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 | 7.11 | ||
Character | \(\chi\) | \(=\) | 100.7 |
Dual form | 100.4.e.f.43.11 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.38148 | − | 1.52596i | 0.841980 | − | 0.539509i | ||||
\(3\) | 0.243692 | + | 0.243692i | 0.0468986 | + | 0.0468986i | 0.730167 | − | 0.683269i | \(-0.239442\pi\) |
−0.683269 | + | 0.730167i | \(0.739442\pi\) | |||||||
\(4\) | 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 | −0.401106 | − | 0.916032i | \(-0.631374\pi\) |
0.916032 | + | 0.401106i | \(0.131374\pi\) | |||||||
\(8\) | −3.12986 | − | 22.4099i | −0.138322 | − | 0.990387i | ||||
\(9\) | − | 26.8812i | − | 0.995601i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 42.2652i | 1.15849i | 0.815152 | + | 0.579247i | \(0.196653\pi\) | ||||
−0.815152 | + | 0.579247i | \(0.803347\pi\) | |||||||
\(12\) | 2.58581 | − | 0.956545i | 0.0622049 | − | 0.0230109i | ||||
\(13\) | 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 | \(0.638054\pi\) | |||||||
\(18\) | −41.0198 | − | 64.0170i | −0.537136 | − | 0.838276i | ||||
\(19\) | −130.653 | −1.57757 | −0.788784 | − | 0.614670i | \(-0.789289\pi\) | ||||
−0.788784 | + | 0.614670i | \(0.789289\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.64797 | 0.0482986 | ||||||||
\(22\) | 64.4951 | + | 100.654i | 0.625018 | + | 0.975428i | ||||
\(23\) | 107.427 | + | 107.427i | 0.973918 | + | 0.973918i | 0.999668 | − | 0.0257506i | \(-0.00819758\pi\) |
−0.0257506 | + | 0.999668i | \(0.508198\pi\) | |||||||
\(24\) | 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 | ||||
\(28\) | −37.4331 | − | 101.192i | −0.252650 | − | 0.682982i | ||||
\(29\) | 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 | \(0.290725\pi\) | ||||
−0.611105 | + | 0.791550i | \(0.709275\pi\) | |||||||
\(32\) | −173.340 | − | 52.1653i | −0.957578 | − | 0.288175i | ||||
\(33\) | −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 | \(0.888876\pi\) | |||||||
\(38\) | −311.147 | + | 199.371i | −1.32828 | + | 0.851113i | ||||
\(39\) | 20.3297 | 0.0834708 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 155.583 | 0.592635 | 0.296317 | − | 0.955090i | \(-0.404241\pi\) | ||||
0.296317 | + | 0.955090i | \(0.404241\pi\) | |||||||
\(42\) | 11.0690 | − | 7.09263i | 0.0406664 | − | 0.0260575i | ||||
\(43\) | 223.543 | + | 223.543i | 0.792789 | + | 0.792789i | 0.981947 | − | 0.189157i | \(-0.0605756\pi\) |
−0.189157 | + | 0.981947i | \(0.560576\pi\) | |||||||
\(44\) | 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 | −0.586287 | − | 0.810103i | \(-0.699411\pi\) |
0.810103 | + | 0.586287i | \(0.199411\pi\) | |||||||
\(48\) | 1.69177 | − | 21.9915i | 0.00508721 | − | 0.0661292i | ||||
\(49\) | 161.108i | 0.469703i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 16.6429i | 0.0456955i | ||||||||
\(52\) | −163.728 | − | 442.604i | −0.436636 | − | 1.18035i | ||||
\(53\) | −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 | ||||
\(58\) | 122.703 | + | 191.496i | 0.277789 | + | 0.433528i | ||||
\(59\) | 177.142 | 0.390880 | 0.195440 | − | 0.980716i | \(-0.437387\pi\) | ||||
0.195440 | + | 0.980716i | \(0.437387\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −41.4688 | −0.0870416 | −0.0435208 | − | 0.999053i | \(-0.513857\pi\) | ||||
−0.0435208 | + | 0.999053i | \(0.513857\pi\) | |||||||
\(62\) | 416.960 | + | 650.725i | 0.854097 | + | 1.33294i | ||||
\(63\) | −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 | −0.904258 | − | 0.426987i | \(-0.859575\pi\) |
0.426987 | + | 0.904258i | \(0.359575\pi\) | |||||||
\(68\) | 362.337 | − | 134.036i | 0.646174 | − | 0.239033i | ||||
\(69\) | 52.3583i | 0.0913507i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 741.456i | − | 1.23936i | −0.784854 | − | 0.619680i | \(-0.787262\pi\) | ||
0.784854 | − | 0.619680i | \(-0.212738\pi\) | |||||||
\(72\) | −602.406 | + | 84.1346i | −0.986031 | + | 0.137713i | ||||
\(73\) | 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 | ||||
\(78\) | 48.4148 | − | 31.0224i | 0.0702807 | − | 0.0450333i | ||||
\(79\) | −222.727 | −0.317200 | −0.158600 | − | 0.987343i | \(-0.550698\pi\) | ||||
−0.158600 | + | 0.987343i | \(0.550698\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −719.394 | −0.986822 | ||||||||
\(82\) | 370.518 | − | 237.414i | 0.498986 | − | 0.319732i | ||||
\(83\) | −824.724 | − | 824.724i | −1.09066 | − | 1.09066i | −0.995457 | − | 0.0952072i | \(-0.969649\pi\) |
−0.0952072 | − | 0.995457i | \(-0.530351\pi\) | |||||||
\(84\) | 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 | ||||
\(88\) | 947.158 | − | 132.284i | 1.14736 | − | 0.160245i | ||||
\(89\) | − | 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 | ||||||
\(92\) | 1139.91 | − | 421.675i | 1.29178 | − | 0.477855i | ||||
\(93\) | −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 | \(0.703599\pi\) | |||||||
\(98\) | 245.845 | + | 383.676i | 0.253409 | + | 0.395481i | ||||
\(99\) | 1136.14 | 1.15340 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 594.739 | 0.585928 | 0.292964 | − | 0.956123i | \(-0.405358\pi\) | ||||
0.292964 | + | 0.956123i | \(0.405358\pi\) | |||||||
\(102\) | 25.3965 | + | 39.6347i | 0.0246532 | + | 0.0384747i | ||||
\(103\) | −499.830 | − | 499.830i | −0.478153 | − | 0.478153i | 0.426388 | − | 0.904540i | \(-0.359786\pi\) |
−0.904540 | + | 0.426388i | \(0.859786\pi\) | |||||||
\(104\) | −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 | −0.304989 | − | 0.952356i | \(-0.598653\pi\) |
0.952356 | + | 0.304989i | \(0.0986527\pi\) | |||||||
\(108\) | −51.5398 | − | 139.327i | −0.0459206 | − | 0.124136i | ||||
