.715460 | − | 0.519812i | ||||
\(924\) | 298.877 | 0.0106410 | ||||||||
\(925\) | −23297.8 | − | 26353.7i | −0.828136 | − | 0.936760i | ||||
\(926\) | −9046.76 | −0.321053 | ||||||||
\(927\) | 14692.4 | + | 10674.7i | 0.520563 | + | 0.378211i | ||||
\(928\) | −280.888 | − | 864.483i | −0.00993598 | − | 0.0305798i | ||||
\(929\) | 6866.91 | + | 21134.2i | 0.242514 | + | 0.746383i | 0.996035 | + | 0.0889586i | \(0.0283539\pi\) |
−0.753521 | + | 0.657424i | \(0.771646\pi\) | |||||||
\(930\) | −52420.2 | + | 10893.0i | −1.84831 | + | 0.384080i | ||||
\(931\) | −9645.01 | + | 29684.3i | −0.339530 | + | 1.04497i | ||||
\(932\) | 44101.4 | 1.54999 | ||||||||
\(933\) | 6549.79 | − | 20158.2i | 0.229829 | − | 0.707341i | ||||
\(934\) | −15294.6 | + | 11112.2i | −0.535818 | + | 0.389295i | ||||
\(935\) | −953.562 | + | 8691.53i | −0.0333527 | + | 0.304004i | ||||
\(936\) | 8357.15 | + | 6071.83i | 0.291840 | + | 0.212034i | ||||
\(937\) | −6572.08 | + | 4774.90i | −0.229136 | + | 0.166477i | −0.696430 | − | 0.717625i | \(-0.745229\pi\) |
0.467293 | + | 0.884102i | \(0.345229\pi\) | |||||||
\(938\) | −96.1755 | + | 69.8756i | −0.00334781 | + | 0.00243232i | ||||
\(939\) | −5008.96 | − | 3639.22i | −0.174080 | − | 0.126477i | ||||
\(940\) | −1370.54 | + | 12492.2i | −0.0475554 | + | 0.433458i | ||||
\(941\) | 33838.2 | − | 24584.9i | 1.17226 | − | 0.851694i | 0.180979 | − | 0.983487i | \(-0.442073\pi\) |
0.991277 | + | 0.131793i | \(0.0420734\pi\) | |||||||
\(942\) | −9087.83 | + | 27969.5i | −0.314328 | + | 0.967403i | ||||
\(943\) | −20296.2 | −0.700885 | ||||||||
\(944\) | −3353.37 | + | 10320.6i | −0.115617 | + | 0.355834i | ||||
\(945\) | −41.5315 | + | 8.63026i | −0.00142965 | + | 0.000297082i | ||||
\(946\) | 37157.3 | + | 114359.i | 1.27705 | + | 3.93035i | ||||
\(947\) | 10149.2 | + | 31236.0i | 0.348263 | + | 1.07184i | 0.959814 | + | 0.280638i | \(0.0905459\pi\) |
−0.611551 | + | 0.791205i | \(0.709454\pi\) | |||||||
\(948\) | −22082.6 | − | 16043.9i | −0.756549 | − | 0.549665i | ||||
\(949\) | −83.8885 | −0.00286948 | ||||||||
\(950\) | −36111.6 | − | 40848.2i | −1.23328 | − | 1.39504i | ||||
\(951\) | 25789.5 | 0.879370 | ||||||||
\(952\) | 62.7537 | + | 45.5932i | 0.00213641 | + | 0.00155219i | ||||
\(953\) | −3887.24 | − | 11963.7i | −0.132130 | − | 0.406655i | 0.863002 | − | 0.505200i | \(-0.168581\pi\) |
−0.995133 | + | 0.0985447i | \(0.968581\pi\) | |||||||
\(954\) | 3324.87 | + | 10232.9i | 0.112837 | + | 0.347277i | ||||
\(955\) | −2047.76 | + | 18664.9i | −0.0693863 | + | 0.632442i | ||||
\(956\) | 10061.4 | − | 30965.8i | 0.340386 | − | 1.04760i | ||||
\(957\) | −1751.88 | −0.0591746 | ||||||||
\(958\) | 15935.6 | − | 49044.8i | 0.537429 | − | 1.65404i | ||||
\(959\) | 179.568 | − | 130.464i | 0.00604645 | − | 0.00439300i | ||||
\(960\) | 11255.9 | + | 19702.5i | 0.378420 | + | 0.662392i | ||||
\(961\) | −65630.2 | − | 47683.1i | −2.20302 | − | 1.60059i | ||||
\(962\) | −37473.5 | + | 27226.1i | −1.25592 | + | 0.912479i | ||||
\(963\) | −12230.3 | + | 8885.80i | −0.409257 | + | 0.297343i | ||||
\(964\) | −27869.2 | − | 20248.1i | −0.931126 | − | 0.676502i | ||||
\(965\) | −10899.5 | + | 11994.8i | −0.363593 | + | 0.400131i | ||||
\(966\) | −264.130 | + | 191.902i | −0.00879735 | + | 0.00639165i | ||||
