Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [100,4,Mod(7,100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(100, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("100.7");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 100 = 2^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 100.e (of order \(4\), 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: | \(5.90019100057\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.5 | ||
Character | \(\chi\) | \(=\) | 100.7 |
Dual form | 100.4.e.f.43.5 |
$q$-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 \(\left(\mathbb{Z}/100\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(77\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.52596 | + | 2.38148i | −0.539509 | + | 0.841980i | ||||
\(3\) | −0.243692 | − | 0.243692i | −0.0468986 | − | 0.0468986i | 0.683269 | − | 0.730167i | \(-0.260558\pi\) |
−0.730167 | + | 0.683269i | \(0.760558\pi\) | |||||||
\(4\) | −3.34287 | − | 7.26809i | −0.417859 | − | 0.908512i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.952213 | − | 0.208482i | 0.0647899 | − | 0.0141854i | ||||
\(7\) | −9.53656 | + | 9.53656i | −0.514926 | + | 0.514926i | −0.916032 | − | 0.401106i | \(-0.868626\pi\) |
0.401106 | + | 0.916032i | \(0.368626\pi\) | |||||||
\(8\) | 22.4099 | + | 3.12986i | 0.990387 | + | 0.138322i | ||||
\(9\) | − | 26.8812i | − | 0.995601i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 42.2652i | − | 1.15849i | −0.815152 | − | 0.579247i | \(-0.803347\pi\) | ||
0.815152 | − | 0.579247i | \(-0.196653\pi\) | |||||||
\(12\) | −0.956545 | + | 2.58581i | −0.0230109 | + | 0.0622049i | ||||
\(13\) | 41.7119 | − | 41.7119i | 0.889908 | − | 0.889908i | −0.104606 | − | 0.994514i | \(-0.533358\pi\) |
0.994514 | + | 0.104606i | \(0.0333582\pi\) | |||||||
\(14\) | −8.15866 | − | 37.2635i | −0.155750 | − | 0.711364i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −41.6504 | + | 48.5926i | −0.650787 | + | 0.759260i | ||||
\(17\) | 34.1474 | + | 34.1474i | 0.487174 | + | 0.487174i | 0.907413 | − | 0.420239i | \(-0.138054\pi\) |
−0.420239 | + | 0.907413i | \(0.638054\pi\) | |||||||
\(18\) | 64.0170 | + | 41.0198i | 0.838276 | + | 0.537136i | ||||
\(19\) | 130.653 | 1.57757 | 0.788784 | − | 0.614670i | \(-0.210711\pi\) | ||||
0.788784 | + | 0.614670i | \(0.210711\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.64797 | 0.0482986 | ||||||||
\(22\) | 100.654 | + | 64.4951i | 0.975428 | + | 0.625018i | ||||
\(23\) | −107.427 | − | 107.427i | −0.973918 | − | 0.973918i | 0.0257506 | − | 0.999668i | \(-0.491802\pi\) |
−0.999668 | + | 0.0257506i | \(0.991802\pi\) | |||||||
\(24\) | −4.69839 | − | 6.22384i | −0.0399607 | − | 0.0529348i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 35.6852 | + | 162.987i | 0.269171 | + | 1.22940i | ||||
\(27\) | −13.1304 | + | 13.1304i | −0.0935908 | + | 0.0935908i | ||||
\(28\) | 101.192 | + | 37.4331i | 0.682982 | + | 0.252650i | ||||
\(29\) | 80.4104i | 0.514891i | 0.966293 | + | 0.257446i | \(0.0828808\pi\) | ||||
−0.966293 | + | 0.257446i | \(0.917119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 273.244i | − | 1.58310i | −0.611105 | − | 0.791550i | \(-0.709275\pi\) | ||
0.611105 | − | 0.791550i | \(-0.290725\pi\) | |||||||
\(32\) | −52.1653 | − | 173.340i | −0.288175 | − | 0.957578i | ||||
\(33\) | −10.2997 | + | 10.2997i | −0.0543317 | + | 0.0543317i | ||||
\(34\) | −133.429 | + | 29.2136i | −0.673026 | + | 0.147356i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −195.375 | + | 89.8605i | −0.904515 | + | 0.416021i | ||||
\(37\) | −134.502 | − | 134.502i | −0.597620 | − | 0.597620i | 0.342059 | − | 0.939679i | \(-0.388876\pi\) |
−0.939679 | + | 0.342059i | \(0.888876\pi\) | |||||||
\(38\) | −199.371 | + | 311.147i | −0.851113 | + | 1.32828i | ||||
\(39\) | −20.3297 | −0.0834708 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 155.583 | 0.592635 | 0.296317 | − | 0.955090i | \(-0.404241\pi\) | ||||
0.296317 | + | 0.955090i | \(0.404241\pi\) | |||||||
\(42\) | −7.09263 | + | 11.0690i | −0.0260575 | + | 0.0406664i | ||||
\(43\) | −223.543 | − | 223.543i | −0.792789 | − | 0.792789i | 0.189157 | − | 0.981947i | \(-0.439424\pi\) |
−0.981947 | + | 0.189157i | \(0.939424\pi\) | |||||||
\(44\) | −307.187 | + | 141.287i | −1.05250 | + | 0.484087i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 419.765 | − | 91.9055i | 1.34546 | − | 0.294581i | ||||
\(47\) | −72.1171 | + | 72.1171i | −0.223816 | + | 0.223816i | −0.810103 | − | 0.586287i | \(-0.800589\pi\) |
0.586287 | + | 0.810103i | \(0.300589\pi\) | |||||||
\(48\) | 21.9915 | − | 1.69177i | 0.0661292 | − | 0.00508721i | ||||
\(49\) | 161.108i | 0.469703i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 16.6429i | − | 0.0456955i | ||||||
\(52\) | −442.604 | − | 163.728i | −1.18035 | − | 0.436636i | ||||
\(53\) | −305.746 | + | 305.746i | −0.792403 | + | 0.792403i | −0.981884 | − | 0.189481i | \(-0.939319\pi\) |
0.189481 | + | 0.981884i | \(0.439319\pi\) | |||||||
\(54\) | −11.2333 | − | 51.3064i | −0.0283084 | − | 0.129295i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −243.561 | + | 183.865i | −0.581201 | + | 0.438750i | ||||
\(57\) | −31.8391 | − | 31.8391i | −0.0739857 | − | 0.0739857i | ||||
\(58\) | −191.496 | − | 122.703i | −0.433528 | − | 0.277789i | ||||
\(59\) | −177.142 | −0.390880 | −0.195440 | − | 0.980716i | \(-0.562613\pi\) | ||||
−0.195440 | + | 0.980716i | \(0.562613\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −41.4688 | −0.0870416 | −0.0435208 | − | 0.999053i | \(-0.513857\pi\) | ||||
−0.0435208 | + | 0.999053i | \(0.513857\pi\) | |||||||
\(62\) | 650.725 | + | 416.960i | 1.33294 | + | 0.854097i | ||||
\(63\) | 256.354 | + | 256.354i | 0.512660 | + | 0.512660i | ||||
\(64\) | 492.408 | + | 140.280i | 0.961734 | + | 0.273984i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.81153 | − | 40.2454i | −0.0164337 | − | 0.0750586i | ||||
\(67\) | 261.744 | − | 261.744i | 0.477271 | − | 0.477271i | −0.426987 | − | 0.904258i | \(-0.640425\pi\) |
0.904258 | + | 0.426987i | \(0.140425\pi\) | |||||||
\(68\) | 134.036 | − | 362.337i | 0.239033 | − | 0.646174i | ||||
\(69\) | 52.3583i | 0.0913507i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 741.456i | 1.23936i | 0.784854 | + | 0.619680i | \(0.212738\pi\) | ||||
−0.784854 | + | 0.619680i | \(0.787262\pi\) | |||||||
\(72\) | 84.1346 | − | 602.406i | 0.137713 | − | 0.986031i | ||||
\(73\) | 516.828 | − | 516.828i | 0.828631 | − | 0.828631i | −0.158696 | − | 0.987327i | \(-0.550729\pi\) |
0.987327 | + | 0.158696i | \(0.0507290\pi\) | |||||||
\(74\) | 525.557 | − | 115.068i | 0.825605 | − | 0.180762i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −436.756 | − | 949.597i | −0.659202 | − | 1.43324i | ||||
\(77\) | 403.064 | + | 403.064i | 0.596538 | + | 0.596538i | ||||
\(78\) | 31.0224 | − | 48.4148i | 0.0450333 | − | 0.0702807i | ||||
\(79\) | 222.727 | 0.317200 | 0.158600 | − | 0.987343i | \(-0.449302\pi\) | ||||
0.158600 | + | 0.987343i | \(0.449302\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −719.394 | −0.986822 | ||||||||
\(82\) | −237.414 | + | 370.518i | −0.319732 | + | 0.498986i | ||||
\(83\) | 824.724 | + | 824.724i | 1.09066 | + | 1.09066i | 0.995457 | + | 0.0952072i | \(0.0303514\pi\) |
0.0952072 | + | 0.995457i | \(0.469649\pi\) | |||||||
\(84\) | −15.5376 | − | 33.7819i | −0.0201820 | − | 0.0438798i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 873.480 | − | 191.244i | 1.09523 | − | 0.239795i | ||||
\(87\) | 19.5954 | − | 19.5954i | 0.0241477 | − | 0.0241477i | ||||
\(88\) | 132.284 | − | 947.158i | 0.160245 | − | 1.14736i | ||||
\(89\) | − | 1447.03i | − | 1.72342i | −0.507400 | − | 0.861711i | \(-0.669393\pi\) | ||
0.507400 | − | 0.861711i | \(-0.330607\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 795.576i | 0.916473i | ||||||||
\(92\) | −421.675 | + | 1139.91i | −0.477855 | + | 1.29178i | ||||
\(93\) | −66.5874 | + | 66.5874i | −0.0742451 | + | 0.0742451i | ||||
\(94\) | −61.6973 | − | 281.793i | −0.0676977 | − | 0.309200i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −29.5293 | + | 54.9539i | −0.0313940 | + | 0.0584240i | ||||
\(97\) | 196.252 | + | 196.252i | 0.205426 | + | 0.205426i | 0.802320 | − | 0.596894i | \(-0.203599\pi\) |
−0.596894 | + | 0.802320i | \(0.703599\pi\) | |||||||
\(98\) | −383.676 | − | 245.845i | −0.395481 | − | 0.253409i | ||||
\(99\) | −1136.14 | −1.15340 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 594.739 | 0.585928 | 0.292964 | − | 0.956123i | \(-0.405358\pi\) | ||||
0.292964 | + | 0.956123i | \(0.405358\pi\) | |||||||
\(102\) | 39.6347 | + | 25.3965i | 0.0384747 | + | 0.0246532i | ||||
\(103\) | 499.830 | + | 499.830i | 0.478153 | + | 0.478153i | 0.904540 | − | 0.426388i | \(-0.140214\pi\) |
−0.426388 | + | 0.904540i | \(0.640214\pi\) | |||||||
\(104\) | 1065.31 | − | 804.207i | 1.00445 | − | 0.758260i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −261.570 | − | 1194.68i | −0.239678 | − | 1.09470i | ||||
\(107\) | −716.517 | + | 716.517i | −0.647367 | + | 0.647367i | −0.952356 | − | 0.304989i | \(-0.901347\pi\) |
0.304989 | + | 0.952356i | \(0.401347\pi\) | |||||||
\(108\) | 139.327 | + | 51.5398i | 0.124136 | + | 0.0459206i | ||||
