Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(34,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.34");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.i (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: | \(0.726638658394\) |
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: | \( x^{12} + 35x^{8} + 295x^{4} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 83.2 | ||
Root | \(-0.626770 - 0.626770i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.83 |
Dual form | 91.2.i.a.34.1 |
$q$-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 \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.45161 | + | 1.45161i | −1.02644 | + | 1.02644i | −0.0267996 | + | 0.999641i | \(0.508532\pi\) |
−0.999641 | + | 0.0267996i | \(0.991468\pi\) | |||||||
\(3\) | 1.81964i | 1.05057i | 0.850926 | + | 0.525286i | \(0.176042\pi\) | ||||
−0.850926 | + | 0.525286i | \(0.823958\pi\) | |||||||
\(4\) | − | 2.21432i | − | 1.10716i | ||||||
\(5\) | 2.01464 | + | 2.01464i | 0.900973 | + | 0.900973i | 0.995520 | − | 0.0945469i | \(-0.0301402\pi\) |
−0.0945469 | + | 0.995520i | \(0.530140\pi\) | |||||||
\(6\) | −2.64141 | − | 2.64141i | −1.07835 | − | 1.07835i | ||||
\(7\) | −2.38948 | − | 1.13594i | −0.903140 | − | 0.429347i | ||||
\(8\) | 0.311108 | + | 0.311108i | 0.109993 | + | 0.109993i | ||||
\(9\) | −0.311108 | −0.103703 | ||||||||
\(10\) | −5.84892 | −1.84959 | ||||||||
\(11\) | 0.451606 | + | 0.451606i | 0.136164 | + | 0.136164i | 0.771904 | − | 0.635739i | \(-0.219305\pi\) |
−0.635739 | + | 0.771904i | \(0.719305\pi\) | |||||||
\(12\) | 4.02928 | 1.16315 | ||||||||
\(13\) | −3.40251 | − | 1.19288i | −0.943685 | − | 0.330844i | ||||
\(14\) | 5.11753 | − | 1.81964i | 1.36772 | − | 0.486321i | ||||
\(15\) | −3.66593 | + | 3.66593i | −0.946538 | + | 0.946538i | ||||
\(16\) | 3.52543 | 0.881357 | ||||||||
\(17\) | 4.32672 | 1.04938 | 0.524692 | − | 0.851292i | \(-0.324180\pi\) | ||||
0.524692 | + | 0.851292i | \(0.324180\pi\) | |||||||
\(18\) | 0.451606 | − | 0.451606i | 0.106445 | − | 0.106445i | ||||
\(19\) | 3.40251 | + | 3.40251i | 0.780588 | + | 0.780588i | 0.979930 | − | 0.199342i | \(-0.0638803\pi\) |
−0.199342 | + | 0.979930i | \(0.563880\pi\) | |||||||
\(20\) | 4.46105 | − | 4.46105i | 0.997522 | − | 0.997522i | ||||
\(21\) | 2.06702 | − | 4.34801i | 0.451060 | − | 0.948814i | ||||
\(22\) | −1.31111 | −0.279529 | ||||||||
\(23\) | 0.933323i | 0.194611i | 0.995255 | + | 0.0973057i | \(0.0310225\pi\) | ||||
−0.995255 | + | 0.0973057i | \(0.968978\pi\) | |||||||
\(24\) | −0.566106 | + | 0.566106i | −0.115556 | + | 0.115556i | ||||
\(25\) | 3.11753i | 0.623506i | ||||||||
\(26\) | 6.67068 | − | 3.20751i | 1.30823 | − | 0.629045i | ||||
\(27\) | 4.89283i | 0.941625i | ||||||||
\(28\) | −2.51534 | + | 5.29108i | −0.475355 | + | 0.999920i | ||||
\(29\) | 6.33185 | 1.17580 | 0.587898 | − | 0.808935i | \(-0.299956\pi\) | ||||
0.587898 | + | 0.808935i | \(0.299956\pi\) | |||||||
\(30\) | − | 10.6430i | − | 1.94313i | ||||||
\(31\) | −5.47781 | − | 5.47781i | −0.983843 | − | 0.983843i | 0.0160282 | − | 0.999872i | \(-0.494898\pi\) |
−0.999872 | + | 0.0160282i | \(0.994898\pi\) | |||||||
\(32\) | −5.73975 | + | 5.73975i | −1.01465 | + | 1.01465i | ||||
\(33\) | −0.821763 | + | 0.821763i | −0.143050 | + | 0.143050i | ||||
\(34\) | −6.28070 | + | 6.28070i | −1.07713 | + | 1.07713i | ||||
\(35\) | −2.52543 | − | 7.10246i | −0.426875 | − | 1.20053i | ||||
\(36\) | 0.688892i | 0.114815i | ||||||||
\(37\) | 2.14050 | + | 2.14050i | 0.351896 | + | 0.351896i | 0.860815 | − | 0.508919i | \(-0.169955\pi\) |
−0.508919 | + | 0.860815i | \(0.669955\pi\) | |||||||
\(38\) | −9.87820 | −1.60246 | ||||||||
\(39\) | 2.17061 | − | 6.19135i | 0.347576 | − | 0.991410i | ||||
\(40\) | 1.25354i | 0.198202i | ||||||||
\(41\) | −1.81964 | − | 1.81964i | −0.284181 | − | 0.284181i | 0.550593 | − | 0.834774i | \(-0.314402\pi\) |
−0.834774 | + | 0.550593i | \(0.814402\pi\) | |||||||
\(42\) | 3.31111 | + | 9.31209i | 0.510915 | + | 1.43689i | ||||
\(43\) | − | 10.4795i | − | 1.59811i | −0.601259 | − | 0.799054i | \(-0.705334\pi\) | ||
0.601259 | − | 0.799054i | \(-0.294666\pi\) | |||||||
\(44\) | 1.00000 | − | 1.00000i | 0.150756 | − | 0.150756i | ||||
\(45\) | −0.626770 | − | 0.626770i | −0.0934333 | − | 0.0934333i | ||||
\(46\) | −1.35482 | − | 1.35482i | −0.199757 | − | 0.199757i | ||||
\(47\) | −5.90958 | + | 5.90958i | −0.862002 | + | 0.862002i | −0.991570 | − | 0.129569i | \(-0.958641\pi\) |
0.129569 | + | 0.991570i | \(0.458641\pi\) | |||||||
\(48\) | 6.41503i | 0.925929i | ||||||||
\(49\) | 4.41926 | + | 5.42864i | 0.631323 | + | 0.775520i | ||||
\(50\) | −4.52543 | − | 4.52543i | −0.639992 | − | 0.639992i | ||||
\(51\) | 7.87310i | 1.10245i | ||||||||
\(52\) | −2.64141 | + | 7.53424i | −0.366297 | + | 1.04481i | ||||
\(53\) | 3.36196 | 0.461801 | 0.230901 | − | 0.972977i | \(-0.425833\pi\) | ||||
0.230901 | + | 0.972977i | \(0.425833\pi\) | |||||||
\(54\) | −7.10246 | − | 7.10246i | −0.966522 | − | 0.966522i | ||||
\(55\) | 1.81964i | 0.245361i | ||||||||
\(56\) | −0.389986 | − | 1.09679i | −0.0521141 | − | 0.146564i | ||||
\(57\) | −6.19135 | + | 6.19135i | −0.820065 | + | 0.820065i | ||||
\(58\) | −9.19135 | + | 9.19135i | −1.20688 | + | 1.20688i | ||||
\(59\) | 0.255657 | − | 0.255657i | 0.0332837 | − | 0.0332837i | −0.690269 | − | 0.723553i | \(-0.742508\pi\) |
0.723553 | + | 0.690269i | \(0.242508\pi\) | |||||||
\(60\) | 8.11753 | + | 8.11753i | 1.04797 | + | 1.04797i | ||||
\(61\) | − | 7.78989i | − | 0.997394i | −0.866776 | − | 0.498697i | \(-0.833812\pi\) | ||
0.866776 | − | 0.498697i | \(-0.166188\pi\) | |||||||
\(62\) | 15.9032 | 2.01971 | ||||||||
\(63\) | 0.743387 | + | 0.353401i | 0.0936580 | + | 0.0445244i | ||||
\(64\) | − | 9.61285i | − | 1.20161i | ||||||
\(65\) | −4.45161 | − | 9.25803i | −0.552154 | − | 1.14832i | ||||
\(66\) | − | 2.38575i | − | 0.293666i | ||||||
\(67\) | 7.28100 | − | 7.28100i | 0.889515 | − | 0.889515i | −0.104961 | − | 0.994476i | \(-0.533472\pi\) |
0.994476 | + | 0.104961i | \(0.0334718\pi\) | |||||||
\(68\) | − | 9.58075i | − | 1.16184i | ||||||
\(69\) | −1.69832 | −0.204453 | ||||||||
\(70\) | 13.9759 | + | 6.64405i | 1.67044 | + | 0.794116i | ||||
\(71\) | 5.56914 | − | 5.56914i | 0.660935 | − | 0.660935i | −0.294665 | − | 0.955600i | \(-0.595208\pi\) |
0.955600 | + | 0.294665i | \(0.0952082\pi\) | |||||||
\(72\) | −0.0967881 | − | 0.0967881i | −0.0114066 | − | 0.0114066i | ||||
\(73\) | 8.86144 | − | 8.86144i | 1.03715 | − | 1.03715i | 0.0378706 | − | 0.999283i | \(-0.487943\pi\) |
0.999283 | − | 0.0378706i | \(-0.0120575\pi\) | |||||||
\(74\) | −6.21432 | −0.722400 | ||||||||
\(75\) | −5.67280 | −0.655039 | ||||||||
\(76\) | 7.53424 | − | 7.53424i | 0.864236 | − | 0.864236i | ||||
\(77\) | −0.566106 | − | 1.59210i | −0.0645137 | − | 0.181437i | ||||
\(78\) | 5.83654 | + | 12.1383i | 0.660857 | + | 1.37439i | ||||
\(79\) | −13.7971 | −1.55229 | −0.776145 | − | 0.630554i | \(-0.782828\pi\) | ||||
−0.776145 | + | 0.630554i | \(0.782828\pi\) | |||||||
\(80\) | 7.10246 | + | 7.10246i | 0.794079 | + | 0.794079i | ||||
\(81\) | −9.83654 | −1.09295 | ||||||||
\(82\) | 5.28281 | 0.583389 | ||||||||
\(83\) | −4.30785 | − | 4.30785i | −0.472848 | − | 0.472848i | 0.429987 | − | 0.902835i | \(-0.358518\pi\) |
−0.902835 | + | 0.429987i | \(0.858518\pi\) | |||||||
\(84\) | −9.62789 | − | 4.57703i | −1.05049 | − | 0.499395i | ||||
\(85\) | 8.71678 | + | 8.71678i | 0.945468 | + | 0.945468i | ||||
\(86\) | 15.2121 | + | 15.2121i | 1.64036 | + | 1.64036i | ||||
\(87\) | 11.5217i | 1.23526i | ||||||||
\(88\) | 0.280996i | 0.0299543i | ||||||||
\(89\) | −5.61214 | + | 5.61214i | −0.594885 | + | 0.594885i | −0.938947 | − | 0.344062i | \(-0.888197\pi\) |
0.344062 | + | 0.938947i | \(0.388197\pi\) | |||||||
\(90\) | 1.81964 | 0.191807 | ||||||||
\(91\) | 6.77519 | + | 6.71541i | 0.710233 | + | 0.703967i | ||||
\(92\) | 2.06668 | 0.215466 | ||||||||
\(93\) | 9.96767 | − | 9.96767i | 1.03360 | − | 1.03360i | ||||
\(94\) | − | 17.1568i | − | 1.76959i | ||||||
\(95\) | 13.7096i | 1.40658i | ||||||||
\(96\) | −10.4443 | − | 10.4443i | −1.06597 | − | 1.06597i | ||||
\(97\) | 0.236784 | + | 0.236784i | 0.0240417 | + | 0.0240417i | 0.719025 | − | 0.694984i | \(-0.244588\pi\) |
−0.694984 | + | 0.719025i | \(0.744588\pi\) | |||||||
\(98\) | −14.2953 | − | 1.46522i | −1.44404 | − | 0.148009i | ||||
\(99\) | −0.140498 | − | 0.140498i | −0.0141206 | − | 0.0141206i | ||||
\(100\) | 6.90321 | 0.690321 | ||||||||
\(101\) | −9.21955 | −0.917380 | −0.458690 | − | 0.888596i | \(-0.651681\pi\) | ||||
−0.458690 | + | 0.888596i | \(0.651681\pi\) | |||||||
\(102\) | −11.4286 | − | 11.4286i | −1.13160 | − | 1.13160i | ||||
\(103\) | 2.50708 | 0.247030 | 0.123515 | − | 0.992343i | \(-0.460583\pi\) | ||||
0.123515 | + | 0.992343i | \(0.460583\pi\) | |||||||
\(104\) | −0.687433 | − | 1.42966i | −0.0674084 | − | 0.140190i | ||||
\(105\) | 12.9240 | − | 4.59538i | 1.26125 | − | 0.448463i | ||||
\(106\) | −4.88025 | + | 4.88025i | −0.474011 | + | 0.474011i | ||||
\(107\) | 2.88247 | 0.278659 | 0.139329 | − | 0.990246i | \(-0.455505\pi\) | ||||
0.139329 | + | 0.990246i | \(0.455505\pi\) | |||||||
\(108\) | 10.8343 | 1.04253 | ||||||||
\(109\) | −3.54839 | + | 3.54839i | −0.339875 | + | 0.339875i | −0.856320 | − | 0.516446i | \(-0.827255\pi\) |
0.516446 | + | 0.856320i | \(0.327255\pi\) | |||||||
\(110\) | −2.64141 | − | 2.64141i | −0.251848 | − | 0.251848i | ||||
\(111\) | −3.89495 | + | 3.89495i | −0.369692 | + | 0.369692i | ||||
