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.a.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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.06378 | + | 1.76887i | −1.08321 | + | 0.625391i | −0.931760 | − | 0.363075i | \(-0.881727\pi\) |
−0.151448 | + | 0.988465i | \(0.548394\pi\) | |||||||
\(3\) | −0.433556 | + | 5.17803i | −0.0834379 | + | 0.996513i | ||||
\(4\) | 2.25781 | − | 3.91065i | 0.282227 | − | 0.488831i | ||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | −7.83096 | − | 16.6312i | −0.532829 | − | 1.13161i | ||||
\(7\) | 5.77785 | − | 17.5959i | 0.311975 | − | 0.950090i | ||||
\(8\) | − | 12.3268i | − | 0.544773i | ||||||
\(9\) | −26.6241 | − | 4.48993i | −0.986076 | − | 0.166294i | ||||
\(10\) | 15.3189 | + | 8.84436i | 0.484425 | + | 0.279683i | ||||
\(11\) | 3.05657 | + | 1.76471i | 0.0837811 | + | 0.0483710i | 0.541305 | − | 0.840826i | \(-0.317930\pi\) |
−0.457524 | + | 0.889197i | \(0.651264\pi\) | |||||||
\(12\) | 19.2706 | + | 13.3865i | 0.463578 | + | 0.322030i | ||||
\(13\) | − | 14.5404i | − | 0.310214i | −0.987898 | − | 0.155107i | \(-0.950428\pi\) | ||
0.987898 | − | 0.155107i | \(-0.0495723\pi\) | |||||||
\(14\) | 13.4229 | + | 64.1302i | 0.256244 | + | 1.22425i | ||||
\(15\) | 23.5054 | − | 11.0677i | 0.404605 | − | 0.190512i | ||||
\(16\) | 39.8671 | + | 69.0518i | 0.622923 | + | 1.07893i | ||||
\(17\) | 30.9412 | − | 53.5917i | 0.441432 | − | 0.764582i | −0.556364 | − | 0.830939i | \(-0.687804\pi\) |
0.997796 | + | 0.0663561i | \(0.0211373\pi\) | |||||||
\(18\) | 89.5123 | − | 33.3384i | 1.17212 | − | 0.436552i | ||||
\(19\) | −39.8972 | + | 23.0346i | −0.481739 | + | 0.278132i | −0.721141 | − | 0.692788i | \(-0.756382\pi\) |
0.239402 | + | 0.970921i | \(0.423049\pi\) | |||||||
\(20\) | −22.5781 | −0.252431 | ||||||||
\(21\) | 88.6072 | + | 37.5467i | 0.920747 | + | 0.390160i | ||||
\(22\) | −12.4862 | −0.121003 | ||||||||
\(23\) | 99.5813 | − | 57.4933i | 0.902788 | − | 0.521225i | 0.0246846 | − | 0.999695i | \(-0.492142\pi\) |
0.878104 | + | 0.478470i | \(0.158809\pi\) | |||||||
\(24\) | 63.8287 | + | 5.34436i | 0.542874 | + | 0.0454547i | ||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 25.7201 | + | 44.5486i | 0.194005 | + | 0.336027i | ||||
\(27\) | 34.7920 | − | 135.914i | 0.247990 | − | 0.968763i | ||||
\(28\) | −55.7661 | − | 62.3234i | −0.376386 | − | 0.420644i | ||||
\(29\) | − | 127.376i | − | 0.815628i | −0.913065 | − | 0.407814i | \(-0.866291\pi\) | ||
0.913065 | − | 0.407814i | \(-0.133709\pi\) | |||||||
\(30\) | −52.4380 | + | 75.4871i | −0.319127 | + | 0.459400i | ||||
\(31\) | 183.725 | + | 106.074i | 1.06445 | + | 0.614561i | 0.926660 | − | 0.375900i | \(-0.122666\pi\) |
0.137791 | + | 0.990461i | \(0.456000\pi\) | |||||||
\(32\) | −158.885 | − | 91.7322i | −0.877723 | − | 0.506753i | ||||
\(33\) | −10.4629 | + | 15.0619i | −0.0551929 | + | 0.0794529i | ||||
\(34\) | 218.924i | 1.10427i | ||||||||
\(35\) | −90.6372 | + | 18.9710i | −0.437728 | + | 0.0916194i | ||||
\(36\) | −77.6707 | + | 93.9799i | −0.359587 | + | 0.435092i | ||||
\(37\) | −142.232 | − | 246.353i | −0.631969 | − | 1.09460i | −0.987149 | − | 0.159804i | \(-0.948914\pi\) |
0.355180 | − | 0.934798i | \(-0.384419\pi\) | |||||||
\(38\) | 81.4907 | − | 141.146i | 0.347882 | − | 0.602550i | ||||
\(39\) | 75.2907 | + | 6.30408i | 0.309132 | + | 0.0258836i | ||||
\(40\) | −53.3767 | + | 30.8170i | −0.210990 | + | 0.121815i | ||||
\(41\) | −328.199 | −1.25015 | −0.625075 | − | 0.780565i | \(-0.714932\pi\) | ||||
−0.625075 | + | 0.780565i | \(0.714932\pi\) | |||||||
\(42\) | −337.888 | + | 41.7001i | −1.24136 | + | 0.153202i | ||||
\(43\) | −108.351 | −0.384264 | −0.192132 | − | 0.981369i | \(-0.561540\pi\) | ||||
−0.192132 | + | 0.981369i | \(0.561540\pi\) | |||||||
\(44\) | 13.8023 | − | 7.96879i | 0.0472905 | − | 0.0273032i | ||||
\(45\) | 47.1182 | + | 126.510i | 0.156088 | + | 0.419090i | ||||
\(46\) | −203.396 | + | 352.293i | −0.651939 | + | 1.12919i | ||||
\(47\) | −194.765 | − | 337.343i | −0.604455 | − | 1.04695i | −0.992137 | − | 0.125154i | \(-0.960058\pi\) |
0.387682 | − | 0.921793i | \(-0.373276\pi\) | |||||||
\(48\) | −374.837 | + | 176.495i | −1.12715 | + | 0.530727i | ||||
\(49\) | −276.233 | − | 203.333i | −0.805344 | − | 0.592808i | ||||
\(50\) | − | 88.4436i | − | 0.250156i | ||||||
\(51\) | 264.085 | + | 183.450i | 0.725084 | + | 0.503688i | ||||
\(52\) | −56.8624 | − | 32.8295i | −0.151642 | − | 0.0875507i | ||||
\(53\) | 514.874 | + | 297.263i | 1.33440 | + | 0.770418i | 0.985971 | − | 0.166915i | \(-0.0533807\pi\) |
0.348433 | + | 0.937334i | \(0.386714\pi\) | |||||||
\(54\) | 133.819 | + | 477.951i | 0.337230 | + | 1.20446i | ||||
\(55\) | − | 17.6471i | − | 0.0432643i | ||||||
\(56\) | −216.902 | − | 71.2225i | −0.517584 | − | 0.169955i | ||||
\(57\) | −101.976 | − | 216.576i | −0.236967 | − | 0.503266i | ||||
\(58\) | 225.313 | + | 390.253i | 0.510086 | + | 0.883495i | ||||
\(59\) | 275.460 | − | 477.110i | 0.607827 | − | 1.05279i | −0.383770 | − | 0.923429i | \(-0.625375\pi\) |
0.991598 | − | 0.129359i | \(-0.0412921\pi\) | |||||||
\(60\) | 9.78888 | − | 116.910i | 0.0210623 | − | 0.251551i | ||||
\(61\) | 411.663 | − | 237.674i | 0.864067 | − | 0.498869i | −0.00130515 | − | 0.999999i | \(-0.500415\pi\) |
0.865372 | + | 0.501130i | \(0.167082\pi\) | |||||||
\(62\) | −750.523 | −1.53736 | ||||||||
\(63\) | −232.834 | + | 442.533i | −0.465625 | + | 0.884982i | ||||
\(64\) | 11.1767 | 0.0218295 | ||||||||
\(65\) | −62.9618 | + | 36.3510i | −0.120145 | + | 0.0693660i | ||||
\(66\) | 5.41347 | − | 64.6540i | 0.0100962 | − | 0.120581i | ||||
\(67\) | 208.025 | − | 360.310i | 0.379318 | − | 0.656998i | −0.611645 | − | 0.791132i | \(-0.709492\pi\) |
0.990963 | + | 0.134134i | \(0.0428253\pi\) | |||||||
\(68\) | −139.719 | − | 242.000i | −0.249168 | − | 0.431571i | ||||
\(69\) | 254.528 | + | 540.562i | 0.444081 | + | 0.943130i | ||||
\(70\) | 244.135 | − | 218.448i | 0.416853 | − | 0.372994i | ||||
\(71\) | − | 399.916i | − | 0.668470i | −0.942490 | − | 0.334235i | \(-0.891522\pi\) | ||
0.942490 | − | 0.334235i | \(-0.108478\pi\) | |||||||
\(72\) | −55.3466 | + | 328.190i | −0.0905925 | + | 0.537188i | ||||
\(73\) | −134.493 | − | 77.6498i | −0.215634 | − | 0.124496i | 0.388293 | − | 0.921536i | \(-0.373065\pi\) |
−0.603927 | + | 0.797040i | \(0.706398\pi\) | |||||||
\(74\) | 871.535 | + | 503.181i | 1.36911 | + | 0.790454i | ||||
\(75\) | −106.688 | − | 74.1122i | −0.164257 | − | 0.114103i | ||||
\(76\) | 208.032i | 0.313985i | ||||||||
\(77\) | 48.7122 | − | 43.5870i | 0.0720944 | − | 0.0645090i | ||||
\(78\) | −241.825 | + | 113.865i | −0.351042 | + | 0.165291i | ||||
\(79\) | −586.016 | − | 1015.01i | −0.834581 | − | 1.44554i | −0.894371 | − | 0.447326i | \(-0.852376\pi\) |
0.0597897 | − | 0.998211i | \(-0.480957\pi\) | |||||||
\(80\) | 199.335 | − | 345.259i | 0.278580 | − | 0.482514i | ||||
\(81\) | 688.681 | + | 239.080i | 0.944693 | + | 0.327957i | ||||
\(82\) | 1005.53 | − | 580.543i | 1.35417 | − | 0.781832i | ||||
\(83\) | 4.43096 | 0.00585977 | 0.00292988 | − | 0.999996i | \(-0.499067\pi\) | ||||
0.00292988 | + | 0.999996i | \(0.499067\pi\) | |||||||
\(84\) | 346.891 | − | 261.738i | 0.450582 | − | 0.339976i | ||||
\(85\) | −309.412 | −0.394829 | ||||||||
\(86\) | 331.963 | − | 191.659i | 0.416238 | − | 0.240315i | ||||
\(87\) | 659.560 | + | 55.2248i | 0.812784 | + | 0.0680543i | ||||
\(88\) | 21.7533 | − | 37.6778i | 0.0263512 | − | 0.0456417i | ||||
\(89\) | 505.709 | + | 875.913i | 0.602303 | + | 1.04322i | 0.992471 | + | 0.122476i | \(0.0390836\pi\) |
−0.390168 | + | 0.920744i | \(0.627583\pi\) | |||||||
\(90\) | −368.140 | − | 304.253i | −0.431171 | − | 0.356346i | ||||
\(91\) | −255.852 | − | 84.0123i | −0.294732 | − | 0.0967789i | ||||
\(92\) | − | 519.236i | − | 0.588415i | ||||||
\(93\) | −628.908 | + | 905.346i | −0.701234 | + | 1.00946i | ||||
\(94\) | 1193.43 | + | 689.028i | 1.30950 | + | 0.756041i | ||||
\(95\) | 199.486 | + | 115.173i | 0.215440 | + | 0.124384i | ||||
\(96\) | 543.878 | − | 782.940i | 0.578222 | − | 0.832380i | ||||
\(97\) | − | 27.5269i | − | 0.0288137i | −0.999896 | − | 0.0144069i | \(-0.995414\pi\) | ||
0.999896 | − | 0.0144069i | \(-0.00458600\pi\) | |||||||
\(98\) | 1205.99 | + | 134.347i | 1.24309 | + | 0.138480i | ||||
\(99\) | −73.4549 | − | 60.7076i | −0.0745707 | − | 0.0616298i | ||||
\(100\) | 56.4453 | + | 97.7662i | 0.0564453 | + | 0.0977662i | ||||
\(101\) | −953.191 | + | 1650.97i | −0.939069 | + | 1.62652i | −0.171858 | + | 0.985122i | \(0.554977\pi\) |
−0.767211 | + | 0.641394i | \(0.778356\pi\) | |||||||
\(102\) | −1133.60 | − | 94.9158i | −1.10042 | − | 0.0921379i | ||||
\(103\) | 1509.53 | − | 871.529i | 1.44407 | − | 0.833732i | 0.445948 | − | 0.895059i | \(-0.352867\pi\) |
0.998118 | + | 0.0613274i | \(0.0195334\pi\) | |||||||
\(104\) | −179.237 | −0.168996 | ||||||||
\(105\) | −58.9361 | − | 477.547i | −0.0547769 | − | 0.443846i | ||||
\(106\) | −2103.28 | −1.92725 | ||||||||
\(107\) | −1554.57 | + | 897.534i | −1.40455 | + | 0.810915i | −0.994855 | − | 0.101310i | \(-0.967697\pi\) |
−0.409690 | + | 0.912225i | \(0.634363\pi\) | |||||||
\(108\) | −452.956 | − | 442.927i | −0.403572 | − | 0.394636i | ||||
\(109\) | −382.680 | + | 662.821i | −0.336276 | + | 0.582447i | −0.983729 | − | 0.179658i | \(-0.942501\pi\) |
0.647453 | + | 0.762105i | \(0.275834\pi\) | |||||||
\(110\) | 31.2155 | + | 54.0669i | 0.0270571 | + | 0.0468643i | ||||
\(111\) | 1337.29 | − | 629.675i | 1.14351 | − | 0.538434i | ||||
\(112\) | 1445.38 | − | 302.527i | 1.21942 | − | 0.255233i | ||||
\(113\) | − | 142.010i | − | 0.118222i | −0.998251 | − | 0.0591112i | \(-0.981173\pi\) | ||
0.998251 | − | 0.0591112i | \(-0.0188267\pi\) | |||||||
\(114\) | 695.528 | + | 483.156i | 0.571422 | + | 0.396945i | ||||
\(115\) | −497.906 | − | 287.466i | −0.403739 | − | 0.233099i | ||||
\(116\) | −498.124 | − | 287.592i | −0.398704 | − | 0.230192i | ||||
