Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [13,7,Mod(5,13)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(13, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("13.5");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 13 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 13.d (of order \(4\), degree \(2\), 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: | \(2.99070308706\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 18 x^{10} + 488 x^{9} + 36205 x^{8} - 155430 x^{7} + 399962 x^{6} + 9502784 x^{5} + \cdots + 56070144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 5^{2}\cdot 13^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 8.4 | ||
Root | \(0.388469 - 0.388469i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 13.8 |
Dual form | 13.7.d.a.5.4 |
$q$-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 \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.611531 | + | 0.611531i | 0.0764414 | + | 0.0764414i | 0.744294 | − | 0.667852i | \(-0.232786\pi\) |
−0.667852 | + | 0.744294i | \(0.732786\pi\) | |||||||
\(3\) | 18.7379 | 0.693997 | 0.346998 | − | 0.937866i | \(-0.387201\pi\) | ||||
0.346998 | + | 0.937866i | \(0.387201\pi\) | |||||||
\(4\) | − | 63.2521i | − | 0.988313i | ||||||
\(5\) | 134.607 | + | 134.607i | 1.07686 | + | 1.07686i | 0.996789 | + | 0.0800682i | \(0.0255138\pi\) |
0.0800682 | + | 0.996789i | \(0.474486\pi\) | |||||||
\(6\) | 11.4588 | + | 11.4588i | 0.0530501 | + | 0.0530501i | ||||
\(7\) | 241.226 | − | 241.226i | 0.703282 | − | 0.703282i | −0.261832 | − | 0.965114i | \(-0.584327\pi\) |
0.965114 | + | 0.261832i | \(0.0843265\pi\) | |||||||
\(8\) | 77.8186 | − | 77.8186i | 0.151990 | − | 0.151990i | ||||
\(9\) | −377.891 | −0.518369 | ||||||||
\(10\) | 164.633i | 0.164633i | ||||||||
\(11\) | −1796.54 | + | 1796.54i | −1.34976 | + | 1.34976i | −0.463849 | + | 0.885914i | \(0.653532\pi\) |
−0.885914 | + | 0.463849i | \(0.846468\pi\) | |||||||
\(12\) | − | 1185.21i | − | 0.685886i | ||||||
\(13\) | −375.320 | − | 2164.70i | −0.170833 | − | 0.985300i | ||||
\(14\) | 295.034 | 0.107520 | ||||||||
\(15\) | 2522.26 | + | 2522.26i | 0.747336 | + | 0.747336i | ||||
\(16\) | −3952.95 | −0.965077 | ||||||||
\(17\) | 789.421i | 0.160680i | 0.996768 | + | 0.0803400i | \(0.0256006\pi\) | ||||
−0.996768 | + | 0.0803400i | \(0.974399\pi\) | |||||||
\(18\) | −231.092 | − | 231.092i | −0.0396248 | − | 0.0396248i | ||||
\(19\) | 4083.16 | + | 4083.16i | 0.595299 | + | 0.595299i | 0.939058 | − | 0.343759i | \(-0.111700\pi\) |
−0.343759 | + | 0.939058i | \(0.611700\pi\) | |||||||
\(20\) | 8514.18 | − | 8514.18i | 1.06427 | − | 1.06427i | ||||
\(21\) | 4520.07 | − | 4520.07i | 0.488075 | − | 0.488075i | ||||
\(22\) | −2197.28 | −0.206356 | ||||||||
\(23\) | 1432.88i | 0.117767i | 0.998265 | + | 0.0588837i | \(0.0187541\pi\) | ||||
−0.998265 | + | 0.0588837i | \(0.981246\pi\) | |||||||
\(24\) | 1458.16 | − | 1458.16i | 0.105480 | − | 0.105480i | ||||
\(25\) | 20613.2i | 1.31924i | ||||||||
\(26\) | 1094.26 | − | 1553.30i | 0.0622590 | − | 0.0883765i | ||||
\(27\) | −20740.8 | −1.05374 | ||||||||
\(28\) | −15258.0 | − | 15258.0i | −0.695063 | − | 0.695063i | ||||
\(29\) | 6913.74 | 0.283478 | 0.141739 | − | 0.989904i | \(-0.454731\pi\) | ||||
0.141739 | + | 0.989904i | \(0.454731\pi\) | |||||||
\(30\) | 3084.88i | 0.114255i | ||||||||
\(31\) | −11888.4 | − | 11888.4i | −0.399060 | − | 0.399060i | 0.478841 | − | 0.877902i | \(-0.341057\pi\) |
−0.877902 | + | 0.478841i | \(0.841057\pi\) | |||||||
\(32\) | −7397.75 | − | 7397.75i | −0.225761 | − | 0.225761i | ||||
\(33\) | −33663.3 | + | 33663.3i | −0.936731 | + | 0.936731i | ||||
\(34\) | −482.756 | + | 482.756i | −0.0122826 | + | 0.0122826i | ||||
\(35\) | 64941.4 | 1.51467 | ||||||||
\(36\) | 23902.4i | 0.512311i | ||||||||
\(37\) | 29823.4 | − | 29823.4i | 0.588779 | − | 0.588779i | −0.348521 | − | 0.937301i | \(-0.613316\pi\) |
0.937301 | + | 0.348521i | \(0.113316\pi\) | |||||||
\(38\) | 4993.96i | 0.0910111i | ||||||||
\(39\) | −7032.71 | − | 40562.0i | −0.118558 | − | 0.683795i | ||||
\(40\) | 20949.9 | 0.327342 | ||||||||
\(41\) | −29513.5 | − | 29513.5i | −0.428222 | − | 0.428222i | 0.459800 | − | 0.888022i | \(-0.347921\pi\) |
−0.888022 | + | 0.459800i | \(0.847921\pi\) | |||||||
\(42\) | 5528.32 | 0.0746183 | ||||||||
\(43\) | 33537.0i | 0.421811i | 0.977506 | + | 0.210906i | \(0.0676413\pi\) | ||||
−0.977506 | + | 0.210906i | \(0.932359\pi\) | |||||||
\(44\) | 113635. | + | 113635.i | 1.33399 | + | 1.33399i | ||||
\(45\) | −50866.8 | − | 50866.8i | −0.558209 | − | 0.558209i | ||||
\(46\) | −876.249 | + | 876.249i | −0.00900232 | + | 0.00900232i | ||||
\(47\) | 76861.6 | − | 76861.6i | 0.740314 | − | 0.740314i | −0.232325 | − | 0.972638i | \(-0.574633\pi\) |
0.972638 | + | 0.232325i | \(0.0746331\pi\) | |||||||
\(48\) | −74070.1 | −0.669760 | ||||||||
\(49\) | 1269.32i | 0.0107891i | ||||||||
\(50\) | −12605.6 | + | 12605.6i | −0.100845 | + | 0.100845i | ||||
\(51\) | 14792.1i | 0.111511i | ||||||||
\(52\) | −136922. | + | 23739.8i | −0.973785 | + | 0.168837i | ||||
\(53\) | 142559. | 0.957564 | 0.478782 | − | 0.877934i | \(-0.341078\pi\) | ||||
0.478782 | + | 0.877934i | \(0.341078\pi\) | |||||||
\(54\) | −12683.7 | − | 12683.7i | −0.0805496 | − | 0.0805496i | ||||
\(55\) | −483653. | −2.90701 | ||||||||
\(56\) | − | 37543.7i | − | 0.213783i | ||||||
\(57\) | 76509.9 | + | 76509.9i | 0.413136 | + | 0.413136i | ||||
\(58\) | 4227.97 | + | 4227.97i | 0.0216695 | + | 0.0216695i | ||||
\(59\) | −82531.1 | + | 82531.1i | −0.401848 | + | 0.401848i | −0.878884 | − | 0.477036i | \(-0.841711\pi\) |
0.477036 | + | 0.878884i | \(0.341711\pi\) | |||||||
\(60\) | 159538. | − | 159538.i | 0.738602 | − | 0.738602i | ||||
\(61\) | 305962. | 1.34796 | 0.673982 | − | 0.738748i | \(-0.264582\pi\) | ||||
0.673982 | + | 0.738748i | \(0.264582\pi\) | |||||||
\(62\) | − | 14540.3i | − | 0.0610095i | ||||||
\(63\) | −91156.9 | + | 91156.9i | −0.364559 | + | 0.364559i | ||||
\(64\) | 243941.i | 0.930562i | ||||||||
\(65\) | 240864. | − | 341906.i | 0.877065 | − | 1.24499i | ||||
\(66\) | −41172.3 | −0.143210 | ||||||||
\(67\) | 53061.6 | + | 53061.6i | 0.176423 | + | 0.176423i | 0.789795 | − | 0.613371i | \(-0.210187\pi\) |
−0.613371 | + | 0.789795i | \(0.710187\pi\) | |||||||
\(68\) | 49932.5 | 0.158802 | ||||||||
\(69\) | 26849.1i | 0.0817303i | ||||||||
\(70\) | 39713.7 | + | 39713.7i | 0.115783 | + | 0.115783i | ||||
\(71\) | −192797. | − | 192797.i | −0.538672 | − | 0.538672i | 0.384467 | − | 0.923139i | \(-0.374385\pi\) |
−0.923139 | + | 0.384467i | \(0.874385\pi\) | |||||||
\(72\) | −29406.9 | + | 29406.9i | −0.0787866 | + | 0.0787866i | ||||
\(73\) | 390480. | − | 390480.i | 1.00376 | − | 1.00376i | 0.00376728 | − | 0.999993i | \(-0.498801\pi\) |
0.999993 | − | 0.00376728i | \(-0.00119916\pi\) | |||||||
\(74\) | 36475.9 | 0.0900143 | ||||||||
\(75\) | 386248.i | 0.915551i | ||||||||
\(76\) | 258268. | − | 258268.i | 0.588342 | − | 0.588342i | ||||
\(77\) | 866741.i | 1.89853i | ||||||||
\(78\) | 20504.2 | − | 29105.7i | 0.0432076 | − | 0.0613330i | ||||
\(79\) | −531901. | −1.07882 | −0.539411 | − | 0.842043i | \(-0.681353\pi\) | ||||
−0.539411 | + | 0.842043i | \(0.681353\pi\) | |||||||
\(80\) | −532096. | − | 532096.i | −1.03925 | − | 1.03925i | ||||
\(81\) | −113157. | −0.212925 | ||||||||
\(82\) | − | 36096.9i | − | 0.0654679i | ||||||
\(83\) | 188950. | + | 188950.i | 0.330455 | + | 0.330455i | 0.852759 | − | 0.522305i | \(-0.174928\pi\) |
−0.522305 | + | 0.852759i | \(0.674928\pi\) | |||||||
\(84\) | −285903. | − | 285903.i | −0.482371 | − | 0.482371i | ||||
\(85\) | −106262. | + | 106262.i | −0.173029 | + | 0.173029i | ||||
\(86\) | −20508.9 | + | 20508.9i | −0.0322439 | + | 0.0322439i | ||||
\(87\) | 129549. | 0.196733 | ||||||||
\(88\) | 279608.i | 0.410300i | ||||||||
\(89\) | −45096.2 | + | 45096.2i | −0.0639691 | + | 0.0639691i | −0.738368 | − | 0.674398i | \(-0.764403\pi\) |
0.674398 | + | 0.738368i | \(0.264403\pi\) | |||||||
\(90\) | − | 62213.3i | − | 0.0853406i | ||||||
\(91\) | −612719. | − | 431645.i | −0.813087 | − | 0.572800i | ||||
\(92\) | 90632.4 | 0.116391 | ||||||||
\(93\) | −222764. | − | 222764.i | −0.276947 | − | 0.276947i | ||||
\(94\) | 94006.6 | 0.113181 | ||||||||
\(95\) | 1.09925e6i | 1.28211i | ||||||||
\(96\) | −138618. | − | 138618.i | −0.156678 | − | 0.156678i | ||||
\(97\) | 730591. | + | 730591.i | 0.800496 | + | 0.800496i | 0.983173 | − | 0.182677i | \(-0.0584762\pi\) |
−0.182677 | + | 0.983173i | \(0.558476\pi\) | |||||||
\(98\) | −776.232 | + | 776.232i | −0.000824732 | + | 0.000824732i | ||||
\(99\) | 678894. | − | 678894.i | 0.699675 | − | 0.699675i | ||||
\(100\) | 1.30383e6 | 1.30383 | ||||||||
\(101\) | − | 957084.i | − | 0.928937i | −0.885590 | − | 0.464468i | \(-0.846245\pi\) | ||
0.885590 | − | 0.464468i | \(-0.153755\pi\) | |||||||
\(102\) | −9045.83 | + | 9045.83i | −0.00852409 | + | 0.00852409i | ||||
\(103\) | − | 1.00285e6i | − | 0.917746i | −0.888502 | − | 0.458873i | \(-0.848253\pi\) | ||
0.888502 | − | 0.458873i | \(-0.151747\pi\) | |||||||
\(104\) | −197661. | − | 139247.i | −0.175720 | − | 0.123790i | ||||
\(105\) | 1.21687e6 | 1.05118 | ||||||||
\(106\) | 87179.4 | + | 87179.4i | 0.0731975 | + | 0.0731975i | ||||
\(107\) | −949187. | −0.774820 | −0.387410 | − | 0.921908i | \(-0.626630\pi\) | ||||
−0.387410 | + | 0.921908i | \(0.626630\pi\) | |||||||
\(108\) | 1.31190e6i | 1.04143i | ||||||||
\(109\) | 850682. | + | 850682.i | 0.656882 | + | 0.656882i | 0.954641 | − | 0.297759i | \(-0.0962391\pi\) |
−0.297759 | + | 0.954641i | \(0.596239\pi\) | |||||||
