Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,4,Mod(4,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, 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("33.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.e (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: | \(1.94706303019\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.682515625.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 4.1 | ||
Root | \(0.581882 + 1.79085i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.4 |
Dual form | 33.4.e.b.25.1 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.02339 | − | 1.47008i | −0.715376 | − | 0.519751i | 0.169528 | − | 0.985525i | \(-0.445776\pi\) |
−0.884903 | + | 0.465775i | \(0.845776\pi\) | |||||||
\(3\) | 0.927051 | − | 2.85317i | 0.178411 | − | 0.549093i | ||||
\(4\) | −0.539165 | − | 1.65938i | −0.0673956 | − | 0.207422i | ||||
\(5\) | −8.44146 | + | 6.13308i | −0.755027 | + | 0.548559i | −0.897381 | − | 0.441257i | \(-0.854533\pi\) |
0.142354 | + | 0.989816i | \(0.454533\pi\) | |||||||
\(6\) | −6.07016 | + | 4.41023i | −0.413022 | + | 0.300078i | ||||
\(7\) | −10.1220 | − | 31.1524i | −0.546539 | − | 1.68207i | −0.717302 | − | 0.696762i | \(-0.754623\pi\) |
0.170763 | − | 0.985312i | \(-0.445377\pi\) | |||||||
\(8\) | −7.53140 | + | 23.1793i | −0.332844 | + | 1.02439i | ||||
\(9\) | −7.28115 | − | 5.29007i | −0.269672 | − | 0.195928i | ||||
\(10\) | 26.0964 | 0.825242 | ||||||||
\(11\) | 12.6666 | − | 34.2134i | 0.347194 | − | 0.937793i | ||||
\(12\) | −5.23432 | −0.125918 | ||||||||
\(13\) | 59.2672 | + | 43.0601i | 1.26444 | + | 0.918672i | 0.998967 | − | 0.0454454i | \(-0.0144707\pi\) |
0.265477 | + | 0.964117i | \(0.414471\pi\) | |||||||
\(14\) | −25.3157 | + | 77.9137i | −0.483279 | + | 1.48738i | ||||
\(15\) | 9.67305 | + | 29.7706i | 0.166505 | + | 0.512449i | ||||
\(16\) | 38.0218 | − | 27.6245i | 0.594091 | − | 0.431633i | ||||
\(17\) | 44.7200 | − | 32.4909i | 0.638011 | − | 0.463542i | −0.221155 | − | 0.975239i | \(-0.570983\pi\) |
0.859166 | + | 0.511697i | \(0.170983\pi\) | |||||||
\(18\) | 6.95579 | + | 21.4077i | 0.0910831 | + | 0.280325i | ||||
\(19\) | 27.9834 | − | 86.1240i | 0.337886 | − | 1.03990i | −0.627398 | − | 0.778699i | \(-0.715880\pi\) |
0.965283 | − | 0.261206i | \(-0.0841201\pi\) | |||||||
\(20\) | 14.7284 | + | 10.7008i | 0.164669 | + | 0.119639i | ||||
\(21\) | −98.2669 | −1.02112 | ||||||||
\(22\) | −75.9259 | + | 50.6060i | −0.735793 | + | 0.490420i | ||||
\(23\) | −91.1987 | −0.826793 | −0.413397 | − | 0.910551i | \(-0.635658\pi\) | ||||
−0.413397 | + | 0.910551i | \(0.635658\pi\) | |||||||
\(24\) | 59.1524 | + | 42.9767i | 0.503101 | + | 0.365524i | ||||
\(25\) | −4.98357 | + | 15.3379i | −0.0398686 | + | 0.122703i | ||||
\(26\) | −56.6188 | − | 174.255i | −0.427072 | − | 1.31439i | ||||
\(27\) | −21.8435 | + | 15.8702i | −0.155695 | + | 0.113119i | ||||
\(28\) | −46.2362 | + | 33.5926i | −0.312065 | + | 0.226729i | ||||
\(29\) | −23.7073 | − | 72.9635i | −0.151805 | − | 0.467206i | 0.846019 | − | 0.533153i | \(-0.178993\pi\) |
−0.997823 | + | 0.0659470i | \(0.978993\pi\) | |||||||
\(30\) | 24.1927 | − | 74.4576i | 0.147232 | − | 0.453134i | ||||
\(31\) | −18.6296 | − | 13.5352i | −0.107935 | − | 0.0784193i | 0.532509 | − | 0.846425i | \(-0.321249\pi\) |
−0.640443 | + | 0.768005i | \(0.721249\pi\) | |||||||
\(32\) | 77.4339 | 0.427766 | ||||||||
\(33\) | −85.8740 | − | 67.8576i | −0.452992 | − | 0.357954i | ||||
\(34\) | −138.250 | −0.697344 | ||||||||
\(35\) | 276.505 | + | 200.893i | 1.33537 | + | 0.970202i | ||||
\(36\) | −4.85248 | + | 14.9344i | −0.0224652 | + | 0.0691408i | ||||
\(37\) | 38.8841 | + | 119.673i | 0.172770 | + | 0.531732i | 0.999525 | − | 0.0308308i | \(-0.00981532\pi\) |
−0.826754 | + | 0.562563i | \(0.809815\pi\) | |||||||
\(38\) | −183.230 | + | 133.124i | −0.782207 | + | 0.568306i | ||||
\(39\) | 177.802 | − | 129.180i | 0.730027 | − | 0.530395i | ||||
\(40\) | −78.5842 | − | 241.857i | −0.310631 | − | 0.956025i | ||||
\(41\) | 43.2807 | − | 133.204i | 0.164861 | − | 0.507391i | −0.834165 | − | 0.551515i | \(-0.814050\pi\) |
0.999026 | + | 0.0441244i | \(0.0140498\pi\) | |||||||
\(42\) | 198.832 | + | 144.460i | 0.730487 | + | 0.530730i | ||||
\(43\) | 146.015 | 0.517838 | 0.258919 | − | 0.965899i | \(-0.416634\pi\) | ||||
0.258919 | + | 0.965899i | \(0.416634\pi\) | |||||||
\(44\) | −63.6024 | − | 2.57208i | −0.217919 | − | 0.00881262i | ||||
\(45\) | 93.9079 | 0.311088 | ||||||||
\(46\) | 184.530 | + | 134.069i | 0.591468 | + | 0.429727i | ||||
\(47\) | −68.4490 | + | 210.664i | −0.212432 | + | 0.653799i | 0.786894 | + | 0.617088i | \(0.211688\pi\) |
−0.999326 | + | 0.0367105i | \(0.988312\pi\) | |||||||
\(48\) | −43.5692 | − | 134.092i | −0.131014 | − | 0.403219i | ||||
\(49\) | −590.526 | + | 429.042i | −1.72165 | + | 1.25085i | ||||
\(50\) | 32.6315 | − | 23.7082i | 0.0922959 | − | 0.0670569i | ||||
\(51\) | −51.2445 | − | 157.714i | −0.140699 | − | 0.433028i | ||||
\(52\) | 39.4983 | − | 121.563i | 0.105335 | − | 0.324188i | ||||
\(53\) | 35.5597 | + | 25.8356i | 0.0921604 | + | 0.0669585i | 0.632911 | − | 0.774224i | \(-0.281860\pi\) |
−0.540751 | + | 0.841183i | \(0.681860\pi\) | |||||||
\(54\) | 67.5282 | 0.170175 | ||||||||
\(55\) | 102.909 | + | 366.496i | 0.252294 | + | 0.898516i | ||||
\(56\) | 798.324 | 1.90501 | ||||||||
\(57\) | −219.784 | − | 159.683i | −0.510722 | − | 0.371061i | ||||
\(58\) | −59.2930 | + | 182.485i | −0.134234 | + | 0.413129i | ||||
\(59\) | −124.159 | − | 382.121i | −0.273967 | − | 0.843184i | −0.989491 | − | 0.144596i | \(-0.953812\pi\) |
0.715524 | − | 0.698589i | \(-0.246188\pi\) | |||||||
\(60\) | 44.1853 | − | 32.1025i | 0.0950716 | − | 0.0690736i | ||||
\(61\) | 328.861 | − | 238.932i | 0.690269 | − | 0.501509i | −0.186480 | − | 0.982459i | \(-0.559708\pi\) |
0.876748 | + | 0.480949i | \(0.159708\pi\) | |||||||
\(62\) | 17.7972 | + | 54.7740i | 0.0364555 | + | 0.112199i | ||||
\(63\) | −91.0984 | + | 280.372i | −0.182180 | + | 0.560691i | ||||
\(64\) | −460.853 | − | 334.830i | −0.900104 | − | 0.653964i | ||||
\(65\) | −764.393 | −1.45863 | ||||||||
\(66\) | 74.0005 | + | 263.544i | 0.138013 | + | 0.491515i | ||||
\(67\) | 221.234 | 0.403404 | 0.201702 | − | 0.979447i | \(-0.435353\pi\) | ||||
0.201702 | + | 0.979447i | \(0.435353\pi\) | |||||||
\(68\) | −78.0262 | − | 56.6893i | −0.139148 | − | 0.101097i | ||||
\(69\) | −84.5459 | + | 260.205i | −0.147509 | + | 0.453986i | ||||
\(70\) | −264.149 | − | 812.968i | −0.451027 | − | 1.38812i | ||||
\(71\) | 606.376 | − | 440.558i | 1.01357 | − | 0.736403i | 0.0486165 | − | 0.998818i | \(-0.484519\pi\) |
0.964955 | + | 0.262415i | \(0.0845188\pi\) | |||||||
\(72\) | 177.457 | − | 128.930i | 0.290466 | − | 0.211036i | ||||
\(73\) | −68.6023 | − | 211.136i | −0.109990 | − | 0.338516i | 0.880879 | − | 0.473342i | \(-0.156952\pi\) |
−0.990869 | + | 0.134826i | \(0.956952\pi\) | |||||||
\(74\) | 97.2508 | − | 299.307i | 0.152773 | − | 0.470186i | ||||
\(75\) | 39.1415 | + | 28.4379i | 0.0602622 | + | 0.0437831i | ||||
\(76\) | −158.000 | −0.238471 | ||||||||
\(77\) | −1194.04 | − | 48.2871i | −1.76719 | − | 0.0714652i | ||||
\(78\) | −549.667 | −0.797917 | ||||||||
\(79\) | 954.850 | + | 693.739i | 1.35986 | + | 0.987997i | 0.998454 | + | 0.0555887i | \(0.0177036\pi\) |
0.361407 | + | 0.932408i | \(0.382296\pi\) | |||||||
\(80\) | −151.537 | + | 466.382i | −0.211779 | + | 0.651788i | ||||
\(81\) | 25.0304 | + | 77.0356i | 0.0343352 | + | 0.105673i | ||||
\(82\) | −283.394 | + | 205.898i | −0.381655 | + | 0.277288i | ||||
\(83\) | −547.425 | + | 397.728i | −0.723948 | + | 0.525979i | −0.887643 | − | 0.460532i | \(-0.847659\pi\) |
0.163695 | + | 0.986511i | \(0.447659\pi\) | |||||||
\(84\) | 52.9820 | + | 163.062i | 0.0688192 | + | 0.211804i | ||||
\(85\) | −178.232 | + | 548.542i | −0.227435 | + | 0.699973i | ||||
\(86\) | −295.444 | − | 214.653i | −0.370449 | − | 0.269147i | ||||
\(87\) | −230.155 | −0.283623 | ||||||||
\(88\) | 697.644 | + | 551.278i | 0.845103 | + | 0.667800i | ||||
\(89\) | 1054.06 | 1.25539 | 0.627695 | − | 0.778460i | \(-0.283999\pi\) | ||||
0.627695 | + | 0.778460i | \(0.283999\pi\) | |||||||
\(90\) | −190.012 | − | 138.052i | −0.222545 | − | 0.161688i | ||||
\(91\) | 741.524 | − | 2282.17i | 0.854207 | − | 2.62898i | ||||
\(92\) | 49.1711 | + | 151.333i | 0.0557222 | + | 0.171495i | ||||
\(93\) | −55.8889 | + | 40.6057i | −0.0623162 | + | 0.0452754i | ||||
\(94\) | 448.192 | − | 325.630i | 0.491781 | − | 0.357300i | ||||
\(95\) | 291.985 | + | 898.636i | 0.315337 | + | 0.970506i | ||||
\(96\) | 71.7852 | − | 220.932i | 0.0763181 | − | 0.234883i | ||||
\(97\) | 198.573 | + | 144.272i | 0.207857 | + | 0.151017i | 0.686843 | − | 0.726805i | \(-0.258996\pi\) |
−0.478987 | + | 0.877822i | \(0.658996\pi\) | |||||||
\(98\) | 1825.59 | 1.88176 | ||||||||
\(99\) | −273.219 | + | 182.106i | −0.277369 | + | 0.184872i | ||||
\(100\) | 28.1383 | 0.0281383 | ||||||||
\(101\) | −18.3580 | − | 13.3379i | −0.0180860 | − | 0.0131403i | 0.578706 | − | 0.815537i | \(-0.303558\pi\) |
−0.596792 | + | 0.802396i | \(0.703558\pi\) | |||||||
\(102\) | −128.165 | + | 394.451i | −0.124414 | + | 0.382906i | ||||
\(103\) | 303.269 | + | 933.366i | 0.290116 | + | 0.892886i | 0.984818 | + | 0.173588i | \(0.0555363\pi\) |
−0.694702 | + | 0.719298i | \(0.744464\pi\) | |||||||
\(104\) | −1444.47 | + | 1049.47i | −1.36194 | + | 0.989507i | ||||
\(105\) | 829.515 | − | 602.678i | 0.770975 | − | 0.560146i | ||||
\(106\) | −33.9707 | − | 104.551i | −0.0311276 | − | 0.0958009i | ||||
\(107\) | −205.796 | + | 633.375i | −0.185935 | + | 0.572249i | −0.999963 | − | 0.00857617i | \(-0.997270\pi\) |
0.814028 | + | 0.580825i | \(0.197270\pi\) | |||||||
\(108\) | 38.1119 | + | 27.6899i | 0.0339566 | + | 0.0246709i | ||||
\(109\) | 85.6516 | 0.0752654 | 0.0376327 | − | 0.999292i | \(-0.488018\pi\) | ||||
0.0376327 | + | 0.999292i | \(0.488018\pi\) | |||||||
\(110\) | 330.554 | − | 892.848i | 0.286519 | − | 0.773906i | ||||
\(111\) | 377.494 | 0.322794 | ||||||||
