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 | 16.2 | ||
Character | \(\chi\) | \(=\) | 75.16 |
Dual form | 75.4.g.b.61.2 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.16070 | − | 2.29638i | −1.11748 | − | 0.811894i | −0.133651 | − | 0.991028i | \(-0.542670\pi\) |
−0.983825 | + | 0.179135i | \(0.942670\pi\) | |||||||
\(3\) | 0.927051 | + | 2.85317i | 0.178411 | + | 0.549093i | ||||
\(4\) | 2.24451 | + | 6.90789i | 0.280564 | + | 0.863487i | ||||
\(5\) | −11.0852 | − | 1.45535i | −0.991492 | − | 0.130171i | ||||
\(6\) | 3.62184 | − | 11.1469i | 0.246435 | − | 0.758449i | ||||
\(7\) | 22.0918 | 1.19284 | 0.596422 | − | 0.802671i | \(-0.296589\pi\) | ||||
0.596422 | + | 0.802671i | \(0.296589\pi\) | |||||||
\(8\) | −0.889297 | + | 2.73697i | −0.0393017 | + | 0.120958i | ||||
\(9\) | −7.28115 | + | 5.29007i | −0.269672 | + | 0.195928i | ||||
\(10\) | 31.6950 | + | 30.0558i | 1.00228 | + | 0.950448i | ||||
\(11\) | 31.5999 | + | 22.9587i | 0.866158 | + | 0.629301i | 0.929553 | − | 0.368688i | \(-0.120193\pi\) |
−0.0633953 | + | 0.997988i | \(0.520193\pi\) | |||||||
\(12\) | −17.6286 | + | 12.8079i | −0.424079 | + | 0.308111i | ||||
\(13\) | 55.3321 | − | 40.2012i | 1.18049 | − | 0.857676i | 0.188264 | − | 0.982119i | \(-0.439714\pi\) |
0.992227 | + | 0.124442i | \(0.0397141\pi\) | |||||||
\(14\) | −69.8255 | − | 50.7312i | −1.33297 | − | 0.968462i | ||||
\(15\) | −6.12419 | − | 32.9772i | −0.105417 | − | 0.567645i | ||||
\(16\) | 56.1056 | − | 40.7631i | 0.876650 | − | 0.636923i | ||||
\(17\) | 31.1744 | − | 95.9450i | 0.444759 | − | 1.36883i | −0.437988 | − | 0.898981i | \(-0.644309\pi\) |
0.882747 | − | 0.469848i | \(-0.155691\pi\) | |||||||
\(18\) | 35.1615 | 0.460425 | ||||||||
\(19\) | −29.0621 | + | 89.4438i | −0.350910 | + | 1.07999i | 0.607433 | + | 0.794371i | \(0.292199\pi\) |
−0.958343 | + | 0.285619i | \(0.907801\pi\) | |||||||
\(20\) | −14.8275 | − | 79.8420i | −0.165776 | − | 0.892661i | ||||
\(21\) | 20.4802 | + | 63.0316i | 0.212817 | + | 0.654982i | ||||
\(22\) | −47.1559 | − | 145.131i | −0.456985 | − | 1.40646i | ||||
\(23\) | 130.565 | + | 94.8612i | 1.18368 | + | 0.859997i | 0.992582 | − | 0.121573i | \(-0.0387939\pi\) |
0.191102 | + | 0.981570i | \(0.438794\pi\) | |||||||
\(24\) | −8.63347 | −0.0734292 | ||||||||
\(25\) | 120.764 | + | 32.2658i | 0.966111 | + | 0.258126i | ||||
\(26\) | −267.205 | −2.01551 | ||||||||
\(27\) | −21.8435 | − | 15.8702i | −0.155695 | − | 0.113119i | ||||
\(28\) | 49.5852 | + | 152.608i | 0.334669 | + | 1.03000i | ||||
\(29\) | −15.8462 | − | 48.7695i | −0.101468 | − | 0.312285i | 0.887418 | − | 0.460966i | \(-0.152497\pi\) |
−0.988885 | + | 0.148681i | \(0.952497\pi\) | |||||||
\(30\) | −56.3715 | + | 118.294i | −0.343066 | + | 0.719917i | ||||
\(31\) | −80.4233 | + | 247.517i | −0.465950 | + | 1.43405i | 0.391834 | + | 0.920036i | \(0.371841\pi\) |
−0.857784 | + | 0.514011i | \(0.828159\pi\) | |||||||
\(32\) | −247.918 | −1.36957 | ||||||||
\(33\) | −36.2103 | + | 111.444i | −0.191012 | + | 0.587875i | ||||
\(34\) | −318.859 | + | 231.665i | −1.60835 | + | 1.16854i | ||||
\(35\) | −244.892 | − | 32.1513i | −1.18269 | − | 0.155273i | ||||
\(36\) | −52.8858 | − | 38.4238i | −0.244842 | − | 0.177888i | ||||
\(37\) | 70.1129 | − | 50.9400i | 0.311527 | − | 0.226337i | −0.421025 | − | 0.907049i | \(-0.638329\pi\) |
0.732551 | + | 0.680712i | \(0.238329\pi\) | |||||||
\(38\) | 297.254 | − | 215.967i | 1.26897 | − | 0.921961i | ||||
\(39\) | 165.996 | + | 120.603i | 0.681556 | + | 0.495180i | ||||
\(40\) | 13.8413 | − | 29.0457i | 0.0547126 | − | 0.114813i | ||||
\(41\) | 42.4765 | − | 30.8610i | 0.161798 | − | 0.117553i | −0.503940 | − | 0.863739i | \(-0.668117\pi\) |
0.665738 | + | 0.746185i | \(0.268117\pi\) | |||||||
\(42\) | 80.0128 | − | 246.254i | 0.293958 | − | 0.904711i | ||||
\(43\) | −53.3748 | −0.189293 | −0.0946463 | − | 0.995511i | \(-0.530172\pi\) | ||||
−0.0946463 | + | 0.995511i | \(0.530172\pi\) | |||||||
\(44\) | −87.6698 | + | 269.820i | −0.300380 | + | 0.924475i | ||||
\(45\) | 88.4120 | − | 48.0449i | 0.292882 | − | 0.159158i | ||||
\(46\) | −194.840 | − | 599.656i | −0.624512 | − | 1.92205i | ||||
\(47\) | 74.7809 | + | 230.152i | 0.232083 | + | 0.714279i | 0.997495 | + | 0.0707380i | \(0.0225354\pi\) |
−0.765412 | + | 0.643541i | \(0.777465\pi\) | |||||||
\(48\) | 168.317 | + | 122.289i | 0.506134 | + | 0.367728i | ||||
\(49\) | 145.047 | 0.422876 | ||||||||
\(50\) | −307.604 | − | 379.302i | −0.870035 | − | 1.07283i | ||||
\(51\) | 302.648 | 0.830964 | ||||||||
\(52\) | 401.899 | + | 291.997i | 1.07179 | + | 0.778705i | ||||
\(53\) | 18.2798 | + | 56.2594i | 0.0473759 | + | 0.145808i | 0.971946 | − | 0.235204i | \(-0.0755757\pi\) |
−0.924570 | + | 0.381012i | \(0.875576\pi\) | |||||||
\(54\) | 32.5965 | + | 100.322i | 0.0821450 | + | 0.252816i | ||||
\(55\) | −316.879 | − | 300.491i | −0.776872 | − | 0.736695i | ||||
\(56\) | −19.6461 | + | 60.4646i | −0.0468808 | + | 0.144284i | ||||
\(57\) | −282.140 | −0.655621 | ||||||||
\(58\) | −61.9084 | + | 190.534i | −0.140155 | + | 0.431352i | ||||
\(59\) | 524.396 | − | 380.996i | 1.15713 | − | 0.840703i | 0.167716 | − | 0.985835i | \(-0.446361\pi\) |
0.989412 | + | 0.145132i | \(0.0463607\pi\) | |||||||
\(60\) | 214.057 | − | 116.323i | 0.460577 | − | 0.250287i | ||||
\(61\) | −530.204 | − | 385.216i | −1.11288 | − | 0.808555i | −0.129765 | − | 0.991545i | \(-0.541422\pi\) |
−0.983115 | + | 0.182990i | \(0.941422\pi\) | |||||||
\(62\) | 822.588 | − | 597.645i | 1.68498 | − | 1.22421i | ||||
\(63\) | −160.854 | + | 116.867i | −0.321677 | + | 0.233712i | ||||
\(64\) | 334.749 | + | 243.209i | 0.653807 | + | 0.475018i | ||||
\(65\) | −671.875 | + | 365.111i | −1.28209 | + | 0.696714i | ||||
\(66\) | 370.367 | − | 269.088i | 0.690744 | − | 0.501855i | ||||
\(67\) | 240.635 | − | 740.598i | 0.438779 | − | 1.35042i | −0.450384 | − | 0.892835i | \(-0.648713\pi\) |
0.889164 | − | 0.457589i | \(-0.151287\pi\) | |||||||
\(68\) | 732.749 | 1.30675 | ||||||||
\(69\) | −149.614 | + | 460.466i | −0.261036 | + | 0.803385i | ||||
\(70\) | 700.198 | + | 663.986i | 1.19557 | + | 1.13374i | ||||
\(71\) | 69.2398 | + | 213.098i | 0.115736 | + | 0.356199i | 0.992100 | − | 0.125451i | \(-0.0400378\pi\) |
−0.876364 | + | 0.481650i | \(0.840038\pi\) | |||||||
\(72\) | −8.00367 | − | 24.6328i | −0.0131006 | − | 0.0403194i | ||||
\(73\) | −281.749 | − | 204.703i | −0.451729 | − | 0.328200i | 0.338549 | − | 0.940949i | \(-0.390064\pi\) |
−0.790278 | + | 0.612748i | \(0.790064\pi\) | |||||||
\(74\) | −338.583 | −0.531886 | ||||||||
\(75\) | 19.8946 | + | 374.472i | 0.0306297 | + | 0.576537i | ||||
\(76\) | −683.098 | −1.03101 | ||||||||
\(77\) | 698.099 | + | 507.198i | 1.03319 | + | 0.750657i | ||||
\(78\) | −247.713 | − | 762.382i | −0.359590 | − | 1.10670i | ||||
\(79\) | 49.9257 | + | 153.655i | 0.0711022 | + | 0.218830i | 0.980293 | − | 0.197550i | \(-0.0632985\pi\) |
−0.909191 | + | 0.416380i | \(0.863299\pi\) | |||||||
\(80\) | −681.267 | + | 370.214i | −0.952099 | + | 0.517390i | ||||
\(81\) | 25.0304 | − | 77.0356i | 0.0343352 | − | 0.105673i | ||||
\(82\) | −205.124 | −0.276246 | ||||||||
\(83\) | −12.3245 | + | 37.9308i | −0.0162986 | + | 0.0501620i | −0.958875 | − | 0.283829i | \(-0.908395\pi\) |
0.942576 | + | 0.333991i | \(0.108395\pi\) | |||||||
\(84\) | −389.447 | + | 282.950i | −0.505859 | + | 0.367528i | ||||
\(85\) | −485.209 | + | 1018.20i | −0.619156 | + | 1.29929i | ||||
\(86\) | 168.702 | + | 122.569i | 0.211530 | + | 0.153685i | ||||
\(87\) | 124.457 | − | 90.4236i | 0.153370 | − | 0.111430i | ||||
\(88\) | −90.9391 | + | 66.0711i | −0.110161 | + | 0.0800364i | ||||
\(89\) | 375.213 | + | 272.608i | 0.446882 | + | 0.324679i | 0.788364 | − | 0.615210i | \(-0.210929\pi\) |
−0.341481 | + | 0.939889i | \(0.610929\pi\) | |||||||
\(90\) | −389.773 | − | 51.1724i | −0.456508 | − | 0.0599339i | ||||
\(91\) | 1222.39 | − | 888.115i | 1.40814 | − | 1.02307i | ||||
\(92\) | −362.236 | + | 1114.85i | −0.410497 | + | 1.26338i | ||||
\(93\) | −780.766 | −0.870555 | ||||||||
\(94\) | 292.157 | − | 899.167i | 0.320571 | − | 0.986617i | ||||
\(95\) | 452.331 | − | 949.208i | 0.488508 | − | 1.02512i | ||||
\(96\) | −229.832 | − | 707.352i | −0.244346 | − | 0.752018i | ||||
\(97\) | 177.512 | + | 546.326i | 0.185810 | + | 0.571866i | 0.999961 | − | 0.00878766i | \(-0.00279724\pi\) |
−0.814151 | + | 0.580653i | \(0.802797\pi\) | |||||||
\(98\) | −458.449 | − | 333.082i | −0.472554 | − | 0.343331i | ||||
\(99\) | −351.537 | −0.356877 | ||||||||
\(100\) | 48.1674 | + | 906.645i | 0.0481674 | + | 0.906645i | ||||
\(101\) | −1074.69 | −1.05877 | −0.529383 | − | 0.848383i | \(-0.677577\pi\) | ||||
−0.529383 | + | 0.848383i | \(0.677577\pi\) | |||||||
\(102\) | −956.578 | − | 694.995i | −0.928582 | − | 0.674654i | ||||
\(103\) | 288.232 | + | 887.086i | 0.275731 | + | 0.848613i | 0.989025 | + | 0.147748i | \(0.0472025\pi\) |
−0.713294 | + | 0.700865i | \(0.752797\pi\) | |||||||
\(104\) | 60.8228 | + | 187.193i | 0.0573478 | + | 0.176498i | ||||
\(105\) | −135.294 | − | 728.524i | −0.125746 | − | 0.677111i | ||||
\(106\) | 71.4162 | − | 219.797i | 0.0654392 | − | 0.201401i | ||||
\(107\) | −1102.95 | −0.996511 | −0.498255 | − | 0.867030i | \(-0.666026\pi\) | ||||
−0.498255 | + | 0.867030i | \(0.666026\pi\) | |||||||
\(108\) | 60.6018 | − | 186.513i | 0.0539945 | − | 0.166178i | ||||
\(109\) | 1186.41 | − | 861.976i | 1.04254 | − | 0.757453i | 0.0717636 | − | 0.997422i | \(-0.477137\pi\) |
0.970781 | + | 0.239969i | \(0.0771373\pi\) | |||||||
\(110\) | 311.517 | + | 1677.44i | 0.270018 | + | 1.45398i | ||||
\(111\) | 210.339 | + | 152.820i | 0.179860 | + | 0.130676i | ||||
\(112\) | 1239.47 | − | 900.529i | 1.04571 | − | 0.759750i | ||||
\(113\) | 1253.89 | − | 911.005i | 1.04386 | − | 0.758408i | 0.0728243 | − | 0.997345i | \(-0.476799\pi\) |
0.971035 | + | 0.238936i | \(0.0767988\pi\) | |||||||
\(114\) | 891.761 | + | 647.902i | 0.732641 | + | 0.532295i | ||||
\(115\) | −1309.29 | − | 1241.58i | −1.06167 | − | 1.00676i | ||||
