Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(43,1110)]
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, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.l (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 | 697.11 | ||
Character | \(\chi\) | \(=\) | 1110.697 |
Dual form | 1110.2.l.a.43.11 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.0221544 | − | 2.23596i | −0.00990775 | − | 0.999951i | ||||
\(6\) | 0.707107 | − | 0.707107i | 0.288675 | − | 0.288675i | ||||
\(7\) | −0.281427 | − | 0.281427i | −0.106369 | − | 0.106369i | 0.651919 | − | 0.758289i | \(-0.273964\pi\) |
−0.758289 | + | 0.651919i | \(0.773964\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 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 | ||||
\(13\) | − | 3.15714i | − | 0.875634i | −0.899064 | − | 0.437817i | \(-0.855752\pi\) | ||
0.899064 | − | 0.437817i | \(-0.144248\pi\) | |||||||
\(14\) | −0.281427 | + | 0.281427i | −0.0752146 | + | 0.0752146i | ||||
\(15\) | 1.56540 | − | 1.59673i | 0.404183 | − | 0.412273i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.44561 | 0.835684 | 0.417842 | − | 0.908520i | \(-0.362787\pi\) | ||||
0.417842 | + | 0.908520i | \(0.362787\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.85024 | + | 1.85024i | 0.424475 | + | 0.424475i | 0.886741 | − | 0.462266i | \(-0.152964\pi\) |
−0.462266 | + | 0.886741i | \(0.652964\pi\) | |||||||
\(20\) | 0.0221544 | + | 2.23596i | 0.00495387 | + | 0.499975i | ||||
\(21\) | − | 0.397998i | − | 0.0868503i | ||||||
\(22\) | −1.64708 | −0.351159 | ||||||||
\(23\) | − | 3.91265i | − | 0.815844i | −0.913017 | − | 0.407922i | \(-0.866253\pi\) | ||
0.913017 | − | 0.407922i | \(-0.133747\pi\) | |||||||
\(24\) | −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 | −0.910247 | − | 0.414066i | \(-0.864108\pi\) |
0.414066 | + | 0.910247i | \(0.364108\pi\) | |||||||
\(30\) | −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 | \(-0.579611\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 1.16466 | − | 1.16466i | 0.202742 | − | 0.202742i | ||||
\(34\) | − | 3.44561i | − | 0.590917i | ||||||
\(35\) | −0.623024 | + | 0.635494i | −0.105310 | + | 0.107418i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | −6.01195 | + | 0.925435i | −0.988359 | + | 0.152141i | ||||
\(38\) | 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 | \(-0.238435\pi\) | |||||||
\(42\) | −0.397998 | −0.0614124 | ||||||||
\(43\) | − | 1.27639i | − | 0.194647i | −0.995253 | − | 0.0973237i | \(-0.968972\pi\) | ||
0.995253 | − | 0.0973237i | \(-0.0310282\pi\) | |||||||
\(44\) | 1.64708i | 0.248307i | ||||||||
\(45\) | 2.23596 | − | 0.0221544i | 0.333317 | − | 0.00330258i | ||||
\(46\) | −3.91265 | −0.576889 | ||||||||
\(47\) | −0.752821 | − | 0.752821i | −0.109810 | − | 0.109810i | 0.650067 | − | 0.759877i | \(-0.274741\pi\) |
−0.759877 | + | 0.650067i | \(0.774741\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | − | 6.84160i | − | 0.977371i | ||||||
\(50\) | 0.0990726 | + | 4.99902i | 0.0140110 | + | 0.706968i | ||||
\(51\) | 2.43642 | + | 2.43642i | 0.341166 | + | 0.341166i | ||||
\(52\) | 3.15714i | 0.437817i | ||||||||
\(53\) | 3.88760 | − | 3.88760i | 0.534003 | − | 0.534003i | −0.387758 | − | 0.921761i | \(-0.626750\pi\) |
0.921761 | + | 0.387758i | \(0.126750\pi\) | |||||||
\(54\) | 0.707107 | + | 0.707107i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | −3.68281 | + | 0.0364901i | −0.496590 | + | 0.00492033i | ||||
\(56\) | 0.281427 | − | 0.281427i | 0.0376073 | − | 0.0376073i | ||||
\(57\) | 2.61664i | 0.346582i | ||||||||
\(58\) | 2.67202 | + | 2.67202i | 0.350853 | + | 0.350853i | ||||
\(59\) | 6.53793 | + | 6.53793i | 0.851166 | + | 0.851166i | 0.990277 | − | 0.139111i | \(-0.0444244\pi\) |
−0.139111 | + | 0.990277i | \(0.544424\pi\) | |||||||
\(60\) | −1.56540 | + | 1.59673i | −0.202092 | + | 0.206137i | ||||
\(61\) | −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 | \(-0.736451\pi\) |
0.736555 | + | 0.676377i | \(0.236451\pi\) | |||||||
\(68\) | −3.44561 | −0.417842 | ||||||||
\(69\) | 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 | \(0.268095\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −0.804916 | − | 0.804916i | −0.0942083 | − | 0.0942083i | 0.658432 | − | 0.752640i | \(-0.271220\pi\) |
−0.752640 | + | 0.658432i | \(0.771220\pi\) | |||||||
\(74\) | 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 | 0.527446 | − | 0.849588i | \(-0.323150\pi\) |
−0.849588 | + | 0.527446i | \(0.823150\pi\) | |||||||
\(80\) | −0.0221544 | − | 2.23596i | −0.00247694 | − | 0.249988i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −8.72049 | −0.963017 | ||||||||
\(83\) | 3.45461 | − | 3.45461i | 0.379192 | − | 0.379192i | −0.491618 | − | 0.870811i | \(-0.663594\pi\) |
0.870811 | + | 0.491618i | \(0.163594\pi\) | |||||||
\(84\) | 0.397998i | 0.0434251i | ||||||||
\(85\) | −0.0763355 | − | 7.70424i | −0.00827974 | − | 0.835643i | ||||
\(86\) | −1.27639 | −0.137636 | ||||||||
\(87\) | −3.77880 | −0.405130 | ||||||||
\(88\) | 1.64708 | 0.175580 | ||||||||
\(89\) | −12.5832 | + | 12.5832i | −1.33381 | + | 1.33381i | −0.431885 | + | 0.901929i | \(0.642151\pi\) |
−0.901929 | + | 0.431885i | \(0.857849\pi\) | |||||||
\(90\) | −0.0221544 | − | 2.23596i | −0.00233528 | − | 0.235691i | ||||
\(91\) | −0.888506 | + | 0.888506i | −0.0931407 | + | 0.0931407i | ||||
\(92\) | 3.91265i | 0.407922i | ||||||||
\(93\) | − | 9.57788i | − | 0.993180i | ||||||
\(94\) | −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 | ||||
\(97\) | −6.92746 | −0.703377 | −0.351689 | − | 0.936117i | \(-0.614392\pi\) | ||||
−0.351689 | + | 0.936117i | \(0.614392\pi\) | |||||||
\(98\) | −6.84160 | −0.691106 | ||||||||
\(99\) | 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 | ||||
\(103\) | 11.2563 | 1.10912 | 0.554560 | − | 0.832144i | \(-0.312887\pi\) | ||||
0.554560 | + | 0.832144i | \(0.312887\pi\) | |||||||
\(104\) | 3.15714 | 0.309583 | ||||||||
\(105\) | −0.889907 | + | 0.00881741i | −0.0868460 | + | 0.000860491i | ||||
\(106\) | −3.88760 | − | 3.88760i | −0.377597 | − | 0.377597i | ||||
\(107\) | 8.88960 | + | 8.88960i | 0.859390 | + | 0.859390i | 0.991266 | − | 0.131876i | \(-0.0421001\pi\) |
−0.131876 | + | 0.991266i | \(0.542100\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | −8.94425 | − | 8.94425i | −0.856704 | − | 0.856704i | 0.134244 | − | 0.990948i | \(-0.457139\pi\) |
−0.990948 | + | 0.134244i | \(0.957139\pi\) | |||||||
\(110\) | 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 | ||||
\(113\) | −0.196751 | −0.0185088 | −0.00925440 | − | 0.999957i | \(-0.502946\pi\) | ||||
−0.00925440 | + | 0.999957i | \(0.502946\pi\) | |||||||
\(114\) | 2.61664 | 0.245071 | ||||||||
\(115\) | −8.74853 | + | 0.0866825i | −0.815804 | + | 0.00808318i | ||||
\(116\) | 2.67202 | − | 2.67202i | 0.248090 | − | 0.248090i | ||||
\(117\) | 3.15714 | 0.291878 | ||||||||
