Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,41,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 41, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 41);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 41 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(30.4026855589\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 249659905422 x^{10} + \cdots + 12\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{63}\cdot 3^{98}\cdot 5^{6}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.6 | ||
Root | \(-18015.5i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.41.b.a.2.7 |
$q$-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 \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 108093.i | − | 0.103085i | −0.998671 | − | 0.0515427i | \(-0.983586\pi\) | ||
0.998671 | − | 0.0515427i | \(-0.0164138\pi\) | |||||||
\(3\) | −2.05308e9 | − | 2.81825e9i | −0.588819 | − | 0.808265i | ||||
\(4\) | 1.08783e12 | 0.989373 | ||||||||
\(5\) | − | 1.13503e14i | − | 1.19016i | −0.803665 | − | 0.595082i | \(-0.797119\pi\) | ||
0.803665 | − | 0.595082i | \(-0.202881\pi\) | |||||||
\(6\) | −3.04633e14 | + | 2.21924e14i | −0.0833204 | + | 0.0606987i | ||||
\(7\) | −1.19157e17 | −1.49334 | −0.746669 | − | 0.665196i | \(-0.768348\pi\) | ||||
−0.746669 | + | 0.665196i | \(0.768348\pi\) | |||||||
\(8\) | − | 2.36436e17i | − | 0.205076i | ||||||
\(9\) | −3.72735e18 | + | 1.15722e19i | −0.306585 | + | 0.951843i | ||||
\(10\) | −1.22689e19 | −0.122689 | ||||||||
\(11\) | − | 1.08238e21i | − | 1.60889i | −0.594024 | − | 0.804447i | \(-0.702462\pi\) | ||
0.594024 | − | 0.804447i | \(-0.297538\pi\) | |||||||
\(12\) | −2.23340e21 | − | 3.06577e21i | −0.582562 | − | 0.799676i | ||||
\(13\) | 9.34761e21 | 0.491851 | 0.245925 | − | 0.969289i | \(-0.420908\pi\) | ||||
0.245925 | + | 0.969289i | \(0.420908\pi\) | |||||||
\(14\) | 1.28800e22i | 0.153941i | ||||||||
\(15\) | −3.19879e23 | + | 2.33031e23i | −0.961969 | + | 0.700792i | ||||
\(16\) | 1.17052e24 | 0.968233 | ||||||||
\(17\) | − | 1.14562e24i | − | 0.281879i | −0.990018 | − | 0.140940i | \(-0.954988\pi\) | ||
0.990018 | − | 0.140940i | \(-0.0450124\pi\) | |||||||
\(18\) | 1.25087e24 | + | 4.02901e23i | 0.0981212 | + | 0.0316044i | ||||
\(19\) | −4.02644e25 | −1.07115 | −0.535574 | − | 0.844489i | \(-0.679905\pi\) | ||||
−0.535574 | + | 0.844489i | \(0.679905\pi\) | |||||||
\(20\) | − | 1.23472e26i | − | 1.17752i | ||||||
\(21\) | 2.44639e26 | + | 3.35813e26i | 0.879305 | + | 1.20701i | ||||
\(22\) | −1.16998e26 | −0.165854 | ||||||||
\(23\) | 1.54324e26i | 0.0899241i | 0.998989 | + | 0.0449620i | \(0.0143167\pi\) | ||||
−0.998989 | + | 0.0449620i | \(0.985683\pi\) | |||||||
\(24\) | −6.66335e26 | + | 4.85423e26i | −0.165755 | + | 0.120752i | ||||
\(25\) | −3.78798e27 | −0.416493 | ||||||||
\(26\) | − | 1.01041e27i | − | 0.0507027i | ||||||
\(27\) | 4.02659e28 | − | 1.32541e28i | 0.949865 | − | 0.312662i | ||||
\(28\) | −1.29622e29 | −1.47747 | ||||||||
\(29\) | 3.32449e29i | 1.87830i | 0.343509 | + | 0.939149i | \(0.388384\pi\) | ||||
−0.343509 | + | 0.939149i | \(0.611616\pi\) | |||||||
\(30\) | 2.51890e28 | + | 3.45767e28i | 0.0722414 | + | 0.0991650i | ||||
\(31\) | −2.50582e29 | −0.373006 | −0.186503 | − | 0.982454i | \(-0.559715\pi\) | ||||
−0.186503 | + | 0.982454i | \(0.559715\pi\) | |||||||
\(32\) | − | 3.86489e29i | − | 0.304886i | ||||||
\(33\) | −3.05042e30 | + | 2.22223e30i | −1.30041 | + | 0.947347i | ||||
\(34\) | −1.23834e29 | −0.0290577 | ||||||||
\(35\) | 1.35246e31i | 1.77732i | ||||||||
\(36\) | −4.05472e30 | + | 1.25886e31i | −0.303327 | + | 0.941728i | ||||
\(37\) | −2.26165e31 | −0.978117 | −0.489059 | − | 0.872251i | \(-0.662660\pi\) | ||||
−0.489059 | + | 0.872251i | \(0.662660\pi\) | |||||||
\(38\) | 4.35230e30i | 0.110420i | ||||||||
\(39\) | −1.91914e31 | − | 2.63439e31i | −0.289611 | − | 0.397546i | ||||
\(40\) | −2.68362e31 | −0.244074 | ||||||||
\(41\) | 2.34363e32i | 1.30080i | 0.759590 | + | 0.650402i | \(0.225400\pi\) | ||||
−0.759590 | + | 0.650402i | \(0.774600\pi\) | |||||||
\(42\) | 3.62990e31 | − | 2.64437e31i | 0.124425 | − | 0.0906436i | ||||
\(43\) | 8.11516e31 | 0.173751 | 0.0868756 | − | 0.996219i | \(-0.472312\pi\) | ||||
0.0868756 | + | 0.996219i | \(0.472312\pi\) | |||||||
\(44\) | − | 1.17745e33i | − | 1.59180i | ||||||
\(45\) | 1.31348e33 | + | 4.23066e32i | 1.13285 | + | 0.364886i | ||||
\(46\) | 1.66813e31 | 0.00926987 | ||||||||
\(47\) | − | 2.91765e33i | − | 1.05457i | −0.849688 | − | 0.527286i | \(-0.823209\pi\) | ||
0.849688 | − | 0.527286i | \(-0.176791\pi\) | |||||||
\(48\) | −2.40318e33 | − | 3.29882e33i | −0.570114 | − | 0.782589i | ||||
\(49\) | 7.83153e33 | 1.23006 | ||||||||
\(50\) | 4.09454e32i | 0.0429344i | ||||||||
\(51\) | −3.22865e33 | + | 2.35206e33i | −0.227833 | + | 0.165976i | ||||
\(52\) | 1.01686e34 | 0.486624 | ||||||||
\(53\) | 1.51489e34i | 0.495294i | 0.968850 | + | 0.247647i | \(0.0796573\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(54\) | −1.43267e33 | − | 4.35246e33i | −0.0322309 | − | 0.0979173i | ||||
\(55\) | −1.22854e35 | −1.91485 | ||||||||
\(56\) | 2.81729e34i | 0.306247i | ||||||||
\(57\) | 8.26662e34 | + | 1.13475e35i | 0.630712 | + | 0.865771i | ||||
\(58\) | 3.59354e34 | 0.193625 | ||||||||
\(59\) | 7.34418e34i | 0.281127i | 0.990072 | + | 0.140564i | \(0.0448915\pi\) | ||||
−0.990072 | + | 0.140564i | \(0.955109\pi\) | |||||||
\(60\) | −3.47974e35 | + | 2.53498e35i | −0.951746 | + | 0.693345i | ||||
\(61\) | −1.65923e35 | −0.326070 | −0.163035 | − | 0.986620i | \(-0.552128\pi\) | ||||
−0.163035 | + | 0.986620i | \(0.552128\pi\) | |||||||
\(62\) | 2.70861e34i | 0.0384515i | ||||||||
\(63\) | 4.44140e35 | − | 1.37891e36i | 0.457834 | − | 1.42142i | ||||
\(64\) | 1.24523e36 | 0.936804 | ||||||||
\(65\) | − | 1.06098e36i | − | 0.585384i | ||||||
\(66\) | 2.40207e35 | + | 3.29729e35i | 0.0976578 | + | 0.134054i | ||||
\(67\) | 8.14731e35 | 0.245199 | 0.122599 | − | 0.992456i | \(-0.460877\pi\) | ||||
0.122599 | + | 0.992456i | \(0.460877\pi\) | |||||||
\(68\) | − | 1.24624e36i | − | 0.278884i | ||||||
\(69\) | 4.34922e35 | − | 3.16840e35i | 0.0726825 | − | 0.0529490i | ||||
\(70\) | 1.46192e36 | 0.183216 | ||||||||
\(71\) | − | 3.89618e36i | − | 0.367682i | −0.982956 | − | 0.183841i | \(-0.941147\pi\) | ||
0.982956 | − | 0.183841i | \(-0.0588532\pi\) | |||||||
\(72\) | 2.73608e36 | + | 8.81281e35i | 0.195200 | + | 0.0628730i | ||||
\(73\) | −1.48310e37 | −0.802995 | −0.401498 | − | 0.915860i | \(-0.631510\pi\) | ||||
−0.401498 | + | 0.915860i | \(0.631510\pi\) | |||||||
\(74\) | 2.44468e36i | 0.100830i | ||||||||
\(75\) | 7.77704e36 | + | 1.06755e37i | 0.245239 | + | 0.336636i | ||||
\(76\) | −4.38007e37 | −1.05976 | ||||||||
\(77\) | 1.28973e38i | 2.40262i | ||||||||
\(78\) | −2.84759e36 | + | 2.07446e36i | −0.0409812 | + | 0.0298547i | ||||
\(79\) | 5.20652e37 | 0.580772 | 0.290386 | − | 0.956910i | \(-0.406216\pi\) | ||||
0.290386 | + | 0.956910i | \(0.406216\pi\) | |||||||
\(80\) | − | 1.32858e38i | − | 1.15236i | ||||||
\(81\) | −1.20022e38 | − | 8.62673e37i | −0.812012 | − | 0.583641i | ||||
\(82\) | 2.53330e37 | 0.134094 | ||||||||
\(83\) | − | 2.17493e38i | − | 0.903405i | −0.892169 | − | 0.451703i | \(-0.850817\pi\) | ||
0.892169 | − | 0.451703i | \(-0.149183\pi\) | |||||||
\(84\) | 2.66125e38 | + | 3.65307e38i | 0.869961 | + | 1.19419i | ||||
\(85\) | −1.30032e38 | −0.335483 | ||||||||
\(86\) | − | 8.77192e36i | − | 0.0179112i | ||||||
\(87\) | 9.36922e38 | − | 6.82545e38i | 1.51816 | − | 1.10598i | ||||
\(88\) | −2.55914e38 | −0.329945 | ||||||||
\(89\) | − | 3.50974e38i | − | 0.360973i | −0.983577 | − | 0.180487i | \(-0.942233\pi\) | ||
0.983577 | − | 0.180487i | \(-0.0577673\pi\) | |||||||
\(90\) | 4.57304e37 | − | 1.41978e38i | 0.0376145 | − | 0.116780i | ||||
\(91\) | −1.11383e39 | −0.734499 | ||||||||
\(92\) | 1.67878e38i | 0.0889685i | ||||||||
\(93\) | 5.14465e38 | + | 7.06201e38i | 0.219633 | + | 0.301487i | ||||
\(94\) | −3.15378e38 | −0.108711 | ||||||||
\(95\) | 4.57013e39i | 1.27484i | ||||||||
\(96\) | −1.08922e39 | + | 7.93495e38i | −0.246429 | + | 0.179523i | ||||
\(97\) | −7.87477e39 | −1.44812 | −0.724058 | − | 0.689740i | \(-0.757725\pi\) | ||||
−0.724058 | + | 0.689740i | \(0.757725\pi\) | |||||||
\(98\) | − | 8.46533e38i | − | 0.126801i | ||||||
\(99\) | 1.25256e40 | + | 4.03443e39i | 1.53142 | + | 0.493263i | ||||
\(100\) | −4.12067e39 | −0.412067 | ||||||||
\(101\) | − | 4.39351e39i | − | 0.360068i | −0.983660 | − | 0.180034i | \(-0.942379\pi\) | ||
0.983660 | − | 0.180034i | \(-0.0576207\pi\) | |||||||
\(102\) | 2.54241e38 | + | 3.48994e38i | 0.0171097 | + | 0.0234863i | ||||
\(103\) | −1.79465e40 | −0.993654 | −0.496827 | − | 0.867850i | \(-0.665502\pi\) | ||||
−0.496827 | + | 0.867850i | \(0.665502\pi\) | |||||||
\(104\) | − | 2.21011e39i | − | 0.100867i | ||||||
\(105\) | 3.81158e40 | − | 2.77672e40i | 1.43654 | − | 1.04652i | ||||
\(106\) | 1.63749e39 | 0.0510576 | ||||||||
\(107\) | − | 7.12764e39i | − | 0.184192i | −0.995750 | − | 0.0920959i | \(-0.970643\pi\) | ||
