Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,7,Mod(19,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.19");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.8032450172\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.1 | ||
Character | \(\chi\) | \(=\) | 60.19 |
Dual form | 60.7.f.a.19.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.93273 | − | 1.03526i | −0.991592 | − | 0.129407i | ||||
\(3\) | 15.5885 | 0.577350 | ||||||||
\(4\) | 61.8565 | + | 16.4248i | 0.966508 | + | 0.256638i | ||||
\(5\) | −80.2400 | + | 95.8465i | −0.641920 | + | 0.766772i | ||||
\(6\) | −123.659 | − | 16.1381i | −0.572496 | − | 0.0747132i | ||||
\(7\) | −143.606 | −0.418676 | −0.209338 | − | 0.977843i | \(-0.567131\pi\) | ||||
−0.209338 | + | 0.977843i | \(0.567131\pi\) | |||||||
\(8\) | −473.687 | − | 194.331i | −0.925170 | − | 0.379553i | ||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | 735.748 | − | 677.255i | 0.735748 | − | 0.677255i | ||||
\(11\) | − | 1568.78i | − | 1.17865i | −0.807897 | − | 0.589324i | \(-0.799394\pi\) | ||
0.807897 | − | 0.589324i | \(-0.200606\pi\) | |||||||
\(12\) | 964.247 | + | 256.038i | 0.558013 | + | 0.148170i | ||||
\(13\) | 3878.76i | 1.76548i | 0.469860 | + | 0.882741i | \(0.344305\pi\) | ||||
−0.469860 | + | 0.882741i | \(0.655695\pi\) | |||||||
\(14\) | 1139.19 | + | 148.669i | 0.415155 | + | 0.0541796i | ||||
\(15\) | −1250.82 | + | 1494.10i | −0.370613 | + | 0.442696i | ||||
\(16\) | 3556.45 | + | 2031.96i | 0.868274 | + | 0.496085i | ||||
\(17\) | − | 5035.60i | − | 1.02495i | −0.858701 | − | 0.512477i | \(-0.828728\pi\) | ||
0.858701 | − | 0.512477i | \(-0.171272\pi\) | |||||||
\(18\) | −1927.65 | − | 251.567i | −0.330531 | − | 0.0431357i | ||||
\(19\) | − | 11740.4i | − | 1.71167i | −0.517247 | − | 0.855836i | \(-0.673043\pi\) | ||
0.517247 | − | 0.855836i | \(-0.326957\pi\) | |||||||
\(20\) | −6537.63 | + | 4610.80i | −0.817203 | + | 0.576350i | ||||
\(21\) | −2238.59 | −0.241723 | ||||||||
\(22\) | −1624.09 | + | 12444.7i | −0.152525 | + | 1.16874i | ||||
\(23\) | −21747.5 | −1.78741 | −0.893706 | − | 0.448652i | \(-0.851904\pi\) | ||||
−0.893706 | + | 0.448652i | \(0.851904\pi\) | |||||||
\(24\) | −7384.05 | − | 3029.32i | −0.534147 | − | 0.219135i | ||||
\(25\) | −2748.09 | − | 15381.4i | −0.175878 | − | 0.984412i | ||||
\(26\) | 4015.52 | − | 30769.2i | 0.228466 | − | 1.75064i | ||||
\(27\) | 3788.00 | 0.192450 | ||||||||
\(28\) | −8882.95 | − | 2358.70i | −0.404653 | − | 0.107448i | ||||
\(29\) | −40105.7 | −1.64442 | −0.822208 | − | 0.569187i | \(-0.807258\pi\) | ||||
−0.822208 | + | 0.569187i | \(0.807258\pi\) | |||||||
\(30\) | 11469.2 | − | 10557.4i | 0.424784 | − | 0.391014i | ||||
\(31\) | 223.114i | 0.00748930i | 0.999993 | + | 0.00374465i | \(0.00119196\pi\) | ||||
−0.999993 | + | 0.00374465i | \(0.998808\pi\) | |||||||
\(32\) | −26108.8 | − | 19800.9i | −0.796776 | − | 0.604275i | ||||
\(33\) | − | 24454.9i | − | 0.680492i | ||||||
\(34\) | −5213.14 | + | 39946.1i | −0.132636 | + | 1.01634i | ||||
\(35\) | 11522.9 | − | 13764.1i | 0.268756 | − | 0.321029i | ||||
\(36\) | 15031.1 | + | 3991.23i | 0.322169 | + | 0.0855460i | ||||
\(37\) | − | 17396.7i | − | 0.343448i | −0.985145 | − | 0.171724i | \(-0.945066\pi\) | ||
0.985145 | − | 0.171724i | \(-0.0549337\pi\) | |||||||
\(38\) | −12154.3 | + | 93133.1i | −0.221503 | + | 1.69728i | ||||
\(39\) | 60464.0i | 1.01930i | ||||||||
\(40\) | 56634.6 | − | 29808.1i | 0.884915 | − | 0.465752i | ||||
\(41\) | 2197.54 | 0.0318849 | 0.0159425 | − | 0.999873i | \(-0.494925\pi\) | ||||
0.0159425 | + | 0.999873i | \(0.494925\pi\) | |||||||
\(42\) | 17758.2 | + | 2317.52i | 0.239690 | + | 0.0312806i | ||||
\(43\) | −3196.47 | −0.0402036 | −0.0201018 | − | 0.999798i | \(-0.506399\pi\) | ||||
−0.0201018 | + | 0.999798i | \(0.506399\pi\) | |||||||
\(44\) | 25766.9 | − | 97039.2i | 0.302486 | − | 1.13917i | ||||
\(45\) | −19498.3 | + | 23290.7i | −0.213973 | + | 0.255591i | ||||
\(46\) | 172517. | + | 22514.2i | 1.77238 | + | 0.231304i | ||||
\(47\) | 10495.8 | 0.101093 | 0.0505467 | − | 0.998722i | \(-0.483904\pi\) | ||||
0.0505467 | + | 0.998722i | \(0.483904\pi\) | |||||||
\(48\) | 55439.6 | + | 31675.2i | 0.501298 | + | 0.286415i | ||||
\(49\) | −97026.4 | −0.824711 | ||||||||
\(50\) | 5876.12 | + | 124862.i | 0.0470090 | + | 0.998894i | ||||
\(51\) | − | 78497.3i | − | 0.591758i | ||||||
\(52\) | −63708.0 | + | 239927.i | −0.453090 | + | 1.70635i | ||||
\(53\) | − | 199848.i | − | 1.34237i | −0.741289 | − | 0.671186i | \(-0.765785\pi\) | ||
0.741289 | − | 0.671186i | \(-0.234215\pi\) | |||||||
\(54\) | −30049.2 | − | 3921.55i | −0.190832 | − | 0.0249044i | ||||
\(55\) | 150362. | + | 125879.i | 0.903753 | + | 0.756597i | ||||
\(56\) | 68024.2 | + | 27907.1i | 0.387346 | + | 0.158910i | ||||
\(57\) | − | 183014.i | − | 0.988235i | ||||||
\(58\) | 318148. | + | 41519.7i | 1.63059 | + | 0.212799i | ||||
\(59\) | 149784.i | 0.729304i | 0.931144 | + | 0.364652i | \(0.118812\pi\) | ||||
−0.931144 | + | 0.364652i | \(0.881188\pi\) | |||||||
\(60\) | −101911. | + | 71875.2i | −0.471812 | + | 0.332756i | ||||
\(61\) | 226558. | 0.998137 | 0.499068 | − | 0.866563i | \(-0.333676\pi\) | ||||
0.499068 | + | 0.866563i | \(0.333676\pi\) | |||||||
\(62\) | 230.980 | − | 1769.90i | 0.000969168 | − | 0.00742632i | ||||
\(63\) | −34896.2 | −0.139559 | ||||||||
\(64\) | 186615. | + | 184104.i | 0.711879 | + | 0.702302i | ||||
\(65\) | −371766. | − | 311232.i | −1.35372 | − | 1.13330i | ||||
\(66\) | −25317.0 | + | 193994.i | −0.0880605 | + | 0.674770i | ||||
\(67\) | −235597. | −0.783330 | −0.391665 | − | 0.920108i | \(-0.628101\pi\) | ||||
−0.391665 | + | 0.920108i | \(0.628101\pi\) | |||||||
\(68\) | 82708.9 | − | 311485.i | 0.263042 | − | 0.990626i | ||||
\(69\) | −339009. | −1.03196 | ||||||||
\(70\) | −105658. | + | 97257.8i | −0.308040 | + | 0.283550i | ||||
\(71\) | 170700.i | 0.476934i | 0.971151 | + | 0.238467i | \(0.0766448\pi\) | ||||
−0.971151 | + | 0.238467i | \(0.923355\pi\) | |||||||
\(72\) | −115106. | − | 47222.5i | −0.308390 | − | 0.126518i | ||||
\(73\) | 245829.i | 0.631923i | 0.948772 | + | 0.315962i | \(0.102327\pi\) | ||||
−0.948772 | + | 0.315962i | \(0.897673\pi\) | |||||||
\(74\) | −18010.0 | + | 138003.i | −0.0444446 | + | 0.340560i | ||||
\(75\) | −42838.5 | − | 239773.i | −0.101543 | − | 0.568351i | ||||
\(76\) | 192833. | − | 726217.i | 0.439280 | − | 1.65434i | ||||
\(77\) | 225286.i | 0.493471i | ||||||||
\(78\) | 62595.7 | − | 479644.i | 0.131905 | − | 1.01073i | ||||
\(79\) | − | 373075.i | − | 0.756684i | −0.925666 | − | 0.378342i | \(-0.876494\pi\) | ||
0.925666 | − | 0.378342i | \(-0.123506\pi\) | |||||||
\(80\) | −480126. | + | 177828.i | −0.937746 | + | 0.347321i | ||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | −17432.5 | − | 2275.02i | −0.0316168 | − | 0.00412614i | ||||
\(83\) | 380458. | 0.665384 | 0.332692 | − | 0.943036i | \(-0.392043\pi\) | ||||
0.332692 | + | 0.943036i | \(0.392043\pi\) | |||||||
\(84\) | −138471. | − | 36768.5i | −0.233627 | − | 0.0620352i | ||||
\(85\) | 482645. | + | 404057.i | 0.785906 | + | 0.657939i | ||||
\(86\) | 25356.8 | + | 3309.17i | 0.0398656 | + | 0.00520264i | ||||
\(87\) | −625186. | −0.949404 | ||||||||
\(88\) | −304863. | + | 743111.i | −0.447359 | + | 1.09045i | ||||
\(89\) | 421299. | 0.597614 | 0.298807 | − | 0.954314i | \(-0.403411\pi\) | ||||
0.298807 | + | 0.954314i | \(0.403411\pi\) | |||||||
\(90\) | 178787. | − | 164573.i | 0.245249 | − | 0.225752i | ||||
\(91\) | − | 557013.i | − | 0.739165i | ||||||
\(92\) | −1.34522e6 | − | 357198.i | −1.72755 | − | 0.458718i | ||||
\(93\) | 3478.00i | 0.00432395i | ||||||||
\(94\) | −83260.6 | − | 10865.9i | −0.100243 | − | 0.0130822i | ||||
\(95\) | 1.12527e6 | + | 942046.i | 1.31246 | + | 1.09876i | ||||
\(96\) | −406995. | − | 308665.i | −0.460019 | − | 0.348878i | ||||
\(97\) | 855309.i | 0.937147i | 0.883425 | + | 0.468573i | \(0.155232\pi\) | ||||
−0.883425 | + | 0.468573i | \(0.844768\pi\) | |||||||
\(98\) | 769684. | + | 100447.i | 0.817776 | + | 0.106723i | ||||
\(99\) | − | 381213.i | − | 0.392882i | ||||||
\(100\) | 82650.3 | − | 996579.i | 0.0826503 | − | 0.996579i | ||||
\(101\) | 514825. | 0.499684 | 0.249842 | − | 0.968287i | \(-0.419621\pi\) | ||||
0.249842 | + | 0.968287i | \(0.419621\pi\) | |||||||
\(102\) | −81264.8 | + | 622698.i | −0.0765776 | + | 0.586782i | ||||
\(103\) | −1.35064e6 | −1.23603 | −0.618015 | − | 0.786166i | \(-0.712063\pi\) | ||||
−0.618015 | + | 0.786166i | \(0.712063\pi\) | |||||||
\(104\) | 753765. | − | 1.83732e6i | 0.670094 | − | 1.63337i | ||||
\(105\) | 179625. | − | 214561.i | 0.155166 | − | 0.185346i | ||||
\(106\) | −206894. | + | 1.58534e6i | −0.173712 | + | 1.33108i | ||||
\(107\) | −717435. | −0.585641 | −0.292820 | − | 0.956167i | \(-0.594594\pi\) | ||||
−0.292820 | + | 0.956167i | \(0.594594\pi\) | |||||||
\(108\) | 234312. | + | 62217.2i | 0.186004 | + | 0.0493900i | ||||
\(109\) | 339995. | 0.262538 | 0.131269 | − | 0.991347i | \(-0.458095\pi\) | ||||
0.131269 | + | 0.991347i | \(0.458095\pi\) | |||||||
\(110\) | −1.06246e6 | − | 1.15423e6i | −0.798245 | − | 0.867187i | ||||
\(111\) | − | 271187.i | − | 0.198290i | ||||||
\(112\) | −510727. | − | 291802.i | −0.363525 | − | 0.207699i | ||||
\(113\) | 465203.i | 0.322409i | 0.986921 | + | 0.161205i | \(0.0515379\pi\) | ||||
−0.986921 | + | 0.161205i | \(0.948462\pi\) | |||||||
\(114\) | −189467. | + | 1.45180e6i | −0.127885 | + | 0.979925i | ||||
\(115\) | 1.74502e6 | − | 2.08442e6i | 1.14738 | − | 1.37054i | ||||
\(116\) | −2.48080e6 | − | 658729.i | −1.58934 | − | 0.422020i | ||||
\(117\) | 942540.i | 0.588494i | ||||||||
\(118\) | 155065. | − | 1.18819e6i | 0.0943771 | − | 0.723171i | ||||
