Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [693,2,Mod(64,693)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(693, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("693.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 693.m (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.53363286007\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 631.3 | ||
Root | \(0.901622 + 0.655067i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 693.631 |
Dual form | 693.2.m.i.190.3 |
$q$-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 \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(442\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.901622 | + | 0.655067i | 0.637543 | + | 0.463202i | 0.859005 | − | 0.511967i | \(-0.171083\pi\) |
−0.221462 | + | 0.975169i | \(0.571083\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.234224 | − | 0.720867i | −0.117112 | − | 0.360433i | ||||
\(5\) | 2.79603 | − | 2.03143i | 1.25042 | − | 0.908484i | 0.252174 | − | 0.967682i | \(-0.418854\pi\) |
0.998246 | + | 0.0591979i | \(0.0188543\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.309017 | + | 0.951057i | 0.116797 | + | 0.359466i | ||||
\(8\) | 0.949813 | − | 2.92322i | 0.335810 | − | 1.03352i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.85168 | 1.21801 | ||||||||
\(11\) | −3.31530 | + | 0.0938970i | −0.999599 | + | 0.0283110i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.66629 | + | 1.21063i | 0.462147 | + | 0.335769i | 0.794373 | − | 0.607430i | \(-0.207800\pi\) |
−0.332226 | + | 0.943200i | \(0.607800\pi\) | |||||||
\(14\) | −0.344389 | + | 1.05992i | −0.0920419 | + | 0.283276i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.54487 | − | 1.12241i | 0.386217 | − | 0.280603i | ||||
\(17\) | 1.56442 | − | 1.13662i | 0.379427 | − | 0.275670i | −0.381682 | − | 0.924294i | \(-0.624655\pi\) |
0.761109 | + | 0.648624i | \(0.224655\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.501522 | − | 1.54353i | 0.115057 | − | 0.354109i | −0.876902 | − | 0.480669i | \(-0.840394\pi\) |
0.991959 | + | 0.126560i | \(0.0403937\pi\) | |||||||
\(20\) | −2.11929 | − | 1.53975i | −0.473887 | − | 0.344299i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.05065 | − | 2.08708i | −0.650401 | − | 0.444967i | ||||
\(23\) | 0.807136 | 0.168299 | 0.0841497 | − | 0.996453i | \(-0.473183\pi\) | ||||
0.0841497 | + | 0.996453i | \(0.473183\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.14596 | − | 6.60459i | 0.429192 | − | 1.32092i | ||||
\(26\) | 0.709322 | + | 2.18307i | 0.139109 | + | 0.428135i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.613206 | − | 0.445520i | 0.115885 | − | 0.0841954i | ||||
\(29\) | −2.46400 | − | 7.58342i | −0.457554 | − | 1.40821i | −0.868111 | − | 0.496371i | \(-0.834666\pi\) |
0.410557 | − | 0.911835i | \(-0.365334\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.637845 | − | 0.463421i | −0.114560 | − | 0.0832330i | 0.529030 | − | 0.848603i | \(-0.322556\pi\) |
−0.643590 | + | 0.765370i | \(0.722556\pi\) | |||||||
\(32\) | −4.01918 | −0.710497 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.15508 | 0.369592 | ||||||||
\(35\) | 2.79603 | + | 2.03143i | 0.472615 | + | 0.343375i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.10926 | + | 9.56931i | 0.511159 | + | 1.57318i | 0.790164 | + | 0.612895i | \(0.209995\pi\) |
−0.279005 | + | 0.960290i | \(0.590005\pi\) | |||||||
\(38\) | 1.46330 | − | 1.06315i | 0.237378 | − | 0.172465i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.28263 | − | 10.1029i | −0.519029 | − | 1.59741i | ||||
\(41\) | 0.657011 | − | 2.02207i | 0.102608 | − | 0.315795i | −0.886554 | − | 0.462626i | \(-0.846907\pi\) |
0.989162 | + | 0.146831i | \(0.0469074\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.08043 | 0.469761 | 0.234880 | − | 0.972024i | \(-0.424530\pi\) | ||||
0.234880 | + | 0.972024i | \(0.424530\pi\) | |||||||
\(44\) | 0.844208 | + | 2.36789i | 0.127269 | + | 0.356973i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.727732 | + | 0.528728i | 0.107298 | + | 0.0779567i | ||||
\(47\) | −2.33812 | + | 7.19600i | −0.341050 | + | 1.04964i | 0.622615 | + | 0.782529i | \(0.286070\pi\) |
−0.963665 | + | 0.267115i | \(0.913930\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 6.26129 | − | 4.54910i | 0.885481 | − | 0.643339i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.482420 | − | 1.48474i | 0.0668996 | − | 0.205896i | ||||
\(53\) | 8.75554 | + | 6.36127i | 1.20267 | + | 0.873788i | 0.994544 | − | 0.104315i | \(-0.0332649\pi\) |
0.208122 | + | 0.978103i | \(0.433265\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.07891 | + | 6.99733i | −1.22420 | + | 0.943520i | ||||
\(56\) | 3.07366 | 0.410735 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.74605 | − | 8.45147i | 0.360574 | − | 1.10973i | ||||
\(59\) | 1.01872 | + | 3.13529i | 0.132626 | + | 0.408180i | 0.995213 | − | 0.0977281i | \(-0.0311576\pi\) |
−0.862587 | + | 0.505908i | \(0.831158\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.871010 | − | 0.632826i | 0.111521 | − | 0.0810250i | −0.530627 | − | 0.847606i | \(-0.678043\pi\) |
0.642148 | + | 0.766581i | \(0.278043\pi\) | |||||||
\(62\) | −0.271523 | − | 0.835662i | −0.0344835 | − | 0.106129i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.71351 | − | 4.87765i | −0.839189 | − | 0.609707i | ||||
\(65\) | 7.11832 | 0.882919 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.40314 | 0.293590 | 0.146795 | − | 0.989167i | \(-0.453104\pi\) | ||||
0.146795 | + | 0.989167i | \(0.453104\pi\) | |||||||
\(68\) | −1.18577 | − | 0.861515i | −0.143796 | − | 0.104474i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.19024 | + | 3.66317i | 0.142260 | + | 0.437832i | ||||
\(71\) | −2.57963 | + | 1.87421i | −0.306145 | + | 0.222428i | −0.730241 | − | 0.683190i | \(-0.760592\pi\) |
0.424095 | + | 0.905618i | \(0.360592\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.378940 | + | 1.16626i | 0.0443516 | + | 0.136500i | 0.970780 | − | 0.239970i | \(-0.0771377\pi\) |
−0.926429 | + | 0.376470i | \(0.877138\pi\) | |||||||
\(74\) | −3.46516 | + | 10.6647i | −0.402817 | + | 1.23974i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.23015 | −0.141107 | ||||||||
\(77\) | −1.11378 | − | 3.12402i | −0.126927 | − | 0.356015i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.67096 | + | 5.57328i | 0.863050 | + | 0.627043i | 0.928713 | − | 0.370799i | \(-0.120916\pi\) |
−0.0656630 | + | 0.997842i | \(0.520916\pi\) | |||||||
\(80\) | 2.03939 | − | 6.27659i | 0.228010 | − | 0.701744i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.91697 | − | 1.39276i | 0.211694 | − | 0.153805i | ||||
\(83\) | −13.0004 | + | 9.44536i | −1.42698 | + | 1.03676i | −0.436412 | + | 0.899747i | \(0.643751\pi\) |
−0.990569 | + | 0.137016i | \(0.956249\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.06520 | − | 6.35602i | 0.224002 | − | 0.689407i | ||||
\(86\) | 2.77738 | + | 2.01789i | 0.299493 | + | 0.217594i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.87443 | + | 9.78053i | −0.306415 | + | 1.04261i | ||||
\(89\) | 4.43830 | 0.470459 | 0.235230 | − | 0.971940i | \(-0.424416\pi\) | ||||
0.235230 | + | 0.971940i | \(0.424416\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.636468 | + | 1.95885i | −0.0667199 | + | 0.205343i | ||||
\(92\) | −0.189050 | − | 0.581837i | −0.0197099 | − | 0.0606607i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.82196 | + | 4.95645i | −0.703632 | + | 0.511218i | ||||
\(95\) | −1.73330 | − | 5.33455i | −0.177833 | − | 0.547313i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.23278 | − | 3.80184i | −0.531308 | − | 0.386018i | 0.289539 | − | 0.957166i | \(-0.406498\pi\) |
−0.820847 | + | 0.571148i | \(0.806498\pi\) | |||||||
\(98\) | −1.11447 | −0.112578 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.26366 | −0.526366 | ||||||||
\(101\) | −12.4952 | − | 9.07828i | −1.24332 | − | 0.903323i | −0.245503 | − | 0.969396i | \(-0.578953\pi\) |
−0.997815 | + | 0.0660728i | \(0.978953\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.75276 | + | 8.47213i | 0.271238 | + | 0.834784i | 0.990190 | + | 0.139725i | \(0.0446218\pi\) |
−0.718953 | + | 0.695059i | \(0.755378\pi\) | |||||||
\(104\) | 5.12162 | − | 3.72107i | 0.502216 | − | 0.364881i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.72713 | + | 11.4709i | 0.362011 | + | 1.11416i | ||||
\(107\) | −1.08533 | + | 3.34029i | −0.104922 | + | 0.322918i | −0.989712 | − | 0.143072i | \(-0.954302\pi\) |
0.884790 | + | 0.465990i | \(0.154302\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.87655 | 0.371306 | 0.185653 | − | 0.982615i | \(-0.440560\pi\) | ||||
0.185653 | + | 0.982615i | \(0.440560\pi\) | |||||||
\(110\) | −12.7695 | + | 0.361662i | −1.21752 | + | 0.0344831i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.54487 | + | 1.12241i | 0.145976 | + | 0.106058i | ||||