\(109\) | 680.181i | 0.597702i | 0.954300 | + | 0.298851i | \(0.0966034\pi\) | ||||
−0.954300 | + | 0.298851i | \(0.903397\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 65.5540i | 0.0560550i | ||||||||
\(112\) | −66.2051 | − | 860.608i | −0.0558553 | − | 0.726070i | ||||
\(113\) | 30.3535 | − | 30.3535i | 0.0252692 | − | 0.0252692i | −0.694359 | − | 0.719629i | \(-0.744312\pi\) |
0.719629 | + | 0.694359i | \(0.244312\pi\) | |||||||
\(114\) | 124.409 | − | 27.2388i | 0.102210 | − | 0.0223785i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 584.431 | − | 268.802i | 0.467785 | − | 0.215152i | ||||
\(117\) | −1121.27 | − | 1121.27i | −0.885993 | − | 0.885993i | ||||
\(118\) | 270.312 | − | 421.859i | 0.210883 | − | 0.329113i | ||||
\(119\) | −651.297 | −0.501717 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −455.344 | −0.342107 | ||||||||
\(122\) | 63.2799 | − | 98.7571i | 0.0469598 | − | 0.0732872i | ||||
\(123\) | −37.9144 | − | 37.9144i | −0.0277937 | − | 0.0277937i | ||||
\(124\) | −1985.96 | + | 913.420i | −1.43826 | + | 0.661513i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1001.69 | + | 219.315i | −0.708235 | + | 0.155064i | ||||
\(127\) | 1252.53 | − | 1252.53i | 0.875147 | − | 0.875147i | −0.117880 | − | 0.993028i | \(-0.537610\pi\) |
0.993028 | + | 0.117880i | \(0.0376100\pi\) | |||||||
\(128\) | −1085.47 | + | 958.596i | −0.749554 | + | 0.661943i | ||||
\(129\) | 108.951i | 0.0743614i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 262.746i | − | 0.175238i | −0.996154 | − | 0.0876192i | \(-0.972074\pi\) | ||
0.996154 | − | 0.0876192i | \(-0.0279259\pi\) | |||||||
\(132\) | 109.290 | + | 40.4285i | 0.0720640 | + | 0.0266580i | ||||
\(133\) | −1245.98 | + | 1245.98i | −0.812331 | + | 0.812331i | ||||
\(134\) | 223.926 | + | 1022.75i | 0.144360 | + | 0.659345i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 658.363 | + | 872.117i | 0.415104 | + | 0.549878i | ||||
\(137\) | 1252.60 | + | 1252.60i | 0.781146 | + | 0.781146i | 0.980024 | − | 0.198878i | \(-0.0637298\pi\) |
−0.198878 | + | 0.980024i | \(0.563730\pi\) | |||||||
\(138\) | −124.690 | − | 79.8968i | −0.0769154 | − | 0.0492846i | ||||
\(139\) | 2028.30 | 1.23768 | 0.618842 | − | 0.785516i | \(-0.287602\pi\) | ||||
0.618842 | + | 0.785516i | \(0.287602\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 35.1487 | 0.0209933 | ||||||||
\(142\) | −1765.76 | − | 1131.43i | −1.04352 | − | 0.668647i | ||||
\(143\) | −1762.96 | − | 1762.96i | −1.03095 | − | 1.03095i | ||||
\(144\) | 1306.23 | + | 1119.61i | 0.755920 | + | 0.647925i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 442.154 | + | 2019.47i | 0.250636 | + | 1.14475i | ||||
\(147\) | 39.2608 | − | 39.2608i | 0.0220284 | − | 0.0220284i | ||||
\(148\) | −527.948 | + | 1427.19i | −0.293224 | + | 0.792665i | ||||
\(149\) | 2992.83i | 1.64552i | 0.568392 | + | 0.822758i | \(0.307566\pi\) | ||||
−0.568392 | + | 0.822758i | \(0.692434\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 184.103i | − | 0.0992192i | −0.998769 | − | 0.0496096i | \(-0.984202\pi\) | ||
0.998769 | − | 0.0496096i | \(-0.0157977\pi\) | |||||||
\(152\) | 2927.92 | + | 408.926i | 1.56240 | + | 0.218212i | ||||
\(153\) | 917.924 | − | 917.924i | 0.485031 | − | 0.485031i | ||||
\(154\) | −1574.95 | + | 344.827i | −0.824110 | + | 0.180435i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 67.9597 | + | 147.758i | 0.0348790 | + | 0.0758342i | ||||
\(157\) | −1301.36 | − | 1301.36i | −0.661530 | − | 0.661530i | 0.294211 | − | 0.955741i | \(-0.404943\pi\) |
−0.955741 | + | 0.294211i | \(0.904943\pi\) | |||||||
\(158\) | −339.874 | + | 530.420i | −0.171132 | + | 0.267076i | ||||
\(159\) | 149.016 | 0.0743252 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2048.97 | 1.00299 | ||||||||
\(162\) | 1097.77 | − | 1713.22i | 0.532400 | − | 0.830884i | ||||
\(163\) | −1460.57 | − | 1460.57i | −0.701843 | − | 0.701843i | 0.262963 | − | 0.964806i | \(-0.415300\pi\) |
−0.964806 | + | 0.262963i | \(0.915300\pi\) | |||||||
\(164\) | −520.095 | − | 1130.79i | −0.247638 | − | 0.538416i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3222.56 | + | 705.563i | −1.50674 | + | 0.329894i | ||||
\(167\) | −1656.63 | + | 1656.63i | −0.767626 | + | 0.767626i | −0.977688 | − | 0.210062i | \(-0.932633\pi\) |
0.210062 | + | 0.977688i | \(0.432633\pi\) | |||||||
\(168\) | 104.161 | + | 14.5475i | 0.0478343 | + | 0.00668074i | ||||
\(169\) | − | 1282.77i | − | 0.583872i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 3512.11i | − | 1.57063i | ||||||
\(172\) | −877.455 | + | 2372.00i | −0.388984 | + | 1.05153i | ||||
\(173\) | −1601.81 | + | 1601.81i | −0.703952 | + | 0.703952i | −0.965256 | − | 0.261304i | \(-0.915847\pi\) |
0.261304 | + | 0.965256i | \(0.415847\pi\) | |||||||
\(174\) | 16.7641 | + | 76.5678i | 0.00730395 | + | 0.0333597i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2053.78 | + | 1760.36i | 0.879598 | + | 0.753933i | ||||
\(177\) | 43.1681 | + | 43.1681i | 0.0183317 | + | 0.0183317i | ||||
\(178\) | 3446.06 | + | 2208.11i | 1.45109 | + | 0.929802i | ||||
\(179\) | 37.6748 | 0.0157316 | 0.00786578 | − | 0.999969i | \(-0.497496\pi\) | ||||
0.00786578 | + | 0.999969i | \(0.497496\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1360.64 | −0.558762 | −0.279381 | − | 0.960180i | \(-0.590129\pi\) | ||||
−0.279381 | + | 0.960180i | \(0.590129\pi\) | |||||||
\(182\) | −1894.65 | − | 1214.02i | −0.771651 | − | 0.494446i | ||||
\(183\) | 10.1056 | + | 10.1056i | 0.00408213 | + | 0.00408213i | ||||
\(184\) | −2071.20 | − | 2743.66i | −0.829842 | − | 1.09927i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −56.9665 | − | 260.186i | −0.0224569 | − | 0.102569i | ||||
\(187\) | 1443.24 | − | 1443.24i | 0.564388 | − | 0.564388i | ||||
\(188\) | 765.232 | + | 283.076i | 0.296863 | + | 0.109816i | ||||
\(189\) | − | 250.438i | − | 0.0963846i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3587.14i | − | 1.35893i | −0.733706 | − | 0.679467i | \(-0.762211\pi\) | ||
0.733706 | − | 0.679467i | \(-0.237789\pi\) | |||||||
\(192\) | −85.8108 | − | 154.181i | −0.0322545 | − | 0.0579534i | ||||
\(193\) | 3631.68 | − | 3631.68i | 1.35448 | − | 1.35448i | 0.473894 | − | 0.880582i | \(-0.342848\pi\) |
0.880582 | − | 0.473894i | \(-0.157152\pi\) | |||||||
\(194\) | −766.843 | + | 167.896i | −0.283794 | + | 0.0621354i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1170.95 | − | 538.564i | 0.426731 | − | 0.196270i | ||||
\(197\) | −235.786 | − | 235.786i | −0.0852746 | − | 0.0852746i | 0.663183 | − | 0.748457i | \(-0.269205\pi\) |
−0.748457 | + | 0.663183i | \(0.769205\pi\) | |||||||
\(198\) | 1733.71 | − | 2705.69i | 0.622269 | − | 0.971137i | ||||
\(199\) | 2893.75 | 1.03081 | 0.515407 | − | 0.856945i | \(-0.327641\pi\) | ||||
0.515407 | + | 0.856945i | \(0.327641\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −127.570 | −0.0447667 | ||||||||
\(202\) | −907.550 | + | 1416.36i | −0.316114 | + | 0.493340i | ||||
\(203\) | −766.838 | − | 766.838i | −0.265131 | − | 0.265131i | ||||
\(204\) | −120.962 | + | 55.6351i | −0.0415149 | + | 0.0190943i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1953.06 | + | 427.612i | −0.660563 | + | 0.144627i | ||||
\(207\) | −2887.77 | + | 2887.77i | −0.969634 | + | 0.969634i | ||||
\(208\) | 289.574 | + | 3764.21i | 0.0965306 | + | 1.25481i | ||||
\(209\) | − | 5522.06i | − | 1.82760i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2956.45i | 0.964599i | 0.876006 | + | 0.482300i | \(0.160198\pi\) | ||||
−0.876006 | + | 0.482300i | \(0.839802\pi\) | |||||||
\(212\) | 3244.26 | + | 1200.12i | 1.05102 | + | 0.388795i | ||||
\(213\) | 180.687 | − | 180.687i | 0.0581242 | − | 0.0581242i | ||||
\(214\) | −612.991 | − | 2799.75i | −0.195809 | − | 0.894331i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −335.348 | + | 253.155i | −0.105637 | + | 0.0797455i | ||||
\(217\) | 2605.81 | + | 2605.81i | 0.815178 | + | 0.815178i | ||||
\(218\) | −1619.84 | − | 1037.93i | −0.503253 | − | 0.322466i | ||||
\(219\) | −251.894 | −0.0777233 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2848.71 | 0.867080 | ||||||||
\(222\) | −156.115 | − | 100.033i | −0.0471972 | − | 0.0302422i | ||||
\(223\) | 1581.62 | + | 1581.62i | 0.474946 | + | 0.474946i | 0.903511 | − | 0.428565i | \(-0.140981\pi\) |
−0.428565 | + | 0.903511i | \(0.640981\pi\) | |||||||
\(224\) | 2150.54 | + | 1155.59i | 0.641470 | + | 0.344692i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 25.9679 | + | 118.605i | 0.00764318 | + | 0.0349091i | ||||
\(227\) | −668.464 | + | 668.464i | −0.195452 | + | 0.195452i | −0.798047 | − | 0.602595i | \(-0.794133\pi\) |
0.602595 | + | 0.798047i | \(0.294133\pi\) | |||||||
\(228\) | −124.975 | + | 337.843i | −0.0363013 | + | 0.0981325i | ||||
\(229\) | 3515.88i | 1.01457i | 0.861779 | + | 0.507284i | \(0.169350\pi\) | ||||
−0.861779 | + | 0.507284i | \(0.830650\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 196.447i | − | 0.0559535i | ||||||
\(232\) | −251.674 | + | 1801.99i | −0.0712206 | + | 0.509942i | ||||
\(233\) | 1658.86 | − | 1658.86i | 0.466420 | − | 0.466420i | −0.434333 | − | 0.900752i | \(-0.643016\pi\) |
0.900752 | + | 0.434333i | \(0.143016\pi\) | |||||||
