Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,9,Mod(11,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.11");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.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: | \(8.14757220122\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 5 x^{15} + 26 x^{14} - 834 x^{13} + 4390 x^{12} - 61783 x^{11} + 466168 x^{10} + \cdots + 206161212459445 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{58}\cdot 5^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.15 | ||
Root | \(-5.64565 + 3.35245i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 20.11 |
Dual form | 20.9.b.a.11.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 14.5274 | − | 6.70489i | 0.907961 | − | 0.419056i | ||||
\(3\) | − | 150.211i | − | 1.85446i | −0.374496 | − | 0.927228i | \(-0.622184\pi\) | ||
0.374496 | − | 0.927228i | \(-0.377816\pi\) | |||||||
\(4\) | 166.089 | − | 194.809i | 0.648785 | − | 0.760972i | ||||
\(5\) | 279.508 | 0.447214 | ||||||||
\(6\) | −1007.15 | − | 2182.17i | −0.777121 | − | 1.68377i | ||||
\(7\) | 2626.96i | 1.09411i | 0.837097 | + | 0.547055i | \(0.184251\pi\) | ||||
−0.837097 | + | 0.547055i | \(0.815749\pi\) | |||||||
\(8\) | 1106.66 | − | 3943.67i | 0.270181 | − | 0.962810i | ||||
\(9\) | −16002.3 | −2.43901 | ||||||||
\(10\) | 4060.52 | − | 1874.07i | 0.406052 | − | 0.187407i | ||||
\(11\) | 2300.68i | 0.157140i | 0.996909 | + | 0.0785699i | \(0.0250354\pi\) | ||||
−0.996909 | + | 0.0785699i | \(0.974965\pi\) | |||||||
\(12\) | −29262.4 | − | 24948.4i | −1.41119 | − | 1.20314i | ||||
\(13\) | 47058.2 | 1.64764 | 0.823820 | − | 0.566852i | \(-0.191839\pi\) | ||||
0.823820 | + | 0.566852i | \(0.191839\pi\) | |||||||
\(14\) | 17613.5 | + | 38162.8i | 0.458493 | + | 0.993408i | ||||
\(15\) | − | 41985.3i | − | 0.829338i | ||||||
\(16\) | −10365.0 | − | 64711.2i | −0.158157 | − | 0.987414i | ||||
\(17\) | −51967.0 | −0.622202 | −0.311101 | − | 0.950377i | \(-0.600698\pi\) | ||||
−0.311101 | + | 0.950377i | \(0.600698\pi\) | |||||||
\(18\) | −232472. | + | 107294.i | −2.21452 | + | 1.02208i | ||||
\(19\) | − | 59554.7i | − | 0.456985i | −0.973546 | − | 0.228492i | \(-0.926620\pi\) | ||
0.973546 | − | 0.228492i | \(-0.0733796\pi\) | |||||||
\(20\) | 46423.2 | − | 54450.7i | 0.290145 | − | 0.340317i | ||||
\(21\) | 394598. | 2.02898 | ||||||||
\(22\) | 15425.8 | + | 33422.9i | 0.0658503 | + | 0.142677i | ||||
\(23\) | 77570.5i | 0.277195i | 0.990349 | + | 0.138597i | \(0.0442594\pi\) | ||||
−0.990349 | + | 0.138597i | \(0.955741\pi\) | |||||||
\(24\) | −592382. | − | 166233.i | −1.78549 | − | 0.501039i | ||||
\(25\) | 78125.0 | 0.200000 | ||||||||
\(26\) | 683632. | − | 315520.i | 1.49599 | − | 0.690453i | ||||
\(27\) | 1.41819e6i | 2.66858i | ||||||||
\(28\) | 511754. | + | 436308.i | 0.832587 | + | 0.709841i | ||||
\(29\) | 902211. | 1.27561 | 0.637803 | − | 0.770200i | \(-0.279844\pi\) | ||||
0.637803 | + | 0.770200i | \(0.279844\pi\) | |||||||
\(30\) | −281507. | − | 609935.i | −0.347539 | − | 0.753006i | ||||
\(31\) | 340014.i | 0.368171i | 0.982910 | + | 0.184086i | \(0.0589324\pi\) | ||||
−0.982910 | + | 0.184086i | \(0.941068\pi\) | |||||||
\(32\) | −584457. | − | 870587.i | −0.557382 | − | 0.830256i | ||||
\(33\) | 345588. | 0.291409 | ||||||||
\(34\) | −754943. | + | 348433.i | −0.564935 | + | 0.260737i | ||||
\(35\) | 734257.i | 0.489301i | ||||||||
\(36\) | −2.65781e6 | + | 3.11740e6i | −1.58239 | + | 1.85602i | ||||
\(37\) | −584324. | −0.311779 | −0.155890 | − | 0.987774i | \(-0.549824\pi\) | ||||
−0.155890 | + | 0.987774i | \(0.549824\pi\) | |||||||
\(38\) | −399308. | − | 865173.i | −0.191502 | − | 0.414924i | ||||
\(39\) | − | 7.06866e6i | − | 3.05548i | ||||||
\(40\) | 309321. | − | 1.10229e6i | 0.120829 | − | 0.430582i | ||||
\(41\) | 293985. | 0.104037 | 0.0520187 | − | 0.998646i | \(-0.483434\pi\) | ||||
0.0520187 | + | 0.998646i | \(0.483434\pi\) | |||||||
\(42\) | 5.73247e6 | − | 2.64573e6i | 1.84223 | − | 0.850255i | ||||
\(43\) | − | 2.95292e6i | − | 0.863731i | −0.901938 | − | 0.431866i | \(-0.857856\pi\) | ||
0.901938 | − | 0.431866i | \(-0.142144\pi\) | |||||||
\(44\) | 448194. | + | 382118.i | 0.119579 | + | 0.101950i | ||||
\(45\) | −4.47279e6 | −1.09076 | ||||||||
\(46\) | 520102. | + | 1.12689e6i | 0.116160 | + | 0.251682i | ||||
\(47\) | 5.03746e6i | 1.03233i | 0.856488 | + | 0.516167i | \(0.172642\pi\) | ||||
−0.856488 | + | 0.516167i | \(0.827358\pi\) | |||||||
\(48\) | −9.72033e6 | + | 1.55693e6i | −1.83112 | + | 0.293295i | ||||
\(49\) | −1.13610e6 | −0.197075 | ||||||||
\(50\) | 1.13495e6 | − | 523820.i | 0.181592 | − | 0.0838111i | ||||
\(51\) | 7.80601e6i | 1.15385i | ||||||||
\(52\) | 7.81585e6 | − | 9.16736e6i | 1.06896 | − | 1.25381i | ||||
\(53\) | −7.54985e6 | −0.956830 | −0.478415 | − | 0.878134i | \(-0.658789\pi\) | ||||
−0.478415 | + | 0.878134i | \(0.658789\pi\) | |||||||
\(54\) | 9.50883e6 | + | 2.06026e7i | 1.11828 | + | 2.42297i | ||||
\(55\) | 643061.i | 0.0702751i | ||||||||
\(56\) | 1.03598e7 | + | 2.90715e6i | 1.05342 | + | 0.295608i | ||||
\(57\) | −8.94577e6 | −0.847458 | ||||||||
\(58\) | 1.31068e7 | − | 6.04923e6i | 1.15820 | − | 0.534550i | ||||
\(59\) | 8.82594e6i | 0.728372i | 0.931326 | + | 0.364186i | \(0.118653\pi\) | ||||
−0.931326 | + | 0.364186i | \(0.881347\pi\) | |||||||
\(60\) | −8.17910e6 | − | 6.97328e6i | −0.631103 | − | 0.538062i | ||||
\(61\) | 1.08173e7 | 0.781269 | 0.390634 | − | 0.920546i | \(-0.372256\pi\) | ||||
0.390634 | + | 0.920546i | \(0.372256\pi\) | |||||||
\(62\) | 2.27976e6 | + | 4.93951e6i | 0.154284 | + | 0.334285i | ||||
\(63\) | − | 4.20375e7i | − | 2.66854i | ||||||
\(64\) | −1.43278e7 | − | 8.72861e6i | −0.854004 | − | 0.520266i | ||||
\(65\) | 1.31532e7 | 0.736847 | ||||||||
\(66\) | 5.02049e6 | − | 2.31713e6i | 0.264588 | − | 0.122117i | ||||
\(67\) | 1.44347e7i | 0.716324i | 0.933659 | + | 0.358162i | \(0.116596\pi\) | ||||
−0.933659 | + | 0.358162i | \(0.883404\pi\) | |||||||
\(68\) | −8.63113e6 | + | 1.01236e7i | −0.403675 | + | 0.473479i | ||||
\(69\) | 1.16519e7 | 0.514046 | ||||||||
\(70\) | 4.92311e6 | + | 1.06668e7i | 0.205044 | + | 0.444266i | ||||
\(71\) | − | 3.71149e6i | − | 0.146054i | −0.997330 | − | 0.0730272i | \(-0.976734\pi\) | ||
0.997330 | − | 0.0730272i | \(-0.0232660\pi\) | |||||||
\(72\) | −1.77092e7 | + | 6.31079e7i | −0.658975 | + | 2.34830i | ||||
\(73\) | −3.62775e7 | −1.27746 | −0.638728 | − | 0.769433i | \(-0.720539\pi\) | ||||
−0.638728 | + | 0.769433i | \(0.720539\pi\) | |||||||
\(74\) | −8.48869e6 | + | 3.91783e6i | −0.283083 | + | 0.130653i | ||||
\(75\) | − | 1.17352e7i | − | 0.370891i | ||||||
\(76\) | −1.16018e7 | − | 9.89137e6i | −0.347752 | − | 0.296485i | ||||
\(77\) | −6.04380e6 | −0.171928 | ||||||||
\(78\) | −4.73946e7 | − | 1.02689e8i | −1.28041 | − | 2.77425i | ||||
\(79\) | 4.88562e7i | 1.25433i | 0.778887 | + | 0.627164i | \(0.215785\pi\) | ||||
−0.778887 | + | 0.627164i | \(0.784215\pi\) | |||||||
\(80\) | −2.89710e6 | − | 1.80873e7i | −0.0707300 | − | 0.441585i | ||||
\(81\) | 1.08037e8 | 2.50976 | ||||||||
\(82\) | 4.27083e6 | − | 1.97114e6i | 0.0944619 | − | 0.0435975i | ||||
\(83\) | 6.93862e7i | 1.46205i | 0.682353 | + | 0.731023i | \(0.260957\pi\) | ||||
−0.682353 | + | 0.731023i | \(0.739043\pi\) | |||||||
\(84\) | 6.55383e7 | − | 7.68711e7i | 1.31637 | − | 1.54400i | ||||
\(85\) | −1.45252e7 | −0.278257 | ||||||||
\(86\) | −1.97990e7 | − | 4.28982e7i | −0.361951 | − | 0.784234i | ||||
\(87\) | − | 1.35522e8i | − | 2.36555i | ||||||
\(88\) | 9.07314e6 | + | 2.54608e6i | 0.151296 | + | 0.0424562i | ||||
\(89\) | −1.05906e8 | −1.68796 | −0.843979 | − | 0.536377i | \(-0.819793\pi\) | ||||
−0.843979 | + | 0.536377i | \(0.819793\pi\) | |||||||
\(90\) | −6.49779e7 | + | 2.99896e7i | −0.990366 | + | 0.457089i | ||||
\(91\) | 1.23620e8i | 1.80270i | ||||||||
\(92\) | 1.51114e7 | + | 1.28836e7i | 0.210938 | + | 0.179840i | ||||
\(93\) | 5.10738e7 | 0.682758 | ||||||||
\(94\) | 3.37756e7 | + | 7.31810e7i | 0.432605 | + | 0.937319i | ||||
\(95\) | − | 1.66460e7i | − | 0.204370i | ||||||
\(96\) | −1.30772e8 | + | 8.77919e7i | −1.53967 | + | 1.03364i | ||||
\(97\) | 1.33519e8 | 1.50819 | 0.754093 | − | 0.656768i | \(-0.228077\pi\) | ||||
0.754093 | + | 0.656768i | \(0.228077\pi\) | |||||||
\(98\) | −1.65045e7 | + | 7.61742e6i | −0.178936 | + | 0.0825854i | ||||
\(99\) | − | 3.68163e7i | − | 0.383266i | ||||||
\(100\) | 1.29757e7 | − | 1.52194e7i | 0.129757 | − | 0.152194i | ||||
\(101\) | −6.08853e7 | −0.585096 | −0.292548 | − | 0.956251i | \(-0.594503\pi\) | ||||
−0.292548 | + | 0.956251i | \(0.594503\pi\) | |||||||
\(102\) | 5.23384e7 | + | 1.13401e8i | 0.483526 | + | 1.04765i | ||||
\(103\) | 2.63324e7i | 0.233960i | 0.993134 | + | 0.116980i | \(0.0373214\pi\) | ||||
−0.993134 | + | 0.116980i | \(0.962679\pi\) | |||||||
\(104\) | 5.20776e7 | − | 1.85582e8i | 0.445161 | − | 1.58636i | ||||
\(105\) | 1.10293e8 | 0.907387 | ||||||||
\(106\) | −1.09679e8 | + | 5.06209e7i | −0.868764 | + | 0.400965i | ||||
\(107\) | − | 1.26375e8i | − | 0.964108i | −0.876141 | − | 0.482054i | \(-0.839891\pi\) | ||
0.876141 | − | 0.482054i | \(-0.160109\pi\) | |||||||
\(108\) | 2.76277e8 | + | 2.35546e8i | 2.03072 | + | 1.73133i | ||||
\(109\) | 7.75869e7 | 0.549645 | 0.274822 | − | 0.961495i | \(-0.411381\pi\) | ||||
0.274822 | + | 0.961495i | \(0.411381\pi\) | |||||||
\(110\) | 4.31165e6 | + | 9.34198e6i | 0.0294492 | + | 0.0638070i | ||||
\(111\) | 8.77719e7i | 0.578181i | ||||||||
\(112\) | 1.69993e8 | − | 2.72283e7i | 1.08034 | − | 0.173041i | ||||
\(113\) | −9.07281e7 | −0.556453 | −0.278226 | − | 0.960516i | \(-0.589747\pi\) | ||||
