Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(53,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.ce (of order \(12\), 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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 107.1 | ||
Character | \(\chi\) | \(=\) | 315.107 |
Dual form | 315.2.ce.a.53.1 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.695956 | − | 2.59734i | −0.492115 | − | 1.83660i | −0.545621 | − | 0.838032i | \(-0.683706\pi\) |
0.0535055 | − | 0.998568i | \(-0.482961\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.52979 | + | 2.61528i | −2.26490 | + | 1.30764i | ||||
\(5\) | 1.27254 | + | 1.83865i | 0.569098 | + | 0.822270i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.50727 | + | 2.17442i | −0.569696 | + | 0.821855i | ||||
\(8\) | 6.14253 | + | 6.14253i | 2.17171 | + | 2.17171i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.88997 | − | 4.58485i | 1.23012 | − | 1.44986i | ||||
\(11\) | 3.60099 | − | 2.07903i | 1.08574 | − | 0.626852i | 0.153300 | − | 0.988180i | \(-0.451010\pi\) |
0.932439 | + | 0.361328i | \(0.117677\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.702126 | + | 0.702126i | −0.194735 | + | 0.194735i | −0.797738 | − | 0.603004i | \(-0.793970\pi\) |
0.603004 | + | 0.797738i | \(0.293970\pi\) | |||||||
\(14\) | 6.69673 | + | 2.40161i | 1.78978 | + | 0.641856i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.44878 | − | 11.1696i | 1.61220 | − | 2.79241i | ||||
\(17\) | 1.31583 | + | 0.352577i | 0.319137 | + | 0.0855124i | 0.414831 | − | 0.909898i | \(-0.363841\pi\) |
−0.0956947 | + | 0.995411i | \(0.530507\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.22461 | + | 3.01643i | 1.19861 | + | 0.692016i | 0.960245 | − | 0.279160i | \(-0.0900559\pi\) |
0.238363 | + | 0.971176i | \(0.423389\pi\) | |||||||
\(20\) | −10.5729 | − | 5.00065i | −2.36418 | − | 1.11818i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.90609 | − | 7.90609i | −1.68558 | − | 1.68558i | ||||
\(23\) | 0.205581 | − | 0.0550852i | 0.0428665 | − | 0.0114861i | −0.237322 | − | 0.971431i | \(-0.576270\pi\) |
0.280189 | + | 0.959945i | \(0.409603\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.76127 | + | 4.67952i | −0.352254 | + | 0.935904i | ||||
\(26\) | 2.31231 | + | 1.33501i | 0.453482 | + | 0.261818i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.14092 | − | 13.7916i | 0.215613 | − | 2.60637i | ||||
\(29\) | −0.879133 | −0.163251 | −0.0816255 | − | 0.996663i | \(-0.526011\pi\) | ||||
−0.0816255 | + | 0.996663i | \(0.526011\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.76368 | + | 8.25093i | 0.855582 | + | 1.48191i | 0.876104 | + | 0.482122i | \(0.160134\pi\) |
−0.0205224 | + | 0.999789i | \(0.506533\pi\) | |||||||
\(32\) | −16.7177 | − | 4.47950i | −2.95530 | − | 0.791871i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 3.66305i | − | 0.628208i | ||||||
\(35\) | −5.91608 | − | 0.00430290i | −1.00000 | − | 0.000727323i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.13636 | + | 0.840384i | −0.515614 | + | 0.138158i | −0.507237 | − | 0.861807i | \(-0.669333\pi\) |
−0.00837687 | + | 0.999965i | \(0.502666\pi\) | |||||||
\(38\) | 4.19861 | − | 15.6694i | 0.681104 | − | 2.54191i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.47734 | + | 19.1106i | −0.549815 | + | 3.02165i | ||||
\(41\) | − | 1.25212i | − | 0.195548i | −0.995209 | − | 0.0977742i | \(-0.968828\pi\) | ||
0.995209 | − | 0.0977742i | \(-0.0311723\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.28935 | + | 4.28935i | −0.654120 | + | 0.654120i | −0.953982 | − | 0.299862i | \(-0.903059\pi\) |
0.299862 | + | 0.953982i | \(0.403059\pi\) | |||||||
\(44\) | −10.8745 | + | 18.8352i | −1.63939 | + | 2.83951i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.286150 | − | 0.495627i | −0.0421906 | − | 0.0730762i | ||||
\(47\) | 0.0279906 | + | 0.104462i | 0.00408285 | + | 0.0152374i | 0.967937 | − | 0.251192i | \(-0.0808226\pi\) |
−0.963854 | + | 0.266430i | \(0.914156\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.45625 | − | 6.55491i | −0.350893 | − | 0.936416i | ||||
\(50\) | 13.3801 | + | 1.31789i | 1.89223 | + | 0.186377i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.34423 | − | 5.01674i | 0.186411 | − | 0.695697i | ||||
\(53\) | 1.29555 | − | 4.83507i | 0.177958 | − | 0.664148i | −0.818071 | − | 0.575117i | \(-0.804956\pi\) |
0.996029 | − | 0.0890305i | \(-0.0283769\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.40502 | + | 3.97530i | 1.13333 | + | 0.536030i | ||||
\(56\) | −22.6150 | + | 4.09799i | −3.02205 | + | 0.547618i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.611838 | + | 2.28341i | 0.0803383 | + | 0.299827i | ||||
\(59\) | −0.113063 | − | 0.195831i | −0.0147196 | − | 0.0254951i | 0.858572 | − | 0.512693i | \(-0.171352\pi\) |
−0.873291 | + | 0.487198i | \(0.838019\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.96760 | − | 10.3362i | 0.764073 | − | 1.32341i | −0.176662 | − | 0.984272i | \(-0.556530\pi\) |
0.940735 | − | 0.339142i | \(-0.110137\pi\) | |||||||
\(62\) | 18.1152 | − | 18.1152i | 2.30063 | − | 2.30063i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 20.7441i | 2.59301i | ||||||||
\(65\) | −2.18445 | − | 0.397480i | −0.270948 | − | 0.0493013i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.825199 | − | 3.07969i | 0.100814 | − | 0.376243i | −0.897023 | − | 0.441985i | \(-0.854275\pi\) |
0.997837 | + | 0.0657413i | \(0.0209412\pi\) | |||||||
\(68\) | −6.88254 | + | 1.84417i | −0.834630 | + | 0.223639i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.10616 | + | 15.3691i | 0.490779 | + | 1.83696i | ||||
\(71\) | 9.78757i | 1.16157i | 0.814057 | + | 0.580785i | \(0.197254\pi\) | ||||
−0.814057 | + | 0.580785i | \(0.802746\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.60621 | − | 1.77013i | −0.773198 | − | 0.207178i | −0.149414 | − | 0.988775i | \(-0.547739\pi\) |
−0.623784 | + | 0.781597i | \(0.714406\pi\) | |||||||
\(74\) | 4.36553 | + | 7.56133i | 0.507483 | + | 0.878986i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −31.5552 | −3.61963 | ||||||||
\(77\) | −0.906979 | + | 10.9637i | −0.103360 | + | 1.24944i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.88223 | + | 1.08671i | 0.211767 | + | 0.122264i | 0.602132 | − | 0.798396i | \(-0.294318\pi\) |
−0.390365 | + | 0.920660i | \(0.627651\pi\) | |||||||
\(80\) | 28.7434 | − | 2.35676i | 3.21361 | − | 0.263493i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.25219 | + | 0.871421i | −0.359144 | + | 0.0962324i | ||||
\(83\) | 3.75964 | + | 3.75964i | 0.412674 | + | 0.412674i | 0.882669 | − | 0.469995i | \(-0.155744\pi\) |
−0.469995 | + | 0.882669i | \(0.655744\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.02619 | + | 2.86803i | 0.111306 | + | 0.311081i | ||||
\(86\) | 14.1261 | + | 8.15572i | 1.52326 | + | 0.879454i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 34.8897 | + | 9.34867i | 3.71925 | + | 0.996571i | ||||
\(89\) | 7.19793 | − | 12.4672i | 0.762979 | − | 1.32152i | −0.178330 | − | 0.983971i | \(-0.557069\pi\) |
0.941309 | − | 0.337547i | \(-0.109597\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.468424 | − | 2.58502i | −0.0491042 | − | 0.270984i | ||||
\(92\) | −0.787175 | + | 0.787175i | −0.0820686 | + | 0.0820686i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.251845 | − | 0.145403i | 0.0259758 | − | 0.0149971i | ||||
\(95\) | 1.10238 | + | 13.4448i | 0.113101 | + | 1.37940i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.88891 | + | 3.88891i | 0.394859 | + | 0.394859i | 0.876415 | − | 0.481556i | \(-0.159928\pi\) |
−0.481556 | + | 0.876415i | \(0.659928\pi\) | |||||||
\(98\) | −15.3159 | + | 10.9417i | −1.54714 | + | 1.10527i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.26005 | − | 25.8035i | −0.426005 | − | 2.58035i | ||||
\(101\) | −7.89380 | + | 4.55749i | −0.785463 | + | 0.453487i | −0.838363 | − | 0.545113i | \(-0.816487\pi\) |
0.0528999 | + | 0.998600i | \(0.483154\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.32007 | + | 8.65861i | 0.228603 | + | 0.853158i | 0.980929 | + | 0.194367i | \(0.0622652\pi\) |
−0.752326 | + | 0.658791i | \(0.771068\pi\) | |||||||
\(104\) | −8.62567 | −0.845816 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.4600 | −1.30735 | ||||||||
\(107\) | −3.50023 | − | 13.0630i | −0.338380 | − | 1.26285i | −0.900158 | − | 0.435564i | \(-0.856549\pi\) |
0.561778 | − | 0.827288i | \(-0.310118\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.19131 | + | 1.84250i | −0.305672 | + | 0.176480i | −0.644988 | − | 0.764192i | \(-0.723138\pi\) |
0.339316 | + | 0.940672i | \(0.389804\pi\) | |||||||
\(110\) | 4.47570 | − | 24.5974i | 0.426741 | − | 2.34527i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 14.5674 | + | 30.8581i | 1.37649 | + | 2.91581i | ||||
\(113\) | −13.2212 | − | 13.2212i | −1.24375 | − | 1.24375i | −0.958434 | − | 0.285316i | \(-0.907901\pi\) |
