Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,2,Mod(31,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, 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("150.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.g (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.19775603032\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 150.61 |
Dual form | 150.2.g.b.91.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | − | 0.587785i | 0.572061 | − | 0.415627i | ||||
\(3\) | −0.309017 | + | 0.951057i | −0.178411 | + | 0.549093i | ||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 0.690983 | + | 2.12663i | 0.309017 | + | 0.951057i | ||||
\(6\) | 0.309017 | + | 0.951057i | 0.126156 | + | 0.388267i | ||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | −0.309017 | − | 0.951057i | −0.109254 | − | 0.336249i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | 1.80902 | + | 1.31433i | 0.572061 | + | 0.415627i | ||||
\(11\) | 0.618034 | − | 0.449028i | 0.186344 | − | 0.135387i | −0.490702 | − | 0.871327i | \(-0.663260\pi\) |
0.677046 | + | 0.735940i | \(0.263260\pi\) | |||||||
\(12\) | 0.809017 | + | 0.587785i | 0.233543 | + | 0.169679i | ||||
\(13\) | −1.50000 | − | 1.08981i | −0.416025 | − | 0.302260i | 0.360011 | − | 0.932948i | \(-0.382773\pi\) |
−0.776037 | + | 0.630688i | \(0.782773\pi\) | |||||||
\(14\) | 1.61803 | − | 1.17557i | 0.432438 | − | 0.314184i | ||||
\(15\) | −2.23607 | −0.577350 | ||||||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | 0.354102 | + | 1.08981i | 0.0858823 | + | 0.264319i | 0.984770 | − | 0.173860i | \(-0.0556239\pi\) |
−0.898888 | + | 0.438178i | \(0.855624\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.23607 | − | 6.88191i | −0.512989 | − | 1.57882i | −0.786911 | − | 0.617066i | \(-0.788321\pi\) |
0.273922 | − | 0.961752i | \(-0.411679\pi\) | |||||||
\(20\) | 2.23607 | 0.500000 | ||||||||
\(21\) | −0.618034 | + | 1.90211i | −0.134866 | + | 0.415075i | ||||
\(22\) | 0.236068 | − | 0.726543i | 0.0503299 | − | 0.154899i | ||||
\(23\) | −4.85410 | + | 3.52671i | −1.01215 | + | 0.735370i | −0.964659 | − | 0.263501i | \(-0.915123\pi\) |
−0.0474912 | + | 0.998872i | \(0.515123\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.04508 | + | 2.93893i | −0.809017 | + | 0.587785i | ||||
\(26\) | −1.85410 | −0.363619 | ||||||||
\(27\) | 0.809017 | − | 0.587785i | 0.155695 | − | 0.113119i | ||||
\(28\) | 0.618034 | − | 1.90211i | 0.116797 | − | 0.359466i | ||||
\(29\) | −1.11803 | + | 3.44095i | −0.207614 | + | 0.638969i | 0.791982 | + | 0.610544i | \(0.209049\pi\) |
−0.999596 | + | 0.0284251i | \(0.990951\pi\) | |||||||
\(30\) | −1.80902 | + | 1.31433i | −0.330280 | + | 0.239962i | ||||
\(31\) | −3.00000 | − | 9.23305i | −0.538816 | − | 1.65830i | −0.735256 | − | 0.677789i | \(-0.762938\pi\) |
0.196440 | − | 0.980516i | \(-0.437062\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.236068 | + | 0.726543i | 0.0410942 | + | 0.126475i | ||||
\(34\) | 0.927051 | + | 0.673542i | 0.158988 | + | 0.115511i | ||||
\(35\) | 1.38197 | + | 4.25325i | 0.233595 | + | 0.718931i | ||||
\(36\) | −0.809017 | + | 0.587785i | −0.134836 | + | 0.0979642i | ||||
\(37\) | 7.16312 | + | 5.20431i | 1.17761 | + | 0.855583i | 0.991900 | − | 0.127021i | \(-0.0405417\pi\) |
0.185710 | + | 0.982605i | \(0.440542\pi\) | |||||||
\(38\) | −5.85410 | − | 4.25325i | −0.949661 | − | 0.689969i | ||||
\(39\) | 1.50000 | − | 1.08981i | 0.240192 | − | 0.174510i | ||||
\(40\) | 1.80902 | − | 1.31433i | 0.286031 | − | 0.207813i | ||||
\(41\) | −4.11803 | − | 2.99193i | −0.643129 | − | 0.467260i | 0.217795 | − | 0.975995i | \(-0.430114\pi\) |
−0.860924 | + | 0.508734i | \(0.830114\pi\) | |||||||
\(42\) | 0.618034 | + | 1.90211i | 0.0953647 | + | 0.293502i | ||||
\(43\) | 3.23607 | 0.493496 | 0.246748 | − | 0.969080i | \(-0.420638\pi\) | ||||
0.246748 | + | 0.969080i | \(0.420638\pi\) | |||||||
\(44\) | −0.236068 | − | 0.726543i | −0.0355886 | − | 0.109530i | ||||
\(45\) | 0.690983 | − | 2.12663i | 0.103006 | − | 0.317019i | ||||
\(46\) | −1.85410 | + | 5.70634i | −0.273372 | + | 0.841354i | ||||
\(47\) | 2.85410 | − | 8.78402i | 0.416314 | − | 1.28128i | −0.494757 | − | 0.869031i | \(-0.664743\pi\) |
0.911071 | − | 0.412250i | \(-0.135257\pi\) | |||||||
\(48\) | 0.809017 | − | 0.587785i | 0.116772 | − | 0.0848395i | ||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | −1.54508 | + | 4.75528i | −0.218508 | + | 0.672499i | ||||
\(51\) | −1.14590 | −0.160458 | ||||||||
\(52\) | −1.50000 | + | 1.08981i | −0.208013 | + | 0.151130i | ||||
\(53\) | −3.57295 | + | 10.9964i | −0.490782 | + | 1.51047i | 0.332646 | + | 0.943052i | \(0.392059\pi\) |
−0.823428 | + | 0.567421i | \(0.807941\pi\) | |||||||
\(54\) | 0.309017 | − | 0.951057i | 0.0420519 | − | 0.129422i | ||||
\(55\) | 1.38197 | + | 1.00406i | 0.186344 | + | 0.135387i | ||||
\(56\) | −0.618034 | − | 1.90211i | −0.0825883 | − | 0.254181i | ||||
\(57\) | 7.23607 | 0.958441 | ||||||||
\(58\) | 1.11803 | + | 3.44095i | 0.146805 | + | 0.451820i | ||||
\(59\) | 7.23607 | + | 5.25731i | 0.942056 | + | 0.684444i | 0.948915 | − | 0.315533i | \(-0.102183\pi\) |
−0.00685884 | + | 0.999976i | \(0.502183\pi\) | |||||||
\(60\) | −0.690983 | + | 2.12663i | −0.0892055 | + | 0.274546i | ||||
\(61\) | 1.73607 | − | 1.26133i | 0.222281 | − | 0.161496i | −0.471072 | − | 0.882095i | \(-0.656133\pi\) |
0.693353 | + | 0.720598i | \(0.256133\pi\) | |||||||
\(62\) | −7.85410 | − | 5.70634i | −0.997472 | − | 0.724706i | ||||
\(63\) | −1.61803 | − | 1.17557i | −0.203853 | − | 0.148108i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 1.28115 | − | 3.94298i | 0.158907 | − | 0.489067i | ||||
\(66\) | 0.618034 | + | 0.449028i | 0.0760747 | + | 0.0552715i | ||||
\(67\) | 1.14590 | + | 3.52671i | 0.139994 | + | 0.430856i | 0.996333 | − | 0.0855568i | \(-0.0272669\pi\) |
−0.856340 | + | 0.516413i | \(0.827267\pi\) | |||||||
\(68\) | 1.14590 | 0.138961 | ||||||||
\(69\) | −1.85410 | − | 5.70634i | −0.223208 | − | 0.686963i | ||||
\(70\) | 3.61803 | + | 2.62866i | 0.432438 | + | 0.314184i | ||||
\(71\) | 2.52786 | − | 7.77997i | 0.300002 | − | 0.923312i | −0.681493 | − | 0.731825i | \(-0.738669\pi\) |
0.981495 | − | 0.191487i | \(-0.0613311\pi\) | |||||||
\(72\) | −0.309017 | + | 0.951057i | −0.0364180 | + | 0.112083i | ||||
\(73\) | 7.97214 | − | 5.79210i | 0.933068 | − | 0.677914i | −0.0136741 | − | 0.999907i | \(-0.504353\pi\) |
0.946742 | + | 0.321993i | \(0.104353\pi\) | |||||||
\(74\) | 8.85410 | 1.02927 | ||||||||
\(75\) | −1.54508 | − | 4.75528i | −0.178411 | − | 0.549093i | ||||
\(76\) | −7.23607 | −0.830034 | ||||||||
\(77\) | 1.23607 | − | 0.898056i | 0.140863 | − | 0.102343i | ||||
\(78\) | 0.572949 | − | 1.76336i | 0.0648737 | − | 0.199661i | ||||
\(79\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(80\) | 0.690983 | − | 2.12663i | 0.0772542 | − | 0.237764i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | −5.09017 | −0.562115 | ||||||||
\(83\) | 1.85410 | + | 5.70634i | 0.203514 | + | 0.626352i | 0.999771 | + | 0.0213936i | \(0.00681031\pi\) |
−0.796257 | + | 0.604959i | \(0.793190\pi\) | |||||||
\(84\) | 1.61803 | + | 1.17557i | 0.176542 | + | 0.128265i | ||||
\(85\) | −2.07295 | + | 1.50609i | −0.224843 | + | 0.163358i | ||||
\(86\) | 2.61803 | − | 1.90211i | 0.282310 | − | 0.205110i | ||||
\(87\) | −2.92705 | − | 2.12663i | −0.313813 | − | 0.227998i | ||||
\(88\) | −0.618034 | − | 0.449028i | −0.0658826 | − | 0.0478665i | ||||
\(89\) | −2.92705 | + | 2.12663i | −0.310267 | + | 0.225422i | −0.732011 | − | 0.681293i | \(-0.761418\pi\) |
0.421744 | + | 0.906715i | \(0.361418\pi\) | |||||||
\(90\) | −0.690983 | − | 2.12663i | −0.0728360 | − | 0.224166i | ||||
\(91\) | −3.00000 | − | 2.17963i | −0.314485 | − | 0.228487i | ||||
\(92\) | 1.85410 | + | 5.70634i | 0.193303 | + | 0.594927i | ||||
\(93\) | 9.70820 | 1.00669 | ||||||||
\(94\) | −2.85410 | − | 8.78402i | −0.294378 | − | 0.906003i | ||||
\(95\) | 13.0902 | − | 9.51057i | 1.34302 | − | 0.975763i | ||||
\(96\) | 0.309017 | − | 0.951057i | 0.0315389 | − | 0.0970668i | ||||
\(97\) | −2.20820 | + | 6.79615i | −0.224209 | + | 0.690045i | 0.774162 | + | 0.632988i | \(0.218172\pi\) |
−0.998371 | + | 0.0570570i | \(0.981828\pi\) | |||||||
\(98\) | −2.42705 | + | 1.76336i | −0.245169 | + | 0.178126i | ||||
\(99\) | −0.763932 | −0.0767781 | ||||||||
\(100\) | 1.54508 | + | 4.75528i | 0.154508 | + | 0.475528i | ||||
\(101\) | 17.3262 | 1.72403 | 0.862013 | − | 0.506887i | \(-0.169204\pi\) | ||||
