Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(265,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.265");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.o (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.7442857984.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 26x^{6} + 205x^{4} + 540x^{2} + 324 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.1 | ||
Root | \(3.73923i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.307 |
Dual form | 546.2.o.a.265.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −1.80230 | + | 1.80230i | −0.806015 | + | 0.806015i | −0.984028 | − | 0.178014i | \(-0.943033\pi\) |
0.178014 | + | 0.984028i | \(0.443033\pi\) | |||||||
\(6\) | −0.707107 | + | 0.707107i | −0.288675 | + | 0.288675i | ||||
\(7\) | 1.93693 | − | 1.80230i | 0.732091 | − | 0.681207i | ||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.54884 | 0.806015 | ||||||||
\(11\) | 0.936931 | − | 0.936931i | 0.282495 | − | 0.282495i | −0.551608 | − | 0.834103i | \(-0.685986\pi\) |
0.834103 | + | 0.551608i | \(0.185986\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 2.00000 | + | 3.00000i | 0.554700 | + | 0.832050i | ||||
\(14\) | −2.64404 | − | 0.0951965i | −0.706649 | − | 0.0254423i | ||||
\(15\) | 1.80230 | + | 1.80230i | 0.465353 | + | 0.465353i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.496594 | −0.120442 | −0.0602209 | − | 0.998185i | \(-0.519180\pi\) | ||||
−0.0602209 | + | 0.998185i | \(0.519180\pi\) | |||||||
\(18\) | 0.707107 | + | 0.707107i | 0.166667 | + | 0.166667i | ||||
\(19\) | 3.07156 | − | 3.07156i | 0.704664 | − | 0.704664i | −0.260744 | − | 0.965408i | \(-0.583968\pi\) |
0.965408 | + | 0.260744i | \(0.0839678\pi\) | |||||||
\(20\) | −1.80230 | − | 1.80230i | −0.403007 | − | 0.403007i | ||||
\(21\) | −1.80230 | − | 1.93693i | −0.393295 | − | 0.422673i | ||||
\(22\) | −1.32502 | −0.282495 | ||||||||
\(23\) | − | 7.37727i | − | 1.53827i | −0.639088 | − | 0.769133i | \(-0.720688\pi\) | ||
0.639088 | − | 0.769133i | \(-0.279312\pi\) | |||||||
\(24\) | −0.707107 | − | 0.707107i | −0.144338 | − | 0.144338i | ||||
\(25\) | − | 1.49659i | − | 0.299319i | ||||||
\(26\) | 0.707107 | − | 3.53553i | 0.138675 | − | 0.693375i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 1.80230 | + | 1.93693i | 0.340603 | + | 0.366046i | ||||
\(29\) | 7.25113 | 1.34650 | 0.673251 | − | 0.739414i | \(-0.264897\pi\) | ||||
0.673251 | + | 0.739414i | \(0.264897\pi\) | |||||||
\(30\) | − | 2.54884i | − | 0.465353i | ||||||
\(31\) | 5.73923 | − | 5.73923i | 1.03080 | − | 1.03080i | 0.0312865 | − | 0.999510i | \(-0.490040\pi\) |
0.999510 | − | 0.0312865i | \(-0.00996043\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −0.936931 | − | 0.936931i | −0.163099 | − | 0.163099i | ||||
\(34\) | 0.351145 | + | 0.351145i | 0.0602209 | + | 0.0602209i | ||||
\(35\) | −0.242641 | + | 6.73923i | −0.0410138 | + | 1.13914i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | 3.54154 | − | 3.54154i | 0.582225 | − | 0.582225i | −0.353289 | − | 0.935514i | \(-0.614937\pi\) |
0.935514 | + | 0.353289i | \(0.114937\pi\) | |||||||
\(38\) | −4.34384 | −0.704664 | ||||||||
\(39\) | 3.00000 | − | 2.00000i | 0.480384 | − | 0.320256i | ||||
\(40\) | 2.54884i | 0.403007i | ||||||||
\(41\) | −6.11650 | + | 6.11650i | −0.955237 | + | 0.955237i | −0.999040 | − | 0.0438029i | \(-0.986053\pi\) |
0.0438029 | + | 0.999040i | \(0.486053\pi\) | |||||||
\(42\) | −0.0951965 | + | 2.64404i | −0.0146891 | + | 0.407984i | ||||
\(43\) | − | 6.85574i | − | 1.04549i | −0.852489 | − | 0.522745i | \(-0.824908\pi\) | ||
0.852489 | − | 0.522745i | \(-0.175092\pi\) | |||||||
\(44\) | 0.936931 | + | 0.936931i | 0.141248 | + | 0.141248i | ||||
\(45\) | 1.80230 | − | 1.80230i | 0.268672 | − | 0.268672i | ||||
\(46\) | −5.21652 | + | 5.21652i | −0.769133 | + | 0.769133i | ||||
\(47\) | −5.87386 | − | 5.87386i | −0.856791 | − | 0.856791i | 0.134168 | − | 0.990959i | \(-0.457164\pi\) |
−0.990959 | + | 0.134168i | \(0.957164\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 0.503406 | − | 6.98188i | 0.0719152 | − | 0.997411i | ||||
\(50\) | −1.05825 | + | 1.05825i | −0.149659 | + | 0.149659i | ||||
\(51\) | 0.496594i | 0.0695371i | ||||||||
\(52\) | −3.00000 | + | 2.00000i | −0.416025 | + | 0.277350i | ||||
\(53\) | −4.26926 | −0.586427 | −0.293214 | − | 0.956047i | \(-0.594725\pi\) | ||||
−0.293214 | + | 0.956047i | \(0.594725\pi\) | |||||||
\(54\) | 0.707107 | − | 0.707107i | 0.0962250 | − | 0.0962250i | ||||
\(55\) | 3.37727i | 0.455391i | ||||||||
\(56\) | 0.0951965 | − | 2.64404i | 0.0127212 | − | 0.353324i | ||||
\(57\) | −3.07156 | − | 3.07156i | −0.406838 | − | 0.406838i | ||||
\(58\) | −5.12732 | − | 5.12732i | −0.673251 | − | 0.673251i | ||||
\(59\) | −1.37727 | − | 1.37727i | −0.179305 | − | 0.179305i | 0.611748 | − | 0.791053i | \(-0.290467\pi\) |
−0.791053 | + | 0.611748i | \(0.790467\pi\) | |||||||
\(60\) | −1.80230 | + | 1.80230i | −0.232676 | + | 0.232676i | ||||
\(61\) | 0.496594i | 0.0635823i | 0.999495 | + | 0.0317912i | \(0.0101211\pi\) | ||||
−0.999495 | + | 0.0317912i | \(0.989879\pi\) | |||||||
\(62\) | −8.11650 | −1.03080 | ||||||||
\(63\) | −1.93693 | + | 1.80230i | −0.244030 | + | 0.227069i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −9.01152 | − | 1.80230i | −1.11774 | − | 0.223548i | ||||
\(66\) | 1.32502i | 0.163099i | ||||||||
\(67\) | 9.11650 | + | 9.11650i | 1.11376 | + | 1.11376i | 0.992638 | + | 0.121120i | \(0.0386487\pi\) |
0.121120 | + | 0.992638i | \(0.461351\pi\) | |||||||
\(68\) | − | 0.496594i | − | 0.0602209i | ||||||
\(69\) | −7.37727 | −0.888119 | ||||||||
\(70\) | 4.93693 | − | 4.59379i | 0.590076 | − | 0.549062i | ||||
\(71\) | 11.3773 | + | 11.3773i | 1.35023 | + | 1.35023i | 0.885396 | + | 0.464837i | \(0.153887\pi\) |
0.464837 | + | 0.885396i | \(0.346113\pi\) | |||||||
\(72\) | −0.707107 | + | 0.707107i | −0.0833333 | + | 0.0833333i | ||||
\(73\) | 3.54154 | + | 3.54154i | 0.414506 | + | 0.414506i | 0.883305 | − | 0.468799i | \(-0.155313\pi\) |
−0.468799 | + | 0.883305i | \(0.655313\pi\) | |||||||
\(74\) | −5.00849 | −0.582225 | ||||||||
\(75\) | −1.49659 | −0.172812 | ||||||||
\(76\) | 3.07156 | + | 3.07156i | 0.352332 | + | 0.352332i | ||||
\(77\) | 0.126137 | − | 3.50341i | 0.0143747 | − | 0.399250i | ||||
\(78\) | −3.53553 | − | 0.707107i | −0.400320 | − | 0.0800641i | ||||
\(79\) | −13.1499 | −1.47948 | −0.739741 | − | 0.672891i | \(-0.765052\pi\) | ||||
−0.739741 | + | 0.672891i | \(0.765052\pi\) | |||||||
\(80\) | 1.80230 | − | 1.80230i | 0.201504 | − | 0.201504i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.65004 | 0.955237 | ||||||||
\(83\) | 7.87386 | − | 7.87386i | 0.864269 | − | 0.864269i | −0.127562 | − | 0.991831i | \(-0.540715\pi\) |
0.991831 | + | 0.127562i | \(0.0407151\pi\) | |||||||
\(84\) | 1.93693 | − | 1.80230i | 0.211337 | − | 0.196647i | ||||
\(85\) | 0.895013 | − | 0.895013i | 0.0970778 | − | 0.0970778i | ||||
\(86\) | −4.84774 | + | 4.84774i | −0.522745 | + | 0.522745i | ||||
\(87\) | − | 7.25113i | − | 0.777403i | ||||||
\(88\) | − | 1.32502i | − | 0.141248i | ||||||
\(89\) | 10.2177 | + | 10.2177i | 1.08307 | + | 1.08307i | 0.996221 | + | 0.0868533i | \(0.0276811\pi\) |
0.0868533 | + | 0.996221i | \(0.472319\pi\) | |||||||
\(90\) | −2.54884 | −0.268672 | ||||||||
\(91\) | 9.28077 | + | 2.20619i | 0.972889 | + | 0.231271i | ||||
\(92\) | 7.37727 | 0.769133 | ||||||||
\(93\) | −5.73923 | − | 5.73923i | −0.595131 | − | 0.595131i | ||||
\(94\) | 8.30690i | 0.856791i | ||||||||
\(95\) | 11.0718i | 1.13594i | ||||||||
\(96\) | 0.707107 | − | 0.707107i | 0.0721688 | − | 0.0721688i | ||||
\(97\) | 9.46034 | − | 9.46034i | 0.960552 | − | 0.960552i | −0.0386985 | − | 0.999251i | \(-0.512321\pi\) |
0.999251 | + | 0.0386985i | \(0.0123212\pi\) | |||||||
\(98\) | −5.29289 | + | 4.58097i | −0.534663 | + | 0.462748i | ||||
\(99\) | −0.936931 | + | 0.936931i | −0.0941651 | + | 0.0941651i | ||||
\(100\) | 1.49659 | 0.149659 | ||||||||
\(101\) | −4.66465 | −0.464150 | −0.232075 | − | 0.972698i | \(-0.574551\pi\) | ||||
−0.232075 | + | 0.972698i | \(0.574551\pi\) | |||||||
\(102\) | 0.351145 | − | 0.351145i | 0.0347685 | − | 0.0347685i | ||||
\(103\) | −18.5865 | −1.83138 | −0.915690 | − | 0.401885i | \(-0.868355\pi\) | ||||
−0.915690 | + | 0.401885i | \(0.868355\pi\) | |||||||
\(104\) | 3.53553 | + | 0.707107i | 0.346688 | + | 0.0693375i | ||||
\(105\) | 6.73923 | + | 0.242641i | 0.657682 | + | 0.0236793i | ||||
\(106\) | 3.01882 | + | 3.01882i | 0.293214 | + | 0.293214i | ||||
\(107\) | 6.95694 | 0.672553 | 0.336276 | − | 0.941763i | \(-0.390832\pi\) | ||||
0.336276 | + | 0.941763i | \(0.390832\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 2.94374 | + | 2.94374i | 0.281959 | + | 0.281959i | 0.833890 | − | 0.551931i | \(-0.186109\pi\) |
−0.551931 | + | 0.833890i | \(0.686109\pi\) | |||||||
\(110\) | 2.38809 | − | 2.38809i | 0.227695 | − | 0.227695i | ||||
\(111\) | −3.54154 | − | 3.54154i | −0.336148 | − | 0.336148i | ||||
\(112\) | −1.93693 | + | 1.80230i | −0.183023 | + | 0.170302i | ||||
\(113\) | −2.93996 | −0.276568 | −0.138284 | − | 0.990393i | \(-0.544159\pi\) | ||||
−0.138284 | + | 0.990393i | \(0.544159\pi\) | |||||||
\(114\) | 4.34384i | 0.406838i | ||||||||
\(115\) | 13.2961 | + | 13.2961i | 1.23987 | + | 1.23987i | ||||
\(116\) | 7.25113i | 0.673251i | ||||||||
\(117\) | −2.00000 | − | 3.00000i | −0.184900 | − | 0.277350i | ||||