\(118\) | 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 | ||||
\(125\) | 0.332273 | + | 11.1754i | 0.0297194 | + | 0.999558i | ||||
\(126\) | −0.281427 | − | 0.281427i | −0.0250715 | − | 0.0250715i | ||||
\(127\) | 6.37075 | + | 6.37075i | 0.565313 | + | 0.565313i | 0.930812 | − | 0.365499i | \(-0.119102\pi\) |
−0.365499 | + | 0.930812i | \(0.619102\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0.902543 | − | 0.902543i | 0.0794644 | − | 0.0794644i | ||||
\(130\) | 0.0699446 | + | 7.05924i | 0.00613455 | + | 0.619136i | ||||
\(131\) | −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 | ||||
\(133\) | − | 1.04142i | − | 0.0903023i | ||||||
\(134\) | −0.492575 | − | 0.492575i | −0.0425520 | − | 0.0425520i | ||||
\(135\) | 1.59673 | + | 1.56540i | 0.137424 | + | 0.134728i | ||||
\(136\) | 3.44561i | 0.295459i | ||||||||
\(137\) | 15.3866 | + | 15.3866i | 1.31456 | + | 1.31456i | 0.918012 | + | 0.396553i | \(0.129794\pi\) |
0.396553 | + | 0.918012i | \(0.370206\pi\) | |||||||
\(138\) | −2.76666 | − | 2.76666i | −0.235514 | − | 0.235514i | ||||
\(139\) | 2.99885 | 0.254359 | 0.127180 | − | 0.991880i | \(-0.459408\pi\) | ||||
0.127180 | + | 0.991880i | \(0.459408\pi\) | |||||||
\(140\) | 0.623024 | − | 0.635494i | 0.0526552 | − | 0.0537091i | ||||
\(141\) | − | 1.06465i | − | 0.0896597i | ||||||
\(142\) | − | 11.2201i | − | 0.941569i | ||||||
\(143\) | −5.20007 | −0.434852 | ||||||||
\(144\) | 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 | ||||
\(148\) | 6.01195 | − | 0.925435i | 0.494179 | − | 0.0760703i | ||||
\(149\) | − | 8.60756i | − | 0.705159i | −0.935782 | − | 0.352579i | \(-0.885305\pi\) | ||
0.935782 | − | 0.352579i | \(-0.114695\pi\) | |||||||
\(150\) | −3.46478 | + | 3.60489i | −0.282898 | + | 0.294338i | ||||
\(151\) | 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 | ||||
\(153\) | 3.44561i | 0.278561i | ||||||||
\(154\) | 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 | 0.509283 | − | 0.860599i | \(-0.329911\pi\) |
−0.860599 | + | 0.509283i | \(0.829911\pi\) | |||||||
\(158\) | −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 | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 10.2487 | 0.802740 | 0.401370 | − | 0.915916i | \(-0.368534\pi\) | ||||
0.401370 | + | 0.915916i | \(0.368534\pi\) | |||||||
\(164\) | 8.72049i | 0.680956i | ||||||||
\(165\) | −2.62994 | − | 2.57834i | −0.204741 | − | 0.200723i | ||||
\(166\) | −3.45461 | − | 3.45461i | −0.268130 | − | 0.268130i | ||||
\(167\) | −2.97278 | −0.230040 | −0.115020 | − | 0.993363i | \(-0.536693\pi\) | ||||
−0.115020 | + | 0.993363i | \(0.536693\pi\) | |||||||
\(168\) | 0.397998 | 0.0307062 | ||||||||
\(169\) | 3.03245 | 0.233265 | ||||||||
\(170\) | −7.70424 | + | 0.0763355i | −0.590888 | + | 0.00585466i | ||||
\(171\) | −1.85024 | + | 1.85024i | −0.141492 | + | 0.141492i | ||||
\(172\) | 1.27639i | 0.0973237i | ||||||||
\(173\) | 5.83257 | + | 5.83257i | 0.443442 | + | 0.443442i | 0.893167 | − | 0.449725i | \(-0.148478\pi\) |
−0.449725 | + | 0.893167i | \(0.648478\pi\) | |||||||
\(174\) | 3.77880i | 0.286470i | ||||||||
\(175\) | 1.43474 | + | 1.37898i | 0.108456 | + | 0.104241i | ||||
\(176\) | − | 1.64708i | − | 0.124153i | ||||||
\(177\) | 9.24603i | 0.694974i | ||||||||
\(178\) | 12.5832 | + | 12.5832i | 0.943149 | + | 0.943149i | ||||
\(179\) | 4.52269 | − | 4.52269i | 0.338042 | − | 0.338042i | −0.517588 | − | 0.855630i | \(-0.673170\pi\) |
0.855630 | + | 0.517588i | \(0.173170\pi\) | |||||||
\(180\) | −2.23596 | + | 0.0221544i | −0.166658 | + | 0.00165129i | ||||
\(181\) | −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 | ||||
\(183\) | − | 0.204701i | − | 0.0151320i | ||||||
\(184\) | 3.91265 | 0.288445 | ||||||||
\(185\) | 2.20243 | + | 13.4220i | 0.161926 | + | 0.986803i | ||||
\(186\) | −9.57788 | −0.702284 | ||||||||
\(187\) | − | 5.67521i | − | 0.415012i | ||||||
\(188\) | 0.752821 | + | 0.752821i | 0.0549051 | + | 0.0549051i | ||||
\(189\) | 0.397998 | 0.0289501 | ||||||||
\(190\) | −4.17806 | − | 4.09608i | −0.303108 | − | 0.297161i | ||||
\(191\) | −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 | ||||
\(193\) | 17.1049i | 1.23124i | 0.788043 | + | 0.615620i | \(0.211094\pi\) | ||||
−0.788043 | + | 0.615620i | \(0.788906\pi\) | |||||||
\(194\) | 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 | 0.686995 | − | 0.726662i | \(-0.258929\pi\) |
−0.726662 | + | 0.686995i | \(0.758929\pi\) | |||||||
\(198\) | − | 1.64708i | − | 0.117053i | ||||||
\(199\) | 7.91159 | − | 7.91159i | 0.560838 | − | 0.560838i | −0.368707 | − | 0.929546i | \(-0.620200\pi\) |
0.929546 | + | 0.368707i | \(0.120200\pi\) | |||||||
\(200\) | −0.0990726 | − | 4.99902i | −0.00700549 | − | 0.353484i | ||||
\(201\) | 0.696607 | 0.0491349 | ||||||||
\(202\) | −6.04485 | −0.425314 | ||||||||
\(203\) | 1.50396 | 0.105557 | ||||||||
\(204\) | −2.43642 | − | 2.43642i | −0.170583 | − | 0.170583i | ||||
\(205\) | −19.4986 | + | 0.193197i | −1.36184 | + | 0.0134935i | ||||
\(206\) | − | 11.2563i | − | 0.784266i | ||||||
\(207\) | 3.91265 | 0.271948 | ||||||||
\(208\) | − | 3.15714i | − | 0.218908i | ||||||
\(209\) | 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 | ||||
\(217\) | 3.81198i | 0.258774i | ||||||||
\(218\) | −8.94425 | + | 8.94425i | −0.605781 | + | 0.605781i | ||||
\(219\) | − | 1.13832i | − | 0.0769207i | ||||||
\(220\) | 3.68281 | − | 0.0364901i | 0.248295 | − | 0.00246016i | ||||
\(221\) | − | 10.8783i | − | 0.731753i | ||||||
\(222\) | −3.59671 | + | 4.90547i | −0.241395 | + | 0.329234i | ||||
\(223\) | −3.07126 | + | 3.07126i | −0.205667 | + | 0.205667i | −0.802423 | − | 0.596756i | \(-0.796456\pi\) |
0.596756 | + | 0.802423i | \(0.296456\pi\) | |||||||
\(224\) | −0.281427 | + | 0.281427i | −0.0188036 | + | 0.0188036i | ||||
\(225\) | −0.0990726 | − | 4.99902i | −0.00660484 | − | 0.333268i | ||||
\(226\) | 0.196751i | 0.0130877i | ||||||||
\(227\) | 24.6591 | 1.63668 | 0.818342 | − | 0.574732i | \(-0.194894\pi\) | ||||
0.818342 | + | 0.574732i | \(0.194894\pi\) | |||||||
\(228\) | − | 2.61664i | − | 0.173291i | ||||||
\(229\) | 14.8812i | 0.983377i | 0.870771 | + | 0.491689i | \(0.163620\pi\) | ||||
−0.870771 | + | 0.491689i | \(0.836380\pi\) | |||||||
\(230\) | 0.0866825 | + | 8.74853i | 0.00571567 | + | 0.576861i | ||||
\(231\) | −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 | \(-0.0118916\pi\) |
−0.0373500 | + | 0.999302i | \(0.511892\pi\) | |||||||
\(234\) | − | 3.15714i | − | 0.206389i | ||||||
\(235\) | −1.66660 | + | 1.69995i | −0.108717 | + | 0.110893i | ||||
\(236\) | −6.53793 | − | 6.53793i | −0.425583 | − | 0.425583i | ||||
\(237\) | − | 4.04926i | − | 0.263028i | ||||||
\(238\) | −0.969688 | + | 0.969688i | −0.0628556 | + | 0.0628556i | ||||
\(239\) | 11.8998 | + | 11.8998i | 0.769736 | + | 0.769736i | 0.978060 | − | 0.208324i | \(-0.0668009\pi\) |
