Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(49,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.k (of order \(6\), degree \(2\), not 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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.7 | ||
Character | \(\chi\) | \(=\) | 225.49 |
Dual form | 225.4.k.d.124.7 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.195072 | + | 0.112625i | −0.0689684 | + | 0.0398189i | −0.534088 | − | 0.845429i | \(-0.679345\pi\) |
0.465119 | + | 0.885248i | \(0.346011\pi\) | |||||||
\(3\) | 4.76710 | − | 2.06755i | 0.917429 | − | 0.397899i | ||||
\(4\) | −3.97463 | + | 6.88426i | −0.496829 | + | 0.860533i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.697071 | + | 0.940215i | −0.0474297 | + | 0.0639735i | ||||
\(7\) | −27.0148 | + | 15.5970i | −1.45866 | + | 0.842159i | −0.998946 | − | 0.0459062i | \(-0.985382\pi\) |
−0.459717 | + | 0.888066i | \(0.652049\pi\) | |||||||
\(8\) | − | 3.59257i | − | 0.158771i | ||||||
\(9\) | 18.4505 | − | 19.7124i | 0.683352 | − | 0.730089i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.06424 | − | 15.6997i | −0.248452 | − | 0.430331i | 0.714645 | − | 0.699488i | \(-0.246588\pi\) |
−0.963096 | + | 0.269156i | \(0.913255\pi\) | |||||||
\(12\) | −4.71394 | + | 41.0357i | −0.113400 | + | 0.987166i | ||||
\(13\) | −43.4366 | − | 25.0781i | −0.926702 | − | 0.535032i | −0.0409353 | − | 0.999162i | \(-0.513034\pi\) |
−0.885767 | + | 0.464130i | \(0.846367\pi\) | |||||||
\(14\) | 3.51322 | − | 6.08508i | 0.0670678 | − | 0.116165i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −31.3924 | − | 54.3733i | −0.490507 | − | 0.849583i | ||||
\(17\) | − | 131.631i | − | 1.87795i | −0.343981 | − | 0.938977i | \(-0.611776\pi\) | ||
0.343981 | − | 0.938977i | \(-0.388224\pi\) | |||||||
\(18\) | −1.37907 | + | 5.92333i | −0.0180583 | + | 0.0775634i | ||||
\(19\) | −23.2428 | −0.280646 | −0.140323 | − | 0.990106i | \(-0.544814\pi\) | ||||
−0.140323 | + | 0.990106i | \(0.544814\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −96.5348 | + | 130.207i | −1.00312 | + | 1.35302i | ||||
\(22\) | 3.53636 | + | 2.04172i | 0.0342707 | + | 0.0197862i | ||||
\(23\) | −28.5664 | − | 16.4928i | −0.258978 | − | 0.149521i | 0.364890 | − | 0.931051i | \(-0.381107\pi\) |
−0.623868 | + | 0.781529i | \(0.714440\pi\) | |||||||
\(24\) | −7.42780 | − | 17.1261i | −0.0631747 | − | 0.145661i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 11.2977 | 0.0852176 | ||||||||
\(27\) | 47.1991 | − | 132.118i | 0.336425 | − | 0.941710i | ||||
\(28\) | − | 247.969i | − | 1.67364i | ||||||
\(29\) | 62.9087 | + | 108.961i | 0.402823 | + | 0.697709i | 0.994065 | − | 0.108784i | \(-0.0346958\pi\) |
−0.591243 | + | 0.806494i | \(0.701363\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −62.5563 | + | 108.351i | −0.362434 | + | 0.627754i | −0.988361 | − | 0.152128i | \(-0.951387\pi\) |
0.625927 | + | 0.779882i | \(0.284721\pi\) | |||||||
\(32\) | 37.1376 | + | 21.4414i | 0.205158 | + | 0.118448i | ||||
\(33\) | −75.6700 | − | 56.1014i | −0.399166 | − | 0.295940i | ||||
\(34\) | 14.8249 | + | 25.6775i | 0.0747781 | + | 0.129519i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 62.3714 | + | 205.368i | 0.288757 | + | 0.950776i | ||||
\(37\) | 99.9894i | 0.444274i | 0.975015 | + | 0.222137i | \(0.0713033\pi\) | ||||
−0.975015 | + | 0.222137i | \(0.928697\pi\) | |||||||
\(38\) | 4.53402 | − | 2.61772i | 0.0193557 | − | 0.0111750i | ||||
\(39\) | −258.917 | − | 29.7428i | −1.06307 | − | 0.122119i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −122.663 | + | 212.458i | −0.467237 | + | 0.809278i | −0.999299 | − | 0.0374272i | \(-0.988084\pi\) |
0.532063 | + | 0.846705i | \(0.321417\pi\) | |||||||
\(42\) | 4.16670 | − | 36.2720i | 0.0153080 | − | 0.133259i | ||||
\(43\) | −120.530 | + | 69.5882i | −0.427458 | + | 0.246793i | −0.698263 | − | 0.715841i | \(-0.746043\pi\) |
0.270805 | + | 0.962634i | \(0.412710\pi\) | |||||||
\(44\) | 144.108 | 0.493752 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.43001 | 0.0238151 | ||||||||
\(47\) | −409.596 | + | 236.480i | −1.27119 | + | 0.733919i | −0.975211 | − | 0.221276i | \(-0.928978\pi\) |
−0.295975 | + | 0.955196i | \(0.595644\pi\) | |||||||
\(48\) | −262.070 | − | 194.298i | −0.788054 | − | 0.584259i | ||||
\(49\) | 315.033 | − | 545.654i | 0.918465 | − | 1.59083i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −272.153 | − | 627.498i | −0.747237 | − | 1.72289i | ||||
\(52\) | 345.289 | − | 199.352i | 0.920825 | − | 0.531639i | ||||
\(53\) | − | 421.529i | − | 1.09248i | −0.837628 | − | 0.546240i | \(-0.816059\pi\) | ||
0.837628 | − | 0.546240i | \(-0.183941\pi\) | |||||||
\(54\) | 5.67258 | + | 31.0884i | 0.0142952 | + | 0.0783443i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 56.0333 | + | 97.0526i | 0.133710 | + | 0.231593i | ||||
\(57\) | −110.801 | + | 48.0556i | −0.257472 | + | 0.111669i | ||||
\(58\) | −24.5435 | − | 14.1702i | −0.0555641 | − | 0.0320799i | ||||
\(59\) | −371.207 | + | 642.949i | −0.819101 | + | 1.41873i | 0.0872437 | + | 0.996187i | \(0.472194\pi\) |
−0.906345 | + | 0.422538i | \(0.861139\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.48868 | − | 7.77462i | −0.00942158 | − | 0.0163187i | 0.861276 | − | 0.508137i | \(-0.169666\pi\) |
−0.870698 | + | 0.491818i | \(0.836332\pi\) | |||||||
\(62\) | − | 28.1816i | − | 0.0577269i | ||||||
\(63\) | −190.982 | + | 820.300i | −0.381929 | + | 1.64044i | ||||
\(64\) | 492.620 | 0.962148 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 21.0795 | + | 2.42149i | 0.0393138 | + | 0.00451613i | ||||
\(67\) | −510.008 | − | 294.453i | −0.929960 | − | 0.536913i | −0.0431613 | − | 0.999068i | \(-0.513743\pi\) |
−0.886799 | + | 0.462155i | \(0.847076\pi\) | |||||||
\(68\) | 906.182 | + | 523.185i | 1.61604 | + | 0.933021i | ||||
\(69\) | −170.279 | − | 19.5606i | −0.297089 | − | 0.0341278i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −48.5526 | −0.0811568 | −0.0405784 | − | 0.999176i | \(-0.512920\pi\) | ||||
−0.0405784 | + | 0.999176i | \(0.512920\pi\) | |||||||
\(72\) | −70.8182 | − | 66.2847i | −0.115917 | − | 0.108496i | ||||
\(73\) | − | 409.800i | − | 0.657034i | −0.944498 | − | 0.328517i | \(-0.893451\pi\) | ||
0.944498 | − | 0.328517i | \(-0.106549\pi\) | |||||||
\(74\) | −11.2613 | − | 19.5051i | −0.0176905 | − | 0.0306409i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 92.3816 | − | 160.010i | 0.139433 | − | 0.241505i | ||||
\(77\) | 489.737 | + | 282.750i | 0.724815 | + | 0.418472i | ||||
\(78\) | 53.8572 | − | 23.3585i | 0.0781811 | − | 0.0339080i | ||||
\(79\) | 265.263 | + | 459.449i | 0.377778 | + | 0.654330i | 0.990739 | − | 0.135783i | \(-0.0433550\pi\) |
−0.612961 | + | 0.790113i | \(0.710022\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −48.1577 | − | 727.408i | −0.0660600 | − | 0.997816i | ||||
\(82\) | − | 55.2595i | − | 0.0744195i | ||||||
\(83\) | 255.122 | − | 147.295i | 0.337389 | − | 0.194792i | −0.321728 | − | 0.946832i | \(-0.604264\pi\) |
0.659117 | + | 0.752040i | \(0.270930\pi\) | |||||||
\(84\) | −512.688 | − | 1182.10i | −0.665939 | − | 1.53544i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 15.6747 | − | 27.1494i | 0.0196541 | − | 0.0340418i | ||||
\(87\) | 525.174 | + | 389.362i | 0.647179 | + | 0.479816i | ||||
\(88\) | −56.4023 | + | 32.5639i | −0.0683240 | + | 0.0394469i | ||||
\(89\) | −852.817 | −1.01571 | −0.507856 | − | 0.861442i | \(-0.669562\pi\) | ||||
−0.507856 | + | 0.861442i | \(0.669562\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1564.57 | 1.80233 | ||||||||
\(92\) | 227.082 | − | 131.106i | 0.257336 | − | 0.148573i | ||||
\(93\) | −74.1922 | + | 645.857i | −0.0827244 | + | 0.720132i | ||||
\(94\) | 53.2672 | − | 92.2615i | 0.0584478 | − | 0.101234i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 221.370 | + | 25.4296i | 0.235349 | + | 0.0270354i | ||||
\(97\) | −336.096 | + | 194.045i | −0.351808 | + | 0.203117i | −0.665481 | − | 0.746414i | \(-0.731774\pi\) |
0.313673 | + | 0.949531i | \(0.398440\pi\) | |||||||
\(98\) | 141.922i | 0.146289i | ||||||||
\(99\) | −476.719 | − | 110.990i | −0.483960 | − | 0.112676i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 539.997 | + | 935.302i | 0.531997 | + | 0.921446i | 0.999302 | + | 0.0373500i | \(0.0118916\pi\) |
−0.467305 | + | 0.884096i | \(0.654775\pi\) | |||||||
\(102\) | 123.761 | + | 91.7562i | 0.120139 | + | 0.0890707i | ||||
\(103\) | −515.282 | − | 297.498i | −0.492935 | − | 0.284596i | 0.232856 | − | 0.972511i | \(-0.425193\pi\) |
−0.725791 | + | 0.687915i | \(0.758526\pi\) | |||||||
\(104\) | −90.0948 | + | 156.049i | −0.0849473 | + | 0.147133i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 47.4747 | + | 82.2286i | 0.0435014 | + | 0.0753467i | ||||
\(107\) | − | 498.693i | − | 0.450565i | −0.974293 | − | 0.225282i | \(-0.927670\pi\) | ||
0.974293 | − | 0.225282i | \(-0.0723305\pi\) | |||||||
\(108\) | 721.938 | + | 850.053i | 0.643227 | + | 0.757374i | ||||
\(109\) | 959.301 | 0.842976 | 0.421488 | − | 0.906834i | \(-0.361508\pi\) | ||||
0.421488 | + | 0.906834i | \(0.361508\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 206.733 | + | 476.660i | 0.176777 | + | 0.407590i | ||||
\(112\) | 1696.12 | + | 979.256i | 1.43097 | + | 0.826170i | ||||
