Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [13,5,Mod(2,13)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(13, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("13.2");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 13 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 13.f (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.34380952009\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 152 x^{14} + 9190 x^{12} + 285720 x^{10} + 4862025 x^{8} + 43573680 x^{6} + 169417008 x^{4} + \cdots + 3779136 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2}\cdot 13^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 7.2 | ||
Root | \(-5.33868i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 13.7 |
Dual form | 13.5.f.a.2.2 |
$q$-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 \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{11}{12}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.41998 | + | 0.916381i | −0.854996 | + | 0.229095i | −0.659589 | − | 0.751627i | \(-0.729269\pi\) |
−0.195407 | + | 0.980722i | \(0.562603\pi\) | |||||||
\(3\) | −5.16500 | + | 8.94604i | −0.573889 | + | 0.994005i | 0.422272 | + | 0.906469i | \(0.361233\pi\) |
−0.996161 | + | 0.0875358i | \(0.972101\pi\) | |||||||
\(4\) | −2.99988 | + | 1.73198i | −0.187493 | + | 0.108249i | ||||
\(5\) | 8.65321 | + | 8.65321i | 0.346129 | + | 0.346129i | 0.858665 | − | 0.512537i | \(-0.171294\pi\) |
−0.512537 | + | 0.858665i | \(0.671294\pi\) | |||||||
\(6\) | 9.46622 | − | 35.3284i | 0.262951 | − | 0.981345i | ||||
\(7\) | −2.94871 | − | 0.790103i | −0.0601777 | − | 0.0161246i | 0.228605 | − | 0.973519i | \(-0.426584\pi\) |
−0.288782 | + | 0.957395i | \(0.593250\pi\) | |||||||
\(8\) | 48.7300 | − | 48.7300i | 0.761406 | − | 0.761406i | ||||
\(9\) | −12.8545 | − | 22.2646i | −0.158697 | − | 0.274871i | ||||
\(10\) | −37.5235 | − | 21.6642i | −0.375235 | − | 0.216642i | ||||
\(11\) | 53.6740 | + | 200.314i | 0.443587 | + | 1.65549i | 0.719640 | + | 0.694347i | \(0.244307\pi\) |
−0.276053 | + | 0.961142i | \(0.589027\pi\) | |||||||
\(12\) | − | 35.7828i | − | 0.248491i | ||||||
\(13\) | −168.828 | + | 7.63056i | −0.998980 | + | 0.0451512i | ||||
\(14\) | 10.8086 | 0.0551457 | ||||||||
\(15\) | −122.106 | + | 32.7182i | −0.542693 | + | 0.145414i | ||||
\(16\) | −94.2887 | + | 163.313i | −0.368315 | + | 0.637941i | ||||
\(17\) | 419.914 | − | 242.437i | 1.45299 | − | 0.838884i | 0.454340 | − | 0.890828i | \(-0.349875\pi\) |
0.998650 | + | 0.0519444i | \(0.0165419\pi\) | |||||||
\(18\) | 64.3648 | + | 64.3648i | 0.198657 | + | 0.198657i | ||||
\(19\) | −4.81436 | + | 17.9674i | −0.0133362 | + | 0.0497713i | −0.972273 | − | 0.233847i | \(-0.924868\pi\) |
0.958937 | + | 0.283619i | \(0.0915350\pi\) | |||||||
\(20\) | −40.9458 | − | 10.9714i | −0.102365 | − | 0.0274285i | ||||
\(21\) | 22.2984 | − | 22.2984i | 0.0505632 | − | 0.0505632i | ||||
\(22\) | −367.129 | − | 635.885i | −0.758530 | − | 1.31381i | ||||
\(23\) | 100.029 | + | 57.7520i | 0.189092 | + | 0.109172i | 0.591557 | − | 0.806263i | \(-0.298513\pi\) |
−0.402466 | + | 0.915435i | \(0.631847\pi\) | |||||||
\(24\) | 184.250 | + | 687.631i | 0.319879 | + | 1.19380i | ||||
\(25\) | − | 475.244i | − | 0.760390i | ||||||
\(26\) | 570.395 | − | 180.807i | 0.843780 | − | 0.267466i | ||||
\(27\) | −571.157 | −0.783480 | ||||||||
\(28\) | 10.2142 | − | 2.73689i | 0.0130283 | − | 0.00349093i | ||||
\(29\) | −59.3250 | + | 102.754i | −0.0705410 | + | 0.122181i | −0.899139 | − | 0.437664i | \(-0.855806\pi\) |
0.828598 | + | 0.559845i | \(0.189139\pi\) | |||||||
\(30\) | 387.618 | − | 223.791i | 0.430686 | − | 0.248657i | ||||
\(31\) | 1056.86 | + | 1056.86i | 1.09975 | + | 1.09975i | 0.994439 | + | 0.105310i | \(0.0335836\pi\) |
0.105310 | + | 0.994439i | \(0.466416\pi\) | |||||||
\(32\) | −112.574 | + | 420.131i | −0.109935 | + | 0.410284i | ||||
\(33\) | −2069.25 | − | 554.453i | −1.90013 | − | 0.509139i | ||||
\(34\) | −1213.93 | + | 1213.93i | −1.05012 | + | 1.05012i | ||||
\(35\) | −18.6788 | − | 32.3527i | −0.0152480 | − | 0.0264104i | ||||
\(36\) | 77.1237 | + | 44.5274i | 0.0595090 | + | 0.0343576i | ||||
\(37\) | 6.33806 | + | 23.6540i | 0.00462970 | + | 0.0172783i | 0.968202 | − | 0.250170i | \(-0.0804864\pi\) |
−0.963572 | + | 0.267448i | \(0.913820\pi\) | |||||||
\(38\) | − | 65.8601i | − | 0.0456095i | ||||||
\(39\) | 803.732 | − | 1549.75i | 0.528423 | − | 1.01890i | ||||
\(40\) | 843.342 | 0.527089 | ||||||||
\(41\) | 1705.47 | − | 456.980i | 1.01456 | − | 0.271850i | 0.287025 | − | 0.957923i | \(-0.407334\pi\) |
0.727533 | + | 0.686073i | \(0.240667\pi\) | |||||||
\(42\) | −55.8262 | + | 96.6938i | −0.0316475 | + | 0.0548151i | ||||
\(43\) | 1797.41 | − | 1037.74i | 0.972099 | − | 0.561242i | 0.0722236 | − | 0.997388i | \(-0.476990\pi\) |
0.899876 | + | 0.436147i | \(0.143657\pi\) | |||||||
\(44\) | −507.957 | − | 507.957i | −0.262374 | − | 0.262374i | ||||
\(45\) | 81.4277 | − | 303.892i | 0.0402112 | − | 0.150070i | ||||
\(46\) | −395.022 | − | 105.846i | −0.186683 | − | 0.0500216i | ||||
\(47\) | −507.246 | + | 507.246i | −0.229627 | + | 0.229627i | −0.812537 | − | 0.582910i | \(-0.801914\pi\) |
0.582910 | + | 0.812537i | \(0.301914\pi\) | |||||||
\(48\) | −974.003 | − | 1687.02i | −0.422744 | − | 0.732214i | ||||
\(49\) | −2071.26 | − | 1195.84i | −0.862664 | − | 0.498059i | ||||
\(50\) | 435.505 | + | 1625.33i | 0.174202 | + | 0.650130i | ||||
\(51\) | 5008.76i | 1.92571i | ||||||||
\(52\) | 493.247 | − | 315.297i | 0.182414 | − | 0.116604i | ||||
\(53\) | −2094.89 | −0.745779 | −0.372890 | − | 0.927876i | \(-0.621633\pi\) | ||||
−0.372890 | + | 0.927876i | \(0.621633\pi\) | |||||||
\(54\) | 1953.35 | − | 523.398i | 0.669872 | − | 0.179492i | ||||
\(55\) | −1268.91 | + | 2197.81i | −0.419474 | + | 0.726550i | ||||
\(56\) | −182.192 | + | 105.189i | −0.0580970 | + | 0.0335423i | ||||
\(57\) | −135.871 | − | 135.871i | −0.0418194 | − | 0.0418194i | ||||
\(58\) | 108.729 | − | 405.781i | 0.0323212 | − | 0.120624i | ||||
\(59\) | 1551.77 | + | 415.796i | 0.445783 | + | 0.119447i | 0.474726 | − | 0.880134i | \(-0.342547\pi\) |
−0.0289423 | + | 0.999581i | \(0.509214\pi\) | |||||||
\(60\) | 309.636 | − | 309.636i | 0.0860100 | − | 0.0860100i | ||||
\(61\) | 1643.56 | + | 2846.73i | 0.441699 | + | 0.765045i | 0.997816 | − | 0.0660589i | \(-0.0210425\pi\) |
−0.556117 | + | 0.831104i | \(0.687709\pi\) | |||||||
\(62\) | −4582.93 | − | 2645.95i | −1.19223 | − | 0.688334i | ||||
\(63\) | 20.3127 | + | 75.8080i | 0.00511783 | + | 0.0191000i | ||||
\(64\) | − | 4557.24i | − | 1.11261i | ||||||
\(65\) | −1526.93 | − | 1394.87i | −0.361404 | − | 0.330147i | ||||
\(66\) | 7584.88 | 1.74125 | ||||||||
\(67\) | −1181.79 | + | 316.660i | −0.263263 | + | 0.0705412i | −0.388036 | − | 0.921644i | \(-0.626846\pi\) |
0.124773 | + | 0.992185i | \(0.460180\pi\) | |||||||
\(68\) | −839.795 | + | 1454.57i | −0.181617 | + | 0.314569i | ||||
\(69\) | −1033.30 | + | 596.578i | −0.217035 | + | 0.125305i | ||||
\(70\) | 93.5287 | + | 93.5287i | 0.0190875 | + | 0.0190875i | ||||
\(71\) | 263.562 | − | 983.628i | 0.0522838 | − | 0.195126i | −0.934844 | − | 0.355058i | \(-0.884461\pi\) |
0.987128 | + | 0.159933i | \(0.0511277\pi\) | |||||||
\(72\) | −1711.35 | − | 458.555i | −0.330121 | − | 0.0884558i | ||||
\(73\) | 5166.15 | − | 5166.15i | 0.969442 | − | 0.969442i | −0.0301052 | − | 0.999547i | \(-0.509584\pi\) |
0.999547 | + | 0.0301052i | \(0.00958423\pi\) | |||||||
\(74\) | −43.3521 | − | 75.0881i | −0.00791675 | − | 0.0137122i | ||||
\(75\) | 4251.55 | + | 2454.63i | 0.755831 | + | 0.436379i | ||||
\(76\) | −16.6768 | − | 62.2386i | −0.00288725 | − | 0.0107754i | ||||
\(77\) | − | 633.076i | − | 0.106776i | ||||||
\(78\) | −1328.58 | + | 6036.65i | −0.218373 | + | 0.992217i | ||||
\(79\) | −8149.63 | −1.30582 | −0.652911 | − | 0.757435i | \(-0.726452\pi\) | ||||
−0.652911 | + | 0.757435i | \(0.726452\pi\) | |||||||
\(80\) | −2229.08 | + | 597.281i | −0.348294 | + | 0.0933251i | ||||
\(81\) | 3991.24 | − | 6913.02i | 0.608327 | − | 1.05365i | ||||
\(82\) | −5413.92 | + | 3125.73i | −0.805163 | + | 0.464861i | ||||
\(83\) | −1321.43 | − | 1321.43i | −0.191818 | − | 0.191818i | 0.604663 | − | 0.796481i | \(-0.293308\pi\) |
−0.796481 | + | 0.604663i | \(0.793308\pi\) | |||||||
\(84\) | −28.2721 | + | 105.513i | −0.00400681 | + | 0.0149536i | ||||
\(85\) | 5731.47 | + | 1535.74i | 0.793283 | + | 0.212560i | ||||
\(86\) | −5196.15 | + | 5196.15i | −0.702563 | + | 0.702563i | ||||
\(87\) | −612.827 | − | 1061.45i | −0.0809654 | − | 0.140236i | ||||
\(88\) | 12376.8 | + | 7145.78i | 1.59825 | + | 0.922750i | ||||
\(89\) | −1137.68 | − | 4245.89i | −0.143629 | − | 0.536030i | −0.999813 | − | 0.0193585i | \(-0.993838\pi\) |
0.856184 | − | 0.516671i | \(-0.172829\pi\) | |||||||
\(90\) | 1113.93i | 0.137522i | ||||||||
\(91\) | 503.852 | + | 110.891i | 0.0608443 | + | 0.0133910i | ||||
\(92\) | −400.102 | −0.0472710 | ||||||||
\(93\) | −14913.4 | + | 3996.03i | −1.72429 | + | 0.462022i | ||||
\(94\) | 1269.94 | − | 2199.60i | 0.143724 | − | 0.248936i | ||||
\(95\) | −197.136 | + | 113.816i | −0.0218433 | + | 0.0126112i | ||||
\(96\) | −3177.07 | − | 3177.07i | −0.344734 | − | 0.344734i | ||||
\(97\) | −1714.28 | + | 6397.78i | −0.182196 | + | 0.679964i | 0.813018 | + | 0.582239i | \(0.197823\pi\) |
−0.995213 | + | 0.0977249i | \(0.968843\pi\) | |||||||
\(98\) | 8179.51 | + | 2191.69i | 0.851677 | + | 0.228206i | ||||
\(99\) | 3769.96 | − | 3769.96i | 0.384650 | − | 0.384650i | ||||
\(100\) | 823.114 | + | 1425.68i | 0.0823114 | + | 0.142568i | ||||
\(101\) | 5427.32 | + | 3133.47i | 0.532038 | + | 0.307172i | 0.741846 | − | 0.670570i | \(-0.233951\pi\) |
−0.209808 | + | 0.977743i | \(0.567284\pi\) | |||||||
\(102\) | −4589.93 | − | 17129.9i | −0.441170 | − | 1.64647i | ||||
\(103\) | − | 13218.9i | − | 1.24601i | −0.782218 | − | 0.623005i | \(-0.785912\pi\) | ||
0.782218 | − | 0.623005i | \(-0.214088\pi\) | |||||||
\(104\) | −7855.13 | + | 8598.81i | −0.726251 | + | 0.795008i | ||||
\(105\) | 385.905 | 0.0350027 | ||||||||
\(106\) | 7164.50 | − | 1919.72i | 0.637638 | − | 0.170855i | ||||
\(107\) | 5199.02 | − | 9004.96i | 0.454102 | − | 0.786528i | −0.544534 | − | 0.838739i | \(-0.683293\pi\) |
0.998636 | + | 0.0522108i | \(0.0166268\pi\) | |||||||
