Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,6,Mod(5,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.5");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.e (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.56614111701\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 5 x^{16} - 30 x^{15} - 42 x^{14} - 344 x^{13} + 2904 x^{12} + 5344 x^{11} + 16576 x^{10} - 297472 x^{9} + 265216 x^{8} + 1368064 x^{7} + 11894784 x^{6} + \cdots + 68719476736 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{36} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(-1.58716 + 3.67164i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.5 |
Dual form | 16.6.e.a.13.1 |
$q$-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 \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(15\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.25880 | + | 2.08448i | −0.929632 | + | 0.368488i | ||||
\(3\) | −3.18000 | + | 3.18000i | −0.203997 | + | 0.203997i | −0.801710 | − | 0.597713i | \(-0.796076\pi\) |
0.597713 | + | 0.801710i | \(0.296076\pi\) | |||||||
\(4\) | 23.3098 | − | 21.9238i | 0.728433 | − | 0.685117i | ||||
\(5\) | −67.3647 | − | 67.3647i | −1.20506 | − | 1.20506i | −0.972609 | − | 0.232447i | \(-0.925327\pi\) |
−0.232447 | − | 0.972609i | \(-0.574673\pi\) | |||||||
\(6\) | 10.0943 | − | 23.3517i | 0.114472 | − | 0.264813i | ||||
\(7\) | − | 148.379i | − | 1.14453i | −0.820069 | − | 0.572265i | \(-0.806065\pi\) | ||
0.820069 | − | 0.572265i | \(-0.193935\pi\) | |||||||
\(8\) | −76.8820 | + | 163.882i | −0.424717 | + | 0.905326i | ||||
\(9\) | 222.775i | 0.916770i | ||||||||
\(10\) | 494.678 | + | 213.836i | 1.56431 | + | 0.676210i | ||||
\(11\) | −256.205 | − | 256.205i | −0.638420 | − | 0.638420i | 0.311745 | − | 0.950166i | \(-0.399086\pi\) |
−0.950166 | + | 0.311745i | \(0.899086\pi\) | |||||||
\(12\) | −4.40780 | + | 143.843i | −0.00883626 | + | 0.288360i | ||||
\(13\) | −218.586 | + | 218.586i | −0.358727 | + | 0.358727i | −0.863343 | − | 0.504617i | \(-0.831634\pi\) |
0.504617 | + | 0.863343i | \(0.331634\pi\) | |||||||
\(14\) | 309.293 | + | 780.294i | 0.421746 | + | 1.06399i | ||||
\(15\) | 428.440 | 0.491657 | ||||||||
\(16\) | 62.6982 | − | 1022.08i | 0.0612287 | − | 0.998124i | ||||
\(17\) | −463.168 | −0.388701 | −0.194351 | − | 0.980932i | \(-0.562260\pi\) | ||||
−0.194351 | + | 0.980932i | \(0.562260\pi\) | |||||||
\(18\) | −464.371 | − | 1171.53i | −0.337819 | − | 0.852259i | ||||
\(19\) | 920.791 | − | 920.791i | 0.585163 | − | 0.585163i | −0.351154 | − | 0.936318i | \(-0.614211\pi\) |
0.936318 | + | 0.351154i | \(0.114211\pi\) | |||||||
\(20\) | −3047.15 | − | 93.3741i | −1.70341 | − | 0.0521977i | ||||
\(21\) | 471.845 | + | 471.845i | 0.233481 | + | 0.233481i | ||||
\(22\) | 1881.39 | + | 813.276i | 0.828746 | + | 0.358246i | ||||
\(23\) | − | 1053.65i | − | 0.415315i | −0.978202 | − | 0.207657i | \(-0.933416\pi\) | ||
0.978202 | − | 0.207657i | \(-0.0665839\pi\) | |||||||
\(24\) | −276.659 | − | 765.629i | −0.0980430 | − | 0.271325i | ||||
\(25\) | 5951.00i | 1.90432i | ||||||||
\(26\) | 693.860 | − | 1605.14i | 0.201297 | − | 0.465671i | ||||
\(27\) | −1481.17 | − | 1481.17i | −0.391016 | − | 0.391016i | ||||
\(28\) | −3253.02 | − | 3458.69i | −0.784137 | − | 0.833713i | ||||
\(29\) | 1290.79 | − | 1290.79i | 0.285010 | − | 0.285010i | −0.550093 | − | 0.835103i | \(-0.685408\pi\) |
0.835103 | + | 0.550093i | \(0.185408\pi\) | |||||||
\(30\) | −2253.08 | + | 893.076i | −0.457060 | + | 0.181170i | ||||
\(31\) | 10036.9 | 1.87584 | 0.937921 | − | 0.346848i | \(-0.112748\pi\) | ||||
0.937921 | + | 0.346848i | \(0.112748\pi\) | |||||||
\(32\) | 1800.79 | + | 5505.60i | 0.310877 | + | 0.950450i | ||||
\(33\) | 1629.47 | 0.260472 | ||||||||
\(34\) | 2435.71 | − | 965.466i | 0.361349 | − | 0.143232i | ||||
\(35\) | −9995.50 | + | 9995.50i | −1.37922 | + | 1.37922i | ||||
\(36\) | 4884.07 | + | 5192.86i | 0.628095 | + | 0.667805i | ||||
\(37\) | −9409.85 | − | 9409.85i | −1.13000 | − | 1.13000i | −0.990176 | − | 0.139824i | \(-0.955346\pi\) |
−0.139824 | − | 0.990176i | \(-0.544654\pi\) | |||||||
\(38\) | −2922.88 | + | 6761.62i | −0.328361 | + | 0.759612i | ||||
\(39\) | − | 1390.21i | − | 0.146359i | ||||||
\(40\) | 16219.0 | − | 5860.70i | 1.60278 | − | 0.579161i | ||||
\(41\) | − | 368.682i | − | 0.0342525i | −0.999853 | − | 0.0171263i | \(-0.994548\pi\) | ||
0.999853 | − | 0.0171263i | \(-0.00545173\pi\) | |||||||
\(42\) | −3464.89 | − | 1497.78i | −0.303086 | − | 0.131016i | ||||
\(43\) | −9168.57 | − | 9168.57i | −0.756189 | − | 0.756189i | 0.219438 | − | 0.975627i | \(-0.429578\pi\) |
−0.975627 | + | 0.219438i | \(0.929578\pi\) | |||||||
\(44\) | −11589.1 | − | 355.126i | −0.902439 | − | 0.0276535i | ||||
\(45\) | 15007.2 | − | 15007.2i | 1.10476 | − | 1.10476i | ||||
\(46\) | 2196.32 | + | 5540.94i | 0.153039 | + | 0.386090i | ||||
\(47\) | −7638.65 | −0.504396 | −0.252198 | − | 0.967676i | \(-0.581153\pi\) | ||||
−0.252198 | + | 0.967676i | \(0.581153\pi\) | |||||||
\(48\) | 3050.83 | + | 3449.59i | 0.191124 | + | 0.216105i | ||||
\(49\) | −5209.29 | −0.309948 | ||||||||
\(50\) | −12404.8 | − | 31295.1i | −0.701720 | − | 1.77032i | ||||
\(51\) | 1472.88 | − | 1472.88i | 0.0792941 | − | 0.0792941i | ||||
\(52\) | −302.982 | + | 9887.43i | −0.0155385 | + | 0.507078i | ||||
\(53\) | −1242.05 | − | 1242.05i | −0.0607363 | − | 0.0607363i | 0.676086 | − | 0.736823i | \(-0.263675\pi\) |
−0.736823 | + | 0.676086i | \(0.763675\pi\) | |||||||
\(54\) | 10876.6 | + | 4701.68i | 0.507586 | + | 0.219416i | ||||
\(55\) | 34518.4i | 1.53866i | ||||||||
\(56\) | 24316.6 | + | 11407.7i | 1.03617 | + | 0.486101i | ||||
\(57\) | 5856.24i | 0.238743i | ||||||||
\(58\) | −4097.36 | + | 9478.62i | −0.159932 | + | 0.369977i | ||||
\(59\) | 16255.3 | + | 16255.3i | 0.607945 | + | 0.607945i | 0.942409 | − | 0.334464i | \(-0.108555\pi\) |
−0.334464 | + | 0.942409i | \(0.608555\pi\) | |||||||
\(60\) | 9986.87 | − | 9393.01i | 0.358139 | − | 0.336842i | ||||
\(61\) | −1394.11 | + | 1394.11i | −0.0479704 | + | 0.0479704i | −0.730685 | − | 0.682715i | \(-0.760799\pi\) |
0.682715 | + | 0.730685i | \(0.260799\pi\) | |||||||
\(62\) | −52782.1 | + | 20921.8i | −1.74384 | + | 0.691226i | ||||
\(63\) | 33055.1 | 1.04927 | ||||||||
\(64\) | −20946.3 | − | 25199.1i | −0.639231 | − | 0.769015i | ||||
\(65\) | 29449.9 | 0.864572 | ||||||||
\(66\) | −8569.04 | + | 3396.60i | −0.242143 | + | 0.0959809i | ||||
\(67\) | −17400.9 | + | 17400.9i | −0.473569 | + | 0.473569i | −0.903068 | − | 0.429498i | \(-0.858690\pi\) |
0.429498 | + | 0.903068i | \(0.358690\pi\) | |||||||
\(68\) | −10796.4 | + | 10154.4i | −0.283143 | + | 0.266306i | ||||
\(69\) | 3350.62 | + | 3350.62i | 0.0847231 | + | 0.0847231i | ||||
\(70\) | 31728.8 | − | 73399.7i | 0.773943 | − | 1.79040i | ||||
\(71\) | − | 67414.6i | − | 1.58711i | −0.608495 | − | 0.793557i | \(-0.708227\pi\) | ||
0.608495 | − | 0.793557i | \(-0.291773\pi\) | |||||||
\(72\) | −36508.7 | − | 17127.4i | −0.829976 | − | 0.389368i | ||||
\(73\) | 19543.2i | 0.429228i | 0.976699 | + | 0.214614i | \(0.0688494\pi\) | ||||
−0.976699 | + | 0.214614i | \(0.931151\pi\) | |||||||
\(74\) | 69099.2 | + | 29869.8i | 1.46688 | + | 0.634093i | ||||
\(75\) | −18924.2 | − | 18924.2i | −0.388476 | − | 0.388476i | ||||
\(76\) | 1276.31 | − | 41650.7i | 0.0253467 | − | 0.827157i | ||||
\(77\) | −38015.5 | + | 38015.5i | −0.730691 | + | 0.730691i | ||||
\(78\) | 2897.87 | + | 7310.82i | 0.0539314 | + | 0.136060i | ||||
\(79\) | −43996.5 | −0.793140 | −0.396570 | − | 0.918004i | \(-0.629800\pi\) | ||||
−0.396570 | + | 0.918004i | \(0.629800\pi\) | |||||||
\(80\) | −73075.7 | + | 64628.4i | −1.27658 | + | 1.12901i | ||||
\(81\) | −44714.1 | −0.757238 | ||||||||
\(82\) | 768.512 | + | 1938.82i | 0.0126217 | + | 0.0318423i | ||||
\(83\) | 73286.1 | − | 73286.1i | 1.16769 | − | 1.16769i | 0.184937 | − | 0.982750i | \(-0.440792\pi\) |
0.982750 | − | 0.184937i | \(-0.0592080\pi\) | |||||||
\(84\) | 21343.3 | + | 654.024i | 0.330037 | + | 0.0101134i | ||||
\(85\) | 31201.2 | + | 31201.2i | 0.468407 | + | 0.468407i | ||||
\(86\) | 67327.4 | + | 29103.9i | 0.981625 | + | 0.424331i | ||||
\(87\) | 8209.42i | 0.116283i | ||||||||
\(88\) | 61684.9 | − | 22289.8i | 0.849126 | − | 0.306831i | ||||
\(89\) | − | 88671.1i | − | 1.18661i | −0.804979 | − | 0.593304i | \(-0.797823\pi\) | ||
0.804979 | − | 0.593304i | \(-0.202177\pi\) | |||||||
\(90\) | −47637.4 | + | 110202.i | −0.619929 | + | 1.43411i | ||||
\(91\) | 32433.5 | + | 32433.5i | 0.410573 | + | 0.410573i | ||||
\(92\) | −23100.0 | − | 24560.5i | −0.284539 | − | 0.302529i | ||||
\(93\) | −31917.5 | + | 31917.5i | −0.382667 | + | 0.382667i | ||||
\(94\) | 40170.1 | − | 15922.6i | 0.468903 | − | 0.185864i | ||||
\(95\) | −124058. | −1.41031 | ||||||||
\(96\) | −23234.3 | − | 11781.3i | −0.257307 | − | 0.130471i | ||||
\(97\) | −73610.3 | −0.794345 | −0.397173 | − | 0.917744i | \(-0.630009\pi\) | ||||
−0.397173 | + | 0.917744i | \(0.630009\pi\) | |||||||
\(98\) | 27394.6 | − | 10858.7i | 0.288137 | − | 0.114212i | ||||
\(99\) | 57076.2 | − | 57076.2i | 0.585285 | − | 0.585285i | ||||
\(100\) | 130468. | + | 138717.i | 1.30468 | + | 1.38717i | ||||
\(101\) | 78062.3 | + | 78062.3i | 0.761444 | + | 0.761444i | 0.976583 | − | 0.215139i | \(-0.0690206\pi\) |
−0.215139 | + | 0.976583i | \(0.569021\pi\) | |||||||
\(102\) | −4675.37 | + | 10815.7i | −0.0444954 | + | 0.102933i | ||||
\(103\) | − | 3655.48i | − | 0.0339509i | −0.999856 | − | 0.0169754i | \(-0.994596\pi\) | ||
0.999856 | − | 0.0169754i | \(-0.00540371\pi\) | |||||||
\(104\) | −19016.9 | − | 52627.5i | −0.172407 | − | 0.477122i | ||||
\(105\) | − | 63571.4i | − | 0.562715i | ||||||
\(106\) | 9120.70 | + | 3942.64i | 0.0788431 | + | 0.0340818i | ||||
\(107\) | 44702.0 | + | 44702.0i | 0.377457 | + | 0.377457i | 0.870184 | − | 0.492727i | \(-0.164000\pi\) |
−0.492727 | + | 0.870184i | \(0.664000\pi\) | |||||||
\(108\) | −66998.5 | − | 2053.04i | −0.552721 | − | 0.0169371i | ||||
\(109\) | −68265.8 | + | 68265.8i | −0.550348 | + | 0.550348i | −0.926541 | − | 0.376193i | \(-0.877233\pi\) |
0.376193 | + | 0.926541i | \(0.377233\pi\) | |||||||
\(110\) | −71953.1 | − | 181525.i | −0.566980 | − | 1.43039i | ||||
\(111\) | 59846.7 | 0.461034 | ||||||||
