Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(253,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.o (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 253.8 | ||
Character | \(\chi\) | \(=\) | 1110.253 |
Dual form | 1110.2.o.a.487.8 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.23596 | + | 0.0221544i | 0.999951 | + | 0.00990775i | ||||
\(6\) | 0.707107 | − | 0.707107i | 0.288675 | − | 0.288675i | ||||
\(7\) | −0.281427 | + | 0.281427i | −0.106369 | + | 0.106369i | −0.758289 | − | 0.651919i | \(-0.773964\pi\) |
0.651919 | + | 0.758289i | \(0.273964\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −2.23596 | − | 0.0221544i | −0.707072 | − | 0.00700584i | ||||
\(11\) | − | 1.64708i | − | 0.496614i | −0.968681 | − | 0.248307i | \(-0.920126\pi\) | ||
0.968681 | − | 0.248307i | \(-0.0798742\pi\) | |||||||
\(12\) | −0.707107 | + | 0.707107i | −0.204124 | + | 0.204124i | ||||
\(13\) | 3.15714 | 0.875634 | 0.437817 | − | 0.899064i | \(-0.355752\pi\) | ||||
0.437817 | + | 0.899064i | \(0.355752\pi\) | |||||||
\(14\) | 0.281427 | − | 0.281427i | 0.0752146 | − | 0.0752146i | ||||
\(15\) | −1.59673 | + | 1.56540i | −0.412273 | + | 0.404183i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 3.44561i | − | 0.835684i | −0.908520 | − | 0.417842i | \(-0.862787\pi\) | ||
0.908520 | − | 0.417842i | \(-0.137213\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −1.85024 | − | 1.85024i | −0.424475 | − | 0.424475i | 0.462266 | − | 0.886741i | \(-0.347036\pi\) |
−0.886741 | + | 0.462266i | \(0.847036\pi\) | |||||||
\(20\) | 2.23596 | + | 0.0221544i | 0.499975 | + | 0.00495387i | ||||
\(21\) | − | 0.397998i | − | 0.0868503i | ||||||
\(22\) | 1.64708i | 0.351159i | ||||||||
\(23\) | 3.91265 | 0.815844 | 0.407922 | − | 0.913017i | \(-0.366253\pi\) | ||||
0.407922 | + | 0.913017i | \(0.366253\pi\) | |||||||
\(24\) | 0.707107 | − | 0.707107i | 0.144338 | − | 0.144338i | ||||
\(25\) | 4.99902 | + | 0.0990726i | 0.999804 | + | 0.0198145i | ||||
\(26\) | −3.15714 | −0.619167 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | −0.281427 | + | 0.281427i | −0.0531847 | + | 0.0531847i | ||||
\(29\) | 2.67202 | − | 2.67202i | 0.496181 | − | 0.496181i | −0.414066 | − | 0.910247i | \(-0.635892\pi\) |
0.910247 | + | 0.414066i | \(0.135892\pi\) | |||||||
\(30\) | 1.59673 | − | 1.56540i | 0.291521 | − | 0.285801i | ||||
\(31\) | −6.77259 | − | 6.77259i | −1.21639 | − | 1.21639i | −0.968886 | − | 0.247506i | \(-0.920389\pi\) |
−0.247506 | − | 0.968886i | \(-0.579611\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.16466 | + | 1.16466i | 0.202742 | + | 0.202742i | ||||
\(34\) | 3.44561i | 0.590917i | ||||||||
\(35\) | −0.635494 | + | 0.623024i | −0.107418 | + | 0.105310i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | 0.925435 | + | 6.01195i | 0.152141 | + | 0.988359i | ||||
\(38\) | 1.85024 | + | 1.85024i | 0.300149 | + | 0.300149i | ||||
\(39\) | −2.23244 | + | 2.23244i | −0.357476 | + | 0.357476i | ||||
\(40\) | −2.23596 | − | 0.0221544i | −0.353536 | − | 0.00350292i | ||||
\(41\) | − | 8.72049i | − | 1.36191i | −0.732325 | − | 0.680956i | \(-0.761565\pi\) | ||
0.732325 | − | 0.680956i | \(-0.238435\pi\) | |||||||
\(42\) | 0.397998i | 0.0614124i | ||||||||
\(43\) | 1.27639 | 0.194647 | 0.0973237 | − | 0.995253i | \(-0.468972\pi\) | ||||
0.0973237 | + | 0.995253i | \(0.468972\pi\) | |||||||
\(44\) | − | 1.64708i | − | 0.248307i | ||||||
\(45\) | 0.0221544 | − | 2.23596i | 0.00330258 | − | 0.333317i | ||||
\(46\) | −3.91265 | −0.576889 | ||||||||
\(47\) | −0.752821 | + | 0.752821i | −0.109810 | + | 0.109810i | −0.759877 | − | 0.650067i | \(-0.774741\pi\) |
0.650067 | + | 0.759877i | \(0.274741\pi\) | |||||||
\(48\) | −0.707107 | + | 0.707107i | −0.102062 | + | 0.102062i | ||||
\(49\) | 6.84160i | 0.977371i | ||||||||
\(50\) | −4.99902 | − | 0.0990726i | −0.706968 | − | 0.0140110i | ||||
\(51\) | 2.43642 | + | 2.43642i | 0.341166 | + | 0.341166i | ||||
\(52\) | 3.15714 | 0.437817 | ||||||||
\(53\) | 3.88760 | + | 3.88760i | 0.534003 | + | 0.534003i | 0.921761 | − | 0.387758i | \(-0.126750\pi\) |
−0.387758 | + | 0.921761i | \(0.626750\pi\) | |||||||
\(54\) | −0.707107 | − | 0.707107i | −0.0962250 | − | 0.0962250i | ||||
\(55\) | 0.0364901 | − | 3.68281i | 0.00492033 | − | 0.496590i | ||||
\(56\) | 0.281427 | − | 0.281427i | 0.0376073 | − | 0.0376073i | ||||
\(57\) | 2.61664 | 0.346582 | ||||||||
\(58\) | −2.67202 | + | 2.67202i | −0.350853 | + | 0.350853i | ||||
\(59\) | −6.53793 | − | 6.53793i | −0.851166 | − | 0.851166i | 0.139111 | − | 0.990277i | \(-0.455576\pi\) |
−0.990277 | + | 0.139111i | \(0.955576\pi\) | |||||||
\(60\) | −1.59673 | + | 1.56540i | −0.206137 | + | 0.202092i | ||||
\(61\) | −0.144746 | − | 0.144746i | −0.0185328 | − | 0.0185328i | 0.697780 | − | 0.716312i | \(-0.254171\pi\) |
−0.716312 | + | 0.697780i | \(0.754171\pi\) | |||||||
\(62\) | 6.77259 | + | 6.77259i | 0.860119 | + | 0.860119i | ||||
\(63\) | 0.281427 | + | 0.281427i | 0.0354565 | + | 0.0354565i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.05924 | + | 0.0699446i | 0.875591 | + | 0.00867556i | ||||
\(66\) | −1.16466 | − | 1.16466i | −0.143360 | − | 0.143360i | ||||
\(67\) | −0.492575 | − | 0.492575i | −0.0601777 | − | 0.0601777i | 0.676377 | − | 0.736555i | \(-0.263549\pi\) |
−0.736555 | + | 0.676377i | \(0.763549\pi\) | |||||||
\(68\) | − | 3.44561i | − | 0.417842i | ||||||
\(69\) | −2.76666 | + | 2.76666i | −0.333067 | + | 0.333067i | ||||
\(70\) | 0.635494 | − | 0.623024i | 0.0759561 | − | 0.0744657i | ||||
\(71\) | 11.2201 | 1.33158 | 0.665790 | − | 0.746140i | \(-0.268095\pi\) | ||||
0.665790 | + | 0.746140i | \(0.268095\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 0.804916 | − | 0.804916i | 0.0942083 | − | 0.0942083i | −0.658432 | − | 0.752640i | \(-0.728780\pi\) |
0.752640 | + | 0.658432i | \(0.228780\pi\) | |||||||
\(74\) | −0.925435 | − | 6.01195i | −0.107580 | − | 0.698875i | ||||
\(75\) | −3.60489 | + | 3.46478i | −0.416257 | + | 0.400079i | ||||
\(76\) | −1.85024 | − | 1.85024i | −0.212237 | − | 0.212237i | ||||
\(77\) | 0.463534 | + | 0.463534i | 0.0528246 | + | 0.0528246i | ||||
\(78\) | 2.23244 | − | 2.23244i | 0.252774 | − | 0.252774i | ||||
\(79\) | 2.86326 | + | 2.86326i | 0.322142 | + | 0.322142i | 0.849588 | − | 0.527446i | \(-0.176850\pi\) |
−0.527446 | + | 0.849588i | \(0.676850\pi\) | |||||||
\(80\) | 2.23596 | + | 0.0221544i | 0.249988 | + | 0.00247694i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 8.72049i | 0.963017i | ||||||||
\(83\) | 3.45461 | + | 3.45461i | 0.379192 | + | 0.379192i | 0.870811 | − | 0.491618i | \(-0.163594\pi\) |
−0.491618 | + | 0.870811i | \(0.663594\pi\) | |||||||
\(84\) | − | 0.397998i | − | 0.0434251i | ||||||
\(85\) | 0.0763355 | − | 7.70424i | 0.00827974 | − | 0.835643i | ||||
\(86\) | −1.27639 | −0.137636 | ||||||||
\(87\) | 3.77880i | 0.405130i | ||||||||
\(88\) | 1.64708i | 0.175580i | ||||||||
\(89\) | 12.5832 | − | 12.5832i | 1.33381 | − | 1.33381i | 0.431885 | − | 0.901929i | \(-0.357849\pi\) |
0.901929 | − | 0.431885i | \(-0.142151\pi\) | |||||||
\(90\) | −0.0221544 | + | 2.23596i | −0.00233528 | + | 0.235691i | ||||
\(91\) | −0.888506 | + | 0.888506i | −0.0931407 | + | 0.0931407i | ||||
\(92\) | 3.91265 | 0.407922 | ||||||||
\(93\) | 9.57788 | 0.993180 | ||||||||
\(94\) | 0.752821 | − | 0.752821i | 0.0776476 | − | 0.0776476i | ||||
\(95\) | −4.09608 | − | 4.17806i | −0.420248 | − | 0.428660i | ||||
\(96\) | 0.707107 | − | 0.707107i | 0.0721688 | − | 0.0721688i | ||||
\(97\) | 6.92746i | 0.703377i | 0.936117 | + | 0.351689i | \(0.114392\pi\) | ||||
−0.936117 | + | 0.351689i | \(0.885608\pi\) | |||||||
\(98\) | − | 6.84160i | − | 0.691106i | ||||||
\(99\) | −1.64708 | −0.165538 | ||||||||
\(100\) | 4.99902 | + | 0.0990726i | 0.499902 | + | 0.00990726i | ||||
\(101\) | − | 6.04485i | − | 0.601486i | −0.953705 | − | 0.300743i | \(-0.902765\pi\) | ||
0.953705 | − | 0.300743i | \(-0.0972346\pi\) | |||||||
\(102\) | −2.43642 | − | 2.43642i | −0.241241 | − | 0.241241i | ||||
\(103\) | 11.2563i | 1.10912i | 0.832144 | + | 0.554560i | \(0.187113\pi\) | ||||
−0.832144 | + | 0.554560i | \(0.812887\pi\) | |||||||
\(104\) | −3.15714 | −0.309583 | ||||||||
\(105\) | 0.00881741 | − | 0.889907i | 0.000860491 | − | 0.0868460i | ||||
\(106\) | −3.88760 | − | 3.88760i | −0.377597 | − | 0.377597i | ||||
\(107\) | 8.88960 | − | 8.88960i | 0.859390 | − | 0.859390i | −0.131876 | − | 0.991266i | \(-0.542100\pi\) |
0.991266 | + | 0.131876i | \(0.0421001\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | 8.94425 | + | 8.94425i | 0.856704 | + | 0.856704i | 0.990948 | − | 0.134244i | \(-0.0428607\pi\) |
−0.134244 | + | 0.990948i | \(0.542861\pi\) | |||||||
\(110\) | −0.0364901 | + | 3.68281i | −0.00347920 | + | 0.351142i | ||||
\(111\) | −4.90547 | − | 3.59671i | −0.465607 | − | 0.341385i | ||||
\(112\) | −0.281427 | + | 0.281427i | −0.0265924 | + | 0.0265924i | ||||
\(113\) | − | 0.196751i | − | 0.0185088i | −0.999957 | − | 0.00925440i | \(-0.997054\pi\) | ||
0.999957 | − | 0.00925440i | \(-0.00294581\pi\) | |||||||
\(114\) | −2.61664 | −0.245071 | ||||||||
\(115\) | 8.74853 | + | 0.0866825i | 0.815804 | + | 0.00808318i | ||||
\(116\) | 2.67202 | − | 2.67202i | 0.248090 | − | 0.248090i | ||||
\(117\) | − | 3.15714i | − | 0.291878i | ||||||
\(118\) | 6.53793 | + | 6.53793i | 0.601865 | + | 0.601865i | ||||
\(119\) | 0.969688 | + | 0.969688i | 0.0888912 | + | 0.0888912i | ||||
