Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(481,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.481");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.n (of order \(5\), degree \(4\), 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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 16 x^{10} - 6 x^{9} + 161 x^{8} - 180 x^{7} + 1725 x^{6} - 2255 x^{5} + 17635 x^{4} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 901.1 | ||
Root | \(2.41709 - 1.75612i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.901 |
Dual form | 930.2.n.e.481.1 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | + | 0.587785i | 0.572061 | + | 0.415627i | ||||
\(3\) | −0.809017 | + | 0.587785i | −0.467086 | + | 0.339358i | ||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.23226 | − | 3.79252i | −0.465752 | − | 1.43344i | −0.858034 | − | 0.513592i | \(-0.828314\pi\) |
0.392282 | − | 0.919845i | \(-0.371686\pi\) | |||||||
\(8\) | −0.309017 | + | 0.951057i | −0.109254 | + | 0.336249i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | 0.809017 | + | 0.587785i | 0.255834 | + | 0.185874i | ||||
\(11\) | −0.732264 | − | 2.25368i | −0.220786 | − | 0.679509i | −0.998692 | − | 0.0511286i | \(-0.983718\pi\) |
0.777906 | − | 0.628380i | \(-0.216282\pi\) | |||||||
\(12\) | −0.809017 | − | 0.587785i | −0.233543 | − | 0.169679i | ||||
\(13\) | 1.55840 | − | 1.13224i | 0.432223 | − | 0.314028i | −0.350314 | − | 0.936632i | \(-0.613925\pi\) |
0.782537 | + | 0.622604i | \(0.213925\pi\) | |||||||
\(14\) | 1.23226 | − | 3.79252i | 0.329336 | − | 1.01359i | ||||
\(15\) | −0.809017 | + | 0.587785i | −0.208887 | + | 0.151765i | ||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | 0.485923 | − | 1.49552i | 0.117854 | − | 0.362716i | −0.874678 | − | 0.484705i | \(-0.838927\pi\) |
0.992531 | + | 0.121989i | \(0.0389271\pi\) | |||||||
\(18\) | 0.809017 | − | 0.587785i | 0.190687 | − | 0.138542i | ||||
\(19\) | −4.47549 | − | 3.25164i | −1.02675 | − | 0.745976i | −0.0590932 | − | 0.998252i | \(-0.518821\pi\) |
−0.967655 | + | 0.252276i | \(0.918821\pi\) | |||||||
\(20\) | 0.309017 | + | 0.951057i | 0.0690983 | + | 0.212663i | ||||
\(21\) | 3.22611 | + | 2.34391i | 0.703995 | + | 0.511482i | ||||
\(22\) | 0.732264 | − | 2.25368i | 0.156119 | − | 0.480485i | ||||
\(23\) | 1.18483 | − | 3.64653i | 0.247054 | − | 0.760353i | −0.748238 | − | 0.663430i | \(-0.769100\pi\) |
0.995292 | − | 0.0969229i | \(-0.0309000\pi\) | |||||||
\(24\) | −0.309017 | − | 0.951057i | −0.0630778 | − | 0.194134i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.92629 | 0.377776 | ||||||||
\(27\) | 0.309017 | + | 0.951057i | 0.0594703 | + | 0.183031i | ||||
\(28\) | 3.22611 | − | 2.34391i | 0.609677 | − | 0.442956i | ||||
\(29\) | −0.786239 | − | 0.571236i | −0.146001 | − | 0.106076i | 0.512387 | − | 0.858755i | \(-0.328761\pi\) |
−0.658388 | + | 0.752679i | \(0.728761\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −1.29494 | − | 5.41508i | −0.232578 | − | 0.972578i | ||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.91709 | + | 1.39285i | 0.333723 | + | 0.242464i | ||||
\(34\) | 1.27216 | − | 0.924280i | 0.218174 | − | 0.158513i | ||||
\(35\) | −1.23226 | − | 3.79252i | −0.208291 | − | 0.641053i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.72598 | −0.283750 | −0.141875 | − | 0.989885i | \(-0.545313\pi\) | ||||
−0.141875 | + | 0.989885i | \(0.545313\pi\) | |||||||
\(38\) | −1.70949 | − | 5.26126i | −0.277315 | − | 0.853489i | ||||
\(39\) | −0.595256 | + | 1.83201i | −0.0953173 | + | 0.293356i | ||||
\(40\) | −0.309017 | + | 0.951057i | −0.0488599 | + | 0.150375i | ||||
\(41\) | 9.22818 | + | 6.70467i | 1.44120 | + | 1.04709i | 0.987790 | + | 0.155791i | \(0.0497927\pi\) |
0.453410 | + | 0.891302i | \(0.350207\pi\) | |||||||
\(42\) | 1.23226 | + | 3.79252i | 0.190142 | + | 0.585198i | ||||
\(43\) | 4.55225 | + | 3.30740i | 0.694211 | + | 0.504374i | 0.878042 | − | 0.478584i | \(-0.158850\pi\) |
−0.183831 | + | 0.982958i | \(0.558850\pi\) | |||||||
\(44\) | 1.91709 | − | 1.39285i | 0.289012 | − | 0.209980i | ||||
\(45\) | 0.309017 | − | 0.951057i | 0.0460655 | − | 0.141775i | ||||
\(46\) | 3.10192 | − | 2.25368i | 0.457353 | − | 0.332286i | ||||
\(47\) | 3.24323 | − | 2.35634i | 0.473074 | − | 0.343708i | −0.325564 | − | 0.945520i | \(-0.605554\pi\) |
0.798638 | + | 0.601812i | \(0.205554\pi\) | |||||||
\(48\) | 0.309017 | − | 0.951057i | 0.0446028 | − | 0.137273i | ||||
\(49\) | −7.20160 | + | 5.23227i | −1.02880 | + | 0.747467i | ||||
\(50\) | 0.809017 | + | 0.587785i | 0.114412 | + | 0.0831254i | ||||
\(51\) | 0.485923 | + | 1.49552i | 0.0680428 | + | 0.209414i | ||||
\(52\) | 1.55840 | + | 1.13224i | 0.216111 | + | 0.157014i | ||||
\(53\) | 0.978605 | − | 3.01184i | 0.134422 | − | 0.413708i | −0.861078 | − | 0.508473i | \(-0.830210\pi\) |
0.995500 | + | 0.0947655i | \(0.0302101\pi\) | |||||||
\(54\) | −0.309017 | + | 0.951057i | −0.0420519 | + | 0.129422i | ||||
\(55\) | −0.732264 | − | 2.25368i | −0.0987384 | − | 0.303886i | ||||
\(56\) | 3.98769 | 0.532877 | ||||||||
\(57\) | 5.53201 | 0.732733 | ||||||||
\(58\) | −0.300317 | − | 0.924280i | −0.0394335 | − | 0.121364i | ||||
\(59\) | −1.77578 | + | 1.29018i | −0.231187 | + | 0.167967i | −0.697348 | − | 0.716733i | \(-0.745637\pi\) |
0.466161 | + | 0.884700i | \(0.345637\pi\) | |||||||
\(60\) | −0.809017 | − | 0.587785i | −0.104444 | − | 0.0758827i | ||||
\(61\) | −5.27402 | −0.675268 | −0.337634 | − | 0.941277i | \(-0.609627\pi\) | ||||
−0.337634 | + | 0.941277i | \(0.609627\pi\) | |||||||
\(62\) | 2.13528 | − | 5.14204i | 0.271181 | − | 0.653040i | ||||
\(63\) | −3.98769 | −0.502402 | ||||||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | 1.55840 | − | 1.13224i | 0.193296 | − | 0.140438i | ||||
\(66\) | 0.732264 | + | 2.25368i | 0.0901355 | + | 0.277408i | ||||
\(67\) | 11.8088 | 1.44267 | 0.721337 | − | 0.692584i | \(-0.243528\pi\) | ||||
0.721337 | + | 0.692584i | \(0.243528\pi\) | |||||||
\(68\) | 1.57248 | 0.190691 | ||||||||
\(69\) | 1.18483 | + | 3.64653i | 0.142637 | + | 0.438990i | ||||
\(70\) | 1.23226 | − | 3.79252i | 0.147284 | − | 0.453293i | ||||
\(71\) | −1.36818 | + | 4.21082i | −0.162373 | + | 0.499733i | −0.998833 | − | 0.0482951i | \(-0.984621\pi\) |
0.836460 | + | 0.548028i | \(0.184621\pi\) | |||||||
\(72\) | 0.809017 | + | 0.587785i | 0.0953436 | + | 0.0692712i | ||||
\(73\) | 1.05186 | + | 3.23730i | 0.123111 | + | 0.378897i | 0.993552 | − | 0.113376i | \(-0.0361663\pi\) |
−0.870441 | + | 0.492273i | \(0.836166\pi\) | |||||||
\(74\) | −1.39635 | − | 1.01451i | −0.162323 | − | 0.117934i | ||||
\(75\) | −0.809017 | + | 0.587785i | −0.0934172 | + | 0.0678716i | ||||
\(76\) | 1.70949 | − | 5.26126i | 0.196092 | − | 0.603508i | ||||
\(77\) | −7.64477 | + | 5.55425i | −0.871202 | + | 0.632965i | ||||
\(78\) | −1.55840 | + | 1.13224i | −0.176454 | + | 0.128201i | ||||
\(79\) | −1.87836 | + | 5.78099i | −0.211332 | + | 0.650412i | 0.788062 | + | 0.615596i | \(0.211085\pi\) |
−0.999394 | + | 0.0348160i | \(0.988915\pi\) | |||||||
\(80\) | −0.809017 | + | 0.587785i | −0.0904508 | + | 0.0657164i | ||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 3.52485 | + | 10.8484i | 0.389255 | + | 1.19800i | ||||
\(83\) | −6.51982 | − | 4.73692i | −0.715643 | − | 0.519945i | 0.169346 | − | 0.985557i | \(-0.445834\pi\) |
−0.884989 | + | 0.465612i | \(0.845834\pi\) | |||||||
\(84\) | −1.23226 | + | 3.79252i | −0.134451 | + | 0.413798i | ||||
\(85\) | 0.485923 | − | 1.49552i | 0.0527057 | − | 0.162211i | ||||
\(86\) | 1.73880 | + | 5.35149i | 0.187500 | + | 0.577066i | ||||
\(87\) | 0.971845 | 0.104193 | ||||||||
\(88\) | 2.36966 | 0.252606 | ||||||||
\(89\) | 2.02504 | + | 6.23244i | 0.214654 | + | 0.660637i | 0.999178 | + | 0.0405387i | \(0.0129074\pi\) |
−0.784524 | + | 0.620099i | \(0.787093\pi\) | |||||||
\(90\) | 0.809017 | − | 0.587785i | 0.0852779 | − | 0.0619580i | ||||
\(91\) | −6.21442 | − | 4.51504i | −0.651448 | − | 0.473305i | ||||
\(92\) | 3.83418 | 0.399741 | ||||||||
\(93\) | 4.23053 | + | 3.61975i | 0.438686 | + | 0.375350i | ||||
\(94\) | 4.00885 | 0.413481 | ||||||||
\(95\) | −4.47549 | − | 3.25164i | −0.459176 | − | 0.333611i | ||||
\(96\) | 0.809017 | − | 0.587785i | 0.0825700 | − | 0.0599906i | ||||
\(97\) | −1.61145 | − | 4.95952i | −0.163618 | − | 0.503563i | 0.835314 | − | 0.549773i | \(-0.185286\pi\) |
−0.998932 | + | 0.0462096i | \(0.985286\pi\) | |||||||
\(98\) | −8.90167 | −0.899204 | ||||||||
\(99\) | −2.36966 | −0.238159 | ||||||||
\(100\) | 0.309017 | + | 0.951057i | 0.0309017 | + | 0.0951057i | ||||
\(101\) | 5.10270 | − | 15.7045i | 0.507737 | − | 1.56266i | −0.288382 | − | 0.957515i | \(-0.593117\pi\) |
0.796119 | − | 0.605140i | \(-0.206883\pi\) | |||||||
\(102\) | −0.485923 | + | 1.49552i | −0.0481135 | + | 0.148078i | ||||
\(103\) | 9.82263 | + | 7.13656i | 0.967853 | + | 0.703186i | 0.954961 | − | 0.296731i | \(-0.0958963\pi\) |
0.0128917 | + | 0.999917i | \(0.495896\pi\) | |||||||
\(104\) | 0.595256 | + | 1.83201i | 0.0583697 | + | 0.179643i | ||||
\(105\) | 3.22611 | + | 2.34391i | 0.314836 | + | 0.228742i | ||||
\(106\) | 2.56202 | − | 1.86142i | 0.248846 | − | 0.180797i | ||||
\(107\) | 4.16978 | − | 12.8333i | 0.403108 | − | 1.24064i | −0.519357 | − | 0.854558i | \(-0.673828\pi\) |
0.922465 | − | 0.386081i | \(-0.126172\pi\) | |||||||
\(108\) | −0.809017 | + | 0.587785i | −0.0778477 | + | 0.0565597i | ||||
\(109\) | −14.4292 | + | 10.4834i | −1.38207 | + | 1.00413i | −0.385386 | + | 0.922756i | \(0.625932\pi\) |
−0.996683 | + | 0.0813763i | \(0.974068\pi\) | |||||||
\(110\) | 0.732264 | − | 2.25368i | 0.0698186 | − | 0.214880i | ||||
\(111\) | 1.39635 | − | 1.01451i | 0.132536 | − | 0.0962929i | ||||
\(112\) | 3.22611 | + | 2.34391i | 0.304839 | + | 0.221478i | ||||
\(113\) | −1.21819 | − | 3.74919i | −0.114597 | − | 0.352694i | 0.877265 | − | 0.480005i | \(-0.159365\pi\) |
−0.991863 | + | 0.127311i | \(0.959365\pi\) | |||||||