\(112\) | −151655. | − | 9303.09i | −1.14238 | − | 0.0700781i | ||||
\(113\) | 176086. | 1.29726 | 0.648632 | − | 0.761102i | \(-0.275341\pi\) | ||||
0.648632 | + | 0.761102i | \(0.275341\pi\) | |||||||
\(114\) | −12207.2 | − | 30796.8i | −0.0879742 | − | 0.221944i | ||||
\(115\) | −70978.9 | + | 70978.9i | −0.500478 | + | 0.500478i | ||||
\(116\) | 1789.16 | − | 58387.0i | 0.0123454 | − | 0.402876i | ||||
\(117\) | −48695.5 | − | 48695.5i | −0.328870 | − | 0.328870i | ||||
\(118\) | −119367. | − | 51599.3i | −0.789186 | − | 0.341145i | ||||
\(119\) | 68724.3i | 0.444880i | ||||||||
\(120\) | −32939.3 | + | 70213.4i | −0.208815 | + | 0.445110i | ||||
\(121\) | − | 29768.6i | − | 0.184839i | ||||||
\(122\) | 4425.35 | − | 10237.4i | 0.0269183 | − | 0.0622714i | ||||
\(123\) | 1172.41 | + | 1172.41i | 0.00698743 | + | 0.00698743i | ||||
\(124\) | 233959. | − | 220047.i | 1.36643 | − | 1.28517i | ||||
\(125\) | 190373. | − | 190373.i | 1.08976 | − | 1.08976i | ||||
\(126\) | −173830. | + | 68902.9i | −0.975436 | + | 0.386644i | ||||
\(127\) | −77564.5 | −0.426730 | −0.213365 | − | 0.976973i | \(-0.568442\pi\) | ||||
−0.213365 | + | 0.976973i | \(0.568442\pi\) | |||||||
\(128\) | 162679. | + | 88854.5i | 0.877623 | + | 0.479352i | ||||
\(129\) | 58312.2 | 0.308521 | ||||||||
\(130\) | −154871. | + | 61388.0i | −0.803734 | + | 0.318585i | ||||
\(131\) | −102943. | + | 102943.i | −0.524105 | + | 0.524105i | −0.918809 | − | 0.394703i | \(-0.870847\pi\) |
0.394703 | + | 0.918809i | \(0.370847\pi\) | |||||||
\(132\) | 37982.7 | − | 35724.1i | 0.189736 | − | 0.178454i | ||||
\(133\) | −136626. | − | 136626.i | −0.669737 | − | 0.669737i | ||||
\(134\) | 55235.7 | − | 127779.i | 0.265741 | − | 0.614750i | ||||
\(135\) | 199557.i | 0.942393i | ||||||||
\(136\) | 35609.3 | − | 75904.7i | 0.165088 | − | 0.351902i | ||||
\(137\) | 103866.i | 0.472792i | 0.971657 | + | 0.236396i | \(0.0759662\pi\) | ||||
−0.971657 | + | 0.236396i | \(0.924034\pi\) | |||||||
\(138\) | −24604.5 | − | 10635.9i | −0.109981 | − | 0.0475419i | ||||
\(139\) | 199447. | + | 199447.i | 0.875569 | + | 0.875569i | 0.993072 | − | 0.117503i | \(-0.0374891\pi\) |
−0.117503 | + | 0.993072i | \(0.537489\pi\) | |||||||
\(140\) | −13854.7 | + | 452132.i | −0.0597418 | + | 1.94960i | ||||
\(141\) | 24290.9 | − | 24290.9i | 0.102895 | − | 0.102895i | ||||
\(142\) | 140525. | + | 354520.i | 0.584833 | + | 1.47543i | ||||
\(143\) | 112006. | 0.458037 | ||||||||
\(144\) | 227694. | + | 13967.6i | 0.915050 | + | 0.0561327i | ||||
\(145\) | −173907. | −0.686906 | ||||||||
\(146\) | −40737.5 | − | 102774.i | −0.158166 | − | 0.399025i | ||||
\(147\) | 16565.6 | − | 16565.6i | 0.0632285 | − | 0.0632285i | ||||
\(148\) | −425642. | − | 13043.0i | −1.59731 | − | 0.0489466i | ||||
\(149\) | 111883. | + | 111883.i | 0.412855 | + | 0.412855i | 0.882732 | − | 0.469877i | \(-0.155702\pi\) |
−0.469877 | + | 0.882732i | \(0.655702\pi\) | |||||||
\(150\) | 138966. | + | 60071.3i | 0.504289 | + | 0.217991i | ||||
\(151\) | − | 270469.i | − | 0.965330i | −0.875805 | − | 0.482665i | \(-0.839669\pi\) | ||
0.875805 | − | 0.482665i | \(-0.160331\pi\) | |||||||
\(152\) | 80108.4 | + | 221693.i | 0.281235 | + | 0.778292i | ||||
\(153\) | − | 103182.i | − | 0.356350i | ||||||
\(154\) | 120673. | − | 279158.i | 0.410023 | − | 0.948525i | ||||
\(155\) | −676134. | − | 676134.i | −2.26050 | − | 2.26050i | ||||
\(156\) | −30478.6 | − | 32405.5i | −0.100273 | − | 0.106612i | ||||
\(157\) | −105844. | + | 105844.i | −0.342703 | + | 0.342703i | −0.857383 | − | 0.514679i | \(-0.827911\pi\) |
0.514679 | + | 0.857383i | \(0.327911\pi\) | |||||||
\(158\) | 231368. | − | 91709.9i | 0.737329 | − | 0.292263i | ||||
\(159\) | 7899.43 | 0.0247801 | ||||||||
\(160\) | 249573. | − | 492192.i | 0.770722 | − | 1.51997i | ||||
\(161\) | −156340. | −0.475340 | ||||||||
\(162\) | 235142. | − | 93205.9i | 0.703953 | − | 0.279033i | ||||
\(163\) | 3832.26 | − | 3832.26i | 0.0112976 | − | 0.0112976i | −0.701435 | − | 0.712733i | \(-0.747457\pi\) |
0.712733 | + | 0.701435i | \(0.247457\pi\) | |||||||
\(164\) | −8082.90 | − | 8593.93i | −0.0234670 | − | 0.0249507i | ||||
\(165\) | −109769. | − | 109769.i | −0.313883 | − | 0.313883i | ||||
\(166\) | −232633. | + | 538160.i | −0.655241 | + | 1.51580i | ||||
\(167\) | − | 94932.2i | − | 0.263404i | −0.991289 | − | 0.131702i | \(-0.957956\pi\) | ||
0.991289 | − | 0.131702i | \(-0.0420442\pi\) | |||||||
\(168\) | −113603. | + | 41050.3i | −0.310540 | + | 0.112213i | ||||
\(169\) | 275733.i | 0.742630i | ||||||||
\(170\) | −229119. | − | 99042.2i | −0.608049 | − | 0.262844i | ||||
\(171\) | 205129. | + | 205129.i | 0.536460 | + | 0.536460i | ||||
\(172\) | −414727. | − | 12708.5i | −1.06891 | − | 0.0327548i | ||||
\(173\) | 267579. | − | 267579.i | 0.679732 | − | 0.679732i | −0.280208 | − | 0.959939i | \(-0.590403\pi\) |
0.959939 | + | 0.280208i | \(0.0904034\pi\) | |||||||
\(174\) | −17112.4 | − | 43171.7i | −0.0428487 | − | 0.108100i | ||||
\(175\) | 883003. | 2.17955 | ||||||||
\(176\) | −277926. | + | 245798.i | −0.676312 | + | 0.598133i | ||||
\(177\) | −103384. | −0.248038 | ||||||||
\(178\) | 184834. | + | 466303.i | 0.437251 | + | 1.10311i | ||||
\(179\) | −153517. | + | 153517.i | −0.358116 | + | 0.358116i | −0.863118 | − | 0.505002i | \(-0.831492\pi\) |
0.505002 | + | 0.863118i | \(0.331492\pi\) | |||||||
\(180\) | 20801.4 | − | 678829.i | 0.0478533 | − | 1.56163i | ||||
\(181\) | −286803. | − | 286803.i | −0.650711 | − | 0.650711i | 0.302453 | − | 0.953164i | \(-0.402194\pi\) |
−0.953164 | + | 0.302453i | \(0.902194\pi\) | |||||||
\(182\) | −238169. | − | 102954.i | −0.532974 | − | 0.230391i | ||||
\(183\) | − | 8866.57i | − | 0.0195717i | ||||||
\(184\) | 172674. | + | 81006.9i | 0.375995 | + | 0.176391i | ||||
\(185\) | 1.26778e6i | 2.72343i | ||||||||
\(186\) | 101316. | − | 234379.i | 0.214731 | − | 0.496748i | ||||
\(187\) | 118666. | + | 118666.i | 0.248155 | + | 0.248155i | ||||
\(188\) | −178056. | + | 167468.i | −0.367419 | + | 0.345571i | ||||
\(189\) | −219774. | + | 219774.i | −0.447529 | + | 0.447529i | ||||
\(190\) | 652393. | − | 258596.i | 1.31107 | − | 0.519682i | ||||
\(191\) | −266466. | −0.528517 | −0.264258 | − | 0.964452i | \(-0.585127\pi\) | ||||
−0.264258 | + | 0.964452i | \(0.585127\pi\) | |||||||
\(192\) | 146743. | + | 13523.8i | 0.287278 | + | 0.0264756i | ||||
\(193\) | 953848. | 1.84326 | 0.921628 | − | 0.388074i | \(-0.126859\pi\) | ||||
0.921628 | + | 0.388074i | \(0.126859\pi\) | |||||||
\(194\) | 387101. | − | 153440.i | 0.738449 | − | 0.292707i | ||||
\(195\) | −93650.9 | + | 93650.9i | −0.176370 | + | 0.176370i | ||||
\(196\) | −121428. | + | 114207.i | −0.225776 | + | 0.212351i | ||||
\(197\) | 223796. | + | 223796.i | 0.410853 | + | 0.410853i | 0.882036 | − | 0.471183i | \(-0.156173\pi\) |
−0.471183 | + | 0.882036i | \(0.656173\pi\) | |||||||
\(198\) | −181178. | + | 419126.i | −0.328429 | + | 0.759770i | ||||
\(199\) | − | 562835.i | − | 1.00751i | −0.863847 | − | 0.503754i | \(-0.831952\pi\) | ||
0.863847 | − | 0.503754i | \(-0.168048\pi\) | |||||||
\(200\) | −975259. | − | 457525.i | −1.72403 | − | 0.808798i | ||||
\(201\) | − | 110670.i | − | 0.193214i | ||||||
\(202\) | −573233. | − | 247794.i | −0.988446 | − | 0.427280i | ||||
\(203\) | −191526. | − | 191526.i | −0.326202 | − | 0.326202i | ||||
\(204\) | 2041.55 | − | 66623.5i | 0.00343467 | − | 0.112086i | ||||
\(205\) | −24836.2 | + | 24836.2i | −0.0412762 | + | 0.0412762i | ||||
\(206\) | 7619.79 | + | 19223.4i | 0.0125105 | + | 0.0315619i | ||||
\(207\) | 234727. | 0.380748 | ||||||||
\(208\) | 209707. | + | 237117.i | 0.336089 | + | 0.380018i | ||||
\(209\) | −471823. | −0.747160 | ||||||||
\(210\) | 132514. | + | 334309.i | 0.207354 | + | 0.523118i | ||||
\(211\) | 507141. | − | 507141.i | 0.784192 | − | 0.784192i | −0.196343 | − | 0.980535i | \(-0.562907\pi\) |
0.980535 | + | 0.196343i | \(0.0629067\pi\) | |||||||
\(212\) | −56182.3 | − | 1721.60i | −0.0858538 | − | 0.00263083i | ||||
\(213\) | 214379. | + | 214379.i | 0.323767 | + | 0.323767i | ||||
\(214\) | −328259. | − | 141898.i | −0.489985 | − | 0.211808i | ||||
\(215\) | 1.23528e6i | 1.82250i | ||||||||
\(216\) | 356611. | − | 128861.i | 0.520068 | − | 0.187926i | ||||
\(217\) | − | 1.48927e6i | − | 2.14696i | ||||||
\(218\) | 216697. | − | 501295.i | 0.308824 | − | 0.714418i | ||||
\(219\) | −62147.4 | − | 62147.4i | −0.0875615 | − | 0.0875615i | ||||
\(220\) | 756773. | + | 804619.i | 1.05417 | + | 1.12081i | ||||
\(221\) | 101242. | − | 101242.i | 0.139438 | − | 0.139438i | ||||
\(222\) | −314722. | + | 124750.i | −0.428592 | + | 0.169886i | ||||
\(223\) | −963165. | −1.29700 | −0.648498 | − | 0.761217i | \(-0.724602\pi\) | ||||
−0.648498 | + | 0.761217i | \(0.724602\pi\) | |||||||
\(224\) | 816914. | − | 267199.i | 1.08782 | − | 0.355808i | ||||
\(225\) | −1.32574e6 | −1.74582 | ||||||||
\(226\) | −926000. | + | 367048.i | −1.20598 | + | 0.478027i | ||||
\(227\) | −288197. | + | 288197.i | −0.371214 | + | 0.371214i | −0.867919 | − | 0.496705i | \(-0.834543\pi\) |
0.496705 | + | 0.867919i | \(0.334543\pi\) | |||||||
\(228\) | 128391. | + | 136508.i | 0.163567 | + | 0.173909i | ||||
\(229\) | −294327. | − | 294327.i | −0.370887 | − | 0.370887i | 0.496913 | − | 0.867800i | \(-0.334467\pi\) |
−0.867800 | + | 0.496913i | \(0.834467\pi\) | |||||||
\(230\) | 225309. | − | 521218.i | 0.280840 | − | 0.649681i | ||||
\(231\) | − | 241779.i | − | 0.298118i | ||||||
\(232\) | 112298. | + | 310775.i | 0.136978 | + | 0.379075i | ||||
\(233\) | − | 1.27046e6i | − | 1.53311i | −0.642180 | − | 0.766554i | \(-0.721970\pi\) | ||
0.642180 | − | 0.766554i | \(-0.278030\pi\) | |||||||
\(234\) | 357585. | + | 154575.i | 0.426913 | + | 0.184543i | ||||
\(235\) | 514575. | + | 514575.i | 0.607826 | + | 0.607826i | ||||
\(236\) | 735285. | + | 22531.4i | 0.859361 | + | 0.0263335i | ||||
\(237\) | 139909. | − | 139909.i | 0.161799 | − | 0.161799i | ||||
\(238\) | −143255. | − | 361407.i | −0.163933 | − | 0.413575i | ||||
\(239\) | −1.09946e6 | −1.24504 | −0.622522 | − | 0.782603i | \(-0.713892\pi\) | ||||
−0.622522 | + | 0.782603i | \(0.713892\pi\) | |||||||
\(240\) | 26862.4 | − | 437899.i | 0.0301035 | − | 0.490734i | ||||
