Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(26,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.26");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.4 | ||
Character | \(\chi\) | \(=\) | 105.101 |
Dual form | 105.4.s.b.26.4 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.53626 | + | 2.04166i | −1.25026 | + | 0.721836i | −0.971160 | − | 0.238427i | \(-0.923368\pi\) |
−0.279096 | + | 0.960263i | \(0.590035\pi\) | |||||||
\(3\) | −5.19608 | + | 0.0272697i | −0.999986 | + | 0.00524805i | ||||
\(4\) | 4.33676 | − | 7.51148i | 0.542095 | − | 0.938935i | ||||
\(5\) | 2.50000 | + | 4.33013i | 0.223607 | + | 0.387298i | ||||
\(6\) | 18.3190 | − | 10.7051i | 1.24645 | − | 0.728388i | ||||
\(7\) | 0.627588 | − | 18.5096i | 0.0338866 | − | 0.999426i | ||||
\(8\) | 2.75017i | 0.121542i | ||||||||
\(9\) | 26.9985 | − | 0.283391i | 0.999945 | − | 0.0104960i | ||||
\(10\) | −17.6813 | − | 10.2083i | −0.559132 | − | 0.322815i | ||||
\(11\) | 7.33279 | + | 4.23359i | 0.200993 | + | 0.116043i | 0.597118 | − | 0.802153i | \(-0.296312\pi\) |
−0.396126 | + | 0.918196i | \(0.629646\pi\) | |||||||
\(12\) | −22.3293 | + | 39.1485i | −0.537160 | + | 0.941767i | ||||
\(13\) | − | 5.50408i | − | 0.117427i | −0.998275 | − | 0.0587137i | \(-0.981300\pi\) | ||
0.998275 | − | 0.0587137i | \(-0.0186999\pi\) | |||||||
\(14\) | 35.5711 | + | 66.7362i | 0.679055 | + | 1.27400i | ||||
\(15\) | −13.1083 | − | 22.4315i | −0.225636 | − | 0.386120i | ||||
\(16\) | 29.0791 | + | 50.3665i | 0.454361 | + | 0.786977i | ||||
\(17\) | −60.2944 | + | 104.433i | −0.860208 | + | 1.48992i | 0.0115198 | + | 0.999934i | \(0.496333\pi\) |
−0.871728 | + | 0.489990i | \(0.837000\pi\) | |||||||
\(18\) | −94.8952 | + | 56.1239i | −1.24261 | + | 0.734919i | ||||
\(19\) | 23.3904 | − | 13.5044i | 0.282427 | − | 0.163059i | −0.352095 | − | 0.935964i | \(-0.614530\pi\) |
0.634522 | + | 0.772905i | \(0.281197\pi\) | |||||||
\(20\) | 43.3676 | 0.484864 | ||||||||
\(21\) | −2.75625 | + | 96.1946i | −0.0286411 | + | 0.999590i | ||||
\(22\) | −34.5742 | −0.335057 | ||||||||
\(23\) | 2.98204 | − | 1.72168i | 0.0270347 | − | 0.0156085i | −0.486422 | − | 0.873724i | \(-0.661698\pi\) |
0.513456 | + | 0.858116i | \(0.328365\pi\) | |||||||
\(24\) | −0.0749963 | − | 14.2901i | −0.000637857 | − | 0.121540i | ||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 11.2375 | + | 19.4639i | 0.0847634 | + | 0.146814i | ||||
\(27\) | −140.279 | + | 2.20876i | −0.999876 | + | 0.0157436i | ||||
\(28\) | −136.313 | − | 84.9859i | −0.920026 | − | 0.573601i | ||||
\(29\) | 72.7598i | 0.465902i | 0.972489 | + | 0.232951i | \(0.0748381\pi\) | ||||
−0.972489 | + | 0.232951i | \(0.925162\pi\) | |||||||
\(30\) | 92.1518 | + | 52.5610i | 0.560818 | + | 0.319876i | ||||
\(31\) | 242.287 | + | 139.885i | 1.40374 | + | 0.810452i | 0.994775 | − | 0.102095i | \(-0.0325546\pi\) |
0.408970 | + | 0.912548i | \(0.365888\pi\) | |||||||
\(32\) | −224.717 | − | 129.740i | −1.24140 | − | 0.716720i | ||||
\(33\) | −38.2172 | − | 21.7981i | −0.201599 | − | 0.114987i | ||||
\(34\) | − | 492.403i | − | 2.48372i | ||||||
\(35\) | 81.7180 | − | 43.5565i | 0.394653 | − | 0.210354i | ||||
\(36\) | 114.957 | − | 204.028i | 0.532210 | − | 0.944574i | ||||
\(37\) | 44.8944 | + | 77.7594i | 0.199476 | + | 0.345502i | 0.948359 | − | 0.317200i | \(-0.102743\pi\) |
−0.748883 | + | 0.662702i | \(0.769409\pi\) | |||||||
\(38\) | −55.1429 | + | 95.5104i | −0.235404 | + | 0.407732i | ||||
\(39\) | 0.150094 | + | 28.5996i | 0.000616265 | + | 0.117426i | ||||
\(40\) | −11.9086 | + | 6.87544i | −0.0470729 | + | 0.0271775i | ||||
\(41\) | 221.251 | 0.842770 | 0.421385 | − | 0.906882i | \(-0.361544\pi\) | ||||
0.421385 | + | 0.906882i | \(0.361544\pi\) | |||||||
\(42\) | −186.650 | − | 345.796i | −0.685731 | − | 1.27042i | ||||
\(43\) | 495.285 | 1.75652 | 0.878259 | − | 0.478185i | \(-0.158705\pi\) | ||||
0.878259 | + | 0.478185i | \(0.158705\pi\) | |||||||
\(44\) | 63.6010 | − | 36.7201i | 0.217914 | − | 0.125813i | ||||
\(45\) | 68.7234 | + | 116.199i | 0.227660 | + | 0.384930i | ||||
\(46\) | −7.03018 | + | 12.1766i | −0.0225336 | + | 0.0390293i | ||||
\(47\) | 100.415 | + | 173.923i | 0.311638 | + | 0.539773i | 0.978717 | − | 0.205214i | \(-0.0657889\pi\) |
−0.667079 | + | 0.744987i | \(0.732456\pi\) | |||||||
\(48\) | −152.471 | − | 260.916i | −0.458485 | − | 0.784582i | ||||
\(49\) | −342.212 | − | 23.2328i | −0.997703 | − | 0.0677342i | ||||
\(50\) | − | 102.083i | − | 0.288734i | ||||||
\(51\) | 310.447 | − | 544.286i | 0.852377 | − | 1.49442i | ||||
\(52\) | −41.3438 | − | 23.8699i | −0.110257 | − | 0.0636568i | ||||
\(53\) | 63.3970 | + | 36.6023i | 0.164307 | + | 0.0948625i | 0.579899 | − | 0.814689i | \(-0.303092\pi\) |
−0.415592 | + | 0.909551i | \(0.636426\pi\) | |||||||
\(54\) | 491.553 | − | 294.212i | 1.23874 | − | 0.741430i | ||||
\(55\) | 42.3359i | 0.103792i | ||||||||
\(56\) | 50.9047 | + | 1.72598i | 0.121472 | + | 0.00411863i | ||||
\(57\) | −121.170 | + | 70.8080i | −0.281568 | + | 0.164539i | ||||
\(58\) | −148.551 | − | 257.297i | −0.336305 | − | 0.582497i | ||||
\(59\) | −180.462 | + | 312.570i | −0.398207 | + | 0.689714i | −0.993505 | − | 0.113791i | \(-0.963701\pi\) |
0.595298 | + | 0.803505i | \(0.297034\pi\) | |||||||
\(60\) | −225.341 | + | 1.18262i | −0.484857 | + | 0.00254459i | ||||
\(61\) | −586.446 | + | 338.585i | −1.23093 | + | 0.710678i | −0.967224 | − | 0.253925i | \(-0.918278\pi\) |
−0.263706 | + | 0.964603i | \(0.584945\pi\) | |||||||
\(62\) | −1142.39 | −2.34006 | ||||||||
\(63\) | 11.6985 | − | 499.910i | 0.0233948 | − | 0.999726i | ||||
\(64\) | 594.275 | 1.16069 | ||||||||
\(65\) | 23.8334 | − | 13.7602i | 0.0454795 | − | 0.0262576i | ||||
\(66\) | 179.650 | − | 0.942827i | 0.335052 | − | 0.00175839i | ||||
\(67\) | −385.932 | + | 668.453i | −0.703717 | + | 1.21887i | 0.263435 | + | 0.964677i | \(0.415145\pi\) |
−0.967152 | + | 0.254197i | \(0.918189\pi\) | |||||||
\(68\) | 522.964 | + | 905.801i | 0.932628 | + | 1.61536i | ||||
\(69\) | −15.4480 | + | 9.02732i | −0.0269524 | + | 0.0157502i | ||||
\(70\) | −200.048 | + | 320.868i | −0.341577 | + | 0.547872i | ||||
\(71\) | − | 801.257i | − | 1.33932i | −0.742668 | − | 0.669660i | \(-0.766440\pi\) | ||
0.742668 | − | 0.669660i | \(-0.233560\pi\) | |||||||
\(72\) | 0.779374 | + | 74.2506i | 0.00127570 | + | 0.121535i | ||||
\(73\) | 881.784 | + | 509.098i | 1.41377 | + | 0.816239i | 0.995741 | − | 0.0921954i | \(-0.0293884\pi\) |
0.418027 | + | 0.908435i | \(0.362722\pi\) | |||||||
\(74\) | −317.517 | − | 183.318i | −0.498791 | − | 0.287977i | ||||
\(75\) | 64.3606 | − | 112.839i | 0.0990896 | − | 0.173728i | ||||
\(76\) | − | 234.262i | − | 0.353575i | ||||||
\(77\) | 82.9641 | − | 133.070i | 0.122787 | − | 0.196945i | ||||
\(78\) | −58.9215 | − | 100.829i | −0.0855327 | − | 0.146368i | ||||
\(79\) | 96.8783 | + | 167.798i | 0.137970 | + | 0.238972i | 0.926728 | − | 0.375732i | \(-0.122609\pi\) |
−0.788758 | + | 0.614704i | \(0.789275\pi\) | |||||||
\(80\) | −145.396 | + | 251.833i | −0.203197 | + | 0.351947i | ||||
\(81\) | 728.839 | − | 15.3023i | 0.999780 | − | 0.0209908i | ||||
\(82\) | −782.400 | + | 451.719i | −1.05368 | + | 0.608342i | ||||
\(83\) | 1419.66 | 1.87745 | 0.938724 | − | 0.344670i | \(-0.112009\pi\) | ||||
0.938724 | + | 0.344670i | \(0.112009\pi\) | |||||||
\(84\) | 710.611 | + | 437.876i | 0.923024 | + | 0.568764i | ||||
\(85\) | −602.944 | −0.769393 | ||||||||
\(86\) | −1751.46 | + | 1011.20i | −2.19610 | + | 1.26792i | ||||
\(87\) | −1.98413 | − | 378.066i | −0.00244508 | − | 0.465895i | ||||
\(88\) | −11.6431 | + | 20.1664i | −0.0141041 | + | 0.0244290i | ||||
\(89\) | 310.733 | + | 538.205i | 0.370085 | + | 0.641007i | 0.989578 | − | 0.143995i | \(-0.0459951\pi\) |
−0.619493 | + | 0.785002i | \(0.712662\pi\) | |||||||
\(90\) | −480.262 | − | 270.598i | −0.562489 | − | 0.316929i | ||||
\(91\) | −101.878 | − | 3.45429i | −0.117360 | − | 0.00397921i | ||||
\(92\) | − | 29.8661i | − | 0.0338451i | ||||||
\(93\) | −1262.76 | − | 720.245i | −1.40798 | − | 0.803074i | ||||
\(94\) | −710.186 | − | 410.026i | −0.779256 | − | 0.449904i | ||||
\(95\) | 116.952 | + | 67.5222i | 0.126305 | + | 0.0729224i | ||||
\(96\) | 1171.18 | + | 668.012i | 1.24514 | + | 0.710195i | ||||
\(97\) | − | 30.4414i | − | 0.0318644i | −0.999873 | − | 0.0159322i | \(-0.994928\pi\) | ||
0.999873 | − | 0.0159322i | \(-0.00507160\pi\) | |||||||
\(98\) | 1257.59 | − | 616.524i | 1.29628 | − | 0.635493i | ||||
\(99\) | 199.174 | + | 112.223i | 0.202200 | + | 0.113927i | ||||
\(100\) | 108.419 | + | 187.787i | 0.108419 | + | 0.187787i | ||||
\(101\) | −485.210 | + | 840.409i | −0.478022 | + | 0.827959i | −0.999683 | − | 0.0251945i | \(-0.991979\pi\) |
0.521660 | + | 0.853153i | \(0.325313\pi\) | |||||||
\(102\) | 13.4277 | + | 2558.56i | 0.0130347 | + | 2.48368i | ||||
\(103\) | −895.886 | + | 517.240i | −0.857032 | + | 0.494808i | −0.863017 | − | 0.505175i | \(-0.831428\pi\) |
0.00598542 | + | 0.999982i | \(0.498095\pi\) | |||||||
\(104\) | 15.1372 | 0.0142723 | ||||||||
\(105\) | −423.425 | + | 228.552i | −0.393544 | + | 0.212422i | ||||
\(106\) | −298.918 | −0.273901 | ||||||||
\(107\) | 299.147 | − | 172.713i | 0.270277 | − | 0.156045i | −0.358736 | − | 0.933439i | \(-0.616792\pi\) |
0.629014 | + | 0.777394i | \(0.283459\pi\) | |||||||
\(108\) | −591.764 | + | 1063.28i | −0.527245 | + | 0.947354i | ||||
\(109\) | 381.979 | − | 661.607i | 0.335660 | − | 0.581380i | −0.647951 | − | 0.761682i | \(-0.724374\pi\) |
0.983611 | + | 0.180301i | \(0.0577073\pi\) | |||||||
\(110\) | −86.4355 | − | 149.711i | −0.0749209 | − | 0.129767i | ||||
\(111\) | −235.396 | − | 402.820i | −0.201286 | − | 0.344450i | ||||
\(112\) | 950.515 | − | 506.634i | 0.801922 | − | 0.427433i | ||||
\(113\) | − | 1127.01i | − | 0.938229i | −0.883137 | − | 0.469114i | \(-0.844573\pi\) | ||
0.883137 | − | 0.469114i | \(-0.155427\pi\) | |||||||
\(114\) | 283.923 | − | 497.783i | 0.233261 | − | 0.408962i | ||||
\(115\) | 14.9102 | + | 8.60841i | 0.0120903 | + | 0.00698033i | ||||