\(112\) | −1245.43 | − | 904.857i | −1.05073 | − | 0.763401i | ||||
\(113\) | −136.056 | + | 418.736i | −0.113266 | + | 0.348597i | −0.991581 | − | 0.129485i | \(-0.958668\pi\) |
0.878315 | + | 0.478081i | \(0.158668\pi\) | |||||||
\(114\) | 209.963 | + | 646.200i | 0.172499 | + | 0.530896i | ||||
\(115\) | 769.850 | − | 559.329i | 0.624251 | − | 0.453545i | ||||
\(116\) | −108.292 | + | 78.6787i | −0.0866780 | + | 0.0629753i | ||||
\(117\) | −203.743 | − | 627.055i | −0.160991 | − | 0.495481i | ||||
\(118\) | −310.526 | + | 955.701i | −0.242256 | + | 0.745588i | ||||
\(119\) | −1464.83 | − | 1064.26i | −1.12841 | − | 0.819838i | ||||
\(120\) | −762.912 | −0.580367 | ||||||||
\(121\) | −1010.11 | − | 866.737i | −0.758913 | − | 0.651192i | ||||
\(122\) | −1016.66 | −0.754461 | ||||||||
\(123\) | −339.931 | − | 246.974i | −0.249192 | − | 0.181048i | ||||
\(124\) | −12.4156 | + | 38.2113i | −0.00899157 | + | 0.0276732i | ||||
\(125\) | −455.043 | − | 1400.48i | −0.325603 | − | 1.00210i | ||||
\(126\) | 596.496 | − | 433.380i | 0.421747 | − | 0.306417i | ||||
\(127\) | −1314.97 | + | 955.382i | −0.918778 | + | 0.667531i | −0.943219 | − | 0.332170i | \(-0.892219\pi\) |
0.0244418 | + | 0.999701i | \(0.492219\pi\) | |||||||
\(128\) | 248.833 | + | 765.829i | 0.171828 | + | 0.528831i | ||||
\(129\) | 135.363 | − | 416.605i | 0.0923880 | − | 0.284341i | ||||
\(130\) | 1546.66 | + | 1123.72i | 1.04347 | + | 0.758127i | ||||
\(131\) | 1049.60 | 0.700030 | 0.350015 | − | 0.936744i | \(-0.386177\pi\) | ||||
0.350015 | + | 0.936744i | \(0.386177\pi\) | |||||||
\(132\) | −66.3012 | + | 179.084i | −0.0437180 | + | 0.118085i | ||||
\(133\) | −2966.22 | −1.93386 | ||||||||
\(134\) | −447.642 | − | 325.231i | −0.288585 | − | 0.209669i | ||||
\(135\) | 87.0574 | − | 267.935i | 0.0555016 | − | 0.170816i | ||||
\(136\) | 416.312 | + | 1281.28i | 0.262489 | + | 0.807858i | ||||
\(137\) | 2486.37 | − | 1806.45i | 1.55055 | − | 1.12654i | 0.607287 | − | 0.794483i | \(-0.292258\pi\) |
0.943260 | − | 0.332055i | \(-0.107742\pi\) | |||||||
\(138\) | 553.591 | − | 402.208i | 0.341484 | − | 0.248103i | ||||
\(139\) | −329.681 | − | 1014.65i | −0.201174 | − | 0.619149i | −0.999849 | − | 0.0173866i | \(-0.994465\pi\) |
0.798675 | − | 0.601762i | \(-0.205535\pi\) | |||||||
\(140\) | 184.275 | − | 567.141i | 0.111244 | − | 0.342372i | ||||
\(141\) | 537.605 | + | 390.593i | 0.321096 | + | 0.233290i | ||||
\(142\) | −1874.59 | −1.10783 | ||||||||
\(143\) | 2223.95 | − | 1482.31i | 1.30053 | − | 0.866829i | ||||
\(144\) | −422.978 | −0.244779 | ||||||||
\(145\) | 647.615 | + | 470.520i | 0.370907 | + | 0.269480i | ||||
\(146\) | −171.578 | + | 528.061i | −0.0972593 | + | 0.299333i | ||||
\(147\) | 676.683 | + | 2082.62i | 0.379673 | + | 1.16851i | ||||
\(148\) | 177.618 | − | 129.047i | 0.0986492 | − | 0.0716728i | ||||
\(149\) | −1706.92 | + | 1240.15i | −0.938501 | + | 0.681861i | −0.948059 | − | 0.318094i | \(-0.896957\pi\) |
0.00955863 | + | 0.999954i | \(0.496957\pi\) | |||||||
\(150\) | −37.3924 | − | 115.082i | −0.0203538 | − | 0.0626427i | ||||
\(151\) | 366.835 | − | 1129.00i | 0.197699 | − | 0.608456i | −0.802235 | − | 0.597008i | \(-0.796356\pi\) |
0.999934 | − | 0.0114476i | \(-0.00364398\pi\) | |||||||
\(152\) | 1785.54 | + | 1297.27i | 0.952803 | + | 0.692252i | ||||
\(153\) | −497.492 | −0.262875 | ||||||||
\(154\) | 2345.03 | + | 1853.04i | 1.22706 | + | 0.969624i | ||||
\(155\) | 240.274 | 0.124511 | ||||||||
\(156\) | −310.223 | − | 225.391i | −0.159216 | − | 0.115677i | ||||
\(157\) | −571.355 | + | 1758.45i | −0.290440 | + | 0.893882i | 0.694275 | + | 0.719710i | \(0.255725\pi\) |
−0.984715 | + | 0.174173i | \(0.944275\pi\) | |||||||
\(158\) | −912.182 | − | 2807.41i | −0.459299 | − | 1.41358i | ||||
\(159\) | 106.679 | − | 77.5069i | 0.0532088 | − | 0.0386585i | ||||
\(160\) | −653.655 | + | 474.908i | −0.322975 | + | 0.234655i | ||||
\(161\) | 923.117 | + | 2841.06i | 0.451875 | + | 1.39073i | ||||
\(162\) | 62.6021 | − | 192.669i | 0.0303610 | − | 0.0934416i | ||||
\(163\) | −1466.71 | − | 1065.63i | −0.704796 | − | 0.512064i | 0.176695 | − | 0.984266i | \(-0.443459\pi\) |
−0.881491 | + | 0.472202i | \(0.843459\pi\) | |||||||
\(164\) | −244.372 | −0.116355 | ||||||||
\(165\) | 1141.08 | + | 46.1452i | 0.538380 | + | 0.0217721i | ||||
\(166\) | 1692.34 | 0.791273 | ||||||||
\(167\) | −213.891 | − | 155.401i | −0.0991100 | − | 0.0720076i | 0.537127 | − | 0.843502i | \(-0.319510\pi\) |
−0.636237 | + | 0.771494i | \(0.719510\pi\) | |||||||
\(168\) | 740.087 | − | 2277.75i | 0.339875 | − | 1.04603i | ||||
\(169\) | 979.515 | + | 3014.64i | 0.445842 | + | 1.37216i | ||||
\(170\) | 1167.03 | − | 847.898i | 0.526513 | − | 0.382534i | ||||
\(171\) | −659.353 | + | 479.048i | −0.294865 | + | 0.214232i | ||||
\(172\) | −78.7260 | − | 242.294i | −0.0349000 | − | 0.107411i | ||||
\(173\) | −205.545 | + | 632.602i | −0.0903311 | + | 0.278011i | −0.986009 | − | 0.166693i | \(-0.946691\pi\) |
0.895678 | + | 0.444704i | \(0.146691\pi\) | |||||||
\(174\) | 465.693 | + | 338.346i | 0.202897 | + | 0.147413i | ||||
\(175\) | 528.256 | 0.228185 | ||||||||
\(176\) | −463.519 | − | 1650.77i | −0.198517 | − | 0.706995i | ||||
\(177\) | −1205.36 | −0.511865 | ||||||||
\(178\) | −2132.76 | − | 1549.54i | −0.898075 | − | 0.652490i | ||||
\(179\) | −20.1093 | + | 61.8901i | −0.00839688 | + | 0.0258429i | −0.955167 | − | 0.296067i | \(-0.904325\pi\) |
0.946770 | + | 0.321910i | \(0.104325\pi\) | |||||||
\(180\) | −50.6318 | − | 155.829i | −0.0209660 | − | 0.0645266i | ||||
\(181\) | 33.1354 | − | 24.0743i | 0.0136074 | − | 0.00988634i | −0.580961 | − | 0.813932i | \(-0.697323\pi\) |
0.594568 | + | 0.804045i | \(0.297323\pi\) | |||||||
\(182\) | −4855.36 | + | 3527.63i | −1.97749 | + | 1.43673i | ||||
\(183\) | −376.842 | − | 1159.80i | −0.152224 | − | 0.468496i | ||||
\(184\) | 686.854 | − | 2113.92i | 0.275193 | − | 0.846958i | ||||
\(185\) | −1062.20 | − | 771.734i | −0.422133 | − | 0.306697i | ||||
\(186\) | 172.778 | 0.0681114 | ||||||||
\(187\) | −545.175 | − | 1941.57i | −0.213193 | − | 0.759261i | ||||
\(188\) | 386.477 | 0.149929 | ||||||||
\(189\) | 715.496 | + | 519.838i | 0.275369 | + | 0.200067i | ||||
\(190\) | 730.266 | − | 2247.53i | 0.278837 | − | 0.858173i | ||||
\(191\) | 1415.27 | + | 4355.76i | 0.536155 | + | 1.65012i | 0.741140 | + | 0.671351i | \(0.234285\pi\) |
−0.204985 | + | 0.978765i | \(0.565715\pi\) | |||||||
\(192\) | −1382.56 | + | 1004.49i | −0.519676 | + | 0.377566i | ||||
\(193\) | 4081.18 | − | 2965.15i | 1.52212 | − | 1.10589i | 0.561703 | − | 0.827339i | \(-0.310146\pi\) |
0.960422 | − | 0.278550i | \(-0.0898536\pi\) | |||||||
\(194\) | −189.700 | − | 583.837i | −0.0702045 | − | 0.216067i | ||||
\(195\) | −708.631 | + | 2180.94i | −0.260237 | + | 0.800926i | ||||
\(196\) | 1030.33 | + | 748.582i | 0.375486 | + | 0.272807i | ||||
\(197\) | 1703.26 | 0.616001 | 0.308000 | − | 0.951386i | \(-0.400340\pi\) | ||||
0.308000 | + | 0.951386i | \(0.400340\pi\) | |||||||
\(198\) | 820.537 | + | 33.1825i | 0.294510 | + | 0.0119100i | ||||
\(199\) | −3326.11 | −1.18483 | −0.592416 | − | 0.805632i | \(-0.701826\pi\) | ||||
−0.592416 | + | 0.805632i | \(0.701826\pi\) | |||||||
\(200\) | −317.987 | − | 231.031i | −0.112425 | − | 0.0816818i | ||||
\(201\) | 205.095 | − | 631.218i | 0.0719716 | − | 0.221506i | ||||
\(202\) | 17.5376 | + | 53.9753i | 0.00610863 | + | 0.0188004i | ||||
\(203\) | −2033.03 | + | 1477.08i | −0.702909 | + | 0.510693i | ||||
\(204\) | −234.079 | + | 170.068i | −0.0803371 | + | 0.0583684i | ||||
\(205\) | 451.600 | + | 1389.88i | 0.153859 | + | 0.473530i | ||||
\(206\) | 758.489 | − | 2334.39i | 0.256536 | − | 0.789537i | ||||
\(207\) | 664.032 | + | 482.447i | 0.222963 | + | 0.161992i | ||||
\(208\) | 3442.96 | 1.14772 | ||||||||
\(209\) | −2592.14 | − | 2048.31i | −0.857904 | − | 0.677915i | ||||
\(210\) | −2564.42 | −0.842674 | ||||||||
\(211\) | −4013.48 | − | 2915.96i | −1.30947 | − | 0.951389i | −1.00000 | 0.000481181i | \(-0.999847\pi\) | |
−0.309475 | − | 0.950908i | \(-0.600153\pi\) | |||||||
\(212\) | 23.6986 | − | 72.9367i | 0.00767747 | − | 0.0236288i | ||||
\(213\) | −694.845 | − | 2138.51i | −0.223521 | − | 0.687927i | ||||
\(214\) | 1347.52 | − | 979.027i | 0.430440 | − | 0.312733i | ||||
\(215\) | −1232.58 | + | 895.520i | −0.390982 | + | 0.284065i | ||||
\(216\) | −203.348 | − | 625.840i | −0.0640558 | − | 0.197144i | ||||
\(217\) | −233.085 | + | 717.363i | −0.0729164 | + | 0.224414i | ||||
\(218\) | −173.306 | − | 125.914i | −0.0538431 | − | 0.0391193i | ||||
\(219\) | −666.006 | −0.205500 | ||||||||
\(220\) | 552.671 | − | 368.366i | 0.169369 | − | 0.112887i | ||||
\(221\) | 4049.49 | 1.23257 | ||||||||
\(222\) | −763.818 | − | 554.946i | −0.230919 | − | 0.167773i | ||||
\(223\) | −1136.92 | + | 3499.07i | −0.341406 | + | 1.05074i | 0.622074 | + | 0.782959i | \(0.286290\pi\) |
−0.963480 | + | 0.267781i | \(0.913710\pi\) | |||||||
\(224\) | −783.789 | − | 2412.25i | −0.233791 | − | 0.719534i | ||||
\(225\) | 117.424 | − | 85.3138i | 0.0347924 | − | 0.0252782i | ||||
\(226\) | 890.869 | − | 647.254i | 0.262211 | − | 0.190507i | ||||
\(227\) | 124.139 | + | 382.062i | 0.0362970 | + | 0.111711i | 0.967563 | − | 0.252628i | \(-0.0812950\pi\) |
−0.931266 | + | 0.364339i | \(0.881295\pi\) | |||||||
\(228\) | −146.474 | + | 450.800i | −0.0425459 | + | 0.130943i | ||||
\(229\) | 2388.11 | + | 1735.06i | 0.689129 | + | 0.500681i | 0.876374 | − | 0.481632i | \(-0.159956\pi\) |
−0.187245 | + | 0.982313i | \(0.559956\pi\) | |||||||
\(230\) | −2379.96 | −0.682305 | ||||||||
\(231\) | −1244.71 | + | 3362.04i | −0.354528 | + | 0.957603i | ||||
\(232\) | 1869.79 | 0.529128 | ||||||||
\(233\) | 1994.88 | + | 1449.36i | 0.560896 | + | 0.407515i | 0.831787 | − | 0.555095i | \(-0.187318\pi\) |
−0.270891 | + | 0.962610i | \(0.587318\pi\) | |||||||
\(234\) | −509.569 | + | 1568.29i | −0.142357 | + | 0.438130i | ||||
\(235\) | −714.211 | − | 2198.12i | −0.198255 | − | 0.610167i | ||||
\(236\) | −567.141 | + | 412.052i | −0.156431 | + | 0.113654i | ||||
\(237\) | 2864.55 | − | 2081.22i | 0.785116 | − | 0.570420i | ||||
