Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,4,Mod(9,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.9");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.e (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.95009550029\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 9.6 | ||
Character | \(\chi\) | \(=\) | 50.9 |
Dual form | 50.4.e.a.39.6 |
$q$-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 \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).
\(n\) | \(27\) |
\(\chi(n)\) | \(e\left(\frac{7}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.17557 | − | 1.61803i | 0.415627 | − | 0.572061i | ||||
\(3\) | −4.16531 | + | 1.35339i | −0.801615 | + | 0.260461i | −0.681042 | − | 0.732244i | \(-0.738473\pi\) |
−0.120573 | + | 0.992704i | \(0.538473\pi\) | |||||||
\(4\) | −1.23607 | − | 3.80423i | −0.154508 | − | 0.475528i | ||||
\(5\) | −1.15597 | − | 11.1204i | −0.103393 | − | 0.994641i | ||||
\(6\) | −2.70679 | + | 8.33063i | −0.184173 | + | 0.566828i | ||||
\(7\) | − | 31.2051i | − | 1.68492i | −0.538761 | − | 0.842459i | \(-0.681107\pi\) | ||
0.538761 | − | 0.842459i | \(-0.318893\pi\) | |||||||
\(8\) | −7.60845 | − | 2.47214i | −0.336249 | − | 0.109254i | ||||
\(9\) | −6.32528 | + | 4.59559i | −0.234270 | + | 0.170207i | ||||
\(10\) | −19.3521 | − | 11.2024i | −0.611968 | − | 0.354252i | ||||
\(11\) | 12.0574 | + | 8.76021i | 0.330495 | + | 0.240118i | 0.740640 | − | 0.671902i | \(-0.234522\pi\) |
−0.410146 | + | 0.912020i | \(0.634522\pi\) | |||||||
\(12\) | 10.2972 | + | 14.1729i | 0.247713 | + | 0.340947i | ||||
\(13\) | 25.0832 | + | 34.5241i | 0.535141 | + | 0.736558i | 0.987903 | − | 0.155073i | \(-0.0495613\pi\) |
−0.452762 | + | 0.891631i | \(0.649561\pi\) | |||||||
\(14\) | −50.4909 | − | 36.6838i | −0.963876 | − | 0.700297i | ||||
\(15\) | 19.8653 | + | 44.7556i | 0.341946 | + | 0.770389i | ||||
\(16\) | −12.9443 | + | 9.40456i | −0.202254 | + | 0.146946i | ||||
\(17\) | 27.6773 | + | 8.99290i | 0.394867 | + | 0.128300i | 0.499718 | − | 0.866188i | \(-0.333437\pi\) |
−0.104852 | + | 0.994488i | \(0.533437\pi\) | |||||||
\(18\) | 15.6370i | 0.204759i | ||||||||
\(19\) | 15.9076 | − | 48.9587i | 0.192077 | − | 0.591152i | −0.807921 | − | 0.589290i | \(-0.799407\pi\) |
0.999998 | − | 0.00186182i | \(-0.000592636\pi\) | |||||||
\(20\) | −40.8757 | + | 18.1432i | −0.457005 | + | 0.202847i | ||||
\(21\) | 42.2328 | + | 129.979i | 0.438855 | + | 1.35066i | ||||
\(22\) | 28.3486 | − | 9.21103i | 0.274725 | − | 0.0892636i | ||||
\(23\) | 109.187 | − | 150.283i | 0.989874 | − | 1.36244i | 0.0585368 | − | 0.998285i | \(-0.481356\pi\) |
0.931337 | − | 0.364159i | \(-0.118644\pi\) | |||||||
\(24\) | 35.0374 | 0.297999 | ||||||||
\(25\) | −122.327 | + | 25.7097i | −0.978620 | + | 0.205677i | ||||
\(26\) | 85.3482 | 0.643775 | ||||||||
\(27\) | 89.6334 | − | 123.370i | 0.638887 | − | 0.879353i | ||||
\(28\) | −118.711 | + | 38.5716i | −0.801226 | + | 0.260334i | ||||
\(29\) | 23.7789 | + | 73.1839i | 0.152263 | + | 0.468618i | 0.997873 | − | 0.0651831i | \(-0.0207631\pi\) |
−0.845610 | + | 0.533801i | \(0.820763\pi\) | |||||||
\(30\) | 95.7691 | + | 20.4707i | 0.582832 | + | 0.124581i | ||||
\(31\) | −80.3709 | + | 247.356i | −0.465646 | + | 1.43311i | 0.392522 | + | 0.919743i | \(0.371603\pi\) |
−0.858168 | + | 0.513369i | \(0.828397\pi\) | |||||||
\(32\) | 32.0000i | 0.176777i | ||||||||
\(33\) | −62.0789 | − | 20.1706i | −0.327471 | − | 0.106402i | ||||
\(34\) | 47.0875 | − | 34.2110i | 0.237513 | − | 0.172563i | ||||
\(35\) | −347.014 | + | 36.0721i | −1.67589 | + | 0.174208i | ||||
\(36\) | 25.3011 | + | 18.3823i | 0.117135 | + | 0.0851035i | ||||
\(37\) | 70.7618 | + | 97.3953i | 0.314410 | + | 0.432748i | 0.936750 | − | 0.349999i | \(-0.113818\pi\) |
−0.622340 | + | 0.782747i | \(0.713818\pi\) | |||||||
\(38\) | −60.5163 | − | 83.2935i | −0.258343 | − | 0.355579i | ||||
\(39\) | −151.204 | − | 109.856i | −0.620821 | − | 0.451053i | ||||
\(40\) | −18.6961 | + | 87.4669i | −0.0739027 | + | 0.345743i | ||||
\(41\) | 248.032 | − | 180.206i | 0.944783 | − | 0.686425i | −0.00478394 | − | 0.999989i | \(-0.501523\pi\) |
0.949567 | + | 0.313563i | \(0.101523\pi\) | |||||||
\(42\) | 259.958 | + | 84.4656i | 0.955058 | + | 0.310317i | ||||
\(43\) | − | 504.394i | − | 1.78882i | −0.447246 | − | 0.894411i | \(-0.647595\pi\) | ||
0.447246 | − | 0.894411i | \(-0.352405\pi\) | |||||||
\(44\) | 18.4221 | − | 56.6973i | 0.0631189 | − | 0.194260i | ||||
\(45\) | 58.4167 | + | 65.0275i | 0.193516 | + | 0.215416i | ||||
\(46\) | −114.806 | − | 353.337i | −0.367984 | − | 1.13254i | ||||
\(47\) | −186.822 | + | 60.7022i | −0.579804 | + | 0.188390i | −0.584213 | − | 0.811600i | \(-0.698597\pi\) |
0.00440862 | + | 0.999990i | \(0.498597\pi\) | |||||||
\(48\) | 41.1889 | − | 56.6917i | 0.123856 | − | 0.170474i | ||||
\(49\) | −630.759 | −1.83895 | ||||||||
\(50\) | −102.205 | + | 228.154i | −0.289081 | + | 0.645316i | ||||
\(51\) | −127.456 | −0.349948 | ||||||||
\(52\) | 100.333 | − | 138.096i | 0.267570 | − | 0.368279i | ||||
\(53\) | 430.808 | − | 139.978i | 1.11653 | − | 0.362782i | 0.308087 | − | 0.951358i | \(-0.400311\pi\) |
0.808442 | + | 0.588576i | \(0.200311\pi\) | |||||||
\(54\) | −94.2462 | − | 290.060i | −0.237505 | − | 0.730966i | ||||
\(55\) | 83.4793 | − | 144.210i | 0.204661 | − | 0.353550i | ||||
\(56\) | −77.1433 | + | 237.423i | −0.184084 | + | 0.566552i | ||||
\(57\) | 225.458i | 0.523905i | ||||||||
\(58\) | 146.368 | + | 47.5578i | 0.331363 | + | 0.107666i | ||||
\(59\) | 51.9655 | − | 37.7552i | 0.114667 | − | 0.0833102i | −0.528974 | − | 0.848638i | \(-0.677423\pi\) |
0.643641 | + | 0.765328i | \(0.277423\pi\) | |||||||
\(60\) | 145.706 | − | 130.893i | 0.313508 | − | 0.281637i | ||||
\(61\) | 110.566 | + | 80.3305i | 0.232073 | + | 0.168611i | 0.697744 | − | 0.716347i | \(-0.254187\pi\) |
−0.465671 | + | 0.884958i | \(0.654187\pi\) | |||||||
\(62\) | 305.749 | + | 420.827i | 0.626293 | + | 0.862018i | ||||
\(63\) | 143.406 | + | 197.381i | 0.286785 | + | 0.394725i | ||||
\(64\) | 51.7771 | + | 37.6183i | 0.101127 | + | 0.0734732i | ||||
\(65\) | 354.927 | − | 318.844i | 0.677281 | − | 0.608428i | ||||
\(66\) | −105.615 | + | 76.7337i | −0.196974 | + | 0.143110i | ||||
\(67\) | −223.555 | − | 72.6375i | −0.407636 | − | 0.132449i | 0.0980193 | − | 0.995185i | \(-0.468749\pi\) |
−0.505656 | + | 0.862735i | \(0.668749\pi\) | |||||||
\(68\) | − | 116.407i | − | 0.207594i | ||||||
\(69\) | −251.407 | + | 773.750i | −0.438635 | + | 1.34998i | ||||
\(70\) | −349.574 | + | 603.886i | −0.596886 | + | 1.03112i | ||||
\(71\) | 166.664 | + | 512.939i | 0.278583 | + | 0.857390i | 0.988249 | + | 0.152852i | \(0.0488458\pi\) |
−0.709666 | + | 0.704538i | \(0.751154\pi\) | |||||||
\(72\) | 59.4865 | − | 19.3283i | 0.0973688 | − | 0.0316370i | ||||
\(73\) | −614.830 | + | 846.241i | −0.985759 | + | 1.35678i | −0.0520909 | + | 0.998642i | \(0.516589\pi\) |
−0.933668 | + | 0.358139i | \(0.883411\pi\) | |||||||
\(74\) | 240.774 | 0.378236 | ||||||||
\(75\) | 474.737 | − | 272.646i | 0.730906 | − | 0.419766i | ||||
\(76\) | −205.913 | −0.310787 | ||||||||
\(77\) | 273.363 | − | 376.252i | 0.404580 | − | 0.556856i | ||||
\(78\) | −355.502 | + | 115.510i | −0.516060 | + | 0.167678i | ||||
\(79\) | −109.157 | − | 335.949i | −0.155457 | − | 0.478446i | 0.842750 | − | 0.538305i | \(-0.180935\pi\) |
−0.998207 | + | 0.0598585i | \(0.980935\pi\) | |||||||
\(80\) | 119.546 | + | 133.074i | 0.167070 | + | 0.185977i | ||||
\(81\) | −141.150 | + | 434.416i | −0.193622 | + | 0.595907i | ||||
\(82\) | − | 613.169i | − | 0.825771i | ||||||
\(83\) | 928.944 | + | 301.832i | 1.22849 | + | 0.399161i | 0.850168 | − | 0.526512i | \(-0.176500\pi\) |
0.378325 | + | 0.925673i | \(0.376500\pi\) | |||||||
\(84\) | 442.267 | − | 321.326i | 0.574468 | − | 0.417376i | ||||
\(85\) | 68.0108 | − | 318.179i | 0.0867860 | − | 0.406016i | ||||
\(86\) | −816.127 | − | 592.951i | −1.02332 | − | 0.743483i | ||||
\(87\) | −198.093 | − | 272.652i | −0.244113 | − | 0.335993i | ||||
\(88\) | −70.0817 | − | 96.4592i | −0.0848947 | − | 0.116848i | ||||
\(89\) | 891.118 | + | 647.435i | 1.06133 | + | 0.771101i | 0.974334 | − | 0.225108i | \(-0.0722735\pi\) |
0.0869953 | + | 0.996209i | \(0.472273\pi\) | |||||||
\(90\) | 173.890 | − | 18.0758i | 0.203662 | − | 0.0211706i | ||||
\(91\) | 1077.33 | − | 782.724i | 1.24104 | − | 0.901668i | ||||
\(92\) | −706.674 | − | 229.612i | −0.800825 | − | 0.260204i | ||||
\(93\) | − | 1139.09i | − | 1.27009i | ||||||
\(94\) | −121.404 | + | 373.644i | −0.133212 | + | 0.409984i | ||||
\(95\) | −562.830 | − | 120.305i | −0.607843 | − | 0.129927i | ||||
\(96\) | −43.3086 | − | 133.290i | −0.0460434 | − | 0.141707i | ||||
\(97\) | −1379.77 | + | 448.316i | −1.44428 | + | 0.469274i | −0.923228 | − | 0.384253i | \(-0.874459\pi\) |
−0.521048 | + | 0.853527i | \(0.674459\pi\) | |||||||
\(98\) | −741.502 | + | 1020.59i | −0.764316 | + | 1.05199i | ||||
\(99\) | −116.525 | −0.118295 | ||||||||
\(100\) | 249.010 | + | 433.583i | 0.249010 | + | 0.433583i | ||||
\(101\) | −305.774 | −0.301244 | −0.150622 | − | 0.988591i | \(-0.548128\pi\) | ||||
−0.150622 | + | 0.988591i | \(0.548128\pi\) | |||||||
\(102\) | −149.833 | + | 206.228i | −0.145448 | + | 0.200192i | ||||
\(103\) | −337.914 | + | 109.795i | −0.323259 | + | 0.105033i | −0.466151 | − | 0.884705i | \(-0.654360\pi\) |
0.142892 | + | 0.989738i | \(0.454360\pi\) | |||||||
\(104\) | −105.496 | − | 324.684i | −0.0994688 | − | 0.306133i | ||||
\(105\) | 1396.60 | − | 619.898i | 1.29804 | − | 0.576151i | ||||
\(106\) | 279.956 | − | 861.616i | 0.256526 | − | 0.789505i | ||||
\(107\) | − | 254.177i | − | 0.229647i | −0.993386 | − | 0.114823i | \(-0.963370\pi\) | ||
0.993386 | − | 0.114823i | \(-0.0366302\pi\) | |||||||
\(108\) | −580.120 | − | 188.492i | −0.516871 | − | 0.167942i | ||||
\(109\) | 723.625 | − | 525.744i | 0.635878 | − | 0.461992i | −0.222554 | − | 0.974920i | \(-0.571439\pi\) |
0.858432 | + | 0.512928i | \(0.171439\pi\) | |||||||
\(110\) | −135.201 | − | 304.601i | −0.117190 | − | 0.264023i | ||||
\(111\) | −426.559 | − | 309.914i | −0.364750 | − | 0.265006i | ||||
\(112\) | 293.470 | + | 403.927i | 0.247592 | + | 0.340782i | ||||