\(116\) | 546.534 | + | 315.541i | 0.437452 | + | 0.252563i | ||||
\(117\) | −1.55981 | − | 148.602i | −0.00123251 | − | 0.117421i | ||||
\(118\) | − | 1473.77i | − | 1.14976i | ||||||
\(119\) | 1895.17 | + | 1181.57i | 1.45992 | + | 0.910202i | ||||
\(120\) | 61.6906 | − | 36.0501i | 0.0469296 | − | 0.0274242i | ||||
\(121\) | −629.653 | − | 1090.59i | −0.473068 | − | 0.819378i | ||||
\(122\) | 1382.55 | − | 2394.65i | 1.02599 | − | 1.77706i | ||||
\(123\) | −1149.64 | + | 6.03343i | −0.842758 | + | 0.00442290i | ||||
\(124\) | 2101.48 | − | 1213.29i | 1.52193 | − | 0.878684i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 979.278 | + | 1791.70i | 0.692389 | + | 1.26680i | ||||
\(127\) | 1904.91 | 1.33097 | 0.665485 | − | 0.746411i | \(-0.268225\pi\) | ||||
0.665485 | + | 0.746411i | \(0.268225\pi\) | |||||||
\(128\) | −303.780 | + | 175.387i | −0.209770 | + | 0.121111i | ||||
\(129\) | −2573.54 | + | 13.5063i | −1.75649 | + | 0.00921829i | ||||
\(130\) | −56.1873 | + | 97.3193i | −0.0379073 | + | 0.0656574i | ||||
\(131\) | −1022.16 | − | 1770.44i | −0.681731 | − | 1.18079i | −0.974452 | − | 0.224595i | \(-0.927894\pi\) |
0.292721 | − | 0.956198i | \(-0.405439\pi\) | |||||||
\(132\) | −329.475 | + | 192.535i | −0.217251 | + | 0.126955i | ||||
\(133\) | −235.282 | − | 441.422i | −0.153395 | − | 0.287791i | ||||
\(134\) | − | 3151.77i | − | 2.03187i | ||||||
\(135\) | −360.261 | − | 601.903i | −0.229677 | − | 0.383730i | ||||
\(136\) | −287.209 | − | 165.820i | −0.181088 | − | 0.104551i | ||||
\(137\) | −135.672 | − | 78.3304i | −0.0846078 | − | 0.0488483i | 0.457099 | − | 0.889416i | \(-0.348888\pi\) |
−0.541707 | + | 0.840567i | \(0.682222\pi\) | |||||||
\(138\) | 36.1973 | − | 63.4625i | 0.0223284 | − | 0.0391470i | ||||
\(139\) | 1051.68i | 0.641746i | 0.947122 | + | 0.320873i | \(0.103976\pi\) | ||||
−0.947122 | + | 0.320873i | \(0.896024\pi\) | |||||||
\(140\) | 27.2170 | − | 802.717i | 0.0164304 | − | 0.484586i | ||||
\(141\) | −526.506 | − | 900.982i | −0.314467 | − | 0.538130i | ||||
\(142\) | 1635.90 | + | 2833.45i | 0.966770 | + | 1.67449i | ||||
\(143\) | 23.3020 | − | 40.3603i | 0.0136267 | − | 0.0236021i | ||||
\(144\) | 799.367 | + | 1351.58i | 0.462597 | + | 0.782165i | ||||
\(145\) | −315.059 | + | 181.899i | −0.180443 | + | 0.104179i | ||||
\(146\) | −4157.63 | −2.35676 | ||||||||
\(147\) | 1778.80 | + | 111.388i | 0.998045 | + | 0.0624973i | ||||
\(148\) | 778.785 | 0.432539 | ||||||||
\(149\) | −945.006 | + | 545.599i | −0.519583 | + | 0.299982i | −0.736764 | − | 0.676150i | \(-0.763647\pi\) |
0.217181 | + | 0.976131i | \(0.430314\pi\) | |||||||
\(150\) | 2.78377 | + | 530.432i | 0.00151529 | + | 0.288730i | ||||
\(151\) | 1672.45 | − | 2896.76i | 0.901336 | − | 1.56116i | 0.0755736 | − | 0.997140i | \(-0.475921\pi\) |
0.825762 | − | 0.564019i | \(-0.190745\pi\) | |||||||
\(152\) | 37.1395 | + | 64.3276i | 0.0198185 | + | 0.0343267i | ||||
\(153\) | −1598.26 | + | 2836.62i | −0.844522 | + | 1.49887i | ||||
\(154\) | −21.6983 | + | 639.955i | −0.0113539 | + | 0.334864i | ||||
\(155\) | 1398.85i | 0.724891i | ||||||||
\(156\) | 215.477 | + | 122.902i | 0.110589 | + | 0.0630773i | ||||
\(157\) | −1817.80 | − | 1049.51i | −0.924055 | − | 0.533503i | −0.0391283 | − | 0.999234i | \(-0.512458\pi\) |
−0.884926 | + | 0.465731i | \(0.845791\pi\) | |||||||
\(158\) | −685.174 | − | 395.585i | −0.344997 | − | 0.199184i | ||||
\(159\) | −330.414 | − | 188.460i | −0.164802 | − | 0.0939989i | ||||
\(160\) | − | 1297.40i | − | 0.641054i | ||||||
\(161\) | −29.9962 | − | 56.2769i | −0.0146834 | − | 0.0275481i | ||||
\(162\) | −2546.12 | + | 1542.16i | −1.23483 | + | 0.747921i | ||||
\(163\) | 1248.73 | + | 2162.87i | 0.600050 | + | 1.03932i | 0.992813 | + | 0.119678i | \(0.0381862\pi\) |
−0.392762 | + | 0.919640i | \(0.628480\pi\) | |||||||
\(164\) | 959.511 | − | 1661.92i | 0.456861 | − | 0.791306i | ||||
\(165\) | −1.15449 | − | 219.981i | −0.000544706 | − | 0.103791i | ||||
\(166\) | −5020.29 | + | 2898.47i | −2.34729 | + | 1.35521i | ||||
\(167\) | −3329.30 | −1.54269 | −0.771345 | − | 0.636417i | \(-0.780416\pi\) | ||||
−0.771345 | + | 0.636417i | \(0.780416\pi\) | |||||||
\(168\) | −264.552 | − | 7.58016i | −0.121492 | − | 0.00348108i | ||||
\(169\) | 2166.71 | 0.986211 | ||||||||
\(170\) | 2132.17 | − | 1231.01i | 0.961939 | − | 0.555376i | ||||
\(171\) | 627.678 | − | 371.228i | 0.280700 | − | 0.166015i | ||||
\(172\) | 2147.93 | − | 3720.33i | 0.952199 | − | 1.64926i | ||||
\(173\) | 134.286 | + | 232.590i | 0.0590149 | + | 0.102217i | 0.894023 | − | 0.448020i | \(-0.147871\pi\) |
−0.835009 | + | 0.550237i | \(0.814537\pi\) | |||||||
\(174\) | 778.898 | + | 1332.89i | 0.339357 | + | 0.580724i | ||||
\(175\) | 392.900 | + | 244.958i | 0.169717 | + | 0.105812i | ||||
\(176\) | 492.436i | 0.210902i | ||||||||
\(177\) | 929.174 | − | 1629.06i | 0.394582 | − | 0.691795i | ||||
\(178\) | −2197.66 | − | 1268.82i | −0.925404 | − | 0.534282i | ||||
\(179\) | −1472.14 | − | 849.943i | −0.614711 | − | 0.354904i | 0.160096 | − | 0.987101i | \(-0.448820\pi\) |
−0.774807 | + | 0.632198i | \(0.782153\pi\) | |||||||
\(180\) | 1170.86 | − | 12.2900i | 0.484837 | − | 0.00508911i | ||||
\(181\) | 2624.64i | 1.07783i | 0.842359 | + | 0.538917i | \(0.181166\pi\) | ||||
−0.842359 | + | 0.538917i | \(0.818834\pi\) | |||||||
\(182\) | 367.321 | − | 195.786i | 0.149603 | − | 0.0797397i | ||||
\(183\) | 3037.99 | − | 1775.31i | 1.22718 | − | 0.717128i | ||||
\(184\) | 4.73493 | + | 8.20113i | 0.00189708 | + | 0.00328584i | ||||
\(185\) | −224.472 | + | 388.797i | −0.0892082 | + | 0.154513i | ||||
\(186\) | 5935.94 | − | 31.1525i | 2.34002 | − | 0.0122807i | ||||
\(187\) | −884.252 | + | 510.523i | −0.345791 | + | 0.199642i | ||||
\(188\) | 1741.90 | 0.675750 | ||||||||
\(189\) | −47.1539 | + | 2597.89i | −0.0181478 | + | 0.999835i | ||||
\(190\) | −551.429 | −0.210552 | ||||||||
\(191\) | 2142.24 | − | 1236.82i | 0.811554 | − | 0.468551i | −0.0359413 | − | 0.999354i | \(-0.511443\pi\) |
0.847495 | + | 0.530803i | \(0.178110\pi\) | |||||||
\(192\) | −3087.90 | + | 16.2057i | −1.16068 | + | 0.00609138i | ||||
\(193\) | 839.123 | − | 1453.40i | 0.312961 | − | 0.542064i | −0.666041 | − | 0.745915i | \(-0.732013\pi\) |
0.979002 | + | 0.203851i | \(0.0653459\pi\) | |||||||
\(194\) | 62.1509 | + | 107.649i | 0.0230009 | + | 0.0398387i | ||||
\(195\) | −123.465 | + | 72.1490i | −0.0453410 | + | 0.0264959i | ||||
\(196\) | −1658.60 | + | 2469.77i | −0.604448 | + | 0.900061i | ||||
\(197\) | 4518.62i | 1.63420i | 0.576493 | + | 0.817102i | \(0.304421\pi\) | ||||
−0.576493 | + | 0.817102i | \(0.695579\pi\) | |||||||
\(198\) | −933.452 | + | 9.79801i | −0.335038 | + | 0.00351674i | ||||
\(199\) | 442.348 | + | 255.390i | 0.157574 | + | 0.0909754i | 0.576714 | − | 0.816946i | \(-0.304335\pi\) |
−0.419140 | + | 0.907922i | \(0.637668\pi\) | |||||||
\(200\) | −59.5430 | − | 34.3772i | −0.0210516 | − | 0.0121542i | ||||
\(201\) | 1987.10 | − | 3483.86i | 0.697311 | − | 1.22255i | ||||
\(202\) | − | 3962.54i | − | 1.38021i | ||||||
\(203\) | 1346.76 | + | 45.6632i | 0.465634 | + | 0.0157878i | ||||
\(204\) | −2742.07 | − | 4692.35i | −0.941093 | − | 1.61044i | ||||
\(205\) | 553.127 | + | 958.044i | 0.188449 | + | 0.326403i | ||||
\(206\) | 2112.06 | − | 3658.19i | 0.714340 | − | 1.23727i | ||||
\(207\) | 80.0227 | − | 47.3279i | 0.0268694 | − | 0.0158914i | ||||
\(208\) | 277.221 | − | 160.054i | 0.0924127 | − | 0.0533545i | ||||
\(209\) | 228.689 | 0.0756877 | ||||||||
\(210\) | 1030.72 | − | 1672.71i | 0.338697 | − | 0.549657i | ||||
\(211\) | −2859.26 | −0.932889 | −0.466444 | − | 0.884550i | \(-0.654465\pi\) | ||||
−0.466444 | + | 0.884550i | \(0.654465\pi\) | |||||||
\(212\) | 549.875 | − | 317.471i | 0.178140 | − | 0.102849i | ||||
\(213\) | 21.8500 | + | 4163.40i | 0.00702882 | + | 1.33930i | ||||
\(214\) | −705.241 | + | 1221.51i | −0.225277 | + | 0.390191i | ||||
\(215\) | 1238.21 | + | 2144.65i | 0.392769 | + | 0.680296i | ||||
\(216\) | −6.07448 | − | 385.791i | −0.00191350 | − | 0.121527i | ||||
\(217\) | 2741.27 | − | 4396.86i | 0.857555 | − | 1.37548i | ||||
\(218\) | 3119.49i | 0.969166i | ||||||||
\(219\) | −4595.71 | − | 2621.27i | −1.41803 | − | 0.808808i | ||||
\(220\) | 318.005 | + | 183.600i | 0.0974541 | + | 0.0562652i | ||||
\(221\) | 574.807 | + | 331.865i | 0.174958 | + | 0.101012i | ||||
\(222\) | 1654.84 | + | 943.878i | 0.500296 | + | 0.285356i | ||||
\(223\) | 45.7328i | 0.0137332i | 0.999976 | + | 0.00686658i | \(0.00218572\pi\) | ||||
−0.999976 | + | 0.00686658i | \(0.997814\pi\) | |||||||
\(224\) | −2542.47 | + | 4077.99i | −0.758375 | + | 1.21640i | ||||
\(225\) | −331.346 | + | 588.077i | −0.0981765 | + | 0.174245i | ||||
\(226\) | 2300.96 | + | 3985.39i | 0.677247 | + | 1.17303i | ||||
\(227\) | 285.201 | − | 493.982i | 0.0833896 | − | 0.144435i | −0.821314 | − | 0.570476i | \(-0.806759\pi\) |
0.904704 | + | 0.426041i | \(0.140092\pi\) | |||||||
\(228\) | 6.38824 | + | 1217.24i | 0.00185558 | + | 0.353570i | ||||
\(229\) | −4897.01 | + | 2827.29i | −1.41311 | + | 0.815862i | −0.995681 | − | 0.0928450i | \(-0.970404\pi\) |
−0.417434 | + | 0.908707i | \(0.637071\pi\) | |||||||
\(230\) | −70.3018 | −0.0201546 | ||||||||
\(231\) | −427.459 | + | 693.706i | −0.121752 | + | 0.197587i | ||||
\(232\) | −200.102 | −0.0566265 | ||||||||
\(233\) | −588.268 | + | 339.637i | −0.165402 | + | 0.0954951i | −0.580416 | − | 0.814320i | \(-0.697110\pi\) |
0.415014 | + | 0.909815i | \(0.363777\pi\) | |||||||
\(234\) | 308.911 | + | 522.311i | 0.0862997 | + | 0.145917i | ||||
\(235\) | −502.074 | + | 869.617i | −0.139369 | + | 0.241394i | ||||
\(236\) | 1565.24 | + | 2711.08i | 0.431732 | + | 0.747781i | ||||
\(237\) | −507.963 | − | 869.251i | −0.139223 | − | 0.238244i | ||||
\(238\) | −9114.19 | − | 309.026i | −2.48229 | − | 0.0841646i | ||||
\(239\) | 211.837i | 0.0573332i | 0.999589 | + | 0.0286666i | \(0.00912611\pi\) | ||||
−0.999589 | + | 0.0286666i | \(0.990874\pi\) | |||||||