0.862013 | + | 0.506887i | \(0.169204\pi\) | |||||||
\(102\) | −0.927051 | + | 0.673542i | −0.0917917 | + | 0.0666906i | ||||
\(103\) | −4.85410 | + | 14.9394i | −0.478289 | + | 1.47202i | 0.363181 | + | 0.931718i | \(0.381691\pi\) |
−0.841470 | + | 0.540303i | \(0.818309\pi\) | |||||||
\(104\) | −0.572949 | + | 1.76336i | −0.0561823 | + | 0.172911i | ||||
\(105\) | −4.47214 | −0.436436 | ||||||||
\(106\) | 3.57295 | + | 10.9964i | 0.347035 | + | 1.06807i | ||||
\(107\) | −6.94427 | −0.671328 | −0.335664 | − | 0.941982i | \(-0.608961\pi\) | ||||
−0.335664 | + | 0.941982i | \(0.608961\pi\) | |||||||
\(108\) | −0.309017 | − | 0.951057i | −0.0297352 | − | 0.0915155i | ||||
\(109\) | 14.2082 | + | 10.3229i | 1.36090 | + | 0.988751i | 0.998387 | + | 0.0567720i | \(0.0180808\pi\) |
0.362512 | + | 0.931979i | \(0.381919\pi\) | |||||||
\(110\) | 1.70820 | 0.162871 | ||||||||
\(111\) | −7.16312 | + | 5.20431i | −0.679893 | + | 0.493971i | ||||
\(112\) | −1.61803 | − | 1.17557i | −0.152890 | − | 0.111081i | ||||
\(113\) | −6.92705 | − | 5.03280i | −0.651642 | − | 0.473446i | 0.212188 | − | 0.977229i | \(-0.431941\pi\) |
−0.863830 | + | 0.503783i | \(0.831941\pi\) | |||||||
\(114\) | 5.85410 | − | 4.25325i | 0.548287 | − | 0.398354i | ||||
\(115\) | −10.8541 | − | 7.88597i | −1.01215 | − | 0.735370i | ||||
\(116\) | 2.92705 | + | 2.12663i | 0.271770 | + | 0.197452i | ||||
\(117\) | 0.572949 | + | 1.76336i | 0.0529692 | + | 0.163022i | ||||
\(118\) | 8.94427 | 0.823387 | ||||||||
\(119\) | 0.708204 | + | 2.17963i | 0.0649209 | + | 0.199806i | ||||
\(120\) | 0.690983 | + | 2.12663i | 0.0630778 | + | 0.194134i | ||||
\(121\) | −3.21885 | + | 9.90659i | −0.292622 | + | 0.900599i | ||||
\(122\) | 0.663119 | − | 2.04087i | 0.0600360 | − | 0.184772i | ||||
\(123\) | 4.11803 | − | 2.99193i | 0.371311 | − | 0.269773i | ||||
\(124\) | −9.70820 | −0.871822 | ||||||||
\(125\) | −9.04508 | − | 6.57164i | −0.809017 | − | 0.587785i | ||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | −11.0902 | + | 8.05748i | −0.984093 | + | 0.714986i | −0.958620 | − | 0.284690i | \(-0.908109\pi\) |
−0.0254737 | + | 0.999675i | \(0.508109\pi\) | |||||||
\(128\) | −0.309017 | + | 0.951057i | −0.0273135 | + | 0.0840623i | ||||
\(129\) | −1.00000 | + | 3.07768i | −0.0880451 | + | 0.270975i | ||||
\(130\) | −1.28115 | − | 3.94298i | −0.112365 | − | 0.345823i | ||||
\(131\) | −1.61803 | − | 4.97980i | −0.141368 | − | 0.435087i | 0.855158 | − | 0.518368i | \(-0.173460\pi\) |
−0.996526 | + | 0.0832809i | \(0.973460\pi\) | |||||||
\(132\) | 0.763932 | 0.0664917 | ||||||||
\(133\) | −4.47214 | − | 13.7638i | −0.387783 | − | 1.19347i | ||||
\(134\) | 3.00000 | + | 2.17963i | 0.259161 | + | 0.188291i | ||||
\(135\) | 1.80902 | + | 1.31433i | 0.155695 | + | 0.113119i | ||||
\(136\) | 0.927051 | − | 0.673542i | 0.0794940 | − | 0.0577557i | ||||
\(137\) | −11.3541 | − | 8.24924i | −0.970046 | − | 0.704780i | −0.0145842 | − | 0.999894i | \(-0.504642\pi\) |
−0.955462 | + | 0.295114i | \(0.904642\pi\) | |||||||
\(138\) | −4.85410 | − | 3.52671i | −0.413209 | − | 0.300214i | ||||
\(139\) | −10.8541 | + | 7.88597i | −0.920633 | + | 0.668879i | −0.943681 | − | 0.330855i | \(-0.892663\pi\) |
0.0230486 | + | 0.999734i | \(0.492663\pi\) | |||||||
\(140\) | 4.47214 | 0.377964 | ||||||||
\(141\) | 7.47214 | + | 5.42882i | 0.629267 | + | 0.457190i | ||||
\(142\) | −2.52786 | − | 7.77997i | −0.212134 | − | 0.652880i | ||||
\(143\) | −1.41641 | −0.118446 | ||||||||
\(144\) | 0.309017 | + | 0.951057i | 0.0257514 | + | 0.0792547i | ||||
\(145\) | −8.09017 | −0.671852 | ||||||||
\(146\) | 3.04508 | − | 9.37181i | 0.252013 | − | 0.775616i | ||||
\(147\) | 0.927051 | − | 2.85317i | 0.0764619 | − | 0.235325i | ||||
\(148\) | 7.16312 | − | 5.20431i | 0.588805 | − | 0.427792i | ||||
\(149\) | −22.0344 | −1.80513 | −0.902566 | − | 0.430552i | \(-0.858319\pi\) | ||||
−0.902566 | + | 0.430552i | \(0.858319\pi\) | |||||||
\(150\) | −4.04508 | − | 2.93893i | −0.330280 | − | 0.239962i | ||||
\(151\) | 10.9443 | 0.890632 | 0.445316 | − | 0.895373i | \(-0.353091\pi\) | ||||
0.445316 | + | 0.895373i | \(0.353091\pi\) | |||||||
\(152\) | −5.85410 | + | 4.25325i | −0.474830 | + | 0.344984i | ||||
\(153\) | 0.354102 | − | 1.08981i | 0.0286274 | − | 0.0881062i | ||||
\(154\) | 0.472136 | − | 1.45309i | 0.0380458 | − | 0.117093i | ||||
\(155\) | 17.5623 | − | 12.7598i | 1.41064 | − | 1.02489i | ||||
\(156\) | −0.572949 | − | 1.76336i | −0.0458726 | − | 0.141181i | ||||
\(157\) | 11.1459 | 0.889540 | 0.444770 | − | 0.895645i | \(-0.353286\pi\) | ||||
0.444770 | + | 0.895645i | \(0.353286\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.35410 | − | 6.79615i | −0.741829 | − | 0.538970i | ||||
\(160\) | −0.690983 | − | 2.12663i | −0.0546270 | − | 0.168125i | ||||
\(161\) | −9.70820 | + | 7.05342i | −0.765114 | + | 0.555888i | ||||
\(162\) | 0.809017 | + | 0.587785i | 0.0635624 | + | 0.0461808i | ||||
\(163\) | −9.32624 | − | 6.77591i | −0.730487 | − | 0.530730i | 0.159230 | − | 0.987241i | \(-0.449099\pi\) |
−0.889718 | + | 0.456511i | \(0.849099\pi\) | |||||||
\(164\) | −4.11803 | + | 2.99193i | −0.321564 | + | 0.233630i | ||||
\(165\) | −1.38197 | + | 1.00406i | −0.107586 | + | 0.0781657i | ||||
\(166\) | 4.85410 | + | 3.52671i | 0.376751 | + | 0.273726i | ||||
\(167\) | −0.763932 | − | 2.35114i | −0.0591148 | − | 0.181937i | 0.917139 | − | 0.398569i | \(-0.130493\pi\) |
−0.976253 | + | 0.216632i | \(0.930493\pi\) | |||||||
\(168\) | 2.00000 | 0.154303 | ||||||||
\(169\) | −2.95492 | − | 9.09429i | −0.227301 | − | 0.699561i | ||||
\(170\) | −0.791796 | + | 2.43690i | −0.0607280 | + | 0.186902i | ||||
\(171\) | −2.23607 | + | 6.88191i | −0.170996 | + | 0.526273i | ||||
\(172\) | 1.00000 | − | 3.07768i | 0.0762493 | − | 0.234671i | ||||
\(173\) | 17.8713 | − | 12.9843i | 1.35873 | − | 0.987176i | 0.360207 | − | 0.932872i | \(-0.382706\pi\) |
0.998524 | − | 0.0543039i | \(-0.0172940\pi\) | |||||||
\(174\) | −3.61803 | −0.274282 | ||||||||
\(175\) | −8.09017 | + | 5.87785i | −0.611559 | + | 0.444324i | ||||
\(176\) | −0.763932 | −0.0575835 | ||||||||
\(177\) | −7.23607 | + | 5.25731i | −0.543896 | + | 0.395164i | ||||
\(178\) | −1.11803 | + | 3.44095i | −0.0838002 | + | 0.257910i | ||||
\(179\) | −8.09017 | + | 24.8990i | −0.604688 | + | 1.86104i | −0.105764 | + | 0.994391i | \(0.533729\pi\) |
−0.498923 | + | 0.866646i | \(0.666271\pi\) | |||||||
\(180\) | −1.80902 | − | 1.31433i | −0.134836 | − | 0.0979642i | ||||
\(181\) | 2.79180 | + | 8.59226i | 0.207513 | + | 0.638658i | 0.999601 | + | 0.0282515i | \(0.00899392\pi\) |
−0.792088 | + | 0.610407i | \(0.791006\pi\) | |||||||
\(182\) | −3.70820 | −0.274870 | ||||||||
\(183\) | 0.663119 | + | 2.04087i | 0.0490192 | + | 0.150865i | ||||
\(184\) | 4.85410 | + | 3.52671i | 0.357849 | + | 0.259993i | ||||
\(185\) | −6.11803 | + | 18.8294i | −0.449807 | + | 1.38436i | ||||
\(186\) | 7.85410 | − | 5.70634i | 0.575891 | − | 0.418409i | ||||
\(187\) | 0.708204 | + | 0.514540i | 0.0517890 | + | 0.0376269i | ||||
\(188\) | −7.47214 | − | 5.42882i | −0.544962 | − | 0.395938i | ||||
\(189\) | 1.61803 | − | 1.17557i | 0.117695 | − | 0.0855102i | ||||
\(190\) | 5.00000 | − | 15.3884i | 0.362738 | − | 1.11639i | ||||
\(191\) | 4.23607 | + | 3.07768i | 0.306511 | + | 0.222693i | 0.730398 | − | 0.683022i | \(-0.239335\pi\) |
−0.423887 | + | 0.905715i | \(0.639335\pi\) | |||||||
\(192\) | −0.309017 | − | 0.951057i | −0.0223014 | − | 0.0686366i | ||||
\(193\) | 4.61803 | 0.332413 | 0.166207 | − | 0.986091i | \(-0.446848\pi\) | ||||
0.166207 | + | 0.986091i | \(0.446848\pi\) | |||||||
\(194\) | 2.20820 | + | 6.79615i | 0.158540 | + | 0.487935i | ||||
\(195\) | 3.35410 | + | 2.43690i | 0.240192 | + | 0.174510i | ||||
\(196\) | −0.927051 | + | 2.85317i | −0.0662179 | + | 0.203798i | ||||
\(197\) | 0.718847 | − | 2.21238i | 0.0512157 | − | 0.157626i | −0.922177 | − | 0.386767i | \(-0.873592\pi\) |
0.973393 | + | 0.229141i | \(0.0735918\pi\) | |||||||
\(198\) | −0.618034 | + | 0.449028i | −0.0439218 | + | 0.0319110i | ||||
\(199\) | 16.1803 | 1.14699 | 0.573497 | − | 0.819208i | \(-0.305586\pi\) | ||||
0.573497 | + | 0.819208i | \(0.305586\pi\) | |||||||
\(200\) | 4.04508 | + | 2.93893i | 0.286031 | + | 0.207813i | ||||
\(201\) | −3.70820 | −0.261557 | ||||||||
\(202\) | 14.0172 | − | 10.1841i | 0.986248 | − | 0.716551i | ||||
\(203\) | −2.23607 | + | 6.88191i | −0.156941 | + | 0.483015i | ||||
\(204\) | −0.354102 | + | 1.08981i | −0.0247921 | + | 0.0763022i | ||||
\(205\) | 3.51722 | − | 10.8249i | 0.245653 | − | 0.756043i | ||||