\(234\) | 4381.29 | − | 959.261i | 1.22399 | − | 0.267986i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 592.163 | + | 1287.48i | 0.163333 | + | 0.355119i | ||||
\(237\) | −54.2769 | − | 54.2769i | −0.0148762 | − | 0.0148762i | ||||
\(238\) | 993.855 | − | 1551.05i | 0.270681 | − | 0.422435i | ||||
\(239\) | −1712.05 | −0.463360 | −0.231680 | − | 0.972792i | \(-0.574422\pi\) | ||||
−0.231680 | + | 0.972792i | \(0.574422\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5796.70 | −1.54937 | −0.774685 | − | 0.632348i | \(-0.782091\pi\) | ||||
−0.774685 | + | 0.632348i | \(0.782091\pi\) | |||||||
\(242\) | 694.838 | − | 1084.39i | 0.184570 | − | 0.288047i | ||||
\(243\) | 529.832 | + | 529.832i | 0.139871 | + | 0.139871i | ||||
\(244\) | 138.625 | + | 301.399i | 0.0363711 | + | 0.0790783i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 148.148 | − | 32.4364i | 0.0383967 | − | 0.00840677i | ||||
\(247\) | 5449.78 | − | 5449.78i | 1.40389 | − | 1.40389i | ||||
\(248\) | 855.217 | − | 6123.37i | 0.218977 | − | 1.56788i | ||||
\(249\) | − | 401.957i | − | 0.102301i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2040.48i | 0.513123i | 0.966528 | + | 0.256562i | \(0.0825897\pi\) | ||||
−0.966528 | + | 0.256562i | \(0.917410\pi\) | |||||||
\(252\) | 1006.25 | − | 2720.17i | 0.251538 | − | 0.679978i | ||||
\(253\) | −4540.43 | + | 4540.43i | −1.12828 | + | 1.12828i | ||||
\(254\) | 1071.55 | + | 4894.17i | 0.264706 | + | 1.20901i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −626.489 | − | 4047.81i | −0.152952 | − | 0.988234i | ||||
\(257\) | −757.135 | − | 757.135i | −0.183770 | − | 0.183770i | 0.609227 | − | 0.792996i | \(-0.291480\pi\) |
−0.792996 | + | 0.609227i | \(0.791480\pi\) | |||||||
\(258\) | −259.465 | − | 166.256i | −0.0626108 | − | 0.0401187i | ||||
\(259\) | 2565.36 | 0.615459 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2161.53 | 0.512626 | ||||||||
\(262\) | 625.724 | + | 400.941i | 0.147547 | + | 0.0945428i | ||||
\(263\) | 1842.73 | + | 1842.73i | 0.432045 | + | 0.432045i | 0.889323 | − | 0.457279i | \(-0.151176\pi\) |
−0.457279 | + | 0.889323i | \(0.651176\pi\) | |||||||
\(264\) | −263.052 | + | 198.578i | −0.0613247 | + | 0.0462942i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1065.95 | − | 4868.58i | −0.245706 | − | 1.12223i | ||||
\(267\) | −352.629 | + | 352.629i | −0.0808260 | + | 0.0808260i | ||||
\(268\) | −2777.36 | − | 1027.40i | −0.633039 | − | 0.234174i | ||||
\(269\) | 4651.65i | 1.05433i | 0.849762 | + | 0.527167i | \(0.176746\pi\) | ||||
−0.849762 | + | 0.527167i | \(0.823254\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8533.48i | 1.91281i | 0.292040 | + | 0.956406i | \(0.405666\pi\) | ||||
−0.292040 | + | 0.956406i | \(0.594334\pi\) | |||||||
\(272\) | −3081.56 | + | 237.060i | −0.686939 | + | 0.0528450i | ||||
\(273\) | 193.876 | − | 193.876i | 0.0429813 | − | 0.0429813i | ||||
\(274\) | −4894.47 | + | 1071.62i | −1.07914 | + | 0.236273i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 380.545 | − | 175.027i | 0.0829932 | − | 0.0381717i | ||||
\(277\) | −1883.72 | − | 1883.72i | −0.408598 | − | 0.408598i | 0.472652 | − | 0.881249i | \(-0.343297\pi\) |
−0.881249 | + | 0.472652i | \(0.843297\pi\) | |||||||
\(278\) | −3095.11 | + | 4830.35i | −0.667742 | + | 1.04210i | ||||
\(279\) | −7345.13 | −1.57614 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1365.56 | −0.289902 | −0.144951 | − | 0.989439i | \(-0.546303\pi\) | ||||
−0.144951 | + | 0.989439i | \(0.546303\pi\) | |||||||
\(282\) | −53.6357 | + | 83.7060i | −0.0113261 | + | 0.0176759i | ||||
\(283\) | 2275.91 | + | 2275.91i | 0.478052 | + | 0.478052i | 0.904508 | − | 0.426456i | \(-0.140238\pi\) |
−0.426456 | + | 0.904508i | \(0.640238\pi\) | |||||||
\(284\) | 5388.97 | − | 2478.59i | 1.12597 | − | 0.517878i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6888.66 | − | 1508.24i | 1.42425 | − | 0.311832i | ||||
\(287\) | −1483.73 | + | 1483.73i | −0.305163 | + | 0.305163i | ||||
\(288\) | −4659.59 | + | 1402.27i | −0.953365 | + | 0.286908i | ||||
\(289\) | − | 2580.91i | − | 0.525323i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 95.6501i | − | 0.0192684i | ||||||
\(292\) | −5484.04 | − | 2028.66i | −1.09907 | − | 0.406570i | ||||
\(293\) | −2859.58 | + | 2859.58i | −0.570165 | + | 0.570165i | −0.932175 | − | 0.362009i | \(-0.882091\pi\) |
0.362009 | + | 0.932175i | \(0.382091\pi\) | |||||||
\(294\) | 33.5882 | + | 153.409i | 0.00666294 | + | 0.0304320i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2593.20 | − | 3435.14i | −0.509211 | − | 0.674539i | ||||
\(297\) | 554.960 | + | 554.960i | 0.108424 | + | 0.108424i | ||||
\(298\) | −7127.35 | − | 4566.94i | −1.38549 | − | 0.887771i | ||||
\(299\) | −8961.98 | −1.73339 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4263.66 | 0.816455 | ||||||||
\(302\) | 438.437 | + | 280.935i | 0.0835405 | + | 0.0535297i | ||||
\(303\) | −144.933 | − | 144.933i | −0.0274792 | − | 0.0274792i | ||||
\(304\) | −5441.74 | + | 6348.76i | −1.02666 | + | 1.19778i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 785.297 | + | 3586.73i | 0.146707 | + | 0.670065i | ||||
\(307\) | −528.300 | + | 528.300i | −0.0982139 | + | 0.0982139i | −0.754507 | − | 0.656293i | \(-0.772124\pi\) |
0.656293 | + | 0.754507i | \(0.272124\pi\) | |||||||
\(308\) | 1582.12 | − | 4276.90i | 0.292693 | − | 0.791230i | ||||
\(309\) | − | 243.609i | − | 0.0448494i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 395.402i | 0.0720938i | 0.999350 | + | 0.0360469i | \(0.0114766\pi\) | ||||
−0.999350 | + | 0.0360469i | \(0.988523\pi\) | |||||||
\(312\) | −455.587 | − | 63.6293i | −0.0826684 | − | 0.0115458i | ||||
\(313\) | −804.658 | + | 804.658i | −0.145310 | + | 0.145310i | −0.776019 | − | 0.630709i | \(-0.782764\pi\) |
0.630709 | + | 0.776019i | \(0.282764\pi\) | |||||||
\(314\) | 5085.00 | − | 1113.34i | 0.913896 | − | 0.200093i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −744.549 | − | 1618.80i | −0.132545 | − | 0.288180i | ||||
\(317\) | −3696.00 | − | 3696.00i | −0.654852 | − | 0.654852i | 0.299305 | − | 0.954157i | \(-0.403245\pi\) |
−0.954157 | + | 0.299305i | \(0.903245\pi\) | |||||||
\(318\) | −227.392 | + | 354.877i | −0.0400991 | + | 0.0625803i | ||||
\(319\) | 3398.56 | 0.596498 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 349.219 | 0.0607212 | ||||||||
\(322\) | −3126.65 | + | 4879.58i | −0.541123 | + | 0.844497i | ||||
\(323\) | 4461.45 | + | 4461.45i | 0.768551 | + | 0.768551i | ||||
\(324\) | 2404.84 | + | 5228.62i | 0.412353 | + | 0.896540i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5707.08 | − | 1249.54i | 0.969588 | − | 0.212287i | ||||
\(327\) | 165.755 | − | 165.755i | 0.0280314 | − | 0.0280314i | ||||
\(328\) | 3486.61 | + | 486.955i | 0.586938 | + | 0.0819743i | ||||
\(329\) | − | 1375.50i | − | 0.230497i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1388.78i | 0.230617i | 0.993330 | + | 0.115308i | \(0.0367856\pi\) | ||||
−0.993330 | + | 0.115308i | \(0.963214\pi\) | |||||||
\(332\) | 3237.22 | − | 8751.11i | 0.535137 | − | 1.44663i | ||||
\(333\) | −3615.57 | + | 3615.57i | −0.594991 | + | 0.594991i | ||||
\(334\) | −1417.27 | − | 6473.17i | −0.232184 | − | 1.06047i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −193.590 | + | 225.857i | −0.0314321 | + | 0.0366712i | ||||
\(337\) | 2766.70 | + | 2766.70i | 0.447216 | + | 0.447216i | 0.894428 | − | 0.447212i | \(-0.147583\pi\) |
−0.447212 | + | 0.894428i | \(0.647583\pi\) | |||||||
\(338\) | 3054.88 | + | 1957.45i | 0.491608 | + | 0.315004i | ||||
\(339\) | −14.7938 | −0.00237018 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11548.7 | −1.83401 | ||||||||
\(342\) | 8364.01 | + | 5359.35i | 1.32244 | + | 0.847369i | ||||
\(343\) | −4807.46 | − | 4807.46i | −0.756788 | − | 0.756788i | ||||
\(344\) | −4309.91 | − | 5709.23i | −0.675509 | − | 0.894829i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1370.38 | − | 6259.00i | −0.212925 | − | 0.972502i | ||||
\(347\) | 2069.91 | − | 2069.91i | 0.320227 | − | 0.320227i | −0.528627 | − | 0.848854i | \(-0.677293\pi\) |
0.848854 | + | 0.528627i | \(0.177293\pi\) | |||||||
\(348\) | −207.926 | − | 76.9162i | −0.0320288 | − | 0.0118481i | ||||
\(349\) | 5774.64i | 0.885700i | 0.896596 | + | 0.442850i | \(0.146033\pi\) | ||||
−0.896596 | + | 0.442850i | \(0.853967\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1095.39i | 0.166574i | ||||||||
\(352\) | −7326.25 | + | 2204.78i | −1.10935 | + | 0.333849i | ||||
\(353\) | 7965.11 | − | 7965.11i | 1.20096 | − | 1.20096i | 0.227089 | − | 0.973874i | \(-0.427079\pi\) |
0.973874 | − | 0.227089i | \(-0.0729208\pi\) | |||||||
\(354\) | −168.677 | + | 36.9309i | −0.0253250 | + | 0.00554479i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10517.1 | + | 4837.23i | −1.56575 | + | 0.720148i | ||||
\(357\) | 158.716 | + | 158.716i | 0.0235298 | + | 0.0235298i | ||||
\(358\) | −57.4904 | + | 89.7218i | −0.00848733 | + | 0.0132457i | ||||
\(359\) | 6227.61 | 0.915545 | 0.457773 | − | 0.889069i | \(-0.348647\pi\) | ||||
0.457773 | + | 0.889069i | \(0.348647\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10211.2 | 1.48872 | ||||||||
\(362\) | 2076.29 | − | 3240.35i | 0.301457 | − | 0.470466i | ||||