0.995750 | − | 0.0920959i | \(-0.0293566\pi\) | |||||||
\(108\) | 4.38023e40 | − | 1.44182e40i | 0.939771 | − | 0.309339i | ||||
\(109\) | −2.25766e40 | −0.402836 | −0.201418 | − | 0.979505i | \(-0.564555\pi\) | ||||
−0.201418 | + | 0.979505i | \(0.564555\pi\) | |||||||
\(110\) | 1.32796e40i | 0.197393i | ||||||||
\(111\) | 4.64336e40 | + | 6.37388e40i | 0.575934 | + | 0.790578i | ||||
\(112\) | −1.39476e41 | −1.44590 | ||||||||
\(113\) | − | 1.88589e41i | − | 1.63662i | −0.574780 | − | 0.818308i | \(-0.694912\pi\) | ||
0.574780 | − | 0.818308i | \(-0.305088\pi\) | |||||||
\(114\) | 1.22658e40 | − | 8.93563e39i | 0.0892484 | − | 0.0650172i | ||||
\(115\) | 1.75162e40 | 0.107025 | ||||||||
\(116\) | 3.61647e41i | 1.85834i | ||||||||
\(117\) | −3.48418e40 | + | 1.08172e41i | −0.150794 | + | 0.468165i | ||||
\(118\) | 7.93855e39 | 0.0289802 | ||||||||
\(119\) | 1.36509e41i | 0.420941i | ||||||||
\(120\) | 5.50970e40 | + | 7.56310e40i | 0.143715 | + | 0.197276i | ||||
\(121\) | −7.18962e41 | −1.58854 | ||||||||
\(122\) | 1.79351e40i | 0.0336131i | ||||||||
\(123\) | 6.60493e41 | − | 4.81167e41i | 1.05139 | − | 0.765938i | ||||
\(124\) | −2.72590e41 | −0.369042 | ||||||||
\(125\) | − | 6.02357e41i | − | 0.694470i | ||||||
\(126\) | −1.49050e41 | − | 4.80084e40i | −0.146528 | − | 0.0471961i | ||||
\(127\) | 2.05337e42 | 1.72342 | 0.861712 | − | 0.507398i | \(-0.169392\pi\) | ||||
0.861712 | + | 0.507398i | \(0.169392\pi\) | |||||||
\(128\) | − | 5.59550e41i | − | 0.401457i | ||||||
\(129\) | −1.66611e41 | − | 2.28705e41i | −0.102308 | − | 0.140437i | ||||
\(130\) | −1.14685e41 | −0.0603446 | ||||||||
\(131\) | − | 6.40342e41i | − | 0.289059i | −0.989500 | − | 0.144529i | \(-0.953833\pi\) | ||
0.989500 | − | 0.144529i | \(-0.0461668\pi\) | |||||||
\(132\) | −3.31833e42 | + | 2.41740e42i | −1.28659 | + | 0.937280i | ||||
\(133\) | 4.79777e42 | 1.59958 | ||||||||
\(134\) | − | 8.80667e40i | − | 0.0252764i | ||||||
\(135\) | −1.50438e42 | − | 4.57030e42i | −0.372119 | − | 1.13050i | ||||
\(136\) | −2.70867e41 | −0.0578066 | ||||||||
\(137\) | 1.12866e42i | 0.208042i | 0.994575 | + | 0.104021i | \(0.0331710\pi\) | ||||
−0.994575 | + | 0.104021i | \(0.966829\pi\) | |||||||
\(138\) | −3.42481e40 | − | 4.70120e40i | −0.00545827 | − | 0.00749251i | ||||
\(139\) | −5.82513e42 | −0.803544 | −0.401772 | − | 0.915740i | \(-0.631605\pi\) | ||||
−0.401772 | + | 0.915740i | \(0.631605\pi\) | |||||||
\(140\) | 1.47125e43i | 1.75843i | ||||||||
\(141\) | −8.22267e42 | + | 5.99019e42i | −0.852374 | + | 0.620952i | ||||
\(142\) | −4.21150e41 | −0.0379027 | ||||||||
\(143\) | − | 1.01177e43i | − | 0.791336i | ||||||
\(144\) | −4.36295e42 | + | 1.35455e43i | −0.296846 | + | 0.921606i | ||||
\(145\) | 3.77339e43 | 2.23549 | ||||||||
\(146\) | 1.60313e42i | 0.0827771i | ||||||||
\(147\) | −1.60788e43 | − | 2.20712e43i | −0.724280 | − | 0.994212i | ||||
\(148\) | −2.46028e43 | −0.967723 | ||||||||
\(149\) | − | 4.17735e43i | − | 1.43607i | −0.696007 | − | 0.718035i | \(-0.745042\pi\) | ||
0.696007 | − | 0.718035i | \(-0.254958\pi\) | |||||||
\(150\) | 1.15394e42 | − | 8.40643e41i | 0.0347023 | − | 0.0252806i | ||||
\(151\) | 4.60012e43 | 1.21124 | 0.605620 | − | 0.795754i | \(-0.292925\pi\) | ||||
0.605620 | + | 0.795754i | \(0.292925\pi\) | |||||||
\(152\) | 9.51995e42i | 0.219666i | ||||||||
\(153\) | 1.32574e43 | + | 4.27014e42i | 0.268305 | + | 0.0864199i | ||||
\(154\) | 1.39411e43 | 0.247675 | ||||||||
\(155\) | 2.84418e43i | 0.443938i | ||||||||
\(156\) | −2.08770e43 | − | 2.86576e43i | −0.286533 | − | 0.393321i | ||||
\(157\) | 1.47730e41 | 0.00178434 | 0.000892168 | − | 1.00000i | \(-0.499716\pi\) | ||||
0.000892168 | 1.00000i | \(0.499716\pi\) | ||||||||
\(158\) | − | 5.62788e42i | − | 0.0598692i | ||||||
\(159\) | 4.26933e43 | − | 3.11019e43i | 0.400329 | − | 0.291638i | ||||
\(160\) | −4.38677e43 | −0.362865 | ||||||||
\(161\) | − | 1.83887e43i | − | 0.134287i | ||||||
\(162\) | −9.32489e42 | + | 1.29736e43i | −0.0601650 | + | 0.0837066i | ||||
\(163\) | −3.33578e44 | −1.90303 | −0.951514 | − | 0.307605i | \(-0.900473\pi\) | ||||
−0.951514 | + | 0.307605i | \(0.900473\pi\) | |||||||
\(164\) | 2.54947e44i | 1.28698i | ||||||||
\(165\) | 2.52229e44 | + | 3.46232e44i | 1.12750 | + | 1.54771i | ||||
\(166\) | −2.35094e43 | −0.0931280 | ||||||||
\(167\) | − | 2.38931e44i | − | 0.839348i | −0.907675 | − | 0.419674i | \(-0.862144\pi\) | ||
0.907675 | − | 0.419674i | \(-0.137856\pi\) | |||||||
\(168\) | 7.93983e43 | − | 5.78414e43i | 0.247529 | − | 0.180324i | ||||
\(169\) | −2.73811e44 | −0.758083 | ||||||||
\(170\) | 1.40555e43i | 0.0345834i | ||||||||
\(171\) | 1.50080e44 | − | 4.65947e44i | 0.328397 | − | 1.01956i | ||||
\(172\) | 8.82790e43 | 0.171905 | ||||||||
\(173\) | 5.45959e44i | 0.946756i | 0.880860 | + | 0.473378i | \(0.156965\pi\) | ||||
−0.880860 | + | 0.473378i | \(0.843035\pi\) | |||||||
\(174\) | −7.37783e43 | − | 1.01275e44i | −0.114010 | − | 0.156501i | ||||
\(175\) | 4.51363e44 | 0.621964 | ||||||||
\(176\) | − | 1.26695e45i | − | 1.55778i | ||||||
\(177\) | 2.06977e44 | − | 1.50782e44i | 0.227226 | − | 0.165533i | ||||
\(178\) | −3.79379e43 | −0.0372111 | ||||||||
\(179\) | − | 4.75963e44i | − | 0.417362i | −0.977984 | − | 0.208681i | \(-0.933083\pi\) | ||
0.977984 | − | 0.208681i | \(-0.0669170\pi\) | |||||||
\(180\) | 1.42884e45 | + | 4.60223e44i | 1.12081 | + | 0.361009i | ||||
\(181\) | −1.39046e45 | −0.976305 | −0.488153 | − | 0.872758i | \(-0.662329\pi\) | ||||
−0.488153 | + | 0.872758i | \(0.662329\pi\) | |||||||
\(182\) | 1.20397e44i | 0.0757162i | ||||||||
\(183\) | 3.40655e44 | + | 4.67613e44i | 0.191996 | + | 0.263551i | ||||
\(184\) | 3.64877e43 | 0.0184412 | ||||||||
\(185\) | 2.56704e45i | 1.16412i | ||||||||
\(186\) | 7.63354e43 | − | 5.56101e43i | 0.0310790 | − | 0.0226410i | ||||
\(187\) | −1.24000e45 | −0.453514 | ||||||||
\(188\) | − | 3.17390e45i | − | 1.04337i | ||||||
\(189\) | −4.79795e45 | + | 1.57931e45i | −1.41847 | + | 0.466909i | ||||
\(190\) | 4.93999e44 | 0.131418 | ||||||||
\(191\) | 5.74210e45i | 1.37532i | 0.726033 | + | 0.687660i | \(0.241362\pi\) | ||||
−0.726033 | + | 0.687660i | \(0.758638\pi\) | |||||||
\(192\) | −2.55655e45 | − | 3.50935e45i | −0.551608 | − | 0.757186i | ||||
\(193\) | 5.42847e45 | 1.05568 | 0.527839 | − | 0.849344i | \(-0.323002\pi\) | ||||
0.527839 | + | 0.849344i | \(0.323002\pi\) | |||||||
\(194\) | 8.51207e44i | 0.149280i | ||||||||
\(195\) | −2.99011e45 | + | 2.17828e45i | −0.473145 | + | 0.344685i | ||||
\(196\) | 8.51935e45 | 1.21699 | ||||||||
\(197\) | 9.09772e44i | 0.117384i | 0.998276 | + | 0.0586919i | \(0.0186930\pi\) | ||||
−0.998276 | + | 0.0586919i | \(0.981307\pi\) | |||||||
\(198\) | 4.36093e44 | − | 1.35392e45i | 0.0508482 | − | 0.157867i | ||||
\(199\) | −4.16830e45 | −0.439438 | −0.219719 | − | 0.975563i | \(-0.570514\pi\) | ||||
−0.219719 | + | 0.975563i | \(0.570514\pi\) | |||||||
\(200\) | 8.95615e44i | 0.0854125i | ||||||||
\(201\) | −1.67271e45 | − | 2.29611e45i | −0.144378 | − | 0.198186i | ||||
\(202\) | −4.74908e44 | −0.0371178 | ||||||||
\(203\) | − | 3.96135e46i | − | 2.80493i | ||||||
\(204\) | −3.51221e45 | + | 2.55864e45i | −0.225412 | + | 0.164212i | ||||
\(205\) | 2.66009e46 | 1.54817 | ||||||||
\(206\) | 1.93989e45i | 0.102431i | ||||||||
\(207\) | −1.78586e45 | − | 5.75219e44i | −0.0855937 | − | 0.0275694i | ||||
\(208\) | 1.09416e46 | 0.476226 | ||||||||
\(209\) | 4.35815e46i | 1.72336i | ||||||||
\(210\) | −3.00144e45 | − | 4.12005e45i | −0.107881 | − | 0.148087i | ||||
\(211\) | −4.23119e46 | −1.38297 | −0.691486 | − | 0.722390i | \(-0.743044\pi\) | ||||
−0.691486 | + | 0.722390i | \(0.743044\pi\) | |||||||
\(212\) | 1.64794e46i | 0.490031i | ||||||||
\(213\) | −1.09804e46 | + | 7.99920e45i | −0.297185 | + | 0.216498i | ||||
\(214\) | −7.70448e44 | −0.0189875 | ||||||||
\(215\) | − | 9.21095e45i | − | 0.206793i | ||||||
\(216\) | −3.13374e45 | − | 9.52030e45i | −0.0641192 | − | 0.194794i | ||||
\(217\) | 2.98585e46 | 0.557023 | ||||||||
\(218\) | 2.44037e45i | 0.0415266i | ||||||||
\(219\) | 3.04493e46 | + | 4.17974e46i | 0.472819 | + | 0.649033i | ||||
\(220\) | −1.33644e47 | −1.89450 | ||||||||
\(221\) | − | 1.07088e46i | − | 0.138643i | ||||||
\(222\) | 6.88972e45 | − | 5.01914e45i | 0.0814971 | − | 0.0593704i | ||||
\(223\) | 7.95251e46 | 0.859818 | 0.429909 | − | 0.902872i | \(-0.358546\pi\) | ||||
0.429909 | + | 0.902872i | \(0.358546\pi\) | |||||||
\(224\) | 4.60528e46i | 0.455298i | ||||||||
\(225\) | 1.41191e46 | − | 4.38352e46i | 0.127690 | − | 0.396436i | ||||
\(226\) | −2.03851e46 | −0.168711 | ||||||||
\(227\) | − | 1.10749e47i | − | 0.839118i | −0.907728 | − | 0.419559i | \(-0.862185\pi\) | ||
0.907728 | − | 0.419559i | \(-0.137815\pi\) | |||||||
\(228\) | 8.99266e46 | + | 1.23441e47i | 0.624009 | + | 0.856570i | ||||
\(229\) | −1.39153e47 | −0.884672 | −0.442336 | − | 0.896849i | \(-0.645850\pi\) | ||||
−0.442336 | + | 0.896849i | \(0.645850\pi\) | |||||||
\(230\) | − | 1.89338e45i | − | 0.0110327i | ||||||
\(231\) | 3.63479e47 | − | 2.64793e47i | 1.94196 | − | 1.41471i | ||||