\(240\) | 748.620 | − | 1312.51i | 0.201347 | − | 0.353008i | ||||
\(241\) | −99.2273 | − | 57.2889i | −0.0265220 | − | 0.0153125i | 0.486680 | − | 0.873580i | \(-0.338208\pi\) |
−0.513202 | + | 0.858268i | \(0.671541\pi\) | |||||||
\(242\) | 4453.24 | + | 2571.08i | 1.18291 | + | 0.682955i | ||||
\(243\) | −3786.69 | + | 99.3870i | −0.999656 | + | 0.0262374i | ||||
\(244\) | 5873.44i | 1.54102i | ||||||||
\(245\) | −754.930 | − | 1539.90i | −0.196860 | − | 0.401555i | ||||
\(246\) | 4053.10 | − | 2368.50i | 1.05047 | − | 0.613863i | ||||
\(247\) | −74.3295 | − | 128.742i | −0.0191477 | − | 0.0331647i | ||||
\(248\) | −384.707 | + | 666.332i | −0.0985038 | + | 0.170614i | ||||
\(249\) | −7376.68 | + | 38.7137i | −1.87742 | + | 0.00985294i | ||||
\(250\) | 442.033 | − | 255.208i | 0.111826 | − | 0.0645630i | ||||
\(251\) | 6671.72 | 1.67775 | 0.838875 | − | 0.544324i | \(-0.183214\pi\) | ||||
0.838875 | + | 0.544324i | \(0.183214\pi\) | |||||||
\(252\) | −3704.33 | − | 2255.86i | −0.925996 | − | 0.563912i | ||||
\(253\) | 29.1556 | 0.00724504 | ||||||||
\(254\) | −6736.25 | + | 3889.17i | −1.66405 | + | 0.960742i | ||||
\(255\) | 3132.95 | − | 16.4421i | 0.769383 | − | 0.00403782i | ||||
\(256\) | −1660.94 | + | 2876.83i | −0.405502 | + | 0.702351i | ||||
\(257\) | 1173.99 | + | 2033.40i | 0.284946 | + | 0.493542i | 0.972596 | − | 0.232501i | \(-0.0746908\pi\) |
−0.687650 | + | 0.726043i | \(0.741358\pi\) | |||||||
\(258\) | 9073.14 | − | 5302.06i | 2.18941 | − | 1.27943i | ||||
\(259\) | 1467.47 | − | 782.178i | 0.352063 | − | 0.187653i | ||||
\(260\) | − | 238.699i | − | 0.0569364i | ||||||
\(261\) | 20.6195 | + | 1964.41i | 0.00489008 | + | 0.465876i | ||||
\(262\) | 7229.26 | + | 4173.82i | 1.70468 | + | 0.984196i | ||||
\(263\) | −6281.95 | − | 3626.88i | −1.47286 | − | 0.850354i | −0.473323 | − | 0.880889i | \(-0.656946\pi\) |
−0.999534 | + | 0.0305344i | \(0.990279\pi\) | |||||||
\(264\) | 59.9486 | − | 105.104i | 0.0139757 | − | 0.0245027i | ||||
\(265\) | 366.023i | 0.0848476i | ||||||||
\(266\) | 1733.25 | + | 1080.62i | 0.399521 | + | 0.249086i | ||||
\(267\) | −1629.27 | − | 2788.08i | −0.373444 | − | 0.639056i | ||||
\(268\) | 3347.38 | + | 5797.84i | 0.762963 | + | 1.32149i | ||||
\(269\) | 797.075 | − | 1380.57i | 0.180664 | − | 0.312918i | −0.761443 | − | 0.648232i | \(-0.775509\pi\) |
0.942107 | + | 0.335313i | \(0.108842\pi\) | |||||||
\(270\) | 2502.86 | + | 1392.95i | 0.564145 | + | 0.313972i | ||||
\(271\) | −2302.55 | + | 1329.38i | −0.516124 | + | 0.297984i | −0.735347 | − | 0.677690i | \(-0.762981\pi\) |
0.219223 | + | 0.975675i | \(0.429648\pi\) | |||||||
\(272\) | −7013.23 | −1.56338 | ||||||||
\(273\) | 529.463 | + | 15.1706i | 0.117379 | + | 0.00336325i | ||||
\(274\) | 639.697 | 0.141042 | ||||||||
\(275\) | −183.320 | + | 105.840i | −0.0401985 | + | 0.0232086i | ||||
\(276\) | 0.814438 | + | 155.186i | 0.000177621 | + | 0.0338447i | ||||
\(277\) | −261.315 | + | 452.611i | −0.0566820 | + | 0.0981760i | −0.892974 | − | 0.450108i | \(-0.851385\pi\) |
0.836292 | + | 0.548284i | \(0.184719\pi\) | |||||||
\(278\) | −2147.18 | − | 3719.03i | −0.463235 | − | 0.802347i | ||||
\(279\) | 6581.04 | + | 3708.02i | 1.41217 | + | 0.795674i | ||||
\(280\) | 119.788 | + | 224.739i | 0.0255668 | + | 0.0479668i | ||||
\(281\) | 3626.44i | 0.769876i | 0.922943 | + | 0.384938i | \(0.125777\pi\) | ||||
−0.922943 | + | 0.384938i | \(0.874223\pi\) | |||||||
\(282\) | 3701.36 | + | 2111.16i | 0.781606 | + | 0.445808i | ||||
\(283\) | 720.958 | + | 416.246i | 0.151437 | + | 0.0874319i | 0.573804 | − | 0.818993i | \(-0.305467\pi\) |
−0.422367 | + | 0.906425i | \(0.638801\pi\) | |||||||
\(284\) | −6018.63 | − | 3474.86i | −1.25754 | − | 0.726038i | ||||
\(285\) | −609.532 | − | 347.661i | −0.126686 | − | 0.0722585i | ||||
\(286\) | 190.299i | 0.0393448i | ||||||||
\(287\) | 138.854 | − | 4095.27i | 0.0285586 | − | 0.842286i | ||||
\(288\) | −6103.78 | − | 3439.11i | −1.24885 | − | 0.703651i | ||||
\(289\) | −4814.33 | − | 8338.66i | −0.979916 | − | 1.69726i | ||||
\(290\) | 742.754 | − | 1286.49i | 0.150400 | − | 0.260501i | ||||
\(291\) | 0.830126 | + | 158.176i | 0.000167226 | + | 0.0318640i | ||||
\(292\) | 7648.17 | − | 4415.67i | 1.53279 | − | 0.884958i | ||||
\(293\) | 1490.52 | 0.297191 | 0.148595 | − | 0.988898i | \(-0.452525\pi\) | ||||
0.148595 | + | 0.988898i | \(0.452525\pi\) | |||||||
\(294\) | −6517.70 | + | 3237.80i | −1.29293 | + | 0.642287i | ||||
\(295\) | −1804.62 | −0.356167 | ||||||||
\(296\) | −213.852 | + | 123.467i | −0.0419929 | + | 0.0242446i | ||||
\(297\) | −1037.99 | − | 577.686i | −0.202795 | − | 0.112864i | ||||
\(298\) | 2227.86 | − | 3858.76i | 0.433075 | − | 0.750108i | ||||
\(299\) | −9.47627 | − | 16.4134i | −0.00183287 | − | 0.00317462i | ||||
\(300\) | −568.474 | − | 972.800i | −0.109403 | − | 0.187216i | ||||
\(301\) | 310.835 | − | 9167.54i | 0.0595223 | − | 1.75551i | ||||
\(302\) | 13658.3i | 2.60247i | ||||||||
\(303\) | 2498.28 | − | 4380.07i | 0.473670 | − | 0.830456i | ||||
\(304\) | 1360.34 | + | 785.394i | 0.256648 | + | 0.148176i | ||||
\(305\) | −2932.23 | − | 1692.92i | −0.550489 | − | 0.317825i | ||||
\(306\) | −139.542 | − | 13294.1i | −0.0260690 | − | 2.48358i | ||||
\(307\) | − | 9583.15i | − | 1.78156i | −0.454434 | − | 0.890780i | \(-0.650159\pi\) | ||
0.454434 | − | 0.890780i | \(-0.349841\pi\) | |||||||
\(308\) | −639.760 | − | 1200.28i | −0.118356 | − | 0.222052i | ||||
\(309\) | 4640.99 | − | 2712.05i | 0.854423 | − | 0.499298i | ||||
\(310\) | −2855.97 | − | 4946.69i | −0.523252 | − | 0.906300i | ||||
\(311\) | −1149.87 | + | 1991.63i | −0.209656 | + | 0.363136i | −0.951606 | − | 0.307320i | \(-0.900568\pi\) |
0.741950 | + | 0.670455i | \(0.233901\pi\) | |||||||
\(312\) | −78.6540 | + | 0.412786i | −0.0142721 | + | 7.49019e-5i | ||||
\(313\) | 4770.46 | − | 2754.23i | 0.861478 | − | 0.497374i | −0.00302927 | − | 0.999995i | \(-0.500964\pi\) |
0.864507 | + | 0.502621i | \(0.167631\pi\) | |||||||
\(314\) | 8570.97 | 1.54041 | ||||||||
\(315\) | 2193.92 | − | 1199.12i | 0.392424 | − | 0.214485i | ||||
\(316\) | 1680.55 | 0.299172 | ||||||||
\(317\) | 3604.26 | − | 2080.92i | 0.638598 | − | 0.368694i | −0.145477 | − | 0.989362i | \(-0.546472\pi\) |
0.784074 | + | 0.620667i | \(0.213138\pi\) | |||||||
\(318\) | 1553.20 | − | 8.15139i | 0.273897 | − | 0.00143744i | ||||
\(319\) | −308.035 | + | 533.532i | −0.0540647 | + | 0.0936428i | ||||
\(320\) | 1485.69 | + | 2573.29i | 0.259539 | + | 0.449535i | ||||
\(321\) | −1549.68 | + | 905.587i | −0.269454 | + | 0.157461i | ||||
\(322\) | 220.973 | + | 137.768i | 0.0382433 | + | 0.0238432i | ||||
\(323\) | 3256.97i | 0.561060i | ||||||||
\(324\) | 3045.86 | − | 5541.03i | 0.522266 | − | 0.950108i | ||||
\(325\) | 119.167 | + | 68.8010i | 0.0203390 | + | 0.0117427i | ||||
\(326\) | −8831.68 | − | 5098.97i | −1.50043 | − | 0.866276i | ||||
\(327\) | −1966.75 | + | 3448.18i | −0.332604 | + | 0.583134i | ||||
\(328\) | 608.478i | 0.102432i | ||||||||
\(329\) | 3282.28 | − | 1749.49i | 0.550024 | − | 0.293168i | ||||
\(330\) | 453.208 | + | 775.552i | 0.0756009 | + | 0.129372i | ||||
\(331\) | −2185.70 | − | 3785.75i | −0.362952 | − | 0.628651i | 0.625493 | − | 0.780229i | \(-0.284898\pi\) |
−0.988445 | + | 0.151578i | \(0.951564\pi\) | |||||||
\(332\) | 6156.73 | − | 10663.8i | 1.01775 | − | 1.76280i | ||||
\(333\) | 1234.12 | + | 2086.67i | 0.203091 | + | 0.343389i | ||||
\(334\) | 11773.3 | − | 6797.31i | 1.92876 | − | 1.11357i | ||||
\(335\) | −3859.32 | −0.629424 | ||||||||
\(336\) | −4925.14 | + | 2658.43i | −0.799668 | + | 0.431635i | ||||
\(337\) | −3888.74 | −0.628584 | −0.314292 | − | 0.949326i | \(-0.601767\pi\) | ||||
−0.314292 | + | 0.949326i | \(0.601767\pi\) | |||||||
\(338\) | −7662.03 | + | 4423.68i | −1.23302 | + | 0.711883i | ||||
\(339\) | 30.7331 | + | 5856.02i | 0.00492387 | + | 0.938216i | ||||
\(340\) | −2614.82 | + | 4529.00i | −0.417084 | + | 0.722411i | ||||
\(341\) | 1184.43 | + | 2051.49i | 0.188095 | + | 0.325790i | ||||
\(342\) | −1461.71 | + | 2594.27i | −0.231112 | + | 0.410181i | ||||
\(343\) | −644.799 | + | 6319.64i | −0.101504 | + | 0.994835i | ||||
\(344\) | 1362.12i | 0.213490i | ||||||||
\(345\) | −77.7094 | − | 44.3234i | −0.0121268 | − | 0.00691679i | ||||
\(346\) | −949.741 | − | 548.333i | −0.147568 | − | 0.0851982i | ||||
\(347\) | 8390.19 | + | 4844.08i | 1.29801 | + | 0.749406i | 0.980060 | − | 0.198702i | \(-0.0636727\pi\) |
0.317949 | + | 0.948108i | \(0.397006\pi\) | |||||||
\(348\) | −2848.44 | − | 1624.68i | −0.438771 | − | 0.250264i | ||||
\(349\) | 5564.36i | 0.853447i | 0.904382 | + | 0.426724i | \(0.140332\pi\) | ||||
−0.904382 | + | 0.426724i | \(0.859668\pi\) | |||||||
\(350\) | −1889.52 | − | 64.0661i | −0.288569 | − | 0.00978422i | ||||
\(351\) | 12.1572 | + | 772.105i | 0.00184873 | + | 0.117413i | ||||
\(352\) | −1098.53 | − | 1902.71i | −0.166341 | − | 0.288111i | ||||
\(353\) | −3784.55 | + | 6555.03i | −0.570627 | + | 0.988355i | 0.425875 | + | 0.904782i | \(0.359966\pi\) |
−0.996502 | + | 0.0835727i | \(0.973367\pi\) | |||||||
\(354\) | 40.1893 | + | 7657.84i | 0.00603400 | + | 1.14974i | ||||
\(355\) | 3469.55 | − | 2003.14i | 0.518716 | − | 0.299481i | ||||
\(356\) | 5390.29 | 0.802485 | ||||||||
\(357\) | −9879.70 | − | 6087.84i | −1.46468 | − | 0.902528i | ||||
\(358\) | 6941.18 | 1.02473 | ||||||||
\(359\) | 8900.82 | − | 5138.89i | 1.30854 | − | 0.755488i | 0.326691 | − | 0.945131i | \(-0.394066\pi\) |
0.981853 | + | 0.189643i | \(0.0607330\pi\) | |||||||
\(360\) | −319.566 | + | 189.001i | −0.0467850 | + | 0.0276701i | ||||
\(361\) | −3064.76 | + | 5308.32i | −0.446823 | + | 0.773921i | ||||
\(362\) | −5358.62 | − | 9281.41i | −0.778019 | − | 1.34757i | ||||
\(363\) | 3301.47 | + | 5649.63i | 0.477362 | + | 0.816884i | ||||
\(364\) | −467.769 | + | 750.278i | −0.0673565 | + | 0.108036i | ||||
\(365\) | 5090.98i | 0.730067i | ||||||||
\(366\) | −7118.55 | + | 12480.5i | −1.01665 | + | 1.78242i | ||||