\(241\) | 1.31349e6 | 1.45675 | 0.728376 | − | 0.685178i | \(-0.240275\pi\) | ||||
0.728376 | + | 0.685178i | \(0.240275\pi\) | |||||||
\(242\) | 62052.1 | + | 156547.i | 0.0681111 | + | 0.171833i | ||||
\(243\) | 502115. | − | 502115.i | 0.545491 | − | 0.545491i | ||||
\(244\) | −1932.38 | + | 63060.8i | −0.00207787 | + | 0.0678086i | ||||
\(245\) | 350922. | + | 350922.i | 0.373504 | + | 0.373504i | ||||
\(246\) | −8609.34 | − | 3721.60i | −0.00907052 | − | 0.00392095i | ||||
\(247\) | 402544.i | 0.419827i | ||||||||
\(248\) | −771659. | + | 1.64487e6i | −0.796703 | + | 1.69825i | ||||
\(249\) | 466100.i | 0.476410i | ||||||||
\(250\) | −604302. | + | 1.39796e6i | −0.611511 | + | 1.41464i | ||||
\(251\) | 444145. | + | 444145.i | 0.444980 | + | 0.444980i | 0.893682 | − | 0.448701i | \(-0.148113\pi\) |
−0.448701 | + | 0.893682i | \(0.648113\pi\) | |||||||
\(252\) | 770510. | − | 724692.i | 0.764323 | − | 0.718873i | ||||
\(253\) | −269951. | + | 269951.i | −0.265145 | + | 0.265145i | ||||
\(254\) | 407896. | − | 161682.i | 0.396702 | − | 0.157245i | ||||
\(255\) | −198440. | −0.191108 | ||||||||
\(256\) | −1.04071e6 | − | 128165.i | −0.992502 | − | 0.122228i | ||||
\(257\) | 664856. | 0.627906 | 0.313953 | − | 0.949438i | \(-0.398347\pi\) | ||||
0.313953 | + | 0.949438i | \(0.398347\pi\) | |||||||
\(258\) | −306652. | + | 121551.i | −0.286811 | + | 0.113686i | ||||
\(259\) | −1.39622e6 | + | 1.39622e6i | −1.29332 | + | 1.29332i | ||||
\(260\) | 686474. | − | 645653.i | 0.629783 | − | 0.592333i | ||||
\(261\) | 287555. | + | 287555.i | 0.261289 | + | 0.261289i | ||||
\(262\) | 326773. | − | 755939.i | 0.294099 | − | 0.680352i | ||||
\(263\) | − | 1.50708e6i | − | 1.34353i | −0.740765 | − | 0.671764i | \(-0.765537\pi\) | ||
0.740765 | − | 0.671764i | \(-0.234463\pi\) | |||||||
\(264\) | −125277. | + | 267040.i | −0.110627 | + | 0.235812i | ||||
\(265\) | 167340.i | 0.146381i | ||||||||
\(266\) | 1.00328e6 | + | 433693.i | 0.869399 | + | 0.375819i | ||||
\(267\) | 281975. | + | 281975.i | 0.242065 | + | 0.242065i | ||||
\(268\) | −24119.3 | + | 787103.i | −0.0205129 | + | 0.669414i | ||||
\(269\) | −581250. | + | 581250.i | −0.489759 | + | 0.489759i | −0.908230 | − | 0.418471i | \(-0.862566\pi\) |
0.418471 | + | 0.908230i | \(0.362566\pi\) | |||||||
\(270\) | −415973. | − | 1.04943e6i | −0.347261 | − | 0.876079i | ||||
\(271\) | 821841. | 0.679774 | 0.339887 | − | 0.940466i | \(-0.389611\pi\) | ||||
0.339887 | + | 0.940466i | \(0.389611\pi\) | |||||||
\(272\) | −29039.8 | + | 473394.i | −0.0237997 | + | 0.387972i | ||||
\(273\) | −206278. | −0.167512 | ||||||||
\(274\) | −216506. | − | 546207.i | −0.174218 | − | 0.439523i | ||||
\(275\) | 1.52468e6 | − | 1.52468e6i | 1.21576 | − | 1.21576i | ||||
\(276\) | 151560. | + | 4644.28i | 0.119760 | + | 0.00366983i | ||||
\(277\) | −285729. | − | 285729.i | −0.223746 | − | 0.223746i | 0.586328 | − | 0.810074i | \(-0.300573\pi\) |
−0.810074 | + | 0.586328i | \(0.800573\pi\) | |||||||
\(278\) | −1.46459e6 | − | 633107.i | −1.13659 | − | 0.491320i | ||||
\(279\) | 2.23598e6i | 1.71972i | ||||||||
\(280\) | −869604. | − | 2.40655e6i | −0.662867 | − | 1.83443i | ||||
\(281\) | − | 1.38882e6i | − | 1.04925i | −0.851334 | − | 0.524625i | \(-0.824206\pi\) | ||
0.851334 | − | 0.524625i | \(-0.175794\pi\) | |||||||
\(282\) | −77107.0 | + | 178375.i | −0.0577392 | + | 0.133571i | ||||
\(283\) | 62485.8 | + | 62485.8i | 0.0463784 | + | 0.0463784i | 0.729916 | − | 0.683537i | \(-0.239559\pi\) |
−0.683537 | + | 0.729916i | \(0.739559\pi\) | |||||||
\(284\) | −1.47798e6 | − | 1.57142e6i | −1.08736 | − | 1.15611i | ||||
\(285\) | 394504. | − | 394504.i | 0.287699 | − | 0.287699i | ||||
\(286\) | −589016. | + | 233474.i | −0.425806 | + | 0.168781i | ||||
\(287\) | −54704.7 | −0.0392030 | ||||||||
\(288\) | −1.22651e6 | + | 401171.i | −0.871344 | + | 0.285002i | ||||
\(289\) | −1.20533e6 | −0.848911 | ||||||||
\(290\) | 914542. | − | 362507.i | 0.638570 | − | 0.253117i | ||||
\(291\) | 234081. | − | 234081.i | 0.162044 | − | 0.162044i | ||||
\(292\) | 428460. | + | 455549.i | 0.294072 | + | 0.312664i | ||||
\(293\) | 1.58326e6 | + | 1.58326e6i | 1.07741 | + | 1.07741i | 0.996741 | + | 0.0806745i | \(0.0257074\pi\) |
0.0806745 | + | 0.996741i | \(0.474293\pi\) | |||||||
\(294\) | −52584.3 | + | 121646.i | −0.0354803 | + | 0.0820782i | ||||
\(295\) | − | 2.19006e6i | − | 1.46522i | ||||||
\(296\) | 2.26555e6 | − | 818653.i | 1.50295 | − | 0.543088i | ||||
\(297\) | 758966.i | 0.499265i | ||||||||
\(298\) | −821586. | − | 355150.i | −0.535935 | − | 0.231671i | ||||
\(299\) | 230313. | + | 230313.i | 0.148985 | + | 0.148985i | ||||
\(300\) | −856010. | − | 26230.8i | −0.549131 | − | 0.0168271i | ||||
\(301\) | −1.36042e6 | + | 1.36042e6i | −0.865481 | + | 0.865481i | ||||
\(302\) | 563789. | + | 1.42234e6i | 0.355713 | + | 0.897402i | ||||
\(303\) | −496477. | −0.310665 | ||||||||
\(304\) | −883389. | − | 998853.i | −0.548236 | − | 0.619894i | ||||
\(305\) | 187828. | 0.115614 | ||||||||
\(306\) | 215082. | + | 542615.i | 0.131311 | + | 0.331274i | ||||
\(307\) | 1.31667e6 | − | 1.31667e6i | 0.797314 | − | 0.797314i | −0.185357 | − | 0.982671i | \(-0.559344\pi\) |
0.982671 | + | 0.185357i | \(0.0593441\pi\) | |||||||
\(308\) | −52693.2 | + | 1.71958e6i | −0.0316503 | + | 1.03287i | ||||
\(309\) | 11624.4 | + | 11624.4i | 0.00692589 | + | 0.00692589i | ||||
\(310\) | 4.96504e6 | + | 2.14626e6i | 2.93440 | + | 1.26846i | ||||
\(311\) | 564228.i | 0.330791i | 0.986227 | + | 0.165395i | \(0.0528900\pi\) | ||||
−0.986227 | + | 0.165395i | \(0.947110\pi\) | |||||||
\(312\) | 227829. | + | 106882.i | 0.132502 | + | 0.0621610i | ||||
\(313\) | 2.17165e6i | 1.25294i | 0.779446 | + | 0.626469i | \(0.215500\pi\) | ||||
−0.779446 | + | 0.626469i | \(0.784500\pi\) | |||||||
\(314\) | 335983. | − | 777244.i | 0.192306 | − | 0.444870i | ||||
\(315\) | −2.22675e6 | − | 2.22675e6i | −1.26443 | − | 1.26443i | ||||
\(316\) | −1.02555e6 | + | 964568.i | −0.577749 | + | 0.543394i | ||||
\(317\) | −266259. | + | 266259.i | −0.148818 | + | 0.148818i | −0.777590 | − | 0.628772i | \(-0.783558\pi\) |
0.628772 | + | 0.777590i | \(0.283558\pi\) | |||||||
\(318\) | −41541.5 | + | 16466.2i | −0.0230364 | + | 0.00913117i | ||||
\(319\) | −661414. | −0.363912 | ||||||||
\(320\) | −286486. | + | 3.10857e6i | −0.156397 | + | 1.69702i | ||||
\(321\) | −284305. | −0.154000 | ||||||||
\(322\) | 822158. | − | 325888.i | 0.441892 | − | 0.175157i | ||||
\(323\) | −426481. | + | 426481.i | −0.227454 | + | 0.227454i | ||||
\(324\) | −1.04228e6 | + | 980301.i | −0.551597 | + | 0.518797i | ||||
\(325\) | −1.30081e6 | − | 1.30081e6i | −0.683131 | − | 0.683131i | ||||
\(326\) | −12164.8 | + | 28141.4i | −0.00633958 | + | 0.0146656i | ||||
\(327\) | − | 434171.i | − | 0.224539i | ||||||
\(328\) | 60420.2 | + | 28345.0i | 0.0310097 | + | 0.0145476i | ||||
\(329\) | 1.13341e6i | 0.577296i | ||||||||
\(330\) | 806062. | + | 348440.i | 0.407459 | + | 0.176134i | ||||
\(331\) | 1.05180e6 | + | 1.05180e6i | 0.527670 | + | 0.527670i | 0.919877 | − | 0.392207i | \(-0.128288\pi\) |
−0.392207 | + | 0.919877i | \(0.628288\pi\) | |||||||
\(332\) | 101582. | − | 3.31500e6i | 0.0505790 | − | 1.65058i | ||||
\(333\) | 2.09628e6 | − | 2.09628e6i | 1.03595 | − | 1.03595i | ||||
\(334\) | 197885. | + | 499229.i | 0.0970613 | + | 0.244869i | ||||
\(335\) | 2.34441e6 | 1.14136 | ||||||||
\(336\) | 511847. | − | 452679.i | 0.247339 | − | 0.218747i | ||||
\(337\) | 228933. | 0.109808 | 0.0549040 | − | 0.998492i | \(-0.482515\pi\) | ||||
0.0549040 | + | 0.998492i | \(0.482515\pi\) | |||||||
\(338\) | −574762. | − | 1.45003e6i | −0.273650 | − | 0.690373i | ||||
\(339\) | −559954. | + | 559954.i | −0.264639 | + | 0.264639i | ||||
\(340\) | 1.41134e6 | + | 43247.9i | 0.662117 | + | 0.0202893i | ||||
\(341\) | −2.57151e6 | − | 2.57151e6i | −1.19758 | − | 1.19758i | ||||
\(342\) | −1.50632e6 | − | 651144.i | −0.696390 | − | 0.301031i | ||||
\(343\) | − | 1.72085e6i | − | 0.789785i | ||||||
\(344\) | 2.20746e6 | − | 797661.i | 1.00576 | − | 0.363431i | ||||
\(345\) | − | 451427.i | − | 0.204192i | ||||||
\(346\) | −849380. | + | 1.96491e6i | −0.381427 | + | 0.882374i | ||||
\(347\) | −1.61497e6 | − | 1.61497e6i | −0.720014 | − | 0.720014i | 0.248594 | − | 0.968608i | \(-0.420031\pi\) |
−0.968608 | + | 0.248594i | \(0.920031\pi\) | |||||||
\(348\) | 179981. | + | 191360.i | 0.0796672 | + | 0.0847040i | ||||
\(349\) | 341998. | − | 341998.i | 0.150300 | − | 0.150300i | −0.627952 | − | 0.778252i | \(-0.716107\pi\) |
0.778252 | + | 0.627952i | \(0.216107\pi\) | |||||||
\(350\) | −4.64353e6 | + | 1.84061e6i | −2.02618 | + | 0.803139i | ||||
\(351\) | 647524. | 0.280536 | ||||||||
\(352\) | 949191. | − | 1.87194e6i | 0.408317 | − | 0.805257i | ||||
\(353\) | −1986.21 | −0.000848377 | −0.000424188 | − | 1.00000i | \(-0.500135\pi\) | ||||
−0.000424188 | 1.00000i | \(0.500135\pi\) | ||||||||
\(354\) | 543674. | − | 215502.i | 0.230585 | − | 0.0913992i | ||||
\(355\) | −4.54137e6 | + | 4.54137e6i | −1.91256 | + | 1.91256i | ||||
\(356\) | −1.94400e6 | − | 2.06691e6i | −0.812965 | − | 0.864364i | ||||
\(357\) | −218544. | − | 218544.i | −0.0907544 | − | 0.0907544i | ||||
\(358\) | 487311. | − | 1.12732e6i | 0.200955 | − | 0.464878i | ||||
\(359\) | 1.77409e6i | 0.726505i | 0.931691 | + | 0.363253i | \(0.118334\pi\) | ||||
−0.931691 | + | 0.363253i | \(0.881666\pi\) | |||||||
\(360\) | 1.30562e6 | + | 3.61318e6i | 0.530957 | + | 1.46938i | ||||
\(361\) | 780387.i | 0.315168i | ||||||||
\(362\) | 2.10608e6 | + | 910403.i | 0.844701 | + | 0.365142i | ||||
\(363\) | 94664.1 | + | 94664.1i | 0.0377067 | + | 0.0377067i | ||||
\(364\) | 1.46709e6 | + | 44956.1i | 0.580366 | + | 0.0177842i | ||||
\(365\) | 1.31652e6 | − | 1.31652e6i | 0.517244 | − | 0.517244i | ||||
\(366\) | 18482.2 | + | 46627.5i | 0.00721193 | + | 0.0181945i | ||||
\(367\) | 4.40691e6 | 1.70793 | 0.853963 | − | 0.520334i | \(-0.174193\pi\) | ||||
0.853963 | + | 0.520334i | \(0.174193\pi\) | |||||||
\(368\) | −1.07692e6 | − | 66062.1i | −0.414536 | − | 0.0254292i | ||||
\(369\) | 82133.3 | 0.0314017 | ||||||||
\(370\) | −2.64268e6 | − | 6.66702e6i | −1.00355 | − | 2.53179i | ||||
\(371\) | −184294. | + | 184294.i | −0.0695145 | + | 0.0695145i | ||||
