Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not 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: | \(6.76332905120\) |
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: | \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} - 1175 x^{7} + 2135 x^{6} - 2300 x^{5} + 1850 x^{4} - 925 x^{3} + 700 x^{2} + \cdots + 25 \) |
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 | 323.3 | ||
Root | \(0.901622 + 0.655067i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.323 |
Dual form | 847.2.f.x.729.3 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 | \(0.571083\pi\) | |||||||
\(3\) | −0.883423 | + | 2.71890i | −0.510045 | + | 1.56976i | 0.282076 | + | 0.959392i | \(0.408977\pi\) |
−0.792121 | + | 0.610364i | \(0.791023\pi\) | |||||||
\(4\) | −0.234224 | − | 0.720867i | −0.117112 | − | 0.360433i | ||||
\(5\) | −2.79603 | + | 2.03143i | −1.25042 | + | 0.908484i | −0.998246 | − | 0.0591979i | \(-0.981146\pi\) |
−0.252174 | + | 0.967682i | \(0.581146\pi\) | |||||||
\(6\) | −2.57757 | + | 1.87272i | −1.05229 | + | 0.764534i | ||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | 0.949813 | − | 2.92322i | 0.335810 | − | 1.03352i | ||||
\(9\) | −4.18492 | − | 3.04052i | −1.39497 | − | 1.01351i | ||||
\(10\) | −3.85168 | −1.21801 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.16688 | 0.625525 | ||||||||
\(13\) | −1.66629 | − | 1.21063i | −0.462147 | − | 0.335769i | 0.332226 | − | 0.943200i | \(-0.392200\pi\) |
−0.794373 | + | 0.607430i | \(0.792200\pi\) | |||||||
\(14\) | 0.344389 | − | 1.05992i | 0.0920419 | − | 0.283276i | ||||
\(15\) | −3.05318 | − | 9.39672i | −0.788328 | − | 2.42622i | ||||
\(16\) | 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 | \(0.224655\pi\) | |||||||
\(18\) | −1.78147 | − | 5.48280i | −0.419897 | − | 1.29231i | ||||
\(19\) | −0.501522 | + | 1.54353i | −0.115057 | + | 0.354109i | −0.991959 | − | 0.126560i | \(-0.959606\pi\) |
0.876902 | + | 0.480669i | \(0.159606\pi\) | |||||||
\(20\) | 2.11929 | + | 1.53975i | 0.473887 | + | 0.344299i | ||||
\(21\) | 2.85882 | 0.623845 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.807136 | −0.168299 | −0.0841497 | − | 0.996453i | \(-0.526817\pi\) | ||||
−0.0841497 | + | 0.996453i | \(0.526817\pi\) | |||||||
\(24\) | 7.10886 | + | 5.16489i | 1.45109 | + | 1.05428i | ||||
\(25\) | 2.14596 | − | 6.60459i | 0.429192 | − | 1.32092i | ||||
\(26\) | −0.709322 | − | 2.18307i | −0.139109 | − | 0.428135i | ||||
\(27\) | 5.02542 | − | 3.65118i | 0.967142 | − | 0.702670i | ||||
\(28\) | −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 | \(-0.365334\pi\) | |||||||
\(30\) | 3.40267 | − | 10.4723i | 0.621239 | − | 1.91198i | ||||
\(31\) | −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 | ||||
\(36\) | −1.21160 | + | 3.72893i | −0.201934 | + | 0.621488i | ||||
\(37\) | 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 | ||||
\(39\) | 4.76363 | − | 3.46098i | 0.762792 | − | 0.554200i | ||||
\(40\) | 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 | \(0.0469074\pi\) | |||||||
\(42\) | 2.57757 | + | 1.87272i | 0.397728 | + | 0.288967i | ||||
\(43\) | −3.08043 | −0.469761 | −0.234880 | − | 0.972024i | \(-0.575470\pi\) | ||||
−0.234880 | + | 0.972024i | \(0.575470\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 17.8777 | 2.66506 | ||||||||
\(46\) | −0.727732 | − | 0.528728i | −0.107298 | − | 0.0779567i | ||||
\(47\) | 2.33812 | − | 7.19600i | 0.341050 | − | 1.04964i | −0.622615 | − | 0.782529i | \(-0.713930\pi\) |
0.963665 | − | 0.267115i | \(-0.0860705\pi\) | |||||||
\(48\) | 1.68695 | + | 5.19190i | 0.243490 | + | 0.749387i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 6.26129 | − | 4.54910i | 0.885481 | − | 0.643339i | ||||
\(51\) | 1.70830 | + | 5.25761i | 0.239210 | + | 0.736213i | ||||
\(52\) | −0.482420 | + | 1.48474i | −0.0668996 | + | 0.205896i | ||||
\(53\) | −8.75554 | − | 6.36127i | −1.20267 | − | 0.873788i | −0.208122 | − | 0.978103i | \(-0.566735\pi\) |
−0.994544 | + | 0.104315i | \(0.966735\pi\) | |||||||
\(54\) | 6.92280 | 0.942073 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.07366 | −0.410735 | ||||||||
\(57\) | −3.75363 | − | 2.72717i | −0.497181 | − | 0.361223i | ||||
\(58\) | 2.74605 | − | 8.45147i | 0.360574 | − | 1.10973i | ||||
\(59\) | −1.01872 | − | 3.13529i | −0.132626 | − | 0.408180i | 0.862587 | − | 0.505908i | \(-0.168842\pi\) |
−0.995213 | + | 0.0977281i | \(0.968842\pi\) | |||||||
\(60\) | −6.05866 | + | 4.40187i | −0.782169 | + | 0.568279i | ||||
\(61\) | −0.871010 | + | 0.632826i | −0.111521 | + | 0.0810250i | −0.642148 | − | 0.766581i | \(-0.721957\pi\) |
0.530627 | + | 0.847606i | \(0.321957\pi\) | |||||||
\(62\) | −0.271523 | − | 0.835662i | −0.0344835 | − | 0.106129i | ||||
\(63\) | −1.59850 | + | 4.91966i | −0.201392 | + | 0.619819i | ||||
\(64\) | −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 | ||||
\(69\) | 0.713042 | − | 2.19452i | 0.0858402 | − | 0.264189i | ||||
\(70\) | 1.19024 | + | 3.66317i | 0.142260 | + | 0.437832i | ||||
\(71\) | 2.57963 | − | 1.87421i | 0.306145 | − | 0.222428i | −0.424095 | − | 0.905618i | \(-0.639408\pi\) |
0.730241 | + | 0.683190i | \(0.239408\pi\) | |||||||
\(72\) | −12.8630 | + | 9.34552i | −1.51592 | + | 1.10138i | ||||
\(73\) | −0.378940 | − | 1.16626i | −0.0443516 | − | 0.136500i | 0.926429 | − | 0.376470i | \(-0.122862\pi\) |
−0.970780 | + | 0.239970i | \(0.922862\pi\) | |||||||
\(74\) | −3.46516 | + | 10.6647i | −0.402817 | + | 1.23974i | ||||
\(75\) | 16.0614 | + | 11.6693i | 1.85461 | + | 1.34745i | ||||
\(76\) | 1.23015 | 0.141107 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.56217 | 0.743020 | ||||||||
\(79\) | −7.67096 | − | 5.57328i | −0.863050 | − | 0.627043i | 0.0656630 | − | 0.997842i | \(-0.479084\pi\) |
−0.928713 | + | 0.370799i | \(0.879084\pi\) | |||||||
\(80\) | −2.03939 | + | 6.27659i | −0.228010 | + | 0.701744i | ||||
\(81\) | 0.692124 | + | 2.13014i | 0.0769027 | + | 0.236682i | ||||
\(82\) | 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 | \(0.956249\pi\) | |||||||
\(84\) | −0.669603 | − | 2.06083i | −0.0730597 | − | 0.224855i | ||||
\(85\) | −2.06520 | + | 6.35602i | −0.224002 | + | 0.689407i | ||||
\(86\) | −2.77738 | − | 2.01789i | −0.299493 | − | 0.217594i | ||||
\(87\) | 22.7953 | 2.44391 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.43830 | −0.470459 | −0.235230 | − | 0.971940i | \(-0.575584\pi\) | ||||
−0.235230 | + | 0.971940i | \(0.575584\pi\) | |||||||
\(90\) | 16.1190 | + | 11.7111i | 1.69909 | + | 1.23446i | ||||
\(91\) | −0.636468 | + | 1.95885i | −0.0667199 | + | 0.205343i | ||||
\(92\) | 0.189050 | + | 0.581837i | 0.0197099 | + | 0.0606607i | ||||
\(93\) | 1.82348 | − | 1.32484i | 0.189086 | − | 0.137379i | ||||
\(94\) | 6.82196 | − | 4.95645i | 0.703632 | − | 0.511218i | ||||
\(95\) | −1.73330 | − | 5.33455i | −0.177833 | − | 0.547313i | ||||
\(96\) | 3.55063 | − | 10.9277i | 0.362385 | − | 1.11531i | ||||
\(97\) | −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 | \(0.978953\pi\) | |||||||
\(102\) | −1.90384 | + | 5.85943i | −0.188509 | + | 0.580170i | ||||
\(103\) | 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 | ||||
\(105\) | −7.99333 | + | 5.80749i | −0.780069 | + | 0.566753i | ||||
\(106\) | −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 | \(0.154302\pi\) | |||||||
\(108\) | −3.80909 | − | 2.76746i | −0.366530 | − | 0.266299i | ||||
\(109\) | −3.87655 | −0.371306 | −0.185653 | − | 0.982615i | \(-0.559440\pi\) | ||||
−0.185653 | + | 0.982615i | \(0.559440\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −28.7648 | −2.73023 | ||||||||
\(112\) | −1.54487 | − | 1.12241i | −0.145976 | − | 0.106058i | ||||
\(113\) | 3.29224 | − | 10.1325i | 0.309708 | − | 0.953183i | −0.668170 | − | 0.744008i | \(-0.732922\pi\) |
0.977878 | − | 0.209175i | \(-0.0670777\pi\) | |||||||
\(114\) | −1.59788 | − | 4.91776i | −0.149655 | − | 0.460591i | ||||
\(115\) | 2.25677 | − | 1.63964i | 0.210445 | − | 0.152897i | ||||