\(119\) | 723141.i | 0.429124i | ||||||||
\(120\) | 882846. | − | 464662.i | 0.510906 | − | 0.268902i | ||||
\(121\) | −689508. | −0.389209 | ||||||||
\(122\) | −1.79722e6 | − | 234546.i | −0.989744 | − | 0.129166i | ||||
\(123\) | 34256.3 | 0.0184088 | ||||||||
\(124\) | −3664.60 | + | 13801.0i | −0.00192204 | + | 0.00723846i | ||||
\(125\) | 1.69476e6 | + | 970812.i | 0.867719 | + | 0.497056i | ||||
\(126\) | 276822. | + | 36126.5i | 0.138385 | + | 0.0180599i | ||||
\(127\) | −1.03009e6 | −0.502878 | −0.251439 | − | 0.967873i | \(-0.580904\pi\) | ||||
−0.251439 | + | 0.967873i | \(0.580904\pi\) | |||||||
\(128\) | −1.28977e6 | − | 1.65364e6i | −0.615010 | − | 0.788519i | ||||
\(129\) | −49828.1 | −0.0232116 | ||||||||
\(130\) | 2.62691e6 | + | 2.85379e6i | 1.19568 | + | 1.29895i | ||||
\(131\) | 2.41236e6i | 1.07307i | 0.843878 | + | 0.536536i | \(0.180267\pi\) | ||||
−0.843878 | + | 0.536536i | \(0.819733\pi\) | |||||||
\(132\) | 401667. | − | 1.51269e6i | 0.174640 | − | 0.657701i | ||||
\(133\) | 1.68598e6i | 0.716636i | ||||||||
\(134\) | 1.86892e6 | + | 243903.i | 0.776743 | + | 0.101368i | ||||
\(135\) | −303949. | + | 363066.i | −0.123538 | + | 0.147565i | ||||
\(136\) | −978574. | + | 2.38530e6i | −0.389024 | + | 0.948257i | ||||
\(137\) | 527604.i | 0.205185i | 0.994723 | + | 0.102593i | \(0.0327138\pi\) | ||||
−0.994723 | + | 0.102593i | \(0.967286\pi\) | |||||||
\(138\) | 2.68927e6 | + | 350962.i | 1.02329 | + | 0.133543i | ||||
\(139\) | 2.19739e6i | 0.818204i | 0.912489 | + | 0.409102i | \(0.134158\pi\) | ||||
−0.912489 | + | 0.409102i | \(0.865842\pi\) | |||||||
\(140\) | 938841. | − | 662137.i | 0.342143 | − | 0.241304i | ||||
\(141\) | 163614. | 0.0583663 | ||||||||
\(142\) | 176718. | − | 1.35412e6i | 0.0617186 | − | 0.472924i | ||||
\(143\) | 6.08493e6 | 2.08088 | ||||||||
\(144\) | 864217. | + | 493767.i | 0.289425 | + | 0.165362i | ||||
\(145\) | 3.21808e6 | − | 3.84399e6i | 1.05558 | − | 1.26089i | ||||
\(146\) | 254496. | − | 1.95009e6i | 0.0817753 | − | 0.626610i | ||||
\(147\) | −1.51249e6 | −0.476147 | ||||||||
\(148\) | 285737. | − | 1.07610e6i | 0.0881417 | − | 0.331945i | ||||
\(149\) | −3.55467e6 | −1.07458 | −0.537292 | − | 0.843396i | \(-0.680553\pi\) | ||||
−0.537292 | + | 0.843396i | \(0.680553\pi\) | |||||||
\(150\) | 91599.7 | + | 1.94640e6i | 0.0271406 | + | 0.576712i | ||||
\(151\) | 28179.2i | 0.00818459i | 0.999992 | + | 0.00409230i | \(0.00130262\pi\) | ||||
−0.999992 | + | 0.00409230i | \(0.998697\pi\) | |||||||
\(152\) | −2.28152e6 | + | 5.56126e6i | −0.649670 | + | 1.58359i | ||||
\(153\) | − | 1.22365e6i | − | 0.341652i | ||||||
\(154\) | 233229. | − | 1.78713e6i | 0.0638586 | − | 0.489322i | ||||
\(155\) | −21384.7 | − | 17902.6i | −0.00574258 | − | 0.00480753i | ||||
\(156\) | −993110. | + | 3.74009e6i | −0.261591 | + | 0.985163i | ||||
\(157\) | − | 2.51703e6i | − | 0.650413i | −0.945643 | − | 0.325207i | \(-0.894566\pi\) | ||
0.945643 | − | 0.325207i | \(-0.105434\pi\) | |||||||
\(158\) | −386228. | + | 2.95950e6i | −0.0979203 | + | 0.750322i | ||||
\(159\) | − | 3.11533e6i | − | 0.775019i | ||||||
\(160\) | 3.99281e6 | − | 913611.i | 0.974807 | − | 0.223050i | ||||
\(161\) | 3.12306e6 | 0.748346 | ||||||||
\(162\) | −468420. | − | 61130.9i | −0.110177 | − | 0.0143786i | ||||
\(163\) | −2.44319e6 | −0.564150 | −0.282075 | − | 0.959392i | \(-0.591023\pi\) | ||||
−0.282075 | + | 0.959392i | \(0.591023\pi\) | |||||||
\(164\) | 135932. | + | 36094.2i | 0.0308170 | + | 0.00818288i | ||||
\(165\) | 2.34391e6 | + | 1.96226e6i | 0.521782 | + | 0.436822i | ||||
\(166\) | −3.01807e6 | − | 393871.i | −0.659789 | − | 0.0861054i | ||||
\(167\) | −595753. | −0.127914 | −0.0639569 | − | 0.997953i | \(-0.520372\pi\) | ||||
−0.0639569 | + | 0.997953i | \(0.520372\pi\) | |||||||
\(168\) | 1.06039e6 | + | 435028.i | 0.223634 | + | 0.0917465i | ||||
\(169\) | −1.02180e7 | −2.11693 | ||||||||
\(170\) | −3.41039e6 | − | 3.70493e6i | −0.694156 | − | 0.754108i | ||||
\(171\) | − | 2.85291e6i | − | 0.570557i | ||||||
\(172\) | −197722. | − | 52501.5i | −0.0388571 | − | 0.0103178i | ||||
\(173\) | − | 3.88556e6i | − | 0.750440i | −0.926936 | − | 0.375220i | \(-0.877567\pi\) | ||
0.926936 | − | 0.375220i | \(-0.122433\pi\) | |||||||
\(174\) | 4.95943e6 | + | 647228.i | 0.941421 | + | 0.122860i | ||||
\(175\) | 394641. | + | 2.20886e6i | 0.0736357 | + | 0.412149i | ||||
\(176\) | 3.18770e6 | − | 5.57929e6i | 0.584709 | − | 1.02339i | ||||
\(177\) | 2.33490e6i | 0.421064i | ||||||||
\(178\) | −3.34205e6 | − | 436153.i | −0.592589 | − | 0.0773354i | ||||
\(179\) | 4.77301e6i | 0.832211i | 0.909316 | + | 0.416106i | \(0.136605\pi\) | ||||
−0.909316 | + | 0.416106i | \(0.863395\pi\) | |||||||
\(180\) | −1.58864e6 | + | 1.12042e6i | −0.272401 | + | 0.192117i | ||||
\(181\) | −5.55733e6 | −0.937196 | −0.468598 | − | 0.883412i | \(-0.655241\pi\) | ||||
−0.468598 | + | 0.883412i | \(0.655241\pi\) | |||||||
\(182\) | −576651. | + | 4.41863e6i | −0.0956531 | + | 0.732949i | ||||
\(183\) | 3.53169e6 | 0.576275 | ||||||||
\(184\) | 1.03015e7 | + | 4.22621e6i | 1.65366 | + | 0.678418i | ||||
\(185\) | 1.66741e6 | + | 1.39591e6i | 0.263346 | + | 0.220466i | ||||
\(186\) | 3600.62 | − | 27590.0i | 0.000559549 | − | 0.00428759i | ||||
\(187\) | −7.89975e6 | −1.20806 | ||||||||
\(188\) | 649235. | + | 172392.i | 0.0977076 | + | 0.0259444i | ||||
\(189\) | −543978. | −0.0805742 | ||||||||
\(190\) | −7.95122e6 | − | 8.63795e6i | −1.15924 | − | 1.25936i | ||||
\(191\) | 2.75996e6i | 0.396098i | 0.980192 | + | 0.198049i | \(0.0634605\pi\) | ||||
−0.980192 | + | 0.198049i | \(0.936540\pi\) | |||||||
\(192\) | 2.90904e6 | + | 2.86990e6i | 0.411004 | + | 0.405474i | ||||
\(193\) | − | 1.01132e7i | − | 1.40675i | −0.710820 | − | 0.703374i | \(-0.751676\pi\) | ||
0.710820 | − | 0.703374i | \(-0.248324\pi\) | |||||||
\(194\) | 885464. | − | 6.78493e6i | 0.121273 | − | 0.929267i | ||||
\(195\) | −5.79526e6 | − | 4.85163e6i | −0.781572 | − | 0.654310i | ||||
\(196\) | −6.00171e6 | − | 1.59364e6i | −0.797089 | − | 0.211652i | ||||
\(197\) | − | 5.31570e6i | − | 0.695284i | −0.937627 | − | 0.347642i | \(-0.886983\pi\) | ||
0.937627 | − | 0.347642i | \(-0.113017\pi\) | |||||||
\(198\) | −394654. | + | 3.02406e6i | −0.0508418 | + | 0.389579i | ||||
\(199\) | − | 1.03986e7i | − | 1.31952i | −0.751477 | − | 0.659759i | \(-0.770658\pi\) | ||
0.751477 | − | 0.659759i | \(-0.229342\pi\) | |||||||
\(200\) | −1.68736e6 | + | 7.82003e6i | −0.210920 | + | 0.977503i | ||||
\(201\) | −3.67259e6 | −0.452256 | ||||||||
\(202\) | −4.08397e6 | − | 532976.i | −0.495483 | − | 0.0646627i | ||||
\(203\) | 5.75941e6 | 0.688477 | ||||||||
\(204\) | 1.28930e6 | − | 4.85556e6i | 0.151867 | − | 0.571938i | ||||
\(205\) | −176331. | + | 210627.i | −0.0204676 | + | 0.0244485i | ||||
\(206\) | 1.07143e7 | + | 1.39826e6i | 1.22564 | + | 0.159951i | ||||
\(207\) | −5.28463e6 | −0.595804 | ||||||||
\(208\) | −7.88151e6 | + | 1.37946e7i | −0.875829 | + | 1.53292i | ||||
\(209\) | −1.84180e7 | −2.01746 | ||||||||
\(210\) | −1.64704e6 | + | 1.51610e6i | −0.177847 | + | 0.163708i | ||||
\(211\) | − | 5.65069e6i | − | 0.601525i | −0.953699 | − | 0.300763i | \(-0.902759\pi\) | ||
0.953699 | − | 0.300763i | \(-0.0972412\pi\) | |||||||
\(212\) | 3.28247e6 | − | 1.23619e7i | 0.344504 | − | 1.29741i | ||||
\(213\) | 2.66095e6i | 0.275358i | ||||||||
\(214\) | 5.69122e6 | + | 742729.i | 0.580716 | + | 0.0757860i | ||||
\(215\) | 256485. | − | 306370.i | 0.0258075 | − | 0.0308270i | ||||
\(216\) | −1.79432e6 | − | 736125.i | −0.178049 | − | 0.0730450i | ||||
\(217\) | − | 32040.4i | − | 0.00313559i | ||||||
\(218\) | −2.69709e6 | − | 351982.i | −0.260331 | − | 0.0339743i | ||||
\(219\) | 3.83209e6i | 0.364841i | ||||||||
\(220\) | 7.23332e6 | + | 1.02561e7i | 0.679313 | + | 0.963194i | ||||
\(221\) | 1.95319e7 | 1.80954 | ||||||||
\(222\) | −280748. | + | 2.15125e6i | −0.0256601 | + | 0.196622i | ||||
\(223\) | −1.20891e7 | −1.09013 | −0.545065 | − | 0.838394i | \(-0.683495\pi\) | ||||
−0.545065 | + | 0.838394i | \(0.683495\pi\) | |||||||
\(224\) | 3.74937e6 | + | 2.84352e6i | 0.333591 | + | 0.252995i | ||||
\(225\) | −667786. | − | 3.73769e6i | −0.0586259 | − | 0.328137i | ||||
\(226\) | 481604. | − | 3.69033e6i | 0.0417220 | − | 0.319698i | ||||
\(227\) | 5.54653e6 | 0.474181 | 0.237090 | − | 0.971488i | \(-0.423806\pi\) | ||||
0.237090 | + | 0.971488i | \(0.423806\pi\) | |||||||
\(228\) | 3.00598e6 | − | 1.13206e7i | 0.253618 | − | 0.955136i | ||||
\(229\) | −5.82739e6 | −0.485252 | −0.242626 | − | 0.970120i | \(-0.578009\pi\) | ||||
−0.242626 | + | 0.970120i | \(0.578009\pi\) | |||||||
\(230\) | −1.60006e7 | + | 1.47286e7i | −1.31509 | + | 1.21053i | ||||
\(231\) | 3.51186e6i | 0.284906i | ||||||||
\(232\) | 1.89975e7 | + | 7.79378e6i | 1.52136 | + | 0.624143i | ||||
\(233\) | 6.44278e6i | 0.509338i | 0.967028 | + | 0.254669i | \(0.0819664\pi\) | ||||
−0.967028 | + | 0.254669i | \(0.918034\pi\) | |||||||
\(234\) | 975771. | − | 7.47692e6i | 0.0761553 | − | 0.583546i | ||||
\(235\) | −842185. | + | 1.00599e6i | −0.0648939 | + | 0.0775156i | ||||
\(236\) | −2.46017e6 | + | 9.26509e6i | −0.187167 | + | 0.704878i | ||||
\(237\) | − | 5.81566e6i | − | 0.436872i | ||||||
\(238\) | 748637. | − | 5.73649e6i | 0.0555316 | − | 0.425515i | ||||
\(239\) | 2.58807e7i | 1.89576i | 0.318632 | + | 0.947878i | \(0.396777\pi\) | ||||
−0.318632 | + | 0.947878i | \(0.603223\pi\) | |||||||
\(240\) | −7.48443e6 | + | 2.77207e6i | −0.541408 | + | 0.200526i | ||||
\(241\) | 2.39919e7 | 1.71401 | 0.857005 | − | 0.515308i | \(-0.172323\pi\) | ||||
0.857005 | + | 0.515308i | \(0.172323\pi\) | |||||||
\(242\) | 5.46968e6 | + | 713818.i | 0.385937 | + | 0.0503664i | ||||
\(243\) | 920483. | 0.0641500 | ||||||||