\(238\) | 1399.37 | + | 4306.83i | 0.381125 | + | 1.17298i | ||||
\(239\) | −1311.91 | + | 4037.64i | −0.355064 | + | 1.09278i | 0.600908 | + | 0.799318i | \(0.294806\pi\) |
−0.955972 | + | 0.293457i | \(0.905194\pi\) | |||||||
\(240\) | 1190.18 | + | 864.719i | 0.320109 | + | 0.232572i | ||||
\(241\) | −2686.25 | −0.717994 | −0.358997 | − | 0.933339i | \(-0.616881\pi\) | ||||
−0.358997 | + | 0.933339i | \(0.616881\pi\) | |||||||
\(242\) | 769.680 | + | 3238.69i | 0.204450 | + | 0.860293i | ||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −573.789 | − | 416.882i | −0.150545 | − | 0.109378i | ||||
\(245\) | 2353.55 | − | 7243.49i | 0.613726 | − | 1.88885i | ||||
\(246\) | 324.741 | + | 999.450i | 0.0841656 | + | 0.259035i | ||||
\(247\) | 5367.01 | − | 3899.36i | 1.38257 | − | 1.00449i | ||||
\(248\) | 454.044 | − | 329.882i | 0.116257 | − | 0.0844659i | ||||
\(249\) | 627.293 | + | 1930.61i | 0.159651 | + | 0.491355i | ||||
\(250\) | −1138.08 | + | 3502.66i | −0.287915 | + | 0.886111i | ||||
\(251\) | −5951.11 | − | 4323.74i | −1.49654 | − | 1.08730i | −0.971735 | − | 0.236074i | \(-0.924139\pi\) |
−0.524802 | − | 0.851224i | \(-0.675861\pi\) | |||||||
\(252\) | 514.360 | 0.128578 | ||||||||
\(253\) | −1155.18 | + | 3120.22i | −0.287058 | + | 0.775361i | ||||
\(254\) | 4065.18 | 1.00422 | ||||||||
\(255\) | 1399.85 | + | 1017.05i | 0.343773 | + | 0.249766i | ||||
\(256\) | −785.901 | + | 2418.75i | −0.191870 | + | 0.590516i | ||||
\(257\) | −147.792 | − | 454.856i | −0.0358716 | − | 0.110401i | 0.931517 | − | 0.363697i | \(-0.118486\pi\) |
−0.967389 | + | 0.253295i | \(0.918486\pi\) | |||||||
\(258\) | −886.333 | + | 643.959i | −0.213879 | + | 0.155392i | ||||
\(259\) | 3334.52 | − | 2422.67i | 0.799987 | − | 0.581225i | ||||
\(260\) | 412.133 | + | 1268.42i | 0.0983055 | + | 0.302553i | ||||
\(261\) | −213.366 | + | 656.672i | −0.0506015 | + | 0.155735i | ||||
\(262\) | −2123.75 | − | 1542.99i | −0.500784 | − | 0.363841i | ||||
\(263\) | 3955.38 | 0.927373 | 0.463686 | − | 0.885999i | \(-0.346526\pi\) | ||||
0.463686 | + | 0.885999i | \(0.346526\pi\) | |||||||
\(264\) | 2219.64 | − | 1479.43i | 0.517460 | − | 0.344897i | ||||
\(265\) | −458.628 | −0.106314 | ||||||||
\(266\) | 6001.82 | + | 4360.57i | 1.38344 | + | 1.00513i | ||||
\(267\) | 977.163 | − | 3007.40i | 0.223975 | − | 0.689325i | ||||
\(268\) | −119.282 | − | 367.111i | −0.0271876 | − | 0.0836749i | ||||
\(269\) | 1059.90 | − | 770.065i | 0.240236 | − | 0.174542i | −0.461153 | − | 0.887321i | \(-0.652564\pi\) |
0.701388 | + | 0.712779i | \(0.252564\pi\) | |||||||
\(270\) | −570.037 | + | 414.156i | −0.128486 | + | 0.0933508i | ||||
\(271\) | −1685.61 | − | 5187.78i | −0.377836 | − | 1.16286i | −0.941545 | − | 0.336887i | \(-0.890626\pi\) |
0.563709 | − | 0.825974i | \(-0.309374\pi\) | |||||||
\(272\) | 802.789 | − | 2470.73i | 0.178957 | − | 0.550772i | ||||
\(273\) | −5824.00 | − | 4231.38i | −1.29115 | − | 0.938077i | ||||
\(274\) | −7686.52 | −1.69474 | ||||||||
\(275\) | 461.635 | + | 364.784i | 0.101228 | + | 0.0799901i | ||||
\(276\) | 477.363 | 0.104108 | ||||||||
\(277\) | 3852.71 | + | 2799.16i | 0.835693 | + | 0.607167i | 0.921164 | − | 0.389174i | \(-0.127240\pi\) |
−0.0854711 | + | 0.996341i | \(0.527240\pi\) | |||||||
\(278\) | −824.546 | + | 2537.69i | −0.177888 | + | 0.547484i | ||||
\(279\) | 64.0430 | + | 197.104i | 0.0137425 | + | 0.0422950i | ||||
\(280\) | −6739.02 | + | 4896.18i | −1.43833 | + | 1.04501i | ||||
\(281\) | 451.960 | − | 328.368i | 0.0959490 | − | 0.0697110i | −0.538776 | − | 0.842449i | \(-0.681113\pi\) |
0.634725 | + | 0.772738i | \(0.281113\pi\) | |||||||
\(282\) | −513.582 | − | 1580.64i | −0.108452 | − | 0.333780i | ||||
\(283\) | −638.145 | + | 1964.01i | −0.134042 | + | 0.412538i | −0.995440 | − | 0.0953928i | \(-0.969589\pi\) |
0.861398 | + | 0.507930i | \(0.169589\pi\) | |||||||
\(284\) | −1057.99 | − | 768.674i | −0.221057 | − | 0.160607i | ||||
\(285\) | 2834.65 | 0.589157 | ||||||||
\(286\) | −6679.02 | − | 270.099i | −1.38090 | − | 0.0558437i | ||||
\(287\) | −4587.73 | −0.943572 | ||||||||
\(288\) | −563.808 | − | 409.630i | −0.115357 | − | 0.0838115i | ||||
\(289\) | −573.988 | + | 1766.55i | −0.116830 | + | 0.359567i | ||||
\(290\) | −618.676 | − | 1904.09i | −0.125275 | − | 0.385558i | ||||
\(291\) | 595.720 | − | 432.816i | 0.120006 | − | 0.0871895i | ||||
\(292\) | −313.367 | + | 227.674i | −0.0628028 | + | 0.0456289i | ||||
\(293\) | −2316.44 | − | 7129.26i | −0.461869 | − | 1.42149i | −0.862877 | − | 0.505413i | \(-0.831340\pi\) |
0.401008 | − | 0.916074i | \(-0.368660\pi\) | |||||||
\(294\) | 1692.41 | − | 5208.72i | 0.335727 | − | 1.03326i | ||||
\(295\) | 3391.65 | + | 2464.18i | 0.669389 | + | 0.486340i | ||||
\(296\) | −3066.78 | −0.602206 | ||||||||
\(297\) | 266.290 | + | 948.361i | 0.0520261 | + | 0.185284i | ||||
\(298\) | 5276.89 | 1.02578 | ||||||||
\(299\) | −5405.09 | − | 3927.03i | −1.04543 | − | 0.759552i | ||||
\(300\) | 26.0856 | − | 80.2832i | 0.00502018 | − | 0.0154505i | ||||
\(301\) | −1477.97 | − | 4548.72i | −0.283019 | − | 0.871042i | ||||
\(302\) | −2401.97 | + | 1745.13i | −0.457675 | + | 0.332520i | ||||
\(303\) | −55.0739 | + | 40.0136i | −0.0104420 | + | 0.00758653i | ||||
\(304\) | −1315.15 | − | 4047.62i | −0.248122 | − | 0.763641i | ||||
\(305\) | −1310.68 | + | 4033.86i | −0.246064 | + | 0.757306i | ||||
\(306\) | 1006.62 | + | 731.352i | 0.188054 | + | 0.136629i | ||||
\(307\) | 1036.23 | 0.192640 | 0.0963201 | − | 0.995350i | \(-0.469293\pi\) | ||||
0.0963201 | + | 0.995350i | \(0.469293\pi\) | |||||||
\(308\) | 563.659 | + | 2007.40i | 0.104277 | + | 0.371372i | ||||
\(309\) | 2944.20 | 0.542037 | ||||||||
\(310\) | −486.167 | − | 353.221i | −0.0890724 | − | 0.0647149i | ||||
\(311\) | −3193.59 | + | 9828.85i | −0.582288 | + | 1.79210i | 0.0276089 | + | 0.999619i | \(0.491211\pi\) |
−0.609897 | + | 0.792481i | \(0.708789\pi\) | |||||||
\(312\) | 1655.21 | + | 5094.22i | 0.300346 | + | 0.924370i | ||||
\(313\) | −5769.05 | + | 4191.46i | −1.04181 | + | 0.756918i | −0.970638 | − | 0.240546i | \(-0.922674\pi\) |
−0.0711707 | + | 0.997464i | \(0.522674\pi\) | |||||||
\(314\) | 3741.13 | − | 2718.09i | 0.672370 | − | 0.488505i | ||||
\(315\) | −950.540 | − | 2925.46i | −0.170022 | − | 0.523273i | ||||
\(316\) | 636.354 | − | 1958.50i | 0.113284 | − | 0.348652i | ||||
\(317\) | 5215.16 | + | 3789.04i | 0.924014 | + | 0.671336i | 0.944520 | − | 0.328454i | \(-0.106528\pi\) |
−0.0205056 | + | 0.999790i | \(0.506528\pi\) | |||||||
\(318\) | −329.794 | −0.0581571 | ||||||||
\(319\) | −2796.62 | − | 113.095i | −0.490849 | − | 0.0198499i | ||||
\(320\) | 5943.81 | 1.03834 | ||||||||
\(321\) | 1616.34 | + | 1174.34i | 0.281045 | + | 0.204191i | ||||
\(322\) | 2308.76 | − | 7105.63i | 0.399572 | − | 1.22976i | ||||
\(323\) | −1546.83 | − | 4760.67i | −0.266465 | − | 0.820095i | ||||
\(324\) | 114.336 | − | 83.0697i | 0.0196049 | − | 0.0142438i | ||||
\(325\) | −955.812 | + | 694.438i | −0.163135 | + | 0.118525i | ||||
\(326\) | 1401.17 | + | 4312.36i | 0.238048 | + | 0.732636i | ||||
\(327\) | 79.4034 | − | 244.378i | 0.0134282 | − | 0.0413277i | ||||
\(328\) | 2761.61 | + | 2006.43i | 0.464892 | + | 0.337764i | ||||
\(329\) | 7255.55 | 1.21584 | ||||||||
\(330\) | −2241.01 | − | 1770.84i | −0.373828 | − | 0.295399i | ||||
\(331\) | 5634.51 | 0.935652 | 0.467826 | − | 0.883821i | \(-0.345037\pi\) | ||||
0.467826 | + | 0.883821i | \(0.345037\pi\) | |||||||
\(332\) | 955.133 | + | 693.945i | 0.157891 | + | 0.114714i | ||||
\(333\) | 349.957 | − | 1077.06i | 0.0575901 | − | 0.177244i | ||||
\(334\) | 204.333 | + | 628.872i | 0.0334749 | + | 0.103025i | ||||
\(335\) | −1867.54 | + | 1356.85i | −0.304580 | + | 0.221291i | ||||
\(336\) | −3736.29 | + | 2714.57i | −0.606640 | + | 0.440750i | ||||
\(337\) | 945.112 | + | 2908.76i | 0.152770 | + | 0.470178i | 0.997928 | − | 0.0643383i | \(-0.0204937\pi\) |
−0.845158 | + | 0.534517i | \(0.820494\pi\) | |||||||
\(338\) | 2449.81 | − | 7539.74i | 0.394237 | − | 1.21334i | ||||
\(339\) | 1068.60 | + | 776.380i | 0.171204 | + | 0.124387i | ||||
\(340\) | 1006.33 | 0.160518 | ||||||||
\(341\) | −699.061 | + | 465.937i | −0.111015 | + | 0.0739939i | ||||
\(342\) | 2038.36 | 0.322287 | ||||||||
\(343\) | 10253.6 | + | 7449.68i | 1.61412 | + | 1.17273i | ||||
\(344\) | −1099.70 | + | 3384.51i | −0.172359 | + | 0.530467i | ||||
\(345\) | −882.170 | − | 2715.04i | −0.137665 | − | 0.423689i | ||||
\(346\) | 1345.87 | − | 977.832i | 0.209117 | − | 0.151932i | ||||
\(347\) | 8507.85 | − | 6181.32i | 1.31621 | − | 0.956284i | 0.316241 | − | 0.948679i | \(-0.397579\pi\) |
0.999971 | − | 0.00760501i | \(-0.00242077\pi\) | |||||||
\(348\) | 124.092 | + | 381.914i | 0.0191150 | + | 0.0588298i | ||||
\(349\) | 465.051 | − | 1431.28i | 0.0713283 | − | 0.219526i | −0.909037 | − | 0.416715i | \(-0.863181\pi\) |
0.980365 | + | 0.197189i | \(0.0631813\pi\) | |||||||
\(350\) | −1068.87 | − | 776.577i | −0.163238 | − | 0.118599i | ||||
\(351\) | −1977.97 | −0.300788 | ||||||||
\(352\) | 980.826 | − | 2649.28i | 0.148518 | − | 0.401156i | ||||
\(353\) | −11810.2 | −1.78071 | −0.890356 | − | 0.455264i | \(-0.849545\pi\) | ||||
−0.890356 | + | 0.455264i | \(0.849545\pi\) | |||||||
\(354\) | 2438.90 | + | 1771.97i | 0.366176 | + | 0.266042i | ||||
\(355\) | −2416.72 | + | 7437.90i | −0.361313 | + | 1.11201i | ||||
\(356\) | −568.309 | − | 1749.08i | −0.0846077 | − | 0.260396i | ||||
\(357\) | −4394.49 | + | 3192.78i | −0.651488 | + | 0.473333i | ||||
\(358\) | 131.672 | − | 95.6655i | 0.0194388 | − | 0.0141231i | ||||
\(359\) | 1021.81 | + | 3144.82i | 0.150221 | + | 0.462332i | 0.997645 | − | 0.0685836i | \(-0.0218480\pi\) |
−0.847424 | + | 0.530916i | \(0.821848\pi\) | |||||||
\(360\) | −707.258 | + | 2176.72i | −0.103544 | + | 0.318675i | ||||
\(361\) | −1085.22 | − | 788.459i | −0.158218 | − | 0.114952i | ||||
\(362\) | −102.437 | −0.0148728 | ||||||||
\(363\) | −3409.37 | + | 2078.51i | −0.492963 | + | 0.300534i | ||||
\(364\) | −4186.79 | −0.602878 | ||||||||