\(113\) | 1497.18 | + | 864.396i | 1.24640 | + | 0.719607i | 0.970389 | − | 0.241549i | \(-0.0776554\pi\) |
0.276007 | + | 0.961156i | \(0.410989\pi\) | |||||||
\(114\) | 16.2019 | − | 21.8532i | 0.0133109 | − | 0.0179539i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1000.16 | −0.800536 | ||||||||
\(117\) | −1295.78 | + | 393.535i | −1.02388 | + | 0.310960i | ||||
\(118\) | − | 167.228i | − | 0.130463i | ||||||
\(119\) | 2053.05 | + | 3555.99i | 1.58154 | + | 2.73930i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 501.179 | − | 868.068i | 0.376543 | − | 0.652192i | ||||
\(122\) | 1.75123 | + | 1.01107i | 0.00129958 | + | 0.000750315i | ||||
\(123\) | −145.479 | + | 1266.42i | −0.106645 | + | 0.928368i | ||||
\(124\) | −497.277 | − | 861.309i | −0.360135 | − | 0.623773i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −55.1308 | − | 181.527i | −0.0389797 | − | 0.128347i | ||||
\(127\) | 1019.95i | 0.712647i | 0.934363 | + | 0.356324i | \(0.115970\pi\) | ||||
−0.934363 | + | 0.356324i | \(0.884030\pi\) | |||||||
\(128\) | −393.197 | + | 227.013i | −0.271516 | + | 0.156760i | ||||
\(129\) | −430.703 | + | 580.936i | −0.293964 | + | 0.396500i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 851.196 | − | 1474.31i | 0.567705 | − | 0.983294i | −0.429088 | − | 0.903263i | \(-0.641165\pi\) |
0.996792 | − | 0.0800308i | \(-0.0255019\pi\) | |||||||
\(132\) | 686.977 | − | 297.950i | 0.452983 | − | 0.196464i | ||||
\(133\) | 627.900 | − | 362.518i | 0.409367 | − | 0.236348i | ||||
\(134\) | 132.651 | 0.0855172 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −472.893 | −0.298164 | ||||||||
\(137\) | −909.049 | + | 524.839i | −0.566900 | + | 0.327300i | −0.755910 | − | 0.654675i | \(-0.772805\pi\) |
0.189010 | + | 0.981975i | \(0.439472\pi\) | |||||||
\(138\) | 35.4196 | − | 15.3619i | 0.0218487 | − | 0.00947602i | ||||
\(139\) | 717.411 | − | 1242.59i | 0.437770 | − | 0.758240i | −0.559747 | − | 0.828663i | \(-0.689102\pi\) |
0.997517 | + | 0.0704236i | \(0.0224351\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1463.65 | + | 1974.18i | −0.874197 | + | 1.17912i | ||||
\(142\) | 9.47126 | − | 5.46823i | 0.00559726 | − | 0.00323158i | ||||
\(143\) | 909.256i | 0.531719i | ||||||||
\(144\) | −1651.03 | − | 384.394i | −0.955460 | − | 0.222450i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 46.1537 | + | 79.9406i | 0.0261624 | + | 0.0453146i | ||||
\(147\) | 373.631 | − | 3252.53i | 0.209637 | − | 1.82493i | ||||
\(148\) | −688.353 | − | 397.421i | −0.382313 | − | 0.220728i | ||||
\(149\) | 609.231 | − | 1055.22i | 0.334968 | − | 0.580181i | −0.648511 | − | 0.761205i | \(-0.724608\pi\) |
0.983479 | + | 0.181024i | \(0.0579413\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −804.751 | − | 1393.87i | −0.433707 | − | 0.751202i | 0.563482 | − | 0.826128i | \(-0.309461\pi\) |
−0.997189 | + | 0.0749258i | \(0.976128\pi\) | |||||||
\(152\) | 83.5014i | 0.0445583i | ||||||||
\(153\) | −2594.76 | − | 2428.66i | −1.37107 | − | 1.28330i | ||||
\(154\) | −127.379 | −0.0666524 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1233.86 | − | 1664.23i | 0.633253 | − | 0.854137i | ||||
\(157\) | −1114.00 | − | 643.168i | −0.566286 | − | 0.326945i | 0.189379 | − | 0.981904i | \(-0.439353\pi\) |
−0.755664 | + | 0.654959i | \(0.772686\pi\) | |||||||
\(158\) | −103.491 | − | 59.7505i | −0.0521095 | − | 0.0300854i | ||||
\(159\) | −871.531 | − | 2009.47i | −0.434698 | − | 1.00227i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1028.95 | 0.503683 | ||||||||
\(162\) | 91.3185 | + | 136.473i | 0.0442880 | + | 0.0661873i | ||||
\(163\) | − | 1416.84i | − | 0.680830i | −0.940275 | − | 0.340415i | \(-0.889432\pi\) | ||
0.940275 | − | 0.340415i | \(-0.110568\pi\) | |||||||
\(164\) | −975.079 | − | 1688.89i | −0.464273 | − | 0.804145i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −33.1782 | + | 57.4663i | −0.0155128 | + | 0.0268690i | ||||
\(167\) | −775.071 | − | 447.487i | −0.359142 | − | 0.207351i | 0.309562 | − | 0.950879i | \(-0.399818\pi\) |
−0.668704 | + | 0.743528i | \(0.733151\pi\) | |||||||
\(168\) | 467.777 | + | 346.808i | 0.214820 | + | 0.159267i | ||||
\(169\) | 159.323 | + | 275.955i | 0.0725183 | + | 0.125605i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −428.842 | + | 458.172i | −0.191780 | + | 0.204896i | ||||
\(172\) | − | 1106.35i | − | 0.490456i | ||||||
\(173\) | 1502.64 | − | 867.548i | 0.660367 | − | 0.381263i | −0.132050 | − | 0.991243i | \(-0.542156\pi\) |
0.792417 | + | 0.609980i | \(0.208823\pi\) | |||||||
\(174\) | −146.299 | − | 16.8059i | −0.0637407 | − | 0.00732214i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −569.097 | + | 985.705i | −0.243735 | + | 0.422161i | ||||
\(177\) | −440.253 | + | 3832.49i | −0.186957 | + | 1.62750i | ||||
\(178\) | 166.361 | − | 96.0485i | 0.0700521 | − | 0.0404446i | ||||
\(179\) | −2133.37 | −0.890815 | −0.445408 | − | 0.895328i | \(-0.646941\pi\) | ||||
−0.445408 | + | 0.895328i | \(0.646941\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3611.98 | −1.48330 | −0.741648 | − | 0.670789i | \(-0.765955\pi\) | ||||
−0.741648 | + | 0.670789i | \(0.765955\pi\) | |||||||
\(182\) | −305.205 | + | 176.210i | −0.124304 | + | 0.0717668i | ||||
\(183\) | −37.4724 | − | 27.7819i | −0.0151368 | − | 0.0112224i | ||||
\(184\) | −59.2516 | + | 102.627i | −0.0237396 | + | 0.0411182i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −58.2668 | − | 134.345i | −0.0229695 | − | 0.0529603i | ||||
\(187\) | −2066.57 | + | 1193.13i | −0.808142 | + | 0.466581i | ||||
\(188\) | − | 3759.69i | − | 1.45853i | ||||||
\(189\) | 785.575 | + | 4305.32i | 0.302340 | + | 1.65696i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 298.495 | + | 517.008i | 0.113080 | + | 0.195861i | 0.917011 | − | 0.398863i | \(-0.130595\pi\) |
−0.803930 | + | 0.594723i | \(0.797262\pi\) | |||||||
\(192\) | 2348.37 | − | 1018.51i | 0.882702 | − | 0.382838i | ||||
\(193\) | −1045.94 | − | 603.872i | −0.390094 | − | 0.225221i | 0.292107 | − | 0.956386i | \(-0.405644\pi\) |
−0.682201 | + | 0.731165i | \(0.738977\pi\) | |||||||
\(194\) | 43.7087 | − | 75.7056i | 0.0161758 | − | 0.0280173i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2504.28 | + | 4337.54i | 0.912639 | + | 1.58074i | ||||
\(197\) | − | 3268.56i | − | 1.18211i | −0.806632 | − | 0.591054i | \(-0.798712\pi\) | ||
0.806632 | − | 0.591054i | \(-0.201288\pi\) | |||||||
\(198\) | 105.495 | − | 32.0394i | 0.0378646 | − | 0.0114997i | ||||
\(199\) | 2109.88 | 0.751585 | 0.375793 | − | 0.926704i | \(-0.377371\pi\) | ||||
0.375793 | + | 0.926704i | \(0.377371\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3040.05 | − | 349.223i | −1.06681 | − | 0.122549i | ||||
\(202\) | −210.677 | − | 121.634i | −0.0733820 | − | 0.0423671i | ||||
\(203\) | −3398.93 | − | 1962.38i | −1.17516 | − | 0.678482i | ||||
\(204\) | 5401.57 | + | 620.500i | 1.85385 | + | 0.212959i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 134.023 | 0.0453292 | ||||||||
\(207\) | −852.177 | + | 258.811i | −0.286137 | + | 0.0869017i | ||||
\(208\) | 3149.05i | 1.04975i | ||||||||
\(209\) | 210.678 | + | 364.906i | 0.0697269 | + | 0.120771i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −329.321 | + | 570.400i | −0.107447 | + | 0.186104i | −0.914735 | − | 0.404053i | \(-0.867601\pi\) |
0.807288 | + | 0.590157i | \(0.200934\pi\) | |||||||
\(212\) | 2901.92 | + | 1675.42i | 0.940116 | + | 0.542776i | ||||
\(213\) | −231.455 | + | 100.385i | −0.0744556 | + | 0.0322923i | ||||
\(214\) | 56.1652 | + | 97.2810i | 0.0179410 | + | 0.0310747i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −474.644 | − | 169.566i | −0.149516 | − | 0.0534144i | ||||
\(217\) | − | 3902.77i | − | 1.22091i | ||||||
\(218\) | −187.133 | + | 108.041i | −0.0581387 | + | 0.0335664i | ||||
\(219\) | −847.281 | − | 1953.56i | −0.261434 | − | 0.602783i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3301.06 | + | 5717.60i | −1.00476 | + | 1.74030i | ||||
\(222\) | −94.0115 | − | 69.6997i | −0.0284218 | − | 0.0210718i | ||||
\(223\) | −1055.51 | + | 609.397i | −0.316959 | + | 0.182997i | −0.650036 | − | 0.759903i | \(-0.725246\pi\) |
0.333077 | + | 0.942900i | \(0.391913\pi\) | |||||||
\(224\) | −1337.69 | −0.399009 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −389.410 | −0.114616 | ||||||||
\(227\) | −1321.18 | + | 762.785i | −0.386299 | + | 0.223030i | −0.680555 | − | 0.732697i | \(-0.738261\pi\) |
0.294256 | + | 0.955727i | \(0.404928\pi\) | |||||||
\(228\) | 109.565 | − | 953.785i | 0.0318251 | − | 0.277044i | ||||
\(229\) | −3091.33 | + | 5354.33i | −0.892055 | + | 1.54508i | −0.0546469 | + | 0.998506i | \(0.517403\pi\) |
−0.837408 | + | 0.546578i | \(0.815930\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2919.23 | + | 335.343i | 0.831476 | + | 0.0955150i | ||||
\(232\) | 391.450 | − | 226.004i | 0.110776 | − | 0.0639564i | ||||
\(233\) | 2013.82i | 0.566222i | 0.959087 | + | 0.283111i | \(0.0913665\pi\) | ||||
−0.959087 | + | 0.283111i | \(0.908633\pi\) | |||||||
\(234\) | 208.448 | − | 222.704i | 0.0582336 | − | 0.0622164i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2950.82 | − | 5110.97i | −0.813906 | − | 1.40973i | ||||
\(237\) | 2214.47 | + | 1641.80i | 0.606942 | + | 0.449984i | ||||
\(238\) | −800.985 | − | 462.449i | −0.218152 | − | 0.125950i | ||||
