Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,7,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (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: | \(9.89232559565\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 1038 x^{18} + 455829 x^{16} + 110435384 x^{14} + 16133606976 x^{12} + 1458210485616 x^{10} + \cdots + 64\!\cdots\!40 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.5 | ||
Root | \(-11.0119i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.7.b.b.42.16 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 11.0119i | − | 1.37649i | −0.725478 | − | 0.688245i | \(-0.758381\pi\) | ||
0.725478 | − | 0.688245i | \(-0.241619\pi\) | |||||||
\(3\) | − | 50.0401i | − | 1.85334i | −0.375880 | − | 0.926668i | \(-0.622660\pi\) | ||
0.375880 | − | 0.926668i | \(-0.377340\pi\) | |||||||
\(4\) | −57.2623 | −0.894724 | ||||||||
\(5\) | 30.3065i | 0.242452i | 0.992625 | + | 0.121226i | \(0.0386826\pi\) | ||||
−0.992625 | + | 0.121226i | \(0.961317\pi\) | |||||||
\(6\) | −551.037 | −2.55110 | ||||||||
\(7\) | − | 75.1486i | − | 0.219092i | −0.993982 | − | 0.109546i | \(-0.965060\pi\) | ||
0.993982 | − | 0.109546i | \(-0.0349397\pi\) | |||||||
\(8\) | − | 74.1946i | − | 0.144911i | ||||||
\(9\) | −1775.01 | −2.43486 | ||||||||
\(10\) | 333.733 | 0.333733 | ||||||||
\(11\) | 604.862 | 0.454442 | 0.227221 | − | 0.973843i | \(-0.427036\pi\) | ||||
0.227221 | + | 0.973843i | \(0.427036\pi\) | |||||||
\(12\) | 2865.41i | 1.65822i | ||||||||
\(13\) | 2635.68 | 1.19967 | 0.599836 | − | 0.800123i | \(-0.295233\pi\) | ||||
0.599836 | + | 0.800123i | \(0.295233\pi\) | |||||||
\(14\) | −827.530 | −0.301578 | ||||||||
\(15\) | 1516.54 | 0.449345 | ||||||||
\(16\) | −4481.81 | −1.09419 | ||||||||
\(17\) | 4989.55 | 1.01558 | 0.507791 | − | 0.861481i | \(-0.330462\pi\) | ||||
0.507791 | + | 0.861481i | \(0.330462\pi\) | |||||||
\(18\) | 19546.3i | 3.35155i | ||||||||
\(19\) | − | 3038.63i | − | 0.443014i | −0.975159 | − | 0.221507i | \(-0.928902\pi\) | ||
0.975159 | − | 0.221507i | \(-0.0710975\pi\) | |||||||
\(20\) | − | 1735.42i | − | 0.216928i | ||||||
\(21\) | −3760.44 | −0.406051 | ||||||||
\(22\) | − | 6660.70i | − | 0.625535i | ||||||
\(23\) | −12445.5 | −1.02289 | −0.511443 | − | 0.859317i | \(-0.670889\pi\) | ||||
−0.511443 | + | 0.859317i | \(0.670889\pi\) | |||||||
\(24\) | −3712.70 | −0.268569 | ||||||||
\(25\) | 14706.5 | 0.941217 | ||||||||
\(26\) | − | 29023.9i | − | 1.65134i | ||||||
\(27\) | 52342.4i | 2.65927i | ||||||||
\(28\) | 4303.18i | 0.196027i | ||||||||
\(29\) | 4449.10i | 0.182422i | 0.995832 | + | 0.0912111i | \(0.0290738\pi\) | ||||
−0.995832 | + | 0.0912111i | \(0.970926\pi\) | |||||||
\(30\) | − | 16700.0i | − | 0.618519i | ||||||
\(31\) | −29312.5 | −0.983939 | −0.491969 | − | 0.870612i | \(-0.663723\pi\) | ||||
−0.491969 | + | 0.870612i | \(0.663723\pi\) | |||||||
\(32\) | 44604.9i | 1.36123i | ||||||||
\(33\) | − | 30267.4i | − | 0.842234i | ||||||
\(34\) | − | 54944.5i | − | 1.39794i | ||||||
\(35\) | 2277.49 | 0.0531193 | ||||||||
\(36\) | 101641. | 2.17852 | ||||||||
\(37\) | − | 83027.3i | − | 1.63914i | −0.572980 | − | 0.819570i | \(-0.694213\pi\) | ||
0.572980 | − | 0.819570i | \(-0.305787\pi\) | |||||||
\(38\) | −33461.2 | −0.609804 | ||||||||
\(39\) | − | 131890.i | − | 2.22339i | ||||||
\(40\) | 2248.58 | 0.0351340 | ||||||||
\(41\) | −33442.2 | −0.485225 | −0.242612 | − | 0.970123i | \(-0.578004\pi\) | ||||
−0.242612 | + | 0.970123i | \(0.578004\pi\) | |||||||
\(42\) | 41409.7i | 0.558925i | ||||||||
\(43\) | 30046.7 | + | 73610.9i | 0.377912 | + | 0.925841i | ||||
\(44\) | −34635.8 | −0.406600 | ||||||||
\(45\) | − | 53794.4i | − | 0.590336i | ||||||
\(46\) | 137048.i | 1.40799i | ||||||||
\(47\) | −157085. | −1.51301 | −0.756503 | − | 0.653991i | \(-0.773093\pi\) | ||||
−0.756503 | + | 0.653991i | \(0.773093\pi\) | |||||||
\(48\) | 224270.i | 2.02791i | ||||||||
\(49\) | 112002. | 0.951999 | ||||||||
\(50\) | − | 161947.i | − | 1.29558i | ||||||
\(51\) | − | 249678.i | − | 1.88221i | ||||||
\(52\) | −150925. | −1.07337 | ||||||||
\(53\) | 212620. | 1.42816 | 0.714078 | − | 0.700066i | \(-0.246846\pi\) | ||||
0.714078 | + | 0.700066i | \(0.246846\pi\) | |||||||
\(54\) | 576391. | 3.66046 | ||||||||
\(55\) | 18331.3i | 0.110180i | ||||||||
\(56\) | −5575.61 | −0.0317489 | ||||||||
\(57\) | −152053. | −0.821054 | ||||||||
\(58\) | 48993.1 | 0.251102 | ||||||||
\(59\) | −263304. | −1.28204 | −0.641019 | − | 0.767525i | \(-0.721488\pi\) | ||||
−0.641019 | + | 0.767525i | \(0.721488\pi\) | |||||||
\(60\) | −86840.7 | −0.402040 | ||||||||
\(61\) | 133532.i | 0.588296i | 0.955760 | + | 0.294148i | \(0.0950359\pi\) | ||||
−0.955760 | + | 0.294148i | \(0.904964\pi\) | |||||||
\(62\) | 322787.i | 1.35438i | ||||||||
\(63\) | 133389.i | 0.533457i | ||||||||
\(64\) | 204350. | 0.779532 | ||||||||
\(65\) | 79878.2i | 0.290863i | ||||||||
\(66\) | −333302. | −1.15933 | ||||||||
\(67\) | −157955. | −0.525182 | −0.262591 | − | 0.964907i | \(-0.584577\pi\) | ||||
−0.262591 | + | 0.964907i | \(0.584577\pi\) | |||||||
\(68\) | −285713. | −0.908665 | ||||||||
\(69\) | 622771.i | 1.89575i | ||||||||
\(70\) | − | 25079.5i | − | 0.0731182i | ||||||
\(71\) | − | 485322.i | − | 1.35599i | −0.735068 | − | 0.677993i | \(-0.762850\pi\) | ||
0.735068 | − | 0.677993i | \(-0.237150\pi\) | |||||||
\(72\) | 131696.i | 0.352838i | ||||||||
\(73\) | 48573.5i | 0.124862i | 0.998049 | + | 0.0624310i | \(0.0198853\pi\) | ||||
−0.998049 | + | 0.0624310i | \(0.980115\pi\) | |||||||
\(74\) | −914290. | −2.25626 | ||||||||
\(75\) | − | 735915.i | − | 1.74439i | ||||||
\(76\) | 173999.i | 0.396375i | ||||||||
\(77\) | − | 45454.5i | − | 0.0995646i | ||||||
\(78\) | −1.45236e6 | −3.06048 | ||||||||
\(79\) | 762200. | 1.54592 | 0.772961 | − | 0.634454i | \(-0.218775\pi\) | ||||
0.772961 | + | 0.634454i | \(0.218775\pi\) | |||||||
\(80\) | − | 135828.i | − | 0.265289i | ||||||
\(81\) | 1.32524e6 | 2.49367 | ||||||||
\(82\) | 368262.i | 0.667907i | ||||||||
\(83\) | 268573. | 0.469708 | 0.234854 | − | 0.972031i | \(-0.424539\pi\) | ||||
0.234854 | + | 0.972031i | \(0.424539\pi\) | |||||||
\(84\) | 215332. | 0.363304 | ||||||||
\(85\) | 151216.i | 0.246230i | ||||||||
\(86\) | 810597. | − | 330872.i | 1.27441 | − | 0.520192i | ||||
\(87\) | 222633. | 0.338090 | ||||||||
\(88\) | − | 44877.5i | − | 0.0658538i | ||||||
\(89\) | − | 1.32878e6i | − | 1.88488i | −0.334381 | − | 0.942438i | \(-0.608527\pi\) | ||
0.334381 | − | 0.942438i | \(-0.391473\pi\) | |||||||
\(90\) | −592379. | −0.812592 | ||||||||
\(91\) | − | 198067.i | − | 0.262838i | ||||||
\(92\) | 712656. | 0.915201 | ||||||||
\(93\) | 1.46680e6i | 1.82357i | ||||||||
\(94\) | 1.72980e6i | 2.08264i | ||||||||
\(95\) | 92090.4 | 0.107410 | ||||||||
\(96\) | 2.23203e6 | 2.52282 | ||||||||
\(97\) | 1.43066e6 | 1.56755 | 0.783774 | − | 0.621046i | \(-0.213292\pi\) | ||||
0.783774 | + | 0.621046i | \(0.213292\pi\) | |||||||
\(98\) | − | 1.23335e6i | − | 1.31042i | ||||||
\(99\) | −1.07364e6 | −1.10650 | ||||||||
\(100\) | −842129. | −0.842129 | ||||||||
\(101\) | 909346. | 0.882602 | 0.441301 | − | 0.897359i | \(-0.354517\pi\) | ||||
0.441301 | + | 0.897359i | \(0.354517\pi\) | |||||||
\(102\) | −2.74943e6 | −2.59085 | ||||||||
\(103\) | 634146. | 0.580333 | 0.290167 | − | 0.956976i | \(-0.406289\pi\) | ||||
0.290167 | + | 0.956976i | \(0.406289\pi\) | |||||||
\(104\) | − | 195553.i | − | 0.173846i | ||||||
\(105\) | − | 113966.i | − | 0.0984480i | ||||||
\(106\) | − | 2.34135e6i | − | 1.96584i | ||||||
\(107\) | −481718. | −0.393225 | −0.196613 | − | 0.980481i | \(-0.562994\pi\) | ||||
−0.196613 | + | 0.980481i | \(0.562994\pi\) | |||||||
\(108\) | − | 2.99725e6i | − | 2.37931i | ||||||