\(372\) | −44240.7 | + | 1.44374e6i | −0.0165754 | + | 0.540919i | ||||
\(373\) | 1.23878e6 | + | 1.23878e6i | 0.461024 | + | 0.461024i | 0.898991 | − | 0.437967i | \(-0.144301\pi\) |
−0.437967 | + | 0.898991i | \(0.644301\pi\) | |||||||
\(374\) | −871399. | − | 376683.i | −0.322135 | − | 0.139251i | ||||
\(375\) | 1.21077e6i | 0.444615i | ||||||||
\(376\) | 587275. | − | 1.25183e6i | 0.214226 | − | 0.456643i | ||||
\(377\) | 564296.i | 0.204481i | ||||||||
\(378\) | 697631. | − | 1.61386e6i | 0.251128 | − | 0.580947i | ||||
\(379\) | −608015. | − | 608015.i | −0.217428 | − | 0.217428i | 0.589986 | − | 0.807414i | \(-0.299133\pi\) |
−0.807414 | + | 0.589986i | \(0.799133\pi\) | |||||||
\(380\) | −2.89176e6 | + | 2.71981e6i | −1.02732 | + | 0.966227i | ||||
\(381\) | 246655. | − | 246655.i | 0.0870519 | − | 0.0870519i | ||||
\(382\) | 1.40129e6 | − | 555445.i | 0.491326 | − | 0.194752i | ||||
\(383\) | −1.17463e6 | −0.409172 | −0.204586 | − | 0.978849i | \(-0.565585\pi\) | ||||
−0.204586 | + | 0.978849i | \(0.565585\pi\) | |||||||
\(384\) | −799879. | + | 234764.i | −0.276819 | + | 0.0812461i | ||||
\(385\) | 5.12180e6 | 1.76105 | ||||||||
\(386\) | −5.01609e6 | + | 1.98828e6i | −1.71355 | + | 0.679218i | ||||
\(387\) | 2.04253e6 | − | 2.04253e6i | 0.693252 | − | 0.693252i | ||||
\(388\) | −1.71585e6 | + | 1.61381e6i | −0.578627 | + | 0.544220i | ||||
\(389\) | −612458. | − | 612458.i | −0.205212 | − | 0.205212i | 0.597017 | − | 0.802229i | \(-0.296353\pi\) |
−0.802229 | + | 0.597017i | \(0.796353\pi\) | |||||||
\(390\) | 297277. | − | 687705.i | 0.0989692 | − | 0.228950i | ||||
\(391\) | 488018.i | 0.161434i | ||||||||
\(392\) | 400501. | − | 853707.i | 0.131640 | − | 0.280604i | ||||
\(393\) | − | 654718.i | − | 0.213832i | ||||||
\(394\) | −1.64339e6 | − | 710397.i | −0.533337 | − | 0.230548i | ||||
\(395\) | 2.96381e6 | + | 2.96381e6i | 0.955779 | + | 0.955779i | ||||
\(396\) | 79113.2 | − | 2.58176e6i | 0.0253519 | − | 0.827329i | ||||
\(397\) | −127882. | + | 127882.i | −0.0407224 | + | 0.0407224i | −0.727175 | − | 0.686452i | \(-0.759167\pi\) |
0.686452 | + | 0.727175i | \(0.259167\pi\) | |||||||
\(398\) | 1.17322e6 | + | 2.95983e6i | 0.371255 | + | 0.936612i | ||||
\(399\) | 868942. | 0.273249 | ||||||||
\(400\) | 6.08239e6 | + | 373117.i | 1.90075 | + | 0.116599i | ||||
\(401\) | −5.67113e6 | −1.76120 | −0.880600 | − | 0.473861i | \(-0.842860\pi\) | ||||
−0.880600 | + | 0.473861i | \(0.842860\pi\) | |||||||
\(402\) | 230689. | + | 581989.i | 0.0711970 | + | 0.179618i | ||||
\(403\) | −2.19393e6 | + | 2.19393e6i | −0.672915 | + | 0.672915i | ||||
\(404\) | 3.53104e6 | + | 108202.i | 1.07634 | + | 0.0329824i | ||||
\(405\) | 3.01215e6 | + | 3.01215e6i | 0.912514 | + | 0.912514i | ||||
\(406\) | 1.40643e6 | + | 607962.i | 0.423450 | + | 0.183046i | ||||
\(407\) | 4.82171e6i | 1.44283i | ||||||||
\(408\) | 128139. | + | 354615.i | 0.0381094 | + | 0.105465i | ||||
\(409\) | 156604.i | 0.0462907i | 0.999732 | + | 0.0231453i | \(0.00736805\pi\) | ||||
−0.999732 | + | 0.0231453i | \(0.992632\pi\) | |||||||
\(410\) | 78837.7 | − | 182379.i | 0.0231619 | − | 0.0535815i | ||||
\(411\) | −330293. | − | 330293.i | −0.0964483 | − | 0.0964483i | ||||
\(412\) | −80141.8 | − | 85208.7i | −0.0232603 | − | 0.0247309i | ||||
\(413\) | 2.41194e6 | − | 2.41194e6i | 0.695811 | − | 0.695811i | ||||
\(414\) | −1.23438e6 | + | 489286.i | −0.353956 | + | 0.140301i | ||||
\(415\) | −9.87379e6 | −2.81426 | ||||||||
\(416\) | −1.59707e6 | − | 809818.i | −0.452472 | − | 0.229432i | ||||
\(417\) | −1.26848e6 | −0.357227 | ||||||||
\(418\) | 2.48122e6 | − | 983508.i | 0.694584 | − | 0.275320i | ||||
\(419\) | 3.22837e6 | − | 3.22837e6i | 0.898357 | − | 0.898357i | −0.0969342 | − | 0.995291i | \(-0.530904\pi\) |
0.995291 | + | 0.0969342i | \(0.0309036\pi\) | |||||||
\(420\) | −1.39372e6 | − | 1.48184e6i | −0.385526 | − | 0.409900i | ||||
\(421\) | −3.16092e6 | − | 3.16092e6i | −0.869176 | − | 0.869176i | 0.123205 | − | 0.992381i | \(-0.460683\pi\) |
−0.992381 | + | 0.123205i | \(0.960683\pi\) | |||||||
\(422\) | −1.60982e6 | + | 3.72408e6i | −0.440045 | + | 1.01798i | ||||
\(423\) | − | 1.70170e6i | − | 0.462415i | ||||||
\(424\) | 299040. | − | 108058.i | 0.0807819 | − | 0.0291904i | ||||
\(425\) | − | 2.75631e6i | − | 0.740212i | ||||||
\(426\) | −1.57424e6 | − | 680505.i | −0.420289 | − | 0.181680i | ||||
\(427\) | 206857. | + | 206857.i | 0.0549036 | + | 0.0549036i | ||||
\(428\) | 2.02203e6 | + | 61961.3i | 0.533554 | + | 0.0163498i | ||||
\(429\) | −356179. | + | 356179.i | −0.0934383 | + | 0.0934383i | ||||
\(430\) | −2.57491e6 | − | 6.49606e6i | −0.671570 | − | 1.69426i | ||||
\(431\) | 6.23411e6 | 1.61652 | 0.808260 | − | 0.588826i | \(-0.200410\pi\) | ||||
0.808260 | + | 0.588826i | \(0.200410\pi\) | |||||||
\(432\) | −1.60674e6 | + | 1.42100e6i | −0.414224 | + | 0.366341i | ||||
\(433\) | 4.15896e6 | 1.06602 | 0.533010 | − | 0.846109i | \(-0.321061\pi\) | ||||
0.533010 | + | 0.846109i | \(0.321061\pi\) | |||||||
\(434\) | 3.10436e6 | + | 7.83175e6i | 0.791129 | + | 1.99588i | ||||
\(435\) | 553025. | − | 553025.i | 0.140127 | − | 0.140127i | ||||
\(436\) | −94623.1 | + | 3.08791e6i | −0.0238386 | + | 0.777944i | ||||
\(437\) | −970193. | − | 970193.i | −0.243027 | − | 0.243027i | ||||
\(438\) | 456366. | + | 197275.i | 0.113665 | + | 0.0491346i | ||||
\(439\) | − | 5.80927e6i | − | 1.43867i | −0.694664 | − | 0.719334i | \(-0.744447\pi\) | ||
0.694664 | − | 0.719334i | \(-0.255553\pi\) | |||||||
\(440\) | −5.65693e6 | − | 2.65384e6i | −1.39299 | − | 0.653497i | ||||
\(441\) | − | 1.16050e6i | − | 0.284151i | ||||||
\(442\) | −321374. | + | 743448.i | −0.0782446 | + | 0.181007i | ||||
\(443\) | −4.91288e6 | − | 4.91288e6i | −1.18940 | − | 1.18940i | −0.977234 | − | 0.212162i | \(-0.931949\pi\) |
−0.212162 | − | 0.977234i | \(-0.568051\pi\) | |||||||
\(444\) | 1.39502e6 | − | 1.31207e6i | 0.335832 | − | 0.315862i | ||||
\(445\) | −5.97330e6 | + | 5.97330e6i | −1.42993 | + | 1.42993i | ||||
\(446\) | 5.06509e6 | − | 2.00770e6i | 1.20573 | − | 0.477928i | ||||
\(447\) | −711575. | −0.168443 | ||||||||
\(448\) | −3.73901e6 | + | 3.10799e6i | −0.880160 | + | 0.731618i | ||||
\(449\) | −5.08115e6 | −1.18945 | −0.594725 | − | 0.803929i | \(-0.702739\pi\) | ||||
−0.594725 | + | 0.803929i | \(0.702739\pi\) | |||||||
\(450\) | 6.97177e6 | − | 2.76348e6i | 1.62298 | − | 0.643316i | ||||
\(451\) | −94458.4 | + | 94458.4i | −0.0218675 | + | 0.0218675i | ||||
\(452\) | 4.10454e6 | − | 3.86047e6i | 0.944970 | − | 0.888779i | ||||
\(453\) | 860094. | + | 860094.i | 0.196925 | + | 0.196925i | ||||
\(454\) | 914825. | − | 2.11631e6i | 0.208304 | − | 0.481880i | ||||
\(455\) | − | 4.36975e6i | − | 0.989528i | ||||||
\(456\) | −959729. | − | 450239.i | −0.216141 | − | 0.101398i | ||||
\(457\) | − | 166114.i | − | 0.0372061i | −0.999827 | − | 0.0186031i | \(-0.994078\pi\) | ||
0.999827 | − | 0.0186031i | \(-0.00592188\pi\) | |||||||
\(458\) | 2.16133e6 | + | 934286.i | 0.481456 | + | 0.208121i | ||||
\(459\) | 686029. | + | 686029.i | 0.151988 | + | 0.151988i | ||||
\(460\) | −98383.8 | + | 3.21063e6i | −0.0216785 | + | 0.707450i | ||||
\(461\) | −3.52977e6 | + | 3.52977e6i | −0.773560 | + | 0.773560i | −0.978727 | − | 0.205167i | \(-0.934226\pi\) |
0.205167 | + | 0.978727i | \(0.434226\pi\) | |||||||
\(462\) | 503984. | + | 1.27146e6i | 0.109853 | + | 0.277140i | ||||
\(463\) | −3.31500e6 | −0.718673 | −0.359337 | − | 0.933208i | \(-0.616997\pi\) | ||||
−0.359337 | + | 0.933208i | \(0.616997\pi\) | |||||||
\(464\) | −1.23836e6 | − | 1.40022e6i | −0.267024 | − | 0.301926i | ||||
\(465\) | 4.30022e6 | 0.922270 | ||||||||
\(466\) | 2.64826e6 | + | 6.68111e6i | 0.564932 | + | 1.42523i | ||||
\(467\) | 1.83160e6 | − | 1.83160e6i | 0.388632 | − | 0.388632i | −0.485567 | − | 0.874199i | \(-0.661387\pi\) |
0.874199 | + | 0.485567i | \(0.161387\pi\) | |||||||
\(468\) | −2.20267e6 | − | 67496.8i | −0.464874 | − | 0.0142452i | ||||
\(469\) | 2.58192e6 | + | 2.58192e6i | 0.542014 | + | 0.542014i | ||||
\(470\) | −3.77867e6 | − | 1.63342e6i | −0.789031 | − | 0.341078i | ||||
\(471\) | − | 673171.i | − | 0.139821i | ||||||
\(472\) | −3.91368e6 | + | 1.41420e6i | −0.808593 | + | 0.292184i | ||||
\(473\) | 4.69807e6i | 0.965533i | ||||||||
\(474\) | −444114. | + | 1.02739e6i | −0.0907923 | + | 0.210034i | ||||
\(475\) | 5.47963e6 | + | 5.47963e6i | 1.11434 | + | 1.11434i | ||||
\(476\) | 1.50670e6 | + | 1.60195e6i | 0.304795 | + | 0.324065i | ||||
\(477\) | 276697. | − | 276697.i | 0.0556812 | − | 0.0556812i | ||||
\(478\) | 5.78183e6 | − | 2.29181e6i | 1.15743 | − | 0.458784i | ||||
\(479\) | 2.00716e6 | 0.399708 | 0.199854 | − | 0.979826i | \(-0.435953\pi\) | ||||
0.199854 | + | 0.979826i | \(0.435953\pi\) | |||||||
\(480\) | 771530. | + | 2.35882e6i | 0.152845 | + | 0.467295i | ||||
\(481\) | 4.11372e6 | 0.810723 | ||||||||
\(482\) | −6.90740e6 | + | 2.73796e6i | −1.35424 | + | 0.536796i | ||||
\(483\) | 497161. | − | 497161.i | 0.0969681 | − | 0.0969681i | ||||
\(484\) | −652639. | − | 693901.i | −0.126637 | − | 0.134643i | ||||
\(485\) | 4.95874e6 | + | 4.95874e6i | 0.957231 | + | 0.957231i | ||||
\(486\) | −1.59387e6 | + | 3.68717e6i | −0.306099 | + | 0.708113i | ||||
\(487\) | 2.41202e6i | 0.460850i | 0.973090 | + | 0.230425i | \(0.0740116\pi\) | ||||
−0.973090 | + | 0.230425i | \(0.925988\pi\) | |||||||
\(488\) | −121287. | − | 335652.i | −0.0230550 | − | 0.0638027i | ||||
\(489\) | 24373.2i | 0.00460936i | ||||||||
\(490\) | −2.57692e6 | − | 1.11394e6i | −0.484854 | − | 0.209590i | ||||
\(491\) | 5.10857e6 | + | 5.10857e6i | 0.956303 | + | 0.956303i | 0.999084 | − | 0.0427811i | \(-0.0136218\pi\) |
−0.0427811 | + | 0.999084i | \(0.513622\pi\) | |||||||
\(492\) | 53032.4 | + | 1625.08i | 0.00987708 | + | 0.000302664i | ||||
\(493\) | −597852. | + | 597852.i | −0.110784 | + | 0.110784i | ||||
\(494\) | −839096. | − | 2.11690e6i | −0.154701 | − | 0.390285i | ||||
\(495\) | −7.68984e6 | −1.41060 | ||||||||
\(496\) | 629297. | − | 1.02585e7i | 0.114855 | − | 1.87232i | ||||
\(497\) | −1.00029e7 | −1.81650 | ||||||||
\(498\) | −971579. | − | 2.45113e6i | −0.175552 | − | 0.442886i | ||||
\(499\) | 7.47209e6 | − | 7.47209e6i | 1.34335 | − | 1.34335i | 0.450658 | − | 0.892697i | \(-0.351189\pi\) |