\(109\) | 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 | ||||||
\(112\) | −860.608 | − | 66.2051i | −0.726070 | − | 0.0558553i | ||||
\(113\) | 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 | ||||
\(118\) | 421.859 | − | 270.312i | 0.329113 | − | 0.210883i | ||||
\(119\) | 651.297 | 0.501717 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −455.344 | −0.342107 | ||||||||
\(122\) | −98.7571 | + | 63.2799i | −0.0732872 | + | 0.0469598i | ||||
\(123\) | 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 | −0.993028 | − | 0.117880i | \(-0.962390\pi\) |
0.117880 | + | 0.993028i | \(0.462390\pi\) | |||||||
\(128\) | −958.596 | + | 1085.47i | −0.661943 | + | 0.749554i | ||||
\(129\) | 108.951i | 0.0743614i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 262.746i | 0.175238i | 0.996154 | + | 0.0876192i | \(0.0279259\pi\) | ||||
−0.996154 | + | 0.0876192i | \(0.972074\pi\) | |||||||
\(132\) | 40.4285 | + | 109.290i | 0.0266580 | + | 0.0720640i | ||||
\(133\) | −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 | \(0.563730\pi\) | |||||||
\(138\) | 79.8968 | + | 124.690i | 0.0492846 | + | 0.0769154i | ||||
\(139\) | −2028.30 | −1.23768 | −0.618842 | − | 0.785516i | \(-0.712398\pi\) | ||||
−0.618842 | + | 0.785516i | \(0.712398\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 35.1487 | 0.0209933 | ||||||||
\(142\) | −1131.43 | − | 1765.76i | −0.668647 | − | 1.04352i | ||||
\(143\) | 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 | ||||
\(148\) | −1427.19 | + | 527.948i | −0.792665 | + | 0.293224i | ||||
\(149\) | 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 | \(0.0157977\pi\) | ||||
−0.998769 | + | 0.0496096i | \(0.984202\pi\) | |||||||
\(152\) | 408.926 | + | 2927.92i | 0.218212 | + | 1.56240i | ||||
\(153\) | 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 | \(0.904943\pi\) | |||||||
\(158\) | −530.420 | + | 339.874i | −0.267076 | + | 0.171132i | ||||
\(159\) | −149.016 | −0.0743252 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2048.97 | 1.00299 | ||||||||
\(162\) | −1713.22 | + | 1097.77i | −0.830884 | + | 0.532400i | ||||
\(163\) | 1460.57 | + | 1460.57i | 0.701843 | + | 0.701843i | 0.964806 | − | 0.262963i | \(-0.0846997\pi\) |
−0.262963 | + | 0.964806i | \(0.584700\pi\) | |||||||
\(164\) | 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 | −0.210062 | − | 0.977688i | \(-0.567367\pi\) |
0.977688 | + | 0.210062i | \(0.0673665\pi\) | |||||||
\(168\) | −14.5475 | − | 104.161i | −0.00668074 | − | 0.0478343i | ||||
\(169\) | − | 1282.77i | − | 0.583872i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3512.11i | 1.57063i | ||||||||
\(172\) | 2372.00 | − | 877.455i | 1.05153 | − | 0.388984i | ||||
\(173\) | −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 | ||||
\(178\) | −2208.11 | − | 3446.06i | −0.929802 | − | 1.45109i | ||||
\(179\) | −37.6748 | −0.0157316 | −0.00786578 | − | 0.999969i | \(-0.502504\pi\) | ||||
−0.00786578 | + | 0.999969i | \(0.502504\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1360.64 | −0.558762 | −0.279381 | − | 0.960180i | \(-0.590129\pi\) | ||||
−0.279381 | + | 0.960180i | \(0.590129\pi\) | |||||||
\(182\) | −1214.02 | − | 1894.65i | −0.494446 | − | 0.771651i | ||||
\(183\) | −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 | ||||
\(188\) | −283.076 | − | 765.232i | −0.109816 | − | 0.296863i | ||||
\(189\) | − | 250.438i | − | 0.0963846i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3587.14i | 1.35893i | 0.733706 | + | 0.679467i | \(0.237789\pi\) | ||||
−0.733706 | + | 0.679467i | \(0.762211\pi\) | |||||||
\(192\) | −154.181 | − | 85.8108i | −0.0579534 | − | 0.0322545i | ||||
\(193\) | 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 | \(0.769205\pi\) | |||||||
\(198\) | 2705.69 | − | 1733.71i | 0.971137 | − | 0.622269i | ||||
\(199\) | −2893.75 | −1.03081 | −0.515407 | − | 0.856945i | \(-0.672359\pi\) | ||||
−0.515407 | + | 0.856945i | \(0.672359\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −127.570 | −0.0447667 | ||||||||
\(202\) | 1416.36 | − | 907.550i | 0.493340 | − | 0.316114i | ||||
\(203\) | 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 | ||||
\(208\) | −3764.21 | − | 289.574i | −1.25481 | − | 0.0965306i | ||||
\(209\) | − | 5522.06i | − | 1.82760i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 2956.45i | − | 0.964599i | −0.876006 | − | 0.482300i | \(-0.839802\pi\) | ||
0.876006 | − | 0.482300i | \(-0.160198\pi\) | |||||||
\(212\) | 1200.12 | + | 3244.26i | 0.388795 | + | 1.05102i | ||||
\(213\) | 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 | ||||
\(218\) | 1037.93 | + | 1619.84i | 0.322466 | + | 0.503253i | ||||
\(219\) | 251.894 | 0.0777233 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2848.71 | 0.867080 | ||||||||
\(222\) | −100.033 | − | 156.115i | −0.0302422 | − | 0.0471972i | ||||
\(223\) | −1581.62 | − | 1581.62i | −0.474946 | − | 0.474946i | 0.428565 | − | 0.903511i | \(-0.359019\pi\) |
−0.903511 | + | 0.428565i | \(0.859019\pi\) | |||||||
\(224\) | −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 | −0.602595 | − | 0.798047i | \(-0.705867\pi\) |
0.798047 | + | 0.602595i | \(0.205867\pi\) | |||||||
\(228\) | −337.843 | + | 124.975i | −0.0981325 | + | 0.0363013i | ||||
\(229\) | 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 | ||||||||
\(232\) | 1801.99 | − | 251.674i | 0.509942 | − | 0.0712206i | ||||
\(233\) | 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 | ||||
\(238\) | 1551.05 | − | 993.855i | 0.422435 | − | 0.270681i | ||||
\(239\) | 1712.05 | 0.463360 | 0.231680 | − | 0.972792i | \(-0.425578\pi\) | ||||