\(109\) | 1.74683e6 | 1.34888 | 0.674438 | − | 0.738332i | \(-0.264386\pi\) | ||||
0.674438 | + | 0.738332i | \(0.264386\pi\) | |||||||
\(110\) | 201863. | 0.151662 | ||||||||
\(111\) | −4.15469e6 | −3.03788 | ||||||||
\(112\) | 336802.i | 0.239729i | ||||||||
\(113\) | − | 1.35156e6i | − | 0.936701i | −0.883543 | − | 0.468350i | \(-0.844849\pi\) | ||
0.883543 | − | 0.468350i | \(-0.155151\pi\) | |||||||
\(114\) | 1.67440e6i | 1.13017i | ||||||||
\(115\) | − | 377178.i | − | 0.248001i | ||||||
\(116\) | − | 254766.i | − | 0.163218i | ||||||
\(117\) | −4.67835e6 | −2.92103 | ||||||||
\(118\) | 2.89948e6i | 1.76471i | ||||||||
\(119\) | − | 374958.i | − | 0.222506i | ||||||
\(120\) | − | 112519.i | − | 0.0651152i | ||||||
\(121\) | −1.40570e6 | −0.793482 | ||||||||
\(122\) | 1.47044e6 | 0.809783 | ||||||||
\(123\) | 1.67345e6i | 0.899284i | ||||||||
\(124\) | 1.67850e6 | 0.880354 | ||||||||
\(125\) | 919243.i | 0.470652i | ||||||||
\(126\) | 1.46887e6 | 0.734299 | ||||||||
\(127\) | −376971. | −0.184034 | −0.0920168 | − | 0.995757i | \(-0.529331\pi\) | ||||
−0.0920168 | + | 0.995757i | \(0.529331\pi\) | |||||||
\(128\) | 604434.i | 0.288216i | ||||||||
\(129\) | 3.68349e6 | − | 1.50354e6i | 1.71590 | − | 0.700399i | ||||
\(130\) | 879613. | 0.400370 | ||||||||
\(131\) | 1.97348e6i | 0.877847i | 0.898524 | + | 0.438923i | \(0.144640\pi\) | ||||
−0.898524 | + | 0.438923i | \(0.855360\pi\) | |||||||
\(132\) | 1.73318e6i | 0.753567i | ||||||||
\(133\) | −228349. | −0.0970608 | ||||||||
\(134\) | 1.73939e6i | 0.722907i | ||||||||
\(135\) | −1.58632e6 | −0.644746 | ||||||||
\(136\) | − | 370197.i | − | 0.147169i | ||||||
\(137\) | − | 3.58675e6i | − | 1.39489i | −0.716638 | − | 0.697445i | \(-0.754320\pi\) | ||
0.716638 | − | 0.697445i | \(-0.245680\pi\) | |||||||
\(138\) | 6.85791e6 | 2.60948 | ||||||||
\(139\) | −952415. | −0.354635 | −0.177318 | − | 0.984154i | \(-0.556742\pi\) | ||||
−0.177318 | + | 0.984154i | \(0.556742\pi\) | |||||||
\(140\) | −130414. | −0.0475271 | ||||||||
\(141\) | 7.86053e6i | 2.80411i | ||||||||
\(142\) | −5.34433e6 | −1.86650 | ||||||||
\(143\) | 1.59422e6 | 0.545181 | ||||||||
\(144\) | 7.95527e6 | 2.66420 | ||||||||
\(145\) | −134837. | −0.0442287 | ||||||||
\(146\) | 534887. | 0.171871 | ||||||||
\(147\) | − | 5.60457e6i | − | 1.76437i | ||||||
\(148\) | 4.75434e6i | 1.46658i | ||||||||
\(149\) | 3.30681e6i | 0.999656i | 0.866125 | + | 0.499828i | \(0.166604\pi\) | ||||
−0.866125 | + | 0.499828i | \(0.833396\pi\) | |||||||
\(150\) | −8.10384e6 | −2.40114 | ||||||||
\(151\) | 5.46323e6i | 1.58679i | 0.608709 | + | 0.793393i | \(0.291688\pi\) | ||||
−0.608709 | + | 0.793393i | \(0.708312\pi\) | |||||||
\(152\) | −225450. | −0.0641977 | ||||||||
\(153\) | −8.85650e6 | −2.47279 | ||||||||
\(154\) | −500542. | −0.137050 | ||||||||
\(155\) | − | 888361.i | − | 0.238558i | ||||||
\(156\) | 7.55230e6i | 1.98932i | ||||||||
\(157\) | − | 833342.i | − | 0.215340i | −0.994187 | − | 0.107670i | \(-0.965661\pi\) | ||
0.994187 | − | 0.107670i | \(-0.0343390\pi\) | |||||||
\(158\) | − | 8.39328e6i | − | 2.12795i | ||||||
\(159\) | − | 1.06395e7i | − | 2.64685i | ||||||
\(160\) | −1.35182e6 | −0.330034 | ||||||||
\(161\) | 935258.i | 0.224106i | ||||||||
\(162\) | − | 1.45934e7i | − | 3.43251i | ||||||
\(163\) | − | 1.39941e6i | − | 0.323134i | −0.986862 | − | 0.161567i | \(-0.948345\pi\) | ||
0.986862 | − | 0.161567i | \(-0.0516547\pi\) | |||||||
\(164\) | 1.91498e6 | 0.434142 | ||||||||
\(165\) | 917299. | 0.204202 | ||||||||
\(166\) | − | 2.95750e6i | − | 0.646548i | ||||||
\(167\) | 6.41130e6 | 1.37657 | 0.688283 | − | 0.725442i | \(-0.258365\pi\) | ||||
0.688283 | + | 0.725442i | \(0.258365\pi\) | |||||||
\(168\) | 279004.i | 0.0588414i | ||||||||
\(169\) | 2.11999e6 | 0.439211 | ||||||||
\(170\) | 1.66518e6 | 0.338933 | ||||||||
\(171\) | 5.39360e6i | 1.07867i | ||||||||
\(172\) | −1.72054e6 | − | 4.21513e6i | −0.338127 | − | 0.828373i | ||||
\(173\) | −5.06186e6 | −0.977624 | −0.488812 | − | 0.872389i | \(-0.662570\pi\) | ||||
−0.488812 | + | 0.872389i | \(0.662570\pi\) | |||||||
\(174\) | − | 2.45162e6i | − | 0.465377i | ||||||
\(175\) | − | 1.10517e6i | − | 0.206213i | ||||||
\(176\) | −2.71088e6 | −0.497247 | ||||||||
\(177\) | 1.31757e7i | 2.37605i | ||||||||
\(178\) | −1.46324e7 | −2.59451 | ||||||||
\(179\) | 428340.i | 0.0746843i | 0.999303 | + | 0.0373422i | \(0.0118891\pi\) | ||||
−0.999303 | + | 0.0373422i | \(0.988111\pi\) | |||||||
\(180\) | 3.08039e6i | 0.528188i | ||||||||
\(181\) | 2.17931e6 | 0.367522 | 0.183761 | − | 0.982971i | \(-0.441173\pi\) | ||||
0.183761 | + | 0.982971i | \(0.441173\pi\) | |||||||
\(182\) | −2.18110e6 | −0.361794 | ||||||||
\(183\) | 6.68195e6 | 1.09031 | ||||||||
\(184\) | 923385.i | 0.148228i | ||||||||
\(185\) | 2.51627e6 | 0.397413 | ||||||||
\(186\) | 1.61523e7 | 2.51013 | ||||||||
\(187\) | 3.01799e6 | 0.461523 | ||||||||
\(188\) | 8.99504e6 | 1.35372 | ||||||||
\(189\) | 3.93346e6 | 0.582625 | ||||||||
\(190\) | − | 1.01409e6i | − | 0.147848i | ||||||
\(191\) | 4.92816e6i | 0.707269i | 0.935384 | + | 0.353635i | \(0.115054\pi\) | ||||
−0.935384 | + | 0.353635i | \(0.884946\pi\) | |||||||
\(192\) | − | 1.02257e7i | − | 1.44473i | ||||||
\(193\) | −3.40731e6 | −0.473958 | −0.236979 | − | 0.971515i | \(-0.576157\pi\) | ||||
−0.236979 | + | 0.971515i | \(0.576157\pi\) | |||||||
\(194\) | − | 1.57543e7i | − | 2.15772i | ||||||
\(195\) | 3.99711e6 | 0.539067 | ||||||||
\(196\) | −6.41348e6 | −0.851776 | ||||||||
\(197\) | −646332. | −0.0845390 | −0.0422695 | − | 0.999106i | \(-0.513459\pi\) | ||||
−0.0422695 | + | 0.999106i | \(0.513459\pi\) | |||||||
\(198\) | 1.18228e7i | 1.52309i | ||||||||
\(199\) | − | 6.52813e6i | − | 0.828379i | −0.910191 | − | 0.414190i | \(-0.864065\pi\) | ||
0.910191 | − | 0.414190i | \(-0.135935\pi\) | |||||||
\(200\) | − | 1.09114e6i | − | 0.136393i | ||||||
\(201\) | 7.90409e6i | 0.973338i | ||||||||
\(202\) | − | 1.00136e7i | − | 1.21489i | ||||||
\(203\) | 334343. | 0.0399673 | ||||||||
\(204\) | 1.42971e7i | 1.68406i | ||||||||
\(205\) | − | 1.01352e6i | − | 0.117644i | ||||||
\(206\) | − | 6.98316e6i | − | 0.798823i | ||||||
\(207\) | 2.20908e7 | 2.49058 | ||||||||
\(208\) | −1.18126e7 | −1.31267 | ||||||||
\(209\) | − | 1.83795e6i | − | 0.201324i | ||||||
\(210\) | −1.25498e6 | −0.135513 | ||||||||
\(211\) | 2.63536e6i | 0.280539i | 0.990113 | + | 0.140269i | \(0.0447968\pi\) | ||||
−0.990113 | + | 0.140269i | \(0.955203\pi\) | |||||||
\(212\) | −1.21751e7 | −1.27781 | ||||||||
\(213\) | −2.42856e7 | −2.51310 | ||||||||
\(214\) | 5.30464e6i | 0.541271i | ||||||||
\(215\) | −2.23089e6 | + | 910610.i | −0.224472 | + | 0.0916257i | ||||
\(216\) | 3.88352e6 | 0.385358 | ||||||||
\(217\) | 2.20279e6i | 0.215573i | ||||||||
\(218\) | − | 1.92360e7i | − | 1.85671i | ||||||
\(219\) | 2.43062e6 | 0.231411 | ||||||||
\(220\) | − | 1.04969e6i | − | 0.0985811i | ||||||
\(221\) | 1.31508e7 | 1.21836 | ||||||||
\(222\) | 4.57512e7i | 4.18161i | ||||||||
\(223\) | 1.69760e7i | 1.53081i | 0.643551 | + | 0.765403i | \(0.277460\pi\) | ||||
−0.643551 | + | 0.765403i | \(0.722540\pi\) | |||||||
\(224\) | 3.35200e6 | 0.298235 | ||||||||
\(225\) | −2.61042e7 | −2.29173 | ||||||||
\(226\) | −1.48833e7 | −1.28936 | ||||||||
\(227\) | − | 1.01092e7i | − | 0.864247i | −0.901814 | − | 0.432124i | \(-0.857764\pi\) | ||
0.901814 | − | 0.432124i | \(-0.142236\pi\) | |||||||
\(228\) | 8.70693e6 | 0.734616 | ||||||||
\(229\) | 7.19101e6 | 0.598802 | 0.299401 | − | 0.954127i | \(-0.403213\pi\) | ||||
0.299401 | + | 0.954127i | \(0.403213\pi\) | |||||||
\(230\) | −4.15346e6 | −0.341371 | ||||||||
\(231\) | −2.27455e6 | −0.184527 | ||||||||
\(232\) | 330099. | 0.0264350 | ||||||||
\(233\) | − | 1.30168e7i | − | 1.02905i | −0.857475 | − | 0.514526i | \(-0.827968\pi\) | ||
