Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [36,5,Mod(7,36)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(36, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("36.7");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 36.f (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.72131867102\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.20 | ||
Character | \(\chi\) | \(=\) | 36.31 |
Dual form | 36.5.f.a.7.20 |
$q$-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 \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).
\(n\) | \(19\) | \(29\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.68138 | + | 1.56444i | 0.920344 | + | 0.391110i | ||||
\(3\) | 4.25251 | − | 7.93197i | 0.472501 | − | 0.881330i | ||||
\(4\) | 11.1051 | + | 11.5186i | 0.694066 | + | 0.719911i | ||||
\(5\) | 1.01545 | − | 1.75881i | 0.0406181 | − | 0.0703525i | −0.845002 | − | 0.534764i | \(-0.820401\pi\) |
0.885620 | + | 0.464411i | \(0.153734\pi\) | |||||||
\(6\) | 28.0642 | − | 22.5478i | 0.779560 | − | 0.626327i | ||||
\(7\) | 20.0352 | − | 11.5673i | 0.408882 | − | 0.236068i | −0.281427 | − | 0.959583i | \(-0.590808\pi\) |
0.690309 | + | 0.723514i | \(0.257474\pi\) | |||||||
\(8\) | 22.8618 | + | 59.7774i | 0.357216 | + | 0.934022i | ||||
\(9\) | −44.8324 | − | 67.4615i | −0.553486 | − | 0.832859i | ||||
\(10\) | 6.48981 | − | 4.88624i | 0.0648981 | − | 0.0488624i | ||||
\(11\) | 4.32958 | − | 2.49968i | 0.0357816 | − | 0.0206585i | −0.482002 | − | 0.876170i | \(-0.660090\pi\) |
0.517784 | + | 0.855511i | \(0.326757\pi\) | |||||||
\(12\) | 138.589 | − | 39.1022i | 0.962426 | − | 0.271543i | ||||
\(13\) | −137.824 | + | 238.718i | −0.815527 | + | 1.41253i | 0.0934218 | + | 0.995627i | \(0.470219\pi\) |
−0.908949 | + | 0.416908i | \(0.863114\pi\) | |||||||
\(14\) | 91.8536 | − | 11.2399i | 0.468641 | − | 0.0573462i | ||||
\(15\) | −9.63264 | − | 15.5339i | −0.0428117 | − | 0.0690395i | ||||
\(16\) | −9.35520 | + | 255.829i | −0.0365438 | + | 0.999332i | ||||
\(17\) | −266.009 | −0.920447 | −0.460224 | − | 0.887803i | \(-0.652231\pi\) | ||||
−0.460224 | + | 0.887803i | \(0.652231\pi\) | |||||||
\(18\) | −59.5053 | − | 318.489i | −0.183658 | − | 0.982990i | ||||
\(19\) | − | 367.194i | − | 1.01716i | −0.861015 | − | 0.508579i | \(-0.830171\pi\) | ||
0.861015 | − | 0.508579i | \(-0.169829\pi\) | |||||||
\(20\) | 31.5357 | − | 7.83518i | 0.0788392 | − | 0.0195879i | ||||
\(21\) | −6.55189 | − | 208.109i | −0.0148569 | − | 0.471902i | ||||
\(22\) | 19.8494 | − | 2.42891i | 0.0410111 | − | 0.00501841i | ||||
\(23\) | −544.473 | − | 314.352i | −1.02925 | − | 0.594238i | −0.112481 | − | 0.993654i | \(-0.535880\pi\) |
−0.916770 | + | 0.399416i | \(0.869213\pi\) | |||||||
\(24\) | 571.373 | + | 72.8647i | 0.991966 | + | 0.126501i | ||||
\(25\) | 310.438 | + | 537.694i | 0.496700 | + | 0.860310i | ||||
\(26\) | −880.842 | + | 663.194i | −1.30302 | + | 0.981057i | ||||
\(27\) | −725.753 | + | 68.7283i | −0.995546 | + | 0.0942775i | ||||
\(28\) | 355.732 | + | 102.321i | 0.453739 | + | 0.130512i | ||||
\(29\) | −319.481 | − | 553.357i | −0.379882 | − | 0.657975i | 0.611163 | − | 0.791505i | \(-0.290702\pi\) |
−0.991045 | + | 0.133530i | \(0.957369\pi\) | |||||||
\(30\) | −11.1595 | − | 72.2558i | −0.0123995 | − | 0.0802842i | ||||
\(31\) | 1191.19 | + | 687.735i | 1.23953 | + | 0.715645i | 0.968999 | − | 0.247065i | \(-0.0794660\pi\) |
0.270535 | + | 0.962710i | \(0.412799\pi\) | |||||||
\(32\) | −434.669 | + | 927.167i | −0.424481 | + | 0.905437i | ||||
\(33\) | −1.41585 | − | 44.9720i | −0.00130014 | − | 0.0412966i | ||||
\(34\) | −979.280 | − | 416.155i | −0.847128 | − | 0.359996i | ||||
\(35\) | − | 46.9843i | − | 0.0383545i | ||||||
\(36\) | 279.195 | − | 1265.57i | 0.215428 | − | 0.976520i | ||||
\(37\) | 1466.19 | 1.07099 | 0.535496 | − | 0.844538i | \(-0.320125\pi\) | ||||
0.535496 | + | 0.844538i | \(0.320125\pi\) | |||||||
\(38\) | 574.453 | − | 1351.78i | 0.397820 | − | 0.936135i | ||||
\(39\) | 1307.41 | + | 2108.37i | 0.859572 | + | 1.38617i | ||||
\(40\) | 128.352 | + | 20.4914i | 0.0802202 | + | 0.0128071i | ||||
\(41\) | 593.019 | − | 1027.14i | 0.352777 | − | 0.611028i | −0.633958 | − | 0.773368i | \(-0.718571\pi\) |
0.986735 | + | 0.162339i | \(0.0519040\pi\) | |||||||
\(42\) | 301.454 | − | 776.378i | 0.170892 | − | 0.440123i | ||||
\(43\) | 1430.33 | − | 825.804i | 0.773572 | − | 0.446622i | −0.0605755 | − | 0.998164i | \(-0.519294\pi\) |
0.834147 | + | 0.551542i | \(0.185960\pi\) | |||||||
\(44\) | 76.8730 | + | 22.1114i | 0.0397071 | + | 0.0114212i | ||||
\(45\) | −164.177 | + | 10.3478i | −0.0810752 | + | 0.00511004i | ||||
\(46\) | −1512.63 | − | 2009.04i | −0.714852 | − | 0.949453i | ||||
\(47\) | 307.864 | − | 177.745i | 0.139368 | − | 0.0804642i | −0.428695 | − | 0.903449i | \(-0.641026\pi\) |
0.568063 | + | 0.822985i | \(0.307693\pi\) | |||||||
\(48\) | 1989.45 | + | 1162.12i | 0.863475 | + | 0.504392i | ||||
\(49\) | −932.893 | + | 1615.82i | −0.388544 | + | 0.672977i | ||||
\(50\) | 301.649 | + | 2465.11i | 0.120660 | + | 0.986046i | ||||
\(51\) | −1131.21 | + | 2109.98i | −0.434912 | + | 0.811218i | ||||
\(52\) | −4280.24 | + | 1063.44i | −1.58293 | + | 0.393286i | ||||
\(53\) | 5297.49 | 1.88590 | 0.942950 | − | 0.332934i | \(-0.108039\pi\) | ||||
0.942950 | + | 0.332934i | \(0.108039\pi\) | |||||||
\(54\) | −2779.29 | − | 882.381i | −0.953118 | − | 0.302600i | ||||
\(55\) | − | 10.1532i | − | 0.00335644i | ||||||
\(56\) | 1149.51 | + | 933.203i | 0.366552 | + | 0.297578i | ||||
\(57\) | −2912.57 | − | 1561.50i | −0.896452 | − | 0.480608i | ||||
\(58\) | −310.436 | − | 2536.92i | −0.0922818 | − | 0.754139i | ||||
\(59\) | −5223.32 | − | 3015.68i | −1.50052 | − | 0.866327i | −1.00000 | 0.000603027i | \(-0.999808\pi\) | |
−0.500522 | − | 0.865724i | \(-0.666859\pi\) | |||||||
\(60\) | 71.9573 | − | 283.459i | 0.0199881 | − | 0.0787387i | ||||
\(61\) | −833.364 | − | 1443.43i | −0.223962 | − | 0.387914i | 0.732045 | − | 0.681256i | \(-0.238566\pi\) |
−0.956008 | + | 0.293342i | \(0.905233\pi\) | |||||||
\(62\) | 3309.31 | + | 4395.36i | 0.860902 | + | 1.14343i | ||||
\(63\) | −1678.58 | − | 833.016i | −0.422922 | − | 0.209880i | ||||
\(64\) | −3050.68 | + | 2733.24i | −0.744794 | + | 0.667295i | ||||
\(65\) | 279.907 | + | 484.814i | 0.0662502 | + | 0.114749i | ||||
\(66\) | 65.1436 | − | 167.774i | 0.0149549 | − | 0.0385156i | ||||
\(67\) | −1908.36 | − | 1101.79i | −0.425119 | − | 0.245443i | 0.272146 | − | 0.962256i | \(-0.412267\pi\) |
−0.697265 | + | 0.716813i | \(0.745600\pi\) | |||||||
\(68\) | −2954.05 | − | 3064.05i | −0.638852 | − | 0.662640i | ||||
\(69\) | −4808.81 | + | 2981.96i | −1.01004 | + | 0.626332i | ||||
\(70\) | 73.5040 | − | 172.967i | 0.0150008 | − | 0.0352993i | ||||
\(71\) | 524.299i | 0.104007i | 0.998647 | + | 0.0520035i | \(0.0165607\pi\) | ||||
−0.998647 | + | 0.0520035i | \(0.983439\pi\) | |||||||
\(72\) | 3007.73 | − | 4222.25i | 0.580194 | − | 0.814478i | ||||
\(73\) | −1492.29 | −0.280032 | −0.140016 | − | 0.990149i | \(-0.544715\pi\) | ||||
−0.140016 | + | 0.990149i | \(0.544715\pi\) | |||||||
\(74\) | 5397.59 | + | 2293.76i | 0.985680 | + | 0.418875i | ||||
\(75\) | 5585.11 | − | 175.836i | 0.992909 | − | 0.0312597i | ||||
\(76\) | 4229.55 | − | 4077.71i | 0.732263 | − | 0.705975i | ||||
\(77\) | 57.8293 | − | 100.163i | 0.00975364 | − | 0.0168938i | ||||
\(78\) | 1514.65 | + | 9807.06i | 0.248956 | + | 1.61194i | ||||
\(79\) | 4448.35 | − | 2568.25i | 0.712762 | − | 0.411513i | −0.0993209 | − | 0.995055i | \(-0.531667\pi\) |
0.812083 | + | 0.583542i | \(0.198334\pi\) | |||||||
\(80\) | 440.456 | + | 276.236i | 0.0688212 | + | 0.0431619i | ||||
\(81\) | −2541.12 | + | 6048.92i | −0.387307 | + | 0.921951i | ||||
\(82\) | 3790.02 | − | 2853.54i | 0.563656 | − | 0.424382i | ||||
\(83\) | 6918.39 | − | 3994.33i | 1.00427 | − | 0.579813i | 0.0947580 | − | 0.995500i | \(-0.469792\pi\) |
0.909508 | + | 0.415687i | \(0.136459\pi\) | |||||||
\(84\) | 2324.36 | − | 2386.53i | 0.329416 | − | 0.338227i | ||||
\(85\) | −270.120 | + | 467.861i | −0.0373868 | + | 0.0647558i | ||||
\(86\) | 6557.52 | − | 802.424i | 0.886630 | − | 0.108494i | ||||
\(87\) | −5747.81 | + | 180.958i | −0.759388 | + | 0.0239078i | ||||
\(88\) | 248.406 | + | 201.664i | 0.0320773 | + | 0.0260413i | ||||
\(89\) | −8860.17 | −1.11857 | −0.559283 | − | 0.828977i | \(-0.688924\pi\) | ||||
−0.559283 | + | 0.828977i | \(0.688924\pi\) | |||||||
\(90\) | −620.587 | − | 218.751i | −0.0766157 | − | 0.0270063i | ||||
\(91\) | 6377.03i | 0.770080i | ||||||||
\(92\) | −2425.53 | − | 9762.46i | −0.286570 | − | 1.15341i | ||||
\(93\) | 10520.7 | − | 6523.91i | 1.21640 | − | 0.754296i | ||||
\(94\) | 1411.44 | − | 172.713i | 0.159737 | − | 0.0195465i | ||||
\(95\) | −645.826 | − | 372.868i | −0.0715596 | − | 0.0413150i | ||||
\(96\) | 5505.83 | + | 7390.57i | 0.597421 | + | 0.801928i | ||||
\(97\) | −3409.33 | − | 5905.14i | −0.362348 | − | 0.627606i | 0.625999 | − | 0.779824i | \(-0.284692\pi\) |
−0.988347 | + | 0.152219i | \(0.951358\pi\) | |||||||
\(98\) | −5962.18 | + | 4488.98i | −0.620802 | + | 0.467408i | ||||
\(99\) | −362.737 | − | 180.013i | −0.0370103 | − | 0.0183668i | ||||
\(100\) | −2746.04 | + | 9546.92i | −0.274604 | + | 0.954692i | ||||
\(101\) | −1545.53 | − | 2676.93i | −0.151507 | − | 0.262418i | 0.780274 | − | 0.625437i | \(-0.215079\pi\) |
−0.931782 | + | 0.363019i | \(0.881746\pi\) | |||||||
\(102\) | −7465.33 | + | 5997.92i | −0.717544 | + | 0.576501i | ||||
\(103\) | −9409.35 | − | 5432.49i | −0.886922 | − | 0.512065i | −0.0139875 | − | 0.999902i | \(-0.504453\pi\) |
−0.872934 | + | 0.487838i | \(0.837786\pi\) | |||||||
\(104\) | −17420.9 | − | 2781.23i | −1.61066 | − | 0.257141i | ||||
\(105\) | −372.678 | − | 199.801i | −0.0338030 | − | 0.0181225i | ||||
\(106\) | 19502.1 | + | 8287.61i | 1.73568 | + | 0.737594i | ||||
\(107\) | 14106.5i | 1.23212i | 0.787699 | + | 0.616060i | \(0.211272\pi\) | ||||
−0.787699 | + | 0.616060i | \(0.788728\pi\) | |||||||
\(108\) | −8851.18 | − | 7596.41i | −0.758846 | − | 0.651270i | ||||
\(109\) | 16328.3 | 1.37432 | 0.687160 | − | 0.726506i | \(-0.258857\pi\) | ||||
0.687160 | + | 0.726506i | \(0.258857\pi\) | |||||||
\(110\) | 15.8841 | − | 37.3778i | 0.00131273 | − | 0.00308908i | ||||
\(111\) | 6234.97 | − | 11629.8i | 0.506044 | − | 0.943897i | ||||
\(112\) | 2771.83 | + | 5233.81i | 0.220968 | + | 0.417236i | ||||