\(367\) | 5323.65 | + | 3073.61i | 0.757199 | + | 0.437169i | 0.828289 | − | 0.560301i | \(-0.189314\pi\) |
−0.0710901 | + | 0.997470i | \(0.522648\pi\) | |||||||
\(368\) | 173.430 | + | 100.130i | 0.0245671 | + | 0.0141838i | ||||
\(369\) | 5973.44 | − | 62.7004i | 0.842723 | − | 0.00884567i | ||||
\(370\) | − | 1833.18i | − | 0.257575i | ||||||
\(371\) | 717.282 | − | 1150.48i | 0.100376 | − | 0.160998i | ||||
\(372\) | −10886.4 | + | 6361.67i | −1.51729 | + | 0.886659i | ||||
\(373\) | 4214.93 | + | 7300.47i | 0.585096 | + | 1.01342i | 0.994864 | + | 0.101225i | \(0.0322764\pi\) |
−0.409768 | + | 0.912190i | \(0.634390\pi\) | |||||||
\(374\) | 2084.63 | − | 3610.68i | 0.288218 | − | 0.499209i | ||||
\(375\) | 649.510 | − | 3.40871i | 0.0894415 | − | 0.000469400i | ||||
\(376\) | −478.320 | + | 276.158i | −0.0656050 | + | 0.0378770i | ||||
\(377\) | 400.476 | 0.0547097 | ||||||||
\(378\) | −5137.27 | − | 9283.10i | −0.699028 | − | 1.26315i | ||||
\(379\) | −7676.46 | −1.04040 | −0.520202 | − | 0.854043i | \(-0.674143\pi\) | ||||
−0.520202 | + | 0.854043i | \(0.674143\pi\) | |||||||
\(380\) | 1014.38 | − | 585.654i | 0.136939 | − | 0.0790617i | ||||
\(381\) | −9898.05 | + | 51.9462i | −1.33095 | + | 0.00698500i | ||||
\(382\) | −5050.34 | + | 8747.44i | −0.676434 | + | 1.17162i | ||||
\(383\) | −5802.30 | − | 10049.9i | −0.774109 | − | 1.34080i | −0.935294 | − | 0.353871i | \(-0.884865\pi\) |
0.161186 | − | 0.986924i | \(-0.448468\pi\) | |||||||
\(384\) | 1573.68 | − | 919.611i | 0.209132 | − | 0.122210i | ||||
\(385\) | 783.621 | + | 26.5695i | 0.103733 | + | 0.00351716i | ||||
\(386\) | 6852.82i | 0.903625i | ||||||||
\(387\) | 13372.0 | − | 140.359i | 1.75642 | − | 0.0184363i | ||||
\(388\) | −228.660 | − | 132.017i | −0.0299187 | − | 0.0172735i | ||||
\(389\) | 694.507 | + | 400.974i | 0.0905217 | + | 0.0522627i | 0.544578 | − | 0.838711i | \(-0.316690\pi\) |
−0.454056 | + | 0.890973i | \(0.650023\pi\) | |||||||
\(390\) | 289.300 | − | 507.211i | 0.0375622 | − | 0.0658555i | ||||
\(391\) | 415.231i | 0.0537062i | ||||||||
\(392\) | 63.8943 | − | 941.143i | 0.00823253 | − | 0.121263i | ||||
\(393\) | 5359.52 | + | 9171.46i | 0.687918 | + | 1.17720i | ||||
\(394\) | −9225.49 | − | 15979.0i | −1.17963 | − | 2.04318i | ||||
\(395\) | −484.391 | + | 838.991i | −0.0617022 | + | 0.106871i | ||||
\(396\) | 1706.73 | − | 1009.41i | 0.216582 | − | 0.128093i | ||||
\(397\) | −7984.56 | + | 4609.89i | −1.00940 | + | 0.582780i | −0.911017 | − | 0.412368i | \(-0.864702\pi\) |
−0.0983871 | + | 0.995148i | \(0.531368\pi\) | |||||||
\(398\) | −2085.68 | −0.262677 | ||||||||
\(399\) | 1234.58 | + | 2287.25i | 0.154904 | + | 0.286982i | ||||
\(400\) | −1453.96 | −0.181745 | ||||||||
\(401\) | −1886.94 | + | 1089.43i | −0.234986 | + | 0.135669i | −0.612870 | − | 0.790184i | \(-0.709985\pi\) |
0.377884 | + | 0.925853i | \(0.376652\pi\) | |||||||
\(402\) | 85.9476 | + | 16376.8i | 0.0106634 | + | 2.03185i | ||||
\(403\) | 769.936 | − | 1333.57i | 0.0951694 | − | 0.164838i | ||||
\(404\) | 4208.48 | + | 7289.30i | 0.518267 | + | 0.897664i | ||||
\(405\) | 1888.36 | + | 3117.71i | 0.231687 | + | 0.382519i | ||||
\(406\) | −4855.71 | + | 2588.14i | −0.593559 | + | 0.316373i | ||||
\(407\) | 760.258i | 0.0925911i | ||||||||
\(408\) | 1496.88 | + | 853.782i | 0.181634 | + | 0.103599i | ||||
\(409\) | 2406.40 | + | 1389.34i | 0.290926 | + | 0.167966i | 0.638360 | − | 0.769738i | \(-0.279613\pi\) |
−0.347433 | + | 0.937705i | \(0.612947\pi\) | |||||||
\(410\) | −3912.00 | − | 2258.59i | −0.471219 | − | 0.272059i | ||||
\(411\) | 707.100 | + | 403.312i | 0.0848630 | + | 0.0484036i | ||||
\(412\) | 8972.58i | 1.07293i | ||||||||
\(413\) | 5672.30 | + | 3536.46i | 0.675825 | + | 0.421350i | ||||
\(414\) | −186.354 | + | 330.743i | −0.0221227 | + | 0.0392636i | ||||
\(415\) | 3549.15 | + | 6147.32i | 0.419810 | + | 0.727132i | ||||
\(416\) | −714.100 | + | 1236.86i | −0.0841626 | + | 0.145774i | ||||
\(417\) | −28.6791 | − | 5464.64i | −0.00336791 | − | 0.641737i | ||||
\(418\) | −808.703 | + | 466.905i | −0.0946291 | + | 0.0546341i | ||||
\(419\) | 2105.13 | 0.245448 | 0.122724 | − | 0.992441i | \(-0.460837\pi\) | ||||
0.122724 | + | 0.992441i | \(0.460837\pi\) | |||||||
\(420\) | −119.532 | + | 4171.73i | −0.0138870 | + | 0.484665i | ||||
\(421\) | −913.228 | −0.105720 | −0.0528599 | − | 0.998602i | \(-0.516834\pi\) | ||||
−0.0528599 | + | 0.998602i | \(0.516834\pi\) | |||||||
\(422\) | 10111.1 | − | 5837.64i | 1.16635 | − | 0.673393i | ||||
\(423\) | 2760.34 | + | 4667.22i | 0.317287 | + | 0.536473i | ||||
\(424\) | −100.663 | + | 174.353i | −0.0115297 | + | 0.0199701i | ||||
\(425\) | −1507.36 | − | 2610.82i | −0.172042 | − | 0.297985i | ||||
\(426\) | −8577.51 | − | 14678.2i | −0.975544 | − | 1.66940i | ||||
\(427\) | 5899.03 | + | 11067.4i | 0.668558 | + | 1.25431i | ||||
\(428\) | − | 2996.05i | − | 0.338364i | ||||||
\(429\) | −119.978 | + | 210.351i | −0.0135026 | + | 0.0236732i | ||||
\(430\) | −8757.28 | − | 5056.02i | −0.982125 | − | 0.567030i | ||||
\(431\) | −11007.2 | − | 6355.00i | −1.23016 | − | 0.710231i | −0.263093 | − | 0.964770i | \(-0.584743\pi\) |
−0.967062 | + | 0.254540i | \(0.918076\pi\) | |||||||
\(432\) | −4190.43 | − | 7001.12i | −0.466695 | − | 0.779726i | ||||
\(433\) | − | 3578.00i | − | 0.397108i | −0.980090 | − | 0.198554i | \(-0.936375\pi\) | ||
0.980090 | − | 0.198554i | \(-0.0636245\pi\) | |||||||
\(434\) | −716.949 | + | 21145.2i | −0.0792964 | + | 2.33871i | ||||
\(435\) | 1632.11 | − | 953.756i | 0.179894 | − | 0.105124i | ||||
\(436\) | −3313.10 | − | 5738.46i | −0.363919 | − | 0.630326i | ||||
\(437\) | 46.5007 | − | 80.5415i | 0.00509023 | − | 0.00881653i | ||||
\(438\) | 21603.4 | − | 113.377i | 2.35673 | − | 0.0123684i | ||||
\(439\) | 11240.4 | − | 6489.62i | 1.22203 | − | 0.705542i | 0.256683 | − | 0.966496i | \(-0.417370\pi\) |
0.965351 | + | 0.260954i | \(0.0840371\pi\) | |||||||
\(440\) | −116.431 | −0.0126151 | ||||||||
\(441\) | −9245.81 | − | 530.272i | −0.998359 | − | 0.0572586i | ||||
\(442\) | −2710.22 | −0.291657 | ||||||||
\(443\) | −9761.27 | + | 5635.67i | −1.04689 | + | 0.604421i | −0.921777 | − | 0.387721i | \(-0.873262\pi\) |
−0.125112 | + | 0.992143i | \(0.539929\pi\) | |||||||
\(444\) | −4046.63 | + | 21.2372i | −0.432533 | + | 0.00226998i | ||||
\(445\) | −1553.66 | + | 2691.02i | −0.165507 | + | 0.286667i | ||||
\(446\) | −93.3708 | − | 161.723i | −0.00991308 | − | 0.0171700i | ||||
\(447\) | 4895.45 | − | 2860.75i | 0.518002 | − | 0.302704i | ||||
\(448\) | 372.960 | − | 10999.8i | 0.0393319 | − | 1.16003i | ||||
\(449\) | − | 14311.8i | − | 1.50427i | −0.659012 | − | 0.752133i | \(-0.729025\pi\) | ||
0.659012 | − | 0.752133i | \(-0.270975\pi\) | |||||||
\(450\) | −28.9294 | − | 2756.09i | −0.00303054 | − | 0.288719i | ||||
\(451\) | 1622.38 | + | 936.684i | 0.169391 | + | 0.0977977i | ||||
\(452\) | −8465.49 | − | 4887.55i | −0.880936 | − | 0.508609i | ||||
\(453\) | −8611.17 | + | 15097.4i | −0.893130 | + | 1.56587i | ||||
\(454\) | 2329.13i | 0.240774i | ||||||||
\(455\) | −239.739 | − | 449.782i | −0.0247014 | − | 0.0463431i | ||||
\(456\) | −194.734 | − | 333.239i | −0.0199984 | − | 0.0342222i | ||||
\(457\) | 810.931 | + | 1404.57i | 0.0830061 | + | 0.143771i | 0.904540 | − | 0.426389i | \(-0.140215\pi\) |
−0.821534 | + | 0.570160i | \(0.806881\pi\) | |||||||
\(458\) | 11544.7 | − | 19996.0i | 1.17784 | − | 2.04007i | ||||
\(459\) | 8227.35 | − | 14782.9i | 0.836645 | − | 1.50328i | ||||
\(460\) | 129.324 | − | 74.6652i | 0.0131082 | − | 0.00756800i | ||||
\(461\) | 18238.0 | 1.84258 | 0.921290 | − | 0.388877i | \(-0.127137\pi\) | ||||
0.921290 | + | 0.388877i | \(0.127137\pi\) | |||||||
\(462\) | 95.2950 | − | 3325.85i | 0.00959637 | − | 0.334919i | ||||
\(463\) | −14765.4 | −1.48209 | −0.741046 | − | 0.671455i | \(-0.765670\pi\) | ||||
−0.741046 | + | 0.671455i | \(0.765670\pi\) | |||||||
\(464\) | −3664.66 | + | 2115.79i | −0.366654 | + | 0.211688i | ||||
\(465\) | −38.1461 | − | 7268.52i | −0.00380426 | − | 0.724881i | ||||
\(466\) | 1386.85 | − | 2402.09i | 0.137864 | − | 0.238787i | ||||
\(467\) | 3767.85 | + | 6526.10i | 0.373352 | + | 0.646664i | 0.990079 | − | 0.140513i | \(-0.0448752\pi\) |
−0.616727 | + | 0.787177i | \(0.711542\pi\) | |||||||
\(468\) | −1122.99 | − | 632.734i | −0.110919 | − | 0.0624960i | ||||
\(469\) | 12130.6 | + | 7562.96i | 1.19433 | + | 0.744617i | ||||
\(470\) | − | 4100.26i | − | 0.402406i | ||||||
\(471\) | 9474.08 | + | 5403.77i | 0.926842 | + | 0.528646i | ||||
\(472\) | −859.622 | − | 496.303i | −0.0838291 | − | 0.0483987i | ||||
\(473\) | 3631.82 | + | 2096.83i | 0.353047 | + | 0.203832i | ||||
\(474\) | 3571.01 | + | 2036.81i | 0.346037 | + | 0.197371i | ||||
\(475\) | 675.222i | 0.0652238i | ||||||||
\(476\) | 17094.2 | − | 9111.40i | 1.64604 | − | 0.877354i | ||||
\(477\) | 1722.00 | + | 970.241i | 0.165293 | + | 0.0931327i | ||||
\(478\) | −432.500 | − | 749.112i | −0.0413851 | − | 0.0716812i | ||||
\(479\) | 1641.79 | − | 2843.66i | 0.156608 | − | 0.271253i | −0.777035 | − | 0.629457i | \(-0.783277\pi\) |
0.933643 | + | 0.358204i | \(0.116611\pi\) | |||||||
\(480\) | 35.3797 | + | 6741.40i | 0.00336428 | + | 0.641045i | ||||
\(481\) | 427.994 | − | 247.102i | 0.0405714 | − | 0.0234239i | ||||
\(482\) | 467.858 | 0.0442123 | ||||||||
\(483\) | 157.397 | + | 291.602i | 0.0148278 | + | 0.0274707i | ||||
\(484\) | −10922.6 | −1.02579 | ||||||||
\(485\) | 131.815 | − | 76.1034i | 0.0123410 | − | 0.00712511i | ||||
\(486\) | 13187.8 | − | 8082.60i | 1.23089 | − | 0.754391i | ||||
\(487\) | 5107.21 | − | 8845.95i | 0.475215 | − | 0.823097i | −0.524382 | − | 0.851483i | \(-0.675704\pi\) |
0.999597 | + | 0.0283864i | \(0.00903690\pi\) | |||||||
\(488\) | −931.168 | − | 1612.83i | −0.0863770 | − | 0.149609i | ||||
\(489\) | −6547.49 | − | 11204.4i | −0.605497 | − | 1.03615i | ||||
\(490\) | 5813.59 | + | 3904.19i | 0.535982 | + | 0.359946i | ||||
\(491\) | − | 1347.56i | − | 0.123858i | −0.998081 | − | 0.0619292i | \(-0.980275\pi\) | ||
