Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [539,2,Mod(148,539)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(539, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("539.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 539 = 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 539.f (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: | \(4.30393666895\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.159390625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 246.2 | ||
Root | \(0.453245 + 1.39494i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 539.246 |
Dual form | 539.2.f.d.344.2 |
$q$-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 \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(442\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.18661 | + | 0.862123i | 0.839061 | + | 0.609613i | 0.922108 | − | 0.386932i | \(-0.126465\pi\) |
−0.0830475 | + | 0.996546i | \(0.526465\pi\) | |||||||
\(3\) | 0.500000 | − | 1.53884i | 0.288675 | − | 0.888451i | −0.696598 | − | 0.717462i | \(-0.745304\pi\) |
0.985273 | − | 0.170989i | \(-0.0546962\pi\) | |||||||
\(4\) | 0.0467549 | + | 0.143897i | 0.0233775 | + | 0.0719485i | ||||
\(5\) | 0.377594 | − | 0.274338i | 0.168865 | − | 0.122688i | −0.500143 | − | 0.865943i | \(-0.666719\pi\) |
0.669008 | + | 0.743255i | \(0.266719\pi\) | |||||||
\(6\) | 1.91998 | − | 1.39494i | 0.783827 | − | 0.569484i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.837913 | − | 2.57883i | 0.296247 | − | 0.911755i | ||||
\(9\) | 0.309017 | + | 0.224514i | 0.103006 | + | 0.0748380i | ||||
\(10\) | 0.684570 | 0.216480 | ||||||||
\(11\) | −2.22899 | − | 2.45593i | −0.672067 | − | 0.740490i | ||||
\(12\) | 0.244812 | 0.0706712 | ||||||||
\(13\) | −1.28012 | − | 0.930062i | −0.355042 | − | 0.257953i | 0.395939 | − | 0.918277i | \(-0.370419\pi\) |
−0.750981 | + | 0.660324i | \(0.770419\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.233366 | − | 0.718226i | −0.0602548 | − | 0.185445i | ||||
\(16\) | 3.46236 | − | 2.51555i | 0.865590 | − | 0.628888i | ||||
\(17\) | 4.22899 | − | 3.07254i | 1.02568 | − | 0.745201i | 0.0582418 | − | 0.998303i | \(-0.481451\pi\) |
0.967440 | + | 0.253101i | \(0.0814505\pi\) | |||||||
\(18\) | 0.173124 | + | 0.532822i | 0.0408058 | + | 0.125587i | ||||
\(19\) | −1.30464 | + | 4.01528i | −0.299306 | + | 0.921169i | 0.682435 | + | 0.730946i | \(0.260921\pi\) |
−0.981741 | + | 0.190223i | \(0.939079\pi\) | |||||||
\(20\) | 0.0571308 | + | 0.0415079i | 0.0127748 | + | 0.00928146i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.527635 | − | 4.83590i | −0.112492 | − | 1.03102i | ||||
\(23\) | −1.80505 | −0.376380 | −0.188190 | − | 0.982133i | \(-0.560262\pi\) | ||||
−0.188190 | + | 0.982133i | \(0.560262\pi\) | |||||||
\(24\) | −3.54946 | − | 2.57883i | −0.724530 | − | 0.526402i | ||||
\(25\) | −1.47777 | + | 4.54811i | −0.295554 | + | 0.909621i | ||||
\(26\) | −0.717177 | − | 2.20724i | −0.140650 | − | 0.432876i | ||||
\(27\) | 4.42705 | − | 3.21644i | 0.851986 | − | 0.619004i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.840363 | + | 2.58637i | 0.156051 | + | 0.480277i | 0.998266 | − | 0.0588657i | \(-0.0187484\pi\) |
−0.842215 | + | 0.539143i | \(0.818748\pi\) | |||||||
\(30\) | 0.342285 | − | 1.05345i | 0.0624924 | − | 0.192332i | ||||
\(31\) | 1.04675 | + | 0.760512i | 0.188003 | + | 0.136592i | 0.677805 | − | 0.735241i | \(-0.262931\pi\) |
−0.489803 | + | 0.871833i | \(0.662931\pi\) | |||||||
\(32\) | 0.854102 | 0.150985 | ||||||||
\(33\) | −4.89378 | + | 2.20210i | −0.851898 | + | 0.383337i | ||||
\(34\) | 7.66708 | 1.31489 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.0178588 | + | 0.0549637i | −0.00297647 | + | 0.00916062i | ||||
\(37\) | −0.600175 | − | 1.84715i | −0.0986682 | − | 0.303669i | 0.889524 | − | 0.456888i | \(-0.151036\pi\) |
−0.988192 | + | 0.153219i | \(0.951036\pi\) | |||||||
\(38\) | −5.00978 | + | 3.63982i | −0.812693 | + | 0.590456i | ||||
\(39\) | −2.07128 | + | 1.50487i | −0.331670 | + | 0.240972i | ||||
\(40\) | −0.391081 | − | 1.20362i | −0.0618353 | − | 0.190309i | ||||
\(41\) | 0.321724 | − | 0.990166i | 0.0502449 | − | 0.154638i | −0.922786 | − | 0.385313i | \(-0.874093\pi\) |
0.973031 | + | 0.230675i | \(0.0740935\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.70820 | 1.32799 | 0.663994 | − | 0.747738i | \(-0.268860\pi\) | ||||
0.663994 | + | 0.747738i | \(0.268860\pi\) | |||||||
\(44\) | 0.249184 | − | 0.435572i | 0.0375659 | − | 0.0656650i | ||||
\(45\) | 0.178276 | 0.0265758 | ||||||||
\(46\) | −2.14190 | − | 1.55618i | −0.315805 | − | 0.229446i | ||||
\(47\) | 1.97626 | − | 6.08229i | 0.288266 | − | 0.887193i | −0.697134 | − | 0.716941i | \(-0.745542\pi\) |
0.985401 | − | 0.170252i | \(-0.0544582\pi\) | |||||||
\(48\) | −2.13986 | − | 6.58580i | −0.308862 | − | 0.950578i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.67457 | + | 4.12281i | −0.802505 | + | 0.583054i | ||||
\(51\) | −2.61366 | − | 8.04402i | −0.365986 | − | 1.12639i | ||||
\(52\) | 0.0739811 | − | 0.227690i | 0.0102593 | − | 0.0315750i | ||||
\(53\) | 10.6826 | + | 7.76137i | 1.46737 | + | 1.06611i | 0.981366 | + | 0.192149i | \(0.0615458\pi\) |
0.486004 | + | 0.873957i | \(0.338454\pi\) | |||||||
\(54\) | 8.02616 | 1.09222 | ||||||||
\(55\) | −1.51541 | − | 0.315846i | −0.204338 | − | 0.0425887i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.52656 | + | 4.01528i | 0.732011 | + | 0.531837i | ||||
\(58\) | −1.23259 | + | 3.79351i | −0.161847 | + | 0.498112i | ||||
\(59\) | 2.65875 | + | 8.18278i | 0.346139 | + | 1.06531i | 0.960971 | + | 0.276649i | \(0.0892239\pi\) |
−0.614832 | + | 0.788658i | \(0.710776\pi\) | |||||||
\(60\) | 0.0924396 | − | 0.0671613i | 0.0119339 | − | 0.00867048i | ||||
\(61\) | −12.3295 | + | 8.95793i | −1.57864 | + | 1.14695i | −0.660399 | + | 0.750915i | \(0.729613\pi\) |
−0.918237 | + | 0.396031i | \(0.870387\pi\) | |||||||
\(62\) | 0.586436 | + | 1.80486i | 0.0744774 | + | 0.229218i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.91123 | − | 4.29476i | −0.738904 | − | 0.536845i | ||||
\(65\) | −0.738517 | −0.0916018 | ||||||||
\(66\) | −7.70550 | − | 1.60600i | −0.948482 | − | 0.197685i | ||||
\(67\) | −4.67583 | −0.571243 | −0.285622 | − | 0.958342i | \(-0.592200\pi\) | ||||
−0.285622 | + | 0.958342i | \(0.592200\pi\) | |||||||
\(68\) | 0.639856 | + | 0.464883i | 0.0775939 | + | 0.0563753i | ||||
\(69\) | −0.902527 | + | 2.77769i | −0.108651 | + | 0.334395i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.88234 | + | 5.72685i | −0.935461 | + | 0.679652i | −0.947324 | − | 0.320277i | \(-0.896224\pi\) |
0.0118626 | + | 0.999930i | \(0.496224\pi\) | |||||||
\(72\) | 0.837913 | − | 0.608780i | 0.0987490 | − | 0.0717454i | ||||
\(73\) | 4.11611 | + | 12.6681i | 0.481754 | + | 1.48269i | 0.836627 | + | 0.547773i | \(0.184524\pi\) |
−0.354873 | + | 0.934915i | \(0.615476\pi\) | |||||||
\(74\) | 0.880296 | − | 2.70927i | 0.102332 | − | 0.314947i | ||||
\(75\) | 6.25993 | + | 4.54811i | 0.722835 | + | 0.525170i | ||||
\(76\) | −0.638786 | −0.0732737 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.75519 | −0.425191 | ||||||||
\(79\) | −2.89815 | − | 2.10563i | −0.326068 | − | 0.236902i | 0.412692 | − | 0.910870i | \(-0.364588\pi\) |
−0.738760 | + | 0.673968i | \(0.764588\pi\) | |||||||
\(80\) | 0.617255 | − | 1.89971i | 0.0690112 | − | 0.212395i | ||||
\(81\) | −2.38197 | − | 7.33094i | −0.264663 | − | 0.814549i | ||||
\(82\) | 1.23541 | − | 0.897575i | 0.136428 | − | 0.0991206i | ||||
\(83\) | −13.9627 | + | 10.1445i | −1.53261 | + | 1.11351i | −0.577842 | + | 0.816148i | \(0.696105\pi\) |
−0.954766 | + | 0.297357i | \(0.903895\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.753927 | − | 2.32035i | 0.0817748 | − | 0.251677i | ||||
\(86\) | 10.3333 | + | 7.50755i | 1.11426 | + | 0.809559i | ||||
\(87\) | 4.40020 | 0.471750 | ||||||||
\(88\) | −8.20113 | + | 3.69034i | −0.874243 | + | 0.393392i | ||||
\(89\) | 8.91982 | 0.945499 | 0.472750 | − | 0.881197i | \(-0.343262\pi\) | ||||
0.472750 | + | 0.881197i | \(0.343262\pi\) | |||||||
\(90\) | 0.211544 | + | 0.153696i | 0.0222987 | + | 0.0162009i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.0843952 | − | 0.259742i | −0.00879881 | − | 0.0270799i | ||||
\(93\) | 1.69369 | − | 1.23053i | 0.175627 | − | 0.127600i | ||||
\(94\) | 7.58873 | − | 5.51353i | 0.782718 | − | 0.568678i | ||||
\(95\) | 0.608919 | + | 1.87406i | 0.0624738 | + | 0.192275i | ||||
\(96\) | 0.427051 | − | 1.31433i | 0.0435857 | − | 0.134143i | ||||
\(97\) | −2.18727 | − | 1.58915i | −0.222084 | − | 0.161353i | 0.471180 | − | 0.882037i | \(-0.343828\pi\) |
−0.693264 | + | 0.720684i | \(0.743828\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.137407 | − | 1.25936i | −0.0138099 | − | 0.126571i | ||||
\(100\) | −0.723551 | −0.0723551 | ||||||||
\(101\) | 0.144637 | + | 0.105085i | 0.0143919 | + | 0.0104563i | 0.594958 | − | 0.803757i | \(-0.297169\pi\) |
−0.580566 | + | 0.814213i | \(0.697169\pi\) | |||||||
\(102\) | 3.83354 | − | 11.7984i | 0.379577 | − | 1.16822i | ||||
\(103\) | −5.21535 | − | 16.0512i | −0.513884 | − | 1.58157i | −0.785304 | − | 0.619111i | \(-0.787493\pi\) |
0.271420 | − | 0.962461i | \(-0.412507\pi\) | |||||||
\(104\) | −3.47110 | + | 2.52190i | −0.340370 | + | 0.247293i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.98484 | + | 18.4195i | 0.581299 | + | 1.78906i | ||||
\(107\) | −4.78241 | + | 14.7188i | −0.462333 | + | 1.42292i | 0.399972 | + | 0.916527i | \(0.369020\pi\) |
−0.862305 | + | 0.506389i | \(0.830980\pi\) | |||||||
\(108\) | 0.669822 | + | 0.486655i | 0.0644537 | + | 0.0468284i | ||||
\(109\) | 11.0349 | 1.05695 | 0.528476 | − | 0.848948i | \(-0.322764\pi\) | ||||
0.528476 | + | 0.848948i | \(0.322764\pi\) | |||||||
\(110\) | −1.52590 | − | 1.68126i | −0.145489 | − | 0.160301i | ||||