0.231680 | + | 0.972792i | \(0.425578\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5796.70 | −1.54937 | −0.774685 | − | 0.632348i | \(-0.782091\pi\) | ||||
−0.774685 | + | 0.632348i | \(0.782091\pi\) | |||||||
\(242\) | −1084.39 | + | 694.838i | −0.288047 | + | 0.184570i | ||||
\(243\) | −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 | ||||
\(248\) | 6123.37 | − | 855.217i | 1.56788 | − | 0.218977i | ||||
\(249\) | − | 401.957i | − | 0.102301i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2040.48i | − | 0.513123i | −0.966528 | − | 0.256562i | \(-0.917410\pi\) | ||
0.966528 | − | 0.256562i | \(-0.0825897\pi\) | |||||||
\(252\) | −2720.17 | + | 1006.25i | −0.679978 | + | 0.251538i | ||||
\(253\) | −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 | \(0.791480\pi\) | |||||||
\(258\) | 166.256 | + | 259.465i | 0.0401187 | + | 0.0626108i | ||||
\(259\) | −2565.36 | −0.615459 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2161.53 | 0.512626 | ||||||||
\(262\) | 400.941 | + | 625.724i | 0.0945428 | + | 0.147547i | ||||
\(263\) | −1842.73 | − | 1842.73i | −0.432045 | − | 0.432045i | 0.457279 | − | 0.889323i | \(-0.348824\pi\) |
−0.889323 | + | 0.457279i | \(0.848824\pi\) | |||||||
\(264\) | 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 | ||||
\(268\) | 1027.40 | + | 2777.36i | 0.234174 | + | 0.633039i | ||||
\(269\) | 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 | \(-0.594334\pi\) | ||
0.292040 | − | 0.956406i | \(-0.405666\pi\) | |||||||
\(272\) | 237.060 | − | 3081.56i | 0.0528450 | − | 0.686939i | ||||
\(273\) | 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 | \(0.843297\pi\) | |||||||
\(278\) | −4830.35 | + | 3095.11i | −1.04210 | + | 0.667742i | ||||
\(279\) | 7345.13 | 1.57614 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1365.56 | −0.289902 | −0.144951 | − | 0.989439i | \(-0.546303\pi\) | ||||
−0.144951 | + | 0.989439i | \(0.546303\pi\) | |||||||
\(282\) | 83.7060 | − | 53.6357i | 0.0176759 | − | 0.0113261i | ||||
\(283\) | −2275.91 | − | 2275.91i | −0.478052 | − | 0.478052i | 0.426456 | − | 0.904508i | \(-0.359762\pi\) |
−0.904508 | + | 0.426456i | \(0.859762\pi\) | |||||||
\(284\) | −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 | ||||
\(288\) | −1402.27 | + | 4659.59i | −0.286908 | + | 0.953365i | ||||
\(289\) | − | 2580.91i | − | 0.525323i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 95.6501i | 0.0192684i | ||||||||
\(292\) | −2028.66 | − | 5484.04i | −0.406570 | − | 1.09907i | ||||
\(293\) | −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 | ||||
\(298\) | 4566.94 | + | 7127.35i | 0.887771 | + | 1.38549i | ||||
\(299\) | 8961.98 | 1.73339 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4263.66 | 0.816455 | ||||||||
\(302\) | 280.935 | + | 438.437i | 0.0535297 | + | 0.0835405i | ||||
\(303\) | 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 | −0.656293 | − | 0.754507i | \(-0.727876\pi\) |
0.754507 | + | 0.656293i | \(0.227876\pi\) | |||||||
\(308\) | 4276.90 | − | 1582.12i | 0.791230 | − | 0.292693i | ||||
\(309\) | − | 243.609i | − | 0.0448494i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 395.402i | − | 0.0720938i | −0.999350 | − | 0.0360469i | \(-0.988523\pi\) | ||
0.999350 | − | 0.0360469i | \(-0.0114766\pi\) | |||||||
\(312\) | −63.6293 | − | 455.587i | −0.0115458 | − | 0.0826684i | ||||
\(313\) | −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 | \(0.903245\pi\) | |||||||
\(318\) | −354.877 | + | 227.392i | −0.0625803 | + | 0.0400991i | ||||
\(319\) | −3398.56 | −0.596498 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 349.219 | 0.0607212 | ||||||||
\(322\) | 4879.58 | − | 3126.65i | 0.844497 | − | 0.541123i | ||||
\(323\) | −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 | ||||
\(328\) | −486.955 | − | 3486.61i | −0.0819743 | − | 0.586938i | ||||
\(329\) | − | 1375.50i | − | 0.230497i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1388.78i | − | 0.230617i | −0.993330 | − | 0.115308i | \(-0.963214\pi\) | ||
0.993330 | − | 0.115308i | \(-0.0367856\pi\) | |||||||
\(332\) | −8751.11 | + | 3237.22i | −1.44663 | + | 0.535137i | ||||
\(333\) | −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 | \(0.647583\pi\) | |||||||
\(338\) | −1957.45 | − | 3054.88i | −0.315004 | − | 0.491608i | ||||
\(339\) | 14.7938 | 0.00237018 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11548.7 | −1.83401 | ||||||||
\(342\) | 5359.35 | + | 8364.01i | 0.847369 | + | 1.32244i | ||||
\(343\) | 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 | −0.848854 | − | 0.528627i | \(-0.822707\pi\) |
0.528627 | + | 0.848854i | \(0.322707\pi\) | |||||||
\(348\) | 76.9162 | + | 207.926i | 0.0118481 | + | 0.0320288i | ||||
\(349\) | 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 | ||||||
\(352\) | 2204.78 | − | 7326.25i | 0.333849 | − | 1.10935i | ||||
\(353\) | 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 | ||||
\(358\) | −89.7218 | + | 57.4904i | −0.0132457 | + | 0.00848733i | ||||
\(359\) | −6227.61 | −0.915545 | −0.457773 | − | 0.889069i | \(-0.651353\pi\) | ||||
−0.457773 | + | 0.889069i | \(0.651353\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10211.2 | 1.48872 | ||||||||
\(362\) | −3240.35 | + | 2076.29i | −0.470466 | + | 0.301457i | ||||
\(363\) | −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 | −0.907474 | − | 0.420109i | \(-0.861992\pi\) |
0.420109 | + | 0.907474i | \(0.361992\pi\) | |||||||
\(368\) | 745.786 | − | 9694.55i | 0.105643 | − | 1.37327i | ||||