0.857475 | − | 0.514526i | \(-0.172032\pi\) | |||||||
\(234\) | 5.15177e7i | 4.02076i | ||||||||
\(235\) | − | 4.76069e6i | − | 0.366831i | ||||||
\(236\) | 1.50774e7 | 1.14707 | ||||||||
\(237\) | − | 3.81405e7i | − | 2.86511i | ||||||
\(238\) | −4.12900e6 | −0.306277 | ||||||||
\(239\) | −5.98455e6 | −0.438367 | −0.219183 | − | 0.975684i | \(-0.570339\pi\) | ||||
−0.219183 | + | 0.975684i | \(0.570339\pi\) | |||||||
\(240\) | −6.79686e6 | −0.491671 | ||||||||
\(241\) | 1.94706e7i | 1.39101i | 0.718523 | + | 0.695503i | \(0.244818\pi\) | ||||
−0.718523 | + | 0.695503i | \(0.755182\pi\) | |||||||
\(242\) | 1.54795e7i | 1.09222i | ||||||||
\(243\) | − | 2.81574e7i | − | 1.96233i | ||||||
\(244\) | − | 7.64636e6i | − | 0.526363i | ||||||
\(245\) | 3.39438e6i | 0.230814i | ||||||||
\(246\) | 1.84279e7 | 1.23786 | ||||||||
\(247\) | − | 8.00885e6i | − | 0.531471i | ||||||
\(248\) | 2.17483e6i | 0.142584i | ||||||||
\(249\) | − | 1.34394e7i | − | 0.870527i | ||||||
\(250\) | 1.01226e7 | 0.647848 | ||||||||
\(251\) | −6.05694e6 | −0.383029 | −0.191515 | − | 0.981490i | \(-0.561340\pi\) | ||||
−0.191515 | + | 0.981490i | \(0.561340\pi\) | |||||||
\(252\) | − | 7.63819e6i | − | 0.477297i | ||||||
\(253\) | −7.52779e6 | −0.464842 | ||||||||
\(254\) | 4.15118e6i | 0.253320i | ||||||||
\(255\) | 7.56686e6 | 0.456347 | ||||||||
\(256\) | 1.97343e7 | 1.17626 | ||||||||
\(257\) | 1.73952e7i | 1.02478i | 0.858754 | + | 0.512388i | \(0.171239\pi\) | ||||
−0.858754 | + | 0.512388i | \(0.828761\pi\) | |||||||
\(258\) | −1.65568e7 | − | 4.05623e7i | −0.964092 | − | 2.36191i | ||||
\(259\) | −6.23938e6 | −0.359122 | ||||||||
\(260\) | − | 4.57402e6i | − | 0.260242i | ||||||
\(261\) | − | 7.89719e6i | − | 0.444172i | ||||||
\(262\) | 2.17318e7 | 1.20835 | ||||||||
\(263\) | 2.18225e7i | 1.19960i | 0.800149 | + | 0.599801i | \(0.204754\pi\) | ||||
−0.800149 | + | 0.599801i | \(0.795246\pi\) | |||||||
\(264\) | −2.24567e6 | −0.122049 | ||||||||
\(265\) | 6.44376e6i | 0.346259i | ||||||||
\(266\) | 2.51456e6i | 0.133603i | ||||||||
\(267\) | −6.64922e7 | −3.49331 | ||||||||
\(268\) | 9.04488e6 | 0.469893 | ||||||||
\(269\) | 759715. | 0.0390296 | 0.0195148 | − | 0.999810i | \(-0.493788\pi\) | ||||
0.0195148 | + | 0.999810i | \(0.493788\pi\) | |||||||
\(270\) | 1.74684e7i | 0.887486i | ||||||||
\(271\) | 3.82518e7 | 1.92196 | 0.960978 | − | 0.276624i | \(-0.0892155\pi\) | ||||
0.960978 | + | 0.276624i | \(0.0892155\pi\) | |||||||
\(272\) | −2.23622e7 | −1.11124 | ||||||||
\(273\) | −9.91131e6 | −0.487128 | ||||||||
\(274\) | −3.94970e7 | −1.92005 | ||||||||
\(275\) | 8.89542e6 | 0.427729 | ||||||||
\(276\) | − | 3.56614e7i | − | 1.69617i | ||||||
\(277\) | 2.70372e7i | 1.27210i | 0.771647 | + | 0.636052i | \(0.219433\pi\) | ||||
−0.771647 | + | 0.636052i | \(0.780567\pi\) | |||||||
\(278\) | 1.04879e7i | 0.488152i | ||||||||
\(279\) | 5.20300e7 | 2.39575 | ||||||||
\(280\) | − | 168977.i | − | 0.00769759i | ||||||
\(281\) | −1.84904e7 | −0.833352 | −0.416676 | − | 0.909055i | \(-0.636805\pi\) | ||||
−0.416676 | + | 0.909055i | \(0.636805\pi\) | |||||||
\(282\) | 8.65595e7 | 3.85983 | ||||||||
\(283\) | 3.01118e7 | 1.32855 | 0.664274 | − | 0.747489i | \(-0.268741\pi\) | ||||
0.664274 | + | 0.747489i | \(0.268741\pi\) | |||||||
\(284\) | 2.77907e7i | 1.21323i | ||||||||
\(285\) | − | 4.60821e6i | − | 0.199066i | ||||||
\(286\) | − | 1.75555e7i | − | 0.750436i | ||||||
\(287\) | 2.51313e6i | 0.106309i | ||||||||
\(288\) | − | 7.91742e7i | − | 3.31441i | ||||||
\(289\) | 758046. | 0.0314052 | ||||||||
\(290\) | 1.48481e6i | 0.0608803i | ||||||||
\(291\) | − | 7.15903e7i | − | 2.90520i | ||||||
\(292\) | − | 2.78143e6i | − | 0.111717i | ||||||
\(293\) | 1.61065e6 | 0.0640324 | 0.0320162 | − | 0.999487i | \(-0.489807\pi\) | ||||
0.0320162 | + | 0.999487i | \(0.489807\pi\) | |||||||
\(294\) | −6.17171e7 | −2.42864 | ||||||||
\(295\) | − | 7.97982e6i | − | 0.310833i | ||||||
\(296\) | −6.16018e6 | −0.237530 | ||||||||
\(297\) | 3.16600e7i | 1.20848i | ||||||||
\(298\) | 3.64143e7 | 1.37602 | ||||||||
\(299\) | −3.28022e7 | −1.22713 | ||||||||
\(300\) | 4.21402e7i | 1.56075i | ||||||||
\(301\) | 5.53175e6 | − | 2.25796e6i | 0.202844 | − | 0.0827976i | ||||
\(302\) | 6.01606e7 | 2.18420 | ||||||||
\(303\) | − | 4.55037e7i | − | 1.63576i | ||||||
\(304\) | 1.36186e7i | 0.484743i | ||||||||
\(305\) | −4.04689e6 | −0.142634 | ||||||||
\(306\) | 9.75271e7i | 3.40378i | ||||||||
\(307\) | 3.91736e7 | 1.35388 | 0.676938 | − | 0.736040i | \(-0.263307\pi\) | ||||
0.676938 | + | 0.736040i | \(0.263307\pi\) | |||||||
\(308\) | 2.60283e6i | 0.0890829i | ||||||||
\(309\) | − | 3.17327e7i | − | 1.07555i | ||||||
\(310\) | −9.78256e6 | −0.328373 | ||||||||
\(311\) | −2.65437e7 | −0.882429 | −0.441215 | − | 0.897402i | \(-0.645452\pi\) | ||||
−0.441215 | + | 0.897402i | \(0.645452\pi\) | |||||||
\(312\) | −9.78549e6 | −0.322195 | ||||||||
\(313\) | 3.65208e7i | 1.19099i | 0.803359 | + | 0.595495i | \(0.203044\pi\) | ||||
−0.803359 | + | 0.595495i | \(0.796956\pi\) | |||||||
\(314\) | −9.17669e6 | −0.296413 | ||||||||
\(315\) | −4.04257e6 | −0.129338 | ||||||||
\(316\) | −4.36453e7 | −1.38317 | ||||||||
\(317\) | 3.58851e7 | 1.12651 | 0.563257 | − | 0.826282i | \(-0.309548\pi\) | ||||
0.563257 | + | 0.826282i | \(0.309548\pi\) | |||||||
\(318\) | −1.17161e8 | −3.64337 | ||||||||
\(319\) | 2.69109e6i | 0.0829004i | ||||||||
\(320\) | 6.19313e6i | 0.188999i | ||||||||
\(321\) | 2.41052e7i | 0.728779i | ||||||||
\(322\) | 1.02990e7 | 0.308480 | ||||||||
\(323\) | − | 1.51614e7i | − | 0.449916i | ||||||
\(324\) | −7.58862e7 | −2.23114 | ||||||||
\(325\) | 3.87616e7 | 1.12915 | ||||||||
\(326\) | −1.54102e7 | −0.444790 | ||||||||
\(327\) | − | 8.74117e7i | − | 2.49992i | ||||||
\(328\) | 2.48123e6i | 0.0703145i | ||||||||
\(329\) | 1.18047e7i | 0.331487i | ||||||||
\(330\) | − | 1.01012e7i | − | 0.281081i | ||||||
\(331\) | − | 4.13224e7i | − | 1.13947i | −0.821829 | − | 0.569734i | \(-0.807046\pi\) | ||
0.821829 | − | 0.569734i | \(-0.192954\pi\) | |||||||
\(332\) | −1.53791e7 | −0.420259 | ||||||||
\(333\) | 1.47374e8i | 3.99107i | ||||||||
\(334\) | − | 7.06008e7i | − | 1.89483i | ||||||
\(335\) | − | 4.78707e6i | − | 0.127331i | ||||||
\(336\) | 1.68536e7 | 0.444298 | ||||||||
\(337\) | 5.37649e7 | 1.40478 | 0.702392 | − | 0.711790i | \(-0.252115\pi\) | ||||
0.702392 | + | 0.711790i | \(0.252115\pi\) | |||||||
\(338\) | − | 2.33452e7i | − | 0.604570i | ||||||
\(339\) | −6.76323e7 | −1.73602 | ||||||||
\(340\) | − | 8.65898e6i | − | 0.220308i | ||||||
\(341\) | −1.77300e7 | −0.447143 | ||||||||
\(342\) | 5.93939e7 | 1.48478 | ||||||||
\(343\) | − | 1.72579e7i | − | 0.427667i | ||||||
\(344\) | 5.46153e6 | − | 2.22930e6i | 0.134165 | − | 0.0547637i | ||||
\(345\) | −1.88740e7 | −0.459629 | ||||||||
\(346\) | 5.57408e7i | 1.34569i | ||||||||
\(347\) | 7.03541e7i | 1.68384i | 0.539603 | + | 0.841920i | \(0.318574\pi\) | ||||
−0.539603 | + | 0.841920i | \(0.681426\pi\) | |||||||
\(348\) | −1.27485e7 | −0.302497 | ||||||||
\(349\) | − | 5.74051e7i | − | 1.35044i | −0.737618 | − | 0.675218i | \(-0.764049\pi\) | ||
0.737618 | − | 0.675218i | \(-0.235951\pi\) | |||||||
\(350\) | −1.21701e7 | −0.283850 | ||||||||
\(351\) | 1.37958e8i | 3.19025i | ||||||||
\(352\) | 2.69798e7i | 0.618602i | ||||||||
\(353\) | −6.11985e7 | −1.39129 | −0.695644 | − | 0.718387i | \(-0.744881\pi\) | ||||
−0.695644 | + | 0.718387i | \(0.744881\pi\) | |||||||
\(354\) | 1.45090e8 | 3.27061 | ||||||||
\(355\) | 1.47084e7 | 0.328762 | ||||||||
\(356\) | 7.60890e7i | 1.68644i | ||||||||
\(357\) | −1.87629e7 | −0.412378 | ||||||||
\(358\) | 4.71684e6 | 0.102802 | ||||||||
\(359\) | 1.65832e7 | 0.358414 | 0.179207 | − | 0.983811i | \(-0.442647\pi\) | ||||