\(111\) | −3.14256 | −0.298278 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.546984 | − | 1.68344i | 0.0514559 | − | 0.158365i | −0.922027 | − | 0.387127i | \(-0.873468\pi\) |
0.973482 | + | 0.228762i | \(0.0734676\pi\) | |||||||
\(114\) | 3.09621 | + | 9.52916i | 0.289987 | + | 0.892488i | ||||
\(115\) | −0.681577 | + | 0.495195i | −0.0635574 | + | 0.0461772i | ||||
\(116\) | −0.332880 | + | 0.241851i | −0.0309071 | + | 0.0224553i | ||||
\(117\) | −0.186767 | − | 0.574810i | −0.0172666 | − | 0.0531412i | ||||
\(118\) | −3.89967 | + | 12.0019i | −0.358994 | + | 1.10487i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.04773 | −0.186931 | ||||||||
\(121\) | −1.06317 | + | 10.9485i | −0.0966521 | + | 0.995318i | ||||
\(122\) | −22.3532 | −2.02376 | ||||||||
\(123\) | −1.36285 | − | 0.990166i | −0.122884 | − | 0.0892802i | ||||
\(124\) | −0.0604944 | + | 0.186183i | −0.00543255 | + | 0.0167197i | ||||
\(125\) | 1.41086 | + | 4.34219i | 0.126191 | + | 0.388377i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.90919 | − | 5.01982i | 0.613092 | − | 0.445437i | −0.237410 | − | 0.971410i | \(-0.576298\pi\) |
0.850502 | + | 0.525972i | \(0.176298\pi\) | |||||||
\(128\) | −3.83958 | − | 11.8170i | −0.339374 | − | 1.04449i | ||||
\(129\) | 4.35410 | − | 13.4005i | 0.383357 | − | 1.17985i | ||||
\(130\) | −0.876333 | − | 0.636693i | −0.0768595 | − | 0.0558417i | ||||
\(131\) | 9.66708 | 0.844617 | 0.422308 | − | 0.906452i | \(-0.361220\pi\) | ||||
0.422308 | + | 0.906452i | \(0.361220\pi\) | |||||||
\(132\) | −0.545685 | − | 0.601241i | −0.0474957 | − | 0.0523313i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.54839 | − | 4.03114i | −0.479308 | − | 0.348237i | ||||
\(135\) | 0.789236 | − | 2.42902i | 0.0679266 | − | 0.209057i | ||||
\(136\) | −4.38004 | − | 13.4804i | −0.375586 | − | 1.15593i | ||||
\(137\) | 11.3350 | − | 8.23535i | 0.968413 | − | 0.703593i | 0.0133236 | − | 0.999911i | \(-0.495759\pi\) |
0.955089 | + | 0.296318i | \(0.0957589\pi\) | |||||||
\(138\) | −3.46566 | + | 2.51795i | −0.295017 | + | 0.214342i | ||||
\(139\) | −2.95966 | − | 9.10889i | −0.251035 | − | 0.772606i | −0.994585 | − | 0.103926i | \(-0.966860\pi\) |
0.743550 | − | 0.668680i | \(-0.233140\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.37155 | − | 6.08229i | −0.705012 | − | 0.512221i | ||||
\(142\) | −14.2905 | −1.19923 | ||||||||
\(143\) | 0.569215 | + | 5.21699i | 0.0476001 | + | 0.436267i | ||||
\(144\) | 1.63470 | 0.136225 | ||||||||
\(145\) | 1.02686 | + | 0.746054i | 0.0852757 | + | 0.0619564i | ||||
\(146\) | −6.03723 | + | 18.5807i | −0.499645 | + | 1.53775i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.237738 | − | 0.172727i | 0.0195419 | − | 0.0141980i | ||||
\(149\) | −12.1049 | + | 8.79474i | −0.991674 | + | 0.720493i | −0.960287 | − | 0.279014i | \(-0.909992\pi\) |
−0.0313866 | + | 0.999507i | \(0.509992\pi\) | |||||||
\(150\) | 3.50707 | + | 10.7937i | 0.286351 | + | 0.881299i | ||||
\(151\) | −0.887599 | + | 2.73175i | −0.0722318 | + | 0.222307i | −0.980655 | − | 0.195746i | \(-0.937287\pi\) |
0.908423 | + | 0.418053i | \(0.137287\pi\) | |||||||
\(152\) | 9.26156 | + | 6.72892i | 0.751212 | + | 0.545787i | ||||
\(153\) | 1.99666 | 0.161420 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.603886 | 0.0485053 | ||||||||
\(156\) | −0.313389 | − | 0.227690i | −0.0250912 | − | 0.0182298i | ||||
\(157\) | 5.83496 | − | 17.9582i | 0.465680 | − | 1.43322i | −0.392444 | − | 0.919776i | \(-0.628370\pi\) |
0.858125 | − | 0.513441i | \(-0.171630\pi\) | |||||||
\(158\) | −1.62367 | − | 4.99713i | −0.129172 | − | 0.397551i | ||||
\(159\) | 17.2848 | − | 12.5582i | 1.37078 | − | 0.995927i | ||||
\(160\) | 0.322504 | − | 0.234313i | 0.0254962 | − | 0.0185240i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.49371 | − | 10.7525i | 0.274491 | − | 0.844798i | ||||
\(163\) | −9.38067 | − | 6.81545i | −0.734751 | − | 0.533827i | 0.156312 | − | 0.987708i | \(-0.450039\pi\) |
−0.891063 | + | 0.453880i | \(0.850039\pi\) | |||||||
\(164\) | 0.157524 | 0.0123006 | ||||||||
\(165\) | −1.24374 | + | 2.17405i | −0.0968252 | + | 0.169250i | ||||
\(166\) | −25.3142 | −1.96476 | ||||||||
\(167\) | 5.11696 | + | 3.71769i | 0.395963 | + | 0.287684i | 0.767894 | − | 0.640576i | \(-0.221305\pi\) |
−0.371932 | + | 0.928260i | \(0.621305\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.24353 | − | 9.98255i | −0.249502 | − | 0.767889i | ||||
\(170\) | 2.89504 | − | 2.10337i | 0.222040 | − | 0.161321i | ||||
\(171\) | −1.30464 | + | 0.947880i | −0.0997687 | + | 0.0724862i | ||||
\(172\) | 0.407152 | + | 1.25308i | 0.0310450 | + | 0.0955467i | ||||
\(173\) | −0.413793 | + | 1.27352i | −0.0314601 | + | 0.0968243i | −0.965554 | − | 0.260204i | \(-0.916210\pi\) |
0.934093 | + | 0.357029i | \(0.116210\pi\) | |||||||
\(174\) | 5.22132 | + | 3.79351i | 0.395827 | + | 0.287585i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.8956 | − | 2.89616i | −1.04742 | − | 0.218306i | ||||
\(177\) | 13.9214 | 1.04639 | ||||||||
\(178\) | 10.5844 | + | 7.68999i | 0.793331 | + | 0.576389i | ||||
\(179\) | 5.49705 | − | 16.9182i | 0.410868 | − | 1.26452i | −0.505026 | − | 0.863104i | \(-0.668517\pi\) |
0.915895 | − | 0.401419i | \(-0.131483\pi\) | |||||||
\(180\) | 0.00833527 | + | 0.0256533i | 0.000621274 | + | 0.00191209i | ||||
\(181\) | −0.779712 | + | 0.566494i | −0.0579555 | + | 0.0421072i | −0.616386 | − | 0.787444i | \(-0.711404\pi\) |
0.558430 | + | 0.829551i | \(0.311404\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.62007 | + | 23.4522i | 0.563292 | + | 1.73363i | ||||
\(184\) | −1.51248 | + | 4.65493i | −0.111501 | + | 0.343166i | ||||
\(185\) | −0.733366 | − | 0.532822i | −0.0539181 | − | 0.0391738i | ||||
\(186\) | 3.07062 | 0.225149 | ||||||||
\(187\) | −16.9724 | − | 3.53743i | −1.24114 | − | 0.258682i | ||||
\(188\) | 0.967622 | 0.0705711 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.893121 | + | 2.74874i | −0.0647938 | + | 0.199415i | ||||
\(191\) | −4.97173 | − | 15.3014i | −0.359742 | − | 1.10717i | −0.953209 | − | 0.302313i | \(-0.902241\pi\) |
0.593467 | − | 0.804858i | \(-0.297759\pi\) | |||||||
\(192\) | −9.56458 | + | 6.94907i | −0.690264 | + | 0.501506i | ||||
\(193\) | −9.82750 | + | 7.14010i | −0.707399 | + | 0.513955i | −0.882333 | − | 0.470625i | \(-0.844029\pi\) |
0.174935 | + | 0.984580i | \(0.444029\pi\) | |||||||
\(194\) | −1.22540 | − | 3.77140i | −0.0879787 | − | 0.270771i | ||||
\(195\) | −0.369259 | + | 1.13646i | −0.0264432 | + | 0.0813837i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.30179 | −0.163996 | −0.0819978 | − | 0.996633i | \(-0.526130\pi\) | ||||
−0.0819978 | + | 0.996633i | \(0.526130\pi\) | |||||||
\(198\) | 0.922679 | − | 1.61284i | 0.0655719 | − | 0.114619i | ||||
\(199\) | −20.2797 | −1.43759 | −0.718795 | − | 0.695222i | \(-0.755306\pi\) | ||||
−0.718795 | + | 0.695222i | \(0.755306\pi\) | |||||||
\(200\) | 10.4906 | + | 7.62184i | 0.741794 | + | 0.538945i | ||||
\(201\) | −2.33791 | + | 7.19536i | −0.164904 | + | 0.507521i | ||||
\(202\) | 0.0810316 | + | 0.249390i | 0.00570136 | + | 0.0175470i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.03531 | − | 0.752196i | 0.0724861 | − | 0.0526642i | ||||
\(205\) | −0.150159 | − | 0.462142i | −0.0104876 | − | 0.0322774i | ||||
\(206\) | 7.64952 | − | 23.5428i | 0.532967 | − | 1.64030i | ||||
\(207\) | −0.557792 | − | 0.405260i | −0.0387692 | − | 0.0281675i | ||||
\(208\) | −6.77186 | −0.469544 | ||||||||
\(209\) | 12.7693 | − | 5.74593i | 0.883271 | − | 0.397454i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.34062 | − | 3.15364i | −0.298820 | − | 0.217106i | 0.428264 | − | 0.903654i | \(-0.359125\pi\) |
−0.727085 | + | 0.686548i | \(0.759125\pi\) | |||||||
\(212\) | −0.617372 | + | 1.90008i | −0.0424013 | + | 0.130498i | ||||
\(213\) | 4.87155 | + | 14.9931i | 0.333793 | + | 1.02731i | ||||
\(214\) | −18.3642 | + | 13.3424i | −1.25535 | + | 0.912068i | ||||
\(215\) | 3.28817 | − | 2.38899i | 0.224251 | − | 0.162928i | ||||
\(216\) | −4.58517 | − | 14.1117i | −0.311982 | − | 0.960181i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 13.0941 | + | 9.51344i | 0.886847 | + | 0.644332i | ||||
\(219\) | 21.5522 | 1.45637 | ||||||||
\(220\) | −0.0254036 | − | 0.232830i | −0.00171271 | − | 0.0156974i | ||||
\(221\) | −8.27128 | −0.556387 | ||||||||
\(222\) | −3.72899 | − | 2.70927i | −0.250274 | − | 0.181834i | ||||
\(223\) | 7.85614 | − | 24.1787i | 0.526086 | − | 1.61913i | −0.236072 | − | 0.971736i | \(-0.575860\pi\) |
0.762158 | − | 0.647391i | \(-0.224140\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.47777 | + | 1.07366i | −0.0985179 | + | 0.0715775i | ||||
\(226\) | 2.10039 | − | 1.52602i | 0.139716 | − | 0.101510i | ||||
\(227\) | 6.70869 | + | 20.6472i | 0.445271 | + | 1.37040i | 0.882186 | + | 0.470901i | \(0.156071\pi\) |
−0.436915 | + | 0.899503i | \(0.643929\pi\) | |||||||
\(228\) | −0.319393 | + | 0.982990i | −0.0211523 | + | 0.0651001i | ||||
\(229\) | 16.6097 | + | 12.0676i | 1.09760 | + | 0.797451i | 0.980666 | − | 0.195689i | \(-0.0626943\pi\) |
0.116931 | + | 0.993140i | \(0.462694\pi\) | |||||||
\(230\) | −1.23569 | −0.0814787 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.37396 | 0.484124 | ||||||||
\(233\) | −0.561503 | − | 0.407956i | −0.0367853 | − | 0.0267261i | 0.569241 | − | 0.822171i | \(-0.307237\pi\) |
−0.606026 | + | 0.795445i | \(0.707237\pi\) | |||||||
\(234\) | 0.273937 | − | 0.843092i | 0.0179078 | − | 0.0551147i | ||||
\(235\) | −0.922381 | − | 2.83880i | −0.0601695 | − | 0.185183i | ||||
\(236\) | −1.05317 | + | 0.765171i | −0.0685554 | + | 0.0498084i | ||||
\(237\) | −4.68931 | + | 3.40699i | −0.304604 | + | 0.221307i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.107093 | − | 0.329599i | 0.00692728 | − | 0.0213200i | −0.947533 | − | 0.319658i | \(-0.896432\pi\) |