\(206\) | 4.85410 | + | 14.9394i | 0.338201 | + | 1.04088i | ||||
\(207\) | 6.00000 | 0.417029 | ||||||||
\(208\) | 0.572949 | + | 1.76336i | 0.0397269 | + | 0.122267i | ||||
\(209\) | −4.47214 | − | 3.24920i | −0.309344 | − | 0.224752i | ||||
\(210\) | −3.61803 | + | 2.62866i | −0.249668 | + | 0.181394i | ||||
\(211\) | 6.47214 | − | 4.70228i | 0.445560 | − | 0.323718i | −0.342280 | − | 0.939598i | \(-0.611199\pi\) |
0.787840 | + | 0.615880i | \(0.211199\pi\) | |||||||
\(212\) | 9.35410 | + | 6.79615i | 0.642442 | + | 0.466762i | ||||
\(213\) | 6.61803 | + | 4.80828i | 0.453460 | + | 0.329458i | ||||
\(214\) | −5.61803 | + | 4.08174i | −0.384041 | + | 0.279022i | ||||
\(215\) | 2.23607 | + | 6.88191i | 0.152499 | + | 0.469342i | ||||
\(216\) | −0.809017 | − | 0.587785i | −0.0550466 | − | 0.0399937i | ||||
\(217\) | −6.00000 | − | 18.4661i | −0.407307 | − | 1.25356i | ||||
\(218\) | 17.5623 | 1.18947 | ||||||||
\(219\) | 3.04508 | + | 9.37181i | 0.205768 | + | 0.633288i | ||||
\(220\) | 1.38197 | − | 1.00406i | 0.0931721 | − | 0.0676935i | ||||
\(221\) | 0.656541 | − | 2.02063i | 0.0441637 | − | 0.135922i | ||||
\(222\) | −2.73607 | + | 8.42075i | −0.183633 | + | 0.565164i | ||||
\(223\) | 12.7082 | − | 9.23305i | 0.851004 | − | 0.618291i | −0.0744185 | − | 0.997227i | \(-0.523710\pi\) |
0.925423 | + | 0.378936i | \(0.123710\pi\) | |||||||
\(224\) | −2.00000 | −0.133631 | ||||||||
\(225\) | 5.00000 | 0.333333 | ||||||||
\(226\) | −8.56231 | −0.569556 | ||||||||
\(227\) | −0.763932 | + | 0.555029i | −0.0507039 | + | 0.0368386i | −0.612849 | − | 0.790200i | \(-0.709976\pi\) |
0.562145 | + | 0.827039i | \(0.309976\pi\) | |||||||
\(228\) | 2.23607 | − | 6.88191i | 0.148087 | − | 0.455766i | ||||
\(229\) | 2.86475 | − | 8.81678i | 0.189308 | − | 0.582629i | −0.810688 | − | 0.585478i | \(-0.800907\pi\) |
0.999996 | + | 0.00284891i | \(0.000906837\pi\) | |||||||
\(230\) | −13.4164 | −0.884652 | ||||||||
\(231\) | 0.472136 | + | 1.45309i | 0.0310643 | + | 0.0956060i | ||||
\(232\) | 3.61803 | 0.237536 | ||||||||
\(233\) | −3.37132 | − | 10.3759i | −0.220863 | − | 0.679746i | −0.998685 | − | 0.0512616i | \(-0.983676\pi\) |
0.777823 | − | 0.628484i | \(-0.216324\pi\) | |||||||
\(234\) | 1.50000 | + | 1.08981i | 0.0980581 | + | 0.0712434i | ||||
\(235\) | 20.6525 | 1.34722 | ||||||||
\(236\) | 7.23607 | − | 5.25731i | 0.471028 | − | 0.342222i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.85410 | + | 1.34708i | 0.120184 | + | 0.0873185i | ||||
\(239\) | 21.7082 | − | 15.7719i | 1.40419 | − | 1.02020i | 0.410051 | − | 0.912063i | \(-0.365511\pi\) |
0.994136 | − | 0.108139i | \(-0.0344892\pi\) | |||||||
\(240\) | 1.80902 | + | 1.31433i | 0.116772 | + | 0.0848395i | ||||
\(241\) | 5.78115 | + | 4.20025i | 0.372397 | + | 0.270562i | 0.758204 | − | 0.652017i | \(-0.226077\pi\) |
−0.385807 | + | 0.922579i | \(0.626077\pi\) | |||||||
\(242\) | 3.21885 | + | 9.90659i | 0.206915 | + | 0.636820i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.663119 | − | 2.04087i | −0.0424518 | − | 0.130653i | ||||
\(245\) | −2.07295 | − | 6.37988i | −0.132436 | − | 0.407596i | ||||
\(246\) | 1.57295 | − | 4.84104i | 0.100288 | − | 0.308653i | ||||
\(247\) | −4.14590 | + | 12.7598i | −0.263797 | + | 0.811884i | ||||
\(248\) | −7.85410 | + | 5.70634i | −0.498736 | + | 0.362353i | ||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | −11.1803 | −0.707107 | ||||||||
\(251\) | −3.52786 | −0.222677 | −0.111338 | − | 0.993783i | \(-0.535514\pi\) | ||||
−0.111338 | + | 0.993783i | \(0.535514\pi\) | |||||||
\(252\) | −1.61803 | + | 1.17557i | −0.101927 | + | 0.0740540i | ||||
\(253\) | −1.41641 | + | 4.35926i | −0.0890488 | + | 0.274064i | ||||
\(254\) | −4.23607 | + | 13.0373i | −0.265795 | + | 0.818031i | ||||
\(255\) | −0.791796 | − | 2.43690i | −0.0495842 | − | 0.152604i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | −9.38197 | −0.585231 | −0.292615 | − | 0.956230i | \(-0.594526\pi\) | ||||
−0.292615 | + | 0.956230i | \(0.594526\pi\) | |||||||
\(258\) | 1.00000 | + | 3.07768i | 0.0622573 | + | 0.191608i | ||||
\(259\) | 14.3262 | + | 10.4086i | 0.890189 | + | 0.646760i | ||||
\(260\) | −3.35410 | − | 2.43690i | −0.208013 | − | 0.151130i | ||||
\(261\) | 2.92705 | − | 2.12663i | 0.181180 | − | 0.131635i | ||||
\(262\) | −4.23607 | − | 3.07768i | −0.261705 | − | 0.190140i | ||||
\(263\) | 6.85410 | + | 4.97980i | 0.422642 | + | 0.307067i | 0.778700 | − | 0.627396i | \(-0.215879\pi\) |
−0.356058 | + | 0.934464i | \(0.615879\pi\) | |||||||
\(264\) | 0.618034 | − | 0.449028i | 0.0380374 | − | 0.0276358i | ||||
\(265\) | −25.8541 | −1.58820 | ||||||||
\(266\) | −11.7082 | − | 8.50651i | −0.717876 | − | 0.521567i | ||||
\(267\) | −1.11803 | − | 3.44095i | −0.0684226 | − | 0.210583i | ||||
\(268\) | 3.70820 | 0.226515 | ||||||||
\(269\) | −4.04508 | − | 12.4495i | −0.246633 | − | 0.759059i | −0.995364 | − | 0.0961842i | \(-0.969336\pi\) |
0.748730 | − | 0.662875i | \(-0.230664\pi\) | |||||||
\(270\) | 2.23607 | 0.136083 | ||||||||
\(271\) | 1.79837 | − | 5.53483i | 0.109243 | − | 0.336217i | −0.881460 | − | 0.472260i | \(-0.843438\pi\) |
0.990703 | + | 0.136043i | \(0.0434385\pi\) | |||||||
\(272\) | 0.354102 | − | 1.08981i | 0.0214706 | − | 0.0660797i | ||||
\(273\) | 3.00000 | − | 2.17963i | 0.181568 | − | 0.131917i | ||||
\(274\) | −14.0344 | −0.847852 | ||||||||
\(275\) | −1.18034 | + | 3.63271i | −0.0711772 | + | 0.219061i | ||||
\(276\) | −6.00000 | −0.361158 | ||||||||
\(277\) | 23.3435 | − | 16.9600i | 1.40257 | − | 1.01903i | 0.408222 | − | 0.912883i | \(-0.366149\pi\) |
0.994351 | − | 0.106146i | \(-0.0338510\pi\) | |||||||
\(278\) | −4.14590 | + | 12.7598i | −0.248654 | + | 0.765280i | ||||
\(279\) | −3.00000 | + | 9.23305i | −0.179605 | + | 0.552768i | ||||
\(280\) | 3.61803 | − | 2.62866i | 0.216219 | − | 0.157092i | ||||
\(281\) | 1.57295 | + | 4.84104i | 0.0938343 | + | 0.288792i | 0.986948 | − | 0.161038i | \(-0.0514843\pi\) |
−0.893114 | + | 0.449831i | \(0.851484\pi\) | |||||||
\(282\) | 9.23607 | 0.550000 | ||||||||
\(283\) | −0.381966 | − | 1.17557i | −0.0227055 | − | 0.0698804i | 0.939062 | − | 0.343749i | \(-0.111697\pi\) |
−0.961767 | + | 0.273868i | \(0.911697\pi\) | |||||||
\(284\) | −6.61803 | − | 4.80828i | −0.392708 | − | 0.285319i | ||||
\(285\) | 5.00000 | + | 15.3884i | 0.296174 | + | 0.911531i | ||||
\(286\) | −1.14590 | + | 0.832544i | −0.0677584 | + | 0.0492293i | ||||
\(287\) | −8.23607 | − | 5.98385i | −0.486160 | − | 0.353216i | ||||
\(288\) | 0.809017 | + | 0.587785i | 0.0476718 | + | 0.0346356i | ||||
\(289\) | 12.6910 | − | 9.22054i | 0.746528 | − | 0.542385i | ||||
\(290\) | −6.54508 | + | 4.75528i | −0.384341 | + | 0.279240i | ||||
\(291\) | −5.78115 | − | 4.20025i | −0.338897 | − | 0.246223i | ||||
\(292\) | −3.04508 | − | 9.37181i | −0.178200 | − | 0.548444i | ||||
\(293\) | −4.20163 | −0.245462 | −0.122731 | − | 0.992440i | \(-0.539165\pi\) | ||||
−0.122731 | + | 0.992440i | \(0.539165\pi\) | |||||||
\(294\) | −0.927051 | − | 2.85317i | −0.0540667 | − | 0.166400i | ||||
\(295\) | −6.18034 | + | 19.0211i | −0.359833 | + | 1.10745i | ||||
\(296\) | 2.73607 | − | 8.42075i | 0.159031 | − | 0.489446i | ||||
\(297\) | 0.236068 | − | 0.726543i | 0.0136981 | − | 0.0421583i | ||||
\(298\) | −17.8262 | + | 12.9515i | −1.03265 | + | 0.750261i | ||||
\(299\) | 11.1246 | 0.643353 | ||||||||
\(300\) | −5.00000 | −0.288675 | ||||||||
\(301\) | 6.47214 | 0.373048 | ||||||||
\(302\) | 8.85410 | − | 6.43288i | 0.509496 | − | 0.370171i | ||||
\(303\) | −5.35410 | + | 16.4782i | −0.307585 | + | 0.946650i | ||||
\(304\) | −2.23607 | + | 6.88191i | −0.128247 | + | 0.394705i | ||||
\(305\) | 3.88197 | + | 2.82041i | 0.222281 | + | 0.161496i | ||||
\(306\) | −0.354102 | − | 1.08981i | −0.0202427 | − | 0.0623005i | ||||
\(307\) | −29.7082 | −1.69554 | −0.847768 | − | 0.530367i | \(-0.822054\pi\) | ||||
−0.847768 | + | 0.530367i | \(0.822054\pi\) | |||||||
\(308\) | −0.472136 | − | 1.45309i | −0.0269024 | − | 0.0827972i | ||||
\(309\) | −12.7082 | − | 9.23305i | −0.722944 | − | 0.525250i | ||||
\(310\) | 6.70820 | − | 20.6457i | 0.381000 | − | 1.17260i | ||||
\(311\) | −10.2361 | + | 7.43694i | −0.580434 | + | 0.421710i | −0.838881 | − | 0.544315i | \(-0.816789\pi\) |
0.258446 | + | 0.966026i | \(0.416789\pi\) | |||||||
\(312\) | −1.50000 | − | 1.08981i | −0.0849208 | − | 0.0616986i | ||||
\(313\) | −14.8541 | − | 10.7921i | −0.839603 | − | 0.610008i | 0.0826564 | − | 0.996578i | \(-0.473660\pi\) |
