Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(49,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.i (of order \(10\), 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: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 274.3 | ||
Character | \(\chi\) | \(=\) | 375.274 |
Dual form | 375.2.i.d.349.3 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.234682 | − | 0.0762527i | −0.165945 | − | 0.0539188i | 0.224866 | − | 0.974390i | \(-0.427805\pi\) |
−0.390811 | + | 0.920471i | \(0.627805\pi\) | |||||||
\(3\) | −0.587785 | + | 0.809017i | −0.339358 | + | 0.467086i | ||||
\(4\) | −1.56877 | − | 1.13978i | −0.784386 | − | 0.569890i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.199632 | − | 0.145041i | 0.0814995 | − | 0.0592129i | ||||
\(7\) | 1.24676i | 0.471231i | 0.971846 | + | 0.235615i | \(0.0757105\pi\) | ||||
−0.971846 | + | 0.235615i | \(0.924289\pi\) | |||||||
\(8\) | 0.571334 | + | 0.786373i | 0.201997 | + | 0.278025i | ||||
\(9\) | −0.309017 | − | 0.951057i | −0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.794084 | − | 2.44394i | 0.239425 | − | 0.736876i | −0.757078 | − | 0.653324i | \(-0.773374\pi\) |
0.996503 | − | 0.0835513i | \(-0.0266262\pi\) | |||||||
\(12\) | 1.84420 | − | 0.599218i | 0.532376 | − | 0.172979i | ||||
\(13\) | 4.45215 | − | 1.44659i | 1.23480 | − | 0.401212i | 0.382351 | − | 0.924017i | \(-0.375115\pi\) |
0.852452 | + | 0.522805i | \(0.175115\pi\) | |||||||
\(14\) | 0.0950687 | − | 0.292592i | 0.0254082 | − | 0.0781984i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.12432 | + | 3.46029i | 0.281079 | + | 0.865073i | ||||
\(17\) | 3.43216 | + | 4.72397i | 0.832422 | + | 1.14573i | 0.987467 | + | 0.157823i | \(0.0504474\pi\) |
−0.155046 | + | 0.987907i | \(0.549553\pi\) | |||||||
\(18\) | 0.246759i | 0.0581616i | ||||||||
\(19\) | 3.37244 | − | 2.45022i | 0.773692 | − | 0.562120i | −0.129387 | − | 0.991594i | \(-0.541301\pi\) |
0.903079 | + | 0.429474i | \(0.141301\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00865 | − | 0.732827i | −0.220105 | − | 0.159916i | ||||
\(22\) | −0.372714 | + | 0.512997i | −0.0794629 | + | 0.109371i | ||||
\(23\) | 1.52689 | + | 0.496117i | 0.318379 | + | 0.103447i | 0.463847 | − | 0.885915i | \(-0.346469\pi\) |
−0.145468 | + | 0.989363i | \(0.546469\pi\) | |||||||
\(24\) | −0.972011 | −0.198411 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.15514 | −0.226542 | ||||||||
\(27\) | 0.951057 | + | 0.309017i | 0.183031 | + | 0.0594703i | ||||
\(28\) | 1.42103 | − | 1.95588i | 0.268550 | − | 0.369627i | ||||
\(29\) | −2.60158 | − | 1.89016i | −0.483102 | − | 0.350994i | 0.319423 | − | 0.947612i | \(-0.396511\pi\) |
−0.802525 | + | 0.596618i | \(0.796511\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.43739 | − | 5.40358i | 1.33579 | − | 0.970512i | 0.336207 | − | 0.941788i | \(-0.390856\pi\) |
0.999587 | − | 0.0287236i | \(-0.00914425\pi\) | |||||||
\(32\) | − | 2.84182i | − | 0.502368i | ||||||
\(33\) | 1.51044 | + | 2.07894i | 0.262934 | + | 0.361897i | ||||
\(34\) | −0.445250 | − | 1.37034i | −0.0763598 | − | 0.235011i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.599218 | + | 1.84420i | −0.0998697 | + | 0.307367i | ||||
\(37\) | −1.21524 | + | 0.394857i | −0.199785 | + | 0.0649141i | −0.407200 | − | 0.913339i | \(-0.633495\pi\) |
0.207415 | + | 0.978253i | \(0.433495\pi\) | |||||||
\(38\) | −0.978287 | + | 0.317865i | −0.158699 | + | 0.0515645i | ||||
\(39\) | −1.44659 | + | 4.45215i | −0.231640 | + | 0.712914i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.68719 | + | 8.27031i | 0.419668 | + | 1.29161i | 0.908008 | + | 0.418953i | \(0.137603\pi\) |
−0.488340 | + | 0.872654i | \(0.662397\pi\) | |||||||
\(42\) | 0.180832 | + | 0.248893i | 0.0279029 | + | 0.0384051i | ||||
\(43\) | − | 3.88086i | − | 0.591825i | −0.955215 | − | 0.295913i | \(-0.904376\pi\) | ||
0.955215 | − | 0.295913i | \(-0.0956237\pi\) | |||||||
\(44\) | −4.03129 | + | 2.92891i | −0.607740 | + | 0.441549i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.320503 | − | 0.232859i | −0.0472556 | − | 0.0343332i | ||||
\(47\) | 1.88651 | − | 2.59656i | 0.275176 | − | 0.378747i | −0.648953 | − | 0.760829i | \(-0.724793\pi\) |
0.924129 | + | 0.382082i | \(0.124793\pi\) | |||||||
\(48\) | −3.46029 | − | 1.12432i | −0.499450 | − | 0.162281i | ||||
\(49\) | 5.44559 | 0.777942 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.83914 | −0.817643 | ||||||||
\(52\) | −8.63320 | − | 2.80510i | −1.19721 | − | 0.388997i | ||||
\(53\) | −7.83770 | + | 10.7877i | −1.07659 | + | 1.48180i | −0.213371 | + | 0.976971i | \(0.568444\pi\) |
−0.863219 | + | 0.504829i | \(0.831556\pi\) | |||||||
\(54\) | −0.199632 | − | 0.145041i | −0.0271665 | − | 0.0197376i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.980418 | + | 0.712315i | −0.131014 | + | 0.0951871i | ||||
\(57\) | 4.16857i | 0.552141i | ||||||||
\(58\) | 0.466414 | + | 0.641964i | 0.0612432 | + | 0.0842940i | ||||
\(59\) | 1.97548 | + | 6.07990i | 0.257186 | + | 0.791536i | 0.993391 | + | 0.114778i | \(0.0366157\pi\) |
−0.736206 | + | 0.676758i | \(0.763384\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.18258 | − | 3.63961i | 0.151414 | − | 0.466005i | −0.846366 | − | 0.532602i | \(-0.821214\pi\) |
0.997780 | + | 0.0665973i | \(0.0212143\pi\) | |||||||
\(62\) | −2.15746 | + | 0.701000i | −0.273997 | + | 0.0890271i | ||||
\(63\) | 1.18574 | − | 0.385270i | 0.149389 | − | 0.0485394i | ||||
\(64\) | 2.03194 | − | 6.25366i | 0.253992 | − | 0.781708i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.195947 | − | 0.603064i | −0.0241195 | − | 0.0742321i | ||||
\(67\) | −5.95063 | − | 8.19034i | −0.726985 | − | 1.00061i | −0.999263 | − | 0.0383907i | \(-0.987777\pi\) |
0.272277 | − | 0.962219i | \(-0.412223\pi\) | |||||||
\(68\) | − | 11.3227i | − | 1.37308i | ||||||
\(69\) | −1.29885 | + | 0.943670i | −0.156363 | + | 0.113605i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.2284 | − | 8.15794i | −1.33257 | − | 0.968169i | −0.999682 | − | 0.0252028i | \(-0.991977\pi\) |
−0.332888 | − | 0.942966i | \(-0.608023\pi\) | |||||||
\(72\) | 0.571334 | − | 0.786373i | 0.0673323 | − | 0.0926750i | ||||
\(73\) | −10.8243 | − | 3.51704i | −1.26689 | − | 0.411638i | −0.402947 | − | 0.915223i | \(-0.632014\pi\) |
−0.863946 | + | 0.503585i | \(0.832014\pi\) | |||||||
\(74\) | 0.315305 | 0.0366534 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.08332 | −0.927220 | ||||||||
\(77\) | 3.04700 | + | 0.990032i | 0.347238 | + | 0.112825i | ||||
\(78\) | 0.678976 | − | 0.934531i | 0.0768789 | − | 0.105815i | ||||
\(79\) | 9.29008 | + | 6.74964i | 1.04522 | + | 0.759394i | 0.971297 | − | 0.237871i | \(-0.0764494\pi\) |
0.0739188 | + | 0.997264i | \(0.476449\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | − | 2.14580i | − | 0.236964i | ||||||
\(83\) | 1.66478 | + | 2.29137i | 0.182733 | + | 0.251511i | 0.890550 | − | 0.454885i | \(-0.150320\pi\) |
−0.707817 | + | 0.706396i | \(0.750320\pi\) | |||||||
\(84\) | 0.747080 | + | 2.29928i | 0.0815131 | + | 0.250872i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.295926 | + | 0.910766i | −0.0319105 | + | 0.0982105i | ||||
\(87\) | 3.05835 | − | 0.993717i | 0.327889 | − | 0.106538i | ||||
\(88\) | 2.37554 | − | 0.771858i | 0.253233 | − | 0.0822804i | ||||
\(89\) | 0.426682 | − | 1.31319i | 0.0452282 | − | 0.139198i | −0.925892 | − | 0.377788i | \(-0.876685\pi\) |
0.971121 | + | 0.238589i | \(0.0766850\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.80355 | + | 5.55075i | 0.189063 | + | 0.581877i | ||||
\(92\) | −1.82988 | − | 2.51861i | −0.190778 | − | 0.262584i | ||||
\(93\) | 9.19312i | 0.953282i | ||||||||
\(94\) | −0.640724 | + | 0.465513i | −0.0660857 | + | 0.0480140i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.29908 | + | 1.67038i | 0.234649 | + | 0.170483i | ||||
\(97\) | −0.0179322 | + | 0.0246815i | −0.00182074 | + | 0.00250603i | −0.809926 | − | 0.586532i | \(-0.800493\pi\) |
0.808106 | + | 0.589038i | \(0.200493\pi\) | |||||||
\(98\) | −1.27798 | − | 0.415241i | −0.129096 | − | 0.0419457i | ||||
\(99\) | −2.56971 | −0.258266 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.2308 | −1.11750 | −0.558751 | − | 0.829336i | \(-0.688719\pi\) | ||||
−0.558751 | + | 0.829336i | \(0.688719\pi\) | |||||||
\(102\) | 1.37034 | + | 0.445250i | 0.135684 | + | 0.0440864i | ||||
\(103\) | −0.423783 | + | 0.583288i | −0.0417566 | + | 0.0574730i | −0.829385 | − | 0.558678i | \(-0.811309\pi\) |
0.787628 | + | 0.616151i | \(0.211309\pi\) | |||||||
\(104\) | 3.68122 | + | 2.67456i | 0.360973 | + | 0.262262i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.66195 | − | 1.93402i | 0.258552 | − | 0.187849i | ||||
\(107\) | − | 2.11668i | − | 0.204627i | −0.994752 | − | 0.102313i | \(-0.967376\pi\) | ||
0.994752 | − | 0.102313i | \(-0.0326244\pi\) | |||||||
\(108\) | −1.13978 | − | 1.56877i | −0.109675 | − | 0.150955i | ||||
\(109\) | −0.690602 | − | 2.12545i | −0.0661477 | − | 0.203582i | 0.912520 | − | 0.409033i | \(-0.134134\pi\) |
−0.978667 | + | 0.205451i | \(0.934134\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.394857 | − | 1.21524i | 0.0374782 | − | 0.115346i | ||||
\(112\) | −4.31415 | + | 1.40175i | −0.407649 | + | 0.132453i | ||||
\(113\) | 2.99525 | − | 0.973217i | 0.281770 | − | 0.0915526i | −0.164723 | − | 0.986340i | \(-0.552673\pi\) |
0.446493 | + | 0.894787i | \(0.352673\pi\) | |||||||