0.179207 | + | 0.983811i | \(0.442647\pi\) | |||||||
\(360\) | −3.99125e6 | −0.0855464 | ||||||||
\(361\) | 3.78126e7 | 0.803739 | ||||||||
\(362\) | − | 2.39984e7i | − | 0.505891i | ||||||
\(363\) | 7.03415e7i | 1.47059i | ||||||||
\(364\) | 1.13418e7i | 0.235168i | ||||||||
\(365\) | −1.47209e6 | −0.0302731 | ||||||||
\(366\) | − | 7.35811e7i | − | 1.50080i | ||||||
\(367\) | −7.49850e6 | −0.151697 | −0.0758484 | − | 0.997119i | \(-0.524166\pi\) | ||||
−0.0758484 | + | 0.997119i | \(0.524166\pi\) | |||||||
\(368\) | 5.57782e7 | 1.11923 | ||||||||
\(369\) | 5.93602e7 | 1.18145 | ||||||||
\(370\) | − | 2.77090e7i | − | 0.547035i | ||||||
\(371\) | − | 1.59780e7i | − | 0.312897i | ||||||
\(372\) | − | 8.39925e7i | − | 1.63159i | ||||||
\(373\) | − | 2.28773e7i | − | 0.440837i | −0.975405 | − | 0.220419i | \(-0.929258\pi\) | ||
0.975405 | − | 0.220419i | \(-0.0707423\pi\) | |||||||
\(374\) | − | 3.32339e7i | − | 0.635282i | ||||||
\(375\) | 4.59990e7 | 0.872277 | ||||||||
\(376\) | 1.16548e7i | 0.219251i | ||||||||
\(377\) | 1.17264e7i | 0.218847i | ||||||||
\(378\) | − | 4.33149e7i | − | 0.801977i | ||||||
\(379\) | −3.49753e7 | −0.642457 | −0.321228 | − | 0.947002i | \(-0.604096\pi\) | ||||
−0.321228 | + | 0.947002i | \(0.604096\pi\) | |||||||
\(380\) | −5.27331e6 | −0.0961020 | ||||||||
\(381\) | 1.88637e7i | 0.341076i | ||||||||
\(382\) | 5.42685e7 | 0.973549 | ||||||||
\(383\) | 3.06385e7i | 0.545345i | 0.962107 | + | 0.272672i | \(0.0879075\pi\) | ||||
−0.962107 | + | 0.272672i | \(0.912093\pi\) | |||||||
\(384\) | 3.02459e7 | 0.534162 | ||||||||
\(385\) | 1.37757e6 | 0.0241397 | ||||||||
\(386\) | 3.75210e7i | 0.652398i | ||||||||
\(387\) | −5.33332e7 | − | 1.30660e8i | −0.920162 | − | 2.25429i | ||||
\(388\) | −8.19229e7 | −1.40252 | ||||||||
\(389\) | − | 8.00209e6i | − | 0.135942i | −0.997687 | − | 0.0679711i | \(-0.978347\pi\) | ||
0.997687 | − | 0.0679711i | \(-0.0216526\pi\) | |||||||
\(390\) | − | 4.40159e7i | − | 0.742020i | ||||||
\(391\) | −6.20972e7 | −1.03882 | ||||||||
\(392\) | − | 8.30992e6i | − | 0.137955i | ||||||
\(393\) | 9.87531e7 | 1.62695 | ||||||||
\(394\) | 7.11736e6i | 0.116367i | ||||||||
\(395\) | 2.30996e7i | 0.374812i | ||||||||
\(396\) | 6.14790e7 | 0.990013 | ||||||||
\(397\) | −7.52627e7 | −1.20284 | −0.601421 | − | 0.798932i | \(-0.705399\pi\) | ||||
−0.601421 | + | 0.798932i | \(0.705399\pi\) | |||||||
\(398\) | −7.18872e7 | −1.14026 | ||||||||
\(399\) | 1.14266e7i | 0.179886i | ||||||||
\(400\) | −6.59119e7 | −1.02987 | ||||||||
\(401\) | −3.64743e7 | −0.565658 | −0.282829 | − | 0.959170i | \(-0.591273\pi\) | ||||
−0.282829 | + | 0.959170i | \(0.591273\pi\) | |||||||
\(402\) | 8.70392e7 | 1.33979 | ||||||||
\(403\) | −7.72584e7 | −1.18040 | ||||||||
\(404\) | −5.20713e7 | −0.789685 | ||||||||
\(405\) | 4.01633e7i | 0.604595i | ||||||||
\(406\) | − | 3.68176e6i | − | 0.0550145i | ||||||
\(407\) | − | 5.02201e7i | − | 0.744894i | ||||||
\(408\) | −1.85247e7 | −0.272754 | ||||||||
\(409\) | − | 1.19043e8i | − | 1.73993i | −0.493111 | − | 0.869966i | \(-0.664140\pi\) | ||
0.493111 | − | 0.869966i | \(-0.335860\pi\) | |||||||
\(410\) | −1.11608e7 | −0.161935 | ||||||||
\(411\) | −1.79481e8 | −2.58520 | ||||||||
\(412\) | −3.63127e7 | −0.519238 | ||||||||
\(413\) | 1.97869e7i | 0.280884i | ||||||||
\(414\) | − | 2.43262e8i | − | 3.42826i | ||||||
\(415\) | 8.13951e6i | 0.113882i | ||||||||
\(416\) | 1.17564e8i | 1.63303i | ||||||||
\(417\) | 4.76589e7i | 0.657258i | ||||||||
\(418\) | −2.02394e7 | −0.277121 | ||||||||
\(419\) | − | 1.30796e8i | − | 1.77809i | −0.457824 | − | 0.889043i | \(-0.651371\pi\) | ||
0.457824 | − | 0.889043i | \(-0.348629\pi\) | |||||||
\(420\) | 6.52595e6i | 0.0880838i | ||||||||
\(421\) | 1.08991e8i | 1.46064i | 0.683105 | + | 0.730320i | \(0.260629\pi\) | ||||
−0.683105 | + | 0.730320i | \(0.739371\pi\) | |||||||
\(422\) | 2.90204e7 | 0.386159 | ||||||||
\(423\) | 2.78827e8 | 3.68395 | ||||||||
\(424\) | − | 1.57752e7i | − | 0.206956i | ||||||
\(425\) | 7.33789e7 | 0.955882 | ||||||||
\(426\) | 2.67431e8i | 3.45925i | ||||||||
\(427\) | 1.00347e7 | 0.128891 | ||||||||
\(428\) | 2.75843e7 | 0.351828 | ||||||||
\(429\) | − | 7.97750e7i | − | 1.01040i | ||||||
\(430\) | 1.00276e7 | + | 2.45664e7i | 0.126122 | + | 0.308984i | ||||
\(431\) | −2.84336e7 | −0.355141 | −0.177570 | − | 0.984108i | \(-0.556824\pi\) | ||||
−0.177570 | + | 0.984108i | \(0.556824\pi\) | |||||||
\(432\) | − | 2.34589e8i | − | 2.90976i | ||||||
\(433\) | 1.31732e7i | 0.162266i | 0.996703 | + | 0.0811330i | \(0.0258539\pi\) | ||||
−0.996703 | + | 0.0811330i | \(0.974146\pi\) | |||||||
\(434\) | 2.42570e7 | 0.296734 | ||||||||
\(435\) | 6.74724e6i | 0.0819706i | ||||||||
\(436\) | −1.00028e8 | −1.20687 | ||||||||
\(437\) | 3.78171e7i | 0.453153i | ||||||||
\(438\) | − | 2.67658e7i | − | 0.318535i | ||||||
\(439\) | 9.21820e7 | 1.08956 | 0.544782 | − | 0.838578i | \(-0.316612\pi\) | ||||
0.544782 | + | 0.838578i | \(0.316612\pi\) | |||||||
\(440\) | 1.36008e6 | 0.0159664 | ||||||||
\(441\) | −1.98804e8 | −2.31798 | ||||||||
\(442\) | − | 1.44816e8i | − | 1.67707i | ||||||
\(443\) | −1.32293e8 | −1.52169 | −0.760843 | − | 0.648935i | \(-0.775214\pi\) | ||||
−0.760843 | + | 0.648935i | \(0.775214\pi\) | |||||||
\(444\) | 2.37908e8 | 2.71806 | ||||||||
\(445\) | 4.02707e7 | 0.456992 | ||||||||
\(446\) | 1.86938e8 | 2.10714 | ||||||||
\(447\) | 1.65473e8 | 1.85270 | ||||||||
\(448\) | − | 1.53566e7i | − | 0.170789i | ||||||
\(449\) | 8.50172e7i | 0.939221i | 0.882874 | + | 0.469610i | \(0.155606\pi\) | ||||
−0.882874 | + | 0.469610i | \(0.844394\pi\) | |||||||
\(450\) | 2.87457e8i | 3.15454i | ||||||||
\(451\) | −2.02279e7 | −0.220506 | ||||||||
\(452\) | 7.73936e7i | 0.838089i | ||||||||
\(453\) | 2.73380e8 | 2.94085 | ||||||||
\(454\) | −1.11321e8 | −1.18963 | ||||||||
\(455\) | 6.00273e6 | 0.0637257 | ||||||||
\(456\) | 1.12815e7i | 0.118980i | ||||||||
\(457\) | − | 923905.i | − | 0.00968008i | −0.999988 | − | 0.00484004i | \(-0.998459\pi\) | ||
0.999988 | − | 0.00484004i | \(-0.00154064\pi\) | |||||||
\(458\) | − | 7.91868e7i | − | 0.824245i | ||||||
\(459\) | 2.61165e8i | 2.70071i | ||||||||
\(460\) | 2.15981e7i | 0.221892i | ||||||||
\(461\) | −6.17034e7 | −0.629806 | −0.314903 | − | 0.949124i | \(-0.601972\pi\) | ||||
−0.314903 | + | 0.949124i | \(0.601972\pi\) | |||||||
\(462\) | 2.50471e7i | 0.253999i | ||||||||
\(463\) | 1.17785e8i | 1.18672i | 0.804938 | + | 0.593358i | \(0.202198\pi\) | ||||
−0.804938 | + | 0.593358i | \(0.797802\pi\) | |||||||
\(464\) | − | 1.99400e7i | − | 0.199605i | ||||||
\(465\) | −4.44536e7 | −0.442129 | ||||||||
\(466\) | −1.43340e8 | −1.41648 | ||||||||
\(467\) | − | 2.00013e6i | − | 0.0196385i | −0.999952 | − | 0.00981923i | \(-0.996874\pi\) | ||
0.999952 | − | 0.00981923i | \(-0.00312561\pi\) | |||||||
\(468\) | 2.67894e8 | 2.61351 | ||||||||
\(469\) | 1.18701e7i | 0.115063i | ||||||||
\(470\) | −5.24243e7 | −0.504940 | ||||||||
\(471\) | −4.17005e7 | −0.399097 | ||||||||
\(472\) | 1.95357e7i | 0.185782i | ||||||||
\(473\) | 1.81741e7 | + | 4.45245e7i | 0.171739 | + | 0.420741i | ||||
\(474\) | −4.20001e8 | −3.94380 | ||||||||
\(475\) | − | 4.46877e7i | − | 0.416972i | ||||||
\(476\) | 2.14709e7i | 0.199081i | ||||||||
\(477\) | −3.77402e8 | −3.47735 | ||||||||
\(478\) | 6.59014e7i | 0.603408i | ||||||||
\(479\) | 5.60261e7 | 0.509781 | 0.254890 | − | 0.966970i | \(-0.417961\pi\) | ||||
0.254890 | + | 0.966970i | \(0.417961\pi\) | |||||||
\(480\) | 6.76452e7i | 0.611664i | ||||||||
\(481\) | − | 2.18833e8i | − | 1.96643i | ||||||
\(482\) | 2.14409e8 | 1.91471 | ||||||||
\(483\) | 4.68004e7 | 0.415344 | ||||||||
\(484\) | 8.04938e7 | 0.709948 | ||||||||
\(485\) | 4.33583e7i | 0.380056i | ||||||||