\(113\) | −3.29224 | + | 10.1325i | −0.309708 | + | 0.953183i | 0.668170 | + | 0.744008i | \(0.267078\pi\) |
−0.977878 | + | 0.209175i | \(0.932922\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.25677 | − | 1.63964i | 0.210445 | − | 0.152897i | ||||
\(116\) | −4.88951 | + | 3.55243i | −0.453979 | + | 0.329835i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.13533 | + | 3.49417i | −0.104515 | + | 0.321665i | ||||
\(119\) | 1.56442 | + | 1.13662i | 0.143410 | + | 0.104194i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9824 | − | 0.622593i | 0.998397 | − | 0.0565993i | ||||
\(122\) | 1.19987 | 0.108631 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.184667 | + | 0.568346i | −0.0165836 | + | 0.0510389i | ||||
\(125\) | −2.07667 | − | 6.39134i | −0.185743 | − | 0.571659i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.7361 | + | 11.4330i | −1.39635 | + | 1.01451i | −0.401220 | + | 0.915982i | \(0.631414\pi\) |
−0.995134 | + | 0.0985289i | \(0.968586\pi\) | |||||||
\(128\) | −0.373878 | − | 1.15068i | −0.0330464 | − | 0.101706i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.41804 | + | 4.66298i | 0.562899 | + | 0.408970i | ||||
\(131\) | −5.11284 | −0.446711 | −0.223355 | − | 0.974737i | \(-0.571701\pi\) | ||||
−0.223355 | + | 0.974737i | \(0.571701\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.62296 | 0.140728 | ||||||||
\(134\) | 2.16672 | + | 1.57422i | 0.187176 | + | 0.135992i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.83668 | − | 5.65272i | −0.157494 | − | 0.484717i | ||||
\(137\) | 7.36247 | − | 5.34915i | 0.629019 | − | 0.457009i | −0.227042 | − | 0.973885i | \(-0.572905\pi\) |
0.856060 | + | 0.516876i | \(0.172905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.02234 | − | 12.3795i | −0.341171 | − | 1.05002i | −0.963602 | − | 0.267341i | \(-0.913855\pi\) |
0.622431 | − | 0.782675i | \(-0.286145\pi\) | |||||||
\(140\) | 0.809496 | − | 2.49137i | 0.0684149 | − | 0.210559i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.55358 | −0.298210 | ||||||||
\(143\) | −5.63793 | − | 3.85715i | −0.471468 | − | 0.322551i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.2946 | − | 16.1980i | −1.85147 | − | 1.34517i | ||||
\(146\) | −0.422316 | + | 1.29975i | −0.0349511 | + | 0.107568i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.16994 | − | 4.48272i | 0.507166 | − | 0.368477i | ||||
\(149\) | −2.54557 | + | 1.84947i | −0.208541 | + | 0.151514i | −0.687153 | − | 0.726512i | \(-0.741140\pi\) |
0.478612 | + | 0.878026i | \(0.341140\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.885940 | − | 2.72664i | 0.0720968 | − | 0.221891i | −0.908515 | − | 0.417853i | \(-0.862783\pi\) |
0.980612 | + | 0.195962i | \(0.0627828\pi\) | |||||||
\(152\) | −4.03572 | − | 2.93212i | −0.327340 | − | 0.237827i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.04223 | − | 3.54629i | 0.0839851 | − | 0.285768i | ||||
\(155\) | −2.72484 | −0.218864 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.64062 | + | 20.4377i | −0.529979 | + | 1.63111i | 0.224275 | + | 0.974526i | \(0.427999\pi\) |
−0.754254 | + | 0.656582i | \(0.772001\pi\) | |||||||
\(158\) | 3.26544 | + | 10.0500i | 0.259784 | + | 0.799534i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −11.2377 | + | 8.16468i | −0.888420 | + | 0.645475i | ||||
\(161\) | 0.249419 | + | 0.767632i | 0.0196569 | + | 0.0604978i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.65210 | + | 4.83304i | 0.521033 | + | 0.378553i | 0.816993 | − | 0.576648i | \(-0.195639\pi\) |
−0.295960 | + | 0.955200i | \(0.595639\pi\) | |||||||
\(164\) | −1.61153 | −0.125840 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.9088 | −1.38999 | ||||||||
\(167\) | −17.5626 | − | 12.7600i | −1.35904 | − | 0.987397i | −0.998506 | − | 0.0546489i | \(-0.982596\pi\) |
−0.360529 | − | 0.932748i | \(-0.617404\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.70632 | − | 8.32919i | −0.208178 | − | 0.640707i | ||||
\(170\) | 6.02565 | − | 4.37789i | 0.462146 | − | 0.335769i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.721509 | − | 2.22058i | −0.0550146 | − | 0.169317i | ||||
\(173\) | 2.48624 | − | 7.65185i | 0.189025 | − | 0.581760i | −0.810969 | − | 0.585089i | \(-0.801060\pi\) |
0.999994 | + | 0.00332915i | \(0.00105970\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.94447 | 0.524953 | ||||||||
\(176\) | −5.01630 | + | 3.86619i | −0.378118 | + | 0.291425i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.00167 | + | 2.90739i | 0.299938 | + | 0.217918i | ||||
\(179\) | 1.11892 | − | 3.44369i | 0.0836322 | − | 0.257393i | −0.900493 | − | 0.434871i | \(-0.856794\pi\) |
0.984125 | + | 0.177478i | \(0.0567938\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.7970 | + | 9.29753i | −0.951190 | + | 0.691080i | −0.951088 | − | 0.308920i | \(-0.900033\pi\) |
−0.000102207 | 1.00000i | \(0.500033\pi\) | ||||||||
\(182\) | −1.85703 | + | 1.34921i | −0.137652 | + | 0.100010i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.766628 | − | 2.35944i | 0.0565165 | − | 0.173940i | ||||
\(185\) | 28.1330 | + | 20.4398i | 2.06838 | + | 1.50276i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.07979 | + | 3.91512i | −0.371471 | + | 0.286302i | ||||
\(188\) | 5.73500 | 0.418268 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.93170 | − | 5.94518i | 0.140141 | − | 0.431308i | ||||
\(191\) | −0.132593 | − | 0.408080i | −0.00959411 | − | 0.0295276i | 0.946145 | − | 0.323744i | \(-0.104942\pi\) |
−0.955739 | + | 0.294216i | \(0.904942\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.2767 | − | 8.91954i | 0.883696 | − | 0.642042i | −0.0505310 | − | 0.998722i | \(-0.516091\pi\) |
0.934227 | + | 0.356680i | \(0.116091\pi\) | |||||||
\(194\) | −2.22753 | − | 6.85564i | −0.159927 | − | 0.492206i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.613206 | + | 0.445520i | 0.0438004 | + | 0.0318229i | ||||
\(197\) | 20.8082 | 1.48252 | 0.741262 | − | 0.671216i | \(-0.234228\pi\) | ||||
0.741262 | + | 0.671216i | \(0.234228\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.44567 | 0.598698 | 0.299349 | − | 0.954144i | \(-0.403231\pi\) | ||||
0.299349 | + | 0.954144i | \(0.403231\pi\) | |||||||
\(200\) | −17.2684 | − | 12.5462i | −1.22106 | − | 0.887153i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.31906 | − | 16.3704i | −0.374247 | − | 1.15182i | ||||
\(203\) | 6.45084 | − | 4.68681i | 0.452760 | − | 0.328950i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.27068 | − | 6.98844i | −0.158591 | − | 0.488094i | ||||
\(206\) | −3.06786 | + | 9.44190i | −0.213748 | + | 0.657849i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.93303 | 0.272707 | ||||||||
\(209\) | −1.51776 | + | 5.16434i | −0.104986 | + | 0.357225i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.97632 | + | 5.79513i | 0.549112 | + | 0.398953i | 0.827458 | − | 0.561528i | \(-0.189786\pi\) |
−0.278346 | + | 0.960481i | \(0.589786\pi\) | |||||||
\(212\) | 2.53487 | − | 7.80154i | 0.174096 | − | 0.535812i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.16667 | + | 2.30072i | −0.216469 | + | 0.157274i | ||||
\(215\) | 8.61295 | − | 6.25768i | 0.587399 | − | 0.426770i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.243635 | − | 0.749832i | 0.0165390 | − | 0.0509019i | ||||
\(218\) | 3.49518 | + | 2.53940i | 0.236724 | + | 0.171990i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.17064 | + | 4.90574i | 0.483445 | + | 0.330745i | ||||
\(221\) | 3.98281 | 0.267913 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.37562 | − | 16.5445i | 0.359978 | − | 1.10790i | −0.593088 | − | 0.805138i | \(-0.702091\pi\) |
0.953066 | − | 0.302762i | \(-0.0979087\pi\) | |||||||
\(224\) | −1.24199 | − | 3.82246i | −0.0829842 | − | 0.255399i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.60581 | + | 6.97903i | −0.638969 | + | 0.464238i | ||||
\(227\) | 3.90334 | + | 12.0133i | 0.259074 | + | 0.797348i | 0.993000 | + | 0.118118i | \(0.0376861\pi\) |
−0.733926 | + | 0.679230i | \(0.762314\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.69997 | − | 2.68819i | −0.244501 | − | 0.177640i | 0.458785 | − | 0.888547i | \(-0.348285\pi\) |
−0.703286 | + | 0.710907i | \(0.748285\pi\) | |||||||
\(230\) | 3.10883 | 0.204990 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −24.5084 | −1.60905 | ||||||||
\(233\) | 19.3006 | + | 14.0227i | 1.26443 | + | 0.918659i | 0.998966 | − | 0.0454624i | \(-0.0144761\pi\) |
0.265460 | + | 0.964122i | \(0.414476\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.08073 | + | 24.8699i | 0.527129 | + | 1.62234i | ||||
\(236\) | 2.02152 | − | 1.46872i | 0.131590 | − | 0.0956054i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.665955 | + | 2.04960i | 0.0431675 | + | 0.132856i | ||||
\(239\) | −2.73114 | + | 8.40558i | −0.176663 | + | 0.543711i | −0.999705 | − | 0.0242677i | \(-0.992275\pi\) |
0.823043 | + | 0.567979i | \(0.192275\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.9464 | 1.22045 | 0.610224 | − | 0.792229i | \(-0.291079\pi\) | ||||