0.998081 | − | 0.0619292i | \(-0.0197253\pi\) | |||||||
\(492\) | −4940.38 | + | 8661.64i | −0.452702 | + | 0.793693i | ||||
\(493\) | −7598.52 | − | 4387.01i | −0.694158 | − | 0.400772i | ||||
\(494\) | 525.697 | + | 303.511i | 0.0478790 | + | 0.0276429i | ||||
\(495\) | 11.9976 | + | 1143.01i | 0.00108940 | + | 0.103786i | ||||
\(496\) | 16270.9i | 1.47295i | ||||||||
\(497\) | −14831.0 | − | 502.859i | −1.33855 | − | 0.0453849i | ||||
\(498\) | 26006.8 | − | 15197.6i | 2.34015 | − | 1.36751i | ||||
\(499\) | 6255.74 | + | 10835.3i | 0.561213 | + | 0.972050i | 0.997391 | + | 0.0721893i | \(0.0229986\pi\) |
−0.436178 | + | 0.899861i | \(0.643668\pi\) | |||||||
\(500\) | −542.095 | + | 938.935i | −0.0484864 | + | 0.0839809i | ||||
\(501\) | 17299.3 | − | 90.7890i | 1.54267 | − | 0.00809611i | ||||
\(502\) | −23592.9 | + | 13621.4i | −2.09762 | + | 1.21106i | ||||
\(503\) | −3030.57 | −0.268641 | −0.134320 | − | 0.990938i | \(-0.542885\pi\) | ||||
−0.134320 | + | 0.990938i | \(0.542885\pi\) | |||||||
\(504\) | 1374.84 | + | 32.1729i | 0.121508 | + | 0.00284344i | ||||
\(505\) | −4852.10 | −0.427556 | ||||||||
\(506\) | −103.102 | + | 59.5258i | −0.00905816 | + | 0.00522973i | ||||
\(507\) | −11258.4 | + | 59.0853i | −0.986197 | + | 0.00517568i | ||||
\(508\) | 8261.12 | − | 14308.7i | 0.721512 | − | 1.24969i | ||||
\(509\) | −6228.25 | − | 10787.7i | −0.542362 | − | 0.939399i | −0.998768 | − | 0.0496273i | \(-0.984197\pi\) |
0.456405 | − | 0.889772i | \(-0.349137\pi\) | |||||||
\(510\) | −11045.3 | + | 6454.55i | −0.959011 | + | 0.560417i | ||||
\(511\) | 9976.62 | − | 16002.0i | 0.863678 | − | 1.38530i | ||||
\(512\) | − | 16370.5i | − | 1.41305i | ||||||
\(513\) | −3251.34 | + | 1946.05i | −0.279825 | + | 0.167486i | ||||
\(514\) | −8303.04 | − | 4793.76i | −0.712512 | − | 0.411369i | ||||
\(515\) | −4479.43 | − | 2586.20i | −0.383276 | − | 0.221285i | ||||
\(516\) | −11059.4 | + | 19389.7i | −0.943530 | + | 1.65423i | ||||
\(517\) | 1700.46i | 0.144654i | ||||||||
\(518\) | −3592.42 | + | 5762.07i | −0.304714 | + | 0.488746i | ||||
\(519\) | −704.104 | − | 1204.90i | −0.0595506 | − | 0.101906i | ||||
\(520\) | 37.8429 | + | 65.5459i | 0.00319139 | + | 0.00552765i | ||||
\(521\) | −3119.32 | + | 5402.82i | −0.262303 | + | 0.454322i | −0.966854 | − | 0.255332i | \(-0.917815\pi\) |
0.704551 | + | 0.709654i | \(0.251149\pi\) | |||||||
\(522\) | −4083.57 | − | 6904.55i | −0.342400 | − | 0.578935i | ||||
\(523\) | −6897.77 | + | 3982.43i | −0.576708 | + | 0.332962i | −0.759824 | − | 0.650129i | \(-0.774715\pi\) |
0.183116 | + | 0.983091i | \(0.441382\pi\) | |||||||
\(524\) | −17731.5 | −1.47825 | ||||||||
\(525\) | −2048.22 | − | 1262.11i | −0.170270 | − | 0.104920i | ||||
\(526\) | 29619.5 | 2.45527 | ||||||||
\(527\) | −29217.1 | + | 16868.5i | −2.41503 | + | 1.39432i | ||||
\(528\) | −13.4286 | − | 2558.74i | −0.00110682 | − | 0.210899i | ||||
\(529\) | −6077.57 | + | 10526.7i | −0.499513 | + | 0.865181i | ||||
\(530\) | −747.295 | − | 1294.35i | −0.0612461 | − | 0.106081i | ||||
\(531\) | −4783.64 | + | 8490.07i | −0.390946 | + | 0.693856i | ||||
\(532\) | −4336.10 | − | 147.020i | −0.353372 | − | 0.0119814i | ||||
\(533\) | − | 1217.78i | − | 0.0989643i | ||||||
\(534\) | 11453.8 | + | 6532.97i | 0.928195 | + | 0.529418i | ||||
\(535\) | 1495.74 | + | 863.563i | 0.120872 | + | 0.0697852i | ||||
\(536\) | −1838.36 | − | 1061.38i | −0.148144 | − | 0.0855310i | ||||
\(537\) | 7672.56 | + | 4376.23i | 0.616565 | + | 0.351673i | ||||
\(538\) | 6509.42i | 0.521638i | ||||||||
\(539\) | −2411.01 | − | 1619.15i | −0.192671 | − | 0.129391i | ||||
\(540\) | −6083.55 | + | 95.7886i | −0.484804 | + | 0.00763349i | ||||
\(541\) | 3018.33 | + | 5227.90i | 0.239867 | + | 0.415462i | 0.960676 | − | 0.277672i | \(-0.0895627\pi\) |
−0.720809 | + | 0.693134i | \(0.756229\pi\) | |||||||
\(542\) | 5428.27 | − | 9402.03i | 0.430192 | − | 0.745114i | ||||
\(543\) | −71.5731 | − | 13637.8i | −0.00565653 | − | 1.07782i | ||||
\(544\) | 27098.3 | − | 15645.2i | 2.13572 | − | 1.23306i | ||||
\(545\) | 3819.79 | 0.300224 | ||||||||
\(546\) | −1903.29 | + | 1027.34i | −0.149182 | + | 0.0805237i | ||||
\(547\) | 620.134 | 0.0484735 | 0.0242368 | − | 0.999706i | \(-0.492284\pi\) | ||||
0.0242368 | + | 0.999706i | \(0.492284\pi\) | |||||||
\(548\) | −1176.76 | + | 679.400i | −0.0917308 | + | 0.0529608i | ||||
\(549\) | −15737.2 | + | 9307.48i | −1.22340 | + | 0.723559i | ||||
\(550\) | 432.177 | − | 748.553i | 0.0335057 | − | 0.0580335i | ||||
\(551\) | 982.580 | + | 1701.88i | 0.0759697 | + | 0.131583i | ||||
\(552\) | −24.8267 | − | 42.4846i | −0.00191430 | − | 0.00327584i | ||||
\(553\) | 3166.68 | − | 1687.87i | 0.243510 | − | 0.129793i | ||||
\(554\) | − | 2134.07i | − | 0.163660i | ||||||
\(555\) | 1155.77 | − | 2026.34i | 0.0883961 | − | 0.154979i | ||||
\(556\) | 7899.71 | + | 4560.90i | 0.602558 | + | 0.347887i | ||||
\(557\) | 863.961 | + | 498.808i | 0.0657221 | + | 0.0379447i | 0.532501 | − | 0.846429i | \(-0.321252\pi\) |
−0.466779 | + | 0.884374i | \(0.654586\pi\) | |||||||
\(558\) | −30842.8 | + | 323.742i | −2.33993 | + | 0.0245611i | ||||
\(559\) | − | 2726.09i | − | 0.206263i | ||||||
\(560\) | 4570.08 | + | 2849.27i | 0.344859 | + | 0.215006i | ||||
\(561\) | 4580.72 | − | 2676.83i | 0.344738 | − | 0.201454i | ||||
\(562\) | −7403.95 | − | 12824.0i | −0.555724 | − | 0.962542i | ||||
\(563\) | 5884.96 | − | 10193.0i | 0.440535 | − | 0.763030i | −0.557194 | − | 0.830382i | \(-0.688122\pi\) |
0.997729 | + | 0.0673528i | \(0.0214553\pi\) | |||||||
\(564\) | −9051.04 | + | 47.5010i | −0.675741 | + | 0.00354637i | ||||
\(565\) | 4880.08 | − | 2817.52i | 0.363374 | − | 0.209794i | ||||
\(566\) | −3399.33 | −0.252446 | ||||||||
\(567\) | 174.172 | − | 13500.1i | 0.0129004 | − | 0.999917i | ||||
\(568\) | 2203.60 | 0.162783 | ||||||||
\(569\) | 12969.2 | − | 7487.79i | 0.955534 | − | 0.551678i | 0.0607380 | − | 0.998154i | \(-0.480655\pi\) |
0.894796 | + | 0.446476i | \(0.147321\pi\) | |||||||
\(570\) | 2865.27 | − | 15.0373i | 0.210549 | − | 0.00110499i | ||||
\(571\) | −3729.38 | + | 6459.47i | −0.273327 | + | 0.473416i | −0.969712 | − | 0.244253i | \(-0.921457\pi\) |
0.696385 | + | 0.717669i | \(0.254791\pi\) | |||||||
\(572\) | −202.110 | − | 350.065i | −0.0147739 | − | 0.0255891i | ||||
\(573\) | −11097.5 | + | 6485.04i | −0.809084 | + | 0.472804i | ||||
\(574\) | 7870.12 | + | 14765.4i | 0.572287 | + | 1.07369i | ||||
\(575\) | 86.0841i | 0.00624340i | ||||||||
\(576\) | 16044.5 | − | 168.412i | 1.16063 | − | 0.0121826i | ||||
\(577\) | −15285.7 | − | 8825.21i | −1.10286 | − | 0.636739i | −0.165892 | − | 0.986144i | \(-0.553050\pi\) |
−0.936972 | + | 0.349405i | \(0.886384\pi\) | |||||||
\(578\) | 34049.4 | + | 19658.4i | 2.45029 | + | 1.41468i | ||||
\(579\) | −4320.52 | + | 7574.88i | −0.310111 | + | 0.543698i | ||||
\(580\) | 3155.41i | 0.225899i | ||||||||
\(581\) | 890.963 | − | 26277.4i | 0.0636202 | − | 1.87637i | ||||
\(582\) | −325.877 | − | 557.656i | −0.0232097 | − | 0.0397175i | ||||
\(583\) | 309.918 | + | 536.794i | 0.0220163 | + | 0.0381333i | ||||
\(584\) | −1400.11 | + | 2425.06i | −0.0992071 | + | 0.171832i | ||||
\(585\) | 639.566 | − | 378.259i | 0.0452014 | − | 0.0267335i | ||||
\(586\) | −5270.85 | + | 3043.13i | −0.371565 | + | 0.214523i | ||||
\(587\) | −19139.8 | −1.34580 | −0.672900 | − | 0.739734i | \(-0.734951\pi\) | ||||
−0.672900 | + | 0.739734i | \(0.734951\pi\) | |||||||
\(588\) | 8550.89 | − | 12878.3i | 0.599716 | − | 0.903221i | ||||
\(589\) | 7556.25 | 0.528608 | ||||||||
\(590\) | 6381.62 | − | 3684.43i | 0.445300 | − | 0.257094i | ||||
\(591\) | −123.221 | − | 23479.1i | −0.00857639 | − | 1.63418i | ||||
\(592\) | −2610.98 | + | 4522.35i | −0.181268 | + | 0.313966i | ||||
\(593\) | 9205.87 | + | 15945.0i | 0.637504 | + | 1.10419i | 0.985979 | + | 0.166871i | \(0.0533663\pi\) |
−0.348475 | + | 0.937318i | \(0.613300\pi\) | |||||||
\(594\) | 4850.02 | − | 76.3662i | 0.335015 | − | 0.00527499i | ||||
\(595\) | −378.400 | + | 11160.3i | −0.0260721 | + | 0.768952i | ||||
\(596\) | 9464.53i | 0.650473i | ||||||||
\(597\) | −2305.44 | − | 1314.96i | −0.158049 | − | 0.0901472i | ||||
\(598\) | 67.0211 | + | 38.6947i | 0.00458311 | + | 0.00264606i | ||||
\(599\) | −9319.12 | − | 5380.39i | −0.635674 | − | 0.367007i | 0.147272 | − | 0.989096i | \(-0.452951\pi\) |
−0.782946 | + | 0.622089i | \(0.786284\pi\) | |||||||
\(600\) | 310.328 | + | 177.003i | 0.0211151 | + | 0.0120435i | ||||
\(601\) | − | 16893.6i | − | 1.14660i | −0.819347 | − | 0.573298i | \(-0.805664\pi\) | ||
0.819347 | − | 0.573298i | \(-0.194336\pi\) | |||||||
\(602\) | 17617.8 | + | 33053.4i | 1.19277 | + | 2.23780i | ||||
\(603\) | −10230.1 | + | 18156.6i | −0.690885 | + | 1.22619i | ||||
\(604\) | −14506.0 | − | 25125.1i | −0.977218 | − | 1.69259i | ||||
\(605\) | 3148.27 | − | 5452.96i | 0.211562 | − | 0.366437i | ||||
\(606\) | 108.057 | + | 20589.7i | 0.00724344 | + | 1.38020i | ||||
\(607\) | 10522.5 | − | 6075.17i | 0.703617 | − | 0.406233i | −0.105076 | − | 0.994464i | \(-0.533509\pi\) |
0.808693 | + | 0.588231i | \(0.200175\pi\) | |||||||
\(608\) | −7008.27 | −0.467472 | ||||||||
\(609\) | −6999.10 | − | 200.544i | −0.465711 | − | 0.0133439i | ||||
\(610\) | 13825.5 | 0.917670 | ||||||||
\(611\) | 957.289 | − | 552.691i | 0.0633842 | − | 0.0365949i | ||||
\(612\) | 14376.0 | + | 24307.1i | 0.949532 | + | 1.60548i | ||||
\(613\) | 10068.8 | − | 17439.6i | 0.663416 | − | 1.14907i | −0.316296 | − | 0.948661i | \(-0.602439\pi\) |
0.979712 | − | 0.200410i | \(-0.0642274\pi\) | |||||||
\(614\) | 19565.5 | + | 33888.5i | 1.28599 | + | 2.22741i | ||||
\(615\) | −2900.22 | − | 4962.99i | −0.190159 | − | 0.325410i | ||||
\(616\) | 365.966 | + | 228.166i | 0.0239370 | + | 0.0149238i | ||||
\(617\) | − | 17281.4i | − | 1.12759i | −0.825914 | − | 0.563796i | \(-0.809341\pi\) | ||
0.825914 | − | 0.563796i | \(-0.190659\pi\) | |||||||
\(618\) | −10874.7 | + | 19065.8i | −0.707837 | + | 1.24100i | ||||