\(114\) | 4.47549 | + | 3.25164i | 0.419168 | + | 0.304544i | ||||
\(115\) | 1.18483 | − | 3.64653i | 0.110486 | − | 0.340040i | ||||
\(116\) | 0.300317 | − | 0.924280i | 0.0278837 | − | 0.0858172i | ||||
\(117\) | −0.595256 | − | 1.83201i | −0.0550315 | − | 0.169369i | ||||
\(118\) | −2.19499 | −0.202065 | ||||||||
\(119\) | −6.27056 | −0.574821 | ||||||||
\(120\) | −0.309017 | − | 0.951057i | −0.0282093 | − | 0.0868192i | ||||
\(121\) | 4.35634 | − | 3.16507i | 0.396031 | − | 0.287733i | ||||
\(122\) | −4.26677 | − | 3.09999i | −0.386295 | − | 0.280660i | ||||
\(123\) | −11.4067 | −1.02850 | ||||||||
\(124\) | 4.74989 | − | 2.90491i | 0.426553 | − | 0.260869i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −3.22611 | − | 2.34391i | −0.287405 | − | 0.208812i | ||||
\(127\) | −7.97911 | + | 5.79717i | −0.708032 | + | 0.514415i | −0.882538 | − | 0.470241i | \(-0.844167\pi\) |
0.174506 | + | 0.984656i | \(0.444167\pi\) | |||||||
\(128\) | −0.309017 | − | 0.951057i | −0.0273135 | − | 0.0840623i | ||||
\(129\) | −5.62689 | −0.495420 | ||||||||
\(130\) | 1.92629 | 0.168947 | ||||||||
\(131\) | −2.69657 | − | 8.29919i | −0.235601 | − | 0.725104i | −0.997041 | − | 0.0768692i | \(-0.975508\pi\) |
0.761441 | − | 0.648235i | \(-0.224492\pi\) | |||||||
\(132\) | −0.732264 | + | 2.25368i | −0.0637354 | + | 0.196157i | ||||
\(133\) | −6.81690 | + | 20.9803i | −0.591100 | + | 1.81922i | ||||
\(134\) | 9.55352 | + | 6.94104i | 0.825298 | + | 0.599614i | ||||
\(135\) | 0.309017 | + | 0.951057i | 0.0265959 | + | 0.0818539i | ||||
\(136\) | 1.27216 | + | 0.924280i | 0.109087 | + | 0.0792563i | ||||
\(137\) | 5.70022 | − | 4.14145i | 0.487003 | − | 0.353828i | −0.317028 | − | 0.948416i | \(-0.602685\pi\) |
0.804030 | + | 0.594588i | \(0.202685\pi\) | |||||||
\(138\) | −1.18483 | + | 3.64653i | −0.100859 | + | 0.310413i | ||||
\(139\) | −10.0551 | + | 7.30549i | −0.852866 | + | 0.619643i | −0.925935 | − | 0.377683i | \(-0.876721\pi\) |
0.0730687 | + | 0.997327i | \(0.476721\pi\) | |||||||
\(140\) | 3.22611 | − | 2.34391i | 0.272656 | − | 0.198096i | ||||
\(141\) | −1.23880 | + | 3.81264i | −0.104326 | + | 0.321083i | ||||
\(142\) | −3.58194 | + | 2.60243i | −0.300590 | + | 0.218391i | ||||
\(143\) | −3.69287 | − | 2.68303i | −0.308814 | − | 0.224366i | ||||
\(144\) | 0.309017 | + | 0.951057i | 0.0257514 | + | 0.0792547i | ||||
\(145\) | −0.786239 | − | 0.571236i | −0.0652936 | − | 0.0474386i | ||||
\(146\) | −1.05186 | + | 3.23730i | −0.0870527 | + | 0.267921i | ||||
\(147\) | 2.75077 | − | 8.46599i | 0.226879 | − | 0.698263i | ||||
\(148\) | −0.533359 | − | 1.64151i | −0.0438418 | − | 0.134931i | ||||
\(149\) | −8.01770 | −0.656836 | −0.328418 | − | 0.944533i | \(-0.606515\pi\) | ||||
−0.328418 | + | 0.944533i | \(0.606515\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | −4.71700 | − | 14.5174i | −0.383864 | − | 1.18141i | −0.937301 | − | 0.348521i | \(-0.886684\pi\) |
0.553437 | − | 0.832891i | \(-0.313316\pi\) | |||||||
\(152\) | 4.47549 | − | 3.25164i | 0.363010 | − | 0.263742i | ||||
\(153\) | −1.27216 | − | 0.924280i | −0.102848 | − | 0.0747236i | ||||
\(154\) | −9.44945 | −0.761459 | ||||||||
\(155\) | −1.29494 | − | 5.41508i | −0.104012 | − | 0.434950i | ||||
\(156\) | −1.92629 | −0.154227 | ||||||||
\(157\) | 1.35410 | + | 0.983813i | 0.108069 | + | 0.0785168i | 0.640507 | − | 0.767952i | \(-0.278724\pi\) |
−0.532438 | + | 0.846469i | \(0.678724\pi\) | |||||||
\(158\) | −4.91760 | + | 3.57285i | −0.391223 | + | 0.284240i | ||||
\(159\) | 0.978605 | + | 3.01184i | 0.0776084 | + | 0.238854i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −15.2895 | −1.20498 | ||||||||
\(162\) | −0.309017 | − | 0.951057i | −0.0242787 | − | 0.0747221i | ||||
\(163\) | −2.94194 | + | 9.05437i | −0.230431 | + | 0.709193i | 0.767264 | + | 0.641332i | \(0.221618\pi\) |
−0.997695 | + | 0.0678617i | \(0.978382\pi\) | |||||||
\(164\) | −3.52485 | + | 10.8484i | −0.275245 | + | 0.847116i | ||||
\(165\) | 1.91709 | + | 1.39285i | 0.149245 | + | 0.108433i | ||||
\(166\) | −2.49035 | − | 7.66450i | −0.193289 | − | 0.594881i | ||||
\(167\) | 10.9383 | + | 7.94716i | 0.846433 | + | 0.614969i | 0.924160 | − | 0.382005i | \(-0.124766\pi\) |
−0.0777273 | + | 0.996975i | \(0.524766\pi\) | |||||||
\(168\) | −3.22611 | + | 2.34391i | −0.248900 | + | 0.180836i | ||||
\(169\) | −2.87058 | + | 8.83475i | −0.220814 | + | 0.679596i | ||||
\(170\) | 1.27216 | − | 0.924280i | 0.0975704 | − | 0.0708890i | ||||
\(171\) | −4.47549 | + | 3.25164i | −0.342249 | + | 0.248659i | ||||
\(172\) | −1.73880 | + | 5.35149i | −0.132583 | + | 0.408047i | ||||
\(173\) | 12.9464 | − | 9.40611i | 0.984296 | − | 0.715133i | 0.0256317 | − | 0.999671i | \(-0.491840\pi\) |
0.958665 | + | 0.284538i | \(0.0918403\pi\) | |||||||
\(174\) | 0.786239 | + | 0.571236i | 0.0596046 | + | 0.0433053i | ||||
\(175\) | −1.23226 | − | 3.79252i | −0.0931504 | − | 0.286687i | ||||
\(176\) | 1.91709 | + | 1.39285i | 0.144506 | + | 0.104990i | ||||
\(177\) | 0.678289 | − | 2.08756i | 0.0509833 | − | 0.156910i | ||||
\(178\) | −2.02504 | + | 6.23244i | −0.151783 | + | 0.467141i | ||||
\(179\) | −2.00635 | − | 6.17491i | −0.149962 | − | 0.461534i | 0.847654 | − | 0.530549i | \(-0.178014\pi\) |
−0.997616 | + | 0.0690151i | \(0.978014\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −20.7709 | −1.54389 | −0.771945 | − | 0.635689i | \(-0.780716\pi\) | ||||
−0.771945 | + | 0.635689i | \(0.780716\pi\) | |||||||
\(182\) | −2.37370 | − | 7.30549i | −0.175950 | − | 0.541519i | ||||
\(183\) | 4.26677 | − | 3.09999i | 0.315409 | − | 0.229158i | ||||
\(184\) | 3.10192 | + | 2.25368i | 0.228677 | + | 0.166143i | ||||
\(185\) | −1.72598 | −0.126897 | ||||||||
\(186\) | 1.29494 | + | 5.41508i | 0.0949496 | + | 0.397053i | ||||
\(187\) | −3.72623 | −0.272489 | ||||||||
\(188\) | 3.24323 | + | 2.35634i | 0.236537 | + | 0.171854i | ||||
\(189\) | 3.22611 | − | 2.34391i | 0.234665 | − | 0.170494i | ||||
\(190\) | −1.70949 | − | 5.26126i | −0.124019 | − | 0.381692i | ||||
\(191\) | 0.842019 | 0.0609263 | 0.0304632 | − | 0.999536i | \(-0.490302\pi\) | ||||
0.0304632 | + | 0.999536i | \(0.490302\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 5.22942 | + | 16.0945i | 0.376422 | + | 1.15851i | 0.942514 | + | 0.334166i | \(0.108455\pi\) |
−0.566092 | + | 0.824342i | \(0.691545\pi\) | |||||||
\(194\) | 1.61145 | − | 4.95952i | 0.115695 | − | 0.356073i | ||||
\(195\) | −0.595256 | + | 1.83201i | −0.0426272 | + | 0.131193i | ||||
\(196\) | −7.20160 | − | 5.23227i | −0.514400 | − | 0.373734i | ||||
\(197\) | 7.82857 | + | 24.0939i | 0.557762 | + | 1.71662i | 0.688534 | + | 0.725204i | \(0.258254\pi\) |
−0.130772 | + | 0.991412i | \(0.541746\pi\) | |||||||
\(198\) | −1.91709 | − | 1.39285i | −0.136242 | − | 0.0989854i | ||||
\(199\) | −12.3422 | + | 8.96712i | −0.874914 | + | 0.635663i | −0.931901 | − | 0.362712i | \(-0.881851\pi\) |
0.0569867 | + | 0.998375i | \(0.481851\pi\) | |||||||
\(200\) | −0.309017 | + | 0.951057i | −0.0218508 | + | 0.0672499i | ||||
\(201\) | −9.55352 | + | 6.94104i | −0.673853 | + | 0.489583i | ||||
\(202\) | 13.3590 | − | 9.70591i | 0.939938 | − | 0.682905i | ||||
\(203\) | −1.19757 | + | 3.68574i | −0.0840529 | + | 0.258688i | ||||
\(204\) | −1.27216 | + | 0.924280i | −0.0890691 | + | 0.0647125i | ||||
\(205\) | 9.22818 | + | 6.70467i | 0.644524 | + | 0.468274i | ||||
\(206\) | 3.75191 | + | 11.5472i | 0.261408 | + | 0.804531i | ||||
\(207\) | −3.10192 | − | 2.25368i | −0.215598 | − | 0.156641i | ||||
\(208\) | −0.595256 | + | 1.83201i | −0.0412736 | + | 0.127027i | ||||
\(209\) | −4.05089 | + | 12.4674i | −0.280206 | + | 0.862386i | ||||
\(210\) | 1.23226 | + | 3.79252i | 0.0850343 | + | 0.261709i | ||||
\(211\) | 12.2482 | 0.843201 | 0.421601 | − | 0.906782i | \(-0.361468\pi\) | ||||
0.421601 | + | 0.906782i | \(0.361468\pi\) | |||||||
\(212\) | 3.16683 | 0.217499 | ||||||||
\(213\) | −1.36818 | − | 4.21082i | −0.0937461 | − | 0.288521i | ||||
\(214\) | 10.9166 | − | 7.93140i | 0.746246 | − | 0.542179i | ||||
\(215\) | 4.55225 | + | 3.30740i | 0.310461 | + | 0.225563i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −18.9411 | + | 11.5839i | −1.28581 | + | 0.786366i | ||||
\(218\) | −17.8355 | −1.20797 | ||||||||
\(219\) | −2.75381 | − | 2.00076i | −0.186085 | − | 0.135199i | ||||
\(220\) | 1.91709 | − | 1.39285i | 0.129250 | − | 0.0939058i | ||||
\(221\) | −0.936028 | − | 2.88080i | −0.0629640 | − | 0.193783i | ||||
\(222\) | 1.72598 | 0.115841 | ||||||||
\(223\) | 0.264851 | 0.0177357 | 0.00886787 | − | 0.999961i | \(-0.497177\pi\) | ||||
0.00886787 | + | 0.999961i | \(0.497177\pi\) | |||||||
\(224\) | 1.23226 | + | 3.79252i | 0.0823341 | + | 0.253398i | ||||
\(225\) | 0.309017 | − | 0.951057i | 0.0206011 | − | 0.0634038i | ||||
\(226\) | 1.21819 | − | 3.74919i | 0.0810326 | − | 0.249393i | ||||
\(227\) | 13.9174 | + | 10.1116i | 0.923729 | + | 0.671128i | 0.944449 | − | 0.328657i | \(-0.106596\pi\) |
−0.0207206 | + | 0.999785i | \(0.506596\pi\) | |||||||
\(228\) | 1.70949 | + | 5.26126i | 0.113213 | + | 0.348435i | ||||
\(229\) | −19.4070 | − | 14.1000i | −1.28245 | − | 0.931755i | −0.282827 | − | 0.959171i | \(-0.591272\pi\) |
−0.999624 | + | 0.0274156i | \(0.991272\pi\) | |||||||
\(230\) | 3.10192 | − | 2.25368i | 0.204535 | − | 0.148603i | ||||
\(231\) | 2.92004 | − | 8.98696i | 0.192125 | − | 0.591299i | ||||
\(232\) | 0.786239 | − | 0.571236i | 0.0516191 | − | 0.0375035i | ||||
\(233\) | 11.6293 | − | 8.44916i | 0.761859 | − | 0.553523i | −0.137621 | − | 0.990485i | \(-0.543946\pi\) |
0.899480 | + | 0.436962i | \(0.143946\pi\) | |||||||
\(234\) | 0.595256 | − | 1.83201i | 0.0389131 | − | 0.119762i | ||||
\(235\) | 3.24323 | − | 2.35634i | 0.211565 | − | 0.153711i | ||||
\(236\) | −1.77578 | − | 1.29018i | −0.115594 | − | 0.0839837i | ||||
\(237\) | −1.87836 | − | 5.78099i | −0.122012 | − | 0.375515i | ||||
\(238\) | −5.07299 | − | 3.68574i | −0.328833 | − | 0.238911i | ||||