\(365\) | 1874.02 | + | 1361.55i | 0.268741 | + | 0.195252i | ||||
\(366\) | −942.498 | + | 2900.71i | −0.134604 | + | 0.414269i | ||||
\(367\) | −1108.64 | − | 3412.03i | −0.157685 | − | 0.485304i | 0.840738 | − | 0.541442i | \(-0.182121\pi\) |
−0.998423 | + | 0.0561380i | \(0.982121\pi\) | |||||||
\(368\) | −3467.54 | + | 2519.32i | −0.491191 | + | 0.356871i | ||||
\(369\) | −1019.79 | + | 740.923i | −0.143871 | + | 0.104528i | ||||
\(370\) | 1014.74 | + | 3123.04i | 0.142577 | + | 0.438808i | ||||
\(371\) | 444.906 | − | 1369.28i | 0.0622598 | − | 0.191616i | ||||
\(372\) | 97.5135 | + | 70.8477i | 0.0135910 | + | 0.00987441i | ||||
\(373\) | −2022.36 | −0.280734 | −0.140367 | − | 0.990100i | \(-0.544828\pi\) | ||||
−0.140367 | + | 0.990100i | \(0.544828\pi\) | |||||||
\(374\) | −1751.16 | + | 4730.00i | −0.242113 | + | 0.653964i | ||||
\(375\) | −4417.65 | −0.608338 | ||||||||
\(376\) | −4367.53 | − | 3173.19i | −0.599037 | − | 0.435226i | ||||
\(377\) | 1736.76 | − | 5345.18i | 0.237261 | − | 0.730215i | ||||
\(378\) | −683.524 | − | 2103.67i | −0.0930070 | − | 0.286246i | ||||
\(379\) | 4696.18 | − | 3411.97i | 0.636482 | − | 0.462431i | −0.222158 | − | 0.975011i | \(-0.571310\pi\) |
0.858640 | + | 0.512580i | \(0.171310\pi\) | |||||||
\(380\) | 1333.75 | − | 969.025i | 0.180052 | − | 0.130816i | ||||
\(381\) | 1506.82 | + | 4637.52i | 0.202616 | + | 0.623589i | ||||
\(382\) | 3539.66 | − | 10894.0i | 0.474097 | − | 1.45912i | ||||
\(383\) | 4237.83 | + | 3078.96i | 0.565387 | + | 0.410777i | 0.833426 | − | 0.552630i | \(-0.186376\pi\) |
−0.268040 | + | 0.963408i | \(0.586376\pi\) | |||||||
\(384\) | 2415.72 | 0.321033 | ||||||||
\(385\) | 10375.6 | − | 6915.55i | 1.37348 | − | 0.915452i | ||||
\(386\) | −12616.8 | −1.66368 | ||||||||
\(387\) | −1063.16 | − | 772.428i | −0.139647 | − | 0.101459i | ||||
\(388\) | 132.338 | − | 407.295i | 0.0173156 | − | 0.0532919i | ||||
\(389\) | −26.2617 | − | 80.8251i | −0.00342293 | − | 0.0105347i | 0.949330 | − | 0.314280i | \(-0.101763\pi\) |
−0.952753 | + | 0.303745i | \(0.901763\pi\) | |||||||
\(390\) | 4639.99 | − | 3371.15i | 0.602449 | − | 0.437705i | ||||
\(391\) | −4078.40 | + | 2963.13i | −0.527503 | + | 0.383253i | ||||
\(392\) | −5497.40 | − | 16919.3i | −0.708318 | − | 2.17998i | ||||
\(393\) | 973.032 | − | 2994.68i | 0.124893 | − | 0.384381i | ||||
\(394\) | −3446.35 | − | 2503.92i | −0.440672 | − | 0.320167i | ||||
\(395\) | −12315.1 | −1.56871 | ||||||||
\(396\) | 449.492 | + | 355.188i | 0.0570400 | + | 0.0450730i | ||||
\(397\) | −7187.71 | −0.908667 | −0.454334 | − | 0.890832i | \(-0.650123\pi\) | ||||
−0.454334 | + | 0.890832i | \(0.650123\pi\) | |||||||
\(398\) | 6730.01 | + | 4889.64i | 0.847600 | + | 0.615818i | ||||
\(399\) | −2749.84 | + | 8463.13i | −0.345023 | + | 1.06187i | ||||
\(400\) | 234.216 | + | 720.842i | 0.0292770 | + | 0.0901052i | ||||
\(401\) | −1839.76 | + | 1336.66i | −0.229110 | + | 0.166458i | −0.696418 | − | 0.717636i | \(-0.745224\pi\) |
0.467308 | + | 0.884095i | \(0.345224\pi\) | |||||||
\(402\) | −1342.93 | + | 975.693i | −0.166615 | + | 0.121053i | ||||
\(403\) | −521.298 | − | 1604.39i | −0.0644360 | − | 0.198314i | ||||
\(404\) | −12.2346 | + | 37.6541i | −0.00150666 | + | 0.00463704i | ||||
\(405\) | −683.758 | − | 496.779i | −0.0838919 | − | 0.0609510i | ||||
\(406\) | 6285.02 | 0.768277 | ||||||||
\(407\) | 4586.94 | + | 185.496i | 0.558640 | + | 0.0225914i | ||||
\(408\) | 4041.65 | 0.490420 | ||||||||
\(409\) | 7772.40 | + | 5646.98i | 0.939659 | + | 0.682702i | 0.948339 | − | 0.317260i | \(-0.102763\pi\) |
−0.00867953 | + | 0.999962i | \(0.502763\pi\) | |||||||
\(410\) | 1129.47 | − | 3476.16i | 0.136050 | − | 0.418720i | ||||
\(411\) | −2849.13 | − | 8768.71i | −0.341939 | − | 1.05238i | ||||
\(412\) | 1385.30 | − | 1006.48i | 0.165652 | − | 0.120353i | ||||
\(413\) | −10647.3 | + | 7735.68i | −1.26856 | + | 0.921666i | ||||
\(414\) | −634.359 | − | 1952.36i | −0.0753069 | − | 0.231771i | ||||
\(415\) | 2181.77 | − | 6714.80i | 0.258070 | − | 0.794257i | ||||
\(416\) | 4589.29 | + | 3334.31i | 0.540886 | + | 0.392976i | ||||
\(417\) | −3200.61 | −0.375862 | ||||||||
\(418\) | 2233.73 | + | 7955.16i | 0.261377 | + | 0.930861i | ||||
\(419\) | 10777.3 | 1.25658 | 0.628291 | − | 0.777979i | \(-0.283755\pi\) | ||||
0.628291 | + | 0.777979i | \(0.283755\pi\) | |||||||
\(420\) | −1447.32 | − | 1051.54i | −0.168147 | − | 0.122166i | ||||
\(421\) | 380.512 | − | 1171.10i | 0.0440500 | − | 0.135572i | −0.926613 | − | 0.376017i | \(-0.877293\pi\) |
0.970663 | + | 0.240445i | \(0.0772934\pi\) | |||||||
\(422\) | 3834.13 | + | 11800.2i | 0.442281 | + | 1.36120i | ||||
\(423\) | 1612.82 | − | 1171.78i | 0.185385 | − | 0.134690i | ||||
\(424\) | −866.665 | + | 629.669i | −0.0992665 | + | 0.0721213i | ||||
\(425\) | 275.476 | + | 847.829i | 0.0314413 | + | 0.0967665i | ||||
\(426\) | −1737.84 | + | 5348.52i | −0.197649 | + | 0.608302i | ||||
\(427\) | −10772.1 | − | 7826.36i | −1.22083 | − | 0.886988i | ||||
\(428\) | 1161.97 | 0.131228 | ||||||||
\(429\) | −2167.55 | − | 7719.48i | −0.243941 | − | 0.868764i | ||||
\(430\) | 3810.46 | 0.427342 | ||||||||
\(431\) | −7047.38 | − | 5120.22i | −0.787611 | − | 0.572233i | 0.119643 | − | 0.992817i | \(-0.461825\pi\) |
−0.907253 | + | 0.420584i | \(0.861825\pi\) | |||||||
\(432\) | −392.122 | + | 1206.83i | −0.0436713 | + | 0.134406i | ||||
\(433\) | 2313.66 | + | 7120.71i | 0.256784 | + | 0.790299i | 0.993473 | + | 0.114068i | \(0.0363880\pi\) |
−0.736689 | + | 0.676231i | \(0.763612\pi\) | |||||||
\(434\) | 1526.20 | − | 1108.85i | 0.168802 | − | 0.122642i | ||||
\(435\) | 1942.84 | − | 1411.56i | 0.214143 | − | 0.155584i | ||||
\(436\) | −46.1803 | − | 142.128i | −0.00507256 | − | 0.0156117i | ||||
\(437\) | −2552.05 | + | 7854.40i | −0.279362 | + | 0.859787i | ||||
\(438\) | 1347.59 | + | 979.080i | 0.147010 | + | 0.106809i | ||||
\(439\) | 9595.95 | 1.04326 | 0.521628 | − | 0.853173i | \(-0.325325\pi\) | ||||
0.521628 | + | 0.853173i | \(0.325325\pi\) | |||||||
\(440\) | −9270.16 | − | 374.885i | −1.00440 | − | 0.0406180i | ||||
\(441\) | 6569.38 | 0.709359 | ||||||||
\(442\) | −8193.69 | − | 5953.07i | −0.881752 | − | 0.640630i | ||||
\(443\) | 2871.05 | − | 8836.18i | 0.307918 | − | 0.947674i | −0.670654 | − | 0.741770i | \(-0.733987\pi\) |
0.978572 | − | 0.205904i | \(-0.0660133\pi\) | |||||||
\(444\) | −203.532 | − | 626.406i | −0.0217549 | − | 0.0669548i | ||||
\(445\) | −8897.76 | + | 6464.60i | −0.947853 | + | 0.688655i | ||||
\(446\) | 7444.32 | − | 5408.62i | 0.790356 | − | 0.574227i | ||||
\(447\) | 1955.96 | + | 6019.83i | 0.206966 | + | 0.636975i | ||||
\(448\) | −5765.98 | + | 17745.9i | −0.608074 | + | 1.87146i | ||||
\(449\) | 5550.31 | + | 4032.54i | 0.583375 | + | 0.423847i | 0.839939 | − | 0.542680i | \(-0.182591\pi\) |
−0.256564 | + | 0.966527i | \(0.582591\pi\) | |||||||
\(450\) | −363.013 | −0.0380280 | ||||||||
\(451\) | −4009.15 | − | 3168.03i | −0.418589 | − | 0.330769i | ||||
\(452\) | 768.199 | 0.0799403 | ||||||||
\(453\) | −2881.16 | − | 2093.28i | −0.298827 | − | 0.217110i | ||||
\(454\) | 310.478 | − | 955.553i | 0.0320957 | − | 0.0987805i | ||||
\(455\) | 7737.22 | + | 23812.7i | 0.797201 | + | 2.45353i | ||||
\(456\) | 5356.61 | − | 3891.80i | 0.550101 | − | 0.399672i | ||||
\(457\) | −935.459 | + | 679.650i | −0.0957525 | + | 0.0695683i | −0.634631 | − | 0.772815i | \(-0.718848\pi\) |
0.538879 | + | 0.842383i | \(0.318848\pi\) | |||||||
\(458\) | −2281.39 | − | 7021.40i | −0.232756 | − | 0.716351i | ||||
\(459\) | −461.201 | + | 1419.43i | −0.0468998 | + | 0.144343i | ||||
\(460\) | −1343.21 | − | 975.902i | −0.136147 | − | 0.0989167i | ||||
\(461\) | −8394.87 | −0.848131 | −0.424065 | − | 0.905632i | \(-0.639397\pi\) | ||||
−0.424065 | + | 0.905632i | \(0.639397\pi\) | |||||||
\(462\) | 7460.99 | − | 4972.90i | 0.751335 | − | 0.500779i | ||||
\(463\) | 1801.45 | 0.180822 | 0.0904108 | − | 0.995905i | \(-0.471182\pi\) | ||||
0.0904108 | + | 0.995905i | \(0.471182\pi\) | |||||||
\(464\) | −2916.97 | − | 2119.31i | −0.291847 | − | 0.212039i | ||||
\(465\) | 222.746 | − | 685.542i | 0.0222142 | − | 0.0683683i | ||||
\(466\) | −1905.73 | − | 5865.25i | −0.189445 | − | 0.583052i | ||||
\(467\) | 15389.4 | − | 11181.0i | 1.52492 | − | 1.10792i | 0.565934 | − | 0.824451i | \(-0.308516\pi\) |
0.958982 | − | 0.283466i | \(-0.0914842\pi\) | |||||||
\(468\) | −930.670 | + | 676.172i | −0.0919236 | + | 0.0667864i | ||||
\(469\) | −2239.34 | − | 6891.98i | −0.220476 | − | 0.678555i | ||||
\(470\) | −1786.27 | + | 5497.59i | −0.175308 | + | 0.539542i | ||||
\(471\) | 4487.48 | + | 3260.34i | 0.439007 | + | 0.318957i | ||||
\(472\) | 9792.36 | 0.954936 | ||||||||
\(473\) | 1849.51 | − | 4995.66i | 0.179790 | − | 0.485625i | ||||
\(474\) | −8855.65 | −0.858129 | ||||||||
\(475\) | 1181.50 | + | 858.410i | 0.114128 | + | 0.0829190i | ||||
\(476\) | −976.227 | + | 3004.52i | −0.0940027 | + | 0.289311i | ||||
\(477\) | −122.243 | − | 376.226i | −0.0117340 | − | 0.0361137i | ||||
\(478\) | 8590.15 | − | 6241.11i | 0.821976 | − | 0.597200i | ||||
\(479\) | 13686.9 | − | 9944.13i | 1.30558 | − | 0.948557i | 0.305583 | − | 0.952165i | \(-0.401149\pi\) |
0.999993 | + | 0.00360855i | \(0.00114864\pi\) | |||||||
\(480\) | 749.022 | + | 2305.25i | 0.0712250 | + | 0.219208i | ||||
\(481\) | −2848.58 | + | 8767.03i | −0.270029 | + | 0.831065i | ||||
\(482\) | 5435.33 | + | 3949.00i | 0.513636 | + | 0.373178i | ||||
\(483\) | 8961.81 | 0.844258 | ||||||||
\(484\) | −893.627 | + | 2143.47i | −0.0839244 | + | 0.201303i | ||||
\(485\) | −2561.08 | −0.239779 | ||||||||
\(486\) | −491.683 | − | 357.229i | −0.0458914 | − | 0.0333420i | ||||
\(487\) | −2844.77 | + | 8755.32i | −0.264700 | + | 0.814664i | 0.727062 | + | 0.686572i | \(0.240885\pi\) |
−0.991762 | + | 0.128092i | \(0.959115\pi\) | |||||||
\(488\) | 3061.48 | + | 9422.25i | 0.283989 | + | 0.874027i | ||||
\(489\) | −4400.13 | + | 3196.88i | −0.406914 | + | 0.295640i | ||||
\(490\) | −15410.6 | + | 11196.5i | −1.42078 | + | 1.03226i | ||||