\(118\) | 1.94775i | 0.179305i | ||||||||
\(119\) | −0.961868 | + | 0.895013i | −0.0881743 | + | 0.0820457i | ||||
\(120\) | 2.54884 | 0.232676 | ||||||||
\(121\) | 9.24432i | 0.840393i | ||||||||
\(122\) | 0.351145 | − | 0.351145i | 0.0317912 | − | 0.0317912i | ||||
\(123\) | 6.11650 | + | 6.11650i | 0.551507 | + | 0.551507i | ||||
\(124\) | 5.73923 | + | 5.73923i | 0.515398 | + | 0.515398i | ||||
\(125\) | −6.31420 | − | 6.31420i | −0.564759 | − | 0.564759i | ||||
\(126\) | 2.64404 | + | 0.0951965i | 0.235550 | + | 0.00848077i | ||||
\(127\) | 19.8376i | 1.76030i | 0.474692 | + | 0.880152i | \(0.342559\pi\) | ||||
−0.474692 | + | 0.880152i | \(0.657441\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −6.85574 | −0.603614 | ||||||||
\(130\) | 5.09768 | + | 7.64653i | 0.447096 | + | 0.670645i | ||||
\(131\) | − | 5.10801i | − | 0.446289i | −0.974785 | − | 0.223145i | \(-0.928368\pi\) | ||
0.974785 | − | 0.223145i | \(-0.0716322\pi\) | |||||||
\(132\) | 0.936931 | − | 0.936931i | 0.0815494 | − | 0.0815494i | ||||
\(133\) | 0.413518 | − | 11.4853i | 0.0358566 | − | 0.995900i | ||||
\(134\) | − | 12.8927i | − | 1.11376i | ||||||
\(135\) | −1.80230 | − | 1.80230i | −0.155118 | − | 0.155118i | ||||
\(136\) | −0.351145 | + | 0.351145i | −0.0301104 | + | 0.0301104i | ||||
\(137\) | 3.80230 | − | 3.80230i | 0.324853 | − | 0.324853i | −0.525773 | − | 0.850625i | \(-0.676224\pi\) |
0.850625 | + | 0.525773i | \(0.176224\pi\) | |||||||
\(138\) | 5.21652 | + | 5.21652i | 0.444059 | + | 0.444059i | ||||
\(139\) | 2.93996i | 0.249364i | 0.992197 | + | 0.124682i | \(0.0397910\pi\) | ||||
−0.992197 | + | 0.124682i | \(0.960209\pi\) | |||||||
\(140\) | −6.73923 | − | 0.242641i | −0.569569 | − | 0.0205069i | ||||
\(141\) | −5.87386 | + | 5.87386i | −0.494668 | + | 0.494668i | ||||
\(142\) | − | 16.0899i | − | 1.35023i | ||||||
\(143\) | 4.68466 | + | 0.936931i | 0.391751 | + | 0.0783501i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −13.0687 | + | 13.0687i | −1.08530 | + | 1.08530i | ||||
\(146\) | − | 5.00849i | − | 0.414506i | ||||||
\(147\) | −6.98188 | − | 0.503406i | −0.575855 | − | 0.0415202i | ||||
\(148\) | 3.54154 | + | 3.54154i | 0.291113 | + | 0.291113i | ||||
\(149\) | −1.74605 | − | 1.74605i | −0.143042 | − | 0.143042i | 0.631960 | − | 0.775001i | \(-0.282251\pi\) |
−0.775001 | + | 0.631960i | \(0.782251\pi\) | |||||||
\(150\) | 1.05825 | + | 1.05825i | 0.0864059 | + | 0.0864059i | ||||
\(151\) | −6.55003 | + | 6.55003i | −0.533034 | + | 0.533034i | −0.921474 | − | 0.388440i | \(-0.873014\pi\) |
0.388440 | + | 0.921474i | \(0.373014\pi\) | |||||||
\(152\) | − | 4.34384i | − | 0.352332i | ||||||
\(153\) | 0.496594 | 0.0401472 | ||||||||
\(154\) | −2.56647 | + | 2.38809i | −0.206812 | + | 0.192438i | ||||
\(155\) | 20.6877i | 1.66167i | ||||||||
\(156\) | 2.00000 | + | 3.00000i | 0.160128 | + | 0.240192i | ||||
\(157\) | − | 1.70581i | − | 0.136138i | −0.997681 | − | 0.0680691i | \(-0.978316\pi\) | ||
0.997681 | − | 0.0680691i | \(-0.0216838\pi\) | |||||||
\(158\) | 9.29841 | + | 9.29841i | 0.739741 | + | 0.739741i | ||||
\(159\) | 4.26926i | 0.338574i | ||||||||
\(160\) | −2.54884 | −0.201504 | ||||||||
\(161\) | −13.2961 | − | 14.2893i | −1.04788 | − | 1.12615i | ||||
\(162\) | −0.707107 | − | 0.707107i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | −4.23583 | + | 4.23583i | −0.331776 | + | 0.331776i | −0.853261 | − | 0.521485i | \(-0.825378\pi\) |
0.521485 | + | 0.853261i | \(0.325378\pi\) | |||||||
\(164\) | −6.11650 | − | 6.11650i | −0.477619 | − | 0.477619i | ||||
\(165\) | 3.37727 | 0.262920 | ||||||||
\(166\) | −11.1353 | −0.864269 | ||||||||
\(167\) | 8.02001 | + | 8.02001i | 0.620607 | + | 0.620607i | 0.945687 | − | 0.325080i | \(-0.105391\pi\) |
−0.325080 | + | 0.945687i | \(0.605391\pi\) | |||||||
\(168\) | −2.64404 | − | 0.0951965i | −0.203992 | − | 0.00734457i | ||||
\(169\) | −5.00000 | + | 12.0000i | −0.384615 | + | 0.923077i | ||||
\(170\) | −1.26574 | −0.0970778 | ||||||||
\(171\) | −3.07156 | + | 3.07156i | −0.234888 | + | 0.234888i | ||||
\(172\) | 6.85574 | 0.522745 | ||||||||
\(173\) | 4.21603 | 0.320538 | 0.160269 | − | 0.987073i | \(-0.448764\pi\) | ||||
0.160269 | + | 0.987073i | \(0.448764\pi\) | |||||||
\(174\) | −5.12732 | + | 5.12732i | −0.388701 | + | 0.388701i | ||||
\(175\) | −2.69732 | − | 2.89880i | −0.203898 | − | 0.219129i | ||||
\(176\) | −0.936931 | + | 0.936931i | −0.0706239 | + | 0.0706239i | ||||
\(177\) | −1.37727 | + | 1.37727i | −0.103522 | + | 0.103522i | ||||
\(178\) | − | 14.4500i | − | 1.08307i | ||||||
\(179\) | 5.33535i | 0.398783i | 0.979920 | + | 0.199391i | \(0.0638965\pi\) | ||||
−0.979920 | + | 0.199391i | \(0.936103\pi\) | |||||||
\(180\) | 1.80230 | + | 1.80230i | 0.134336 | + | 0.134336i | ||||
\(181\) | 1.79760 | 0.133615 | 0.0668073 | − | 0.997766i | \(-0.478719\pi\) | ||||
0.0668073 | + | 0.997766i | \(0.478719\pi\) | |||||||
\(182\) | −5.00249 | − | 8.12251i | −0.370809 | − | 0.602080i | ||||
\(183\) | 0.496594 | 0.0367093 | ||||||||
\(184\) | −5.21652 | − | 5.21652i | −0.384567 | − | 0.384567i | ||||
\(185\) | 12.7659i | 0.938564i | ||||||||
\(186\) | 8.11650i | 0.595131i | ||||||||
\(187\) | −0.465274 | + | 0.465274i | −0.0340242 | + | 0.0340242i | ||||
\(188\) | 5.87386 | − | 5.87386i | 0.428395 | − | 0.428395i | ||||
\(189\) | 1.80230 | + | 1.93693i | 0.131098 | + | 0.140891i | ||||
\(190\) | 7.82892 | − | 7.82892i | 0.567969 | − | 0.567969i | ||||
\(191\) | −18.7889 | −1.35952 | −0.679758 | − | 0.733437i | \(-0.737915\pi\) | ||||
−0.679758 | + | 0.733437i | \(0.737915\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 1.37046 | − | 1.37046i | 0.0986476 | − | 0.0986476i | −0.656061 | − | 0.754708i | \(-0.727778\pi\) |
0.754708 | + | 0.656061i | \(0.227778\pi\) | |||||||
\(194\) | −13.3789 | −0.960552 | ||||||||
\(195\) | −1.80230 | + | 9.01152i | −0.129066 | + | 0.645328i | ||||
\(196\) | 6.98188 | + | 0.503406i | 0.498705 | + | 0.0359576i | ||||
\(197\) | −2.86537 | − | 2.86537i | −0.204149 | − | 0.204149i | 0.597626 | − | 0.801775i | \(-0.296111\pi\) |
−0.801775 | + | 0.597626i | \(0.796111\pi\) | |||||||
\(198\) | 1.32502 | 0.0941651 | ||||||||
\(199\) | −14.0650 | −0.997038 | −0.498519 | − | 0.866879i | \(-0.666123\pi\) | ||||
−0.498519 | + | 0.866879i | \(0.666123\pi\) | |||||||
\(200\) | −1.05825 | − | 1.05825i | −0.0748297 | − | 0.0748297i | ||||
\(201\) | 9.11650 | − | 9.11650i | 0.643029 | − | 0.643029i | ||||
\(202\) | 3.29841 | + | 3.29841i | 0.232075 | + | 0.232075i | ||||
\(203\) | 14.0449 | − | 13.0687i | 0.985762 | − | 0.917246i | ||||
\(204\) | −0.496594 | −0.0347685 | ||||||||
\(205\) | − | 22.0476i | − | 1.53987i | ||||||
\(206\) | 13.1426 | + | 13.1426i | 0.915690 | + | 0.915690i | ||||
\(207\) | 7.37727i | 0.512756i | ||||||||
\(208\) | −2.00000 | − | 3.00000i | −0.138675 | − | 0.208013i | ||||
\(209\) | − | 5.75568i | − | 0.398129i | ||||||
\(210\) | −4.59379 | − | 4.93693i | −0.317001 | − | 0.340681i | ||||
\(211\) | −14.8557 | −1.02271 | −0.511356 | − | 0.859369i | \(-0.670856\pi\) | ||||
−0.511356 | + | 0.859369i | \(0.670856\pi\) | |||||||
\(212\) | − | 4.26926i | − | 0.293214i | ||||||
\(213\) | 11.3773 | − | 11.3773i | 0.779558 | − | 0.779558i | ||||
\(214\) | −4.91930 | − | 4.91930i | −0.336276 | − | 0.336276i | ||||
\(215\) | 12.3561 | + | 12.3561i | 0.842680 | + | 0.842680i | ||||
\(216\) | 0.707107 | + | 0.707107i | 0.0481125 | + | 0.0481125i | ||||
\(217\) | 0.772662 | − | 21.4603i | 0.0524517 | − | 1.45682i | ||||
\(218\) | − | 4.16308i | − | 0.281959i | ||||||
\(219\) | 3.54154 | − | 3.54154i | 0.239315 | − | 0.239315i | ||||
\(220\) | −3.37727 | −0.227695 | ||||||||
\(221\) | −0.993188 | − | 1.48978i | −0.0668090 | − | 0.100214i | ||||
\(222\) | 5.00849i | 0.336148i | ||||||||
\(223\) | 6.24945 | − | 6.24945i | 0.418494 | − | 0.418494i | −0.466190 | − | 0.884685i | \(-0.654374\pi\) |
0.884685 | + | 0.466190i | \(0.154374\pi\) | |||||||
\(224\) | 2.64404 | + | 0.0951965i | 0.176662 | + | 0.00636058i | ||||
\(225\) | 1.49659i | 0.0997729i | ||||||||
\(226\) | 2.07886 | + | 2.07886i | 0.138284 | + | 0.138284i | ||||
\(227\) | −5.50341 | + | 5.50341i | −0.365274 | + | 0.365274i | −0.865750 | − | 0.500476i | \(-0.833158\pi\) |
0.500476 | + | 0.865750i | \(0.333158\pi\) | |||||||
\(228\) | 3.07156 | − | 3.07156i | 0.203419 | − | 0.203419i | ||||
\(229\) | −2.50341 | − | 2.50341i | −0.165430 | − | 0.165430i | 0.619537 | − | 0.784967i | \(-0.287320\pi\) |
−0.784967 | + | 0.619537i | \(0.787320\pi\) | |||||||
\(230\) | − | 18.8035i | − | 1.23987i | ||||||
\(231\) | −3.50341 | − | 0.126137i | −0.230507 | − | 0.00829923i | ||||
\(232\) | 5.12732 | − | 5.12732i | 0.336625 | − | 0.336625i | ||||
\(233\) | − | 16.5615i | − | 1.08498i | −0.840061 | − | 0.542491i | \(-0.817481\pi\) | ||
0.840061 | − | 0.542491i | \(-0.182519\pi\) | |||||||
\(234\) | −0.707107 | + | 3.53553i | −0.0462250 | + | 0.231125i | ||||
\(235\) | 21.1730 | 1.38117 | ||||||||
\(236\) | 1.37727 | − | 1.37727i | 0.0896526 | − | 0.0896526i | ||||
\(237\) | 13.1499i | 0.854180i | ||||||||
\(238\) | 1.31301 | + | 0.0472740i | 0.0851100 | + | 0.00306432i | ||||
\(239\) | −2.41238 | − | 2.41238i | −0.156044 | − | 0.156044i | 0.624767 | − | 0.780811i | \(-0.285194\pi\) |
−0.780811 | + | 0.624767i | \(0.785194\pi\) | |||||||
\(240\) | −1.80230 | − | 1.80230i | −0.116338 | − | 0.116338i | ||||