\(369\) | − | 4182.27i | − | 0.590028i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5831.52i | 0.816058i | ||||||||
\(372\) | 261.370 | + | 706.557i | 0.0364285 | + | 0.0984765i | ||||
\(373\) | 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 | ||||
\(378\) | −382.159 | − | 596.413i | −0.0520004 | − | 0.0811539i | ||||
\(379\) | −10644.7 | −1.44269 | −0.721347 | − | 0.692574i | \(-0.756477\pi\) | ||||
−0.721347 | + | 0.692574i | \(0.756477\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −610.461 | −0.0820863 | ||||||||
\(382\) | 5473.85 | + | 8542.70i | 0.733158 | + | 1.14419i | ||||
\(383\) | −2301.02 | − | 2301.02i | −0.306988 | − | 0.306988i | 0.536752 | − | 0.843740i | \(-0.319651\pi\) |
−0.843740 | + | 0.536752i | \(0.819651\pi\) | |||||||
\(384\) | −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 | ||||
\(388\) | 2082.42 | − | 770.332i | 0.272472 | − | 0.100793i | ||||
\(389\) | − | 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 | ||||||||
\(392\) | 3610.42 | − | 504.247i | 0.465188 | − | 0.0649702i | ||||
\(393\) | −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 | \(0.551275\pi\) | |||||||
\(398\) | −6891.39 | + | 4415.75i | −0.867925 | + | 0.556134i | ||||
\(399\) | −607.270 | −0.0761943 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5980.28 | −0.744740 | −0.372370 | − | 0.928084i | \(-0.621455\pi\) | ||||
−0.372370 | + | 0.928084i | \(0.621455\pi\) | |||||||
\(402\) | −303.805 | + | 194.667i | −0.0376926 | + | 0.0241521i | ||||
\(403\) | 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 | ||||
\(408\) | 372.966 | − | 52.0900i | 0.0452563 | − | 0.00632069i | ||||
\(409\) | − | 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 | ||||||||
\(412\) | −5303.68 | + | 1961.94i | −0.634208 | + | 0.234607i | ||||
\(413\) | 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 | ||||
\(418\) | −8426.46 | − | 13150.7i | −0.986009 | − | 1.53880i | ||||
\(419\) | 3080.65 | 0.359188 | 0.179594 | − | 0.983741i | \(-0.442522\pi\) | ||||
0.179594 | + | 0.983741i | \(0.442522\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5636.62 | 0.652523 | 0.326261 | − | 0.945280i | \(-0.394211\pi\) | ||||
0.326261 | + | 0.945280i | \(0.394211\pi\) | |||||||
\(422\) | −4511.43 | − | 7040.72i | −0.520410 | − | 0.812173i | ||||
\(423\) | −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 | ||||
\(428\) | −2812.49 | − | 7602.94i | −0.317632 | − | 0.858649i | ||||
\(429\) | 859.239i | 0.0967004i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12970.7i | 1.44959i | 0.688963 | + | 0.724797i | \(0.258066\pi\) | ||||
−0.688963 | + | 0.724797i | \(0.741934\pi\) | |||||||
\(432\) | −1184.93 | − | 91.1547i | −0.131968 | − | 0.0101520i | ||||
\(433\) | −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 | ||||
\(438\) | 599.879 | − | 384.380i | 0.0654414 | − | 0.0419324i | ||||
\(439\) | −5465.06 | −0.594153 | −0.297076 | − | 0.954854i | \(-0.596012\pi\) | ||||
−0.297076 | + | 0.954854i | \(0.596012\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4330.79 | 0.467637 | ||||||||
\(442\) | 6784.13 | − | 4347.02i | 0.730064 | − | 0.467798i | ||||
\(443\) | 4982.88 | + | 4982.88i | 0.534410 | + | 0.534410i | 0.921882 | − | 0.387472i | \(-0.126651\pi\) |
−0.387472 | + | 0.921882i | \(0.626651\pi\) | |||||||
\(444\) | −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 | ||||
\(448\) | −3358.09 | + | 6033.66i | −0.354140 | + | 0.636303i | ||||
\(449\) | 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 | ||||||||
\(452\) | −119.144 | − | 322.080i | −0.0123984 | − | 0.0335164i | ||||
\(453\) | −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 | \(0.781397\pi\) | |||||||
\(458\) | 5365.10 | + | 8372.99i | 0.547369 | + | 0.854245i | ||||
\(459\) | 896.740 | 0.0911901 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8133.56 | 0.821730 | 0.410865 | − | 0.911696i | \(-0.365227\pi\) | ||||
0.410865 | + | 0.911696i | \(0.365227\pi\) | |||||||
\(462\) | 299.771 | + | 467.834i | 0.0301875 | + | 0.0471117i | ||||
\(463\) | 1938.32 | + | 1938.32i | 0.194560 | + | 0.194560i | 0.797663 | − | 0.603103i | \(-0.206069\pi\) |
−0.603103 | + | 0.797663i | \(0.706069\pi\) | |||||||
\(464\) | 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 | −0.988668 | − | 0.150116i | \(-0.952035\pi\) |
0.150116 | + | 0.988668i | \(0.452035\pi\) | |||||||
\(468\) | −11897.7 | + | 4401.22i | −1.17516 | + | 0.434715i | ||||
\(469\) | 4992.28i | 0.491518i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 634.264i | − | 0.0620496i | ||||||
\(472\) | −554.430 | − | 3969.73i | −0.0540671 | − | 0.387122i | ||||
\(473\) | −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 | ||||
\(478\) | 4077.20 | − | 2612.52i | 0.390140 | − | 0.249987i | ||||
\(479\) | 7570.70 | 0.722158 | 0.361079 | − | 0.932535i | \(-0.382408\pi\) | ||||
0.361079 | + | 0.932535i | \(0.382408\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11220.6 | −1.06365 | ||||||||
\(482\) | −13804.7 | + | 8845.55i | −1.30454 | + | 0.835899i | ||||
\(483\) | 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 | −0.109776 | − | 0.993956i | \(-0.535013\pi\) |
0.993956 | + | 0.109776i | \(0.0350133\pi\) | |||||||
\(488\) | 129.792 | + | 929.312i | 0.0120397 | + | 0.0862049i | ||||
\(489\) | 711.857i | 0.0658309i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 8188.17i | − | 0.752601i | −0.926498 | − | 0.376300i | \(-0.877196\pi\) | ||
0.926498 | − | 0.376300i | \(-0.122804\pi\) | |||||||
\(492\) | 402.309 | − | 148.823i | 0.0368648 | − | 0.0136371i | ||||
\(493\) | −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 | ||||