−0.922260 | + | 0.386570i | \(0.873660\pi\) | |||||||
\(314\) | 9.01722 | − | 6.55139i | 0.508871 | − | 0.369717i | ||||
\(315\) | 1.38197 | − | 4.25325i | 0.0778650 | − | 0.239644i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.38197 | + | 10.4086i | 0.189950 | + | 0.584606i | 0.999998 | − | 0.00175672i | \(-0.000559182\pi\) |
−0.810048 | + | 0.586363i | \(0.800559\pi\) | |||||||
\(318\) | −11.5623 | −0.648382 | ||||||||
\(319\) | 0.854102 | + | 2.62866i | 0.0478205 | + | 0.147176i | ||||
\(320\) | −1.80902 | − | 1.31433i | −0.101127 | − | 0.0734732i | ||||
\(321\) | 2.14590 | − | 6.60440i | 0.119772 | − | 0.368621i | ||||
\(322\) | −3.70820 | + | 11.4127i | −0.206650 | + | 0.636004i | ||||
\(323\) | 6.70820 | − | 4.87380i | 0.373254 | − | 0.271185i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 9.27051 | 0.514235 | ||||||||
\(326\) | −11.5279 | −0.638469 | ||||||||
\(327\) | −14.2082 | + | 10.3229i | −0.785715 | + | 0.570856i | ||||
\(328\) | −1.57295 | + | 4.84104i | −0.0868516 | + | 0.267302i | ||||
\(329\) | 5.70820 | − | 17.5680i | 0.314703 | − | 0.968558i | ||||
\(330\) | −0.527864 | + | 1.62460i | −0.0290580 | + | 0.0894312i | ||||
\(331\) | −7.27051 | − | 22.3763i | −0.399623 | − | 1.22991i | −0.925302 | − | 0.379231i | \(-0.876189\pi\) |
0.525679 | − | 0.850683i | \(-0.323811\pi\) | |||||||
\(332\) | 6.00000 | 0.329293 | ||||||||
\(333\) | −2.73607 | − | 8.42075i | −0.149936 | − | 0.461454i | ||||
\(334\) | −2.00000 | − | 1.45309i | −0.109435 | − | 0.0795093i | ||||
\(335\) | −6.70820 | + | 4.87380i | −0.366508 | + | 0.266284i | ||||
\(336\) | 1.61803 | − | 1.17557i | 0.0882710 | − | 0.0641326i | ||||
\(337\) | 20.0902 | + | 14.5964i | 1.09438 | + | 0.795115i | 0.980134 | − | 0.198338i | \(-0.0635543\pi\) |
0.114248 | + | 0.993452i | \(0.463554\pi\) | |||||||
\(338\) | −7.73607 | − | 5.62058i | −0.420787 | − | 0.305719i | ||||
\(339\) | 6.92705 | − | 5.03280i | 0.376226 | − | 0.273344i | ||||
\(340\) | 0.791796 | + | 2.43690i | 0.0429412 | + | 0.132159i | ||||
\(341\) | −6.00000 | − | 4.35926i | −0.324918 | − | 0.236067i | ||||
\(342\) | 2.23607 | + | 6.88191i | 0.120913 | + | 0.372131i | ||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | −1.00000 | − | 3.07768i | −0.0539164 | − | 0.165938i | ||||
\(345\) | 10.8541 | − | 7.88597i | 0.584365 | − | 0.424566i | ||||
\(346\) | 6.82624 | − | 21.0090i | 0.366981 | − | 1.12945i | ||||
\(347\) | −0.236068 | + | 0.726543i | −0.0126728 | + | 0.0390028i | −0.957193 | − | 0.289451i | \(-0.906527\pi\) |
0.944520 | + | 0.328453i | \(0.106527\pi\) | |||||||
\(348\) | −2.92705 | + | 2.12663i | −0.156906 | + | 0.113999i | ||||
\(349\) | −9.79837 | −0.524495 | −0.262247 | − | 0.965001i | \(-0.584464\pi\) | ||||
−0.262247 | + | 0.965001i | \(0.584464\pi\) | |||||||
\(350\) | −3.09017 | + | 9.51057i | −0.165177 | + | 0.508361i | ||||
\(351\) | −1.85410 | −0.0989646 | ||||||||
\(352\) | −0.618034 | + | 0.449028i | −0.0329413 | + | 0.0239333i | ||||
\(353\) | 3.56231 | − | 10.9637i | 0.189602 | − | 0.583536i | −0.810395 | − | 0.585884i | \(-0.800747\pi\) |
0.999997 | + | 0.00234791i | \(0.000747364\pi\) | |||||||
\(354\) | −2.76393 | + | 8.50651i | −0.146901 | + | 0.452116i | ||||
\(355\) | 18.2918 | 0.970828 | ||||||||
\(356\) | 1.11803 | + | 3.44095i | 0.0592557 | + | 0.182370i | ||||
\(357\) | −2.29180 | −0.121295 | ||||||||
\(358\) | 8.09017 | + | 24.8990i | 0.427579 | + | 1.31595i | ||||
\(359\) | −6.38197 | − | 4.63677i | −0.336827 | − | 0.244719i | 0.406495 | − | 0.913653i | \(-0.366751\pi\) |
−0.743322 | + | 0.668934i | \(0.766751\pi\) | |||||||
\(360\) | −2.23607 | −0.117851 | ||||||||
\(361\) | −26.9894 | + | 19.6089i | −1.42049 | + | 1.03205i | ||||
\(362\) | 7.30902 | + | 5.31031i | 0.384153 | + | 0.279104i | ||||
\(363\) | −8.42705 | − | 6.12261i | −0.442305 | − | 0.321354i | ||||
\(364\) | −3.00000 | + | 2.17963i | −0.157243 | + | 0.114244i | ||||
\(365\) | 17.8262 | + | 12.9515i | 0.933068 | + | 0.677914i | ||||
\(366\) | 1.73607 | + | 1.26133i | 0.0907457 | + | 0.0659306i | ||||
\(367\) | −1.09017 | − | 3.35520i | −0.0569064 | − | 0.175140i | 0.918563 | − | 0.395274i | \(-0.129350\pi\) |
−0.975470 | + | 0.220134i | \(0.929350\pi\) | |||||||
\(368\) | 6.00000 | 0.312772 | ||||||||
\(369\) | 1.57295 | + | 4.84104i | 0.0818845 | + | 0.252014i | ||||
\(370\) | 6.11803 | + | 18.8294i | 0.318061 | + | 0.978892i | ||||
\(371\) | −7.14590 | + | 21.9928i | −0.370997 | + | 1.14181i | ||||
\(372\) | 3.00000 | − | 9.23305i | 0.155543 | − | 0.478711i | ||||
\(373\) | −23.7984 | + | 17.2905i | −1.23223 | + | 0.895270i | −0.997056 | − | 0.0766827i | \(-0.975567\pi\) |
−0.235178 | + | 0.971952i | \(0.575567\pi\) | |||||||
\(374\) | 0.875388 | 0.0452652 | ||||||||
\(375\) | 9.04508 | − | 6.57164i | 0.467086 | − | 0.339358i | ||||
\(376\) | −9.23607 | −0.476314 | ||||||||
\(377\) | 5.42705 | − | 3.94298i | 0.279507 | − | 0.203074i | ||||
\(378\) | 0.618034 | − | 1.90211i | 0.0317882 | − | 0.0978341i | ||||
\(379\) | 7.23607 | − | 22.2703i | 0.371692 | − | 1.14395i | −0.573992 | − | 0.818861i | \(-0.694606\pi\) |
0.945684 | − | 0.325089i | \(-0.105394\pi\) | |||||||
\(380\) | −5.00000 | − | 15.3884i | −0.256495 | − | 0.789409i | ||||
\(381\) | −4.23607 | − | 13.0373i | −0.217020 | − | 0.667920i | ||||
\(382\) | 5.23607 | 0.267901 | ||||||||
\(383\) | 3.56231 | + | 10.9637i | 0.182025 | + | 0.560216i | 0.999884 | − | 0.0152022i | \(-0.00483919\pi\) |
−0.817859 | + | 0.575419i | \(0.804839\pi\) | |||||||
\(384\) | −0.809017 | − | 0.587785i | −0.0412850 | − | 0.0299953i | ||||
\(385\) | 2.76393 | + | 2.00811i | 0.140863 | + | 0.102343i | ||||
\(386\) | 3.73607 | − | 2.71441i | 0.190161 | − | 0.138160i | ||||
\(387\) | −2.61803 | − | 1.90211i | −0.133082 | − | 0.0966898i | ||||
\(388\) | 5.78115 | + | 4.20025i | 0.293494 | + | 0.213236i | ||||
\(389\) | 25.0623 | − | 18.2088i | 1.27071 | − | 0.923224i | 0.271479 | − | 0.962444i | \(-0.412487\pi\) |
0.999231 | + | 0.0392200i | \(0.0124873\pi\) | |||||||
\(390\) | 4.14590 | 0.209936 | ||||||||
\(391\) | −5.56231 | − | 4.04125i | −0.281298 | − | 0.204375i | ||||
\(392\) | 0.927051 | + | 2.85317i | 0.0468231 | + | 0.144107i | ||||
\(393\) | 5.23607 | 0.264125 | ||||||||
\(394\) | −0.718847 | − | 2.21238i | −0.0362150 | − | 0.111458i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.236068 | + | 0.726543i | −0.0118629 | + | 0.0365101i | ||||
\(397\) | −7.67376 | + | 23.6174i | −0.385135 | + | 1.18532i | 0.551247 | + | 0.834342i | \(0.314152\pi\) |
−0.936382 | + | 0.350982i | \(0.885848\pi\) | |||||||
\(398\) | 13.0902 | − | 9.51057i | 0.656151 | − | 0.476722i | ||||
\(399\) | 14.4721 | 0.724513 | ||||||||
\(400\) | 5.00000 | 0.250000 | ||||||||
\(401\) | −14.9098 | −0.744561 | −0.372281 | − | 0.928120i | \(-0.621424\pi\) | ||||
−0.372281 | + | 0.928120i | \(0.621424\pi\) | |||||||
\(402\) | −3.00000 | + | 2.17963i | −0.149626 | + | 0.108710i | ||||
\(403\) | −5.56231 | + | 17.1190i | −0.277078 | + | 0.852759i | ||||
\(404\) | 5.35410 | − | 16.4782i | 0.266377 | − | 0.819823i | ||||
\(405\) | −1.80902 | + | 1.31433i | −0.0898908 | + | 0.0653095i | ||||
\(406\) | 2.23607 | + | 6.88191i | 0.110974 | + | 0.341543i | ||||
\(407\) | 6.76393 | 0.335276 | ||||||||
\(408\) | 0.354102 | + | 1.08981i | 0.0175307 | + | 0.0539538i | ||||
\(409\) | 21.0172 | + | 15.2699i | 1.03923 | + | 0.755048i | 0.970136 | − | 0.242562i | \(-0.0779877\pi\) |
0.0690987 | + | 0.997610i | \(0.477988\pi\) | |||||||
\(410\) | −3.51722 | − | 10.8249i | −0.173703 | − | 0.534603i | ||||
\(411\) | 11.3541 | − | 8.24924i | 0.560057 | − | 0.406905i | ||||
\(412\) | 12.7082 | + | 9.23305i | 0.626088 | + | 0.454880i | ||||
\(413\) | 14.4721 | + | 10.5146i | 0.712127 | + | 0.517391i | ||||
\(414\) | 4.85410 | − | 3.52671i | 0.238566 | − | 0.173328i | ||||
\(415\) | −10.8541 | + | 7.88597i | −0.532807 | + | 0.387107i | ||||
\(416\) | 1.50000 | + | 1.08981i | 0.0735436 | + | 0.0534325i | ||||
\(417\) | −4.14590 | − | 12.7598i | −0.203026 | − | 0.624848i | ||||
\(418\) | −5.52786 | −0.270377 | ||||||||
\(419\) | −0.652476 | − | 2.00811i | −0.0318755 | − | 0.0981028i | 0.933853 | − | 0.357657i | \(-0.116424\pi\) |
−0.965729 | + | 0.259554i | \(0.916424\pi\) | |||||||
\(420\) | −1.38197 | + | 4.25325i | −0.0674330 | + | 0.207538i | ||||
\(421\) | 0.0278640 | − | 0.0857567i | 0.00135801 | − | 0.00417953i | −0.950375 | − | 0.311106i | \(-0.899301\pi\) |
0.951733 | + | 0.306926i | \(0.0993006\pi\) | |||||||
\(422\) | 2.47214 | − | 7.60845i | 0.120342 | − | 0.370374i | ||||