−0.208324 | + | 0.978060i | \(0.566801\pi\) | |||||||
\(240\) | 1.56540 | − | 1.59673i | 0.101046 | − | 0.103068i | ||||
\(241\) | 15.6655 | − | 15.6655i | 1.00910 | − | 1.00910i | 0.00914615 | − | 0.999958i | \(-0.497089\pi\) |
0.999958 | − | 0.00914615i | \(-0.00291135\pi\) | |||||||
\(242\) | − | 8.28712i | − | 0.532716i | ||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0.144746 | + | 0.144746i | 0.00926640 | + | 0.00926640i | ||||
\(245\) | −15.2975 | + | 0.151571i | −0.977323 | + | 0.00968355i | ||||
\(246\) | −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 | ||||
\(253\) | −6.44446 | −0.405160 | ||||||||
\(254\) | 6.37075 | − | 6.37075i | 0.399737 | − | 0.399737i | ||||
\(255\) | 5.39375 | − | 5.50170i | 0.337769 | − | 0.344530i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.24215 | 0.264618 | 0.132309 | − | 0.991209i | \(-0.457761\pi\) | ||||
0.132309 | + | 0.991209i | \(0.457761\pi\) | |||||||
\(258\) | −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 | 0.842223 | + | 0.539129i | \(0.181246\pi\) |
0.539129 | + | 0.842223i | \(0.318754\pi\) | |||||||
\(264\) | 1.16466 | + | 1.16466i | 0.0716801 | + | 0.0716801i | ||||
\(265\) | −8.77864 | − | 8.60638i | −0.539267 | − | 0.528686i | ||||
\(266\) | −1.04142 | −0.0638534 | ||||||||
\(267\) | −17.7953 | −1.08905 | ||||||||
\(268\) | −0.492575 | + | 0.492575i | −0.0300888 | + | 0.0300888i | ||||
\(269\) | − | 15.2647i | − | 0.930706i | −0.885125 | − | 0.465353i | \(-0.845927\pi\) | ||
0.885125 | − | 0.465353i | \(-0.154073\pi\) | |||||||
\(270\) | 1.56540 | − | 1.59673i | 0.0952669 | − | 0.0971737i | ||||
\(271\) | 14.7969 | 0.898849 | 0.449424 | − | 0.893318i | \(-0.351629\pi\) | ||||
0.449424 | + | 0.893318i | \(0.351629\pi\) | |||||||
\(272\) | 3.44561 | 0.208921 | ||||||||
\(273\) | −1.25654 | −0.0760491 | ||||||||
\(274\) | 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 | ||||
\(277\) | 3.00385i | 0.180484i | 0.995920 | + | 0.0902420i | \(0.0287640\pi\) | ||||
−0.995920 | + | 0.0902420i | \(0.971236\pi\) | |||||||
\(278\) | − | 2.99885i | − | 0.179859i | ||||||
\(279\) | 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 | \(0.364678\pi\) | |||||||
\(282\) | −1.06465 | −0.0633990 | ||||||||
\(283\) | 3.86949 | 0.230018 | 0.115009 | − | 0.993364i | \(-0.463310\pi\) | ||||
0.115009 | + | 0.993364i | \(0.463310\pi\) | |||||||
\(284\) | −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 | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −5.12776 | −0.301633 | ||||||||
\(290\) | 5.91532 | − | 6.03371i | 0.347359 | − | 0.354312i | ||||
\(291\) | −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 | −0.319448 | − | 0.947604i | \(-0.603498\pi\) |
0.947604 | + | 0.319448i | \(0.103498\pi\) | |||||||
\(294\) | −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 | ||||
\(298\) | −8.60756 | −0.498622 | ||||||||
\(299\) | −12.3528 | −0.714381 | ||||||||
\(300\) | 3.60489 | + | 3.46478i | 0.208129 | + | 0.200039i | ||||
\(301\) | −0.359210 | + | 0.359210i | −0.0207045 | + | 0.0207045i | ||||
\(302\) | 2.73615 | 0.157448 | ||||||||
\(303\) | 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 | 0.112652 | − | 0.993634i | \(-0.464065\pi\) |
0.993634 | − | 0.112652i | \(-0.0359347\pi\) | |||||||
\(308\) | 0.463534 | − | 0.463534i | 0.0264123 | − | 0.0264123i | ||||
\(309\) | 7.95943 | + | 7.95943i | 0.452796 | + | 0.452796i | ||||
\(310\) | 15.2933 | + | 14.9932i | 0.868599 | + | 0.851555i | ||||
\(311\) | −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 | ||||
\(313\) | 20.7779i | 1.17444i | 0.809429 | + | 0.587218i | \(0.199777\pi\) | ||||
−0.809429 | + | 0.587218i | \(0.800223\pi\) | |||||||
\(314\) | −4.40198 | + | 4.40198i | −0.248418 | + | 0.248418i | ||||
\(315\) | −0.635494 | − | 0.623024i | −0.0358060 | − | 0.0351034i | ||||
\(316\) | 2.86326 | + | 2.86326i | 0.161071 | + | 0.161071i | ||||
\(317\) | 3.25873 | − | 3.25873i | 0.183029 | − | 0.183029i | −0.609646 | − | 0.792674i | \(-0.708688\pi\) |
0.792674 | + | 0.609646i | \(0.208688\pi\) | |||||||
\(318\) | − | 5.49790i | − | 0.308307i | ||||||
\(319\) | 4.40103 | + | 4.40103i | 0.246410 | + | 0.246410i | ||||
\(320\) | 0.0221544 | + | 2.23596i | 0.00123847 | + | 0.124994i | ||||
\(321\) | 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 | ||||||||
\(325\) | 0.312786 | + | 15.7826i | 0.0173503 | + | 0.875462i | ||||
\(326\) | − | 10.2487i | − | 0.567623i | ||||||
\(327\) | − | 12.6491i | − | 0.699496i | ||||||
\(328\) | 8.72049 | 0.481508 | ||||||||
\(329\) | 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 | ||||
\(333\) | −0.925435 | − | 6.01195i | −0.0507135 | − | 0.329453i | ||||
\(334\) | 2.97278i | 0.162663i | ||||||||
\(335\) | −1.11229 | − | 1.09047i | −0.0607709 | − | 0.0595785i | ||||
\(336\) | − | 0.397998i | − | 0.0217126i | ||||||
\(337\) | −8.49643 | + | 8.49643i | −0.462830 | + | 0.462830i | −0.899582 | − | 0.436752i | \(-0.856129\pi\) |
0.436752 | + | 0.899582i | \(0.356129\pi\) | |||||||
\(338\) | − | 3.03245i | − | 0.164944i | ||||||
\(339\) | −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 | ||||
\(347\) | − | 0.455842i | − | 0.0244709i | −0.999925 | − | 0.0122354i | \(-0.996105\pi\) | ||
0.999925 | − | 0.0122354i | \(-0.00389476\pi\) | |||||||
\(348\) | 3.77880 | 0.202565 | ||||||||
\(349\) | − | 18.0258i | − | 0.964899i | −0.875924 | − | 0.482450i | \(-0.839747\pi\) | ||
0.875924 | − | 0.482450i | \(-0.160253\pi\) | |||||||
\(350\) | 1.37898 | − | 1.43474i | 0.0737095 | − | 0.0766901i | ||||
\(351\) | 2.23244 | + | 2.23244i | 0.119159 | + | 0.119159i | ||||
\(352\) | −1.64708 | −0.0877898 | ||||||||
\(353\) | 16.2235 | 0.863489 | 0.431745 | − | 0.901996i | \(-0.357898\pi\) | ||||
0.431745 | + | 0.901996i | \(0.357898\pi\) | |||||||
\(354\) | 9.24603 | 0.491421 | ||||||||
\(355\) | −0.248574 | − | 25.0876i | −0.0131930 | − | 1.33151i | ||||
\(356\) | 12.5832 | − | 12.5832i | 0.666907 | − | 0.666907i | ||||
\(357\) | − | 1.37135i | − | 0.0725794i | ||||||
\(358\) | −4.52269 | − | 4.52269i | −0.239031 | − | 0.239031i | ||||
\(359\) | − | 19.2940i | − | 1.01830i | −0.860678 | − | 0.509149i | \(-0.829960\pi\) | ||
0.860678 | − | 0.509149i | \(-0.170040\pi\) | |||||||
\(360\) | 0.0221544 | + | 2.23596i | 0.00116764 | + | 0.117845i | ||||
\(361\) | − | 12.1532i | − | 0.639642i | ||||||
\(362\) | 16.8840i | 0.887401i | ||||||||
\(363\) | 5.85988 | + | 5.85988i | 0.307564 | + | 0.307564i | ||||
\(364\) | 0.888506 | − | 0.888506i | 0.0465703 | − | 0.0465703i | ||||
\(365\) | −1.78193 | + | 1.81759i | −0.0932703 | + | 0.0951370i | ||||
\(366\) | −0.204701 | −0.0106999 | ||||||||
\(367\) | −3.21053 | − | 3.21053i | −0.167588 | − | 0.167588i | 0.618330 | − | 0.785919i | \(-0.287810\pi\) |
−0.785919 | + | 0.618330i | \(0.787810\pi\) | |||||||
\(368\) | − | 3.91265i | − | 0.203961i | ||||||
\(369\) | 8.72049 | 0.453970 | ||||||||