\(239\) | 2543.15 | − | 4404.87i | 0.688297 | − | 1.19216i | −0.284092 | − | 0.958797i | \(-0.591692\pi\) |
0.972389 | − | 0.233368i | \(-0.0749746\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1643.41 | − | 2846.47i | −0.439259 | − | 0.760820i | 0.558373 | − | 0.829590i | \(-0.311426\pi\) |
−0.997633 | + | 0.0687703i | \(0.978092\pi\) | |||||||
\(242\) | 225.781i | 0.0599742i | ||||||||
\(243\) | −1733.52 | − | 3368.06i | −0.457636 | − | 0.889140i | ||||
\(244\) | 71.3634 | 0.0187237 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −114.252 | − | 263.428i | −0.0296115 | − | 0.0682746i | ||||
\(247\) | 1009.59 | + | 582.886i | 0.260075 | + | 0.150154i | ||||
\(248\) | 389.258 | + | 224.738i | 0.0996689 | + | 0.0575439i | ||||
\(249\) | 911.655 | − | 1229.65i | 0.232023 | − | 0.312955i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3480.55 | 0.875260 | 0.437630 | − | 0.899155i | \(-0.355818\pi\) | ||||
0.437630 | + | 0.899155i | \(0.355818\pi\) | |||||||
\(252\) | −4888.07 | − | 4575.16i | −1.22190 | − | 1.14368i | ||||
\(253\) | 597.979i | 0.148595i | ||||||||
\(254\) | −114.872 | − | 198.964i | −0.0283768 | − | 0.0491501i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1919.34 | + | 3324.40i | −0.468590 | + | 0.811621i | ||||
\(257\) | 5884.62 | + | 3397.49i | 1.42830 | + | 0.824628i | 0.996987 | − | 0.0775746i | \(-0.0247176\pi\) |
0.431312 | + | 0.902203i | \(0.358051\pi\) | |||||||
\(258\) | 18.5903 | − | 161.832i | 0.00448598 | − | 0.0390513i | ||||
\(259\) | −1559.54 | − | 2701.19i | −0.374150 | − | 0.648047i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3308.58 | + | 770.305i | 0.784659 | + | 0.182685i | ||||
\(262\) | 383.464i | 0.0904216i | ||||||||
\(263\) | −4645.56 | + | 2682.12i | −1.08919 | + | 0.628846i | −0.933362 | − | 0.358938i | \(-0.883139\pi\) |
−0.155832 | + | 0.987784i | \(0.549806\pi\) | |||||||
\(264\) | −201.548 | + | 271.850i | −0.0469865 | + | 0.0633758i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −81.6572 | + | 141.434i | −0.0188223 | + | 0.0326011i | ||||
\(267\) | −4065.47 | + | 1763.24i | −0.931845 | + | 0.404152i | ||||
\(268\) | 4054.18 | − | 2340.68i | 0.924062 | − | 0.533508i | ||||
\(269\) | −48.4985 | −0.0109926 | −0.00549629 | − | 0.999985i | \(-0.501750\pi\) | ||||
−0.00549629 | + | 0.999985i | \(0.501750\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7643.16 | 1.71324 | 0.856622 | − | 0.515945i | \(-0.172559\pi\) | ||||
0.856622 | + | 0.515945i | \(0.172559\pi\) | |||||||
\(272\) | −7157.21 | + | 4132.22i | −1.59548 | + | 0.921149i | ||||
\(273\) | 7458.48 | − | 3234.83i | 1.65351 | − | 0.717145i | ||||
\(274\) | 118.220 | − | 204.763i | 0.0260654 | − | 0.0451467i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 811.454 | − | 1094.50i | 0.176970 | − | 0.238699i | ||||
\(277\) | 4456.59 | − | 2573.01i | 0.966680 | − | 0.558113i | 0.0684576 | − | 0.997654i | \(-0.478192\pi\) |
0.898223 | + | 0.439541i | \(0.144859\pi\) | |||||||
\(278\) | 323.193i | 0.0697261i | ||||||||
\(279\) | 981.658 | + | 3232.26i | 0.210646 | + | 0.693586i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2927.37 | − | 5070.35i | −0.621467 | − | 1.07641i | −0.989213 | − | 0.146486i | \(-0.953204\pi\) |
0.367746 | − | 0.929926i | \(-0.380130\pi\) | |||||||
\(282\) | 63.1752 | − | 549.952i | 0.0133405 | − | 0.116132i | ||||
\(283\) | 8135.31 | + | 4696.92i | 1.70881 | + | 0.986583i | 0.936036 | + | 0.351904i | \(0.114466\pi\) |
0.772776 | + | 0.634679i | \(0.218868\pi\) | |||||||
\(284\) | 192.979 | − | 334.249i | 0.0403211 | − | 0.0698381i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −102.405 | − | 177.370i | −0.0211725 | − | 0.0366718i | ||||
\(287\) | − | 7652.69i | − | 1.57395i | ||||||
\(288\) | 1107.87 | − | 336.467i | 0.226673 | − | 0.0688420i | ||||
\(289\) | −12413.7 | −2.52671 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1201.01 | + | 1619.93i | −0.241939 | + | 0.326329i | ||||
\(292\) | 2821.17 | + | 1628.81i | 0.565400 | + | 0.326434i | ||||
\(293\) | −1542.03 | − | 890.291i | −0.307462 | − | 0.177513i | 0.338328 | − | 0.941028i | \(-0.390139\pi\) |
−0.645790 | + | 0.763515i | \(0.723472\pi\) | |||||||
\(294\) | 293.431 | + | 676.559i | 0.0582083 | + | 0.134210i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 359.219 | 0.0705377 | ||||||||
\(297\) | −2502.04 | + | 456.539i | −0.488833 | + | 0.0891955i | ||||
\(298\) | 274.458i | 0.0533522i | ||||||||
\(299\) | 827.217 | + | 1432.78i | 0.159997 | + | 0.277123i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2170.74 | − | 3759.82i | 0.415678 | − | 0.719976i | ||||
\(302\) | 313.969 | + | 181.270i | 0.0598241 | + | 0.0345395i | ||||
\(303\) | 4508.00 | + | 3342.21i | 0.854713 | + | 0.633680i | ||||
\(304\) | 729.649 | + | 1263.79i | 0.137659 | + | 0.238432i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 779.693 | + | 181.528i | 0.145660 | + | 0.0339127i | ||||
\(307\) | 8480.18i | 1.57651i | 0.615347 | + | 0.788256i | \(0.289016\pi\) | ||||
−0.615347 | + | 0.788256i | \(0.710984\pi\) | |||||||
\(308\) | −3893.05 | + | 2247.65i | −0.720218 | + | 0.415818i | ||||
\(309\) | −3071.50 | − | 352.835i | −0.565473 | − | 0.0649582i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3405.40 | − | 5898.32i | 0.620908 | − | 1.07544i | −0.368409 | − | 0.929664i | \(-0.620097\pi\) |
0.989317 | − | 0.145780i | \(-0.0465692\pi\) | |||||||
\(312\) | −106.853 | + | 930.176i | −0.0193890 | + | 0.168785i | ||||
\(313\) | −6968.74 | + | 4023.41i | −1.25846 | + | 0.726570i | −0.972774 | − | 0.231755i | \(-0.925553\pi\) |
−0.285682 | + | 0.958325i | \(0.592220\pi\) | |||||||
\(314\) | 289.747 | 0.0520744 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4217.30 | −0.750764 | ||||||||
\(317\) | 1356.39 | − | 783.112i | 0.240323 | − | 0.138751i | −0.375002 | − | 0.927024i | \(-0.622358\pi\) |
0.615325 | + | 0.788273i | \(0.289025\pi\) | |||||||
\(318\) | 396.328 | + | 293.836i | 0.0698898 | + | 0.0518160i | ||||
\(319\) | 1140.44 | − | 1975.30i | 0.200164 | − | 0.346694i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1031.07 | − | 2377.32i | −0.179280 | − | 0.413361i | ||||
\(322\) | −200.720 | + | 115.886i | −0.0347382 | + | 0.0200561i | ||||
\(323\) | 3059.47i | 0.527039i | ||||||||
\(324\) | 5199.07 | + | 2559.65i | 0.891474 | + | 0.438897i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 159.571 | + | 276.385i | 0.0271099 | + | 0.0469557i | ||||
\(327\) | 4573.08 | − | 1983.40i | 0.773371 | − | 0.335420i | ||||
\(328\) | 763.271 | + | 440.674i | 0.128490 | + | 0.0741835i | ||||
\(329\) | 7376.77 | − | 12776.9i | 1.23615 | − | 2.14108i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1221.28 | − | 2115.32i | −0.202802 | − | 0.351264i | 0.746628 | − | 0.665242i | \(-0.231672\pi\) |
−0.949430 | + | 0.313978i | \(0.898338\pi\) | |||||||
\(332\) | 2341.77i | 0.387113i | ||||||||
\(333\) | 1971.03 | + | 1844.85i | 0.324360 | + | 0.303596i | ||||
\(334\) | 201.593 | 0.0330260 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 10110.2 | + | 1161.40i | 1.64154 | + | 0.188571i | ||||
\(337\) | −8203.84 | − | 4736.49i | −1.32609 | − | 0.765617i | −0.341396 | − | 0.939920i | \(-0.610900\pi\) |
−0.984692 | + | 0.174302i | \(0.944233\pi\) | |||||||
\(338\) | −62.1588 | − | 35.8874i | −0.0100029 | − | 0.00577520i | ||||
\(339\) | 8924.38 | + | 1025.18i | 1.42981 | + | 0.164248i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2268.10 | 0.360190 | ||||||||
\(342\) | 32.0535 | − | 137.675i | 0.00506799 | − | 0.0217678i | ||||
\(343\) | 8954.76i | 1.40966i | ||||||||
\(344\) | 250.000 | + | 433.013i | 0.0391835 | + | 0.0678678i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −195.415 | + | 338.469i | −0.0303630 | + | 0.0525902i | ||||
\(347\) | 2868.68 | + | 1656.23i | 0.443801 | + | 0.256229i | 0.705209 | − | 0.709000i | \(-0.250853\pi\) |
−0.261408 | + | 0.965229i | \(0.584187\pi\) | |||||||
\(348\) | −4767.84 | + | 2067.87i | −0.734435 | + | 0.318533i | ||||
\(349\) | 2834.48 | + | 4909.46i | 0.434745 | + | 0.753001i | 0.997275 | − | 0.0737765i | \(-0.0235052\pi\) |
−0.562530 | + | 0.826777i | \(0.690172\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5363.44 | + | 4555.10i | −0.815611 | + | 0.692687i | ||||
\(352\) | − | 777.400i | − | 0.117715i | ||||||
\(353\) | 1506.09 | − | 869.541i | 0.227085 | − | 0.131108i | −0.382142 | − | 0.924104i | \(-0.624813\pi\) |
0.609227 | + | 0.792996i | \(0.291480\pi\) | |||||||
\(354\) | −345.753 | − | 797.195i | −0.0519111 | − | 0.119690i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3389.63 | − | 5871.02i | 0.504636 | − | 0.874054i | ||||
\(357\) | 17139.3 | + | 12707.0i | 2.54091 | + | 1.88382i | ||||
\(358\) | 416.162 | − | 240.271i | 0.0614381 | − | 0.0354713i | ||||
\(359\) | −8624.58 | −1.26793 | −0.633966 | − | 0.773361i | \(-0.718574\pi\) | ||||
−0.633966 | + | 0.773361i | \(0.718574\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6318.77 | −0.921238 | ||||||||
\(362\) | 704.597 | − | 406.799i | 0.102301 | − | 0.0590632i | ||||
\(363\) | 594.401 | − | 5174.38i | 0.0859449 | − | 0.748166i | ||||
\(364\) | −6218.60 | + | 10770.9i | −0.895449 | + | 1.55096i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.4387 | + | 1.19914i | 0.00149083 | + | 0.000171257i | ||||
\(367\) | −5290.70 | + | 3054.59i | −0.752513 | + | 0.434463i | −0.826601 | − | 0.562788i | \(-0.809729\pi\) |