0.610224 | + | 0.792229i | \(0.291079\pi\) | |||||||
\(242\) | 10.3098 | + | 6.63284i | 0.662738 | + | 0.426375i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.660194 | − | 0.479659i | −0.0422646 | − | 0.0307070i | ||||
\(245\) | −1.06799 | + | 3.28693i | −0.0682312 | + | 0.209994i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.70433 | − | 1.96481i | 0.172072 | − | 0.125018i | ||||
\(248\) | −1.96052 | + | 1.42440i | −0.124493 | + | 0.0904495i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.31438 | − | 7.12294i | 0.146374 | − | 0.450494i | ||||
\(251\) | −2.31938 | − | 1.68513i | −0.146398 | − | 0.106364i | 0.512175 | − | 0.858881i | \(-0.328840\pi\) |
−0.658573 | + | 0.752516i | \(0.728840\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.67589 | + | 0.0757876i | −0.168232 | + | 0.00476473i | ||||
\(254\) | −21.6774 | −1.36016 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.71199 | + | 14.5020i | −0.294500 | + | 0.906377i | ||||
\(257\) | −6.92689 | − | 21.3188i | −0.432087 | − | 1.32983i | −0.896042 | − | 0.443969i | \(-0.853570\pi\) |
0.463955 | − | 0.885859i | \(-0.346430\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.14014 | + | 5.91416i | −0.505804 | + | 0.367488i | ||||
\(260\) | −1.66728 | − | 5.13136i | −0.103400 | − | 0.318234i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.60985 | − | 3.34925i | −0.284797 | − | 0.206917i | ||||
\(263\) | −0.990706 | −0.0610895 | −0.0305448 | − | 0.999533i | \(-0.509724\pi\) | ||||
−0.0305448 | + | 0.999533i | \(0.509724\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37.4032 | 2.29766 | ||||||||
\(266\) | 1.46330 | + | 1.06315i | 0.0897205 | + | 0.0651858i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.562873 | − | 1.73234i | −0.0343829 | − | 0.105820i | ||||
\(269\) | −5.81713 | + | 4.22639i | −0.354677 | + | 0.257688i | −0.750828 | − | 0.660497i | \(-0.770345\pi\) |
0.396152 | + | 0.918185i | \(0.370345\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.39423 | − | 25.8348i | −0.509913 | − | 1.56935i | −0.792351 | − | 0.610065i | \(-0.791143\pi\) |
0.282438 | − | 0.959285i | \(-0.408857\pi\) | |||||||
\(272\) | 1.14107 | − | 3.51185i | 0.0691874 | − | 0.212937i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.1422 | 0.612714 | ||||||||
\(275\) | −6.49434 | + | 22.0977i | −0.391624 | + | 1.33254i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.9777 | − | 12.3350i | −1.02009 | − | 0.741140i | −0.0537900 | − | 0.998552i | \(-0.517130\pi\) |
−0.966302 | + | 0.257412i | \(0.917130\pi\) | |||||||
\(278\) | 4.48277 | − | 13.7965i | 0.268859 | − | 0.827462i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.59403 | − | 6.24393i | 0.513592 | − | 0.373146i | ||||
\(281\) | −22.7803 | + | 16.5509i | −1.35896 | + | 0.987341i | −0.360448 | + | 0.932779i | \(0.617376\pi\) |
−0.998510 | + | 0.0545621i | \(0.982624\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.09369 | + | 24.9098i | −0.481120 | + | 1.48074i | 0.356403 | + | 0.934332i | \(0.384003\pi\) |
−0.837523 | + | 0.546403i | \(0.815997\pi\) | |||||||
\(284\) | 1.95527 | + | 1.42058i | 0.116024 | + | 0.0842961i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.55660 | − | 7.17091i | −0.151175 | − | 0.424025i | ||||
\(287\) | 2.12613 | 0.125502 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.09778 | + | 12.6117i | −0.241046 | + | 0.741863i | ||||
\(290\) | −9.49056 | − | 29.2089i | −0.557305 | − | 1.71521i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.751959 | − | 0.546331i | 0.0440051 | − | 0.0319716i | ||||
\(293\) | 1.37941 | + | 4.24538i | 0.0805858 | + | 0.248017i | 0.983230 | − | 0.182370i | \(-0.0583769\pi\) |
−0.902644 | + | 0.430388i | \(0.858377\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.21748 | + | 6.69689i | 0.536663 | + | 0.389908i | ||||
\(296\) | 30.9264 | 1.79756 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.50667 | −0.203136 | ||||||||
\(299\) | 1.34493 | + | 0.977145i | 0.0777790 | + | 0.0565098i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.951904 | + | 2.92966i | 0.0548669 | + | 0.168863i | ||||
\(302\) | 2.58492 | − | 1.87805i | 0.148745 | − | 0.108070i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.957688 | − | 2.94746i | −0.0549271 | − | 0.169048i | ||||
\(305\) | 1.14982 | − | 3.53879i | 0.0658387 | − | 0.202631i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.8841 | 0.735334 | 0.367667 | − | 0.929957i | \(-0.380157\pi\) | ||||
0.367667 | + | 0.929957i | \(0.380157\pi\) | |||||||
\(308\) | −1.99113 | + | 1.53461i | −0.113455 | + | 0.0874425i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.45678 | − | 1.78495i | −0.139536 | − | 0.101379i | ||||
\(311\) | −8.28779 | + | 25.5072i | −0.469957 | + | 1.44638i | 0.382682 | + | 0.923880i | \(0.375001\pi\) |
−0.852639 | + | 0.522500i | \(0.824999\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.90331 | + | 2.10938i | −0.164105 | + | 0.119229i | −0.666807 | − | 0.745231i | \(-0.732339\pi\) |
0.502702 | + | 0.864460i | \(0.332339\pi\) | |||||||
\(314\) | −19.3754 | + | 14.0771i | −1.09342 | + | 0.794415i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.22087 | − | 6.83513i | 0.124934 | − | 0.384506i | ||||
\(317\) | −13.6870 | − | 9.94418i | −0.768738 | − | 0.558521i | 0.132840 | − | 0.991138i | \(-0.457590\pi\) |
−0.901578 | + | 0.432617i | \(0.857590\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.88095 | + | 24.9099i | 0.497238 | + | 1.39469i | ||||
\(320\) | −28.6798 | −1.60325 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.277969 | + | 0.855500i | −0.0154906 | + | 0.0476751i | ||||
\(323\) | −0.969808 | − | 2.98476i | −0.0539616 | − | 0.166077i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.5715 | − | 8.40721i | 0.641873 | − | 0.466348i | ||||
\(326\) | 2.83172 | + | 8.71515i | 0.156835 | + | 0.482687i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.28693 | − | 3.84118i | −0.291922 | − | 0.212094i | ||||
\(329\) | −7.56632 | −0.417145 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.23826 | −0.0680610 | −0.0340305 | − | 0.999421i | \(-0.510834\pi\) | ||||
−0.0340305 | + | 0.999421i | \(0.510834\pi\) | |||||||
\(332\) | 9.85385 | + | 7.15924i | 0.540800 | + | 0.392914i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.47620 | − | 23.0094i | −0.409079 | − | 1.25902i | ||||
\(335\) | 6.71924 | − | 4.88181i | 0.367111 | − | 0.266722i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.32885 | − | 19.4782i | −0.344754 | − | 1.06104i | −0.961715 | − | 0.274051i | \(-0.911636\pi\) |
0.616961 | − | 0.786994i | \(-0.288364\pi\) | |||||||
\(338\) | 3.01610 | − | 9.28261i | 0.164054 | − | 0.504907i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.06556 | −0.274719 | ||||||||
\(341\) | 2.15816 | + | 1.47649i | 0.116871 | + | 0.0799563i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.809017 | − | 0.587785i | −0.0436828 | − | 0.0317374i | ||||
\(344\) | 2.92583 | − | 9.00478i | 0.157750 | − | 0.485505i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.25412 | − | 5.27043i | 0.389984 | − | 0.283340i | ||||
\(347\) | 22.0618 | − | 16.0288i | 1.18434 | − | 0.860472i | 0.191684 | − | 0.981457i | \(-0.438605\pi\) |
0.992654 | + | 0.120985i | \(0.0386052\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.46730 | − | 7.59356i | 0.132071 | − | 0.406474i | −0.863052 | − | 0.505116i | \(-0.831450\pi\) |
0.995123 | + | 0.0986418i | \(0.0314498\pi\) | |||||||
\(350\) | 6.26129 | + | 4.54910i | 0.334680 | + | 0.243159i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.3248 | − | 0.377388i | 0.710212 | − | 0.0201149i | ||||
\(353\) | −5.93472 | −0.315873 | −0.157937 | − | 0.987449i | \(-0.550484\pi\) | ||||
−0.157937 | + | 0.987449i | \(0.550484\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.40538 | + | 10.4807i | −0.180739 | + | 0.556256i | ||||
\(356\) | −1.03956 | − | 3.19942i | −0.0550964 | − | 0.169569i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.26469 | − | 2.37194i | 0.172544 | − | 0.125361i | ||||
\(359\) | −8.78235 | − | 27.0293i | −0.463515 | − | 1.42655i | −0.860841 | − | 0.508874i | \(-0.830062\pi\) |
0.397326 | − | 0.917677i | \(-0.369938\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.2404 | + | 9.61969i | 0.696862 | + | 0.506300i | ||||
\(362\) | −17.6285 | −0.926535 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.56114 | 0.0818261 | ||||||||
\(365\) | 3.42870 | + | 2.49109i | 0.179466 | + | 0.130390i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.39456 | − | 28.9135i | −0.490392 | − | 1.50927i | −0.824017 | − | 0.566565i | \(-0.808272\pi\) |
0.333625 | − | 0.942706i | \(-0.391728\pi\) | |||||||
\(368\) | 1.24692 | − | 0.905939i | 0.0650001 | − | 0.0472253i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11.9759 | + | 36.8580i | 0.622596 | + | 1.91615i | ||||