\(116\) | −4.88951 | + | 3.55243i | −0.453979 | + | 0.329835i | ||||
\(117\) | 3.29235 | + | 10.1328i | 0.304378 | + | 0.936778i | ||||
\(118\) | 1.13533 | − | 3.49417i | 0.104515 | − | 0.321665i | ||||
\(119\) | −1.56442 | − | 1.13662i | −0.143410 | − | 0.104194i | ||||
\(120\) | −30.3687 | −2.77227 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.19987 | −0.108631 | ||||||||
\(123\) | 4.91739 | + | 3.57269i | 0.443386 | + | 0.322139i | ||||
\(124\) | −0.184667 | + | 0.568346i | −0.0165836 | + | 0.0510389i | ||||
\(125\) | 2.07667 | + | 6.39134i | 0.185743 | + | 0.571659i | ||||
\(126\) | −4.66395 | + | 3.38856i | −0.415498 | + | 0.301877i | ||||
\(127\) | 15.7361 | − | 11.4330i | 1.39635 | − | 1.01451i | 0.401220 | − | 0.915982i | \(-0.368586\pi\) |
0.995134 | − | 0.0985289i | \(-0.0314137\pi\) | |||||||
\(128\) | −0.373878 | − | 1.15068i | −0.0330464 | − | 0.101706i | ||||
\(129\) | 2.72132 | − | 8.37537i | 0.239599 | − | 0.737410i | ||||
\(130\) | 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 | ||||
\(135\) | −6.63407 | + | 20.4176i | −0.570970 | + | 1.75727i | ||||
\(136\) | −1.83668 | − | 5.65272i | −0.157494 | − | 0.484717i | ||||
\(137\) | −7.36247 | + | 5.34915i | −0.629019 | + | 0.457009i | −0.856060 | − | 0.516876i | \(-0.827095\pi\) |
0.227042 | + | 0.973885i | \(0.427095\pi\) | |||||||
\(138\) | 2.08045 | − | 1.51154i | 0.177100 | − | 0.128671i | ||||
\(139\) | 4.02234 | + | 12.3795i | 0.341171 | + | 1.05002i | 0.963602 | + | 0.267341i | \(0.0861450\pi\) |
−0.622431 | + | 0.782675i | \(0.713855\pi\) | |||||||
\(140\) | 0.809496 | − | 2.49137i | 0.0684149 | − | 0.210559i | ||||
\(141\) | 17.4996 | + | 12.7142i | 1.47373 | + | 1.07073i | ||||
\(142\) | 3.55358 | 0.298210 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −9.87786 | −0.823155 | ||||||||
\(145\) | 22.2946 | + | 16.1980i | 1.85147 | + | 1.34517i | ||||
\(146\) | 0.422316 | − | 1.29975i | 0.0349511 | − | 0.107568i | ||||
\(147\) | −0.883423 | − | 2.71890i | −0.0728635 | − | 0.224251i | ||||
\(148\) | 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 | \(0.341140\pi\) | |||||||
\(150\) | 6.83715 | + | 21.0426i | 0.558251 | + | 1.71812i | ||||
\(151\) | −0.885940 | + | 2.72664i | −0.0720968 | + | 0.221891i | −0.980612 | − | 0.195962i | \(-0.937217\pi\) |
0.908515 | + | 0.417853i | \(0.137217\pi\) | |||||||
\(152\) | 4.03572 | + | 2.93212i | 0.327340 | + | 0.237827i | ||||
\(153\) | −10.0029 | −0.808684 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.72484 | 0.218864 | ||||||||
\(156\) | −3.61066 | − | 2.62330i | −0.289084 | − | 0.210032i | ||||
\(157\) | −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 | ||||
\(159\) | 25.0305 | − | 18.1857i | 1.98505 | − | 1.44222i | ||||
\(160\) | 11.2377 | − | 8.16468i | 0.888420 | − | 0.645475i | ||||
\(161\) | 0.249419 | + | 0.767632i | 0.0196569 | + | 0.0604978i | ||||
\(162\) | −0.771349 | + | 2.37397i | −0.0606029 | + | 0.186517i | ||||
\(163\) | 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 | \(-0.617404\pi\) | |||||||
\(168\) | 2.71534 | − | 8.35696i | 0.209493 | − | 0.644754i | ||||
\(169\) | −2.70632 | − | 8.32919i | −0.208178 | − | 0.640707i | ||||
\(170\) | −6.02565 | + | 4.37789i | −0.462146 | + | 0.335769i | ||||
\(171\) | 6.79195 | − | 4.93464i | 0.519393 | − | 0.377361i | ||||
\(172\) | 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 | \(0.00105970\pi\) | |||||||
\(174\) | 20.5527 | + | 14.9324i | 1.55810 | + | 1.13203i | ||||
\(175\) | −6.94447 | −0.524953 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.42449 | 0.708388 | ||||||||
\(178\) | −4.00167 | − | 2.90739i | −0.299938 | − | 0.217918i | ||||
\(179\) | −1.11892 | + | 3.44369i | −0.0836322 | + | 0.257393i | −0.984125 | − | 0.177478i | \(-0.943206\pi\) |
0.900493 | + | 0.434871i | \(0.143206\pi\) | |||||||
\(180\) | −4.18739 | − | 12.8875i | −0.312110 | − | 0.960575i | ||||
\(181\) | −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 | ||||
\(183\) | −0.951118 | − | 2.92724i | −0.0703087 | − | 0.216388i | ||||
\(184\) | −0.766628 | + | 2.35944i | −0.0565165 | + | 0.173940i | ||||
\(185\) | −28.1330 | − | 20.4398i | −2.06838 | − | 1.50276i | ||||
\(186\) | 2.51195 | 0.184185 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −5.73500 | −0.418268 | ||||||||
\(189\) | −5.02542 | − | 3.65118i | −0.365545 | − | 0.265584i | ||||
\(190\) | 1.93170 | − | 5.94518i | 0.140141 | − | 0.431308i | ||||
\(191\) | 0.132593 | + | 0.408080i | 0.00959411 | + | 0.0295276i | 0.955739 | − | 0.294216i | \(-0.0950585\pi\) |
−0.946145 | + | 0.323744i | \(0.895058\pi\) | |||||||
\(192\) | 19.1927 | − | 13.9443i | 1.38511 | − | 1.00634i | ||||
\(193\) | −12.2767 | + | 8.91954i | −0.883696 | + | 0.642042i | −0.934227 | − | 0.356680i | \(-0.883909\pi\) |
0.0505310 | + | 0.998722i | \(0.483909\pi\) | |||||||
\(194\) | −2.22753 | − | 6.85564i | −0.159927 | − | 0.492206i | ||||
\(195\) | −6.28849 | + | 19.3540i | −0.450328 | + | 1.38597i | ||||
\(196\) | 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 | ||||
\(201\) | −2.12299 | + | 6.53389i | −0.149744 | + | 0.460865i | ||||
\(202\) | −5.31906 | − | 16.3704i | −0.374247 | − | 1.15182i | ||||
\(203\) | −6.45084 | + | 4.68681i | −0.452760 | + | 0.328950i | ||||
\(204\) | 3.38991 | − | 2.46292i | 0.237341 | − | 0.172439i | ||||
\(205\) | 2.27068 | + | 6.98844i | 0.158591 | + | 0.488094i | ||||
\(206\) | −3.06786 | + | 9.44190i | −0.213748 | + | 0.657849i | ||||
\(207\) | 3.37779 | + | 2.45411i | 0.234773 | + | 0.170573i | ||||
\(208\) | −3.93303 | −0.272707 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −11.0113 | −0.759849 | ||||||||
\(211\) | −7.97632 | − | 5.79513i | −0.549112 | − | 0.398953i | 0.278346 | − | 0.960481i | \(-0.410214\pi\) |
−0.827458 | + | 0.561528i | \(0.810214\pi\) | |||||||
\(212\) | −2.53487 | + | 7.80154i | −0.174096 | + | 0.535812i | ||||
\(213\) | 2.81688 | + | 8.66946i | 0.193009 | + | 0.594022i | ||||
\(214\) | −3.16667 | + | 2.30072i | −0.216469 | + | 0.157274i | ||||
\(215\) | 8.61295 | − | 6.25768i | 0.587399 | − | 0.426770i | ||||
\(216\) | −5.90001 | − | 18.1584i | −0.401445 | − | 1.23552i | ||||
\(217\) | −0.243635 | + | 0.749832i | −0.0165390 | + | 0.0509019i | ||||
\(218\) | −3.49518 | − | 2.53940i | −0.236724 | − | 0.171990i | ||||
\(219\) | 3.50570 | 0.236893 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.98281 | −0.267913 | ||||||||
\(222\) | −25.9350 | − | 18.8429i | −1.74064 | − | 1.26465i | ||||
\(223\) | 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 | ||||
\(225\) | −29.0620 | + | 21.1148i | −1.93747 | + | 1.40765i | ||||
\(226\) | 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 | \(0.762314\pi\) | |||||||
\(228\) | −1.08674 | + | 3.34464i | −0.0719711 | + | 0.221504i | ||||
\(229\) | −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 | \(0.414476\pi\) | |||||||
\(234\) | −3.66921 | + | 11.2927i | −0.239864 | + | 0.738225i | ||||
\(235\) | 8.08073 | + | 24.8699i | 0.527129 | + | 1.62234i | ||||
\(236\) | −2.02152 | + | 1.46872i | −0.131590 | + | 0.0956054i | ||||
\(237\) | 21.9299 | − | 15.9330i | 1.42450 | − | 1.03496i | ||||
\(238\) | −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 | \(0.192275\pi\) | |||||||
\(240\) | −15.2638 | − | 11.0898i | −0.985271 | − | 0.715841i | ||||
\(241\) | −18.9464 | −1.22045 | −0.610224 | − | 0.792229i | \(-0.708921\pi\) | ||||
−0.610224 | + | 0.792229i | \(0.708921\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.2322 | 0.784696 | ||||||||
\(244\) | 0.660194 | + | 0.479659i | 0.0422646 | + | 0.0307070i | ||||
\(245\) | 1.06799 | − | 3.28693i | 0.0682312 | − | 0.209994i | ||||
\(246\) | 2.09328 | + | 6.44244i | 0.133462 | + | 0.410755i | ||||
\(247\) | 2.70433 | − | 1.96481i | 0.172072 | − | 0.125018i | ||||
\(248\) | −1.96052 | + | 1.42440i | −0.124493 | + | 0.0904495i | ||||
\(249\) | −14.1961 | − | 43.6911i | −0.899640 | − | 2.76881i | ||||