\(112\) | −8.42395 | − | 4.00469i | −0.795989 | − | 0.378408i | ||||
\(113\) | −16.3526 | −1.53832 | −0.769161 | − | 0.639055i | \(-0.779326\pi\) | ||||
−0.769161 | + | 0.639055i | \(0.779326\pi\) | |||||||
\(114\) | − | 17.9748i | − | 1.68350i | ||||||
\(115\) | −1.88031 | + | 1.88031i | −0.175340 | + | 0.175340i | ||||
\(116\) | − | 14.0207i | − | 1.30179i | ||||||
\(117\) | 1.05855 | + | 0.371113i | 0.0978626 | + | 0.0343094i | ||||
\(118\) | 0.742226i | 0.0683274i | ||||||||
\(119\) | −10.3386 | − | 4.91492i | −0.947741 | − | 0.450550i | ||||
\(120\) | −2.28100 | −0.208226 | ||||||||
\(121\) | − | 10.5921i | − | 0.962919i | ||||||
\(122\) | 11.3079 | + | 11.3079i | 1.02377 | + | 1.02377i | ||||
\(123\) | 3.31111 | − | 3.31111i | 0.298553 | − | 0.298553i | ||||
\(124\) | −12.1296 | + | 12.1296i | −1.08927 | + | 1.08927i | ||||
\(125\) | 3.79249 | − | 3.79249i | 0.339211 | − | 0.339211i | ||||
\(126\) | −1.59210 | + | 0.566106i | −0.141836 | + | 0.0504327i | ||||
\(127\) | 13.8272i | 1.22696i | 0.789709 | + | 0.613481i | \(0.210231\pi\) | ||||
−0.789709 | + | 0.613481i | \(0.789769\pi\) | |||||||
\(128\) | 2.47457 | + | 2.47457i | 0.218723 | + | 0.218723i | ||||
\(129\) | 19.0690 | 1.67893 | ||||||||
\(130\) | 19.9010 | + | 6.97703i | 1.74543 | + | 0.611926i | ||||
\(131\) | 12.8301i | 1.12097i | 0.828166 | + | 0.560483i | \(0.189385\pi\) | ||||
−0.828166 | + | 0.560483i | \(0.810615\pi\) | |||||||
\(132\) | 1.81964 | + | 1.81964i | 0.158380 | + | 0.158380i | ||||
\(133\) | −4.26517 | − | 11.9953i | −0.369838 | − | 1.04012i | ||||
\(134\) | 21.1383i | 1.82607i | ||||||||
\(135\) | −9.85728 | + | 9.85728i | −0.848379 | + | 0.848379i | ||||
\(136\) | 1.34608 | + | 1.34608i | 0.115425 | + | 0.115425i | ||||
\(137\) | 2.40075 | + | 2.40075i | 0.205110 | + | 0.205110i | 0.802185 | − | 0.597075i | \(-0.203671\pi\) |
−0.597075 | + | 0.802185i | \(0.703671\pi\) | |||||||
\(138\) | 2.46529 | − | 2.46529i | 0.209859 | − | 0.209859i | ||||
\(139\) | − | 3.34184i | − | 0.283451i | −0.989906 | − | 0.141726i | \(-0.954735\pi\) | ||
0.989906 | − | 0.141726i | \(-0.0452651\pi\) | |||||||
\(140\) | −15.7271 | + | 5.59210i | −1.32918 | + | 0.472619i | ||||
\(141\) | −10.7533 | − | 10.7533i | −0.905595 | − | 0.905595i | ||||
\(142\) | 16.1684i | 1.35682i | ||||||||
\(143\) | −0.997882 | − | 2.07530i | −0.0834471 | − | 0.173545i | ||||
\(144\) | −1.09679 | −0.0913990 | ||||||||
\(145\) | 12.7564 | + | 12.7564i | 1.05936 | + | 1.05936i | ||||
\(146\) | 25.7266i | 2.12915i | ||||||||
\(147\) | −9.87820 | + | 8.04149i | −0.814740 | + | 0.663251i | ||||
\(148\) | 4.73975 | − | 4.73975i | 0.389605 | − | 0.389605i | ||||
\(149\) | 2.62936 | − | 2.62936i | 0.215406 | − | 0.215406i | −0.591153 | − | 0.806559i | \(-0.701327\pi\) |
0.806559 | + | 0.591153i | \(0.201327\pi\) | |||||||
\(150\) | 8.23467 | − | 8.23467i | 0.672358 | − | 0.672358i | ||||
\(151\) | −4.78346 | − | 4.78346i | −0.389272 | − | 0.389272i | 0.485156 | − | 0.874428i | \(-0.338763\pi\) |
−0.874428 | + | 0.485156i | \(0.838763\pi\) | |||||||
\(152\) | 2.11709i | 0.171719i | ||||||||
\(153\) | −1.34608 | −0.108824 | ||||||||
\(154\) | 3.13287 | + | 1.48935i | 0.252454 | + | 0.120015i | ||||
\(155\) | − | 22.0716i | − | 1.77283i | ||||||
\(156\) | −13.7096 | − | 4.80642i | −1.09765 | − | 0.384822i | ||||
\(157\) | − | 3.42542i | − | 0.273379i | −0.990614 | − | 0.136689i | \(-0.956354\pi\) | ||
0.990614 | − | 0.136689i | \(-0.0436462\pi\) | |||||||
\(158\) | 20.0279 | − | 20.0279i | 1.59333 | − | 1.59333i | ||||
\(159\) | 6.11758i | 0.485156i | ||||||||
\(160\) | −23.1270 | −1.82835 | ||||||||
\(161\) | 1.06020 | − | 2.23016i | 0.0835557 | − | 0.175761i | ||||
\(162\) | 14.2788 | − | 14.2788i | 1.12185 | − | 1.12185i | ||||
\(163\) | 10.4494 | + | 10.4494i | 0.818459 | + | 0.818459i | 0.985885 | − | 0.167426i | \(-0.0535455\pi\) |
−0.167426 | + | 0.985885i | \(0.553545\pi\) | |||||||
\(164\) | −4.02928 | + | 4.02928i | −0.314634 | + | 0.314634i | ||||
\(165\) | −3.31111 | −0.257769 | ||||||||
\(166\) | 12.5066 | 0.970701 | ||||||||
\(167\) | 16.2326 | − | 16.2326i | 1.25611 | − | 1.25611i | 0.303180 | − | 0.952933i | \(-0.401952\pi\) |
0.952933 | − | 0.303180i | \(-0.0980483\pi\) | |||||||
\(168\) | 1.99576 | − | 0.709636i | 0.153977 | − | 0.0547496i | ||||
\(169\) | 10.1541 | + | 8.11753i | 0.781084 | + | 0.624426i | ||||
\(170\) | −25.3067 | −1.94093 | ||||||||
\(171\) | −1.05855 | − | 1.05855i | −0.0809491 | − | 0.0809491i | ||||
\(172\) | −23.2050 | −1.76936 | ||||||||
\(173\) | −14.3810 | −1.09337 | −0.546685 | − | 0.837338i | \(-0.684111\pi\) | ||||
−0.546685 | + | 0.837338i | \(0.684111\pi\) | |||||||
\(174\) | −16.7250 | − | 16.7250i | −1.26792 | − | 1.26792i | ||||
\(175\) | 3.54134 | − | 7.44929i | 0.267700 | − | 0.563113i | ||||
\(176\) | 1.59210 | + | 1.59210i | 0.120009 | + | 0.120009i | ||||
\(177\) | 0.465205 | + | 0.465205i | 0.0349669 | + | 0.0349669i | ||||
\(178\) | − | 16.2932i | − | 1.22123i | ||||||
\(179\) | 4.11108i | 0.307276i | 0.988127 | + | 0.153638i | \(0.0490990\pi\) | ||||
−0.988127 | + | 0.153638i | \(0.950901\pi\) | |||||||
\(180\) | −1.38787 | + | 1.38787i | −0.103446 | + | 0.103446i | ||||
\(181\) | −21.5760 | −1.60373 | −0.801867 | − | 0.597502i | \(-0.796160\pi\) | ||||
−0.801867 | + | 0.597502i | \(0.796160\pi\) | |||||||
\(182\) | −19.5830 | + | 0.0867758i | −1.45159 | + | 0.00643225i | ||||
\(183\) | 14.1748 | 1.04783 | ||||||||
\(184\) | −0.290364 | + | 0.290364i | −0.0214059 | + | 0.0214059i | ||||
\(185\) | 8.62466i | 0.634097i | ||||||||
\(186\) | 28.9382i | 2.12186i | ||||||||
\(187\) | 1.95397 | + | 1.95397i | 0.142889 | + | 0.142889i | ||||
\(188\) | 13.0857 | + | 13.0857i | 0.954373 | + | 0.954373i | ||||
\(189\) | 5.55798 | − | 11.6913i | 0.404284 | − | 0.850419i | ||||
\(190\) | −19.9010 | − | 19.9010i | −1.44377 | − | 1.44377i | ||||
\(191\) | 10.3017 | 0.745408 | 0.372704 | − | 0.927950i | \(-0.378431\pi\) | ||||
0.372704 | + | 0.927950i | \(0.378431\pi\) | |||||||
\(192\) | 17.4920 | 1.26237 | ||||||||
\(193\) | 6.28592 | + | 6.28592i | 0.452470 | + | 0.452470i | 0.896174 | − | 0.443703i | \(-0.146336\pi\) |
−0.443703 | + | 0.896174i | \(0.646336\pi\) | |||||||
\(194\) | −0.687433 | −0.0493548 | ||||||||
\(195\) | 16.8463 | − | 8.10034i | 1.20639 | − | 0.580078i | ||||
\(196\) | 12.0207 | − | 9.78566i | 0.858625 | − | 0.698976i | ||||
\(197\) | −3.25088 | + | 3.25088i | −0.231616 | + | 0.231616i | −0.813367 | − | 0.581751i | \(-0.802368\pi\) |
0.581751 | + | 0.813367i | \(0.302368\pi\) | |||||||
\(198\) | 0.407896 | 0.0289879 | ||||||||
\(199\) | 6.20116 | 0.439589 | 0.219794 | − | 0.975546i | \(-0.429461\pi\) | ||||
0.219794 | + | 0.975546i | \(0.429461\pi\) | |||||||
\(200\) | −0.969888 | + | 0.969888i | −0.0685815 | + | 0.0685815i | ||||
\(201\) | 13.2488 | + | 13.2488i | 0.934500 | + | 0.934500i | ||||
\(202\) | 13.3832 | − | 13.3832i | 0.941636 | − | 0.941636i | ||||
\(203\) | −15.1299 | − | 7.19263i | −1.06191 | − | 0.504824i | ||||
\(204\) | 17.4336 | 1.22059 | ||||||||
\(205\) | − | 7.33185i | − | 0.512079i | ||||||
\(206\) | −3.63929 | + | 3.63929i | −0.253561 | + | 0.253561i | ||||
\(207\) | − | 0.290364i | − | 0.0201817i | ||||||
\(208\) | −11.9953 | − | 4.20540i | −0.831724 | − | 0.291592i | ||||
\(209\) | 3.07318i | 0.212577i | ||||||||
\(210\) | −12.0898 | + | 25.4312i | −0.834276 | + | 1.75492i | ||||
\(211\) | −9.55554 | −0.657830 | −0.328915 | − | 0.944359i | \(-0.606683\pi\) | ||||
−0.328915 | + | 0.944359i | \(0.606683\pi\) | |||||||
\(212\) | − | 7.44446i | − | 0.511288i | ||||||
\(213\) | 10.1339 | + | 10.1339i | 0.694360 | + | 0.694360i | ||||
\(214\) | −4.18421 | + | 4.18421i | −0.286027 | + | 0.286027i | ||||
\(215\) | 21.1124 | − | 21.1124i | 1.43985 | − | 1.43985i | ||||
\(216\) | −1.52220 | + | 1.52220i | −0.103572 | + | 0.103572i | ||||
\(217\) | 6.86665 | + | 19.3116i | 0.466138 | + | 1.31096i | ||||
\(218\) | − | 10.3017i | − | 0.697722i | ||||||
\(219\) | 16.1247 | + | 16.1247i | 1.08960 | + | 1.08960i | ||||
\(220\) | 4.02928 | 0.271654 | ||||||||
\(221\) | −14.7217 | − | 5.16124i | −0.990289 | − | 0.347183i | ||||
\(222\) | − | 11.3079i | − | 0.758934i | ||||||
\(223\) | 2.58074 | + | 2.58074i | 0.172819 | + | 0.172819i | 0.788217 | − | 0.615398i | \(-0.211005\pi\) |
−0.615398 | + | 0.788217i | \(0.711005\pi\) | |||||||
\(224\) | 20.2351 | − | 7.19500i | 1.35201 | − | 0.480736i | ||||
\(225\) | − | 0.969888i | − | 0.0646592i | ||||||
\(226\) | 23.7375 | − | 23.7375i | 1.57900 | − | 1.57900i | ||||
\(227\) | −5.25403 | − | 5.25403i | −0.348722 | − | 0.348722i | 0.510911 | − | 0.859633i | \(-0.329308\pi\) |
−0.859633 | + | 0.510911i | \(0.829308\pi\) | |||||||
\(228\) | 13.7096 | + | 13.7096i | 0.907943 | + | 0.907943i | ||||
\(229\) | 0.729224 | − | 0.729224i | 0.0481885 | − | 0.0481885i | −0.682602 | − | 0.730790i | \(-0.739152\pi\) |
0.730790 | + | 0.682602i | \(0.239152\pi\) | |||||||
\(230\) | − | 5.45893i | − | 0.359952i | ||||||
\(231\) | 2.89706 | − | 1.03011i | 0.190613 | − | 0.0677764i | ||||
\(232\) | 1.96989 | + | 1.96989i | 0.129330 | + | 0.129330i | ||||
\(233\) | 24.6128i | 1.61244i | 0.591615 | + | 0.806221i | \(0.298491\pi\) | ||||
−0.591615 | + | 0.806221i | \(0.701509\pi\) | |||||||
\(234\) | −2.07530 | + | 0.997882i | −0.135667 | + | 0.0652336i | ||||
\(235\) | −23.8113 | −1.55328 | ||||||||
\(236\) | −0.566106 | − | 0.566106i | −0.0368503 | − | 0.0368503i | ||||
\(237\) | − | 25.1057i | − | 1.63079i | ||||||
\(238\) | 22.1421 | − | 7.87310i | 1.43526 | − | 0.510337i | ||||