\(371\) | −3.34432 | + | 10.2928i | −0.173628 | + | 0.534373i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.4226 | 0.746772 | 0.373386 | − | 0.927676i | \(-0.378197\pi\) | ||||
0.373386 | + | 0.927676i | \(0.378197\pi\) | |||||||
\(374\) | −7.14471 | + | 0.202355i | −0.369444 | + | 0.0104635i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.8147 | + | 13.6697i | 0.970296 | + | 0.704961i | ||||
\(377\) | 5.07499 | − | 15.6192i | 0.261375 | − | 0.804430i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.1278 | − | 13.1706i | 0.931163 | − | 0.676529i | −0.0151144 | − | 0.999886i | \(-0.504811\pi\) |
0.946277 | + | 0.323356i | \(0.104811\pi\) | |||||||
\(380\) | −3.43952 | + | 2.49896i | −0.176444 | + | 0.128194i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.147771 | − | 0.454792i | 0.00756061 | − | 0.0232692i | ||||
\(383\) | 27.2465 | + | 19.7957i | 1.39223 | + | 1.01152i | 0.995616 | + | 0.0935305i | \(0.0298153\pi\) |
0.396615 | + | 0.917985i | \(0.370185\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.46040 | − | 6.47226i | −0.482146 | − | 0.329857i | ||||
\(386\) | 16.9118 | 0.860790 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.51498 | + | 4.66262i | −0.0769112 | + | 0.236708i | ||||
\(389\) | −0.750241 | − | 2.30900i | −0.0380387 | − | 0.117071i | 0.930234 | − | 0.366967i | \(-0.119604\pi\) |
−0.968273 | + | 0.249896i | \(0.919604\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.26270 | − | 0.917404i | 0.0638574 | − | 0.0463951i | ||||
\(392\) | 0.949813 | + | 2.92322i | 0.0479728 | + | 0.147645i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.7611 | + | 13.6308i | 0.945173 | + | 0.686708i | ||||
\(395\) | 32.7699 | 1.64883 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.89696 | −0.295960 | −0.147980 | − | 0.988990i | \(-0.547277\pi\) | ||||
−0.147980 | + | 0.988990i | \(0.547277\pi\) | |||||||
\(398\) | 7.61481 | + | 5.53248i | 0.381696 | + | 0.277318i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.09784 | − | 12.6119i | −0.204892 | − | 0.630593i | ||||
\(401\) | 9.09302 | − | 6.60646i | 0.454084 | − | 0.329911i | −0.337122 | − | 0.941461i | \(-0.609454\pi\) |
0.791206 | + | 0.611550i | \(0.209454\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.501804 | − | 1.54439i | −0.0249966 | − | 0.0769317i | ||||
\(404\) | −3.61756 | + | 11.1337i | −0.179981 | + | 0.553923i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.88640 | 0.441025 | ||||||||
\(407\) | −11.2066 | − | 31.4331i | −0.555492 | − | 1.55808i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.7320 | − | 17.2423i | −1.17347 | − | 0.852578i | −0.182052 | − | 0.983289i | \(-0.558274\pi\) |
−0.991421 | + | 0.130711i | \(0.958274\pi\) | |||||||
\(410\) | 2.53060 | − | 7.78839i | 0.124977 | − | 0.384641i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.46251 | − | 3.96875i | 0.269119 | − | 0.195526i | ||||
\(413\) | −2.66704 | + | 1.93771i | −0.131236 | + | 0.0953487i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.1619 | + | 52.8189i | −0.842445 | + | 2.59278i | ||||
\(416\) | −6.69713 | − | 4.86575i | −0.328354 | − | 0.238563i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.75144 | + | 3.66205i | −0.232400 | + | 0.179117i | ||||
\(419\) | 20.2858 | 0.991027 | 0.495514 | − | 0.868600i | \(-0.334980\pi\) | ||||
0.495514 | + | 0.868600i | \(0.334980\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.945600 | + | 2.91026i | −0.0460857 | + | 0.141837i | −0.971452 | − | 0.237238i | \(-0.923758\pi\) |
0.925366 | + | 0.379075i | \(0.123758\pi\) | |||||||
\(422\) | 3.39542 | + | 10.4500i | 0.165287 | + | 0.508700i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 26.9116 | − | 19.5524i | 1.30694 | − | 0.949548i | ||||
\(425\) | −4.14971 | − | 12.7715i | −0.201290 | − | 0.619508i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.871010 | + | 0.632826i | 0.0421511 | + | 0.0306246i | ||||
\(428\) | 2.66211 | 0.128678 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.8648 | 0.572173 | ||||||||
\(431\) | 6.10158 | + | 4.43306i | 0.293903 | + | 0.213533i | 0.724959 | − | 0.688792i | \(-0.241859\pi\) |
−0.431056 | + | 0.902325i | \(0.641859\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.93848 | − | 30.5875i | −0.477613 | − | 1.46994i | −0.842401 | − | 0.538851i | \(-0.818859\pi\) |
0.364788 | − | 0.931091i | \(-0.381141\pi\) | |||||||
\(434\) | 0.710857 | − | 0.516468i | 0.0341222 | − | 0.0247912i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.907980 | − | 2.79447i | −0.0434844 | − | 0.133831i | ||||
\(437\) | 0.404796 | − | 1.24584i | 0.0193640 | − | 0.0595964i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.66725 | −0.222756 | −0.111378 | − | 0.993778i | \(-0.535526\pi\) | ||||
−0.111378 | + | 0.993778i | \(0.535526\pi\) | |||||||
\(440\) | 11.8315 | + | 33.1858i | 0.564045 | + | 1.58207i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.59099 | + | 2.60901i | 0.170806 | + | 0.124098i | ||||
\(443\) | −5.33893 | + | 16.4315i | −0.253660 | + | 0.780686i | 0.740430 | + | 0.672133i | \(0.234622\pi\) |
−0.994091 | + | 0.108553i | \(0.965378\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.4096 | − | 9.01611i | 0.588272 | − | 0.427404i | ||||
\(446\) | 15.6845 | − | 11.3955i | 0.742684 | − | 0.539591i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.56433 | − | 7.89221i | 0.121153 | − | 0.372872i | ||||
\(449\) | −13.5430 | − | 9.83957i | −0.639134 | − | 0.464358i | 0.220418 | − | 0.975405i | \(-0.429258\pi\) |
−0.859553 | + | 0.511047i | \(0.829258\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.98832 | + | 6.76546i | −0.0936264 | + | 0.318573i | ||||
\(452\) | 8.07529 | 0.379829 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.35015 | + | 13.3884i | −0.204162 | + | 0.628347i | ||||
\(455\) | 2.19968 | + | 6.76992i | 0.103123 | + | 0.317379i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.5536 | − | 12.7534i | 0.821121 | − | 0.596580i | −0.0959121 | − | 0.995390i | \(-0.530577\pi\) |
0.917033 | + | 0.398810i | \(0.130577\pi\) | |||||||
\(458\) | −1.57503 | − | 4.84746i | −0.0735965 | − | 0.226507i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.71055 | − | 1.24279i | −0.0797549 | − | 0.0579453i | ||||
\(461\) | 6.07778 | 0.283070 | 0.141535 | − | 0.989933i | \(-0.454796\pi\) | ||||
0.141535 | + | 0.989933i | \(0.454796\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.14719 | −0.239210 | −0.119605 | − | 0.992822i | \(-0.538163\pi\) | ||||
−0.119605 | + | 0.992822i | \(0.538163\pi\) | |||||||
\(464\) | −12.3183 | − | 8.94975i | −0.571862 | − | 0.415482i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.21605 | + | 25.2864i | 0.380601 | + | 1.17137i | ||||
\(467\) | −3.17076 | + | 2.30369i | −0.146725 | + | 0.106602i | −0.658726 | − | 0.752383i | \(-0.728904\pi\) |
0.512001 | + | 0.858985i | \(0.328904\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.742611 | + | 2.28552i | 0.0342906 | + | 0.105536i | ||||
\(470\) | −9.00570 | + | 27.7167i | −0.415402 | + | 1.27848i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.1327 | 0.466397 | ||||||||
\(473\) | −10.2125 | + | 0.289243i | −0.469572 | + | 0.0132994i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.11811 | − | 6.62469i | −0.418368 | − | 0.303962i | ||||
\(476\) | 0.452925 | − | 1.39396i | 0.0207598 | − | 0.0638921i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.96867 | + | 5.78958i | −0.364478 | + | 0.264809i | ||||
\(479\) | −12.2266 | + | 8.88315i | −0.558648 | + | 0.405882i | −0.830964 | − | 0.556326i | \(-0.812210\pi\) |
0.272316 | + | 0.962208i | \(0.412210\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.40399 | + | 19.7095i | −0.291997 | + | 0.898674i | ||||
\(482\) | 17.0825 | + | 12.4112i | 0.778088 | + | 0.565314i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.02114 | − | 7.77100i | −0.137324 | − | 0.353227i | ||||
\(485\) | −22.3541 | −1.01505 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.74916 | − | 23.8495i | 0.351148 | − | 1.08072i | −0.607062 | − | 0.794655i | \(-0.707652\pi\) |
0.958210 | − | 0.286067i | \(-0.0923480\pi\) | |||||||
\(488\) | −1.02259 | − | 3.14722i | −0.0462907 | − | 0.142468i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.11608 | + | 2.26396i | −0.140770 | + | 0.102275i | ||||
\(491\) | −11.5019 | − | 35.3991i | −0.519071 | − | 1.59754i | −0.775750 | − | 0.631040i | \(-0.782628\pi\) |
0.256679 | − | 0.966497i | \(-0.417372\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.4742 | − | 9.06302i | −0.561809 | − | 0.408178i | ||||
\(494\) | 3.72536 | 0.167612 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.50554 | −0.0676006 | ||||||||
\(497\) | −2.57963 | − | 1.87421i | −0.115712 | − | 0.0840698i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.83087 | − | 30.2563i | −0.440090 | − | 1.35446i | −0.887780 | − | 0.460269i | \(-0.847753\pi\) |
0.447689 | − | 0.894189i | \(-0.352247\pi\) | |||||||
\(500\) | −4.12090 | + | 2.99401i | −0.184292 | + | 0.133896i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.987334 | − | 3.03870i | −0.0440669 | − | 0.135624i | ||||