−0.278226 | + | 0.960516i | \(0.589747\pi\) | |||||||
\(114\) | −1.29958e8 | + | 5.99804e7i | −0.769459 | + | 0.355132i | ||||
\(115\) | 2.16816e7i | 0.123965i | ||||||||
\(116\) | 1.49847e8 | − | 1.75759e8i | 0.827593 | − | 0.970700i | ||||
\(117\) | −7.53042e8 | −4.01861 | ||||||||
\(118\) | 5.91770e7 | + | 1.28218e8i | 0.305228 | + | 0.661333i | ||||
\(119\) | − | 1.36515e8i | − | 0.680757i | ||||||
\(120\) | −1.65576e8 | − | 4.64635e7i | −0.798495 | − | 0.224072i | ||||
\(121\) | 2.09066e8 | 0.975307 | ||||||||
\(122\) | 1.57147e8 | − | 7.25290e7i | 0.709361 | − | 0.327395i | ||||
\(123\) | − | 4.41598e7i | − | 0.192933i | ||||||
\(124\) | 6.62377e7 | + | 5.64725e7i | 0.280168 | + | 0.238864i | ||||
\(125\) | 2.18366e7 | 0.0894427 | ||||||||
\(126\) | −2.81857e8 | − | 6.10694e8i | −1.11827 | − | 2.42293i | ||||
\(127\) | 3.10844e8i | 1.19489i | 0.801910 | + | 0.597445i | \(0.203817\pi\) | ||||
−0.801910 | + | 0.597445i | \(0.796183\pi\) | |||||||
\(128\) | −2.66670e8 | − | 3.07374e7i | −0.993423 | − | 0.114506i | ||||
\(129\) | −4.43562e8 | −1.60175 | ||||||||
\(130\) | 1.91081e8 | − | 8.81906e7i | 0.669028 | − | 0.308780i | ||||
\(131\) | − | 5.44781e8i | − | 1.84985i | −0.380150 | − | 0.924925i | \(-0.624128\pi\) | ||
0.380150 | − | 0.924925i | \(-0.375872\pi\) | |||||||
\(132\) | 5.73983e7 | − | 6.73236e7i | 0.189062 | − | 0.221754i | ||||
\(133\) | 1.56448e8 | 0.499991 | ||||||||
\(134\) | 9.67833e7 | + | 2.09699e8i | 0.300180 | + | 0.650394i | ||||
\(135\) | 3.96397e8i | 1.19343i | ||||||||
\(136\) | −5.75099e7 | + | 2.04940e8i | −0.168107 | + | 0.599062i | ||||
\(137\) | −1.23319e8 | −0.350065 | −0.175033 | − | 0.984563i | \(-0.556003\pi\) | ||||
−0.175033 | + | 0.984563i | \(0.556003\pi\) | |||||||
\(138\) | 1.69272e8 | − | 7.81250e7i | 0.466733 | − | 0.215414i | ||||
\(139\) | − | 6.72621e8i | − | 1.80182i | −0.434008 | − | 0.900909i | \(-0.642901\pi\) | ||
0.434008 | − | 0.900909i | \(-0.357099\pi\) | |||||||
\(140\) | 1.43040e8 | + | 1.21952e8i | 0.372344 | + | 0.317451i | ||||
\(141\) | 7.56682e8 | 1.91442 | ||||||||
\(142\) | −2.48851e7 | − | 5.39181e7i | −0.0612049 | − | 0.132612i | ||||
\(143\) | 1.08266e8i | 0.258910i | ||||||||
\(144\) | 1.65864e8 | + | 1.03553e9i | 0.385746 | + | 2.40831i | ||||
\(145\) | 2.52176e8 | 0.570468 | ||||||||
\(146\) | −5.27017e8 | + | 2.43237e8i | −1.15988 | + | 0.535325i | ||||
\(147\) | 1.70655e8i | 0.365467i | ||||||||
\(148\) | −9.70497e7 | + | 1.13832e8i | −0.202277 | + | 0.237255i | ||||
\(149\) | 2.47048e8 | 0.501229 | 0.250615 | − | 0.968087i | \(-0.419367\pi\) | ||||
0.250615 | + | 0.968087i | \(0.419367\pi\) | |||||||
\(150\) | −7.86835e7 | − | 1.70482e8i | −0.155424 | − | 0.336755i | ||||
\(151\) | 4.00056e8i | 0.769508i | 0.923019 | + | 0.384754i | \(0.125714\pi\) | ||||
−0.923019 | + | 0.384754i | \(0.874286\pi\) | |||||||
\(152\) | −2.34864e8 | − | 6.59069e7i | −0.439989 | − | 0.123469i | ||||
\(153\) | 8.31593e8 | 1.51756 | ||||||||
\(154\) | −8.78005e7 | + | 4.05230e7i | −0.156104 | + | 0.0720475i | ||||
\(155\) | 9.50368e7i | 0.164651i | ||||||||
\(156\) | −1.37704e9 | − | 1.17403e9i | −2.32513 | − | 1.98235i | ||||
\(157\) | −7.00538e8 | −1.15301 | −0.576505 | − | 0.817094i | \(-0.695584\pi\) | ||||
−0.576505 | + | 0.817094i | \(0.695584\pi\) | |||||||
\(158\) | 3.27575e8 | + | 7.09752e8i | 0.525634 | + | 1.13888i | ||||
\(159\) | 1.13407e9i | 1.77440i | ||||||||
\(160\) | −1.63361e8 | − | 2.43336e8i | −0.249269 | − | 0.371302i | ||||
\(161\) | −2.03774e8 | −0.303281 | ||||||||
\(162\) | 1.56949e9 | − | 7.24376e8i | 2.27876 | − | 1.05173i | ||||
\(163\) | 2.24412e8i | 0.317903i | 0.987286 | + | 0.158952i | \(0.0508114\pi\) | ||||
−0.987286 | + | 0.158952i | \(0.949189\pi\) | |||||||
\(164\) | 4.88277e7 | − | 5.72709e7i | 0.0674979 | − | 0.0791696i | ||||
\(165\) | 9.65948e7 | 0.130322 | ||||||||
\(166\) | 4.65227e8 | + | 1.00800e9i | 0.612678 | + | 1.32748i | ||||
\(167\) | − | 1.11919e9i | − | 1.43893i | −0.694530 | − | 0.719464i | \(-0.744387\pi\) | ||
0.694530 | − | 0.719464i | \(-0.255613\pi\) | |||||||
\(168\) | 4.36686e8 | − | 1.55616e9i | 0.548192 | − | 1.95352i | ||||
\(169\) | 1.39875e9 | 1.71472 | ||||||||
\(170\) | −2.11013e8 | + | 9.73899e7i | −0.252647 | + | 0.116605i | ||||
\(171\) | 9.53015e8i | 1.11459i | ||||||||
\(172\) | −5.75256e8 | − | 4.90448e8i | −0.657275 | − | 0.560375i | ||||
\(173\) | −1.58033e9 | −1.76426 | −0.882130 | − | 0.471005i | \(-0.843891\pi\) | ||||
−0.882130 | + | 0.471005i | \(0.843891\pi\) | |||||||
\(174\) | −9.08661e8 | − | 1.96878e9i | −0.991299 | − | 2.14783i | ||||
\(175\) | 2.05231e8i | 0.218822i | ||||||||
\(176\) | 1.48880e8 | − | 2.38465e7i | 0.155162 | − | 0.0248528i | ||||
\(177\) | 1.32575e9 | 1.35073 | ||||||||
\(178\) | −1.53854e9 | + | 7.10090e8i | −1.53260 | + | 0.707348i | ||||
\(179\) | − | 4.43340e8i | − | 0.431841i | −0.976411 | − | 0.215921i | \(-0.930725\pi\) | ||
0.976411 | − | 0.215921i | \(-0.0692753\pi\) | |||||||
\(180\) | −7.42881e8 | + | 8.71339e8i | −0.707667 | + | 0.830037i | ||||
\(181\) | −1.87230e8 | −0.174446 | −0.0872232 | − | 0.996189i | \(-0.527799\pi\) | ||||
−0.0872232 | + | 0.996189i | \(0.527799\pi\) | |||||||
\(182\) | 8.28858e8 | + | 1.79587e9i | 0.755431 | + | 1.63678i | ||||
\(183\) | − | 1.62488e9i | − | 1.44883i | ||||||
\(184\) | 3.05912e8 | + | 8.58443e7i | 0.266886 | + | 0.0748928i | ||||
\(185\) | −1.63324e8 | −0.139432 | ||||||||
\(186\) | 7.41968e8 | − | 3.42444e8i | 0.619917 | − | 0.286114i | ||||
\(187\) | − | 1.19560e8i | − | 0.0977728i | ||||||
\(188\) | 9.81342e8 | + | 8.36666e8i | 0.785577 | + | 0.669762i | ||||
\(189\) | −3.72553e9 | −2.91972 | ||||||||
\(190\) | −1.11610e8 | − | 2.41823e8i | −0.0856423 | − | 0.185560i | ||||
\(191\) | 5.22344e8i | 0.392485i | 0.980555 | + | 0.196242i | \(0.0628740\pi\) | ||||
−0.980555 | + | 0.196242i | \(0.937126\pi\) | |||||||
\(192\) | −1.31113e9 | + | 2.15220e9i | −0.964811 | + | 1.58371i | ||||
\(193\) | 5.01793e7 | 0.0361655 | 0.0180828 | − | 0.999836i | \(-0.494244\pi\) | ||||
0.0180828 | + | 0.999836i | \(0.494244\pi\) | |||||||
\(194\) | 1.93967e9 | − | 8.95227e8i | 1.36937 | − | 0.632014i | ||||
\(195\) | − | 1.97575e9i | − | 1.36645i | ||||||
\(196\) | −1.88693e8 | + | 2.21322e8i | −0.127859 | + | 0.149969i | ||||
\(197\) | −2.63629e8 | −0.175036 | −0.0875181 | − | 0.996163i | \(-0.527894\pi\) | ||||
−0.0875181 | + | 0.996163i | \(0.527894\pi\) | |||||||
\(198\) | −2.46850e8 | − | 5.34845e8i | −0.160610 | − | 0.347990i | ||||
\(199\) | − | 1.26573e9i | − | 0.807105i | −0.914956 | − | 0.403553i | \(-0.867775\pi\) | ||
0.914956 | − | 0.403553i | \(-0.132225\pi\) | |||||||
\(200\) | 8.64580e7 | − | 3.08099e8i | 0.0540362 | − | 0.192562i | ||||
\(201\) | 2.16826e9 | 1.32839 | ||||||||
\(202\) | −8.84503e8 | + | 4.08229e8i | −0.531244 | + | 0.245188i | ||||
\(203\) | 2.37007e9i | 1.39565i | ||||||||
\(204\) | 1.52068e9 | + | 1.29649e9i | 0.878046 | + | 0.748598i | ||||
\(205\) | 8.21713e7 | 0.0465270 | ||||||||
\(206\) | 1.76556e8 | + | 3.82541e8i | 0.0980423 | + | 0.212427i | ||||
\(207\) | − | 1.24131e9i | − | 0.676081i | ||||||
\(208\) | −4.87757e8 | − | 3.04519e9i | −0.260586 | − | 1.62690i | ||||
\(209\) | 1.37017e8 | 0.0718105 | ||||||||
\(210\) | 1.60227e9 | − | 7.39505e8i | 0.823871 | − | 0.380246i | ||||
\(211\) | − | 9.34053e8i | − | 0.471240i | −0.971845 | − | 0.235620i | \(-0.924288\pi\) | ||
0.971845 | − | 0.235620i | \(-0.0757120\pi\) | |||||||
\(212\) | −1.25395e9 | + | 1.47078e9i | −0.620777 | + | 0.728121i | ||||
\(213\) | −5.57506e8 | −0.270852 | ||||||||
\(214\) | −8.47330e8 | − | 1.83590e9i | −0.404015 | − | 0.875372i | ||||
\(215\) | − | 8.25367e8i | − | 0.386272i | ||||||
\(216\) | 5.59288e9 | + | 1.56946e9i | 2.56934 | + | 0.721000i | ||||
\(217\) | −8.93202e8 | −0.402820 | ||||||||
\(218\) | 1.12713e9 | − | 5.20212e8i | 0.499056 | − | 0.230332i | ||||
\(219\) | 5.44928e9i | 2.36899i | ||||||||
\(220\) | 1.25274e8 | + | 1.06805e8i | 0.0534774 | + | 0.0455934i | ||||
\(221\) | −2.44547e9 | −1.02517 | ||||||||
\(222\) | 5.88501e8 | + | 1.27509e9i | 0.242290 | + | 0.524965i | ||||
\(223\) | 5.22225e8i | 0.211173i | 0.994410 | + | 0.105586i | \(0.0336720\pi\) | ||||
−0.994410 | + | 0.105586i | \(0.966328\pi\) | |||||||
\(224\) | 2.28699e9 | − | 1.53534e9i | 0.908391 | − | 0.609837i | ||||
\(225\) | −1.25018e9 | −0.487802 | ||||||||
\(226\) | −1.31804e9 | + | 6.08322e8i | −0.505237 | + | 0.233185i | ||||
\(227\) | 3.46698e9i | 1.30571i | 0.757482 | + | 0.652856i | \(0.226430\pi\) | ||||
−0.757482 | + | 0.652856i | \(0.773570\pi\) | |||||||
\(228\) | −1.48579e9 | + | 1.74271e9i | −0.549818 | + | 0.644892i | ||||
\(229\) | 1.31243e9 | 0.477239 | 0.238619 | − | 0.971113i | \(-0.423305\pi\) | ||||
0.238619 | + | 0.971113i | \(0.423305\pi\) | |||||||
\(230\) | 1.45373e8 | + | 3.14977e8i | 0.0519484 | + | 0.112556i | ||||
\(231\) | 9.07845e8i | 0.318833i | ||||||||
\(232\) | 9.98443e8 | − | 3.55802e9i | 0.344644 | − | 1.22816i | ||||
\(233\) | −2.43802e9 | −0.827207 | −0.413604 | − | 0.910457i | \(-0.635730\pi\) | ||||
−0.413604 | + | 0.910457i | \(0.635730\pi\) | |||||||
\(234\) | −1.09397e10 | + | 5.04906e9i | −3.64874 | + | 1.68402i | ||||
\(235\) | 1.40801e9i | 0.461674i | ||||||||
\(236\) | 1.71937e9 | + | 1.46589e9i | 0.554271 | + | 0.472556i | ||||
\(237\) | 7.33874e9 | 2.32610 | ||||||||
\(238\) | −9.15318e8 | − | 1.98320e9i | −0.285275 | − | 0.618101i | ||||
\(239\) | − | 2.78783e9i | − | 0.854427i | −0.904151 | − | 0.427214i | \(-0.859495\pi\) | ||
0.904151 | − | 0.427214i | \(-0.140505\pi\) | |||||||
\(240\) | −2.71691e9 | + | 4.35176e8i | −0.818900 | + | 0.131166i | ||||