\(239\) | 2.11238 | − | 6.50123i | 0.136638 | − | 0.420529i | −0.859203 | − | 0.511635i | \(-0.829040\pi\) |
0.995841 | + | 0.0911055i | \(0.0290401\pi\) | |||||||
\(240\) | 0.309017 | − | 0.951057i | 0.0199470 | − | 0.0613904i | ||||
\(241\) | 9.08178 | + | 27.9509i | 0.585009 | + | 1.80047i | 0.599234 | + | 0.800574i | \(0.295472\pi\) |
−0.0142247 | + | 0.999899i | \(0.504528\pi\) | |||||||
\(242\) | 5.38473 | 0.346144 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.62976 | − | 5.01589i | −0.104335 | − | 0.321109i | ||||
\(245\) | −7.20160 | + | 5.23227i | −0.460093 | + | 0.334277i | ||||
\(246\) | −9.22818 | − | 6.70467i | −0.588367 | − | 0.427474i | ||||
\(247\) | −10.6563 | −0.678042 | ||||||||
\(248\) | 5.55021 | + | 0.441792i | 0.352439 | + | 0.0280538i | ||||
\(249\) | 8.05894 | 0.510714 | ||||||||
\(250\) | 0.809017 | + | 0.587785i | 0.0511667 | + | 0.0371748i | ||||
\(251\) | 0.0529801 | − | 0.0384923i | 0.00334407 | − | 0.00242961i | −0.586112 | − | 0.810230i | \(-0.699342\pi\) |
0.589456 | + | 0.807800i | \(0.299342\pi\) | |||||||
\(252\) | −1.23226 | − | 3.79252i | −0.0776253 | − | 0.238906i | ||||
\(253\) | −9.08569 | −0.571213 | ||||||||
\(254\) | −9.86273 | −0.618843 | ||||||||
\(255\) | 0.485923 | + | 1.49552i | 0.0304297 | + | 0.0936528i | ||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | 2.09148 | − | 6.43690i | 0.130463 | − | 0.401523i | −0.864394 | − | 0.502815i | \(-0.832298\pi\) |
0.994857 | + | 0.101292i | \(0.0322977\pi\) | |||||||
\(258\) | −4.55225 | − | 3.30740i | −0.283410 | − | 0.205910i | ||||
\(259\) | 2.12687 | + | 6.54583i | 0.132157 | + | 0.406738i | ||||
\(260\) | 1.55840 | + | 1.13224i | 0.0966479 | + | 0.0702188i | ||||
\(261\) | −0.786239 | + | 0.571236i | −0.0486670 | + | 0.0353586i | ||||
\(262\) | 2.69657 | − | 8.29919i | 0.166595 | − | 0.512726i | ||||
\(263\) | −6.89481 | + | 5.00937i | −0.425152 | + | 0.308891i | −0.779707 | − | 0.626144i | \(-0.784632\pi\) |
0.354556 | + | 0.935035i | \(0.384632\pi\) | |||||||
\(264\) | −1.91709 | + | 1.39285i | −0.117989 | + | 0.0857239i | ||||
\(265\) | 0.978605 | − | 3.01184i | 0.0601152 | − | 0.185016i | ||||
\(266\) | −17.8469 | + | 12.9665i | −1.09426 | + | 0.795028i | ||||
\(267\) | −5.30163 | − | 3.85186i | −0.324454 | − | 0.235730i | ||||
\(268\) | 3.64912 | + | 11.2308i | 0.222905 | + | 0.686032i | ||||
\(269\) | 0.466614 | + | 0.339015i | 0.0284500 | + | 0.0206701i | 0.601919 | − | 0.798557i | \(-0.294403\pi\) |
−0.573469 | + | 0.819227i | \(0.694403\pi\) | |||||||
\(270\) | −0.309017 | + | 0.951057i | −0.0188062 | + | 0.0578795i | ||||
\(271\) | 3.32144 | − | 10.2223i | 0.201763 | − | 0.620963i | −0.798068 | − | 0.602568i | \(-0.794144\pi\) |
0.999831 | − | 0.0183954i | \(-0.00585575\pi\) | |||||||
\(272\) | 0.485923 | + | 1.49552i | 0.0294634 | + | 0.0906790i | ||||
\(273\) | 7.68145 | 0.464902 | ||||||||
\(274\) | 7.04586 | 0.425656 | ||||||||
\(275\) | −0.732264 | − | 2.25368i | −0.0441572 | − | 0.135902i | ||||
\(276\) | −3.10192 | + | 2.25368i | −0.186714 | + | 0.135655i | ||||
\(277\) | 23.1956 | + | 16.8526i | 1.39369 | + | 1.01257i | 0.995449 | + | 0.0952930i | \(0.0303788\pi\) |
0.398240 | + | 0.917281i | \(0.369621\pi\) | |||||||
\(278\) | −12.4288 | −0.745432 | ||||||||
\(279\) | −5.55021 | − | 0.441792i | −0.332282 | − | 0.0264494i | ||||
\(280\) | 3.98769 | 0.238310 | ||||||||
\(281\) | 1.30606 | + | 0.948905i | 0.0779128 | + | 0.0566069i | 0.626060 | − | 0.779775i | \(-0.284667\pi\) |
−0.548147 | + | 0.836382i | \(0.684667\pi\) | |||||||
\(282\) | −3.24323 | + | 2.35634i | −0.193131 | + | 0.140318i | ||||
\(283\) | −5.71376 | − | 17.5851i | −0.339648 | − | 1.04533i | −0.964387 | − | 0.264495i | \(-0.914795\pi\) |
0.624739 | − | 0.780833i | \(-0.285205\pi\) | |||||||
\(284\) | −4.42752 | −0.262725 | ||||||||
\(285\) | 5.53201 | 0.327688 | ||||||||
\(286\) | −1.41055 | − | 4.34123i | −0.0834077 | − | 0.256703i | ||||
\(287\) | 14.0560 | − | 43.2600i | 0.829700 | − | 2.55356i | ||||
\(288\) | −0.309017 | + | 0.951057i | −0.0182090 | + | 0.0560415i | ||||
\(289\) | 11.7528 | + | 8.53894i | 0.691344 | + | 0.502291i | ||||
\(290\) | −0.300317 | − | 0.924280i | −0.0176352 | − | 0.0542756i | ||||
\(291\) | 4.21882 | + | 3.06515i | 0.247312 | + | 0.179683i | ||||
\(292\) | −2.75381 | + | 2.00076i | −0.161155 | + | 0.117086i | ||||
\(293\) | 3.70628 | − | 11.4068i | 0.216523 | − | 0.666390i | −0.782519 | − | 0.622627i | \(-0.786065\pi\) |
0.999042 | − | 0.0437629i | \(-0.0139346\pi\) | |||||||
\(294\) | 7.20160 | − | 5.23227i | 0.420006 | − | 0.305152i | ||||
\(295\) | −1.77578 | + | 1.29018i | −0.103390 | + | 0.0751173i | ||||
\(296\) | 0.533359 | − | 1.64151i | 0.0310008 | − | 0.0954108i | ||||
\(297\) | 1.91709 | − | 1.39285i | 0.111241 | − | 0.0808213i | ||||
\(298\) | −6.48646 | − | 4.71269i | −0.375750 | − | 0.272999i | ||||
\(299\) | −2.28232 | − | 7.02426i | −0.131990 | − | 0.406224i | ||||
\(300\) | −0.809017 | − | 0.587785i | −0.0467086 | − | 0.0339358i | ||||
\(301\) | 6.93381 | − | 21.3401i | 0.399658 | − | 1.23002i | ||||
\(302\) | 4.71700 | − | 14.5174i | 0.271433 | − | 0.835384i | ||||
\(303\) | 5.10270 | + | 15.7045i | 0.293142 | + | 0.902199i | ||||
\(304\) | 5.53201 | 0.317283 | ||||||||
\(305\) | −5.27402 | −0.301989 | ||||||||
\(306\) | −0.485923 | − | 1.49552i | −0.0277783 | − | 0.0854930i | ||||
\(307\) | 12.1638 | − | 8.83750i | 0.694223 | − | 0.504383i | −0.183822 | − | 0.982959i | \(-0.558847\pi\) |
0.878046 | + | 0.478577i | \(0.158847\pi\) | |||||||
\(308\) | −7.64477 | − | 5.55425i | −0.435601 | − | 0.316483i | ||||
\(309\) | −12.1414 | −0.690703 | ||||||||
\(310\) | 2.13528 | − | 5.14204i | 0.121276 | − | 0.292048i | ||||
\(311\) | 28.1086 | 1.59389 | 0.796946 | − | 0.604051i | \(-0.206448\pi\) | ||||
0.796946 | + | 0.604051i | \(0.206448\pi\) | |||||||
\(312\) | −1.55840 | − | 1.13224i | −0.0882271 | − | 0.0641007i | ||||
\(313\) | 3.32610 | − | 2.41656i | 0.188003 | − | 0.136592i | −0.489803 | − | 0.871833i | \(-0.662931\pi\) |
0.677805 | + | 0.735241i | \(0.262931\pi\) | |||||||
\(314\) | 0.517221 | + | 1.59184i | 0.0291885 | + | 0.0898329i | ||||
\(315\) | −3.98769 | −0.224681 | ||||||||
\(316\) | −6.07849 | −0.341942 | ||||||||
\(317\) | −6.12446 | − | 18.8491i | −0.343984 | − | 1.05867i | −0.962125 | − | 0.272607i | \(-0.912114\pi\) |
0.618142 | − | 0.786067i | \(-0.287886\pi\) | |||||||
\(318\) | −0.978605 | + | 3.01184i | −0.0548775 | + | 0.168895i | ||||
\(319\) | −0.711647 | + | 2.19022i | −0.0398446 | + | 0.122629i | ||||
\(320\) | −0.809017 | − | 0.587785i | −0.0452254 | − | 0.0328582i | ||||
\(321\) | 4.16978 | + | 12.8333i | 0.232735 | + | 0.716283i | ||||
\(322\) | −12.3695 | − | 8.98696i | −0.689325 | − | 0.500824i | ||||
\(323\) | −7.03762 | + | 5.11313i | −0.391583 | + | 0.284502i | ||||
\(324\) | 0.309017 | − | 0.951057i | 0.0171676 | − | 0.0528365i | ||||
\(325\) | 1.55840 | − | 1.13224i | 0.0864445 | − | 0.0628056i | ||||
\(326\) | −7.70211 | + | 5.59591i | −0.426580 | + | 0.309929i | ||||
\(327\) | 5.51147 | − | 16.9626i | 0.304785 | − | 0.938032i | ||||
\(328\) | −9.22818 | + | 6.70467i | −0.509541 | + | 0.370203i | ||||
\(329\) | −12.9330 | − | 9.39637i | −0.713019 | − | 0.518039i | ||||
\(330\) | 0.732264 | + | 2.25368i | 0.0403098 | + | 0.124061i | ||||
\(331\) | 22.1696 | + | 16.1072i | 1.21855 | + | 0.885329i | 0.995979 | − | 0.0895870i | \(-0.0285547\pi\) |
0.222572 | + | 0.974916i | \(0.428555\pi\) | |||||||
\(332\) | 2.49035 | − | 7.66450i | 0.136676 | − | 0.420644i | ||||
\(333\) | −0.533359 | + | 1.64151i | −0.0292279 | + | 0.0899541i | ||||
\(334\) | 4.17807 | + | 12.8588i | 0.228614 | + | 0.703601i | ||||
\(335\) | 11.8088 | 0.645183 | ||||||||
\(336\) | −3.98769 | −0.217546 | ||||||||
\(337\) | −1.43367 | − | 4.41237i | −0.0780968 | − | 0.240357i | 0.904384 | − | 0.426719i | \(-0.140331\pi\) |
−0.982481 | + | 0.186361i | \(0.940331\pi\) | |||||||
\(338\) | −7.51529 | + | 5.46018i | −0.408778 | + | 0.296994i | ||||
\(339\) | 3.18925 | + | 2.31713i | 0.173216 | + | 0.125849i | ||||
\(340\) | 1.57248 | 0.0852796 | ||||||||
\(341\) | −11.2556 | + | 6.88365i | −0.609525 | + | 0.372770i | ||||
\(342\) | −5.53201 | −0.299137 | ||||||||
\(343\) | 6.13499 | + | 4.45733i | 0.331258 | + | 0.240673i | ||||
\(344\) | −4.55225 | + | 3.30740i | −0.245441 | + | 0.178323i | ||||
\(345\) | 1.18483 | + | 3.64653i | 0.0637890 | + | 0.196322i | ||||
\(346\) | 16.0026 | 0.860307 | ||||||||
\(347\) | −20.7000 | −1.11124 | −0.555618 | − | 0.831438i | \(-0.687518\pi\) | ||||
−0.555618 | + | 0.831438i | \(0.687518\pi\) | |||||||
\(348\) | 0.300317 | + | 0.924280i | 0.0160987 | + | 0.0495466i | ||||
\(349\) | 3.97421 | − | 12.2314i | 0.212734 | − | 0.654729i | −0.786572 | − | 0.617498i | \(-0.788146\pi\) |
0.999307 | − | 0.0372310i | \(-0.0118537\pi\) | |||||||
\(350\) | 1.23226 | − | 3.79252i | 0.0658673 | − | 0.202719i | ||||
\(351\) | 1.55840 | + | 1.13224i | 0.0831813 | + | 0.0604348i | ||||
\(352\) | 0.732264 | + | 2.25368i | 0.0390298 | + | 0.120121i | ||||
\(353\) | 20.3797 | + | 14.8067i | 1.08470 | + | 0.788081i | 0.978497 | − | 0.206263i | \(-0.0661302\pi\) |
0.106204 | + | 0.994344i | \(0.466130\pi\) | |||||||
\(354\) | 1.77578 | − | 1.29018i | 0.0943818 | − | 0.0685724i | ||||
\(355\) | −1.36818 | + | 4.21082i | −0.0726154 | + | 0.223487i | ||||
\(356\) | −5.30163 | + | 3.85186i | −0.280986 | + | 0.204148i | ||||
\(357\) | 5.07299 | − | 3.68574i | 0.268491 | − | 0.195070i | ||||
\(358\) | 2.00635 | − | 6.17491i | 0.106039 | − | 0.326354i | ||||
\(359\) | −4.09631 | + | 2.97615i | −0.216195 | + | 0.157075i | −0.690612 | − | 0.723225i | \(-0.742659\pi\) |
0.474417 | + | 0.880300i | \(0.342659\pi\) | |||||||
\(360\) | 0.809017 | + | 0.587785i | 0.0426389 | + | 0.0309790i | ||||
\(361\) | 3.58558 | + | 11.0353i | 0.188715 | + | 0.580804i | ||||
\(362\) | −16.8040 | − | 12.2088i | −0.883200 | − | 0.641682i | ||||
\(363\) | −1.66397 | + | 5.12118i | −0.0873360 | + | 0.268792i | ||||