\(244\) | 1.40141e7 | + | 3.72118e6i | 0.964707 | + | 0.256160i | ||||
\(245\) | 7.78540e6 | − | 9.29964e6i | 0.529398 | − | 0.632365i | ||||
\(246\) | −271746. | − | 35464.0i | −0.0182540 | − | 0.00238223i | ||||
\(247\) | 4.55381e7 | 3.02193 | ||||||||
\(248\) | 43357.9 | − | 105686.i | 0.00284258 | − | 0.00692887i | ||||
\(249\) | 5.93075e6 | 0.384159 | ||||||||
\(250\) | −1.24391e7 | − | 9.45570e6i | −0.796100 | − | 0.605165i | ||||
\(251\) | − | 2.34272e7i | − | 1.48149i | −0.671787 | − | 0.740744i | \(-0.734473\pi\) | ||
0.671787 | − | 0.740744i | \(-0.265527\pi\) | |||||||
\(252\) | −2.15856e6 | − | 573164.i | −0.134884 | − | 0.0358160i | ||||
\(253\) | 3.41170e7i | 2.10673i | ||||||||
\(254\) | 8.17141e6 | + | 1.06640e6i | 0.498650 | + | 0.0650760i | ||||
\(255\) | 7.52368e6 | + | 6.29862e6i | 0.453743 | + | 0.379861i | ||||
\(256\) | 8.51946e6 | + | 1.44532e7i | 0.507799 | + | 0.861475i | ||||
\(257\) | 1.57956e7i | 0.930544i | 0.885168 | + | 0.465272i | \(0.154043\pi\) | ||||
−0.885168 | + | 0.465272i | \(0.845957\pi\) | |||||||
\(258\) | 395273. | + | 51584.8i | 0.0230164 | + | 0.00300374i | ||||
\(259\) | 2.49826e6i | 0.143793i | ||||||||
\(260\) | −1.78842e7 | − | 2.53579e7i | −1.01754 | − | 1.44276i | ||||
\(261\) | −9.74568e6 | −0.548139 | ||||||||
\(262\) | 2.49741e6 | − | 1.91366e7i | 0.138863 | − | 1.06405i | ||||
\(263\) | −8.68016e6 | −0.477156 | −0.238578 | − | 0.971123i | \(-0.576681\pi\) | ||||
−0.238578 | + | 0.971123i | \(0.576681\pi\) | |||||||
\(264\) | −4.75234e6 | + | 1.15839e7i | −0.258283 | + | 0.629571i | ||||
\(265\) | 1.91548e7 | + | 1.60358e7i | 1.02929 | + | 0.861695i | ||||
\(266\) | 1.74543e6 | − | 1.33745e7i | 0.0927377 | − | 0.710610i | ||||
\(267\) | 6.56740e6 | 0.345032 | ||||||||
\(268\) | −1.45732e7 | − | 3.86963e6i | −0.757094 | − | 0.201032i | ||||
\(269\) | −3.33952e7 | −1.71564 | −0.857822 | − | 0.513946i | \(-0.828183\pi\) | ||||
−0.857822 | + | 0.513946i | \(0.828183\pi\) | |||||||
\(270\) | 2.78701e6 | − | 2.56544e6i | 0.141595 | − | 0.130338i | ||||
\(271\) | 2.69520e7i | 1.35420i | 0.735889 | + | 0.677102i | \(0.236764\pi\) | ||||
−0.735889 | + | 0.677102i | \(0.763236\pi\) | |||||||
\(272\) | 1.02322e7 | − | 1.79089e7i | 0.508465 | − | 0.889941i | ||||
\(273\) | − | 8.68297e6i | − | 0.426757i | ||||||
\(274\) | 546205. | − | 4.18534e6i | 0.0265524 | − | 0.203460i | ||||
\(275\) | −2.41301e7 | + | 4.31115e6i | −1.16027 | + | 0.207298i | ||||
\(276\) | −2.09699e7 | − | 5.56817e6i | −0.997400 | − | 0.264841i | ||||
\(277\) | − | 9.32384e6i | − | 0.438688i | −0.975648 | − | 0.219344i | \(-0.929608\pi\) | ||
0.975648 | − | 0.219344i | \(-0.0703917\pi\) | |||||||
\(278\) | 2.27486e6 | − | 1.74313e7i | 0.105881 | − | 0.811324i | ||||
\(279\) | 54216.6i | 0.00249643i | ||||||||
\(280\) | −8.13305e6 | + | 4.28062e6i | −0.370493 | + | 0.194999i | ||||
\(281\) | 2.95827e7 | 1.33327 | 0.666636 | − | 0.745384i | \(-0.267734\pi\) | ||||
0.666636 | + | 0.745384i | \(0.267734\pi\) | |||||||
\(282\) | −1.29790e6 | − | 169382.i | −0.0578756 | − | 0.00755302i | ||||
\(283\) | −8.93801e6 | −0.394350 | −0.197175 | − | 0.980368i | \(-0.563177\pi\) | ||||
−0.197175 | + | 0.980368i | \(0.563177\pi\) | |||||||
\(284\) | −2.80372e6 | + | 1.05589e7i | −0.122399 | + | 0.460960i | ||||
\(285\) | 1.75413e7 | + | 1.46851e7i | 0.757750 | + | 0.634367i | ||||
\(286\) | −4.82701e7 | − | 6.29946e6i | −2.06338 | − | 0.269281i | ||||
\(287\) | −315580. | −0.0133494 | ||||||||
\(288\) | −6.34443e6 | − | 4.81161e6i | −0.265592 | − | 0.201425i | ||||
\(289\) | −1.21971e6 | −0.0505318 | ||||||||
\(290\) | −2.95077e7 | + | 2.71618e7i | −1.20988 | + | 1.11369i | ||||
\(291\) | 1.33329e7i | 0.541062i | ||||||||
\(292\) | −4.03770e6 | + | 1.52061e7i | −0.162175 | + | 0.610759i | ||||
\(293\) | − | 2.26330e7i | − | 0.899787i | −0.893082 | − | 0.449894i | \(-0.851462\pi\) | ||
0.893082 | − | 0.449894i | \(-0.148538\pi\) | |||||||
\(294\) | 1.19982e7 | + | 1.56582e6i | 0.472143 | + | 0.0616168i | ||||
\(295\) | −1.43562e7 | − | 1.20186e7i | −0.559209 | − | 0.468155i | ||||
\(296\) | −3.38071e6 | + | 8.24057e6i | −0.130357 | + | 0.317748i | ||||
\(297\) | − | 5.94253e6i | − | 0.226831i | ||||||
\(298\) | 2.81982e7 | + | 3.68000e6i | 1.06555 | + | 0.139059i | ||||
\(299\) | − | 8.43532e7i | − | 3.15565i | ||||||
\(300\) | 1.28839e6 | − | 1.55351e7i | 0.0477182 | − | 0.575375i | ||||
\(301\) | 459032. | 0.0168323 | ||||||||
\(302\) | 29172.7 | − | 223538.i | 0.00105914 | − | 0.00811577i | ||||
\(303\) | 8.02533e6 | 0.288493 | ||||||||
\(304\) | 2.38560e7 | − | 4.17540e7i | 0.849135 | − | 1.48620i | ||||
\(305\) | −1.81790e7 | + | 2.17148e7i | −0.640724 | + | 0.765343i | ||||
\(306\) | −1.26679e6 | + | 9.70690e6i | −0.0442121 | + | 0.338779i | ||||
\(307\) | 9.53548e6 | 0.329555 | 0.164777 | − | 0.986331i | \(-0.447309\pi\) | ||||
0.164777 | + | 0.986331i | \(0.447309\pi\) | |||||||
\(308\) | −3.70028e6 | + | 1.39354e7i | −0.126643 | + | 0.476943i | ||||
\(309\) | −2.10544e7 | −0.713622 | ||||||||
\(310\) | 151105. | + | 164155.i | 0.00507217 | + | 0.00551024i | ||||
\(311\) | − | 1.49513e7i | − | 0.497047i | −0.968626 | − | 0.248523i | \(-0.920055\pi\) | ||
0.968626 | − | 0.248523i | \(-0.0799453\pi\) | |||||||
\(312\) | 1.17500e7 | − | 2.86410e7i | 0.386879 | − | 0.943027i | ||||
\(313\) | 5.65882e6i | 0.184541i | 0.995734 | + | 0.0922706i | \(0.0294125\pi\) | ||||
−0.995734 | + | 0.0922706i | \(0.970588\pi\) | |||||||
\(314\) | −2.60577e6 | + | 1.99669e7i | −0.0841681 | + | 0.644944i | ||||
\(315\) | 2.80007e6 | − | 3.34468e6i | 0.0895854 | − | 0.107010i | ||||
\(316\) | 6.12769e6 | − | 2.30771e7i | 0.194194 | − | 0.731341i | ||||
\(317\) | 1.34418e7i | 0.421969i | 0.977489 | + | 0.210984i | \(0.0676669\pi\) | ||||
−0.977489 | + | 0.210984i | \(0.932333\pi\) | |||||||
\(318\) | −3.22516e6 | + | 2.47131e7i | −0.100293 | + | 0.768502i | ||||
\(319\) | 6.29170e7i | 1.93819i | ||||||||
\(320\) | −3.26197e7 | + | 3.11385e6i | −0.995475 | + | 0.0950272i | ||||
\(321\) | −1.11837e7 | −0.338120 | ||||||||
\(322\) | −2.47744e7 | − | 3.23317e6i | −0.742054 | − | 0.0968413i | ||||
\(323\) | −5.91198e7 | −1.75439 | ||||||||
\(324\) | 3.65256e6 | + | 969870.i | 0.107390 | + | 0.0285153i | ||||
\(325\) | 5.96610e7 | − | 1.06592e7i | 1.73796 | − | 0.310509i | ||||
\(326\) | 1.93812e7 | + | 2.52933e6i | 0.559407 | + | 0.0730050i | ||||
\(327\) | 5.29999e6 | 0.151577 | ||||||||
\(328\) | −1.04095e6 | − | 427051.i | −0.0294990 | − | 0.0121020i | ||||
\(329\) | −1.50726e6 | −0.0423254 | ||||||||
\(330\) | −1.65622e7 | − | 1.79926e7i | −0.460867 | − | 0.500671i | ||||
\(331\) | − | 4.96648e7i | − | 1.36951i | −0.728774 | − | 0.684755i | \(-0.759909\pi\) | ||
0.728774 | − | 0.684755i | \(-0.240091\pi\) | |||||||
\(332\) | 2.35338e7 | + | 6.24895e6i | 0.643098 | + | 0.170763i | ||||
\(333\) | − | 4.22739e6i | − | 0.114483i | ||||||
\(334\) | 4.72595e6 | + | 616758.i | 0.126838 | + | 0.0165529i | ||||
\(335\) | 1.89043e7 | − | 2.25811e7i | 0.502835 | − | 0.600635i | ||||
\(336\) | −7.96144e6 | − | 4.54874e6i | −0.209881 | − | 0.119915i | ||||
\(337\) | 2.90061e7i | 0.757878i | 0.925422 | + | 0.378939i | \(0.123711\pi\) | ||||
−0.925422 | + | 0.378939i | \(0.876289\pi\) | |||||||
\(338\) | 8.10567e7 | + | 1.05783e7i | 2.09913 | + | 0.273945i | ||||
\(339\) | 7.25180e6i | 0.186143i | ||||||||
\(340\) | 2.32181e7 | + | 3.29209e7i | 0.590732 | + | 0.837596i | ||||
\(341\) | 350016. | 0.00882724 | ||||||||
\(342\) | −2.95349e6 | + | 2.26314e7i | −0.0738342 | + | 0.565760i | ||||
\(343\) | 3.08286e7 | 0.763962 | ||||||||
\(344\) | 1.51413e6 | + | 621174.i | 0.0371952 | + | 0.0152594i | ||||
\(345\) | 2.72021e7 | − | 3.24928e7i | 0.662438 | − | 0.791280i | ||||
\(346\) | −4.02256e6 | + | 3.08231e7i | −0.0971122 | + | 0.744130i | ||||
\(347\) | −2.93928e7 | −0.703481 | −0.351740 | − | 0.936098i | \(-0.614410\pi\) | ||||
−0.351740 | + | 0.936098i | \(0.614410\pi\) | |||||||
\(348\) | −3.86718e7 | − | 1.02686e7i | −0.917607 | − | 0.243653i | ||||
\(349\) | −4.15224e7 | −0.976801 | −0.488401 | − | 0.872620i | \(-0.662419\pi\) | ||||
−0.488401 | + | 0.872620i | \(0.662419\pi\) | |||||||
\(350\) | −843845. | − | 1.79309e7i | −0.0196815 | − | 0.418213i | ||||
\(351\) | 1.46927e7i | 0.339767i | ||||||||
\(352\) | −3.10632e7 | + | 4.09589e7i | −0.712226 | + | 0.939118i | ||||
\(353\) | 5.41710e7i | 1.23152i | 0.787933 | + | 0.615761i | \(0.211152\pi\) | ||||
−0.787933 | + | 0.615761i | \(0.788848\pi\) | |||||||
\(354\) | 2.41722e6 | − | 1.85221e7i | 0.0544886 | − | 0.417523i | ||||
\(355\) | −1.63610e7 | − | 1.36970e7i | −0.365699 | − | 0.306153i | ||||
\(356\) | 2.60601e7 | + | 6.91976e6i | 0.577598 | + | 0.153370i | ||||
\(357\) | 1.12727e7i | 0.247755i | ||||||||
\(358\) | 4.94130e6 | − | 3.78630e7i | 0.107694 | − | 0.825214i | ||||
\(359\) | 5.22320e7i | 1.12890i | 0.825469 | + | 0.564448i | \(0.190911\pi\) | ||||
−0.825469 | + | 0.564448i | \(0.809089\pi\) | |||||||
\(360\) | 1.37622e7 | − | 7.24337e6i | 0.294972 | − | 0.155251i | ||||
\(361\) | −9.07902e7 | −1.92982 | ||||||||
\(362\) | 4.40848e7 | + | 5.75326e6i | 0.929315 | + | 0.121280i | ||||
\(363\) | −1.07484e7 | −0.224710 | ||||||||
\(364\) | 9.14884e6 | − | 3.44549e7i | 0.189698 | − | 0.714408i | ||||
\(365\) | −2.35618e7 | − | 1.97253e7i | −0.484541 | − | 0.405644i | ||||
\(366\) | −2.80160e7 | − | 3.65621e6i | −0.571429 | − | 0.0745740i | ||||
\(367\) | 3.08439e7 | 0.623980 | 0.311990 | − | 0.950085i | \(-0.399004\pi\) | ||||
0.311990 | + | 0.950085i | \(0.399004\pi\) | |||||||
\(368\) | −7.73437e7 | − | 4.41900e7i | −1.55196 | − | 0.886709i | ||||
\(369\) | 534003. | 0.0106283 | ||||||||
\(370\) | −1.17820e7 | − | 1.27996e7i | −0.232602 | − | 0.252691i | ||||
\(371\) | 2.86994e7i | 0.562019i | ||||||||
