Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 13.10 | ||
Character | \(\chi\) | \(=\) | 76.13 |
Dual form | 76.7.j.a.41.10 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 17.6351 | − | 48.4521i | 0.653152 | − | 1.79452i | 0.0473893 | − | 0.998876i | \(-0.484910\pi\) |
0.605763 | − | 0.795645i | \(-0.292868\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 11.8840 | + | 67.3972i | 0.0950716 | + | 0.539178i | 0.994725 | + | 0.102574i | \(0.0327078\pi\) |
−0.899654 | + | 0.436604i | \(0.856181\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −186.943 | + | 323.795i | −0.545023 | + | 0.944008i | 0.453582 | + | 0.891214i | \(0.350146\pi\) |
−0.998605 | + | 0.0527935i | \(0.983188\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1478.16 | − | 1240.32i | −2.02765 | − | 1.70140i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −462.506 | − | 801.084i | −0.347488 | − | 0.601867i | 0.638315 | − | 0.769776i | \(-0.279632\pi\) |
−0.985803 | + | 0.167909i | \(0.946299\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1082.59 | − | 2974.39i | −0.492757 | − | 1.35384i | −0.898147 | − | 0.439695i | \(-0.855086\pi\) |
0.405390 | − | 0.914144i | \(-0.367136\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3475.11 | + | 612.756i | 1.02966 | + | 0.181557i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6881.88 | + | 5774.58i | −1.40075 | + | 1.17537i | −0.439983 | + | 0.898006i | \(0.645015\pi\) |
−0.960766 | + | 0.277361i | \(0.910540\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6577.56 | + | 1944.62i | −0.958968 | + | 0.283513i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12391.8 | + | 14767.9i | 1.33806 | + | 1.59464i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −209.854 | + | 1190.14i | −0.0172478 | + | 0.0978171i | −0.992216 | − | 0.124525i | \(-0.960259\pi\) |
0.974969 | + | 0.222342i | \(0.0713703\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10281.5 | − | 3742.17i | 0.658018 | − | 0.239499i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −53611.3 | + | 30952.5i | −2.72373 | + | 1.57255i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 20758.8 | − | 24739.4i | 0.851153 | − | 1.01437i | −0.148523 | − | 0.988909i | \(-0.547452\pi\) |
0.999676 | − | 0.0254561i | \(-0.00810381\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10305.9 | + | 5950.12i | 0.345940 | + | 0.199729i | 0.662896 | − | 0.748712i | \(-0.269327\pi\) |
−0.316955 | + | 0.948440i | \(0.602661\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −46970.6 | + | 8282.18i | −1.30703 | + | 0.230464i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −24044.5 | − | 8751.48i | −0.560804 | − | 0.204116i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 35746.8i | 0.705719i | 0.935676 | + | 0.352860i | \(0.114791\pi\) | ||||
−0.935676 | + | 0.352860i | \(0.885209\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −163207. | −2.75134 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18775.8 | − | 51586.2i | 0.272426 | − | 0.748483i | −0.725742 | − | 0.687967i | \(-0.758503\pi\) |
0.998167 | − | 0.0605158i | \(-0.0192746\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6291.43 | − | 35680.4i | −0.0791305 | − | 0.448771i | −0.998470 | − | 0.0553049i | \(-0.982387\pi\) |
0.919339 | − | 0.393466i | \(-0.128724\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 66028.0 | − | 114364.i | 0.724587 | − | 1.25502i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −105148. | − | 88229.4i | −1.01276 | − | 0.849806i | −0.0240587 | − | 0.999711i | \(-0.507659\pi\) |
−0.988700 | + | 0.149905i | \(0.952103\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11070.8 | − | 19175.3i | −0.0941006 | − | 0.162987i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 158428. | + | 435277.i | 1.19432 | + | 3.28137i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 115562. | + | 20376.6i | 0.776222 | + | 0.136869i | 0.547705 | − | 0.836671i | \(-0.315501\pi\) |
0.228516 | + | 0.973540i | \(0.426613\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 48494.5 | − | 40691.7i | 0.291477 | − | 0.244578i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −21775.4 | + | 352990.i | −0.117582 | + | 1.90607i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12651.0 | − | 15076.9i | −0.0615985 | − | 0.0734102i | 0.734365 | − | 0.678754i | \(-0.237480\pi\) |
−0.795964 | + | 0.605344i | \(0.793035\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 37645.8 | − | 213500.i | 0.165854 | − | 0.940607i | −0.782325 | − | 0.622871i | \(-0.785966\pi\) |
0.948179 | − | 0.317736i | \(-0.102923\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 677942. | − | 246751.i | 2.71126 | − | 0.986817i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 187600. | − | 108311.i | 0.683113 | − | 0.394396i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 179950. | − | 214456.i | 0.598310 | − | 0.713039i | −0.378870 | − | 0.925450i | \(-0.623687\pi\) |
0.977180 | + | 0.212411i | \(0.0681317\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 53964.0 | + | 31156.1i | 0.164270 | + | 0.0948411i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −598154. | + | 105471.i | −1.67124 | + | 0.294684i | −0.927510 | − | 0.373799i | \(-0.878055\pi\) |
−0.743727 | + | 0.668484i | \(0.766944\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −444320. | − | 161719.i | −1.14216 | − | 0.415712i | −0.299467 | − | 0.954107i | \(-0.596809\pi\) |
−0.842693 | + | 0.538394i | \(0.819031\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 564156.i | − | 1.33726i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 345849. | 0.757556 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 174270. | − | 478802.i | 0.353460 | − | 0.971124i | −0.627789 | − | 0.778383i | \(-0.716040\pi\) |
0.981250 | − | 0.192741i | \(-0.0617377\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 310004. | + | 1.75812e6i | 0.583327 | + | 3.30821i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 154246. | − | 267163.i | 0.269762 | − | 0.467242i | −0.699038 | − | 0.715084i | \(-0.746388\pi\) |
0.968800 | + | 0.247843i | \(0.0797216\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −470975. | − | 395195.i | −0.766904 | − | 0.643509i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −832590. | − | 1.44209e6i | −1.26437 | − | 2.18995i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 156769. | + | 430720.i | 0.222377 | + | 0.610977i | 0.999839 | − | 0.0179539i | \(-0.00571521\pi\) |
−0.777462 | + | 0.628931i | \(0.783493\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.16547e6 | + | 205504.i | 1.54660 | + | 0.272707i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 470042. | − | 394412.i | 0.584370 | − | 0.490344i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −209229. | − | 420200.i | −0.244035 | − | 0.490100i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −242174. | − | 288612.i | −0.265346 | − | 0.316227i | 0.616876 | − | 0.787060i | \(-0.288398\pi\) |
−0.882222 | + | 0.470833i | \(0.843954\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −309946. | + | 1.75779e6i | −0.319433 | + | 1.81160i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 84977.2 | − | 30929.2i | 0.0824780 | − | 0.0300195i | −0.300452 | − | 0.953797i | \(-0.597137\pi\) |
0.382930 | + | 0.923778i | \(0.374915\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −801514. | + | 462754.i | −0.733499 | + | 0.423486i | −0.819701 | − | 0.572792i | \(-0.805860\pi\) |
0.0862019 | + | 0.996278i | \(0.472527\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −848055. | + | 1.01067e6i | −0.732581 | + | 0.873057i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 991191. | + | 572265.i | 0.809107 | + | 0.467138i | 0.846646 | − | 0.532157i | \(-0.178618\pi\) |
−0.0375385 | + | 0.999295i | \(0.511952\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.05836e6 | + | 186617.i | −0.817245 | + | 0.144102i | −0.566617 | − | 0.823981i | \(-0.691748\pi\) |
−0.250628 | + | 0.968083i | \(0.580637\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.73201e6 | + | 630399.i | 1.26643 | + | 0.460942i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 695217.i | − | 0.481820i | −0.970547 | − | 0.240910i | \(-0.922554\pi\) | ||