\(364\) | 2.37370 | − | 7.30549i | 0.124416 | − | 0.382912i | ||||
\(365\) | 1.05186 | + | 3.23730i | 0.0550570 | + | 0.169448i | ||||
\(366\) | 5.27402 | 0.275677 | ||||||||
\(367\) | 23.1771 | 1.20983 | 0.604916 | − | 0.796289i | \(-0.293207\pi\) | ||||
0.604916 | + | 0.796289i | \(0.293207\pi\) | |||||||
\(368\) | 1.18483 | + | 3.64653i | 0.0617634 | + | 0.190088i | ||||
\(369\) | 9.22818 | − | 6.70467i | 0.480400 | − | 0.349031i | ||||
\(370\) | −1.39635 | − | 1.01451i | −0.0725928 | − | 0.0527418i | ||||
\(371\) | −12.6283 | −0.655631 | ||||||||
\(372\) | −2.13528 | + | 5.14204i | −0.110709 | + | 0.266602i | ||||
\(373\) | 22.0764 | 1.14307 | 0.571536 | − | 0.820577i | \(-0.306348\pi\) | ||||
0.571536 | + | 0.820577i | \(0.306348\pi\) | |||||||
\(374\) | −3.01459 | − | 2.19022i | −0.155881 | − | 0.113254i | ||||
\(375\) | −0.809017 | + | 0.587785i | −0.0417775 | + | 0.0303531i | ||||
\(376\) | 1.23880 | + | 3.81264i | 0.0638864 | + | 0.196622i | ||||
\(377\) | −1.87206 | −0.0964158 | ||||||||
\(378\) | 3.98769 | 0.205105 | ||||||||
\(379\) | 7.99701 | + | 24.6123i | 0.410779 | + | 1.26425i | 0.915972 | + | 0.401241i | \(0.131421\pi\) |
−0.505193 | + | 0.863006i | \(0.668579\pi\) | |||||||
\(380\) | 1.70949 | − | 5.26126i | 0.0876948 | − | 0.269897i | ||||
\(381\) | 3.04775 | − | 9.38001i | 0.156141 | − | 0.480552i | ||||
\(382\) | 0.681207 | + | 0.494926i | 0.0348536 | + | 0.0253226i | ||||
\(383\) | −7.95037 | − | 24.4687i | −0.406245 | − | 1.25029i | −0.919851 | − | 0.392267i | \(-0.871691\pi\) |
0.513606 | − | 0.858026i | \(-0.328309\pi\) | |||||||
\(384\) | 0.809017 | + | 0.587785i | 0.0412850 | + | 0.0299953i | ||||
\(385\) | −7.64477 | + | 5.55425i | −0.389613 | + | 0.283071i | ||||
\(386\) | −5.22942 | + | 16.0945i | −0.266171 | + | 0.819189i | ||||
\(387\) | 4.55225 | − | 3.30740i | 0.231404 | − | 0.168125i | ||||
\(388\) | 4.21882 | − | 3.06515i | 0.214178 | − | 0.155610i | ||||
\(389\) | −1.68719 | + | 5.19263i | −0.0855439 | + | 0.263277i | −0.984674 | − | 0.174404i | \(-0.944200\pi\) |
0.899130 | + | 0.437681i | \(0.144200\pi\) | |||||||
\(390\) | −1.55840 | + | 1.13224i | −0.0789127 | + | 0.0573334i | ||||
\(391\) | −4.87770 | − | 3.54386i | −0.246676 | − | 0.179221i | ||||
\(392\) | −2.75077 | − | 8.46599i | −0.138935 | − | 0.427597i | ||||
\(393\) | 7.05971 | + | 5.12918i | 0.356115 | + | 0.258733i | ||||
\(394\) | −7.82857 | + | 24.0939i | −0.394398 | + | 1.21383i | ||||
\(395\) | −1.87836 | + | 5.78099i | −0.0945103 | + | 0.290873i | ||||
\(396\) | −0.732264 | − | 2.25368i | −0.0367976 | − | 0.113252i | ||||
\(397\) | −10.3275 | −0.518322 | −0.259161 | − | 0.965834i | \(-0.583446\pi\) | ||||
−0.259161 | + | 0.965834i | \(0.583446\pi\) | |||||||
\(398\) | −15.2558 | −0.764703 | ||||||||
\(399\) | −6.81690 | − | 20.9803i | −0.341272 | − | 1.05033i | ||||
\(400\) | −0.809017 | + | 0.587785i | −0.0404508 | + | 0.0293893i | ||||
\(401\) | 25.3541 | + | 18.4208i | 1.26612 | + | 0.919892i | 0.999041 | − | 0.0437825i | \(-0.0139409\pi\) |
0.267081 | + | 0.963674i | \(0.413941\pi\) | |||||||
\(402\) | −11.8088 | −0.588969 | ||||||||
\(403\) | −8.14924 | − | 6.97268i | −0.405942 | − | 0.347334i | ||||
\(404\) | 16.5127 | 0.821536 | ||||||||
\(405\) | −0.809017 | − | 0.587785i | −0.0402004 | − | 0.0292073i | ||||
\(406\) | −3.13528 | + | 2.27791i | −0.155601 | + | 0.113051i | ||||
\(407\) | 1.26388 | + | 3.88981i | 0.0626480 | + | 0.192811i | ||||
\(408\) | −1.57248 | −0.0778493 | ||||||||
\(409\) | −0.820443 | −0.0405683 | −0.0202841 | − | 0.999794i | \(-0.506457\pi\) | ||||
−0.0202841 | + | 0.999794i | \(0.506457\pi\) | |||||||
\(410\) | 3.52485 | + | 10.8484i | 0.174080 | + | 0.535763i | ||||
\(411\) | −2.17729 | + | 6.70101i | −0.107398 | + | 0.330536i | ||||
\(412\) | −3.75191 | + | 11.5472i | −0.184843 | + | 0.568890i | ||||
\(413\) | 7.08127 | + | 5.14484i | 0.348446 | + | 0.253161i | ||||
\(414\) | −1.18483 | − | 3.64653i | −0.0582311 | − | 0.179217i | ||||
\(415\) | −6.51982 | − | 4.73692i | −0.320045 | − | 0.232526i | ||||
\(416\) | −1.55840 | + | 1.13224i | −0.0764069 | + | 0.0555129i | ||||
\(417\) | 3.84072 | − | 11.8205i | 0.188081 | − | 0.578854i | ||||
\(418\) | −10.6054 | + | 7.70526i | −0.518726 | + | 0.376876i | ||||
\(419\) | 7.29651 | − | 5.30122i | 0.356458 | − | 0.258982i | −0.395115 | − | 0.918631i | \(-0.629295\pi\) |
0.751573 | + | 0.659650i | \(0.229295\pi\) | |||||||
\(420\) | −1.23226 | + | 3.79252i | −0.0601283 | + | 0.185056i | ||||
\(421\) | 5.77485 | − | 4.19568i | 0.281449 | − | 0.204485i | −0.438100 | − | 0.898926i | \(-0.644348\pi\) |
0.719549 | + | 0.694441i | \(0.244348\pi\) | |||||||
\(422\) | 9.90901 | + | 7.19931i | 0.482363 | + | 0.350457i | ||||
\(423\) | −1.23880 | − | 3.81264i | −0.0602327 | − | 0.185377i | ||||
\(424\) | 2.56202 | + | 1.86142i | 0.124423 | + | 0.0903984i | ||||
\(425\) | 0.485923 | − | 1.49552i | 0.0235707 | − | 0.0725432i | ||||
\(426\) | 1.36818 | − | 4.21082i | 0.0662885 | − | 0.204015i | ||||
\(427\) | 6.49898 | + | 20.0018i | 0.314508 | + | 0.967955i | ||||
\(428\) | 13.4937 | 0.652243 | ||||||||
\(429\) | 4.56464 | 0.220383 | ||||||||
\(430\) | 1.73880 | + | 5.35149i | 0.0838525 | + | 0.258072i | ||||
\(431\) | −22.7816 | + | 16.5518i | −1.09735 | + | 0.797273i | −0.980626 | − | 0.195891i | \(-0.937240\pi\) |
−0.116726 | + | 0.993164i | \(0.537240\pi\) | |||||||
\(432\) | −0.809017 | − | 0.587785i | −0.0389238 | − | 0.0282798i | ||||
\(433\) | −21.6103 | −1.03852 | −0.519261 | − | 0.854616i | \(-0.673793\pi\) | ||||
−0.519261 | + | 0.854616i | \(0.673793\pi\) | |||||||
\(434\) | −22.1325 | − | 1.76173i | −1.06239 | − | 0.0845657i | ||||
\(435\) | 0.971845 | 0.0465964 | ||||||||
\(436\) | −14.4292 | − | 10.4834i | −0.691035 | − | 0.502066i | ||||
\(437\) | −17.1599 | + | 12.4674i | −0.820867 | + | 0.596395i | ||||
\(438\) | −1.05186 | − | 3.23730i | −0.0502599 | − | 0.154684i | ||||
\(439\) | 17.9892 | 0.858577 | 0.429289 | − | 0.903167i | \(-0.358764\pi\) | ||||
0.429289 | + | 0.903167i | \(0.358764\pi\) | |||||||
\(440\) | 2.36966 | 0.112969 | ||||||||
\(441\) | 2.75077 | + | 8.46599i | 0.130989 | + | 0.403142i | ||||
\(442\) | 0.936028 | − | 2.88080i | 0.0445223 | − | 0.137026i | ||||
\(443\) | −8.95142 | + | 27.5496i | −0.425295 | + | 1.30892i | 0.477417 | + | 0.878677i | \(0.341573\pi\) |
−0.902712 | + | 0.430246i | \(0.858427\pi\) | |||||||
\(444\) | 1.39635 | + | 1.01451i | 0.0662679 | + | 0.0481464i | ||||
\(445\) | 2.02504 | + | 6.23244i | 0.0959962 | + | 0.295446i | ||||
\(446\) | 0.214269 | + | 0.155675i | 0.0101459 | + | 0.00737145i | ||||
\(447\) | 6.48646 | − | 4.71269i | 0.306799 | − | 0.222902i | ||||
\(448\) | −1.23226 | + | 3.79252i | −0.0582190 | + | 0.179180i | ||||
\(449\) | 23.7140 | − | 17.2293i | 1.11913 | − | 0.813099i | 0.135057 | − | 0.990838i | \(-0.456878\pi\) |
0.984078 | + | 0.177739i | \(0.0568783\pi\) | |||||||
\(450\) | 0.809017 | − | 0.587785i | 0.0381374 | − | 0.0277085i | ||||
\(451\) | 8.35269 | − | 25.7069i | 0.393313 | − | 1.21049i | ||||
\(452\) | 3.18925 | − | 2.31713i | 0.150010 | − | 0.108989i | ||||
\(453\) | 12.3493 | + | 8.97226i | 0.580219 | + | 0.421554i | ||||
\(454\) | 5.31596 | + | 16.3609i | 0.249491 | + | 0.767853i | ||||
\(455\) | −6.21442 | − | 4.51504i | −0.291337 | − | 0.211668i | ||||
\(456\) | −1.70949 | + | 5.26126i | −0.0800540 | + | 0.246381i | ||||
\(457\) | 7.89556 | − | 24.3000i | 0.369339 | − | 1.13671i | −0.577880 | − | 0.816121i | \(-0.696120\pi\) |
0.947219 | − | 0.320587i | \(-0.103880\pi\) | |||||||
\(458\) | −7.41282 | − | 22.8143i | −0.346378 | − | 1.06604i | ||||
\(459\) | 1.57248 | 0.0733970 | ||||||||
\(460\) | 3.83418 | 0.178770 | ||||||||
\(461\) | 11.0777 | + | 34.0937i | 0.515940 | + | 1.58790i | 0.781565 | + | 0.623823i | \(0.214422\pi\) |
−0.265625 | + | 0.964076i | \(0.585578\pi\) | |||||||
\(462\) | 7.64477 | − | 5.55425i | 0.355667 | − | 0.258407i | ||||
\(463\) | −8.01228 | − | 5.82126i | −0.372362 | − | 0.270537i | 0.385828 | − | 0.922571i | \(-0.373916\pi\) |
−0.758190 | + | 0.652034i | \(0.773916\pi\) | |||||||
\(464\) | 0.971845 | 0.0451168 | ||||||||
\(465\) | 4.23053 | + | 3.61975i | 0.196186 | + | 0.167862i | ||||
\(466\) | 14.3746 | 0.665889 | ||||||||
\(467\) | 16.5030 | + | 11.9901i | 0.763668 | + | 0.554837i | 0.900033 | − | 0.435822i | \(-0.143542\pi\) |
−0.136365 | + | 0.990659i | \(0.543542\pi\) | |||||||
\(468\) | 1.55840 | − | 1.13224i | 0.0720371 | − | 0.0523380i | ||||
\(469\) | −14.5516 | − | 44.7851i | −0.671928 | − | 2.06798i | ||||
\(470\) | 4.00885 | 0.184915 | ||||||||
\(471\) | −1.67376 | −0.0771229 | ||||||||
\(472\) | −0.678289 | − | 2.08756i | −0.0312208 | − | 0.0960876i | ||||
\(473\) | 4.12037 | − | 12.6812i | 0.189455 | − | 0.583081i | ||||
\(474\) | 1.87836 | − | 5.78099i | 0.0862757 | − | 0.265529i | ||||
\(475\) | −4.47549 | − | 3.25164i | −0.205350 | − | 0.149195i | ||||
\(476\) | −1.93771 | − | 5.96365i | −0.0888147 | − | 0.273344i | ||||
\(477\) | −2.56202 | − | 1.86142i | −0.117307 | − | 0.0852285i | ||||
\(478\) | 5.53027 | − | 4.01798i | 0.252949 | − | 0.183778i | ||||
\(479\) | 5.39362 | − | 16.5999i | 0.246441 | − | 0.758467i | −0.748955 | − | 0.662620i | \(-0.769444\pi\) |
0.995396 | − | 0.0958463i | \(-0.0305557\pi\) | |||||||
\(480\) | 0.809017 | − | 0.587785i | 0.0369264 | − | 0.0268286i | ||||
\(481\) | −2.68978 | + | 1.95424i | −0.122643 | + | 0.0891055i | ||||
\(482\) | −9.08178 | + | 27.9509i | −0.413664 | + | 1.27313i | ||||
\(483\) | 12.3695 | − | 8.98696i | 0.562831 | − | 0.408921i | ||||
\(484\) | 4.35634 | + | 3.16507i | 0.198015 | + | 0.143867i | ||||
\(485\) | −1.61145 | − | 4.95952i | −0.0731721 | − | 0.225200i | ||||
\(486\) | 0.809017 | + | 0.587785i | 0.0366978 | + | 0.0266625i | ||||
\(487\) | −5.39415 | + | 16.6015i | −0.244432 | + | 0.752285i | 0.751297 | + | 0.659964i | \(0.229428\pi\) |
−0.995729 | + | 0.0923207i | \(0.970572\pi\) | |||||||
\(488\) | 1.62976 | − | 5.01589i | 0.0737758 | − | 0.227059i | ||||