\(619\) | −12324.5 | − | 7115.55i | −0.800264 | − | 0.462033i | 0.0432995 | − | 0.999062i | \(-0.486213\pi\) |
−0.843563 | + | 0.537030i | \(0.819546\pi\) | |||||||
\(620\) | 10507.4 | + | 6066.46i | 0.680626 | + | 0.392959i | ||||
\(621\) | −414.514 | + | 248.102i | −0.0267856 | + | 0.0160322i | ||||
\(622\) | − | 9390.58i | − | 0.605350i | ||||||
\(623\) | 10157.0 | − | 5413.77i | 0.653180 | − | 0.348151i | ||||
\(624\) | −1436.10 | + | 839.213i | −0.0921315 | + | 0.0538388i | ||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −11246.4 | + | 19479.3i | −0.718045 | + | 1.24369i | ||||
\(627\) | −1188.29 | + | 6.23627i | −0.0756867 | + | 0.000397213i | ||||
\(628\) | −15766.8 | + | 9102.94i | −1.00185 | + | 0.578418i | ||||
\(629\) | −10827.5 | −0.686362 | ||||||||
\(630\) | −5310.08 | + | 8719.64i | −0.335807 | + | 0.551427i | ||||
\(631\) | −17950.2 | −1.13247 | −0.566233 | − | 0.824245i | \(-0.691600\pi\) | ||||
−0.566233 | + | 0.824245i | \(0.691600\pi\) | |||||||
\(632\) | −461.474 | + | 266.432i | −0.0290450 | + | 0.0167692i | ||||
\(633\) | 14856.9 | − | 77.9711i | 0.932876 | − | 0.00489585i | ||||
\(634\) | −8497.07 | + | 14717.4i | −0.532274 | + | 0.921926i | ||||
\(635\) | 4762.27 | + | 8248.49i | 0.297614 | + | 0.515482i | ||||
\(636\) | −2848.54 | + | 1664.60i | −0.177597 | + | 0.103782i | ||||
\(637\) | −127.875 | + | 1883.56i | −0.00795385 | + | 0.117158i | ||||
\(638\) | − | 2515.61i | − | 0.156103i | ||||||
\(639\) | −227.069 | − | 21632.7i | −0.0140574 | − | 1.33925i | ||||
\(640\) | −1518.90 | − | 876.937i | −0.0938121 | − | 0.0541625i | ||||
\(641\) | −2290.70 | − | 1322.53i | −0.141150 | − | 0.0814929i | 0.427762 | − | 0.903891i | \(-0.359302\pi\) |
−0.568912 | + | 0.822399i | \(0.692635\pi\) | |||||||
\(642\) | 3631.18 | − | 6366.32i | 0.223226 | − | 0.391368i | ||||
\(643\) | − | 9632.67i | − | 0.590786i | −0.955376 | − | 0.295393i | \(-0.904549\pi\) | ||
0.955376 | − | 0.295393i | \(-0.0954506\pi\) | |||||||
\(644\) | −552.810 | − | 18.7436i | −0.0338257 | − | 0.00114690i | ||||
\(645\) | −6492.34 | − | 11110.0i | −0.396334 | − | 0.678226i | ||||
\(646\) | −6649.62 | − | 11517.5i | −0.404993 | − | 0.701469i | ||||
\(647\) | −6135.42 | + | 10626.9i | −0.372810 | + | 0.645726i | −0.989997 | − | 0.141091i | \(-0.954939\pi\) |
0.617187 | + | 0.786817i | \(0.288272\pi\) | |||||||
\(648\) | 42.0839 | + | 2004.44i | 0.00255125 | + | 0.121515i | ||||
\(649\) | −2646.59 | + | 1528.01i | −0.160073 | + | 0.0924183i | ||||
\(650\) | −561.873 | −0.0339054 | ||||||||
\(651\) | −14124.0 | + | 22921.2i | −0.850325 | + | 1.37996i | ||||
\(652\) | 21661.8 | 1.30114 | ||||||||
\(653\) | −7275.75 | + | 4200.66i | −0.436022 | + | 0.251737i | −0.701909 | − | 0.712267i | \(-0.747669\pi\) |
0.265887 | + | 0.964004i | \(0.414335\pi\) | |||||||
\(654\) | −85.0673 | − | 16209.1i | −0.00508623 | − | 0.969153i | ||||
\(655\) | 5110.81 | − | 8852.19i | 0.304879 | − | 0.528066i | ||||
\(656\) | 6433.78 | + | 11143.6i | 0.382922 | + | 0.663241i | ||||
\(657\) | 23951.1 | + | 13495.0i | 1.42226 | + | 0.801355i | ||||
\(658\) | −8035.13 | + | 12887.9i | −0.476051 | + | 0.763563i | ||||
\(659\) | 29704.2i | 1.75586i | 0.478792 | + | 0.877929i | \(0.341075\pi\) | ||||
−0.478792 | + | 0.877929i | \(0.658925\pi\) | |||||||
\(660\) | −1657.39 | − | 945.331i | −0.0977481 | − | 0.0557529i | ||||
\(661\) | −1377.33 | − | 795.203i | −0.0810469 | − | 0.0467924i | 0.458929 | − | 0.888473i | \(-0.348233\pi\) |
−0.539976 | + | 0.841681i | \(0.681567\pi\) | |||||||
\(662\) | 15458.4 | + | 8924.93i | 0.907566 | + | 0.523984i | ||||
\(663\) | −2995.79 | − | 1708.72i | −0.175486 | − | 0.100092i | ||||
\(664\) | 3904.32i | 0.228188i | ||||||||
\(665\) | 1323.21 | − | 2122.36i | 0.0771606 | − | 0.123762i | ||||
\(666\) | −8624.43 | − | 4859.34i | −0.501787 | − | 0.282726i | ||||
\(667\) | 125.269 | + | 216.973i | 0.00727203 | + | 0.0125955i | ||||
\(668\) | −14438.4 | + | 25008.0i | −0.836284 | + | 1.44849i | ||||
\(669\) | −1.24712 | − | 237.631i | −7.20723e−5 | − | 0.0137330i | ||||
\(670\) | 13647.5 | − | 7879.42i | 0.786942 | − | 0.454341i | ||||
\(671\) | −5733.72 | −0.329877 | ||||||||
\(672\) | 13099.7 | − | 21258.9i | 0.751981 | − | 1.22036i | ||||
\(673\) | 12890.7 | 0.738338 | 0.369169 | − | 0.929362i | \(-0.379642\pi\) | ||||
0.369169 | + | 0.929362i | \(0.379642\pi\) | |||||||
\(674\) | 13751.6 | − | 7939.48i | 0.785892 | − | 0.453735i | ||||
\(675\) | 1705.66 | − | 3064.73i | 0.0972607 | − | 0.174758i | ||||
\(676\) | 9396.47 | − | 16275.2i | 0.534620 | − | 0.925988i | ||||
\(677\) | −1264.76 | − | 2190.62i | −0.0718000 | − | 0.124361i | 0.827890 | − | 0.560890i | \(-0.189541\pi\) |
−0.899690 | + | 0.436529i | \(0.856208\pi\) | |||||||
\(678\) | −12064.7 | − | 20645.7i | −0.683394 | − | 1.16946i | ||||
\(679\) | −563.458 | − | 19.1046i | −0.0318461 | − | 0.00107978i | ||||
\(680\) | − | 1658.20i | − | 0.0935134i | ||||||
\(681\) | −1468.46 | + | 2574.55i | −0.0826305 | + | 0.144871i | ||||
\(682\) | −8376.89 | − | 4836.40i | −0.470334 | − | 0.271547i | ||||
\(683\) | −9705.06 | − | 5603.22i | −0.543710 | − | 0.313911i | 0.202871 | − | 0.979205i | \(-0.434973\pi\) |
−0.746581 | + | 0.665294i | \(0.768306\pi\) | |||||||
\(684\) | −66.3876 | − | 6324.72i | −0.00371110 | − | 0.353555i | ||||
\(685\) | − | 783.304i | − | 0.0436913i | ||||||
\(686\) | −10622.4 | − | 23664.3i | −0.591202 | − | 1.31707i | ||||
\(687\) | 25368.1 | − | 14824.4i | 1.40881 | − | 0.823267i | ||||
\(688\) | 14402.5 | + | 24945.8i | 0.798094 | + | 1.38234i | ||||
\(689\) | 201.462 | − | 348.942i | 0.0111395 | − | 0.0192941i | ||||
\(690\) | 365.294 | − | 1.91711i | 0.0201543 | − | 0.000105772i | ||||
\(691\) | 6536.69 | − | 3773.96i | 0.359866 | − | 0.207769i | −0.309156 | − | 0.951011i | \(-0.600046\pi\) |
0.669022 | + | 0.743243i | \(0.266713\pi\) | |||||||
\(692\) | 2329.47 | 0.127967 | ||||||||
\(693\) | 2202.20 | − | 3616.21i | 0.120714 | − | 0.198223i | ||||
\(694\) | −39559.9 | −2.16379 | ||||||||
\(695\) | −4553.93 | + | 2629.21i | −0.248547 | + | 0.143499i | ||||
\(696\) | 1039.75 | − | 5.45672i | 0.0566257 | − | 0.000297179i | ||||
\(697\) | −13340.2 | + | 23105.9i | −0.724957 | + | 1.25566i | ||||
\(698\) | −11360.5 | − | 19677.0i | −0.616049 | − | 1.06703i | ||||
\(699\) | 3047.43 | − | 1780.82i | 0.164899 | − | 0.0963618i | ||||
\(700\) | 3543.91 | − | 1888.94i | 0.191353 | − | 0.101993i | ||||
\(701\) | − | 6104.85i | − | 0.328926i | −0.986383 | − | 0.164463i | \(-0.947411\pi\) | ||
0.986383 | − | 0.164463i | \(-0.0525891\pi\) | |||||||
\(702\) | −1619.37 | − | 2705.54i | −0.0870643 | − | 0.145462i | ||||
\(703\) | 2100.19 | + | 1212.55i | 0.112675 | + | 0.0650528i | ||||
\(704\) | 4357.70 | + | 2515.92i | 0.233291 | + | 0.134691i | ||||
\(705\) | 2585.10 | − | 4532.29i | 0.138100 | − | 0.242122i | ||||
\(706\) | − | 30907.1i | − | 1.64760i | ||||||
\(707\) | 15251.1 | + | 9508.49i | 0.811285 | + | 0.505804i | ||||
\(708\) | −8207.06 | − | 14044.3i | −0.435650 | − | 0.745505i | ||||
\(709\) | 9505.45 | + | 16463.9i | 0.503505 | + | 0.872096i | 0.999992 | + | 0.00405149i | \(0.00128963\pi\) |
−0.496487 | + | 0.868044i | \(0.665377\pi\) | |||||||
\(710\) | −8179.48 | + | 14167.3i | −0.432352 | + | 0.748856i | ||||
\(711\) | 2663.12 | + | 4502.85i | 0.140471 | + | 0.237510i | ||||
\(712\) | −1480.16 | + | 854.569i | −0.0779090 | + | 0.0449808i | ||||
\(713\) | 963.348 | 0.0505998 | ||||||||
\(714\) | 47366.5 | + | 1357.18i | 2.48270 | + | 0.0711363i | ||||
\(715\) | 233.020 | 0.0121880 | ||||||||
\(716\) | −12768.7 | + | 7371.99i | −0.666463 | + | 0.384783i | ||||
\(717\) | −5.77674 | − | 1100.72i | −0.000300887 | − | 0.0573324i | ||||
\(718\) | −20983.7 | + | 36344.9i | −1.09068 | + | 1.88911i | ||||
\(719\) | −10904.9 | − | 18887.9i | −0.565625 | − | 0.979691i | −0.996991 | − | 0.0775144i | \(-0.975302\pi\) |
0.431366 | − | 0.902177i | \(-0.358032\pi\) | |||||||
\(720\) | −3854.10 | + | 6840.31i | −0.199491 | + | 0.354060i | ||||
\(721\) | 9011.67 | + | 16907.1i | 0.465481 | + | 0.873307i | ||||
\(722\) | − | 25028.8i | − | 1.29013i | ||||||
\(723\) | 517.155 | + | 294.972i | 0.0266020 | + | 0.0151731i | ||||
\(724\) | 19714.9 | + | 11382.4i | 1.01202 | + | 0.584288i | ||||
\(725\) | −1575.30 | − | 909.497i | −0.0806966 | − | 0.0465902i | ||||
\(726\) | −23209.5 | − | 13238.1i | −1.18648 | − | 0.676738i | ||||
\(727\) | 1336.38i | 0.0681757i | 0.999419 | + | 0.0340878i | \(0.0108526\pi\) | ||||
−0.999419 | + | 0.0340878i | \(0.989147\pi\) | |||||||
\(728\) | 9.49991 | − | 280.183i | 0.000483640 | − | 0.0142641i | ||||
\(729\) | 19673.2 | − | 619.685i | 0.999504 | − | 0.0314832i | ||||
\(730\) | −10394.1 | − | 18003.0i | −0.526988 | − | 0.912771i | ||||
\(731\) | −29862.9 | + | 51724.1i | −1.51097 | + | 2.61708i | ||||
\(732\) | −160.167 | − | 30518.9i | −0.00808734 | − | 1.54100i | ||||
\(733\) | 4426.94 | − | 2555.90i | 0.223074 | − | 0.128792i | −0.384299 | − | 0.923209i | \(-0.625557\pi\) |
0.607373 | + | 0.794417i | \(0.292224\pi\) | |||||||
\(734\) | −25101.1 | −1.26226 | ||||||||
\(735\) | 3964.67 | + | 7980.88i | 0.198965 | + | 0.400516i | ||||
\(736\) | −893.485 | −0.0447477 | ||||||||
\(737\) | −5659.91 | + | 3267.75i | −0.282884 | + | 0.163323i | ||||
\(738\) | −20995.6 | + | 12417.5i | −1.04724 | + | 0.619367i | ||||
\(739\) | −12541.2 | + | 21721.9i | −0.624268 | + | 1.08126i | 0.364414 | + | 0.931237i | \(0.381269\pi\) |
−0.988682 | + | 0.150027i | \(0.952064\pi\) | |||||||
\(740\) | 1946.96 | + | 3372.24i | 0.0967186 | + | 0.167521i | ||||
\(741\) | 389.733 | + | 666.929i | 0.0193214 | + | 0.0330638i | ||||
\(742\) | −187.597 | + | 5532.86i | −0.00928155 | + | 0.273743i | ||||
\(743\) | 10848.7i | 0.535664i | 0.963466 | + | 0.267832i | \(0.0863073\pi\) | ||||
−0.963466 | + | 0.267832i | \(0.913693\pi\) | |||||||
\(744\) | 1980.80 | − | 3472.81i | 0.0976070 | − | 0.171128i | ||||
\(745\) | −4725.03 | − | 2728.00i | −0.232365 | − | 0.134156i | ||||
\(746\) | −29810.2 | − | 17210.9i | −1.46304 | − | 0.844686i | ||||
\(747\) | 38328.8 | − | 402.319i | 1.87734 | − | 0.0197056i | ||||