\(241\) | 1.16299e9 | 0.344753 | 0.172376 | − | 0.985031i | \(-0.444856\pi\) | ||||
0.172376 | + | 0.985031i | \(0.444856\pi\) | |||||||
\(242\) | 3.03717e9 | − | 1.40176e9i | 0.885540 | − | 0.408708i | ||||
\(243\) | − | 6.92356e9i | − | 1.98566i | ||||||
\(244\) | 1.79664e9 | − | 2.10731e9i | 0.506875 | − | 0.594524i | ||||
\(245\) | −3.17549e8 | −0.0881347 | ||||||||
\(246\) | −2.96087e8 | − | 6.41526e8i | −0.0808497 | − | 0.175176i | ||||
\(247\) | − | 2.80254e9i | − | 0.752946i | ||||||
\(248\) | 1.34090e9 | + | 3.76281e8i | 0.354479 | + | 0.0994729i | ||||
\(249\) | 1.04226e10 | 2.71130 | ||||||||
\(250\) | 3.17228e8 | − | 1.46412e8i | 0.0812105 | − | 0.0374815i | ||||
\(251\) | − | 6.20014e9i | − | 1.56209i | −0.624474 | − | 0.781046i | \(-0.714687\pi\) | ||
0.624474 | − | 0.781046i | \(-0.285313\pi\) | |||||||
\(252\) | −8.18927e9 | − | 6.98195e9i | −2.03069 | − | 1.73131i | ||||
\(253\) | −1.78465e8 | −0.0435584 | ||||||||
\(254\) | 2.08418e9 | + | 4.51575e9i | 0.500725 | + | 1.08491i | ||||
\(255\) | 2.18185e9i | 0.516016i | ||||||||
\(256\) | −4.08010e9 | + | 1.34146e9i | −0.949973 | + | 0.312333i | ||||
\(257\) | −1.12108e9 | −0.256983 | −0.128491 | − | 0.991711i | \(-0.541013\pi\) | ||||
−0.128491 | + | 0.991711i | \(0.541013\pi\) | |||||||
\(258\) | −6.44378e9 | + | 2.97403e9i | −1.45433 | + | 0.671223i | ||||
\(259\) | − | 1.53499e9i | − | 0.341120i | ||||||
\(260\) | 2.18460e9 | − | 2.56235e9i | 0.478055 | − | 0.560720i | ||||
\(261\) | −1.44375e10 | −3.11121 | ||||||||
\(262\) | −3.65269e9 | − | 7.91423e9i | −0.775190 | − | 1.67959i | ||||
\(263\) | − | 1.51480e9i | − | 0.316616i | −0.987390 | − | 0.158308i | \(-0.949396\pi\) | ||
0.987390 | − | 0.158308i | \(-0.0506038\pi\) | |||||||
\(264\) | 3.82449e8 | − | 1.36288e9i | 0.0787332 | − | 0.280571i | ||||
\(265\) | −2.11025e9 | −0.427907 | ||||||||
\(266\) | 2.27277e9 | − | 1.04896e9i | 0.453972 | − | 0.209524i | ||||
\(267\) | 1.59083e10i | 3.13024i | ||||||||
\(268\) | 2.81201e9 | + | 2.39745e9i | 0.545102 | + | 0.464740i | ||||
\(269\) | −2.73389e9 | −0.522121 | −0.261060 | − | 0.965322i | \(-0.584072\pi\) | ||||
−0.261060 | + | 0.965322i | \(0.584072\pi\) | |||||||
\(270\) | 2.65780e9 | + | 5.75861e9i | 0.500112 | + | 1.08358i | ||||
\(271\) | 9.38092e9i | 1.73927i | 0.493691 | + | 0.869637i | \(0.335647\pi\) | ||||
−0.493691 | + | 0.869637i | \(0.664353\pi\) | |||||||
\(272\) | 5.38636e8 | + | 3.36284e9i | 0.0984056 | + | 0.614371i | ||||
\(273\) | 1.85691e10 | 3.34302 | ||||||||
\(274\) | −1.79151e9 | + | 8.26843e8i | −0.317845 | + | 0.146697i | ||||
\(275\) | 1.79741e8i | 0.0314280i | ||||||||
\(276\) | 1.93526e9 | − | 2.26990e9i | 0.333505 | − | 0.391174i | ||||
\(277\) | 1.88891e9 | 0.320842 | 0.160421 | − | 0.987049i | \(-0.448715\pi\) | ||||
0.160421 | + | 0.987049i | \(0.448715\pi\) | |||||||
\(278\) | −4.50985e9 | − | 9.77141e9i | −0.755062 | − | 1.63598i | ||||
\(279\) | − | 5.44102e9i | − | 0.897973i | ||||||
\(280\) | 2.89566e9 | + | 8.12574e8i | 0.471103 | + | 0.132200i | ||||
\(281\) | −1.65526e9 | −0.265485 | −0.132743 | − | 0.991151i | \(-0.542378\pi\) | ||||
−0.132743 | + | 0.991151i | \(0.542378\pi\) | |||||||
\(282\) | 1.09926e10 | − | 5.07347e9i | 1.73822 | − | 0.802248i | ||||
\(283\) | 8.61833e9i | 1.34362i | 0.740722 | + | 0.671811i | \(0.234483\pi\) | ||||
−0.740722 | + | 0.671811i | \(0.765517\pi\) | |||||||
\(284\) | −7.23031e8 | − | 6.16437e8i | −0.111143 | − | 0.0947578i | ||||
\(285\) | −2.50042e9 | −0.378995 | ||||||||
\(286\) | 7.25913e8 | + | 1.57282e9i | 0.108498 | + | 0.235080i | ||||
\(287\) | 7.72286e8i | 0.113828i | ||||||||
\(288\) | 9.35268e9 | + | 1.39314e10i | 1.35946 | + | 2.02500i | ||||
\(289\) | −4.27519e9 | −0.612864 | ||||||||
\(290\) | 3.66345e9 | − | 1.69081e9i | 0.517962 | − | 0.239058i | ||||
\(291\) | − | 2.00560e10i | − | 2.79686i | ||||||
\(292\) | −6.02529e9 | + | 7.06718e9i | −0.828794 | + | 0.972108i | ||||
\(293\) | −5.51315e9 | −0.748048 | −0.374024 | − | 0.927419i | \(-0.622022\pi\) | ||||
−0.374024 | + | 0.927419i | \(0.622022\pi\) | |||||||
\(294\) | 1.14422e9 | + | 2.47916e9i | 0.153151 | + | 0.331830i | ||||
\(295\) | 2.46693e9i | 0.325738i | ||||||||
\(296\) | −6.46649e8 | + | 2.30438e9i | −0.0842368 | + | 0.300184i | ||||
\(297\) | −3.26282e9 | −0.419341 | ||||||||
\(298\) | 3.58896e9 | − | 1.65643e9i | 0.455096 | − | 0.210043i | ||||
\(299\) | 3.65033e9i | 0.456717i | ||||||||
\(300\) | −2.28613e9 | − | 1.94909e9i | −0.282238 | − | 0.240629i | ||||
\(301\) | 7.75720e9 | 0.945016 | ||||||||
\(302\) | 2.68233e9 | + | 5.81177e9i | 0.322467 | + | 0.698683i | ||||
\(303\) | 9.14564e9i | 1.08504i | ||||||||
\(304\) | −3.85385e9 | + | 6.17283e8i | −0.451233 | + | 0.0722753i | ||||
\(305\) | 3.02353e9 | 0.349394 | ||||||||
\(306\) | 1.20809e10 | − | 5.57574e9i | 1.37788 | − | 0.635941i | ||||
\(307\) | − | 1.53502e10i | − | 1.72806i | −0.503437 | − | 0.864032i | \(-0.667931\pi\) | ||
0.503437 | − | 0.864032i | \(-0.332069\pi\) | |||||||
\(308\) | −1.00381e9 | + | 1.17739e9i | −0.111544 | + | 0.130833i | ||||
\(309\) | 3.95542e9 | 0.433869 | ||||||||
\(310\) | 6.37211e8 | + | 1.38063e9i | 0.0689980 | + | 0.149497i | ||||
\(311\) | − | 5.55831e9i | − | 0.594157i | −0.954853 | − | 0.297079i | \(-0.903988\pi\) | ||
0.954853 | − | 0.297079i | \(-0.0960123\pi\) | |||||||
\(312\) | −2.78765e10 | − | 7.82262e9i | −2.94184 | − | 0.825532i | ||||
\(313\) | −1.76829e10 | −1.84237 | −0.921183 | − | 0.389131i | \(-0.872775\pi\) | ||||
−0.921183 | + | 0.389131i | \(0.872775\pi\) | |||||||
\(314\) | −1.01770e10 | + | 4.69703e9i | −1.04689 | + | 0.483176i | ||||
\(315\) | − | 1.17498e10i | − | 1.19341i | ||||||
\(316\) | 9.51762e9 | + | 8.11447e9i | 0.954509 | + | 0.813789i | ||||
\(317\) | −2.84291e9 | −0.281531 | −0.140766 | − | 0.990043i | \(-0.544956\pi\) | ||||
−0.140766 | + | 0.990043i | \(0.544956\pi\) | |||||||
\(318\) | 7.60382e9 | + | 1.64751e10i | 0.743572 | + | 1.61109i | ||||
\(319\) | 2.07570e9i | 0.200448i | ||||||||
\(320\) | −4.00475e9 | − | 2.43972e9i | −0.381922 | − | 0.232670i | ||||
\(321\) | −1.89829e10 | −1.78790 | ||||||||
\(322\) | −2.96030e9 | + | 1.36628e9i | −0.275368 | + | 0.127092i | ||||
\(323\) | 3.09488e9i | 0.284337i | ||||||||
\(324\) | 1.79437e10 | − | 2.10465e10i | 1.62829 | − | 1.90986i | ||||
\(325\) | 3.67642e9 | 0.329528 | ||||||||
\(326\) | 1.50466e9 | + | 3.26011e9i | 0.133219 | + | 0.288643i | ||||
\(327\) | − | 1.16544e10i | − | 1.01929i | ||||||
\(328\) | 3.25342e8 | − | 1.15938e9i | 0.0281090 | − | 0.100168i | ||||
\(329\) | −1.32332e10 | −1.12949 | ||||||||
\(330\) | 1.40327e9 | − | 6.47658e8i | 0.118327 | − | 0.0546122i | ||||
\(331\) | − | 1.16323e10i | − | 0.969068i | −0.874773 | − | 0.484534i | \(-0.838989\pi\) | ||
0.874773 | − | 0.484534i | \(-0.161011\pi\) | |||||||
\(332\) | 1.35171e10 | + | 1.15243e10i | 1.11258 | + | 0.948553i | ||||
\(333\) | 9.35056e9 | 0.760432 | ||||||||
\(334\) | −7.50407e9 | − | 1.62589e10i | −0.602991 | − | 1.30649i | ||||
\(335\) | 4.03463e9i | 0.320350i | ||||||||
\(336\) | −4.09000e9 | − | 2.55349e10i | −0.320897 | − | 2.00344i | ||||
\(337\) | 2.09960e10 | 1.62786 | 0.813930 | − | 0.580963i | \(-0.197324\pi\) | ||||
0.813930 | + | 0.580963i | \(0.197324\pi\) | |||||||
\(338\) | 2.03201e10 | − | 9.37844e9i | 1.55689 | − | 0.718561i | ||||
\(339\) | 1.36284e10i | 1.03192i | ||||||||
\(340\) | −2.41248e9 | + | 2.82964e9i | −0.180529 | + | 0.211746i | ||||
\(341\) | −7.82265e8 | −0.0578544 | ||||||||
\(342\) | 6.38986e9 | + | 1.38448e10i | 0.467075 | + | 1.01200i | ||||
\(343\) | 1.21594e10i | 0.878488i | ||||||||
\(344\) | −1.16454e10 | − | 3.26789e9i | −0.831608 | − | 0.233364i | ||||
\(345\) | 3.25682e9 | 0.229888 | ||||||||
\(346\) | −2.29580e10 | + | 1.05959e10i | −1.60188 | + | 0.739324i | ||||
\(347\) | 7.43114e9i | 0.512552i | 0.966604 | + | 0.256276i | \(0.0824955\pi\) | ||||
−0.966604 | + | 0.256276i | \(0.917504\pi\) | |||||||
\(348\) | −2.64009e10 | − | 2.25087e10i | −1.80012 | − | 1.53474i | ||||
\(349\) | 5.43305e9 | 0.366220 | 0.183110 | − | 0.983092i | \(-0.441384\pi\) | ||||
0.183110 | + | 0.983092i | \(0.441384\pi\) | |||||||
\(350\) | 1.37605e9 | + | 2.98147e9i | 0.0916985 | + | 0.198682i | ||||
\(351\) | 6.67377e10i | 4.39686i | ||||||||
\(352\) | 2.00295e9 | − | 1.34465e9i | 0.130466 | − | 0.0875869i | ||||
\(353\) | 7.17687e9 | 0.462207 | 0.231103 | − | 0.972929i | \(-0.425766\pi\) | ||||
0.231103 | + | 0.972929i | \(0.425766\pi\) | |||||||
\(354\) | 1.92597e10 | − | 8.88904e9i | 1.22641 | − | 0.566033i | ||||
\(355\) | − | 1.03739e9i | − | 0.0653175i | ||||||
\(356\) | −1.75898e10 | + | 2.06315e10i | −1.09512 | + | 1.28449i | ||||
\(357\) | −2.05060e10 | −1.26244 | ||||||||
\(358\) | −2.97254e9 | − | 6.44056e9i | −0.180966 | − | 0.392095i | ||||
\(359\) | − | 1.10278e10i | − | 0.663913i | −0.943295 | − | 0.331957i | \(-0.892291\pi\) | ||
0.943295 | − | 0.331957i | \(-0.107709\pi\) | |||||||
\(360\) | −4.94987e9 | + | 1.76392e10i | −0.294702 | + | 1.05019i | ||||
\(361\) | 1.34368e10 | 0.791165 | ||||||||
\(362\) | −2.71996e9 | + | 1.25536e9i | −0.158390 | + | 0.0731027i | ||||
\(363\) | − | 3.14040e10i | − | 1.80866i | ||||||
\(364\) | 2.40823e10 | + | 2.05319e10i | 1.37180 | + | 1.16956i | ||||
\(365\) | −1.01399e10 | −0.571296 | ||||||||
\(366\) | −1.08947e10 | − | 2.36052e10i | −0.607140 | − | 1.31548i | ||||
\(367\) | − | 3.39042e10i | − | 1.86891i | −0.356076 | − | 0.934457i | \(-0.615886\pi\) | ||
0.356076 | − | 0.934457i | \(-0.384114\pi\) | |||||||
\(368\) | 5.01968e9 | − | 8.04016e8i | 0.273706 | − | 0.0438403i | ||||
\(369\) | −4.70445e9 | −0.253748 | ||||||||