\(372\) | −57125.5 | + | 215137.i | −0.00110969 | + | 0.00417913i | ||||
\(373\) | − | 9.32456e7i | − | 1.79681i | −0.439170 | − | 0.898404i | \(-0.644727\pi\) | ||
0.439170 | − | 0.898404i | \(-0.355273\pi\) | |||||||
\(374\) | 6.26666e7 | + | 8.17827e6i | 1.19790 | + | 0.156331i | ||||
\(375\) | 2.64187e7 | + | 1.51335e7i | 0.500978 | + | 0.286975i | ||||
\(376\) | −4.97174e6 | − | 2.03967e6i | −0.0935287 | − | 0.0383703i | ||||
\(377\) | − | 1.55560e8i | − | 2.90319i | ||||||
\(378\) | 4.31523e6 | + | 563157.i | 0.0798967 | + | 0.0104269i | ||||
\(379\) | − | 3.66043e7i | − | 0.672379i | −0.941794 | − | 0.336189i | \(-0.890862\pi\) | ||
0.941794 | − | 0.336189i | \(-0.109138\pi\) | |||||||
\(380\) | 5.41324e7 | + | 7.67541e7i | 0.986522 | + | 1.39878i | ||||
\(381\) | −1.60575e7 | −0.290337 | ||||||||
\(382\) | 2.85726e6 | − | 2.18940e7i | 0.0512578 | − | 0.392767i | ||||
\(383\) | 3.75898e7 | 0.669073 | 0.334537 | − | 0.942383i | \(-0.391420\pi\) | ||||
0.334537 | + | 0.942383i | \(0.391420\pi\) | |||||||
\(384\) | −2.01055e7 | − | 2.57778e7i | −0.355076 | − | 0.455252i | ||||
\(385\) | −2.15928e7 | − | 1.80769e7i | −0.378380 | − | 0.316769i | ||||
\(386\) | −1.04698e7 | + | 8.02253e7i | −0.182043 | + | 1.39492i | ||||
\(387\) | −776743. | −0.0134012 | ||||||||
\(388\) | −1.40483e7 | + | 5.29064e7i | −0.240507 | + | 0.905760i | ||||
\(389\) | −1.40687e7 | −0.239005 | −0.119502 | − | 0.992834i | \(-0.538130\pi\) | ||||
−0.119502 | + | 0.992834i | \(0.538130\pi\) | |||||||
\(390\) | 4.09495e7 | + | 4.44862e7i | 0.690328 | + | 0.749949i | ||||
\(391\) | 1.09511e8i | 1.83202i | ||||||||
\(392\) | 4.59601e7 | + | 1.88552e7i | 0.762998 | + | 0.313021i | ||||
\(393\) | 3.76050e7i | 0.619538i | ||||||||
\(394\) | −5.50312e6 | + | 4.21680e7i | −0.0899746 | + | 0.689437i | ||||
\(395\) | 3.57579e7 | + | 2.99355e7i | 0.580204 | + | 0.485731i | ||||
\(396\) | 6.26136e6 | − | 2.35805e7i | 0.100829 | − | 0.379724i | ||||
\(397\) | − | 5.35899e7i | − | 0.856469i | −0.903668 | − | 0.428234i | \(-0.859136\pi\) | ||
0.903668 | − | 0.428234i | \(-0.140864\pi\) | |||||||
\(398\) | −1.07652e7 | + | 8.24893e7i | −0.170755 | + | 1.30842i | ||||
\(399\) | 2.62819e7i | 0.413750i | ||||||||
\(400\) | 2.14811e7 | − | 6.02873e7i | 0.335642 | − | 0.941990i | ||||
\(401\) | 6.63361e7 | 1.02877 | 0.514384 | − | 0.857560i | \(-0.328021\pi\) | ||||
0.514384 | + | 0.857560i | \(0.328021\pi\) | |||||||
\(402\) | 2.91337e7 | + | 3.80207e6i | 0.448453 | + | 0.0585251i | ||||
\(403\) | −865405. | −0.0132222 | ||||||||
\(404\) | 3.18453e7 | + | 8.45591e6i | 0.482949 | + | 0.128238i | ||||
\(405\) | −4.73809e6 | + | 5.65964e6i | −0.0713244 | + | 0.0851969i | ||||
\(406\) | −4.56878e7 | − | 5.96246e6i | −0.682688 | − | 0.0890938i | ||||
\(407\) | −2.72915e7 | −0.404804 | ||||||||
\(408\) | −1.52545e7 | + | 3.71831e7i | −0.224603 | + | 0.547477i | ||||
\(409\) | 4.77129e7 | 0.697374 | 0.348687 | − | 0.937239i | \(-0.386628\pi\) | ||||
0.348687 | + | 0.937239i | \(0.386628\pi\) | |||||||
\(410\) | 1.61684e6 | − | 1.48830e6i | 0.0234593 | − | 0.0215942i | ||||
\(411\) | 8.22453e6i | 0.118464i | ||||||||
\(412\) | −8.35460e7 | − | 2.21841e7i | −1.19463 | − | 0.317212i | ||||
\(413\) | − | 2.15098e7i | − | 0.305342i | ||||||
\(414\) | 4.19216e7 | + | 5.47095e6i | 0.590794 | + | 0.0771013i | ||||
\(415\) | −3.05279e7 | + | 3.64655e7i | −0.427123 | + | 0.510197i | ||||
\(416\) | 7.68029e7 | − | 1.01270e8i | 1.06684 | − | 1.40669i | ||||
\(417\) | 3.42538e7i | 0.472390i | ||||||||
\(418\) | 1.46105e8 | + | 1.90674e7i | 2.00049 | + | 0.261073i | ||||
\(419\) | − | 4.33308e7i | − | 0.589053i | −0.955643 | − | 0.294526i | \(-0.904838\pi\) | ||
0.955643 | − | 0.294526i | \(-0.0951619\pi\) | |||||||
\(420\) | 1.46351e7 | − | 1.03217e7i | 0.197536 | − | 0.139317i | ||||
\(421\) | −5.83065e7 | −0.781395 | −0.390697 | − | 0.920519i | \(-0.627766\pi\) | ||||
−0.390697 | + | 0.920519i | \(0.627766\pi\) | |||||||
\(422\) | −5.84991e6 | + | 4.48254e7i | −0.0778416 | + | 0.596467i | ||||
\(423\) | 2.55049e6 | 0.0336978 | ||||||||
\(424\) | −3.88367e7 | + | 9.46656e7i | −0.509501 | + | 1.24192i | ||||
\(425\) | −7.74548e7 | + | 1.38383e7i | −1.00898 | + | 0.180267i | ||||
\(426\) | 2.75476e6 | − | 2.11086e7i | 0.0356333 | − | 0.273043i | ||||
\(427\) | −3.25350e7 | −0.417896 | ||||||||
\(428\) | −4.43780e7 | − | 1.17837e7i | −0.566026 | − | 0.150298i | ||||
\(429\) | 9.48546e7 | 1.20140 | ||||||||
\(430\) | −2.35180e6 | + | 2.16483e6i | −0.0295798 | + | 0.0272281i | ||||
\(431\) | − | 1.41316e8i | − | 1.76506i | −0.470255 | − | 0.882531i | \(-0.655838\pi\) | ||
0.470255 | − | 0.882531i | \(-0.344162\pi\) | |||||||
\(432\) | 1.34718e7 | + | 7.69707e6i | 0.167099 | + | 0.0954716i | ||||
\(433\) | − | 6.37747e7i | − | 0.785569i | −0.919631 | − | 0.392785i | \(-0.871512\pi\) | ||
0.919631 | − | 0.392785i | \(-0.128488\pi\) | |||||||
\(434\) | −33170.0 | + | 254168.i | −0.000405767 | + | 0.00310922i | ||||
\(435\) | 5.01649e7 | − | 5.99218e7i | 0.609442 | − | 0.727976i | ||||
\(436\) | 2.10309e7 | + | 5.58435e6i | 0.253745 | + | 0.0673773i | ||||
\(437\) | 2.55323e8i | 3.05947i | ||||||||
\(438\) | 3.96720e6 | − | 3.03990e7i | 0.0472130 | − | 0.361773i | ||||
\(439\) | − | 8.13434e7i | − | 0.961455i | −0.876870 | − | 0.480728i | \(-0.840373\pi\) | ||
0.876870 | − | 0.480728i | \(-0.159627\pi\) | |||||||
\(440\) | −4.67623e7 | − | 8.88472e7i | −0.548957 | − | 1.04300i | ||||
\(441\) | −2.35774e7 | −0.274904 | ||||||||
\(442\) | −1.54941e8 | − | 2.02205e7i | −1.79432 | − | 0.234167i | ||||
\(443\) | −2.93915e7 | −0.338073 | −0.169036 | − | 0.985610i | \(-0.554066\pi\) | ||||
−0.169036 | + | 0.985610i | \(0.554066\pi\) | |||||||
\(444\) | 4.45420e6 | − | 1.67747e7i | 0.0508887 | − | 0.191648i | ||||
\(445\) | −3.38050e7 | + | 4.03800e7i | −0.383620 | + | 0.458233i | ||||
\(446\) | 9.58993e7 | + | 1.25153e7i | 1.08096 | + | 0.141070i | ||||
\(447\) | −5.54118e7 | −0.620412 | ||||||||
\(448\) | −2.67990e7 | − | 2.64384e7i | −0.298046 | − | 0.294037i | ||||
\(449\) | −6.13990e6 | −0.0678300 | −0.0339150 | − | 0.999425i | \(-0.510798\pi\) | ||||
−0.0339150 | + | 0.999425i | \(0.510798\pi\) | |||||||
\(450\) | 1.42790e6 | + | 3.03414e7i | 0.0156697 | + | 0.332965i | ||||
\(451\) | − | 3.44746e6i | − | 0.0375811i | ||||||
\(452\) | −7.64088e6 | + | 2.87758e7i | −0.0827424 | + | 0.311611i | ||||
\(453\) | 439270.i | 0.00472538i | ||||||||
\(454\) | −4.39991e7 | − | 5.74208e6i | −0.470193 | − | 0.0613623i | ||||
\(455\) | 5.33877e7 | + | 4.46947e7i | 0.566770 | + | 0.474484i | ||||
\(456\) | −3.55653e7 | + | 8.66914e7i | −0.375087 | + | 0.914285i | ||||
\(457\) | 1.81452e7i | 0.190113i | 0.995472 | + | 0.0950567i | \(0.0303032\pi\) | ||||
−0.995472 | + | 0.0950567i | \(0.969697\pi\) | |||||||
\(458\) | 4.62271e7 | + | 6.03284e6i | 0.481172 | + | 0.0627951i | ||||
\(459\) | − | 1.90748e7i | − | 0.197253i | ||||||
\(460\) | 1.42177e8 | − | 1.00273e8i | 1.46068 | − | 1.03017i | ||||
\(461\) | 1.58024e8 | 1.61294 | 0.806472 | − | 0.591272i | \(-0.201374\pi\) | ||||
0.806472 | + | 0.591272i | \(0.201374\pi\) | |||||||
\(462\) | 3.63567e6 | − | 2.78586e7i | 0.0368688 | − | 0.282510i | ||||
\(463\) | 1.30644e8 | 1.31627 | 0.658137 | − | 0.752898i | \(-0.271345\pi\) | ||||
0.658137 | + | 0.752898i | \(0.271345\pi\) | |||||||
\(464\) | −1.42634e8 | − | 8.14933e7i | −1.42780 | − | 0.815770i | ||||
\(465\) | −333354. | − | 279074.i | −0.00331548 | − | 0.00277563i | ||||
\(466\) | 6.66993e6 | − | 5.11089e7i | 0.0659119 | − | 0.505055i | ||||
\(467\) | −1.60687e8 | −1.57772 | −0.788859 | − | 0.614574i | \(-0.789328\pi\) | ||||
−0.788859 | + | 0.614574i | \(0.789328\pi\) | |||||||
\(468\) | −1.54811e7 | + | 5.83022e7i | −0.151030 | + | 0.568784i | ||||
\(469\) | 3.38330e7 | 0.327961 | ||||||||
\(470\) | 7.72229e6 | − | 7.10836e6i | 0.0743793 | − | 0.0684661i | ||||
\(471\) | − | 3.92366e7i | − | 0.375516i | ||||||
\(472\) | 2.91076e7 | − | 7.09506e7i | 0.276809 | − | 0.674730i | ||||
\(473\) | 5.01456e6i | 0.0473859i | ||||||||
\(474\) | −6.02070e6 | + | 4.61341e7i | −0.0565343 | + | 0.433199i | ||||
\(475\) | −1.80584e8 | + | 3.22636e7i | −1.68499 | + | 0.301045i | ||||
\(476\) | −1.18775e7 | + | 4.47310e7i | −0.110129 | + | 0.414751i | ||||
\(477\) | − | 4.85631e7i | − | 0.447457i | ||||||
\(478\) | 2.67932e7 | − | 2.05305e8i | 0.245324 | − | 1.87982i | ||||
\(479\) | 8.69380e7i | 0.791048i | 0.918456 | + | 0.395524i | \(0.129437\pi\) | ||||
−0.918456 | + | 0.395524i | \(0.870563\pi\) | |||||||
\(480\) | 6.22417e7 | − | 1.42418e7i | 0.562805 | − | 0.128778i | ||||
\(481\) | 6.74776e7 | 0.606351 | ||||||||
\(482\) | −1.90321e8 | − | 2.48378e7i | −1.69960 | − | 0.221805i | ||||
\(483\) | 4.86837e7 | 0.432058 | ||||||||
\(484\) | −4.26505e7 | − | 1.13250e7i | −0.376174 | − | 0.0998859i | ||||
\(485\) | −8.19783e7 | − | 6.86300e7i | −0.718578 | − | 0.601573i | ||||
\(486\) | −7.30194e6 | − | 952936.i | −0.0636106 | − | 0.00830147i | ||||
\(487\) | 9.33645e6 | 0.0808342 | 0.0404171 | − | 0.999183i | \(-0.487131\pi\) | ||||
0.0404171 | + | 0.999183i | \(0.487131\pi\) | |||||||
\(488\) | −1.07318e8 | − | 4.40273e7i | −0.923446 | − | 0.378846i | ||||
\(489\) | −3.80856e7 | −0.325712 | ||||||||
\(490\) | −7.13870e7 | + | 6.57116e7i | −0.606779 | + | 0.558540i | ||||
\(491\) | − | 4.23949e7i | − | 0.358154i | −0.983835 | − | 0.179077i | \(-0.942689\pi\) | ||
0.983835 | − | 0.179077i | \(-0.0573111\pi\) | |||||||
\(492\) | 2.11897e6 | + | 562653.i | 0.0177922 | + | 0.00472439i | ||||
\(493\) | 2.01956e8i | 1.68545i | ||||||||
\(494\) | −3.61242e8 | − | 4.71436e7i | −2.99652 | − | 0.391059i | ||||
\(495\) | 3.65380e7 | + | 3.05886e7i | 0.301251 | + | 0.252199i | ||||
\(496\) | −453359. | + | 793493.i | −0.00371533 | + | 0.00650276i | ||||