\(423\) | −7.47214 | + | 5.42882i | −0.363308 | + | 0.263958i | ||||
\(424\) | 11.5623 | 0.561515 | ||||||||
\(425\) | −4.63525 | − | 3.36771i | −0.224843 | − | 0.163358i | ||||
\(426\) | 8.18034 | 0.396339 | ||||||||
\(427\) | 3.47214 | − | 2.52265i | 0.168028 | − | 0.122080i | ||||
\(428\) | −2.14590 | + | 6.60440i | −0.103726 | + | 0.319235i | ||||
\(429\) | 0.437694 | − | 1.34708i | 0.0211321 | − | 0.0650378i | ||||
\(430\) | 5.85410 | + | 4.25325i | 0.282310 | + | 0.205110i | ||||
\(431\) | −3.00000 | − | 9.23305i | −0.144505 | − | 0.444740i | 0.852442 | − | 0.522822i | \(-0.175121\pi\) |
−0.996947 | + | 0.0780813i | \(0.975121\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −9.22542 | − | 28.3929i | −0.443346 | − | 1.36448i | −0.884288 | − | 0.466942i | \(-0.845356\pi\) |
0.440942 | − | 0.897535i | \(-0.354644\pi\) | |||||||
\(434\) | −15.7082 | − | 11.4127i | −0.754018 | − | 0.547826i | ||||
\(435\) | 2.50000 | − | 7.69421i | 0.119866 | − | 0.368909i | ||||
\(436\) | 14.2082 | − | 10.3229i | 0.680450 | − | 0.494376i | ||||
\(437\) | 35.1246 | + | 25.5195i | 1.68024 | + | 1.22076i | ||||
\(438\) | 7.97214 | + | 5.79210i | 0.380923 | + | 0.276757i | ||||
\(439\) | −12.2361 | + | 8.89002i | −0.583996 | + | 0.424298i | −0.840162 | − | 0.542335i | \(-0.817540\pi\) |
0.256167 | + | 0.966633i | \(0.417540\pi\) | |||||||
\(440\) | 0.527864 | − | 1.62460i | 0.0251649 | − | 0.0774497i | ||||
\(441\) | 2.42705 | + | 1.76336i | 0.115574 | + | 0.0839693i | ||||
\(442\) | −0.656541 | − | 2.02063i | −0.0312285 | − | 0.0961114i | ||||
\(443\) | −28.0689 | −1.33359 | −0.666796 | − | 0.745240i | \(-0.732335\pi\) | ||||
−0.666796 | + | 0.745240i | \(0.732335\pi\) | |||||||
\(444\) | 2.73607 | + | 8.42075i | 0.129848 | + | 0.399631i | ||||
\(445\) | −6.54508 | − | 4.75528i | −0.310267 | − | 0.225422i | ||||
\(446\) | 4.85410 | − | 14.9394i | 0.229848 | − | 0.707401i | ||||
\(447\) | 6.80902 | − | 20.9560i | 0.322055 | − | 0.991185i | ||||
\(448\) | −1.61803 | + | 1.17557i | −0.0764449 | + | 0.0555405i | ||||
\(449\) | −19.7984 | −0.934343 | −0.467172 | − | 0.884167i | \(-0.654727\pi\) | ||||
−0.467172 | + | 0.884167i | \(0.654727\pi\) | |||||||
\(450\) | 4.04508 | − | 2.93893i | 0.190687 | − | 0.138542i | ||||
\(451\) | −3.88854 | −0.183104 | ||||||||
\(452\) | −6.92705 | + | 5.03280i | −0.325821 | + | 0.236723i | ||||
\(453\) | −3.38197 | + | 10.4086i | −0.158899 | + | 0.489040i | ||||
\(454\) | −0.291796 | + | 0.898056i | −0.0136947 | + | 0.0421479i | ||||
\(455\) | 2.56231 | − | 7.88597i | 0.120123 | − | 0.369700i | ||||
\(456\) | −2.23607 | − | 6.88191i | −0.104713 | − | 0.322275i | ||||
\(457\) | −3.52786 | −0.165027 | −0.0825133 | − | 0.996590i | \(-0.526295\pi\) | ||||
−0.0825133 | + | 0.996590i | \(0.526295\pi\) | |||||||
\(458\) | −2.86475 | − | 8.81678i | −0.133861 | − | 0.411981i | ||||
\(459\) | 0.927051 | + | 0.673542i | 0.0432710 | + | 0.0314382i | ||||
\(460\) | −10.8541 | + | 7.88597i | −0.506075 | + | 0.367685i | ||||
\(461\) | −11.2533 | + | 8.17599i | −0.524118 | + | 0.380794i | −0.818153 | − | 0.575001i | \(-0.805002\pi\) |
0.294035 | + | 0.955795i | \(0.405002\pi\) | |||||||
\(462\) | 1.23607 | + | 0.898056i | 0.0575071 | + | 0.0417813i | ||||
\(463\) | 20.7984 | + | 15.1109i | 0.966582 | + | 0.702263i | 0.954670 | − | 0.297666i | \(-0.0962081\pi\) |
0.0119123 | + | 0.999929i | \(0.496208\pi\) | |||||||
\(464\) | 2.92705 | − | 2.12663i | 0.135885 | − | 0.0987262i | ||||
\(465\) | 6.70820 | + | 20.6457i | 0.311086 | + | 0.957423i | ||||
\(466\) | −8.82624 | − | 6.41264i | −0.408868 | − | 0.297060i | ||||
\(467\) | 11.7984 | + | 36.3117i | 0.545964 | + | 1.68030i | 0.718688 | + | 0.695333i | \(0.244743\pi\) |
−0.172724 | + | 0.984970i | \(0.555257\pi\) | |||||||
\(468\) | 1.85410 | 0.0857059 | ||||||||
\(469\) | 2.29180 | + | 7.05342i | 0.105825 | + | 0.325697i | ||||
\(470\) | 16.7082 | − | 12.1392i | 0.770692 | − | 0.559940i | ||||
\(471\) | −3.44427 | + | 10.6004i | −0.158704 | + | 0.488440i | ||||
\(472\) | 2.76393 | − | 8.50651i | 0.127220 | − | 0.391544i | ||||
\(473\) | 2.00000 | − | 1.45309i | 0.0919601 | − | 0.0668129i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.2705 | + | 21.2663i | 1.34302 | + | 0.975763i | ||||
\(476\) | 2.29180 | 0.105044 | ||||||||
\(477\) | 9.35410 | − | 6.79615i | 0.428295 | − | 0.311174i | ||||
\(478\) | 8.29180 | − | 25.5195i | 0.379258 | − | 1.16724i | ||||
\(479\) | −1.38197 | + | 4.25325i | −0.0631436 | + | 0.194336i | −0.977652 | − | 0.210232i | \(-0.932578\pi\) |
0.914508 | + | 0.404568i | \(0.132578\pi\) | |||||||
\(480\) | 2.23607 | 0.102062 | ||||||||
\(481\) | −5.07295 | − | 15.6129i | −0.231307 | − | 0.711888i | ||||
\(482\) | 7.14590 | 0.325487 | ||||||||
\(483\) | −3.70820 | − | 11.4127i | −0.168729 | − | 0.519295i | ||||
\(484\) | 8.42705 | + | 6.12261i | 0.383048 | + | 0.278300i | ||||
\(485\) | −15.9787 | −0.725556 | ||||||||
\(486\) | −0.809017 | + | 0.587785i | −0.0366978 | + | 0.0266625i | ||||
\(487\) | −19.1803 | − | 13.9353i | −0.869144 | − | 0.631470i | 0.0612130 | − | 0.998125i | \(-0.480503\pi\) |
−0.930357 | + | 0.366655i | \(0.880503\pi\) | |||||||
\(488\) | −1.73607 | − | 1.26133i | −0.0785881 | − | 0.0570976i | ||||
\(489\) | 9.32624 | − | 6.77591i | 0.421747 | − | 0.306417i | ||||
\(490\) | −5.42705 | − | 3.94298i | −0.245169 | − | 0.178126i | ||||
\(491\) | 4.76393 | + | 3.46120i | 0.214993 | + | 0.156202i | 0.690070 | − | 0.723743i | \(-0.257580\pi\) |
−0.475077 | + | 0.879944i | \(0.657580\pi\) | |||||||
\(492\) | −1.57295 | − | 4.84104i | −0.0709140 | − | 0.218251i | ||||
\(493\) | −4.14590 | −0.186722 | ||||||||
\(494\) | 4.14590 | + | 12.7598i | 0.186533 | + | 0.574089i | ||||
\(495\) | −0.527864 | − | 1.62460i | −0.0237257 | − | 0.0730203i | ||||
\(496\) | −3.00000 | + | 9.23305i | −0.134704 | + | 0.414576i | ||||
\(497\) | 5.05573 | − | 15.5599i | 0.226780 | − | 0.697958i | ||||
\(498\) | −4.85410 | + | 3.52671i | −0.217518 | + | 0.158036i | ||||
\(499\) | −6.58359 | −0.294722 | −0.147361 | − | 0.989083i | \(-0.547078\pi\) | ||||
−0.147361 | + | 0.989083i | \(0.547078\pi\) | |||||||
\(500\) | −9.04508 | + | 6.57164i | −0.404508 | + | 0.293893i | ||||
\(501\) | 2.47214 | 0.110447 | ||||||||
\(502\) | −2.85410 | + | 2.07363i | −0.127385 | + | 0.0925505i | ||||
\(503\) | 9.41641 | − | 28.9807i | 0.419857 | − | 1.29219i | −0.487977 | − | 0.872857i | \(-0.662265\pi\) |
0.907834 | − | 0.419330i | \(-0.137735\pi\) | |||||||
\(504\) | −0.618034 | + | 1.90211i | −0.0275294 | + | 0.0847268i | ||||
\(505\) | 11.9721 | + | 36.8464i | 0.532753 | + | 1.63965i | ||||
\(506\) | 1.41641 | + | 4.35926i | 0.0629670 | + | 0.193793i | ||||
\(507\) | 9.56231 | 0.424677 | ||||||||
\(508\) | 4.23607 | + | 13.0373i | 0.187945 | + | 0.578436i | ||||
\(509\) | −23.2533 | − | 16.8945i | −1.03068 | − | 0.748836i | −0.0622385 | − | 0.998061i | \(-0.519824\pi\) |
−0.968445 | + | 0.249226i | \(0.919824\pi\) | |||||||
\(510\) | −2.07295 | − | 1.50609i | −0.0917917 | − | 0.0666906i | ||||
\(511\) | 15.9443 | − | 11.5842i | 0.705333 | − | 0.512454i | ||||
\(512\) | 0.809017 | + | 0.587785i | 0.0357538 | + | 0.0259767i | ||||
\(513\) | −5.85410 | − | 4.25325i | −0.258465 | − | 0.187786i | ||||
\(514\) | −7.59017 | + | 5.51458i | −0.334788 | + | 0.243238i | ||||
\(515\) | −35.1246 | −1.54778 | ||||||||
\(516\) | 2.61803 | + | 1.90211i | 0.115253 | + | 0.0837359i | ||||
\(517\) | −2.18034 | − | 6.71040i | −0.0958912 | − | 0.295123i | ||||
\(518\) | 17.7082 | 0.778054 | ||||||||
\(519\) | 6.82624 | + | 21.0090i | 0.299639 | + | 0.922193i | ||||
\(520\) | −4.14590 | −0.181810 | ||||||||
\(521\) | −8.42705 | + | 25.9358i | −0.369196 | + | 1.13627i | 0.578116 | + | 0.815955i | \(0.303788\pi\) |
−0.947312 | + | 0.320313i | \(0.896212\pi\) | |||||||
\(522\) | 1.11803 | − | 3.44095i | 0.0489350 | − | 0.150607i | ||||
\(523\) | 12.7082 | − | 9.23305i | 0.555691 | − | 0.403733i | −0.274188 | − | 0.961676i | \(-0.588409\pi\) |
0.829879 | + | 0.557943i | \(0.188409\pi\) | |||||||
\(524\) | −5.23607 | −0.228739 | ||||||||
\(525\) | −3.09017 | − | 9.51057i | −0.134866 | − | 0.415075i | ||||
\(526\) | 8.47214 | 0.369403 | ||||||||
\(527\) | 9.00000 | − | 6.53888i | 0.392046 | − | 0.284838i | ||||
\(528\) | 0.236068 | − | 0.726543i | 0.0102735 | − | 0.0316187i | ||||
\(529\) | 4.01722 | − | 12.3637i | 0.174662 | − | 0.537554i | ||||
\(530\) | −20.9164 | + | 15.1967i | −0.908551 | + | 0.660101i | ||||
\(531\) | −2.76393 | − | 8.50651i | −0.119944 | − | 0.369151i | ||||
\(532\) | −14.4721 | −0.627447 | ||||||||