\(241\) | −8.37727 | − | 8.37727i | −0.539627 | − | 0.539627i | 0.383792 | − | 0.923419i | \(-0.374618\pi\) |
−0.923419 | + | 0.383792i | \(0.874618\pi\) | |||||||
\(242\) | 6.53672 | − | 6.53672i | 0.420196 | − | 0.420196i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −0.496594 | −0.0317912 | ||||||||
\(245\) | 11.6762 | + | 13.4907i | 0.745963 | + | 0.861892i | ||||
\(246\) | − | 8.65004i | − | 0.551507i | ||||||
\(247\) | 15.3578 | + | 3.07156i | 0.977193 | + | 0.195439i | ||||
\(248\) | − | 8.11650i | − | 0.515398i | ||||||
\(249\) | −7.87386 | − | 7.87386i | −0.498986 | − | 0.498986i | ||||
\(250\) | 8.92963i | 0.564759i | ||||||||
\(251\) | 26.8727 | 1.69619 | 0.848096 | − | 0.529843i | \(-0.177749\pi\) | ||||
0.848096 | + | 0.529843i | \(0.177749\pi\) | |||||||
\(252\) | −1.80230 | − | 1.93693i | −0.113534 | − | 0.122015i | ||||
\(253\) | −6.91199 | − | 6.91199i | −0.434553 | − | 0.434553i | ||||
\(254\) | 14.0273 | − | 14.0273i | 0.880152 | − | 0.880152i | ||||
\(255\) | −0.895013 | − | 0.895013i | −0.0560479 | − | 0.0560479i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.98302 | 0.497967 | 0.248984 | − | 0.968508i | \(-0.419904\pi\) | ||||
0.248984 | + | 0.968508i | \(0.419904\pi\) | |||||||
\(258\) | 4.84774 | + | 4.84774i | 0.301807 | + | 0.301807i | ||||
\(259\) | 0.476791 | − | 13.2426i | 0.0296263 | − | 0.822858i | ||||
\(260\) | 1.80230 | − | 9.01152i | 0.111774 | − | 0.558871i | ||||
\(261\) | −7.25113 | −0.448834 | ||||||||
\(262\) | −3.61191 | + | 3.61191i | −0.223145 | + | 0.223145i | ||||
\(263\) | −2.47166 | −0.152409 | −0.0762044 | − | 0.997092i | \(-0.524280\pi\) | ||||
−0.0762044 | + | 0.997092i | \(0.524280\pi\) | |||||||
\(264\) | −1.32502 | −0.0815494 | ||||||||
\(265\) | 7.69449 | − | 7.69449i | 0.472669 | − | 0.472669i | ||||
\(266\) | −8.41372 | + | 7.82892i | −0.515878 | + | 0.480022i | ||||
\(267\) | 10.2177 | − | 10.2177i | 0.625313 | − | 0.625313i | ||||
\(268\) | −9.11650 | + | 9.11650i | −0.556879 | + | 0.556879i | ||||
\(269\) | 5.83761i | 0.355926i | 0.984037 | + | 0.177963i | \(0.0569507\pi\) | ||||
−0.984037 | + | 0.177963i | \(0.943049\pi\) | |||||||
\(270\) | 2.54884i | 0.155118i | ||||||||
\(271\) | −8.57799 | − | 8.57799i | −0.521076 | − | 0.521076i | 0.396820 | − | 0.917896i | \(-0.370114\pi\) |
−0.917896 | + | 0.396820i | \(0.870114\pi\) | |||||||
\(272\) | 0.496594 | 0.0301104 | ||||||||
\(273\) | 2.20619 | − | 9.28077i | 0.133525 | − | 0.561698i | ||||
\(274\) | −5.37727 | −0.324853 | ||||||||
\(275\) | −1.40221 | − | 1.40221i | −0.0845562 | − | 0.0845562i | ||||
\(276\) | − | 7.37727i | − | 0.444059i | ||||||
\(277\) | − | 2.66465i | − | 0.160103i | −0.996791 | − | 0.0800516i | \(-0.974491\pi\) | ||
0.996791 | − | 0.0800516i | \(-0.0255085\pi\) | |||||||
\(278\) | 2.07886 | − | 2.07886i | 0.124682 | − | 0.124682i | ||||
\(279\) | −5.73923 | + | 5.73923i | −0.343599 | + | 0.343599i | ||||
\(280\) | 4.59379 | + | 4.93693i | 0.274531 | + | 0.295038i | ||||
\(281\) | −8.09952 | + | 8.09952i | −0.483177 | + | 0.483177i | −0.906145 | − | 0.422968i | \(-0.860988\pi\) |
0.422968 | + | 0.906145i | \(0.360988\pi\) | |||||||
\(282\) | 8.30690 | 0.494668 | ||||||||
\(283\) | −30.2730 | −1.79954 | −0.899772 | − | 0.436360i | \(-0.856267\pi\) | ||||
−0.899772 | + | 0.436360i | \(0.856267\pi\) | |||||||
\(284\) | −11.3773 | + | 11.3773i | −0.675117 | + | 0.675117i | ||||
\(285\) | 11.0718 | 0.655835 | ||||||||
\(286\) | −2.65004 | − | 3.97506i | −0.156700 | − | 0.235050i | ||||
\(287\) | −0.823453 | + | 22.8710i | −0.0486069 | + | 1.35003i | ||||
\(288\) | −0.707107 | − | 0.707107i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | −16.7534 | −0.985494 | ||||||||
\(290\) | 18.4820 | 1.08530 | ||||||||
\(291\) | −9.46034 | − | 9.46034i | −0.554575 | − | 0.554575i | ||||
\(292\) | −3.54154 | + | 3.54154i | −0.207253 | + | 0.207253i | ||||
\(293\) | −17.9235 | − | 17.9235i | −1.04710 | − | 1.04710i | −0.998834 | − | 0.0482683i | \(-0.984630\pi\) |
−0.0482683 | − | 0.998834i | \(-0.515370\pi\) | |||||||
\(294\) | 4.58097 | + | 5.29289i | 0.267168 | + | 0.308688i | ||||
\(295\) | 4.96451 | 0.289045 | ||||||||
\(296\) | − | 5.00849i | − | 0.291113i | ||||||
\(297\) | 0.936931 | + | 0.936931i | 0.0543663 | + | 0.0543663i | ||||
\(298\) | 2.46928i | 0.143042i | ||||||||
\(299\) | 22.1318 | − | 14.7545i | 1.27992 | − | 0.853277i | ||||
\(300\) | − | 1.49659i | − | 0.0864059i | ||||||
\(301\) | −12.3561 | − | 13.2791i | −0.712195 | − | 0.765394i | ||||
\(302\) | 9.26314 | 0.533034 | ||||||||
\(303\) | 4.66465i | 0.267977i | ||||||||
\(304\) | −3.07156 | + | 3.07156i | −0.176166 | + | 0.176166i | ||||
\(305\) | −0.895013 | − | 0.895013i | −0.0512483 | − | 0.0512483i | ||||
\(306\) | −0.351145 | − | 0.351145i | −0.0200736 | − | 0.0200736i | ||||
\(307\) | −5.09157 | − | 5.09157i | −0.290591 | − | 0.290591i | 0.546723 | − | 0.837314i | \(-0.315875\pi\) |
−0.837314 | + | 0.546723i | \(0.815875\pi\) | |||||||
\(308\) | 3.50341 | + | 0.126137i | 0.199625 | + | 0.00718734i | ||||
\(309\) | 18.5865i | 1.05735i | ||||||||
\(310\) | 14.6284 | − | 14.6284i | 0.830837 | − | 0.830837i | ||||
\(311\) | −14.0729 | −0.798001 | −0.399001 | − | 0.916951i | \(-0.630643\pi\) | ||||
−0.399001 | + | 0.916951i | \(0.630643\pi\) | |||||||
\(312\) | 0.707107 | − | 3.53553i | 0.0400320 | − | 0.200160i | ||||
\(313\) | 28.3059i | 1.59994i | 0.600037 | + | 0.799972i | \(0.295153\pi\) | ||||
−0.600037 | + | 0.799972i | \(0.704847\pi\) | |||||||
\(314\) | −1.20619 | + | 1.20619i | −0.0680691 | + | 0.0680691i | ||||
\(315\) | 0.242641 | − | 6.73923i | 0.0136713 | − | 0.379713i | ||||
\(316\) | − | 13.1499i | − | 0.739741i | ||||||
\(317\) | 20.5119 | + | 20.5119i | 1.15206 | + | 1.15206i | 0.986138 | + | 0.165924i | \(0.0530608\pi\) |
0.165924 | + | 0.986138i | \(0.446939\pi\) | |||||||
\(318\) | 3.01882 | − | 3.01882i | 0.169287 | − | 0.169287i | ||||
\(319\) | 6.79381 | − | 6.79381i | 0.380380 | − | 0.380380i | ||||
\(320\) | 1.80230 | + | 1.80230i | 0.100752 | + | 0.100752i | ||||
\(321\) | − | 6.95694i | − | 0.388298i | ||||||
\(322\) | −0.702290 | + | 19.5058i | −0.0391371 | + | 1.08701i | ||||
\(323\) | −1.52532 | + | 1.52532i | −0.0848709 | + | 0.0848709i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | 4.48978 | − | 2.99319i | 0.249048 | − | 0.166032i | ||||
\(326\) | 5.99037 | 0.331776 | ||||||||
\(327\) | 2.94374 | − | 2.94374i | 0.162789 | − | 0.162789i | ||||
\(328\) | 8.65004i | 0.477619i | ||||||||
\(329\) | −21.9638 | − | 0.790787i | −1.21090 | − | 0.0435975i | ||||
\(330\) | −2.38809 | − | 2.38809i | −0.131460 | − | 0.131460i | ||||
\(331\) | −9.65502 | − | 9.65502i | −0.530688 | − | 0.530688i | 0.390089 | − | 0.920777i | \(-0.372444\pi\) |
−0.920777 | + | 0.390089i | \(0.872444\pi\) | |||||||
\(332\) | 7.87386 | + | 7.87386i | 0.432134 | + | 0.432134i | ||||
\(333\) | −3.54154 | + | 3.54154i | −0.194075 | + | 0.194075i | ||||
\(334\) | − | 11.3420i | − | 0.620607i | ||||||
\(335\) | −32.8614 | −1.79541 | ||||||||
\(336\) | 1.80230 | + | 1.93693i | 0.0983237 | + | 0.105668i | ||||
\(337\) | − | 7.25113i | − | 0.394994i | −0.980303 | − | 0.197497i | \(-0.936719\pi\) | ||
0.980303 | − | 0.197497i | \(-0.0632813\pi\) | |||||||
\(338\) | 12.0208 | − | 4.94975i | 0.653846 | − | 0.269231i | ||||
\(339\) | 2.93996i | 0.159677i | ||||||||
\(340\) | 0.895013 | + | 0.895013i | 0.0485389 | + | 0.0485389i | ||||
\(341\) | − | 10.7545i | − | 0.582391i | ||||||
\(342\) | 4.34384 | 0.234888 | ||||||||
\(343\) | −11.6084 | − | 14.4307i | −0.626794 | − | 0.779185i | ||||
\(344\) | −4.84774 | − | 4.84774i | −0.261373 | − | 0.261373i | ||||
\(345\) | 13.2961 | − | 13.2961i | 0.715837 | − | 0.715837i | ||||
\(346\) | −2.98118 | − | 2.98118i | −0.160269 | − | 0.160269i | ||||
\(347\) | 29.7647 | 1.59785 | 0.798927 | − | 0.601429i | \(-0.205402\pi\) | ||||
0.798927 | + | 0.601429i | \(0.205402\pi\) | |||||||
\(348\) | 7.25113 | 0.388701 | ||||||||
\(349\) | 13.1431 | + | 13.1431i | 0.703535 | + | 0.703535i | 0.965168 | − | 0.261633i | \(-0.0842608\pi\) |
−0.261633 | + | 0.965168i | \(0.584261\pi\) | |||||||
\(350\) | −0.142470 | + | 3.95705i | −0.00761536 | + | 0.211513i | ||||
\(351\) | −3.00000 | + | 2.00000i | −0.160128 | + | 0.106752i | ||||
\(352\) | 1.32502 | 0.0706239 | ||||||||
\(353\) | −13.5531 | + | 13.5531i | −0.721356 | + | 0.721356i | −0.968881 | − | 0.247525i | \(-0.920383\pi\) |
0.247525 | + | 0.968881i | \(0.420383\pi\) | |||||||
\(354\) | 1.94775 | 0.103522 | ||||||||
\(355\) | −41.0106 | −2.17662 | ||||||||
\(356\) | −10.2177 | + | 10.2177i | −0.541537 | + | 0.541537i | ||||
\(357\) | 0.895013 | + | 0.961868i | 0.0473691 | + | 0.0509075i | ||||
\(358\) | 3.77266 | − | 3.77266i | 0.199391 | − | 0.199391i | ||||
\(359\) | −4.04192 | + | 4.04192i | −0.213324 | + | 0.213324i | −0.805678 | − | 0.592354i | \(-0.798199\pi\) |
0.592354 | + | 0.805678i | \(0.298199\pi\) | |||||||
\(360\) | − | 2.54884i | − | 0.134336i | ||||||
\(361\) | 0.131045i | 0.00689710i | ||||||||
\(362\) | −1.27109 | − | 1.27109i | −0.0668073 | − | 0.0668073i | ||||
\(363\) | 9.24432 | 0.485201 | ||||||||
\(364\) | −2.20619 | + | 9.28077i | −0.115636 | + | 0.486445i | ||||
\(365\) | −12.7659 | −0.668195 | ||||||||
\(366\) | −0.351145 | − | 0.351145i | −0.0183546 | − | 0.0183546i | ||||
\(367\) | − | 4.26926i | − | 0.222853i | −0.993773 | − | 0.111427i | \(-0.964458\pi\) | ||
0.993773 | − | 0.111427i | \(-0.0355420\pi\) | |||||||