\(113\) | 785.716 | + | 1081.45i | 0.654106 | + | 0.900300i | 0.999268 | − | 0.0382434i | \(-0.0121762\pi\) |
−0.345163 | + | 0.938543i | \(0.612176\pi\) | |||||||
\(114\) | 364.798 | + | 265.041i | 0.299706 | + | 0.217749i | ||||
\(115\) | −1797.43 | − | 1040.48i | −1.45749 | − | 0.843702i | ||||
\(116\) | 249.016 | − | 180.921i | 0.199315 | − | 0.144811i | ||||
\(117\) | −317.317 | − | 103.102i | −0.250735 | − | 0.0814686i | ||||
\(118\) | − | 128.466i | − | 0.100222i | ||||||
\(119\) | 280.625 | − | 863.674i | 0.216175 | − | 0.665318i | ||||
\(120\) | −40.5020 | − | 389.630i | −0.0308109 | − | 0.296402i | ||||
\(121\) | −342.662 | − | 1054.61i | −0.257447 | − | 0.792341i | ||||
\(122\) | 259.955 | − | 84.4645i | 0.192912 | − | 0.0626808i | ||||
\(123\) | −789.243 | + | 1086.30i | −0.578566 | + | 0.796328i | ||||
\(124\) | 1040.34 | 0.753431 | ||||||||
\(125\) | 427.309 | + | 1330.61i | 0.305757 | + | 0.952110i | ||||
\(126\) | 487.953 | 0.345002 | ||||||||
\(127\) | −891.078 | + | 1226.46i | −0.622601 | + | 0.856937i | −0.997539 | − | 0.0701127i | \(-0.977664\pi\) |
0.374938 | + | 0.927050i | \(0.377664\pi\) | |||||||
\(128\) | 121.735 | − | 39.5542i | 0.0840623 | − | 0.0273135i | ||||
\(129\) | 682.643 | + | 2100.96i | 0.465918 | + | 1.43395i | ||||
\(130\) | −98.6596 | − | 949.108i | −0.0665617 | − | 0.640325i | ||||
\(131\) | −385.607 | + | 1186.78i | −0.257180 | + | 0.791519i | 0.736212 | + | 0.676751i | \(0.236613\pi\) |
−0.993392 | + | 0.114768i | \(0.963387\pi\) | |||||||
\(132\) | 261.094i | 0.172162i | ||||||||
\(133\) | −1527.76 | − | 496.400i | −0.996043 | − | 0.323634i | ||||
\(134\) | −380.335 | + | 276.330i | −0.245194 | + | 0.178144i | ||||
\(135\) | −1475.54 | − | 854.150i | −0.940697 | − | 0.544545i | ||||
\(136\) | −188.350 | − | 136.844i | −0.118756 | − | 0.0862815i | ||||
\(137\) | −1405.06 | − | 1933.90i | −0.876222 | − | 1.20602i | −0.977453 | − | 0.211154i | \(-0.932278\pi\) |
0.101231 | − | 0.994863i | \(-0.467722\pi\) | |||||||
\(138\) | 956.408 | + | 1316.38i | 0.589962 | + | 0.812014i | ||||
\(139\) | 1423.34 | + | 1034.12i | 0.868534 | + | 0.631027i | 0.930193 | − | 0.367071i | \(-0.119639\pi\) |
−0.0616594 | + | 0.998097i | \(0.519639\pi\) | |||||||
\(140\) | 566.159 | + | 1275.53i | 0.341780 | + | 0.770015i | ||||
\(141\) | 696.019 | − | 505.687i | 0.415712 | − | 0.302032i | ||||
\(142\) | 1025.88 | + | 333.328i | 0.606266 | + | 0.196988i | ||||
\(143\) | 636.005i | 0.371926i | ||||||||
\(144\) | 38.6567 | − | 118.973i | 0.0223708 | − | 0.0688501i | ||||
\(145\) | 786.349 | − | 349.030i | 0.450363 | − | 0.199899i | ||||
\(146\) | 646.471 | + | 1989.63i | 0.366454 | + | 1.12783i | ||||
\(147\) | 2627.31 | − | 853.665i | 1.47413 | − | 0.478973i | ||||
\(148\) | 283.047 | − | 389.581i | 0.157205 | − | 0.216374i | ||||
\(149\) | −391.623 | −0.215322 | −0.107661 | − | 0.994188i | \(-0.534336\pi\) | ||||
−0.107661 | + | 0.994188i | \(0.534336\pi\) | |||||||
\(150\) | 116.937 | − | 1088.66i | 0.0636523 | − | 0.592589i | ||||
\(151\) | 1937.43 | 1.04414 | 0.522072 | − | 0.852901i | \(-0.325159\pi\) | ||||
0.522072 | + | 0.852901i | \(0.325159\pi\) | |||||||
\(152\) | −242.065 | + | 333.174i | −0.129172 | + | 0.177789i | ||||
\(153\) | −216.394 | + | 70.3108i | −0.114343 | + | 0.0371522i | ||||
\(154\) | −287.431 | − | 884.622i | −0.150402 | − | 0.462889i | ||||
\(155\) | 2843.61 | + | 607.823i | 1.47358 | + | 0.314977i | ||||
\(156\) | −231.019 | + | 711.004i | −0.118566 | + | 0.364910i | ||||
\(157\) | 1798.13i | 0.914052i | 0.889453 | + | 0.457026i | \(0.151085\pi\) | ||||
−0.889453 | + | 0.457026i | \(0.848915\pi\) | |||||||
\(158\) | −671.899 | − | 218.313i | −0.338313 | − | 0.109924i | ||||
\(159\) | −1605.01 | + | 1166.10i | −0.800536 | + | 0.581623i | ||||
\(160\) | 355.853 | − | 36.9909i | 0.175829 | − | 0.0182774i | ||||
\(161\) | −4689.60 | − | 3407.20i | −2.29561 | − | 1.66786i | ||||
\(162\) | 536.968 | + | 739.073i | 0.260421 | + | 0.358439i | ||||
\(163\) | 784.182 | + | 1079.33i | 0.376821 | + | 0.518650i | 0.954739 | − | 0.297445i | \(-0.0961345\pi\) |
−0.577917 | + | 0.816095i | \(0.696134\pi\) | |||||||
\(164\) | −992.129 | − | 720.824i | −0.472392 | − | 0.343213i | ||||
\(165\) | −152.545 | + | 713.659i | −0.0719734 | + | 0.336717i | ||||
\(166\) | 1580.41 | − | 1148.24i | 0.738939 | − | 0.536871i | ||||
\(167\) | −1535.29 | − | 498.847i | −0.711404 | − | 0.231149i | −0.0691116 | − | 0.997609i | \(-0.522016\pi\) |
−0.642292 | + | 0.766460i | \(0.722016\pi\) | |||||||
\(168\) | − | 1093.35i | − | 0.502104i | ||||||
\(169\) | 116.166 | − | 357.522i | 0.0528748 | − | 0.162732i | ||||
\(170\) | −434.873 | − | 484.085i | −0.196195 | − | 0.218398i | ||||
\(171\) | 124.374 | + | 382.782i | 0.0556204 | + | 0.171182i | ||||
\(172\) | −1918.83 | + | 623.465i | −0.850636 | + | 0.276388i | ||||
\(173\) | 1941.29 | − | 2671.96i | 0.853142 | − | 1.17425i | −0.130020 | − | 0.991511i | \(-0.541504\pi\) |
0.983162 | − | 0.182738i | \(-0.0584960\pi\) | |||||||
\(174\) | −674.033 | −0.293668 | ||||||||
\(175\) | 802.273 | + | 3817.24i | 0.346549 | + | 1.64889i | ||||
\(176\) | −238.460 | −0.102128 | ||||||||
\(177\) | −165.355 | + | 227.592i | −0.0702195 | + | 0.0966489i | ||||
\(178\) | 2095.14 | − | 680.753i | 0.882234 | − | 0.286655i | ||||
\(179\) | −854.933 | − | 2631.21i | −0.356987 | − | 1.09869i | −0.954848 | − | 0.297094i | \(-0.903983\pi\) |
0.597861 | − | 0.801600i | \(-0.296017\pi\) | |||||||
\(180\) | 175.172 | − | 302.609i | 0.0725365 | − | 0.125306i | ||||
\(181\) | −1009.96 | + | 3108.33i | −0.414749 | + | 1.27647i | 0.497726 | + | 0.867334i | \(0.334168\pi\) |
−0.912475 | + | 0.409132i | \(0.865832\pi\) | |||||||
\(182\) | − | 2663.30i | − | 1.08471i | ||||||
\(183\) | −569.259 | − | 184.963i | −0.229950 | − | 0.0747153i | ||||
\(184\) | −1202.27 | + | 873.497i | −0.481697 | + | 0.349973i | ||||
\(185\) | 1001.28 | − | 899.487i | 0.397921 | − | 0.357468i | ||||
\(186\) | −1843.09 | − | 1339.08i | −0.726568 | − | 0.527882i | ||||
\(187\) | 254.937 | + | 350.890i | 0.0996941 | + | 0.137217i | ||||
\(188\) | 461.850 | + | 635.681i | 0.179169 | + | 0.246605i | ||||
\(189\) | −3849.77 | − | 2797.02i | −1.48164 | − | 1.07647i | ||||
\(190\) | −856.304 | + | 769.251i | −0.326962 | + | 0.293723i | ||||
\(191\) | −286.949 | + | 208.481i | −0.108706 | + | 0.0789797i | −0.640810 | − | 0.767699i | \(-0.721401\pi\) |
0.532104 | + | 0.846679i | \(0.321401\pi\) | |||||||
\(192\) | −266.580 | − | 86.6171i | −0.100202 | − | 0.0325576i | ||||
\(193\) | − | 2907.82i | − | 1.08451i | −0.840216 | − | 0.542253i | \(-0.817572\pi\) | ||
0.840216 | − | 0.542253i | \(-0.182428\pi\) | |||||||
\(194\) | −896.631 | + | 2759.55i | −0.331827 | + | 1.02126i | ||||
\(195\) | −1046.86 | + | 1808.44i | −0.384447 | + | 0.664130i | ||||
\(196\) | 779.661 | + | 2399.55i | 0.284133 | + | 0.874472i | ||||
\(197\) | 3974.94 | − | 1291.54i | 1.43758 | − | 0.467098i | 0.516437 | − | 0.856325i | \(-0.327258\pi\) |
0.921142 | + | 0.389228i | \(0.127258\pi\) | |||||||
\(198\) | −136.983 | + | 188.541i | −0.0491665 | + | 0.0676718i | ||||
\(199\) | 1052.08 | 0.374772 | 0.187386 | − | 0.982286i | \(-0.439998\pi\) | ||||
0.187386 | + | 0.982286i | \(0.439998\pi\) | |||||||
\(200\) | 994.281 | + | 106.799i | 0.351531 | + | 0.0377593i | ||||
\(201\) | 1029.49 | 0.361265 | ||||||||
\(202\) | −359.459 | + | 494.753i | −0.125205 | + | 0.172330i | ||||
\(203\) | 2283.71 | − | 742.023i | 0.789583 | − | 0.256551i | ||||
\(204\) | 157.544 | + | 484.870i | 0.0540700 | + | 0.166410i | ||||
\(205\) | −2290.68 | − | 2549.91i | −0.780430 | − | 0.868749i | ||||
\(206\) | −219.590 | + | 675.828i | −0.0742697 | + | 0.228579i | ||||
\(207\) | 1452.36i | 0.487663i | ||||||||
\(208\) | −649.368 | − | 210.992i | −0.216469 | − | 0.0703350i | ||||
\(209\) | 620.693 | − | 450.960i | 0.205427 | − | 0.149251i | ||||
\(210\) | 638.790 | − | 2988.48i | 0.209908 | − | 0.982024i | ||||
\(211\) | 1074.58 | + | 780.728i | 0.350602 | + | 0.254727i | 0.749122 | − | 0.662432i | \(-0.230476\pi\) |
−0.398519 | + | 0.917160i | \(0.630476\pi\) | |||||||
\(212\) | −1065.02 | − | 1465.87i | −0.345026 | − | 0.474888i | ||||
\(213\) | −1388.42 | − | 1910.99i | −0.446633 | − | 0.614737i | ||||
\(214\) | −411.267 | − | 298.803i | −0.131372 | − | 0.0954474i | ||||
\(215\) | −5609.07 | + | 583.062i | −1.77924 | + | 0.184951i | ||||
\(216\) | −986.959 | + | 717.067i | −0.310898 | + | 0.225881i | ||||
\(217\) | 7718.77 | + | 2507.98i | 2.41468 | + | 0.784576i | ||||
\(218\) | − | 1788.90i | − | 0.555778i | ||||||
\(219\) | 1415.66 | − | 4356.97i | 0.436812 | − | 1.34437i | ||||
\(220\) | −651.793 | − | 139.321i | −0.199745 | − | 0.0426955i | ||||
\(221\) | 383.764 | + | 1181.10i | 0.116809 | + | 0.359501i | ||||
\(222\) | −1002.90 | + | 325.862i | −0.303200 | + | 0.0985155i | ||||
\(223\) | −2625.59 | + | 3613.82i | −0.788442 | + | 1.08520i | 0.205858 | + | 0.978582i | \(0.434001\pi\) |
−0.994300 | + | 0.106616i | \(0.965999\pi\) | |||||||
\(224\) | 998.564 | 0.297854 | ||||||||
\(225\) | 655.605 | − | 724.787i | 0.194253 | − | 0.214752i | ||||
\(226\) | 2673.48 | 0.786891 | ||||||||
\(227\) | 1085.71 | − | 1494.35i | 0.317449 | − | 0.436931i | −0.620237 | − | 0.784414i | \(-0.712964\pi\) |
0.937686 | + | 0.347483i | \(0.112964\pi\) | |||||||
\(228\) | 857.692 | − | 278.681i | 0.249132 | − | 0.0809478i | ||||
\(229\) | 80.0296 | + | 246.306i | 0.0230939 | + | 0.0710757i | 0.961939 | − | 0.273263i | \(-0.0881030\pi\) |
−0.938845 | + | 0.344339i | \(0.888103\pi\) | |||||||
\(230\) | −3796.54 | + | 1685.14i | −1.08842 | + | 0.483108i | ||||
\(231\) | −629.427 | + | 1937.18i | −0.179278 | + | 0.551762i | ||||
\(232\) | − | 615.601i | − | 0.174208i | ||||||
\(233\) | −3222.33 | − | 1047.00i | −0.906018 | − | 0.294383i | −0.181299 | − | 0.983428i | \(-0.558030\pi\) |
−0.724719 | + | 0.689045i | \(0.758030\pi\) | |||||||
\(234\) | −539.852 | + | 392.225i | −0.150817 | + | 0.109575i | ||||
\(235\) | 890.994 | + | 2007.37i | 0.247328 | + | 0.557219i | ||||
\(236\) | −207.862 | − | 151.021i | −0.0573333 | − | 0.0416551i | ||||
\(237\) | 909.343 | + | 1251.60i | 0.249233 | + | 0.343040i | ||||