\(108\) | 1713.40 | − | 989.234i | 0.146897 | − | 0.0848109i | ||||
\(109\) | 4906.68 | + | 4906.68i | 0.412985 | + | 0.412985i | 0.882777 | − | 0.469792i | \(-0.155671\pi\) |
−0.469792 | + | 0.882777i | \(0.655671\pi\) | |||||||
\(110\) | 2325.61 | − | 8679.29i | 0.192199 | − | 0.717297i | ||||
\(111\) | −244.346 | − | 65.4722i | −0.0198316 | − | 0.00531387i | ||||
\(112\) | 407.064 | − | 407.064i | 0.0324509 | − | 0.0324509i | ||||
\(113\) | 6966.43 | + | 12066.2i | 0.545574 | + | 0.944961i | 0.998571 | + | 0.0534491i | \(0.0170215\pi\) |
−0.452997 | + | 0.891512i | \(0.649645\pi\) | |||||||
\(114\) | 589.187 | + | 340.167i | 0.0453360 | + | 0.0261748i | ||||
\(115\) | 365.835 | + | 1365.32i | 0.0276624 | + | 0.103238i | ||||
\(116\) | − | 410.999i | − | 0.0305439i | ||||||
\(117\) | 2340.08 | + | 3660.79i | 0.170946 | + | 0.267425i | ||||
\(118\) | −5688.06 | −0.408508 | ||||||||
\(119\) | −1429.75 | + | 383.101i | −0.100964 | + | 0.0270533i | ||||
\(120\) | −4355.86 | + | 7544.57i | −0.302490 | + | 0.523929i | ||||
\(121\) | −24565.4 | + | 14182.8i | −1.67785 | + | 0.968708i | ||||
\(122\) | −8229.65 | − | 8229.65i | −0.552919 | − | 0.552919i | ||||
\(123\) | −4720.60 | + | 17617.5i | −0.312023 | + | 1.16449i | ||||
\(124\) | −5000.92 | − | 1339.99i | −0.325242 | − | 0.0871483i | ||||
\(125\) | 9520.64 | − | 9520.64i | 0.609321 | − | 0.609321i | ||||
\(126\) | −138.938 | − | 240.648i | −0.00875145 | − | 0.0151580i | ||||
\(127\) | −22842.8 | − | 13188.3i | −1.41625 | − | 0.817674i | −0.420286 | − | 0.907392i | \(-0.638070\pi\) |
−0.995967 | + | 0.0897173i | \(0.971404\pi\) | |||||||
\(128\) | 2374.99 | + | 8863.59i | 0.144958 | + | 0.540990i | ||||
\(129\) | 21439.6i | 1.28836i | ||||||||
\(130\) | 6500.31 | + | 3371.19i | 0.384634 | + | 0.199479i | ||||
\(131\) | 18082.0 | 1.05367 | 0.526833 | − | 0.849969i | \(-0.323379\pi\) | ||||
0.526833 | + | 0.849969i | \(0.323379\pi\) | |||||||
\(132\) | 7167.80 | − | 1920.61i | 0.411375 | − | 0.110228i | ||||
\(133\) | 28.3923 | − | 49.1768i | 0.00160508 | − | 0.00278008i | ||||
\(134\) | 3751.52 | − | 2165.94i | 0.208928 | − | 0.120625i | ||||
\(135\) | −4942.34 | − | 4942.34i | −0.271185 | − | 0.271185i | ||||
\(136\) | 8648.43 | − | 32276.4i | 0.467584 | − | 1.74505i | ||||
\(137\) | 24479.3 | + | 6559.21i | 1.30424 | + | 0.349470i | 0.843052 | − | 0.537832i | \(-0.180756\pi\) |
0.461189 | + | 0.887302i | \(0.347423\pi\) | |||||||
\(138\) | 2987.19 | − | 2987.19i | 0.156857 | − | 0.156857i | ||||
\(139\) | 369.245 | + | 639.551i | 0.0191111 | + | 0.0331013i | 0.875423 | − | 0.483358i | \(-0.160583\pi\) |
−0.856312 | + | 0.516459i | \(0.827250\pi\) | |||||||
\(140\) | 112.069 | + | 64.7029i | 0.00571779 | + | 0.00330117i | ||||
\(141\) | −1917.92 | − | 7157.77i | −0.0964699 | − | 0.360031i | ||||
\(142\) | 3605.52i | 0.178810i | ||||||||
\(143\) | −10590.2 | − | 33409.0i | −0.517882 | − | 1.63377i | ||||
\(144\) | 4848.12 | 0.233802 | ||||||||
\(145\) | −1402.50 | + | 375.799i | −0.0667064 | + | 0.0178739i | ||||
\(146\) | −12934.0 | + | 22402.3i | −0.606774 | + | 1.05096i | ||||
\(147\) | 21396.1 | − | 12353.0i | 0.990147 | − | 0.571661i | ||||
\(148\) | −59.9817 | − | 59.9817i | −0.00273839 | − | 0.00273839i | ||||
\(149\) | −207.438 | + | 774.170i | −0.00934365 | + | 0.0348710i | −0.970440 | − | 0.241341i | \(-0.922413\pi\) |
0.961097 | + | 0.276212i | \(0.0890793\pi\) | |||||||
\(150\) | −16789.6 | − | 4498.76i | −0.746205 | − | 0.199945i | ||||
\(151\) | −19015.3 | + | 19015.3i | −0.833967 | + | 0.833967i | −0.988057 | − | 0.154090i | \(-0.950756\pi\) |
0.154090 | + | 0.988057i | \(0.450756\pi\) | |||||||
\(152\) | 640.949 | + | 1110.16i | 0.0277419 | + | 0.0480504i | ||||
\(153\) | −10795.5 | − | 6232.80i | −0.461170 | − | 0.266257i | ||||
\(154\) | 580.139 | + | 2165.11i | 0.0244619 | + | 0.0912931i | ||||
\(155\) | 18290.5i | 0.761309i | ||||||||
\(156\) | 273.043 | + | 6041.12i | 0.0112197 | + | 0.248238i | ||||
\(157\) | 9205.74 | 0.373473 | 0.186737 | − | 0.982410i | \(-0.440209\pi\) | ||||
0.186737 | + | 0.982410i | \(0.440209\pi\) | |||||||
\(158\) | 27871.6 | − | 7468.17i | 1.11647 | − | 0.299158i | ||||
\(159\) | 10820.1 | − | 18741.0i | 0.427994 | − | 0.741308i | ||||
\(160\) | −4609.61 | + | 2661.36i | −0.180063 | + | 0.103959i | ||||
\(161\) | −249.327 | − | 249.327i | −0.00961874 | − | 0.00961874i | ||||
\(162\) | −7314.99 | + | 27299.9i | −0.278730 | + | 1.04023i | ||||
\(163\) | −19216.5 | − | 5149.05i | −0.723268 | − | 0.193799i | −0.121638 | − | 0.992574i | \(-0.538815\pi\) |
−0.601629 | + | 0.798775i | \(0.705482\pi\) | |||||||
\(164\) | −4324.73 | + | 4324.73i | −0.160795 | + | 0.160795i | ||||
\(165\) | −13107.8 | − | 22703.4i | −0.481463 | − | 0.833918i | ||||
\(166\) | 5730.21 | + | 3308.34i | 0.207948 | + | 0.120059i | ||||
\(167\) | 10641.6 | + | 39714.8i | 0.381568 | + | 1.42403i | 0.843506 | + | 0.537120i | \(0.180488\pi\) |
−0.461937 | + | 0.886913i | \(0.652846\pi\) | |||||||
\(168\) | − | 2173.20i | − | 0.0769982i | ||||||
\(169\) | 28444.5 | − | 2576.50i | 0.995923 | − | 0.0902104i | ||||
\(170\) | −21008.8 | −0.726950 | ||||||||
\(171\) | 461.923 | − | 123.772i | 0.0157971 | − | 0.00423282i | ||||
\(172\) | −3594.68 | + | 6226.17i | −0.121508 | + | 0.210457i | ||||
\(173\) | 9931.57 | − | 5733.99i | 0.331838 | − | 0.191587i | −0.324819 | − | 0.945776i | \(-0.605303\pi\) |
0.656657 | + | 0.754190i | \(0.271970\pi\) | |||||||
\(174\) | 3068.55 | + | 3068.55i | 0.101352 | + | 0.101352i | ||||
\(175\) | −375.492 | + | 1401.35i | −0.0122610 | + | 0.0457585i | ||||
\(176\) | −37774.8 | − | 10121.7i | −1.21948 | − | 0.326760i | ||||
\(177\) | −11734.6 | + | 11734.6i | −0.374561 | + | 0.374561i | ||||
\(178\) | 7781.71 | + | 13478.3i | 0.245604 | + | 0.425398i | ||||
\(179\) | −20163.5 | − | 11641.4i | −0.629303 | − | 0.363328i | 0.151179 | − | 0.988506i | \(-0.451693\pi\) |
−0.780482 | + | 0.625178i | \(0.785026\pi\) | |||||||
\(180\) | 282.063 | + | 1052.67i | 0.00870564 | + | 0.0324899i | ||||
\(181\) | − | 37461.2i | − | 1.14347i | −0.820438 | − | 0.571735i | \(-0.806270\pi\) | ||
0.820438 | − | 0.571735i | \(-0.193730\pi\) | |||||||
\(182\) | −1824.78 | + | 82.4753i | −0.0550895 | + | 0.00248990i | ||||
\(183\) | −33956.0 | −1.01395 | ||||||||
\(184\) | 7688.69 | − | 2060.18i | 0.227100 | − | 0.0608512i | ||||
\(185\) | −149.838 | + | 259.527i | −0.00437803 | + | 0.00758298i | ||||
\(186\) | 47341.6 | − | 27332.7i | 1.36841 | − | 0.790054i | ||||
\(187\) | 71102.2 | + | 71102.2i | 2.03329 | + | 2.03329i | ||||
\(188\) | 643.137 | − | 2400.22i | 0.0181965 | − | 0.0679102i | ||||
\(189\) | 1684.17 | + | 451.273i | 0.0471480 | + | 0.0126333i | ||||
\(190\) | 569.901 | − | 569.901i | 0.0157867 | − | 0.0157867i | ||||
\(191\) | −26753.1 | − | 46337.8i | −0.733344 | − | 1.27019i | −0.955446 | − | 0.295166i | \(-0.904625\pi\) |
0.222102 | − | 0.975023i | \(-0.428708\pi\) | |||||||
\(192\) | 40769.3 | + | 23538.2i | 1.10594 | + | 0.638513i | ||||
\(193\) | −9330.72 | − | 34822.7i | −0.250496 | − | 0.934864i | −0.970541 | − | 0.240936i | \(-0.922546\pi\) |
0.720045 | − | 0.693927i | \(-0.244121\pi\) | |||||||
\(194\) | − | 23451.2i | − | 0.623106i | ||||||
\(195\) | 20365.2 | − | 6455.47i | 0.535574 | − | 0.169769i | ||||
\(196\) | 8284.70 | 0.215658 | ||||||||
\(197\) | −43914.8 | + | 11766.9i | −1.13156 | + | 0.303201i | −0.775554 | − | 0.631282i | \(-0.782529\pi\) |
−0.356008 | + | 0.934483i | \(0.615863\pi\) | |||||||
\(198\) | −9438.47 | + | 16347.9i | −0.240753 | + | 0.416996i | ||||
\(199\) | 9076.93 | − | 5240.57i | 0.229210 | − | 0.132334i | −0.380998 | − | 0.924576i | \(-0.624419\pi\) |
0.610207 | + | 0.792242i | \(0.291086\pi\) | |||||||
\(200\) | −23158.6 | − | 23158.6i | −0.578966 | − | 0.578966i | ||||
\(201\) | 3271.09 | − | 12207.9i | 0.0809656 | − | 0.302168i | ||||
\(202\) | −21432.8 | − | 5742.90i | −0.525262 | − | 0.140744i | ||||
\(203\) | 256.118 | − | 256.118i | 0.00621510 | − | 0.00621510i | ||||
\(204\) | −8675.09 | − | 15025.7i | −0.208456 | − | 0.361056i | ||||
\(205\) | 18712.2 | + | 10803.5i | 0.445262 | + | 0.257072i | ||||
\(206\) | 12113.6 | + | 45208.5i | 0.285455 | + | 1.06533i | ||||
\(207\) | − | 2969.48i | − | 0.0693011i | ||||||
\(208\) | 14672.4 | − | 28291.2i | 0.339136 | − | 0.653920i | ||||
\(209\) | −3857.54 | −0.0883116 | ||||||||
\(210\) | −1319.79 | + | 353.636i | −0.0299272 | + | 0.00801896i | ||||
\(211\) | −10189.4 | + | 17648.5i | −0.228867 | + | 0.396409i | −0.957473 | − | 0.288524i | \(-0.906835\pi\) |
0.728606 | + | 0.684933i | \(0.240169\pi\) | |||||||
\(212\) | 6284.43 | − | 3628.32i | 0.139828 | − | 0.0807298i | ||||
\(213\) | 7438.28 | + | 7438.28i | 0.163951 | + | 0.163951i | ||||
\(214\) | −9528.56 | + | 35561.1i | −0.208065 | + | 0.776511i | ||||
\(215\) | 24533.1 | + | 6573.63i | 0.530733 | + | 0.142209i | ||||
\(216\) | −27832.5 | + | 27832.5i | −0.596547 | + | 0.596547i | ||||
\(217\) | −2281.34 | − | 3951.39i | −0.0484474 | − | 0.0839133i | ||||
\(218\) | −21277.1 | − | 12284.4i | −0.447714 | − | 0.258488i | ||||
\(219\) | 19533.4 | + | 72899.8i | 0.407278 | + | 1.51998i | ||||
\(220\) | − | 8790.92i | − | 0.181630i | ||||||
\(221\) | −69043.2 | + | 44134.3i | −1.41363 | + | 0.903633i | ||||
\(222\) | 895.655 | 0.0181733 | ||||||||
\(223\) | 6722.49 | − | 1801.28i | 0.135182 | − | 0.0362220i | −0.190593 | − | 0.981669i | \(-0.561041\pi\) |
0.325776 | + | 0.945447i | \(0.394375\pi\) | |||||||
\(224\) | 663.894 | − | 1149.90i | 0.0132313 | − | 0.0229173i | ||||
\(225\) | −10581.1 | + | 6109.00i | −0.209009 | + | 0.120672i | ||||
\(226\) | −34882.3 | − | 34882.3i | −0.682949 | − | 0.682949i | ||||
\(227\) | 10437.2 | − | 38952.3i | 0.202551 | − | 0.755930i | −0.787631 | − | 0.616147i | \(-0.788693\pi\) |
0.990182 | − | 0.139783i | \(-0.0446405\pi\) | |||||||
\(228\) | 642.925 | + | 172.271i | 0.0123677 | + | 0.00331393i | ||||
\(229\) | 32415.8 | − | 32415.8i | 0.618138 | − | 0.618138i | −0.326916 | − | 0.945053i | \(-0.606009\pi\) |
0.945053 | + | 0.326916i | \(0.106009\pi\) | |||||||
\(230\) | −2502.30 | − | 4334.11i | −0.0473025 | − | 0.0819303i | ||||
\(231\) | 5663.52 | + | 3269.84i | 0.106136 | + | 0.0612776i | ||||
\(232\) | 2116.29 | + | 7898.10i | 0.0393187 | + | 0.146739i | ||||
\(233\) | 81886.8i | 1.50835i | 0.656673 | + | 0.754175i | \(0.271963\pi\) | ||||