\(120\) | 1.59673 | − | 1.56540i | 0.145761 | − | 0.142900i | ||||
\(121\) | 8.28712 | 0.753375 | ||||||||
\(122\) | 0.144746 | + | 0.144746i | 0.0131047 | + | 0.0131047i | ||||
\(123\) | 6.16632 | + | 6.16632i | 0.555998 | + | 0.555998i | ||||
\(124\) | −6.77259 | − | 6.77259i | −0.608196 | − | 0.608196i | ||||
\(125\) | 11.1754 | + | 0.332273i | 0.999558 | + | 0.0297194i | ||||
\(126\) | −0.281427 | − | 0.281427i | −0.0250715 | − | 0.0250715i | ||||
\(127\) | 6.37075 | − | 6.37075i | 0.565313 | − | 0.565313i | −0.365499 | − | 0.930812i | \(-0.619102\pi\) |
0.930812 | + | 0.365499i | \(0.119102\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.902543 | + | 0.902543i | −0.0794644 | + | 0.0794644i | ||||
\(130\) | −7.05924 | − | 0.0699446i | −0.619136 | − | 0.00613455i | ||||
\(131\) | −2.48554 | − | 2.48554i | −0.217162 | − | 0.217162i | 0.590139 | − | 0.807302i | \(-0.299073\pi\) |
−0.807302 | + | 0.590139i | \(0.799073\pi\) | |||||||
\(132\) | 1.16466 | + | 1.16466i | 0.101371 | + | 0.101371i | ||||
\(133\) | 1.04142 | 0.0903023 | ||||||||
\(134\) | 0.492575 | + | 0.492575i | 0.0425520 | + | 0.0425520i | ||||
\(135\) | 1.56540 | + | 1.59673i | 0.134728 | + | 0.137424i | ||||
\(136\) | 3.44561i | 0.295459i | ||||||||
\(137\) | 15.3866 | − | 15.3866i | 1.31456 | − | 1.31456i | 0.396553 | − | 0.918012i | \(-0.370206\pi\) |
0.918012 | − | 0.396553i | \(-0.129794\pi\) | |||||||
\(138\) | 2.76666 | − | 2.76666i | 0.235514 | − | 0.235514i | ||||
\(139\) | −2.99885 | −0.254359 | −0.127180 | − | 0.991880i | \(-0.540592\pi\) | ||||
−0.127180 | + | 0.991880i | \(0.540592\pi\) | |||||||
\(140\) | −0.635494 | + | 0.623024i | −0.0537091 | + | 0.0526552i | ||||
\(141\) | − | 1.06465i | − | 0.0896597i | ||||||
\(142\) | −11.2201 | −0.941569 | ||||||||
\(143\) | − | 5.20007i | − | 0.434852i | ||||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 6.03371 | − | 5.91532i | 0.501073 | − | 0.491240i | ||||
\(146\) | −0.804916 | + | 0.804916i | −0.0666153 | + | 0.0666153i | ||||
\(147\) | −4.83774 | − | 4.83774i | −0.399010 | − | 0.399010i | ||||
\(148\) | 0.925435 | + | 6.01195i | 0.0760703 | + | 0.494179i | ||||
\(149\) | 8.60756i | 0.705159i | 0.935782 | + | 0.352579i | \(0.114695\pi\) | ||||
−0.935782 | + | 0.352579i | \(0.885305\pi\) | |||||||
\(150\) | 3.60489 | − | 3.46478i | 0.294338 | − | 0.282898i | ||||
\(151\) | 2.73615i | 0.222665i | 0.993783 | + | 0.111332i | \(0.0355118\pi\) | ||||
−0.993783 | + | 0.111332i | \(0.964488\pi\) | |||||||
\(152\) | 1.85024 | + | 1.85024i | 0.150075 | + | 0.150075i | ||||
\(153\) | −3.44561 | −0.278561 | ||||||||
\(154\) | −0.463534 | − | 0.463534i | −0.0373526 | − | 0.0373526i | ||||
\(155\) | −14.9932 | − | 15.2933i | −1.20428 | − | 1.22838i | ||||
\(156\) | −2.23244 | + | 2.23244i | −0.178738 | + | 0.178738i | ||||
\(157\) | −4.40198 | + | 4.40198i | −0.351317 | + | 0.351317i | −0.860599 | − | 0.509283i | \(-0.829911\pi\) |
0.509283 | + | 0.860599i | \(0.329911\pi\) | |||||||
\(158\) | −2.86326 | − | 2.86326i | −0.227789 | − | 0.227789i | ||||
\(159\) | −5.49790 | −0.436011 | ||||||||
\(160\) | −2.23596 | − | 0.0221544i | −0.176768 | − | 0.00175146i | ||||
\(161\) | −1.10113 | + | 1.10113i | −0.0867809 | + | 0.0867809i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 10.2487i | 0.802740i | 0.915916 | + | 0.401370i | \(0.131466\pi\) | ||||
−0.915916 | + | 0.401370i | \(0.868534\pi\) | |||||||
\(164\) | − | 8.72049i | − | 0.680956i | ||||||
\(165\) | 2.57834 | + | 2.62994i | 0.200723 | + | 0.204741i | ||||
\(166\) | −3.45461 | − | 3.45461i | −0.268130 | − | 0.268130i | ||||
\(167\) | 2.97278i | 0.230040i | 0.993363 | + | 0.115020i | \(0.0366933\pi\) | ||||
−0.993363 | + | 0.115020i | \(0.963307\pi\) | |||||||
\(168\) | 0.397998i | 0.0307062i | ||||||||
\(169\) | −3.03245 | −0.233265 | ||||||||
\(170\) | −0.0763355 | + | 7.70424i | −0.00585466 | + | 0.590888i | ||||
\(171\) | −1.85024 | + | 1.85024i | −0.141492 | + | 0.141492i | ||||
\(172\) | 1.27639 | 0.0973237 | ||||||||
\(173\) | −5.83257 | + | 5.83257i | −0.443442 | + | 0.443442i | −0.893167 | − | 0.449725i | \(-0.851522\pi\) |
0.449725 | + | 0.893167i | \(0.351522\pi\) | |||||||
\(174\) | − | 3.77880i | − | 0.286470i | ||||||
\(175\) | −1.43474 | + | 1.37898i | −0.108456 | + | 0.104241i | ||||
\(176\) | − | 1.64708i | − | 0.124153i | ||||||
\(177\) | 9.24603 | 0.694974 | ||||||||
\(178\) | −12.5832 | + | 12.5832i | −0.943149 | + | 0.943149i | ||||
\(179\) | −4.52269 | + | 4.52269i | −0.338042 | + | 0.338042i | −0.855630 | − | 0.517588i | \(-0.826830\pi\) |
0.517588 | + | 0.855630i | \(0.326830\pi\) | |||||||
\(180\) | 0.0221544 | − | 2.23596i | 0.00165129 | − | 0.166658i | ||||
\(181\) | −16.8840 | −1.25497 | −0.627487 | − | 0.778627i | \(-0.715917\pi\) | ||||
−0.627487 | + | 0.778627i | \(0.715917\pi\) | |||||||
\(182\) | 0.888506 | − | 0.888506i | 0.0658604 | − | 0.0658604i | ||||
\(183\) | 0.204701 | 0.0151320 | ||||||||
\(184\) | −3.91265 | −0.288445 | ||||||||
\(185\) | 1.93604 | + | 13.4630i | 0.142341 | + | 0.989818i | ||||
\(186\) | −9.57788 | −0.702284 | ||||||||
\(187\) | −5.67521 | −0.415012 | ||||||||
\(188\) | −0.752821 | + | 0.752821i | −0.0549051 | + | 0.0549051i | ||||
\(189\) | −0.397998 | −0.0289501 | ||||||||
\(190\) | 4.09608 | + | 4.17806i | 0.297161 | + | 0.303108i | ||||
\(191\) | −18.5005 | + | 18.5005i | −1.33865 | + | 1.33865i | −0.441274 | + | 0.897372i | \(0.645473\pi\) |
−0.897372 | + | 0.441274i | \(0.854527\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | −17.1049 | −1.23124 | −0.615620 | − | 0.788043i | \(-0.711094\pi\) | ||||
−0.615620 | + | 0.788043i | \(0.711094\pi\) | |||||||
\(194\) | − | 6.92746i | − | 0.497363i | ||||||
\(195\) | −5.04109 | + | 4.94218i | −0.361000 | + | 0.353917i | ||||
\(196\) | 6.84160i | 0.488686i | ||||||||
\(197\) | −0.556751 | + | 0.556751i | −0.0396669 | + | 0.0396669i | −0.726662 | − | 0.686995i | \(-0.758929\pi\) |
0.686995 | + | 0.726662i | \(0.258929\pi\) | |||||||
\(198\) | 1.64708 | 0.117053 | ||||||||
\(199\) | −7.91159 | + | 7.91159i | −0.560838 | + | 0.560838i | −0.929546 | − | 0.368707i | \(-0.879800\pi\) |
0.368707 | + | 0.929546i | \(0.379800\pi\) | |||||||
\(200\) | −4.99902 | − | 0.0990726i | −0.353484 | − | 0.00700549i | ||||
\(201\) | 0.696607 | 0.0491349 | ||||||||
\(202\) | 6.04485i | 0.425314i | ||||||||
\(203\) | 1.50396i | 0.105557i | ||||||||
\(204\) | 2.43642 | + | 2.43642i | 0.170583 | + | 0.170583i | ||||
\(205\) | 0.193197 | − | 19.4986i | 0.0134935 | − | 1.36184i | ||||
\(206\) | − | 11.2563i | − | 0.784266i | ||||||
\(207\) | − | 3.91265i | − | 0.271948i | ||||||
\(208\) | 3.15714 | 0.218908 | ||||||||
\(209\) | −3.04750 | + | 3.04750i | −0.210800 | + | 0.210800i | ||||
\(210\) | −0.00881741 | + | 0.889907i | −0.000608459 | + | 0.0614094i | ||||
\(211\) | −1.32938 | −0.0915183 | −0.0457592 | − | 0.998953i | \(-0.514571\pi\) | ||||
−0.0457592 | + | 0.998953i | \(0.514571\pi\) | |||||||
\(212\) | 3.88760 | + | 3.88760i | 0.267001 | + | 0.267001i | ||||
\(213\) | −7.93380 | + | 7.93380i | −0.543615 | + | 0.543615i | ||||
\(214\) | −8.88960 | + | 8.88960i | −0.607681 | + | 0.607681i | ||||
\(215\) | 2.85395 | + | 0.0282776i | 0.194638 | + | 0.00192852i | ||||
\(216\) | −0.707107 | − | 0.707107i | −0.0481125 | − | 0.0481125i | ||||
\(217\) | 3.81198 | 0.258774 | ||||||||
\(218\) | −8.94425 | − | 8.94425i | −0.605781 | − | 0.605781i | ||||
\(219\) | 1.13832i | 0.0769207i | ||||||||
\(220\) | 0.0364901 | − | 3.68281i | 0.00246016 | − | 0.248295i | ||||
\(221\) | − | 10.8783i | − | 0.731753i | ||||||
\(222\) | 4.90547 | + | 3.59671i | 0.329234 | + | 0.241395i | ||||
\(223\) | −3.07126 | − | 3.07126i | −0.205667 | − | 0.205667i | 0.596756 | − | 0.802423i | \(-0.296456\pi\) |
−0.802423 | + | 0.596756i | \(0.796456\pi\) | |||||||
\(224\) | 0.281427 | − | 0.281427i | 0.0188036 | − | 0.0188036i | ||||
\(225\) | 0.0990726 | − | 4.99902i | 0.00660484 | − | 0.333268i | ||||
\(226\) | 0.196751i | 0.0130877i | ||||||||
\(227\) | − | 24.6591i | − | 1.63668i | −0.574732 | − | 0.818342i | \(-0.694894\pi\) | ||
0.574732 | − | 0.818342i | \(-0.305106\pi\) | |||||||
\(228\) | 2.61664 | 0.173291 | ||||||||
\(229\) | − | 14.8812i | − | 0.983377i | −0.870771 | − | 0.491689i | \(-0.836380\pi\) | ||
0.870771 | − | 0.491689i | \(-0.163620\pi\) | |||||||
\(230\) | −8.74853 | − | 0.0866825i | −0.576861 | − | 0.00571567i | ||||
\(231\) | −0.655535 | −0.0431311 | ||||||||
\(232\) | −2.67202 | + | 2.67202i | −0.175426 | + | 0.175426i | ||||
\(233\) | −14.6836 | + | 14.6836i | −0.961952 | + | 0.961952i | −0.999302 | − | 0.0373500i | \(-0.988108\pi\) |
0.0373500 | + | 0.999302i | \(0.488108\pi\) | |||||||
\(234\) | 3.15714i | 0.206389i | ||||||||
\(235\) | −1.69995 | + | 1.66660i | −0.110893 | + | 0.108717i | ||||
\(236\) | −6.53793 | − | 6.53793i | −0.425583 | − | 0.425583i | ||||
\(237\) | −4.04926 | −0.263028 | ||||||||
\(238\) | −0.969688 | − | 0.969688i | −0.0628556 | − | 0.0628556i | ||||
\(239\) | −11.8998 | − | 11.8998i | −0.769736 | − | 0.769736i | 0.208324 | − | 0.978060i | \(-0.433199\pi\) |
−0.978060 | + | 0.208324i | \(0.933199\pi\) | |||||||
\(240\) | −1.59673 | + | 1.56540i | −0.103068 | + | 0.101046i | ||||
\(241\) | 15.6655 | − | 15.6655i | 1.00910 | − | 1.00910i | 0.00914615 | − | 0.999958i | \(-0.497089\pi\) |
0.999958 | − | 0.00914615i | \(-0.00291135\pi\) | |||||||