\(232\) | 7.86028e46 | 0.385193 | ||||||||
\(233\) | − | 2.19142e47i | − | 0.985386i | −0.870203 | − | 0.492693i | \(-0.836013\pi\) | ||
0.870203 | − | 0.492693i | \(-0.163987\pi\) | |||||||
\(234\) | 1.16927e46 | + | 3.76616e45i | 0.0482610 | + | 0.0155447i | ||||
\(235\) | −3.31162e47 | −1.25512 | ||||||||
\(236\) | 7.98921e46i | 0.278140i | ||||||||
\(237\) | −1.06894e47 | − | 1.46733e47i | −0.341970 | − | 0.469418i | ||||
\(238\) | 1.47556e46 | 0.0433929 | ||||||||
\(239\) | 6.15537e47i | 1.66455i | 0.554365 | + | 0.832273i | \(0.312961\pi\) | ||||
−0.554365 | + | 0.832273i | \(0.687039\pi\) | |||||||
\(240\) | −3.74426e47 | + | 2.72768e47i | −0.931410 | + | 0.678530i | ||||
\(241\) | 5.24429e47 | 1.20046 | 0.600228 | − | 0.799829i | \(-0.295077\pi\) | ||||
0.600228 | + | 0.799829i | \(0.295077\pi\) | |||||||
\(242\) | 7.77147e46i | 0.163756i | ||||||||
\(243\) | 3.29368e45 | + | 5.15367e47i | 0.00639082 | + | 0.999980i | ||||
\(244\) | −1.80496e47 | −0.322605 | ||||||||
\(245\) | − | 8.88902e47i | − | 1.46397i | ||||||
\(246\) | −5.20108e46 | − | 7.13946e46i | −0.0789571 | − | 0.108384i | ||||
\(247\) | −3.76376e47 | −0.526845 | ||||||||
\(248\) | 5.92465e46i | 0.0764943i | ||||||||
\(249\) | −6.12947e47 | + | 4.46531e47i | −0.730191 | + | 0.531942i | ||||
\(250\) | −6.51105e46 | −0.0715898 | ||||||||
\(251\) | 1.18485e48i | 1.20278i | 0.798954 | + | 0.601392i | \(0.205387\pi\) | ||||
−0.798954 | + | 0.601392i | \(0.794613\pi\) | |||||||
\(252\) | 4.83147e47 | − | 1.50001e48i | 0.452969 | − | 1.40632i | ||||
\(253\) | 1.67038e47 | 0.144678 | ||||||||
\(254\) | − | 2.21955e47i | − | 0.177660i | ||||||
\(255\) | 2.66966e47 | + | 3.66461e47i | 0.197539 | + | 0.271159i | ||||
\(256\) | 1.30866e48 | 0.895419 | ||||||||
\(257\) | − | 4.52221e47i | − | 0.286212i | −0.989707 | − | 0.143106i | \(-0.954291\pi\) | ||
0.989707 | − | 0.143106i | \(-0.0457090\pi\) | |||||||
\(258\) | −2.47214e46 | + | 1.80095e46i | −0.0144770 | + | 0.0105465i | ||||
\(259\) | 2.69491e48 | 1.46066 | ||||||||
\(260\) | − | 1.15416e48i | − | 0.579163i | ||||||
\(261\) | −3.84716e48 | − | 1.23915e48i | −1.78785 | − | 0.575858i | ||||
\(262\) | −6.92165e46 | −0.0297978 | ||||||||
\(263\) | − | 1.78553e48i | − | 0.712280i | −0.934433 | − | 0.356140i | \(-0.884093\pi\) | ||
0.934433 | − | 0.356140i | \(-0.115907\pi\) | |||||||
\(264\) | 5.25414e47 | + | 7.21230e47i | 0.194278 | + | 0.266683i | ||||
\(265\) | 1.71944e48 | 0.589482 | ||||||||
\(266\) | − | 5.18606e47i | − | 0.164894i | ||||||
\(267\) | −9.89132e47 | + | 7.20580e47i | −0.291762 | + | 0.212548i | ||||
\(268\) | 8.86287e47 | 0.242593 | ||||||||
\(269\) | 5.13521e48i | 1.30471i | 0.757915 | + | 0.652353i | \(0.226218\pi\) | ||||
−0.757915 | + | 0.652353i | \(0.773782\pi\) | |||||||
\(270\) | −4.94017e47 | + | 1.62613e47i | −0.116538 | + | 0.0383601i | ||||
\(271\) | −5.29935e48 | −1.16101 | −0.580506 | − | 0.814256i | \(-0.697145\pi\) | ||||
−0.580506 | + | 0.814256i | \(0.697145\pi\) | |||||||
\(272\) | − | 1.34098e48i | − | 0.272925i | ||||||
\(273\) | 2.28679e48 | + | 3.13905e48i | 0.432487 | + | 0.593670i | ||||
\(274\) | 1.22000e47 | 0.0214462 | ||||||||
\(275\) | 4.10005e48i | 0.670093i | ||||||||
\(276\) | 4.73120e47 | − | 3.44667e47i | 0.0719101 | − | 0.0523863i | ||||
\(277\) | −5.34662e48 | −0.755934 | −0.377967 | − | 0.925819i | \(-0.623377\pi\) | ||||
−0.377967 | + | 0.925819i | \(0.623377\pi\) | |||||||
\(278\) | 6.29655e47i | 0.0828337i | ||||||||
\(279\) | 9.34007e47 | − | 2.89978e48i | 0.114358 | − | 0.355043i | ||||
\(280\) | 3.19771e48 | 0.364484 | ||||||||
\(281\) | 6.38334e48i | 0.677520i | 0.940873 | + | 0.338760i | \(0.110007\pi\) | ||||
−0.940873 | + | 0.338760i | \(0.889993\pi\) | |||||||
\(282\) | 6.47497e47 | + | 8.88812e47i | 0.0640112 | + | 0.0878674i | ||||
\(283\) | −1.29528e49 | −1.19298 | −0.596492 | − | 0.802619i | \(-0.703439\pi\) | ||||
−0.596492 | + | 0.802619i | \(0.703439\pi\) | |||||||
\(284\) | − | 4.23838e48i | − | 0.363775i | ||||||
\(285\) | 1.28797e49 | − | 9.38286e48i | 1.03041 | − | 0.750651i | ||||
\(286\) | −1.09365e48 | −0.0815753 | ||||||||
\(287\) | − | 2.79259e49i | − | 1.94254i | ||||||
\(288\) | 4.47253e48 | + | 1.44058e48i | 0.290204 | + | 0.0934735i | ||||
\(289\) | 1.52055e49 | 0.920544 | ||||||||
\(290\) | − | 4.07877e48i | − | 0.230446i | ||||||
\(291\) | 1.61676e49 | + | 2.21930e49i | 0.852678 | + | 1.17046i | ||||
\(292\) | −1.61336e49 | −0.794462 | ||||||||
\(293\) | 1.44357e49i | 0.663875i | 0.943301 | + | 0.331937i | \(0.107702\pi\) | ||||
−0.943301 | + | 0.331937i | \(0.892298\pi\) | |||||||
\(294\) | −2.38574e48 | + | 1.73800e48i | −0.102489 | + | 0.0746628i | ||||
\(295\) | 8.33587e48 | 0.334588 | ||||||||
\(296\) | 5.34735e48i | 0.200588i | ||||||||
\(297\) | −1.43460e49 | − | 4.35831e49i | −0.503039 | − | 1.52823i | ||||
\(298\) | −4.51542e48 | −0.148038 | ||||||||
\(299\) | 1.44256e48i | 0.0442292i | ||||||||
\(300\) | 8.46008e48 | + | 1.16131e49i | 0.242633 | + | 0.333059i | ||||
\(301\) | −9.66976e48 | −0.259469 | ||||||||
\(302\) | − | 4.97241e48i | − | 0.124861i | ||||||
\(303\) | −1.23820e49 | + | 9.02025e48i | −0.291030 | + | 0.212015i | ||||
\(304\) | −4.71304e49 | −1.03712 | ||||||||
\(305\) | 1.88328e49i | 0.388077i | ||||||||
\(306\) | 4.61573e47 | − | 1.43303e48i | 0.00890864 | − | 0.0276584i | ||||
\(307\) | 2.03168e49 | 0.367357 | 0.183678 | − | 0.982986i | \(-0.441200\pi\) | ||||
0.183678 | + | 0.982986i | \(0.441200\pi\) | |||||||
\(308\) | 1.40301e50i | 2.37709i | ||||||||
\(309\) | 3.68457e49 | + | 5.05776e49i | 0.585082 | + | 0.803136i | ||||
\(310\) | 3.07436e48 | 0.0457636 | ||||||||
\(311\) | − | 1.26635e50i | − | 1.76745i | −0.468009 | − | 0.883724i | \(-0.655029\pi\) | ||
0.468009 | − | 0.883724i | \(-0.344971\pi\) | |||||||
\(312\) | −6.22864e48 | + | 4.53754e48i | −0.0815269 | + | 0.0593921i | ||||
\(313\) | −3.21332e49 | −0.394518 | −0.197259 | − | 0.980351i | \(-0.563204\pi\) | ||||
−0.197259 | + | 0.980351i | \(0.563204\pi\) | |||||||
\(314\) | − | 1.59686e46i | − | 0.000183939i | ||||||
\(315\) | −1.56510e50 | − | 5.04112e49i | −1.69173 | − | 0.544899i | ||||
\(316\) | 5.66380e49 | 0.574600 | ||||||||
\(317\) | − | 6.96883e49i | − | 0.663705i | −0.943331 | − | 0.331852i | \(-0.892326\pi\) | ||
0.943331 | − | 0.331852i | \(-0.107674\pi\) | |||||||
\(318\) | −3.36190e48 | − | 4.61484e48i | −0.0300637 | − | 0.0412681i | ||||
\(319\) | 3.59837e50 | 3.02198 | ||||||||
\(320\) | − | 1.41337e50i | − | 1.11495i | ||||||
\(321\) | −2.00874e49 | + | 1.46336e49i | −0.148876 | + | 0.108456i | ||||
\(322\) | −1.98769e48 | −0.0138430 | ||||||||
\(323\) | 4.61278e49i | 0.301934i | ||||||||
\(324\) | −1.30564e50 | − | 9.38440e49i | −0.803383 | − | 0.577439i | ||||
\(325\) | −3.54085e49 | −0.204852 | ||||||||
\(326\) | 3.60574e49i | 0.196175i | ||||||||
\(327\) | 4.63517e49 | + | 6.36264e49i | 0.237198 | + | 0.325598i | ||||
\(328\) | 5.54119e49 | 0.266763 | ||||||||
\(329\) | 3.47658e50i | 1.57483i | ||||||||
\(330\) | 3.74253e49 | − | 2.72642e49i | 0.159546 | − | 0.116229i | ||||
\(331\) | −2.72248e50 | −1.09246 | −0.546230 | − | 0.837636i | \(-0.683937\pi\) | ||||
−0.546230 | + | 0.837636i | \(0.683937\pi\) | |||||||
\(332\) | − | 2.36594e50i | − | 0.893805i | ||||||
\(333\) | 8.42997e49 | − | 2.61722e50i | 0.299876 | − | 0.931014i | ||||
\(334\) | −2.58267e49 | −0.0865246 | ||||||||
\(335\) | − | 9.24744e49i | − | 0.291827i | ||||||
\(336\) | 2.86355e50 | + | 3.93077e50i | 0.851372 | + | 1.16867i | ||||
\(337\) | −5.28872e49 | −0.148167 | −0.0740837 | − | 0.997252i | \(-0.523603\pi\) | ||||
−0.0740837 | + | 0.997252i | \(0.523603\pi\) | |||||||
\(338\) | 2.95970e49i | 0.0781473i | ||||||||
\(339\) | −5.31489e50 | + | 3.87189e50i | −1.32282 | + | 0.963671i | ||||
\(340\) | −1.41452e50 | −0.331918 | ||||||||
\(341\) | 2.71226e50i | 0.600127i | ||||||||
\(342\) | −5.03656e49 | − | 1.62226e49i | −0.105102 | − | 0.0338530i | ||||
\(343\) | −1.74532e50 | −0.343552 | ||||||||
\(344\) | − | 1.91872e49i | − | 0.0356321i | ||||||
\(345\) | −3.59622e49 | − | 4.93650e49i | −0.0630180 | − | 0.0865042i | ||||
\(346\) | 5.90143e49 | 0.0975968 | ||||||||
\(347\) | 4.99538e50i | 0.779793i | 0.920859 | + | 0.389896i | \(0.127489\pi\) | ||||
−0.920859 | + | 0.389896i | \(0.872511\pi\) | |||||||
\(348\) | 1.01921e51 | − | 7.42491e50i | 1.50203 | − | 1.09422i | ||||
\(349\) | 1.76342e50 | 0.245384 | 0.122692 | − | 0.992445i | \(-0.460847\pi\) | ||||
0.122692 | + | 0.992445i | \(0.460847\pi\) | |||||||
\(350\) | − | 4.87892e49i | − | 0.0641155i | ||||||
\(351\) | 3.76389e50 | − | 1.23894e50i | 0.467192 | − | 0.153783i | ||||
\(352\) | −4.18330e50 | −0.490530 | ||||||||
\(353\) | − | 1.29915e51i | − | 1.43935i | −0.694311 | − | 0.719675i | \(-0.744291\pi\) | ||
0.694311 | − | 0.719675i | \(-0.255709\pi\) | |||||||
\(354\) | −1.62985e49 | − | 2.23728e49i | −0.0170641 | − | 0.0234237i | ||||
\(355\) | −4.42229e50 | −0.437602 | ||||||||
\(356\) | − | 3.81800e50i | − | 0.357137i | ||||||
\(357\) | 3.84715e50 | − | 2.80264e50i | 0.340232 | − | 0.247858i | ||||