\(117\) | −65.2855 | + | 387.125i | −0.0515867 | + | 0.305895i | ||||
\(118\) | 1949.01i | 1.52052i | ||||||||
\(119\) | −764.222 | − | 854.084i | −0.588707 | − | 0.657931i | ||||
\(120\) | −136.430 | − | 289.747i | −0.103786 | − | 0.220418i | ||||
\(121\) | −659.272 | − | 1141.89i | −0.495320 | − | 0.857920i | ||||
\(122\) | −840.829 | + | 1456.36i | −0.623976 | + | 1.08076i | ||||
\(123\) | 142.293 | − | 1699.43i | 0.104310 | − | 1.24579i | ||||
\(124\) | 829.634 | − | 478.989i | 0.600833 | − | 0.346891i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −69.4314 | − | 1767.67i | −0.0490908 | − | 1.24982i | ||||
\(127\) | −2291.18 | −1.60086 | −0.800430 | − | 0.599426i | \(-0.795396\pi\) | ||||
−0.800430 | + | 0.599426i | \(0.795396\pi\) | |||||||
\(128\) | 1236.84 | − | 714.087i | 0.854077 | − | 0.493101i | ||||
\(129\) | 46.9762 | − | 561.045i | 0.0320622 | − | 0.382925i | ||||
\(130\) | 128.601 | − | 222.743i | 0.0867617 | − | 0.150276i | ||||
\(131\) | 259.146 | + | 448.855i | 0.172838 | + | 0.299364i | 0.939411 | − | 0.342793i | \(-0.111373\pi\) |
−0.766573 | + | 0.642157i | \(0.778040\pi\) | |||||||
\(132\) | 35.2786 | + | 74.9239i | 0.0232622 | + | 0.0494037i | ||||
\(133\) | 174.796 | + | 835.118i | 0.113960 | + | 0.544466i | ||||
\(134\) | 1471.88i | 0.948888i | ||||||||
\(135\) | −675.503 | + | 189.130i | −0.430652 | + | 0.120576i | ||||
\(136\) | −660.615 | − | 381.406i | −0.416524 | − | 0.240480i | ||||
\(137\) | −1012.79 | − | 584.732i | −0.631593 | − | 0.364650i | 0.149776 | − | 0.988720i | \(-0.452145\pi\) |
−0.781369 | + | 0.624070i | \(0.785478\pi\) | |||||||
\(138\) | −1736.00 | − | 1205.93i | −1.07086 | − | 0.743883i | ||||
\(139\) | 2599.73i | 1.58638i | 0.608977 | + | 0.793188i | \(0.291580\pi\) | ||||
−0.608977 | + | 0.793188i | \(0.708420\pi\) | |||||||
\(140\) | −130.453 | + | 397.283i | −0.0787521 | + | 0.239833i | ||||
\(141\) | 1831.21 | − | 862.243i | 1.09373 | − | 0.514992i | ||||
\(142\) | 707.401 | + | 1225.25i | 0.418055 | + | 0.724092i | ||||
\(143\) | 25.6597 | − | 44.4438i | 0.0150054 | − | 0.0259901i | ||||
\(144\) | −751.385 | − | 2017.44i | −0.434829 | − | 1.16750i | ||||
\(145\) | −551.556 | + | 318.441i | −0.315891 | + | 0.182380i | ||||
\(146\) | 549.410 | 0.311435 | ||||||||
\(147\) | 1172.63 | − | 1342.19i | 0.657937 | − | 0.753073i | ||||
\(148\) | −1284.54 | −0.713434 | ||||||||
\(149\) | 435.444 | − | 251.404i | 0.239416 | − | 0.138227i | −0.375492 | − | 0.926825i | \(-0.622526\pi\) |
0.614908 | + | 0.788599i | \(0.289193\pi\) | |||||||
\(150\) | 457.964 | + | 38.3452i | 0.249284 | + | 0.0208725i | ||||
\(151\) | −1175.38 | + | 2035.82i | −0.633452 | + | 1.09717i | 0.353389 | + | 0.935477i | \(0.385029\pi\) |
−0.986841 | + | 0.161695i | \(0.948304\pi\) | |||||||
\(152\) | 283.944 | + | 491.805i | 0.151519 | + | 0.262439i | ||||
\(153\) | −1064.40 | + | 1287.91i | −0.562431 | + | 0.680529i | ||||
\(154\) | −72.1434 | + | 219.706i | −0.0377499 | + | 0.114964i | ||||
\(155\) | − | 1060.74i | − | 0.549680i | ||||||
\(156\) | 194.645 | − | 280.202i | 0.0998981 | − | 0.143808i | ||||
\(157\) | 2469.13 | + | 1425.55i | 1.25515 | + | 0.724659i | 0.972127 | − | 0.234455i | \(-0.0753306\pi\) |
0.283019 | + | 0.959114i | \(0.408664\pi\) | |||||||
\(158\) | 3590.84 | + | 2073.17i | 1.80805 | + | 1.04388i | ||||
\(159\) | −1762.46 | + | 2537.16i | −0.879072 | + | 1.26547i | ||||
\(160\) | 917.322i | 0.453254i | ||||||||
\(161\) | −436.282 | − | 2084.41i | −0.213564 | − | 1.02034i | ||||
\(162\) | −2532.87 | + | 485.699i | −1.22840 | + | 0.235556i | ||||
\(163\) | −1119.63 | − | 1939.25i | −0.538011 | − | 0.931863i | −0.999011 | − | 0.0444628i | \(-0.985842\pi\) |
0.461000 | − | 0.887400i | \(-0.347491\pi\) | |||||||
\(164\) | −741.013 | + | 1283.47i | −0.352826 | + | 0.611112i | ||||
\(165\) | 91.3775 | + | 7.65102i | 0.0431135 | + | 0.00360988i | ||||
\(166\) | −13.5755 | + | 7.83779i | −0.00634735 | + | 0.00366464i | ||||
\(167\) | 2469.34 | 1.14421 | 0.572105 | − | 0.820181i | \(-0.306127\pi\) | ||||
0.572105 | + | 0.820181i | \(0.306127\pi\) | |||||||
\(168\) | 462.831 | − | 1092.25i | 0.212549 | − | 0.501599i | ||||
\(169\) | 1985.58 | 0.903767 | ||||||||
\(170\) | 947.969 | − | 547.310i | 0.427682 | − | 0.246922i | ||||
\(171\) | 1165.65 | − | 434.140i | 0.521283 | − | 0.194149i | ||||
\(172\) | −244.636 | + | 423.723i | −0.108450 | + | 0.187840i | ||||
\(173\) | 373.114 | + | 646.252i | 0.163973 | + | 0.284009i | 0.936290 | − | 0.351228i | \(-0.114236\pi\) |
−0.772317 | + | 0.635237i | \(0.780902\pi\) | |||||||
\(174\) | −2118.43 | + | 997.480i | −0.922975 | + | 0.434590i | ||||
\(175\) | 308.740 | + | 345.043i | 0.133363 | + | 0.149045i | ||||
\(176\) | 281.416i | 0.120526i | ||||||||
\(177\) | 2351.07 | + | 1633.19i | 0.998401 | + | 0.693550i | ||||
\(178\) | −3098.76 | − | 1789.07i | −1.30484 | − | 0.753350i | ||||
\(179\) | −2952.97 | − | 1704.90i | −1.23305 | − | 0.711901i | −0.265384 | − | 0.964143i | \(-0.585499\pi\) |
−0.967664 | + | 0.252242i | \(0.918832\pi\) | |||||||
\(180\) | 601.122 | + | 101.374i | 0.248916 | + | 0.0419778i | ||||
\(181\) | 2937.61i | 1.20636i | 0.797607 | + | 0.603178i | \(0.206099\pi\) | ||||
−0.797607 | + | 0.603178i | \(0.793901\pi\) | |||||||
\(182\) | 932.480 | − | 195.174i | 0.379780 | − | 0.0794906i | ||||
\(183\) | 1052.20 | + | 2234.65i | 0.425034 | + | 0.902679i | ||||
\(184\) | −708.709 | − | 1227.52i | −0.283950 | − | 0.491815i | ||||
\(185\) | −711.161 | + | 1231.77i | −0.282625 | + | 0.489521i | ||||
\(186\) | 325.394 | − | 3886.23i | 0.128274 | − | 1.53200i | ||||
\(187\) | 189.148 | − | 109.205i | 0.0739673 | − | 0.0427050i | ||||
\(188\) | −1758.97 | −0.682374 | ||||||||
\(189\) | −2190.50 | − | 1397.49i | −0.843045 | − | 0.537842i | ||||
\(190\) | −814.907 | −0.311155 | ||||||||
\(191\) | 92.6615 | − | 53.4982i | 0.0351034 | − | 0.0202670i | −0.482346 | − | 0.875981i | \(-0.660215\pi\) |
0.517449 | + | 0.855714i | \(0.326882\pi\) | |||||||
\(192\) | −4.84573 | + | 57.8735i | −0.00182141 | + | 0.0217534i | ||||
\(193\) | 1091.15 | − | 1889.93i | 0.406958 | − | 0.704871i | −0.587590 | − | 0.809159i | \(-0.699923\pi\) |
0.994547 | + | 0.104288i | \(0.0332563\pi\) | |||||||
\(194\) | 48.6915 | + | 84.3362i | 0.0180198 | + | 0.0312113i | ||||
\(195\) | −160.929 | − | 341.779i | −0.0590994 | − | 0.125514i | ||||
\(196\) | −1418.85 | + | 621.161i | −0.517073 | + | 0.226371i | ||||
\(197\) | − | 205.038i | − | 0.0741541i | −0.999312 | − | 0.0370771i | \(-0.988195\pi\) | ||
0.999312 | − | 0.0370771i | \(-0.0118047\pi\) | |||||||
\(198\) | 332.433 | + | 56.0622i | 0.119318 | + | 0.0201221i | ||||
\(199\) | −2307.14 | − | 1332.03i | −0.821854 | − | 0.474498i | 0.0292011 | − | 0.999574i | \(-0.490704\pi\) |
−0.851056 | + | 0.525076i | \(0.824037\pi\) | |||||||
\(200\) | 266.883 | + | 154.085i | 0.0943575 | + | 0.0544773i | ||||
\(201\) | 1775.51 | + | 1233.38i | 0.623058 | + | 0.432814i | ||||
\(202\) | − | 6744.29i | − | 2.34914i | ||||||
\(203\) | −2241.31 | − | 735.962i | −0.774920 | − | 0.254455i | ||||
\(204\) | 1313.66 | − | 618.549i | 0.450856 | − | 0.212290i | ||||
\(205\) | 820.499 | + | 1421.15i | 0.279542 | + | 0.484181i | ||||
\(206\) | −3083.25 | + | 5340.34i | −1.04282 | + | 1.80621i | ||||
\(207\) | −2909.40 | + | 1083.59i | −0.976895 | + | 0.363840i | ||||
\(208\) | 1004.04 | − | 579.683i | 0.334701 | − | 0.193239i | ||||
\(209\) | −162.598 | −0.0538141 | ||||||||
\(210\) | 1025.29 | + | 1358.85i | 0.336912 | + | 0.446521i | ||||
\(211\) | 3884.53 | 1.26740 | 0.633701 | − | 0.773578i | \(-0.281535\pi\) | ||||
0.633701 | + | 0.773578i | \(0.281535\pi\) | |||||||
\(212\) | 2324.98 | − | 1342.33i | 0.753209 | − | 0.434865i | ||||
\(213\) | 2070.78 | + | 173.386i | 0.666139 | + | 0.0557757i | ||||
\(214\) | 3175.24 | − | 5499.68i | 1.01428 | − | 1.75678i | ||||
\(215\) | 270.877 | + | 469.174i | 0.0859241 | + | 0.148825i | ||||
\(216\) | −1675.38 | − | 428.875i | −0.527756 | − | 0.135098i | ||||
\(217\) | 2928.00 | − | 2619.93i | 0.915971 | − | 0.819598i | ||||
\(218\) | − | 2707.65i | − | 0.841216i | ||||||
\(219\) | 460.384 | − | 662.746i | 0.142054 | − | 0.204494i | ||||
\(220\) | −69.0117 | − | 39.8439i | −0.0211490 | − | 0.0122104i | ||||
\(221\) | −779.246 | − | 449.898i | −0.237184 | − | 0.136938i | ||||
\(222\) | −2983.35 | + | 4294.68i | −0.901933 | + | 1.29838i | ||||
\(223\) | 563.780i | 0.169298i | 0.996411 | + | 0.0846490i | \(0.0269769\pi\) | ||||
−0.996411 | + | 0.0846490i | \(0.973023\pi\) | |||||||
\(224\) | −2532.12 | + | 2265.71i | −0.755289 | + | 0.675822i | ||||
\(225\) | 430.011 | − | 520.304i | 0.127411 | − | 0.154164i | ||||
\(226\) | 251.197 | + | 435.085i | 0.0739352 | + | 0.128059i | ||||
\(227\) | 437.969 | − | 758.584i | 0.128057 | − | 0.221802i | −0.794867 | − | 0.606784i | \(-0.792459\pi\) |
0.922924 | + | 0.384982i | \(0.125793\pi\) | |||||||
\(228\) | −1077.20 | − | 90.1934i | −0.312890 | − | 0.0261983i | ||||
\(229\) | 4417.95 | − | 2550.70i | 1.27487 | − | 0.736049i | 0.298973 | − | 0.954262i | \(-0.403356\pi\) |
0.975901 | + | 0.218213i | \(0.0700227\pi\) | |||||||
\(230\) | 2033.96 | 0.583112 | ||||||||
\(231\) | 204.575 | + | 271.131i | 0.0582687 | + | 0.0772255i | ||||
\(232\) | −1570.15 | −0.444332 | ||||||||
\(233\) | −5036.52 | + | 2907.84i | −1.41611 | + | 0.817591i | −0.995954 | − | 0.0898610i | \(-0.971358\pi\) |
−0.420155 | + | 0.907452i | \(0.638024\pi\) | |||||||
\(234\) | −484.754 | − | 1301.54i | −0.135425 | − | 0.363610i | ||||
\(235\) | −973.825 | + | 1686.71i | −0.270321 | + | 0.468209i | ||||
\(236\) | −1243.87 | − | 2154.45i | −0.343090 | − | 0.594250i | ||||
\(237\) | 5509.82 | − | 2594.35i | 1.51013 | − | 0.711059i | ||||
\(238\) | 3852.17 | + | 1264.91i | 1.04916 | + | 0.344504i | ||||
\(239\) | − | 3786.80i | − | 1.02489i | −0.858721 | − | 0.512443i | \(-0.828741\pi\) | ||
0.858721 | − | 0.512443i | \(-0.171259\pi\) | |||||||
\(240\) | 1701.34 | + | 1181.85i | 0.457587 | + | 0.317868i | ||||