−0.285316 | − | 0.958434i | \(-0.592099\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.362893 | + | 0.307893i | 0.0338399 | + | 0.0287112i | ||||
\(116\) | 3.98229 | − | 2.29918i | 0.369746 | − | 0.213473i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.429954 | + | 0.429954i | −0.0395805 | + | 0.0395805i | ||||
\(119\) | −2.74997 | + | 2.32975i | −0.252090 | + | 0.213568i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.14474 | − | 5.44685i | 0.285886 | − | 0.495169i | ||||
\(122\) | −30.9998 | − | 8.30638i | −2.80659 | − | 0.752024i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −43.1569 | − | 24.9167i | −3.87561 | − | 2.23758i | ||||
\(125\) | −10.8453 | + | 2.71653i | −0.970033 | + | 0.242973i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.70267 | − | 5.70267i | −0.506030 | − | 0.506030i | 0.407275 | − | 0.913305i | \(-0.366479\pi\) |
−0.913305 | + | 0.407275i | \(0.866479\pi\) | |||||||
\(128\) | 20.4440 | − | 5.47796i | 1.80701 | − | 0.484188i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.487891 | + | 5.95040i | 0.0427909 | + | 0.521885i | ||||
\(131\) | −16.3919 | − | 9.46386i | −1.43217 | − | 0.826862i | −0.434880 | − | 0.900488i | \(-0.643209\pi\) |
−0.997286 | + | 0.0736266i | \(0.976543\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.4339 | + | 6.81393i | −1.25158 | + | 0.590843i | ||||
\(134\) | −8.57330 | −0.740621 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.91684 | + | 10.2483i | 0.507365 | + | 0.878782i | ||||
\(137\) | 11.5217 | + | 3.08722i | 0.984361 | + | 0.263759i | 0.714880 | − | 0.699247i | \(-0.246481\pi\) |
0.269481 | + | 0.963006i | \(0.413148\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 17.0047i | − | 1.44232i | −0.692767 | − | 0.721161i | \(-0.743609\pi\) | ||
0.692767 | − | 0.721161i | \(-0.256391\pi\) | |||||||
\(140\) | 26.8098 | − | 15.4527i | 2.26585 | − | 1.30599i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 25.4217 | − | 6.81172i | 2.13334 | − | 0.571627i | ||||
\(143\) | −1.06861 | + | 3.98809i | −0.0893613 | + | 0.333501i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.11873 | − | 1.61642i | −0.0929058 | − | 0.134236i | ||||
\(146\) | 18.3905i | 1.52201i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 12.0092 | − | 12.0092i | 0.987150 | − | 0.987150i | ||||
\(149\) | 5.31610 | − | 9.20775i | 0.435512 | − | 0.754328i | −0.561826 | − | 0.827256i | \(-0.689901\pi\) |
0.997337 | + | 0.0729275i | \(0.0232342\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.91806 | + | 11.9824i | 0.562984 | + | 0.975116i | 0.997234 | + | 0.0743241i | \(0.0236799\pi\) |
−0.434251 | + | 0.900792i | \(0.642987\pi\) | |||||||
\(152\) | 13.5638 | + | 50.6208i | 1.10017 | + | 4.10589i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 29.1078 | − | 5.27455i | 2.34558 | − | 0.425036i | ||||
\(155\) | −9.10860 | + | 19.2584i | −0.731620 | + | 1.54687i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.26351 | − | 19.6437i | 0.420074 | − | 1.56774i | −0.354376 | − | 0.935103i | \(-0.615307\pi\) |
0.774450 | − | 0.632635i | \(-0.218027\pi\) | |||||||
\(158\) | 1.51260 | − | 5.64509i | 0.120336 | − | 0.449100i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13.0378 | − | 36.4384i | −1.03073 | − | 2.88071i | ||||
\(161\) | −0.190088 | + | 0.530048i | −0.0149810 | + | 0.0417737i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.444770 | + | 1.65991i | 0.0348371 | + | 0.130014i | 0.981154 | − | 0.193225i | \(-0.0618948\pi\) |
−0.946317 | + | 0.323239i | \(0.895228\pi\) | |||||||
\(164\) | 3.27464 | + | 5.67185i | 0.255707 | + | 0.442897i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.14854 | − | 12.3816i | 0.554834 | − | 0.961001i | ||||
\(167\) | 4.75534 | − | 4.75534i | 0.367980 | − | 0.367980i | −0.498760 | − | 0.866740i | \(-0.666211\pi\) |
0.866740 | + | 0.498760i | \(0.166211\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0140i | 0.924157i | ||||||||
\(170\) | 6.73507 | − | 4.66139i | 0.516556 | − | 0.357512i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.21203 | − | 30.6477i | 0.626161 | − | 2.33687i | ||||
\(173\) | 0.263351 | − | 0.0705647i | 0.0200222 | − | 0.00536494i | −0.248794 | − | 0.968556i | \(-0.580034\pi\) |
0.268816 | + | 0.963191i | \(0.413368\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.52055 | − | 10.8831i | −0.568500 | − | 0.822683i | ||||
\(176\) | − | 53.6289i | − | 4.04243i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −37.3910 | − | 10.0189i | −2.80257 | − | 0.750947i | ||||
\(179\) | 8.58944 | + | 14.8773i | 0.642005 | + | 1.11199i | 0.984985 | + | 0.172642i | \(0.0552305\pi\) |
−0.342980 | + | 0.939343i | \(0.611436\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.07537 | −0.302920 | −0.151460 | − | 0.988463i | \(-0.548397\pi\) | ||||
−0.151460 | + | 0.988463i | \(0.548397\pi\) | |||||||
\(182\) | −6.38818 | + | 3.01572i | −0.473523 | + | 0.223540i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.60115 | + | 0.924424i | 0.118038 | + | 0.0681494i | ||||
\(185\) | −5.53632 | − | 4.69724i | −0.407038 | − | 0.345348i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.47132 | − | 1.46604i | 0.400103 | − | 0.107207i | ||||
\(188\) | −0.399990 | − | 0.399990i | −0.0291723 | − | 0.0291723i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 34.1535 | − | 12.2202i | 2.47775 | − | 0.886548i | ||||
\(191\) | −8.15870 | − | 4.71043i | −0.590343 | − | 0.340834i | 0.174890 | − | 0.984588i | \(-0.444043\pi\) |
−0.765233 | + | 0.643753i | \(0.777376\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.2504 | − | 3.01454i | −0.809824 | − | 0.216992i | −0.169931 | − | 0.985456i | \(-0.554355\pi\) |
−0.639893 | + | 0.768464i | \(0.721021\pi\) | |||||||
\(194\) | 7.39433 | − | 12.8073i | 0.530882 | − | 0.919514i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 28.2692 | + | 23.2686i | 2.01923 | + | 1.66204i | ||||
\(197\) | −8.07168 | + | 8.07168i | −0.575083 | + | 0.575083i | −0.933545 | − | 0.358461i | \(-0.883301\pi\) |
0.358461 | + | 0.933545i | \(0.383301\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.4380 | − | 9.49049i | 1.16526 | − | 0.672763i | 0.212701 | − | 0.977117i | \(-0.431774\pi\) |
0.952559 | + | 0.304354i | \(0.0984407\pi\) | |||||||
\(200\) | −39.5628 | + | 17.9254i | −2.79751 | + | 1.26752i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 17.3311 | + | 17.3311i | 1.21941 | + | 1.21941i | ||||
\(203\) | 1.32509 | − | 1.91161i | 0.0930034 | − | 0.134169i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.30221 | − | 1.59338i | 0.160794 | − | 0.111286i | ||||
\(206\) | 20.8747 | − | 12.0520i | 1.45441 | − | 0.839704i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.31463 | + | 12.3703i | 0.229828 | + | 0.857729i | ||||
\(209\) | 25.0850 | 1.73517 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.43148 | 0.511604 | 0.255802 | − | 0.966729i | \(-0.417660\pi\) | ||||
0.255802 | + | 0.966729i | \(0.417660\pi\) | |||||||
\(212\) | 6.77645 | + | 25.2901i | 0.465409 | + | 1.73693i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −31.4932 | + | 18.1826i | −2.15283 | + | 1.24294i | ||||
\(215\) | −13.3450 | − | 2.42824i | −0.910122 | − | 0.165604i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −25.1212 | − | 2.07816i | −1.70534 | − | 0.141075i | ||||
\(218\) | 7.00663 | + | 7.00663i | 0.474549 | + | 0.474549i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −48.4695 | + | 3.97416i | −3.26781 | + | 0.267938i | ||||
\(221\) | −1.17144 | + | 0.676328i | −0.0787993 | + | 0.0454948i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.70762 | + | 9.70762i | −0.650071 | + | 0.650071i | −0.953010 | − | 0.302939i | \(-0.902032\pi\) |
0.302939 | + | 0.953010i | \(0.402032\pi\) | |||||||
\(224\) | 34.9385 | − | 29.5996i | 2.33443 | − | 1.97771i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −25.1387 | + | 43.5415i | −1.67220 | + | 2.89634i | ||||
\(227\) | 10.4034 | + | 2.78758i | 0.690498 | + | 0.185018i | 0.586971 | − | 0.809608i | \(-0.300320\pi\) |
0.103527 | + | 0.994627i | \(0.466987\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.41630 | + | 3.70445i | 0.424001 | + | 0.244797i | 0.696788 | − | 0.717277i | \(-0.254612\pi\) |
−0.272787 | + | 0.962075i | \(0.587945\pi\) | |||||||
\(230\) | 0.547146 | − | 1.15684i | 0.0360778 | − | 0.0762796i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.40010 | − | 5.40010i | −0.354534 | − | 0.354534i | ||||
\(233\) | 21.5398 | − | 5.77156i | 1.41112 | − | 0.378107i | 0.528793 | − | 0.848751i | \(-0.322645\pi\) |
0.882324 | + | 0.470643i | \(0.155978\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.156451 | + | 0.184398i | −0.0102057 | + | 0.0120288i | ||||
\(236\) | 1.02431 | + | 0.591383i | 0.0666766 | + | 0.0384958i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.96503 | + | 5.52122i | 0.516296 | + | 0.357888i | ||||