\(113\) | −5911.44 | + | 10238.9i | −0.462952 | + | 0.801857i | −0.999107 | − | 0.0422631i | \(-0.986543\pi\) |
0.536154 | + | 0.844120i | \(0.319877\pi\) | |||||||
\(114\) | −8279.41 | − | 10305.0i | −0.637074 | − | 0.792936i | ||||
\(115\) | −1105.77 | + | 638.418i | −0.0836123 | + | 0.0482736i | ||||
\(116\) | 2826.03 | − | 9825.03i | 0.210020 | − | 0.730160i | ||||
\(117\) | 22283.3 | − | 1404.48i | 1.62782 | − | 0.102599i | ||||
\(118\) | −14511.1 | − | 19273.4i | −1.04217 | − | 1.38419i | ||||
\(119\) | −5329.56 | + | 3077.02i | −0.376354 | + | 0.217288i | ||||
\(120\) | 708.356 | − | 930.947i | 0.0491914 | − | 0.0646491i | ||||
\(121\) | −7308.00 | + | 12657.8i | −0.499146 | + | 0.864547i | ||||
\(122\) | −809.770 | − | 6617.55i | −0.0544054 | − | 0.444608i | ||||
\(123\) | −5625.42 | − | 9071.72i | −0.371830 | − | 0.599625i | ||||
\(124\) | 5306.53 | + | 21358.2i | 0.345118 | + | 1.38906i | ||||
\(125\) | 2530.25 | 0.161936 | ||||||||
\(126\) | −4876.27 | − | 5692.67i | −0.307147 | − | 0.358571i | ||||
\(127\) | 20979.9i | 1.30076i | 0.759609 | + | 0.650379i | \(0.225390\pi\) | ||||
−0.759609 | + | 0.650379i | \(0.774610\pi\) | |||||||
\(128\) | −15506.7 | + | 5289.48i | −0.946452 | + | 0.322844i | ||||
\(129\) | −467.746 | − | 14857.1i | −0.0281081 | − | 0.892802i | ||||
\(130\) | 271.983 | + | 2222.68i | 0.0160936 | + | 0.131519i | ||||
\(131\) | 24723.9 | + | 14274.3i | 1.44070 | + | 0.831789i | 0.997896 | − | 0.0648298i | \(-0.0206504\pi\) |
0.442804 | + | 0.896618i | \(0.353984\pi\) | |||||||
\(132\) | 502.290 | − | 515.725i | 0.0288275 | − | 0.0295986i | ||||
\(133\) | −4247.46 | − | 7356.81i | −0.240119 | − | 0.415898i | ||||
\(134\) | −5301.70 | − | 7041.62i | −0.295261 | − | 0.392160i | ||||
\(135\) | −616.087 | + | 1346.25i | −0.0338045 | + | 0.0738685i | ||||
\(136\) | −6081.45 | − | 15901.3i | −0.328798 | − | 0.859718i | ||||
\(137\) | 309.436 | + | 535.959i | 0.0164866 | + | 0.0285556i | 0.874151 | − | 0.485654i | \(-0.161419\pi\) |
−0.857664 | + | 0.514210i | \(0.828085\pi\) | |||||||
\(138\) | −22368.1 | + | 3454.65i | −1.17455 | + | 0.181403i | ||||
\(139\) | −16819.9 | − | 9710.99i | −0.870552 | − | 0.502613i | −0.00302027 | − | 0.999995i | \(-0.500961\pi\) |
−0.867532 | + | 0.497382i | \(0.834295\pi\) | |||||||
\(140\) | 541.192 | − | 521.763i | 0.0276118 | − | 0.0266206i | ||||
\(141\) | −100.677 | − | 3197.83i | −0.00506400 | − | 0.160849i | ||||
\(142\) | −820.234 | + | 1930.14i | −0.0406781 | + | 0.0957222i | ||||
\(143\) | 1378.07i | 0.0673903i | ||||||||
\(144\) | 17678.0 | − | 10838.3i | 0.852529 | − | 0.522680i | ||||
\(145\) | −1297.67 | −0.0617203 | ||||||||
\(146\) | −5493.69 | − | 2334.60i | −0.257726 | − | 0.109523i | ||||
\(147\) | 8849.49 | + | 14271.0i | 0.409528 | + | 0.660418i | ||||
\(148\) | 16282.1 | + | 16888.4i | 0.743339 | + | 0.771018i | ||||
\(149\) | −309.641 | + | 536.313i | −0.0139471 | + | 0.0241572i | −0.872915 | − | 0.487873i | \(-0.837773\pi\) |
0.858968 | + | 0.512030i | \(0.171106\pi\) | |||||||
\(150\) | 20836.0 | + | 8090.25i | 0.926044 | + | 0.359567i | ||||
\(151\) | −3758.08 | + | 2169.73i | −0.164821 | + | 0.0951593i | −0.580141 | − | 0.814516i | \(-0.697003\pi\) |
0.415321 | + | 0.909675i | \(0.363669\pi\) | |||||||
\(152\) | 21949.9 | − | 8394.72i | 0.950048 | − | 0.363345i | ||||
\(153\) | 11925.8 | + | 17945.4i | 0.509455 | + | 0.766603i | ||||
\(154\) | 369.591 | − | 278.268i | 0.0155840 | − | 0.0117334i | ||||
\(155\) | 2419.20 | − | 1396.72i | 0.100695 | − | 0.0581362i | ||||
\(156\) | −9766.54 | + | 38473.0i | −0.401321 | + | 1.58091i | ||||
\(157\) | 3103.88 | − | 5376.08i | 0.125923 | − | 0.218105i | −0.796170 | − | 0.605073i | \(-0.793144\pi\) |
0.922093 | + | 0.386967i | \(0.126477\pi\) | |||||||
\(158\) | 20393.9 | − | 2495.54i | 0.816933 | − | 0.0999657i | ||||
\(159\) | 22527.6 | − | 42019.6i | 0.891090 | − | 1.66210i | ||||
\(160\) | 1189.33 | + | 1705.99i | 0.0464582 | + | 0.0666404i | ||||
\(161\) | −14544.9 | −0.561123 | ||||||||
\(162\) | −18818.0 | + | 18292.9i | −0.717039 | + | 0.697033i | ||||
\(163\) | − | 15857.0i | − | 0.596824i | −0.954437 | − | 0.298412i | \(-0.903543\pi\) | ||
0.954437 | − | 0.298412i | \(-0.0964569\pi\) | |||||||
\(164\) | 18416.7 | − | 4575.71i | 0.684737 | − | 0.170126i | ||||
\(165\) | −80.5351 | − | 43.1766i | −0.00295813 | − | 0.00158592i | ||||
\(166\) | 31718.1 | − | 3881.25i | 1.15104 | − | 0.140849i | ||||
\(167\) | −362.861 | − | 209.498i | −0.0130109 | − | 0.00751186i | 0.493480 | − | 0.869757i | \(-0.335724\pi\) |
−0.506491 | + | 0.862245i | \(0.669058\pi\) | |||||||
\(168\) | 12290.4 | − | 5149.40i | 0.435460 | − | 0.182448i | ||||
\(169\) | −23710.4 | − | 41067.7i | −0.830169 | − | 1.43789i | ||||
\(170\) | −1726.35 | + | 1299.79i | −0.0597353 | + | 0.0449753i | ||||
\(171\) | −24771.5 | + | 16462.2i | −0.847149 | + | 0.562983i | ||||
\(172\) | 25396.0 | + | 7304.81i | 0.858438 | + | 0.246918i | ||||
\(173\) | 9600.40 | + | 16628.4i | 0.320772 | + | 0.555594i | 0.980648 | − | 0.195781i | \(-0.0627242\pi\) |
−0.659875 | + | 0.751375i | \(0.729391\pi\) | |||||||
\(174\) | −21442.9 | − | 8325.92i | −0.708249 | − | 0.275001i | ||||
\(175\) | 12439.4 | + | 7181.88i | 0.406184 | + | 0.234510i | ||||
\(176\) | 598.987 | + | 1131.02i | 0.0193371 | + | 0.0365127i | ||||
\(177\) | −46132.5 | + | 28607.0i | −1.47252 | + | 0.913115i | ||||
\(178\) | −32617.6 | − | 13861.2i | −1.02947 | − | 0.437482i | ||||
\(179\) | − | 49821.7i | − | 1.55494i | −0.628922 | − | 0.777468i | \(-0.716504\pi\) | ||
0.628922 | − | 0.777468i | \(-0.283496\pi\) | |||||||
\(180\) | −1942.39 | − | 1776.18i | −0.0599504 | − | 0.0548202i | ||||
\(181\) | 13970.7 | 0.426443 | 0.213222 | − | 0.977004i | \(-0.431604\pi\) | ||||
0.213222 | + | 0.977004i | \(0.431604\pi\) | |||||||
\(182\) | −9976.48 | + | 23476.3i | −0.301186 | + | 0.708738i | ||||
\(183\) | −14993.1 | + | 472.028i | −0.447703 | + | 0.0140950i | ||||
\(184\) | 6343.50 | − | 39733.9i | 0.187367 | − | 1.17361i | ||||
\(185\) | 1488.84 | − | 2578.75i | 0.0435016 | − | 0.0753469i | ||||
\(186\) | 48936.7 | − | 7558.03i | 1.41452 | − | 0.218466i | ||||
\(187\) | −1151.71 | + | 664.939i | −0.0329351 | + | 0.0190151i | ||||
\(188\) | 5466.22 | + | 1572.28i | 0.154658 | + | 0.0444851i | ||||
\(189\) | −13745.6 | + | 9772.02i | −0.384805 | + | 0.273565i | ||||
\(190\) | −1794.20 | − | 2383.02i | −0.0497008 | − | 0.0660117i | ||||
\(191\) | −26994.8 | + | 15585.5i | −0.739969 | + | 0.427221i | −0.822058 | − | 0.569404i | \(-0.807174\pi\) |
0.0820893 | + | 0.996625i | \(0.473841\pi\) | |||||||
\(192\) | 8706.95 | + | 35821.0i | 0.236191 | + | 0.971707i | ||||
\(193\) | −13498.2 | + | 23379.5i | −0.362377 | + | 0.627655i | −0.988351 | − | 0.152189i | \(-0.951368\pi\) |
0.625975 | + | 0.779843i | \(0.284701\pi\) | |||||||
\(194\) | −3312.81 | − | 27072.7i | −0.0880224 | − | 0.719331i | ||||
\(195\) | 5035.84 | − | 158.543i | 0.132435 | − | 0.00416944i | ||||
\(196\) | −28971.8 | + | 7198.16i | −0.754159 | + | 0.187374i | ||||
\(197\) | 10416.4 | 0.268402 | 0.134201 | − | 0.990954i | \(-0.457153\pi\) | ||||
0.134201 | + | 0.990954i | \(0.457153\pi\) | |||||||
\(198\) | −1053.75 | − | 1230.18i | −0.0268787 | − | 0.0313789i | ||||
\(199\) | 8438.68i | 0.213093i | 0.994308 | + | 0.106546i | \(0.0339793\pi\) | ||||
−0.994308 | + | 0.106546i | \(0.966021\pi\) | |||||||
\(200\) | −25044.8 | + | 30849.8i | −0.626119 | + | 0.771245i | ||||
\(201\) | −16854.7 | + | 10451.7i | −0.417185 | + | 0.258699i | ||||
\(202\) | −1501.77 | − | 12272.7i | −0.0368045 | − | 0.300771i | ||||
\(203\) | −12801.7 | − | 7391.09i | −0.310654 | − | 0.179356i | ||||
\(204\) | −36866.1 | + | 10401.6i | −0.885863 | + | 0.249941i | ||||
\(205\) | −1204.36 | − | 2086.02i | −0.0286583 | − | 0.0496376i | ||||
\(206\) | −26140.6 | − | 34719.4i | −0.616000 | − | 0.818159i | ||||
\(207\) | 3203.37 | + | 50824.2i | 0.0747594 | + | 1.18612i | ||||
\(208\) | −59781.7 | − | 37492.7i | −1.38179 | − | 0.866602i | ||||
\(209\) | −917.868 | − | 1589.79i | −0.0210130 | − | 0.0363956i | ||||
\(210\) | −1059.39 | − | 1318.57i | −0.0240225 | − | 0.0298997i | ||||
\(211\) | −19871.6 | − | 11472.8i | −0.446341 | − | 0.257695i | 0.259943 | − | 0.965624i | \(-0.416296\pi\) |
−0.706284 | + | 0.707929i | \(0.749630\pi\) | |||||||
\(212\) | 58829.0 | + | 61019.6i | 1.30894 | + | 1.35768i | ||||
\(213\) | 4158.73 | + | 2229.59i | 0.0916645 | + | 0.0491434i | ||||
\(214\) | −22068.8 | + | 51931.5i | −0.481894 | + | 1.13397i | ||||
\(215\) | − | 3354.25i | − | 0.0725637i | ||||||
\(216\) | −20700.4 | − | 41812.4i | −0.443682 | − | 0.896184i | ||||
\(217\) | 31821.1 | 0.675764 | ||||||||
\(218\) | 60110.6 | + | 25544.6i | 1.26485 | + | 0.537510i | ||||
\(219\) | −6345.99 | + | 11836.8i | −0.132316 | + | 0.246801i | ||||
\(220\) | 116.951 | − | 112.752i | 0.00241634 | − | 0.00232959i | ||||
\(221\) | 36662.5 | − | 63501.3i | 0.750650 | − | 1.30016i | ||||
\(222\) | 41147.3 | − | 33059.3i | 0.834902 | − | 0.670791i | ||||
\(223\) | 55651.0 | − | 32130.1i | 1.11909 | − | 0.646105i | 0.177919 | − | 0.984045i | \(-0.443064\pi\) |
0.941167 | + | 0.337941i | \(0.109730\pi\) | |||||||
\(224\) | 2016.17 | + | 23604.0i | 0.0401820 | + | 0.470423i | ||||
\(225\) | 22356.0 | − | 45048.7i | 0.441600 | − | 0.889851i | ||||
\(226\) | −37780.4 | + | 28445.2i | −0.739690 | + | 0.556919i | ||||
\(227\) | 5807.02 | − | 3352.69i | 0.112694 | − | 0.0650641i | −0.442593 | − | 0.896722i | \(-0.645941\pi\) |
0.555288 | + | 0.831658i | \(0.312608\pi\) | |||||||
\(228\) | −14358.1 | − | 50889.2i | −0.276202 | − | 0.978940i | ||||
\(229\) | −17775.1 | + | 30787.4i | −0.338955 | + | 0.587087i | −0.984236 | − | 0.176858i | \(-0.943407\pi\) |
0.645281 | + | 0.763945i | \(0.276740\pi\) | |||||||
\(230\) | −5069.53 | + | 620.344i | −0.0958323 | + | 0.0117267i | ||||
\(231\) | −548.573 | − | 884.646i | −0.0102804 | − | 0.0165785i | ||||
\(232\) | 25774.4 | − | 31748.5i | 0.478864 | − | 0.589857i | ||||
\(233\) | 62439.9 | 1.15014 | 0.575070 | − | 0.818105i | \(-0.304975\pi\) | ||||
0.575070 | + | 0.818105i | \(0.304975\pi\) | |||||||
\(234\) | 84230.4 | + | 29690.4i | 1.53829 | + | 0.542231i | ||||
\(235\) | − | 721.967i | − | 0.0130732i | ||||||
\(236\) | −23268.9 | − | 93654.5i | −0.417784 | − | 1.68153i | ||||
\(237\) | −1454.69 | − | 46205.7i | −0.0258985 | − | 0.822619i | ||||
\(238\) | −24433.9 | + | 2989.91i | −0.431359 | + | 0.0527841i | ||||