\(533\) | 2.91641 | + | 8.97578i | 0.126324 | + | 0.388784i | ||||
\(534\) | −2.92705 | − | 2.12663i | −0.126666 | − | 0.0920282i | ||||
\(535\) | −4.79837 | − | 14.7679i | −0.207452 | − | 0.638471i | ||||
\(536\) | 3.00000 | − | 2.17963i | 0.129580 | − | 0.0941456i | ||||
\(537\) | −21.1803 | − | 15.3884i | −0.913999 | − | 0.664059i | ||||
\(538\) | −10.5902 | − | 7.69421i | −0.456575 | − | 0.331721i | ||||
\(539\) | −1.85410 | + | 1.34708i | −0.0798618 | + | 0.0580230i | ||||
\(540\) | 1.80902 | − | 1.31433i | 0.0778477 | − | 0.0565597i | ||||
\(541\) | 9.92705 | + | 7.21242i | 0.426797 | + | 0.310086i | 0.780367 | − | 0.625322i | \(-0.215032\pi\) |
−0.353570 | + | 0.935408i | \(0.615032\pi\) | |||||||
\(542\) | −1.79837 | − | 5.53483i | −0.0772468 | − | 0.237741i | ||||
\(543\) | −9.03444 | −0.387705 | ||||||||
\(544\) | −0.354102 | − | 1.08981i | −0.0151820 | − | 0.0467254i | ||||
\(545\) | −12.1353 | + | 37.3485i | −0.519817 | + | 1.59983i | ||||
\(546\) | 1.14590 | − | 3.52671i | 0.0490399 | − | 0.150929i | ||||
\(547\) | 0.618034 | − | 1.90211i | 0.0264252 | − | 0.0813285i | −0.936974 | − | 0.349399i | \(-0.886386\pi\) |
0.963399 | + | 0.268070i | \(0.0863859\pi\) | |||||||
\(548\) | −11.3541 | + | 8.24924i | −0.485023 | + | 0.352390i | ||||
\(549\) | −2.14590 | −0.0915847 | ||||||||
\(550\) | 1.18034 | + | 3.63271i | 0.0503299 | + | 0.154899i | ||||
\(551\) | 26.1803 | 1.11532 | ||||||||
\(552\) | −4.85410 | + | 3.52671i | −0.206604 | + | 0.150107i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8.91641 | − | 27.4419i | 0.378822 | − | 1.16589i | ||||
\(555\) | −16.0172 | − | 11.6372i | −0.679893 | − | 0.493971i | ||||
\(556\) | 4.14590 | + | 12.7598i | 0.175825 | + | 0.541134i | ||||
\(557\) | 6.27051 | 0.265690 | 0.132845 | − | 0.991137i | \(-0.457589\pi\) | ||||
0.132845 | + | 0.991137i | \(0.457589\pi\) | |||||||
\(558\) | 3.00000 | + | 9.23305i | 0.127000 | + | 0.390866i | ||||
\(559\) | −4.85410 | − | 3.52671i | −0.205307 | − | 0.149164i | ||||
\(560\) | 1.38197 | − | 4.25325i | 0.0583987 | − | 0.179733i | ||||
\(561\) | −0.708204 | + | 0.514540i | −0.0299004 | + | 0.0217239i | ||||
\(562\) | 4.11803 | + | 2.99193i | 0.173709 | + | 0.126207i | ||||
\(563\) | −1.23607 | − | 0.898056i | −0.0520941 | − | 0.0378485i | 0.561434 | − | 0.827522i | \(-0.310250\pi\) |
−0.613528 | + | 0.789673i | \(0.710250\pi\) | |||||||
\(564\) | 7.47214 | − | 5.42882i | 0.314634 | − | 0.228595i | ||||
\(565\) | 5.91641 | − | 18.2088i | 0.248905 | − | 0.766051i | ||||
\(566\) | −1.00000 | − | 0.726543i | −0.0420331 | − | 0.0305389i | ||||
\(567\) | 0.618034 | + | 1.90211i | 0.0259550 | + | 0.0798812i | ||||
\(568\) | −8.18034 | −0.343239 | ||||||||
\(569\) | 7.29837 | + | 22.4621i | 0.305964 | + | 0.941660i | 0.979316 | + | 0.202338i | \(0.0648538\pi\) |
−0.673352 | + | 0.739322i | \(0.735146\pi\) | |||||||
\(570\) | 13.0902 | + | 9.51057i | 0.548287 | + | 0.398354i | ||||
\(571\) | 6.27051 | − | 19.2986i | 0.262413 | − | 0.807623i | −0.729866 | − | 0.683591i | \(-0.760417\pi\) |
0.992278 | − | 0.124032i | \(-0.0395827\pi\) | |||||||
\(572\) | −0.437694 | + | 1.34708i | −0.0183009 | + | 0.0563244i | ||||
\(573\) | −4.23607 | + | 3.07768i | −0.176964 | + | 0.128572i | ||||
\(574\) | −10.1803 | −0.424919 | ||||||||
\(575\) | 9.27051 | − | 28.5317i | 0.386607 | − | 1.18985i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 20.0902 | − | 14.5964i | 0.836365 | − | 0.607655i | −0.0849881 | − | 0.996382i | \(-0.527085\pi\) |
0.921353 | + | 0.388727i | \(0.127085\pi\) | |||||||
\(578\) | 4.84752 | − | 14.9191i | 0.201630 | − | 0.620555i | ||||
\(579\) | −1.42705 | + | 4.39201i | −0.0593062 | + | 0.182526i | ||||
\(580\) | −2.50000 | + | 7.69421i | −0.103807 | + | 0.319485i | ||||
\(581\) | 3.70820 | + | 11.4127i | 0.153842 | + | 0.473478i | ||||
\(582\) | −7.14590 | −0.296207 | ||||||||
\(583\) | 2.72949 | + | 8.40051i | 0.113044 | + | 0.347913i | ||||
\(584\) | −7.97214 | − | 5.79210i | −0.329889 | − | 0.239679i | ||||
\(585\) | −3.35410 | + | 2.43690i | −0.138675 | + | 0.100753i | ||||
\(586\) | −3.39919 | + | 2.46965i | −0.140419 | + | 0.102020i | ||||
\(587\) | −16.0902 | − | 11.6902i | −0.664112 | − | 0.482506i | 0.203937 | − | 0.978984i | \(-0.434626\pi\) |
−0.868049 | + | 0.496478i | \(0.834626\pi\) | |||||||
\(588\) | −2.42705 | − | 1.76336i | −0.100090 | − | 0.0727196i | ||||
\(589\) | −56.8328 | + | 41.2915i | −2.34176 | + | 1.70138i | ||||
\(590\) | 6.18034 | + | 19.0211i | 0.254441 | + | 0.783088i | ||||
\(591\) | 1.88197 | + | 1.36733i | 0.0774137 | + | 0.0562444i | ||||
\(592\) | −2.73607 | − | 8.42075i | −0.112452 | − | 0.346091i | ||||
\(593\) | 23.0344 | 0.945911 | 0.472956 | − | 0.881086i | \(-0.343187\pi\) | ||||
0.472956 | + | 0.881086i | \(0.343187\pi\) | |||||||
\(594\) | −0.236068 | − | 0.726543i | −0.00968599 | − | 0.0298104i | ||||
\(595\) | −4.14590 | + | 3.01217i | −0.169965 | + | 0.123487i | ||||
\(596\) | −6.80902 | + | 20.9560i | −0.278908 | + | 0.858391i | ||||
\(597\) | −5.00000 | + | 15.3884i | −0.204636 | + | 0.629806i | ||||
\(598\) | 9.00000 | − | 6.53888i | 0.368037 | − | 0.267395i | ||||
\(599\) | 18.9443 | 0.774042 | 0.387021 | − | 0.922071i | \(-0.373504\pi\) | ||||
0.387021 | + | 0.922071i | \(0.373504\pi\) | |||||||
\(600\) | −4.04508 | + | 2.93893i | −0.165140 | + | 0.119981i | ||||
\(601\) | −8.32624 | −0.339634 | −0.169817 | − | 0.985476i | \(-0.554318\pi\) | ||||
−0.169817 | + | 0.985476i | \(0.554318\pi\) | |||||||
\(602\) | 5.23607 | − | 3.80423i | 0.213406 | − | 0.155049i | ||||
\(603\) | 1.14590 | − | 3.52671i | 0.0466646 | − | 0.143619i | ||||
\(604\) | 3.38197 | − | 10.4086i | 0.137610 | − | 0.423521i | ||||
\(605\) | −23.2918 | −0.946946 | ||||||||
\(606\) | 5.35410 | + | 16.4782i | 0.217496 | + | 0.669382i | ||||
\(607\) | −24.1803 | −0.981450 | −0.490725 | − | 0.871315i | \(-0.663268\pi\) | ||||
−0.490725 | + | 0.871315i | \(0.663268\pi\) | |||||||
\(608\) | 2.23607 | + | 6.88191i | 0.0906845 | + | 0.279098i | ||||
\(609\) | −5.85410 | − | 4.25325i | −0.237220 | − | 0.172351i | ||||
\(610\) | 4.79837 | 0.194280 | ||||||||
\(611\) | −13.8541 | + | 10.0656i | −0.560477 | + | 0.407210i | ||||
\(612\) | −0.927051 | − | 0.673542i | −0.0374738 | − | 0.0272263i | ||||
\(613\) | 1.16312 | + | 0.845055i | 0.0469779 | + | 0.0341315i | 0.611026 | − | 0.791610i | \(-0.290757\pi\) |
−0.564048 | + | 0.825742i | \(0.690757\pi\) | |||||||
\(614\) | −24.0344 | + | 17.4620i | −0.969951 | + | 0.704711i | ||||
\(615\) | 9.20820 | + | 6.69015i | 0.371311 | + | 0.269773i | ||||
\(616\) | −1.23607 | − | 0.898056i | −0.0498026 | − | 0.0361837i | ||||
\(617\) | 3.28115 | + | 10.0984i | 0.132094 | + | 0.406544i | 0.995127 | − | 0.0986041i | \(-0.0314378\pi\) |
−0.863032 | + | 0.505148i | \(0.831438\pi\) | |||||||
\(618\) | −15.7082 | −0.631877 | ||||||||
\(619\) | −7.23607 | − | 22.2703i | −0.290842 | − | 0.895120i | −0.984586 | − | 0.174899i | \(-0.944040\pi\) |
0.693744 | − | 0.720221i | \(-0.255960\pi\) | |||||||
\(620\) | −6.70820 | − | 20.6457i | −0.269408 | − | 0.829152i | ||||
\(621\) | −1.85410 | + | 5.70634i | −0.0744025 | + | 0.228988i | ||||
\(622\) | −3.90983 | + | 12.0332i | −0.156770 | + | 0.482488i | ||||
\(623\) | −5.85410 | + | 4.25325i | −0.234540 | + | 0.170403i | ||||
\(624\) | −1.85410 | −0.0742235 | ||||||||
\(625\) | 7.72542 | − | 23.7764i | 0.309017 | − | 0.951057i | ||||
\(626\) | −18.3607 | −0.733840 | ||||||||
\(627\) | 4.47214 | − | 3.24920i | 0.178600 | − | 0.129760i | ||||
\(628\) | 3.44427 | − | 10.6004i | 0.137441 | − | 0.423001i | ||||
\(629\) | −3.13525 | + | 9.64932i | −0.125011 | + | 0.384744i | ||||
\(630\) | −1.38197 | − | 4.25325i | −0.0550588 | − | 0.169454i | ||||
\(631\) | −0.888544 | − | 2.73466i | −0.0353724 | − | 0.108865i | 0.931811 | − | 0.362943i | \(-0.118228\pi\) |
−0.967184 | + | 0.254078i | \(0.918228\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.47214 | + | 7.60845i | 0.0982586 | + | 0.302409i | ||||
\(634\) | 8.85410 | + | 6.43288i | 0.351641 | + | 0.255482i | ||||
\(635\) | −24.7984 | − | 18.0171i | −0.984093 | − | 0.714986i | ||||
\(636\) | −9.35410 | + | 6.79615i | −0.370914 | + | 0.269485i | ||||
\(637\) | 4.50000 | + | 3.26944i | 0.178296 | + | 0.129540i | ||||
\(638\) | 2.23607 | + | 1.62460i | 0.0885268 | + | 0.0643185i | ||||
\(639\) | −6.61803 | + | 4.80828i | −0.261805 | + | 0.190213i | ||||
\(640\) | −2.23607 | −0.0883883 | ||||||||
\(641\) | 7.32624 | + | 5.32282i | 0.289369 | + | 0.210239i | 0.722994 | − | 0.690855i | \(-0.242766\pi\) |