\(239\) | −6.52543 | + | 6.52543i | −0.422095 | + | 0.422095i | −0.885924 | − | 0.463830i | \(-0.846475\pi\) |
0.463830 | + | 0.885924i | \(0.346475\pi\) | |||||||
\(240\) | −12.9240 | + | 12.9240i | −0.834238 | + | 0.834238i | ||||
\(241\) | −20.1563 | + | 20.1563i | −1.29838 | + | 1.29838i | −0.368920 | + | 0.929461i | \(0.620272\pi\) |
−0.929461 | + | 0.368920i | \(0.879728\pi\) | |||||||
\(242\) | 15.3756 | + | 15.3756i | 0.988379 | + | 0.988379i | ||||
\(243\) | − | 3.22051i | − | 0.206596i | ||||||
\(244\) | −17.2493 | −1.10427 | ||||||||
\(245\) | −2.03353 | + | 19.8400i | −0.129918 | + | 1.26753i | ||||
\(246\) | 9.61285i | 0.612893i | ||||||||
\(247\) | −7.51828 | − | 15.6358i | −0.478377 | − | 0.994883i | ||||
\(248\) | − | 3.40838i | − | 0.216432i | ||||||
\(249\) | 7.83876 | − | 7.83876i | 0.496761 | − | 0.496761i | ||||
\(250\) | 11.0104i | 0.696359i | ||||||||
\(251\) | 14.4448 | 0.911747 | 0.455873 | − | 0.890045i | \(-0.349327\pi\) | ||||
0.455873 | + | 0.890045i | \(0.349327\pi\) | |||||||
\(252\) | 0.782543 | − | 1.64610i | 0.0492956 | − | 0.103694i | ||||
\(253\) | −0.421494 | + | 0.421494i | −0.0264991 | + | 0.0264991i | ||||
\(254\) | −20.0716 | − | 20.0716i | −1.25940 | − | 1.25940i | ||||
\(255\) | −15.8614 | + | 15.8614i | −0.993282 | + | 0.993282i | ||||
\(256\) | 12.0415 | 0.752593 | ||||||||
\(257\) | −14.6237 | −0.912201 | −0.456101 | − | 0.889928i | \(-0.650754\pi\) | ||||
−0.456101 | + | 0.889928i | \(0.650754\pi\) | |||||||
\(258\) | −27.6806 | + | 27.6806i | −1.72332 | + | 1.72332i | ||||
\(259\) | −2.68320 | − | 7.54617i | −0.166726 | − | 0.468896i | ||||
\(260\) | −20.5002 | + | 9.85728i | −1.27137 | + | 0.611322i | ||||
\(261\) | −1.96989 | −0.121933 | ||||||||
\(262\) | −18.6242 | − | 18.6242i | −1.15061 | − | 1.15061i | ||||
\(263\) | −2.61729 | −0.161389 | −0.0806946 | − | 0.996739i | \(-0.525714\pi\) | ||||
−0.0806946 | + | 0.996739i | \(0.525714\pi\) | |||||||
\(264\) | −0.511313 | −0.0314692 | ||||||||
\(265\) | 6.77314 | + | 6.77314i | 0.416071 | + | 0.416071i | ||||
\(266\) | 23.6038 | + | 11.2211i | 1.44724 | + | 0.688009i | ||||
\(267\) | −10.2121 | − | 10.2121i | −0.624970 | − | 0.624970i | ||||
\(268\) | −16.1225 | − | 16.1225i | −0.984836 | − | 0.984836i | ||||
\(269\) | − | 9.82340i | − | 0.598944i | −0.954105 | − | 0.299472i | \(-0.903190\pi\) | ||
0.954105 | − | 0.299472i | \(-0.0968104\pi\) | |||||||
\(270\) | − | 28.6178i | − | 1.74162i | ||||||
\(271\) | 3.43438 | − | 3.43438i | 0.208624 | − | 0.208624i | −0.595059 | − | 0.803682i | \(-0.702871\pi\) |
0.803682 | + | 0.595059i | \(0.202871\pi\) | |||||||
\(272\) | 15.2535 | 0.924882 | ||||||||
\(273\) | −12.2197 | + | 12.3284i | −0.739568 | + | 0.746151i | ||||
\(274\) | −6.96989 | −0.421066 | ||||||||
\(275\) | −1.40790 | + | 1.40790i | −0.0848993 | + | 0.0848993i | ||||
\(276\) | 3.76062i | 0.226363i | ||||||||
\(277\) | − | 5.89877i | − | 0.354423i | −0.984173 | − | 0.177211i | \(-0.943292\pi\) | ||
0.984173 | − | 0.177211i | \(-0.0567076\pi\) | |||||||
\(278\) | 4.85104 | + | 4.85104i | 0.290946 | + | 0.290946i | ||||
\(279\) | 1.70419 | + | 1.70419i | 0.102027 | + | 0.102027i | ||||
\(280\) | 1.42395 | − | 2.99531i | 0.0850973 | − | 0.179004i | ||||
\(281\) | 9.23729 | + | 9.23729i | 0.551050 | + | 0.551050i | 0.926744 | − | 0.375694i | \(-0.122595\pi\) |
−0.375694 | + | 0.926744i | \(0.622595\pi\) | |||||||
\(282\) | 31.2192 | 1.85908 | ||||||||
\(283\) | −8.32721 | −0.495001 | −0.247501 | − | 0.968888i | \(-0.579609\pi\) | ||||
−0.247501 | + | 0.968888i | \(0.579609\pi\) | |||||||
\(284\) | −12.3319 | − | 12.3319i | −0.731761 | − | 0.731761i | ||||
\(285\) | −24.9467 | −1.47771 | ||||||||
\(286\) | 4.46105 | + | 1.56399i | 0.263788 | + | 0.0924806i | ||||
\(287\) | 2.28100 | + | 6.41503i | 0.134643 | + | 0.378667i | ||||
\(288\) | 1.78568 | − | 1.78568i | 0.105222 | − | 0.105222i | ||||
\(289\) | 1.72054 | 0.101208 | ||||||||
\(290\) | −37.0345 | −2.17474 | ||||||||
\(291\) | −0.430862 | + | 0.430862i | −0.0252576 | + | 0.0252576i | ||||
\(292\) | −19.6221 | − | 19.6221i | −1.14829 | − | 1.14829i | ||||
\(293\) | −15.4903 | + | 15.4903i | −0.904955 | + | 0.904955i | −0.995860 | − | 0.0909047i | \(-0.971024\pi\) |
0.0909047 | + | 0.995860i | \(0.471024\pi\) | |||||||
\(294\) | 2.66618 | − | 26.0123i | 0.155495 | − | 1.51707i | ||||
\(295\) | 1.03011 | 0.0599754 | ||||||||
\(296\) | 1.33185i | 0.0774123i | ||||||||
\(297\) | −2.20963 | + | 2.20963i | −0.128216 | + | 0.128216i | ||||
\(298\) | 7.63359i | 0.442202i | ||||||||
\(299\) | 1.11334 | − | 3.17564i | 0.0643860 | − | 0.183652i | ||||
\(300\) | 12.5614i | 0.725232i | ||||||||
\(301\) | −11.9041 | + | 25.0406i | −0.686142 | + | 1.44331i | ||||
\(302\) | 13.8874 | 0.799130 | ||||||||
\(303\) | − | 16.7763i | − | 0.963774i | ||||||
\(304\) | 11.9953 | + | 11.9953i | 0.687977 | + | 0.687977i | ||||
\(305\) | 15.6938 | − | 15.6938i | 0.898625 | − | 0.898625i | ||||
\(306\) | 1.95397 | − | 1.95397i | 0.111701 | − | 0.111701i | ||||
\(307\) | 5.77526 | − | 5.77526i | 0.329611 | − | 0.329611i | −0.522827 | − | 0.852439i | \(-0.675123\pi\) |
0.852439 | + | 0.522827i | \(0.175123\pi\) | |||||||
\(308\) | −3.52543 | + | 1.25354i | −0.200880 | + | 0.0714270i | ||||
\(309\) | 4.56199i | 0.259523i | ||||||||
\(310\) | 32.0393 | + | 32.0393i | 1.81971 | + | 1.81971i | ||||
\(311\) | −2.62562 | −0.148885 | −0.0744426 | − | 0.997225i | \(-0.523718\pi\) | ||||
−0.0744426 | + | 0.997225i | \(0.523718\pi\) | |||||||
\(312\) | 2.60147 | − | 1.25088i | 0.147279 | − | 0.0708174i | ||||
\(313\) | − | 19.8489i | − | 1.12193i | −0.827840 | − | 0.560964i | \(-0.810431\pi\) | ||
0.827840 | − | 0.560964i | \(-0.189569\pi\) | |||||||
\(314\) | 4.97237 | + | 4.97237i | 0.280607 | + | 0.280607i | ||||
\(315\) | 0.785680 | + | 2.20963i | 0.0442681 | + | 0.124499i | ||||
\(316\) | 30.5511i | 1.71863i | ||||||||
\(317\) | 1.14764 | − | 1.14764i | 0.0644581 | − | 0.0644581i | −0.674143 | − | 0.738601i | \(-0.735487\pi\) |
0.738601 | + | 0.674143i | \(0.235487\pi\) | |||||||
\(318\) | −8.88031 | − | 8.88031i | −0.497983 | − | 0.497983i | ||||
\(319\) | 2.85950 | + | 2.85950i | 0.160101 | + | 0.160101i | ||||
\(320\) | 19.3664 | − | 19.3664i | 1.08262 | − | 1.08262i | ||||
\(321\) | 5.24507i | 0.292751i | ||||||||
\(322\) | 1.69832 | + | 4.77631i | 0.0946435 | + | 0.266173i | ||||
\(323\) | 14.7217 | + | 14.7217i | 0.819137 | + | 0.819137i | ||||
\(324\) | 21.7812i | 1.21007i | ||||||||
\(325\) | 3.71883 | − | 10.6074i | 0.206283 | − | 0.588394i | ||||
\(326\) | −30.3368 | −1.68020 | ||||||||
\(327\) | −6.45682 | − | 6.45682i | −0.357063 | − | 0.357063i | ||||
\(328\) | − | 1.13221i | − | 0.0625159i | ||||||
\(329\) | 20.8338 | − | 7.40790i | 1.14861 | − | 0.408411i | ||||
\(330\) | 4.80642 | − | 4.80642i | 0.264585 | − | 0.264585i | ||||
\(331\) | −2.90321 | + | 2.90321i | −0.159575 | + | 0.159575i | −0.782378 | − | 0.622803i | \(-0.785994\pi\) |
0.622803 | + | 0.782378i | \(0.285994\pi\) | |||||||
\(332\) | −9.53896 | + | 9.53896i | −0.523518 | + | 0.523518i | ||||
\(333\) | −0.665926 | − | 0.665926i | −0.0364925 | − | 0.0364925i | ||||
\(334\) | 47.1266i | 2.57865i | ||||||||
\(335\) | 29.3371 | 1.60286 | ||||||||
\(336\) | 7.28711 | − | 15.3286i | 0.397545 | − | 0.836244i | ||||
\(337\) | 4.47304i | 0.243662i | 0.992551 | + | 0.121831i | \(0.0388766\pi\) | ||||
−0.992551 | + | 0.121831i | \(0.961123\pi\) | |||||||
\(338\) | −26.5232 | + | 2.95629i | −1.44267 | + | 0.160801i | ||||
\(339\) | − | 29.7559i | − | 1.61612i | ||||||
\(340\) | 19.3017 | − | 19.3017i | 1.04678 | − | 1.04678i | ||||
\(341\) | − | 4.94762i | − | 0.267929i | ||||||
\(342\) | 3.07318 | 0.166179 | ||||||||
\(343\) | −4.39312 | − | 17.9917i | −0.237206 | − | 0.971459i | ||||
\(344\) | 3.26025 | − | 3.26025i | 0.175781 | − | 0.175781i | ||||
\(345\) | −3.42149 | − | 3.42149i | −0.184207 | − | 0.184207i | ||||
\(346\) | 20.8756 | − | 20.8756i | 1.12228 | − | 1.12228i | ||||
\(347\) | 8.81135 | 0.473018 | 0.236509 | − | 0.971629i | \(-0.423997\pi\) | ||||
0.236509 | + | 0.971629i | \(0.423997\pi\) | |||||||
\(348\) | 25.5128 | 1.36763 | ||||||||
\(349\) | −11.8133 | + | 11.8133i | −0.632351 | + | 0.632351i | −0.948657 | − | 0.316306i | \(-0.897557\pi\) |
0.316306 | + | 0.948657i | \(0.397557\pi\) | |||||||
\(350\) | 5.67280 | + | 15.9541i | 0.303224 | + | 0.852781i | ||||
\(351\) | 5.83654 | − | 16.6479i | 0.311531 | − | 0.888598i | ||||
\(352\) | −5.18421 | −0.276319 | ||||||||
\(353\) | −2.91007 | − | 2.91007i | −0.154887 | − | 0.154887i | 0.625410 | − | 0.780297i | \(-0.284932\pi\) |
−0.780297 | + | 0.625410i | \(0.784932\pi\) | |||||||
\(354\) | −1.35059 | −0.0717829 | ||||||||
\(355\) | 22.4396 | 1.19097 | ||||||||
\(356\) | 12.4271 | + | 12.4271i | 0.658633 | + | 0.658633i | ||||
\(357\) | 8.94340 | − | 18.8126i | 0.473335 | − | 0.995671i | ||||
\(358\) | −5.96767 | − | 5.96767i | −0.315401 | − | 0.315401i | ||||
\(359\) | 3.52320 | + | 3.52320i | 0.185948 | + | 0.185948i | 0.793942 | − | 0.607994i | \(-0.208026\pi\) |
−0.607994 | + | 0.793942i | \(0.708026\pi\) | |||||||
\(360\) | − | 0.389986i | − | 0.0205541i | ||||||
\(361\) | 4.15410i | 0.218637i | ||||||||
\(362\) | 31.3199 | − | 31.3199i | 1.64614 | − | 1.64614i | ||||
\(363\) | 19.2739 | 1.01162 | ||||||||
\(364\) | 14.8701 | − | 15.0024i | 0.779404 | − | 0.786342i | ||||
\(365\) | 35.7052 | 1.86890 | ||||||||
\(366\) | −20.5763 | + | 20.5763i | −1.07554 | + | 1.07554i | ||||
\(367\) | 19.8112i | 1.03414i | 0.855944 | + | 0.517068i | \(0.172976\pi\) | ||||