0.954460 | + | 0.298338i | \(0.0964321\pi\) | |||||||
\(240\) | −2.61473 | − | 1.89971i | −0.168780 | − | 0.122626i | ||||
\(241\) | 10.4372 | 0.672317 | 0.336158 | − | 0.941806i | \(-0.390872\pi\) | ||||
0.336158 | + | 0.941806i | \(0.390872\pi\) | |||||||
\(242\) | −10.7005 | + | 12.0750i | −0.687856 | + | 0.776212i | ||||
\(243\) | 3.94427 | 0.253025 | ||||||||
\(244\) | −1.86549 | − | 1.35536i | −0.119426 | − | 0.0867677i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.763523 | − | 2.34988i | −0.0486805 | − | 0.149823i | ||||
\(247\) | 5.40457 | − | 3.92665i | 0.343884 | − | 0.249847i | ||||
\(248\) | 2.83832 | − | 2.06216i | 0.180234 | − | 0.130947i | ||||
\(249\) | 8.62944 | + | 26.5587i | 0.546869 | + | 1.68309i | ||||
\(250\) | −2.06936 | + | 6.36882i | −0.130878 | + | 0.402800i | ||||
\(251\) | −5.65909 | − | 4.11157i | −0.357199 | − | 0.259520i | 0.394684 | − | 0.918817i | \(-0.370854\pi\) |
−0.751883 | + | 0.659297i | \(0.770854\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.02345 | + | 4.43308i | 0.252952 | + | 0.278706i | ||||
\(254\) | 12.5262 | 0.785965 | ||||||||
\(255\) | −3.19369 | − | 2.32035i | −0.199996 | − | 0.145306i | ||||
\(256\) | 1.11586 | − | 3.43426i | 0.0697412 | − | 0.214641i | ||||
\(257\) | 3.07423 | + | 9.46152i | 0.191765 | + | 0.590193i | 0.999999 | + | 0.00133144i | \(0.000423809\pi\) |
−0.808234 | + | 0.588862i | \(0.799576\pi\) | |||||||
\(258\) | 16.7196 | − | 12.1475i | 1.04091 | − | 0.756268i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.0345293 | − | 0.106270i | −0.00214142 | − | 0.00659061i | ||||
\(261\) | −0.320990 | + | 0.987905i | −0.0198688 | + | 0.0611498i | ||||
\(262\) | 11.4711 | + | 8.33422i | 0.708685 | + | 0.514890i | ||||
\(263\) | 14.1803 | 0.874397 | 0.437199 | − | 0.899365i | \(-0.355971\pi\) | ||||
0.437199 | + | 0.899365i | \(0.355971\pi\) | |||||||
\(264\) | 1.57829 | + | 14.4654i | 0.0971371 | + | 0.890285i | ||||
\(265\) | 6.16293 | 0.378586 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.45991 | − | 13.7262i | 0.272942 | − | 0.840029i | ||||
\(268\) | −0.218618 | − | 0.672837i | −0.0133542 | − | 0.0411001i | ||||
\(269\) | −14.8884 | + | 10.8171i | −0.907762 | + | 0.659528i | −0.940448 | − | 0.339938i | \(-0.889594\pi\) |
0.0326859 | + | 0.999466i | \(0.489594\pi\) | |||||||
\(270\) | 3.03063 | − | 2.20188i | 0.184438 | − | 0.134002i | ||||
\(271\) | −0.225765 | − | 0.694833i | −0.0137142 | − | 0.0422081i | 0.943965 | − | 0.330045i | \(-0.107064\pi\) |
−0.957679 | + | 0.287837i | \(0.907064\pi\) | |||||||
\(272\) | 6.91316 | − | 21.2765i | 0.419172 | − | 1.29008i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.5501 | 1.24148 | ||||||||
\(275\) | 14.4638 | − | 6.50840i | 0.872198 | − | 0.392472i | ||||
\(276\) | −0.441899 | −0.0265992 | ||||||||
\(277\) | −12.1874 | − | 8.85463i | −0.732267 | − | 0.532023i | 0.158013 | − | 0.987437i | \(-0.449491\pi\) |
−0.890280 | + | 0.455414i | \(0.849491\pi\) | |||||||
\(278\) | 4.34102 | − | 13.3603i | 0.260357 | − | 0.801297i | ||||
\(279\) | 0.152719 | + | 0.470022i | 0.00914308 | + | 0.0281395i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.65334 | − | 6.28702i | 0.516215 | − | 0.375052i | −0.298961 | − | 0.954265i | \(-0.596640\pi\) |
0.815176 | + | 0.579213i | \(0.196640\pi\) | |||||||
\(282\) | −4.69009 | − | 14.4346i | −0.279291 | − | 0.859569i | ||||
\(283\) | −2.81481 | + | 8.66308i | −0.167323 | + | 0.514967i | −0.999200 | − | 0.0399931i | \(-0.987266\pi\) |
0.831877 | + | 0.554960i | \(0.187266\pi\) | |||||||
\(284\) | −1.19261 | − | 0.866485i | −0.0707687 | − | 0.0514164i | ||||
\(285\) | 3.18834 | 0.188861 | ||||||||
\(286\) | −3.82225 | + | 6.68127i | −0.226014 | + | 0.395072i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.263932 | + | 0.191758i | 0.0155523 | + | 0.0112994i | ||||
\(289\) | 3.19057 | − | 9.81958i | 0.187681 | − | 0.577622i | ||||
\(290\) | 0.575287 | + | 1.77055i | 0.0337820 | + | 0.103970i | ||||
\(291\) | −3.53908 | + | 2.57129i | −0.207465 | + | 0.150732i | ||||
\(292\) | −1.63045 | + | 1.18459i | −0.0954149 | + | 0.0693230i | ||||
\(293\) | −3.67390 | − | 11.3071i | −0.214632 | − | 0.660569i | −0.999180 | − | 0.0405002i | \(-0.987105\pi\) |
0.784548 | − | 0.620068i | \(-0.212895\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.24878 | + | 2.36037i | 0.189151 | + | 0.137426i | ||||
\(296\) | −5.26638 | −0.306102 | ||||||||
\(297\) | −17.7672 | − | 3.70310i | −1.03096 | − | 0.214875i | ||||
\(298\) | −21.9460 | −1.27130 | ||||||||
\(299\) | 2.31069 | + | 1.67881i | 0.133630 | + | 0.0970882i | ||||
\(300\) | −0.361776 | + | 1.11343i | −0.0208871 | + | 0.0642840i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.40834 | + | 2.47630i | −0.196128 | + | 0.142495i | ||||
\(303\) | 0.234027 | − | 0.170031i | 0.0134445 | − | 0.00976802i | ||||
\(304\) | 5.58350 | + | 17.1843i | 0.320236 | + | 0.985585i | ||||
\(305\) | −2.19806 | + | 6.76492i | −0.125860 | + | 0.387358i | ||||
\(306\) | 2.36926 | + | 1.72137i | 0.135442 | + | 0.0984040i | ||||
\(307\) | −2.22072 | −0.126743 | −0.0633716 | − | 0.997990i | \(-0.520185\pi\) | ||||
−0.0633716 | + | 0.997990i | \(0.520185\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −27.3079 | −1.55349 | ||||||||
\(310\) | 0.716577 | + | 0.520624i | 0.0406989 | + | 0.0295695i | ||||
\(311\) | 6.61685 | − | 20.3646i | 0.375207 | − | 1.15477i | −0.568132 | − | 0.822937i | \(-0.692334\pi\) |
0.943339 | − | 0.331831i | \(-0.107666\pi\) | |||||||
\(312\) | 2.14526 | + | 6.60243i | 0.121451 | + | 0.373789i | ||||
\(313\) | −25.5283 | + | 18.5474i | −1.44295 | + | 1.04836i | −0.455531 | + | 0.890220i | \(0.650550\pi\) |
−0.987416 | + | 0.158142i | \(0.949450\pi\) | |||||||
\(314\) | 22.4060 | − | 16.2789i | 1.26444 | − | 0.918671i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.167491 | − | 0.515484i | 0.00942211 | − | 0.0289983i | ||||
\(317\) | 10.6796 | + | 7.75915i | 0.599824 | + | 0.435798i | 0.845816 | − | 0.533474i | \(-0.179114\pi\) |
−0.245992 | + | 0.969272i | \(0.579114\pi\) | |||||||
\(318\) | 31.3370 | 1.75729 | ||||||||
\(319\) | 4.47878 | − | 7.82887i | 0.250763 | − | 0.438333i | ||||
\(320\) | −3.41026 | −0.190639 | ||||||||
\(321\) | 20.2586 | + | 14.7188i | 1.13073 | + | 0.821521i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.81980 | + | 20.9892i | 0.379464 | + | 1.16787i | ||||
\(324\) | 0.943531 | − | 0.685515i | 0.0524184 | − | 0.0380842i | ||||
\(325\) | 6.12174 | − | 4.44771i | 0.339573 | − | 0.246714i | ||||
\(326\) | −5.25544 | − | 16.1746i | −0.291072 | − | 0.895827i | ||||
\(327\) | 5.51745 | − | 16.9810i | 0.305116 | − | 0.939050i | ||||
\(328\) | −2.28389 | − | 1.65935i | −0.126107 | − | 0.0916220i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.35014 | + | 1.50750i | −0.184419 | + | 0.0829849i | ||||
\(331\) | 9.47653 | 0.520877 | 0.260439 | − | 0.965490i | \(-0.416133\pi\) | ||||
0.260439 | + | 0.965490i | \(0.416133\pi\) | |||||||
\(332\) | −2.11259 | − | 1.53489i | −0.115944 | − | 0.0842379i | ||||
\(333\) | 0.229247 | − | 0.705548i | 0.0125626 | − | 0.0386638i | ||||
\(334\) | 2.86674 | + | 8.82291i | 0.156861 | + | 0.482768i | ||||
\(335\) | −1.76556 | + | 1.28276i | −0.0964631 | + | 0.0700845i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.93346 | − | 18.2613i | −0.323216 | − | 0.994758i | −0.972239 | − | 0.233989i | \(-0.924822\pi\) |
0.649023 | − | 0.760769i | \(-0.275178\pi\) | |||||||
\(338\) | 4.75738 | − | 14.6417i | 0.258768 | − | 0.796405i | ||||
\(339\) | −2.31706 | − | 1.68344i | −0.125845 | − | 0.0914321i | ||||
\(340\) | 0.369141 | 0.0200195 | ||||||||
\(341\) | −0.465447 | − | 4.26593i | −0.0252054 | − | 0.231013i | ||||
\(342\) | −2.36530 | −0.127901 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7.29672 | − | 22.4570i | 0.393413 | − | 1.21080i | ||||
\(345\) | 0.421238 | + | 1.29644i | 0.0226787 | + | 0.0697978i | ||||
\(346\) | −1.58895 | + | 1.15444i | −0.0854223 | + | 0.0620629i | ||||
\(347\) | −2.46613 | + | 1.79175i | −0.132389 | + | 0.0961862i | −0.652009 | − | 0.758211i | \(-0.726074\pi\) |
0.519620 | + | 0.854397i | \(0.326074\pi\) | |||||||
\(348\) | 0.205731 | + | 0.633175i | 0.0110283 | + | 0.0339417i | ||||
\(349\) | −5.99373 | + | 18.4468i | −0.320837 | + | 0.987435i | 0.652448 | + | 0.757834i | \(0.273742\pi\) |
−0.973285 | + | 0.229601i | \(0.926258\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.65865 | −0.462165 | ||||||||
\(352\) | −1.90379 | − | 2.09761i | −0.101472 | − | 0.111803i | ||||
\(353\) | 10.7585 | 0.572619 | 0.286309 | − | 0.958137i | \(-0.407572\pi\) | ||||
0.286309 | + | 0.958137i | \(0.407572\pi\) | |||||||
\(354\) | 16.5193 | + | 12.0019i | 0.877989 | + | 0.637896i | ||||
\(355\) | −1.40523 | + | 4.32485i | −0.0745818 | + | 0.229539i | ||||
\(356\) | 0.417046 | + | 1.28353i | 0.0221034 | + | 0.0680272i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 21.1084 | − | 15.3361i | 1.11561 | − | 0.810541i | ||||
\(359\) | 0.187643 | + | 0.577506i | 0.00990342 | + | 0.0304796i | 0.955886 | − | 0.293738i | \(-0.0948992\pi\) |
−0.945983 | + | 0.324217i | \(0.894899\pi\) | |||||||
\(360\) | 0.149380 | − | 0.459743i | 0.00787299 | − | 0.0242306i | ||||
\(361\) | 0.950914 | + | 0.690879i | 0.0500481 | + | 0.0363621i | ||||
\(362\) | −1.41360 | −0.0742973 | ||||||||
\(363\) | 16.3164 | + | 7.11030i | 0.856390 | + | 0.373194i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.02956 | + | 3.65419i | 0.263259 | + | 0.191269i | ||||
\(366\) | −11.1766 | + | 34.3981i | −0.584211 | + | 1.79802i | ||||
\(367\) | −8.54829 | − | 26.3089i | −0.446217 | − | 1.37332i | −0.881143 | − | 0.472849i | \(-0.843226\pi\) |
0.434926 | − | 0.900466i | \(-0.356774\pi\) | |||||||
\(368\) | −6.24975 | + | 4.54071i | −0.325791 | + | 0.236701i | ||||