\(497\) | − | 2.45135e7i | − | 0.199681i | ||||||
\(498\) | −4.70470e7 | − | 6.13985e6i | −0.380929 | − | 0.0497130i | ||||
\(499\) | 2.31844e7i | 0.186592i | 0.995638 | + | 0.0932962i | \(0.0297404\pi\) | ||||
−0.995638 | + | 0.0932962i | \(0.970260\pi\) | |||||||
\(500\) | 8.88867e7 | + | 8.78872e7i | 0.711093 | + | 0.703098i | ||||
\(501\) | −9.28688e6 | −0.0738510 | ||||||||
\(502\) | −2.42531e7 | + | 1.85841e8i | −0.191715 | + | 1.46903i | ||||
\(503\) | 1.79093e8 | 1.40726 | 0.703632 | − | 0.710565i | \(-0.251561\pi\) | ||||
0.703632 | + | 0.710565i | \(0.251561\pi\) | |||||||
\(504\) | 1.65299e7 | + | 6.78142e6i | 0.129115 | + | 0.0529699i | ||||
\(505\) | −4.13096e7 | + | 4.93442e7i | −0.320757 | + | 0.383144i | ||||
\(506\) | 3.53198e7 | − | 2.70641e8i | 0.272626 | − | 2.08901i | ||||
\(507\) | −1.59283e8 | −1.22221 | ||||||||
\(508\) | −6.37176e7 | − | 1.69190e7i | −0.486036 | − | 0.129058i | ||||
\(509\) | 1.21665e8 | 0.922595 | 0.461298 | − | 0.887245i | \(-0.347384\pi\) | ||||
0.461298 | + | 0.887245i | \(0.347384\pi\) | |||||||
\(510\) | −5.31627e7 | − | 5.77542e7i | −0.400771 | − | 0.435385i | ||||
\(511\) | − | 3.53024e7i | − | 0.264571i | ||||||
\(512\) | −5.26199e7 | − | 1.23473e8i | −0.392048 | − | 0.919945i | ||||
\(513\) | − | 4.44724e7i | − | 0.329412i | ||||||
\(514\) | 1.63525e7 | − | 1.25302e8i | 0.120419 | − | 0.922719i | ||||
\(515\) | 1.08376e8 | − | 1.29454e8i | 0.793432 | − | 0.947753i | ||||
\(516\) | −3.08219e6 | − | 818417.i | −0.0224342 | − | 0.00595697i | ||||
\(517\) | − | 1.64656e7i | − | 0.119154i | ||||||
\(518\) | 2.58634e6 | − | 1.98180e7i | 0.0186079 | − | 0.142584i | ||||
\(519\) | − | 6.05700e7i | − | 0.433267i | ||||||
\(520\) | 1.15619e8 | + | 2.19672e8i | 0.822276 | + | 1.56230i | ||||
\(521\) | −6.60811e7 | −0.467266 | −0.233633 | − | 0.972325i | \(-0.575061\pi\) | ||||
−0.233633 | + | 0.972325i | \(0.575061\pi\) | |||||||
\(522\) | 7.73099e7 | + | 1.00893e7i | 0.543530 | + | 0.0709330i | ||||
\(523\) | −7.09676e7 | −0.496083 | −0.248042 | − | 0.968749i | \(-0.579787\pi\) | ||||
−0.248042 | + | 0.968749i | \(0.579787\pi\) | |||||||
\(524\) | −3.96226e7 | + | 1.49220e8i | −0.275391 | + | 1.03713i | ||||
\(525\) | 6.15185e6 | + | 3.44328e7i | 0.0425136 | + | 0.237955i | ||||
\(526\) | 6.88574e7 | + | 8.98619e6i | 0.473144 | + | 0.0617474i | ||||
\(527\) | 1.12351e6 | 0.00767619 | ||||||||
\(528\) | 4.96914e7 | − | 8.69725e7i | 0.337582 | − | 0.590854i | ||||
\(529\) | 3.24916e8 | 2.19484 | ||||||||
\(530\) | −1.35348e8 | − | 1.47038e8i | −0.909129 | − | 0.987648i | ||||
\(531\) | 3.63974e7i | 0.243101i | ||||||||
\(532\) | −2.76920e7 | + | 1.04289e8i | −0.183916 | + | 0.692634i | ||||
\(533\) | 8.52375e6i | 0.0562923i | ||||||||
\(534\) | −5.20974e7 | − | 6.79895e6i | −0.342131 | − | 0.0446496i | ||||
\(535\) | 5.75670e7 | − | 6.87636e7i | 0.375934 | − | 0.449053i | ||||
\(536\) | 1.11599e8 | + | 4.57837e7i | 0.724713 | + | 0.297315i | ||||
\(537\) | 7.44039e7i | 0.480478i | ||||||||
\(538\) | 2.64915e8 | + | 3.45726e7i | 1.70122 | + | 0.222017i | ||||
\(539\) | 1.52213e8i | 0.972043i | ||||||||
\(540\) | −2.47645e7 | + | 1.74657e7i | −0.157271 | + | 0.110919i | ||||
\(541\) | −1.30210e7 | −0.0822345 | −0.0411172 | − | 0.999154i | \(-0.513092\pi\) | ||||
−0.0411172 | + | 0.999154i | \(0.513092\pi\) | |||||||
\(542\) | 2.79023e7 | − | 2.13803e8i | 0.175243 | − | 1.34282i | ||||
\(543\) | −8.66302e7 | −0.541090 | ||||||||
\(544\) | −9.97093e7 | + | 1.31473e8i | −0.619354 | + | 0.816659i | ||||
\(545\) | −2.72812e7 | + | 3.25873e7i | −0.168529 | + | 0.201307i | ||||
\(546\) | −8.98910e6 | + | 6.88797e7i | −0.0552254 | + | 0.423168i | ||||
\(547\) | 2.06228e8 | 1.26004 | 0.630021 | − | 0.776578i | \(-0.283046\pi\) | ||||
0.630021 | + | 0.776578i | \(0.283046\pi\) | |||||||
\(548\) | −8.66580e6 | + | 3.26357e7i | −0.0526583 | + | 0.198313i | ||||
\(549\) | 5.50536e7 | 0.332712 | ||||||||
\(550\) | 1.95881e8 | − | 9.21834e6i | 1.17734 | − | 0.0554070i | ||||
\(551\) | 4.70855e8i | 2.81470i | ||||||||
\(552\) | 1.60584e8 | + | 6.58800e7i | 0.954741 | + | 0.391685i | ||||
\(553\) | 5.35757e7i | 0.316805i | ||||||||
\(554\) | −9.65257e6 | + | 7.39635e7i | −0.0567693 | + | 0.434999i | ||||
\(555\) | 2.59923e7 | + | 2.17601e7i | 0.152043 | + | 0.127286i | ||||
\(556\) | −3.60917e7 | + | 1.35923e8i | −0.209982 | + | 0.790801i | ||||
\(557\) | 2.48107e6i | 0.0143573i | 0.999974 | + | 0.00717865i | \(0.00228505\pi\) | ||||
−0.999974 | + | 0.00717865i | \(0.997715\pi\) | |||||||
\(558\) | 56128.1 | − | 430086.i | 0.000323056 | − | 0.00247544i | ||||
\(559\) | − | 1.23984e7i | − | 0.0709788i | ||||||
\(560\) | 6.89489e7 | − | 2.55372e7i | 0.392612 | − | 0.145415i | ||||
\(561\) | −1.23145e8 | −0.697474 | ||||||||
\(562\) | −2.34671e8 | − | 3.06257e7i | −1.32206 | − | 0.172535i | ||||
\(563\) | 1.47289e8 | 0.825361 | 0.412680 | − | 0.910876i | \(-0.364593\pi\) | ||||
0.412680 | + | 0.910876i | \(0.364593\pi\) | |||||||
\(564\) | 1.01206e7 | + | 2.68733e6i | 0.0564115 | + | 0.0149790i | ||||
\(565\) | −4.45881e7 | − | 3.73279e7i | −0.247214 | − | 0.206961i | ||||
\(566\) | 7.09028e7 | + | 9.25313e6i | 0.391034 | + | 0.0510316i | ||||
\(567\) | −8.47978e6 | −0.0465195 | ||||||||
\(568\) | 3.31723e7 | − | 8.08583e7i | 0.181022 | − | 0.441245i | ||||
\(569\) | 9.59654e7 | 0.520928 | 0.260464 | − | 0.965484i | \(-0.416124\pi\) | ||||
0.260464 | + | 0.965484i | \(0.416124\pi\) | |||||||
\(570\) | −1.23947e8 | − | 1.34652e8i | −0.669287 | − | 0.727092i | ||||
\(571\) | − | 3.67358e8i | − | 1.97325i | −0.163011 | − | 0.986624i | \(-0.552121\pi\) | ||
0.163011 | − | 0.986624i | \(-0.447879\pi\) | |||||||
\(572\) | 3.76392e8 | + | 9.99439e7i | 2.01119 | + | 0.534033i | ||||
\(573\) | 4.30235e7i | 0.228687i | ||||||||
\(574\) | 2.50341e6 | + | 326706.i | 0.0132372 | + | 0.00172751i | ||||
\(575\) | 5.97639e7 | + | 3.34507e8i | 0.314366 | + | 1.75955i | ||||
\(576\) | 4.53474e7 | + | 4.47373e7i | 0.237293 | + | 0.234101i | ||||
\(577\) | 2.14798e8i | 1.11816i | 0.829115 | + | 0.559078i | \(0.188845\pi\) | ||||
−0.829115 | + | 0.559078i | \(0.811155\pi\) | |||||||
\(578\) | 9.67567e6 | + | 1.26272e6i | 0.0501069 | + | 0.00653917i | ||||
\(579\) | − | 1.57649e8i | − | 0.812187i | ||||||
\(580\) | 2.62196e8 | − | 1.84919e8i | 1.34382 | − | 0.947759i | ||||
\(581\) | −5.46359e7 | −0.278580 | ||||||||
\(582\) | 1.38030e7 | − | 1.05767e8i | 0.0700173 | − | 0.536513i | ||||
\(583\) | −3.13518e8 | −1.58218 | ||||||||
\(584\) | 4.77722e7 | − | 1.16446e8i | 0.239848 | − | 0.584636i | ||||
\(585\) | −9.03391e7 | − | 7.56294e7i | −0.451241 | − | 0.377766i | ||||
\(586\) | −2.34310e7 | + | 1.79542e8i | −0.116439 | + | 0.892222i | ||||
\(587\) | 1.34919e8 | 0.667050 | 0.333525 | − | 0.942741i | \(-0.391762\pi\) | ||||
0.333525 | + | 0.942741i | \(0.391762\pi\) | |||||||
\(588\) | −9.35574e7 | − | 2.48424e7i | −0.460200 | − | 0.122197i | ||||
\(589\) | 2.61943e6 | 0.0128192 | ||||||||
\(590\) | 1.01442e8 | + | 1.10203e8i | 0.493925 | + | 0.536584i | ||||
\(591\) | − | 8.28636e7i | − | 0.401422i | ||||||
\(592\) | 3.53494e7 | − | 6.18704e7i | 0.170379 | − | 0.298207i | ||||
\(593\) | − | 2.80226e8i | − | 1.34383i | −0.740628 | − | 0.671915i | \(-0.765472\pi\) | ||
0.740628 | − | 0.671915i | \(-0.234528\pi\) | |||||||
\(594\) | −6.15204e6 | + | 4.71405e7i | −0.0293535 | + | 0.224923i | ||||
\(595\) | −6.93105e7 | − | 5.80249e7i | −0.329040 | − | 0.275463i | ||||
\(596\) | −2.19879e8 | − | 5.83848e7i | −1.03859 | − | 0.275779i | ||||
\(597\) | − | 1.62098e8i | − | 0.761824i | ||||||
\(598\) | −8.73273e7 | + | 6.69152e8i | −0.408363 | + | 3.12911i | ||||
\(599\) | − | 1.49142e8i | − | 0.693937i | −0.937877 | − | 0.346969i | \(-0.887211\pi\) | ||
0.937877 | − | 0.346969i | \(-0.112789\pi\) | |||||||
\(600\) | −2.63033e7 | + | 1.21902e8i | −0.121775 | + | 0.564362i | ||||
\(601\) | −2.09302e8 | −0.964161 | −0.482080 | − | 0.876127i | \(-0.660119\pi\) | ||||
−0.482080 | + | 0.876127i | \(0.660119\pi\) | |||||||
\(602\) | −3.64138e6 | − | 475216.i | −0.0166908 | − | 0.00217822i | ||||
\(603\) | −5.72500e7 | −0.261110 | ||||||||
\(604\) | −462838. | + | 1.74306e6i | −0.00210048 | + | 0.00791047i | ||||
\(605\) | 5.53261e7 | − | 6.60869e7i | 0.249841 | − | 0.298435i | ||||
\(606\) | −6.36628e7 | − | 8.30828e6i | −0.286067 | − | 0.0373330i | ||||
\(607\) | 1.45876e8 | 0.652258 | 0.326129 | − | 0.945325i | \(-0.394256\pi\) | ||||
0.326129 | + | 0.945325i | \(0.394256\pi\) | |||||||
\(608\) | −2.32469e8 | + | 3.06526e8i | −1.03432 | + | 1.36382i | ||||
\(609\) | 8.97803e7 | 0.397493 | ||||||||
\(610\) | 1.66690e8 | − | 1.53438e8i | 0.734377 | − | 0.675993i | ||||
\(611\) | 4.07108e7i | 0.178479i | ||||||||
\(612\) | 2.00983e7 | − | 7.56908e7i | 0.0876807 | − | 0.330209i | ||||
\(613\) | − | 2.18756e8i | − | 0.949684i | −0.880071 | − | 0.474842i | \(-0.842505\pi\) | ||
0.880071 | − | 0.474842i | \(-0.157495\pi\) | |||||||
\(614\) | −7.56424e7 | − | 9.87167e6i | −0.326784 | − | 0.0426467i | ||||
\(615\) | −2.74872e6 | + | 3.28334e6i | −0.0118170 | + | 0.0141153i | ||||
\(616\) | 4.37800e7 | − | 1.06715e8i | 0.187298 | − | 0.456545i | ||||
\(617\) | − | 2.56428e8i | − | 1.09172i | −0.837877 | − | 0.545859i | \(-0.816203\pi\) | ||
0.837877 | − | 0.545859i | \(-0.183797\pi\) | |||||||
\(618\) | 1.67019e8 | + | 2.17968e7i | 0.707622 | + | 0.0923478i | ||||
\(619\) | − | 5.25164e7i | − | 0.221423i | −0.993853 | − | 0.110712i | \(-0.964687\pi\) | ||
0.993853 | − | 0.110712i | \(-0.0353130\pi\) | |||||||
\(620\) | −1.02873e6 | − | 1.45863e6i | −0.00431645 | − | 0.00612028i | ||||
\(621\) | −8.23792e7 | −0.343988 | ||||||||
\(622\) | −1.54784e7 | + | 1.18605e8i | −0.0643214 | + | 0.492867i | ||||
\(623\) | −6.05010e7 | −0.250206 | ||||||||
