Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(97,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.m (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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 97.7 | ||
Root | \(0.277956 - 0.213283i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.97 |
Dual form | 1470.2.m.e.1273.7 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 1.36519 | − | 1.77095i | 0.610532 | − | 0.791991i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 2.21758 | − | 0.286912i | 0.701262 | − | 0.0907294i | ||||
\(11\) | 5.48630 | 1.65418 | 0.827091 | − | 0.562068i | \(-0.189994\pi\) | ||||
0.827091 | + | 0.562068i | \(0.189994\pi\) | |||||||
\(12\) | −0.707107 | + | 0.707107i | −0.204124 | + | 0.204124i | ||||
\(13\) | −2.41668 | − | 2.41668i | −0.670266 | − | 0.670266i | 0.287511 | − | 0.957777i | \(-0.407172\pi\) |
−0.957777 | + | 0.287511i | \(0.907172\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.21758 | − | 0.286912i | 0.572578 | − | 0.0740803i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.49783 | + | 1.49783i | −0.363276 | + | 0.363276i | −0.865018 | − | 0.501742i | \(-0.832693\pi\) |
0.501742 | + | 0.865018i | \(0.332693\pi\) | |||||||
\(18\) | −0.707107 | + | 0.707107i | −0.166667 | + | 0.166667i | ||||
\(19\) | 6.99593 | 1.60498 | 0.802489 | − | 0.596668i | \(-0.203509\pi\) | ||||
0.802489 | + | 0.596668i | \(0.203509\pi\) | |||||||
\(20\) | 1.77095 | + | 1.36519i | 0.395996 | + | 0.305266i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.87940 | + | 3.87940i | 0.827091 | + | 0.827091i | ||||
\(23\) | −1.24054 | + | 1.24054i | −0.258670 | + | 0.258670i | −0.824513 | − | 0.565843i | \(-0.808551\pi\) |
0.565843 | + | 0.824513i | \(0.308551\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −1.27250 | − | 4.83536i | −0.254500 | − | 0.967073i | ||||
\(26\) | − | 3.41770i | − | 0.670266i | ||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.684610i | 0.127129i | 0.997978 | + | 0.0635644i | \(0.0202468\pi\) | ||||
−0.997978 | + | 0.0635644i | \(0.979753\pi\) | |||||||
\(30\) | 1.77095 | + | 1.36519i | 0.323329 | + | 0.249249i | ||||
\(31\) | − | 5.57642i | − | 1.00155i | −0.865576 | − | 0.500777i | \(-0.833048\pi\) | ||
0.865576 | − | 0.500777i | \(-0.166952\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 3.87940 | + | 3.87940i | 0.675317 | + | 0.675317i | ||||
\(34\) | −2.11825 | −0.363276 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 6.92974 | + | 6.92974i | 1.13924 | + | 1.13924i | 0.988586 | + | 0.150656i | \(0.0481386\pi\) |
0.150656 | + | 0.988586i | \(0.451861\pi\) | |||||||
\(38\) | 4.94687 | + | 4.94687i | 0.802489 | + | 0.802489i | ||||
\(39\) | − | 3.41770i | − | 0.547270i | ||||||
\(40\) | 0.286912 | + | 2.21758i | 0.0453647 | + | 0.350631i | ||||
\(41\) | − | 2.50597i | − | 0.391366i | −0.980667 | − | 0.195683i | \(-0.937308\pi\) | ||
0.980667 | − | 0.195683i | \(-0.0626924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.95305 | + | 1.95305i | −0.297837 | + | 0.297837i | −0.840166 | − | 0.542329i | \(-0.817543\pi\) |
0.542329 | + | 0.840166i | \(0.317543\pi\) | |||||||
\(44\) | 5.48630i | 0.827091i | ||||||||
\(45\) | 1.77095 | + | 1.36519i | 0.263997 | + | 0.203511i | ||||
\(46\) | −1.75439 | −0.258670 | ||||||||
\(47\) | 2.49268 | − | 2.49268i | 0.363594 | − | 0.363594i | −0.501540 | − | 0.865134i | \(-0.667233\pi\) |
0.865134 | + | 0.501540i | \(0.167233\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.51932 | − | 4.31891i | 0.356286 | − | 0.610787i | ||||
\(51\) | −2.11825 | −0.296614 | ||||||||
\(52\) | 2.41668 | − | 2.41668i | 0.335133 | − | 0.335133i | ||||
\(53\) | −6.64852 | + | 6.64852i | −0.913244 | + | 0.913244i | −0.996526 | − | 0.0832822i | \(-0.973460\pi\) |
0.0832822 | + | 0.996526i | \(0.473460\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 7.48985 | − | 9.71594i | 1.00993 | − | 1.31010i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.94687 | + | 4.94687i | 0.655229 | + | 0.655229i | ||||
\(58\) | −0.484092 | + | 0.484092i | −0.0635644 | + | 0.0635644i | ||||
\(59\) | 10.1603 | 1.32276 | 0.661379 | − | 0.750052i | \(-0.269972\pi\) | ||||
0.661379 | + | 0.750052i | \(0.269972\pi\) | |||||||
\(60\) | 0.286912 | + | 2.21758i | 0.0370401 | + | 0.286289i | ||||
\(61\) | 1.17166i | 0.150016i | 0.997183 | + | 0.0750079i | \(0.0238982\pi\) | ||||
−0.997183 | + | 0.0750079i | \(0.976102\pi\) | |||||||
\(62\) | 3.94312 | − | 3.94312i | 0.500777 | − | 0.500777i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −7.57904 | + | 0.980578i | −0.940064 | + | 0.121626i | ||||
\(66\) | 5.48630i | 0.675317i | ||||||||
\(67\) | 7.03792 | + | 7.03792i | 0.859819 | + | 0.859819i | 0.991317 | − | 0.131497i | \(-0.0419784\pi\) |
−0.131497 | + | 0.991317i | \(0.541978\pi\) | |||||||
\(68\) | −1.49783 | − | 1.49783i | −0.181638 | − | 0.181638i | ||||
\(69\) | −1.75439 | −0.211204 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.9716 | −1.42077 | −0.710383 | − | 0.703816i | \(-0.751478\pi\) | ||||
−0.710383 | + | 0.703816i | \(0.751478\pi\) | |||||||
\(72\) | −0.707107 | − | 0.707107i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | −3.44417 | − | 3.44417i | −0.403109 | − | 0.403109i | 0.476218 | − | 0.879327i | \(-0.342007\pi\) |
−0.879327 | + | 0.476218i | \(0.842007\pi\) | |||||||
\(74\) | 9.80013i | 1.13924i | ||||||||
\(75\) | 2.51932 | − | 4.31891i | 0.290906 | − | 0.498705i | ||||
\(76\) | 6.99593i | 0.802489i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.41668 | − | 2.41668i | 0.273635 | − | 0.273635i | ||||
\(79\) | 8.33087i | 0.937296i | 0.883385 | + | 0.468648i | \(0.155259\pi\) | ||||
−0.883385 | + | 0.468648i | \(0.844741\pi\) | |||||||
\(80\) | −1.36519 | + | 1.77095i | −0.152633 | + | 0.197998i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 1.77199 | − | 1.77199i | 0.195683 | − | 0.195683i | ||||
\(83\) | −4.05281 | − | 4.05281i | −0.444854 | − | 0.444854i | 0.448786 | − | 0.893639i | \(-0.351857\pi\) |
−0.893639 | + | 0.448786i | \(0.851857\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.607749 | + | 4.69739i | 0.0659197 | + | 0.509503i | ||||
\(86\) | −2.76202 | −0.297837 | ||||||||
\(87\) | −0.484092 | + | 0.484092i | −0.0519001 | + | 0.0519001i | ||||
\(88\) | −3.87940 | + | 3.87940i | −0.413545 | + | 0.413545i | ||||
\(89\) | 7.18356 | 0.761456 | 0.380728 | − | 0.924687i | \(-0.375673\pi\) | ||||
0.380728 | + | 0.924687i | \(0.375673\pi\) | |||||||
\(90\) | 0.286912 | + | 2.21758i | 0.0302431 | + | 0.233754i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.24054 | − | 1.24054i | −0.129335 | − | 0.129335i | ||||
\(93\) | 3.94312 | − | 3.94312i | 0.408883 | − | 0.408883i | ||||
\(94\) | 3.52518 | 0.363594 | ||||||||
\(95\) | 9.55079 | − | 12.3894i | 0.979891 | − | 1.27113i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | −13.1212 | + | 13.1212i | −1.33226 | + | 1.33226i | −0.428909 | + | 0.903348i | \(0.641102\pi\) |
−0.903348 | + | 0.428909i | \(0.858898\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.48630i | 0.551394i | ||||||||
\(100\) | 4.83536 | − | 1.27250i | 0.483536 | − | 0.127250i | ||||
\(101\) | − | 8.26766i | − | 0.822663i | −0.911486 | − | 0.411332i | \(-0.865064\pi\) | ||
0.911486 | − | 0.411332i | \(-0.134936\pi\) | |||||||
\(102\) | −1.49783 | − | 1.49783i | −0.148307 | − | 0.148307i | ||||
\(103\) | −6.58048 | − | 6.58048i | −0.648394 | − | 0.648394i | 0.304211 | − | 0.952605i | \(-0.401607\pi\) |
−0.952605 | + | 0.304211i | \(0.901607\pi\) | |||||||
\(104\) | 3.41770 | 0.335133 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.40242 | −0.913244 | ||||||||
\(107\) | −8.67454 | − | 8.67454i | −0.838600 | − | 0.838600i | 0.150075 | − | 0.988675i | \(-0.452049\pi\) |
−0.988675 | + | 0.150075i | \(0.952049\pi\) | |||||||
\(108\) | −0.707107 | − | 0.707107i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | 0.336622i | 0.0322425i | 0.999870 | + | 0.0161213i | \(0.00513178\pi\) | ||||
−0.999870 | + | 0.0161213i | \(0.994868\pi\) | |||||||
\(110\) | 12.1663 | − | 1.57408i | 1.16001 | − | 0.150083i | ||||
\(111\) | 9.80013i | 0.930188i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.1896 | − | 10.1896i | 0.958555 | − | 0.958555i | −0.0406198 | − | 0.999175i | \(-0.512933\pi\) |
0.999175 | + | 0.0406198i | \(0.0129332\pi\) | |||||||
\(114\) | 6.99593i | 0.655229i | ||||||||
\(115\) | 0.503355 | + | 3.89051i | 0.0469380 | + | 0.362792i | ||||
\(116\) | −0.684610 | −0.0635644 | ||||||||
\(117\) | 2.41668 | − | 2.41668i | 0.223422 | − | 0.223422i | ||||
\(118\) | 7.18441 | + | 7.18441i | 0.661379 | + | 0.661379i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.36519 | + | 1.77095i | −0.124624 | + | 0.161665i | ||||
\(121\) | 19.0995 | 1.73632 | ||||||||
\(122\) | −0.828489 | + | 0.828489i | −0.0750079 | + | 0.0750079i | ||||
\(123\) | 1.77199 | − | 1.77199i | 0.159775 | − | 0.159775i | ||||
\(124\) | 5.57642 | 0.500777 | ||||||||