\(369\) | 0.321724 | − | 0.233746i | 0.0167483 | − | 0.0121684i | ||||
\(370\) | −0.410862 | − | 1.26450i | −0.0213597 | − | 0.0657384i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.256258 | + | 0.186183i | 0.0132864 | + | 0.00965311i | ||||
\(373\) | −29.4513 | −1.52493 | −0.762465 | − | 0.647029i | \(-0.776011\pi\) | ||||
−0.762465 | + | 0.647029i | \(0.776011\pi\) | |||||||
\(374\) | −17.0899 | − | 18.8298i | −0.883697 | − | 0.973666i | ||||
\(375\) | 7.38737 | 0.381482 | ||||||||
\(376\) | −14.0293 | − | 10.1929i | −0.723504 | − | 0.525657i | ||||
\(377\) | 1.32972 | − | 4.09246i | 0.0684840 | − | 0.210772i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.5034 | + | 14.8966i | −1.05319 | + | 0.765188i | −0.972817 | − | 0.231577i | \(-0.925612\pi\) |
−0.0803745 | + | 0.996765i | \(0.525612\pi\) | |||||||
\(380\) | −0.241202 | + | 0.175243i | −0.0123734 | + | 0.00898979i | ||||
\(381\) | −4.27012 | − | 13.1421i | −0.218765 | − | 0.673288i | ||||
\(382\) | 7.29219 | − | 22.4431i | 0.373101 | − | 1.14829i | ||||
\(383\) | −25.8337 | − | 18.7693i | −1.32004 | − | 0.959065i | −0.999932 | − | 0.0116837i | \(-0.996281\pi\) |
−0.320108 | − | 0.947381i | \(-0.603719\pi\) | |||||||
\(384\) | −20.1043 | −1.02594 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.8171 | −0.906865 | ||||||||
\(387\) | 2.69098 | + | 1.95511i | 0.136790 | + | 0.0993840i | ||||
\(388\) | 0.126407 | − | 0.389042i | 0.00641737 | − | 0.0197506i | ||||
\(389\) | 5.48558 | + | 16.8829i | 0.278130 | + | 0.855996i | 0.988374 | + | 0.152040i | \(0.0485844\pi\) |
−0.710244 | + | 0.703955i | \(0.751416\pi\) | |||||||
\(390\) | −1.41794 | + | 1.03019i | −0.0718000 | + | 0.0521657i | ||||
\(391\) | −7.63356 | + | 5.54611i | −0.386046 | + | 0.280479i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.83354 | − | 14.8761i | 0.243820 | − | 0.750400i | ||||
\(394\) | −2.73133 | − | 1.98442i | −0.137602 | − | 0.0999738i | ||||
\(395\) | −1.67198 | −0.0841265 | ||||||||
\(396\) | 0.174794 | − | 0.0786539i | 0.00878374 | − | 0.00395251i | ||||
\(397\) | 13.3047 | 0.667742 | 0.333871 | − | 0.942619i | \(-0.391645\pi\) | ||||
0.333871 | + | 0.942619i | \(0.391645\pi\) | |||||||
\(398\) | −24.0641 | − | 17.4836i | −1.20623 | − | 0.876374i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.32443 | + | 19.4646i | 0.316221 | + | 0.973229i | ||||
\(401\) | 2.82317 | − | 2.05115i | 0.140982 | − | 0.102430i | −0.515059 | − | 0.857155i | \(-0.672230\pi\) |
0.656041 | + | 0.754725i | \(0.272230\pi\) | |||||||
\(402\) | −8.97748 | + | 6.52252i | −0.447756 | + | 0.325314i | ||||
\(403\) | −0.632649 | − | 1.94709i | −0.0315145 | − | 0.0969917i | ||||
\(404\) | −0.00835890 | + | 0.0257260i | −0.000415871 | + | 0.00127992i | ||||
\(405\) | −2.91057 | − | 2.11465i | −0.144627 | − | 0.105078i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.19868 | + | 5.59127i | −0.158553 | + | 0.277149i | ||||
\(408\) | −22.9342 | −1.13541 | ||||||||
\(409\) | −23.9675 | − | 17.4134i | −1.18512 | − | 0.861039i | −0.192379 | − | 0.981321i | \(-0.561620\pi\) |
−0.992740 | + | 0.120282i | \(0.961620\pi\) | |||||||
\(410\) | 0.220243 | − | 0.677838i | 0.0108770 | − | 0.0334760i | ||||
\(411\) | −7.00540 | − | 21.5604i | −0.345551 | − | 1.06350i | ||||
\(412\) | 2.06587 | − | 1.50095i | 0.101778 | − | 0.0739463i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.312499 | − | 0.961771i | −0.0153585 | − | 0.0472685i | ||||
\(415\) | −2.48922 | + | 7.66102i | −0.122191 | + | 0.376065i | ||||
\(416\) | −1.09335 | − | 0.794368i | −0.0536061 | − | 0.0389471i | ||||
\(417\) | −15.4970 | −0.758890 | ||||||||
\(418\) | 20.1059 | + | 4.19053i | 0.983411 | + | 0.204965i | ||||
\(419\) | 11.6452 | 0.568907 | 0.284454 | − | 0.958690i | \(-0.408188\pi\) | ||||
0.284454 | + | 0.958690i | \(0.408188\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.14475 | − | 18.9116i | 0.299477 | − | 0.921696i | −0.682204 | − | 0.731162i | \(-0.738978\pi\) |
0.981681 | − | 0.190533i | \(-0.0610217\pi\) | |||||||
\(422\) | −2.43179 | − | 7.48429i | −0.118378 | − | 0.364330i | ||||
\(423\) | 1.97626 | − | 1.43583i | 0.0960888 | − | 0.0698126i | ||||
\(424\) | 28.9664 | − | 21.0453i | 1.40673 | − | 1.02205i | ||||
\(425\) | 7.72478 | + | 23.7744i | 0.374707 | + | 1.15323i | ||||
\(426\) | −7.14526 | + | 21.9908i | −0.346189 | + | 1.06546i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.34159 | −0.113185 | ||||||||
\(429\) | 8.31273 | + | 1.73256i | 0.401342 | + | 0.0836489i | ||||
\(430\) | 5.96138 | 0.287483 | ||||||||
\(431\) | −24.4698 | − | 17.7784i | −1.17867 | − | 0.856354i | −0.186649 | − | 0.982427i | \(-0.559763\pi\) |
−0.992021 | + | 0.126073i | \(0.959763\pi\) | |||||||
\(432\) | 7.23692 | − | 22.2730i | 0.348186 | − | 1.07161i | ||||
\(433\) | 1.76362 | + | 5.42786i | 0.0847542 | + | 0.260846i | 0.984448 | − | 0.175674i | \(-0.0562106\pi\) |
−0.899694 | + | 0.436521i | \(0.856211\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.66149 | − | 1.20714i | 0.0796622 | − | 0.0578780i | ||||
\(436\) | 0.515936 | + | 1.58789i | 0.0247089 | + | 0.0760461i | ||||
\(437\) | 2.35495 | − | 7.24780i | 0.112653 | − | 0.346709i | ||||
\(438\) | 25.5741 | + | 18.5807i | 1.22198 | + | 0.887820i | ||||
\(439\) | −6.84875 | −0.326873 | −0.163436 | − | 0.986554i | \(-0.552258\pi\) | ||||
−0.163436 | + | 0.986554i | \(0.552258\pi\) | |||||||
\(440\) | −2.08430 | + | 3.64333i | −0.0993649 | + | 0.173689i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.81479 | − | 7.13086i | −0.466842 | − | 0.339181i | ||||
\(443\) | 0.0311165 | − | 0.0957668i | 0.00147839 | − | 0.00455002i | −0.950315 | − | 0.311291i | \(-0.899239\pi\) |
0.951793 | + | 0.306741i | \(0.0992386\pi\) | |||||||
\(444\) | −0.146930 | − | 0.452204i | −0.00697300 | − | 0.0214607i | ||||
\(445\) | 3.36807 | − | 2.44705i | 0.159662 | − | 0.116001i | ||||
\(446\) | 30.1672 | − | 21.9178i | 1.42846 | − | 1.03784i | ||||
\(447\) | 7.48125 | + | 23.0249i | 0.353851 | + | 1.08904i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.9216 | + | 18.1066i | 1.17612 | + | 0.854502i | 0.991729 | − | 0.128351i | \(-0.0409683\pi\) |
0.184392 | + | 0.982853i | \(0.440968\pi\) | |||||||
\(450\) | −2.67917 | −0.126297 | ||||||||
\(451\) | −3.14890 | + | 1.41694i | −0.148276 | + | 0.0667211i | ||||
\(452\) | 0.267817 | 0.0125970 | ||||||||
\(453\) | 3.75993 | + | 2.73175i | 0.176657 | + | 0.128349i | ||||
\(454\) | −9.83984 | + | 30.2839i | −0.461807 | + | 1.42129i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.9855 | − | 10.8876i | 0.701761 | − | 0.509859i | ||||
\(457\) | −18.7171 | + | 13.5987i | −0.875547 | + | 0.636122i | −0.932070 | − | 0.362279i | \(-0.881999\pi\) |
0.0565223 | + | 0.998401i | \(0.481999\pi\) | |||||||
\(458\) | 9.30542 | + | 28.6392i | 0.434814 | + | 1.33822i | ||||
\(459\) | 8.83932 | − | 27.2046i | 0.412584 | − | 1.26980i | ||||
\(460\) | −0.103124 | − | 0.0749241i | −0.00480819 | − | 0.00349335i | ||||
\(461\) | 2.77839 | 0.129403 | 0.0647013 | − | 0.997905i | \(-0.479391\pi\) | ||||
0.0647013 | + | 0.997905i | \(0.479391\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.0950 | −1.21274 | −0.606369 | − | 0.795184i | \(-0.707374\pi\) | ||||
−0.606369 | + | 0.795184i | \(0.707374\pi\) | |||||||
\(464\) | 9.41578 | + | 6.84097i | 0.437117 | + | 0.317584i | ||||
\(465\) | 0.301943 | − | 0.929285i | 0.0140023 | − | 0.0430945i | ||||
\(466\) | −0.314577 | − | 0.968169i | −0.0145725 | − | 0.0448496i | ||||
\(467\) | −2.15060 | + | 1.56250i | −0.0995180 | + | 0.0723041i | −0.636431 | − | 0.771333i | \(-0.719590\pi\) |
0.536913 | + | 0.843637i | \(0.319590\pi\) | |||||||
\(468\) | 0.0739811 | − | 0.0537504i | 0.00341978 | − | 0.00248461i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.35289 | − | 4.16375i | 0.0624040 | − | 0.192060i | ||||
\(471\) | −24.7173 | − | 17.9582i | −1.13891 | − | 0.827468i | ||||
\(472\) | 23.3298 | 1.07384 | ||||||||
\(473\) | −19.4105 | − | 21.3867i | −0.892497 | − | 0.983363i | ||||
\(474\) | −8.50163 | −0.390493 | ||||||||
\(475\) | −16.3340 | − | 11.8673i | −0.749454 | − | 0.544510i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.55857 | + | 4.79679i | 0.0713621 | + | 0.219630i | ||||
\(478\) | 0.411233 | − | 0.298778i | 0.0188093 | − | 0.0136658i | ||||
\(479\) | −6.70047 | + | 4.86818i | −0.306152 | + | 0.222433i | −0.730244 | − | 0.683187i | \(-0.760593\pi\) |
0.424091 | + | 0.905619i | \(0.360593\pi\) | |||||||
\(480\) | −0.199318 | − | 0.613439i | −0.00909759 | − | 0.0279995i | ||||
\(481\) | −0.949667 | + | 2.92277i | −0.0433011 | + | 0.133267i | ||||
\(482\) | 12.3848 | + | 8.99812i | 0.564114 | + | 0.409853i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.62516 | + | 0.358909i | −0.0738711 | + | 0.0163141i | ||||
\(485\) | −1.26186 | −0.0572983 | ||||||||
\(486\) | 4.68032 | + | 3.40045i | 0.212303 | + | 0.154247i | ||||
\(487\) | −6.05536 | + | 18.6365i | −0.274395 | + | 0.844500i | 0.714984 | + | 0.699141i | \(0.246434\pi\) |
−0.989379 | + | 0.145360i | \(0.953566\pi\) | |||||||
\(488\) | 12.7699 | + | 39.3018i | 0.578067 | + | 1.77911i | ||||
\(489\) | −15.1782 | + | 11.0276i | −0.686384 | + | 0.498687i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.86312 | − | 27.2779i | −0.399987 | − | 1.23103i | −0.925009 | − | 0.379945i | \(-0.875943\pi\) |
0.525022 | − | 0.851089i | \(-0.324057\pi\) | |||||||
\(492\) | 0.0787620 | − | 0.242405i | 0.00355087 | − | 0.0109284i | ||||
\(493\) | 11.5006 | + | 8.35569i | 0.517962 | + | 0.376321i | ||||
\(494\) | 9.79837 | 0.440850 | ||||||||
\(495\) | −0.397375 | − | 0.437832i | −0.0178607 | − | 0.0196791i | ||||
\(496\) | 5.53735 | 0.248634 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −12.6571 | + | 38.9545i | −0.567177 | + | 1.74559i | ||||
\(499\) | 8.63700 | + | 26.5819i | 0.386645 | + | 1.18997i | 0.935280 | + | 0.353909i | \(0.115148\pi\) |