\(110\) | −295769. | − | 295769.i | −0.222216 | − | 0.222216i | ||||
\(111\) | 558829. | − | 558829.i | 0.408611 | − | 0.408611i | ||||
\(112\) | −953554. | + | 953554.i | −0.678721 | + | 0.678721i | ||||
\(113\) | −2.43128e6 | −1.68500 | −0.842498 | − | 0.538699i | \(-0.818916\pi\) | ||||
−0.842498 | + | 0.538699i | \(0.818916\pi\) | |||||||
\(114\) | 93576.4i | 0.0631614i | ||||||||
\(115\) | −192876. | + | 192876.i | −0.126819 | + | 0.126819i | ||||
\(116\) | − | 437308.i | − | 0.280165i | ||||||
\(117\) | 141830. | + | 818021.i | 0.0885544 | + | 0.510749i | ||||
\(118\) | −100941. | −0.0614357 | ||||||||
\(119\) | 190429. | + | 190429.i | 0.113003 | + | 0.113003i | ||||
\(120\) | 392557. | 0.227174 | ||||||||
\(121\) | − | 4.68352e6i | − | 2.64372i | ||||||
\(122\) | 187106. | + | 187106.i | 0.103040 | + | 0.103040i | ||||
\(123\) | −553022. | − | 553022.i | −0.297185 | − | 0.297185i | ||||
\(124\) | −751966. | + | 751966.i | −0.394397 | + | 0.394397i | ||||
\(125\) | −671447. | + | 671447.i | −0.343781 | + | 0.343781i | ||||
\(126\) | −111491. | −0.0557349 | ||||||||
\(127\) | 2.27446e6i | 1.11037i | 0.831728 | + | 0.555184i | \(0.187352\pi\) | ||||
−0.831728 | + | 0.555184i | \(0.812648\pi\) | |||||||
\(128\) | −622634. | + | 622634.i | −0.296895 | + | 0.296895i | ||||
\(129\) | 628413.i | 0.292736i | ||||||||
\(130\) | 356382. | − | 61790.1i | 0.162213 | − | 0.0281248i | ||||
\(131\) | −1.76457e6 | −0.784919 | −0.392460 | − | 0.919769i | \(-0.628376\pi\) | ||||
−0.392460 | + | 0.919769i | \(0.628376\pi\) | |||||||
\(132\) | 2.12927e6 | + | 2.12927e6i | 0.925784 | + | 0.925784i | ||||
\(133\) | 1.96993e6 | 0.837327 | ||||||||
\(134\) | 64897.7i | 0.0269721i | ||||||||
\(135\) | −2.79186e6 | − | 2.79186e6i | −1.13473 | − | 1.13473i | ||||
\(136\) | 61431.6 | + | 61431.6i | 0.0244217 | + | 0.0244217i | ||||
\(137\) | 136280. | − | 136280.i | 0.0529994 | − | 0.0529994i | −0.680110 | − | 0.733110i | \(-0.738068\pi\) |
0.733110 | + | 0.680110i | \(0.238068\pi\) | |||||||
\(138\) | −16419.1 | + | 16419.1i | −0.00624758 | + | 0.00624758i | ||||
\(139\) | 960906. | 0.357797 | 0.178898 | − | 0.983868i | \(-0.442747\pi\) | ||||
0.178898 | + | 0.983868i | \(0.442747\pi\) | |||||||
\(140\) | − | 4.10768e6i | − | 1.49697i | ||||||
\(141\) | 1.44023e6 | − | 1.44023e6i | 0.513775 | − | 0.513775i | ||||
\(142\) | − | 235803.i | − | 0.0823538i | ||||||
\(143\) | 4.56324e6 | + | 3.21469e6i | 1.56051 | + | 1.09934i | ||||
\(144\) | 1.49378e6 | 0.500265 | ||||||||
\(145\) | 930639. | + | 930639.i | 0.305265 | + | 0.305265i | ||||
\(146\) | 477581. | 0.153458 | ||||||||
\(147\) | 23784.5i | 0.00748758i | ||||||||
\(148\) | −1.88639e6 | − | 1.88639e6i | −0.581899 | − | 0.581899i | ||||
\(149\) | 2.10179e6 | + | 2.10179e6i | 0.635374 | + | 0.635374i | 0.949411 | − | 0.314036i | \(-0.101681\pi\) |
−0.314036 | + | 0.949411i | \(0.601681\pi\) | |||||||
\(150\) | −236203. | + | 236203.i | −0.0699860 | + | 0.0699860i | ||||
\(151\) | −3.16039e6 | + | 3.16039e6i | −0.917930 | + | 0.917930i | −0.996879 | − | 0.0789491i | \(-0.974844\pi\) |
0.0789491 | + | 0.996879i | \(0.474844\pi\) | |||||||
\(152\) | 635492. | 0.180959 | ||||||||
\(153\) | − | 298315.i | − | 0.0832915i | ||||||
\(154\) | −530039. | + | 530039.i | −0.145126 | + | 0.145126i | ||||
\(155\) | − | 3.20053e6i | − | 0.859462i | ||||||
\(156\) | −2.56563e6 | + | 444834.i | −0.675804 | + | 0.117172i | ||||
\(157\) | −2.14207e6 | −0.553522 | −0.276761 | − | 0.960939i | \(-0.589261\pi\) | ||||
−0.276761 | + | 0.960939i | \(0.589261\pi\) | |||||||
\(158\) | −325274. | − | 325274.i | −0.0824667 | − | 0.0824667i | ||||
\(159\) | 2.67126e6 | 0.664546 | ||||||||
\(160\) | − | 1.99158e6i | − | 0.486226i | ||||||
\(161\) | 345647. | + | 345647.i | 0.0828238 | + | 0.0828238i | ||||
\(162\) | −69199.3 | − | 69199.3i | −0.0162763 | − | 0.0162763i | ||||
\(163\) | 1.17045e6 | − | 1.17045e6i | 0.270266 | − | 0.270266i | −0.558941 | − | 0.829207i | \(-0.688792\pi\) |
0.829207 | + | 0.558941i | \(0.188792\pi\) | |||||||
\(164\) | −1.86679e6 | + | 1.86679e6i | −0.423218 | + | 0.423218i | ||||
\(165\) | −9.06265e6 | −2.01745 | ||||||||
\(166\) | 231097.i | 0.0505208i | ||||||||
\(167\) | 471034. | − | 471034.i | 0.101135 | − | 0.101135i | −0.654729 | − | 0.755864i | \(-0.727217\pi\) |
0.755864 | + | 0.654729i | \(0.227217\pi\) | |||||||
\(168\) | − | 703491.i | − | 0.148365i | ||||||
\(169\) | −4.54508e6 | + | 1.62491e6i | −0.941632 | + | 0.336643i | ||||
\(170\) | −129965. | −0.0264532 | ||||||||
\(171\) | −1.54299e6 | − | 1.54299e6i | −0.308585 | − | 0.308585i | ||||
\(172\) | 2.12128e6 | 0.416882 | ||||||||
\(173\) | 7.65909e6i | 1.47924i | 0.673025 | + | 0.739620i | \(0.264995\pi\) | ||||
−0.673025 | + | 0.739620i | \(0.735005\pi\) | |||||||
\(174\) | 79223.3 | + | 79223.3i | 0.0150385 | + | 0.0150385i | ||||
\(175\) | 4.97243e6 | + | 4.97243e6i | 0.927801 | + | 0.927801i | ||||
\(176\) | 7.10162e6 | − | 7.10162e6i | 1.30263 | − | 1.30263i | ||||
\(177\) | −1.54646e6 | + | 1.54646e6i | −0.278881 | + | 0.278881i | ||||
\(178\) | −55155.5 | −0.00977978 | ||||||||
\(179\) | − | 1.06052e6i | − | 0.184910i | −0.995717 | − | 0.0924552i | \(-0.970529\pi\) | ||
0.995717 | − | 0.0924552i | \(-0.0294715\pi\) | |||||||
\(180\) | −3.21743e6 | + | 3.21743e6i | −0.551686 | + | 0.551686i | ||||
\(181\) | − | 1.01426e7i | − | 1.71046i | −0.518253 | − | 0.855228i | \(-0.673417\pi\) | ||
0.518253 | − | 0.855228i | \(-0.326583\pi\) | |||||||
\(182\) | −110732. | − | 638662.i | −0.0183679 | − | 0.105939i | ||||
\(183\) | 5.73310e6 | 0.935483 | ||||||||
\(184\) | 111505. | + | 111505.i | 0.0178994 | + | 0.0178994i | ||||
\(185\) | 8.02890e6 | 1.26806 | ||||||||
\(186\) | − | 272454.i | − | 0.0423404i | ||||||
\(187\) | −1.41822e6 | − | 1.41822e6i | −0.216880 | − | 0.216880i | ||||
\(188\) | −4.86165e6 | − | 4.86165e6i | −0.731662 | − | 0.731662i | ||||
\(189\) | −5.00322e6 | + | 5.00322e6i | −0.741078 | + | 0.741078i | ||||
\(190\) | −672223. | + | 672223.i | −0.0980060 | + | 0.0980060i | ||||
\(191\) | 6.10706e6 | 0.876460 | 0.438230 | − | 0.898863i | \(-0.355606\pi\) | ||||
0.438230 | + | 0.898863i | \(0.355606\pi\) | |||||||
\(192\) | 4.57095e6i | 0.645807i | ||||||||
\(193\) | −1.87431e6 | + | 1.87431e6i | −0.260717 | + | 0.260717i | −0.825345 | − | 0.564628i | \(-0.809020\pi\) |
0.564628 | + | 0.825345i | \(0.309020\pi\) | |||||||
\(194\) | 893559.i | 0.122382i | ||||||||
\(195\) | 4.51329e6 | − | 6.40660e6i | 0.608680 | − | 0.864019i | ||||
\(196\) | 80287.4 | 0.0106630 | ||||||||
\(197\) | 3.59068e6 | + | 3.59068e6i | 0.469654 | + | 0.469654i | 0.901802 | − | 0.432148i | \(-0.142244\pi\) |
−0.432148 | + | 0.901802i | \(0.642244\pi\) | |||||||
\(198\) | 830330. | 0.106968 | ||||||||
\(199\) | 2.17903e6i | 0.276506i | 0.990397 | + | 0.138253i | \(0.0441487\pi\) | ||||
−0.990397 | + | 0.138253i | \(0.955851\pi\) | |||||||
\(200\) | 1.60409e6 | + | 1.60409e6i | 0.200511 | + | 0.200511i | ||||
\(201\) | 994263. | + | 994263.i | 0.122437 | + | 0.122437i | ||||
\(202\) | 585287. | − | 585287.i | 0.0710092 | − | 0.0710092i | ||||
\(203\) | 1.66777e6 | − | 1.66777e6i | 0.199365 | − | 0.199365i | ||||
\(204\) | 935631. | 0.110208 | ||||||||
\(205\) | − | 7.94546e6i | − | 0.922269i | ||||||
\(206\) | 613272. | − | 613272.i | 0.0701538 | − | 0.0701538i | ||||
\(207\) | − | 541471.i | − | 0.0610470i | ||||||
\(208\) | 1.48362e6 | + | 8.55698e6i | 0.164867 | + | 0.950890i | ||||
\(209\) | −1.46711e7 | −1.60703 | ||||||||
\(210\) | 744152. | + | 744152.i | 0.0803533 | + | 0.0803533i | ||||
\(211\) | −1.24296e7 | −1.32315 | −0.661574 | − | 0.749880i | \(-0.730111\pi\) | ||||
−0.661574 | + | 0.749880i | \(0.730111\pi\) | |||||||
\(212\) | − | 9.01716e6i | − | 0.946373i | ||||||
\(213\) | −3.61261e6 | − | 3.61261e6i | −0.373837 | − | 0.373837i | ||||
\(214\) | −580458. | − | 580458.i | −0.0592283 | − | 0.0592283i | ||||
\(215\) | −4.51432e6 | + | 4.51432e6i | −0.454231 | + | 0.454231i | ||||
\(216\) | −1.61402e6 | + | 1.61402e6i | −0.160158 | + | 0.160158i | ||||
\(217\) | −5.73558e6 | −0.561304 | ||||||||
\(218\) | 1.04044e6i | 0.100426i | ||||||||
\(219\) | 7.31678e6 | − | 7.31678e6i | 0.696606 | − | 0.696606i | ||||
\(220\) | 3.05921e7i | 2.87303i | ||||||||
\(221\) | 1.70886e6 | − | 296285.i | 0.158318 | − | 0.0274494i | ||||
\(222\) | 683483. | 0.0624696 | ||||||||
\(223\) | −8.35639e6 | − | 8.35639e6i | −0.753537 | − | 0.753537i | 0.221601 | − | 0.975137i | \(-0.428872\pi\) |
−0.975137 | + | 0.221601i | \(0.928872\pi\) | |||||||
\(224\) | −3.56905e6 | −0.317548 | ||||||||
\(225\) | − | 7.78953e6i | − | 0.683855i | ||||||
\(226\) | −1.48680e6 | − | 1.48680e6i | −0.128804 | − | 0.128804i | ||||
\(227\) | 540807. | + | 540807.i | 0.0462343 | + | 0.0462343i | 0.729846 | − | 0.683612i | \(-0.239592\pi\) |
−0.683612 | + | 0.729846i | \(0.739592\pi\) | |||||||
\(228\) | 4.83941e6 | − | 4.83941e6i | 0.408308 | − | 0.408308i | ||||
\(229\) | 1.52151e7 | − | 1.52151e7i | 1.26697 | − | 1.26697i | 0.319332 | − | 0.947643i | \(-0.396542\pi\) |
0.947643 | − | 0.319332i | \(-0.103458\pi\) | |||||||
\(230\) | −235899. | −0.0193884 | ||||||||
\(231\) | 1.62409e7i | 1.31757i | ||||||||
\(232\) | 538018. | − | 538018.i | 0.0430857 | − | 0.0430857i | ||||
\(233\) | − | 1.83092e6i | − | 0.144744i | −0.997378 | − | 0.0723720i | \(-0.976943\pi\) | ||
0.997378 | − | 0.0723720i | \(-0.0230569\pi\) | |||||||
\(234\) | −413512. | + | 586979.i | −0.0322731 | + | 0.0458116i | ||||
\(235\) | 2.06922e7 | 1.59442 | ||||||||
\(236\) | 5.22026e6 | + | 5.22026e6i | 0.397152 | + | 0.397152i | ||||