\(114\) | 0.317865 | − | 0.978287i | 0.0297708 | − | 0.0916250i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.92693 | + | 5.93047i | 0.178911 | + | 0.550630i | ||||
\(117\) | −2.75158 | − | 3.78722i | −0.254383 | − | 0.350129i | ||||
\(118\) | − | 1.57748i | − | 0.145219i | ||||||
\(119\) | −5.88965 | + | 4.27908i | −0.539903 | + | 0.392262i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.55691 | + | 2.58425i | 0.323356 | + | 0.234932i | ||||
\(122\) | −0.555061 | + | 0.763975i | −0.0502528 | + | 0.0691671i | ||||
\(123\) | −8.27031 | − | 2.68719i | −0.745709 | − | 0.242296i | ||||
\(124\) | −17.8265 | −1.60086 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.307649 | −0.0274075 | ||||||||
\(127\) | 14.8938 | + | 4.83929i | 1.32161 | + | 0.429418i | 0.883048 | − | 0.469282i | \(-0.155487\pi\) |
0.438564 | + | 0.898700i | \(0.355487\pi\) | |||||||
\(128\) | −4.29448 | + | 5.91084i | −0.379582 | + | 0.522450i | ||||
\(129\) | 3.13968 | + | 2.28111i | 0.276433 | + | 0.200841i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.1000 | − | 8.79116i | 1.05718 | − | 0.768087i | 0.0836161 | − | 0.996498i | \(-0.473353\pi\) |
0.973565 | + | 0.228411i | \(0.0733530\pi\) | |||||||
\(132\) | − | 4.98295i | − | 0.433710i | ||||||
\(133\) | 3.05484 | + | 4.20463i | 0.264888 | + | 0.364587i | ||||
\(134\) | 0.771969 | + | 2.37588i | 0.0666879 | + | 0.205244i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.75389 | + | 5.39792i | −0.150395 | + | 0.462868i | ||||
\(137\) | −9.98092 | + | 3.24300i | −0.852727 | + | 0.277068i | −0.702588 | − | 0.711597i | \(-0.747972\pi\) |
−0.150139 | + | 0.988665i | \(0.547972\pi\) | |||||||
\(138\) | 0.376774 | − | 0.122421i | 0.0320731 | − | 0.0104212i | ||||
\(139\) | −3.84749 | + | 11.8414i | −0.326340 | + | 1.00437i | 0.644492 | + | 0.764611i | \(0.277069\pi\) |
−0.970832 | + | 0.239761i | \(0.922931\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.991798 | + | 3.05244i | 0.0835244 | + | 0.257062i | ||||
\(142\) | 2.01304 | + | 2.77072i | 0.168931 | + | 0.232513i | ||||
\(143\) | − | 12.0295i | − | 1.00596i | ||||||
\(144\) | 2.94350 | − | 2.13858i | 0.245292 | − | 0.178215i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.27209 | + | 1.65077i | 0.188039 | + | 0.136619i | ||||
\(147\) | −3.20084 | + | 4.40558i | −0.264001 | + | 0.363366i | ||||
\(148\) | 2.35649 | + | 0.765671i | 0.193703 | + | 0.0629378i | ||||
\(149\) | 17.0680 | 1.39826 | 0.699131 | − | 0.714994i | \(-0.253570\pi\) | ||||
0.699131 | + | 0.714994i | \(0.253570\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.57516 | −0.128185 | −0.0640923 | − | 0.997944i | \(-0.520415\pi\) | ||||
−0.0640923 | + | 0.997944i | \(0.520415\pi\) | |||||||
\(152\) | 3.85358 | + | 1.25210i | 0.312567 | + | 0.101559i | ||||
\(153\) | 3.43216 | − | 4.72397i | 0.277474 | − | 0.381910i | ||||
\(154\) | −0.639584 | − | 0.464685i | −0.0515391 | − | 0.0374454i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.34384 | − | 5.33561i | 0.587978 | − | 0.427191i | ||||
\(157\) | 9.20058i | 0.734286i | 0.930164 | + | 0.367143i | \(0.119664\pi\) | ||||
−0.930164 | + | 0.367143i | \(0.880336\pi\) | |||||||
\(158\) | −1.66553 | − | 2.29241i | −0.132503 | − | 0.182374i | ||||
\(159\) | −4.12052 | − | 12.6817i | −0.326779 | − | 1.00572i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.618538 | + | 1.90366i | −0.0487476 | + | 0.150030i | ||||
\(162\) | 0.234682 | − | 0.0762527i | 0.0184383 | − | 0.00599098i | ||||
\(163\) | 4.35656 | − | 1.41553i | 0.341232 | − | 0.110873i | −0.133388 | − | 0.991064i | \(-0.542586\pi\) |
0.474620 | + | 0.880191i | \(0.342586\pi\) | |||||||
\(164\) | 5.21075 | − | 16.0370i | 0.406891 | − | 1.25228i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.215970 | − | 0.664687i | −0.0167625 | − | 0.0515897i | ||||
\(167\) | 0.0837776 | + | 0.115310i | 0.00648291 | + | 0.00892296i | 0.812246 | − | 0.583315i | \(-0.198245\pi\) |
−0.805763 | + | 0.592238i | \(0.798245\pi\) | |||||||
\(168\) | − | 1.21186i | − | 0.0934973i | ||||||
\(169\) | 7.21176 | − | 5.23965i | 0.554751 | − | 0.403050i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.37244 | − | 2.45022i | −0.257897 | − | 0.187373i | ||||
\(172\) | −4.42333 | + | 6.08819i | −0.337275 | + | 0.464220i | ||||
\(173\) | 23.4176 | + | 7.60885i | 1.78041 | + | 0.578490i | 0.998965 | − | 0.0454831i | \(-0.0144827\pi\) |
0.781445 | + | 0.623974i | \(0.214483\pi\) | |||||||
\(174\) | −0.793511 | −0.0601559 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.34955 | 0.704749 | ||||||||
\(177\) | −6.07990 | − | 1.97548i | −0.456993 | − | 0.148486i | ||||
\(178\) | −0.200269 | + | 0.275647i | −0.0150108 | + | 0.0206606i | ||||
\(179\) | −19.5420 | − | 14.1981i | −1.46064 | − | 1.06122i | −0.983195 | − | 0.182557i | \(-0.941563\pi\) |
−0.477446 | − | 0.878661i | \(-0.658437\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.59218 | + | 1.15679i | −0.118346 | + | 0.0859834i | −0.645384 | − | 0.763858i | \(-0.723303\pi\) |
0.527038 | + | 0.849842i | \(0.323303\pi\) | |||||||
\(182\) | − | 1.44019i | − | 0.106754i | ||||||
\(183\) | 2.24940 | + | 3.09604i | 0.166281 | + | 0.228866i | ||||
\(184\) | 0.482231 | + | 1.48415i | 0.0355505 | + | 0.109413i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.701000 | − | 2.15746i | 0.0513998 | − | 0.158192i | ||||
\(187\) | 14.2705 | − | 4.63677i | 1.04356 | − | 0.339074i | ||||
\(188\) | −5.91901 | + | 1.92320i | −0.431689 | + | 0.140264i | ||||
\(189\) | −0.385270 | + | 1.18574i | −0.0280242 | + | 0.0862498i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.40061 | − | 7.38832i | −0.173702 | − | 0.534600i | 0.825870 | − | 0.563861i | \(-0.190685\pi\) |
−0.999572 | + | 0.0292607i | \(0.990685\pi\) | |||||||
\(192\) | 3.86498 | + | 5.31968i | 0.278931 | + | 0.383915i | ||||
\(193\) | 14.3458i | 1.03264i | 0.856397 | + | 0.516318i | \(0.172698\pi\) | ||||
−0.856397 | + | 0.516318i | \(0.827302\pi\) | |||||||
\(194\) | 0.00609039 | − | 0.00442493i | 0.000437265 | − | 0.000317691i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.54290 | − | 6.20678i | −0.610207 | − | 0.443341i | ||||
\(197\) | −0.0961264 | + | 0.132307i | −0.00684872 | + | 0.00942645i | −0.812428 | − | 0.583062i | \(-0.801854\pi\) |
0.805579 | + | 0.592489i | \(0.201854\pi\) | |||||||
\(198\) | 0.603064 | + | 0.195947i | 0.0428579 | + | 0.0139254i | ||||
\(199\) | −4.96974 | −0.352295 | −0.176148 | − | 0.984364i | \(-0.556364\pi\) | ||||
−0.176148 | + | 0.984364i | \(0.556364\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.1238 | 0.714079 | ||||||||
\(202\) | 2.63565 | + | 0.856375i | 0.185444 | + | 0.0602543i | ||||
\(203\) | 2.35658 | − | 3.24355i | 0.165399 | − | 0.227652i | ||||
\(204\) | 9.16029 | + | 6.65534i | 0.641348 | + | 0.465967i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.143931 | − | 0.104572i | 0.0100282 | − | 0.00728590i | ||||
\(207\) | − | 1.60547i | − | 0.111588i | ||||||
\(208\) | 10.0112 | + | 13.7793i | 0.694155 | + | 0.955423i | ||||
\(209\) | −3.31020 | − | 10.1877i | −0.228971 | − | 0.704701i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.01784 | − | 3.13260i | 0.0700713 | − | 0.215657i | −0.909888 | − | 0.414853i | \(-0.863833\pi\) |
0.979960 | + | 0.199196i | \(0.0638330\pi\) | |||||||
\(212\) | 24.5911 | − | 7.99015i | 1.68893 | − | 0.548766i | ||||
\(213\) | 13.1998 | − | 4.28888i | 0.904437 | − | 0.293869i | ||||
\(214\) | −0.161402 | + | 0.496745i | −0.0110332 | + | 0.0339568i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.300368 | + | 0.924437i | 0.0204374 | + | 0.0629000i | ||||
\(217\) | 6.73696 | + | 9.27263i | 0.457335 | + | 0.629467i | ||||
\(218\) | 0.551465i | 0.0373500i | ||||||||
\(219\) | 9.20773 | − | 6.68981i | 0.622201 | − | 0.452055i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.1141 | + | 16.0669i | 1.48756 | + | 1.08077i | ||||
\(222\) | −0.185331 | + | 0.255087i | −0.0124386 | + | 0.0171203i | ||||
\(223\) | −15.0012 | − | 4.87419i | −1.00456 | − | 0.326400i | −0.239872 | − | 0.970805i | \(-0.577105\pi\) |
−0.764685 | + | 0.644404i | \(0.777105\pi\) | |||||||
\(224\) | 3.54307 | 0.236731 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.777142 | −0.0516947 | ||||||||
\(227\) | −12.8779 | − | 4.18427i | −0.854734 | − | 0.277720i | −0.151307 | − | 0.988487i | \(-0.548348\pi\) |
−0.703428 | + | 0.710767i | \(0.748348\pi\) | |||||||
\(228\) | 4.75125 | − | 6.53954i | 0.314660 | − | 0.433092i | ||||
\(229\) | −11.9596 | − | 8.68915i | −0.790312 | − | 0.574195i | 0.117744 | − | 0.993044i | \(-0.462434\pi\) |
−0.908056 | + | 0.418849i | \(0.862434\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.59194 | + | 1.88315i | −0.170537 | + | 0.123902i | ||||
\(232\) | − | 3.12573i | − | 0.205214i | ||||||
\(233\) | −0.305049 | − | 0.419864i | −0.0199844 | − | 0.0275062i | 0.798908 | − | 0.601453i | \(-0.205411\pi\) |
−0.818892 | + | 0.573947i | \(0.805411\pi\) | |||||||
\(234\) | 0.356959 | + | 1.09861i | 0.0233351 | + | 0.0718182i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.83067 | − | 11.7896i | 0.249356 | − | 0.767438i | ||||
\(237\) | −10.9211 | + | 3.54849i | −0.709405 | + | 0.230500i | ||||
\(238\) | 1.70848 | − | 0.555120i | 0.110745 | − | 0.0359831i | ||||
\(239\) | −2.54331 | + | 7.82750i | −0.164513 | + | 0.506319i | −0.999000 | − | 0.0447086i | \(-0.985764\pi\) |