−0.855944 | + | 0.517068i | \(0.827024\pi\) | |||||||
\(368\) | 3.29036i | 0.171522i | ||||||||
\(369\) | 0.566106 | + | 0.566106i | 0.0294703 | + | 0.0294703i | ||||
\(370\) | −12.5196 | − | 12.5196i | −0.650863 | − | 0.650863i | ||||
\(371\) | −8.03335 | − | 3.81900i | −0.417071 | − | 0.198273i | ||||
\(372\) | −22.0716 | − | 22.0716i | −1.14436 | − | 1.14436i | ||||
\(373\) | −24.5368 | −1.27047 | −0.635234 | − | 0.772320i | \(-0.719096\pi\) | ||||
−0.635234 | + | 0.772320i | \(0.719096\pi\) | |||||||
\(374\) | −5.67280 | −0.293334 | ||||||||
\(375\) | 6.90099 | + | 6.90099i | 0.356366 | + | 0.356366i | ||||
\(376\) | −3.67704 | −0.189629 | ||||||||
\(377\) | −21.5442 | − | 7.55311i | −1.10958 | − | 0.389005i | ||||
\(378\) | 8.90321 | + | 25.0392i | 0.457932 | + | 1.28788i | ||||
\(379\) | −8.78346 | + | 8.78346i | −0.451176 | + | 0.451176i | −0.895745 | − | 0.444569i | \(-0.853357\pi\) |
0.444569 | + | 0.895745i | \(0.353357\pi\) | |||||||
\(380\) | 30.3575 | 1.55731 | ||||||||
\(381\) | −25.1605 | −1.28901 | ||||||||
\(382\) | −14.9541 | + | 14.9541i | −0.765117 | + | 0.765117i | ||||
\(383\) | −17.8990 | − | 17.8990i | −0.914596 | − | 0.914596i | 0.0820333 | − | 0.996630i | \(-0.473859\pi\) |
−0.996630 | + | 0.0820333i | \(0.973859\pi\) | |||||||
\(384\) | −4.50284 | + | 4.50284i | −0.229785 | + | 0.229785i | ||||
\(385\) | 2.06702 | − | 4.34801i | 0.105345 | − | 0.221595i | ||||
\(386\) | −18.2494 | −0.928868 | ||||||||
\(387\) | 3.26025i | 0.165728i | ||||||||
\(388\) | 0.524315 | − | 0.524315i | 0.0266181 | − | 0.0266181i | ||||
\(389\) | − | 12.0667i | − | 0.611805i | −0.952063 | − | 0.305902i | \(-0.901042\pi\) | ||
0.952063 | − | 0.305902i | \(-0.0989581\pi\) | |||||||
\(390\) | −12.6957 | + | 36.2127i | −0.642873 | + | 1.83370i | ||||
\(391\) | 4.03823i | 0.204222i | ||||||||
\(392\) | −0.314025 | + | 3.06376i | −0.0158607 | + | 0.154743i | ||||
\(393\) | −23.3461 | −1.17766 | ||||||||
\(394\) | − | 9.43801i | − | 0.475480i | ||||||
\(395\) | −27.7961 | − | 27.7961i | −1.39857 | − | 1.39857i | ||||
\(396\) | −0.311108 | + | 0.311108i | −0.0156338 | + | 0.0156338i | ||||
\(397\) | 7.82177 | − | 7.82177i | 0.392563 | − | 0.392563i | −0.483037 | − | 0.875600i | \(-0.660466\pi\) |
0.875600 | + | 0.483037i | \(0.160466\pi\) | |||||||
\(398\) | −9.00164 | + | 9.00164i | −0.451212 | + | 0.451212i | ||||
\(399\) | 21.8272 | − | 7.76110i | 1.09273 | − | 0.388541i | ||||
\(400\) | 10.9906i | 0.549532i | ||||||||
\(401\) | −17.6178 | − | 17.6178i | −0.879789 | − | 0.879789i | 0.113723 | − | 0.993512i | \(-0.463722\pi\) |
−0.993512 | + | 0.113723i | \(0.963722\pi\) | |||||||
\(402\) | −38.4642 | −1.91842 | ||||||||
\(403\) | 12.1039 | + | 25.1726i | 0.602940 | + | 1.25394i | ||||
\(404\) | 20.4150i | 1.01569i | ||||||||
\(405\) | −19.8171 | − | 19.8171i | −0.984717 | − | 0.984717i | ||||
\(406\) | 32.4035 | − | 11.5217i | 1.60816 | − | 0.571813i | ||||
\(407\) | 1.93332i | 0.0958313i | ||||||||
\(408\) | −2.44938 | + | 2.44938i | −0.121263 | + | 0.121263i | ||||
\(409\) | 24.0225 | + | 24.0225i | 1.18783 | + | 1.18783i | 0.977665 | + | 0.210169i | \(0.0674013\pi\) |
0.210169 | + | 0.977665i | \(0.432599\pi\) | |||||||
\(410\) | 10.6430 | + | 10.6430i | 0.525618 | + | 0.525618i | ||||
\(411\) | −4.36851 | + | 4.36851i | −0.215483 | + | 0.215483i | ||||
\(412\) | − | 5.55147i | − | 0.273501i | ||||||
\(413\) | −0.901299 | + | 0.320476i | −0.0443500 | + | 0.0157696i | ||||
\(414\) | 0.421494 | + | 0.421494i | 0.0207153 | + | 0.0207153i | ||||
\(415\) | − | 17.3575i | − | 0.852047i | ||||||
\(416\) | 26.3763 | − | 12.6827i | 1.29321 | − | 0.621822i | ||||
\(417\) | 6.08097 | 0.297786 | ||||||||
\(418\) | −4.46105 | − | 4.46105i | −0.218197 | − | 0.218197i | ||||
\(419\) | − | 19.6899i | − | 0.961912i | −0.876745 | − | 0.480956i | \(-0.840290\pi\) | ||
0.876745 | − | 0.480956i | \(-0.159710\pi\) | |||||||
\(420\) | −10.1756 | − | 28.6178i | −0.496521 | − | 1.39640i | ||||
\(421\) | 26.6042 | − | 26.6042i | 1.29661 | − | 1.29661i | 0.365989 | − | 0.930619i | \(-0.380731\pi\) |
0.930619 | − | 0.365989i | \(-0.119269\pi\) | |||||||
\(422\) | 13.8709 | − | 13.8709i | 0.675224 | − | 0.675224i | ||||
\(423\) | 1.83852 | − | 1.83852i | 0.0893918 | − | 0.0893918i | ||||
\(424\) | 1.04593 | + | 1.04593i | 0.0507950 | + | 0.0507950i | ||||
\(425\) | 13.4887i | 0.654298i | ||||||||
\(426\) | −29.4207 | −1.42544 | ||||||||
\(427\) | −8.84888 | + | 18.6138i | −0.428228 | + | 0.900786i | ||||
\(428\) | − | 6.38271i | − | 0.308520i | ||||||
\(429\) | 3.77631 | − | 1.81579i | 0.182322 | − | 0.0876673i | ||||
\(430\) | 61.2937i | 2.95585i | ||||||||
\(431\) | −4.81135 | + | 4.81135i | −0.231754 | + | 0.231754i | −0.813425 | − | 0.581670i | \(-0.802399\pi\) |
0.581670 | + | 0.813425i | \(0.302399\pi\) | |||||||
\(432\) | 17.2493i | 0.829908i | ||||||||
\(433\) | 8.34704 | 0.401133 | 0.200567 | − | 0.979680i | \(-0.435722\pi\) | ||||
0.200567 | + | 0.979680i | \(0.435722\pi\) | |||||||
\(434\) | −38.0005 | − | 18.0652i | −1.82408 | − | 0.867157i | ||||
\(435\) | −23.2121 | + | 23.2121i | −1.11293 | + | 1.11293i | ||||
\(436\) | 7.85728 | + | 7.85728i | 0.376295 | + | 0.376295i | ||||
\(437\) | −3.17564 | + | 3.17564i | −0.151911 | + | 0.151911i | ||||
\(438\) | −46.8134 | −2.23683 | ||||||||
\(439\) | 2.42350 | 0.115667 | 0.0578336 | − | 0.998326i | \(-0.481581\pi\) | ||||
0.0578336 | + | 0.998326i | \(0.481581\pi\) | |||||||
\(440\) | −0.566106 | + | 0.566106i | −0.0269880 | + | 0.0269880i | ||||
\(441\) | −1.37487 | − | 1.68889i | −0.0654698 | − | 0.0804234i | ||||
\(442\) | 28.8622 | − | 13.8780i | 1.37283 | − | 0.660110i | ||||
\(443\) | 13.7763 | 0.654532 | 0.327266 | − | 0.944932i | \(-0.393873\pi\) | ||||
0.327266 | + | 0.944932i | \(0.393873\pi\) | |||||||
\(444\) | 8.62466 | + | 8.62466i | 0.409308 | + | 0.409308i | ||||
\(445\) | −22.6128 | −1.07195 | ||||||||
\(446\) | −7.49245 | −0.354778 | ||||||||
\(447\) | 4.78450 | + | 4.78450i | 0.226299 | + | 0.226299i | ||||
\(448\) | −10.9197 | + | 22.9697i | −0.515905 | + | 1.08522i | ||||
\(449\) | −24.7447 | − | 24.7447i | −1.16777 | − | 1.16777i | −0.982730 | − | 0.185043i | \(-0.940758\pi\) |
−0.185043 | − | 0.982730i | \(-0.559242\pi\) | |||||||
\(450\) | 1.40790 | + | 1.40790i | 0.0663688 | + | 0.0663688i | ||||
\(451\) | − | 1.64353i | − | 0.0773906i | ||||||
\(452\) | 36.2099i | 1.70317i | ||||||||
\(453\) | 8.70419 | − | 8.70419i | 0.408959 | − | 0.408959i | ||||
\(454\) | 15.2535 | 0.715885 | ||||||||
\(455\) | 0.120433 | + | 27.1787i | 0.00564600 | + | 1.27416i | ||||
\(456\) | −3.85236 | −0.180403 | ||||||||
\(457\) | −2.84521 | + | 2.84521i | −0.133093 | + | 0.133093i | −0.770515 | − | 0.637422i | \(-0.780001\pi\) |
0.637422 | + | 0.770515i | \(0.280001\pi\) | |||||||
\(458\) | 2.11709i | 0.0989252i | ||||||||
\(459\) | 21.1699i | 0.988127i | ||||||||
\(460\) | 4.16360 | + | 4.16360i | 0.194129 | + | 0.194129i | ||||
\(461\) | 2.38575 | + | 2.38575i | 0.111115 | + | 0.111115i | 0.760479 | − | 0.649363i | \(-0.224964\pi\) |
−0.649363 | + | 0.760479i | \(0.724964\pi\) | |||||||
\(462\) | −2.71008 | + | 5.70071i | −0.126084 | + | 0.265221i | ||||
\(463\) | 17.5899 | + | 17.5899i | 0.817471 | + | 0.817471i | 0.985741 | − | 0.168270i | \(-0.0538180\pi\) |
−0.168270 | + | 0.985741i | \(0.553818\pi\) | |||||||
\(464\) | 22.3225 | 1.03630 | ||||||||
\(465\) | 40.1625 | 1.86249 | ||||||||
\(466\) | −35.7282 | − | 35.7282i | −1.65507 | − | 1.65507i | ||||
\(467\) | 21.4287 | 0.991602 | 0.495801 | − | 0.868436i | \(-0.334874\pi\) | ||||
0.495801 | + | 0.868436i | \(0.334874\pi\) | |||||||
\(468\) | 0.821763 | − | 2.34396i | 0.0379860 | − | 0.108350i | ||||
\(469\) | −25.6686 | + | 9.12701i | −1.18527 | + | 0.421446i | ||||
\(470\) | 34.5647 | − | 34.5647i | 1.59435 | − | 1.59435i | ||||
\(471\) | 6.23306 | 0.287204 | ||||||||
\(472\) | 0.159074 | 0.00732196 | ||||||||
\(473\) | 4.73260 | − | 4.73260i | 0.217605 | − | 0.217605i | ||||
\(474\) | 36.4436 | + | 36.4436i | 1.67391 | + | 1.67391i | ||||
\(475\) | −10.6074 | + | 10.6074i | −0.486702 | + | 0.486702i | ||||
\(476\) | −10.8832 | + | 22.8930i | −0.498830 | + | 1.04930i | ||||
\(477\) | −1.04593 | −0.0478900 | ||||||||
\(478\) | − | 18.9447i | − | 0.866510i | ||||||
\(479\) | −4.61425 | + | 4.61425i | −0.210831 | + | 0.210831i | −0.804620 | − | 0.593790i | \(-0.797631\pi\) |
0.593790 | + | 0.804620i | \(0.297631\pi\) | |||||||
\(480\) | − | 42.0830i | − | 1.92082i | ||||||
\(481\) | −4.72971 | − | 9.83641i | −0.215656 | − | 0.448501i | ||||
\(482\) | − | 58.5180i | − | 2.66542i | ||||||
\(483\) | 4.05810 | + | 1.92919i | 0.184650 | + | 0.0877814i | ||||
\(484\) | −23.4543 | −1.06610 | ||||||||
\(485\) | 0.954067i | 0.0433220i | ||||||||
\(486\) | 4.67492 | + | 4.67492i | 0.212059 | + | 0.212059i | ||||
\(487\) | 9.62867 | − | 9.62867i | 0.436317 | − | 0.436317i | −0.454454 | − | 0.890770i | \(-0.650166\pi\) |
0.890770 | + | 0.454454i | \(0.150166\pi\) | |||||||
\(488\) | 2.42350 | − | 2.42350i | 0.109707 | − | 0.109707i | ||||
\(489\) | −19.0142 | + | 19.0142i | −0.859850 | + | 0.859850i | ||||
\(490\) | −25.8479 | − | 31.7517i | −1.16769 | − | 1.43439i | ||||
\(491\) | 9.21924i | 0.416059i | 0.978123 | + | 0.208029i | \(0.0667049\pi\) | ||||
−0.978123 | + | 0.208029i | \(0.933295\pi\) | |||||||
\(492\) | −7.33185 | − | 7.33185i | −0.330545 | − | 0.330545i | ||||
\(493\) | 27.3962 | 1.23386 | ||||||||
\(494\) | 33.6106 | + | 11.7835i | 1.51221 | + | 0.530163i | ||||
\(495\) | − | 0.566106i | − | 0.0254446i | ||||||
\(496\) | −19.3116 | − | 19.3116i | −0.867117 | − | 0.867117i | ||||