\(237\) | −9.96672e6 | −0.748699 | ||||||||
\(238\) | 232906.i | 0.0172763i | ||||||||
\(239\) | 9.23971e6 | + | 9.23971e6i | 0.676806 | + | 0.676806i | 0.959276 | − | 0.282470i | \(-0.0911537\pi\) |
−0.282470 | + | 0.959276i | \(0.591154\pi\) | |||||||
\(240\) | −9.97037e6 | − | 9.97037e6i | −0.721236 | − | 0.721236i | ||||
\(241\) | −1.23613e7 | + | 1.23613e7i | −0.883107 | + | 0.883107i | −0.993849 | − | 0.110743i | \(-0.964677\pi\) |
0.110743 | + | 0.993849i | \(0.464677\pi\) | |||||||
\(242\) | 2.86412e6 | − | 2.86412e6i | 0.202090 | − | 0.202090i | ||||
\(243\) | 1.29997e7 | 0.905973 | ||||||||
\(244\) | − | 1.93527e7i | − | 1.33221i | ||||||
\(245\) | −170860. | + | 170860.i | −0.0116183 | + | 0.0116183i | ||||
\(246\) | − | 676380.i | − | 0.0454345i | ||||||
\(247\) | 7.30634e6 | − | 1.03713e7i | 0.484852 | − | 0.688245i | ||||
\(248\) | −1.85028e6 | −0.121306 | ||||||||
\(249\) | 3.54052e6 | + | 3.54052e6i | 0.229334 | + | 0.229334i | ||||
\(250\) | −821222. | −0.0525582 | ||||||||
\(251\) | 1.03150e7i | 0.652300i | 0.945318 | + | 0.326150i | \(0.105752\pi\) | ||||
−0.945318 | + | 0.326150i | \(0.894248\pi\) | |||||||
\(252\) | 5.76586e6 | + | 5.76586e6i | 0.360299 | + | 0.360299i | ||||
\(253\) | −2.57421e6 | − | 2.57421e6i | −0.158958 | − | 0.158958i | ||||
\(254\) | −1.39090e6 | + | 1.39090e6i | −0.0848780 | + | 0.0848780i | ||||
\(255\) | −1.99112e6 | + | 1.99112e6i | −0.120082 | + | 0.120082i | ||||
\(256\) | 1.48507e7 | 0.885172 | ||||||||
\(257\) | 1.57226e7i | 0.926244i | 0.886294 | + | 0.463122i | \(0.153271\pi\) | ||||
−0.886294 | + | 0.463122i | \(0.846729\pi\) | |||||||
\(258\) | −384294. | + | 384294.i | −0.0223771 | + | 0.0223771i | ||||
\(259\) | − | 1.43884e7i | − | 0.828156i | ||||||
\(260\) | −2.16262e7 | − | 1.52351e7i | −1.23044 | − | 0.866815i | ||||
\(261\) | −2.61264e6 | −0.146946 | ||||||||
\(262\) | −1.07909e6 | − | 1.07909e6i | −0.0600004 | − | 0.0600004i | ||||
\(263\) | −2.43214e7 | −1.33697 | −0.668484 | − | 0.743727i | \(-0.733056\pi\) | ||||
−0.668484 | + | 0.743727i | \(0.733056\pi\) | |||||||
\(264\) | 5.23927e6i | 0.284747i | ||||||||
\(265\) | 1.91895e7 | + | 1.91895e7i | 1.03116 | + | 1.03116i | ||||
\(266\) | 1.20467e6 | + | 1.20467e6i | 0.0640064 | + | 0.0640064i | ||||
\(267\) | −845009. | + | 845009.i | −0.0443943 | + | 0.0443943i | ||||
\(268\) | 3.35626e6 | − | 3.35626e6i | 0.174361 | − | 0.174361i | ||||
\(269\) | −974208. | −0.0500489 | −0.0250245 | − | 0.999687i | \(-0.507966\pi\) | ||||
−0.0250245 | + | 0.999687i | \(0.507966\pi\) | |||||||
\(270\) | − | 3.41462e6i | − | 0.173481i | ||||||
\(271\) | −8.06718e6 | + | 8.06718e6i | −0.405335 | + | 0.405335i | −0.880108 | − | 0.474773i | \(-0.842530\pi\) |
0.474773 | + | 0.880108i | \(0.342530\pi\) | |||||||
\(272\) | − | 3.12054e6i | − | 0.155069i | ||||||
\(273\) | −1.14811e7 | − | 8.08813e6i | −0.564280 | − | 0.397521i | ||||
\(274\) | 166679. | 0.00810270 | ||||||||
\(275\) | −3.70323e7 | − | 3.70323e7i | −1.78067 | − | 1.78067i | ||||
\(276\) | 1.69826e6 | 0.0807751 | ||||||||
\(277\) | 1.85917e7i | 0.874741i | 0.899281 | + | 0.437371i | \(0.144090\pi\) | ||||
−0.899281 | + | 0.437371i | \(0.855910\pi\) | |||||||
\(278\) | 587624. | + | 587624.i | 0.0273505 | + | 0.0273505i | ||||
\(279\) | 4.49252e6 | + | 4.49252e6i | 0.206860 | + | 0.206860i | ||||
\(280\) | 5.05365e6 | − | 5.05365e6i | 0.230214 | − | 0.230214i | ||||
\(281\) | 1.38680e7 | − | 1.38680e7i | 0.625020 | − | 0.625020i | −0.321791 | − | 0.946811i | \(-0.604285\pi\) |
0.946811 | + | 0.321791i | \(0.104285\pi\) | |||||||
\(282\) | 1.76149e6 | 0.0785474 | ||||||||
\(283\) | 2.29361e7i | 1.01195i | 0.862547 | + | 0.505976i | \(0.168868\pi\) | ||||
−0.862547 | + | 0.505976i | \(0.831132\pi\) | |||||||
\(284\) | −1.21948e7 | + | 1.21948e7i | −0.532377 | + | 0.532377i | ||||
\(285\) | 2.05976e7i | 0.889777i | ||||||||
\(286\) | 824681. | + | 4.75645e6i | 0.0352524 | + | 0.203322i | ||||
\(287\) | −1.42388e7 | −0.602322 | ||||||||
\(288\) | 2.79554e6 | + | 2.79554e6i | 0.117028 | + | 0.117028i | ||||
\(289\) | 2.35144e7 | 0.974182 | ||||||||
\(290\) | 1.13823e6i | 0.0466698i | ||||||||
\(291\) | 1.36898e7 | + | 1.36898e7i | 0.555542 | + | 0.555542i | ||||
\(292\) | −2.46986e7 | − | 2.46986e7i | −0.992030 | − | 0.992030i | ||||
\(293\) | 4.68843e6 | − | 4.68843e6i | 0.186391 | − | 0.186391i | −0.607743 | − | 0.794134i | \(-0.707925\pi\) |
0.794134 | + | 0.607743i | \(0.207925\pi\) | |||||||
\(294\) | −14545.0 | + | 14545.0i | −0.000572362 | + | 0.000572362i | ||||
\(295\) | −2.22186e7 | −0.865466 | ||||||||
\(296\) | − | 4.64164e6i | − | 0.178977i | ||||||
\(297\) | 3.72616e7 | − | 3.72616e7i | 1.42230 | − | 1.42230i | ||||
\(298\) | 2.57062e6i | 0.0971379i | ||||||||
\(299\) | 3.10176e6 | − | 537788.i | 0.116036 | − | 0.0201186i | ||||
\(300\) | 2.44310e7 | 0.904852 | ||||||||
\(301\) | 8.08998e6 | + | 8.08998e6i | 0.296652 | + | 0.296652i | ||||
\(302\) | −3.86535e6 | −0.140336 | ||||||||
\(303\) | − | 1.79338e7i | − | 0.644679i | ||||||
\(304\) | −1.61405e7 | − | 1.61405e7i | −0.574510 | − | 0.574510i | ||||
\(305\) | 4.11847e7 | + | 4.11847e7i | 1.45157 | + | 1.45157i | ||||
\(306\) | 182429. | − | 182429.i | 0.00636692 | − | 0.00636692i | ||||
\(307\) | 2.66439e7 | − | 2.66439e7i | 0.920838 | − | 0.920838i | −0.0762504 | − | 0.997089i | \(-0.524295\pi\) |
0.997089 | + | 0.0762504i | \(0.0242948\pi\) | |||||||
\(308\) | 5.48231e7 | 1.87634 | ||||||||
\(309\) | − | 1.87912e7i | − | 0.636913i | ||||||
\(310\) | 1.95723e6 | − | 1.95723e6i | 0.0656985 | − | 0.0656985i | ||||
\(311\) | 4.76858e7i | 1.58529i | 0.609685 | + | 0.792644i | \(0.291296\pi\) | ||||
−0.609685 | + | 0.792644i | \(0.708704\pi\) | |||||||
\(312\) | −3.70376e6 | − | 2.60921e6i | −0.121949 | − | 0.0859102i | ||||
\(313\) | −3.30144e7 | −1.07664 | −0.538320 | − | 0.842741i | \(-0.680941\pi\) | ||||
−0.538320 | + | 0.842741i | \(0.680941\pi\) | |||||||
\(314\) | −1.30994e6 | − | 1.30994e6i | −0.0423120 | − | 0.0423120i | ||||
\(315\) | −2.45408e7 | −0.785157 | ||||||||
\(316\) | 3.36438e7i | 1.06621i | ||||||||
\(317\) | −4.35163e7 | − | 4.35163e7i | −1.36607 | − | 1.36607i | −0.865961 | − | 0.500112i | \(-0.833292\pi\) |
−0.500112 | − | 0.865961i | \(-0.666708\pi\) | |||||||
\(318\) | 1.63356e6 | + | 1.63356e6i | 0.0507989 | + | 0.0507989i | ||||
\(319\) | −1.24208e7 | + | 1.24208e7i | −0.382628 | + | 0.382628i | ||||
\(320\) | −3.28362e7 | + | 3.28362e7i | −1.00208 | + | 1.00208i | ||||
\(321\) | −1.77858e7 | −0.537722 | ||||||||
\(322\) | 422748.i | 0.0126623i | ||||||||
\(323\) | −3.22333e6 | + | 3.22333e6i | −0.0956527 | + | 0.0956527i | ||||
\(324\) | 7.15743e6i | 0.210437i | ||||||||
\(325\) | 4.46215e7 | − | 7.73655e6i | 1.29985 | − | 0.225370i | ||||
\(326\) | 1.43154e6 | 0.0413190 | ||||||||
\(327\) | 1.59400e7 | + | 1.59400e7i | 0.455874 | + | 0.455874i | ||||
\(328\) | −4.59340e6 | −0.130171 | ||||||||
\(329\) | − | 3.70820e7i | − | 1.04130i | ||||||
\(330\) | −5.54209e6 | − | 5.54209e6i | −0.154217 | − | 0.154217i | ||||
\(331\) | −3.16932e7 | − | 3.16932e7i | −0.873940 | − | 0.873940i | 0.118959 | − | 0.992899i | \(-0.462044\pi\) |
−0.992899 | + | 0.118959i | \(0.962044\pi\) | |||||||
\(332\) | 1.19515e7 | − | 1.19515e7i | 0.326593 | − | 0.326593i | ||||
\(333\) | −1.12700e7 | + | 1.12700e7i | −0.305205 | + | 0.305205i | ||||
\(334\) | 576105. | 0.0154619 | ||||||||
\(335\) | 1.42849e7i | 0.379965i | ||||||||
\(336\) | −1.78676e7 | + | 1.78676e7i | −0.471030 | + | 0.471030i | ||||
\(337\) | − | 4.31706e7i | − | 1.12797i | −0.825784 | − | 0.563986i | \(-0.809267\pi\) | ||
0.825784 | − | 0.563986i | \(-0.190733\pi\) | |||||||
\(338\) | −3.77314e6 | − | 1.78577e6i | −0.0977132 | − | 0.0462462i | ||||
\(339\) | −4.55571e7 | −1.16938 | ||||||||
\(340\) | 6.72127e6 | + | 6.72127e6i | 0.171007 | + | 0.171007i | ||||
\(341\) | 4.27159e7 | 1.07727 | ||||||||
\(342\) | − | 1.88717e6i | − | 0.0471773i | ||||||
\(343\) | 2.86862e7 | + | 2.86862e7i | 0.710870 | + | 0.710870i | ||||
\(344\) | 2.60980e6 | + | 2.60980e6i | 0.0641109 | + | 0.0641109i | ||||
\(345\) | −3.61409e6 | + | 3.61409e6i | −0.0880118 | + | 0.0880118i | ||||
\(346\) | −4.68377e6 | + | 4.68377e6i | −0.113075 | + | 0.113075i | ||||
\(347\) | −5.94985e7 | −1.42403 | −0.712013 | − | 0.702167i | \(-0.752216\pi\) | ||||
−0.712013 | + | 0.702167i | \(0.752216\pi\) | |||||||
\(348\) | − | 8.19425e6i | − | 0.194434i | ||||||
\(349\) | −3.01005e7 | + | 3.01005e7i | −0.708105 | + | 0.708105i | −0.966136 | − | 0.258032i | \(-0.916926\pi\) |
0.258032 | + | 0.966136i | \(0.416926\pi\) | |||||||
\(350\) | 6.08160e6i | 0.141845i | ||||||||
\(351\) | 7.78445e6 | + | 4.48977e7i | 0.180014 | + | 1.03825i | ||||
\(352\) | 2.65806e7 | 0.609449 | ||||||||
\(353\) | 1.53500e7 | + | 1.53500e7i | 0.348966 | + | 0.348966i | 0.859725 | − | 0.510758i | \(-0.170635\pi\) |
−0.510758 | + | 0.859725i | \(0.670635\pi\) | |||||||
\(354\) | −1.89142e6 | −0.0426361 | ||||||||
\(355\) | − | 5.19037e7i | − | 1.16015i | ||||||
\(356\) | 2.85243e6 | + | 2.85243e6i | 0.0632215 | + | 0.0632215i | ||||
\(357\) | 3.56823e6 | + | 3.56823e6i | 0.0784239 | + | 0.0784239i | ||||
\(358\) | 648544. | − | 648544.i | 0.0141348 | − | 0.0141348i | ||||
\(359\) | 2.38598e7 | − | 2.38598e7i | 0.515685 | − | 0.515685i | −0.400578 | − | 0.916263i | \(-0.631191\pi\) |
0.916263 | + | 0.400578i | \(0.131191\pi\) | |||||||
\(360\) | −7.91677e6 | −0.169684 | ||||||||
\(361\) | − | 1.37015e7i | − | 0.291237i | ||||||
\(362\) | 6.20249e6 | − | 6.20249e6i | 0.130750 | − | 0.130750i | ||||
\(363\) | − | 8.77593e7i | − | 1.83473i | ||||||