0.834487 | + | 0.551027i | \(0.185764\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.395906 | − | 1.21847i | −0.0255025 | − | 0.0784888i | 0.937495 | − | 0.347998i | \(-0.113138\pi\) |
−0.962998 | + | 0.269509i | \(0.913138\pi\) | |||||||
\(242\) | −0.637686 | − | 0.877700i | −0.0409920 | − | 0.0564207i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −6.00356 | + | 4.36184i | −0.384339 | + | 0.279238i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.73599 | + | 1.26127i | 0.110682 | + | 0.0804155i | ||||
\(247\) | 11.4701 | − | 15.7873i | 0.729828 | − | 1.00452i | ||||
\(248\) | 8.49846 | + | 2.76132i | 0.539653 | + | 0.175344i | ||||
\(249\) | −2.83229 | −0.179489 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.63494 | 0.292555 | 0.146277 | − | 0.989244i | \(-0.453271\pi\) | ||||
0.146277 | + | 0.989244i | \(0.453271\pi\) | |||||||
\(252\) | −2.29928 | − | 0.747080i | −0.144841 | − | 0.0470616i | ||||
\(253\) | 2.42496 | − | 3.33767i | 0.152456 | − | 0.209837i | ||||
\(254\) | −3.12630 | − | 2.27139i | −0.196161 | − | 0.142519i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.18081 | + | 6.67025i | −0.573801 | + | 0.416891i | ||||
\(257\) | 18.3001i | 1.14153i | 0.821113 | + | 0.570766i | \(0.193353\pi\) | ||||
−0.821113 | + | 0.570766i | \(0.806647\pi\) | |||||||
\(258\) | −0.562885 | − | 0.774744i | −0.0350437 | − | 0.0482335i | ||||
\(259\) | −0.492291 | − | 1.51512i | −0.0305895 | − | 0.0941448i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.993717 | + | 3.05835i | −0.0615095 | + | 0.189307i | ||||
\(262\) | −3.51000 | + | 1.14047i | −0.216848 | + | 0.0704583i | ||||
\(263\) | −15.8509 | + | 5.15027i | −0.977409 | + | 0.317579i | −0.753803 | − | 0.657100i | \(-0.771783\pi\) |
−0.223606 | + | 0.974680i | \(0.571783\pi\) | |||||||
\(264\) | −0.771858 | + | 2.37554i | −0.0475046 | + | 0.146204i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.396301 | − | 1.21969i | −0.0242988 | − | 0.0747839i | ||||
\(267\) | 0.811598 | + | 1.11707i | 0.0496690 | + | 0.0683635i | ||||
\(268\) | 19.6312i | 1.19917i | ||||||||
\(269\) | 2.12942 | − | 1.54712i | 0.129833 | − | 0.0943294i | −0.520973 | − | 0.853573i | \(-0.674431\pi\) |
0.650807 | + | 0.759244i | \(0.274431\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.69192 | − | 2.68233i | −0.224268 | − | 0.162940i | 0.469978 | − | 0.882678i | \(-0.344262\pi\) |
−0.694246 | + | 0.719738i | \(0.744262\pi\) | |||||||
\(272\) | −12.4875 | + | 17.1875i | −0.757164 | + | 1.04215i | ||||
\(273\) | −5.55075 | − | 1.80355i | −0.335947 | − | 0.109156i | ||||
\(274\) | 2.58963 | 0.156445 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.11318 | 0.187391 | ||||||||
\(277\) | −1.19762 | − | 0.389132i | −0.0719583 | − | 0.0233807i | 0.272817 | − | 0.962066i | \(-0.412045\pi\) |
−0.344775 | + | 0.938685i | \(0.612045\pi\) | |||||||
\(278\) | 1.80587 | − | 2.48557i | 0.108309 | − | 0.149075i | ||||
\(279\) | −7.43739 | − | 5.40358i | −0.445265 | − | 0.323504i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.8543 | + | 7.88611i | −0.647513 | + | 0.470446i | −0.862423 | − | 0.506188i | \(-0.831054\pi\) |
0.214910 | + | 0.976634i | \(0.431054\pi\) | |||||||
\(282\) | − | 0.791979i | − | 0.0471617i | ||||||
\(283\) | −14.1591 | − | 19.4884i | −0.841674 | − | 1.15846i | −0.985636 | − | 0.168882i | \(-0.945984\pi\) |
0.143962 | − | 0.989583i | \(-0.454016\pi\) | |||||||
\(284\) | 8.31661 | + | 25.5959i | 0.493500 | + | 1.51884i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.917281 | + | 2.82310i | −0.0542400 | + | 0.166934i | ||||
\(287\) | −10.3111 | + | 3.35028i | −0.608644 | + | 0.197761i | ||||
\(288\) | −2.70273 | + | 0.878171i | −0.159260 | + | 0.0517467i | ||||
\(289\) | −5.28283 | + | 16.2589i | −0.310754 | + | 0.956404i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.00942751 | − | 0.0290149i | −0.000552651 | − | 0.00170088i | ||||
\(292\) | 12.9723 | + | 17.8548i | 0.759145 | + | 1.04487i | ||||
\(293\) | − | 32.1727i | − | 1.87955i | −0.341792 | − | 0.939776i | \(-0.611034\pi\) | ||
0.341792 | − | 0.939776i | \(-0.388966\pi\) | |||||||
\(294\) | 1.08712 | − | 0.789836i | 0.0634019 | − | 0.0460641i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.00481 | − | 0.730041i | −0.0584037 | − | 0.0424328i | ||||
\(297\) | 1.51044 | − | 2.07894i | 0.0876445 | − | 0.120632i | ||||
\(298\) | −4.00554 | − | 1.30148i | −0.232035 | − | 0.0753926i | ||||
\(299\) | 7.51561 | 0.434639 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.83849 | 0.278886 | ||||||||
\(302\) | 0.369661 | + | 0.120110i | 0.0212716 | + | 0.00691156i | ||||
\(303\) | 6.60127 | − | 9.08587i | 0.379233 | − | 0.521970i | ||||
\(304\) | 12.2702 | + | 8.91482i | 0.703744 | + | 0.511300i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.16568 | + | 0.846917i | −0.0666375 | + | 0.0484150i | ||||
\(307\) | − | 20.2962i | − | 1.15837i | −0.815198 | − | 0.579183i | \(-0.803372\pi\) | ||
0.815198 | − | 0.579183i | \(-0.196628\pi\) | |||||||
\(308\) | −3.65164 | − | 5.02605i | −0.208071 | − | 0.286386i | ||||
\(309\) | −0.222796 | − | 0.685696i | −0.0126744 | − | 0.0390079i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.78554 | + | 17.8061i | −0.328068 | + | 1.00969i | 0.641969 | + | 0.766731i | \(0.278118\pi\) |
−0.970037 | + | 0.242959i | \(0.921882\pi\) | |||||||
\(312\) | −4.32753 | + | 1.40610i | −0.244998 | + | 0.0796048i | ||||
\(313\) | −23.6660 | + | 7.68955i | −1.33768 | + | 0.434639i | −0.888531 | − | 0.458817i | \(-0.848274\pi\) |
−0.449151 | + | 0.893456i | \(0.648274\pi\) | |||||||
\(314\) | 0.701569 | − | 2.15921i | 0.0395919 | − | 0.121851i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.88092 | − | 21.1773i | −0.387082 | − | 1.19132i | ||||
\(317\) | −14.8052 | − | 20.3775i | −0.831540 | − | 1.14452i | −0.987634 | − | 0.156775i | \(-0.949890\pi\) |
0.156094 | − | 0.987742i | \(-0.450110\pi\) | |||||||
\(318\) | 3.29036i | 0.184514i | ||||||||
\(319\) | −6.68532 | + | 4.85717i | −0.374306 | + | 0.271949i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.71243 | + | 1.24415i | 0.0955783 | + | 0.0694417i | ||||
\(322\) | 0.290319 | − | 0.399590i | 0.0161788 | − | 0.0222683i | ||||
\(323\) | 23.1496 | + | 7.52174i | 1.28808 | + | 0.418521i | ||||
\(324\) | 1.93911 | 0.107728 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.13034 | −0.0626039 | ||||||||
\(327\) | 2.12545 | + | 0.690602i | 0.117538 | + | 0.0381904i | ||||
\(328\) | −4.96827 | + | 6.83824i | −0.274327 | + | 0.377579i | ||||
\(329\) | 3.23728 | + | 2.35202i | 0.178477 | + | 0.129671i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.6097 | + | 17.8800i | −1.35267 | + | 0.982773i | −0.353797 | + | 0.935322i | \(0.615110\pi\) |
−0.998874 | + | 0.0474508i | \(0.984890\pi\) | |||||||
\(332\) | − | 5.49212i | − | 0.301419i | ||||||
\(333\) | 0.751062 | + | 1.03375i | 0.0411580 | + | 0.0566491i | ||||
\(334\) | −0.0108684 | − | 0.0334494i | −0.000594691 | − | 0.00183027i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.40175 | − | 4.31415i | 0.0764719 | − | 0.235356i | ||||
\(337\) | −4.35066 | + | 1.41361i | −0.236995 | + | 0.0770045i | −0.425107 | − | 0.905143i | \(-0.639763\pi\) |
0.188111 | + | 0.982148i | \(0.439763\pi\) | |||||||
\(338\) | −2.09200 | + | 0.679734i | −0.113790 | + | 0.0369726i | ||||
\(339\) | −0.973217 | + | 2.99525i | −0.0528579 | + | 0.162680i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.30011 | − | 22.4674i | −0.395323 | − | 1.21668i | ||||
\(342\) | 0.604615 | + | 0.832181i | 0.0326938 | + | 0.0449992i | ||||
\(343\) | 15.5167i | 0.837821i | ||||||||
\(344\) | 3.05180 | − | 2.21726i | 0.164542 | − | 0.119547i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.91550 | − | 3.57132i | −0.264259 | − | 0.191995i | ||||
\(347\) | 9.88377 | − | 13.6038i | 0.530589 | − | 0.730293i | −0.456631 | − | 0.889656i | \(-0.650944\pi\) |
0.987220 | + | 0.159363i | \(0.0509442\pi\) | |||||||
\(348\) | −5.93047 | − | 1.92693i | −0.317906 | − | 0.103294i | ||||
\(349\) | −0.373581 | −0.0199973 | −0.00999866 | − | 0.999950i | \(-0.503183\pi\) | ||||
−0.00999866 | + | 0.999950i | \(0.503183\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.68126 | 0.249867 | ||||||||
\(352\) | −6.94524 | − | 2.25665i | −0.370183 | − | 0.120280i | ||||
\(353\) | −14.0883 | + | 19.3909i | −0.749847 | + | 1.03208i | 0.248144 | + | 0.968723i | \(0.420179\pi\) |
−0.997991 | + | 0.0633526i | \(0.979821\pi\) | |||||||
\(354\) | 1.27621 | + | 0.927218i | 0.0678296 | + | 0.0492811i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.16612 | + | 1.57378i | −0.114804 | + | 0.0834101i | ||||
\(357\) | − | 7.28000i | − | 0.385299i | ||||||
\(358\) | 3.50352 | + | 4.82218i | 0.185167 | + | 0.254860i | ||||
\(359\) | 1.46789 | + | 4.51771i | 0.0774724 | + | 0.238435i | 0.982291 | − | 0.187362i | \(-0.0599937\pi\) |
−0.904819 | + | 0.425797i | \(0.859994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.501540 | + | 1.54358i | −0.0263969 | + | 0.0812412i | ||||
\(362\) | 0.461865 | − | 0.150069i | 0.0242751 | − | 0.00788744i | ||||
\(363\) | −4.18140 | + | 1.35862i | −0.219467 | + | 0.0713090i | ||||
\(364\) | 3.49728 | − | 10.7635i | 0.183307 | − | 0.564162i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.291813 | − | 0.898107i | −0.0152533 | − | 0.0469448i | ||||
\(367\) | −10.2098 | − | 14.0526i | −0.532948 | − | 0.733540i | 0.454628 | − | 0.890681i | \(-0.349772\pi\) |
−0.987576 | + | 0.157141i | \(0.949772\pi\) | |||||||