\(486\) | −3.10066e8 | −2.70113 | ||||||||
\(487\) | −8.02252e7 | −0.694582 | −0.347291 | − | 0.937757i | \(-0.612898\pi\) | ||||
−0.347291 | + | 0.937757i | \(0.612898\pi\) | |||||||
\(488\) | 9.90735e6 | 0.0852507 | ||||||||
\(489\) | −7.00266e7 | −0.598875 | ||||||||
\(490\) | 3.73787e7 | 0.317713 | ||||||||
\(491\) | 4.73660e7i | 0.400149i | 0.979781 | + | 0.200075i | \(0.0641185\pi\) | ||||
−0.979781 | + | 0.200075i | \(0.935882\pi\) | |||||||
\(492\) | − | 9.58256e7i | − | 0.804611i | ||||||
\(493\) | 2.21990e7i | 0.185265i | ||||||||
\(494\) | −8.81928e7 | −0.731564 | ||||||||
\(495\) | − | 3.25382e7i | − | 0.268274i | ||||||
\(496\) | 1.31373e8 | 1.07662 | ||||||||
\(497\) | −3.64713e7 | −0.297086 | ||||||||
\(498\) | −1.47994e8 | −1.19827 | ||||||||
\(499\) | − | 1.29386e8i | − | 1.04132i | −0.853763 | − | 0.520662i | \(-0.825685\pi\) | ||
0.853763 | − | 0.520662i | \(-0.174315\pi\) | |||||||
\(500\) | − | 5.26380e7i | − | 0.421104i | ||||||
\(501\) | − | 3.20822e8i | − | 2.55124i | ||||||
\(502\) | 6.66985e7i | 0.527236i | ||||||||
\(503\) | − | 4.95506e7i | − | 0.389355i | −0.980867 | − | 0.194677i | \(-0.937634\pi\) | ||
0.980867 | − | 0.194677i | \(-0.0623660\pi\) | |||||||
\(504\) | 9.89677e6 | 0.0773040 | ||||||||
\(505\) | 2.75591e7i | 0.213989i | ||||||||
\(506\) | 8.28954e7i | 0.639851i | ||||||||
\(507\) | − | 1.06084e8i | − | 0.814007i | ||||||
\(508\) | 2.15863e7 | 0.164659 | ||||||||
\(509\) | 1.13027e8 | 0.857098 | 0.428549 | − | 0.903519i | \(-0.359025\pi\) | ||||
0.428549 | + | 0.903519i | \(0.359025\pi\) | |||||||
\(510\) | − | 8.33256e7i | − | 0.628157i | ||||||
\(511\) | 3.65022e6 | 0.0273563 | ||||||||
\(512\) | − | 1.78629e8i | − | 1.33089i | ||||||
\(513\) | 1.59049e8 | 1.17809 | ||||||||
\(514\) | 1.91554e8 | 1.41059 | ||||||||
\(515\) | 1.92188e7i | 0.140703i | ||||||||
\(516\) | −2.10925e8 | + | 8.60961e7i | −1.53525 | + | 0.626664i | ||||
\(517\) | −9.50147e7 | −0.687573 | ||||||||
\(518\) | 6.87076e7i | 0.494328i | ||||||||
\(519\) | 2.53296e8i | 1.81187i | ||||||||
\(520\) | 5.92653e6 | 0.0421493 | ||||||||
\(521\) | − | 3.09027e7i | − | 0.218516i | −0.994013 | − | 0.109258i | \(-0.965152\pi\) | ||
0.994013 | − | 0.109258i | \(-0.0348475\pi\) | |||||||
\(522\) | −8.69632e7 | −0.611398 | ||||||||
\(523\) | − | 1.39183e8i | − | 0.972932i | −0.873699 | − | 0.486466i | \(-0.838286\pi\) | ||
0.873699 | − | 0.486466i | \(-0.161714\pi\) | |||||||
\(524\) | − | 1.13006e8i | − | 0.785431i | ||||||
\(525\) | −5.53030e7 | −0.382182 | ||||||||
\(526\) | 2.40308e8 | 1.65124 | ||||||||
\(527\) | −1.46256e8 | −0.999270 | ||||||||
\(528\) | 1.35653e8i | 0.921567i | ||||||||
\(529\) | 6.85340e6 | 0.0462955 | ||||||||
\(530\) | 7.09581e7 | 0.476623 | ||||||||
\(531\) | 4.67367e8 | 3.12158 | ||||||||
\(532\) | 1.30758e7 | 0.0868426 | ||||||||
\(533\) | −8.81428e7 | −0.582110 | ||||||||
\(534\) | 7.32207e8i | 4.80850i | ||||||||
\(535\) | − | 1.45992e7i | − | 0.0953383i | ||||||
\(536\) | 1.17194e7i | 0.0761047i | ||||||||
\(537\) | 2.14342e7 | 0.138415 | ||||||||
\(538\) | − | 8.36591e6i | − | 0.0537238i | ||||||
\(539\) | 6.77456e7 | 0.432628 | ||||||||
\(540\) | 9.08362e7 | 0.576870 | ||||||||
\(541\) | 6.32657e7 | 0.399555 | 0.199777 | − | 0.979841i | \(-0.435978\pi\) | ||||
0.199777 | + | 0.979841i | \(0.435978\pi\) | |||||||
\(542\) | − | 4.21225e8i | − | 2.64555i | ||||||
\(543\) | − | 1.09053e8i | − | 0.681143i | ||||||
\(544\) | 2.22558e8i | 1.38244i | ||||||||
\(545\) | 5.29405e7i | 0.327038i | ||||||||
\(546\) | 1.09143e8i | 0.670527i | ||||||||
\(547\) | −1.95485e8 | −1.19441 | −0.597203 | − | 0.802090i | \(-0.703721\pi\) | ||||
−0.597203 | + | 0.802090i | \(0.703721\pi\) | |||||||
\(548\) | 2.05386e8i | 1.24804i | ||||||||
\(549\) | − | 2.37021e8i | − | 1.43242i | ||||||
\(550\) | − | 9.79556e7i | − | 0.588764i | ||||||
\(551\) | 1.35192e7 | 0.0808156 | ||||||||
\(552\) | 4.62063e7 | 0.274716 | ||||||||
\(553\) | − | 5.72782e7i | − | 0.338699i | ||||||
\(554\) | 2.97731e8 | 1.75104 | ||||||||
\(555\) | − | 1.25914e8i | − | 0.736540i | ||||||
\(556\) | 5.45375e7 | 0.317301 | ||||||||
\(557\) | 3.96240e7 | 0.229294 | 0.114647 | − | 0.993406i | \(-0.463426\pi\) | ||||
0.114647 | + | 0.993406i | \(0.463426\pi\) | |||||||
\(558\) | − | 5.72950e8i | − | 3.29772i | ||||||
\(559\) | 7.91934e7 | + | 1.94015e8i | 0.453371 | + | 1.11071i | ||||
\(560\) | −1.02073e7 | −0.0581228 | ||||||||
\(561\) | − | 1.51021e8i | − | 0.855357i | ||||||
\(562\) | 2.03615e8i | 1.14710i | ||||||||
\(563\) | 2.83973e8 | 1.59130 | 0.795649 | − | 0.605758i | \(-0.207130\pi\) | ||||
0.795649 | + | 0.605758i | \(0.207130\pi\) | |||||||
\(564\) | − | 4.50112e8i | − | 2.50890i | ||||||
\(565\) | 4.09612e7 | 0.227105 | ||||||||
\(566\) | − | 3.31589e8i | − | 1.82873i | ||||||
\(567\) | − | 9.95897e7i | − | 0.546343i | ||||||
\(568\) | −3.60083e7 | −0.196498 | ||||||||
\(569\) | −1.60879e8 | −0.873296 | −0.436648 | − | 0.899632i | \(-0.643834\pi\) | ||||
−0.436648 | + | 0.899632i | \(0.643834\pi\) | |||||||
\(570\) | −5.07452e7 | −0.274013 | ||||||||
\(571\) | 2.43494e8i | 1.30792i | 0.756530 | + | 0.653959i | \(0.226893\pi\) | ||||
−0.756530 | + | 0.653959i | \(0.773107\pi\) | |||||||
\(572\) | −9.12889e7 | −0.487787 | ||||||||
\(573\) | 2.46606e8 | 1.31081 | ||||||||
\(574\) | 2.76744e7 | 0.146333 | ||||||||
\(575\) | −1.83029e8 | −0.962758 | ||||||||
\(576\) | −3.62723e8 | −1.89805 | ||||||||
\(577\) | − | 2.31171e8i | − | 1.20339i | −0.798727 | − | 0.601693i | \(-0.794493\pi\) | ||
0.798727 | − | 0.601693i | \(-0.205507\pi\) | |||||||
\(578\) | − | 8.34754e6i | − | 0.0432290i | ||||||
\(579\) | 1.70502e8i | 0.878403i | ||||||||
\(580\) | 7.72106e6 | 0.0395725 | ||||||||
\(581\) | − | 2.01829e7i | − | 0.102909i | ||||||
\(582\) | −7.88347e8 | −3.99897 | ||||||||
\(583\) | 1.28606e8 | 0.649014 | ||||||||
\(584\) | 3.60389e6 | 0.0180939 | ||||||||
\(585\) | − | 1.41785e8i | − | 0.708209i | ||||||
\(586\) | − | 1.77364e7i | − | 0.0881399i | ||||||
\(587\) | 2.10877e8i | 1.04259i | 0.853375 | + | 0.521297i | \(0.174552\pi\) | ||||
−0.853375 | + | 0.521297i | \(0.825448\pi\) | |||||||
\(588\) | 3.20931e8i | 1.57863i | ||||||||
\(589\) | 8.90700e7i | 0.435898i | ||||||||
\(590\) | −8.78732e7 | −0.427859 | ||||||||
\(591\) | 3.23425e7i | 0.156679i | ||||||||
\(592\) | 3.72113e8i | 1.79353i | ||||||||
\(593\) | 2.60310e8i | 1.24832i | 0.781295 | + | 0.624162i | \(0.214560\pi\) | ||||
−0.781295 | + | 0.624162i | \(0.785440\pi\) | |||||||
\(594\) | 3.48637e8 | 1.66347 | ||||||||
\(595\) | 1.13637e7 | 0.0539470 | ||||||||
\(596\) | − | 1.89356e8i | − | 0.894417i | ||||||
\(597\) | −3.26668e8 | −1.53527 | ||||||||
\(598\) | 3.61215e8i | 1.68913i | ||||||||
\(599\) | 1.98069e8 | 0.921587 | 0.460794 | − | 0.887507i | \(-0.347565\pi\) | ||||
0.460794 | + | 0.887507i | \(0.347565\pi\) | |||||||
\(600\) | −5.46009e7 | −0.252782 | ||||||||
\(601\) | 2.10475e8i | 0.969565i | 0.874635 | + | 0.484783i | \(0.161101\pi\) | ||||
−0.874635 | + | 0.484783i | \(0.838899\pi\) | |||||||
\(602\) | −2.48645e7 | − | 6.09152e7i | −0.113970 | − | 0.279213i | ||||
\(603\) | 2.80372e8 | 1.27874 | ||||||||
\(604\) | − | 3.12837e8i | − | 1.41974i | ||||||
\(605\) | − | 4.26020e7i | − | 0.192382i | ||||||
\(606\) | −5.01083e8 | −2.25160 | ||||||||
\(607\) | 6.23544e7i | 0.278805i | 0.990236 | + | 0.139403i | \(0.0445182\pi\) | ||||
−0.990236 | + | 0.139403i | \(0.955482\pi\) | |||||||
\(608\) | 1.35538e8 | 0.603045 | ||||||||
\(609\) | − | 1.67306e7i | − | 0.0740728i | ||||||
\(610\) | 4.45640e7i | 0.196334i | ||||||||
\(611\) | −4.14025e8 | −1.81511 | ||||||||
\(612\) | 5.07144e8 | 2.21247 | ||||||||
\(613\) | −3.02341e7 | −0.131255 | −0.0656276 | − | 0.997844i | \(-0.520905\pi\) | ||||
−0.0656276 | + | 0.997844i | \(0.520905\pi\) | |||||||