\(239\) | −11.9368 | −0.772124 | −0.386062 | − | 0.922473i | \(-0.626165\pi\) | ||||
−0.386062 | + | 0.922473i | \(0.626165\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.36327 | − | 12.7536i | −0.474310 | − | 0.821529i | 0.525257 | − | 0.850943i | \(-0.323969\pi\) |
−0.999567 | + | 0.0294146i | \(0.990636\pi\) | |||||||
\(242\) | −16.3360 | − | 4.37721i | −1.05012 | − | 0.281377i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 62.4277i | 3.99652i | ||||||||
\(245\) | 8.92651 | − | 12.8576i | 0.570294 | − | 0.821441i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.78625 | + | 1.55042i | −0.368170 | + | 0.0986510i | ||||
\(248\) | −21.4206 | + | 79.9427i | −1.36021 | + | 5.07636i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.6036 | + | 26.2784i | 0.923613 | + | 1.66199i | ||||
\(251\) | − | 18.8368i | − | 1.18897i | −0.804108 | − | 0.594483i | \(-0.797357\pi\) | ||
0.804108 | − | 0.594483i | \(-0.202643\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.625770 | − | 0.625770i | 0.0393418 | − | 0.0393418i | ||||
\(254\) | −10.8430 | + | 18.7806i | −0.680350 | + | 1.17840i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.71224 | − | 13.3580i | −0.482015 | − | 0.834874i | ||||
\(257\) | −3.87251 | − | 14.4524i | −0.241561 | − | 0.901517i | −0.975081 | − | 0.221849i | \(-0.928791\pi\) |
0.733520 | − | 0.679668i | \(-0.237876\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.90000 | − | 8.08646i | 0.180197 | − | 0.502468i | ||||
\(260\) | 10.9346 | − | 3.91244i | 0.678137 | − | 0.242639i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.1729 | + | 49.1618i | −0.813823 | + | 3.03723i | ||||
\(263\) | 2.88720 | − | 10.7752i | 0.178032 | − | 0.664426i | −0.817983 | − | 0.575243i | \(-0.804908\pi\) |
0.996015 | − | 0.0891835i | \(-0.0284257\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.5386 | − | 3.77076i | 0.647384 | − | 0.231636i | ||||
\(266\) | 27.7435 | + | 32.7477i | 1.70106 | + | 2.00789i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.31625 | + | 16.1085i | 0.263657 | + | 0.983980i | ||||
\(269\) | 8.34045 | + | 14.4461i | 0.508526 | + | 0.880793i | 0.999951 | + | 0.00987349i | \(0.00314288\pi\) |
−0.491425 | + | 0.870920i | \(0.663524\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.86722 | − | 10.1623i | 0.356408 | − | 0.617317i | −0.630950 | − | 0.775824i | \(-0.717335\pi\) |
0.987358 | + | 0.158507i | \(0.0506679\pi\) | |||||||
\(272\) | 12.4237 | − | 12.4237i | 0.753296 | − | 0.753296i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 32.0743i | − | 1.93768i | ||||||
\(275\) | 3.38655 | + | 20.5126i | 0.204217 | + | 1.23696i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.17485 | + | 11.8487i | −0.190758 | + | 0.711919i | 0.802566 | + | 0.596563i | \(0.203468\pi\) |
−0.993324 | + | 0.115356i | \(0.963199\pi\) | |||||||
\(278\) | −44.1671 | + | 11.8345i | −2.64897 | + | 0.709789i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −36.3133 | − | 36.3661i | −2.17013 | − | 2.17329i | ||||
\(281\) | − | 20.0929i | − | 1.19864i | −0.800509 | − | 0.599320i | \(-0.795438\pi\) | ||
0.800509 | − | 0.599320i | \(-0.204562\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.6875 | + | 8.22270i | 1.82418 | + | 0.488789i | 0.997290 | − | 0.0735682i | \(-0.0234387\pi\) |
0.826895 | + | 0.562357i | \(0.190105\pi\) | |||||||
\(284\) | −25.5972 | − | 44.3356i | −1.51891 | − | 2.63084i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.1021 | 0.656484 | ||||||||
\(287\) | 2.72264 | + | 1.88729i | 0.160713 | + | 0.111403i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.1153 | − | 7.57214i | −0.771490 | − | 0.445420i | ||||
\(290\) | −3.41981 | + | 4.03069i | −0.200818 | + | 0.236691i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 34.5541 | − | 9.25875i | 2.02213 | − | 0.541827i | ||||
\(293\) | 3.32527 | + | 3.32527i | 0.194265 | + | 0.194265i | 0.797536 | − | 0.603271i | \(-0.206136\pi\) |
−0.603271 | + | 0.797536i | \(0.706136\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.216188 | − | 0.457088i | 0.0125869 | − | 0.0266127i | ||||
\(296\) | −24.4273 | − | 14.1031i | −1.41981 | − | 0.819725i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −27.6155 | − | 7.39954i | −1.59972 | − | 0.428644i | ||||
\(299\) | −0.105667 | + | 0.183020i | −0.00611087 | + | 0.0105843i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.86164 | − | 15.7921i | −0.164942 | − | 0.910242i | ||||
\(302\) | 26.3078 | − | 26.3078i | 1.51385 | − | 1.51385i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 67.3848 | − | 38.9046i | 3.86478 | − | 2.23133i | ||||
\(305\) | 26.5987 | − | 2.18090i | 1.52304 | − | 0.124878i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.96830 | − | 2.96830i | −0.169410 | − | 0.169410i | 0.617310 | − | 0.786720i | \(-0.288222\pi\) |
−0.786720 | + | 0.617310i | \(0.788222\pi\) | |||||||
\(308\) | −24.5648 | − | 52.0355i | −1.39971 | − | 2.96500i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 56.3599 | + | 10.2552i | 3.20103 | + | 0.582454i | ||||
\(311\) | −8.09571 | + | 4.67406i | −0.459065 | + | 0.265042i | −0.711651 | − | 0.702533i | \(-0.752052\pi\) |
0.252586 | + | 0.967575i | \(0.418719\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.38565 | + | 20.0995i | 0.304415 | + | 1.13609i | 0.933448 | + | 0.358714i | \(0.116785\pi\) |
−0.629032 | + | 0.777379i | \(0.716549\pi\) | |||||||
\(314\) | −54.6846 | −3.08603 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.3681 | −0.639507 | ||||||||
\(317\) | 3.73583 | + | 13.9423i | 0.209825 | + | 0.783078i | 0.987924 | + | 0.154937i | \(0.0495173\pi\) |
−0.778099 | + | 0.628141i | \(0.783816\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.16575 | + | 1.82775i | −0.177248 | + | 0.102334i | ||||
\(320\) | −38.1411 | + | 26.3977i | −2.13215 | + | 1.47568i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.50901 | + | 0.124833i | 0.0840939 | + | 0.00695669i | ||||
\(323\) | 5.81120 | + | 5.81120i | 0.323344 | + | 0.323344i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.04898 | − | 4.52225i | −0.113657 | − | 0.250849i | ||||
\(326\) | 4.00180 | − | 2.31044i | 0.221639 | − | 0.127964i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.69119 | − | 7.69119i | 0.424675 | − | 0.424675i | ||||
\(329\) | −0.269335 | − | 0.0965901i | −0.0148489 | − | 0.00532518i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.77389 | + | 10.0007i | −0.317362 | + | 0.549687i | −0.979937 | − | 0.199309i | \(-0.936130\pi\) |
0.662575 | + | 0.748996i | \(0.269464\pi\) | |||||||
\(332\) | −26.8629 | − | 7.19789i | −1.47429 | − | 0.395036i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −15.6608 | − | 9.04175i | −0.856919 | − | 0.494743i | ||||
\(335\) | 6.71257 | − | 2.40178i | 0.366747 | − | 0.131223i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.7098 | − | 20.7098i | −1.12813 | − | 1.12813i | −0.990481 | − | 0.137653i | \(-0.956044\pi\) |
−0.137653 | − | 0.990481i | \(-0.543956\pi\) | |||||||
\(338\) | 31.2046 | − | 8.36124i | 1.69731 | − | 0.454792i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.1491 | − | 10.3078i | −0.658878 | − | 0.559019i | ||||
\(341\) | 34.3079 | + | 19.8077i | 1.85788 | + | 1.07265i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.9554 | + | 4.53912i | 0.969500 | + | 0.245089i | ||||
\(344\) | −52.6950 | −2.84112 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.366562 | − | 0.634904i | −0.0197065 | − | 0.0341326i | ||||
\(347\) | 20.5602 | + | 5.50909i | 1.10373 | + | 0.295743i | 0.764282 | − | 0.644882i | \(-0.223093\pi\) |
0.339447 | + | 0.940625i | \(0.389760\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.84619i | 0.366468i | 0.983069 | + | 0.183234i | \(0.0586566\pi\) | ||||
−0.983069 | + | 0.183234i | \(0.941343\pi\) | |||||||
\(350\) | −23.0331 | + | 27.1076i | −1.23117 | + | 1.44896i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −69.5133 | + | 18.6260i | −3.70507 | + | 0.992771i | ||||
\(353\) | 5.27279 | − | 19.6783i | 0.280642 | − | 1.04737i | −0.671323 | − | 0.741165i | \(-0.734274\pi\) |
0.951965 | − | 0.306206i | \(-0.0990597\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.9959 | + | 12.4551i | −0.955124 | + | 0.661048i | ||||
\(356\) | 75.2983i | 3.99080i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 32.6637 | − | 32.6637i | 1.72633 | − | 1.72633i | ||||
\(359\) | 7.96815 | − | 13.8012i | 0.420543 | − | 0.728402i | −0.575450 | − | 0.817837i | \(-0.695173\pi\) |
0.995993 | + | 0.0894353i | \(0.0285062\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.69770 | + | 15.0649i | 0.457774 | + | 0.792887i | ||||
\(362\) | 2.83628 | + | 10.5851i | 0.149072 | + | 0.556343i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.88240 | + | 10.4845i | 0.465564 | + | 0.549539i | ||||
\(365\) | −5.15203 | − | 14.3991i | −0.269670 | − | 0.753682i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.90688 | + | 10.8486i | −0.151738 | + | 0.566294i | 0.847625 | + | 0.530596i | \(0.178032\pi\) |