−0.548635 | + | 0.836062i | \(0.684852\pi\) | |||||||
\(500\) | −0.558863 | + | 0.406037i | −0.0249931 | + | 0.0181585i | ||||
\(501\) | 8.27942 | − | 6.01535i | 0.369897 | − | 0.268746i | ||||
\(502\) | −3.17046 | − | 9.75767i | −0.141505 | − | 0.435506i | ||||
\(503\) | 2.50222 | − | 7.70104i | 0.111568 | − | 0.343373i | −0.879647 | − | 0.475626i | \(-0.842221\pi\) |
0.991216 | + | 0.132254i | \(0.0422214\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.0834428 | 0.00371316 | ||||||||
\(506\) | 0.952410 | + | 8.72906i | 0.0423398 | + | 0.388054i | ||||
\(507\) | −16.9833 | −0.754256 | ||||||||
\(508\) | 1.04538 | + | 0.759510i | 0.0463811 | + | 0.0336978i | ||||
\(509\) | −5.03702 | + | 15.5024i | −0.223262 | + | 0.687130i | 0.775201 | + | 0.631714i | \(0.217648\pi\) |
−0.998463 | + | 0.0554159i | \(0.982352\pi\) | |||||||
\(510\) | −1.78924 | − | 5.50670i | −0.0792287 | − | 0.243841i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −15.8195 | + | 11.4935i | −0.699129 | + | 0.507947i | ||||
\(513\) | 7.13919 | + | 21.9722i | 0.315203 | + | 0.970096i | ||||
\(514\) | −4.50908 | + | 13.8775i | −0.198887 | + | 0.612111i | ||||
\(515\) | −6.37274 | − | 4.63007i | −0.280816 | − | 0.204025i | ||||
\(516\) | 2.13187 | 0.0938505 | ||||||||
\(517\) | −19.3427 | + | 8.70384i | −0.850692 | + | 0.382795i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.75286 | + | 1.27352i | 0.0769419 | + | 0.0559015i | ||||
\(520\) | −0.618813 | + | 1.90451i | −0.0271368 | + | 0.0835184i | ||||
\(521\) | −2.37512 | − | 7.30987i | −0.104056 | − | 0.320251i | 0.885452 | − | 0.464731i | \(-0.153849\pi\) |
−0.989508 | + | 0.144480i | \(0.953849\pi\) | |||||||
\(522\) | −1.23259 | + | 0.895526i | −0.0539488 | + | 0.0391961i | ||||
\(523\) | 21.1339 | − | 15.3547i | 0.924121 | − | 0.671413i | −0.0204256 | − | 0.999791i | \(-0.506502\pi\) |
0.944546 | + | 0.328378i | \(0.106502\pi\) | |||||||
\(524\) | 0.451984 | + | 1.39106i | 0.0197450 | + | 0.0607689i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.8265 | + | 12.2252i | 0.733672 | + | 0.533044i | ||||
\(527\) | 6.76343 | 0.294619 | ||||||||
\(528\) | −11.4045 | + | 19.9350i | −0.496318 | + | 0.867561i | ||||
\(529\) | −19.7418 | −0.858338 | ||||||||
\(530\) | 7.31300 | + | 5.31320i | 0.317656 | + | 0.230791i | ||||
\(531\) | −1.01555 | + | 3.12554i | −0.0440712 | + | 0.135637i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.33276 | + | 0.968308i | −0.0577283 | + | 0.0419421i | ||||
\(534\) | 17.1258 | − | 12.4427i | 0.741108 | − | 0.538446i | ||||
\(535\) | 2.23210 | + | 6.86971i | 0.0965023 | + | 0.297004i | ||||
\(536\) | −3.91794 | + | 12.0582i | −0.169229 | + | 0.520834i | ||||
\(537\) | −23.2859 | − | 16.9182i | −1.00486 | − | 0.730073i | ||||
\(538\) | −26.9924 | −1.16372 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.386429 | 0.0166292 | ||||||||
\(541\) | 20.9355 | + | 15.2105i | 0.900086 | + | 0.653951i | 0.938488 | − | 0.345312i | \(-0.112227\pi\) |
−0.0384021 | + | 0.999262i | \(0.512227\pi\) | |||||||
\(542\) | 0.331137 | − | 1.01913i | 0.0142235 | − | 0.0437756i | ||||
\(543\) | 0.481889 | + | 1.48310i | 0.0206798 | + | 0.0636459i | ||||
\(544\) | 3.61199 | − | 2.62427i | 0.154863 | − | 0.112514i | ||||
\(545\) | 4.16671 | − | 3.02729i | 0.178482 | − | 0.129675i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.7726 | + | 36.2322i | −0.503359 | + | 1.54918i | 0.300154 | + | 0.953891i | \(0.402962\pi\) |
−0.803513 | + | 0.595288i | \(0.797038\pi\) | |||||||
\(548\) | 1.71501 | + | 1.24603i | 0.0732615 | + | 0.0532276i | ||||
\(549\) | −5.82122 | −0.248444 | ||||||||
\(550\) | 22.7739 | + | 4.74660i | 0.971083 | + | 0.202396i | ||||
\(551\) | −11.4814 | −0.489123 | ||||||||
\(552\) | 6.40696 | + | 4.65493i | 0.272698 | + | 0.198127i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.82786 | − | 21.0140i | −0.290088 | − | 0.892799i | ||||
\(555\) | −1.18661 | + | 0.862123i | −0.0503688 | + | 0.0365951i | ||||
\(556\) | 1.17236 | − | 0.851771i | 0.0497192 | − | 0.0361231i | ||||
\(557\) | 10.6741 | + | 32.8516i | 0.452277 | + | 1.39197i | 0.874303 | + | 0.485381i | \(0.161319\pi\) |
−0.422026 | + | 0.906584i | \(0.638681\pi\) | |||||||
\(558\) | −0.223999 | + | 0.689397i | −0.00948261 | + | 0.0291845i | ||||
\(559\) | −11.1476 | − | 8.09917i | −0.471491 | − | 0.342558i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.9297 | + | 24.3490i | −0.588113 | + | 1.02802i | ||||
\(562\) | 15.6883 | 0.661773 | ||||||||
\(563\) | 15.7612 | + | 11.4512i | 0.664256 | + | 0.482610i | 0.868098 | − | 0.496394i | \(-0.165343\pi\) |
−0.203842 | + | 0.979004i | \(0.565343\pi\) | |||||||
\(564\) | 0.483811 | − | 1.48902i | 0.0203721 | − | 0.0626990i | ||||
\(565\) | −0.255295 | − | 0.785717i | −0.0107403 | − | 0.0330553i | ||||
\(566\) | −10.8087 | + | 7.85300i | −0.454325 | + | 0.330086i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.16387 | + | 25.1258i | 0.342549 | + | 1.05426i | ||||
\(569\) | 5.29308 | − | 16.2904i | 0.221897 | − | 0.682930i | −0.776694 | − | 0.629878i | \(-0.783105\pi\) |
0.998592 | − | 0.0530524i | \(-0.0168950\pi\) | |||||||
\(570\) | 3.78332 | + | 2.74874i | 0.158466 | + | 0.115132i | ||||
\(571\) | −3.85581 | −0.161360 | −0.0806802 | − | 0.996740i | \(-0.525709\pi\) | ||||
−0.0806802 | + | 0.996740i | \(0.525709\pi\) | |||||||
\(572\) | −0.724095 | + | 0.325828i | −0.0302759 | + | 0.0136236i | ||||
\(573\) | −26.0323 | −1.08751 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.66745 | − | 8.20958i | 0.111240 | − | 0.342363i | ||||
\(576\) | −0.862437 | − | 2.65431i | −0.0359349 | − | 0.110596i | ||||
\(577\) | −7.91368 | + | 5.74963i | −0.329451 | + | 0.239360i | −0.740198 | − | 0.672389i | \(-0.765268\pi\) |
0.410747 | + | 0.911750i | \(0.365268\pi\) | |||||||
\(578\) | 12.2517 | − | 8.90135i | 0.509602 | − | 0.370247i | ||||
\(579\) | 6.07373 | + | 18.6930i | 0.252416 | + | 0.776855i | ||||
\(580\) | −0.0593443 | + | 0.182643i | −0.00246414 | + | 0.00758384i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.41628 | −0.265964 | ||||||||
\(583\) | −4.75010 | − | 43.5358i | −0.196729 | − | 1.80307i | ||||
\(584\) | 36.1178 | 1.49457 | ||||||||
\(585\) | −0.228214 | − | 0.165807i | −0.00943551 | − | 0.00685530i | ||||
\(586\) | 5.38863 | − | 16.5845i | 0.222602 | − | 0.685099i | ||||
\(587\) | 1.88467 | + | 5.80041i | 0.0777886 | + | 0.239409i | 0.982387 | − | 0.186855i | \(-0.0598295\pi\) |
−0.904599 | + | 0.426264i | \(0.859830\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.41932 | + | 3.21082i | −0.182095 | + | 0.132300i | ||||
\(590\) | 1.82010 | + | 5.60169i | 0.0749323 | + | 0.230618i | ||||
\(591\) | −1.15089 | + | 3.54209i | −0.0473414 | + | 0.145702i | ||||
\(592\) | −6.72462 | − | 4.88572i | −0.276380 | − | 0.200802i | ||||
\(593\) | −13.2330 | −0.543413 | −0.271706 | − | 0.962380i | \(-0.587588\pi\) | ||||
−0.271706 | + | 0.962380i | \(0.587588\pi\) | |||||||
\(594\) | −17.8903 | − | 19.7117i | −0.734046 | − | 0.808780i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.83150 | − | 1.33066i | −0.0750212 | − | 0.0545061i | ||||
\(597\) | −10.1399 | + | 31.2073i | −0.414997 | + | 1.27723i | ||||
\(598\) | 1.29454 | + | 3.98419i | 0.0529378 | + | 0.162926i | ||||
\(599\) | 4.79355 | − | 3.48271i | 0.195859 | − | 0.142300i | −0.485534 | − | 0.874218i | \(-0.661375\pi\) |
0.681393 | + | 0.731918i | \(0.261375\pi\) | |||||||
\(600\) | 16.9741 | − | 12.3324i | 0.692964 | − | 0.503468i | ||||
\(601\) | −3.93712 | − | 12.1172i | −0.160599 | − | 0.494272i | 0.838086 | − | 0.545538i | \(-0.183674\pi\) |
−0.998685 | + | 0.0512657i | \(0.983674\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.44491 | − | 1.04979i | −0.0588413 | − | 0.0427507i | ||||
\(604\) | −0.434590 | −0.0176832 | ||||||||
\(605\) | 2.60214 | + | 4.42576i | 0.105792 | + | 0.179933i | ||||
\(606\) | 0.424287 | 0.0172355 | ||||||||
\(607\) | 6.76452 | + | 4.91471i | 0.274563 | + | 0.199482i | 0.716543 | − | 0.697543i | \(-0.245724\pi\) |
−0.441979 | + | 0.897025i | \(0.645724\pi\) | |||||||
\(608\) | −1.11430 | + | 3.42946i | −0.0451908 | + | 0.139083i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.44044 | + | 6.13234i | −0.341743 | + | 0.248291i | ||||
\(611\) | −8.18675 | + | 5.94802i | −0.331201 | + | 0.240631i | ||||
\(612\) | 0.0933537 | + | 0.287313i | 0.00377360 | + | 0.0116139i | ||||
\(613\) | −2.06514 | + | 6.35585i | −0.0834102 | + | 0.256710i | −0.984060 | − | 0.177835i | \(-0.943091\pi\) |
0.900650 | + | 0.434545i | \(0.143091\pi\) | |||||||
\(614\) | −2.63513 | − | 1.91453i | −0.106345 | − | 0.0772643i | ||||
\(615\) | −0.786243 | −0.0317044 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.8669 | 0.477741 | 0.238871 | − | 0.971051i | \(-0.423223\pi\) | ||||
0.238871 | + | 0.971051i | \(0.423223\pi\) | |||||||
\(618\) | −32.4039 | − | 23.5428i | −1.30348 | − | 0.947031i | ||||
\(619\) | −6.37213 | + | 19.6114i | −0.256118 | + | 0.788249i | 0.737490 | + | 0.675358i | \(0.236011\pi\) |
−0.993607 | + | 0.112891i | \(0.963989\pi\) | |||||||
\(620\) | 0.0282346 | + | 0.0868973i | 0.00113393 | + | 0.00348988i | ||||
\(621\) | −7.99107 | + | 5.80585i | −0.320670 | + | 0.232981i | ||||
\(622\) | 25.4084 | − | 18.4603i | 1.01878 | − | 0.740189i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.38593 | + | 10.4208i | −0.135546 | + | 0.417167i | ||||
\(625\) | −17.6203 | − | 12.8019i | −0.704812 | − | 0.512076i | ||||
\(626\) | −46.2824 | −1.84982 | ||||||||
\(627\) | −2.45743 | − | 22.5229i | −0.0981402 | − | 0.899478i | ||||
\(628\) | 2.85694 | 0.114004 | ||||||||
\(629\) | −8.21358 | − | 5.96752i | −0.327497 | − | 0.237941i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.78342 | − | 14.7219i | −0.190425 | − | 0.586068i | 0.809575 | − | 0.587017i | \(-0.199698\pi\) |
−1.00000 | 0.000949112i | \(0.999698\pi\) | ||||||||