\(614\) | − | 4.31377e8i | − | 1.86360i | ||||||
\(615\) | −5.07164e7 | −0.218033 | ||||||||
\(616\) | −3.37248e6 | −0.0144280 | ||||||||
\(617\) | 5.23405e7 | 0.222834 | 0.111417 | − | 0.993774i | \(-0.464461\pi\) | ||||
0.111417 | + | 0.993774i | \(0.464461\pi\) | |||||||
\(618\) | −3.49438e8 | −1.48049 | ||||||||
\(619\) | −6.04729e7 | −0.254970 | −0.127485 | − | 0.991841i | \(-0.540690\pi\) | ||||
−0.127485 | + | 0.991841i | \(0.540690\pi\) | |||||||
\(620\) | 5.08696e7i | 0.213444i | ||||||||
\(621\) | − | 6.51425e8i | − | 2.72013i | ||||||
\(622\) | 2.92297e8i | 1.21465i | ||||||||
\(623\) | −9.98558e7 | −0.412961 | ||||||||
\(624\) | 5.91104e8i | 2.43282i | ||||||||
\(625\) | 2.01930e8 | 0.827106 | ||||||||
\(626\) | 4.02165e8 | 1.63938 | ||||||||
\(627\) | −9.19714e7 | −0.373121 | ||||||||
\(628\) | 4.77191e7i | 0.192670i | ||||||||
\(629\) | − | 4.14269e8i | − | 1.66468i | ||||||
\(630\) | 4.45165e7i | 0.178032i | ||||||||
\(631\) | 5.68881e7i | 0.226430i | 0.993571 | + | 0.113215i | \(0.0361149\pi\) | ||||
−0.993571 | + | 0.113215i | \(0.963885\pi\) | |||||||
\(632\) | − | 5.65511e7i | − | 0.224021i | ||||||
\(633\) | 1.31874e8 | 0.519933 | ||||||||
\(634\) | − | 3.95164e8i | − | 1.55064i | ||||||
\(635\) | − | 1.14247e7i | − | 0.0446194i | ||||||
\(636\) | 6.09243e8i | 2.36820i | ||||||||
\(637\) | 2.95200e8 | 1.14209 | ||||||||
\(638\) | 2.96341e7 | 0.114111 | ||||||||
\(639\) | 8.61452e8i | 3.30163i | ||||||||
\(640\) | −1.83183e7 | −0.0698787 | ||||||||
\(641\) | 5.01358e8i | 1.90359i | 0.306734 | + | 0.951795i | \(0.400764\pi\) | ||||
−0.306734 | + | 0.951795i | \(0.599236\pi\) | |||||||
\(642\) | 2.65445e8 | 1.00316 | ||||||||
\(643\) | −2.03232e8 | −0.764468 | −0.382234 | − | 0.924065i | \(-0.624845\pi\) | ||||
−0.382234 | + | 0.924065i | \(0.624845\pi\) | |||||||
\(644\) | − | 5.35550e7i | − | 0.200513i | ||||||
\(645\) | 4.55670e7 | + | 1.11634e8i | 0.169813 | + | 0.416023i | ||||
\(646\) | −1.66956e8 | −0.619305 | ||||||||
\(647\) | 1.76979e8i | 0.653443i | 0.945121 | + | 0.326722i | \(0.105944\pi\) | ||||
−0.945121 | + | 0.326722i | \(0.894056\pi\) | |||||||
\(648\) | − | 9.83254e7i | − | 0.361361i | ||||||
\(649\) | −1.59263e8 | −0.582612 | ||||||||
\(650\) | − | 4.26840e8i | − | 1.55426i | ||||||
\(651\) | 1.10228e8 | 0.399530 | ||||||||
\(652\) | 8.01335e7i | 0.289115i | ||||||||
\(653\) | 7.16442e7i | 0.257301i | 0.991690 | + | 0.128651i | \(0.0410646\pi\) | ||||
−0.991690 | + | 0.128651i | \(0.958935\pi\) | |||||||
\(654\) | −9.62570e8 | −3.44112 | ||||||||
\(655\) | −5.98093e7 | −0.212836 | ||||||||
\(656\) | 1.49882e8 | 0.530929 | ||||||||
\(657\) | − | 8.62184e7i | − | 0.304021i | ||||||
\(658\) | 1.29992e8 | 0.456289 | ||||||||
\(659\) | −4.47258e8 | −1.56279 | −0.781397 | − | 0.624035i | \(-0.785492\pi\) | ||||
−0.781397 | + | 0.624035i | \(0.785492\pi\) | |||||||
\(660\) | −5.25267e7 | −0.182704 | ||||||||
\(661\) | −1.23912e8 | −0.429049 | −0.214525 | − | 0.976719i | \(-0.568820\pi\) | ||||
−0.214525 | + | 0.976719i | \(0.568820\pi\) | |||||||
\(662\) | −4.55039e8 | −1.56847 | ||||||||
\(663\) | − | 6.58070e8i | − | 2.25804i | ||||||
\(664\) | − | 1.99266e7i | − | 0.0680659i | ||||||
\(665\) | − | 6.92046e6i | − | 0.0235326i | ||||||
\(666\) | 1.62287e9 | 5.49366 | ||||||||
\(667\) | − | 5.53710e7i | − | 0.186597i | ||||||
\(668\) | −3.67126e8 | −1.23165 | ||||||||
\(669\) | 8.49480e8 | 2.83710 | ||||||||
\(670\) | −5.27148e7 | −0.175270 | ||||||||
\(671\) | 8.07685e7i | 0.267346i | ||||||||
\(672\) | − | 1.67734e8i | − | 0.552731i | ||||||
\(673\) | − | 1.92398e7i | − | 0.0631185i | −0.999502 | − | 0.0315592i | \(-0.989953\pi\) | ||
0.999502 | − | 0.0315592i | \(-0.0100473\pi\) | |||||||
\(674\) | − | 5.92055e8i | − | 1.93367i | ||||||
\(675\) | 7.69775e8i | 2.50295i | ||||||||
\(676\) | −1.21396e8 | −0.392973 | ||||||||
\(677\) | − | 4.42129e8i | − | 1.42490i | −0.701725 | − | 0.712448i | \(-0.747586\pi\) | ||
0.701725 | − | 0.712448i | \(-0.252414\pi\) | |||||||
\(678\) | 7.44761e8i | 2.38962i | ||||||||
\(679\) | − | 1.07512e8i | − | 0.343437i | ||||||
\(680\) | 1.12194e7 | 0.0356815 | ||||||||
\(681\) | −5.05864e8 | −1.60174 | ||||||||
\(682\) | 1.95242e8i | 0.615488i | ||||||||
\(683\) | 9.46019e6 | 0.0296919 | 0.0148459 | − | 0.999890i | \(-0.495274\pi\) | ||||
0.0148459 | + | 0.999890i | \(0.495274\pi\) | |||||||
\(684\) | − | 3.08850e8i | − | 0.965116i | ||||||
\(685\) | 1.08702e8 | 0.338194 | ||||||||
\(686\) | −1.90043e8 | −0.588680 | ||||||||
\(687\) | − | 3.59839e8i | − | 1.10978i | ||||||
\(688\) | −1.34664e8 | − | 3.29910e8i | −0.413509 | − | 1.01305i | ||||
\(689\) | 5.60397e8 | 1.71332 | ||||||||
\(690\) | 2.07839e8i | 0.632675i | ||||||||
\(691\) | − | 4.38108e8i | − | 1.32784i | −0.747802 | − | 0.663922i | \(-0.768891\pi\) | ||
0.747802 | − | 0.663922i | \(-0.231109\pi\) | |||||||
\(692\) | 2.89854e8 | 0.874703 | ||||||||
\(693\) | 8.06823e7i | 0.242426i | ||||||||
\(694\) | 7.74733e8 | 2.31779 | ||||||||
\(695\) | − | 2.88644e7i | − | 0.0859821i | ||||||
\(696\) | − | 1.65182e7i | − | 0.0489930i | ||||||
\(697\) | −1.66861e8 | −0.492785 | ||||||||
\(698\) | −6.32140e8 | −1.85886 | ||||||||
\(699\) | −6.51363e8 | −1.90718 | ||||||||
\(700\) | 6.32848e7i | 0.184504i | ||||||||
\(701\) | 1.11880e8 | 0.324786 | 0.162393 | − | 0.986726i | \(-0.448079\pi\) | ||||
0.162393 | + | 0.986726i | \(0.448079\pi\) | |||||||
\(702\) | 1.51918e9 | 4.39135 | ||||||||
\(703\) | −2.52289e8 | −0.726161 | ||||||||
\(704\) | 1.23603e8 | 0.354252 | ||||||||
\(705\) | −2.38225e8 | −0.679862 | ||||||||
\(706\) | 6.73913e8i | 1.91509i | ||||||||
\(707\) | − | 6.83360e7i | − | 0.193371i | ||||||
\(708\) | − | 7.54474e8i | − | 2.12591i | ||||||
\(709\) | −1.44384e8 | −0.405117 | −0.202559 | − | 0.979270i | \(-0.564926\pi\) | ||||
−0.202559 | + | 0.979270i | \(0.564926\pi\) | |||||||
\(710\) | − | 1.61968e8i | − | 0.452537i | ||||||
\(711\) | −1.35291e9 | −3.76410 | ||||||||
\(712\) | −9.85882e7 | −0.273140 | ||||||||
\(713\) | 3.64808e8 | 1.00646 | ||||||||
\(714\) | 2.06616e8i | 0.567634i | ||||||||
\(715\) | 4.83154e7i | 0.132180i | ||||||||
\(716\) | − | 2.45277e7i | − | 0.0668219i | ||||||
\(717\) | 2.99467e8i | 0.812441i | ||||||||
\(718\) | − | 1.82613e8i | − | 0.493353i | ||||||
\(719\) | 1.65815e8 | 0.446105 | 0.223052 | − | 0.974806i | \(-0.428398\pi\) | ||||
0.223052 | + | 0.974806i | \(0.428398\pi\) | |||||||
\(720\) | 2.41096e8i | 0.645942i | ||||||||
\(721\) | − | 4.76551e7i | − | 0.127146i | ||||||
\(722\) | − | 4.16389e8i | − | 1.10634i | ||||||
\(723\) | 9.74312e8 | 2.57800 | ||||||||
\(724\) | −1.24793e8 | −0.328831 | ||||||||
\(725\) | 6.54307e7i | 0.171699i | ||||||||
\(726\) | 7.74594e8 | 2.02425 | ||||||||
\(727\) | − | 6.29238e8i | − | 1.63761i | −0.574069 | − | 0.818807i | \(-0.694636\pi\) | ||
0.574069 | − | 0.818807i | \(-0.305364\pi\) | |||||||
\(728\) | −1.46955e7 | −0.0380882 | ||||||||
\(729\) | −4.42898e8 | −1.14320 | ||||||||
\(730\) | 1.62106e7i | 0.0416706i | ||||||||
\(731\) | 1.49919e8 | + | 3.67285e8i | 0.383801 | + | 0.940267i | ||||
\(732\) | −3.82624e8 | −0.975527 | ||||||||
\(733\) | 5.55695e8i | 1.41099i | 0.708714 | + | 0.705495i | \(0.249275\pi\) | ||||
−0.708714 | + | 0.705495i | \(0.750725\pi\) | |||||||
\(734\) | 8.25729e7i | 0.208809i | ||||||||
\(735\) | 1.69855e8 | 0.427776 | ||||||||
\(736\) | − | 5.55128e8i | − | 1.39239i | ||||||
\(737\) | −9.55412e7 | −0.238665 | ||||||||
\(738\) | − | 6.53669e8i | − | 1.62626i | ||||||
\(739\) | 1.18378e8i | 0.293318i | 0.989187 | + | 0.146659i | \(0.0468519\pi\) | ||||
−0.989187 | + | 0.146659i | \(0.953148\pi\) | |||||||
\(740\) | −1.44087e8 | −0.355575 | ||||||||
\(741\) | −4.00764e8 | −0.984994 | ||||||||
\(742\) | −1.75949e8 | −0.430700 | ||||||||