−0.999363 | + | 0.0356974i | \(0.988635\pi\) | |||||||
\(368\) | 0.710465 | − | 2.65149i | 0.0370356 | − | 0.138219i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.34731 | + | 17.6488i | −0.433956 | + | 0.917518i | ||||
\(371\) | 8.56074 | + | 10.1049i | 0.444451 | + | 0.524618i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.97059 | − | 29.7467i | −0.412702 | − | 1.54022i | −0.789395 | − | 0.613885i | \(-0.789606\pi\) |
0.376694 | − | 0.926338i | \(-0.377061\pi\) | |||||||
\(374\) | −7.61560 | − | 13.1906i | −0.393793 | − | 0.682070i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.469731 | + | 0.813598i | −0.0242245 | + | 0.0419581i | ||||
\(377\) | 0.617263 | − | 0.617263i | 0.0317906 | − | 0.0317906i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.79809i | 0.297828i | 0.988850 | + | 0.148914i | \(0.0475777\pi\) | ||||
−0.988850 | + | 0.148914i | \(0.952422\pi\) | |||||||
\(380\) | −40.1553 | − | 58.0190i | −2.05992 | − | 2.97631i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.55650 | + | 24.4692i | −0.335460 | + | 1.25195i | ||||
\(383\) | −9.09525 | + | 2.43707i | −0.464746 | + | 0.124528i | −0.483591 | − | 0.875294i | \(-0.660668\pi\) |
0.0188451 | + | 0.999822i | \(0.494001\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.3127 | + | 12.2842i | −1.08619 | + | 0.626062i | ||||
\(386\) | 31.3192i | 1.59411i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −27.7865 | − | 7.44538i | −1.41065 | − | 0.377982i | ||||
\(389\) | −4.94348 | − | 8.56236i | −0.250644 | − | 0.434129i | 0.713059 | − | 0.701104i | \(-0.247309\pi\) |
−0.963703 | + | 0.266975i | \(0.913976\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.289932 | 0.0146625 | ||||||||
\(392\) | 25.1762 | − | 55.3513i | 1.27159 | − | 2.79566i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 26.5825 | + | 15.3474i | 1.33920 | + | 0.773190i | ||||
\(395\) | 0.397144 | + | 4.84364i | 0.0199825 | + | 0.243710i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.9026 | − | 5.60083i | 1.04907 | − | 0.281097i | 0.307202 | − | 0.951644i | \(-0.400607\pi\) |
0.741867 | + | 0.670547i | \(0.233940\pi\) | |||||||
\(398\) | −36.0902 | − | 36.0902i | −1.80904 | − | 1.80904i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 40.9104 | + | 49.8500i | 2.04552 | + | 2.49250i | ||||
\(401\) | −18.9003 | − | 10.9121i | −0.943836 | − | 0.544924i | −0.0526753 | − | 0.998612i | \(-0.516775\pi\) |
−0.891161 | + | 0.453688i | \(0.850108\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.13790 | − | 2.44849i | −0.455191 | − | 0.121968i | ||||
\(404\) | 23.8382 | − | 41.2890i | 1.18599 | − | 2.05420i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.88731 | − | 2.11133i | −0.292182 | − | 0.104784i | ||||
\(407\) | −9.54680 | + | 9.54680i | −0.473217 | + | 0.473217i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.24712 | − | 1.29738i | 0.111113 | − | 0.0641512i | −0.443414 | − | 0.896317i | \(-0.646233\pi\) |
0.554527 | + | 0.832166i | \(0.312899\pi\) | |||||||
\(410\) | −5.74079 | − | 4.87072i | −0.283517 | − | 0.240548i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −33.1541 | − | 33.1541i | −1.63338 | − | 1.63338i | ||||
\(413\) | 0.596238 | + | 0.0493239i | 0.0293390 | + | 0.00242707i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.12836 | + | 11.6970i | −0.104477 | + | 0.574182i | ||||
\(416\) | 14.8831 | − | 8.59278i | 0.729705 | − | 0.421295i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −17.4581 | − | 65.1544i | −0.853902 | − | 3.18681i | ||||
\(419\) | 9.23892 | 0.451351 | 0.225675 | − | 0.974203i | \(-0.427541\pi\) | ||||
0.225675 | + | 0.974203i | \(0.427541\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.60198 | −0.224287 | −0.112143 | − | 0.993692i | \(-0.535772\pi\) | ||||
−0.112143 | + | 0.993692i | \(0.535772\pi\) | |||||||
\(422\) | −5.17199 | − | 19.3021i | −0.251768 | − | 0.939612i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 37.6575 | − | 21.7416i | 1.82881 | − | 1.05586i | ||||
\(425\) | −3.96743 | + | 5.53649i | −0.192449 | + | 0.268559i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.4805 | + | 28.5556i | 0.652365 | + | 1.38190i | ||||
\(428\) | 50.0188 | + | 50.0188i | 2.41775 | + | 2.41775i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.98057 | + | 36.3515i | 0.143736 | + | 1.75303i | ||||
\(431\) | 1.04639 | − | 0.604133i | 0.0504027 | − | 0.0291000i | −0.474587 | − | 0.880209i | \(-0.657403\pi\) |
0.524990 | + | 0.851109i | \(0.324069\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.2085 | − | 21.2085i | 1.01922 | − | 1.01922i | 0.0194062 | − | 0.999812i | \(-0.493822\pi\) |
0.999812 | − | 0.0194062i | \(-0.00617756\pi\) | |||||||
\(434\) | 12.0856 | + | 66.6947i | 0.580126 | + | 3.20145i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.63732 | − | 16.6923i | 0.461544 | − | 0.799417i | ||||
\(437\) | 1.24024 | + | 0.332321i | 0.0593287 | + | 0.0158971i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.26004 | + | 4.19158i | 0.346503 | + | 0.200053i | 0.663144 | − | 0.748492i | \(-0.269222\pi\) |
−0.316641 | + | 0.948545i | \(0.602555\pi\) | |||||||
\(440\) | 27.2097 | + | 76.0465i | 1.29717 | + | 3.62538i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.57193 | + | 2.57193i | 0.122334 | + | 0.122334i | ||||
\(443\) | −5.19257 | + | 1.39135i | −0.246707 | + | 0.0661048i | −0.380053 | − | 0.924965i | \(-0.624094\pi\) |
0.133347 | + | 0.991069i | \(0.457428\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 32.0824 | − | 2.63054i | 1.52085 | − | 0.124699i | ||||
\(446\) | 31.9701 | + | 18.4580i | 1.51383 | + | 0.874010i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −45.1064 | − | 31.2670i | −2.13108 | − | 1.47723i | ||||
\(449\) | −3.34892 | −0.158045 | −0.0790227 | − | 0.996873i | \(-0.525180\pi\) | ||||
−0.0790227 | + | 0.996873i | \(0.525180\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.60320 | − | 4.50887i | −0.122580 | − | 0.212315i | ||||
\(452\) | 94.4666 | + | 25.3123i | 4.44334 | + | 1.19059i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 28.9613i | − | 1.35922i | ||||||
\(455\) | 4.15686 | − | 4.15081i | 0.194876 | − | 0.194593i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.01059 | + | 0.270788i | −0.0472736 | + | 0.0126669i | −0.282378 | − | 0.959303i | \(-0.591123\pi\) |
0.235105 | + | 0.971970i | \(0.424457\pi\) | |||||||
\(458\) | 5.15628 | − | 19.2435i | 0.240937 | − | 0.899189i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.44905 | − | 0.445626i | −0.114188 | − | 0.0207774i | ||||
\(461\) | − | 23.0551i | − | 1.07378i | −0.843651 | − | 0.536891i | \(-0.819599\pi\) | ||
0.843651 | − | 0.536891i | \(-0.180401\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.8069 | + | 25.8069i | −1.19935 | + | 1.19935i | −0.224987 | + | 0.974362i | \(0.572234\pi\) |
−0.974362 | + | 0.224987i | \(0.927766\pi\) | |||||||
\(464\) | −5.66934 | + | 9.81958i | −0.263192 | + | 0.455863i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −29.9815 | − | 51.9294i | −1.38886 | − | 2.40558i | ||||
\(467\) | −6.24612 | − | 23.3108i | −0.289036 | − | 1.07870i | −0.945839 | − | 0.324635i | \(-0.894758\pi\) |
0.656803 | − | 0.754062i | \(-0.271908\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.45274 | + | 6.43626i | 0.251784 | + | 0.297199i | ||||
\(470\) | 0.587828 | + | 0.278024i | 0.0271145 | + | 0.0128243i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.508405 | − | 1.89740i | 0.0234013 | − | 0.0873347i | ||||
\(473\) | −6.52821 | + | 24.3636i | −0.300167 | + | 1.12024i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.3174 | + | 19.1359i | −1.06988 | + | 0.878016i | ||||
\(476\) | 6.36386 | − | 17.7452i | 0.291687 | − | 0.813351i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.30746 | + | 31.0039i | 0.379974 | + | 1.41808i | ||||
\(479\) | −9.61925 | − | 16.6610i | −0.439515 | − | 0.761262i | 0.558137 | − | 0.829749i | \(-0.311516\pi\) |
−0.997652 | + | 0.0684867i | \(0.978183\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.61206 | − | 2.79218i | 0.0735038 | − | 0.127312i | ||||
\(482\) | −28.0009 | + | 28.0009i | −1.27540 | + | 1.27540i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 32.8975i | 1.49534i | ||||||||
\(485\) | −2.20154 | + | 12.0991i | −0.0999670 | + | 0.549394i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.55036 | − | 28.1783i | 0.342140 | − | 1.27688i | −0.553779 | − | 0.832664i | \(-0.686815\pi\) |
0.895918 | − | 0.444219i | \(-0.146519\pi\) | |||||||
\(488\) | 100.147 | − | 26.8342i | 4.53342 | − | 1.21473i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −39.6080 | − | 14.2369i | −1.78931 | − | 0.643158i | ||||
\(491\) | − | 7.79240i | − | 0.351666i | −0.984420 | − | 0.175833i | \(-0.943738\pi\) | ||