\(363\) | 110.964 | + | 110.964i | 0.0160443 | + | 0.0160443i | ||||
\(364\) | 5782.32 | − | 2659.51i | 0.832626 | − | 0.382956i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −39.4871 | + | 8.64551i | −0.00563941 | + | 0.00123472i | ||||
\(367\) | 3426.52 | − | 3426.52i | 0.487365 | − | 0.487365i | −0.420109 | − | 0.907474i | \(-0.638008\pi\) |
0.907474 | + | 0.420109i | \(0.138008\pi\) | |||||||
\(368\) | 9694.55 | − | 745.786i | 1.37327 | − | 0.105643i | ||||
\(369\) | − | 4182.27i | − | 0.590028i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 5831.52i | − | 0.816058i | ||||||
\(372\) | 706.557 | + | 261.370i | 0.0984765 | + | 0.0364285i | ||||
\(373\) | 4631.53 | − | 4631.53i | 0.642926 | − | 0.642926i | −0.308347 | − | 0.951274i | \(-0.599776\pi\) |
0.951274 | + | 0.308347i | \(0.0997759\pi\) | |||||||
\(374\) | 1234.72 | + | 5639.39i | 0.170710 | + | 0.779696i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1841.85 | + | 1390.42i | −0.252623 | + | 0.190706i | ||||
\(377\) | 3354.07 | + | 3354.07i | 0.458206 | + | 0.458206i | ||||
\(378\) | 596.413 | + | 382.159i | 0.0811539 | + | 0.0520004i | ||||
\(379\) | 10644.7 | 1.44269 | 0.721347 | − | 0.692574i | \(-0.243523\pi\) | ||||
0.721347 | + | 0.692574i | \(0.243523\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −610.461 | −0.0820863 | ||||||||
\(382\) | 8542.70 | + | 5473.85i | 1.14419 | + | 0.733158i | ||||
\(383\) | 2301.02 | + | 2301.02i | 0.306988 | + | 0.306988i | 0.843740 | − | 0.536752i | \(-0.180349\pi\) |
−0.536752 | + | 0.843740i | \(0.680349\pi\) | |||||||
\(384\) | 498.123 | + | 30.9180i | 0.0661972 | + | 0.00410880i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3106.95 | + | 14190.6i | 0.409688 | + | 1.87119i | ||||
\(387\) | −6009.10 | + | 6009.10i | −0.789302 | + | 0.789302i | ||||
\(388\) | 770.332 | − | 2082.42i | 0.100793 | − | 0.272472i | ||||
\(389\) | − | 5636.87i | − | 0.734706i | −0.930082 | − | 0.367353i | \(-0.880264\pi\) | ||
0.930082 | − | 0.367353i | \(-0.119736\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7336.71i | − | 0.948935i | ||||||
\(392\) | −504.247 | + | 3610.42i | −0.0649702 | + | 0.465188i | ||||
\(393\) | −64.0291 | + | 64.0291i | −0.00821843 | + | 0.00821843i | ||||
\(394\) | 921.322 | − | 201.719i | 0.117806 | − | 0.0257930i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3797.97 | + | 8257.57i | 0.481958 | + | 1.04787i | ||||
\(397\) | 6539.04 | + | 6539.04i | 0.826663 | + | 0.826663i | 0.987054 | − | 0.160391i | \(-0.0512754\pi\) |
−0.160391 | + | 0.987054i | \(0.551275\pi\) | |||||||
\(398\) | −4415.75 | + | 6891.39i | −0.556134 | + | 0.867925i | ||||
\(399\) | 607.270 | 0.0761943 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5980.28 | −0.744740 | −0.372370 | − | 0.928084i | \(-0.621455\pi\) | ||||
−0.372370 | + | 0.928084i | \(0.621455\pi\) | |||||||
\(402\) | 194.667 | − | 303.805i | 0.0241521 | − | 0.0376926i | ||||
\(403\) | −11397.5 | − | 11397.5i | −1.40881 | − | 1.40881i | ||||
\(404\) | −1988.14 | − | 4322.62i | −0.244835 | − | 0.532323i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2996.38 | − | 656.042i | 0.366275 | − | 0.0801941i | ||||
\(407\) | −5684.73 | + | 5684.73i | −0.692338 | + | 0.692338i | ||||
\(408\) | 52.0900 | − | 372.966i | 0.00632069 | − | 0.0452563i | ||||
\(409\) | − | 5150.66i | − | 0.622698i | −0.950296 | − | 0.311349i | \(-0.899219\pi\) | ||
0.950296 | − | 0.311349i | \(-0.100781\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 610.499i | − | 0.0732693i | ||||||
\(412\) | 1961.94 | − | 5303.68i | 0.234607 | − | 0.634208i | ||||
\(413\) | 1689.32 | − | 1689.32i | 0.201274 | − | 0.201274i | ||||
\(414\) | −2470.53 | − | 11283.8i | −0.293285 | − | 1.33954i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9406.26 | − | 5054.43i | −1.10861 | − | 0.595706i | ||||
\(417\) | −494.280 | − | 494.280i | −0.0580456 | − | 0.0580456i | ||||
\(418\) | 13150.7 | + | 8426.46i | 1.53880 | + | 0.986009i | ||||
\(419\) | −3080.65 | −0.359188 | −0.179594 | − | 0.983741i | \(-0.557478\pi\) | ||||
−0.179594 | + | 0.983741i | \(0.557478\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5636.62 | 0.652523 | 0.326261 | − | 0.945280i | \(-0.394211\pi\) | ||||
0.326261 | + | 0.945280i | \(0.394211\pi\) | |||||||
\(422\) | −7040.72 | − | 4511.43i | −0.812173 | − | 0.520410i | ||||
\(423\) | 1938.60 | + | 1938.60i | 0.222832 | + | 0.222832i | ||||
\(424\) | −7808.67 | + | 5894.79i | −0.894393 | + | 0.675180i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 154.580 | + | 706.023i | 0.0175808 | + | 0.0802980i | ||||
\(427\) | 395.470 | − | 395.470i | 0.0448199 | − | 0.0448199i | ||||
\(428\) | 7602.94 | + | 2812.49i | 0.858649 | + | 0.317632i | ||||
\(429\) | 859.239i | 0.0967004i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 12970.7i | − | 1.44959i | −0.688963 | − | 0.724797i | \(-0.741934\pi\) | ||
0.688963 | − | 0.724797i | \(-0.258066\pi\) | |||||||
\(432\) | −91.1547 | − | 1184.93i | −0.0101520 | − | 0.131968i | ||||
\(433\) | −181.752 | + | 181.752i | −0.0201719 | + | 0.0201719i | −0.717121 | − | 0.696949i | \(-0.754540\pi\) |
0.696949 | + | 0.717121i | \(0.254540\pi\) | |||||||
\(434\) | −10182.0 | + | 2229.31i | −1.12616 | + | 0.246567i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4943.62 | − | 2273.76i | 0.543020 | − | 0.249755i | ||||
\(437\) | −14035.7 | − | 14035.7i | −1.53642 | − | 1.53642i | ||||
\(438\) | 384.380 | − | 599.879i | 0.0419324 | − | 0.0654414i | ||||
\(439\) | 5465.06 | 0.594153 | 0.297076 | − | 0.954854i | \(-0.403988\pi\) | ||||
0.297076 | + | 0.954854i | \(0.403988\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4330.79 | 0.467637 | ||||||||
\(442\) | −4347.02 | + | 6784.13i | −0.467798 | + | 0.730064i | ||||
\(443\) | −4982.88 | − | 4982.88i | −0.534410 | − | 0.534410i | 0.387472 | − | 0.921882i | \(-0.373349\pi\) |
−0.921882 | + | 0.387472i | \(0.873349\pi\) | |||||||
\(444\) | 476.452 | − | 219.139i | 0.0509266 | − | 0.0234231i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6180.07 | + | 1353.10i | −0.656132 | + | 0.143657i | ||||
\(447\) | 729.328 | − | 729.328i | 0.0771724 | − | 0.0771724i | ||||
\(448\) | −6033.66 | + | 3358.09i | −0.636303 | + | 0.354140i | ||||
\(449\) | 11884.7i | 1.24916i | 0.780960 | + | 0.624581i | \(0.214730\pi\) | ||||
−0.780960 | + | 0.624581i | \(0.785270\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 6575.75i | − | 0.686563i | ||||||
\(452\) | −322.080 | − | 119.144i | −0.0335164 | − | 0.0123984i | ||||
\(453\) | −44.8645 | + | 44.8645i | −0.00465324 | + | 0.00465324i | ||||
\(454\) | −571.881 | − | 2611.98i | −0.0591183 | − | 0.270014i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −613.858 | − | 813.162i | −0.0630407 | − | 0.0835084i | ||||
\(457\) | −1360.58 | − | 1360.58i | −0.139267 | − | 0.139267i | 0.634036 | − | 0.773303i | \(-0.281397\pi\) |
−0.773303 | + | 0.634036i | \(0.781397\pi\) | |||||||
\(458\) | −8372.99 | − | 5365.10i | −0.854245 | − | 0.547369i | ||||
\(459\) | −896.740 | −0.0911901 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8133.56 | 0.821730 | 0.410865 | − | 0.911696i | \(-0.365227\pi\) | ||||
0.410865 | + | 0.911696i | \(0.365227\pi\) | |||||||
\(462\) | 467.834 | + | 299.771i | 0.0471117 | + | 0.0301875i | ||||
\(463\) | −1938.32 | − | 1938.32i | −0.194560 | − | 0.194560i | 0.603103 | − | 0.797663i | \(-0.293931\pi\) |
−0.797663 | + | 0.603103i | \(0.793931\pi\) | |||||||
\(464\) | −3907.35 | − | 3349.13i | −0.390936 | − | 0.335085i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1419.18 | + | 6481.91i | 0.141078 | + | 0.644354i | ||||
\(467\) | 8462.63 | − | 8462.63i | 0.838552 | − | 0.838552i | −0.150116 | − | 0.988668i | \(-0.547965\pi\) |
0.988668 | + | 0.150116i | \(0.0479648\pi\) | |||||||
\(468\) | −4401.22 | + | 11897.7i | −0.434715 | + | 1.17516i | ||||
\(469\) | 4992.28i | 0.491518i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 634.264i | 0.0620496i | ||||||||
\(472\) | −3969.73 | − | 554.430i | −0.387122 | − | 0.0540671i | ||||
\(473\) | −9448.07 | + | 9448.07i | −0.918441 | + | 0.918441i | ||||
\(474\) | 212.084 | − | 46.4347i | 0.0205513 | − | 0.00449961i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2177.20 | + | 4733.69i | 0.209647 | + | 0.455816i | ||||
\(477\) | 8218.81 | + | 8218.81i | 0.788918 | + | 0.788918i | ||||
\(478\) | 2612.52 | − | 4077.20i | 0.249987 | − | 0.390140i | ||||
\(479\) | −7570.70 | −0.722158 | −0.361079 | − | 0.932535i | \(-0.617592\pi\) | ||||
−0.361079 | + | 0.932535i | \(0.617592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11220.6 | −1.06365 | ||||||||
\(482\) | 8845.55 | − | 13804.7i | 0.835899 | − | 1.30454i | ||||
\(483\) | −499.318 | − | 499.318i | −0.0470388 | − | 0.0470388i | ||||
\(484\) | 1522.16 | + | 3309.48i | 0.142952 | + | 0.310808i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2070.29 | + | 453.279i | −0.193231 | + | 0.0423069i | ||||
\(487\) | −9502.42 | + | 9502.42i | −0.884181 | + | 0.884181i | −0.993956 | − | 0.109776i | \(-0.964987\pi\) |
0.109776 | + | 0.993956i | \(0.464987\pi\) | |||||||
\(488\) | −929.312 | − | 129.792i | −0.0862049 | − | 0.0120397i | ||||