\(238\) | −1067.56 | − | 1469.37i | −0.290755 | − | 0.400189i | ||||
\(239\) | 2332.67 | + | 1694.79i | 0.631330 | + | 0.458688i | 0.856861 | − | 0.515548i | \(-0.172411\pi\) |
−0.225530 | + | 0.974236i | \(0.572411\pi\) | |||||||
\(240\) | −678.048 | − | 392.504i | −0.182366 | − | 0.105567i | ||||
\(241\) | 5114.13 | − | 3715.63i | 1.36693 | − | 0.993133i | 0.368960 | − | 0.929445i | \(-0.379714\pi\) |
0.997970 | − | 0.0636877i | \(-0.0202861\pi\) | |||||||
\(242\) | −2109.21 | − | 685.324i | −0.560270 | − | 0.182043i | ||||
\(243\) | 2116.81i | 0.558821i | ||||||||
\(244\) | 168.929 | − | 519.910i | 0.0443220 | − | 0.136409i | ||||
\(245\) | 729.136 | + | 7014.31i | 0.190134 | + | 1.82909i | ||||
\(246\) | 829.859 | + | 2554.04i | 0.215081 | + | 0.661951i | ||||
\(247\) | 2089.27 | − | 678.844i | 0.538206 | − | 0.174874i | ||||
\(248\) | 1223.00 | − | 1683.31i | 0.313146 | − | 0.431009i | ||||
\(249\) | −4277.84 | −1.08874 | ||||||||
\(250\) | 2655.31 | + | 872.830i | 0.671746 | + | 0.220811i | ||||
\(251\) | 1232.70 | 0.309990 | 0.154995 | − | 0.987915i | \(-0.450464\pi\) | ||||
0.154995 | + | 0.987915i | \(0.450464\pi\) | |||||||
\(252\) | 573.623 | − | 789.525i | 0.143392 | − | 0.197363i | ||||
\(253\) | 2633.02 | − | 855.522i | 0.654296 | − | 0.212594i | ||||
\(254\) | 936.935 | + | 2883.59i | 0.231451 | + | 0.712332i | ||||
\(255\) | 147.334 | + | 1417.36i | 0.0361821 | + | 0.348073i | ||||
\(256\) | 79.1084 | − | 243.470i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | 6483.90i | 1.57375i | 0.617110 | + | 0.786877i | \(0.288303\pi\) | ||||
−0.617110 | + | 0.786877i | \(0.711697\pi\) | |||||||
\(258\) | 4201.92 | + | 1365.29i | 1.01395 | + | 0.329454i | ||||
\(259\) | 3039.23 | − | 2208.13i | 0.729145 | − | 0.529755i | ||||
\(260\) | −1651.67 | − | 956.109i | −0.393970 | − | 0.228059i | ||||
\(261\) | −486.731 | − | 353.631i | −0.115433 | − | 0.0838667i | ||||
\(262\) | 1466.93 | + | 2019.06i | 0.345907 | + | 0.476100i | ||||
\(263\) | −469.694 | − | 646.478i | −0.110124 | − | 0.151572i | 0.750398 | − | 0.660987i | \(-0.229862\pi\) |
−0.860521 | + | 0.509414i | \(0.829862\pi\) | |||||||
\(264\) | 422.459 | + | 306.935i | 0.0984870 | + | 0.0715550i | ||||
\(265\) | −2054.61 | − | 4628.95i | −0.476279 | − | 1.07304i | ||||
\(266\) | −2599.18 | + | 1888.42i | −0.599121 | + | 0.435287i | ||||
\(267\) | −4588.02 | − | 1490.74i | −1.05162 | − | 0.341692i | ||||
\(268\) | 940.240i | 0.214307i | ||||||||
\(269\) | −1260.60 | + | 3879.74i | −0.285727 | + | 0.879376i | 0.700453 | + | 0.713698i | \(0.252981\pi\) |
−0.986180 | + | 0.165678i | \(0.947019\pi\) | |||||||
\(270\) | −3116.64 | + | 1383.36i | −0.702492 | + | 0.311809i | ||||
\(271\) | 135.829 | + | 418.040i | 0.0304467 | + | 0.0937052i | 0.965125 | − | 0.261789i | \(-0.0843125\pi\) |
−0.934678 | + | 0.355494i | \(0.884313\pi\) | |||||||
\(272\) | −442.837 | + | 143.886i | −0.0987167 | + | 0.0320750i | ||||
\(273\) | −3428.08 | + | 4718.34i | −0.759987 | + | 1.04603i | ||||
\(274\) | −4780.86 | −1.05410 | ||||||||
\(275\) | −1700.17 | − | 761.623i | −0.372816 | − | 0.167009i | ||||
\(276\) | 3254.28 | 0.709726 | ||||||||
\(277\) | 37.7190 | − | 51.9157i | 0.00818164 | − | 0.0112611i | −0.804907 | − | 0.593402i | \(-0.797785\pi\) |
0.813088 | + | 0.582140i | \(0.197785\pi\) | |||||||
\(278\) | 3346.47 | − | 1087.34i | 0.721972 | − | 0.234583i | ||||
\(279\) | −628.378 | − | 1933.95i | −0.134839 | − | 0.414991i | ||||
\(280\) | 2729.41 | + | 583.413i | 0.582549 | + | 0.124520i | ||||
\(281\) | −552.262 | + | 1699.69i | −0.117243 | + | 0.360836i | −0.992408 | − | 0.122988i | \(-0.960752\pi\) |
0.875166 | + | 0.483824i | \(0.160752\pi\) | |||||||
\(282\) | − | 1720.65i | − | 0.363345i | ||||||
\(283\) | −5937.78 | − | 1929.30i | −1.24722 | − | 0.405248i | −0.390299 | − | 0.920688i | \(-0.627628\pi\) |
−0.856926 | + | 0.515440i | \(0.827628\pi\) | |||||||
\(284\) | 1745.33 | − | 1268.06i | 0.364670 | − | 0.264948i | ||||
\(285\) | 2507.18 | − | 260.621i | 0.521097 | − | 0.0541680i | ||||
\(286\) | 1029.08 | + | 747.668i | 0.212764 | + | 0.154582i | ||||
\(287\) | −5623.35 | − | 7739.87i | −1.15657 | − | 1.59188i | ||||
\(288\) | −147.059 | − | 202.409i | −0.0300886 | − | 0.0414134i | ||||
\(289\) | −3289.54 | − | 2389.99i | −0.669558 | − | 0.486462i | ||||
\(290\) | 359.667 | − | 1682.65i | 0.0728288 | − | 0.340719i | ||||
\(291\) | 5140.44 | − | 3734.75i | 1.03553 | − | 0.752354i | ||||
\(292\) | 3979.26 | + | 1292.94i | 0.797496 | + | 0.259122i | ||||
\(293\) | − | 2442.29i | − | 0.486963i | −0.969905 | − | 0.243482i | \(-0.921710\pi\) | ||
0.969905 | − | 0.243482i | \(-0.0782896\pi\) | |||||||
\(294\) | 1707.33 | − | 5254.62i | 0.338685 | − | 1.04237i | ||||
\(295\) | −479.924 | − | 534.235i | −0.0947194 | − | 0.105438i | ||||
\(296\) | −297.614 | − | 915.960i | −0.0584407 | − | 0.179862i | ||||
\(297\) | 2161.49 | − | 702.311i | 0.422298 | − | 0.137213i | ||||
\(298\) | −460.381 | + | 633.660i | −0.0894937 | + | 0.123178i | ||||
\(299\) | 7927.15 | 1.53324 | ||||||||
\(300\) | −1624.01 | − | 1469.00i | −0.312542 | − | 0.282709i | ||||
\(301\) | −15739.7 | −3.01402 | ||||||||
\(302\) | 2277.59 | − | 3134.83i | 0.433975 | − | 0.597315i | ||||
\(303\) | 1273.65 | − | 413.832i | 0.241482 | − | 0.0784622i | ||||
\(304\) | 254.522 | + | 783.339i | 0.0480193 | + | 0.147788i | ||||
\(305\) | 765.499 | − | 1322.39i | 0.143713 | − | 0.248263i | ||||
\(306\) | −140.622 | + | 432.789i | −0.0262706 | + | 0.0808526i | ||||
\(307\) | − | 6382.66i | − | 1.18657i | −0.804992 | − | 0.593286i | \(-0.797830\pi\) | ||
0.804992 | − | 0.593286i | \(-0.202170\pi\) | |||||||
\(308\) | −1769.24 | − | 574.862i | −0.327312 | − | 0.106350i | ||||
\(309\) | 1258.92 | − | 914.661i | 0.231772 | − | 0.168392i | ||||
\(310\) | 4326.34 | − | 3886.52i | 0.792644 | − | 0.712063i | ||||
\(311\) | −2487.41 | − | 1807.21i | −0.453531 | − | 0.329510i | 0.337457 | − | 0.941341i | \(-0.390433\pi\) |
−0.790988 | + | 0.611831i | \(0.790433\pi\) | |||||||
\(312\) | 878.850 | + | 1209.63i | 0.159471 | + | 0.219494i | ||||
\(313\) | 3265.88 | + | 4495.09i | 0.589771 | + | 0.811750i | 0.994724 | − | 0.102587i | \(-0.0327122\pi\) |
−0.404953 | + | 0.914337i | \(0.632712\pi\) | |||||||
\(314\) | 2909.43 | + | 2113.82i | 0.522894 | + | 0.379904i | ||||
\(315\) | 2029.19 | − | 1822.90i | 0.362958 | − | 0.326059i | ||||
\(316\) | −1143.10 | + | 830.513i | −0.203495 | + | 0.147848i | ||||
\(317\) | −3164.57 | − | 1028.23i | −0.560693 | − | 0.182180i | 0.0149397 | − | 0.999888i | \(-0.495244\pi\) |
−0.575633 | + | 0.817708i | \(0.695244\pi\) | |||||||
\(318\) | 3967.79i | 0.699694i | ||||||||
\(319\) | −354.395 | + | 1090.72i | −0.0622016 | + | 0.191437i | ||||
\(320\) | 358.478 | − | 619.268i | 0.0626236 | − | 0.108182i | ||||
\(321\) | 344.001 | + | 1058.73i | 0.0598140 | + | 0.184088i | ||||
\(322\) | −11025.9 | + | 3582.54i | −1.90823 | + | 0.620022i | ||||
\(323\) | 880.562 | − | 1211.99i | 0.151690 | − | 0.208783i | ||||
\(324\) | 1827.09 | 0.313287 | ||||||||
\(325\) | −3955.97 | − | 3578.36i | −0.675193 | − | 0.610744i | ||||
\(326\) | 2668.26 | 0.453317 | ||||||||
\(327\) | −2302.59 | + | 3169.24i | −0.389399 | + | 0.535961i | ||||
\(328\) | −2332.63 | + | 757.919i | −0.392677 | + | 0.127589i | ||||
\(329\) | 1894.22 | + | 5829.80i | 0.317421 | + | 0.976923i | ||||
\(330\) | 975.398 | + | 1085.78i | 0.162709 | + | 0.181122i | ||||
\(331\) | −266.427 | + | 819.978i | −0.0442422 | + | 0.136163i | −0.970738 | − | 0.240143i | \(-0.922806\pi\) |
0.926495 | + | 0.376306i | \(0.122806\pi\) | |||||||
\(332\) | − | 3907.00i | − | 0.645857i | ||||||
\(333\) | −895.177 | − | 290.861i | −0.147313 | − | 0.0478651i | ||||
\(334\) | −2611.99 | + | 1897.73i | −0.427910 | + | 0.310895i | ||||
\(335\) | −549.337 | + | 2570.00i | −0.0895926 | + | 0.419146i | ||||
\(336\) | −1769.07 | − | 1285.30i | −0.287234 | − | 0.208688i | ||||
\(337\) | 3366.82 | + | 4634.03i | 0.544221 | + | 0.749056i | 0.989214 | − | 0.146478i | \(-0.0467939\pi\) |
−0.444993 | + | 0.895534i | \(0.646794\pi\) | |||||||
\(338\) | −441.921 | − | 608.253i | −0.0711164 | − | 0.0978834i | ||||
\(339\) | −4736.38 | − | 3441.18i | −0.758834 | − | 0.551325i | ||||
\(340\) | −1294.49 | + | 134.562i | −0.206481 | + | 0.0214637i | ||||
\(341\) | −3135.95 | + | 2278.40i | −0.498010 | + | 0.361826i | ||||
\(342\) | 765.565 | + | 248.747i | 0.121044 | + | 0.0393295i | ||||
\(343\) | 8979.56i | 1.41356i | ||||||||
\(344\) | −1246.93 | + | 3837.66i | −0.195436 | + | 0.601490i | ||||
\(345\) | 8895.04 | + | 1901.32i | 1.38810 | + | 0.296706i | ||||
\(346\) | −2041.19 | − | 6282.15i | −0.317154 | − | 0.976099i | ||||
\(347\) | −2202.29 | + | 715.567i | −0.340706 | + | 0.110702i | −0.474373 | − | 0.880324i | \(-0.657325\pi\) |
0.133666 | + | 0.991026i | \(0.457325\pi\) | |||||||
\(348\) | −792.373 | + | 1090.61i | −0.122056 | + | 0.167996i | ||||
\(349\) | 4454.14 | 0.683166 | 0.341583 | − | 0.939852i | \(-0.389037\pi\) | ||||
0.341583 | + | 0.939852i | \(0.389037\pi\) | |||||||
\(350\) | 7119.56 | + | 3189.33i | 1.08730 | + | 0.487077i | ||||
\(351\) | 6507.52 | 0.989589 | ||||||||
\(352\) | −280.327 | + | 385.837i | −0.0424473 | + | 0.0584238i | ||||
\(353\) | 7220.26 | − | 2346.00i | 1.08866 | − | 0.353726i | 0.290929 | − | 0.956745i | \(-0.406036\pi\) |
0.797727 | + | 0.603019i | \(0.206036\pi\) | |||||||
\(354\) | 173.865 | + | 535.101i | 0.0261040 | + | 0.0803398i | ||||
\(355\) | 5511.44 | − | 2446.31i | 0.823991 | − | 0.365738i | ||||
\(356\) | 1361.51 | − | 4190.29i | 0.202696 | − | 0.623834i | ||||
\(357\) | 3977.27i | 0.589634i | ||||||||
\(358\) | −5262.43 | − | 1709.87i | −0.776894 | − | 0.252428i | ||||
\(359\) | −7535.11 | + | 5474.58i | −1.10777 | + | 0.804839i | −0.982310 | − | 0.187261i | \(-0.940039\pi\) |
−0.125455 | + | 0.992099i | \(0.540039\pi\) | |||||||
\(360\) | −283.704 | − | 639.172i | −0.0415347 | − | 0.0935759i | ||||
\(361\) | 3405.15 | + | 2473.98i | 0.496450 | + | 0.360692i | ||||
\(362\) | 3842.11 | + | 5288.21i | 0.557836 | + | 0.767796i | ||||
\(363\) | 2854.59 | + | 3929.01i | 0.412747 | + | 0.568098i | ||||
\(364\) | −4309.31 | − | 3130.90i | −0.620520 | − | 0.450834i | ||||
\(365\) | 10121.3 | + | 5858.94i | 1.45143 | + | 0.840195i | ||||