0.892697 | − | 0.450658i | \(-0.148811\pi\) | |||||||
\(500\) | 263875. | − | 8.61125e6i | 0.0472035 | − | 1.54043i | ||||
\(501\) | 301885. | + | 301885.i | 0.0537337 | + | 0.0537337i | ||||
\(502\) | −3.26148e6 | − | 1.40986e6i | −0.577638 | − | 0.249698i | ||||
\(503\) | 7.72508e6i | 1.36139i | 0.732566 | + | 0.680696i | \(0.238322\pi\) | ||||
−0.732566 | + | 0.680696i | \(0.761678\pi\) | |||||||
\(504\) | −2.54134e6 | + | 5.41712e6i | −0.445643 | + | 0.949932i | ||||
\(505\) | − | 1.05173e7i | − | 1.83517i | ||||||
\(506\) | 856909. | − | 1.98233e6i | 0.148785 | − | 0.344191i | ||||
\(507\) | −876833. | − | 876833.i | −0.151495 | − | 0.151495i | ||||
\(508\) | −1.80802e6 | + | 1.70050e6i | −0.310844 | + | 0.292360i | ||||
\(509\) | 3.58467e6 | − | 3.58467e6i | 0.613274 | − | 0.613274i | −0.330524 | − | 0.943798i | \(-0.607225\pi\) |
0.943798 | + | 0.330524i | \(0.107225\pi\) | |||||||
\(510\) | 1.04355e6 | − | 413644.i | 0.177660 | − | 0.0704209i | ||||
\(511\) | 2.89980e6 | 0.491265 | ||||||||
\(512\) | 5.74006e6 | − | 1.49536e6i | 0.967702 | − | 0.252099i | ||||
\(513\) | −2.72769e6 | −0.457616 | ||||||||
\(514\) | −3.49634e6 | + | 1.38588e6i | −0.583722 | + | 0.231376i | ||||
\(515\) | −246250. | + | 246250.i | −0.0409127 | + | 0.0409127i | ||||
\(516\) | 1.35925e6 | − | 1.27842e6i | 0.224737 | − | 0.211373i | ||||
\(517\) | 1.95706e6 | + | 1.95706e6i | 0.322017 | + | 0.322017i | ||||
\(518\) | 4.43205e6 | − | 1.02529e7i | 0.725738 | − | 1.67888i | ||||
\(519\) | 1.70181e6i | 0.277327i | ||||||||
\(520\) | −2.26417e6 | + | 4.82630e6i | −0.367198 | + | 0.782720i | ||||
\(521\) | − | 2.53713e6i | − | 0.409495i | −0.978815 | − | 0.204748i | \(-0.934363\pi\) | ||
0.978815 | − | 0.204748i | \(-0.0656374\pi\) | |||||||
\(522\) | −2.11160e6 | − | 912790.i | −0.339184 | − | 0.146621i | ||||
\(523\) | −4.65944e6 | − | 4.65944e6i | −0.744868 | − | 0.744868i | 0.228642 | − | 0.973510i | \(-0.426571\pi\) |
−0.973510 | + | 0.228642i | \(0.926571\pi\) | |||||||
\(524\) | −142689. | + | 4.65648e6i | −0.0227019 | + | 0.740849i | ||||
\(525\) | −2.80795e6 | + | 2.80795e6i | −0.444623 | + | 0.444623i | ||||
\(526\) | 3.14148e6 | + | 7.92542e6i | 0.495074 | + | 1.24899i | ||||
\(527\) | −4.64878e6 | −0.729143 | ||||||||
\(528\) | 102165. | − | 1.66545e6i | 0.0159484 | − | 0.259983i | ||||
\(529\) | 5.32616e6 | 0.827514 | ||||||||
\(530\) | −348818. | − | 880008.i | −0.0539398 | − | 0.136081i | ||||
\(531\) | −3.62127e6 | + | 3.62127e6i | −0.557346 | + | 0.557346i | ||||
\(532\) | −6.18008e6 | − | 189377.i | −0.946706 | − | 0.0290100i | ||||
\(533\) | 80588.8 | + | 80588.8i | 0.0122873 | + | 0.0122873i | ||||
\(534\) | −2.07062e6 | − | 895075.i | −0.314229 | − | 0.135833i | ||||
\(535\) | − | 6.02267e6i | − | 0.909714i | ||||||
\(536\) | −1.51387e6 | − | 4.18949e6i | −0.227602 | − | 0.629868i | ||||
\(537\) | − | 976370.i | − | 0.146110i | ||||||
\(538\) | 1.84507e6 | − | 4.26828e6i | 0.274825 | − | 0.635766i | ||||
\(539\) | 1.33465e6 | + | 1.33465e6i | 0.197877 | + | 0.197877i | ||||
\(540\) | 4.37503e6 | + | 4.65164e6i | 0.645649 | + | 0.686470i | ||||
\(541\) | 2.06112e6 | − | 2.06112e6i | 0.302768 | − | 0.302768i | −0.539328 | − | 0.842096i | \(-0.681322\pi\) |
0.842096 | + | 0.539328i | \(0.181322\pi\) | |||||||
\(542\) | −4.32189e6 | + | 1.71311e6i | −0.631940 | + | 0.250489i | ||||
\(543\) | 1.82407e6 | 0.265486 | ||||||||
\(544\) | −834068. | − | 2.55002e6i | −0.120838 | − | 0.369441i | ||||
\(545\) | 9.19741e6 | 1.32640 | ||||||||
\(546\) | 1.08477e6 | − | 429982.i | 0.155724 | − | 0.0617261i | ||||
\(547\) | −7.60525e6 | + | 7.60525e6i | −1.08679 | + | 1.08679i | −0.0909315 | + | 0.995857i | \(0.528984\pi\) |
−0.995857 | + | 0.0909315i | \(0.971016\pi\) | |||||||
\(548\) | 2.27712e6 | + | 2.42109e6i | 0.323918 | + | 0.344397i | ||||
\(549\) | −310574. | − | 310574.i | −0.0439779 | − | 0.0439779i | ||||
\(550\) | −4.83981e6 | + | 1.11961e7i | −0.682215 | + | 1.57820i | ||||
\(551\) | − | 2.37709e6i | − | 0.333555i | ||||||
\(552\) | −806706. | + | 291502.i | −0.112685 | + | 0.0407187i | ||||
\(553\) | 6.52815e6i | 0.907773i | ||||||||
\(554\) | 2.09819e6 | + | 906992.i | 0.290449 | + | 0.125554i | ||||
\(555\) | −4.03156e6 | − | 4.03156e6i | −0.555572 | − | 0.555572i | ||||
\(556\) | 9.02170e6 | + | 276453.i | 1.23766 | + | 0.0379258i | ||||
\(557\) | 2.69598e6 | − | 2.69598e6i | 0.368196 | − | 0.368196i | −0.498623 | − | 0.866819i | \(-0.666161\pi\) |
0.866819 | + | 0.498623i | \(0.166161\pi\) | |||||||
\(558\) | −4.66086e6 | − | 1.17585e7i | −0.633695 | − | 1.59870i | ||||
\(559\) | 4.00824e6 | 0.542531 | ||||||||
\(560\) | 9.58949e6 | + | 1.08429e7i | 1.29219 | + | 1.46108i | ||||
\(561\) | −754718. | −0.101246 | ||||||||
\(562\) | 2.89496e6 | + | 7.30350e6i | 0.386636 | + | 0.975416i | ||||
\(563\) | −4.79425e6 | + | 4.79425e6i | −0.637455 | + | 0.637455i | −0.949927 | − | 0.312472i | \(-0.898843\pi\) |
0.312472 | + | 0.949927i | \(0.398843\pi\) | |||||||
\(564\) | 33669.6 | − | 1.09877e6i | 0.00445698 | − | 0.145448i | ||||
\(565\) | −1.18620e7 | − | 1.18620e7i | −1.56328 | − | 1.56328i | ||||
\(566\) | −458851. | − | 198349.i | −0.0602047 | − | 0.0260249i | ||||
\(567\) | 6.63463e6i | 0.866681i | ||||||||
\(568\) | 1.10480e7 | + | 5.18297e6i | 1.43686 | + | 0.674075i | ||||
\(569\) | − | 5.78452e6i | − | 0.749008i | −0.927225 | − | 0.374504i | \(-0.877813\pi\) | ||
0.927225 | − | 0.374504i | \(-0.122187\pi\) | |||||||
\(570\) | −1.25228e6 | + | 2.89695e6i | −0.161441 | + | 0.373468i | ||||
\(571\) | 6.78200e6 | + | 6.78200e6i | 0.870498 | + | 0.870498i | 0.992527 | − | 0.122029i | \(-0.0389401\pi\) |
−0.122029 | + | 0.992527i | \(0.538940\pi\) | |||||||
\(572\) | 2.61084e6 | − | 2.45559e6i | 0.333649 | − | 0.313809i | ||||
\(573\) | 847364. | − | 847364.i | 0.107816 | − | 0.107816i | ||||
\(574\) | 287681. | − | 114031.i | 0.0364444 | − | 0.0144459i | ||||
\(575\) | 6.27028e6 | 0.790893 | ||||||||
\(576\) | 5.61373e6 | − | 4.66632e6i | 0.705010 | − | 0.586028i | ||||
\(577\) | −1.33602e7 | −1.67060 | −0.835300 | − | 0.549795i | \(-0.814706\pi\) | ||||
−0.835300 | + | 0.549795i | \(0.814706\pi\) | |||||||
\(578\) | 6.33860e6 | − | 2.51250e6i | 0.789175 | − | 0.312814i | ||||
\(579\) | −3.03324e6 | + | 3.03324e6i | −0.376019 | + | 0.376019i | ||||
\(580\) | −4.05375e6 | + | 3.81269e6i | −0.500365 | + | 0.470611i | ||||
\(581\) | −1.08741e7 | − | 1.08741e7i | −1.33645 | − | 1.33645i | ||||
\(582\) | −743046. | + | 1.71892e6i | −0.0909302 | + | 0.210353i | ||||
\(583\) | 636438.i | 0.0775506i | ||||||||
\(584\) | −3.20277e6 | − | 1.50252e6i | −0.388592 | − | 0.182301i | ||||
\(585\) | 6.56072e6i | 0.792614i | ||||||||
\(586\) | −1.16263e7 | − | 5.02576e6i | −1.39861 | − | 0.604585i | ||||
\(587\) | −4.29558e6 | − | 4.29558e6i | −0.514549 | − | 0.514549i | 0.401368 | − | 0.915917i | \(-0.368535\pi\) |
−0.915917 | + | 0.401368i | \(0.868535\pi\) | |||||||
\(588\) | 22961.5 | − | 749320.i | 0.00273878 | − | 0.0893767i | ||||
\(589\) | 9.24191e6 | − | 9.24191e6i | 1.09767 | − | 1.09767i | ||||
\(590\) | 4.56515e6 | + | 1.15171e7i | 0.539915 | + | 1.36211i | ||||
\(591\) | −1.42334e6 | −0.167626 | ||||||||
\(592\) | −1.02076e7 | + | 9.02763e6i | −1.19707 | + | 1.05869i | ||||
\(593\) | 1.13393e7 | 1.32418 | 0.662092 | − | 0.749423i | \(-0.269669\pi\) | ||||
0.662092 | + | 0.749423i | \(0.269669\pi\) | |||||||
\(594\) | −1.58205e6 | − | 3.99125e6i | −0.183973 | − | 0.464133i | ||||
\(595\) | 4.62959e6 | − | 4.62959e6i | 0.536106 | − | 0.536106i | ||||
\(596\) | 5.06086e6 | + | 155080.i | 0.583591 | + | 0.0178830i | ||||
\(597\) | 1.78982e6 | + | 1.78982e6i | 0.205529 | + | 0.205529i | ||||
\(598\) | −1.69126e6 | − | 731086.i | −0.193400 | − | 0.0836018i | ||||
\(599\) | 1.32953e6i | 0.151402i | 0.997131 | + | 0.0757011i | \(0.0241195\pi\) | ||||
−0.997131 | + | 0.0757011i | \(0.975881\pi\) | |||||||
\(600\) | 4.55626e6 | − | 1.64640e6i | 0.516690 | − | 0.186705i | ||||
\(601\) | 1.21817e7i | 1.37569i | 0.725858 | + | 0.687845i | \(0.241443\pi\) | ||||
−0.725858 | + | 0.687845i | \(0.758557\pi\) | |||||||
\(602\) | 4.31840e6 | − | 9.98996e6i | 0.485659 | − | 1.12350i | ||||
\(603\) | −3.87648e6 | − | 3.87648e6i | −0.434154 | − | 0.434154i | ||||
\(604\) | −5.92970e6 | − | 6.30460e6i | −0.661364 | − | 0.703178i | ||||
\(605\) | −2.00535e6 | + | 2.00535e6i | −0.222742 | + | 0.222742i | ||||
\(606\) | 2.61087e6 | − | 1.03490e6i | 0.288804 | − | 0.114476i | ||||
\(607\) | 8.54612e6 | 0.941450 | 0.470725 | − | 0.882280i | \(-0.343992\pi\) | ||||
0.470725 | + | 0.882280i | \(0.343992\pi\) | |||||||
\(608\) | 6.72765e6 | + | 3.41135e6i | 0.738082 | + | 0.374255i | ||||
\(609\) | 1.21810e6 | 0.133089 | ||||||||
\(610\) | −987749. | + | 391525.i | −0.107479 | + | 0.0426024i | ||||
\(611\) | 1.66970e6 | − | 1.66970e6i | 0.180940 | − | 0.180940i | ||||
\(612\) | −2.26214e6 | − | 2.40516e6i | −0.244141 | − | 0.259577i | ||||
\(613\) | 1.05598e7 | + | 1.05598e7i | 1.13502 | + | 1.13502i | 0.989331 | + | 0.145688i | \(0.0465395\pi\) |
0.145688 | + | 0.989331i | \(0.453460\pi\) | |||||||
\(614\) | −4.17951e6 | + | 9.66864e6i | −0.447408 | + | 1.03501i | ||||
\(615\) | − | 157958.i | − | 0.0168405i | ||||||
\(616\) | −3.30733e6 | − | 9.15274e6i | −0.351177 | − | 0.971850i | ||||
\(617\) | 3.42350e6i | 0.362041i | 0.983479 | + | 0.181021i | \(0.0579401\pi\) | ||||
−0.983479 | + | 0.181021i | \(0.942060\pi\) | |||||||
\(618\) | −85361.5 | − | 36899.6i | −0.00899064 | − | 0.00388642i | ||||
\(619\) | −9.52048e6 | − | 9.52048e6i | −0.998693 | − | 0.998693i | 0.00130592 | − | 0.999999i | \(-0.499584\pi\) |
−0.999999 | + | 0.00130592i | \(0.999584\pi\) | |||||||
\(620\) | −3.05840e7 | − | 937189.i | −3.19532 | − | 0.0979147i | ||||
\(621\) | −1.56063e6 | + | 1.56063e6i | −0.162395 | + | 0.162395i | ||||
\(622\) | −1.17612e6 | − | 2.96716e6i | −0.121893 | − | 0.307514i | ||||
\(623\) | −1.31569e7 | −1.35811 | ||||||||
\(624\) | −1.42090e6 | − | 87163.6i | −0.146084 | − | 0.00896135i | ||||
\(625\) | −7.05193e6 | −0.722117 | ||||||||
\(626\) | −4.52678e6 | − | 1.14203e7i | −0.461693 | − | 1.16477i | ||||
\(627\) | 1.50040e6 | − | 1.50040e6i | 0.152419 | − | 0.152419i | ||||
\(628\) | −146711. | + | 4.78772e6i | −0.0148444 | + | 0.484428i | ||||
\(629\) | 4.35834e6 | + | 4.35834e6i | 0.439233 | + | 0.439233i | ||||