\(368\) | 7.37727i | 0.384567i | ||||||||
\(369\) | 6.11650 | − | 6.11650i | 0.318412 | − | 0.318412i | ||||
\(370\) | 9.02682 | − | 9.02682i | 0.469282 | − | 0.469282i | ||||
\(371\) | −8.26926 | + | 7.69449i | −0.429318 | + | 0.399478i | ||||
\(372\) | 5.73923 | − | 5.73923i | 0.297565 | − | 0.297565i | ||||
\(373\) | 9.67146 | 0.500769 | 0.250385 | − | 0.968146i | \(-0.419443\pi\) | ||||
0.250385 | + | 0.968146i | \(0.419443\pi\) | |||||||
\(374\) | 0.657997 | 0.0340242 | ||||||||
\(375\) | −6.31420 | + | 6.31420i | −0.326064 | + | 0.326064i | ||||
\(376\) | −8.30690 | −0.428395 | ||||||||
\(377\) | 14.5023 | + | 21.7534i | 0.746905 | + | 1.12036i | ||||
\(378\) | 0.0951965 | − | 2.64404i | 0.00489638 | − | 0.135995i | ||||
\(379\) | −0.746047 | − | 0.746047i | −0.0383218 | − | 0.0383218i | 0.687686 | − | 0.726008i | \(-0.258627\pi\) |
−0.726008 | + | 0.687686i | \(0.758627\pi\) | |||||||
\(380\) | −11.0718 | −0.567969 | ||||||||
\(381\) | 19.8376 | 1.01631 | ||||||||
\(382\) | 13.2857 | + | 13.2857i | 0.679758 | + | 0.679758i | ||||
\(383\) | 18.1461 | − | 18.1461i | 0.927225 | − | 0.927225i | −0.0703012 | − | 0.997526i | \(-0.522396\pi\) |
0.997526 | + | 0.0703012i | \(0.0223960\pi\) | |||||||
\(384\) | 0.707107 | + | 0.707107i | 0.0360844 | + | 0.0360844i | ||||
\(385\) | 6.08686 | + | 6.54154i | 0.310215 | + | 0.333388i | ||||
\(386\) | −1.93812 | −0.0986476 | ||||||||
\(387\) | 6.85574i | 0.348497i | ||||||||
\(388\) | 9.46034 | + | 9.46034i | 0.480276 | + | 0.480276i | ||||
\(389\) | − | 6.73756i | − | 0.341608i | −0.985305 | − | 0.170804i | \(-0.945364\pi\) | ||
0.985305 | − | 0.170804i | \(-0.0546364\pi\) | |||||||
\(390\) | 7.64653 | − | 5.09768i | 0.387197 | − | 0.258131i | ||||
\(391\) | 3.66351i | 0.185271i | ||||||||
\(392\) | −4.58097 | − | 5.29289i | −0.231374 | − | 0.267331i | ||||
\(393\) | −5.10801 | −0.257665 | ||||||||
\(394\) | 4.05225i | 0.204149i | ||||||||
\(395\) | 23.7002 | − | 23.7002i | 1.19248 | − | 1.19248i | ||||
\(396\) | −0.936931 | − | 0.936931i | −0.0470826 | − | 0.0470826i | ||||
\(397\) | −21.7715 | − | 21.7715i | −1.09268 | − | 1.09268i | −0.995241 | − | 0.0974398i | \(-0.968935\pi\) |
−0.0974398 | − | 0.995241i | \(-0.531065\pi\) | |||||||
\(398\) | 9.94542 | + | 9.94542i | 0.498519 | + | 0.498519i | ||||
\(399\) | −11.4853 | − | 0.413518i | −0.574983 | − | 0.0207018i | ||||
\(400\) | 1.49659i | 0.0748297i | ||||||||
\(401\) | 16.5119 | − | 16.5119i | 0.824565 | − | 0.824565i | −0.162194 | − | 0.986759i | \(-0.551857\pi\) |
0.986759 | + | 0.162194i | \(0.0518571\pi\) | |||||||
\(402\) | −12.8927 | −0.643029 | ||||||||
\(403\) | 28.6962 | + | 5.73923i | 1.42946 | + | 0.285892i | ||||
\(404\) | − | 4.66465i | − | 0.232075i | ||||||
\(405\) | −1.80230 | + | 1.80230i | −0.0895572 | + | 0.0895572i | ||||
\(406\) | −19.1723 | − | 0.690282i | −0.951504 | − | 0.0342581i | ||||
\(407\) | − | 6.63636i | − | 0.328952i | ||||||
\(408\) | 0.351145 | + | 0.351145i | 0.0173843 | + | 0.0173843i | ||||
\(409\) | 4.00379 | − | 4.00379i | 0.197975 | − | 0.197975i | −0.601157 | − | 0.799131i | \(-0.705293\pi\) |
0.799131 | + | 0.601157i | \(0.205293\pi\) | |||||||
\(410\) | −15.5900 | + | 15.5900i | −0.769935 | + | 0.769935i | ||||
\(411\) | −3.80230 | − | 3.80230i | −0.187554 | − | 0.187554i | ||||
\(412\) | − | 18.5865i | − | 0.915690i | ||||||
\(413\) | −5.14993 | − | 0.185419i | −0.253412 | − | 0.00912388i | ||||
\(414\) | 5.21652 | − | 5.21652i | 0.256378 | − | 0.256378i | ||||
\(415\) | 28.3822i | 1.39323i | ||||||||
\(416\) | −0.707107 | + | 3.53553i | −0.0346688 | + | 0.173344i | ||||
\(417\) | 2.93996 | 0.143970 | ||||||||
\(418\) | −4.06988 | + | 4.06988i | −0.199064 | + | 0.199064i | ||||
\(419\) | − | 15.1782i | − | 0.741505i | −0.928732 | − | 0.370752i | \(-0.879100\pi\) | ||
0.928732 | − | 0.370752i | \(-0.120900\pi\) | |||||||
\(420\) | −0.242641 | + | 6.73923i | −0.0118397 | + | 0.328841i | ||||
\(421\) | 11.0650 | + | 11.0650i | 0.539273 | + | 0.539273i | 0.923315 | − | 0.384043i | \(-0.125468\pi\) |
−0.384043 | + | 0.923315i | \(0.625468\pi\) | |||||||
\(422\) | 10.5046 | + | 10.5046i | 0.511356 | + | 0.511356i | ||||
\(423\) | 5.87386 | + | 5.87386i | 0.285597 | + | 0.285597i | ||||
\(424\) | −3.01882 | + | 3.01882i | −0.146607 | + | 0.146607i | ||||
\(425\) | 0.743199i | 0.0360505i | ||||||||
\(426\) | −16.0899 | −0.779558 | ||||||||
\(427\) | 0.895013 | + | 0.961868i | 0.0433127 | + | 0.0465481i | ||||
\(428\) | 6.95694i | 0.336276i | ||||||||
\(429\) | 0.936931 | − | 4.68466i | 0.0452355 | − | 0.226177i | ||||
\(430\) | − | 17.4742i | − | 0.842680i | ||||||
\(431\) | 9.60461 | + | 9.60461i | 0.462638 | + | 0.462638i | 0.899519 | − | 0.436881i | \(-0.143917\pi\) |
−0.436881 | + | 0.899519i | \(0.643917\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | −6.52489 | −0.313566 | −0.156783 | − | 0.987633i | \(-0.550112\pi\) | ||||
−0.156783 | + | 0.987633i | \(0.550112\pi\) | |||||||
\(434\) | −15.7211 | + | 14.6284i | −0.754637 | + | 0.702186i | ||||
\(435\) | 13.0687 | + | 13.0687i | 0.626598 | + | 0.626598i | ||||
\(436\) | −2.94374 | + | 2.94374i | −0.140980 | + | 0.140980i | ||||
\(437\) | −22.6597 | − | 22.6597i | −1.08396 | − | 1.08396i | ||||
\(438\) | −5.00849 | −0.239315 | ||||||||
\(439\) | 1.61592 | 0.0771236 | 0.0385618 | − | 0.999256i | \(-0.487722\pi\) | ||||
0.0385618 | + | 0.999256i | \(0.487722\pi\) | |||||||
\(440\) | 2.38809 | + | 2.38809i | 0.113848 | + | 0.113848i | ||||
\(441\) | −0.503406 | + | 6.98188i | −0.0239717 | + | 0.332470i | ||||
\(442\) | −0.351145 | + | 1.75572i | −0.0167023 | + | 0.0835113i | ||||
\(443\) | −19.0408 | −0.904655 | −0.452327 | − | 0.891852i | \(-0.649406\pi\) | ||||
−0.452327 | + | 0.891852i | \(0.649406\pi\) | |||||||
\(444\) | 3.54154 | − | 3.54154i | 0.168074 | − | 0.168074i | ||||
\(445\) | −36.8308 | −1.74595 | ||||||||
\(446\) | −8.83806 | −0.418494 | ||||||||
\(447\) | −1.74605 | + | 1.74605i | −0.0825852 | + | 0.0825852i | ||||
\(448\) | −1.80230 | − | 1.93693i | −0.0851508 | − | 0.0915114i | ||||
\(449\) | −10.3408 | + | 10.3408i | −0.488013 | + | 0.488013i | −0.907679 | − | 0.419666i | \(-0.862147\pi\) |
0.419666 | + | 0.907679i | \(0.362147\pi\) | |||||||
\(450\) | 1.05825 | − | 1.05825i | 0.0498865 | − | 0.0498865i | ||||
\(451\) | 11.4615i | 0.539700i | ||||||||
\(452\) | − | 2.93996i | − | 0.138284i | ||||||
\(453\) | 6.55003 | + | 6.55003i | 0.307747 | + | 0.307747i | ||||
\(454\) | 7.78299 | 0.365274 | ||||||||
\(455\) | −20.7030 | + | 12.7505i | −0.970571 | + | 0.597755i | ||||
\(456\) | −4.34384 | −0.203419 | ||||||||
\(457\) | 20.0718 | + | 20.0718i | 0.938917 | + | 0.938917i | 0.998239 | − | 0.0593215i | \(-0.0188937\pi\) |
−0.0593215 | + | 0.998239i | \(0.518894\pi\) | |||||||
\(458\) | 3.54035i | 0.165430i | ||||||||
\(459\) | − | 0.496594i | − | 0.0231790i | ||||||
\(460\) | −13.2961 | + | 13.2961i | −0.619933 | + | 0.619933i | ||||
\(461\) | −13.4069 | + | 13.4069i | −0.624422 | + | 0.624422i | −0.946659 | − | 0.322237i | \(-0.895565\pi\) |
0.322237 | + | 0.946659i | \(0.395565\pi\) | |||||||
\(462\) | 2.38809 | + | 2.56647i | 0.111104 | + | 0.119403i | ||||
\(463\) | −17.7592 | + | 17.7592i | −0.825342 | + | 0.825342i | −0.986868 | − | 0.161526i | \(-0.948358\pi\) |
0.161526 | + | 0.986868i | \(0.448358\pi\) | |||||||
\(464\) | −7.25113 | −0.336625 | ||||||||
\(465\) | 20.6877 | 0.959368 | ||||||||
\(466\) | −11.7108 | + | 11.7108i | −0.542491 | + | 0.542491i | ||||
\(467\) | 39.5072 | 1.82817 | 0.914087 | − | 0.405518i | \(-0.132909\pi\) | ||||
0.914087 | + | 0.405518i | \(0.132909\pi\) | |||||||
\(468\) | 3.00000 | − | 2.00000i | 0.138675 | − | 0.0924500i | ||||
\(469\) | 34.0887 | + | 1.22734i | 1.57407 | + | 0.0566732i | ||||
\(470\) | −14.9715 | − | 14.9715i | −0.690586 | − | 0.690586i | ||||
\(471\) | −1.70581 | −0.0785994 | ||||||||
\(472\) | −1.94775 | −0.0896526 | ||||||||
\(473\) | −6.42336 | − | 6.42336i | −0.295346 | − | 0.295346i | ||||
\(474\) | 9.29841 | − | 9.29841i | 0.427090 | − | 0.427090i | ||||
\(475\) | −4.59688 | − | 4.59688i | −0.210919 | − | 0.210919i | ||||
\(476\) | −0.895013 | − | 0.961868i | −0.0410228 | − | 0.0440872i | ||||
\(477\) | 4.26926 | 0.195476 | ||||||||
\(478\) | 3.41161i | 0.156044i | ||||||||
\(479\) | 20.1768 | + | 20.1768i | 0.921899 | + | 0.921899i | 0.997164 | − | 0.0752644i | \(-0.0239801\pi\) |
−0.0752644 | + | 0.997164i | \(0.523980\pi\) | |||||||
\(480\) | 2.54884i | 0.116338i | ||||||||
\(481\) | 17.7077 | + | 3.54154i | 0.807401 | + | 0.161480i | ||||
\(482\) | 11.8472i | 0.539627i | ||||||||
\(483\) | −14.2893 | + | 13.2961i | −0.650184 | + | 0.604992i | ||||
\(484\) | −9.24432 | −0.420196 | ||||||||
\(485\) | 34.1008i | 1.54844i | ||||||||
\(486\) | −0.707107 | + | 0.707107i | −0.0320750 | + | 0.0320750i | ||||
\(487\) | −14.5837 | − | 14.5837i | −0.660849 | − | 0.660849i | 0.294731 | − | 0.955580i | \(-0.404770\pi\) |
−0.955580 | + | 0.294731i | \(0.904770\pi\) | |||||||
\(488\) | 0.351145 | + | 0.351145i | 0.0158956 | + | 0.0158956i | ||||
\(489\) | 4.23583 | + | 4.23583i | 0.191551 | + | 0.191551i | ||||
\(490\) | 1.28310 | − | 17.7957i | 0.0579647 | − | 0.803928i | ||||
\(491\) | − | 10.3591i | − | 0.467502i | −0.972297 | − | 0.233751i | \(-0.924900\pi\) | ||
0.972297 | − | 0.233751i | \(-0.0751000\pi\) | |||||||
\(492\) | −6.11650 | + | 6.11650i | −0.275753 | + | 0.275753i | ||||
\(493\) | −3.60087 | −0.162175 | ||||||||