0.984420 | − | 0.175833i | \(-0.0562619\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.15679 | − | 0.309962i | −0.0520993 | − | 0.0139600i | ||||
\(494\) | 8.05396 | + | 13.9499i | 0.362365 | + | 0.627634i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 122.880 | 5.51746 | ||||||||
\(497\) | −21.2823 | − | 14.7525i | −0.954643 | − | 0.661742i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.52229 | − | 2.61095i | −0.202446 | − | 0.116882i | 0.395350 | − | 0.918530i | \(-0.370623\pi\) |
−0.597796 | + | 0.801649i | \(0.703957\pi\) | |||||||
\(500\) | 42.0225 | − | 40.6687i | 1.87930 | − | 1.81876i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −48.9256 | + | 13.1096i | −2.18366 | + | 0.585109i | ||||
\(503\) | 25.6241 | + | 25.6241i | 1.14252 | + | 1.14252i | 0.987987 | + | 0.154535i | \(0.0493879\pi\) |
0.154535 | + | 0.987987i | \(0.450612\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.4248 | − | 8.71435i | −0.819894 | − | 0.387783i | ||||
\(506\) | −2.06085 | − | 1.18983i | −0.0916159 | − | 0.0528945i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 40.7460 | + | 10.9178i | 1.80781 | + | 0.484401i | ||||
\(509\) | −17.7901 | + | 30.8133i | −0.788532 | + | 1.36578i | 0.138335 | + | 0.990385i | \(0.455825\pi\) |
−0.926866 | + | 0.375391i | \(0.877508\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.8064 | − | 11.6966i | 0.610758 | − | 0.517429i | ||||
\(512\) | 0.604217 | − | 0.604217i | 0.0267029 | − | 0.0267029i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −34.8428 | + | 20.1165i | −1.53685 | + | 0.887300i | ||||
\(515\) | −12.9678 | + | 15.2842i | −0.571428 | + | 0.673504i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.317975 | + | 0.317975i | 0.0139845 | + | 0.0139845i | ||||
\(518\) | −23.0216 | − | 1.90447i | −1.01151 | − | 0.0836775i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.9765 | − | 15.8596i | −0.481353 | − | 0.695489i | ||||
\(521\) | −20.0749 | + | 11.5902i | −0.879495 | + | 0.507777i | −0.870492 | − | 0.492183i | \(-0.836199\pi\) |
−0.00900344 | + | 0.999959i | \(0.502866\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.305268 | + | 1.13928i | 0.0133485 | + | 0.0498171i | 0.972279 | − | 0.233824i | \(-0.0751241\pi\) |
−0.958930 | + | 0.283642i | \(0.908457\pi\) | |||||||
\(524\) | 99.0025 | 4.32494 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −29.9962 | −1.30790 | ||||||||
\(527\) | 3.35912 | + | 12.5364i | 0.146326 | + | 0.546095i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.8794 | + | 11.4774i | −0.864320 | + | 0.499015i | ||||
\(530\) | −17.1284 | − | 24.7482i | −0.744010 | − | 1.07499i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 47.5623 | − | 68.6144i | 2.06209 | − | 2.97481i | ||||
\(533\) | 0.879147 | + | 0.879147i | 0.0380801 | + | 0.0380801i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.5642 | − | 23.0590i | 0.845833 | − | 0.996926i | ||||
\(536\) | 23.9859 | − | 13.8483i | 1.03603 | − | 0.598153i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 31.7169 | − | 31.7169i | 1.36741 | − | 1.36741i | ||||
\(539\) | −22.4728 | − | 18.4975i | −0.967971 | − | 0.796745i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.51761 | − | 7.82473i | 0.194227 | − | 0.336411i | −0.752420 | − | 0.658684i | \(-0.771113\pi\) |
0.946647 | + | 0.322273i | \(0.104447\pi\) | |||||||
\(542\) | −30.4784 | − | 8.16666i | −1.30916 | − | 0.350788i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −20.4184 | − | 11.7886i | −0.875430 | − | 0.505430i | ||||
\(545\) | −7.44880 | − | 3.52304i | −0.319072 | − | 0.150911i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.6405 | + | 22.6405i | 0.968036 | + | 0.968036i | 0.999505 | − | 0.0314683i | \(-0.0100183\pi\) |
−0.0314683 | + | 0.999505i | \(0.510018\pi\) | |||||||
\(548\) | −60.2646 | + | 16.1479i | −2.57438 | + | 0.689802i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 50.9215 | − | 23.0719i | 2.17130 | − | 0.983791i | ||||
\(551\) | −4.59313 | − | 2.65184i | −0.195674 | − | 0.112972i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.19999 | + | 2.45480i | −0.221126 | + | 0.104389i | ||||
\(554\) | 32.9847 | 1.40139 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 44.4721 | + | 77.0279i | 1.88604 | + | 3.26671i | ||||
\(557\) | −29.0377 | − | 7.78063i | −1.23037 | − | 0.329676i | −0.415645 | − | 0.909527i | \(-0.636444\pi\) |
−0.814723 | + | 0.579851i | \(0.803111\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.02334i | − | 0.254760i | ||||||
\(560\) | −38.1996 | + | 66.0526i | −1.61423 | + | 2.79123i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −52.1881 | + | 13.9838i | −2.20142 | + | 0.589870i | ||||
\(563\) | −4.47706 | + | 16.7086i | −0.188685 | + | 0.704184i | 0.805126 | + | 0.593104i | \(0.202098\pi\) |
−0.993811 | + | 0.111080i | \(0.964569\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.48465 | − | 41.1338i | 0.314882 | − | 1.73051i | ||||
\(566\) | − | 85.4287i | − | 3.59084i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −60.1204 | + | 60.1204i | −2.52260 | + | 2.52260i | ||||
\(569\) | 7.00255 | − | 12.1288i | 0.293562 | − | 0.508465i | −0.681087 | − | 0.732202i | \(-0.738493\pi\) |
0.974649 | + | 0.223738i | \(0.0718259\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.55183 | − | 4.41990i | −0.106791 | − | 0.184967i | 0.807678 | − | 0.589624i | \(-0.200724\pi\) |
−0.914468 | + | 0.404657i | \(0.867391\pi\) | |||||||
\(572\) | −5.58940 | − | 20.8599i | −0.233705 | − | 0.872197i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.00710 | − | 8.38511i | 0.125514 | − | 0.349988i | ||||
\(575\) | −0.104311 | + | 1.05904i | −0.00435008 | + | 0.0441650i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.25944 | + | 12.1644i | −0.135692 | + | 0.506411i | 0.864302 | + | 0.502974i | \(0.167761\pi\) |
−0.999994 | + | 0.00343709i | \(0.998906\pi\) | |||||||
\(578\) | −10.5398 | + | 39.3349i | −0.438396 | + | 1.63612i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.29501 | + | 4.39624i | 0.385954 | + | 0.182544i | ||||
\(581\) | −13.8419 | + | 2.50825i | −0.574258 | + | 0.104060i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.38699 | − | 20.1045i | −0.223106 | − | 0.832644i | ||||
\(584\) | −29.7058 | − | 51.4519i | −1.22923 | − | 2.12910i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.32263 | − | 10.9511i | 0.261186 | − | 0.452387i | ||||
\(587\) | −29.0630 | + | 29.0630i | −1.19956 | + | 1.19956i | −0.225260 | + | 0.974299i | \(0.572323\pi\) |
−0.974299 | + | 0.225260i | \(0.927677\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 57.4772i | 2.36831i | ||||||||
\(590\) | −1.33767 | − | 0.243401i | −0.0550710 | − | 0.0100206i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.8389 | + | 40.4514i | −0.445477 | + | 1.66254i | ||||
\(593\) | 27.3282 | − | 7.32257i | 1.12224 | − | 0.300702i | 0.350448 | − | 0.936582i | \(-0.386029\pi\) |
0.771788 | + | 0.635880i | \(0.219363\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.78306 | − | 2.09153i | −0.319074 | − | 0.0857445i | ||||
\(596\) | 55.6122i | 2.27797i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.548907 | + | 0.147079i | 0.0224465 | + | 0.00601451i | ||||
\(599\) | −13.6860 | − | 23.7049i | −0.559195 | − | 0.968554i | −0.997564 | − | 0.0697592i | \(-0.977777\pi\) |
0.438369 | − | 0.898795i | \(-0.355556\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.4893 | −1.61080 | −0.805401 | − | 0.592731i | \(-0.798050\pi\) | ||||
−0.805401 | + | 0.592731i | \(0.798050\pi\) | |||||||
\(602\) | −39.0260 | + | 18.4233i | −1.59058 | + | 0.750877i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −62.6747 | − | 36.1853i | −2.55020 | − | 1.47236i | ||||
\(605\) | 14.0167 | − | 1.14927i | 0.569859 | − | 0.0467245i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.88660 | + | 1.04141i | −0.157752 | + | 0.0422696i | −0.336831 | − | 0.941565i | \(-0.609355\pi\) |
0.179079 | + | 0.983835i | \(0.442688\pi\) | |||||||
\(608\) | −73.8314 | − | 73.8314i | −2.99426 | − | 2.99426i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24.1761 | − | 67.5681i | −0.978861 | − | 2.73575i | ||||
\(611\) | −0.0929988 | − | 0.0536929i | −0.00376233 | − | 0.00217218i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.6850 | + | 4.73869i | 0.714292 | + | 0.191394i | 0.597623 | − | 0.801777i | \(-0.296112\pi\) |
0.116668 | + | 0.993171i | \(0.462779\pi\) | |||||||
\(614\) | −5.64388 | + | 9.77549i | −0.227769 | + | 0.394507i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −72.9163 | + | 61.7740i | −2.93788 | + | 2.48895i | ||||
\(617\) | −21.3229 | + | 21.3229i | −0.858426 | + | 0.858426i | −0.991153 | − | 0.132727i | \(-0.957627\pi\) |
0.132727 | + | 0.991153i | \(0.457627\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.61954 | − | 1.51239i | 0.105288 | − | 0.0607883i | −0.446431 | − | 0.894818i | \(-0.647305\pi\) |
0.551720 | + | 0.834030i | \(0.313972\pi\) | |||||||