\(370\) | −2.37266e9 | + | 1.09507e9i | −0.126599 | + | 0.0584297i | ||||
\(371\) | − | 1.98331e10i | − | 1.04688i | ||||||
\(372\) | 8.48279e9 | − | 9.94963e9i | 0.442963 | − | 0.519560i | ||||
\(373\) | 3.19254e10 | 1.64930 | 0.824651 | − | 0.565641i | \(-0.191371\pi\) | ||||
0.824651 | + | 0.565641i | \(0.191371\pi\) | |||||||
\(374\) | −8.01634e8 | − | 1.73689e9i | −0.0409722 | − | 0.0887738i | ||||
\(375\) | − | 3.28010e9i | − | 0.165868i | ||||||
\(376\) | 1.98661e10 | + | 5.57477e9i | 0.993941 | + | 0.278917i | ||||
\(377\) | 4.24565e10 | 2.10174 | ||||||||
\(378\) | −5.41222e10 | + | 2.49793e10i | −2.65099 | + | 1.22353i | ||||
\(379\) | 2.66340e10i | 1.29086i | 0.763819 | + | 0.645430i | \(0.223322\pi\) | ||||
−0.763819 | + | 0.645430i | \(0.776678\pi\) | |||||||
\(380\) | −3.24280e9 | − | 2.76472e9i | −0.155520 | − | 0.132592i | ||||
\(381\) | 4.66922e10 | 2.21587 | ||||||||
\(382\) | 3.50226e9 | + | 7.58828e9i | 0.164473 | + | 0.356361i | ||||
\(383\) | − | 1.61064e10i | − | 0.748518i | −0.927324 | − | 0.374259i | \(-0.877897\pi\) | ||
0.927324 | − | 0.374259i | \(-0.122103\pi\) | |||||||
\(384\) | −4.61709e9 | + | 4.00567e10i | −0.212346 | + | 1.84226i | ||||
\(385\) | −1.68929e9 | −0.0768886 | ||||||||
\(386\) | 7.28973e8 | − | 3.36446e8i | 0.0328369 | − | 0.0151554i | ||||
\(387\) | 4.72537e10i | 2.10665i | ||||||||
\(388\) | 2.21759e10 | − | 2.60106e10i | 0.978487 | − | 1.14769i | ||||
\(389\) | 1.81674e10 | 0.793405 | 0.396702 | − | 0.917947i | \(-0.370154\pi\) | ||||
0.396702 | + | 0.917947i | \(0.370154\pi\) | |||||||
\(390\) | −1.32472e10 | − | 2.87025e10i | −0.572619 | − | 1.24068i | ||||
\(391\) | − | 4.03110e9i | − | 0.172471i | ||||||
\(392\) | −1.25728e9 | + | 4.48040e9i | −0.0532460 | + | 0.189746i | ||||
\(393\) | −8.18320e10 | −3.43047 | ||||||||
\(394\) | −3.82983e9 | + | 1.76760e9i | −0.158926 | + | 0.0733499i | ||||
\(395\) | 1.36557e10i | 0.560953i | ||||||||
\(396\) | −7.17215e9 | − | 6.11479e9i | −0.291654 | − | 0.248657i | ||||
\(397\) | −4.03325e10 | −1.62365 | −0.811827 | − | 0.583898i | \(-0.801527\pi\) | ||||
−0.811827 | + | 0.583898i | \(0.801527\pi\) | |||||||
\(398\) | −8.48661e9 | − | 1.83878e10i | −0.338222 | − | 0.732820i | ||||
\(399\) | − | 2.35001e10i | − | 0.927212i | ||||||
\(400\) | −8.09764e8 | − | 5.05556e9i | −0.0316314 | − | 0.197483i | ||||
\(401\) | 1.86384e10 | 0.720826 | 0.360413 | − | 0.932793i | \(-0.382636\pi\) | ||||
0.360413 | + | 0.932793i | \(0.382636\pi\) | |||||||
\(402\) | 3.14990e10 | − | 1.45379e10i | 1.20613 | − | 0.556670i | ||||
\(403\) | 1.60005e10i | 0.606614i | ||||||||
\(404\) | −1.01124e10 | + | 1.18610e10i | −0.379601 | + | 0.445242i | ||||
\(405\) | 3.01972e10 | 1.12240 | ||||||||
\(406\) | 1.58911e10 | + | 3.44309e10i | 0.584856 | + | 1.26720i | ||||
\(407\) | − | 1.34435e9i | − | 0.0489929i | ||||||
\(408\) | 3.07843e10 | + | 8.63861e9i | 1.11094 | + | 0.311748i | ||||
\(409\) | −1.95383e10 | −0.698222 | −0.349111 | − | 0.937081i | \(-0.613516\pi\) | ||||
−0.349111 | + | 0.937081i | \(0.613516\pi\) | |||||||
\(410\) | 1.19373e9 | − | 5.50950e8i | 0.0422447 | − | 0.0194974i | ||||
\(411\) | 1.85239e10i | 0.649181i | ||||||||
\(412\) | 5.12979e9 | + | 4.37352e9i | 0.178037 | + | 0.151790i | ||||
\(413\) | −2.31854e10 | −0.796918 | ||||||||
\(414\) | −8.32284e9 | − | 1.80330e10i | −0.283316 | − | 0.613855i | ||||
\(415\) | 1.93940e10i | 0.653847i | ||||||||
\(416\) | −2.75035e10 | − | 4.09683e10i | −0.918364 | − | 1.36796i | ||||
\(417\) | −1.01035e11 | −3.34139 | ||||||||
\(418\) | 1.99049e9 | − | 9.18681e8i | 0.0652011 | − | 0.0300926i | ||||
\(419\) | − | 1.60399e10i | − | 0.520410i | −0.965553 | − | 0.260205i | \(-0.916210\pi\) | ||
0.965553 | − | 0.260205i | \(-0.0837901\pi\) | |||||||
\(420\) | 1.83185e10 | − | 2.14861e10i | 0.588699 | − | 0.690496i | ||||
\(421\) | 8.80074e9 | 0.280150 | 0.140075 | − | 0.990141i | \(-0.455266\pi\) | ||||
0.140075 | + | 0.990141i | \(0.455266\pi\) | |||||||
\(422\) | −6.26273e9 | − | 1.35693e10i | −0.197476 | − | 0.427867i | ||||
\(423\) | − | 8.06112e10i | − | 2.51787i | ||||||
\(424\) | −8.35513e9 | + | 2.97741e10i | −0.258517 | + | 0.921245i | ||||
\(425\) | −4.05992e9 | −0.124440 | ||||||||
\(426\) | −8.09910e9 | + | 3.73802e9i | −0.245922 | + | 0.113502i | ||||
\(427\) | 2.84166e10i | 0.854794i | ||||||||
\(428\) | −2.46190e10 | − | 2.09895e10i | −0.733659 | − | 0.625499i | ||||
\(429\) | 1.62628e10 | 0.480137 | ||||||||
\(430\) | −5.53400e9 | − | 1.19904e10i | −0.161870 | − | 0.350720i | ||||
\(431\) | − | 2.17255e10i | − | 0.629593i | −0.949159 | − | 0.314797i | \(-0.898064\pi\) | ||
0.949159 | − | 0.314797i | \(-0.101936\pi\) | |||||||
\(432\) | 9.17730e10 | − | 1.46995e10i | 2.63499 | − | 0.422055i | ||||
\(433\) | 2.50658e10 | 0.713066 | 0.356533 | − | 0.934283i | \(-0.383959\pi\) | ||||
0.356533 | + | 0.934283i | \(0.383959\pi\) | |||||||
\(434\) | −1.29759e10 | + | 5.98882e9i | −0.365744 | + | 0.168804i | ||||
\(435\) | − | 3.78796e10i | − | 1.05791i | ||||||
\(436\) | 1.28863e10 | − | 1.51146e10i | 0.356601 | − | 0.418264i | ||||
\(437\) | 4.61969e9 | 0.126674 | ||||||||
\(438\) | 3.65368e10 | + | 7.91637e10i | 0.992738 | + | 2.15095i | ||||
\(439\) | − | 2.69059e10i | − | 0.724419i | −0.932097 | − | 0.362210i | \(-0.882022\pi\) | ||
0.932097 | − | 0.362210i | \(-0.117978\pi\) | |||||||
\(440\) | 2.53602e9 | + | 7.11651e8i | 0.0676615 | + | 0.0189870i | ||||
\(441\) | 1.81802e10 | 0.480668 | ||||||||
\(442\) | −3.55263e10 | + | 1.63966e10i | −0.930809 | + | 0.429601i | ||||
\(443\) | 5.16514e10i | 1.34112i | 0.741856 | + | 0.670560i | \(0.233946\pi\) | ||||
−0.741856 | + | 0.670560i | \(0.766054\pi\) | |||||||
\(444\) | 1.70987e10 | + | 1.45779e10i | 0.439979 | + | 0.375115i | ||||
\(445\) | −2.96017e10 | −0.754878 | ||||||||
\(446\) | 3.50146e9 | + | 7.58655e9i | 0.0884932 | + | 0.191737i | ||||
\(447\) | − | 3.71093e10i | − | 0.929508i | ||||||
\(448\) | 2.29297e10 | − | 3.76385e10i | 0.569228 | − | 0.934374i | ||||
\(449\) | −4.61561e10 | −1.13565 | −0.567825 | − | 0.823150i | \(-0.692215\pi\) | ||||
−0.567825 | + | 0.823150i | \(0.692215\pi\) | |||||||
\(450\) | −1.81619e10 | + | 8.38234e9i | −0.442905 | + | 0.204416i | ||||
\(451\) | 6.76367e8i | 0.0163484i | ||||||||
\(452\) | −1.50689e10 | + | 1.76746e10i | −0.361018 | + | 0.423445i | ||||
\(453\) | 6.00929e10 | 1.42702 | ||||||||
\(454\) | 2.32457e10 | + | 5.03661e10i | 0.547166 | + | 1.18554i | ||||
\(455\) | 3.45528e10i | 0.806191i | ||||||||
\(456\) | −9.89994e9 | + | 3.52791e10i | −0.228967 | + | 0.815941i | ||||
\(457\) | −3.11288e10 | −0.713669 | −0.356835 | − | 0.934168i | \(-0.616144\pi\) | ||||
−0.356835 | + | 0.934168i | \(0.616144\pi\) | |||||||
\(458\) | 1.90662e10 | − | 8.79973e9i | 0.433314 | − | 0.199990i | ||||
\(459\) | − | 7.36992e10i | − | 1.66040i | ||||||
\(460\) | 4.22377e9 | + | 3.60107e9i | 0.0943341 | + | 0.0804268i | ||||
\(461\) | 4.68016e10 | 1.03623 | 0.518116 | − | 0.855310i | \(-0.326634\pi\) | ||||
0.518116 | + | 0.855310i | \(0.326634\pi\) | |||||||
\(462\) | 6.08700e9 | + | 1.31886e10i | 0.133609 | + | 0.289488i | ||||
\(463\) | 2.03332e10i | 0.442468i | 0.975221 | + | 0.221234i | \(0.0710085\pi\) | ||||
−0.975221 | + | 0.221234i | \(0.928992\pi\) | |||||||
\(464\) | −9.35140e9 | − | 5.83831e10i | −0.201746 | − | 1.25955i | ||||
\(465\) | 1.42756e10 | 0.305339 | ||||||||
\(466\) | −3.54181e10 | + | 1.63467e10i | −0.751072 | + | 0.346646i | ||||
\(467\) | 5.89675e10i | 1.23978i | 0.784688 | + | 0.619891i | \(0.212823\pi\) | ||||
−0.784688 | + | 0.619891i | \(0.787177\pi\) | |||||||
\(468\) | −1.25072e11 | + | 1.46699e11i | −2.60721 | + | 3.05805i | ||||
\(469\) | −3.79194e10 | −0.783737 | ||||||||
\(470\) | 9.44057e9 | + | 2.04547e10i | 0.193467 | + | 0.419182i | ||||
\(471\) | 1.05229e11i | 2.13821i | ||||||||
\(472\) | 3.48066e10 | + | 9.76734e9i | 0.701283 | + | 0.196792i | ||||
\(473\) | 6.79375e9 | 0.135727 | ||||||||
\(474\) | 1.06613e11 | − | 4.92054e10i | 2.11201 | − | 0.974765i | ||||
\(475\) | − | 4.65271e9i | − | 0.0913969i | ||||||
\(476\) | −2.65943e10 | − | 2.26736e10i | −0.518037 | − | 0.441665i | ||||
\(477\) | 1.20815e11 | 2.33372 | ||||||||
\(478\) | −1.86921e10 | − | 4.04999e10i | −0.358053 | − | 0.775786i | ||||
\(479\) | 1.20229e10i | 0.228384i | 0.993459 | + | 0.114192i | \(0.0364279\pi\) | ||||
−0.993459 | + | 0.114192i | \(0.963572\pi\) | |||||||
\(480\) | −3.65518e10 | + | 2.45386e10i | −0.688563 | + | 0.462258i | ||||
\(481\) | −2.74973e10 | −0.513699 | ||||||||
\(482\) | 1.68952e10 | − | 7.79772e9i | 0.313022 | − | 0.144471i | ||||
\(483\) | 3.06091e10i | 0.562422i | ||||||||
\(484\) | 3.47235e10 | − | 4.07279e10i | 0.632764 | − | 0.742181i | ||||
\(485\) | 3.73196e10 | 0.674481 | ||||||||
\(486\) | −4.64217e10 | − | 1.00581e11i | −0.832102 | − | 1.80290i | ||||
\(487\) | − | 4.85939e10i | − | 0.863905i | −0.901896 | − | 0.431953i | \(-0.857825\pi\) | ||
0.901896 | − | 0.431953i | \(-0.142175\pi\) | |||||||
\(488\) | 1.19711e10 | − | 4.26599e10i | 0.211084 | − | 0.752213i | ||||
\(489\) | 3.37091e10 | 0.589538 | ||||||||
\(490\) | −4.61315e9 | + | 2.12913e9i | −0.0800228 | + | 0.0369333i | ||||
\(491\) | − | 1.71586e9i | − | 0.0295226i | −0.999891 | − | 0.0147613i | \(-0.995301\pi\) | ||
0.999891 | − | 0.0147613i | \(-0.00469884\pi\) | |||||||
\(492\) | −8.60272e9 | − | 7.33445e9i | −0.146817 | − | 0.125172i | ||||
\(493\) | −4.68852e10 | −0.793685 | ||||||||
\(494\) | −1.87907e10 | − | 4.07135e10i | −0.315526 | − | 0.683645i | ||||
\(495\) | − | 1.02905e10i | − | 0.171402i | ||||||
\(496\) | 2.20027e10 | − | 3.52424e9i | 0.363537 | − | 0.0582289i | ||||