\(489\) | −2.94194 | − | 9.05437i | −0.133039 | − | 0.409453i | ||||
\(490\) | −8.90167 | −0.402136 | ||||||||
\(491\) | −31.7750 | −1.43399 | −0.716993 | − | 0.697080i | \(-0.754482\pi\) | ||||
−0.716993 | + | 0.697080i | \(0.754482\pi\) | |||||||
\(492\) | −3.52485 | − | 10.8484i | −0.158913 | − | 0.489083i | ||||
\(493\) | −1.23634 | + | 0.898257i | −0.0556821 | + | 0.0404554i | ||||
\(494\) | −8.62110 | − | 6.26359i | −0.387881 | − | 0.281812i | ||||
\(495\) | −2.36966 | −0.106508 | ||||||||
\(496\) | 4.23053 | + | 3.61975i | 0.189957 | + | 0.162531i | ||||
\(497\) | 17.6556 | 0.791961 | ||||||||
\(498\) | 6.51982 | + | 4.73692i | 0.292160 | + | 0.212267i | ||||
\(499\) | −15.4482 | + | 11.2238i | −0.691555 | + | 0.502444i | −0.877171 | − | 0.480178i | \(-0.840572\pi\) |
0.185616 | + | 0.982622i | \(0.440572\pi\) | |||||||
\(500\) | 0.309017 | + | 0.951057i | 0.0138197 | + | 0.0425325i | ||||
\(501\) | −13.5205 | −0.604052 | ||||||||
\(502\) | 0.0654870 | 0.00292283 | ||||||||
\(503\) | 3.56903 | + | 10.9843i | 0.159135 | + | 0.489768i | 0.998556 | − | 0.0537137i | \(-0.0171058\pi\) |
−0.839421 | + | 0.543481i | \(0.817106\pi\) | |||||||
\(504\) | 1.23226 | − | 3.79252i | 0.0548894 | − | 0.168932i | ||||
\(505\) | 5.10270 | − | 15.7045i | 0.227067 | − | 0.698841i | ||||
\(506\) | −7.35048 | − | 5.34044i | −0.326769 | − | 0.237411i | ||||
\(507\) | −2.87058 | − | 8.83475i | −0.127487 | − | 0.392365i | ||||
\(508\) | −7.97911 | − | 5.79717i | −0.354016 | − | 0.257208i | ||||
\(509\) | 17.2315 | − | 12.5194i | 0.763774 | − | 0.554915i | −0.136291 | − | 0.990669i | \(-0.543518\pi\) |
0.900066 | + | 0.435754i | \(0.143518\pi\) | |||||||
\(510\) | −0.485923 | + | 1.49552i | −0.0215170 | + | 0.0662226i | ||||
\(511\) | 10.9813 | − | 7.97841i | 0.485786 | − | 0.352944i | ||||
\(512\) | 0.809017 | − | 0.587785i | 0.0357538 | − | 0.0259767i | ||||
\(513\) | 1.70949 | − | 5.26126i | 0.0754757 | − | 0.232290i | ||||
\(514\) | 5.47555 | − | 3.97822i | 0.241516 | − | 0.175472i | ||||
\(515\) | 9.82263 | + | 7.13656i | 0.432837 | + | 0.314474i | ||||
\(516\) | −1.73880 | − | 5.35149i | −0.0765465 | − | 0.235586i | ||||
\(517\) | −7.68534 | − | 5.58372i | −0.338001 | − | 0.245572i | ||||
\(518\) | −2.12687 | + | 6.54583i | −0.0934492 | + | 0.287607i | ||||
\(519\) | −4.94508 | + | 15.2194i | −0.217065 | + | 0.668058i | ||||
\(520\) | 0.595256 | + | 1.83201i | 0.0261037 | + | 0.0803390i | ||||
\(521\) | 15.2854 | 0.669667 | 0.334833 | − | 0.942277i | \(-0.391320\pi\) | ||||
0.334833 | + | 0.942277i | \(0.391320\pi\) | |||||||
\(522\) | −0.971845 | −0.0425365 | ||||||||
\(523\) | −9.49286 | − | 29.2160i | −0.415094 | − | 1.27753i | −0.912167 | − | 0.409819i | \(-0.865592\pi\) |
0.497073 | − | 0.867709i | \(-0.334408\pi\) | |||||||
\(524\) | 7.05971 | − | 5.12918i | 0.308405 | − | 0.224069i | ||||
\(525\) | 3.22611 | + | 2.34391i | 0.140799 | + | 0.102296i | ||||
\(526\) | −8.52245 | −0.371596 | ||||||||
\(527\) | −8.72758 | − | 0.694709i | −0.380180 | − | 0.0302620i | ||||
\(528\) | −2.36966 | −0.103126 | ||||||||
\(529\) | 6.71406 | + | 4.87805i | 0.291916 | + | 0.212089i | ||||
\(530\) | 2.56202 | − | 1.86142i | 0.111287 | − | 0.0808548i | ||||
\(531\) | 0.678289 | + | 2.08756i | 0.0294352 | + | 0.0905923i | ||||
\(532\) | −22.0600 | −0.956420 | ||||||||
\(533\) | 21.9725 | 0.951736 | ||||||||
\(534\) | −2.02504 | − | 6.23244i | −0.0876322 | − | 0.269704i | ||||
\(535\) | 4.16978 | − | 12.8333i | 0.180275 | − | 0.554831i | ||||
\(536\) | −3.64912 | + | 11.2308i | −0.157618 | + | 0.485098i | ||||
\(537\) | 5.25269 | + | 3.81630i | 0.226670 | + | 0.164686i | ||||
\(538\) | 0.178231 | + | 0.548538i | 0.00768407 | + | 0.0236491i | ||||
\(539\) | 17.0653 | + | 12.3987i | 0.735055 | + | 0.534049i | ||||
\(540\) | −0.809017 | + | 0.587785i | −0.0348145 | + | 0.0252942i | ||||
\(541\) | 3.31413 | − | 10.1999i | 0.142486 | − | 0.438526i | −0.854193 | − | 0.519956i | \(-0.825949\pi\) |
0.996679 | + | 0.0814294i | \(0.0259485\pi\) | |||||||
\(542\) | 8.69565 | − | 6.31776i | 0.373510 | − | 0.271371i | ||||
\(543\) | 16.8040 | − | 12.2088i | 0.721130 | − | 0.523932i | ||||
\(544\) | −0.485923 | + | 1.49552i | −0.0208338 | + | 0.0641197i | ||||
\(545\) | −14.4292 | + | 10.4834i | −0.618080 | + | 0.449061i | ||||
\(546\) | 6.21442 | + | 4.51504i | 0.265953 | + | 0.193226i | ||||
\(547\) | 4.69708 | + | 14.4561i | 0.200832 | + | 0.618099i | 0.999859 | + | 0.0168027i | \(0.00534872\pi\) |
−0.799026 | + | 0.601296i | \(0.794651\pi\) | |||||||
\(548\) | 5.70022 | + | 4.14145i | 0.243501 | + | 0.176914i | ||||
\(549\) | −1.62976 | + | 5.01589i | −0.0695565 | + | 0.214073i | ||||
\(550\) | 0.732264 | − | 2.25368i | 0.0312238 | − | 0.0960971i | ||||
\(551\) | 1.66136 | + | 5.11313i | 0.0707761 | + | 0.217827i | ||||
\(552\) | −3.83418 | −0.163194 | ||||||||
\(553\) | 24.2391 | 1.03075 | ||||||||
\(554\) | 8.85993 | + | 27.2681i | 0.376423 | + | 1.15851i | ||||
\(555\) | 1.39635 | − | 1.01451i | 0.0592718 | − | 0.0430635i | ||||
\(556\) | −10.0551 | − | 7.30549i | −0.426433 | − | 0.309822i | ||||
\(557\) | 16.2233 | 0.687402 | 0.343701 | − | 0.939079i | \(-0.388319\pi\) | ||||
0.343701 | + | 0.939079i | \(0.388319\pi\) | |||||||
\(558\) | −4.23053 | − | 3.61975i | −0.179093 | − | 0.153236i | ||||
\(559\) | 10.8390 | 0.458441 | ||||||||
\(560\) | 3.22611 | + | 2.34391i | 0.136328 | + | 0.0990481i | ||||
\(561\) | 3.01459 | − | 2.19022i | 0.127276 | − | 0.0924714i | ||||
\(562\) | 0.498869 | + | 1.53536i | 0.0210435 | + | 0.0647653i | ||||
\(563\) | −34.2000 | −1.44136 | −0.720678 | − | 0.693270i | \(-0.756170\pi\) | ||||
−0.720678 | + | 0.693270i | \(0.756170\pi\) | |||||||
\(564\) | −4.00885 | −0.168803 | ||||||||
\(565\) | −1.21819 | − | 3.74919i | −0.0512495 | − | 0.157730i | ||||
\(566\) | 5.71376 | − | 17.5851i | 0.240167 | − | 0.739159i | ||||
\(567\) | −1.23226 | + | 3.79252i | −0.0517502 | + | 0.159271i | ||||
\(568\) | −3.58194 | − | 2.60243i | −0.150295 | − | 0.109196i | ||||
\(569\) | 10.5183 | + | 32.3721i | 0.440951 | + | 1.35711i | 0.886863 | + | 0.462032i | \(0.152879\pi\) |
−0.445912 | + | 0.895077i | \(0.647121\pi\) | |||||||
\(570\) | 4.47549 | + | 3.25164i | 0.187458 | + | 0.136196i | ||||
\(571\) | 7.52561 | − | 5.46768i | 0.314937 | − | 0.228815i | −0.419075 | − | 0.907952i | \(-0.637646\pi\) |
0.734012 | + | 0.679136i | \(0.237646\pi\) | |||||||
\(572\) | 1.41055 | − | 4.34123i | 0.0589782 | − | 0.181516i | ||||
\(573\) | −0.681207 | + | 0.494926i | −0.0284578 | + | 0.0206758i | ||||
\(574\) | 36.7991 | − | 26.7361i | 1.53597 | − | 1.11594i | ||||
\(575\) | 1.18483 | − | 3.64653i | 0.0494107 | − | 0.152071i | ||||
\(576\) | −0.809017 | + | 0.587785i | −0.0337090 | + | 0.0244911i | ||||
\(577\) | 8.04567 | + | 5.84552i | 0.334946 | + | 0.243352i | 0.742526 | − | 0.669817i | \(-0.233627\pi\) |
−0.407581 | + | 0.913169i | \(0.633627\pi\) | |||||||
\(578\) | 4.48919 | + | 13.8163i | 0.186726 | + | 0.574682i | ||||
\(579\) | −13.6908 | − | 9.94695i | −0.568970 | − | 0.413381i | ||||
\(580\) | 0.300317 | − | 0.924280i | 0.0124700 | − | 0.0383786i | ||||
\(581\) | −9.93074 | + | 30.5637i | −0.411996 | + | 1.26799i | ||||
\(582\) | 1.61145 | + | 4.95952i | 0.0667966 | + | 0.205579i | ||||
\(583\) | −7.50430 | −0.310797 | ||||||||
\(584\) | −3.40390 | −0.140854 | ||||||||
\(585\) | −0.595256 | − | 1.83201i | −0.0246108 | − | 0.0757443i | ||||
\(586\) | 9.70317 | − | 7.04976i | 0.400834 | − | 0.291223i | ||||
\(587\) | −23.6886 | − | 17.2108i | −0.977732 | − | 0.710364i | −0.0205313 | − | 0.999789i | \(-0.506536\pi\) |
−0.957201 | + | 0.289425i | \(0.906536\pi\) | |||||||
\(588\) | 8.90167 | 0.367099 | ||||||||
\(589\) | −11.8124 | + | 28.4458i | −0.486721 | + | 1.17209i | ||||
\(590\) | −2.19499 | −0.0903662 | ||||||||
\(591\) | −20.4955 | − | 14.8908i | −0.843071 | − | 0.612527i | ||||
\(592\) | 1.39635 | − | 1.01451i | 0.0573897 | − | 0.0416960i | ||||
\(593\) | −11.4394 | − | 35.2069i | −0.469760 | − | 1.44577i | −0.852896 | − | 0.522081i | \(-0.825156\pi\) |
0.383136 | − | 0.923692i | \(-0.374844\pi\) | |||||||
\(594\) | 2.36966 | 0.0972282 | ||||||||
\(595\) | −6.27056 | −0.257068 | ||||||||
\(596\) | −2.47761 | − | 7.62529i | −0.101487 | − | 0.312344i | ||||
\(597\) | 4.71430 | − | 14.5091i | 0.192943 | − | 0.593818i | ||||
\(598\) | 2.28232 | − | 7.02426i | 0.0933311 | − | 0.287244i | ||||
\(599\) | −2.29187 | − | 1.66514i | −0.0936433 | − | 0.0680359i | 0.539978 | − | 0.841679i | \(-0.318432\pi\) |
−0.633622 | + | 0.773643i | \(0.718432\pi\) | |||||||
\(600\) | −0.309017 | − | 0.951057i | −0.0126156 | − | 0.0388267i | ||||
\(601\) | 0.443279 | + | 0.322061i | 0.0180817 | + | 0.0131371i | 0.596789 | − | 0.802398i | \(-0.296443\pi\) |
−0.578708 | + | 0.815535i | \(0.696443\pi\) | |||||||
\(602\) | 18.1529 | − | 13.1889i | 0.739859 | − | 0.537539i | ||||
\(603\) | 3.64912 | − | 11.2308i | 0.148604 | − | 0.457355i | ||||
\(604\) | 12.3493 | − | 8.97226i | 0.502484 | − | 0.365076i | ||||
\(605\) | 4.35634 | − | 3.16507i | 0.177110 | − | 0.128678i | ||||
\(606\) | −5.10270 | + | 15.7045i | −0.207283 | + | 0.637951i | ||||
\(607\) | 30.6648 | − | 22.2793i | 1.24465 | − | 0.904289i | 0.246748 | − | 0.969080i | \(-0.420638\pi\) |
0.997899 | + | 0.0647909i | \(0.0206381\pi\) | |||||||
\(608\) | 4.47549 | + | 3.25164i | 0.181505 | + | 0.131871i | ||||
\(609\) | −1.19757 | − | 3.68574i | −0.0485280 | − | 0.149354i | ||||
\(610\) | −4.26677 | − | 3.09999i | −0.172756 | − | 0.125515i | ||||
\(611\) | 2.38629 | − | 7.34426i | 0.0965391 | − | 0.297117i | ||||
\(612\) | 0.485923 | − | 1.49552i | 0.0196423 | − | 0.0604526i | ||||
\(613\) | −11.5976 | − | 35.6938i | −0.468424 | − | 1.44166i | −0.854625 | − | 0.519246i | \(-0.826213\pi\) |
0.386201 | − | 0.922415i | \(-0.373787\pi\) | |||||||
\(614\) | 15.0353 | 0.606774 | ||||||||
\(615\) | −11.4067 | −0.459961 | ||||||||
\(616\) | −2.92004 | − | 8.98696i | −0.117652 | − | 0.362095i | ||||