\(366\) | −968.481 | + | 703.643i | −0.138315 | + | 0.100492i | ||||
\(367\) | −7331.03 | − | 2382.00i | −1.04272 | − | 0.338799i | −0.262910 | − | 0.964820i | \(-0.584682\pi\) |
−0.779806 | + | 0.626022i | \(0.784682\pi\) | |||||||
\(368\) | 2972.16i | 0.421018i | ||||||||
\(369\) | −740.722 | + | 2279.71i | −0.104500 | + | 0.321617i | ||||
\(370\) | −278.327 | − | 2677.51i | −0.0391068 | − | 0.376209i | ||||
\(371\) | −4368.03 | − | 13443.4i | −0.611258 | − | 1.88126i | ||||
\(372\) | −4333.35 | + | 1407.99i | −0.603962 | + | 0.196239i | ||||
\(373\) | 5249.03 | − | 7224.67i | 0.728644 | − | 1.00289i | −0.270548 | − | 0.962707i | \(-0.587205\pi\) |
0.999192 | − | 0.0401863i | \(-0.0127951\pi\) | |||||||
\(374\) | 867.448 | 0.119932 | ||||||||
\(375\) | −3580.72 | − | 4964.11i | −0.493087 | − | 0.683588i | ||||
\(376\) | 1571.49 | 0.215541 | ||||||||
\(377\) | −1930.16 | + | 2656.63i | −0.263682 | + | 0.362927i | ||||
\(378\) | −9051.35 | + | 2940.96i | −1.23162 | + | 0.400177i | ||||
\(379\) | 1311.50 | + | 4036.39i | 0.177750 | + | 0.547059i | 0.999748 | − | 0.0224313i | \(-0.00714069\pi\) |
−0.821998 | + | 0.569490i | \(0.807141\pi\) | |||||||
\(380\) | 238.028 | + | 2289.84i | 0.0321331 | + | 0.309122i | ||||
\(381\) | 2051.73 | − | 6314.59i | 0.275888 | − | 0.849097i | ||||
\(382\) | 709.377i | 0.0950127i | ||||||||
\(383\) | 5191.55 | + | 1686.84i | 0.692626 | + | 0.225048i | 0.634115 | − | 0.773239i | \(-0.281365\pi\) |
0.0585112 | + | 0.998287i | \(0.481365\pi\) | |||||||
\(384\) | −453.533 | + | 329.511i | −0.0602715 | + | 0.0437898i | ||||
\(385\) | −4500.08 | − | 2604.98i | −0.595703 | − | 0.344837i | ||||
\(386\) | −4704.95 | − | 3418.35i | −0.620403 | − | 0.450749i | ||||
\(387\) | 2317.99 | + | 3190.43i | 0.304470 | + | 0.419067i | ||||
\(388\) | 3410.99 | + | 4694.82i | 0.446306 | + | 0.614287i | ||||
\(389\) | 10460.1 | + | 7599.69i | 1.36336 | + | 0.990538i | 0.998223 | + | 0.0595840i | \(0.0189774\pi\) |
0.365136 | + | 0.930954i | \(0.381023\pi\) | |||||||
\(390\) | 1695.46 | + | 3819.81i | 0.220136 | + | 0.495958i | ||||
\(391\) | 4373.49 | − | 3177.53i | 0.565670 | − | 0.410983i | ||||
\(392\) | 4799.10 | + | 1559.32i | 0.618345 | + | 0.200912i | ||||
\(393\) | − | 5465.17i | − | 0.701479i | ||||||
\(394\) | 2583.07 | − | 7949.89i | 0.330288 | − | 1.01652i | ||||
\(395\) | −3609.72 | + | 1602.21i | −0.459809 | + | 0.204091i | ||||
\(396\) | 144.032 | + | 443.286i | 0.0182775 | + | 0.0562525i | ||||
\(397\) | −1933.04 | + | 628.083i | −0.244374 | + | 0.0794020i | −0.428643 | − | 0.903474i | \(-0.641008\pi\) |
0.184269 | + | 0.982876i | \(0.441008\pi\) | |||||||
\(398\) | 1236.79 | − | 1702.29i | 0.155765 | − | 0.214393i | ||||
\(399\) | 7035.43 | 0.882737 | ||||||||
\(400\) | 1341.65 | − | 1483.23i | 0.167707 | − | 0.185404i | ||||
\(401\) | −8972.43 | −1.11736 | −0.558681 | − | 0.829383i | \(-0.688692\pi\) | ||||
−0.558681 | + | 0.829383i | \(0.688692\pi\) | |||||||
\(402\) | 1210.23 | − | 1665.74i | 0.150152 | − | 0.206666i | ||||
\(403\) | −10555.7 | + | 3429.75i | −1.30476 | + | 0.423941i | ||||
\(404\) | 377.958 | + | 1163.23i | 0.0465448 | + | 0.143250i | ||||
\(405\) | 4994.06 | + | 1067.48i | 0.612733 | + | 0.130972i | ||||
\(406\) | 1484.05 | − | 4567.43i | 0.181409 | − | 0.558319i | ||||
\(407\) | 1794.22i | 0.218517i | ||||||||
\(408\) | 969.740 | + | 315.088i | 0.117670 | + | 0.0382332i | ||||
\(409\) | −7002.65 | + | 5087.72i | −0.846599 | + | 0.615090i | −0.924206 | − | 0.381894i | \(-0.875272\pi\) |
0.0776075 | + | 0.996984i | \(0.475272\pi\) | |||||||
\(410\) | −6818.70 | + | 708.803i | −0.821345 | + | 0.0853787i | ||||
\(411\) | 8469.85 | + | 6153.71i | 1.01651 | + | 0.738540i | ||||
\(412\) | 835.370 | + | 1149.79i | 0.0998925 | + | 0.137490i | ||||
\(413\) | −1178.15 | − | 1621.59i | −0.140371 | − | 0.193204i | ||||
\(414\) | 2349.97 | + | 1707.35i | 0.278973 | + | 0.202686i | ||||
\(415\) | 2282.67 | − | 10679.2i | 0.270005 | − | 1.26318i | ||||
\(416\) | −1104.77 | + | 802.663i | −0.130206 | + | 0.0946004i | ||||
\(417\) | −7328.23 | − | 2381.09i | −0.860587 | − | 0.279622i | ||||
\(418\) | − | 1534.44i | − | 0.179550i | ||||||
\(419\) | 1774.40 | − | 5461.04i | 0.206886 | − | 0.636729i | −0.792745 | − | 0.609554i | \(-0.791349\pi\) |
0.999631 | − | 0.0271754i | \(-0.00865126\pi\) | |||||||
\(420\) | −4084.53 | − | 4546.76i | −0.474535 | − | 0.528236i | ||||
\(421\) | 1139.25 | + | 3506.25i | 0.131885 | + | 0.405901i | 0.995093 | − | 0.0989486i | \(-0.0315479\pi\) |
−0.863207 | + | 0.504850i | \(0.831548\pi\) | |||||||
\(422\) | 2526.49 | − | 820.905i | 0.291440 | − | 0.0946944i | ||||
\(423\) | 902.740 | − | 1242.52i | 0.103765 | − | 0.142821i | ||||
\(424\) | −3623.83 | −0.415067 | ||||||||
\(425\) | −3616.90 | − | 388.505i | −0.412813 | − | 0.0443418i | ||||
\(426\) | −4724.23 | −0.537300 | ||||||||
\(427\) | 2506.72 | − | 3450.21i | 0.284096 | − | 0.391024i | ||||
\(428\) | −966.947 | + | 314.180i | −0.109204 | + | 0.0354824i | ||||
\(429\) | −860.764 | − | 2649.16i | −0.0968720 | − | 0.298141i | ||||
\(430\) | −5650.45 | + | 9761.10i | −0.633695 | + | 1.09470i | ||||
\(431\) | −2973.01 | + | 9149.99i | −0.332262 | + | 1.02260i | 0.635793 | + | 0.771859i | \(0.280673\pi\) |
−0.968055 | + | 0.250738i | \(0.919327\pi\) | |||||||
\(432\) | 2439.90i | 0.271735i | ||||||||
\(433\) | −1505.50 | − | 489.167i | −0.167090 | − | 0.0542907i | 0.224278 | − | 0.974525i | \(-0.427998\pi\) |
−0.391367 | + | 0.920235i | \(0.627998\pi\) | |||||||
\(434\) | 13132.0 | − | 9540.93i | 1.45243 | − | 1.05525i | ||||
\(435\) | −2803.02 | + | 2518.06i | −0.308952 | + | 0.277544i | ||||
\(436\) | −2894.50 | − | 2102.98i | −0.317939 | − | 0.230996i | ||||
\(437\) | −5620.76 | − | 7736.31i | −0.615280 | − | 0.846860i | ||||
\(438\) | −5385.51 | − | 7412.52i | −0.587510 | − | 0.808639i | ||||
\(439\) | 1345.66 | + | 977.681i | 0.146298 | + | 0.106292i | 0.658527 | − | 0.752557i | \(-0.271180\pi\) |
−0.512229 | + | 0.858849i | \(0.671180\pi\) | |||||||
\(440\) | −991.654 | + | 890.841i | −0.107444 | + | 0.0965209i | ||||
\(441\) | 3989.73 | − | 2898.71i | 0.430810 | − | 0.313002i | ||||
\(442\) | 2362.21 | + | 767.528i | 0.254205 | + | 0.0825964i | ||||
\(443\) | 6466.22i | 0.693497i | 0.937958 | + | 0.346748i | \(0.112714\pi\) | ||||
−0.937958 | + | 0.346748i | \(0.887286\pi\) | |||||||
\(444\) | −651.725 | + | 2005.80i | −0.0696610 | + | 0.214395i | ||||
\(445\) | 6169.65 | − | 10658.0i | 0.657234 | − | 1.13537i | ||||
\(446\) | 2760.71 | + | 8496.59i | 0.293102 | + | 0.902075i | ||||
\(447\) | 1631.23 | − | 530.020i | 0.172606 | − | 0.0560830i | ||||
\(448\) | 1173.88 | − | 1615.71i | 0.123796 | − | 0.170391i | ||||
\(449\) | −5559.14 | −0.584303 | −0.292151 | − | 0.956372i | \(-0.594371\pi\) | ||||
−0.292151 | + | 0.956372i | \(0.594371\pi\) | |||||||
\(450\) | −402.021 | − | 1912.83i | −0.0421143 | − | 0.200381i | ||||
\(451\) | 4569.26 | 0.477069 | ||||||||
\(452\) | 3142.87 | − | 4325.78i | 0.327053 | − | 0.450150i | ||||
\(453\) | −8070.01 | + | 2622.11i | −0.837002 | + | 0.271959i | ||||
\(454\) | −1141.58 | − | 3513.42i | −0.118011 | − | 0.363201i | ||||
\(455\) | −9949.58 | − | 11075.5i | −1.02515 | − | 1.14116i | ||||
\(456\) | 557.362 | − | 1715.38i | 0.0572387 | − | 0.176163i | ||||
\(457\) | − | 1317.36i | − | 0.134843i | −0.997725 | − | 0.0674216i | \(-0.978523\pi\) | ||
0.997725 | − | 0.0674216i | \(-0.0214773\pi\) | |||||||
\(458\) | 492.611 | + | 160.059i | 0.0502581 | + | 0.0163299i | ||||
\(459\) | 3590.27 | − | 2608.48i | 0.365096 | − | 0.265258i | ||||
\(460\) | −1736.49 | + | 8123.94i | −0.176010 | + | 0.823436i | ||||
\(461\) | 6845.97 | + | 4973.89i | 0.691646 | + | 0.502510i | 0.877201 | − | 0.480124i | \(-0.159408\pi\) |
−0.185555 | + | 0.982634i | \(0.559408\pi\) | |||||||
\(462\) | 2394.48 | + | 3295.72i | 0.241129 | + | 0.331885i | ||||
\(463\) | −7458.64 | − | 10265.9i | −0.748666 | − | 1.03045i | −0.998073 | − | 0.0620519i | \(-0.980236\pi\) |
0.249407 | − | 0.968399i | \(-0.419764\pi\) | |||||||
\(464\) | −996.064 | − | 723.683i | −0.0996575 | − | 0.0724054i | ||||
\(465\) | −12667.2 | + | 1316.75i | −1.26328 | + | 0.131318i | ||||
\(466\) | −5482.16 | + | 3983.02i | −0.544971 | + | 0.395944i | ||||
\(467\) | 781.175 | + | 253.819i | 0.0774057 | + | 0.0251506i | 0.347464 | − | 0.937693i | \(-0.387043\pi\) |
−0.270058 | + | 0.962844i | \(0.587043\pi\) | |||||||
\(468\) | 1334.59i | 0.131819i | ||||||||
\(469\) | −2266.66 | + | 6976.07i | −0.223166 | + | 0.686834i | ||||
\(470\) | 4295.42 | + | 918.147i | 0.421559 | + | 0.0901085i | ||||
\(471\) | −2433.57 | − | 7489.76i | −0.238074 | − | 0.732718i | ||||
\(472\) | −488.713 | + | 158.792i | −0.0476586 | + | 0.0154852i | ||||
\(473\) | 4418.60 | − | 6081.68i | 0.429529 | − | 0.591196i | ||||
\(474\) | 3094.13 | 0.299828 | ||||||||
\(475\) | −687.231 | + | 6397.97i | −0.0663838 | + | 0.618019i | ||||
\(476\) | −3632.48 | −0.349778 | ||||||||
\(477\) | −2081.70 | + | 2865.21i | −0.199821 | + | 0.275030i | ||||
\(478\) | 5484.44 | − | 1782.00i | 0.524796 | − | 0.170517i | ||||
\(479\) | −3405.28 | − | 10480.4i | −0.324825 | − | 0.999710i | −0.971519 | − | 0.236960i | \(-0.923849\pi\) |
0.646694 | − | 0.762750i | \(-0.276151\pi\) | |||||||
\(480\) | −1432.18 | + | 635.688i | −0.136187 | + | 0.0604481i | ||||
\(481\) | −1587.55 | + | 4885.97i | −0.150491 | + | 0.463163i | ||||
\(482\) | − | 12642.8i | − | 1.19474i | ||||||
\(483\) | 24145.0 | + | 7845.17i | 2.27460 | + | 0.739064i | ||||
\(484\) | −3588.40 | + | 2607.13i | −0.337003 | + | 0.244847i | ||||
\(485\) | 6580.43 | + | 14825.4i | 0.616086 | + | 1.38802i | ||||
\(486\) | 3425.07 | + | 2488.46i | 0.319680 | + | 0.232261i | ||||
\(487\) | −4616.73 | − | 6354.39i | −0.429577 | − | 0.591262i | 0.538279 | − | 0.842767i | \(-0.319075\pi\) |
−0.967856 | + | 0.251504i | \(0.919075\pi\) | |||||||
\(488\) | −642.644 | − | 884.524i | −0.0596130 | − | 0.0820503i | ||||
\(489\) | −4727.13 | − | 3434.46i | −0.437154 | − | 0.317611i | ||||
\(490\) | 12206.5 | + | 7066.04i | 1.12538 | + | 0.651452i | ||||
\(491\) | −16604.1 | + | 12063.6i | −1.52614 | + | 1.10881i | −0.567803 | + | 0.823164i | \(0.692206\pi\) |