\(125\) | −10.3004 | − | 4.34767i | −0.921294 | − | 0.388867i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.77054 | − | 4.77054i | −0.423317 | − | 0.423317i | 0.463027 | − | 0.886344i | \(-0.346763\pi\) |
−0.886344 | + | 0.463027i | \(0.846763\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −2.76202 | −0.243183 | ||||||||
\(130\) | −6.05256 | − | 4.66582i | −0.530845 | − | 0.409219i | ||||
\(131\) | 18.2091i | 1.59094i | 0.605996 | + | 0.795468i | \(0.292775\pi\) | ||||
−0.605996 | + | 0.795468i | \(0.707225\pi\) | |||||||
\(132\) | −3.87940 | + | 3.87940i | −0.337658 | + | 0.337658i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 9.95313i | 0.859819i | ||||||||
\(135\) | 0.286912 | + | 2.21758i | 0.0246934 | + | 0.190859i | ||||
\(136\) | − | 2.11825i | − | 0.181638i | ||||||
\(137\) | 1.54481 | + | 1.54481i | 0.131982 | + | 0.131982i | 0.770012 | − | 0.638030i | \(-0.220250\pi\) |
−0.638030 | + | 0.770012i | \(0.720250\pi\) | |||||||
\(138\) | −1.24054 | − | 1.24054i | −0.105602 | − | 0.105602i | ||||
\(139\) | −18.1446 | −1.53900 | −0.769501 | − | 0.638645i | \(-0.779495\pi\) | ||||
−0.769501 | + | 0.638645i | \(0.779495\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.52518 | 0.296873 | ||||||||
\(142\) | −8.46519 | − | 8.46519i | −0.710383 | − | 0.710383i | ||||
\(143\) | −13.2586 | − | 13.2586i | −1.10874 | − | 1.10874i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 1.21241 | + | 0.934623i | 0.100685 | + | 0.0776163i | ||||
\(146\) | − | 4.87079i | − | 0.403109i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.92974 | + | 6.92974i | −0.569621 | + | 0.569621i | ||||
\(149\) | − | 0.193656i | − | 0.0158649i | −0.999969 | − | 0.00793245i | \(-0.997475\pi\) | ||
0.999969 | − | 0.00793245i | \(-0.00252500\pi\) | |||||||
\(150\) | 4.83536 | − | 1.27250i | 0.394806 | − | 0.103899i | ||||
\(151\) | −21.3227 | −1.73522 | −0.867610 | − | 0.497245i | \(-0.834345\pi\) | ||||
−0.867610 | + | 0.497245i | \(0.834345\pi\) | |||||||
\(152\) | −4.94687 | + | 4.94687i | −0.401244 | + | 0.401244i | ||||
\(153\) | −1.49783 | − | 1.49783i | −0.121092 | − | 0.121092i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.87553 | − | 7.61288i | −0.793222 | − | 0.611481i | ||||
\(156\) | 3.41770 | 0.273635 | ||||||||
\(157\) | −2.60217 | + | 2.60217i | −0.207676 | + | 0.207676i | −0.803279 | − | 0.595603i | \(-0.796913\pi\) |
0.595603 | + | 0.803279i | \(0.296913\pi\) | |||||||
\(158\) | −5.89081 | + | 5.89081i | −0.468648 | + | 0.468648i | ||||
\(159\) | −9.40242 | −0.745660 | ||||||||
\(160\) | −2.21758 | + | 0.286912i | −0.175315 | + | 0.0226824i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.707107 | − | 0.707107i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | −9.95676 | + | 9.95676i | −0.779874 | + | 0.779874i | −0.979809 | − | 0.199935i | \(-0.935927\pi\) |
0.199935 | + | 0.979809i | \(0.435927\pi\) | |||||||
\(164\) | 2.50597 | 0.195683 | ||||||||
\(165\) | 12.1663 | − | 1.57408i | 0.947148 | − | 0.122542i | ||||
\(166\) | − | 5.73154i | − | 0.444854i | ||||||
\(167\) | 6.07259 | − | 6.07259i | 0.469911 | − | 0.469911i | −0.431974 | − | 0.901886i | \(-0.642183\pi\) |
0.901886 | + | 0.431974i | \(0.142183\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.31933i | − | 0.101487i | ||||||
\(170\) | −2.89181 | + | 3.75130i | −0.221792 | + | 0.287711i | ||||
\(171\) | 6.99593i | 0.534992i | ||||||||
\(172\) | −1.95305 | − | 1.95305i | −0.148918 | − | 0.148918i | ||||
\(173\) | −2.86311 | − | 2.86311i | −0.217678 | − | 0.217678i | 0.589841 | − | 0.807519i | \(-0.299190\pi\) |
−0.807519 | + | 0.589841i | \(0.799190\pi\) | |||||||
\(174\) | −0.684610 | −0.0519001 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.48630 | −0.413545 | ||||||||
\(177\) | 7.18441 | + | 7.18441i | 0.540014 | + | 0.540014i | ||||
\(178\) | 5.07954 | + | 5.07954i | 0.380728 | + | 0.380728i | ||||
\(179\) | − | 3.66534i | − | 0.273960i | −0.990574 | − | 0.136980i | \(-0.956260\pi\) | ||
0.990574 | − | 0.136980i | \(-0.0437396\pi\) | |||||||
\(180\) | −1.36519 | + | 1.77095i | −0.101755 | + | 0.131999i | ||||
\(181\) | 2.39985i | 0.178379i | 0.996015 | + | 0.0891896i | \(0.0284277\pi\) | ||||
−0.996015 | + | 0.0891896i | \(0.971572\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.828489 | + | 0.828489i | −0.0612437 | + | 0.0612437i | ||||
\(184\) | − | 1.75439i | − | 0.129335i | ||||||
\(185\) | 21.7326 | − | 2.81177i | 1.59781 | − | 0.206726i | ||||
\(186\) | 5.57642 | 0.408883 | ||||||||
\(187\) | −8.21752 | + | 8.21752i | −0.600925 | + | 0.600925i | ||||
\(188\) | 2.49268 | + | 2.49268i | 0.181797 | + | 0.181797i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 15.5141 | − | 2.00721i | 1.12551 | − | 0.145619i | ||||
\(191\) | 8.07532 | 0.584310 | 0.292155 | − | 0.956371i | \(-0.405628\pi\) | ||||
0.292155 | + | 0.956371i | \(0.405628\pi\) | |||||||
\(192\) | 0.707107 | − | 0.707107i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | −1.21801 | + | 1.21801i | −0.0876740 | + | 0.0876740i | −0.749584 | − | 0.661910i | \(-0.769746\pi\) |
0.661910 | + | 0.749584i | \(0.269746\pi\) | |||||||
\(194\) | −18.5562 | −1.33226 | ||||||||
\(195\) | −6.05256 | − | 4.66582i | −0.433433 | − | 0.334126i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.01174 | + | 6.01174i | 0.428319 | + | 0.428319i | 0.888055 | − | 0.459737i | \(-0.152056\pi\) |
−0.459737 | + | 0.888055i | \(0.652056\pi\) | |||||||
\(198\) | −3.87940 | + | 3.87940i | −0.275697 | + | 0.275697i | ||||
\(199\) | −11.0179 | −0.781041 | −0.390520 | − | 0.920594i | \(-0.627705\pi\) | ||||
−0.390520 | + | 0.920594i | \(0.627705\pi\) | |||||||
\(200\) | 4.31891 | + | 2.51932i | 0.305393 | + | 0.178143i | ||||
\(201\) | 9.95313i | 0.702040i | ||||||||
\(202\) | 5.84612 | − | 5.84612i | 0.411332 | − | 0.411332i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 2.11825i | − | 0.148307i | ||||||
\(205\) | −4.43793 | − | 3.42113i | −0.309959 | − | 0.238942i | ||||
\(206\) | − | 9.30620i | − | 0.648394i | ||||||
\(207\) | −1.24054 | − | 1.24054i | −0.0862235 | − | 0.0862235i | ||||
\(208\) | 2.41668 | + | 2.41668i | 0.167566 | + | 0.167566i | ||||
\(209\) | 38.3818 | 2.65492 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3323 | 0.711302 | 0.355651 | − | 0.934619i | \(-0.384259\pi\) | ||||
0.355651 | + | 0.934619i | \(0.384259\pi\) | |||||||
\(212\) | −6.64852 | − | 6.64852i | −0.456622 | − | 0.456622i | ||||
\(213\) | −8.46519 | − | 8.46519i | −0.580025 | − | 0.580025i | ||||
\(214\) | − | 12.2677i | − | 0.838600i | ||||||
\(215\) | 0.792457 | + | 6.12502i | 0.0540451 | + | 0.417723i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.238027 | + | 0.238027i | −0.0161213 | + | 0.0161213i | ||||
\(219\) | − | 4.87079i | − | 0.329137i | ||||||
\(220\) | 9.71594 | + | 7.48985i | 0.655049 | + | 0.504966i | ||||
\(221\) | 7.23953 | 0.486983 | ||||||||
\(222\) | −6.92974 | + | 6.92974i | −0.465094 | + | 0.465094i | ||||
\(223\) | 3.41183 | + | 3.41183i | 0.228473 | + | 0.228473i | 0.812054 | − | 0.583582i | \(-0.198349\pi\) |
−0.583582 | + | 0.812054i | \(0.698349\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.83536 | − | 1.27250i | 0.322358 | − | 0.0848334i | ||||
\(226\) | 14.4102 | 0.958555 | ||||||||
\(227\) | −12.7942 | + | 12.7942i | −0.849182 | + | 0.849182i | −0.990031 | − | 0.140849i | \(-0.955017\pi\) |
0.140849 | + | 0.990031i | \(0.455017\pi\) | |||||||
\(228\) | −4.94687 | + | 4.94687i | −0.327615 | + | 0.327615i | ||||
\(229\) | −9.64749 | −0.637524 | −0.318762 | − | 0.947835i | \(-0.603267\pi\) | ||||
−0.318762 | + | 0.947835i | \(0.603267\pi\) | |||||||
\(230\) | −2.39508 | + | 3.10693i | −0.157927 | + | 0.204865i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.484092 | − | 0.484092i | −0.0317822 | − | 0.0317822i | ||||
\(233\) | 10.2342 | − | 10.2342i | 0.670463 | − | 0.670463i | −0.287360 | − | 0.957823i | \(-0.592777\pi\) |
0.957823 | + | 0.287360i | \(0.0927775\pi\) | |||||||
\(234\) | 3.41770 | 0.223422 | ||||||||
\(235\) | −1.01141 | − | 7.81738i | −0.0659774 | − | 0.509949i | ||||
\(236\) | 10.1603i | 0.661379i | ||||||||
\(237\) | −5.89081 | + | 5.89081i | −0.382649 | + | 0.382649i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 29.9736i | − | 1.93883i | −0.245427 | − | 0.969415i | \(-0.578928\pi\) | ||
0.245427 | − | 0.969415i | \(-0.421072\pi\) | |||||||
\(240\) | −2.21758 | + | 0.286912i | −0.143144 | + | 0.0185201i | ||||
\(241\) | − | 16.6201i | − | 1.07059i | −0.844664 | − | 0.535296i | \(-0.820200\pi\) | ||
0.844664 | − | 0.535296i | \(-0.179800\pi\) | |||||||
\(242\) | 13.5054 | + | 13.5054i | 0.868158 | + | 0.868158i | ||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | −1.17166 | −0.0750079 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.50597 | 0.159775 | ||||||||
\(247\) | −16.9069 | − | 16.9069i | −1.07576 | − | 1.07576i | ||||
\(248\) | 3.94312 | + | 3.94312i | 0.250388 | + | 0.250388i | ||||