−0.656673 | + | 0.754175i | \(0.728037\pi\) | |||||||
\(234\) | −11357.7 | − | 10375.4i | −0.207424 | − | 0.189485i | ||||
\(235\) | −8778.61 | −0.158961 | ||||||||
\(236\) | −5375.29 | + | 1440.30i | −0.0965112 | + | 0.0258601i | ||||
\(237\) | 42092.8 | − | 72907.0i | 0.749396 | − | 1.29799i | ||||
\(238\) | 4538.66 | − | 2620.40i | 0.0801261 | − | 0.0462608i | ||||
\(239\) | −7149.22 | − | 7149.22i | −0.125159 | − | 0.125159i | 0.641753 | − | 0.766912i | \(-0.278208\pi\) |
−0.766912 | + | 0.641753i | \(0.778208\pi\) | |||||||
\(240\) | 6169.91 | − | 23026.4i | 0.107116 | − | 0.399764i | ||||
\(241\) | −24011.5 | − | 6433.86i | −0.413414 | − | 0.110774i | 0.0461164 | − | 0.998936i | \(-0.485315\pi\) |
−0.459530 | + | 0.888162i | \(0.651982\pi\) | |||||||
\(242\) | 71016.4 | − | 71016.4i | 1.21263 | − | 1.21263i | ||||
\(243\) | 18097.6 | + | 31346.0i | 0.306485 | + | 0.530847i | ||||
\(244\) | −9860.99 | − | 5693.25i | −0.165631 | − | 0.0956269i | ||||
\(245\) | −7575.16 | − | 28270.9i | −0.126200 | − | 0.470985i | ||||
\(246\) | − | 64577.5i | − | 1.06711i | ||||||
\(247\) | 675.695 | − | 3070.14i | 0.0110753 | − | 0.0503227i | ||||
\(248\) | 103002. | 1.67471 | ||||||||
\(249\) | 18646.8 | − | 4996.39i | 0.300750 | − | 0.0805857i | ||||
\(250\) | −23835.9 | + | 41285.0i | −0.381374 | + | 0.660560i | ||||
\(251\) | 9123.99 | − | 5267.74i | 0.144823 | − | 0.0836136i | −0.425838 | − | 0.904800i | \(-0.640021\pi\) |
0.570661 | + | 0.821186i | \(0.306687\pi\) | |||||||
\(252\) | −192.234 | − | 192.234i | −0.00302711 | − | 0.00302711i | ||||
\(253\) | −6199.57 | + | 23137.1i | −0.0968546 | + | 0.361466i | ||||
\(254\) | 90207.3 | + | 24171.0i | 1.39822 | + | 0.374651i | ||||
\(255\) | −43341.9 | + | 43341.9i | −0.666541 | + | 0.666541i | ||||
\(256\) | 20213.1 | + | 35010.1i | 0.308427 | + | 0.534211i | ||||
\(257\) | −80836.7 | − | 46671.1i | −1.22389 | − | 0.706613i | −0.258145 | − | 0.966106i | \(-0.583111\pi\) |
−0.965745 | + | 0.259493i | \(0.916445\pi\) | |||||||
\(258\) | −19646.9 | − | 73323.1i | −0.295158 | − | 1.10154i | ||||
\(259\) | − | 74.7563i | − | 0.00111442i | ||||||
\(260\) | 6996.51 | + | 1539.84i | 0.103499 | + | 0.0227787i | ||||
\(261\) | 3050.36 | 0.0447785 | ||||||||
\(262\) | −61840.0 | + | 16570.0i | −0.900880 | + | 0.241390i | ||||
\(263\) | −42725.6 | + | 74002.8i | −0.617698 | + | 1.06988i | 0.372207 | + | 0.928150i | \(0.378601\pi\) |
−0.989905 | + | 0.141735i | \(0.954732\pi\) | |||||||
\(264\) | −127853. | + | 73815.9i | −1.83444 | + | 1.05911i | ||||
\(265\) | −18127.6 | − | 18127.6i | −0.258135 | − | 0.258135i | ||||
\(266\) | −52.0363 | + | 194.202i | −0.000735433 | + | 0.00274467i | ||||
\(267\) | 43860.1 | + | 11752.3i | 0.615243 | + | 0.164854i | ||||
\(268\) | 2996.78 | − | 2996.78i | 0.0417239 | − | 0.0417239i | ||||
\(269\) | 31229.8 | + | 54091.5i | 0.431583 | + | 0.747523i | 0.997010 | − | 0.0772751i | \(-0.0246220\pi\) |
−0.565427 | + | 0.824798i | \(0.691289\pi\) | |||||||
\(270\) | 21431.8 | + | 12373.7i | 0.293989 | + | 0.169735i | ||||
\(271\) | −26380.8 | − | 98454.6i | −0.359211 | − | 1.34059i | −0.875101 | − | 0.483940i | \(-0.839205\pi\) |
0.515890 | − | 0.856655i | \(-0.327461\pi\) | |||||||
\(272\) | 91436.5i | 1.23590i | ||||||||
\(273\) | −3594.43 | + | 3934.73i | −0.0482286 | + | 0.0527946i | ||||
\(274\) | −89729.5 | −1.19518 | ||||||||
\(275\) | 95198.1 | − | 25508.3i | 1.25882 | − | 0.337299i | ||||
\(276\) | 2066.53 | − | 3579.33i | 0.0271283 | − | 0.0469876i | ||||
\(277\) | −47081.3 | + | 27182.4i | −0.613605 | + | 0.354265i | −0.774375 | − | 0.632727i | \(-0.781936\pi\) |
0.160770 | + | 0.986992i | \(0.448602\pi\) | |||||||
\(278\) | −1848.88 | − | 1848.88i | −0.0239232 | − | 0.0239232i | ||||
\(279\) | 9945.17 | − | 37115.9i | 0.127763 | − | 0.476816i | ||||
\(280\) | −2486.77 | − | 666.327i | −0.0317190 | − | 0.00849907i | ||||
\(281\) | 48013.6 | − | 48013.6i | 0.608067 | − | 0.608067i | −0.334374 | − | 0.942441i | \(-0.608525\pi\) |
0.942441 | + | 0.334374i | \(0.108525\pi\) | |||||||
\(282\) | 13118.5 | + | 22721.9i | 0.164963 | + | 0.285724i | ||||
\(283\) | 42224.4 | + | 24378.3i | 0.527219 | + | 0.304390i | 0.739883 | − | 0.672735i | \(-0.234881\pi\) |
−0.212664 | + | 0.977125i | \(0.568214\pi\) | |||||||
\(284\) | 912.971 | + | 3407.26i | 0.0113193 | + | 0.0422443i | ||||
\(285\) | − | 2351.45i | − | 0.0289498i | ||||||
\(286\) | 66833.6 | + | 104554.i | 0.817077 | + | 1.27822i | ||||
\(287\) | −5390.00 | −0.0654372 | ||||||||
\(288\) | 10801.1 | − | 2894.15i | 0.130222 | − | 0.0348928i | ||||
\(289\) | 75791.4 | − | 131275.i | 0.907453 | − | 1.57175i | ||||
\(290\) | 4452.16 | − | 2570.45i | 0.0529389 | − | 0.0305643i | ||||
\(291\) | −48380.6 | − | 48380.6i | −0.571327 | − | 0.571327i | ||||
\(292\) | −6550.16 | + | 24445.5i | −0.0768222 | + | 0.286704i | ||||
\(293\) | −15114.0 | − | 4049.79i | −0.176054 | − | 0.0471734i | 0.169715 | − | 0.985493i | \(-0.445715\pi\) |
−0.345769 | + | 0.938320i | \(0.612382\pi\) | |||||||
\(294\) | −61854.1 | + | 61854.1i | −0.715606 | + | 0.715606i | ||||
\(295\) | 9829.84 | + | 17025.8i | 0.112954 | + | 0.195642i | ||||
\(296\) | 1461.51 | + | 843.804i | 0.0166809 | + | 0.00963071i | ||||
\(297\) | −30656.3 | − | 114411.i | −0.347542 | − | 1.29704i | ||||
\(298\) | − | 2837.74i | − | 0.0319551i | ||||||
\(299\) | −17328.4 | − | 8986.86i | −0.193828 | − | 0.100523i | ||||
\(300\) | −17005.5 | −0.188950 | ||||||||
\(301\) | −6119.95 | + | 1639.84i | −0.0675484 | + | 0.0180995i | ||||
\(302\) | 47606.7 | − | 82457.2i | 0.521980 | − | 0.904096i | ||||
\(303\) | −56064.2 | + | 32368.7i | −0.610662 | + | 0.352566i | ||||
\(304\) | −2480.37 | − | 2480.37i | −0.0268392 | − | 0.0268392i | ||||
\(305\) | −10411.3 | + | 38855.5i | −0.111919 | + | 0.417689i | ||||
\(306\) | 42632.1 | + | 11423.2i | 0.455297 | + | 0.121996i | ||||
\(307\) | −54125.4 | + | 54125.4i | −0.574281 | + | 0.574281i | −0.933322 | − | 0.359041i | \(-0.883104\pi\) |
0.359041 | + | 0.933322i | \(0.383104\pi\) | |||||||
\(308\) | 1096.48 | + | 1899.15i | 0.0115584 | + | 0.0200197i | ||||
\(309\) | 118257. | + | 68275.7i | 1.23854 | + | 0.715071i | ||||
\(310\) | −16761.0 | − | 62553.0i | −0.174412 | − | 0.650916i | ||||
\(311\) | − | 62698.1i | − | 0.648237i | −0.946017 | − | 0.324118i | \(-0.894932\pi\) | ||
0.946017 | − | 0.324118i | \(-0.105068\pi\) | |||||||
\(312\) | −36353.5 | − | 114685.i | −0.373454 | − | 1.17814i | ||||
\(313\) | 102335. | 1.04457 | 0.522284 | − | 0.852772i | \(-0.325080\pi\) | ||||
0.522284 | + | 0.852772i | \(0.325080\pi\) | |||||||
\(314\) | −31483.5 | + | 8435.97i | −0.319318 | + | 0.0855610i | ||||
\(315\) | −480.213 | + | 831.753i | −0.00483963 | + | 0.00838249i | ||||
\(316\) | 24447.9 | − | 14115.0i | 0.244832 | − | 0.141354i | ||||
\(317\) | −46963.7 | − | 46963.7i | −0.467351 | − | 0.467351i | 0.433704 | − | 0.901055i | \(-0.357206\pi\) |
−0.901055 | + | 0.433704i | \(0.857206\pi\) | |||||||
\(318\) | −19830.7 | + | 74009.3i | −0.196103 | + | 0.731866i | ||||
\(319\) | −23767.3 | − | 6368.42i | −0.233560 | − | 0.0625821i | ||||
\(320\) | 39434.8 | − | 39434.8i | 0.385105 | − | 0.385105i | ||||
\(321\) | 53705.8 | + | 93021.2i | 0.521208 | + | 0.902759i | ||||
\(322\) | 1081.17 | + | 624.216i | 0.0104276 | + | 0.00602037i | ||||
\(323\) | 2334.36 | + | 8711.96i | 0.0223750 | + | 0.0835047i | ||||
\(324\) | 27651.0i | 0.263403i | ||||||||
\(325\) | 3626.38 | + | 80234.3i | 0.0343326 | + | 0.759615i | ||||
\(326\) | 70438.6 | 0.662789 | ||||||||
\(327\) | −69238.4 | + | 18552.4i | −0.647517 | + | 0.173502i | ||||
\(328\) | 60839.0 | − | 105376.i | 0.565503 | − | 0.979479i | ||||
\(329\) | 1896.49 | − | 1094.94i | 0.0175210 | − | 0.0101158i | ||||
\(330\) | 65633.5 | + | 65633.5i | 0.602695 | + | 0.602695i | ||||
\(331\) | −1935.38 | + | 7222.92i | −0.0176648 | + | 0.0659260i | −0.974196 | − | 0.225705i | \(-0.927531\pi\) |
0.956531 | + | 0.291631i | \(0.0941980\pi\) | |||||||
\(332\) | 6252.84 | + | 1675.44i | 0.0567285 | + | 0.0152004i | ||||
\(333\) | 445.173 | − | 445.173i | 0.00401458 | − | 0.00401458i | ||||
\(334\) | −72787.9 | − | 126072.i | −0.652479 | − | 1.13013i | ||||
\(335\) | −12966.4 | − | 7486.15i | −0.115539 | − | 0.0667066i | ||||
\(336\) | 1539.13 | + | 5744.09i | 0.0136331 | + | 0.0508795i | ||||
\(337\) | 33199.1i | 0.292325i | 0.989261 | + | 0.146162i | \(0.0466922\pi\) | ||||
−0.989261 | + | 0.146162i | \(0.953308\pi\) | |||||||
\(338\) | −94918.8 | + | 34877.6i | −0.830843 | + | 0.305291i | ||||
\(339\) | −143926. | −1.25239 | ||||||||
\(340\) | −19853.6 | + | 5319.76i | −0.171744 | + | 0.0460187i | ||||
\(341\) | −154978. | + | 268430.i | −1.33279 | + | 2.30846i | ||||
\(342\) | −1466.35 | + | 846.595i | −0.0125367 | + | 0.00723808i | ||||
\(343\) | 10345.5 | + | 10345.5i | 0.0879352 | + | 0.0879352i | ||||
\(344\) | 37019.0 | − | 138157.i | 0.312829 | − | 1.16750i | ||||
\(345\) | −14103.7 | − | 3779.08i | −0.118494 | − | 0.0317503i | ||||
\(346\) | −28711.3 | + | 28711.3i | −0.239828 | + | 0.239828i | ||||
\(347\) | 4436.36 | + | 7684.00i | 0.0368441 | + | 0.0638158i | 0.883859 | − | 0.467753i | \(-0.154936\pi\) |
−0.847015 | + | 0.531568i | \(0.821603\pi\) | |||||||
\(348\) | 3676.82 | + | 2122.81i | 0.0303608 | + | 0.0175288i | ||||
\(349\) | 40393.6 | + | 150751.i | 0.331636 | + | 1.23768i | 0.907470 | + | 0.420117i | \(0.138011\pi\) |
−0.575834 | + | 0.817567i | \(0.695322\pi\) | |||||||
\(350\) | − | 5136.70i | − | 0.0419322i | ||||||
\(351\) | 96427.1 | − | 4358.25i | 0.782681 | − | 0.0353751i | ||||
\(352\) | −90200.5 | −0.727987 | ||||||||
\(353\) | −104409. | + | 27976.4i | −0.837895 | + | 0.224513i | −0.652155 | − | 0.758086i | \(-0.726135\pi\) |
−0.185740 | + | 0.982599i | \(0.559468\pi\) | |||||||
\(354\) | 29378.8 | − | 50885.6i | 0.234438 | − | 0.406059i | ||||
\(355\) | 10792.2 | − | 6230.88i | 0.0856354 | − | 0.0494416i | ||||
\(356\) | 10766.7 | + | 10766.7i | 0.0849540 | + | 0.0849540i | ||||
\(357\) | 3957.44 | − | 14769.4i | 0.0310511 | − | 0.115884i | ||||
\(358\) | 79626.8 | + | 21335.9i | 0.621288 | + | 0.166474i | ||||
\(359\) | 157573. | − | 157573.i | 1.22262 | − | 1.22262i | 0.255926 | − | 0.966696i | \(-0.417620\pi\) |
0.966696 | − | 0.255926i | \(-0.0823803\pi\) | |||||||
\(360\) | −10840.7 | − | 18776.6i | −0.0836474 | − | 0.144882i | ||||