\(368\) | 5.84128i | 0.304498i | ||||||||
\(369\) | 7.03515 | − | 5.11134i | 0.366235 | − | 0.266085i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.4496 | − | 9.77172i | −0.698270 | − | 0.507323i | ||||
\(372\) | 10.4781 | − | 14.4219i | 0.543266 | − | 0.747742i | ||||
\(373\) | 2.00556 | + | 0.651645i | 0.103844 | + | 0.0337409i | 0.360478 | − | 0.932768i | \(-0.382614\pi\) |
−0.256634 | + | 0.966509i | \(0.582614\pi\) | |||||||
\(374\) | −3.70260 | −0.191457 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.11969 | 0.160886 | ||||||||
\(377\) | −14.3169 | − | 4.65185i | −0.737359 | − | 0.239582i | ||||
\(378\) | 0.180832 | − | 0.248893i | 0.00930097 | − | 0.0128017i | ||||
\(379\) | 10.0391 | + | 7.29380i | 0.515671 | + | 0.374657i | 0.814971 | − | 0.579502i | \(-0.196753\pi\) |
−0.299299 | + | 0.954159i | \(0.596753\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.6694 | + | 9.20488i | −0.649075 | + | 0.471580i | ||||
\(382\) | 1.91696i | 0.0980801i | ||||||||
\(383\) | −19.5766 | − | 26.9448i | −1.00032 | − | 1.37682i | −0.925132 | − | 0.379646i | \(-0.876046\pi\) |
−0.0751836 | − | 0.997170i | \(-0.523954\pi\) | |||||||
\(384\) | −2.25774 | − | 6.94861i | −0.115215 | − | 0.354595i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.09391 | − | 3.36671i | 0.0556785 | − | 0.171361i | ||||
\(387\) | −3.69092 | + | 1.19925i | −0.187620 | + | 0.0609614i | ||||
\(388\) | 0.0562631 | − | 0.0182810i | 0.00285633 | − | 0.000928076i | ||||
\(389\) | 5.24639 | − | 16.1467i | 0.266002 | − | 0.818671i | −0.725459 | − | 0.688266i | \(-0.758372\pi\) |
0.991461 | − | 0.130405i | \(-0.0416278\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.89690 | + | 8.91573i | 0.146502 | + | 0.450888i | ||||
\(392\) | 3.11125 | + | 4.28227i | 0.157142 | + | 0.216287i | ||||
\(393\) | 14.9564i | 0.754451i | ||||||||
\(394\) | 0.0326478 | − | 0.0237200i | 0.00164477 | − | 0.00119500i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.03129 | + | 2.92891i | 0.202580 | + | 0.147183i | ||||
\(397\) | 0.509357 | − | 0.701070i | 0.0255639 | − | 0.0351857i | −0.796044 | − | 0.605239i | \(-0.793078\pi\) |
0.821608 | + | 0.570053i | \(0.193078\pi\) | |||||||
\(398\) | 1.16631 | + | 0.378956i | 0.0584617 | + | 0.0189953i | ||||
\(399\) | −5.19720 | −0.260186 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.68680 | 0.483736 | 0.241868 | − | 0.970309i | \(-0.422240\pi\) | ||||
0.241868 | + | 0.970309i | \(0.422240\pi\) | |||||||
\(402\) | −2.37588 | − | 0.771969i | −0.118498 | − | 0.0385023i | ||||
\(403\) | 25.2956 | − | 34.8164i | 1.26006 | − | 1.73433i | ||||
\(404\) | 17.6185 | + | 12.8006i | 0.876553 | + | 0.636853i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.800374 | + | 0.581506i | −0.0397219 | + | 0.0288597i | ||||
\(407\) | 3.28353i | 0.162759i | ||||||||
\(408\) | −3.33610 | − | 4.59174i | −0.165161 | − | 0.227325i | ||||
\(409\) | −0.469043 | − | 1.44357i | −0.0231927 | − | 0.0713797i | 0.938790 | − | 0.344489i | \(-0.111948\pi\) |
−0.961983 | + | 0.273109i | \(0.911948\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.24300 | − | 9.98092i | 0.159965 | − | 0.492322i | ||||
\(412\) | 1.32964 | − | 0.432026i | 0.0655066 | − | 0.0212844i | ||||
\(413\) | −7.58017 | + | 2.46295i | −0.372996 | + | 0.121194i | ||||
\(414\) | −0.122421 | + | 0.376774i | −0.00601667 | + | 0.0185174i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.11095 | − | 12.6522i | −0.201556 | − | 0.620325i | ||||
\(417\) | −7.31837 | − | 10.0729i | −0.358382 | − | 0.493271i | ||||
\(418\) | 2.64329i | 0.129287i | ||||||||
\(419\) | −24.7252 | + | 17.9639i | −1.20790 | + | 0.877594i | −0.995039 | − | 0.0994875i | \(-0.968280\pi\) |
−0.212866 | + | 0.977081i | \(0.568280\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.64016 | + | 4.09782i | 0.274885 | + | 0.199715i | 0.716683 | − | 0.697399i | \(-0.245659\pi\) |
−0.441799 | + | 0.897114i | \(0.645659\pi\) | |||||||
\(422\) | −0.477739 | + | 0.657551i | −0.0232560 | + | 0.0320091i | ||||
\(423\) | −3.05244 | − | 0.991798i | −0.148415 | − | 0.0482228i | ||||
\(424\) | −12.9611 | −0.629445 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.42480 | −0.165932 | ||||||||
\(427\) | 4.53772 | + | 1.47439i | 0.219596 | + | 0.0713510i | ||||
\(428\) | −2.41255 | + | 3.32058i | −0.116615 | + | 0.160506i | ||||
\(429\) | 9.73206 | + | 7.07076i | 0.469868 | + | 0.341379i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.85650 | + | 6.43463i | −0.426603 | + | 0.309945i | −0.780289 | − | 0.625419i | \(-0.784928\pi\) |
0.353686 | + | 0.935364i | \(0.384928\pi\) | |||||||
\(432\) | 3.63837i | 0.175051i | ||||||||
\(433\) | −6.13609 | − | 8.44561i | −0.294882 | − | 0.405870i | 0.635710 | − | 0.771928i | \(-0.280707\pi\) |
−0.930592 | + | 0.366058i | \(0.880707\pi\) | |||||||
\(434\) | −0.873978 | − | 2.68983i | −0.0419523 | − | 0.129116i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.33915 | + | 4.12149i | −0.0641338 | + | 0.197384i | ||||
\(437\) | 6.36495 | − | 2.06810i | 0.304477 | − | 0.0989305i | ||||
\(438\) | −2.67100 | + | 0.867861i | −0.127625 | + | 0.0414680i | ||||
\(439\) | −4.76917 | + | 14.6780i | −0.227620 | + | 0.700543i | 0.770395 | + | 0.637567i | \(0.220059\pi\) |
−0.998015 | + | 0.0629758i | \(0.979941\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.68278 | − | 5.17907i | −0.0801324 | − | 0.246622i | ||||
\(442\) | −3.96464 | − | 5.45686i | −0.188579 | − | 0.259556i | ||||
\(443\) | 18.9105i | 0.898463i | 0.893415 | + | 0.449231i | \(0.148302\pi\) | ||||
−0.893415 | + | 0.449231i | \(0.851698\pi\) | |||||||
\(444\) | −2.00455 | + | 1.45639i | −0.0951318 | + | 0.0691173i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.14884 | + | 2.28777i | 0.149102 | + | 0.108329i | ||||
\(447\) | −10.0323 | + | 13.8083i | −0.474511 | + | 0.653109i | ||||
\(448\) | 7.79681 | + | 2.53334i | 0.368365 | + | 0.119689i | ||||
\(449\) | 11.4152 | 0.538714 | 0.269357 | − | 0.963040i | \(-0.413189\pi\) | ||||
0.269357 | + | 0.963040i | \(0.413189\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.3460 | 1.05223 | ||||||||
\(452\) | −5.80813 | − | 1.88717i | −0.273191 | − | 0.0887652i | ||||
\(453\) | 0.925855 | − | 1.27433i | 0.0435005 | − | 0.0598733i | ||||
\(454\) | 2.70314 | + | 1.96395i | 0.126865 | + | 0.0921725i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.27805 | + | 2.38164i | −0.153509 | + | 0.111531i | ||||
\(457\) | 33.9739i | 1.58923i | 0.607112 | + | 0.794616i | \(0.292328\pi\) | ||||
−0.607112 | + | 0.794616i | \(0.707672\pi\) | |||||||
\(458\) | 2.14413 | + | 2.95114i | 0.100188 | + | 0.137898i | ||||
\(459\) | 1.80439 | + | 5.55335i | 0.0842219 | + | 0.259208i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.62985 | + | 23.4823i | −0.355358 | + | 1.09368i | 0.600444 | + | 0.799667i | \(0.294991\pi\) |
−0.955802 | + | 0.294012i | \(0.905009\pi\) | |||||||
\(462\) | 0.751876 | − | 0.244299i | 0.0349804 | − | 0.0113658i | ||||
\(463\) | 12.9643 | − | 4.21237i | 0.602504 | − | 0.195765i | 0.00814689 | − | 0.999967i | \(-0.497407\pi\) |
0.594357 | + | 0.804202i | \(0.297407\pi\) | |||||||
\(464\) | 3.61551 | − | 11.1274i | 0.167846 | − | 0.516576i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.0395737 | + | 0.121795i | 0.00183321 | + | 0.00564205i | ||||
\(467\) | 5.56700 | + | 7.66232i | 0.257610 | + | 0.354570i | 0.918158 | − | 0.396214i | \(-0.129676\pi\) |
−0.660548 | + | 0.750784i | \(0.729676\pi\) | |||||||
\(468\) | 9.07748i | 0.419607i | ||||||||
\(469\) | 10.2114 | − | 7.41900i | 0.471518 | − | 0.342578i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.44343 | − | 5.40797i | −0.342975 | − | 0.249186i | ||||
\(472\) | −3.65241 | + | 5.02712i | −0.168116 | + | 0.231392i | ||||
\(473\) | −9.48459 | − | 3.08173i | −0.436102 | − | 0.141698i | ||||
\(474\) | 2.83358 | 0.130150 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 14.1167 | 0.647039 | ||||||||
\(477\) | 12.6817 | + | 4.12052i | 0.580654 | + | 0.188666i | ||||
\(478\) | 1.19374 | − | 1.64304i | 0.0546002 | − | 0.0751508i | ||||
\(479\) | −20.8149 | − | 15.1229i | −0.951055 | − | 0.690982i | 1.08775e−6 | − | 1.00000i | \(-0.500000\pi\) |
−0.951056 | + | 0.309018i | \(0.900000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.83925 | + | 3.51592i | −0.220651 | + | 0.160312i | ||||
\(482\) | 0.316142i | 0.0143999i | ||||||||
\(483\) | −1.17653 | − | 1.61935i | −0.0535339 | − | 0.0736831i | ||||
\(484\) | −2.63451 | − | 8.10820i | −0.119751 | − | 0.368554i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.0762527 | + | 0.234682i | −0.00345889 | + | 0.0106454i | ||||
\(487\) | −27.0144 | + | 8.77751i | −1.22414 | + | 0.397747i | −0.848588 | − | 0.529055i | \(-0.822547\pi\) |
−0.375551 | + | 0.926802i | \(0.622547\pi\) | |||||||
\(488\) | 3.53774 | − | 1.14948i | 0.160146 | − | 0.0520346i | ||||
\(489\) | −1.41553 | + | 4.35656i | −0.0640126 | + | 0.197010i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.88593 | − | 5.80429i | −0.0851107 | − | 0.261944i | 0.899440 | − | 0.437045i | \(-0.143975\pi\) |
−0.984551 | + | 0.175101i | \(0.943975\pi\) | |||||||
\(492\) | 9.91144 | + | 13.6419i | 0.446842 | + | 0.615026i | ||||
\(493\) | − | 18.7771i | − | 0.845679i | ||||||
\(494\) | −3.89566 | + | 2.83036i | −0.175274 | + | 0.127344i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 27.0600 | + | 19.6602i | 1.21503 | + | 0.882770i | ||||