\(250\) | −2.31438 | + | 7.12294i | −0.146374 | + | 0.450494i | ||||
\(251\) | 2.31938 | + | 1.68513i | 0.146398 | + | 0.106364i | 0.658573 | − | 0.752516i | \(-0.271160\pi\) |
−0.512175 | + | 0.858881i | \(0.671160\pi\) | |||||||
\(252\) | 3.92083 | 0.246989 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 21.6774 | 1.36016 | ||||||||
\(255\) | −15.4569 | − | 11.2301i | −0.967950 | − | 0.703257i | ||||
\(256\) | −4.71199 | + | 14.5020i | −0.294500 | + | 0.906377i | ||||
\(257\) | 6.92689 | + | 21.3188i | 0.432087 | + | 1.32983i | 0.896042 | + | 0.443969i | \(0.146430\pi\) |
−0.463955 | + | 0.885859i | \(0.653570\pi\) | |||||||
\(258\) | 7.94003 | − | 5.76877i | 0.494325 | − | 0.359148i | ||||
\(259\) | 8.14014 | − | 5.91416i | 0.505804 | − | 0.367488i | ||||
\(260\) | −1.66728 | − | 5.13136i | −0.103400 | − | 0.318234i | ||||
\(261\) | −12.7459 | + | 39.2278i | −0.788951 | + | 2.42814i | ||||
\(262\) | −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 | ||||
\(267\) | 3.92090 | − | 12.0673i | 0.239955 | − | 0.738506i | ||||
\(268\) | −0.562873 | − | 1.73234i | −0.0343829 | − | 0.105820i | ||||
\(269\) | 5.81713 | − | 4.22639i | 0.354677 | − | 0.257688i | −0.396152 | − | 0.918185i | \(-0.629655\pi\) |
0.750828 | + | 0.660497i | \(0.229655\pi\) | |||||||
\(270\) | −19.3563 | + | 14.0632i | −1.17799 | + | 0.855858i | ||||
\(271\) | 8.39423 | + | 25.8348i | 0.509913 | + | 1.56935i | 0.792351 | + | 0.610065i | \(0.208857\pi\) |
−0.282438 | + | 0.959285i | \(0.591143\pi\) | |||||||
\(272\) | 1.14107 | − | 3.51185i | 0.0691874 | − | 0.212937i | ||||
\(273\) | −4.76363 | − | 3.46098i | −0.288308 | − | 0.209468i | ||||
\(274\) | −10.1422 | −0.612714 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.74897 | −0.105275 | ||||||||
\(277\) | 16.9777 | + | 12.3350i | 1.02009 | + | 0.741140i | 0.966302 | − | 0.257412i | \(-0.0828698\pi\) |
0.0537900 | + | 0.998552i | \(0.482870\pi\) | |||||||
\(278\) | −4.48277 | + | 13.7965i | −0.268859 | + | 0.827462i | ||||
\(279\) | 1.26029 | + | 3.87876i | 0.0754513 | + | 0.232215i | ||||
\(280\) | 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 | \(0.982624\pi\) | |||||||
\(282\) | 7.44939 | + | 22.9269i | 0.443605 | + | 1.36527i | ||||
\(283\) | 8.09369 | − | 24.9098i | 0.481120 | − | 1.48074i | −0.356403 | − | 0.934332i | \(-0.615997\pi\) |
0.837523 | − | 0.546403i | \(-0.184003\pi\) | |||||||
\(284\) | −1.95527 | − | 1.42058i | −0.116024 | − | 0.0842961i | ||||
\(285\) | 16.0353 | 0.949851 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.12613 | −0.125502 | ||||||||
\(288\) | 16.8199 | + | 12.2204i | 0.991123 | + | 0.720093i | ||||
\(289\) | −4.09778 | + | 12.6117i | −0.241046 | + | 0.741863i | ||||
\(290\) | 9.49056 | + | 29.2089i | 0.557305 | + | 1.71521i | ||||
\(291\) | 14.9596 | − | 10.8688i | 0.876945 | − | 0.637138i | ||||
\(292\) | −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 | \(0.858377\pi\) | |||||||
\(294\) | 0.984546 | − | 3.03012i | 0.0574199 | − | 0.176720i | ||||
\(295\) | 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 | ||||
\(300\) | 4.65004 | − | 14.3114i | 0.268470 | − | 0.826267i | ||||
\(301\) | 0.951904 | + | 2.92966i | 0.0548669 | + | 0.168863i | ||||
\(302\) | −2.58492 | + | 1.87805i | −0.148745 | + | 0.108070i | ||||
\(303\) | 35.7215 | − | 25.9532i | 2.05214 | − | 1.49097i | ||||
\(304\) | 0.957688 | + | 2.94746i | 0.0549271 | + | 0.169048i | ||||
\(305\) | 1.14982 | − | 3.53879i | 0.0658387 | − | 0.202631i | ||||
\(306\) | −9.01881 | − | 6.55255i | −0.515571 | − | 0.374584i | ||||
\(307\) | −12.8841 | −0.735334 | −0.367667 | − | 0.929957i | \(-0.619843\pi\) | ||||
−0.367667 | + | 0.929957i | \(0.619843\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.4667 | −1.44875 | ||||||||
\(310\) | 2.45678 | + | 1.78495i | 0.139536 | + | 0.101379i | ||||
\(311\) | 8.28779 | − | 25.5072i | 0.469957 | − | 1.44638i | −0.382682 | − | 0.923880i | \(-0.624999\pi\) |
0.852639 | − | 0.522500i | \(-0.175001\pi\) | |||||||
\(312\) | −5.59266 | − | 17.2124i | −0.316622 | − | 0.974463i | ||||
\(313\) | −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 | ||||
\(315\) | −5.52453 | − | 17.0027i | −0.311272 | − | 0.957996i | ||||
\(316\) | −2.22087 | + | 6.83513i | −0.124934 | + | 0.384506i | ||||
\(317\) | 13.6870 | + | 9.94418i | 0.768738 | + | 0.558521i | 0.901578 | − | 0.432617i | \(-0.142410\pi\) |
−0.132840 | + | 0.991138i | \(0.542410\pi\) | |||||||
\(318\) | 34.4809 | 1.93359 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 28.6798 | 1.60325 | ||||||||
\(321\) | −8.12311 | − | 5.90178i | −0.453388 | − | 0.329405i | ||||
\(322\) | −0.277969 | + | 0.855500i | −0.0154906 | + | 0.0476751i | ||||
\(323\) | 0.969808 | + | 2.98476i | 0.0539616 | + | 0.166077i | ||||
\(324\) | 1.37343 | − | 0.997859i | 0.0763019 | − | 0.0554366i | ||||
\(325\) | −11.5715 | + | 8.40721i | −0.641873 | + | 0.466348i | ||||
\(326\) | 2.83172 | + | 8.71515i | 0.156835 | + | 0.482687i | ||||
\(327\) | 3.42463 | − | 10.5399i | 0.189383 | − | 0.582860i | ||||
\(328\) | −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 | ||||
\(333\) | 16.0837 | − | 49.5005i | 0.881381 | − | 2.71261i | ||||
\(334\) | −7.47620 | − | 23.0094i | −0.409079 | − | 1.25902i | ||||
\(335\) | −6.71924 | + | 4.88181i | −0.367111 | + | 0.266722i | ||||
\(336\) | 4.41650 | − | 3.20877i | 0.240940 | − | 0.175053i | ||||
\(337\) | 6.32885 | + | 19.4782i | 0.344754 | + | 1.06104i | 0.961715 | + | 0.274051i | \(0.0883637\pi\) |
−0.616961 | + | 0.786994i | \(0.711636\pi\) | |||||||
\(338\) | 3.01610 | − | 9.28261i | 0.164054 | − | 0.504907i | ||||
\(339\) | 24.6407 | + | 17.9025i | 1.33830 | + | 0.972332i | ||||
\(340\) | 5.06556 | 0.274719 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 9.35630 | 0.505931 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | −2.92583 | + | 9.00478i | −0.157750 | + | 0.485505i | ||||
\(345\) | 2.46433 | + | 7.58443i | 0.132675 | + | 0.408332i | ||||
\(346\) | 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 | \(0.0386052\pi\) | |||||||
\(348\) | −5.33920 | − | 16.4324i | −0.286211 | − | 0.880868i | ||||
\(349\) | −2.46730 | + | 7.59356i | −0.132071 | + | 0.406474i | −0.995123 | − | 0.0986418i | \(-0.968550\pi\) |
0.863052 | + | 0.505116i | \(0.168550\pi\) | |||||||
\(350\) | −6.26129 | − | 4.54910i | −0.334680 | − | 0.243159i | ||||
\(351\) | −12.7941 | −0.682897 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.93472 | 0.315873 | 0.157937 | − | 0.987449i | \(-0.449516\pi\) | ||||
0.157937 | + | 0.987449i | \(0.449516\pi\) | |||||||
\(354\) | 8.49733 | + | 6.17367i | 0.451628 | + | 0.328127i | ||||
\(355\) | −3.40538 | + | 10.4807i | −0.180739 | + | 0.556256i | ||||
\(356\) | 1.03956 | + | 3.19942i | 0.0550964 | + | 0.169569i | ||||
\(357\) | 4.47239 | − | 3.24938i | 0.236704 | − | 0.171976i | ||||
\(358\) | −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 | \(-0.369938\pi\) | |||||||
\(360\) | 16.9805 | − | 52.2606i | 0.894951 | − | 2.75438i | ||||
\(361\) | 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 | ||||
\(366\) | 1.05999 | − | 3.26231i | 0.0554065 | − | 0.170524i | ||||
\(367\) | −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 | ||||
\(369\) | −8.89769 | + | 6.46455i | −0.463195 | + | 0.336531i | ||||
\(370\) | −11.9759 | − | 36.8580i | −0.622596 | − | 1.91615i | ||||
\(371\) | −3.34432 | + | 10.2928i | −0.173628 | + | 0.534373i | ||||
\(372\) | −1.38213 | − | 1.00418i | −0.0716603 | − | 0.0520643i | ||||
\(373\) | −14.4226 | −0.746772 | −0.373386 | − | 0.927676i | \(-0.621803\pi\) | ||||
−0.373386 | + | 0.927676i | \(0.621803\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −19.2120 | −0.992103 | ||||||||
\(376\) | −18.8147 | − | 13.6697i | −0.970296 | − | 0.704961i | ||||
\(377\) | −5.07499 | + | 15.6192i | −0.261375 | + | 0.804430i | ||||
\(378\) | −2.13926 | − | 6.58397i | −0.110032 | − | 0.338643i | ||||
\(379\) | 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 | ||||