0.970547 | − | 0.240910i | \(-0.0774459\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −82706.1 | −0.0543806 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.08896e6 | + | 5.73938e6i | −1.30429 | + | 3.58350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −583260. | − | 3.30783e6i | −0.346116 | − | 1.96292i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 457956. | − | 793204.i | 0.258504 | − | 0.447743i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.16834e6 | − | 1.81946e6i | −1.16523 | − | 0.977747i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 909061. | + | 1.57454e6i | 0.465439 | + | 0.806164i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −31432.5 | − | 86360.1i | −0.0153450 | − | 0.0421601i | 0.931784 | − | 0.363014i | \(-0.118252\pi\) |
−0.947129 | + | 0.320854i | \(0.896030\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.83974e6 | − | 324396.i | −0.857014 | − | 0.151115i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.16831e6 | − | 980326.i | 0.519688 | − | 0.436070i | −0.344835 | − | 0.938663i | \(-0.612065\pi\) |
0.864523 | + | 0.502593i | \(0.167621\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 599973. | − | 2.49331e6i | 0.255021 | − | 1.05979i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.72323e6 | − | 3.24541e6i | −1.10683 | − | 1.31907i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 548281. | − | 3.10946e6i | 0.213227 | − | 1.20927i | −0.670731 | − | 0.741701i | \(-0.734019\pi\) |
0.883957 | − | 0.467567i | \(-0.154870\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.47990e6 | + | 1.63055e6i | −1.66811 | + | 0.607142i | −0.991606 | − | 0.129299i | \(-0.958727\pi\) |
−0.676502 | + | 0.736441i | \(0.736505\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.12919e6 | + | 3.53869e6i | −2.18648 | + | 1.26237i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.88203e6 | + | 2.24292e6i | −0.643604 | + | 0.767017i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.91406e6 | + | 1.10508e6i | 0.627844 | + | 0.362486i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.12432e6 | + | 198247.i | −0.353946 | + | 0.0624102i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.90020e6 | + | 1.41956e6i | 1.17904 | + | 0.429135i | 0.855862 | − | 0.517204i | \(-0.173027\pi\) |
0.323176 | + | 0.946339i | \(0.395249\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.63776e6i | − | 0.766133i | −0.923721 | − | 0.383066i | \(-0.874868\pi\) | ||
0.923721 | − | 0.383066i | \(-0.125132\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.73349e7 | 4.84001 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −278547. | + | 765301.i | −0.0748002 | + | 0.205512i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −82450.1 | − | 467598.i | −0.0213055 | − | 0.120830i | 0.972300 | − | 0.233736i | \(-0.0750951\pi\) |
−0.993606 | + | 0.112906i | \(0.963984\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.02523e6 | − | 5.23985e6i | 0.752605 | − | 1.30355i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −346131. | − | 290438.i | −0.0829397 | − | 0.0695947i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.38569e6 | + | 4.13213e6i | 0.550872 | + | 0.954139i | 0.998212 | + | 0.0597748i | \(0.0190383\pi\) |
−0.447339 | + | 0.894364i | \(0.647628\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.11639e6 | − | 3.06726e6i | −0.248522 | − | 0.682808i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −507839. | − | 89545.8i | −0.109038 | − | 0.0192263i | 0.118863 | − | 0.992911i | \(-0.462075\pi\) |
−0.227901 | + | 0.973684i | \(0.573186\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.97742e6 | + | 3.33745e6i | −0.824027 | + | 0.691441i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.21346e7 | + | 5.28386e6i | 2.42683 | + | 1.05673i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.82939e6 | + | 4.56369e6i | 0.739590 | + | 0.881410i | 0.996376 | − | 0.0850589i | \(-0.0271078\pi\) |
−0.256786 | + | 0.966468i | \(0.582663\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −710365. | + | 4.02868e6i | −0.132546 | + | 0.751707i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −953610. | + | 347086.i | −0.171969 | + | 0.0625917i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.16232e6 | + | 2.40312e6i | −0.725732 | + | 0.419002i | −0.816859 | − | 0.576838i | \(-0.804287\pi\) |
0.0911266 | + | 0.995839i | \(0.470953\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.70797e6 | − | 5.61074e6i | 0.793958 | − | 0.946202i | −0.205515 | − | 0.978654i | \(-0.565887\pi\) |
0.999473 | + | 0.0324514i | \(0.0103314\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.68063e6 | − | 5.58911e6i | −1.57961 | − | 0.911989i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.40923e6 | + | 424813.i | −0.380508 | + | 0.0670938i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.80884e6 | + | 2.84218e6i | 1.19416 | + | 0.434638i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 2.31454e7i | − | 3.42830i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.39203e6 | 1.20439 | 0.602195 | − | 0.798349i | \(-0.294293\pi\) | ||||
0.602195 | + | 0.798349i | \(0.294293\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.44669e6 | + | 1.22172e7i | −0.618537 | + | 1.69942i | 0.0920037 | + | 0.995759i | \(0.470673\pi\) |
−0.710540 | + | 0.703657i | \(0.751549\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.93954e6 | − | 1.09997e7i | −0.261574 | − | 1.48346i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.52150e6 | − | 6.09942e6i | 0.460606 | − | 0.797793i | −0.538385 | − | 0.842699i | \(-0.680966\pi\) |
0.998991 | + | 0.0449061i | \(0.0142989\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.12660e7 | − | 9.45330e6i | −1.42959 | − | 1.19957i | −0.945956 | − | 0.324294i | \(-0.894873\pi\) |
−0.483631 | − | 0.875272i | \(-0.660682\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.21739e6 | − | 1.25009e7i | −0.888775 | − | 1.53940i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.12976e6 | + | 1.13464e7i | 0.493670 | + | 1.35635i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.69990e6 | + | 652392.i | 0.429465 | + | 0.0757264i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.78636e6 | − | 1.49893e6i | 0.201399 | − | 0.168994i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.59997e6 | + | 4.36979e6i | 0.503867 | + | 0.478654i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.17515e7 | − | 1.40048e7i | −1.25096 | − | 1.49084i | −0.802042 | − | 0.597267i | \(-0.796253\pi\) |
−0.448920 | − | 0.893572i | \(-0.648191\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.43824e6 | + | 3.08418e7i | −0.562755 | + | 3.19154i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.33000e6 | − | 848049.i | 0.234444 | − | 0.0853308i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.85324e6 | + | 2.22467e6i | −0.377091 | + | 0.217714i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.56713e7 | + | 1.86763e7i | −1.49201 | + | 1.77811i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.46261e7 | + | 1.42179e7i | 2.28149 | + | 1.31722i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.92753e6 | − | 1.04518e6i | 0.534514 | − | 0.0942492i | 0.100125 | − | 0.994975i | \(-0.468076\pi\) |
0.434388 | + | 0.900726i | \(0.356965\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.98393e7 | − | 7.22090e6i | −1.74172 | − | 0.633934i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.74521e6i | 0.320184i | 0.987102 | + | 0.160092i | \(0.0511790\pi\) | ||||
−0.987102 | + | 0.160092i | \(0.948821\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.94412e7 | −1.61888 | −0.809442 | − | 0.587200i | \(-0.800230\pi\) | ||||
−0.809442 | + | 0.587200i | \(0.800230\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.09909e6 | − | 1.67571e7i | 0.494799 | − | 1.35945i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.20270e6 | + | 1.24921e7i | 0.174136 | + | 0.987572i | 0.939137 | + | 0.343543i | \(0.111627\pi\) |
−0.765001 | + | 0.644029i | \(0.777262\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.69685e6 | − | 8.13518e6i | 0.361912 | − | 0.626850i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.01257e7 | − | 1.68875e7i | −1.51184 | − | 1.26858i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.77010e6 | + | 3.06589e6i | 0.129659 | + | 0.224576i | 0.923545 | − | 0.383491i | \(-0.125278\pi\) |