\(748\) | 8856.06i | 0.432900i | ||||||||
\(749\) | −3009.11 | − | 5645.49i | −0.146796 | − | 0.275410i | ||||
\(750\) | −2289.88 | + | 1338.13i | −0.111486 | + | 0.0651490i | ||||
\(751\) | 8500.44 | + | 14723.2i | 0.413030 | + | 0.715389i | 0.995219 | − | 0.0976641i | \(-0.0311371\pi\) |
−0.582189 | + | 0.813053i | \(0.697804\pi\) | |||||||
\(752\) | −5839.95 | + | 10115.1i | −0.283193 | + | 0.490504i | ||||
\(753\) | −34666.8 | + | 181.936i | −1.67773 | + | 0.00880491i | ||||
\(754\) | −1416.19 | + | 817.635i | −0.0684011 | + | 0.0394914i | ||||
\(755\) | 16724.5 | 0.806179 | ||||||||
\(756\) | 19309.5 | + | 11620.6i | 0.928943 | + | 0.559045i | ||||
\(757\) | 4378.07 | 0.210203 | 0.105102 | − | 0.994461i | \(-0.466483\pi\) | ||||
0.105102 | + | 0.994461i | \(0.466483\pi\) | |||||||
\(758\) | 27146.0 | − | 15672.7i | 1.30077 | − | 0.751001i | ||||
\(759\) | −151.495 | + | 0.795062i | −0.00724494 | + | 3.80223e-5i | ||||
\(760\) | −185.698 | + | 321.638i | −0.00886311 | + | 0.0153514i | ||||
\(761\) | −7619.87 | − | 13198.0i | −0.362970 | − | 0.628682i | 0.625478 | − | 0.780241i | \(-0.284904\pi\) |
−0.988448 | + | 0.151560i | \(0.951570\pi\) | |||||||
\(762\) | 34896.0 | − | 20392.2i | 1.65899 | − | 0.969462i | ||||
\(763\) | −12006.4 | − | 7485.50i | −0.569672 | − | 0.355168i | ||||
\(764\) | − | 21455.2i | − | 1.01600i | ||||||
\(765\) | −16278.6 | + | 170.869i | −0.769351 | + | 0.00807552i | ||||
\(766\) | 41036.9 | + | 23692.6i | 1.93567 | + | 1.11756i | ||||
\(767\) | 1720.41 | + | 993.279i | 0.0809914 | + | 0.0467604i | ||||
\(768\) | 8551.92 | − | 14993.5i | 0.401811 | − | 0.704469i | ||||
\(769\) | 16240.8i | 0.761583i | 0.924661 | + | 0.380792i | \(0.124348\pi\) | ||||
−0.924661 | + | 0.380792i | \(0.875652\pi\) | |||||||
\(770\) | −2825.33 | + | 1505.93i | −0.132231 | + | 0.0704805i | ||||
\(771\) | −6155.58 | − | 10533.7i | −0.287533 | − | 0.492040i | ||||
\(772\) | −7278.14 | − | 12606.1i | −0.339308 | − | 0.587699i | ||||
\(773\) | 20102.7 | − | 34819.0i | 0.935375 | − | 1.62012i | 0.161412 | − | 0.986887i | \(-0.448395\pi\) |
0.773963 | − | 0.633230i | \(-0.218271\pi\) | |||||||
\(774\) | −47000.2 | + | 27797.4i | −2.18267 | + | 1.29090i | ||||
\(775\) | −6057.18 | + | 3497.12i | −0.280749 | + | 0.162090i | ||||
\(776\) | 83.7190 | 0.00387286 | ||||||||
\(777\) | −7603.78 | + | 4104.28i | −0.351073 | + | 0.189498i | ||||
\(778\) | −3274.61 | −0.150900 | ||||||||
\(779\) | 5175.14 | − | 2987.87i | 0.238021 | − | 0.137422i | ||||
\(780\) | 6.50923 | + | 1240.30i | 0.000298805 | + | 0.0569356i | ||||
\(781\) | 3392.19 | − | 5875.45i | 0.155419 | − | 0.269193i | ||||
\(782\) | −847.761 | − | 1468.36i | −0.0387671 | − | 0.0671466i | ||||
\(783\) | −160.709 | − | 10206.6i | −0.00733496 | − | 0.465844i | ||||
\(784\) | −8781.08 | − | 17911.6i | −0.400013 | − | 0.815946i | ||||
\(785\) | − | 10495.1i | − | 0.477180i | ||||||
\(786\) | −37677.7 | − | 21490.4i | −1.70982 | − | 0.975236i | ||||
\(787\) | −5358.79 | − | 3093.90i | −0.242719 | − | 0.140134i | 0.373707 | − | 0.927547i | \(-0.378087\pi\) |
−0.616426 | + | 0.787413i | \(0.711420\pi\) | |||||||
\(788\) | 33941.5 | + | 19596.2i | 1.53441 | + | 0.885894i | ||||
\(789\) | 32740.4 | + | 18674.3i | 1.47730 | + | 0.842613i | ||||
\(790\) | − | 3955.85i | − | 0.178156i | ||||||
\(791\) | −20860.5 | − | 707.296i | −0.937690 | − | 0.0317933i | ||||
\(792\) | −308.631 | + | 547.764i | −0.0138469 | + | 0.0245757i | ||||
\(793\) | 1863.60 | + | 3227.85i | 0.0834531 | + | 0.144545i | ||||
\(794\) | 18823.7 | − | 32603.5i | 0.841343 | − | 1.45725i | ||||
\(795\) | −9.98132 | − | 1901.88i | −0.000445284 | − | 0.0848464i | ||||
\(796\) | 3836.71 | − | 2215.13i | 0.170840 | − | 0.0986346i | ||||
\(797\) | 34131.6 | 1.51694 | 0.758471 | − | 0.651707i | \(-0.225947\pi\) | ||||
0.758471 | + | 0.651707i | \(0.225947\pi\) | |||||||
\(798\) | −9035.60 | − | 5567.70i | −0.400823 | − | 0.246986i | ||||
\(799\) | −24217.8 | −1.07230 | ||||||||
\(800\) | 5617.91 | − | 3243.50i | 0.248279 | − | 0.143344i | ||||
\(801\) | 8541.84 | + | 14442.7i | 0.376793 | + | 0.637087i | ||||
\(802\) | 4448.48 | − | 7705.00i | 0.195862 | − | 0.339243i | ||||
\(803\) | 4310.63 | + | 7466.22i | 0.189438 | + | 0.328116i | ||||
\(804\) | −17551.4 | − | 30034.8i | −0.769888 | − | 1.31747i | ||||
\(805\) | 168.696 | − | 270.580i | 0.00738602 | − | 0.0118468i | ||||
\(806\) | 6287.80i | 0.274787i | ||||||||
\(807\) | −4104.02 | + | 7195.31i | −0.179019 | + | 0.313862i | ||||
\(808\) | −2311.27 | − | 1334.41i | −0.100632 | − | 0.0580996i | ||||
\(809\) | 27867.5 | + | 16089.3i | 1.21109 | + | 0.699222i | 0.962996 | − | 0.269515i | \(-0.0868633\pi\) |
0.248091 | + | 0.968737i | \(0.420197\pi\) | |||||||
\(810\) | −13043.0 | − | 7169.65i | −0.565785 | − | 0.311007i | ||||
\(811\) | − | 19444.4i | − | 0.841906i | −0.907083 | − | 0.420953i | \(-0.861696\pi\) | ||
0.907083 | − | 0.420953i | \(-0.138304\pi\) | |||||||
\(812\) | 6183.55 | − | 9918.11i | 0.267242 | − | 0.428642i | ||||
\(813\) | 11928.0 | − | 6970.33i | 0.514553 | − | 0.300689i | ||||
\(814\) | −1552.19 | − | 2688.47i | −0.0668356 | − | 0.115763i | ||||
\(815\) | −6243.66 | + | 10814.3i | −0.268351 | + | 0.464797i | ||||
\(816\) | 36441.3 | − | 191.249i | 1.56336 | − | 0.00820470i | ||||
\(817\) | 11584.9 | − | 6688.54i | 0.496089 | − | 0.286417i | ||||
\(818\) | −11346.2 | −0.484977 | ||||||||
\(819\) | −2751.55 | − | 64.3894i | −0.117395 | − | 0.00274719i | ||||
\(820\) | 9595.11 | 0.408629 | ||||||||
\(821\) | 319.413 | − | 184.413i | 0.0135781 | − | 0.00783931i | −0.493196 | − | 0.869918i | \(-0.664171\pi\) |
0.506774 | + | 0.862079i | \(0.330838\pi\) | |||||||
\(822\) | −3323.92 | + | 17.4443i | −0.141040 | + | 0.000740195i | ||||
\(823\) | 6812.44 | − | 11799.5i | 0.288538 | − | 0.499762i | −0.684923 | − | 0.728615i | \(-0.740164\pi\) |
0.973461 | + | 0.228853i | \(0.0734975\pi\) | |||||||
\(824\) | −1422.50 | − | 2463.84i | −0.0601397 | − | 0.104165i | ||||
\(825\) | 949.658 | − | 554.951i | 0.0400762 | − | 0.0234193i | ||||
\(826\) | −27279.0 | − | 924.921i | −1.14910 | − | 0.0389614i | ||||
\(827\) | 25985.7i | 1.09264i | 0.837578 | + | 0.546318i | \(0.183971\pi\) | ||||
−0.837578 | + | 0.546318i | \(0.816029\pi\) | |||||||
\(828\) | −8.46377 | − | 806.339i | −0.000355237 | − | 0.0338433i | ||||
\(829\) | 20752.9 | + | 11981.7i | 0.869455 | + | 0.501980i | 0.867167 | − | 0.498017i | \(-0.165938\pi\) |
0.00228780 | + | 0.999997i | \(0.499272\pi\) | |||||||
\(830\) | −25101.5 | − | 14492.3i | −1.04974 | − | 0.606068i | ||||
\(831\) | 1345.47 | − | 2358.93i | 0.0561659 | − | 0.0984721i | ||||
\(832\) | − | 3270.94i | − | 0.136297i | ||||||
\(833\) | 23059.8 | − | 34337.4i | 0.959151 | − | 1.42824i | ||||
\(834\) | 11258.3 | + | 19265.8i | 0.467440 | + | 0.799905i | ||||
\(835\) | −8323.26 | − | 14416.3i | −0.344956 | − | 0.597481i | ||||
\(836\) | 991.768 | − | 1717.79i | 0.0410299 | − | 0.0710659i | ||||
\(837\) | −34296.7 | − | 19087.7i | −1.41633 | − | 0.788252i | ||||
\(838\) | −7444.30 | + | 4297.97i | −0.306872 | + | 0.177173i | ||||
\(839\) | −26831.1 | −1.10407 | −0.552034 | − | 0.833822i | \(-0.686148\pi\) | ||||
−0.552034 | + | 0.833822i | \(0.686148\pi\) | |||||||
\(840\) | −628.557 | − | 1164.49i | −0.0258182 | − | 0.0478320i | ||||
\(841\) | 19095.0 | 0.782936 | ||||||||
\(842\) | 3229.41 | − | 1864.50i | 0.132177 | − | 0.0763123i | ||||
\(843\) | −98.8917 | − | 18843.3i | −0.00404035 | − | 0.769865i | ||||
\(844\) | −12399.9 | + | 21477.3i | −0.505714 | + | 0.875922i | ||||
\(845\) | 5416.76 | + | 9382.11i | 0.220523 | + | 0.381958i | ||||
\(846\) | −19290.2 | − | 10868.8i | −0.783935 | − | 0.441700i | ||||
\(847\) | −20581.6 | + | 10970.2i | −0.834938 | + | 0.445030i | ||||
\(848\) | 4257.45i | 0.172407i | ||||||||
\(849\) | −3757.51 | − | 2143.19i | −0.151893 | − | 0.0866360i | ||||
\(850\) | 10660.8 | + | 6155.03i | 0.430192 | + | 0.248372i | ||||
\(851\) | 267.754 | + | 154.588i | 0.0107855 | + | 0.00622703i | ||||
\(852\) | 31368.0 | + | 17891.5i | 1.26133 | + | 0.719429i | ||||
\(853\) | − | 27485.0i | − | 1.10324i | −0.834094 | − | 0.551622i | \(-0.814009\pi\) | ||
0.834094 | − | 0.551622i | \(-0.185991\pi\) | |||||||
\(854\) | −43456.4 | − | 27093.4i | −1.74127 | − | 1.08562i | ||||
\(855\) | 3176.66 | + | 1789.86i | 0.127064 | + | 0.0715927i | ||||
\(856\) | 474.990 | + | 822.707i | 0.0189659 | + | 0.0328499i | ||||
\(857\) | 23661.3 | − | 40982.6i | 0.943122 | − | 1.63353i | 0.183652 | − | 0.982991i | \(-0.441208\pi\) |
0.759469 | − | 0.650543i | \(-0.225459\pi\) | |||||||
\(858\) | −5.18939 | − | 988.810i | −0.000206484 | − | 0.0393443i | ||||
\(859\) | −24680.1 | + | 14249.1i | −0.980295 | + | 0.565974i | −0.902359 | − | 0.430985i | \(-0.858166\pi\) |
−0.0779360 | + | 0.996958i | \(0.524833\pi\) | |||||||
\(860\) | 21479.3 | 0.851673 | ||||||||
\(861\) | −609.821 | + | 21283.1i | −0.0241378 | + | 0.842424i | ||||
\(862\) | 51899.0 | 2.05068 | ||||||||
\(863\) | 9407.77 | − | 5431.58i | 0.371082 | − | 0.214245i | −0.302849 | − | 0.953039i | \(-0.597938\pi\) |
0.673931 | + | 0.738794i | \(0.264604\pi\) | |||||||
\(864\) | 31809.5 | + | 17703.4i | 1.25253 | + | 0.697087i | ||||
\(865\) | −671.431 | + | 1162.95i | −0.0263923 | + | 0.0457128i | ||||
\(866\) | 7305.06 | + | 12652.7i | 0.286647 | + | 0.496487i | ||||
\(867\) | 25243.0 | + | 43197.1i | 0.988810 | + | 1.69210i | ||||
\(868\) | −21138.7 | − | 39659.1i | −0.826606 | − | 1.55083i | ||||
\(869\) | 1640.57i | 0.0640421i | ||||||||
\(870\) | −3824.33 | + | 6704.95i | −0.149031 | + | 0.261286i | ||||
\(871\) | 3679.22 | + | 2124.20i | 0.143129 | + | 0.0826357i | ||||
\(872\) | 1819.53 | + | 1050.51i | 0.0706619 | + | 0.0407967i | ||||
\(873\) | −8.62680 | − | 821.871i | −0.000334448 | − | 0.0318627i | ||||
\(874\) | 379.754i | 0.0146972i | ||||||||
\(875\) | −78.4485 | + | 2313.70i | −0.00303091 | + | 0.0893914i | ||||
\(876\) | −39620.1 | + | 23152.8i | −1.52813 | + | 0.892990i | ||||