\(370\) | 13.4220 | − | 2.20243i | 0.697775 | − | 0.114499i | ||||
\(371\) | −2.18815 | −0.113603 | ||||||||
\(372\) | 9.57788i | 0.496590i | ||||||||
\(373\) | 2.94440 | + | 2.94440i | 0.152455 | + | 0.152455i | 0.779214 | − | 0.626759i | \(-0.215619\pi\) |
−0.626759 | + | 0.779214i | \(0.715619\pi\) | |||||||
\(374\) | −5.67521 | −0.293458 | ||||||||
\(375\) | −7.66725 | + | 8.13715i | −0.395935 | + | 0.420201i | ||||
\(376\) | 0.752821 | − | 0.752821i | 0.0388238 | − | 0.0388238i | ||||
\(377\) | 8.43593 | + | 8.43593i | 0.434473 | + | 0.434473i | ||||
\(378\) | − | 0.397998i | − | 0.0204708i | ||||||
\(379\) | − | 25.1637i | − | 1.29257i | −0.763094 | − | 0.646287i | \(-0.776321\pi\) | ||
0.763094 | − | 0.646287i | \(-0.223679\pi\) | |||||||
\(380\) | −4.09608 | + | 4.17806i | −0.210124 | + | 0.214330i | ||||
\(381\) | 9.00960i | 0.461576i | ||||||||
\(382\) | 18.5005 | + | 18.5005i | 0.946566 | + | 0.946566i | ||||
\(383\) | 0.995617i | 0.0508736i | 0.999676 | + | 0.0254368i | \(0.00809766\pi\) | ||||
−0.999676 | + | 0.0254368i | \(0.991902\pi\) | |||||||
\(384\) | −0.707107 | + | 0.707107i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | 1.04671 | + | 1.02617i | 0.0533453 | + | 0.0522986i | ||||
\(386\) | 17.1049 | 0.870618 | ||||||||
\(387\) | 1.27639 | 0.0648824 | ||||||||
\(388\) | 6.92746 | 0.351689 | ||||||||
\(389\) | 19.4231 | + | 19.4231i | 0.984788 | + | 0.984788i | 0.999886 | − | 0.0150980i | \(-0.00480602\pi\) |
−0.0150980 | + | 0.999886i | \(0.504806\pi\) | |||||||
\(390\) | −4.94218 | + | 5.04109i | −0.250257 | + | 0.255266i | ||||
\(391\) | − | 13.4815i | − | 0.681788i | ||||||
\(392\) | 6.84160 | 0.345553 | ||||||||
\(393\) | − | 3.51508i | − | 0.177312i | ||||||
\(394\) | −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 | \(-0.824066\pi\) |
0.524999 | + | 0.851103i | \(0.324066\pi\) | |||||||
\(398\) | −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 | \(-0.577678\pi\) | |||||||
\(402\) | − | 0.696607i | − | 0.0347436i | ||||||
\(403\) | −21.3820 | + | 21.3820i | −1.06511 | + | 1.06511i | ||||
\(404\) | 6.04485i | 0.300743i | ||||||||
\(405\) | 0.0221544 | + | 2.23596i | 0.00110086 | + | 0.111106i | ||||
\(406\) | − | 1.50396i | − | 0.0746401i | ||||||
\(407\) | 1.52427 | + | 9.90218i | 0.0755551 | + | 0.490833i | ||||
\(408\) | −2.43642 | + | 2.43642i | −0.120621 | + | 0.120621i | ||||
\(409\) | −24.0003 | + | 24.0003i | −1.18674 | + | 1.18674i | −0.208776 | + | 0.977963i | \(0.566948\pi\) |
−0.977963 | + | 0.208776i | \(0.933052\pi\) | |||||||
\(410\) | 0.193197 | + | 19.4986i | 0.00954133 | + | 0.962969i | ||||
\(411\) | 21.7599i | 1.07334i | ||||||||
\(412\) | −11.2563 | −0.554560 | ||||||||
\(413\) | − | 3.67990i | − | 0.181076i | ||||||
\(414\) | − | 3.91265i | − | 0.192296i | ||||||
\(415\) | −7.80089 | − | 7.64782i | −0.382931 | − | 0.375417i | ||||
\(416\) | −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 | \(-0.711276\pi\) | ||
0.616070 | − | 0.787692i | \(-0.288724\pi\) | |||||||
\(420\) | 0.889907 | − | 0.00881741i | 0.0434230 | − | 0.000430245i | ||||
\(421\) | −3.85720 | − | 3.85720i | −0.187988 | − | 0.187988i | 0.606838 | − | 0.794826i | \(-0.292438\pi\) |
−0.794826 | + | 0.606838i | \(0.792438\pi\) | |||||||
\(422\) | 1.32938i | 0.0647132i | ||||||||
\(423\) | 0.752821 | − | 0.752821i | 0.0366034 | − | 0.0366034i | ||||
\(424\) | 3.88760 | + | 3.88760i | 0.188798 | + | 0.188798i | ||||
\(425\) | −17.2247 | + | 0.341366i | −0.835519 | + | 0.0165587i | ||||
\(426\) | 7.93380 | − | 7.93380i | 0.384394 | − | 0.384394i | ||||
\(427\) | 0.0814708i | 0.00394265i | ||||||||
\(428\) | −8.88960 | − | 8.88960i | −0.429695 | − | 0.429695i | ||||
\(429\) | −3.67701 | − | 3.67701i | −0.177528 | − | 0.177528i | ||||
\(430\) | 0.0282776 | + | 2.85395i | 0.00136367 | + | 0.137630i | ||||
\(431\) | −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 | −0.432130 | + | 0.901811i | \(0.642238\pi\) |
−0.901811 | + | 0.432130i | \(0.857762\pi\) | |||||||
\(434\) | 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 | ||||
\(438\) | −1.13832 | −0.0543912 | ||||||||
\(439\) | −17.1813 | + | 17.1813i | −0.820020 | + | 0.820020i | −0.986110 | − | 0.166091i | \(-0.946885\pi\) |
0.166091 | + | 0.986110i | \(0.446885\pi\) | |||||||
\(440\) | −0.0364901 | − | 3.68281i | −0.00173960 | − | 0.175571i | ||||
\(441\) | 6.84160 | 0.325790 | ||||||||
\(442\) | −10.8783 | −0.517427 | ||||||||
\(443\) | 7.22878 | + | 7.22878i | 0.343450 | + | 0.343450i | 0.857663 | − | 0.514213i | \(-0.171916\pi\) |
−0.514213 | + | 0.857663i | \(0.671916\pi\) | |||||||
\(444\) | 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 | 0.438116 | − | 0.898918i | \(-0.355646\pi\) |
−0.898918 | + | 0.438116i | \(0.855646\pi\) | |||||||
\(450\) | −4.99902 | + | 0.0990726i | −0.235656 | + | 0.00467033i | ||||
\(451\) | −14.3634 | −0.676344 | ||||||||
\(452\) | 0.196751 | 0.00925440 | ||||||||
\(453\) | −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 | ||||||||
\(457\) | −20.5176 | −0.959771 | −0.479886 | − | 0.877331i | \(-0.659322\pi\) | ||||
−0.479886 | + | 0.877331i | \(0.659322\pi\) | |||||||
\(458\) | 14.8812 | 0.695353 | ||||||||
\(459\) | −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 | \(-0.00221127\pi\) | |||||||
\(462\) | 0.655535i | 0.0304983i | ||||||||
\(463\) | − | 1.38040i | − | 0.0641527i | −0.999485 | − | 0.0320764i | \(-0.989788\pi\) | ||
0.999485 | − | 0.0320764i | \(-0.0102120\pi\) | |||||||
\(464\) | −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 | ||||
\(467\) | 0.453871 | 0.0210026 | 0.0105013 | − | 0.999945i | \(-0.496657\pi\) | ||||
0.0105013 | + | 0.999945i | \(0.496657\pi\) | |||||||
\(468\) | −3.15714 | −0.145939 | ||||||||
\(469\) | −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 | ||||
\(473\) | −2.10232 | −0.0966646 | ||||||||
\(474\) | −4.04926 | −0.185989 | ||||||||
\(475\) | −9.43271 | − | 9.06609i | −0.432802 | − | 0.415981i | ||||
\(476\) | 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 | 0.417521 | − | 0.908667i | \(-0.362899\pi\) |
−0.908667 | + | 0.417521i | \(0.862899\pi\) | |||||||
\(480\) | −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 | ||||
\(483\) | −1.55723 | −0.0708563 | ||||||||
\(484\) | −8.28712 | −0.376687 | ||||||||
\(485\) | 0.153474 | + | 15.4895i | 0.00696888 | + | 0.703343i | ||||
\(486\) | −0.707107 | + | 0.707107i | −0.0320750 | + | 0.0320750i | ||||
\(487\) | 13.2268 | 0.599365 | 0.299682 | − | 0.954039i | \(-0.403119\pi\) | ||||
0.299682 | + | 0.954039i | \(0.403119\pi\) | |||||||
\(488\) | 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 | ||||
\(495\) | −0.0364901 | − | 3.68281i | −0.00164011 | − | 0.165530i | ||||
\(496\) | −6.77259 | − | 6.77259i | −0.304098 | − | 0.304098i | ||||
\(497\) | −3.15764 | − | 3.15764i | −0.141639 | − | 0.141639i | ||||
\(498\) | − | 4.88555i | − | 0.218927i | ||||||