\(632\) | −7.85847 | + | 5.70952i | −0.312593 | + | 0.227112i | ||||
\(633\) | −7.02326 | + | 5.10270i | −0.279150 | + | 0.202814i | ||||
\(634\) | 5.98314 | + | 18.4142i | 0.237621 | + | 0.731321i | ||||
\(635\) | 1.23174 | − | 3.79091i | 0.0488801 | − | 0.150438i | ||||
\(636\) | 2.61523 | + | 1.90008i | 0.103701 | + | 0.0753430i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12.0640 | − | 5.42857i | 0.477619 | − | 0.214919i | ||||
\(639\) | −3.72153 | −0.147222 | ||||||||
\(640\) | −4.69166 | − | 3.40869i | −0.185454 | − | 0.134740i | ||||
\(641\) | −7.28615 | + | 22.4245i | −0.287786 | + | 0.885713i | 0.697764 | + | 0.716327i | \(0.254178\pi\) |
−0.985550 | + | 0.169385i | \(0.945822\pi\) | |||||||
\(642\) | 11.3497 | + | 34.9309i | 0.447938 | + | 1.37861i | ||||
\(643\) | 23.2031 | − | 16.8581i | 0.915042 | − | 0.664817i | −0.0272428 | − | 0.999629i | \(-0.508673\pi\) |
0.942285 | + | 0.334812i | \(0.108673\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.03220 | − | 6.25446i | −0.0800177 | − | 0.246269i | ||||
\(646\) | −10.0028 | + | 30.7855i | −0.393556 | + | 1.21124i | ||||
\(647\) | 4.39104 | + | 3.19028i | 0.172630 | + | 0.125423i | 0.670745 | − | 0.741688i | \(-0.265974\pi\) |
−0.498115 | + | 0.867111i | \(0.665974\pi\) | |||||||
\(648\) | −20.9011 | −0.821074 | ||||||||
\(649\) | 14.1700 | − | 24.7691i | 0.556221 | − | 0.972271i | ||||
\(650\) | 11.0986 | 0.435323 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.542130 | − | 1.66851i | 0.0212315 | − | 0.0653437i | ||||
\(653\) | −3.81392 | − | 11.7380i | −0.149250 | − | 0.459344i | 0.848283 | − | 0.529543i | \(-0.177637\pi\) |
−0.997533 | + | 0.0701988i | \(0.977637\pi\) | |||||||
\(654\) | 21.1868 | − | 15.3931i | 0.828468 | − | 0.601917i | ||||
\(655\) | 3.65023 | − | 2.65205i | 0.142626 | − | 0.103624i | ||||
\(656\) | −1.37689 | − | 4.23762i | −0.0537584 | − | 0.165451i | ||||
\(657\) | −1.57221 | + | 4.83878i | −0.0613379 | + | 0.188779i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.2115 | 0.631512 | 0.315756 | − | 0.948840i | \(-0.397742\pi\) | ||||
0.315756 | + | 0.948840i | \(0.397742\pi\) | |||||||
\(660\) | −0.370991 | − | 0.0773229i | −0.0144408 | − | 0.00300979i | ||||
\(661\) | −43.7050 | −1.69993 | −0.849964 | − | 0.526840i | \(-0.823377\pi\) | ||||
−0.849964 | + | 0.526840i | \(0.823377\pi\) | |||||||
\(662\) | 11.2450 | + | 8.16994i | 0.437048 | + | 0.317534i | ||||
\(663\) | −4.13564 | + | 12.7282i | −0.160615 | + | 0.494322i | ||||
\(664\) | 14.4614 | + | 44.5078i | 0.561213 | + | 1.72724i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.880296 | − | 0.639573i | 0.0341108 | − | 0.0247829i | ||||
\(667\) | −1.51690 | − | 4.66854i | −0.0587346 | − | 0.180766i | ||||
\(668\) | −0.295721 | + | 0.910136i | −0.0114418 | + | 0.0352142i | ||||
\(669\) | −33.2792 | − | 24.1787i | −1.28665 | − | 0.934803i | ||||
\(670\) | −3.20093 | −0.123663 | ||||||||
\(671\) | 49.4825 | + | 10.3133i | 1.91025 | + | 0.398140i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.74166 | + | 3.44502i | 0.182778 | + | 0.132796i | 0.675412 | − | 0.737441i | \(-0.263966\pi\) |
−0.492634 | + | 0.870237i | \(0.663966\pi\) | |||||||
\(674\) | 8.70280 | − | 26.7845i | 0.335219 | − | 1.03170i | ||||
\(675\) | 8.08655 | + | 24.8879i | 0.311252 | + | 0.957934i | ||||
\(676\) | 1.28481 | − | 0.933467i | 0.0494157 | − | 0.0359026i | ||||
\(677\) | −16.6074 | + | 12.0660i | −0.638275 | + | 0.463734i | −0.859257 | − | 0.511544i | \(-0.829074\pi\) |
0.220982 | + | 0.975278i | \(0.429074\pi\) | |||||||
\(678\) | −1.29811 | − | 3.99519i | −0.0498538 | − | 0.153434i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5.35206 | − | 3.88850i | −0.205242 | − | 0.149117i | ||||
\(681\) | 35.1271 | 1.34607 | ||||||||
\(682\) | 3.12546 | − | 5.46327i | 0.119680 | − | 0.209200i | ||||
\(683\) | 38.7055 | 1.48103 | 0.740513 | − | 0.672042i | \(-0.234583\pi\) | ||||
0.740513 | + | 0.672042i | \(0.234583\pi\) | |||||||
\(684\) | −0.197396 | − | 0.143416i | −0.00754761 | − | 0.00548366i | ||||
\(685\) | 2.02075 | − | 6.21923i | 0.0772090 | − | 0.237625i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.8750 | − | 19.5258i | 1.02535 | − | 0.744957i | ||||
\(688\) | 30.1509 | − | 21.9059i | 1.14949 | − | 0.835156i | ||||
\(689\) | −6.45647 | − | 19.8710i | −0.245972 | − | 0.757024i | ||||
\(690\) | −0.617843 | + | 1.90153i | −0.0235209 | + | 0.0723898i | ||||
\(691\) | −18.7126 | − | 13.5955i | −0.711860 | − | 0.517197i | 0.171913 | − | 0.985112i | \(-0.445005\pi\) |
−0.883773 | + | 0.467916i | \(0.845005\pi\) | |||||||
\(692\) | −0.202603 | −0.00770182 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.47105 | −0.169719 | ||||||||
\(695\) | −3.61646 | − | 2.62751i | −0.137180 | − | 0.0996673i | ||||
\(696\) | 3.68698 | − | 11.3474i | 0.139755 | − | 0.430121i | ||||
\(697\) | −1.68176 | − | 5.17592i | −0.0637011 | − | 0.196052i | ||||
\(698\) | −23.0156 | + | 16.7218i | −0.871155 | + | 0.632931i | ||||
\(699\) | −0.908531 | + | 0.660086i | −0.0343638 | + | 0.0249668i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.9734 | − | 33.7727i | 0.414460 | − | 1.27558i | −0.498273 | − | 0.867020i | \(-0.666032\pi\) |
0.912733 | − | 0.408557i | \(-0.133968\pi\) | |||||||
\(702\) | −10.2744 | − | 7.46482i | −0.387784 | − | 0.281742i | ||||
\(703\) | 8.19985 | 0.309263 | ||||||||
\(704\) | 2.62847 | + | 24.0906i | 0.0990643 | + | 0.907947i | ||||
\(705\) | −4.82965 | −0.181895 | ||||||||
\(706\) | 12.7662 | + | 9.27518i | 0.480462 | + | 0.349076i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.650893 | + | 2.00324i | 0.0244621 | + | 0.0752865i | ||||
\(709\) | −35.4386 | + | 25.7476i | −1.33092 | + | 0.966972i | −0.331197 | + | 0.943562i | \(0.607453\pi\) |
−0.999726 | + | 0.0234107i | \(0.992547\pi\) | |||||||
\(710\) | −5.39601 | + | 3.92043i | −0.202509 | + | 0.147131i | ||||
\(711\) | −0.422835 | − | 1.30135i | −0.0158576 | − | 0.0488045i | ||||
\(712\) | 7.47403 | − | 23.0027i | 0.280101 | − | 0.862063i | ||||
\(713\) | −1.88945 | − | 1.37277i | −0.0707604 | − | 0.0514105i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.64615 | + | 1.81375i | 0.0615625 | + | 0.0678303i | ||||
\(716\) | 2.69149 | 0.100586 | ||||||||
\(717\) | −0.453654 | − | 0.329599i | −0.0169420 | − | 0.0123091i | ||||
\(718\) | −0.275222 | + | 0.847046i | −0.0102712 | + | 0.0316115i | ||||
\(719\) | −4.90115 | − | 15.0842i | −0.182782 | − | 0.562546i | 0.817121 | − | 0.576466i | \(-0.195569\pi\) |
−0.999903 | + | 0.0139205i | \(0.995569\pi\) | |||||||
\(720\) | 0.617255 | − | 0.448462i | 0.0230037 | − | 0.0167132i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.532741 | + | 1.63961i | 0.0198266 | + | 0.0610199i | ||||
\(723\) | 5.21858 | − | 16.0611i | 0.194081 | − | 0.597320i | ||||
\(724\) | −0.117972 | − | 0.0857118i | −0.00438440 | − | 0.00318545i | ||||
\(725\) | −13.0049 | −0.482992 | ||||||||
\(726\) | 13.2313 | + | 22.5039i | 0.491059 | + | 0.835199i | ||||
\(727\) | −13.7719 | −0.510770 | −0.255385 | − | 0.966839i | \(-0.582202\pi\) | ||||
−0.255385 | + | 0.966839i | \(0.582202\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.11803 | − | 28.0624i | 0.337705 | − | 1.03935i | ||||
\(730\) | 2.81777 | + | 8.67220i | 0.104290 | + | 0.320972i | ||||
\(731\) | 36.8269 | − | 26.7563i | 1.36209 | − | 0.989619i | ||||
\(732\) | −3.01842 | + | 2.19301i | −0.111564 | + | 0.0810560i | ||||
\(733\) | 6.04675 | + | 18.6100i | 0.223342 | + | 0.687376i | 0.998456 | + | 0.0555542i | \(0.0176926\pi\) |
−0.775114 | + | 0.631822i | \(0.782307\pi\) | |||||||
\(734\) | 12.5380 | − | 38.5881i | 0.462788 | − | 1.42431i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.54170 | −0.0568278 | ||||||||
\(737\) | 10.4224 | + | 11.4835i | 0.383914 | + | 0.423000i | ||||
\(738\) | 0.583280 | 0.0214708 | ||||||||
\(739\) | 9.02392 | + | 6.55626i | 0.331950 | + | 0.241176i | 0.741258 | − | 0.671220i | \(-0.234230\pi\) |
−0.409307 | + | 0.912397i | \(0.634230\pi\) | |||||||
\(740\) | 0.0423829 | − | 0.130441i | 0.00155803 | − | 0.00479511i | ||||
\(741\) | −3.34021 | − | 10.2801i | −0.122706 | − | 0.377649i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.7102 | + | 12.1407i | −0.613038 | + | 0.445398i | −0.850483 | − | 0.526003i | \(-0.823690\pi\) |
0.237445 | + | 0.971401i | \(0.423690\pi\) | |||||||
\(744\) | −1.75418 | − | 5.39881i | −0.0643113 | − | 0.197930i | ||||
\(745\) | −2.15801 | + | 6.64168i | −0.0790635 | + | 0.243332i | ||||
\(746\) | −34.9472 | − | 25.3907i | −1.27951 | − | 0.929618i | ||||
\(747\) | −6.59231 | −0.241200 | ||||||||
\(748\) | −0.284517 | − | 2.60766i | −0.0104030 | − | 0.0953455i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 8.76593 | + | 6.36882i | 0.320087 | + | 0.232557i | ||||
\(751\) | 8.21957 | − | 25.2972i | 0.299936 | − | 0.923109i | −0.681582 | − | 0.731742i | \(-0.738708\pi\) |
0.981518 | − | 0.191367i | \(-0.0612922\pi\) | |||||||
\(752\) | −8.45780 | − | 26.0304i | −0.308424 | − | 0.949233i | ||||
\(753\) | −9.15661 | + | 6.65266i | −0.333685 | + | 0.242437i | ||||
\(754\) | 5.10606 | − | 3.70977i | 0.185952 | − | 0.135102i | ||||
\(755\) | 0.414271 | + | 1.27499i | 0.0150769 | + | 0.0464018i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.0702 | − | 12.4022i | −0.620427 | − | 0.450767i | 0.232644 | − | 0.972562i | \(-0.425262\pi\) |
−0.853071 | + | 0.521796i | \(0.825262\pi\) | |||||||
\(758\) | −37.1723 | −1.35016 | ||||||||
\(759\) | 8.83354 | − | 3.97492i | 0.320637 | − | 0.144280i | ||||
\(760\) | 5.34311 | 0.193815 | ||||||||
\(761\) | −6.47006 | − | 4.70077i | −0.234539 | − | 0.170403i | 0.464308 | − | 0.885674i | \(-0.346303\pi\) |
−0.698847 | + | 0.715271i | \(0.746303\pi\) | |||||||
\(762\) | 6.26311 | − | 19.2759i | 0.226889 | − | 0.698292i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.96937 | − | 1.43083i | 0.0712494 | − | 0.0517657i | ||||