\(361\) | 112562. | + | 64987.5i | 0.863726 | + | 0.498672i | ||||
\(362\) | 34328.8 | + | 128117.i | 0.261964 | + | 0.977662i | ||||
\(363\) | − | 293018.i | − | 2.22372i | ||||||
\(364\) | −1703.56 | + | 540.003i | −0.0128574 | + | 0.00407562i | ||||
\(365\) | 89407.7 | 0.671103 | ||||||||
\(366\) | 116129. | − | 31116.7i | 0.866918 | − | 0.232290i | ||||
\(367\) | −22964.2 | + | 39775.1i | −0.170498 | + | 0.295311i | −0.938594 | − | 0.345024i | \(-0.887871\pi\) |
0.768096 | + | 0.640334i | \(0.221204\pi\) | |||||||
\(368\) | −18863.3 | + | 10890.7i | −0.139291 | + | 0.0804195i | ||||
\(369\) | −32097.4 | − | 32097.4i | −0.235731 | − | 0.235731i | ||||
\(370\) | 274.618 | − | 1024.89i | 0.00200597 | − | 0.00748640i | ||||
\(371\) | 6177.22 | + | 1655.18i | 0.0448792 | + | 0.0120254i | ||||
\(372\) | 37817.4 | − | 37817.4i | 0.273278 | − | 0.273278i | ||||
\(373\) | −124163. | − | 215056.i | −0.892428 | − | 1.54573i | −0.836956 | − | 0.547270i | \(-0.815667\pi\) |
−0.0554716 | − | 0.998460i | \(-0.517666\pi\) | |||||||
\(374\) | −308325. | − | 178011.i | −2.20427 | − | 1.27264i | ||||
\(375\) | 35998.0 | + | 134346.i | 0.255985 | + | 0.955351i | ||||
\(376\) | 49436.2i | 0.349679i | ||||||||
\(377\) | 9231.62 | − | 17800.4i | 0.0649524 | − | 0.125241i | ||||
\(378\) | −6173.38 | −0.0432056 | ||||||||
\(379\) | 65151.5 | − | 17457.3i | 0.453572 | − | 0.121534i | −0.0247984 | − | 0.999692i | \(-0.507894\pi\) |
0.478370 | + | 0.878158i | \(0.341228\pi\) | |||||||
\(380\) | 394.256 | − | 682.871i | 0.00273030 | − | 0.00472903i | ||||
\(381\) | 235966. | − | 136235.i | 1.62554 | − | 0.938508i | ||||
\(382\) | 133958. | + | 133958.i | 0.918000 | + | 0.918000i | ||||
\(383\) | 8150.00 | − | 30416.2i | 0.0555597 | − | 0.207352i | −0.932566 | − | 0.361000i | \(-0.882436\pi\) |
0.988126 | + | 0.153648i | \(0.0491022\pi\) | |||||||
\(384\) | −91560.8 | − | 24533.7i | −0.620937 | − | 0.166379i | ||||
\(385\) | 5478.14 | − | 5478.14i | 0.0369583 | − | 0.0369583i | ||||
\(386\) | 63821.8 | + | 110543.i | 0.428346 | + | 0.741917i | ||||
\(387\) | −46209.5 | − | 26679.0i | −0.308538 | − | 0.178135i | ||||
\(388\) | −5938.21 | − | 22161.7i | −0.0394450 | − | 0.147211i | ||||
\(389\) | 150495.i | 0.994541i | 0.867595 | + | 0.497271i | \(0.165664\pi\) | ||||
−0.867595 | + | 0.497271i | \(0.834336\pi\) | |||||||
\(390\) | −63732.9 | + | 40739.9i | −0.419020 | + | 0.267849i | ||||
\(391\) | 56005.0 | 0.366331 | ||||||||
\(392\) | −159206. | + | 42659.0i | −1.03606 | + | 0.277612i | ||||
\(393\) | −93393.4 | + | 161762.i | −0.604688 | + | 1.04735i | ||||
\(394\) | 139405. | − | 80485.4i | 0.898019 | − | 0.518471i | ||||
\(395\) | −70520.5 | − | 70520.5i | −0.451982 | − | 0.451982i | ||||
\(396\) | −4779.93 | + | 17838.9i | −0.0304811 | + | 0.113757i | ||||
\(397\) | −157302. | − | 42148.9i | −0.998051 | − | 0.267427i | −0.277422 | − | 0.960748i | \(-0.589480\pi\) |
−0.720629 | + | 0.693321i | \(0.756147\pi\) | |||||||
\(398\) | −26240.6 | + | 26240.6i | −0.165656 | + | 0.165656i | ||||
\(399\) | 293.292 | + | 507.997i | 0.00184227 | + | 0.00319091i | ||||
\(400\) | 77613.4 | + | 44810.1i | 0.485084 | + | 0.280063i | ||||
\(401\) | 32839.7 | + | 122559.i | 0.204226 | + | 0.762180i | 0.989684 | + | 0.143266i | \(0.0457604\pi\) |
−0.785459 | + | 0.618914i | \(0.787573\pi\) | |||||||
\(402\) | 44748.3i | 0.276901i | ||||||||
\(403\) | −186492. | − | 170363.i | −1.14828 | − | 1.04897i | ||||
\(404\) | −21708.4 | −0.133004 | ||||||||
\(405\) | 94356.9 | − | 25282.9i | 0.575259 | − | 0.154140i | ||||
\(406\) | −641.217 | + | 1110.62i | −0.00389003 | + | 0.00673773i | ||||
\(407\) | −4398.04 | + | 2539.21i | −0.0265503 | + | 0.0153288i | ||||
\(408\) | 244077. | + | 244077.i | 1.46624 | + | 1.46624i | ||||
\(409\) | −39413.4 | + | 147093.i | −0.235612 | + | 0.879315i | 0.742260 | + | 0.670111i | \(0.233754\pi\) |
−0.977872 | + | 0.209203i | \(0.932913\pi\) | |||||||
\(410\) | −73895.3 | − | 19800.2i | −0.439592 | − | 0.117788i | ||||
\(411\) | −185115. | + | 185115.i | −1.09586 | + | 1.09586i | ||||
\(412\) | 22895.0 | + | 39655.2i | 0.134879 | + | 0.233618i | ||||
\(413\) | −4247.20 | − | 2452.12i | −0.0249002 | − | 0.0143761i | ||||
\(414\) | 2721.18 | + | 10155.6i | 0.0158766 | + | 0.0592521i | ||||
\(415\) | − | 22869.3i | − | 0.132787i | ||||||
\(416\) | 15799.7 | − | 71788.7i | 0.0912984 | − | 0.414830i | ||||
\(417\) | −7628.60 | −0.0438705 | ||||||||
\(418\) | 13192.7 | − | 3534.98i | 0.0755060 | − | 0.0202318i | ||||
\(419\) | 37475.9 | − | 64910.2i | 0.213464 | − | 0.369730i | −0.739332 | − | 0.673341i | \(-0.764859\pi\) |
0.952796 | + | 0.303610i | \(0.0981921\pi\) | |||||||
\(420\) | −1157.67 | + | 668.381i | −0.00656275 | + | 0.00378901i | ||||
\(421\) | −207945. | − | 207945.i | −1.17323 | − | 1.17323i | −0.981435 | − | 0.191797i | \(-0.938568\pi\) |
−0.191797 | − | 0.981435i | \(-0.561432\pi\) | |||||||
\(422\) | 18674.7 | − | 69695.0i | 0.104865 | − | 0.391360i | ||||
\(423\) | 17814.0 | + | 4773.24i | 0.0995589 | + | 0.0266767i | ||||
\(424\) | −102084. | + | 102084.i | −0.567841 | + | 0.567841i | ||||
\(425\) | −115217. | − | 199562.i | −0.637879 | − | 1.10484i | ||||
\(426\) | −32255.1 | − | 18622.5i | −0.177738 | − | 0.102617i | ||||
\(427\) | −2597.17 | − | 9692.76i | −0.0142444 | − | 0.0531608i | ||||
\(428\) | 36018.4i | 0.196624i | ||||||||
\(429\) | 353577. | + | 77817.5i | 1.92118 | + | 0.422827i | ||||
\(430\) | −89926.8 | −0.486354 | ||||||||
\(431\) | 249819. | − | 66938.7i | 1.34484 | − | 0.360348i | 0.486611 | − | 0.873619i | \(-0.338233\pi\) |
0.858227 | + | 0.513270i | \(0.171566\pi\) | |||||||
\(432\) | 53853.7 | − | 93277.3i | 0.288568 | − | 0.499814i | ||||
\(433\) | 111565. | − | 64412.4i | 0.595051 | − | 0.343553i | −0.172041 | − | 0.985090i | \(-0.555036\pi\) |
0.767092 | + | 0.641537i | \(0.221703\pi\) | |||||||
\(434\) | 11423.1 | + | 11423.1i | 0.0606465 | + | 0.0606465i | ||||
\(435\) | 3882.01 | − | 14487.9i | 0.0205153 | − | 0.0765641i | ||||
\(436\) | −23217.8 | − | 6221.18i | −0.122137 | − | 0.0327265i | ||||
\(437\) | −1519.23 | + | 1519.23i | −0.00795539 | + | 0.00795539i | ||||
\(438\) | −133608. | − | 231416.i | −0.696441 | − | 1.20627i | ||||
\(439\) | 151706. | + | 87587.8i | 0.787182 | + | 0.454480i | 0.838970 | − | 0.544178i | \(-0.183159\pi\) |
−0.0517876 | + | 0.998658i | \(0.516492\pi\) | |||||||
\(440\) | 45265.6 | + | 168933.i | 0.233810 | + | 0.872590i | ||||
\(441\) | 61487.5i | 0.316162i | ||||||||
\(442\) | 195683. | − | 214209.i | 1.00163 | − | 1.09646i | ||||
\(443\) | 4105.84 | 0.0209216 | 0.0104608 | − | 0.999945i | \(-0.496670\pi\) | ||||
0.0104608 | + | 0.999945i | \(0.496670\pi\) | |||||||
\(444\) | 846.405 | − | 226.793i | 0.00429351 | − | 0.00115044i | ||||
\(445\) | 26896.0 | − | 46585.2i | 0.135821 | − | 0.235249i | ||||
\(446\) | −21340.1 | + | 12320.7i | −0.107282 | + | 0.0619393i | ||||
\(447\) | −5854.34 | − | 5854.34i | −0.0292997 | − | 0.0292997i | ||||
\(448\) | −3600.69 | + | 13438.0i | −0.0179403 | + | 0.0669541i | ||||
\(449\) | −194809. | − | 52198.8i | −0.966308 | − | 0.258922i | −0.259040 | − | 0.965867i | \(-0.583406\pi\) |
−0.707268 | + | 0.706945i | \(0.750073\pi\) | |||||||
\(450\) | 30589.0 | − | 30589.0i | 0.151057 | − | 0.151057i | ||||
\(451\) | 183079. | + | 317102.i | 0.900090 | + | 1.55900i | ||||
\(452\) | −41796.9 | − | 24131.5i | −0.204582 | − | 0.118116i | ||||
\(453\) | −71897.6 | − | 268326.i | −0.350363 | − | 1.30757i | ||||
\(454\) | 142781.i | 0.692720i | ||||||||
\(455\) | 3400.37 | + | 5319.50i | 0.0164249 | + | 0.0256950i | ||||
\(456\) | −13242.0 | −0.0636831 | ||||||||
\(457\) | 69439.6 | − | 18606.3i | 0.332487 | − | 0.0890897i | −0.0887134 | − | 0.996057i | \(-0.528276\pi\) |
0.421201 | + | 0.906968i | \(0.361609\pi\) | |||||||
\(458\) | −81156.1 | + | 140567.i | −0.386893 | + | 0.670118i | ||||
\(459\) | −239837. | + | 138470.i | −1.13839 | + | 0.657249i | ||||
\(460\) | −3462.17 | − | 3462.17i | −0.0163619 | − | 0.0163619i | ||||
\(461\) | 54042.0 | − | 201688.i | 0.254290 | − | 0.949025i | −0.714193 | − | 0.699948i | \(-0.753206\pi\) |
0.968484 | − | 0.249076i | \(-0.0801270\pi\) | |||||||
\(462\) | −22365.6 | − | 5992.83i | −0.104784 | − | 0.0280768i | ||||
\(463\) | −209384. | + | 209384.i | −0.976747 | + | 0.976747i | −0.999736 | − | 0.0229886i | \(-0.992682\pi\) |
0.0229886 | + | 0.999736i | \(0.492682\pi\) | |||||||
\(464\) | −11187.4 | − | 19377.1i | −0.0519627 | − | 0.0900020i | ||||
\(465\) | −163627. | − | 94470.2i | −0.756745 | − | 0.436907i | ||||
\(466\) | −75039.6 | − | 280052.i | −0.345556 | − | 1.28963i | ||||
\(467\) | − | 161789.i | − | 0.741847i | −0.928663 | − | 0.370924i | \(-0.879041\pi\) | ||
0.928663 | − | 0.370924i | \(-0.120959\pi\) | |||||||
\(468\) | −13360.4 | − | 6928.96i | −0.0609996 | − | 0.0316356i | ||||
\(469\) | 3734.94 | 0.0169800 | ||||||||
\(470\) | 30022.7 | − | 8044.56i | 0.135911 | − | 0.0364172i | ||||
\(471\) | −47547.6 | + | 82354.9i | −0.214332 | + | 0.371234i | ||||
\(472\) | 95879.6 | − | 55356.1i | 0.430370 | − | 0.248474i | ||||
\(473\) | 304348. | + | 304348.i | 1.36034 | + | 1.36034i | ||||
\(474\) | −77146.2 | + | 287914.i | −0.343367 | + | 1.28146i | ||||
\(475\) | 8538.91 | + | 2287.99i | 0.0378456 | + | 0.0101407i | ||||
\(476\) | 3625.57 | − | 3625.57i | 0.0160016 | − | 0.0160016i | ||||
\(477\) | 26928.7 | + | 46641.9i | 0.118353 | + | 0.204993i | ||||
\(478\) | 31001.6 | + | 17898.8i | 0.135684 | + | 0.0783371i | ||||
\(479\) | 25884.6 | + | 96602.8i | 0.112816 | + | 0.421035i | 0.999114 | − | 0.0420796i | \(-0.0133983\pi\) |
−0.886298 | + | 0.463115i | \(0.846732\pi\) | |||||||
\(480\) | − | 54983.7i | − | 0.238644i | ||||||
\(481\) | −1250.53 | − | 3945.08i | −0.00540512 | − | 0.0170516i | ||||
\(482\) | 88014.7 | 0.378845 | ||||||||
\(483\) | 3518.27 | − | 942.717i | 0.0150812 | − | 0.00404098i | ||||
\(484\) | 49128.9 | − | 85093.8i | 0.209723 | − | 0.363251i | ||||
\(485\) | −70195.4 | + | 40527.3i | −0.298418 | + | 0.172292i | ||||
\(486\) | −90618.4 | − | 90618.4i | −0.383658 | − | 0.383658i | ||||
\(487\) | −41248.4 | + | 153941.i | −0.173920 | + | 0.649078i | 0.822813 | + | 0.568312i | \(0.192403\pi\) |
−0.996733 | + | 0.0807659i | \(0.974263\pi\) | |||||||
\(488\) | 218812. | + | 58630.5i | 0.918823 | + | 0.246198i | ||||