\(494\) | −8.68768 | − | 13.0315i | −0.390877 | − | 0.586316i | ||||
\(495\) | − | 3.37727i | − | 0.151797i | ||||||
\(496\) | −5.73923 | + | 5.73923i | −0.257699 | + | 0.257699i | ||||
\(497\) | 42.5423 | + | 1.53170i | 1.90828 | + | 0.0687061i | ||||
\(498\) | 11.1353i | 0.498986i | ||||||||
\(499\) | 30.2834 | + | 30.2834i | 1.35567 | + | 1.35567i | 0.879178 | + | 0.476494i | \(0.158093\pi\) |
0.476494 | + | 0.879178i | \(0.341907\pi\) | |||||||
\(500\) | 6.31420 | − | 6.31420i | 0.282380 | − | 0.282380i | ||||
\(501\) | 8.02001 | − | 8.02001i | 0.358307 | − | 0.358307i | ||||
\(502\) | −19.0019 | − | 19.0019i | −0.848096 | − | 0.848096i | ||||
\(503\) | − | 12.0000i | − | 0.535054i | −0.963550 | − | 0.267527i | \(-0.913794\pi\) | ||
0.963550 | − | 0.267527i | \(-0.0862064\pi\) | |||||||
\(504\) | −0.0951965 | + | 2.64404i | −0.00424039 | + | 0.117775i | ||||
\(505\) | 8.40711 | − | 8.40711i | 0.374112 | − | 0.374112i | ||||
\(506\) | 9.77504i | 0.434553i | ||||||||
\(507\) | 12.0000 | + | 5.00000i | 0.532939 | + | 0.222058i | ||||
\(508\) | −19.8376 | −0.880152 | ||||||||
\(509\) | −27.9685 | + | 27.9685i | −1.23968 | + | 1.23968i | −0.279548 | + | 0.960132i | \(0.590185\pi\) |
−0.960132 | + | 0.279548i | \(0.909815\pi\) | |||||||
\(510\) | 1.26574i | 0.0560479i | ||||||||
\(511\) | 13.2426 | + | 0.476791i | 0.585820 | + | 0.0210920i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 3.07156 | + | 3.07156i | 0.135613 | + | 0.135613i | ||||
\(514\) | −5.64485 | − | 5.64485i | −0.248984 | − | 0.248984i | ||||
\(515\) | 33.4985 | − | 33.4985i | 1.47612 | − | 1.47612i | ||||
\(516\) | − | 6.85574i | − | 0.301807i | ||||||
\(517\) | −11.0068 | −0.484079 | ||||||||
\(518\) | −9.70110 | + | 9.02682i | −0.426242 | + | 0.396616i | ||||
\(519\) | − | 4.21603i | − | 0.185063i | ||||||
\(520\) | −7.64653 | + | 5.09768i | −0.335322 | + | 0.223548i | ||||
\(521\) | 18.7160i | 0.819962i | 0.912094 | + | 0.409981i | \(0.134465\pi\) | ||||
−0.912094 | + | 0.409981i | \(0.865535\pi\) | |||||||
\(522\) | 5.12732 | + | 5.12732i | 0.224417 | + | 0.224417i | ||||
\(523\) | 5.69449i | 0.249003i | 0.992219 | + | 0.124501i | \(0.0397331\pi\) | ||||
−0.992219 | + | 0.124501i | \(0.960267\pi\) | |||||||
\(524\) | 5.10801 | 0.223145 | ||||||||
\(525\) | −2.89880 | + | 2.69732i | −0.126514 | + | 0.117721i | ||||
\(526\) | 1.74773 | + | 1.74773i | 0.0762044 | + | 0.0762044i | ||||
\(527\) | −2.85007 | + | 2.85007i | −0.124151 | + | 0.124151i | ||||
\(528\) | 0.936931 | + | 0.936931i | 0.0407747 | + | 0.0407747i | ||||
\(529\) | −31.4241 | −1.36626 | ||||||||
\(530\) | −10.8817 | −0.472669 | ||||||||
\(531\) | 1.37727 | + | 1.37727i | 0.0597684 | + | 0.0597684i | ||||
\(532\) | 11.4853 | + | 0.413518i | 0.497950 | + | 0.0179283i | ||||
\(533\) | −30.5825 | − | 6.11650i | −1.32468 | − | 0.264935i | ||||
\(534\) | −14.4500 | −0.625313 | ||||||||
\(535\) | −12.5385 | + | 12.5385i | −0.542087 | + | 0.542087i | ||||
\(536\) | 12.8927 | 0.556879 | ||||||||
\(537\) | 5.33535 | 0.230237 | ||||||||
\(538\) | 4.12782 | − | 4.12782i | 0.177963 | − | 0.177963i | ||||
\(539\) | −6.06988 | − | 7.01319i | −0.261448 | − | 0.302080i | ||||
\(540\) | 1.80230 | − | 1.80230i | 0.0775588 | − | 0.0775588i | ||||
\(541\) | 6.48149 | − | 6.48149i | 0.278661 | − | 0.278661i | −0.553913 | − | 0.832574i | \(-0.686866\pi\) |
0.832574 | + | 0.553913i | \(0.186866\pi\) | |||||||
\(542\) | 12.1311i | 0.521076i | ||||||||
\(543\) | − | 1.79760i | − | 0.0771424i | ||||||
\(544\) | −0.351145 | − | 0.351145i | −0.0150552 | − | 0.0150552i | ||||
\(545\) | −10.6110 | −0.454527 | ||||||||
\(546\) | −8.12251 | + | 5.00249i | −0.347611 | + | 0.214087i | ||||
\(547\) | 39.5294 | 1.69016 | 0.845078 | − | 0.534643i | \(-0.179554\pi\) | ||||
0.845078 | + | 0.534643i | \(0.179554\pi\) | |||||||
\(548\) | 3.80230 | + | 3.80230i | 0.162426 | + | 0.162426i | ||||
\(549\) | − | 0.496594i | − | 0.0211941i | ||||||
\(550\) | 1.98302i | 0.0845562i | ||||||||
\(551\) | 22.2723 | − | 22.2723i | 0.948831 | − | 0.948831i | ||||
\(552\) | −5.21652 | + | 5.21652i | −0.222030 | + | 0.222030i | ||||
\(553\) | −25.4705 | + | 23.7002i | −1.08312 | + | 1.00783i | ||||
\(554\) | −1.88419 | + | 1.88419i | −0.0800516 | + | 0.0800516i | ||||
\(555\) | 12.7659 | 0.541880 | ||||||||
\(556\) | −2.93996 | −0.124682 | ||||||||
\(557\) | −0.806090 | + | 0.806090i | −0.0341551 | + | 0.0341551i | −0.723978 | − | 0.689823i | \(-0.757688\pi\) |
0.689823 | + | 0.723978i | \(0.257688\pi\) | |||||||
\(558\) | 8.11650 | 0.343599 | ||||||||
\(559\) | 20.5672 | − | 13.7115i | 0.869900 | − | 0.579934i | ||||
\(560\) | 0.242641 | − | 6.73923i | 0.0102534 | − | 0.284785i | ||||
\(561\) | 0.465274 | + | 0.465274i | 0.0196439 | + | 0.0196439i | ||||
\(562\) | 11.4545 | 0.483177 | ||||||||
\(563\) | −44.4350 | −1.87271 | −0.936357 | − | 0.351050i | \(-0.885825\pi\) | ||||
−0.936357 | + | 0.351050i | \(0.885825\pi\) | |||||||
\(564\) | −5.87386 | − | 5.87386i | −0.247334 | − | 0.247334i | ||||
\(565\) | 5.29869 | − | 5.29869i | 0.222918 | − | 0.222918i | ||||
\(566\) | 21.4063 | + | 21.4063i | 0.899772 | + | 0.899772i | ||||
\(567\) | 1.93693 | − | 1.80230i | 0.0813435 | − | 0.0756896i | ||||
\(568\) | 16.0899 | 0.675117 | ||||||||
\(569\) | 5.40826i | 0.226726i | 0.993554 | + | 0.113363i | \(0.0361623\pi\) | ||||
−0.993554 | + | 0.113363i | \(0.963838\pi\) | |||||||
\(570\) | −7.82892 | − | 7.82892i | −0.327917 | − | 0.327917i | ||||
\(571\) | 2.46830i | 0.103295i | 0.998665 | + | 0.0516476i | \(0.0164472\pi\) | ||||
−0.998665 | + | 0.0516476i | \(0.983553\pi\) | |||||||
\(572\) | −0.936931 | + | 4.68466i | −0.0391751 | + | 0.195875i | ||||
\(573\) | 18.7889i | 0.784917i | ||||||||
\(574\) | 16.7545 | − | 15.5900i | 0.699321 | − | 0.650714i | ||||
\(575\) | −11.0408 | −0.460432 | ||||||||
\(576\) | 1.00000i | 0.0416667i | ||||||||
\(577\) | 27.0650 | − | 27.0650i | 1.12673 | − | 1.12673i | 0.136023 | − | 0.990706i | \(-0.456568\pi\) |
0.990706 | − | 0.136023i | \(-0.0434321\pi\) | |||||||
\(578\) | 11.8464 | + | 11.8464i | 0.492747 | + | 0.492747i | ||||
\(579\) | −1.37046 | − | 1.37046i | −0.0569542 | − | 0.0569542i | ||||
\(580\) | −13.0687 | − | 13.0687i | −0.542650 | − | 0.542650i | ||||
\(581\) | 1.06004 | − | 29.4422i | 0.0439780 | − | 1.22147i | ||||
\(582\) | 13.3789i | 0.554575i | ||||||||
\(583\) | −4.00000 | + | 4.00000i | −0.165663 | + | 0.165663i | ||||
\(584\) | 5.00849 | 0.207253 | ||||||||
\(585\) | 9.01152 | + | 1.80230i | 0.372580 | + | 0.0745161i | ||||
\(586\) | 25.3477i | 1.04710i | ||||||||
\(587\) | −10.6533 | + | 10.6533i | −0.439710 | + | 0.439710i | −0.891914 | − | 0.452204i | \(-0.850638\pi\) |
0.452204 | + | 0.891914i | \(0.350638\pi\) | |||||||
\(588\) | 0.503406 | − | 6.98188i | 0.0207601 | − | 0.287928i | ||||
\(589\) | − | 35.2568i | − | 1.45273i | ||||||
\(590\) | −3.51044 | − | 3.51044i | −0.144523 | − | 0.144523i | ||||
\(591\) | −2.86537 | + | 2.86537i | −0.117866 | + | 0.117866i | ||||
\(592\) | −3.54154 | + | 3.54154i | −0.145556 | + | 0.145556i | ||||
\(593\) | 11.4938 | + | 11.4938i | 0.471993 | + | 0.471993i | 0.902559 | − | 0.430566i | \(-0.141686\pi\) |
−0.430566 | + | 0.902559i | \(0.641686\pi\) | |||||||
\(594\) | − | 1.32502i | − | 0.0543663i | ||||||
\(595\) | 0.120494 | − | 3.34666i | 0.00493977 | − | 0.137200i | ||||
\(596\) | 1.74605 | − | 1.74605i | 0.0715209 | − | 0.0715209i | ||||
\(597\) | 14.0650i | 0.575640i | ||||||||
\(598\) | −26.0826 | − | 5.21652i | −1.06660 | − | 0.213319i | ||||
\(599\) | −30.3149 | −1.23863 | −0.619317 | − | 0.785141i | \(-0.712591\pi\) | ||||
−0.619317 | + | 0.785141i | \(0.712591\pi\) | |||||||
\(600\) | −1.05825 | + | 1.05825i | −0.0432029 | + | 0.0432029i | ||||
\(601\) | 11.9638i | 0.488012i | 0.969774 | + | 0.244006i | \(0.0784616\pi\) | ||||
−0.969774 | + | 0.244006i | \(0.921538\pi\) | |||||||
\(602\) | −0.652642 | + | 18.1268i | −0.0265997 | + | 0.738795i | ||||
\(603\) | −9.11650 | − | 9.11650i | −0.371253 | − | 0.371253i | ||||
\(604\) | −6.55003 | − | 6.55003i | −0.266517 | − | 0.266517i | ||||
\(605\) | −16.6611 | − | 16.6611i | −0.677369 | − | 0.677369i | ||||
\(606\) | 3.29841 | − | 3.29841i | 0.133989 | − | 0.133989i | ||||
\(607\) | 41.6103i | 1.68891i | 0.535627 | + | 0.844454i | \(0.320075\pi\) | ||||
−0.535627 | + | 0.844454i | \(0.679925\pi\) | |||||||
\(608\) | 4.34384 | 0.176166 | ||||||||
\(609\) | −13.0687 | − | 14.0449i | −0.529572 | − | 0.569130i | ||||
\(610\) | 1.26574i | 0.0512483i | ||||||||
\(611\) | 5.87386 | − | 29.3693i | 0.237631 | − | 1.18816i | ||||
\(612\) | 0.496594i | 0.0200736i | ||||||||
\(613\) | −27.9736 | − | 27.9736i | −1.12984 | − | 1.12984i | −0.990202 | − | 0.139640i | \(-0.955405\pi\) |
−0.139640 | − | 0.990202i | \(-0.544595\pi\) | |||||||
\(614\) | 7.20056i | 0.290591i | ||||||||
\(615\) | −22.0476 | −0.889045 | ||||||||
\(616\) | −2.38809 | − | 2.56647i | −0.0962189 | − | 0.103406i | ||||
\(617\) | 15.7830 | + | 15.7830i | 0.635401 | + | 0.635401i | 0.949418 | − | 0.314016i | \(-0.101675\pi\) |
−0.314016 | + | 0.949418i | \(0.601675\pi\) | |||||||
\(618\) | 13.1426 | − | 13.1426i | 0.528674 | − | 0.528674i | ||||
\(619\) | −0.473765 | − | 0.473765i | −0.0190422 | − | 0.0190422i | 0.697522 | − | 0.716564i | \(-0.254286\pi\) |
−0.716564 | + | 0.697522i | \(0.754286\pi\) | |||||||
\(620\) | −20.6877 | −0.830837 | ||||||||
\(621\) | 7.37727 | 0.296040 | ||||||||