\(242\) | −8.28712 | −0.532716 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −0.144746 | − | 0.144746i | −0.00926640 | − | 0.00926640i | ||||
\(245\) | −0.151571 | + | 15.2975i | −0.00968355 | + | 0.977323i | ||||
\(246\) | −6.16632 | − | 6.16632i | −0.393150 | − | 0.393150i | ||||
\(247\) | −5.84148 | − | 5.84148i | −0.371685 | − | 0.371685i | ||||
\(248\) | 6.77259 | + | 6.77259i | 0.430060 | + | 0.430060i | ||||
\(249\) | −4.88555 | −0.309609 | ||||||||
\(250\) | −11.1754 | − | 0.332273i | −0.706794 | − | 0.0210148i | ||||
\(251\) | 8.27735 | + | 8.27735i | 0.522462 | + | 0.522462i | 0.918314 | − | 0.395852i | \(-0.129551\pi\) |
−0.395852 | + | 0.918314i | \(0.629551\pi\) | |||||||
\(252\) | 0.281427 | + | 0.281427i | 0.0177282 | + | 0.0177282i | ||||
\(253\) | − | 6.44446i | − | 0.405160i | ||||||
\(254\) | −6.37075 | + | 6.37075i | −0.399737 | + | 0.399737i | ||||
\(255\) | 5.39375 | + | 5.50170i | 0.337769 | + | 0.344530i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 4.24215i | − | 0.264618i | −0.991209 | − | 0.132309i | \(-0.957761\pi\) | ||
0.991209 | − | 0.132309i | \(-0.0422391\pi\) | |||||||
\(258\) | 0.902543 | − | 0.902543i | 0.0561898 | − | 0.0561898i | ||||
\(259\) | −1.95237 | − | 1.43148i | −0.121314 | − | 0.0889481i | ||||
\(260\) | 7.05924 | + | 0.0699446i | 0.437795 | + | 0.00433778i | ||||
\(261\) | −2.67202 | − | 2.67202i | −0.165394 | − | 0.165394i | ||||
\(262\) | 2.48554 | + | 2.48554i | 0.153557 | + | 0.153557i | ||||
\(263\) | −22.4018 | + | 22.4018i | −1.38135 | + | 1.38135i | −0.539129 | + | 0.842223i | \(0.681246\pi\) |
−0.842223 | + | 0.539129i | \(0.818754\pi\) | |||||||
\(264\) | −1.16466 | − | 1.16466i | −0.0716801 | − | 0.0716801i | ||||
\(265\) | 8.60638 | + | 8.77864i | 0.528686 | + | 0.539267i | ||||
\(266\) | −1.04142 | −0.0638534 | ||||||||
\(267\) | 17.7953i | 1.08905i | ||||||||
\(268\) | −0.492575 | − | 0.492575i | −0.0300888 | − | 0.0300888i | ||||
\(269\) | 15.2647i | 0.930706i | 0.885125 | + | 0.465353i | \(0.154073\pi\) | ||||
−0.885125 | + | 0.465353i | \(0.845927\pi\) | |||||||
\(270\) | −1.56540 | − | 1.59673i | −0.0952669 | − | 0.0971737i | ||||
\(271\) | 14.7969 | 0.898849 | 0.449424 | − | 0.893318i | \(-0.351629\pi\) | ||||
0.449424 | + | 0.893318i | \(0.351629\pi\) | |||||||
\(272\) | − | 3.44561i | − | 0.208921i | ||||||
\(273\) | − | 1.25654i | − | 0.0760491i | ||||||
\(274\) | −15.3866 | + | 15.3866i | −0.929538 | + | 0.929538i | ||||
\(275\) | 0.163181 | − | 8.23379i | 0.00984017 | − | 0.496516i | ||||
\(276\) | −2.76666 | + | 2.76666i | −0.166534 | + | 0.166534i | ||||
\(277\) | 3.00385 | 0.180484 | 0.0902420 | − | 0.995920i | \(-0.471236\pi\) | ||||
0.0902420 | + | 0.995920i | \(0.471236\pi\) | |||||||
\(278\) | 2.99885 | 0.179859 | ||||||||
\(279\) | −6.77259 | + | 6.77259i | −0.405464 | + | 0.405464i | ||||
\(280\) | 0.635494 | − | 0.623024i | 0.0379780 | − | 0.0372328i | ||||
\(281\) | −8.35723 | + | 8.35723i | −0.498551 | + | 0.498551i | −0.910987 | − | 0.412436i | \(-0.864678\pi\) |
0.412436 | + | 0.910987i | \(0.364678\pi\) | |||||||
\(282\) | 1.06465i | 0.0633990i | ||||||||
\(283\) | 3.86949i | 0.230018i | 0.993364 | + | 0.115009i | \(0.0366896\pi\) | ||||
−0.993364 | + | 0.115009i | \(0.963310\pi\) | |||||||
\(284\) | 11.2201 | 0.665790 | ||||||||
\(285\) | 5.85070 | + | 0.0579701i | 0.346565 | + | 0.00343385i | ||||
\(286\) | 5.20007i | 0.307487i | ||||||||
\(287\) | 2.45418 | + | 2.45418i | 0.144866 | + | 0.144866i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 5.12776 | 0.301633 | ||||||||
\(290\) | −6.03371 | + | 5.91532i | −0.354312 | + | 0.347359i | ||||
\(291\) | −4.89845 | − | 4.89845i | −0.287152 | − | 0.287152i | ||||
\(292\) | 0.804916 | − | 0.804916i | 0.0471041 | − | 0.0471041i | ||||
\(293\) | 10.7523 | + | 10.7523i | 0.628156 | + | 0.628156i | 0.947604 | − | 0.319448i | \(-0.103498\pi\) |
−0.319448 | + | 0.947604i | \(0.603498\pi\) | |||||||
\(294\) | 4.83774 | + | 4.83774i | 0.282143 | + | 0.282143i | ||||
\(295\) | −14.4737 | − | 14.7634i | −0.842691 | − | 0.859557i | ||||
\(296\) | −0.925435 | − | 6.01195i | −0.0537898 | − | 0.349438i | ||||
\(297\) | 1.16466 | − | 1.16466i | 0.0675806 | − | 0.0675806i | ||||
\(298\) | − | 8.60756i | − | 0.498622i | ||||||
\(299\) | 12.3528 | 0.714381 | ||||||||
\(300\) | −3.60489 | + | 3.46478i | −0.208129 | + | 0.200039i | ||||
\(301\) | −0.359210 | + | 0.359210i | −0.0207045 | + | 0.0207045i | ||||
\(302\) | − | 2.73615i | − | 0.157448i | ||||||
\(303\) | 4.27436 | + | 4.27436i | 0.245555 | + | 0.245555i | ||||
\(304\) | −1.85024 | − | 1.85024i | −0.106119 | − | 0.106119i | ||||
\(305\) | −0.320439 | − | 0.326852i | −0.0183483 | − | 0.0187155i | ||||
\(306\) | 3.44561 | 0.196972 | ||||||||
\(307\) | −19.3837 | − | 19.3837i | −1.10629 | − | 1.10629i | −0.993634 | − | 0.112652i | \(-0.964065\pi\) |
−0.112652 | − | 0.993634i | \(-0.535935\pi\) | |||||||
\(308\) | 0.463534 | + | 0.463534i | 0.0264123 | + | 0.0264123i | ||||
\(309\) | −7.95943 | − | 7.95943i | −0.452796 | − | 0.452796i | ||||
\(310\) | 14.9932 | + | 15.2933i | 0.851555 | + | 0.868599i | ||||
\(311\) | −9.43851 | − | 9.43851i | −0.535209 | − | 0.535209i | 0.386909 | − | 0.922118i | \(-0.373543\pi\) |
−0.922118 | + | 0.386909i | \(0.873543\pi\) | |||||||
\(312\) | 2.23244 | − | 2.23244i | 0.126387 | − | 0.126387i | ||||
\(313\) | −20.7779 | −1.17444 | −0.587218 | − | 0.809429i | \(-0.699777\pi\) | ||||
−0.587218 | + | 0.809429i | \(0.699777\pi\) | |||||||
\(314\) | 4.40198 | − | 4.40198i | 0.248418 | − | 0.248418i | ||||
\(315\) | 0.623024 | + | 0.635494i | 0.0351034 | + | 0.0358060i | ||||
\(316\) | 2.86326 | + | 2.86326i | 0.161071 | + | 0.161071i | ||||
\(317\) | −3.25873 | − | 3.25873i | −0.183029 | − | 0.183029i | 0.609646 | − | 0.792674i | \(-0.291312\pi\) |
−0.792674 | + | 0.609646i | \(0.791312\pi\) | |||||||
\(318\) | 5.49790 | 0.308307 | ||||||||
\(319\) | −4.40103 | − | 4.40103i | −0.246410 | − | 0.246410i | ||||
\(320\) | 2.23596 | + | 0.0221544i | 0.124994 | + | 0.00123847i | ||||
\(321\) | 12.5718i | 0.701689i | ||||||||
\(322\) | 1.10113 | − | 1.10113i | 0.0613634 | − | 0.0613634i | ||||
\(323\) | −6.37522 | + | 6.37522i | −0.354727 | + | 0.354727i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 15.7826 | + | 0.312786i | 0.875462 | + | 0.0173503i | ||||
\(326\) | − | 10.2487i | − | 0.567623i | ||||||
\(327\) | −12.6491 | −0.699496 | ||||||||
\(328\) | 8.72049i | 0.481508i | ||||||||
\(329\) | − | 0.423728i | − | 0.0233609i | ||||||
\(330\) | −2.57834 | − | 2.62994i | −0.141933 | − | 0.144773i | ||||
\(331\) | 2.00568 | − | 2.00568i | 0.110242 | − | 0.110242i | −0.649834 | − | 0.760076i | \(-0.725162\pi\) |
0.760076 | + | 0.649834i | \(0.225162\pi\) | |||||||
\(332\) | 3.45461 | + | 3.45461i | 0.189596 | + | 0.189596i | ||||
\(333\) | 6.01195 | − | 0.925435i | 0.329453 | − | 0.0507135i | ||||
\(334\) | − | 2.97278i | − | 0.162663i | ||||||
\(335\) | −1.09047 | − | 1.11229i | −0.0595785 | − | 0.0607709i | ||||
\(336\) | − | 0.397998i | − | 0.0217126i | ||||||
\(337\) | 8.49643 | + | 8.49643i | 0.462830 | + | 0.462830i | 0.899582 | − | 0.436752i | \(-0.143871\pi\) |
−0.436752 | + | 0.899582i | \(0.643871\pi\) | |||||||
\(338\) | 3.03245 | 0.164944 | ||||||||
\(339\) | 0.139124 | + | 0.139124i | 0.00755619 | + | 0.00755619i | ||||
\(340\) | 0.0763355 | − | 7.70424i | 0.00413987 | − | 0.417821i | ||||
\(341\) | −11.1550 | + | 11.1550i | −0.604077 | + | 0.604077i | ||||
\(342\) | 1.85024 | − | 1.85024i | 0.100050 | − | 0.100050i | ||||
\(343\) | −3.89540 | − | 3.89540i | −0.210332 | − | 0.210332i | ||||
\(344\) | −1.27639 | −0.0688182 | ||||||||
\(345\) | −6.24744 | + | 6.12485i | −0.336351 | + | 0.329751i | ||||
\(346\) | 5.83257 | − | 5.83257i | 0.313561 | − | 0.313561i | ||||
\(347\) | −0.455842 | −0.0244709 | −0.0122354 | − | 0.999925i | \(-0.503895\pi\) | ||||
−0.0122354 | + | 0.999925i | \(0.503895\pi\) | |||||||
\(348\) | 3.77880i | 0.202565i | ||||||||
\(349\) | 18.0258i | 0.964899i | 0.875924 | + | 0.482450i | \(0.160253\pi\) | ||||
−0.875924 | + | 0.482450i | \(0.839747\pi\) | |||||||
\(350\) | 1.43474 | − | 1.37898i | 0.0766901 | − | 0.0737095i | ||||
\(351\) | 2.23244 | + | 2.23244i | 0.119159 | + | 0.119159i | ||||
\(352\) | 1.64708i | 0.0877898i | ||||||||
\(353\) | 16.2235i | 0.863489i | 0.901996 | + | 0.431745i | \(0.142102\pi\) | ||||
−0.901996 | + | 0.431745i | \(0.857898\pi\) | |||||||
\(354\) | −9.24603 | −0.491421 | ||||||||
\(355\) | 25.0876 | + | 0.248574i | 1.33151 | + | 0.0131930i | ||||
\(356\) | 12.5832 | − | 12.5832i | 0.666907 | − | 0.666907i | ||||
\(357\) | −1.37135 | −0.0725794 | ||||||||
\(358\) | 4.52269 | − | 4.52269i | 0.239031 | − | 0.239031i | ||||
\(359\) | 19.2940i | 1.01830i | 0.860678 | + | 0.509149i | \(0.170040\pi\) | ||||
−0.860678 | + | 0.509149i | \(0.829960\pi\) | |||||||
\(360\) | −0.0221544 | + | 2.23596i | −0.00116764 | + | 0.117845i | ||||
\(361\) | − | 12.1532i | − | 0.639642i | ||||||
\(362\) | 16.8840 | 0.887401 | ||||||||
\(363\) | −5.85988 | + | 5.85988i | −0.307564 | + | 0.307564i | ||||
\(364\) | −0.888506 | + | 0.888506i | −0.0465703 | + | 0.0465703i | ||||
\(365\) | 1.81759 | − | 1.78193i | 0.0951370 | − | 0.0932703i | ||||
\(366\) | −0.204701 | −0.0106999 | ||||||||
\(367\) | −3.21053 | + | 3.21053i | −0.167588 | + | 0.167588i | −0.785919 | − | 0.618330i | \(-0.787810\pi\) |
0.618330 | + | 0.785919i | \(0.287810\pi\) | |||||||
\(368\) | 3.91265 | 0.203961 | ||||||||