\(358\) | −5.14482e49 | −0.0430239 | ||||||||
\(359\) | − | 1.20829e50i | − | 0.0955613i | −0.998858 | − | 0.0477806i | \(-0.984785\pi\) | ||
0.998858 | − | 0.0477806i | \(-0.0152148\pi\) | |||||||
\(360\) | 1.00028e50 | − | 3.10554e50i | 0.0748293 | − | 0.232320i | ||||
\(361\) | 2.08215e50 | 0.147356 | ||||||||
\(362\) | 1.50298e50i | 0.100643i | ||||||||
\(363\) | 1.47609e51 | + | 2.02621e51i | 0.935363 | + | 1.28396i | ||||
\(364\) | −1.21166e51 | −0.726694 | ||||||||
\(365\) | 1.68336e51i | 0.955697i | ||||||||
\(366\) | 5.05457e49 | − | 3.68224e49i | 0.0271683 | − | 0.0197920i | ||||
\(367\) | 1.03875e51 | 0.528677 | 0.264339 | − | 0.964430i | \(-0.414846\pi\) | ||||
0.264339 | + | 0.964430i | \(0.414846\pi\) | |||||||
\(368\) | 1.80639e50i | 0.0870675i | ||||||||
\(369\) | −2.71209e51 | − | 8.73554e50i | −1.23816 | − | 0.398807i | ||||
\(370\) | 2.77479e50 | 0.120004 | ||||||||
\(371\) | − | 1.80509e51i | − | 0.739641i | ||||||
\(372\) | 5.59650e50 | + | 7.68225e50i | 0.217299 | + | 0.298284i | ||||
\(373\) | −3.34287e51 | −1.23011 | −0.615053 | − | 0.788486i | \(-0.710865\pi\) | ||||
−0.615053 | + | 0.788486i | \(0.710865\pi\) | |||||||
\(374\) | 1.34036e50i | 0.0467507i | ||||||||
\(375\) | −1.69759e51 | + | 1.23669e51i | −0.561316 | + | 0.408917i | ||||
\(376\) | −6.89838e50 | −0.216267 | ||||||||
\(377\) | 3.10760e51i | 0.923843i | ||||||||
\(378\) | 1.70713e50 | + | 5.18625e50i | 0.0481316 | + | 0.146224i | ||||
\(379\) | 5.71675e51 | 1.52885 | 0.764425 | − | 0.644713i | \(-0.223023\pi\) | ||||
0.764425 | + | 0.644713i | \(0.223023\pi\) | |||||||
\(380\) | 4.97151e51i | 1.26129i | ||||||||
\(381\) | −4.21574e51 | − | 5.78689e51i | −1.01478 | − | 1.39298i | ||||
\(382\) | 6.20681e50 | 0.141776 | ||||||||
\(383\) | − | 5.35561e51i | − | 1.16100i | −0.814259 | − | 0.580502i | \(-0.802857\pi\) | ||
0.814259 | − | 0.580502i | \(-0.197143\pi\) | |||||||
\(384\) | −1.57695e51 | + | 1.14880e51i | −0.324484 | + | 0.236386i | ||||
\(385\) | 1.46389e52 | 2.85952 | ||||||||
\(386\) | − | 5.86780e50i | − | 0.108825i | ||||||
\(387\) | −3.02481e50 | + | 9.39102e50i | −0.0532695 | + | 0.165384i | ||||
\(388\) | −8.56639e51 | −1.43273 | ||||||||
\(389\) | − | 6.15052e51i | − | 0.977056i | −0.872548 | − | 0.488528i | \(-0.837534\pi\) | ||
0.872548 | − | 0.488528i | \(-0.162466\pi\) | |||||||
\(390\) | 2.35457e50 | + | 3.23209e50i | 0.0355320 | + | 0.0487744i | ||||
\(391\) | 1.76797e50 | 0.0253478 | ||||||||
\(392\) | − | 1.85166e51i | − | 0.252254i | ||||||
\(393\) | −1.80464e51 | + | 1.31468e51i | −0.233636 | + | 0.170203i | ||||
\(394\) | 9.83400e49 | 0.0121006 | ||||||||
\(395\) | − | 5.90956e51i | − | 0.691215i | ||||||
\(396\) | 1.36256e52 | + | 4.38876e51i | 1.51514 | + | 0.488021i | ||||
\(397\) | 3.02413e51 | 0.319735 | 0.159868 | − | 0.987138i | \(-0.448893\pi\) | ||||
0.159868 | + | 0.987138i | \(0.448893\pi\) | |||||||
\(398\) | 4.50564e50i | 0.0452997i | ||||||||
\(399\) | −9.85024e51 | − | 1.35213e52i | −0.941865 | − | 1.29289i | ||||
\(400\) | −4.43391e51 | −0.403262 | ||||||||
\(401\) | 1.73505e52i | 1.50116i | 0.660782 | + | 0.750578i | \(0.270225\pi\) | ||||
−0.660782 | + | 0.750578i | \(0.729775\pi\) | |||||||
\(402\) | −2.48194e50 | + | 1.80808e50i | −0.0204301 | + | 0.0148832i | ||||
\(403\) | −2.34234e51 | −0.183463 | ||||||||
\(404\) | − | 4.77938e51i | − | 0.356241i | ||||||
\(405\) | −9.79160e51 | + | 1.36229e52i | −0.694629 | + | 0.966428i | ||||
\(406\) | −4.28194e51 | −0.289148 | ||||||||
\(407\) | 2.44797e52i | 1.57369i | ||||||||
\(408\) | 5.56112e50 | + | 7.63369e50i | 0.0340376 | + | 0.0467230i | ||||
\(409\) | 1.71171e52 | 0.997619 | 0.498809 | − | 0.866712i | \(-0.333771\pi\) | ||||
0.498809 | + | 0.866712i | \(0.333771\pi\) | |||||||
\(410\) | − | 2.87537e51i | − | 0.159594i | ||||||
\(411\) | 3.18084e51 | − | 2.31724e51i | 0.168153 | − | 0.122499i | ||||
\(412\) | −1.95227e52 | −0.983095 | ||||||||
\(413\) | − | 8.75109e51i | − | 0.419818i | ||||||
\(414\) | −6.21772e49 | + | 1.93039e50i | −0.00284200 | + | 0.00882346i | ||||
\(415\) | −2.46861e52 | −1.07520 | ||||||||
\(416\) | − | 3.61275e51i | − | 0.149959i | ||||||
\(417\) | 1.19595e52 | + | 1.64166e52i | 0.473142 | + | 0.649476i | ||||
\(418\) | 4.71086e51 | 0.177654 | ||||||||
\(419\) | − | 3.31810e52i | − | 1.19291i | −0.802645 | − | 0.596457i | \(-0.796575\pi\) | ||
0.802645 | − | 0.596457i | \(-0.203425\pi\) | |||||||
\(420\) | 4.14634e52 | − | 3.02060e52i | 1.42128 | − | 1.03540i | ||||
\(421\) | −3.09470e52 | −1.01152 | −0.505762 | − | 0.862673i | \(-0.668789\pi\) | ||||
−0.505762 | + | 0.862673i | \(0.668789\pi\) | |||||||
\(422\) | 4.57362e51i | 0.142564i | ||||||||
\(423\) | 3.37637e52 | + | 1.08751e52i | 1.00379 | + | 0.323316i | ||||
\(424\) | 3.58174e51 | 0.101573 | ||||||||
\(425\) | 4.33960e51i | 0.117401i | ||||||||
\(426\) | 8.64657e50 | + | 1.18690e51i | 0.0223178 | + | 0.0306354i | ||||
\(427\) | 1.97709e52 | 0.486932 | ||||||||
\(428\) | − | 7.75364e51i | − | 0.182234i | ||||||
\(429\) | −2.85142e52 | + | 2.07725e52i | −0.639609 | + | 0.465954i | ||||
\(430\) | −9.95639e50 | −0.0213173 | ||||||||
\(431\) | 9.81535e50i | 0.0200614i | 0.999950 | + | 0.0100307i | \(0.00319292\pi\) | ||||
−0.999950 | + | 0.0100307i | \(0.996807\pi\) | |||||||
\(432\) | 4.71321e52 | − | 1.55142e52i | 0.919690 | − | 0.302729i | ||||
\(433\) | 5.74733e51 | 0.107080 | 0.0535399 | − | 0.998566i | \(-0.482950\pi\) | ||||
0.0535399 | + | 0.998566i | \(0.482950\pi\) | |||||||
\(434\) | − | 3.22749e51i | − | 0.0574210i | ||||||
\(435\) | −7.74709e52 | − | 1.06343e53i | −1.31630 | − | 1.80686i | ||||
\(436\) | −2.45594e52 | −0.398555 | ||||||||
\(437\) | − | 6.21375e51i | − | 0.0963219i | ||||||
\(438\) | 4.51800e51 | − | 3.29135e51i | 0.0669059 | − | 0.0487407i | ||||
\(439\) | 6.68531e52 | 0.945869 | 0.472935 | − | 0.881098i | \(-0.343195\pi\) | ||||
0.472935 | + | 0.881098i | \(0.343195\pi\) | |||||||
\(440\) | 2.90471e52i | 0.392689i | ||||||||
\(441\) | −2.91909e52 | + | 9.06280e52i | −0.377117 | + | 1.17082i | ||||
\(442\) | −1.15755e51 | −0.0142920 | ||||||||
\(443\) | 1.09893e53i | 1.29687i | 0.761269 | + | 0.648436i | \(0.224577\pi\) | ||||
−0.761269 | + | 0.648436i | \(0.775423\pi\) | |||||||
\(444\) | 5.05117e52 | + | 6.93369e52i | 0.569814 | + | 0.782177i | ||||
\(445\) | −3.98366e52 | −0.429618 | ||||||||
\(446\) | − | 8.59610e51i | − | 0.0886348i | ||||||
\(447\) | −1.17728e53 | + | 8.57646e52i | −1.16073 | + | 0.845585i | ||||
\(448\) | −1.48377e53 | −1.39896 | ||||||||
\(449\) | 7.85528e51i | 0.0708329i | 0.999373 | + | 0.0354164i | \(0.0112758\pi\) | ||||
−0.999373 | + | 0.0354164i | \(0.988724\pi\) | |||||||
\(450\) | −4.73828e51 | − | 1.52618e51i | −0.0408668 | − | 0.0131630i | ||||
\(451\) | 2.53671e53 | 2.09286 | ||||||||
\(452\) | − | 2.05152e53i | − | 1.61922i | ||||||
\(453\) | −9.44443e52 | − | 1.29643e53i | −0.713201 | − | 0.979003i | ||||
\(454\) | −1.19712e52 | −0.0865009 | ||||||||
\(455\) | 1.26423e53i | 0.874175i | ||||||||
\(456\) | 2.68296e52 | − | 1.95453e52i | 0.177548 | − | 0.129344i | ||||
\(457\) | 6.95029e52 | 0.440229 | 0.220115 | − | 0.975474i | \(-0.429357\pi\) | ||||
0.220115 | + | 0.975474i | \(0.429357\pi\) | |||||||
\(458\) | 1.50414e52i | 0.0911969i | ||||||||
\(459\) | −1.51842e52 | − | 4.61295e52i | −0.0881329 | − | 0.267747i | ||||
\(460\) | 1.90546e52 | 0.105887 | ||||||||
\(461\) | − | 2.62065e53i | − | 1.39441i | −0.716871 | − | 0.697206i | \(-0.754426\pi\) | ||
0.716871 | − | 0.697206i | \(-0.245574\pi\) | |||||||
\(462\) | −2.86223e52 | − | 3.92895e52i | −0.145836 | − | 0.200187i | ||||
\(463\) | 2.26385e53 | 1.10466 | 0.552329 | − | 0.833626i | \(-0.313739\pi\) | ||||
0.552329 | + | 0.833626i | \(0.313739\pi\) | |||||||
\(464\) | 3.89138e53i | 1.81863i | ||||||||
\(465\) | 8.01559e52 | − | 5.83934e52i | 0.358820 | − | 0.261399i | ||||
\(466\) | −2.36877e52 | −0.101579 | ||||||||
\(467\) | − | 3.37419e53i | − | 1.38622i | −0.720833 | − | 0.693109i | \(-0.756241\pi\) | ||
0.720833 | − | 0.693109i | \(-0.243759\pi\) | |||||||
\(468\) | −3.79019e52 | + | 1.17673e53i | −0.149192 | + | 0.463190i | ||||
\(469\) | −9.70807e52 | −0.366164 | ||||||||
\(470\) | 3.57963e52i | 0.129384i | ||||||||
\(471\) | −3.03303e50 | − | 4.16340e50i | −0.00105065 | − | 0.00144222i | ||||
\(472\) | 1.73643e52 | 0.0576524 | ||||||||
\(473\) | − | 8.78372e52i | − | 0.279547i | ||||||
\(474\) | −1.58608e52 | + | 1.15545e52i | −0.0483902 | + | 0.0352521i | ||||
\(475\) | 1.52521e53 | 0.446125 | ||||||||
\(476\) | 1.48498e53i | 0.416468i | ||||||||
\(477\) | −1.75306e53 | − | 5.64652e52i | −0.471442 | − | 0.151850i | ||||
\(478\) | 6.65352e52 | 0.171591 | ||||||||
\(479\) | − | 1.29204e53i | − | 0.319569i | −0.987152 | − | 0.159784i | \(-0.948920\pi\) | ||
0.987152 | − | 0.159784i | \(-0.0510799\pi\) | |||||||
\(480\) | 9.00641e52 | + | 1.23630e53i | 0.213662 | + | 0.293291i | ||||
\(481\) | −2.11410e53 | −0.481088 | ||||||||
\(482\) | − | 5.66871e52i | − | 0.123750i | ||||||
\(483\) | −5.18239e52 | + | 3.77536e52i | −0.108539 | + | 0.0790707i | ||||
\(484\) | −7.82107e53 | −1.57166 | ||||||||