\(249\) | − | 5.73154i | − | 0.363222i | ||||||
\(250\) | −4.20920 | − | 10.3577i | −0.266213 | − | 0.655081i | ||||
\(251\) | − | 10.7660i | − | 0.679546i | −0.940508 | − | 0.339773i | \(-0.889650\pi\) | ||
0.940508 | − | 0.339773i | \(-0.110350\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.80597 | + | 6.80597i | −0.427888 | + | 0.427888i | ||||
\(254\) | − | 6.74657i | − | 0.423317i | ||||||
\(255\) | −2.89181 | + | 3.75130i | −0.181092 | + | 0.234915i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.6366 | − | 10.6366i | 0.663495 | − | 0.663495i | −0.292707 | − | 0.956202i | \(-0.594556\pi\) |
0.956202 | + | 0.292707i | \(0.0945560\pi\) | |||||||
\(258\) | −1.95305 | − | 1.95305i | −0.121591 | − | 0.121591i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.980578 | − | 7.57904i | −0.0608128 | − | 0.470032i | ||||
\(261\) | −0.684610 | −0.0423763 | ||||||||
\(262\) | −12.8758 | + | 12.8758i | −0.795468 | + | 0.795468i | ||||
\(263\) | 15.9321 | − | 15.9321i | 0.982418 | − | 0.982418i | −0.0174300 | − | 0.999848i | \(-0.505548\pi\) |
0.999848 | + | 0.0174300i | \(0.00554843\pi\) | |||||||
\(264\) | −5.48630 | −0.337658 | ||||||||
\(265\) | 2.69766 | + | 20.8507i | 0.165716 | + | 1.28085i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.07954 | + | 5.07954i | 0.310863 | + | 0.310863i | ||||
\(268\) | −7.03792 | + | 7.03792i | −0.429910 | + | 0.429910i | ||||
\(269\) | −11.0424 | −0.673270 | −0.336635 | − | 0.941635i | \(-0.609289\pi\) | ||||
−0.336635 | + | 0.941635i | \(0.609289\pi\) | |||||||
\(270\) | −1.36519 | + | 1.77095i | −0.0830829 | + | 0.107776i | ||||
\(271\) | 5.01640i | 0.304724i | 0.988325 | + | 0.152362i | \(0.0486880\pi\) | ||||
−0.988325 | + | 0.152362i | \(0.951312\pi\) | |||||||
\(272\) | 1.49783 | − | 1.49783i | 0.0908190 | − | 0.0908190i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.18468i | 0.131982i | ||||||||
\(275\) | −6.98132 | − | 26.5283i | −0.420990 | − | 1.59971i | ||||
\(276\) | − | 1.75439i | − | 0.105602i | ||||||
\(277\) | 4.47957 | + | 4.47957i | 0.269151 | + | 0.269151i | 0.828758 | − | 0.559607i | \(-0.189048\pi\) |
−0.559607 | + | 0.828758i | \(0.689048\pi\) | |||||||
\(278\) | −12.8302 | − | 12.8302i | −0.769501 | − | 0.769501i | ||||
\(279\) | 5.57642 | 0.333851 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.4723 | −1.75817 | −0.879085 | − | 0.476665i | \(-0.841846\pi\) | ||||
−0.879085 | + | 0.476665i | \(0.841846\pi\) | |||||||
\(282\) | 2.49268 | + | 2.49268i | 0.148437 | + | 0.148437i | ||||
\(283\) | 0.0691733 | + | 0.0691733i | 0.00411193 | + | 0.00411193i | 0.709160 | − | 0.705048i | \(-0.249074\pi\) |
−0.705048 | + | 0.709160i | \(0.749074\pi\) | |||||||
\(284\) | − | 11.9716i | − | 0.710383i | ||||||
\(285\) | 15.5141 | − | 2.00721i | 0.918974 | − | 0.118897i | ||||
\(286\) | − | 18.7505i | − | 1.10874i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.707107 | − | 0.707107i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | 12.5130i | 0.736061i | ||||||||
\(290\) | 0.196422 | + | 1.51818i | 0.0115343 | + | 0.0891506i | ||||
\(291\) | −18.5562 | −1.08778 | ||||||||
\(292\) | 3.44417 | − | 3.44417i | 0.201555 | − | 0.201555i | ||||
\(293\) | −14.0076 | − | 14.0076i | −0.818330 | − | 0.818330i | 0.167536 | − | 0.985866i | \(-0.446419\pi\) |
−0.985866 | + | 0.167536i | \(0.946419\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.8708 | − | 17.9933i | 0.807587 | − | 1.04761i | ||||
\(296\) | −9.80013 | −0.569621 | ||||||||
\(297\) | −3.87940 | + | 3.87940i | −0.225106 | + | 0.225106i | ||||
\(298\) | 0.136935 | − | 0.136935i | 0.00793245 | − | 0.00793245i | ||||
\(299\) | 5.99597 | 0.346756 | ||||||||
\(300\) | 4.31891 | + | 2.51932i | 0.249353 | + | 0.145453i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −15.0775 | − | 15.0775i | −0.867610 | − | 0.867610i | ||||
\(303\) | 5.84612 | − | 5.84612i | 0.335851 | − | 0.335851i | ||||
\(304\) | −6.99593 | −0.401244 | ||||||||
\(305\) | 2.07495 | + | 1.59954i | 0.118811 | + | 0.0915895i | ||||
\(306\) | − | 2.11825i | − | 0.121092i | ||||||
\(307\) | −3.05320 | + | 3.05320i | −0.174255 | + | 0.174255i | −0.788846 | − | 0.614591i | \(-0.789321\pi\) |
0.614591 | + | 0.788846i | \(0.289321\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 9.30620i | − | 0.529411i | ||||||
\(310\) | −1.59994 | − | 12.3662i | −0.0908704 | − | 0.702351i | ||||
\(311\) | 8.44532i | 0.478890i | 0.970910 | + | 0.239445i | \(0.0769655\pi\) | ||||
−0.970910 | + | 0.239445i | \(0.923035\pi\) | |||||||
\(312\) | 2.41668 | + | 2.41668i | 0.136817 | + | 0.136817i | ||||
\(313\) | −13.7247 | − | 13.7247i | −0.775764 | − | 0.775764i | 0.203343 | − | 0.979107i | \(-0.434819\pi\) |
−0.979107 | + | 0.203343i | \(0.934819\pi\) | |||||||
\(314\) | −3.68003 | −0.207676 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.33087 | −0.468648 | ||||||||
\(317\) | −10.9957 | − | 10.9957i | −0.617581 | − | 0.617581i | 0.327329 | − | 0.944910i | \(-0.393851\pi\) |
−0.944910 | + | 0.327329i | \(0.893851\pi\) | |||||||
\(318\) | −6.64852 | − | 6.64852i | −0.372830 | − | 0.372830i | ||||
\(319\) | 3.75597i | 0.210294i | ||||||||
\(320\) | −1.77095 | − | 1.36519i | −0.0989989 | − | 0.0763166i | ||||
\(321\) | − | 12.2677i | − | 0.684714i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.4787 | + | 10.4787i | −0.583050 | + | 0.583050i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | −8.61029 | + | 14.7607i | −0.477613 | + | 0.818779i | ||||
\(326\) | −14.0810 | −0.779874 | ||||||||
\(327\) | −0.238027 | + | 0.238027i | −0.0131629 | + | 0.0131629i | ||||
\(328\) | 1.77199 | + | 1.77199i | 0.0978416 | + | 0.0978416i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 9.71594 | + | 7.48985i | 0.534845 | + | 0.412303i | ||||
\(331\) | 16.1859 | 0.889659 | 0.444830 | − | 0.895615i | \(-0.353264\pi\) | ||||
0.444830 | + | 0.895615i | \(0.353264\pi\) | |||||||
\(332\) | 4.05281 | − | 4.05281i | 0.222427 | − | 0.222427i | ||||
\(333\) | −6.92974 | + | 6.92974i | −0.379747 | + | 0.379747i | ||||
\(334\) | 8.58794 | 0.469911 | ||||||||
\(335\) | 22.0719 | − | 2.85567i | 1.20592 | − | 0.156022i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.2055 | + | 19.2055i | 1.04619 | + | 1.04619i | 0.998880 | + | 0.0473073i | \(0.0150640\pi\) |
0.0473073 | + | 0.998880i | \(0.484936\pi\) | |||||||
\(338\) | 0.932908 | − | 0.932908i | 0.0507435 | − | 0.0507435i | ||||
\(339\) | 14.4102 | 0.782657 | ||||||||
\(340\) | −4.69739 | + | 0.607749i | −0.254752 | + | 0.0329598i | ||||
\(341\) | − | 30.5939i | − | 1.65675i | ||||||
\(342\) | −4.94687 | + | 4.94687i | −0.267496 | + | 0.267496i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 2.76202i | − | 0.148918i | ||||||
\(345\) | −2.39508 | + | 3.10693i | −0.128947 | + | 0.167271i | ||||
\(346\) | − | 4.04905i | − | 0.217678i | ||||||
\(347\) | 7.25896 | + | 7.25896i | 0.389681 | + | 0.389681i | 0.874574 | − | 0.484892i | \(-0.161141\pi\) |
−0.484892 | + | 0.874574i | \(0.661141\pi\) | |||||||
\(348\) | −0.484092 | − | 0.484092i | −0.0259501 | − | 0.0259501i | ||||
\(349\) | 6.61441 | 0.354061 | 0.177031 | − | 0.984205i | \(-0.443351\pi\) | ||||
0.177031 | + | 0.984205i | \(0.443351\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.41770 | 0.182423 | ||||||||
\(352\) | −3.87940 | − | 3.87940i | −0.206773 | − | 0.206773i | ||||
\(353\) | −9.63411 | − | 9.63411i | −0.512772 | − | 0.512772i | 0.402603 | − | 0.915375i | \(-0.368106\pi\) |
−0.915375 | + | 0.402603i | \(0.868106\pi\) | |||||||
\(354\) | 10.1603i | 0.540014i | ||||||||
\(355\) | −16.3435 | + | 21.2010i | −0.867423 | + | 1.12523i | ||||
\(356\) | 7.18356i | 0.380728i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.59178 | − | 2.59178i | 0.136980 | − | 0.136980i | ||||
\(359\) | − | 17.2964i | − | 0.912871i | −0.889757 | − | 0.456435i | \(-0.849126\pi\) | ||
0.889757 | − | 0.456435i | \(-0.150874\pi\) | |||||||
\(360\) | −2.21758 | + | 0.286912i | −0.116877 | + | 0.0151216i | ||||
\(361\) | 29.9431 | 1.57595 | ||||||||
\(362\) | −1.69695 | + | 1.69695i | −0.0891896 | + | 0.0891896i | ||||
\(363\) | 13.5054 | + | 13.5054i | 0.708848 | + | 0.708848i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.8014 | + | 1.39749i | −0.565370 | + | 0.0731477i | ||||
\(366\) | −1.17166 | −0.0612437 | ||||||||
\(367\) | −18.3007 | + | 18.3007i | −0.955288 | + | 0.955288i | −0.999042 | − | 0.0437539i | \(-0.986068\pi\) |
0.0437539 | + | 0.999042i | \(0.486068\pi\) | |||||||
\(368\) | 1.24054 | − | 1.24054i | 0.0646676 | − | 0.0646676i | ||||
\(369\) | 2.50597 | 0.130455 | ||||||||
\(370\) | 17.3555 | + | 13.3791i | 0.902270 | + | 0.695544i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.94312 | + | 3.94312i | 0.204441 | + | 0.204441i | ||||
\(373\) | 6.48161 | − | 6.48161i | 0.335605 | − | 0.335605i | −0.519105 | − | 0.854710i | \(-0.673735\pi\) |
0.854710 | + | 0.519105i | \(0.173735\pi\) | |||||||