\(497\) | −19.6336 | + | 6.98113i | −0.880687 | + | 0.313147i | ||||
\(498\) | 22.7576i | 1.01979i | ||||||||
\(499\) | −6.65947 | + | 6.65947i | −0.298119 | + | 0.298119i | −0.840277 | − | 0.542158i | \(-0.817608\pi\) |
0.542158 | + | 0.840277i | \(0.317608\pi\) | |||||||
\(500\) | −8.39779 | − | 8.39779i | −0.375561 | − | 0.375561i | ||||
\(501\) | 29.5375 | + | 29.5375i | 1.31964 | + | 1.31964i | ||||
\(502\) | −20.9681 | + | 20.9681i | −0.935854 | + | 0.935854i | ||||
\(503\) | − | 1.81069i | − | 0.0807346i | −0.999185 | − | 0.0403673i | \(-0.987147\pi\) | ||
0.999185 | − | 0.0403673i | \(-0.0128528\pi\) | |||||||
\(504\) | 0.121328 | + | 0.341219i | 0.00540436 | + | 0.0151991i | ||||
\(505\) | −18.5741 | − | 18.5741i | −0.826535 | − | 0.826535i | ||||
\(506\) | − | 1.22369i | − | 0.0543996i | ||||||
\(507\) | −14.7710 | + | 18.4769i | −0.656004 | + | 0.820586i | ||||
\(508\) | 30.6178 | 1.35844 | ||||||||
\(509\) | 22.2864 | + | 22.2864i | 0.987827 | + | 0.987827i | 0.999927 | − | 0.0121000i | \(-0.00385163\pi\) |
−0.0121000 | + | 0.999927i | \(0.503852\pi\) | |||||||
\(510\) | − | 46.0491i | − | 2.03909i | ||||||
\(511\) | −31.2404 | + | 11.1082i | −1.38199 | + | 0.491396i | ||||
\(512\) | −22.4286 | + | 22.4286i | −0.991215 | + | 0.991215i | ||||
\(513\) | −16.6479 | + | 16.6479i | −0.735022 | + | 0.735022i | ||||
\(514\) | 21.2278 | − | 21.2278i | 0.936320 | − | 0.936320i | ||||
\(515\) | 5.05086 | + | 5.05086i | 0.222567 | + | 0.222567i | ||||
\(516\) | − | 42.2248i | − | 1.85884i | ||||||
\(517\) | −5.33761 | −0.234748 | ||||||||
\(518\) | 14.8490 | + | 7.05912i | 0.652428 | + | 0.310160i | ||||
\(519\) | − | 26.1684i | − | 1.14866i | ||||||
\(520\) | 1.49532 | − | 4.26517i | 0.0655739 | − | 0.187040i | ||||
\(521\) | − | 15.8744i | − | 0.695472i | −0.937592 | − | 0.347736i | \(-0.886951\pi\) | ||
0.937592 | − | 0.347736i | \(-0.113049\pi\) | |||||||
\(522\) | 2.85950 | − | 2.85950i | 0.125157 | − | 0.125157i | ||||
\(523\) | − | 3.90795i | − | 0.170883i | −0.996343 | − | 0.0854413i | \(-0.972770\pi\) | ||
0.996343 | − | 0.0854413i | \(-0.0272300\pi\) | |||||||
\(524\) | 28.4098 | 1.24109 | ||||||||
\(525\) | 13.5551 | + | 6.44399i | 0.591591 | + | 0.281239i | ||||
\(526\) | 3.79928 | − | 3.79928i | 0.165656 | − | 0.165656i | ||||
\(527\) | −23.7010 | − | 23.7010i | −1.03243 | − | 1.03243i | ||||
\(528\) | −2.89706 | + | 2.89706i | −0.126079 | + | 0.126079i | ||||
\(529\) | 22.1289 | 0.962126 | ||||||||
\(530\) | −19.6639 | −0.854143 | ||||||||
\(531\) | −0.0795368 | + | 0.0795368i | −0.00345160 | + | 0.00345160i | ||||
\(532\) | −26.5614 | + | 9.44446i | −1.15158 | + | 0.409469i | ||||
\(533\) | 4.02074 | + | 8.36196i | 0.174158 | + | 0.362197i | ||||
\(534\) | 29.6479 | 1.28299 | ||||||||
\(535\) | 5.80713 | + | 5.80713i | 0.251064 | + | 0.251064i | ||||
\(536\) | 4.53035 | 0.195681 | ||||||||
\(537\) | −7.48070 | −0.322816 | ||||||||
\(538\) | 14.2597 | + | 14.2597i | 0.614780 | + | 0.614780i | ||||
\(539\) | −0.455841 | + | 4.44737i | −0.0196345 | + | 0.191562i | ||||
\(540\) | 21.8272 | + | 21.8272i | 0.939292 | + | 0.939292i | ||||
\(541\) | 8.57406 | + | 8.57406i | 0.368628 | + | 0.368628i | 0.866977 | − | 0.498349i | \(-0.166060\pi\) |
−0.498349 | + | 0.866977i | \(0.666060\pi\) | |||||||
\(542\) | 9.97073i | 0.428280i | ||||||||
\(543\) | − | 39.2607i | − | 1.68484i | ||||||
\(544\) | −24.8343 | + | 24.8343i | −1.06476 | + | 1.06476i | ||||
\(545\) | −14.2975 | −0.612436 | ||||||||
\(546\) | −0.157901 | − | 35.6342i | −0.00675754 | − | 1.52500i | ||||
\(547\) | −4.72546 | −0.202046 | −0.101023 | − | 0.994884i | \(-0.532212\pi\) | ||||
−0.101023 | + | 0.994884i | \(0.532212\pi\) | |||||||
\(548\) | 5.31603 | − | 5.31603i | 0.227090 | − | 0.227090i | ||||
\(549\) | 2.42350i | 0.103432i | ||||||||
\(550\) | − | 4.08742i | − | 0.174288i | ||||||
\(551\) | 21.5442 | + | 21.5442i | 0.917812 | + | 0.917812i | ||||
\(552\) | −0.528360 | − | 0.528360i | −0.0224885 | − | 0.0224885i | ||||
\(553\) | 32.9678 | + | 15.6727i | 1.40193 | + | 0.666470i | ||||
\(554\) | 8.56268 | + | 8.56268i | 0.363794 | + | 0.363794i | ||||
\(555\) | −15.6938 | −0.666165 | ||||||||
\(556\) | −7.39991 | −0.313826 | ||||||||
\(557\) | −23.8415 | − | 23.8415i | −1.01019 | − | 1.01019i | −0.999947 | − | 0.0102475i | \(-0.996738\pi\) |
−0.0102475 | − | 0.999947i | \(-0.503262\pi\) | |||||||
\(558\) | −4.94762 | −0.209450 | ||||||||
\(559\) | −12.5007 | + | 35.6565i | −0.528725 | + | 1.50811i | ||||
\(560\) | −8.90321 | − | 25.0392i | −0.376229 | − | 1.05810i | ||||
\(561\) | −3.55554 | + | 3.55554i | −0.150115 | + | 0.150115i | ||||
\(562\) | −26.8178 | −1.13124 | ||||||||
\(563\) | 41.2776 | 1.73965 | 0.869823 | − | 0.493365i | \(-0.164233\pi\) | ||||
0.869823 | + | 0.493365i | \(0.164233\pi\) | |||||||
\(564\) | −23.8113 | + | 23.8113i | −1.00264 | + | 1.00264i | ||||
\(565\) | −32.9446 | − | 32.9446i | −1.38599 | − | 1.38599i | ||||
\(566\) | 12.0878 | − | 12.0878i | 0.508089 | − | 0.508089i | ||||
\(567\) | 23.5042 | + | 11.1738i | 0.987085 | + | 0.469254i | ||||
\(568\) | 3.46520 | 0.145397 | ||||||||
\(569\) | 43.5402i | 1.82530i | 0.408742 | + | 0.912650i | \(0.365968\pi\) | ||||
−0.408742 | + | 0.912650i | \(0.634032\pi\) | |||||||
\(570\) | 36.2127 | − | 36.2127i | 1.51678 | − | 1.51678i | ||||
\(571\) | − | 21.2701i | − | 0.890126i | −0.895499 | − | 0.445063i | \(-0.853181\pi\) | ||
0.895499 | − | 0.445063i | \(-0.146819\pi\) | |||||||
\(572\) | −4.59538 | + | 2.20963i | −0.192143 | + | 0.0923893i | ||||
\(573\) | 18.7455i | 0.783105i | ||||||||
\(574\) | −12.6232 | − | 6.00098i | −0.526882 | − | 0.250476i | ||||
\(575\) | −2.90967 | −0.121341 | ||||||||
\(576\) | 2.99063i | 0.124610i | ||||||||
\(577\) | −8.73703 | − | 8.73703i | −0.363727 | − | 0.363727i | 0.501456 | − | 0.865183i | \(-0.332798\pi\) |
−0.865183 | + | 0.501456i | \(0.832798\pi\) | |||||||
\(578\) | −2.49754 | + | 2.49754i | −0.103884 | + | 0.103884i | ||||
\(579\) | −11.4381 | + | 11.4381i | −0.475353 | + | 0.475353i | ||||
\(580\) | 28.2467 | − | 28.2467i | 1.17288 | − | 1.17288i | ||||
\(581\) | 5.40006 | + | 15.1870i | 0.224032 | + | 0.630064i | ||||
\(582\) | − | 1.25088i | − | 0.0518508i | ||||||
\(583\) | 1.51828 | + | 1.51828i | 0.0628808 | + | 0.0628808i | ||||
\(584\) | 5.51373 | 0.228160 | ||||||||
\(585\) | 1.38493 | + | 2.88025i | 0.0572598 | + | 0.119083i | ||||
\(586\) | − | 44.9717i | − | 1.85776i | ||||||
\(587\) | 30.6931 | + | 30.6931i | 1.26684 | + | 1.26684i | 0.947711 | + | 0.319131i | \(0.103391\pi\) |
0.319131 | + | 0.947711i | \(0.396609\pi\) | |||||||
\(588\) | 17.8064 | + | 21.8735i | 0.734325 | + | 0.902047i | ||||
\(589\) | − | 37.2766i | − | 1.53595i | ||||||
\(590\) | −1.49532 | + | 1.49532i | −0.0615612 | + | 0.0615612i | ||||
\(591\) | −5.91546 | − | 5.91546i | −0.243329 | − | 0.243329i | ||||
\(592\) | 7.54617 | + | 7.54617i | 0.310146 | + | 0.310146i | ||||
\(593\) | 5.18036 | − | 5.18036i | 0.212732 | − | 0.212732i | −0.592695 | − | 0.805427i | \(-0.701936\pi\) |
0.805427 | + | 0.592695i | \(0.201936\pi\) | |||||||
\(594\) | − | 6.41503i | − | 0.263212i | ||||||
\(595\) | −10.9268 | − | 30.7304i | −0.447956 | − | 1.25982i | ||||
\(596\) | −5.82225 | − | 5.82225i | −0.238488 | − | 0.238488i | ||||
\(597\) | 11.2839i | 0.461820i | ||||||||
\(598\) | 2.99365 | + | 6.22591i | 0.122419 | + | 0.254596i | ||||
\(599\) | −18.5254 | −0.756928 | −0.378464 | − | 0.925616i | \(-0.623548\pi\) | ||||
−0.378464 | + | 0.925616i | \(0.623548\pi\) | |||||||
\(600\) | −1.76485 | − | 1.76485i | −0.0720498 | − | 0.0720498i | ||||
\(601\) | 30.9807i | 1.26373i | 0.775079 | + | 0.631864i | \(0.217710\pi\) | ||||
−0.775079 | + | 0.631864i | \(0.782290\pi\) | |||||||
\(602\) | −19.0690 | − | 53.6291i | −0.777193 | − | 2.18576i | ||||
\(603\) | −2.26517 | + | 2.26517i | −0.0922451 | + | 0.0922451i | ||||
\(604\) | −10.5921 | + | 10.5921i | −0.430987 | + | 0.430987i | ||||
\(605\) | 21.3393 | − | 21.3393i | 0.867564 | − | 0.867564i | ||||
\(606\) | 24.3526 | + | 24.3526i | 0.989257 | + | 0.989257i | ||||
\(607\) | − | 29.4674i | − | 1.19605i | −0.801479 | − | 0.598023i | \(-0.795953\pi\) | ||
0.801479 | − | 0.598023i | \(-0.204047\pi\) | |||||||
\(608\) | −39.0591 | −1.58405 | ||||||||
\(609\) | 13.0880 | − | 27.5310i | 0.530354 | − | 1.11561i | ||||
\(610\) | 45.5625i | 1.84477i | ||||||||
\(611\) | 27.1568 | − | 13.0580i | 1.09865 | − | 0.528270i | ||||
\(612\) | 2.98065i | 0.120485i | ||||||||
\(613\) | 13.9398 | − | 13.9398i | 0.563022 | − | 0.563022i | −0.367142 | − | 0.930165i | \(-0.619664\pi\) |
0.930165 | + | 0.367142i | \(0.119664\pi\) | |||||||
\(614\) | 16.7668i | 0.676653i | ||||||||
\(615\) | 13.3414 | 0.537976 | ||||||||
\(616\) | 0.319196 | − | 0.671436i | 0.0128608 | − | 0.0270529i | ||||
\(617\) | −27.7052 | + | 27.7052i | −1.11537 | + | 1.11537i | −0.122957 | + | 0.992412i | \(0.539238\pi\) |
−0.992412 | + | 0.122957i | \(0.960762\pi\) | |||||||
\(618\) | −6.62222 | − | 6.62222i | −0.266385 | − | 0.266385i | ||||
\(619\) | −4.58642 | + | 4.58642i | −0.184344 | + | 0.184344i | −0.793246 | − | 0.608902i | \(-0.791610\pi\) |
0.608902 | + | 0.793246i | \(0.291610\pi\) | |||||||
\(620\) | −48.8736 | −1.96281 | ||||||||
\(621\) | −4.56659 | −0.183251 | ||||||||
\(622\) | 3.81137 | − | 3.81137i | 0.152822 | − | 0.152822i | ||||
\(623\) | 19.7852 | − | 7.03503i | 0.792677 | − | 0.281853i | ||||
\(624\) | 7.65233 | − | 21.8272i | 0.306338 | − | 0.873786i | ||||
\(625\) | 30.8687 | 1.23475 | ||||||||