−0.793885 | + | 0.608067i | \(0.791945\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.43684e6 | + | 1.21901e7i | 0.316973 | + | 0.870877i | 0.991202 | + | 0.132355i | \(0.0422539\pi\) |
−0.674229 | + | 0.738522i | \(0.735524\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.62084e7 | + | 8.14779e6i | 3.22034 | + | 0.567833i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.16079e6 | − | 974022.i | 0.0789327 | − | 0.0662324i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.29048e7 | + | 1.74590e7i | 0.856370 | + | 1.15859i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.02244e7 | − | 1.21850e7i | −0.662279 | − | 0.789274i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.94585e6 | + | 1.67068e7i | −0.186290 | + | 1.05650i | 0.737996 | + | 0.674805i | \(0.235772\pi\) |
−0.924286 | + | 0.381700i | \(0.875339\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.05046e6 | − | 382337.i | 0.0648663 | − | 0.0236094i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.74537e7 | + | 1.58504e7i | −1.65569 | + | 0.955916i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 915461. | − | 1.09100e6i | 0.0539312 | − | 0.0642727i | −0.738404 | − | 0.674358i | \(-0.764420\pi\) |
0.792336 | + | 0.610085i | \(0.208865\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.15746e7 | − | 6.68261e6i | −0.666204 | − | 0.384633i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.13696e7 | + | 1.08211e7i | −3.45169 | + | 0.608626i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.09611e6 | − | 1.12689e6i | −0.170196 | − | 0.0619463i | 0.255517 | − | 0.966805i | \(-0.417754\pi\) |
−0.425713 | + | 0.904858i | \(0.639977\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.03068e6i | 0.431534i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.36339e7 | 1.24166 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.00178e6 | − | 1.37423e7i | 0.256961 | − | 0.705995i | −0.742390 | − | 0.669968i | \(-0.766308\pi\) |
0.999351 | − | 0.0360265i | \(-0.0114701\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.05273e6 | + | 1.16416e7i | 0.103139 | + | 0.584931i | 0.991947 | + | 0.126652i | \(0.0404230\pi\) |
−0.888808 | + | 0.458279i | \(0.848466\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.05103e7 | − | 5.28455e7i | 1.49954 | − | 2.59729i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.75307e6 | − | 6.50560e6i | −0.372800 | − | 0.312816i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.02602e7 | − | 1.77712e7i | −0.482744 | − | 0.836137i | 0.517060 | − | 0.855949i | \(-0.327026\pi\) |
−0.999804 | + | 0.0198123i | \(0.993693\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.85371e6 | − | 2.15779e7i | −0.361628 | − | 0.993566i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.84040e6 | − | 1.02982e6i | −0.263223 | − | 0.0464133i | 0.0404791 | − | 0.999180i | \(-0.487112\pi\) |
−0.303702 | + | 0.952767i | \(0.598223\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.31441e7 | + | 1.94202e7i | −1.02113 | + | 0.856830i | −0.989769 | − | 0.142678i | \(-0.954429\pi\) |
−0.0313613 | + | 0.999508i | \(0.509984\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.40493e7 | + | 2.72732e6i | −1.03889 | + | 0.117815i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.31933e7 | + | 1.57232e7i | 0.558096 | + | 0.665113i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.82301e6 | − | 5.57091e7i | 0.406959 | − | 2.30798i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.82546e7 | + | 6.64415e6i | −0.740789 | + | 0.269625i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.62506e7 | − | 2.09293e7i | 1.44116 | − | 0.832054i | 0.443233 | − | 0.896406i | \(-0.353831\pi\) |
0.997927 | + | 0.0643522i | \(0.0204981\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 865798. | − | 1.03182e6i | 0.0337249 | − | 0.0401918i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.95911e7 | + | 2.86314e7i | 1.89293 | + | 1.09288i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.76712e6 | − | 664246.i | 0.140928 | − | 0.0248494i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.27293e7 | + | 4.63308e6i | 0.466771 | + | 0.169891i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 4.66276e6i | − | 0.167616i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.48367e7 | 0.522923 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.57275e6 | + | 9.81606e6i | −0.123478 | + | 0.339252i | −0.985995 | − | 0.166776i | \(-0.946664\pi\) |
0.862517 | + | 0.506028i | \(0.168887\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.28662e6 | + | 4.69958e7i | 0.280868 | + | 1.59288i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.12886e6 | − | 3.68729e6i | 0.0707726 | − | 0.122582i | −0.828467 | − | 0.560037i | \(-0.810787\pi\) |
0.899240 | + | 0.437455i | \(0.144120\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.28451e7 | + | 1.07784e7i | 0.418896 | + | 0.351495i | 0.827743 | − | 0.561108i | \(-0.189625\pi\) |
−0.408847 | + | 0.912603i | \(0.634069\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.46869e7 | + | 4.27590e7i | 0.789834 | + | 1.36803i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.08084e7 | + | 2.96959e7i | 0.339301 | + | 0.932222i | 0.985593 | + | 0.169132i | \(0.0540964\pi\) |
−0.646293 | + | 0.763090i | \(0.723681\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.94194e7 | − | 5.18743e6i | −0.906278 | − | 0.159801i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.52072e7 | − | 3.79333e7i | 1.36676 | − | 1.14685i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.40366e7 | − | 5.13653e7i | 1.01004 | − | 1.52427i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.22613e7 | − | 2.65300e7i | −0.648487 | − | 0.772836i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.62226e6 | + | 5.45706e7i | −0.275191 | + | 1.56068i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.82248e7 | − | 1.75524e7i | 1.35420 | − | 0.492889i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.98972e7 | + | 1.14876e7i | −0.548665 | + | 0.316772i | −0.748583 | − | 0.663041i | \(-0.769266\pi\) |
0.199919 | + | 0.979813i | \(0.435932\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.43376e7 | − | 5.28395e7i | 1.20071 | − | 1.43095i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.65922e7 | + | 9.57953e6i | 0.441337 | + | 0.254806i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.17348e7 | − | 2.06916e6i | 0.306609 | − | 0.0540635i | −0.0182267 | − | 0.999834i | \(-0.505802\pi\) |
0.324836 | + | 0.945770i | \(0.394691\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.36847e7 | − | 1.22602e7i | −0.864636 | − | 0.314702i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.10079e7i | − | 0.277613i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.57088e7 | −0.884898 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.45853e6 | + | 4.00728e6i | −0.0355188 | + | 0.0975872i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.38023e7 | − | 7.82766e7i | −0.330341 | − | 1.87346i | −0.469122 | − | 0.883133i | \(-0.655430\pi\) |
0.138782 | − | 0.990323i | \(-0.455681\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.97314e7 | + | 5.14963e7i | −0.699422 | + | 1.21143i | 0.269246 | + | 0.963072i | \(0.413226\pi\) |
−0.968667 | + | 0.248362i | \(0.920108\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.50104e8 | + | 1.25952e8i | 3.47112 | + | 2.91261i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.00325e7 | + | 1.73768e7i | 0.228079 | + | 0.395044i | 0.957239 | − | 0.289299i | \(-0.0934223\pi\) |
−0.729160 | + | 0.684343i | \(0.760089\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.42169e7 | − | 3.90605e7i | −0.317774 | − | 0.873078i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.70557e8 | − | 3.00738e7i | −3.74857 | − | 0.660974i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.40990e6 | + | 6.21765e6i | −0.160151 | + | 0.134382i | −0.719342 | − | 0.694657i | \(-0.755556\pi\) |
0.559191 | + | 0.829039i | \(0.311112\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.94828e7 | − | 2.55817e7i | 0.839241 | − | 0.543760i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.03563e7 | − | 3.61772e7i | −0.634641 | − | 0.756336i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.61915e6 | − | 3.18678e7i | 0.115556 | − | 0.655350i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.83850e7 | + | 1.03313e7i | −0.574237 | + | 0.209005i | −0.612782 | − | 0.790252i | \(-0.709950\pi\) |