\(743\) | 2.35083e8i | 0.573132i | 0.958060 | + | 0.286566i | \(0.0925138\pi\) | ||||
−0.958060 | + | 0.286566i | \(0.907486\pi\) | |||||||
\(744\) | 1.08829e8 | 0.264256 | ||||||||
\(745\) | −1.00218e8 | −0.242369 | ||||||||
\(746\) | −2.51923e8 | −0.606808 | ||||||||
\(747\) | −4.76719e8 | −1.14367 | ||||||||
\(748\) | −1.72817e8 | −0.412936 | ||||||||
\(749\) | 3.62004e7i | 0.0861525i | ||||||||
\(750\) | − | 5.06537e8i | − | 1.20068i | ||||||
\(751\) | − | 2.67999e8i | − | 0.632722i | −0.948639 | − | 0.316361i | \(-0.897539\pi\) | ||
0.948639 | − | 0.316361i | \(-0.102461\pi\) | |||||||
\(752\) | 7.04025e8 | 1.65552 | ||||||||
\(753\) | 3.03090e8i | 0.709882i | ||||||||
\(754\) | 1.29130e8 | 0.301240 | ||||||||
\(755\) | −1.65571e8 | −0.384720 | ||||||||
\(756\) | −2.25239e8 | −0.521289 | ||||||||
\(757\) | − | 3.48844e8i | − | 0.804162i | −0.915604 | − | 0.402081i | \(-0.868287\pi\) | ||
0.915604 | − | 0.402081i | \(-0.131713\pi\) | |||||||
\(758\) | 3.85145e8i | 0.884335i | ||||||||
\(759\) | 3.76691e8i | 0.861509i | ||||||||
\(760\) | − | 6.83260e6i | − | 0.0155649i | ||||||
\(761\) | 3.74723e8i | 0.850269i | 0.905130 | + | 0.425135i | \(0.139773\pi\) | ||||
−0.905130 | + | 0.425135i | \(0.860227\pi\) | |||||||
\(762\) | 2.07725e8 | 0.469488 | ||||||||
\(763\) | − | 1.31272e8i | − | 0.295528i | ||||||
\(764\) | − | 2.82198e8i | − | 0.632811i | ||||||
\(765\) | − | 2.68410e8i | − | 0.599534i | ||||||
\(766\) | 3.37389e8 | 0.750661 | ||||||||
\(767\) | −6.93984e8 | −1.53803 | ||||||||
\(768\) | − | 9.87508e8i | − | 2.18000i | ||||||
\(769\) | 1.68131e8 | 0.369716 | 0.184858 | − | 0.982765i | \(-0.440817\pi\) | ||||
0.184858 | + | 0.982765i | \(0.440817\pi\) | |||||||
\(770\) | − | 1.51697e7i | − | 0.0332280i | ||||||
\(771\) | 8.70456e8 | 1.89926 | ||||||||
\(772\) | 1.95111e8 | 0.424061 | ||||||||
\(773\) | 1.56150e8i | 0.338068i | 0.985610 | + | 0.169034i | \(0.0540647\pi\) | ||||
−0.985610 | + | 0.169034i | \(0.945935\pi\) | |||||||
\(774\) | −1.43882e9 | + | 5.87300e8i | −3.10301 | + | 1.26659i | ||||
\(775\) | −4.31085e8 | −0.926100 | ||||||||
\(776\) | − | 1.06147e8i | − | 0.227155i | ||||||
\(777\) | 3.12219e8i | 0.665574i | ||||||||
\(778\) | −8.81183e7 | −0.187123 | ||||||||
\(779\) | 1.01618e8i | 0.214961i | ||||||||
\(780\) | −2.28884e8 | −0.482316 | ||||||||
\(781\) | − | 2.93553e8i | − | 0.616217i | ||||||
\(782\) | 6.83809e8i | 1.42993i | ||||||||
\(783\) | −2.32877e8 | −0.485110 | ||||||||
\(784\) | −5.01971e8 | −1.04167 | ||||||||
\(785\) | 2.52557e7 | 0.0522096 | ||||||||
\(786\) | − | 1.08746e9i | − | 2.23947i | ||||||
\(787\) | 3.87835e8 | 0.795650 | 0.397825 | − | 0.917461i | \(-0.369765\pi\) | ||||
0.397825 | + | 0.917461i | \(0.369765\pi\) | |||||||
\(788\) | 3.70105e7 | 0.0756391 | ||||||||
\(789\) | 1.09200e9 | 2.22327 | ||||||||
\(790\) | 2.54371e8 | 0.515925 | ||||||||
\(791\) | −1.01568e8 | −0.205224 | ||||||||
\(792\) | 7.96580e7i | 0.160344i | ||||||||
\(793\) | 3.51947e8i | 0.705762i | ||||||||
\(794\) | 8.28787e8i | 1.65570i | ||||||||
\(795\) | 3.22446e8 | 0.641735 | ||||||||
\(796\) | 3.73816e8i | 0.741171i | ||||||||
\(797\) | 8.28482e8 | 1.63647 | 0.818235 | − | 0.574883i | \(-0.194953\pi\) | ||||
0.818235 | + | 0.574883i | \(0.194953\pi\) | |||||||
\(798\) | 1.25829e8 | 0.247612 | ||||||||
\(799\) | −7.83782e8 | −1.53658 | ||||||||
\(800\) | 6.55983e8i | 1.28122i | ||||||||
\(801\) | 2.35860e9i | 4.58940i | ||||||||
\(802\) | 4.01652e8i | 0.778623i | ||||||||
\(803\) | 2.93803e7i | 0.0567426i | ||||||||
\(804\) | − | 4.52607e8i | − | 0.870869i | ||||||
\(805\) | −2.83444e7 | −0.0543350 | ||||||||
\(806\) | 8.50763e8i | 1.62481i | ||||||||
\(807\) | − | 3.80162e7i | − | 0.0723349i | ||||||
\(808\) | − | 6.74685e7i | − | 0.127899i | ||||||
\(809\) | 5.00126e8 | 0.944569 | 0.472284 | − | 0.881446i | \(-0.343430\pi\) | ||||
0.472284 | + | 0.881446i | \(0.343430\pi\) | |||||||
\(810\) | 4.42275e8 | 0.832219 | ||||||||
\(811\) | − | 6.53394e8i | − | 1.22493i | −0.790496 | − | 0.612467i | \(-0.790177\pi\) | ||
0.790496 | − | 0.612467i | \(-0.209823\pi\) | |||||||
\(812\) | −1.91453e7 | −0.0357597 | ||||||||
\(813\) | − | 1.91412e9i | − | 3.56203i | ||||||
\(814\) | −5.53020e8 | −1.02534 | ||||||||
\(815\) | 4.24113e7 | 0.0783445 | ||||||||
\(816\) | 1.11901e9i | 2.05950i | ||||||||
\(817\) | 2.23676e8 | − | 9.13008e7i | 0.410160 | − | 0.167420i | ||||
\(818\) | −1.31089e9 | −2.39500 | ||||||||
\(819\) | 3.51572e8i | 0.639974i | ||||||||
\(820\) | 5.80363e7i | 0.105259i | ||||||||
\(821\) | 6.62105e7 | 0.119646 | 0.0598229 | − | 0.998209i | \(-0.480946\pi\) | ||||
0.0598229 | + | 0.998209i | \(0.480946\pi\) | |||||||
\(822\) | 1.97644e9i | 3.55850i | ||||||||
\(823\) | 1.68404e7 | 0.0302102 | 0.0151051 | − | 0.999886i | \(-0.495192\pi\) | ||||
0.0151051 | + | 0.999886i | \(0.495192\pi\) | |||||||
\(824\) | − | 4.70502e7i | − | 0.0840968i | ||||||
\(825\) | − | 4.45128e8i | − | 0.792725i | ||||||
\(826\) | 2.17892e8 | 0.386634 | ||||||||
\(827\) | 5.77846e8 | 1.02163 | 0.510817 | − | 0.859689i | \(-0.329343\pi\) | ||||
0.510817 | + | 0.859689i | \(0.329343\pi\) | |||||||
\(828\) | −1.26497e9 | −2.22838 | ||||||||
\(829\) | 1.53214e8i | 0.268927i | 0.990919 | + | 0.134464i | \(0.0429311\pi\) | ||||
−0.990919 | + | 0.134464i | \(0.957069\pi\) | |||||||
\(830\) | 8.96316e7 | 0.156757 | ||||||||
\(831\) | 1.35294e9 | 2.35764 | ||||||||
\(832\) | 5.38600e8 | 0.935182 | ||||||||
\(833\) | 5.58838e8 | 0.966832 | ||||||||
\(834\) | 5.24816e8 | 0.904709 | ||||||||
\(835\) | 1.94304e8i | 0.333751i | ||||||||
\(836\) | 1.05246e8i | 0.180130i | ||||||||
\(837\) | − | 1.53429e9i | − | 2.61656i | ||||||
\(838\) | −1.44032e9 | −2.44752 | ||||||||
\(839\) | − | 4.17573e8i | − | 0.707044i | −0.935426 | − | 0.353522i | \(-0.884984\pi\) | ||
0.935426 | − | 0.353522i | \(-0.115016\pi\) | |||||||
\(840\) | −8.45565e6 | −0.0142662 | ||||||||
\(841\) | 5.75029e8 | 0.966722 | ||||||||
\(842\) | 1.20020e9 | 2.01056 | ||||||||
\(843\) | 9.25263e8i | 1.54448i | ||||||||
\(844\) | − | 1.50907e8i | − | 0.251005i | ||||||
\(845\) | 6.42495e7i | 0.106488i | ||||||||
\(846\) | − | 3.07042e9i | − | 5.07092i | ||||||
\(847\) | 1.05637e8i | 0.173846i | ||||||||
\(848\) | −9.52921e8 | −1.56268 | ||||||||
\(849\) | − | 1.50680e9i | − | 2.46225i | ||||||
\(850\) | − | 8.08042e8i | − | 1.31576i | ||||||
\(851\) | 1.03331e9i | 1.67665i | ||||||||
\(852\) | 1.39065e9 | 2.24853 | ||||||||
\(853\) | −1.66126e8 | −0.267665 | −0.133832 | − | 0.991004i | \(-0.542728\pi\) | ||||
−0.133832 | + | 0.991004i | \(0.542728\pi\) | |||||||
\(854\) | − | 1.10502e8i | − | 0.177417i | ||||||
\(855\) | −1.63461e8 | −0.261527 | ||||||||
\(856\) | 3.57408e7i | 0.0569828i | ||||||||
\(857\) | −3.66098e8 | −0.581640 | −0.290820 | − | 0.956778i | \(-0.593928\pi\) | ||||
−0.290820 | + | 0.956778i | \(0.593928\pi\) | |||||||
\(858\) | −8.78476e8 | −1.39081 | ||||||||
\(859\) | − | 1.53078e8i | − | 0.241509i | −0.992682 | − | 0.120754i | \(-0.961469\pi\) | ||
0.992682 | − | 0.120754i | \(-0.0385314\pi\) | |||||||
\(860\) | 1.27746e8 | − | 5.21437e7i | 0.200841 | − | 0.0819797i | ||||
\(861\) | 1.25757e8 | 0.197026 | ||||||||
\(862\) | 3.13109e8i | 0.488848i | ||||||||
\(863\) | 3.72244e8i | 0.579155i | 0.957155 | + | 0.289578i | \(0.0935149\pi\) | ||||
−0.957155 | + | 0.289578i | \(0.906485\pi\) | |||||||
\(864\) | −2.33473e9 | −3.61989 | ||||||||
\(865\) | − | 1.53407e8i | − | 0.237027i | ||||||
\(866\) | 1.45062e8 | 0.223357 | ||||||||
\(867\) | − | 3.79327e7i | − | 0.0582044i | ||||||
\(868\) | − | 1.26137e8i | − | 0.192878i | ||||||
\(869\) | 4.61026e8 | 0.702532 | ||||||||
\(870\) | 7.43000e7 | 0.112832 | ||||||||
\(871\) | −4.16319e8 | −0.630045 | ||||||||
\(872\) | − | 1.29606e8i | − | 0.195467i | ||||||