\(967\) | 12942.6 | − | 39833.2i | 0.430409 | − | 1.32466i | −0.467309 | − | 0.884094i | \(-0.654777\pi\) |
0.897718 | − | 0.440570i | \(-0.145223\pi\) | |||||||
\(968\) | −30449.2 | −1.01103 | ||||||||
\(969\) | 1393.38 | − | 4288.39i | 0.0461939 | − | 0.142170i | ||||
\(970\) | −38044.6 | − | 66593.9i | −1.25932 | − | 2.20433i | ||||
\(971\) | 17116.5 | + | 52679.3i | 0.565701 | + | 1.74105i | 0.665860 | + | 0.746077i | \(0.268065\pi\) |
−0.100159 | + | 0.994971i | \(0.531935\pi\) | |||||||
\(972\) | 1124.34 | + | 3460.36i | 0.0371020 | + | 0.114188i | ||||
\(973\) | −177.942 | − | 129.283i | −0.00586287 | − | 0.00425963i | ||||
\(974\) | −15296.2 | −0.503204 | ||||||||
\(975\) | −6540.53 | + | 11093.9i | −0.214835 | + | 0.364399i | ||||
\(976\) | 14944.2 | 0.490117 | ||||||||
\(977\) | 28690.5 | + | 20844.9i | 0.939498 | + | 0.682585i | 0.948300 | − | 0.317376i | \(-0.102802\pi\) |
−0.00880161 | + | 0.999961i | \(0.502802\pi\) | |||||||
\(978\) | −3768.03 | − | 11596.8i | −0.123199 | − | 0.379167i | ||||
\(979\) | −19570.9 | − | 60233.0i | −0.638906 | − | 1.96635i | ||||
\(980\) | −52345.2 | − | 23591.8i | −1.70623 | − | 0.768994i | ||||
\(981\) | 56.2581 | − | 173.145i | 0.00183097 | − | 0.00563515i | ||||
\(982\) | −4476.20 | −0.145459 | ||||||||
\(983\) | −10713.9 | + | 32974.0i | −0.347630 | + | 1.06989i | 0.612531 | + | 0.790447i | \(0.290151\pi\) |
−0.960161 | + | 0.279448i | \(0.909849\pi\) | |||||||
\(984\) | 10189.0 | − | 7402.71i | 0.330093 | − | 0.239827i | ||||
\(985\) | −10810.9 | − | 4872.43i | −0.349709 | − | 0.157613i | ||||
\(986\) | −789.842 | − | 573.854i | −0.0255108 | − | 0.0185347i | ||||
\(987\) | −25.6030 | + | 18.6017i | −0.000825687 | + | 0.000599896i | ||||
\(988\) | −37857.1 | + | 27504.8i | −1.21902 | + | 0.885673i | ||||
\(989\) | −69259.4 | − | 50319.9i | −2.22682 | − | 1.61788i | ||||
\(990\) | 22358.9 | − | 4646.19i | 0.717790 | − | 0.149157i | ||||
\(991\) | 30160.4 | − | 21912.8i | 0.966778 | − | 0.702405i | 0.0120626 | − | 0.999927i | \(-0.496160\pi\) |
0.954715 | + | 0.297522i | \(0.0961603\pi\) | |||||||
\(992\) | −7585.22 | + | 23344.9i | −0.242773 | + | 0.747179i | ||||
\(993\) | 778.884 | 0.0248914 | ||||||||
\(994\) | −150.290 | + | 462.544i | −0.00479567 | + | 0.0147596i | ||||
\(995\) | −1376.53 | + | 1514.86i | −0.0438583 | + | 0.0482656i | ||||
\(996\) | −17608.5 | − | 54193.3i | −0.560186 | − | 1.72408i | ||||
\(997\) | −10625.0 | − | 32700.3i | −0.337509 | − | 1.03875i | −0.965473 | − | 0.260503i | \(-0.916111\pi\) |
0.627964 | − | 0.778242i | \(-0.283889\pi\) | |||||||
\(998\) | 21323.5 | + | 15492.4i | 0.676335 | + | 0.491386i | ||||
\(999\) | −7597.86 | −0.240626 |
(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 | 75.4.g.b.16.7 | ✓ | 28 | |
3.2 | odd | 2 | 225.4.h.a.91.1 | 28 | |||
25.6 | even | 5 | 1875.4.a.g.1.2 | 14 | |||
25.11 | even | 5 | inner | 75.4.g.b.61.7 | yes | 28 | |
25.19 | even | 10 | 1875.4.a.f.1.13 | 14 | |||
75.11 | odd | 10 | 225.4.h.a.136.1 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.g.b.16.7 | ✓ | 28 | 1.1 | even | 1 | trivial | |
75.4.g.b.61.7 | yes | 28 | 25.11 | even | 5 | inner | |
225.4.h.a.91.1 | 28 | 3.2 | odd | 2 | |||
225.4.h.a.136.1 | 28 | 75.11 | odd | 10 | |||
1875.4.a.f.1.13 | 14 | 25.19 | even | 10 | |||
1875.4.a.g.1.2 | 14 | 25.6 | even | 5 |