\(381\) | 17.1834 | + | 52.8850i | 0.880331 | + | 2.70938i | ||||
\(382\) | −0.147771 | + | 0.454792i | −0.00756061 | + | 0.0232692i | ||||
\(383\) | −27.2465 | − | 19.7957i | −1.39223 | − | 1.01152i | −0.995616 | − | 0.0935305i | \(-0.970185\pi\) |
−0.396615 | − | 0.917985i | \(-0.629815\pi\) | |||||||
\(384\) | 3.45887 | 0.176510 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.9118 | −0.860790 | ||||||||
\(387\) | 12.8913 | + | 9.36610i | 0.655303 | + | 0.476106i | ||||
\(388\) | −1.51498 | + | 4.66262i | −0.0769112 | + | 0.236708i | ||||
\(389\) | 0.750241 | + | 2.30900i | 0.0380387 | + | 0.117071i | 0.968273 | − | 0.249896i | \(-0.0803963\pi\) |
−0.930234 | + | 0.366967i | \(0.880396\pi\) | |||||||
\(390\) | −18.3480 | + | 13.3306i | −0.929087 | + | 0.675021i | ||||
\(391\) | −1.26270 | + | 0.917404i | −0.0638574 | + | 0.0463951i | ||||
\(392\) | 0.949813 | + | 2.92322i | 0.0479728 | + | 0.147645i | ||||
\(393\) | 4.51680 | − | 13.9013i | 0.227842 | − | 0.701227i | ||||
\(394\) | 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 | ||||
\(399\) | −1.43376 | + | 4.41266i | −0.0717778 | + | 0.220909i | ||||
\(400\) | −4.09784 | − | 12.6119i | −0.204892 | − | 0.630593i | ||||
\(401\) | −9.09302 | + | 6.60646i | −0.454084 | + | 0.329911i | −0.791206 | − | 0.611550i | \(-0.790546\pi\) |
0.337122 | + | 0.941461i | \(0.390546\pi\) | |||||||
\(402\) | −6.19427 | + | 4.50040i | −0.308942 | + | 0.224460i | ||||
\(403\) | 0.501804 | + | 1.54439i | 0.0249966 | + | 0.0769317i | ||||
\(404\) | −3.61756 | + | 11.1337i | −0.179981 | + | 0.553923i | ||||
\(405\) | −6.26243 | − | 4.54992i | −0.311183 | − | 0.226087i | ||||
\(406\) | −8.88640 | −0.441025 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 16.9917 | 0.841216 | ||||||||
\(409\) | 23.7320 | + | 17.2423i | 1.17347 | + | 0.852578i | 0.991421 | − | 0.130711i | \(-0.0417260\pi\) |
0.182052 | + | 0.983289i | \(0.441726\pi\) | |||||||
\(410\) | −2.53060 | + | 7.78839i | −0.124977 | + | 0.384641i | ||||
\(411\) | −8.03961 | − | 24.7434i | −0.396565 | − | 1.22050i | ||||
\(412\) | 5.46251 | − | 3.96875i | 0.269119 | − | 0.195526i | ||||
\(413\) | −2.66704 | + | 1.93771i | −0.131236 | + | 0.0953487i | ||||
\(414\) | 1.43789 | + | 4.42536i | 0.0706683 | + | 0.217495i | ||||
\(415\) | 17.1619 | − | 52.8189i | 0.842445 | − | 2.59278i | ||||
\(416\) | 6.69713 | + | 4.86575i | 0.328354 | + | 0.238563i | ||||
\(417\) | −37.2120 | −1.82228 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.2858 | −0.991027 | −0.495514 | − | 0.868600i | \(-0.665020\pi\) | ||||
−0.495514 | + | 0.868600i | \(0.665020\pi\) | |||||||
\(420\) | 6.05866 | + | 4.40187i | 0.295632 | + | 0.214789i | ||||
\(421\) | −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 | ||||
\(423\) | −31.6644 | + | 23.0055i | −1.53958 | + | 1.11857i | ||||
\(424\) | −26.9116 | + | 19.5524i | −1.30694 | + | 0.949548i | ||||
\(425\) | −4.14971 | − | 12.7715i | −0.201290 | − | 0.619508i | ||||
\(426\) | −3.13932 | + | 9.66183i | −0.152100 | + | 0.468117i | ||||
\(427\) | 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 | \(0.641859\pi\) | |||||||
\(432\) | 3.66548 | − | 11.2812i | 0.176355 | − | 0.542766i | ||||
\(433\) | −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 | ||||
\(435\) | −63.7362 | + | 46.3071i | −3.05592 | + | 2.22025i | ||||
\(436\) | 0.907980 | + | 2.79447i | 0.0434844 | + | 0.133831i | ||||
\(437\) | 0.404796 | − | 1.24584i | 0.0193640 | − | 0.0595964i | ||||
\(438\) | 3.16082 | + | 2.29647i | 0.151030 | + | 0.109729i | ||||
\(439\) | 4.66725 | 0.222756 | 0.111378 | − | 0.993778i | \(-0.464474\pi\) | ||||
0.111378 | + | 0.993778i | \(0.464474\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.17284 | 0.246326 | ||||||||
\(442\) | −3.59099 | − | 2.60901i | −0.170806 | − | 0.124098i | ||||
\(443\) | 5.33893 | − | 16.4315i | 0.253660 | − | 0.780686i | −0.740430 | − | 0.672133i | \(-0.765378\pi\) |
0.994091 | − | 0.108553i | \(-0.0346218\pi\) | |||||||
\(444\) | 6.73739 | + | 20.7356i | 0.319743 | + | 0.984066i | ||||
\(445\) | 12.4096 | − | 9.01611i | 0.588272 | − | 0.427404i | ||||
\(446\) | 15.6845 | − | 11.3955i | 0.742684 | − | 0.539591i | ||||
\(447\) | −2.77969 | − | 8.55501i | −0.131475 | − | 0.404638i | ||||
\(448\) | −2.56433 | + | 7.89221i | −0.121153 | + | 0.372872i | ||||
\(449\) | 13.5430 | + | 9.83957i | 0.639134 | + | 0.464358i | 0.859553 | − | 0.511047i | \(-0.170742\pi\) |
−0.220418 | + | 0.975405i | \(0.570742\pi\) | |||||||
\(450\) | −40.0346 | −1.88725 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −8.07529 | −0.379829 | ||||||||
\(453\) | −6.63080 | − | 4.81756i | −0.311542 | − | 0.226349i | ||||
\(454\) | −4.35015 | + | 13.3884i | −0.204162 | + | 0.628347i | ||||
\(455\) | −2.19968 | − | 6.76992i | −0.103123 | − | 0.317379i | ||||
\(456\) | −11.5374 | + | 8.38241i | −0.540288 | + | 0.392542i | ||||
\(457\) | −17.5536 | + | 12.7534i | −0.821121 | + | 0.596580i | −0.917033 | − | 0.398810i | \(-0.869423\pi\) |
0.0959121 | + | 0.995390i | \(0.469423\pi\) | |||||||
\(458\) | −1.57503 | − | 4.84746i | −0.0735965 | − | 0.226507i | ||||
\(459\) | 3.71187 | − | 11.4240i | 0.173255 | − | 0.533224i | ||||
\(460\) | −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 | ||||
\(465\) | −2.40719 | + | 7.40856i | −0.111631 | + | 0.343564i | ||||
\(466\) | 8.21605 | + | 25.2864i | 0.380601 | + | 1.17137i | ||||
\(467\) | 3.17076 | − | 2.30369i | 0.146725 | − | 0.106602i | −0.512001 | − | 0.858985i | \(-0.671096\pi\) |
0.658726 | + | 0.752383i | \(0.271096\pi\) | |||||||
\(468\) | 6.53325 | − | 4.74669i | 0.302000 | − | 0.219416i | ||||
\(469\) | −0.742611 | − | 2.28552i | −0.0342906 | − | 0.105536i | ||||
\(470\) | −9.00570 | + | 27.7167i | −0.415402 | + | 1.27848i | ||||
\(471\) | −49.7016 | − | 36.1103i | −2.29013 | − | 1.66388i | ||||
\(472\) | −10.1327 | −0.466397 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 30.2096 | 1.38757 | ||||||||
\(475\) | 9.11811 | + | 6.62469i | 0.418368 | + | 0.303962i | ||||
\(476\) | −0.452925 | + | 1.39396i | −0.0207598 | + | 0.0638921i | ||||
\(477\) | 17.2996 | + | 53.2428i | 0.792096 | + | 2.43782i | ||||
\(478\) | −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 | \(0.412210\pi\) | |||||||
\(480\) | 12.2713 | + | 37.7671i | 0.560104 | + | 1.72382i | ||||
\(481\) | 6.40399 | − | 19.7095i | 0.291997 | − | 0.898674i | ||||
\(482\) | −17.0825 | − | 12.4112i | −0.778088 | − | 0.565314i | ||||
\(483\) | −2.30745 | −0.104993 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.3541 | 1.01505 | ||||||||
\(486\) | 11.0288 | + | 8.01291i | 0.500278 | + | 0.363473i | ||||
\(487\) | 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 | ||||
\(489\) | −19.0172 | + | 13.8168i | −0.859985 | + | 0.624816i | ||||
\(490\) | 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 | \(-0.417372\pi\) | |||||||
\(492\) | 1.42367 | − | 4.38159i | 0.0641838 | − | 0.197538i | ||||
\(493\) | −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 | ||||
\(498\) | 15.8211 | − | 48.6922i | 0.708959 | − | 2.18195i | ||||
\(499\) | −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 | ||||
\(501\) | 50.2083 | − | 36.4785i | 2.24314 | − | 1.62974i | ||||
\(502\) | 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 | \(-0.0408426\pi\) | |||||||
\(504\) | 12.8630 | + | 9.34552i | 0.572964 | + | 0.416283i | ||||
\(505\) | 53.3788 | 2.37532 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.0370 | 1.11193 | ||||||||
\(508\) | −11.9274 | − | 8.66577i | −0.529193 | − | 0.384481i | ||||
\(509\) | 0.777328 | − | 2.39237i | 0.0344545 | − | 0.106040i | −0.932350 | − | 0.361556i | \(-0.882246\pi\) |
0.966805 | + | 0.255516i | \(0.0822455\pi\) | |||||||
\(510\) | −6.57984 | − | 20.2506i | −0.291360 | − | 0.896714i | ||||
\(511\) | −0.992078 | + | 0.720787i | −0.0438869 | + | 0.0318857i | ||||
\(512\) | −15.7059 | + | 11.4110i | −0.694109 | + | 0.504300i | ||||
\(513\) | 3.11533 | + | 9.58801i | 0.137545 | + | 0.423321i | ||||