\(489\) | 711.857i | 0.0658309i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8188.17i | 0.752601i | 0.926498 | + | 0.376300i | \(0.122804\pi\) | ||||
−0.926498 | + | 0.376300i | \(0.877196\pi\) | |||||||
\(492\) | −148.823 | + | 402.309i | −0.0136371 | + | 0.0368648i | ||||
\(493\) | −2745.81 | + | 2745.81i | −0.250842 | + | 0.250842i | ||||
\(494\) | 4662.36 | + | 21294.7i | 0.424635 | + | 1.93946i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13277.6 | + | 11380.7i | 1.20198 | + | 1.03026i | ||||
\(497\) | −7070.93 | − | 7070.93i | −0.638178 | − | 0.638178i | ||||
\(498\) | 957.252 | + | 613.372i | 0.0861355 | + | 0.0551925i | ||||
\(499\) | 429.740 | 0.0385527 | 0.0192764 | − | 0.999814i | \(-0.493864\pi\) | ||||
0.0192764 | + | 0.999814i | \(0.493864\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 807.414 | 0.0720012 | ||||||||
\(502\) | −4859.36 | − | 3113.70i | −0.432039 | − | 0.276835i | ||||
\(503\) | −8511.42 | − | 8511.42i | −0.754484 | − | 0.754484i | 0.220829 | − | 0.975313i | \(-0.429124\pi\) |
−0.975313 | + | 0.220829i | \(0.929124\pi\) | |||||||
\(504\) | 4942.52 | + | 6547.23i | 0.436820 | + | 0.578645i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3884.40 | − | 17741.4i | −0.341270 | − | 1.55870i | ||||
\(507\) | −312.600 | + | 312.600i | −0.0273827 | + | 0.0273827i | ||||
\(508\) | −13290.5 | − | 4916.44i | −1.16077 | − | 0.429393i | ||||
\(509\) | − | 3762.37i | − | 0.327631i | −0.986491 | − | 0.163816i | \(-0.947620\pi\) | ||
0.986491 | − | 0.163816i | \(-0.0523802\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9857.51i | 0.853367i | ||||||||
\(512\) | 10595.8 | + | 4684.83i | 0.914591 | + | 0.404379i | ||||
\(513\) | −1715.53 | + | 1715.53i | −0.147646 | + | 0.147646i | ||||
\(514\) | 2958.46 | − | 647.740i | 0.253876 | − | 0.0555848i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 791.868 | − | 364.210i | 0.0675582 | − | 0.0310726i | ||||
\(517\) | 3048.04 | + | 3048.04i | 0.259290 | + | 0.259290i | ||||
\(518\) | −3914.65 | + | 6109.36i | −0.332046 | + | 0.518204i | ||||
\(519\) | 780.699 | 0.0660287 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 818.504 | 0.0688279 | 0.0344139 | − | 0.999408i | \(-0.489044\pi\) | ||||
0.0344139 | + | 0.999408i | \(0.489044\pi\) | |||||||
\(522\) | −3298.42 | + | 5147.64i | −0.276567 | + | 0.431621i | ||||
\(523\) | 14975.1 | + | 14975.1i | 1.25203 | + | 1.25203i | 0.954807 | + | 0.297227i | \(0.0960618\pi\) |
0.297227 | + | 0.954807i | \(0.403938\pi\) | |||||||
\(524\) | −1909.66 | + | 878.327i | −0.159206 | + | 0.0732250i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7200.37 | + | 1576.48i | −0.596865 | + | 0.130681i | ||||
\(527\) | 9330.57 | − | 9330.57i | 0.771245 | − | 0.771245i | ||||
\(528\) | −71.5030 | − | 929.475i | −0.00589350 | − | 0.0766102i | ||||
\(529\) | 10914.2i | 0.897032i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4761.79i | 0.389160i | ||||||||
\(532\) | 13221.0 | + | 4890.74i | 1.07745 | + | 0.398572i | ||||
\(533\) | 6489.68 | − | 6489.68i | 0.527390 | − | 0.527390i | ||||
\(534\) | −301.679 | − | 1377.88i | −0.0244475 | − | 0.111660i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6684.89 | − | 5046.45i | 0.538701 | − | 0.406666i | ||||
\(537\) | −9.18106 | − | 9.18106i | −0.000737788 | − | 0.000737788i | ||||
\(538\) | −11077.8 | − | 7098.24i | −0.887728 | − | 0.568823i | ||||
\(539\) | 6809.26 | 0.544148 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1894.75 | −0.150576 | −0.0752879 | − | 0.997162i | \(-0.523988\pi\) | ||||
−0.0752879 | + | 0.997162i | \(0.523988\pi\) | |||||||
\(542\) | −20322.3 | − | 13021.8i | −1.61055 | − | 1.03198i | ||||
\(543\) | 331.578 | + | 331.578i | 0.0262051 | + | 0.0262051i | ||||
\(544\) | 4137.80 | − | 7700.42i | 0.326115 | − | 0.606899i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 165.863 | + | 757.557i | 0.0130005 | + | 0.0593781i | ||||
\(547\) | 8079.10 | − | 8079.10i | 0.631513 | − | 0.631513i | −0.316935 | − | 0.948447i | \(-0.602654\pi\) |
0.948447 | + | 0.316935i | \(0.102654\pi\) | |||||||
\(548\) | 4916.74 | − | 13291.3i | 0.383271 | − | 1.03609i | ||||
\(549\) | 1114.73i | 0.0866587i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10505.8i | 0.812276i | ||||||||
\(552\) | −163.874 | + | 1173.34i | −0.0126358 | + | 0.0904726i | ||||
\(553\) | −2124.05 | + | 2124.05i | −0.163334 | + | 0.163334i | ||||
\(554\) | 7360.51 | − | 1611.55i | 0.564473 | − | 0.123589i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6780.34 | − | 14741.9i | −0.517177 | − | 1.12445i | ||||
\(557\) | 11900.0 | + | 11900.0i | 0.905243 | + | 0.905243i | 0.995884 | − | 0.0906404i | \(-0.0288914\pi\) |
−0.0906404 | + | 0.995884i | \(0.528891\pi\) | |||||||
\(558\) | 11208.4 | − | 17492.3i | 0.850340 | − | 1.32707i | ||||
\(559\) | −18648.8 | −1.41102 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −703.415 | −0.0529380 | ||||||||
\(562\) | 2083.80 | − | 3252.06i | 0.156405 | − | 0.244092i | ||||
\(563\) | 11749.3 | + | 11749.3i | 0.879526 | + | 0.879526i | 0.993485 | − | 0.113959i | \(-0.0363533\pi\) |
−0.113959 | + | 0.993485i | \(0.536353\pi\) | |||||||
\(564\) | −117.498 | − | 255.464i | −0.00877225 | − | 0.0190727i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8892.97 | + | 1947.07i | −0.660423 | + | 0.144596i | ||||
\(567\) | 6860.54 | − | 6860.54i | 0.508140 | − | 0.508140i | ||||
\(568\) | −2320.66 | + | 16616.0i | −0.171431 | + | 1.22745i | ||||
\(569\) | − | 2172.30i | − | 0.160049i | −0.996793 | − | 0.0800243i | \(-0.974500\pi\) | ||
0.996793 | − | 0.0800243i | \(-0.0254998\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5608.37i | 0.411039i | 0.978653 | + | 0.205519i | \(0.0658884\pi\) | ||||
−0.978653 | + | 0.205519i | \(0.934112\pi\) | |||||||
\(572\) | −6920.01 | + | 18706.7i | −0.505839 | + | 1.36742i | ||||
\(573\) | −874.158 | + | 874.158i | −0.0637321 | + | 0.0637321i | ||||
\(574\) | −1269.35 | − | 5797.58i | −0.0923027 | − | 0.421579i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3770.90 | − | 13236.5i | 0.272779 | − | 0.957504i | ||||
\(577\) | −16686.9 | − | 16686.9i | −1.20396 | − | 1.20396i | −0.972951 | − | 0.231010i | \(-0.925797\pi\) |
−0.231010 | − | 0.972951i | \(-0.574203\pi\) | |||||||
\(578\) | 6146.38 | + | 3938.38i | 0.442311 | + | 0.283417i | ||||
\(579\) | −1770.02 | −0.127046 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15730.0 | −1.12322 | ||||||||
\(582\) | 227.789 | + | 145.959i | 0.0162236 | + | 0.0103955i | ||||
\(583\) | 12922.4 | + | 12922.4i | 0.917994 | + | 0.917994i | ||||
\(584\) | 13199.7 | − | 9964.46i | 0.935284 | − | 0.706048i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2446.41 | − | 11173.6i | −0.172458 | − | 0.787677i | ||||
\(587\) | −19717.2 | + | 19717.2i | −1.38640 | + | 1.38640i | −0.553650 | + | 0.832749i | \(0.686766\pi\) |
−0.832749 | + | 0.553650i | \(0.813234\pi\) | |||||||
\(588\) | −416.595 | − | 154.107i | −0.0292178 | − | 0.0108083i | ||||
\(589\) | − | 35700.1i | − | 2.49745i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 114.919i | 0.00799851i | ||||||||
\(592\) | 12137.8 | − | 933.743i | 0.842672 | − | 0.0648254i | ||||
\(593\) | −168.200 | + | 168.200i | −0.0116478 | + | 0.0116478i | −0.712907 | − | 0.701259i | \(-0.752622\pi\) |
0.701259 | + | 0.712907i | \(0.252622\pi\) | |||||||
\(594\) | −2168.47 | + | 474.776i | −0.149787 | + | 0.0327951i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 21752.1 | − | 10004.6i | 1.49497 | − | 0.687594i | ||||
\(597\) | −705.183 | − | 705.183i | −0.0483438 | − | 0.0483438i | ||||
\(598\) | 13675.7 | − | 21342.8i | 0.935182 | − | 1.45948i | ||||
\(599\) | −3488.67 | −0.237969 | −0.118984 | − | 0.992896i | \(-0.537964\pi\) | ||||
−0.118984 | + | 0.992896i | \(0.537964\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10909.5 | 0.740443 | 0.370222 | − | 0.928943i | \(-0.379282\pi\) | ||||
0.370222 | + | 0.928943i | \(0.379282\pi\) | |||||||
\(602\) | −6506.18 | + | 10153.8i | −0.440485 | + | 0.687439i | ||||
\(603\) | −7036.01 | − | 7036.01i | −0.475172 | − | 0.475172i | ||||
\(604\) | −1338.08 | + | 615.433i | −0.0901418 | + | 0.0414596i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 566.318 | − | 123.993i | 0.0379622 | − | 0.00831164i | ||||
\(607\) | −12048.9 | + | 12048.9i | −0.805683 | + | 0.805683i | −0.983977 | − | 0.178294i | \(-0.942942\pi\) |
0.178294 | + | 0.983977i | \(0.442942\pi\) | |||||||
\(608\) | −6815.55 | − | 22647.4i | −0.454617 | − | 1.51064i | ||||
\(609\) | 373.745i | 0.0248685i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6016.28i | 0.398352i | ||||||||
\(612\) | −9740.06 | − | 3603.05i | −0.643331 | − | 0.237982i | ||||
\(613\) | 7796.28 | − | 7796.28i | 0.513685 | − | 0.513685i | −0.401969 | − | 0.915653i | \(-0.631674\pi\) |
0.915653 | + | 0.401969i | \(0.131674\pi\) | |||||||
\(614\) | −451.969 | − | 2064.30i | −0.0297068 | − | 0.135681i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7771.09 | + | 10294.2i | 0.508289 | + | 0.673318i | ||||
\(617\) | 20235.1 | + | 20235.1i | 1.32031 | + | 1.32031i | 0.913521 | + | 0.406791i | \(0.133352\pi\) |
0.406791 | + | 0.913521i | \(0.366648\pi\) | |||||||
\(618\) | 580.150 | + | 371.739i | 0.0377622 | + | 0.0241967i | ||||