\(626\) | 28.8128 | + | 28.8128i | 1.15159 | + | 1.15159i | ||||
\(627\) | −5.59210 | −0.223327 | ||||||||
\(628\) | −7.58498 | −0.302674 | ||||||||
\(629\) | 9.26134 | + | 9.26134i | 0.369274 | + | 0.369274i | ||||
\(630\) | −4.34801 | − | 2.06702i | −0.173229 | − | 0.0823519i | ||||
\(631\) | 11.1175 | + | 11.1175i | 0.442582 | + | 0.442582i | 0.892879 | − | 0.450297i | \(-0.148682\pi\) |
−0.450297 | + | 0.892879i | \(0.648682\pi\) | |||||||
\(632\) | −4.29237 | − | 4.29237i | −0.170741 | − | 0.170741i | ||||
\(633\) | − | 17.3877i | − | 0.691099i | ||||||
\(634\) | 3.33185i | 0.132325i | ||||||||
\(635\) | −27.8567 | + | 27.8567i | −1.10546 | + | 1.10546i | ||||
\(636\) | 13.5463 | 0.537145 | ||||||||
\(637\) | −8.56087 | − | 23.7426i | −0.339194 | − | 0.940716i | ||||
\(638\) | −8.30174 | −0.328669 | ||||||||
\(639\) | −1.73260 | + | 1.73260i | −0.0685407 | + | 0.0685407i | ||||
\(640\) | 9.97073i | 0.394128i | ||||||||
\(641\) | 22.3590i | 0.883129i | 0.897229 | + | 0.441565i | \(0.145576\pi\) | ||||
−0.897229 | + | 0.441565i | \(0.854424\pi\) | |||||||
\(642\) | −7.61377 | − | 7.61377i | −0.300492 | − | 0.300492i | ||||
\(643\) | 5.69880 | + | 5.69880i | 0.224739 | + | 0.224739i | 0.810491 | − | 0.585752i | \(-0.199201\pi\) |
−0.585752 | + | 0.810491i | \(0.699201\pi\) | |||||||
\(644\) | −4.93829 | − | 2.34763i | −0.194596 | − | 0.0925096i | ||||
\(645\) | 38.4170 | + | 38.4170i | 1.51267 | + | 1.51267i | ||||
\(646\) | −42.7402 | −1.68159 | ||||||||
\(647\) | −7.73510 | −0.304098 | −0.152049 | − | 0.988373i | \(-0.548587\pi\) | ||||
−0.152049 | + | 0.988373i | \(0.548587\pi\) | |||||||
\(648\) | −3.06022 | − | 3.06022i | −0.120217 | − | 0.120217i | ||||
\(649\) | 0.230912 | 0.00906410 | ||||||||
\(650\) | 9.99952 | + | 20.7961i | 0.392214 | + | 0.815689i | ||||
\(651\) | −35.1403 | + | 12.4949i | −1.37726 | + | 0.489712i | ||||
\(652\) | 23.1383 | − | 23.1383i | 0.906165 | − | 0.906165i | ||||
\(653\) | 21.3921 | 0.837137 | 0.418568 | − | 0.908185i | \(-0.362532\pi\) | ||||
0.418568 | + | 0.908185i | \(0.362532\pi\) | |||||||
\(654\) | 18.7455 | 0.733007 | ||||||||
\(655\) | −25.8479 | + | 25.8479i | −1.00996 | + | 1.00996i | ||||
\(656\) | −6.41503 | − | 6.41503i | −0.250465 | − | 0.250465i | ||||
\(657\) | −2.75686 | + | 2.75686i | −0.107555 | + | 0.107555i | ||||
\(658\) | −19.4891 | + | 40.9958i | −0.759766 | + | 1.59818i | ||||
\(659\) | −1.68445 | −0.0656167 | −0.0328084 | − | 0.999462i | \(-0.510445\pi\) | ||||
−0.0328084 | + | 0.999462i | \(0.510445\pi\) | |||||||
\(660\) | 7.33185i | 0.285392i | ||||||||
\(661\) | 23.4056 | − | 23.4056i | 0.910372 | − | 0.910372i | −0.0859290 | − | 0.996301i | \(-0.527386\pi\) |
0.996301 | + | 0.0859290i | \(0.0273858\pi\) | |||||||
\(662\) | − | 8.42864i | − | 0.327588i | ||||||
\(663\) | 9.39163 | − | 26.7883i | 0.364741 | − | 1.04037i | ||||
\(664\) | − | 2.68041i | − | 0.104020i | ||||||
\(665\) | 15.5734 | − | 32.7589i | 0.603910 | − | 1.27034i | ||||
\(666\) | 1.93332 | 0.0749148 | ||||||||
\(667\) | 5.90967i | 0.228823i | ||||||||
\(668\) | −35.9441 | − | 35.9441i | −1.39072 | − | 1.39072i | ||||
\(669\) | −4.69604 | + | 4.69604i | −0.181559 | + | 0.181559i | ||||
\(670\) | −42.5860 | + | 42.5860i | −1.64524 | + | 1.64524i | ||||
\(671\) | 3.51796 | − | 3.51796i | 0.135809 | − | 0.135809i | ||||
\(672\) | 13.0923 | + | 36.8206i | 0.505048 | + | 1.42039i | ||||
\(673\) | − | 26.2464i | − | 1.01173i | −0.862614 | − | 0.505863i | \(-0.831174\pi\) | ||
0.862614 | − | 0.505863i | \(-0.168826\pi\) | |||||||
\(674\) | −6.49309 | − | 6.49309i | −0.250105 | − | 0.250105i | ||||
\(675\) | −15.2535 | −0.587109 | ||||||||
\(676\) | 17.9748 | − | 22.4844i | 0.691339 | − | 0.864785i | ||||
\(677\) | 36.7658i | 1.41303i | 0.707700 | + | 0.706513i | \(0.249733\pi\) | ||||
−0.707700 | + | 0.706513i | \(0.750267\pi\) | |||||||
\(678\) | 43.1939 | + | 43.1939i | 1.65885 | + | 1.65885i | ||||
\(679\) | −0.296818 | − | 0.834764i | −0.0113908 | − | 0.0320353i | ||||
\(680\) | 5.42372i | 0.207990i | ||||||||
\(681\) | 9.56046 | − | 9.56046i | 0.366358 | − | 0.366358i | ||||
\(682\) | 7.18200 | + | 7.18200i | 0.275013 | + | 0.275013i | ||||
\(683\) | −14.5812 | − | 14.5812i | −0.557934 | − | 0.557934i | 0.370785 | − | 0.928719i | \(-0.379089\pi\) |
−0.928719 | + | 0.370785i | \(0.879089\pi\) | |||||||
\(684\) | −2.34396 | + | 2.34396i | −0.0896235 | + | 0.0896235i | ||||
\(685\) | 9.67329i | 0.369597i | ||||||||
\(686\) | 32.4939 | + | 19.7397i | 1.24062 | + | 0.753667i | ||||
\(687\) | 1.32693 | + | 1.32693i | 0.0506255 | + | 0.0506255i | ||||
\(688\) | − | 36.9447i | − | 1.40850i | ||||||
\(689\) | −11.4391 | − | 4.01040i | −0.435795 | − | 0.152784i | ||||
\(690\) | 9.93332 | 0.378155 | ||||||||
\(691\) | −30.4663 | − | 30.4663i | −1.15899 | − | 1.15899i | −0.984693 | − | 0.174299i | \(-0.944234\pi\) |
−0.174299 | − | 0.984693i | \(-0.555766\pi\) | |||||||
\(692\) | 31.8442i | 1.21054i | ||||||||
\(693\) | 0.176120 | + | 0.495316i | 0.00669024 | + | 0.0188155i | ||||
\(694\) | −12.7906 | + | 12.7906i | −0.485525 | + | 0.485525i | ||||
\(695\) | 6.73260 | − | 6.73260i | 0.255382 | − | 0.255382i | ||||
\(696\) | −3.58450 | + | 3.58450i | −0.135870 | + | 0.135870i | ||||
\(697\) | −7.87310 | − | 7.87310i | −0.298215 | − | 0.298215i | ||||
\(698\) | − | 34.2965i | − | 1.29814i | ||||||
\(699\) | −44.7866 | −1.69399 | ||||||||
\(700\) | −16.4951 | − | 7.84166i | −0.623457 | − | 0.296387i | ||||
\(701\) | 17.7368i | 0.669911i | 0.942234 | + | 0.334955i | \(0.108721\pi\) | ||||
−0.942234 | + | 0.334955i | \(0.891279\pi\) | |||||||
\(702\) | 15.6938 | + | 32.6385i | 0.592325 | + | 1.23186i | ||||
\(703\) | 14.5661i | 0.549371i | ||||||||
\(704\) | 4.34122 | − | 4.34122i | 0.163616 | − | 0.163616i | ||||
\(705\) | − | 43.3282i | − | 1.63183i | ||||||
\(706\) | 8.44854 | 0.317965 | ||||||||
\(707\) | 22.0300 | + | 10.4729i | 0.828522 | + | 0.393874i | ||||
\(708\) | 1.03011 | − | 1.03011i | 0.0387140 | − | 0.0387140i | ||||
\(709\) | 19.2422 | + | 19.2422i | 0.722656 | + | 0.722656i | 0.969146 | − | 0.246489i | \(-0.0792770\pi\) |
−0.246489 | + | 0.969146i | \(0.579277\pi\) | |||||||
\(710\) | −32.5734 | + | 32.5734i | −1.22246 | + | 1.22246i | ||||
\(711\) | 4.29237 | 0.160977 | ||||||||
\(712\) | −3.49196 | −0.130867 | ||||||||
\(713\) | 5.11257 | − | 5.11257i | 0.191467 | − | 0.191467i | ||||
\(714\) | 14.3262 | + | 40.2908i | 0.536146 | + | 1.50785i | ||||
\(715\) | 2.17061 | − | 6.19135i | 0.0811762 | − | 0.231543i | ||||
\(716\) | 9.10324 | 0.340204 | ||||||||
\(717\) | −11.8740 | − | 11.8740i | −0.443441 | − | 0.443441i | ||||
\(718\) | −10.2286 | −0.381728 | ||||||||
\(719\) | −42.3551 | −1.57958 | −0.789789 | − | 0.613379i | \(-0.789810\pi\) | ||||
−0.789789 | + | 0.613379i | \(0.789810\pi\) | |||||||
\(720\) | −2.20963 | − | 2.20963i | −0.0823481 | − | 0.0823481i | ||||
\(721\) | −5.99062 | − | 2.84790i | −0.223102 | − | 0.106061i | ||||
\(722\) | −6.03011 | − | 6.03011i | −0.224418 | − | 0.224418i | ||||
\(723\) | −36.6773 | − | 36.6773i | −1.36404 | − | 1.36404i | ||||
\(724\) | 47.7762i | 1.77559i | ||||||||
\(725\) | 19.7397i | 0.733116i | ||||||||
\(726\) | −27.9781 | + | 27.9781i | −1.03836 | + | 1.03836i | ||||
\(727\) | −23.2484 | −0.862234 | −0.431117 | − | 0.902296i | \(-0.641880\pi\) | ||||
−0.431117 | + | 0.902296i | \(0.641880\pi\) | |||||||
\(728\) | 0.0185978 | + | 4.19703i | 0.000689279 | + | 0.155552i | ||||
\(729\) | −23.6494 | −0.875904 | ||||||||
\(730\) | −51.8299 | + | 51.8299i | −1.91831 | + | 1.91831i | ||||
\(731\) | − | 45.3419i | − | 1.67703i | ||||||
\(732\) | − | 31.3876i | − | 1.16012i | ||||||
\(733\) | −24.1280 | − | 24.1280i | −0.891188 | − | 0.891188i | 0.103447 | − | 0.994635i | \(-0.467013\pi\) |
−0.994635 | + | 0.103447i | \(0.967013\pi\) | |||||||
\(734\) | −28.7580 | − | 28.7580i | −1.06148 | − | 1.06148i | ||||
\(735\) | −36.1017 | − | 3.70030i | −1.33163 | − | 0.136488i | ||||
\(736\) | −5.35704 | − | 5.35704i | −0.197463 | − | 0.197463i | ||||
\(737\) | 6.57628 | 0.242240 | ||||||||
\(738\) | −1.64353 | −0.0604990 | ||||||||
\(739\) | 4.46590 | + | 4.46590i | 0.164281 | + | 0.164281i | 0.784460 | − | 0.620179i | \(-0.212940\pi\) |
−0.620179 | + | 0.784460i | \(0.712940\pi\) | |||||||
\(740\) | 19.0977 | 0.702047 | ||||||||
\(741\) | 28.4516 | − | 13.6806i | 1.04520 | − | 0.502570i | ||||
\(742\) | 17.2050 | − | 6.11758i | 0.631614 | − | 0.224583i | ||||
\(743\) | 10.0114 | − | 10.0114i | 0.367282 | − | 0.367282i | −0.499203 | − | 0.866485i | \(-0.666374\pi\) |
0.866485 | + | 0.499203i | \(0.166374\pi\) | |||||||
\(744\) | 6.20204 | 0.227378 | ||||||||
\(745\) | 10.5944 | 0.388149 | ||||||||
\(746\) | 35.6178 | − | 35.6178i | 1.30406 | − | 1.30406i | ||||
\(747\) | 1.34021 | + | 1.34021i | 0.0490356 | + | 0.0490356i | ||||
\(748\) | 4.32672 | − | 4.32672i | 0.158201 | − | 0.158201i | ||||
\(749\) | −6.88761 | − | 3.27432i | −0.251668 | − | 0.119641i | ||||
\(750\) | −20.0350 | −0.731576 | ||||||||
\(751\) | − | 8.16686i | − | 0.298013i | −0.988836 | − | 0.149006i | \(-0.952392\pi\) | ||
0.988836 | − | 0.149006i | \(-0.0476075\pi\) | |||||||
\(752\) | −20.8338 | + | 20.8338i | −0.759731 | + | 0.759731i | ||||
\(753\) | 26.2844i | 0.957856i | ||||||||
\(754\) | 42.2378 | − | 20.3095i | 1.53821 | − | 0.739628i | ||||
\(755\) | − | 19.2739i | − | 0.701448i | ||||||
\(756\) | −25.8884 | − | 12.3071i | −0.941550 | − | 0.447607i | ||||
\(757\) | 10.5210 | 0.382392 | 0.191196 | − | 0.981552i | \(-0.438763\pi\) | ||||
0.191196 | + | 0.981552i | \(0.438763\pi\) | |||||||