\(514\) | −7.71978 | + | 23.7590i | −0.340505 | + | 1.04797i | ||||
\(515\) | −24.9073 | − | 18.0962i | −1.09755 | − | 0.797416i | ||||
\(516\) | −6.67492 | −0.293847 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 11.2135 | 0.492693 | ||||||||
\(519\) | 18.6082 | + | 13.5196i | 0.816809 | + | 0.593447i | ||||
\(520\) | 6.76107 | − | 20.8084i | 0.296493 | − | 0.912510i | ||||
\(521\) | 4.60335 | + | 14.1677i | 0.201677 | + | 0.620697i | 0.999834 | + | 0.0182471i | \(0.00580856\pi\) |
−0.798157 | + | 0.602450i | \(0.794191\pi\) | |||||||
\(522\) | −37.1888 | + | 27.0193i | −1.62771 | + | 1.18260i | ||||
\(523\) | −8.01333 | + | 5.82203i | −0.350399 | + | 0.254579i | −0.749036 | − | 0.662529i | \(-0.769483\pi\) |
0.398638 | + | 0.917109i | \(0.369483\pi\) | |||||||
\(524\) | 1.19755 | + | 3.68567i | 0.0523151 | + | 0.161009i | ||||
\(525\) | 6.13491 | − | 18.8813i | 0.267749 | − | 0.824048i | ||||
\(526\) | −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 | ||||
\(531\) | −5.26966 | + | 16.2183i | −0.228684 | + | 0.703816i | ||||
\(532\) | −0.380136 | − | 1.16994i | −0.0164810 | − | 0.0507232i | ||||
\(533\) | −3.54276 | + | 2.57397i | −0.153454 | + | 0.111491i | ||||
\(534\) | 11.4401 | − | 8.31169i | 0.495060 | − | 0.359682i | ||||
\(535\) | −3.75097 | − | 11.5443i | −0.162169 | − | 0.499104i | ||||
\(536\) | 2.28253 | − | 7.02491i | 0.0985904 | − | 0.303430i | ||||
\(537\) | −8.37456 | − | 6.08447i | −0.361389 | − | 0.262564i | ||||
\(538\) | 8.01342 | 0.345483 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 16.2722 | 0.700245 | ||||||||
\(541\) | −17.8052 | − | 12.9362i | −0.765503 | − | 0.556171i | 0.135090 | − | 0.990833i | \(-0.456868\pi\) |
−0.900593 | + | 0.434663i | \(0.856868\pi\) | |||||||
\(542\) | −9.35508 | + | 28.7920i | −0.401835 | + | 1.23672i | ||||
\(543\) | −13.9739 | − | 43.0073i | −0.599678 | − | 1.84562i | ||||
\(544\) | −6.28768 | + | 4.56826i | −0.269582 | + | 0.195863i | ||||
\(545\) | 10.8389 | − | 7.87494i | 0.464289 | − | 0.337325i | ||||
\(546\) | −2.02782 | − | 6.24100i | −0.0867828 | − | 0.267090i | ||||
\(547\) | 3.35724 | − | 10.3325i | 0.143545 | − | 0.441787i | −0.853276 | − | 0.521460i | \(-0.825388\pi\) |
0.996821 | + | 0.0796728i | \(0.0253875\pi\) | |||||||
\(548\) | 5.58049 | + | 4.05446i | 0.238387 | + | 0.173198i | ||||
\(549\) | 5.56922 | 0.237689 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.9410 | 0.551303 | ||||||||
\(552\) | −5.73781 | − | 4.16876i | −0.244218 | − | 0.177434i | ||||
\(553\) | −2.93004 | + | 9.01775i | −0.124598 | + | 0.383474i | ||||
\(554\) | 7.22721 | + | 22.2431i | 0.307055 | + | 0.945018i | ||||
\(555\) | 80.4270 | − | 58.4337i | 3.41394 | − | 2.48037i | ||||
\(556\) | 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 | \(-0.352258\pi\) | |||||||
\(558\) | −1.40455 | + | 4.32275i | −0.0594592 | + | 0.182997i | ||||
\(559\) | 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 | \(0.713778\pi\) | |||||||
\(564\) | 5.06643 | − | 15.5929i | 0.213335 | − | 0.656578i | ||||
\(565\) | 11.3782 | + | 35.0186i | 0.478686 | + | 1.47324i | ||||
\(566\) | 23.6151 | − | 17.1573i | 0.992615 | − | 0.721177i | ||||
\(567\) | 1.81200 | − | 1.31650i | 0.0760971 | − | 0.0552877i | ||||
\(568\) | −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 | \(0.121863\pi\) | |||||||
\(570\) | 14.4578 | + | 10.5042i | 0.605571 | + | 0.439973i | ||||
\(571\) | 43.8897 | 1.83673 | 0.918363 | − | 0.395738i | \(-0.129511\pi\) | ||||
0.918363 | + | 0.395738i | \(0.129511\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.22666 | −0.0512446 | ||||||||
\(574\) | −1.91697 | − | 1.39276i | −0.0800128 | − | 0.0581327i | ||||
\(575\) | −1.73208 | + | 5.33080i | −0.0722328 | + | 0.222310i | ||||
\(576\) | 13.2649 | + | 40.8251i | 0.552704 | + | 1.70105i | ||||
\(577\) | 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 | ||||
\(579\) | −13.4058 | − | 41.2588i | −0.557126 | − | 1.71466i | ||||
\(580\) | 6.45466 | − | 19.8654i | 0.268015 | − | 0.824866i | ||||
\(581\) | 13.0004 | + | 9.44536i | 0.539348 | + | 0.391859i | ||||
\(582\) | 20.6076 | 0.854214 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −3.76915 | −0.155969 | ||||||||
\(585\) | −29.7896 | − | 21.6434i | −1.23165 | − | 0.894844i | ||||
\(586\) | −1.53730 | + | 4.73133i | −0.0635054 | + | 0.195449i | ||||
\(587\) | 0.862670 | + | 2.65503i | 0.0356062 | + | 0.109585i | 0.967280 | − | 0.253711i | \(-0.0816513\pi\) |
−0.931674 | + | 0.363296i | \(0.881651\pi\) | |||||||
\(588\) | −1.75304 | + | 1.27366i | −0.0722943 | + | 0.0525249i | ||||
\(589\) | 1.03520 | − | 0.752114i | 0.0426545 | − | 0.0309903i | ||||
\(590\) | 3.92378 | + | 12.0761i | 0.161539 | + | 0.497167i | ||||
\(591\) | −18.3825 | + | 56.5754i | −0.756153 | + | 2.32720i | ||||
\(592\) | 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 | ||||
\(597\) | −7.46111 | + | 22.9629i | −0.305363 | + | 0.939810i | ||||
\(598\) | 0.572519 | + | 1.76203i | 0.0234120 | + | 0.0720549i | ||||
\(599\) | −8.46187 | + | 6.14791i | −0.345743 | + | 0.251197i | −0.747081 | − | 0.664733i | \(-0.768545\pi\) |
0.401338 | + | 0.915930i | \(0.368545\pi\) | |||||||
\(600\) | 49.3673 | − | 35.8674i | 2.01541 | − | 1.46428i | ||||
\(601\) | −6.89406 | − | 21.2177i | −0.281215 | − | 0.865489i | −0.987508 | − | 0.157570i | \(-0.949634\pi\) |
0.706293 | − | 0.707919i | \(-0.250366\pi\) | |||||||
\(602\) | −1.06087 | + | 3.26501i | −0.0432376 | + | 0.133072i | ||||
\(603\) | −10.0569 | − | 7.30679i | −0.409550 | − | 0.297556i | ||||
\(604\) | 2.17306 | 0.0884204 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 49.2083 | 1.99895 | ||||||||
\(607\) | 15.3619 | + | 11.1611i | 0.623522 | + | 0.453015i | 0.854150 | − | 0.520027i | \(-0.174078\pi\) |
−0.230628 | + | 0.973042i | \(0.574078\pi\) | |||||||
\(608\) | 2.01571 | − | 6.20370i | 0.0817477 | − | 0.251593i | ||||
\(609\) | −7.04413 | − | 21.6796i | −0.285443 | − | 0.878502i | ||||
\(610\) | 3.35485 | − | 2.43744i | 0.135834 | − | 0.0986892i | ||||
\(611\) | −12.6077 | + | 9.16004i | −0.510053 | + | 0.370576i | ||||
\(612\) | 2.34291 | + | 7.21074i | 0.0947066 | + | 0.291477i | ||||
\(613\) | −6.23030 | + | 19.1749i | −0.251639 | + | 0.774467i | 0.742834 | + | 0.669476i | \(0.233481\pi\) |
−0.994473 | + | 0.104991i | \(0.966519\pi\) | |||||||
\(614\) | −11.6166 | − | 8.43995i | −0.468807 | − | 0.340608i | ||||
\(615\) | −21.0068 | −0.847077 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.03919 | 0.283387 | 0.141694 | − | 0.989911i | \(-0.454745\pi\) | ||||
0.141694 | + | 0.989911i | \(0.454745\pi\) | |||||||
\(618\) | −22.9614 | − | 16.6824i | −0.923641 | − | 0.671064i | ||||
\(619\) | −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 | ||||
\(621\) | −4.05619 | + | 2.94700i | −0.162769 | + | 0.118259i | ||||
\(622\) | 24.1814 | − | 17.5688i | 0.969585 | − | 0.704445i | ||||
\(623\) | 1.37151 | + | 4.22108i | 0.0549484 | + | 0.169114i | ||||
\(624\) | 3.47453 | − | 10.6935i | 0.139093 | − | 0.428083i | ||||
\(625\) | 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 | ||||
\(630\) | 6.15690 | − | 18.9490i | 0.245297 | − | 0.754946i | ||||
\(631\) | 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 | ||||
\(633\) | 22.8028 | − | 16.5672i | 0.906331 | − | 0.658488i | ||||
\(634\) | 5.82639 | + | 17.9318i | 0.231396 | + | 0.712163i | ||||
\(635\) | −20.7733 | + | 63.9337i | −0.824364 | + | 2.53713i | ||||
\(636\) | −18.9722 | − | 13.7841i | −0.752298 | − | 0.546576i | ||||
\(637\) | 2.05965 | 0.0816064 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.4941 | −0.652496 | ||||||||
\(640\) | 3.38290 | + | 2.45782i | 0.133721 | + | 0.0971538i | ||||
\(641\) | −4.10713 | + | 12.6404i | −0.162222 | + | 0.499267i | −0.998821 | − | 0.0485485i | \(-0.984540\pi\) |
0.836599 | + | 0.547816i | \(0.184540\pi\) | |||||||
\(642\) | −3.45791 | − | 10.6424i | −0.136473 | − | 0.420020i | ||||
\(643\) | −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 | ||||