−0.958337 | + | 0.285641i | \(0.907794\pi\) | |||||||
\(492\) | 5108.09 | + | 1659.72i | 0.468070 | + | 0.152085i | ||||
\(493\) | 2239.38i | 0.204577i | ||||||||
\(494\) | 1357.69 | − | 4178.54i | 0.123654 | − | 0.380569i | ||||
\(495\) | 134.699 | + | 1295.80i | 0.0122308 | + | 0.117661i | ||||
\(496\) | −1285.93 | − | 3957.70i | −0.116412 | − | 0.358278i | ||||
\(497\) | 16006.3 | − | 5200.77i | 1.44463 | − | 0.469389i | ||||
\(498\) | −5028.91 | + | 6921.70i | −0.452511 | + | 0.622829i | ||||
\(499\) | −20672.7 | −1.85458 | −0.927291 | − | 0.374341i | \(-0.877869\pi\) | ||||
−0.927291 | + | 0.374341i | \(0.877869\pi\) | |||||||
\(500\) | 4533.77 | − | 3270.31i | 0.405513 | − | 0.292505i | ||||
\(501\) | 7070.11 | 0.630477 | ||||||||
\(502\) | 1449.13 | − | 1994.55i | 0.128840 | − | 0.177333i | ||||
\(503\) | 3087.72 | − | 1003.26i | 0.273707 | − | 0.0889329i | −0.168947 | − | 0.985625i | \(-0.554037\pi\) |
0.442655 | + | 0.896692i | \(0.354037\pi\) | |||||||
\(504\) | −603.143 | − | 1856.28i | −0.0533058 | − | 0.164058i | ||||
\(505\) | 353.464 | + | 3400.34i | 0.0311465 | + | 0.299630i | ||||
\(506\) | 1711.04 | − | 5266.05i | 0.150326 | − | 0.462657i | ||||
\(507\) | 1646.41i | 0.144220i | ||||||||
\(508\) | 5767.18 | + | 1873.87i | 0.503695 | + | 0.163660i | ||||
\(509\) | 43.4872 | − | 31.5953i | 0.00378691 | − | 0.00275135i | −0.585890 | − | 0.810390i | \(-0.699255\pi\) |
0.589677 | + | 0.807639i | \(0.299255\pi\) | |||||||
\(510\) | 2466.54 | + | 1427.81i | 0.214157 | + | 0.123970i | ||||
\(511\) | 26407.1 | + | 19185.8i | 2.28606 | + | 1.66092i | ||||
\(512\) | −300.946 | − | 414.217i | −0.0259767 | − | 0.0357538i | ||||
\(513\) | −4614.17 | − | 6350.86i | −0.397116 | − | 0.546583i | ||||
\(514\) | 10491.2 | + | 7622.28i | 0.900284 | + | 0.654094i | ||||
\(515\) | 1611.58 | + | 3630.83i | 0.137893 | + | 0.310667i | ||||
\(516\) | 7148.73 | − | 5193.86i | 0.609894 | − | 0.443114i | ||||
\(517\) | −2784.35 | − | 904.691i | −0.236858 | − | 0.0769599i | ||||
\(518\) | − | 7513.39i | − | 0.637296i | ||||||
\(519\) | −4469.88 | + | 13756.9i | −0.378046 | + | 1.16351i | ||||
\(520\) | −3488.67 | + | 1548.49i | −0.294208 | + | 0.130588i | ||||
\(521\) | 1555.45 | + | 4787.17i | 0.130797 | + | 0.402553i | 0.994913 | − | 0.100741i | \(-0.0321214\pi\) |
−0.864115 | + | 0.503294i | \(0.832121\pi\) | |||||||
\(522\) | −1144.37 | + | 371.830i | −0.0959538 | + | 0.0311773i | ||||
\(523\) | −3493.99 | + | 4809.07i | −0.292126 | + | 0.402076i | −0.929703 | − | 0.368310i | \(-0.879937\pi\) |
0.637577 | + | 0.770386i | \(0.279937\pi\) | |||||||
\(524\) | 4991.40 | 0.416126 | ||||||||
\(525\) | −8507.95 | − | 14814.2i | −0.707271 | − | 1.23152i | ||||
\(526\) | −1598.18 | −0.132479 | ||||||||
\(527\) | −4448.90 | + | 6123.38i | −0.367736 | + | 0.506146i | ||||
\(528\) | 993.262 | − | 322.730i | 0.0818677 | − | 0.0266004i | ||||
\(529\) | −6903.40 | − | 21246.5i | −0.567387 | − | 1.74624i | ||||
\(530\) | −9905.15 | − | 2117.23i | −0.811796 | − | 0.173522i | ||||
\(531\) | −155.189 | + | 477.624i | −0.0126830 | + | 0.0390341i | ||||
\(532\) | 6425.53i | 0.523651i | ||||||||
\(533\) | 12442.9 | + | 4042.94i | 1.01118 | + | 0.328554i | ||||
\(534\) | −7805.61 | + | 5671.10i | −0.632550 | + | 0.459574i | ||||
\(535\) | −2826.55 | + | 293.820i | −0.228416 | + | 0.0237438i | ||||
\(536\) | 1521.34 | + | 1105.32i | 0.122597 | + | 0.0890718i | ||||
\(537\) | 7122.13 | + | 9802.77i | 0.572333 | + | 0.787748i | ||||
\(538\) | 4795.63 | + | 6600.61i | 0.384301 | + | 0.528945i | ||||
\(539\) | −7605.31 | − | 5525.58i | −0.607762 | − | 0.441565i | ||||
\(540\) | −1425.52 | + | 6669.07i | −0.113601 | + | 0.531465i | ||||
\(541\) | −16453.2 | + | 11953.9i | −1.30754 | + | 0.949982i | −0.999999 | − | 0.00155356i | \(-0.999505\pi\) |
−0.307539 | + | 0.951535i | \(0.599505\pi\) | |||||||
\(542\) | 836.080 | + | 271.659i | 0.0662596 | + | 0.0215290i | ||||
\(543\) | − | 14314.0i | − | 1.13126i | ||||||
\(544\) | −287.773 | + | 885.674i | −0.0226804 | + | 0.0698032i | ||||
\(545\) | −6682.98 | − | 7439.27i | −0.525262 | − | 0.584703i | ||||
\(546\) | 3604.49 | + | 11093.5i | 0.282524 | + | 0.869519i | ||||
\(547\) | 17348.4 | − | 5636.82i | 1.35606 | − | 0.440609i | 0.461331 | − | 0.887228i | \(-0.347372\pi\) |
0.894724 | + | 0.446619i | \(0.147372\pi\) | |||||||
\(548\) | −5620.24 | + | 7735.60i | −0.438111 | + | 0.603008i | ||||
\(549\) | −1068.52 | −0.0830665 | ||||||||
\(550\) | −3231.00 | + | 1855.60i | −0.250492 | + | 0.143860i | ||||
\(551\) | 3961.26 | 0.306271 | ||||||||
\(552\) | 3825.63 | − | 5265.53i | 0.294981 | − | 0.406007i | ||||
\(553\) | −10483.3 | + | 3406.24i | −0.806143 | + | 0.261932i | ||||
\(554\) | −39.6601 | − | 122.061i | −0.00304151 | − | 0.00936080i | ||||
\(555\) | −2953.28 | + | 5101.77i | −0.225873 | + | 0.390195i | ||||
\(556\) | 2174.67 | − | 6692.95i | 0.165875 | − | 0.510511i | ||||
\(557\) | 2617.19i | 0.199092i | 0.995033 | + | 0.0995458i | \(0.0317390\pi\) | ||||
−0.995033 | + | 0.0995458i | \(0.968261\pi\) | |||||||
\(558\) | −3867.90 | − | 1256.76i | −0.293443 | − | 0.0953454i | ||||
\(559\) | 17413.7 | − | 12651.8i | 1.31757 | − | 0.957272i | ||||
\(560\) | 4152.60 | − | 3730.44i | 0.313356 | − | 0.281500i | ||||
\(561\) | −1536.78 | − | 1116.54i | −0.115656 | − | 0.0840290i | ||||
\(562\) | 2100.93 | + | 2891.68i | 0.157691 | + | 0.217043i | ||||
\(563\) | −9201.70 | − | 12665.1i | −0.688820 | − | 0.948079i | 0.311178 | − | 0.950352i | \(-0.399277\pi\) |
−0.999997 | + | 0.00227286i | \(0.999277\pi\) | |||||||
\(564\) | −2784.08 | − | 2022.75i | −0.207856 | − | 0.151016i | ||||
\(565\) | 11117.9 | − | 9987.61i | 0.827845 | − | 0.743685i | ||||
\(566\) | −10102.0 | + | 7339.50i | −0.750207 | + | 0.545057i | ||||
\(567\) | 13556.0 | + | 4404.62i | 1.00405 | + | 0.326237i | ||||
\(568\) | − | 4314.69i | − | 0.318733i | ||||||
\(569\) | −2209.54 | + | 6800.27i | −0.162792 | + | 0.501023i | −0.998867 | − | 0.0475929i | \(-0.984845\pi\) |
0.836075 | + | 0.548616i | \(0.184845\pi\) | |||||||
\(570\) | 2525.68 | − | 4363.09i | 0.185595 | − | 0.320613i | ||||
\(571\) | 2342.24 | + | 7208.67i | 0.171663 | + | 0.528325i | 0.999465 | − | 0.0326951i | \(-0.0104090\pi\) |
−0.827802 | + | 0.561020i | \(0.810409\pi\) | |||||||
\(572\) | 2419.51 | − | 786.145i | 0.176861 | − | 0.0574657i | ||||
\(573\) | 913.076 | − | 1256.74i | 0.0665695 | − | 0.0916250i | ||||
\(574\) | −19134.0 | −1.39136 | ||||||||
\(575\) | −9492.86 | + | 21190.9i | −0.688486 | + | 1.53691i | ||||
\(576\) | −500.383 | −0.0361967 | ||||||||
\(577\) | 4557.21 | − | 6272.46i | 0.328803 | − | 0.452558i | −0.612327 | − | 0.790605i | \(-0.709766\pi\) |
0.941129 | + | 0.338047i | \(0.109766\pi\) | |||||||
\(578\) | −7734.17 | + | 2512.98i | −0.556573 | + | 0.180841i | ||||
\(579\) | 3935.42 | + | 12112.0i | 0.282471 | + | 0.869356i | ||||
\(580\) | −2299.77 | − | 2560.02i | −0.164643 | − | 0.183274i | ||||
\(581\) | 9418.71 | − | 28987.8i | 0.672554 | − | 2.06991i | ||||
\(582\) | − | 12707.9i | − | 0.905083i | ||||||
\(583\) | 6420.66 | + | 2086.20i | 0.456117 | + | 0.148202i | ||||
\(584\) | 6769.93 | − | 4918.64i | 0.479695 | − | 0.348519i | ||||
\(585\) | −779.735 | + | 3647.88i | −0.0551078 | + | 0.257814i | ||||
\(586\) | −3951.71 | − | 2871.09i | −0.278573 | − | 0.202395i | ||||
\(587\) | −5047.27 | − | 6946.97i | −0.354894 | − | 0.488470i | 0.593823 | − | 0.804596i | \(-0.297618\pi\) |
−0.948717 | + | 0.316126i | \(0.897618\pi\) | |||||||
\(588\) | −6495.07 | − | 8939.70i | −0.455531 | − | 0.626984i | ||||
\(589\) | 10831.7 | + | 7869.70i | 0.757747 | + | 0.550536i | ||||
\(590\) | −1428.59 | + | 148.502i | −0.0996852 | + | 0.0103623i | ||||
\(591\) | −14808.9 | + | 10759.3i | −1.03072 | + | 0.748865i | ||||
\(592\) | −1831.92 | − | 595.227i | −0.127182 | − | 0.0413238i | ||||
\(593\) | − | 7557.43i | − | 0.523350i | −0.965156 | − | 0.261675i | \(-0.915725\pi\) | ||
0.965156 | − | 0.261675i | \(-0.0842748\pi\) | |||||||
\(594\) | 1404.62 | − | 4322.98i | 0.0970241 | − | 0.298610i | ||||
\(595\) | −9928.81 | − | 2122.29i | −0.684103 | − | 0.146227i | ||||
\(596\) | 484.073 | + | 1489.82i | 0.0332691 | + | 0.102392i | ||||
\(597\) | −4382.22 | + | 1423.87i | −0.300423 | + | 0.0976133i | ||||
\(598\) | 9318.93 | − | 12826.4i | 0.637256 | − | 0.877108i | ||||
\(599\) | 1555.67 | 0.106115 | 0.0530577 | − | 0.998591i | \(-0.483103\pi\) | ||||
0.0530577 | + | 0.998591i | \(0.483103\pi\) | |||||||
\(600\) | −4286.03 | + | 900.799i | −0.291628 | + | 0.0612916i | ||||
\(601\) | 3958.20 | 0.268650 | 0.134325 | − | 0.990937i | \(-0.457113\pi\) | ||||
0.134325 | + | 0.990937i | \(0.457113\pi\) | |||||||
\(602\) | −18503.1 | + | 25467.3i | −1.25271 | + | 1.72420i | ||||
\(603\) | 1747.86 | − | 567.915i | 0.118041 | − | 0.0383537i | ||||
\(604\) | −2394.80 | − | 7370.42i | −0.161329 | − | 0.496520i | ||||
\(605\) | −11331.6 | + | 5029.64i | −0.761476 | + | 0.337990i | ||||
\(606\) | 827.665 | − | 2547.29i | 0.0554812 | − | 0.170753i | ||||
\(607\) | 23128.2i | 1.54653i | 0.634081 | + | 0.773266i | \(0.281378\pi\) | ||||
−0.634081 | + | 0.773266i | \(0.718622\pi\) | |||||||
\(608\) | 1566.68 | + | 509.045i | 0.104502 | + | 0.0339547i | ||||
\(609\) | −8508.14 | + | 6181.52i | −0.566120 | + | 0.411310i | ||||
\(610\) | −1239.78 | − | 2793.17i | −0.0822906 | − | 0.185397i | ||||
\(611\) | −6781.78 | − | 4927.25i | −0.449037 | − | 0.326244i | ||||
\(612\) | 534.957 | + | 736.305i | 0.0353339 | + | 0.0486329i | ||||
\(613\) | 5456.58 | + | 7510.33i | 0.359525 | + | 0.494844i | 0.950016 | − | 0.312200i | \(-0.101066\pi\) |
−0.590491 | + | 0.807044i | \(0.701066\pi\) | |||||||
\(614\) | −10327.4 | − | 7503.26i | −0.678792 | − | 0.493171i | ||||
\(615\) | 12992.4 | + | 7520.99i | 0.851880 | + | 0.493131i | ||||
\(616\) | −3010.02 | + | 2186.91i | −0.196878 | + | 0.143041i | ||||
\(617\) | 5259.91 | + | 1709.05i | 0.343203 | + | 0.111513i | 0.475547 | − | 0.879691i | \(-0.342250\pi\) |
−0.132344 | + | 0.991204i | \(0.542250\pi\) | |||||||
\(618\) | − | 3112.23i | − | 0.202576i | ||||||
\(619\) | 4872.99 | − | 14997.5i | 0.316417 | − | 0.973831i | −0.658750 | − | 0.752361i | \(-0.728915\pi\) |
0.975167 | − | 0.221469i | \(-0.0710853\pi\) | |||||||