\(503\) | 5.93493 | − | 18.2658i | 0.264626 | − | 0.814434i | −0.727154 | − | 0.686474i | \(-0.759157\pi\) |
0.991779 | − | 0.127959i | \(-0.0408426\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −53.3788 | −2.37532 | ||||||||
\(506\) | −2.46229 | − | 1.68456i | −0.109462 | − | 0.0748877i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.9274 | + | 8.66577i | 0.529193 | + | 0.384481i | ||||
\(509\) | −0.777328 | + | 2.39237i | −0.0344545 | + | 0.106040i | −0.966805 | − | 0.255516i | \(-0.917754\pi\) |
0.932350 | + | 0.361556i | \(0.117754\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.992078 | + | 0.720787i | −0.0438869 | + | 0.0318857i | ||||
\(512\) | −15.7059 | + | 11.4110i | −0.694109 | + | 0.504300i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.71978 | − | 23.7590i | 0.340505 | − | 1.04797i | ||||
\(515\) | 24.9073 | + | 18.0962i | 1.09755 | + | 0.797416i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.07588 | − | 24.0764i | 0.311197 | − | 1.05888i | ||||
\(518\) | −11.2135 | −0.492693 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.76107 | − | 20.8084i | 0.296493 | − | 0.912510i | ||||
\(521\) | −4.60335 | − | 14.1677i | −0.201677 | − | 0.620697i | −0.999834 | − | 0.0182471i | \(-0.994191\pi\) |
0.798157 | − | 0.602450i | \(-0.205809\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.01333 | − | 5.82203i | 0.350399 | − | 0.254579i | −0.398638 | − | 0.917109i | \(-0.630517\pi\) |
0.749036 | + | 0.662529i | \(0.230517\pi\) | |||||||
\(524\) | 1.19755 | + | 3.68567i | 0.0523151 | + | 0.161009i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.893242 | − | 0.648979i | −0.0389472 | − | 0.0282968i | ||||
\(527\) | −1.52459 | −0.0664122 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3485 | −0.971675 | ||||||||
\(530\) | 33.7236 | + | 24.5016i | 1.46486 | + | 1.06428i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.380136 | − | 1.16994i | −0.0164810 | − | 0.0507232i | ||||
\(533\) | 3.54276 | − | 2.57397i | 0.153454 | − | 0.111491i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.75097 | + | 11.5443i | 0.162169 | + | 0.499104i | ||||
\(536\) | 2.28253 | − | 7.02491i | 0.0985904 | − | 0.303430i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.01342 | −0.345483 | ||||||||
\(539\) | 2.62694 | − | 2.02465i | 0.113150 | − | 0.0872077i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.8052 | + | 12.9362i | 0.765503 | + | 0.556171i | 0.900593 | − | 0.434663i | \(-0.143132\pi\) |
−0.135090 | + | 0.990833i | \(0.543132\pi\) | |||||||
\(542\) | 9.35508 | − | 28.7920i | 0.401835 | − | 1.23672i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.28768 | + | 4.56826i | −0.269582 | + | 0.195863i | ||||
\(545\) | 10.8389 | − | 7.87494i | 0.464289 | − | 0.337325i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.35724 | + | 10.3325i | −0.143545 | + | 0.441787i | −0.996821 | − | 0.0796728i | \(-0.974612\pi\) |
0.853276 | + | 0.521460i | \(0.174612\pi\) | |||||||
\(548\) | −5.58049 | − | 4.05446i | −0.238387 | − | 0.173198i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −20.3309 | + | 15.6695i | −0.866912 | + | 0.668150i | ||||
\(551\) | −12.9410 | −0.551303 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.93004 | + | 9.01775i | −0.124598 | + | 0.383474i | ||||
\(554\) | −7.22721 | − | 22.2431i | −0.307055 | − | 0.945018i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.98184 | + | 5.79915i | −0.338506 | + | 0.245939i | ||||
\(557\) | −10.3869 | − | 31.9675i | −0.440105 | − | 1.35451i | −0.887763 | − | 0.460300i | \(-0.847742\pi\) |
0.447658 | − | 0.894205i | \(-0.352258\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.13290 | + | 3.72927i | 0.217098 | + | 0.157731i | ||||
\(560\) | 6.59959 | 0.278884 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −31.3811 | −1.32373 | ||||||||
\(563\) | −1.66130 | − | 1.20701i | −0.0700155 | − | 0.0508693i | 0.552227 | − | 0.833694i | \(-0.313778\pi\) |
−0.622242 | + | 0.782825i | \(0.713778\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.3782 | + | 35.0186i | 0.478686 | + | 1.47324i | ||||
\(566\) | −23.6151 | + | 17.1573i | −0.992615 | + | 0.721177i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.02857 | + | 9.32098i | 0.127076 | + | 0.391099i | ||||
\(569\) | −1.01177 | + | 3.11391i | −0.0424156 | + | 0.130542i | −0.970022 | − | 0.243017i | \(-0.921863\pi\) |
0.927606 | + | 0.373559i | \(0.121863\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.8897 | −1.83673 | −0.918363 | − | 0.395738i | \(-0.870489\pi\) | ||||
−0.918363 | + | 0.395738i | \(0.870489\pi\) | |||||||
\(572\) | −1.45995 | + | 4.96763i | −0.0610437 | + | 0.207707i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.91697 | + | 1.39276i | 0.0800128 | + | 0.0581327i | ||||
\(575\) | 1.73208 | − | 5.33080i | 0.0722328 | − | 0.222310i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.5081 | − | 25.7981i | 1.47822 | − | 1.07399i | 0.500096 | − | 0.865970i | \(-0.333298\pi\) |
0.978125 | − | 0.208020i | \(-0.0667019\pi\) | |||||||
\(578\) | −11.9561 | + | 8.68664i | −0.497310 | + | 0.361317i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.45466 | + | 19.8654i | −0.268015 | + | 0.824866i | ||||
\(581\) | −13.0004 | − | 9.44536i | −0.539348 | − | 0.391859i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29.6245 | − | 20.2674i | −1.22692 | − | 0.839389i | ||||
\(584\) | 3.76915 | 0.155969 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.53730 | + | 4.73133i | −0.0635054 | + | 0.195449i | ||||
\(587\) | −0.862670 | − | 2.65503i | −0.0356062 | − | 0.109585i | 0.931674 | − | 0.363296i | \(-0.118349\pi\) |
−0.967280 | + | 0.253711i | \(0.918349\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.03520 | + | 0.752114i | −0.0426545 | + | 0.0309903i | ||||
\(590\) | 3.92378 | + | 12.0761i | 0.161539 | + | 0.497167i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 15.5441 | + | 11.2935i | 0.638859 | + | 0.464158i | ||||
\(593\) | −23.2526 | −0.954871 | −0.477435 | − | 0.878667i | \(-0.658434\pi\) | ||||
−0.477435 | + | 0.878667i | \(0.658434\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.68312 | 0.273981 | ||||||||
\(596\) | 1.92945 | + | 1.40183i | 0.0790334 | + | 0.0574211i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.572519 | + | 1.76203i | 0.0234120 | + | 0.0720549i | ||||
\(599\) | 8.46187 | − | 6.14791i | 0.345743 | − | 0.251197i | −0.401338 | − | 0.915930i | \(-0.631455\pi\) |
0.747081 | + | 0.664733i | \(0.231455\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.89406 | + | 21.2177i | 0.281215 | + | 0.865489i | 0.987508 | + | 0.157570i | \(0.0503660\pi\) |
−0.706293 | + | 0.707919i | \(0.749634\pi\) | |||||||
\(602\) | −1.06087 | + | 3.26501i | −0.0432376 | + | 0.133072i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.17306 | −0.0884204 | ||||||||
\(605\) | 29.4422 | − | 24.0507i | 1.19700 | − | 0.977800i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.3619 | − | 11.1611i | −0.623522 | − | 0.453015i | 0.230628 | − | 0.973042i | \(-0.425922\pi\) |
−0.854150 | + | 0.520027i | \(0.825922\pi\) | |||||||
\(608\) | −2.01571 | + | 6.20370i | −0.0817477 | + | 0.251593i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.35485 | − | 2.43744i | 0.135834 | − | 0.0986892i | ||||
\(611\) | −12.6077 | + | 9.16004i | −0.510053 | + | 0.370576i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.23030 | − | 19.1749i | 0.251639 | − | 0.774467i | −0.742834 | − | 0.669476i | \(-0.766519\pi\) |
0.994473 | − | 0.104991i | \(-0.0334813\pi\) | |||||||
\(614\) | 11.6166 | + | 8.43995i | 0.468807 | + | 0.340608i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.1901 | + | 0.288607i | −0.410570 | + | 0.0116283i | ||||
\(617\) | −7.03919 | −0.283387 | −0.141694 | − | 0.989911i | \(-0.545255\pi\) | ||||
−0.141694 | + | 0.989911i | \(0.545255\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.60520 | + | 29.5618i | −0.386066 | + | 1.18819i | 0.549639 | + | 0.835402i | \(0.314765\pi\) |
−0.935704 | + | 0.352785i | \(0.885235\pi\) | |||||||
\(620\) | 0.638222 | + | 1.96425i | 0.0256316 | + | 0.0788860i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.1814 | + | 17.5688i | −0.969585 | + | 0.704445i | ||||
\(623\) | 1.37151 | + | 4.22108i | 0.0549484 | + | 0.169114i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.30098 | + | 6.75756i | 0.372039 | + | 0.270302i | ||||
\(626\) | −3.99947 | −0.159851 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.2883 | 0.649973 | ||||||||
\(629\) | 15.7408 | + | 11.4364i | 0.627628 | + | 0.455998i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.78971 | + | 20.8966i | 0.270294 | + | 0.831880i | 0.990426 | + | 0.138043i | \(0.0440812\pi\) |
−0.720132 | + | 0.693837i | \(0.755919\pi\) | |||||||
\(632\) | 23.5779 | − | 17.1303i | 0.937879 | − | 0.681409i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.82639 | − | 17.9318i | −0.231396 | − | 0.712163i | ||||