\(645\) | 9.40510 | + | 28.9459i | 0.370325 | + | 1.13974i | ||||
\(646\) | −1.08082 | + | 3.32642i | −0.0425242 | + | 0.130876i | ||||
\(647\) | 4.97160 | + | 3.61208i | 0.195454 | + | 0.142005i | 0.681208 | − | 0.732090i | \(-0.261455\pi\) |
−0.485754 | + | 0.874095i | \(0.661455\pi\) | |||||||
\(648\) | 6.88426 | 0.270439 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −15.9404 | −0.625236 | ||||||||
\(651\) | −1.82348 | − | 1.32484i | −0.0714679 | − | 0.0519245i | ||||
\(652\) | 1.92589 | − | 5.92729i | 0.0754238 | − | 0.232131i | ||||
\(653\) | −12.5674 | − | 38.6786i | −0.491802 | − | 1.51361i | −0.821882 | − | 0.569658i | \(-0.807076\pi\) |
0.330079 | − | 0.943953i | \(-0.392924\pi\) | |||||||
\(654\) | 9.99209 | − | 7.25968i | 0.390722 | − | 0.283876i | ||||
\(655\) | 14.2956 | − | 10.3864i | 0.558576 | − | 0.405829i | ||||
\(656\) | −1.25460 | − | 3.86127i | −0.0489841 | − | 0.150757i | ||||
\(657\) | −1.96020 | + | 6.03286i | −0.0764745 | + | 0.235364i | ||||
\(658\) | −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 | ||||
\(663\) | 3.51851 | − | 10.8289i | 0.136647 | − | 0.420558i | ||||
\(664\) | 15.2629 | + | 46.9744i | 0.592316 | + | 1.82296i | ||||
\(665\) | −4.53784 | + | 3.29693i | −0.175970 | + | 0.127850i | ||||
\(666\) | 46.9276 | − | 34.0949i | 1.81841 | − | 1.32115i | ||||
\(667\) | 1.98878 | + | 6.12085i | 0.0770060 | + | 0.237000i | ||||
\(668\) | −5.08466 | + | 15.6490i | −0.196732 | + | 0.605478i | ||||
\(669\) | 40.2338 | + | 29.2315i | 1.55553 | + | 1.13016i | ||||
\(670\) | −9.25613 | −0.357596 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −11.4901 | −0.443240 | ||||||||
\(673\) | −18.7632 | − | 13.6322i | −0.723268 | − | 0.525485i | 0.164159 | − | 0.986434i | \(-0.447509\pi\) |
−0.887426 | + | 0.460949i | \(0.847509\pi\) | |||||||
\(674\) | −7.05329 | + | 21.7078i | −0.271683 | + | 0.836153i | ||||
\(675\) | −13.3302 | − | 41.0261i | −0.513079 | − | 1.57910i | ||||
\(676\) | −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 | \(0.477737\pi\) | |||||||
\(678\) | 10.4893 | + | 32.2826i | 0.402838 | + | 1.23981i | ||||
\(679\) | −1.99874 | + | 6.15150i | −0.0767047 | + | 0.236073i | ||||
\(680\) | 16.6185 | + | 12.0741i | 0.637291 | + | 0.463019i | ||||
\(681\) | −36.1111 | −1.38378 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.9351 | 0.839322 | 0.419661 | − | 0.907681i | \(-0.362149\pi\) | ||||
0.419661 | + | 0.907681i | \(0.362149\pi\) | |||||||
\(684\) | −5.14806 | − | 3.74028i | −0.196841 | − | 0.143013i | ||||
\(685\) | 9.71923 | − | 29.9127i | 0.371353 | − | 1.14291i | ||||
\(686\) | 0.344389 | + | 1.05992i | 0.0131488 | + | 0.0404680i | ||||
\(687\) | 10.5775 | − | 7.68503i | 0.403558 | − | 0.293202i | ||||
\(688\) | −4.75885 | + | 3.45751i | −0.181430 | + | 0.131816i | ||||
\(689\) | 6.88814 | + | 21.1995i | 0.262417 | + | 0.807637i | ||||
\(690\) | −2.74641 | + | 8.45259i | −0.104554 | + | 0.321785i | ||||
\(691\) | 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 | ||||
\(696\) | 21.6513 | − | 66.6357i | 0.820689 | − | 2.52582i | ||||
\(697\) | −1.27048 | − | 3.91014i | −0.0481229 | − | 0.148107i | ||||
\(698\) | −7.19886 | + | 5.23028i | −0.272481 | + | 0.197969i | ||||
\(699\) | −55.1770 | + | 40.0884i | −2.08699 | + | 1.51628i | ||||
\(700\) | 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 | \(-0.0130485\pi\) | |||||||
\(702\) | −11.5354 | − | 8.38097i | −0.435376 | − | 0.316319i | ||||
\(703\) | −16.3298 | −0.615892 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −74.7575 | −2.81553 | ||||||||
\(706\) | 5.35087 | + | 3.88764i | 0.201383 | + | 0.146313i | ||||
\(707\) | −4.77274 | + | 14.6890i | −0.179497 | + | 0.552436i | ||||
\(708\) | −2.20744 | − | 6.79380i | −0.0829607 | − | 0.255327i | ||||
\(709\) | −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 | ||||
\(711\) | 15.1567 | + | 46.6474i | 0.568419 | + | 1.74941i | ||||
\(712\) | −4.21556 | + | 12.9741i | −0.157985 | + | 0.486227i | ||||
\(713\) | 0.514827 | + | 0.374044i | 0.0192804 | + | 0.0140081i | ||||
\(714\) | 6.16097 | 0.230569 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.74452 | 0.102568 | ||||||||
\(717\) | −20.4411 | − | 14.8514i | −0.763389 | − | 0.554634i | ||||
\(718\) | 9.78763 | − | 30.1232i | 0.365271 | − | 1.12419i | ||||
\(719\) | 3.43696 | + | 10.5779i | 0.128177 | + | 0.394488i | 0.994467 | − | 0.105054i | \(-0.0335015\pi\) |
−0.866289 | + | 0.499542i | \(0.833502\pi\) | |||||||
\(720\) | 27.6187 | − | 20.0662i | 1.02929 | − | 0.747823i | ||||
\(721\) | 7.20682 | − | 5.23606i | 0.268396 | − | 0.195001i | ||||
\(722\) | 5.63627 | + | 17.3467i | 0.209760 | + | 0.645576i | ||||
\(723\) | 16.7377 | − | 51.5135i | 0.622483 | − | 1.91581i | ||||
\(724\) | 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 | ||||
\(729\) | −12.8826 | + | 39.6485i | −0.477133 | + | 1.46846i | ||||
\(730\) | 1.45956 | + | 4.49205i | 0.0540206 | + | 0.166258i | ||||
\(731\) | −4.81908 | + | 3.50127i | −0.178240 | + | 0.129499i | ||||
\(732\) | −1.88738 | + | 1.37126i | −0.0697594 | + | 0.0506832i | ||||
\(733\) | −6.85660 | − | 21.1025i | −0.253254 | − | 0.779437i | −0.994169 | − | 0.107837i | \(-0.965607\pi\) |
0.740914 | − | 0.671600i | \(-0.234393\pi\) | |||||||
\(734\) | 10.4699 | − | 32.2231i | 0.386452 | − | 1.18938i | ||||
\(735\) | 7.99333 | + | 5.80749i | 0.294838 | + | 0.214213i | ||||
\(736\) | 3.24402 | 0.119576 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −12.2571 | −0.451189 | ||||||||
\(739\) | 23.8240 | + | 17.3092i | 0.876381 | + | 0.636728i | 0.932292 | − | 0.361708i | \(-0.117806\pi\) |
−0.0559106 | + | 0.998436i | \(0.517806\pi\) | |||||||
\(740\) | −8.14496 | + | 25.0676i | −0.299415 | + | 0.921504i | ||||
\(741\) | 2.95305 | + | 9.08855i | 0.108483 | + | 0.333876i | ||||
\(742\) | −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 | \(0.199635\pi\) | |||||||
\(744\) | −2.14083 | − | 6.58879i | −0.0784866 | − | 0.241557i | ||||
\(745\) | 3.36042 | − | 10.3423i | 0.123116 | − | 0.378913i | ||||
\(746\) | −13.0037 | − | 9.44774i | −0.476099 | − | 0.345906i | ||||
\(747\) | 83.1244 | 3.04136 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.51219 | 0.128333 | ||||||||
\(750\) | −17.3220 | − | 12.5851i | −0.632508 | − | 0.459544i | ||||
\(751\) | −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 | ||||
\(753\) | −6.63069 | + | 4.81748i | −0.241636 | + | 0.175559i | ||||
\(754\) | −14.8074 | + | 10.7582i | −0.539252 | + | 0.391789i | ||||
\(755\) | −3.06188 | − | 9.42349i | −0.111433 | − | 0.342956i | ||||
\(756\) | −1.45494 | + | 4.47785i | −0.0529157 | + | 0.162858i | ||||
\(757\) | −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 | \(0.752358\pi\) | |||||||
\(762\) | −19.1503 | + | 58.9386i | −0.693742 | + | 2.13512i | ||||
\(763\) | 1.19792 | + | 3.68682i | 0.0433676 | + | 0.133472i | ||||
\(764\) | 0.263115 | − | 0.191164i | 0.00951916 | − | 0.00691608i | ||||
\(765\) | 27.9683 | − | 20.3201i | 1.01120 | − | 0.734677i | ||||
\(766\) | −11.5985 | − | 35.6966i | −0.419072 | − | 1.28977i | ||||
\(767\) | −2.09820 | + | 6.45761i | −0.0757617 | + | 0.233171i | ||||
\(768\) | −35.2668 | − | 25.6229i | −1.27258 | − | 0.924585i | ||||
\(769\) | 16.1383 | 0.581963 | 0.290981 | − | 0.956729i | \(-0.406018\pi\) | ||||
0.290981 | + | 0.956729i | \(0.406018\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −64.0829 | −2.30789 | ||||||||
\(772\) | 9.30529 | + | 6.76069i | 0.334905 | + | 0.243323i | ||||
\(773\) | −5.69007 | + | 17.5122i | −0.204657 | + | 0.629871i | 0.795070 | + | 0.606518i | \(0.207434\pi\) |
−0.999727 | + | 0.0233530i | \(0.992566\pi\) | |||||||
\(774\) | 5.48769 | + | 16.8894i | 0.197251 | + | 0.607076i | ||||
\(775\) | −4.42950 | + | 3.21822i | −0.159112 | + | 0.115602i | ||||
\(776\) | −16.0838 | + | 11.6855i | −0.577374 | + | 0.419487i | ||||
\(777\) | 8.88880 | + | 27.3569i | 0.318884 | + | 0.981424i | ||||