\(758\) | − | 25.5002i | − | 0.926210i | ||||||
\(759\) | −0.766970 | − | 0.766970i | −0.0278393 | − | 0.0278393i | ||||
\(760\) | −4.26517 | + | 4.26517i | −0.154714 | + | 0.154714i | ||||
\(761\) | −5.95138 | + | 5.95138i | −0.215737 | + | 0.215737i | −0.806699 | − | 0.590962i | \(-0.798748\pi\) |
0.590962 | + | 0.806699i | \(0.298748\pi\) | |||||||
\(762\) | 36.5232 | − | 36.5232i | 1.32310 | − | 1.32310i | ||||
\(763\) | 12.5096 | − | 4.44805i | 0.452878 | − | 0.161030i | ||||
\(764\) | − | 22.8113i | − | 0.825286i | ||||||
\(765\) | −2.71186 | − | 2.71186i | −0.0980475 | − | 0.0980475i | ||||
\(766\) | 51.9646 | 1.87756 | ||||||||
\(767\) | −1.17484 | + | 0.564907i | −0.0424210 | + | 0.0203976i | ||||
\(768\) | 21.9112i | 0.790653i | ||||||||
\(769\) | −9.73800 | − | 9.73800i | −0.351161 | − | 0.351161i | 0.509380 | − | 0.860541i | \(-0.329875\pi\) |
−0.860541 | + | 0.509380i | \(0.829875\pi\) | |||||||
\(770\) | 3.31111 | + | 9.31209i | 0.119324 | + | 0.335584i | ||||
\(771\) | − | 26.6099i | − | 0.958333i | ||||||
\(772\) | 13.9190 | − | 13.9190i | 0.500957 | − | 0.500957i | ||||
\(773\) | 16.0246 | + | 16.0246i | 0.576364 | + | 0.576364i | 0.933899 | − | 0.357536i | \(-0.116383\pi\) |
−0.357536 | + | 0.933899i | \(0.616383\pi\) | |||||||
\(774\) | −4.73260 | − | 4.73260i | −0.170110 | − | 0.170110i | ||||
\(775\) | 17.0772 | − | 17.0772i | 0.613433 | − | 0.613433i | ||||
\(776\) | 0.147331i | 0.00528886i | ||||||||
\(777\) | 13.7314 | − | 4.88247i | 0.492610 | − | 0.175158i | ||||
\(778\) | 17.5161 | + | 17.5161i | 0.627981 | + | 0.627981i | ||||
\(779\) | − | 12.3827i | − | 0.443657i | ||||||
\(780\) | −17.9367 | − | 37.3032i | −0.642239 | − | 1.33567i | ||||
\(781\) | 5.03011 | 0.179992 | ||||||||
\(782\) | −5.86192 | − | 5.86192i | −0.209622 | − | 0.209622i | ||||
\(783\) | 30.9807i | 1.10716i | ||||||||
\(784\) | 15.5798 | + | 19.1383i | 0.556421 | + | 0.683510i | ||||
\(785\) | 6.90099 | − | 6.90099i | 0.246307 | − | 0.246307i | ||||
\(786\) | 33.8894 | − | 33.8894i | 1.20879 | − | 1.20879i | ||||
\(787\) | 17.9844 | − | 17.9844i | 0.641075 | − | 0.641075i | −0.309745 | − | 0.950820i | \(-0.600244\pi\) |
0.950820 | + | 0.309745i | \(0.100244\pi\) | |||||||
\(788\) | 7.19850 | + | 7.19850i | 0.256436 | + | 0.256436i | ||||
\(789\) | − | 4.76254i | − | 0.169551i | ||||||
\(790\) | 80.6979 | 2.87110 | ||||||||
\(791\) | 39.0743 | + | 18.5756i | 1.38932 | + | 0.660474i | ||||
\(792\) | − | 0.0874201i | − | 0.00310634i | ||||||
\(793\) | −9.29237 | + | 26.5052i | −0.329982 | + | 0.941226i | ||||
\(794\) | 22.7082i | 0.805886i | ||||||||
\(795\) | −12.3247 | + | 12.3247i | −0.437112 | + | 0.437112i | ||||
\(796\) | − | 13.7314i | − | 0.486695i | ||||||
\(797\) | −43.9698 | −1.55749 | −0.778745 | − | 0.627341i | \(-0.784143\pi\) | ||||
−0.778745 | + | 0.627341i | \(0.784143\pi\) | |||||||
\(798\) | −20.4184 | + | 42.9505i | −0.722803 | + | 1.52043i | ||||
\(799\) | −25.5691 | + | 25.5691i | −0.904571 | + | 0.904571i | ||||
\(800\) | −17.8938 | − | 17.8938i | −0.632643 | − | 0.632643i | ||||
\(801\) | 1.74598 | − | 1.74598i | 0.0616912 | − | 0.0616912i | ||||
\(802\) | 51.1481 | 1.80610 | ||||||||
\(803\) | 8.00376 | 0.282447 | ||||||||
\(804\) | 29.3371 | − | 29.3371i | 1.03464 | − | 1.03464i | ||||
\(805\) | 6.62889 | − | 2.35704i | 0.233638 | − | 0.0830748i | ||||
\(806\) | −54.1109 | − | 18.9706i | −1.90597 | − | 0.668210i | ||||
\(807\) | 17.8751 | 0.629234 | ||||||||
\(808\) | −2.86827 | − | 2.86827i | −0.100906 | − | 0.100906i | ||||
\(809\) | 12.0509 | 0.423686 | 0.211843 | − | 0.977304i | \(-0.432054\pi\) | ||||
0.211843 | + | 0.977304i | \(0.432054\pi\) | |||||||
\(810\) | 57.5331 | 2.02151 | ||||||||
\(811\) | 1.07742 | + | 1.07742i | 0.0378333 | + | 0.0378333i | 0.725770 | − | 0.687937i | \(-0.241483\pi\) |
−0.687937 | + | 0.725770i | \(0.741483\pi\) | |||||||
\(812\) | −15.9268 | + | 33.5023i | −0.558920 | + | 1.17570i | ||||
\(813\) | 6.24935 | + | 6.24935i | 0.219174 | + | 0.219174i | ||||
\(814\) | −2.80642 | − | 2.80642i | −0.0983651 | − | 0.0983651i | ||||
\(815\) | 42.1034i | 1.47482i | ||||||||
\(816\) | 27.7560i | 0.971656i | ||||||||
\(817\) | 35.6565 | − | 35.6565i | 1.24746 | − | 1.24746i | ||||
\(818\) | −69.7423 | −2.43848 | ||||||||
\(819\) | −2.10782 | − | 2.08922i | −0.0736530 | − | 0.0730032i | ||||
\(820\) | −16.2351 | −0.566953 | ||||||||
\(821\) | −34.1847 | + | 34.1847i | −1.19305 | + | 1.19305i | −0.216848 | + | 0.976205i | \(0.569578\pi\) |
−0.976205 | + | 0.216848i | \(0.930422\pi\) | |||||||
\(822\) | − | 12.6827i | − | 0.442361i | ||||||
\(823\) | − | 4.71609i | − | 0.164393i | −0.996616 | − | 0.0821963i | \(-0.973807\pi\) | ||
0.996616 | − | 0.0821963i | \(-0.0261934\pi\) | |||||||
\(824\) | 0.779972 | + | 0.779972i | 0.0271716 | + | 0.0271716i | ||||
\(825\) | −2.56187 | − | 2.56187i | −0.0891929 | − | 0.0891929i | ||||
\(826\) | 0.843127 | − | 1.77354i | 0.0293361 | − | 0.0617092i | ||||
\(827\) | 24.0939 | + | 24.0939i | 0.837826 | + | 0.837826i | 0.988572 | − | 0.150746i | \(-0.0481677\pi\) |
−0.150746 | + | 0.988572i | \(0.548168\pi\) | |||||||
\(828\) | −0.642959 | −0.0223444 | ||||||||
\(829\) | 12.4689 | 0.433061 | 0.216531 | − | 0.976276i | \(-0.430526\pi\) | ||||
0.216531 | + | 0.976276i | \(0.430526\pi\) | |||||||
\(830\) | 25.1963 | + | 25.1963i | 0.874575 | + | 0.874575i | ||||
\(831\) | 10.7337 | 0.372347 | ||||||||
\(832\) | −11.4669 | + | 32.7078i | −0.397544 | + | 1.13394i | ||||
\(833\) | 19.1209 | + | 23.4882i | 0.662501 | + | 0.813819i | ||||
\(834\) | −8.82717 | + | 8.82717i | −0.305660 | + | 0.305660i | ||||
\(835\) | 65.4055 | 2.26345 | ||||||||
\(836\) | 6.80501 | 0.235356 | ||||||||
\(837\) | 26.8020 | − | 26.8020i | 0.926412 | − | 0.926412i | ||||
\(838\) | 28.5819 | + | 28.5819i | 0.987346 | + | 0.987346i | ||||
\(839\) | 26.1454 | − | 26.1454i | 0.902640 | − | 0.902640i | −0.0930239 | − | 0.995664i | \(-0.529653\pi\) |
0.995664 | + | 0.0930239i | \(0.0296533\pi\) | |||||||
\(840\) | 5.45040 | + | 2.59108i | 0.188057 | + | 0.0894009i | ||||
\(841\) | 11.0923 | 0.382495 | ||||||||
\(842\) | 77.2375i | 2.66178i | ||||||||
\(843\) | −16.8086 | + | 16.8086i | −0.578918 | + | 0.578918i | ||||
\(844\) | 21.1590i | 0.728323i | ||||||||
\(845\) | 4.10294 | + | 36.8107i | 0.141145 | + | 1.26633i | ||||
\(846\) | 5.33761i | 0.183511i | ||||||||
\(847\) | −12.0320 | + | 25.3097i | −0.413426 | + | 0.869650i | ||||
\(848\) | 11.8524 | 0.407012 | ||||||||
\(849\) | − | 15.1526i | − | 0.520035i | ||||||
\(850\) | −19.5803 | − | 19.5803i | −0.671598 | − | 0.671598i | ||||
\(851\) | −1.99778 | + | 1.99778i | −0.0684829 | + | 0.0684829i | ||||
\(852\) | 22.4396 | − | 22.4396i | 0.768768 | − | 0.768768i | ||||
\(853\) | 15.4396 | − | 15.4396i | 0.528641 | − | 0.528641i | −0.391526 | − | 0.920167i | \(-0.628053\pi\) |
0.920167 | + | 0.391526i | \(0.128053\pi\) | |||||||
\(854\) | −14.1748 | − | 39.8650i | −0.485053 | − | 1.36415i | ||||
\(855\) | − | 4.26517i | − | 0.145866i | ||||||
\(856\) | 0.896758 | + | 0.896758i | 0.0306506 | + | 0.0306506i | ||||
\(857\) | −35.9311 | −1.22738 | −0.613691 | − | 0.789546i | \(-0.710316\pi\) | ||||
−0.613691 | + | 0.789546i | \(0.710316\pi\) | |||||||
\(858\) | −2.84590 | + | 8.11753i | −0.0971575 | + | 0.277128i | ||||
\(859\) | 6.05104i | 0.206459i | 0.994658 | + | 0.103229i | \(0.0329176\pi\) | ||||
−0.994658 | + | 0.103229i | \(0.967082\pi\) | |||||||
\(860\) | −46.7496 | − | 46.7496i | −1.59415 | − | 1.59415i | ||||
\(861\) | −11.6731 | + | 4.15060i | −0.397817 | + | 0.141452i | ||||
\(862\) | − | 13.9684i | − | 0.475764i | ||||||
\(863\) | −11.8524 | + | 11.8524i | −0.403459 | + | 0.403459i | −0.879450 | − | 0.475991i | \(-0.842089\pi\) |
0.475991 | + | 0.879450i | \(0.342089\pi\) | |||||||
\(864\) | −28.0836 | − | 28.0836i | −0.955424 | − | 0.955424i | ||||
\(865\) | −28.9726 | − | 28.9726i | −0.985098 | − | 0.985098i | ||||
\(866\) | −12.1166 | + | 12.1166i | −0.411739 | + | 0.411739i | ||||
\(867\) | 3.13076i | 0.106326i | ||||||||
\(868\) | 42.7621 | − | 15.2050i | 1.45144 | − | 0.516090i | ||||
\(869\) | −6.23083 | − | 6.23083i | −0.211367 | − | 0.211367i | ||||
\(870\) | − | 67.3896i | − | 2.28472i | ||||||
\(871\) | −33.4590 | + | 16.0883i | −1.13371 | + | 0.545132i | ||||
\(872\) | −2.20787 | −0.0747678 | ||||||||
\(873\) | −0.0736653 | − | 0.0736653i | −0.00249319 | − | 0.00249319i | ||||
\(874\) | − | 9.21955i | − | 0.311856i | ||||||
\(875\) | −13.3702 | + | 4.75404i | −0.451994 | + | 0.160716i | ||||
\(876\) | 35.7052 | − | 35.7052i | 1.20637 | − | 1.20637i | ||||
\(877\) | 29.7741 | − | 29.7741i | 1.00540 | − | 1.00540i | 0.00541422 | − | 0.999985i | \(-0.498277\pi\) |
0.999985 | − | 0.00541422i | \(-0.00172341\pi\) | |||||||
\(878\) | −3.51796 | + | 3.51796i | −0.118725 | + | 0.118725i | ||||
\(879\) | −28.1869 | − | 28.1869i | −0.950721 | − | 0.950721i | ||||
\(880\) | 6.41503i | 0.216251i | ||||||||
\(881\) | −18.8928 | −0.636516 | −0.318258 | − | 0.948004i | \(-0.603098\pi\) | ||||
−0.318258 | + | 0.948004i | \(0.603098\pi\) | |||||||
\(882\) | 4.44737 | + | 0.455841i | 0.149751 | + | 0.0153490i | ||||
\(883\) | − | 7.28391i | − | 0.245123i | −0.992461 | − | 0.122562i | \(-0.960889\pi\) | ||
0.992461 | − | 0.122562i | \(-0.0391109\pi\) | |||||||
\(884\) | −11.4286 | + | 32.5986i | −0.384387 | + | 1.09641i | ||||
\(885\) | 1.87444i | 0.0630085i | ||||||||
\(886\) | −19.9978 | + | 19.9978i | −0.671838 | + | 0.671838i | ||||
\(887\) | 36.5520i | 1.22730i | 0.789580 | + | 0.613648i | \(0.210298\pi\) | ||||