\(489\) | 145317. | − | 145317.i | 0.607712 | − | 0.607712i | ||||
\(490\) | 51813.8 | + | 89744.2i | 0.215801 | + | 0.373778i | ||||
\(491\) | −44308.9 | − | 25581.7i | −0.183792 | − | 0.106113i | 0.405281 | − | 0.914192i | \(-0.367174\pi\) |
−0.589073 | + | 0.808080i | \(0.700507\pi\) | |||||||
\(492\) | −16352.0 | − | 61026.5i | −0.0675524 | − | 0.252109i | ||||
\(493\) | 57530.4i | 0.236703i | ||||||||
\(494\) | 502.549 | + | 11119.0i | 0.00205932 | + | 0.0455630i | ||||
\(495\) | 65244.5 | 0.266277 | ||||||||
\(496\) | −272249. | + | 72948.8i | −1.10663 | + | 0.296521i | ||||
\(497\) | −1554.34 | + | 2692.19i | −0.00629263 | + | 0.0108992i | ||||
\(498\) | −59193.1 | + | 34175.2i | −0.238678 | + | 0.137801i | ||||
\(499\) | −149225. | − | 149225.i | −0.599294 | − | 0.599294i | 0.340831 | − | 0.940125i | \(-0.389292\pi\) |
−0.940125 | + | 0.340831i | \(0.889292\pi\) | |||||||
\(500\) | −12071.2 | + | 45050.4i | −0.0482849 | + | 0.180202i | ||||
\(501\) | −410254. | − | 109927.i | −1.63447 | − | 0.437956i | ||||
\(502\) | −26376.6 | + | 26376.6i | −0.104668 | + | 0.104668i | ||||
\(503\) | 82545.1 | + | 142972.i | 0.326254 | + | 0.565088i | 0.981765 | − | 0.190097i | \(-0.0608803\pi\) |
−0.655512 | + | 0.755185i | \(0.727547\pi\) | |||||||
\(504\) | 4683.96 | + | 2704.29i | 0.0184396 | + | 0.0106461i | ||||
\(505\) | 19849.2 | + | 74078.3i | 0.0778325 | + | 0.290475i | ||||
\(506\) | − | 84809.7i | − | 0.331241i | ||||||
\(507\) | −123867. | + | 267774.i | −0.481879 | + | 1.04172i | ||||
\(508\) | 91367.4 | 0.354050 | ||||||||
\(509\) | 158359. | − | 42432.1i | 0.611233 | − | 0.163779i | 0.0600938 | − | 0.998193i | \(-0.480860\pi\) |
0.551139 | + | 0.834413i | \(0.314193\pi\) | |||||||
\(510\) | 108511. | − | 187946.i | 0.417188 | − | 0.722591i | ||||
\(511\) | −19315.3 | + | 11151.7i | −0.0739705 | + | 0.0427069i | ||||
\(512\) | −205028. | − | 205028.i | −0.782122 | − | 0.782122i | ||||
\(513\) | 2749.76 | − | 10262.2i | 0.0104486 | − | 0.0389948i | ||||
\(514\) | 319229. | + | 85537.1i | 1.20830 | + | 0.323764i | ||||
\(515\) | 114386. | − | 114386.i | 0.431280 | − | 0.431280i | ||||
\(516\) | −37133.1 | − | 64316.4i | −0.139464 | − | 0.241558i | ||||
\(517\) | −128834. | − | 74382.6i | −0.482004 | − | 0.278285i | ||||
\(518\) | 68.5053 | + | 255.665i | 0.000255308 | + | 0.000952823i | ||||
\(519\) | 118464.i | 0.439798i | ||||||||
\(520\) | −142379. | + | 6435.17i | −0.526551 | + | 0.0237987i | ||||
\(521\) | −25950.8 | −0.0956038 | −0.0478019 | − | 0.998857i | \(-0.515222\pi\) | ||||
−0.0478019 | + | 0.998857i | \(0.515222\pi\) | |||||||
\(522\) | −10432.2 | + | 2795.29i | −0.0382855 | + | 0.0102586i | ||||
\(523\) | 8718.04 | − | 15100.1i | 0.0318725 | − | 0.0552047i | −0.849649 | − | 0.527348i | \(-0.823186\pi\) |
0.881522 | + | 0.472144i | \(0.156520\pi\) | |||||||
\(524\) | −54243.8 | + | 31317.7i | −0.197555 | + | 0.114058i | ||||
\(525\) | −10597.2 | − | 10597.2i | −0.0384477 | − | 0.0384477i | ||||
\(526\) | 78305.8 | − | 292241.i | 0.283024 | − | 1.05626i | ||||
\(527\) | 700013. | + | 187568.i | 2.52049 | + | 0.675363i | ||||
\(528\) | 285656. | − | 285656.i | 1.02465 | − | 1.02465i | ||||
\(529\) | −133250. | − | 230796.i | −0.476163 | − | 0.824738i | ||||
\(530\) | 78607.7 | + | 45384.2i | 0.279842 | + | 0.161567i | ||||
\(531\) | −10689.7 | − | 39894.4i | −0.0379118 | − | 0.141489i | ||||
\(532\) | 196.700i | 0.000694993i | ||||||||
\(533\) | −284444. | + | 90164.5i | −1.00125 | + | 0.317381i | ||||
\(534\) | −160770. | −0.563797 | ||||||||
\(535\) | 122910. | − | 32933.6i | 0.429417 | − | 0.115062i | ||||
\(536\) | −42157.8 | + | 73019.4i | −0.146740 | + | 0.254161i | ||||
\(537\) | 208289. | − | 120256.i | 0.722300 | − | 0.417020i | ||||
\(538\) | −156374. | − | 156374.i | −0.540255 | − | 0.540255i | ||||
\(539\) | 128371. | − | 479088.i | 0.441865 | − | 1.64906i | ||||
\(540\) | 23386.5 | + | 6266.40i | 0.0802006 | + | 0.0214897i | ||||
\(541\) | −9872.14 | + | 9872.14i | −0.0337300 | + | 0.0337300i | −0.723771 | − | 0.690041i | \(-0.757593\pi\) |
0.690041 | + | 0.723771i | \(0.257593\pi\) | |||||||
\(542\) | 180444. | + | 312538.i | 0.614248 | + | 1.06391i | ||||
\(543\) | 335130. | + | 193487.i | 1.13662 | + | 0.656225i | ||||
\(544\) | 54584.2 | + | 203711.i | 0.184446 | + | 0.688362i | ||||
\(545\) | 84917.1i | 0.285892i | ||||||||
\(546\) | 8687.18 | − | 16750.6i | 0.0291403 | − | 0.0561881i | ||||
\(547\) | −146316. | −0.489009 | −0.244505 | − | 0.969648i | \(-0.578625\pi\) | ||||
−0.244505 | + | 0.969648i | \(0.578625\pi\) | |||||||
\(548\) | −84795.5 | + | 22720.9i | −0.282365 | + | 0.0756596i | ||||
\(549\) | 42254.2 | − | 73186.4i | 0.140193 | − | 0.242821i | ||||
\(550\) | −302201. | + | 174476.i | −0.999010 | + | 0.576779i | ||||
\(551\) | −1560.61 | − | 1560.61i | −0.00514034 | − | 0.00514034i | ||||
\(552\) | −21281.6 | + | 79424.2i | −0.0698437 | + | 0.260660i | ||||
\(553\) | 24030.9 | + | 6439.05i | 0.0785813 | + | 0.0210558i | ||||
\(554\) | 136108. | − | 136108.i | 0.443469 | − | 0.443469i | ||||
\(555\) | −1547.83 | − | 2680.92i | −0.00502501 | − | 0.00870357i | ||||
\(556\) | −2215.38 | − | 1279.05i | −0.00716637 | − | 0.00413751i | ||||
\(557\) | −49582.1 | − | 185043.i | −0.159814 | − | 0.596434i | −0.998645 | − | 0.0520417i | \(-0.983427\pi\) |
0.838831 | − | 0.544392i | \(-0.183240\pi\) | |||||||
\(558\) | 136049.i | 0.436946i | ||||||||
\(559\) | −295534. | + | 188914.i | −0.945767 | + | 0.604561i | ||||
\(560\) | 7044.82 | 0.0224643 | ||||||||
\(561\) | −1.00333e6 | + | 268840.i | −3.18798 | + | 0.854218i | ||||
\(562\) | −120207. | + | 208204.i | −0.380589 | + | 0.659200i | ||||
\(563\) | −222626. | + | 128533.i | −0.702357 | + | 0.405506i | −0.808225 | − | 0.588874i | \(-0.799571\pi\) |
0.105867 | + | 0.994380i | \(0.466238\pi\) | |||||||
\(564\) | 18150.7 | + | 18150.7i | 0.0570603 | + | 0.0570603i | ||||
\(565\) | −44129.5 | + | 164693.i | −0.138239 | + | 0.515917i | ||||
\(566\) | −166747. | − | 44679.6i | −0.520504 | − | 0.139469i | ||||
\(567\) | −17231.0 | + | 17231.0i | −0.0535974 | + | 0.0535974i | ||||
\(568\) | −35088.8 | − | 60775.6i | −0.108761 | − | 0.188379i | ||||
\(569\) | 88592.0 | + | 51148.6i | 0.273634 | + | 0.157983i | 0.630538 | − | 0.776158i | \(-0.282834\pi\) |
−0.356904 | + | 0.934141i | \(0.616168\pi\) | |||||||
\(570\) | 2154.82 | + | 8041.90i | 0.00663226 | + | 0.0247519i | ||||
\(571\) | − | 297882.i | − | 0.913633i | −0.889561 | − | 0.456817i | \(-0.848990\pi\) | ||
0.889561 | − | 0.456817i | \(-0.151010\pi\) | |||||||
\(572\) | 89633.1 | + | 81881.1i | 0.273953 | + | 0.250260i | ||||
\(573\) | 552719. | 1.68343 | ||||||||
\(574\) | 18433.7 | − | 4939.29i | 0.0559485 | − | 0.0149914i | ||||
\(575\) | 27446.3 | − | 47538.4i | 0.0830134 | − | 0.143783i | ||||
\(576\) | −101465. | + | 58580.8i | −0.305824 | + | 0.176567i | ||||
\(577\) | 217932. | + | 217932.i | 0.654591 | + | 0.654591i | 0.954095 | − | 0.299504i | \(-0.0968212\pi\) |
−0.299504 | + | 0.954095i | \(0.596821\pi\) | |||||||
\(578\) | −138908. | + | 518410.i | −0.415787 | + | 1.55174i | ||||
\(579\) | 359719. | + | 96386.4i | 1.07302 | + | 0.287514i | ||||
\(580\) | 3556.46 | − | 3556.46i | 0.0105721 | − | 0.0105721i | ||||
\(581\) | 2852.45 | + | 4940.58i | 0.00845017 | + | 0.0146361i | ||||
\(582\) | 209796. | + | 121126.i | 0.619371 | + | 0.357594i | ||||
\(583\) | −112441. | − | 419637.i | −0.330818 | − | 1.23463i | ||||
\(584\) | − | 503493.i | − | 1.47628i | ||||||
\(585\) | −11428.4 | + | 51926.8i | −0.0333943 | + | 0.151733i | ||||
\(586\) | 55400.8 | 0.161332 | ||||||||
\(587\) | −131119. | + | 35133.2i | −0.380530 | + | 0.101963i | −0.444013 | − | 0.896020i | \(-0.646446\pi\) |
0.0634831 | + | 0.997983i | \(0.479779\pi\) | |||||||
\(588\) | −42790.5 | + | 74115.3i | −0.123763 | + | 0.214365i | ||||
\(589\) | −24077.2 | + | 13901.0i | −0.0694024 | + | 0.0400695i | ||||
\(590\) | −49220.0 | − | 49220.0i | −0.141396 | − | 0.141396i | ||||
\(591\) | 121552. | − | 453640.i | 0.348008 | − | 1.29878i | ||||
\(592\) | −4460.61 | − | 1195.22i | −0.0127277 | − | 0.00341038i | ||||
\(593\) | 143981. | − | 143981.i | 0.409444 | − | 0.409444i | −0.472101 | − | 0.881545i | \(-0.656504\pi\) |
0.881545 | + | 0.472101i | \(0.156504\pi\) | |||||||
\(594\) | 209688. | + | 363190.i | 0.594293 | + | 1.02935i | ||||
\(595\) | −15687.0 | − | 9056.90i | −0.0443105 | − | 0.0255827i | ||||
\(596\) | −718.559 | − | 2681.70i | −0.00202288 | − | 0.00754949i | ||||
\(597\) | 108270.i | 0.303781i | ||||||||
\(598\) | 67498.3 | + | 14855.5i | 0.188751 | + | 0.0415416i | ||||
\(599\) | −583382. | −1.62592 | −0.812961 | − | 0.582319i | \(-0.802146\pi\) | ||||
−0.812961 | + | 0.582319i | \(0.802146\pi\) | |||||||
\(600\) | 326792. | − | 87563.8i | 0.907757 | − | 0.243233i | ||||
\(601\) | 332297. | − | 575556.i | 0.919979 | − | 1.59345i | 0.120535 | − | 0.992709i | \(-0.461539\pi\) |
0.799444 | − | 0.600741i | \(-0.205128\pi\) | |||||||
\(602\) | 19427.4 | − | 11216.4i | 0.0536071 | − | 0.0309501i | ||||
\(603\) | 22241.5 | + | 22241.5i | 0.0611688 | + | 0.0611688i | ||||
\(604\) | 24109.5 | − | 89977.8i | 0.0660867 | − | 0.246639i | ||||
\(605\) | −335297. | − | 89842.5i | −0.916049 | − | 0.245455i | ||||
\(606\) | 162077. | − | 162077.i | 0.441342 | − | 0.441342i | ||||
\(607\) | −13999.5 | − | 24247.8i | −0.0379957 | − | 0.0658105i | 0.846402 | − | 0.532544i | \(-0.178764\pi\) |
−0.884398 | + | 0.466734i | \(0.845431\pi\) | |||||||
\(608\) | −7006.71 | − | 4045.32i | −0.0189543 | − | 0.0109432i | ||||
\(609\) | 968.393 | + | 3614.09i | 0.00261106 | + | 0.00974461i | ||||
\(610\) | − | 142426.i | − | 0.382762i | ||||||
\(611\) | 81766.5 | − | 89507.7i | 0.219025 | − | 0.239761i | ||||
\(612\) | 43180.4 | 0.115288 | ||||||||
\(613\) | 645104. | − | 172855.i | 1.71676 | − | 0.460004i | 0.739692 | − | 0.672946i | \(-0.234971\pi\) |
0.977065 | + | 0.212942i | \(0.0683046\pi\) | |||||||
\(614\) | 135508. | − | 234707.i | 0.359442 | − | 0.622573i | ||||
\(615\) | −193297. | + | 111600.i | −0.511062 | + | 0.295062i | ||||
\(616\) | −30849.8 | − | 30849.8i | −0.0813000 | − | 0.0813000i | ||||
\(617\) | −45280.8 | + | 168990.i | −0.118944 | + | 0.443906i | −0.999552 | − | 0.0299404i | \(-0.990468\pi\) |
0.880607 | + | 0.473847i | \(0.157135\pi\) | |||||||