\(497\) | 9.74991e9 | 0.159799 | ||||||||
\(498\) | 1.51413e11 | − | 6.98822e10i | 2.46175 | − | 1.13619i | ||||
\(499\) | 6.25565e10i | 1.00895i | 0.863426 | + | 0.504476i | \(0.168314\pi\) | ||||
−0.863426 | + | 0.504476i | \(0.831686\pi\) | |||||||
\(500\) | 3.62682e9 | − | 4.25396e9i | 0.0580291 | − | 0.0680634i | ||||
\(501\) | −1.68115e11 | −2.66843 | ||||||||
\(502\) | −4.15712e10 | − | 9.00717e10i | −0.654603 | − | 1.41832i | ||||
\(503\) | 8.60985e10i | 1.34500i | 0.740095 | + | 0.672502i | \(0.234780\pi\) | ||||
−0.740095 | + | 0.672502i | \(0.765220\pi\) | |||||||
\(504\) | −1.65782e11 | − | 4.65213e10i | −2.56930 | − | 0.720990i | ||||
\(505\) | −1.70180e10 | −0.261663 | ||||||||
\(506\) | −2.59263e9 | + | 1.19659e9i | −0.0395493 | + | 0.0182534i | ||||
\(507\) | − | 2.10107e11i | − | 3.17987i | ||||||
\(508\) | 6.05552e10 | + | 5.16277e10i | 0.909278 | + | 0.775226i | ||||
\(509\) | 5.17187e10 | 0.770506 | 0.385253 | − | 0.922811i | \(-0.374114\pi\) | ||||
0.385253 | + | 0.922811i | \(0.374114\pi\) | |||||||
\(510\) | 1.46290e10 | + | 3.16965e10i | 0.216240 | + | 0.468522i | ||||
\(511\) | − | 9.52994e10i | − | 1.39768i | ||||||
\(512\) | −5.02788e10 | + | 4.68445e10i | −0.731653 | + | 0.681677i | ||||
\(513\) | 8.44601e10 | 1.21950 | ||||||||
\(514\) | −1.62863e10 | + | 7.51672e9i | −0.233330 | + | 0.107690i | ||||
\(515\) | 7.36013e9i | 0.104630i | ||||||||
\(516\) | −7.36707e10 | + | 8.64098e10i | −1.03919 | + | 1.21889i | ||||
\(517\) | −1.15896e10 | −0.162221 | ||||||||
\(518\) | −1.02920e10 | − | 2.22994e10i | −0.142948 | − | 0.309724i | ||||
\(519\) | 2.37383e11i | 3.27175i | ||||||||
\(520\) | 1.45561e10 | − | 5.18717e10i | 0.199082 | − | 0.709443i | ||||
\(521\) | 6.36828e10 | 0.864313 | 0.432157 | − | 0.901799i | \(-0.357753\pi\) | ||||
0.432157 | + | 0.901799i | \(0.357753\pi\) | |||||||
\(522\) | −2.09739e11 | + | 9.68018e10i | −2.82486 | + | 1.30377i | ||||
\(523\) | − | 3.05582e10i | − | 0.408434i | −0.978926 | − | 0.204217i | \(-0.934535\pi\) | ||
0.978926 | − | 0.204217i | \(-0.0654648\pi\) | |||||||
\(524\) | −1.06128e11 | − | 9.04820e10i | −1.40768 | − | 1.20015i | ||||
\(525\) | 3.08279e10 | 0.405796 | ||||||||
\(526\) | −1.01566e10 | − | 2.20061e10i | −0.132680 | − | 0.287474i | ||||
\(527\) | − | 1.76695e10i | − | 0.229077i | ||||||
\(528\) | −3.58201e9 | − | 2.23634e10i | −0.0460884 | − | 0.287741i | ||||
\(529\) | 7.22938e10 | 0.923163 | ||||||||
\(530\) | −3.06563e10 | + | 1.41490e10i | −0.388523 | + | 0.179317i | ||||
\(531\) | − | 1.41236e11i | − | 1.77651i | ||||||
\(532\) | 2.59842e10 | − | 3.04774e10i | 0.324387 | − | 0.380479i | ||||
\(533\) | 1.38344e10 | 0.171416 | ||||||||
\(534\) | 1.06663e11 | + | 2.31105e11i | 1.31175 | + | 2.84214i | ||||
\(535\) | − | 3.53229e10i | − | 0.431162i | ||||||
\(536\) | 5.69258e10 | + | 1.59744e10i | 0.689683 | + | 0.193537i | ||||
\(537\) | −6.65945e10 | −0.800831 | ||||||||
\(538\) | −3.97162e10 | + | 1.83304e10i | −0.474065 | + | 0.218798i | ||||
\(539\) | − | 2.61380e9i | − | 0.0309683i | ||||||
\(540\) | 7.72217e10 | + | 6.58372e10i | 0.908164 | + | 0.774276i | ||||
\(541\) | 2.53545e10 | 0.295982 | 0.147991 | − | 0.988989i | \(-0.452719\pi\) | ||||
0.147991 | + | 0.988989i | \(0.452719\pi\) | |||||||
\(542\) | 6.28980e10 | + | 1.36280e11i | 0.728853 | + | 1.57919i | ||||
\(543\) | 2.81240e10i | 0.323503i | ||||||||
\(544\) | 3.03725e10 | + | 4.52418e10i | 0.346804 | + | 0.516587i | ||||
\(545\) | 2.16862e10 | 0.245809 | ||||||||
\(546\) | 2.69760e11 | − | 1.24504e11i | 3.03533 | − | 1.40091i | ||||
\(547\) | 5.79915e10i | 0.647762i | 0.946098 | + | 0.323881i | \(0.104988\pi\) | ||||
−0.946098 | + | 0.323881i | \(0.895012\pi\) | |||||||
\(548\) | −2.04820e10 | + | 2.40237e10i | −0.227117 | + | 0.266390i | ||||
\(549\) | −1.73103e11 | −1.90552 | ||||||||
\(550\) | 1.20514e9 | + | 2.61116e9i | 0.0131701 | + | 0.0285354i | ||||
\(551\) | − | 5.37309e10i | − | 0.582932i | ||||||
\(552\) | 1.28948e10 | − | 4.59514e10i | 0.138885 | − | 0.494928i | ||||
\(553\) | −1.28343e11 | −1.37237 | ||||||||
\(554\) | 2.74408e10 | − | 1.26649e10i | 0.291312 | − | 0.134451i | ||||
\(555\) | 2.45330e10i | 0.258570i | ||||||||
\(556\) | −1.31032e11 | − | 1.11715e11i | −1.37113 | − | 1.16899i | ||||
\(557\) | 1.71554e11 | 1.78230 | 0.891149 | − | 0.453710i | \(-0.149900\pi\) | ||||
0.891149 | + | 0.453710i | \(0.149900\pi\) | |||||||
\(558\) | −3.64814e10 | − | 7.90437e10i | −0.376301 | − | 0.815324i | ||||
\(559\) | − | 1.38959e11i | − | 1.42312i | ||||||
\(560\) | 4.75146e10 | − | 7.61055e9i | 0.483142 | − | 0.0773863i | ||||
\(561\) | −1.79592e10 | −0.181315 | ||||||||
\(562\) | −2.40465e10 | + | 1.10983e10i | −0.241050 | + | 0.111253i | ||||
\(563\) | 5.49966e8i | 0.00547397i | 0.999996 | + | 0.00273698i | \(0.000871210\pi\) | ||||
−0.999996 | + | 0.00273698i | \(0.999129\pi\) | |||||||
\(564\) | 1.25676e11 | − | 1.47408e11i | 1.24205 | − | 1.45682i | ||||
\(565\) | −2.53593e10 | −0.248853 | ||||||||
\(566\) | 5.77850e10 | + | 1.25202e11i | 0.563053 | + | 1.21996i | ||||
\(567\) | 2.83808e11i | 2.74595i | ||||||||
\(568\) | −1.46369e10 | − | 4.10736e9i | −0.140623 | − | 0.0394611i | ||||
\(569\) | −1.48683e10 | −0.141845 | −0.0709223 | − | 0.997482i | \(-0.522594\pi\) | ||||
−0.0709223 | + | 0.997482i | \(0.522594\pi\) | |||||||
\(570\) | −3.63245e10 | + | 1.67650e10i | −0.344112 | + | 0.158820i | ||||
\(571\) | 3.55169e10i | 0.334111i | 0.985947 | + | 0.167056i | \(0.0534259\pi\) | ||||
−0.985947 | + | 0.167056i | \(0.946574\pi\) | |||||||
\(572\) | 2.10912e10 | + | 1.79818e10i | 0.197023 | + | 0.167977i | ||||
\(573\) | 7.84618e10 | 0.727846 | ||||||||
\(574\) | 5.17809e9 | + | 1.12193e10i | 0.0477004 | + | 0.103352i | ||||
\(575\) | 6.06019e9i | 0.0554390i | ||||||||
\(576\) | 2.29279e11 | + | 1.39678e11i | 2.08292 | + | 1.26893i | ||||
\(577\) | 4.14670e10 | 0.374110 | 0.187055 | − | 0.982349i | \(-0.440106\pi\) | ||||
0.187055 | + | 0.982349i | \(0.440106\pi\) | |||||||
\(578\) | −6.21073e10 | + | 2.86647e10i | −0.556457 | + | 0.256824i | ||||
\(579\) | − | 7.53748e9i | − | 0.0670674i | ||||||
\(580\) | 4.18836e10 | − | 4.91261e10i | 0.370111 | − | 0.434110i | ||||
\(581\) | −1.82275e11 | −1.59964 | ||||||||
\(582\) | −1.34473e11 | − | 2.91360e11i | −1.17204 | − | 2.53944i | ||||
\(583\) | − | 1.73698e10i | − | 0.150356i | ||||||
\(584\) | −4.01469e10 | + | 1.43066e11i | −0.345145 | + | 1.22995i | ||||
\(585\) | −2.10482e11 | −1.79718 | ||||||||
\(586\) | −8.00916e10 | + | 3.69651e10i | −0.679198 | + | 0.313474i | ||||
\(587\) | 2.88322e10i | 0.242843i | 0.992601 | + | 0.121421i | \(0.0387453\pi\) | ||||
−0.992601 | + | 0.121421i | \(0.961255\pi\) | |||||||
\(588\) | 3.32450e10 | + | 2.83438e10i | 0.278110 | + | 0.237110i | ||||
\(589\) | 2.02494e10 | 0.168249 | ||||||||
\(590\) | 1.65405e10 | + | 3.58379e10i | 0.136502 | + | 0.295757i | ||||
\(591\) | 3.95999e10i | 0.324597i | ||||||||
\(592\) | 6.05651e9 | + | 3.78123e10i | 0.0493100 | + | 0.307855i | ||||
\(593\) | −4.33851e10 | −0.350850 | −0.175425 | − | 0.984493i | \(-0.556130\pi\) | ||||
−0.175425 | + | 0.984493i | \(0.556130\pi\) | |||||||
\(594\) | −4.74001e10 | + | 2.18768e10i | −0.380745 | + | 0.175727i | ||||
\(595\) | − | 3.81571e10i | − | 0.304444i | ||||||
\(596\) | 4.10319e10 | − | 4.81272e10i | 0.325190 | − | 0.381422i | ||||
\(597\) | −1.90127e11 | −1.49674 | ||||||||
\(598\) | 2.44751e10 | + | 5.30297e10i | 0.191390 | + | 0.414681i | ||||
\(599\) | − | 1.41612e11i | − | 1.10000i | −0.835164 | − | 0.550000i | \(-0.814628\pi\) | ||
0.835164 | − | 0.550000i | \(-0.185372\pi\) | |||||||
\(600\) | −4.62799e10 | − | 1.29869e10i | −0.357098 | − | 0.100208i | ||||
\(601\) | −1.16789e11 | −0.895170 | −0.447585 | − | 0.894241i | \(-0.647716\pi\) | ||||
−0.447585 | + | 0.894241i | \(0.647716\pi\) | |||||||
\(602\) | 1.12692e11 | − | 5.20112e10i | 0.858037 | − | 0.396014i | ||||
\(603\) | − | 2.30989e11i | − | 1.74712i | ||||||
\(604\) | 7.79345e10 | + | 6.64449e10i | 0.585574 | + | 0.499245i | ||||
\(605\) | 5.84356e10 | 0.436171 | ||||||||
\(606\) | 6.13205e10 | + | 1.32862e11i | 0.454690 | + | 0.985169i | ||||
\(607\) | 4.19809e10i | 0.309241i | 0.987974 | + | 0.154620i | \(0.0494155\pi\) | ||||
−0.987974 | + | 0.154620i | \(0.950585\pi\) | |||||||
\(608\) | −5.18475e10 | + | 3.48072e10i | −0.379414 | + | 0.254715i | ||||
\(609\) | 3.56011e11 | 2.58818 | ||||||||
\(610\) | 4.39240e10 | − | 2.02725e10i | 0.317236 | − | 0.146416i | ||||
\(611\) | 2.37054e11i | 1.70091i | ||||||||
\(612\) | 1.38118e11 | − | 1.62002e11i | 0.984568 | − | 1.15482i | ||||
\(613\) | 1.73299e11 | 1.22731 | 0.613655 | − | 0.789575i | \(-0.289699\pi\) | ||||
0.613655 | + | 0.789575i | \(0.289699\pi\) | |||||||
\(614\) | −1.02921e11 | − | 2.22998e11i | −0.724155 | − | 1.56901i | ||||
\(615\) | − | 1.23430e10i | − | 0.0862823i | ||||||
\(616\) | −6.68844e9 | + | 2.38347e10i | −0.0464518 | + | 0.165534i | ||||
\(617\) | 2.09205e11 | 1.44355 | 0.721773 | − | 0.692130i | \(-0.243328\pi\) | ||||
0.721773 | + | 0.692130i | \(0.243328\pi\) | |||||||
\(618\) | 5.74618e10 | − | 2.65206e10i | 0.393936 | − | 0.181815i | ||||
\(619\) | − | 1.25079e11i | − | 0.851965i | −0.904731 | − | 0.425983i | \(-0.859928\pi\) | ||
0.904731 | − | 0.425983i | \(-0.140072\pi\) | |||||||
\(620\) | 1.85140e10 | + | 1.57846e10i | 0.125295 | + | 0.106823i | ||||
\(621\) | −1.10010e11 | −0.739717 | ||||||||
\(622\) | −3.72679e10 | − | 8.07476e10i | −0.248985 | − | 0.539471i | ||||
\(623\) | − | 2.78211e11i | − | 1.84681i | ||||||
\(624\) | −4.57421e11 | + | 7.32665e10i | −3.01702 | + | 0.483245i | ||||