\(620\) | −1202.60 | − | 11569.0i | −0.0778993 | − | 0.749394i | ||||
\(621\) | −8753.60 | − | 26940.8i | −0.565652 | − | 1.74090i | ||||
\(622\) | −5848.26 | + | 1900.21i | −0.377000 | + | 0.122495i | ||||
\(623\) | 20203.3 | − | 27807.4i | 1.29924 | − | 1.78825i | ||||
\(624\) | 2990.38 | 0.191844 | ||||||||
\(625\) | 14303.0 | − | 6290.00i | 0.915394 | − | 0.402560i | ||||
\(626\) | 11112.5 | 0.709496 | ||||||||
\(627\) | −1975.06 | + | 2718.43i | −0.125799 | + | 0.173148i | ||||
\(628\) | 6840.48 | − | 2222.61i | 0.434657 | − | 0.141229i | ||||
\(629\) | 1082.63 | + | 3331.99i | 0.0686285 | + | 0.211217i | ||||
\(630\) | −564.057 | − | 5426.24i | −0.0356708 | − | 0.343153i | ||||
\(631\) | 6785.23 | − | 20882.8i | 0.428075 | − | 1.31748i | −0.471943 | − | 0.881629i | \(-0.656447\pi\) |
0.900019 | − | 0.435852i | \(-0.143553\pi\) | |||||||
\(632\) | 2825.90i | 0.177861i | ||||||||
\(633\) | −5532.59 | − | 1797.65i | −0.347395 | − | 0.112875i | ||||
\(634\) | −5383.88 | + | 3911.62i | −0.337258 | + | 0.245032i | ||||
\(635\) | 14668.8 | + | 8491.41i | 0.916717 | + | 0.530664i | ||||
\(636\) | 6420.02 | + | 4664.42i | 0.400268 | + | 0.290812i | ||||
\(637\) | −15821.5 | − | 21776.4i | −0.984096 | − | 1.35449i | ||||
\(638\) | 1348.20 | + | 1855.64i | 0.0836610 | + | 0.115149i | ||||
\(639\) | −3411.45 | − | 2478.57i | −0.211197 | − | 0.153444i | ||||
\(640\) | −580.581 | − | 1308.02i | −0.0358586 | − | 0.0807878i | ||||
\(641\) | 23240.6 | − | 16885.3i | 1.43205 | − | 1.04045i | 0.442425 | − | 0.896806i | \(-0.354118\pi\) |
0.989630 | − | 0.143643i | \(-0.0458817\pi\) | |||||||
\(642\) | 2117.45 | + | 688.003i | 0.130170 | + | 0.0422949i | ||||
\(643\) | 19485.8i | 1.19509i | 0.801834 | + | 0.597547i | \(0.203858\pi\) | ||||
−0.801834 | + | 0.597547i | \(0.796142\pi\) | |||||||
\(644\) | −7165.08 | + | 22051.8i | −0.438422 | + | 1.34932i | ||||
\(645\) | 22574.4 | − | 10019.9i | 1.37809 | − | 0.611680i | ||||
\(646\) | −925.877 | − | 2849.56i | −0.0563903 | − | 0.173552i | ||||
\(647\) | −17212.8 | + | 5592.78i | −1.04591 | + | 0.339838i | −0.781063 | − | 0.624452i | \(-0.785322\pi\) |
−0.264850 | + | 0.964290i | \(0.585322\pi\) | |||||||
\(648\) | 2147.87 | − | 2956.29i | 0.130211 | − | 0.179219i | ||||
\(649\) | 957.312 | 0.0579010 | ||||||||
\(650\) | −10440.4 | + | 2194.27i | −0.630011 | + | 0.132410i | ||||
\(651\) | −35545.4 | −2.13999 | ||||||||
\(652\) | 3136.73 | − | 4317.34i | 0.188411 | − | 0.259325i | ||||
\(653\) | −25011.1 | + | 8126.61i | −1.49887 | + | 0.487012i | −0.939688 | − | 0.342033i | \(-0.888885\pi\) |
−0.559181 | + | 0.829045i | \(0.688885\pi\) | |||||||
\(654\) | 2421.08 | + | 7451.33i | 0.144758 | + | 0.445520i | ||||
\(655\) | 13643.2 | + | 2916.24i | 0.813868 | + | 0.173965i | ||||
\(656\) | −1515.84 | + | 4665.27i | −0.0902188 | + | 0.277665i | ||||
\(657\) | − | 8178.22i | − | 0.485636i | ||||||
\(658\) | 11659.6 | + | 3788.44i | 0.690789 | + | 0.224451i | ||||
\(659\) | −832.956 | + | 605.178i | −0.0492373 | + | 0.0357730i | −0.612132 | − | 0.790756i | \(-0.709688\pi\) |
0.562894 | + | 0.826529i | \(0.309688\pi\) | |||||||
\(660\) | 2903.48 | − | 301.816i | 0.171239 | − | 0.0178003i | ||||
\(661\) | 3435.86 | + | 2496.30i | 0.202178 | + | 0.146891i | 0.684267 | − | 0.729231i | \(-0.260122\pi\) |
−0.482090 | + | 0.876122i | \(0.660122\pi\) | |||||||
\(662\) | 1013.55 | + | 1395.03i | 0.0595056 | + | 0.0819024i | ||||
\(663\) | −3197.00 | − | 4400.29i | −0.187272 | − | 0.257757i | ||||
\(664\) | −6321.66 | − | 4592.95i | −0.369470 | − | 0.268435i | ||||
\(665\) | −3754.13 | + | 17563.2i | −0.218916 | + | 1.02417i | ||||
\(666\) | −1522.97 | + | 1106.50i | −0.0886092 | + | 0.0643784i | ||||
\(667\) | 13594.7 | + | 4417.18i | 0.789187 | + | 0.256422i | ||||
\(668\) | 6457.21i | 0.374007i | ||||||||
\(669\) | 6045.50 | − | 18606.1i | 0.349376 | − | 1.07527i | ||||
\(670\) | 3512.56 | + | 3910.06i | 0.202540 | + | 0.225461i | ||||
\(671\) | 629.420 | + | 1937.15i | 0.0362123 | + | 0.111450i | ||||
\(672\) | −4159.33 | + | 1351.45i | −0.238764 | + | 0.0775793i | ||||
\(673\) | −8195.71 | + | 11280.4i | −0.469422 | + | 0.646105i | −0.976429 | − | 0.215837i | \(-0.930752\pi\) |
0.507007 | + | 0.861942i | \(0.330752\pi\) | |||||||
\(674\) | 11456.0 | 0.654699 | ||||||||
\(675\) | −7792.84 | + | 17396.0i | −0.444365 | + | 0.991957i | ||||
\(676\) | −1503.68 | −0.0855532 | ||||||||
\(677\) | −7907.76 | + | 10884.1i | −0.448921 | + | 0.617887i | −0.972165 | − | 0.234296i | \(-0.924722\pi\) |
0.523244 | + | 0.852183i | \(0.324722\pi\) | |||||||
\(678\) | −11135.9 | + | 3618.27i | −0.630784 | + | 0.204954i | ||||
\(679\) | 13989.7 | + | 43056.0i | 0.790688 | + | 2.43349i | ||||
\(680\) | −1304.04 | + | 2252.72i | −0.0735406 | + | 0.127041i | ||||
\(681\) | −2499.87 | + | 7693.82i | −0.140669 | + | 0.432934i | ||||
\(682\) | 7752.51i | 0.435277i | ||||||||
\(683\) | −18301.2 | − | 5946.43i | −1.02530 | − | 0.333139i | −0.252367 | − | 0.967632i | \(-0.581209\pi\) |
−0.772928 | + | 0.634493i | \(0.781209\pi\) | |||||||
\(684\) | 1302.46 | − | 946.290i | 0.0728080 | − | 0.0528981i | ||||
\(685\) | −19881.6 | + | 17860.4i | −1.10896 | + | 0.996220i | ||||
\(686\) | 14529.2 | + | 10556.1i | 0.808642 | + | 0.587513i | ||||
\(687\) | −666.697 | − | 917.629i | −0.0370248 | − | 0.0509603i | ||||
\(688\) | 4743.61 | + | 6529.01i | 0.262861 | + | 0.361797i | ||||
\(689\) | 15638.7 | + | 11362.1i | 0.864710 | + | 0.628249i | ||||
\(690\) | 13533.1 | − | 12157.3i | 0.746664 | − | 0.670757i | ||||
\(691\) | −18585.0 | + | 13502.8i | −1.02316 | + | 0.743373i | −0.966929 | − | 0.255045i | \(-0.917910\pi\) |
−0.0562356 | + | 0.998418i | \(0.517910\pi\) | |||||||
\(692\) | −12564.3 | − | 4082.39i | −0.690206 | − | 0.224262i | ||||
\(693\) | 3636.17i | 0.199317i | ||||||||
\(694\) | −1431.13 | + | 4404.58i | −0.0782783 | + | 0.240916i | ||||
\(695\) | 9854.49 | − | 17023.6i | 0.537845 | − | 0.929122i | ||||
\(696\) | 833.150 | + | 2564.17i | 0.0453743 | + | 0.139648i | ||||
\(697\) | 8485.44 | − | 2757.09i | 0.461132 | − | 0.149831i | ||||
\(698\) | 5236.16 | − | 7206.96i | 0.283942 | − | 0.390813i | ||||
\(699\) | 14839.0 | 0.802953 | ||||||||
\(700\) | 13530.0 | − | 7770.40i | 0.730551 | − | 0.419562i | ||||
\(701\) | −4226.67 | −0.227730 | −0.113865 | − | 0.993496i | \(-0.536323\pi\) | ||||
−0.113865 | + | 0.993496i | \(0.536323\pi\) | |||||||
\(702\) | 7650.05 | − | 10529.4i | 0.411300 | − | 0.566106i | ||||
\(703\) | 5894.00 | − | 1915.08i | 0.316211 | − | 0.102743i | ||||
\(704\) | 294.753 | + | 907.156i | 0.0157797 | + | 0.0485650i | ||||
\(705\) | −6428.03 | − | 7155.47i | −0.343395 | − | 0.382256i | ||||
\(706\) | 4692.01 | − | 14440.5i | 0.250122 | − | 0.769796i | ||||
\(707\) | 9541.71i | 0.507572i | ||||||||
\(708\) | 1070.20 | + | 347.729i | 0.0568088 | + | 0.0184583i | ||||
\(709\) | 18626.9 | − | 13533.2i | 0.986668 | − | 0.716856i | 0.0274791 | − | 0.999622i | \(-0.491252\pi\) |
0.959189 | + | 0.282766i | \(0.0912520\pi\) | |||||||
\(710\) | 2520.87 | − | 11793.5i | 0.133249 | − | 0.623384i | ||||
\(711\) | 2234.33 | + | 1623.34i | 0.117854 | + | 0.0856257i | ||||
\(712\) | −5179.48 | − | 7128.94i | −0.272625 | − | 0.375236i | ||||
\(713\) | 28398.0 | + | 39086.5i | 1.49160 | + | 2.05302i | ||||
\(714\) | 6435.35 | + | 4675.56i | 0.337307 | + | 0.245068i | ||||
\(715\) | 7072.64 | − | 735.200i | 0.369932 | − | 0.0384544i | ||||
\(716\) | −8952.98 | + | 6504.72i | −0.467302 | + | 0.339515i | ||||
\(717\) | −12010.0 | − | 3902.29i | −0.625554 | − | 0.203255i | ||||
\(718\) | 18627.8i | 0.968222i | ||||||||
\(719\) | 1901.30 | − | 5851.59i | 0.0986181 | − | 0.303515i | −0.889562 | − | 0.456815i | \(-0.848990\pi\) |
0.988180 | + | 0.153300i | \(0.0489901\pi\) | |||||||
\(720\) | −1367.72 | − | 292.350i | −0.0707941 | − | 0.0151323i | ||||
\(721\) | 3426.16 | + | 10544.7i | 0.176972 | + | 0.544665i | ||||
\(722\) | 8005.98 | − | 2601.30i | 0.412676 | − | 0.134086i | ||||
\(723\) | −16273.3 | + | 22398.2i | −0.837080 | + | 1.15214i | ||||
\(724\) | 13073.2 | 0.671078 | ||||||||
\(725\) | −4790.35 | − | 8341.06i | −0.245392 | − | 0.427282i | ||||
\(726\) | 9713.04 | 0.496536 | ||||||||
\(727\) | 16997.0 | − | 23394.3i | 0.867101 | − | 1.19346i | −0.112729 | − | 0.993626i | \(-0.535959\pi\) |
0.979829 | − | 0.199836i | \(-0.0640410\pi\) | |||||||
\(728\) | −10131.8 | + | 3292.02i | −0.515810 | + | 0.167597i | ||||
\(729\) | −6675.94 | − | 20546.4i | −0.339173 | − | 1.04387i | ||||
\(730\) | 21378.2 | − | 9488.97i | 1.08390 | − | 0.481100i | ||||
\(731\) | 4535.97 | − | 13960.3i | 0.229506 | − | 0.706346i | ||||
\(732\) | 2394.22i | 0.120892i | ||||||||
\(733\) | −10380.1 | − | 3372.68i | −0.523051 | − | 0.169949i | 0.0355788 | − | 0.999367i | \(-0.488673\pi\) |
−0.558629 | + | 0.829417i | \(0.688673\pi\) | |||||||
\(734\) | −12472.3 | + | 9061.65i | −0.627194 | + | 0.455683i | ||||
\(735\) | −12530.2 | − | 28230.0i | −0.628821 | − | 1.41671i | ||||
\(736\) | 4809.06 | + | 3493.99i | 0.240848 | + | 0.174987i | ||||
\(737\) | −2059.17 | − | 2834.21i | −0.102918 | − | 0.141655i | ||||
\(738\) | 2817.87 | + | 3878.47i | 0.140552 | + | 0.193453i | ||||
\(739\) | −11697.6 | − | 8498.82i | −0.582278 | − | 0.423050i | 0.257266 | − | 0.966341i | \(-0.417178\pi\) |
−0.839545 | + | 0.543290i | \(0.817178\pi\) | |||||||
\(740\) | −4659.50 | − | 2697.26i | −0.231468 | − | 0.133991i | ||||
\(741\) | −7783.72 | + | 5655.20i | −0.385887 | + | 0.280363i | ||||
\(742\) | −26886.8 | − | 8736.06i | −1.33025 | − | 0.432225i | ||||
\(743\) | 22720.1i | 1.12183i | 0.827874 | + | 0.560915i | \(0.189550\pi\) | ||||
−0.827874 | + | 0.560915i | \(0.810450\pi\) | |||||||
\(744\) | −2815.98 | + | 8666.71i | −0.138762 | + | 0.427066i | ||||
\(745\) | 452.703 | + | 4355.01i | 0.0222628 | + | 0.214168i | ||||
\(746\) | −5519.15 | − | 16986.2i | −0.270872 | − | 0.833659i | ||||
\(747\) | −7262.93 | + | 2359.87i | −0.355739 | + | 0.115586i | ||||
\(748\) | 1019.75 | − | 1403.56i | 0.0498471 | − | 0.0686086i | ||||
\(749\) | −7931.62 | −0.386936 | ||||||||
\(750\) | −12241.5 | − | 41.9359i | −0.595994 | − | 0.00204171i | ||||
\(751\) | 400.556 | 0.0194627 | 0.00973135 | − | 0.999953i | \(-0.496902\pi\) | ||||