\(619\) | −22702.2 | −1.47411 | −0.737057 | − | 0.675830i | \(-0.763785\pi\) | ||||
−0.737057 | + | 0.675830i | \(0.763785\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2821.13 | 0.182300 | ||||||||
\(622\) | −941.641 | − | 603.369i | −0.0607015 | − | 0.0388953i | ||||
\(623\) | 13799.7 | + | 13799.7i | 0.887434 | + | 0.887434i | ||||
\(624\) | 846.741 | − | 987.875i | 0.0543218 | − | 0.0633760i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −688.397 | − | 3144.15i | −0.0439519 | − | 0.200744i | ||||
\(627\) | −1345.68 | + | 1345.68i | −0.0857120 | + | 0.0857120i | ||||
\(628\) | −5108.14 | + | 13808.7i | −0.324581 | + | 0.877434i | ||||
\(629\) | − | 9185.76i | − | 0.582289i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5787.42i | 0.365125i | 0.983194 | + | 0.182562i | \(0.0584391\pi\) | ||||
−0.983194 | + | 0.182562i | \(0.941561\pi\) | |||||||
\(632\) | 4991.30 | + | 697.106i | 0.314151 | + | 0.0438756i | ||||
\(633\) | 720.464 | − | 720.464i | 0.0452383 | − | 0.0452383i | ||||
\(634\) | 14441.9 | − | 3161.98i | 0.904671 | − | 0.198073i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −498.140 | − | 1083.06i | −0.0310575 | − | 0.0675253i | ||||
\(637\) | 6720.13 | + | 6720.13i | 0.417993 | + | 0.417993i | ||||
\(638\) | −5186.08 | + | 8093.59i | −0.321816 | + | 0.502239i | ||||
\(639\) | 19931.2 | 1.23391 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8721.43 | 0.537404 | 0.268702 | − | 0.963223i | \(-0.413405\pi\) | ||||
0.268702 | + | 0.963223i | \(0.413405\pi\) | |||||||
\(642\) | −532.895 | + | 831.658i | −0.0327597 | + | 0.0511260i | ||||
\(643\) | 2937.61 | + | 2937.61i | 0.180168 | + | 0.180168i | 0.791429 | − | 0.611261i | \(-0.209337\pi\) |
−0.611261 | + | 0.791429i | \(0.709337\pi\) | |||||||
\(644\) | −6849.45 | − | 14892.1i | −0.419109 | − | 0.911229i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17432.9 | + | 3816.84i | −1.06174 | + | 0.232464i | ||||
\(647\) | 18130.5 | − | 18130.5i | 1.10167 | − | 1.10167i | 0.107465 | − | 0.994209i | \(-0.465727\pi\) |
0.994209 | − | 0.107465i | \(-0.0342733\pi\) | |||||||
\(648\) | −16121.5 | − | 2251.60i | −0.977337 | − | 0.136499i | ||||
\(649\) | 7486.92i | 0.452831i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 1270.03i | − | 0.0764614i | ||||||
\(652\) | −5733.05 | + | 15498.0i | −0.344361 | + | 0.930904i | ||||
\(653\) | 14359.8 | − | 14359.8i | 0.860555 | − | 0.860555i | −0.130847 | − | 0.991403i | \(-0.541770\pi\) |
0.991403 | + | 0.130847i | \(0.0417698\pi\) | |||||||
\(654\) | 141.806 | + | 647.677i | 0.00847866 | + | 0.0387251i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6480.11 | + | 7560.20i | −0.385679 | + | 0.449964i | ||||
\(657\) | −13893.0 | − | 13893.0i | −0.824986 | − | 0.824986i | ||||
\(658\) | 3275.72 | + | 2098.96i | 0.194074 | + | 0.124356i | ||||
\(659\) | 14608.8 | 0.863550 | 0.431775 | − | 0.901981i | \(-0.357887\pi\) | ||||
0.431775 | + | 0.901981i | \(0.357887\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26434.7 | −1.55551 | −0.777755 | − | 0.628567i | \(-0.783642\pi\) | ||||
−0.777755 | + | 0.628567i | \(0.783642\pi\) | |||||||
\(662\) | −3307.34 | − | 2119.22i | −0.194175 | − | 0.124420i | ||||
\(663\) | −694.207 | − | 694.207i | −0.0406648 | − | 0.0406648i | ||||
\(664\) | 15900.7 | + | 21063.3i | 0.929318 | + | 1.23104i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3093.17 | − | 14127.6i | −0.179967 | − | 0.821973i | ||||
\(667\) | 8638.26 | − | 8638.26i | 0.501462 | − | 0.501462i | ||||
\(668\) | 17578.4 | + | 6502.62i | 1.01816 | + | 0.376638i | ||||
\(669\) | − | 770.855i | − | 0.0445485i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1752.69i | 0.100837i | ||||||||
\(672\) | −242.463 | − | 805.679i | −0.0139185 | − | 0.0462496i | ||||
\(673\) | −16012.9 | + | 16012.9i | −0.917167 | + | 0.917167i | −0.996822 | − | 0.0796554i | \(-0.974618\pi\) |
0.0796554 | + | 0.996822i | \(0.474618\pi\) | |||||||
\(674\) | −10810.7 | + | 2366.95i | −0.617824 | + | 0.135269i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9323.26 | + | 4288.12i | −0.530454 | + | 0.243976i | ||||
\(677\) | −5496.28 | − | 5496.28i | −0.312023 | − | 0.312023i | 0.533670 | − | 0.845693i | \(-0.320812\pi\) |
−0.845693 | + | 0.533670i | \(0.820812\pi\) | |||||||
\(678\) | 22.5749 | − | 35.2312i | 0.00127873 | − | 0.00199564i | ||||
\(679\) | −3743.14 | −0.211559 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 325.799 | 0.0183328 | ||||||||
\(682\) | 17622.9 | − | 27503.0i | 0.989465 | − | 1.54420i | ||||
\(683\) | −12875.9 | − | 12875.9i | −0.721351 | − | 0.721351i | 0.247530 | − | 0.968880i | \(-0.420381\pi\) |
−0.968880 | + | 0.247530i | \(0.920381\pi\) | |||||||
\(684\) | −25526.3 | + | 11740.5i | −1.42694 | + | 0.656302i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18784.9 | − | 4112.85i | 1.04549 | − | 0.228906i | ||||
\(687\) | 856.792 | − | 856.792i | 0.0475818 | − | 0.0475818i | ||||
\(688\) | 20173.2 | − | 1551.89i | 1.11787 | − | 0.0859959i | ||||
\(689\) | 25506.5i | 1.41033i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 9091.60i | − | 0.500522i | −0.968178 | − | 0.250261i | \(-0.919484\pi\) | ||
0.968178 | − | 0.250261i | \(-0.0805164\pi\) | |||||||
\(692\) | 16996.8 | + | 6287.48i | 0.933702 | + | 0.345396i | ||||
\(693\) | 10834.9 | − | 10834.9i | 0.593914 | − | 0.593914i | ||||
\(694\) | 1770.84 | + | 8088.07i | 0.0968592 | + | 0.442390i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 500.462 | − | 377.800i | 0.0272557 | − | 0.0205754i | ||||
\(697\) | 5312.76 | + | 5312.76i | 0.288716 | + | 0.288716i | ||||
\(698\) | −13752.2 | − | 8811.88i | −0.745741 | − | 0.477843i | ||||
\(699\) | −808.504 | −0.0437488 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19437.4 | 1.04728 | 0.523639 | − | 0.851941i | \(-0.324574\pi\) | ||||
0.523639 | + | 0.851941i | \(0.324574\pi\) | |||||||
\(702\) | −2608.65 | − | 1671.53i | −0.140252 | − | 0.0898685i | ||||
\(703\) | −17573.0 | − | 17573.0i | −0.942786 | − | 0.942786i | ||||
\(704\) | 5928.95 | − | 20811.7i | 0.317409 | − | 1.11416i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6814.27 | + | 31123.2i | 0.363255 | + | 1.65912i | ||||
\(707\) | −5671.76 | + | 5671.76i | −0.301709 | + | 0.301709i | ||||
\(708\) | 169.444 | − | 458.055i | 0.00899449 | − | 0.0243146i | ||||
\(709\) | 10638.6i | 0.563525i | 0.959484 | + | 0.281763i | \(0.0909190\pi\) | ||||
−0.959484 | + | 0.281763i | \(0.909081\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 5987.18i | − | 0.315804i | ||||||
\(712\) | 4529.00 | − | 32427.7i | 0.238387 | − | 1.70685i | ||||
\(713\) | −29353.8 | + | 29353.8i | −1.54181 | + | 1.54181i | ||||
\(714\) | −620.173 | + | 135.784i | −0.0325062 | + | 0.00711706i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −125.942 | − | 273.824i | −0.00657358 | − | 0.0142923i | ||||
\(717\) | 417.213 | + | 417.213i | 0.0217309 | + | 0.0217309i | ||||
\(718\) | −9503.10 | + | 14830.9i | −0.493945 | + | 0.770870i | ||||
\(719\) | 26377.6 | 1.36818 | 0.684089 | − | 0.729399i | \(-0.260200\pi\) | ||||
0.684089 | + | 0.729399i | \(0.260200\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9533.32 | −0.492426 | ||||||||
\(722\) | −15581.8 | + | 24317.6i | −0.803180 | + | 1.25347i | ||||
\(723\) | 1412.61 | + | 1412.61i | 0.0726632 | + | 0.0726632i | ||||
\(724\) | 4548.46 | + | 9889.29i | 0.233484 | + | 0.507642i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −433.584 | + | 94.9311i | −0.0221650 | + | 0.00485292i | ||||
\(727\) | −15452.7 | + | 15452.7i | −0.788321 | + | 0.788321i | −0.981219 | − | 0.192898i | \(-0.938211\pi\) |
0.192898 | + | 0.981219i | \(0.438211\pi\) | |||||||
\(728\) | −2490.04 | + | 17828.8i | −0.126768 | + | 0.907663i | ||||
\(729\) | 19165.4i | 0.973703i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 15266.8i | − | 0.772453i | ||||||
\(732\) | 39.6668 | − | 107.230i | 0.00200291 | − | 0.00541441i | ||||
\(733\) | 628.566 | − | 628.566i | 0.0316734 | − | 0.0316734i | −0.691093 | − | 0.722766i | \(-0.742870\pi\) |
0.722766 | + | 0.691093i | \(0.242870\pi\) | |||||||
\(734\) | 2931.44 | + | 13388.9i | 0.147413 | + | 0.673290i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13017.5 | + | 24225.4i | −0.651943 | + | 1.21326i | ||||
\(737\) | −11062.7 | − | 11062.7i | −0.552916 | − | 0.552916i | ||||
\(738\) | 9959.98 | + | 6381.99i | 0.496791 | + | 0.318326i | ||||
\(739\) | −27295.7 | −1.35871 | −0.679356 | − | 0.733809i | \(-0.737741\pi\) | ||||
−0.679356 | + | 0.733809i | \(0.737741\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2656.14 | −0.131681 | ||||||||
\(742\) | 13887.6 | + | 8898.68i | 0.687104 | + | 0.440271i | ||||
\(743\) | −19570.2 | − | 19570.2i | −0.966300 | − | 0.966300i | 0.0331505 | − | 0.999450i | \(-0.489446\pi\) |
−0.999450 | + | 0.0331505i | \(0.989446\pi\) | |||||||
\(744\) | −1700.63 | + | 1283.81i | −0.0838011 | + | 0.0632617i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3962.34 | + | 18097.4i | 0.194466 | + | 0.888196i | ||||
\(747\) | 22169.6 | − | 22169.6i | 1.08587 | − | 1.08587i | ||||
\(748\) | −15314.2 | − | 5665.06i | −0.748588 | − | 0.276918i | ||||
\(749\) | − | 13666.2i | − | 0.666692i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 23982.8i | − | 1.16530i | −0.812722 | − | 0.582652i | \(-0.802015\pi\) | ||