\(625\) | 6.10352e9 | 0.0400000 | ||||||||
\(626\) | −2.56886e11 | + | 1.18562e11i | −1.67279 | + | 0.772054i | ||||
\(627\) | − | 2.05814e10i | − | 0.133169i | ||||||
\(628\) | −1.16352e11 | + | 1.36471e11i | −0.748055 | + | 0.877409i | ||||
\(629\) | 3.03656e10 | 0.193990 | ||||||||
\(630\) | −7.87813e10 | − | 1.70694e11i | −0.500105 | − | 1.08357i | ||||
\(631\) | − | 2.63720e11i | − | 1.66351i | −0.555143 | − | 0.831755i | \(-0.687337\pi\) | ||
0.555143 | − | 0.831755i | \(-0.312663\pi\) | |||||||
\(632\) | 1.92673e11 | + | 5.40673e10i | 1.20768 | + | 0.338896i | ||||
\(633\) | −1.40305e11 | −0.873894 | ||||||||
\(634\) | −4.13001e10 | + | 1.90614e10i | −0.255619 | + | 0.117977i | ||||
\(635\) | 8.68836e10i | 0.534371i | ||||||||
\(636\) | 2.20927e11 | + | 1.88356e11i | 1.35027 | + | 1.15120i | ||||
\(637\) | −5.34628e10 | −0.324709 | ||||||||
\(638\) | 1.39174e10 | + | 3.01545e10i | 0.0839990 | + | 0.181999i | ||||
\(639\) | 5.93925e10i | 0.356228i | ||||||||
\(640\) | −7.45365e10 | − | 8.59135e9i | −0.444272 | − | 0.0512085i | ||||
\(641\) | 1.68400e10 | 0.0997495 | 0.0498748 | − | 0.998755i | \(-0.484118\pi\) | ||||
0.0498748 | + | 0.998755i | \(0.484118\pi\) | |||||||
\(642\) | −2.75772e11 | + | 1.27278e11i | −1.62334 | + | 0.749228i | ||||
\(643\) | 2.84422e11i | 1.66387i | 0.554871 | + | 0.831936i | \(0.312767\pi\) | ||||
−0.554871 | + | 0.831936i | \(0.687233\pi\) | |||||||
\(644\) | −3.38446e10 | + | 3.96970e10i | −0.196764 | + | 0.230789i | ||||
\(645\) | −1.23979e11 | −0.716325 | ||||||||
\(646\) | 2.07508e10 | + | 4.49604e10i | 0.119153 | + | 0.258167i | ||||
\(647\) | 2.11657e11i | 1.20785i | 0.797040 | + | 0.603927i | \(0.206398\pi\) | ||||
−0.797040 | + | 0.603927i | \(0.793602\pi\) | |||||||
\(648\) | 1.19560e11 | − | 4.26062e11i | 0.678090 | − | 2.41642i | ||||
\(649\) | −2.03057e10 | −0.114456 | ||||||||
\(650\) | 5.34088e10 | − | 2.46500e10i | 0.299198 | − | 0.138091i | ||||
\(651\) | 1.34169e11i | 0.747012i | ||||||||
\(652\) | 4.37174e10 | + | 3.72723e10i | 0.241915 | + | 0.206251i | ||||
\(653\) | −2.94426e11 | −1.61929 | −0.809644 | − | 0.586922i | \(-0.800340\pi\) | ||||
−0.809644 | + | 0.586922i | \(0.800340\pi\) | |||||||
\(654\) | −7.81415e10 | − | 1.69308e11i | −0.427140 | − | 0.925478i | ||||
\(655\) | − | 1.52271e11i | − | 0.827278i | ||||||
\(656\) | −3.04715e9 | − | 1.90241e10i | −0.0164543 | − | 0.102728i | ||||
\(657\) | 5.80525e11 | 3.11573 | ||||||||
\(658\) | −1.92243e11 | + | 8.87271e10i | −1.02553 | + | 0.473318i | ||||
\(659\) | − | 1.18352e11i | − | 0.627529i | −0.949501 | − | 0.313765i | \(-0.898410\pi\) | ||
0.949501 | − | 0.313765i | \(-0.101590\pi\) | |||||||
\(660\) | 1.60433e10 | − | 1.88175e10i | 0.0845510 | − | 0.0991715i | ||||
\(661\) | 2.01300e11 | 1.05448 | 0.527239 | − | 0.849717i | \(-0.323227\pi\) | ||||
0.527239 | + | 0.849717i | \(0.323227\pi\) | |||||||
\(662\) | −7.79934e10 | − | 1.68987e11i | −0.406093 | − | 0.879875i | ||||
\(663\) | 3.67337e11i | 1.90112i | ||||||||
\(664\) | 2.73636e11 | + | 7.67871e10i | 1.40767 | + | 0.395017i | ||||
\(665\) | 4.37284e10 | 0.223603 | ||||||||
\(666\) | 1.35839e11 | − | 6.26945e10i | 0.690442 | − | 0.318663i | ||||
\(667\) | 6.99850e10i | 0.353591i | ||||||||
\(668\) | −2.18029e11 | − | 1.85886e11i | −1.09498 | − | 0.933555i | ||||
\(669\) | 7.84439e10 | 0.391611 | ||||||||
\(670\) | 2.70518e10 | + | 5.86125e10i | 0.134244 | + | 0.290865i | ||||
\(671\) | 2.48873e10i | 0.122768i | ||||||||
\(672\) | −2.30625e11 | − | 3.43532e11i | −1.13092 | − | 1.68457i | ||||
\(673\) | 2.21745e11 | 1.08092 | 0.540461 | − | 0.841369i | \(-0.318250\pi\) | ||||
0.540461 | + | 0.841369i | \(0.318250\pi\) | |||||||
\(674\) | 3.05017e11 | − | 1.40776e11i | 1.47803 | − | 0.682164i | ||||
\(675\) | 1.10796e11i | 0.533716i | ||||||||
\(676\) | 2.32316e11 | − | 2.72488e11i | 1.11248 | − | 1.30485i | ||||
\(677\) | −3.56145e11 | −1.69540 | −0.847701 | − | 0.530475i | \(-0.822014\pi\) | ||||
−0.847701 | + | 0.530475i | \(0.822014\pi\) | |||||||
\(678\) | 9.13767e10 | + | 1.97984e11i | 0.432431 | + | 0.936940i | ||||
\(679\) | 3.50747e11i | 1.65012i | ||||||||
\(680\) | −1.60745e10 | + | 5.72826e10i | −0.0751799 | + | 0.267909i | ||||
\(681\) | 5.20778e11 | 2.42139 | ||||||||
\(682\) | −1.13642e10 | + | 5.24500e9i | −0.0525295 | + | 0.0242442i | ||||
\(683\) | − | 2.15409e11i | − | 0.989878i | −0.868928 | − | 0.494939i | \(-0.835190\pi\) | ||
0.868928 | − | 0.494939i | \(-0.164810\pi\) | |||||||
\(684\) | 1.85656e11 | + | 1.58285e11i | 0.848172 | + | 0.723129i | ||||
\(685\) | −3.44688e10 | −0.156554 | ||||||||
\(686\) | 8.15274e10 | + | 1.76644e11i | 0.368135 | + | 0.797632i | ||||
\(687\) | − | 1.97142e11i | − | 0.885018i | ||||||
\(688\) | −1.91087e11 | + | 3.06070e10i | −0.852860 | + | 0.136605i | ||||
\(689\) | −3.55283e11 | −1.57651 | ||||||||
\(690\) | 4.73130e10 | − | 2.18366e10i | 0.208729 | − | 0.0963360i | ||||
\(691\) | 2.64031e11i | 1.15809i | 0.815296 | + | 0.579045i | \(0.196574\pi\) | ||||
−0.815296 | + | 0.579045i | \(0.803426\pi\) | |||||||
\(692\) | −2.62475e11 | + | 3.07862e11i | −1.14463 | + | 1.34255i | ||||
\(693\) | 9.67149e10 | 0.419334 | ||||||||
\(694\) | 4.98250e10 | + | 1.07955e11i | 0.214788 | + | 0.465377i | ||||
\(695\) | − | 1.88003e11i | − | 0.805797i | ||||||
\(696\) | −5.34454e11 | − | 1.49977e11i | −2.27758 | − | 0.639128i | ||||
\(697\) | −1.52775e10 | −0.0647324 | ||||||||
\(698\) | 7.89280e10 | − | 3.64280e10i | 0.332514 | − | 0.153467i | ||||
\(699\) | 3.66218e11i | 1.53402i | ||||||||
\(700\) | 3.99808e10 | + | 3.40866e10i | 0.166517 | + | 0.141968i | ||||
\(701\) | −1.98676e11 | −0.822758 | −0.411379 | − | 0.911464i | \(-0.634953\pi\) | ||||
−0.411379 | + | 0.911464i | \(0.634953\pi\) | |||||||
\(702\) | 4.47469e11 | + | 9.69523e11i | 1.84253 | + | 3.99218i | ||||
\(703\) | 3.47992e10i | 0.142478i | ||||||||
\(704\) | 2.00818e10 | − | 3.29638e10i | 0.0817545 | − | 0.134198i | ||||
\(705\) | 2.11499e11 | 0.856154 | ||||||||
\(706\) | 1.04261e11 | − | 4.81201e10i | 0.419666 | − | 0.193690i | ||||
\(707\) | − | 1.59943e11i | − | 0.640159i | ||||||
\(708\) | 2.20193e11 | − | 2.58269e11i | 0.876335 | − | 1.02787i | ||||
\(709\) | −1.08511e11 | −0.429427 | −0.214713 | − | 0.976677i | \(-0.568882\pi\) | ||||
−0.214713 | + | 0.976677i | \(0.568882\pi\) | |||||||
\(710\) | −6.95560e9 | − | 1.50706e10i | −0.0273717 | − | 0.0593057i | ||||
\(711\) | − | 7.81814e11i | − | 3.05932i | ||||||
\(712\) | −1.17202e11 | + | 4.17659e11i | −0.456054 | + | 1.62518i | ||||
\(713\) | −2.63750e10 | −0.102055 | ||||||||
\(714\) | −2.97899e11 | + | 1.37491e11i | −1.14624 | + | 0.529031i | ||||
\(715\) | 3.02613e10i | 0.115788i | ||||||||
\(716\) | −8.63665e10 | − | 7.36338e10i | −0.328619 | − | 0.280172i | ||||
\(717\) | −4.18763e11 | −1.58450 | ||||||||
\(718\) | −7.39403e10 | − | 1.60205e11i | −0.278217 | − | 0.602807i | ||||
\(719\) | − | 3.56644e11i | − | 1.33450i | −0.744832 | − | 0.667252i | \(-0.767471\pi\) | ||
0.744832 | − | 0.667252i | \(-0.232529\pi\) | |||||||
\(720\) | 4.63604e10 | + | 2.89440e11i | 0.172511 | + | 1.07703i | ||||
\(721\) | −6.91741e10 | −0.255978 | ||||||||
\(722\) | 1.95201e11 | − | 9.00923e10i | 0.718347 | − | 0.331542i | ||||
\(723\) | − | 1.74694e11i | − | 0.639329i | ||||||
\(724\) | −3.10969e10 | + | 3.64741e10i | −0.113178 | + | 0.132749i | ||||
\(725\) | 7.04853e10 | 0.255121 | ||||||||
\(726\) | −2.10560e11 | − | 4.56217e11i | −0.757931 | − | 1.64220i | ||||
\(727\) | − | 8.05781e10i | − | 0.288456i | −0.989544 | − | 0.144228i | \(-0.953930\pi\) | ||
0.989544 | − | 0.144228i | \(-0.0460699\pi\) | |||||||
\(728\) | 4.87516e11 | + | 1.36805e11i | 1.73565 | + | 0.487055i | ||||
\(729\) | −3.31165e11 | −1.17256 | ||||||||
\(730\) | −1.47306e11 | + | 6.79867e10i | −0.518714 | + | 0.239405i | ||||
\(731\) | 1.53455e11i | 0.537415i | ||||||||
\(732\) | −3.16541e11 | − | 2.69875e11i | −1.10252 | − | 0.939978i | ||||
\(733\) | 3.80343e11 | 1.31753 | 0.658763 | − | 0.752351i | \(-0.271080\pi\) | ||||
0.658763 | + | 0.752351i | \(0.271080\pi\) | |||||||
\(734\) | −2.27324e11 | − | 4.92539e11i | −0.783179 | − | 1.69690i | ||||
\(735\) | 4.76994e10i | 0.163442i | ||||||||
\(736\) | 6.75318e10 | − | 4.53366e10i | 0.230143 | − | 0.154503i | ||||
\(737\) | −3.32098e10 | −0.112563 | ||||||||
\(738\) | −6.83433e10 | + | 3.15428e10i | −0.230394 | + | 0.106335i | ||||
\(739\) | 4.01614e11i | 1.34658i | 0.739381 | + | 0.673288i | \(0.235118\pi\) | ||||
−0.739381 | + | 0.673288i | \(0.764882\pi\) | |||||||
\(740\) | −2.71262e10 | + | 3.18169e10i | −0.0904612 | + | 0.106104i | ||||
\(741\) | −4.20972e11 | −1.39631 | ||||||||
\(742\) | −1.32979e11 | − | 2.88123e11i | −0.438700 | − | 0.950523i | ||||
\(743\) | − | 3.54474e11i | − | 1.16313i | −0.813499 | − | 0.581566i | \(-0.802440\pi\) | ||
0.813499 | − | 0.581566i | \(-0.197560\pi\) | |||||||
\(744\) | 5.65215e10 | − | 2.01418e11i | 0.184468 | − | 0.657366i | ||||
\(745\) | 6.90521e10 | 0.224157 | ||||||||
\(746\) | 4.63791e11 | − | 2.14056e11i | 1.49750 | − | 0.691150i | ||||
\(747\) | − | 1.11034e12i | − | 3.56594i | ||||||
\(748\) | −2.32913e10 | − | 1.98575e10i | −0.0744024 | − | 0.0634335i | ||||
\(749\) | 3.31981e11 | 1.05484 | ||||||||
\(750\) | −2.19927e10 | − | 4.76512e10i | −0.0695078 | − | 0.150601i | ||||
\(751\) | 4.84888e11i | 1.52434i | 0.647378 | + | 0.762169i | \(0.275866\pi\) | ||||
−0.647378 | + | 0.762169i | \(0.724134\pi\) | |||||||
\(752\) | 3.25980e11 | − | 5.22132e10i | 1.01934 | − | 0.163271i | ||||
\(753\) | −9.31329e11 | −2.89683 | ||||||||
\(754\) | 6.16781e11 | − | 2.84666e11i | 1.90829 | − | 0.880745i | ||||