0.0740883 | + | 0.997252i | \(0.476395\pi\) | |||||||
\(368\) | 2071.00i | 0.293365i | ||||||||
\(369\) | 1924.87 | + | 6337.94i | 0.271558 | + | 0.894146i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6574.59 | + | 11387.5i | 0.920043 | + | 1.59356i | ||||
\(372\) | −4151.36 | − | 3077.80i | −0.578597 | − | 0.428969i | ||||
\(373\) | 5677.08 | + | 3277.67i | 0.788065 | + | 0.454990i | 0.839281 | − | 0.543698i | \(-0.182976\pi\) |
−0.0512159 | + | 0.998688i | \(0.516310\pi\) | |||||||
\(374\) | 268.753 | − | 465.494i | 0.0371575 | − | 0.0643587i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 849.572 | + | 1471.50i | 0.116525 | + | 0.201827i | ||||
\(377\) | − | 6310.52i | − | 0.862092i | ||||||
\(378\) | −638.130 | − | 751.372i | −0.0868303 | − | 0.102239i | ||||
\(379\) | −5032.40 | −0.682050 | −0.341025 | − | 0.940054i | \(-0.610774\pi\) | ||||
−0.341025 | + | 0.940054i | \(0.610774\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2108.80 | + | 4862.22i | 0.283562 | + | 0.653803i | ||||
\(382\) | −116.456 | − | 67.2359i | −0.0155979 | − | 0.00900547i | ||||
\(383\) | 3172.24 | + | 1831.49i | 0.423222 | + | 0.244347i | 0.696455 | − | 0.717601i | \(-0.254760\pi\) |
−0.273233 | + | 0.961948i | \(0.588093\pi\) | |||||||
\(384\) | −1405.05 | + | 1895.15i | −0.186722 | + | 0.251852i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 272.044 | 0.0358722 | ||||||||
\(387\) | −852.094 | + | 3659.88i | −0.111923 | + | 0.480729i | ||||
\(388\) | − | 3085.03i | − | 0.403657i | ||||||
\(389\) | −2435.48 | − | 4218.37i | −0.317439 | − | 0.549820i | 0.662514 | − | 0.749049i | \(-0.269489\pi\) |
−0.979953 | + | 0.199229i | \(0.936156\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2170.97 | + | 3760.22i | −0.280794 | + | 0.486349i | ||||
\(392\) | −1960.30 | − | 1131.78i | −0.252577 | − | 0.145825i | ||||
\(393\) | 1009.52 | − | 8788.09i | 0.129577 | − | 1.12799i | ||||
\(394\) | 368.121 | + | 637.605i | 0.0470703 | + | 0.0815281i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2658.87 | − | 2840.72i | 0.337407 | − | 0.360483i | ||||
\(397\) | − | 3744.62i | − | 0.473393i | −0.971584 | − | 0.236696i | \(-0.923935\pi\) | ||
0.971584 | − | 0.236696i | \(-0.0760647\pi\) | |||||||
\(398\) | −411.579 | + | 237.625i | −0.0518356 | + | 0.0299273i | ||||
\(399\) | 2243.74 | − | 3026.37i | 0.281523 | − | 0.379720i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 900.435 | − | 1559.60i | 0.112134 | − | 0.194221i | −0.804497 | − | 0.593957i | \(-0.797565\pi\) |
0.916630 | + | 0.399736i | \(0.130898\pi\) | |||||||
\(402\) | 632.361 | − | 274.262i | 0.0784559 | − | 0.0340272i | ||||
\(403\) | 5434.46 | − | 3137.59i | 0.671737 | − | 0.387827i | ||||
\(404\) | −8585.16 | −1.05725 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 884.049 | 0.108066 | ||||||||
\(407\) | 1569.81 | − | 906.328i | 0.191185 | − | 0.110381i | ||||
\(408\) | −2254.33 | + | 977.729i | −0.273544 | + | 0.118639i | ||||
\(409\) | 7965.99 | − | 13797.5i | 0.963064 | − | 1.66808i | 0.248334 | − | 0.968675i | \(-0.420117\pi\) |
0.714730 | − | 0.699401i | \(-0.246550\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3248.40 | + | 4381.46i | −0.389858 | + | 0.525843i | ||||
\(412\) | 4096.12 | − | 2364.89i | 0.489809 | − | 0.282791i | ||||
\(413\) | − | 23158.8i | − | 2.75926i | ||||||
\(414\) | 137.087 | − | 146.463i | 0.0162741 | − | 0.0173871i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1075.42 | − | 1862.68i | −0.126747 | − | 0.219532i | ||||
\(417\) | 850.854 | − | 7406.84i | 0.0999196 | − | 0.869820i | ||||
\(418\) | −82.1949 | − | 47.4553i | −0.00961791 | − | 0.00555290i | ||||
\(419\) | −1723.87 | + | 2985.84i | −0.200995 | + | 0.348133i | −0.948849 | − | 0.315730i | \(-0.897751\pi\) |
0.747854 | + | 0.663863i | \(0.231084\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2807.99 | − | 4863.58i | −0.325066 | − | 0.563032i | 0.656459 | − | 0.754361i | \(-0.272053\pi\) |
−0.981526 | + | 0.191330i | \(0.938720\pi\) | |||||||
\(422\) | − | 148.359i | − | 0.0171137i | ||||||
\(423\) | −2895.66 | + | 12437.3i | −0.332841 | + | 1.42960i | ||||
\(424\) | −1514.37 | −0.173454 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 33.8446 | − | 45.6499i | 0.00384924 | − | 0.00519189i | ||||
\(427\) | 242.522 | + | 140.020i | 0.0274858 | + | 0.0158689i | ||||
\(428\) | 3433.13 | + | 1982.12i | 0.387726 | + | 0.223854i | ||||
\(429\) | 1879.93 | + | 4334.51i | 0.211571 | + | 0.487814i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3534.04 | −0.394962 | −0.197481 | − | 0.980307i | \(-0.563276\pi\) | ||||
−0.197481 | + | 0.980307i | \(0.563276\pi\) | |||||||
\(432\) | −8665.40 | + | 1581.14i | −0.965080 | + | 0.176094i | ||||
\(433\) | − | 6674.80i | − | 0.740809i | −0.928871 | − | 0.370405i | \(-0.879219\pi\) | ||
0.928871 | − | 0.370405i | \(-0.120781\pi\) | |||||||
\(434\) | 439.549 | + | 761.321i | 0.0486153 | + | 0.0842041i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3812.87 | + | 6604.08i | −0.418815 | + | 0.725408i | ||||
\(437\) | 663.963 | + | 383.339i | 0.0726812 | + | 0.0419625i | ||||
\(438\) | 385.301 | + | 285.660i | 0.0420328 | + | 0.0311629i | ||||
\(439\) | −3271.76 | − | 5666.85i | −0.355700 | − | 0.616091i | 0.631537 | − | 0.775346i | \(-0.282424\pi\) |
−0.987238 | + | 0.159254i | \(0.949091\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4943.62 | − | 16277.7i | −0.533811 | − | 1.75766i | ||||
\(442\) | − | 1487.12i | − | 0.160035i | ||||||
\(443\) | −12392.6 | + | 7154.86i | −1.32909 | + | 0.767353i | −0.985160 | − | 0.171640i | \(-0.945093\pi\) |
−0.343935 | + | 0.938993i | \(0.611760\pi\) | |||||||
\(444\) | −4103.14 | − | 471.344i | −0.438573 | − | 0.0503806i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 137.267 | − | 237.753i | 0.0145734 | − | 0.0252420i | ||||
\(447\) | 722.552 | − | 6289.95i | 0.0764553 | − | 0.665558i | ||||
\(448\) | −13308.0 | + | 7683.39i | −1.40345 | + | 0.810282i | ||||
\(449\) | 14587.4 | 1.53324 | 0.766618 | − | 0.642104i | \(-0.221938\pi\) | ||||
0.766618 | + | 0.642104i | \(0.221938\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4447.38 | 0.464343 | ||||||||
\(452\) | −11901.5 | + | 6871.31i | −1.23849 | + | 0.715043i | ||||
\(453\) | −6718.22 | − | 4980.86i | −0.696798 | − | 0.516603i | ||||
\(454\) | 171.817 | − | 297.596i | 0.0177616 | − | 0.0307640i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 172.643 | + | 398.060i | 0.0177297 | + | 0.0408791i | ||||
\(457\) | 1754.37 | − | 1012.89i | 0.179576 | − | 0.103678i | −0.407518 | − | 0.913197i | \(-0.633606\pi\) |
0.587093 | + | 0.809519i | \(0.300272\pi\) | |||||||
\(458\) | − | 1392.64i | − | 0.142083i | ||||||
\(459\) | −17390.9 | − | 6212.87i | −1.76849 | − | 0.631790i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1778.09 | + | 3079.75i | 0.179640 | + | 0.311146i | 0.941757 | − | 0.336293i | \(-0.109173\pi\) |
−0.762117 | + | 0.647439i | \(0.775840\pi\) | |||||||
\(462\) | −607.228 | + | 263.362i | −0.0611489 | + | 0.0265210i | ||||
\(463\) | −8905.07 | − | 5141.34i | −0.893852 | − | 0.516066i | −0.0186517 | − | 0.999826i | \(-0.505937\pi\) |
−0.875201 | + | 0.483760i | \(0.839271\pi\) | |||||||
\(464\) | 3949.72 | − | 6841.11i | 0.395174 | − | 0.684462i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −226.806 | − | 392.840i | −0.0225464 | − | 0.0390514i | ||||
\(467\) | 8217.44i | 0.814256i | 0.913371 | + | 0.407128i | \(0.133470\pi\) | ||||
−0.913371 | + | 0.407128i | \(0.866530\pi\) | |||||||
\(468\) | 2441.03 | − | 10484.6i | 0.241104 | − | 1.03558i | ||||
\(469\) | 18370.3 | 1.80866 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6640.33 | − | 762.801i | −0.649618 | − | 0.0746242i | ||||
\(472\) | 2309.84 | + | 1333.59i | 0.225252 | + | 0.130049i | ||||
\(473\) | 2185.03 | + | 1261.53i | 0.212406 | + | 0.122632i | ||||
\(474\) | −616.889 | − | 70.8645i | −0.0597777 | − | 0.00686690i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −32640.5 | −3.14301 | ||||||||
\(477\) | −8309.35 | − | 7777.43i | −0.797608 | − | 0.746549i | ||||
\(478\) | 1145.69i | 0.109629i | ||||||||
\(479\) | 6842.59 | + | 11851.7i | 0.652705 | + | 1.13052i | 0.982464 | + | 0.186453i | \(0.0596993\pi\) |
−0.329759 | + | 0.944065i | \(0.606967\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2507.54 | − | 4343.19i | 0.237701 | − | 0.411710i | ||||
\(482\) | 641.168 | + | 370.178i | 0.0605900 | + | 0.0349817i | ||||
\(483\) | 4905.13 | − | 2127.41i | 0.462093 | − | 0.200415i | ||||
\(484\) | 3984.00 | + | 6900.50i | 0.374155 | + | 0.648056i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 717.489 | + | 461.776i | 0.0669670 | + | 0.0431000i | ||||
\(487\) | − | 3239.59i | − | 0.301437i | −0.988577 | − | 0.150718i | \(-0.951841\pi\) | ||
0.988577 | − | 0.150718i | \(-0.0481587\pi\) | |||||||
\(488\) | −27.9309 | + | 16.1259i | −0.00259092 | + | 0.00149587i | ||||
\(489\) | −2929.38 | − | 6754.21i | −0.270902 | − | 0.624613i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5564.04 | + | 9637.20i | −0.511409 | + | 0.885786i | 0.488504 | + | 0.872562i | \(0.337543\pi\) |
−0.999913 | + | 0.0132239i | \(0.995791\pi\) | |||||||
\(492\) | −8140.15 | − | 6035.07i | −0.745907 | − | 0.553012i | ||||
\(493\) | 14342.7 | − | 8280.74i | 1.31027 | − | 0.756482i | ||||