\(622\) | 9.95105 | + | 9.95105i | 0.399001 | + | 0.399001i | ||||
\(623\) | 38.2064 | + | 1.37559i | 1.53071 | + | 0.0551119i | ||||
\(624\) | −3.00000 | + | 2.00000i | −0.120096 | + | 0.0800641i | ||||
\(625\) | 30.2432 | 1.20973 | ||||||||
\(626\) | 20.0153 | − | 20.0153i | 0.799972 | − | 0.799972i | ||||
\(627\) | −5.75568 | −0.229860 | ||||||||
\(628\) | 1.70581 | 0.0680691 | ||||||||
\(629\) | −1.75871 | + | 1.75871i | −0.0701242 | + | 0.0701242i | ||||
\(630\) | −4.93693 | + | 4.59379i | −0.196692 | + | 0.183021i | ||||
\(631\) | −30.2978 | + | 30.2978i | −1.20613 | + | 1.20613i | −0.233866 | + | 0.972269i | \(0.575138\pi\) |
−0.972269 | + | 0.233866i | \(0.924862\pi\) | |||||||
\(632\) | −9.29841 | + | 9.29841i | −0.369871 | + | 0.369871i | ||||
\(633\) | 14.8557i | 0.590463i | ||||||||
\(634\) | − | 29.0082i | − | 1.15206i | ||||||
\(635\) | −35.7534 | − | 35.7534i | −1.41883 | − | 1.41883i | ||||
\(636\) | −4.26926 | −0.169287 | ||||||||
\(637\) | 21.9524 | − | 12.4535i | 0.869787 | − | 0.493427i | ||||
\(638\) | −9.60790 | −0.380380 | ||||||||
\(639\) | −11.3773 | − | 11.3773i | −0.450078 | − | 0.450078i | ||||
\(640\) | − | 2.54884i | − | 0.100752i | ||||||
\(641\) | 5.40556i | 0.213507i | 0.994286 | + | 0.106753i | \(0.0340456\pi\) | ||||
−0.994286 | + | 0.106753i | \(0.965954\pi\) | |||||||
\(642\) | −4.91930 | + | 4.91930i | −0.194149 | + | 0.194149i | ||||
\(643\) | 9.08518 | − | 9.08518i | 0.358285 | − | 0.358285i | −0.504896 | − | 0.863180i | \(-0.668469\pi\) |
0.863180 | + | 0.504896i | \(0.168469\pi\) | |||||||
\(644\) | 14.2893 | − | 13.2961i | 0.563076 | − | 0.523939i | ||||
\(645\) | 12.3561 | − | 12.3561i | 0.486522 | − | 0.486522i | ||||
\(646\) | 2.15712 | 0.0848709 | ||||||||
\(647\) | 15.0468 | 0.591552 | 0.295776 | − | 0.955257i | \(-0.404422\pi\) | ||||
0.295776 | + | 0.955257i | \(0.404422\pi\) | |||||||
\(648\) | 0.707107 | − | 0.707107i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | −2.58081 | −0.101306 | ||||||||
\(650\) | −5.29126 | − | 1.05825i | −0.207540 | − | 0.0415080i | ||||
\(651\) | −21.4603 | − | 0.772662i | −0.841097 | − | 0.0302830i | ||||
\(652\) | −4.23583 | − | 4.23583i | −0.165888 | − | 0.165888i | ||||
\(653\) | 6.17411 | 0.241611 | 0.120806 | − | 0.992676i | \(-0.461452\pi\) | ||||
0.120806 | + | 0.992676i | \(0.461452\pi\) | |||||||
\(654\) | −4.16308 | −0.162789 | ||||||||
\(655\) | 9.20619 | + | 9.20619i | 0.359716 | + | 0.359716i | ||||
\(656\) | 6.11650 | − | 6.11650i | 0.238809 | − | 0.238809i | ||||
\(657\) | −3.54154 | − | 3.54154i | −0.138169 | − | 0.138169i | ||||
\(658\) | 14.9715 | + | 16.0899i | 0.583652 | + | 0.627249i | ||||
\(659\) | 2.70131 | 0.105228 | 0.0526140 | − | 0.998615i | \(-0.483245\pi\) | ||||
0.0526140 | + | 0.998615i | \(0.483245\pi\) | |||||||
\(660\) | 3.37727i | 0.131460i | ||||||||
\(661\) | 15.1148 | + | 15.1148i | 0.587899 | + | 0.587899i | 0.937062 | − | 0.349163i | \(-0.113534\pi\) |
−0.349163 | + | 0.937062i | \(0.613534\pi\) | |||||||
\(662\) | 13.6543i | 0.530688i | ||||||||
\(663\) | −1.48978 | + | 0.993188i | −0.0578583 | + | 0.0385722i | ||||
\(664\) | − | 11.1353i | − | 0.432134i | ||||||
\(665\) | 19.9547 | + | 21.4452i | 0.773809 | + | 0.831611i | ||||
\(666\) | 5.00849 | 0.194075 | ||||||||
\(667\) | − | 53.4935i | − | 2.07128i | ||||||
\(668\) | −8.02001 | + | 8.02001i | −0.310303 | + | 0.310303i | ||||
\(669\) | −6.24945 | − | 6.24945i | −0.241618 | − | 0.241618i | ||||
\(670\) | 23.2365 | + | 23.2365i | 0.897705 | + | 0.897705i | ||||
\(671\) | 0.465274 | + | 0.465274i | 0.0179617 | + | 0.0179617i | ||||
\(672\) | 0.0951965 | − | 2.64404i | 0.00367228 | − | 0.101996i | ||||
\(673\) | 18.7262i | 0.721844i | 0.932596 | + | 0.360922i | \(0.117538\pi\) | ||||
−0.932596 | + | 0.360922i | \(0.882462\pi\) | |||||||
\(674\) | −5.12732 | + | 5.12732i | −0.197497 | + | 0.197497i | ||||
\(675\) | 1.49659 | 0.0576039 | ||||||||
\(676\) | −12.0000 | − | 5.00000i | −0.461538 | − | 0.192308i | ||||
\(677\) | 25.6884i | 0.987287i | 0.869664 | + | 0.493644i | \(0.164335\pi\) | ||||
−0.869664 | + | 0.493644i | \(0.835665\pi\) | |||||||
\(678\) | 2.07886 | − | 2.07886i | 0.0798383 | − | 0.0798383i | ||||
\(679\) | 1.27363 | − | 35.3744i | 0.0488774 | − | 1.35755i | ||||
\(680\) | − | 1.26574i | − | 0.0485389i | ||||||
\(681\) | 5.50341 | + | 5.50341i | 0.210891 | + | 0.210891i | ||||
\(682\) | −7.60461 | + | 7.60461i | −0.291195 | + | 0.291195i | ||||
\(683\) | 10.6677 | − | 10.6677i | 0.408187 | − | 0.408187i | −0.472919 | − | 0.881106i | \(-0.656800\pi\) |
0.881106 | + | 0.472919i | \(0.156800\pi\) | |||||||
\(684\) | −3.07156 | − | 3.07156i | −0.117444 | − | 0.117444i | ||||
\(685\) | 13.7058i | 0.523672i | ||||||||
\(686\) | −1.99567 | + | 18.4124i | −0.0761952 | + | 0.702990i | ||||
\(687\) | −2.50341 | + | 2.50341i | −0.0955109 | + | 0.0955109i | ||||
\(688\) | 6.85574i | 0.261373i | ||||||||
\(689\) | −8.53851 | − | 12.8078i | −0.325291 | − | 0.487937i | ||||
\(690\) | −18.8035 | −0.715837 | ||||||||
\(691\) | −18.7630 | + | 18.7630i | −0.713779 | + | 0.713779i | −0.967324 | − | 0.253544i | \(-0.918404\pi\) |
0.253544 | + | 0.967324i | \(0.418404\pi\) | |||||||
\(692\) | 4.21603i | 0.160269i | ||||||||
\(693\) | −0.126137 | + | 3.50341i | −0.00479156 | + | 0.133083i | ||||
\(694\) | −21.0468 | − | 21.0468i | −0.798927 | − | 0.798927i | ||||
\(695\) | −5.29869 | − | 5.29869i | −0.200991 | − | 0.200991i | ||||
\(696\) | −5.12732 | − | 5.12732i | −0.194351 | − | 0.194351i | ||||
\(697\) | 3.03742 | − | 3.03742i | 0.115050 | − | 0.115050i | ||||
\(698\) | − | 18.5872i | − | 0.703535i | ||||||
\(699\) | −16.5615 | −0.626415 | ||||||||
\(700\) | 2.89880 | − | 2.69732i | 0.109564 | − | 0.101949i | ||||
\(701\) | − | 30.4354i | − | 1.14953i | −0.818319 | − | 0.574765i | \(-0.805094\pi\) | ||
0.818319 | − | 0.574765i | \(-0.194906\pi\) | |||||||
\(702\) | 3.53553 | + | 0.707107i | 0.133440 | + | 0.0266880i | ||||
\(703\) | − | 21.7561i | − | 0.820546i | ||||||
\(704\) | −0.936931 | − | 0.936931i | −0.0353119 | − | 0.0353119i | ||||
\(705\) | − | 21.1730i | − | 0.797420i | ||||||
\(706\) | 19.1669 | 0.721356 | ||||||||
\(707\) | −9.03511 | + | 8.40711i | −0.339800 | + | 0.316182i | ||||
\(708\) | −1.37727 | − | 1.37727i | −0.0517609 | − | 0.0517609i | ||||
\(709\) | −31.7070 | + | 31.7070i | −1.19078 | + | 1.19078i | −0.213932 | + | 0.976849i | \(0.568627\pi\) |
−0.976849 | + | 0.213932i | \(0.931373\pi\) | |||||||
\(710\) | 28.9989 | + | 28.9989i | 1.08831 | + | 1.08831i | ||||
\(711\) | 13.1499 | 0.493161 | ||||||||
\(712\) | 14.4500 | 0.541537 | ||||||||
\(713\) | −42.3399 | − | 42.3399i | −1.58564 | − | 1.58564i | ||||
\(714\) | 0.0472740 | − | 1.31301i | 0.00176918 | − | 0.0491383i | ||||
\(715\) | −10.1318 | + | 6.75454i | −0.378908 | + | 0.252605i | ||||
\(716\) | −5.33535 | −0.199391 | ||||||||
\(717\) | −2.41238 | + | 2.41238i | −0.0900918 | + | 0.0900918i | ||||
\(718\) | 5.71614 | 0.213324 | ||||||||
\(719\) | −0.575169 | −0.0214502 | −0.0107251 | − | 0.999942i | \(-0.503414\pi\) | ||||
−0.0107251 | + | 0.999942i | \(0.503414\pi\) | |||||||
\(720\) | −1.80230 | + | 1.80230i | −0.0671679 | + | 0.0671679i | ||||
\(721\) | −36.0007 | + | 33.4985i | −1.34074 | + | 1.24755i | ||||
\(722\) | 0.0926627 | − | 0.0926627i | 0.00344855 | − | 0.00344855i | ||||
\(723\) | −8.37727 | + | 8.37727i | −0.311554 | + | 0.311554i | ||||
\(724\) | 1.79760i | 0.0668073i | ||||||||
\(725\) | − | 10.8520i | − | 0.403033i | ||||||
\(726\) | −6.53672 | − | 6.53672i | −0.242600 | − | 0.242600i | ||||
\(727\) | 32.1850 | 1.19368 | 0.596838 | − | 0.802361i | \(-0.296423\pi\) | ||||
0.596838 | + | 0.802361i | \(0.296423\pi\) | |||||||
\(728\) | 8.12251 | − | 5.00249i | 0.301040 | − | 0.185404i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 9.02682 | + | 9.02682i | 0.334098 | + | 0.334098i | ||||
\(731\) | 3.40452i | 0.125921i | ||||||||
\(732\) | 0.496594i | 0.0183546i | ||||||||
\(733\) | −31.3478 | + | 31.3478i | −1.15786 | + | 1.15786i | −0.172923 | + | 0.984935i | \(0.555321\pi\) |
−0.984935 | + | 0.172923i | \(0.944679\pi\) | |||||||
\(734\) | −3.01882 | + | 3.01882i | −0.111427 | + | 0.111427i | ||||
\(735\) | 13.4907 | − | 11.6762i | 0.497614 | − | 0.430682i | ||||
\(736\) | 5.21652 | − | 5.21652i | 0.192283 | − | 0.192283i | ||||
\(737\) | 17.0831 | 0.629263 | ||||||||
\(738\) | −8.65004 | −0.318412 | ||||||||
\(739\) | 18.7211 | − | 18.7211i | 0.688667 | − | 0.688667i | −0.273270 | − | 0.961937i | \(-0.588105\pi\) |
0.961937 | + | 0.273270i | \(0.0881053\pi\) | |||||||
\(740\) | −12.7659 | −0.469282 | ||||||||
\(741\) | 3.07156 | − | 15.3578i | 0.112837 | − | 0.564183i | ||||
\(742\) | 11.2881 | + | 0.406418i | 0.414398 | + | 0.0149201i | ||||
\(743\) | 20.3172 | + | 20.3172i | 0.745367 | + | 0.745367i | 0.973605 | − | 0.228239i | \(-0.0732966\pi\) |
−0.228239 | + | 0.973605i | \(0.573297\pi\) | |||||||
\(744\) | −8.11650 | −0.297565 | ||||||||
\(745\) | 6.29381 | 0.230587 | ||||||||
\(746\) | −6.83876 | − | 6.83876i | −0.250385 | − | 0.250385i | ||||
\(747\) | −7.87386 | + | 7.87386i | −0.288090 | + | 0.288090i | ||||
\(748\) | −0.465274 | − | 0.465274i | −0.0170121 | − | 0.0170121i | ||||
\(749\) | 13.4751 | − | 12.5385i | 0.492370 | − | 0.458147i | ||||
\(750\) | 8.92963 | 0.326064 | ||||||||
\(751\) | − | 37.6220i | − | 1.37285i | −0.727202 | − | 0.686423i | \(-0.759180\pi\) | ||
0.727202 | − | 0.686423i | \(-0.240820\pi\) | |||||||