\(755\) | 1.11819e11i | 0.344135i | ||||||||
\(756\) | −6.18770e11 | + | 7.25767e11i | −1.89427 | + | 2.22183i | ||||
\(757\) | 1.22819e11 | 0.374009 | 0.187004 | − | 0.982359i | \(-0.440122\pi\) | ||||
0.187004 | + | 0.982359i | \(0.440122\pi\) | |||||||
\(758\) | 1.78578e11 | + | 3.86922e11i | 0.540942 | + | 1.17205i | ||||
\(759\) | 2.68074e10i | 0.0807771i | ||||||||
\(760\) | −6.56465e10 | − | 1.84215e10i | −0.196769 | − | 0.0552168i | ||||
\(761\) | −1.93019e11 | −0.575521 | −0.287761 | − | 0.957702i | \(-0.592911\pi\) | ||||
−0.287761 | + | 0.957702i | \(0.592911\pi\) | |||||||
\(762\) | 6.78315e11 | − | 3.13066e11i | 2.01192 | − | 0.928573i | ||||
\(763\) | 2.03817e11i | 0.601372i | ||||||||
\(764\) | 1.01757e11 | + | 8.67555e10i | 0.298670 | + | 0.254638i | ||||
\(765\) | 2.32437e11 | 0.678672 | ||||||||
\(766\) | −1.07991e11 | − | 2.33983e11i | −0.313671 | − | 0.679625i | ||||
\(767\) | 4.15333e11i | 1.20009i | ||||||||
\(768\) | 2.01502e11 | + | 6.12876e11i | 0.579208 | + | 1.76168i | ||||
\(769\) | 1.34359e11 | 0.384202 | 0.192101 | − | 0.981375i | \(-0.438470\pi\) | ||||
0.192101 | + | 0.981375i | \(0.438470\pi\) | |||||||
\(770\) | −2.45410e10 | + | 1.13265e10i | −0.0698118 | + | 0.0322206i | ||||
\(771\) | 1.68399e11i | 0.476564i | ||||||||
\(772\) | 8.33422e9 | − | 9.77536e9i | 0.0234636 | − | 0.0275210i | ||||
\(773\) | −1.97017e11 | −0.551804 | −0.275902 | − | 0.961186i | \(-0.588976\pi\) | ||||
−0.275902 | + | 0.961186i | \(0.588976\pi\) | |||||||
\(774\) | 3.16831e11 | + | 6.86472e11i | 0.882803 | + | 1.91275i | ||||
\(775\) | 2.65636e10i | 0.0736343i | ||||||||
\(776\) | 1.47760e11 | − | 5.26553e11i | 0.407483 | − | 1.45210i | ||||
\(777\) | −2.30573e11 | −0.632593 | ||||||||
\(778\) | 2.63925e11 | − | 1.21811e11i | 0.720380 | − | 0.332481i | ||||
\(779\) | − | 1.75082e10i | − | 0.0475435i | ||||||
\(780\) | −3.84894e11 | − | 3.28150e11i | −1.03983 | − | 0.886532i | ||||
\(781\) | 8.53896e9 | 0.0229510 | ||||||||
\(782\) | −2.70281e10 | − | 5.85613e10i | −0.0722751 | − | 0.156597i | ||||
\(783\) | 1.27951e12i | 3.40406i | ||||||||
\(784\) | 1.17756e10 | + | 7.35183e10i | 0.0311688 | + | 0.194595i | ||||
\(785\) | −1.95806e11 | −0.515642 | ||||||||
\(786\) | −1.18880e12 | + | 5.48675e11i | −3.11473 | + | 1.43756i | ||||
\(787\) | − | 3.63175e11i | − | 0.946711i | −0.880871 | − | 0.473356i | \(-0.843043\pi\) | ||
0.880871 | − | 0.473356i | \(-0.156957\pi\) | |||||||
\(788\) | −4.37858e10 | + | 5.13572e10i | −0.113561 | + | 0.133198i | ||||
\(789\) | −2.27540e11 | −0.587150 | ||||||||
\(790\) | 9.15601e10 | + | 1.98382e11i | 0.235070 | + | 0.509323i | ||||
\(791\) | − | 2.38339e11i | − | 0.608820i | ||||||
\(792\) | −1.45191e11 | − | 4.07433e10i | −0.369012 | − | 0.103551i | ||||
\(793\) | 5.09044e11 | 1.28725 | ||||||||
\(794\) | −5.85926e11 | + | 2.70425e11i | −1.47421 | + | 0.680402i | ||||
\(795\) | 3.16982e11i | 0.793536i | ||||||||
\(796\) | −2.46576e11 | − | 2.10224e11i | −0.614184 | − | 0.523637i | ||||
\(797\) | −5.78264e10 | −0.143316 | −0.0716578 | − | 0.997429i | \(-0.522829\pi\) | ||||
−0.0716578 | + | 0.997429i | \(0.522829\pi\) | |||||||
\(798\) | −1.57566e11 | − | 3.41395e11i | −0.388553 | − | 0.841872i | ||||
\(799\) | − | 2.61782e11i | − | 0.642321i | ||||||
\(800\) | −4.56607e10 | − | 6.80146e10i | −0.111476 | − | 0.166051i | ||||
\(801\) | 1.69475e12 | 4.11694 | ||||||||
\(802\) | 2.70766e11 | − | 1.24968e11i | 0.654481 | − | 0.302066i | ||||
\(803\) | − | 8.34631e10i | − | 0.200739i | ||||||
\(804\) | 3.60123e11 | − | 4.22395e11i | 0.861840 | − | 1.01087i | ||||
\(805\) | −5.69566e10 | −0.135632 | ||||||||
\(806\) | 1.07281e11 | + | 2.32444e11i | 0.254205 | + | 0.550781i | ||||
\(807\) | 4.10660e11i | 0.968251i | ||||||||
\(808\) | −6.73795e10 | + | 2.40111e11i | −0.158082 | + | 0.563336i | ||||
\(809\) | −1.75206e11 | −0.409031 | −0.204515 | − | 0.978863i | \(-0.565562\pi\) | ||||
−0.204515 | + | 0.978863i | \(0.565562\pi\) | |||||||
\(810\) | 4.38686e11 | − | 2.02469e11i | 1.01909 | − | 0.470347i | ||||
\(811\) | 1.53398e11i | 0.354599i | 0.984157 | + | 0.177299i | \(0.0567361\pi\) | ||||
−0.984157 | + | 0.177299i | \(0.943264\pi\) | |||||||
\(812\) | 4.61711e11 | + | 3.93642e11i | 1.06205 | + | 0.905477i | ||||
\(813\) | 1.40912e12 | 3.22541 | ||||||||
\(814\) | −9.01369e9 | − | 1.95298e10i | −0.0205308 | − | 0.0444836i | ||||
\(815\) | 6.27249e10i | 0.142171i | ||||||||
\(816\) | 5.05136e11 | − | 8.09091e10i | 1.13932 | − | 0.182489i | ||||
\(817\) | −1.75860e11 | −0.394712 | ||||||||
\(818\) | −2.83840e11 | + | 1.31002e11i | −0.633958 | + | 0.292594i | ||||
\(819\) | − | 1.97821e12i | − | 4.39680i | ||||||
\(820\) | 1.36477e10 | − | 1.60077e10i | 0.0301860 | − | 0.0354057i | ||||
\(821\) | −3.12544e11 | −0.687922 | −0.343961 | − | 0.938984i | \(-0.611769\pi\) | ||||
−0.343961 | + | 0.938984i | \(0.611769\pi\) | |||||||
\(822\) | 1.24201e11 | + | 2.69104e11i | 0.272043 | + | 0.589431i | ||||
\(823\) | − | 6.75905e11i | − | 1.47328i | −0.676283 | − | 0.736641i | \(-0.736411\pi\) | ||
0.676283 | − | 0.736641i | \(-0.263589\pi\) | |||||||
\(824\) | 1.03846e11 | + | 2.91411e10i | 0.225259 | + | 0.0632116i | ||||
\(825\) | 2.69991e10 | 0.0582818 | ||||||||
\(826\) | −3.36822e11 | + | 1.55455e11i | −0.723570 | + | 0.333953i | ||||
\(827\) | 7.49212e11i | 1.60171i | 0.598861 | + | 0.800853i | \(0.295620\pi\) | ||||
−0.598861 | + | 0.800853i | \(0.704380\pi\) | |||||||
\(828\) | −2.41818e11 | − | 2.06168e11i | −0.514479 | − | 0.438631i | ||||
\(829\) | −6.27639e11 | −1.32890 | −0.664449 | − | 0.747333i | \(-0.731334\pi\) | ||||
−0.664449 | + | 0.747333i | \(0.731334\pi\) | |||||||
\(830\) | 1.30035e11 | + | 2.81744e11i | 0.273998 | + | 0.593667i | ||||
\(831\) | − | 2.83735e11i | − | 0.594988i | ||||||
\(832\) | −6.74242e11 | − | 4.10753e11i | −1.40709 | − | 0.857211i | ||||
\(833\) | 5.90396e10 | 0.122621 | ||||||||
\(834\) | −1.46777e12 | + | 6.77429e11i | −3.03385 | + | 1.40023i | ||||
\(835\) | − | 3.12824e11i | − | 0.643508i | ||||||
\(836\) | 2.27569e10 | − | 2.66920e10i | 0.0465895 | − | 0.0546458i | ||||
\(837\) | −4.82206e11 | −0.982495 | ||||||||
\(838\) | −1.07546e11 | − | 2.33018e11i | −0.218081 | − | 0.472512i | ||||
\(839\) | 8.86257e11i | 1.78860i | 0.447473 | + | 0.894298i | \(0.352324\pi\) | ||||
−0.447473 | + | 0.894298i | \(0.647676\pi\) | |||||||
\(840\) | 1.22058e11 | − | 4.34961e11i | 0.245159 | − | 0.873641i | ||||
\(841\) | 3.13739e11 | 0.627168 | ||||||||
\(842\) | 1.27852e11 | − | 5.90080e10i | 0.254365 | − | 0.117398i | ||||
\(843\) | 2.48638e11i | 0.492331i | ||||||||
\(844\) | −1.81962e11 | − | 1.55136e11i | −0.358600 | − | 0.305733i | ||||
\(845\) | 3.90961e11 | 0.766844 | ||||||||
\(846\) | −5.40489e11 | − | 1.17107e12i | −1.05513 | − | 2.28613i | ||||
\(847\) | 5.49207e11i | 1.06709i | ||||||||
\(848\) | 7.82540e10 | + | 4.88560e11i | 0.151329 | + | 0.944787i | ||||
\(849\) | 1.29457e12 | 2.49169 | ||||||||
\(850\) | −5.89799e10 | + | 2.72213e10i | −0.112987 | + | 0.0521475i | ||||
\(851\) | − | 4.53263e10i | − | 0.0864235i | ||||||
\(852\) | −9.25956e10 | + | 1.08607e11i | −0.175724 | + | 0.206110i | ||||
\(853\) | −4.42385e10 | −0.0835611 | −0.0417805 | − | 0.999127i | \(-0.513303\pi\) | ||||
−0.0417805 | + | 0.999127i | \(0.513303\pi\) | |||||||
\(854\) | 1.90530e11 | + | 4.12819e11i | 0.358206 | + | 0.776119i | ||||
\(855\) | 2.66376e11i | 0.498460i | ||||||||
\(856\) | −4.98381e11 | − | 1.39854e11i | −0.928253 | − | 0.260484i | ||||
\(857\) | −1.03847e12 | −1.92517 | −0.962586 | − | 0.270976i | \(-0.912654\pi\) | ||||
−0.962586 | + | 0.270976i | \(0.912654\pi\) | |||||||
\(858\) | 2.36255e11 | − | 1.09040e11i | 0.435945 | − | 0.201204i | ||||
\(859\) | − | 5.28066e11i | − | 0.969874i | −0.874549 | − | 0.484937i | \(-0.838842\pi\) | ||
0.874549 | − | 0.484937i | \(-0.161158\pi\) | |||||||
\(860\) | −1.60789e11 | − | 1.37084e11i | −0.293942 | − | 0.250608i | ||||
\(861\) | 1.16006e11 | 0.211090 | ||||||||
\(862\) | −1.45667e11 | − | 3.15614e11i | −0.263835 | − | 0.571646i | ||||
\(863\) | − | 1.90850e11i | − | 0.344072i | −0.985091 | − | 0.172036i | \(-0.944965\pi\) | ||
0.985091 | − | 0.172036i | \(-0.0550346\pi\) | |||||||
\(864\) | 1.23466e12 | − | 8.28873e11i | 2.21561 | − | 1.48742i | ||||
\(865\) | −4.41715e11 | −0.789001 | ||||||||
\(866\) | 3.64140e11 | − | 1.68063e11i | 0.647436 | − | 0.298814i | ||||
\(867\) | 6.42181e11i | 1.13653i | ||||||||
\(868\) | −1.48351e11 | + | 1.74004e11i | −0.261343 | + | 0.306534i | ||||
\(869\) | −1.12403e11 | −0.197105 | ||||||||
\(870\) | −2.53978e11 | − | 5.50290e11i | −0.443322 | − | 0.960539i | ||||
\(871\) | 6.79273e11i | 1.18024i | ||||||||
\(872\) | 8.58624e10 | − | 3.05977e11i | 0.148504 | − | 0.529203i | ||||
\(873\) | −2.13661e12 | −3.67848 | ||||||||
\(874\) | 6.71119e10 | − | 3.09745e10i | 0.115015 | − | 0.0530834i | ||||
\(875\) | 5.73638e10i | 0.0978601i | ||||||||
\(876\) | 1.06157e12 | + | 9.05065e11i | 1.80273 | + | 1.53696i | ||||
\(877\) | 2.36707e11 | 0.400140 | 0.200070 | − | 0.979782i | \(-0.435883\pi\) | ||||
0.200070 | + | 0.979782i | \(0.435883\pi\) | |||||||
\(878\) | −1.80401e11 | − | 3.90872e11i | −0.303572 | − | 0.657744i | ||||
\(879\) | 8.28136e11i | 1.38722i | ||||||||
\(880\) | 4.16132e10 | − | 6.66531e9i | 0.0693906 | − | 0.0111145i | ||||
\(881\) | 3.49205e11 | 0.579665 | 0.289832 | − | 0.957077i | \(-0.406400\pi\) | ||||
0.289832 | + | 0.957077i | \(0.406400\pi\) | |||||||
\(882\) | 2.64111e11 | − | 1.21897e11i | 0.436428 | − | 0.201427i | ||||
\(883\) | − | 5.98818e11i | − | 0.985035i | −0.870302 | − | 0.492518i | \(-0.836077\pi\) | ||
0.870302 | − | 0.492518i | \(-0.163923\pi\) | |||||||