0.0385456 | + | 0.999257i | \(0.487728\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.17373e7 | + | 5.29646e7i | −1.82586 | + | 1.05416i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.82013e7 | + | 3.36090e7i | −0.552264 | + | 0.658163i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.78611e6 | + | 1.60856e6i | 0.0536873 | + | 0.0309964i | 0.526603 | − | 0.850111i | \(-0.323465\pi\) |
−0.472916 | + | 0.881107i | \(0.656799\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.23211e7 | − | 1.62787e7i | 1.75068 | − | 0.308693i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.60576e7 | − | 3.49621e7i | −1.79270 | − | 0.652489i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7.47670e7i | − | 1.37338i | −0.726948 | − | 0.686692i | \(-0.759062\pi\) | ||
0.726948 | − | 0.686692i | \(-0.240938\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.73864e6 | −0.0856799 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.01017e7 | + | 2.77542e7i | −0.179803 | + | 0.494006i | −0.996550 | − | 0.0829903i | \(-0.973553\pi\) |
0.816747 | + | 0.576996i | \(0.195775\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.11005e6 | + | 2.33093e7i | 0.0720220 | + | 0.408457i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.49556e7 | + | 6.05448e7i | −0.603092 | + | 1.04459i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.07001e7 | + | 3.41515e7i | 0.691428 | + | 0.580177i | 0.919321 | − | 0.393509i | \(-0.128739\pi\) |
−0.227893 | + | 0.973686i | \(0.573183\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.42838e6 | − | 9.40222e6i | −0.0908113 | − | 0.157290i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.68956e7 | − | 7.38951e7i | −0.443102 | − | 1.21741i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.43410e7 | + | 6.05524e6i | 0.557213 | + | 0.0982516i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.92475e7 | − | 2.45415e7i | 0.467430 | − | 0.392220i | −0.378426 | − | 0.925631i | \(-0.623535\pi\) |
0.845856 | + | 0.533411i | \(0.179090\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.10226e8 | − | 7.30398e7i | −1.73526 | − | 1.14985i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.58690e7 | + | 9.04171e7i | 1.17661 | + | 1.40222i | 0.896955 | + | 0.442122i | \(0.145774\pi\) |
0.279651 | + | 0.960102i | \(0.409781\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.54090e6 | − | 3.70953e7i | 0.0999361 | − | 0.566766i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.14808e8 | + | 4.17868e7i | −1.72826 | + | 0.629034i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.86362e7 | − | 1.65331e7i | 0.424749 | − | 0.245229i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.82835e7 | − | 2.17894e7i | 0.267232 | − | 0.318475i | −0.615695 | − | 0.787984i | \(-0.711125\pi\) |
0.882928 | + | 0.469509i | \(0.155569\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.40991e8 | − | 8.14010e7i | −2.03079 | − | 1.17248i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.24685e6 | − | 1.27781e6i | 0.102872 | − | 0.0181392i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.98391e7 | + | 7.22083e6i | 0.277573 | + | 0.101028i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.45816e8i | 3.39001i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.25519e7 | 0.578465 | 0.289232 | − | 0.957259i | \(-0.406600\pi\) | ||||
0.289232 | + | 0.957259i | \(0.406600\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.38147e7 | − | 9.29052e7i | 0.453168 | − | 1.24507i | −0.477314 | − | 0.878733i | \(-0.658390\pi\) |
0.930482 | − | 0.366337i | \(-0.119388\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.59921e7 | + | 2.60834e8i | 0.607663 | + | 3.44623i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.91468e7 | + | 8.51248e7i | −0.640219 | + | 1.10889i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.20925e7 | + | 5.21018e7i | 0.797546 | + | 0.669221i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.54841e7 | + | 1.30742e8i | 0.956057 | + | 1.65594i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.11223e7 | − | 3.05582e7i | −0.138919 | − | 0.381677i | 0.850651 | − | 0.525731i | \(-0.176208\pi\) |
−0.989570 | + | 0.144054i | \(0.953986\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.07697e7 | + | 1.07153e7i | 0.748554 | + | 0.131990i | 0.534896 | − | 0.844918i | \(-0.320351\pi\) |
0.213659 | + | 0.976908i | \(0.431462\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.72982e7 | − | 7.32519e7i | 1.06057 | − | 0.889921i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −934039. | − | 8.23632e6i | −0.0111923 | − | 0.0986935i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.90147e7 | − | 9.41660e7i | −0.933930 | − | 1.11301i | −0.993391 | − | 0.114783i | \(-0.963383\pi\) |
0.0594610 | − | 0.998231i | \(-0.481062\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.41905e6 | + | 4.20755e7i | −0.0865033 | + | 0.490585i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.83024e7 | + | 3.57791e7i | −1.13071 | + | 0.411546i | −0.838552 | − | 0.544822i | \(-0.816597\pi\) |
−0.292163 | + | 0.956369i | \(0.594375\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.71663e7 | + | 1.56845e7i | −0.308283 | + | 0.177987i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.37561e8 | − | 1.63939e8i | 1.54018 | − | 1.83552i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.38886e7 | + | 2.53391e7i | 0.484856 | + | 0.279932i | 0.722438 | − | 0.691436i | \(-0.243021\pi\) |
−0.237582 | + | 0.971368i | \(0.576355\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.00089e7 | + | 8.81791e6i | −0.545152 | + | 0.0961249i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.27805e8 | − | 4.65172e7i | −1.37484 | − | 0.500401i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.09918e7i | 0.859819i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.35007e8 | −1.41452 | −0.707260 | − | 0.706954i | \(-0.750069\pi\) | ||||
−0.707260 | + | 0.706954i | \(0.750069\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.90209e8 | − | 5.22594e8i | 1.96694 | − | 5.40414i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.52231e7 | − | 1.43047e8i | −0.257451 | − | 1.46008i | −0.789702 | − | 0.613491i | \(-0.789765\pi\) |
0.532250 | − | 0.846587i | \(-0.321347\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.56343e6 | − | 1.48323e7i | 0.0862790 | − | 0.149440i | −0.819657 | − | 0.572855i | \(-0.805836\pi\) |
0.905935 | + | 0.423416i | \(0.139169\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.21682e7 | + | 2.69923e7i | 0.319940 | + | 0.268461i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.16672e7 | + | 7.21697e7i | 0.409113 | + | 0.708605i | 0.994791 | − | 0.101939i | \(-0.0325047\pi\) |
−0.585677 | + | 0.810544i | \(0.699171\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.57993e7 | + | 9.83577e7i | 0.347021 | + | 0.953432i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.41101e7 | − | 4.25126e6i | −0.230747 | − | 0.0406869i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.56732e7 | + | 2.15424e7i | −0.242603 | + | 0.203569i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.03504e7 | + | 4.46080e7i | −0.563118 | + | 0.416229i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.45545e8 | − | 1.73454e8i | −1.34104 | − | 1.59819i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.50462e6 | + | 2.55469e7i | −0.0409875 | + | 0.232452i | −0.998419 | − | 0.0562089i | \(-0.982099\pi\) |
0.957432 | + | 0.288660i | \(0.0932098\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.06325e8 | − | 3.86990e7i | 0.955430 | − | 0.347748i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.01764e7 | + | 1.16488e7i | −0.179061 | + | 0.103381i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.65737e7 | − | 1.97517e7i | 0.145276 | − | 0.173133i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.53672e7 | − | 1.46457e7i | −0.219627 | − | 0.126802i | 0.386151 | − | 0.922436i | \(-0.373804\pi\) |