\(630\) | 1.63516e7 | + | 7.06839e6i | 1.64138 | + | 0.709527i | ||||
\(631\) | − | 7.08377e6i | − | 0.708257i | −0.935197 | − | 0.354129i | \(-0.884777\pi\) | ||
0.935197 | − | 0.354129i | \(-0.115223\pi\) | |||||||
\(632\) | 3.38254e6 | − | 7.21021e6i | 0.336860 | − | 0.718051i | ||||
\(633\) | 3.22542e6i | 0.319946i | ||||||||
\(634\) | 845190. | − | 1.95522e6i | 0.0835086 | − | 0.193184i | ||||
\(635\) | 5.22511e6 | + | 5.22511e6i | 0.514234 | + | 0.514234i | ||||
\(636\) | 184135. | − | 173185.i | 0.0180506 | − | 0.0169773i | ||||
\(637\) | 1.13868e6 | − | 1.13868e6i | 0.111187 | − | 0.111187i | ||||
\(638\) | 3.47824e6 | − | 1.37871e6i | 0.338304 | − | 0.134097i | ||||
\(639\) | 1.50183e7 | 1.45502 | ||||||||
\(640\) | −4.97319e6 | − | 1.69445e7i | −0.479938 | − | 1.63523i | ||||
\(641\) | 1.32658e6 | 0.127523 | 0.0637617 | − | 0.997965i | \(-0.479690\pi\) | ||||
0.0637617 | + | 0.997965i | \(0.479690\pi\) | |||||||
\(642\) | 1.49510e6 | − | 592629.i | 0.143164 | − | 0.0567473i | ||||
\(643\) | 2.06573e6 | − | 2.06573e6i | 0.197036 | − | 0.197036i | −0.601692 | − | 0.798728i | \(-0.705507\pi\) |
0.798728 | + | 0.601692i | \(0.205507\pi\) | |||||||
\(644\) | −3.64425e6 | + | 3.42755e6i | −0.346253 | + | 0.325664i | ||||
\(645\) | −3.92818e6 | − | 3.92818e6i | −0.371785 | − | 0.371785i | ||||
\(646\) | 1.35378e6 | − | 3.13177e6i | 0.127634 | − | 0.295262i | ||||
\(647\) | − | 879558.i | − | 0.0826046i | −0.999147 | − | 0.0413023i | \(-0.986849\pi\) | ||
0.999147 | − | 0.0413023i | \(-0.0131507\pi\) | |||||||
\(648\) | 3.43771e6 | − | 7.32782e6i | 0.321612 | − | 0.685547i | ||||
\(649\) | − | 8.32938e6i | − | 0.776249i | ||||||
\(650\) | 9.55218e6 | + | 4.12916e6i | 0.886786 | + | 0.383335i | ||||
\(651\) | 4.73588e6 | + | 4.73588e6i | 0.437974 | + | 0.437974i | ||||
\(652\) | 5311.89 | − | 173347.i | 0.000489362 | − | 0.0159697i | ||||
\(653\) | −9.65093e6 | + | 9.65093e6i | −0.885699 | + | 0.885699i | −0.994107 | − | 0.108407i | \(-0.965425\pi\) |
0.108407 | + | 0.994107i | \(0.465425\pi\) | |||||||
\(654\) | 905023. | + | 2.28322e6i | 0.0827400 | + | 0.208739i | ||||
\(655\) | 1.38694e7 | 1.26315 | ||||||||
\(656\) | −376822. | − | 23115.7i | −0.0341883 | − | 0.00209724i | ||||
\(657\) | −4.35374e6 | −0.393504 | ||||||||
\(658\) | −2.36258e6 | − | 5.96039e6i | −0.212727 | − | 0.536673i | ||||
\(659\) | −7.38827e6 | + | 7.38827e6i | −0.662719 | + | 0.662719i | −0.956020 | − | 0.293301i | \(-0.905246\pi\) |
0.293301 | + | 0.956020i | \(0.405246\pi\) | |||||||
\(660\) | −4.96523e6 | − | 152150.i | −0.443690 | − | 0.0135960i | ||||
\(661\) | 4.31263e6 | + | 4.31263e6i | 0.383918 | + | 0.383918i | 0.872512 | − | 0.488593i | \(-0.162490\pi\) |
−0.488593 | + | 0.872512i | \(0.662490\pi\) | |||||||
\(662\) | −7.72364e6 | − | 3.33873e6i | −0.684979 | − | 0.296099i | ||||
\(663\) | 643900.i | 0.0568898i | ||||||||
\(664\) | 6.37586e6 | + | 1.76446e7i | 0.561201 | + | 1.55307i | ||||
\(665\) | 1.84075e7i | 1.61414i | ||||||||
\(666\) | −6.65425e6 | + | 1.53936e7i | −0.581318 | + | 1.34479i | ||||
\(667\) | −1.36004e6 | − | 1.36004e6i | −0.118369 | − | 0.118369i | ||||
\(668\) | −2.08127e6 | − | 2.21286e6i | −0.180463 | − | 0.191872i | ||||
\(669\) | 3.06287e6 | − | 3.06287e6i | 0.264584 | − | 0.264584i | ||||
\(670\) | −1.23288e7 | + | 4.88688e6i | −1.06104 | + | 0.420576i | ||||
\(671\) | 714359. | 0.0612506 | ||||||||
\(672\) | −1.74810e6 | + | 3.44748e6i | −0.149328 | + | 0.294496i | ||||
\(673\) | 3.04784e6 | 0.259390 | 0.129695 | − | 0.991554i | \(-0.458600\pi\) | ||||
0.129695 | + | 0.991554i | \(0.458600\pi\) | |||||||
\(674\) | −1.20391e6 | + | 477208.i | −0.102081 | + | 0.0404630i | ||||
\(675\) | 8.81443e6 | − | 8.81443e6i | 0.744620 | − | 0.744620i | ||||
\(676\) | 6.04511e6 | + | 6.42730e6i | 0.508789 | + | 0.540956i | ||||
\(677\) | 2.15140e6 | + | 2.15140e6i | 0.180405 | + | 0.180405i | 0.791533 | − | 0.611127i | \(-0.209284\pi\) |
−0.611127 | + | 0.791533i | \(0.709284\pi\) | |||||||
\(678\) | 1.77747e6 | − | 4.11190e6i | 0.148500 | − | 0.343533i | ||||
\(679\) | 1.09222e7i | 0.909151i | ||||||||
\(680\) | −7.51210e6 | + | 2.71449e6i | −0.623002 | + | 0.225121i | ||||
\(681\) | − | 1.83293e6i | − | 0.151453i | ||||||
\(682\) | 1.88834e7 | + | 8.16279e6i | 1.55460 | + | 0.672013i | ||||
\(683\) | −6.10507e6 | − | 6.10507e6i | −0.500770 | − | 0.500770i | 0.410907 | − | 0.911677i | \(-0.365212\pi\) |
−0.911677 | + | 0.410907i | \(0.865212\pi\) | |||||||
\(684\) | 9.27874e6 | + | 284329.i | 0.758313 | + | 0.0232371i | ||||
\(685\) | 6.99687e6 | − | 6.99687e6i | 0.569741 | − | 0.569741i | ||||
\(686\) | 3.58710e6 | + | 9.04962e6i | 0.291027 | + | 0.734210i | ||||
\(687\) | 1.87192e6 | 0.151320 | ||||||||
\(688\) | −9.94585e6 | + | 8.79615e6i | −0.801071 | + | 0.708470i | ||||
\(689\) | 542988. | 0.0435755 | ||||||||
\(690\) | 940992. | + | 2.37396e6i | 0.0752425 | + | 0.189824i | ||||
\(691\) | −1.26085e7 | + | 1.26085e7i | −1.00454 | + | 1.00454i | −0.00455145 | + | 0.999990i | \(0.501449\pi\) |
−0.999990 | + | 0.00455145i | \(0.998551\pi\) | |||||||
\(692\) | 370891. | − | 1.21036e7i | 0.0294430 | − | 0.960835i | ||||
\(693\) | −8.46890e6 | − | 8.46890e6i | −0.669875 | − | 0.669875i | ||||
\(694\) | 1.18592e7 | + | 5.12642e6i | 0.934665 | + | 0.404031i | ||||
\(695\) | − | 2.68714e7i | − | 2.11022i | ||||||
\(696\) | −1.34537e6 | − | 631157.i | −0.105274 | − | 0.0493872i | ||||
\(697\) | 170762.i | 0.0133140i | ||||||||
\(698\) | −1.08561e6 | + | 2.51138e6i | −0.0843401 | + | 0.195108i | ||||
\(699\) | 4.04008e6 | + | 4.04008e6i | 0.312750 | + | 0.312750i | ||||
\(700\) | 2.05827e7 | − | 1.93587e7i | 1.58766 | − | 1.49325i | ||||
\(701\) | −1.59123e7 | + | 1.59123e7i | −1.22303 | + | 1.22303i | −0.256487 | + | 0.966548i | \(0.582565\pi\) |
−0.966548 | + | 0.256487i | \(0.917435\pi\) | |||||||
\(702\) | −3.40520e6 | + | 1.34975e6i | −0.260795 | + | 0.103374i | ||||
\(703\) | −1.73290e7 | −1.32247 | ||||||||
\(704\) | −1.08958e6 | + | 1.18227e7i | −0.0828568 | + | 0.899053i | ||||
\(705\) | −3.27270e6 | −0.247990 | ||||||||
\(706\) | 10445.1 | − | 4140.23i | 0.000788678 | − | 0.000312617i | ||||
\(707\) | 1.15828e7 | − | 1.15828e7i | 0.871495 | − | 0.871495i | ||||
\(708\) | −2.40986e6 | + | 2.26656e6i | −0.180679 | + | 0.169935i | ||||
\(709\) | −1.02088e7 | − | 1.02088e7i | −0.762709 | − | 0.762709i | 0.214103 | − | 0.976811i | \(-0.431317\pi\) |
−0.976811 | + | 0.214103i | \(0.931317\pi\) | |||||||
\(710\) | 1.44157e7 | − | 3.33485e7i | 1.07322 | − | 2.48274i | ||||
\(711\) | − | 9.80132e6i | − | 0.727127i | ||||||
\(712\) | 1.45316e7 | + | 6.81721e6i | 1.07427 | + | 0.503973i | ||||
\(713\) | − | 1.05754e7i | − | 0.779066i | ||||||
\(714\) | 1.60483e6 | + | 693725.i | 0.117810 | + | 0.0509263i | ||||
\(715\) | −7.54524e6 | − | 7.54524e6i | −0.551960 | − | 0.551960i | ||||
\(716\) | −212790. | + | 6.94413e6i | −0.0155120 | + | 0.506215i | ||||
\(717\) | 3.49629e6 | − | 3.49629e6i | 0.253986 | − | 0.253986i | ||||
\(718\) | −3.69806e6 | − | 9.32956e6i | −0.267709 | − | 0.675383i | ||||
\(719\) | −1.72580e7 | −1.24499 | −0.622497 | − | 0.782622i | \(-0.713882\pi\) | ||||
−0.622497 | + | 0.782622i | \(0.713882\pi\) | |||||||
\(720\) | −1.43976e7 | − | 1.62794e7i | −1.03504 | − | 1.17033i | ||||
\(721\) | −542396. | −0.0388578 | ||||||||
\(722\) | −1.62671e6 | − | 4.10390e6i | −0.116136 | − | 0.292990i | ||||
\(723\) | −4.17692e6 | + | 4.17692e6i | −0.297174 | + | 0.297174i | ||||
\(724\) | −1.29732e7 | − | 397538.i | −0.919812 | − | 0.0281859i | ||||
\(725\) | 7.68148e6 | + | 7.68148e6i | 0.542750 | + | 0.542750i | ||||
\(726\) | −695145. | − | 300493.i | −0.0489479 | − | 0.0211589i | ||||
\(727\) | 1.06169e7i | 0.745012i | 0.928030 | + | 0.372506i | \(0.121501\pi\) | ||||
−0.928030 | + | 0.372506i | \(0.878499\pi\) | |||||||
\(728\) | −7.80881e6 | + | 2.82170e6i | −0.546080 | + | 0.197325i | ||||
\(729\) | − | 7.67208e6i | − | 0.534680i | ||||||
\(730\) | −4.17905e6 | + | 9.66758e6i | −0.290249 | + | 0.671446i | ||||
\(731\) | 4.24659e6 | + | 4.24659e6i | 0.293932 | + | 0.293932i | ||||
\(732\) | −194389. | − | 206678.i | −0.0134089 | − | 0.0142567i | ||||
\(733\) | 3.65326e6 | − | 3.65326e6i | 0.251143 | − | 0.251143i | −0.570296 | − | 0.821439i | \(-0.693172\pi\) |
0.821439 | + | 0.570296i | \(0.193172\pi\) | |||||||
\(734\) | −2.31750e7 | + | 9.18613e6i | −1.58774 | + | 0.629350i | ||||
\(735\) | −2.23187e6 | −0.152388 | ||||||||
\(736\) | 5.80098e6 | − | 1.89741e6i | 0.394736 | − | 0.129112i | ||||
\(737\) | 8.91639e6 | 0.604673 | ||||||||
\(738\) | −431922. | + | 171205.i | −0.0291920 | + | 0.0115712i | ||||
\(739\) | 1.91916e7 | − | 1.91916e7i | 1.29271 | − | 1.29271i | 0.359600 | − | 0.933106i | \(-0.382913\pi\) |
0.933106 | − | 0.359600i | \(-0.117087\pi\) | |||||||
\(740\) | 2.77946e7 | + | 2.95519e7i | 1.86587 | + | 1.98383i | ||||
\(741\) | −1.28009e6 | − | 1.28009e6i | −0.0856437 | − | 0.0856437i | ||||
\(742\) | 585005. | − | 1.35332e6i | 0.0390077 | − | 0.0902382i | ||||
\(743\) | 1.62809e7i | 1.08195i | 0.841039 | + | 0.540974i | \(0.181944\pi\) | ||||
−0.841039 | + | 0.540974i | \(0.818056\pi\) | |||||||
\(744\) | −2.77680e6 | − | 7.68456e6i | −0.183913 | − | 0.508964i | ||||
\(745\) | − | 1.50739e7i | − | 0.995026i | ||||||
\(746\) | −9.09674e6 | − | 3.93229e6i | −0.598465 | − | 0.258701i | ||||
\(747\) | 1.63263e7 | + | 1.63263e7i | 1.07050 | + | 1.07050i | ||||
\(748\) | 5.36770e6 | + | 164483.i | 0.350779 | + | 0.0107490i | ||||
\(749\) | 6.63283e6 | − | 6.63283e6i | 0.432011 | − | 0.432011i | ||||
\(750\) | −2.52384e6 | − | 6.36720e6i | −0.163836 | − | 0.413329i | ||||
\(751\) | −9.94826e6 | −0.643646 | −0.321823 | − | 0.946800i | \(-0.604296\pi\) | ||||
−0.321823 | + | 0.946800i | \(0.604296\pi\) | |||||||
\(752\) | −478930. | + | 7.80730e6i | −0.0308835 | + | 0.503450i | ||||
\(753\) | −2.82477e6 | −0.181550 | ||||||||
\(754\) | −1.17627e6 | − | 2.96752e6i | −0.0753490 | − | 0.190092i | ||||
\(755\) | −1.82201e7 | + | 1.82201e7i | −1.16328 | + | 1.16328i | ||||
\(756\) | −304628. | + | 9.94116e6i | −0.0193850 | + | 0.632605i | ||||
\(757\) | 1.01751e7 | + | 1.01751e7i | 0.645356 | + | 0.645356i | 0.951867 | − | 0.306511i | \(-0.0991616\pi\) |
−0.306511 | + | 0.951867i | \(0.599162\pi\) | |||||||