−0.433625 | + | 0.901094i | \(0.642766\pi\) | |||||||
\(642\) | −2.14590 | − | 6.60440i | −0.0846918 | − | 0.260655i | ||||
\(643\) | 31.7771 | 1.25317 | 0.626583 | − | 0.779355i | \(-0.284453\pi\) | ||||
0.626583 | + | 0.779355i | \(0.284453\pi\) | |||||||
\(644\) | 3.70820 | + | 11.4127i | 0.146124 | + | 0.449723i | ||||
\(645\) | −7.23607 | −0.284920 | ||||||||
\(646\) | 2.56231 | − | 7.88597i | 0.100813 | − | 0.310269i | ||||
\(647\) | −0.0344419 | + | 0.106001i | −0.00135405 | + | 0.00416733i | −0.951731 | − | 0.306933i | \(-0.900697\pi\) |
0.950377 | + | 0.311100i | \(0.100697\pi\) | |||||||
\(648\) | 0.809017 | − | 0.587785i | 0.0317812 | − | 0.0230904i | ||||
\(649\) | 6.83282 | 0.268211 | ||||||||
\(650\) | 7.50000 | − | 5.44907i | 0.294174 | − | 0.213730i | ||||
\(651\) | 19.4164 | 0.760989 | ||||||||
\(652\) | −9.32624 | + | 6.77591i | −0.365244 | + | 0.265365i | ||||
\(653\) | 5.93769 | − | 18.2743i | 0.232360 | − | 0.715130i | −0.765101 | − | 0.643911i | \(-0.777311\pi\) |
0.997461 | − | 0.0712197i | \(-0.0226891\pi\) | |||||||
\(654\) | −5.42705 | + | 16.7027i | −0.212214 | + | 0.653129i | ||||
\(655\) | 9.47214 | − | 6.88191i | 0.370107 | − | 0.268898i | ||||
\(656\) | 1.57295 | + | 4.84104i | 0.0614133 | + | 0.189011i | ||||
\(657\) | −9.85410 | −0.384445 | ||||||||
\(658\) | −5.70820 | − | 17.5680i | −0.222529 | − | 0.684874i | ||||
\(659\) | −17.0344 | − | 12.3762i | −0.663568 | − | 0.482110i | 0.204298 | − | 0.978909i | \(-0.434509\pi\) |
−0.867866 | + | 0.496799i | \(0.834509\pi\) | |||||||
\(660\) | 0.527864 | + | 1.62460i | 0.0205471 | + | 0.0632374i | ||||
\(661\) | 26.2705 | − | 19.0866i | 1.02180 | − | 0.742384i | 0.0551524 | − | 0.998478i | \(-0.482436\pi\) |
0.966652 | + | 0.256094i | \(0.0824355\pi\) | |||||||
\(662\) | −19.0344 | − | 13.8293i | −0.739795 | − | 0.537492i | ||||
\(663\) | 1.71885 | + | 1.24882i | 0.0667545 | + | 0.0485000i | ||||
\(664\) | 4.85410 | − | 3.52671i | 0.188376 | − | 0.136863i | ||||
\(665\) | 26.1803 | − | 19.0211i | 1.01523 | − | 0.737608i | ||||
\(666\) | −7.16312 | − | 5.20431i | −0.277565 | − | 0.201663i | ||||
\(667\) | −6.70820 | − | 20.6457i | −0.259743 | − | 0.799406i | ||||
\(668\) | −2.47214 | −0.0956498 | ||||||||
\(669\) | 4.85410 | + | 14.9394i | 0.187670 | + | 0.577590i | ||||
\(670\) | −2.56231 | + | 7.88597i | −0.0989905 | + | 0.304661i | ||||
\(671\) | 0.506578 | − | 1.55909i | 0.0195562 | − | 0.0601879i | ||||
\(672\) | 0.618034 | − | 1.90211i | 0.0238412 | − | 0.0733756i | ||||
\(673\) | −4.69098 | + | 3.40820i | −0.180824 | + | 0.131376i | −0.674515 | − | 0.738261i | \(-0.735647\pi\) |
0.493691 | + | 0.869637i | \(0.335647\pi\) | |||||||
\(674\) | 24.8328 | 0.956524 | ||||||||
\(675\) | −1.54508 | + | 4.75528i | −0.0594703 | + | 0.183031i | ||||
\(676\) | −9.56231 | −0.367781 | ||||||||
\(677\) | −22.2705 | + | 16.1805i | −0.855925 | + | 0.621866i | −0.926773 | − | 0.375621i | \(-0.877429\pi\) |
0.0708481 | + | 0.997487i | \(0.477429\pi\) | |||||||
\(678\) | 2.64590 | − | 8.14324i | 0.101615 | − | 0.312739i | ||||
\(679\) | −4.41641 | + | 13.5923i | −0.169486 | + | 0.521625i | ||||
\(680\) | 2.07295 | + | 1.50609i | 0.0794940 | + | 0.0577557i | ||||
\(681\) | −0.291796 | − | 0.898056i | −0.0111816 | − | 0.0344136i | ||||
\(682\) | −7.41641 | −0.283989 | ||||||||
\(683\) | −2.29180 | − | 7.05342i | −0.0876931 | − | 0.269892i | 0.897588 | − | 0.440836i | \(-0.145318\pi\) |
−0.985281 | + | 0.170945i | \(0.945318\pi\) | |||||||
\(684\) | 5.85410 | + | 4.25325i | 0.223837 | + | 0.162627i | ||||
\(685\) | 9.69756 | − | 29.8460i | 0.370525 | − | 1.14036i | ||||
\(686\) | −16.1803 | + | 11.7557i | −0.617768 | + | 0.448835i | ||||
\(687\) | 7.50000 | + | 5.44907i | 0.286143 | + | 0.207895i | ||||
\(688\) | −2.61803 | − | 1.90211i | −0.0998116 | − | 0.0725174i | ||||
\(689\) | 17.3435 | − | 12.6008i | 0.660733 | − | 0.480051i | ||||
\(690\) | 4.14590 | − | 12.7598i | 0.157832 | − | 0.485756i | ||||
\(691\) | 1.47214 | + | 1.06957i | 0.0560027 | + | 0.0406883i | 0.615434 | − | 0.788188i | \(-0.288981\pi\) |
−0.559432 | + | 0.828876i | \(0.688981\pi\) | |||||||
\(692\) | −6.82624 | − | 21.0090i | −0.259495 | − | 0.798642i | ||||
\(693\) | −1.52786 | −0.0580388 | ||||||||
\(694\) | 0.236068 | + | 0.726543i | 0.00896102 | + | 0.0275792i | ||||
\(695\) | −24.2705 | − | 17.6336i | −0.920633 | − | 0.668879i | ||||
\(696\) | −1.11803 | + | 3.44095i | −0.0423790 | + | 0.130429i | ||||
\(697\) | 1.80244 | − | 5.54734i | 0.0682723 | − | 0.210120i | ||||
\(698\) | −7.92705 | + | 5.75934i | −0.300043 | + | 0.217994i | ||||
\(699\) | 10.9098 | 0.412648 | ||||||||
\(700\) | 3.09017 | + | 9.51057i | 0.116797 | + | 0.359466i | ||||
\(701\) | 49.1591 | 1.85671 | 0.928356 | − | 0.371692i | \(-0.121222\pi\) | ||||
0.928356 | + | 0.371692i | \(0.121222\pi\) | |||||||
\(702\) | −1.50000 | + | 1.08981i | −0.0566139 | + | 0.0411324i | ||||
\(703\) | 19.7984 | − | 60.9331i | 0.746710 | − | 2.29814i | ||||
\(704\) | −0.236068 | + | 0.726543i | −0.00889715 | + | 0.0273826i | ||||
\(705\) | −6.38197 | + | 19.6417i | −0.240359 | + | 0.739748i | ||||
\(706\) | −3.56231 | − | 10.9637i | −0.134069 | − | 0.412622i | ||||
\(707\) | 34.6525 | 1.30324 | ||||||||
\(708\) | 2.76393 | + | 8.50651i | 0.103875 | + | 0.319694i | ||||
\(709\) | 4.20820 | + | 3.05744i | 0.158042 | + | 0.114825i | 0.663996 | − | 0.747736i | \(-0.268859\pi\) |
−0.505953 | + | 0.862561i | \(0.668859\pi\) | |||||||
\(710\) | 14.7984 | − | 10.7516i | 0.555373 | − | 0.403502i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.92705 | + | 2.12663i | 0.109696 | + | 0.0796987i | ||||
\(713\) | 47.1246 | + | 34.2380i | 1.76483 | + | 1.28222i | ||||
\(714\) | −1.85410 | + | 1.34708i | −0.0693880 | + | 0.0504133i | ||||
\(715\) | −0.978714 | − | 3.01217i | −0.0366018 | − | 0.112649i | ||||
\(716\) | 21.1803 | + | 15.3884i | 0.791546 | + | 0.575092i | ||||
\(717\) | 8.29180 | + | 25.5195i | 0.309663 | + | 0.953044i | ||||
\(718\) | −7.88854 | −0.294398 | ||||||||
\(719\) | −6.90983 | − | 21.2663i | −0.257693 | − | 0.793098i | −0.993287 | − | 0.115675i | \(-0.963097\pi\) |
0.735594 | − | 0.677423i | \(-0.236903\pi\) | |||||||
\(720\) | −1.80902 | + | 1.31433i | −0.0674181 | + | 0.0489821i | ||||
\(721\) | −9.70820 | + | 29.8788i | −0.361552 | + | 1.11274i | ||||
\(722\) | −10.3090 | + | 31.7279i | −0.383662 | + | 1.18079i | ||||
\(723\) | −5.78115 | + | 4.20025i | −0.215003 | + | 0.156209i | ||||
\(724\) | 9.03444 | 0.335762 | ||||||||
\(725\) | −5.59017 | − | 17.2048i | −0.207614 | − | 0.638969i | ||||
\(726\) | −10.4164 | −0.386589 | ||||||||
\(727\) | −19.1803 | + | 13.9353i | −0.711359 | + | 0.516833i | −0.883612 | − | 0.468220i | \(-0.844895\pi\) |
0.172253 | + | 0.985053i | \(0.444895\pi\) | |||||||
\(728\) | −1.14590 | + | 3.52671i | −0.0424698 | + | 0.130709i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | 22.0344 | 0.815531 | ||||||||
\(731\) | 1.14590 | + | 3.52671i | 0.0423826 | + | 0.130440i | ||||
\(732\) | 2.14590 | 0.0793147 | ||||||||
\(733\) | 11.8541 | + | 36.4832i | 0.437841 | + | 1.34754i | 0.890147 | + | 0.455674i | \(0.150602\pi\) |
−0.452306 | + | 0.891863i | \(0.649398\pi\) | |||||||
\(734\) | −2.85410 | − | 2.07363i | −0.105347 | − | 0.0765389i | ||||
\(735\) | 6.70820 | 0.247436 | ||||||||
\(736\) | 4.85410 | − | 3.52671i | 0.178925 | − | 0.129996i | ||||
\(737\) | 2.29180 | + | 1.66509i | 0.0844194 | + | 0.0613343i | ||||
\(738\) | 4.11803 | + | 2.99193i | 0.151587 | + | 0.110134i | ||||
\(739\) | −17.5623 | + | 12.7598i | −0.646040 | + | 0.469375i | −0.861920 | − | 0.507044i | \(-0.830738\pi\) |
0.215880 | + | 0.976420i | \(0.430738\pi\) | |||||||
\(740\) | 16.0172 | + | 11.6372i | 0.588805 | + | 0.427792i | ||||
\(741\) | −10.8541 | − | 7.88597i | −0.398735 | − | 0.289698i | ||||
\(742\) | 7.14590 | + | 21.9928i | 0.262334 | + | 0.807382i | ||||
\(743\) | −24.6525 | −0.904412 | −0.452206 | − | 0.891914i | \(-0.649363\pi\) | ||||
−0.452206 | + | 0.891914i | \(0.649363\pi\) | |||||||
\(744\) | −3.00000 | − | 9.23305i | −0.109985 | − | 0.338500i | ||||
\(745\) | −15.2254 | − | 46.8590i | −0.557816 | − | 1.71678i | ||||
\(746\) | −9.09017 | + | 27.9767i | −0.332815 | + | 1.02430i | ||||
\(747\) | 1.85410 | − | 5.70634i | 0.0678380 | − | 0.208784i | ||||
\(748\) | 0.708204 | − | 0.514540i | 0.0258945 | − | 0.0188135i | ||||
\(749\) | −13.8885 | −0.507476 | ||||||||
\(750\) | 3.45492 | − | 10.6331i | 0.126156 | − | 0.388267i | ||||
\(751\) | 19.2361 | 0.701934 | 0.350967 | − | 0.936388i | \(-0.385853\pi\) | ||||