\(618\) | −467004. | − | 125133.i | −1.22277 | − | 0.327639i | ||||
\(619\) | −171025. | + | 171025.i | −0.446352 | + | 0.446352i | −0.894140 | − | 0.447788i | \(-0.852212\pi\) |
0.447788 | + | 0.894140i | \(0.352212\pi\) | |||||||
\(620\) | −31678.8 | − | 54869.2i | −0.0824109 | − | 0.142740i | ||||
\(621\) | −57132.5 | − | 32985.5i | −0.148150 | − | 0.0855342i | ||||
\(622\) | 57455.4 | + | 214426.i | 0.148508 | + | 0.554240i | ||||
\(623\) | 13418.8i | 0.0345730i | ||||||||
\(624\) | 177312. | + | 277384.i | 0.455373 | + | 0.712380i | ||||
\(625\) | −132259. | −0.338583 | ||||||||
\(626\) | −349985. | + | 93778.1i | −0.893101 | + | 0.239306i | ||||
\(627\) | 19924.2 | − | 34509.7i | 0.0506810 | − | 0.0877821i | ||||
\(628\) | −27616.1 | + | 15944.2i | −0.0700235 | + | 0.0404281i | ||||
\(629\) | 8396.05 | + | 8396.05i | 0.0212214 | + | 0.0212214i | ||||
\(630\) | 880.116 | − | 3284.64i | 0.00221747 | − | 0.00827573i | ||||
\(631\) | 612582. | + | 164141.i | 1.53853 | + | 0.412248i | 0.925790 | − | 0.378038i | \(-0.123401\pi\) |
0.612739 | + | 0.790286i | \(0.290068\pi\) | |||||||
\(632\) | −397132. | + | 397132.i | −0.994261 | + | 0.994261i | ||||
\(633\) | −105256. | − | 182309.i | −0.262688 | − | 0.454989i | ||||
\(634\) | 203652. | + | 117578.i | 0.506651 | + | 0.292515i | ||||
\(635\) | −83542.3 | − | 311784.i | −0.207185 | − | 0.773226i | ||||
\(636\) | 74961.1i | 0.185320i | ||||||||
\(637\) | 358810. | + | 186086.i | 0.884272 | + | 0.458601i | ||||
\(638\) | 87119.5 | 0.214030 | ||||||||
\(639\) | −25288.0 | + | 6775.90i | −0.0619317 | + | 0.0165945i | ||||
\(640\) | −56147.2 | + | 97249.8i | −0.137078 | + | 0.237426i | ||||
\(641\) | 196060. | − | 113195.i | 0.477169 | − | 0.275494i | −0.242067 | − | 0.970260i | \(-0.577825\pi\) |
0.719236 | + | 0.694766i | \(0.244492\pi\) | |||||||
\(642\) | −268916. | − | 268916.i | −0.652449 | − | 0.652449i | ||||
\(643\) | −145903. | + | 544516.i | −0.352892 | + | 1.31701i | 0.530225 | + | 0.847857i | \(0.322107\pi\) |
−0.883117 | + | 0.469153i | \(0.844559\pi\) | |||||||
\(644\) | 1179.78 | + | 316.122i | 0.00284466 | + | 0.000762225i | ||||
\(645\) | −185522. | + | 185522.i | −0.445939 | + | 0.445939i | ||||
\(646\) | −15967.0 | − | 27655.6i | −0.0382611 | − | 0.0662701i | ||||
\(647\) | −38867.8 | − | 22440.4i | −0.0928500 | − | 0.0536070i | 0.452856 | − | 0.891584i | \(-0.350405\pi\) |
−0.545706 | + | 0.837977i | \(0.683738\pi\) | |||||||
\(648\) | −142379. | − | 531365.i | −0.339074 | − | 1.26544i | ||||
\(649\) | 333159.i | 0.790975i | ||||||||
\(650\) | −85927.4 | − | 271077.i | −0.203378 | − | 0.641602i | ||||
\(651\) | 47132.5 | 0.111214 | ||||||||
\(652\) | 66565.3 | − | 17836.1i | 0.156586 | − | 0.0419571i | ||||
\(653\) | −321240. | + | 556404.i | −0.753362 | + | 1.30486i | 0.192823 | + | 0.981234i | \(0.438236\pi\) |
−0.946185 | + | 0.323627i | \(0.895098\pi\) | |||||||
\(654\) | 219793. | − | 126898.i | 0.513876 | − | 0.296686i | ||||
\(655\) | 156467. | + | 156467.i | 0.364704 | + | 0.364704i | ||||
\(656\) | −86176.1 | + | 321614.i | −0.200253 | + | 0.747355i | ||||
\(657\) | −181430. | − | 48614.1i | −0.420319 | − | 0.112624i | ||||
\(658\) | −5482.59 | + | 5482.59i | −0.0126629 | + | 0.0126629i | ||||
\(659\) | −61574.5 | − | 106650.i | −0.141785 | − | 0.245579i | 0.786384 | − | 0.617738i | \(-0.211951\pi\) |
−0.928169 | + | 0.372159i | \(0.878618\pi\) | |||||||
\(660\) | 78643.9 | + | 45405.1i | 0.180542 | + | 0.104236i | ||||
\(661\) | 98643.4 | + | 368142.i | 0.225770 | + | 0.842583i | 0.982095 | + | 0.188388i | \(0.0603261\pi\) |
−0.756325 | + | 0.654196i | \(0.773007\pi\) | |||||||
\(662\) | − | 26475.8i | − | 0.0604134i | ||||||
\(663\) | −38219.6 | − | 845617.i | −0.0869480 | − | 1.92374i | ||||
\(664\) | −128787. | −0.292103 | ||||||||
\(665\) | 671.222 | − | 179.853i | 0.00151783 | − | 0.000406701i | ||||
\(666\) | −1114.54 | + | 1930.43i | −0.00251273 | + | 0.00435217i | ||||
\(667\) | −11868.5 | + | 6852.27i | −0.0266774 | + | 0.0154022i | ||||
\(668\) | −100709. | − | 100709.i | −0.225691 | − | 0.225691i | ||||
\(669\) | −18607.3 | + | 69443.3i | −0.0415748 | + | 0.155159i | ||||
\(670\) | 51205.0 | + | 13720.3i | 0.114068 | + | 0.0305644i | ||||
\(671\) | −482025. | + | 482025.i | −1.07059 | + | 1.07059i | ||||
\(672\) | 6858.02 | + | 11878.4i | 0.0151866 | + | 0.0263040i | ||||
\(673\) | −401413. | − | 231756.i | −0.886260 | − | 0.511682i | −0.0135427 | − | 0.999908i | \(-0.504311\pi\) |
−0.872717 | + | 0.488226i | \(0.837644\pi\) | |||||||
\(674\) | −30423.0 | − | 113540.i | −0.0669703 | − | 0.249937i | ||||
\(675\) | 271439.i | 0.595751i | ||||||||
\(676\) | −80867.9 | + | 56994.7i | −0.176963 | + | 0.124721i | ||||
\(677\) | 291789. | 0.636636 | 0.318318 | − | 0.947984i | \(-0.396882\pi\) | ||||
0.318318 | + | 0.947984i | \(0.396882\pi\) | |||||||
\(678\) | 492226. | − | 131892.i | 1.07079 | − | 0.286918i | ||||
\(679\) | 10109.8 | − | 17510.7i | 0.0219282 | − | 0.0379808i | ||||
\(680\) | 354131. | − | 204458.i | 0.765855 | − | 0.442166i | ||||
\(681\) | 294561. | + | 294561.i | 0.635156 | + | 0.635156i | ||||
\(682\) | 284038. | − | 1.06004e6i | 0.610672 | − | 2.27906i | ||||
\(683\) | −94711.9 | − | 25378.0i | −0.203031 | − | 0.0544021i | 0.155870 | − | 0.987778i | \(-0.450182\pi\) |
−0.358901 | + | 0.933375i | \(0.616849\pi\) | |||||||
\(684\) | −1171.34 | + | 1171.34i | −0.00250364 | + | 0.00250364i | ||||
\(685\) | 155066. | + | 268583.i | 0.330473 | + | 0.572397i | ||||
\(686\) | −44861.8 | − | 25901.0i | −0.0953298 | − | 0.0550387i | ||||
\(687\) | 122565. | + | 457420.i | 0.259689 | + | 0.969174i | ||||
\(688\) | 391387.i | 0.826856i | ||||||||
\(689\) | 353676. | − | 15985.2i | 0.745018 | − | 0.0336728i | ||||
\(690\) | 51697.6 | 0.108585 | ||||||||
\(691\) | −287965. | + | 77159.9i | −0.603091 | + | 0.161598i | −0.547429 | − | 0.836852i | \(-0.684394\pi\) |
−0.0556618 | + | 0.998450i | \(0.517727\pi\) | |||||||
\(692\) | −19862.4 | + | 34402.6i | −0.0414781 | + | 0.0718422i | ||||
\(693\) | −14095.2 | + | 8137.84i | −0.0293497 | + | 0.0169450i | ||||
\(694\) | −22213.8 | − | 22213.8i | −0.0461215 | − | 0.0461215i | ||||
\(695\) | −2339.02 | + | 8729.32i | −0.00484243 | + | 0.0180722i | ||||
\(696\) | −81587.4 | − | 21861.3i | −0.168424 | − | 0.0451291i | ||||
\(697\) | 605363. | − | 605363.i | 1.24609 | − | 1.24609i | ||||
\(698\) | −276291. | − | 478550.i | −0.567095 | − | 0.982238i | ||||
\(699\) | −732563. | − | 422946.i | −1.49931 | − | 0.865626i | ||||
\(700\) | −1300.69 | − | 4854.24i | −0.00265447 | − | 0.00990662i | ||||
\(701\) | 512051.i | 1.04202i | 0.853550 | + | 0.521011i | \(0.174445\pi\) | ||||
−0.853550 | + | 0.521011i | \(0.825555\pi\) | |||||||
\(702\) | −325785. | + | 103269.i | −0.661085 | + | 0.209554i | ||||
\(703\) | −455.515 | −0.000921705 | ||||||||
\(704\) | 912880. | − | 244606.i | 1.84191 | − | 0.493538i | ||||
\(705\) | 45341.5 | − | 78533.8i | 0.0912259 | − | 0.158008i | ||||
\(706\) | 331441. | − | 191357.i | 0.664961 | − | 0.383916i | ||||
\(707\) | −13527.8 | − | 13527.8i | −0.0270638 | − | 0.0270638i | ||||
\(708\) | 14878.3 | − | 55526.7i | 0.0296816 | − | 0.110773i | ||||
\(709\) | −819797. | − | 219664.i | −1.63085 | − | 0.436985i | −0.676686 | − | 0.736271i | \(-0.736585\pi\) |
−0.954163 | + | 0.299287i | \(0.903251\pi\) | |||||||
\(710\) | −31199.3 | + | 31199.3i | −0.0618911 | + | 0.0618911i | ||||
\(711\) | 104759. | + | 181448.i | 0.207230 | + | 0.358933i | ||||
\(712\) | −262342. | − | 151463.i | −0.517496 | − | 0.298777i | ||||
\(713\) | 44681.3 | + | 166753.i | 0.0878915 | + | 0.328015i | ||||
\(714\) | 54137.4i | 0.106194i | ||||||||
\(715\) | 197456. | − | 380734.i | 0.386242 | − | 0.744749i | ||||
\(716\) | 80650.8 | 0.157320 | ||||||||
\(717\) | 100883. | − | 27031.5i | 0.196236 | − | 0.0525813i | ||||
\(718\) | −394499. | + | 683293.i | −0.765239 | + | 1.32543i | ||||
\(719\) | −245795. | + | 141910.i | −0.475461 | + | 0.274508i | −0.718523 | − | 0.695503i | \(-0.755182\pi\) |
0.243062 | + | 0.970011i | \(0.421848\pi\) | |||||||
\(720\) | 41951.8 | + | 41951.8i | 0.0809256 | + | 0.0809256i | ||||
\(721\) | −10444.3 | + | 38978.7i | −0.0200914 | + | 0.0749820i | ||||
\(722\) | −444512. | − | 119107.i | −0.852726 | − | 0.228487i | ||||
\(723\) | 181577. | − | 181577.i | 0.347363 | − | 0.347363i | ||||
\(724\) | 64882.2 | + | 112379.i | 0.123779 | + | 0.214392i | ||||
\(725\) | 48833.1 | + | 28193.8i | 0.0929049 | + | 0.0536387i | ||||
\(726\) | 268516. | + | 1.00212e6i | 0.509444 | + | 1.90127i | ||||
\(727\) | − | 1.02808e6i | − | 1.94517i | −0.232538 | − | 0.972587i | \(-0.574703\pi\) | ||
0.232538 | − | 0.972587i | \(-0.425297\pi\) | |||||||
\(728\) | 29956.4 | − | 19149.0i | 0.0565233 | − | 0.0361313i | ||||
\(729\) | 272684. | 0.513102 | ||||||||
\(730\) | −305773. | + | 81931.5i | −0.573790 | + | 0.153747i | ||||
\(731\) | 503172. | − | 871520.i | 0.941633 | − | 1.63096i | ||||
\(732\) | 101864. | − | 58811.2i | 0.190107 | − | 0.109758i | ||||
\(733\) | −61040.7 | − | 61040.7i | −0.113609 | − | 0.113609i | 0.648017 | − | 0.761626i | \(-0.275599\pi\) |
−0.761626 | + | 0.648017i | \(0.775599\pi\) | |||||||
\(734\) | 42087.9 | − | 157074.i | 0.0781205 | − | 0.291550i | ||||
\(735\) | 292038. | + | 78251.4i | 0.540586 | + | 0.144850i | ||||
\(736\) | −35524.1 | + | 35524.1i | −0.0655794 | + | 0.0655794i | ||||
\(737\) | −126863. | − | 219733.i | −0.233560 | − | 0.404539i | ||||
\(738\) | 139186. | + | 80359.0i | 0.255554 | + | 0.147544i | ||||
\(739\) | 238112. | + | 888646.i | 0.436006 | + | 1.62720i | 0.738647 | + | 0.674092i | \(0.235465\pi\) |
−0.302641 | + | 0.953105i | \(0.597868\pi\) | |||||||
\(740\) | − | 1038.07i | − | 0.00189567i | ||||||
\(741\) | 23975.6 | + | 21902.1i | 0.0436650 | + | 0.0398886i | ||||
\(742\) | −22642.8 | −0.0411265 | ||||||||
\(743\) | 333151. | − | 89267.6i | 0.603481 | − | 0.161702i | 0.0558740 | − | 0.998438i | \(-0.482206\pi\) |
0.547607 | + | 0.836736i | \(0.315539\pi\) | |||||||
\(744\) | −532003. | + | 921456.i | −0.961099 | + | 1.66467i | ||||
\(745\) | −8494.07 | + | 4904.05i | −0.0153039 | + | 0.00883573i | ||||
\(746\) | 621707. | + | 621707.i | 1.11714 | + | 1.11714i | ||||
\(747\) | −12434.8 | + | 46407.4i | −0.0222843 | + | 0.0831661i | ||||
\(748\) | −336446. | − | 90150.4i | −0.601329 | − | 0.161126i | ||||