\(241\) | 2248.22 | + | 1298.01i | 0.600915 | + | 0.346938i | 0.769401 | − | 0.638766i | \(-0.220555\pi\) |
−0.168486 | + | 0.985704i | \(0.553888\pi\) | |||||||
\(242\) | 4039.72 | + | 2332.33i | 1.07307 | + | 0.619538i | ||||
\(243\) | −1536.55 | + | 3462.36i | −0.405636 | + | 0.914035i | ||||
\(244\) | − | 2146.49i | − | 0.563177i | ||||||
\(245\) | −189.876 | + | 1704.46i | −0.0495133 | + | 0.444464i | ||||
\(246\) | 2570.12 | + | 5458.36i | 0.666116 | + | 1.41469i | ||||
\(247\) | 334.933 | + | 580.121i | 0.0862805 | + | 0.149442i | ||||
\(248\) | 1307.55 | − | 2264.74i | 0.334797 | − | 0.579885i | ||||
\(249\) | −1.92107 | + | 22.9436i | −0.000488926 | + | 0.00583933i | ||||
\(250\) | −382.972 | + | 221.109i | −0.0968851 | + | 0.0559366i | ||||
\(251\) | 4377.60 | 1.10084 | 0.550422 | − | 0.834887i | \(-0.314467\pi\) | ||||
0.550422 | + | 0.834887i | \(0.314467\pi\) | |||||||
\(252\) | 1204.89 | + | 1909.69i | 0.301195 | + | 0.477377i | ||||
\(253\) | 405.837 | 0.100849 | ||||||||
\(254\) | 7019.66 | − | 4052.80i | 1.73407 | − | 1.00116i | ||||
\(255\) | 134.147 | − | 1602.15i | 0.0329437 | − | 0.393452i | ||||
\(256\) | −2570.96 | + | 4453.04i | −0.627677 | + | 1.08717i | ||||
\(257\) | 283.243 | + | 490.592i | 0.0687480 | + | 0.119075i | 0.898350 | − | 0.439280i | \(-0.144766\pi\) |
−0.829602 | + | 0.558355i | \(0.811433\pi\) | |||||||
\(258\) | 848.492 | + | 1802.01i | 0.204747 | + | 0.434838i | ||||
\(259\) | −5156.61 | + | 1079.31i | −1.23713 | + | 0.258939i | ||||
\(260\) | 328.295i | 0.0783077i | ||||||||
\(261\) | −571.912 | + | 3391.28i | −0.135634 | + | 0.804271i | ||||
\(262\) | −1587.93 | − | 916.794i | −0.374438 | − | 0.216182i | ||||
\(263\) | 1051.70 | + | 607.199i | 0.246580 | + | 0.142363i | 0.618197 | − | 0.786023i | \(-0.287863\pi\) |
−0.371617 | + | 0.928386i | \(0.621197\pi\) | |||||||
\(264\) | 185.666 | + | 128.975i | 0.0432838 | + | 0.0300676i | ||||
\(265\) | − | 2972.63i | − | 0.689083i | ||||||
\(266\) | −2012.75 | − | 2249.42i | −0.463946 | − | 0.518500i | ||||
\(267\) | −4754.76 | + | 2238.82i | −1.08984 | + | 0.513159i | ||||
\(268\) | −939.364 | − | 1627.03i | −0.214107 | − | 0.370845i | ||||
\(269\) | 454.101 | − | 786.526i | 0.102926 | − | 0.178273i | −0.809963 | − | 0.586481i | \(-0.800513\pi\) |
0.912889 | + | 0.408208i | \(0.133846\pi\) | |||||||
\(270\) | 1735.04 | − | 1774.33i | 0.391079 | − | 0.399935i | ||||
\(271\) | −3758.84 | + | 2170.17i | −0.842558 | + | 0.486451i | −0.858133 | − | 0.513427i | \(-0.828376\pi\) |
0.0155746 | + | 0.999879i | \(0.495042\pi\) | |||||||
\(272\) | 4934.14 | 1.09991 | ||||||||
\(273\) | 545.945 | − | 1288.39i | 0.121033 | − | 0.285629i | ||||
\(274\) | 4137.27 | 0.912195 | ||||||||
\(275\) | −76.4143 | + | 44.1178i | −0.0167562 | + | 0.00967420i | ||||
\(276\) | 2688.62 | + | 225.118i | 0.586363 | + | 0.0490961i | ||||
\(277\) | −3194.05 | + | 5532.26i | −0.692823 | + | 1.20001i | 0.278086 | + | 0.960556i | \(0.410300\pi\) |
−0.970909 | + | 0.239449i | \(0.923033\pi\) | |||||||
\(278\) | −4598.59 | − | 7964.99i | −0.992105 | − | 1.71838i | ||||
\(279\) | −4415.24 | − | 3649.03i | −0.947433 | − | 0.783016i | ||||
\(280\) | 233.852 | + | 1117.27i | 0.0499118 | + | 0.238463i | ||||
\(281\) | − | 3345.41i | − | 0.710216i | −0.934825 | − | 0.355108i | \(-0.884444\pi\) | ||
0.934825 | − | 0.355108i | \(-0.115556\pi\) | |||||||
\(282\) | −4085.23 | + | 5880.90i | −0.862667 | + | 1.24185i | ||||
\(283\) | 949.320 | + | 548.090i | 0.199404 | + | 0.115126i | 0.596377 | − | 0.802704i | \(-0.296606\pi\) |
−0.396974 | + | 0.917830i | \(0.629940\pi\) | |||||||
\(284\) | −1563.93 | − | 902.937i | −0.326769 | − | 0.188660i | ||||
\(285\) | −682.859 | + | 983.010i | −0.141927 | + | 0.204311i | ||||
\(286\) | 181.555i | 0.0375369i | ||||||||
\(287\) | −1896.29 | + | 5774.97i | −0.390015 | + | 1.18776i | ||||
\(288\) | 3818.29 | + | 3155.66i | 0.781232 | + | 0.645657i | ||||
\(289\) | 541.785 | + | 938.399i | 0.110276 | + | 0.191003i | ||||
\(290\) | 1126.56 | − | 1951.26i | 0.228117 | − | 0.395111i | ||||
\(291\) | 142.535 | + | 11.9344i | 0.0287132 | + | 0.00240415i | ||||
\(292\) | −607.322 | + | 350.638i | −0.121715 | + | 0.0702723i | ||||
\(293\) | −4350.28 | −0.867392 | −0.433696 | − | 0.901059i | \(-0.642791\pi\) | ||||
−0.433696 | + | 0.901059i | \(0.642791\pi\) | |||||||
\(294\) | −1218.51 | + | 6186.39i | −0.241718 | + | 1.22720i | ||||
\(295\) | −2754.60 | −0.543657 | ||||||||
\(296\) | −3036.75 | + | 1753.27i | −0.596310 | + | 0.344280i | ||||
\(297\) | 346.193 | − | 354.032i | 0.0676369 | − | 0.0691684i | ||||
\(298\) | −889.402 | + | 1540.49i | −0.172891 | + | 0.299457i | ||||
\(299\) | −835.976 | − | 1447.95i | −0.161691 | − | 0.280058i | ||||
\(300\) | −530.709 | + | 249.889i | −0.102135 | + | 0.0480911i | ||||
\(301\) | −626.036 | + | 1906.54i | −0.119881 | + | 0.365086i | ||||
\(302\) | − | 8316.40i | − | 1.58462i | ||||||
\(303\) | −8135.54 | − | 5651.44i | −1.54249 | − | 1.07151i | ||||
\(304\) | −3181.17 | − | 1836.65i | −0.600172 | − | 0.346510i | ||||
\(305\) | −2058.32 | − | 1188.37i | −0.386422 | − | 0.223101i | ||||
\(306\) | 982.954 | − | 5828.65i | 0.183633 | − | 1.08889i | ||||
\(307\) | − | 5750.86i | − | 1.06912i | −0.845132 | − | 0.534558i | \(-0.820478\pi\) | ||
0.845132 | − | 0.534558i | \(-0.179522\pi\) | |||||||
\(308\) | −60.4703 | − | 288.907i | −0.0111871 | − | 0.0534482i | ||||
\(309\) | 3858.34 | + | 8194.27i | 0.710335 | + | 1.50859i | ||||
\(310\) | 1876.31 | + | 3249.86i | 0.343765 | + | 0.595418i | ||||
\(311\) | 2750.86 | − | 4764.63i | 0.501565 | − | 0.868737i | −0.498433 | − | 0.866928i | \(-0.666091\pi\) |
0.999998 | − | 0.00180853i | \(-0.000575673\pi\) | |||||||
\(312\) | 77.7092 | − | 928.095i | 0.0141007 | − | 0.168407i | ||||
\(313\) | 623.841 | − | 360.175i | 0.112657 | − | 0.0650424i | −0.442613 | − | 0.896713i | \(-0.645948\pi\) |
0.555270 | + | 0.831670i | \(0.312615\pi\) | |||||||
\(314\) | −10086.5 | −1.81278 | ||||||||
\(315\) | 2498.31 | − | 98.1295i | 0.446869 | − | 0.0175523i | ||||
\(316\) | −5292.46 | −0.942164 | ||||||||
\(317\) | −106.684 | + | 61.5942i | −0.0189022 | + | 0.0109132i | −0.509421 | − | 0.860517i | \(-0.670141\pi\) |
0.490519 | + | 0.871430i | \(0.336807\pi\) | |||||||
\(318\) | 911.889 | − | 10890.8i | 0.160806 | − | 1.92053i | ||||
\(319\) | 224.783 | − | 389.335i | 0.0394528 | − | 0.0683342i | ||||
\(320\) | −27.9418 | − | 48.3966i | −0.00488123 | − | 0.00845454i | ||||
\(321\) | −3973.47 | − | 8438.77i | −0.690895 | − | 1.46731i | ||||
\(322\) | 5023.73 | + | 5614.44i | 0.869445 | + | 0.971679i | ||||
\(323\) | 2850.88i | 0.491105i | ||||||||
\(324\) | 2489.87 | − | 2153.39i | 0.426933 | − | 0.369237i | ||||
\(325\) | 314.809 | + | 181.755i | 0.0537307 | + | 0.0310214i | ||||
\(326\) | 6860.56 | + | 3960.95i | 1.16556 | + | 0.672935i | ||||
\(327\) | −3266.20 | − | 2268.90i | −0.552358 | − | 0.383702i | ||||
\(328\) | 4045.65i | 0.681048i | ||||||||
\(329\) | −7061.18 | + | 1477.95i | −1.18327 | + | 0.247666i | ||||
\(330\) | −293.494 | + | 138.194i | −0.0489585 | + | 0.0230525i | ||||
\(331\) | −4816.06 | − | 8341.66i | −0.799742 | − | 1.38519i | −0.919784 | − | 0.392425i | \(-0.871636\pi\) |
0.120042 | − | 0.992769i | \(-0.461697\pi\) | |||||||
\(332\) | 10.0043 | − | 17.3279i | 0.00165378 | − | 0.00286443i | ||||
\(333\) | 2680.69 | + | 7197.54i | 0.441144 | + | 1.18445i | ||||
\(334\) | −7565.49 | + | 4367.94i | −1.23942 | + | 0.715578i | ||||
\(335\) | −2080.25 | −0.339272 | ||||||||
\(336\) | 939.843 | + | 7615.37i | 0.152597 | + | 1.23647i | ||||
\(337\) | 4977.75 | 0.804615 | 0.402308 | − | 0.915505i | \(-0.368208\pi\) | ||||
0.402308 | + | 0.915505i | \(0.368208\pi\) | |||||||
\(338\) | −6083.36 | + | 3512.23i | −0.978968 | + | 0.565207i | ||||
\(339\) | 735.330 | + | 61.5691i | 0.117810 | + | 0.00986422i | ||||
\(340\) | −698.595 | + | 1210.00i | −0.111431 | + | 0.193005i | ||||
\(341\) | 374.379 | + | 648.444i | 0.0594539 | + | 0.102977i | ||||
\(342\) | −2803.35 | + | 3391.99i | −0.443239 | + | 0.536309i | ||||
\(343\) | −5173.87 | + | 3685.74i | −0.814468 | + | 0.580208i | ||||
\(344\) | 1335.62i | 0.209337i | ||||||||
\(345\) | 1704.38 | − | 2453.54i | 0.265973 | − | 0.382882i | ||||
\(346\) | −2286.27 | − | 1319.98i | −0.355234 | − | 0.205094i | ||||
\(347\) | 5974.28 | + | 3449.25i | 0.924254 | + | 0.533618i | 0.884990 | − | 0.465610i | \(-0.154165\pi\) |
0.0392645 | + | 0.999229i | \(0.487499\pi\) | |||||||
\(348\) | 1705.13 | − | 2454.62i | 0.262656 | − | 0.378107i | ||||
\(349\) | 5143.79i | 0.788942i | 0.918908 | + | 0.394471i | \(0.129072\pi\) | ||||
−0.918908 | + | 0.394471i | \(0.870928\pi\) | |||||||
\(350\) | −1556.25 | − | 511.014i | −0.237671 | − | 0.0780424i | ||||
\(351\) | −1976.24 | − | 505.890i | −0.300524 | − | 0.0769300i | ||||
\(352\) | −323.762 | − | 560.772i | −0.0490244 | − | 0.0849127i | ||||
\(353\) | −2903.48 | + | 5028.97i | −0.437781 | + | 0.758258i | −0.997518 | − | 0.0704119i | \(-0.977569\pi\) |
0.559737 | + | 0.828670i | \(0.310902\pi\) | |||||||
\(354\) | −10092.1 | − | 845.006i | −1.51522 | − | 0.126869i | ||||
\(355\) | −1731.69 | + | 999.791i | −0.258897 | + | 0.149474i | ||||
\(356\) | 4567.18 | 0.679944 | ||||||||
\(357\) | 4753.81 | − | 3586.87i | 0.704757 | − | 0.531758i | ||||
\(358\) | 12063.0 | 1.78086 | ||||||||
\(359\) | 6501.82 | − | 3753.83i | 0.955857 | − | 0.551864i | 0.0609616 | − | 0.998140i | \(-0.480583\pi\) |
0.894896 | + | 0.446276i | \(0.147250\pi\) | |||||||
\(360\) | 1559.47 | − | 580.817i | 0.228309 | − | 0.0850326i | ||||
\(361\) | −2368.31 | + | 4102.03i | −0.345285 | + | 0.598051i | ||||
\(362\) | −5196.25 | − | 9000.16i | −0.754444 | − | 1.30674i | ||||
\(363\) | 6198.59 | − | 2918.66i | 0.896257 | − | 0.422010i | ||||
\(364\) | −906.208 | + | 810.863i | −0.130490 | + | 0.116760i | ||||
\(365\) | 776.498i | 0.111353i | ||||||||
\(366\) | −7176.53 | − | 4985.25i | −1.02493 | − | 0.711977i | ||||
\(367\) | 8497.92 | + | 4906.28i | 1.20869 | + | 0.697835i | 0.962472 | − | 0.271380i | \(-0.0874800\pi\) |