\(778\) | −0.836118 | + | 2.57331i | −0.0299763 | + | 0.0922575i | ||||
\(779\) | 2.79162 | + | 2.02823i | 0.100020 | + | 0.0726689i | ||||
\(780\) | 15.4246 | 0.552288 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.73944 | −0.0622022 | ||||||||
\(783\) | −40.0711 | − | 29.1133i | −1.43202 | − | 1.04043i | ||||
\(784\) | −0.590087 | + | 1.81610i | −0.0210745 | + | 0.0648608i | ||||
\(785\) | −22.9505 | − | 70.6344i | −0.819139 | − | 2.52105i | ||||
\(786\) | 13.1787 | − | 9.57490i | 0.470069 | − | 0.341525i | ||||
\(787\) | 38.0133 | − | 27.6183i | 1.35503 | − | 0.984486i | 0.356284 | − | 0.934378i | \(-0.384043\pi\) |
0.998744 | − | 0.0501080i | \(-0.0159565\pi\) | |||||||
\(788\) | −4.87378 | − | 14.9999i | −0.173621 | − | 0.534351i | ||||
\(789\) | 0.875212 | − | 2.69363i | 0.0311584 | − | 0.0958957i | ||||
\(790\) | 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 | ||||
\(795\) | −33.0429 | + | 101.696i | −1.17191 | + | 3.60677i | ||||
\(796\) | −1.97818 | − | 6.08821i | −0.0701147 | − | 0.215791i | ||||
\(797\) | 2.52781 | − | 1.83656i | 0.0895395 | − | 0.0650543i | −0.542115 | − | 0.840304i | \(-0.682376\pi\) |
0.631654 | + | 0.775250i | \(0.282376\pi\) | |||||||
\(798\) | −4.18330 | + | 3.03935i | −0.148087 | + | 0.107592i | ||||
\(799\) | −4.52129 | − | 13.9151i | −0.159952 | − | 0.492281i | ||||
\(800\) | −8.62499 | + | 26.5450i | −0.304940 | + | 0.938507i | ||||
\(801\) | 18.5739 | + | 13.4947i | 0.656277 | + | 0.476813i | ||||
\(802\) | −12.5261 | −0.442314 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 5.20732 | 0.183648 | ||||||||
\(805\) | −2.25677 | − | 1.63964i | −0.0795408 | − | 0.0577897i | ||||
\(806\) | −0.559243 | + | 1.72117i | −0.0196985 | + | 0.0606258i | ||||
\(807\) | 6.35214 | + | 19.5499i | 0.223606 | + | 0.688188i | ||||
\(808\) | −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 | \(0.495109\pi\) | |||||||
\(810\) | −2.66584 | − | 8.20462i | −0.0936682 | − | 0.288281i | ||||
\(811\) | −10.0929 | + | 31.0627i | −0.354410 | + | 1.09076i | 0.601941 | + | 0.798540i | \(0.294394\pi\) |
−0.956351 | + | 0.292220i | \(0.905606\pi\) | |||||||
\(812\) | 4.88951 | + | 3.55243i | 0.171588 | + | 0.124666i | ||||
\(813\) | −77.6578 | −2.72358 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.4174 | −0.995419 | ||||||||
\(816\) | 8.54031 | + | 6.20490i | 0.298970 | + | 0.217215i | ||||
\(817\) | 1.54490 | − | 4.75472i | 0.0540493 | − | 0.166347i | ||||
\(818\) | 10.1024 | + | 31.0921i | 0.353224 | + | 1.08711i | ||||
\(819\) | 8.61947 | − | 6.26241i | 0.301189 | − | 0.218826i | ||||
\(820\) | 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 | \(0.858605\pi\) | |||||||
\(822\) | 8.95988 | − | 27.5757i | 0.312512 | − | 0.961812i | ||||
\(823\) | −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 | \(0.563873\pi\) | |||||||
\(828\) | 0.977928 | − | 3.00975i | 0.0339853 | − | 0.104596i | ||||
\(829\) | −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 | ||||
\(831\) | −48.5362 | + | 35.2636i | −1.68370 | + | 1.22328i | ||||
\(832\) | 5.28164 | + | 16.2552i | 0.183108 | + | 0.563548i | ||||
\(833\) | −0.597555 | + | 1.83909i | −0.0207041 | + | 0.0637205i | ||||
\(834\) | −33.5512 | − | 24.3764i | −1.16178 | − | 0.844085i | ||||
\(835\) | 75.0265 | 2.59640 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.89747 | −0.169281 | ||||||||
\(838\) | −18.2901 | − | 13.2886i | −0.631823 | − | 0.459046i | ||||
\(839\) | 10.5959 | − | 32.6107i | 0.365810 | − | 1.12585i | −0.583662 | − | 0.811997i | \(-0.698381\pi\) |
0.949472 | − | 0.313851i | \(-0.101619\pi\) | |||||||
\(840\) | 9.38443 | + | 28.8823i | 0.323794 | + | 0.996535i | ||||
\(841\) | −27.9754 | + | 20.3253i | −0.964670 | + | 0.700874i | ||||
\(842\) | −2.75899 | + | 2.00452i | −0.0950810 | + | 0.0690804i | ||||
\(843\) | −24.8754 | − | 76.5587i | −0.856755 | − | 2.63682i | ||||
\(844\) | −2.30928 | + | 7.10722i | −0.0794885 | + | 0.244641i | ||||
\(845\) | 24.4871 | + | 17.7909i | 0.842383 | + | 0.612027i | ||||
\(846\) | −43.6195 | −1.49967 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −20.6661 | −0.709678 | ||||||||
\(849\) | 60.5771 | + | 44.0118i | 2.07900 | + | 1.51048i | ||||
\(850\) | 4.62471 | − | 14.2334i | 0.158626 | − | 0.488201i | ||||
\(851\) | −2.50959 | − | 7.72373i | −0.0860277 | − | 0.264766i | ||||
\(852\) | 5.58975 | − | 4.06119i | 0.191502 | − | 0.139134i | ||||
\(853\) | 17.3002 | − | 12.5693i | 0.592347 | − | 0.430365i | −0.250807 | − | 0.968037i | \(-0.580696\pi\) |
0.843154 | + | 0.537672i | \(0.180696\pi\) | |||||||
\(854\) | 0.370779 | + | 1.14114i | 0.0126878 | + | 0.0390490i | ||||
\(855\) | −8.96608 | + | 27.5948i | −0.306634 | + | 0.943721i | ||||
\(856\) | 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 | ||||
\(861\) | 1.87828 | − | 5.78074i | 0.0640115 | − | 0.197007i | ||||
\(862\) | 2.59737 | + | 7.99389i | 0.0884668 | + | 0.272273i | ||||
\(863\) | −9.56130 | + | 6.94669i | −0.325471 | + | 0.236468i | −0.738506 | − | 0.674247i | \(-0.764468\pi\) |
0.413036 | + | 0.910715i | \(0.364468\pi\) | |||||||
\(864\) | −20.1980 | + | 14.6747i | −0.687151 | + | 0.499244i | ||||
\(865\) | 8.59263 | + | 26.4454i | 0.292158 | + | 0.899170i | ||||
\(866\) | 11.0761 | − | 34.0887i | 0.376381 | − | 1.15838i | ||||
\(867\) | −30.6698 | − | 22.2829i | −1.04160 | − | 0.756766i | ||||
\(868\) | 0.597594 | 0.0202837 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −87.8003 | −2.97671 | ||||||||
\(871\) | −4.00434 | − | 2.90932i | −0.135682 | − | 0.0985786i | ||||
\(872\) | −3.68200 | + | 11.3320i | −0.124688 | + | 0.383750i | ||||
\(873\) | 10.3392 | + | 31.8207i | 0.349928 | + | 1.07697i | ||||
\(874\) | 1.18108 | − | 0.858104i | 0.0399506 | − | 0.0290258i | ||||
\(875\) | 5.43680 | − | 3.95007i | 0.183797 | − | 0.133537i | ||||
\(876\) | −0.821118 | − | 2.52714i | −0.0277430 | − | 0.0853842i | ||||
\(877\) | 2.84446 | − | 8.75436i | 0.0960507 | − | 0.295614i | −0.891475 | − | 0.453069i | \(-0.850329\pi\) |
0.987526 | + | 0.157455i | \(0.0503291\pi\) | |||||||
\(878\) | 4.20810 | + | 3.05736i | 0.142016 | + | 0.103181i | ||||
\(879\) | −12.7613 | −0.430429 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.9030 | −1.41175 | −0.705874 | − | 0.708338i | \(-0.749445\pi\) | ||||
−0.705874 | + | 0.708338i | \(0.749445\pi\) | |||||||
\(882\) | 4.66395 | + | 3.38856i | 0.157043 | + | 0.114099i | ||||
\(883\) | −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 | ||||
\(885\) | −26.3511 | + | 19.1452i | −0.885783 | + | 0.643559i | ||||
\(886\) | 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 | \(0.707618\pi\) | |||||||
\(888\) | −27.3211 | + | 84.0858i | −0.916838 | + | 2.82174i | ||||
\(889\) | −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 | ||||
\(894\) | 3.09787 | − | 9.53427i | 0.103608 | − | 0.318874i | ||||
\(895\) | −3.86708 | − | 11.9017i | −0.129262 | − | 0.397829i | ||||
\(896\) | −0.978825 | + | 0.711158i | −0.0327002 | + | 0.0237581i | ||||
\(897\) | −3.84490 | + | 2.79348i | −0.128377 | + | 0.0932716i | ||||
\(898\) | 5.76510 | + | 17.7432i | 0.192384 | + | 0.592097i | ||||
\(899\) | −1.94267 | + | 5.97892i | −0.0647916 | + | 0.199408i | ||||
\(900\) | 22.0280 | + | 16.0043i | 0.734266 | + | 0.533476i | ||||
\(901\) | −20.9277 | −0.697202 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.80638 | −0.293058 | ||||||||
\(904\) | −26.4925 | − | 19.2479i | −0.881127 | − | 0.640176i | ||||
\(905\) | 16.8933 | − | 51.9923i | 0.561553 | − | 1.72828i | ||||
\(906\) | −2.82266 | − | 8.68724i | −0.0937765 | − | 0.288614i | ||||
\(907\) | 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 | ||||
\(909\) | 24.6886 | + | 75.9837i | 0.818869 | + | 2.52022i | ||||
\(910\) | 2.45147 | − | 7.54486i | 0.0812655 | − | 0.250110i | ||||
\(911\) | −40.1075 | − | 29.1398i | −1.32882 | − | 0.965446i | −0.999777 | − | 0.0211316i | \(-0.993273\pi\) |
−0.329045 | − | 0.944314i | \(-0.606727\pi\) | |||||||