\(485\) | 8.93810e53i | 1.72350i | ||||||||
\(486\) | 5.57076e52 | − | 3.56024e50i | 0.103083 | − | 0.000658800i | ||||
\(487\) | −5.88712e53 | −1.04550 | −0.522749 | − | 0.852487i | \(-0.675094\pi\) | ||||
−0.522749 | + | 0.852487i | \(0.675094\pi\) | |||||||
\(488\) | 3.92303e52i | 0.0668690i | ||||||||
\(489\) | 6.84864e53 | + | 9.40105e53i | 1.12054 | + | 1.53815i | ||||
\(490\) | −9.60841e52 | −0.150914 | ||||||||
\(491\) | − | 2.12361e53i | − | 0.320217i | −0.987099 | − | 0.160108i | \(-0.948816\pi\) | ||
0.987099 | − | 0.160108i | \(-0.0511844\pi\) | |||||||
\(492\) | 7.18502e53 | − | 5.23427e53i | 1.04022 | − | 0.757799i | ||||
\(493\) | 3.80861e53 | 0.529454 | ||||||||
\(494\) | 4.06836e52i | 0.0543100i | ||||||||
\(495\) | 4.57920e53 | − | 1.42169e54i | 0.587064 | − | 1.82264i | ||||
\(496\) | −2.93311e53 | −0.361156 | ||||||||
\(497\) | 4.64257e53i | 0.549073i | ||||||||
\(498\) | 4.82668e52 | + | 6.62553e52i | 0.0548355 | + | 0.0752721i | ||||
\(499\) | −2.91330e53 | −0.317961 | −0.158980 | − | 0.987282i | \(-0.550821\pi\) | ||||
−0.158980 | + | 0.987282i | \(0.550821\pi\) | |||||||
\(500\) | − | 6.55260e53i | − | 0.687090i | ||||||
\(501\) | −6.73365e53 | + | 4.90544e53i | −0.678416 | + | 0.494224i | ||||
\(502\) | 1.28074e53 | 0.123990 | ||||||||
\(503\) | − | 1.95537e54i | − | 1.81915i | −0.415535 | − | 0.909577i | \(-0.636406\pi\) | ||
0.415535 | − | 0.909577i | \(-0.363594\pi\) | |||||||
\(504\) | −3.26023e53 | − | 1.05011e53i | −0.291499 | − | 0.0938907i | ||||
\(505\) | −4.98676e53 | −0.428540 | ||||||||
\(506\) | − | 1.80556e52i | − | 0.0149142i | ||||||
\(507\) | 5.62157e53 | + | 7.71666e53i | 0.446373 | + | 0.612732i | ||||
\(508\) | 2.23371e54 | 1.70511 | ||||||||
\(509\) | 3.00436e53i | 0.220494i | 0.993904 | + | 0.110247i | \(0.0351642\pi\) | ||||
−0.993904 | + | 0.110247i | \(0.964836\pi\) | |||||||
\(510\) | 3.96119e52 | − | 2.88571e52i | 0.0279526 | − | 0.0203634i | ||||
\(511\) | 1.76721e54 | 1.19914 | ||||||||
\(512\) | − | 7.56688e53i | − | 0.493762i | ||||||
\(513\) | −1.62128e54 | + | 5.33668e53i | −1.01744 | + | 0.334906i | ||||
\(514\) | −4.88819e52 | −0.0295043 | ||||||||
\(515\) | 2.03698e54i | 1.18261i | ||||||||
\(516\) | −1.81244e53 | − | 2.48792e53i | −0.101221 | − | 0.138945i | ||||
\(517\) | −3.15802e54 | −1.69670 | ||||||||
\(518\) | − | 2.91301e53i | − | 0.150573i | ||||||
\(519\) | 1.53865e54 | − | 1.12090e54i | 0.765229 | − | 0.557468i | ||||
\(520\) | −2.50854e53 | −0.120048 | ||||||||
\(521\) | 2.81714e54i | 1.29734i | 0.761069 | + | 0.648671i | \(0.224675\pi\) | ||||
−0.761069 | + | 0.648671i | \(0.775325\pi\) | |||||||
\(522\) | −1.33944e53 | + | 4.15851e53i | −0.0593626 | + | 0.184301i | ||||
\(523\) | −1.35385e54 | −0.577481 | −0.288741 | − | 0.957407i | \(-0.593237\pi\) | ||||
−0.288741 | + | 0.957407i | \(0.593237\pi\) | |||||||
\(524\) | − | 6.96582e53i | − | 0.285987i | ||||||
\(525\) | −9.26687e53 | − | 1.27205e54i | −0.366224 | − | 0.502712i | ||||
\(526\) | −1.93003e53 | −0.0734258 | ||||||||
\(527\) | 2.87072e53i | 0.105143i | ||||||||
\(528\) | −3.57059e54 | + | 2.60116e54i | −1.25910 | + | 0.917253i | ||||
\(529\) | 2.92138e54 | 0.991914 | ||||||||
\(530\) | − | 1.85860e53i | − | 0.0607670i | ||||||
\(531\) | −8.49883e53 | − | 2.73744e53i | −0.267589 | − | 0.0861894i | ||||
\(532\) | 5.21915e54 | 1.58259 | ||||||||
\(533\) | 2.19073e54i | 0.639802i | ||||||||
\(534\) | 7.78896e52 | + | 1.06918e53i | 0.0219106 | + | 0.0300764i | ||||
\(535\) | −8.09008e53 | −0.219219 | ||||||||
\(536\) | − | 1.92632e53i | − | 0.0502843i | ||||||
\(537\) | −1.34138e54 | + | 9.77192e53i | −0.337339 | + | 0.245750i | ||||
\(538\) | 5.55080e53 | 0.134496 | ||||||||
\(539\) | − | 8.47672e54i | − | 1.97903i | ||||||
\(540\) | −1.63650e54 | − | 4.97169e54i | −0.368164 | − | 1.11848i | ||||
\(541\) | 1.57638e54 | 0.341756 | 0.170878 | − | 0.985292i | \(-0.445340\pi\) | ||||
0.170878 | + | 0.985292i | \(0.445340\pi\) | |||||||
\(542\) | 5.72822e53i | 0.119683i | ||||||||
\(543\) | 2.85472e54 | + | 3.91865e54i | 0.574867 | + | 0.789113i | ||||
\(544\) | −4.42771e53 | −0.0859412 | ||||||||
\(545\) | 2.56251e54i | 0.479442i | ||||||||
\(546\) | 3.39309e53 | − | 2.47186e53i | 0.0611988 | − | 0.0445831i | ||||
\(547\) | 4.38693e54 | 0.762806 | 0.381403 | − | 0.924409i | \(-0.375441\pi\) | ||||
0.381403 | + | 0.924409i | \(0.375441\pi\) | |||||||
\(548\) | 1.22779e54i | 0.205832i | ||||||||
\(549\) | 6.18455e53 | − | 1.92010e54i | 0.0999681 | − | 0.310368i | ||||
\(550\) | 4.43186e53 | 0.0690768 | ||||||||
\(551\) | − | 1.33858e55i | − | 2.01193i | ||||||
\(552\) | −7.49123e52 | − | 1.02831e53i | −0.0108585 | − | 0.0149054i | ||||
\(553\) | −6.20392e54 | −0.867289 | ||||||||
\(554\) | 5.77932e53i | 0.0779258i | ||||||||
\(555\) | 7.23455e54 | − | 5.27035e54i | 0.940918 | − | 0.685456i | ||||
\(556\) | −6.33673e54 | −0.795005 | ||||||||
\(557\) | 1.43649e55i | 1.73859i | 0.494293 | + | 0.869295i | \(0.335427\pi\) | ||||
−0.494293 | + | 0.869295i | \(0.664573\pi\) | |||||||
\(558\) | −3.13446e53 | − | 1.00960e53i | −0.0365998 | − | 0.0117886i | ||||
\(559\) | 7.58573e53 | 0.0854597 | ||||||||
\(560\) | 1.58309e55i | 1.72086i | ||||||||
\(561\) | 2.54583e54 | + | 3.49464e54i | 0.267038 | + | 0.366560i | ||||
\(562\) | 6.89995e53 | 0.0698424 | ||||||||
\(563\) | − | 5.10238e54i | − | 0.498431i | −0.968448 | − | 0.249215i | \(-0.919827\pi\) | ||
0.968448 | − | 0.249215i | \(-0.0801727\pi\) | |||||||
\(564\) | −8.94484e54 | + | 6.51629e54i | −0.843317 | + | 0.614354i | ||||
\(565\) | −2.14054e55 | −1.94784 | ||||||||
\(566\) | 1.40011e54i | 0.122979i | ||||||||
\(567\) | 1.43015e55 | + | 1.02793e55i | 1.21261 | + | 0.871573i | ||||
\(568\) | −9.21198e53 | −0.0754026 | ||||||||
\(569\) | − | 1.08403e55i | − | 0.856634i | −0.903628 | − | 0.428317i | \(-0.859107\pi\) | ||
0.903628 | − | 0.428317i | \(-0.140893\pi\) | |||||||
\(570\) | −1.01422e54 | − | 1.39221e54i | −0.0773812 | − | 0.106220i | ||||
\(571\) | 1.56093e53 | 0.0114990 | 0.00574951 | − | 0.999983i | \(-0.498170\pi\) | ||||
0.00574951 | + | 0.999983i | \(0.498170\pi\) | |||||||
\(572\) | − | 1.10063e55i | − | 0.782927i | ||||||
\(573\) | 1.61827e55 | − | 1.17890e55i | 1.11162 | − | 0.809814i | ||||
\(574\) | −3.01860e54 | −0.200248 | ||||||||
\(575\) | − | 5.84575e53i | − | 0.0374527i | ||||||
\(576\) | −4.64140e54 | + | 1.44100e55i | −0.287210 | + | 0.891690i | ||||
\(577\) | −2.64011e55 | −1.57800 | −0.788999 | − | 0.614395i | \(-0.789400\pi\) | ||||
−0.788999 | + | 0.614395i | \(0.789400\pi\) | |||||||
\(578\) | − | 1.64361e54i | − | 0.0948947i | ||||||
\(579\) | −1.11451e55 | − | 1.52988e55i | −0.621603 | − | 0.853268i | ||||
\(580\) | 4.10480e55 | 2.21173 | ||||||||
\(581\) | 2.59157e55i | 1.34909i | ||||||||
\(582\) | 2.39891e54 | − | 1.74760e54i | 0.120658 | − | 0.0878987i | ||||
\(583\) | 1.63969e55 | 0.796876 | ||||||||
\(584\) | 3.50658e54i | 0.164675i | ||||||||
\(585\) | 1.22779e55 | + | 3.95465e54i | 0.557193 | + | 0.179470i | ||||
\(586\) | 1.56040e54 | 0.0684359 | ||||||||
\(587\) | − | 1.90360e55i | − | 0.806889i | −0.915004 | − | 0.403445i | \(-0.867813\pi\) | ||
0.915004 | − | 0.403445i | \(-0.132187\pi\) | |||||||
\(588\) | −1.74910e55 | − | 2.40096e55i | −0.716584 | − | 0.983647i | ||||
\(589\) | 1.00895e55 | 0.399544 | ||||||||
\(590\) | − | 9.01049e53i | − | 0.0344912i | ||||||
\(591\) | 2.56396e54 | − | 1.86784e54i | 0.0948772 | − | 0.0691178i | ||||
\(592\) | −2.64731e55 | −0.947045 | ||||||||
\(593\) | − | 1.61772e55i | − | 0.559511i | −0.960071 | − | 0.279755i | \(-0.909747\pi\) | ||
0.960071 | − | 0.279755i | \(-0.0902534\pi\) | |||||||
\(594\) | −4.71103e54 | + | 1.55070e54i | −0.157539 | + | 0.0518561i | ||||
\(595\) | 1.54942e55 | 0.500989 | ||||||||
\(596\) | − | 4.54424e55i | − | 1.42081i | ||||||
\(597\) | 8.55788e54 | + | 1.17473e55i | 0.258749 | + | 0.355182i | ||||
\(598\) | 1.55930e53 | 0.00455939 | ||||||||
\(599\) | 3.38952e55i | 0.958521i | 0.877673 | + | 0.479261i | \(0.159095\pi\) | ||||
−0.877673 | + | 0.479261i | \(0.840905\pi\) | |||||||
\(600\) | 2.52406e54 | − | 1.83877e54i | 0.0690359 | − | 0.0502925i | ||||
\(601\) | −3.44925e55 | −0.912506 | −0.456253 | − | 0.889850i | \(-0.650809\pi\) | ||||
−0.456253 | + | 0.889850i | \(0.650809\pi\) | |||||||
\(602\) | 1.04523e54i | 0.0267475i | ||||||||
\(603\) | −3.03679e54 | + | 9.42822e54i | −0.0751742 | + | 0.233391i | ||||
\(604\) | 5.00414e55 | 1.19837 | ||||||||
\(605\) | 8.16043e55i | 1.89063i | ||||||||
\(606\) | 9.75025e53 | + | 1.33841e54i | 0.0218556 | + | 0.0300010i | ||||
\(607\) | −1.09354e55 | −0.237170 | −0.118585 | − | 0.992944i | \(-0.537836\pi\) | ||||
−0.118585 | + | 0.992944i | \(0.537836\pi\) | |||||||
\(608\) | 1.55618e55i | 0.326578i | ||||||||
\(609\) | −1.11641e56 | + | 8.13299e55i | −2.26713 | + | 1.65160i | ||||
\(610\) | 2.03569e54 | 0.0400051 | ||||||||
\(611\) | − | 2.72731e55i | − | 0.518693i | ||||||
\(612\) | 1.44217e55 | + | 4.64518e54i | 0.265454 | + | 0.0855016i | ||||
\(613\) | 1.75716e55 | 0.313042 | 0.156521 | − | 0.987675i | \(-0.449972\pi\) | ||||