\(624\) | −1.22861e8 | + | 2.15037e8i | −0.505660 | + | 0.885033i | ||||
\(625\) | −2.29037e8 | + | 8.45391e7i | −0.938134 | + | 0.346272i | ||||
\(626\) | 5.85834e6 | − | 4.48899e7i | 0.0238809 | − | 0.182989i | ||||
\(627\) | −2.87109e8 | −1.16478 | ||||||||
\(628\) | 4.13418e7 | − | 1.55695e8i | 0.166921 | − | 0.628629i | ||||
\(629\) | −8.76027e7 | −0.352018 | ||||||||
\(630\) | −2.56748e7 | + | 2.36336e7i | −0.102680 | + | 0.0945168i | ||||
\(631\) | 3.92931e8i | 1.56397i | 0.623297 | + | 0.781985i | \(0.285793\pi\) | ||||
−0.623297 | + | 0.781985i | \(0.714207\pi\) | |||||||
\(632\) | −7.25001e7 | + | 1.76721e8i | −0.287202 | + | 0.700062i | ||||
\(633\) | − | 8.80855e7i | − | 0.347291i | ||||||
\(634\) | 1.39157e7 | − | 1.06630e8i | 0.0546058 | − | 0.418421i | ||||
\(635\) | 8.26542e7 | − | 9.87302e7i | 0.322807 | − | 0.385593i | ||||
\(636\) | 5.11687e7 | − | 1.92703e8i | 0.198899 | − | 0.749062i | ||||
\(637\) | − | 3.76343e8i | − | 1.45601i | ||||||
\(638\) | 6.51352e7 | − | 4.99103e8i | 0.250815 | − | 1.92189i | ||||
\(639\) | 4.14801e7i | 0.158978i | ||||||||
\(640\) | 2.61987e8 | + | 9.06843e6i | 0.999401 | + | 0.0345933i | ||||
\(641\) | −4.43610e8 | −1.68433 | −0.842165 | − | 0.539219i | \(-0.818719\pi\) | ||||
−0.842165 | + | 0.539219i | \(0.818719\pi\) | |||||||
\(642\) | 8.87173e7 | + | 1.15780e7i | 0.335277 | + | 0.0437551i | ||||
\(643\) | −4.69895e8 | −1.76753 | −0.883767 | − | 0.467927i | \(-0.845001\pi\) | ||||
−0.883767 | + | 0.467927i | \(0.845001\pi\) | |||||||
\(644\) | 1.93181e8 | + | 5.12957e7i | 0.723282 | + | 0.192054i | ||||
\(645\) | 3.99820e6 | − | 4.77584e6i | 0.0149000 | − | 0.0177980i | ||||
\(646\) | 4.68981e8 | + | 6.12041e7i | 1.73963 | + | 0.227030i | ||||
\(647\) | −7.12899e7 | −0.263218 | −0.131609 | − | 0.991302i | \(-0.542014\pi\) | ||||
−0.131609 | + | 0.991302i | \(0.542014\pi\) | |||||||
\(648\) | −2.79707e7 | − | 1.14751e7i | −0.102797 | − | 0.0421725i | ||||
\(649\) | 2.34978e8 | 0.859592 | ||||||||
\(650\) | −4.84310e8 | + | 2.27921e7i | −1.76353 | + | 0.0829935i | ||||
\(651\) | − | 499460.i | − | 0.00181033i | ||||||
\(652\) | −1.51127e8 | − | 4.01290e7i | −0.545255 | − | 0.144782i | ||||
\(653\) | 3.07313e8i | 1.10367i | 0.833952 | + | 0.551837i | \(0.186073\pi\) | ||||
−0.833952 | + | 0.551837i | \(0.813927\pi\) | |||||||
\(654\) | −4.20434e7 | − | 5.48685e6i | −0.150302 | − | 0.0196151i | ||||
\(655\) | −2.31216e8 | − | 1.93568e8i | −0.822801 | − | 0.688826i | ||||
\(656\) | 7.81545e6 | + | 4.46533e6i | 0.0276849 | + | 0.0158176i | ||||
\(657\) | 5.97364e7i | 0.210641i | ||||||||
\(658\) | 1.19567e7 | + | 1.56040e6i | 0.0419695 | + | 0.00547720i | ||||
\(659\) | 1.56295e8i | 0.546122i | 0.961997 | + | 0.273061i | \(0.0880360\pi\) | ||||
−0.961997 | + | 0.273061i | \(0.911964\pi\) | |||||||
\(660\) | 1.12756e8 | + | 1.59877e8i | 0.392202 | + | 0.556100i | ||||
\(661\) | 2.76572e7 | 0.0957644 | 0.0478822 | − | 0.998853i | \(-0.484753\pi\) | ||||
0.0478822 | + | 0.998853i | \(0.484753\pi\) | |||||||
\(662\) | −5.14158e7 | + | 3.93978e8i | −0.177224 | + | 1.35799i | ||||
\(663\) | 3.04472e8 | 1.04474 | ||||||||
\(664\) | −1.80218e8 | − | 7.39348e7i | −0.615593 | − | 0.252548i | ||||
\(665\) | −1.61596e8 | − | 1.35283e8i | −0.549496 | − | 0.460023i | ||||
\(666\) | −4.37643e6 | + | 3.35347e7i | −0.0148149 | + | 0.113520i | ||||
\(667\) | 8.72196e8 | 2.93925 | ||||||||
\(668\) | −3.68512e7 | − | 9.78515e6i | −0.123630 | − | 0.0328275i | ||||
\(669\) | −1.88450e8 | −0.629386 | ||||||||
\(670\) | −1.73340e8 | + | 1.59559e8i | −0.576333 | + | 0.530514i | ||||
\(671\) | − | 3.55420e8i | − | 1.17645i | ||||||
\(672\) | 5.84469e7 | + | 4.43261e7i | 0.192599 | + | 0.146067i | ||||
\(673\) | 2.88925e8i | 0.947851i | 0.880565 | + | 0.473926i | \(0.157163\pi\) | ||||
−0.880565 | + | 0.473926i | \(0.842837\pi\) | |||||||
\(674\) | 3.00288e7 | − | 2.30098e8i | 0.0980748 | − | 0.751506i | ||||
\(675\) | −1.04097e7 | − | 5.82648e7i | −0.0338477 | − | 0.189450i | ||||
\(676\) | −6.32050e8 | − | 1.67829e8i | −2.04603 | − | 0.543284i | ||||
\(677\) | − | 1.02252e8i | − | 0.329540i | −0.986332 | − | 0.164770i | \(-0.947312\pi\) | ||
0.986332 | − | 0.164770i | \(-0.0526881\pi\) | |||||||
\(678\) | 7.50747e6 | − | 5.75266e7i | 0.0240882 | − | 0.184578i | ||||
\(679\) | − | 1.22827e8i | − | 0.392361i | ||||||
\(680\) | −1.50102e8 | − | 2.85189e8i | −0.477374 | − | 0.906998i | ||||
\(681\) | 8.64618e7 | 0.273768 | ||||||||
\(682\) | −2.77658e6 | − | 362356.i | −0.00875302 | − | 0.00114231i | ||||
\(683\) | −1.71355e8 | −0.537818 | −0.268909 | − | 0.963166i | \(-0.586663\pi\) | ||||
−0.268909 | + | 0.963166i | \(0.586663\pi\) | |||||||
\(684\) | 4.68585e7 | − | 1.76471e8i | 0.146427 | − | 0.551448i | ||||
\(685\) | −5.05690e7 | − | 4.23349e7i | −0.157330 | − | 0.131712i | ||||
\(686\) | −2.44555e8 | − | 3.19155e7i | −0.757538 | − | 0.0988621i | ||||
\(687\) | −9.08400e7 | −0.280161 | ||||||||
\(688\) | −1.13681e7 | − | 6.49512e6i | −0.0349078 | − | 0.0199444i | ||||
\(689\) | 7.75165e8 | 2.36993 | ||||||||
\(690\) | −2.49425e8 | + | 2.29596e8i | −0.759265 | + | 0.698903i | ||||
\(691\) | 1.78401e8i | 0.540708i | 0.962761 | + | 0.270354i | \(0.0871408\pi\) | ||||
−0.962761 | + | 0.270354i | \(0.912859\pi\) | |||||||
\(692\) | 6.38197e7 | − | 2.40347e8i | 0.192591 | − | 0.725306i | ||||
\(693\) | 5.47444e7i | 0.164490i | ||||||||
\(694\) | 2.33165e8 | + | 3.04291e7i | 0.697566 | + | 0.0910354i | ||||
\(695\) | −2.10612e8 | − | 1.76318e8i | −0.627376 | − | 0.525222i | ||||
\(696\) | 2.96142e8 | + | 1.21493e8i | 0.878360 | + | 0.360349i | ||||
\(697\) | − | 1.10659e7i | − | 0.0326806i | ||||||
\(698\) | 3.29386e8 | + | 4.29863e7i | 0.968588 | + | 0.126405i | ||||
\(699\) | 1.00433e8i | 0.294066i | ||||||||
\(700\) | −1.18691e7 | + | 1.43114e8i | −0.0346037 | + | 0.417243i | ||||
\(701\) | −3.64044e8 | −1.05682 | −0.528408 | − | 0.848991i | \(-0.677211\pi\) | ||||
−0.528408 | + | 0.848991i | \(0.677211\pi\) | |||||||
\(702\) | 1.52108e7 | − | 1.16554e8i | 0.0439683 | − | 0.336910i | ||||
\(703\) | −2.04243e8 | −0.587870 | ||||||||
\(704\) | 2.88819e8 | − | 2.92758e8i | 0.827766 | − | 0.839054i | ||||
\(705\) | −1.31284e7 | + | 1.56818e7i | −0.0374665 | + | 0.0447537i | ||||
\(706\) | 5.60809e7 | − | 4.29724e8i | 0.159368 | − | 1.22117i | ||||
\(707\) | −7.39319e7 | −0.209206 | ||||||||
\(708\) | −3.83503e7 | + | 1.44428e8i | −0.108061 | + | 0.406961i | ||||
\(709\) | −4.12018e8 | −1.15605 | −0.578026 | − | 0.816018i | \(-0.696177\pi\) | ||||
−0.578026 | + | 0.816018i | \(0.696177\pi\) | |||||||
\(710\) | 1.15607e8 | + | 1.25592e8i | 0.323006 | + | 0.350903i | ||||
\(711\) | − | 9.06572e7i | − | 0.252228i | ||||||
\(712\) | −1.99564e8 | − | 8.18715e7i | −0.552894 | − | 0.226826i | ||||
\(713\) | − | 4.85215e6i | − | 0.0133865i | ||||||
\(714\) | 1.16701e7 | − | 8.94230e7i | 0.0320612 | − | 0.245671i | ||||
\(715\) | −4.88254e8 | + | 5.83219e8i | −1.33576 | + | 1.59556i | ||||
\(716\) | −7.83959e7 | + | 2.95242e8i | −0.213577 | + | 0.804339i | ||||
\(717\) | 4.03440e8i | 1.09452i | ||||||||
\(718\) | 5.40736e7 | − | 4.14343e8i | 0.146087 | − | 1.11940i | ||||
\(719\) | − | 3.87039e8i | − | 1.04128i | −0.853776 | − | 0.520641i | \(-0.825693\pi\) | ||
0.853776 | − | 0.520641i | \(-0.174307\pi\) | |||||||
\(720\) | −1.16671e8 | + | 4.32123e7i | −0.312582 | + | 0.115774i | ||||
\(721\) | 1.93960e8 | 0.517496 | ||||||||
\(722\) | 7.20214e8 | + | 9.39912e7i | 1.91360 | + | 0.249733i | ||||
\(723\) | 3.73997e8 | 0.989584 | ||||||||
\(724\) | −3.43757e8 | − | 9.12781e7i | −0.905807 | − | 0.240520i | ||||
\(725\) | 1.10214e8 | + | 6.16883e8i | 0.289216 | + | 1.61878i | ||||
\(726\) | 8.52639e7 | + | 1.11273e7i | 0.222821 | + | 0.0290791i | ||||
\(727\) | 4.91602e8 | 1.27941 | 0.639706 | − | 0.768619i | \(-0.279056\pi\) | ||||
0.639706 | + | 0.768619i | \(0.279056\pi\) | |||||||
\(728\) | −1.08245e8 | + | 2.63850e8i | −0.280552 | + | 0.683853i | ||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 1.66489e8 | + | 1.80868e8i | 0.427973 | + | 0.464936i | ||||
\(731\) | 1.60962e7i | 0.0412069i | ||||||||
\(732\) | 2.18458e8 | + | 5.80074e7i | 0.556974 | + | 0.147894i | ||||
\(733\) | − | 2.92669e8i | − | 0.743130i | −0.928407 | − | 0.371565i | \(-0.878821\pi\) | ||
0.928407 | − | 0.371565i | \(-0.121179\pi\) | |||||||
\(734\) | −2.44676e8 | − | 3.19313e7i | −0.618733 | − | 0.0807474i | ||||
\(735\) | 1.21362e8 | − | 1.44967e8i | 0.305648 | − | 0.365096i | ||||
\(736\) | 5.67799e8 | + | 4.30618e8i | 1.42417 | + | 1.08009i | ||||
\(737\) | 3.69599e8i | 0.923269i | ||||||||
\(738\) | −4.23610e6 | − | 552830.i | −0.0105389 | − | 0.00137538i | ||||
\(739\) | 2.64415e8i | 0.655167i | 0.944822 | + | 0.327583i | \(0.106234\pi\) | ||||
−0.944822 | + | 0.327583i | \(0.893766\pi\) | |||||||
\(740\) | 8.02125e7 | + | 1.13733e8i | 0.197946 | + | 0.280667i | ||||
\(741\) | 7.09869e8 | 1.74471 | ||||||||
\(742\) | 2.97112e7 | − | 2.27664e8i | 0.0727292 | − | 0.557293i | ||||
\(743\) | 2.47114e8 | 0.602464 | 0.301232 | − | 0.953551i | \(-0.402602\pi\) | ||||
0.301232 | + | 0.953551i | \(0.402602\pi\) | |||||||
\(744\) | 675883. | − | 1.64748e6i | 0.00164117 | − | 0.00400039i | ||||
\(745\) | 2.85227e8 | − | 3.40703e8i | 0.689797 | − | 0.823961i | ||||
\(746\) | −9.65331e7 | + | 7.39692e8i | −0.232520 | + | 1.78170i | ||||
\(747\) | 9.24512e7 | 0.221795 | ||||||||
\(748\) | −4.88651e8 | − | 1.29752e8i | −1.16760 | − | 0.310034i | ||||
\(749\) | 1.03028e8 | 0.245193 | ||||||||
\(750\) | −1.93906e8 | − | 1.47400e8i | −0.459629 | − | 0.349392i | ||||
\(751\) | − | 3.88949e8i | − | 0.918276i | −0.888365 | − | 0.459138i | \(-0.848158\pi\) | ||
0.888365 | − | 0.459138i | \(-0.151842\pi\) | |||||||
\(752\) | 3.73279e7 | + | 2.13271e7i | 0.0877768 | + | 0.0501510i | ||||