\(620\) | −9.10598 | − | 111.058i | −0.365705 | − | 4.46020i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.7744 | + | 17.7744i | 0.712688 | + | 0.712688i | ||||
\(623\) | 16.2597 | + | 34.4428i | 0.651431 | + | 1.37992i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.7958 | − | 16.4838i | −0.751834 | − | 0.659353i | ||||
\(626\) | 48.4572 | − | 27.9768i | 1.93674 | − | 1.11818i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 27.5311 | + | 102.747i | 1.09861 | + | 4.10007i | ||||
\(629\) | −4.42323 | −0.176366 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.5296 | 1.61346 | 0.806730 | − | 0.590921i | \(-0.201235\pi\) | ||||
0.806730 | + | 0.590921i | \(0.201235\pi\) | |||||||
\(632\) | 4.88653 | + | 18.2368i | 0.194376 | + | 0.725420i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 33.6130 | − | 19.4065i | 1.33494 | − | 0.770729i | ||||
\(635\) | 3.22833 | − | 17.7421i | 0.128112 | − | 0.704074i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.32697 | + | 2.87778i | 0.250684 | + | 0.114022i | ||||
\(638\) | 6.95051 | + | 6.95051i | 0.275173 | + | 0.275173i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 36.0879 | + | 30.6185i | 1.42650 | + | 1.21030i | ||||
\(641\) | −37.2313 | + | 21.4955i | −1.47055 | + | 0.849022i | −0.999453 | − | 0.0330603i | \(-0.989475\pi\) |
−0.471096 | + | 0.882082i | \(0.656141\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.4639 | − | 31.4639i | 1.24082 | − | 1.24082i | 0.281152 | − | 0.959663i | \(-0.409283\pi\) |
0.959663 | − | 0.281152i | \(-0.0907166\pi\) | |||||||
\(644\) | −0.525164 | − | 2.89814i | −0.0206944 | − | 0.114203i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.0493 | − | 19.1380i | 0.434730 | − | 0.752975i | ||||
\(647\) | 16.5816 | + | 4.44301i | 0.651888 | + | 0.174673i | 0.569582 | − | 0.821934i | \(-0.307105\pi\) |
0.0823057 | + | 0.996607i | \(0.473772\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.814279 | − | 0.470124i | −0.0319632 | − | 0.0184540i | ||||
\(650\) | −10.3198 | + | 8.46920i | −0.404778 | + | 0.332189i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.35583 | − | 6.35583i | −0.248913 | − | 0.248913i | ||||
\(653\) | −26.6769 | + | 7.14804i | −1.04395 | + | 0.279724i | −0.739748 | − | 0.672884i | \(-0.765055\pi\) |
−0.304198 | + | 0.952609i | \(0.598389\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.45864 | − | 42.1821i | −0.135140 | − | 1.64819i | ||||
\(656\) | −13.9857 | − | 8.07466i | −0.546051 | − | 0.315262i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.0634320 | + | 0.766779i | −0.00247284 | + | 0.0298922i | ||||
\(659\) | −6.44855 | −0.251200 | −0.125600 | − | 0.992081i | \(-0.540086\pi\) | ||||
−0.125600 | + | 0.992081i | \(0.540086\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.39721 | + | 5.88414i | 0.132136 | + | 0.228867i | 0.924500 | − | 0.381182i | \(-0.124483\pi\) |
−0.792364 | + | 0.610049i | \(0.791150\pi\) | |||||||
\(662\) | 29.9936 | + | 8.03675i | 1.16573 | + | 0.312357i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 46.1875i | 1.79242i | ||||||||
\(665\) | −30.8962 | − | 17.8679i | −1.19810 | − | 0.692888i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.180733 | + | 0.0484272i | −0.00699800 | + | 0.00187511i | ||||
\(668\) | −9.10418 | + | 33.9772i | −0.352251 | + | 1.31462i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.9099 | − | 15.7633i | −0.421486 | − | 0.608990i | ||||
\(671\) | − | 49.6273i | − | 1.91584i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.7865 | − | 15.7865i | 0.608524 | − | 0.608524i | −0.334036 | − | 0.942560i | \(-0.608411\pi\) |
0.942560 | + | 0.334036i | \(0.108411\pi\) | |||||||
\(674\) | −39.3773 | + | 68.2035i | −1.51676 | + | 2.62710i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −31.4200 | − | 54.4211i | −1.20846 | − | 2.09312i | ||||
\(677\) | 4.56513 | + | 17.0373i | 0.175452 | + | 0.654797i | 0.996474 | + | 0.0839000i | \(0.0267376\pi\) |
−0.821022 | + | 0.570897i | \(0.806596\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.3178 | + | 2.59449i | −0.549467 | + | 0.0995673i | ||||
\(680\) | −11.3136 | + | 23.9204i | −0.433855 | + | 0.917304i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 27.5705 | − | 102.895i | 1.05573 | − | 3.94004i | ||||
\(683\) | 6.77169 | − | 25.2723i | 0.259111 | − | 0.967017i | −0.706645 | − | 0.707568i | \(-0.749792\pi\) |
0.965757 | − | 0.259449i | \(-0.0835410\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.98548 | + | 25.1129i | 0.343318 | + | 0.959515i | ||||
\(686\) | −0.706516 | − | 49.7954i | −0.0269749 | − | 1.90120i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20.2493 | + | 75.5716i | 0.771999 | + | 2.88114i | ||||
\(689\) | 2.48519 | + | 4.30447i | 0.0946781 | + | 0.163987i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.25564 | + | 10.8351i | −0.237976 | + | 0.412186i | −0.960133 | − | 0.279543i | \(-0.909817\pi\) |
0.722158 | + | 0.691729i | \(0.243151\pi\) | |||||||
\(692\) | −1.00838 | + | 1.00838i | −0.0383328 | + | 0.0383328i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 57.2360i | − | 2.17265i | ||||||
\(695\) | 31.2658 | − | 21.6392i | 1.18598 | − | 0.820823i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.441469 | − | 1.64758i | 0.0167218 | − | 0.0624067i | ||||
\(698\) | 17.7819 | − | 4.76465i | 0.673055 | − | 0.180344i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 62.5288 | + | 29.6297i | 2.36336 | + | 1.11990i | ||||
\(701\) | 15.0496i | 0.568417i | 0.958763 | + | 0.284208i | \(0.0917307\pi\) | ||||
−0.958763 | + | 0.284208i | \(0.908269\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.9212 | − | 5.06992i | −0.713627 | − | 0.191216i | ||||
\(704\) | 43.1275 | + | 74.6991i | 1.62543 | + | 2.81533i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −54.7810 | −2.06171 | ||||||||
\(707\) | 1.98821 | − | 24.0339i | 0.0747743 | − | 0.903887i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.3774 | + | 21.0025i | 1.36618 | + | 0.788766i | 0.990438 | − | 0.137958i | \(-0.0440539\pi\) |
0.375744 | + | 0.926724i | \(0.377387\pi\) | |||||||
\(710\) | 44.8745 | + | 38.0734i | 1.68411 | + | 1.42887i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 120.794 | − | 32.3665i | 4.52693 | − | 1.21299i | ||||
\(713\) | 1.43382 | + | 1.43382i | 0.0536972 | + | 0.0536972i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.69255 | + | 3.11022i | −0.325083 | + | 0.116316i | ||||
\(716\) | −77.8167 | − | 44.9275i | −2.90815 | − | 1.67902i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −41.3921 | − | 11.0910i | −1.54474 | − | 0.413911i | ||||
\(719\) | −20.7737 | + | 35.9811i | −0.774729 | + | 1.34187i | 0.160217 | + | 0.987082i | \(0.448780\pi\) |
−0.934947 | + | 0.354788i | \(0.884553\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.3245 | − | 8.00608i | −0.831406 | − | 0.298162i | ||||
\(722\) | 33.0754 | − | 33.0754i | 1.23094 | − | 1.23094i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.4606 | − | 10.6582i | 0.686082 | − | 0.396110i | ||||
\(725\) | 1.54839 | − | 4.11392i | 0.0575058 | − | 0.152787i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.40873 | + | 5.40873i | 0.200599 | + | 0.200599i | 0.800256 | − | 0.599658i | \(-0.204697\pi\) |
−0.599658 | + | 0.800256i | \(0.704697\pi\) | |||||||
\(728\) | 13.0012 | − | 18.7559i | 0.481858 | − | 0.695139i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −33.8138 | + | 23.4027i | −1.25150 | + | 0.866174i | ||||
\(731\) | −7.15640 | + | 4.13175i | −0.264689 | + | 0.152818i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.15765 | + | 34.1768i | 0.338246 | + | 1.26235i | 0.900307 | + | 0.435255i | \(0.143342\pi\) |
−0.562062 | + | 0.827095i | \(0.689992\pi\) | |||||||
\(734\) | 30.2007 | 1.11473 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.68359 | −0.135779 | ||||||||
\(737\) | −3.43123 | − | 12.8055i | −0.126391 | − | 0.471698i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.4398 | + | 10.0689i | −0.641535 | + | 0.370390i | −0.785205 | − | 0.619235i | \(-0.787443\pi\) |
0.143671 | + | 0.989626i | \(0.454109\pi\) | |||||||
\(740\) | 37.3630 | + | 6.79851i | 1.37349 | + | 0.249918i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20.2879 | − | 29.2677i | 0.744792 | − | 1.07445i | ||||
\(743\) | −4.81639 | − | 4.81639i | −0.176696 | − | 0.176696i | 0.613218 | − | 0.789914i | \(-0.289875\pi\) |
−0.789914 | + | 0.613218i | \(0.789875\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.6948 | − | 1.94281i | 0.868110 | − | 0.0711789i | ||||
\(746\) | −71.7151 | + | 41.4047i | −2.62568 | + | 1.51594i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −20.9498 | + | 20.9498i | −0.766002 | + | 0.766002i | ||||
\(749\) | 33.6804 | + | 12.0786i | 1.23066 | + | 0.441342i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.34330 | − | 2.32666i | 0.0490177 | − | 0.0849012i | −0.840476 | − | 0.541850i | \(-0.817724\pi\) |
0.889493 | + | 0.456948i | \(0.151058\pi\) | |||||||