\(635\) | −20.7733 | + | 63.9337i | −0.824364 | + | 2.53713i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.05965 | −0.0816064 | ||||||||
\(638\) | −8.31039 | + | 28.2770i | −0.329012 | + | 1.11950i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.38290 | − | 2.45782i | −0.133721 | − | 0.0971538i | ||||
\(641\) | 4.10713 | − | 12.6404i | 0.162222 | − | 0.499267i | −0.836599 | − | 0.547816i | \(-0.815460\pi\) |
0.998821 | + | 0.0485485i | \(0.0154595\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.8848 | + | 8.63480i | −0.468690 | + | 0.340523i | −0.796930 | − | 0.604071i | \(-0.793544\pi\) |
0.328241 | + | 0.944594i | \(0.393544\pi\) | |||||||
\(644\) | 0.494940 | − | 0.359595i | 0.0195034 | − | 0.0141700i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.08082 | − | 3.32642i | 0.0425242 | − | 0.130876i | ||||
\(647\) | −4.97160 | − | 3.61208i | −0.195454 | − | 0.142005i | 0.485754 | − | 0.874095i | \(-0.338545\pi\) |
−0.681208 | + | 0.732090i | \(0.738545\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.67174 | − | 10.2988i | −0.144128 | − | 0.404261i | ||||
\(650\) | 15.9404 | 0.625236 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.92589 | − | 5.92729i | 0.0754238 | − | 0.232131i | ||||
\(653\) | 12.5674 | + | 38.6786i | 0.491802 | + | 1.51361i | 0.821882 | + | 0.569658i | \(0.192924\pi\) |
−0.330079 | + | 0.943953i | \(0.607076\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.2956 | + | 10.3864i | −0.558576 | + | 0.405829i | ||||
\(656\) | −1.25460 | − | 3.86127i | −0.0489841 | − | 0.150757i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.82196 | − | 4.95645i | −0.265948 | − | 0.193222i | ||||
\(659\) | −18.0090 | −0.701531 | −0.350765 | − | 0.936463i | \(-0.614079\pi\) | ||||
−0.350765 | + | 0.936463i | \(0.614079\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.1420 | −0.666745 | −0.333373 | − | 0.942795i | \(-0.608187\pi\) | ||||
−0.333373 | + | 0.942795i | \(0.608187\pi\) | |||||||
\(662\) | −1.11644 | − | 0.811145i | −0.0433919 | − | 0.0315260i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.2629 | + | 46.9744i | 0.592316 | + | 1.82296i | ||||
\(665\) | 4.53784 | − | 3.29693i | 0.175970 | − | 0.127850i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.98878 | − | 6.12085i | −0.0770060 | − | 0.237000i | ||||
\(668\) | −5.08466 | + | 15.6490i | −0.196732 | + | 0.605478i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.25613 | 0.357596 | ||||||||
\(671\) | −2.82823 | + | 2.17979i | −0.109183 | + | 0.0841498i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.7632 | + | 13.6322i | 0.723268 | + | 0.525485i | 0.887426 | − | 0.460949i | \(-0.152491\pi\) |
−0.164159 | + | 0.986434i | \(0.552491\pi\) | |||||||
\(674\) | 7.05329 | − | 21.7078i | 0.271683 | − | 0.836153i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.37035 | + | 3.90179i | −0.206552 | + | 0.150069i | ||||
\(677\) | −22.3050 | + | 16.2056i | −0.857252 | + | 0.622830i | −0.927136 | − | 0.374725i | \(-0.877737\pi\) |
0.0698841 | + | 0.997555i | \(0.477737\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.99874 | − | 6.15150i | 0.0767047 | − | 0.236073i | ||||
\(680\) | −16.6185 | − | 12.0741i | −0.637291 | − | 0.463019i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.978646 | + | 2.74497i | 0.0374743 | + | 0.105110i | ||||
\(683\) | −21.9351 | −0.839322 | −0.419661 | − | 0.907681i | \(-0.637851\pi\) | ||||
−0.419661 | + | 0.907681i | \(0.637851\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.71923 | − | 29.9127i | 0.371353 | − | 1.14291i | ||||
\(686\) | −0.344389 | − | 1.05992i | −0.0131488 | − | 0.0404680i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.75885 | − | 3.45751i | 0.181430 | − | 0.131816i | ||||
\(689\) | 6.88814 | + | 21.1995i | 0.262417 | + | 0.807637i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.7647 | + | 15.0865i | 0.789928 | + | 0.573916i | 0.907942 | − | 0.419096i | \(-0.137653\pi\) |
−0.118014 | + | 0.993012i | \(0.537653\pi\) | |||||||
\(692\) | −6.09830 | −0.231823 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.3913 | 1.15364 | ||||||||
\(695\) | −36.3947 | − | 26.4423i | −1.38053 | − | 1.00301i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.27048 | − | 3.91014i | −0.0481229 | − | 0.148107i | ||||
\(698\) | 7.19886 | − | 5.23028i | 0.272481 | − | 0.197969i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.62656 | − | 5.00604i | −0.0614782 | − | 0.189211i | ||||
\(701\) | 5.69007 | − | 17.5122i | 0.214911 | − | 0.661428i | −0.784249 | − | 0.620446i | \(-0.786951\pi\) |
0.999160 | − | 0.0409817i | \(-0.0130485\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.3298 | 0.615892 | ||||||||
\(704\) | 22.7153 | + | 15.5405i | 0.856114 | + | 0.585704i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.35087 | − | 3.88764i | −0.201383 | − | 0.146313i | ||||
\(707\) | 4.77274 | − | 14.6890i | 0.179497 | − | 0.552436i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.1430 | + | 13.9082i | −0.718930 | + | 0.522334i | −0.886042 | − | 0.463604i | \(-0.846556\pi\) |
0.167112 | + | 0.985938i | \(0.446556\pi\) | |||||||
\(710\) | −9.93591 | + | 7.21886i | −0.372888 | + | 0.270919i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.21556 | − | 12.9741i | 0.157985 | − | 0.486227i | ||||
\(713\) | −0.514827 | − | 0.374044i | −0.0192804 | − | 0.0140081i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.5993 | + | 0.668389i | −0.882565 | + | 0.0249963i | ||||
\(716\) | −2.74452 | −0.102568 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.78763 | − | 30.1232i | 0.365271 | − | 1.12419i | ||||
\(719\) | −3.43696 | − | 10.5779i | −0.128177 | − | 0.394488i | 0.866289 | − | 0.499542i | \(-0.166498\pi\) |
−0.994467 | + | 0.105054i | \(0.966498\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.20682 | + | 5.23606i | −0.268396 | + | 0.195001i | ||||
\(722\) | 5.63627 | + | 17.3467i | 0.209760 | + | 0.645576i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.69964 | + | 7.04720i | 0.360484 | + | 0.261907i | ||||
\(725\) | −55.3730 | −2.05650 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.4803 | 1.57551 | 0.787753 | − | 0.615991i | \(-0.211244\pi\) | ||||
0.787753 | + | 0.615991i | \(0.211244\pi\) | |||||||
\(728\) | 5.12162 | + | 3.72107i | 0.189820 | + | 0.137912i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.45956 | + | 4.49205i | 0.0540206 | + | 0.166258i | ||||
\(731\) | 4.81908 | − | 3.50127i | 0.178240 | − | 0.129499i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.85660 | + | 21.1025i | 0.253254 | + | 0.779437i | 0.994169 | + | 0.107837i | \(0.0343925\pi\) |
−0.740914 | + | 0.671600i | \(0.765607\pi\) | |||||||
\(734\) | 10.4699 | − | 32.2231i | 0.386452 | − | 1.18938i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.24402 | −0.119576 | ||||||||
\(737\) | −7.96712 | + | 0.225648i | −0.293473 | + | 0.00831184i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.8240 | − | 17.3092i | −0.876381 | − | 0.636728i | 0.0559106 | − | 0.998436i | \(-0.482194\pi\) |
−0.932292 | + | 0.361708i | \(0.882194\pi\) | |||||||
\(740\) | 8.14496 | − | 25.0676i | 0.299415 | − | 0.921504i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.75776 | + | 7.08943i | −0.358219 | + | 0.260261i | ||||
\(743\) | 13.6772 | − | 9.93704i | 0.501766 | − | 0.364555i | −0.307925 | − | 0.951411i | \(-0.599635\pi\) |
0.809691 | + | 0.586856i | \(0.199635\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.36042 | + | 10.3423i | −0.123116 | + | 0.378913i | ||||
\(746\) | 13.0037 | + | 9.44774i | 0.476099 | + | 0.345906i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.01208 | + | 2.74484i | 0.146696 | + | 0.100361i | ||||
\(749\) | −3.51219 | −0.128333 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.479429 | + | 1.47553i | −0.0174946 | + | 0.0538429i | −0.959423 | − | 0.281972i | \(-0.909012\pi\) |
0.941928 | + | 0.335815i | \(0.109012\pi\) | |||||||
\(752\) | 4.46479 | + | 13.7412i | 0.162814 | + | 0.501090i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14.8074 | − | 10.7582i | 0.539252 | − | 0.391789i | ||||
\(755\) | −3.06188 | − | 9.42349i | −0.111433 | − | 0.342956i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.1505 | − | 7.37474i | −0.368925 | − | 0.268040i | 0.387840 | − | 0.921727i | \(-0.373221\pi\) |
−0.756765 | + | 0.653687i | \(0.773221\pi\) | |||||||
\(758\) | 24.9721 | 0.907027 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −17.2404 | −0.625375 | ||||||||
\(761\) | −7.30895 | − | 5.31026i | −0.264949 | − | 0.192497i | 0.447377 | − | 0.894346i | \(-0.352358\pi\) |
−0.712326 | + | 0.701849i | \(0.752358\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.19792 | + | 3.68682i | 0.0433676 | + | 0.133472i | ||||
\(764\) | −0.263115 | + | 0.191164i | −0.00951916 | + | 0.00691608i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.5985 | + | 35.6966i | 0.419072 | + | 1.28977i | ||||