\(369\) | −8.72049 | −0.453970 | ||||||||
\(370\) | −1.93604 | − | 13.4630i | −0.100650 | − | 0.699907i | ||||
\(371\) | −2.18815 | −0.113603 | ||||||||
\(372\) | 9.57788 | 0.496590 | ||||||||
\(373\) | −2.94440 | + | 2.94440i | −0.152455 | + | 0.152455i | −0.779214 | − | 0.626759i | \(-0.784381\pi\) |
0.626759 | + | 0.779214i | \(0.284381\pi\) | |||||||
\(374\) | 5.67521 | 0.293458 | ||||||||
\(375\) | −8.13715 | + | 7.66725i | −0.420201 | + | 0.395935i | ||||
\(376\) | 0.752821 | − | 0.752821i | 0.0388238 | − | 0.0388238i | ||||
\(377\) | 8.43593 | − | 8.43593i | 0.434473 | − | 0.434473i | ||||
\(378\) | 0.397998 | 0.0204708 | ||||||||
\(379\) | 25.1637i | 1.29257i | 0.763094 | + | 0.646287i | \(0.223679\pi\) | ||||
−0.763094 | + | 0.646287i | \(0.776321\pi\) | |||||||
\(380\) | −4.09608 | − | 4.17806i | −0.210124 | − | 0.214330i | ||||
\(381\) | 9.00960i | 0.461576i | ||||||||
\(382\) | 18.5005 | − | 18.5005i | 0.946566 | − | 0.946566i | ||||
\(383\) | −0.995617 | −0.0508736 | −0.0254368 | − | 0.999676i | \(-0.508098\pi\) | ||||
−0.0254368 | + | 0.999676i | \(0.508098\pi\) | |||||||
\(384\) | 0.707107 | − | 0.707107i | 0.0360844 | − | 0.0360844i | ||||
\(385\) | 1.02617 | + | 1.04671i | 0.0522986 | + | 0.0533453i | ||||
\(386\) | 17.1049 | 0.870618 | ||||||||
\(387\) | − | 1.27639i | − | 0.0648824i | ||||||
\(388\) | 6.92746i | 0.351689i | ||||||||
\(389\) | −19.4231 | − | 19.4231i | −0.984788 | − | 0.984788i | 0.0150980 | − | 0.999886i | \(-0.495194\pi\) |
−0.999886 | + | 0.0150980i | \(0.995194\pi\) | |||||||
\(390\) | 5.04109 | − | 4.94218i | 0.255266 | − | 0.250257i | ||||
\(391\) | − | 13.4815i | − | 0.681788i | ||||||
\(392\) | − | 6.84160i | − | 0.345553i | ||||||
\(393\) | 3.51508 | 0.177312 | ||||||||
\(394\) | 0.556751 | − | 0.556751i | 0.0280487 | − | 0.0280487i | ||||
\(395\) | 6.33870 | + | 6.46557i | 0.318935 | + | 0.325318i | ||||
\(396\) | −1.64708 | −0.0827690 | ||||||||
\(397\) | 6.49757 | + | 6.49757i | 0.326104 | + | 0.326104i | 0.851103 | − | 0.524999i | \(-0.175934\pi\) |
−0.524999 | + | 0.851103i | \(0.675934\pi\) | |||||||
\(398\) | 7.91159 | − | 7.91159i | 0.396572 | − | 0.396572i | ||||
\(399\) | −0.736393 | + | 0.736393i | −0.0368658 | + | 0.0368658i | ||||
\(400\) | 4.99902 | + | 0.0990726i | 0.249951 | + | 0.00495363i | ||||
\(401\) | −24.2700 | − | 24.2700i | −1.21199 | − | 1.21199i | −0.970372 | − | 0.241616i | \(-0.922322\pi\) |
−0.241616 | − | 0.970372i | \(-0.577678\pi\) | |||||||
\(402\) | −0.696607 | −0.0347436 | ||||||||
\(403\) | −21.3820 | − | 21.3820i | −1.06511 | − | 1.06511i | ||||
\(404\) | − | 6.04485i | − | 0.300743i | ||||||
\(405\) | −2.23596 | − | 0.0221544i | −0.111106 | − | 0.00110086i | ||||
\(406\) | − | 1.50396i | − | 0.0746401i | ||||||
\(407\) | 9.90218 | − | 1.52427i | 0.490833 | − | 0.0755551i | ||||
\(408\) | −2.43642 | − | 2.43642i | −0.120621 | − | 0.120621i | ||||
\(409\) | 24.0003 | − | 24.0003i | 1.18674 | − | 1.18674i | 0.208776 | − | 0.977963i | \(-0.433052\pi\) |
0.977963 | − | 0.208776i | \(-0.0669481\pi\) | |||||||
\(410\) | −0.193197 | + | 19.4986i | −0.00954133 | + | 0.962969i | ||||
\(411\) | 21.7599i | 1.07334i | ||||||||
\(412\) | 11.2563i | 0.554560i | ||||||||
\(413\) | 3.67990 | 0.181076 | ||||||||
\(414\) | 3.91265i | 0.192296i | ||||||||
\(415\) | 7.64782 | + | 7.80089i | 0.375417 | + | 0.382931i | ||||
\(416\) | −3.15714 | −0.154792 | ||||||||
\(417\) | 2.12051 | − | 2.12051i | 0.103842 | − | 0.103842i | ||||
\(418\) | 3.04750 | − | 3.04750i | 0.149058 | − | 0.149058i | ||||
\(419\) | 32.2473i | 1.57538i | 0.616070 | + | 0.787692i | \(0.288724\pi\) | ||||
−0.616070 | + | 0.787692i | \(0.711276\pi\) | |||||||
\(420\) | 0.00881741 | − | 0.889907i | 0.000430245 | − | 0.0434230i | ||||
\(421\) | −3.85720 | − | 3.85720i | −0.187988 | − | 0.187988i | 0.606838 | − | 0.794826i | \(-0.292438\pi\) |
−0.794826 | + | 0.606838i | \(0.792438\pi\) | |||||||
\(422\) | 1.32938 | 0.0647132 | ||||||||
\(423\) | 0.752821 | + | 0.752821i | 0.0366034 | + | 0.0366034i | ||||
\(424\) | −3.88760 | − | 3.88760i | −0.188798 | − | 0.188798i | ||||
\(425\) | 0.341366 | − | 17.2247i | 0.0165587 | − | 0.835519i | ||||
\(426\) | 7.93380 | − | 7.93380i | 0.384394 | − | 0.384394i | ||||
\(427\) | 0.0814708 | 0.00394265 | ||||||||
\(428\) | 8.88960 | − | 8.88960i | 0.429695 | − | 0.429695i | ||||
\(429\) | 3.67701 | + | 3.67701i | 0.177528 | + | 0.177528i | ||||
\(430\) | −2.85395 | − | 0.0282776i | −0.137630 | − | 0.00136367i | ||||
\(431\) | −15.1362 | − | 15.1362i | −0.729087 | − | 0.729087i | 0.241351 | − | 0.970438i | \(-0.422410\pi\) |
−0.970438 | + | 0.241351i | \(0.922410\pi\) | |||||||
\(432\) | 0.707107 | + | 0.707107i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | −27.7575 | − | 27.7575i | −1.33394 | − | 1.33394i | −0.901811 | − | 0.432130i | \(-0.857762\pi\) |
−0.432130 | − | 0.901811i | \(-0.642238\pi\) | |||||||
\(434\) | −3.81198 | −0.182981 | ||||||||
\(435\) | −0.0837171 | + | 8.44924i | −0.00401393 | + | 0.405110i | ||||
\(436\) | 8.94425 | + | 8.94425i | 0.428352 | + | 0.428352i | ||||
\(437\) | −7.23936 | − | 7.23936i | −0.346306 | − | 0.346306i | ||||
\(438\) | − | 1.13832i | − | 0.0543912i | ||||||
\(439\) | 17.1813 | − | 17.1813i | 0.820020 | − | 0.820020i | −0.166091 | − | 0.986110i | \(-0.553115\pi\) |
0.986110 | + | 0.166091i | \(0.0531145\pi\) | |||||||
\(440\) | −0.0364901 | + | 3.68281i | −0.00173960 | + | 0.175571i | ||||
\(441\) | 6.84160 | 0.325790 | ||||||||
\(442\) | 10.8783i | 0.517427i | ||||||||
\(443\) | −7.22878 | + | 7.22878i | −0.343450 | + | 0.343450i | −0.857663 | − | 0.514213i | \(-0.828084\pi\) |
0.514213 | + | 0.857663i | \(0.328084\pi\) | |||||||
\(444\) | −4.90547 | − | 3.59671i | −0.232803 | − | 0.170692i | ||||
\(445\) | 28.4142 | − | 27.8567i | 1.34696 | − | 1.32053i | ||||
\(446\) | 3.07126 | + | 3.07126i | 0.145429 | + | 0.145429i | ||||
\(447\) | −6.08646 | − | 6.08646i | −0.287880 | − | 0.287880i | ||||
\(448\) | −0.281427 | + | 0.281427i | −0.0132962 | + | 0.0132962i | ||||
\(449\) | 9.76421 | + | 9.76421i | 0.460802 | + | 0.460802i | 0.898918 | − | 0.438116i | \(-0.144354\pi\) |
−0.438116 | + | 0.898918i | \(0.644354\pi\) | |||||||
\(450\) | −0.0990726 | + | 4.99902i | −0.00467033 | + | 0.235656i | ||||
\(451\) | −14.3634 | −0.676344 | ||||||||
\(452\) | − | 0.196751i | − | 0.00925440i | ||||||
\(453\) | −1.93475 | − | 1.93475i | −0.0909024 | − | 0.0909024i | ||||
\(454\) | 24.6591i | 1.15731i | ||||||||
\(455\) | −2.00635 | + | 1.96698i | −0.0940589 | + | 0.0922133i | ||||
\(456\) | −2.61664 | −0.122535 | ||||||||
\(457\) | 20.5176i | 0.959771i | 0.877331 | + | 0.479886i | \(0.159322\pi\) | ||||
−0.877331 | + | 0.479886i | \(0.840678\pi\) | |||||||
\(458\) | 14.8812i | 0.695353i | ||||||||
\(459\) | 2.43642 | − | 2.43642i | 0.113722 | − | 0.113722i | ||||
\(460\) | 8.74853 | + | 0.0866825i | 0.407902 | + | 0.00404159i | ||||
\(461\) | 21.6195 | − | 21.6195i | 1.00692 | − | 1.00692i | 0.00694687 | − | 0.999976i | \(-0.497789\pi\) |
0.999976 | − | 0.00694687i | \(-0.00221127\pi\) | |||||||
\(462\) | 0.655535 | 0.0304983 | ||||||||
\(463\) | 1.38040 | 0.0641527 | 0.0320764 | − | 0.999485i | \(-0.489788\pi\) | ||||
0.0320764 | + | 0.999485i | \(0.489788\pi\) | |||||||
\(464\) | 2.67202 | − | 2.67202i | 0.124045 | − | 0.124045i | ||||
\(465\) | 21.4157 | + | 0.212192i | 0.993131 | + | 0.00984018i | ||||
\(466\) | 14.6836 | − | 14.6836i | 0.680203 | − | 0.680203i | ||||
\(467\) | − | 0.453871i | − | 0.0210026i | −0.999945 | − | 0.0105013i | \(-0.996657\pi\) | ||
0.999945 | − | 0.0105013i | \(-0.00334274\pi\) | |||||||
\(468\) | − | 3.15714i | − | 0.145939i | ||||||
\(469\) | 0.277248 | 0.0128021 | ||||||||
\(470\) | 1.69995 | − | 1.66660i | 0.0784131 | − | 0.0768744i | ||||
\(471\) | − | 6.22534i | − | 0.286849i | ||||||
\(472\) | 6.53793 | + | 6.53793i | 0.300933 | + | 0.300933i | ||||
\(473\) | − | 2.10232i | − | 0.0966646i | ||||||
\(474\) | 4.04926 | 0.185989 | ||||||||
\(475\) | −9.06609 | − | 9.43271i | −0.415981 | − | 0.432802i | ||||
\(476\) | 0.969688 | + | 0.969688i | 0.0444456 | + | 0.0444456i | ||||
\(477\) | 3.88760 | − | 3.88760i | 0.178001 | − | 0.178001i | ||||
\(478\) | 11.8998 | + | 11.8998i | 0.544285 | + | 0.544285i | ||||
\(479\) | 10.7493 | + | 10.7493i | 0.491147 | + | 0.491147i | 0.908667 | − | 0.417521i | \(-0.137101\pi\) |
−0.417521 | + | 0.908667i | \(0.637101\pi\) | |||||||
\(480\) | 1.59673 | − | 1.56540i | 0.0728803 | − | 0.0714502i | ||||
\(481\) | 2.92173 | + | 18.9806i | 0.133219 | + | 0.865440i | ||||
\(482\) | −15.6655 | + | 15.6655i | −0.713545 | + | 0.713545i | ||||
\(483\) | − | 1.55723i | − | 0.0708563i | ||||||
\(484\) | 8.28712 | 0.376687 | ||||||||
\(485\) | −0.153474 | + | 15.4895i | −0.00696888 | + | 0.703343i | ||||
\(486\) | −0.707107 | + | 0.707107i | −0.0320750 | + | 0.0320750i | ||||
\(487\) | − | 13.2268i | − | 0.599365i | −0.954039 | − | 0.299682i | \(-0.903119\pi\) | ||
0.954039 | − | 0.299682i | \(-0.0968807\pi\) | |||||||
\(488\) | 0.144746 | + | 0.144746i | 0.00655233 | + | 0.00655233i | ||||
\(489\) | −7.24692 | − | 7.24692i | −0.327717 | − | 0.327717i | ||||
\(490\) | 0.151571 | − | 15.2975i | 0.00684730 | − | 0.691072i | ||||
\(491\) | −30.4522 | −1.37429 | −0.687145 | − | 0.726520i | \(-0.741136\pi\) | ||||
−0.687145 | + | 0.726520i | \(0.741136\pi\) | |||||||
\(492\) | 6.16632 | + | 6.16632i | 0.277999 | + | 0.277999i | ||||