0.246214 | + | 0.969215i | \(0.420813\pi\) | |||||||
\(368\) | 7940.03 | + | 4584.18i | 1.12474 | + | 0.649366i | ||||
\(369\) | 8738.00 | + | 1473.59i | 1.23274 | + | 0.207892i | ||||
\(370\) | − | 5031.81i | − | 0.707004i | ||||||
\(371\) | 8205.48 | − | 7342.14i | 1.14827 | − | 1.02745i | ||||
\(372\) | 2120.53 | + | 4503.54i | 0.295549 | + | 0.627682i | ||||
\(373\) | −2300.91 | − | 3985.29i | −0.319401 | − | 0.553219i | 0.660962 | − | 0.750419i | \(-0.270148\pi\) |
−0.980363 | + | 0.197200i | \(0.936815\pi\) | |||||||
\(374\) | −386.338 | + | 669.157i | −0.0534146 | + | 0.0925169i | ||||
\(375\) | −54.1945 | + | 647.254i | −0.00746291 | + | 0.0891308i | ||||
\(376\) | −4158.36 | + | 2400.83i | −0.570349 | + | 0.329291i | ||||
\(377\) | −1852.11 | −0.253019 | ||||||||
\(378\) | 9183.18 | + | 406.868i | 1.24956 | + | 0.0553625i | ||||
\(379\) | 10325.6 | 1.39945 | 0.699726 | − | 0.714412i | \(-0.253306\pi\) | ||||
0.699726 | + | 0.714412i | \(0.253306\pi\) | |||||||
\(380\) | 900.804 | − | 520.079i | 0.121606 | − | 0.0702092i | ||||
\(381\) | 993.354 | − | 11863.8i | 0.133572 | − | 1.59528i | ||||
\(382\) | −189.263 | + | 327.813i | −0.0253495 | + | 0.0439067i | ||||
\(383\) | −1615.63 | − | 2798.35i | −0.215548 | − | 0.373339i | 0.737894 | − | 0.674916i | \(-0.235820\pi\) |
−0.953442 | + | 0.301577i | \(0.902487\pi\) | |||||||
\(384\) | 3161.33 | + | 6713.97i | 0.420120 | + | 0.892242i | ||||
\(385\) | −310.518 | − | 101.963i | −0.0411050 | − | 0.0134974i | ||||
\(386\) | 7720.43i | 1.01803i | ||||||||
\(387\) | 2884.74 | + | 486.489i | 0.378914 | + | 0.0639008i | ||||
\(388\) | −107.648 | − | 62.1506i | −0.0140850 | − | 0.00813200i | ||||
\(389\) | 10881.5 | + | 6282.46i | 1.41829 | + | 0.818851i | 0.996149 | − | 0.0876781i | \(-0.0279447\pi\) |
0.422143 | + | 0.906529i | \(0.361278\pi\) | |||||||
\(390\) | 1097.61 | + | 762.470i | 0.142512 | + | 0.0989978i | ||||
\(391\) | − | 7115.64i | − | 0.920342i | ||||||
\(392\) | −2506.45 | + | 3405.07i | −0.322946 | + | 0.438730i | ||||
\(393\) | −2436.54 | + | 1147.27i | −0.312741 | + | 0.147257i | ||||
\(394\) | 362.686 | + | 628.191i | 0.0463753 | + | 0.0803244i | ||||
\(395\) | −2930.08 | + | 5075.04i | −0.373236 | + | 0.646464i | ||||
\(396\) | −403.254 | + | 150.190i | −0.0511724 | + | 0.0190589i | ||||
\(397\) | 1052.09 | − | 607.424i | 0.133005 | − | 0.0767903i | −0.432021 | − | 0.901863i | \(-0.642199\pi\) |
0.565026 | + | 0.825073i | \(0.308866\pi\) | |||||||
\(398\) | 9424.76 | 1.18699 | ||||||||
\(399\) | −4400.05 | + | 543.029i | −0.552076 | + | 0.0681339i | ||||
\(400\) | −1993.35 | −0.249169 | ||||||||
\(401\) | 7615.66 | − | 4396.91i | 0.948399 | − | 0.547559i | 0.0558160 | − | 0.998441i | \(-0.482224\pi\) |
0.892583 | + | 0.450882i | \(0.148891\pi\) | |||||||
\(402\) | −7621.44 | − | 638.142i | −0.945579 | − | 0.0791731i | ||||
\(403\) | 1542.36 | − | 2671.44i | 0.190646 | − | 0.330208i | ||||
\(404\) | 4304.25 | + | 7455.19i | 0.530061 | + | 0.918093i | ||||
\(405\) | −686.454 | − | 3579.78i | −0.0842226 | − | 0.439211i | ||||
\(406\) | 8168.68 | − | 1709.76i | 0.998534 | − | 0.209000i | ||||
\(407\) | − | 1004.00i | − | 0.122276i | ||||||
\(408\) | 2261.35 | − | 3255.33i | 0.274396 | − | 0.395007i | ||||
\(409\) | 4831.45 | + | 2789.44i | 0.584107 | + | 0.337234i | 0.762764 | − | 0.646677i | \(-0.223842\pi\) |
−0.178657 | + | 0.983911i | \(0.557175\pi\) | |||||||
\(410\) | −5027.65 | − | 2902.71i | −0.605604 | − | 0.349646i | ||||
\(411\) | 3466.86 | − | 4990.73i | 0.416077 | − | 0.598965i | ||||
\(412\) | − | 7871.00i | − | 0.941205i | ||||||
\(413\) | −6803.63 | − | 7603.64i | −0.810617 | − | 0.905934i | ||||
\(414\) | 6997.01 | − | 8466.23i | 0.830639 | − | 1.00505i | ||||
\(415\) | −11.0774 | − | 19.1866i | −0.00131028 | − | 0.00226948i | ||||
\(416\) | −1333.82 | + | 2310.25i | −0.157202 | + | 0.272282i | ||||
\(417\) | −13461.5 | − | 1127.13i | −1.58084 | − | 0.132364i | ||||
\(418\) | 498.164 | − | 287.615i | 0.0582919 | − | 0.0336548i | ||||
\(419\) | 5449.56 | 0.635390 | 0.317695 | − | 0.948193i | \(-0.397091\pi\) | ||||
0.317695 | + | 0.948193i | \(0.397091\pi\) | |||||||
\(420\) | −2000.59 | − | 847.735i | −0.232425 | − | 0.0984886i | ||||
\(421\) | 2759.33 | 0.319433 | 0.159717 | − | 0.987163i | \(-0.448942\pi\) | ||||
0.159717 | + | 0.987163i | \(0.448942\pi\) | |||||||
\(422\) | −11901.3 | + | 6871.23i | −1.37286 | + | 0.792621i | ||||
\(423\) | 3670.79 | + | 9855.92i | 0.421938 | + | 1.13289i | ||||
\(424\) | 3664.30 | − | 6346.76i | 0.419703 | − | 0.726948i | ||||
\(425\) | 773.530 | + | 1339.79i | 0.0882864 | + | 0.152916i | ||||
\(426\) | −6651.10 | + | 3131.73i | −0.756449 | + | 0.356180i | ||||
\(427\) | −1803.56 | − | 8616.84i | −0.204404 | − | 0.976576i | ||||
\(428\) | 8105.86i | 0.915447i | ||||||||
\(429\) | 219.007 | + | 152.135i | 0.0246474 | + | 0.0171216i | ||||
\(430\) | −1659.82 | − | 958.295i | −0.186147 | − | 0.107472i | ||||
\(431\) | −3948.36 | − | 2279.59i | −0.441267 | − | 0.254766i | 0.262868 | − | 0.964832i | \(-0.415332\pi\) |
−0.704135 | + | 0.710066i | \(0.748665\pi\) | |||||||
\(432\) | 10772.1 | − | 3016.03i | 1.19971 | − | 0.335899i | ||||
\(433\) | − | 7442.63i | − | 0.826027i | −0.910725 | − | 0.413014i | \(-0.864476\pi\) | ||
0.910725 | − | 0.413014i | \(-0.135524\pi\) | |||||||
\(434\) | −4336.41 | + | 13206.1i | −0.479618 | + | 1.46063i | ||||
\(435\) | −1409.77 | − | 2994.04i | −0.155387 | − | 0.330007i | ||||
\(436\) | 1728.04 | + | 2993.05i | 0.189812 | + | 0.328764i | ||||
\(437\) | −2648.67 | + | 4587.64i | −0.289939 | + | 0.502189i | ||||
\(438\) | −238.200 | + | 2844.87i | −0.0259855 | + | 0.310349i | ||||
\(439\) | −5233.12 | + | 3021.35i | −0.568937 | + | 0.328476i | −0.756725 | − | 0.653734i | \(-0.773202\pi\) |
0.187788 | + | 0.982210i | \(0.439868\pi\) | |||||||
\(440\) | −217.533 | −0.0235693 | ||||||||
\(441\) | 6441.49 | + | 6653.82i | 0.695550 | + | 0.718478i | ||||
\(442\) | 3183.24 | 0.342560 | ||||||||
\(443\) | 3456.00 | − | 1995.32i | 0.370653 | − | 0.213997i | −0.303091 | − | 0.952962i | \(-0.598018\pi\) |
0.673744 | + | 0.738965i | \(0.264685\pi\) | |||||||
\(444\) | 556.918 | − | 6651.37i | 0.0595274 | − | 0.710946i | ||||
\(445\) | 2528.54 | − | 4379.56i | 0.269358 | − | 0.466542i | ||||
\(446\) | −997.254 | − | 1727.29i | −0.105877 | − | 0.183385i | ||||
\(447\) | 1112.99 | + | 2363.74i | 0.117768 | + | 0.250114i | ||||
\(448\) | 64.5774 | − | 196.665i | 0.00681026 | − | 0.0207400i | ||||
\(449\) | − | 897.052i | − | 0.0942862i | −0.998888 | − | 0.0471431i | \(-0.984988\pi\) | ||
0.998888 | − | 0.0471431i | \(-0.0150117\pi\) | |||||||
\(450\) | −397.106 | + | 2354.73i | −0.0415994 | + | 0.246673i | ||||
\(451\) | −1003.17 | − | 579.178i | −0.104739 | − | 0.0604710i | ||||
\(452\) | −555.349 | − | 320.631i | −0.0577908 | − | 0.0333655i | ||||
\(453\) | −10032.0 | − | 6968.81i | −1.04049 | − | 0.722789i | ||||
\(454\) | 3098.84i | 0.320343i | ||||||||
\(455\) | 275.846 | + | 1317.90i | 0.0284216 | + | 0.135789i | ||||
\(456\) | −2669.69 | + | 1257.05i | −0.274166 | + | 0.129093i | ||||
\(457\) | 1123.05 | + | 1945.18i | 0.114954 | + | 0.199106i | 0.917761 | − | 0.397132i | \(-0.129995\pi\) |
−0.802807 | + | 0.596239i | \(0.796661\pi\) | |||||||
\(458\) | −9023.73 | + | 15629.6i | −0.920636 | + | 1.59459i | ||||
\(459\) | −6207.34 | − | 6069.90i | −0.631228 | − | 0.617252i | ||||
\(460\) | −2248.36 | + | 1298.09i | −0.227892 | + | 0.131574i | ||||
\(461\) | 6503.45 | 0.657041 | 0.328520 | − | 0.944497i | \(-0.393450\pi\) | ||||
0.328520 | + | 0.944497i | \(0.393450\pi\) | |||||||
\(462\) | −1106.37 | − | 468.816i | −0.111413 | − | 0.0472106i | ||||
\(463\) | −12869.8 | −1.29181 | −0.645906 | − | 0.763417i | \(-0.723520\pi\) | ||||
−0.645906 | + | 0.763417i | \(0.723520\pi\) | |||||||
\(464\) | 8795.57 | − | 5078.13i | 0.880009 | − | 0.508073i | ||||
\(465\) | 5492.53 | + | 459.889i | 0.547764 | + | 0.0458641i | ||||
\(466\) | 10287.2 | − | 17817.9i | 1.02263 | − | 1.77124i | ||||
\(467\) | 14.4148 | + | 24.9672i | 0.00142835 | + | 0.00247397i | 0.866739 | − | 0.498763i | \(-0.166212\pi\) |
−0.865310 | + | 0.501236i | \(0.832879\pi\) | |||||||
\(468\) | 1366.51 | + | 1129.36i | 0.134972 | + | 0.111549i | ||||
\(469\) | −5138.05 | − | 5742.21i | −0.505870 | − | 0.565353i | ||||
\(470\) | − | 6890.28i | − | 0.676224i | ||||||
\(471\) | −8452.06 | + | 12167.2i | −0.826859 | + | 1.19031i | ||||
\(472\) | −5881.25 | − | 3395.54i | −0.573531 | − | 0.331128i | ||||
\(473\) | −331.183 | − | 191.208i | −0.0321941 | − | 0.0185873i | ||||
\(474\) | −12291.8 | + | 17694.7i | −1.19110 | + | 1.71465i | ||||
\(475\) | − | 1151.73i | − | 0.111253i | ||||||
\(476\) | −5065.49 | + | 1060.24i | −0.487766 | + | 0.102093i | ||||
\(477\) | −12373.3 | − | 10226.1i | −1.18771 | − | 0.981594i | ||||
\(478\) | 6698.36 | + | 11601.9i | 0.640954 | + | 1.11016i | ||||
\(479\) | 4994.02 | − | 8649.90i | 0.476373 | − | 0.825102i | −0.523260 | − | 0.852173i | \(-0.675285\pi\) |
0.999634 | + | 0.0270705i | \(0.00861785\pi\) | |||||||
\(480\) | −4749.92 | − | 397.710i | −0.451674 | − | 0.0378185i | ||||
\(481\) | −3582.08 | + | 2068.11i | −0.339561 | + | 0.196046i | ||||
\(482\) | −9184.05 | −0.867888 | ||||||||
\(483\) | 10982.3 | − | 1355.37i | 1.03460 | − | 0.127684i | ||||
\(484\) | −5954.05 | −0.559171 | ||||||||
\(485\) | −119.195 | + | 68.8172i | −0.0111595 | + | 0.00644294i | ||||
\(486\) | −1416.83 | − | 13325.8i | −0.132240 | − | 1.24377i | ||||
\(487\) | 2079.06 | − | 3601.04i | 0.193452 | − | 0.335069i | −0.752940 | − | 0.658089i | \(-0.771365\pi\) |
0.946392 | + | 0.323020i | \(0.104698\pi\) | |||||||
\(488\) | −2929.76 | − | 5074.50i | −0.271771 | − | 0.470721i | ||||
\(489\) | 10526.9 | − | 4956.69i | 0.973504 | − | 0.458383i | ||||
\(490\) | −2433.23 | − | 5557.94i | −0.224331 | − | 0.512412i | ||||
\(491\) | 4981.52i | 0.457867i | 0.973442 | + | 0.228934i | \(0.0735238\pi\) | ||||
−0.973442 | + | 0.228934i | \(0.926476\pi\) | |||||||