\(239\) | −3250.59 | − | 1876.73i | −0.0569070 | − | 0.0328553i | 0.471277 | − | 0.881985i | \(-0.343793\pi\) |
−0.528184 | + | 0.849130i | \(0.677127\pi\) | |||||||
\(240\) | 4064.14 | − | 2318.99i | 0.0705579 | − | 0.0402602i | ||||
\(241\) | 44832.6 | + | 77652.3i | 0.771898 | + | 1.33697i | 0.936522 | + | 0.350610i | \(0.114026\pi\) |
−0.164624 | + | 0.986356i | \(0.552641\pi\) | |||||||
\(242\) | −46705.9 | + | 35165.3i | −0.797519 | + | 0.600460i | ||||
\(243\) | 37173.7 | + | 45879.2i | 0.629541 | + | 0.776968i | ||||
\(244\) | 7371.68 | − | 25628.5i | 0.123819 | − | 0.430471i | ||||
\(245\) | 1894.62 | + | 3281.57i | 0.0315638 | + | 0.0546701i | ||||
\(246\) | −6517.12 | − | 42197.1i | −0.107693 | − | 0.697288i | ||||
\(247\) | 87655.9 | + | 50608.2i | 1.43677 | + | 0.829520i | ||||
\(248\) | −13878.2 | + | 86929.3i | −0.225647 | + | 1.41339i | ||||
\(249\) | −2262.44 | − | 71862.4i | −0.0364904 | − | 1.15905i | ||||
\(250\) | 9314.81 | + | 3958.42i | 0.149037 | + | 0.0633348i | ||||
\(251\) | − | 9246.49i | − | 0.146767i | −0.997304 | − | 0.0733836i | \(-0.976620\pi\) | ||
0.997304 | − | 0.0733836i | \(-0.0233798\pi\) | |||||||
\(252\) | −9045.54 | − | 28585.5i | −0.142441 | − | 0.450137i | ||||
\(253\) | −3143.12 | −0.0491043 | ||||||||
\(254\) | −32821.8 | + | 77235.1i | −0.508739 | + | 1.19715i | ||||
\(255\) | 2562.37 | + | 4132.16i | 0.0394060 | + | 0.0635473i | ||||
\(256\) | −65361.0 | − | 4786.66i | −0.997329 | − | 0.0730387i | ||||
\(257\) | −7624.85 | + | 13206.6i | −0.115442 | + | 0.199952i | −0.917956 | − | 0.396681i | \(-0.870162\pi\) |
0.802514 | + | 0.596633i | \(0.203495\pi\) | |||||||
\(258\) | 21521.1 | − | 55426.4i | 0.323314 | − | 0.832678i | ||||
\(259\) | 29375.4 | − | 16959.9i | 0.437909 | − | 0.252827i | ||||
\(260\) | −2475.97 | + | 8608.02i | −0.0366268 | + | 0.127338i | ||||
\(261\) | −23007.2 | + | 46361.0i | −0.337741 | + | 0.680568i | ||||
\(262\) | 68686.5 | + | 91228.1i | 1.00062 | + | 1.32900i | ||||
\(263\) | −89478.0 | + | 51660.2i | −1.29361 | + | 0.746869i | −0.979293 | − | 0.202448i | \(-0.935110\pi\) |
−0.314322 | + | 0.949317i | \(0.601777\pi\) | |||||||
\(264\) | 2655.94 | − | 1112.78i | 0.0381075 | − | 0.0159661i | ||||
\(265\) | 5379.35 | − | 9317.30i | 0.0766016 | − | 0.132678i | ||||
\(266\) | −4127.21 | − | 33728.1i | −0.0583301 | − | 0.476682i | ||||
\(267\) | −37677.9 | + | 70278.6i | −0.528524 | + | 0.985826i | ||||
\(268\) | −8501.38 | − | 34217.1i | −0.118364 | − | 0.476402i | ||||
\(269\) | −86017.8 | −1.18873 | −0.594366 | − | 0.804195i | \(-0.702597\pi\) | ||||
−0.594366 | + | 0.804195i | \(0.702597\pi\) | |||||||
\(270\) | −4374.18 | + | 3992.24i | −0.0600025 | + | 0.0547632i | ||||
\(271\) | 15629.0i | 0.212810i | 0.994323 | + | 0.106405i | \(0.0339340\pi\) | ||||
−0.994323 | + | 0.106405i | \(0.966066\pi\) | |||||||
\(272\) | 2488.57 | − | 68052.9i | 0.0336366 | − | 0.919833i | ||||
\(273\) | 50582.4 | + | 27118.4i | 0.678695 | + | 0.363863i | ||||
\(274\) | 300.676 | + | 2457.16i | 0.00400495 | + | 0.0327290i | ||||
\(275\) | 2688.13 | + | 1551.99i | 0.0355455 | + | 0.0205222i | ||||
\(276\) | −87750.1 | − | 22275.7i | −1.15194 | − | 0.292424i | ||||
\(277\) | 28307.3 | + | 49029.7i | 0.368926 | + | 0.638998i | 0.989398 | − | 0.145231i | \(-0.0463924\pi\) |
−0.620472 | + | 0.784228i | \(0.713059\pi\) | |||||||
\(278\) | −46728.2 | − | 62063.6i | −0.604630 | − | 0.803059i | ||||
\(279\) | −7008.29 | − | 111192.i | −0.0900334 | − | 1.42846i | ||||
\(280\) | 2808.60 | − | 1074.15i | 0.0358240 | − | 0.0137008i | ||||
\(281\) | −55533.5 | − | 96186.8i | −0.703303 | − | 1.21816i | −0.967301 | − | 0.253633i | \(-0.918374\pi\) |
0.263998 | − | 0.964523i | \(-0.414959\pi\) | |||||||
\(282\) | 4632.18 | − | 11929.9i | 0.0582489 | − | 0.150017i | ||||
\(283\) | −78979.6 | − | 45598.9i | −0.986148 | − | 0.569353i | −0.0820271 | − | 0.996630i | \(-0.526139\pi\) |
−0.904121 | + | 0.427278i | \(0.859473\pi\) | |||||||
\(284\) | −6039.18 | + | 5822.37i | −0.0748758 | + | 0.0721877i | ||||
\(285\) | −5703.95 | + | 3537.05i | −0.0702241 | + | 0.0435463i | ||||
\(286\) | −2155.90 | + | 5073.18i | −0.0263570 | + | 0.0620223i | ||||
\(287\) | − | 27438.6i | − | 0.333118i | ||||||
\(288\) | 82035.4 | − | 12243.7i | 0.989045 | − | 0.147614i | ||||
\(289\) | −12760.0 | −0.152776 | ||||||||
\(290\) | −4777.21 | − | 2030.12i | −0.0568039 | − | 0.0241394i | ||||
\(291\) | −61337.6 | + | 1931.09i | −0.724338 | + | 0.0228043i | ||||
\(292\) | −16572.0 | − | 17189.1i | −0.194361 | − | 0.201598i | ||||
\(293\) | −41507.5 | + | 71893.1i | −0.483494 | + | 0.837436i | −0.999820 | − | 0.0189556i | \(-0.993966\pi\) |
0.516326 | + | 0.856392i | \(0.327299\pi\) | |||||||
\(294\) | 10252.3 | + | 66381.3i | 0.118611 | + | 0.767982i | ||||
\(295\) | −10608.0 | + | 6124.56i | −0.121897 | + | 0.0703770i | ||||
\(296\) | 33519.7 | + | 87644.8i | 0.382575 | + | 1.00033i | ||||
\(297\) | −2970.40 | + | 2111.72i | −0.0336746 | + | 0.0239399i | ||||
\(298\) | −1978.93 | + | 1489.96i | −0.0222843 | + | 0.0167780i | ||||
\(299\) | 150083. | − | 86650.5i | 1.67876 | − | 0.969234i | ||||
\(300\) | 64048.4 | + | 62379.9i | 0.711649 | + | 0.693110i | ||||
\(301\) | 19104.7 | − | 33090.3i | 0.210866 | − | 0.365231i | ||||
\(302\) | −17229.3 | + | 2108.30i | −0.188910 | + | 0.0231163i | ||||
\(303\) | −27805.7 | + | 875.407i | −0.302865 | + | 0.00953508i | ||||
\(304\) | 93938.9 | + | 3435.17i | 1.01648 | + | 0.0371708i | ||||
\(305\) | −3384.96 | −0.0363876 | ||||||||
\(306\) | 15829.0 | + | 84721.0i | 0.169048 | + | 0.904791i | ||||
\(307\) | − | 65201.8i | − | 0.691803i | −0.938271 | − | 0.345902i | \(-0.887573\pi\) | ||
0.938271 | − | 0.345902i | \(-0.112427\pi\) | |||||||
\(308\) | 1795.94 | − | 446.209i | 0.0189317 | − | 0.00470367i | ||||
\(309\) | −83103.7 | + | 51533.0i | −0.870369 | + | 0.539720i | ||||
\(310\) | 11091.1 | − | 1357.18i | 0.115412 | − | 0.0141226i | ||||
\(311\) | −115786. | − | 66849.3i | −1.19712 | − | 0.691156i | −0.237206 | − | 0.971459i | \(-0.576232\pi\) |
−0.959911 | + | 0.280303i | \(0.909565\pi\) | |||||||
\(312\) | −96143.0 | + | 126355.i | −0.987663 | + | 1.29802i | ||||
\(313\) | −5620.04 | − | 9734.19i | −0.0573655 | − | 0.0993599i | 0.835917 | − | 0.548857i | \(-0.184937\pi\) |
−0.893282 | + | 0.449497i | \(0.851603\pi\) | |||||||
\(314\) | 19837.1 | − | 14935.5i | 0.201196 | − | 0.151482i | ||||
\(315\) | −3169.63 | + | 2106.42i | −0.0319439 | + | 0.0212287i | ||||
\(316\) | 78981.8 | + | 22718.0i | 0.790957 | + | 0.227508i | ||||
\(317\) | 19603.1 | + | 33953.5i | 0.195077 | + | 0.337883i | 0.946926 | − | 0.321452i | \(-0.104171\pi\) |
−0.751849 | + | 0.659336i | \(0.770838\pi\) | |||||||
\(318\) | 148670. | − | 119447.i | 1.47017 | − | 1.18119i | ||||
\(319\) | −2766.43 | − | 1597.20i | −0.0271856 | − | 0.0156956i | ||||
\(320\) | 1709.44 | + | 8141.04i | 0.0166938 | + | 0.0795023i | ||||
\(321\) | 111893. | + | 59988.2i | 1.08590 | + | 0.582178i | ||||
\(322\) | −53545.1 | − | 22754.5i | −0.516426 | − | 0.219461i | ||||
\(323\) | 97677.0i | 0.936240i | ||||||||
\(324\) | −97894.2 | + | 37903.6i | −0.932539 | + | 0.361069i | ||||
\(325\) | −171143. | −1.62029 | ||||||||
\(326\) | 24807.3 | − | 58375.6i | 0.233424 | − | 0.549283i | ||||
\(327\) | 69436.2 | − | 129516.i | 0.649367 | − | 1.21123i | ||||
\(328\) | 74957.2 | + | 11966.9i | 0.696732 | + | 0.111233i | ||||
\(329\) | 4112.08 | − | 7122.34i | 0.0379901 | − | 0.0658007i | ||||
\(330\) | −228.933 | − | 284.942i | −0.00210223 | − | 0.00261654i | ||||
\(331\) | −64736.6 | + | 37375.7i | −0.590873 | + | 0.341141i | −0.765443 | − | 0.643504i | \(-0.777480\pi\) |
0.174570 | + | 0.984645i | \(0.444147\pi\) | |||||||
\(332\) | 122838. | + | 35332.7i | 1.11444 | + | 0.320553i | ||||
\(333\) | −65732.6 | − | 98911.2i | −0.592779 | − | 0.891984i | ||||
\(334\) | −1008.08 | − | 1338.92i | −0.00903656 | − | 0.0120022i | ||||
\(335\) | −3875.69 | + | 2237.63i | −0.0345350 | + | 0.0199388i | ||||
\(336\) | 53301.6 | + | 270.738i | 0.472130 | + | 0.00239812i | ||||
\(337\) | 70909.1 | − | 122818.i | 0.624370 | − | 1.08144i | −0.364293 | − | 0.931285i | \(-0.618689\pi\) |
0.988662 | − | 0.150156i | \(-0.0479775\pi\) | |||||||
\(338\) | −23039.2 | − | 188279.i | −0.201666 | − | 1.64804i | ||||
\(339\) | 56076.3 | + | 90430.4i | 0.487955 | + | 0.786892i | ||||
\(340\) | −8388.78 | + | 2084.23i | −0.0725673 | + | 0.0180297i | ||||
\(341\) | 6876.48 | 0.0591367 | ||||||||
\(342\) | −116947. | + | 21850.0i | −0.999856 | + | 0.186810i | ||||
\(343\) | 98710.7i | 0.839027i | ||||||||
\(344\) | 82064.4 | + | 66622.3i | 0.693487 | + | 0.562993i | ||||
\(345\) | 361.608 | + | 11485.8i | 0.00303809 | + | 0.0964994i | ||||
\(346\) | 9328.60 | + | 76234.5i | 0.0779227 | + | 0.636795i | ||||
\(347\) | 158508. | + | 91514.6i | 1.31641 | + | 0.760032i | 0.983150 | − | 0.182802i | \(-0.0585168\pi\) |
0.333264 | + | 0.942834i | \(0.391850\pi\) | |||||||
\(348\) | −65914.2 | − | 64197.0i | −0.544277 | − | 0.530098i | ||||
\(349\) | −67279.0 | − | 116531.i | −0.552368 | − | 0.956729i | −0.998103 | − | 0.0615644i | \(-0.980391\pi\) |
0.445735 | − | 0.895165i | \(-0.352942\pi\) | |||||||
\(350\) | 34558.4 | + | 45899.8i | 0.282110 | + | 0.374693i | ||||
\(351\) | 83619.5 | − | 182723.i | 0.678724 | − | 1.48313i | ||||
\(352\) | 435.691 | + | 5100.77i | 0.00351636 | + | 0.0411671i | ||||
\(353\) | 100139. | + | 173446.i | 0.803626 | + | 1.39192i | 0.917215 | + | 0.398393i | \(0.130432\pi\) |
−0.113589 | + | 0.993528i | \(0.536235\pi\) | |||||||
\(354\) | −214585. | + | 33141.6i | −1.71235 | + | 0.264464i | ||||
\(355\) | 922.144 | + | 532.400i | 0.00731715 | + | 0.00422456i | ||||
\(356\) | −98392.7 | − | 102056.i | −0.776359 | − | 0.805268i | ||||
\(357\) | 1742.86 | + | 55358.9i | 0.0136750 | + | 0.434361i | ||||
\(358\) | 77943.1 | − | 183413.i | 0.608151 | − | 1.43108i | ||||
\(359\) | 161179.i | 1.25060i | 0.780385 | + | 0.625300i | \(0.215023\pi\) | ||||
−0.780385 | + | 0.625300i | \(0.784977\pi\) | |||||||
\(360\) | −4371.96 | − | 9577.52i | −0.0337342 | − | 0.0739006i | ||||
\(361\) | −4510.46 | −0.0346104 | ||||||||
\(362\) | 51431.4 | + | 21856.3i | 0.392474 | + | 0.166786i | ||||
\(363\) | 69324.2 | + | 111794.i | 0.526104 | + | 0.848412i | ||||
\(364\) | −73454.3 | + | 70817.3i | −0.554389 | + | 0.534487i | ||||
\(365\) | −1515.35 | + | 2624.66i | −0.0113744 | + | 0.0197010i | ||||
\(366\) | −55933.8 | − | 21718.1i | −0.417553 | − | 0.162129i | ||||