\(912\) | −8.85988 | −0.293380 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −24.1810 | −0.799837 | ||||||||
\(915\) | 8.60584 | + | 6.25251i | 0.284500 | + | 0.206702i | ||||
\(916\) | −1.07120 | + | 3.29682i | −0.0353935 | + | 0.108930i | ||||
\(917\) | 1.57995 | + | 4.86260i | 0.0521746 | + | 0.160577i | ||||
\(918\) | 10.8302 | − | 7.86857i | 0.357448 | − | 0.259701i | ||||
\(919\) | −33.0019 | + | 23.9773i | −1.08863 | + | 0.790939i | −0.979168 | − | 0.203052i | \(-0.934914\pi\) |
−0.109466 | + | 0.993991i | \(0.534914\pi\) | |||||||
\(920\) | −2.64953 | − | 8.15440i | −0.0873523 | − | 0.268843i | ||||
\(921\) | 11.3821 | − | 35.0305i | 0.375053 | − | 1.15430i | ||||
\(922\) | 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 | ||||
\(927\) | 14.2396 | − | 43.8250i | 0.467690 | − | 1.43940i | ||||
\(928\) | 9.90326 | + | 30.4791i | 0.325090 | + | 1.00053i | ||||
\(929\) | −33.4876 | + | 24.3301i | −1.09869 | + | 0.798246i | −0.980846 | − | 0.194786i | \(-0.937599\pi\) |
−0.117846 | + | 0.993032i | \(0.537599\pi\) | |||||||
\(930\) | −7.02348 | + | 5.10286i | −0.230309 | + | 0.167329i | ||||
\(931\) | −0.501522 | − | 1.54353i | −0.0164367 | − | 0.0505870i | ||||
\(932\) | 5.58785 | − | 17.1976i | 0.183036 | − | 0.563327i | ||||
\(933\) | 62.0298 | + | 45.0673i | 2.03077 | + | 1.47544i | ||||
\(934\) | 4.36790 | 0.142922 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 32.7476 | 1.07039 | ||||||||
\(937\) | 1.29155 | + | 0.938364i | 0.0421930 | + | 0.0306550i | 0.608682 | − | 0.793414i | \(-0.291699\pi\) |
−0.566489 | + | 0.824069i | \(0.691699\pi\) | |||||||
\(938\) | 0.827615 | − | 2.54714i | 0.0270226 | − | 0.0831670i | ||||
\(939\) | −3.17033 | − | 9.75727i | −0.103460 | − | 0.318416i | ||||
\(940\) | 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 | \(0.263039\pi\) | |||||||
\(942\) | −21.1574 | − | 65.1158i | −0.689345 | − | 2.12159i | ||||
\(943\) | −0.530297 | + | 1.63209i | −0.0172689 | + | 0.0531481i | ||||
\(944\) | −5.09287 | − | 3.70019i | −0.165759 | − | 0.120431i | ||||
\(945\) | 21.4683 | 0.698364 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.45986 | −0.0799347 | −0.0399674 | − | 0.999201i | \(-0.512725\pi\) | ||||
−0.0399674 | + | 0.999201i | \(0.512725\pi\) | |||||||
\(948\) | −16.6221 | − | 12.0766i | −0.539859 | − | 0.392231i | ||||
\(949\) | −0.780485 | + | 2.40209i | −0.0253356 | + | 0.0779750i | ||||
\(950\) | 3.88147 | + | 11.9459i | 0.125932 | + | 0.387578i | ||||
\(951\) | −39.1286 | + | 28.4286i | −1.26883 | + | 0.921861i | ||||
\(952\) | −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 | \(0.746693\pi\) | |||||||
\(954\) | −19.2799 | + | 59.3373i | −0.624209 | + | 1.92112i | ||||
\(955\) | −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 | ||||
\(960\) | −25.3364 | + | 77.9774i | −0.817728 | + | 2.51671i | ||||
\(961\) | −9.38744 | − | 28.8916i | −0.302821 | − | 0.931986i | ||||
\(962\) | 18.6850 | − | 13.5754i | 0.602428 | − | 0.437690i | ||||
\(963\) | 14.6982 | − | 10.6789i | 0.473644 | − | 0.344122i | ||||
\(964\) | 4.43771 | + | 13.6579i | 0.142929 | + | 0.439890i | ||||
\(965\) | 16.2065 | − | 49.8785i | 0.521706 | − | 1.60565i | ||||
\(966\) | −2.08045 | − | 1.51154i | −0.0669374 | − | 0.0486329i | ||||
\(967\) | 0.213338 | 0.00686047 | 0.00343024 | − | 0.999994i | \(-0.498908\pi\) | ||||
0.00343024 | + | 0.999994i | \(0.498908\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.97201 | −0.288223 | ||||||||
\(970\) | 20.1550 | + | 14.6435i | 0.647138 | + | 0.470173i | ||||
\(971\) | −0.255927 | + | 0.787664i | −0.00821310 | + | 0.0252773i | −0.955079 | − | 0.296351i | \(-0.904230\pi\) |
0.946866 | + | 0.321628i | \(0.104230\pi\) | |||||||
\(972\) | −2.86507 | − | 8.81779i | −0.0918973 | − | 0.282831i | ||||
\(973\) | 10.5306 | − | 7.65095i | 0.337597 | − | 0.245278i | ||||
\(974\) | 22.6098 | − | 16.4270i | 0.724465 | − | 0.526354i | ||||
\(975\) | −12.6358 | − | 38.8890i | −0.404669 | − | 1.24544i | ||||
\(976\) | −0.635304 | + | 1.95526i | −0.0203356 | + | 0.0625865i | ||||
\(977\) | −7.89369 | − | 5.73510i | −0.252542 | − | 0.183482i | 0.454311 | − | 0.890843i | \(-0.349886\pi\) |
−0.706852 | + | 0.707361i | \(0.749886\pi\) | |||||||
\(978\) | −26.1972 | −0.837694 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2.61958 | −0.0836795 | ||||||||
\(981\) | 16.2230 | + | 11.7867i | 0.517961 | + | 0.376321i | ||||
\(982\) | 12.8184 | − | 39.4511i | 0.409052 | − | 1.25893i | ||||
\(983\) | 13.9428 | + | 42.9114i | 0.444705 | + | 1.36866i | 0.882807 | + | 0.469737i | \(0.155651\pi\) |
−0.438101 | + | 0.898926i | \(0.644349\pi\) | |||||||
\(984\) | 15.1144 | − | 10.9812i | 0.481829 | − | 0.350069i | ||||
\(985\) | −58.1803 | + | 42.2704i | −1.85378 | + | 1.34685i | ||||
\(986\) | −5.31011 | − | 16.3428i | −0.169108 | − | 0.520462i | ||||
\(987\) | 6.68426 | − | 20.5720i | 0.212762 | − | 0.654815i | ||||
\(988\) | −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 | ||||
\(993\) | 1.09391 | − | 3.36671i | 0.0347142 | − | 0.106839i | ||||
\(994\) | −1.09812 | − | 3.37966i | −0.0348302 | − | 0.107196i | ||||
\(995\) | −23.6143 | + | 17.1568i | −0.748624 | + | 0.543907i | ||||
\(996\) | −28.1704 | + | 20.4670i | −0.892612 | + | 0.648521i | ||||
\(997\) | 9.62918 | + | 29.6356i | 0.304959 | + | 0.938568i | 0.979692 | + | 0.200506i | \(0.0642587\pi\) |
−0.674733 | + | 0.738062i | \(0.735741\pi\) | |||||||
\(998\) | 10.9562 | − | 33.7196i | 0.346812 | − | 1.06738i | ||||
\(999\) | 50.5646 | + | 36.7373i | 1.59979 | + | 1.16232i |
(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 | 847.2.f.x.323.3 | 16 | ||
11.2 | odd | 10 | 847.2.f.w.148.3 | 16 | |||
11.3 | even | 5 | inner | 847.2.f.x.729.3 | 16 | ||
11.4 | even | 5 | 847.2.f.v.372.2 | 16 | |||
11.5 | even | 5 | 847.2.a.o.1.3 | 8 | |||
11.6 | odd | 10 | 847.2.a.p.1.6 | 8 | |||
11.7 | odd | 10 | 847.2.f.w.372.3 | 16 | |||
11.8 | odd | 10 | 77.2.f.b.36.2 | yes | 16 | ||
11.9 | even | 5 | 847.2.f.v.148.2 | 16 | |||
11.10 | odd | 2 | 77.2.f.b.15.2 | ✓ | 16 | ||
33.5 | odd | 10 | 7623.2.a.cw.1.6 | 8 | |||
33.8 | even | 10 | 693.2.m.i.190.3 | 16 | |||
33.17 | even | 10 | 7623.2.a.ct.1.3 | 8 | |||
33.32 | even | 2 | 693.2.m.i.631.3 | 16 | |||
77.6 | even | 10 | 5929.2.a.bt.1.6 | 8 | |||
77.10 | even | 6 | 539.2.q.f.422.3 | 32 | |||
77.19 | even | 30 | 539.2.q.f.410.3 | 32 | |||
77.27 | odd | 10 | 5929.2.a.bs.1.3 | 8 | |||
77.30 | odd | 30 | 539.2.q.g.410.3 | 32 | |||
77.32 | odd | 6 | 539.2.q.g.422.3 | 32 | |||
77.41 | even | 10 | 539.2.f.e.344.2 | 16 | |||
77.52 | even | 30 | 539.2.q.f.520.2 | 32 | |||
77.54 | even | 6 | 539.2.q.f.312.2 | 32 | |||
77.65 | odd | 6 | 539.2.q.g.312.2 | 32 | |||
77.74 | odd | 30 | 539.2.q.g.520.2 | 32 | |||
77.76 | even | 2 | 539.2.f.e.246.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.15.2 | ✓ | 16 | 11.10 | odd | 2 | ||
77.2.f.b.36.2 | yes | 16 | 11.8 | odd | 10 | ||
539.2.f.e.246.2 | 16 | 77.76 | even | 2 | |||
539.2.f.e.344.2 | 16 | 77.41 | even | 10 | |||
539.2.q.f.312.2 | 32 | 77.54 | even | 6 | |||
539.2.q.f.410.3 | 32 | 77.19 | even | 30 | |||
539.2.q.f.422.3 | 32 | 77.10 | even | 6 | |||
539.2.q.f.520.2 | 32 | 77.52 | even | 30 | |||
539.2.q.g.312.2 | 32 | 77.65 | odd | 6 | |||
539.2.q.g.410.3 | 32 | 77.30 | odd | 30 | |||
539.2.q.g.422.3 | 32 | 77.32 | odd | 6 | |||
539.2.q.g.520.2 | 32 | 77.74 | odd | 30 | |||
693.2.m.i.190.3 | 16 | 33.8 | even | 10 | |||
693.2.m.i.631.3 | 16 | 33.32 | even | 2 | |||
847.2.a.o.1.3 | 8 | 11.5 | even | 5 | |||
847.2.a.p.1.6 | 8 | 11.6 | odd | 10 | |||
847.2.f.v.148.2 | 16 | 11.9 | even | 5 | |||
847.2.f.v.372.2 | 16 | 11.4 | even | 5 | |||
847.2.f.w.148.3 | 16 | 11.2 | odd | 10 | |||
847.2.f.w.372.3 | 16 | 11.7 | odd | 10 | |||
847.2.f.x.323.3 | 16 | 1.1 | even | 1 | trivial | ||
847.2.f.x.729.3 | 16 | 11.3 | even | 5 | inner | ||
5929.2.a.bs.1.3 | 8 | 77.27 | odd | 10 | |||
5929.2.a.bt.1.6 | 8 | 77.6 | even | 10 | |||
7623.2.a.ct.1.3 | 8 | 33.17 | even | 10 | |||
7623.2.a.cw.1.6 | 8 | 33.5 | odd | 10 |