\(492\) | −6324.59 | − | 4393.45i | −0.579542 | − | 0.402585i | ||||
\(493\) | −6826.32 | − | 3941.18i | −0.623615 | − | 0.360044i | ||||
\(494\) | −2052.32 | − | 1184.91i | −0.186920 | − | 0.107918i | ||||
\(495\) | −79.2345 | + | 469.838i | −0.00719459 | + | 0.0426619i | ||||
\(496\) | 16915.4i | 1.53130i | ||||||||
\(497\) | −7036.90 | − | 2310.66i | −0.635107 | − | 0.208546i | ||||
\(498\) | −34.6986 | − | 73.6923i | −0.00312225 | − | 0.00663098i | ||||
\(499\) | 4098.39 | + | 7098.62i | 0.367674 | + | 0.636830i | 0.989201 | − | 0.146563i | \(-0.0468210\pi\) |
−0.621528 | + | 0.783392i | \(0.713488\pi\) | |||||||
\(500\) | 282.227 | − | 488.831i | 0.0252431 | − | 0.0437224i | ||||
\(501\) | −1070.60 | + | 12786.3i | −0.0954704 | + | 1.14022i | ||||
\(502\) | −13412.0 | + | 7743.41i | −1.19244 | + | 0.688457i | ||||
\(503\) | 2582.86 | 0.228954 | 0.114477 | − | 0.993426i | \(-0.463481\pi\) | ||||
0.114477 | + | 0.993426i | \(0.463481\pi\) | |||||||
\(504\) | 5455.02 | + | 2870.11i | 0.482115 | + | 0.253660i | ||||
\(505\) | 9531.91 | 0.839929 | ||||||||
\(506\) | −1243.39 | + | 717.873i | −0.109240 | + | 0.0630699i | ||||
\(507\) | −860.858 | + | 10281.4i | −0.0754084 | + | 0.900616i | ||||
\(508\) | −5173.06 | + | 8960.00i | −0.451806 | + | 0.782550i | ||||
\(509\) | 10831.6 | + | 18760.8i | 0.943224 | + | 1.63371i | 0.759269 | + | 0.650777i | \(0.225557\pi\) |
0.183955 | + | 0.982935i | \(0.441110\pi\) | |||||||
\(510\) | 2422.99 | + | 5145.90i | 0.210376 | + | 0.446793i | ||||
\(511\) | −2143.40 | + | 1917.89i | −0.185555 | + | 0.166032i | ||||
\(512\) | − | 6765.43i | − | 0.583970i | ||||||
\(513\) | 1742.62 | + | 6223.99i | 0.149978 | + | 0.535665i | ||||
\(514\) | −1735.59 | − | 1002.04i | −0.148937 | − | 0.0859886i | ||||
\(515\) | −7547.67 | − | 4357.65i | −0.645806 | − | 0.372856i | ||||
\(516\) | −2087.99 | − | 1450.44i | −0.178137 | − | 0.123745i | ||||
\(517\) | − | 1374.82i | − | 0.116952i | ||||||
\(518\) | 13889.5 | − | 12428.2i | 1.17813 | − | 1.05417i | ||||
\(519\) | −3508.08 | + | 1651.81i | −0.296701 | + | 0.139704i | ||||
\(520\) | 448.092 | + | 776.119i | 0.0377888 | + | 0.0654520i | ||||
\(521\) | −9770.62 | + | 16923.2i | −0.821610 | + | 1.42307i | 0.0828730 | + | 0.996560i | \(0.473590\pi\) |
−0.904483 | + | 0.426510i | \(0.859743\pi\) | |||||||
\(522\) | −4246.53 | − | 11401.8i | −0.356064 | − | 0.956018i | ||||
\(523\) | 13158.2 | − | 7596.91i | 1.10013 | − | 0.635162i | 0.163877 | − | 0.986481i | \(-0.447600\pi\) |
0.936256 | + | 0.351319i | \(0.114267\pi\) | |||||||
\(524\) | 2340.42 | 0.195118 | ||||||||
\(525\) | −1920.50 | + | 1449.07i | −0.159652 | + | 0.120462i | ||||
\(526\) | −4296.23 | −0.356130 | ||||||||
\(527\) | 11369.3 | − | 6564.09i | 0.939766 | − | 0.542574i | ||||
\(528\) | −1457.18 | − | 122.009i | −0.120105 | − | 0.0100564i | ||||
\(529\) | 527.456 | − | 913.580i | 0.0433513 | − | 0.0750867i | ||||
\(530\) | 5258.20 | + | 9107.46i | 0.430946 | + | 0.746421i | ||||
\(531\) | −9476.05 | + | 11465.8i | −0.774436 | + | 0.937051i | ||||
\(532\) | 3660.51 | + | 1201.98i | 0.298314 | + | 0.0979554i | ||||
\(533\) | 4772.15i | 0.387814i | ||||||||
\(534\) | 10607.3 | − | 15269.8i | 0.859596 | − | 1.23743i | ||||
\(535\) | 7772.87 | + | 4487.67i | 0.628132 | + | 0.362652i | ||||
\(536\) | −4441.48 | − | 2564.29i | −0.357915 | − | 0.206642i | ||||
\(537\) | 10108.3 | − | 14551.4i | 0.812301 | − | 1.16935i | ||||
\(538\) | 3212.99i | 0.257475i | ||||||||
\(539\) | −485.501 | − | 1108.97i | −0.0387978 | − | 0.0886214i | ||||
\(540\) | −785.539 | + | 3068.68i | −0.0626004 | + | 0.244546i | ||||
\(541\) | 7087.52 | + | 12276.0i | 0.563247 | + | 0.975572i | 0.997210 | + | 0.0746416i | \(0.0237813\pi\) |
−0.433964 | + | 0.900930i | \(0.642885\pi\) | |||||||
\(542\) | 7677.50 | − | 13297.8i | 0.608444 | − | 1.05386i | ||||
\(543\) | −15211.0 | − | 1273.62i | −1.20215 | − | 0.100656i | ||||
\(544\) | −9832.17 | + | 5676.61i | −0.774910 | + | 0.447394i | ||||
\(545\) | 3826.80 | 0.300775 | ||||||||
\(546\) | 606.337 | + | 4913.03i | 0.0475253 | + | 0.385088i | ||||
\(547\) | −3915.65 | −0.306072 | −0.153036 | − | 0.988221i | \(-0.548905\pi\) | ||||
−0.153036 | + | 0.988221i | \(0.548905\pi\) | |||||||
\(548\) | −4573.37 | + | 2640.43i | −0.356505 | + | 0.205828i | ||||
\(549\) | −12027.3 | + | 4479.50i | −0.934995 | + | 0.348234i | ||||
\(550\) | 156.078 | − | 270.334i | 0.0121003 | − | 0.0209584i | ||||
\(551\) | 2934.07 | + | 5081.96i | 0.226852 | + | 0.392920i | ||||
\(552\) | 6663.41 | − | 3137.52i | 0.513792 | − | 0.241923i | ||||
\(553\) | −21245.9 | + | 4446.92i | −1.63376 | + | 0.341957i | ||||
\(554\) | − | 22599.5i | − | 1.73314i | ||||||
\(555\) | −6069.80 | − | 4216.46i | −0.464232 | − | 0.322484i | ||||
\(556\) | 10166.6 | + | 5869.71i | 0.775470 | + | 0.447718i | ||||
\(557\) | 9426.69 | + | 5442.50i | 0.717094 | + | 0.414015i | 0.813682 | − | 0.581310i | \(-0.197460\pi\) |
−0.0965880 | + | 0.995324i | \(0.530793\pi\) | |||||||
\(558\) | 19982.0 | + | 3369.80i | 1.51596 | + | 0.255654i | ||||
\(559\) | 1575.47i | 0.119204i | ||||||||
\(560\) | −4923.42 | − | 5502.34i | −0.371522 | − | 0.415208i | ||||
\(561\) | 483.459 | + | 1026.76i | 0.0363844 | + | 0.0772725i | ||||
\(562\) | 5917.61 | + | 10249.6i | 0.444162 | + | 0.769311i | ||||
\(563\) | −1235.82 | + | 2140.51i | −0.0925111 | + | 0.160234i | −0.908567 | − | 0.417739i | \(-0.862823\pi\) |
0.816056 | + | 0.577973i | \(0.196156\pi\) | |||||||
\(564\) | 762.613 | − | 9108.02i | 0.0569358 | − | 0.679994i | ||||
\(565\) | −614.919 | + | 355.024i | −0.0457873 | + | 0.0264353i | ||||
\(566\) | −3878.00 | −0.287994 | ||||||||
\(567\) | 8185.94 | − | 10736.6i | 0.606309 | − | 0.795229i | ||||
\(568\) | −4929.70 | −0.364165 | ||||||||
\(569\) | 5773.89 | − | 3333.56i | 0.425403 | − | 0.245606i | −0.271984 | − | 0.962302i | \(-0.587680\pi\) |
0.697386 | + | 0.716696i | \(0.254346\pi\) | |||||||
\(570\) | 353.307 | − | 4219.61i | 0.0259621 | − | 0.310070i | ||||
\(571\) | 1897.30 | − | 3286.22i | 0.139053 | − | 0.240848i | −0.788085 | − | 0.615566i | \(-0.788927\pi\) |
0.927139 | + | 0.374719i | \(0.122261\pi\) | |||||||
\(572\) | −115.869 | − | 200.692i | −0.00846983 | − | 0.0146702i | ||||
\(573\) | 236.841 | + | 502.999i | 0.0172673 | + | 0.0366720i | ||||
\(574\) | −4405.39 | − | 21047.5i | −0.320344 | − | 1.53050i | ||||
\(575\) | 2874.66i | 0.208490i | ||||||||
\(576\) | −297.570 | − | 50.1827i | −0.0215256 | − | 0.00363012i | ||||
\(577\) | −20022.1 | − | 11559.8i | −1.44459 | − | 0.834037i | −0.446443 | − | 0.894812i | \(-0.647309\pi\) |
−0.998151 | + | 0.0607751i | \(0.980643\pi\) | |||||||
\(578\) | −3319.81 | − | 1916.70i | −0.238903 | − | 0.137931i | ||||
\(579\) | 9313.05 | + | 6469.41i | 0.668458 | + | 0.464351i | ||||
\(580\) | 2875.92i | 0.205890i | ||||||||
\(581\) | 25.6014 | − | 77.9667i | 0.00182810 | − | 0.00556731i | ||||
\(582\) | −457.806 | + | 215.562i | −0.0326060 | + | 0.0153528i | ||||
\(583\) | 1049.17 | + | 1817.21i | 0.0745318 | + | 0.129093i | ||||
\(584\) | −957.175 | + | 1657.88i | −0.0678223 | + | 0.117472i | ||||
\(585\) | 1839.51 | − | 685.117i | 0.130008 | − | 0.0484207i | ||||
\(586\) | 13328.3 | − | 7695.08i | 0.939567 | − | 0.542459i | ||||
\(587\) | −16772.1 | −1.17932 | −0.589659 | − | 0.807653i | \(-0.700738\pi\) | ||||
−0.589659 | + | 0.807653i | \(0.700738\pi\) | |||||||
\(588\) | −2601.24 | − | 7616.14i | −0.182438 | − | 0.534157i | ||||
\(589\) | −9773.48 | −0.683717 | ||||||||
\(590\) | 8439.47 | − | 4872.53i | 0.588894 | − | 0.339998i | ||||
\(591\) | 1061.69 | + | 88.8955i | 0.0738956 | + | 0.00618726i | ||||
\(592\) | 11340.8 | − | 19642.8i | 0.787335 | − | 1.36370i | ||||
\(593\) | −2564.12 | − | 4441.19i | −0.177565 | − | 0.307551i | 0.763481 | − | 0.645830i | \(-0.223489\pi\) |
−0.941046 | + | 0.338279i | \(0.890155\pi\) | |||||||
\(594\) | −434.421 | + | 1697.05i | −0.0300076 | + | 0.117223i | ||||
\(595\) | −1787.74 | + | 5444.39i | −0.123177 | + | 0.375123i | ||||
\(596\) | − | 2270.49i | − | 0.156045i | ||||||
\(597\) | 7897.57 | − | 11369.0i | 0.541417 | − | 0.779398i | ||||
\(598\) | 5122.49 | + | 2957.47i | 0.350291 | + | 0.202241i | ||||
\(599\) | −18075.2 | − | 10435.7i | −1.23294 | − | 0.711839i | −0.265300 | − | 0.964166i | \(-0.585471\pi\) |
−0.967642 | + | 0.252327i | \(0.918804\pi\) | |||||||
\(600\) | −913.567 | + | 1315.13i | −0.0621604 | + | 0.0894830i | ||||
\(601\) | 5784.11i | 0.392577i | 0.980546 | + | 0.196288i | \(0.0628889\pi\) | ||||
−0.980546 | + | 0.196288i | \(0.937111\pi\) | |||||||
\(602\) | −1454.38 | − | 6948.57i | −0.0984655 | − | 0.470436i | ||||
\(603\) | −7156.24 | + | 8658.90i | −0.483291 | + | 0.584772i | ||||
\(604\) | 5307.59 | + | 9193.01i | 0.357554 | + | 0.619302i | ||||
\(605\) | −3296.36 | + | 5709.46i | −0.221514 | + | 0.383674i | ||||
\(606\) | 34922.1 | + | 2924.03i | 2.34095 | + | 0.196007i | ||||
\(607\) | −16931.6 | + | 9775.46i | −1.13218 | + | 0.653664i | −0.944482 | − | 0.328563i | \(-0.893436\pi\) |
−0.187697 | + | 0.982227i | \(0.560102\pi\) | |||||||
\(608\) | 8452.07 | 0.563778 | ||||||||
\(609\) | 4782.57 | − | 11286.5i | 0.318226 | − | 0.750987i | ||||
\(610\) | 8408.29 | 0.558101 | ||||||||
\(611\) | −4905.10 | + | 2831.96i | −0.324778 | + | 0.187511i | ||||
\(612\) | 2633.32 | + | 7070.36i | 0.173931 | + | 0.466997i | ||||
\(613\) | −1564.33 | + | 2709.50i | −0.103071 | + | 0.178525i | −0.912949 | − | 0.408075i | \(-0.866200\pi\) |
0.809877 | + | 0.586599i | \(0.199534\pi\) | |||||||
\(614\) | 10172.5 | + | 17619.3i | 0.668615 | + | 1.15808i | ||||
\(615\) | −7714.47 | + | 3632.42i | −0.505817 | + | 0.238168i | ||||
\(616\) | −537.289 | − | 600.466i | −0.0351428 | − | 0.0392751i | ||||
\(617\) | 19251.3i | 1.25613i | 0.778163 | + | 0.628063i | \(0.216152\pi\) | ||||
−0.778163 | + | 0.628063i | \(0.783848\pi\) | |||||||
\(618\) | −26315.7 | − | 18280.5i | −1.71290 | − | 1.18989i | ||||
\(619\) | 22828.6 | + | 13180.1i | 1.48232 | + | 0.855820i | 0.999799 | − | 0.0200617i | \(-0.00638628\pi\) |