\(497\) | 10.1710 | − | 13.9992i | 0.456231 | − | 0.627948i | ||||
\(498\) | 0.664687 | + | 0.215970i | 0.0297853 | + | 0.00967784i | ||||
\(499\) | 20.3163 | 0.909481 | 0.454740 | − | 0.890624i | \(-0.349732\pi\) | ||||
0.454740 | + | 0.890624i | \(0.349732\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.142531 | −0.00636782 | ||||||||
\(502\) | −1.08773 | − | 0.353426i | −0.0485480 | − | 0.0157742i | ||||
\(503\) | 8.59734 | − | 11.8332i | 0.383336 | − | 0.527617i | −0.573128 | − | 0.819466i | \(-0.694270\pi\) |
0.956465 | + | 0.291848i | \(0.0942703\pi\) | |||||||
\(504\) | 0.980418 | + | 0.712315i | 0.0436713 | + | 0.0317290i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.823600 | + | 0.598380i | −0.0366135 | + | 0.0266012i | ||||
\(507\) | 8.91422i | 0.395894i | ||||||||
\(508\) | −17.8493 | − | 24.5674i | −0.791934 | − | 1.09000i | ||||
\(509\) | 1.33058 | + | 4.09510i | 0.0589768 | + | 0.181512i | 0.976205 | − | 0.216851i | \(-0.0695785\pi\) |
−0.917228 | + | 0.398363i | \(0.869578\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.38490 | − | 13.4953i | 0.193977 | − | 0.596999i | ||||
\(512\) | 16.5604 | − | 5.38081i | 0.731874 | − | 0.237800i | ||||
\(513\) | 3.96455 | − | 1.28816i | 0.175039 | − | 0.0568736i | ||||
\(514\) | 1.39543 | − | 4.29471i | 0.0615500 | − | 0.189431i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.32548 | − | 7.15709i | −0.102374 | − | 0.315073i | ||||
\(517\) | −4.84779 | − | 6.67241i | −0.213205 | − | 0.293452i | ||||
\(518\) | 0.393109i | 0.0172722i | ||||||||
\(519\) | −19.9202 | + | 14.4729i | −0.874401 | + | 0.635290i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.0705 | + | 23.3006i | 1.40503 | + | 1.02082i | 0.994021 | + | 0.109186i | \(0.0348243\pi\) |
0.411011 | + | 0.911630i | \(0.365176\pi\) | |||||||
\(522\) | 0.466414 | − | 0.641964i | 0.0204144 | − | 0.0280980i | ||||
\(523\) | 34.5114 | + | 11.2134i | 1.50908 | + | 0.490329i | 0.942650 | − | 0.333782i | \(-0.108325\pi\) |
0.566428 | + | 0.824111i | \(0.308325\pi\) | |||||||
\(524\) | −29.0021 | −1.26696 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.11264 | 0.179320 | ||||||||
\(527\) | 51.0526 | + | 16.5880i | 2.22389 | + | 0.722585i | ||||
\(528\) | −5.49553 | + | 7.56395i | −0.239162 | + | 0.329179i | ||||
\(529\) | −16.5221 | − | 12.0040i | −0.718353 | − | 0.521914i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.17187 | − | 3.75759i | 0.224440 | − | 0.163065i | ||||
\(532\) | − | 10.0779i | − | 0.436934i | ||||||
\(533\) | 23.9275 | + | 32.9334i | 1.03642 | + | 1.42650i | ||||
\(534\) | −0.105288 | − | 0.324042i | −0.00455625 | − | 0.0140227i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.04087 | − | 9.35883i | 0.131346 | − | 0.404240i | ||||
\(537\) | 22.9731 | − | 7.46440i | 0.991360 | − | 0.322113i | ||||
\(538\) | −0.617709 | + | 0.200706i | −0.0266313 | + | 0.00865304i | ||||
\(539\) | 4.32426 | − | 13.3087i | 0.186259 | − | 0.573246i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.9294 | − | 36.7150i | −0.512886 | − | 1.57850i | −0.787096 | − | 0.616830i | \(-0.788417\pi\) |
0.274211 | − | 0.961670i | \(-0.411583\pi\) | |||||||
\(542\) | 0.661890 | + | 0.911014i | 0.0284306 | + | 0.0391314i | ||||
\(543\) | − | 1.96805i | − | 0.0844570i | ||||||
\(544\) | 13.4247 | − | 9.75359i | 0.575578 | − | 0.418182i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.16513 | + | 0.846520i | 0.0498632 | + | 0.0362277i | ||||
\(547\) | −6.09063 | + | 8.38303i | −0.260416 | + | 0.358433i | −0.919125 | − | 0.393965i | \(-0.871103\pi\) |
0.658709 | + | 0.752398i | \(0.271103\pi\) | |||||||
\(548\) | 19.3541 | + | 6.28853i | 0.826766 | + | 0.268633i | ||||
\(549\) | −3.82692 | −0.163329 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.4050 | −0.571073 | ||||||||
\(552\) | −1.48415 | − | 0.482231i | −0.0631698 | − | 0.0205251i | ||||
\(553\) | −8.41517 | + | 11.5825i | −0.357850 | + | 0.492538i | ||||
\(554\) | 0.251388 | + | 0.182644i | 0.0106805 | + | 0.00775981i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.5324 | − | 14.1911i | 0.828359 | − | 0.601838i | ||||
\(557\) | − | 12.6830i | − | 0.537398i | −0.963224 | − | 0.268699i | \(-0.913406\pi\) | ||
0.963224 | − | 0.268699i | \(-0.0865936\pi\) | |||||||
\(558\) | 1.33338 | + | 1.83524i | 0.0564465 | + | 0.0776920i | ||||
\(559\) | −5.61401 | − | 17.2781i | −0.237447 | − | 0.730788i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.63677 | + | 14.2705i | −0.195765 | + | 0.602502i | ||||
\(562\) | 3.14864 | − | 1.02306i | 0.132817 | − | 0.0431550i | ||||
\(563\) | −12.4486 | + | 4.04480i | −0.524646 | + | 0.170468i | −0.559353 | − | 0.828930i | \(-0.688950\pi\) |
0.0347068 | + | 0.999398i | \(0.488950\pi\) | |||||||
\(564\) | 1.92320 | − | 5.91901i | 0.0809815 | − | 0.249235i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.83685 | + | 5.65324i | 0.0772086 | + | 0.237624i | ||||
\(567\) | −0.732827 | − | 1.00865i | −0.0307758 | − | 0.0423593i | ||||
\(568\) | − | 13.4906i | − | 0.566055i | ||||||
\(569\) | −2.09376 | + | 1.52120i | −0.0877748 | + | 0.0637721i | −0.630807 | − | 0.775940i | \(-0.717276\pi\) |
0.543032 | + | 0.839712i | \(0.317276\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.55571 | + | 6.21609i | 0.358045 | + | 0.260135i | 0.752236 | − | 0.658893i | \(-0.228975\pi\) |
−0.394191 | + | 0.919029i | \(0.628975\pi\) | |||||||
\(572\) | −13.7110 | + | 18.8715i | −0.573285 | + | 0.789059i | ||||
\(573\) | 7.38832 | + | 2.40061i | 0.308652 | + | 0.100287i | ||||
\(574\) | 2.67529 | 0.111665 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.57549 | −0.273979 | ||||||||
\(577\) | 0.0135910 | + | 0.00441597i | 0.000565800 | + | 0.000183839i | 0.309300 | − | 0.950965i | \(-0.399905\pi\) |
−0.308734 | + | 0.951148i | \(0.599905\pi\) | |||||||
\(578\) | 2.47957 | − | 3.41283i | 0.103136 | − | 0.141955i | ||||
\(579\) | −11.6060 | − | 8.43227i | −0.482330 | − | 0.350433i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.85679 | + | 2.07558i | −0.118519 | + | 0.0861094i | ||||
\(582\) | 0.00752814i | 0.000312051i | ||||||||
\(583\) | 20.1406 | + | 27.7212i | 0.834139 | + | 1.14809i | ||||
\(584\) | −3.41860 | − | 10.5214i | −0.141463 | − | 0.435377i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.45326 | + | 7.55035i | −0.101343 | + | 0.311902i | ||||
\(587\) | −21.5309 | + | 6.99581i | −0.888675 | + | 0.288748i | −0.717555 | − | 0.696502i | \(-0.754739\pi\) |
−0.171120 | + | 0.985250i | \(0.554739\pi\) | |||||||
\(588\) | 10.0428 | − | 3.26310i | 0.414157 | − | 0.134568i | ||||
\(589\) | 11.8422 | − | 36.4465i | 0.487949 | − | 1.50175i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.0505366 | − | 0.155536i | −0.00207880 | − | 0.00639788i | ||||
\(592\) | −2.73264 | − | 3.76116i | −0.112311 | − | 0.154583i | ||||
\(593\) | 12.7423i | 0.523264i | 0.965168 | + | 0.261632i | \(0.0842606\pi\) | ||||
−0.965168 | + | 0.261632i | \(0.915739\pi\) | |||||||
\(594\) | −0.512997 | + | 0.372714i | −0.0210485 | + | 0.0152926i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −26.7758 | − | 19.4537i | −1.09678 | − | 0.796856i | ||||
\(597\) | 2.92114 | − | 4.02060i | 0.119554 | − | 0.164552i | ||||
\(598\) | −1.76378 | − | 0.573086i | −0.0721262 | − | 0.0234352i | ||||
\(599\) | 6.83599 | 0.279311 | 0.139656 | − | 0.990200i | \(-0.455400\pi\) | ||||
0.139656 | + | 0.990200i | \(0.455400\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.8422 | 1.29887 | 0.649435 | − | 0.760417i | \(-0.275005\pi\) | ||||
0.649435 | + | 0.760417i | \(0.275005\pi\) | |||||||
\(602\) | −1.13551 | − | 0.368948i | −0.0462798 | − | 0.0150372i | ||||
\(603\) | −5.95063 | + | 8.19034i | −0.242328 | + | 0.333537i | ||||
\(604\) | 2.47107 | + | 1.79534i | 0.100546 | + | 0.0730511i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.24202 | + | 1.62892i | −0.0910758 | + | 0.0661705i | ||||
\(607\) | − | 27.7763i | − | 1.12741i | −0.825977 | − | 0.563703i | \(-0.809376\pi\) | ||
0.825977 | − | 0.563703i | \(-0.190624\pi\) | |||||||
\(608\) | −6.96310 | − | 9.58388i | −0.282391 | − | 0.388678i | ||||
\(609\) | 1.23892 | + | 3.81302i | 0.0502038 | + | 0.154511i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.64286 | − | 14.2893i | 0.187830 | − | 0.578082i | ||||
\(612\) | −10.7686 | + | 3.49892i | −0.435293 | + | 0.141435i | ||||
\(613\) | 3.43991 | − | 1.11769i | 0.138937 | − | 0.0451433i | −0.238723 | − | 0.971088i | \(-0.576729\pi\) |
0.377660 | + | 0.925944i | \(0.376729\pi\) | |||||||
\(614\) | −1.54764 | + | 4.76315i | −0.0624577 | + | 0.192225i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.962321 | + | 2.96172i | 0.0387730 | + | 0.119331i | ||||
\(617\) | 26.2402 | + | 36.1166i | 1.05639 | + | 1.45400i | 0.883133 | + | 0.469122i | \(0.155430\pi\) |
0.173259 | + | 0.984876i | \(0.444570\pi\) | |||||||
\(618\) | 0.177909i | 0.00715655i | ||||||||
\(619\) | 16.5917 | − | 12.0546i | 0.666878 | − | 0.484515i | −0.202101 | − | 0.979365i | \(-0.564777\pi\) |
0.868979 | + | 0.494850i | \(0.164777\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.29885 | + | 0.943670i | 0.0521211 | + | 0.0378682i | ||||
\(622\) | 2.71552 | − | 3.73760i | 0.108883 | − | 0.149864i | ||||
\(623\) | 1.63724 | + | 0.531970i | 0.0655945 | + | 0.0213129i | ||||
\(624\) | −17.0322 | −0.681832 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.14033 | 0.245417 | ||||||||
\(627\) | 10.1877 | + | 3.31020i | 0.406859 | + | 0.132197i | ||||