\(499\) | 6.74452 | − | 6.74452i | 0.301926 | − | 0.301926i | −0.539841 | − | 0.841767i | \(-0.681516\pi\) |
0.841767 | + | 0.539841i | \(0.181516\pi\) | |||||||
\(500\) | −0.332273 | − | 11.1754i | −0.0148597 | − | 0.499779i | ||||
\(501\) | −2.10207 | − | 2.10207i | −0.0939136 | − | 0.0939136i | ||||
\(502\) | 8.27735 | − | 8.27735i | 0.369436 | − | 0.369436i | ||||
\(503\) | − | 31.0691i | − | 1.38530i | −0.721272 | − | 0.692652i | \(-0.756442\pi\) | ||
0.721272 | − | 0.692652i | \(-0.243558\pi\) | |||||||
\(504\) | 0.281427 | + | 0.281427i | 0.0125358 | + | 0.0125358i | ||||
\(505\) | −13.5160 | + | 0.133920i | −0.601456 | + | 0.00595937i | ||||
\(506\) | 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 | \(-0.420986\pi\) | ||||
0.245688 | + | 0.969349i | \(0.420986\pi\) | |||||||
\(510\) | −5.50170 | − | 5.39375i | −0.243619 | − | 0.238839i | ||||
\(511\) | 0.453050i | 0.0200418i | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −2.61664 | −0.115527 | ||||||||
\(514\) | − | 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 | ||||
\(518\) | 1.43148 | − | 1.95237i | 0.0628958 | − | 0.0857822i | ||||
\(519\) | 8.24851i | 0.362069i | ||||||||
\(520\) | −0.0699446 | − | 7.05924i | −0.00306727 | − | 0.309568i | ||||
\(521\) | 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 | ||||
\(523\) | 9.72492i | 0.425241i | 0.977135 | + | 0.212620i | \(0.0681998\pi\) | ||||
−0.977135 | + | 0.212620i | \(0.931800\pi\) | |||||||
\(524\) | 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 | ||||
\(532\) | 1.04142i | 0.0451512i | ||||||||
\(533\) | −27.5318 | −1.19254 | ||||||||
\(534\) | 17.7953i | 0.770078i | ||||||||
\(535\) | 19.6798 | − | 20.0737i | 0.850833 | − | 0.867863i | ||||
\(536\) | 0.492575 | + | 0.492575i | 0.0212760 | + | 0.0212760i | ||||
\(537\) | 6.39605 | 0.276010 | ||||||||
\(538\) | −15.2647 | −0.658108 | ||||||||
\(539\) | −11.2687 | −0.485376 | ||||||||
\(540\) | −1.59673 | − | 1.56540i | −0.0687122 | − | 0.0673639i | ||||
\(541\) | −22.2929 | + | 22.2929i | −0.958445 | + | 0.958445i | −0.999170 | − | 0.0407258i | \(-0.987033\pi\) |
0.0407258 | + | 0.999170i | \(0.487033\pi\) | |||||||
\(542\) | − | 14.7969i | − | 0.635582i | ||||||
\(543\) | −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 | ||||||||
\(547\) | 33.1369i | 1.41683i | 0.705795 | + | 0.708416i | \(0.250590\pi\) | ||||
−0.705795 | + | 0.708416i | \(0.749410\pi\) | |||||||
\(548\) | −15.3866 | − | 15.3866i | −0.657282 | − | 0.657282i | ||||
\(549\) | 0.144746 | − | 0.144746i | 0.00617760 | − | 0.00617760i | ||||
\(550\) | 8.23379 | − | 0.163181i | 0.351090 | − | 0.00695805i | ||||
\(551\) | −9.88776 | −0.421233 | ||||||||
\(552\) | 2.76666 | + | 2.76666i | 0.117757 | + | 0.117757i | ||||
\(553\) | 1.61160i | 0.0685322i | ||||||||
\(554\) | 3.00385 | 0.127621 | ||||||||
\(555\) | −7.93342 | + | 11.0481i | −0.336755 | + | 0.468966i | ||||
\(556\) | −2.99885 | −0.127180 | ||||||||
\(557\) | 3.42489i | 0.145117i | 0.997364 | + | 0.0725586i | \(0.0231164\pi\) | ||||
−0.997364 | + | 0.0725586i | \(0.976884\pi\) | |||||||
\(558\) | −6.77259 | − | 6.77259i | −0.286706 | − | 0.286706i | ||||
\(559\) | −4.02974 | −0.170440 | ||||||||
\(560\) | −0.623024 | + | 0.635494i | −0.0263276 | + | 0.0268545i | ||||
\(561\) | 4.01298 | − | 4.01298i | 0.169428 | − | 0.169428i | ||||
\(562\) | 8.35723 | + | 8.35723i | 0.352529 | + | 0.352529i | ||||
\(563\) | − | 17.6124i | − | 0.742273i | −0.928578 | − | 0.371136i | \(-0.878968\pi\) | ||
0.928578 | − | 0.371136i | \(-0.121032\pi\) | |||||||
\(564\) | 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 | ||||
\(568\) | 11.2201i | 0.470784i | ||||||||
\(569\) | 13.6557 | − | 13.6557i | 0.572477 | − | 0.572477i | −0.360343 | − | 0.932820i | \(-0.617340\pi\) |
0.932820 | + | 0.360343i | \(0.117340\pi\) | |||||||
\(570\) | −0.0579701 | − | 5.85070i | −0.00242810 | − | 0.245059i | ||||
\(571\) | 36.6093 | 1.53205 | 0.766025 | − | 0.642811i | \(-0.222232\pi\) | ||||
0.766025 | + | 0.642811i | \(0.222232\pi\) | |||||||
\(572\) | 5.20007 | 0.217426 | ||||||||
\(573\) | −26.1636 | −1.09300 | ||||||||
\(574\) | 2.45418 | + | 2.45418i | 0.102436 | + | 0.102436i | ||||
\(575\) | 0.387637 | + | 19.5594i | 0.0161656 | + | 0.815684i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | −28.6229 | −1.19159 | −0.595794 | − | 0.803137i | \(-0.703163\pi\) | ||||
−0.595794 | + | 0.803137i | \(0.703163\pi\) | |||||||
\(578\) | 5.12776i | 0.213287i | ||||||||
\(579\) | −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 | ||||
\(587\) | − | 17.5944i | − | 0.726197i | −0.931751 | − | 0.363099i | \(-0.881719\pi\) | ||
0.931751 | − | 0.363099i | \(-0.118281\pi\) | |||||||
\(588\) | −4.83774 | + | 4.83774i | −0.199505 | + | 0.199505i | ||||
\(589\) | − | 25.0619i | − | 1.03266i | ||||||
\(590\) | −14.7634 | − | 14.4737i | −0.607799 | − | 0.595873i | ||||
\(591\) | − | 0.787365i | − | 0.0323879i | ||||||
\(592\) | −6.01195 | + | 0.925435i | −0.247090 | + | 0.0380351i | ||||
\(593\) | −5.00469 | + | 5.00469i | −0.205518 | + | 0.205518i | −0.802359 | − | 0.596841i | \(-0.796422\pi\) |
0.596841 | + | 0.802359i | \(0.296422\pi\) | |||||||
\(594\) | 1.16466 | − | 1.16466i | 0.0477867 | − | 0.0477867i | ||||
\(595\) | −2.14670 | + | 2.18967i | −0.0880061 | + | 0.0897675i | ||||
\(596\) | 8.60756i | 0.352579i | ||||||||
\(597\) | 11.1887 | 0.457922 | ||||||||
\(598\) | 12.3528i | 0.505144i | ||||||||
\(599\) | 35.1064i | 1.43441i | 0.696863 | + | 0.717204i | \(0.254579\pi\) | ||||
−0.696863 | + | 0.717204i | \(0.745421\pi\) | |||||||
\(600\) | 3.46478 | − | 3.60489i | 0.141449 | − | 0.147169i | ||||
\(601\) | −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 | ||||||
\(605\) | −0.183596 | − | 18.5297i | −0.00746425 | − | 0.753338i | ||||
\(606\) | −4.27436 | − | 4.27436i | −0.173634 | − | 0.173634i | ||||
\(607\) | − | 2.58147i | − | 0.104779i | −0.998627 | − | 0.0523894i | \(-0.983316\pi\) | ||
0.998627 | − | 0.0523894i | \(-0.0166837\pi\) | |||||||
\(608\) | 1.85024 | − | 1.85024i | 0.0750373 | − | 0.0750373i | ||||
\(609\) | 1.06346 | + | 1.06346i | 0.0430935 | + | 0.0430935i | ||||
\(610\) | 0.326852 | + | 0.320439i | 0.0132339 | + | 0.0129742i | ||||
\(611\) | −2.37676 | + | 2.37676i | −0.0961535 | + | 0.0961535i | ||||
\(612\) | − | 3.44561i | − | 0.139281i | ||||||
\(613\) | −7.76986 | − | 7.76986i | −0.313822 | − | 0.313822i | 0.532566 | − | 0.846388i | \(-0.321228\pi\) |
−0.846388 | + | 0.532566i | \(0.821228\pi\) | |||||||
\(614\) | −19.3837 | − | 19.3837i | −0.782263 | − | 0.782263i | ||||
\(615\) | −13.9242 | − | 13.6510i | −0.561479 | − | 0.550462i | ||||
\(616\) | −0.463534 | − | 0.463534i | −0.0186763 | − | 0.0186763i | ||||
\(617\) | 19.3110 | − | 19.3110i | 0.777430 | − | 0.777430i | −0.201963 | − | 0.979393i | \(-0.564732\pi\) |
0.979393 | + | 0.201963i | \(0.0647322\pi\) | |||||||