0.482525 | + | 0.875882i | \(0.339720\pi\) | |||||||
\(620\) | −4148.17 | − | 2394.95i | −0.268701 | − | 0.155134i | ||||
\(621\) | −4349.48 | − | 15534.8i | −0.281061 | − | 1.00385i | ||||
\(622\) | 19463.7i | 1.25470i | ||||||||
\(623\) | 18334.4 | − | 3837.51i | 1.17906 | − | 0.246785i | ||||
\(624\) | 2566.31 | + | 5450.28i | 0.164639 | + | 0.349657i | ||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −1274.21 | + | 2206.99i | −0.0813538 | + | 0.140909i | ||||
\(627\) | 70.4954 | − | 841.939i | 0.00449013 | − | 0.0536265i | ||||
\(628\) | 11149.7 | − | 6437.26i | 0.708472 | − | 0.409036i | ||||
\(629\) | −17603.3 | −1.11588 | ||||||||
\(630\) | −7480.68 | + | 4719.83i | −0.473075 | + | 0.298480i | ||||
\(631\) | 18010.0 | 1.13624 | 0.568118 | − | 0.822947i | \(-0.307672\pi\) | ||||
0.568118 | + | 0.822947i | \(0.307672\pi\) | |||||||
\(632\) | −12511.8 | + | 7223.71i | −0.787490 | + | 0.454658i | ||||
\(633\) | −1684.16 | + | 20114.2i | −0.105749 | + | 1.26298i | ||||
\(634\) | 217.904 | − | 377.422i | 0.0136500 | − | 0.0236425i | ||||
\(635\) | 5727.95 | + | 9921.10i | 0.357963 | + | 0.620011i | ||||
\(636\) | 5942.61 | + | 12620.8i | 0.370503 | + | 0.786867i | ||||
\(637\) | −2956.55 | + | 4016.54i | −0.183897 | + | 0.249829i | ||||
\(638\) | 1590.45i | 0.0986935i | ||||||||
\(639\) | −1795.60 | + | 10647.4i | −0.111162 | + | 0.659162i | ||||
\(640\) | −6184.18 | − | 3570.44i | −0.381955 | − | 0.220522i | ||||
\(641\) | −14086.0 | − | 8132.54i | −0.867961 | − | 0.501117i | −0.00129064 | − | 0.999999i | \(-0.500411\pi\) |
−0.866670 | + | 0.498882i | \(0.833744\pi\) | |||||||
\(642\) | 27100.9 | + | 18825.9i | 1.66602 | + | 1.15732i | ||||
\(643\) | − | 3133.59i | − | 0.192188i | −0.995372 | − | 0.0960939i | \(-0.969365\pi\) | ||
0.995372 | − | 0.0960939i | \(-0.0306349\pi\) | |||||||
\(644\) | −9136.44 | − | 3000.07i | −0.559047 | − | 0.183570i | ||||
\(645\) | −2546.84 | + | 1199.20i | −0.155475 | + | 0.0732069i | ||||
\(646\) | −5042.84 | − | 8734.45i | −0.307133 | − | 0.531970i | ||||
\(647\) | −150.407 | + | 260.513i | −0.00913928 | + | 0.0158297i | −0.870559 | − | 0.492064i | \(-0.836242\pi\) |
0.861420 | + | 0.507894i | \(0.169576\pi\) | |||||||
\(648\) | 2947.10 | − | 8489.24i | 0.178662 | − | 0.514644i | ||||
\(649\) | 1683.93 | − | 972.215i | 0.101849 | − | 0.0588025i | ||||
\(650\) | −1286.01 | −0.0776020 | ||||||||
\(651\) | 12296.7 | + | 16297.2i | 0.740313 | + | 0.981162i | ||||
\(652\) | −10111.6 | −0.607365 | ||||||||
\(653\) | 4968.97 | − | 2868.83i | 0.297780 | − | 0.171924i | −0.343665 | − | 0.939092i | \(-0.611668\pi\) |
0.641445 | + | 0.767169i | \(0.278335\pi\) | |||||||
\(654\) | 14020.3 | + | 1173.92i | 0.838282 | + | 0.0701892i | ||||
\(655\) | 1295.73 | − | 2244.27i | 0.0772954 | − | 0.133879i | ||||
\(656\) | −13084.3 | − | 22662.8i | −0.778747 | − | 1.34883i | ||||
\(657\) | 3232.12 | + | 2671.22i | 0.191928 | + | 0.158621i | ||||
\(658\) | 19019.6 | − | 17018.4i | 1.12684 | − | 1.00828i | ||||
\(659\) | − | 12643.0i | − | 0.747346i | −0.927561 | − | 0.373673i | \(-0.878098\pi\) | ||
0.927561 | − | 0.373673i | \(-0.121902\pi\) | |||||||
\(660\) | 236.234 | − | 340.070i | 0.0139324 | − | 0.0200564i | ||||
\(661\) | −13547.8 | − | 7821.85i | −0.797201 | − | 0.460264i | 0.0452905 | − | 0.998974i | \(-0.485579\pi\) |
−0.842491 | + | 0.538710i | \(0.818912\pi\) | |||||||
\(662\) | 29510.7 | + | 17038.0i | 1.73257 | + | 1.00030i | ||||
\(663\) | 2667.43 | − | 3839.90i | 0.156251 | − | 0.224931i | ||||
\(664\) | − | 54.6196i | − | 0.00319224i | ||||||
\(665\) | 3179.18 | − | 2844.68i | 0.185388 | − | 0.165883i | ||||
\(666\) | −20944.6 | − | 17309.9i | −1.21860 | − | 1.00712i | ||||
\(667\) | −7323.29 | − | 12684.3i | −0.425126 | − | 0.736340i | ||||
\(668\) | 5575.30 | − | 9656.71i | 0.322927 | − | 0.559325i | ||||
\(669\) | −2919.27 | − | 244.430i | −0.168708 | − | 0.0141259i | ||||
\(670\) | 6373.42 | − | 3679.70i | 0.367503 | − | 0.212178i | ||||
\(671\) | 1677.71 | 0.0965233 | ||||||||
\(672\) | −10634.1 | − | 14093.7i | −0.610445 | − | 0.809044i | ||||
\(673\) | −11596.1 | −0.664188 | −0.332094 | − | 0.943246i | \(-0.607755\pi\) | ||||
−0.332094 | + | 0.943246i | \(0.607755\pi\) | |||||||
\(674\) | −15250.7 | + | 8805.00i | −0.871566 | + | 0.503199i | ||||
\(675\) | 2507.72 | + | 2452.19i | 0.142996 | + | 0.139829i | ||||
\(676\) | 4483.06 | − | 7764.89i | 0.255067 | − | 0.441789i | ||||
\(677\) | −16444.2 | − | 28482.1i | −0.933532 | − | 1.61692i | −0.777231 | − | 0.629215i | \(-0.783377\pi\) |
−0.156300 | − | 0.987710i | \(-0.549957\pi\) | |||||||
\(678\) | −2361.79 | + | 1112.07i | −0.133782 | + | 0.0629924i | ||||
\(679\) | −484.361 | − | 159.046i | −0.0273756 | − | 0.00898915i | ||||
\(680\) | 3814.06i | 0.215092i | ||||||||
\(681\) | 3738.09 | + | 2596.71i | 0.210344 | + | 0.146117i | ||||
\(682\) | −2294.03 | − | 1324.46i | −0.128802 | − | 0.0743638i | ||||
\(683\) | 17140.8 | + | 9896.23i | 0.960283 | + | 0.554420i | 0.896260 | − | 0.443529i | \(-0.146274\pi\) |
0.0640229 | + | 0.997948i | \(0.479607\pi\) | |||||||
\(684\) | 934.048 | − | 5538.65i | 0.0522138 | − | 0.309613i | ||||
\(685\) | 5847.32i | 0.326153i | ||||||||
\(686\) | 9331.96 | − | 20444.2i | 0.519382 | − | 1.13785i | ||||
\(687\) | 11292.2 | + | 23982.1i | 0.627109 | + | 1.33184i | ||||
\(688\) | −4319.64 | − | 7481.83i | −0.239367 | − | 0.414596i | ||||
\(689\) | 4322.32 | − | 7486.48i | 0.238995 | − | 0.413951i | ||||
\(690\) | −881.837 | + | 10531.9i | −0.0486536 | + | 0.581078i | ||||
\(691\) | 19063.9 | − | 11006.5i | 1.04953 | − | 0.605945i | 0.127010 | − | 0.991901i | \(-0.459462\pi\) |
0.922517 | + | 0.385956i | \(0.126128\pi\) | |||||||
\(692\) | 3369.69 | 0.185110 | ||||||||
\(693\) | −1492.62 | + | 941.748i | −0.0818180 | + | 0.0516220i | ||||
\(694\) | −24405.1 | −1.33488 | ||||||||
\(695\) | 11257.2 | − | 6499.33i | 0.614401 | − | 0.354725i | ||||
\(696\) | 680.746 | − | 8130.27i | 0.0370741 | − | 0.442783i | ||||
\(697\) | −10154.9 | + | 17588.8i | −0.551856 | + | 0.955843i | ||||
\(698\) | −9098.70 | − | 15759.4i | −0.493397 | − | 0.854588i | ||||
\(699\) | −12873.3 | − | 27340.0i | −0.696583 | − | 1.47939i | ||||
\(700\) | 2046.42 | − | 428.329i | 0.110496 | − | 0.0231276i | ||||
\(701\) | − | 10015.2i | − | 0.539612i | −0.962915 | − | 0.269806i | \(-0.913040\pi\) | ||
0.962915 | − | 0.269806i | \(-0.0869596\pi\) | |||||||
\(702\) | 6949.61 | − | 1945.78i | 0.373641 | − | 0.104614i | ||||
\(703\) | 11349.3 | + | 6552.54i | 0.608888 | + | 0.351541i | ||||
\(704\) | 34.1625 | + | 19.7237i | 0.00182890 | + | 0.00105592i | ||||
\(705\) | −8311.65 | − | 5773.78i | −0.444021 | − | 0.308444i | ||||
\(706\) | − | 20543.5i | − | 1.09514i | ||||||
\(707\) | 23543.0 | + | 26311.4i | 1.25237 | + | 1.39963i | ||||
\(708\) | 11695.1 | − | 5506.75i | 0.620804 | − | 0.292311i | ||||
\(709\) | 8975.91 | + | 15546.7i | 0.475455 | + | 0.823511i | 0.999605 | − | 0.0281144i | \(-0.00895028\pi\) |
−0.524150 | + | 0.851626i | \(0.675617\pi\) | |||||||
\(710\) | 3537.00 | − | 6126.27i | 0.186960 | − | 0.323824i | ||||
\(711\) | 11044.8 | + | 29654.8i | 0.582577 | + | 1.56420i | ||||
\(712\) | 10797.2 | − | 6233.78i | 0.568319 | − | 0.328119i | ||||
\(713\) | 24394.1 | 1.28130 | ||||||||
\(714\) | −8219.88 | + | 19398.3i | −0.430842 | + | 1.01675i | ||||
\(715\) | −256.597 | −0.0134212 | ||||||||
\(716\) | −13334.5 | + | 7698.69i | −0.695998 | + | 0.401835i | ||||
\(717\) | 19608.2 | + | 1641.79i | 1.02131 | + | 0.0855143i | ||||
\(718\) | −13280.1 | + | 23001.8i | −0.690262 | + | 1.19557i | ||||
\(719\) | −8242.13 | − | 14275.8i | −0.427510 | − | 0.740468i | 0.569142 | − | 0.822240i | \(-0.307276\pi\) |
−0.996651 | + | 0.0817712i | \(0.973942\pi\) | |||||||
\(720\) | −6857.30 | + | 8297.19i | −0.354940 | + | 0.429470i | ||||
\(721\) | −6613.51 | − | 31597.2i | −0.341609 | − | 1.63210i | ||||
\(722\) | − | 16756.9i | − | 0.863752i | ||||||
\(723\) | −7695.87 | + | 11078.6i | −0.395868 | + | 0.569872i | ||||
\(724\) | 11487.9 | + | 6632.57i | 0.589704 | + | 0.340466i | ||||
\(725\) | 2757.78 | + | 1592.21i | 0.141271 | + | 0.0815628i | ||||
\(726\) | −13828.3 | + | 19906.6i | −0.706912 | + | 1.01764i | ||||
\(727\) | 36315.4i | 1.85263i | 0.376744 | + | 0.926317i | \(0.377044\pi\) | ||||
−0.376744 | + | 0.926317i | \(0.622956\pi\) | |||||||
\(728\) | −1035.60 | + | 3153.84i | −0.0527226 | + | 0.160562i | ||||
\(729\) | −17262.0 | − | 9457.42i | −0.877002 | − | 0.480487i | ||||
\(730\) | −1373.53 | − | 2379.02i | −0.0696390 | − | 0.120618i | ||||
\(731\) | −3352.51 | + | 5806.72i | −0.169627 | + | 0.293802i | ||||
\(732\) | 11114.6 | + | 930.625i | 0.561213 | + | 0.0469903i | ||||
\(733\) | 19183.5 | − | 11075.6i | 0.966657 | − | 0.558100i | 0.0684416 | − | 0.997655i | \(-0.478197\pi\) |
0.898215 | + | 0.439555i | \(0.144864\pi\) | |||||||
\(734\) | −34714.3 | −1.74568 | ||||||||
\(735\) | −8743.41 | − | 1722.16i | −0.438783 | − | 0.0864258i | ||||
\(736\) | −21095.9 | −1.05653 | ||||||||
\(737\) | 1271.69 | − | 734.209i | 0.0635593 | − | 0.0366960i | ||||
\(738\) | −29377.9 | + | 10941.6i | −1.46533 | + | 0.545755i | ||||
\(739\) | −3079.43 | + | 5333.73i | −0.153287 | + | 0.265500i | −0.932434 | − | 0.361341i | \(-0.882319\pi\) |
0.779147 | + | 0.626841i | \(0.215652\pi\) | |||||||
\(740\) | 3211.34 | + | 5562.20i | 0.159529 | + | 0.276312i | ||||
\(741\) | −3149.10 | + | 1482.78i | −0.156120 | + | 0.0735105i | ||||
\(742\) | −12152.4 | + | 37009.1i | −0.601253 | + | 1.83106i | ||||
\(743\) | − | 31402.5i | − | 1.55053i | −0.631634 | − | 0.775267i | \(-0.717615\pi\) | ||
0.631634 | − | 0.775267i | \(-0.282385\pi\) | |||||||
\(744\) | 11160.0 | + | 7752.44i | 0.549928 | + | 0.382014i | ||||
\(745\) | −2177.22 | − | 1257.02i | −0.107070 | − | 0.0618169i | ||||
\(746\) | 14098.9 | + | 8140.03i | 0.691956 | + | 0.399501i | ||||
\(747\) | −117.970 | − | 19.8947i | −0.00577818 | − | 0.000974443i | ||||
\(748\) | − | 986.255i | − | 0.0482100i | ||||||