0.156521 | + | 0.987675i | \(0.449972\pi\) | |||||||
\(614\) | − | 2.19610e54i | − | 0.0378691i | ||||||
\(615\) | −5.46139e55 | − | 7.49679e55i | −0.911593 | − | 1.25133i | ||||
\(616\) | 3.04939e55 | 0.492719 | ||||||||
\(617\) | − | 8.39830e55i | − | 1.31368i | −0.754032 | − | 0.656838i | \(-0.771894\pi\) | ||
0.754032 | − | 0.656838i | \(-0.228106\pi\) | |||||||
\(618\) | 5.46709e54 | − | 3.98276e54i | 0.0827916 | − | 0.0603135i | ||||
\(619\) | 1.05937e56 | 1.55323 | 0.776617 | − | 0.629974i | \(-0.216934\pi\) | ||||
0.776617 | + | 0.629974i | \(0.216934\pi\) | |||||||
\(620\) | 3.09397e55i | 0.439221i | ||||||||
\(621\) | 2.04542e54 | + | 6.21398e54i | 0.0281158 | + | 0.0854157i | ||||
\(622\) | −1.36884e55 | −0.182198 | ||||||||
\(623\) | 4.18210e55i | 0.539055i | ||||||||
\(624\) | −2.24640e55 | − | 3.08361e55i | −0.280411 | − | 0.384917i | ||||
\(625\) | −1.02821e56 | −1.24303 | ||||||||
\(626\) | 3.47337e54i | 0.0406691i | ||||||||
\(627\) | 1.22823e56 | − | 8.94765e55i | 1.39293 | − | 1.01475i | ||||
\(628\) | 1.60705e53 | 0.00176537 | ||||||||
\(629\) | 2.59100e55i | 0.275711i | ||||||||
\(630\) | −5.44909e54 | + | 1.69176e55i | −0.0561711 | + | 0.174393i | ||||
\(631\) | −2.26793e55 | −0.226487 | −0.113243 | − | 0.993567i | \(-0.536124\pi\) | ||||
−0.113243 | + | 0.993567i | \(0.536124\pi\) | |||||||
\(632\) | − | 1.23101e55i | − | 0.119102i | ||||||
\(633\) | 8.68699e55 | + | 1.19245e56i | 0.814320 | + | 1.11781i | ||||
\(634\) | −7.53282e54 | −0.0684183 | ||||||||
\(635\) | − | 2.33063e56i | − | 2.05116i | ||||||
\(636\) | 4.64429e55 | − | 3.38335e55i | 0.396075 | − | 0.288539i | ||||
\(637\) | 7.32061e55 | 0.605004 | ||||||||
\(638\) | − | 3.88959e55i | − | 0.311523i | ||||||
\(639\) | 4.50874e55 | + | 1.45225e55i | 0.349976 | + | 0.112726i | ||||
\(640\) | −6.35106e55 | −0.477800 | ||||||||
\(641\) | 1.60220e56i | 1.16830i | 0.811645 | + | 0.584151i | \(0.198573\pi\) | ||||
−0.811645 | + | 0.584151i | \(0.801427\pi\) | |||||||
\(642\) | 1.58179e54 | + | 2.17131e54i | 0.0111802 | + | 0.0153469i | ||||
\(643\) | −1.34900e56 | −0.924256 | −0.462128 | − | 0.886813i | \(-0.652914\pi\) | ||||
−0.462128 | + | 0.886813i | \(0.652914\pi\) | |||||||
\(644\) | − | 2.00038e55i | − | 0.132860i | ||||||
\(645\) | −2.59587e55 | + | 1.89109e55i | −0.167143 | + | 0.121763i | ||||
\(646\) | 4.98609e54 | 0.0311250 | ||||||||
\(647\) | 3.06483e55i | 0.185490i | 0.995690 | + | 0.0927452i | \(0.0295642\pi\) | ||||
−0.995690 | + | 0.0927452i | \(0.970436\pi\) | |||||||
\(648\) | −2.03967e55 | + | 2.83776e55i | −0.119691 | + | 0.166524i | ||||
\(649\) | 7.94923e55 | 0.452304 | ||||||||
\(650\) | 3.82741e54i | 0.0211173i | ||||||||
\(651\) | −6.13020e55 | − | 8.41486e55i | −0.327986 | − | 0.450223i | ||||
\(652\) | −3.62875e56 | −1.88281 | ||||||||
\(653\) | 1.79299e56i | 0.902222i | 0.892468 | + | 0.451111i | \(0.148972\pi\) | ||||
−0.892468 | + | 0.451111i | \(0.851028\pi\) | |||||||
\(654\) | 6.87757e54 | − | 5.01029e54i | 0.0335645 | − | 0.0244516i | ||||
\(655\) | −7.26808e55 | −0.344028 | ||||||||
\(656\) | 2.74327e56i | 1.25948i | ||||||||
\(657\) | 5.52804e55 | − | 1.71627e56i | 0.246186 | − | 0.764326i | ||||
\(658\) | 3.75794e55 | 0.162342 | ||||||||
\(659\) | 6.55167e55i | 0.274564i | 0.990532 | + | 0.137282i | \(0.0438367\pi\) | ||||
−0.990532 | + | 0.137282i | \(0.956163\pi\) | |||||||
\(660\) | 2.74382e56 | + | 3.76641e56i | 1.11552 | + | 1.53126i | ||||
\(661\) | 1.73011e56 | 0.682409 | 0.341205 | − | 0.939989i | \(-0.389165\pi\) | ||||
0.341205 | + | 0.939989i | \(0.389165\pi\) | |||||||
\(662\) | 2.94281e55i | 0.112617i | ||||||||
\(663\) | −3.01801e55 | + | 2.19861e55i | −0.112060 | + | 0.0816354i | ||||
\(664\) | −5.14231e55 | −0.185266 | ||||||||
\(665\) | − | 5.44562e56i | − | 1.90377i | ||||||
\(666\) | −2.82904e55 | − | 9.11221e54i | −0.0959741 | − | 0.0309128i | ||||
\(667\) | −5.13047e55 | −0.168904 | ||||||||
\(668\) | − | 2.59915e56i | − | 0.830429i | ||||||
\(669\) | −1.63272e56 | − | 2.24121e56i | −0.506277 | − | 0.694961i | ||||
\(670\) | −9.99583e54 | −0.0300831 | ||||||||
\(671\) | 1.79593e56i | 0.524612i | ||||||||
\(672\) | 1.29788e56 | − | 9.45503e55i | 0.368002 | − | 0.268088i | ||||
\(673\) | 2.41957e56 | 0.665943 | 0.332971 | − | 0.942937i | \(-0.391949\pi\) | ||||
0.332971 | + | 0.942937i | \(0.391949\pi\) | |||||||
\(674\) | 5.71674e54i | 0.0152739i | ||||||||
\(675\) | −1.52526e56 | + | 5.02062e55i | −0.395612 | + | 0.130221i | ||||
\(676\) | −2.97859e56 | −0.750027 | ||||||||
\(677\) | − | 3.89497e56i | − | 0.952206i | −0.879389 | − | 0.476103i | \(-0.842049\pi\) | ||
0.879389 | − | 0.476103i | \(-0.157951\pi\) | |||||||
\(678\) | 4.18524e55 | + | 5.74503e55i | 0.0993405 | + | 0.136364i | ||||
\(679\) | 9.38332e56 | 2.16252 | ||||||||
\(680\) | 3.07442e55i | 0.0687994i | ||||||||
\(681\) | −3.12118e56 | + | 2.27377e56i | −0.678230 | + | 0.494088i | ||||
\(682\) | 2.93176e55 | 0.0618644 | ||||||||
\(683\) | − | 2.39575e55i | − | 0.0490938i | −0.999699 | − | 0.0245469i | \(-0.992186\pi\) | ||
0.999699 | − | 0.0245469i | \(-0.00781431\pi\) | |||||||
\(684\) | 1.63261e56 | − | 5.06870e56i | 0.324908 | − | 1.00873i | ||||
\(685\) | 1.28106e56 | 0.247605 | ||||||||
\(686\) | 1.88657e55i | 0.0354152i | ||||||||
\(687\) | 2.85693e56 | + | 3.92167e56i | 0.520912 | + | 0.715050i | ||||
\(688\) | 9.49897e55 | 0.168232 | ||||||||
\(689\) | 1.41606e56i | 0.243611i | ||||||||
\(690\) | −5.33601e54 | + | 3.88727e54i | −0.00891732 | + | 0.00649625i | ||||
\(691\) | −6.14613e56 | −0.997794 | −0.498897 | − | 0.866661i | \(-0.666261\pi\) | ||||
−0.498897 | + | 0.866661i | \(0.666261\pi\) | |||||||
\(692\) | 5.93909e56i | 0.936695i | ||||||||
\(693\) | −1.49250e57 | − | 4.80729e56i | −2.28692 | − | 0.736607i | ||||
\(694\) | 5.39966e55 | 0.0803853 | ||||||||
\(695\) | 6.61169e56i | 0.956349i | ||||||||
\(696\) | −1.61378e56 | − | 2.21522e56i | −0.226809 | − | 0.311338i | ||||
\(697\) | 2.68492e56 | 0.366670 | ||||||||
\(698\) | − | 1.90613e55i | − | 0.0252956i | ||||||
\(699\) | −6.17595e56 | + | 4.49916e56i | −0.796453 | + | 0.580214i | ||||
\(700\) | 4.91005e56 | 0.615355 | ||||||||
\(701\) | 2.87457e56i | 0.350117i | 0.984558 | + | 0.175058i | \(0.0560114\pi\) | ||||
−0.984558 | + | 0.175058i | \(0.943989\pi\) | |||||||
\(702\) | −1.33921e55 | − | 4.06851e55i | −0.0158528 | − | 0.0481607i | ||||
\(703\) | 9.10639e56 | 1.04771 | ||||||||
\(704\) | − | 1.34781e57i | − | 1.50722i | ||||||
\(705\) | 6.79904e56 | + | 9.33297e56i | 0.739036 | + | 1.01447i | ||||
\(706\) | −1.40429e56 | −0.148376 | ||||||||
\(707\) | 5.23517e56i | 0.537703i | ||||||||
\(708\) | 2.25155e56 | − | 1.64025e56i | 0.224811 | − | 0.163774i | ||||
\(709\) | −1.38335e57 | −1.34279 | −0.671395 | − | 0.741100i | \(-0.734305\pi\) | ||||
−0.671395 | + | 0.741100i | \(0.734305\pi\) | |||||||
\(710\) | 4.78018e55i | 0.0451105i | ||||||||
\(711\) | −1.94066e56 | + | 6.02509e56i | −0.178056 | + | 0.552804i | ||||
\(712\) | −8.29830e55 | −0.0740268 | ||||||||
\(713\) | − | 3.86707e55i | − | 0.0335422i | ||||||
\(714\) | −3.02946e55 | − | 4.15850e55i | −0.0255506 | − | 0.0350730i | ||||
\(715\) | −1.14839e57 | −0.941820 | ||||||||
\(716\) | − | 5.17766e56i | − | 0.412926i | ||||||
\(717\) | 1.73473e57 | − | 1.26375e57i | 1.34539 | − | 0.980116i | ||||
\(718\) | −1.30608e55 | −0.00985098 | ||||||||
\(719\) | − | 1.40918e56i | − | 0.103369i | −0.998663 | − | 0.0516844i | \(-0.983541\pi\) | ||
0.998663 | − | 0.0516844i | \(-0.0164590\pi\) | |||||||
\(720\) | 1.53746e57 | + | 4.95208e56i | 1.09686 | + | 0.353295i | ||||
\(721\) | 2.13845e57 | 1.48386 | ||||||||
\(722\) | − | 2.25066e55i | − | 0.0151903i | ||||||
\(723\) | −1.07670e57 | − | 1.47797e57i | −0.706851 | − | 0.970286i | ||||
\(724\) | −1.51258e57 | −0.965930 | ||||||||
\(725\) | − | 1.25931e57i | − | 0.782298i | ||||||
\(726\) | 2.19019e56 | − | 1.59555e56i | 0.132358 | − | 0.0964224i | ||||
\(727\) | −1.00482e57 | −0.590742 | −0.295371 | − | 0.955383i | \(-0.595443\pi\) | ||||
−0.295371 | + | 0.955383i | \(0.595443\pi\) | |||||||
\(728\) | 2.63350e56i | 0.150628i | ||||||||
\(729\) | 1.44567e57 | − | 1.06737e57i | 0.804486 | − | 0.593972i | ||||
\(730\) | 1.81960e56 | 0.0985185 | ||||||||
\(731\) | − | 9.29692e55i | − | 0.0489769i | ||||||
\(732\) | 3.70573e56 | + | 5.08682e56i | 0.189956 | + | 0.260750i | ||||
\(733\) | 1.26612e57 | 0.631532 | 0.315766 | − | 0.948837i | \(-0.397739\pi\) | ||||
0.315766 | + | 0.948837i | \(0.397739\pi\) | |||||||
\(734\) | − | 1.12282e56i | − | 0.0544990i | ||||||
\(735\) | −2.50514e57 | + | 1.82499e57i | −1.18328 | + | 0.862013i | ||||
\(736\) | 5.96445e55 | 0.0274166 | ||||||||
\(737\) | − | 8.81851e56i | − | 0.394499i | ||||||
\(738\) | −9.44251e55 | + | 2.93158e56i | −0.0411112 | + | 0.127637i | ||||
\(739\) | 4.06472e55 | 0.0172243 | 0.00861215 | − | 0.999963i | \(-0.497259\pi\) | ||||
0.00861215 | + | 0.999963i | \(0.497259\pi\) | |||||||
\(740\) | 2.79250e57i | 1.15175i | ||||||||
\(741\) | 7.72731e56 | + | 1.06072e57i | 0.310216 | + | 0.425830i | ||||
\(742\) | −1.95118e56 | −0.0762463 | ||||||||