−0.789580 | + | 0.613648i | \(0.789702\pi\) | |||||||
\(888\) | −2.42350 | −0.0813272 | ||||||||
\(889\) | 15.7069 | − | 33.0398i | 0.526792 | − | 1.10812i | ||||
\(890\) | 32.8249 | − | 32.8249i | 1.10029 | − | 1.10029i | ||||
\(891\) | −4.44224 | − | 4.44224i | −0.148821 | − | 0.148821i | ||||
\(892\) | 5.71459 | − | 5.71459i | 0.191339 | − | 0.191339i | ||||
\(893\) | −40.2148 | −1.34574 | ||||||||
\(894\) | −13.8904 | −0.464565 | ||||||||
\(895\) | −8.28233 | + | 8.28233i | −0.276848 | + | 0.276848i | ||||
\(896\) | −3.10197 | − | 8.72393i | −0.103630 | − | 0.291446i | ||||
\(897\) | 5.77854 | + | 2.02588i | 0.192940 | + | 0.0676422i | ||||
\(898\) | 71.8390 | 2.39730 | ||||||||
\(899\) | −34.6847 | − | 34.6847i | −1.15680 | − | 1.15680i | ||||
\(900\) | −2.14764 | −0.0715881 | ||||||||
\(901\) | 14.5463 | 0.484607 | ||||||||
\(902\) | 2.38575 | + | 2.38575i | 0.0794368 | + | 0.0794368i | ||||
\(903\) | −45.5650 | − | 21.6613i | −1.51631 | − | 0.720842i | ||||
\(904\) | −5.08742 | − | 5.08742i | −0.169205 | − | 0.169205i | ||||
\(905\) | −43.4679 | − | 43.4679i | −1.44492 | − | 1.44492i | ||||
\(906\) | 25.2701i | 0.839544i | ||||||||
\(907\) | − | 8.45875i | − | 0.280868i | −0.990090 | − | 0.140434i | \(-0.955150\pi\) | ||
0.990090 | − | 0.140434i | \(-0.0448498\pi\) | |||||||
\(908\) | −11.6341 | + | 11.6341i | −0.386091 | + | 0.386091i | ||||
\(909\) | 2.86827 | 0.0951347 | ||||||||
\(910\) | −39.6276 | − | 39.2779i | −1.31364 | − | 1.30205i | ||||
\(911\) | −11.0973 | −0.367669 | −0.183834 | − | 0.982957i | \(-0.558851\pi\) | ||||
−0.183834 | + | 0.982957i | \(0.558851\pi\) | |||||||
\(912\) | −21.8272 | + | 21.8272i | −0.722770 | + | 0.722770i | ||||
\(913\) | − | 3.89090i | − | 0.128770i | ||||||
\(914\) | − | 8.26025i | − | 0.273225i | ||||||
\(915\) | 28.5572 | + | 28.5572i | 0.944071 | + | 0.944071i | ||||
\(916\) | −1.61474 | − | 1.61474i | −0.0533524 | − | 0.0533524i | ||||
\(917\) | 14.5742 | − | 30.6572i | 0.481283 | − | 1.01239i | ||||
\(918\) | −30.7304 | − | 30.7304i | −1.01425 | − | 1.01425i | ||||
\(919\) | −30.7225 | −1.01344 | −0.506722 | − | 0.862110i | \(-0.669143\pi\) | ||||
−0.506722 | + | 0.862110i | \(0.669143\pi\) | |||||||
\(920\) | −1.16996 | −0.0385724 | ||||||||
\(921\) | 10.5089 | + | 10.5089i | 0.346281 | + | 0.346281i | ||||
\(922\) | −6.92634 | −0.228107 | ||||||||
\(923\) | −25.5923 | + | 12.3057i | −0.842381 | + | 0.405048i | ||||
\(924\) | −2.28100 | − | 6.41503i | −0.0750393 | − | 0.211039i | ||||
\(925\) | −6.67307 | + | 6.67307i | −0.219409 | + | 0.219409i | ||||
\(926\) | −51.0672 | −1.67817 | ||||||||
\(927\) | −0.779972 | −0.0256176 | ||||||||
\(928\) | −36.3432 | + | 36.3432i | −1.19302 | + | 1.19302i | ||||
\(929\) | 24.7606 | + | 24.7606i | 0.812370 | + | 0.812370i | 0.984989 | − | 0.172619i | \(-0.0552228\pi\) |
−0.172619 | + | 0.984989i | \(0.555223\pi\) | |||||||
\(930\) | −58.3001 | + | 58.3001i | −1.91174 | + | 1.91174i | ||||
\(931\) | −3.43441 | + | 33.5075i | −0.112558 | + | 1.09817i | ||||
\(932\) | 54.5007 | 1.78523 | ||||||||
\(933\) | − | 4.77770i | − | 0.156415i | ||||||
\(934\) | −31.1060 | + | 31.1060i | −1.01782 | + | 1.01782i | ||||
\(935\) | 7.87310i | 0.257478i | ||||||||
\(936\) | 0.213866 | + | 0.444778i | 0.00699043 | + | 0.0145380i | ||||
\(937\) | − | 18.9594i | − | 0.619376i | −0.950838 | − | 0.309688i | \(-0.899775\pi\) | ||
0.950838 | − | 0.309688i | \(-0.100225\pi\) | |||||||
\(938\) | 24.0119 | − | 50.5096i | 0.784016 | − | 1.64920i | ||||
\(939\) | 36.1180 | 1.17867 | ||||||||
\(940\) | 52.7259i | 1.71973i | ||||||||
\(941\) | 32.7842 | + | 32.7842i | 1.06874 | + | 1.06874i | 0.997456 | + | 0.0712788i | \(0.0227080\pi\) |
0.0712788 | + | 0.997456i | \(0.477292\pi\) | |||||||
\(942\) | −9.04794 | + | 9.04794i | −0.294798 | + | 0.294798i | ||||
\(943\) | 1.69832 | − | 1.69832i | 0.0553048 | − | 0.0553048i | ||||
\(944\) | 0.901299 | − | 0.901299i | 0.0293348 | − | 0.0293348i | ||||
\(945\) | 34.7511 | − | 12.3565i | 1.13045 | − | 0.401957i | ||||
\(946\) | 13.7397i | 0.446718i | ||||||||
\(947\) | −29.9748 | − | 29.9748i | −0.974050 | − | 0.974050i | 0.0256213 | − | 0.999672i | \(-0.491844\pi\) |
−0.999672 | + | 0.0256213i | \(0.991844\pi\) | |||||||
\(948\) | −55.5921 | −1.80555 | ||||||||
\(949\) | −40.7217 | + | 19.5805i | −1.32188 | + | 0.635610i | ||||
\(950\) | − | 30.7956i | − | 0.999141i | ||||||
\(951\) | 2.08830 | + | 2.08830i | 0.0677179 | + | 0.0677179i | ||||
\(952\) | −1.68736 | − | 4.74550i | −0.0546877 | − | 0.153802i | ||||
\(953\) | − | 41.0785i | − | 1.33066i | −0.746548 | − | 0.665332i | \(-0.768290\pi\) | ||
0.746548 | − | 0.665332i | \(-0.231710\pi\) | |||||||
\(954\) | 1.51828 | − | 1.51828i | 0.0491562 | − | 0.0491562i | ||||
\(955\) | 20.7543 | + | 20.7543i | 0.671593 | + | 0.671593i | ||||
\(956\) | 14.4494 | + | 14.4494i | 0.467326 | + | 0.467326i | ||||
\(957\) | −5.20328 | + | 5.20328i | −0.168198 | + | 0.168198i | ||||
\(958\) | − | 13.3962i | − | 0.432810i | ||||||
\(959\) | −3.00944 | − | 8.46367i | −0.0971797 | − | 0.273306i | ||||
\(960\) | 35.2400 | + | 35.2400i | 1.13737 | + | 1.13737i | ||||
\(961\) | 29.0128i | 0.935895i | ||||||||
\(962\) | 21.1443 | + | 7.41291i | 0.681718 | + | 0.239002i | ||||
\(963\) | −0.896758 | −0.0288976 | ||||||||
\(964\) | 44.6325 | + | 44.6325i | 1.43752 | + | 1.43752i | ||||
\(965\) | 25.3277i | 0.815327i | ||||||||
\(966\) | −8.69119 | + | 3.09033i | −0.279635 | + | 0.0994299i | ||||
\(967\) | −43.8412 | + | 43.8412i | −1.40984 | + | 1.40984i | −0.649347 | + | 0.760492i | \(0.724958\pi\) |
−0.760492 | + | 0.649347i | \(0.775042\pi\) | |||||||
\(968\) | 3.29529 | − | 3.29529i | 0.105915 | − | 0.105915i | ||||
\(969\) | −26.7883 | + | 26.7883i | −0.860563 | + | 0.860563i | ||||
\(970\) | −1.38493 | − | 1.38493i | −0.0444674 | − | 0.0444674i | ||||
\(971\) | 44.2843i | 1.42115i | 0.703621 | + | 0.710575i | \(0.251565\pi\) | ||||
−0.703621 | + | 0.710575i | \(0.748435\pi\) | |||||||
\(972\) | −7.13125 | −0.228735 | ||||||||
\(973\) | −3.79615 | + | 7.98528i | −0.121699 | + | 0.255996i | ||||
\(974\) | 27.9541i | 0.895706i | ||||||||
\(975\) | 19.3017 | + | 6.76694i | 0.618150 | + | 0.216716i | ||||
\(976\) | − | 27.4627i | − | 0.879060i | ||||||
\(977\) | 7.01207 | − | 7.01207i | 0.224336 | − | 0.224336i | −0.585986 | − | 0.810321i | \(-0.699292\pi\) |
0.810321 | + | 0.585986i | \(0.199292\pi\) | |||||||
\(978\) | − | 55.2022i | − | 1.76517i | ||||||
\(979\) | −5.06895 | −0.162004 | ||||||||
\(980\) | 43.9320 | + | 4.50289i | 1.40336 | + | 0.143839i | ||||
\(981\) | 1.10393 | − | 1.10393i | 0.0352459 | − | 0.0352459i | ||||
\(982\) | −13.3827 | − | 13.3827i | −0.427059 | − | 0.427059i | ||||
\(983\) | 31.8034 | − | 31.8034i | 1.01437 | − | 1.01437i | 0.0144754 | − | 0.999895i | \(-0.495392\pi\) |
0.999895 | − | 0.0144754i | \(-0.00460781\pi\) | |||||||
\(984\) | 2.06022 | 0.0656775 | ||||||||
\(985\) | −13.0987 | −0.417360 | ||||||||
\(986\) | −39.7684 | + | 39.7684i | −1.26649 | + | 1.26649i | ||||
\(987\) | 13.4797 | + | 37.9101i | 0.429065 | + | 1.20669i | ||||
\(988\) | −34.6227 | + | 16.6479i | −1.10149 | + | 0.529640i | ||||
\(989\) | 9.78076 | 0.311010 | ||||||||
\(990\) | 0.821763 | + | 0.821763i | 0.0261173 | + | 0.0261173i | ||||
\(991\) | 42.1367 | 1.33852 | 0.669259 | − | 0.743029i | \(-0.266612\pi\) | ||||
0.669259 | + | 0.743029i | \(0.266612\pi\) | |||||||
\(992\) | 62.8825 | 1.99652 | ||||||||
\(993\) | −5.28281 | − | 5.28281i | −0.167645 | − | 0.167645i | ||||
\(994\) | 18.3664 | − | 38.6341i | 0.582546 | − | 1.22540i | ||||
\(995\) | 12.4931 | + | 12.4931i | 0.396058 | + | 0.396058i | ||||
\(996\) | −17.3575 | − | 17.3575i | −0.549994 | − | 0.549994i | ||||
\(997\) | − | 27.7314i | − | 0.878261i | −0.898423 | − | 0.439131i | \(-0.855287\pi\) | ||
0.898423 | − | 0.439131i | \(-0.144713\pi\) | |||||||
\(998\) | − | 19.3339i | − | 0.612003i | ||||||
\(999\) | −10.4731 | + | 10.4731i | −0.331354 | + | 0.331354i |
(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 | 91.2.i.a.83.2 | yes | 12 | |
3.2 | odd | 2 | 819.2.y.h.811.5 | 12 | |||
7.2 | even | 3 | 637.2.bc.a.31.5 | 24 | |||
7.3 | odd | 6 | 637.2.bc.a.460.1 | 24 | |||
7.4 | even | 3 | 637.2.bc.a.460.2 | 24 | |||
7.5 | odd | 6 | 637.2.bc.a.31.6 | 24 | |||
7.6 | odd | 2 | inner | 91.2.i.a.83.1 | yes | 12 | |
13.8 | odd | 4 | inner | 91.2.i.a.34.2 | yes | 12 | |
21.20 | even | 2 | 819.2.y.h.811.6 | 12 | |||
39.8 | even | 4 | 819.2.y.h.307.6 | 12 | |||
91.34 | even | 4 | inner | 91.2.i.a.34.1 | ✓ | 12 | |
91.47 | even | 12 | 637.2.bc.a.619.2 | 24 | |||
91.60 | odd | 12 | 637.2.bc.a.411.6 | 24 | |||
91.73 | even | 12 | 637.2.bc.a.411.5 | 24 | |||
91.86 | odd | 12 | 637.2.bc.a.619.1 | 24 | |||
273.125 | odd | 4 | 819.2.y.h.307.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.i.a.34.1 | ✓ | 12 | 91.34 | even | 4 | inner | |
91.2.i.a.34.2 | yes | 12 | 13.8 | odd | 4 | inner | |
91.2.i.a.83.1 | yes | 12 | 7.6 | odd | 2 | inner | |
91.2.i.a.83.2 | yes | 12 | 1.1 | even | 1 | trivial | |
637.2.bc.a.31.5 | 24 | 7.2 | even | 3 | |||
637.2.bc.a.31.6 | 24 | 7.5 | odd | 6 | |||
637.2.bc.a.411.5 | 24 | 91.73 | even | 12 | |||
637.2.bc.a.411.6 | 24 | 91.60 | odd | 12 | |||
637.2.bc.a.460.1 | 24 | 7.3 | odd | 6 | |||
637.2.bc.a.460.2 | 24 | 7.4 | even | 3 | |||
637.2.bc.a.619.1 | 24 | 91.86 | odd | 12 | |||
637.2.bc.a.619.2 | 24 | 91.47 | even | 12 | |||
819.2.y.h.307.5 | 12 | 273.125 | odd | 4 | |||
819.2.y.h.307.6 | 12 | 39.8 | even | 4 | |||
819.2.y.h.811.5 | 12 | 3.2 | odd | 2 | |||
819.2.y.h.811.6 | 12 | 21.20 | even | 2 |