\(491\) | 5069.27 | + | 15601.6i | 0.465933 | + | 1.43399i | 0.857805 | + | 0.513975i | \(0.171827\pi\) |
−0.391872 | + | 0.920020i | \(0.628173\pi\) | |||||||
\(492\) | −226.545 | + | 697.234i | −0.0207590 | + | 0.0638897i | ||||
\(493\) | −3430.84 | − | 2492.65i | −0.313423 | − | 0.227715i | ||||
\(494\) | −16591.9 | −1.51114 | ||||||||
\(495\) | 1189.50 | − | 3212.91i | 0.108008 | − | 0.291736i | ||||
\(496\) | −1082.24 | −0.0979715 | ||||||||
\(497\) | −19862.2 | − | 14430.7i | −1.79264 | − | 1.30243i | ||||
\(498\) | 1568.89 | − | 4828.54i | 0.141172 | − | 0.434482i | ||||
\(499\) | −1431.17 | − | 4404.69i | −0.128393 | − | 0.395152i | 0.866111 | − | 0.499851i | \(-0.166612\pi\) |
−0.994504 | + | 0.104699i | \(0.966612\pi\) | |||||||
\(500\) | −2078.58 | + | 1510.18i | −0.185914 | + | 0.135074i | ||||
\(501\) | −641.673 | + | 466.202i | −0.0572212 | + | 0.0415736i | ||||
\(502\) | 5685.18 | + | 17497.2i | 0.505462 | + | 1.55565i | ||||
\(503\) | 6057.33 | − | 18642.5i | 0.536944 | − | 1.65255i | −0.202465 | − | 0.979289i | \(-0.564895\pi\) |
0.739410 | − | 0.673256i | \(-0.235105\pi\) | |||||||
\(504\) | −5812.72 | − | 4223.19i | −0.513728 | − | 0.373245i | ||||
\(505\) | 236.770 | 0.0208636 | ||||||||
\(506\) | 6924.34 | − | 4615.21i | 0.608349 | − | 0.405476i | ||||
\(507\) | 9509.33 | 0.832987 | ||||||||
\(508\) | 2294.33 | + | 1666.93i | 0.200382 | + | 0.145586i | ||||
\(509\) | 5031.84 | − | 15486.4i | 0.438178 | − | 1.34857i | −0.451617 | − | 0.892212i | \(-0.649153\pi\) |
0.889795 | − | 0.456360i | \(-0.150847\pi\) | |||||||
\(510\) | −1337.30 | − | 4115.78i | −0.116111 | − | 0.357353i | ||||
\(511\) | −5883.02 | + | 4274.26i | −0.509294 | + | 0.370024i | ||||
\(512\) | 10357.6 | − | 7525.21i | 0.894031 | − | 0.649551i | ||||
\(513\) | 755.551 | + | 2325.35i | 0.0650261 | + | 0.200130i | ||||
\(514\) | −369.634 | + | 1137.62i | −0.0317196 | + | 0.0976227i | ||||
\(515\) | −8284.44 | − | 6019.00i | −0.708846 | − | 0.515007i | ||||
\(516\) | −764.288 | −0.0652052 | ||||||||
\(517\) | 6340.52 | + | 5010.28i | 0.539373 | + | 0.426212i | ||||
\(518\) | −10308.5 | −0.874384 | ||||||||
\(519\) | 1614.37 | + | 1172.91i | 0.136538 | + | 0.0992003i | ||||
\(520\) | 5756.95 | − | 17718.1i | 0.485498 | − | 1.49421i | ||||
\(521\) | −3170.21 | − | 9756.91i | −0.266583 | − | 0.820457i | −0.991325 | − | 0.131436i | \(-0.958041\pi\) |
0.724742 | − | 0.689020i | \(-0.241959\pi\) | |||||||
\(522\) | 1397.08 | − | 1015.04i | 0.117143 | − | 0.0851092i | ||||
\(523\) | −17290.3 | + | 12562.2i | −1.44561 | + | 1.05030i | −0.458776 | + | 0.888552i | \(0.651712\pi\) |
−0.986833 | + | 0.161744i | \(0.948288\pi\) | |||||||
\(524\) | −565.907 | − | 1741.68i | −0.0471789 | − | 0.145202i | ||||
\(525\) | 489.720 | − | 1507.20i | 0.0407107 | − | 0.125295i | ||||
\(526\) | −8003.27 | − | 5814.71i | −0.663420 | − | 0.482003i | ||||
\(527\) | −1272.89 | −0.105214 | ||||||||
\(528\) | −5139.62 | − | 207.846i | −0.423624 | − | 0.0171313i | ||||
\(529\) | −3849.79 | −0.316413 | ||||||||
\(530\) | 927.982 | + | 674.218i | 0.0760546 | + | 0.0552569i | ||||
\(531\) | −1117.43 | + | 3439.09i | −0.0913224 | + | 0.281061i | ||||
\(532\) | 1599.28 | + | 4922.08i | 0.130334 | + | 0.401127i | ||||
\(533\) | 8300.93 | − | 6030.98i | 0.674584 | − | 0.490114i | ||||
\(534\) | −6398.29 | + | 4648.63i | −0.518504 | + | 0.376715i | ||||
\(535\) | −2147.32 | − | 6608.77i | −0.173527 | − | 0.534060i | ||||
\(536\) | −1666.20 | + | 5128.04i | −0.134270 | + | 0.413242i | ||||
\(537\) | 157.941 | + | 114.751i | 0.0126921 | + | 0.00922133i | ||||
\(538\) | −3276.65 | −0.262577 | ||||||||
\(539\) | 7199.02 | + | 25638.4i | 0.575295 | + | 2.04884i | ||||
\(540\) | −491.544 | −0.0391717 | ||||||||
\(541\) | −17097.0 | − | 12421.7i | −1.35870 | − | 0.987157i | −0.998526 | − | 0.0542736i | \(-0.982716\pi\) |
−0.360179 | − | 0.932883i | \(-0.617284\pi\) | |||||||
\(542\) | −4215.79 | + | 12974.9i | −0.334103 | + | 1.02826i | ||||
\(543\) | −37.9698 | − | 116.859i | −0.00300081 | − | 0.00923555i | ||||
\(544\) | 3462.84 | − | 2515.90i | 0.272919 | − | 0.198287i | ||||
\(545\) | −723.024 | + | 525.308i | −0.0568274 | + | 0.0412875i | ||||
\(546\) | 5563.75 | + | 17123.5i | 0.436093 | + | 1.34216i | ||||
\(547\) | 214.684 | − | 660.729i | 0.0167810 | − | 0.0516467i | −0.942315 | − | 0.334726i | \(-0.891356\pi\) |
0.959096 | + | 0.283080i | \(0.0913561\pi\) | |||||||
\(548\) | −4338.15 | − | 3151.85i | −0.338169 | − | 0.245694i | ||||
\(549\) | −3658.45 | −0.284406 | ||||||||
\(550\) | −397.806 | − | 1416.74i | −0.0308409 | − | 0.109836i | ||||
\(551\) | −6947.32 | −0.537143 | ||||||||
\(552\) | −5394.62 | − | 3919.42i | −0.415961 | − | 0.302213i | ||||
\(553\) | 11946.6 | − | 36768.0i | 0.918667 | − | 2.82737i | ||||
\(554\) | −3680.55 | − | 11327.6i | −0.282259 | − | 0.868704i | ||||
\(555\) | −3186.60 | + | 2315.20i | −0.243718 | + | 0.177072i | ||||
\(556\) | −1505.94 | + | 1094.13i | −0.114867 | + | 0.0834558i | ||||
\(557\) | 5531.72 | + | 17024.9i | 0.420801 | + | 1.29509i | 0.906958 | + | 0.421222i | \(0.138399\pi\) |
−0.486156 | + | 0.873872i | \(0.661601\pi\) | |||||||
\(558\) | 160.174 | − | 492.966i | 0.0121518 | − | 0.0373995i | ||||
\(559\) | 8653.88 | + | 6287.42i | 0.654777 | + | 0.475723i | ||||
\(560\) | 16062.8 | 1.21210 | ||||||||
\(561\) | −6045.04 | − | 244.461i | −0.454941 | − | 0.0183978i | ||||
\(562\) | −1397.22 | −0.104872 | ||||||||
\(563\) | −12328.2 | − | 8956.97i | −0.922864 | − | 0.670500i | 0.0213713 | − | 0.999772i | \(-0.493197\pi\) |
−0.944235 | + | 0.329272i | \(0.893197\pi\) | |||||||
\(564\) | 358.284 | − | 1102.68i | 0.0267491 | − | 0.0823252i | ||||
\(565\) | −1419.63 | − | 4369.19i | −0.105707 | − | 0.325333i | ||||
\(566\) | 4178.46 | − | 3035.83i | 0.310307 | − | 0.225451i | ||||
\(567\) | 2146.49 | − | 1559.51i | 0.158984 | − | 0.115509i | ||||
\(568\) | 5644.95 | + | 17373.4i | 0.417001 | + | 1.28340i | ||||
\(569\) | −7618.38 | + | 23447.0i | −0.561299 | + | 1.72750i | 0.117401 | + | 0.993085i | \(0.462544\pi\) |
−0.678700 | + | 0.734416i | \(0.737456\pi\) | |||||||
\(570\) | −5735.59 | − | 4167.15i | −0.421469 | − | 0.306215i | ||||
\(571\) | 20893.8 | 1.53131 | 0.765656 | − | 0.643250i | \(-0.222415\pi\) | ||||
0.765656 | + | 0.643250i | \(0.222415\pi\) | |||||||
\(572\) | −3658.78 | − | 2891.17i | −0.267450 | − | 0.211339i | ||||
\(573\) | 13739.8 | 1.00172 | ||||||||
\(574\) | 9282.76 | + | 6744.32i | 0.675009 | + | 0.490422i | ||||
\(575\) | 454.495 | − | 1398.79i | 0.0329631 | − | 0.101450i | ||||
\(576\) | 1584.27 | + | 4875.89i | 0.114603 | + | 0.352712i | ||||
\(577\) | 11720.4 | − | 8515.35i | 0.845624 | − | 0.614382i | −0.0783117 | − | 0.996929i | \(-0.524953\pi\) |
0.923936 | + | 0.382547i | \(0.124953\pi\) | |||||||
\(578\) | 3758.37 | − | 2730.62i | 0.270463 | − | 0.196503i | ||||
\(579\) | −4676.62 | − | 14393.2i | −0.335671 | − | 1.03309i | ||||
\(580\) | 431.599 | − | 1328.33i | 0.0308986 | − | 0.0950961i | ||||
\(581\) | 17931.2 | + | 13027.8i | 1.28040 | + | 0.930266i | ||||
\(582\) | −1841.65 | −0.131166 | ||||||||
\(583\) | 1334.35 | − | 889.368i | 0.0947907 | − | 0.0631798i | ||||
\(584\) | 5410.65 | 0.383381 | ||||||||
\(585\) | 5565.66 | + | 4043.69i | 0.393353 | + | 0.285788i | ||||
\(586\) | −5793.51 | + | 17830.6i | −0.408409 | + | 1.25695i | ||||
\(587\) | 2950.00 | + | 9079.16i | 0.207427 | + | 0.638394i | 0.999605 | + | 0.0281041i | \(0.00894698\pi\) |
−0.792178 | + | 0.610290i | \(0.791053\pi\) | |||||||
\(588\) | 3091.00 | − | 2245.75i | 0.216787 | − | 0.157505i | ||||
\(589\) | −1687.03 | + | 1225.70i | −0.118018 | + | 0.0857453i | ||||
\(590\) | −3240.10 | − | 9971.99i | −0.226089 | − | 0.695831i | ||||
\(591\) | 1579.01 | − | 4859.68i | 0.109901 | − | 0.338242i | ||||
\(592\) | 4784.34 | + | 3476.03i | 0.332154 | + | 0.241324i | ||||
\(593\) | −15771.0 | −1.09213 | −0.546067 | − | 0.837741i | \(-0.683876\pi\) | ||||
−0.546067 | + | 0.837741i | \(0.683876\pi\) | |||||||
\(594\) | 855.355 | − | 2310.37i | 0.0590836 | − | 0.159589i | ||||
\(595\) | 18892.5 | 1.30171 | ||||||||
\(596\) | 2978.19 | + | 2163.78i | 0.204684 | + | 0.148712i | ||||
\(597\) | −3083.47 | + | 9489.95i | −0.211387 | + | 0.650583i | ||||
\(598\) | 5163.56 | + | 15891.8i | 0.353100 | + | 1.08673i | ||||
\(599\) | −15970.3 | + | 11603.1i | −1.08936 | + | 0.791469i | −0.979292 | − | 0.202455i | \(-0.935108\pi\) |
−0.110072 | + | 0.993924i | \(0.535108\pi\) | |||||||
\(600\) | −953.961 | + | 693.093i | −0.0649088 | + | 0.0471590i | ||||
\(601\) | 667.170 | + | 2053.34i | 0.0452819 | + | 0.139363i | 0.971141 | − | 0.238505i | \(-0.0766573\pi\) |
−0.925859 | + | 0.377868i | \(0.876657\pi\) | |||||||
\(602\) | −3696.46 | + | 11376.5i | −0.250260 | + | 0.770221i | ||||
\(603\) | −1610.84 | − | 1170.34i | −0.108787 | − | 0.0790382i | ||||
\(604\) | −2071.22 | −0.139531 | ||||||||
\(605\) | 13842.6 | + | 1121.42i | 0.930217 | + | 0.0753591i | ||||
\(606\) | 170.259 | 0.0114130 | ||||||||
\(607\) | −4096.74 | − | 2976.46i | −0.273940 | − | 0.199029i | 0.442330 | − | 0.896852i | \(-0.354152\pi\) |
−0.716270 | + | 0.697823i | \(0.754152\pi\) | |||||||
\(608\) | 2166.86 | − | 6668.91i | 0.144536 | − | 0.444836i | ||||
\(609\) | 2329.64 | + | 7169.90i | 0.155011 | + | 0.477075i | ||||
\(610\) | 8582.11 | − | 6235.27i | 0.569639 | − | 0.413867i | ||||
\(611\) | −13128.0 | + | 9538.06i | −0.869235 | + | 0.631536i | ||||
\(612\) | 268.230 | + | 825.528i | 0.0177166 | + | 0.0545261i | ||||
\(613\) | 7547.95 | − | 23230.2i | 0.497323 | − | 1.53060i | −0.315982 | − | 0.948765i | \(-0.602334\pi\) |
0.813305 | − | 0.581837i | \(-0.197666\pi\) | |||||||
\(614\) | −2096.69 | − | 1523.33i | −0.137810 | − | 0.100125i | ||||
\(615\) | 4384.23 | 0.287462 | ||||||||
\(616\) | 10112.1 | − | 27313.4i | 0.661408 | − | 1.78650i | ||||
\(617\) | −13814.4 | −0.901369 | −0.450685 | − | 0.892683i | \(-0.648820\pi\) | ||||
−0.450685 | + | 0.892683i | \(0.648820\pi\) | |||||||
\(618\) | −5957.25 | − | 4328.20i | −0.387760 | − | 0.281724i | ||||
\(619\) | −1351.02 | + | 4158.01i | −0.0877255 | + | 0.269991i | −0.985290 | − | 0.170892i | \(-0.945335\pi\) |