\(743\) | 2.79186e57i | 1.06198i | 0.847378 | + | 0.530991i | \(0.178180\pi\) | ||||
−0.847378 | + | 0.530991i | \(0.821820\pi\) | |||||||
\(744\) | 1.66971e56 | − | 1.21638e56i | 0.0618277 | − | 0.0450413i | ||||
\(745\) | −4.74142e57 | −1.70916 | ||||||||
\(746\) | 3.61341e56i | 0.126806i | ||||||||
\(747\) | 2.51687e57 | + | 8.10672e56i | 0.859900 | + | 0.276970i | ||||
\(748\) | −1.34891e57 | −0.448695 | ||||||||
\(749\) | 8.49307e56i | 0.275060i | ||||||||
\(750\) | 1.33677e56 | + | 1.83497e56i | 0.0421534 | + | 0.0578635i | ||||
\(751\) | −3.61104e57 | −1.10875 | −0.554374 | − | 0.832268i | \(-0.687042\pi\) | ||||
−0.554374 | + | 0.832268i | \(0.687042\pi\) | |||||||
\(752\) | − | 3.41518e57i | − | 1.02107i | ||||||
\(753\) | 3.33919e57 | − | 2.43259e57i | 0.972168 | − | 0.708222i | ||||
\(754\) | 3.35910e56 | 0.0952348 | ||||||||
\(755\) | − | 5.22127e57i | − | 1.44158i | ||||||
\(756\) | −5.21934e57 | + | 1.71802e57i | −1.40339 | + | 0.461948i | ||||
\(757\) | 4.20138e57 | 1.10021 | 0.550104 | − | 0.835096i | \(-0.314588\pi\) | ||||
0.550104 | + | 0.835096i | \(0.314588\pi\) | |||||||
\(758\) | − | 6.17940e56i | − | 0.157602i | ||||||
\(759\) | −3.42942e56 | − | 4.70753e56i | −0.0851894 | − | 0.116938i | ||||
\(760\) | 1.08054e57 | 0.261439 | ||||||||
\(761\) | 5.80497e57i | 1.36807i | 0.729451 | + | 0.684033i | \(0.239776\pi\) | ||||
−0.729451 | + | 0.684033i | \(0.760224\pi\) | |||||||
\(762\) | −6.25522e56 | + | 4.55691e56i | −0.143596 | + | 0.104610i | ||||
\(763\) | 2.69015e57 | 0.601570 | ||||||||
\(764\) | 6.24642e57i | 1.36070i | ||||||||
\(765\) | 4.84674e56 | − | 1.50475e57i | 0.102854 | − | 0.319327i | ||||
\(766\) | −5.78904e56 | −0.119683 | ||||||||
\(767\) | 6.86505e56i | 0.138273i | ||||||||
\(768\) | −2.68678e57 | − | 3.68812e57i | −0.527240 | − | 0.723736i | ||||
\(769\) | 7.43323e57 | 1.42119 | 0.710593 | − | 0.703603i | \(-0.248427\pi\) | ||||
0.710593 | + | 0.703603i | \(0.248427\pi\) | |||||||
\(770\) | − | 1.58236e57i | − | 0.294775i | ||||||
\(771\) | −1.27447e57 | + | 9.28447e56i | −0.231335 | + | 0.168527i | ||||
\(772\) | 5.90524e57 | 1.04446 | ||||||||
\(773\) | − | 1.13457e58i | − | 1.95543i | −0.209927 | − | 0.977717i | \(-0.567323\pi\) | ||
0.209927 | − | 0.977717i | \(-0.432677\pi\) | |||||||
\(774\) | 1.01510e56 | + | 3.26961e55i | 0.0170487 | + | 0.00549131i | ||||
\(775\) | 9.49198e56 | 0.155354 | ||||||||
\(776\) | 1.86188e57i | 0.296973i | ||||||||
\(777\) | −5.53287e57 | − | 7.59492e57i | −0.860063 | − | 1.18060i | ||||
\(778\) | −6.64828e56 | −0.100720 | ||||||||
\(779\) | − | 9.43648e57i | − | 1.39335i | ||||||
\(780\) | −3.25272e57 | + | 2.36960e57i | −0.468117 | + | 0.341022i | ||||
\(781\) | −4.21717e57 | −0.591562 | ||||||||
\(782\) | − | 1.91105e55i | − | 0.00261299i | ||||||
\(783\) | 4.40630e57 | + | 1.33863e58i | 0.587272 | + | 1.78413i | ||||
\(784\) | 9.16698e57 | 1.19098 | ||||||||
\(785\) | − | 1.67678e55i | − | 0.00212365i | ||||||
\(786\) | 1.42107e56 | + | 1.95069e56i | 0.0175455 | + | 0.0240845i | ||||
\(787\) | −5.94377e57 | −0.715430 | −0.357715 | − | 0.933831i | \(-0.616444\pi\) | ||||
−0.357715 | + | 0.933831i | \(0.616444\pi\) | |||||||
\(788\) | 9.89675e56i | 0.116136i | ||||||||
\(789\) | −5.03205e57 | + | 3.66583e57i | −0.575711 | + | 0.419404i | ||||
\(790\) | −6.38781e56 | −0.0712542 | ||||||||
\(791\) | 2.24716e58i | 2.44402i | ||||||||
\(792\) | 9.53884e56 | − | 2.96149e57i | 0.101156 | − | 0.314056i | ||||
\(793\) | −1.55099e57 | −0.160378 | ||||||||
\(794\) | − | 3.26888e56i | − | 0.0329601i | ||||||
\(795\) | −3.53016e57 | − | 4.84581e57i | −0.347098 | − | 0.476457i | ||||
\(796\) | −4.53439e57 | −0.434768 | ||||||||
\(797\) | − | 4.16698e57i | − | 0.389632i | −0.980840 | − | 0.194816i | \(-0.937589\pi\) | ||
0.980840 | − | 0.194816i | \(-0.0624110\pi\) | |||||||
\(798\) | −1.46156e57 | + | 1.06474e57i | −0.133278 | + | 0.0970926i | ||||
\(799\) | −3.34253e57 | −0.297262 | ||||||||
\(800\) | 1.46401e57i | 0.126983i | ||||||||
\(801\) | 4.06154e57 | + | 1.30821e57i | 0.343590 | + | 0.110669i | ||||
\(802\) | 1.87547e57 | 0.154747 | ||||||||
\(803\) | 1.60528e58i | 1.29193i | ||||||||
\(804\) | −1.81962e57 | − | 2.49777e57i | −0.142843 | − | 0.196079i | ||||
\(805\) | −2.08717e57 | −0.159824 | ||||||||
\(806\) | 2.53190e56i | 0.0189124i | ||||||||
\(807\) | 1.44723e58 | − | 1.05430e58i | 1.05455 | − | 0.768235i | ||||
\(808\) | −1.03878e57 | −0.0738411 | ||||||||
\(809\) | − | 1.41711e58i | − | 0.982728i | −0.870954 | − | 0.491364i | \(-0.836499\pi\) | ||
0.870954 | − | 0.491364i | \(-0.163501\pi\) | |||||||
\(810\) | 1.47254e57 | + | 1.05840e57i | 0.0996247 | + | 0.0716062i | ||||
\(811\) | −1.58235e58 | −1.04444 | −0.522221 | − | 0.852810i | \(-0.674896\pi\) | ||||
−0.522221 | + | 0.852810i | \(0.674896\pi\) | |||||||
\(812\) | − | 4.30927e58i | − | 2.77513i | ||||||
\(813\) | 1.08800e58 | + | 1.49349e58i | 0.683626 | + | 0.938405i | ||||
\(814\) | 2.64609e57 | 0.162224 | ||||||||
\(815\) | 3.78621e58i | 2.26492i | ||||||||
\(816\) | −3.77920e57 | + | 2.75314e57i | −0.220596 | + | 0.160703i | ||||
\(817\) | −3.26752e57 | −0.186113 | ||||||||
\(818\) | − | 1.85024e57i | − | 0.102840i | ||||||
\(819\) | 4.15164e57 | − | 1.28895e58i | 0.225186 | − | 0.699128i | ||||
\(820\) | 2.89372e58 | 1.53172 | ||||||||
\(821\) | − | 8.62420e57i | − | 0.445508i | −0.974875 | − | 0.222754i | \(-0.928495\pi\) | ||
0.974875 | − | 0.222754i | \(-0.0715047\pi\) | |||||||
\(822\) | −2.50477e56 | − | 3.43827e56i | −0.0126279 | − | 0.0173342i | ||||
\(823\) | −3.14799e58 | −1.54895 | −0.774474 | − | 0.632606i | \(-0.781985\pi\) | ||||
−0.774474 | + | 0.632606i | \(0.781985\pi\) | |||||||
\(824\) | 4.24320e57i | 0.203774i | ||||||||
\(825\) | 1.15549e58 | − | 8.41774e57i | 0.541613 | − | 0.394563i | ||||
\(826\) | −9.45932e56 | −0.0432772 | ||||||||
\(827\) | − | 3.29187e58i | − | 1.47005i | −0.678040 | − | 0.735025i | \(-0.737170\pi\) | ||
0.678040 | − | 0.735025i | \(-0.262830\pi\) | |||||||
\(828\) | −1.94271e57 | − | 6.25740e56i | −0.0846841 | − | 0.0272764i | ||||
\(829\) | 3.25021e58 | 1.38300 | 0.691499 | − | 0.722378i | \(-0.256951\pi\) | ||||
0.691499 | + | 0.722378i | \(0.256951\pi\) | |||||||
\(830\) | 2.66839e57i | 0.110838i | ||||||||
\(831\) | 1.09771e58 | + | 1.50681e58i | 0.445108 | + | 0.610995i | ||||
\(832\) | 1.16399e58 | 0.460768 | ||||||||
\(833\) | − | 8.97198e57i | − | 0.346728i | ||||||
\(834\) | 1.77452e57 | − | 1.29274e57i | 0.0669516 | − | 0.0487740i | ||||
\(835\) | −2.71193e58 | −0.998963 | ||||||||
\(836\) | 4.74092e58i | 1.70505i | ||||||||
\(837\) | −1.00899e58 | + | 3.32123e57i | −0.354305 | + | 0.116625i | ||||
\(838\) | −3.58663e57 | −0.122972 | ||||||||
\(839\) | − | 8.79650e57i | − | 0.294490i | −0.989100 | − | 0.147245i | \(-0.952959\pi\) | ||
0.989100 | − | 0.147245i | \(-0.0470406\pi\) | |||||||
\(840\) | −6.56518e57 | − | 9.01194e57i | −0.214615 | − | 0.294600i | ||||
\(841\) | −7.91950e58 | −2.52801 | ||||||||
\(842\) | 3.34515e57i | 0.104273i | ||||||||
\(843\) | 1.79898e58 | − | 1.31055e58i | 0.547615 | − | 0.398936i | ||||
\(844\) | −4.60280e58 | −1.36828 | ||||||||
\(845\) | 3.10784e58i | 0.902244i | ||||||||
\(846\) | 1.17553e57 | − | 3.64961e57i | 0.0333292 | − | 0.103476i | ||||
\(847\) | 8.56692e58 | 2.37223 | ||||||||
\(848\) | 1.77321e58i | 0.479560i | ||||||||
\(849\) | 2.65932e58 | + | 3.65042e58i | 0.702452 | + | 0.964248i | ||||
\(850\) | 4.69080e56 | 0.0121023 | ||||||||
\(851\) | − | 3.49026e57i | − | 0.0879563i | ||||||
\(852\) | −1.19448e58 | + | 8.70174e57i | −0.294027 | + | 0.214198i | ||||
\(853\) | 5.31286e57 | 0.127746 | 0.0638731 | − | 0.997958i | \(-0.479655\pi\) | ||||
0.0638731 | + | 0.997958i | \(0.479655\pi\) | |||||||
\(854\) | − | 2.13709e57i | − | 0.0501957i | ||||||
\(855\) | −5.28864e58 | − | 1.70345e58i | −1.21345 | − | 0.390847i | ||||
\(856\) | −1.68523e57 | −0.0377732 | ||||||||
\(857\) | 1.38461e58i | 0.303187i | 0.988443 | + | 0.151593i | \(0.0484404\pi\) | ||||
−0.988443 | + | 0.151593i | \(0.951560\pi\) | |||||||
\(858\) | 2.24536e57 | + | 3.08218e57i | 0.0480331 | + | 0.0659344i | ||||
\(859\) | 5.63532e58 | 1.17776 | 0.588878 | − | 0.808222i | \(-0.299570\pi\) | ||||
0.588878 | + | 0.808222i | \(0.299570\pi\) | |||||||
\(860\) | − | 1.00199e58i | − | 0.204595i | ||||||
\(861\) | −7.87022e58 | + | 5.73343e58i | −1.57009 | + | 1.14380i | ||||
\(862\) | 1.06097e56 | 0.00206804 | ||||||||
\(863\) | − | 9.71213e58i | − | 1.84969i | −0.380347 | − | 0.924844i | \(-0.624196\pi\) | ||
0.380347 | − | 0.924844i | \(-0.375804\pi\) | |||||||
\(864\) | −5.12256e57 | − | 1.55623e58i | −0.0953262 | − | 0.289601i | ||||
\(865\) | 6.19680e58 | 1.12680 | ||||||||
\(866\) | − | 6.21246e56i | − | 0.0110384i | ||||||
\(867\) | −3.12182e58 | − | 4.28529e58i | −0.542034 | − | 0.744044i | ||||
\(868\) | 3.24809e58 | 0.551104 | ||||||||
\(869\) | − | 5.63545e58i | − | 0.934401i | ||||||
\(870\) | −1.14950e58 | + | 8.37406e57i | −0.186262 | + | 0.135691i | ||||
\(871\) | 7.61578e57 | 0.120601 | ||||||||
\(872\) | 5.33792e57i | 0.0826119i | ||||||||