\(116\) | 301.327 | − | 218.927i | 0.241186 | − | 0.175232i | ||||
\(117\) | −190.215 | + | 585.422i | −0.150302 | + | 0.462583i | ||||
\(118\) | −2532.37 | −1.97563 | ||||||||
\(119\) | 688.699 | − | 2119.60i | 0.530528 | − | 1.63280i | ||||
\(120\) | 95.7039 | + | 12.5647i | 0.0728044 | + | 0.00955832i | ||||
\(121\) | 60.1524 | + | 185.130i | 0.0451934 | + | 0.139091i | ||||
\(122\) | 791.213 | + | 2435.10i | 0.587156 | + | 1.80708i | ||||
\(123\) | 127.430 | + | 92.5830i | 0.0934142 | + | 0.0678694i | ||||
\(124\) | −1890.33 | −1.36901 | ||||||||
\(125\) | −1291.74 | − | 533.427i | −0.924291 | − | 0.381689i | ||||
\(126\) | 776.781 | 0.549216 | ||||||||
\(127\) | −786.360 | − | 571.324i | −0.549434 | − | 0.399187i | 0.278143 | − | 0.960540i | \(-0.410281\pi\) |
−0.827577 | + | 0.561352i | \(0.810281\pi\) | |||||||
\(128\) | 113.347 | + | 348.848i | 0.0782703 | + | 0.240891i | ||||
\(129\) | −49.4811 | − | 152.287i | −0.0337719 | − | 0.103939i | ||||
\(130\) | 2962.03 | + | 388.878i | 1.99836 | + | 0.262360i | ||||
\(131\) | −360.986 | + | 1111.00i | −0.240760 | + | 0.740982i | 0.755545 | + | 0.655096i | \(0.227372\pi\) |
−0.996305 | + | 0.0858855i | \(0.972628\pi\) | |||||||
\(132\) | −851.116 | −0.561213 | ||||||||
\(133\) | −642.032 | + | 1975.97i | −0.418581 | + | 1.28826i | ||||
\(134\) | −2461.27 | + | 1788.22i | −1.58673 | + | 1.15282i | ||||
\(135\) | 219.043 | + | 207.714i | 0.139646 | + | 0.132424i | ||||
\(136\) | 234.876 | + | 170.647i | 0.148091 | + | 0.107595i | ||||
\(137\) | −867.865 | + | 630.541i | −0.541217 | + | 0.393217i | −0.824537 | − | 0.565808i | \(-0.808564\pi\) |
0.283320 | + | 0.959025i | \(0.408564\pi\) | |||||||
\(138\) | 1530.29 | − | 1111.82i | 0.943965 | − | 0.685831i | ||||
\(139\) | 276.953 | + | 201.218i | 0.168999 | + | 0.122785i | 0.669070 | − | 0.743200i | \(-0.266693\pi\) |
−0.500071 | + | 0.865984i | \(0.666693\pi\) | |||||||
\(140\) | −327.565 | − | 1763.85i | −0.197745 | − | 1.06480i | ||||
\(141\) | −587.337 | + | 426.725i | −0.350799 | + | 0.254871i | ||||
\(142\) | 270.509 | − | 832.540i | 0.159863 | − | 0.492009i | ||||
\(143\) | 2671.46 | 1.56223 | ||||||||
\(144\) | −192.874 | + | 593.604i | −0.111617 | + | 0.343521i | ||||
\(145\) | 104.681 | + | 563.682i | 0.0599539 | + | 0.322836i | ||||
\(146\) | 420.448 | + | 1294.01i | 0.238333 | + | 0.733512i | ||||
\(147\) | 134.466 | + | 413.843i | 0.0754458 | + | 0.232198i | ||||
\(148\) | 509.257 | + | 369.997i | 0.282842 | + | 0.205497i | ||||
\(149\) | 1268.97 | 0.697704 | 0.348852 | − | 0.937178i | \(-0.386572\pi\) | ||||
0.348852 | + | 0.937178i | \(0.386572\pi\) | |||||||
\(150\) | 797.050 | − | 1229.28i | 0.433859 | − | 0.669134i | ||||
\(151\) | −1863.93 | −1.00453 | −0.502266 | − | 0.864713i | \(-0.667500\pi\) | ||||
−0.502266 | + | 0.864713i | \(0.667500\pi\) | |||||||
\(152\) | −218.961 | − | 159.084i | −0.116842 | − | 0.0848910i | ||||
\(153\) | 280.570 | + | 863.505i | 0.148253 | + | 0.456276i | ||||
\(154\) | −1041.76 | − | 3206.20i | −0.545112 | − | 1.67768i | ||||
\(155\) | 1251.73 | − | 2626.74i | 0.648656 | − | 1.36119i | ||||
\(156\) | −460.535 | + | 1417.38i | −0.236361 | + | 0.727444i | ||||
\(157\) | −1891.87 | −0.961705 | −0.480852 | − | 0.876802i | \(-0.659673\pi\) | ||||
−0.480852 | + | 0.876802i | \(0.659673\pi\) | |||||||
\(158\) | 195.051 | − | 600.307i | 0.0982118 | − | 0.302265i | ||||
\(159\) | −143.571 | + | 104.311i | −0.0716098 | + | 0.0520275i | ||||
\(160\) | 2748.22 | + | 360.808i | 1.35791 | + | 0.178277i | ||||
\(161\) | 2884.42 | + | 2095.65i | 1.41195 | + | 1.02584i | ||||
\(162\) | −256.017 | + | 186.007i | −0.124164 | + | 0.0902104i | ||||
\(163\) | −2559.85 | + | 1859.84i | −1.23008 | + | 0.893705i | −0.996896 | − | 0.0787280i | \(-0.974914\pi\) |
−0.233183 | + | 0.972433i | \(0.574914\pi\) | |||||||
\(164\) | 308.524 | + | 224.155i | 0.146900 | + | 0.106729i | ||||
\(165\) | 563.589 | − | 1182.68i | 0.265911 | − | 0.558009i | ||||
\(166\) | 126.057 | − | 91.5861i | 0.0589395 | − | 0.0428220i | ||||
\(167\) | 1089.41 | − | 3352.87i | 0.504798 | − | 1.55361i | −0.296312 | − | 0.955091i | \(-0.595757\pi\) |
0.801110 | − | 0.598517i | \(-0.204243\pi\) | |||||||
\(168\) | −190.729 | −0.0875896 | ||||||||
\(169\) | 766.603 | − | 2359.36i | 0.348932 | − | 1.07390i | ||||
\(170\) | 3871.78 | − | 2104.00i | 1.74678 | − | 0.949233i | ||||
\(171\) | −261.559 | − | 804.994i | −0.116970 | − | 0.359997i | ||||
\(172\) | −119.800 | − | 368.707i | −0.0531086 | − | 0.163452i | ||||
\(173\) | −3140.81 | − | 2281.93i | −1.38030 | − | 1.00285i | −0.996852 | − | 0.0792825i | \(-0.974737\pi\) |
−0.383446 | − | 0.923563i | \(-0.625263\pi\) | |||||||
\(174\) | −601.019 | −0.261857 | ||||||||
\(175\) | 2667.89 | + | 712.808i | 1.15242 | + | 0.307904i | ||||
\(176\) | 2708.80 | 1.16013 | ||||||||
\(177\) | 1573.19 | + | 1142.99i | 0.668069 | + | 0.485380i | ||||
\(178\) | −559.923 | − | 1723.27i | −0.235775 | − | 0.725641i | ||||
\(179\) | 154.209 | + | 474.606i | 0.0643917 | + | 0.198177i | 0.978076 | − | 0.208247i | \(-0.0667756\pi\) |
−0.913685 | + | 0.406424i | \(0.866776\pi\) | |||||||
\(180\) | 530.331 | + | 502.904i | 0.219603 | + | 0.208246i | ||||
\(181\) | −1375.55 | + | 4233.49i | −0.564881 | + | 1.73853i | 0.103422 | + | 0.994638i | \(0.467021\pi\) |
−0.668304 | + | 0.743888i | \(0.732979\pi\) | |||||||
\(182\) | −5903.04 | −2.40419 | ||||||||
\(183\) | 607.560 | − | 1869.88i | 0.245421 | − | 0.755330i | ||||
\(184\) | −375.744 | + | 272.994i | −0.150545 | + | 0.109377i | ||||
\(185\) | −851.352 | + | 462.642i | −0.338339 | + | 0.183860i | ||||
\(186\) | 2467.77 | + | 1792.94i | 0.972824 | + | 0.706798i | ||||
\(187\) | 3187.88 | − | 2316.13i | 1.24664 | − | 0.905734i | ||||
\(188\) | −1422.02 | + | 1033.16i | −0.551656 | + | 0.400802i | ||||
\(189\) | −482.561 | − | 350.601i | −0.185720 | − | 0.134934i | ||||
\(190\) | −3609.43 | + | 1961.44i | −1.37819 | + | 0.748934i | ||||
\(191\) | −3212.06 | + | 2333.70i | −1.21684 | + | 0.884088i | −0.995834 | − | 0.0911844i | \(-0.970935\pi\) |
−0.221008 | + | 0.975272i | \(0.570935\pi\) | |||||||
\(192\) | −383.588 | + | 1180.56i | −0.144183 | + | 0.443749i | ||||
\(193\) | 3115.35 | 1.16190 | 0.580952 | − | 0.813938i | \(-0.302680\pi\) | ||||
0.580952 | + | 0.813938i | \(0.302680\pi\) | |||||||
\(194\) | 693.510 | − | 2134.41i | 0.256655 | − | 0.789904i | ||||
\(195\) | −1664.59 | − | 1578.50i | −0.611300 | − | 0.579685i | ||||
\(196\) | 325.559 | + | 1001.97i | 0.118644 | + | 0.365148i | ||||
\(197\) | −445.849 | − | 1372.18i | −0.161246 | − | 0.496263i | 0.837494 | − | 0.546446i | \(-0.184020\pi\) |
−0.998740 | + | 0.0501827i | \(0.984020\pi\) | |||||||
\(198\) | 1111.10 | + | 807.263i | 0.398801 | + | 0.289746i | ||||
\(199\) | −2015.36 | −0.717916 | −0.358958 | − | 0.933354i | \(-0.616868\pi\) | ||||
−0.358958 | + | 0.933354i | \(0.616868\pi\) | |||||||
\(200\) | −195.706 | + | 301.834i | −0.0691924 | + | 0.106714i | ||||
\(201\) | 2336.13 | 0.819791 | ||||||||
\(202\) | 3396.76 | + | 2467.89i | 1.18315 | + | 0.859606i | ||||
\(203\) | −350.070 | − | 1077.40i | −0.121035 | − | 0.372507i | ||||
\(204\) | 679.296 | + | 2090.66i | 0.233138 | + | 0.717526i | ||||
\(205\) | −515.775 | + | 280.283i | −0.175723 | + | 0.0954916i | ||||
\(206\) | 1126.07 | − | 3465.70i | 0.380861 | − | 1.17217i | ||||
\(207\) | −1452.49 | −0.487705 | ||||||||
\(208\) | 1465.72 | − | 4511.02i | 0.488602 | − | 1.50376i | ||||
\(209\) | −2971.87 | + | 2159.19i | −0.983582 | + | 0.714614i | ||||
\(210\) | −1245.35 | + | 2613.33i | −0.409224 | + | 0.858748i | ||||
\(211\) | 192.025 | + | 139.514i | 0.0626517 | + | 0.0455192i | 0.618670 | − | 0.785651i | \(-0.287672\pi\) |
−0.556019 | + | 0.831170i | \(0.687672\pi\) | |||||||
\(212\) | −347.605 | + | 252.550i | −0.112611 | + | 0.0818169i | ||||
\(213\) | −543.816 | + | 395.106i | −0.174937 | + | 0.127100i | ||||
\(214\) | 3486.11 | + | 2532.80i | 1.11358 | + | 0.809061i | ||||
\(215\) | 591.671 | + | 77.6791i | 0.187682 | + | 0.0246403i | ||||
\(216\) | 62.8616 | − | 45.6717i | 0.0198018 | − | 0.0143869i | ||||
\(217\) | −1776.69 | + | 5468.10i | −0.555806 | + | 1.71059i | ||||
\(218\) | −5729.31 | −1.77999 | ||||||||
\(219\) | 322.856 | − | 993.647i | 0.0996190 | − | 0.306596i | ||||
\(220\) | 1364.52 | − | 2863.42i | 0.418164 | − | 0.877508i | ||||
\(221\) | −2132.15 | − | 6562.09i | −0.648978 | − | 1.99735i | ||||
\(222\) | −313.884 | − | 966.036i | −0.0948943 | − | 0.292054i | ||||
\(223\) | 236.890 | + | 172.111i | 0.0711361 | + | 0.0516834i | 0.622785 | − | 0.782393i | \(-0.286001\pi\) |
−0.551649 | + | 0.834076i | \(0.686001\pi\) | |||||||
\(224\) | −5476.95 | −1.63368 | ||||||||
\(225\) | −1049.99 | + | 403.917i | −0.311108 | + | 0.119679i | ||||
\(226\) | −6055.19 | −1.78223 | ||||||||
\(227\) | −172.374 | − | 125.237i | −0.0504003 | − | 0.0366180i | 0.562300 | − | 0.826933i | \(-0.309917\pi\) |
−0.612700 | + | 0.790315i | \(0.709917\pi\) | |||||||
\(228\) | −633.267 | − | 1949.00i | −0.183944 | − | 0.566120i | ||||
\(229\) | −1001.94 | − | 3083.67i | −0.289128 | − | 0.889845i | −0.985131 | − | 0.171806i | \(-0.945040\pi\) |
0.696003 | − | 0.718039i | \(-0.254960\pi\) | |||||||
\(230\) | 1287.13 | + | 6930.87i | 0.369004 | + | 1.98699i | ||||
\(231\) | −799.950 | + | 2461.99i | −0.227848 | + | 0.701243i | ||||
\(232\) | 147.573 | 0.0417613 | ||||||||
\(233\) | −1229.34 | + | 3783.53i | −0.345652 | + | 1.06381i | 0.615582 | + | 0.788073i | \(0.288921\pi\) |
−0.961234 | + | 0.275735i | \(0.911079\pi\) | |||||||
\(234\) | 1945.56 | − | 1413.53i | 0.543528 | − | 0.394896i | ||||
\(235\) | −494.010 | − | 2660.12i | −0.137131 | − | 0.738412i | ||||
\(236\) | 3808.89 | + | 2767.32i | 1.05058 | + | 0.763294i | ||||
\(237\) | −392.121 | + | 284.893i | −0.107473 | + | 0.0780834i | ||||
\(238\) | −7044.17 | + | 5117.89i | −1.91851 | + | 1.39388i | ||||
\(239\) | 3905.56 | + | 2837.55i | 1.05703 | + | 0.767975i | 0.973536 | − | 0.228533i | \(-0.0733929\pi\) |
0.0834914 | + | 0.996508i | \(0.473393\pi\) | |||||||
\(240\) | −1687.85 | − | 1600.56i | −0.453960 | − | 0.430483i | ||||