\(767\) | −2.09820 | + | 6.45761i | −0.0757617 | + | 0.233171i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.1383 | −0.581963 | −0.290981 | − | 0.956729i | \(-0.593982\pi\) | ||||
−0.290981 | + | 0.956729i | \(0.593982\pi\) | |||||||
\(770\) | −4.28994 | − | 12.0327i | −0.154599 | − | 0.433629i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.30529 | − | 6.76069i | −0.334905 | − | 0.243323i | ||||
\(773\) | 5.69007 | − | 17.5122i | 0.204657 | − | 0.629871i | −0.795070 | − | 0.606518i | \(-0.792566\pi\) |
0.999727 | − | 0.0233530i | \(-0.00743416\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.42950 | + | 3.21822i | −0.159112 | + | 0.115602i | ||||
\(776\) | −16.0838 | + | 11.6855i | −0.577374 | + | 0.419487i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.836118 | − | 2.57331i | 0.0299763 | − | 0.0922575i | ||||
\(779\) | −2.79162 | − | 2.02823i | −0.100020 | − | 0.0726689i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.37624 | − | 6.45578i | 0.299726 | − | 0.231006i | ||||
\(782\) | 1.73944 | 0.0622022 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.590087 | + | 1.81610i | −0.0210745 | + | 0.0648608i | ||||
\(785\) | 22.9505 | + | 70.6344i | 0.819139 | + | 2.52105i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.0133 | + | 27.6183i | −1.35503 | + | 0.984486i | −0.356284 | + | 0.934378i | \(0.615957\pi\) |
−0.998744 | + | 0.0501080i | \(0.984043\pi\) | |||||||
\(788\) | −4.87378 | − | 14.9999i | −0.173621 | − | 0.534351i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 29.5461 | + | 21.4665i | 1.05120 | + | 0.763744i | ||||
\(791\) | −10.6539 | −0.378810 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.21748 | 0.0787450 | ||||||||
\(794\) | −5.31683 | − | 3.86291i | −0.188687 | − | 0.137089i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.97818 | − | 6.08821i | −0.0701147 | − | 0.215791i | ||||
\(797\) | −2.52781 | + | 1.83656i | −0.0895395 | + | 0.0650543i | −0.631654 | − | 0.775250i | \(-0.717624\pi\) |
0.542115 | + | 0.840304i | \(0.317624\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.52129 | + | 13.9151i | 0.159952 | + | 0.492281i | ||||
\(800\) | −8.62499 | + | 26.5450i | −0.304940 | + | 0.938507i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.5261 | 0.442314 | ||||||||
\(803\) | −1.36581 | − | 3.83091i | −0.0481982 | − | 0.135190i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.25677 | + | 1.63964i | 0.0795408 | + | 0.0577897i | ||||
\(806\) | 0.559243 | − | 1.72117i | 0.0196985 | − | 0.0606258i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −38.4059 | + | 27.9036i | −1.35112 | + | 0.981643i | ||||
\(809\) | −26.4756 | + | 19.2357i | −0.930833 | + | 0.676290i | −0.946197 | − | 0.323592i | \(-0.895109\pi\) |
0.0153636 | + | 0.999882i | \(0.495109\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.0929 | − | 31.0627i | 0.354410 | − | 1.09076i | −0.601941 | − | 0.798540i | \(-0.705606\pi\) |
0.956351 | − | 0.292220i | \(-0.0943941\pi\) | |||||||
\(812\) | −4.88951 | − | 3.55243i | −0.171588 | − | 0.124666i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.4867 | − | 35.6819i | 0.367557 | − | 1.25065i | ||||
\(815\) | 28.4174 | 0.995419 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.54490 | − | 4.75472i | 0.0540493 | − | 0.166347i | ||||
\(818\) | −10.1024 | − | 31.0921i | −0.353224 | − | 1.08711i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.50589 | + | 3.27372i | −0.157352 | + | 0.114323i | ||||
\(821\) | 2.29644 | + | 7.06770i | 0.0801461 | + | 0.246664i | 0.983099 | − | 0.183075i | \(-0.0586053\pi\) |
−0.902953 | + | 0.429740i | \(0.858605\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.30607 | − | 3.85509i | −0.184958 | − | 0.134380i | 0.491453 | − | 0.870904i | \(-0.336466\pi\) |
−0.676411 | + | 0.736524i | \(0.736466\pi\) | |||||||
\(824\) | 27.3805 | 0.953846 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.67399 | −0.127835 | ||||||||
\(827\) | 19.2982 | + | 14.0209i | 0.671063 | + | 0.487556i | 0.870381 | − | 0.492379i | \(-0.163873\pi\) |
−0.199318 | + | 0.979935i | \(0.563873\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.07867 | − | 24.8636i | −0.280584 | − | 0.863549i | −0.987688 | − | 0.156439i | \(-0.949999\pi\) |
0.707104 | − | 0.707110i | \(-0.250001\pi\) | |||||||
\(830\) | −50.0735 | + | 36.3805i | −1.73808 | + | 1.26279i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.28164 | − | 16.2552i | −0.183108 | − | 0.563548i | ||||
\(833\) | −0.597555 | + | 1.83909i | −0.0207041 | + | 0.0637205i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −75.0265 | −2.59640 | ||||||||
\(836\) | 4.07830 | − | 0.115507i | 0.141051 | − | 0.00399489i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18.2901 | + | 13.2886i | 0.631823 | + | 0.459046i | ||||
\(839\) | −10.5959 | + | 32.6107i | −0.365810 | + | 1.12585i | 0.583662 | + | 0.811997i | \(0.301619\pi\) |
−0.949472 | + | 0.313851i | \(0.898381\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9754 | + | 20.3253i | −0.964670 | + | 0.700874i | ||||
\(842\) | −2.75899 | + | 2.00452i | −0.0950810 | + | 0.0690804i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.30928 | − | 7.10722i | 0.0794885 | − | 0.244641i | ||||
\(845\) | −24.4871 | − | 17.7909i | −0.842383 | − | 0.612027i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.98586 | + | 10.2525i | 0.136956 | + | 0.352279i | ||||
\(848\) | 20.6661 | 0.709678 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.62471 | − | 14.2334i | 0.158626 | − | 0.488201i | ||||
\(851\) | 2.50959 | + | 7.72373i | 0.0860277 | + | 0.264766i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.3002 | + | 12.5693i | −0.592347 | + | 0.430365i | −0.843154 | − | 0.537672i | \(-0.819304\pi\) |
0.250807 | + | 0.968037i | \(0.419304\pi\) | |||||||
\(854\) | 0.370779 | + | 1.14114i | 0.0126878 | + | 0.0390490i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.73356 | + | 6.34530i | 0.298507 | + | 0.216878i | ||||
\(857\) | −42.8697 | −1.46440 | −0.732200 | − | 0.681090i | \(-0.761506\pi\) | ||||
−0.732200 | + | 0.681090i | \(0.761506\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.3915 | −1.03695 | −0.518473 | − | 0.855094i | \(-0.673499\pi\) | ||||
−0.518473 | + | 0.855094i | \(0.673499\pi\) | |||||||
\(860\) | −6.52831 | − | 4.74310i | −0.222614 | − | 0.161738i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.59737 | + | 7.99389i | 0.0884668 | + | 0.272273i | ||||
\(863\) | 9.56130 | − | 6.94669i | 0.325471 | − | 0.236468i | −0.413036 | − | 0.910715i | \(-0.635532\pi\) |
0.738506 | + | 0.674247i | \(0.235532\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.59263 | − | 26.4454i | −0.292158 | − | 0.899170i | ||||
\(866\) | 11.0761 | − | 34.0887i | 0.376381 | − | 1.15838i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.597594 | −0.0202837 | ||||||||
\(869\) | −25.9548 | − | 17.7568i | −0.880456 | − | 0.602357i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.00434 | + | 2.90932i | 0.135682 | + | 0.0985786i | ||||
\(872\) | 3.68200 | − | 11.3320i | 0.124688 | − | 0.383750i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.18108 | − | 0.858104i | 0.0399506 | − | 0.0290258i | ||||
\(875\) | 5.43680 | − | 3.95007i | 0.183797 | − | 0.133537i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.84446 | + | 8.75436i | −0.0960507 | + | 0.295614i | −0.987526 | − | 0.157455i | \(-0.949671\pi\) |
0.891475 | + | 0.453069i | \(0.149671\pi\) | |||||||
\(878\) | −4.20810 | − | 3.05736i | −0.142016 | − | 0.103181i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.17182 | + | 21.0002i | −0.208052 | + | 0.707918i | ||||
\(881\) | 41.9030 | 1.41175 | 0.705874 | − | 0.708338i | \(-0.250555\pi\) | ||||
0.705874 | + | 0.708338i | \(0.250555\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.95906 | + | 15.2624i | −0.166886 | + | 0.513621i | −0.999170 | − | 0.0407275i | \(-0.987032\pi\) |
0.832285 | + | 0.554348i | \(0.187032\pi\) | |||||||
\(884\) | −0.932869 | − | 2.87108i | −0.0313758 | − | 0.0965647i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.5775 | + | 11.3177i | −0.523335 | + | 0.380225i | ||||
\(887\) | 10.4597 | + | 32.1917i | 0.351203 | + | 1.08089i | 0.958179 | + | 0.286171i | \(0.0923825\pi\) |
−0.606976 | + | 0.794720i | \(0.707618\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.7361 | − | 11.4330i | −0.527772 | − | 0.383449i | ||||
\(890\) | 17.0949 | 0.573024 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.1855 | −0.441482 | ||||||||
\(893\) | 9.93459 | + | 7.21790i | 0.332448 | + | 0.241538i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.86708 | − | 11.9017i | −0.129262 | − | 0.397829i | ||||
\(896\) | 0.978825 | − | 0.711158i | 0.0327002 | − | 0.0237581i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.76510 | − | 17.7432i | −0.192384 | − | 0.592097i | ||||
\(899\) | −1.94267 | + | 5.97892i | −0.0647916 | + | 0.199408i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.9277 | 0.697202 | ||||||||