\(873\) | 2.93521e58 | − | 9.11283e58i | 0.443970 | − | 1.37838i | ||||
\(874\) | −6.71663e56 | −0.00992939 | ||||||||
\(875\) | 7.17749e58i | 1.03708i | ||||||||
\(876\) | 3.31236e58 | + | 4.54683e58i | 0.467794 | + | 0.642136i | ||||
\(877\) | 1.00937e59 | 1.39335 | 0.696676 | − | 0.717386i | \(-0.254662\pi\) | ||||
0.696676 | + | 0.717386i | \(0.254662\pi\) | |||||||
\(878\) | − | 7.22635e57i | − | 0.0975054i | ||||||
\(879\) | 4.06834e58 | − | 2.96378e58i | 0.536587 | − | 0.390902i | ||||
\(880\) | −1.43803e59 | −1.85402 | ||||||||
\(881\) | 1.09043e59i | 1.37430i | 0.726516 | + | 0.687150i | \(0.241138\pi\) | ||||
−0.726516 | + | 0.687150i | \(0.758862\pi\) | |||||||
\(882\) | 9.79625e57 | + | 3.15533e57i | 0.120695 | + | 0.0388752i | ||||
\(883\) | 1.03905e59 | 1.25147 | 0.625736 | − | 0.780035i | \(-0.284799\pi\) | ||||
0.625736 | + | 0.780035i | \(0.284799\pi\) | |||||||
\(884\) | − | 1.16494e58i | − | 0.137169i | ||||||
\(885\) | −1.71142e58 | − | 2.34925e58i | −0.197012 | − | 0.270436i | ||||
\(886\) | 1.18787e58 | 0.133689 | ||||||||
\(887\) | − | 1.39065e59i | − | 1.53019i | −0.643916 | − | 0.765096i | \(-0.722692\pi\) | ||
0.643916 | − | 0.765096i | \(-0.277308\pi\) | |||||||
\(888\) | 1.50702e58 | − | 1.09786e58i | 0.162128 | − | 0.118110i | ||||
\(889\) | −2.44673e59 | −2.57365 | ||||||||
\(890\) | 4.30606e57i | 0.0442874i | ||||||||
\(891\) | −9.33744e58 | + | 1.29910e59i | −0.939017 | + | 1.30644i | ||||
\(892\) | 8.65096e58 | 0.850682 | ||||||||
\(893\) | 1.17478e59i | 1.12960i | ||||||||
\(894\) | 9.27055e57 | + | 1.27256e58i | 0.0871676 | + | 0.119654i | ||||
\(895\) | −5.40232e58 | −0.496729 | ||||||||
\(896\) | 6.66741e58i | 0.599511i | ||||||||
\(897\) | 4.06548e57 | − | 2.96169e57i | 0.0357489 | − | 0.0260430i | ||||
\(898\) | 8.49101e56 | 0.00730184 | ||||||||
\(899\) | − | 8.33056e58i | − | 0.700616i | ||||||
\(900\) | 1.53592e58 | − | 4.76852e58i | 0.126333 | − | 0.392223i | ||||
\(901\) | 1.73549e58 | 0.139613 | ||||||||
\(902\) | − | 2.74200e58i | − | 0.215743i | ||||||
\(903\) | 1.98528e58 | + | 2.72518e58i | 0.152780 | + | 0.209720i | ||||
\(904\) | −4.45892e58 | −0.335630 | ||||||||
\(905\) | 1.57821e59i | 1.16196i | ||||||||
\(906\) | −1.40135e58 | + | 1.02088e58i | −0.100921 | + | 0.0735207i | ||||
\(907\) | 6.22392e58 | 0.438448 | 0.219224 | − | 0.975675i | \(-0.429647\pi\) | ||||
0.219224 | + | 0.975675i | \(0.429647\pi\) | |||||||
\(908\) | − | 1.20476e59i | − | 0.830201i | ||||||
\(909\) | 5.08425e58 | + | 1.63762e58i | 0.342728 | + | 0.110391i | ||||
\(910\) | 1.36654e58 | 0.0901148 | ||||||||
\(911\) | − | 2.53157e58i | − | 0.163313i | −0.996661 | − | 0.0816567i | \(-0.973979\pi\) | ||
0.996661 | − | 0.0816567i | \(-0.0260211\pi\) | |||||||
\(912\) | 9.67626e58 | + | 1.32825e59i | 0.610676 | + | 0.838268i | ||||
\(913\) | −2.35410e59 | −1.45348 | ||||||||
\(914\) | − | 7.51278e57i | − | 0.0453813i | ||||||
\(915\) | 5.30754e58 | − | 3.86653e58i | 0.313669 | − | 0.228507i | ||||
\(916\) | −1.51374e59 | −0.875271 | ||||||||
\(917\) | 7.63011e58i | 0.431662i | ||||||||
\(918\) | −4.98628e57 | + | 1.64130e57i | −0.0276009 | + | 0.00908522i | ||||
\(919\) | 1.77477e59 | 0.961241 | 0.480621 | − | 0.876929i | \(-0.340411\pi\) | ||||
0.480621 | + | 0.876929i | \(0.340411\pi\) | |||||||
\(920\) | − | 4.14146e57i | − | 0.0219481i | ||||||
\(921\) | −4.17121e58 | − | 5.72577e58i | −0.216306 | − | 0.296921i | ||||
\(922\) | −2.83274e58 | −0.143744 | ||||||||
\(923\) | − | 3.64200e58i | − | 0.180845i | ||||||
\(924\) | 3.95402e59 | − | 2.88049e59i | 1.92132 | − | 1.39968i | ||||
\(925\) | 8.56708e58 | 0.407379 | ||||||||
\(926\) | − | 2.44706e58i | − | 0.113874i | ||||||
\(927\) | 6.68929e58 | − | 2.07680e59i | 0.304639 | − | 0.945803i | ||||
\(928\) | 1.28488e59 | 0.572668 | ||||||||
\(929\) | − | 2.44892e59i | − | 1.06822i | −0.845415 | − | 0.534110i | \(-0.820647\pi\) | ||
0.845415 | − | 0.534110i | \(-0.179353\pi\) | |||||||
\(930\) | −6.31191e57 | − | 8.66429e57i | −0.0269465 | − | 0.0369891i | ||||
\(931\) | −3.15332e59 | −1.31757 | ||||||||
\(932\) | − | 2.38388e59i | − | 0.974915i | ||||||
\(933\) | −3.56889e59 | + | 2.59993e59i | −1.42857 | + | 1.04071i | ||||
\(934\) | −3.64726e58 | −0.142899 | ||||||||
\(935\) | 1.40744e59i | 0.539757i | ||||||||
\(936\) | 2.55758e58 | + | 8.23787e57i | 0.0960092 | + | 0.0309242i | ||||
\(937\) | 4.70534e59 | 1.72902 | 0.864509 | − | 0.502617i | \(-0.167630\pi\) | ||||
0.864509 | + | 0.502617i | \(0.167630\pi\) | |||||||
\(938\) | 1.04937e58i | 0.0377462i | ||||||||
\(939\) | 6.59722e58 | + | 9.05593e58i | 0.232300 | + | 0.318876i | ||||
\(940\) | −3.60248e59 | −1.24178 | ||||||||
\(941\) | 4.64871e59i | 1.56870i | 0.620319 | + | 0.784350i | \(0.287003\pi\) | ||||
−0.620319 | + | 0.784350i | \(0.712997\pi\) | |||||||
\(942\) | −4.50035e55 | + | 3.27849e55i | −0.000148672 | + | 0.000108307i | ||||
\(943\) | −3.61678e58 | −0.116974 | ||||||||
\(944\) | 8.59653e58i | 0.272197i | ||||||||
\(945\) | 1.79257e59 | + | 5.44582e59i | 0.555699 | + | 1.68821i | ||||
\(946\) | −9.49458e57 | −0.0288173 | ||||||||
\(947\) | − | 3.33540e59i | − | 0.991171i | −0.868559 | − | 0.495586i | \(-0.834954\pi\) | ||
0.868559 | − | 0.495586i | \(-0.165046\pi\) | |||||||
\(948\) | −1.16283e59 | − | 1.59620e59i | −0.338336 | − | 0.464429i | ||||
\(949\) | −1.38634e59 | −0.394954 | ||||||||
\(950\) | − | 1.64864e58i | − | 0.0459890i | ||||||
\(951\) | −1.96399e59 | + | 1.43076e59i | −0.536449 | + | 0.390802i | ||||
\(952\) | 3.22756e58 | 0.0863247 | ||||||||
\(953\) | 9.58504e58i | 0.251036i | 0.992091 | + | 0.125518i | \(0.0400593\pi\) | ||||
−0.992091 | + | 0.125518i | \(0.959941\pi\) | |||||||
\(954\) | −6.10350e57 | + | 1.89493e58i | −0.0156535 | + | 0.0485989i | ||||
\(955\) | 6.51746e59 | 1.63686 | ||||||||
\(956\) | 6.69598e59i | 1.64686i | ||||||||
\(957\) | −7.38776e59 | − | 1.01411e60i | −1.77940 | − | 2.44256i | ||||
\(958\) | −1.39660e58 | −0.0329429 | ||||||||
\(959\) | − | 1.34488e59i | − | 0.310678i | ||||||
\(960\) | −3.98322e59 | + | 2.90176e59i | −0.901176 | + | 0.656504i | ||||
\(961\) | −3.88511e59 | −0.860867 | ||||||||
\(962\) | 2.28519e58i | 0.0495932i | ||||||||
\(963\) | 8.24824e58 | + | 2.65672e58i | 0.175322 | + | 0.0564704i | ||||
\(964\) | 5.70489e59 | 1.18770 | ||||||||
\(965\) | − | 6.16148e59i | − | 1.25643i | ||||||
\(966\) | 4.08090e57 | + | 5.60180e57i | 0.00815104 | + | 0.0111888i | ||||
\(967\) | 1.45692e59 | 0.285040 | 0.142520 | − | 0.989792i | \(-0.454480\pi\) | ||||
0.142520 | + | 0.989792i | \(0.454480\pi\) | |||||||
\(968\) | 1.69988e59i | 0.325771i | ||||||||
\(969\) | 1.30000e59 | − | 9.47043e58i | 0.244043 | − | 0.177785i | ||||
\(970\) | 9.66145e58 | 0.177667 | ||||||||
\(971\) | 6.17773e59i | 1.11287i | 0.830891 | + | 0.556435i | \(0.187831\pi\) | ||||
−0.830891 | + | 0.556435i | \(0.812169\pi\) | |||||||
\(972\) | 3.58296e57 | + | 5.60630e59i | 0.00632290 | + | 0.989353i | ||||
\(973\) | 6.94103e59 | 1.19996 | ||||||||
\(974\) | 6.36356e58i | 0.107776i | ||||||||
\(975\) | 7.26967e58 | + | 9.97900e58i | 0.120621 | + | 0.165575i | ||||
\(976\) | −1.94217e59 | −0.315712 | ||||||||
\(977\) | − | 5.80301e59i | − | 0.924192i | −0.886830 | − | 0.462096i | \(-0.847098\pi\) | ||
0.886830 | − | 0.462096i | \(-0.152902\pi\) | |||||||
\(978\) | 1.01619e59 | − | 7.40290e58i | 0.158561 | − | 0.115511i | ||||
\(979\) | −3.79889e59 | −0.580768 | ||||||||
\(980\) | − | 9.66972e59i | − | 1.44841i | ||||||
\(981\) | 8.41510e58 | − | 2.61261e59i | 0.123503 | − | 0.383437i | ||||
\(982\) | −2.29547e58 | −0.0330097 | ||||||||
\(983\) | − | 4.95264e59i | − | 0.697857i | −0.937149 | − | 0.348929i | \(-0.886546\pi\) | ||
0.937149 | − | 0.348929i | \(-0.113454\pi\) | |||||||
\(984\) | −1.13765e59 | − | 1.56164e59i | −0.157075 | − | 0.215615i | ||||
\(985\) | 1.03262e59 | 0.139706 | ||||||||
\(986\) | − | 4.11684e58i | − | 0.0545790i | ||||||
\(987\) | 9.79786e59 | − | 7.13772e59i | 1.27288 | − | 0.927291i | ||||
\(988\) | −4.09432e59 | −0.521246 | ||||||||
\(989\) | 1.25236e58i | 0.0156244i | ||||||||
\(990\) | −1.53674e59 | − | 4.94979e58i | −0.187887 | − | 0.0605178i | ||||
\(991\) | 4.47741e59 | 0.536481 | 0.268240 | − | 0.963352i | \(-0.413558\pi\) | ||||
0.268240 | + | 0.963352i | \(0.413558\pi\) | |||||||
\(992\) | 9.68472e58i | 0.113724i | ||||||||
\(993\) | 5.58949e59 | + | 7.67263e59i | 0.643261 | + | 0.882997i | ||||
\(994\) | 5.01829e58 | 0.0566015 | ||||||||
\(995\) | 4.73115e59i | 0.523004i | ||||||||
\(996\) | −6.66781e59 | + | 4.85748e59i | −0.722431 | + | 0.526289i | ||||
\(997\) | −9.25444e59 | −0.982758 | −0.491379 | − | 0.870946i | \(-0.663507\pi\) | ||||
−0.491379 | + | 0.870946i | \(0.663507\pi\) | |||||||
\(998\) | 3.14907e58i | 0.0327771i | ||||||||
\(999\) | −9.10673e59 | + | 2.99761e59i | −0.929079 | + | 0.305820i |
(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 | 3.41.b.a.2.6 | ✓ | 12 | |
3.2 | odd | 2 | inner | 3.41.b.a.2.7 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.41.b.a.2.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
3.41.b.a.2.7 | yes | 12 | 3.2 | odd | 2 | inner |