\(877\) | 1474.02 | + | 2553.08i | 0.0567550 | + | 0.0983026i | 0.893007 | − | 0.450043i | \(-0.148591\pi\) |
−0.836252 | + | 0.548345i | \(0.815258\pi\) | |||||||
\(878\) | −26499.2 | + | 45898.0i | −1.01857 | + | 1.76422i | ||||
\(879\) | −7744.84 | + | 40.6459i | −0.297187 | + | 0.00155967i | ||||
\(880\) | −2132.31 | + | 1231.09i | −0.0816820 | + | 0.0471591i | ||||
\(881\) | 30150.3 | 1.15299 | 0.576497 | − | 0.817099i | \(-0.304419\pi\) | ||||
0.576497 | + | 0.817099i | \(0.304419\pi\) | |||||||
\(882\) | 33778.2 | − | 17001.6i | 1.28954 | − | 0.649064i | ||||
\(883\) | −13452.4 | −0.512693 | −0.256347 | − | 0.966585i | \(-0.582519\pi\) | ||||
−0.256347 | + | 0.966585i | \(0.582519\pi\) | |||||||
\(884\) | 4985.60 | − | 2878.44i | 0.189688 | − | 0.109516i | ||||
\(885\) | 9376.97 | − | 49.2115i | 0.356162 | − | 0.00186918i | ||||
\(886\) | 23012.2 | − | 39858.4i | 0.872586 | − | 1.51136i | ||||
\(887\) | −11083.7 | − | 19197.6i | −0.419566 | − | 0.726710i | 0.576330 | − | 0.817217i | \(-0.304484\pi\) |
−0.995896 | + | 0.0905075i | \(0.971151\pi\) | |||||||
\(888\) | 1107.83 | − | 647.379i | 0.0418651 | − | 0.0244646i | ||||
\(889\) | 1195.50 | − | 35259.1i | 0.0451020 | − | 1.33021i | ||||
\(890\) | − | 12688.2i | − | 0.477876i | ||||||
\(891\) | 5409.21 | + | 2973.40i | 0.203384 | + | 0.111799i | ||||
\(892\) | 343.521 | + | 198.332i | 0.0128945 | + | 0.00744467i | ||||
\(893\) | 4697.48 | + | 2712.09i | 0.176030 | + | 0.101631i | ||||
\(894\) | −11470.9 | + | 20111.2i | −0.429132 | + | 0.752370i | ||||
\(895\) | − | 8499.43i | − | 0.317435i | ||||||
\(896\) | 3055.71 | + | 5732.92i | 0.113933 | + | 0.213754i | ||||
\(897\) | 49.6871 | + | 85.0269i | 0.00184950 | + | 0.00316496i | ||||
\(898\) | 29219.8 | + | 50610.2i | 1.08583 | + | 1.88072i | ||||
\(899\) | −10178.0 | + | 17628.8i | −0.377591 | + | 0.654007i | ||||
\(900\) | 2980.37 | + | 5039.25i | 0.110384 | + | 0.186639i | ||||
\(901\) | −7644.97 | + | 4413.83i | −0.282676 | + | 0.163203i | ||||
\(902\) | −7649.57 | −0.282376 | ||||||||
\(903\) | −1365.13 | + | 47643.8i | −0.0503085 | + | 1.75580i | ||||
\(904\) | 3099.46 | 0.114034 | ||||||||
\(905\) | −11365.0 | + | 6561.60i | −0.417443 | + | 0.241011i | ||||
\(906\) | −372.456 | − | 70969.4i | −0.0136579 | − | 2.60243i | ||||
\(907\) | 6575.84 | − | 11389.7i | 0.240736 | − | 0.416966i | −0.720188 | − | 0.693778i | \(-0.755945\pi\) |
0.960924 | + | 0.276812i | \(0.0892780\pi\) | |||||||
\(908\) | −2473.69 | − | 4284.56i | −0.0904101 | − | 0.156595i | ||||
\(909\) | −12861.8 | + | 22827.3i | −0.469306 | + | 0.832930i | ||||
\(910\) | 1766.08 | + | 1101.08i | 0.0643352 | + | 0.0401105i | ||||
\(911\) | − | 34821.8i | − | 1.26641i | −0.773985 | − | 0.633204i | \(-0.781739\pi\) | ||
0.773985 | − | 0.633204i | \(-0.218261\pi\) | |||||||
\(912\) | −7089.87 | − | 4043.88i | −0.257422 | − | 0.146827i | ||||
\(913\) | 10410.1 | + | 6010.26i | 0.377353 | + | 0.217865i | ||||
\(914\) | −5735.33 | − | 3311.29i | −0.207558 | − | 0.119834i | ||||
\(915\) | 15282.3 | + | 8716.61i | 0.552149 | + | 0.314931i | ||||
\(916\) | 49045.0i | 1.76910i | ||||||||
\(917\) | −33411.6 | + | 17808.7i | −1.20322 | + | 0.641326i | ||||
\(918\) | 1087.60 | + | 69073.6i | 0.0391026 | + | 2.48341i | ||||
\(919\) | −10471.5 | − | 18137.1i | −0.375867 | − | 0.651021i | 0.614589 | − | 0.788847i | \(-0.289322\pi\) |
−0.990456 | + | 0.137826i | \(0.955988\pi\) | |||||||
\(920\) | −23.6746 | + | 41.0057i | −0.000848401 | + | 0.00146947i | ||||
\(921\) | 261.329 | + | 49794.8i | 0.00934972 | + | 1.78154i | ||||
\(922\) | −64494.4 | + | 37235.8i | −2.30370 | + | 1.33004i | ||||
\(923\) | −4410.18 | −0.157273 | ||||||||
\(924\) | 3356.97 | + | 6219.29i | 0.119520 | + | 0.221428i | ||||
\(925\) | −2244.72 | −0.0797902 | ||||||||
\(926\) | 52214.4 | − | 30146.0i | 1.85299 | − | 1.06983i | ||||
\(927\) | −24041.0 | + | 14218.6i | −0.851791 | + | 0.503776i | ||||
\(928\) | 9439.86 | − | 16350.3i | 0.333921 | − | 0.578368i | ||||
\(929\) | 19211.5 | + | 33275.3i | 0.678482 | + | 1.17516i | 0.975438 | + | 0.220273i | \(0.0706950\pi\) |
−0.296957 | + | 0.954891i | \(0.595972\pi\) | |||||||
\(930\) | 14974.7 | + | 25625.5i | 0.528001 | + | 0.903541i | ||||
\(931\) | −8318.22 | + | 4077.96i | −0.292823 | + | 0.143555i | ||||
\(932\) | 5891.69i | 0.207069i | ||||||||
\(933\) | 5920.51 | − | 10380.0i | 0.207748 | − | 0.364231i | ||||
\(934\) | −26648.2 | − | 15385.3i | −0.933571 | − | 0.538997i | ||||
\(935\) | −4421.26 | − | 2552.62i | −0.154642 | − | 0.0892828i | ||||
\(936\) | 408.681 | − | 4.28974i | 0.0142715 | − | 0.000149802i | ||||
\(937\) | 2693.78i | 0.0939188i | 0.998897 | + | 0.0469594i | \(0.0149531\pi\) | ||||
−0.998897 | + | 0.0469594i | \(0.985047\pi\) | |||||||
\(938\) | −58338.0 | − | 1978.01i | −2.03071 | − | 0.0688532i | ||||
\(939\) | −24712.6 | + | 14441.3i | −0.858855 | + | 0.501889i | ||||
\(940\) | 4354.74 | + | 7542.64i | 0.151102 | + | 0.261717i | ||||
\(941\) | −3096.77 | + | 5363.75i | −0.107281 | + | 0.185817i | −0.914668 | − | 0.404206i | \(-0.867548\pi\) |
0.807387 | + | 0.590023i | \(0.200881\pi\) | |||||||
\(942\) | −44535.5 | + | 233.728i | −1.54039 | + | 0.00808413i | ||||
\(943\) | 659.779 | − | 380.923i | 0.0227840 | − | 0.0131544i | ||||
\(944\) | −20990.8 | −0.723719 | ||||||||
\(945\) | −11367.1 | + | 6290.55i | −0.391293 | + | 0.216541i | ||||
\(946\) | −17124.1 | −0.588533 | ||||||||
\(947\) | −23917.9 | + | 13809.0i | −0.820726 | + | 0.473846i | −0.850667 | − | 0.525705i | \(-0.823801\pi\) |
0.0299408 | + | 0.999552i | \(0.490468\pi\) | |||||||
\(948\) | −8732.28 | + | 45.8280i | −0.299168 | + | 0.00157007i | ||||
\(949\) | 2802.12 | − | 4853.41i | 0.0958489 | − | 0.166015i | ||||
\(950\) | −1378.57 | − | 2387.76i | −0.0470809 | − | 0.0815465i | ||||
\(951\) | −18671.3 | + | 10910.9i | −0.636654 | + | 0.372041i | ||||
\(952\) | −3249.52 | + | 5212.06i | −0.110628 | + | 0.177441i | ||||
\(953\) | 27371.0i | 0.930361i | 0.885216 | + | 0.465181i | \(0.154011\pi\) | ||||
−0.885216 | + | 0.465181i | \(0.845989\pi\) | |||||||
\(954\) | −8070.34 | + | 84.7106i | −0.273886 | + | 0.00287485i | ||||
\(955\) | 10711.2 | + | 6184.10i | 0.362938 | + | 0.209542i | ||||
\(956\) | 1591.21 | + | 918.688i | 0.0538321 | + | 0.0310800i | ||||
\(957\) | 1586.02 | − | 2780.68i | 0.0535725 | − | 0.0939253i | ||||
\(958\) | 13407.9i | 0.452181i | ||||||||
\(959\) | −1535.01 | + | 2462.08i | −0.0516873 | + | 0.0829039i | ||||
\(960\) | −7789.93 | − | 13330.5i | −0.261895 | − | 0.448167i | ||||
\(961\) | 24239.9 | + | 41984.8i | 0.813666 | + | 1.40931i | ||||
\(962\) | −1009.00 | + | 1747.64i | −0.0338165 | + | 0.0585718i | ||||
\(963\) | 8027.58 | − | 4747.76i | 0.268624 | − | 0.158873i | ||||
\(964\) | −860.649 | + | 496.896i | −0.0287548 | + | 0.0166016i | ||||
\(965\) | 8391.23 | 0.279920 | ||||||||
\(966\) | −1151.95 | − | 709.827i | −0.0383679 | − | 0.0236421i | ||||
\(967\) | 46696.9 | 1.55292 | 0.776458 | − | 0.630169i | \(-0.217014\pi\) | ||||
0.776458 | + | 0.630169i | \(0.217014\pi\) | |||||||
\(968\) | 2999.32 | − | 1731.66i | 0.0995886 | − | 0.0574975i | ||||
\(969\) | −88.8164 | − | 16923.5i | −0.00294447 | − | 0.561052i | ||||
\(970\) | −310.755 | + | 538.243i | −0.0102863 | + | 0.0178164i | ||||
\(971\) | 1836.88 | + | 3181.58i | 0.0607090 | + | 0.105151i | 0.894783 | − | 0.446502i | \(-0.147331\pi\) |
−0.834074 | + | 0.551653i | \(0.813997\pi\) | |||||||
\(972\) | −15675.4 | + | 28874.7i | −0.517273 | + | 0.952835i | ||||
\(973\) | 19466.3 | + | 660.024i | 0.641377 | + | 0.0217466i | ||||
\(974\) | 41708.8i | 1.37211i | ||||||||
\(975\) | −621.077 | − | 354.246i | −0.0204004 | − | 0.0116358i | ||||
\(976\) | −34106.7 | − | 19691.5i | −1.11857 | − | 0.645809i | ||||
\(977\) | 49808.3 | + | 28756.9i | 1.63102 | + | 0.941672i | 0.983778 | + | 0.179390i | \(0.0574122\pi\) |
0.647245 | + | 0.762282i | \(0.275921\pi\) | |||||||
\(978\) | 46029.2 | + | 26253.8i | 1.50496 | + | 0.858390i | ||||
\(979\) | 5262.06i | 0.171784i | ||||||||
\(980\) | −14840.9 | − | 1007.55i | −0.483751 | − | 0.0328419i | ||||
\(981\) | 10125.4 | − | 17970.7i | 0.329539 | − | 0.584871i | ||||
\(982\) | 2751.26 | + | 4765.32i | 0.0894055 | + | 0.154855i | ||||
\(983\) | 12783.7 | − | 22142.1i | 0.414790 | − | 0.718437i | −0.580617 | − | 0.814177i | \(-0.697188\pi\) |
0.995406 | + | 0.0957402i | \(0.0305218\pi\) | |||||||
\(984\) | −16.5930 | − | 3161.70i | −0.000537566 | − | 0.102430i | ||||
\(985\) | −19566.2 | + | 11296.5i | −0.632925 | + | 0.365419i | ||||
\(986\) | 35827.1 | 1.15717 | ||||||||
\(987\) | −17007.3 | + | 9179.98i | −0.548478 | + | 0.296051i | ||||
\(988\) | −1289.40 | −0.0415194 | ||||||||
\(989\) | 1476.96 | − | 852.723i | 0.0474870 | − | 0.0274166i | ||||
\(990\) | −2376.06 | − | 4017.47i | −0.0762788 | − | 0.128973i | ||||
\(991\) | 12003.2 | − | 20790.2i | 0.384757 | − | 0.666419i | −0.606978 | − | 0.794719i | \(-0.707618\pi\) |
0.991736 | + | 0.128299i | \(0.0409518\pi\) | |||||||
\(992\) | −36297.3 | − | 62868.8i | −1.16173 | − | 2.01218i | ||||
\(993\) | 11460.3 | + | 19611.4i | 0.366246 | + | 0.626738i | ||||
\(994\) | 53472.8 | − | 28501.6i | 1.70629 | − | 0.909471i | ||||
\(995\) | 2553.90i | 0.0813709i | ||||||||
\(996\) | −31700.1 | + | 55577.7i | −1.00849 | + | 1.76812i | ||||
\(997\) | −49562.8 | − | 28615.1i | −1.57439 | − | 0.908976i | −0.995621 | − | 0.0934855i | \(-0.970199\pi\) |
−0.578771 | − | 0.815490i | \(-0.696468\pi\) | |||||||
\(998\) | −44243.9 | − | 25544.2i | −1.40332 | − | 0.810208i | ||||
\(999\) | −6469.48 | − | 10808.8i | −0.204890 | − | 0.342319i |
(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 | 105.4.s.b.101.4 | yes | 32 | |
3.2 | odd | 2 | 105.4.s.a.101.13 | yes | 32 | ||
7.5 | odd | 6 | 105.4.s.a.26.13 | ✓ | 32 | ||
21.5 | even | 6 | inner | 105.4.s.b.26.4 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.s.a.26.13 | ✓ | 32 | 7.5 | odd | 6 | ||
105.4.s.a.101.13 | yes | 32 | 3.2 | odd | 2 | ||
105.4.s.b.26.4 | yes | 32 | 21.5 | even | 6 | inner | |
105.4.s.b.101.4 | yes | 32 | 1.1 | even | 1 | trivial |