\(374\) | −11.6213 | −0.600925 | ||||||||
\(375\) | −4.20920 | − | 10.3577i | −0.217362 | − | 0.534871i | ||||
\(376\) | 3.52518i | 0.181797i | ||||||||
\(377\) | 1.65448 | − | 1.65448i | 0.0852101 | − | 0.0852101i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 18.6871i | − | 0.959891i | −0.877298 | − | 0.479946i | \(-0.840656\pi\) | ||
0.877298 | − | 0.479946i | \(-0.159344\pi\) | |||||||
\(380\) | 12.3894 | + | 9.55079i | 0.635564 | + | 0.489945i | ||||
\(381\) | − | 6.74657i | − | 0.345637i | ||||||
\(382\) | 5.71012 | + | 5.71012i | 0.292155 | + | 0.292155i | ||||
\(383\) | −14.0300 | − | 14.0300i | −0.716900 | − | 0.716900i | 0.251069 | − | 0.967969i | \(-0.419218\pi\) |
−0.967969 | + | 0.251069i | \(0.919218\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.72252 | −0.0876740 | ||||||||
\(387\) | −1.95305 | − | 1.95305i | −0.0992789 | − | 0.0992789i | ||||
\(388\) | −13.1212 | − | 13.1212i | −0.666128 | − | 0.666128i | ||||
\(389\) | 5.12717i | 0.259958i | 0.991517 | + | 0.129979i | \(0.0414910\pi\) | ||||
−0.991517 | + | 0.129979i | \(0.958509\pi\) | |||||||
\(390\) | −0.980578 | − | 7.57904i | −0.0496535 | − | 0.383779i | ||||
\(391\) | − | 3.71623i | − | 0.187938i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.8758 | + | 12.8758i | −0.649497 | + | 0.649497i | ||||
\(394\) | 8.50188i | 0.428319i | ||||||||
\(395\) | 14.7535 | + | 11.3732i | 0.742330 | + | 0.572249i | ||||
\(396\) | −5.48630 | −0.275697 | ||||||||
\(397\) | −18.6630 | + | 18.6630i | −0.936668 | + | 0.936668i | −0.998111 | − | 0.0614422i | \(-0.980430\pi\) |
0.0614422 | + | 0.998111i | \(0.480430\pi\) | |||||||
\(398\) | −7.79086 | − | 7.79086i | −0.390520 | − | 0.390520i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.27250 | + | 4.83536i | 0.0636251 | + | 0.241768i | ||||
\(401\) | −17.2294 | −0.860396 | −0.430198 | − | 0.902735i | \(-0.641556\pi\) | ||||
−0.430198 | + | 0.902735i | \(0.641556\pi\) | |||||||
\(402\) | −7.03792 | + | 7.03792i | −0.351020 | + | 0.351020i | ||||
\(403\) | −13.4764 | + | 13.4764i | −0.671307 | + | 0.671307i | ||||
\(404\) | 8.26766 | 0.411332 | ||||||||
\(405\) | −1.36519 | + | 1.77095i | −0.0678369 | + | 0.0879990i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 38.0186 | + | 38.0186i | 1.88451 | + | 1.88451i | ||||
\(408\) | 1.49783 | − | 1.49783i | 0.0741534 | − | 0.0741534i | ||||
\(409\) | 35.7138 | 1.76593 | 0.882967 | − | 0.469436i | \(-0.155543\pi\) | ||||
0.882967 | + | 0.469436i | \(0.155543\pi\) | |||||||
\(410\) | −0.718991 | − | 5.55719i | −0.0355084 | − | 0.274450i | ||||
\(411\) | 2.18468i | 0.107763i | ||||||||
\(412\) | 6.58048 | − | 6.58048i | 0.324197 | − | 0.324197i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 1.75439i | − | 0.0862235i | ||||||
\(415\) | −12.7102 | + | 1.64445i | −0.623918 | + | 0.0807227i | ||||
\(416\) | 3.41770i | 0.167566i | ||||||||
\(417\) | −12.8302 | − | 12.8302i | −0.628295 | − | 0.628295i | ||||
\(418\) | 27.1400 | + | 27.1400i | 1.32746 | + | 1.32746i | ||||
\(419\) | 14.0414 | 0.685966 | 0.342983 | − | 0.939342i | \(-0.388563\pi\) | ||||
0.342983 | + | 0.939342i | \(0.388563\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.4332 | 1.19080 | 0.595401 | − | 0.803429i | \(-0.296993\pi\) | ||||
0.595401 | + | 0.803429i | \(0.296993\pi\) | |||||||
\(422\) | 7.30601 | + | 7.30601i | 0.355651 | + | 0.355651i | ||||
\(423\) | 2.49268 | + | 2.49268i | 0.121198 | + | 0.121198i | ||||
\(424\) | − | 9.40242i | − | 0.456622i | ||||||
\(425\) | 9.14852 | + | 5.33655i | 0.443768 | + | 0.258861i | ||||
\(426\) | − | 11.9716i | − | 0.580025i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.67454 | − | 8.67454i | 0.419300 | − | 0.419300i | ||||
\(429\) | − | 18.7505i | − | 0.905284i | ||||||
\(430\) | −3.77069 | + | 4.89140i | −0.181839 | + | 0.235884i | ||||
\(431\) | −38.7771 | −1.86783 | −0.933914 | − | 0.357498i | \(-0.883630\pi\) | ||||
−0.933914 | + | 0.357498i | \(0.883630\pi\) | |||||||
\(432\) | 0.707107 | − | 0.707107i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | −7.85700 | − | 7.85700i | −0.377583 | − | 0.377583i | 0.492646 | − | 0.870230i | \(-0.336030\pi\) |
−0.870230 | + | 0.492646i | \(0.836030\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.196422 | + | 1.51818i | 0.00941774 | + | 0.0727911i | ||||
\(436\) | −0.336622 | −0.0161213 | ||||||||
\(437\) | −8.67874 | + | 8.67874i | −0.415160 | + | 0.415160i | ||||
\(438\) | 3.44417 | − | 3.44417i | 0.164569 | − | 0.164569i | ||||
\(439\) | −21.1279 | −1.00838 | −0.504190 | − | 0.863593i | \(-0.668209\pi\) | ||||
−0.504190 | + | 0.863593i | \(0.668209\pi\) | |||||||
\(440\) | 1.57408 | + | 12.1663i | 0.0750415 | + | 0.580007i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.11912 | + | 5.11912i | 0.243492 | + | 0.243492i | ||||
\(443\) | 4.74580 | − | 4.74580i | 0.225480 | − | 0.225480i | −0.585321 | − | 0.810801i | \(-0.699032\pi\) |
0.810801 | + | 0.585321i | \(0.199032\pi\) | |||||||
\(444\) | −9.80013 | −0.465094 | ||||||||
\(445\) | 9.80694 | − | 12.7217i | 0.464894 | − | 0.603066i | ||||
\(446\) | 4.82505i | 0.228473i | ||||||||
\(447\) | 0.136935 | − | 0.136935i | 0.00647682 | − | 0.00647682i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.28979i | 0.391219i | 0.980682 | + | 0.195610i | \(0.0626685\pi\) | ||||
−0.980682 | + | 0.195610i | \(0.937331\pi\) | |||||||
\(450\) | 4.31891 | + | 2.51932i | 0.203596 | + | 0.118762i | ||||
\(451\) | − | 13.7485i | − | 0.647391i | ||||||
\(452\) | 10.1896 | + | 10.1896i | 0.479277 | + | 0.479277i | ||||
\(453\) | −15.0775 | − | 15.0775i | −0.708401 | − | 0.708401i | ||||
\(454\) | −18.0938 | −0.849182 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.99593 | −0.327615 | ||||||||
\(457\) | 15.6143 | + | 15.6143i | 0.730407 | + | 0.730407i | 0.970700 | − | 0.240293i | \(-0.0772436\pi\) |
−0.240293 | + | 0.970700i | \(0.577244\pi\) | |||||||
\(458\) | −6.82181 | − | 6.82181i | −0.318762 | − | 0.318762i | ||||
\(459\) | − | 2.11825i | − | 0.0988712i | ||||||
\(460\) | −3.89051 | + | 0.503355i | −0.181396 | + | 0.0234690i | ||||
\(461\) | 19.0130i | 0.885524i | 0.896639 | + | 0.442762i | \(0.146001\pi\) | ||||
−0.896639 | + | 0.442762i | \(0.853999\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.6091 | + | 16.6091i | −0.771891 | + | 0.771891i | −0.978437 | − | 0.206546i | \(-0.933778\pi\) |
0.206546 | + | 0.978437i | \(0.433778\pi\) | |||||||
\(464\) | − | 0.684610i | − | 0.0317822i | ||||||
\(465\) | −1.59994 | − | 12.3662i | −0.0741954 | − | 0.573468i | ||||
\(466\) | 14.4733 | 0.670463 | ||||||||
\(467\) | −11.3062 | + | 11.3062i | −0.523190 | + | 0.523190i | −0.918533 | − | 0.395343i | \(-0.870626\pi\) |
0.395343 | + | 0.918533i | \(0.370626\pi\) | |||||||
\(468\) | 2.41668 | + | 2.41668i | 0.111711 | + | 0.111711i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.81254 | − | 6.24290i | 0.221986 | − | 0.287963i | ||||
\(471\) | −3.68003 | −0.169567 | ||||||||
\(472\) | −7.18441 | + | 7.18441i | −0.330689 | + | 0.330689i | ||||
\(473\) | −10.7150 | + | 10.7150i | −0.492676 | + | 0.492676i | ||||
\(474\) | −8.33087 | −0.382649 | ||||||||
\(475\) | −8.90234 | − | 33.8279i | −0.408467 | − | 1.55213i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.64852 | − | 6.64852i | −0.304415 | − | 0.304415i | ||||
\(478\) | 21.1945 | − | 21.1945i | 0.969415 | − | 0.969415i | ||||
\(479\) | −9.01051 | −0.411701 | −0.205850 | − | 0.978583i | \(-0.565996\pi\) | ||||
−0.205850 | + | 0.978583i | \(0.565996\pi\) | |||||||
\(480\) | −1.77095 | − | 1.36519i | −0.0808323 | − | 0.0623122i | ||||
\(481\) | − | 33.4939i | − | 1.52719i | ||||||
\(482\) | 11.7522 | − | 11.7522i | 0.535296 | − | 0.535296i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.0995i | 0.868158i | ||||||||
\(485\) | 5.32399 | + | 41.1499i | 0.241750 | + | 1.86852i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 6.60446 | + | 6.60446i | 0.299277 | + | 0.299277i | 0.840731 | − | 0.541454i | \(-0.182126\pi\) |
−0.541454 | + | 0.840731i | \(0.682126\pi\) | |||||||
\(488\) | −0.828489 | − | 0.828489i | −0.0375039 | − | 0.0375039i | ||||
\(489\) | −14.0810 | −0.636764 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.08535 | 0.0941107 | 0.0470554 | − | 0.998892i | \(-0.485016\pi\) | ||||
0.0470554 | + | 0.998892i | \(0.485016\pi\) | |||||||
\(492\) | 1.77199 | + | 1.77199i | 0.0798873 | + | 0.0798873i | ||||
\(493\) | −1.02543 | − | 1.02543i | −0.0461829 | − | 0.0461829i | ||||
\(494\) | − | 23.9100i | − | 1.07576i | ||||||
\(495\) | 9.71594 | + | 7.48985i | 0.436699 | + | 0.336644i | ||||
\(496\) | 5.57642i | 0.250388i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.05281 | − | 4.05281i | 0.181611 | − | 0.181611i | ||||
\(499\) | − | 13.4246i | − | 0.600966i | −0.953787 | − | 0.300483i | \(-0.902852\pi\) | ||
0.953787 | − | 0.300483i | \(-0.0971479\pi\) | |||||||
\(500\) | 4.34767 | − | 10.3004i | 0.194434 | − | 0.460647i | ||||