\(498\) | −613.372 | − | 957.252i | −0.0551925 | − | 0.0861355i | ||||
\(499\) | −429.740 | −0.0385527 | −0.0192764 | − | 0.999814i | \(-0.506136\pi\) | ||||
−0.0192764 | + | 0.999814i | \(0.506136\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 807.414 | 0.0720012 | ||||||||
\(502\) | −3113.70 | − | 4859.36i | −0.276835 | − | 0.432039i | ||||
\(503\) | 8511.42 | + | 8511.42i | 0.754484 | + | 0.754484i | 0.975313 | − | 0.220829i | \(-0.0708762\pi\) |
−0.220829 | + | 0.975313i | \(0.570876\pi\) | |||||||
\(504\) | −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 | ||||
\(508\) | 4916.44 | + | 13290.5i | 0.429393 | + | 1.16077i | ||||
\(509\) | − | 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 | ||||||
\(512\) | 4684.83 | + | 10595.8i | 0.404379 | + | 0.914591i | ||||
\(513\) | −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 | ||||
\(518\) | −6109.36 | + | 3914.65i | −0.518204 | + | 0.332046i | ||||
\(519\) | −780.699 | −0.0660287 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 818.504 | 0.0688279 | 0.0344139 | − | 0.999408i | \(-0.489044\pi\) | ||||
0.0344139 | + | 0.999408i | \(0.489044\pi\) | |||||||
\(522\) | 5147.64 | − | 3298.42i | 0.431621 | − | 0.276567i | ||||
\(523\) | −14975.1 | − | 14975.1i | −1.25203 | − | 1.25203i | −0.954807 | − | 0.297227i | \(-0.903938\pi\) |
−0.297227 | − | 0.954807i | \(-0.596062\pi\) | |||||||
\(524\) | 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 | ||||
\(528\) | 929.475 | + | 71.5030i | 0.0766102 | + | 0.00589350i | ||||
\(529\) | 10914.2i | 0.897032i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 4761.79i | − | 0.389160i | ||||||
\(532\) | 4890.74 | + | 13221.0i | 0.398572 | + | 1.07745i | ||||
\(533\) | 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 | ||||
\(538\) | 7098.24 | + | 11077.8i | 0.568823 | + | 0.887728i | ||||
\(539\) | −6809.26 | −0.544148 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1894.75 | −0.150576 | −0.0752879 | − | 0.997162i | \(-0.523988\pi\) | ||||
−0.0752879 | + | 0.997162i | \(0.523988\pi\) | |||||||
\(542\) | −13021.8 | − | 20322.3i | −1.03198 | − | 1.61055i | ||||
\(543\) | −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 | −0.948447 | − | 0.316935i | \(-0.897346\pi\) |
0.316935 | + | 0.948447i | \(0.397346\pi\) | |||||||
\(548\) | 13291.3 | − | 4916.74i | 1.03609 | − | 0.383271i | ||||
\(549\) | 1114.73i | 0.0866587i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10505.8i | − | 0.812276i | ||||||
\(552\) | 1173.34 | − | 163.874i | 0.0904726 | − | 0.0126358i | ||||
\(553\) | −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 | \(0.528891\pi\) | |||||||
\(558\) | 17492.3 | − | 11208.4i | 1.32707 | − | 0.850340i | ||||
\(559\) | 18648.8 | 1.41102 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −703.415 | −0.0529380 | ||||||||
\(562\) | −3252.06 | + | 2083.80i | −0.244092 | + | 0.156405i | ||||
\(563\) | −11749.3 | − | 11749.3i | −0.879526 | − | 0.879526i | 0.113959 | − | 0.993485i | \(-0.463647\pi\) |
−0.993485 | + | 0.113959i | \(0.963647\pi\) | |||||||
\(564\) | 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 | ||||
\(568\) | −16616.0 | + | 2320.66i | −1.22745 | + | 0.171431i | ||||
\(569\) | − | 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 | \(-0.934112\pi\) | ||
0.978653 | − | 0.205519i | \(-0.0658884\pi\) | |||||||
\(572\) | 18706.7 | − | 6920.01i | 1.36742 | − | 0.505839i | ||||
\(573\) | −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 | \(-0.574203\pi\) | |||||||
\(578\) | −3938.38 | − | 6146.38i | −0.283417 | − | 0.442311i | ||||
\(579\) | 1770.02 | 0.127046 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15730.0 | −1.12322 | ||||||||
\(582\) | 145.959 | + | 227.789i | 0.0103955 | + | 0.0162236i | ||||
\(583\) | −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 | \(-0.313234\pi\) |
0.832749 | − | 0.553650i | \(-0.186766\pi\) | |||||||
\(588\) | 154.107 | + | 416.595i | 0.0108083 | + | 0.0292178i | ||||
\(589\) | − | 35700.1i | − | 2.49745i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 114.919i | − | 0.00799851i | ||||||
\(592\) | −933.743 | + | 12137.8i | −0.0648254 | + | 0.842672i | ||||
\(593\) | −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 | ||||
\(598\) | 21342.8 | − | 13675.7i | 1.45948 | − | 0.935182i | ||||
\(599\) | 3488.67 | 0.237969 | 0.118984 | − | 0.992896i | \(-0.462036\pi\) | ||||
0.118984 | + | 0.992896i | \(0.462036\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10909.5 | 0.740443 | 0.370222 | − | 0.928943i | \(-0.379282\pi\) | ||||
0.370222 | + | 0.928943i | \(0.379282\pi\) | |||||||
\(602\) | 10153.8 | − | 6506.18i | 0.687439 | − | 0.440485i | ||||
\(603\) | 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 | −0.178294 | − | 0.983977i | \(-0.557058\pi\) |
0.983977 | + | 0.178294i | \(0.0570578\pi\) | |||||||
\(608\) | 22647.4 | + | 6815.55i | 1.51064 | + | 0.454617i | ||||
\(609\) | 373.745i | 0.0248685i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 6016.28i | − | 0.398352i | ||||||
\(612\) | −3603.05 | − | 9740.06i | −0.237982 | − | 0.643331i | ||||
\(613\) | 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 | \(0.366648\pi\) | |||||||
\(618\) | −371.739 | − | 580.150i | −0.0241967 | − | 0.0377622i | ||||
\(619\) | 22702.2 | 1.47411 | 0.737057 | − | 0.675830i | \(-0.236215\pi\) | ||||
0.737057 | + | 0.675830i | \(0.236215\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2821.13 | 0.182300 | ||||||||
\(622\) | −603.369 | − | 941.641i | −0.0388953 | − | 0.0607015i | ||||
\(623\) | −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 | ||||