\(752\) | 5.87386 | + | 5.87386i | 0.214198 | + | 0.214198i | ||||
\(753\) | − | 26.8727i | − | 0.979296i | ||||||
\(754\) | 5.12732 | − | 25.6366i | 0.186726 | − | 0.933631i | ||||
\(755\) | − | 23.6103i | − | 0.859266i | ||||||
\(756\) | −1.93693 | + | 1.80230i | −0.0704455 | + | 0.0655491i | ||||
\(757\) | 18.5249 | 0.673299 | 0.336649 | − | 0.941630i | \(-0.390706\pi\) | ||||
0.336649 | + | 0.941630i | \(0.390706\pi\) | |||||||
\(758\) | 1.05507i | 0.0383218i | ||||||||
\(759\) | −6.91199 | + | 6.91199i | −0.250890 | + | 0.250890i | ||||
\(760\) | 7.82892 | + | 7.82892i | 0.283985 | + | 0.283985i | ||||
\(761\) | 20.0153 | + | 20.0153i | 0.725554 | + | 0.725554i | 0.969731 | − | 0.244177i | \(-0.0785177\pi\) |
−0.244177 | + | 0.969731i | \(0.578518\pi\) | |||||||
\(762\) | −14.0273 | − | 14.0273i | −0.508156 | − | 0.508156i | ||||
\(763\) | 11.0073 | + | 0.396311i | 0.398493 | + | 0.0143474i | ||||
\(764\) | − | 18.7889i | − | 0.679758i | ||||||
\(765\) | −0.895013 | + | 0.895013i | −0.0323593 | + | 0.0323593i | ||||
\(766\) | −25.6625 | −0.927225 | ||||||||
\(767\) | 1.37727 | − | 6.88634i | 0.0497303 | − | 0.248651i | ||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 22.3493 | − | 22.3493i | 0.805937 | − | 0.805937i | −0.178079 | − | 0.984016i | \(-0.556988\pi\) |
0.984016 | + | 0.178079i | \(0.0569884\pi\) | |||||||
\(770\) | 0.321504 | − | 8.92963i | 0.0115862 | − | 0.321801i | ||||
\(771\) | − | 7.98302i | − | 0.287501i | ||||||
\(772\) | 1.37046 | + | 1.37046i | 0.0493238 | + | 0.0493238i | ||||
\(773\) | 27.6399 | − | 27.6399i | 0.994139 | − | 0.994139i | −0.00584422 | − | 0.999983i | \(-0.501860\pi\) |
0.999983 | + | 0.00584422i | \(0.00186029\pi\) | |||||||
\(774\) | 4.84774 | − | 4.84774i | 0.174248 | − | 0.174248i | ||||
\(775\) | −8.58930 | − | 8.58930i | −0.308537 | − | 0.308537i | ||||
\(776\) | − | 13.3789i | − | 0.480276i | ||||||
\(777\) | −13.2426 | − | 0.476791i | −0.475077 | − | 0.0171048i | ||||
\(778\) | −4.76417 | + | 4.76417i | −0.170804 | + | 0.170804i | ||||
\(779\) | 37.5744i | 1.34624i | ||||||||
\(780\) | −9.01152 | − | 1.80230i | −0.322664 | − | 0.0645328i | ||||
\(781\) | 21.3194 | 0.762870 | ||||||||
\(782\) | 2.59049 | − | 2.59049i | 0.0926357 | − | 0.0926357i | ||||
\(783\) | 7.25113i | 0.259134i | ||||||||
\(784\) | −0.503406 | + | 6.98188i | −0.0179788 | + | 0.249353i | ||||
\(785\) | 3.07438 | + | 3.07438i | 0.109729 | + | 0.109729i | ||||
\(786\) | 3.61191 | + | 3.61191i | 0.128833 | + | 0.128833i | ||||
\(787\) | 29.7592 | + | 29.7592i | 1.06080 | + | 1.06080i | 0.998028 | + | 0.0627747i | \(0.0199949\pi\) |
0.0627747 | + | 0.998028i | \(0.480005\pi\) | |||||||
\(788\) | 2.86537 | − | 2.86537i | 0.102075 | − | 0.102075i | ||||
\(789\) | 2.47166i | 0.0879933i | ||||||||
\(790\) | −33.5171 | −1.19248 | ||||||||
\(791\) | −5.69449 | + | 5.29869i | −0.202473 | + | 0.188400i | ||||
\(792\) | 1.32502i | 0.0470826i | ||||||||
\(793\) | −1.48978 | + | 0.993188i | −0.0529037 | + | 0.0352691i | ||||
\(794\) | 30.7896i | 1.09268i | ||||||||
\(795\) | −7.69449 | − | 7.69449i | −0.272896 | − | 0.272896i | ||||
\(796\) | − | 14.0650i | − | 0.498519i | ||||||
\(797\) | −19.9732 | −0.707486 | −0.353743 | − | 0.935343i | \(-0.615091\pi\) | ||||
−0.353743 | + | 0.935343i | \(0.615091\pi\) | |||||||
\(798\) | 7.82892 | + | 8.41372i | 0.277141 | + | 0.297843i | ||||
\(799\) | 2.91692 | + | 2.91692i | 0.103193 | + | 0.103193i | ||||
\(800\) | 1.05825 | − | 1.05825i | 0.0374148 | − | 0.0374148i | ||||
\(801\) | −10.2177 | − | 10.2177i | −0.361025 | − | 0.361025i | ||||
\(802\) | −23.3513 | −0.824565 | ||||||||
\(803\) | 6.63636 | 0.234192 | ||||||||
\(804\) | 9.11650 | + | 9.11650i | 0.321514 | + | 0.321514i | ||||
\(805\) | 49.7171 | + | 1.79003i | 1.75230 | + | 0.0630901i | ||||
\(806\) | −16.2330 | − | 24.3495i | −0.571783 | − | 0.857675i | ||||
\(807\) | 5.83761 | 0.205494 | ||||||||
\(808\) | −3.29841 | + | 3.29841i | −0.116037 | + | 0.116037i | ||||
\(809\) | 1.89084 | 0.0664785 | 0.0332393 | − | 0.999447i | \(-0.489418\pi\) | ||||
0.0332393 | + | 0.999447i | \(0.489418\pi\) | |||||||
\(810\) | 2.54884 | 0.0895572 | ||||||||
\(811\) | −7.61007 | + | 7.61007i | −0.267226 | + | 0.267226i | −0.827981 | − | 0.560756i | \(-0.810511\pi\) |
0.560756 | + | 0.827981i | \(0.310511\pi\) | |||||||
\(812\) | 13.0687 | + | 14.0449i | 0.458623 | + | 0.492881i | ||||
\(813\) | −8.57799 | + | 8.57799i | −0.300843 | + | 0.300843i | ||||
\(814\) | −4.69261 | + | 4.69261i | −0.164476 | + | 0.164476i | ||||
\(815\) | − | 15.2685i | − | 0.534832i | ||||||
\(816\) | − | 0.496594i | − | 0.0173843i | ||||||
\(817\) | −21.0578 | − | 21.0578i | −0.736719 | − | 0.736719i | ||||
\(818\) | −5.66221 | −0.197975 | ||||||||
\(819\) | −9.28077 | − | 2.20619i | −0.324296 | − | 0.0770904i | ||||
\(820\) | 22.0476 | 0.769935 | ||||||||
\(821\) | 32.0304 | + | 32.0304i | 1.11787 | + | 1.11787i | 0.992054 | + | 0.125814i | \(0.0401543\pi\) |
0.125814 | + | 0.992054i | \(0.459846\pi\) | |||||||
\(822\) | 5.37727i | 0.187554i | ||||||||
\(823\) | − | 54.2791i | − | 1.89205i | −0.324094 | − | 0.946025i | \(-0.605060\pi\) | ||
0.324094 | − | 0.946025i | \(-0.394940\pi\) | |||||||
\(824\) | −13.1426 | + | 13.1426i | −0.457845 | + | 0.457845i | ||||
\(825\) | −1.40221 | + | 1.40221i | −0.0488185 | + | 0.0488185i | ||||
\(826\) | 3.51044 | + | 3.77266i | 0.122144 | + | 0.131268i | ||||
\(827\) | 27.2462 | − | 27.2462i | 0.947443 | − | 0.947443i | −0.0512430 | − | 0.998686i | \(-0.516318\pi\) |
0.998686 | + | 0.0512430i | \(0.0163183\pi\) | |||||||
\(828\) | −7.37727 | −0.256378 | ||||||||
\(829\) | 41.4649 | 1.44013 | 0.720067 | − | 0.693904i | \(-0.244111\pi\) | ||||
0.720067 | + | 0.693904i | \(0.244111\pi\) | |||||||
\(830\) | 20.0692 | − | 20.0692i | 0.696613 | − | 0.696613i | ||||
\(831\) | −2.66465 | −0.0924357 | ||||||||
\(832\) | 3.00000 | − | 2.00000i | 0.104006 | − | 0.0693375i | ||||
\(833\) | −0.249988 | + | 3.46716i | −0.00866158 | + | 0.120130i | ||||
\(834\) | −2.07886 | − | 2.07886i | −0.0719851 | − | 0.0719851i | ||||
\(835\) | −28.9090 | −1.00044 | ||||||||
\(836\) | 5.75568 | 0.199064 | ||||||||
\(837\) | 5.73923 | + | 5.73923i | 0.198377 | + | 0.198377i | ||||
\(838\) | −10.7326 | + | 10.7326i | −0.370752 | + | 0.370752i | ||||
\(839\) | 0.0702127 | + | 0.0702127i | 0.00242401 | + | 0.00242401i | 0.708318 | − | 0.705894i | \(-0.249454\pi\) |
−0.705894 | + | 0.708318i | \(0.749454\pi\) | |||||||
\(840\) | 4.93693 | − | 4.59379i | 0.170340 | − | 0.158501i | ||||
\(841\) | 23.5789 | 0.813066 | ||||||||
\(842\) | − | 15.6482i | − | 0.539273i | ||||||
\(843\) | 8.09952 | + | 8.09952i | 0.278962 | + | 0.278962i | ||||
\(844\) | − | 14.8557i | − | 0.511356i | ||||||
\(845\) | −12.6161 | − | 30.6392i | −0.434008 | − | 1.05402i | ||||
\(846\) | − | 8.30690i | − | 0.285597i | ||||||
\(847\) | 16.6611 | + | 17.9056i | 0.572481 | + | 0.615244i | ||||
\(848\) | 4.26926 | 0.146607 | ||||||||
\(849\) | 30.2730i | 1.03897i | ||||||||
\(850\) | 0.525521 | − | 0.525521i | 0.0180252 | − | 0.0180252i | ||||
\(851\) | −26.1269 | − | 26.1269i | −0.895618 | − | 0.895618i | ||||
\(852\) | 11.3773 | + | 11.3773i | 0.389779 | + | 0.389779i | ||||
\(853\) | 27.4773 | + | 27.4773i | 0.940806 | + | 0.940806i | 0.998343 | − | 0.0575376i | \(-0.0183249\pi\) |
−0.0575376 | + | 0.998343i | \(0.518325\pi\) | |||||||
\(854\) | 0.0472740 | − | 1.31301i | 0.00161768 | − | 0.0449304i | ||||
\(855\) | − | 11.0718i | − | 0.378646i | ||||||
\(856\) | 4.91930 | − | 4.91930i | 0.168138 | − | 0.168138i | ||||
\(857\) | −50.2104 | −1.71515 | −0.857577 | − | 0.514356i | \(-0.828031\pi\) | ||||
−0.857577 | + | 0.514356i | \(0.828031\pi\) | |||||||
\(858\) | −3.97506 | + | 2.65004i | −0.135706 | + | 0.0904709i | ||||
\(859\) | 41.3127i | 1.40957i | 0.709420 | + | 0.704786i | \(0.248957\pi\) | ||||
−0.709420 | + | 0.704786i | \(0.751043\pi\) | |||||||
\(860\) | −12.3561 | + | 12.3561i | −0.421340 | + | 0.421340i | ||||
\(861\) | 22.8710 | + | 0.823453i | 0.779443 | + | 0.0280632i | ||||
\(862\) | − | 13.5830i | − | 0.462638i | ||||||
\(863\) | −12.8421 | − | 12.8421i | −0.437151 | − | 0.437151i | 0.453901 | − | 0.891052i | \(-0.350032\pi\) |
−0.891052 | + | 0.453901i | \(0.850032\pi\) | |||||||
\(864\) | −0.707107 | + | 0.707107i | −0.0240563 | + | 0.0240563i | ||||
\(865\) | −7.59856 | + | 7.59856i | −0.258359 | + | 0.258359i | ||||
\(866\) | 4.61379 | + | 4.61379i | 0.156783 | + | 0.156783i | ||||
\(867\) | 16.7534i | 0.568975i | ||||||||
\(868\) | 21.4603 | + | 0.772662i | 0.728412 | + | 0.0262259i | ||||
\(869\) | −12.3206 | + | 12.3206i | −0.417947 | + | 0.417947i | ||||
\(870\) | − | 18.4820i | − | 0.626598i | ||||||
\(871\) | −9.11650 | + | 45.5825i | −0.308901 | + | 1.54450i | ||||
\(872\) | 4.16308 | 0.140980 | ||||||||
\(873\) | −9.46034 | + | 9.46034i | −0.320184 | + | 0.320184i | ||||
\(874\) | 32.0457i | 1.08396i | ||||||||
\(875\) | −23.6103 | − | 0.850069i | −0.798173 | − | 0.0287376i | ||||
\(876\) | 3.54154 | + | 3.54154i | 0.119657 | + | 0.119657i | ||||
\(877\) | 12.9294 | + | 12.9294i | 0.436595 | + | 0.436595i | 0.890864 | − | 0.454269i | \(-0.150100\pi\) |
−0.454269 | + | 0.890864i | \(0.650100\pi\) | |||||||
\(878\) | −1.14263 | − | 1.14263i | −0.0385618 | − | 0.0385618i | ||||
\(879\) | −17.9235 | + | 17.9235i | −0.604545 | + | 0.604545i | ||||
\(880\) | − | 3.37727i | − | 0.113848i | ||||||