\(494\) | −262.590 | −0.0239159 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7855.18 | 0.711105 | ||||||||
\(497\) | 1311.64 | − | 757.276i | 0.118380 | − | 0.0683470i | ||||
\(498\) | −39.3495 | + | 342.545i | −0.00354075 | + | 0.0308229i | ||||
\(499\) | −2713.61 | + | 4700.11i | −0.243443 | + | 0.421655i | −0.961693 | − | 0.274130i | \(-0.911610\pi\) |
0.718250 | + | 0.695785i | \(0.244943\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4620.04 | − | 530.723i | −0.411992 | − | 0.0473272i | ||||
\(502\) | −678.958 | + | 391.997i | −0.0603653 | + | 0.0348519i | ||||
\(503\) | 9600.22i | 0.850999i | 0.904959 | + | 0.425500i | \(0.139902\pi\) | ||||
−0.904959 | + | 0.425500i | \(0.860098\pi\) | |||||||
\(504\) | 2946.98 | + | 686.117i | 0.260454 | + | 0.0606391i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −67.3474 | − | 116.649i | −0.00591691 | − | 0.0102484i | ||||
\(507\) | 1330.06 | + | 986.098i | 0.116509 | + | 0.0863790i | ||||
\(508\) | −7021.62 | − | 4053.94i | −0.613256 | − | 0.354064i | ||||
\(509\) | −9469.94 | + | 16402.4i | −0.824652 | + | 1.42834i | 0.0775333 | + | 0.996990i | \(0.475296\pi\) |
−0.902185 | + | 0.431349i | \(0.858038\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6391.66 | + | 11070.7i | 0.553328 | + | 0.958392i | ||||
\(512\) | − | 4496.87i | − | 0.388155i | ||||||
\(513\) | −1097.04 | + | 3070.80i | −0.0944162 | + | 0.264287i | ||||
\(514\) | −1530.57 | −0.131343 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2287.43 | − | 5274.08i | −0.195152 | − | 0.449958i | ||||
\(517\) | 7425.35 | + | 4287.03i | 0.631657 | + | 0.364687i | ||||
\(518\) | 608.444 | + | 351.285i | 0.0516090 | + | 0.0297965i | ||||
\(519\) | 5369.53 | − | 7242.46i | 0.454135 | − | 0.612541i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19292.6 | 1.62231 | 0.811155 | − | 0.584831i | \(-0.198839\pi\) | ||||
0.811155 | + | 0.584831i | \(0.198839\pi\) | |||||||
\(522\) | −732.168 | + | 222.364i | −0.0613910 | + | 0.0186448i | ||||
\(523\) | − | 17967.5i | − | 1.50223i | −0.660172 | − | 0.751114i | \(-0.729517\pi\) | ||
0.660172 | − | 0.751114i | \(-0.270483\pi\) | |||||||
\(524\) | 6766.38 | + | 11719.7i | 0.564104 | + | 0.977057i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 604.147 | − | 1046.41i | 0.0500799 | − | 0.0867410i | ||||
\(527\) | 14262.3 | + | 8234.35i | 1.17889 | + | 0.680634i | ||||
\(528\) | −674.952 | + | 5875.59i | −0.0556317 | + | 0.484285i | ||||
\(529\) | −5539.47 | − | 9594.65i | −0.455287 | − | 0.788580i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5825.11 | + | 19180.1i | 0.476061 | + | 1.56751i | ||||
\(532\) | 5763.51i | 0.469699i | ||||||||
\(533\) | 10656.1 | − | 6152.30i | 0.865979 | − | 0.499973i | ||||
\(534\) | 594.474 | − | 801.832i | 0.0481749 | − | 0.0649787i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1057.84 | + | 1832.24i | −0.0852460 | + | 0.147650i | ||||
\(537\) | −10170.0 | + | 4410.85i | −0.817260 | + | 0.354455i | ||||
\(538\) | 9.46070 | − | 5.46214i | 0.000758141 | − | 0.000437713i | ||||
\(539\) | −11422.1 | −0.912777 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8299.36 | −0.659552 | −0.329776 | − | 0.944059i | \(-0.606973\pi\) | ||||
−0.329776 | + | 0.944059i | \(0.606973\pi\) | |||||||
\(542\) | −1490.97 | + | 860.811i | −0.118160 | + | 0.0682195i | ||||
\(543\) | −17218.7 | + | 7467.94i | −1.36082 | + | 0.590203i | ||||
\(544\) | 2822.35 | − | 4888.46i | 0.222440 | − | 0.385278i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1090.62 | + | 1471.04i | −0.0854839 | + | 0.115301i | ||||
\(547\) | 73.3706 | − | 42.3605i | 0.00573510 | − | 0.00331116i | −0.497130 | − | 0.867676i | \(-0.665613\pi\) |
0.502865 | + | 0.864365i | \(0.332279\pi\) | |||||||
\(548\) | − | 8344.17i | − | 0.650448i | ||||||
\(549\) | −236.075 | − | 54.9630i | −0.0183523 | − | 0.00427280i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1462.18 | − | 2532.56i | −0.113050 | − | 0.195809i | ||||
\(552\) | −70.2727 | + | 611.737i | −0.00541849 | + | 0.0471690i | ||||
\(553\) | −14332.1 | − | 8274.63i | −1.10210 | − | 0.636298i | ||||
\(554\) | −579.571 | + | 1003.85i | −0.0444469 | + | 0.0769843i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5702.89 | + | 9877.69i | 0.434994 | + | 0.753431i | ||||
\(557\) | − | 20914.0i | − | 1.59094i | −0.605994 | − | 0.795469i | \(-0.707224\pi\) | ||
0.605994 | − | 0.795469i | \(-0.292776\pi\) | |||||||
\(558\) | −555.527 | − | 519.965i | −0.0421458 | − | 0.0394478i | ||||
\(559\) | 6980.56 | 0.528169 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7384.69 | + | 9960.52i | −0.555761 | + | 0.749614i | ||||
\(562\) | 1142.10 | + | 659.389i | 0.0857231 | + | 0.0494923i | ||||
\(563\) | 9561.76 | + | 5520.48i | 0.715773 | + | 0.413252i | 0.813195 | − | 0.581991i | \(-0.197726\pi\) |
−0.0974220 | + | 0.995243i | \(0.531060\pi\) | |||||||
\(564\) | −7773.33 | − | 17922.8i | −0.580348 | − | 1.33810i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2115.96 | −0.157139 | ||||||||
\(567\) | 12646.4 | + | 18899.7i | 0.936679 | + | 1.39984i | ||||
\(568\) | 174.429i | 0.0128853i | ||||||||
\(569\) | −3007.31 | − | 5208.81i | −0.221569 | − | 0.383770i | 0.733715 | − | 0.679457i | \(-0.237785\pi\) |
−0.955285 | + | 0.295688i | \(0.904451\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10968.7 | − | 18998.3i | 0.803896 | − | 1.39239i | −0.113137 | − | 0.993579i | \(-0.536090\pi\) |
0.917034 | − | 0.398810i | \(-0.130577\pi\) | |||||||
\(572\) | −6259.56 | − | 3613.96i | −0.457561 | − | 0.264173i | ||||
\(573\) | 2491.89 | + | 1847.48i | 0.181676 | + | 0.134694i | ||||
\(574\) | 861.884 | + | 1492.83i | 0.0626730 | + | 0.108553i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 9089.08 | − | 9710.72i | 0.657486 | − | 0.702454i | ||||
\(577\) | 473.507i | 0.0341635i | 0.999854 | + | 0.0170818i | \(0.00543756\pi\) | ||||
−0.999854 | + | 0.0170818i | \(0.994562\pi\) | |||||||
\(578\) | 2421.57 | − | 1398.09i | 0.174263 | − | 0.100611i | ||||
\(579\) | −6234.62 | − | 716.196i | −0.447499 | − | 0.0514060i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4594.72 | + | 7958.29i | −0.328092 | + | 0.568271i | ||||
\(582\) | 51.8387 | − | 451.266i | 0.00369207 | − | 0.0321402i | ||||
\(583\) | −6617.89 | + | 3820.84i | −0.470129 | + | 0.271429i | ||||
\(584\) | −1472.24 | −0.104318 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 401.076 | 0.0282735 | ||||||||
\(587\) | 11275.9 | − | 6510.17i | 0.792859 | − | 0.457757i | −0.0481093 | − | 0.998842i | \(-0.515320\pi\) |
0.840968 | + | 0.541085i | \(0.181986\pi\) | |||||||
\(588\) | 20906.2 | + | 15499.8i | 1.46626 | + | 1.08708i | ||||
\(589\) | 1453.99 | − | 2518.38i | 0.101715 | − | 0.176176i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6757.90 | − | 15581.6i | −0.470360 | − | 1.08450i | ||||
\(592\) | 5436.75 | − | 3138.91i | 0.377448 | − | 0.217920i | ||||
\(593\) | 12887.3i | 0.892441i | 0.894923 | + | 0.446220i | \(0.147230\pi\) | ||||
−0.894923 | + | 0.446220i | \(0.852770\pi\) | |||||||
\(594\) | 436.661 | − | 370.851i | 0.0301623 | − | 0.0256165i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4842.94 | + | 8388.22i | 0.332843 | + | 0.576501i | ||||
\(597\) | 10058.0 | − | 4362.28i | 0.689526 | − | 0.299055i | ||||
\(598\) | −322.734 | − | 186.330i | −0.0220695 | − | 0.0127418i | ||||
\(599\) | −4337.24 | + | 7512.32i | −0.295851 | + | 0.512429i | −0.975182 | − | 0.221403i | \(-0.928937\pi\) |
0.679332 | + | 0.733832i | \(0.262270\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5467.86 | − | 9470.61i | −0.371112 | − | 0.642786i | 0.618625 | − | 0.785687i | \(-0.287690\pi\) |
−0.989737 | + | 0.142901i | \(0.954357\pi\) | |||||||
\(602\) | 977.916i | 0.0662074i | ||||||||
\(603\) | −15214.3 | + | 4620.67i | −1.02748 | + | 0.312053i | ||||
\(604\) | 12794.4 | 0.861913 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1255.80 | − | 144.259i | −0.0841806 | − | 0.00967016i | ||||
\(607\) | −18767.1 | − | 10835.2i | −1.25492 | − | 0.724527i | −0.282836 | − | 0.959168i | \(-0.591275\pi\) |
−0.972082 | + | 0.234641i | \(0.924608\pi\) | |||||||
\(608\) | −863.183 | − | 498.359i | −0.0575768 | − | 0.0332420i | ||||
\(609\) | −20260.4 | − | 2327.39i | −1.34810 | − | 0.154861i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23721.9 | 1.57068 | ||||||||
\(612\) | 27032.7 | − | 8210.01i | 1.78551 | − | 0.542271i | ||||
\(613\) | 15571.2i | 1.02596i | 0.858399 | + | 0.512982i | \(0.171459\pi\) | ||||
−0.858399 | + | 0.512982i | \(0.828541\pi\) | |||||||
\(614\) | −955.079 | − | 1654.25i | −0.0627750 | − | 0.108730i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1015.80 | − | 1759.42i | 0.0664411 | − | 0.115079i | ||||
\(617\) | −8423.43 | − | 4863.27i | −0.549618 | − | 0.317322i | 0.199350 | − | 0.979928i | \(-0.436117\pi\) |
−0.748968 | + | 0.662606i | \(0.769450\pi\) | |||||||
\(618\) | 638.901 | − | 277.099i | 0.0415864 | − | 0.0180365i | ||||
\(619\) | 3148.79 | + | 5453.87i | 0.204460 | + | 0.354135i | 0.949961 | − | 0.312370i | \(-0.101123\pi\) |
−0.745501 | + | 0.666505i | \(0.767790\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3527.31 | + | 2995.70i | −0.227933 | + | 0.193580i | ||||
\(622\) | 1534.13i | 0.0988955i | ||||||||
\(623\) | 23038.7 | − | 13301.4i | 1.48158 | − | 0.855392i | ||||