\(758\) | 4.46482e6 | + | 1.93003e6i | 0.282248 | + | 0.122009i | ||||
\(759\) | − | 1.71689e6i | − | 0.108178i | ||||||
\(760\) | 9.53780e6 | − | 2.03307e7i | 0.598982 | − | 1.27679i | ||||
\(761\) | − | 3.04334e7i | − | 1.90497i | −0.304583 | − | 0.952486i | \(-0.598517\pi\) | ||
0.304583 | − | 0.952486i | \(-0.401483\pi\) | |||||||
\(762\) | −782961. | + | 1.81126e6i | −0.0488487 | + | 0.113004i | ||||
\(763\) | 1.01292e7 | + | 1.01292e7i | 0.629889 | + | 0.629889i | ||||
\(764\) | −6.21129e6 | + | 5.84194e6i | −0.384989 | + | 0.362096i | ||||
\(765\) | −6.95084e6 | + | 6.95084e6i | −0.429422 | + | 0.429422i | ||||
\(766\) | 6.17716e6 | − | 2.44851e6i | 0.380379 | − | 0.150775i | ||||
\(767\) | −7.10635e6 | −0.436172 | ||||||||
\(768\) | 3.71704e6 | − | 2.90191e6i | 0.227402 | − | 0.177534i | ||||
\(769\) | −1.22268e7 | −0.745587 | −0.372794 | − | 0.927914i | \(-0.621600\pi\) | ||||
−0.372794 | + | 0.927914i | \(0.621600\pi\) | |||||||
\(770\) | −2.69345e7 | + | 1.06763e7i | −1.63713 | + | 0.648925i | ||||
\(771\) | −2.11424e6 | + | 2.11424e6i | −0.128091 | + | 0.128091i | ||||
\(772\) | 2.22340e7 | − | 2.09119e7i | 1.34269 | − | 1.26285i | ||||
\(773\) | 1.62595e7 | + | 1.62595e7i | 0.978722 | + | 0.978722i | 0.999778 | − | 0.0210561i | \(-0.00670287\pi\) |
−0.0210561 | + | 0.999778i | \(0.506703\pi\) | |||||||
\(774\) | −6.48362e6 | + | 1.49989e7i | −0.389014 | + | 0.899924i | ||||
\(775\) | 5.97298e7i | 3.57221i | ||||||||
\(776\) | 5.65931e6 | − | 1.20634e7i | 0.337372 | − | 0.719141i | ||||
\(777\) | − | 8.87999e6i | − | 0.527667i | ||||||
\(778\) | 4.49745e6 | + | 1.94413e6i | 0.266390 | + | 0.115153i | ||||
\(779\) | −339479. | − | 339479.i | −0.0200433 | − | 0.0200433i | ||||
\(780\) | −129809. | + | 4.23617e6i | −0.00763958 | + | 0.249308i | ||||
\(781\) | −1.72720e7 | + | 1.72720e7i | −1.01325 | + | 1.01325i | ||||
\(782\) | −1.01727e6 | − | 2.56639e6i | −0.0594864 | − | 0.150074i | ||||
\(783\) | −3.82374e6 | −0.222887 | ||||||||
\(784\) | −326613. | + | 5.32431e6i | −0.0189777 | + | 0.309366i | ||||
\(785\) | 1.42603e7 | 0.825954 | ||||||||
\(786\) | 1.36475e6 | + | 3.44303e6i | 0.0787947 | + | 0.198785i | ||||
\(787\) | 1.80208e7 | − | 1.80208e7i | 1.03714 | − | 1.03714i | 0.0378547 | − | 0.999283i | \(-0.487948\pi\) |
0.999283 | − | 0.0378547i | \(-0.0120524\pi\) | |||||||
\(788\) | 1.01231e7 | + | 310203.i | 0.580761 | + | 0.0177963i | ||||
\(789\) | 4.79252e6 | + | 4.79252e6i | 0.274076 | + | 0.274076i | ||||
\(790\) | −2.17641e7 | − | 9.40805e6i | −1.24072 | − | 0.536330i | ||||
\(791\) | − | 2.61274e7i | − | 1.48476i | ||||||
\(792\) | 4.96560e6 | + | 1.37419e7i | 0.281293 | + | 0.778454i | ||||
\(793\) | − | 609467.i | − | 0.0344166i | ||||||
\(794\) | 405938. | − | 939074.i | 0.0228511 | − | 0.0528626i | ||||
\(795\) | −532143. | − | 532143.i | −0.0298614 | − | 0.0298614i | ||||
\(796\) | −1.23395e7 | − | 1.31196e7i | −0.690261 | − | 0.733902i | ||||
\(797\) | 2.43391e7 | − | 2.43391e7i | 1.35725 | − | 1.35725i | 0.479953 | − | 0.877294i | \(-0.340654\pi\) |
0.877294 | − | 0.479953i | \(-0.159346\pi\) | |||||||
\(798\) | −4.56959e6 | + | 1.81130e6i | −0.254021 | + | 0.100689i | ||||
\(799\) | 3.53798e6 | 0.196060 | ||||||||
\(800\) | −3.27638e7 | + | 1.07165e7i | −1.80996 | + | 0.592009i | ||||
\(801\) | 1.97537e7 | 1.08785 | ||||||||
\(802\) | 2.98233e7 | − | 1.18214e7i | 1.63727 | − | 0.648981i | ||||
\(803\) | 5.00707e6 | − | 5.00707e6i | 0.274028 | − | 0.274028i | ||||
\(804\) | −2.42629e6 | − | 2.57969e6i | −0.132374 | − | 0.140743i | ||||
\(805\) | 1.05318e7 | + | 1.05318e7i | 0.572812 | + | 0.572812i | ||||
\(806\) | 6.96422e6 | − | 1.61106e7i | 0.377602 | − | 0.873525i | ||||
\(807\) | − | 3.69675e6i | − | 0.199819i | ||||||
\(808\) | −1.87946e7 | + | 6.79138e6i | −1.01275 | + | 0.365957i | ||||
\(809\) | 2.45540e7i | 1.31902i | 0.751696 | + | 0.659509i | \(0.229236\pi\) | ||||
−0.751696 | + | 0.659509i | \(0.770764\pi\) | |||||||
\(810\) | −2.21191e7 | − | 9.56151e6i | −1.18455 | − | 0.512052i | ||||
\(811\) | 5.58766e6 | + | 5.58766e6i | 0.298317 | + | 0.298317i | 0.840354 | − | 0.542037i | \(-0.182347\pi\) |
−0.542037 | + | 0.840354i | \(0.682347\pi\) | |||||||
\(812\) | −8.66340e6 | − | 265473.i | −0.461103 | − | 0.0141296i | ||||
\(813\) | −2.61346e6 | + | 2.61346e6i | −0.138672 | + | 0.138672i | ||||
\(814\) | −1.00508e7 | − | 2.53564e7i | −0.531666 | − | 1.34130i | ||||
\(815\) | −516318. | −0.0272285 | ||||||||
\(816\) | −1.41305e6 | − | 1.59774e6i | −0.0742902 | − | 0.0840004i | ||||
\(817\) | −1.68847e7 | −0.884988 | ||||||||
\(818\) | −326438. | − | 823546.i | −0.0170576 | − | 0.0430333i | ||||
\(819\) | −7.22539e6 | + | 7.22539e6i | −0.376401 | + | 0.376401i | ||||
\(820\) | −34425.4 | + | 1.12343e6i | −0.00178790 | + | 0.0583460i | ||||
\(821\) | −2.26326e7 | − | 2.26326e7i | −1.17186 | − | 1.17186i | −0.981766 | − | 0.190094i | \(-0.939121\pi\) |
−0.190094 | − | 0.981766i | \(-0.560879\pi\) | |||||||
\(822\) | 2.42543e6 | + | 1.04845e6i | 0.125202 | + | 0.0541214i | ||||
\(823\) | − | 2.57524e7i | − | 1.32531i | −0.748923 | − | 0.662657i | \(-0.769429\pi\) | ||
0.748923 | − | 0.662657i | \(-0.230571\pi\) | |||||||
\(824\) | 599066. | + | 281041.i | 0.0307366 | + | 0.0144195i | ||||
\(825\) | 9.69697e6i | 0.496022i | ||||||||
\(826\) | −7.65625e6 | + | 1.77115e7i | −0.390450 | + | 0.903247i | ||||
\(827\) | −6.00028e6 | − | 6.00028e6i | −0.305076 | − | 0.305076i | 0.537920 | − | 0.842996i | \(-0.319210\pi\) |
−0.842996 | + | 0.537920i | \(0.819210\pi\) | |||||||
\(828\) | 5.47146e6 | − | 5.14611e6i | 0.277350 | − | 0.260857i | ||||
\(829\) | −2.48171e7 | + | 2.48171e7i | −1.25419 | + | 1.25419i | −0.300368 | + | 0.953823i | \(0.597110\pi\) |
−0.953823 | + | 0.300368i | \(0.902890\pi\) | |||||||
\(830\) | 5.19243e7 | − | 2.05818e7i | 2.61622 | − | 1.03702i | ||||
\(831\) | 1.81724e6 | 0.0912871 | ||||||||
\(832\) | 1.00867e7 | + | 929595.i | 0.505175 | + | 0.0465571i | ||||
\(833\) | 2.41278e6 | 0.120477 | ||||||||
\(834\) | 6.67070e6 | − | 2.64414e6i | 0.332090 | − | 0.131634i | ||||
\(835\) | −6.39508e6 | + | 6.39508e6i | −0.317417 | + | 0.317417i | ||||
\(836\) | −1.09981e7 | + | 1.03441e7i | −0.544256 | + | 0.511892i | ||||
\(837\) | −1.48664e7 | − | 1.48664e7i | −0.733485 | − | 0.733485i | ||||
\(838\) | −1.02479e7 | + | 2.37069e7i | −0.504108 | + | 1.16618i | ||||
\(839\) | − | 7.34159e6i | − | 0.360069i | −0.983660 | − | 0.180034i | \(-0.942379\pi\) | ||
0.983660 | − | 0.180034i | \(-0.0576209\pi\) | |||||||
\(840\) | 1.04182e7 | + | 4.88750e6i | 0.509441 | + | 0.238995i | ||||
\(841\) | 1.71789e7i | 0.837539i | ||||||||
\(842\) | 2.32115e7 | + | 1.00337e7i | 1.12830 | + | 0.487733i | ||||
\(843\) | 4.41644e6 | + | 4.41644e6i | 0.214044 | + | 0.214044i | ||||
\(844\) | 702947. | − | 2.29398e7i | 0.0339677 | − | 1.10849i | ||||
\(845\) | 1.85747e7 | − | 1.85747e7i | 0.894911 | − | 0.894911i | ||||
\(846\) | 3.54717e6 | + | 8.94890e6i | 0.170395 | + | 0.429876i | ||||
\(847\) | −4.41703e6 | −0.211554 | ||||||||
\(848\) | −1.34734e6 | + | 1.19160e6i | −0.0643412 | + | 0.0569035i | ||||
\(849\) | −397410. | −0.0189221 | ||||||||
\(850\) | 5.74549e6 | + | 1.44949e7i | 0.272760 | + | 0.688125i | ||||
\(851\) | −9.91471e6 | + | 9.91471e6i | −0.469306 | + | 0.469306i | ||||
\(852\) | 9.69713e6 | + | 297150.i | 0.457661 | + | 0.0140242i | ||||
\(853\) | −1.13091e7 | − | 1.13091e7i | −0.532175 | − | 0.532175i | 0.389044 | − | 0.921219i | \(-0.372805\pi\) |
−0.921219 | + | 0.389044i | \(0.872805\pi\) | |||||||
\(854\) | −1.51901e6 | − | 656628.i | −0.0712715 | − | 0.0308088i | ||||
\(855\) | − | 2.76369e7i | − | 1.29293i | ||||||
\(856\) | −1.07626e7 | + | 3.88905e6i | −0.502034 | + | 0.181409i | ||||
\(857\) | − | 9.03234e6i | − | 0.420096i | −0.977691 | − | 0.210048i | \(-0.932638\pi\) | ||
0.977691 | − | 0.210048i | \(-0.0673620\pi\) | |||||||
\(858\) | 1.13062e6 | − | 2.61552e6i | 0.0524324 | − | 0.121294i | ||||
\(859\) | −9.00166e6 | − | 9.00166e6i | −0.416236 | − | 0.416236i | 0.467668 | − | 0.883904i | \(-0.345094\pi\) |
−0.883904 | + | 0.467668i | \(0.845094\pi\) | |||||||
\(860\) | 2.70819e7 | + | 2.87941e7i | 1.24863 | + | 1.32757i | ||||
\(861\) | 173961. | − | 173961.i | 0.00799731 | − | 0.00799731i | ||||
\(862\) | −3.27839e7 | + | 1.29949e7i | −1.50277 | + | 0.595669i | ||||
\(863\) | 3.76885e7 | 1.72259 | 0.861296 | − | 0.508104i | \(-0.169654\pi\) | ||||
0.861296 | + | 0.508104i | \(0.169654\pi\) | |||||||
\(864\) | 5.48744e6 | − | 1.08220e7i | 0.250084 | − | 0.493199i | ||||
\(865\) | −3.60508e7 | −1.63823 | ||||||||
\(866\) | −2.18711e7 | + | 8.66929e6i | −0.991006 | + | 0.392816i | ||||
\(867\) | 3.83296e6 | − | 3.83296e6i | 0.173176 | − | 0.173176i | ||||
\(868\) | −3.26503e7 | − | 3.47146e7i | −1.47092 | − | 1.56391i | ||||
\(869\) | 1.12721e7 | + | 1.12721e7i | 0.506357 | + | 0.506357i | ||||
\(870\) | −1.75547e6 | + | 4.06102e6i | −0.0786314 | + | 0.181902i | ||||
\(871\) | − | 7.60716e6i | − | 0.339764i | ||||||
\(872\) | −5.93910e6 | − | 1.64359e7i | −0.264502 | − | 0.731986i | ||||
\(873\) | − | 1.63985e7i | − | 0.728232i | ||||||
\(874\) | 7.12440e6 | + | 3.07969e6i | 0.315478 | + | 0.136373i | ||||
\(875\) | −2.82473e7 | − | 2.82473e7i | −1.24726 | − | 1.24726i | ||||
\(876\) | −2.81115e6 | − | 86142.5i | −0.123773 | − | 0.00379277i | ||||
\(877\) | −7.81571e6 | + | 7.81571e6i | −0.343139 | + | 0.343139i | −0.857546 | − | 0.514407i | \(-0.828012\pi\) |
0.514407 | + | 0.857546i | \(0.328012\pi\) | |||||||
\(878\) | 1.21093e7 | + | 3.05498e7i | 0.530132 | + | 1.33743i | ||||
\(879\) | −1.00695e7 | −0.439580 | ||||||||
\(880\) | 3.52805e7 | + | 2.16424e6i | 1.53578 | + | 0.0942105i | ||||
\(881\) | 3.50352e7 | 1.52077 | 0.760387 | − | 0.649470i | \(-0.225009\pi\) | ||||
0.760387 | + | 0.649470i | \(0.225009\pi\) | |||||||
\(882\) | 2.41905e6 | + | 6.10284e6i | 0.104706 | + | 0.264156i | ||||
\(883\) | 1.00918e6 | − | 1.00918e6i | 0.0435581 | − | 0.0435581i | −0.684992 | − | 0.728550i | \(-0.740194\pi\) |
0.728550 | + | 0.684992i | \(0.240194\pi\) | |||||||
\(884\) | 140331. | − | 4.57954e6i | 0.00603982 | − | 0.197102i | ||||
\(885\) | 6.96441e6 | + | 6.96441e6i | 0.298900 | + | 0.298900i | ||||
\(886\) | 3.60766e7 | + | 1.55950e7i | 1.54398 | + | 0.667423i | ||||