\(501\) | 8.58794 | 0.383681 | ||||||||
\(502\) | 7.61273 | − | 7.61273i | 0.339773 | − | 0.339773i | ||||
\(503\) | −7.19669 | − | 7.19669i | −0.320885 | − | 0.320885i | 0.528222 | − | 0.849106i | \(-0.322859\pi\) |
−0.849106 | + | 0.528222i | \(0.822859\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.6416 | − | 11.2869i | −0.651542 | − | 0.502263i | ||||
\(506\) | −9.62510 | −0.427888 | ||||||||
\(507\) | 0.932908 | − | 0.932908i | 0.0414319 | − | 0.0414319i | ||||
\(508\) | 4.77054 | − | 4.77054i | 0.211659 | − | 0.211659i | ||||
\(509\) | −4.28156 | −0.189777 | −0.0948884 | − | 0.995488i | \(-0.530249\pi\) | ||||
−0.0948884 | + | 0.995488i | \(0.530249\pi\) | |||||||
\(510\) | −4.69739 | + | 0.607749i | −0.208004 | + | 0.0269116i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −4.94687 | + | 4.94687i | −0.218410 | + | 0.218410i | ||||
\(514\) | 15.0425 | 0.663495 | ||||||||
\(515\) | −20.6373 | + | 2.67006i | −0.909388 | + | 0.117657i | ||||
\(516\) | − | 2.76202i | − | 0.121591i | ||||||
\(517\) | 13.6756 | − | 13.6756i | 0.601451 | − | 0.601451i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 4.04905i | − | 0.177733i | ||||||
\(520\) | 4.66582 | − | 6.05256i | 0.204610 | − | 0.265422i | ||||
\(521\) | 14.5754i | 0.638558i | 0.947661 | + | 0.319279i | \(0.103441\pi\) | ||||
−0.947661 | + | 0.319279i | \(0.896559\pi\) | |||||||
\(522\) | −0.484092 | − | 0.484092i | −0.0211881 | − | 0.0211881i | ||||
\(523\) | 26.9324 | + | 26.9324i | 1.17767 | + | 1.17767i | 0.980336 | + | 0.197336i | \(0.0632290\pi\) |
0.197336 | + | 0.980336i | \(0.436771\pi\) | |||||||
\(524\) | −18.2091 | −0.795468 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.5315 | 0.982418 | ||||||||
\(527\) | 8.35250 | + | 8.35250i | 0.363841 | + | 0.363841i | ||||
\(528\) | −3.87940 | − | 3.87940i | −0.168829 | − | 0.168829i | ||||
\(529\) | 19.9221i | 0.866179i | ||||||||
\(530\) | −12.8361 | + | 16.6512i | −0.557565 | + | 0.723281i | ||||
\(531\) | 10.1603i | 0.440919i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.05612 | + | 6.05612i | −0.262319 | + | 0.262319i | ||||
\(534\) | 7.18356i | 0.310863i | ||||||||
\(535\) | −27.2046 | + | 3.51973i | −1.17616 | + | 0.152171i | ||||
\(536\) | −9.95313 | −0.429910 | ||||||||
\(537\) | 2.59178 | − | 2.59178i | 0.111844 | − | 0.111844i | ||||
\(538\) | −7.80819 | − | 7.80819i | −0.336635 | − | 0.336635i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.21758 | + | 0.286912i | −0.0954296 | + | 0.0123467i | ||||
\(541\) | 16.8603 | 0.724882 | 0.362441 | − | 0.932007i | \(-0.381944\pi\) | ||||
0.362441 | + | 0.932007i | \(0.381944\pi\) | |||||||
\(542\) | −3.54713 | + | 3.54713i | −0.152362 | + | 0.152362i | ||||
\(543\) | −1.69695 | + | 1.69695i | −0.0728230 | + | 0.0728230i | ||||
\(544\) | 2.11825 | 0.0908190 | ||||||||
\(545\) | 0.596139 | + | 0.459553i | 0.0255358 | + | 0.0196851i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.04444 | − | 2.04444i | −0.0874141 | − | 0.0874141i | 0.662048 | − | 0.749462i | \(-0.269688\pi\) |
−0.749462 | + | 0.662048i | \(0.769688\pi\) | |||||||
\(548\) | −1.54481 | + | 1.54481i | −0.0659908 | + | 0.0659908i | ||||
\(549\) | −1.17166 | −0.0500052 | ||||||||
\(550\) | 13.8218 | − | 23.6948i | 0.589362 | − | 1.01035i | ||||
\(551\) | 4.78948i | 0.204039i | ||||||||
\(552\) | 1.24054 | − | 1.24054i | 0.0528009 | − | 0.0528009i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.33506i | 0.269151i | ||||||||
\(555\) | 17.3555 | + | 13.3791i | 0.736700 | + | 0.567910i | ||||
\(556\) | − | 18.1446i | − | 0.769501i | ||||||
\(557\) | 2.95885 | + | 2.95885i | 0.125371 | + | 0.125371i | 0.767008 | − | 0.641637i | \(-0.221745\pi\) |
−0.641637 | + | 0.767008i | \(0.721745\pi\) | |||||||
\(558\) | 3.94312 | + | 3.94312i | 0.166926 | + | 0.166926i | ||||
\(559\) | 9.43977 | 0.399260 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.6213 | −0.490653 | ||||||||
\(562\) | −20.8401 | − | 20.8401i | −0.879085 | − | 0.879085i | ||||
\(563\) | −17.7096 | − | 17.7096i | −0.746372 | − | 0.746372i | 0.227424 | − | 0.973796i | \(-0.426970\pi\) |
−0.973796 | + | 0.227424i | \(0.926970\pi\) | |||||||
\(564\) | 3.52518i | 0.148437i | ||||||||
\(565\) | −4.13447 | − | 31.9559i | −0.173938 | − | 1.34440i | ||||
\(566\) | 0.0978259i | 0.00411193i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.46519 | − | 8.46519i | 0.355191 | − | 0.355191i | ||||
\(569\) | − | 2.30741i | − | 0.0967316i | −0.998830 | − | 0.0483658i | \(-0.984599\pi\) | ||
0.998830 | − | 0.0483658i | \(-0.0154013\pi\) | |||||||
\(570\) | 12.3894 | + | 9.55079i | 0.518936 | + | 0.400039i | ||||
\(571\) | 15.8865 | 0.664830 | 0.332415 | − | 0.943133i | \(-0.392137\pi\) | ||||
0.332415 | + | 0.943133i | \(0.392137\pi\) | |||||||
\(572\) | 13.2586 | − | 13.2586i | 0.554371 | − | 0.554371i | ||||
\(573\) | 5.71012 | + | 5.71012i | 0.238544 | + | 0.238544i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.57705 | + | 4.41987i | 0.315985 | + | 0.184321i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 2.82904 | − | 2.82904i | 0.117774 | − | 0.117774i | −0.645763 | − | 0.763538i | \(-0.723461\pi\) |
0.763538 | + | 0.645763i | \(0.223461\pi\) | |||||||
\(578\) | −8.84805 | + | 8.84805i | −0.368030 | + | 0.368030i | ||||
\(579\) | −1.72252 | −0.0715855 | ||||||||
\(580\) | −0.934623 | + | 1.21241i | −0.0388081 | + | 0.0503425i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −13.1212 | − | 13.1212i | −0.543891 | − | 0.543891i | ||||
\(583\) | −36.4757 | + | 36.4757i | −1.51067 | + | 1.51067i | ||||
\(584\) | 4.87079 | 0.201555 | ||||||||
\(585\) | −0.980578 | − | 7.57904i | −0.0405419 | − | 0.313355i | ||||
\(586\) | − | 19.8097i | − | 0.818330i | ||||||
\(587\) | −5.31785 | + | 5.31785i | −0.219491 | + | 0.219491i | −0.808284 | − | 0.588793i | \(-0.799603\pi\) |
0.588793 | + | 0.808284i | \(0.299603\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 39.0122i | − | 1.60747i | ||||||
\(590\) | 22.5313 | − | 2.91511i | 0.927600 | − | 0.120013i | ||||
\(591\) | 8.50188i | 0.349721i | ||||||||
\(592\) | −6.92974 | − | 6.92974i | −0.284811 | − | 0.284811i | ||||
\(593\) | 12.5171 | + | 12.5171i | 0.514014 | + | 0.514014i | 0.915754 | − | 0.401740i | \(-0.131594\pi\) |
−0.401740 | + | 0.915754i | \(0.631594\pi\) | |||||||
\(594\) | −5.48630 | −0.225106 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.193656 | 0.00793245 | ||||||||
\(597\) | −7.79086 | − | 7.79086i | −0.318858 | − | 0.318858i | ||||
\(598\) | 4.23979 | + | 4.23979i | 0.173378 | + | 0.173378i | ||||
\(599\) | 31.2892i | 1.27844i | 0.769024 | + | 0.639220i | \(0.220743\pi\) | ||||
−0.769024 | + | 0.639220i | \(0.779257\pi\) | |||||||
\(600\) | 1.27250 | + | 4.83536i | 0.0519497 | + | 0.197403i | ||||
\(601\) | 47.5637i | 1.94016i | 0.242776 | + | 0.970082i | \(0.421942\pi\) | ||||
−0.242776 | + | 0.970082i | \(0.578058\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.03792 | + | 7.03792i | −0.286606 | + | 0.286606i | ||||
\(604\) | − | 21.3227i | − | 0.867610i | ||||||
\(605\) | 26.0745 | − | 33.8242i | 1.06008 | − | 1.37515i | ||||
\(606\) | 8.26766 | 0.335851 | ||||||||
\(607\) | −17.3556 | + | 17.3556i | −0.704443 | + | 0.704443i | −0.965361 | − | 0.260918i | \(-0.915975\pi\) |
0.260918 | + | 0.965361i | \(0.415975\pi\) | |||||||
\(608\) | −4.94687 | − | 4.94687i | −0.200622 | − | 0.200622i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.336163 | + | 2.59826i | 0.0136108 | + | 0.105200i | ||||
\(611\) | −12.0480 | −0.487410 | ||||||||
\(612\) | 1.49783 | − | 1.49783i | 0.0605460 | − | 0.0605460i | ||||
\(613\) | −19.6837 | + | 19.6837i | −0.795016 | + | 0.795016i | −0.982305 | − | 0.187289i | \(-0.940030\pi\) |
0.187289 | + | 0.982305i | \(0.440030\pi\) | |||||||
\(614\) | −4.31788 | −0.174255 | ||||||||
\(615\) | −0.718991 | − | 5.55719i | −0.0289925 | − | 0.224088i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.4884 | − | 24.4884i | −0.985865 | − | 0.985865i | 0.0140365 | − | 0.999901i | \(-0.495532\pi\) |
−0.999901 | + | 0.0140365i | \(0.995532\pi\) | |||||||
\(618\) | 6.58048 | − | 6.58048i | 0.264706 | − | 0.264706i | ||||
\(619\) | 31.8275 | 1.27925 | 0.639627 | − | 0.768686i | \(-0.279089\pi\) | ||||
0.639627 | + | 0.768686i | \(0.279089\pi\) | |||||||
\(620\) | 7.61288 | − | 9.87553i | 0.305741 | − | 0.396611i | ||||
\(621\) | − | 1.75439i | − | 0.0704012i | ||||||
\(622\) | −5.97174 | + | 5.97174i | −0.239445 | + | 0.239445i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.41770i | 0.136817i | ||||||||
\(625\) | −21.7615 | + | 12.3060i | −0.870459 | + | 0.492241i | ||||
\(626\) | − | 19.4096i | − | 0.775764i | ||||||
\(627\) | 27.1400 | + | 27.1400i | 1.08387 | + | 1.08387i | ||||
\(628\) | −2.60217 | − | 2.60217i | −0.103838 | − | 0.103838i | ||||
\(629\) | −20.7591 | −0.827719 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.9471 | −1.39122 | −0.695610 | − | 0.718419i | \(-0.744866\pi\) | ||||