\(618\) | 7.95943 | − | 7.95943i | 0.320175 | − | 0.320175i | ||||
\(619\) | −22.9273 | −0.921528 | −0.460764 | − | 0.887523i | \(-0.652425\pi\) | ||||
−0.460764 | + | 0.887523i | \(0.652425\pi\) | |||||||
\(620\) | 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 | ||||
\(623\) | 7.08249 | 0.283754 | ||||||||
\(624\) | 2.23244 | − | 2.23244i | 0.0893690 | − | 0.0893690i | ||||
\(625\) | 24.9804 | − | 0.990532i | 0.999215 | − | 0.0396213i | ||||
\(626\) | 20.7779 | 0.830451 | ||||||||
\(627\) | 4.30982 | 0.172118 | ||||||||
\(628\) | 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 | ||||
\(635\) | 14.1036 | − | 14.3859i | 0.559684 | − | 0.570886i | ||||
\(636\) | −5.49790 | −0.218006 | ||||||||
\(637\) | −21.5999 | −0.855819 | ||||||||
\(638\) | 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 | \(0.457214\pi\) | |||||||
\(642\) | 12.5718 | 0.496169 | ||||||||
\(643\) | 36.8670 | 1.45389 | 0.726945 | − | 0.686695i | \(-0.240939\pi\) | ||||
0.726945 | + | 0.686695i | \(0.240939\pi\) | |||||||
\(644\) | 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 | ||||
\(647\) | − | 19.1501i | − | 0.752868i | −0.926443 | − | 0.376434i | \(-0.877150\pi\) | ||
0.926443 | − | 0.376434i | \(-0.122850\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | 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 | ||||
\(652\) | −10.2487 | −0.401370 | ||||||||
\(653\) | −19.8305 | −0.776029 | −0.388015 | − | 0.921653i | \(-0.626839\pi\) | ||||
−0.388015 | + | 0.921653i | \(0.626839\pi\) | |||||||
\(654\) | −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 | ||||
\(658\) | 0.423728 | 0.0165187 | ||||||||
\(659\) | −21.4129 | −0.834127 | −0.417064 | − | 0.908877i | \(-0.636941\pi\) | ||||
−0.417064 | + | 0.908877i | \(0.636941\pi\) | |||||||
\(660\) | 2.62994 | + | 2.57834i | 0.102370 | + | 0.100362i | ||||
\(661\) | 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 | ||||
\(668\) | 2.97278 | 0.115020 | ||||||||
\(669\) | −4.34342 | −0.167926 | ||||||||
\(670\) | −1.09047 | + | 1.11229i | −0.0421284 | + | 0.0429715i | ||||
\(671\) | −0.238408 | + | 0.238408i | −0.00920365 | + | 0.00920365i | ||||
\(672\) | −0.397998 | −0.0153531 | ||||||||
\(673\) | −19.4561 | + | 19.4561i | −0.749979 | + | 0.749979i | −0.974475 | − | 0.224496i | \(-0.927926\pi\) |
0.224496 | + | 0.974475i | \(0.427926\pi\) | |||||||
\(674\) | 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 | \(-0.790938\pi\) |
0.610577 | + | 0.791957i | \(0.290938\pi\) | |||||||
\(678\) | −0.139124 | + | 0.139124i | −0.00534303 | + | 0.00534303i | ||||
\(679\) | 1.94958 | + | 1.94958i | 0.0748178 | + | 0.0748178i | ||||
\(680\) | 7.70424 | − | 0.0763355i | 0.295444 | − | 0.00292733i | ||||
\(681\) | 17.4366 | + | 17.4366i | 0.668173 | + | 0.668173i | ||||
\(682\) | 11.1550 | + | 11.1550i | 0.427147 | + | 0.427147i | ||||
\(683\) | − | 23.5379i | − | 0.900653i | −0.892864 | − | 0.450327i | \(-0.851308\pi\) | ||
0.892864 | − | 0.450327i | \(-0.148692\pi\) | |||||||
\(684\) | 1.85024 | − | 1.85024i | 0.0707458 | − | 0.0707458i | ||||
\(685\) | 34.0629 | − | 34.7446i | 1.30148 | − | 1.32752i | ||||
\(686\) | 3.89540 | + | 3.89540i | 0.148727 | + | 0.148727i | ||||
\(687\) | −10.5226 | + | 10.5226i | −0.401462 | + | 0.401462i | ||||
\(688\) | − | 1.27639i | − | 0.0486618i | ||||||
\(689\) | −12.2737 | − | 12.2737i | −0.467591 | − | 0.467591i | ||||
\(690\) | −6.12485 | + | 6.24744i | −0.233169 | + | 0.237836i | ||||
\(691\) | 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 | ||||||||
\(695\) | −0.0664378 | − | 6.70531i | −0.00252013 | − | 0.254347i | ||||
\(696\) | − | 3.77880i | − | 0.143235i | ||||||
\(697\) | − | 30.0474i | − | 1.13813i | ||||||
\(698\) | −18.0258 | −0.682287 | ||||||||
\(699\) | 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 | ||||
\(703\) | −12.8359 | − | 9.41129i | −0.484113 | − | 0.354954i | ||||
\(704\) | 1.64708i | 0.0620767i | ||||||||
\(705\) | −2.38051 | + | 0.0235867i | −0.0896553 | + | 0.000888326i | ||||
\(706\) | − | 16.2235i | − | 0.610579i | ||||||
\(707\) | −1.70119 | + | 1.70119i | −0.0639797 | + | 0.0639797i | ||||
\(708\) | − | 9.24603i | − | 0.347487i | ||||||
\(709\) | −17.6567 | − | 17.6567i | −0.663111 | − | 0.663111i | 0.293001 | − | 0.956112i | \(-0.405346\pi\) |
−0.956112 | + | 0.293001i | \(0.905346\pi\) | |||||||
\(710\) | −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 | ||||
\(717\) | 16.8289i | 0.628486i | ||||||||
\(718\) | −19.2940 | −0.720046 | ||||||||
\(719\) | − | 7.51201i | − | 0.280151i | −0.990141 | − | 0.140075i | \(-0.955266\pi\) | ||
0.990141 | − | 0.140075i | \(-0.0447345\pi\) | |||||||
\(720\) | 2.23596 | − | 0.0221544i | 0.0833292 | − | 0.000825646i | ||||
\(721\) | −3.16784 | − | 3.16784i | −0.117976 | − | 0.117976i | ||||
\(722\) | −12.1532 | −0.452295 | ||||||||
\(723\) | 22.1544 | 0.823930 | ||||||||
\(724\) | 16.8840 | 0.627487 | ||||||||
\(725\) | 13.0927 | − | 13.6222i | 0.486252 | − | 0.505915i | ||||
\(726\) | 5.85988 | − | 5.85988i | 0.217481 | − | 0.217481i | ||||
\(727\) | − | 44.5433i | − | 1.65202i | −0.563655 | − | 0.826010i | \(-0.690605\pi\) | ||
0.563655 | − | 0.826010i | \(-0.309395\pi\) | |||||||
\(728\) | −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 | ||||||
\(732\) | 0.204701i | 0.00756598i | ||||||||
\(733\) | 21.8867 | + | 21.8867i | 0.808404 | + | 0.808404i | 0.984392 | − | 0.175988i | \(-0.0563121\pi\) |
−0.175988 | + | 0.984392i | \(0.556312\pi\) | |||||||
\(734\) | −3.21053 | + | 3.21053i | −0.118503 | + | 0.118503i | ||||
\(735\) | −10.9242 | − | 10.7098i | −0.402944 | − | 0.395037i | ||||
\(736\) | −3.91265 | −0.144222 | ||||||||
\(737\) | −0.811312 | − | 0.811312i | −0.0298851 | − | 0.0298851i | ||||
\(738\) | − | 8.72049i | − | 0.321006i | ||||||
\(739\) | 4.64271 | 0.170785 | 0.0853925 | − | 0.996347i | \(-0.472786\pi\) | ||||
0.0853925 | + | 0.996347i | \(0.472786\pi\) | |||||||
\(740\) | −2.20243 | − | 13.4220i | −0.0809628 | − | 0.493401i | ||||
\(741\) | 8.26110 | 0.303479 | ||||||||
\(742\) | 2.18815i | 0.0803296i | ||||||||
\(743\) | 38.1619 | + | 38.1619i | 1.40003 | + | 1.40003i | 0.799921 | + | 0.600105i | \(0.204874\pi\) |
0.600105 | + | 0.799921i | \(0.295126\pi\) | |||||||
\(744\) | 9.57788 | 0.351142 | ||||||||
\(745\) | −19.2461 | + | 0.190695i | −0.705124 | + | 0.00698653i | ||||
\(746\) | 2.94440 | − | 2.94440i | 0.107802 | − | 0.107802i | ||||
\(747\) | 3.45461 | + | 3.45461i | 0.126397 | + | 0.126397i | ||||
\(748\) | 5.67521i | 0.207506i | ||||||||
\(749\) | − | 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 | ||||
\(753\) | 11.7059i | 0.426588i | ||||||||
\(754\) | 8.43593 | − | 8.43593i | 0.307219 | − | 0.307219i | ||||
\(755\) | 6.11791 | − | 0.0606177i | 0.222654 | − | 0.00220610i | ||||
\(756\) | −0.397998 | −0.0144750 | ||||||||
\(757\) | 17.1425 | 0.623054 | 0.311527 | − | 0.950237i | \(-0.399160\pi\) | ||||