0.897564 | + | 0.440884i | \(0.145335\pi\) | |||||||
\(620\) | −129.547 | − | 398.705i | −0.00839151 | − | 0.0258264i | ||||
\(621\) | 1992.10 | − | 1447.34i | 0.128728 | − | 0.0935263i | ||||
\(622\) | 20911.0 | − | 15192.8i | 1.34800 | − | 0.979379i | ||||
\(623\) | −10669.2 | − | 32836.4i | −0.686119 | − | 2.11166i | ||||
\(624\) | 3191.80 | − | 9823.36i | 0.204767 | − | 0.630207i | ||||
\(625\) | 10799.6 | + | 7846.36i | 0.691173 | + | 0.502167i | ||||
\(626\) | 17834.8 | 1.13869 | ||||||||
\(627\) | −8247.21 | + | 5496.93i | −0.525298 | + | 0.350121i | ||||
\(628\) | 3225.99 | 0.204985 | ||||||||
\(629\) | 5627.18 | + | 4088.38i | 0.356710 | + | 0.259165i | ||||
\(630\) | −2377.34 | + | 7316.71i | −0.150342 | + | 0.462706i | ||||
\(631\) | −714.402 | − | 2198.70i | −0.0450711 | − | 0.138715i | 0.925989 | − | 0.377552i | \(-0.123234\pi\) |
−0.971060 | + | 0.238837i | \(0.923234\pi\) | |||||||
\(632\) | −23271.7 | + | 16907.9i | −1.46471 | + | 1.06418i | ||||
\(633\) | −12040.4 | + | 8747.88i | −0.756025 | + | 0.549285i | ||||
\(634\) | −4982.12 | − | 15333.4i | −0.312090 | − | 0.960514i | ||||
\(635\) | 5240.84 | − | 16129.6i | 0.327522 | − | 1.00801i | ||||
\(636\) | −186.131 | − | 135.232i | −0.0116047 | − | 0.00843129i | ||||
\(637\) | −53473.5 | −3.32605 | ||||||||
\(638\) | 5492.39 | + | 4340.09i | 0.340824 | + | 0.269319i | ||||
\(639\) | −6745.70 | −0.417615 | ||||||||
\(640\) | −6797.40 | − | 4938.60i | −0.419829 | − | 0.305024i | ||||
\(641\) | −5704.03 | + | 17555.2i | −0.351475 | + | 1.08173i | 0.606550 | + | 0.795045i | \(0.292553\pi\) |
−0.958025 | + | 0.286684i | \(0.907447\pi\) | |||||||
\(642\) | −1544.12 | − | 4752.30i | −0.0949242 | − | 0.292147i | ||||
\(643\) | −23792.8 | + | 17286.4i | −1.45925 | + | 1.06020i | −0.475686 | + | 0.879615i | \(0.657800\pi\) |
−0.983559 | + | 0.180589i | \(0.942200\pi\) | |||||||
\(644\) | 4216.69 | − | 3063.60i | 0.258014 | − | 0.187458i | ||||
\(645\) | 1412.41 | + | 4346.94i | 0.0862225 | + | 0.265365i | ||||
\(646\) | −3868.70 | + | 11906.6i | −0.235622 | + | 0.725171i | ||||
\(647\) | 1793.76 | + | 1303.24i | 0.108995 | + | 0.0791897i | 0.640948 | − | 0.767585i | \(-0.278542\pi\) |
−0.531953 | + | 0.846774i | \(0.678542\pi\) | |||||||
\(648\) | −1974.14 | −0.119678 | ||||||||
\(649\) | −14646.3 | − | 592.297i | −0.885852 | − | 0.0358238i | ||||
\(650\) | 2954.86 | 0.178306 | ||||||||
\(651\) | 1830.68 | + | 1330.06i | 0.110215 | + | 0.0800758i | ||||
\(652\) | −977.481 | + | 3008.38i | −0.0587134 | + | 0.180701i | ||||
\(653\) | 6953.29 | + | 21400.0i | 0.416697 | + | 1.28246i | 0.910724 | + | 0.413015i | \(0.135524\pi\) |
−0.494027 | + | 0.869447i | \(0.664476\pi\) | |||||||
\(654\) | −519.919 | + | 377.743i | −0.0310863 | + | 0.0225855i | ||||
\(655\) | −8860.14 | + | 6437.27i | −0.528541 | + | 0.384008i | ||||
\(656\) | −2034.09 | − | 6260.28i | −0.121064 | − | 0.372596i | ||||
\(657\) | −617.421 | + | 1900.23i | −0.0366635 | + | 0.112839i | ||||
\(658\) | −14680.8 | − | 10666.2i | −0.869783 | − | 0.631934i | ||||
\(659\) | 5908.12 | 0.349238 | 0.174619 | − | 0.984636i | \(-0.444131\pi\) | ||||
0.174619 | + | 0.984636i | \(0.444131\pi\) | |||||||
\(660\) | −538.656 | − | 1918.36i | −0.0317684 | − | 0.113139i | ||||
\(661\) | 22387.2 | 1.31734 | 0.658670 | − | 0.752432i | \(-0.271120\pi\) | ||||
0.658670 | + | 0.752432i | \(0.271120\pi\) | |||||||
\(662\) | −11400.8 | − | 8283.17i | −0.669343 | − | 0.486306i | ||||
\(663\) | 3754.09 | − | 11553.9i | 0.219904 | − | 0.676796i | ||||
\(664\) | −5096.16 | − | 15684.4i | −0.297845 | − | 0.916673i | ||||
\(665\) | 25039.2 | − | 18192.1i | 1.46012 | − | 1.06084i | ||||
\(666\) | −2291.45 | + | 1664.84i | −0.133321 | + | 0.0968636i | ||||
\(667\) | 2162.07 | + | 6654.18i | 0.125511 | + | 0.386283i | ||||
\(668\) | −142.546 | + | 438.712i | −0.00825641 | + | 0.0254106i | ||||
\(669\) | 8929.45 | + | 6487.63i | 0.516043 | + | 0.374927i | ||||
\(670\) | 5773.42 | 0.332906 | ||||||||
\(671\) | −4009.10 | − | 14277.9i | −0.230655 | − | 0.821450i | ||||
\(672\) | −7609.18 | −0.436802 | ||||||||
\(673\) | 25692.3 | + | 18666.6i | 1.47157 | + | 1.06916i | 0.980155 | + | 0.198233i | \(0.0635204\pi\) |
0.491416 | + | 0.870925i | \(0.336480\pi\) | |||||||
\(674\) | 2363.77 | − | 7274.93i | 0.135087 | − | 0.415757i | ||||
\(675\) | −134.556 | − | 414.122i | −0.00767271 | − | 0.0236142i | ||||
\(676\) | 4474.30 | − | 3250.77i | 0.254569 | − | 0.184955i | ||||
\(677\) | 2970.62 | − | 2158.28i | 0.168641 | − | 0.122525i | −0.500263 | − | 0.865873i | \(-0.666763\pi\) |
0.668905 | + | 0.743348i | \(0.266763\pi\) | |||||||
\(678\) | −1020.84 | − | 3141.84i | −0.0578249 | − | 0.177967i | ||||
\(679\) | 2484.46 | − | 7646.38i | 0.140419 | − | 0.432166i | ||||
\(680\) | −11372.5 | − | 8262.58i | −0.641344 | − | 0.465964i | ||||
\(681\) | 1205.17 | 0.0678153 | ||||||||
\(682\) | 2099.44 | + | 84.9011i | 0.117876 | + | 0.00476691i | ||||
\(683\) | −11719.2 | −0.656549 | −0.328274 | − | 0.944582i | \(-0.606467\pi\) | ||||
−0.328274 | + | 0.944582i | \(0.606467\pi\) | |||||||
\(684\) | 1150.42 | + | 835.830i | 0.0643091 | + | 0.0467233i | ||||
\(685\) | −9909.46 | + | 30498.2i | −0.552732 | + | 1.70113i | ||||
\(686\) | −9795.42 | − | 30147.2i | −0.545176 | − | 1.67788i | ||||
\(687\) | 7164.32 | − | 5205.18i | 0.397869 | − | 0.289069i | ||||
\(688\) | 5551.75 | − | 4033.58i | 0.307643 | − | 0.223516i | ||||
\(689\) | 995.038 | + | 3062.41i | 0.0550188 | + | 0.169330i | ||||
\(690\) | −2206.35 | + | 6790.44i | −0.121731 | + | 0.374649i | ||||
\(691\) | −495.853 | − | 360.259i | −0.0272983 | − | 0.0198334i | 0.574052 | − | 0.818819i | \(-0.305371\pi\) |
−0.601351 | + | 0.798985i | \(0.705371\pi\) | |||||||
\(692\) | 1160.55 | 0.0637535 | ||||||||
\(693\) | 8438.57 | + | 6668.15i | 0.462561 | + | 0.365515i | ||||
\(694\) | −26301.7 | −1.43862 | ||||||||
\(695\) | 9005.93 | + | 6543.19i | 0.491531 | + | 0.357119i | ||||
\(696\) | 1733.39 | − | 5334.83i | 0.0944023 | − | 0.290540i | ||||
\(697\) | −2392.42 | − | 7363.13i | −0.130014 | − | 0.400141i | ||||
\(698\) | −3045.07 | + | 2212.37i | −0.165125 | + | 0.119971i | ||||
\(699\) | 5984.63 | − | 4348.09i | 0.323833 | − | 0.235279i | ||||
\(700\) | −284.817 | − | 876.576i | −0.0153787 | − | 0.0473306i | ||||
\(701\) | 8657.42 | − | 26644.8i | 0.466457 | − | 1.43561i | −0.390684 | − | 0.920525i | \(-0.627762\pi\) |
0.857141 | − | 0.515082i | \(-0.172238\pi\) | |||||||
\(702\) | 4002.21 | + | 2907.77i | 0.215176 | + | 0.156335i | ||||
\(703\) | 11394.8 | 0.611328 | ||||||||
\(704\) | −17293.1 | + | 11526.2i | −0.925794 | + | 0.617060i | ||||
\(705\) | −6933.71 | −0.370409 | ||||||||
\(706\) | 23896.5 | + | 17361.9i | 1.27388 | + | 0.925527i | ||||
\(707\) | −229.686 | + | 706.902i | −0.0122182 | + | 0.0376037i | ||||
\(708\) | 649.886 | + | 2000.14i | 0.0344974 | + | 0.106172i | ||||
\(709\) | −9146.28 | + | 6645.16i | −0.484479 | + | 0.351995i | −0.803057 | − | 0.595902i | \(-0.796795\pi\) |
0.318578 | + | 0.947897i | \(0.396795\pi\) | |||||||
\(710\) | 15824.3 | − | 11497.0i | 0.836442 | − | 0.607711i | ||||
\(711\) | −3282.48 | − | 10102.4i | −0.173140 | − | 0.532871i | ||||
\(712\) | −7938.51 | + | 24432.2i | −0.417849 | + | 1.28601i | ||||
\(713\) | 1699.00 | + | 1234.40i | 0.0892399 | + | 0.0648366i | ||||
\(714\) | 13585.4 | 0.712074 | ||||||||
\(715\) | −9682.28 | + | 26152.5i | −0.506429 | + | 1.36790i | ||||
\(716\) | 113.541 | 0.00592631 | ||||||||
\(717\) | 10303.9 | + | 7486.20i | 0.536688 | + | 0.389927i | ||||
\(718\) | 2555.60 | − | 7865.34i | 0.132833 | − | 0.408819i | ||||
\(719\) | 3455.04 | + | 10633.5i | 0.179209 | + | 0.551549i | 0.999801 | − | 0.0199662i | \(-0.00635588\pi\) |
−0.820592 | + | 0.571515i | \(0.806356\pi\) | |||||||
\(720\) | 3570.55 | − | 2594.16i | 0.184815 | − | 0.134276i | ||||
\(721\) | 26006.9 | − | 18895.1i | 1.34334 | − | 0.975994i | ||||
\(722\) | 1036.73 | + | 3190.72i | 0.0534390 | + | 0.164468i | ||||
\(723\) | −2490.29 | + | 7664.33i | −0.128098 | + | 0.394246i | ||||
\(724\) | −57.8138 | − | 42.0042i | −0.00296772 | − | 0.00215618i | ||||
\(725\) | 1237.25 | 0.0633798 | ||||||||
\(726\) | 9954.06 | + | 806.403i | 0.508857 | + | 0.0412237i | ||||
\(727\) | −31428.7 | −1.60334 | −0.801669 | − | 0.597769i | \(-0.796054\pi\) | ||||
−0.801669 | + | 0.597769i | \(0.796054\pi\) | |||||||
\(728\) | 47314.4 | + | 34375.9i | 2.40878 | + | 1.75008i | ||||
\(729\) | 225.273 | − | 693.320i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | −1790.28 | − | 5509.91i | −0.0907687 | − | 0.279357i | ||||
\(731\) | 6529.77 | − | 4744.16i | 0.330386 | − | 0.240040i | ||||
\(732\) | −1721.37 | + | 1250.65i | −0.0869174 | + | 0.0631492i | ||||
\(733\) | 392.631 | + | 1208.39i | 0.0197847 | + | 0.0608910i | 0.960461 | − | 0.278413i | \(-0.0898084\pi\) |
−0.940677 | + | 0.339304i | \(0.889808\pi\) | |||||||
\(734\) | −2772.75 | + | 8533.64i | −0.139433 | + | 0.429131i | ||||
\(735\) | −18485.0 | − | 13430.2i | −0.927661 | − | 0.673985i | ||||
\(736\) | −7061.87 | −0.353674 | ||||||||
\(737\) | 2802.29 | − | 7569.17i | 0.140059 | − | 0.378309i | ||||
\(738\) | 3152.65 | 0.157250 | ||||||||
\(739\) | −10929.8 | − | 7940.95i | −0.544057 | − | 0.395281i | 0.281532 | − | 0.959552i | \(-0.409157\pi\) |
−0.825590 | + | 0.564271i | \(0.809157\pi\) | |||||||
\(740\) | −707.898 | + | 2178.68i | −0.0351660 | + | 0.108230i | ||||
\(741\) | −6150.04 | − | 18927.9i | −0.304895 | − | 0.938371i | ||||
\(742\) | −2913.17 | + | 2116.54i | −0.144132 | + | 0.104718i | ||||
\(743\) | −25972.0 | + | 18869.8i | −1.28240 | + | 0.931716i | −0.999623 | − | 0.0274700i | \(-0.991255\pi\) |
−0.282775 | + | 0.959186i | \(0.591255\pi\) | |||||||
\(744\) | −520.288 | − | 1601.28i | −0.0256380 | − | 0.0789057i | ||||
\(745\) | 6802.97 | − | 20937.4i | 0.334552 | − | 1.02965i | ||||
\(746\) | 4092.02 | + | 2973.03i | 0.200830 | + | 0.145912i | ||||
\(747\) | 6089.89 | 0.298283 | ||||||||
\(748\) | −2927.86 | + | 1951.48i | −0.143119 | + | 0.0953918i | ||||
\(749\) | 21814.3 | 1.06419 | ||||||||