\(367\) | −172828. | + | 99782.5i | −1.28317 | + | 0.740836i | −0.977426 | − | 0.211279i | \(-0.932237\pi\) |
−0.305740 | + | 0.952115i | \(0.598904\pi\) | |||||||
\(368\) | 85514.0 | − | 136351.i | 0.631454 | − | 1.00685i | ||||
\(369\) | −95878.8 | + | 6043.09i | −0.704158 | + | 0.0443820i | ||||
\(370\) | 9515.28 | − | 7164.14i | 0.0695053 | − | 0.0523312i | ||||
\(371\) | 106136. | − | 61277.9i | 0.771111 | − | 0.445201i | ||||
\(372\) | 191979. | + | 48734.6i | 1.38729 | + | 0.352169i | ||||
\(373\) | 2894.35 | − | 5013.15i | 0.0208033 | − | 0.0360324i | −0.855436 | − | 0.517908i | \(-0.826711\pi\) |
0.876240 | + | 0.481876i | \(0.160044\pi\) | |||||||
\(374\) | −5280.12 | + | 646.113i | −0.0377486 | + | 0.00461919i | ||||
\(375\) | 10759.9 | − | 20069.9i | 0.0765149 | − | 0.142719i | ||||
\(376\) | 17663.5 | + | 14339.7i | 0.124940 | + | 0.101430i | ||||
\(377\) | 176129. | 1.23922 | ||||||||
\(378\) | −65890.5 | + | 14470.3i | −0.461147 | + | 0.101273i | ||||
\(379\) | − | 217930.i | − | 1.51719i | −0.651565 | − | 0.758593i | \(-0.725887\pi\) | ||
0.651565 | − | 0.758593i | \(-0.274113\pi\) | |||||||
\(380\) | −2877.03 | − | 11579.7i | −0.0199240 | − | 0.0801919i | ||||
\(381\) | 166412. | + | 89217.4i | 1.14640 | + | 0.614610i | ||||
\(382\) | −123760. | + | 15144.2i | −0.848116 | + | 0.103781i | ||||
\(383\) | −60187.2 | − | 34749.1i | −0.410305 | − | 0.236890i | 0.280616 | − | 0.959820i | \(-0.409461\pi\) |
−0.690921 | + | 0.722930i | \(0.742795\pi\) | |||||||
\(384\) | −23986.2 | + | 145492.i | −0.162667 | + | 0.986681i | ||||
\(385\) | −117.446 | − | 203.422i | −0.000792348 | − | 0.00137239i | ||||
\(386\) | −86267.6 | + | 64951.7i | −0.578993 | + | 0.435929i | ||||
\(387\) | −119835. | − | 59469.8i | −0.800134 | − | 0.397077i | ||||
\(388\) | 30157.9 | − | 104848.i | 0.200326 | − | 0.696458i | ||||
\(389\) | −28733.0 | − | 49767.0i | −0.189881 | − | 0.328884i | 0.755329 | − | 0.655345i | \(-0.227477\pi\) |
−0.945210 | + | 0.326462i | \(0.894144\pi\) | |||||||
\(390\) | 18786.8 | + | 7294.60i | 0.123516 | + | 0.0479592i | ||||
\(391\) | 144835. | + | 83620.5i | 0.947371 | + | 0.546965i | ||||
\(392\) | −117917. | − | 18825.4i | −0.767369 | − | 0.122510i | ||||
\(393\) | 218362. | − | 135407.i | 1.41381 | − | 0.876712i | ||||
\(394\) | 38346.8 | + | 16295.9i | 0.247023 | + | 0.104975i | ||||
\(395\) | − | 10431.7i | − | 0.0668595i | ||||||
\(396\) | −1954.73 | − | 6177.28i | −0.0124651 | − | 0.0393919i | ||||
\(397\) | 13255.8 | 0.0841056 | 0.0420528 | − | 0.999115i | \(-0.486610\pi\) | ||||
0.0420528 | + | 0.999115i | \(0.486610\pi\) | |||||||
\(398\) | −13201.8 | + | 31066.0i | −0.0833426 | + | 0.196119i | ||||
\(399\) | −76416.4 | + | 2405.82i | −0.479999 | + | 0.0151118i | ||||
\(400\) | −140462. | + | 74388.7i | −0.877887 | + | 0.464930i | ||||
\(401\) | 2687.66 | − | 4655.16i | 0.0167142 | − | 0.0289498i | −0.857547 | − | 0.514405i | \(-0.828013\pi\) |
0.874262 | + | 0.485455i | \(0.161346\pi\) | |||||||
\(402\) | −78399.5 | + | 12108.4i | −0.485133 | + | 0.0749265i | ||||
\(403\) | −328350. | + | 189573.i | −2.02175 | + | 1.16726i | ||||
\(404\) | 13671.3 | − | 47529.7i | 0.0837618 | − | 0.291208i | ||||
\(405\) | 8058.54 | + | 10611.7i | 0.0491299 | + | 0.0646959i | ||||
\(406\) | −35565.1 | − | 47236.9i | −0.215761 | − | 0.286569i | ||||
\(407\) | 6347.97 | − | 3665.00i | 0.0383218 | − | 0.0221251i | ||||
\(408\) | −151990. | − | 19382.7i | −0.913053 | − | 0.116438i | ||||
\(409\) | 120347. | − | 208446.i | 0.719427 | − | 1.24608i | −0.241800 | − | 0.970326i | \(-0.577738\pi\) |
0.961227 | − | 0.275758i | \(-0.0889289\pi\) | |||||||
\(410\) | −1170.27 | − | 9563.57i | −0.00696173 | − | 0.0568922i | ||||
\(411\) | 5567.10 | − | 175.269i | 0.0329568 | − | 0.00103758i | ||||
\(412\) | −41916.9 | − | 168711.i | −0.246942 | − | 0.993912i | ||||
\(413\) | −139534. | −0.818049 | ||||||||
\(414\) | −67718.5 | + | 192114.i | −0.395100 | + | 1.12088i | ||||
\(415\) | − | 16224.2i | − | 0.0942035i | ||||||
\(416\) | −161424. | − | 231549.i | −0.932784 | − | 1.33800i | ||||
\(417\) | −148554. | + | 92119.2i | −0.854305 | + | 0.529758i | ||||
\(418\) | −891.882 | − | 7288.58i | −0.00510452 | − | 0.0417148i | ||||
\(419\) | 30669.6 | + | 17707.1i | 0.174695 | + | 0.100860i | 0.584798 | − | 0.811179i | \(-0.301174\pi\) |
−0.410103 | + | 0.912039i | \(0.634507\pi\) | |||||||
\(420\) | −1837.19 | − | 6511.52i | −0.0104149 | − | 0.0369134i | ||||
\(421\) | 82548.0 | + | 142977.i | 0.465739 | + | 0.806683i | 0.999235 | − | 0.0391198i | \(-0.0124554\pi\) |
−0.533496 | + | 0.845803i | \(0.679122\pi\) | |||||||
\(422\) | −55206.1 | − | 73323.7i | −0.310000 | − | 0.411737i | ||||
\(423\) | −25793.3 | − | 12800.2i | −0.144154 | − | 0.0715381i | ||||
\(424\) | 121110. | + | 316670.i | 0.673673 | + | 1.76147i | ||||
\(425\) | −82579.3 | − | 143032.i | −0.457187 | − | 0.791870i | ||||
\(426\) | 11821.8 | + | 14714.0i | 0.0651424 | + | 0.0810797i | ||||
\(427\) | −33393.2 | − | 19279.6i | −0.183148 | − | 0.105741i | ||||
\(428\) | −162487. | + | 156654.i | −0.887017 | + | 0.855173i | ||||
\(429\) | 10930.8 | + | 5860.23i | 0.0593931 | + | 0.0318420i | ||||
\(430\) | 5247.53 | − | 12348.3i | 0.0283803 | − | 0.0667835i | ||||
\(431\) | 161673.i | 0.870327i | 0.900351 | + | 0.435163i | \(0.143309\pi\) | ||||
−0.900351 | + | 0.435163i | \(0.856691\pi\) | |||||||
\(432\) | −10793.1 | − | 186312.i | −0.0578336 | − | 0.998326i | ||||
\(433\) | −61835.3 | −0.329808 | −0.164904 | − | 0.986310i | \(-0.552731\pi\) | ||||
−0.164904 | + | 0.986310i | \(0.552731\pi\) | |||||||
\(434\) | 117145. | + | 49782.1i | 0.621936 | + | 0.264298i | ||||
\(435\) | −5518.35 | + | 10293.1i | −0.0291629 | + | 0.0543960i | ||||
\(436\) | 181327. | + | 188079.i | 0.953869 | + | 0.989388i | ||||
\(437\) | −115428. | + | 199927.i | −0.604434 | + | 1.04691i | ||||
\(438\) | −41880.0 | + | 33647.9i | −0.218302 | + | 0.175392i | ||||
\(439\) | 268021. | − | 154742.i | 1.39072 | − | 0.802933i | 0.397326 | − | 0.917677i | \(-0.369938\pi\) |
0.993395 | + | 0.114744i | \(0.0366049\pi\) | |||||||
\(440\) | 606.933 | − | 232.121i | 0.00313499 | − | 0.00119897i | ||||
\(441\) | 150829. | − | 9506.54i | 0.775548 | − | 0.0488816i | ||||
\(442\) | 234312. | − | 176416.i | 1.19936 | − | 0.903011i | ||||
\(443\) | −40615.5 | + | 23449.4i | −0.206959 | + | 0.119488i | −0.599897 | − | 0.800077i | \(-0.704792\pi\) |
0.392938 | + | 0.919565i | \(0.371459\pi\) | |||||||
\(444\) | 203198. | − | 57331.1i | 1.03075 | − | 0.290820i | ||||
\(445\) | −8997.07 | + | 15583.4i | −0.0454340 | + | 0.0786940i | ||||
\(446\) | 255138. | − | 31220.5i | 1.28264 | − | 0.156953i | ||||
\(447\) | 2937.27 | + | 4736.74i | 0.0147004 | + | 0.0237063i | ||||
\(448\) | −29504.7 | + | 90049.2i | −0.147006 | + | 0.448667i | ||||
\(449\) | −124857. | −0.619328 | −0.309664 | − | 0.950846i | \(-0.600217\pi\) | ||||
−0.309664 | + | 0.950846i | \(0.600217\pi\) | |||||||
\(450\) | 152777. | − | 130867.i | 0.754453 | − | 0.646255i | ||||
\(451\) | − | 5929.43i | − | 0.0291514i | ||||||
\(452\) | −183585. | + | 45612.4i | −0.898585 | + | 0.223257i | ||||
\(453\) | 1228.96 | + | 39035.8i | 0.00598883 | + | 0.190224i | ||||
\(454\) | 26622.9 | − | 3257.77i | 0.129165 | − | 0.0158055i | ||||
\(455\) | 11216.0 | + | 6475.56i | 0.0541771 | + | 0.0312791i | ||||
\(456\) | 26755.5 | − | 209805.i | 0.128672 | − | 1.00899i | ||||
\(457\) | 62748.5 | + | 108684.i | 0.300449 | + | 0.520393i | 0.976238 | − | 0.216703i | \(-0.0695302\pi\) |
−0.675789 | + | 0.737095i | \(0.736197\pi\) | |||||||
\(458\) | −113602. | + | 85532.1i | −0.541571 | + | 0.407754i | ||||
\(459\) | 193057. | − | 18282.4i | 0.916348 | − | 0.0867775i | ||||
\(460\) | −19633.3 | − | 5647.25i | −0.0927852 | − | 0.0266883i | ||||
\(461\) | −51647.4 | − | 89455.9i | −0.243022 | − | 0.420927i | 0.718551 | − | 0.695474i | \(-0.244806\pi\) |
−0.961574 | + | 0.274547i | \(0.911472\pi\) | |||||||
\(462\) | −635.530 | − | 4114.92i | −0.00297750 | − | 0.0192787i | ||||
\(463\) | 277564. | + | 160252.i | 1.29480 | + | 0.747552i | 0.979501 | − | 0.201442i | \(-0.0645626\pi\) |
0.315297 | + | 0.948993i | \(0.397896\pi\) | |||||||
\(464\) | 144554. | − | 76555.7i | 0.671418 | − | 0.355584i | ||||
\(465\) | −791.122 | − | 25128.6i | −0.00365879 | − | 0.116215i | ||||
\(466\) | 229865. | + | 97683.4i | 1.05852 | + | 0.449831i | ||||
\(467\) | − | 427381.i | − | 1.95967i | −0.199820 | − | 0.979833i | \(-0.564036\pi\) | ||
0.199820 | − | 0.979833i | \(-0.435964\pi\) | |||||||
\(468\) | 263635. | + | 241075.i | 1.20368 | + | 1.10068i | ||||
\(469\) | −50979.2 | −0.231765 | ||||||||
\(470\) | 1129.47 | − | 2657.83i | 0.00511305 | − | 0.0120318i | ||||
\(471\) | −29443.6 | − | 47481.7i | −0.132724 | − | 0.214035i | ||||
\(472\) | 60855.3 | − | 381180.i | 0.273158 | − | 1.71099i | ||||
\(473\) | 4128.49 | − | 7150.76i | 0.0184531 | − | 0.0319617i | ||||
\(474\) | 66930.7 | − | 172376.i | 0.297899 | − | 0.767222i | ||||
\(475\) | 197438. | − | 113991.i | 0.875071 | − | 0.505223i | ||||
\(476\) | −94627.9 | − | 27218.4i | −0.417643 | − | 0.120129i | ||||
\(477\) | −237499. | − | 357377.i | −1.04382 | − | 1.57069i | ||||
\(478\) | −9030.61 | − | 11994.3i | −0.0395240 | − | 0.0524951i | ||||
\(479\) | −166330. | + | 96030.5i | −0.724935 | + | 0.418541i | −0.816566 | − | 0.577252i | \(-0.804125\pi\) |
0.0916316 | + | 0.995793i | \(0.470792\pi\) | |||||||
\(480\) | 18589.5 | − | 2178.97i | 0.0806837 | − | 0.00945733i | ||||
\(481\) | −202076. | + | 350006.i | −0.873422 | + | 1.51281i | ||||
\(482\) | 43563.3 | + | 356005.i | 0.187511 | + | 1.53237i | ||||
\(483\) | −61852.1 | + | 115369.i | −0.265131 | + | 0.494534i | ||||
\(484\) | −226956. | + | 56388.2i | −0.968838 | + | 0.240712i | ||||
\(485\) | −13848.1 | −0.0588715 | ||||||||
\(486\) | 65075.4 | + | 227055.i | 0.275514 | + | 0.961297i | ||||
\(487\) | − | 52885.1i | − | 0.222985i | −0.993765 | − | 0.111492i | \(-0.964437\pi\) | ||
0.993765 | − | 0.111492i | \(-0.0355631\pi\) | |||||||
\(488\) | 67232.2 | − | 82815.7i | 0.282317 | − | 0.347755i | ||||
\(489\) | −125777. | − | 67432.0i | −0.525999 | − | 0.282000i | ||||
\(490\) | 1840.98 | + | 15044.7i | 0.00766754 | + | 0.0626602i | ||||
\(491\) | 6368.89 | + | 3677.08i | 0.0264180 | + | 0.0152525i | 0.513151 | − | 0.858298i | \(-0.328478\pi\) |
−0.486733 | + | 0.873551i | \(0.661811\pi\) | |||||||
\(492\) | 42022.7 | − | 165539.i | 0.173602 | − | 0.683864i | ||||