−0.605777 | + | 0.795634i | \(0.707138\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.42282e8 | − | 4.27209e7i | 2.07203 | − | 0.365354i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.73330e8 | − | 6.30869e7i | −1.46430 | − | 0.532960i | −0.517751 | − | 0.855531i | \(-0.673231\pi\) |
−0.946545 | + | 0.322571i | \(0.895453\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.90126e8i | 2.42129i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.22153e8 | −1.00714 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.76698e7 | − | 2.13396e8i | 0.632679 | − | 1.73827i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.95251e7 | + | 1.10733e8i | 0.157142 | + | 0.891197i | 0.956801 | + | 0.290743i | \(0.0939024\pi\) |
−0.799659 | + | 0.600454i | \(0.794986\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.32945e7 | + | 2.30267e7i | −0.105720 | + | 0.183113i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.85948e7 | + | 4.91669e7i | 0.460421 | + | 0.386339i | 0.843286 | − | 0.537465i | \(-0.180618\pi\) |
−0.382865 | + | 0.923804i | \(0.625062\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.09440e6 | + | 5.35966e6i | 0.0240272 | + | 0.0416163i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.15643e7 | + | 2.51571e8i | 0.702590 | + | 1.93035i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.15054e7 | + | 1.08451e7i | 0.466402 | + | 0.0822392i | 0.401910 | − | 0.915679i | \(-0.368346\pi\) |
0.0644914 | + | 0.997918i | \(0.479458\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.35426e8 | − | 1.13636e8i | 1.01494 | − | 0.851635i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.92441e8 | − | 3.07845e8i | 2.16614 | − | 2.28024i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.07135e7 | − | 4.85205e7i | −0.298069 | − | 0.355225i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.20477e7 | + | 1.25039e8i | −0.159548 | + | 0.904843i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.88652e8 | − | 1.05061e8i | 2.06477 | − | 0.751516i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.47933e7 | − | 3.16349e7i | 0.387449 | − | 0.223694i | −0.293605 | − | 0.955927i | \(-0.594855\pi\) |
0.681054 | + | 0.732233i | \(0.261522\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.93338e7 | + | 5.87937e7i | −0.344857 | + | 0.410985i | −0.910397 | − | 0.413736i | \(-0.864224\pi\) |
0.565540 | + | 0.824721i | \(0.308668\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.82671e8 | + | 1.05465e8i | 1.26238 | + | 0.728836i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.05283e8 | + | 1.85643e7i | −0.719330 | + | 0.126837i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.37736e8 | + | 5.01317e7i | 0.930422 | + | 0.338646i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.79775e7i | 0.253655i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.73764e8 | −1.14757 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.67898e7 | + | 7.36043e7i | −0.174948 | + | 0.480664i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.30330e7 | + | 2.44052e8i | 0.277894 | + | 1.57601i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.02407e7 | + | 1.77374e7i | −0.0653976 | + | 0.113272i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.64458e6 | − | 3.89726e6i | −0.0293329 | − | 0.0246132i | 0.628003 | − | 0.778211i | \(-0.283872\pi\) |
−0.657336 | + | 0.753597i | \(0.728317\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.88826e8 | − | 3.27057e8i | −1.17941 | − | 2.04279i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.51549e7 | − | 6.91125e7i | −0.155394 | − | 0.426940i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.47598e7 | + | 1.67087e7i | 0.578978 | + | 0.102089i | 0.455465 | − | 0.890253i | \(-0.349473\pi\) |
0.123513 | + | 0.992343i | \(0.460584\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.20456e8 | + | 2.68894e8i | −1.93665 | + | 1.62504i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.84337e7 | + | 2.03093e8i | −0.528643 | + | 1.21406i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.22455e8 | + | 1.45936e8i | 0.724105 | + | 0.862955i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.19041e7 | + | 1.24224e8i | −0.128128 | + | 0.726652i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.45478e8 | + | 5.29497e7i | −0.841845 | + | 0.306407i | −0.726711 | − | 0.686943i | \(-0.758952\pi\) |
−0.115134 | + | 0.993350i | \(0.536730\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.93164e7 | + | 5.73403e7i | −0.568572 | + | 0.328265i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.75420e8 | − | 3.28232e8i | 1.55993 | − | 1.85906i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.39192e7 | − | 4.84508e7i | −0.470258 | − | 0.271504i | 0.246090 | − | 0.969247i | \(-0.420854\pi\) |
−0.716348 | + | 0.697743i | \(0.754188\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.68557e7 | − | 8.26192e6i | 0.259787 | − | 0.0458074i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.27223e8 | − | 2.28290e8i | −3.44090 | − | 1.25239i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.03600e8i | − | 0.562371i | −0.959653 | − | 0.281186i | \(-0.909272\pi\) | ||
0.959653 | − | 0.281186i | \(-0.0907276\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.80698e7 | 0.150776 | 0.0753879 | − | 0.997154i | \(-0.475980\pi\) | ||||
0.0753879 | + | 0.997154i | \(0.475980\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.47994e8 | − | 4.06612e8i | 0.786650 | − | 2.16130i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.29609e6 | + | 1.30218e7i | 0.0120777 | + | 0.0684963i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.88306e7 | − | 1.19218e8i | 0.358306 | − | 0.620604i | −0.629372 | − | 0.777104i | \(-0.716688\pi\) |
0.987678 | + | 0.156500i | \(0.0500211\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.13530e8 | + | 4.30903e8i | 2.64564 | + | 2.21995i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.76706e7 | + | 9.98883e7i | 0.294053 | + | 0.509315i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.71246e7 | − | 1.01999e8i | −0.187351 | − | 0.514742i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.11643e8 | − | 7.25838e7i | −2.05614 | − | 0.362554i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.59612e6 | + | 2.17841e6i | −0.0128354 | + | 0.0107702i | −0.649183 | − | 0.760632i | \(-0.724889\pi\) |
0.636347 | + | 0.771403i | \(0.280445\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.93585e7 | − | 1.90963e7i | −0.388372 | − | 0.0934550i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.33428e8 | − | 2.78188e8i | −1.13081 | − | 1.34765i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.86783e7 | + | 1.05930e8i | −0.0895721 | + | 0.507989i | 0.906704 | + | 0.421768i | \(0.138590\pi\) |
−0.996276 | + | 0.0862210i | \(0.972521\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.16007e8 | − | 7.86202e7i | 1.02546 | − | 0.373236i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.56709e8 | + | 3.79151e8i | −3.08639 | + | 1.78193i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.49660e7 | + | 2.97533e7i | −0.116163 | + | 0.138438i | −0.820992 | − | 0.570939i | \(-0.806579\pi\) |
0.704829 | + | 0.709377i | \(0.251024\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.13553e8 | − | 1.81030e8i | −1.44440 | − | 0.833924i | −0.446260 | − | 0.894903i | \(-0.647244\pi\) |
−0.998139 | + | 0.0609791i | \(0.980578\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.31989e8 | + | 9.38040e7i | −2.42633 | + | 0.427828i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.89021e7 | + | 2.14386e7i | 0.265989 | + | 0.0968122i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3.23222e8i | − | 1.44522i | −0.691253 | − | 0.722612i | \(-0.742941\pi\) | ||
0.691253 | − | 0.722612i | \(-0.257059\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.22587e8 | 2.75644 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.48597e8 | + | 4.08266e8i | −0.651456 | + | 1.78986i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.08979e6 | + | 3.45369e7i | 0.0264375 | + | 0.149935i | 0.995169 | − | 0.0981770i | \(-0.0313011\pi\) |
−0.968731 | + | 0.248112i | \(0.920190\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.68579e7 | − | 1.67763e8i | 0.416399 | − | 0.721224i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.80289e7 | + | 2.35190e7i | 0.119330 | + | 0.100130i | 0.700500 | − | 0.713652i | \(-0.252960\pi\) |