0.311527 | + | 0.950237i | \(0.399160\pi\) | |||||||
\(758\) | −25.1637 | −0.913989 | ||||||||
\(759\) | −4.55692 | − | 4.55692i | −0.165406 | − | 0.165406i | ||||
\(760\) | 4.17806 | + | 4.09608i | 0.151554 | + | 0.148580i | ||||
\(761\) | 35.6476i | 1.29222i | 0.763243 | + | 0.646112i | \(0.223606\pi\) | ||||
−0.763243 | + | 0.646112i | \(0.776394\pi\) | |||||||
\(762\) | 9.00960 | 0.326384 | ||||||||
\(763\) | 5.03431i | 0.182254i | ||||||||
\(764\) | 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 | −0.898830 | − | 0.438297i | \(-0.855582\pi\) |
0.438297 | + | 0.898830i | \(0.355582\pi\) | |||||||
\(770\) | 1.02617 | − | 1.04671i | 0.0369807 | − | 0.0377208i | ||||
\(771\) | 2.99965 | + | 2.99965i | 0.108030 | + | 0.108030i | ||||
\(772\) | − | 17.1049i | − | 0.615620i | ||||||
\(773\) | 11.0549 | − | 11.0549i | 0.397617 | − | 0.397617i | −0.479775 | − | 0.877392i | \(-0.659282\pi\) |
0.877392 | + | 0.479775i | \(0.159282\pi\) | |||||||
\(774\) | − | 1.27639i | − | 0.0458788i | ||||||
\(775\) | 34.5273 | + | 33.1853i | 1.24026 | + | 1.19205i | ||||
\(776\) | − | 6.92746i | − | 0.248681i | ||||||
\(777\) | 0.368321 | + | 2.39275i | 0.0132135 | + | 0.0858393i | ||||
\(778\) | 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 | ||||||
\(782\) | −13.4815 | −0.482097 | ||||||||
\(783\) | − | 3.77880i | − | 0.135043i | ||||||
\(784\) | − | 6.84160i | − | 0.244343i | ||||||
\(785\) | −9.74513 | + | 9.94017i | −0.347819 | + | 0.354780i | ||||
\(786\) | −3.51508 | −0.125379 | ||||||||
\(787\) | 13.1009 | + | 13.1009i | 0.466997 | + | 0.466997i | 0.900940 | − | 0.433944i | \(-0.142878\pi\) |
−0.433944 | + | 0.900940i | \(0.642878\pi\) | |||||||
\(788\) | 0.556751 | + | 0.556751i | 0.0198334 | + | 0.0198334i | ||||
\(789\) | 31.6809i | 1.12787i | ||||||||
\(790\) | 6.46557 | + | 6.33870i | 0.230035 | + | 0.225521i | ||||
\(791\) | 0.0553711 | + | 0.0553711i | 0.00196877 | + | 0.00196877i | ||||
\(792\) | 1.64708i | 0.0585265i | ||||||||
\(793\) | −0.456983 | + | 0.456983i | −0.0162279 | + | 0.0162279i | ||||
\(794\) | 6.49757 | + | 6.49757i | 0.230590 | + | 0.230590i | ||||
\(795\) | −0.121803 | − | 12.2931i | −0.00431989 | − | 0.435990i | ||||
\(796\) | −7.91159 | + | 7.91159i | −0.280419 | + | 0.280419i | ||||
\(797\) | 19.8808i | 0.704216i | 0.935959 | + | 0.352108i | \(0.114535\pi\) | ||||
−0.935959 | + | 0.352108i | \(0.885465\pi\) | |||||||
\(798\) | −0.736393 | − | 0.736393i | −0.0260680 | − | 0.0260680i | ||||
\(799\) | −2.59393 | − | 2.59393i | −0.0917666 | − | 0.0917666i | ||||
\(800\) | 0.0990726 | + | 4.99902i | 0.00350275 | + | 0.176742i | ||||
\(801\) | −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 | ||||
\(808\) | 6.04485 | 0.212657 | ||||||||
\(809\) | 9.85033 | − | 9.85033i | 0.346319 | − | 0.346319i | −0.512417 | − | 0.858737i | \(-0.671250\pi\) |
0.858737 | + | 0.512417i | \(0.171250\pi\) | |||||||
\(810\) | 2.23596 | − | 0.0221544i | 0.0785636 | − | 0.000778426i | ||||
\(811\) | 33.2668 | 1.16815 | 0.584077 | − | 0.811698i | \(-0.301456\pi\) | ||||
0.584077 | + | 0.811698i | \(0.301456\pi\) | |||||||
\(812\) | −1.50396 | −0.0527785 | ||||||||
\(813\) | 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 | ||||
\(820\) | 19.4986 | − | 0.193197i | 0.680922 | − | 0.00674674i | ||||
\(821\) | −14.4484 | −0.504251 | −0.252126 | − | 0.967694i | \(-0.581130\pi\) | ||||
−0.252126 | + | 0.967694i | \(0.581130\pi\) | |||||||
\(822\) | 21.7599 | 0.758964 | ||||||||
\(823\) | 8.70320 | − | 8.70320i | 0.303375 | − | 0.303375i | −0.538958 | − | 0.842333i | \(-0.681182\pi\) |
0.842333 | + | 0.538958i | \(0.181182\pi\) | |||||||
\(824\) | 11.2563i | 0.392133i | ||||||||
\(825\) | −5.70679 | + | 5.93756i | −0.198685 | + | 0.206719i | ||||
\(826\) | −3.67990 | −0.128040 | ||||||||
\(827\) | −30.1185 | −1.04732 | −0.523661 | − | 0.851927i | \(-0.675434\pi\) | ||||
−0.523661 | + | 0.851927i | \(0.675434\pi\) | |||||||
\(828\) | −3.91265 | −0.135974 | ||||||||
\(829\) | −23.9359 | + | 23.9359i | −0.831329 | + | 0.831329i | −0.987699 | − | 0.156370i | \(-0.950021\pi\) |
0.156370 | + | 0.987699i | \(0.450021\pi\) | |||||||
\(830\) | −7.64782 | + | 7.80089i | −0.265460 | + | 0.270773i | ||||
\(831\) | −2.12404 | + | 2.12404i | −0.0736823 | + | 0.0736823i | ||||
\(832\) | 3.15714i | 0.109454i | ||||||||
\(833\) | − | 23.5735i | − | 0.816773i | ||||||
\(834\) | 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 | ||||
\(837\) | 9.57788 | 0.331060 | ||||||||
\(838\) | −32.2473 | −1.11396 | ||||||||
\(839\) | 24.1682 | 0.834380 | 0.417190 | − | 0.908819i | \(-0.363015\pi\) | ||||
0.417190 | + | 0.908819i | \(0.363015\pi\) | |||||||
\(840\) | −0.00881741 | − | 0.889907i | −0.000304229 | − | 0.0307047i | ||||
\(841\) | 14.7207i | 0.507609i | ||||||||
\(842\) | −3.85720 | + | 3.85720i | −0.132928 | + | 0.132928i | ||||
\(843\) | −11.8189 | −0.407065 | ||||||||
\(844\) | 1.32938 | 0.0457592 | ||||||||
\(845\) | −0.0671821 | − | 6.78043i | −0.00231114 | − | 0.233254i | ||||
\(846\) | −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 | ||||
\(853\) | −40.9694 | −1.40276 | −0.701382 | − | 0.712785i | \(-0.747433\pi\) | ||||
−0.701382 | + | 0.712785i | \(0.747433\pi\) | |||||||
\(854\) | 0.0814708 | 0.00278787 | ||||||||
\(855\) | 4.17806 | + | 4.09608i | 0.142887 | + | 0.140083i | ||||
\(856\) | −8.88960 | + | 8.88960i | −0.303840 | + | 0.303840i | ||||
\(857\) | 10.8481 | 0.370563 | 0.185281 | − | 0.982686i | \(-0.440680\pi\) | ||||
0.185281 | + | 0.982686i | \(0.440680\pi\) | |||||||
\(858\) | −3.67701 | + | 3.67701i | −0.125531 | + | 0.125531i | ||||
\(859\) | 11.6985 | + | 11.6985i | 0.399147 | + | 0.399147i | 0.877932 | − | 0.478785i | \(-0.158923\pi\) |
−0.478785 | + | 0.877932i | \(0.658923\pi\) | |||||||
\(860\) | 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 | 0.302924 | − | 0.953015i | \(-0.402037\pi\) |
0.953015 | − | 0.302924i | \(-0.0979629\pi\) | |||||||
\(864\) | 0.707107 | + | 0.707107i | 0.0240563 | + | 0.0240563i | ||||
\(865\) | 12.9122 | − | 13.1706i | 0.439027 | − | 0.447814i | ||||
\(866\) | 27.7575 | + | 27.7575i | 0.943239 | + | 0.943239i | ||||
\(867\) | −3.62588 | − | 3.62588i | −0.123141 | − | 0.123141i | ||||
\(868\) | − | 3.81198i | − | 0.129387i | ||||||
\(869\) | −4.71603 | + | 4.71603i | −0.159980 | + | 0.159980i | ||||
\(870\) | 8.44924 | − | 0.0837171i | 0.286456 | − | 0.00283827i | ||||
\(871\) | −1.55513 | − | 1.55513i | −0.0526936 | − | 0.0526936i | ||||
\(872\) | 8.94425 | − | 8.94425i | 0.302891 | − | 0.302891i | ||||
\(873\) | − | 6.92746i | − | 0.234459i | ||||||
\(874\) | −7.23936 | − | 7.23936i | −0.244875 | − | 0.244875i | ||||
\(875\) | 3.05155 | − | 3.23857i | 0.103161 | − | 0.109484i | ||||
\(876\) | 1.13832i | 0.0384604i | ||||||||
\(877\) | −25.8706 | − | 25.8706i | −0.873589 | − | 0.873589i | 0.119273 | − | 0.992862i | \(-0.461944\pi\) |
−0.992862 | + | 0.119273i | \(0.961944\pi\) | |||||||