\(493\) | 84984.9 | + | 147198.i | 0.349662 | + | 0.605632i | ||||
\(494\) | 243521. | + | 323440.i | 0.997890 | + | 1.32538i | ||||
\(495\) | −684.952 | + | 455.193i | −0.00279544 | + | 0.00185774i | ||||
\(496\) | −187086. | + | 298308.i | −0.760465 | + | 1.21255i | ||||
\(497\) | 6064.75 | + | 10504.4i | 0.0245527 | + | 0.0425266i | ||||
\(498\) | 104095. | − | 268092.i | 0.419733 | − | 1.08100i | ||||
\(499\) | −359442. | − | 207524.i | −1.44354 | − | 0.833426i | −0.445452 | − | 0.895306i | \(-0.646957\pi\) |
−0.998084 | + | 0.0618804i | \(0.980290\pi\) | |||||||
\(500\) | 28098.6 | + | 29144.9i | 0.112394 | + | 0.116580i | ||||
\(501\) | −3204.80 | + | 1987.31i | −0.0127681 | + | 0.00791756i | ||||
\(502\) | 14465.6 | − | 34039.8i | 0.0574021 | − | 0.135076i | ||||
\(503\) | − | 53242.3i | − | 0.210436i | −0.994449 | − | 0.105218i | \(-0.966446\pi\) | ||
0.994449 | − | 0.105218i | \(-0.0335541\pi\) | |||||||
\(504\) | 11420.2 | − | 119385.i | 0.0449587 | − | 0.469991i | ||||
\(505\) | −6277.63 | −0.0246157 | ||||||||
\(506\) | −11571.0 | − | 4917.22i | −0.0451929 | − | 0.0192052i | ||||
\(507\) | −426577. | + | 13429.9i | −1.65952 | + | 0.0522465i | ||||
\(508\) | −241659. | + | 232984.i | −0.936431 | + | 0.902813i | ||||
\(509\) | 248630. | − | 430640.i | 0.959662 | − | 1.66218i | 0.236344 | − | 0.971669i | \(-0.424051\pi\) |
0.723319 | − | 0.690515i | \(-0.242616\pi\) | |||||||
\(510\) | 2968.54 | + | 19220.7i | 0.0114131 | + | 0.0738974i | ||||
\(511\) | −29898.4 | + | 17261.9i | −0.114500 | + | 0.0661068i | ||||
\(512\) | −233130. | − | 119875.i | −0.889320 | − | 0.457286i | ||||
\(513\) | 25236.6 | + | 266492.i | 0.0958952 | + | 1.01263i | ||||
\(514\) | −48730.9 | + | 36689.9i | −0.184450 | + | 0.138874i | ||||
\(515\) | −19109.5 | + | 11032.9i | −0.0720501 | + | 0.0415981i | ||||
\(516\) | 165938. | − | 170377.i | 0.623229 | − | 0.639899i | ||||
\(517\) | 888.614 | − | 1539.12i | 0.00332454 | − | 0.00575828i | ||||
\(518\) | 134675. | − | 16479.7i | 0.501910 | − | 0.0614173i | ||||
\(519\) | 172722. | − | 5437.79i | 0.641227 | − | 0.0201877i | ||||
\(520\) | −22581.7 | + | 27815.8i | −0.0835123 | + | 0.102869i | ||||
\(521\) | −58965.8 | −0.217233 | −0.108616 | − | 0.994084i | \(-0.534642\pi\) | ||||
−0.108616 | + | 0.994084i | \(0.534642\pi\) | |||||||
\(522\) | −157227. | + | 134679.i | −0.577015 | + | 0.494263i | ||||
\(523\) | − | 117488.i | − | 0.429527i | −0.976666 | − | 0.214763i | \(-0.931102\pi\) | ||
0.976666 | − | 0.214763i | \(-0.0688980\pi\) | |||||||
\(524\) | 110140. | + | 443301.i | 0.401128 | + | 1.61449i | ||||
\(525\) | 109865. | − | 68127.8i | 0.398603 | − | 0.247176i | ||||
\(526\) | −410222. | + | 50197.6i | −1.48268 | + | 0.181431i | ||||
\(527\) | −316868. | − | 182944.i | −1.14093 | − | 0.658714i | ||||
\(528\) | 11518.4 | + | 58.5059i | 0.0413165 | + | 0.000209861i | ||||
\(529\) | 57713.8 | + | 99963.2i | 0.206238 | + | 0.357214i | ||||
\(530\) | 34379.8 | − | 25884.8i | 0.122391 | − | 0.0921497i | ||||
\(531\) | 30731.0 | + | 487573.i | 0.108990 | + | 1.72922i | ||||
\(532\) | 37571.7 | − | 130623.i | 0.132751 | − | 0.461525i | ||||
\(533\) | 163465. | + | 283129.i | 0.575399 | + | 0.996620i | ||||
\(534\) | −248653. | + | 199777.i | −0.871990 | + | 0.700589i | ||||
\(535\) | 24810.8 | + | 14324.5i | 0.0866828 | + | 0.0500463i | ||||
\(536\) | 22233.7 | − | 139266.i | 0.0773896 | − | 0.484747i | ||||
\(537\) | −395185. | − | 211867.i | −1.37041 | − | 0.734709i | ||||
\(538\) | −316664. | − | 134570.i | −1.09404 | − | 0.464925i | ||||
\(539\) | 9327.75i | 0.0321070i | ||||||||
\(540\) | −22348.6 | + | 7853.80i | −0.0766413 | + | 0.0269335i | ||||
\(541\) | −16461.8 | −0.0562448 | −0.0281224 | − | 0.999604i | \(-0.508953\pi\) | ||||
−0.0281224 | + | 0.999604i | \(0.508953\pi\) | |||||||
\(542\) | −24450.6 | + | 57536.2i | −0.0832322 | + | 0.195859i | ||||
\(543\) | 59410.5 | − | 110815.i | 0.201495 | − | 0.375837i | ||||
\(544\) | 115626. | − | 246635.i | 0.390713 | − | 0.833407i | ||||
\(545\) | 16580.6 | − | 28718.4i | 0.0558222 | − | 0.0966869i | ||||
\(546\) | 143788. | + | 178966.i | 0.482322 | + | 0.600324i | ||||
\(547\) | 337391. | − | 194793.i | 1.12761 | − | 0.651026i | 0.184277 | − | 0.982874i | \(-0.441006\pi\) |
0.943333 | + | 0.331848i | \(0.107672\pi\) | |||||||
\(548\) | −2737.18 | + | 9516.13i | −0.00911470 | + | 0.0316883i | ||||
\(549\) | −60014.2 | + | 120932.i | −0.199118 | + | 0.401234i | ||||
\(550\) | 7468.01 | + | 9918.87i | 0.0246876 | + | 0.0327897i | ||||
\(551\) | −203189. | + | 117312.i | −0.669265 | + | 0.386400i | ||||
\(552\) | −288192. | − | 219285.i | −0.945810 | − | 0.719666i | ||||
\(553\) | 59415.7 | − | 102911.i | 0.194290 | − | 0.336521i | ||||
\(554\) | 27505.9 | + | 224782.i | 0.0896202 | + | 0.732388i | ||||
\(555\) | −14123.3 | − | 22775.6i | −0.0458510 | − | 0.0739407i | ||||
\(556\) | −74929.6 | − | 301583.i | −0.242384 | − | 0.975567i | ||||
\(557\) | 434133. | 1.39931 | 0.699653 | − | 0.714483i | \(-0.253338\pi\) | ||||
0.699653 | + | 0.714483i | \(0.253338\pi\) | |||||||
\(558\) | 148154. | − | 420305.i | 0.475821 | − | 1.34988i | ||||
\(559\) | 455263.i | 1.45693i | ||||||||
\(560\) | 12019.9 | + | 439.547i | 0.0383289 | + | 0.00140162i | ||||
\(561\) | 376.630 | + | 11963.0i | 0.00119671 | + | 0.0380113i | ||||
\(562\) | −53961.3 | − | 440979.i | −0.170848 | − | 1.39619i | ||||
\(563\) | 192477. | + | 111127.i | 0.607244 | + | 0.350592i | 0.771886 | − | 0.635761i | \(-0.219314\pi\) |
−0.164642 | + | 0.986353i | \(0.552647\pi\) | |||||||
\(564\) | 35716.5 | − | 36671.8i | 0.112282 | − | 0.115285i | ||||
\(565\) | 12005.6 | + | 20794.2i | 0.0376084 | + | 0.0651397i | ||||
\(566\) | −219417. | − | 291425.i | −0.684916 | − | 0.909692i | ||||
\(567\) | 19058.0 | + | 150585.i | 0.0592805 | + | 0.468400i | ||||
\(568\) | −31341.2 | + | 11986.4i | −0.0971448 | + | 0.0371529i | ||||
\(569\) | −1962.56 | − | 3399.25i | −0.00606175 | − | 0.0104993i | 0.862979 | − | 0.505240i | \(-0.168596\pi\) |
−0.869040 | + | 0.494741i | \(0.835263\pi\) | |||||||
\(570\) | −26531.9 | + | 4097.72i | −0.0816617 | + | 0.0126123i | ||||
\(571\) | 331554. | + | 191423.i | 1.01691 | + | 0.587112i | 0.913207 | − | 0.407496i | \(-0.133598\pi\) |
0.103702 | + | 0.994608i | \(0.466931\pi\) | |||||||
\(572\) | −15873.3 | + | 15303.5i | −0.0485151 | + | 0.0467734i | ||||
\(573\) | 8827.80 | + | 280399.i | 0.0268871 | + | 0.854019i | ||||
\(574\) | 42926.0 | − | 101012.i | 0.130286 | − | 0.306583i | ||||
\(575\) | − | 390347.i | − | 1.18063i | ||||||
\(576\) | 321157. | + | 83265.8i | 0.967995 | + | 0.250970i | ||||
\(577\) | 18219.2 | 0.0547239 | 0.0273620 | − | 0.999626i | \(-0.491289\pi\) | ||||
0.0273620 | + | 0.999626i | \(0.491289\pi\) | |||||||
\(578\) | −46974.5 | − | 19962.3i | −0.140607 | − | 0.0597524i | ||||
\(579\) | 128045. | + | 206489.i | 0.381948 | + | 0.615941i | ||||
\(580\) | −14410.7 | − | 14947.3i | −0.0428380 | − | 0.0444331i | ||||
\(581\) | 92407.6 | − | 160055.i | 0.273751 | − | 0.474150i | ||||
\(582\) | −228828. | − | 88849.9i | −0.675559 | − | 0.262308i | ||||
\(583\) | 22935.9 | − | 13242.0i | 0.0674806 | − | 0.0389599i | ||||
\(584\) | −34116.5 | − | 89205.4i | −0.100032 | − | 0.261556i | ||||
\(585\) | 20157.4 | − | 40618.3i | 0.0589009 | − | 0.118689i | ||||
\(586\) | −265277. | + | 199730.i | −0.772510 | + | 0.581630i | ||||
\(587\) | 45835.0 | − | 26462.8i | 0.133021 | − | 0.0767998i | −0.432013 | − | 0.901868i | \(-0.642196\pi\) |
0.565034 | + | 0.825068i | \(0.308863\pi\) | |||||||
\(588\) | −66107.0 | + | 260413.i | −0.191202 | + | 0.753197i | ||||
\(589\) | 252532. | − | 437399.i | 0.727924 | − | 1.26080i | ||||
\(590\) | −48633.7 | + | 5951.16i | −0.139712 | + | 0.0170961i | ||||
\(591\) | 44295.9 | − | 82622.8i | 0.126820 | − | 0.236551i | ||||
\(592\) | −13716.5 | + | 375093.i | −0.0391380 | + | 1.07028i | ||||
\(593\) | 216280. | 0.615046 | 0.307523 | − | 0.951541i | \(-0.400500\pi\) | ||||
0.307523 | + | 0.951541i | \(0.400500\pi\) | |||||||
\(594\) | −14238.8 | + | 3127.01i | −0.0403554 | + | 0.00886249i | ||||
\(595\) | 12498.3i | 0.0353033i | ||||||||
\(596\) | −9616.14 | + | 2389.17i | −0.0270713 | + | 0.00672597i | ||||
\(597\) | 66935.4 | + | 35885.6i | 0.187805 | + | 0.100686i | ||||
\(598\) | 688072. | − | 84197.3i | 1.92412 | − | 0.235448i | ||||
\(599\) | 260151. | + | 150198.i | 0.725057 | + | 0.418612i | 0.816611 | − | 0.577188i | \(-0.195850\pi\) |
−0.0915543 | + | 0.995800i | \(0.529184\pi\) | |||||||
\(600\) | 138197. | + | 329844.i | 0.383880 | + | 0.916232i | ||||
\(601\) | −255485. | − | 442514.i | −0.707322 | − | 1.22512i | −0.965847 | − | 0.259113i | \(-0.916570\pi\) |
0.258525 | − | 0.966005i | \(-0.416764\pi\) | |||||||
\(602\) | 122099. | − | 91929.8i | 0.336915 | − | 0.253667i | ||||
\(603\) | 11227.7 | + | 178137.i | 0.0308785 | + | 0.489913i | ||||
\(604\) | −66725.9 | − | 19192.8i | −0.182903 | − | 0.0526094i | ||||
\(605\) | 14841.8 | + | 25706.8i | 0.0405487 | + | 0.0702324i | ||||
\(606\) | −103733. | − | 40277.6i | −0.282469 | − | 0.109678i | ||||
\(607\) | −154217. | − | 89037.5i | −0.418558 | − | 0.241655i | 0.275902 | − | 0.961186i | \(-0.411024\pi\) |
−0.694460 | + | 0.719531i | \(0.744357\pi\) | |||||||
\(608\) | 340450. | + | 159608.i | 0.920972 | + | 0.431765i | ||||
\(609\) | −113065. | + | 70112.4i | −0.304856 | + | 0.189043i | ||||
\(610\) | −12461.3 | − | 5295.56i | −0.0334892 | − | 0.0142316i | ||||
\(611\) | 97990.4i | 0.262483i | ||||||||
\(612\) | −74268.4 | + | 336653.i | −0.198290 | + | 0.898835i | ||||
\(613\) | 570495. | 1.51821 | 0.759103 | − | 0.650970i | \(-0.225638\pi\) | ||||
0.759103 | + | 0.650970i | \(0.225638\pi\) | |||||||
\(614\) | 102004. | − | 240032.i | 0.270571 | − | 0.636697i | ||||
\(615\) | −21667.8 | + | 682.167i | −0.0572881 | + | 0.00180360i | ||||
\(616\) | 7309.59 | + | 1166.97i | 0.0192633 | + | 0.00307538i | ||||
\(617\) | −107951. | + | 186976.i | −0.283567 | + | 0.491153i | −0.972261 | − | 0.233900i | \(-0.924851\pi\) |
0.688694 | + | 0.725052i | \(0.258185\pi\) | |||||||
\(618\) | −386556. | + | 59701.7i | −1.01213 | + | 0.156318i | ||||
\(619\) | −158318. | + | 91404.9i | −0.413189 | + | 0.238555i | −0.692159 | − | 0.721745i | \(-0.743340\pi\) |
0.278970 | + | 0.960300i | \(0.410007\pi\) | |||||||
\(620\) | 42953.6 | + | 12355.0i | 0.111742 | + | 0.0321410i | ||||
\(621\) | 416758. | + | 190721.i | 1.08069 | + | 0.494556i | ||||
\(622\) | −321672. | − | 427238.i | −0.831442 | − | 1.10431i | ||||