\(749\) | −22445.2 | + | 22445.2i | −0.0400092 | + | 0.0400092i | ||||
\(750\) | −246225. | − | 426474.i | −0.437733 | − | 0.758176i | ||||
\(751\) | −484025. | − | 279452.i | −0.858198 | − | 0.495481i | 0.00521022 | − | 0.999986i | \(-0.498342\pi\) |
−0.863409 | + | 0.504505i | \(0.831675\pi\) | |||||||
\(752\) | −35012.2 | − | 130667.i | −0.0619133 | − | 0.231064i | ||||
\(753\) | 108832.i | 0.191940i | ||||||||
\(754\) | −15260.1 | + | 69336.7i | −0.0268419 | + | 0.121961i | ||||
\(755\) | −329087. | −0.577320 | ||||||||
\(756\) | −5833.92 | + | 1563.19i | −0.0102074 | + | 0.00273508i | ||||
\(757\) | −313828. | + | 543567.i | −0.547647 | + | 0.948552i | 0.450788 | + | 0.892631i | \(0.351143\pi\) |
−0.998435 | + | 0.0559213i | \(0.982190\pi\) | |||||||
\(758\) | −206819. | + | 119407.i | −0.359959 | + | 0.207822i | ||||
\(759\) | −174965. | − | 174965.i | −0.303716 | − | 0.303716i | ||||
\(760\) | −4060.15 | + | 15152.7i | −0.00702935 | + | 0.0262339i | ||||
\(761\) | 532223. | + | 142609.i | 0.919018 | + | 0.246250i | 0.687166 | − | 0.726501i | \(-0.258855\pi\) |
0.231852 | + | 0.972751i | \(0.425521\pi\) | |||||||
\(762\) | −682155. | + | 682155.i | −1.17483 | + | 1.17483i | ||||
\(763\) | −10591.6 | − | 18345.1i | −0.0181933 | − | 0.0315117i | ||||
\(764\) | 160512. | + | 92671.9i | 0.274993 | + | 0.158767i | ||||
\(765\) | −39482.3 | − | 147350.i | −0.0674651 | − | 0.251783i | ||||
\(766\) | 111491.i | 0.190013i | ||||||||
\(767\) | −265155. | − | 58357.0i | −0.450722 | − | 0.0991978i | ||||
\(768\) | −417602. | −0.708011 | ||||||||
\(769\) | −1.02476e6 | + | 274583.i | −1.73288 | + | 0.464324i | −0.980844 | − | 0.194797i | \(-0.937595\pi\) |
−0.752037 | + | 0.659121i | \(0.770928\pi\) | |||||||
\(770\) | −13715.1 | + | 23755.2i | −0.0231322 | + | 0.0400661i | ||||
\(771\) | 835044. | − | 482113.i | 1.40475 | − | 0.811035i | ||||
\(772\) | 88303.5 | + | 88303.5i | 0.148164 | + | 0.148164i | ||||
\(773\) | −126326. | + | 471456.i | −0.211415 | + | 0.789010i | 0.775983 | + | 0.630753i | \(0.217254\pi\) |
−0.987398 | + | 0.158257i | \(0.949413\pi\) | |||||||
\(774\) | 182484. | + | 48896.4i | 0.304609 | + | 0.0816197i | ||||
\(775\) | 502266. | − | 502266.i | 0.836239 | − | 0.836239i | ||||
\(776\) | 228227. | + | 395301.i | 0.379004 | + | 0.656454i | ||||
\(777\) | 668.773 | + | 386.116i | 0.00110774 | + | 0.000639552i | ||||
\(778\) | −137911. | − | 514690.i | −0.227845 | − | 0.850328i | ||||
\(779\) | 32843.0i | 0.0541213i | ||||||||
\(780\) | −49912.4 | + | 54637.8i | −0.0820388 | + | 0.0898057i | ||||
\(781\) | 211181. | 0.346221 | ||||||||
\(782\) | −191536. | + | 51322.0i | −0.313211 | + | 0.0839247i | ||||
\(783\) | 33883.9 | − | 58688.6i | 0.0552675 | − | 0.0957260i | ||||
\(784\) | 390592. | − | 225509.i | 0.635465 | − | 0.366886i | ||||
\(785\) | 79659.2 | + | 79659.2i | 0.129270 | + | 0.129270i | ||||
\(786\) | 171168. | − | 638808.i | 0.277062 | − | 1.03401i | ||||
\(787\) | −582792. | − | 156159.i | −0.940944 | − | 0.252125i | −0.244429 | − | 0.969667i | \(-0.578601\pi\) |
−0.696515 | + | 0.717542i | \(0.745267\pi\) | |||||||
\(788\) | 111359. | − | 111359.i | 0.179338 | − | 0.179338i | ||||
\(789\) | −441355. | − | 764449.i | −0.708980 | − | 1.22799i | ||||
\(790\) | 305803. | + | 176555.i | 0.489990 | + | 0.282896i | ||||
\(791\) | −11008.4 | − | 41083.9i | −0.0175943 | − | 0.0656627i | ||||
\(792\) | − | 367420.i | − | 0.585750i | ||||||
\(793\) | −299201. | − | 468066.i | −0.475791 | − | 0.744322i | ||||
\(794\) | 576594. | 0.914596 | ||||||||
\(795\) | 255799. | − | 68541.1i | 0.404729 | − | 0.108447i | ||||
\(796\) | −18153.2 | + | 31442.2i | −0.0286501 | + | 0.0496234i | ||||
\(797\) | 782111. | − | 451552.i | 1.23127 | − | 0.710872i | 0.263972 | − | 0.964530i | \(-0.414967\pi\) |
0.967294 | + | 0.253659i | \(0.0816341\pi\) | |||||||
\(798\) | −1468.57 | − | 1468.57i | −0.00230616 | − | 0.00230616i | ||||
\(799\) | −90024.2 | + | 335975.i | −0.141015 | + | 0.526276i | ||||
\(800\) | 199665. | + | 53500.0i | 0.311976 | + | 0.0835937i | ||||
\(801\) | −79908.6 | + | 79908.6i | −0.124546 | + | 0.124546i | ||||
\(802\) | −224622. | − | 389057.i | −0.349224 | − | 0.604873i | ||||
\(803\) | 1.31214e6 | + | 757566.i | 2.03493 | + | 1.17487i | ||||
\(804\) | 11331.0 | + | 42287.7i | 0.0175289 | + | 0.0654187i | ||||
\(805\) | − | 4314.96i | − | 0.00665864i | ||||||
\(806\) | 793915. | + | 411740.i | 1.22209 | + | 0.633801i | ||||
\(807\) | −645207. | −0.990722 | ||||||||
\(808\) | 417167. | − | 111780.i | 0.638980 | − | 0.171214i | ||||
\(809\) | 565491. | − | 979460.i | 0.864030 | − | 1.49654i | −0.00397645 | − | 0.999992i | \(-0.501266\pi\) |
0.868007 | − | 0.496552i | \(-0.165401\pi\) | |||||||
\(810\) | −299530. | + | 172934.i | −0.456531 | + | 0.263578i | ||||
\(811\) | 268656. | + | 268656.i | 0.408465 | + | 0.408465i | 0.881203 | − | 0.472738i | \(-0.156734\pi\) |
−0.472738 | + | 0.881203i | \(0.656734\pi\) | |||||||
\(812\) | −324.732 | + | 1211.92i | −0.000492508 | + | 0.00183806i | ||||
\(813\) | 1.01704e6 | + | 272514.i | 1.53870 | + | 0.412295i | ||||
\(814\) | 12714.3 | − | 12714.3i | 0.0191887 | − | 0.0191887i | ||||
\(815\) | −121729. | − | 210840.i | −0.183264 | − | 0.317423i | ||||
\(816\) | −817995. | − | 472270.i | −1.22849 | − | 0.709267i | ||||
\(817\) | 9992.07 | + | 37290.9i | 0.0149696 | + | 0.0558674i | ||||
\(818\) | − | 539172.i | − | 0.805788i | ||||||
\(819\) | −4007.80 | − | 12643.5i | −0.00597500 | − | 0.0188495i | ||||
\(820\) | −74845.7 | −0.111311 | ||||||||
\(821\) | −989836. | + | 265226.i | −1.46851 | + | 0.393486i | −0.902420 | − | 0.430858i | \(-0.858211\pi\) |
−0.566090 | + | 0.824344i | \(0.691544\pi\) | |||||||
\(822\) | 463453. | − | 802724.i | 0.685902 | − | 1.18802i | ||||
\(823\) | −636907. | + | 367719.i | −0.940322 | + | 0.542895i | −0.890061 | − | 0.455841i | \(-0.849339\pi\) |
−0.0502608 | + | 0.998736i | \(0.516005\pi\) | |||||||
\(824\) | −644158. | − | 644158.i | −0.948720 | − | 0.948720i | ||||
\(825\) | −263500. | + | 983396.i | −0.387145 | + | 1.44484i | ||||
\(826\) | 16772.4 | + | 4494.15i | 0.0245830 | + | 0.00658700i | ||||
\(827\) | −699704. | + | 699704.i | −1.02307 | + | 1.02307i | −0.0233382 | + | 0.999728i | \(0.507429\pi\) |
−0.999728 | + | 0.0233382i | \(0.992571\pi\) | |||||||
\(828\) | 5143.09 | + | 8908.10i | 0.00750177 | + | 0.0129934i | ||||
\(829\) | 492127. | + | 284130.i | 0.716091 | + | 0.413435i | 0.813312 | − | 0.581828i | \(-0.197662\pi\) |
−0.0972215 | + | 0.995263i | \(0.530996\pi\) | |||||||
\(830\) | 20957.0 | + | 78212.5i | 0.0304209 | + | 0.113532i | ||||
\(831\) | − | 561588.i | − | 0.813235i | ||||||
\(832\) | 34774.3 | + | 769388.i | 0.0502356 | + | 1.11147i | ||||
\(833\) | −1.15967e6 | −1.67126 | ||||||||
\(834\) | 26089.7 | − | 6990.71i | 0.0375091 | − | 0.0100505i | ||||
\(835\) | −251577. | + | 435745.i | −0.360827 | + | 0.624970i | ||||
\(836\) | 11572.2 | − | 6681.19i | 0.0165578 | − | 0.00955964i | ||||
\(837\) | −603633. | − | 603633.i | −0.861632 | − | 0.861632i | ||||
\(838\) | −68684.5 | + | 256334.i | −0.0978072 | + | 0.365021i | ||||
\(839\) | −1.23115e6 | − | 329887.i | −1.74900 | − | 0.468642i | −0.764585 | − | 0.644523i | \(-0.777056\pi\) |
−0.984411 | + | 0.175881i | \(0.943722\pi\) | |||||||
\(840\) | 18805.1 | − | 18805.1i | 0.0266513 | − | 0.0266513i | ||||
\(841\) | 346602. | + | 600332.i | 0.490048 | + | 0.848788i | ||||
\(842\) | 901724. | + | 520611.i | 1.27189 | + | 0.734326i | ||||
\(843\) | 181541. | + | 677522.i | 0.255459 | + | 0.953385i | ||||
\(844\) | − | 70591.3i | − | 0.0990984i | ||||||
\(845\) | 268432. | + | 223842.i | 0.375942 | + | 0.313493i | ||||
\(846\) | −65297.6 | −0.0912339 | ||||||||
\(847\) | 83642.1 | − | 22411.8i | 0.116589 | − | 0.0312400i | ||||
\(848\) | 197525. | − | 342123.i | 0.274682 | − | 0.475763i | ||||
\(849\) | −436178. | + | 251828.i | −0.605130 | + | 0.349372i | ||||
\(850\) | 576914. | + | 576914.i | 0.798497 | + | 0.798497i | ||||
\(851\) | −732.072 | + | 2732.13i | −0.00101087 | + | 0.00377261i | ||||
\(852\) | −35197.0 | − | 9430.99i | −0.0484871 | − | 0.0129921i | ||||
\(853\) | 784615. | − | 784615.i | 1.07835 | − | 1.07835i | 0.0816891 | − | 0.996658i | \(-0.473969\pi\) |
0.996658 | − | 0.0816891i | \(-0.0260314\pi\) | |||||||
\(854\) | 17764.5 | + | 30769.1i | 0.0243578 | + | 0.0421890i | ||||
\(855\) | 5068.14 | + | 2926.09i | 0.00693293 | + | 0.00400273i | ||||
\(856\) | −185464. | − | 692160.i | −0.253111 | − | 0.944624i | ||||
\(857\) | 690735.i | 0.940480i | 0.882539 | + | 0.470240i | \(0.155833\pi\) | ||||
−0.882539 | + | 0.470240i | \(0.844167\pi\) | |||||||
\(858\) | −1.28054e6 | + | 57876.8i | −1.73947 | + | 0.0786195i | ||||
\(859\) | 1.01145e6 | 1.37075 | 0.685376 | − | 0.728189i | \(-0.259638\pi\) | ||||
0.685376 | + | 0.728189i | \(0.259638\pi\) | |||||||
\(860\) | −84981.9 | + | 22770.8i | −0.114903 | + | 0.0307881i | ||||
\(861\) | 27839.3 | − | 48219.1i | 0.0375537 | − | 0.0650449i | ||||
\(862\) | −793034. | + | 457858.i | −1.06728 | + | 0.616193i | ||||
\(863\) | 781879. | + | 781879.i | 1.04983 | + | 1.04983i | 0.998692 | + | 0.0511362i | \(0.0162843\pi\) |
0.0511362 | + | 0.998692i | \(0.483716\pi\) | |||||||
\(864\) | 64297.3 | − | 239961.i | 0.0861322 | − | 0.321450i | ||||
\(865\) | 135557. | + | 36322.5i | 0.181172 | + | 0.0485449i | ||||
\(866\) | −322526. | + | 322526.i | −0.430059 | + | 0.430059i | ||||
\(867\) | 782925. | + | 1.35607e6i | 1.04155 | + | 1.80403i | ||||
\(868\) | 13687.5 | + | 7902.48i | 0.0181671 | + | 0.0104888i | ||||
\(869\) | −437424. | − | 1.63249e6i | −0.579246 | − | 2.16177i | ||||
\(870\) | 53105.6i | 0.0701620i | ||||||||
\(871\) | 197102. | − | 62478.6i | 0.259810 | − | 0.0823559i | ||||
\(872\) | 478205. | 0.628899 | ||||||||
\(873\) | 164480. | − | 44072.3i | 0.215816 | − | 0.0578278i | ||||
\(874\) | 3803.55 | − | 6587.95i | 0.00497928 | − | 0.00862437i | ||||
\(875\) | −35595.9 | + | 20551.3i | −0.0464926 | + | 0.0268425i | ||||
\(876\) | −184859. | − | 184859.i | −0.240898 | − | 0.240898i | ||||
\(877\) | 372128. | − | 1.38880e6i | 0.483830 | − | 1.80568i | −0.101442 | − | 0.994841i | \(-0.532346\pi\) |
0.585272 | − | 0.810837i | \(-0.300988\pi\) | |||||||
\(878\) | −599097. | − | 160528.i | −0.777156 | − | 0.208238i | ||||