0.00973135 | + | 0.999953i | \(0.496902\pi\) | |||||||
\(752\) | 1847.40 | − | 2542.73i | 0.0895847 | − | 0.123303i | ||||
\(753\) | −5134.59 | + | 1668.33i | −0.248493 | + | 0.0807401i | ||||
\(754\) | 2029.49 | + | 6246.12i | 0.0980233 | + | 0.301685i | ||||
\(755\) | −2239.60 | − | 21545.0i | −0.107957 | − | 1.03855i | ||||
\(756\) | −5881.92 | + | 18102.7i | −0.282968 | + | 0.870885i | ||||
\(757\) | − | 8445.77i | − | 0.405504i | −0.979230 | − | 0.202752i | \(-0.935011\pi\) | ||
0.979230 | − | 0.202752i | \(-0.0649886\pi\) | |||||||
\(758\) | 8072.77 | + | 2623.00i | 0.386829 | + | 0.125688i | ||||
\(759\) | −9809.52 | + | 7127.03i | −0.469121 | + | 0.340837i | ||||
\(760\) | 3984.85 | + | 2306.73i | 0.190192 | + | 0.110097i | ||||
\(761\) | −7569.25 | − | 5499.38i | −0.360559 | − | 0.261961i | 0.392726 | − | 0.919655i | \(-0.371532\pi\) |
−0.753285 | + | 0.657694i | \(0.771532\pi\) | |||||||
\(762\) | −7805.26 | − | 10743.0i | −0.371069 | − | 0.510733i | ||||
\(763\) | −16405.9 | − | 22580.8i | −0.778419 | − | 1.07140i | ||||
\(764\) | 1147.80 | + | 833.922i | 0.0543531 | + | 0.0394898i | ||||
\(765\) | 1032.03 | + | 2325.12i | 0.0487754 | + | 0.109889i | ||||
\(766\) | 8832.39 | − | 6417.11i | 0.416615 | − | 0.302689i | ||||
\(767\) | 2606.92 | + | 847.041i | 0.122726 | + | 0.0398760i | ||||
\(768\) | 1121.20i | 0.0526793i | ||||||||
\(769\) | 3534.39 | − | 10877.7i | 0.165739 | − | 0.510092i | −0.833351 | − | 0.552744i | \(-0.813581\pi\) |
0.999090 | + | 0.0426520i | \(0.0135807\pi\) | |||||||
\(770\) | −9505.11 | + | 4218.95i | −0.444858 | + | 0.197455i | ||||
\(771\) | −8775.26 | − | 27007.5i | −0.409901 | − | 1.26154i | ||||
\(772\) | −11062.0 | + | 3594.26i | −0.515713 | + | 0.167565i | ||||
\(773\) | −2210.68 | + | 3042.74i | −0.102862 | + | 0.141578i | −0.857345 | − | 0.514742i | \(-0.827888\pi\) |
0.754483 | + | 0.656320i | \(0.227888\pi\) | |||||||
\(774\) | 7887.19 | 0.366278 | ||||||||
\(775\) | 3472.13 | − | 32324.8i | 0.160932 | − | 1.49824i | ||||
\(776\) | 11606.2 | 0.536907 | ||||||||
\(777\) | −9670.89 | + | 13310.8i | −0.446514 | + | 0.614573i | ||||
\(778\) | 24593.1 | − | 7990.78i | 1.13330 | − | 0.368231i | ||||
\(779\) | −4877.04 | − | 15010.0i | −0.224311 | − | 0.690357i | ||||
\(780\) | 8173.72 | + | 1747.13i | 0.375213 | + | 0.0802019i | ||||
\(781\) | −2483.92 | + | 7644.72i | −0.113805 | + | 0.350256i | ||||
\(782\) | − | 10811.9i | − | 0.494413i | ||||||
\(783\) | 11160.1 | + | 3626.13i | 0.509360 | + | 0.165501i | ||||
\(784\) | 8164.72 | − | 5932.01i | 0.371935 | − | 0.270227i | ||||
\(785\) | 19995.9 | − | 2078.57i | 0.909153 | − | 0.0945063i | ||||
\(786\) | −8842.83 | − | 6424.69i | −0.401289 | − | 0.291554i | ||||
\(787\) | 13423.6 | + | 18476.0i | 0.608005 | + | 0.836848i | 0.996412 | − | 0.0846407i | \(-0.0269742\pi\) |
−0.388406 | + | 0.921488i | \(0.626974\pi\) | |||||||
\(788\) | −9826.60 | − | 13525.2i | −0.444236 | − | 0.611439i | ||||
\(789\) | 2831.36 | + | 2057.10i | 0.127756 | + | 0.0928198i | ||||
\(790\) | −1651.04 | + | 7724.16i | −0.0743562 | + | 0.347865i | ||||
\(791\) | 33746.6 | − | 24518.4i | 1.51693 | − | 1.10211i | ||||
\(792\) | 886.573 | + | 288.065i | 0.0397765 | + | 0.0129242i | ||||
\(793\) | 5832.12i | 0.261166i | ||||||||
\(794\) | −1256.17 | + | 3866.08i | −0.0561457 | + | 0.172799i | ||||
\(795\) | 14822.9 | + | 16500.4i | 0.661276 | + | 0.736110i | ||||
\(796\) | −1300.44 | − | 4002.33i | −0.0579055 | − | 0.178215i | ||||
\(797\) | −153.415 | + | 49.8475i | −0.00681836 | + | 0.00221542i | −0.312424 | − | 0.949943i | \(-0.601141\pi\) |
0.305606 | + | 0.952158i | \(0.401141\pi\) | |||||||
\(798\) | 8270.65 | − | 11383.6i | 0.366889 | − | 0.504980i | ||||
\(799\) | −5716.62 | −0.253116 | ||||||||
\(800\) | −822.709 | − | 3914.48i | −0.0363589 | − | 0.172997i | ||||
\(801\) | −8611.91 | −0.379884 | ||||||||
\(802\) | −10547.7 | + | 14517.7i | −0.464405 | + | 0.639199i | ||||
\(803\) | −14826.5 | + | 4817.42i | −0.651576 | + | 0.211710i | ||||
\(804\) | −1272.51 | − | 3916.40i | −0.0558185 | − | 0.171792i | ||||
\(805\) | −32468.4 | + | 56089.0i | −1.42157 | + | 2.45575i | ||||
\(806\) | −6859.51 | + | 21111.4i | −0.299772 | + | 0.922602i | ||||
\(807\) | − | 17866.4i | − | 0.779342i | ||||||
\(808\) | 2326.47 | + | 755.915i | 0.101293 | + | 0.0329121i | ||||
\(809\) | 8390.60 | − | 6096.13i | 0.364645 | − | 0.264930i | −0.390342 | − | 0.920670i | \(-0.627643\pi\) |
0.754987 | + | 0.655740i | \(0.227643\pi\) | |||||||
\(810\) | 7598.09 | − | 6825.66i | 0.329592 | − | 0.296085i | ||||
\(811\) | −34337.8 | − | 24947.9i | −1.48676 | − | 1.08020i | −0.975299 | − | 0.220890i | \(-0.929104\pi\) |
−0.511463 | − | 0.859305i | \(-0.670896\pi\) | |||||||
\(812\) | −5645.65 | − | 7770.57i | −0.243994 | − | 0.335830i | ||||
\(813\) | −1131.54 | − | 1557.44i | −0.0488130 | − | 0.0671854i | ||||
\(814\) | 2903.11 | + | 2109.23i | 0.125005 | + | 0.0908214i | ||||
\(815\) | 11096.2 | − | 9968.11i | 0.476910 | − | 0.428427i | ||||
\(816\) | 1649.82 | − | 1198.66i | 0.0707785 | − | 0.0514236i | ||||
\(817\) | −24694.5 | − | 8023.72i | −1.05747 | − | 0.343592i | ||||
\(818\) | 17311.5i | 0.739954i | ||||||||
\(819\) | −3217.32 | + | 9901.91i | −0.137268 | + | 0.422467i | ||||
\(820\) | −6869.00 | + | 11866.1i | −0.292531 | + | 0.505346i | ||||
\(821\) | 8552.50 | + | 26321.9i | 0.363562 | + | 1.11893i | 0.950877 | + | 0.309570i | \(0.100185\pi\) |
−0.587315 | + | 0.809359i | \(0.699815\pi\) | |||||||
\(822\) | 19913.8 | − | 6470.39i | 0.844980 | − | 0.274551i | ||||
\(823\) | −6684.48 | + | 9200.39i | −0.283118 | + | 0.389679i | −0.926764 | − | 0.375645i | \(-0.877421\pi\) |
0.643645 | + | 0.765324i | \(0.277421\pi\) | |||||||
\(824\) | 2842.43 | 0.120171 | ||||||||
\(825\) | 8112.53 | + | 871.398i | 0.342354 | + | 0.0367736i | ||||
\(826\) | −4008.79 | −0.168866 | ||||||||
\(827\) | 1946.09 | − | 2678.57i | 0.0818287 | − | 0.112628i | −0.766140 | − | 0.642673i | \(-0.777825\pi\) |
0.847969 | + | 0.530046i | \(0.177825\pi\) | |||||||
\(828\) | 5525.12 | − | 1795.22i | 0.231897 | − | 0.0753480i | ||||
\(829\) | 7520.64 | + | 23146.2i | 0.315082 | + | 0.969722i | 0.975721 | + | 0.219018i | \(0.0702854\pi\) |
−0.660639 | + | 0.750704i | \(0.729715\pi\) | |||||||
\(830\) | −14595.8 | − | 16247.5i | −0.610395 | − | 0.679471i | ||||
\(831\) | −86.8491 | + | 267.294i | −0.00362547 | + | 0.0111580i | ||||
\(832\) | 2731.14i | 0.113804i | ||||||||
\(833\) | −17457.7 | − | 5672.36i | −0.726139 | − | 0.235937i | ||||
\(834\) | −12467.5 | + | 9058.19i | −0.517644 | + | 0.376090i | ||||
\(835\) | −3772.64 | + | 17649.7i | −0.156356 | + | 0.731490i | ||||
\(836\) | −2482.77 | − | 1803.84i | −0.102713 | − | 0.0746257i | ||||
\(837\) | 23312.4 | + | 32086.7i | 0.962716 | + | 1.32506i | ||||
\(838\) | −6750.22 | − | 9290.88i | −0.278261 | − | 0.382993i | ||||
\(839\) | −11147.2 | − | 8098.89i | −0.458692 | − | 0.333260i | 0.334326 | − | 0.942458i | \(-0.391491\pi\) |
−0.793018 | + | 0.609198i | \(0.791491\pi\) | |||||||
\(840\) | −12158.5 | + | 1263.87i | −0.499413 | + | 0.0519139i | ||||
\(841\) | 14940.7 | − | 10855.0i | 0.612598 | − | 0.445079i | ||||
\(842\) | 7012.51 | + | 2278.50i | 0.287015 | + | 0.0932570i | ||||
\(843\) | − | 7827.16i | − | 0.319789i | ||||||
\(844\) | 1641.81 | − | 5052.97i | 0.0669591 | − | 0.206079i | ||||
\(845\) | −4110.08 | − | 878.530i | −0.167327 | − | 0.0357661i | ||||
\(846\) | −949.197 | − | 2921.33i | −0.0385746 | − | 0.118720i | ||||
\(847\) | −32909.1 | + | 10692.8i | −1.33503 | + | 0.433777i | ||||
\(848\) | −4260.06 | + | 5863.47i | −0.172513 | + | 0.237444i | ||||
\(849\) | 27343.8 | 1.10535 | ||||||||
\(850\) | −4880.54 | + | 5395.55i | −0.196942 | + | 0.217725i | ||||
\(851\) | 22363.2 | 0.900822 | ||||||||
\(852\) | −5553.67 | + | 7643.97i | −0.223316 | + | 0.307369i | ||||
\(853\) | 12442.5 | − | 4042.80i | 0.499439 | − | 0.162278i | −0.0484548 | − | 0.998825i | \(-0.515430\pi\) |
0.547894 | + | 0.836548i | \(0.315430\pi\) | |||||||
\(854\) | −2635.73 | − | 8111.93i | −0.105612 | − | 0.325040i | ||||
\(855\) | 4112.93 | − | 1825.57i | 0.164514 | − | 0.0730213i | ||||
\(856\) | −628.360 | + | 1933.89i | −0.0250898 | + | 0.0772186i | ||||
\(857\) | − | 17624.7i | − | 0.702508i | −0.936280 | − | 0.351254i | \(-0.885755\pi\) | ||
0.936280 | − | 0.351254i | \(-0.114245\pi\) | |||||||
\(858\) | −5298.32 | − | 1721.53i | −0.210818 | − | 0.0684988i | ||||
\(859\) | −834.395 | + | 606.224i | −0.0331423 | + | 0.0240793i | −0.604233 | − | 0.796808i | \(-0.706520\pi\) |
0.571091 | + | 0.820887i | \(0.306520\pi\) | |||||||
\(860\) | 9151.30 | + | 20617.5i | 0.362857 | + | 0.817500i | ||||
\(861\) | 33898.1 | + | 24628.4i | 1.34175 | + | 0.974836i | ||||
\(862\) | 11310.0 | + | 15566.9i | 0.446891 | + | 0.615093i | ||||
\(863\) | −21765.5 | − | 29957.6i | −0.858523 | − | 1.18166i | −0.981920 | − | 0.189299i | \(-0.939379\pi\) |
0.123396 | − | 0.992357i | \(-0.460621\pi\) | |||||||
\(864\) | 3947.83 | + | 2868.27i | 0.155449 | + | 0.112940i | ||||
\(865\) | −31957.4 | − | 18499.3i | −1.25616 | − | 0.727161i | ||||
\(866\) | −2561.31 | + | 1860.90i | −0.100505 | + | 0.0730209i | ||||
\(867\) | 16936.6 | + | 5503.02i | 0.663432 | + | 0.215562i | ||||
\(868\) | − | 32464.0i | − | 1.26947i | ||||||
\(869\) | 1626.84 | − | 5006.91i | 0.0635062 | − | 0.195452i | ||||
\(870\) | 779.159 | + | 7495.53i | 0.0303632 | + | 0.292094i | ||||
\(871\) | −3099.74 | − | 9540.02i | −0.120586 | − | 0.371127i | ||||
\(872\) | −6805.38 | + | 2211.20i | −0.264288 | + | 0.0858724i | ||||
\(873\) | 6667.18 | − | 9176.59i | 0.258477 | − | 0.355762i | ||||
\(874\) | −19125.2 | −0.740183 | ||||||||
\(875\) | 41521.9 | − | 13334.2i | 1.60423 | − | 0.515176i | ||||
\(876\) | −18324.7 | −0.706776 | ||||||||
\(877\) | 24803.1 | − | 34138.6i | 0.955008 | − | 1.31446i | 0.00574075 | − | 0.999984i | \(-0.498173\pi\) |
0.949267 | − | 0.314472i | \(-0.101827\pi\) | |||||||
\(878\) | 3163.84 | − | 1027.99i | 0.121611 | − | 0.0395138i | ||||
\(879\) | 3305.38 | + | 10172.9i | 0.126835 | + | 0.390357i | ||||
\(880\) | 275.652 | + | 2651.78i | 0.0105593 | + | 0.101581i | ||||
\(881\) | −2050.56 | + | 6310.96i | −0.0784165 | + | 0.241341i | −0.982578 | − | 0.185849i | \(-0.940497\pi\) |