−0.581170 | + | 0.813782i | \(0.697405\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.00007e8 | + | 3.46422e8i | 0.843281 | + | 1.46061i | 0.887106 | + | 0.461567i | \(0.152712\pi\) |
−0.0438243 | + | 0.999039i | \(0.513954\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.55873e7 | − | 7.03005e7i | −0.106844 | − | 0.293551i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.68772e8 | − | 2.97590e7i | −0.697968 | − | 0.123071i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.56459e7 | − | 2.99105e7i | 0.146006 | − | 0.122513i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.92846e8 | − | 1.45816e8i | 1.18806 | − | 0.591566i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.06423e8 | − | 2.46005e8i | −0.829479 | − | 0.988535i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.07315e7 | + | 1.74287e8i | −0.122320 | + | 0.693709i | 0.860544 | + | 0.509376i | \(0.170124\pi\) |
−0.982864 | + | 0.184333i | \(0.940987\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.85802e8 | + | 3.22406e8i | −3.49241 | + | 1.27113i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.44689e6 | − | 3.14476e6i | 0.0212729 | − | 0.0122819i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.50494e7 | + | 5.36878e7i | −0.174289 | + | 0.207710i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.01499e9 | + | 5.86002e8i | 3.89007 | + | 2.24593i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.94355e8 | + | 5.19027e7i | −1.11763 | + | 0.197068i | −0.701799 | − | 0.712375i | \(-0.747620\pi\) |
−0.415829 | + | 0.909443i | \(0.636509\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.69490e7 | − | 6.16895e6i | −0.0637547 | − | 0.0232048i | 0.309946 | − | 0.950754i | \(-0.399689\pi\) |
−0.373701 | + | 0.927549i | \(0.621911\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1.27849e8i | − | 0.476450i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.46840e6 | 0.0201905 | 0.0100953 | − | 0.999949i | \(-0.496787\pi\) | ||||
0.0100953 | + | 0.999949i | \(0.496787\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.22670e6 | + | 1.71077e7i | −0.0227784 | + | 0.0625832i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.98375e7 | + | 2.25930e8i | 0.144394 | + | 0.818898i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.76619e8 | − | 3.05914e8i | 0.634306 | − | 1.09865i | −0.352355 | − | 0.935866i | \(-0.614619\pi\) |
0.986662 | − | 0.162785i | \(-0.0520476\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.99554e7 | + | 6.70905e7i | 0.284527 | + | 0.238747i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.56192e8 | + | 7.90147e8i | 1.60861 | + | 2.78620i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.90229e8 | − | 5.22651e8i | −0.664694 | − | 1.82623i | −0.554253 | − | 0.832348i | \(-0.686996\pi\) |
−0.110440 | − | 0.993883i | \(-0.535226\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.69015e8 | − | 2.98018e7i | −0.585221 | − | 0.103190i | −0.126804 | − | 0.991928i | \(-0.540472\pi\) |
−0.458416 | + | 0.888737i | \(0.651583\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.12317e9 | − | 9.42450e8i | 3.85393 | − | 3.23384i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.75172e8 | + | 1.08061e7i | 0.595663 | + | 0.0367455i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.50870e7 | + | 2.98975e7i | 0.0845418 | + | 0.100753i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.38913e7 | − | 3.05633e8i | 0.179987 | − | 1.02076i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.88443e8 | + | 6.85876e7i | −0.623753 | + | 0.227027i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.90333e8 | − | 1.09889e8i | 0.624409 | − | 0.360503i | −0.154175 | − | 0.988044i | \(-0.549272\pi\) |
0.778584 | + | 0.627541i | \(0.215938\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.35377e8 | + | 5.18862e8i | −1.41564 | + | 1.68710i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.78519e8 | + | 1.60803e8i | 0.897613 | + | 0.518237i | 0.876425 | − | 0.481538i | \(-0.159922\pi\) |
0.0211880 | + | 0.999776i | \(0.493255\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.38724e8 | − | 2.44608e7i | 0.443141 | − | 0.0781377i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.81463e8 | + | 6.60473e7i | 0.574576 | + | 0.209129i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 4.05444e8i | − | 1.27253i | −0.771470 | − | 0.636266i | \(-0.780478\pi\) | ||
0.771470 | − | 0.636266i | \(-0.219522\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.16084e8 | 0.672283 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.42847e8 | + | 9.41964e8i | −1.05738 | + | 2.90512i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.44976e7 | − | 3.65784e8i | −0.197190 | − | 1.11832i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.13606e8 | − | 1.96772e8i | 0.344325 | − | 0.596389i | −0.640906 | − | 0.767620i | \(-0.721441\pi\) |
0.985231 | + | 0.171231i | \(0.0547744\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.11221e8 | − | 4.28965e8i | −1.53606 | − | 1.28891i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.63134e8 | − | 2.82556e8i | −0.485947 | − | 0.841685i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.68676e8 | + | 4.63433e8i | 0.498143 | + | 1.36864i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.44115e8 | + | 1.13575e8i | 1.88596 | + | 0.332545i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.53751e8 | + | 2.96832e8i | −1.02694 | + | 0.861702i | −0.990483 | − | 0.137634i | \(-0.956050\pi\) |
−0.0364528 | + | 0.999335i | \(0.511606\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.95138e7 | − | 2.35127e8i | −0.200081 | − | 0.676762i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.11337e8 | − | 3.71037e8i | −0.888512 | − | 1.05889i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.87118e6 | + | 3.32971e7i | −0.0166137 | + | 0.0942212i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.64727e8 | − | 9.63528e7i | 0.742780 | − | 0.270350i | 0.0572154 | − | 0.998362i | \(-0.481778\pi\) |
0.685564 | + | 0.728012i | \(0.259556\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.51468e8 | + | 4.91595e8i | −2.36897 | + | 1.36773i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.24422e6 | + | 1.10168e7i | −0.0255036 | + | 0.0303940i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.73532e8 | − | 1.00189e8i | −0.474747 | − | 0.274095i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.79765e8 | − | 3.16974e7i | 0.487694 | − | 0.0859936i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.28341e8 | − | 1.19506e8i | −0.883362 | − | 0.321518i | −0.139796 | − | 0.990180i | \(-0.544645\pi\) |
−0.743566 | + | 0.668663i | \(0.766867\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 3.46035e8i | − | 0.923238i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.68881e8 | 1.76984 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.20853e8 | − | 3.32042e8i | 0.317135 | − | 0.871321i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.28109e7 | − | 1.29367e8i | −0.0593661 | − | 0.336682i | 0.940630 | − | 0.339433i | \(-0.110235\pi\) |
−0.999996 | + | 0.00275141i | \(0.999124\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.58947e8 | − | 9.68125e8i | 1.44274 | − | 2.49890i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.49336e8 | + | 2.09218e8i | 0.638313 | + | 0.535608i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.87149e8 | − | 4.97357e8i | −0.729114 | − | 1.26286i | −0.957258 | − | 0.289236i | \(-0.906599\pi\) |
0.228144 | − | 0.973628i | \(-0.426734\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.67226e7 | − | 7.34199e7i | −0.0673004 | − | 0.184906i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.55025e8 | − | 4.49678e7i | −0.637060 | − | 0.112331i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.65457e7 | + | 6.42295e7i | −0.189665 | + | 0.159148i | −0.732676 | − | 0.680578i | \(-0.761729\pi\) |
0.543011 | + | 0.839726i | \(0.317284\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.07350e9 | − | 3.17374e8i | 2.63845 | − | 0.780041i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.78895e6 | + | 5.70725e6i | 0.0116755 | + | 0.0139143i | 0.771851 | − | 0.635804i | \(-0.219331\pi\) |