\(628\) | −13808.7 | + | 5108.14i | −0.877434 | + | 0.324581i | ||||
\(629\) | − | 9185.76i | − | 0.582289i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 5787.42i | − | 0.365125i | −0.983194 | − | 0.182562i | \(-0.941561\pi\) | ||
0.983194 | − | 0.182562i | \(-0.0584391\pi\) | |||||||
\(632\) | 697.106 | + | 4991.30i | 0.0438756 | + | 0.314151i | ||||
\(633\) | 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 | ||||
\(638\) | −8093.59 | + | 5186.08i | −0.502239 | + | 0.321816i | ||||
\(639\) | −19931.2 | −1.23391 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8721.43 | 0.537404 | 0.268702 | − | 0.963223i | \(-0.413405\pi\) | ||||
0.268702 | + | 0.963223i | \(0.413405\pi\) | |||||||
\(642\) | 831.658 | − | 532.895i | 0.0511260 | − | 0.0327597i | ||||
\(643\) | −2937.61 | − | 2937.61i | −0.180168 | − | 0.180168i | 0.611261 | − | 0.791429i | \(-0.290663\pi\) |
−0.791429 | + | 0.611261i | \(0.790663\pi\) | |||||||
\(644\) | 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 | \(0.534273\pi\) |
−0.994209 | + | 0.107465i | \(0.965727\pi\) | |||||||
\(648\) | 2251.60 | + | 16121.5i | 0.136499 | + | 0.977337i | ||||
\(649\) | 7486.92i | 0.452831i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1270.03i | 0.0764614i | ||||||||
\(652\) | 15498.0 | − | 5733.05i | 0.930904 | − | 0.344361i | ||||
\(653\) | 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 | ||||
\(658\) | −2098.96 | − | 3275.72i | −0.124356 | − | 0.194074i | ||||
\(659\) | −14608.8 | −0.863550 | −0.431775 | − | 0.901981i | \(-0.642113\pi\) | ||||
−0.431775 | + | 0.901981i | \(0.642113\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26434.7 | −1.55551 | −0.777755 | − | 0.628567i | \(-0.783642\pi\) | ||||
−0.777755 | + | 0.628567i | \(0.783642\pi\) | |||||||
\(662\) | −2119.22 | − | 3307.34i | −0.124420 | − | 0.194175i | ||||
\(663\) | 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 | ||||
\(668\) | −6502.62 | − | 17578.4i | −0.376638 | − | 1.01816i | ||||
\(669\) | − | 770.855i | − | 0.0445485i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1752.69i | − | 0.100837i | ||||||
\(672\) | −805.679 | − | 242.463i | −0.0462496 | − | 0.0139185i | ||||
\(673\) | −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 | \(0.820812\pi\) | |||||||
\(678\) | 35.2312 | − | 22.5749i | 0.00199564 | − | 0.00127873i | ||||
\(679\) | 3743.14 | 0.211559 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 325.799 | 0.0183328 | ||||||||
\(682\) | −27503.0 | + | 17622.9i | −1.54420 | + | 0.989465i | ||||
\(683\) | 12875.9 | + | 12875.9i | 0.721351 | + | 0.721351i | 0.968880 | − | 0.247530i | \(-0.0796187\pi\) |
−0.247530 | + | 0.968880i | \(0.579619\pi\) | |||||||
\(684\) | 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 | ||||
\(688\) | 1551.89 | − | 20173.2i | 0.0859959 | − | 1.11787i | ||||
\(689\) | 25506.5i | 1.41033i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9091.60i | 0.500522i | 0.968178 | + | 0.250261i | \(0.0805164\pi\) | ||||
−0.968178 | + | 0.250261i | \(0.919484\pi\) | |||||||
\(692\) | 6287.48 | + | 16996.8i | 0.345396 | + | 0.933702i | ||||
\(693\) | 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 | ||||
\(698\) | 8811.88 | + | 13752.2i | 0.477843 | + | 0.745741i | ||||
\(699\) | 808.504 | 0.0437488 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19437.4 | 1.04728 | 0.523639 | − | 0.851941i | \(-0.324574\pi\) | ||||
0.523639 | + | 0.851941i | \(0.324574\pi\) | |||||||
\(702\) | −1671.53 | − | 2608.65i | −0.0898685 | − | 0.140252i | ||||
\(703\) | 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 | ||||
\(708\) | 458.055 | − | 169.444i | 0.0243146 | − | 0.00899449i | ||||
\(709\) | 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 | ||||||||
\(712\) | −32427.7 | + | 4529.00i | −1.70685 | + | 0.238387i | ||||
\(713\) | −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 | ||||
\(718\) | −14830.9 | + | 9503.10i | −0.770870 | + | 0.493945i | ||||
\(719\) | −26377.6 | −1.36818 | −0.684089 | − | 0.729399i | \(-0.739800\pi\) | ||||
−0.684089 | + | 0.729399i | \(0.739800\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9533.32 | −0.492426 | ||||||||
\(722\) | 24317.6 | − | 15581.8i | 1.25347 | − | 0.803180i | ||||
\(723\) | −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 | −0.192898 | − | 0.981219i | \(-0.561789\pi\) |
0.981219 | + | 0.192898i | \(0.0617885\pi\) | |||||||
\(728\) | −17828.8 | + | 2490.04i | −0.907663 | + | 0.126768i | ||||
\(729\) | 19165.4i | 0.973703i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15266.8i | 0.772453i | ||||||||
\(732\) | −107.230 | + | 39.6668i | −0.00541441 | + | 0.00200291i | ||||
\(733\) | 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 | ||||
\(738\) | −6381.99 | − | 9959.98i | −0.318326 | − | 0.496791i | ||||
\(739\) | 27295.7 | 1.35871 | 0.679356 | − | 0.733809i | \(-0.262259\pi\) | ||||
0.679356 | + | 0.733809i | \(0.262259\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2656.14 | −0.131681 | ||||||||
\(742\) | 8898.68 | + | 13887.6i | 0.440271 | + | 0.687104i | ||||
\(743\) | 19570.2 | + | 19570.2i | 0.966300 | + | 0.966300i | 0.999450 | − | 0.0331505i | \(-0.0105541\pi\) |
−0.0331505 | + | 0.999450i | \(0.510554\pi\) | |||||||
\(744\) | 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 | ||||
\(748\) | 5665.06 | + | 15314.2i | 0.276918 | + | 0.748588i | ||||
\(749\) | − | 13666.2i | − | 0.666692i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23982.8i | 1.16530i | 0.812722 | + | 0.582652i | \(0.197985\pi\) | ||||
−0.812722 | + | 0.582652i | \(0.802015\pi\) | |||||||