\(881\) | 42.1888 | 1.42138 | 0.710688 | − | 0.703507i | \(-0.248384\pi\) | ||||
0.710688 | + | 0.703507i | \(0.248384\pi\) | |||||||
\(882\) | 5.29289 | − | 4.58097i | 0.178221 | − | 0.154249i | ||||
\(883\) | − | 15.6635i | − | 0.527119i | −0.964643 | − | 0.263559i | \(-0.915103\pi\) | ||
0.964643 | − | 0.263559i | \(-0.0848965\pi\) | |||||||
\(884\) | 1.48978 | − | 0.993188i | 0.0501068 | − | 0.0334045i | ||||
\(885\) | − | 4.96451i | − | 0.166880i | ||||||
\(886\) | 13.4639 | + | 13.4639i | 0.452327 | + | 0.452327i | ||||
\(887\) | − | 25.2662i | − | 0.848356i | −0.905579 | − | 0.424178i | \(-0.860563\pi\) | ||
0.905579 | − | 0.424178i | \(-0.139437\pi\) | |||||||
\(888\) | −5.00849 | −0.168074 | ||||||||
\(889\) | 35.7534 | + | 38.4241i | 1.19913 | + | 1.28870i | ||||
\(890\) | 26.0433 | + | 26.0433i | 0.872974 | + | 0.872974i | ||||
\(891\) | 0.936931 | − | 0.936931i | 0.0313884 | − | 0.0313884i | ||||
\(892\) | 6.24945 | + | 6.24945i | 0.209247 | + | 0.209247i | ||||
\(893\) | −36.0838 | −1.20750 | ||||||||
\(894\) | 2.46928 | 0.0825852 | ||||||||
\(895\) | −9.61592 | − | 9.61592i | −0.321425 | − | 0.321425i | ||||
\(896\) | −0.0951965 | + | 2.64404i | −0.00318029 | + | 0.0883311i | ||||
\(897\) | −14.7545 | − | 22.1318i | −0.492640 | − | 0.738960i | ||||
\(898\) | 14.6241 | 0.488013 | ||||||||
\(899\) | 41.6159 | − | 41.6159i | 1.38797 | − | 1.38797i | ||||
\(900\) | −1.49659 | −0.0498865 | ||||||||
\(901\) | 2.12009 | 0.0706303 | ||||||||
\(902\) | 8.10450 | − | 8.10450i | 0.269850 | − | 0.269850i | ||||
\(903\) | −13.2791 | + | 12.3561i | −0.441901 | + | 0.411186i | ||||
\(904\) | −2.07886 | + | 2.07886i | −0.0691420 | + | 0.0691420i | ||||
\(905\) | −3.23982 | + | 3.23982i | −0.107695 | + | 0.107695i | ||||
\(906\) | − | 9.26314i | − | 0.307747i | ||||||
\(907\) | − | 8.71829i | − | 0.289486i | −0.989469 | − | 0.144743i | \(-0.953764\pi\) | ||
0.989469 | − | 0.144743i | \(-0.0462355\pi\) | |||||||
\(908\) | −5.50341 | − | 5.50341i | −0.182637 | − | 0.182637i | ||||
\(909\) | 4.66465 | 0.154717 | ||||||||
\(910\) | 23.6552 | + | 5.62322i | 0.784163 | + | 0.186408i | ||||
\(911\) | −53.1847 | −1.76209 | −0.881044 | − | 0.473035i | \(-0.843158\pi\) | ||||
−0.881044 | + | 0.473035i | \(0.843158\pi\) | |||||||
\(912\) | 3.07156 | + | 3.07156i | 0.101709 | + | 0.101709i | ||||
\(913\) | − | 14.7545i | − | 0.488304i | ||||||
\(914\) | − | 28.3858i | − | 0.938917i | ||||||
\(915\) | −0.895013 | + | 0.895013i | −0.0295882 | + | 0.0295882i | ||||
\(916\) | 2.50341 | − | 2.50341i | 0.0827149 | − | 0.0827149i | ||||
\(917\) | −9.20619 | − | 9.89387i | −0.304015 | − | 0.326724i | ||||
\(918\) | −0.351145 | + | 0.351145i | −0.0115895 | + | 0.0115895i | ||||
\(919\) | −37.9468 | −1.25175 | −0.625874 | − | 0.779924i | \(-0.715258\pi\) | ||||
−0.625874 | + | 0.779924i | \(0.715258\pi\) | |||||||
\(920\) | 18.8035 | 0.619933 | ||||||||
\(921\) | −5.09157 | + | 5.09157i | −0.167773 | + | 0.167773i | ||||
\(922\) | 18.9602 | 0.624422 | ||||||||
\(923\) | −11.3773 | + | 56.8863i | −0.374487 | + | 1.87244i | ||||
\(924\) | 0.126137 | − | 3.50341i | 0.00414961 | − | 0.115254i | ||||
\(925\) | −5.30024 | − | 5.30024i | −0.174271 | − | 0.174271i | ||||
\(926\) | 25.1154 | 0.825342 | ||||||||
\(927\) | 18.5865 | 0.610460 | ||||||||
\(928\) | 5.12732 | + | 5.12732i | 0.168313 | + | 0.168313i | ||||
\(929\) | 3.27439 | − | 3.27439i | 0.107429 | − | 0.107429i | −0.651349 | − | 0.758778i | \(-0.725797\pi\) |
0.758778 | + | 0.651349i | \(0.225797\pi\) | |||||||
\(930\) | −14.6284 | − | 14.6284i | −0.479684 | − | 0.479684i | ||||
\(931\) | −19.8990 | − | 22.9915i | −0.652163 | − | 0.753516i | ||||
\(932\) | 16.5615 | 0.542491 | ||||||||
\(933\) | 14.0729i | 0.460726i | ||||||||
\(934\) | −27.9358 | − | 27.9358i | −0.914087 | − | 0.914087i | ||||
\(935\) | − | 1.67713i | − | 0.0548481i | ||||||
\(936\) | −3.53553 | − | 0.707107i | −0.115563 | − | 0.0231125i | ||||
\(937\) | − | 50.1699i | − | 1.63898i | −0.573094 | − | 0.819490i | \(-0.694257\pi\) | ||
0.573094 | − | 0.819490i | \(-0.305743\pi\) | |||||||
\(938\) | −23.2365 | − | 24.9722i | −0.758699 | − | 0.815373i | ||||
\(939\) | 28.3059 | 0.923729 | ||||||||
\(940\) | 21.1730i | 0.690586i | ||||||||
\(941\) | 4.98020 | − | 4.98020i | 0.162350 | − | 0.162350i | −0.621257 | − | 0.783607i | \(-0.713378\pi\) |
0.783607 | + | 0.621257i | \(0.213378\pi\) | |||||||
\(942\) | 1.20619 | + | 1.20619i | 0.0392997 | + | 0.0392997i | ||||
\(943\) | 45.1231 | + | 45.1231i | 1.46941 | + | 1.46941i | ||||
\(944\) | 1.37727 | + | 1.37727i | 0.0448263 | + | 0.0448263i | ||||
\(945\) | −6.73923 | − | 0.242641i | −0.219227 | − | 0.00789310i | ||||
\(946\) | 9.08400i | 0.295346i | ||||||||
\(947\) | 4.66768 | − | 4.66768i | 0.151679 | − | 0.151679i | −0.627188 | − | 0.778868i | \(-0.715794\pi\) |
0.778868 | + | 0.627188i | \(0.215794\pi\) | |||||||
\(948\) | −13.1499 | −0.427090 | ||||||||
\(949\) | −3.54154 | + | 17.7077i | −0.114963 | + | 0.574816i | ||||
\(950\) | 6.50097i | 0.210919i | ||||||||
\(951\) | 20.5119 | − | 20.5119i | 0.665144 | − | 0.665144i | ||||
\(952\) | −0.0472740 | + | 1.31301i | −0.00153216 | + | 0.0425550i | ||||
\(953\) | 16.3818i | 0.530658i | 0.964158 | + | 0.265329i | \(0.0854805\pi\) | ||||
−0.964158 | + | 0.265329i | \(0.914520\pi\) | |||||||
\(954\) | −3.01882 | − | 3.01882i | −0.0977379 | − | 0.0977379i | ||||
\(955\) | 33.8633 | − | 33.8633i | 1.09579 | − | 1.09579i | ||||
\(956\) | 2.41238 | − | 2.41238i | 0.0780218 | − | 0.0780218i | ||||
\(957\) | −6.79381 | − | 6.79381i | −0.219613 | − | 0.219613i | ||||
\(958\) | − | 28.5342i | − | 0.921899i | ||||||
\(959\) | 0.511897 | − | 14.2177i | 0.0165300 | − | 0.459114i | ||||
\(960\) | 1.80230 | − | 1.80230i | 0.0581691 | − | 0.0581691i | ||||
\(961\) | − | 34.8776i | − | 1.12508i | ||||||
\(962\) | −10.0170 | − | 15.0255i | −0.322960 | − | 0.484441i | ||||
\(963\) | −6.95694 | −0.224184 | ||||||||
\(964\) | 8.37727 | − | 8.37727i | 0.269814 | − | 0.269814i | ||||
\(965\) | 4.93996i | 0.159023i | ||||||||
\(966\) | 19.5058 | + | 0.702290i | 0.627588 | + | 0.0225958i | ||||
\(967\) | −37.7762 | − | 37.7762i | −1.21480 | − | 1.21480i | −0.969429 | − | 0.245373i | \(-0.921090\pi\) |
−0.245373 | − | 0.969429i | \(-0.578910\pi\) | |||||||
\(968\) | 6.53672 | + | 6.53672i | 0.210098 | + | 0.210098i | ||||
\(969\) | 1.52532 | + | 1.52532i | 0.0490003 | + | 0.0490003i | ||||
\(970\) | 24.1129 | − | 24.1129i | 0.774219 | − | 0.774219i | ||||
\(971\) | 23.3617i | 0.749714i | 0.927083 | + | 0.374857i | \(0.122308\pi\) | ||||
−0.927083 | + | 0.374857i | \(0.877692\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 5.29869 | + | 5.69449i | 0.169868 | + | 0.182557i | ||||
\(974\) | 20.6244i | 0.660849i | ||||||||
\(975\) | −2.99319 | − | 4.48978i | −0.0958587 | − | 0.143788i | ||||
\(976\) | − | 0.496594i | − | 0.0158956i | ||||||
\(977\) | −29.3537 | − | 29.3537i | −0.939107 | − | 0.939107i | 0.0591422 | − | 0.998250i | \(-0.481163\pi\) |
−0.998250 | + | 0.0591422i | \(0.981163\pi\) | |||||||
\(978\) | − | 5.99037i | − | 0.191551i | ||||||
\(979\) | 19.1466 | 0.611927 | ||||||||
\(980\) | −13.4907 | + | 11.6762i | −0.430946 | + | 0.372981i | ||||
\(981\) | −2.94374 | − | 2.94374i | −0.0939865 | − | 0.0939865i | ||||
\(982\) | −7.32502 | + | 7.32502i | −0.233751 | + | 0.233751i | ||||
\(983\) | −19.8845 | − | 19.8845i | −0.634216 | − | 0.634216i | 0.314907 | − | 0.949123i | \(-0.398027\pi\) |
−0.949123 | + | 0.314907i | \(0.898027\pi\) | |||||||
\(984\) | 8.65004 | 0.275753 | ||||||||
\(985\) | 10.3285 | 0.329095 | ||||||||
\(986\) | 2.54620 | + | 2.54620i | 0.0810875 | + | 0.0810875i | ||||
\(987\) | −0.790787 | + | 21.9638i | −0.0251710 | + | 0.699114i | ||||
\(988\) | −3.07156 | + | 15.3578i | −0.0977193 | + | 0.488597i | ||||
\(989\) | −50.5766 | −1.60824 | ||||||||
\(990\) | −2.38809 | + | 2.38809i | −0.0758985 | + | 0.0758985i | ||||
\(991\) | 17.8399 | 0.566703 | 0.283352 | − | 0.959016i | \(-0.408554\pi\) | ||||
0.283352 | + | 0.959016i | \(0.408554\pi\) | |||||||
\(992\) | 8.11650 | 0.257699 | ||||||||
\(993\) | −9.65502 | + | 9.65502i | −0.306393 | + | 0.306393i | ||||
\(994\) | −28.9989 | − | 31.1650i | −0.919788 | − | 0.988494i | ||||
\(995\) | 25.3493 | − | 25.3493i | 0.803627 | − | 0.803627i | ||||
\(996\) | 7.87386 | − | 7.87386i | 0.249493 | − | 0.249493i | ||||
\(997\) | 24.4660i | 0.774846i | 0.921902 | + | 0.387423i | \(0.126635\pi\) | ||||
−0.921902 | + | 0.387423i | \(0.873365\pi\) | |||||||
\(998\) | − | 42.8272i | − | 1.35567i | ||||||
\(999\) | 3.54154 | + | 3.54154i | 0.112049 | + | 0.112049i |
(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 | 546.2.o.a.307.1 | yes | 8 | |
3.2 | odd | 2 | 1638.2.x.d.307.4 | 8 | |||
7.6 | odd | 2 | 546.2.o.d.307.2 | yes | 8 | ||
13.5 | odd | 4 | 546.2.o.d.265.2 | yes | 8 | ||
21.20 | even | 2 | 1638.2.x.b.307.3 | 8 | |||
39.5 | even | 4 | 1638.2.x.b.811.3 | 8 | |||
91.83 | even | 4 | inner | 546.2.o.a.265.1 | ✓ | 8 | |
273.83 | odd | 4 | 1638.2.x.d.811.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.o.a.265.1 | ✓ | 8 | 91.83 | even | 4 | inner | |
546.2.o.a.307.1 | yes | 8 | 1.1 | even | 1 | trivial | |
546.2.o.d.265.2 | yes | 8 | 13.5 | odd | 4 | ||
546.2.o.d.307.2 | yes | 8 | 7.6 | odd | 2 | ||
1638.2.x.b.307.3 | 8 | 21.20 | even | 2 | |||
1638.2.x.b.811.3 | 8 | 39.5 | even | 4 | |||
1638.2.x.d.307.4 | 8 | 3.2 | odd | 2 | |||
1638.2.x.d.811.4 | 8 | 273.83 | odd | 4 |