0.812722 | − | 0.582652i | \(-0.197985\pi\) | |||||||
\(752\) | −500.655 | − | 6508.07i | −0.0242779 | − | 0.315591i | ||||
\(753\) | 497.249 | − | 497.249i | 0.0240648 | − | 0.0240648i | ||||
\(754\) | −13105.8 | + | 2869.46i | −0.633006 | + | 0.138594i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1820.21 | + | 837.183i | −0.0875666 | + | 0.0402752i | ||||
\(757\) | −8554.31 | − | 8554.31i | −0.410716 | − | 0.410716i | 0.471272 | − | 0.881988i | \(-0.343795\pi\) |
−0.881988 | + | 0.471272i | \(0.843795\pi\) | |||||||
\(758\) | −16243.4 | + | 25350.1i | −0.778347 | + | 1.21472i | ||||
\(759\) | 2212.93 | 0.105829 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32552.3 | 1.55062 | 0.775308 | − | 0.631583i | \(-0.217594\pi\) | ||||
0.775308 | + | 0.631583i | \(0.217594\pi\) | |||||||
\(762\) | 931.542 | − | 1453.80i | 0.0442863 | − | 0.0691150i | ||||
\(763\) | −6486.59 | − | 6486.59i | −0.307772 | − | 0.307772i | ||||
\(764\) | −26071.7 | + | 11991.4i | −1.23461 | + | 0.567843i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8991.08 | + | 1968.55i | −0.424100 | + | 0.0928547i | ||||
\(767\) | −7388.92 | + | 7388.92i | −0.347847 | + | 0.347847i | ||||
\(768\) | −833.748 | + | 1139.09i | −0.0391735 | + | 0.0535200i | ||||
\(769\) | 1314.72i | 0.0616516i | 0.999525 | + | 0.0308258i | \(0.00981371\pi\) | ||||
−0.999525 | + | 0.0308258i | \(0.990186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 369.016i | 0.0172371i | ||||||||
\(772\) | −38535.6 | − | 14255.1i | −1.79654 | − | 0.664577i | ||||
\(773\) | 12385.8 | − | 12385.8i | 0.576307 | − | 0.576307i | −0.357576 | − | 0.933884i | \(-0.616397\pi\) |
0.933884 | + | 0.357576i | \(0.116397\pi\) | |||||||
\(774\) | −5140.88 | − | 23480.2i | −0.238740 | − | 1.09041i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3783.75 | + | 5012.23i | 0.175037 | + | 0.231867i | ||||
\(777\) | −625.159 | − | 625.159i | −0.0288642 | − | 0.0288642i | ||||
\(778\) | 13424.1 | + | 8601.65i | 0.618607 | + | 0.396381i | ||||
\(779\) | 20327.4 | 0.934922 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31337.7 | 1.43579 | ||||||||
\(782\) | 17472.2 | + | 11195.6i | 0.798984 | + | 0.511959i | ||||
\(783\) | −1055.82 | − | 1055.82i | −0.0481891 | − | 0.0481891i | ||||
\(784\) | −7828.67 | − | 6710.22i | −0.356627 | − | 0.305677i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −54.7779 | − | 250.190i | −0.00248583 | − | 0.0113537i | ||||
\(787\) | −25390.5 | + | 25390.5i | −1.15003 | + | 1.15003i | −0.163485 | + | 0.986546i | \(0.552273\pi\) |
−0.986546 | + | 0.163485i | \(0.947727\pi\) | |||||||
\(788\) | −925.514 | + | 2501.92i | −0.0418402 | + | 0.113106i | ||||
\(789\) | − | 898.119i | − | 0.0405245i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 578.937i | 0.0260235i | ||||||||
\(792\) | −25460.8 | − | 3555.96i | −1.14231 | − | 0.159540i | ||||
\(793\) | −1729.74 | + | 1729.74i | −0.0774590 | + | 0.0774590i | ||||
\(794\) | −25550.9 | + | 5594.25i | −1.14203 | + | 0.250041i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9673.43 | − | 21032.0i | −0.430736 | − | 0.936508i | ||||
\(797\) | 22408.5 | + | 22408.5i | 0.995921 | + | 0.995921i | 0.999992 | − | 0.00407064i | \(-0.00129573\pi\) |
−0.00407064 | + | 0.999992i | \(0.501296\pi\) | |||||||
\(798\) | −926.671 | + | 1446.20i | −0.0411075 | + | 0.0641540i | ||||
\(799\) | −4925.22 | −0.218075 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −38897.9 | −1.71584 | ||||||||
\(802\) | 9125.68 | − | 14241.9i | 0.401794 | − | 0.627056i | ||||
\(803\) | −21843.8 | − | 21843.8i | −0.959964 | − | 0.959964i | ||||
\(804\) | 426.451 | + | 927.192i | 0.0187062 | + | 0.0406711i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 44535.2 | − | 9750.75i | 1.94626 | − | 0.426124i | ||||
\(807\) | 1133.57 | − | 1133.57i | 0.0494468 | − | 0.0494468i | ||||
\(808\) | 13328.0 | + | 1861.45i | 0.580296 | + | 0.0810466i | ||||
\(809\) | − | 1556.16i | − | 0.0676286i | −0.999428 | − | 0.0338143i | \(-0.989235\pi\) | ||
0.999428 | − | 0.0338143i | \(-0.0107655\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 42796.7i | − | 1.85302i | −0.376274 | − | 0.926508i | \(-0.622795\pi\) | ||
0.376274 | − | 0.926508i | \(-0.377205\pi\) | |||||||
\(812\) | −3010.01 | + | 8136.90i | −0.130087 | + | 0.351662i | ||||
\(813\) | 2079.54 | − | 2079.54i | 0.0897082 | − | 0.0897082i | ||||
\(814\) | −4863.37 | − | 22212.8i | −0.209412 | − | 0.956458i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 808.723 | + | 693.183i | 0.0346948 | + | 0.0297381i | ||||
\(817\) | −29206.5 | − | 29206.5i | −1.25068 | − | 1.25068i | ||||
\(818\) | 12266.2 | + | 7859.71i | 0.524299 | + | 0.335952i | ||||
\(819\) | 21386.1 | 0.912441 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23614.4 | −1.00384 | −0.501918 | − | 0.864915i | \(-0.667372\pi\) | ||||
−0.501918 | + | 0.864915i | \(0.667372\pi\) | |||||||
\(822\) | 1453.89 | + | 931.598i | 0.0616912 | + | 0.0395295i | ||||
\(823\) | 23159.2 | + | 23159.2i | 0.980897 | + | 0.980897i | 0.999821 | − | 0.0189236i | \(-0.00602393\pi\) |
−0.0189236 | + | 0.999821i | \(0.506024\pi\) | |||||||
\(824\) | 9636.75 | + | 12765.5i | 0.407417 | + | 0.539695i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1445.24 | + | 6600.93i | 0.0608793 | + | 0.278058i | ||||
\(827\) | 10727.9 | − | 10727.9i | 0.451083 | − | 0.451083i | −0.444631 | − | 0.895714i | \(-0.646665\pi\) |
0.895714 | + | 0.444631i | \(0.146665\pi\) | |||||||
\(828\) | 30642.1 | + | 11335.1i | 1.28609 | + | 0.475753i | ||||
\(829\) | − | 19535.2i | − | 0.818437i | −0.912436 | − | 0.409219i | \(-0.865801\pi\) | ||
0.912436 | − | 0.409219i | \(-0.134199\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 918.094i | 0.0383253i | ||||||||
\(832\) | 26390.6 | − | 14687.9i | 1.09968 | − | 0.612034i | ||||
\(833\) | −5501.43 | + | 5501.43i | −0.228827 | + | 0.228827i | ||||
\(834\) | 1931.37 | − | 422.864i | 0.0801893 | − | 0.0175571i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −40134.9 | + | 18459.6i | −1.66040 | + | 0.763681i | ||||
\(837\) | 3587.81 | + | 3587.81i | 0.148164 | + | 0.148164i | ||||
\(838\) | 4700.96 | − | 7336.50i | 0.193785 | − | 0.302429i | ||||
\(839\) | −25953.9 | −1.06797 | −0.533986 | − | 0.845493i | \(-0.679307\pi\) | ||||
−0.533986 | + | 0.845493i | \(0.679307\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17923.2 | 0.734887 | ||||||||
\(842\) | −8601.27 | + | 13423.5i | −0.352042 | + | 0.549411i | ||||
\(843\) | 332.777 | + | 332.777i | 0.0135960 | + | 0.0135960i | ||||
\(844\) | 21487.8 | − | 9883.04i | 0.876350 | − | 0.403067i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7574.95 | + | 1658.50i | −0.307839 | + | 0.0673999i | ||||
\(847\) | 4342.41 | − | 4342.41i | 0.176159 | − | 0.176159i | ||||
\(848\) | −2122.56 | − | 27591.4i | −0.0859541 | − | 1.11733i | ||||
\(849\) | − | 1109.24i | − | 0.0448399i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28898.2i | 1.16406i | ||||||||
\(852\) | −1917.26 | − | 709.236i | −0.0770943 | − | 0.0285188i | ||||
\(853\) | 18421.1 | − | 18421.1i | 0.739421 | − | 0.739421i | −0.233045 | − | 0.972466i | \(-0.574869\pi\) |
0.972466 | + | 0.233045i | \(0.0748689\pi\) | |||||||
\(854\) | 338.330 | + | 1545.27i | 0.0135567 | + | 0.0619183i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18299.7 | + | 13814.5i | −0.730689 | + | 0.551599i | ||||
\(857\) | 10613.8 | + | 10613.8i | 0.423060 | + | 0.423060i | 0.886256 | − | 0.463196i | \(-0.153297\pi\) |
−0.463196 | + | 0.886256i | \(0.653297\pi\) | |||||||
\(858\) | −2046.26 | − | 1311.17i | −0.0814197 | − | 0.0521708i | ||||
\(859\) | 16534.0 | 0.656732 | 0.328366 | − | 0.944551i | \(-0.393502\pi\) | ||||
0.328366 | + | 0.944551i | \(0.393502\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 723.146 | 0.0286234 | ||||||||
\(862\) | 30889.3 | + | 19792.7i | 1.22053 | + | 0.782069i | ||||
\(863\) | −3057.61 | − | 3057.61i | −0.120605 | − | 0.120605i | 0.644228 | − | 0.764833i | \(-0.277179\pi\) |
−0.764833 | + | 0.644228i | \(0.777179\pi\) | |||||||
\(864\) | 2960.98 | + | 1591.08i | 0.116591 | + | 0.0626499i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −155.491 | − | 710.184i | −0.00610140 | − | 0.0278673i | ||||
\(867\) | −628.948 | + | 628.948i | −0.0246369 | + | 0.0246369i | ||||
\(868\) | 10228.4 | − | 27650.1i | 0.399969 | − | 1.08123i | ||||
\(869\) | − | 9413.60i | − | 0.367474i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 21835.7i | − | 0.849455i | ||||||
\(872\) | −2128.88 | + | 15242.8i | −0.0826753 | + | 0.591957i | ||||
\(873\) | 5275.49 | − | 5275.49i | 0.204523 | − | 0.204523i | ||||
\(874\) | 54843.5 | − | 12007.7i | 2.12255 | − | 0.464722i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 842.049 | + | 1830.79i | 0.0324774 | + | 0.0706125i | ||||
\(877\) | 27748.3 | + | 27748.3i | 1.06841 | + | 1.06841i | 0.997482 | + | 0.0709256i | \(0.0225953\pi\) |
0.0709256 | + | 0.997482i | \(0.477405\pi\) | |||||||
\(878\) | −8339.48 | + | 13014.9i | −0.320551 | + | 0.500264i | ||||
\(879\) | 1393.71 | 0.0534799 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11660.4 | 0.445911 | 0.222955 | − | 0.974829i | \(-0.428430\pi\) | ||||