\(753\) | − | 3.65193e8i | − | 0.855338i | ||||||
\(754\) | −1.61045e8 | + | 1.23402e9i | −0.375693 | + | 2.87878i | ||||
\(755\) | −2.70087e6 | − | 2.26110e6i | −0.00627572 | − | 0.00525385i | ||||
\(756\) | −3.36486e7 | − | 8.93474e6i | −0.0778756 | − | 0.0206784i | ||||
\(757\) | − | 3.98638e8i | − | 0.918948i | −0.888191 | − | 0.459474i | \(-0.848038\pi\) | ||
0.888191 | − | 0.459474i | \(-0.151962\pi\) | |||||||
\(758\) | −3.78948e7 | + | 2.90372e8i | −0.0870106 | + | 0.666725i | ||||
\(759\) | 5.31831e8i | 1.21632i | ||||||||
\(760\) | −3.49958e8 | − | 6.64911e8i | −0.797214 | − | 1.51469i | ||||
\(761\) | 2.05271e8 | 0.465773 | 0.232887 | − | 0.972504i | \(-0.425183\pi\) | ||||
0.232887 | + | 0.972504i | \(0.425183\pi\) | |||||||
\(762\) | 1.27380e8 | + | 1.66236e7i | 0.287896 | + | 0.0375716i | ||||
\(763\) | −4.88252e7 | −0.109918 | ||||||||
\(764\) | −4.53318e7 | + | 1.70721e8i | −0.101654 | + | 0.382831i | ||||
\(765\) | 1.17283e8 | + | 9.81858e7i | 0.261969 | + | 0.219313i | ||||
\(766\) | −2.98190e8 | − | 3.89151e7i | −0.663447 | − | 0.0865828i | ||||
\(767\) | −5.80976e8 | −1.28757 | ||||||||
\(768\) | 1.32805e8 | + | 2.25302e8i | 0.293178 | + | 0.497373i | ||||
\(769\) | −5.15212e8 | −1.13294 | −0.566470 | − | 0.824082i | \(-0.691691\pi\) | ||||
−0.566470 | + | 0.824082i | \(0.691691\pi\) | |||||||
\(770\) | 1.52576e8 | + | 1.65754e8i | 0.334206 | + | 0.363070i | ||||
\(771\) | 2.46229e8i | 0.537250i | ||||||||
\(772\) | 1.66107e8 | − | 6.25567e8i | 0.361025 | − | 1.35963i | ||||
\(773\) | − | 2.25469e8i | − | 0.488145i | −0.969757 | − | 0.244072i | \(-0.921517\pi\) | ||
0.969757 | − | 0.244072i | \(-0.0784834\pi\) | |||||||
\(774\) | 6.16169e6 | + | 804128.i | 0.0132885 | + | 0.00173421i | ||||
\(775\) | 3.43181e6 | − | 613136.i | 0.00737255 | − | 0.00131720i | ||||
\(776\) | 1.66213e8 | − | 4.05149e8i | 0.355697 | − | 0.867020i | ||||
\(777\) | 3.89440e7i | 0.0830191i | ||||||||
\(778\) | 1.11603e8 | + | 1.45647e7i | 0.236995 | + | 0.0309289i | ||||
\(779\) | − | 2.57999e7i | − | 0.0545766i | ||||||
\(780\) | −2.78787e8 | − | 3.95291e8i | −0.587474 | − | 0.832977i | ||||
\(781\) | 2.67790e8 | 0.562137 | ||||||||
\(782\) | 1.13373e8 | − | 8.68725e8i | 0.237076 | − | 1.81661i | ||||
\(783\) | −1.51920e8 | −0.316468 | ||||||||
\(784\) | −3.45069e8 | − | 1.97154e8i | −0.716075 | − | 0.409127i | ||||
\(785\) | 2.41248e8 | + | 2.01966e8i | 0.498718 | + | 0.417513i | ||||
\(786\) | 3.89308e7 | − | 2.98310e8i | 0.0801726 | − | 0.614329i | ||||
\(787\) | 8.23340e8 | 1.68910 | 0.844549 | − | 0.535478i | \(-0.179869\pi\) | ||||
0.844549 | + | 0.535478i | \(0.179869\pi\) | |||||||
\(788\) | 8.73095e7 | − | 3.28811e8i | 0.178436 | − | 0.671997i | ||||
\(789\) | −1.35310e8 | −0.275486 | ||||||||
\(790\) | −2.52667e8 | − | 2.74489e8i | −0.512469 | − | 0.556729i | ||||
\(791\) | − | 6.68058e7i | − | 0.134985i | ||||||
\(792\) | −7.40816e7 | + | 1.80576e8i | −0.149120 | + | 0.363483i | ||||
\(793\) | 8.78765e8i | 1.76219i | ||||||||
\(794\) | −5.54793e7 | + | 4.25114e8i | −0.110833 | + | 0.849267i | ||||
\(795\) | 2.98593e8 | + | 2.49974e8i | 0.594262 | + | 0.497500i | ||||
\(796\) | 1.70795e8 | − | 6.43221e8i | 0.338638 | − | 1.27532i | ||||
\(797\) | 1.31438e8i | 0.259624i | 0.991539 | + | 0.129812i | \(0.0414374\pi\) | ||||
−0.991539 | + | 0.129812i | \(0.958563\pi\) | |||||||
\(798\) | 2.72085e7 | − | 2.08487e8i | 0.0535421 | − | 0.410271i | ||||
\(799\) | − | 5.28528e7i | − | 0.103616i | ||||||
\(800\) | −2.32817e8 | + | 4.56005e8i | −0.454720 | + | 0.890634i | ||||
\(801\) | 1.02376e8 | 0.199205 | ||||||||
\(802\) | −5.26227e8 | − | 6.86749e7i | −1.02012 | − | 0.133130i | ||||
\(803\) | 3.85651e8 | 0.744814 | ||||||||
\(804\) | −2.27173e8 | − | 6.03216e7i | −0.437108 | − | 0.116066i | ||||
\(805\) | −2.50594e8 | + | 2.99334e8i | −0.480378 | + | 0.573811i | ||||
\(806\) | 6.86503e6 | + | 895917.i | 0.0131110 | + | 0.00171105i | ||||
\(807\) | −5.20580e8 | −0.990528 | ||||||||
\(808\) | −2.43866e8 | − | 1.00047e8i | −0.462293 | − | 0.189657i | ||||
\(809\) | −6.41573e8 | −1.21172 | −0.605858 | − | 0.795573i | \(-0.707170\pi\) | ||||
−0.605858 | + | 0.795573i | \(0.707170\pi\) | |||||||
\(810\) | 4.34452e7 | − | 3.99913e7i | 0.0817498 | − | 0.0752506i | ||||
\(811\) | 3.32626e8i | 0.623582i | 0.950151 | + | 0.311791i | \(0.100929\pi\) | ||||
−0.950151 | + | 0.311791i | \(0.899071\pi\) | |||||||
\(812\) | 3.56257e8 | + | 9.45973e7i | 0.665418 | + | 0.176689i | ||||
\(813\) | 4.20141e8i | 0.781850i | ||||||||
\(814\) | 2.16496e8 | + | 2.82537e7i | 0.401400 | + | 0.0523845i | ||||
\(815\) | 1.96042e8 | − | 2.34171e8i | 0.362139 | − | 0.432574i | ||||
\(816\) | 1.59504e8 | − | 2.79172e8i | 0.293562 | − | 0.513808i | ||||
\(817\) | 3.75277e7i | 0.0688155i | ||||||||
\(818\) | −3.78494e8 | − | 4.93951e7i | −0.691511 | − | 0.0902452i | ||||
\(819\) | − | 1.35354e8i | − | 0.246388i | ||||||
\(820\) | −1.43667e7 | + | 1.01324e7i | −0.0260565 | + | 0.0183769i | ||||
\(821\) | 6.97205e8 | 1.25988 | 0.629942 | − | 0.776642i | \(-0.283078\pi\) | ||||
0.629942 | + | 0.776642i | \(0.283078\pi\) | |||||||
\(822\) | 8.51450e6 | − | 6.52430e7i | 0.0153300 | − | 0.117468i | ||||
\(823\) | −5.53566e8 | −0.993047 | −0.496523 | − | 0.868023i | \(-0.665390\pi\) | ||||
−0.496523 | + | 0.868023i | \(0.665390\pi\) | |||||||
\(824\) | 6.39782e8 | + | 2.62472e8i | 1.14354 | + | 0.469139i | ||||
\(825\) | −3.76151e8 | + | 6.72041e7i | −0.669885 | + | 0.119683i | ||||
\(826\) | −2.22682e7 | + | 1.70631e8i | −0.0395134 | + | 0.302774i | ||||
\(827\) | −4.25348e8 | −0.752018 | −0.376009 | − | 0.926616i | \(-0.622704\pi\) | ||||
−0.376009 | + | 0.926616i | \(0.622704\pi\) | |||||||
\(828\) | −3.26889e8 | − | 8.67991e7i | −0.575849 | − | 0.152906i | ||||
\(829\) | −1.52812e8 | −0.268222 | −0.134111 | − | 0.990966i | \(-0.542818\pi\) | ||||
−0.134111 | + | 0.990966i | \(0.542818\pi\) | |||||||
\(830\) | 2.79921e8 | − | 2.57667e8i | 0.489555 | − | 0.450635i | ||||
\(831\) | − | 1.45344e8i | − | 0.253277i | ||||||
\(832\) | −7.14097e8 | + | 7.23835e8i | −1.23990 | + | 1.25681i | ||||
\(833\) | 4.88586e8i | 0.845291i | ||||||||
\(834\) | 3.54615e7 | − | 2.71727e8i | 0.0611307 | − | 0.468418i | ||||
\(835\) | 4.78032e7 | − | 5.71009e7i | 0.0821104 | − | 0.0980806i | ||||
\(836\) | −1.13928e9 | − | 3.02513e8i | −1.94989 | − | 0.517756i | ||||
\(837\) | 845153.i | 0.00144132i | ||||||||
\(838\) | −4.48585e7 | + | 3.43731e8i | −0.0762276 | + | 0.584100i | ||||
\(839\) | − | 3.56914e8i | − | 0.604334i | −0.953255 | − | 0.302167i | \(-0.902290\pi\) | ||
0.953255 | − | 0.302167i | \(-0.0977101\pi\) | |||||||
\(840\) | −1.26782e8 | + | 6.67282e7i | −0.213904 | + | 0.112583i | ||||
\(841\) | 1.01364e9 | 1.70411 | ||||||||
\(842\) | 4.62530e8 | + | 6.03622e7i | 0.774824 | + | 0.101118i | ||||
\(843\) | 4.61148e8 | 0.769765 | ||||||||
\(844\) | 9.28116e7 | − | 3.49532e8i | 0.154374 | − | 0.581379i | ||||
\(845\) | 8.19893e8 | − | 9.79360e8i | 1.35890 | − | 1.62320i | ||||
\(846\) | −2.02323e7 | − | 2.64041e6i | −0.0334145 | − | 0.00436074i | ||||
\(847\) | 9.90173e7 | 0.162952 | ||||||||
\(848\) | 4.06085e8 | − | 7.10751e8i | 0.665931 | − | 1.16555i | ||||
\(849\) | −1.39330e8 | −0.227678 | ||||||||
\(850\) | 6.28754e8 | − | 2.95898e7i | 1.02382 | − | 0.0481821i | ||||
\(851\) | 3.78333e8i | 0.613883i | ||||||||
\(852\) | −4.37056e7 | + | 1.64597e8i | −0.0706673 | + | 0.266135i | ||||
\(853\) | − | 5.26433e8i | − | 0.848195i | −0.905617 | − | 0.424098i | \(-0.860591\pi\) | ||
0.905617 | − | 0.424098i | \(-0.139409\pi\) | |||||||
\(854\) | 2.58092e8 | + | 3.36821e7i | 0.414382 | + | 0.0540786i | ||||
\(855\) | 2.73441e8 | + | 2.28917e8i | 0.437487 | + | 0.366252i | ||||
\(856\) | 3.39840e8 | + | 1.39420e8i | 0.541817 | + | 0.222282i | ||||
\(857\) | 6.08907e8i | 0.967405i | 0.875233 | + | 0.483702i | \(0.160708\pi\) | ||||
−0.875233 | + | 0.483702i | \(0.839292\pi\) | |||||||
\(858\) | −7.52456e8 | − | 9.81989e7i | −1.19130 | − | 0.155469i | ||||
\(859\) | 1.36881e8i | 0.215956i | 0.994153 | + | 0.107978i | \(0.0344376\pi\) | ||||
−0.994153 | + | 0.107978i | \(0.965562\pi\) | |||||||
\(860\) | 2.08973e7 | − | 1.47383e7i | 0.0328545 | − | 0.0231714i | ||||
\(861\) | −4.91940e6 | −0.00770731 | ||||||||
\(862\) | −1.46298e8 | + | 1.12102e9i | −0.228411 | + | 1.75022i | ||||
\(863\) | −1.14016e8 | −0.177391 | −0.0886956 | − | 0.996059i | \(-0.528270\pi\) | ||||
−0.0886956 | + | 0.996059i | \(0.528270\pi\) | |||||||
\(864\) | −9.88999e7 | − | 7.50056e7i | −0.153340 | − | 0.116293i | ||||
\(865\) | 3.72418e8 | + | 3.11778e8i | 0.575416 | + | 0.481722i | ||||
\(866\) | −6.60231e7 | + | 5.05907e8i | −0.101658 | + | 0.778964i | ||||
\(867\) | −1.90135e7 | −0.0291745 | ||||||||
\(868\) | 526258. | − | 1.98191e6i | 0.000804710 | − | 0.00303057i | ||||
\(869\) | −5.85272e8 | −0.891864 | ||||||||
\(870\) | −4.59979e8 | + | 4.23410e8i | −0.698522 | + | 0.642989i | ||||
\(871\) | − | 9.13824e8i | − | 1.38295i | ||||||
\(872\) | −1.61051e8 | − | 6.60715e7i | −0.242893 | − | 0.0996472i | ||||
\(873\) | 2.07840e8i | 0.312382i | ||||||||
\(874\) | 2.64325e8 | − | 2.02541e9i | 0.395916 | − | 3.03374i | ||||
\(875\) | −2.43378e8 | − | 1.39414e8i | −0.363293 | − | 0.208105i | ||||
\(876\) | −6.29415e7 | + | 2.37040e8i | −0.0936320 | + | 0.352622i | ||||
\(877\) | 4.75175e8i | 0.704457i | 0.935914 | + | 0.352229i | \(0.114576\pi\) | ||||
−0.935914 | + | 0.352229i | \(0.885424\pi\) | |||||||
\(878\) | −8.42113e7 | + | 6.45276e8i | −0.124419 | + | 0.953371i | ||||
\(879\) | − | 3.52814e8i | − | 0.519493i | ||||||
\(880\) | 2.78974e8 | + | 7.53212e8i | 0.409369 | + | 1.10527i | ||||
\(881\) | −1.06776e9 | −1.56151 | −0.780755 | − | 0.624837i | \(-0.785165\pi\) | ||||