\(617\) | −4.31488 | + | 3.13494i | −0.173710 | + | 0.126208i | −0.671243 | − | 0.741237i | \(-0.734239\pi\) |
0.497533 | + | 0.867445i | \(0.334239\pi\) | |||||||
\(618\) | −9.82263 | − | 7.13656i | −0.395124 | − | 0.287075i | ||||
\(619\) | −48.5852 | −1.95280 | −0.976401 | − | 0.215964i | \(-0.930710\pi\) | ||||
−0.976401 | + | 0.215964i | \(0.930710\pi\) | |||||||
\(620\) | 4.74989 | − | 2.90491i | 0.190760 | − | 0.116664i | ||||
\(621\) | 3.83418 | 0.153860 | ||||||||
\(622\) | 22.7403 | + | 16.5218i | 0.911804 | + | 0.662464i | ||||
\(623\) | 21.1413 | − | 15.3600i | 0.847007 | − | 0.615386i | ||||
\(624\) | −0.595256 | − | 1.83201i | −0.0238293 | − | 0.0733391i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 4.11129 | 0.164320 | ||||||||
\(627\) | −4.05089 | − | 12.4674i | −0.161777 | − | 0.497899i | ||||
\(628\) | −0.517221 | + | 1.59184i | −0.0206394 | + | 0.0635214i | ||||
\(629\) | −0.838695 | + | 2.58124i | −0.0334410 | + | 0.102921i | ||||
\(630\) | −3.22611 | − | 2.34391i | −0.128531 | − | 0.0933834i | ||||
\(631\) | −6.73238 | − | 20.7201i | −0.268012 | − | 0.824855i | −0.990984 | − | 0.133979i | \(-0.957225\pi\) |
0.722972 | − | 0.690877i | \(-0.242775\pi\) | |||||||
\(632\) | −4.91760 | − | 3.57285i | −0.195612 | − | 0.142120i | ||||
\(633\) | −9.90901 | + | 7.19931i | −0.393848 | + | 0.286147i | ||||
\(634\) | 6.12446 | − | 18.8491i | 0.243233 | − | 0.748595i | ||||
\(635\) | −7.97911 | + | 5.79717i | −0.316641 | + | 0.230053i | ||||
\(636\) | −2.56202 | + | 1.86142i | −0.101591 | + | 0.0738100i | ||||
\(637\) | −5.29877 | + | 16.3080i | −0.209945 | + | 0.646145i | ||||
\(638\) | −1.86312 | + | 1.35363i | −0.0737615 | + | 0.0535909i | ||||
\(639\) | 3.58194 | + | 2.60243i | 0.141699 | + | 0.102951i | ||||
\(640\) | −0.309017 | − | 0.951057i | −0.0122150 | − | 0.0375938i | ||||
\(641\) | 28.6760 | + | 20.8343i | 1.13263 | + | 0.822905i | 0.986076 | − | 0.166297i | \(-0.0531810\pi\) |
0.146556 | + | 0.989202i | \(0.453181\pi\) | |||||||
\(642\) | −4.16978 | + | 12.8333i | −0.164568 | + | 0.506489i | ||||
\(643\) | −8.13252 | + | 25.0293i | −0.320715 | + | 0.987060i | 0.652622 | + | 0.757683i | \(0.273669\pi\) |
−0.973338 | + | 0.229377i | \(0.926331\pi\) | |||||||
\(644\) | −4.72473 | − | 14.5412i | −0.186180 | − | 0.573004i | ||||
\(645\) | −5.62689 | −0.221558 | ||||||||
\(646\) | −8.69897 | −0.342256 | ||||||||
\(647\) | 11.4957 | + | 35.3802i | 0.451943 | + | 1.39094i | 0.874687 | + | 0.484689i | \(0.161067\pi\) |
−0.422744 | + | 0.906249i | \(0.638933\pi\) | |||||||
\(648\) | 0.809017 | − | 0.587785i | 0.0317812 | − | 0.0230904i | ||||
\(649\) | 4.20799 | + | 3.05729i | 0.165178 | + | 0.120009i | ||||
\(650\) | 1.92629 | 0.0755553 | ||||||||
\(651\) | 8.51483 | − | 20.5049i | 0.333722 | − | 0.803649i | ||||
\(652\) | −9.52033 | −0.372845 | ||||||||
\(653\) | 22.5181 | + | 16.3604i | 0.881202 | + | 0.640231i | 0.933569 | − | 0.358397i | \(-0.116677\pi\) |
−0.0523672 | + | 0.998628i | \(0.516677\pi\) | |||||||
\(654\) | 14.4292 | − | 10.4834i | 0.564227 | − | 0.409935i | ||||
\(655\) | −2.69657 | − | 8.29919i | −0.105364 | − | 0.324276i | ||||
\(656\) | −11.4067 | −0.445355 | ||||||||
\(657\) | 3.40390 | 0.132799 | ||||||||
\(658\) | −4.93996 | − | 15.2036i | −0.192580 | − | 0.592700i | ||||
\(659\) | −5.20634 | + | 16.0235i | −0.202810 | + | 0.624186i | 0.796986 | + | 0.603998i | \(0.206426\pi\) |
−0.999796 | + | 0.0201880i | \(0.993574\pi\) | |||||||
\(660\) | −0.732264 | + | 2.25368i | −0.0285033 | + | 0.0877242i | ||||
\(661\) | −6.37440 | − | 4.63127i | −0.247935 | − | 0.180136i | 0.456876 | − | 0.889530i | \(-0.348968\pi\) |
−0.704811 | + | 0.709395i | \(0.748968\pi\) | |||||||
\(662\) | 8.46803 | + | 26.0619i | 0.329119 | + | 1.01293i | ||||
\(663\) | 2.45055 | + | 1.78043i | 0.0951716 | + | 0.0691462i | ||||
\(664\) | 6.51982 | − | 4.73692i | 0.253018 | − | 0.183828i | ||||
\(665\) | −6.81690 | + | 20.9803i | −0.264348 | + | 0.813580i | ||||
\(666\) | −1.39635 | + | 1.01451i | −0.0541075 | + | 0.0393114i | ||||
\(667\) | −3.01459 | + | 2.19022i | −0.116725 | + | 0.0848058i | ||||
\(668\) | −4.17807 | + | 12.8588i | −0.161654 | + | 0.497521i | ||||
\(669\) | −0.214269 | + | 0.155675i | −0.00828411 | + | 0.00601876i | ||||
\(670\) | 9.55352 | + | 6.94104i | 0.369085 | + | 0.268156i | ||||
\(671\) | 3.86197 | + | 11.8859i | 0.149090 | + | 0.458851i | ||||
\(672\) | −3.22611 | − | 2.34391i | −0.124450 | − | 0.0904181i | ||||
\(673\) | −4.20344 | + | 12.9369i | −0.162031 | + | 0.498679i | −0.998805 | − | 0.0488683i | \(-0.984439\pi\) |
0.836774 | + | 0.547548i | \(0.184439\pi\) | |||||||
\(674\) | 1.43367 | − | 4.41237i | 0.0552228 | − | 0.169958i | ||||
\(675\) | 0.309017 | + | 0.951057i | 0.0118941 | + | 0.0366062i | ||||
\(676\) | −9.28941 | −0.357285 | ||||||||
\(677\) | 14.2847 | 0.549004 | 0.274502 | − | 0.961586i | \(-0.411487\pi\) | ||||
0.274502 | + | 0.961586i | \(0.411487\pi\) | |||||||
\(678\) | 1.21819 | + | 3.74919i | 0.0467842 | + | 0.143987i | ||||
\(679\) | −16.8234 | + | 12.2229i | −0.645621 | + | 0.469071i | ||||
\(680\) | 1.27216 | + | 0.924280i | 0.0487852 | + | 0.0354445i | ||||
\(681\) | −17.2028 | −0.659214 | ||||||||
\(682\) | −13.1521 | − | 1.04690i | −0.503619 | − | 0.0400877i | ||||
\(683\) | 40.3109 | 1.54245 | 0.771226 | − | 0.636561i | \(-0.219644\pi\) | ||||
0.771226 | + | 0.636561i | \(0.219644\pi\) | |||||||
\(684\) | −4.47549 | − | 3.25164i | −0.171125 | − | 0.124329i | ||||
\(685\) | 5.70022 | − | 4.14145i | 0.217794 | − | 0.158237i | ||||
\(686\) | 2.34336 | + | 7.21211i | 0.0894698 | + | 0.275360i | ||||
\(687\) | 23.9884 | 0.915214 | ||||||||
\(688\) | −5.62689 | −0.214523 | ||||||||
\(689\) | −1.88508 | − | 5.80167i | −0.0718157 | − | 0.221026i | ||||
\(690\) | −1.18483 | + | 3.64653i | −0.0451056 | + | 0.138821i | ||||
\(691\) | 1.56364 | − | 4.81239i | 0.0594837 | − | 0.183072i | −0.916899 | − | 0.399118i | \(-0.869316\pi\) |
0.976383 | + | 0.216046i | \(0.0693162\pi\) | |||||||
\(692\) | 12.9464 | + | 9.40611i | 0.492148 | + | 0.357567i | ||||
\(693\) | 2.92004 | + | 8.98696i | 0.110923 | + | 0.341386i | ||||
\(694\) | −16.7467 | − | 12.1672i | −0.635696 | − | 0.461860i | ||||
\(695\) | −10.0551 | + | 7.30549i | −0.381413 | + | 0.277113i | ||||
\(696\) | −0.300317 | + | 0.924280i | −0.0113835 | + | 0.0350347i | ||||
\(697\) | 14.5111 | − | 10.5429i | 0.549648 | − | 0.399343i | ||||
\(698\) | 10.4046 | − | 7.55939i | 0.393820 | − | 0.286127i | ||||
\(699\) | −4.44199 | + | 13.6710i | −0.168011 | + | 0.517086i | ||||
\(700\) | 3.22611 | − | 2.34391i | 0.121935 | − | 0.0885913i | ||||
\(701\) | 35.4691 | + | 25.7698i | 1.33965 | + | 0.973313i | 0.999457 | + | 0.0329581i | \(0.0104928\pi\) |
0.340194 | + | 0.940355i | \(0.389507\pi\) | |||||||
\(702\) | 0.595256 | + | 1.83201i | 0.0224665 | + | 0.0691448i | ||||
\(703\) | 7.72463 | + | 5.61227i | 0.291340 | + | 0.211671i | ||||
\(704\) | −0.732264 | + | 2.25368i | −0.0275982 | + | 0.0849386i | ||||
\(705\) | −1.23880 | + | 3.81264i | −0.0466560 | + | 0.143592i | ||||
\(706\) | 7.78435 | + | 23.9578i | 0.292968 | + | 0.901662i | ||||
\(707\) | −65.8474 | −2.47645 | ||||||||
\(708\) | 2.19499 | 0.0824927 | ||||||||
\(709\) | −5.05004 | − | 15.5424i | −0.189658 | − | 0.583708i | 0.810339 | − | 0.585961i | \(-0.199283\pi\) |
−0.999997 | + | 0.00225311i | \(0.999283\pi\) | |||||||
\(710\) | −3.58194 | + | 2.60243i | −0.134428 | + | 0.0976675i | ||||
\(711\) | 4.91760 | + | 3.57285i | 0.184424 | + | 0.133992i | ||||
\(712\) | −6.55318 | −0.245591 | ||||||||
\(713\) | −21.2805 | − | 1.69391i | −0.796962 | − | 0.0634375i | ||||
\(714\) | 6.27056 | 0.234670 | ||||||||
\(715\) | −3.69287 | − | 2.68303i | −0.138106 | − | 0.100340i | ||||
\(716\) | 5.25269 | − | 3.81630i | 0.196302 | − | 0.142622i | ||||
\(717\) | 2.11238 | + | 6.50123i | 0.0788881 | + | 0.242793i | ||||
\(718\) | −5.06332 | −0.188962 | ||||||||
\(719\) | 36.7036 | 1.36881 | 0.684406 | − | 0.729101i | \(-0.260062\pi\) | ||||
0.684406 | + | 0.729101i | \(0.260062\pi\) | |||||||
\(720\) | 0.309017 | + | 0.951057i | 0.0115164 | + | 0.0354438i | ||||
\(721\) | 14.9615 | − | 46.0466i | 0.557194 | − | 1.71487i | ||||
\(722\) | −3.58558 | + | 11.0353i | −0.133441 | + | 0.410690i | ||||
\(723\) | −23.7764 | − | 17.2746i | −0.884255 | − | 0.642449i | ||||
\(724\) | −6.41857 | − | 19.7543i | −0.238544 | − | 0.734164i | ||||
\(725\) | −0.786239 | − | 0.571236i | −0.0292002 | − | 0.0212152i | ||||
\(726\) | −4.35634 | + | 3.16507i | −0.161679 | + | 0.117467i | ||||
\(727\) | −6.38069 | + | 19.6377i | −0.236647 | + | 0.728323i | 0.760252 | + | 0.649628i | \(0.225075\pi\) |
−0.996899 | + | 0.0786953i | \(0.974925\pi\) | |||||||
\(728\) | 6.21442 | − | 4.51504i | 0.230322 | − | 0.167339i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | −1.05186 | + | 3.23730i | −0.0389312 | + | 0.119818i | ||||
\(731\) | 7.15831 | − | 5.20082i | 0.264760 | − | 0.192359i | ||||
\(732\) | 4.26677 | + | 3.09999i | 0.157704 | + | 0.114579i | ||||
\(733\) | −11.1559 | − | 34.3344i | −0.412054 | − | 1.26817i | −0.914860 | − | 0.403772i | \(-0.867699\pi\) |
0.502806 | − | 0.864399i | \(-0.332301\pi\) | |||||||
\(734\) | 18.7506 | + | 13.6231i | 0.692098 | + | 0.502839i | ||||
\(735\) | 2.75077 | − | 8.46599i | 0.101464 | − | 0.312273i | ||||
\(736\) | −1.18483 | + | 3.64653i | −0.0436733 | + | 0.134413i | ||||
\(737\) | −8.64715 | − | 26.6132i | −0.318522 | − | 0.980310i | ||||
\(738\) | 11.4067 | 0.419885 | ||||||||
\(739\) | 39.4637 | 1.45170 | 0.725848 | − | 0.687855i | \(-0.241447\pi\) | ||||
0.725848 | + | 0.687855i | \(0.241447\pi\) | |||||||
\(740\) | −0.533359 | − | 1.64151i | −0.0196067 | − | 0.0603431i | ||||
\(741\) | 8.62110 | − | 6.26359i | 0.316704 | − | 0.230099i | ||||
\(742\) | −10.2165 | − | 7.42276i | −0.375061 | − | 0.272498i | ||||
\(743\) | 1.20723 | 0.0442891 | 0.0221445 | − | 0.999755i | \(-0.492951\pi\) | ||||
0.0221445 | + | 0.999755i | \(0.492951\pi\) | |||||||
\(744\) | −4.74989 | + | 2.90491i | −0.174140 | + | 0.106499i | ||||