−0.695610 | + | 0.718419i | \(0.744866\pi\) | |||||||
\(632\) | −5.89081 | − | 5.89081i | −0.234324 | − | 0.234324i | ||||
\(633\) | 7.30601 | + | 7.30601i | 0.290388 | + | 0.290388i | ||||
\(634\) | − | 15.5503i | − | 0.617581i | ||||||
\(635\) | −14.9611 | + | 1.93567i | −0.593713 | + | 0.0768147i | ||||
\(636\) | − | 9.40242i | − | 0.372830i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.65587 | + | 2.65587i | −0.105147 | + | 0.105147i | ||||
\(639\) | − | 11.9716i | − | 0.473589i | ||||||
\(640\) | −0.286912 | − | 2.21758i | −0.0113412 | − | 0.0876577i | ||||
\(641\) | −11.2298 | −0.443549 | −0.221774 | − | 0.975098i | \(-0.571185\pi\) | ||||
−0.221774 | + | 0.975098i | \(0.571185\pi\) | |||||||
\(642\) | 8.67454 | − | 8.67454i | 0.342357 | − | 0.342357i | ||||
\(643\) | 9.89036 | + | 9.89036i | 0.390038 | + | 0.390038i | 0.874701 | − | 0.484663i | \(-0.161058\pi\) |
−0.484663 | + | 0.874701i | \(0.661058\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.77069 | + | 4.89140i | −0.148471 | + | 0.192599i | ||||
\(646\) | −14.8191 | −0.583050 | ||||||||
\(647\) | 11.0962 | − | 11.0962i | 0.436235 | − | 0.436235i | −0.454508 | − | 0.890743i | \(-0.650185\pi\) |
0.890743 | + | 0.454508i | \(0.150185\pi\) | |||||||
\(648\) | 0.707107 | − | 0.707107i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | 55.7424 | 2.18808 | ||||||||
\(650\) | −16.5258 | + | 4.34903i | −0.648196 | + | 0.170583i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.95676 | − | 9.95676i | −0.389937 | − | 0.389937i | ||||
\(653\) | 11.2769 | − | 11.2769i | 0.441297 | − | 0.441297i | −0.451151 | − | 0.892448i | \(-0.648986\pi\) |
0.892448 | + | 0.451151i | \(0.148986\pi\) | |||||||
\(654\) | −0.336622 | −0.0131629 | ||||||||
\(655\) | 32.2473 | + | 24.8589i | 1.26001 | + | 0.971318i | ||||
\(656\) | 2.50597i | 0.0978416i | ||||||||
\(657\) | 3.44417 | − | 3.44417i | 0.134370 | − | 0.134370i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 10.4778i | − | 0.408157i | −0.978955 | − | 0.204078i | \(-0.934580\pi\) | ||
0.978955 | − | 0.204078i | \(-0.0654198\pi\) | |||||||
\(660\) | 1.57408 | + | 12.1663i | 0.0612711 | + | 0.473574i | ||||
\(661\) | 24.2215i | 0.942106i | 0.882105 | + | 0.471053i | \(0.156126\pi\) | ||||
−0.882105 | + | 0.471053i | \(0.843874\pi\) | |||||||
\(662\) | 11.4452 | + | 11.4452i | 0.444830 | + | 0.444830i | ||||
\(663\) | 5.11912 | + | 5.11912i | 0.198810 | + | 0.198810i | ||||
\(664\) | 5.73154 | 0.222427 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.80013 | −0.379747 | ||||||||
\(667\) | −0.849286 | − | 0.849286i | −0.0328845 | − | 0.0328845i | ||||
\(668\) | 6.07259 | + | 6.07259i | 0.234956 | + | 0.234956i | ||||
\(669\) | 4.82505i | 0.186547i | ||||||||
\(670\) | 17.6265 | + | 13.5879i | 0.680969 | + | 0.524948i | ||||
\(671\) | 6.42808i | 0.248153i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.16725 | + | 1.16725i | −0.0449943 | + | 0.0449943i | −0.729246 | − | 0.684252i | \(-0.760129\pi\) |
0.684252 | + | 0.729246i | \(0.260129\pi\) | |||||||
\(674\) | 27.1606i | 1.04619i | ||||||||
\(675\) | 4.31891 | + | 2.51932i | 0.166235 | + | 0.0969688i | ||||
\(676\) | 1.31933 | 0.0507435 | ||||||||
\(677\) | 9.07752 | − | 9.07752i | 0.348877 | − | 0.348877i | −0.510814 | − | 0.859691i | \(-0.670656\pi\) |
0.859691 | + | 0.510814i | \(0.170656\pi\) | |||||||
\(678\) | 10.1896 | + | 10.1896i | 0.391328 | + | 0.391328i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.75130 | − | 2.89181i | −0.143856 | − | 0.110896i | ||||
\(681\) | −18.0938 | −0.693354 | ||||||||
\(682\) | 21.6331 | − | 21.6331i | 0.828376 | − | 0.828376i | ||||
\(683\) | 15.1075 | − | 15.1075i | 0.578073 | − | 0.578073i | −0.356299 | − | 0.934372i | \(-0.615962\pi\) |
0.934372 | + | 0.356299i | \(0.115962\pi\) | |||||||
\(684\) | −6.99593 | −0.267496 | ||||||||
\(685\) | 4.84472 | − | 0.626811i | 0.185107 | − | 0.0239492i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.82181 | − | 6.82181i | −0.260268 | − | 0.260268i | ||||
\(688\) | 1.95305 | − | 1.95305i | 0.0744592 | − | 0.0744592i | ||||
\(689\) | 32.1346 | 1.22423 | ||||||||
\(690\) | −3.89051 | + | 0.503355i | −0.148109 | + | 0.0191624i | ||||
\(691\) | − | 42.7386i | − | 1.62585i | −0.582365 | − | 0.812927i | \(-0.697873\pi\) | ||
0.582365 | − | 0.812927i | \(-0.302127\pi\) | |||||||
\(692\) | 2.86311 | − | 2.86311i | 0.108839 | − | 0.108839i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.2657i | 0.389681i | ||||||||
\(695\) | −24.7708 | + | 32.1331i | −0.939611 | + | 1.21888i | ||||
\(696\) | − | 0.684610i | − | 0.0259501i | ||||||
\(697\) | 3.75350 | + | 3.75350i | 0.142174 | + | 0.142174i | ||||
\(698\) | 4.67709 | + | 4.67709i | 0.177031 | + | 0.177031i | ||||
\(699\) | 14.4733 | 0.547431 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.5959 | 1.68436 | 0.842182 | − | 0.539194i | \(-0.181271\pi\) | ||||
0.842182 | + | 0.539194i | \(0.181271\pi\) | |||||||
\(702\) | 2.41668 | + | 2.41668i | 0.0912116 | + | 0.0912116i | ||||
\(703\) | 48.4800 | + | 48.4800i | 1.82846 | + | 1.82846i | ||||
\(704\) | − | 5.48630i | − | 0.206773i | ||||||
\(705\) | 4.81254 | − | 6.24290i | 0.181251 | − | 0.235121i | ||||
\(706\) | − | 13.6247i | − | 0.512772i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.18441 | + | 7.18441i | −0.270007 | + | 0.270007i | ||||
\(709\) | 41.4249i | 1.55575i | 0.628422 | + | 0.777873i | \(0.283701\pi\) | ||||
−0.628422 | + | 0.777873i | \(0.716299\pi\) | |||||||
\(710\) | −26.5480 | + | 3.43479i | −0.996329 | + | 0.128905i | ||||
\(711\) | −8.33087 | −0.312432 | ||||||||
\(712\) | −5.07954 | + | 5.07954i | −0.190364 | + | 0.190364i | ||||
\(713\) | 6.91777 | + | 6.91777i | 0.259072 | + | 0.259072i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −41.5809 | + | 5.37974i | −1.55504 | + | 0.201191i | ||||
\(716\) | 3.66534 | 0.136980 | ||||||||
\(717\) | 21.1945 | − | 21.1945i | 0.791524 | − | 0.791524i | ||||
\(718\) | 12.2304 | − | 12.2304i | 0.456435 | − | 0.456435i | ||||
\(719\) | 23.5677 | 0.878928 | 0.439464 | − | 0.898260i | \(-0.355168\pi\) | ||||
0.439464 | + | 0.898260i | \(0.355168\pi\) | |||||||
\(720\) | −1.77095 | − | 1.36519i | −0.0659993 | − | 0.0508777i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 21.1730 | + | 21.1730i | 0.787976 | + | 0.787976i | ||||
\(723\) | 11.7522 | − | 11.7522i | 0.437068 | − | 0.437068i | ||||
\(724\) | −2.39985 | −0.0891896 | ||||||||
\(725\) | 3.31034 | − | 0.871167i | 0.122943 | − | 0.0323543i | ||||
\(726\) | 19.0995i | 0.708848i | ||||||||
\(727\) | 3.38556 | − | 3.38556i | 0.125563 | − | 0.125563i | −0.641532 | − | 0.767096i | \(-0.721701\pi\) |
0.767096 | + | 0.641532i | \(0.221701\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −8.62590 | − | 6.64956i | −0.319259 | − | 0.246111i | ||||
\(731\) | − | 5.85065i | − | 0.216394i | ||||||
\(732\) | −0.828489 | − | 0.828489i | −0.0306218 | − | 0.0306218i | ||||
\(733\) | 27.7720 | + | 27.7720i | 1.02578 | + | 1.02578i | 0.999659 | + | 0.0261249i | \(0.00831677\pi\) |
0.0261249 | + | 0.999659i | \(0.491683\pi\) | |||||||
\(734\) | −25.8811 | −0.955288 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.75439 | 0.0646676 | ||||||||
\(737\) | 38.6122 | + | 38.6122i | 1.42230 | + | 1.42230i | ||||
\(738\) | 1.77199 | + | 1.77199i | 0.0652277 | + | 0.0652277i | ||||
\(739\) | − | 44.5958i | − | 1.64048i | −0.572016 | − | 0.820242i | \(-0.693839\pi\) | ||
0.572016 | − | 0.820242i | \(-0.306161\pi\) | |||||||
\(740\) | 2.81177 | + | 21.7326i | 0.103363 | + | 0.798907i | ||||
\(741\) | − | 23.9100i | − | 0.878356i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.7787 | − | 24.7787i | 0.909041 | − | 0.909041i | −0.0871537 | − | 0.996195i | \(-0.527777\pi\) |
0.996195 | + | 0.0871537i | \(0.0277771\pi\) | |||||||
\(744\) | 5.57642i | 0.204441i | ||||||||
\(745\) | −0.342954 | − | 0.264377i | −0.0125649 | − | 0.00968604i | ||||
\(746\) | 9.16638 | 0.335605 | ||||||||
\(747\) | 4.05281 | − | 4.05281i | 0.148285 | − | 0.148285i | ||||
\(748\) | −8.21752 | − | 8.21752i | −0.300462 | − | 0.300462i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4.34767 | − | 10.3004i | 0.158754 | − | 0.376117i | ||||
\(751\) | 5.09462 | 0.185905 | 0.0929526 | − | 0.995671i | \(-0.470369\pi\) | ||||
0.0929526 | + | 0.995671i | \(0.470369\pi\) | |||||||
\(752\) | −2.49268 | + | 2.49268i | −0.0908985 | + | 0.0908985i | ||||
\(753\) | 7.61273 | − | 7.61273i | 0.277423 | − | 0.277423i | ||||
\(754\) | 2.33979 | 0.0852101 | ||||||||
\(755\) | −29.1096 | + | 37.7614i | −1.05941 | + | 1.37428i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.2623 | + | 18.2623i | 0.663754 | + | 0.663754i | 0.956263 | − | 0.292509i | \(-0.0944900\pi\) |
−0.292509 | + | 0.956263i | \(0.594490\pi\) | |||||||
\(758\) | 13.2138 | − | 13.2138i | 0.479946 | − | 0.479946i | ||||
\(759\) | −9.62510 | −0.349369 | ||||||||
\(760\) | 2.00721 | + | 15.5141i | 0.0728093 | + | 0.562755i | ||||