\(623\) | −177515. | + | 102489.i | −0.457362 | + | 0.264058i | ||||
\(624\) | −551613. | + | 314749.i | −1.41666 | + | 0.808342i | ||||
\(625\) | −191454. | + | 331608.i | −0.490123 | + | 0.848918i | ||||
\(626\) | −5460.93 | − | 44627.4i | −0.0139353 | − | 0.113881i | ||||
\(627\) | −16513.4 | + | 519.893i | −0.0420052 | + | 0.00132245i | ||||
\(628\) | 96393.6 | − | 23949.4i | 0.244415 | − | 0.0607261i | ||||
\(629\) | −390019. | −0.985791 | ||||||||
\(630\) | −14964.0 | + | 2795.82i | −0.0377021 | + | 0.00704413i | ||||
\(631\) | − | 153307.i | − | 0.385037i | −0.981293 | − | 0.192518i | \(-0.938335\pi\) | ||
0.981293 | − | 0.192518i | \(-0.0616655\pi\) | |||||||
\(632\) | 255221. | + | 207196.i | 0.638972 | + | 0.518736i | ||||
\(633\) | −175506. | + | 108832.i | −0.438011 | + | 0.271613i | ||||
\(634\) | 19048.1 | + | 155664.i | 0.0473885 | + | 0.387265i | ||||
\(635\) | 36899.8 | + | 21304.1i | 0.0915117 | + | 0.0528343i | ||||
\(636\) | 734176. | − | 207144.i | 1.81504 | − | 0.512103i | ||||
\(637\) | −257150. | − | 445397.i | −0.633736 | − | 1.09766i | ||||
\(638\) | −7685.56 | − | 10207.8i | −0.0188814 | − | 0.0250779i | ||||
\(639\) | 35370.0 | − | 23505.6i | 0.0866231 | − | 0.0575664i | ||||
\(640\) | −6443.06 | + | 32644.5i | −0.0157301 | + | 0.0796986i | ||||
\(641\) | −196626. | − | 340566.i | −0.478547 | − | 0.828869i | 0.521150 | − | 0.853465i | \(-0.325503\pi\) |
−0.999697 | + | 0.0245966i | \(0.992170\pi\) | |||||||
\(642\) | 318071. | + | 395888.i | 0.771711 | + | 0.960512i | ||||
\(643\) | −384971. | − | 222263.i | −0.931120 | − | 0.537583i | −0.0439545 | − | 0.999034i | \(-0.513996\pi\) |
−0.887166 | + | 0.461451i | \(0.847329\pi\) | |||||||
\(644\) | −161522. | − | 167536.i | −0.389456 | − | 0.403958i | ||||
\(645\) | −26605.9 | − | 14264.0i | −0.0639525 | − | 0.0342864i | ||||
\(646\) | −152810. | + | 359586.i | −0.366173 | + | 0.861663i | ||||
\(647\) | − | 152505.i | − | 0.364314i | −0.983269 | − | 0.182157i | \(-0.941692\pi\) | ||
0.983269 | − | 0.182157i | \(-0.0583079\pi\) | |||||||
\(648\) | −419683. | − | 13612.3i | −0.999474 | − | 0.0324176i | ||||
\(649\) | −30153.0 | −0.0715881 | ||||||||
\(650\) | −630042. | − | 267743.i | −1.49122 | − | 0.633711i | ||||
\(651\) | 135319. | − | 252404.i | 0.319299 | − | 0.595572i | ||||
\(652\) | 182650. | − | 176093.i | 0.429660 | − | 0.414235i | ||||
\(653\) | 149617. | − | 259144.i | 0.350876 | − | 0.607736i | −0.635527 | − | 0.772079i | \(-0.719217\pi\) |
0.986403 | + | 0.164343i | \(0.0525504\pi\) | |||||||
\(654\) | 458240. | − | 368167.i | 1.07137 | − | 0.860774i | ||||
\(655\) | 50211.7 | − | 28989.8i | 0.117037 | − | 0.0675713i | ||||
\(656\) | 257224. | + | 161321.i | 0.597728 | + | 0.374871i | ||||
\(657\) | 66903.0 | + | 100672.i | 0.154994 | + | 0.233227i | ||||
\(658\) | 26280.6 | − | 19786.9i | 0.0606992 | − | 0.0457010i | ||||
\(659\) | 361192. | − | 208535.i | 0.831702 | − | 0.480183i | −0.0227330 | − | 0.999742i | \(-0.507237\pi\) |
0.854435 | + | 0.519558i | \(0.173903\pi\) | |||||||
\(660\) | −397.013 | − | 1407.13i | −0.000911417 | − | 0.00323032i | ||||
\(661\) | −379775. | + | 657790.i | −0.869208 | + | 1.50551i | −0.00639999 | + | 0.999980i | \(0.502037\pi\) |
−0.862808 | + | 0.505532i | \(0.831296\pi\) | |||||||
\(662\) | −296792. | + | 36317.5i | −0.677230 | + | 0.0828706i | ||||
\(663\) | −347783. | − | 560846.i | −0.791191 | − | 1.27590i | ||||
\(664\) | 396938. | + | 322246.i | 0.900298 | + | 0.730888i | ||||
\(665\) | −17252.3 | −0.0390126 | ||||||||
\(666\) | −87245.9 | − | 466964.i | −0.196697 | − | 1.05277i | ||||
\(667\) | 401718.i | 0.902962i | ||||||||
\(668\) | −1616.48 | − | 6506.14i | −0.00362257 | − | 0.0145804i | ||||
\(669\) | −18198.9 | − | 578056.i | −0.0406625 | − | 1.29157i | ||||
\(670\) | −17768.5 | + | 2174.28i | −0.0395824 | + | 0.00484358i | ||||
\(671\) | −7216.22 | − | 4166.29i | −0.0160275 | − | 0.00925346i | ||||
\(672\) | 195800. | + | 84383.8i | 0.433584 | + | 0.186862i | ||||
\(673\) | 18836.0 | + | 32624.9i | 0.0415871 | + | 0.0720309i | 0.886070 | − | 0.463552i | \(-0.153425\pi\) |
−0.844483 | + | 0.535583i | \(0.820092\pi\) | |||||||
\(674\) | 453184. | − | 341207.i | 0.997597 | − | 0.751100i | ||||
\(675\) | −262256. | − | 368897.i | −0.575596 | − | 0.809651i | ||||
\(676\) | 209735. | − | 729170.i | 0.458964 | − | 1.59564i | ||||
\(677\) | 347010. | + | 601039.i | 0.757120 | + | 1.31137i | 0.944313 | + | 0.329047i | \(0.106728\pi\) |
−0.187193 | + | 0.982323i | \(0.559939\pi\) | |||||||
\(678\) | 64965.2 | + | 420636.i | 0.141326 | + | 0.915056i | ||||
\(679\) | −136614. | − | 78873.9i | −0.296315 | − | 0.171078i | ||||
\(680\) | −34142.9 | − | 5450.90i | −0.0738385 | − | 0.0117883i | ||||
\(681\) | −1899.01 | − | 60318.5i | −0.00409479 | − | 0.130064i | ||||
\(682\) | 25314.9 | + | 10757.8i | 0.0544261 | + | 0.0231289i | ||||
\(683\) | 357197.i | 0.765714i | 0.923808 | + | 0.382857i | \(0.125060\pi\) | ||||
−0.923808 | + | 0.382857i | \(0.874940\pi\) | |||||||
\(684\) | −464710. | − | 102519.i | −0.993275 | − | 0.219124i | ||||
\(685\) | 1256.87 | 0.00267861 | ||||||||
\(686\) | −154427. | + | 363391.i | −0.328152 | + | 0.772194i | ||||
\(687\) | 168616. | + | 271916.i | 0.357261 | + | 0.576131i | ||||
\(688\) | 197884. | + | 373647.i | 0.418054 | + | 0.789376i | ||||
\(689\) | −730122. | + | 1.26461e6i | −1.53800 | + | 2.66390i | ||||
\(690\) | −16637.7 | + | 42849.4i | −0.0349457 | + | 0.0900008i | ||||
\(691\) | −384473. | + | 221976.i | −0.805212 | + | 0.464889i | −0.845290 | − | 0.534307i | \(-0.820573\pi\) |
0.0400786 | + | 0.999197i | \(0.487239\pi\) | |||||||
\(692\) | −84922.2 | + | 295242.i | −0.177341 | + | 0.616547i | ||||
\(693\) | −9349.80 | + | 589.303i | −0.0194686 | + | 0.00122708i | ||||
\(694\) | 440359. | + | 584876.i | 0.914297 | + | 1.21435i | ||||
\(695\) | −34159.6 | + | 19722.1i | −0.0707202 | + | 0.0408304i | ||||
\(696\) | −142222. | − | 339452.i | −0.293596 | − | 0.700745i | ||||
\(697\) | −157749. | + | 273228.i | −0.324713 | + | 0.562420i | ||||
\(698\) | −65374.2 | − | 534247.i | −0.134182 | − | 1.09656i | ||||
\(699\) | 265526. | − | 495272.i | 0.543442 | − | 1.01365i | ||||
\(700\) | 55415.0 | + | 223039.i | 0.113092 | + | 0.455182i | ||||
\(701\) | −483771. | −0.984474 | −0.492237 | − | 0.870461i | \(-0.663821\pi\) | ||||
−0.492237 | + | 0.870461i | \(0.663821\pi\) | |||||||
\(702\) | 593694. | − | 541854.i | 1.20473 | − | 1.09953i | ||||
\(703\) | − | 538375.i | − | 1.08937i | ||||||
\(704\) | −6375.91 | + | 19459.5i | −0.0128646 | + | 0.0392632i | ||||
\(705\) | −5726.62 | − | 3070.17i | −0.0115218 | − | 0.00617710i | ||||
\(706\) | 97304.0 | + | 795181.i | 0.195219 | + | 1.59535i | ||||
\(707\) | −61929.9 | − | 35755.3i | −0.123897 | − | 0.0715321i | ||||
\(708\) | −841816. | − | 213698.i | −1.67939 | − | 0.426319i | ||||
\(709\) | −79169.5 | − | 137126.i | −0.157494 | − | 0.272788i | 0.776470 | − | 0.630154i | \(-0.217008\pi\) |
−0.933965 | + | 0.357366i | \(0.883675\pi\) | |||||||
\(710\) | 2561.85 | + | 3402.60i | 0.00508203 | + | 0.00674986i | ||||
\(711\) | −372688. | − | 184951.i | −0.737236 | − | 0.365863i | ||||
\(712\) | −202559. | − | 529638.i | −0.399569 | − | 1.04477i | ||||
\(713\) | −432382. | − | 748907.i | −0.850527 | − | 1.47316i | ||||
\(714\) | −80189.5 | + | 206524.i | −0.157297 | + | 0.405110i | ||||
\(715\) | 2423.76 | + | 1399.36i | 0.00474108 | + | 0.00273726i | ||||
\(716\) | 573875. | − | 553273.i | 1.11942 | − | 1.07923i | ||||
\(717\) | −28709.3 | + | 17802.8i | −0.0558450 | + | 0.0346297i | ||||
\(718\) | −252154. | + | 593359.i | −0.489122 | + | 1.15098i | ||||
\(719\) | 781622.i | 1.51196i | 0.654597 | + | 0.755978i | \(0.272838\pi\) | ||||
−0.654597 | + | 0.755978i | \(0.727162\pi\) | |||||||
\(720\) | −1111.37 | − | 42098.1i | −0.00214384 | − | 0.0812078i | ||||
\(721\) | −251358. | −0.483529 | ||||||||
\(722\) | −16604.7 | − | 7056.34i | −0.0318535 | − | 0.0135365i | ||||
\(723\) | 806587. | − | 25393.8i | 1.54303 | − | 0.0485792i | ||||
\(724\) | 155146. | + | 160923.i | 0.295980 | + | 0.307001i | ||||
\(725\) | 198358. | − | 343566.i | 0.377375 | − | 0.653633i | ||||
\(726\) | 80313.1 | + | 520011.i | 0.152375 | + | 0.986595i | ||||
\(727\) | −51590.1 | + | 29785.6i | −0.0976107 | + | 0.0563556i | −0.548011 | − | 0.836471i | \(-0.684615\pi\) |
0.450400 | + | 0.892827i | \(0.351281\pi\) | |||||||
\(728\) | −381202. | + | 145790.i | −0.719271 | + | 0.275085i | ||||
\(729\) | 521994. | − | 99759.6i | 0.982223 | − | 0.187715i | ||||
\(730\) | −9684.71 | + | 7291.71i | −0.0181736 | + | 0.0136831i | ||||
\(731\) | −380482. | + | 219672.i | −0.712032 | + | 0.411092i | ||||
\(732\) | −171937. | − | 167457.i | −0.320883 | − | 0.312523i | ||||
\(733\) | 106923. | − | 185196.i | 0.199004 | − | 0.344685i | −0.749202 | − | 0.662342i | \(-0.769563\pi\) |
0.948206 | + | 0.317657i | \(0.102896\pi\) | |||||||
\(734\) | −792350. | + | 96957.5i | −1.47070 | + | 0.179966i | ||||
\(735\) | 34086.2 | − | 1073.13i | 0.0630963 | − | 0.00198646i | ||||
\(736\) | 528122. | − | 368179.i | 0.974943 | − | 0.679678i | ||||
\(737\) | −11016.5 | −0.0202819 | ||||||||
\(738\) | −362420. | − | 127750.i | −0.665425 | − | 0.234556i | ||||
\(739\) | 218903.i | 0.400832i | 0.979711 | + | 0.200416i | \(0.0642294\pi\) | ||||
−0.979711 | + | 0.200416i | \(0.935771\pi\) | |||||||
\(740\) | 46237.2 | − | 11487.8i | 0.0844361 | − | 0.0209785i | ||||
\(741\) | 774180. | − | 480073.i | 1.40996 | − | 0.874320i | ||||
\(742\) | 486594. | − | 59543.1i | 0.883810 | − | 0.108149i | ||||
\(743\) | 431487. | + | 249119.i | 0.781610 | + | 0.451263i | 0.837001 | − | 0.547202i | \(-0.184307\pi\) |
−0.0553907 | + | 0.998465i | \(0.517640\pi\) | |||||||
\(744\) | 630503. | + | 479749.i | 1.13905 | + | 0.866699i | ||||
\(745\) | 628.850 | + | 1089.20i | 0.00113301 | + | 0.00196243i | ||||
\(746\) | 18497.9 | − | 13927.3i | 0.0332388 | − | 0.0250258i | ||||
\(747\) | −579631. | − | 287650.i | −1.03875 | − | 0.515493i | ||||
\(748\) | −20448.9 | − | 5881.85i | −0.0365483 | − | 0.0105126i | ||||
\(749\) | 163175. | + | 282628.i | 0.290864 | + | 0.503792i | ||||
\(750\) | 71009.4 | − | 57051.6i | 0.126239 | − | 0.101425i | ||||
\(751\) | −534346. | − | 308505.i | −0.947421 | − | 0.546994i | −0.0551419 | − | 0.998479i | \(-0.517561\pi\) |
−0.892279 | + | 0.451485i | \(0.850894\pi\) | |||||||
\(752\) | 42592.3 | + | 80423.4i | 0.0753174 | + | 0.142215i | ||||