\(241\) | 1630.46 | − | 1184.60i | 0.435798 | − | 0.316625i | −0.348165 | − | 0.937433i | \(-0.613195\pi\) |
0.783963 | + | 0.620808i | \(0.213195\pi\) | |||||||
\(242\) | 235.006 | − | 723.273i | 0.0624245 | − | 0.192123i | ||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 1470.98 | − | 4527.21i | 0.385942 | − | 1.18781i | ||||
\(245\) | −1607.87 | − | 211.094i | −0.419278 | − | 0.0550461i | ||||
\(246\) | −190.161 | − | 585.254i | −0.0492854 | − | 0.151685i | ||||
\(247\) | 1987.68 | + | 6117.45i | 0.512036 | + | 1.57589i | ||||
\(248\) | −605.929 | − | 440.233i | −0.155147 | − | 0.112721i | ||||
\(249\) | −119.648 | −0.0304514 | ||||||||
\(250\) | 2857.84 | + | 4652.32i | 0.722981 | + | 1.17695i | ||||
\(251\) | −278.293 | −0.0699830 | −0.0349915 | − | 0.999388i | \(-0.511140\pi\) | ||||
−0.0349915 | + | 0.999388i | \(0.511140\pi\) | |||||||
\(252\) | −1168.34 | − | 848.850i | −0.292058 | − | 0.212193i | ||||
\(253\) | 1947.96 | + | 5995.22i | 0.484061 | + | 1.48979i | ||||
\(254\) | 1173.47 | + | 3611.57i | 0.289882 | + | 0.892165i | ||||
\(255\) | −3354.91 | − | 440.459i | −0.823894 | − | 0.108167i | ||||
\(256\) | 1465.73 | − | 4511.06i | 0.357845 | − | 1.10133i | ||||
\(257\) | −2149.20 | −0.521647 | −0.260823 | − | 0.965387i | \(-0.583994\pi\) | ||||
−0.260823 | + | 0.965387i | \(0.583994\pi\) | |||||||
\(258\) | −193.315 | + | 594.962i | −0.0466483 | + | 0.143569i | ||||
\(259\) | 1548.92 | − | 1125.36i | 0.371603 | − | 0.269985i | ||||
\(260\) | −4030.18 | − | 3821.75i | −0.961311 | − | 0.911595i | ||||
\(261\) | 373.372 | + | 271.271i | 0.0885485 | + | 0.0643342i | ||||
\(262\) | 3692.25 | − | 2682.58i | 0.870641 | − | 0.632558i | ||||
\(263\) | 5778.91 | − | 4198.62i | 1.35492 | − | 0.984404i | 0.356165 | − | 0.934423i | \(-0.384084\pi\) |
0.998750 | − | 0.0499805i | \(-0.0159159\pi\) | |||||||
\(264\) | −272.817 | − | 198.213i | −0.0636013 | − | 0.0462090i | ||||
\(265\) | −120.758 | − | 650.251i | −0.0279929 | − | 0.150734i | ||||
\(266\) | 6566.86 | − | 4771.10i | 1.51368 | − | 1.09976i | ||||
\(267\) | −429.956 | + | 1323.27i | −0.0985501 | + | 0.303306i | ||||
\(268\) | 5656.08 | 1.28918 | ||||||||
\(269\) | 273.812 | − | 842.706i | 0.0620617 | − | 0.191006i | −0.915218 | − | 0.402958i | \(-0.867982\pi\) |
0.977280 | + | 0.211952i | \(0.0679820\pi\) | |||||||
\(270\) | −215.336 | − | 1159.53i | −0.0485368 | − | 0.261358i | ||||
\(271\) | −238.067 | − | 732.696i | −0.0533637 | − | 0.164237i | 0.920823 | − | 0.389981i | \(-0.127519\pi\) |
−0.974187 | + | 0.225745i | \(0.927519\pi\) | |||||||
\(272\) | −2161.96 | − | 6653.82i | −0.481941 | − | 1.48326i | ||||
\(273\) | 3667.16 | + | 2664.34i | 0.812990 | + | 0.590672i | ||||
\(274\) | 4191.02 | 0.924047 | ||||||||
\(275\) | 3075.35 | + | 3792.18i | 0.674366 | + | 0.831552i | ||||
\(276\) | −3516.66 | −0.766950 | ||||||||
\(277\) | 6061.62 | + | 4404.02i | 1.31483 | + | 0.955278i | 0.999981 | + | 0.00613595i | \(0.00195315\pi\) |
0.314847 | + | 0.949142i | \(0.398047\pi\) | |||||||
\(278\) | −413.291 | − | 1271.98i | −0.0891639 | − | 0.274418i | ||||
\(279\) | −723.810 | − | 2227.66i | −0.155317 | − | 0.478016i | ||||
\(280\) | 305.779 | − | 641.671i | 0.0652635 | − | 0.136954i | ||||
\(281\) | 678.424 | − | 2087.98i | 0.144026 | − | 0.443267i | −0.852858 | − | 0.522143i | \(-0.825133\pi\) |
0.996884 | + | 0.0788752i | \(0.0251329\pi\) | |||||||
\(282\) | 2836.32 | 0.598937 | ||||||||
\(283\) | 1728.33 | − | 5319.25i | 0.363033 | − | 1.11730i | −0.588170 | − | 0.808737i | \(-0.700151\pi\) |
0.951203 | − | 0.308564i | \(-0.0998485\pi\) | |||||||
\(284\) | −1316.65 | + | 956.602i | −0.275101 | + | 0.199873i | ||||
\(285\) | 3127.59 | + | 410.614i | 0.650043 | + | 0.0853426i | ||||
\(286\) | −8443.67 | − | 6134.69i | −1.74575 | − | 1.26836i | ||||
\(287\) | 938.382 | − | 681.775i | 0.193000 | − | 0.140223i | ||||
\(288\) | 1805.13 | − | 1311.50i | 0.369334 | − | 0.268337i | ||||
\(289\) | −4258.90 | − | 3094.27i | −0.866864 | − | 0.629814i | ||||
\(290\) | 963.562 | − | 2022.02i | 0.195111 | − | 0.409437i | ||||
\(291\) | −1394.20 | + | 1012.94i | −0.280857 | + | 0.204054i | ||||
\(292\) | 781.675 | − | 2405.75i | 0.156658 | − | 0.482143i | ||||
\(293\) | −2905.73 | −0.579367 | −0.289684 | − | 0.957122i | \(-0.593550\pi\) | ||||
−0.289684 | + | 0.957122i | \(0.593550\pi\) | |||||||
\(294\) | 525.335 | − | 1616.82i | 0.104211 | − | 0.320730i | ||||
\(295\) | −6367.53 | + | 3460.24i | −1.25672 | + | 0.682926i | ||||
\(296\) | 77.0703 | + | 237.198i | 0.0151339 | + | 0.0465772i | ||||
\(297\) | −325.893 | − | 1002.99i | −0.0636707 | − | 0.195958i | ||||
\(298\) | −4010.83 | − | 2914.04i | −0.779667 | − | 0.566461i | ||||
\(299\) | 11038.0 | 2.13493 | ||||||||
\(300\) | −2542.16 | + | 977.936i | −0.489239 | + | 0.188204i | ||||
\(301\) | −1179.14 | −0.225796 | ||||||||
\(302\) | 5891.32 | + | 4280.29i | 1.12254 | + | 0.815573i | ||||
\(303\) | −996.290 | − | 3066.27i | −0.188896 | − | 0.581361i | ||||
\(304\) | 2015.46 | + | 6202.96i | 0.380246 | + | 1.17028i | ||||
\(305\) | 5316.80 | + | 5041.83i | 0.998161 | + | 0.946540i | ||||
\(306\) | 1096.14 | − | 3373.58i | 0.204778 | − | 0.630243i | ||||
\(307\) | −1896.85 | −0.352635 | −0.176317 | − | 0.984333i | \(-0.556419\pi\) | ||||
−0.176317 | + | 0.984333i | \(0.556419\pi\) | |||||||
\(308\) | −1936.78 | + | 5960.80i | −0.358306 | + | 1.10275i | ||||
\(309\) | −2263.80 | + | 1644.75i | −0.416774 | + | 0.302804i | ||||
\(310\) | −9988.35 | + | 5427.87i | −1.83000 | + | 0.994459i | ||||
\(311\) | −7137.00 | − | 5185.33i | −1.30129 | − | 0.945444i | −0.301325 | − | 0.953522i | \(-0.597429\pi\) |
−0.999967 | + | 0.00807744i | \(0.997429\pi\) | |||||||
\(312\) | −477.709 | + | 347.076i | −0.0866825 | + | 0.0629785i | ||||
\(313\) | 6034.71 | − | 4384.47i | 1.08978 | − | 0.791774i | 0.110420 | − | 0.993885i | \(-0.464780\pi\) |
0.979363 | + | 0.202111i | \(0.0647803\pi\) | |||||||
\(314\) | 5979.63 | + | 4344.46i | 1.07468 | + | 0.780802i | ||||
\(315\) | 1953.18 | − | 1061.40i | 0.349362 | − | 0.189851i | ||||
\(316\) | −949.376 | + | 689.762i | −0.169008 | + | 0.122792i | ||||
\(317\) | −1742.87 | + | 5364.01i | −0.308799 | + | 0.950387i | 0.669433 | + | 0.742873i | \(0.266537\pi\) |
−0.978232 | + | 0.207514i | \(0.933463\pi\) | |||||||
\(318\) | 693.323 | 0.122263 | ||||||||
\(319\) | 618.946 | − | 1904.92i | 0.108634 | − | 0.334342i | ||||
\(320\) | −3356.81 | − | 3183.21i | −0.586410 | − | 0.556083i | ||||
\(321\) | −1022.50 | − | 3146.92i | −0.177788 | − | 0.547177i | ||||
\(322\) | −4304.36 | − | 13247.5i | −0.744946 | − | 2.29271i | ||||
\(323\) | 7675.70 | + | 5576.72i | 1.32225 | + | 0.960672i | ||||
\(324\) | 588.334 | 0.100880 | ||||||||
\(325\) | 7979.25 | − | 3069.51i | 1.36187 | − | 0.523895i | ||||
\(326\) | 12361.8 | 2.10018 | ||||||||
\(327\) | 3559.23 | + | 2585.93i | 0.601913 | + | 0.437316i | ||||
\(328\) | 46.6915 | + | 143.702i | 0.00786009 | + | 0.0241909i | ||||
\(329\) | 1652.04 | + | 5084.47i | 0.276839 | + | 0.852023i | ||||
\(330\) | −4497.22 | + | 2443.88i | −0.750193 | + | 0.407670i | ||||
\(331\) | 1361.95 | − | 4191.66i | 0.226162 | − | 0.696055i | −0.772010 | − | 0.635611i | \(-0.780748\pi\) |
0.998172 | − | 0.0604442i | \(-0.0192517\pi\) | |||||||
\(332\) | −289.684 | −0.0478870 | ||||||||
\(333\) | −241.027 | + | 741.804i | −0.0396642 | + | 0.122074i | ||||
\(334\) | −11142.8 | + | 8095.69i | −1.82546 | + | 1.32628i | ||||
\(335\) | −3745.32 | + | 7859.48i | −0.610832 | + | 1.28182i | ||||
\(336\) | 3718.42 | + | 2701.59i | 0.603739 | + | 0.438642i | ||||
\(337\) | −3620.77 | + | 2630.64i | −0.585269 | + | 0.425223i | −0.840620 | − | 0.541626i | \(-0.817809\pi\) |
0.255351 | + | 0.966848i | \(0.417809\pi\) | |||||||
\(338\) | −7841.00 | + | 5696.82i | −1.26182 | + | 0.916763i | ||||
\(339\) | 3761.67 | + | 2733.02i | 0.602673 | + | 0.437867i | ||||
\(340\) | −8122.68 | − | 1066.41i | −1.29563 | − | 0.170100i | ||||
\(341\) | −8224.05 | + | 5975.12i | −1.30603 | + | 0.948888i | ||||
\(342\) | −1021.87 | + | 3144.98i | −0.161568 | + | 0.497255i | ||||
\(343\) | −4373.14 | −0.688418 | ||||||||
\(344\) | 47.4660 | − | 146.085i | 0.00743952 | − | 0.0228965i | ||||
\(345\) | 2328.65 | − | 4886.62i | 0.363392 | − | 0.762571i | ||||
\(346\) | 4686.97 | + | 14425.0i | 0.728246 | + | 2.24131i | ||||
\(347\) | −216.151 | − | 665.244i | −0.0334397 | − | 0.102917i | 0.932944 | − | 0.360023i | \(-0.117231\pi\) |
−0.966383 | + | 0.257106i | \(0.917231\pi\) | |||||||
\(348\) | 903.982 | + | 656.781i | 0.139249 | + | 0.101170i | ||||
\(349\) | −7119.97 | −1.09204 | −0.546022 | − | 0.837771i | \(-0.683858\pi\) | ||||
−0.546022 | + | 0.837771i | \(0.683858\pi\) | |||||||
\(350\) | −6795.51 | − | 8379.46i | −1.03782 | − | 1.27972i | ||||
\(351\) | −1846.65 | −0.280817 | ||||||||
\(352\) | −7834.19 | − | 5691.87i | −1.18626 | − | 0.861868i | ||||
\(353\) | −1094.30 | − | 3367.90i | −0.164996 | − | 0.507806i | 0.834040 | − | 0.551704i | \(-0.186022\pi\) |
−0.999036 | + | 0.0438984i | \(0.986022\pi\) | |||||||
\(354\) | −2347.64 | − | 7225.29i | −0.352473 | − | 1.08480i | ||||
\(355\) | −457.405 | − | 2463.01i | −0.0683846 | − | 0.368233i | ||||
\(356\) | −1040.98 | + | 3203.80i | −0.154977 | + | 0.476970i | ||||
\(357\) | 6686.03 | 0.991210 | ||||||||
\(358\) | 602.470 | − | 1854.21i | 0.0889428 | − | 0.273738i | ||||
\(359\) | −9430.47 | + | 6851.64i | −1.38641 | + | 1.00729i | −0.390161 | + | 0.920747i | \(0.627581\pi\) |
−0.996248 | + | 0.0865388i | \(0.972419\pi\) | |||||||
\(360\) | 52.8731 | + | 284.708i | 0.00774071 | + | 0.0416817i | ||||
\(361\) | −1606.55 | − | 1167.22i | −0.234224 | − | 0.170174i | ||||
\(362\) | 14069.4 | − | 10222.0i | 2.04274 | − | 1.48414i | ||||
\(363\) | −472.443 | + | 343.250i | −0.0683108 | + | 0.0496307i | ||||
\(364\) | 8878.66 | + | 6450.72i | 1.27848 | + | 0.928873i | ||||
\(365\) | 2825.33 | + | 2679.22i | 0.405164 | + | 0.384210i | ||||
\(366\) | −6214.27 | + | 4514.93i | −0.887500 | + | 0.644806i | ||||