\(628\) | 10.4866 | − | 14.4336i | 0.418463 | − | 0.575964i | ||||
\(629\) | −6.03621 | − | 4.38556i | −0.240679 | − | 0.174864i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.5288 | − | 22.1805i | 1.21533 | − | 0.882991i | 0.219629 | − | 0.975583i | \(-0.429515\pi\) |
0.995704 | + | 0.0925923i | \(0.0295153\pi\) | |||||||
\(632\) | 11.1618i | 0.443991i | ||||||||
\(633\) | 1.93605 | + | 2.66475i | 0.0769512 | + | 0.105914i | ||||
\(634\) | 1.92066 | + | 5.91117i | 0.0762790 | + | 0.234763i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.99015 | + | 24.5911i | −0.316830 | + | 0.975102i | ||||
\(637\) | 24.2446 | − | 7.87754i | 0.960605 | − | 0.312119i | ||||
\(638\) | 1.93929 | − | 0.630115i | 0.0767774 | − | 0.0249465i | ||||
\(639\) | −4.28888 | + | 13.1998i | −0.169666 | + | 0.522177i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.83865 | − | 8.73646i | −0.112120 | − | 0.345070i | 0.879216 | − | 0.476424i | \(-0.158067\pi\) |
−0.991335 | + | 0.131355i | \(0.958067\pi\) | |||||||
\(642\) | −0.307005 | − | 0.422557i | −0.0121165 | − | 0.0166770i | ||||
\(643\) | 3.42111i | 0.134915i | 0.997722 | + | 0.0674577i | \(0.0214888\pi\) | ||||
−0.997722 | + | 0.0674577i | \(0.978511\pi\) | |||||||
\(644\) | 3.14010 | − | 2.28142i | 0.123737 | − | 0.0899005i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.85922 | − | 3.53043i | −0.191184 | − | 0.138903i | ||||
\(647\) | −1.92050 | + | 2.64334i | −0.0755027 | + | 0.103920i | −0.845098 | − | 0.534611i | \(-0.820458\pi\) |
0.769595 | + | 0.638532i | \(0.220458\pi\) | |||||||
\(648\) | −0.924437 | − | 0.300368i | −0.0363153 | − | 0.0117996i | ||||
\(649\) | 16.4276 | 0.644840 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.4616 | −0.449216 | ||||||||
\(652\) | −8.44785 | − | 2.74487i | −0.330843 | − | 0.107498i | ||||
\(653\) | 7.42740 | − | 10.2229i | 0.290656 | − | 0.400054i | −0.638571 | − | 0.769563i | \(-0.720474\pi\) |
0.929227 | + | 0.369509i | \(0.120474\pi\) | |||||||
\(654\) | −0.446145 | − | 0.324143i | −0.0174456 | − | 0.0126750i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −25.5965 | + | 18.5969i | −0.999374 | + | 0.726088i | ||||
\(657\) | 11.3814i | 0.444030i | ||||||||
\(658\) | −0.580383 | − | 0.798829i | −0.0226257 | − | 0.0311416i | ||||
\(659\) | 2.82719 | + | 8.70118i | 0.110131 | + | 0.338950i | 0.990901 | − | 0.134596i | \(-0.0429737\pi\) |
−0.880769 | + | 0.473546i | \(0.842974\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.97487 | − | 6.07804i | 0.0768137 | − | 0.236408i | −0.905275 | − | 0.424825i | \(-0.860336\pi\) |
0.982089 | + | 0.188417i | \(0.0603356\pi\) | |||||||
\(662\) | 7.13884 | − | 2.31955i | 0.277459 | − | 0.0901519i | ||||
\(663\) | −25.9967 | + | 8.44684i | −1.00963 | + | 0.328048i | ||||
\(664\) | −0.850729 | + | 2.61827i | −0.0330147 | + | 0.101609i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.0974345 | − | 0.299872i | −0.00377551 | − | 0.0116198i | ||||
\(667\) | −3.03459 | − | 4.17676i | −0.117500 | − | 0.161725i | ||||
\(668\) | − | 0.276383i | − | 0.0106936i | ||||||
\(669\) | 12.7608 | − | 9.27127i | 0.493361 | − | 0.358448i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.95593 | − | 5.78032i | −0.307135 | − | 0.223147i | ||||
\(672\) | −2.08256 | + | 2.86640i | −0.0803366 | + | 0.110574i | ||||
\(673\) | −32.0566 | − | 10.4158i | −1.23569 | − | 0.401500i | −0.382918 | − | 0.923782i | \(-0.625081\pi\) |
−0.852773 | + | 0.522282i | \(0.825081\pi\) | |||||||
\(674\) | 1.12881 | 0.0434802 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.2857 | −0.664833 | ||||||||
\(677\) | −8.75295 | − | 2.84401i | −0.336403 | − | 0.109304i | 0.135944 | − | 0.990716i | \(-0.456593\pi\) |
−0.472347 | + | 0.881412i | \(0.656593\pi\) | |||||||
\(678\) | 0.456792 | − | 0.628721i | 0.0175430 | − | 0.0241459i | ||||
\(679\) | −0.0307719 | − | 0.0223571i | −0.00118092 | − | 0.000857988i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.9546 | − | 7.95896i | 0.419780 | − | 0.304988i | ||||
\(682\) | 5.82935i | 0.223217i | ||||||||
\(683\) | −16.0005 | − | 22.0227i | −0.612241 | − | 0.842677i | 0.384519 | − | 0.923117i | \(-0.374367\pi\) |
−0.996759 | + | 0.0804402i | \(0.974367\pi\) | |||||||
\(684\) | 2.49788 | + | 7.68769i | 0.0955089 | + | 0.293946i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.18319 | − | 3.64147i | 0.0451743 | − | 0.139032i | ||||
\(687\) | 14.0593 | − | 4.56816i | 0.536397 | − | 0.174286i | ||||
\(688\) | 13.4289 | − | 4.36332i | 0.511972 | − | 0.166350i | ||||
\(689\) | −19.2892 | + | 59.3662i | −0.734862 | + | 2.26167i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.21607 | + | 28.3642i | 0.350596 | + | 1.07902i | 0.958519 | + | 0.285028i | \(0.0920028\pi\) |
−0.607923 | + | 0.793996i | \(0.707997\pi\) | |||||||
\(692\) | −28.0645 | − | 38.6275i | −1.06685 | − | 1.46840i | ||||
\(693\) | − | 3.20381i | − | 0.121703i | ||||||
\(694\) | −3.35687 | + | 2.43891i | −0.127425 | + | 0.0925797i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.52877 | + | 1.83726i | 0.0958527 | + | 0.0696410i | ||||
\(697\) | −29.8458 | + | 41.0792i | −1.13049 | + | 1.55599i | ||||
\(698\) | 0.0876726 | + | 0.0284865i | 0.00331846 | + | 0.00107823i | ||||
\(699\) | 0.518980 | 0.0196296 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.1081 | −0.721704 | −0.360852 | − | 0.932623i | \(-0.617514\pi\) | ||||
−0.360852 | + | 0.932623i | \(0.617514\pi\) | |||||||
\(702\) | −1.09861 | − | 0.356959i | −0.0414642 | − | 0.0134725i | ||||
\(703\) | −3.13086 | + | 4.30925i | −0.118082 | + | 0.162527i | ||||
\(704\) | −13.6700 | − | 9.93187i | −0.515209 | − | 0.374322i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.78489 | − | 3.47642i | 0.180082 | − | 0.130837i | ||||
\(707\) | − | 14.0020i | − | 0.526601i | ||||||
\(708\) | 7.28637 | + | 10.0288i | 0.273839 | + | 0.376907i | ||||
\(709\) | −4.48525 | − | 13.8042i | −0.168447 | − | 0.518427i | 0.830827 | − | 0.556531i | \(-0.187868\pi\) |
−0.999274 | + | 0.0381042i | \(0.987868\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.54849 | − | 10.9211i | 0.133079 | − | 0.409575i | ||||
\(712\) | 1.27644 | − | 0.414740i | 0.0478365 | − | 0.0155430i | ||||
\(713\) | 14.0369 | − | 4.56086i | 0.525685 | − | 0.170806i | ||||
\(714\) | −0.555120 | + | 1.70848i | −0.0207748 | + | 0.0639384i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.4743 | + | 44.5473i | 0.540930 | + | 1.66481i | ||||
\(717\) | −4.83766 | − | 6.65847i | −0.180666 | − | 0.248665i | ||||
\(718\) | − | 1.17215i | − | 0.0437444i | ||||||
\(719\) | 28.1139 | − | 20.4260i | 1.04847 | − | 0.761760i | 0.0765512 | − | 0.997066i | \(-0.475609\pi\) |
0.971921 | + | 0.235306i | \(0.0756091\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.727219 | − | 0.528356i | −0.0270831 | − | 0.0196770i | ||||
\(722\) | 0.235405 | − | 0.324007i | 0.00876086 | − | 0.0120583i | ||||
\(723\) | 1.21847 | + | 0.395906i | 0.0453155 | + | 0.0147239i | ||||
\(724\) | 3.81626 | 0.141830 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.08490 | 0.0402643 | ||||||||
\(727\) | −40.5415 | − | 13.1727i | −1.50360 | − | 0.488550i | −0.562536 | − | 0.826773i | \(-0.690174\pi\) |
−0.941066 | + | 0.338223i | \(0.890174\pi\) | |||||||
\(728\) | −3.33453 | + | 4.58959i | −0.123586 | + | 0.170102i | ||||
\(729\) | 0.809017 | + | 0.587785i | 0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.3330 | − | 13.3197i | 0.678072 | − | 0.492648i | ||||
\(732\) | − | 7.42081i | − | 0.274281i | ||||||
\(733\) | −1.15341 | − | 1.58754i | −0.0426023 | − | 0.0586370i | 0.787184 | − | 0.616718i | \(-0.211538\pi\) |
−0.829787 | + | 0.558081i | \(0.811538\pi\) | |||||||
\(734\) | 1.32451 | + | 4.07642i | 0.0488885 | + | 0.150463i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.40987 | − | 4.33915i | 0.0519687 | − | 0.159943i | ||||
\(737\) | −24.7420 | + | 8.03917i | −0.911384 | + | 0.296127i | ||||
\(738\) | −2.04077 | + | 0.663088i | −0.0751219 | + | 0.0244086i | ||||
\(739\) | −3.81947 | + | 11.7551i | −0.140501 | + | 0.432419i | −0.996405 | − | 0.0847164i | \(-0.973002\pi\) |
0.855904 | + | 0.517135i | \(0.173002\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.03021 | + | 18.5591i | 0.221525 | + | 0.681785i | ||||
\(742\) | 2.41126 | + | 3.31881i | 0.0885201 | + | 0.121838i | ||||
\(743\) | 8.63742i | 0.316876i | 0.987369 | + | 0.158438i | \(0.0506458\pi\) | ||||
−0.987369 | + | 0.158438i | \(0.949354\pi\) | |||||||
\(744\) | −7.22922 | + | 5.25234i | −0.265036 | + | 0.192560i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.420978 | − | 0.305858i | −0.0154131 | − | 0.0111983i | ||||
\(747\) | 1.66478 | − | 2.29137i | 0.0609110 | − | 0.0838369i | ||||
\(748\) | −27.6721 | − | 8.99121i | −1.01179 | − | 0.328751i | ||||
\(749\) | 2.63898 | 0.0964264 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.3654 | −0.889105 | −0.444552 | − | 0.895753i | \(-0.646637\pi\) | ||||
−0.444552 | + | 0.895753i | \(0.646637\pi\) | |||||||
\(752\) | 11.1059 | + | 3.60852i | 0.404990 | + | 0.131589i | ||||
\(753\) | −2.72435 | + | 3.74974i | −0.0992807 | + | 0.136648i | ||||
\(754\) | 3.00520 | + | 2.18341i | 0.109443 | + | 0.0795150i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.95588 | − | 1.42103i | 0.0711347 | − | 0.0516824i | ||||
\(757\) | 5.18352i | 0.188398i | 0.995553 | + | 0.0941991i | \(0.0300290\pi\) | ||||
−0.995553 | + | 0.0941991i | \(0.969971\pi\) | |||||||