\(624\) | 6510.81 | + | 15011.8i | 0.417694 | + | 0.963069i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 906.272 | − | 1569.71i | 0.0578625 | − | 0.100221i | ||||
\(627\) | 1758.78 | + | 1303.95i | 0.112024 | + | 0.0830541i | ||||
\(628\) | 8855.47 | − | 5112.71i | 0.562694 | − | 0.324872i | ||||
\(629\) | 13161.7 | 0.834327 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5670.98 | −0.357778 | −0.178889 | − | 0.983869i | \(-0.557250\pi\) | ||||
−0.178889 | + | 0.983869i | \(0.557250\pi\) | |||||||
\(632\) | 1650.60 | − | 952.977i | 0.103888 | − | 0.0599800i | ||||
\(633\) | −390.576 | + | 3400.04i | −0.0245245 | + | 0.213491i | ||||
\(634\) | −176.396 | + | 305.527i | −0.0110498 | + | 0.0191388i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 17297.7 | + | 1987.06i | 1.07846 | + | 0.123887i | ||||
\(637\) | −27367.9 | + | 15800.9i | −1.70229 | + | 0.982816i | ||||
\(638\) | 513.767i | 0.0318813i | ||||||||
\(639\) | −895.820 | + | 957.089i | −0.0554587 | + | 0.0592517i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10832.3 | − | 18762.0i | −0.667470 | − | 1.15609i | −0.978609 | − | 0.205727i | \(-0.934044\pi\) |
0.311140 | − | 0.950364i | \(-0.399289\pi\) | |||||||
\(642\) | 468.878 | + | 347.624i | 0.0288242 | + | 0.0213701i | ||||
\(643\) | 5389.90 | + | 3111.86i | 0.330570 | + | 0.190855i | 0.656094 | − | 0.754679i | \(-0.272207\pi\) |
−0.325524 | + | 0.945534i | \(0.605541\pi\) | |||||||
\(644\) | −4089.71 | + | 7083.59i | −0.250244 | + | 0.433436i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −344.573 | − | 596.818i | −0.0209861 | − | 0.0363491i | ||||
\(647\) | 20451.9i | 1.24273i | 0.783521 | + | 0.621365i | \(0.213422\pi\) | ||||
−0.783521 | + | 0.621365i | \(0.786578\pi\) | |||||||
\(648\) | −2613.26 | + | 173.010i | −0.158424 | + | 0.0104884i | ||||
\(649\) | 13458.8 | 0.814029 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8069.15 | − | 18604.9i | −0.485799 | − | 1.12010i | ||||
\(652\) | 9753.88 | + | 5631.41i | 0.585876 | + | 0.338256i | ||||
\(653\) | 6450.54 | + | 3724.22i | 0.386568 | + | 0.223185i | 0.680672 | − | 0.732588i | \(-0.261688\pi\) |
−0.294104 | + | 0.955773i | \(0.595021\pi\) | |||||||
\(654\) | −668.701 | + | 901.949i | −0.0399821 | + | 0.0539281i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 15402.7 | 0.916731 | ||||||||
\(657\) | −8078.15 | − | 7561.03i | −0.479694 | − | 0.448986i | ||||
\(658\) | 3323.23i | 0.196889i | ||||||||
\(659\) | 413.185 | + | 715.658i | 0.0244240 | + | 0.0423036i | 0.877979 | − | 0.478699i | \(-0.158891\pi\) |
−0.853555 | + | 0.521003i | \(0.825558\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3129.11 | − | 5419.77i | 0.184127 | − | 0.318918i | −0.759155 | − | 0.650910i | \(-0.774387\pi\) |
0.943282 | + | 0.331992i | \(0.107721\pi\) | |||||||
\(662\) | 476.475 | + | 275.093i | 0.0279739 | + | 0.0161507i | ||||
\(663\) | −3915.07 | + | 34081.4i | −0.229334 | + | 1.99640i | ||||
\(664\) | −529.167 | − | 916.545i | −0.0309272 | − | 0.0535675i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −592.270 | − | 137.892i | −0.0344594 | − | 0.00802286i | ||||
\(667\) | − | 4150.17i | − | 0.240922i | ||||||
\(668\) | 6161.24 | − | 3557.19i | 0.356865 | − | 0.206036i | ||||
\(669\) | −3771.75 | + | 5087.36i | −0.217973 | + | 0.294004i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −81.3729 | + | 140.942i | −0.00468162 | + | 0.00810880i | ||||
\(672\) | −6376.89 | + | 2765.73i | −0.366062 | + | 0.158765i | ||||
\(673\) | 8729.36 | − | 5039.90i | 0.499988 | − | 0.288668i | −0.228720 | − | 0.973492i | \(-0.573454\pi\) |
0.728709 | + | 0.684824i | \(0.240121\pi\) | |||||||
\(674\) | 2133.79 | 0.121944 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2532.99 | −0.144117 | ||||||||
\(677\) | −22265.9 | + | 12855.2i | −1.26403 | + | 0.729788i | −0.973852 | − | 0.227185i | \(-0.927048\pi\) |
−0.290178 | + | 0.956973i | \(0.593715\pi\) | |||||||
\(678\) | −1856.36 | + | 805.124i | −0.105152 | + | 0.0456056i | ||||
\(679\) | 6053.05 | − | 10484.2i | 0.342113 | − | 0.592557i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4721.11 | + | 6367.88i | −0.265659 | + | 0.358322i | ||||
\(682\) | −442.443 | + | 255.445i | −0.0248417 | + | 0.0143424i | ||||
\(683\) | 32091.0i | 1.79784i | 0.438109 | + | 0.898922i | \(0.355648\pi\) | ||||
−0.438109 | + | 0.898922i | \(0.644352\pi\) | |||||||
\(684\) | −1449.69 | − | 4773.32i | −0.0810383 | − | 0.266831i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1008.53 | − | 1746.82i | −0.0561310 | − | 0.0972217i | ||||
\(687\) | −3666.33 | + | 31916.1i | −0.203609 | + | 1.77245i | ||||
\(688\) | 7567.48 | + | 4369.09i | 0.419342 | + | 0.242107i | ||||
\(689\) | −10571.2 | + | 18309.8i | −0.584512 | + | 1.01240i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5282.87 | − | 9150.20i | −0.290839 | − | 0.503748i | 0.683169 | − | 0.730260i | \(-0.260601\pi\) |
−0.974008 | + | 0.226512i | \(0.927268\pi\) | |||||||
\(692\) | 13792.7i | 0.757690i | ||||||||
\(693\) | 14609.6 | − | 4437.02i | 0.800826 | − | 0.243216i | ||||
\(694\) | −746.133 | −0.0408110 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1398.81 | − | 1886.72i | 0.0761806 | − | 0.102753i | ||||
\(697\) | 27966.1 | + | 16146.2i | 1.51979 | + | 0.877449i | ||||
\(698\) | −1105.85 | − | 638.465i | −0.0599673 | − | 0.0346222i | ||||
\(699\) | 4163.67 | + | 9600.09i | 0.225300 | + | 0.519469i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13081.8 | 0.704837 | 0.352419 | − | 0.935842i | \(-0.385359\pi\) | ||||
0.352419 | + | 0.935842i | \(0.385359\pi\) | |||||||
\(702\) | 533.240 | − | 1492.63i | 0.0286693 | − | 0.0802503i | ||||
\(703\) | − | 2324.04i | − | 0.124684i | ||||||
\(704\) | −4465.22 | − | 7733.99i | −0.239047 | − | 0.414042i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −195.864 | + | 339.246i | −0.0104411 | + | 0.0180846i | ||||
\(707\) | −29175.8 | − | 16844.7i | −1.55201 | − | 0.896053i | ||||
\(708\) | −24634.0 | − | 18263.5i | −1.30763 | − | 0.969472i | ||||
\(709\) | −14110.6 | − | 24440.3i | −0.747440 | − | 1.29460i | −0.949046 | − | 0.315137i | \(-0.897949\pi\) |
0.201606 | − | 0.979467i | \(-0.435384\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13951.1 | + | 3248.10i | 0.735875 | + | 0.171327i | ||||
\(712\) | 3063.80i | 0.161265i | ||||||||
\(713\) | 3574.02 | − | 2063.46i | 0.187725 | − | 0.108383i | ||||
\(714\) | −4774.51 | − | 548.467i | −0.250254 | − | 0.0287477i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8479.38 | − | 14686.7i | 0.442583 | − | 0.766576i | ||||
\(717\) | 3016.19 | − | 26256.5i | 0.157102 | − | 1.36760i | ||||
\(718\) | 1682.41 | − | 971.342i | 0.0874473 | − | 0.0504877i | ||||
\(719\) | 11471.4 | 0.595010 | 0.297505 | − | 0.954720i | \(-0.403846\pi\) | ||||
0.297505 | + | 0.954720i | \(0.403846\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18560.3 | 0.958701 | ||||||||
\(722\) | 1232.62 | − | 711.651i | 0.0635363 | − | 0.0366827i | ||||
\(723\) | −13719.5 | − | 10171.6i | −0.705719 | − | 0.523217i | ||||
\(724\) | 14356.3 | − | 24865.8i | 0.736944 | − | 1.27642i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 466.813 | + | 1076.32i | 0.0238637 | + | 0.0550221i | ||||
\(727\) | 18757.5 | − | 10829.6i | 0.956914 | − | 0.552475i | 0.0616922 | − | 0.998095i | \(-0.480350\pi\) |
0.895222 | + | 0.445621i | \(0.147017\pi\) | |||||||
\(728\) | − | 5620.84i | − | 0.286157i | ||||||
\(729\) | −15227.5 | − | 12471.7i | −0.773636 | − | 0.633630i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9159.96 | + | 15865.5i | 0.463466 | + | 0.802746i | ||||
\(732\) | 340.197 | − | 147.547i | 0.0171776 | − | 0.00745013i | ||||
\(733\) | 4920.51 | + | 2840.86i | 0.247944 | + | 0.143151i | 0.618823 | − | 0.785531i | \(-0.287610\pi\) |
−0.370878 | + | 0.928682i | \(0.620943\pi\) | |||||||
\(734\) | 688.045 | − | 1191.73i | 0.0345997 | − | 0.0599285i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −707.259 | − | 1225.01i | −0.0354211 | − | 0.0613511i | ||||
\(737\) | 10676.0i | 0.533588i | ||||||||
\(738\) | −1089.30 | − | 1019.57i | −0.0543328 | − | 0.0508547i | ||||
\(739\) | −261.324 | −0.0130080 | −0.00650402 | − | 0.999979i | \(-0.502070\pi\) | ||||
−0.00650402 | + | 0.999979i | \(0.502070\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6017.95 | + | 691.306i | 0.298347 | + | 0.0342723i | ||||
\(742\) | −2565.04 | − | 1480.93i | −0.126908 | − | 0.0732702i | ||||
\(743\) | −14208.0 | − | 8202.97i | −0.701533 | − | 0.405031i | 0.106385 | − | 0.994325i | \(-0.466072\pi\) |
−0.807918 | + | 0.589294i | \(0.799406\pi\) | |||||||
\(744\) | 2320.29 | + | 266.541i | 0.114336 | + | 0.0131342i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1476.59 | −0.0724688 | ||||||||
\(747\) | 1803.60 | − | 7746.74i | 0.0883403 | − | 0.379436i | ||||
\(748\) | − | 18969.1i | − | 0.927244i | ||||||
\(749\) | 7778.11 | + | 13472.1i | 0.379447 | + | 0.657222i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10737.3 | + | 18597.5i | −0.521716 | + | 0.903639i | 0.477965 | + | 0.878379i | \(0.341375\pi\) |
−0.999681 | + | 0.0252601i | \(0.991959\pi\) | |||||||
\(752\) | 25716.4 | + | 14847.4i | 1.24705 | + | 0.719985i | ||||
\(753\) | 16592.1 | − | 7196.20i | 0.802989 | − | 0.348266i | ||||
\(754\) | 710.722 | + | 1231.01i | 0.0343276 | + | 0.0594571i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −32761.3 | − | 11703.9i | −1.57608 | − | 0.563053i | ||||