\(887\) | 3.68389e7i | 1.57216i | 0.618122 | + | 0.786082i | \(0.287894\pi\) | ||||
−0.618122 | + | 0.786082i | \(0.712106\pi\) | |||||||
\(888\) | −4.60114e6 | + | 9.80778e6i | −0.195809 | + | 0.417386i | ||||
\(889\) | 1.15089e7i | 0.488406i | ||||||||
\(890\) | 1.89611e7 | − | 4.38636e7i | 0.802396 | − | 1.85622i | ||||
\(891\) | 1.14560e7 | + | 1.14560e7i | 0.483436 | + | 0.483436i | ||||
\(892\) | −2.24512e7 | + | 2.11162e7i | −0.944774 | + | 0.888594i | ||||
\(893\) | −7.03360e6 | + | 7.03360e6i | −0.295154 | + | 0.295154i | ||||
\(894\) | 3.74203e6 | − | 1.48327e6i | 0.156590 | − | 0.0620691i | ||||
\(895\) | 2.06833e7 | 0.863101 | ||||||||
\(896\) | 1.31841e7 | − | 2.41382e7i | 0.548633 | − | 1.00446i | ||||
\(897\) | −1.46480e6 | −0.0607849 | ||||||||
\(898\) | 2.67207e7 | − | 1.05916e7i | 1.10575 | − | 0.438298i | ||||
\(899\) | 1.29555e7 | − | 1.29555e7i | 0.534634 | − | 0.534634i | ||||
\(900\) | −3.09027e7 | + | 2.90651e7i | −1.27172 | + | 1.19609i | ||||
\(901\) | 575276. | + | 575276.i | 0.0236083 | + | 0.0236083i | ||||
\(902\) | 299840. | − | 693634.i | 0.0122708 | − | 0.0283867i | ||||
\(903\) | − | 8.65229e6i | − | 0.353111i | ||||||
\(904\) | −1.35378e7 | + | 2.88572e7i | −0.550971 | + | 1.17445i | ||||
\(905\) | 3.86408e7i | 1.56829i | ||||||||
\(906\) | −6.31591e6 | − | 2.73020e6i | −0.255632 | − | 0.110503i | ||||
\(907\) | −3.03199e7 | − | 3.03199e7i | −1.22380 | − | 1.22380i | −0.966271 | − | 0.257527i | \(-0.917093\pi\) |
−0.257527 | − | 0.966271i | \(-0.582907\pi\) | |||||||
\(908\) | −399469. | + | 1.30362e7i | −0.0160793 | + | 0.524729i | ||||
\(909\) | −1.73903e7 | + | 1.73903e7i | −0.698069 | + | 0.698069i | ||||
\(910\) | 9.10868e6 | + | 2.29796e7i | 0.364629 | + | 0.919897i | ||||
\(911\) | −1.32865e6 | −0.0530413 | −0.0265207 | − | 0.999648i | \(-0.508443\pi\) | ||||
−0.0265207 | + | 0.999648i | \(0.508443\pi\) | |||||||
\(912\) | 5.98554e6 | + | 367176.i | 0.238296 | + | 0.0146180i | ||||
\(913\) | −3.75526e7 | −1.49095 | ||||||||
\(914\) | 346261. | + | 873557.i | 0.0137100 | + | 0.0345880i | ||||
\(915\) | −597294. | + | 597294.i | −0.0235850 | + | 0.0235850i | ||||
\(916\) | −1.33135e7 | − | 407966.i | −0.524267 | − | 0.0160652i | ||||
\(917\) | 1.52746e7 | + | 1.52746e7i | 0.599854 | + | 0.599854i | ||||
\(918\) | −5.03770e6 | − | 2.17767e6i | −0.197299 | − | 0.0852875i | ||||
\(919\) | 1.81854e7i | 0.710286i | 0.934812 | + | 0.355143i | \(0.115568\pi\) | ||||
−0.934812 | + | 0.355143i | \(0.884432\pi\) | |||||||
\(920\) | −6.17513e6 | − | 1.70891e7i | −0.240534 | − | 0.665657i | ||||
\(921\) | 8.37400e6i | 0.325300i | ||||||||
\(922\) | 1.12046e7 | − | 2.59201e7i | 0.434079 | − | 1.00417i | ||||
\(923\) | 1.47359e7 | + | 1.47359e7i | 0.569341 | + | 0.569341i | ||||
\(924\) | −5.30070e6 | − | 5.63583e6i | −0.204246 | − | 0.217159i | ||||
\(925\) | 5.59981e7 | − | 5.59981e7i | 2.15188 | − | 2.15188i | ||||
\(926\) | 1.74329e7 | − | 6.91007e6i | 0.668102 | − | 0.264823i | ||||
\(927\) | 814350. | 0.0311252 | ||||||||
\(928\) | 9.43099e6 | + | 4.78212e6i | 0.359491 | + | 0.182285i | ||||
\(929\) | −2.08621e7 | −0.793085 | −0.396542 | − | 0.918016i | \(-0.629790\pi\) | ||||
−0.396542 | + | 0.918016i | \(0.629790\pi\) | |||||||
\(930\) | −2.26140e7 | + | 8.96374e6i | −0.857372 | + | 0.339846i | ||||
\(931\) | −4.79667e6 | + | 4.79667e6i | −0.181370 | + | 0.181370i | ||||
\(932\) | −2.78533e7 | − | 2.96143e7i | −1.05036 | − | 1.11677i | ||||
\(933\) | −1.79425e6 | − | 1.79425e6i | −0.0674804 | − | 0.0674804i | ||||
\(934\) | −5.81408e6 | + | 1.34500e7i | −0.218079 | + | 0.504492i | ||||
\(935\) | − | 1.59878e7i | − | 0.598081i | ||||||
\(936\) | 1.17241e7 | − | 4.23649e6i | 0.437411 | − | 0.158058i | ||||
\(937\) | 8.88420e6i | 0.330574i | 0.986245 | + | 0.165287i | \(0.0528551\pi\) | ||||
−0.986245 | + | 0.165287i | \(0.947145\pi\) | |||||||
\(938\) | −1.89598e7 | − | 8.19581e6i | −0.703600 | − | 0.304148i | ||||
\(939\) | −6.90586e6 | − | 6.90586e6i | −0.255596 | − | 0.255596i | ||||
\(940\) | 2.32761e7 | + | 713252.i | 0.859192 | + | 0.0263283i | ||||
\(941\) | −1.15274e7 | + | 1.15274e7i | −0.424381 | + | 0.424381i | −0.886709 | − | 0.462328i | \(-0.847014\pi\) |
0.462328 | + | 0.886709i | \(0.347014\pi\) | |||||||
\(942\) | 1.40321e6 | + | 3.54007e6i | 0.0515225 | + | 0.129982i | ||||
\(943\) | −388463. | −0.0142256 | ||||||||
\(944\) | 1.76334e7 | − | 1.55950e7i | 0.644028 | − | 0.569581i | ||||
\(945\) | 2.96100e7 | 1.07860 | ||||||||
\(946\) | −9.79306e6 | − | 2.47062e7i | −0.355787 | − | 0.897590i | ||||
\(947\) | 3.66420e6 | − | 3.66420e6i | 0.132771 | − | 0.132771i | −0.637598 | − | 0.770369i | \(-0.720072\pi\) |
0.770369 | + | 0.637598i | \(0.220072\pi\) | |||||||
\(948\) | 193928. | − | 6.32858e6i | 0.00700840 | − | 0.228710i | ||||
\(949\) | −4.27187e6 | − | 4.27187e6i | −0.153976 | − | 0.153976i | ||||
\(950\) | −4.02384e7 | − | 1.73940e7i | −1.44655 | − | 0.625305i | ||||
\(951\) | − | 1.69341e6i | − | 0.0607172i | ||||||
\(952\) | −1.12626e7 | − | 5.28366e6i | −0.402762 | − | 0.188948i | ||||
\(953\) | 2.62115e7i | 0.934887i | 0.884023 | + | 0.467444i | \(0.154825\pi\) | ||||
−0.884023 | + | 0.467444i | \(0.845175\pi\) | |||||||
\(954\) | −878323. | + | 2.03187e6i | −0.0312452 | + | 0.0722810i | ||||
\(955\) | 1.79504e7 | + | 1.79504e7i | 0.636892 | + | 0.636892i | ||||
\(956\) | −2.56282e7 | + | 2.41043e7i | −0.906930 | + | 0.853001i | ||||
\(957\) | 2.10330e6 | − | 2.10330e6i | 0.0742371 | − | 0.0742371i | ||||
\(958\) | −1.05552e7 | + | 4.18389e6i | −0.371582 | + | 0.147288i | ||||
\(959\) | 1.54114e7 | 0.541124 | ||||||||
\(960\) | −8.97424e6 | − | 1.07963e7i | −0.314282 | − | 0.378091i | ||||
\(961\) | 7.21107e7 | 2.51879 | ||||||||
\(962\) | −2.16332e7 | + | 8.57499e6i | −0.753674 | + | 0.298742i | ||||
\(963\) | −9.95849e6 | + | 9.95849e6i | −0.346041 | + | 0.346041i | ||||
\(964\) | 3.06174e7 | − | 2.87967e7i | 1.06115 | − | 0.998046i | ||||
\(965\) | −6.42557e7 | − | 6.42557e7i | −2.22123 | − | 2.22123i | ||||
\(966\) | −1.57814e6 | + | 3.65079e6i | −0.0544131 | + | 0.125876i | ||||
\(967\) | 5.78618e6i | 0.198988i | 0.995038 | + | 0.0994938i | \(0.0317223\pi\) | ||||
−0.995038 | + | 0.0994938i | \(0.968278\pi\) | |||||||
\(968\) | 4.87852e6 | + | 2.28867e6i | 0.167340 | + | 0.0785044i | ||||
\(969\) | − | 2.71242e6i | − | 0.0927999i | ||||||
\(970\) | −3.64134e7 | − | 1.57406e7i | −1.24260 | − | 0.537144i | ||||
\(971\) | 1.05214e7 | + | 1.05214e7i | 0.358116 | + | 0.358116i | 0.863118 | − | 0.505002i | \(-0.168508\pi\) |
−0.505002 | + | 0.863118i | \(0.668508\pi\) | |||||||
\(972\) | 695980. | − | 2.27125e7i | 0.0236282 | − | 0.771078i | ||||
\(973\) | 2.95937e7 | − | 2.95937e7i | 1.00211 | − | 1.00211i | ||||
\(974\) | −5.02783e6 | − | 1.26843e7i | −0.169818 | − | 0.428421i | ||||
\(975\) | 8.27313e6 | 0.278714 | ||||||||
\(976\) | 1.33749e6 | + | 1.51230e6i | 0.0449433 | + | 0.0508176i | ||||
\(977\) | −1.96506e7 | −0.658626 | −0.329313 | − | 0.944221i | \(-0.606817\pi\) | ||||
−0.329313 | + | 0.944221i | \(0.606817\pi\) | |||||||
\(978\) | −50805.6 | − | 128174.i | −0.00169849 | − | 0.00428501i | ||||
\(979\) | −2.27180e7 | + | 2.27180e7i | −0.757554 | + | 0.757554i | ||||
\(980\) | 1.58735e7 | + | 486413.i | 0.527967 | + | 0.0161786i | ||||
\(981\) | −1.52079e7 | − | 1.52079e7i | −0.504542 | − | 0.504542i | ||||
\(982\) | −3.75137e7 | − | 1.62162e7i | −1.24140 | − | 0.536624i | ||||
\(983\) | 8.36026e6i | 0.275954i | 0.990435 | + | 0.137977i | \(0.0440600\pi\) | ||||
−0.990435 | + | 0.137977i | \(0.955940\pi\) | |||||||
\(984\) | −282274. | + | 101999.i | −0.00929358 | + | 0.00335822i | ||||
\(985\) | − | 3.01519e7i | − | 0.990202i | ||||||
\(986\) | 1.89777e6 | − | 4.39019e6i | 0.0621656 | − | 0.143811i | ||||
\(987\) | −3.60426e6 | − | 3.60426e6i | −0.117767 | − | 0.117767i | ||||
\(988\) | 8.82527e6 | + | 9.38324e6i | 0.287631 | + | 0.305816i | ||||
\(989\) | −9.66048e6 | + | 9.66048e6i | −0.314057 | + | 0.314057i | ||||
\(990\) | 4.04393e7 | − | 1.60294e7i | 1.31134 | − | 0.519790i | ||||
\(991\) | 2.37286e7 | 0.767515 | 0.383758 | − | 0.923434i | \(-0.374630\pi\) | ||||
0.383758 | + | 0.923434i | \(0.374630\pi\) | |||||||
\(992\) | 1.80744e7 | + | 5.52593e7i | 0.583156 | + | 1.78290i | ||||
\(993\) | −6.68944e6 | −0.215286 | ||||||||
\(994\) | 5.26032e7 | − | 2.08509e7i | 1.68868 | − | 0.669359i | ||||
\(995\) | −3.79152e7 | + | 3.79152e7i | −1.21410 | + | 1.21410i | ||||
\(996\) | 1.02187e7 | + | 1.08647e7i | 0.326397 | + | 0.347033i | ||||
\(997\) | 3.90437e7 | + | 3.90437e7i | 1.24398 | + | 1.24398i | 0.958336 | + | 0.285644i | \(0.0922074\pi\) |
0.285644 | + | 0.958336i | \(0.407793\pi\) | |||||||
\(998\) | −2.37187e7 | + | 5.48696e7i | −0.753816 | + | 1.74384i | ||||
\(999\) | 2.78751e7i | 0.883697i |
(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 | 16.6.e.a.5.1 | ✓ | 18 | |
3.2 | odd | 2 | 144.6.k.a.37.9 | 18 | |||
4.3 | odd | 2 | 64.6.e.a.49.5 | 18 | |||
8.3 | odd | 2 | 128.6.e.a.97.5 | 18 | |||
8.5 | even | 2 | 128.6.e.b.97.5 | 18 | |||
12.11 | even | 2 | 576.6.k.a.433.9 | 18 | |||
16.3 | odd | 4 | 64.6.e.a.17.5 | 18 | |||
16.5 | even | 4 | 128.6.e.b.33.5 | 18 | |||
16.11 | odd | 4 | 128.6.e.a.33.5 | 18 | |||
16.13 | even | 4 | inner | 16.6.e.a.13.1 | yes | 18 | |
32.3 | odd | 8 | 1024.6.a.l.1.10 | 18 | |||
32.13 | even | 8 | 1024.6.a.k.1.10 | 18 | |||
32.19 | odd | 8 | 1024.6.a.l.1.9 | 18 | |||
32.29 | even | 8 | 1024.6.a.k.1.9 | 18 | |||
48.29 | odd | 4 | 144.6.k.a.109.9 | 18 | |||
48.35 | even | 4 | 576.6.k.a.145.9 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.6.e.a.5.1 | ✓ | 18 | 1.1 | even | 1 | trivial | |
16.6.e.a.13.1 | yes | 18 | 16.13 | even | 4 | inner | |
64.6.e.a.17.5 | 18 | 16.3 | odd | 4 | |||
64.6.e.a.49.5 | 18 | 4.3 | odd | 2 | |||
128.6.e.a.33.5 | 18 | 16.11 | odd | 4 | |||
128.6.e.a.97.5 | 18 | 8.3 | odd | 2 | |||
128.6.e.b.33.5 | 18 | 16.5 | even | 4 | |||
128.6.e.b.97.5 | 18 | 8.5 | even | 2 | |||
144.6.k.a.37.9 | 18 | 3.2 | odd | 2 | |||
144.6.k.a.109.9 | 18 | 48.29 | odd | 4 | |||
576.6.k.a.145.9 | 18 | 48.35 | even | 4 | |||
576.6.k.a.433.9 | 18 | 12.11 | even | 2 | |||
1024.6.a.k.1.9 | 18 | 32.29 | even | 8 | |||
1024.6.a.k.1.10 | 18 | 32.13 | even | 8 | |||
1024.6.a.l.1.9 | 18 | 32.19 | odd | 8 | |||
1024.6.a.l.1.10 | 18 | 32.3 | odd | 8 |