\(758\) | −1.79981 | − | 2.47723i | −0.0653720 | − | 0.0899769i | ||||
\(759\) | 1.27488 | + | 3.92367i | 0.0462751 | + | 0.142420i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.66099 | − | 29.7335i | 0.350211 | − | 1.07784i | −0.608524 | − | 0.793535i | \(-0.708238\pi\) |
0.958735 | − | 0.284302i | \(-0.0917618\pi\) | |||||||
\(762\) | 3.67518 | − | 1.19414i | 0.133138 | − | 0.0432591i | ||||
\(763\) | 2.64993 | − | 0.861014i | 0.0959339 | − | 0.0311708i | ||||
\(764\) | −4.65505 | + | 14.3268i | −0.168414 | + | 0.518324i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.53964 | + | 7.81622i | 0.0917611 | + | 0.282412i | ||||
\(767\) | 17.5903 | + | 24.2109i | 0.635147 | + | 0.874205i | ||||
\(768\) | − | 11.3481i | − | 0.409490i | ||||||
\(769\) | −35.7497 | + | 25.9737i | −1.28917 | + | 0.936636i | −0.999788 | − | 0.0205786i | \(-0.993449\pi\) |
−0.289380 | + | 0.957214i | \(0.593449\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.8051 | − | 10.7566i | −0.533193 | − | 0.387388i | ||||
\(772\) | 16.3511 | − | 22.5054i | 0.588489 | − | 0.809986i | ||||
\(773\) | −20.5315 | − | 6.67110i | −0.738468 | − | 0.239943i | −0.0844563 | − | 0.996427i | \(-0.526915\pi\) |
−0.654012 | + | 0.756484i | \(0.726915\pi\) | |||||||
\(774\) | 0.957636 | 0.0344215 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.0296542 | −0.00106452 | ||||||||
\(777\) | 1.51512 | + | 0.492291i | 0.0543545 | + | 0.0176609i | ||||
\(778\) | −2.46246 | + | 3.38929i | −0.0882835 | + | 0.121512i | ||||
\(779\) | 29.3265 | + | 21.3070i | 1.05073 | + | 0.763401i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.8538 | + | 20.9635i | −1.03247 | + | 0.750135i | ||||
\(782\) | − | 2.31325i | − | 0.0827218i | ||||||
\(783\) | −1.89016 | − | 2.60158i | −0.0675488 | − | 0.0929730i | ||||
\(784\) | 6.12257 | + | 18.8433i | 0.218663 | + | 0.672977i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.14047 | − | 3.51000i | 0.0406791 | − | 0.125197i | ||||
\(787\) | 13.7153 | − | 4.45638i | 0.488899 | − | 0.158853i | −0.0541857 | − | 0.998531i | \(-0.517256\pi\) |
0.543085 | + | 0.839678i | \(0.317256\pi\) | |||||||
\(788\) | 0.301601 | − | 0.0979961i | 0.0107441 | − | 0.00349097i | ||||
\(789\) | 5.15027 | − | 15.8509i | 0.183355 | − | 0.564307i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.21337 | + | 3.73436i | 0.0431424 | + | 0.132779i | ||||
\(792\) | −1.46816 | − | 2.02075i | −0.0521689 | − | 0.0718043i | ||||
\(793\) | − | 17.9148i | − | 0.636173i | ||||||
\(794\) | −0.172995 | + | 0.125688i | −0.00613937 | + | 0.00446052i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.79639 | + | 5.66441i | 0.276336 | + | 0.200770i | ||||
\(797\) | 23.1921 | − | 31.9211i | 0.821505 | − | 1.13070i | −0.167941 | − | 0.985797i | \(-0.553712\pi\) |
0.989445 | − | 0.144907i | \(-0.0462883\pi\) | |||||||
\(798\) | 1.21969 | + | 0.396301i | 0.0431765 | + | 0.0140289i | ||||
\(799\) | 18.7409 | 0.663004 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.38077 | −0.0487872 | ||||||||
\(802\) | −2.27332 | − | 0.738645i | −0.0802736 | − | 0.0260825i | ||||
\(803\) | −17.1909 | + | 23.6612i | −0.606653 | + | 0.834986i | ||||
\(804\) | −15.8820 | − | 11.5389i | −0.560114 | − | 0.406947i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.59125 | + | 6.24191i | −0.302614 | + | 0.219862i | ||||
\(807\) | 2.63211i | 0.0926547i | ||||||||
\(808\) | −6.41650 | − | 8.83156i | −0.225732 | − | 0.310693i | ||||
\(809\) | 1.84237 | + | 5.67024i | 0.0647744 | + | 0.199355i | 0.978206 | − | 0.207638i | \(-0.0665775\pi\) |
−0.913431 | + | 0.406993i | \(0.866577\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.1062 | + | 37.2590i | −0.425105 | + | 1.30834i | 0.477788 | + | 0.878475i | \(0.341439\pi\) |
−0.902893 | + | 0.429865i | \(0.858561\pi\) | |||||||
\(812\) | −7.39386 | + | 2.40241i | −0.259474 | + | 0.0843081i | ||||
\(813\) | 4.34011 | − | 1.41019i | 0.152214 | − | 0.0494574i | ||||
\(814\) | 0.250378 | − | 0.770586i | 0.00877576 | − | 0.0270090i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.56505 | − | 20.2051i | −0.229823 | − | 0.707322i | ||||
\(817\) | −9.50897 | − | 13.0880i | −0.332677 | − | 0.457890i | ||||
\(818\) | 0.374544i | 0.0130956i | ||||||||
\(819\) | 4.72175 | − | 3.43055i | 0.164991 | − | 0.119873i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.6923 | − | 12.1277i | −0.582567 | − | 0.423260i | 0.257082 | − | 0.966390i | \(-0.417239\pi\) |
−0.839649 | + | 0.543130i | \(0.817239\pi\) | |||||||
\(822\) | −1.52214 | + | 2.09505i | −0.0530909 | + | 0.0730733i | ||||
\(823\) | 37.1066 | + | 12.0567i | 1.29345 | + | 0.420269i | 0.873300 | − | 0.487183i | \(-0.161976\pi\) |
0.420155 | + | 0.907452i | \(0.361976\pi\) | |||||||
\(824\) | −0.700803 | −0.0244136 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.96673 | 0.0684314 | ||||||||
\(827\) | −18.6384 | − | 6.05598i | −0.648120 | − | 0.210587i | −0.0335352 | − | 0.999438i | \(-0.510677\pi\) |
−0.614585 | + | 0.788850i | \(0.710677\pi\) | |||||||
\(828\) | −1.82988 | + | 2.51861i | −0.0635927 | + | 0.0875279i | ||||
\(829\) | −7.01831 | − | 5.09910i | −0.243756 | − | 0.177099i | 0.459199 | − | 0.888333i | \(-0.348136\pi\) |
−0.702955 | + | 0.711234i | \(0.748136\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.01876 | − | 0.740173i | 0.0353404 | − | 0.0256763i | ||||
\(832\) | − | 30.7816i | − | 1.06716i | ||||||
\(833\) | 18.6902 | + | 25.7248i | 0.647575 | + | 0.891311i | ||||
\(834\) | 0.949404 | + | 2.92196i | 0.0328752 | + | 0.101179i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.41884 | + | 19.7551i | −0.222000 | + | 0.683246i | ||||
\(837\) | 8.74318 | − | 2.84083i | 0.302208 | − | 0.0981935i | ||||
\(838\) | 7.17235 | − | 2.33044i | 0.247765 | − | 0.0805036i | ||||
\(839\) | 1.19256 | − | 3.67033i | 0.0411718 | − | 0.126714i | −0.928358 | − | 0.371687i | \(-0.878779\pi\) |
0.969530 | + | 0.244974i | \(0.0787793\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.76596 | − | 17.7458i | −0.198826 | − | 0.611925i | ||||
\(842\) | −1.01117 | − | 1.39176i | −0.0348473 | − | 0.0479632i | ||||
\(843\) | − | 13.4167i | − | 0.462094i | ||||||
\(844\) | −5.16724 | + | 3.75422i | −0.177864 | + | 0.129226i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.640724 | + | 0.465513i | 0.0220286 | + | 0.0160047i | ||||
\(847\) | −3.22193 | + | 4.43461i | −0.110707 | + | 0.152375i | ||||
\(848\) | −46.1406 | − | 14.9920i | −1.58447 | − | 0.514827i | ||||
\(849\) | 24.0890 | 0.826732 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.05144 | −0.0703224 | ||||||||
\(852\) | −25.5959 | − | 8.31661i | −0.876901 | − | 0.284922i | ||||
\(853\) | −17.5100 | + | 24.1004i | −0.599531 | + | 0.825183i | −0.995665 | − | 0.0930093i | \(-0.970351\pi\) |
0.396135 | + | 0.918192i | \(0.370351\pi\) | |||||||
\(854\) | −0.952493 | − | 0.692027i | −0.0325936 | − | 0.0236807i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.66450 | − | 1.20933i | 0.0568913 | − | 0.0413340i | ||||
\(857\) | − | 36.2041i | − | 1.23671i | −0.785899 | − | 0.618354i | \(-0.787800\pi\) | ||
0.785899 | − | 0.618354i | \(-0.212200\pi\) | |||||||
\(858\) | −1.74477 | − | 2.40147i | −0.0595656 | − | 0.0819850i | ||||
\(859\) | 11.6355 | + | 35.8104i | 0.396998 | + | 1.22184i | 0.927394 | + | 0.374086i | \(0.122043\pi\) |
−0.530396 | + | 0.847750i | \(0.677957\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.35028 | − | 10.3111i | 0.114177 | − | 0.351401i | ||||
\(862\) | 2.56912 | − | 0.834757i | 0.0875045 | − | 0.0284319i | ||||
\(863\) | 2.37682 | − | 0.772275i | 0.0809078 | − | 0.0262885i | −0.268283 | − | 0.963340i | \(-0.586456\pi\) |
0.349191 | + | 0.937051i | \(0.386456\pi\) | |||||||
\(864\) | 0.878171 | − | 2.70273i | 0.0298760 | − | 0.0919488i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.796028 | + | 2.44992i | 0.0270501 | + | 0.0832518i | ||||
\(867\) | −10.0485 | − | 13.8306i | −0.341266 | − | 0.469712i | ||||
\(868\) | − | 22.2253i | − | 0.754376i | ||||||
\(869\) | 23.8728 | − | 17.3446i | 0.809830 | − | 0.588376i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38.3411 | − | 27.8565i | −1.29914 | − | 0.943881i | ||||
\(872\) | 1.27684 | − | 1.75741i | 0.0432391 | − | 0.0595136i | ||||
\(873\) | 0.0290149 | + | 0.00942751i | 0.000982006 | + | 0.000319073i | ||||
\(874\) | −1.65143 | −0.0558606 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −22.0697 | −0.745668 | ||||||||
\(877\) | 30.8609 | + | 10.0273i | 1.04210 | + | 0.338599i | 0.779563 | − | 0.626323i | \(-0.215441\pi\) |
0.262537 | + | 0.964922i | \(0.415441\pi\) | |||||||
\(878\) | 2.23847 | − | 3.08100i | 0.0755449 | − | 0.103979i | ||||
\(879\) | 26.0283 | + | 18.9107i | 0.877912 | + | 0.637841i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.9099 | − | 19.5512i | 0.906619 | − | 0.658697i | −0.0335388 | − | 0.999437i | \(-0.510678\pi\) |
0.940157 | + | 0.340740i | \(0.110678\pi\) | |||||||
\(882\) | 1.34375i | 0.0452464i | ||||||||
\(883\) | 6.44974 | + | 8.87730i | 0.217051 | + | 0.298745i | 0.903633 | − | 0.428307i | \(-0.140890\pi\) |
−0.686582 | + | 0.727052i | \(0.740890\pi\) | |||||||
\(884\) | −16.3794 | − | 50.4105i | −0.550897 | − | 1.69549i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.44197 | − | 4.43794i | 0.0484440 | − | 0.149095i | ||||
\(887\) | −24.7324 | + | 8.03604i | −0.830432 | + | 0.269824i | −0.693227 | − | 0.720719i | \(-0.743812\pi\) |