\(364\) | −2.73025e7 | + | 3.87557e7i | −0.566106 | + | 0.803585i | ||||
\(365\) | 1.05123e8 | 2.16181 | ||||||||
\(366\) | 3.50597e6 | + | 3.50597e6i | 0.0715096 | + | 0.0715096i | ||||
\(367\) | 1.73262e6 | 0.0350514 | 0.0175257 | − | 0.999846i | \(-0.494421\pi\) | ||||
0.0175257 | + | 0.999846i | \(0.494421\pi\) | |||||||
\(368\) | − | 5.66410e6i | − | 0.113655i | ||||||
\(369\) | 1.11529e7 | + | 1.11529e7i | 0.221977 | + | 0.221977i | ||||
\(370\) | 4.90992e6 | + | 4.90992e6i | 0.0969325 | + | 0.0969325i | ||||
\(371\) | 3.43890e7 | − | 3.43890e7i | 0.673437 | − | 0.673437i | ||||
\(372\) | −1.40903e7 | + | 1.40903e7i | −0.273710 | + | 0.273710i | ||||
\(373\) | −2.27039e7 | −0.437496 | −0.218748 | − | 0.975781i | \(-0.570197\pi\) | ||||
−0.218748 | + | 0.975781i | \(0.570197\pi\) | |||||||
\(374\) | − | 1.73457e6i | − | 0.0331572i | ||||||
\(375\) | −1.25815e7 | + | 1.25815e7i | −0.238583 | + | 0.238583i | ||||
\(376\) | − | 1.19625e7i | − | 0.225040i | ||||||
\(377\) | −2.59487e6 | − | 1.49662e7i | −0.0484274 | − | 0.279311i | ||||
\(378\) | −6.11925e6 | −0.113298 | ||||||||
\(379\) | 2.57526e7 | + | 2.57526e7i | 0.473046 | + | 0.473046i | 0.902899 | − | 0.429853i | \(-0.141435\pi\) |
−0.429853 | + | 0.902899i | \(0.641435\pi\) | |||||||
\(380\) | 6.95295e7 | 1.26712 | ||||||||
\(381\) | 4.26186e7i | 0.770591i | ||||||||
\(382\) | 3.73466e6 | + | 3.73466e6i | 0.0669978 | + | 0.0669978i | ||||
\(383\) | 4.71374e7 | + | 4.71374e7i | 0.839014 | + | 0.839014i | 0.988729 | − | 0.149715i | \(-0.0478355\pi\) |
−0.149715 | + | 0.988729i | \(0.547836\pi\) | |||||||
\(384\) | −1.16669e7 | + | 1.16669e7i | −0.206044 | + | 0.206044i | ||||
\(385\) | −1.16670e8 | + | 1.16670e8i | −2.04444 | + | 2.04444i | ||||
\(386\) | −2.29240e6 | −0.0398592 | ||||||||
\(387\) | − | 1.26733e7i | − | 0.218654i | ||||||
\(388\) | 4.62114e7 | − | 4.62114e7i | 0.791141 | − | 0.791141i | ||||
\(389\) | − | 9.05585e7i | − | 1.53844i | −0.638985 | − | 0.769219i | \(-0.720645\pi\) | ||
0.638985 | − | 0.769219i | \(-0.279355\pi\) | |||||||
\(390\) | 6.67785e6 | − | 1.15782e6i | 0.112575 | − | 0.0195185i | ||||
\(391\) | −1.13114e6 | −0.0189229 | ||||||||
\(392\) | 98777.1 | + | 98777.1i | 0.00163983 | + | 0.00163983i | ||||
\(393\) | −3.30644e7 | −0.544732 | ||||||||
\(394\) | 4.39163e6i | 0.0718021i | ||||||||
\(395\) | −7.15977e7 | − | 7.15977e7i | −1.16174 | − | 1.16174i | ||||
\(396\) | −4.29414e7 | − | 4.29414e7i | −0.691498 | − | 0.691498i | ||||
\(397\) | −2.22106e7 | + | 2.22106e7i | −0.354968 | + | 0.354968i | −0.861954 | − | 0.506986i | \(-0.830760\pi\) |
0.506986 | + | 0.861954i | \(0.330760\pi\) | |||||||
\(398\) | −1.33255e6 | + | 1.33255e6i | −0.0211365 | + | 0.0211365i | ||||
\(399\) | 3.69123e7 | 0.581102 | ||||||||
\(400\) | − | 8.14830e7i | − | 1.27317i | ||||||
\(401\) | −1.67907e7 | + | 1.67907e7i | −0.260397 | + | 0.260397i | −0.825215 | − | 0.564819i | \(-0.808946\pi\) |
0.564819 | + | 0.825215i | \(0.308946\pi\) | |||||||
\(402\) | 1.21605e6i | 0.0187185i | ||||||||
\(403\) | −2.12729e7 | + | 3.01968e7i | −0.325022 | + | 0.461367i | ||||
\(404\) | −6.05376e7 | −0.918081 | ||||||||
\(405\) | −1.52318e7 | − | 1.52318e7i | −0.229290 | − | 0.229290i | ||||
\(406\) | 2.03979e6 | 0.0304795 | ||||||||
\(407\) | 1.07158e8i | 1.58943i | ||||||||
\(408\) | 1.15110e6 | + | 1.15110e6i | 0.0169486 | + | 0.0169486i | ||||
\(409\) | 3.72819e7 | + | 3.72819e7i | 0.544914 | + | 0.544914i | 0.924965 | − | 0.380051i | \(-0.124094\pi\) |
−0.380051 | + | 0.924965i | \(0.624094\pi\) | |||||||
\(410\) | 4.85890e6 | − | 4.85890e6i | 0.0704996 | − | 0.0704996i | ||||
\(411\) | 2.55361e6 | − | 2.55361e6i | 0.0367814 | − | 0.0367814i | ||||
\(412\) | −6.34321e7 | −0.907021 | ||||||||
\(413\) | 3.98173e7i | 0.565225i | ||||||||
\(414\) | 331126. | − | 331126.i | 0.00466652 | − | 0.00466652i | ||||
\(415\) | 5.08680e7i | 0.711705i | ||||||||
\(416\) | −1.32374e7 | + | 1.87905e7i | −0.183875 | + | 0.261010i | ||||
\(417\) | 1.80054e7 | 0.248310 | ||||||||
\(418\) | −8.97182e6 | − | 8.97182e6i | −0.122843 | − | 0.122843i | ||||
\(419\) | 8.72939e7 | 1.18670 | 0.593351 | − | 0.804944i | \(-0.297804\pi\) | ||||
0.593351 | + | 0.804944i | \(0.297804\pi\) | |||||||
\(420\) | − | 7.69693e7i | − | 1.03889i | ||||||
\(421\) | −5.41486e7 | − | 5.41486e7i | −0.725673 | − | 0.725673i | 0.244081 | − | 0.969755i | \(-0.421514\pi\) |
−0.969755 | + | 0.244081i | \(0.921514\pi\) | |||||||
\(422\) | −7.60106e6 | − | 7.60106e6i | −0.101143 | − | 0.101143i | ||||
\(423\) | −2.90453e7 | + | 2.90453e7i | −0.383755 | + | 0.383755i | ||||
\(424\) | 1.10938e7 | − | 1.10938e7i | 0.145540 | − | 0.145540i | ||||
\(425\) | −1.62725e7 | −0.211976 | ||||||||
\(426\) | − | 4.41845e6i | − | 0.0571532i | ||||||
\(427\) | 7.38060e7 | − | 7.38060e7i | 0.947999 | − | 0.947999i | ||||
\(428\) | 6.00381e7i | 0.765765i | ||||||||
\(429\) | 8.55056e7 | + | 6.02366e7i | 1.08299 | + | 0.762937i | ||||
\(430\) | −5.52129e6 | −0.0694441 | ||||||||
\(431\) | 3.81041e6 | + | 3.81041e6i | 0.0475926 | + | 0.0475926i | 0.730503 | − | 0.682910i | \(-0.239286\pi\) |
−0.682910 | + | 0.730503i | \(0.739286\pi\) | |||||||
\(432\) | 8.19875e7 | 1.01694 | ||||||||
\(433\) | − | 9.85826e7i | − | 1.21433i | −0.794576 | − | 0.607165i | \(-0.792307\pi\) | ||
0.794576 | − | 0.607165i | \(-0.207693\pi\) | |||||||
\(434\) | −3.50749e6 | − | 3.50749e6i | −0.0429069 | − | 0.0429069i | ||||
\(435\) | 1.74382e7 | + | 1.74382e7i | 0.211853 | + | 0.211853i | ||||
\(436\) | 5.38074e7 | − | 5.38074e7i | 0.649206 | − | 0.649206i | ||||
\(437\) | −5.85067e6 | + | 5.85067e6i | −0.0701069 | + | 0.0701069i | ||||
\(438\) | 8.94888e6 | 0.106499 | ||||||||
\(439\) | 5.14314e6i | 0.0607903i | 0.999538 | + | 0.0303952i | \(0.00967657\pi\) | ||||
−0.999538 | + | 0.0303952i | \(0.990323\pi\) | |||||||
\(440\) | −3.76372e7 | + | 3.76372e7i | −0.441834 | + | 0.441834i | ||||
\(441\) | − | 479666.i | − | 0.00559272i | ||||||
\(442\) | 1.22621e6 | + | 863835.i | 0.0142003 | + | 0.0100038i | ||||
\(443\) | −1.52839e8 | −1.75802 | −0.879008 | − | 0.476808i | \(-0.841794\pi\) | ||||
−0.879008 | + | 0.476808i | \(0.841794\pi\) | |||||||
\(444\) | −3.53471e7 | − | 3.53471e7i | −0.403836 | − | 0.403836i | ||||
\(445\) | −1.21406e7 | −0.137771 | ||||||||
\(446\) | − | 1.02204e7i | − | 0.115203i | ||||||
\(447\) | 3.93831e7 | + | 3.93831e7i | 0.440948 | + | 0.440948i | ||||
\(448\) | 5.88449e7 | + | 5.88449e7i | 0.654447 | + | 0.654447i | ||||
\(449\) | 8.12560e7 | − | 8.12560e7i | 0.897669 | − | 0.897669i | −0.0975605 | − | 0.995230i | \(-0.531104\pi\) |
0.995230 | + | 0.0975605i | \(0.0311039\pi\) | |||||||
\(450\) | 4.76354e6 | − | 4.76354e6i | 0.0522748 | − | 0.0522748i | ||||
\(451\) | 1.06044e8 | 1.15600 | ||||||||
\(452\) | 1.53783e8i | 1.66531i | ||||||||
\(453\) | −5.92190e7 | + | 5.92190e7i | −0.637040 | + | 0.637040i | ||||
\(454\) | 661441.i | 0.00706844i | ||||||||
\(455\) | −2.43738e7 | − | 1.40579e8i | −0.258755 | − | 1.49240i | ||||
\(456\) | 1.19078e7 | 0.125585 | ||||||||
\(457\) | 6.60613e7 | + | 6.60613e7i | 0.692148 | + | 0.692148i | 0.962704 | − | 0.270556i | \(-0.0872077\pi\) |
−0.270556 | + | 0.962704i | \(0.587208\pi\) | |||||||
\(458\) | 1.86090e7 | 0.193699 | ||||||||
\(459\) | − | 1.63732e7i | − | 0.169315i | ||||||
\(460\) | 1.21998e7 | + | 1.21998e7i | 0.125337 | + | 0.125337i | ||||
\(461\) | −7.29238e7 | − | 7.29238e7i | −0.744332 | − | 0.744332i | 0.229077 | − | 0.973408i | \(-0.426429\pi\) |
−0.973408 | + | 0.229077i | \(0.926429\pi\) | |||||||
\(462\) | −9.93183e6 | + | 9.93183e6i | −0.100717 | + | 0.100717i | ||||
\(463\) | 2.88794e7 | − | 2.88794e7i | 0.290968 | − | 0.290968i | −0.546495 | − | 0.837463i | \(-0.684038\pi\) |
0.837463 | + | 0.546495i | \(0.184038\pi\) | |||||||
\(464\) | −2.73297e7 | −0.273578 | ||||||||
\(465\) | − | 5.99713e7i | − | 0.596464i | ||||||
\(466\) | 1.11966e6 | − | 1.11966e6i | 0.0110644 | − | 0.0110644i | ||||
\(467\) | 2.98298e7i | 0.292886i | 0.989219 | + | 0.146443i | \(0.0467825\pi\) | ||||
−0.989219 | + | 0.146443i | \(0.953217\pi\) | |||||||
\(468\) | 5.17415e7 | − | 8.97104e6i | 0.504780 | − | 0.0875195i | ||||
\(469\) | 2.55996e7 | 0.248151 | ||||||||
\(470\) | 1.26540e7 | + | 1.26540e7i | 0.121880 | + | 0.121880i | ||||
\(471\) | −4.01379e7 | −0.384142 | ||||||||
\(472\) | 1.28449e7i | 0.122153i | ||||||||
\(473\) | −6.02503e7 | − | 6.02503e7i | −0.569346 | − | 0.569346i | ||||
\(474\) | −6.09496e6 | − | 6.09496e6i | −0.0572316 | − | 0.0572316i | ||||
\(475\) | −8.41670e7 | + | 8.41670e7i | −0.785346 | + | 0.785346i | ||||
\(476\) | 1.20450e7 | − | 1.20450e7i | 0.111683 | − | 0.111683i | ||||
\(477\) | −5.38718e7 | −0.496371 | ||||||||
\(478\) | 1.13007e7i | 0.103472i | ||||||||
\(479\) | −6.33389e7 | + | 6.33389e7i | −0.576320 | + | 0.576320i | −0.933887 | − | 0.357567i | \(-0.883606\pi\) |
0.357567 | + | 0.933887i | \(0.383606\pi\) | |||||||
\(480\) | − | 3.73181e7i | − | 0.337439i | ||||||
\(481\) | −7.57523e7 | − | 5.33656e7i | −0.680707 | − | 0.479541i | ||||
\(482\) | −1.51186e7 | −0.135012 | ||||||||
\(483\) | 6.47670e6 | + | 6.47670e6i | 0.0574794 | + | 0.0574794i | ||||
\(484\) | −2.96242e8 | −2.61283 | ||||||||
\(485\) | 1.96686e8i | 1.72404i | ||||||||
\(486\) | 7.94974e6 | + | 7.94974e6i | 0.0692539 | + | 0.0692539i | ||||
\(487\) | −4.86653e6 | − | 4.86653e6i | −0.0421340 | − | 0.0421340i | 0.685726 | − | 0.727860i | \(-0.259485\pi\) |
−0.727860 | + | 0.685726i | \(0.759485\pi\) | |||||||
\(488\) | 2.38096e7 | − | 2.38096e7i | 0.204876 | − | 0.204876i | ||||
\(489\) | 2.19318e7 | − | 2.19318e7i | 0.187564 | − | 0.187564i | ||||
\(490\) | −208973. | −0.00177624 | ||||||||