\(757\) | − | 13643.2i | − | 0.655046i | −0.944843 | − | 0.327523i | \(-0.893786\pi\) | ||
0.944843 | − | 0.327523i | \(-0.106214\pi\) | |||||||
\(758\) | 981.680 | − | 566.773i | 0.0470399 | − | 0.0271585i | ||||
\(759\) | 1236.35 | + | 2850.63i | 0.0591260 | + | 0.136326i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13469.0 | + | 23328.9i | −0.641589 | + | 1.11127i | 0.343489 | + | 0.939157i | \(0.388391\pi\) |
−0.985078 | + | 0.172109i | \(0.944942\pi\) | |||||||
\(762\) | −958.975 | − | 710.980i | −0.0455905 | − | 0.0338006i | ||||
\(763\) | −25915.3 | + | 14962.2i | −1.22962 | + | 0.709920i | ||||
\(764\) | −4745.63 | −0.224726 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −825.088 | −0.0389186 | ||||||||
\(767\) | 32247.9 | − | 18618.3i | 1.51813 | − | 0.876491i | ||||
\(768\) | −2276.35 | + | 19816.1i | −0.106954 | + | 0.931057i | ||||
\(769\) | −14442.7 | + | 25015.5i | −0.677265 | + | 1.17306i | 0.298536 | + | 0.954398i | \(0.403502\pi\) |
−0.975801 | + | 0.218659i | \(0.929832\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35077.1 | + | 4029.44i | 1.63848 | + | 0.188219i | ||||
\(772\) | 8314.43 | − | 4800.34i | 0.387620 | − | 0.223793i | ||||
\(773\) | − | 3031.34i | − | 0.141048i | −0.997510 | − | 0.0705238i | \(-0.977533\pi\) | ||
0.997510 | − | 0.0705238i | \(-0.0224671\pi\) | |||||||
\(774\) | −245.974 | − | 809.907i | −0.0114229 | − | 0.0376118i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 697.121 | + | 1207.45i | 0.0322490 | + | 0.0558568i | ||||
\(777\) | −13019.3 | − | 9652.46i | −0.601113 | − | 0.445663i | ||||
\(778\) | 950.188 | + | 548.591i | 0.0437865 | + | 0.0252801i | ||||
\(779\) | 2851.03 | − | 4938.13i | 0.131128 | − | 0.227120i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 440.092 | + | 762.262i | 0.0201636 | + | 0.0349243i | ||||
\(782\) | − | 978.019i | − | 0.0447236i | ||||||
\(783\) | 17365.0 | − | 3168.52i | 0.792559 | − | 0.144615i | ||||
\(784\) | −39558.7 | −1.80205 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 792.829 | + | 1828.01i | 0.0359787 | + | 0.0829554i | ||||
\(787\) | −13124.4 | − | 7577.38i | −0.594453 | − | 0.343208i | 0.172403 | − | 0.985026i | \(-0.444847\pi\) |
−0.766856 | + | 0.641819i | \(0.778180\pi\) | |||||||
\(788\) | 22501.6 | + | 12991.3i | 1.01724 | + | 0.587306i | ||||
\(789\) | −16600.5 | + | 22390.8i | −0.749040 | + | 1.01031i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −53928.0 | −2.42409 | ||||||||
\(792\) | −398.739 | + | 1712.65i | −0.0178896 | + | 0.0768387i | ||||
\(793\) | 450.270i | 0.0201634i | ||||||||
\(794\) | 421.737 | + | 730.470i | 0.0188500 | + | 0.0326491i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8386.00 | + | 14525.0i | −0.373409 | + | 0.646764i | ||||
\(797\) | −24578.3 | − | 14190.3i | −1.09236 | − | 0.630673i | −0.158155 | − | 0.987414i | \(-0.550555\pi\) |
−0.934203 | + | 0.356741i | \(0.883888\pi\) | |||||||
\(798\) | −96.8459 | + | 843.062i | −0.00429613 | + | 0.0373986i | ||||
\(799\) | 31128.1 | + | 53915.5i | 1.37827 | + | 2.38723i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15734.9 | + | 16811.1i | −0.694089 | + | 0.741561i | ||||
\(802\) | 405.646i | 0.0178602i | ||||||||
\(803\) | −6433.75 | + | 3714.53i | −0.282742 | + | 0.163241i | ||||
\(804\) | 14487.2 | − | 19540.5i | 0.635479 | − | 0.857139i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −706.741 | + | 1224.11i | −0.0308857 | + | 0.0534957i | ||||
\(807\) | −231.197 | + | 100.273i | −0.0100849 | + | 0.00437394i | ||||
\(808\) | 3360.14 | − | 1939.98i | 0.146299 | − | 0.0844655i | ||||
\(809\) | 14569.6 | 0.633175 | 0.316588 | − | 0.948563i | \(-0.397463\pi\) | ||||
0.316588 | + | 0.948563i | \(0.397463\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27927.7 | 1.20921 | 0.604607 | − | 0.796524i | \(-0.293330\pi\) | ||||
0.604607 | + | 0.796524i | \(0.293330\pi\) | |||||||
\(812\) | 27019.0 | − | 15599.4i | 1.16771 | − | 0.674178i | ||||
\(813\) | 36435.7 | − | 15802.6i | 1.57178 | − | 0.681699i | ||||
\(814\) | −204.150 | + | 353.598i | −0.00879049 | + | 0.0152256i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −25575.6 | + | 34496.6i | −1.09721 | + | 1.47993i | ||||
\(817\) | 2801.46 | − | 1617.43i | 0.119964 | − | 0.0692614i | ||||
\(818\) | 3588.68i | 0.153393i | ||||||||
\(819\) | 28867.2 | − | 30841.5i | 1.23162 | − | 1.31586i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9022.03 | − | 15626.6i | −0.383521 | − | 0.664279i | 0.608041 | − | 0.793905i | \(-0.291955\pi\) |
−0.991563 | + | 0.129627i | \(0.958622\pi\) | |||||||
\(822\) | 140.210 | − | 1220.55i | 0.00594936 | − | 0.0517903i | ||||
\(823\) | −27931.8 | − | 16126.4i | −1.18304 | − | 0.683028i | −0.226323 | − | 0.974052i | \(-0.572670\pi\) |
−0.956716 | + | 0.291025i | \(0.906004\pi\) | |||||||
\(824\) | −1068.78 | + | 1851.19i | −0.0451855 | + | 0.0782636i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2608.26 | + | 4517.64i | 0.109871 | + | 0.190301i | ||||
\(827\) | 13569.5i | 0.570566i | 0.958443 | + | 0.285283i | \(0.0920876\pi\) | ||||
−0.958443 | + | 0.285283i | \(0.907912\pi\) | |||||||
\(828\) | 1605.36 | − | 6895.29i | 0.0673795 | − | 0.289406i | ||||
\(829\) | −742.559 | −0.0311099 | −0.0155550 | − | 0.999879i | \(-0.504951\pi\) | ||||
−0.0155550 | + | 0.999879i | \(0.504951\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15925.2 | − | 21480.0i | 0.664788 | − | 0.896671i | ||||
\(832\) | −21397.7 | − | 12354.0i | −0.891625 | − | 0.514780i | ||||
\(833\) | −71824.9 | − | 41468.1i | −2.98750 | − | 1.72483i | ||||
\(834\) | 668.217 | + | 1540.70i | 0.0277440 | + | 0.0639688i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3349.48 | −0.138569 | ||||||||
\(837\) | 11362.5 | + | 13378.9i | 0.469231 | + | 0.552500i | ||||
\(838\) | − | 776.605i | − | 0.0320136i | ||||||
\(839\) | −17752.3 | − | 30747.9i | −0.730487 | − | 1.26524i | −0.956675 | − | 0.291157i | \(-0.905960\pi\) |
0.226189 | − | 0.974083i | \(-0.427373\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4279.49 | − | 7412.29i | 0.175468 | − | 0.303919i | ||||
\(842\) | 1095.52 | + | 632.499i | 0.0448386 | + | 0.0258876i | ||||
\(843\) | −24438.2 | − | 18118.4i | −0.998455 | − | 0.740250i | ||||
\(844\) | −2617.86 | − | 4534.26i | −0.106766 | − | 0.184924i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −835.889 | − | 2752.29i | −0.0339698 | − | 0.111851i | ||||
\(847\) | 31267.6i | 1.26844i | ||||||||
\(848\) | −22919.9 | + | 13232.8i | −0.928153 | + | 0.535869i | ||||
\(849\) | 48492.9 | + | 5570.58i | 1.96027 | + | 0.225185i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1649.11 | − | 2856.34i | 0.0664285 | − | 0.115058i | ||||
\(852\) | 228.874 | − | 1992.39i | 0.00920316 | − | 0.0801153i | ||||
\(853\) | −324.801 | + | 187.524i | −0.0130375 | + | 0.00752719i | −0.506505 | − | 0.862237i | \(-0.669063\pi\) |
0.493467 | + | 0.869764i | \(0.335729\pi\) | |||||||
\(854\) | −63.0790 | −0.00252754 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1791.59 | −0.0715365 | ||||||||
\(857\) | 27881.5 | − | 16097.4i | 1.11133 | − | 0.641629i | 0.172159 | − | 0.985069i | \(-0.444926\pi\) |
0.939174 | + | 0.343440i | \(0.111592\pi\) | |||||||
\(858\) | −854.896 | − | 633.816i | −0.0340159 | − | 0.0252192i | ||||
\(859\) | −14068.8 | + | 24367.8i | −0.558813 | + | 0.967893i | 0.438783 | + | 0.898593i | \(0.355410\pi\) |
−0.997596 | + | 0.0692994i | \(0.977924\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15822.3 | − | 36481.1i | −0.626274 | − | 1.44399i | ||||
\(862\) | 689.392 | − | 398.021i | 0.0272399 | − | 0.0157270i | ||||
\(863\) | − | 15724.6i | − | 0.620244i | −0.950697 | − | 0.310122i | \(-0.899630\pi\) | ||
0.950697 | − | 0.310122i | \(-0.100370\pi\) | |||||||
\(864\) | 4585.67 | − | 3894.54i | 0.180564 | − | 0.153351i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 751.749 | + | 1302.07i | 0.0294982 | + | 0.0510924i | ||||
\(867\) | −59177.4 | + | 25665.9i | −2.31807 | + | 1.00538i | ||||
\(868\) | 26867.7 | + | 15512.1i | 1.05063 | + | 0.606583i | ||||
\(869\) | 4808.82 | − | 8329.12i | 0.187719 | − | 0.325139i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14768.6 | + | 25580.0i | 0.574531 | + | 0.995117i | ||||
\(872\) | − | 3446.35i | − | 0.133840i | ||||||
\(873\) | −2376.05 | + | 10205.5i | −0.0921157 | + | 0.395652i | ||||
\(874\) | −172.694 | −0.00668361 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16816.5 | + | 1931.77i | 0.648602 | + | 0.0745075i | ||||
\(877\) | −13233.3 | − | 7640.23i | −0.509528 | − | 0.294176i | 0.223112 | − | 0.974793i | \(-0.428378\pi\) |
−0.732639 | + | 0.680617i | \(0.761712\pi\) | |||||||
\(878\) | 1276.46 | + | 736.963i | 0.0490642 | + | 0.0283272i | ||||
\(879\) | −9191.72 | − | 1055.89i | −0.352707 | − | 0.0405168i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24687.6 | −0.944092 | −0.472046 | − | 0.881574i | \(-0.656484\pi\) | ||||
−0.472046 | + | 0.881574i | \(0.656484\pi\) | |||||||
\(882\) | 2797.63 | + | 2618.54i | 0.106804 | + | 0.0999669i | ||||
\(883\) | − | 6562.59i | − | 0.250112i | −0.992150 | − | 0.125056i | \(-0.960089\pi\) | ||
0.992150 | − | 0.125056i | \(-0.0399110\pi\) | |||||||
\(884\) | −26241.0 | − | 45450.7i | −0.998392 | − | 1.72927i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1611.63 | − | 2791.43i | 0.0611104 | − | 0.105846i | ||||