−0.780755 | + | 0.624837i | \(0.785165\pi\) | |||||||
\(882\) | 1.87033e8 | + | 2.44087e7i | 0.272592 | + | 0.0355745i | ||||
\(883\) | 1.10522e9 | 1.60534 | 0.802671 | − | 0.596422i | \(-0.203411\pi\) | ||||
0.802671 | + | 0.596422i | \(0.203411\pi\) | |||||||
\(884\) | 1.20818e9 | + | 3.20808e8i | 1.74893 | + | 0.464396i | ||||
\(885\) | −2.23792e8 | − | 1.87352e8i | −0.322860 | − | 0.270289i | ||||
\(886\) | 2.33155e8 | + | 3.04277e7i | 0.335230 | + | 0.0437490i | ||||
\(887\) | −1.10318e9 | −1.58079 | −0.790395 | − | 0.612598i | \(-0.790124\pi\) | ||||
−0.790395 | + | 0.612598i | \(0.790124\pi\) | |||||||
\(888\) | −5.27001e7 | + | 1.28458e8i | −0.0752614 | + | 0.183452i | ||||
\(889\) | 1.47926e8 | 0.210543 | ||||||||
\(890\) | 3.09970e8 | − | 2.85327e8i | 0.439693 | − | 0.404737i | ||||
\(891\) | − | 9.26349e7i | − | 0.130961i | ||||||
\(892\) | −7.47787e8 | − | 1.98561e8i | −1.05362 | − | 0.279768i | ||||
\(893\) | − | 1.23225e8i | − | 0.173039i | ||||||
\(894\) | 4.39567e8 | + | 5.73655e7i | 0.615195 | + | 0.0802856i | ||||
\(895\) | −4.57477e8 | − | 3.82987e8i | −0.638116 | − | 0.534213i | ||||
\(896\) | 1.85218e8 | + | 2.37473e8i | 0.257490 | + | 0.330134i | ||||
\(897\) | − | 1.31494e9i | − | 1.82191i | ||||||
\(898\) | 4.87062e7 | + | 6.35637e6i | 0.0672597 | + | 0.00877769i | ||||
\(899\) | − | 8.94812e6i | − | 0.0123155i | ||||||
\(900\) | 2.00840e7 | − | 2.42169e8i | 0.0275501 | − | 0.332193i | ||||
\(901\) | −1.00636e9 | −1.37587 | ||||||||
\(902\) | −3.56900e6 | + | 2.73478e7i | −0.00486326 | + | 0.0372651i | ||||
\(903\) | 7.15560e6 | 0.00971813 | ||||||||
\(904\) | 9.04034e7 | − | 2.20361e8i | 0.122371 | − | 0.298283i | ||||
\(905\) | 4.45920e8 | − | 5.32650e8i | 0.601605 | − | 0.718615i | ||||
\(906\) | 454757. | − | 3.48461e6i | 0.000611497 | − | 0.00468564i | ||||
\(907\) | −9.34213e8 | −1.25206 | −0.626028 | − | 0.779800i | \(-0.715321\pi\) | ||||
−0.626028 | + | 0.779800i | \(0.715321\pi\) | |||||||
\(908\) | 3.43089e8 | + | 9.11008e7i | 0.458299 | + | 0.121693i | ||||
\(909\) | 1.25103e8 | 0.166561 | ||||||||
\(910\) | −3.77240e8 | − | 4.09821e8i | −0.500603 | − | 0.543839i | ||||
\(911\) | − | 1.26470e9i | − | 1.67275i | −0.548155 | − | 0.836377i | \(-0.684669\pi\) | ||
0.548155 | − | 0.836377i | \(-0.315331\pi\) | |||||||
\(912\) | 3.71878e8 | − | 6.50881e8i | 0.490248 | − | 0.858058i | ||||
\(913\) | − | 5.96854e8i | − | 0.784253i | ||||||
\(914\) | 1.87849e7 | − | 1.43941e8i | 0.0246020 | − | 0.188515i | ||||
\(915\) | −2.83383e8 | + | 3.38500e8i | −0.369922 | + | 0.441871i | ||||
\(916\) | −3.60462e8 | − | 9.57139e7i | −0.469000 | − | 0.124534i | ||||
\(917\) | − | 3.46429e8i | − | 0.449269i | ||||||
\(918\) | −1.97473e7 | + | 1.51316e8i | −0.0255259 | + | 0.195594i | ||||
\(919\) | 1.39700e9i | 1.79990i | 0.435993 | + | 0.899950i | \(0.356397\pi\) | ||||
−0.435993 | + | 0.899950i | \(0.643603\pi\) | |||||||
\(920\) | −1.23166e9 | + | 6.48250e8i | −1.58171 | + | 0.832490i | ||||
\(921\) | 1.48643e8 | 0.190269 | ||||||||
\(922\) | −1.25356e9 | − | 1.63595e8i | −1.59938 | − | 0.208726i | ||||
\(923\) | −6.62105e8 | −0.842018 | ||||||||
\(924\) | −5.76817e7 | + | 2.17231e8i | −0.0731176 | + | 0.275363i | ||||
\(925\) | −2.67586e8 | + | 4.78076e7i | −0.338094 | + | 0.0604048i | ||||
\(926\) | −1.03636e9 | − | 1.35250e8i | −1.30521 | − | 0.170335i | ||||
\(927\) | −3.28206e8 | −0.412010 | ||||||||
\(928\) | 1.04711e9 | + | 7.94127e8i | 1.31023 | + | 0.993679i | ||||
\(929\) | −1.13181e9 | −1.41165 | −0.705825 | − | 0.708386i | \(-0.749423\pi\) | ||||
−0.705825 | + | 0.708386i | \(0.749423\pi\) | |||||||
\(930\) | 2.35549e6 | + | 2.55893e6i | 0.00292842 | + | 0.00318134i | ||||
\(931\) | 1.13912e9i | 1.41163i | ||||||||
\(932\) | −1.05822e8 | + | 3.98528e8i | −0.130715 | + | 0.492279i | ||||
\(933\) | − | 2.33067e8i | − | 0.286970i | ||||||
\(934\) | 1.27468e9 | + | 1.66352e8i | 1.56445 | + | 0.204168i | ||||
\(935\) | 6.33876e8 | − | 7.57163e8i | 0.775478 | − | 0.926306i | ||||
\(936\) | 1.83165e8 | − | 4.46469e8i | 0.223365 | − | 0.544457i | ||||
\(937\) | − | 4.15887e8i | − | 0.505541i | −0.967526 | − | 0.252770i | \(-0.918658\pi\) | ||
0.967526 | − | 0.252770i | \(-0.0813417\pi\) | |||||||
\(938\) | −2.68388e8 | − | 3.50259e7i | −0.325203 | − | 0.0424405i | ||||
\(939\) | 8.82123e7i | 0.106545i | ||||||||
\(940\) | −6.86178e7 | + | 4.83941e7i | −0.0826139 | + | 0.0582652i | ||||
\(941\) | −9.66470e8 | −1.15990 | −0.579949 | − | 0.814653i | \(-0.696927\pi\) | ||||
−0.579949 | + | 0.814653i | \(0.696927\pi\) | |||||||
\(942\) | −4.06199e7 | + | 3.11253e8i | −0.0485944 | + | 0.372359i | ||||
\(943\) | −4.77909e7 | −0.0569915 | ||||||||
\(944\) | −3.04355e8 | + | 5.32698e8i | −0.361797 | + | 0.633235i | ||||
\(945\) | 4.36488e7 | − | 5.21384e7i | 0.0517222 | − | 0.0617820i | ||||
\(946\) | 5.19136e6 | − | 3.97792e7i | 0.00613207 | − | 0.0469875i | ||||
\(947\) | 7.38750e8 | 0.869857 | 0.434928 | − | 0.900465i | \(-0.356774\pi\) | ||||
0.434928 | + | 0.900465i | \(0.356774\pi\) | |||||||
\(948\) | 9.55213e7 | − | 3.59736e8i | 0.112118 | − | 0.422240i | ||||
\(949\) | −9.53512e8 | −1.11565 | ||||||||
\(950\) | 1.46592e9 | − | 6.89878e7i | 1.70978 | − | 0.0804640i | ||||
\(951\) | 2.09537e8i | 0.243624i | ||||||||
\(952\) | 1.40529e8 | − | 3.42543e8i | 0.162875 | − | 0.397012i | ||||
\(953\) | − | 1.55167e9i | − | 1.79275i | −0.443293 | − | 0.896377i | \(-0.646190\pi\) | ||
0.443293 | − | 0.896377i | \(-0.353810\pi\) | |||||||
\(954\) | −5.02753e7 | + | 3.85238e8i | −0.0579041 | + | 0.443695i | ||||
\(955\) | −2.64532e8 | − | 2.21459e8i | −0.303716 | − | 0.254263i | ||||
\(956\) | −4.25086e8 | + | 1.60089e9i | −0.486523 | + | 1.83226i | ||||
\(957\) | 9.80778e8i | 1.11901i | ||||||||
\(958\) | 9.00031e7 | − | 6.89656e8i | 0.102367 | − | 0.784397i | ||||
\(959\) | − | 7.57669e7i | − | 0.0859061i | ||||||
\(960\) | −5.08491e8 | + | 4.85401e7i | −0.574738 | + | 0.0548640i | ||||
\(961\) | 8.87454e8 | 0.999944 | ||||||||
\(962\) | −5.35281e8 | − | 6.98566e7i | −0.601253 | − | 0.0784661i | ||||
\(963\) | −1.74337e8 | −0.195214 | ||||||||
\(964\) | 1.48405e9 | + | 3.94063e8i | 1.65660 | + | 0.439880i | ||||
\(965\) | 9.69314e8 | + | 8.11483e8i | 1.07865 | + | 0.903020i | ||||
\(966\) | −3.86195e8 | − | 5.04001e7i | −0.428425 | − | 0.0559114i | ||||
\(967\) | 7.67779e8 | 0.849096 | 0.424548 | − | 0.905405i | \(-0.360433\pi\) | ||||
0.424548 | + | 0.905405i | \(0.360433\pi\) | |||||||
\(968\) | 3.26611e8 | + | 1.33993e8i | 0.360085 | + | 0.147726i | ||||
\(969\) | −9.21586e8 | −1.01290 | ||||||||
\(970\) | 5.79262e8 | + | 6.29292e8i | 0.634688 | + | 0.689504i | ||||
\(971\) | 8.79174e8i | 0.960323i | 0.877180 | + | 0.480161i | \(0.159422\pi\) | ||||
−0.877180 | + | 0.480161i | \(0.840578\pi\) | |||||||
\(972\) | 5.69378e7 | + | 1.51188e7i | 0.0620015 | + | 0.0164633i | ||||
\(973\) | − | 3.15557e8i | − | 0.342562i | ||||||
\(974\) | −7.40636e7 | − | 9.66562e6i | −0.0801545 | − | 0.0104605i | ||||
\(975\) | 9.30023e8 | − | 1.66160e8i | 1.00341 | − | 0.179272i | ||||
\(976\) | 8.05742e8 | + | 4.60358e8i | 0.866656 | + | 0.495161i | ||||
\(977\) | − | 4.02377e8i | − | 0.431469i | −0.976452 | − | 0.215734i | \(-0.930785\pi\) | ||
0.976452 | − | 0.215734i | \(-0.0692146\pi\) | |||||||
\(978\) | 3.02123e8 | + | 3.94284e7i | 0.322974 | + | 0.0421495i | ||||
\(979\) | − | 6.60925e8i | − | 0.704376i | ||||||
\(980\) | 6.34322e8 | − | 4.47369e8i | 0.673956 | − | 0.475322i | ||||
\(981\) | 8.26187e7 | 0.0875127 | ||||||||
\(982\) | −4.38896e7 | + | 3.36308e8i | −0.0463476 | + | 0.355142i | ||||
\(983\) | 2.86965e8 | 0.302112 | 0.151056 | − | 0.988525i | \(-0.451733\pi\) | ||||
0.151056 | + | 0.988525i | \(0.451733\pi\) | |||||||
\(984\) | −1.62268e7 | − | 6.65706e6i | −0.0170312 | − | 0.00698710i | ||||
\(985\) | 5.09491e8 | + | 4.26532e8i | 0.533124 | + | 0.446316i | ||||
\(986\) | 2.09076e8 | − | 1.60206e9i | 0.218109 | − | 1.67128i | ||||
\(987\) | −2.34959e7 | −0.0244366 | ||||||||
\(988\) | 2.81683e9 | + | 7.47955e8i | 2.92072 | + | 0.775541i | ||||
\(989\) | 6.95151e7 | 0.0718605 | ||||||||
\(990\) | −2.58179e8 | − | 2.80477e8i | −0.266082 | − | 0.289062i | ||||
\(991\) | 5.51206e8i | 0.566360i | 0.959067 | + | 0.283180i | \(0.0913894\pi\) | ||||
−0.959067 | + | 0.283180i | \(0.908611\pi\) | |||||||
\(992\) | 4.41784e6 | − | 5.82522e6i | 0.00452559 | − | 0.00596729i | ||||
\(993\) | − | 7.74198e8i | − | 0.790686i | ||||||
\(994\) | −2.53777e7 | + | 1.94459e8i | −0.0258401 | + | 0.198002i | ||||
\(995\) | 9.96669e8 | + | 8.34383e8i | 1.01177 | + | 0.847025i | ||||
\(996\) | 3.66855e8 | + | 9.74115e7i | 0.371293 | + | 0.0985899i | ||||
\(997\) | 7.29498e8i | 0.736103i | 0.929805 | + | 0.368052i | \(0.119975\pi\) | ||||
−0.929805 | + | 0.368052i | \(0.880025\pi\) | |||||||
\(998\) | 2.40018e7 | − | 1.83916e8i | 0.0241464 | − | 0.185023i | ||||
\(999\) | − | 6.58985e7i | − | 0.0660966i |
(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 | 60.7.f.a.19.1 | ✓ | 36 | |
3.2 | odd | 2 | 180.7.f.g.19.36 | 36 | |||
4.3 | odd | 2 | inner | 60.7.f.a.19.35 | yes | 36 | |
5.4 | even | 2 | inner | 60.7.f.a.19.36 | yes | 36 | |
12.11 | even | 2 | 180.7.f.g.19.2 | 36 | |||
15.14 | odd | 2 | 180.7.f.g.19.1 | 36 | |||
20.19 | odd | 2 | inner | 60.7.f.a.19.2 | yes | 36 | |
60.59 | even | 2 | 180.7.f.g.19.35 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.f.a.19.1 | ✓ | 36 | 1.1 | even | 1 | trivial | |
60.7.f.a.19.2 | yes | 36 | 20.19 | odd | 2 | inner | |
60.7.f.a.19.35 | yes | 36 | 4.3 | odd | 2 | inner | |
60.7.f.a.19.36 | yes | 36 | 5.4 | even | 2 | inner | |
180.7.f.g.19.1 | 36 | 15.14 | odd | 2 | |||
180.7.f.g.19.2 | 36 | 12.11 | even | 2 | |||
180.7.f.g.19.35 | 36 | 60.59 | even | 2 | |||
180.7.f.g.19.36 | 36 | 3.2 | odd | 2 |