\(884\) | −4.06166e11 | + | 4.76400e11i | −0.665111 | + | 0.780122i | ||||
\(885\) | 3.70559e11 | 0.604067 | ||||||||
\(886\) | 3.46317e11 | + | 7.50359e11i | 0.562004 | + | 1.21768i | ||||
\(887\) | − | 5.75931e11i | − | 0.930413i | −0.885202 | − | 0.465207i | \(-0.845980\pi\) | ||
0.885202 | − | 0.465207i | \(-0.154020\pi\) | |||||||
\(888\) | 3.46143e11 | + | 9.71338e10i | 0.556678 | + | 0.156214i | ||||
\(889\) | −8.16574e11 | −1.30734 | ||||||||
\(890\) | −4.30035e11 | + | 1.98476e11i | −0.685399 | + | 0.316336i | ||||
\(891\) | 2.48559e11i | 0.394383i | ||||||||
\(892\) | 1.01734e11 | + | 8.67357e10i | 0.160697 | + | 0.137006i | ||||
\(893\) | 3.00004e11 | 0.471761 | ||||||||
\(894\) | −2.48814e11 | − | 5.39101e11i | −0.389516 | − | 0.843957i | ||||
\(895\) | − | 1.23917e11i | − | 0.193125i | ||||||
\(896\) | 8.07457e10 | − | 7.00530e11i | 0.125282 | − | 1.08691i | ||||
\(897\) | 5.48320e11 | 0.846962 | ||||||||
\(898\) | −6.70527e11 | + | 3.09472e11i | −1.03112 | + | 0.475900i | ||||
\(899\) | 3.06764e11i | 0.469641i | ||||||||
\(900\) | −2.07641e11 | + | 2.43547e11i | −0.316478 | + | 0.371204i | ||||
\(901\) | 3.92343e11 | 0.595342 | ||||||||
\(902\) | 4.53497e9 | + | 9.82583e9i | 0.00685091 | + | 0.0148437i | ||||
\(903\) | − | 1.16522e12i | − | 1.75249i | ||||||
\(904\) | −1.00405e11 | + | 3.57802e11i | −0.150343 | + | 0.535758i | ||||
\(905\) | −5.23325e10 | −0.0780148 | ||||||||
\(906\) | 8.72991e11 | − | 4.02916e11i | 1.29568 | − | 0.598001i | ||||
\(907\) | − | 4.04494e11i | − | 0.597699i | −0.954300 | − | 0.298849i | \(-0.903397\pi\) | ||
0.954300 | − | 0.298849i | \(-0.0966029\pi\) | |||||||
\(908\) | 6.75398e11 | + | 5.75827e11i | 0.993611 | + | 0.847126i | ||||
\(909\) | 9.74308e11 | 1.42705 | ||||||||
\(910\) | 2.31673e11 | + | 5.01961e11i | 0.337839 | + | 0.731989i | ||||
\(911\) | − | 6.18016e11i | − | 0.897276i | −0.893714 | − | 0.448638i | \(-0.851909\pi\) | ||
0.893714 | − | 0.448638i | \(-0.148091\pi\) | |||||||
\(912\) | 9.27227e10 | + | 5.78891e11i | 0.134031 | + | 0.836792i | ||||
\(913\) | −1.59636e11 | −0.229746 | ||||||||
\(914\) | −4.52219e11 | + | 2.08715e11i | −0.647984 | + | 0.299067i | ||||
\(915\) | − | 4.54168e11i | − | 0.647936i | ||||||
\(916\) | 2.17981e11 | − | 2.55674e11i | 0.309625 | − | 0.363165i | ||||
\(917\) | 1.43111e12 | 2.02394 | ||||||||
\(918\) | −4.94145e11 | − | 1.07066e12i | −0.695799 | − | 1.50758i | ||||
\(919\) | − | 5.11050e11i | − | 0.716476i | −0.933630 | − | 0.358238i | \(-0.883378\pi\) | ||
0.933630 | − | 0.358238i | \(-0.116622\pi\) | |||||||
\(920\) | 8.55051e10 | + | 2.39942e10i | 0.119355 | + | 0.0334931i | ||||
\(921\) | −2.30577e12 | −3.20462 | ||||||||
\(922\) | 6.79904e11 | − | 3.13800e11i | 0.940858 | − | 0.434239i | ||||
\(923\) | − | 1.74656e11i | − | 0.240645i | ||||||
\(924\) | 1.76856e11 | + | 1.50783e11i | 0.242623 | + | 0.206854i | ||||
\(925\) | −4.56503e10 | −0.0623558 | ||||||||
\(926\) | 1.36332e11 | + | 2.95388e11i | 0.185419 | + | 0.401744i | ||||
\(927\) | − | 4.21380e11i | − | 0.570631i | ||||||
\(928\) | −5.27304e11 | − | 7.85453e11i | −0.710999 | − | 1.05908i | ||||
\(929\) | 3.49578e11 | 0.469333 | 0.234666 | − | 0.972076i | \(-0.424600\pi\) | ||||
0.234666 | + | 0.972076i | \(0.424600\pi\) | |||||||
\(930\) | 2.07386e11 | − | 9.57161e10i | 0.277235 | − | 0.127954i | ||||
\(931\) | 6.76600e10i | 0.0900603i | ||||||||
\(932\) | −4.04929e11 | + | 4.74949e11i | −0.536680 | + | 0.629482i | ||||
\(933\) | −8.34919e11 | −1.10184 | ||||||||
\(934\) | 3.95371e11 | + | 8.56642e11i | 0.519537 | + | 1.12567i | ||||
\(935\) | − | 3.34179e10i | − | 0.0437253i | ||||||
\(936\) | −8.33363e11 | + | 2.96975e12i | −1.08575 | + | 3.86915i | ||||
\(937\) | −1.37124e11 | −0.177891 | −0.0889457 | − | 0.996036i | \(-0.528350\pi\) | ||||
−0.0889457 | + | 0.996036i | \(0.528350\pi\) | |||||||
\(938\) | −5.50869e11 | + | 2.54245e11i | −0.711602 | + | 0.328429i | ||||
\(939\) | 2.65616e12i | 3.41659i | ||||||||
\(940\) | 2.74293e11 | + | 2.33855e11i | 0.351321 | + | 0.299527i | ||||
\(941\) | −4.32170e10 | −0.0551183 | −0.0275592 | − | 0.999620i | \(-0.508773\pi\) | ||||
−0.0275592 | + | 0.999620i | \(0.508773\pi\) | |||||||
\(942\) | 7.05546e11 | + | 1.52869e12i | 0.896028 | + | 1.94141i | ||||
\(943\) | 2.28046e10i | 0.0288387i | ||||||||
\(944\) | 5.71137e11 | − | 9.14807e10i | 0.719204 | − | 0.115197i | ||||
\(945\) | −1.04132e12 | −1.30574 | ||||||||
\(946\) | 9.86953e10 | − | 4.55513e10i | 0.123234 | − | 0.0568770i | ||||
\(947\) | − | 1.24527e12i | − | 1.54832i | −0.632987 | − | 0.774162i | \(-0.718171\pi\) | ||
0.632987 | − | 0.774162i | \(-0.281829\pi\) | |||||||
\(948\) | 1.21888e12 | − | 1.42965e12i | 1.50914 | − | 1.77010i | ||||
\(949\) | −1.70716e12 | −2.10479 | ||||||||
\(950\) | −3.11959e10 | − | 6.75916e10i | −0.0383004 | − | 0.0829848i | ||||
\(951\) | 4.27037e11i | 0.522088i | ||||||||
\(952\) | −5.38370e11 | − | 1.51076e11i | −0.655440 | − | 0.183928i | ||||
\(953\) | 9.35275e11 | 1.13388 | 0.566941 | − | 0.823759i | \(-0.308127\pi\) | ||||
0.566941 | + | 0.823759i | \(0.308127\pi\) | |||||||
\(954\) | 1.75513e12 | − | 8.10053e11i | 2.11892 | − | 0.977958i | ||||
\(955\) | 1.46000e11i | 0.175525i | ||||||||
\(956\) | −5.43095e11 | − | 4.63028e11i | −0.650195 | − | 0.554339i | ||||
\(957\) | 3.11793e11 | 0.371723 | ||||||||
\(958\) | 8.06120e10 | + | 1.74661e11i | 0.0957057 | + | 0.207364i | ||||
\(959\) | − | 3.23955e11i | − | 0.383010i | ||||||
\(960\) | −3.66473e11 | + | 6.01557e11i | −0.431476 | + | 0.708258i | ||||
\(961\) | 7.37282e11 | 0.864450 | ||||||||
\(962\) | −3.99463e11 | + | 1.84366e11i | −0.466419 | + | 0.215269i | ||||
\(963\) | 2.02229e12i | 2.35147i | ||||||||
\(964\) | 1.93160e11 | − | 2.26561e11i | 0.223670 | − | 0.262347i | ||||
\(965\) | 1.40255e10 | 0.0161737 | ||||||||
\(966\) | 2.05231e11 | + | 4.44670e11i | 0.235686 | + | 0.510657i | ||||
\(967\) | − | 1.52906e12i | − | 1.74871i | −0.485286 | − | 0.874355i | \(-0.661285\pi\) | ||
0.485286 | − | 0.874355i | \(-0.338715\pi\) | |||||||
\(968\) | 2.31365e11 | − | 8.24486e11i | 0.263510 | − | 0.939035i | ||||
\(969\) | 4.64884e11 | 0.527290 | ||||||||
\(970\) | 5.42155e11 | − | 2.50224e11i | 0.612402 | − | 0.282645i | ||||
\(971\) | 5.95468e11i | 0.669856i | 0.942244 | + | 0.334928i | \(0.108712\pi\) | ||||
−0.942244 | + | 0.334928i | \(0.891288\pi\) | |||||||
\(972\) | −1.34877e12 | − | 1.14993e12i | −1.51103 | − | 1.28826i | ||||
\(973\) | 1.76694e12 | 1.97139 | ||||||||
\(974\) | −3.25817e11 | − | 7.05942e11i | −0.362024 | − | 0.784392i | ||||
\(975\) | − | 5.52239e11i | − | 0.611095i | ||||||
\(976\) | −1.12121e11 | − | 7.00002e11i | −0.123563 | − | 0.771436i | ||||
\(977\) | 1.10548e12 | 1.21332 | 0.606659 | − | 0.794962i | \(-0.292509\pi\) | ||||
0.606659 | + | 0.794962i | \(0.292509\pi\) | |||||||
\(978\) | 4.89704e11 | − | 2.26016e11i | 0.535277 | − | 0.247049i | ||||
\(979\) | − | 2.43657e11i | − | 0.265245i | ||||||
\(980\) | −5.27414e10 | + | 6.18614e10i | −0.0571804 | + | 0.0670680i | ||||
\(981\) | −1.24157e12 | −1.34059 | ||||||||
\(982\) | −1.15046e10 | − | 2.49269e10i | −0.0123716 | − | 0.0268054i | ||||
\(983\) | 1.26644e10i | 0.0135634i | 0.999977 | + | 0.00678172i | \(0.00215871\pi\) | ||||
−0.999977 | + | 0.00678172i | \(0.997841\pi\) | |||||||
\(984\) | −1.74152e11 | − | 4.88700e10i | −0.185758 | − | 0.0521269i | ||||
\(985\) | −7.36865e10 | −0.0782786 | ||||||||
\(986\) | −6.81118e11 | + | 3.14360e11i | −0.720634 | + | 0.332598i | ||||
\(987\) | 1.98777e12i | 2.09458i | ||||||||
\(988\) | −5.45959e11 | − | 4.65470e11i | −0.572971 | − | 0.488500i | ||||
\(989\) | 2.29060e11 | 0.239422 | ||||||||
\(990\) | −6.89966e10 | − | 1.49494e11i | −0.0718268 | − | 0.155626i | ||||
\(991\) | 7.11883e11i | 0.738098i | 0.929410 | + | 0.369049i | \(0.120317\pi\) | ||||
−0.929410 | + | 0.369049i | \(0.879683\pi\) | |||||||
\(992\) | 2.96012e11 | − | 1.98724e11i | 0.305677 | − | 0.205212i | ||||
\(993\) | −1.74730e12 | −1.79709 | ||||||||
\(994\) | 1.41641e11 | − | 6.53721e10i | 0.145092 | − | 0.0669649i | ||||
\(995\) | − | 3.53783e11i | − | 0.360948i | ||||||
\(996\) | 1.73107e12 | − | 2.03041e12i | 1.75905 | − | 2.06322i | ||||
\(997\) | 2.60515e11 | 0.263665 | 0.131832 | − | 0.991272i | \(-0.457914\pi\) | ||||
0.131832 | + | 0.991272i | \(0.457914\pi\) | |||||||
\(998\) | 4.19435e11 | + | 9.08782e11i | 0.422807 | + | 0.916089i | ||||
\(999\) | − | 8.28685e11i | − | 0.832008i |
(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 | 20.9.b.a.11.15 | ✓ | 16 | |
3.2 | odd | 2 | 180.9.c.a.91.2 | 16 | |||
4.3 | odd | 2 | inner | 20.9.b.a.11.16 | yes | 16 | |
5.2 | odd | 4 | 100.9.d.c.99.22 | 32 | |||
5.3 | odd | 4 | 100.9.d.c.99.11 | 32 | |||
5.4 | even | 2 | 100.9.b.d.51.2 | 16 | |||
8.3 | odd | 2 | 320.9.b.d.191.1 | 16 | |||
8.5 | even | 2 | 320.9.b.d.191.16 | 16 | |||
12.11 | even | 2 | 180.9.c.a.91.1 | 16 | |||
20.3 | even | 4 | 100.9.d.c.99.21 | 32 | |||
20.7 | even | 4 | 100.9.d.c.99.12 | 32 | |||
20.19 | odd | 2 | 100.9.b.d.51.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.9.b.a.11.15 | ✓ | 16 | 1.1 | even | 1 | trivial | |
20.9.b.a.11.16 | yes | 16 | 4.3 | odd | 2 | inner | |
100.9.b.d.51.1 | 16 | 20.19 | odd | 2 | |||
100.9.b.d.51.2 | 16 | 5.4 | even | 2 | |||
100.9.d.c.99.11 | 32 | 5.3 | odd | 4 | |||
100.9.d.c.99.12 | 32 | 20.7 | even | 4 | |||
100.9.d.c.99.21 | 32 | 20.3 | even | 4 | |||
100.9.d.c.99.22 | 32 | 5.2 | odd | 4 | |||
180.9.c.a.91.1 | 16 | 12.11 | even | 2 | |||
180.9.c.a.91.2 | 16 | 3.2 | odd | 2 | |||
320.9.b.d.191.1 | 16 | 8.3 | odd | 2 | |||
320.9.b.d.191.16 | 16 | 8.5 | even | 2 |