\(493\) | −9.20673 | − | 9.20673i | −0.414650 | − | 0.414650i | ||||
\(494\) | 5.84148 | + | 5.84148i | 0.262821 | + | 0.262821i | ||||
\(495\) | −3.68281 | − | 0.0364901i | −0.165530 | − | 0.00164011i | ||||
\(496\) | −6.77259 | − | 6.77259i | −0.304098 | − | 0.304098i | ||||
\(497\) | −3.15764 | + | 3.15764i | −0.141639 | + | 0.141639i | ||||
\(498\) | 4.88555 | 0.218927 | ||||||||
\(499\) | −6.74452 | + | 6.74452i | −0.301926 | + | 0.301926i | −0.841767 | − | 0.539841i | \(-0.818484\pi\) |
0.539841 | + | 0.841767i | \(0.318484\pi\) | |||||||
\(500\) | 11.1754 | + | 0.332273i | 0.499779 | + | 0.0148597i | ||||
\(501\) | −2.10207 | − | 2.10207i | −0.0939136 | − | 0.0939136i | ||||
\(502\) | −8.27735 | − | 8.27735i | −0.369436 | − | 0.369436i | ||||
\(503\) | 31.0691 | 1.38530 | 0.692652 | − | 0.721272i | \(-0.256442\pi\) | ||||
0.692652 | + | 0.721272i | \(0.256442\pi\) | |||||||
\(504\) | −0.281427 | − | 0.281427i | −0.0125358 | − | 0.0125358i | ||||
\(505\) | 0.133920 | − | 13.5160i | 0.00595937 | − | 0.601456i | ||||
\(506\) | 6.44446i | 0.286491i | ||||||||
\(507\) | 2.14427 | − | 2.14427i | 0.0952302 | − | 0.0952302i | ||||
\(508\) | 6.37075 | − | 6.37075i | 0.282656 | − | 0.282656i | ||||
\(509\) | −11.0860 | −0.491377 | −0.245688 | − | 0.969349i | \(-0.579014\pi\) | ||||
−0.245688 | + | 0.969349i | \(0.579014\pi\) | |||||||
\(510\) | −5.39375 | − | 5.50170i | −0.238839 | − | 0.243619i | ||||
\(511\) | 0.453050i | 0.0200418i | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | − | 2.61664i | − | 0.115527i | ||||||
\(514\) | 4.24215i | 0.187113i | ||||||||
\(515\) | −0.249377 | + | 25.1687i | −0.0109889 | + | 1.10907i | ||||
\(516\) | −0.902543 | + | 0.902543i | −0.0397322 | + | 0.0397322i | ||||
\(517\) | 1.23996 | + | 1.23996i | 0.0545333 | + | 0.0545333i | ||||
\(518\) | 1.95237 | + | 1.43148i | 0.0857822 | + | 0.0628958i | ||||
\(519\) | − | 8.24851i | − | 0.362069i | ||||||
\(520\) | −7.05924 | − | 0.0699446i | −0.309568 | − | 0.00306727i | ||||
\(521\) | 32.8476i | 1.43908i | 0.694451 | + | 0.719540i | \(0.255647\pi\) | ||||
−0.694451 | + | 0.719540i | \(0.744353\pi\) | |||||||
\(522\) | 2.67202 | + | 2.67202i | 0.116951 | + | 0.116951i | ||||
\(523\) | −9.72492 | −0.425241 | −0.212620 | − | 0.977135i | \(-0.568200\pi\) | ||||
−0.212620 | + | 0.977135i | \(0.568200\pi\) | |||||||
\(524\) | −2.48554 | − | 2.48554i | −0.108581 | − | 0.108581i | ||||
\(525\) | 0.0394307 | − | 1.98960i | 0.00172090 | − | 0.0868332i | ||||
\(526\) | 22.4018 | − | 22.4018i | 0.976763 | − | 0.976763i | ||||
\(527\) | −23.3357 | + | 23.3357i | −1.01652 | + | 1.01652i | ||||
\(528\) | 1.16466 | + | 1.16466i | 0.0506854 | + | 0.0506854i | ||||
\(529\) | −7.69115 | −0.334398 | ||||||||
\(530\) | −8.60638 | − | 8.77864i | −0.373837 | − | 0.381320i | ||||
\(531\) | −6.53793 | + | 6.53793i | −0.283722 | + | 0.283722i | ||||
\(532\) | 1.04142 | 0.0451512 | ||||||||
\(533\) | − | 27.5318i | − | 1.19254i | ||||||
\(534\) | − | 17.7953i | − | 0.770078i | ||||||
\(535\) | 20.0737 | − | 19.6798i | 0.867863 | − | 0.850833i | ||||
\(536\) | 0.492575 | + | 0.492575i | 0.0212760 | + | 0.0212760i | ||||
\(537\) | − | 6.39605i | − | 0.276010i | ||||||
\(538\) | − | 15.2647i | − | 0.658108i | ||||||
\(539\) | 11.2687 | 0.485376 | ||||||||
\(540\) | 1.56540 | + | 1.59673i | 0.0673639 | + | 0.0687122i | ||||
\(541\) | −22.2929 | + | 22.2929i | −0.958445 | + | 0.958445i | −0.999170 | − | 0.0407258i | \(-0.987033\pi\) |
0.0407258 | + | 0.999170i | \(0.487033\pi\) | |||||||
\(542\) | −14.7969 | −0.635582 | ||||||||
\(543\) | 11.9388 | − | 11.9388i | 0.512341 | − | 0.512341i | ||||
\(544\) | 3.44561i | 0.147729i | ||||||||
\(545\) | 19.8008 | + | 20.1971i | 0.848174 | + | 0.865150i | ||||
\(546\) | 1.25654i | 0.0537748i | ||||||||
\(547\) | 33.1369 | 1.41683 | 0.708416 | − | 0.705795i | \(-0.249410\pi\) | ||||
0.708416 | + | 0.705795i | \(0.249410\pi\) | |||||||
\(548\) | 15.3866 | − | 15.3866i | 0.657282 | − | 0.657282i | ||||
\(549\) | −0.144746 | + | 0.144746i | −0.00617760 | + | 0.00617760i | ||||
\(550\) | −0.163181 | + | 8.23379i | −0.00695805 | + | 0.351090i | ||||
\(551\) | −9.88776 | −0.421233 | ||||||||
\(552\) | 2.76666 | − | 2.76666i | 0.117757 | − | 0.117757i | ||||
\(553\) | −1.61160 | −0.0685322 | ||||||||
\(554\) | −3.00385 | −0.127621 | ||||||||
\(555\) | −10.8888 | − | 8.15077i | −0.462202 | − | 0.345981i | ||||
\(556\) | −2.99885 | −0.127180 | ||||||||
\(557\) | 3.42489 | 0.145117 | 0.0725586 | − | 0.997364i | \(-0.476884\pi\) | ||||
0.0725586 | + | 0.997364i | \(0.476884\pi\) | |||||||
\(558\) | 6.77259 | − | 6.77259i | 0.286706 | − | 0.286706i | ||||
\(559\) | 4.02974 | 0.170440 | ||||||||
\(560\) | −0.635494 | + | 0.623024i | −0.0268545 | + | 0.0263276i | ||||
\(561\) | 4.01298 | − | 4.01298i | 0.169428 | − | 0.169428i | ||||
\(562\) | 8.35723 | − | 8.35723i | 0.352529 | − | 0.352529i | ||||
\(563\) | 17.6124 | 0.742273 | 0.371136 | − | 0.928578i | \(-0.378968\pi\) | ||||
0.371136 | + | 0.928578i | \(0.378968\pi\) | |||||||
\(564\) | − | 1.06465i | − | 0.0448298i | ||||||
\(565\) | 0.00435891 | − | 0.439928i | 0.000183381 | − | 0.0185079i | ||||
\(566\) | − | 3.86949i | − | 0.162647i | ||||||
\(567\) | 0.281427 | − | 0.281427i | 0.0118188 | − | 0.0118188i | ||||
\(568\) | −11.2201 | −0.470784 | ||||||||
\(569\) | −13.6557 | + | 13.6557i | −0.572477 | + | 0.572477i | −0.932820 | − | 0.360343i | \(-0.882660\pi\) |
0.360343 | + | 0.932820i | \(0.382660\pi\) | |||||||
\(570\) | −5.85070 | − | 0.0579701i | −0.245059 | − | 0.00242810i | ||||
\(571\) | 36.6093 | 1.53205 | 0.766025 | − | 0.642811i | \(-0.222232\pi\) | ||||
0.766025 | + | 0.642811i | \(0.222232\pi\) | |||||||
\(572\) | − | 5.20007i | − | 0.217426i | ||||||
\(573\) | − | 26.1636i | − | 1.09300i | ||||||
\(574\) | −2.45418 | − | 2.45418i | −0.102436 | − | 0.102436i | ||||
\(575\) | 19.5594 | + | 0.387637i | 0.815684 | + | 0.0161656i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | 28.6229i | 1.19159i | 0.803137 | + | 0.595794i | \(0.203163\pi\) | ||||
−0.803137 | + | 0.595794i | \(0.796837\pi\) | |||||||
\(578\) | −5.12776 | −0.213287 | ||||||||
\(579\) | 12.0950 | − | 12.0950i | 0.502652 | − | 0.502652i | ||||
\(580\) | 6.03371 | − | 5.91532i | 0.250536 | − | 0.245620i | ||||
\(581\) | −1.94444 | −0.0806690 | ||||||||
\(582\) | 4.89845 | + | 4.89845i | 0.203047 | + | 0.203047i | ||||
\(583\) | 6.40320 | − | 6.40320i | 0.265193 | − | 0.265193i | ||||
\(584\) | −0.804916 | + | 0.804916i | −0.0333077 | + | 0.0333077i | ||||
\(585\) | 0.0699446 | − | 7.05924i | 0.00289185 | − | 0.291864i | ||||
\(586\) | −10.7523 | − | 10.7523i | −0.444173 | − | 0.444173i | ||||
\(587\) | −17.5944 | −0.726197 | −0.363099 | − | 0.931751i | \(-0.618281\pi\) | ||||
−0.363099 | + | 0.931751i | \(0.618281\pi\) | |||||||
\(588\) | −4.83774 | − | 4.83774i | −0.199505 | − | 0.199505i | ||||
\(589\) | 25.0619i | 1.03266i | ||||||||
\(590\) | 14.4737 | + | 14.7634i | 0.595873 | + | 0.607799i | ||||
\(591\) | − | 0.787365i | − | 0.0323879i | ||||||
\(592\) | 0.925435 | + | 6.01195i | 0.0380351 | + | 0.247090i | ||||
\(593\) | −5.00469 | − | 5.00469i | −0.205518 | − | 0.205518i | 0.596841 | − | 0.802359i | \(-0.296422\pi\) |
−0.802359 | + | 0.596841i | \(0.796422\pi\) | |||||||
\(594\) | −1.16466 | + | 1.16466i | −0.0477867 | + | 0.0477867i | ||||
\(595\) | 2.14670 | + | 2.18967i | 0.0880061 | + | 0.0897675i | ||||
\(596\) | 8.60756i | 0.352579i | ||||||||
\(597\) | − | 11.1887i | − | 0.457922i | ||||||
\(598\) | −12.3528 | −0.505144 | ||||||||
\(599\) | − | 35.1064i | − | 1.43441i | −0.696863 | − | 0.717204i | \(-0.745421\pi\) | ||
0.696863 | − | 0.717204i | \(-0.254579\pi\) | |||||||
\(600\) | 3.60489 | − | 3.46478i | 0.147169 | − | 0.141449i | ||||
\(601\) | −28.3290 | −1.15556 | −0.577782 | − | 0.816191i | \(-0.696082\pi\) | ||||
−0.577782 | + | 0.816191i | \(0.696082\pi\) | |||||||
\(602\) | 0.359210 | − | 0.359210i | 0.0146403 | − | 0.0146403i | ||||
\(603\) | −0.492575 | + | 0.492575i | −0.0200592 | + | 0.0200592i | ||||
\(604\) | 2.73615i | 0.111332i | ||||||||
\(605\) | 18.5297 | + | 0.183596i | 0.753338 | + | 0.00746425i | ||||
\(606\) | −4.27436 | − | 4.27436i | −0.173634 | − | 0.173634i | ||||
\(607\) | −2.58147 | −0.104779 | −0.0523894 | − | 0.998627i | \(-0.516684\pi\) | ||||
−0.0523894 | + | 0.998627i | \(0.516684\pi\) | |||||||
\(608\) | 1.85024 | + | 1.85024i | 0.0750373 | + | 0.0750373i | ||||
\(609\) | −1.06346 | − | 1.06346i | −0.0430935 | − | 0.0430935i | ||||
\(610\) | 0.320439 | + | 0.326852i | 0.0129742 | + | 0.0132339i | ||||
\(611\) | −2.37676 | + | 2.37676i | −0.0961535 | + | 0.0961535i | ||||
\(612\) | −3.44561 | −0.139281 | ||||||||
\(613\) | 7.76986 | − | 7.76986i | 0.313822 | − | 0.313822i | −0.532566 | − | 0.846388i | \(-0.678772\pi\) |
0.846388 | + | 0.532566i | \(0.178772\pi\) | |||||||
\(614\) | 19.3837 | + | 19.3837i | 0.782263 | + | 0.782263i | ||||
\(615\) | 13.6510 | + | 13.9242i | 0.550462 | + | 0.561479i | ||||
\(616\) | −0.463534 | − | 0.463534i | −0.0186763 | − | 0.0186763i | ||||
\(617\) | −19.3110 | − | 19.3110i | −0.777430 | − | 0.777430i | 0.201963 | − | 0.979393i | \(-0.435268\pi\) |
−0.979393 | + | 0.201963i | \(0.935268\pi\) | |||||||
\(618\) | 7.95943 | + | 7.95943i | 0.320175 | + | 0.320175i | ||||
\(619\) | 22.9273 | 0.921528 | 0.460764 | − | 0.887523i | \(-0.347575\pi\) | ||||
0.460764 | + | 0.887523i | \(0.347575\pi\) | |||||||