\(752\) | −6508.07 | − | 500.655i | −0.315591 | − | 0.0242779i | ||||
\(753\) | 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 | \(0.843795\pi\) | |||||||
\(758\) | −25350.1 | + | 16243.4i | −1.21472 | + | 0.778347i | ||||
\(759\) | −2212.93 | −0.105829 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32552.3 | 1.55062 | 0.775308 | − | 0.631583i | \(-0.217594\pi\) | ||||
0.775308 | + | 0.631583i | \(0.217594\pi\) | |||||||
\(762\) | −1453.80 | + | 931.542i | −0.0691150 | + | 0.0442863i | ||||
\(763\) | 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 | ||||
\(768\) | −1139.09 | + | 833.748i | −0.0535200 | + | 0.0391735i | ||||
\(769\) | 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 | ||||||
\(772\) | −14255.1 | − | 38535.6i | −0.664577 | − | 1.79654i | ||||
\(773\) | 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 | ||||
\(778\) | −8601.65 | − | 13424.1i | −0.396381 | − | 0.618607i | ||||
\(779\) | −20327.4 | −0.934922 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31337.7 | 1.43579 | ||||||||
\(782\) | 11195.6 | + | 17472.2i | 0.511959 | + | 0.798984i | ||||
\(783\) | 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 | \(-0.447727\pi\) |
0.986546 | − | 0.163485i | \(-0.0522735\pi\) | |||||||
\(788\) | −2501.92 | + | 925.514i | −0.113106 | + | 0.0418402i | ||||
\(789\) | − | 898.119i | − | 0.0405245i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 578.937i | − | 0.0260235i | ||||||
\(792\) | −3555.96 | − | 25460.8i | −0.159540 | − | 1.14231i | ||||
\(793\) | −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 | \(0.501296\pi\) | |||||||
\(798\) | −1446.20 | + | 926.671i | −0.0641540 | + | 0.0411075i | ||||
\(799\) | 4925.22 | 0.218075 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −38897.9 | −1.71584 | ||||||||
\(802\) | −14241.9 | + | 9125.68i | −0.627056 | + | 0.401794i | ||||
\(803\) | 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 | ||||
\(808\) | −1861.45 | − | 13328.0i | −0.0810466 | − | 0.580296i | ||||
\(809\) | − | 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 | \(0.377205\pi\) | ||||
−0.376274 | + | 0.926508i | \(0.622795\pi\) | |||||||
\(812\) | 8136.90 | − | 3010.01i | 0.351662 | − | 0.130087i | ||||
\(813\) | 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 | ||||
\(818\) | −7859.71 | − | 12266.2i | −0.335952 | − | 0.524299i | ||||
\(819\) | −21386.1 | −0.912441 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23614.4 | −1.00384 | −0.501918 | − | 0.864915i | \(-0.667372\pi\) | ||||
−0.501918 | + | 0.864915i | \(0.667372\pi\) | |||||||
\(822\) | 931.598 | + | 1453.89i | 0.0395295 | + | 0.0616912i | ||||
\(823\) | −23159.2 | − | 23159.2i | −0.980897 | − | 0.980897i | 0.0189236 | − | 0.999821i | \(-0.493976\pi\) |
−0.999821 | + | 0.0189236i | \(0.993976\pi\) | |||||||
\(824\) | −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 | −0.895714 | − | 0.444631i | \(-0.853335\pi\) |
0.444631 | + | 0.895714i | \(0.353335\pi\) | |||||||
\(828\) | −11335.1 | − | 30642.1i | −0.475753 | − | 1.28609i | ||||
\(829\) | − | 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 | ||||||
\(832\) | −14687.9 | + | 26390.6i | −0.612034 | + | 1.09968i | ||||
\(833\) | −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 | ||||
\(838\) | 7336.50 | − | 4700.96i | 0.302429 | − | 0.193785i | ||||
\(839\) | 25953.9 | 1.06797 | 0.533986 | − | 0.845493i | \(-0.320693\pi\) | ||||
0.533986 | + | 0.845493i | \(0.320693\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17923.2 | 0.734887 | ||||||||
\(842\) | 13423.5 | − | 8601.27i | 0.549411 | − | 0.352042i | ||||
\(843\) | −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 | ||||
\(848\) | 27591.4 | + | 2122.56i | 1.11733 | + | 0.0859541i | ||||
\(849\) | − | 1109.24i | − | 0.0448399i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 28898.2i | − | 1.16406i | ||||||
\(852\) | −709.236 | − | 1917.26i | −0.0285188 | − | 0.0770943i | ||||
\(853\) | 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 | \(0.653297\pi\) | |||||||
\(858\) | 1311.17 | + | 2046.26i | 0.0521708 | + | 0.0814197i | ||||
\(859\) | −16534.0 | −0.656732 | −0.328366 | − | 0.944551i | \(-0.606498\pi\) | ||||
−0.328366 | + | 0.944551i | \(0.606498\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 723.146 | 0.0286234 | ||||||||
\(862\) | 19792.7 | + | 30889.3i | 0.782069 | + | 1.22053i | ||||
\(863\) | 3057.61 | + | 3057.61i | 0.120605 | + | 0.120605i | 0.764833 | − | 0.644228i | \(-0.222821\pi\) |
−0.644228 | + | 0.764833i | \(0.722821\pi\) | |||||||
\(864\) | −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 | ||||
\(868\) | 27650.1 | − | 10228.4i | 1.08123 | − | 0.399969i | ||||
\(869\) | − | 9413.60i | − | 0.367474i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21835.7i | 0.849455i | ||||||||
\(872\) | 15242.8 | − | 2128.88i | 0.591957 | − | 0.0826753i | ||||
\(873\) | 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 | \(0.477405\pi\) | |||||||
\(878\) | −13014.9 | + | 8339.48i | −0.500264 | + | 0.320551i | ||||
\(879\) | −1393.71 | −0.0534799 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11660.4 | 0.445911 | 0.222955 | − | 0.974829i | \(-0.428430\pi\) | ||||
0.222955 | + | 0.974829i | \(0.428430\pi\) | |||||||
\(882\) | 10313.7 | − | 6608.62i | 0.393741 | − | 0.252295i | ||||
\(883\) | −15502.9 | − | 15502.9i | −0.590844 | − | 0.590844i | 0.347016 | − | 0.937859i | \(-0.387195\pi\) |
−0.937859 | + | 0.347016i | \(0.887195\pi\) | |||||||
\(884\) | 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 | −0.791836 | − | 0.610733i | \(-0.790875\pi\) |