\(367\) | 22.7126 | − | 69.9022i | 0.00323048 | − | 0.00994241i | −0.949428 | − | 0.313984i | \(-0.898336\pi\) |
0.952659 | + | 0.304042i | \(0.0983362\pi\) | |||||||
\(368\) | 11192.3 | 1.58543 | ||||||||
\(369\) | −146.021 | + | 449.407i | −0.0206005 | + | 0.0634017i | ||||
\(370\) | 3753.27 | + | 492.758i | 0.527360 | + | 0.0692359i | ||||
\(371\) | 403.833 | + | 1242.87i | 0.0565121 | + | 0.173926i | ||||
\(372\) | −1752.44 | − | 5393.45i | −0.244246 | − | 0.751713i | ||||
\(373\) | −2082.90 | − | 1513.32i | −0.289139 | − | 0.210071i | 0.433755 | − | 0.901031i | \(-0.357188\pi\) |
−0.722894 | + | 0.690959i | \(0.757188\pi\) | |||||||
\(374\) | −15394.7 | −2.12845 | ||||||||
\(375\) | 324.453 | − | 4180.05i | 0.0446791 | − | 0.575619i | ||||
\(376\) | −696.422 | −0.0955193 | ||||||||
\(377\) | −2837.39 | − | 2061.48i | −0.387621 | − | 0.281623i | ||||
\(378\) | 720.116 | + | 2216.29i | 0.0979861 | + | 0.301570i | ||||
\(379\) | 18.7531 | + | 57.7162i | 0.00254164 | + | 0.00782238i | 0.952319 | − | 0.305103i | \(-0.0986910\pi\) |
−0.949778 | + | 0.312926i | \(0.898691\pi\) | |||||||
\(380\) | 7572.29 | + | 994.148i | 1.02224 | + | 0.134207i | ||||
\(381\) | 901.088 | − | 2773.26i | 0.121166 | − | 0.372910i | ||||
\(382\) | 15511.4 | 2.07758 | ||||||||
\(383\) | 1174.60 | − | 3615.05i | 0.156708 | − | 0.482299i | −0.841622 | − | 0.540068i | \(-0.818399\pi\) |
0.998330 | + | 0.0577690i | \(0.0183987\pi\) | |||||||
\(384\) | −890.242 | + | 646.799i | −0.118307 | + | 0.0859553i | ||||
\(385\) | −7000.42 | − | 6638.38i | −0.926687 | − | 0.878762i | ||||
\(386\) | −9846.67 | − | 7154.02i | −1.29840 | − | 0.943343i | ||||
\(387\) | 388.630 | − | 282.356i | 0.0510470 | − | 0.0370878i | ||||
\(388\) | −3375.53 | + | 2452.47i | −0.441667 | + | 0.320890i | ||||
\(389\) | −7911.32 | − | 5747.91i | −1.03116 | − | 0.749179i | −0.0626169 | − | 0.998038i | \(-0.519945\pi\) |
−0.968540 | + | 0.248858i | \(0.919945\pi\) | |||||||
\(390\) | 1636.42 | + | 8811.68i | 0.212470 | + | 1.14409i | ||||
\(391\) | 13171.8 | − | 9569.84i | 1.70364 | − | 1.23777i | ||||
\(392\) | −128.989 | + | 396.989i | −0.0166198 | + | 0.0511504i | ||||
\(393\) | −3504.53 | −0.449822 | ||||||||
\(394\) | −1741.86 | + | 5360.89i | −0.222725 | + | 0.685477i | ||||
\(395\) | −329.814 | − | 1775.96i | −0.0420120 | − | 0.226224i | ||||
\(396\) | −789.028 | − | 2428.38i | −0.100127 | − | 0.308158i | ||||
\(397\) | −4430.53 | − | 13635.8i | −0.560106 | − | 1.72383i | −0.682063 | − | 0.731294i | \(-0.738917\pi\) |
0.121957 | − | 0.992535i | \(-0.461083\pi\) | |||||||
\(398\) | 6369.95 | + | 4628.04i | 0.802253 | + | 0.582871i | ||||
\(399\) | −6232.98 | −0.782054 | ||||||||
\(400\) | 8090.78 | − | 3112.42i | 1.01135 | − | 0.389052i | ||||
\(401\) | 2086.59 | 0.259849 | 0.129924 | − | 0.991524i | \(-0.458527\pi\) | ||||
0.129924 | + | 0.991524i | \(0.458527\pi\) | |||||||
\(402\) | −7383.81 | − | 5364.65i | −0.916097 | − | 0.665583i | ||||
\(403\) | 5500.49 | + | 16928.8i | 0.679899 | + | 2.09251i | ||||
\(404\) | −2412.15 | − | 7423.83i | −0.297052 | − | 0.914231i | ||||
\(405\) | −389.581 | + | 817.528i | −0.0477986 | + | 0.100304i | ||||
\(406\) | −1367.67 | + | 4209.24i | −0.167183 | + | 0.514535i | ||||
\(407\) | 3385.08 | 0.412266 | ||||||||
\(408\) | −269.144 | + | 828.339i | −0.0326583 | + | 0.100512i | ||||
\(409\) | 338.014 | − | 245.582i | 0.0408649 | − | 0.0296901i | −0.567165 | − | 0.823604i | \(-0.691960\pi\) |
0.608030 | + | 0.793914i | \(0.291960\pi\) | |||||||
\(410\) | 2273.85 | + | 298.528i | 0.273896 | + | 0.0359591i | ||||
\(411\) | −2603.59 | − | 1891.62i | −0.312472 | − | 0.227024i | ||||
\(412\) | −5480.95 | + | 3982.15i | −0.655406 | + | 0.476180i | ||||
\(413\) | 11584.8 | − | 8416.88i | 1.38027 | − | 1.00283i | ||||
\(414\) | 4590.88 | + | 3335.47i | 0.544998 | + | 0.395964i | ||||
\(415\) | 191.822 | − | 402.534i | 0.0226896 | − | 0.0476136i | ||||
\(416\) | −13717.8 | + | 9966.58i | −1.61676 | + | 1.17464i | ||||
\(417\) | −317.360 | + | 976.733i | −0.0372690 | + | 0.114702i | ||||
\(418\) | 14351.5 | 1.67932 | ||||||||
\(419\) | −385.525 | + | 1186.52i | −0.0449502 | + | 0.138342i | −0.971013 | − | 0.239027i | \(-0.923171\pi\) |
0.926063 | + | 0.377370i | \(0.123171\pi\) | |||||||
\(420\) | 4728.90 | − | 2569.78i | 0.549397 | − | 0.298553i | ||||
\(421\) | 3257.63 | + | 10026.0i | 0.377119 | + | 1.16065i | 0.942038 | + | 0.335507i | \(0.108908\pi\) |
−0.564919 | + | 0.825147i | \(0.691092\pi\) | |||||||
\(422\) | −286.554 | − | 881.924i | −0.0330551 | − | 0.101733i | ||||
\(423\) | −1762.01 | − | 1280.18i | −0.202534 | − | 0.147150i | ||||
\(424\) | −170.237 | −0.0194987 | ||||||||
\(425\) | 6860.49 | − | 10580.8i | 0.783018 | − | 1.20764i | ||||
\(426\) | 2626.15 | 0.298680 | ||||||||
\(427\) | −11713.2 | − | 8510.10i | −1.32749 | − | 0.964480i | ||||
\(428\) | −2475.59 | − | 7619.09i | −0.279585 | − | 0.860473i | ||||
\(429\) | 2476.58 | + | 7622.12i | 0.278719 | + | 0.857808i | ||||
\(430\) | −1691.71 | − | 1604.22i | −0.189725 | − | 0.179913i | ||||
\(431\) | −2759.44 | + | 8492.68i | −0.308393 | + | 0.949137i | 0.669996 | + | 0.742365i | \(0.266296\pi\) |
−0.978389 | + | 0.206772i | \(0.933704\pi\) | |||||||
\(432\) | −1872.46 | −0.208539 | ||||||||
\(433\) | 750.382 | − | 2309.44i | 0.0832819 | − | 0.256315i | −0.900741 | − | 0.434356i | \(-0.856976\pi\) |
0.984023 | + | 0.178041i | \(0.0569759\pi\) | |||||||
\(434\) | 18172.4 | − | 13203.1i | 2.00992 | − | 1.46029i | ||||
\(435\) | −1511.23 | + | 821.235i | −0.166570 | + | 0.0905177i | ||||
\(436\) | 8617.34 | + | 6260.87i | 0.946550 | + | 0.687709i | ||||
\(437\) | −12279.2 | + | 8921.39i | −1.34416 | + | 0.976586i | ||||
\(438\) | −3302.24 | + | 2399.22i | −0.360245 | + | 0.261733i | ||||
\(439\) | 7139.64 | + | 5187.25i | 0.776211 | + | 0.563950i | 0.903839 | − | 0.427872i | \(-0.140737\pi\) |
−0.127629 | + | 0.991822i | \(0.540737\pi\) | |||||||
\(440\) | 1104.24 | − | 600.064i | 0.119642 | − | 0.0650157i | ||||
\(441\) | −1056.11 | + | 767.306i | −0.114038 | + | 0.0828535i | ||||
\(442\) | −8329.98 | + | 25637.0i | −0.896418 | + | 2.75889i | ||||
\(443\) | −11494.3 | −1.23275 | −0.616377 | − | 0.787451i | \(-0.711400\pi\) | ||||
−0.616377 | + | 0.787451i | \(0.711400\pi\) | |||||||
\(444\) | −583.557 | + | 1796.00i | −0.0623747 | + | 0.191970i | ||||
\(445\) | −3762.58 | − | 3567.99i | −0.400816 | − | 0.380087i | ||||
\(446\) | −353.506 | − | 1087.98i | −0.0375314 | − | 0.115510i | ||||
\(447\) | 1176.40 | + | 3620.58i | 0.124478 | + | 0.383104i | ||||
\(448\) | 7395.20 | + | 5372.93i | 0.779889 | + | 0.566623i | ||||
\(449\) | 1582.63 | 0.166345 | 0.0831727 | − | 0.996535i | \(-0.473495\pi\) | ||||
0.0831727 | + | 0.996535i | \(0.473495\pi\) | |||||||
\(450\) | 4246.25 | + | 1134.51i | 0.444822 | + | 0.118848i | ||||
\(451\) | 2050.78 | 0.214119 | ||||||||
\(452\) | 9107.50 | + | 6616.98i | 0.947745 | + | 0.688577i | ||||
\(453\) | −1727.96 | − | 5318.10i | −0.179220 | − | 0.551581i | ||||
\(454\) | 257.230 | + | 791.673i | 0.0265912 | + | 0.0818394i | ||||
\(455\) | −14842.9 | + | 8065.94i | −1.52933 | + | 0.831071i | ||||
\(456\) | 250.907 | − | 772.211i | 0.0257671 | − | 0.0793028i | ||||
\(457\) | 6765.77 | 0.692537 | 0.346269 | − | 0.938135i | \(-0.387449\pi\) | ||||
0.346269 | + | 0.938135i | \(0.387449\pi\) | |||||||
\(458\) | −3914.43 | + | 12047.4i | −0.399366 | + | 1.22912i | ||||
\(459\) | −2203.62 | + | 1601.03i | −0.224088 | + | 0.162809i | ||||
\(460\) | 5637.96 | − | 11831.1i | 0.571459 | − | 1.19920i | ||||
\(461\) | −9394.53 | − | 6825.53i | −0.949126 | − | 0.689580i | 0.00147406 | − | 0.999999i | \(-0.499531\pi\) |
−0.950600 | + | 0.310419i | \(0.899531\pi\) | |||||||
\(462\) | 8182.08 | − | 5944.63i | 0.823949 | − | 0.598634i | ||||
\(463\) | 3221.48 | − | 2340.54i | 0.323358 | − | 0.234934i | −0.414249 | − | 0.910164i | \(-0.635956\pi\) |
0.737607 | + | 0.675230i | \(0.235956\pi\) | |||||||
\(464\) | −2877.05 | − | 2090.30i | −0.287853 | − | 0.209137i | ||||
\(465\) | 8654.95 | + | 1136.29i | 0.863148 | + | 0.113321i | ||||
\(466\) | 12574.0 | − | 9135.55i | 1.24996 | − | 0.908147i | ||||
\(467\) | 3420.76 | − | 10528.0i | 0.338959 | − | 1.04321i | −0.625780 | − | 0.779999i | \(-0.715219\pi\) |
0.964739 | − | 0.263208i | \(-0.0847806\pi\) | |||||||
\(468\) | −4470.97 | −0.441604 | ||||||||
\(469\) | 5316.05 | − | 16361.1i | 0.523395 | − | 1.61085i | ||||
\(470\) | −4547.23 | + | 9542.26i | −0.446272 | + | 0.936493i | ||||
\(471\) | −1753.86 | − | 5397.83i | −0.171579 | − | 0.528065i | ||||
\(472\) | 576.433 | + | 1774.08i | 0.0562129 | + | 0.173005i | ||||
\(473\) | −1686.64 | − | 1225.42i | −0.163957 | − | 0.119122i | ||||
\(474\) | 1893.60 | 0.183493 | ||||||||
\(475\) | −6395.62 | + | 9863.87i | −0.617792 | + | 0.952812i | ||||
\(476\) | 16187.7 | 1.55875 | ||||||||
\(477\) | −430.714 | − | 312.932i | −0.0413439 | − | 0.0300381i | ||||
\(478\) | −5828.19 | − | 17937.3i | −0.557688 | − | 1.71639i | ||||
\(479\) | −305.633 | − | 940.643i | −0.0291540 | − | 0.0897267i | 0.935421 | − | 0.353536i | \(-0.115021\pi\) |
−0.964575 | + | 0.263810i | \(0.915021\pi\) | |||||||
\(480\) | 1518.30 | + | 8175.63i | 0.144376 | + | 0.777427i | ||||
\(481\) | 1831.65 | − | 5637.24i | 0.173630 | − | 0.534378i | ||||
\(482\) | −7873.69 | −0.744059 | ||||||||
\(483\) | −3305.25 | + | 10172.5i | −0.311375 | + | 0.958313i | ||||
\(484\) | −1143.85 | + | 831.052i | −0.107424 | + | 0.0780477i | ||||
\(485\) | −1172.66 | − | 6314.48i | −0.109789 | − | 0.591187i | ||||
\(486\) | −768.050 | − | 558.021i | −0.0716861 | − | 0.0520830i | ||||
\(487\) | −9577.72 | + | 6958.62i | −0.891187 | + | 0.647485i | −0.936187 | − | 0.351502i | \(-0.885671\pi\) |
0.0450004 | + | 0.998987i | \(0.485671\pi\) | |||||||
\(488\) | 1525.83 | − | 1108.58i | 0.141540 | − | 0.102835i | ||||
\(489\) | −7679.55 | − | 5579.52i | −0.710187 | − | 0.515981i | ||||
\(490\) | 4597.25 | + | 4359.49i | 0.423842 | + | 0.401922i | ||||
\(491\) | −10575.2 | + | 7683.33i | −0.971999 | + | 0.706199i | −0.955906 | − | 0.293672i | \(-0.905123\pi\) |