\(765\) | 0.753927 | − | 0.547760i | 0.0272583 | − | 0.0198043i | ||||
\(766\) | −14.4731 | − | 44.5436i | −0.522935 | − | 1.60943i | ||||
\(767\) | 4.20698 | − | 12.9477i | 0.151905 | − | 0.467516i | ||||
\(768\) | −4.72685 | − | 3.43426i | −0.170566 | − | 0.123923i | ||||
\(769\) | 52.0476 | 1.87689 | 0.938443 | − | 0.345435i | \(-0.112269\pi\) | ||||
0.938443 | + | 0.345435i | \(0.112269\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.0969 | 0.579716 | ||||||||
\(772\) | −1.48692 | − | 1.08031i | −0.0535155 | − | 0.0388813i | ||||
\(773\) | 0.488554 | − | 1.50361i | 0.0175721 | − | 0.0540812i | −0.941886 | − | 0.335933i | \(-0.890949\pi\) |
0.959458 | + | 0.281851i | \(0.0909485\pi\) | |||||||
\(774\) | 1.50760 | + | 4.63992i | 0.0541896 | + | 0.166778i | ||||
\(775\) | −5.00575 | + | 3.63689i | −0.179812 | + | 0.130641i | ||||
\(776\) | −5.93089 | + | 4.30904i | −0.212906 | + | 0.154686i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.04587 | + | 24.7626i | −0.288458 | + | 0.887784i | ||||
\(779\) | 3.55606 | + | 2.58363i | 0.127409 | + | 0.0925681i | ||||
\(780\) | −0.180798 | −0.00647361 | ||||||||
\(781\) | 31.6344 | + | 6.59334i | 1.13197 | + | 0.235928i | ||||
\(782\) | −13.8395 | −0.494899 | ||||||||
\(783\) | 12.0392 | + | 8.74702i | 0.430247 | + | 0.312593i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.72336 | − | 8.38164i | −0.0972009 | − | 0.299154i | ||||
\(786\) | 18.5606 | − | 13.4850i | 0.662034 | − | 0.480996i | ||||
\(787\) | 18.9235 | − | 13.7487i | 0.674549 | − | 0.490089i | −0.196996 | − | 0.980404i | \(-0.563118\pi\) |
0.871545 | + | 0.490316i | \(0.163118\pi\) | |||||||
\(788\) | −0.107620 | − | 0.331220i | −0.00383380 | − | 0.0117992i | ||||
\(789\) | 7.09017 | − | 21.8213i | 0.252417 | − | 0.776859i | ||||
\(790\) | −1.98399 | − | 1.44145i | −0.0705872 | − | 0.0512846i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.36282 | − | 0.700889i | −0.119493 | − | 0.0249050i | ||||
\(793\) | 24.1147 | 0.856339 | ||||||||
\(794\) | 15.7875 | + | 11.4703i | 0.560276 | + | 0.407064i | ||||
\(795\) | 3.08146 | − | 9.48377i | 0.109288 | − | 0.336355i | ||||
\(796\) | −0.948177 | − | 2.91819i | −0.0336072 | − | 0.103432i | ||||
\(797\) | −37.3376 | + | 27.1274i | −1.32257 | + | 0.960900i | −0.322669 | + | 0.946512i | \(0.604580\pi\) |
−0.999896 | + | 0.0143887i | \(0.995420\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.3305 | − | 31.7941i | −0.365468 | − | 1.12479i | ||||
\(800\) | −1.26217 | + | 3.88455i | −0.0446243 | + | 0.137339i | ||||
\(801\) | 2.75638 | + | 2.00262i | 0.0973918 | + | 0.0707593i | ||||
\(802\) | 5.11834 | 0.180735 | ||||||||
\(803\) | 21.9371 | − | 38.3460i | 0.774145 | − | 1.35320i | ||||
\(804\) | −1.14470 | −0.0403704 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.927927 | − | 2.85587i | 0.0326848 | − | 0.100594i | ||||
\(807\) | 9.20154 | + | 28.3194i | 0.323910 | + | 0.996891i | ||||
\(808\) | 0.392189 | − | 0.284942i | 0.0137972 | − | 0.0100242i | ||||
\(809\) | −27.3044 | + | 19.8378i | −0.959972 | + | 0.697461i | −0.953144 | − | 0.302516i | \(-0.902173\pi\) |
−0.00682787 | + | 0.999977i | \(0.502173\pi\) | |||||||
\(810\) | −1.63062 | − | 5.01854i | −0.0572943 | − | 0.176334i | ||||
\(811\) | 9.50690 | − | 29.2592i | 0.333833 | − | 1.02743i | −0.633462 | − | 0.773774i | \(-0.718367\pi\) |
0.967294 | − | 0.253657i | \(-0.0816334\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.18212 | −0.0414588 | ||||||||
\(814\) | −8.61596 | + | 3.87701i | −0.301989 | + | 0.135889i | ||||
\(815\) | −5.41182 | −0.189568 | ||||||||
\(816\) | −29.2846 | − | 21.2765i | −1.02517 | − | 0.744827i | ||||
\(817\) | −11.3611 | + | 34.9659i | −0.397475 | + | 1.22330i | ||||
\(818\) | −13.4276 | − | 41.3259i | −0.469485 | − | 1.44493i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0594801 | − | 0.0432148i | 0.00207714 | − | 0.00150913i | ||||
\(821\) | 3.73242 | + | 11.4872i | 0.130262 | + | 0.400906i | 0.994823 | − | 0.101622i | \(-0.0324033\pi\) |
−0.864561 | + | 0.502528i | \(0.832403\pi\) | |||||||
\(822\) | 10.2750 | − | 31.6233i | 0.358383 | − | 1.10299i | ||||
\(823\) | 20.0787 | + | 14.5880i | 0.699900 | + | 0.508507i | 0.879900 | − | 0.475159i | \(-0.157610\pi\) |
−0.179999 | + | 0.983667i | \(0.557610\pi\) | |||||||
\(824\) | −45.7634 | −1.59424 | ||||||||
\(825\) | −2.78352 | − | 25.5116i | −0.0969098 | − | 0.888201i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.18529 | − | 3.04079i | −0.145537 | − | 0.105739i | 0.512634 | − | 0.858607i | \(-0.328670\pi\) |
−0.658171 | + | 0.752868i | \(0.728670\pi\) | |||||||
\(828\) | 0.0322361 | − | 0.0992125i | 0.00112028 | − | 0.00344787i | ||||
\(829\) | −9.75057 | − | 30.0092i | −0.338651 | − | 1.04226i | −0.964895 | − | 0.262635i | \(-0.915409\pi\) |
0.626244 | − | 0.779627i | \(-0.284591\pi\) | |||||||
\(830\) | −9.55847 | + | 6.94464i | −0.331779 | + | 0.241052i | ||||
\(831\) | −19.7196 | + | 14.3271i | −0.684064 | + | 0.497001i | ||||
\(832\) | 3.57270 | + | 10.9956i | 0.123861 | + | 0.381205i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −18.3889 | − | 13.3603i | −0.636755 | − | 0.462629i | ||||
\(835\) | 2.95204 | 0.102160 | ||||||||
\(836\) | 1.42385 | + | 1.56881i | 0.0492449 | + | 0.0542585i | ||||
\(837\) | 7.08018 | 0.244727 | ||||||||
\(838\) | 13.8184 | + | 10.0396i | 0.477348 | + | 0.346813i | ||||
\(839\) | 1.80355 | − | 5.55077i | 0.0622656 | − | 0.191634i | −0.915085 | − | 0.403262i | \(-0.867876\pi\) |
0.977350 | + | 0.211628i | \(0.0678765\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.4784 | − | 12.6988i | 0.602703 | − | 0.437889i | ||||
\(842\) | 23.5956 | − | 17.1432i | 0.813157 | − | 0.590793i | ||||
\(843\) | −5.34806 | − | 16.4596i | −0.184197 | − | 0.566900i | ||||
\(844\) | 0.250854 | − | 0.772050i | 0.00863475 | − | 0.0265750i | ||||
\(845\) | −3.96333 | − | 2.87953i | −0.136343 | − | 0.0990588i | ||||
\(846\) | 3.58291 | 0.123183 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 56.5112 | 1.94060 | ||||||||
\(849\) | 11.9237 | + | 8.66308i | 0.409221 | + | 0.297316i | ||||
\(850\) | −11.3302 | + | 34.8707i | −0.388622 | + | 1.19606i | ||||
\(851\) | 1.08335 | + | 3.33420i | 0.0371367 | + | 0.114295i | ||||
\(852\) | −1.92969 | + | 1.40200i | −0.0661101 | + | 0.0480318i | ||||
\(853\) | −16.4604 | + | 11.9592i | −0.563593 | + | 0.409475i | −0.832772 | − | 0.553616i | \(-0.813248\pi\) |
0.269179 | + | 0.963090i | \(0.413248\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.232586 | + | 0.715828i | −0.00795429 | + | 0.0244808i | ||||
\(856\) | 33.9499 | + | 24.6661i | 1.16039 | + | 0.843069i | ||||
\(857\) | 15.1087 | 0.516104 | 0.258052 | − | 0.966131i | \(-0.416919\pi\) | ||||
0.258052 | + | 0.966131i | \(0.416919\pi\) | |||||||
\(858\) | 8.37029 | + | 9.22247i | 0.285757 | + | 0.314850i | ||||
\(859\) | 33.9641 | 1.15884 | 0.579420 | − | 0.815029i | \(-0.303279\pi\) | ||||
0.579420 | + | 0.815029i | \(0.303279\pi\) | |||||||
\(860\) | 0.497507 | + | 0.361460i | 0.0169648 | + | 0.0123257i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.7090 | − | 42.1920i | −0.466931 | − | 1.43707i | ||||
\(863\) | 2.24691 | − | 1.63248i | 0.0764859 | − | 0.0555702i | −0.548885 | − | 0.835898i | \(-0.684948\pi\) |
0.625371 | + | 0.780327i | \(0.284948\pi\) | |||||||
\(864\) | 3.78115 | − | 2.74717i | 0.128637 | − | 0.0934606i | ||||
\(865\) | 0.193130 | + | 0.594395i | 0.00656663 | + | 0.0202100i | ||||
\(866\) | −2.58676 | + | 7.96122i | −0.0879016 | + | 0.270533i | ||||
\(867\) | −13.5155 | − | 9.81958i | −0.459010 | − | 0.333490i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.28869 | + | 11.8111i | 0.0437156 | + | 0.400664i | ||||
\(870\) | 3.01224 | 0.102125 | ||||||||
\(871\) | 5.98562 | + | 4.34881i | 0.202815 | + | 0.147354i | ||||
\(872\) | 9.24629 | − | 28.4571i | 0.313119 | − | 0.963681i | ||||
\(873\) | −0.319119 | − | 0.982147i | −0.0108005 | − | 0.0332406i | ||||
\(874\) | 9.04292 | − | 6.57006i | 0.305881 | − | 0.222236i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.00767 | + | 3.10130i | 0.0340461 | + | 0.104783i | ||||
\(877\) | 15.3514 | − | 47.2469i | 0.518381 | − | 1.59541i | −0.258662 | − | 0.965968i | \(-0.583282\pi\) |
0.777044 | − | 0.629446i | \(-0.216718\pi\) | |||||||
\(878\) | −8.12680 | − | 5.90446i | −0.274266 | − | 0.199266i | ||||
\(879\) | −19.2368 | −0.648841 | ||||||||
\(880\) | −6.04142 | + | 2.71852i | −0.203656 | + | 0.0916412i | ||||
\(881\) | 27.3064 | 0.919975 | 0.459988 | − | 0.887925i | \(-0.347854\pi\) | ||||
0.459988 | + | 0.887925i | \(0.347854\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.50388 | + | 16.9392i | −0.185220 | + | 0.570049i | −0.999952 | − | 0.00978852i | \(-0.996884\pi\) |
0.814732 | + | 0.579838i | \(0.196884\pi\) | |||||||
\(884\) | −0.386723 | − | 1.19021i | −0.0130069 | − | 0.0400312i | ||||
\(885\) | 5.25663 | − | 3.81916i | 0.176700 | − | 0.128380i | ||||
\(886\) | 0.119486 | − | 0.0868116i | 0.00401421 | − | 0.00291649i | ||||
\(887\) | 5.09040 | + | 15.6666i | 0.170919 | + | 0.526034i | 0.999424 | − | 0.0339479i | \(-0.0108080\pi\) |
−0.828505 | + | 0.559982i | \(0.810808\pi\) | |||||||
\(888\) | −2.63319 | + | 8.10413i | −0.0883641 | + | 0.271957i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.10625 | 0.204682 | ||||||||
\(891\) | −12.6949 | + | 22.1906i | −0.425294 | + | 0.743412i | ||||
\(892\) | 3.84656 | 0.128792 | ||||||||
\(893\) | 21.8438 | + | 15.8705i | 0.730975 | + | 0.531084i | ||||
\(894\) | −10.9730 | + | 33.7714i | −0.366992 | + | 1.12948i | ||||
\(895\) | −2.56565 | − | 7.89625i | −0.0857601 | − | 0.263942i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.73877 | − | 2.71638i | 0.124834 | − | 0.0906971i | ||||
\(898\) | 13.9621 | + | 42.9709i | 0.465921 | + | 1.43396i | ||||
\(899\) | −1.08731 | + | 3.34640i | −0.0362639 | + | 0.111609i | ||||