\(745\) | −8.01770 | −0.293746 | ||||||||
\(746\) | 17.8602 | + | 12.9762i | 0.653908 | + | 0.475092i | ||||
\(747\) | −6.51982 | + | 4.73692i | −0.238548 | + | 0.173315i | ||||
\(748\) | −1.15147 | − | 3.54386i | −0.0421019 | − | 0.129576i | ||||
\(749\) | −53.8087 | −1.96613 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −5.10951 | − | 15.7255i | −0.186449 | − | 0.573830i | 0.813522 | − | 0.581535i | \(-0.197548\pi\) |
−0.999970 | + | 0.00770450i | \(0.997548\pi\) | |||||||
\(752\) | −1.23880 | + | 3.81264i | −0.0451745 | + | 0.139033i | ||||
\(753\) | −0.0202366 | + | 0.0622818i | −0.000737462 | + | 0.00226967i | ||||
\(754\) | −1.51452 | − | 1.10037i | −0.0551557 | − | 0.0400730i | ||||
\(755\) | −4.71700 | − | 14.5174i | −0.171669 | − | 0.528343i | ||||
\(756\) | 3.22611 | + | 2.34391i | 0.117332 | + | 0.0852470i | ||||
\(757\) | −6.27628 | + | 4.55998i | −0.228115 | + | 0.165735i | −0.695972 | − | 0.718069i | \(-0.745026\pi\) |
0.467857 | + | 0.883804i | \(0.345026\pi\) | |||||||
\(758\) | −7.99701 | + | 24.6123i | −0.290465 | + | 0.893958i | ||||
\(759\) | 7.35048 | − | 5.34044i | 0.266806 | − | 0.193846i | ||||
\(760\) | 4.47549 | − | 3.25164i | 0.162343 | − | 0.117949i | ||||
\(761\) | 8.78468 | − | 27.0365i | 0.318445 | − | 0.980071i | −0.655869 | − | 0.754875i | \(-0.727698\pi\) |
0.974313 | − | 0.225197i | \(-0.0723024\pi\) | |||||||
\(762\) | 7.97911 | − | 5.79717i | 0.289053 | − | 0.210009i | ||||
\(763\) | 57.5393 | + | 41.8047i | 2.08306 | + | 1.51343i | ||||
\(764\) | 0.260198 | + | 0.800807i | 0.00941364 | + | 0.0289722i | ||||
\(765\) | −1.27216 | − | 0.924280i | −0.0459951 | − | 0.0334174i | ||||
\(766\) | 7.95037 | − | 24.4687i | 0.287259 | − | 0.884091i | ||||
\(767\) | −1.30658 | + | 4.02124i | −0.0471779 | + | 0.145199i | ||||
\(768\) | 0.309017 | + | 0.951057i | 0.0111507 | + | 0.0343183i | ||||
\(769\) | −31.8616 | −1.14896 | −0.574479 | − | 0.818520i | \(-0.694795\pi\) | ||||
−0.574479 | + | 0.818520i | \(0.694795\pi\) | |||||||
\(770\) | −9.44945 | −0.340535 | ||||||||
\(771\) | 2.09148 | + | 6.43690i | 0.0753226 | + | 0.231819i | ||||
\(772\) | −13.6908 | + | 9.94695i | −0.492743 | + | 0.357999i | ||||
\(773\) | −29.4212 | − | 21.3758i | −1.05821 | − | 0.768833i | −0.0844517 | − | 0.996428i | \(-0.526914\pi\) |
−0.973756 | + | 0.227595i | \(0.926914\pi\) | |||||||
\(774\) | 5.62689 | 0.202254 | ||||||||
\(775\) | −1.29494 | − | 5.41508i | −0.0465156 | − | 0.194516i | ||||
\(776\) | 5.21475 | 0.187199 | ||||||||
\(777\) | −5.56821 | − | 4.04554i | −0.199759 | − | 0.145133i | ||||
\(778\) | −4.41712 | + | 3.20922i | −0.158361 | + | 0.115056i | ||||
\(779\) | −19.4995 | − | 60.0134i | −0.698643 | − | 2.15020i | ||||
\(780\) | −1.92629 | −0.0689722 | ||||||||
\(781\) | 10.4917 | 0.375423 | ||||||||
\(782\) | −1.86312 | − | 5.73408i | −0.0666249 | − | 0.205050i | ||||
\(783\) | 0.300317 | − | 0.924280i | 0.0107324 | − | 0.0330311i | ||||
\(784\) | 2.75077 | − | 8.46599i | 0.0982417 | − | 0.302357i | ||||
\(785\) | 1.35410 | + | 0.983813i | 0.0483300 | + | 0.0351138i | ||||
\(786\) | 2.69657 | + | 8.29919i | 0.0961835 | + | 0.296022i | ||||
\(787\) | 19.4737 | + | 14.1484i | 0.694161 | + | 0.504338i | 0.878025 | − | 0.478614i | \(-0.158861\pi\) |
−0.183864 | + | 0.982952i | \(0.558861\pi\) | |||||||
\(788\) | −20.4955 | + | 14.8908i | −0.730121 | + | 0.530464i | ||||
\(789\) | 2.63358 | − | 8.10533i | 0.0937580 | − | 0.288557i | ||||
\(790\) | −4.91760 | + | 3.57285i | −0.174960 | + | 0.127116i | ||||
\(791\) | −12.7178 | + | 9.23999i | −0.452191 | + | 0.328536i | ||||
\(792\) | 0.732264 | − | 2.25368i | 0.0260199 | − | 0.0800809i | ||||
\(793\) | −8.21903 | + | 5.97148i | −0.291866 | + | 0.212053i | ||||
\(794\) | −8.35512 | − | 6.07035i | −0.296512 | − | 0.215429i | ||||
\(795\) | 0.978605 | + | 3.01184i | 0.0347075 | + | 0.106819i | ||||
\(796\) | −12.3422 | − | 8.96712i | −0.437457 | − | 0.317831i | ||||
\(797\) | −15.2444 | + | 46.9176i | −0.539986 | + | 1.66191i | 0.192636 | + | 0.981270i | \(0.438296\pi\) |
−0.732622 | + | 0.680636i | \(0.761704\pi\) | |||||||
\(798\) | 6.81690 | − | 20.9803i | 0.241316 | − | 0.742693i | ||||
\(799\) | −1.94799 | − | 5.99530i | −0.0689150 | − | 0.212099i | ||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 6.55318 | 0.231545 | ||||||||
\(802\) | 9.68440 | + | 29.8055i | 0.341968 | + | 1.05247i | ||||
\(803\) | 6.52558 | − | 4.74111i | 0.230283 | − | 0.167310i | ||||
\(804\) | −9.55352 | − | 6.94104i | −0.336927 | − | 0.244791i | ||||
\(805\) | −15.2895 | −0.538885 | ||||||||
\(806\) | −2.49443 | − | 10.4310i | −0.0878625 | − | 0.367417i | ||||
\(807\) | −0.576767 | −0.0203032 | ||||||||
\(808\) | 13.3590 | + | 9.70591i | 0.469969 | + | 0.341453i | ||||
\(809\) | −44.6183 | + | 32.4171i | −1.56870 | + | 1.13973i | −0.640307 | + | 0.768119i | \(0.721193\pi\) |
−0.928390 | + | 0.371606i | \(0.878807\pi\) | |||||||
\(810\) | −0.309017 | − | 0.951057i | −0.0108578 | − | 0.0334167i | ||||
\(811\) | −32.0776 | −1.12640 | −0.563199 | − | 0.826322i | \(-0.690429\pi\) | ||||
−0.563199 | + | 0.826322i | \(0.690429\pi\) | |||||||
\(812\) | −3.87542 | −0.136000 | ||||||||
\(813\) | 3.32144 | + | 10.2223i | 0.116488 | + | 0.358513i | ||||
\(814\) | −1.26388 | + | 3.88981i | −0.0442988 | + | 0.136338i | ||||
\(815\) | −2.94194 | + | 9.05437i | −0.103052 | + | 0.317161i | ||||
\(816\) | −1.27216 | − | 0.924280i | −0.0445346 | − | 0.0323563i | ||||
\(817\) | −9.61908 | − | 29.6045i | −0.336529 | − | 1.03573i | ||||
\(818\) | −0.663752 | − | 0.482244i | −0.0232076 | − | 0.0168613i | ||||
\(819\) | −6.21442 | + | 4.51504i | −0.217149 | + | 0.157768i | ||||
\(820\) | −3.52485 | + | 10.8484i | −0.123093 | + | 0.378842i | ||||
\(821\) | −43.9728 | + | 31.9481i | −1.53466 | + | 1.11500i | −0.581084 | + | 0.813843i | \(0.697371\pi\) |
−0.953576 | + | 0.301153i | \(0.902629\pi\) | |||||||
\(822\) | −5.70022 | + | 4.14145i | −0.198818 | + | 0.144450i | ||||
\(823\) | 3.86904 | − | 11.9077i | 0.134866 | − | 0.415076i | −0.860703 | − | 0.509108i | \(-0.829976\pi\) |
0.995569 | + | 0.0940318i | \(0.0299755\pi\) | |||||||
\(824\) | −9.82263 | + | 7.13656i | −0.342188 | + | 0.248614i | ||||
\(825\) | 1.91709 | + | 1.39285i | 0.0667446 | + | 0.0484928i | ||||
\(826\) | 2.70480 | + | 8.32453i | 0.0941122 | + | 0.289647i | ||||
\(827\) | −9.48428 | − | 6.89074i | −0.329801 | − | 0.239614i | 0.410545 | − | 0.911840i | \(-0.365338\pi\) |
−0.740346 | + | 0.672226i | \(0.765338\pi\) | |||||||
\(828\) | 1.18483 | − | 3.64653i | 0.0411756 | − | 0.126726i | ||||
\(829\) | 11.9844 | − | 36.8843i | 0.416237 | − | 1.28104i | −0.494903 | − | 0.868948i | \(-0.664797\pi\) |
0.911140 | − | 0.412097i | \(-0.135203\pi\) | |||||||
\(830\) | −2.49035 | − | 7.66450i | −0.0864413 | − | 0.266039i | ||||
\(831\) | −28.6713 | −0.994598 | ||||||||
\(832\) | −1.92629 | −0.0667821 | ||||||||
\(833\) | 4.32552 | + | 13.3126i | 0.149870 | + | 0.461254i | ||||
\(834\) | 10.0551 | − | 7.30549i | 0.348181 | − | 0.252968i | ||||
\(835\) | 10.9383 | + | 7.94716i | 0.378536 | + | 0.275023i | ||||
\(836\) | −13.1090 | −0.453383 | ||||||||
\(837\) | 4.74989 | − | 2.90491i | 0.164180 | − | 0.100409i | ||||
\(838\) | 9.01898 | 0.311555 | ||||||||
\(839\) | −14.4485 | − | 10.4975i | −0.498818 | − | 0.362412i | 0.309747 | − | 0.950819i | \(-0.399756\pi\) |
−0.808565 | + | 0.588406i | \(0.799756\pi\) | |||||||
\(840\) | −3.22611 | + | 2.34391i | −0.111311 | + | 0.0808724i | ||||
\(841\) | −8.66963 | − | 26.6824i | −0.298953 | − | 0.920082i | ||||
\(842\) | 7.13811 | 0.245996 | ||||||||
\(843\) | −1.61437 | −0.0556020 | ||||||||
\(844\) | 3.78490 | + | 11.6487i | 0.130282 | + | 0.400966i | ||||
\(845\) | −2.87058 | + | 8.83475i | −0.0987511 | + | 0.303925i | ||||
\(846\) | 1.23880 | − | 3.81264i | 0.0425909 | − | 0.131081i | ||||
\(847\) | −17.3717 | − | 12.6213i | −0.596900 | − | 0.433673i | ||||
\(848\) | 0.978605 | + | 3.01184i | 0.0336054 | + | 0.103427i | ||||
\(849\) | 14.9588 | + | 10.8682i | 0.513385 | + | 0.372996i | ||||
\(850\) | 1.27216 | − | 0.924280i | 0.0436348 | − | 0.0317025i | ||||
\(851\) | −2.04499 | + | 6.29385i | −0.0701015 | + | 0.215750i | ||||
\(852\) | 3.58194 | − | 2.60243i | 0.122715 | − | 0.0891578i | ||||
\(853\) | −3.28653 | + | 2.38780i | −0.112529 | + | 0.0817568i | −0.642626 | − | 0.766180i | \(-0.722155\pi\) |
0.530098 | + | 0.847937i | \(0.322155\pi\) | |||||||
\(854\) | −6.49898 | + | 20.0018i | −0.222390 | + | 0.684447i | ||||
\(855\) | −4.47549 | + | 3.25164i | −0.153059 | + | 0.111204i | ||||
\(856\) | 10.9166 | + | 7.93140i | 0.373123 | + | 0.271090i | ||||
\(857\) | −11.1344 | − | 34.2681i | −0.380343 | − | 1.17057i | −0.939803 | − | 0.341717i | \(-0.888991\pi\) |
0.559460 | − | 0.828857i | \(-0.311009\pi\) | |||||||
\(858\) | 3.69287 | + | 2.68303i | 0.126073 | + | 0.0915971i | ||||
\(859\) | −14.2232 | + | 43.7744i | −0.485288 | + | 1.49356i | 0.346275 | + | 0.938133i | \(0.387446\pi\) |
−0.831563 | + | 0.555430i | \(0.812554\pi\) | |||||||
\(860\) | −1.73880 | + | 5.35149i | −0.0592927 | + | 0.182484i | ||||
\(861\) | 14.0560 | + | 43.2600i | 0.479028 | + | 1.47430i | ||||
\(862\) | −28.1596 | −0.959121 | ||||||||
\(863\) | 11.5864 | 0.394406 | 0.197203 | − | 0.980363i | \(-0.436814\pi\) | ||||
0.197203 | + | 0.980363i | \(0.436814\pi\) | |||||||
\(864\) | −0.309017 | − | 0.951057i | −0.0105130 | − | 0.0323556i | ||||
\(865\) | 12.9464 | − | 9.40611i | 0.440191 | − | 0.319817i | ||||
\(866\) | −17.4831 | − | 12.7022i | −0.594099 | − | 0.431638i | ||||
\(867\) | −14.5273 | −0.493373 | ||||||||
\(868\) | −16.8701 | − | 14.4344i | −0.572607 | − | 0.489937i | ||||
\(869\) | 14.4039 | 0.488620 | ||||||||
\(870\) | 0.786239 | + | 0.571236i | 0.0266560 | + | 0.0193667i | ||||
\(871\) | 18.4028 | − | 13.3704i | 0.623556 | − | 0.453040i | ||||
\(872\) | −5.51147 | − | 16.9626i | −0.186642 | − | 0.574425i | ||||
\(873\) | −5.21475 | −0.176493 | ||||||||
\(874\) | −21.2108 | −0.717464 | ||||||||