\(491\) | − | 1.92918e8i | − | 1.62977i | −0.579620 | − | 0.814887i | \(-0.696799\pi\) | ||
0.579620 | − | 0.814887i | \(-0.303201\pi\) | |||||||
\(492\) | −3.49798e7 | + | 3.49798e7i | −0.293712 | + | 0.293712i | ||||
\(493\) | 5.45785e6i | 0.0455492i | ||||||||
\(494\) | 1.08104e7 | − | 1.87433e6i | 0.0896732 | − | 0.0155477i | ||||
\(495\) | 1.82768e8 | 1.50690 | ||||||||
\(496\) | 4.69943e7 | + | 4.69943e7i | 0.385124 | + | 0.385124i | ||||
\(497\) | −9.30151e7 | −0.757677 | ||||||||
\(498\) | 4.33028e6i | 0.0350613i | ||||||||
\(499\) | 1.55886e8 | + | 1.55886e8i | 1.25460 | + | 1.25460i | 0.953636 | + | 0.300962i | \(0.0973077\pi\) |
0.300962 | + | 0.953636i | \(0.402692\pi\) | |||||||
\(500\) | 4.24704e7 | + | 4.24704e7i | 0.339763 | + | 0.339763i | ||||
\(501\) | 8.82620e6 | − | 8.82620e6i | 0.0701876 | − | 0.0701876i | ||||
\(502\) | −6.30794e6 | + | 6.30794e6i | −0.0498628 | + | 0.0498628i | ||||
\(503\) | 9.61748e6 | 0.0755714 | 0.0377857 | − | 0.999286i | \(-0.487970\pi\) | ||||
0.0377857 | + | 0.999286i | \(0.487970\pi\) | |||||||
\(504\) | 1.41874e7i | 0.110818i | ||||||||
\(505\) | 1.28830e8 | − | 1.28830e8i | 1.00033 | − | 1.00033i | ||||
\(506\) | − | 3.14843e6i | − | 0.0243020i | ||||||
\(507\) | −8.51653e7 | + | 3.04475e7i | −0.653490 | + | 0.233629i | ||||
\(508\) | 1.43864e8 | 1.09739 | ||||||||
\(509\) | −1.48532e8 | − | 1.48532e8i | −1.12633 | − | 1.12633i | −0.990769 | − | 0.135560i | \(-0.956717\pi\) |
−0.135560 | − | 0.990769i | \(-0.543283\pi\) | |||||||
\(510\) | −2.43527e6 | −0.0183585 | ||||||||
\(511\) | − | 1.88388e8i | − | 1.41185i | ||||||
\(512\) | 4.89302e7 | + | 4.89302e7i | 0.364559 | + | 0.364559i | ||||
\(513\) | −8.46881e7 | − | 8.46881e7i | −0.627293 | − | 0.627293i | ||||
\(514\) | −9.61487e6 | + | 9.61487e6i | −0.0708034 | + | 0.0708034i | ||||
\(515\) | 1.34990e8 | − | 1.34990e8i | 0.988282 | − | 0.988282i | ||||
\(516\) | 3.97484e7 | 0.289315 | ||||||||
\(517\) | 2.76169e8i | 1.99850i | ||||||||
\(518\) | 8.79893e6 | − | 8.79893e6i | 0.0633054 | − | 0.0633054i | ||||
\(519\) | 1.43515e8i | 1.02659i | ||||||||
\(520\) | −7.86292e6 | − | 4.53503e7i | −0.0559208 | − | 0.322530i | ||||
\(521\) | −1.16210e8 | −0.821731 | −0.410865 | − | 0.911696i | \(-0.634773\pi\) | ||||
−0.410865 | + | 0.911696i | \(0.634773\pi\) | |||||||
\(522\) | −1.59771e6 | − | 1.59771e6i | −0.0112328 | − | 0.0112328i | ||||
\(523\) | 1.16773e8 | 0.816274 | 0.408137 | − | 0.912921i | \(-0.366179\pi\) | ||||
0.408137 | + | 0.912921i | \(0.366179\pi\) | |||||||
\(524\) | 1.11613e8i | 0.775746i | ||||||||
\(525\) | 9.31730e7 | + | 9.31730e7i | 0.643891 | + | 0.643891i | ||||
\(526\) | −1.48733e7 | − | 1.48733e7i | −0.102200 | − | 0.102200i | ||||
\(527\) | 9.38496e6 | − | 9.38496e6i | 0.0641210 | − | 0.0641210i | ||||
\(528\) | 1.33070e8 | − | 1.33070e8i | 0.904018 | − | 0.904018i | ||||
\(529\) | 1.45983e8 | 0.986131 | ||||||||
\(530\) | 2.34700e7i | 0.157647i | ||||||||
\(531\) | 3.11877e7 | − | 3.11877e7i | 0.208305 | − | 0.208305i | ||||
\(532\) | − | 1.24602e8i | − | 0.827541i | ||||||
\(533\) | −5.28110e7 | + | 7.49651e7i | −0.348773 | + | 0.495082i | ||||
\(534\) | −1.03350e6 | −0.00678713 | ||||||||
\(535\) | −1.27767e8 | − | 1.27767e8i | −0.834370 | − | 0.834370i | ||||
\(536\) | 8.25836e6 | 0.0536290 | ||||||||
\(537\) | − | 1.98720e7i | − | 0.128327i | ||||||
\(538\) | −595759. | − | 595759.i | −0.00382581 | − | 0.00382581i | ||||
\(539\) | −2.28039e6 | − | 2.28039e6i | −0.0145627 | − | 0.0145627i | ||||
\(540\) | −1.76591e8 | + | 1.76591e8i | −1.12147 | + | 1.12147i | ||||
\(541\) | −5.07826e7 | + | 5.07826e7i | −0.320718 | + | 0.320718i | −0.849042 | − | 0.528325i | \(-0.822820\pi\) |
0.528325 | + | 0.849042i | \(0.322820\pi\) | |||||||
\(542\) | −9.86667e6 | −0.0619687 | ||||||||
\(543\) | − | 1.90050e8i | − | 1.18705i | ||||||
\(544\) | 5.83994e6 | − | 5.83994e6i | 0.0362753 | − | 0.0362753i | ||||
\(545\) | 2.29016e8i | 1.41474i | ||||||||
\(546\) | −2.07489e6 | − | 1.19672e7i | −0.0127473 | − | 0.0735215i | ||||
\(547\) | 3.77483e7 | 0.230640 | 0.115320 | − | 0.993328i | \(-0.463211\pi\) | ||||
0.115320 | + | 0.993328i | \(0.463211\pi\) | |||||||
\(548\) | −8.62000e6 | − | 8.62000e6i | −0.0523800 | − | 0.0523800i | ||||
\(549\) | −1.15620e8 | −0.698742 | ||||||||
\(550\) | − | 4.52929e7i | − | 0.272234i | ||||||
\(551\) | 2.82299e7 | + | 2.82299e7i | 0.168754 | + | 0.168754i | ||||
\(552\) | 2.08936e6 | + | 2.08936e6i | 0.0124221 | + | 0.0124221i | ||||
\(553\) | −1.28308e8 | + | 1.28308e8i | −0.758716 | + | 0.758716i | ||||
\(554\) | −1.13694e7 | + | 1.13694e7i | −0.0668665 | + | 0.0668665i | ||||
\(555\) | 1.50445e8 | 0.880032 | ||||||||
\(556\) | − | 6.07793e7i | − | 0.353615i | ||||||
\(557\) | 1.59658e8 | − | 1.59658e8i | 0.923903 | − | 0.923903i | −0.0733997 | − | 0.997303i | \(-0.523385\pi\) |
0.997303 | + | 0.0733997i | \(0.0233849\pi\) | |||||||
\(558\) | 5.49463e6i | 0.0316254i | ||||||||
\(559\) | 7.25976e7 | − | 1.25871e7i | 0.415611 | − | 0.0720593i | ||||
\(560\) | −2.56711e8 | −1.46177 | ||||||||
\(561\) | −2.65745e7 | − | 2.65745e7i | −0.150514 | − | 0.150514i | ||||
\(562\) | 1.69614e7 | 0.0955548 | ||||||||
\(563\) | 2.76920e8i | 1.55177i | 0.630872 | + | 0.775887i | \(0.282697\pi\) | ||||
−0.630872 | + | 0.775887i | \(0.717303\pi\) | |||||||
\(564\) | −9.10972e7 | − | 9.10972e7i | −0.507771 | − | 0.507771i | ||||
\(565\) | −3.27267e8 | − | 3.27267e8i | −1.81450 | − | 1.81450i | ||||
\(566\) | −1.40261e7 | + | 1.40261e7i | −0.0773551 | + | 0.0773551i | ||||
\(567\) | −2.72965e7 | + | 2.72965e7i | −0.149747 | + | 0.149747i | ||||
\(568\) | −3.00064e7 | −0.163745 | ||||||||
\(569\) | 2.43629e8i | 1.32249i | 0.750170 | + | 0.661245i | \(0.229971\pi\) | ||||
−0.750170 | + | 0.661245i | \(0.770029\pi\) | |||||||
\(570\) | −1.25961e7 | + | 1.25961e7i | −0.0680158 | + | 0.0680158i | ||||
\(571\) | 1.59255e8i | 0.855432i | 0.903913 | + | 0.427716i | \(0.140682\pi\) | ||||
−0.903913 | + | 0.427716i | \(0.859318\pi\) | |||||||
\(572\) | 2.03336e8 | − | 2.88634e8i | 1.08649 | − | 1.54227i | ||||
\(573\) | 1.14433e8 | 0.608260 | ||||||||
\(574\) | −8.70750e6 | − | 8.70750e6i | −0.0460424 | − | 0.0460424i | ||||
\(575\) | −2.95362e7 | −0.155364 | ||||||||
\(576\) | − | 9.21831e7i | − | 0.482374i | ||||||
\(577\) | −7.58084e6 | − | 7.58084e6i | −0.0394630 | − | 0.0394630i | 0.687100 | − | 0.726563i | \(-0.258883\pi\) |
−0.726563 | + | 0.687100i | \(0.758883\pi\) | |||||||
\(578\) | 1.43798e7 | + | 1.43798e7i | 0.0744679 | + | 0.0744679i | ||||
\(579\) | −3.51206e7 | + | 3.51206e7i | −0.180937 | + | 0.180937i | ||||
\(580\) | 5.88649e7 | − | 5.88649e7i | 0.301698 | − | 0.301698i | ||||
\(581\) | 9.11590e7 | 0.464805 | ||||||||
\(582\) | 1.67434e7i | 0.0849328i | ||||||||
\(583\) | −2.56113e8 | + | 2.56113e8i | −1.29248 | + | 1.29248i | ||||
\(584\) | − | 6.07732e7i | − | 0.305122i | ||||||
\(585\) | −9.10202e7 | + | 1.29203e8i | −0.454643 | + | 0.645364i | ||||
\(586\) | 5.73424e6 | 0.0284960 | ||||||||
\(587\) | 2.37473e7 | + | 2.37473e7i | 0.117409 | + | 0.117409i | 0.763370 | − | 0.645961i | \(-0.223543\pi\) |
−0.645961 | + | 0.763370i | \(0.723543\pi\) | |||||||
\(588\) | 1.50442e6 | 0.00740008 | ||||||||
\(589\) | − | 9.70845e7i | − | 0.475121i | ||||||
\(590\) | −1.35874e7 | − | 1.35874e7i | −0.0661575 | − | 0.0661575i | ||||
\(591\) | 6.72819e7 | + | 6.72819e7i | 0.325938 | + | 0.325938i | ||||
\(592\) | −1.17891e8 | + | 1.17891e8i | −0.568217 | + | 0.568217i | ||||
\(593\) | 7.15224e7 | − | 7.15224e7i | 0.342987 | − | 0.342987i | −0.514502 | − | 0.857489i | \(-0.672023\pi\) |
0.857489 | + | 0.514502i | \(0.172023\pi\) | |||||||
\(594\) | 4.55733e7 | 0.217446 | ||||||||
\(595\) | 5.12661e7i | 0.243377i | ||||||||
\(596\) | 1.32942e8 | − | 1.32942e8i | 0.627949 | − | 0.627949i | ||||
\(597\) | 4.08305e7i | 0.191894i | ||||||||
\(598\) | 2.22569e6 | + | 1.56795e6i | 0.0104079 | + | 0.00733209i | ||||
\(599\) | −4.67139e7 | −0.217353 | −0.108677 | − | 0.994077i | \(-0.534661\pi\) | ||||
−0.108677 | + | 0.994077i | \(0.534661\pi\) | |||||||
\(600\) | 3.00573e7 | + | 3.00573e7i | 0.139154 | + | 0.139154i | ||||
\(601\) | 4.90865e7 | 0.226120 | 0.113060 | − | 0.993588i | \(-0.463935\pi\) | ||||
0.113060 | + | 0.993588i | \(0.463935\pi\) | |||||||
\(602\) | 9.89455e6i | 0.0453531i | ||||||||
\(603\) | −2.00515e7 | − | 2.00515e7i | −0.0914523 | − | 0.0914523i | ||||
\(604\) | 1.99901e8 | + | 1.99901e8i | 0.907202 | + | 0.907202i | ||||
\(605\) | 6.30435e8 | − | 6.30435e8i | 2.84691 | − | 2.84691i | ||||
\(606\) | 1.09671e7 | − | 1.09671e7i | 0.0492802 | − | 0.0492802i | ||||
\(607\) | −1.43011e8 | −0.639446 | −0.319723 | − | 0.947511i | \(-0.603590\pi\) | ||||
−0.319723 | + | 0.947511i | \(0.603590\pi\) | |||||||
\(608\) | − | 6.04124e7i | − | 0.268791i | ||||||
\(609\) | 3.12506e7 | − | 3.12506e7i | 0.138359 | − | 0.138359i | ||||
\(610\) | 5.03715e7i | 0.221920i | ||||||||
\(611\) | −1.95230e8 | − | 1.37535e8i | −0.855901 | − | 0.602961i | ||||
\(612\) | −1.88690e7 | −0.0823181 | ||||||||
\(613\) | 1.01429e8 | + | 1.01429e8i | 0.440333 | + | 0.440333i | 0.892124 | − | 0.451791i | \(-0.149215\pi\) |
−0.451791 | + | 0.892124i | \(0.649215\pi\) | |||||||
\(614\) | 3.25872e7 | 0.140780 | ||||||||
\(615\) | − | 1.48881e8i | − | 0.640052i | ||||||
\(616\) | 6.74486e7 | + | 6.74486e7i | 0.288556 | + | 0.288556i | ||||
\(617\) | 3.13102e8 | + | 3.13102e8i | 1.33300 | + | 1.33300i | 0.902673 | + | 0.430328i | \(0.141602\pi\) |
0.430328 | + | 0.902673i | \(0.358398\pi\) | |||||||
\(618\) | 1.14914e7 | − | 1.14914e7i | 0.0486865 | − | 0.0486865i | ||||