\(873\) | −2.53944e9 | −3.81676 | ||||||||
\(874\) | 4.16439e8 | 0.623760 | ||||||||
\(875\) | 6.90798e7 | 0.103116 | ||||||||
\(876\) | −1.39183e8 | −0.207049 | ||||||||
\(877\) | −8.02743e8 | −1.19008 | −0.595042 | − | 0.803695i | \(-0.702865\pi\) | ||||
−0.595042 | + | 0.803695i | \(0.702865\pi\) | |||||||
\(878\) | − | 1.01510e9i | − | 1.49977i | ||||||
\(879\) | − | 8.05973e7i | − | 0.118674i | ||||||
\(880\) | − | 8.21574e7i | − | 0.120559i | ||||||
\(881\) | −5.95543e8 | −0.870934 | −0.435467 | − | 0.900205i | \(-0.643417\pi\) | ||||
−0.435467 | + | 0.900205i | \(0.643417\pi\) | |||||||
\(882\) | 2.18921e9i | 3.19068i | ||||||||
\(883\) | −1.95039e7 | −0.0283295 | −0.0141647 | − | 0.999900i | \(-0.504509\pi\) | ||||
−0.0141647 | + | 0.999900i | \(0.504509\pi\) | |||||||
\(884\) | −7.53048e8 | −1.09010 | ||||||||
\(885\) | −3.99311e8 | −0.576078 | ||||||||
\(886\) | 1.45680e9i | 2.09459i | ||||||||
\(887\) | 5.45638e8i | 0.781868i | 0.920419 | + | 0.390934i | \(0.127848\pi\) | ||||
−0.920419 | + | 0.390934i | \(0.872152\pi\) | |||||||
\(888\) | 3.08256e8i | 0.440222i | ||||||||
\(889\) | 2.83289e7i | 0.0403203i | ||||||||
\(890\) | − | 4.43457e8i | − | 0.629045i | ||||||
\(891\) | 8.01586e8 | 1.13323 | ||||||||
\(892\) | − | 9.72084e8i | − | 1.36965i | ||||||
\(893\) | 4.77323e8i | 0.670282i | ||||||||
\(894\) | − | 1.82218e9i | − | 2.55022i | ||||||
\(895\) | −1.29815e7 | −0.0181074 | ||||||||
\(896\) | 4.54223e7 | 0.0631459 | ||||||||
\(897\) | 1.64143e9i | 2.27428i | ||||||||
\(898\) | 9.36202e8 | 1.29283 | ||||||||
\(899\) | − | 1.30414e8i | − | 0.179492i | ||||||
\(900\) | 1.49479e9 | 2.05046 | ||||||||
\(901\) | 1.06088e9 | 1.45041 | ||||||||
\(902\) | 2.22748e8i | 0.303525i | ||||||||
\(903\) | −1.12989e8 | − | 2.76809e8i | −0.153452 | − | 0.375939i | ||||
\(904\) | −1.00279e8 | −0.135738 | ||||||||
\(905\) | 6.60474e7i | 0.0891066i | ||||||||
\(906\) | − | 3.01044e9i | − | 4.04805i | ||||||
\(907\) | 9.36250e8 | 1.25479 | 0.627393 | − | 0.778703i | \(-0.284122\pi\) | ||||
0.627393 | + | 0.778703i | \(0.284122\pi\) | |||||||
\(908\) | 5.78875e8i | 0.773263i | ||||||||
\(909\) | −1.61410e9 | −2.14901 | ||||||||
\(910\) | − | 6.61016e7i | − | 0.0877178i | ||||||
\(911\) | − | 9.19474e8i | − | 1.21614i | −0.793883 | − | 0.608071i | \(-0.791944\pi\) | ||
0.793883 | − | 0.608071i | \(-0.208056\pi\) | |||||||
\(912\) | 6.81475e8 | 0.898391 | ||||||||
\(913\) | 1.62450e8 | 0.213455 | ||||||||
\(914\) | −1.01740e7 | −0.0133245 | ||||||||
\(915\) | 2.02507e8i | 0.264348i | ||||||||
\(916\) | −4.11774e8 | −0.535763 | ||||||||
\(917\) | 1.48304e8 | 0.192329 | ||||||||
\(918\) | 2.87593e9 | 3.71749 | ||||||||
\(919\) | 6.53282e8 | 0.841693 | 0.420847 | − | 0.907132i | \(-0.361733\pi\) | ||||
0.420847 | + | 0.907132i | \(0.361733\pi\) | |||||||
\(920\) | −2.79846e7 | −0.0359381 | ||||||||
\(921\) | − | 1.96025e9i | − | 2.50919i | ||||||
\(922\) | 6.79473e8i | 0.866921i | ||||||||
\(923\) | − | 1.27915e9i | − | 1.62674i | ||||||
\(924\) | 1.30246e8 | 0.165101 | ||||||||
\(925\) | − | 1.22104e9i | − | 1.54279i | ||||||
\(926\) | 1.29704e9 | 1.63350 | ||||||||
\(927\) | −1.12562e9 | −1.41303 | ||||||||
\(928\) | −1.98452e8 | −0.248319 | ||||||||
\(929\) | − | 3.68817e8i | − | 0.460007i | −0.973190 | − | 0.230003i | \(-0.926126\pi\) | ||
0.973190 | − | 0.230003i | \(-0.0738737\pi\) | |||||||
\(930\) | 4.89520e8i | 0.608585i | ||||||||
\(931\) | − | 3.40332e8i | − | 0.421749i | ||||||
\(932\) | 7.45373e8i | 0.920717i | ||||||||
\(933\) | 1.32825e9i | 1.63544i | ||||||||
\(934\) | −2.20253e7 | −0.0270321 | ||||||||
\(935\) | 9.14648e7i | 0.111897i | ||||||||
\(936\) | 3.47108e8i | 0.423290i | ||||||||
\(937\) | 3.54151e8i | 0.430497i | 0.976559 | + | 0.215248i | \(0.0690561\pi\) | ||||
−0.976559 | + | 0.215248i | \(0.930944\pi\) | |||||||
\(938\) | 1.30713e8 | 0.158383 | ||||||||
\(939\) | 1.82751e9 | 2.20730 | ||||||||
\(940\) | 2.72608e8i | 0.328213i | ||||||||
\(941\) | 9.86119e8 | 1.18348 | 0.591739 | − | 0.806129i | \(-0.298441\pi\) | ||||
0.591739 | + | 0.806129i | \(0.298441\pi\) | |||||||
\(942\) | 4.59202e8i | 0.549353i | ||||||||
\(943\) | 4.16203e8 | 0.496329 | ||||||||
\(944\) | 1.18008e9 | 1.40280 | ||||||||
\(945\) | 1.19209e8i | 0.141259i | ||||||||
\(946\) | 4.90300e8 | − | 2.00132e8i | 0.579146 | − | 0.236397i | ||||
\(947\) | −1.60092e9 | −1.88503 | −0.942515 | − | 0.334163i | \(-0.891547\pi\) | ||||
−0.942515 | + | 0.334163i | \(0.891547\pi\) | |||||||
\(948\) | 2.18402e9i | 2.56349i | ||||||||
\(949\) | 1.28024e8i | 0.149793i | ||||||||
\(950\) | −4.92097e8 | −0.573958 | ||||||||
\(951\) | − | 1.79569e9i | − | 2.08781i | ||||||
\(952\) | −2.78198e7 | −0.0322436 | ||||||||
\(953\) | 9.21284e8i | 1.06442i | 0.846611 | + | 0.532212i | \(0.178639\pi\) | ||||
−0.846611 | + | 0.532212i | \(0.821361\pi\) | |||||||
\(954\) | 4.15592e9i | 4.78654i | ||||||||
\(955\) | −1.49355e8 | −0.171479 | ||||||||
\(956\) | 3.42689e8 | 0.392217 | ||||||||
\(957\) | 1.34662e8 | 0.153642 | ||||||||
\(958\) | − | 6.16954e8i | − | 0.701708i | ||||||
\(959\) | −2.69539e8 | −0.305609 | ||||||||
\(960\) | 3.09905e8 | 0.350279 | ||||||||
\(961\) | −2.82796e7 | −0.0318642 | ||||||||
\(962\) | −2.40977e9 | −2.70677 | ||||||||
\(963\) | 8.55054e8 | 0.957447 | ||||||||
\(964\) | − | 1.11493e9i | − | 1.24457i | ||||||
\(965\) | − | 1.03264e8i | − | 0.114912i | ||||||
\(966\) | − | 5.15362e8i | − | 0.571717i | ||||||
\(967\) | −6.21408e8 | −0.687223 | −0.343611 | − | 0.939112i | \(-0.611650\pi\) | ||||
−0.343611 | + | 0.939112i | \(0.611650\pi\) | |||||||
\(968\) | 1.04295e8i | 0.114985i | ||||||||
\(969\) | −7.58678e8 | −0.833847 | ||||||||
\(970\) | 4.77458e8 | 0.523143 | ||||||||
\(971\) | −4.82750e8 | −0.527308 | −0.263654 | − | 0.964617i | \(-0.584928\pi\) | ||||
−0.263654 | + | 0.964617i | \(0.584928\pi\) | |||||||
\(972\) | 1.61236e9i | 1.75575i | ||||||||
\(973\) | 7.15726e7i | 0.0776977i | ||||||||
\(974\) | 8.83433e8i | 0.956085i | ||||||||
\(975\) | − | 1.93964e9i | − | 2.09270i | ||||||
\(976\) | − | 5.98466e8i | − | 0.643709i | ||||||
\(977\) | −1.01822e9 | −1.09184 | −0.545921 | − | 0.837837i | \(-0.683820\pi\) | ||||
−0.545921 | + | 0.837837i | \(0.683820\pi\) | |||||||
\(978\) | 7.71127e8i | 0.824346i | ||||||||
\(979\) | − | 8.03729e8i | − | 0.856567i | ||||||
\(980\) | − | 1.94370e8i | − | 0.206515i | ||||||
\(981\) | −3.10065e9 | −3.28432 | ||||||||
\(982\) | 5.21590e8 | 0.550802 | ||||||||
\(983\) | 3.17690e8i | 0.334459i | 0.985918 | + | 0.167229i | \(0.0534821\pi\) | ||||
−0.985918 | + | 0.167229i | \(0.946518\pi\) | |||||||
\(984\) | 1.24161e8 | 0.130316 | ||||||||
\(985\) | − | 1.95881e7i | − | 0.0204967i | ||||||
\(986\) | 2.44453e8 | 0.255015 | ||||||||
\(987\) | 5.90708e8 | 0.614357 | ||||||||
\(988\) | 4.58606e8i | 0.475520i | ||||||||
\(989\) | −3.73944e8 | − | 9.16121e8i | −0.386561 | − | 0.947030i | ||||
\(990\) | −3.58308e8 | −0.369276 | ||||||||
\(991\) | 4.19024e8i | 0.430544i | 0.976554 | + | 0.215272i | \(0.0690638\pi\) | ||||
−0.976554 | + | 0.215272i | \(0.930936\pi\) | |||||||
\(992\) | − | 1.30748e9i | − | 1.33937i | ||||||
\(993\) | −2.06778e9 | −2.11182 | ||||||||
\(994\) | 4.01619e8i | 0.408935i | ||||||||
\(995\) | 1.97845e8 | 0.200842 | ||||||||
\(996\) | 7.69572e8i | 0.778881i | ||||||||
\(997\) | 1.66962e9i | 1.68474i | 0.538900 | + | 0.842370i | \(0.318840\pi\) | ||||
−0.538900 | + | 0.842370i | \(0.681160\pi\) | |||||||
\(998\) | −1.42479e9 | −1.43337 | ||||||||
\(999\) | 4.34585e9 | 4.35892 |
(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 | 43.7.b.b.42.5 | ✓ | 20 | |
43.42 | odd | 2 | inner | 43.7.b.b.42.16 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.7.b.b.42.5 | ✓ | 20 | 1.1 | even | 1 | trivial | |
43.7.b.b.42.16 | yes | 20 | 43.42 | odd | 2 | inner |