\(620\) | −14.9932 | − | 15.2933i | −0.602140 | − | 0.614192i | ||||
\(621\) | 2.76666 | + | 2.76666i | 0.111022 | + | 0.111022i | ||||
\(622\) | 9.43851 | + | 9.43851i | 0.378450 | + | 0.378450i | ||||
\(623\) | 7.08249i | 0.283754i | ||||||||
\(624\) | −2.23244 | + | 2.23244i | −0.0893690 | + | 0.0893690i | ||||
\(625\) | 24.9804 | + | 0.990532i | 0.999215 | + | 0.0396213i | ||||
\(626\) | 20.7779 | 0.830451 | ||||||||
\(627\) | − | 4.30982i | − | 0.172118i | ||||||
\(628\) | −4.40198 | + | 4.40198i | −0.175658 | + | 0.175658i | ||||
\(629\) | 20.7149 | − | 3.18869i | 0.825955 | − | 0.127141i | ||||
\(630\) | −0.623024 | − | 0.635494i | −0.0248219 | − | 0.0253187i | ||||
\(631\) | −18.8706 | − | 18.8706i | −0.751225 | − | 0.751225i | 0.223483 | − | 0.974708i | \(-0.428257\pi\) |
−0.974708 | + | 0.223483i | \(0.928257\pi\) | |||||||
\(632\) | −2.86326 | − | 2.86326i | −0.113894 | − | 0.113894i | ||||
\(633\) | 0.940014 | − | 0.940014i | 0.0373622 | − | 0.0373622i | ||||
\(634\) | 3.25873 | + | 3.25873i | 0.129421 | + | 0.129421i | ||||
\(635\) | 14.3859 | − | 14.1036i | 0.570886 | − | 0.559684i | ||||
\(636\) | −5.49790 | −0.218006 | ||||||||
\(637\) | 21.5999i | 0.855819i | ||||||||
\(638\) | 4.40103 | + | 4.40103i | 0.174238 | + | 0.174238i | ||||
\(639\) | − | 11.2201i | − | 0.443860i | ||||||
\(640\) | −2.23596 | − | 0.0221544i | −0.0883840 | − | 0.000875730i | ||||
\(641\) | 6.78574 | 0.268021 | 0.134010 | − | 0.990980i | \(-0.457214\pi\) | ||||
0.134010 | + | 0.990980i | \(0.457214\pi\) | |||||||
\(642\) | − | 12.5718i | − | 0.496169i | ||||||
\(643\) | 36.8670i | 1.45389i | 0.686695 | + | 0.726945i | \(0.259061\pi\) | ||||
−0.686695 | + | 0.726945i | \(0.740939\pi\) | |||||||
\(644\) | −1.10113 | + | 1.10113i | −0.0433905 | + | 0.0433905i | ||||
\(645\) | −2.03804 | + | 1.99805i | −0.0802479 | + | 0.0786732i | ||||
\(646\) | 6.37522 | − | 6.37522i | 0.250830 | − | 0.250830i | ||||
\(647\) | −19.1501 | −0.752868 | −0.376434 | − | 0.926443i | \(-0.622850\pi\) | ||||
−0.376434 | + | 0.926443i | \(0.622850\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −10.7685 | + | 10.7685i | −0.422701 | + | 0.422701i | ||||
\(650\) | −15.7826 | − | 0.312786i | −0.619045 | − | 0.0122685i | ||||
\(651\) | −2.69548 | + | 2.69548i | −0.105644 | + | 0.105644i | ||||
\(652\) | 10.2487i | 0.401370i | ||||||||
\(653\) | − | 19.8305i | − | 0.776029i | −0.921653 | − | 0.388015i | \(-0.873161\pi\) | ||
0.921653 | − | 0.388015i | \(-0.126839\pi\) | |||||||
\(654\) | 12.6491 | 0.494618 | ||||||||
\(655\) | −5.50249 | − | 5.61263i | −0.215000 | − | 0.219303i | ||||
\(656\) | − | 8.72049i | − | 0.340478i | ||||||
\(657\) | −0.804916 | − | 0.804916i | −0.0314028 | − | 0.0314028i | ||||
\(658\) | 0.423728i | 0.0165187i | ||||||||
\(659\) | 21.4129 | 0.834127 | 0.417064 | − | 0.908877i | \(-0.363059\pi\) | ||||
0.417064 | + | 0.908877i | \(0.363059\pi\) | |||||||
\(660\) | 2.57834 | + | 2.62994i | 0.100362 | + | 0.102370i | ||||
\(661\) | 34.3523 | + | 34.3523i | 1.33615 | + | 1.33615i | 0.899754 | + | 0.436397i | \(0.143746\pi\) |
0.436397 | + | 0.899754i | \(0.356254\pi\) | |||||||
\(662\) | −2.00568 | + | 2.00568i | −0.0779530 | + | 0.0779530i | ||||
\(663\) | 7.69211 | + | 7.69211i | 0.298737 | + | 0.298737i | ||||
\(664\) | −3.45461 | − | 3.45461i | −0.134065 | − | 0.134065i | ||||
\(665\) | 2.32857 | + | 0.0230720i | 0.0902979 | + | 0.000894693i | ||||
\(666\) | −6.01195 | + | 0.925435i | −0.232958 | + | 0.0358599i | ||||
\(667\) | 10.4547 | − | 10.4547i | 0.404806 | − | 0.404806i | ||||
\(668\) | 2.97278i | 0.115020i | ||||||||
\(669\) | 4.34342 | 0.167926 | ||||||||
\(670\) | 1.09047 | + | 1.11229i | 0.0421284 | + | 0.0429715i | ||||
\(671\) | −0.238408 | + | 0.238408i | −0.00920365 | + | 0.00920365i | ||||
\(672\) | 0.397998i | 0.0153531i | ||||||||
\(673\) | −19.4561 | − | 19.4561i | −0.749979 | − | 0.749979i | 0.224496 | − | 0.974475i | \(-0.427926\pi\) |
−0.974475 | + | 0.224496i | \(0.927926\pi\) | |||||||
\(674\) | −8.49643 | − | 8.49643i | −0.327270 | − | 0.327270i | ||||
\(675\) | 3.46478 | + | 3.60489i | 0.133360 | + | 0.138752i | ||||
\(676\) | −3.03245 | −0.116633 | ||||||||
\(677\) | 4.71937 | + | 4.71937i | 0.181380 | + | 0.181380i | 0.791957 | − | 0.610577i | \(-0.209062\pi\) |
−0.610577 | + | 0.791957i | \(0.709062\pi\) | |||||||
\(678\) | −0.139124 | − | 0.139124i | −0.00534303 | − | 0.00534303i | ||||
\(679\) | −1.94958 | − | 1.94958i | −0.0748178 | − | 0.0748178i | ||||
\(680\) | −0.0763355 | + | 7.70424i | −0.00292733 | + | 0.295444i | ||||
\(681\) | 17.4366 | + | 17.4366i | 0.668173 | + | 0.668173i | ||||
\(682\) | 11.1550 | − | 11.1550i | 0.427147 | − | 0.427147i | ||||
\(683\) | 23.5379 | 0.900653 | 0.450327 | − | 0.892864i | \(-0.351308\pi\) | ||||
0.450327 | + | 0.892864i | \(0.351308\pi\) | |||||||
\(684\) | −1.85024 | + | 1.85024i | −0.0707458 | + | 0.0707458i | ||||
\(685\) | 34.7446 | − | 34.0629i | 1.32752 | − | 1.30148i | ||||
\(686\) | 3.89540 | + | 3.89540i | 0.148727 | + | 0.148727i | ||||
\(687\) | 10.5226 | + | 10.5226i | 0.401462 | + | 0.401462i | ||||
\(688\) | 1.27639 | 0.0486618 | ||||||||
\(689\) | 12.2737 | + | 12.2737i | 0.467591 | + | 0.467591i | ||||
\(690\) | 6.24744 | − | 6.12485i | 0.237836 | − | 0.233169i | ||||
\(691\) | 8.31048i | 0.316145i | 0.987427 | + | 0.158073i | \(0.0505280\pi\) | ||||
−0.987427 | + | 0.158073i | \(0.949472\pi\) | |||||||
\(692\) | −5.83257 | + | 5.83257i | −0.221721 | + | 0.221721i | ||||
\(693\) | 0.463534 | − | 0.463534i | 0.0176082 | − | 0.0176082i | ||||
\(694\) | 0.455842 | 0.0173035 | ||||||||
\(695\) | −6.70531 | − | 0.0664378i | −0.254347 | − | 0.00252013i | ||||
\(696\) | − | 3.77880i | − | 0.143235i | ||||||
\(697\) | −30.0474 | −1.13813 | ||||||||
\(698\) | − | 18.0258i | − | 0.682287i | ||||||
\(699\) | − | 20.7657i | − | 0.785431i | ||||||
\(700\) | −1.43474 | + | 1.37898i | −0.0542281 | + | 0.0521205i | ||||
\(701\) | 26.9263 | − | 26.9263i | 1.01699 | − | 1.01699i | 0.0171385 | − | 0.999853i | \(-0.494544\pi\) |
0.999853 | − | 0.0171385i | \(-0.00545561\pi\) | |||||||
\(702\) | −2.23244 | − | 2.23244i | −0.0842579 | − | 0.0842579i | ||||
\(703\) | 9.41129 | − | 12.8359i | 0.354954 | − | 0.484113i | ||||
\(704\) | − | 1.64708i | − | 0.0620767i | ||||||
\(705\) | 0.0235867 | − | 2.38051i | 0.000888326 | − | 0.0896553i | ||||
\(706\) | − | 16.2235i | − | 0.610579i | ||||||
\(707\) | 1.70119 | + | 1.70119i | 0.0639797 | + | 0.0639797i | ||||
\(708\) | 9.24603 | 0.347487 | ||||||||
\(709\) | 17.6567 | + | 17.6567i | 0.663111 | + | 0.663111i | 0.956112 | − | 0.293001i | \(-0.0946539\pi\) |
−0.293001 | + | 0.956112i | \(0.594654\pi\) | |||||||
\(710\) | −25.0876 | − | 0.248574i | −0.941522 | − | 0.00932883i | ||||
\(711\) | 2.86326 | − | 2.86326i | 0.107381 | − | 0.107381i | ||||
\(712\) | −12.5832 | + | 12.5832i | −0.471574 | + | 0.471574i | ||||
\(713\) | −26.4988 | − | 26.4988i | −0.992387 | − | 0.992387i | ||||
\(714\) | 1.37135 | 0.0513214 | ||||||||
\(715\) | 0.115205 | − | 11.6271i | 0.00430840 | − | 0.434831i | ||||
\(716\) | −4.52269 | + | 4.52269i | −0.169021 | + | 0.169021i | ||||
\(717\) | 16.8289 | 0.628486 | ||||||||
\(718\) | − | 19.2940i | − | 0.720046i | ||||||
\(719\) | 7.51201i | 0.280151i | 0.990141 | + | 0.140075i | \(0.0447345\pi\) | ||||
−0.990141 | + | 0.140075i | \(0.955266\pi\) | |||||||
\(720\) | 0.0221544 | − | 2.23596i | 0.000825646 | − | 0.0833292i | ||||
\(721\) | −3.16784 | − | 3.16784i | −0.117976 | − | 0.117976i | ||||
\(722\) | 12.1532i | 0.452295i | ||||||||
\(723\) | 22.1544i | 0.823930i | ||||||||
\(724\) | −16.8840 | −0.627487 | ||||||||
\(725\) | 13.6222 | − | 13.0927i | 0.505915 | − | 0.486252i | ||||
\(726\) | 5.85988 | − | 5.85988i | 0.217481 | − | 0.217481i | ||||
\(727\) | −44.5433 | −1.65202 | −0.826010 | − | 0.563655i | \(-0.809395\pi\) | ||||
−0.826010 | + | 0.563655i | \(0.809395\pi\) | |||||||
\(728\) | 0.888506 | − | 0.888506i | 0.0329302 | − | 0.0329302i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −1.81759 | + | 1.78193i | −0.0672720 | + | 0.0659520i | ||||
\(731\) | − | 4.39794i | − | 0.162664i | ||||||
\(732\) | 0.204701 | 0.00756598 | ||||||||
\(733\) | −21.8867 | + | 21.8867i | −0.808404 | + | 0.808404i | −0.984392 | − | 0.175988i | \(-0.943688\pi\) |
0.175988 | + | 0.984392i | \(0.443688\pi\) | |||||||
\(734\) | 3.21053 | − | 3.21053i | 0.118503 | − | 0.118503i | ||||
\(735\) | −10.7098 | − | 10.9242i | −0.395037 | − | 0.402944i | ||||
\(736\) | −3.91265 | −0.144222 | ||||||||
\(737\) | −0.811312 | + | 0.811312i | −0.0298851 | + | 0.0298851i | ||||
\(738\) | 8.72049 | 0.321006 | ||||||||
\(739\) | −4.64271 | −0.170785 | −0.0853925 | − | 0.996347i | \(-0.527214\pi\) | ||||
−0.0853925 | + | 0.996347i | \(0.527214\pi\) | |||||||
\(740\) | 1.93604 | + | 13.4630i | 0.0711703 | + | 0.494909i | ||||
\(741\) | 8.26110 | 0.303479 | ||||||||
\(742\) | 2.18815 | 0.0803296 | ||||||||
\(743\) | −38.1619 | + | 38.1619i | −1.40003 | + | 1.40003i | −0.600105 | + | 0.799921i | \(0.704874\pi\) |
−0.799921 | + | 0.600105i | \(0.795126\pi\) | |||||||
\(744\) | −9.57788 | −0.351142 | ||||||||
\(745\) | −0.190695 | + | 19.2461i | −0.00698653 | + | 0.705124i | ||||
\(746\) | 2.94440 | − | 2.94440i | 0.107802 | − | 0.107802i | ||||
\(747\) | 3.45461 | − | 3.45461i | 0.126397 | − | 0.126397i | ||||
\(748\) | −5.67521 | −0.207506 | ||||||||
\(749\) | 5.00355i | 0.182826i | ||||||||