\(887\) | −43743.9 | − | 25255.5i | −1.65589 | − | 0.956030i | −0.974581 | − | 0.224035i | \(-0.928077\pi\) |
−0.681311 | − | 0.731994i | \(-0.738590\pi\) | |||||||
\(888\) | 1712.43 | − | 742.702i | 0.0647134 | − | 0.0280669i | ||||
\(889\) | −15908.2 | − | 27553.8i | −0.600162 | − | 1.03951i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10983.6 | + | 7349.46i | −0.412979 | + | 0.276337i | ||||
\(892\) | − | 9688.51i | − | 0.363672i | ||||||
\(893\) | 9520.17 | − | 5496.47i | 0.356753 | − | 0.205971i | ||||
\(894\) | 567.456 | + | 1308.37i | 0.0212288 | + | 0.0489468i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 7081.43 | − | 12265.4i | 0.264034 | − | 0.457320i | ||||
\(897\) | 6905.77 | + | 5119.91i | 0.257053 | + | 0.190578i | ||||
\(898\) | −2845.60 | + | 1642.91i | −0.105745 | + | 0.0610518i | ||||
\(899\) | −15741.4 | −0.583986 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −55486.3 | −2.05163 | ||||||||
\(902\) | −867.559 | + | 500.886i | −0.0320250 | + | 0.0184897i | ||||
\(903\) | 2574.51 | − | 22411.6i | 0.0948773 | − | 0.825925i | ||||
\(904\) | 3105.40 | − | 5378.72i | 0.114252 | − | 0.197891i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1871.51 | + | 214.987i | 0.0686276 | + | 0.00788353i | ||||
\(907\) | −6077.28 | + | 3508.72i | −0.222484 | + | 0.128451i | −0.607100 | − | 0.794626i | \(-0.707667\pi\) |
0.384616 | + | 0.923077i | \(0.374334\pi\) | |||||||
\(908\) | − | 12127.2i | − | 0.443231i | ||||||
\(909\) | 28400.3 | + | 6612.16i | 1.03628 | + | 0.241267i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3062.30 | + | 5304.05i | 0.111370 | + | 0.192899i | 0.916323 | − | 0.400440i | \(-0.131143\pi\) |
−0.804953 | + | 0.593339i | \(0.797809\pi\) | |||||||
\(912\) | 6091.25 | + | 4516.02i | 0.221164 | + | 0.163970i | ||||
\(913\) | −4624.98 | − | 2670.23i | −0.167650 | − | 0.0967928i | ||||
\(914\) | −228.153 | + | 395.172i | −0.00825669 | + | 0.0143010i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24573.8 | − | 42563.0i | −0.886397 | − | 1.53528i | ||||
\(917\) | 53104.4i | 1.91239i | ||||||||
\(918\) | 4092.19 | − | 746.688i | 0.147127 | − | 0.0268457i | ||||
\(919\) | −23780.7 | −0.853594 | −0.426797 | − | 0.904347i | \(-0.640358\pi\) | ||||
−0.426797 | + | 0.904347i | \(0.640358\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17533.2 | + | 40425.9i | 0.627293 | + | 1.44634i | ||||
\(922\) | −693.713 | − | 400.515i | −0.0247790 | − | 0.0143062i | ||||
\(923\) | 2108.96 | + | 1217.61i | 0.0752082 | + | 0.0434215i | ||||
\(924\) | −13911.4 | + | 18763.9i | −0.495295 | + | 0.668058i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2316.17 | 0.0821967 | ||||||||
\(927\) | −15371.6 | + | 4668.46i | −0.544628 | + | 0.165407i | ||||
\(928\) | 5395.41i | 0.190854i | ||||||||
\(929\) | 5094.54 | + | 8824.01i | 0.179921 | + | 0.311632i | 0.941853 | − | 0.336024i | \(-0.109082\pi\) |
−0.761932 | + | 0.647657i | \(0.775749\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7322.26 | + | 12682.5i | −0.257763 | + | 0.446459i | ||||
\(932\) | −13863.7 | − | 8004.19i | −0.487253 | − | 0.281316i | ||||
\(933\) | 4038.82 | − | 35158.7i | 0.141720 | − | 1.23370i | ||||
\(934\) | −925.488 | − | 1602.99i | −0.0324228 | − | 0.0561579i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1413.80 | + | 4655.16i | 0.0493713 | + | 0.162563i | ||||
\(937\) | − | 3880.22i | − | 0.135284i | −0.997710 | − | 0.0676421i | \(-0.978452\pi\) | ||
0.997710 | − | 0.0676421i | \(-0.0215476\pi\) | |||||||
\(938\) | −3583.54 | + | 2068.96i | −0.124741 | + | 0.0720191i | ||||
\(939\) | −24902.1 | + | 33588.2i | −0.865442 | + | 1.16732i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19336.9 | − | 33492.6i | 0.669890 | − | 1.16028i | −0.308045 | − | 0.951372i | \(-0.599675\pi\) |
0.977935 | − | 0.208911i | \(-0.0669919\pi\) | |||||||
\(942\) | 1381.25 | − | 599.065i | 0.0477746 | − | 0.0207204i | ||||
\(943\) | 7008.07 | − | 4046.11i | 0.242008 | − | 0.139724i | ||||
\(944\) | 46612.3 | 1.60710 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −568.318 | −0.0195324 | ||||||||
\(947\) | −6715.92 | + | 3877.44i | −0.230452 | + | 0.133052i | −0.610781 | − | 0.791800i | \(-0.709144\pi\) |
0.380328 | + | 0.924851i | \(0.375811\pi\) | |||||||
\(948\) | −20104.3 | + | 8719.45i | −0.688773 | + | 0.298729i | ||||
\(949\) | −10277.0 | + | 17800.3i | −0.351534 | + | 0.608875i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4846.93 | − | 6537.58i | 0.165271 | − | 0.222918i | ||||
\(952\) | 12775.1 | − | 7375.72i | 0.434920 | − | 0.251101i | ||||
\(953\) | 22527.9i | 0.765739i | 0.923802 | + | 0.382870i | \(0.125064\pi\) | ||||
−0.923802 | + | 0.382870i | \(0.874936\pi\) | |||||||
\(954\) | 2496.85 | + | 581.318i | 0.0847365 | + | 0.0197284i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20216.2 | + | 35015.5i | 0.683931 | + | 1.18460i | ||||
\(957\) | 1352.57 | − | 11774.4i | 0.0456868 | − | 0.397713i | ||||
\(958\) | −2669.60 | − | 1541.29i | −0.0900321 | − | 0.0519800i | ||||
\(959\) | 16371.9 | − | 28356.9i | 0.551277 | − | 0.954840i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7068.91 | + | 12243.7i | 0.237283 | + | 0.410987i | ||||
\(962\) | 1129.65i | 0.0378600i | ||||||||
\(963\) | −9830.43 | − | 9201.13i | −0.328952 | − | 0.307894i | ||||
\(964\) | 26127.8 | 0.872947 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −717.254 | + | 967.438i | −0.0238895 | + | 0.0322224i | ||||
\(967\) | 4895.13 | + | 2826.20i | 0.162789 | + | 0.0939861i | 0.579181 | − | 0.815199i | \(-0.303372\pi\) |
−0.416392 | + | 0.909185i | \(0.636706\pi\) | |||||||
\(968\) | −3118.59 | − | 1800.52i | −0.103549 | − | 0.0597840i | ||||
\(969\) | 6325.60 | + | 14584.8i | 0.209709 | + | 0.483521i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19612.4 | 0.648188 | 0.324094 | − | 0.946025i | \(-0.394941\pi\) | ||||
0.324094 | + | 0.946025i | \(0.394941\pi\) | |||||||
\(972\) | 30076.7 | + | 1452.77i | 0.992501 | + | 0.0479398i | ||||
\(973\) | 44757.9i | 1.47469i | ||||||||
\(974\) | 364.858 | + | 631.953i | 0.0120029 | + | 0.0207896i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −281.821 | + | 488.129i | −0.00924270 | + | 0.0160088i | ||||
\(977\) | 23974.7 | + | 13841.8i | 0.785076 | + | 0.453264i | 0.838226 | − | 0.545323i | \(-0.183593\pi\) |
−0.0531500 | + | 0.998587i | \(0.516926\pi\) | |||||||
\(978\) | 1332.13 | + | 987.636i | 0.0435551 | + | 0.0322915i | ||||
\(979\) | 7730.14 | + | 13389.0i | 0.252356 | + | 0.437093i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17699.6 | − | 18910.1i | 0.576049 | − | 0.615447i | ||||
\(982\) | − | 2506.60i | − | 0.0814549i | ||||||
\(983\) | 26514.6 | − | 15308.2i | 0.860310 | − | 0.496700i | −0.00380619 | − | 0.999993i | \(-0.501212\pi\) |
0.864116 | + | 0.503293i | \(0.167878\pi\) | |||||||
\(984\) | 4549.70 | + | 522.643i | 0.147398 | + | 0.0169321i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1865.23 | + | 3230.68i | −0.0602446 | + | 0.104347i | ||||
\(987\) | 8748.90 | − | 76160.8i | 0.282148 | − | 2.45616i | ||||
\(988\) | −8025.48 | + | 4633.51i | −0.258426 | + | 0.149202i | ||||
\(989\) | 4590.82 | 0.147603 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14462.4 | −0.463587 | −0.231793 | − | 0.972765i | \(-0.574459\pi\) | ||||
−0.231793 | + | 0.972765i | \(0.574459\pi\) | |||||||
\(992\) | −4646.39 | + | 2682.59i | −0.148713 | + | 0.0858593i | ||||
\(993\) | −10195.5 | − | 7558.88i | −0.325824 | − | 0.241565i | ||||
\(994\) | −170.576 | + | 295.447i | −0.00544301 | + | 0.00942756i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4841.72 | + | 11163.5i | 0.154032 | + | 0.355149i | ||||
\(997\) | −5973.20 | + | 3448.63i | −0.189743 | + | 0.109548i | −0.591862 | − | 0.806039i | \(-0.701607\pi\) |
0.402120 | + | 0.915587i | \(0.368274\pi\) | |||||||
\(998\) | − | 1222.48i | − | 0.0387745i | ||||||
\(999\) | 13210.4 | + | 4719.41i | 0.418378 | + | 0.149465i |
(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 | 225.4.k.d.49.7 | 28 | ||
5.2 | odd | 4 | 225.4.e.d.76.4 | 14 | |||
5.3 | odd | 4 | 45.4.e.c.31.4 | yes | 14 | ||
5.4 | even | 2 | inner | 225.4.k.d.49.8 | 28 | ||
9.7 | even | 3 | inner | 225.4.k.d.124.8 | 28 | ||
15.8 | even | 4 | 135.4.e.c.91.4 | 14 | |||
45.7 | odd | 12 | 225.4.e.d.151.4 | 14 | |||
45.13 | odd | 12 | 405.4.a.m.1.4 | 7 | |||
45.22 | odd | 12 | 2025.4.a.bb.1.4 | 7 | |||
45.23 | even | 12 | 405.4.a.n.1.4 | 7 | |||
45.32 | even | 12 | 2025.4.a.ba.1.4 | 7 | |||
45.34 | even | 6 | inner | 225.4.k.d.124.7 | 28 | ||
45.38 | even | 12 | 135.4.e.c.46.4 | 14 | |||
45.43 | odd | 12 | 45.4.e.c.16.4 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.c.16.4 | ✓ | 14 | 45.43 | odd | 12 | ||
45.4.e.c.31.4 | yes | 14 | 5.3 | odd | 4 | ||
135.4.e.c.46.4 | 14 | 45.38 | even | 12 | |||
135.4.e.c.91.4 | 14 | 15.8 | even | 4 | |||
225.4.e.d.76.4 | 14 | 5.2 | odd | 4 | |||
225.4.e.d.151.4 | 14 | 45.7 | odd | 12 | |||
225.4.k.d.49.7 | 28 | 1.1 | even | 1 | trivial | ||
225.4.k.d.49.8 | 28 | 5.4 | even | 2 | inner | ||
225.4.k.d.124.7 | 28 | 45.34 | even | 6 | inner | ||
225.4.k.d.124.8 | 28 | 9.7 | even | 3 | inner | ||
405.4.a.m.1.4 | 7 | 45.13 | odd | 12 | |||
405.4.a.n.1.4 | 7 | 45.23 | even | 12 | |||
2025.4.a.ba.1.4 | 7 | 45.32 | even | 12 | |||
2025.4.a.bb.1.4 | 7 | 45.22 | odd | 12 |