−0.760175 | + | 0.649718i | \(0.774887\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.93244e7 | + | 2.79732e8i | −0.119287 | + | 0.676510i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.59369e8 | + | 2.03594e8i | −1.34195 | + | 0.488430i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.70592e8 | + | 2.13962e8i | −0.881965 | + | 0.509202i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.46321e8 | − | 4.12729e8i | 0.817634 | − | 0.974418i | −0.182327 | − | 0.983238i | \(-0.558363\pi\) |
0.999961 | + | 0.00881953i | \(0.00280738\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.57527e8 | + | 4.37359e8i | 1.77424 | + | 1.02436i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.77778e8 | − | 3.13470e7i | 0.413082 | − | 0.0728375i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.33118e8 | − | 8.48479e7i | −0.537387 | − | 0.195593i | 0.0590466 | − | 0.998255i | \(-0.481194\pi\) |
−0.596434 | + | 0.802662i | \(0.703416\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 5.76396e7i | − | 0.131824i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.92686e7 | −0.157175 | −0.0785873 | − | 0.996907i | \(-0.525041\pi\) | ||||
−0.0785873 | + | 0.996907i | \(0.525041\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.37427e8 | − | 3.77577e8i | 0.309384 | − | 0.850025i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.06007e8 | + | 1.16832e9i | 0.460148 | + | 2.60963i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.11487e7 | + | 5.39511e7i | −0.0690325 | + | 0.119568i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.30828e8 | − | 3.61508e8i | −0.947382 | − | 0.794948i | 0.0314728 | − | 0.999505i | \(-0.489980\pi\) |
−0.978855 | + | 0.204557i | \(0.934425\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.67171e7 | − | 6.35960e7i | −0.0801135 | − | 0.138761i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.09093e8 | − | 2.99729e8i | −0.236187 | − | 0.648920i | −0.999994 | − | 0.00347431i | \(-0.998894\pi\) |
0.763807 | − | 0.645445i | \(-0.223328\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.28227e8 | + | 2.26099e7i | 0.275470 | + | 0.0485728i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.27906e8 | + | 4.42966e8i | −1.12537 | + | 0.944294i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.31840e7 | + | 3.75823e8i | −0.0490428 | + | 0.795008i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.61141e8 | + | 4.30391e8i | 0.758095 | + | 0.903462i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.47160e8 | + | 1.96884e9i | −0.723177 | + | 4.10134i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.05350e7 | − | 1.11138e7i | 0.0631231 | − | 0.0229749i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.71646e8 | + | 1.56835e8i | −0.557287 | + | 0.321750i | −0.752056 | − | 0.659099i | \(-0.770938\pi\) |
0.194769 | + | 0.980849i | \(0.437604\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.09201e8 | + | 1.30140e8i | −0.222328 | + | 0.264960i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.25107e8 | + | 1.29966e8i | 0.454842 | + | 0.262603i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.75786e8 | + | 1.19159e8i | −1.35516 | + | 0.238951i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.89103e8 | + | 1.41622e8i | 0.774397 | + | 0.281857i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 5.50596e8i | − | 1.08757i | −0.839224 | − | 0.543786i | \(-0.816990\pi\) | ||
0.839224 | − | 0.543786i | \(-0.183010\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.23310e9 | 2.41746 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.02502e8 | − | 8.31117e8i | 0.588614 | − | 1.61720i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.59500e7 | + | 4.30734e8i | 0.146683 | + | 0.831883i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.54613e7 | − | 2.67798e7i | 0.0296387 | − | 0.0513357i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.77634e8 | − | 4.84693e8i | −1.09909 | − | 0.922244i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.72042e8 | − | 6.44395e8i | −0.702662 | − | 1.21705i | −0.967529 | − | 0.252761i | \(-0.918661\pi\) |
0.264867 | − | 0.964285i | \(-0.414672\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.07944e8 | + | 8.46069e8i | 0.577310 | + | 1.58615i | 0.792695 | + | 0.609618i | \(0.208677\pi\) |
−0.215385 | + | 0.976529i | \(0.569101\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.00260e8 | + | 1.05842e8i | 1.11704 | + | 0.196964i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.50143e8 | + | 2.09895e8i | −0.462078 | + | 0.387730i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.10767e8 | + | 2.22456e8i | 0.203116 | + | 0.407923i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.46786e9 | − | 1.74933e9i | −2.67198 | − | 3.18435i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.72755e7 | − | 3.81538e8i | 0.121570 | − | 0.689459i | −0.861716 | − | 0.507391i | \(-0.830610\pi\) |
0.983286 | − | 0.182068i | \(-0.0582790\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.49712e8 | − | 1.63682e8i | 0.806743 | − | 0.293630i | 0.0944652 | − | 0.995528i | \(-0.469886\pi\) |
0.712278 | + | 0.701898i | \(0.247664\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.51936e8 | + | 2.60926e8i | −0.804851 | + | 0.464681i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.27485e7 | − | 1.51930e7i | 0.0225393 | − | 0.0268613i | −0.754657 | − | 0.656119i | \(-0.772197\pi\) |
0.777196 | + | 0.629258i | \(0.216641\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.78222e7 | − | 3.33837e7i | −0.101492 | − | 0.0585963i | 0.448395 | − | 0.893836i | \(-0.351996\pi\) |
−0.549887 | + | 0.835239i | \(0.685329\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.04199e9 | + | 1.83731e8i | −1.81577 | + | 0.320169i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.86917e8 | + | 6.80323e7i | 0.323381 | + | 0.117701i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 3.52911e7i | − | 0.0606186i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.36684e8 | −1.25633 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.02866e8 | + | 2.82622e8i | −0.174175 | + | 0.478543i | −0.995807 | − | 0.0914756i | \(-0.970842\pi\) |
0.821632 | + | 0.570018i | \(0.193064\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.78185e7 | − | 4.41331e8i | −0.130826 | − | 0.741953i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.52893e8 | + | 2.64818e8i | −0.255214 | + | 0.442044i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.72203e8 | − | 2.28405e8i | −0.451151 | − | 0.378561i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.71223e8 | + | 2.96568e8i | 0.281782 | + | 0.488060i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.32801e8 | + | 1.46386e9i | 0.870646 | + | 2.39208i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.25437e7 | − | 7.50161e6i | −0.0690314 | − | 0.0121721i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.24011e8 | + | 5.23608e8i | −1.00542 | + | 0.843643i | −0.987725 | − | 0.156200i | \(-0.950076\pi\) |
−0.0176896 | + | 0.999844i | \(0.505631\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.11910e8 | + | 8.80635e8i | −0.339041 | + | 1.40896i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.23699e8 | + | 3.85770e8i | 0.514280 | + | 0.612895i | 0.959218 | − | 0.282666i | \(-0.0912189\pi\) |
−0.444938 | + | 0.895561i | \(0.646774\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.02285e7 | + | 2.28147e8i | −0.0634680 | + | 0.359945i | 0.936489 | + | 0.350696i | \(0.114055\pi\) |
−0.999957 | + | 0.00924849i | \(0.997056\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.94487e8 | − | 3.61964e8i | 1.55808 | − | 0.567095i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.47697e8 | − | 4.31683e8i | 1.16330 | − | 0.671634i | 0.211210 | − | 0.977441i | \(-0.432260\pi\) |
0.952094 | + | 0.305807i | \(0.0989262\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.62072e8 | + | 3.12325e8i | −0.404922 | + | 0.482568i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.52599e9 | − | 1.45838e9i | −3.87592 | − | 2.23776i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.64162e8 | + | 8.18443e7i | −0.707310 | + | 0.124718i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.32685e8 | − | 3.03073e8i | −1.26016 | − | 0.458661i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.26990e8i | 1.09266i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.79770e8 | −1.01470 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.94370e7 | − | 2.18251e8i | 0.117767 | − | 0.323562i | −0.866778 | − | 0.498694i | \(-0.833813\pi\) |