−0.0160929 | + | 0.999871i | \(0.505123\pi\) | |||||||
\(492\) | −353.537 | + | 1088.07i | −0.0323956 | + | 0.0997035i | ||||
\(493\) | −5173.18 | −0.472593 | ||||||||
\(494\) | 7765.54 | − | 23899.9i | 0.707264 | − | 2.17673i | ||||
\(495\) | 3896.86 | + | 511.610i | 0.353840 | + | 0.0464549i | ||||
\(496\) | 5577.38 | + | 17165.4i | 0.504903 | + | 1.55393i | ||||
\(497\) | 1529.63 | + | 4707.72i | 0.138055 | + | 0.424889i | ||||
\(498\) | 378.172 | + | 274.758i | 0.0340287 | + | 0.0247233i | ||||
\(499\) | 107.268 | 0.00962323 | 0.00481162 | − | 0.999988i | \(-0.498468\pi\) | ||||
0.00481162 | + | 0.999988i | \(0.498468\pi\) | |||||||
\(500\) | 785.542 | − | 10120.5i | 0.0702610 | − | 0.905201i | ||||
\(501\) | 10576.2 | 0.943137 | ||||||||
\(502\) | 879.602 | + | 639.068i | 0.0782043 | + | 0.0568187i | ||||
\(503\) | −1599.76 | − | 4923.56i | −0.141809 | − | 0.436443i | 0.854778 | − | 0.518994i | \(-0.173693\pi\) |
−0.996587 | + | 0.0825511i | \(0.973693\pi\) | |||||||
\(504\) | −176.815 | − | 544.182i | −0.0156269 | − | 0.0480948i | ||||
\(505\) | 11913.1 | + | 1564.05i | 1.04976 | + | 0.137820i | ||||
\(506\) | 7610.38 | − | 23422.3i | 0.668622 | − | 2.05781i | ||||
\(507\) | 7442.34 | 0.651925 | ||||||||
\(508\) | 2181.65 | − | 6714.43i | 0.190542 | − | 0.586427i | ||||
\(509\) | 4039.84 | − | 2935.11i | 0.351793 | − | 0.255593i | −0.397828 | − | 0.917460i | \(-0.630236\pi\) |
0.749621 | + | 0.661868i | \(0.230236\pi\) | |||||||
\(510\) | 9592.41 | + | 9096.32i | 0.832861 | + | 0.789788i | ||||
\(511\) | −6224.34 | − | 4522.24i | −0.538842 | − | 0.391492i | ||||
\(512\) | −12617.9 | + | 9167.42i | −1.08913 | + | 0.791302i | ||||
\(513\) | 2054.31 | − | 1492.54i | 0.176803 | − | 0.128455i | ||||
\(514\) | 6792.96 | + | 4935.38i | 0.582928 | + | 0.423522i | ||||
\(515\) | −1904.09 | − | 10253.0i | −0.162921 | − | 0.877285i | ||||
\(516\) | 940.923 | − | 683.621i | 0.0802749 | − | 0.0583231i | ||||
\(517\) | −2920.92 | + | 8989.66i | −0.248475 | + | 0.764729i | ||||
\(518\) | −7479.91 | −0.634456 | ||||||||
\(519\) | 3599.05 | − | 11076.7i | 0.304395 | − | 0.936831i | ||||
\(520\) | −401.802 | − | 2163.60i | −0.0338849 | − | 0.182462i | ||||
\(521\) | 4258.29 | + | 13105.7i | 0.358079 | + | 1.10205i | 0.954203 | + | 0.299161i | \(0.0967068\pi\) |
−0.596124 | + | 0.802893i | \(0.703293\pi\) | |||||||
\(522\) | −557.175 | − | 1714.81i | −0.0467182 | − | 0.143784i | ||||
\(523\) | −17345.4 | − | 12602.2i | −1.45021 | − | 1.05364i | −0.985781 | − | 0.168034i | \(-0.946258\pi\) |
−0.464433 | − | 0.885608i | \(-0.653742\pi\) | |||||||
\(524\) | −8484.91 | −0.707376 | ||||||||
\(525\) | 439.507 | + | 8272.75i | 0.0365365 | + | 0.687719i | ||||
\(526\) | −27907.0 | −2.31332 | ||||||||
\(527\) | 21240.9 | + | 15432.4i | 1.75573 | + | 1.27561i | ||||
\(528\) | 2511.20 | + | 7728.66i | 0.206981 | + | 0.637021i | ||||
\(529\) | 4288.83 | + | 13199.7i | 0.352497 | + | 1.08487i | ||||
\(530\) | −1111.55 | + | 2332.56i | −0.0910990 | + | 0.191169i | ||||
\(531\) | −1802.71 | + | 5548.18i | −0.147328 | + | 0.453429i | ||||
\(532\) | −15090.9 | −1.22983 | ||||||||
\(533\) | 1109.67 | − | 3415.21i | 0.0901785 | − | 0.277541i | ||||
\(534\) | 4397.69 | − | 3195.11i | 0.356380 | − | 0.258925i | ||||
\(535\) | 12226.5 | + | 1605.19i | 0.988032 | + | 0.129716i | ||||
\(536\) | 1813.00 | + | 1317.22i | 0.146100 | + | 0.106148i | ||||
\(537\) | −1211.17 | + | 879.969i | −0.0973296 | + | 0.0707141i | ||||
\(538\) | −2800.61 | + | 2034.76i | −0.224429 | + | 0.163057i | ||||
\(539\) | 4583.46 | + | 3330.08i | 0.366278 | + | 0.266116i | ||||
\(540\) | −943.226 | + | 1979.34i | −0.0751666 | + | 0.157736i | ||||
\(541\) | 19412.5 | − | 14104.0i | 1.54272 | − | 1.12085i | 0.594113 | − | 0.804382i | \(-0.297503\pi\) |
0.948603 | − | 0.316467i | \(-0.102497\pi\) | |||||||
\(542\) | −930.091 | + | 2862.53i | −0.0737100 | + | 0.226856i | ||||
\(543\) | −13354.1 | −1.05539 | ||||||||
\(544\) | −7728.70 | + | 23786.5i | −0.609127 | + | 1.87470i | ||||
\(545\) | −14406.1 | + | 7828.55i | −1.13227 | + | 0.615299i | ||||
\(546\) | −5472.42 | − | 16842.4i | −0.428934 | − | 1.32012i | ||||
\(547\) | −6911.76 | − | 21272.2i | −0.540266 | − | 1.66277i | −0.731987 | − | 0.681319i | \(-0.761407\pi\) |
0.191721 | − | 0.981450i | \(-0.438593\pi\) | |||||||
\(548\) | −6303.64 | − | 4579.86i | −0.491383 | − | 0.357011i | ||||
\(549\) | 5898.32 | 0.458532 | ||||||||
\(550\) | −1011.97 | − | 19048.1i | −0.0784555 | − | 1.47675i | ||||
\(551\) | 4822.65 | 0.372871 | ||||||||
\(552\) | −1127.23 | − | 818.982i | −0.0869170 | − | 0.0631489i | ||||
\(553\) | 1102.95 | + | 3394.52i | 0.0848138 | + | 0.261030i | ||||
\(554\) | −9045.63 | − | 27839.6i | −0.693704 | − | 2.13500i | ||||
\(555\) | −2109.24 | − | 2000.16i | −0.161320 | − | 0.152977i | ||||
\(556\) | −768.369 | + | 2364.80i | −0.0586081 | + | 0.180377i | ||||
\(557\) | 5920.24 | 0.450357 | 0.225178 | − | 0.974318i | \(-0.427703\pi\) | ||||
0.225178 | + | 0.974318i | \(0.427703\pi\) | |||||||
\(558\) | −2827.81 | + | 8703.10i | −0.214535 | + | 0.660271i | ||||
\(559\) | −2953.34 | + | 2145.73i | −0.223458 | + | 0.162352i | ||||
\(560\) | −15050.4 | + | 8178.69i | −1.13571 | + | 0.617165i | ||||
\(561\) | 9563.65 | + | 6948.40i | 0.719746 | + | 0.522926i | ||||
\(562\) | −6939.08 | + | 5041.54i | −0.520832 | + | 0.378407i | ||||
\(563\) | 2602.59 | − | 1890.89i | 0.194824 | − | 0.141548i | −0.486097 | − | 0.873905i | \(-0.661580\pi\) |
0.680921 | + | 0.732357i | \(0.261580\pi\) | |||||||
\(564\) | −4266.06 | − | 3099.47i | −0.318499 | − | 0.231403i | ||||
\(565\) | −15225.5 | + | 8273.83i | −1.13370 | + | 0.616076i | ||||
\(566\) | −17677.7 | + | 12843.6i | −1.31281 | + | 0.953813i | ||||
\(567\) | 552.965 | − | 1701.85i | 0.0409566 | − | 0.126051i | ||||
\(568\) | −644.819 | −0.0476338 | ||||||||
\(569\) | 1869.17 | − | 5752.70i | 0.137714 | − | 0.423841i | −0.858288 | − | 0.513168i | \(-0.828472\pi\) |
0.996002 | + | 0.0893271i | \(0.0284716\pi\) | |||||||
\(570\) | −8942.43 | − | 8479.96i | −0.657118 | − | 0.623134i | ||||
\(571\) | 1450.75 | + | 4464.95i | 0.106326 | + | 0.327237i | 0.990039 | − | 0.140791i | \(-0.0449646\pi\) |
−0.883714 | + | 0.468028i | \(0.844965\pi\) | |||||||
\(572\) | 5996.11 | + | 18454.1i | 0.438304 | + | 1.34896i | ||||
\(573\) | −9636.19 | − | 7001.10i | −0.702544 | − | 0.510428i | ||||
\(574\) | −4531.56 | −0.329518 | ||||||||
\(575\) | 12706.8 | + | 15668.6i | 0.921583 | + | 1.13639i | ||||
\(576\) | −3723.95 | −0.269383 | ||||||||
\(577\) | 15913.7 | + | 11562.0i | 1.14817 | + | 0.834197i | 0.988237 | − | 0.152930i | \(-0.0488709\pi\) |
0.159937 | + | 0.987127i | \(0.448871\pi\) | |||||||
\(578\) | 6355.47 | + | 19560.1i | 0.457358 | + | 1.40760i | ||||
\(579\) | 2888.08 | + | 8888.61i | 0.207297 | + | 0.637993i | ||||
\(580\) | −3658.89 | + | 1988.32i | −0.261944 | + | 0.142345i | ||||
\(581\) | −272.269 | + | 837.958i | −0.0194417 | + | 0.0598354i | ||||
\(582\) | 6732.74 | 0.479521 | ||||||||
\(583\) | −714.003 | + | 2197.47i | −0.0507221 | + | 0.156107i | ||||
\(584\) | 810.824 | − | 589.098i | 0.0574523 | − | 0.0417415i | ||||
\(585\) | 2960.57 | − | 6212.69i | 0.209238 | − | 0.439082i | ||||
\(586\) | 9184.14 | + | 6672.67i | 0.647429 | + | 0.470384i | ||||
\(587\) | 8058.17 | − | 5854.60i | 0.566603 | − | 0.411661i | −0.267266 | − | 0.963623i | \(-0.586120\pi\) |
0.833870 | + | 0.551961i | \(0.186120\pi\) | |||||||
\(588\) | −2556.97 | + | 1857.75i | −0.179333 | + | 0.130293i | ||||
\(589\) | −19801.6 | − | 14386.7i | −1.38525 | − | 1.00644i | ||||
\(590\) | 28071.9 | + | 3685.49i | 1.95882 | + | 0.257168i | ||||
\(591\) | 3501.74 | − | 2544.16i | 0.243727 | − | 0.177078i | ||||
\(592\) | 1857.25 | − | 5716.04i | 0.128940 | − | 0.396837i | ||||
\(593\) | −24115.5 | −1.66999 | −0.834995 | − | 0.550257i | \(-0.814530\pi\) | ||||
−0.834995 | + | 0.550257i | \(0.814530\pi\) | |||||||
\(594\) | −1273.21 | + | 3918.54i | −0.0879469 | + | 0.270673i | ||||
\(595\) | −10719.1 | + | 22493.9i | −0.738557 | + | 1.54985i | ||||
\(596\) | 2848.21 | + | 8765.89i | 0.195750 | + | 0.602458i | ||||
\(597\) | −1868.34 | − | 5750.17i | −0.128084 | − | 0.394202i | ||||
\(598\) | −34887.8 | − | 25347.4i | −2.38573 | − | 1.73333i | ||||
\(599\) | 13381.7 | 0.912790 | 0.456395 | − | 0.889777i | \(-0.349140\pi\) | ||||
0.456395 | + | 0.889777i | \(0.349140\pi\) | |||||||
\(600\) | −1042.61 | − | 278.566i | −0.0709408 | − | 0.0189540i | ||||
\(601\) | 23840.2 | 1.61807 | 0.809037 | − | 0.587758i | \(-0.199989\pi\) | ||||
0.809037 | + | 0.587758i | \(0.199989\pi\) | |||||||
\(602\) | 3726.92 | + | 2707.76i | 0.252322 | + | 0.183323i | ||||
\(603\) | 2165.71 | + | 6665.38i | 0.146260 | + | 0.450141i | ||||
\(604\) | −4183.61 | − | 12875.8i | −0.281835 | − | 0.867400i | ||||
\(605\) | −397.373 | − | 2139.75i | −0.0267033 | − | 0.143790i | ||||
\(606\) | −3892.35 | + | 11979.4i | −0.260917 | + | 0.803020i | ||||
\(607\) | −17213.0 | −1.15100 | −0.575499 | − | 0.817803i | \(-0.695192\pi\) | ||||
−0.575499 | + | 0.817803i | \(0.695192\pi\) | |||||||
\(608\) | 7205.00 | − | 22174.7i | 0.480594 | − | 1.47912i | ||||
\(609\) | 2749.48 | − | 1997.62i | 0.182947 | − | 0.132919i | ||||
\(610\) | −5226.83 | − | 28145.1i | −0.346932 | − | 1.86814i | ||||
\(611\) | 13390.2 | + | 9728.52i | 0.886593 | + | 0.644147i | ||||
\(612\) | −5335.26 | + | 3876.29i | −0.352394 | + | 0.256029i | ||||
\(613\) | −6213.79 | + | 4514.58i | −0.409417 | + | 0.297459i | −0.773366 | − | 0.633960i | \(-0.781428\pi\) |
0.363949 | + | 0.931419i | \(0.381428\pi\) | |||||||
\(614\) | 5995.37 | + | 4355.89i | 0.394061 | + | 0.286302i | ||||
\(615\) | −1277.84 | − | 1211.76i | −0.0837848 | − | 0.0794517i | ||||
\(616\) | −2009.01 | + | 1459.63i | −0.131404 | + | 0.0954709i | ||||
\(617\) | 5822.57 | − | 17920.0i | 0.379915 | − | 1.16926i | −0.560187 | − | 0.828366i | \(-0.689271\pi\) |
0.940102 | − | 0.340893i | \(-0.110729\pi\) | |||||||
\(618\) | 10932.2 | 0.711579 | ||||||||
\(619\) | −8736.42 | + | 26887.9i | −0.567280 | + | 1.74591i | 0.0937989 | + | 0.995591i | \(0.470099\pi\) |