\(900\) | −0.223590 | − | 0.162447i | −0.00745299 | − | 0.00541491i | ||||
\(901\) | 69.0238 | 2.29952 | ||||||||
\(902\) | −4.95809 | − | 1.03338i | −0.165086 | − | 0.0344078i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.88299 | − | 2.82116i | −0.129146 | − | 0.0938304i | ||||
\(905\) | −0.139004 | + | 0.427809i | −0.00462064 | + | 0.0142209i | ||||
\(906\) | 2.10647 | + | 6.48305i | 0.0699828 | + | 0.215385i | ||||
\(907\) | −23.0470 | + | 16.7446i | −0.765264 | + | 0.555997i | −0.900520 | − | 0.434814i | \(-0.856814\pi\) |
0.135257 | + | 0.990811i | \(0.456814\pi\) | |||||||
\(908\) | −2.65741 | + | 1.93072i | −0.0881891 | + | 0.0640731i | ||||
\(909\) | 0.0211022 | + | 0.0649460i | 0.000699917 | + | 0.00215412i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.08955 | + | 6.60394i | 0.301150 | + | 0.218798i | 0.728090 | − | 0.685482i | \(-0.240408\pi\) |
−0.426940 | + | 0.904280i | \(0.640408\pi\) | |||||||
\(912\) | 29.2356 | 0.968088 | ||||||||
\(913\) | 56.0371 | + | 11.6794i | 1.85456 | + | 0.386532i | ||||
\(914\) | −33.9337 | −1.12243 | ||||||||
\(915\) | 9.31112 | + | 6.76492i | 0.307816 | + | 0.223641i | ||||
\(916\) | −0.959910 | + | 2.95430i | −0.0317163 | + | 0.0976128i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 33.9426 | − | 24.6607i | 1.12027 | − | 0.813925i | ||||
\(919\) | −0.631403 | + | 0.458741i | −0.0208281 | + | 0.0151325i | −0.598151 | − | 0.801384i | \(-0.704098\pi\) |
0.577323 | + | 0.816516i | \(0.304098\pi\) | |||||||
\(920\) | 0.705922 | + | 2.17260i | 0.0232735 | + | 0.0716286i | ||||
\(921\) | −1.11036 | + | 3.41734i | −0.0365876 | + | 0.112605i | ||||
\(922\) | 3.29687 | + | 2.39532i | 0.108577 | + | 0.0788856i | ||||
\(923\) | 15.4167 | 0.507446 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.28795 | 0.305386 | ||||||||
\(926\) | −30.9646 | − | 22.4971i | −1.01756 | − | 0.739301i | ||||
\(927\) | 1.99209 | − | 6.13101i | 0.0654287 | − | 0.201369i | ||||
\(928\) | 0.717755 | + | 2.20902i | 0.0235615 | + | 0.0725148i | ||||
\(929\) | 21.5169 | − | 15.6329i | 0.705946 | − | 0.512899i | −0.175918 | − | 0.984405i | \(-0.556289\pi\) |
0.881863 | + | 0.471505i | \(0.156289\pi\) | |||||||
\(930\) | 1.15945 | − | 0.842387i | 0.0380198 | − | 0.0276230i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.0324505 | − | 0.0998725i | 0.00106295 | − | 0.00327143i | ||||
\(933\) | −28.0294 | − | 20.3646i | −0.917642 | − | 0.666706i | ||||
\(934\) | −3.89900 | −0.127579 | ||||||||
\(935\) | −7.37911 | + | 3.32045i | −0.241323 | + | 0.108590i | ||||
\(936\) | −1.63883 | −0.0535669 | ||||||||
\(937\) | 33.9542 | + | 24.6691i | 1.10923 | + | 0.805906i | 0.982543 | − | 0.186036i | \(-0.0595642\pi\) |
0.126691 | + | 0.991942i | \(0.459564\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.7774 | + | 48.5578i | 0.514875 | + | 1.58462i | ||||
\(940\) | 0.365368 | − | 0.265456i | 0.0119170 | − | 0.00865821i | ||||
\(941\) | −39.6685 | + | 28.8209i | −1.29316 | + | 0.939533i | −0.999864 | − | 0.0164899i | \(-0.994751\pi\) |
−0.293292 | + | 0.956023i | \(0.594751\pi\) | |||||||
\(942\) | −13.8477 | − | 42.6187i | −0.451181 | − | 1.38859i | ||||
\(943\) | −0.580730 | + | 1.78730i | −0.0189112 | + | 0.0582026i | ||||
\(944\) | 29.7897 | + | 21.6435i | 0.969574 | + | 0.704437i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.59475 | − | 42.1120i | −0.149388 | − | 1.36918i | ||||
\(947\) | −27.2953 | −0.886978 | −0.443489 | − | 0.896280i | \(-0.646259\pi\) | ||||
−0.443489 | + | 0.896280i | \(0.646259\pi\) | |||||||
\(948\) | −0.709503 | − | 0.515484i | −0.0230436 | − | 0.0167422i | ||||
\(949\) | 6.51299 | − | 20.0449i | 0.211421 | − | 0.650686i | ||||
\(950\) | −9.15097 | − | 28.1638i | −0.296897 | − | 0.913754i | ||||
\(951\) | 17.2799 | − | 12.5546i | 0.560339 | − | 0.407110i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.10023 | + | 18.7746i | 0.197606 | + | 0.608169i | 0.999936 | + | 0.0112883i | \(0.00359326\pi\) |
−0.802330 | + | 0.596880i | \(0.796407\pi\) | |||||||
\(954\) | −2.28601 | + | 7.03561i | −0.0740122 | + | 0.227786i | ||||
\(955\) | −6.07505 | − | 4.41378i | −0.196584 | − | 0.142827i | ||||
\(956\) | 0.0524354 | 0.00169588 | ||||||||
\(957\) | −9.80801 | − | 10.8066i | −0.317048 | − | 0.349327i | ||||
\(958\) | −12.1478 | −0.392478 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.70513 | + | 5.24785i | −0.0550329 | + | 0.169374i | ||||
\(961\) | −9.06221 | − | 27.8906i | −0.292329 | − | 0.899697i | ||||
\(962\) | −3.64668 | + | 2.64947i | −0.117574 | + | 0.0854222i | ||||
\(963\) | −4.78241 | + | 3.47463i | −0.154111 | + | 0.111968i | ||||
\(964\) | 0.487989 | + | 1.50188i | 0.0157171 | + | 0.0483721i | ||||
\(965\) | −1.75200 | + | 5.39211i | −0.0563990 | + | 0.173578i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.6734 | −0.407551 | −0.203775 | − | 0.979018i | \(-0.565321\pi\) | ||||
−0.203775 | + | 0.979018i | \(0.565321\pi\) | |||||||
\(968\) | 27.3435 | + | 11.9156i | 0.878853 | + | 0.382983i | ||||
\(969\) | 35.7089 | 1.14714 | ||||||||
\(970\) | −1.49734 | − | 1.08788i | −0.0480768 | − | 0.0349298i | ||||
\(971\) | −5.16170 | + | 15.8861i | −0.165647 | + | 0.509809i | −0.999083 | − | 0.0428065i | \(-0.986370\pi\) |
0.833436 | + | 0.552615i | \(0.186370\pi\) | |||||||
\(972\) | 0.184414 | + | 0.567569i | 0.00591509 | + | 0.0182048i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −23.2523 | + | 16.8938i | −0.745052 | + | 0.541312i | ||||
\(975\) | −3.78345 | − | 11.6443i | −0.121167 | − | 0.372914i | ||||
\(976\) | −20.1552 | + | 62.0312i | −0.645151 | + | 1.98557i | ||||
\(977\) | −22.1227 | − | 16.0731i | −0.707769 | − | 0.514224i | 0.174684 | − | 0.984625i | \(-0.444110\pi\) |
−0.882453 | + | 0.470400i | \(0.844110\pi\) | |||||||
\(978\) | −27.5178 | −0.879924 | ||||||||
\(979\) | −19.8822 | − | 21.9064i | −0.635439 | − | 0.700133i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.40997 | + | 2.47749i | 0.108872 | + | 0.0791001i | ||||
\(982\) | 12.9998 | − | 40.0093i | 0.414841 | − | 1.27675i | ||||
\(983\) | 16.9979 | + | 52.3143i | 0.542150 | + | 1.66857i | 0.727671 | + | 0.685926i | \(0.240603\pi\) |
−0.185521 | + | 0.982640i | \(0.559397\pi\) | |||||||
\(984\) | −3.69542 | + | 2.68488i | −0.117806 | + | 0.0855908i | ||||
\(985\) | −0.869141 | + | 0.631468i | −0.0276931 | + | 0.0201202i | ||||
\(986\) | 6.44313 | + | 19.8299i | 0.205191 | + | 0.631513i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.817723 | + | 0.594110i | 0.0260152 | + | 0.0189012i | ||||
\(989\) | −15.7188 | −0.499828 | ||||||||
\(990\) | −0.0940645 | − | 0.862123i | −0.00298957 | − | 0.0274001i | ||||
\(991\) | 53.2327 | 1.69099 | 0.845497 | − | 0.533980i | \(-0.179304\pi\) | ||||
0.845497 | + | 0.533980i | \(0.179304\pi\) | |||||||
\(992\) | 0.894035 | + | 0.649555i | 0.0283857 | + | 0.0206234i | ||||
\(993\) | 4.73826 | − | 14.5829i | 0.150364 | − | 0.462774i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.65750 | + | 5.56350i | −0.242759 | + | 0.176375i | ||||
\(996\) | −3.41825 | + | 2.48350i | −0.108311 | + | 0.0786927i | ||||
\(997\) | −10.1217 | − | 31.1515i | −0.320558 | − | 0.986577i | −0.973406 | − | 0.229087i | \(-0.926426\pi\) |
0.652848 | − | 0.757489i | \(-0.273574\pi\) | |||||||
\(998\) | −12.6682 | + | 38.9886i | −0.401004 | + | 1.23416i | ||||
\(999\) | −8.59825 | − | 6.24700i | −0.272037 | − | 0.197646i |
(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 | 539.2.f.d.246.2 | 8 | ||
7.2 | even | 3 | 539.2.q.b.312.2 | 16 | |||
7.3 | odd | 6 | 539.2.q.c.422.1 | 16 | |||
7.4 | even | 3 | 539.2.q.b.422.1 | 16 | |||
7.5 | odd | 6 | 539.2.q.c.312.2 | 16 | |||
7.6 | odd | 2 | 77.2.f.a.15.2 | ✓ | 8 | ||
11.3 | even | 5 | inner | 539.2.f.d.344.2 | 8 | ||
11.5 | even | 5 | 5929.2.a.bi.1.1 | 4 | |||
11.6 | odd | 10 | 5929.2.a.bb.1.4 | 4 | |||
21.20 | even | 2 | 693.2.m.g.631.1 | 8 | |||
77.3 | odd | 30 | 539.2.q.c.520.2 | 16 | |||
77.6 | even | 10 | 847.2.a.k.1.4 | 4 | |||
77.13 | even | 10 | 847.2.f.s.148.2 | 8 | |||
77.20 | odd | 10 | 847.2.f.p.148.1 | 8 | |||
77.25 | even | 15 | 539.2.q.b.520.2 | 16 | |||
77.27 | odd | 10 | 847.2.a.l.1.1 | 4 | |||
77.41 | even | 10 | 847.2.f.q.729.1 | 8 | |||
77.47 | odd | 30 | 539.2.q.c.410.1 | 16 | |||
77.48 | odd | 10 | 847.2.f.p.372.1 | 8 | |||
77.58 | even | 15 | 539.2.q.b.410.1 | 16 | |||
77.62 | even | 10 | 847.2.f.s.372.2 | 8 | |||
77.69 | odd | 10 | 77.2.f.a.36.2 | yes | 8 | ||
77.76 | even | 2 | 847.2.f.q.323.1 | 8 | |||
231.83 | odd | 10 | 7623.2.a.co.1.1 | 4 | |||
231.104 | even | 10 | 7623.2.a.ch.1.4 | 4 | |||
231.146 | even | 10 | 693.2.m.g.190.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.a.15.2 | ✓ | 8 | 7.6 | odd | 2 | ||
77.2.f.a.36.2 | yes | 8 | 77.69 | odd | 10 | ||
539.2.f.d.246.2 | 8 | 1.1 | even | 1 | trivial | ||
539.2.f.d.344.2 | 8 | 11.3 | even | 5 | inner | ||
539.2.q.b.312.2 | 16 | 7.2 | even | 3 | |||
539.2.q.b.410.1 | 16 | 77.58 | even | 15 | |||
539.2.q.b.422.1 | 16 | 7.4 | even | 3 | |||
539.2.q.b.520.2 | 16 | 77.25 | even | 15 | |||
539.2.q.c.312.2 | 16 | 7.5 | odd | 6 | |||
539.2.q.c.410.1 | 16 | 77.47 | odd | 30 | |||
539.2.q.c.422.1 | 16 | 7.3 | odd | 6 | |||
539.2.q.c.520.2 | 16 | 77.3 | odd | 30 | |||
693.2.m.g.190.1 | 8 | 231.146 | even | 10 | |||
693.2.m.g.631.1 | 8 | 21.20 | even | 2 | |||
847.2.a.k.1.4 | 4 | 77.6 | even | 10 | |||
847.2.a.l.1.1 | 4 | 77.27 | odd | 10 | |||
847.2.f.p.148.1 | 8 | 77.20 | odd | 10 | |||
847.2.f.p.372.1 | 8 | 77.48 | odd | 10 | |||
847.2.f.q.323.1 | 8 | 77.76 | even | 2 | |||
847.2.f.q.729.1 | 8 | 77.41 | even | 10 | |||
847.2.f.s.148.2 | 8 | 77.13 | even | 10 | |||
847.2.f.s.372.2 | 8 | 77.62 | even | 10 | |||
5929.2.a.bb.1.4 | 4 | 11.6 | odd | 10 | |||
5929.2.a.bi.1.1 | 4 | 11.5 | even | 5 | |||
7623.2.a.ch.1.4 | 4 | 231.104 | even | 10 | |||
7623.2.a.co.1.1 | 4 | 231.83 | odd | 10 |