\(761\) | 28.1315i | 1.01976i | 0.860244 | + | 0.509882i | \(0.170311\pi\) | ||||
−0.860244 | + | 0.509882i | \(0.829689\pi\) | |||||||
\(762\) | 4.77054 | − | 4.77054i | 0.172819 | − | 0.172819i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 8.07532i | 0.292155i | ||||||||
\(765\) | −4.69739 | + | 0.607749i | −0.169834 | + | 0.0219732i | ||||
\(766\) | − | 19.8414i | − | 0.716900i | ||||||
\(767\) | −24.5542 | − | 24.5542i | −0.886600 | − | 0.886600i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | −3.03517 | −0.109451 | −0.0547256 | − | 0.998501i | \(-0.517428\pi\) | ||||
−0.0547256 | + | 0.998501i | \(0.517428\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.0425 | 0.541742 | ||||||||
\(772\) | −1.21801 | − | 1.21801i | −0.0438370 | − | 0.0438370i | ||||
\(773\) | 34.3021 | + | 34.3021i | 1.23376 | + | 1.23376i | 0.962508 | + | 0.271253i | \(0.0874379\pi\) |
0.271253 | + | 0.962508i | \(0.412562\pi\) | |||||||
\(774\) | − | 2.76202i | − | 0.0992789i | ||||||
\(775\) | −26.9640 | + | 7.09600i | −0.968575 | + | 0.254896i | ||||
\(776\) | − | 18.5562i | − | 0.666128i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.62546 | + | 3.62546i | −0.129979 | + | 0.129979i | ||||
\(779\) | − | 17.5316i | − | 0.628134i | ||||||
\(780\) | 4.66582 | − | 6.05256i | 0.167063 | − | 0.216716i | ||||
\(781\) | −65.6797 | −2.35020 | ||||||||
\(782\) | 2.62777 | − | 2.62777i | 0.0939688 | − | 0.0939688i | ||||
\(783\) | −0.484092 | − | 0.484092i | −0.0173000 | − | 0.0173000i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.05584 | + | 8.16078i | 0.0376847 | + | 0.291271i | ||||
\(786\) | −18.2091 | −0.649497 | ||||||||
\(787\) | −26.8578 | + | 26.8578i | −0.957376 | + | 0.957376i | −0.999128 | − | 0.0417518i | \(-0.986706\pi\) |
0.0417518 | + | 0.999128i | \(0.486706\pi\) | |||||||
\(788\) | −6.01174 | + | 6.01174i | −0.214159 | + | 0.214159i | ||||
\(789\) | 22.5315 | 0.802141 | ||||||||
\(790\) | 2.39022 | + | 18.4744i | 0.0850403 | + | 0.657290i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.87940 | − | 3.87940i | −0.137848 | − | 0.137848i | ||||
\(793\) | 2.83153 | − | 2.83153i | 0.100550 | − | 0.100550i | ||||
\(794\) | −26.3934 | −0.936668 | ||||||||
\(795\) | −12.8361 | + | 16.6512i | −0.455250 | + | 0.590557i | ||||
\(796\) | − | 11.0179i | − | 0.390520i | ||||||
\(797\) | −34.4058 | + | 34.4058i | −1.21871 | + | 1.21871i | −0.250632 | + | 0.968082i | \(0.580638\pi\) |
−0.968082 | + | 0.250632i | \(0.919362\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.46719i | 0.264170i | ||||||||
\(800\) | −2.51932 | + | 4.31891i | −0.0890715 | + | 0.152697i | ||||
\(801\) | 7.18356i | 0.253819i | ||||||||
\(802\) | −12.1830 | − | 12.1830i | −0.430198 | − | 0.430198i | ||||
\(803\) | −18.8957 | − | 18.8957i | −0.666816 | − | 0.666816i | ||||
\(804\) | −9.95313 | −0.351020 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −19.0585 | −0.671307 | ||||||||
\(807\) | −7.80819 | − | 7.80819i | −0.274861 | − | 0.274861i | ||||
\(808\) | 5.84612 | + | 5.84612i | 0.205666 | + | 0.205666i | ||||
\(809\) | − | 38.8636i | − | 1.36637i | −0.730244 | − | 0.683186i | \(-0.760594\pi\) | ||
0.730244 | − | 0.683186i | \(-0.239406\pi\) | |||||||
\(810\) | −2.21758 | + | 0.286912i | −0.0779180 | + | 0.0100810i | ||||
\(811\) | 15.3545i | 0.539168i | 0.962977 | + | 0.269584i | \(0.0868862\pi\) | ||||
−0.962977 | + | 0.269584i | \(0.913114\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.54713 | + | 3.54713i | −0.124403 | + | 0.124403i | ||||
\(814\) | 53.7665i | 1.88451i | ||||||||
\(815\) | 4.04000 | + | 31.2258i | 0.141515 | + | 1.09379i | ||||
\(816\) | 2.11825 | 0.0741534 | ||||||||
\(817\) | −13.6634 | + | 13.6634i | −0.478021 | + | 0.478021i | ||||
\(818\) | 25.2535 | + | 25.2535i | 0.882967 | + | 0.882967i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.42113 | − | 4.43793i | 0.119471 | − | 0.154979i | ||||
\(821\) | 23.9122 | 0.834542 | 0.417271 | − | 0.908782i | \(-0.362987\pi\) | ||||
0.417271 | + | 0.908782i | \(0.362987\pi\) | |||||||
\(822\) | −1.54481 | + | 1.54481i | −0.0538813 | + | 0.0538813i | ||||
\(823\) | −20.0196 | + | 20.0196i | −0.697840 | + | 0.697840i | −0.963944 | − | 0.266105i | \(-0.914263\pi\) |
0.266105 | + | 0.963944i | \(0.414263\pi\) | |||||||
\(824\) | 9.30620 | 0.324197 | ||||||||
\(825\) | 13.8218 | − | 23.6948i | 0.481212 | − | 0.824949i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.7600 | + | 20.7600i | 0.721898 | + | 0.721898i | 0.968992 | − | 0.247094i | \(-0.0794757\pi\) |
−0.247094 | + | 0.968992i | \(0.579476\pi\) | |||||||
\(828\) | 1.24054 | − | 1.24054i | 0.0431117 | − | 0.0431117i | ||||
\(829\) | 8.28212 | 0.287650 | 0.143825 | − | 0.989603i | \(-0.454060\pi\) | ||||
0.143825 | + | 0.989603i | \(0.454060\pi\) | |||||||
\(830\) | −10.1502 | − | 7.82465i | −0.352320 | − | 0.271598i | ||||
\(831\) | 6.33506i | 0.219761i | ||||||||
\(832\) | −2.41668 | + | 2.41668i | −0.0837832 | + | 0.0837832i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 18.1446i | − | 0.628295i | ||||||
\(835\) | −2.46398 | − | 19.0445i | −0.0852696 | − | 0.659062i | ||||
\(836\) | 38.3818i | 1.32746i | ||||||||
\(837\) | 3.94312 | + | 3.94312i | 0.136294 | + | 0.136294i | ||||
\(838\) | 9.92875 | + | 9.92875i | 0.342983 | + | 0.342983i | ||||
\(839\) | −8.03334 | −0.277342 | −0.138671 | − | 0.990339i | \(-0.544283\pi\) | ||||
−0.138671 | + | 0.990339i | \(0.544283\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.5313 | 0.983838 | ||||||||
\(842\) | 17.2769 | + | 17.2769i | 0.595401 | + | 0.595401i | ||||
\(843\) | −20.8401 | − | 20.8401i | −0.717770 | − | 0.717770i | ||||
\(844\) | 10.3323i | 0.355651i | ||||||||
\(845\) | −2.33647 | − | 1.80114i | −0.0803769 | − | 0.0619611i | ||||
\(846\) | 3.52518i | 0.121198i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.64852 | − | 6.64852i | 0.228311 | − | 0.228311i | ||||
\(849\) | 0.0978259i | 0.00335738i | ||||||||
\(850\) | 2.69547 | + | 10.2425i | 0.0924539 | + | 0.351314i | ||||
\(851\) | −17.1932 | −0.589377 | ||||||||
\(852\) | 8.46519 | − | 8.46519i | 0.290013 | − | 0.290013i | ||||
\(853\) | −23.8654 | − | 23.8654i | −0.817136 | − | 0.817136i | 0.168556 | − | 0.985692i | \(-0.446089\pi\) |
−0.985692 | + | 0.168556i | \(0.946089\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.3894 | + | 9.55079i | 0.423709 | + | 0.326630i | ||||
\(856\) | 12.2677 | 0.419300 | ||||||||
\(857\) | 16.9824 | − | 16.9824i | 0.580107 | − | 0.580107i | −0.354826 | − | 0.934933i | \(-0.615460\pi\) |
0.934933 | + | 0.354826i | \(0.115460\pi\) | |||||||
\(858\) | 13.2586 | − | 13.2586i | 0.452642 | − | 0.452642i | ||||
\(859\) | −6.52841 | −0.222747 | −0.111373 | − | 0.993779i | \(-0.535525\pi\) | ||||
−0.111373 | + | 0.993779i | \(0.535525\pi\) | |||||||
\(860\) | −6.12502 | + | 0.792457i | −0.208862 | + | 0.0270226i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27.4196 | − | 27.4196i | −0.933914 | − | 0.933914i | ||||
\(863\) | −11.7091 | + | 11.7091i | −0.398582 | + | 0.398582i | −0.877733 | − | 0.479151i | \(-0.840945\pi\) |
0.479151 | + | 0.877733i | \(0.340945\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −8.97910 | + | 1.16172i | −0.305299 | + | 0.0394996i | ||||
\(866\) | − | 11.1115i | − | 0.377583i | ||||||
\(867\) | −8.84805 | + | 8.84805i | −0.300496 | + | 0.300496i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45.7056i | 1.55046i | ||||||||
\(870\) | −0.934623 | + | 1.21241i | −0.0316867 | + | 0.0411044i | ||||
\(871\) | − | 34.0168i | − | 1.15262i | ||||||
\(872\) | −0.238027 | − | 0.238027i | −0.00806063 | − | 0.00806063i | ||||
\(873\) | −13.1212 | − | 13.1212i | −0.444086 | − | 0.444086i | ||||
\(874\) | −12.2736 | −0.415160 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.87079 | 0.164569 | ||||||||
\(877\) | 26.1379 | + | 26.1379i | 0.882613 | + | 0.882613i | 0.993800 | − | 0.111186i | \(-0.0354651\pi\) |
−0.111186 | + | 0.993800i | \(0.535465\pi\) | |||||||
\(878\) | −14.9397 | − | 14.9397i | −0.504190 | − | 0.504190i | ||||
\(879\) | − | 19.8097i | − | 0.668164i | ||||||
\(880\) | −7.48985 | + | 9.71594i | −0.252483 | + | 0.327524i | ||||
\(881\) | − | 17.4940i | − | 0.589386i | −0.955592 | − | 0.294693i | \(-0.904783\pi\) | ||
0.955592 | − | 0.294693i | \(-0.0952174\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.0857 | + | 14.0857i | −0.474022 | + | 0.474022i | −0.903214 | − | 0.429191i | \(-0.858799\pi\) |
0.429191 | + | 0.903214i | \(0.358799\pi\) | |||||||
\(884\) | 7.23953i | 0.243492i | ||||||||
\(885\) | 22.5313 | − | 2.91511i | 0.757382 | − | 0.0979902i | ||||
\(886\) | 6.71158 | 0.225480 | ||||||||
\(887\) | 29.0011 | − | 29.0011i | 0.973763 | − | 0.973763i | −0.0259017 | − | 0.999664i | \(-0.508246\pi\) |
0.999664 | + | 0.0259017i | \(0.00824569\pi\) | |||||||
\(888\) | −6.92974 | − | 6.92974i | −0.232547 | − | 0.232547i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 15.9302 | − | 2.06105i | 0.533980 | − | 0.0690865i | ||||