−0.661079 | + | 0.750317i | \(0.729901\pi\) | |||||||
\(620\) | 20954.8 | + | 2751.10i | 1.35736 | + | 0.178205i | ||||
\(621\) | −1346.53 | − | 4144.19i | −0.0870119 | − | 0.267795i | ||||
\(622\) | 10650.4 | + | 32778.5i | 0.686562 | + | 2.11302i | ||||
\(623\) | 8289.12 | + | 6022.40i | 0.533060 | + | 0.387291i | ||||
\(624\) | 14229.5 | 0.912878 | ||||||||
\(625\) | 13542.8 | + | 7793.08i | 0.866742 | + | 0.498757i | ||||
\(626\) | −29142.3 | −1.86064 | ||||||||
\(627\) | −8915.62 | − | 6477.57i | −0.567871 | − | 0.412583i | ||||
\(628\) | −4246.32 | − | 13068.8i | −0.269820 | − | 0.830419i | ||||
\(629\) | −2701.71 | − | 8315.01i | −0.171263 | − | 0.527092i | ||||
\(630\) | −8610.78 | − | 1130.49i | −0.544543 | − | 0.0714917i | ||||
\(631\) | −2799.20 | + | 8615.05i | −0.176600 | + | 0.543518i | −0.999703 | − | 0.0243738i | \(-0.992241\pi\) |
0.823103 | + | 0.567892i | \(0.192241\pi\) | |||||||
\(632\) | −464.950 | −0.0292638 | ||||||||
\(633\) | −220.041 | + | 677.215i | −0.0138165 | + | 0.0425227i | ||||
\(634\) | 17826.5 | − | 12951.7i | 1.11669 | − | 0.811322i | ||||
\(635\) | 7885.49 | + | 7477.68i | 0.492797 | + | 0.467311i | ||||
\(636\) | −1042.81 | − | 757.649i | −0.0650162 | − | 0.0472370i | ||||
\(637\) | 8025.74 | − | 5831.04i | 0.499201 | − | 0.362691i | ||||
\(638\) | −6330.72 | + | 4599.54i | −0.392846 | + | 0.285419i | ||||
\(639\) | −1631.45 | − | 1185.32i | −0.101000 | − | 0.0733809i | ||||
\(640\) | −748.785 | − | 4032.01i | −0.0462474 | − | 0.249030i | ||||
\(641\) | 6259.41 | − | 4547.73i | 0.385697 | − | 0.280225i | −0.377993 | − | 0.925809i | \(-0.623386\pi\) |
0.763690 | + | 0.645583i | \(0.223386\pi\) | |||||||
\(642\) | −3994.72 | + | 12294.5i | −0.245575 | + | 0.755802i | ||||
\(643\) | 20694.2 | 1.26921 | 0.634604 | − | 0.772837i | \(-0.281163\pi\) | ||||
0.634604 | + | 0.772837i | \(0.281163\pi\) | |||||||
\(644\) | −8002.44 | + | 24629.0i | −0.489659 | + | 1.50701i | ||||
\(645\) | 326.877 | + | 1760.15i | 0.0199547 | + | 0.107451i | ||||
\(646\) | −11454.3 | − | 35252.7i | −0.697620 | − | 2.14705i | ||||
\(647\) | 2688.19 | + | 8273.39i | 0.163344 | + | 0.502721i | 0.998910 | − | 0.0466682i | \(-0.0148603\pi\) |
−0.835566 | + | 0.549389i | \(0.814860\pi\) | |||||||
\(648\) | 188.585 | + | 137.015i | 0.0114326 | + | 0.00830626i | ||||
\(649\) | 25318.1 | 1.53131 | ||||||||
\(650\) | −32268.8 | − | 8621.59i | −1.94721 | − | 0.520256i | ||||
\(651\) | −17248.5 | −1.03844 | ||||||||
\(652\) | −18593.2 | − | 13508.7i | −1.11682 | − | 0.811416i | ||||
\(653\) | 3741.70 | + | 11515.8i | 0.224233 | + | 0.690118i | 0.998369 | + | 0.0570980i | \(0.0181848\pi\) |
−0.774136 | + | 0.633020i | \(0.781815\pi\) | |||||||
\(654\) | −5311.36 | − | 16346.7i | −0.317570 | − | 0.977379i | ||||
\(655\) | 5618.51 | − | 11790.3i | 0.335165 | − | 0.703337i | ||||
\(656\) | 1125.18 | − | 3462.95i | 0.0669679 | − | 0.206106i | ||||
\(657\) | 3134.35 | 0.186123 | ||||||||
\(658\) | 6454.27 | − | 19864.2i | 0.382391 | − | 1.17688i | ||||
\(659\) | 1436.42 | − | 1043.62i | 0.0849091 | − | 0.0616901i | −0.544521 | − | 0.838747i | \(-0.683288\pi\) |
0.629430 | + | 0.777057i | \(0.283288\pi\) | |||||||
\(660\) | 9434.81 | + | 1238.67i | 0.556438 | + | 0.0730535i | ||||
\(661\) | 9947.42 | + | 7227.23i | 0.585340 | + | 0.425275i | 0.840645 | − | 0.541586i | \(-0.182176\pi\) |
−0.255305 | + | 0.966861i | \(0.582176\pi\) | |||||||
\(662\) | −13930.4 | + | 10121.0i | −0.817853 | + | 0.594205i | ||||
\(663\) | 16746.1 | − | 12166.8i | 0.980945 | − | 0.712698i | ||||
\(664\) | −92.8555 | − | 67.4634i | −0.00542694 | − | 0.00394291i | ||||
\(665\) | 9992.80 | − | 20969.7i | 0.582713 | − | 1.22281i | ||||
\(666\) | 2465.28 | − | 1791.13i | 0.143435 | − | 0.104211i | ||||
\(667\) | 2557.37 | − | 7870.78i | 0.148459 | − | 0.456908i | ||||
\(668\) | 25606.4 | 1.48315 | ||||||||
\(669\) | −271.452 | + | 835.444i | −0.0156875 | + | 0.0482812i | ||||
\(670\) | 29886.2 | − | 16240.8i | 1.72329 | − | 0.936470i | ||||
\(671\) | −7910.36 | − | 24345.6i | −0.455106 | − | 1.40067i | ||||
\(672\) | −5077.41 | − | 15626.7i | −0.291466 | − | 0.897041i | ||||
\(673\) | 23862.6 | + | 17337.2i | 1.36677 | + | 0.993016i | 0.997982 | + | 0.0635025i | \(0.0202271\pi\) |
0.368788 | + | 0.929514i | \(0.379773\pi\) | |||||||
\(674\) | 17485.1 | 0.999260 | ||||||||
\(675\) | −2125.84 | − | 2621.34i | −0.121220 | − | 0.149475i | ||||
\(676\) | 18018.9 | 1.02520 | ||||||||
\(677\) | −27342.4 | − | 19865.4i | −1.55222 | − | 1.12776i | −0.942043 | − | 0.335491i | \(-0.891098\pi\) |
−0.610178 | − | 0.792264i | \(-0.708902\pi\) | |||||||
\(678\) | −5613.47 | − | 17276.5i | −0.317970 | − | 0.978612i | ||||
\(679\) | 3921.55 | + | 12069.3i | 0.221643 | + | 0.682146i | ||||
\(680\) | −2355.30 | − | 2233.49i | −0.132826 | − | 0.125956i | ||||
\(681\) | 197.523 | − | 607.913i | 0.0111147 | − | 0.0342075i | ||||
\(682\) | 39714.9 | 2.22986 | ||||||||
\(683\) | −659.833 | + | 2030.76i | −0.0369661 | + | 0.113770i | −0.967837 | − | 0.251579i | \(-0.919050\pi\) |
0.930871 | + | 0.365349i | \(0.119050\pi\) | |||||||
\(684\) | 4973.74 | − | 3613.64i | 0.278035 | − | 0.202004i | ||||
\(685\) | 10538.1 | − | 5726.63i | 0.587797 | − | 0.319421i | ||||
\(686\) | 13822.2 | + | 10042.4i | 0.769291 | + | 0.558923i | ||||
\(687\) | 7869.37 | − | 5717.43i | 0.437024 | − | 0.317516i | ||||
\(688\) | −2994.62 | + | 2175.72i | −0.165943 | + | 0.120565i | ||||
\(689\) | 3273.16 | + | 2378.09i | 0.180983 | + | 0.131492i | ||||
\(690\) | −18581.7 | + | 10097.7i | −1.02521 | + | 0.557119i | ||||
\(691\) | −17933.3 | + | 13029.3i | −0.987285 | + | 0.717305i | −0.959325 | − | 0.282304i | \(-0.908901\pi\) |
−0.0279602 | + | 0.999609i | \(0.508901\pi\) | |||||||
\(692\) | 8713.77 | − | 26818.2i | 0.478682 | − | 1.47323i | ||||
\(693\) | −7766.08 | −0.425698 | ||||||||
\(694\) | −844.467 | + | 2599.00i | −0.0461895 | + | 0.142157i | ||||
\(695\) | −2777.24 | − | 2633.61i | −0.151578 | − | 0.143739i | ||||
\(696\) | 136.807 | + | 421.050i | 0.00745068 | + | 0.0229308i | ||||
\(697\) | −1636.78 | − | 5037.49i | −0.0889489 | − | 0.273757i | ||||
\(698\) | 22504.1 | + | 16350.2i | 1.22033 | + | 0.886623i | ||||
\(699\) | −11934.7 | −0.645797 | ||||||||
\(700\) | 1064.10 | + | 20029.4i | 0.0574561 | + | 1.08149i | ||||
\(701\) | 12304.2 | 0.662941 | 0.331471 | − | 0.943466i | \(-0.392455\pi\) | ||||
0.331471 | + | 0.943466i | \(0.392455\pi\) | |||||||
\(702\) | 5836.69 | + | 4240.60i | 0.313806 | + | 0.227993i | ||||
\(703\) | 2518.64 | + | 7751.59i | 0.135124 | + | 0.415870i | ||||
\(704\) | 4994.28 | + | 15370.8i | 0.267371 | + | 0.822882i | ||||
\(705\) | 7131.79 | − | 3875.56i | 0.380991 | − | 0.207038i | ||||
\(706\) | −4275.25 | + | 13157.9i | −0.227905 | + | 0.701420i | ||||
\(707\) | −23741.8 | −1.26294 | ||||||||
\(708\) | −4364.60 | + | 13432.9i | −0.231683 | + | 0.713048i | ||||
\(709\) | −9554.64 | + | 6941.85i | −0.506110 | + | 0.367711i | −0.811346 | − | 0.584566i | \(-0.801265\pi\) |
0.305236 | + | 0.952277i | \(0.401265\pi\) | |||||||
\(710\) | −4210.28 | + | 8835.20i | −0.222548 | + | 0.467013i | ||||
\(711\) | −1176.36 | − | 854.678i | −0.0620493 | − | 0.0450815i | ||||
\(712\) | −1079.80 | + | 784.519i | −0.0568358 | + | 0.0412937i | ||||
\(713\) | −33980.3 | + | 24688.1i | −1.78481 | + | 1.29674i | ||||
\(714\) | −21132.5 | − | 15353.7i | −1.10765 | − | 0.804757i | ||||
\(715\) | −29613.7 | − | 3887.91i | −1.54894 | − | 0.203356i | ||||
\(716\) | −2932.41 | + | 2130.52i | −0.153058 | + | 0.111203i | ||||
\(717\) | −4475.37 | + | 13773.8i | −0.233104 | + | 0.717421i | ||||
\(718\) | 45540.8 | 2.36709 | ||||||||
\(719\) | −9386.90 | + | 28889.9i | −0.486888 | + | 1.49849i | 0.342340 | + | 0.939576i | \(0.388781\pi\) |
−0.829228 | + | 0.558911i | \(0.811219\pi\) | |||||||
\(720\) | 3001.95 | − | 6299.53i | 0.155383 | − | 0.326069i | ||||
\(721\) | 6367.55 | + | 19597.3i | 0.328904 | + | 1.01226i | ||||
\(722\) | 2397.42 | + | 7378.48i | 0.123577 | + | 0.380331i | ||||
\(723\) | 4891.38 | + | 3553.80i | 0.251608 | + | 0.182804i | ||||
\(724\) | −32332.0 | −1.65968 | ||||||||
\(725\) | −340.060 | − | 6400.88i | −0.0174200 | − | 0.327893i | ||||
\(726\) | 2281.48 | 0.116631 | ||||||||
\(727\) | −24645.5 | − | 17906.0i | −1.25729 | − | 0.913475i | −0.258668 | − | 0.965966i | \(-0.583284\pi\) |
−0.998621 | + | 0.0524916i | \(0.983284\pi\) | |||||||
\(728\) | 1343.68 | + | 4135.43i | 0.0684069 | + | 0.210535i | ||||
\(729\) | 225.273 | + | 693.320i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | −2777.52 | − | 14956.2i | −0.140823 | − | 0.758295i | ||||
\(731\) | −1663.93 | + | 5121.05i | −0.0841896 | + | 0.259109i | ||||
\(732\) | 14280.6 | 0.721073 | ||||||||
\(733\) | −7869.55 | + | 24220.0i | −0.396546 | + | 1.22044i | 0.531205 | + | 0.847244i | \(0.321740\pi\) |
−0.927751 | + | 0.373200i | \(0.878260\pi\) | |||||||
\(734\) | −232.310 | + | 168.783i | −0.0116822 | + | 0.00848759i | ||||
\(735\) | −888.293 | − | 4783.23i | −0.0445785 | − | 0.240044i | ||||
\(736\) | −32369.5 | − | 23517.8i | −1.62113 | − | 1.17782i | ||||
\(737\) | 24607.2 | − | 17878.2i | 1.22988 | − | 0.893557i | ||||
\(738\) | 1493.54 | − | 1085.12i | 0.0744959 | − | 0.0541245i | ||||
\(739\) | −19811.5 | − | 14393.9i | −0.986167 | − | 0.716492i | −0.0270884 | − | 0.999633i | \(-0.508624\pi\) |
−0.959078 | + | 0.283141i | \(0.908624\pi\) | |||||||
\(740\) | −5106.75 | − | 4842.64i | −0.253686 | − | 0.240566i | ||||
\(741\) | −15611.4 | + | 11342.4i | −0.773955 | + | 0.562311i | ||||
\(742\) | 1577.71 | − | 4855.70i | 0.0780588 | − | 0.240240i | ||||
\(743\) | 11738.9 | 0.579622 | 0.289811 | − | 0.957084i | \(-0.406408\pi\) | ||||
0.289811 | + | 0.957084i | \(0.406408\pi\) | |||||||
\(744\) | 694.332 | − | 2136.94i | 0.0342143 | − | 0.105301i | ||||
\(745\) | −14066.8 | − | 1846.79i | −0.691768 | − | 0.0908206i | ||||
\(746\) | 3108.27 | + | 9566.29i | 0.152550 | + | 0.469499i | ||||
\(747\) | −110.920 | − | 341.377i | −0.00543287 | − | 0.0167207i | ||||
\(748\) | 23154.8 | + | 16823.0i | 1.13185 | + | 0.822338i | ||||