\(619\) | 5.14300e7 | − | 5.14300e7i | 0.216843 | − | 0.216843i | −0.590324 | − | 0.807167i | \(-0.701000\pi\) |
0.807167 | + | 0.590324i | \(0.201000\pi\) | |||||||
\(620\) | −2.02440e8 | −0.849418 | ||||||||
\(621\) | − | 2.97190e7i | − | 0.124097i | ||||||
\(622\) | −2.91614e7 | + | 2.91614e7i | −0.121182 | + | 0.121182i | ||||
\(623\) | 2.17567e7i | 0.0899766i | ||||||||
\(624\) | 2.78000e7 | + | 1.60340e8i | 0.114417 | + | 0.659915i | ||||
\(625\) | 1.41318e8 | 0.578839 | ||||||||
\(626\) | −2.01893e7 | − | 2.01893e7i | −0.0822998 | − | 0.0822998i | ||||
\(627\) | −2.74905e8 | −1.11527 | ||||||||
\(628\) | 1.35490e8i | 0.547053i | ||||||||
\(629\) | 2.35432e7 | + | 2.35432e7i | 0.0946051 | + | 0.0946051i | ||||
\(630\) | −1.50074e7 | − | 1.50074e7i | −0.0600185 | − | 0.0600185i | ||||
\(631\) | 2.06799e7 | − | 2.06799e7i | 0.0823114 | − | 0.0823114i | −0.664752 | − | 0.747064i | \(-0.731463\pi\) |
0.747064 | + | 0.664752i | \(0.231463\pi\) | |||||||
\(632\) | −4.13918e7 | + | 4.13918e7i | −0.163970 | + | 0.163970i | ||||
\(633\) | −2.32904e8 | −0.918260 | ||||||||
\(634\) | − | 5.32231e7i | − | 0.208849i | ||||||
\(635\) | −3.06158e8 | + | 3.06158e8i | −1.19571 | + | 1.19571i | ||||
\(636\) | − | 1.68963e8i | − | 0.656780i | ||||||
\(637\) | 2.74771e6 | − | 476403.i | 0.0106305 | − | 0.00184313i | ||||
\(638\) | −1.51914e7 | −0.0584973 | ||||||||
\(639\) | 7.28561e7 | + | 7.28561e7i | 0.279231 | + | 0.279231i | ||||
\(640\) | −1.67622e8 | −0.639427 | ||||||||
\(641\) | 7.40571e7i | 0.281185i | 0.990068 | + | 0.140593i | \(0.0449008\pi\) | ||||
−0.990068 | + | 0.140593i | \(0.955099\pi\) | |||||||
\(642\) | −1.08766e7 | − | 1.08766e7i | −0.0411043 | − | 0.0411043i | ||||
\(643\) | −1.94452e8 | − | 1.94452e8i | −0.731442 | − | 0.731442i | 0.239463 | − | 0.970905i | \(-0.423028\pi\) |
−0.970905 | + | 0.239463i | \(0.923028\pi\) | |||||||
\(644\) | 2.18629e7 | − | 2.18629e7i | 0.0818558 | − | 0.0818558i | ||||
\(645\) | −8.45889e7 | + | 8.45889e7i | −0.315235 | + | 0.315235i | ||||
\(646\) | −3.94234e6 | −0.0146237 | ||||||||
\(647\) | − | 4.53504e8i | − | 1.67444i | −0.546870 | − | 0.837218i | \(-0.684181\pi\) | ||
0.546870 | − | 0.837218i | \(-0.315819\pi\) | |||||||
\(648\) | −8.80575e6 | + | 8.80575e6i | −0.0323624 | + | 0.0323624i | ||||
\(649\) | − | 2.96540e8i | − | 1.08480i | ||||||
\(650\) | 3.20186e7 | + | 2.25563e7i | 0.116590 | + | 0.0821349i | ||||
\(651\) | −1.07473e8 | −0.389543 | ||||||||
\(652\) | −7.40335e7 | − | 7.40335e7i | −0.267107 | − | 0.267107i | ||||
\(653\) | 3.57842e8 | 1.28515 | 0.642573 | − | 0.766225i | \(-0.277867\pi\) | ||||
0.642573 | + | 0.766225i | \(0.277867\pi\) | |||||||
\(654\) | 1.94956e7i | 0.0696954i | ||||||||
\(655\) | −2.37524e8 | − | 2.37524e8i | −0.845246 | − | 0.845246i | ||||
\(656\) | 1.16666e8 | + | 1.16666e8i | 0.413268 | + | 0.413268i | ||||
\(657\) | −1.47559e8 | + | 1.47559e8i | −0.520318 | + | 0.520318i | ||||
\(658\) | 2.26768e7 | − | 2.26768e7i | 0.0795983 | − | 0.0795983i | ||||
\(659\) | 2.30929e8 | 0.806904 | 0.403452 | − | 0.915001i | \(-0.367810\pi\) | ||||
0.403452 | + | 0.915001i | \(0.367810\pi\) | |||||||
\(660\) | 5.73231e8i | 1.99388i | ||||||||
\(661\) | −7.81262e7 | + | 7.81262e7i | −0.270516 | + | 0.270516i | −0.829308 | − | 0.558792i | \(-0.811265\pi\) |
0.558792 | + | 0.829308i | \(0.311265\pi\) | |||||||
\(662\) | − | 3.87627e7i | − | 0.133610i | ||||||
\(663\) | 3.20205e7 | − | 5.55177e6i | 0.109872 | − | 0.0190498i | ||||
\(664\) | 2.94076e7 | 0.100451 | ||||||||
\(665\) | 2.65166e8 | + | 2.65166e8i | 0.901682 | + | 0.901682i | ||||
\(666\) | −1.37839e7 | −0.0466606 | ||||||||
\(667\) | 9.90654e6i | 0.0333845i | ||||||||
\(668\) | −2.97939e7 | − | 2.97939e7i | −0.0999535 | − | 0.0999535i | ||||
\(669\) | −1.56581e8 | − | 1.56581e8i | −0.522952 | − | 0.522952i | ||||
\(670\) | −8.73569e6 | + | 8.73569e6i | −0.0290451 | + | 0.0290451i | ||||
\(671\) | −5.49672e8 | + | 5.49672e8i | −1.81943 | + | 1.81943i | ||||
\(672\) | −6.68766e7 | −0.220377 | ||||||||
\(673\) | − | 3.05242e8i | − | 1.00138i | −0.865627 | − | 0.500690i | \(-0.833080\pi\) | ||
0.865627 | − | 0.500690i | \(-0.166920\pi\) | |||||||
\(674\) | 2.64002e7 | − | 2.64002e7i | 0.0862238 | − | 0.0862238i | ||||
\(675\) | − | 4.27535e8i | − | 1.39014i | ||||||
\(676\) | 1.02779e8 | + | 2.87486e8i | 0.332709 | + | 0.930628i | ||||
\(677\) | −1.80909e8 | −0.583033 | −0.291517 | − | 0.956566i | \(-0.594160\pi\) | ||||
−0.291517 | + | 0.956566i | \(0.594160\pi\) | |||||||
\(678\) | −2.78596e7 | − | 2.78596e7i | −0.0893893 | − | 0.0893893i | ||||
\(679\) | 3.52475e8 | 1.12595 | ||||||||
\(680\) | 1.65383e7i | 0.0525973i | ||||||||
\(681\) | 1.01336e7 | + | 1.01336e7i | 0.0320865 | + | 0.0320865i | ||||
\(682\) | 2.61221e7 | + | 2.61221e7i | 0.0823484 | + | 0.0823484i | ||||
\(683\) | −8.95873e7 | + | 8.95873e7i | −0.281180 | + | 0.281180i | −0.833579 | − | 0.552400i | \(-0.813712\pi\) |
0.552400 | + | 0.833579i | \(0.313712\pi\) | |||||||
\(684\) | −9.75972e7 | + | 9.75972e7i | −0.304978 | + | 0.304978i | ||||
\(685\) | 3.66886e7 | 0.114146 | ||||||||
\(686\) | 3.50850e7i | 0.108680i | ||||||||
\(687\) | 2.85099e8 | − | 2.85099e8i | 0.879276 | − | 0.879276i | ||||
\(688\) | − | 1.32570e8i | − | 0.407080i | ||||||
\(689\) | −5.35053e7 | − | 3.08599e8i | −0.163583 | − | 0.943488i | ||||
\(690\) | −4.42025e6 | −0.0134555 | ||||||||
\(691\) | 1.52213e8 | + | 1.52213e8i | 0.461336 | + | 0.461336i | 0.899093 | − | 0.437757i | \(-0.144227\pi\) |
−0.437757 | + | 0.899093i | \(0.644227\pi\) | |||||||
\(692\) | 4.84453e8 | 1.46195 | ||||||||
\(693\) | − | 3.27533e8i | − | 0.984137i | ||||||
\(694\) | −3.63852e7 | − | 3.63852e7i | −0.108855 | − | 0.108855i | ||||
\(695\) | 1.29345e8 | + | 1.29345e8i | 0.385296 | + | 0.385296i | ||||
\(696\) | 1.00813e7 | − | 1.00813e7i | 0.0299013 | − | 0.0299013i | ||||
\(697\) | 2.32986e7 | − | 2.32986e7i | 0.0688068 | − | 0.0688068i | ||||
\(698\) | −3.68148e7 | −0.108257 | ||||||||
\(699\) | − | 3.43076e7i | − | 0.100452i | ||||||
\(700\) | 3.14517e8 | − | 3.14517e8i | 0.916958 | − | 0.916958i | ||||
\(701\) | 5.41363e8i | 1.57157i | 0.618498 | + | 0.785786i | \(0.287741\pi\) | ||||
−0.618498 | + | 0.785786i | \(0.712259\pi\) | |||||||
\(702\) | −2.26959e7 | + | 3.22168e7i | −0.0656050 | + | 0.0931260i | ||||
\(703\) | 2.43548e8 | 0.701000 | ||||||||
\(704\) | −4.38249e8 | − | 4.38249e8i | −1.25604 | − | 1.25604i | ||||
\(705\) | 3.87730e8 | 1.10653 | ||||||||
\(706\) | 1.87740e7i | 0.0533510i | ||||||||
\(707\) | −2.30873e8 | − | 2.30873e8i | −0.653304 | − | 0.653304i | ||||
\(708\) | 9.78168e7 | + | 9.78168e7i | 0.275622 | + | 0.275622i | ||||
\(709\) | −1.17076e8 | + | 1.17076e8i | −0.328494 | + | 0.328494i | −0.852014 | − | 0.523520i | \(-0.824619\pi\) |
0.523520 | + | 0.852014i | \(0.324619\pi\) | |||||||
\(710\) | 3.17407e7 | − | 3.17407e7i | 0.0886833 | − | 0.0886833i | ||||
\(711\) | 2.01001e8 | 0.559227 | ||||||||
\(712\) | 7.01865e6i | 0.0194453i | ||||||||
\(713\) | 1.70346e7 | − | 1.70346e7i | 0.0469963 | − | 0.0469963i | ||||
\(714\) | 4.36417e6i | 0.0119897i | ||||||||
\(715\) | 1.81525e8 | + | 1.04697e9i | 0.496612 | + | 2.86427i | ||||
\(716\) | −6.70803e7 | −0.182749 | ||||||||
\(717\) | 1.73133e8 | + | 1.73133e8i | 0.469701 | + | 0.469701i | ||||
\(718\) | 2.91821e7 | 0.0788393 | ||||||||
\(719\) | − | 3.08710e8i | − | 0.830548i | −0.909696 | − | 0.415274i | \(-0.863686\pi\) | ||
0.909696 | − | 0.415274i | \(-0.136314\pi\) | |||||||
\(720\) | 2.01074e8 | + | 2.01074e8i | 0.538715 | + | 0.538715i | ||||
\(721\) | −2.41912e8 | − | 2.41912e8i | −0.645434 | − | 0.645434i | ||||
\(722\) | 8.37890e6 | − | 8.37890e6i | 0.0222626 | − | 0.0222626i | ||||
\(723\) | −2.31625e8 | + | 2.31625e8i | −0.612873 | + | 0.612873i | ||||
\(724\) | −6.41538e8 | −1.69047 | ||||||||
\(725\) | 1.42514e8i | 0.373977i | ||||||||
\(726\) | 5.36676e7 | − | 5.36676e7i | 0.140250 | − | 0.140250i | ||||
\(727\) | − | 2.05083e8i | − | 0.533737i | −0.963733 | − | 0.266868i | \(-0.914011\pi\) | ||
0.963733 | − | 0.266868i | \(-0.0859889\pi\) | |||||||
\(728\) | −8.12710e7 | + | 1.40909e7i | −0.210640 | + | 0.0365212i | ||||
\(729\) | 3.26079e8 | 0.841668 | ||||||||
\(730\) | 6.42859e7 | + | 6.42859e7i | 0.165252 | + | 0.165252i | ||||
\(731\) | −2.64748e7 | −0.0677767 | ||||||||
\(732\) | − | 3.62630e8i | − | 0.924550i | ||||||
\(733\) | −2.32596e8 | − | 2.32596e8i | −0.590596 | − | 0.590596i | 0.347196 | − | 0.937792i | \(-0.387134\pi\) |
−0.937792 | + | 0.347196i | \(0.887134\pi\) | |||||||
\(734\) | 1.05955e6 | + | 1.05955e6i | 0.00267938 | + | 0.00267938i | ||||
\(735\) | −3.20156e6 | + | 3.20156e6i | −0.00806306 | + | 0.00806306i | ||||
\(736\) | 1.06001e7 | − | 1.06001e7i | 0.0265874 | − | 0.0265874i | ||||
\(737\) | −1.90654e8 | −0.476259 | ||||||||
\(738\) | 1.36407e7i | 0.0339365i | ||||||||
\(739\) | −1.11899e8 | + | 1.11899e8i | −0.277263 | + | 0.277263i | −0.832016 | − | 0.554752i | \(-0.812813\pi\) |
0.554752 | + | 0.832016i | \(0.312813\pi\) | |||||||
\(740\) | − | 5.07844e8i | − | 1.25324i | ||||||
\(741\) | 1.36906e8 | − | 1.94337e8i | 0.336486 | − | 0.477640i | ||||
\(742\) | 4.20598e7 | 0.102957 | ||||||||
\(743\) | −2.16522e8 | − | 2.16522e8i | −0.527881 | − | 0.527881i | 0.392059 | − | 0.919940i | \(-0.371763\pi\) |
−0.919940 | + | 0.392059i | \(0.871763\pi\) | |||||||
\(744\) | −3.46704e7 | −0.0841860 | ||||||||
\(745\) | 5.65831e8i | 1.36842i | ||||||||
\(746\) | −1.38841e7 | − | 1.38841e7i | −0.0334428 | − | 0.0334428i | ||||
\(747\) | −7.14023e7 | − | 7.14023e7i | −0.171297 | − | 0.171297i | ||||