\(753\) | −73342.9 | − | 39320.8i | −0.129350 | − | 0.0693477i | ||||
\(754\) | 648396. | + | 275543.i | 1.14051 | + | 0.484670i | ||||
\(755\) | 8813.01i | 0.0154607i | ||||||||
\(756\) | −265206. | − | 49811.1i | −0.464023 | − | 0.0871530i | ||||
\(757\) | 483106. | 0.843045 | 0.421523 | − | 0.906818i | \(-0.361496\pi\) | ||||
0.421523 | + | 0.906818i | \(0.361496\pi\) | |||||||
\(758\) | 340938. | − | 802283.i | 0.593386 | − | 1.39633i | ||||
\(759\) | −13366.1 | + | 24931.1i | −0.0232018 | + | 0.0432771i | ||||
\(760\) | 7524.32 | − | 47130.2i | 0.0130269 | − | 0.0815966i | ||||
\(761\) | 68847.3 | − | 119247.i | 0.118882 | − | 0.205910i | −0.800443 | − | 0.599409i | \(-0.795402\pi\) |
0.919325 | + | 0.393499i | \(0.128736\pi\) | |||||||
\(762\) | 473051. | + | 588785.i | 0.814701 | + | 1.01402i | ||||
\(763\) | 327141. | − | 188875.i | 0.561935 | − | 0.324433i | ||||
\(764\) | −479301. | − | 137864.i | −0.821148 | − | 0.236192i | ||||
\(765\) | 43672.7 | − | 2752.62i | 0.0746255 | − | 0.00470353i | ||||
\(766\) | −167209. | − | 222084.i | −0.284972 | − | 0.378494i | ||||
\(767\) | 1.43980e6 | − | 831268.i | 2.44743 | − | 1.41303i | ||||
\(768\) | −315916. | + | 498086.i | −0.535610 | + | 0.844465i | ||||
\(769\) | 173385. | − | 300311.i | 0.293196 | − | 0.507830i | −0.681368 | − | 0.731941i | \(-0.738614\pi\) |
0.974564 | + | 0.224111i | \(0.0719478\pi\) | |||||||
\(770\) | −114.121 | − | 932.610i | −0.000192479 | − | 0.00157296i | ||||
\(771\) | 72329.9 | + | 116641.i | 0.121677 | + | 0.196220i | ||||
\(772\) | −419197. | + | 104151.i | −0.703369 | + | 0.174755i | ||||
\(773\) | −456941. | −0.764717 | −0.382358 | − | 0.924014i | \(-0.624888\pi\) | ||||
−0.382358 | + | 0.924014i | \(0.624888\pi\) | |||||||
\(774\) | −348122. | − | 406406.i | −0.581098 | − | 0.678388i | ||||
\(775\) | 853996.i | 1.42185i | ||||||||
\(776\) | 275050. | − | 338803.i | 0.456761 | − | 0.562632i | ||||
\(777\) | −9606.30 | − | 305127.i | −0.0159116 | − | 0.505403i | ||||
\(778\) | −27919.5 | − | 228162.i | −0.0461263 | − | 0.376951i | ||||
\(779\) | −377159. | − | 217753.i | −0.621512 | − | 0.358830i | ||||
\(780\) | 57749.5 | + | 56245.0i | 0.0949202 | + | 0.0924474i | ||||
\(781\) | 1310.58 | + | 2269.99i | 0.00214863 | + | 0.00372154i | ||||
\(782\) | 402373. | + | 534424.i | 0.657984 | + | 0.873922i | ||||
\(783\) | 269896. | + | 379643.i | 0.440223 | + | 0.619230i | ||||
\(784\) | −404646. | − | 253777.i | −0.658329 | − | 0.412877i | ||||
\(785\) | −6303.68 | − | 10918.3i | −0.0102295 | − | 0.0177180i | ||||
\(786\) | 1.01571e6 | − | 156871.i | 1.64408 | − | 0.253921i | ||||
\(787\) | 602982. | + | 348132.i | 0.973543 | + | 0.562075i | 0.900314 | − | 0.435240i | \(-0.143337\pi\) |
0.0732283 | + | 0.997315i | \(0.476670\pi\) | |||||||
\(788\) | 115675. | + | 119982.i | 0.186289 | + | 0.193226i | ||||
\(789\) | 29261.0 | + | 929423.i | 0.0470040 | + | 1.49300i | ||||
\(790\) | 16319.8 | − | 38403.2i | 0.0261494 | − | 0.0615337i | ||||
\(791\) | 273518.i | 0.437153i | ||||||||
\(792\) | 2467.89 | − | 25798.9i | 0.00393437 | − | 0.0411293i | ||||
\(793\) | 459430. | 0.730589 | ||||||||
\(794\) | 48799.6 | + | 20737.9i | 0.0774061 | + | 0.0328945i | ||||
\(795\) | −51028.9 | − | 82290.7i | −0.0807387 | − | 0.130202i | ||||
\(796\) | −97201.6 | + | 93712.1i | −0.153408 | + | 0.147900i | ||||
\(797\) | −65680.3 | + | 113762.i | −0.103399 | + | 0.179093i | −0.913083 | − | 0.407773i | \(-0.866305\pi\) |
0.809684 | + | 0.586867i | \(0.199639\pi\) | |||||||
\(798\) | −285081. | − | 110692.i | −0.447675 | − | 0.173824i | ||||
\(799\) | −81894.7 | + | 47281.9i | −0.128281 | + | 0.0740631i | ||||
\(800\) | −633470. | + | 54108.9i | −0.989796 | + | 0.0845451i | ||||
\(801\) | 397222. | + | 597720.i | 0.619111 | + | 0.931608i | ||||
\(802\) | 17177.0 | − | 12932.7i | 0.0267053 | − | 0.0201067i | ||||
\(803\) | −6461.00 | + | 3730.26i | −0.0100200 | + | 0.00578506i | ||||
\(804\) | −307561. | − | 78075.6i | −0.475794 | − | 0.120782i | ||||
\(805\) | −14769.6 | + | 25581.7i | −0.0227917 | + | 0.0394764i | ||||
\(806\) | −1.50536e6 | + | 184206.i | −2.31723 | + | 0.283552i | ||||
\(807\) | −365791. | + | 682291.i | −0.561677 | + | 1.04767i | ||||
\(808\) | 124686. | − | 153587.i | 0.190984 | − | 0.235251i | ||||
\(809\) | 796199. | 1.21653 | 0.608267 | − | 0.793732i | \(-0.291865\pi\) | ||||
0.608267 | + | 0.793732i | \(0.291865\pi\) | |||||||
\(810\) | 13065.1 | + | 51672.9i | 0.0199133 | + | 0.0787576i | ||||
\(811\) | − | 116976.i | − | 0.177851i | −0.996038 | − | 0.0889253i | \(-0.971657\pi\) | ||
0.996038 | − | 0.0889253i | \(-0.0283432\pi\) | |||||||
\(812\) | −57029.3 | − | 229536.i | −0.0864940 | − | 0.348128i | ||||
\(813\) | 123969. | + | 66462.4i | 0.187556 | + | 0.100553i | ||||
\(814\) | 29102.9 | − | 3561.24i | 0.0439226 | − | 0.00537468i | ||||
\(815\) | −27889.5 | − | 16102.0i | −0.0419881 | − | 0.0242418i | ||||
\(816\) | −529211. | − | 309135.i | −0.794783 | − | 0.464267i | ||||
\(817\) | −303230. | − | 525210.i | −0.454285 | − | 0.786845i | ||||
\(818\) | 769142. | − | 579094.i | 1.14948 | − | 0.865451i | ||||
\(819\) | 430204. | − | 285897.i | 0.641368 | − | 0.426228i | ||||
\(820\) | 10653.4 | − | 37037.9i | 0.0158439 | − | 0.0550832i | ||||
\(821\) | −146773. | − | 254219.i | −0.217751 | − | 0.377157i | 0.736369 | − | 0.676580i | \(-0.236539\pi\) |
−0.954120 | + | 0.299424i | \(0.903206\pi\) | |||||||
\(822\) | 20768.8 | + | 8064.15i | 0.0307374 | + | 0.0119348i | ||||
\(823\) | −198711. | − | 114726.i | −0.293375 | − | 0.169380i | 0.346088 | − | 0.938202i | \(-0.387510\pi\) |
−0.639463 | + | 0.768822i | \(0.720843\pi\) | |||||||
\(824\) | 109626. | − | 686663.i | 0.161457 | − | 1.01132i | ||||
\(825\) | 23741.6 | − | 14722.3i | 0.0348821 | − | 0.0216306i | ||||
\(826\) | −513676. | − | 218292.i | −0.752886 | − | 0.319947i | ||||
\(827\) | 673431.i | 0.984651i | 0.870411 | + | 0.492326i | \(0.163853\pi\) | ||||
−0.870411 | + | 0.492326i | \(0.836147\pi\) | |||||||
\(828\) | −549848. | + | 601304.i | −0.802015 | + | 0.877068i | ||||
\(829\) | 268282. | 0.390375 | 0.195188 | − | 0.980766i | \(-0.437468\pi\) | ||||
0.195188 | + | 0.980766i | \(0.437468\pi\) | |||||||
\(830\) | 25381.8 | − | 59727.4i | 0.0368439 | − | 0.0866996i | ||||
\(831\) | 509279. | − | 16033.6i | 0.737486 | − | 0.0232183i | ||||
\(832\) | −232017. | − | 1.10496e6i | −0.335177 | − | 1.59624i | ||||
\(833\) | 248158. | − | 429823.i | 0.357634 | − | 0.619440i | ||||
\(834\) | −690999. | + | 106721.i | −0.993448 | + | 0.153433i | ||||
\(835\) | −736.936 | + | 425.470i | −0.00105696 | + | 0.000610234i | ||||
\(836\) | 8119.18 | − | 28227.3i | 0.0116172 | − | 0.0403884i | ||||
\(837\) | −911778. | − | 417257.i | −1.30148 | − | 0.595598i | ||||
\(838\) | 85204.7 | + | 113167.i | 0.121332 | + | 0.161151i | ||||
\(839\) | −867924. | + | 501096.i | −1.23299 | + | 0.711865i | −0.967651 | − | 0.252292i | \(-0.918816\pi\) |
−0.265334 | + | 0.964156i | \(0.585482\pi\) | |||||||
\(840\) | 3423.49 | − | 26845.5i | 0.00485189 | − | 0.0380464i | ||||
\(841\) | 149504. | − | 258949.i | 0.211379 | − | 0.366119i | ||||
\(842\) | 80210.9 | + | 655494.i | 0.113138 | + | 0.924581i | ||||
\(843\) | −999108. | + | 31454.9i | −1.40591 | + | 0.0442622i | ||||
\(844\) | −88524.0 | − | 356299.i | −0.124273 | − | 0.500183i | ||||
\(845\) | −96307.2 | −0.134879 | ||||||||
\(846\) | −74929.5 | − | 87474.5i | −0.104692 | − | 0.122220i | ||||
\(847\) | 338137.i | 0.471330i | ||||||||
\(848\) | −49559.1 | + | 1.35525e6i | −0.0689179 | + | 1.88464i | ||||
\(849\) | −697550. | + | 432554.i | −0.967743 | + | 0.600102i | ||||
\(850\) | −80241.4 | − | 655743.i | −0.111061 | − | 0.907603i | ||||
\(851\) | −798300. | − | 460899.i | −1.10232 | − | 0.636424i | ||||
\(852\) | 20501.3 | + | 72662.3i | 0.0282424 | + | 0.100099i | ||||
\(853\) | −205795. | − | 356448.i | −0.282837 | − | 0.489889i | 0.689245 | − | 0.724528i | \(-0.257942\pi\) |
−0.972082 | + | 0.234640i | \(0.924609\pi\) | |||||||
\(854\) | −92771.3 | − | 123217.i | −0.127203 | − | 0.168949i | ||||
\(855\) | 3799.67 | + | 60284.9i | 0.00519772 | + | 0.0824663i | ||||
\(856\) | −843253. | + | 322501.i | −1.15083 | + | 0.440133i | ||||
\(857\) | 460403. | + | 797442.i | 0.626869 | + | 1.08577i | 0.988176 | + | 0.153322i | \(0.0489972\pi\) |
−0.361307 | + | 0.932447i | \(0.617669\pi\) | |||||||
\(858\) | 31072.3 | + | 38674.2i | 0.0422084 | + | 0.0525348i | ||||
\(859\) | −520799. | − | 300684.i | −0.705804 | − | 0.407496i | 0.103702 | − | 0.994608i | \(-0.466931\pi\) |
−0.809505 | + | 0.587112i | \(0.800265\pi\) | |||||||
\(860\) | 38636.2 | − | 37249.2i | 0.0522394 | − | 0.0503640i | ||||
\(861\) | −217642. | − | 116683.i | −0.293587 | − | 0.157399i | ||||
\(862\) | −252927. | + | 595178.i | −0.340393 | + | 0.801000i | ||||
\(863\) | − | 1.01872e6i | − | 1.36783i | −0.729560 | − | 0.683917i | \(-0.760275\pi\) | ||
0.729560 | − | 0.683917i | \(-0.239725\pi\) | |||||||
\(864\) | 251740. | − | 702768.i | 0.337228 | − | 0.941423i | ||||
\(865\) | 38994.9 | 0.0521166 | ||||||||
\(866\) | −227639. | − | 96737.6i | −0.303536 | − | 0.128991i | ||||
\(867\) | −54262.2 | + | 101212.i | −0.0721870 | + | 0.134647i | ||||
\(868\) | 353375. | + | 366533.i | 0.469025 | + | 0.486490i | ||||
\(869\) | 12839.6 | − | 22238.9i | 0.0170025 | − | 0.0294492i | ||||
\(870\) | −36418.0 | + | 29259.6i | −0.0481147 | + | 0.0386571i | ||||
\(871\) | 526036. | − | 303707.i | 0.693392 | − | 0.400330i | ||||
\(872\) | 373294. | + | 976063.i | 0.490929 | + | 1.28365i | ||||
\(873\) | −245521. | + | 494740.i | −0.322152 | + | 0.649156i | ||||
\(874\) | −737709. | + | 555428.i | −0.965744 | + | 0.727118i | ||||
\(875\) | 50694.1 | − | 29268.3i | 0.0662128 | − | 0.0382280i | ||||
\(876\) | −206816. | + | 58352.0i | −0.269511 | + | 0.0760409i | ||||
\(877\) | −432672. | + | 749411.i | −0.562549 | + | 0.974363i | 0.434724 | + | 0.900564i | \(0.356846\pi\) |
−0.997273 | + | 0.0737993i | \(0.976488\pi\) | |||||||
\(878\) | 1.22877e6 | − | 150361.i | 1.59398 | − | 0.195050i | ||||
\(879\) | 393743. | + | 634962.i | 0.509607 | + | 0.821807i | ||||
\(880\) | 2597.49 | + | 94.9854i | 0.00335419 | + | 0.000122657i | ||||
\(881\) | 1.46275e6 | 1.88459 | 0.942296 | − | 0.334780i | \(-0.108662\pi\) | ||||
0.942296 | + | 0.334780i | \(0.108662\pi\) | |||||||
\(882\) | 570132. | + | 200966.i | 0.732889 | + | 0.258337i | ||||
\(883\) | 162909.i | 0.208941i | 0.994528 | + | 0.104470i | \(0.0333148\pi\) | ||||