\(878\) | 17.1813 | + | 17.1813i | 0.579841 | + | 0.579841i | ||||
\(879\) | 15.2060 | 0.512887 | ||||||||
\(880\) | −3.68281 | + | 0.0364901i | −0.124147 | + | 0.00123008i | ||||
\(881\) | − | 4.62987i | − | 0.155984i | −0.996954 | − | 0.0779921i | \(-0.975149\pi\) | ||
0.996954 | − | 0.0779921i | \(-0.0248509\pi\) | |||||||
\(882\) | − | 6.84160i | − | 0.230369i | ||||||
\(883\) | −14.3060 | −0.481435 | −0.240718 | − | 0.970595i | \(-0.577383\pi\) | ||||
−0.240718 | + | 0.970595i | \(0.577383\pi\) | |||||||
\(884\) | 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 | \(-0.641231\pi\) |
0.903173 | + | 0.429277i | \(0.141231\pi\) | |||||||
\(888\) | 3.59671 | − | 4.90547i | 0.120698 | − | 0.164617i | ||||
\(889\) | − | 3.58581i | − | 0.120264i | ||||||
\(890\) | 27.8567 | − | 28.4142i | 0.933758 | − | 0.952447i | ||||
\(891\) | 1.64708i | 0.0551793i | ||||||||
\(892\) | 3.07126 | − | 3.07126i | 0.102834 | − | 0.102834i | ||||
\(893\) | − | 2.78580i | − | 0.0932234i | ||||||
\(894\) | −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 | ||||
\(902\) | 14.3634i | 0.478248i | ||||||||
\(903\) | −0.508000 | −0.0169052 | ||||||||
\(904\) | − | 0.196751i | − | 0.00654385i | ||||||
\(905\) | 0.374054 | + | 37.7518i | 0.0124340 | + | 1.25491i | ||||
\(906\) | 1.93475 | + | 1.93475i | 0.0642777 | + | 0.0642777i | ||||
\(907\) | −6.36519 | −0.211353 | −0.105676 | − | 0.994401i | \(-0.533701\pi\) | ||||
−0.105676 | + | 0.994401i | \(0.533701\pi\) | |||||||
\(908\) | −24.6591 | −0.818342 | ||||||||
\(909\) | 6.04485 | 0.200495 | ||||||||
\(910\) | 1.96698 | − | 2.00635i | 0.0652047 | − | 0.0665097i | ||||
\(911\) | −17.2930 | + | 17.2930i | −0.572944 | + | 0.572944i | −0.932950 | − | 0.360006i | \(-0.882775\pi\) |
0.360006 | + | 0.932950i | \(0.382775\pi\) | |||||||
\(912\) | 2.61664i | 0.0866456i | ||||||||
\(913\) | −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 | ||||||
\(917\) | 1.39900i | 0.0461989i | ||||||||
\(918\) | 2.43642 | + | 2.43642i | 0.0804137 | + | 0.0804137i | ||||
\(919\) | −22.2107 | + | 22.2107i | −0.732663 | + | 0.732663i | −0.971146 | − | 0.238484i | \(-0.923350\pi\) |
0.238484 | + | 0.971146i | \(0.423350\pi\) | |||||||
\(920\) | −0.0866825 | − | 8.74853i | −0.00285784 | − | 0.288430i | ||||
\(921\) | 27.4127 | 0.903279 | ||||||||
\(922\) | −21.6195 | − | 21.6195i | −0.712002 | − | 0.712002i | ||||
\(923\) | − | 35.4234i | − | 1.16598i | ||||||
\(924\) | 0.655535 | 0.0215655 | ||||||||
\(925\) | 29.9622 | − | 5.22189i | 0.985150 | − | 0.171695i | ||||
\(926\) | −1.38040 | −0.0453628 | ||||||||
\(927\) | 11.2563i | 0.369707i | ||||||||
\(928\) | 2.67202 | + | 2.67202i | 0.0877132 | + | 0.0877132i | ||||
\(929\) | −1.85414 | −0.0608325 | −0.0304162 | − | 0.999537i | \(-0.509683\pi\) | ||||
−0.0304162 | + | 0.999537i | \(0.509683\pi\) | |||||||
\(930\) | 0.212192 | + | 21.4157i | 0.00695806 | + | 0.702250i | ||||
\(931\) | 12.6586 | − | 12.6586i | 0.414869 | − | 0.414869i | ||||
\(932\) | −14.6836 | − | 14.6836i | −0.480976 | − | 0.480976i | ||||
\(933\) | − | 13.3481i | − | 0.436996i | ||||||
\(934\) | − | 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 | 0.281706 | − | 0.959501i | \(-0.409100\pi\) |
−0.959501 | + | 0.281706i | \(0.909100\pi\) | |||||||
\(938\) | 0.277248i | 0.00905247i | ||||||||
\(939\) | −14.6922 | + | 14.6922i | −0.479461 | + | 0.479461i | ||||
\(940\) | 1.66660 | − | 1.69995i | 0.0543584 | − | 0.0554464i | ||||
\(941\) | 18.4162 | 0.600352 | 0.300176 | − | 0.953884i | \(-0.402955\pi\) | ||||
0.300176 | + | 0.953884i | \(0.402955\pi\) | |||||||
\(942\) | −6.22534 | −0.202833 | ||||||||
\(943\) | −34.1202 | −1.11111 | ||||||||
\(944\) | 6.53793 | + | 6.53793i | 0.212792 | + | 0.212792i | ||||
\(945\) | −0.00881741 | − | 0.889907i | −0.000286830 | − | 0.0289487i | ||||
\(946\) | 2.10232i | 0.0683522i | ||||||||
\(947\) | 35.4933 | 1.15338 | 0.576689 | − | 0.816964i | \(-0.304344\pi\) | ||||
0.576689 | + | 0.816964i | \(0.304344\pi\) | |||||||
\(948\) | 4.04926i | 0.131514i | ||||||||
\(949\) | −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 | \(-0.433368\pi\) |
−0.978170 | + | 0.207806i | \(0.933368\pi\) | |||||||
\(954\) | 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 | ||||
\(957\) | 6.22400i | 0.201193i | ||||||||
\(958\) | −10.7493 | + | 10.7493i | −0.347293 | + | 0.347293i | ||||
\(959\) | − | 8.66041i | − | 0.279659i | ||||||
\(960\) | −1.56540 | + | 1.59673i | −0.0505229 | + | 0.0515341i | ||||
\(961\) | 60.7358i | 1.95922i | ||||||||
\(962\) | 18.9806 | − | 2.92173i | 0.611959 | − | 0.0942004i | ||||
\(963\) | −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 | ||||||||
\(967\) | −23.3872 | −0.752080 | −0.376040 | − | 0.926603i | \(-0.622715\pi\) | ||||
−0.376040 | + | 0.926603i | \(0.622715\pi\) | |||||||
\(968\) | 8.28712i | 0.266358i | ||||||||
\(969\) | 9.01592i | 0.289633i | ||||||||
\(970\) | 15.4895 | − | 0.153474i | 0.497338 | − | 0.00492774i | ||||
\(971\) | −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 | ||||||
\(975\) | −10.9388 | + | 11.3812i | −0.350323 | + | 0.364489i | ||||
\(976\) | −0.144746 | − | 0.144746i | −0.00463320 | − | 0.00463320i | ||||
\(977\) | − | 60.9677i | − | 1.95053i | −0.221043 | − | 0.975264i | \(-0.570946\pi\) | ||
0.221043 | − | 0.975264i | \(-0.429054\pi\) | |||||||
\(978\) | 7.24692 | − | 7.24692i | 0.231731 | − | 0.231731i | ||||
\(979\) | 20.7255 | + | 20.7255i | 0.662390 | + | 0.662390i | ||||
\(980\) | 15.2975 | − | 0.151571i | 0.488662 | − | 0.00484177i | ||||
\(981\) | 8.94425 | − | 8.94425i | 0.285568 | − | 0.285568i | ||||
\(982\) | 30.4522i | 0.971770i | ||||||||
\(983\) | 25.7832 | + | 25.7832i | 0.822357 | + | 0.822357i | 0.986446 | − | 0.164088i | \(-0.0524683\pi\) |
−0.164088 | + | 0.986446i | \(0.552468\pi\) | |||||||
\(984\) | 6.16632 | + | 6.16632i | 0.196575 | + | 0.196575i | ||||
\(985\) | −1.23254 | + | 1.25721i | −0.0392719 | + | 0.0400579i | ||||
\(986\) | 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 | ||||
\(993\) | 2.83646 | 0.0900124 | ||||||||
\(994\) | −3.15764 | + | 3.15764i | −0.100154 | + | 0.100154i | ||||
\(995\) | −17.8653 | − | 17.5147i | −0.566367 | − | 0.555254i | ||||
\(996\) | −4.88555 | −0.154805 | ||||||||
\(997\) | −24.6196 | −0.779711 | −0.389856 | − | 0.920876i | \(-0.627475\pi\) | ||||
−0.389856 | + | 0.920876i | \(0.627475\pi\) | |||||||
\(998\) | −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.l.a.697.11 | yes | 36 | |
5.3 | odd | 4 | 1110.2.o.a.253.8 | yes | 36 | ||
37.6 | odd | 4 | 1110.2.o.a.487.8 | yes | 36 | ||
185.43 | even | 4 | inner | 1110.2.l.a.43.11 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.11 | ✓ | 36 | 185.43 | even | 4 | inner | |
1110.2.l.a.697.11 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.o.a.253.8 | yes | 36 | 5.3 | odd | 4 | ||
1110.2.o.a.487.8 | yes | 36 | 37.6 | odd | 4 |