\(902\) | −6.22455 | + | 4.79741i | −0.207255 | + | 0.159736i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 26.4925 | + | 19.2479i | 0.881127 | + | 0.640176i | ||||
\(905\) | −16.8933 | + | 51.9923i | −0.561553 | + | 1.72828i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.6787 | − | 25.9221i | 1.18469 | − | 0.860730i | 0.192000 | − | 0.981395i | \(-0.438503\pi\) |
0.992693 | + | 0.120665i | \(0.0385027\pi\) | |||||||
\(908\) | 7.74570 | − | 5.62758i | 0.257050 | − | 0.186758i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.45147 | + | 7.54486i | −0.0812655 | + | 0.250110i | ||||
\(911\) | 40.1075 | + | 29.1398i | 1.32882 | + | 0.965446i | 0.999777 | + | 0.0211316i | \(0.00672689\pi\) |
0.329045 | + | 0.944314i | \(0.393273\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.2133 | − | 32.5348i | 1.39706 | − | 1.07675i | ||||
\(914\) | 24.1810 | 0.799837 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.07120 | + | 3.29682i | −0.0353935 | + | 0.108930i | ||||
\(917\) | −1.57995 | − | 4.86260i | −0.0521746 | − | 0.160577i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.0019 | − | 23.9773i | 1.08863 | − | 0.790939i | 0.109466 | − | 0.993991i | \(-0.465086\pi\) |
0.979168 | + | 0.203052i | \(0.0650860\pi\) | |||||||
\(920\) | −2.64953 | − | 8.15440i | −0.0873523 | − | 0.268843i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.47986 | + | 3.98135i | 0.180470 | + | 0.131119i | ||||
\(923\) | −6.56740 | −0.216169 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 69.8737 | 2.29743 | ||||||||
\(926\) | −4.64082 | − | 3.37176i | −0.152507 | − | 0.110803i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.90326 | + | 30.4791i | 0.325090 | + | 1.00053i | ||||
\(929\) | 33.4876 | − | 24.3301i | 1.09869 | − | 0.798246i | 0.117846 | − | 0.993032i | \(-0.462401\pi\) |
0.980846 | + | 0.194786i | \(0.0624012\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.501522 | + | 1.54353i | 0.0164367 | + | 0.0505870i | ||||
\(932\) | 5.58785 | − | 17.1976i | 0.183036 | − | 0.563327i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.36790 | −0.142922 | ||||||||
\(935\) | −6.24993 | + | 21.2660i | −0.204394 | + | 0.695473i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.29155 | − | 0.938364i | −0.0421930 | − | 0.0306550i | 0.566489 | − | 0.824069i | \(-0.308301\pi\) |
−0.608682 | + | 0.793414i | \(0.708301\pi\) | |||||||
\(938\) | −0.827615 | + | 2.54714i | −0.0270226 | + | 0.0831670i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 16.0352 | − | 11.6503i | 0.523011 | − | 0.379990i | ||||
\(941\) | 5.75039 | − | 4.17790i | 0.187457 | − | 0.136196i | −0.490099 | − | 0.871667i | \(-0.663039\pi\) |
0.677556 | + | 0.735471i | \(0.263039\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.530297 | − | 1.63209i | 0.0172689 | − | 0.0531481i | ||||
\(944\) | 5.09287 | + | 3.70019i | 0.165759 | + | 0.120431i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.39731 | − | 6.42910i | −0.305533 | − | 0.209028i | ||||
\(947\) | 2.45986 | 0.0799347 | 0.0399674 | − | 0.999201i | \(-0.487275\pi\) | ||||
0.0399674 | + | 0.999201i | \(0.487275\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.780485 | + | 2.40209i | −0.0253356 | + | 0.0779750i | ||||
\(950\) | −3.88147 | − | 11.9459i | −0.125932 | − | 0.387578i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.80849 | − | 3.49357i | 0.155844 | − | 0.113227i | ||||
\(953\) | 8.83790 | + | 27.2003i | 0.286288 | + | 0.881103i | 0.986010 | + | 0.166688i | \(0.0533071\pi\) |
−0.699722 | + | 0.714415i | \(0.746693\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.19972 | − | 0.871648i | −0.0388221 | − | 0.0282059i | ||||
\(956\) | 6.69900 | 0.216661 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.8428 | −0.544168 | ||||||||
\(959\) | 7.36247 | + | 5.34915i | 0.237747 | + | 0.172733i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.38744 | − | 28.8916i | −0.302821 | − | 0.931986i | ||||
\(962\) | −18.6850 | + | 13.5754i | −0.602428 | + | 0.437690i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.43771 | − | 13.6579i | −0.142929 | − | 0.439890i | ||||
\(965\) | 16.2065 | − | 49.8785i | 0.521706 | − | 1.60565i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.213338 | −0.00686047 | −0.00343024 | − | 0.999994i | \(-0.501092\pi\) | ||||
−0.00343024 | + | 0.999994i | \(0.501092\pi\) | |||||||
\(968\) | 8.61122 | − | 32.6953i | 0.276775 | − | 1.05087i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −20.1550 | − | 14.6435i | −0.647138 | − | 0.470173i | ||||
\(971\) | 0.255927 | − | 0.787664i | 0.00821310 | − | 0.0252773i | −0.946866 | − | 0.321628i | \(-0.895770\pi\) |
0.955079 | + | 0.296351i | \(0.0957698\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.5306 | − | 7.65095i | 0.337597 | − | 0.245278i | ||||
\(974\) | 22.6098 | − | 16.4270i | 0.724465 | − | 0.526354i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.635304 | − | 1.95526i | 0.0203356 | − | 0.0625865i | ||||
\(977\) | 7.89369 | + | 5.73510i | 0.252542 | + | 0.183482i | 0.706852 | − | 0.707361i | \(-0.250114\pi\) |
−0.454311 | + | 0.890843i | \(0.650114\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.7143 | + | 0.416743i | −0.470271 | + | 0.0133192i | ||||
\(980\) | 2.61958 | 0.0836795 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.8184 | − | 39.4511i | 0.409052 | − | 1.25893i | ||||
\(983\) | −13.9428 | − | 42.9114i | −0.444705 | − | 1.36866i | −0.882807 | − | 0.469737i | \(-0.844349\pi\) |
0.438101 | − | 0.898926i | \(-0.355651\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 58.1803 | − | 42.2704i | 1.85378 | − | 1.34685i | ||||
\(986\) | −5.31011 | − | 16.3428i | −0.169108 | − | 0.520462i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.04978 | − | 1.48926i | −0.0652123 | − | 0.0473795i | ||||
\(989\) | 2.48632 | 0.0790604 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.5405 | 1.70077 | 0.850384 | − | 0.526162i | \(-0.176369\pi\) | ||||
0.850384 | + | 0.526162i | \(0.176369\pi\) | |||||||
\(992\) | 2.56361 | + | 1.86257i | 0.0813947 | + | 0.0591367i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.09812 | − | 3.37966i | −0.0348302 | − | 0.107196i | ||||
\(995\) | 23.6143 | − | 17.1568i | 0.748624 | − | 0.543907i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.62918 | − | 29.6356i | −0.304959 | − | 0.938568i | −0.979692 | − | 0.200506i | \(-0.935741\pi\) |
0.674733 | − | 0.738062i | \(-0.264259\pi\) | |||||||
\(998\) | 10.9562 | − | 33.7196i | 0.346812 | − | 1.06738i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 693.2.m.i.631.3 | 16 | ||
3.2 | odd | 2 | 77.2.f.b.15.2 | ✓ | 16 | ||
11.3 | even | 5 | inner | 693.2.m.i.190.3 | 16 | ||
11.5 | even | 5 | 7623.2.a.ct.1.3 | 8 | |||
11.6 | odd | 10 | 7623.2.a.cw.1.6 | 8 | |||
21.2 | odd | 6 | 539.2.q.g.312.2 | 32 | |||
21.5 | even | 6 | 539.2.q.f.312.2 | 32 | |||
21.11 | odd | 6 | 539.2.q.g.422.3 | 32 | |||
21.17 | even | 6 | 539.2.q.f.422.3 | 32 | |||
21.20 | even | 2 | 539.2.f.e.246.2 | 16 | |||
33.2 | even | 10 | 847.2.f.v.148.2 | 16 | |||
33.5 | odd | 10 | 847.2.a.p.1.6 | 8 | |||
33.8 | even | 10 | 847.2.f.x.729.3 | 16 | |||
33.14 | odd | 10 | 77.2.f.b.36.2 | yes | 16 | ||
33.17 | even | 10 | 847.2.a.o.1.3 | 8 | |||
33.20 | odd | 10 | 847.2.f.w.148.3 | 16 | |||
33.26 | odd | 10 | 847.2.f.w.372.3 | 16 | |||
33.29 | even | 10 | 847.2.f.v.372.2 | 16 | |||
33.32 | even | 2 | 847.2.f.x.323.3 | 16 | |||
231.47 | even | 30 | 539.2.q.f.410.3 | 32 | |||
231.80 | even | 30 | 539.2.q.f.520.2 | 32 | |||
231.83 | odd | 10 | 5929.2.a.bs.1.3 | 8 | |||
231.104 | even | 10 | 5929.2.a.bt.1.6 | 8 | |||
231.146 | even | 10 | 539.2.f.e.344.2 | 16 | |||
231.179 | odd | 30 | 539.2.q.g.520.2 | 32 | |||
231.212 | odd | 30 | 539.2.q.g.410.3 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.15.2 | ✓ | 16 | 3.2 | odd | 2 | ||
77.2.f.b.36.2 | yes | 16 | 33.14 | odd | 10 | ||
539.2.f.e.246.2 | 16 | 21.20 | even | 2 | |||
539.2.f.e.344.2 | 16 | 231.146 | even | 10 | |||
539.2.q.f.312.2 | 32 | 21.5 | even | 6 | |||
539.2.q.f.410.3 | 32 | 231.47 | even | 30 | |||
539.2.q.f.422.3 | 32 | 21.17 | even | 6 | |||
539.2.q.f.520.2 | 32 | 231.80 | even | 30 | |||
539.2.q.g.312.2 | 32 | 21.2 | odd | 6 | |||
539.2.q.g.410.3 | 32 | 231.212 | odd | 30 | |||
539.2.q.g.422.3 | 32 | 21.11 | odd | 6 | |||
539.2.q.g.520.2 | 32 | 231.179 | odd | 30 | |||
693.2.m.i.190.3 | 16 | 11.3 | even | 5 | inner | ||
693.2.m.i.631.3 | 16 | 1.1 | even | 1 | trivial | ||
847.2.a.o.1.3 | 8 | 33.17 | even | 10 | |||
847.2.a.p.1.6 | 8 | 33.5 | odd | 10 | |||
847.2.f.v.148.2 | 16 | 33.2 | even | 10 | |||
847.2.f.v.372.2 | 16 | 33.29 | even | 10 | |||
847.2.f.w.148.3 | 16 | 33.20 | odd | 10 | |||
847.2.f.w.372.3 | 16 | 33.26 | odd | 10 | |||
847.2.f.x.323.3 | 16 | 33.32 | even | 2 | |||
847.2.f.x.729.3 | 16 | 33.8 | even | 10 | |||
5929.2.a.bs.1.3 | 8 | 231.83 | odd | 10 | |||
5929.2.a.bt.1.6 | 8 | 231.104 | even | 10 | |||
7623.2.a.ct.1.3 | 8 | 11.5 | even | 5 | |||
7623.2.a.cw.1.6 | 8 | 11.6 | odd | 10 |