\(750\) | 8.13715 | − | 7.66725i | 0.297127 | − | 0.279968i | ||||
\(751\) | 36.4153i | 1.32881i | 0.747371 | + | 0.664406i | \(0.231316\pi\) | ||||
−0.747371 | + | 0.664406i | \(0.768684\pi\) | |||||||
\(752\) | −0.752821 | + | 0.752821i | −0.0274526 | + | 0.0274526i | ||||
\(753\) | −11.7059 | −0.426588 | ||||||||
\(754\) | −8.43593 | + | 8.43593i | −0.307219 | + | 0.307219i | ||||
\(755\) | −0.0606177 | + | 6.11791i | −0.00220610 | + | 0.222654i | ||||
\(756\) | −0.397998 | −0.0144750 | ||||||||
\(757\) | − | 17.1425i | − | 0.623054i | −0.950237 | − | 0.311527i | \(-0.899160\pi\) | ||
0.950237 | − | 0.311527i | \(-0.100840\pi\) | |||||||
\(758\) | − | 25.1637i | − | 0.913989i | ||||||
\(759\) | 4.55692 | + | 4.55692i | 0.165406 | + | 0.165406i | ||||
\(760\) | 4.09608 | + | 4.17806i | 0.148580 | + | 0.151554i | ||||
\(761\) | 35.6476i | 1.29222i | 0.763243 | + | 0.646112i | \(0.223606\pi\) | ||||
−0.763243 | + | 0.646112i | \(0.776394\pi\) | |||||||
\(762\) | − | 9.00960i | − | 0.326384i | ||||||
\(763\) | −5.03431 | −0.182254 | ||||||||
\(764\) | −18.5005 | + | 18.5005i | −0.669323 | + | 0.669323i | ||||
\(765\) | −7.70424 | − | 0.0763355i | −0.278548 | − | 0.00275991i | ||||
\(766\) | 0.995617 | 0.0359731 | ||||||||
\(767\) | −20.6412 | − | 20.6412i | −0.745310 | − | 0.745310i | ||||
\(768\) | −0.707107 | + | 0.707107i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | 12.7710 | − | 12.7710i | 0.460533 | − | 0.460533i | −0.438297 | − | 0.898830i | \(-0.644418\pi\) |
0.898830 | + | 0.438297i | \(0.144418\pi\) | |||||||
\(770\) | −1.02617 | − | 1.04671i | −0.0369807 | − | 0.0377208i | ||||
\(771\) | 2.99965 | + | 2.99965i | 0.108030 | + | 0.108030i | ||||
\(772\) | −17.1049 | −0.615620 | ||||||||
\(773\) | 11.0549 | + | 11.0549i | 0.397617 | + | 0.397617i | 0.877392 | − | 0.479775i | \(-0.159282\pi\) |
−0.479775 | + | 0.877392i | \(0.659282\pi\) | |||||||
\(774\) | 1.27639i | 0.0458788i | ||||||||
\(775\) | −33.1853 | − | 34.5273i | −1.19205 | − | 1.24026i | ||||
\(776\) | − | 6.92746i | − | 0.248681i | ||||||
\(777\) | 2.39275 | − | 0.368321i | 0.0858393 | − | 0.0132135i | ||||
\(778\) | 19.4231 | + | 19.4231i | 0.696350 | + | 0.696350i | ||||
\(779\) | −16.1350 | + | 16.1350i | −0.578097 | + | 0.578097i | ||||
\(780\) | −5.04109 | + | 4.94218i | −0.180500 | + | 0.176958i | ||||
\(781\) | − | 18.4804i | − | 0.661281i | ||||||
\(782\) | 13.4815i | 0.482097i | ||||||||
\(783\) | 3.77880 | 0.135043 | ||||||||
\(784\) | 6.84160i | 0.244343i | ||||||||
\(785\) | −9.94017 | + | 9.74513i | −0.354780 | + | 0.347819i | ||||
\(786\) | −3.51508 | −0.125379 | ||||||||
\(787\) | 13.1009 | − | 13.1009i | 0.466997 | − | 0.466997i | −0.433944 | − | 0.900940i | \(-0.642878\pi\) |
0.900940 | + | 0.433944i | \(0.142878\pi\) | |||||||
\(788\) | −0.556751 | + | 0.556751i | −0.0198334 | + | 0.0198334i | ||||
\(789\) | − | 31.6809i | − | 1.12787i | ||||||
\(790\) | −6.33870 | − | 6.46557i | −0.225521 | − | 0.230035i | ||||
\(791\) | 0.0553711 | + | 0.0553711i | 0.00196877 | + | 0.00196877i | ||||
\(792\) | 1.64708 | 0.0585265 | ||||||||
\(793\) | −0.456983 | − | 0.456983i | −0.0162279 | − | 0.0162279i | ||||
\(794\) | −6.49757 | − | 6.49757i | −0.230590 | − | 0.230590i | ||||
\(795\) | −12.2931 | − | 0.121803i | −0.435990 | − | 0.00431989i | ||||
\(796\) | −7.91159 | + | 7.91159i | −0.280419 | + | 0.280419i | ||||
\(797\) | 19.8808 | 0.704216 | 0.352108 | − | 0.935959i | \(-0.385465\pi\) | ||||
0.352108 | + | 0.935959i | \(0.385465\pi\) | |||||||
\(798\) | 0.736393 | − | 0.736393i | 0.0260680 | − | 0.0260680i | ||||
\(799\) | 2.59393 | + | 2.59393i | 0.0917666 | + | 0.0917666i | ||||
\(800\) | −4.99902 | − | 0.0990726i | −0.176742 | − | 0.00350275i | ||||
\(801\) | −12.5832 | − | 12.5832i | −0.444605 | − | 0.444605i | ||||
\(802\) | 24.2700 | + | 24.2700i | 0.857005 | + | 0.857005i | ||||
\(803\) | −1.32576 | − | 1.32576i | −0.0467851 | − | 0.0467851i | ||||
\(804\) | 0.696607 | 0.0245674 | ||||||||
\(805\) | −2.48647 | + | 2.43768i | −0.0876365 | + | 0.0859169i | ||||
\(806\) | 21.3820 | + | 21.3820i | 0.753149 | + | 0.753149i | ||||
\(807\) | −10.7938 | − | 10.7938i | −0.379959 | − | 0.379959i | ||||
\(808\) | 6.04485i | 0.212657i | ||||||||
\(809\) | −9.85033 | + | 9.85033i | −0.346319 | + | 0.346319i | −0.858737 | − | 0.512417i | \(-0.828750\pi\) |
0.512417 | + | 0.858737i | \(0.328750\pi\) | |||||||
\(810\) | 2.23596 | + | 0.0221544i | 0.0785636 | + | 0.000778426i | ||||
\(811\) | 33.2668 | 1.16815 | 0.584077 | − | 0.811698i | \(-0.301456\pi\) | ||||
0.584077 | + | 0.811698i | \(0.301456\pi\) | |||||||
\(812\) | 1.50396i | 0.0527785i | ||||||||
\(813\) | −10.4630 | + | 10.4630i | −0.366953 | + | 0.366953i | ||||
\(814\) | −9.90218 | + | 1.52427i | −0.347071 | + | 0.0534255i | ||||
\(815\) | −0.227054 | + | 22.9156i | −0.00795334 | + | 0.802700i | ||||
\(816\) | 2.43642 | + | 2.43642i | 0.0852916 | + | 0.0852916i | ||||
\(817\) | −2.36163 | − | 2.36163i | −0.0826229 | − | 0.0826229i | ||||
\(818\) | −24.0003 | + | 24.0003i | −0.839152 | + | 0.839152i | ||||
\(819\) | 0.888506 | + | 0.888506i | 0.0310469 | + | 0.0310469i | ||||
\(820\) | 0.193197 | − | 19.4986i | 0.00674674 | − | 0.680922i | ||||
\(821\) | −14.4484 | −0.504251 | −0.252126 | − | 0.967694i | \(-0.581130\pi\) | ||||
−0.252126 | + | 0.967694i | \(0.581130\pi\) | |||||||
\(822\) | − | 21.7599i | − | 0.758964i | ||||||
\(823\) | 8.70320 | + | 8.70320i | 0.303375 | + | 0.303375i | 0.842333 | − | 0.538958i | \(-0.181182\pi\) |
−0.538958 | + | 0.842333i | \(0.681182\pi\) | |||||||
\(824\) | − | 11.2563i | − | 0.392133i | ||||||
\(825\) | 5.70679 | + | 5.93756i | 0.198685 | + | 0.206719i | ||||
\(826\) | −3.67990 | −0.128040 | ||||||||
\(827\) | 30.1185i | 1.04732i | 0.851927 | + | 0.523661i | \(0.175434\pi\) | ||||
−0.851927 | + | 0.523661i | \(0.824566\pi\) | |||||||
\(828\) | − | 3.91265i | − | 0.135974i | ||||||
\(829\) | 23.9359 | − | 23.9359i | 0.831329 | − | 0.831329i | −0.156370 | − | 0.987699i | \(-0.549979\pi\) |
0.987699 | + | 0.156370i | \(0.0499791\pi\) | |||||||
\(830\) | −7.64782 | − | 7.80089i | −0.265460 | − | 0.270773i | ||||
\(831\) | −2.12404 | + | 2.12404i | −0.0736823 | + | 0.0736823i | ||||
\(832\) | 3.15714 | 0.109454 | ||||||||
\(833\) | 23.5735 | 0.816773 | ||||||||
\(834\) | −2.12051 | + | 2.12051i | −0.0734272 | + | 0.0734272i | ||||
\(835\) | −0.0658601 | + | 6.64701i | −0.00227918 | + | 0.230029i | ||||
\(836\) | −3.04750 | + | 3.04750i | −0.105400 | + | 0.105400i | ||||
\(837\) | − | 9.57788i | − | 0.331060i | ||||||
\(838\) | − | 32.2473i | − | 1.11396i | ||||||
\(839\) | −24.1682 | −0.834380 | −0.417190 | − | 0.908819i | \(-0.636985\pi\) | ||||
−0.417190 | + | 0.908819i | \(0.636985\pi\) | |||||||
\(840\) | −0.00881741 | + | 0.889907i | −0.000304229 | + | 0.0307047i | ||||
\(841\) | 14.7207i | 0.507609i | ||||||||
\(842\) | 3.85720 | + | 3.85720i | 0.132928 | + | 0.132928i | ||||
\(843\) | − | 11.8189i | − | 0.407065i | ||||||
\(844\) | −1.32938 | −0.0457592 | ||||||||
\(845\) | −6.78043 | − | 0.0671821i | −0.233254 | − | 0.00231114i | ||||
\(846\) | −0.752821 | − | 0.752821i | −0.0258825 | − | 0.0258825i | ||||
\(847\) | −2.33222 | + | 2.33222i | −0.0801360 | + | 0.0801360i | ||||
\(848\) | 3.88760 | + | 3.88760i | 0.133501 | + | 0.133501i | ||||
\(849\) | −2.73615 | − | 2.73615i | −0.0939043 | − | 0.0939043i | ||||
\(850\) | −0.341366 | + | 17.2247i | −0.0117087 | + | 0.590801i | ||||
\(851\) | 3.62091 | + | 23.5227i | 0.124123 | + | 0.806347i | ||||
\(852\) | −7.93380 | + | 7.93380i | −0.271807 | + | 0.271807i | ||||
\(853\) | − | 40.9694i | − | 1.40276i | −0.712785 | − | 0.701382i | \(-0.752567\pi\) | ||
0.712785 | − | 0.701382i | \(-0.247433\pi\) | |||||||
\(854\) | −0.0814708 | −0.00278787 | ||||||||
\(855\) | −4.17806 | + | 4.09608i | −0.142887 | + | 0.140083i | ||||
\(856\) | −8.88960 | + | 8.88960i | −0.303840 | + | 0.303840i | ||||
\(857\) | − | 10.8481i | − | 0.370563i | −0.982686 | − | 0.185281i | \(-0.940680\pi\) | ||
0.982686 | − | 0.185281i | \(-0.0593197\pi\) | |||||||
\(858\) | −3.67701 | − | 3.67701i | −0.125531 | − | 0.125531i | ||||
\(859\) | −11.6985 | − | 11.6985i | −0.399147 | − | 0.399147i | 0.478785 | − | 0.877932i | \(-0.341077\pi\) |
−0.877932 | + | 0.478785i | \(0.841077\pi\) | |||||||
\(860\) | 2.85395 | + | 0.0282776i | 0.0973189 | + | 0.000964258i | ||||
\(861\) | −3.47074 | −0.118282 | ||||||||
\(862\) | 15.1362 | + | 15.1362i | 0.515542 | + | 0.515542i | ||||
\(863\) | 36.8955 | + | 36.8955i | 1.25594 | + | 1.25594i | 0.953015 | + | 0.302924i | \(0.0979629\pi\) |
0.302924 | + | 0.953015i | \(0.402037\pi\) | |||||||
\(864\) | −0.707107 | − | 0.707107i | −0.0240563 | − | 0.0240563i | ||||
\(865\) | −13.1706 | + | 12.9122i | −0.447814 | + | 0.439027i | ||||
\(866\) | 27.7575 | + | 27.7575i | 0.943239 | + | 0.943239i | ||||
\(867\) | −3.62588 | + | 3.62588i | −0.123141 | + | 0.123141i | ||||
\(868\) | 3.81198 | 0.129387 | ||||||||
\(869\) | 4.71603 | − | 4.71603i | 0.159980 | − | 0.159980i | ||||
\(870\) | 0.0837171 | − | 8.44924i | 0.00283827 | − | 0.286456i | ||||
\(871\) | −1.55513 | − | 1.55513i | −0.0526936 | − | 0.0526936i | ||||
\(872\) | −8.94425 | − | 8.94425i | −0.302891 | − | 0.302891i | ||||
\(873\) | 6.92746 | 0.234459 | ||||||||
\(874\) | 7.23936 | + | 7.23936i | 0.244875 | + | 0.244875i | ||||
\(875\) | −3.23857 | + | 3.05155i | −0.109484 | + | 0.103161i | ||||
\(876\) | 1.13832i | 0.0384604i | ||||||||