0.984545 | + | 0.175132i | \(0.0560352\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.74784e8 | − | 2.12551e9i | −0.551842 | − | 3.12965i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.20919e8 | − | 9.02258e8i | 0.761802 | − | 1.31948i | −0.180119 | − | 0.983645i | \(-0.557648\pi\) |
0.941921 | − | 0.335835i | \(-0.109018\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.34122e6 | + | 3.64272e6i | 0.00630565 | + | 0.00529107i | 0.645935 | − | 0.763392i | \(-0.276468\pi\) |
−0.639629 | + | 0.768683i | \(0.720912\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.47253e7 | − | 6.01460e7i | −0.0500975 | − | 0.0867714i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.16930e7 | − | 5.96010e7i | −0.0310848 | − | 0.0854049i | 0.923179 | − | 0.384369i | \(-0.125581\pi\) |
−0.954264 | + | 0.298964i | \(0.903359\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.38390e7 | + | 5.96673e6i | 0.0481629 | + | 0.00849241i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.26502e9 | − | 1.06148e9i | 1.78840 | − | 1.50065i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.63188e8 | + | 3.75863e8i | 1.21214 | + | 0.527806i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.11428e8 | − | 2.51970e8i | −0.294913 | − | 0.351464i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.42496e7 | − | 1.94239e8i | 0.0474546 | − | 0.269128i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.61140e8 | − | 1.31444e8i | 0.497046 | − | 0.180910i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.12947e8 | + | 5.27090e8i | −1.24816 | + | 0.720627i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.48965e8 | − | 5.35055e8i | 0.609746 | − | 0.726667i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.34097e8 | + | 2.50626e8i | 0.585654 | + | 0.338128i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.22126e8 | + | 3.91668e7i | −0.297699 | + | 0.0524924i | −0.320503 | − | 0.947248i | \(-0.603852\pi\) |
0.0228036 | + | 0.999740i | \(0.492741\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.63972e8 | − | 5.96809e7i | −0.218312 | − | 0.0794592i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.12572e9i | 1.48894i | 0.667659 | + | 0.744468i | \(0.267297\pi\) | ||||
−0.667659 | + | 0.744468i | \(0.732703\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.85360e8 | −0.374956 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.61647e8 | − | 7.18868e8i | 0.341548 | − | 0.938396i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.90176e7 | + | 5.61557e8i | 0.128412 | + | 0.728258i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.48089e8 | + | 2.56497e8i | −0.190799 | + | 0.330473i | −0.945515 | − | 0.325578i | \(-0.894441\pi\) |
0.754716 | + | 0.656051i | \(0.227774\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.12603e8 | + | 3.46215e8i | 0.528145 | + | 0.443166i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.61265e8 | + | 1.66496e9i | 1.22247 | + | 2.11738i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.33771e8 | + | 3.67532e8i | 0.169019 | + | 0.464376i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.75873e9 | + | 3.10112e8i | 2.20780 | + | 0.389295i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.65352e6 | − | 3.06566e6i | 0.00455684 | − | 0.00382364i | −0.640506 | − | 0.767953i | \(-0.721275\pi\) |
0.645063 | + | 0.764129i | \(0.276831\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.10108e8 | + | 1.04598e8i | 0.136448 | + | 0.129621i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.41114e8 | − | 1.68173e8i | −0.173750 | − | 0.207068i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.87555e7 | + | 5.60071e8i | −0.120817 | + | 0.685185i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.35719e8 | + | 4.93977e7i | −0.164976 | + | 0.0600465i | −0.423188 | − | 0.906042i | \(-0.639089\pi\) |
0.258212 | + | 0.966088i | \(0.416867\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.48759e8 | − | 4.32296e8i | 0.904369 | − | 0.522137i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.03360e8 | − | 3.61530e8i | 0.364073 | − | 0.433886i | −0.552647 | − | 0.833416i | \(-0.686382\pi\) |
0.916720 | + | 0.399530i | \(0.130827\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.74547e7 | + | 3.31715e7i | 0.0685157 | + | 0.0395576i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.55994e9 | − | 2.75059e8i | 1.84846 | − | 0.325934i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.44414e8 | + | 2.70945e8i | 0.876526 | + | 0.319029i | 0.740807 | − | 0.671718i | \(-0.234443\pi\) |
0.135719 | + | 0.990747i | \(0.456666\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.49665e9i | 1.75115i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.62944e9 | 1.89451 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.38447e8 | + | 9.29874e8i | −0.391031 | + | 1.07435i | 0.575500 | + | 0.817801i | \(0.304807\pi\) |
−0.966532 | + | 0.256548i | \(0.917415\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.97305e7 | + | 5.65600e8i | 0.114503 | + | 0.649380i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.70156e8 | + | 1.33395e9i | −0.878704 | + | 1.52196i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.04328e8 | + | 7.58821e8i | 1.02535 | + | 0.860367i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.72944e8 | − | 6.45958e8i | −0.420217 | − | 0.727837i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.55346e8 | − | 2.07530e9i | −0.845799 | − | 2.32381i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.76249e8 | − | 1.54506e8i | −0.975092 | − | 0.171935i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.73764e8 | − | 2.29715e8i | 0.302759 | − | 0.254045i | −0.478733 | − | 0.877961i | \(-0.658904\pi\) |
0.781491 | + | 0.623916i | \(0.214459\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.88851e9 | − | 2.55498e9i | −2.07563 | − | 2.80812i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.98073e8 | + | 8.31931e8i | 0.762506 | + | 0.908719i | 0.998004 | − | 0.0631555i | \(-0.0201164\pi\) |
−0.235498 | + | 0.971875i | \(0.575672\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.09522e8 | − | 1.75539e9i | 0.336011 | − | 1.90561i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.67802e9 | + | 6.10748e8i | −1.81043 | + | 0.658943i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.99279e8 | + | 5.76934e8i | −1.07153 | + | 0.618647i | −0.928598 | − | 0.371086i | \(-0.878985\pi\) |
−0.142929 | + | 0.989733i | \(0.545652\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.72536e8 | − | 3.24796e8i | 0.290453 | − | 0.346148i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.79589e9 | + | 1.03685e9i | 1.90227 | + | 1.09827i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.84567e9 | − | 3.25441e8i | 1.94309 | − | 0.342619i | 0.943140 | − | 0.332395i | \(-0.107857\pi\) |
0.999948 | − | 0.0102233i | \(-0.00325424\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.52934e8 | + | 1.64854e8i | 0.473943 | + | 0.172501i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 2.64613e9i | − | 2.75207i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.37850e7 | 0.0452623 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.93201e8 | − | 1.35506e9i | 0.506760 | − | 1.39231i | −0.377800 | − | 0.925887i | \(-0.623319\pi\) |
0.884560 | − | 0.466425i | \(-0.154458\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.05711e8 | + | 1.16664e9i | 0.210092 | + | 1.19149i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.03242e8 | − | 8.71640e8i | 0.510866 | − | 0.884846i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.39912e8 | + | 2.01310e8i | 0.242084 | + | 0.203133i | 0.755755 | − | 0.654855i | \(-0.227270\pi\) |
−0.513671 | + | 0.857987i | \(0.671715\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.10645e9 | − | 1.91643e9i | −1.10978 | − | 1.92219i |
(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 | 76.7.j.a.13.10 | ✓ | 60 | |
19.3 | odd | 18 | inner | 76.7.j.a.41.10 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.j.a.13.10 | ✓ | 60 | 1.1 | even | 1 | trivial | |
76.7.j.a.41.10 | yes | 60 | 19.3 | odd | 18 | inner |