\(752\) | 1.34731 | + | 0.361011i | 0.0491314 | + | 0.0131647i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.03283 | − | 1.17366i | −0.0740313 | − | 0.0427420i | ||||
\(755\) | −13.2280 | + | 27.9680i | −0.481415 | + | 1.01786i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.4395 | + | 26.4395i | 0.960959 | + | 0.960959i | 0.999266 | − | 0.0383075i | \(-0.0121966\pi\) |
−0.0383075 | + | 0.999266i | \(0.512197\pi\) | |||||||
\(758\) | 15.0596 | − | 4.03521i | 0.546990 | − | 0.146566i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −75.8135 | + | 89.3563i | −2.75005 | + | 3.24129i | ||||
\(761\) | 22.8320 | + | 13.1820i | 0.827658 | + | 0.477849i | 0.853050 | − | 0.521829i | \(-0.174750\pi\) |
−0.0253919 | + | 0.999678i | \(0.508083\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.803794 | − | 9.71643i | 0.0290993 | − | 0.351758i | ||||
\(764\) | 49.2763 | 1.78275 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.6598 | + | 21.9274i | 0.457417 | + | 0.792270i | ||||
\(767\) | 0.216883 | + | 0.0581136i | 0.00783119 | + | 0.00209836i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 3.56245i | − | 0.128465i | −0.997935 | − | 0.0642326i | \(-0.979540\pi\) | ||
0.997935 | − | 0.0642326i | \(-0.0204600\pi\) | |||||||
\(770\) | 46.7390 | + | 46.8071i | 1.68436 | + | 1.68681i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 58.8460 | − | 15.7677i | 2.11791 | − | 0.567493i | ||||
\(773\) | −0.795756 | + | 2.96980i | −0.0286214 | + | 0.106816i | −0.978759 | − | 0.205015i | \(-0.934276\pi\) |
0.950137 | + | 0.311831i | \(0.100942\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −47.0005 | + | 7.75960i | −1.68831 | + | 0.278733i | ||||
\(776\) | 47.7755i | 1.71504i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18.7989 | + | 18.7989i | −0.673975 | + | 0.673975i | ||||
\(779\) | 3.77693 | − | 6.54184i | 0.135323 | − | 0.234386i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.3487 | + | 35.2449i | 0.728132 | + | 1.26116i | ||||
\(782\) | −0.201780 | − | 0.753053i | −0.00721563 | − | 0.0269291i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −89.0557 | − | 14.8358i | −3.18056 | − | 0.529851i | ||||
\(785\) | 42.8159 | − | 15.3197i | 1.52817 | − | 0.546783i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.9823 | + | 40.9866i | −0.391478 | + | 1.46101i | 0.436220 | + | 0.899840i | \(0.356317\pi\) |
−0.827698 | + | 0.561174i | \(0.810350\pi\) | |||||||
\(788\) | 15.4533 | − | 57.6727i | 0.550503 | − | 2.05450i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.3042 | − | 4.40248i | 0.437764 | − | 0.156633i | ||||
\(791\) | 48.6766 | − | 8.82056i | 1.73074 | − | 0.313623i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.06730 | + | 11.4473i | 0.108923 | + | 0.406506i | ||||
\(794\) | −29.0945 | − | 50.3932i | −1.03253 | − | 1.78839i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −49.6405 | + | 85.9799i | −1.75946 | + | 3.04748i | ||||
\(797\) | −37.3428 | + | 37.3428i | −1.32275 | + | 1.32275i | −0.411208 | + | 0.911542i | \(0.634893\pi\) |
−0.911542 | + | 0.411208i | \(0.865107\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.147324i | 0.00521195i | ||||||||
\(800\) | 50.4063 | − | 70.3413i | 1.78213 | − | 2.48694i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15.1887 | + | 56.6849i | −0.536331 | + | 2.00161i | ||||
\(803\) | −27.4690 | + | 7.36031i | −0.969361 | + | 0.259740i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.21647 | + | 0.325004i | −0.0428749 | + | 0.0114549i | ||||
\(806\) | 25.4383i | 0.896027i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −76.4825 | − | 20.4934i | −2.69064 | − | 0.720956i | ||||
\(809\) | −10.5010 | − | 18.1884i | −0.369197 | − | 0.639468i | 0.620243 | − | 0.784410i | \(-0.287034\pi\) |
−0.989440 | + | 0.144941i | \(0.953701\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.4188 | −1.27884 | −0.639419 | − | 0.768858i | \(-0.720825\pi\) | ||||
−0.639419 | + | 0.768858i | \(0.720825\pi\) | |||||||
\(812\) | −1.00302 | + | 12.1247i | −0.0351990 | + | 0.425493i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 31.4405 | + | 18.1522i | 1.10199 | + | 0.636233i | ||||
\(815\) | −2.48600 | + | 2.93008i | −0.0870807 | + | 0.102636i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −35.3487 | + | 9.47166i | −1.23670 | + | 0.331371i | ||||
\(818\) | −4.93364 | − | 4.93364i | −0.172501 | − | 0.172501i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.26142 | + | 13.2386i | −0.218658 | + | 0.462311i | ||||
\(821\) | 21.3394 | + | 12.3203i | 0.744751 | + | 0.429982i | 0.823794 | − | 0.566889i | \(-0.191853\pi\) |
−0.0790431 | + | 0.996871i | \(0.525186\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.4572 | − | 4.67764i | −0.608519 | − | 0.163052i | −0.0586159 | − | 0.998281i | \(-0.518669\pi\) |
−0.549903 | + | 0.835228i | \(0.685335\pi\) | |||||||
\(824\) | −38.9347 | + | 67.4368i | −1.35635 | + | 2.34927i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.286844 | − | 1.58296i | −0.00998059 | − | 0.0550783i | ||||
\(827\) | 25.8068 | − | 25.8068i | 0.897391 | − | 0.897391i | −0.0978136 | − | 0.995205i | \(-0.531185\pi\) |
0.995205 | + | 0.0978136i | \(0.0311849\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.1695 | + | 12.2222i | −0.735248 | + | 0.424496i | −0.820339 | − | 0.571878i | \(-0.806215\pi\) |
0.0850911 | + | 0.996373i | \(0.472882\pi\) | |||||||
\(830\) | 31.8623 | − | 2.61249i | 1.10596 | − | 0.0906808i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −14.5650 | − | 14.5650i | −0.504949 | − | 0.504949i | ||||
\(833\) | −0.920907 | − | 9.49119i | −0.0319075 | − | 0.328850i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.7948 | + | 2.69204i | 0.511995 | + | 0.0931618i | ||||
\(836\) | −113.630 | + | 65.6042i | −3.92997 | + | 2.26897i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.42988 | − | 23.9966i | −0.222117 | − | 0.828950i | ||||
\(839\) | −34.3012 | −1.18421 | −0.592105 | − | 0.805861i | \(-0.701703\pi\) | ||||
−0.592105 | + | 0.805861i | \(0.701703\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2271 | −0.973349 | ||||||||
\(842\) | 3.20278 | + | 11.9529i | 0.110375 | + | 0.411925i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −33.6631 | + | 19.4354i | −1.15873 | + | 0.668993i | ||||
\(845\) | −22.0896 | + | 15.2884i | −0.759906 | + | 0.525936i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.10379 | + | 15.0479i | 0.244089 | + | 0.517052i | ||||
\(848\) | −45.6511 | − | 45.6511i | −1.56767 | − | 1.56767i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 17.1413 | + | 6.45163i | 0.587943 | + | 0.221289i | ||||
\(851\) | −0.598482 | + | 0.345534i | −0.0205157 | + | 0.0118447i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.7234 | − | 38.7234i | 1.32586 | − | 1.32586i | 0.416919 | − | 0.908944i | \(-0.363110\pi\) |
0.908944 | − | 0.416919i | \(-0.136890\pi\) | |||||||
\(854\) | 64.7869 | − | 54.8868i | 2.21696 | − | 1.87819i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 58.7399 | − | 101.740i | 2.00769 | − | 3.47742i | ||||
\(857\) | 36.7630 | + | 9.85063i | 1.25580 | + | 0.336491i | 0.824575 | − | 0.565753i | \(-0.191414\pi\) |
0.431226 | + | 0.902244i | \(0.358081\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.3839 | + | 12.3460i | 0.729608 | + | 0.421239i | 0.818279 | − | 0.574822i | \(-0.194929\pi\) |
−0.0886709 | + | 0.996061i | \(0.528262\pi\) | |||||||
\(860\) | 66.8006 | − | 23.9015i | 2.27788 | − | 0.815033i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.29738 | − | 2.29738i | −0.0782491 | − | 0.0782491i | ||||
\(863\) | 14.5822 | − | 3.90728i | 0.496382 | − | 0.133005i | −0.00193811 | − | 0.999998i | \(-0.500617\pi\) |
0.498321 | + | 0.866993i | \(0.333950\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.464869 | + | 0.394414i | 0.0158060 | + | 0.0134105i | ||||
\(866\) | −69.8461 | − | 40.3257i | −2.37347 | − | 1.37032i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 119.229 | − | 56.2853i | 4.04689 | − | 1.91045i | ||||
\(869\) | 9.03718 | 0.306565 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.58293 | + | 2.74172i | 0.0536357 | + | 0.0928997i | ||||
\(872\) | −30.9204 | − | 8.28509i | −1.04710 | − | 0.280569i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 3.45261i | − | 0.116786i | ||||||
\(875\) | 10.4400 | − | 27.6768i | 0.352935 | − | 0.935648i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.5967 | − | 10.0740i | 1.26955 | − | 0.340175i | 0.439692 | − | 0.898149i | \(-0.355088\pi\) |
0.829859 | + | 0.557973i | \(0.188421\pi\) | |||||||
\(878\) | 5.83432 | − | 21.7740i | 0.196899 | − | 0.734836i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 98.6048 | − | 68.2450i | 3.32397 | − | 2.30054i | ||||
\(881\) | 40.0097i | 1.34796i | 0.738750 | + | 0.673980i | \(0.235417\pi\) | ||||