\(748\) | −8.97055e7 | + | 8.97055e7i | −0.214345 | + | 0.214345i | ||||
\(749\) | −2.28968e8 | + | 2.28968e8i | −0.544917 | + | 0.544917i | ||||
\(750\) | −1.53880e7 | −0.0364752 | ||||||||
\(751\) | − | 3.77813e8i | − | 0.891983i | −0.895037 | − | 0.445991i | \(-0.852851\pi\) | ||
0.895037 | − | 0.445991i | \(-0.147149\pi\) | |||||||
\(752\) | −3.03830e8 | + | 3.03830e8i | −0.714460 | + | 0.714460i | ||||
\(753\) | 1.93281e8i | 0.452694i | ||||||||
\(754\) | 7.56546e6 | − | 1.07391e7i | 0.0176491 | − | 0.0250528i | ||||
\(755\) | −8.50822e8 | −1.97696 | ||||||||
\(756\) | 3.16464e8 | + | 3.16464e8i | 0.732418 | + | 0.732418i | ||||
\(757\) | −6.99389e8 | −1.61225 | −0.806123 | − | 0.591749i | \(-0.798438\pi\) | ||||
−0.806123 | + | 0.591749i | \(0.798438\pi\) | |||||||
\(758\) | 3.14971e7i | 0.0723207i | ||||||||
\(759\) | −4.82354e7 | − | 4.82354e7i | −0.110317 | − | 0.110317i | ||||
\(760\) | 8.55418e7 | + | 8.55418e7i | 0.194867 | + | 0.194867i | ||||
\(761\) | 8.68673e7 | − | 8.68673e7i | 0.197107 | − | 0.197107i | −0.601651 | − | 0.798759i | \(-0.705490\pi\) |
0.798759 | + | 0.601651i | \(0.205490\pi\) | |||||||
\(762\) | −2.60626e7 | + | 2.60626e7i | −0.0589051 | + | 0.0589051i | ||||
\(763\) | 4.10413e8 | 0.923947 | ||||||||
\(764\) | − | 3.86284e8i | − | 0.866217i | ||||||
\(765\) | 4.01553e7 | − | 4.01553e7i | 0.0896930 | − | 0.0896930i | ||||
\(766\) | 5.76520e7i | 0.128271i | ||||||||
\(767\) | 2.09631e8 | + | 1.47680e8i | 0.464590 | + | 0.327292i | ||||
\(768\) | 2.78271e8 | 0.614306 | ||||||||
\(769\) | 2.69755e8 | + | 2.69755e8i | 0.593185 | + | 0.593185i | 0.938490 | − | 0.345305i | \(-0.112225\pi\) |
−0.345305 | + | 0.938490i | \(0.612225\pi\) | |||||||
\(770\) | −1.42694e8 | −0.312561 | ||||||||
\(771\) | 2.94609e8i | 0.642810i | ||||||||
\(772\) | 1.18554e8 | + | 1.18554e8i | 0.257670 | + | 0.257670i | ||||
\(773\) | 5.07426e8 | + | 5.07426e8i | 1.09859 | + | 1.09859i | 0.994576 | + | 0.104011i | \(0.0331678\pi\) |
0.104011 | + | 0.994576i | \(0.466832\pi\) | |||||||
\(774\) | 7.75012e6 | − | 7.75012e6i | 0.0167142 | − | 0.0167142i | ||||
\(775\) | 2.45058e8 | − | 2.45058e8i | 0.526458 | − | 0.526458i | ||||
\(776\) | 1.13707e8 | 0.243334 | ||||||||
\(777\) | − | 2.69608e8i | − | 0.574737i | ||||||
\(778\) | 5.53793e7 | − | 5.53793e7i | 0.117600 | − | 0.117600i | ||||
\(779\) | − | 2.41017e8i | − | 0.509841i | ||||||
\(780\) | −4.05230e8 | − | 2.85475e8i | −0.853922 | − | 0.601567i | ||||
\(781\) | 6.92732e8 | 1.45416 | ||||||||
\(782\) | −691729. | − | 691729.i | −0.00144649 | − | 0.00144649i | ||||
\(783\) | −1.43397e8 | −0.298713 | ||||||||
\(784\) | − | 5.01758e6i | − | 0.0104123i | ||||||
\(785\) | −2.88338e8 | − | 2.88338e8i | −0.596064 | − | 0.596064i | ||||
\(786\) | −2.02199e7 | − | 2.02199e7i | −0.0416401 | − | 0.0416401i | ||||
\(787\) | 6.10621e8 | − | 6.10621e8i | 1.25270 | − | 1.25270i | 0.298196 | − | 0.954505i | \(-0.403615\pi\) |
0.954505 | − | 0.298196i | \(-0.0963849\pi\) | |||||||
\(788\) | 2.27118e8 | − | 2.27118e8i | 0.464165 | − | 0.464165i | ||||
\(789\) | −4.55732e8 | −0.927851 | ||||||||
\(790\) | − | 8.75685e7i | − | 0.177610i | ||||||
\(791\) | −5.86486e8 | + | 5.86486e8i | −1.18503 | + | 1.18503i | ||||
\(792\) | − | 1.05661e8i | − | 0.212686i | ||||||
\(793\) | −1.14834e8 | − | 6.62318e8i | −0.230277 | − | 1.32815i | ||||
\(794\) | −2.71650e7 | −0.0542685 | ||||||||
\(795\) | 3.59571e8 | + | 3.59571e8i | 0.715622 | + | 0.715622i | ||||
\(796\) | 1.37828e8 | 0.273274 | ||||||||
\(797\) | − | 1.40021e8i | − | 0.276578i | −0.990392 | − | 0.138289i | \(-0.955840\pi\) | ||
0.990392 | − | 0.138289i | \(-0.0441602\pi\) | |||||||
\(798\) | 2.25730e7 | + | 2.25730e7i | 0.0444203 | + | 0.0444203i | ||||
\(799\) | 6.06761e7 | + | 6.06761e7i | 0.118954 | + | 0.118954i | ||||
\(800\) | 1.52491e8 | − | 1.52491e8i | 0.297834 | − | 0.297834i | ||||
\(801\) | 1.70414e7 | − | 1.70414e7i | 0.0331596 | − | 0.0331596i | ||||
\(802\) | −2.05361e7 | −0.0398102 | ||||||||
\(803\) | 1.40302e9i | 2.70968i | ||||||||
\(804\) | 6.28892e7 | − | 6.28892e7i | 0.121006 | − | 0.121006i | ||||
\(805\) | 9.30531e7i | 0.178379i | ||||||||
\(806\) | −3.14754e7 | + | 5.45726e6i | −0.0601127 | + | 0.0104224i | ||||
\(807\) | −1.82546e7 | −0.0347338 | ||||||||
\(808\) | −7.44790e7 | − | 7.44790e7i | −0.141189 | − | 0.141189i | ||||
\(809\) | 3.87651e8 | 0.732141 | 0.366071 | − | 0.930587i | \(-0.380703\pi\) | ||||
0.366071 | + | 0.930587i | \(0.380703\pi\) | |||||||
\(810\) | − | 1.86294e7i | − | 0.0350546i | ||||||
\(811\) | 6.59086e8 | + | 6.59086e8i | 1.23561 | + | 1.23561i | 0.961779 | + | 0.273826i | \(0.0882892\pi\) |
0.273826 | + | 0.961779i | \(0.411711\pi\) | |||||||
\(812\) | −1.05490e8 | − | 1.05490e8i | −0.197035 | − | 0.197035i | ||||
\(813\) | −1.51162e8 | + | 1.51162e8i | −0.281301 | + | 0.281301i | ||||
\(814\) | −6.55303e7 | + | 6.55303e7i | −0.121498 | + | 0.121498i | ||||
\(815\) | 3.15103e8 | 0.582075 | ||||||||
\(816\) | − | 5.84725e7i | − | 0.107617i | ||||||
\(817\) | −1.36937e8 | + | 1.36937e8i | −0.251104 | + | 0.251104i | ||||
\(818\) | 4.55981e7i | 0.0833080i | ||||||||
\(819\) | 2.31541e8 | + | 1.63115e8i | 0.421479 | + | 0.296921i | ||||
\(820\) | −5.02567e8 | −0.911491 | ||||||||
\(821\) | −3.15682e8 | − | 3.15682e8i | −0.570454 | − | 0.570454i | 0.361802 | − | 0.932255i | \(-0.382162\pi\) |
−0.932255 | + | 0.361802i | \(0.882162\pi\) | |||||||
\(822\) | 3.12322e6 | 0.00562325 | ||||||||
\(823\) | − | 9.22357e8i | − | 1.65462i | −0.561743 | − | 0.827312i | \(-0.689869\pi\) | ||
0.561743 | − | 0.827312i | \(-0.310131\pi\) | |||||||
\(824\) | −7.80401e7 | − | 7.80401e7i | −0.139488 | − | 0.139488i | ||||
\(825\) | −6.93908e8 | − | 6.93908e8i | −1.23578 | − | 1.23578i | ||||
\(826\) | −2.43495e7 | + | 2.43495e7i | −0.0432066 | + | 0.0432066i | ||||
\(827\) | 6.23270e8 | − | 6.23270e8i | 1.10194 | − | 1.10194i | 0.107768 | − | 0.994176i | \(-0.465630\pi\) |
0.994176 | − | 0.107768i | \(-0.0343703\pi\) | |||||||
\(828\) | −3.42492e7 | −0.0603335 | ||||||||
\(829\) | 1.44545e8i | 0.253712i | 0.991921 | + | 0.126856i | \(0.0404886\pi\) | ||||
−0.991921 | + | 0.126856i | \(0.959511\pi\) | |||||||
\(830\) | −3.11073e7 | + | 3.11073e7i | −0.0544037 | + | 0.0544037i | ||||
\(831\) | 3.48369e8i | 0.607067i | ||||||||
\(832\) | 5.28060e8 | − | 9.15560e7i | 0.916883 | − | 0.158971i | ||||
\(833\) | −1.00203e6 | −0.00173359 | ||||||||
\(834\) | 1.10108e7 | + | 1.10108e7i | 0.0189811 | + | 0.0189811i | ||||
\(835\) | 1.26809e8 | 0.217817 | ||||||||
\(836\) | 9.27976e8i | 1.58825i | ||||||||
\(837\) | 2.46575e8 | + | 2.46575e8i | 0.420507 | + | 0.420507i | ||||
\(838\) | 5.33830e7 | + | 5.33830e7i | 0.0907132 | + | 0.0907132i | ||||
\(839\) | 2.13888e8 | − | 2.13888e8i | 0.362160 | − | 0.362160i | −0.502448 | − | 0.864608i | \(-0.667567\pi\) |
0.864608 | + | 0.502448i | \(0.167567\pi\) | |||||||
\(840\) | 9.46949e7 | − | 9.46949e7i | 0.159768 | − | 0.159768i | ||||
\(841\) | −5.47024e8 | −0.919640 | ||||||||
\(842\) | − | 6.62272e7i | − | 0.110943i | ||||||
\(843\) | 2.59857e8 | − | 2.59857e8i | 0.433762 | − | 0.433762i | ||||
\(844\) | 7.86195e8i | 1.30768i | ||||||||
\(845\) | −8.30525e8 | − | 3.93075e8i | −1.37652 | − | 0.651487i | ||||
\(846\) | −3.55242e7 | −0.0586696 | ||||||||
\(847\) | −1.12978e9 | − | 1.12978e9i | −1.85928 | − | 1.85928i | ||||
\(848\) | −5.63530e8 | −0.924123 | ||||||||
\(849\) | 4.29774e8i | 0.702292i | ||||||||
\(850\) | −9.95113e6 | − | 9.95113e6i | −0.0162038 | − | 0.0162038i | ||||
\(851\) | 4.27333e7 | + | 4.27333e7i | 0.0693391 | + | 0.0693391i | ||||
\(852\) | −2.28505e8 | + | 2.28505e8i | −0.369468 | + | 0.369468i | ||||
\(853\) | −9.88221e7 | + | 9.88221e7i | −0.159224 | + | 0.159224i | −0.782223 | − | 0.622999i | \(-0.785914\pi\) |
0.622999 | + | 0.782223i | \(0.285914\pi\) | |||||||
\(854\) | 9.02693e7 | 0.144933 | ||||||||
\(855\) | − | 4.15395e8i | − | 0.664603i | ||||||
\(856\) | −7.38645e7 | + | 7.38645e7i | −0.117764 | + | 0.117764i | ||||
\(857\) | 6.90476e8i | 1.09700i | 0.836151 | + | 0.548499i | \(0.184801\pi\) | ||||
−0.836151 | + | 0.548499i | \(0.815199\pi\) | |||||||
\(858\) | 1.54528e7 | + | 8.91259e7i | 0.0244650 | + | 0.141105i | ||||
\(859\) | −5.34158e8 | −0.842734 | −0.421367 | − | 0.906890i | \(-0.638450\pi\) | ||||
−0.421367 | + | 0.906890i | \(0.638450\pi\) | |||||||
\(860\) | 2.85540e8 | + | 2.85540e8i | 0.448922 | + | 0.448922i | ||||
\(861\) | −2.66806e8 | −0.418010 | ||||||||
\(862\) | 4.66037e6i | 0.00727610i | ||||||||
\(863\) | −2.78251e8 | − | 2.78251e8i | −0.432917 | − | 0.432917i | 0.456703 | − | 0.889619i | \(-0.349030\pi\) |
−0.889619 | + | 0.456703i | \(0.849030\pi\) | |||||||
\(864\) | 1.53435e8 | + | 1.53435e8i | 0.237894 | + | 0.237894i | ||||
\(865\) | −1.03097e9 | + | 1.03097e9i | −1.59293 | + | 1.59293i | ||||
\(866\) | 6.02863e7 | − | 6.02863e7i | 0.0928251 | − | 0.0928251i | ||||
\(867\) | 4.40610e8 | 0.676079 | ||||||||
\(868\) | 3.62787e8i | 0.554744i | ||||||||
\(869\) | 9.55579e8 | − | 9.55579e8i | 1.45615 | − | 1.45615i | ||||
\(870\) | 2.13281e7i | 0.0323887i | ||||||||
\(871\) | 9.49476e7 | − | 1.34778e8i | 0.143691 | − | 0.203969i | ||||
\(872\) | 1.32398e8 | 0.199678 | ||||||||
\(873\) | −2.76084e8 | − | 2.76084e8i | −0.414952 | − | 0.414952i | ||||
\(874\) | −7.15573e6 | −0.0107181 | ||||||||
\(875\) | 3.23940e8i | 0.483550i | ||||||||
\(876\) | −4.62801e8 | − | 4.62801e8i | −0.688465 | − | 0.688465i | ||||
\(877\) | 3.82228e7 | + | 3.82228e7i | 0.0566661 | + | 0.0566661i | 0.734872 | − | 0.678206i | \(-0.237242\pi\) |
−0.678206 | + | 0.734872i | \(0.737242\pi\) | |||||||