\(750\) | 8938.63 | + | 6494.29i | 0.435190 | + | 0.316184i | ||||
\(751\) | −7329.02 | + | 22556.4i | −0.356111 | + | 1.09600i | 0.599251 | + | 0.800561i | \(0.295465\pi\) |
−0.955362 | + | 0.295437i | \(0.904535\pi\) | |||||||
\(752\) | 3216.94 | + | 9900.71i | 0.155997 | + | 0.480109i | ||||
\(753\) | −17853.3 | + | 12971.2i | −0.864026 | + | 0.627752i | ||||
\(754\) | −11372.0 | + | 8262.21i | −0.549260 | + | 0.399061i | ||||
\(755\) | 3827.63 | + | 11780.2i | 0.184506 | + | 0.567850i | ||||
\(756\) | 476.838 | − | 1467.56i | 0.0229397 | − | 0.0706012i | ||||
\(757\) | 18715.6 | + | 13597.7i | 0.898589 | + | 0.652863i | 0.938103 | − | 0.346356i | \(-0.112581\pi\) |
−0.0395142 | + | 0.999219i | \(0.512581\pi\) | |||||||
\(758\) | −14518.1 | −0.695672 | ||||||||
\(759\) | 7831.60 | + | 6188.53i | 0.374531 | + | 0.295954i | ||||
\(760\) | −23028.8 | −1.09913 | ||||||||
\(761\) | −667.872 | − | 485.238i | −0.0318139 | − | 0.0231141i | 0.571765 | − | 0.820418i | \(-0.306259\pi\) |
−0.603579 | + | 0.797304i | \(0.706259\pi\) | |||||||
\(762\) | 3768.63 | − | 11598.7i | 0.179164 | − | 0.551410i | ||||
\(763\) | −866.969 | − | 2668.26i | −0.0411355 | − | 0.126602i | ||||
\(764\) | 6464.80 | − | 4696.95i | 0.306136 | − | 0.222421i | ||||
\(765\) | 4199.56 | − | 3051.16i | 0.198478 | − | 0.144202i | ||||
\(766\) | −4048.46 | − | 12459.9i | −0.190962 | − | 0.587720i | ||||
\(767\) | 9095.64 | − | 27993.5i | 0.428194 | − | 1.31784i | ||||
\(768\) | 6172.55 | + | 4484.62i | 0.290016 | + | 0.210709i | ||||
\(769\) | 9591.21 | 0.449763 | 0.224882 | − | 0.974386i | \(-0.427800\pi\) | ||||
0.224882 | + | 0.974386i | \(0.427800\pi\) | |||||||
\(770\) | −31160.3 | − | 1260.12i | −1.45836 | − | 0.0589761i | ||||
\(771\) | −1434.79 | −0.0670205 | ||||||||
\(772\) | −7120.74 | − | 5173.52i | −0.331970 | − | 0.241191i | ||||
\(773\) | 724.297 | − | 2229.16i | 0.0337014 | − | 0.103722i | −0.932791 | − | 0.360418i | \(-0.882634\pi\) |
0.966492 | + | 0.256696i | \(0.0826340\pi\) | |||||||
\(774\) | 1015.65 | + | 3125.84i | 0.0471663 | + | 0.145163i | ||||
\(775\) | 300.443 | − | 218.285i | 0.0139255 | − | 0.0101175i | ||||
\(776\) | −4839.66 | + | 3516.22i | −0.223883 | + | 0.162661i | ||||
\(777\) | −3821.02 | − | 11759.9i | −0.176420 | − | 0.542964i | ||||
\(778\) | −65.6816 | + | 202.147i | −0.00302674 | + | 0.00931533i | ||||
\(779\) | −10260.9 | − | 7455.02i | −0.471934 | − | 0.342880i | ||||
\(780\) | 4001.08 | 0.183669 | ||||||||
\(781\) | −7392.24 | − | 26326.6i | −0.338688 | − | 1.20620i | ||||
\(782\) | 12608.2 | 0.576559 | ||||||||
\(783\) | 1675.79 | + | 1217.54i | 0.0764853 | + | 0.0555699i | ||||
\(784\) | −10600.8 | + | 32626.0i | −0.482909 | + | 1.48624i | ||||
\(785\) | −5961.64 | − | 18348.0i | −0.271057 | − | 0.834229i | ||||
\(786\) | −6371.24 | + | 4628.98i | −0.289128 | + | 0.210064i | ||||
\(787\) | 21078.8 | − | 15314.6i | 0.954736 | − | 0.693656i | 0.00281375 | − | 0.999996i | \(-0.499104\pi\) |
0.951922 | + | 0.306340i | \(0.0991044\pi\) | |||||||
\(788\) | −918.337 | − | 2826.35i | −0.0415157 | − | 0.127772i | ||||
\(789\) | 3666.84 | − | 11285.4i | 0.165454 | − | 0.509214i | ||||
\(790\) | 24918.2 | + | 18104.1i | 1.12221 | + | 0.815336i | ||||
\(791\) | 14421.8 | 0.648269 | ||||||||
\(792\) | −2163.35 | − | 7704.52i | −0.0970599 | − | 0.345667i | ||||
\(793\) | 29779.1 | 1.33353 | ||||||||
\(794\) | 14543.5 | + | 10566.5i | 0.650039 | + | 0.472281i | ||||
\(795\) | −425.171 | + | 1308.54i | −0.0189676 | + | 0.0583764i | ||||
\(796\) | 1793.32 | + | 5519.27i | 0.0798525 | + | 0.245761i | ||||
\(797\) | −35109.5 | + | 25508.5i | −1.56040 | + | 1.13370i | −0.624727 | + | 0.780844i | \(0.714790\pi\) |
−0.935677 | + | 0.352856i | \(0.885210\pi\) | |||||||
\(798\) | 18005.4 | − | 13081.7i | 0.798729 | − | 0.580311i | ||||
\(799\) | 3783.65 | + | 11644.9i | 0.167529 | + | 0.515602i | ||||
\(800\) | −385.897 | + | 1187.67i | −0.0170544 | + | 0.0524881i | ||||
\(801\) | −7674.74 | − | 5576.02i | −0.338544 | − | 0.245966i | ||||
\(802\) | 5687.54 | 0.250417 | ||||||||
\(803\) | −8092.65 | − | 327.267i | −0.355646 | − | 0.0143823i | ||||
\(804\) | −1158.01 | −0.0507958 | ||||||||
\(805\) | −25216.9 | − | 18321.2i | −1.10407 | − | 0.802157i | ||||
\(806\) | −1303.79 | + | 4012.65i | −0.0569777 | + | 0.175359i | ||||
\(807\) | −1214.54 | − | 3737.97i | −0.0529788 | − | 0.163052i | ||||
\(808\) | 447.423 | − | 325.072i | 0.0194805 | − | 0.0141534i | ||||
\(809\) | 6863.36 | − | 4986.53i | 0.298273 | − | 0.216708i | −0.428575 | − | 0.903506i | \(-0.640984\pi\) |
0.726848 | + | 0.686798i | \(0.240984\pi\) | |||||||
\(810\) | 653.204 | + | 2010.35i | 0.0283349 | + | 0.0872057i | ||||
\(811\) | 1715.59 | − | 5280.06i | 0.0742820 | − | 0.228616i | −0.907021 | − | 0.421085i | \(-0.861649\pi\) |
0.981303 | + | 0.192469i | \(0.0616494\pi\) | |||||||
\(812\) | 3547.17 | + | 2577.17i | 0.153302 | + | 0.111380i | ||||
\(813\) | −16364.3 | −0.705928 | ||||||||
\(814\) | −9008.48 | − | 7118.49i | −0.387895 | − | 0.306515i | ||||
\(815\) | 18916.8 | 0.813037 | ||||||||
\(816\) | −6305.19 | − | 4580.99i | −0.270497 | − | 0.196528i | ||||
\(817\) | 4085.98 | − | 12575.4i | 0.174970 | − | 0.538502i | ||||
\(818\) | −7425.09 | − | 22852.1i | −0.317374 | − | 0.976777i | ||||
\(819\) | −17472.0 | + | 12694.2i | −0.745447 | + | 0.541599i | ||||
\(820\) | 2062.85 | − | 1498.75i | 0.0878512 | − | 0.0638276i | ||||
\(821\) | −32.7348 | − | 100.748i | −0.00139154 | − | 0.00428272i | 0.950358 | − | 0.311158i | \(-0.100717\pi\) |
−0.951750 | + | 0.306875i | \(0.900717\pi\) | |||||||
\(822\) | −7125.79 | + | 21930.9i | −0.302361 | + | 0.930571i | ||||
\(823\) | −30200.5 | − | 21941.9i | −1.27913 | − | 0.929341i | −0.279602 | − | 0.960116i | \(-0.590202\pi\) |
−0.999526 | + | 0.0307751i | \(0.990202\pi\) | |||||||
\(824\) | −23918.8 | −1.01123 | ||||||||
\(825\) | 1468.75 | − | 978.950i | 0.0619822 | − | 0.0413123i | ||||
\(826\) | 32915.6 | 1.38654 | ||||||||
\(827\) | 1408.83 | + | 1023.58i | 0.0592380 | + | 0.0430389i | 0.617010 | − | 0.786955i | \(-0.288344\pi\) |
−0.557772 | + | 0.829994i | \(0.688344\pi\) | |||||||
\(828\) | 442.540 | − | 1362.00i | 0.0185741 | − | 0.0571651i | ||||
\(829\) | −1629.09 | − | 5013.82i | −0.0682516 | − | 0.210057i | 0.911114 | − | 0.412155i | \(-0.135224\pi\) |
−0.979365 | + | 0.202098i | \(0.935224\pi\) | |||||||
\(830\) | −14285.8 | + | 10379.3i | −0.597432 | + | 0.434060i | ||||
\(831\) | 11558.1 | − | 8397.48i | 0.482488 | − | 0.350548i | ||||
\(832\) | −12895.7 | − | 39688.8i | −0.537353 | − | 1.65380i | ||||
\(833\) | −12468.3 | + | 38373.5i | −0.518609 | + | 1.59611i | ||||
\(834\) | 6476.07 | + | 4705.14i | 0.268882 | + | 0.195355i | ||||
\(835\) | 2758.64 | 0.114331 | ||||||||
\(836\) | −2001.33 | + | 5405.71i | −0.0827958 | + | 0.223637i | ||||
\(837\) | 621.742 | 0.0256757 | ||||||||
\(838\) | −21806.7 | − | 15843.5i | −0.898928 | − | 0.653109i | ||||
\(839\) | 7446.81 | − | 22918.9i | 0.306427 | − | 0.943086i | −0.672714 | − | 0.739903i | \(-0.734871\pi\) |
0.979141 | − | 0.203183i | \(-0.0651286\pi\) | |||||||
\(840\) | 7722.23 | + | 23766.6i | 0.317193 | + | 0.976220i | ||||
\(841\) | 14969.5 | − | 10876.0i | 0.613780 | − | 0.445937i | ||||
\(842\) | −2491.53 | + | 1810.20i | −0.101976 | + | 0.0740898i | ||||
\(843\) | −517.900 | − | 1593.93i | −0.0211595 | − | 0.0651221i | ||||
\(844\) | −2674.76 | + | 8232.06i | −0.109086 | + | 0.335734i | ||||
\(845\) | −26757.5 | − | 19440.5i | −1.08933 | − | 0.791447i | ||||
\(846\) | −4985.96 | −0.202625 | ||||||||
\(847\) | −16776.6 | + | 40240.6i | −0.680578 | + | 1.63245i | ||||
\(848\) | 2065.74 | 0.0836531 | ||||||||
\(849\) | 5012.05 | + | 3641.47i | 0.202607 | + | 0.147203i | ||||
\(850\) | 688.979 | − | 2120.46i | 0.0278021 | − | 0.0855660i | ||||
\(851\) | −3546.18 | − | 10914.0i | −0.142845 | − | 0.439633i | ||||
\(852\) | −3173.97 | + | 2306.02i | −0.127627 | + | 0.0927265i | ||||
\(853\) | 22983.5 | − | 16698.5i | 0.922555 | − | 0.670275i | −0.0216040 | − | 0.999767i | \(-0.506877\pi\) |
0.944159 | + | 0.329491i | \(0.106877\pi\) | |||||||
\(854\) | 10290.7 | + | 31671.5i | 0.412343 | + | 1.26906i | ||||
\(855\) | 2627.86 | − | 8087.72i | 0.105112 | − | 0.323502i | ||||
\(856\) | −13131.2 | − | 9540.40i | −0.524318 | − | 0.380939i | ||||
\(857\) | −6941.16 | −0.276669 | −0.138335 | − | 0.990386i | \(-0.544175\pi\) | ||||
−0.138335 | + | 0.990386i | \(0.544175\pi\) | |||||||
\(858\) | −6962.43 | + | 18806.0i | −0.277032 | + | 0.748281i | ||||
\(859\) | 21637.2 | 0.859430 | 0.429715 | − | 0.902965i | \(-0.358614\pi\) | ||||
0.429715 | + | 0.902965i | \(0.358614\pi\) | |||||||
\(860\) | 2150.57 | + | 1562.48i | 0.0852718 | + | 0.0619536i | ||||
\(861\) | −4253.06 | + | 13089.6i | −0.168344 | + | 0.518109i | ||||
\(862\) | 6732.46 | + | 20720.4i | 0.266019 | + | 0.818723i | ||||
\(863\) | −6019.83 | + | 4373.67i | −0.237448 | + | 0.172516i | −0.700146 | − | 0.714000i | \(-0.746882\pi\) |
0.462698 | + | 0.886516i | \(0.346882\pi\) | |||||||
\(864\) | −1691.42 | + | 1228.89i | −0.0666012 | + | 0.0483886i | ||||
\(865\) | −2144.70 | − | 6600.70i | −0.0843028 | − | 0.259457i | ||||
\(866\) | 5786.56 | − | 17809.2i | 0.227062 | − | 0.698824i | ||||
\(867\) | 4508.16 | + | 3275.37i | 0.176592 | + | 0.128301i | ||||
\(868\) | 1316.05 | 0.0514626 | ||||||||
\(869\) | 35829.9 | − | 23881.3i | 1.39867 | − | 0.932242i | ||||
\(870\) | −6006.23 | −0.234058 | ||||||||
\(871\) | 13111.9 | + | 9526.37i | 0.510081 | + | 0.370595i | ||||
\(872\) | −645.076 | + | 1985.34i | −0.0250516 | + | 0.0771010i | ||||
\(873\) | −682.635 | − | 2100.93i | −0.0264647 | − | 0.0814500i | ||||
\(874\) | 16710.4 | − | 12140.8i | 0.646723 | − | 0.469872i | ||||
\(875\) | −39022.4 | + | 28351.4i | −1.50765 | + | 1.09537i | ||||
\(876\) | 359.087 | + | 1105.15i | 0.0138498 | + | 0.0426253i | ||||
\(877\) | −9984.83 | + | 30730.2i | −0.384451 | + | 1.18322i | 0.552426 | + | 0.833562i | \(0.313702\pi\) |
−0.936877 | + | 0.349658i | \(0.886298\pi\) | |||||||
\(878\) | −19416.3 | − | 14106.8i | −0.746320 | − | 0.542233i | ||||
\(879\) | −22488.4 | −0.862931 | ||||||||