0.610733 | + | 0.791836i | \(0.290875\pi\) | |||||||
\(888\) | −1469.06 | + | 205.175i | −0.0555162 | + | 0.00775363i | ||||
\(889\) | 23889.6i | 0.901272i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 30405.3i | − | 1.14323i | ||||||
\(892\) | −16782.5 | + | 6208.19i | −0.629954 | + | 0.233033i | ||||
\(893\) | −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 | ||||
\(898\) | 18135.6 | + | 28303.1i | 0.673934 | + | 1.05177i | ||||
\(899\) | −21971.7 | −0.815124 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20880.8 | −0.772077 | ||||||||
\(902\) | 10034.4 | + | 15660.0i | 0.370407 | + | 0.578072i | ||||
\(903\) | 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 | −0.00140132 | − | 0.999999i | \(-0.500446\pi\) |
0.999999 | + | 0.00140132i | \(0.000446054\pi\) | |||||||
\(908\) | −2623.87 | − | 7093.05i | −0.0958989 | − | 0.259241i | ||||
\(909\) | − | 15987.3i | − | 0.583351i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 37452.0i | − | 1.36206i | −0.732254 | − | 0.681032i | \(-0.761531\pi\) | ||
0.732254 | − | 0.681032i | \(-0.238469\pi\) | |||||||
\(912\) | −221.035 | + | 2873.25i | −0.00802542 | + | 0.104323i | ||||
\(913\) | 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 | ||||
\(918\) | 2135.57 | − | 1368.39i | 0.0767802 | − | 0.0491979i | ||||
\(919\) | 7803.81 | 0.280113 | 0.140057 | − | 0.990144i | \(-0.455272\pi\) | ||||
0.140057 | + | 0.990144i | \(0.455272\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 257.485 | 0.00921219 | ||||||||
\(922\) | 19369.9 | − | 12411.5i | 0.691880 | − | 0.443331i | ||||
\(923\) | −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 | ||||
\(928\) | 4194.64 | − | 13938.3i | 0.148379 | − | 0.493048i | ||||
\(929\) | − | 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 | ||||||
\(932\) | −6511.41 | − | 17602.1i | −0.228850 | − | 0.618645i | ||||
\(933\) | 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 | \(0.798005\pi\) | |||||||
\(938\) | 7618.04 | + | 11889.0i | 0.265179 | + | 0.413849i | ||||
\(939\) | −392.178 | −0.0136296 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11090.5 | −0.384207 | −0.192103 | − | 0.981375i | \(-0.561531\pi\) | ||||
−0.192103 | + | 0.981375i | \(0.561531\pi\) | |||||||
\(942\) | −967.864 | − | 1510.49i | −0.0334763 | − | 0.0522445i | ||||
\(943\) | 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 | \(0.576127\pi\) |
−0.971537 | + | 0.236886i | \(0.923873\pi\) | |||||||
\(948\) | −575.930 | + | 213.049i | −0.0197314 | + | 0.00729905i | ||||
\(949\) | − | 43115.7i | − | 1.47481i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1801.37i | − | 0.0614233i | ||||||
\(952\) | −2038.47 | − | 14595.5i | −0.0693984 | − | 0.496894i | ||||
\(953\) | −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 | ||||
\(958\) | 18029.4 | − | 11552.6i | 0.608043 | − | 0.389611i | ||||
\(959\) | 23891.0 | 0.804464 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −44871.3 | −1.50620 | ||||||||
\(962\) | −26721.7 | + | 17122.3i | −0.895574 | + | 0.573851i | ||||
\(963\) | −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 | −0.703361 | − | 0.710833i | \(-0.748318\pi\) |
0.710833 | + | 0.703361i | \(0.248318\pi\) | |||||||
\(968\) | 1425.16 | + | 10204.2i | 0.0473208 | + | 0.338818i | ||||
\(969\) | − | 2174.44i | − | 0.0720878i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1315.64i | 0.0434818i | 0.999764 | + | 0.0217409i | \(0.00692089\pi\) | ||||
−0.999764 | + | 0.0217409i | \(0.993079\pi\) | |||||||
\(972\) | −5622.03 | + | 2079.71i | −0.185521 | + | 0.0686283i | ||||
\(973\) | −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 | \(0.730761\pi\) | |||||||
\(978\) | 1086.27 | + | 1695.27i | 0.0355164 | + | 0.0554283i | ||||
\(979\) | 61158.8 | 1.99657 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18284.1 | 0.595073 | ||||||||
\(982\) | −12494.8 | − | 19500.0i | −0.406035 | − | 0.633675i | ||||
\(983\) | −38327.7 | − | 38327.7i | −1.24360 | − | 1.24360i | −0.958495 | − | 0.285109i | \(-0.907970\pi\) |
−0.285109 | − | 0.958495i | \(-0.592030\pi\) | |||||||
\(984\) | 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 | ||||
\(988\) | 21391.6 | + | 57827.4i | 0.688823 | + | 1.86208i | ||||
\(989\) | 48029.1i | 1.54422i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3912.43i | 0.125411i | 0.998032 | + | 0.0627055i | \(0.0199729\pi\) | ||||
−0.998032 | + | 0.0627055i | \(0.980027\pi\) | |||||||
\(992\) | 14253.9 | − | 47364.1i | 0.456210 | − | 1.51594i | ||||
\(993\) | 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 | \(-0.636404\pi\) | |||||||
\(998\) | −1023.42 | + | 655.767i | −0.0324606 | + | 0.0207995i | ||||
\(999\) | −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.7.11 | yes | 24 | |
4.3 | odd | 2 | inner | 100.4.e.f.7.5 | yes | 24 | |
5.2 | odd | 4 | inner | 100.4.e.f.43.8 | yes | 24 | |
5.3 | odd | 4 | inner | 100.4.e.f.43.5 | yes | 24 | |
5.4 | even | 2 | inner | 100.4.e.f.7.2 | ✓ | 24 | |
20.3 | even | 4 | inner | 100.4.e.f.43.11 | yes | 24 | |
20.7 | even | 4 | inner | 100.4.e.f.43.2 | yes | 24 | |
20.19 | odd | 2 | inner | 100.4.e.f.7.8 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
100.4.e.f.7.2 | ✓ | 24 | 5.4 | even | 2 | inner | |
100.4.e.f.7.5 | yes | 24 | 4.3 | odd | 2 | inner | |
100.4.e.f.7.8 | yes | 24 | 20.19 | odd | 2 | inner | |
100.4.e.f.7.11 | yes | 24 | 1.1 | even | 1 | trivial | |
100.4.e.f.43.2 | yes | 24 | 20.7 | even | 4 | inner | |
100.4.e.f.43.5 | yes | 24 | 5.3 | odd | 4 | inner | |
100.4.e.f.43.8 | yes | 24 | 5.2 | odd | 4 | inner | |
100.4.e.f.43.11 | yes | 24 | 20.3 | even | 4 | inner |