\(875\) | −1.23226 | − | 3.79252i | −0.0416581 | − | 0.128211i | ||||
\(876\) | 1.05186 | − | 3.23730i | 0.0355391 | − | 0.109378i | ||||
\(877\) | −14.5519 | + | 44.7861i | −0.491382 | + | 1.51232i | 0.331139 | + | 0.943582i | \(0.392567\pi\) |
−0.822520 | + | 0.568736i | \(0.807433\pi\) | |||||||
\(878\) | 14.5536 | + | 10.5738i | 0.491159 | + | 0.356848i | ||||
\(879\) | 3.70628 | + | 11.4068i | 0.125010 | + | 0.384740i | ||||
\(880\) | 1.91709 | + | 1.39285i | 0.0646251 | + | 0.0469529i | ||||
\(881\) | −7.77009 | + | 5.64530i | −0.261781 | + | 0.190195i | −0.710932 | − | 0.703261i | \(-0.751727\pi\) |
0.449151 | + | 0.893456i | \(0.351727\pi\) | |||||||
\(882\) | −2.75077 | + | 8.46599i | −0.0926231 | + | 0.285065i | ||||
\(883\) | −2.69008 | + | 1.95445i | −0.0905283 | + | 0.0657726i | −0.632129 | − | 0.774863i | \(-0.717819\pi\) |
0.541600 | + | 0.840636i | \(0.317819\pi\) | |||||||
\(884\) | 2.45055 | − | 1.78043i | 0.0824210 | − | 0.0598824i | ||||
\(885\) | 0.678289 | − | 2.08756i | 0.0228004 | − | 0.0701725i | ||||
\(886\) | −23.4351 | + | 17.0266i | −0.787318 | + | 0.572020i | ||||
\(887\) | −23.6358 | − | 17.1724i | −0.793612 | − | 0.576593i | 0.115421 | − | 0.993317i | \(-0.463178\pi\) |
−0.909033 | + | 0.416724i | \(0.863178\pi\) | |||||||
\(888\) | 0.533359 | + | 1.64151i | 0.0178983 | + | 0.0550854i | ||||
\(889\) | 31.8182 | + | 23.1173i | 1.06715 | + | 0.775329i | ||||
\(890\) | −2.02504 | + | 6.23244i | −0.0678796 | + | 0.208912i | ||||
\(891\) | −0.732264 | + | 2.25368i | −0.0245318 | + | 0.0755010i | ||||
\(892\) | 0.0818434 | + | 0.251888i | 0.00274032 | + | 0.00843384i | ||||
\(893\) | −22.1770 | −0.742126 | ||||||||
\(894\) | 8.01770 | 0.268152 | ||||||||
\(895\) | −2.00635 | − | 6.17491i | −0.0670649 | − | 0.206404i | ||||
\(896\) | −3.22611 | + | 2.34391i | −0.107777 | + | 0.0783044i | ||||
\(897\) | 5.97520 | + | 4.34123i | 0.199506 | + | 0.144950i | ||||
\(898\) | 29.3122 | 0.978159 | ||||||||
\(899\) | −2.07516 | + | 4.99727i | −0.0692105 | + | 0.166668i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −4.02872 | − | 2.92704i | −0.134216 | − | 0.0975138i | ||||
\(902\) | 21.8676 | − | 15.8878i | 0.728112 | − | 0.529004i | ||||
\(903\) | 6.93381 | + | 21.3401i | 0.230743 | + | 0.710153i | ||||
\(904\) | 3.94213 | 0.131113 | ||||||||
\(905\) | −20.7709 | −0.690449 | ||||||||
\(906\) | 4.71700 | + | 14.5174i | 0.156712 | + | 0.482309i | ||||
\(907\) | −15.0977 | + | 46.4659i | −0.501310 | + | 1.54287i | 0.305576 | + | 0.952168i | \(0.401151\pi\) |
−0.806886 | + | 0.590707i | \(0.798849\pi\) | |||||||
\(908\) | −5.31596 | + | 16.3609i | −0.176416 | + | 0.542954i | ||||
\(909\) | −13.3590 | − | 9.70591i | −0.443091 | − | 0.321925i | ||||
\(910\) | −2.37370 | − | 7.30549i | −0.0786873 | − | 0.242175i | ||||
\(911\) | 30.7302 | + | 22.3268i | 1.01814 | + | 0.739719i | 0.965900 | − | 0.258916i | \(-0.0833652\pi\) |
0.0522359 | + | 0.998635i | \(0.483365\pi\) | |||||||
\(912\) | −4.47549 | + | 3.25164i | −0.148198 | + | 0.107672i | ||||
\(913\) | −5.90127 | + | 18.1622i | −0.195303 | + | 0.601082i | ||||
\(914\) | 20.6709 | − | 15.0183i | 0.683731 | − | 0.496760i | ||||
\(915\) | 4.26677 | − | 3.09999i | 0.141055 | − | 0.102482i | ||||
\(916\) | 7.41282 | − | 22.8143i | 0.244926 | − | 0.753806i | ||||
\(917\) | −28.1520 | + | 20.4536i | −0.929659 | + | 0.675437i | ||||
\(918\) | 1.27216 | + | 0.924280i | 0.0419876 | + | 0.0305058i | ||||
\(919\) | 6.07964 | + | 18.7112i | 0.200549 | + | 0.617225i | 0.999867 | + | 0.0163173i | \(0.00519420\pi\) |
−0.799318 | + | 0.600908i | \(0.794806\pi\) | |||||||
\(920\) | 3.10192 | + | 2.25368i | 0.102267 | + | 0.0743015i | ||||
\(921\) | −4.64615 | + | 14.2994i | −0.153096 | + | 0.471181i | ||||
\(922\) | −11.0777 | + | 34.0937i | −0.364825 | + | 1.12281i | ||||
\(923\) | 2.63551 | + | 8.11127i | 0.0867489 | + | 0.266986i | ||||
\(924\) | 9.44945 | 0.310864 | ||||||||
\(925\) | −1.72598 | −0.0567500 | ||||||||
\(926\) | −3.06042 | − | 9.41900i | −0.100572 | − | 0.309527i | ||||
\(927\) | 9.82263 | − | 7.13656i | 0.322618 | − | 0.234395i | ||||
\(928\) | 0.786239 | + | 0.571236i | 0.0258096 | + | 0.0187517i | ||||
\(929\) | 25.0883 | 0.823121 | 0.411560 | − | 0.911383i | \(-0.364984\pi\) | ||||
0.411560 | + | 0.911383i | \(0.364984\pi\) | |||||||
\(930\) | 1.29494 | + | 5.41508i | 0.0424627 | + | 0.177568i | ||||
\(931\) | 49.2442 | 1.61391 | ||||||||
\(932\) | 11.6293 | + | 8.44916i | 0.380930 | + | 0.276762i | ||||
\(933\) | −22.7403 | + | 16.5218i | −0.744485 | + | 0.540900i | ||||
\(934\) | 6.30358 | + | 19.4004i | 0.206260 | + | 0.634802i | ||||
\(935\) | −3.72623 | −0.121861 | ||||||||
\(936\) | 1.92629 | 0.0629627 | ||||||||
\(937\) | −12.2553 | − | 37.7180i | −0.400363 | − | 1.23219i | −0.924705 | − | 0.380684i | \(-0.875689\pi\) |
0.524342 | − | 0.851508i | \(-0.324311\pi\) | |||||||
\(938\) | 14.5516 | − | 44.7851i | 0.475125 | − | 1.46228i | ||||
\(939\) | −1.27046 | + | 3.91007i | −0.0414599 | + | 0.127600i | ||||
\(940\) | 3.24323 | + | 2.35634i | 0.105782 | + | 0.0768555i | ||||
\(941\) | 1.40040 | + | 4.30998i | 0.0456517 | + | 0.140501i | 0.971284 | − | 0.237922i | \(-0.0764663\pi\) |
−0.925633 | + | 0.378424i | \(0.876466\pi\) | |||||||
\(942\) | −1.35410 | − | 0.983813i | −0.0441190 | − | 0.0320543i | ||||
\(943\) | 35.3825 | − | 25.7069i | 1.15221 | − | 0.837133i | ||||
\(944\) | 0.678289 | − | 2.08756i | 0.0220764 | − | 0.0679442i | ||||
\(945\) | 3.22611 | − | 2.34391i | 0.104945 | − | 0.0762472i | ||||
\(946\) | 10.7873 | − | 7.83740i | 0.350724 | − | 0.254816i | ||||
\(947\) | −12.0175 | + | 36.9862i | −0.390517 | + | 1.20189i | 0.541881 | + | 0.840455i | \(0.317712\pi\) |
−0.932398 | + | 0.361433i | \(0.882288\pi\) | |||||||
\(948\) | 4.91760 | − | 3.57285i | 0.159716 | − | 0.116041i | ||||
\(949\) | 5.30464 | + | 3.85404i | 0.172196 | + | 0.125108i | ||||
\(950\) | −1.70949 | − | 5.26126i | −0.0554631 | − | 0.170698i | ||||
\(951\) | 16.0340 | + | 11.6494i | 0.519940 | + | 0.377758i | ||||
\(952\) | 1.93771 | − | 5.96365i | 0.0628015 | − | 0.193283i | ||||
\(953\) | 5.24965 | − | 16.1568i | 0.170053 | − | 0.523369i | −0.829320 | − | 0.558774i | \(-0.811272\pi\) |
0.999373 | + | 0.0354047i | \(0.0112720\pi\) | |||||||
\(954\) | −0.978605 | − | 3.01184i | −0.0316835 | − | 0.0975118i | ||||
\(955\) | 0.842019 | 0.0272471 | ||||||||
\(956\) | 6.83579 | 0.221085 | ||||||||
\(957\) | −0.711647 | − | 2.19022i | −0.0230043 | − | 0.0707999i | ||||
\(958\) | 14.1207 | − | 10.2593i | 0.456218 | − | 0.331462i | ||||
\(959\) | −22.7307 | − | 16.5148i | −0.734013 | − | 0.533291i | ||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −27.6463 | + | 14.0244i | −0.891815 | + | 0.452400i | ||||
\(962\) | −3.32475 | −0.107194 | ||||||||
\(963\) | −10.9166 | − | 7.93140i | −0.351784 | − | 0.255586i | ||||
\(964\) | −23.7764 | + | 17.2746i | −0.765787 | + | 0.556377i | ||||
\(965\) | 5.22942 | + | 16.0945i | 0.168341 | + | 0.518101i | ||||
\(966\) | 15.2895 | 0.491933 | ||||||||
\(967\) | −59.2768 | −1.90621 | −0.953107 | − | 0.302634i | \(-0.902134\pi\) | ||||
−0.953107 | + | 0.302634i | \(0.902134\pi\) | |||||||
\(968\) | 1.66397 | + | 5.12118i | 0.0534821 | + | 0.164601i | ||||
\(969\) | 2.68813 | − | 8.27321i | 0.0863552 | − | 0.265774i | ||||
\(970\) | 1.61145 | − | 4.95952i | 0.0517405 | − | 0.159241i | ||||
\(971\) | 8.80009 | + | 6.39364i | 0.282408 | + | 0.205182i | 0.719967 | − | 0.694008i | \(-0.244157\pi\) |
−0.437559 | + | 0.899190i | \(0.644157\pi\) | |||||||
\(972\) | 0.309017 | + | 0.951057i | 0.00991172 | + | 0.0305052i | ||||
\(973\) | 40.0968 | + | 29.1320i | 1.28544 | + | 0.933930i | ||||
\(974\) | −14.1221 | + | 10.2603i | −0.452500 | + | 0.328760i | ||||
\(975\) | −0.595256 | + | 1.83201i | −0.0190635 | + | 0.0586713i | ||||
\(976\) | 4.26677 | − | 3.09999i | 0.136576 | − | 0.0992282i | ||||
\(977\) | −1.80683 | + | 1.31274i | −0.0578056 | + | 0.0419982i | −0.616313 | − | 0.787501i | \(-0.711374\pi\) |
0.558507 | + | 0.829500i | \(0.311374\pi\) | |||||||
\(978\) | 2.94194 | − | 9.05437i | 0.0940730 | − | 0.289527i | ||||
\(979\) | 12.5630 | − | 9.12758i | 0.401516 | − | 0.291719i | ||||
\(980\) | −7.20160 | − | 5.23227i | −0.230047 | − | 0.167139i | ||||
\(981\) | 5.51147 | + | 16.9626i | 0.175968 | + | 0.541573i | ||||
\(982\) | −25.7065 | − | 18.6769i | −0.820328 | − | 0.596003i | ||||
\(983\) | −7.95972 | + | 24.4975i | −0.253876 | + | 0.781349i | 0.740174 | + | 0.672416i | \(0.234743\pi\) |
−0.994049 | + | 0.108933i | \(0.965257\pi\) | |||||||
\(984\) | 3.52485 | − | 10.8484i | 0.112368 | − | 0.345834i | ||||
\(985\) | 7.82857 | + | 24.0939i | 0.249439 | + | 0.767694i | ||||
\(986\) | −1.52821 | −0.0486680 | ||||||||
\(987\) | 15.9861 | 0.508842 | ||||||||
\(988\) | −3.29297 | − | 10.1347i | −0.104763 | − | 0.322428i | ||||
\(989\) | 17.4541 | − | 12.6812i | 0.555010 | − | 0.403238i | ||||
\(990\) | −1.91709 | − | 1.39285i | −0.0609292 | − | 0.0442676i | ||||
\(991\) | −32.9447 | −1.04652 | −0.523261 | − | 0.852172i | \(-0.675285\pi\) | ||||
−0.523261 | + | 0.852172i | \(0.675285\pi\) | |||||||
\(992\) | 1.29494 | + | 5.41508i | 0.0411144 | + | 0.171929i | ||||
\(993\) | −27.4031 | −0.869612 | ||||||||
\(994\) | 14.2837 | + | 10.3777i | 0.453050 | + | 0.329160i | ||||
\(995\) | −12.3422 | + | 8.96712i | −0.391274 | + | 0.284277i | ||||
\(996\) | 2.49035 | + | 7.66450i | 0.0789097 | + | 0.242859i | ||||
\(997\) | 5.16406 | 0.163547 | 0.0817737 | − | 0.996651i | \(-0.473942\pi\) | ||||
0.0817737 | + | 0.996651i | \(0.473942\pi\) | |||||||
\(998\) | −19.0950 | −0.604441 | ||||||||
\(999\) | −0.533359 | − | 1.64151i | −0.0168747 | − | 0.0519350i |
(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 | 930.2.n.e.901.1 | yes | 12 | |
31.16 | even | 5 | inner | 930.2.n.e.481.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.n.e.481.1 | ✓ | 12 | 31.16 | even | 5 | inner | |
930.2.n.e.901.1 | yes | 12 | 1.1 | even | 1 | trivial |