\(877\) | −25.8706 | + | 25.8706i | −0.873589 | + | 0.873589i | −0.992862 | − | 0.119273i | \(-0.961944\pi\) |
0.119273 | + | 0.992862i | \(0.461944\pi\) | |||||||
\(878\) | −17.1813 | + | 17.1813i | −0.579841 | + | 0.579841i | ||||
\(879\) | −15.2060 | −0.512887 | ||||||||
\(880\) | 0.0364901 | − | 3.68281i | 0.00123008 | − | 0.124147i | ||||
\(881\) | − | 4.62987i | − | 0.155984i | −0.996954 | − | 0.0779921i | \(-0.975149\pi\) | ||
0.996954 | − | 0.0779921i | \(-0.0248509\pi\) | |||||||
\(882\) | −6.84160 | −0.230369 | ||||||||
\(883\) | − | 14.3060i | − | 0.481435i | −0.970595 | − | 0.240718i | \(-0.922617\pi\) | ||
0.970595 | − | 0.240718i | \(-0.0773828\pi\) | |||||||
\(884\) | − | 10.8783i | − | 0.365876i | ||||||
\(885\) | 20.6737 | + | 0.204840i | 0.694940 | + | 0.00688563i | ||||
\(886\) | 7.22878 | − | 7.22878i | 0.242855 | − | 0.242855i | ||||
\(887\) | −14.1138 | − | 14.1138i | −0.473896 | − | 0.473896i | 0.429277 | − | 0.903173i | \(-0.358769\pi\) |
−0.903173 | + | 0.429277i | \(0.858769\pi\) | |||||||
\(888\) | 4.90547 | + | 3.59671i | 0.164617 | + | 0.120698i | ||||
\(889\) | 3.58581i | 0.120264i | ||||||||
\(890\) | −28.4142 | + | 27.8567i | −0.952447 | + | 0.933758i | ||||
\(891\) | 1.64708i | 0.0551793i | ||||||||
\(892\) | −3.07126 | − | 3.07126i | −0.102834 | − | 0.102834i | ||||
\(893\) | 2.78580 | 0.0932234 | ||||||||
\(894\) | 6.08646 | + | 6.08646i | 0.203562 | + | 0.203562i | ||||
\(895\) | −10.2127 | + | 10.0123i | −0.341374 | + | 0.334676i | ||||
\(896\) | 0.281427 | − | 0.281427i | 0.00940182 | − | 0.00940182i | ||||
\(897\) | −8.73475 | + | 8.73475i | −0.291645 | + | 0.291645i | ||||
\(898\) | −9.76421 | − | 9.76421i | −0.325836 | − | 0.325836i | ||||
\(899\) | −36.1929 | −1.20710 | ||||||||
\(900\) | 0.0990726 | − | 4.99902i | 0.00330242 | − | 0.166634i | ||||
\(901\) | 13.3952 | − | 13.3952i | 0.446257 | − | 0.446257i | ||||
\(902\) | 14.3634 | 0.478248 | ||||||||
\(903\) | − | 0.508000i | − | 0.0169052i | ||||||
\(904\) | 0.196751i | 0.00654385i | ||||||||
\(905\) | −37.7518 | − | 0.374054i | −1.25491 | − | 0.0124340i | ||||
\(906\) | 1.93475 | + | 1.93475i | 0.0642777 | + | 0.0642777i | ||||
\(907\) | 6.36519i | 0.211353i | 0.994401 | + | 0.105676i | \(0.0337007\pi\) | ||||
−0.994401 | + | 0.105676i | \(0.966299\pi\) | |||||||
\(908\) | − | 24.6591i | − | 0.818342i | ||||||
\(909\) | −6.04485 | −0.200495 | ||||||||
\(910\) | 2.00635 | − | 1.96698i | 0.0665097 | − | 0.0652047i | ||||
\(911\) | −17.2930 | + | 17.2930i | −0.572944 | + | 0.572944i | −0.932950 | − | 0.360006i | \(-0.882775\pi\) |
0.360006 | + | 0.932950i | \(0.382775\pi\) | |||||||
\(912\) | 2.61664 | 0.0866456 | ||||||||
\(913\) | 5.69002 | − | 5.69002i | 0.188312 | − | 0.188312i | ||||
\(914\) | − | 20.5176i | − | 0.678661i | ||||||
\(915\) | 0.457704 | + | 0.00453504i | 0.0151312 | + | 0.000149924i | ||||
\(916\) | − | 14.8812i | − | 0.491689i | ||||||
\(917\) | 1.39900 | 0.0461989 | ||||||||
\(918\) | −2.43642 | + | 2.43642i | −0.0804137 | + | 0.0804137i | ||||
\(919\) | 22.2107 | − | 22.2107i | 0.732663 | − | 0.732663i | −0.238484 | − | 0.971146i | \(-0.576650\pi\) |
0.971146 | + | 0.238484i | \(0.0766504\pi\) | |||||||
\(920\) | −8.74853 | − | 0.0866825i | −0.288430 | − | 0.00285784i | ||||
\(921\) | 27.4127 | 0.903279 | ||||||||
\(922\) | −21.6195 | + | 21.6195i | −0.712002 | + | 0.712002i | ||||
\(923\) | 35.4234 | 1.16598 | ||||||||
\(924\) | −0.655535 | −0.0215655 | ||||||||
\(925\) | 4.03065 | + | 30.1455i | 0.132527 | + | 0.991179i | ||||
\(926\) | −1.38040 | −0.0453628 | ||||||||
\(927\) | 11.2563 | 0.369707 | ||||||||
\(928\) | −2.67202 | + | 2.67202i | −0.0877132 | + | 0.0877132i | ||||
\(929\) | 1.85414 | 0.0608325 | 0.0304162 | − | 0.999537i | \(-0.490317\pi\) | ||||
0.0304162 | + | 0.999537i | \(0.490317\pi\) | |||||||
\(930\) | −21.4157 | − | 0.212192i | −0.702250 | − | 0.00695806i | ||||
\(931\) | 12.6586 | − | 12.6586i | 0.414869 | − | 0.414869i | ||||
\(932\) | −14.6836 | + | 14.6836i | −0.480976 | + | 0.480976i | ||||
\(933\) | 13.3481 | 0.436996 | ||||||||
\(934\) | 0.453871i | 0.0148511i | ||||||||
\(935\) | −12.6895 | − | 0.125731i | −0.414992 | − | 0.00411184i | ||||
\(936\) | 3.15714i | 0.103194i | ||||||||
\(937\) | −20.7476 | + | 20.7476i | −0.677795 | + | 0.677795i | −0.959501 | − | 0.281706i | \(-0.909100\pi\) |
0.281706 | + | 0.959501i | \(0.409100\pi\) | |||||||
\(938\) | −0.277248 | −0.00905247 | ||||||||
\(939\) | 14.6922 | − | 14.6922i | 0.479461 | − | 0.479461i | ||||
\(940\) | −1.69995 | + | 1.66660i | −0.0554464 | + | 0.0543584i | ||||
\(941\) | 18.4162 | 0.600352 | 0.300176 | − | 0.953884i | \(-0.402955\pi\) | ||||
0.300176 | + | 0.953884i | \(0.402955\pi\) | |||||||
\(942\) | 6.22534i | 0.202833i | ||||||||
\(943\) | − | 34.1202i | − | 1.11111i | ||||||
\(944\) | −6.53793 | − | 6.53793i | −0.212792 | − | 0.212792i | ||||
\(945\) | −0.889907 | − | 0.00881741i | −0.0289487 | − | 0.000286830i | ||||
\(946\) | 2.10232i | 0.0683522i | ||||||||
\(947\) | − | 35.4933i | − | 1.15338i | −0.816964 | − | 0.576689i | \(-0.804344\pi\) | ||
0.816964 | − | 0.576689i | \(-0.195656\pi\) | |||||||
\(948\) | −4.04926 | −0.131514 | ||||||||
\(949\) | 2.54123 | − | 2.54123i | 0.0824920 | − | 0.0824920i | ||||
\(950\) | 9.06609 | + | 9.43271i | 0.294143 | + | 0.306037i | ||||
\(951\) | 4.60854 | 0.149442 | ||||||||
\(952\) | −0.969688 | − | 0.969688i | −0.0314278 | − | 0.0314278i | ||||
\(953\) | 23.7817 | − | 23.7817i | 0.770365 | − | 0.770365i | −0.207806 | − | 0.978170i | \(-0.566632\pi\) |
0.978170 | + | 0.207806i | \(0.0666321\pi\) | |||||||
\(954\) | −3.88760 | + | 3.88760i | −0.125866 | + | 0.125866i | ||||
\(955\) | −41.7761 | + | 40.9564i | −1.35184 | + | 1.32532i | ||||
\(956\) | −11.8998 | − | 11.8998i | −0.384868 | − | 0.384868i | ||||
\(957\) | 6.22400 | 0.201193 | ||||||||
\(958\) | −10.7493 | − | 10.7493i | −0.347293 | − | 0.347293i | ||||
\(959\) | 8.66041i | 0.279659i | ||||||||
\(960\) | −1.59673 | + | 1.56540i | −0.0515341 | + | 0.0505229i | ||||
\(961\) | 60.7358i | 1.95922i | ||||||||
\(962\) | −2.92173 | − | 18.9806i | −0.0942004 | − | 0.611959i | ||||
\(963\) | −8.88960 | − | 8.88960i | −0.286463 | − | 0.286463i | ||||
\(964\) | 15.6655 | − | 15.6655i | 0.504552 | − | 0.504552i | ||||
\(965\) | −38.2459 | − | 0.378950i | −1.23118 | − | 0.0121988i | ||||
\(966\) | 1.55723i | 0.0501030i | ||||||||
\(967\) | 23.3872i | 0.752080i | 0.926603 | + | 0.376040i | \(0.122715\pi\) | ||||
−0.926603 | + | 0.376040i | \(0.877285\pi\) | |||||||
\(968\) | −8.28712 | −0.266358 | ||||||||
\(969\) | − | 9.01592i | − | 0.289633i | ||||||
\(970\) | 0.153474 | − | 15.4895i | 0.00492774 | − | 0.497338i | ||||
\(971\) | −10.8563 | −0.348395 | −0.174198 | − | 0.984711i | \(-0.555733\pi\) | ||||
−0.174198 | + | 0.984711i | \(0.555733\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | 0.843958 | − | 0.843958i | 0.0270561 | − | 0.0270561i | ||||
\(974\) | 13.2268i | 0.423815i | ||||||||
\(975\) | −11.3812 | + | 10.9388i | −0.364489 | + | 0.350323i | ||||
\(976\) | −0.144746 | − | 0.144746i | −0.00463320 | − | 0.00463320i | ||||
\(977\) | −60.9677 | −1.95053 | −0.975264 | − | 0.221043i | \(-0.929054\pi\) | ||||
−0.975264 | + | 0.221043i | \(0.929054\pi\) | |||||||
\(978\) | 7.24692 | + | 7.24692i | 0.231731 | + | 0.231731i | ||||
\(979\) | −20.7255 | − | 20.7255i | −0.662390 | − | 0.662390i | ||||
\(980\) | −0.151571 | + | 15.2975i | −0.00484177 | + | 0.488662i | ||||
\(981\) | 8.94425 | − | 8.94425i | 0.285568 | − | 0.285568i | ||||
\(982\) | 30.4522 | 0.971770 | ||||||||
\(983\) | −25.7832 | + | 25.7832i | −0.822357 | + | 0.822357i | −0.986446 | − | 0.164088i | \(-0.947532\pi\) |
0.164088 | + | 0.986446i | \(0.447532\pi\) | |||||||
\(984\) | −6.16632 | − | 6.16632i | −0.196575 | − | 0.196575i | ||||
\(985\) | −1.25721 | + | 1.23254i | −0.0400579 | + | 0.0392719i | ||||
\(986\) | 9.20673 | + | 9.20673i | 0.293202 | + | 0.293202i | ||||
\(987\) | 0.299621 | + | 0.299621i | 0.00953705 | + | 0.00953705i | ||||
\(988\) | −5.84148 | − | 5.84148i | −0.185842 | − | 0.185842i | ||||
\(989\) | 4.99406 | 0.158802 | ||||||||
\(990\) | 3.68281 | + | 0.0364901i | 0.117047 | + | 0.00115973i | ||||
\(991\) | 6.60187 | + | 6.60187i | 0.209715 | + | 0.209715i | 0.804147 | − | 0.594431i | \(-0.202623\pi\) |
−0.594431 | + | 0.804147i | \(0.702623\pi\) | |||||||
\(992\) | 6.77259 | + | 6.77259i | 0.215030 | + | 0.215030i | ||||
\(993\) | 2.83646i | 0.0900124i | ||||||||
\(994\) | 3.15764 | − | 3.15764i | 0.100154 | − | 0.100154i | ||||
\(995\) | −17.8653 | + | 17.5147i | −0.566367 | + | 0.555254i | ||||
\(996\) | −4.88555 | −0.154805 | ||||||||
\(997\) | 24.6196i | 0.779711i | 0.920876 | + | 0.389856i | \(0.127475\pi\) | ||||
−0.920876 | + | 0.389856i | \(0.872525\pi\) | |||||||
\(998\) | 6.74452 | − | 6.74452i | 0.213494 | − | 0.213494i | ||||
\(999\) | −3.59671 | + | 4.90547i | −0.113795 | + | 0.155202i |
(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 | 1110.2.o.a.253.8 | yes | 36 | |
5.2 | odd | 4 | 1110.2.l.a.697.11 | yes | 36 | ||
37.6 | odd | 4 | 1110.2.l.a.43.11 | ✓ | 36 | ||
185.117 | even | 4 | inner | 1110.2.o.a.487.8 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.11 | ✓ | 36 | 37.6 | odd | 4 | ||
1110.2.l.a.697.11 | yes | 36 | 5.2 | odd | 4 | ||
1110.2.o.a.253.8 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.o.a.487.8 | yes | 36 | 185.117 | even | 4 | inner |