\(878\) | −3.14519e6 | + | 3.14519e6i | −0.00464690 | + | 0.00464690i | ||||
\(879\) | 8.78514e7 | − | 8.78514e7i | 0.129355 | − | 0.129355i | ||||
\(880\) | 1.91186e9 | 2.80548 | ||||||||
\(881\) | − | 2.25232e8i | − | 0.329384i | −0.986345 | − | 0.164692i | \(-0.947337\pi\) | ||
0.986345 | − | 0.164692i | \(-0.0526630\pi\) | |||||||
\(882\) | 293331. | − | 293331.i | 0.000427515 | − | 0.000427515i | ||||
\(883\) | − | 4.01767e8i | − | 0.583568i | −0.956484 | − | 0.291784i | \(-0.905751\pi\) | ||
0.956484 | − | 0.291784i | \(-0.0942489\pi\) | |||||||
\(884\) | −1.87407e7 | − | 1.08089e8i | −0.0271287 | − | 0.156468i | ||||
\(885\) | −4.16330e8 | −0.600631 | ||||||||
\(886\) | −9.34658e7 | − | 9.34658e7i | −0.134385 | − | 0.134385i | ||||
\(887\) | 2.67161e8 | 0.382826 | 0.191413 | − | 0.981510i | \(-0.438693\pi\) | ||||
0.191413 | + | 0.981510i | \(0.438693\pi\) | |||||||
\(888\) | − | 8.69746e7i | − | 0.124209i | ||||||
\(889\) | 5.48658e8 | + | 5.48658e8i | 0.780901 | + | 0.780901i | ||||
\(890\) | −7.42433e6 | − | 7.42433e6i | −0.0105314 | − | 0.0105314i | ||||
\(891\) | 2.03291e8 | − | 2.03291e8i | 0.287399 | − | 0.287399i | ||||
\(892\) | −5.28559e8 | + | 5.28559e8i | −0.744730 | + | 0.744730i | ||||
\(893\) | 6.27676e8 | 0.881417 | ||||||||
\(894\) | 4.81680e7i | 0.0674134i | ||||||||
\(895\) | 1.42754e8 | − | 1.42754e8i | 0.199122 | − | 0.199122i | ||||
\(896\) | 3.00390e8i | 0.417602i | ||||||||
\(897\) | 5.81204e7 | − | 1.00770e7i | 0.0805288 | − | 0.0139622i | ||||
\(898\) | 9.93812e7 | 0.137238 | ||||||||
\(899\) | −8.21934e7 | − | 8.21934e7i | −0.113125 | − | 0.113125i | ||||
\(900\) | −4.92704e8 | −0.675863 | ||||||||
\(901\) | 1.12539e8i | 0.153861i | ||||||||
\(902\) | 6.48493e7 | + | 6.48493e7i | 0.0883661 | + | 0.0883661i | ||||
\(903\) | 1.51589e8 | + | 1.51589e8i | 0.205876 | + | 0.205876i | ||||
\(904\) | −1.89199e8 | + | 1.89199e8i | −0.256102 | + | 0.256102i | ||||
\(905\) | 1.36526e9 | − | 1.36526e9i | 1.84192 | − | 1.84192i | ||||
\(906\) | −7.24286e7 | −0.0973925 | ||||||||
\(907\) | − | 1.29431e8i | − | 0.173466i | −0.996232 | − | 0.0867332i | \(-0.972357\pi\) | ||
0.996232 | − | 0.0867332i | \(-0.0276428\pi\) | |||||||
\(908\) | 3.42072e7 | − | 3.42072e7i | 0.0456940 | − | 0.0456940i | ||||
\(909\) | 3.61673e8i | 0.481532i | ||||||||
\(910\) | 7.10631e7 | − | 1.00874e8i | 0.0943018 | − | 0.133861i | ||||
\(911\) | 9.09544e8 | 1.20301 | 0.601504 | − | 0.798870i | \(-0.294568\pi\) | ||||
0.601504 | + | 0.798870i | \(0.294568\pi\) | |||||||
\(912\) | −3.02440e8 | − | 3.02440e8i | −0.398708 | − | 0.398708i | ||||
\(913\) | −6.78909e8 | −0.892071 | ||||||||
\(914\) | 8.07972e7i | 0.105818i | ||||||||
\(915\) | 7.71716e8 | + | 7.71716e8i | 1.00738 | + | 1.00738i | ||||
\(916\) | −9.62386e8 | − | 9.62386e8i | −1.25217 | − | 1.25217i | ||||
\(917\) | −4.25660e8 | + | 4.25660e8i | −0.552020 | + | 0.552020i | ||||
\(918\) | 1.00127e7 | − | 1.00127e7i | 0.0129427 | − | 0.0129427i | ||||
\(919\) | −5.70701e8 | −0.735296 | −0.367648 | − | 0.929965i | \(-0.619837\pi\) | ||||
−0.367648 | + | 0.929965i | \(0.619837\pi\) | |||||||
\(920\) | 3.00186e7i | 0.0385503i | ||||||||
\(921\) | 4.99252e8 | − | 4.99252e8i | 0.639059 | − | 0.639059i | ||||
\(922\) | − | 8.91904e7i | − | 0.113796i | ||||||
\(923\) | −3.44987e8 | + | 4.89708e8i | −0.438731 | + | 0.622777i | ||||
\(924\) | 1.02727e9 | 1.30217 | ||||||||
\(925\) | 6.14756e8 | + | 6.14756e8i | 0.776744 | + | 0.776744i | ||||
\(926\) | 3.53213e7 | 0.0444840 | ||||||||
\(927\) | 3.78966e8i | 0.475731i | ||||||||
\(928\) | −5.11461e7 | − | 5.11461e7i | −0.0639983 | − | 0.0639983i | ||||
\(929\) | −2.60806e8 | − | 2.60806e8i | −0.325290 | − | 0.325290i | 0.525502 | − | 0.850792i | \(-0.323877\pi\) |
−0.850792 | + | 0.525502i | \(0.823877\pi\) | |||||||
\(930\) | 3.66743e7 | − | 3.66743e7i | 0.0455946 | − | 0.0455946i | ||||
\(931\) | −5.18285e6 | + | 5.18285e6i | −0.00642273 | + | 0.00642273i | ||||
\(932\) | −1.15809e8 | −0.143053 | ||||||||
\(933\) | 8.93532e8i | 1.10018i | ||||||||
\(934\) | −1.82418e7 | + | 1.82418e7i | −0.0223886 | + | 0.0223886i | ||||
\(935\) | − | 3.81806e8i | − | 0.467098i | ||||||
\(936\) | 7.46943e7 | + | 5.26203e7i | 0.0910878 | + | 0.0641691i | ||||
\(937\) | −1.85169e8 | −0.225086 | −0.112543 | − | 0.993647i | \(-0.535900\pi\) | ||||
−0.112543 | + | 0.993647i | \(0.535900\pi\) | |||||||
\(938\) | 1.56550e7 | + | 1.56550e7i | 0.0189690 | + | 0.0189690i | ||||
\(939\) | −6.18621e8 | −0.747184 | ||||||||
\(940\) | − | 1.30883e9i | − | 1.57579i | ||||||
\(941\) | 3.91178e8 | + | 3.91178e8i | 0.469468 | + | 0.469468i | 0.901742 | − | 0.432274i | \(-0.142289\pi\) |
−0.432274 | + | 0.901742i | \(0.642289\pi\) | |||||||
\(942\) | −2.45456e7 | − | 2.45456e7i | −0.0293644 | − | 0.0293644i | ||||
\(943\) | 4.22892e7 | − | 4.22892e7i | 0.0504307 | − | 0.0504307i | ||||
\(944\) | 3.26242e8 | − | 3.26242e8i | 0.387814 | − | 0.387814i | ||||
\(945\) | −1.34694e9 | −1.59607 | ||||||||
\(946\) | − | 7.36899e7i | − | 0.0870432i | ||||||
\(947\) | −1.03681e9 | + | 1.03681e9i | −1.22081 | + | 1.22081i | −0.253471 | + | 0.967343i | \(0.581572\pi\) |
−0.967343 | + | 0.253471i | \(0.918428\pi\) | |||||||
\(948\) | 6.30415e8i | 0.739949i | ||||||||
\(949\) | −9.91828e8 | − | 6.98718e8i | −1.16048 | − | 0.817530i | ||||
\(950\) | −1.02941e8 | −0.120066 | ||||||||
\(951\) | −8.15404e8 | − | 8.15404e8i | −0.948050 | − | 0.948050i | ||||
\(952\) | 2.96378e7 | 0.0343506 | ||||||||
\(953\) | − | 2.01631e8i | − | 0.232959i | −0.993193 | − | 0.116479i | \(-0.962839\pi\) | ||
0.993193 | − | 0.116479i | \(-0.0371609\pi\) | |||||||
\(954\) | −3.29443e7 | − | 3.29443e7i | −0.0379433 | − | 0.0379433i | ||||
\(955\) | 8.22054e8 | + | 8.22054e8i | 0.943822 | + | 0.943822i | ||||
\(956\) | 5.84430e8 | − | 5.84430e8i | 0.668897 | − | 0.668897i | ||||
\(957\) | −2.32739e8 | + | 2.32739e8i | −0.265543 | + | 0.265543i | ||||
\(958\) | −7.74674e7 | −0.0881095 | ||||||||
\(959\) | − | 6.57486e7i | − | 0.0745470i | ||||||
\(960\) | −6.15283e8 | + | 6.15283e8i | −0.695442 | + | 0.695442i | ||||
\(961\) | − | 6.04835e8i | − | 0.681502i | ||||||
\(962\) | −1.36902e7 | − | 7.89596e7i | −0.0153774 | − | 0.0886911i | ||||
\(963\) | 3.58689e8 | 0.401642 | ||||||||
\(964\) | 7.81878e8 | + | 7.81878e8i | 0.872786 | + | 0.872786i | ||||
\(965\) | −5.04591e8 | −0.561510 | ||||||||
\(966\) | 7.92141e6i | 0.00878762i | ||||||||
\(967\) | 8.11848e8 | + | 8.11848e8i | 0.897832 | + | 0.897832i | 0.995244 | − | 0.0974120i | \(-0.0310565\pi\) |
−0.0974120 | + | 0.995244i | \(0.531056\pi\) | |||||||
\(968\) | −3.64465e8 | − | 3.64465e8i | −0.401818 | − | 0.401818i | ||||
\(969\) | −6.03985e7 | + | 6.03985e7i | −0.0663827 | + | 0.0663827i | ||||
\(970\) | −1.20279e8 | + | 1.20279e8i | −0.131788 | + | 0.131788i | ||||
\(971\) | −1.57720e8 | −0.172278 | −0.0861388 | − | 0.996283i | \(-0.527453\pi\) | ||||
−0.0861388 | + | 0.996283i | \(0.527453\pi\) | |||||||
\(972\) | − | 8.22259e8i | − | 0.895385i | ||||||
\(973\) | 2.31795e8 | − | 2.31795e8i | 0.251632 | − | 0.251632i | ||||
\(974\) | − | 5.95207e6i | − | 0.00644156i | ||||||
\(975\) | 8.36113e8 | − | 1.44967e8i | 0.902093 | − | 0.156406i | ||||
\(976\) | −1.20946e9 | −1.30089 | ||||||||
\(977\) | 6.27520e8 | + | 6.27520e8i | 0.672890 | + | 0.672890i | 0.958381 | − | 0.285491i | \(-0.0921568\pi\) |
−0.285491 | + | 0.958381i | \(0.592157\pi\) | |||||||
\(978\) | 2.68240e7 | 0.0286752 | ||||||||
\(979\) | − | 1.62034e8i | − | 0.172686i | ||||||
\(980\) | 1.08073e7 | + | 1.08073e7i | 0.0114825 | + | 0.0114825i | ||||
\(981\) | −3.21465e8 | − | 3.21465e8i | −0.340507 | − | 0.340507i | ||||
\(982\) | 1.17975e8 | − | 1.17975e8i | 0.124582 | − | 0.124582i | ||||
\(983\) | −4.70097e8 | + | 4.70097e8i | −0.494911 | + | 0.494911i | −0.909849 | − | 0.414938i | \(-0.863803\pi\) |
0.414938 | + | 0.909849i | \(0.363803\pi\) | |||||||
\(984\) | −8.60708e7 | −0.0903380 | ||||||||
\(985\) | 9.66663e8i | 1.01150i | ||||||||
\(986\) | −3.33765e6 | + | 3.33765e6i | −0.00348185 | + | 0.00348185i | ||||
\(987\) | − | 6.94839e8i | − | 0.722658i | ||||||
\(988\) | −6.56008e8 | − | 4.62141e8i | −0.680202 | − | 0.479186i | ||||
\(989\) | −4.80543e7 | −0.0496757 | ||||||||
\(990\) | 1.11768e8 | + | 1.11768e8i | 0.115190 | + | 0.115190i | ||||
\(991\) | −7.09755e8 | −0.729268 | −0.364634 | − | 0.931151i | \(-0.618806\pi\) | ||||
−0.364634 | + | 0.931151i | \(0.618806\pi\) | |||||||
\(992\) | 1.75895e8i | 0.180185i | ||||||||
\(993\) | −5.93864e8 | − | 5.93864e8i | −0.606512 | − | 0.606512i | ||||
\(994\) | −5.68816e7 | − | 5.68816e7i | −0.0579179 | − | 0.0579179i | ||||
\(995\) | −2.93313e8 | + | 2.93313e8i | −0.297757 | + | 0.297757i | ||||
\(996\) | 2.23945e8 | − | 2.23945e8i | 0.226654 | − | 0.226654i | ||||
\(997\) | 1.40289e9 | 1.41559 | 0.707796 | − | 0.706417i | \(-0.249690\pi\) | ||||
0.707796 | + | 0.706417i | \(0.249690\pi\) | |||||||
\(998\) | 1.90658e8i | 0.191807i | ||||||||
\(999\) | −6.18563e8 | + | 6.18563e8i | −0.620422 | + | 0.620422i |
(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 | 13.7.d.a.8.4 | yes | 12 | |
3.2 | odd | 2 | 117.7.j.b.73.3 | 12 | |||
4.3 | odd | 2 | 208.7.t.c.177.3 | 12 | |||
13.5 | odd | 4 | inner | 13.7.d.a.5.4 | ✓ | 12 | |
39.5 | even | 4 | 117.7.j.b.109.3 | 12 | |||
52.31 | even | 4 | 208.7.t.c.161.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.7.d.a.5.4 | ✓ | 12 | 13.5 | odd | 4 | inner | |
13.7.d.a.8.4 | yes | 12 | 1.1 | even | 1 | trivial | |
117.7.j.b.73.3 | 12 | 3.2 | odd | 2 | |||
117.7.j.b.109.3 | 12 | 39.5 | even | 4 | |||
208.7.t.c.161.3 | 12 | 52.31 | even | 4 | |||
208.7.t.c.177.3 | 12 | 4.3 | odd | 2 |