\(879\) | 114294. | − | 114294.i | 0.147926 | − | 0.147926i | ||||
\(880\) | −239288. | − | 414458.i | −0.308997 | − | 0.535199i | ||||
\(881\) | −468896. | − | 270717.i | −0.604122 | − | 0.348790i | 0.166540 | − | 0.986035i | \(-0.446741\pi\) |
−0.770661 | + | 0.637245i | \(0.780074\pi\) | |||||||
\(882\) | −56346.0 | − | 210286.i | −0.0724312 | − | 0.270317i | ||||
\(883\) | − | 312491.i | − | 0.400790i | −0.979715 | − | 0.200395i | \(-0.935778\pi\) | ||
0.979715 | − | 0.200395i | \(-0.0642225\pi\) | |||||||
\(884\) | 130682. | − | 251979.i | 0.167228 | − | 0.322449i | ||||
\(885\) | −203085. | −0.259293 | ||||||||
\(886\) | −14041.9 | + | 3762.51i | −0.0178879 | + | 0.00479304i | ||||
\(887\) | −415042. | + | 718874.i | −0.527527 | + | 0.913703i | 0.471958 | + | 0.881621i | \(0.343547\pi\) |
−0.999485 | + | 0.0320825i | \(0.989786\pi\) | |||||||
\(888\) | −15097.4 | + | 8716.50i | −0.0191459 | + | 0.0110539i | ||||
\(889\) | 56936.4 | + | 56936.4i | 0.0720422 | + | 0.0720422i | ||||
\(890\) | −49294.0 | + | 183968.i | −0.0622320 | + | 0.232253i | ||||
\(891\) | 1.59900e6 | + | 428452.i | 2.01416 | + | 0.539692i | ||||
\(892\) | −17046.9 | + | 17046.9i | −0.0214247 | + | 0.0214247i | ||||
\(893\) | −6671.84 | − | 11556.0i | −0.00836648 | − | 0.0144912i | ||||
\(894\) | 25386.6 | + | 14656.9i | 0.0317635 | + | 0.0183387i | ||||
\(895\) | −73743.5 | − | 275215.i | −0.0920614 | − | 0.343578i | ||||
\(896\) | − | 28012.6i | − | 0.0348929i | ||||||
\(897\) | 169898. | − | 108604.i | 0.211156 | − | 0.134977i | ||||
\(898\) | 714076. | 0.885507 | ||||||||
\(899\) | −171295. | + | 45898.2i | −0.211945 | + | 0.0567906i | ||||
\(900\) | 21161.4 | − | 36652.6i | 0.0261251 | − | 0.0452501i | ||||
\(901\) | −879675. | + | 507881.i | −1.08361 | + | 0.625622i | ||||
\(902\) | −916714. | − | 916714.i | −1.12673 | − | 1.12673i | ||||
\(903\) | 16939.5 | − | 63219.1i | 0.0207743 | − | 0.0775306i | ||||
\(904\) | 927460. | + | 248512.i | 1.13490 | + | 0.304096i | ||||
\(905\) | 324160. | − | 324160.i | 0.395788 | − | 0.395788i | ||||
\(906\) | 491777. | + | 851783.i | 0.599117 | + | 1.03770i | ||||
\(907\) | −730442. | − | 421721.i | −0.887914 | − | 0.512638i | −0.0146546 | − | 0.999893i | \(-0.504665\pi\) |
−0.873260 | + | 0.487255i | \(0.837998\pi\) | |||||||
\(908\) | 36154.3 | + | 134930.i | 0.0438518 | + | 0.163657i | ||||
\(909\) | − | 161116.i | − | 0.194989i | ||||||
\(910\) | −16503.9 | − | 15076.6i | −0.0199299 | − | 0.0182062i | ||||
\(911\) | −628593. | −0.757413 | −0.378706 | − | 0.925517i | \(-0.623631\pi\) | ||||
−0.378706 | + | 0.925517i | \(0.623631\pi\) | |||||||
\(912\) | 35000.7 | − | 9378.40i | 0.0420810 | − | 0.0112756i | ||||
\(913\) | 193775. | − | 335628.i | 0.232464 | − | 0.402640i | ||||
\(914\) | −220432. | + | 127266.i | −0.263865 | + | 0.152343i | ||||
\(915\) | −293829. | − | 293829.i | −0.350955 | − | 0.350955i | ||||
\(916\) | −41099.9 | + | 153387.i | −0.0489835 | + | 0.182809i | ||||
\(917\) | −53318.4 | − | 14286.6i | −0.0634072 | − | 0.0169899i | ||||
\(918\) | 693347. | − | 693347.i | 0.822745 | − | 0.822745i | ||||
\(919\) | 145322. | + | 251706.i | 0.172069 | + | 0.298031i | 0.939143 | − | 0.343527i | \(-0.111622\pi\) |
−0.767074 | + | 0.641558i | \(0.778288\pi\) | |||||||
\(920\) | 84359.0 | + | 48704.7i | 0.0996681 | + | 0.0575434i | ||||
\(921\) | −204650. | − | 763766.i | −0.241264 | − | 0.900411i | ||||
\(922\) | 739291.i | 0.869669i | ||||||||
\(923\) | −36991.0 | + | 168075.i | −0.0434203 | + | 0.197287i | ||||
\(924\) | −22653.2 | −0.0265330 | ||||||||
\(925\) | 11241.4 | − | 3012.12i | 0.0131382 | − | 0.00352038i | ||||
\(926\) | 524215. | − | 907967.i | 0.611346 | − | 1.05888i | ||||
\(927\) | −294314. | + | 169922.i | −0.342492 | + | 0.197738i | ||||
\(928\) | −36491.7 | − | 36491.7i | −0.0423738 | − | 0.0423738i | ||||
\(929\) | 51907.6 | − | 193722.i | 0.0601450 | − | 0.224464i | −0.929311 | − | 0.369298i | \(-0.879598\pi\) |
0.989456 | + | 0.144834i | \(0.0462648\pi\) | |||||||
\(930\) | 646173. | + | 173142.i | 0.747107 | + | 0.200187i | ||||
\(931\) | 31458.0 | − | 31458.0i | 0.0362937 | − | 0.0362937i | ||||
\(932\) | −141827. | − | 245651.i | −0.163277 | − | 0.282805i | ||||
\(933\) | 560900. | + | 323836.i | 0.644350 | + | 0.372016i | ||||
\(934\) | 148260. | + | 553314.i | 0.169954 | + | 0.634276i | ||||
\(935\) | 1.23052e6i | 1.40756i | ||||||||
\(936\) | 292422. | + | 64358.2i | 0.333779 | + | 0.0734602i | ||||
\(937\) | 968618. | 1.10325 | 0.551624 | − | 0.834093i | \(-0.314008\pi\) | ||||
0.551624 | + | 0.834093i | \(0.314008\pi\) | |||||||
\(938\) | −12773.4 | + | 3422.63i | −0.0145178 | + | 0.00389004i | ||||
\(939\) | −528562. | + | 915495.i | −0.599466 | + | 1.03831i | ||||
\(940\) | 26334.8 | − | 15204.4i | 0.0298040 | − | 0.0172073i | ||||
\(941\) | −694217. | − | 694217.i | −0.784000 | − | 0.784000i | 0.196503 | − | 0.980503i | \(-0.437041\pi\) |
−0.980503 | + | 0.196503i | \(0.937041\pi\) | |||||||
\(942\) | 87143.5 | − | 325224.i | 0.0982050 | − | 0.366506i | ||||
\(943\) | 196989. | + | 52783.0i | 0.221523 | + | 0.0593569i | ||||
\(944\) | −214219. | + | 214219.i | −0.240389 | + | 0.240389i | ||||
\(945\) | 10668.6 | + | 18478.5i | 0.0119465 | + | 0.0206920i | ||||
\(946\) | −1.31976e6 | − | 761965.i | −1.47473 | − | 0.851437i | ||||
\(947\) | −175682. | − | 655655.i | −0.195897 | − | 0.731098i | −0.992033 | − | 0.125980i | \(-0.959793\pi\) |
0.796136 | − | 0.605118i | \(-0.206874\pi\) | |||||||
\(948\) | 291616.i | 0.324486i | ||||||||
\(949\) | −832769. | + | 911610.i | −0.924681 | + | 1.01222i | ||||
\(950\) | −31299.6 | −0.0346810 | ||||||||
\(951\) | 662706. | − | 177572.i | 0.732757 | − | 0.196342i | ||||
\(952\) | −51003.4 | + | 88340.4i | −0.0562762 | + | 0.0974733i | ||||
\(953\) | −447722. | + | 258492.i | −0.492972 | + | 0.284618i | −0.725807 | − | 0.687899i | \(-0.758533\pi\) |
0.232834 | + | 0.972516i | \(0.425200\pi\) | |||||||
\(954\) | −134837. | − | 134837.i | −0.148154 | − | 0.148154i | ||||
\(955\) | 169470. | − | 632471.i | 0.185817 | − | 0.693480i | ||||
\(956\) | 33829.1 | + | 9064.49i | 0.0370148 | + | 0.00991808i | ||||
\(957\) | 179730. | − | 179730.i | 0.196244 | − | 0.196244i | ||||
\(958\) | −177050. | − | 306660.i | −0.192915 | − | 0.334138i | ||||
\(959\) | −66999.8 | − | 38682.3i | −0.0728511 | − | 0.0420606i | ||||
\(960\) | 149105. | + | 556466.i | 0.161789 | + | 0.603804i | ||||
\(961\) | 1.31038e6i | 1.41890i | ||||||||
\(962\) | 7892.00 | + | 12346.1i | 0.00852780 | + | 0.0133408i | ||||
\(963\) | −267322. | −0.288258 | ||||||||
\(964\) | 83174.9 | − | 22286.7i | 0.0895032 | − | 0.0239823i | ||||
\(965\) | 220588. | − | 382069.i | 0.236879 | − | 0.410287i | ||||
\(966\) | −11168.5 | + | 6448.15i | −0.0119686 | + | 0.00691005i | ||||
\(967\) | −508744. | − | 508744.i | −0.544060 | − | 0.544060i | 0.380657 | − | 0.924716i | \(-0.375698\pi\) |
−0.924716 | + | 0.380657i | \(0.875698\pi\) | |||||||
\(968\) | −505942. | + | 1.88820e6i | −0.539946 | + | 2.01511i | ||||
\(969\) | −89994.5 | − | 24114.0i | −0.0958448 | − | 0.0256815i | ||||
\(970\) | 202928. | − | 202928.i | 0.215675 | − | 0.215675i | ||||
\(971\) | 250029. | + | 433063.i | 0.265187 | + | 0.459317i | 0.967613 | − | 0.252440i | \(-0.0812330\pi\) |
−0.702426 | + | 0.711757i | \(0.747900\pi\) | |||||||
\(972\) | −108581. | − | 62689.5i | −0.114927 | − | 0.0663533i | ||||
\(973\) | −583.483 | − | 2177.59i | −0.000616315 | − | 0.00230012i | ||||
\(974\) | − | 564275.i | − | 0.594803i | ||||||
\(975\) | −736510. | − | 381968.i | −0.774764 | − | 0.401808i | ||||
\(976\) | −619878. | −0.650738 | ||||||||
\(977\) | 625260. | − | 167538.i | 0.655046 | − | 0.175519i | 0.0840367 | − | 0.996463i | \(-0.473219\pi\) |
0.571009 | + | 0.820944i | \(0.306552\pi\) | |||||||
\(978\) | −363815. | + | 630146.i | −0.380367 | + | 0.658815i | ||||
\(979\) | 789448. | − | 455788.i | 0.823680 | − | 0.475552i | ||||
\(980\) | 71689.3 | + | 71689.3i | 0.0746452 | + | 0.0746452i | ||||
\(981\) | 46172.4 | − | 172318.i | 0.0479783 | − | 0.179057i | ||||
\(982\) | 174978. | + | 46885.3i | 0.181452 | + | 0.0486198i | ||||
\(983\) | −331095. | + | 331095.i | −0.342646 | + | 0.342646i | −0.857361 | − | 0.514715i | \(-0.827898\pi\) |
0.514715 | + | 0.857361i | \(0.327898\pi\) | |||||||
\(984\) | 628467. | + | 1.08854e6i | 0.649071 | + | 1.12422i | ||||
\(985\) | −481826. | − | 278182.i | −0.496613 | − | 0.286719i | ||||
\(986\) | −52719.8 | − | 196753.i | −0.0542275 | − | 0.202380i | ||||
\(987\) | 22621.5i | 0.0232213i | ||||||||
\(988\) | 3290.42 | + | 10380.3i | 0.00337083 | + | 0.0106340i | ||||
\(989\) | 239725. | 0.245088 | ||||||||
\(990\) | −223135. | + | 59788.9i | −0.227666 | + | 0.0610028i | ||||
\(991\) | 396282. | − | 686381.i | 0.403513 | − | 0.698904i | −0.590635 | − | 0.806939i | \(-0.701122\pi\) |
0.994147 | + | 0.108035i | \(0.0344558\pi\) | |||||||
\(992\) | −562994. | + | 325045.i | −0.572111 | + | 0.330309i | ||||
\(993\) | −54620.3 | − | 54620.3i | −0.0553931 | − | 0.0553931i | ||||
\(994\) | 2848.73 | − | 10631.6i | 0.00288322 | − | 0.0107603i | ||||
\(995\) | 123892. | + | 33196.9i | 0.125141 | + | 0.0335313i | ||||
\(996\) | −47284.5 | + | 47284.5i | −0.0476651 | + | 0.0476651i | ||||
\(997\) | 508715. | + | 881120.i | 0.511781 | + | 0.886431i | 0.999907 | + | 0.0136575i | \(0.00434746\pi\) |
−0.488126 | + | 0.872773i | \(0.662319\pi\) | |||||||
\(998\) | 647093. | + | 373599.i | 0.649689 | + | 0.375098i | ||||
\(999\) | −3620.03 | − | 13510.1i | −0.00362728 | − | 0.0135372i |
(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 | 13.5.f.a.7.2 | yes | 16 | |
3.2 | odd | 2 | 117.5.bd.c.46.3 | 16 | |||
13.2 | odd | 12 | inner | 13.5.f.a.2.2 | ✓ | 16 | |
13.4 | even | 6 | 169.5.d.c.99.3 | 16 | |||
13.6 | odd | 12 | 169.5.d.d.70.6 | 16 | |||
13.7 | odd | 12 | 169.5.d.c.70.3 | 16 | |||
13.9 | even | 3 | 169.5.d.d.99.6 | 16 | |||
39.2 | even | 12 | 117.5.bd.c.28.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.5.f.a.2.2 | ✓ | 16 | 13.2 | odd | 12 | inner | |
13.5.f.a.7.2 | yes | 16 | 1.1 | even | 1 | trivial | |
117.5.bd.c.28.3 | 16 | 39.2 | even | 12 | |||
117.5.bd.c.46.3 | 16 | 3.2 | odd | 2 | |||
169.5.d.c.70.3 | 16 | 13.7 | odd | 12 | |||
169.5.d.c.99.3 | 16 | 13.4 | even | 6 | |||
169.5.d.d.70.6 | 16 | 13.6 | odd | 12 | |||
169.5.d.d.99.6 | 16 | 13.9 | even | 3 |