−0.738750 | + | 0.673980i | \(0.764583\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.2833 | − | 20.2833i | 0.682587 | − | 0.682587i | −0.277995 | − | 0.960582i | \(-0.589670\pi\) |
0.960582 | + | 0.277995i | \(0.0896700\pi\) | |||||||
\(884\) | 3.53757 | − | 6.12725i | 0.118981 | − | 0.206082i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.22761 | + | 12.5186i | 0.242816 | + | 0.420570i | ||||
\(887\) | 2.09272 | + | 7.81012i | 0.0702665 | + | 0.262238i | 0.992118 | − | 0.125304i | \(-0.0399907\pi\) |
−0.921852 | + | 0.387542i | \(0.873324\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.9955 | − | 3.80454i | 0.704167 | − | 0.127600i | ||||
\(890\) | −29.1604 | − | 81.4984i | −0.977458 | − | 2.73183i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18.5854 | − | 69.3616i | 0.622285 | − | 2.32240i | ||||
\(893\) | −0.168864 | + | 0.630208i | −0.00565080 | + | 0.0210891i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.4238 | + | 34.7250i | −0.548988 | + | 1.16073i | ||||
\(896\) | −18.9033 | + | 52.7108i | −0.631516 | + | 1.76094i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.33070 | + | 8.69830i | 0.0777765 | + | 0.290266i | ||||
\(899\) | −4.18791 | − | 7.25367i | −0.139675 | − | 0.241923i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.40946 | − | 5.90537i | 0.113586 | − | 0.196736i | ||||
\(902\) | −9.89938 | + | 9.89938i | −0.329613 | + | 0.329613i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 162.424i | − | 5.40213i | ||||||
\(905\) | −5.18609 | − | 7.49319i | −0.172391 | − | 0.249082i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.38781 | − | 12.6435i | 0.112491 | − | 0.419820i | −0.886596 | − | 0.462544i | \(-0.846937\pi\) |
0.999087 | + | 0.0427234i | \(0.0136034\pi\) | |||||||
\(908\) | −54.4155 | + | 14.5806i | −1.80584 | + | 0.483874i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −13.6741 | − | 7.90800i | −0.453291 | − | 0.262148i | ||||
\(911\) | − | 18.3815i | − | 0.609005i | −0.952512 | − | 0.304502i | \(-0.901510\pi\) | ||
0.952512 | − | 0.304502i | \(-0.0984901\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.3548 | + | 5.72201i | 0.706742 | + | 0.189371i | ||||
\(914\) | 1.40666 | + | 2.43640i | 0.0465281 | + | 0.0805891i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −38.7527 | −1.28042 | ||||||||
\(917\) | 45.2855 | − | 21.3783i | 1.49546 | − | 0.705974i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.5697 | − | 19.3815i | −1.10736 | − | 0.639336i | −0.169218 | − | 0.985579i | \(-0.554124\pi\) |
−0.938145 | + | 0.346242i | \(0.887457\pi\) | |||||||
\(920\) | 0.337838 | + | 4.12032i | 0.0111382 | + | 0.135843i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −59.8820 | + | 16.0453i | −1.97211 | + | 0.528425i | ||||
\(923\) | −6.87211 | − | 6.87211i | −0.226198 | − | 0.226198i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.59138 | − | 16.1568i | 0.0523243 | − | 0.531232i | ||||
\(926\) | 84.9899 | + | 49.0689i | 2.79294 | + | 1.61251i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 14.6971 | + | 3.93808i | 0.482456 | + | 0.129274i | ||||
\(929\) | 4.37286 | − | 7.57402i | 0.143469 | − | 0.248496i | −0.785332 | − | 0.619075i | \(-0.787508\pi\) |
0.928801 | + | 0.370580i | \(0.120841\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.93949 | − | 41.6559i | 0.227433 | − | 1.36522i | ||||
\(932\) | −82.4764 | + | 82.4764i | −2.70160 | + | 2.70160i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −56.1993 | + | 32.4467i | −1.83890 | + | 1.06169i | ||||
\(935\) | 9.65801 | + | 8.19425i | 0.315851 | + | 0.267981i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.8936 | + | 10.8936i | 0.355879 | + | 0.355879i | 0.862291 | − | 0.506413i | \(-0.169029\pi\) |
−0.506413 | + | 0.862291i | \(0.669029\pi\) | |||||||
\(938\) | 12.9223 | − | 18.6420i | 0.421929 | − | 0.608683i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.226438 | − | 1.24445i | 0.00738558 | − | 0.0405894i | ||||
\(941\) | 47.6405 | − | 27.5052i | 1.55304 | − | 0.896646i | 0.555143 | − | 0.831755i | \(-0.312663\pi\) |
0.997892 | − | 0.0648907i | \(-0.0206699\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.0689733 | − | 0.257412i | −0.00224608 | − | 0.00838249i | ||||
\(944\) | −2.91648 | −0.0949234 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 67.8240 | 2.20515 | ||||||||
\(947\) | 11.1538 | + | 41.6265i | 0.362449 | + | 1.35268i | 0.870846 | + | 0.491556i | \(0.163572\pi\) |
−0.508396 | + | 0.861123i | \(0.669762\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.88125 | − | 3.39554i | 0.190913 | − | 0.110224i | ||||
\(950\) | 65.9305 | + | 47.2456i | 2.13907 | + | 1.53285i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −31.2024 | − | 2.58123i | −1.01128 | − | 0.0836580i | ||||
\(953\) | −15.9728 | − | 15.9728i | −0.517408 | − | 0.517408i | 0.399378 | − | 0.916786i | \(-0.369226\pi\) |
−0.916786 | + | 0.399378i | \(0.869226\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.72146 | − | 20.9952i | −0.0557052 | − | 0.679389i | ||||
\(956\) | 54.0710 | − | 31.2179i | 1.74878 | − | 1.00966i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −36.5799 | + | 36.5799i | −1.18184 | + | 1.18184i | ||||
\(959\) | −24.0792 | + | 20.3997i | −0.777559 | + | 0.658740i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.8853 | + | 51.7628i | −0.964040 | + | 1.66977i | ||||
\(962\) | −8.37417 | − | 2.24385i | −0.269994 | − | 0.0723447i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 66.7081 | + | 38.5140i | 2.14852 | + | 1.24045i | ||||
\(965\) | −8.77396 | − | 24.5217i | −0.282444 | − | 0.789383i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.1296 | + | 16.1296i | 0.518694 | + | 0.518694i | 0.917176 | − | 0.398482i | \(-0.130463\pi\) |
−0.398482 | + | 0.917176i | \(0.630463\pi\) | |||||||
\(968\) | 52.7742 | − | 14.1408i | 1.69623 | − | 0.454502i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 32.9578 | − | 2.70231i | 1.05821 | − | 0.0867660i | ||||
\(971\) | 38.0747 | + | 21.9824i | 1.22187 | + | 0.705449i | 0.965317 | − | 0.261080i | \(-0.0840786\pi\) |
0.256557 | + | 0.966529i | \(0.417412\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.9755 | + | 25.6308i | 1.18538 | + | 0.821685i | ||||
\(974\) | −78.4436 | −2.51349 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −76.9676 | − | 133.312i | −2.46367 | − | 4.26720i | ||||
\(977\) | −55.7479 | − | 14.9376i | −1.78353 | − | 0.477896i | −0.792312 | − | 0.610117i | \(-0.791123\pi\) |
−0.991220 | + | 0.132221i | \(0.957789\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 59.8589i | − | 1.91310i | ||||||
\(980\) | −6.80909 | + | 81.5874i | −0.217508 | + | 2.60622i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −20.2395 | + | 5.42317i | −0.645870 | + | 0.173060i | ||||
\(983\) | −1.79419 | + | 6.69600i | −0.0572257 | + | 0.213569i | −0.988618 | − | 0.150448i | \(-0.951928\pi\) |
0.931392 | + | 0.364017i | \(0.118595\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.1125 | − | 4.56944i | −0.800152 | − | 0.145595i | ||||
\(986\) | 3.22031i | 0.102556i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 22.1557 | − | 22.1557i | 0.704868 | − | 0.704868i | ||||
\(989\) | −0.645528 | + | 1.11809i | −0.0205266 | + | 0.0355531i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.8019 | − | 25.6376i | −0.470197 | − | 0.814405i | 0.529222 | − | 0.848483i | \(-0.322484\pi\) |
−0.999419 | + | 0.0340783i | \(0.989150\pi\) | |||||||
\(992\) | −42.6778 | − | 159.276i | −1.35502 | − | 5.05701i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −23.5059 | + | 65.5447i | −0.745561 | + | 2.07895i | ||||
\(995\) | 38.3678 | + | 18.1467i | 1.21634 | + | 0.575289i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.53622 | − | 16.9294i | 0.143663 | − | 0.536159i | −0.856148 | − | 0.516731i | \(-0.827149\pi\) |
0.999811 | − | 0.0194282i | \(-0.00618457\pi\) | |||||||
\(998\) | −3.63421 | + | 13.5631i | −0.115039 | + | 0.429331i | ||||
\(999\) | 0 | 0 |
(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 | 315.2.ce.a.107.1 | yes | 64 | |
3.2 | odd | 2 | inner | 315.2.ce.a.107.16 | yes | 64 | |
5.3 | odd | 4 | inner | 315.2.ce.a.233.1 | yes | 64 | |
7.4 | even | 3 | inner | 315.2.ce.a.242.16 | yes | 64 | |
15.8 | even | 4 | inner | 315.2.ce.a.233.16 | yes | 64 | |
21.11 | odd | 6 | inner | 315.2.ce.a.242.1 | yes | 64 | |
35.18 | odd | 12 | inner | 315.2.ce.a.53.16 | yes | 64 | |
105.53 | even | 12 | inner | 315.2.ce.a.53.1 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.ce.a.53.1 | ✓ | 64 | 105.53 | even | 12 | inner | |
315.2.ce.a.53.16 | yes | 64 | 35.18 | odd | 12 | inner | |
315.2.ce.a.107.1 | yes | 64 | 1.1 | even | 1 | trivial | |
315.2.ce.a.107.16 | yes | 64 | 3.2 | odd | 2 | inner | |
315.2.ce.a.233.1 | yes | 64 | 5.3 | odd | 4 | inner | |
315.2.ce.a.233.16 | yes | 64 | 15.8 | even | 4 | inner | |
315.2.ce.a.242.1 | yes | 64 | 21.11 | odd | 6 | inner | |
315.2.ce.a.242.16 | yes | 64 | 7.4 | even | 3 | inner |