−0.137205 | + | 0.990543i | \(0.543812\pi\) | |||||||
\(888\) | 1.18123 | − | 0.383805i | 0.0396395 | − | 0.0128797i | ||||
\(889\) | −6.03343 | + | 18.5690i | −0.202355 | + | 0.622784i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.794084 | + | 2.44394i | 0.0266028 | + | 0.0818751i | ||||
\(892\) | 17.9780 | + | 24.7446i | 0.601948 | + | 0.828511i | ||||
\(893\) | − | 13.3791i | − | 0.447715i | ||||||
\(894\) | 3.40731 | − | 2.47556i | 0.113958 | − | 0.0827951i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7.36940 | − | 5.35418i | −0.246194 | − | 0.178871i | ||||
\(897\) | −4.41757 | + | 6.08026i | −0.147498 | + | 0.203014i | ||||
\(898\) | −2.67893 | − | 0.870436i | −0.0893970 | − | 0.0290468i | ||||
\(899\) | −29.5626 | −0.985969 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −77.8608 | −2.59392 | ||||||||
\(902\) | −5.24420 | − | 1.70394i | −0.174613 | − | 0.0567351i | ||||
\(903\) | −2.84400 | + | 3.91442i | −0.0946423 | + | 0.130264i | ||||
\(904\) | 2.47660 | + | 1.79936i | 0.0823705 | + | 0.0598457i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.314452 | + | 0.228463i | −0.0104470 | + | 0.00759018i | ||||
\(907\) | 55.0108i | 1.82660i | 0.407283 | + | 0.913302i | \(0.366476\pi\) | ||||
−0.407283 | + | 0.913302i | \(0.633524\pi\) | |||||||
\(908\) | 15.4333 | + | 21.2421i | 0.512172 | + | 0.704944i | ||||
\(909\) | 3.47049 | + | 10.6811i | 0.115109 | + | 0.354269i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.74142 | + | 11.5149i | −0.123959 | + | 0.381506i | −0.993710 | − | 0.111985i | \(-0.964279\pi\) |
0.869751 | + | 0.493490i | \(0.164279\pi\) | |||||||
\(912\) | −14.4245 | + | 4.68680i | −0.477642 | + | 0.155195i | ||||
\(913\) | 6.92195 | − | 2.24908i | 0.229083 | − | 0.0744336i | ||||
\(914\) | 2.59060 | − | 7.97306i | 0.0856895 | − | 0.263725i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.85816 | + | 27.2626i | 0.292682 | + | 0.900782i | ||||
\(917\) | 10.9605 | + | 15.0858i | 0.361946 | + | 0.498176i | ||||
\(918\) | − | 1.44086i | − | 0.0475555i | ||||||
\(919\) | 4.83138 | − | 3.51020i | 0.159372 | − | 0.115791i | −0.505241 | − | 0.862978i | \(-0.668596\pi\) |
0.664613 | + | 0.747188i | \(0.268596\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.4200 | + | 11.9298i | 0.541056 | + | 0.393100i | ||||
\(922\) | 3.58117 | − | 4.92906i | 0.117940 | − | 0.162330i | ||||
\(923\) | −61.7918 | − | 20.0774i | −2.03390 | − | 0.660855i | ||||
\(924\) | 6.21254 | 0.204378 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.36370 | −0.110538 | ||||||||
\(927\) | 0.685696 | + | 0.222796i | 0.0225212 | + | 0.00731758i | ||||
\(928\) | −5.37150 | + | 7.39324i | −0.176328 | + | 0.242695i | ||||
\(929\) | 37.9232 | + | 27.5528i | 1.24422 | + | 0.903979i | 0.997872 | − | 0.0652030i | \(-0.0207695\pi\) |
0.246348 | + | 0.969182i | \(0.420770\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.3650 | − | 13.3429i | 0.601887 | − | 0.437297i | ||||
\(932\) | 1.00636i | 0.0329644i | ||||||||
\(933\) | −11.0048 | − | 15.1468i | −0.360280 | − | 0.495882i | ||||
\(934\) | −0.722201 | − | 2.22271i | −0.0236311 | − | 0.0727291i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.40610 | − | 4.32753i | 0.0459598 | − | 0.141450i | ||||
\(937\) | −18.4823 | + | 6.00528i | −0.603792 | + | 0.196184i | −0.594931 | − | 0.803777i | \(-0.702821\pi\) |
−0.00886093 | + | 0.999961i | \(0.502821\pi\) | |||||||
\(938\) | −2.96214 | + | 0.962459i | −0.0967174 | + | 0.0314254i | ||||
\(939\) | 7.68955 | − | 23.6660i | 0.250939 | − | 0.772311i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.70867 | + | 20.6472i | 0.218696 | + | 0.673078i | 0.998870 | + | 0.0475159i | \(0.0151305\pi\) |
−0.780174 | + | 0.625563i | \(0.784870\pi\) | |||||||
\(942\) | 1.33446 | + | 1.83673i | 0.0434792 | + | 0.0598440i | ||||
\(943\) | 13.9610i | 0.454633i | ||||||||
\(944\) | −18.8172 | + | 13.6715i | −0.612447 | + | 0.444969i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.99087 | + | 1.44645i | 0.0647287 | + | 0.0470282i | ||||
\(947\) | 3.71222 | − | 5.10943i | 0.120631 | − | 0.166034i | −0.744431 | − | 0.667699i | \(-0.767279\pi\) |
0.865062 | + | 0.501665i | \(0.167279\pi\) | |||||||
\(948\) | 21.1773 | + | 6.88092i | 0.687807 | + | 0.223482i | ||||
\(949\) | −53.2792 | −1.72952 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.1880 | 0.816778 | ||||||||
\(952\) | −6.72990 | − | 2.18668i | −0.218117 | − | 0.0708707i | ||||
\(953\) | 12.8147 | − | 17.6380i | 0.415110 | − | 0.571350i | −0.549345 | − | 0.835595i | \(-0.685123\pi\) |
0.964455 | + | 0.264245i | \(0.0851229\pi\) | |||||||
\(954\) | −2.66195 | − | 1.93402i | −0.0861839 | − | 0.0626163i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.9115 | − | 9.38076i | 0.417588 | − | 0.303395i | ||||
\(957\) | − | 8.26351i | − | 0.267121i | ||||||
\(958\) | 3.73171 | + | 5.13625i | 0.120566 | + | 0.165945i | ||||
\(959\) | −4.04324 | − | 12.4438i | −0.130563 | − | 0.401831i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.5366 | − | 50.8943i | 0.533437 | − | 1.64175i | ||||
\(962\) | 1.40378 | − | 0.456116i | 0.0452597 | − | 0.0147058i | ||||
\(963\) | −2.01308 | + | 0.654089i | −0.0648705 | + | 0.0210777i | ||||
\(964\) | −0.767705 | + | 2.36275i | −0.0247261 | + | 0.0760992i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.152630 | + | 0.469746i | 0.00491078 | + | 0.0151138i | ||||
\(967\) | −4.12195 | − | 5.67338i | −0.132553 | − | 0.182444i | 0.737581 | − | 0.675259i | \(-0.235968\pi\) |
−0.870134 | + | 0.492815i | \(0.835968\pi\) | |||||||
\(968\) | 4.27353i | 0.137356i | ||||||||
\(969\) | −19.6922 | + | 14.3072i | −0.632604 | + | 0.459614i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.99504 | − | 4.35565i | −0.192390 | − | 0.139779i | 0.487420 | − | 0.873167i | \(-0.337938\pi\) |
−0.679810 | + | 0.733388i | \(0.737938\pi\) | |||||||
\(972\) | −1.13978 | + | 1.56877i | −0.0365585 | + | 0.0503184i | ||||
\(973\) | −14.7633 | − | 4.79690i | −0.473291 | − | 0.153781i | ||||
\(974\) | 7.00909 | 0.224586 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.9237 | 0.445688 | ||||||||
\(977\) | −37.3370 | − | 12.1315i | −1.19452 | − | 0.388122i | −0.356776 | − | 0.934190i | \(-0.616124\pi\) |
−0.837741 | + | 0.546068i | \(0.816124\pi\) | |||||||
\(978\) | 0.664399 | − | 0.914467i | 0.0212451 | − | 0.0292414i | ||||
\(979\) | −2.87054 | − | 2.08557i | −0.0917430 | − | 0.0666552i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.80802 | + | 1.31360i | −0.0577256 | + | 0.0419401i | ||||
\(982\) | 1.50597i | 0.0480573i | ||||||||
\(983\) | 10.8051 | + | 14.8719i | 0.344629 | + | 0.474341i | 0.945786 | − | 0.324790i | \(-0.105294\pi\) |
−0.601158 | + | 0.799131i | \(0.705294\pi\) | |||||||
\(984\) | −2.61198 | − | 8.03883i | −0.0832667 | − | 0.256269i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.43181 | + | 4.40665i | −0.0455980 | + | 0.140336i | ||||
\(987\) | −3.80566 | + | 1.23653i | −0.121135 | + | 0.0393593i | ||||
\(988\) | −35.9881 | + | 11.6932i | −1.14493 | + | 0.372012i | ||||
\(989\) | 1.92536 | − | 5.92564i | 0.0612228 | − | 0.188424i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.2128 | + | 49.8980i | 0.515018 | + | 1.58506i | 0.783250 | + | 0.621707i | \(0.213560\pi\) |
−0.268233 | + | 0.963354i | \(0.586440\pi\) | |||||||
\(992\) | −15.3560 | − | 21.1357i | −0.487554 | − | 0.671060i | ||||
\(993\) | − | 30.4193i | − | 0.965326i | ||||||
\(994\) | −3.45442 | + | 2.50978i | −0.109567 | + | 0.0796054i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.44322 | + | 3.22819i | 0.140789 | + | 0.102289i | ||||
\(997\) | 21.3789 | − | 29.4256i | 0.677077 | − | 0.931917i | −0.322817 | − | 0.946461i | \(-0.604630\pi\) |
0.999894 | + | 0.0145444i | \(0.00462980\pi\) | |||||||
\(998\) | −4.76785 | − | 1.54917i | −0.150924 | − | 0.0490381i | ||||
\(999\) | −1.27778 | −0.0404273 |
(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 | 375.2.i.d.274.3 | 24 | ||
5.2 | odd | 4 | 75.2.g.c.46.2 | yes | 12 | ||
5.3 | odd | 4 | 375.2.g.c.226.2 | 12 | |||
5.4 | even | 2 | inner | 375.2.i.d.274.4 | 24 | ||
15.2 | even | 4 | 225.2.h.d.46.2 | 12 | |||
25.6 | even | 5 | inner | 375.2.i.d.349.4 | 24 | ||
25.8 | odd | 20 | 375.2.g.c.151.2 | 12 | |||
25.9 | even | 10 | 1875.2.b.f.1249.8 | 12 | |||
25.12 | odd | 20 | 1875.2.a.j.1.4 | 6 | |||
25.13 | odd | 20 | 1875.2.a.k.1.3 | 6 | |||
25.16 | even | 5 | 1875.2.b.f.1249.5 | 12 | |||
25.17 | odd | 20 | 75.2.g.c.31.2 | ✓ | 12 | ||
25.19 | even | 10 | inner | 375.2.i.d.349.3 | 24 | ||
75.17 | even | 20 | 225.2.h.d.181.2 | 12 | |||
75.38 | even | 20 | 5625.2.a.q.1.4 | 6 | |||
75.62 | even | 20 | 5625.2.a.p.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.31.2 | ✓ | 12 | 25.17 | odd | 20 | ||
75.2.g.c.46.2 | yes | 12 | 5.2 | odd | 4 | ||
225.2.h.d.46.2 | 12 | 15.2 | even | 4 | |||
225.2.h.d.181.2 | 12 | 75.17 | even | 20 | |||
375.2.g.c.151.2 | 12 | 25.8 | odd | 20 | |||
375.2.g.c.226.2 | 12 | 5.3 | odd | 4 | |||
375.2.i.d.274.3 | 24 | 1.1 | even | 1 | trivial | ||
375.2.i.d.274.4 | 24 | 5.4 | even | 2 | inner | ||
375.2.i.d.349.3 | 24 | 25.19 | even | 10 | inner | ||
375.2.i.d.349.4 | 24 | 25.6 | even | 5 | inner | ||
1875.2.a.j.1.4 | 6 | 25.12 | odd | 20 | |||
1875.2.a.k.1.3 | 6 | 25.13 | odd | 20 | |||
1875.2.b.f.1249.5 | 12 | 25.16 | even | 5 | |||
1875.2.b.f.1249.8 | 12 | 25.9 | even | 10 | |||
5625.2.a.p.1.3 | 6 | 75.62 | even | 20 | |||
5625.2.a.q.1.4 | 6 | 75.38 | even | 20 |