\(880\) | 14037.0 | + | 11092.1i | 0.537714 | + | 0.424902i | ||||
\(881\) | 21907.4 | 0.837774 | 0.418887 | − | 0.908038i | \(-0.362420\pi\) | ||||
0.418887 | + | 0.908038i | \(0.362420\pi\) | |||||||
\(882\) | −13292.4 | − | 9657.49i | −0.507458 | − | 0.368690i | ||||
\(883\) | −370.914 | + | 1141.56i | −0.0141362 | + | 0.0435067i | −0.957876 | − | 0.287183i | \(-0.907281\pi\) |
0.943740 | + | 0.330689i | \(0.107281\pi\) | |||||||
\(884\) | −2183.34 | − | 6719.64i | −0.0830699 | − | 0.255663i | ||||
\(885\) | 10175.0 | − | 7392.54i | 0.386472 | − | 0.280788i | ||||
\(886\) | −18799.1 | + | 13658.3i | −0.712831 | + | 0.517902i | ||||
\(887\) | −7342.41 | − | 22597.6i | −0.277941 | − | 0.855415i | −0.988426 | − | 0.151703i | \(-0.951524\pi\) |
0.710485 | − | 0.703712i | \(-0.248476\pi\) | |||||||
\(888\) | −2843.06 | + | 8750.04i | −0.107440 | + | 0.330667i | ||||
\(889\) | 43072.7 | + | 31294.1i | 1.62498 | + | 1.18062i | ||||
\(890\) | 27507.1 | 1.03600 | ||||||||
\(891\) | 2952.70 | + | 119.407i | 0.111020 | + | 0.00448966i | ||||
\(892\) | 6419.26 | 0.240956 | ||||||||
\(893\) | 16227.8 | + | 11790.2i | 0.608111 | + | 0.441818i | ||||
\(894\) | 4891.94 | − | 15055.9i | 0.183010 | − | 0.563247i | ||||
\(895\) | −209.825 | − | 645.775i | −0.00783651 | − | 0.0241183i | ||||
\(896\) | 21338.7 | − | 15503.5i | 0.795622 | − | 0.578053i | ||||
\(897\) | −16215.3 | + | 11781.1i | −0.603581 | + | 0.438528i | ||||
\(898\) | −5302.29 | − | 16318.8i | −0.197038 | − | 0.606419i | ||||
\(899\) | −545.919 | + | 1680.17i | −0.0202530 | + | 0.0623323i | ||||
\(900\) | −204.879 | − | 148.853i | −0.00758811 | − | 0.00551308i | ||||
\(901\) | 2429.65 | 0.0898374 | ||||||||
\(902\) | 3454.82 | + | 12303.9i | 0.127531 | + | 0.454186i | ||||
\(903\) | −14348.4 | −0.528777 | ||||||||
\(904\) | −8681.31 | − | 6307.34i | −0.319398 | − | 0.232057i | ||||
\(905\) | −132.062 | + | 406.444i | −0.00485069 | + | 0.0149289i | ||||
\(906\) | 2752.41 | + | 8471.05i | 0.100930 | + | 0.310631i | ||||
\(907\) | 10232.4 | − | 7434.24i | 0.374597 | − | 0.272161i | −0.384517 | − | 0.923118i | \(-0.625632\pi\) |
0.759115 | + | 0.650957i | \(0.225632\pi\) | |||||||
\(908\) | 567.053 | − | 411.988i | 0.0207250 | − | 0.0150576i | ||||
\(909\) | 63.1091 | + | 194.230i | 0.00230275 | + | 0.00708713i | ||||
\(910\) | 19351.1 | − | 59556.6i | 0.704927 | − | 2.16954i | ||||
\(911\) | 10814.5 | + | 7857.18i | 0.393304 | + | 0.285752i | 0.766808 | − | 0.641877i | \(-0.221844\pi\) |
−0.373504 | + | 0.927628i | \(0.621844\pi\) | |||||||
\(912\) | −12767.8 | −0.463577 | ||||||||
\(913\) | 6673.58 | + | 23767.1i | 0.241909 | + | 0.861531i | ||||
\(914\) | 2891.93 | 0.104657 | ||||||||
\(915\) | 10294.2 | + | 7479.20i | 0.371931 | + | 0.270224i | ||||
\(916\) | 1591.54 | − | 4898.26i | 0.0574082 | − | 0.176684i | ||||
\(917\) | −10624.1 | − | 32697.6i | −0.382593 | − | 1.17750i | ||||
\(918\) | 3019.86 | − | 2194.06i | 0.108573 | − | 0.0788830i | ||||
\(919\) | 14994.8 | − | 10894.4i | 0.538230 | − | 0.391047i | −0.285197 | − | 0.958469i | \(-0.592059\pi\) |
0.823427 | + | 0.567422i | \(0.192059\pi\) | |||||||
\(920\) | 7166.78 | + | 22057.1i | 0.256828 | + | 0.790435i | ||||
\(921\) | 960.635 | − | 2956.53i | 0.0343692 | − | 0.105777i | ||||
\(922\) | 16986.1 | + | 12341.1i | 0.606732 | + | 0.440817i | ||||
\(923\) | 54908.7 | 1.95812 | ||||||||
\(924\) | 6250.00 | + | 252.750i | 0.222522 | + | 0.00899877i | ||||
\(925\) | −2029.31 | −0.0721332 | ||||||||
\(926\) | −3645.03 | − | 2648.27i | −0.129355 | − | 0.0939822i | ||||
\(927\) | 2729.42 | − | 8400.29i | 0.0967054 | − | 0.297629i | ||||
\(928\) | −1835.75 | − | 5649.85i | −0.0649368 | − | 0.199855i | ||||
\(929\) | −21222.9 | + | 15419.3i | −0.749517 | + | 0.544556i | −0.895677 | − | 0.444705i | \(-0.853309\pi\) |
0.146160 | + | 0.989261i | \(0.453309\pi\) | |||||||
\(930\) | −1458.50 | + | 1059.66i | −0.0514260 | + | 0.0373632i | ||||
\(931\) | 20425.9 | + | 62864.5i | 0.719047 | + | 2.21300i | ||||
\(932\) | 1329.47 | − | 4091.70i | 0.0467257 | − | 0.143807i | ||||
\(933\) | 25082.8 | + | 18223.7i | 0.880142 | + | 0.639461i | ||||
\(934\) | −47575.7 | −1.66673 | ||||||||
\(935\) | 16509.9 | + | 13046.1i | 0.577466 | + | 0.456314i | ||||
\(936\) | 16069.1 | 0.561150 | ||||||||
\(937\) | 11249.4 | + | 8173.17i | 0.392212 | + | 0.284958i | 0.766361 | − | 0.642410i | \(-0.222065\pi\) |
−0.374150 | + | 0.927368i | \(0.622065\pi\) | |||||||
\(938\) | −5600.69 | + | 17237.2i | −0.194956 | + | 0.600014i | ||||
\(939\) | 6610.74 | + | 20345.8i | 0.229748 | + | 0.707092i | ||||
\(940\) | −3262.43 | + | 2370.29i | −0.113201 | + | 0.0822452i | ||||
\(941\) | −29656.0 | + | 21546.4i | −1.02737 | + | 0.746431i | −0.967781 | − | 0.251792i | \(-0.918980\pi\) |
−0.0595926 | + | 0.998223i | \(0.518980\pi\) | |||||||
\(942\) | −4286.95 | − | 13193.9i | −0.148276 | − | 0.456348i | ||||
\(943\) | −3947.15 | + | 12148.1i | −0.136306 | + | 0.419508i | ||||
\(944\) | −15276.6 | − | 11099.1i | −0.526707 | − | 0.382675i | ||||
\(945\) | −9228.04 | −0.317659 | ||||||||
\(946\) | −11086.3 | + | 7389.23i | −0.381022 | + | 0.253958i | ||||
\(947\) | −9454.30 | −0.324417 | −0.162209 | − | 0.986756i | \(-0.551862\pi\) | ||||
−0.162209 | + | 0.986756i | \(0.551862\pi\) | |||||||
\(948\) | −4997.99 | − | 3631.25i | −0.171231 | − | 0.124407i | ||||
\(949\) | 5025.69 | − | 15467.5i | 0.171908 | − | 0.529079i | ||||
\(950\) | −1128.70 | − | 3473.79i | −0.0385473 | − | 0.118637i | ||||
\(951\) | 15645.5 | − | 11367.1i | 0.533480 | − | 0.387596i | ||||
\(952\) | 35701.0 | − | 25938.3i | 1.21542 | − | 0.883052i | ||||
\(953\) | 9444.38 | + | 29066.8i | 0.321022 | + | 0.988003i | 0.973204 | + | 0.229941i | \(0.0738534\pi\) |
−0.652183 | + | 0.758062i | \(0.726147\pi\) | |||||||
\(954\) | −305.736 | + | 940.959i | −0.0103759 | + | 0.0319336i | ||||
\(955\) | −38661.2 | − | 28089.0i | −1.31000 | − | 0.951769i | ||||
\(956\) | 7407.31 | 0.250596 | ||||||||
\(957\) | −2915.29 | + | 7874.39i | −0.0984723 | + | 0.265980i | ||||
\(958\) | −42312.6 | −1.42699 | ||||||||
\(959\) | −81442.6 | − | 59171.5i | −2.74235 | − | 1.99244i | ||||
\(960\) | 5510.22 | − | 16958.7i | 0.185252 | − | 0.570146i | ||||
\(961\) | −9042.06 | − | 27828.6i | −0.303517 | − | 0.934128i | ||||
\(962\) | 18652.0 | − | 13551.5i | 0.625119 | − | 0.454175i | ||||
\(963\) | 4849.03 | − | 3523.03i | 0.162261 | − | 0.117890i | ||||
\(964\) | 1448.33 | + | 4457.51i | 0.0483897 | + | 0.148928i | ||||
\(965\) | −16265.6 | + | 50060.4i | −0.542600 | + | 1.66995i | ||||
\(966\) | −18133.2 | − | 13174.6i | −0.603962 | − | 0.438804i | ||||
\(967\) | −30119.6 | −1.00164 | −0.500818 | − | 0.865553i | \(-0.666967\pi\) | ||||
−0.500818 | + | 0.865553i | \(0.666967\pi\) | |||||||
\(968\) | 27697.9 | − | 16885.9i | 0.919673 | − | 0.560676i | ||||
\(969\) | −15017.0 | −0.497848 | ||||||||
\(970\) | 5182.06 | + | 3764.99i | 0.171532 | + | 0.124625i | ||||
\(971\) | −9953.51 | + | 30633.7i | −0.328963 | + | 1.01244i | 0.640657 | + | 0.767828i | \(0.278662\pi\) |
−0.969620 | + | 0.244617i | \(0.921338\pi\) | |||||||
\(972\) | −131.017 | − | 403.229i | −0.00432343 | − | 0.0133061i | ||||
\(973\) | −28271.9 | + | 20540.7i | −0.931505 | + | 0.676778i | ||||
\(974\) | 18627.1 | − | 13533.4i | 0.612782 | − | 0.445212i | ||||
\(975\) | 1095.26 | + | 3370.87i | 0.0359759 | + | 0.110722i | ||||
\(976\) | 5903.55 | − | 18169.3i | 0.193615 | − | 0.595885i | ||||
\(977\) | 6868.82 | + | 4990.49i | 0.224926 | + | 0.163419i | 0.694541 | − | 0.719453i | \(-0.255607\pi\) |
−0.469615 | + | 0.882871i | \(0.655607\pi\) | |||||||
\(978\) | 13602.8 | 0.444756 | ||||||||
\(979\) | 13351.3 | − | 36062.8i | 0.435864 | − | 1.17730i | ||||
\(980\) | −13288.6 | −0.433153 | ||||||||
\(981\) | −623.642 | − | 453.103i | −0.0202970 | − | 0.0147466i | ||||
\(982\) | 12678.5 | − | 39020.3i | 0.412003 | − | 1.26801i | ||||
\(983\) | −1043.50 | − | 3211.55i | −0.0338580 | − | 0.104204i | 0.932699 | − | 0.360655i | \(-0.117447\pi\) |
−0.966557 | + | 0.256451i | \(0.917447\pi\) | |||||||
\(984\) | 8284.84 | − | 6019.29i | 0.268406 | − | 0.195008i | ||||
\(985\) | −14378.0 | + | 10446.2i | −0.465097 | + | 0.337913i | ||||
\(986\) | 3277.53 | + | 10087.2i | 0.105860 | + | 0.325803i | ||||
\(987\) | 6726.27 | − | 20701.3i | 0.216919 | − | 0.667609i | ||||
\(988\) | −9364.21 | − | 6803.50i | −0.301534 | − | 0.219077i | ||||
\(989\) | −13316.4 | −0.428145 | ||||||||
\(990\) | −7130.04 | + | 4752.31i | −0.228896 | + | 0.152564i | ||||
\(991\) | −20081.5 | −0.643703 | −0.321851 | − | 0.946790i | \(-0.604305\pi\) | ||||
−0.321851 | + | 0.946790i | \(0.604305\pi\) | |||||||
\(992\) | −1442.57 | − | 1048.08i | −0.0461709 | − | 0.0335451i | ||||
\(993\) | 5223.48 | − | 16076.2i | 0.166931 | − | 0.513760i | ||||
\(994\) | 18974.7 | + | 58398.0i | 0.605473 | + | 1.86345i | ||||
\(995\) | 28077.2 | − | 20399.3i | 0.894580 | − | 0.649951i | ||||
\(996\) | 2865.40 | − | 2081.83i | 0.0911582 | − | 0.0662303i | ||||
\(997\) | −10625.0 | − | 32700.4i | −0.337510 | − | 1.03875i | −0.965472 | − | 0.260506i | \(-0.916111\pi\) |
0.627962 | − | 0.778244i | \(-0.283889\pi\) | |||||||
\(998\) | −3579.42 | + | 11016.3i | −0.113532 | + | 0.349414i | ||||
\(999\) | −2748.59 | − | 1996.97i | −0.0870487 | − | 0.0632446i |
(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 | 33.4.e.b.4.1 | ✓ | 8 | |
3.2 | odd | 2 | 99.4.f.b.37.2 | 8 | |||
11.3 | even | 5 | inner | 33.4.e.b.25.1 | yes | 8 | |
11.5 | even | 5 | 363.4.a.p.1.4 | 4 | |||
11.6 | odd | 10 | 363.4.a.t.1.1 | 4 | |||
33.5 | odd | 10 | 1089.4.a.bg.1.1 | 4 | |||
33.14 | odd | 10 | 99.4.f.b.91.2 | 8 | |||
33.17 | even | 10 | 1089.4.a.z.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.4.e.b.4.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
33.4.e.b.25.1 | yes | 8 | 11.3 | even | 5 | inner | |
99.4.f.b.37.2 | 8 | 3.2 | odd | 2 | |||
99.4.f.b.91.2 | 8 | 33.14 | odd | 10 | |||
363.4.a.p.1.4 | 4 | 11.5 | even | 5 | |||
363.4.a.t.1.1 | 4 | 11.6 | odd | 10 | |||
1089.4.a.z.1.4 | 4 | 33.17 | even | 10 | |||
1089.4.a.bg.1.1 | 4 | 33.5 | odd | 10 |