0.904162 | + | 0.427190i | \(0.140497\pi\) | |||||||
\(882\) | − | 9863.15i | − | 0.376542i | ||||||
\(883\) | −5354.36 | − | 1739.74i | −0.204064 | − | 0.0663044i | 0.205202 | − | 0.978720i | \(-0.434215\pi\) |
−0.409266 | + | 0.912415i | \(0.634215\pi\) | |||||||
\(884\) | 4018.83 | − | 2919.85i | 0.152905 | − | 0.111092i | ||||
\(885\) | 2722.06 | + | 1575.73i | 0.103391 | + | 0.0598504i | ||||
\(886\) | 10462.6 | + | 7601.49i | 0.396723 | + | 0.288236i | ||||
\(887\) | 19343.9 | + | 26624.6i | 0.732250 | + | 1.00786i | 0.999027 | + | 0.0440972i | \(0.0140411\pi\) |
−0.266777 | + | 0.963758i | \(0.585959\pi\) | |||||||
\(888\) | 2479.31 | + | 3412.47i | 0.0936938 | + | 0.128959i | ||||
\(889\) | 38271.9 | + | 27806.2i | 1.44387 | + | 1.04903i | ||||
\(890\) | −9992.18 | − | 22511.9i | −0.376335 | − | 0.847868i | ||||
\(891\) | −5507.49 | + | 4001.42i | −0.207079 | + | 0.150452i | ||||
\(892\) | 16993.2 | + | 5521.42i | 0.637863 | + | 0.207254i | ||||
\(893\) | 10112.2i | 0.378938i | ||||||||
\(894\) | 1060.04 | − | 3262.47i | 0.0396567 | − | 0.122051i | ||||
\(895\) | −28271.9 | + | 12548.8i | −1.05590 | + | 0.468671i | ||||
\(896\) | −1234.29 | − | 3798.76i | −0.0460210 | − | 0.141638i | ||||
\(897\) | −33019.1 | + | 10728.6i | −1.22907 | + | 0.399349i | ||||
\(898\) | −6535.16 | + | 8994.87i | −0.242852 | + | 0.334257i | ||||
\(899\) | −20013.6 | −0.742483 | ||||||||
\(900\) | −3567.63 | − | 1598.18i | −0.132134 | − | 0.0591920i | ||||
\(901\) | 13182.4 | 0.487425 | ||||||||
\(902\) | 5371.49 | − | 7393.22i | 0.198283 | − | 0.272913i | ||||
\(903\) | 65560.7 | − | 21302.0i | 2.41608 | − | 0.785033i | ||||
\(904\) | −3304.60 | − | 10170.5i | −0.121581 | − | 0.374189i | ||||
\(905\) | 35733.4 | + | 7638.03i | 1.31251 | + | 0.280549i | ||||
\(906\) | −5244.21 | + | 16140.0i | −0.192304 | + | 0.591850i | ||||
\(907\) | 23738.5i | 0.869046i | 0.900661 | + | 0.434523i | \(0.143083\pi\) | ||||
−0.900661 | + | 0.434523i | \(0.856917\pi\) | |||||||
\(908\) | −7026.85 | − | 2283.16i | −0.256822 | − | 0.0834464i | ||||
\(909\) | 1934.11 | − | 1405.21i | 0.0705724 | − | 0.0512738i | ||||
\(910\) | −29617.0 | + | 3078.69i | −1.07890 | + | 0.112151i | ||||
\(911\) | −10584.2 | − | 7689.85i | −0.384928 | − | 0.279666i | 0.378446 | − | 0.925623i | \(-0.376459\pi\) |
−0.763374 | + | 0.645957i | \(0.776459\pi\) | |||||||
\(912\) | −2120.33 | − | 2918.39i | −0.0769859 | − | 0.105962i | ||||
\(913\) | 8556.53 | + | 11777.1i | 0.310164 | + | 0.426904i | ||||
\(914\) | −2131.53 | − | 1548.65i | −0.0771386 | − | 0.0560445i | ||||
\(915\) | −1398.83 | + | 6544.21i | −0.0505397 | + | 0.236443i | ||||
\(916\) | 838.081 | − | 608.901i | 0.0302303 | − | 0.0219636i | ||||
\(917\) | 37033.5 | + | 12032.9i | 1.33364 | + | 0.433328i | ||||
\(918\) | − | 8875.62i | − | 0.319106i | ||||||
\(919\) | 983.027 | − | 3025.45i | 0.0352852 | − | 0.108597i | −0.931863 | − | 0.362811i | \(-0.881817\pi\) |
0.967148 | + | 0.254215i | \(0.0818170\pi\) | |||||||
\(920\) | 11103.4 | + | 12360.0i | 0.397901 | + | 0.442930i | ||||
\(921\) | 8638.24 | + | 26585.8i | 0.309055 | + | 0.951174i | ||||
\(922\) | 16095.8 | − | 5229.86i | 0.574933 | − | 0.186807i | ||||
\(923\) | −13528.3 | + | 18620.1i | −0.482436 | + | 0.664017i | ||||
\(924\) | 8147.48 | 0.290078 | ||||||||
\(925\) | −11160.1 | − | 10094.9i | −0.396694 | − | 0.358829i | ||||
\(926\) | −25378.8 | −0.900647 | ||||||||
\(927\) | 1632.83 | − | 2247.40i | 0.0578524 | − | 0.0796270i | ||||
\(928\) | −2341.89 | + | 760.925i | −0.0828407 | + | 0.0269166i | ||||
\(929\) | −12964.0 | − | 39899.2i | −0.457843 | − | 1.40910i | −0.867764 | − | 0.496976i | \(-0.834444\pi\) |
0.409921 | − | 0.912121i | \(-0.365556\pi\) | |||||||
\(930\) | −12760.6 | + | 22043.8i | −0.449931 | + | 0.777253i | ||||
\(931\) | −10033.9 | + | 30881.1i | −0.353220 | + | 1.08710i | ||||
\(932\) | 13552.7i | 0.476322i | ||||||||
\(933\) | 12806.7 | + | 4161.16i | 0.449382 | + | 0.146013i | ||||
\(934\) | 1329.01 | − | 965.585i | 0.0465596 | − | 0.0338275i | ||||
\(935\) | 3607.35 | − | 3240.62i | 0.126174 | − | 0.113347i | ||||
\(936\) | 2159.41 | + | 1568.90i | 0.0754085 | + | 0.0547875i | ||||
\(937\) | −2442.49 | − | 3361.80i | −0.0851577 | − | 0.117210i | 0.764313 | − | 0.644846i | \(-0.223078\pi\) |
−0.849470 | + | 0.527636i | \(0.823078\pi\) | |||||||
\(938\) | 8622.90 | + | 11868.4i | 0.300157 | + | 0.413131i | ||||
\(939\) | −19687.0 | − | 14303.5i | −0.684198 | − | 0.497099i | ||||
\(940\) | 6535.16 | − | 5870.79i | 0.226759 | − | 0.203706i | ||||
\(941\) | −14793.5 | + | 10748.1i | −0.512490 | + | 0.372346i | −0.813767 | − | 0.581191i | \(-0.802587\pi\) |
0.301277 | + | 0.953537i | \(0.402587\pi\) | |||||||
\(942\) | −14979.5 | − | 4867.14i | −0.518110 | − | 0.168344i | ||||
\(943\) | − | 56951.2i | − | 1.96669i | ||||||
\(944\) | −317.585 | + | 977.426i | −0.0109497 | + | 0.0336997i | ||||
\(945\) | −26653.8 | + | 46044.3i | −0.917513 | + | 1.58500i | ||||
\(946\) | −4645.99 | − | 14298.9i | −0.159677 | − | 0.491434i | ||||
\(947\) | 46162.9 | − | 14999.2i | 1.58405 | − | 0.514688i | 0.620953 | − | 0.783848i | \(-0.286746\pi\) |
0.963096 | + | 0.269160i | \(0.0867459\pi\) | |||||||
\(948\) | 3637.37 | − | 5006.41i | 0.124616 | − | 0.171520i | ||||
\(949\) | −44637.6 | −1.52687 | ||||||||
\(950\) | 9544.25 | + | 8633.23i | 0.325954 | + | 0.294841i | ||||
\(951\) | 14573.0 | 0.496911 | ||||||||
\(952\) | −4270.24 | + | 5877.48i | −0.145377 | + | 0.200095i | ||||
\(953\) | 32652.7 | − | 10609.5i | 1.10989 | − | 0.360625i | 0.303988 | − | 0.952676i | \(-0.401682\pi\) |
0.805900 | + | 0.592051i | \(0.201682\pi\) | |||||||
\(954\) | 2188.83 | + | 6736.52i | 0.0742830 | + | 0.228620i | ||||
\(955\) | 2650.09 | + | 2950.00i | 0.0897958 | + | 0.0999577i | ||||
\(956\) | 3564.01 | − | 10968.9i | 0.120573 | − | 0.371087i | ||||
\(957\) | − | 5022.81i | − | 0.169660i | ||||||
\(958\) | −20960.8 | − | 6810.57i | −0.706902 | − | 0.229686i | ||||
\(959\) | −60347.6 | + | 43845.1i | −2.03204 | + | 1.47636i | ||||
\(960\) | −655.061 | + | 3064.61i | −0.0220229 | + | 0.103031i | ||||
\(961\) | −30624.1 | − | 22249.7i | −1.02797 | − | 0.746861i | ||||
\(962\) | 6039.39 | + | 8312.51i | 0.202409 | + | 0.278593i | ||||
\(963\) | 1168.09 | + | 1607.74i | 0.0390875 | + | 0.0537993i | ||||
\(964\) | −20456.5 | − | 14862.5i | −0.683465 | − | 0.496566i | ||||
\(965\) | −32336.2 | + | 3361.34i | −1.07869 | + | 0.112130i | ||||
\(966\) | 41077.9 | − | 29844.8i | 1.36818 | − | 0.994038i | ||||
\(967\) | −6186.33 | − | 2010.06i | −0.205728 | − | 0.0668451i | 0.204340 | − | 0.978900i | \(-0.434495\pi\) |
−0.410068 | + | 0.912055i | \(0.634495\pi\) | |||||||
\(968\) | 8871.02i | 0.294551i | ||||||||
\(969\) | −2027.52 | + | 6240.06i | −0.0672170 | + | 0.206873i | ||||
\(970\) | 31723.8 | + | 6780.97i | 1.05009 | + | 0.224458i | ||||
\(971\) | 8528.41 | + | 26247.7i | 0.281864 | + | 0.867487i | 0.987321 | + | 0.158735i | \(0.0507416\pi\) |
−0.705457 | + | 0.708752i | \(0.749258\pi\) | |||||||
\(972\) | 8052.83 | − | 2616.52i | 0.265735 | − | 0.0863426i | ||||
\(973\) | 32269.8 | − | 44415.5i | 1.06323 | − | 1.46341i | ||||
\(974\) | −15708.9 | −0.516782 | ||||||||
\(975\) | 21320.8 | + | 9551.03i | 0.700320 | + | 0.313721i | ||||
\(976\) | −2186.66 | −0.0717146 | ||||||||
\(977\) | −11978.4 | + | 16486.8i | −0.392244 | + | 0.539877i | −0.958776 | − | 0.284162i | \(-0.908285\pi\) |
0.566533 | + | 0.824039i | \(0.308285\pi\) | |||||||
\(978\) | −11114.1 | + | 3611.21i | −0.363386 | + | 0.118071i | ||||
\(979\) | 5072.89 | + | 15612.8i | 0.165608 | + | 0.509689i | ||||
\(980\) | 25782.7 | − | 11444.0i | 0.840408 | − | 0.373024i | ||||
\(981\) | −2161.03 | + | 6650.96i | −0.0703327 | + | 0.216462i | ||||
\(982\) | 41047.7i | 1.33390i | ||||||||
\(983\) | −4843.95 | − | 1573.89i | −0.157170 | − | 0.0510675i | 0.229375 | − | 0.973338i | \(-0.426332\pi\) |
−0.386545 | + | 0.922270i | \(0.626332\pi\) | |||||||
\(984\) | 8690.40 | − | 6313.94i | 0.281544 | − | 0.204554i | ||||
\(985\) | −18957.3 | − | 42710.1i | −0.613229 | − | 1.38158i | ||||
\(986\) | 3623.39 | + | 2632.54i | 0.117031 | + | 0.0850277i | ||||
\(987\) | −15780.0 | − | 21719.3i | −0.508900 | − | 0.700440i | ||||
\(988\) | −5164.96 | − | 7108.95i | −0.166315 | − | 0.228913i | ||||
\(989\) | −75801.9 | − | 55073.3i | −2.43717 | − | 1.77071i | ||||
\(990\) | 2255.00 | + | 1305.36i | 0.0723926 | + | 0.0419062i | ||||
\(991\) | −1089.49 | + | 791.563i | −0.0349232 | + | 0.0253732i | −0.605110 | − | 0.796142i | \(-0.706871\pi\) |
0.570187 | + | 0.821515i | \(0.306871\pi\) | |||||||
\(992\) | −7915.39 | − | 2571.87i | −0.253341 | − | 0.0823154i | ||||
\(993\) | − | 3776.05i | − | 0.120674i | ||||||
\(994\) | 10401.5 | − | 32012.7i | 0.331908 | − | 1.02151i | ||||
\(995\) | −1216.16 | − | 11699.5i | −0.0387487 | − | 0.372763i | ||||
\(996\) | 5287.71 | + | 16273.9i | 0.168220 | + | 0.517729i | ||||
\(997\) | −21308.2 | + | 6923.45i | −0.676868 | + | 0.219928i | −0.627224 | − | 0.778839i | \(-0.715809\pi\) |
−0.0496443 | + | 0.998767i | \(0.515809\pi\) | |||||||
\(998\) | −24302.2 | + | 33449.1i | −0.770814 | + | 1.06093i | ||||
\(999\) | 18358.3 | 0.581411 |
(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 | 50.4.e.a.9.6 | ✓ | 32 | |
5.2 | odd | 4 | 250.4.d.d.201.6 | 32 | |||
5.3 | odd | 4 | 250.4.d.c.201.3 | 32 | |||
5.4 | even | 2 | 250.4.e.b.49.3 | 32 | |||
25.2 | odd | 20 | 250.4.d.d.51.6 | 32 | |||
25.8 | odd | 20 | 1250.4.a.n.1.5 | 16 | |||
25.11 | even | 5 | 250.4.e.b.199.3 | 32 | |||
25.14 | even | 10 | inner | 50.4.e.a.39.6 | yes | 32 | |
25.17 | odd | 20 | 1250.4.a.m.1.12 | 16 | |||
25.23 | odd | 20 | 250.4.d.c.51.3 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.4.e.a.9.6 | ✓ | 32 | 1.1 | even | 1 | trivial | |
50.4.e.a.39.6 | yes | 32 | 25.14 | even | 10 | inner | |
250.4.d.c.51.3 | 32 | 25.23 | odd | 20 | |||
250.4.d.c.201.3 | 32 | 5.3 | odd | 4 | |||
250.4.d.d.51.6 | 32 | 25.2 | odd | 20 | |||
250.4.d.d.201.6 | 32 | 5.2 | odd | 4 | |||
250.4.e.b.49.3 | 32 | 5.4 | even | 2 | |||
250.4.e.b.199.3 | 32 | 25.11 | even | 5 | |||
1250.4.a.m.1.12 | 16 | 25.17 | odd | 20 | |||
1250.4.a.n.1.5 | 16 | 25.8 | odd | 20 |