\(749\) | 6810.84 | + | 32540.0i | 0.332260 | + | 1.58743i | ||||
\(750\) | −978.870 | − | 2078.90i | −0.0476577 | − | 0.101214i | ||||
\(751\) | −13149.1 | − | 22774.9i | −0.638903 | − | 1.10661i | −0.985674 | − | 0.168663i | \(-0.946055\pi\) |
0.346771 | − | 0.937950i | \(-0.387278\pi\) | |||||||
\(752\) | 15529.4 | − | 26897.7i | 0.753058 | − | 1.30433i | ||||
\(753\) | −1897.93 | + | 22667.4i | −0.0918520 | + | 1.09700i | ||||
\(754\) | 5674.44 | − | 3276.14i | 0.274073 | − | 0.158236i | ||||
\(755\) | 11753.8 | 0.566577 | ||||||||
\(756\) | −10410.8 | + | 5411.02i | −0.500844 | + | 0.260313i | ||||
\(757\) | 40494.0 | 1.94422 | 0.972112 | − | 0.234517i | \(-0.0753507\pi\) | ||||
0.972112 | + | 0.234517i | \(0.0753507\pi\) | |||||||
\(758\) | −31635.4 | + | 18264.7i | −1.51590 | + | 0.875204i | ||||
\(759\) | −175.953 | + | 2101.44i | −0.00841460 | + | 0.100497i | ||||
\(760\) | 1419.72 | − | 2459.03i | 0.0677613 | − | 0.117366i | ||||
\(761\) | 6077.17 | + | 10526.0i | 0.289484 | + | 0.501401i | 0.973687 | − | 0.227891i | \(-0.0731829\pi\) |
−0.684203 | + | 0.729292i | \(0.739850\pi\) | |||||||
\(762\) | 17942.1 | + | 38105.2i | 0.852985 | + | 1.81155i | ||||
\(763\) | 9451.88 | + | 10563.3i | 0.448468 | + | 0.501202i | ||||
\(764\) | − | 483.156i | − | 0.0228795i | ||||||
\(765\) | 8237.80 | + | 1389.24i | 0.389331 | + | 0.0656576i | ||||
\(766\) | 9899.84 | + | 5715.68i | 0.466966 | + | 0.269603i | ||||
\(767\) | −6937.38 | − | 4005.30i | −0.326590 | − | 0.188557i | ||||
\(768\) | −21943.3 | − | 15243.2i | −1.03101 | − | 0.716199i | ||||
\(769\) | − | 4997.38i | − | 0.234344i | −0.993112 | − | 0.117172i | \(-0.962617\pi\) | ||
0.993112 | − | 0.117172i | \(-0.0373828\pi\) | |||||||
\(770\) | 1131.71 | − | 236.876i | 0.0529665 | − | 0.0110862i | ||||
\(771\) | −2663.10 | + | 1253.94i | −0.124396 | + | 0.0585729i | ||||
\(772\) | −4927.23 | − | 8534.22i | −0.229709 | − | 0.397867i | ||||
\(773\) | 8420.67 | − | 14585.0i | 0.391812 | − | 0.678638i | −0.600877 | − | 0.799342i | \(-0.705182\pi\) |
0.992689 | + | 0.120704i | \(0.0385151\pi\) | |||||||
\(774\) | −9698.74 | + | 3612.25i | −0.450406 | + | 0.167751i | ||||
\(775\) | −4593.13 | + | 2651.84i | −0.212890 | + | 0.122912i | ||||
\(776\) | −339.319 | −0.0156969 | ||||||||
\(777\) | −3353.04 | − | 27169.1i | −0.154813 | − | 1.25442i | ||||
\(778\) | −44451.4 | −2.04841 | ||||||||
\(779\) | 13094.2 | − | 7559.96i | 0.602246 | − | 0.347707i | ||||
\(780\) | −1699.92 | − | 142.334i | −0.0780347 | − | 0.00653383i | ||||
\(781\) | 705.738 | − | 1222.37i | 0.0323346 | − | 0.0560051i | ||||
\(782\) | 12586.7 | + | 21800.7i | 0.575573 | + | 0.996922i | ||||
\(783\) | −17312.2 | − | 4431.69i | −0.790150 | − | 0.202268i | ||||
\(784\) | 3027.93 | − | 27180.7i | 0.137934 | − | 1.23819i | ||||
\(785\) | − | 14255.5i | − | 0.648155i | ||||||
\(786\) | 5435.65 | − | 7824.89i | 0.246671 | − | 0.355095i | ||||
\(787\) | 10016.9 | + | 5783.24i | 0.453701 | + | 0.261944i | 0.709392 | − | 0.704814i | \(-0.248970\pi\) |
−0.255691 | + | 0.966759i | \(0.582303\pi\) | |||||||
\(788\) | −801.832 | − | 462.938i | −0.0362488 | − | 0.0209283i | ||||
\(789\) | −3600.07 | + | 5182.48i | −0.162441 | + | 0.233842i | ||||
\(790\) | − | 20731.7i | − | 0.933673i | ||||||
\(791\) | −2498.79 | − | 820.510i | −0.112322 | − | 0.0368824i | ||||
\(792\) | −748.332 | + | 905.466i | −0.0335743 | + | 0.0406241i | ||||
\(793\) | −3455.88 | − | 5985.75i | −0.154756 | − | 0.268046i | ||||
\(794\) | −2148.91 | + | 3722.02i | −0.0960478 | + | 0.166360i | ||||
\(795\) | 15392.4 | + | 1288.80i | 0.686680 | + | 0.0574956i | ||||
\(796\) | −10418.2 | + | 6014.95i | −0.463899 | + | 0.267832i | ||||
\(797\) | −34942.8 | −1.55300 | −0.776498 | − | 0.630120i | \(-0.783006\pi\) | ||||
−0.776498 | + | 0.630120i | \(0.783006\pi\) | |||||||
\(798\) | 12520.2 | − | 9446.85i | 0.555403 | − | 0.419066i | ||||
\(799\) | −24105.0 | −1.06730 | ||||||||
\(800\) | 3972.12 | − | 2293.30i | 0.175545 | − | 0.101351i | ||||
\(801\) | −9531.22 | − | 25591.0i | −0.420436 | − | 1.12885i | ||||
\(802\) | −15555.1 | + | 26942.3i | −0.684876 | + | 1.18624i | ||||
\(803\) | −274.059 | − | 474.685i | −0.0120440 | − | 0.0208609i | ||||
\(804\) | 8832.06 | − | 4158.65i | 0.387416 | − | 0.182418i | ||||
\(805\) | −7935.07 | + | 7100.18i | −0.347422 | + | 0.310868i | ||||
\(806\) | 10912.9i | 0.476912i | ||||||||
\(807\) | 3875.78 | + | 2692.35i | 0.169063 | + | 0.117442i | ||||
\(808\) | 20351.3 | + | 11749.8i | 0.886083 | + | 0.511580i | ||||
\(809\) | −24287.6 | − | 14022.5i | −1.05551 | − | 0.609398i | −0.131322 | − | 0.991340i | \(-0.541922\pi\) |
−0.924186 | + | 0.381942i | \(0.875256\pi\) | |||||||
\(810\) | 8435.31 | + | 9753.39i | 0.365909 | + | 0.423085i | ||||
\(811\) | 2288.12i | 0.0990714i | 0.998772 | + | 0.0495357i | \(0.0157742\pi\) | ||||
−0.998772 | + | 0.0495357i | \(0.984226\pi\) | |||||||
\(812\) | −7938.54 | + | 7103.29i | −0.343089 | + | 0.306991i | ||||
\(813\) | −9607.53 | − | 20404.3i | −0.414454 | − | 0.880209i | ||||
\(814\) | 1775.94 | + | 3076.02i | 0.0764701 | + | 0.132450i | ||||
\(815\) | −5598.13 | + | 9696.24i | −0.240606 | + | 0.416742i | ||||
\(816\) | −2139.22 | + | 25549.1i | −0.0917743 | + | 1.09608i | ||||
\(817\) | 4322.90 | − | 2495.83i | 0.185115 | − | 0.106876i | ||||
\(818\) | −19736.6 | −0.843612 | ||||||||
\(819\) | 6434.61 | + | 3385.51i | 0.274534 | + | 0.144443i | ||||
\(820\) | 7410.13 | 0.315577 | ||||||||
\(821\) | −24342.8 | + | 14054.3i | −1.03480 | + | 0.597441i | −0.918355 | − | 0.395757i | \(-0.870482\pi\) |
−0.116442 | + | 0.993197i | \(0.537149\pi\) | |||||||
\(822\) | −1793.74 | + | 21422.9i | −0.0761116 | + | 0.909014i | ||||
\(823\) | 14845.0 | − | 25712.2i | 0.628752 | − | 1.08903i | −0.359051 | − | 0.933318i | \(-0.616899\pi\) |
0.987802 | − | 0.155712i | \(-0.0497672\pi\) | |||||||
\(824\) | −10743.2 | − | 18607.7i | −0.454195 | − | 0.786689i | ||||
\(825\) | −195.314 | − | 414.804i | −0.00824237 | − | 0.0175050i | ||||
\(826\) | 34294.7 | + | 11261.1i | 1.44463 | + | 0.474363i | ||||
\(827\) | 35131.6i | 1.47720i | 0.674142 | + | 0.738601i | \(0.264513\pi\) | ||||
−0.674142 | + | 0.738601i | \(0.735487\pi\) | |||||||
\(828\) | −2331.34 | + | 13824.2i | −0.0978497 | + | 0.580222i | ||||
\(829\) | −30051.2 | − | 17350.1i | −1.25901 | − | 0.726891i | −0.286130 | − | 0.958191i | \(-0.592369\pi\) |
−0.972883 | + | 0.231300i | \(0.925702\pi\) | |||||||
\(830\) | 67.8773 | + | 39.1890i | 0.00283862 | + | 0.00163888i | ||||
\(831\) | −27261.4 | − | 18937.5i | −1.13801 | − | 0.790533i | ||||
\(832\) | − | 162.514i | − | 0.00677183i | ||||||
\(833\) | −19444.0 | + | 8512.42i | −0.808755 | + | 0.354067i | ||||
\(834\) | 43236.7 | − | 20358.4i | 1.79516 | − | 0.845268i | ||||
\(835\) | −6173.34 | − | 10692.5i | −0.255853 | − | 0.443150i | ||||
\(836\) | −367.116 | + | 635.864i | −0.0151878 | + | 0.0263060i | ||||
\(837\) | 20809.0 | − | 21280.2i | 0.859337 | − | 0.878796i | ||||
\(838\) | −16696.2 | + | 9639.57i | −0.688260 | + | 0.397367i | ||||
\(839\) | 9268.60 | 0.381392 | 0.190696 | − | 0.981649i | \(-0.438926\pi\) | ||||
0.190696 | + | 0.981649i | \(0.438926\pi\) | |||||||
\(840\) | −5886.64 | + | 726.494i | −0.241796 | + | 0.0298410i | ||||
\(841\) | 8164.24 | 0.334751 | ||||||||
\(842\) | −8453.97 | + | 4880.90i | −0.346013 | + | 0.199771i | ||||
\(843\) | 17322.7 | + | 1450.42i | 0.707739 | + | 0.0592589i | ||||
\(844\) | 8770.54 | − | 15191.0i | 0.357695 | − | 0.619546i | ||||
\(845\) | −4963.94 | − | 8597.80i | −0.202088 | − | 0.350028i | ||||
\(846\) | −28680.3 | − | 23703.2i | −1.16554 | − | 0.963276i | ||||
\(847\) | −23901.8 | + | 5002.81i | −0.969629 | + | 0.202950i | ||||
\(848\) | 47404.0i | 1.91964i | ||||||||
\(849\) | −3249.61 | + | 4677.98i | −0.131362 | + | 0.189102i | ||||
\(850\) | −4739.84 | − | 2736.55i | −0.191265 | − | 0.110427i | ||||
\(851\) | −28327.3 | − | 16354.8i | −1.14107 | − | 0.658796i | ||||
\(852\) | 5353.49 | − | 7706.62i | 0.215267 | − | 0.309888i | ||||
\(853\) | − | 5300.18i | − | 0.212749i | −0.994326 | − | 0.106374i | \(-0.966076\pi\) | ||
0.994326 | − | 0.106374i | \(-0.0339242\pi\) | |||||||
\(854\) | 20767.8 | + | 23209.8i | 0.832154 | + | 0.930003i | ||||
\(855\) | −4794.00 | − | 3962.06i | −0.191756 | − | 0.158479i | ||||
\(856\) | 11063.7 | + | 19162.9i | 0.441765 | + | 0.765159i | ||||
\(857\) | 15912.3 | − | 27560.9i | 0.634251 | − | 1.09856i | −0.352422 | − | 0.935841i | \(-0.614642\pi\) |
0.986673 | − | 0.162714i | \(-0.0520248\pi\) | |||||||
\(858\) | −940.096 | − | 78.7140i | −0.0374060 | − | 0.00313200i | ||||
\(859\) | 13397.4 | − | 7734.97i | 0.532145 | − | 0.307234i | −0.209745 | − | 0.977756i | \(-0.567263\pi\) |
0.741889 | + | 0.670522i | \(0.233930\pi\) | |||||||
\(860\) | 2446.36 | 0.0970004 | ||||||||
\(861\) | −29080.9 | − | 12322.8i | −1.15107 | − | 0.487759i | ||||
\(862\) | 16129.2 | 0.637312 | ||||||||
\(863\) | 188.260 | − | 108.692i | 0.00742576 | − | 0.00428727i | −0.496283 | − | 0.868161i | \(-0.665302\pi\) |
0.503708 | + | 0.863874i | \(0.331969\pi\) | |||||||
\(864\) | −17995.6 | + | 18403.1i | −0.708590 | + | 0.724635i | ||||
\(865\) | 1865.57 | − | 3231.26i | 0.0733309 | − | 0.127013i | ||||
\(866\) | 13165.0 | + | 22802.5i | 0.516590 | + | 0.894759i | ||||
\(867\) | −5093.95 | + | 2398.53i | −0.199538 | + | 0.0939543i | ||||
\(868\) | −3634.76 | − | 17365.7i | −0.142133 | − | 0.679067i | ||||
\(869\) | − | 4136.60i | − | 0.161478i | ||||||
\(870\) | 9615.28 | + | 6679.36i | 0.374700 | + | 0.260289i | ||||
\(871\) | −5239.05 | − | 3024.77i | −0.203810 | − | 0.117670i | ||||
\(872\) | 8170.48 | + | 4717.23i | 0.317302 | + | 0.183194i | ||||
\(873\) | −123.594 | + | 732.877i | −0.00479154 | + | 0.0284125i | ||||
\(874\) | − | 18740.7i | − | 0.725300i | ||||||
\(875\) | 722.231 | − | 2199.49i | 0.0279039 | − | 0.0849787i | ||||
\(876\) | −1552.31 | − | 3296.76i | −0.0598716 | − | 0.127154i | ||||