\(891\) | −5.48630 | −0.183798 | ||||||||
\(892\) | −3.41183 | + | 3.41183i | −0.114236 | + | 0.114236i | ||||
\(893\) | 17.4386 | − | 17.4386i | 0.583560 | − | 0.583560i | ||||
\(894\) | 0.193656 | 0.00647682 | ||||||||
\(895\) | −6.49112 | − | 5.00389i | −0.216974 | − | 0.167262i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.23979 | + | 4.23979i | 0.141563 | + | 0.141563i | ||||
\(898\) | −5.86176 | + | 5.86176i | −0.195610 | + | 0.195610i | ||||
\(899\) | 3.81767 | 0.127326 | ||||||||
\(900\) | 1.27250 | + | 4.83536i | 0.0424167 | + | 0.161179i | ||||
\(901\) | − | 19.9166i | − | 0.663519i | ||||||
\(902\) | 9.72165 | − | 9.72165i | 0.323695 | − | 0.323695i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.4102i | 0.479277i | ||||||||
\(905\) | 4.25000 | + | 3.27625i | 0.141275 | + | 0.108906i | ||||
\(906\) | − | 21.3227i | − | 0.708401i | ||||||
\(907\) | 14.1293 | + | 14.1293i | 0.469156 | + | 0.469156i | 0.901641 | − | 0.432485i | \(-0.142363\pi\) |
−0.432485 | + | 0.901641i | \(0.642363\pi\) | |||||||
\(908\) | −12.7942 | − | 12.7942i | −0.424591 | − | 0.424591i | ||||
\(909\) | 8.26766 | 0.274221 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.3131 | −0.706136 | −0.353068 | − | 0.935598i | \(-0.614862\pi\) | ||||
−0.353068 | + | 0.935598i | \(0.614862\pi\) | |||||||
\(912\) | −4.94687 | − | 4.94687i | −0.163807 | − | 0.163807i | ||||
\(913\) | −22.2349 | − | 22.2349i | −0.735869 | − | 0.735869i | ||||
\(914\) | 22.0820i | 0.730407i | ||||||||
\(915\) | 0.336163 | + | 2.59826i | 0.0111132 | + | 0.0858957i | ||||
\(916\) | − | 9.64749i | − | 0.318762i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.49783 | − | 1.49783i | 0.0494356 | − | 0.0494356i | ||||
\(919\) | − | 13.1648i | − | 0.434266i | −0.976142 | − | 0.217133i | \(-0.930330\pi\) | ||
0.976142 | − | 0.217133i | \(-0.0696705\pi\) | |||||||
\(920\) | −3.10693 | − | 2.39508i | −0.102432 | − | 0.0789634i | ||||
\(921\) | −4.31788 | −0.142279 | ||||||||
\(922\) | −13.4442 | + | 13.4442i | −0.442762 | + | 0.442762i | ||||
\(923\) | 28.9315 | + | 28.9315i | 0.952291 | + | 0.952291i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.6897 | − | 42.3259i | 0.811793 | − | 1.39167i | ||||
\(926\) | −23.4888 | −0.771891 | ||||||||
\(927\) | 6.58048 | − | 6.58048i | 0.216131 | − | 0.216131i | ||||
\(928\) | 0.484092 | − | 0.484092i | 0.0158911 | − | 0.0158911i | ||||
\(929\) | −5.19844 | −0.170555 | −0.0852777 | − | 0.996357i | \(-0.527178\pi\) | ||||
−0.0852777 | + | 0.996357i | \(0.527178\pi\) | |||||||
\(930\) | 7.61288 | − | 9.87553i | 0.249636 | − | 0.323831i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 10.2342 | + | 10.2342i | 0.335232 | + | 0.335232i | ||||
\(933\) | −5.97174 | + | 5.97174i | −0.195506 | + | 0.195506i | ||||
\(934\) | −15.9894 | −0.523190 | ||||||||
\(935\) | 3.33429 | + | 25.7713i | 0.109043 | + | 0.842811i | ||||
\(936\) | 3.41770i | 0.111711i | ||||||||
\(937\) | −3.54515 | + | 3.54515i | −0.115815 | + | 0.115815i | −0.762639 | − | 0.646824i | \(-0.776097\pi\) |
0.646824 | + | 0.762639i | \(0.276097\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 19.4096i | − | 0.633409i | ||||||
\(940\) | 7.81738 | − | 1.01141i | 0.254975 | − | 0.0329887i | ||||
\(941\) | − | 10.2591i | − | 0.334437i | −0.985920 | − | 0.167219i | \(-0.946521\pi\) | ||
0.985920 | − | 0.167219i | \(-0.0534786\pi\) | |||||||
\(942\) | −2.60217 | − | 2.60217i | −0.0847834 | − | 0.0847834i | ||||
\(943\) | 3.10875 | + | 3.10875i | 0.101235 | + | 0.101235i | ||||
\(944\) | −10.1603 | −0.330689 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.1533 | −0.492676 | ||||||||
\(947\) | 19.8496 | + | 19.8496i | 0.645025 | + | 0.645025i | 0.951786 | − | 0.306761i | \(-0.0992454\pi\) |
−0.306761 | + | 0.951786i | \(0.599245\pi\) | |||||||
\(948\) | −5.89081 | − | 5.89081i | −0.191325 | − | 0.191325i | ||||
\(949\) | 16.6469i | 0.540381i | ||||||||
\(950\) | 17.6250 | − | 30.2148i | 0.571831 | − | 0.980298i | ||||
\(951\) | − | 15.5503i | − | 0.504253i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.6648 | + | 29.6648i | −0.960937 | + | 0.960937i | −0.999265 | − | 0.0383279i | \(-0.987797\pi\) |
0.0383279 | + | 0.999265i | \(0.487797\pi\) | |||||||
\(954\) | − | 9.40242i | − | 0.304415i | ||||||
\(955\) | 11.0244 | − | 14.3010i | 0.356740 | − | 0.462768i | ||||
\(956\) | 29.9736 | 0.969415 | ||||||||
\(957\) | −2.65587 | + | 2.65587i | −0.0858522 | + | 0.0858522i | ||||
\(958\) | −6.37140 | − | 6.37140i | −0.205850 | − | 0.205850i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.286912 | − | 2.21758i | −0.00926003 | − | 0.0715722i | ||||
\(961\) | −0.0964085 | −0.00310995 | ||||||||
\(962\) | 23.6838 | − | 23.6838i | 0.763595 | − | 0.763595i | ||||
\(963\) | 8.67454 | − | 8.67454i | 0.279533 | − | 0.279533i | ||||
\(964\) | 16.6201 | 0.535296 | ||||||||
\(965\) | 0.494211 | + | 3.81984i | 0.0159092 | + | 0.122965i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.20889 | − | 3.20889i | −0.103191 | − | 0.103191i | 0.653626 | − | 0.756817i | \(-0.273247\pi\) |
−0.756817 | + | 0.653626i | \(0.773247\pi\) | |||||||
\(968\) | −13.5054 | + | 13.5054i | −0.434079 | + | 0.434079i | ||||
\(969\) | −14.8191 | −0.476058 | ||||||||
\(970\) | −25.3328 | + | 32.8620i | −0.813386 | + | 1.05514i | ||||
\(971\) | 59.0859i | 1.89616i | 0.318036 | + | 0.948079i | \(0.396977\pi\) | ||||
−0.318036 | + | 0.948079i | \(0.603023\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 9.34012i | 0.299277i | ||||||||
\(975\) | −16.5258 | + | 4.34903i | −0.529250 | + | 0.139280i | ||||
\(976\) | − | 1.17166i | − | 0.0375039i | ||||||
\(977\) | −8.36251 | − | 8.36251i | −0.267540 | − | 0.267540i | 0.560568 | − | 0.828108i | \(-0.310583\pi\) |
−0.828108 | + | 0.560568i | \(0.810583\pi\) | |||||||
\(978\) | −9.95676 | − | 9.95676i | −0.318382 | − | 0.318382i | ||||
\(979\) | 39.4112 | 1.25959 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.336622 | −0.0107475 | ||||||||
\(982\) | 1.47457 | + | 1.47457i | 0.0470554 | + | 0.0470554i | ||||
\(983\) | 26.8714 | + | 26.8714i | 0.857064 | + | 0.857064i | 0.990991 | − | 0.133927i | \(-0.0427587\pi\) |
−0.133927 | + | 0.990991i | \(0.542759\pi\) | |||||||
\(984\) | 2.50597i | 0.0798873i | ||||||||
\(985\) | 18.8536 | − | 2.43929i | 0.600727 | − | 0.0777222i | ||||
\(986\) | − | 1.45017i | − | 0.0461829i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.9069 | − | 16.9069i | 0.537881 | − | 0.537881i | ||||
\(989\) | − | 4.84566i | − | 0.154083i | ||||||
\(990\) | 1.57408 | + | 12.1663i | 0.0500276 | + | 0.386671i | ||||
\(991\) | 8.01259 | 0.254528 | 0.127264 | − | 0.991869i | \(-0.459380\pi\) | ||||
0.127264 | + | 0.991869i | \(0.459380\pi\) | |||||||
\(992\) | −3.94312 | + | 3.94312i | −0.125194 | + | 0.125194i | ||||
\(993\) | 11.4452 | + | 11.4452i | 0.363202 | + | 0.363202i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.0416 | + | 19.5122i | −0.476851 | + | 0.618577i | ||||
\(996\) | 5.73154 | 0.181611 | ||||||||
\(997\) | 30.0935 | − | 30.0935i | 0.953072 | − | 0.953072i | −0.0458749 | − | 0.998947i | \(-0.514608\pi\) |
0.998947 | + | 0.0458749i | \(0.0146076\pi\) | |||||||
\(998\) | 9.49260 | − | 9.49260i | 0.300483 | − | 0.300483i | ||||
\(999\) | −9.80013 | −0.310063 |
(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 | 1470.2.m.e.97.7 | 16 | ||
5.3 | odd | 4 | 1470.2.m.d.1273.6 | 16 | |||
7.2 | even | 3 | 210.2.u.b.157.3 | yes | 16 | ||
7.3 | odd | 6 | 210.2.u.a.187.1 | yes | 16 | ||
7.6 | odd | 2 | 1470.2.m.d.97.6 | 16 | |||
21.2 | odd | 6 | 630.2.bv.b.577.2 | 16 | |||
21.17 | even | 6 | 630.2.bv.a.397.4 | 16 | |||
35.2 | odd | 12 | 1050.2.bc.h.493.3 | 16 | |||
35.3 | even | 12 | 210.2.u.b.103.3 | yes | 16 | ||
35.9 | even | 6 | 1050.2.bc.g.157.2 | 16 | |||
35.13 | even | 4 | inner | 1470.2.m.e.1273.7 | 16 | ||
35.17 | even | 12 | 1050.2.bc.g.943.2 | 16 | |||
35.23 | odd | 12 | 210.2.u.a.73.1 | ✓ | 16 | ||
35.24 | odd | 6 | 1050.2.bc.h.607.3 | 16 | |||
105.23 | even | 12 | 630.2.bv.a.73.4 | 16 | |||
105.38 | odd | 12 | 630.2.bv.b.523.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.u.a.73.1 | ✓ | 16 | 35.23 | odd | 12 | ||
210.2.u.a.187.1 | yes | 16 | 7.3 | odd | 6 | ||
210.2.u.b.103.3 | yes | 16 | 35.3 | even | 12 | ||
210.2.u.b.157.3 | yes | 16 | 7.2 | even | 3 | ||
630.2.bv.a.73.4 | 16 | 105.23 | even | 12 | |||
630.2.bv.a.397.4 | 16 | 21.17 | even | 6 | |||
630.2.bv.b.523.2 | 16 | 105.38 | odd | 12 | |||
630.2.bv.b.577.2 | 16 | 21.2 | odd | 6 | |||
1050.2.bc.g.157.2 | 16 | 35.9 | even | 6 | |||
1050.2.bc.g.943.2 | 16 | 35.17 | even | 12 | |||
1050.2.bc.h.493.3 | 16 | 35.2 | odd | 12 | |||
1050.2.bc.h.607.3 | 16 | 35.24 | odd | 6 | |||
1470.2.m.d.97.6 | 16 | 7.6 | odd | 2 | |||
1470.2.m.d.1273.6 | 16 | 5.3 | odd | 4 | |||
1470.2.m.e.97.7 | 16 | 1.1 | even | 1 | trivial | ||
1470.2.m.e.1273.7 | 16 | 35.13 | even | 4 | inner |