\(749\) | −24366.2 | −1.18868 | ||||||||
\(750\) | −10624.5 | + | 12466.8i | −0.517269 | + | 0.606965i | ||||
\(751\) | −12224.7 | −0.593989 | −0.296995 | − | 0.954879i | \(-0.595984\pi\) | ||||
−0.296995 | + | 0.954879i | \(0.595984\pi\) | |||||||
\(752\) | 13577.3 | + | 9864.51i | 0.658397 | + | 0.478353i | ||||
\(753\) | −257.992 | − | 794.018i | −0.0124857 | − | 0.0384271i | ||||
\(754\) | 4234.18 | + | 13031.5i | 0.204509 | + | 0.629414i | ||||
\(755\) | 20662.0 | + | 2712.67i | 0.995985 | + | 0.130761i | ||||
\(756\) | 1338.80 | − | 4120.41i | 0.0644070 | − | 0.198224i | ||||
\(757\) | −22653.2 | −1.08764 | −0.543822 | − | 0.839201i | \(-0.683023\pi\) | ||||
−0.543822 | + | 0.839201i | \(0.683023\pi\) | |||||||
\(758\) | 73.2654 | − | 225.488i | 0.00351071 | − | 0.0108049i | ||||
\(759\) | −15299.5 | + | 11115.7i | −0.731669 | + | 0.531589i | ||||
\(760\) | 2195.70 | + | 2082.15i | 0.104798 | + | 0.0993782i | ||||
\(761\) | −6237.17 | − | 4531.57i | −0.297106 | − | 0.215860i | 0.429238 | − | 0.903191i | \(-0.358782\pi\) |
−0.726344 | + | 0.687331i | \(0.758782\pi\) | |||||||
\(762\) | −9216.54 | + | 6696.21i | −0.438163 | + | 0.318344i | ||||
\(763\) | 26209.9 | − | 19042.6i | 1.24359 | − | 0.903523i | ||||
\(764\) | −23330.5 | − | 16950.6i | −1.10480 | − | 0.802684i | ||||
\(765\) | −1853.47 | − | 9980.47i | −0.0875980 | − | 0.471692i | ||||
\(766\) | −12014.1 | + | 8728.75i | −0.566693 | + | 0.411727i | ||||
\(767\) | 13699.5 | − | 42162.7i | 0.644928 | − | 1.98488i | ||||
\(768\) | 14229.6 | 0.668577 | ||||||||
\(769\) | 8640.68 | − | 26593.3i | 0.405190 | − | 1.24705i | −0.515547 | − | 0.856861i | \(-0.672411\pi\) |
0.920737 | − | 0.390184i | \(-0.127589\pi\) | |||||||
\(770\) | 6881.96 | + | 37057.6i | 0.322089 | + | 1.73437i | ||||
\(771\) | −1992.42 | − | 6132.02i | −0.0930675 | − | 0.286432i | ||||
\(772\) | 6992.42 | + | 21520.5i | 0.325988 | + | 1.00329i | ||||
\(773\) | −31856.0 | − | 23144.7i | −1.48225 | − | 1.07692i | −0.976823 | − | 0.214049i | \(-0.931335\pi\) |
−0.505428 | − | 0.862869i | \(-0.668665\pi\) | |||||||
\(774\) | −1876.74 | −0.0871551 | ||||||||
\(775\) | −17698.6 | + | 27296.3i | −0.820324 | + | 1.26517i | ||||
\(776\) | −1653.14 | −0.0764746 | ||||||||
\(777\) | 4646.76 | + | 3376.07i | 0.214545 | + | 0.155876i | ||||
\(778\) | 11805.9 | + | 36334.8i | 0.544039 | + | 1.67438i | ||||
\(779\) | 1525.87 | + | 4696.15i | 0.0701797 | + | 0.215991i | ||||
\(780\) | 7167.92 | − | 15041.7i | 0.329042 | − | 0.690488i | ||||
\(781\) | −2704.48 | + | 8323.54i | −0.123910 | + | 0.381357i | ||||
\(782\) | −63608.0 | −2.90872 | ||||||||
\(783\) | −427.846 | + | 1316.78i | −0.0195274 | + | 0.0600993i | ||||
\(784\) | 8137.92 | − | 5912.55i | 0.370714 | − | 0.269340i | ||||
\(785\) | 20971.8 | + | 2753.34i | 0.953522 | + | 0.125186i | ||||
\(786\) | 11076.8 | + | 8047.73i | 0.502665 | + | 0.365208i | ||||
\(787\) | 16986.5 | − | 12341.4i | 0.769381 | − | 0.558988i | −0.132392 | − | 0.991197i | \(-0.542266\pi\) |
0.901773 | + | 0.432210i | \(0.142266\pi\) | |||||||
\(788\) | 8478.17 | − | 6159.75i | 0.383277 | − | 0.278467i | ||||
\(789\) | 17336.7 | + | 12595.9i | 0.782261 | + | 0.568346i | ||||
\(790\) | −3035.84 | + | 6370.66i | −0.136722 | + | 0.286909i | ||||
\(791\) | 27700.7 | − | 20125.7i | 1.24516 | − | 0.904663i | ||||
\(792\) | 312.621 | − | 962.148i | 0.0140259 | − | 0.0431672i | ||||
\(793\) | −44823.5 | −2.00722 | ||||||||
\(794\) | −17309.4 | + | 53272.8i | −0.773661 | + | 2.38108i | ||||
\(795\) | 1743.33 | − | 947.360i | 0.0777729 | − | 0.0422634i | ||||
\(796\) | −4523.50 | − | 13921.9i | −0.201421 | − | 0.619911i | ||||
\(797\) | 8542.84 | + | 26292.1i | 0.379677 | + | 1.16853i | 0.940268 | + | 0.340434i | \(0.110574\pi\) |
−0.560591 | + | 0.828093i | \(0.689426\pi\) | |||||||
\(798\) | 19700.6 | + | 14313.3i | 0.873926 | + | 0.634944i | ||||
\(799\) | 24413.2 | 1.08095 | ||||||||
\(800\) | −29939.5 | − | 7999.26i | −1.32315 | − | 0.353521i | ||||
\(801\) | −4174.10 | −0.184126 | ||||||||
\(802\) | −6595.08 | − | 4791.61i | −0.290375 | − | 0.210970i | ||||
\(803\) | −4203.54 | − | 12937.2i | −0.184732 | − | 0.568547i | ||||
\(804\) | 5243.47 | + | 16137.7i | 0.230004 | + | 0.707879i | ||||
\(805\) | −28924.5 | − | 27428.6i | −1.26640 | − | 1.20091i | ||||
\(806\) | 21489.5 | − | 66138.0i | 0.939128 | − | 2.89034i | ||||
\(807\) | 2658.22 | 0.115953 | ||||||||
\(808\) | 955.716 | − | 2941.39i | 0.0416114 | − | 0.128067i | ||||
\(809\) | −15121.8 | + | 10986.6i | −0.657174 | + | 0.477465i | −0.865707 | − | 0.500551i | \(-0.833131\pi\) |
0.208534 | + | 0.978015i | \(0.433131\pi\) | |||||||
\(810\) | 3108.70 | − | 1689.33i | 0.134850 | − | 0.0732804i | ||||
\(811\) | 20567.9 | + | 14943.4i | 0.890549 | + | 0.647022i | 0.936021 | − | 0.351944i | \(-0.114479\pi\) |
−0.0454722 | + | 0.998966i | \(0.514479\pi\) | |||||||
\(812\) | 6656.86 | − | 4836.49i | 0.287697 | − | 0.209024i | ||||
\(813\) | 1869.81 | − | 1358.49i | 0.0806604 | − | 0.0586032i | ||||
\(814\) | −10699.2 | − | 7773.43i | −0.460697 | − | 0.334716i | ||||
\(815\) | 31083.2 | − | 16891.2i | 1.33595 | − | 0.725981i | ||||
\(816\) | 16980.2 | − | 12336.9i | 0.728464 | − | 0.529260i | ||||
\(817\) | 1551.18 | − | 4774.04i | 0.0664247 | − | 0.204434i | ||||
\(818\) | −1632.31 | −0.0697707 | ||||||||
\(819\) | −4202.19 | + | 12933.0i | −0.179287 | + | 0.551790i | ||||
\(820\) | −3093.82 | − | 2933.82i | −0.131757 | − | 0.124943i | ||||
\(821\) | 2291.56 | + | 7052.69i | 0.0974128 | + | 0.299806i | 0.987875 | − | 0.155252i | \(-0.0496188\pi\) |
−0.890462 | + | 0.455057i | \(0.849619\pi\) | |||||||
\(822\) | 3885.29 | + | 11957.7i | 0.164860 | + | 0.507388i | ||||
\(823\) | 1178.99 | + | 856.588i | 0.0499357 | + | 0.0362804i | 0.612473 | − | 0.790491i | \(-0.290175\pi\) |
−0.562537 | + | 0.826772i | \(0.690175\pi\) | |||||||
\(824\) | −2684.25 | −0.113484 | ||||||||
\(825\) | −7968.72 | + | 12290.0i | −0.336285 | + | 0.518648i | ||||
\(826\) | −55944.6 | −2.35661 | ||||||||
\(827\) | −10460.3 | − | 7599.87i | −0.439832 | − | 0.319557i | 0.345736 | − | 0.938332i | \(-0.387629\pi\) |
−0.785568 | + | 0.618775i | \(0.787629\pi\) | |||||||
\(828\) | −3260.12 | − | 10033.6i | −0.136832 | − | 0.421127i | ||||
\(829\) | −7478.70 | − | 23017.1i | −0.313325 | − | 0.964314i | −0.976439 | − | 0.215795i | \(-0.930766\pi\) |
0.663114 | − | 0.748518i | \(-0.269234\pi\) | |||||||
\(830\) | −1530.66 | + | 831.793i | −0.0640122 | + | 0.0347855i | ||||
\(831\) | −6946.00 | + | 21377.6i | −0.289957 | + | 0.892395i | ||||
\(832\) | 28299.7 | 1.17922 | ||||||||
\(833\) | 4521.74 | − | 13916.5i | 0.188078 | − | 0.578845i | ||||
\(834\) | 3246.03 | − | 2358.38i | 0.134773 | − | 0.0979184i | ||||
\(835\) | −16956.0 | + | 35581.8i | −0.702737 | + | 1.47468i | ||||
\(836\) | −21585.9 | − | 15683.0i | −0.893017 | − | 0.648815i | ||||
\(837\) | 5684.87 | − | 4130.30i | 0.234765 | − | 0.170567i | ||||
\(838\) | 3943.24 | − | 2864.93i | 0.162550 | − | 0.118100i | ||||
\(839\) | 5241.08 | + | 3807.87i | 0.215664 | + | 0.156689i | 0.690373 | − | 0.723454i | \(-0.257447\pi\) |
−0.474709 | + | 0.880143i | \(0.657447\pi\) | |||||||
\(840\) | 2114.27 | + | 277.577i | 0.0868443 | + | 0.0114016i | ||||
\(841\) | 17603.8 | − | 12789.9i | 0.721791 | − | 0.524412i | ||||
\(842\) | 12727.0 | − | 39169.8i | 0.520906 | − | 1.60318i | ||||
\(843\) | 6586.28 | 0.269091 | ||||||||
\(844\) | −532.747 | + | 1639.63i | −0.0217274 | + | 0.0668700i | ||||
\(845\) | −11931.7 | + | 25038.3i | −0.485753 | + | 1.01934i | ||||
\(846\) | 2629.41 | + | 8092.50i | 0.106857 | + | 0.328872i | ||||
\(847\) | 1328.87 | + | 4089.85i | 0.0539086 | + | 0.165914i | ||||
\(848\) | 3318.91 | + | 2411.33i | 0.134401 | + | 0.0976478i | ||||
\(849\) | 16779.0 | 0.678271 | ||||||||
\(850\) | −45981.6 | + | 17688.5i | −1.85548 | + | 0.713778i | ||||
\(851\) | 13986.5 | 0.563399 | ||||||||
\(852\) | −3949.95 | − | 2869.81i | −0.158830 | − | 0.115397i | ||||
\(853\) | −644.676 | − | 1984.11i | −0.0258772 | − | 0.0796420i | 0.937284 | − | 0.348567i | \(-0.113332\pi\) |
−0.963161 | + | 0.268925i | \(0.913332\pi\) | |||||||
\(854\) | 17479.3 | + | 53795.8i | 0.700386 | + | 2.15557i | ||||
\(855\) | 1727.88 | + | 9304.19i | 0.0691138 | + | 0.372160i | ||||
\(856\) | 980.854 | − | 3018.76i | 0.0391646 | − | 0.120536i | ||||
\(857\) | 19021.1 | 0.758167 | 0.379083 | − | 0.925363i | \(-0.376239\pi\) | ||||
0.379083 | + | 0.925363i | \(0.376239\pi\) | |||||||
\(858\) | 9675.59 | − | 29778.4i | 0.384987 | − | 1.18487i | ||||
\(859\) | 26210.6 | − | 19043.1i | 1.04109 | − | 0.756395i | 0.0705911 | − | 0.997505i | \(-0.477511\pi\) |
0.970498 | + | 0.241110i | \(0.0775114\pi\) | |||||||
\(860\) | 791.413 | + | 4261.55i | 0.0313802 | + | 0.168974i | ||||
\(861\) | 2815.15 | + | 2045.32i | 0.111428 | + | 0.0809575i | ||||
\(862\) | 28224.2 | − | 20506.1i | 1.11522 | − | 0.810255i | ||||
\(863\) | 14847.6 | − | 10787.4i | 0.585654 | − | 0.425503i | −0.255104 | − | 0.966914i | \(-0.582110\pi\) |
0.840758 | + | 0.541411i | \(0.182110\pi\) | |||||||
\(864\) | 5415.38 | + | 3934.51i | 0.213235 | + | 0.154924i | ||||
\(865\) | 31495.6 | + | 29866.7i | 1.23801 | + | 1.17399i | ||||
\(866\) | −7675.08 | + | 5576.28i | −0.301166 | + | 0.218810i | ||||
\(867\) | 4880.27 | − | 15019.9i | 0.191168 | − | 0.588354i | ||||
\(868\) | −41760.9 | −1.63301 | ||||||||
\(869\) | −1950.08 | + | 6001.73i | −0.0761242 | + | 0.234286i | ||||
\(870\) | 6662.43 | + | 874.694i | 0.259629 | + | 0.0340861i | ||||
\(871\) | −16458.0 | − | 50652.7i | −0.640252 | − | 1.97049i | ||||
\(872\) | 1304.14 | + | 4013.72i | 0.0506464 | + | 0.155874i | ||||
\(873\) | −4182.59 | − | 3038.83i | −0.162153 | − | 0.117811i | ||||
\(874\) | 59297.9 | 2.29495 | ||||||||
\(875\) | −28536.7 | − | 11784.3i | −1.10253 | − | 0.455296i | ||||
\(876\) | 7588.66 | 0.292691 | ||||||||
\(877\) | 11926.6 | + | 8665.21i | 0.459218 | + | 0.333641i | 0.793224 | − | 0.608929i | \(-0.208401\pi\) |
−0.334007 | + | 0.942571i | \(0.608401\pi\) | |||||||