\(877\) | −23221.7 | − | 40221.2i | −0.894119 | − | 1.54866i | −0.834891 | − | 0.550415i | \(-0.814470\pi\) |
−0.0592274 | − | 0.998245i | \(-0.518864\pi\) | |||||||
\(878\) | 10688.7 | − | 18513.5i | 0.410852 | − | 0.711616i | ||||
\(879\) | 1886.09 | − | 22525.9i | 0.0723734 | − | 0.864368i | ||||
\(880\) | 1218.57 | − | 703.539i | 0.0466794 | − | 0.0269504i | ||||
\(881\) | 29022.7 | 1.10988 | 0.554938 | − | 0.831892i | \(-0.312742\pi\) | ||||
0.554938 | + | 0.831892i | \(0.312742\pi\) | |||||||
\(882\) | −31505.0 | − | 8991.65i | −1.20275 | − | 0.343271i | ||||
\(883\) | 33524.8 | 1.27769 | 0.638845 | − | 0.769336i | \(-0.279413\pi\) | ||||
0.638845 | + | 0.769336i | \(0.279413\pi\) | |||||||
\(884\) | −3518.78 | + | 2031.57i | −0.133879 | + | 0.0772954i | ||||
\(885\) | 1194.27 | − | 14263.4i | 0.0453616 | − | 0.541762i | ||||
\(886\) | −7058.93 | + | 12226.4i | −0.267663 | + | 0.463606i | ||||
\(887\) | 23054.8 | + | 39932.2i | 0.872724 | + | 1.51160i | 0.859168 | + | 0.511694i | \(0.170982\pi\) |
0.0135557 | + | 0.999908i | \(0.495685\pi\) | |||||||
\(888\) | −7761.89 | − | 16484.6i | −0.293324 | − | 0.622956i | ||||
\(889\) | −13238.1 | + | 40315.4i | −0.499428 | + | 1.52096i | ||||
\(890\) | 17890.7i | 0.673816i | ||||||||
\(891\) | 1683.10 | + | 1946.09i | 0.0632838 | + | 0.0731723i | ||||
\(892\) | 2204.74 | + | 1272.91i | 0.0827581 | + | 0.0477804i | ||||
\(893\) | 15541.1 | + | 8972.68i | 0.582379 | + | 0.336237i | ||||
\(894\) | −7591.10 | − | 5273.24i | −0.283987 | − | 0.197275i | ||||
\(895\) | 17049.0i | 0.636743i | ||||||||
\(896\) | −5418.77 | − | 25889.1i | −0.202041 | − | 0.965285i | ||||
\(897\) | 7859.99 | − | 3700.94i | 0.292572 | − | 0.137760i | ||||
\(898\) | 1586.77 | + | 2748.36i | 0.0589657 | + | 0.102132i | ||||
\(899\) | 13511.3 | − | 23402.2i | 0.501253 | − | 0.868196i | ||||
\(900\) | −1063.84 | − | 2856.37i | −0.0394015 | − | 0.105791i | ||||
\(901\) | 31861.6 | − | 18395.3i | 1.17810 | − | 0.680174i | ||||
\(902\) | 4097.97 | 0.151272 | ||||||||
\(903\) | −9600.68 | − | 4068.22i | −0.353810 | − | 0.149925i | ||||
\(904\) | −1750.53 | −0.0644044 | ||||||||
\(905\) | 12720.2 | − | 7344.01i | 0.467220 | − | 0.269749i | ||||
\(906\) | 43062.6 | + | 3605.62i | 1.57909 | + | 0.132217i | ||||
\(907\) | 1333.54 | − | 2309.77i | 0.0488198 | − | 0.0845585i | −0.840583 | − | 0.541683i | \(-0.817787\pi\) |
0.889403 | + | 0.457125i | \(0.151121\pi\) | |||||||
\(908\) | −1977.70 | − | 3425.48i | −0.0722824 | − | 0.125197i | ||||
\(909\) | 32790.6 | − | 39675.9i | 1.19647 | − | 1.44771i | ||||
\(910\) | −3176.33 | − | 3549.82i | −0.115708 | − | 0.129314i | ||||
\(911\) | 8098.22i | 0.294518i | 0.989098 | + | 0.147259i | \(0.0470451\pi\) | ||||
−0.989098 | + | 0.147259i | \(0.952955\pi\) | |||||||
\(912\) | 10889.4 | − | 15675.9i | 0.395378 | − | 0.569168i | ||||
\(913\) | 13.5435 | + | 7.81937i | 0.000490937 | + | 0.000283443i | ||||
\(914\) | −6881.54 | − | 3973.06i | −0.249038 | − | 0.143782i | ||||
\(915\) | 7045.81 | − | 10142.8i | 0.254565 | − | 0.366460i | ||||
\(916\) | − | 23036.0i | − | 0.830930i | ||||||
\(917\) | 9395.32 | − | 1966.50i | 0.338343 | − | 0.0708176i | ||||
\(918\) | 29754.8 | + | 7616.81i | 1.06977 | + | 0.273848i | ||||
\(919\) | 12254.4 | + | 21225.2i | 0.439864 | + | 0.761867i | 0.997679 | − | 0.0680987i | \(-0.0216933\pi\) |
−0.557815 | + | 0.829966i | \(0.688360\pi\) | |||||||
\(920\) | −3543.55 | + | 6137.60i | −0.126986 | + | 0.219946i | ||||
\(921\) | 29778.1 | + | 2493.32i | 1.06539 | + | 0.0892048i | ||||
\(922\) | −19925.1 | + | 11503.8i | −0.711712 | + | 0.410907i | ||||
\(923\) | −5814.95 | −0.207369 | ||||||||
\(924\) | 1522.19 | − | 187.860i | 0.0541952 | − | 0.00668845i | ||||
\(925\) | 7111.61 | 0.252787 | ||||||||
\(926\) | 39430.1 | − | 22765.0i | 1.39930 | − | 0.807887i | ||||
\(927\) | −44103.0 | + | 16425.9i | −1.56260 | + | 0.581984i | ||||
\(928\) | −11684.5 | + | 20238.2i | −0.413322 | + | 0.715895i | ||||
\(929\) | 16512.6 | + | 28600.7i | 0.583167 | + | 1.01007i | 0.995101 | + | 0.0988613i | \(0.0315200\pi\) |
−0.411934 | + | 0.911214i | \(0.635147\pi\) | |||||||
\(930\) | −17641.4 | + | 8306.59i | −0.622025 | + | 0.292886i | ||||
\(931\) | 15704.6 | + | 1749.49i | 0.552844 | + | 0.0615868i | ||||
\(932\) | 26261.4i | 0.922984i | ||||||||
\(933\) | 23478.7 | + | 16309.8i | 0.823858 | + | 0.572302i | ||||
\(934\) | −88.3275 | − | 50.9959i | −0.00309439 | − | 0.00178655i | ||||
\(935\) | −945.740 | − | 546.023i | −0.0330792 | − | 0.0190983i | ||||
\(936\) | 4772.02 | + | 804.762i | 0.166643 | + | 0.0281031i | ||||
\(937\) | − | 1369.77i | − | 0.0477573i | −0.999715 | − | 0.0238786i | \(-0.992398\pi\) | ||
0.999715 | − | 0.0238786i | \(-0.00760153\pi\) | |||||||
\(938\) | 25899.1 | + | 8504.29i | 0.901529 | + | 0.296029i | ||||
\(939\) | 1594.53 | + | 3386.42i | 0.0554158 | + | 0.117691i | ||||
\(940\) | 4397.43 | + | 7616.57i | 0.152583 | + | 0.264282i | ||||
\(941\) | −19007.3 | + | 32921.7i | −0.658471 | + | 1.14051i | 0.322540 | + | 0.946556i | \(0.395463\pi\) |
−0.981011 | + | 0.193950i | \(0.937870\pi\) | |||||||
\(942\) | 4373.05 | − | 52228.1i | 0.151254 | − | 1.80646i | ||||
\(943\) | −32682.5 | + | 18869.3i | −1.12862 | + | 0.651610i | ||||
\(944\) | 43927.1 | 1.51452 | ||||||||
\(945\) | −575.038 | + | 12978.9i | −0.0197947 | + | 0.446775i | ||||
\(946\) | 1352.89 | 0.0464972 | ||||||||
\(947\) | 12763.0 | − | 7368.74i | 0.437954 | − | 0.252853i | −0.264775 | − | 0.964310i | \(-0.585298\pi\) |
0.702730 | + | 0.711457i | \(0.251964\pi\) | |||||||
\(948\) | 2294.58 | − | 27404.5i | 0.0786122 | − | 0.938879i | ||||
\(949\) | −1129.06 | + | 1955.59i | −0.0386205 | + | 0.0668927i | ||||
\(950\) | 2037.27 | + | 3528.65i | 0.0695765 | + | 0.120510i | ||||
\(951\) | −272.683 | − | 579.119i | −0.00929796 | − | 0.0197468i | ||||
\(952\) | −10528.1 | + | 9420.43i | −0.358423 | + | 0.320712i | ||||
\(953\) | 1184.48i | 0.0402612i | 0.999797 | + | 0.0201306i | \(0.00640820\pi\) | ||||
−0.999797 | + | 0.0201306i | \(0.993592\pi\) | |||||||
\(954\) | 55997.8 | + | 9443.58i | 1.90041 | + | 0.320490i | ||||
\(955\) | −463.308 | − | 267.491i | −0.0156987 | − | 0.00906366i | ||||
\(956\) | −14808.8 | − | 8549.89i | −0.500996 | − | 0.289250i | ||||
\(957\) | 1918.54 | + | 1332.73i | 0.0648040 | + | 0.0450168i | ||||
\(958\) | 35335.1i | 1.19168i | ||||||||
\(959\) | −16140.6 | + | 14442.4i | −0.543491 | + | 0.486308i | ||||
\(960\) | 262.714 | − | 123.701i | 0.00883234 | − | 0.00415878i | ||||
\(961\) | 7607.76 | + | 13177.0i | 0.255371 | + | 0.442316i | ||||
\(962\) | 7316.46 | − | 12672.5i | 0.245210 | − | 0.424716i | ||||
\(963\) | 45418.9 | − | 16916.1i | 1.51984 | − | 0.566056i | ||||
\(964\) | 10152.1 | − | 5861.33i | 0.339189 | − | 0.195831i | ||||
\(965\) | −10911.5 | −0.363994 | ||||||||
\(966\) | −31249.8 | + | 23578.8i | −1.04084 | + | 0.785338i | ||||
\(967\) | 43755.8 | 1.45511 | 0.727555 | − | 0.686050i | \(-0.240657\pi\) | ||||
0.727555 | + | 0.686050i | \(0.240657\pi\) | |||||||
\(968\) | −14075.9 | + | 8126.72i | −0.467372 | + | 0.269837i | ||||
\(969\) | −14761.9 | − | 1236.01i | −0.489393 | − | 0.0409768i | ||||
\(970\) | 243.458 | − | 421.681i | 0.00805871 | − | 0.0139581i | ||||
\(971\) | −640.617 | − | 1109.58i | −0.0211724 | − | 0.0366716i | 0.855245 | − | 0.518224i | \(-0.173407\pi\) |
−0.876417 | + | 0.481552i | \(0.840073\pi\) | |||||||
\(972\) | 10070.8 | + | 13826.3i | 0.332327 | + | 0.456253i | ||||
\(973\) | 45744.7 | + | 15020.9i | 1.50720 | + | 0.494909i | ||||
\(974\) | 14710.4i | 0.483932i | ||||||||
\(975\) | −1077.62 | + | 1551.29i | −0.0353964 | + | 0.0509549i | ||||
\(976\) | 32823.6 | + | 18950.7i | 1.07649 | + | 0.621514i | ||||
\(977\) | −9150.85 | − | 5283.25i | −0.299654 | − | 0.173005i | 0.342634 | − | 0.939469i | \(-0.388681\pi\) |
−0.642287 | + | 0.766464i | \(0.722014\pi\) | |||||||
\(978\) | −23484.4 | + | 33806.9i | −0.767840 | + | 1.10534i | ||||
\(979\) | 3569.72i | 0.116536i | ||||||||
\(980\) | 6236.82 | + | 4590.88i | 0.203294 | + | 0.149643i | ||||
\(981\) | 13164.5 | − | 15928.8i | 0.428451 | − | 0.518417i | ||||
\(982\) | −8811.66 | − | 15262.3i | −0.286346 | − | 0.495965i | ||||
\(983\) | 1262.37 | − | 2186.48i | 0.0409595 | − | 0.0709439i | −0.844819 | − | 0.535052i | \(-0.820292\pi\) |
0.885778 | + | 0.464108i | \(0.153625\pi\) | |||||||
\(984\) | −20948.5 | − | 1754.02i | −0.678674 | − | 0.0568252i | ||||
\(985\) | −887.841 | + | 512.595i | −0.0287198 | + | 0.0165814i | ||||
\(986\) | 27885.8 | 0.900673 | ||||||||
\(987\) | −4591.47 | − | 37203.8i | −0.148073 | − | 1.19981i | ||||
\(988\) | 3024.87 | 0.0974027 | ||||||||
\(989\) | −10789.7 | + | 6229.45i | −0.346910 | + | 0.200288i | ||||
\(990\) | −588.327 | − | 1579.63i | −0.0188871 | − | 0.0507112i | ||||
\(991\) | −22103.9 | + | 38285.1i | −0.708530 | + | 1.22721i | 0.256872 | + | 0.966445i | \(0.417308\pi\) |
−0.965402 | + | 0.260765i | \(0.916025\pi\) | |||||||
\(992\) | −19460.7 | − | 33707.0i | −0.622862 | − | 1.07883i | ||||
\(993\) | 45281.4 | − | 21321.1i | 1.44709 | − | 0.681376i | ||||
\(994\) | 25646.7 | − | 5368.03i | 0.818375 | − | 0.171291i | ||||
\(995\) | 13320.3i | 0.424404i | ||||||||
\(996\) | 85.3871 | + | 59.3151i | 0.00271646 | + | 0.00188702i | ||||
\(997\) | −30636.8 | − | 17688.2i | −0.973196 | − | 0.561875i | −0.0729871 | − | 0.997333i | \(-0.523253\pi\) |
−0.900209 | + | 0.435458i | \(0.856587\pi\) | |||||||
\(998\) | −25113.1 | − | 14499.1i | −0.796534 | − | 0.459879i | ||||
\(999\) | −38431.3 | + | 10760.2i | −1.21713 | + | 0.340777i |
(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.a.101.4 | yes | 32 | |
3.2 | odd | 2 | 105.4.s.b.101.13 | yes | 32 | ||
7.5 | odd | 6 | 105.4.s.b.26.13 | yes | 32 | ||
21.5 | even | 6 | inner | 105.4.s.a.26.4 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.s.a.26.4 | ✓ | 32 | 21.5 | even | 6 | inner | |
105.4.s.a.101.4 | yes | 32 | 1.1 | even | 1 | trivial | |
105.4.s.b.26.13 | yes | 32 | 7.5 | odd | 6 | ||
105.4.s.b.101.13 | yes | 32 | 3.2 | odd | 2 |