−0.994528 | + | 0.104470i | \(0.966685\pi\) | |||||||
\(884\) | 1.13858e6 | − | 282886.i | 1.45700 | − | 0.361999i | ||||
\(885\) | 3469.03 | + | 110187.i | 0.00442916 | + | 0.140684i | ||||
\(886\) | −186206. | + | 22785.5i | −0.237206 | + | 0.0290262i | ||||
\(887\) | −192525. | − | 111154.i | −0.244703 | − | 0.141280i | 0.372633 | − | 0.927979i | \(-0.378455\pi\) |
−0.617337 | + | 0.786699i | \(0.711788\pi\) | |||||||
\(888\) | 837739. | + | 106833.i | 1.06239 | + | 0.135482i | ||||
\(889\) | 242682. | + | 420338.i | 0.307068 | + | 0.531857i | ||||
\(890\) | −57500.8 | + | 43292.9i | −0.0725929 | + | 0.0546559i | ||||
\(891\) | 4118.41 | + | 32541.2i | 0.00518769 | + | 0.0409901i | ||||
\(892\) | 988102. | + | 284213.i | 1.24186 | + | 0.357203i | ||||
\(893\) | −65267.1 | − | 113046.i | −0.0818448 | − | 0.141759i | ||||
\(894\) | 3402.87 | + | 22032.9i | 0.00425766 | + | 0.0275674i | ||||
\(895\) | −87627.1 | − | 50591.5i | −0.109394 | − | 0.0631585i | ||||
\(896\) | −249494. | + | 285347.i | −0.310774 | + | 0.355432i | ||||
\(897\) | −49080.0 | − | 1.55894e6i | −0.0609986 | − | 1.93751i | ||||
\(898\) | −459646. | − | 195332.i | −0.569995 | − | 0.242225i | ||||
\(899\) | − | 878873.i | − | 1.08744i | ||||||
\(900\) | 767162. | − | 242759.i | 0.947113 | − | 0.299703i | ||||
\(901\) | −1.40918e6 | −1.73587 | ||||||||
\(902\) | 9276.24 | − | 21828.5i | 0.0114014 | − | 0.0268294i | ||||
\(903\) | −181229. | − | 292255.i | −0.222255 | − | 0.358415i | ||||
\(904\) | −747202. | − | 119290.i | −0.914326 | − | 0.145972i | ||||
\(905\) | 14186.6 | − | 24571.9i | 0.0173213 | − | 0.0300014i | ||||
\(906\) | −56544.8 | + | 145628.i | −0.0688868 | + | 0.177414i | ||||
\(907\) | 1.03664e6 | − | 598505.i | 1.26013 | − | 0.727534i | 0.287028 | − | 0.957922i | \(-0.407333\pi\) |
0.973099 | + | 0.230388i | \(0.0739995\pi\) | |||||||
\(908\) | 103106. | + | 29656.8i | 0.125058 | + | 0.0359711i | ||||
\(909\) | −111300. | + | 224277.i | −0.134700 | + | 0.271429i | ||||
\(910\) | 31159.7 | + | 41385.7i | 0.0376280 | + | 0.0499767i | ||||
\(911\) | 806036. | − | 465365.i | 0.971220 | − | 0.560734i | 0.0716123 | − | 0.997433i | \(-0.477186\pi\) |
0.899608 | + | 0.436698i | \(0.143852\pi\) | |||||||
\(912\) | 426724. | − | 730513.i | 0.513047 | − | 0.878290i | ||||
\(913\) | 19969.1 | − | 34587.5i | 0.0239562 | − | 0.0414933i | ||||
\(914\) | 60972.0 | + | 498271.i | 0.0729857 | + | 0.596449i | ||||
\(915\) | −14394.6 | + | 26849.4i | −0.0171932 | + | 0.0320695i | ||||
\(916\) | −552022. | + | 137152.i | −0.657908 | + | 0.163460i | ||||
\(917\) | 660464. | 0.785435 | ||||||||
\(918\) | 739317. | + | 234722.i | 0.877295 | + | 0.278527i | ||||
\(919\) | − | 1.46503e6i | − | 1.73467i | −0.497725 | − | 0.867335i | \(-0.665831\pi\) | ||
0.497725 | − | 0.867335i | \(-0.334169\pi\) | |||||||
\(920\) | −63442.9 | − | 51504.8i | −0.0749562 | − | 0.0608516i | ||||
\(921\) | −517178. | − | 277271.i | −0.609707 | − | 0.326878i | ||||
\(922\) | −50185.2 | − | 410120.i | −0.0590355 | − | 0.482446i | ||||
\(923\) | −125160. | − | 72261.0i | −0.146913 | − | 0.0848205i | ||||
\(924\) | 4097.92 | − | 16142.8i | 0.00479976 | − | 0.0189076i | ||||
\(925\) | 455160. | + | 788360.i | 0.531962 | + | 0.921385i | ||||
\(926\) | 771115. | + | 1.02418e6i | 0.899284 | + | 1.19441i | ||||
\(927\) | 55359.2 | + | 878321.i | 0.0644214 | + | 1.02210i | ||||
\(928\) | 651923. | − | 55685.1i | 0.757008 | − | 0.0646611i | ||||
\(929\) | −493591. | − | 854925.i | −0.571921 | − | 0.990596i | −0.996369 | − | 0.0851437i | \(-0.972865\pi\) |
0.424448 | − | 0.905452i | \(-0.360468\pi\) | |||||||
\(930\) | 36399.7 | − | 93745.4i | 0.0420854 | − | 0.108389i | ||||
\(931\) | 593319. | + | 342553.i | 0.684524 | + | 0.395210i | ||||
\(932\) | 693399. | + | 719219.i | 0.798273 | + | 0.827998i | ||||
\(933\) | −1.02263e6 | + | 634137.i | −1.17478 | + | 0.728484i | ||||
\(934\) | 668612. | − | 1.57335e6i | 0.766444 | − | 1.80357i | ||||
\(935\) | 2700.85i | 0.00308942i | ||||||||
\(936\) | 593392. | + | 1.29993e6i | 0.677314 | + | 1.48377i | ||||
\(937\) | −287243. | −0.327167 | −0.163584 | − | 0.986529i | \(-0.552305\pi\) | ||||
−0.163584 | + | 0.986529i | \(0.552305\pi\) | |||||||
\(938\) | −187674. | − | 79753.9i | −0.213303 | − | 0.0906455i | ||||
\(939\) | −101111. | + | 3183.26i | −0.114674 | + | 0.00361028i | ||||
\(940\) | 8316.04 | − | 8017.49i | 0.00941154 | − | 0.00907367i | ||||
\(941\) | 149097. | − | 258244.i | 0.168380 | − | 0.291643i | −0.769470 | − | 0.638683i | \(-0.779480\pi\) |
0.937850 | + | 0.347040i | \(0.112813\pi\) | |||||||
\(942\) | −34110.8 | − | 220861.i | −0.0384407 | − | 0.248895i | ||||
\(943\) | −645766. | + | 372833.i | −0.726193 | + | 0.419267i | ||||
\(944\) | 820364. | − | 1.30806e6i | 0.920583 | − | 1.46786i | ||||
\(945\) | 3229.15 | + | 34099.0i | 0.00361597 | + | 0.0381837i | ||||
\(946\) | 26385.5 | − | 19865.9i | 0.0294837 | − | 0.0221986i | ||||
\(947\) | −904210. | + | 522046.i | −1.00825 | + | 0.582115i | −0.910680 | − | 0.413113i | \(-0.864441\pi\) |
−0.0975732 | + | 0.995228i | \(0.531108\pi\) | |||||||
\(948\) | 516069. | − | 529873.i | 0.574237 | − | 0.589597i | ||||
\(949\) | 205674. | − | 356238.i | 0.228374 | − | 0.395555i | ||||
\(950\) | 905175. | − | 110764.i | 1.00296 | − | 0.122730i | ||||
\(951\) | 352681. | − | 11103.4i | 0.389961 | − | 0.0122771i | ||||
\(952\) | −305780. | − | 248241.i | −0.337392 | − | 0.273905i | ||||
\(953\) | −1.38691e6 | −1.52708 | −0.763539 | − | 0.645762i | \(-0.776540\pi\) | ||||
−0.763539 | + | 0.645762i | \(0.776540\pi\) | |||||||
\(954\) | −315229. | − | 1.68719e6i | −0.346362 | − | 1.85382i | ||||
\(955\) | 63305.1i | 0.0694115i | ||||||||
\(956\) | −14480.7 | − | 58283.3i | −0.0158444 | − | 0.0637717i | ||||
\(957\) | −24433.2 | + | 15151.2i | −0.0266782 | + | 0.0165433i | ||||
\(958\) | −762556. | + | 93311.7i | −0.830885 | + | 0.101673i | ||||
\(959\) | 12399.2 | + | 7158.71i | 0.0134821 | + | 0.00778391i | ||||
\(960\) | 71843.9 | + | 21060.6i | 0.0779556 | + | 0.0228522i | ||||
\(961\) | 484199. | + | 838657.i | 0.524297 | + | 0.908109i | ||||
\(962\) | −1.29148e6 | + | 972367.i | −1.39552 | + | 1.05070i | ||||
\(963\) | 951649. | − | 632430.i | 1.02618 | − | 0.681961i | ||||
\(964\) | −396576. | + | 1.37874e6i | −0.426748 | + | 1.48364i | ||||
\(965\) | 27413.5 | + | 47481.5i | 0.0294381 | + | 0.0509882i | ||||
\(966\) | −408189. | + | 327954.i | −0.437429 | + | 0.351447i | ||||
\(967\) | 697159. | + | 402505.i | 0.745554 | + | 0.430446i | 0.824085 | − | 0.566466i | \(-0.191690\pi\) |
−0.0785311 | + | 0.996912i | \(0.525023\pi\) | |||||||
\(968\) | −923727. | − | 147473.i | −0.985809 | − | 0.157384i | ||||
\(969\) | 774772. | + | 415372.i | 0.825137 | + | 0.442374i | ||||
\(970\) | −50979.9 | − | 21664.4i | −0.0541821 | − | 0.0230252i | ||||
\(971\) | 643421.i | 0.682428i | 0.939986 | + | 0.341214i | \(0.110838\pi\) | ||||
−0.939986 | + | 0.341214i | \(0.889162\pi\) | |||||||
\(972\) | −115646. | + | 937679.i | −0.122405 | + | 0.992480i | ||||
\(973\) | −449321. | −0.474604 | ||||||||
\(974\) | 82735.5 | − | 194690.i | 0.0872116 | − | 0.205223i | ||||
\(975\) | −727788. | + | 1.35750e6i | −0.765588 | + | 1.42801i | ||||
\(976\) | 377067. | − | 199695.i | 0.395839 | − | 0.209637i | ||||
\(977\) | 63505.8 | − | 109995.i | 0.0665311 | − | 0.115235i | −0.830841 | − | 0.556510i | \(-0.812140\pi\) |
0.897372 | + | 0.441275i | \(0.145474\pi\) | |||||||
\(978\) | −357540. | − | 445014.i | −0.373807 | − | 0.465260i | ||||
\(979\) | −38360.8 | + | 22147.6i | −0.0400241 | + | 0.0231079i | ||||
\(980\) | −16759.2 | + | 58265.3i | −0.0174502 | + | 0.0606678i | ||||
\(981\) | −732036. | − | 1.10153e6i | −0.760667 | − | 1.14461i | ||||
\(982\) | 17693.7 | + | 23500.5i | 0.0183483 | + | 0.0243699i | ||||
\(983\) | 158662. | − | 91603.6i | 0.164197 | − | 0.0947994i | −0.415650 | − | 0.909525i | \(-0.636446\pi\) |
0.579847 | + | 0.814725i | \(0.303112\pi\) | |||||||
\(984\) | 413677. | − | 543669.i | 0.427239 | − | 0.561493i | ||||
\(985\) | 10577.4 | − | 18320.6i | 0.0109020 | − | 0.0188828i | ||||
\(986\) | 82578.9 | + | 674846.i | 0.0849406 | + | 0.694146i | ||||
\(987\) | −39007.5 | − | 62904.7i | −0.0400418 | − | 0.0645727i | ||||
\(988\) | 390490. | + | 1.57168e6i | 0.400034 | + | 1.61009i | ||||
\(989\) | −1.03837e6 | −1.06160 | ||||||||
\(990\) | −3233.69 | + | 604.171i | −0.00329934 | + | 0.000616438i | ||||
\(991\) | − | 684255.i | − | 0.696740i | −0.937357 | − | 0.348370i | \(-0.886735\pi\) | ||
0.937357 | − | 0.348370i | \(-0.113265\pi\) | |||||||
\(992\) | −1.15542e6 | + | 805497.i | −1.17413 | + | 0.818542i | ||||
\(993\) | 21170.1 | + | 672429.i | 0.0214696 | + | 0.681943i | ||||
\(994\) | 5893.04 | + | 48158.7i | 0.00596440 | + | 0.0487419i | ||||
\(995\) | 14842.1 | + | 8569.07i | 0.0149916 | + | 0.00865541i | ||||
\(996\) | 802628. | − | 824096.i | 0.809087 | − | 0.830729i | ||||
\(997\) | 271816. | + | 470800.i | 0.273455 | + | 0.473637i | 0.969744 | − | 0.244124i | \(-0.0785003\pi\) |
−0.696289 | + | 0.717761i | \(0.745167\pi\) | |||||||
\(998\) | −998582. | − | 1.32630e6i | −1.00259 | − | 1.33162i | ||||
\(999\) | −1.06409e6 | + | 100769.i | −1.06622 | + | 0.100970i |
(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 | 36.5.f.a.31.20 | yes | 44 | |
3.2 | odd | 2 | 108.5.f.a.91.3 | 44 | |||
4.3 | odd | 2 | inner | 36.5.f.a.31.11 | yes | 44 | |
9.2 | odd | 6 | 108.5.f.a.19.12 | 44 | |||
9.4 | even | 3 | 324.5.d.f.163.6 | 22 | |||
9.5 | odd | 6 | 324.5.d.e.163.17 | 22 | |||
9.7 | even | 3 | inner | 36.5.f.a.7.11 | ✓ | 44 | |
12.11 | even | 2 | 108.5.f.a.91.12 | 44 | |||
36.7 | odd | 6 | inner | 36.5.f.a.7.20 | yes | 44 | |
36.11 | even | 6 | 108.5.f.a.19.3 | 44 | |||
36.23 | even | 6 | 324.5.d.e.163.18 | 22 | |||
36.31 | odd | 6 | 324.5.d.f.163.5 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.11 | ✓ | 44 | 9.7 | even | 3 | inner | |
36.5.f.a.7.20 | yes | 44 | 36.7 | odd | 6 | inner | |
36.5.f.a.31.11 | yes | 44 | 4.3 | odd | 2 | inner | |
36.5.f.a.31.20 | yes | 44 | 1.1 | even | 1 | trivial | |
108.5.f.a.19.3 | 44 | 36.11 | even | 6 | |||
108.5.f.a.19.12 | 44 | 9.2 | odd | 6 | |||
108.5.f.a.91.3 | 44 | 3.2 | odd | 2 | |||
108.5.f.a.91.12 | 44 | 12.11 | even | 2 | |||
324.5.d.e.163.17 | 22 | 9.5 | odd | 6 | |||
324.5.d.e.163.18 | 22 | 36.23 | even | 6 | |||
324.5.d.f.163.5 | 22 | 36.31 | odd | 6 | |||
324.5.d.f.163.6 | 22 | 9.4 | even | 3 |