\(878\) | −10654.3 | − | 32790.7i | −0.409529 | − | 1.26040i | ||||
\(879\) | −2693.76 | − | 8290.54i | −0.103365 | − | 0.318126i | ||||
\(880\) | −30027.6 | − | 3942.26i | −1.15026 | − | 0.151015i | ||||
\(881\) | 1663.04 | − | 5118.31i | 0.0635973 | − | 0.195733i | −0.914209 | − | 0.405243i | \(-0.867187\pi\) |
0.977806 | + | 0.209510i | \(0.0671870\pi\) | |||||||
\(882\) | 5100.06 | 0.194703 | ||||||||
\(883\) | −6500.14 | + | 20005.4i | −0.247732 | + | 0.762440i | 0.747443 | + | 0.664326i | \(0.231281\pi\) |
−0.995175 | + | 0.0981146i | \(0.968719\pi\) | |||||||
\(884\) | 40544.6 | − | 29457.4i | 1.54260 | − | 1.12077i | ||||
\(885\) | −15775.7 | − | 14959.8i | −0.599202 | − | 0.568213i | ||||
\(886\) | 36330.0 | + | 26395.3i | 1.37757 | + | 1.00086i | ||||
\(887\) | −5182.71 | + | 3765.46i | −0.196188 | + | 0.142539i | −0.681542 | − | 0.731779i | \(-0.738690\pi\) |
0.485355 | + | 0.874317i | \(0.338690\pi\) | |||||||
\(888\) | −605.318 | + | 439.789i | −0.0228752 | + | 0.0166198i | ||||
\(889\) | −17372.1 | − | 12621.6i | −0.655389 | − | 0.476168i | ||||
\(890\) | 3698.91 | + | 19917.6i | 0.139312 | + | 0.750158i | ||||
\(891\) | 2559.59 | − | 1859.65i | 0.0962398 | − | 0.0699223i | ||||
\(892\) | −657.221 | + | 2022.72i | −0.0246697 | + | 0.0759255i | ||||
\(893\) | −22759.0 | −0.852855 | ||||||||
\(894\) | 4596.00 | − | 14145.0i | 0.171939 | − | 0.529173i | ||||
\(895\) | −1018.72 | − | 5485.54i | −0.0380470 | − | 0.204873i | ||||
\(896\) | 2504.05 | + | 7706.66i | 0.0933642 | + | 0.287345i | ||||
\(897\) | 10232.8 | + | 31493.2i | 0.380895 | + | 1.17227i | ||||
\(898\) | −5002.23 | − | 3634.33i | −0.185887 | − | 0.135055i | ||||
\(899\) | 13345.7 | 0.495110 | ||||||||
\(900\) | −5146.93 | − | 6346.61i | −0.190627 | − | 0.235060i | ||||
\(901\) | 5967.68 | 0.220657 | ||||||||
\(902\) | −6481.91 | − | 4709.38i | −0.239273 | − | 0.173842i | ||||
\(903\) | −1093.13 | − | 3364.30i | −0.0402846 | − | 0.123983i | ||||
\(904\) | 1378.32 | + | 4242.02i | 0.0507103 | + | 0.156070i | ||||
\(905\) | 21409.4 | − | 44927.3i | 0.786380 | − | 1.65020i | ||||
\(906\) | −6750.85 | + | 20777.0i | −0.247552 | + | 0.761886i | ||||
\(907\) | 21808.6 | 0.798392 | 0.399196 | − | 0.916866i | \(-0.369289\pi\) | ||||
0.399196 | + | 0.916866i | \(0.369289\pi\) | |||||||
\(908\) | 478.229 | − | 1471.84i | 0.0174786 | − | 0.0537936i | ||||
\(909\) | 7824.97 | − | 5685.17i | 0.285520 | − | 0.207442i | ||||
\(910\) | 65436.5 | + | 8591.00i | 2.38373 | + | 0.312955i | ||||
\(911\) | −26349.5 | − | 19144.0i | −0.958285 | − | 0.696235i | −0.00553296 | − | 0.999985i | \(-0.501761\pi\) |
−0.952752 | + | 0.303750i | \(0.901761\pi\) | |||||||
\(912\) | −15829.6 | + | 11500.9i | −0.574750 | + | 0.417580i | ||||
\(913\) | −1260.29 | + | 915.656i | −0.0456841 | + | 0.0331915i | ||||
\(914\) | −21384.6 | − | 15536.8i | −0.773893 | − | 0.562267i | ||||
\(915\) | −9456.26 | + | 19843.8i | −0.341655 | + | 0.716956i | ||||
\(916\) | 19052.8 | − | 13842.6i | 0.687250 | − | 0.499316i | ||||
\(917\) | −7974.82 | + | 24544.0i | −0.287189 | + | 0.883876i | ||||
\(918\) | 10641.6 | 0.382597 | ||||||||
\(919\) | 3712.22 | − | 11425.1i | 0.133248 | − | 0.410095i | −0.862065 | − | 0.506797i | \(-0.830829\pi\) |
0.995313 | + | 0.0967018i | \(0.0308293\pi\) | |||||||
\(920\) | 4562.50 | − | 2479.36i | 0.163501 | − | 0.0888500i | ||||
\(921\) | −1758.48 | − | 5412.03i | −0.0629139 | − | 0.193629i | ||||
\(922\) | 14019.3 | + | 43146.9i | 0.500759 | + | 1.54118i | ||||
\(923\) | 12398.0 | + | 9007.66i | 0.442128 | + | 0.321225i | ||||
\(924\) | −18802.7 | −0.669440 | ||||||||
\(925\) | 10110.7 | − | 3889.47i | 0.359393 | − | 0.138254i | ||||
\(926\) | −15556.9 | −0.552086 | ||||||||
\(927\) | −6791.40 | − | 4934.24i | −0.240625 | − | 0.174824i | ||||
\(928\) | 3928.55 | + | 12090.8i | 0.138966 | + | 0.427695i | ||||
\(929\) | 1471.19 | + | 4527.86i | 0.0519571 | + | 0.159908i | 0.973668 | − | 0.227969i | \(-0.0732086\pi\) |
−0.921711 | + | 0.387877i | \(0.873209\pi\) | |||||||
\(930\) | −24746.4 | − | 23466.5i | −0.872543 | − | 0.827418i | ||||
\(931\) | −4215.35 | + | 12973.5i | −0.148392 | + | 0.456702i | ||||
\(932\) | −28895.5 | −1.01556 | ||||||||
\(933\) | 8178.27 | − | 25170.1i | 0.286972 | − | 0.883208i | ||||
\(934\) | −34988.3 | + | 25420.5i | −1.22575 | + | 0.890561i | ||||
\(935\) | −38709.1 | + | 21035.3i | −1.35393 | + | 0.735753i | ||||
\(936\) | −1433.13 | − | 1041.23i | −0.0500461 | − | 0.0363606i | ||||
\(937\) | −5763.73 | + | 4187.59i | −0.200953 | + | 0.146001i | −0.683711 | − | 0.729753i | \(-0.739635\pi\) |
0.482758 | + | 0.875754i | \(0.339635\pi\) | |||||||
\(938\) | −54373.8 | + | 39504.9i | −1.89272 | + | 1.37514i | ||||
\(939\) | 18104.1 | + | 13153.4i | 0.629186 | + | 0.457131i | ||||
\(940\) | 17267.0 | − | 9383.23i | 0.599135 | − | 0.325582i | ||||
\(941\) | 5831.93 | − | 4237.14i | 0.202036 | − | 0.146787i | −0.482167 | − | 0.876079i | \(-0.660150\pi\) |
0.684203 | + | 0.729292i | \(0.260150\pi\) | |||||||
\(942\) | −6852.05 | + | 21088.4i | −0.236998 | + | 0.729404i | ||||
\(943\) | 8473.47 | 0.292613 | ||||||||
\(944\) | 13891.0 | − | 42752.0i | 0.478933 | − | 1.47400i | ||||
\(945\) | 4839.04 | + | 4588.78i | 0.166576 | + | 0.157961i | ||||
\(946\) | 2516.94 | + | 7746.34i | 0.0865039 | + | 0.266232i | ||||
\(947\) | 2411.20 | + | 7420.91i | 0.0827386 | + | 0.254643i | 0.983865 | − | 0.178914i | \(-0.0572583\pi\) |
−0.901126 | + | 0.433557i | \(0.857258\pi\) | |||||||
\(948\) | −2848.13 | − | 2069.29i | −0.0975769 | − | 0.0708938i | ||||
\(949\) | −23819.1 | −0.814752 | ||||||||
\(950\) | 42865.9 | − | 16489.9i | 1.46395 | − | 0.563163i | ||||
\(951\) | −16920.1 | −0.576944 | ||||||||
\(952\) | 5188.82 | + | 3769.90i | 0.176650 | + | 0.128344i | ||||
\(953\) | 1389.10 | + | 4275.21i | 0.0472165 | + | 0.145317i | 0.971885 | − | 0.235455i | \(-0.0756581\pi\) |
−0.924669 | + | 0.380773i | \(0.875658\pi\) | |||||||
\(954\) | 642.746 | + | 1978.17i | 0.0218131 | + | 0.0671337i | ||||
\(955\) | 39002.8 | − | 21194.9i | 1.32157 | − | 0.718168i | ||||
\(956\) | −10835.5 | + | 33348.1i | −0.366573 | + | 1.12820i | ||||
\(957\) | 6008.85 | 0.202966 | ||||||||
\(958\) | −1194.06 | + | 3674.94i | −0.0402697 | + | 0.123937i | ||||
\(959\) | −19172.7 | + | 13929.8i | −0.645587 | + | 0.469047i | ||||
\(960\) | 5970.29 | − | 12528.5i | 0.200719 | − | 0.421205i | ||||
\(961\) | −30695.6 | − | 22301.6i | −1.03036 | − | 0.748603i | ||||
\(962\) | −18734.5 | + | 13611.4i | −0.627886 | + | 0.456186i | ||||
\(963\) | 8030.78 | − | 5834.70i | 0.268731 | − | 0.195245i | ||||
\(964\) | 11842.7 | + | 8604.20i | 0.395671 | + | 0.287472i | ||||
\(965\) | −34534.3 | − | 4533.92i | −1.15202 | − | 0.151246i | ||||
\(966\) | 33806.9 | − | 24562.1i | 1.12600 | − | 0.818089i | ||||
\(967\) | 3922.61 | − | 12072.6i | 0.130448 | − | 0.401476i | −0.864407 | − | 0.502793i | \(-0.832306\pi\) |
0.994854 | + | 0.101317i | \(0.0323057\pi\) | |||||||
\(968\) | −560.189 | −0.0186004 | ||||||||
\(969\) | −8795.57 | + | 27070.0i | −0.291594 | + | 0.897433i | ||||
\(970\) | −10794.0 | + | 22651.0i | −0.357294 | + | 0.749774i | ||||
\(971\) | −10927.8 | − | 33632.2i | −0.361162 | − | 1.11154i | −0.952349 | − | 0.305009i | \(-0.901341\pi\) |
0.591187 | − | 0.806534i | \(-0.298659\pi\) | |||||||
\(972\) | 545.416 | + | 1678.62i | 0.0179982 | + | 0.0553927i | ||||
\(973\) | 6118.38 | + | 4445.26i | 0.201589 | + | 0.146463i | ||||
\(974\) | 46251.9 | 1.52157 | ||||||||
\(975\) | 16155.0 | + | 19920.5i | 0.530640 | + | 0.654326i | ||||
\(976\) | −45450.0 | −1.49059 | ||||||||
\(977\) | 21437.1 | + | 15575.0i | 0.701979 | + | 0.510018i | 0.880576 | − | 0.473905i | \(-0.157156\pi\) |
−0.178597 | + | 0.983922i | \(0.557156\pi\) | |||||||
\(978\) | 11460.0 | + | 35270.4i | 0.374695 | + | 1.15319i | ||||
\(979\) | 5597.98 | + | 17228.8i | 0.182750 | + | 0.562446i | ||||
\(980\) | −2150.67 | − | 11580.8i | −0.0701028 | − | 0.377485i | ||||
\(981\) | −4078.51 | + | 12552.4i | −0.132739 | + | 0.408528i | ||||
\(982\) | 51068.8 | 1.65954 | ||||||||
\(983\) | −10752.4 | + | 33092.4i | −0.348878 | + | 1.07374i | 0.610597 | + | 0.791942i | \(0.290930\pi\) |
−0.959475 | + | 0.281795i | \(0.909070\pi\) | |||||||
\(984\) | −366.720 | + | 266.438i | −0.0118807 | + | 0.00863183i | ||||
\(985\) | 2945.32 | + | 15859.8i | 0.0952749 | + | 0.513030i | ||||
\(986\) | 16350.9 | + | 11879.6i | 0.528111 | + | 0.383695i | ||||
\(987\) | −12975.3 | + | 9427.12i | −0.418449 | + | 0.304021i | ||||
\(988\) | −37797.3 | + | 27461.3i | −1.21710 | + | 0.884273i | ||||
\(989\) | −6968.89 | − | 5063.20i | −0.224063 | − | 0.162791i | ||||
\(990\) | −11142.0 | − | 10565.7i | −0.357692 | − | 0.339193i | ||||
\(991\) | 5104.81 | − | 3708.86i | 0.163632 | − | 0.118886i | −0.502956 | − | 0.864312i | \(-0.667754\pi\) |
0.666588 | + | 0.745426i | \(0.267754\pi\) | |||||||
\(992\) | 19938.4 | − | 61364.0i | 0.638149 | − | 1.96402i | ||||
\(993\) | 13222.1 | 0.422549 | ||||||||
\(994\) | 5976.02 | − | 18392.3i | 0.190692 | − | 0.586889i | ||||
\(995\) | 22340.7 | + | 2933.06i | 0.711807 | + | 0.0934515i | ||||
\(996\) | −268.552 | − | 826.518i | −0.00854357 | − | 0.0262944i | ||||
\(997\) | −933.590 | − | 2873.29i | −0.0296561 | − | 0.0912720i | 0.935133 | − | 0.354297i | \(-0.115280\pi\) |
−0.964789 | + | 0.263025i | \(0.915280\pi\) | |||||||
\(998\) | −339.043 | − | 246.329i | −0.0107537 | − | 0.00781304i | ||||
\(999\) | −2339.94 | −0.0741064 |
(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.16.2 | ✓ | 28 | |
3.2 | odd | 2 | 225.4.h.a.91.6 | 28 | |||
25.6 | even | 5 | 1875.4.a.g.1.11 | 14 | |||
25.11 | even | 5 | inner | 75.4.g.b.61.2 | yes | 28 | |
25.19 | even | 10 | 1875.4.a.f.1.4 | 14 | |||
75.11 | odd | 10 | 225.4.h.a.136.6 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.g.b.16.2 | ✓ | 28 | 1.1 | even | 1 | trivial | |
75.4.g.b.61.2 | yes | 28 | 25.11 | even | 5 | inner | |
225.4.h.a.91.6 | 28 | 3.2 | odd | 2 | |||
225.4.h.a.136.6 | 28 | 75.11 | odd | 10 | |||
1875.4.a.f.1.4 | 14 | 25.19 | even | 10 | |||
1875.4.a.g.1.11 | 14 | 25.6 | even | 5 |