0.222955 | + | 0.974829i | \(0.428430\pi\) | |||||||
\(882\) | −6608.62 | + | 10313.7i | −0.252295 | + | 0.393741i | ||||
\(883\) | 15502.9 | + | 15502.9i | 0.590844 | + | 0.590844i | 0.937859 | − | 0.347016i | \(-0.112805\pi\) |
−0.347016 | + | 0.937859i | \(0.612805\pi\) | |||||||
\(884\) | −9522.86 | − | 20704.7i | −0.362317 | − | 0.787752i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19470.3 | − | 4262.93i | 0.738282 | − | 0.161643i | ||||
\(887\) | 4784.23 | − | 4784.23i | 0.181103 | − | 0.181103i | −0.610733 | − | 0.791836i | \(-0.709125\pi\) |
0.791836 | + | 0.610733i | \(0.209125\pi\) | |||||||
\(888\) | −205.175 | + | 1469.06i | −0.00775363 | + | 0.0555162i | ||||
\(889\) | 23889.6i | 0.901272i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 30405.3i | 1.14323i | ||||||||
\(892\) | 6208.19 | − | 16782.5i | 0.233033 | − | 0.629954i | ||||
\(893\) | −9422.30 | + | 9422.30i | −0.353085 | + | 0.353085i | ||||
\(894\) | 623.951 | + | 2849.81i | 0.0233423 | + | 0.106613i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1209.93 | − | 19493.4i | 0.0451128 | − | 0.726816i | ||||
\(897\) | 2183.96 | + | 2183.96i | 0.0812937 | + | 0.0812937i | ||||
\(898\) | −28303.1 | − | 18135.6i | −1.05177 | − | 0.673934i | ||||
\(899\) | 21971.7 | 0.815124 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20880.8 | −0.772077 | ||||||||
\(902\) | 15660.0 | + | 10034.4i | 0.578072 | + | 0.370407i | ||||
\(903\) | −1039.02 | − | 1039.02i | −0.0382906 | − | 0.0382906i | ||||
\(904\) | 775.223 | − | 585.218i | 0.0285216 | − | 0.0215310i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −38.3822 | − | 175.305i | −0.00140747 | − | 0.00642840i | ||||
\(907\) | −27277.3 | + | 27277.3i | −0.998598 | + | 0.998598i | −0.999999 | − | 0.00140132i | \(-0.999554\pi\) |
0.00140132 | + | 0.999999i | \(0.499554\pi\) | |||||||
\(908\) | 7093.05 | + | 2623.87i | 0.259241 | + | 0.0958989i | ||||
\(909\) | − | 15987.3i | − | 0.583351i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37452.0i | 1.36206i | 0.732254 | + | 0.681032i | \(0.238469\pi\) | ||||
−0.732254 | + | 0.681032i | \(0.761531\pi\) | |||||||
\(912\) | 2873.25 | − | 221.035i | 0.104323 | − | 0.00802542i | ||||
\(913\) | 34857.1 | − | 34857.1i | 1.26353 | − | 1.26353i | ||||
\(914\) | 5316.37 | − | 1163.99i | 0.192396 | − | 0.0421242i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 25553.7 | − | 11753.1i | 0.921746 | − | 0.423946i | ||||
\(917\) | 2505.69 | + | 2505.69i | 0.0902347 | + | 0.0902347i | ||||
\(918\) | 1368.39 | − | 2135.57i | 0.0491979 | − | 0.0767802i | ||||
\(919\) | −7803.81 | −0.280113 | −0.140057 | − | 0.990144i | \(-0.544728\pi\) | ||||
−0.140057 | + | 0.990144i | \(0.544728\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 257.485 | 0.00921219 | ||||||||
\(922\) | −12411.5 | + | 19369.9i | −0.443331 | + | 0.691880i | ||||
\(923\) | 30927.5 | + | 30927.5i | 1.10292 | + | 1.10292i | ||||
\(924\) | −1427.80 | + | 656.698i | −0.0508345 | + | 0.0233807i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7573.88 | − | 1658.26i | 0.268783 | − | 0.0588487i | ||||
\(927\) | 13436.0 | − | 13436.0i | 0.476049 | − | 0.476049i | ||||
\(928\) | 13938.3 | − | 4194.64i | 0.493048 | − | 0.148379i | ||||
\(929\) | − | 6045.30i | − | 0.213498i | −0.994286 | − | 0.106749i | \(-0.965956\pi\) | ||
0.994286 | − | 0.106749i | \(-0.0340442\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21049.2i | 0.740989i | ||||||||
\(932\) | −17602.1 | − | 6511.41i | −0.618645 | − | 0.228850i | ||||
\(933\) | 96.3563 | − | 96.3563i | 0.00338110 | − | 0.00338110i | ||||
\(934\) | 7239.91 | + | 33067.2i | 0.253637 | + | 1.15845i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −21618.1 | − | 28636.9i | −0.754924 | − | 1.00003i | ||||
\(937\) | −6094.14 | − | 6094.14i | −0.212473 | − | 0.212473i | 0.592844 | − | 0.805317i | \(-0.298005\pi\) |
−0.805317 | + | 0.592844i | \(0.798005\pi\) | |||||||
\(938\) | −11889.0 | − | 7618.04i | −0.413849 | − | 0.265179i | ||||
\(939\) | 392.178 | 0.0136296 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11090.5 | −0.384207 | −0.192103 | − | 0.981375i | \(-0.561531\pi\) | ||||
−0.192103 | + | 0.981375i | \(0.561531\pi\) | |||||||
\(942\) | −1510.49 | − | 967.864i | −0.0522445 | − | 0.0334763i | ||||
\(943\) | −16713.9 | − | 16713.9i | −0.577178 | − | 0.577178i | ||||
\(944\) | 7378.02 | − | 8607.79i | 0.254379 | − | 0.296779i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8082.96 | − | 36917.8i | −0.277801 | − | 1.26882i | ||||
\(947\) | 35216.3 | − | 35216.3i | 1.20842 | − | 1.20842i | 0.236886 | − | 0.971537i | \(-0.423873\pi\) |
0.971537 | − | 0.236886i | \(-0.0761268\pi\) | |||||||
\(948\) | −213.049 | + | 575.930i | −0.00729905 | + | 0.0197314i | ||||
\(949\) | − | 43115.7i | − | 1.47481i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1801.37i | 0.0614233i | ||||||||
\(952\) | −14595.5 | − | 2038.47i | −0.496894 | − | 0.0693984i | ||||
\(953\) | −28821.7 | + | 28821.7i | −0.979670 | + | 0.979670i | −0.999797 | − | 0.0201277i | \(-0.993593\pi\) |
0.0201277 | + | 0.999797i | \(0.493593\pi\) | |||||||
\(954\) | −32114.5 | + | 7031.32i | −1.08988 | + | 0.238624i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5723.16 | + | 12443.3i | 0.193619 | + | 0.420968i | ||||
\(957\) | −828.202 | − | 828.202i | −0.0279749 | − | 0.0279749i | ||||
\(958\) | 11552.6 | − | 18029.4i | 0.389611 | − | 0.608043i | ||||
\(959\) | −23891.0 | −0.804464 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −44871.3 | −1.50620 | ||||||||
\(962\) | 17122.3 | − | 26721.7i | 0.573851 | − | 0.895574i | ||||
\(963\) | 19260.9 | + | 19260.9i | 0.644520 | + | 0.644520i | ||||
\(964\) | 19377.6 | + | 42130.9i | 0.647418 | + | 1.40762i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1951.06 | − | 427.174i | 0.0649836 | − | 0.0142278i | ||||
\(967\) | −224.697 | + | 224.697i | −0.00747237 | + | 0.00747237i | −0.710833 | − | 0.703361i | \(-0.751682\pi\) |
0.703361 | + | 0.710833i | \(0.251682\pi\) | |||||||
\(968\) | −10204.2 | − | 1425.16i | −0.338818 | − | 0.0473208i | ||||
\(969\) | − | 2174.44i | − | 0.0720878i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1315.64i | − | 0.0434818i | −0.999764 | − | 0.0217409i | \(-0.993079\pi\) | ||
0.999764 | − | 0.0217409i | \(-0.00692089\pi\) | |||||||
\(972\) | 2079.71 | − | 5622.03i | 0.0686283 | − | 0.185521i | ||||
\(973\) | −19343.0 | + | 19343.0i | −0.637315 | + | 0.637315i | ||||
\(974\) | −8129.46 | − | 37130.2i | −0.267438 | − | 1.22149i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1727.19 | − | 2015.08i | 0.0566456 | − | 0.0660872i | ||||
\(977\) | 2608.70 | + | 2608.70i | 0.0854246 | + | 0.0854246i | 0.748528 | − | 0.663103i | \(-0.230761\pi\) |
−0.663103 | + | 0.748528i | \(0.730761\pi\) | |||||||
\(978\) | −1695.27 | − | 1086.27i | −0.0554283 | − | 0.0355164i | ||||
\(979\) | −61158.8 | −1.99657 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18284.1 | 0.595073 | ||||||||
\(982\) | −19500.0 | − | 12494.8i | −0.633675 | − | 0.406035i | ||||
\(983\) | 38327.7 | + | 38327.7i | 1.24360 | + | 1.24360i | 0.958495 | + | 0.285109i | \(0.0920297\pi\) |
0.285109 | + | 0.958495i | \(0.407970\pi\) | |||||||
\(984\) | −730.992 | − | 968.326i | −0.0236821 | − | 0.0313710i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2349.08 | − | 10729.1i | −0.0758721 | − | 0.346535i | ||||
\(987\) | −335.198 | + | 335.198i | −0.0108100 | + | 0.0108100i | ||||
\(988\) | −57827.4 | − | 21391.6i | −1.86208 | − | 0.688823i | ||||
\(989\) | 48029.1i | 1.54422i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 3912.43i | − | 0.125411i | −0.998032 | − | 0.0627055i | \(-0.980027\pi\) | ||
0.998032 | − | 0.0627055i | \(-0.0199729\pi\) | |||||||
\(992\) | −47364.1 | + | 14253.9i | −1.51594 | + | 0.456210i | ||||
\(993\) | 338.434 | − | 338.434i | 0.0108156 | − | 0.0108156i | ||||
\(994\) | 27629.2 | − | 6049.29i | 0.881636 | − | 0.193030i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2921.46 | + | 1343.69i | −0.0929419 | + | 0.0427475i | ||||
\(997\) | −41715.2 | − | 41715.2i | −1.32511 | − | 1.32511i | −0.909579 | − | 0.415531i | \(-0.863596\pi\) |
−0.415531 | − | 0.909579i | \(-0.636404\pi\) | |||||||
\(998\) | −655.767 | + | 1023.42i | −0.0207995 | + | 0.0324606i | ||||
\(999\) | 3532.13 | 0.111863 |
(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 | 100.4.e.f.7.5 | yes | 24 | |
4.3 | odd | 2 | inner | 100.4.e.f.7.11 | yes | 24 | |
5.2 | odd | 4 | inner | 100.4.e.f.43.2 | yes | 24 | |
5.3 | odd | 4 | inner | 100.4.e.f.43.11 | yes | 24 | |
5.4 | even | 2 | inner | 100.4.e.f.7.8 | yes | 24 | |
20.3 | even | 4 | inner | 100.4.e.f.43.5 | yes | 24 | |
20.7 | even | 4 | inner | 100.4.e.f.43.8 | yes | 24 | |
20.19 | odd | 2 | inner | 100.4.e.f.7.2 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
100.4.e.f.7.2 | ✓ | 24 | 20.19 | odd | 2 | inner | |
100.4.e.f.7.5 | yes | 24 | 1.1 | even | 1 | trivial | |
100.4.e.f.7.8 | yes | 24 | 5.4 | even | 2 | inner | |
100.4.e.f.7.11 | yes | 24 | 4.3 | odd | 2 | inner | |
100.4.e.f.43.2 | yes | 24 | 5.2 | odd | 4 | inner | |
100.4.e.f.43.5 | yes | 24 | 20.3 | even | 4 | inner | |
100.4.e.f.43.8 | yes | 24 | 20.7 | even | 4 | inner | |
100.4.e.f.43.11 | yes | 24 | 5.3 | odd | 4 | inner |