0.350967 | + | 0.936388i | \(0.385853\pi\) | |||||||
\(752\) | −7.47214 | + | 5.42882i | −0.272481 | + | 0.197969i | ||||
\(753\) | 1.09017 | − | 3.35520i | 0.0397280 | − | 0.122270i | ||||
\(754\) | 2.07295 | − | 6.37988i | 0.0754924 | − | 0.232342i | ||||
\(755\) | 7.56231 | + | 23.2744i | 0.275220 | + | 0.847042i | ||||
\(756\) | −0.618034 | − | 1.90211i | −0.0224777 | − | 0.0691792i | ||||
\(757\) | −22.1459 | −0.804906 | −0.402453 | − | 0.915441i | \(-0.631842\pi\) | ||||
−0.402453 | + | 0.915441i | \(0.631842\pi\) | |||||||
\(758\) | −7.23607 | − | 22.2703i | −0.262826 | − | 0.808895i | ||||
\(759\) | −3.70820 | − | 2.69417i | −0.134599 | − | 0.0977921i | ||||
\(760\) | −13.0902 | − | 9.51057i | −0.474830 | − | 0.344984i | ||||
\(761\) | 36.5344 | − | 26.5438i | 1.32437 | − | 0.962213i | 0.324506 | − | 0.945884i | \(-0.394802\pi\) |
0.999867 | − | 0.0163292i | \(-0.00519799\pi\) | |||||||
\(762\) | −11.0902 | − | 8.05748i | −0.401754 | − | 0.291892i | ||||
\(763\) | 28.4164 | + | 20.6457i | 1.02874 | + | 0.747426i | ||||
\(764\) | 4.23607 | − | 3.07768i | 0.153256 | − | 0.111347i | ||||
\(765\) | 2.56231 | 0.0926404 | ||||||||
\(766\) | 9.32624 | + | 6.77591i | 0.336971 | + | 0.244824i | ||||
\(767\) | −5.12461 | − | 15.7719i | −0.185039 | − | 0.569492i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 13.0902 | + | 40.2874i | 0.472044 | + | 1.45280i | 0.849904 | + | 0.526938i | \(0.176660\pi\) |
−0.377860 | + | 0.925863i | \(0.623340\pi\) | |||||||
\(770\) | 3.41641 | 0.123119 | ||||||||
\(771\) | 2.89919 | − | 8.92278i | 0.104412 | − | 0.321346i | ||||
\(772\) | 1.42705 | − | 4.39201i | 0.0513607 | − | 0.158072i | ||||
\(773\) | −2.35410 | + | 1.71036i | −0.0846712 | + | 0.0615172i | −0.629315 | − | 0.777150i | \(-0.716665\pi\) |
0.544644 | + | 0.838667i | \(0.316665\pi\) | |||||||
\(774\) | −3.23607 | −0.116318 | ||||||||
\(775\) | 39.2705 | + | 28.5317i | 1.41064 | + | 1.02489i | ||||
\(776\) | 7.14590 | 0.256523 | ||||||||
\(777\) | −14.3262 | + | 10.4086i | −0.513951 | + | 0.373407i | ||||
\(778\) | 9.57295 | − | 29.4625i | 0.343207 | − | 1.05628i | ||||
\(779\) | −11.3820 | + | 35.0301i | −0.407801 | + | 1.25508i | ||||
\(780\) | 3.35410 | − | 2.43690i | 0.120096 | − | 0.0872549i | ||||
\(781\) | −1.93112 | − | 5.94336i | −0.0691008 | − | 0.212670i | ||||
\(782\) | −6.87539 | −0.245863 | ||||||||
\(783\) | 1.11803 | + | 3.44095i | 0.0399553 | + | 0.122970i | ||||
\(784\) | 2.42705 | + | 1.76336i | 0.0866804 | + | 0.0629770i | ||||
\(785\) | 7.70163 | + | 23.7032i | 0.274883 | + | 0.846002i | ||||
\(786\) | 4.23607 | − | 3.07768i | 0.151096 | − | 0.109777i | ||||
\(787\) | 29.5623 | + | 21.4783i | 1.05378 | + | 0.765618i | 0.972928 | − | 0.231108i | \(-0.0742351\pi\) |
0.0808543 | + | 0.996726i | \(0.474235\pi\) | |||||||
\(788\) | −1.88197 | − | 1.36733i | −0.0670423 | − | 0.0487091i | ||||
\(789\) | −6.85410 | + | 4.97980i | −0.244012 | + | 0.177285i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.8541 | − | 10.0656i | −0.492595 | − | 0.357891i | ||||
\(792\) | 0.236068 | + | 0.726543i | 0.00838831 | + | 0.0258166i | ||||
\(793\) | −3.97871 | −0.141288 | ||||||||
\(794\) | 7.67376 | + | 23.6174i | 0.272332 | + | 0.838151i | ||||
\(795\) | 7.98936 | − | 24.5887i | 0.283353 | − | 0.872072i | ||||
\(796\) | 5.00000 | − | 15.3884i | 0.177220 | − | 0.545428i | ||||
\(797\) | 0.718847 | − | 2.21238i | 0.0254629 | − | 0.0783667i | −0.937518 | − | 0.347938i | \(-0.886882\pi\) |
0.962980 | + | 0.269571i | \(0.0868820\pi\) | |||||||
\(798\) | 11.7082 | − | 8.50651i | 0.414466 | − | 0.301127i | ||||
\(799\) | 10.5836 | 0.374421 | ||||||||
\(800\) | 4.04508 | − | 2.93893i | 0.143015 | − | 0.103907i | ||||
\(801\) | 3.61803 | 0.127837 | ||||||||
\(802\) | −12.0623 | + | 8.76378i | −0.425935 | + | 0.309460i | ||||
\(803\) | 2.32624 | − | 7.15942i | 0.0820912 | − | 0.252651i | ||||
\(804\) | −1.14590 | + | 3.52671i | −0.0404127 | + | 0.124378i | ||||
\(805\) | −21.7082 | − | 15.7719i | −0.765114 | − | 0.555888i | ||||
\(806\) | 5.56231 | + | 17.1190i | 0.195924 | + | 0.602992i | ||||
\(807\) | 13.0902 | 0.460796 | ||||||||
\(808\) | −5.35410 | − | 16.4782i | −0.188357 | − | 0.579702i | ||||
\(809\) | 34.9615 | + | 25.4010i | 1.22918 | + | 0.893052i | 0.996829 | − | 0.0795797i | \(-0.0253578\pi\) |
0.232352 | + | 0.972632i | \(0.425358\pi\) | |||||||
\(810\) | −0.690983 | + | 2.12663i | −0.0242787 | + | 0.0747221i | ||||
\(811\) | −19.1803 | + | 13.9353i | −0.673513 | + | 0.489336i | −0.871199 | − | 0.490930i | \(-0.836657\pi\) |
0.197686 | + | 0.980265i | \(0.436657\pi\) | |||||||
\(812\) | 5.85410 | + | 4.25325i | 0.205439 | + | 0.149260i | ||||
\(813\) | 4.70820 | + | 3.42071i | 0.165124 | + | 0.119970i | ||||
\(814\) | 5.47214 | − | 3.97574i | 0.191798 | − | 0.139350i | ||||
\(815\) | 7.96556 | − | 24.5155i | 0.279021 | − | 0.858739i | ||||
\(816\) | 0.927051 | + | 0.673542i | 0.0324533 | + | 0.0235787i | ||||
\(817\) | −7.23607 | − | 22.2703i | −0.253158 | − | 0.779140i | ||||
\(818\) | 25.9787 | 0.908324 | ||||||||
\(819\) | 1.14590 | + | 3.52671i | 0.0400409 | + | 0.123233i | ||||
\(820\) | −9.20820 | − | 6.69015i | −0.321564 | − | 0.233630i | ||||
\(821\) | 2.72949 | − | 8.40051i | 0.0952599 | − | 0.293180i | −0.892061 | − | 0.451914i | \(-0.850741\pi\) |
0.987321 | + | 0.158734i | \(0.0507413\pi\) | |||||||
\(822\) | 4.33688 | − | 13.3475i | 0.151266 | − | 0.465549i | ||||
\(823\) | −20.7082 | + | 15.0454i | −0.721843 | + | 0.524449i | −0.886972 | − | 0.461822i | \(-0.847196\pi\) |
0.165130 | + | 0.986272i | \(0.447196\pi\) | |||||||
\(824\) | 15.7082 | 0.547221 | ||||||||
\(825\) | −3.09017 | − | 2.24514i | −0.107586 | − | 0.0781657i | ||||
\(826\) | 17.8885 | 0.622422 | ||||||||
\(827\) | −15.5623 | + | 11.3067i | −0.541154 | + | 0.393172i | −0.824514 | − | 0.565842i | \(-0.808551\pi\) |
0.283359 | + | 0.959014i | \(0.408551\pi\) | |||||||
\(828\) | 1.85410 | − | 5.70634i | 0.0644345 | − | 0.198309i | ||||
\(829\) | 14.1697 | − | 43.6098i | 0.492134 | − | 1.51463i | −0.329242 | − | 0.944245i | \(-0.606793\pi\) |
0.821376 | − | 0.570387i | \(-0.193207\pi\) | |||||||
\(830\) | −4.14590 | + | 12.7598i | −0.143906 | + | 0.442898i | ||||
\(831\) | 8.91641 | + | 27.4419i | 0.309307 | + | 0.951948i | ||||
\(832\) | 1.85410 | 0.0642794 | ||||||||
\(833\) | −1.06231 | − | 3.26944i | −0.0368067 | − | 0.113279i | ||||
\(834\) | −10.8541 | − | 7.88597i | −0.375847 | − | 0.273069i | ||||
\(835\) | 4.47214 | − | 3.24920i | 0.154765 | − | 0.112443i | ||||
\(836\) | −4.47214 | + | 3.24920i | −0.154672 | + | 0.112376i | ||||
\(837\) | −7.85410 | − | 5.70634i | −0.271477 | − | 0.197240i | ||||
\(838\) | −1.70820 | − | 1.24108i | −0.0590089 | − | 0.0428725i | ||||
\(839\) | −28.4164 | + | 20.6457i | −0.981043 | + | 0.712770i | −0.957942 | − | 0.286963i | \(-0.907354\pi\) |
−0.0231018 | + | 0.999733i | \(0.507354\pi\) | |||||||
\(840\) | 1.38197 | + | 4.25325i | 0.0476824 | + | 0.146751i | ||||
\(841\) | 12.8713 | + | 9.35156i | 0.443839 | + | 0.322468i | ||||
\(842\) | −0.0278640 | − | 0.0857567i | −0.000960258 | − | 0.00295537i | ||||
\(843\) | −5.09017 | −0.175315 | ||||||||
\(844\) | −2.47214 | − | 7.60845i | −0.0850944 | − | 0.261894i | ||||
\(845\) | 17.2984 | − | 12.5680i | 0.595082 | − | 0.432352i | ||||
\(846\) | −2.85410 | + | 8.78402i | −0.0981260 | + | 0.302001i | ||||
\(847\) | −6.43769 | + | 19.8132i | −0.221202 | + | 0.680789i | ||||
\(848\) | 9.35410 | − | 6.79615i | 0.321221 | − | 0.233381i | ||||
\(849\) | 1.23607 | 0.0424217 | ||||||||
\(850\) | −5.72949 | −0.196520 | ||||||||
\(851\) | −53.1246 | −1.82109 | ||||||||
\(852\) | 6.61803 | − | 4.80828i | 0.226730 | − | 0.164729i | ||||
\(853\) | −12.1910 | + | 37.5200i | −0.417411 | + | 1.28466i | 0.492665 | + | 0.870219i | \(0.336023\pi\) |
−0.910076 | + | 0.414441i | \(0.863977\pi\) | |||||||
\(854\) | 1.32624 | − | 4.08174i | 0.0453829 | − | 0.139674i | ||||
\(855\) | −16.1803 | −0.553356 | ||||||||
\(856\) | 2.14590 | + | 6.60440i | 0.0733453 | + | 0.225734i | ||||
\(857\) | −39.3050 | −1.34263 | −0.671316 | − | 0.741171i | \(-0.734271\pi\) | ||||
−0.671316 | + | 0.741171i | \(0.734271\pi\) | |||||||
\(858\) | −0.437694 | − | 1.34708i | −0.0149426 | − | 0.0459887i | ||||
\(859\) | −44.0689 | − | 32.0179i | −1.50361 | − | 1.09244i | −0.968915 | − | 0.247393i | \(-0.920426\pi\) |
−0.534696 | − | 0.845045i | \(-0.679574\pi\) | |||||||
\(860\) | 7.23607 | 0.246748 | ||||||||
\(861\) | 8.23607 | − | 5.98385i | 0.280684 | − | 0.203929i | ||||
\(862\) | −7.85410 | − | 5.70634i | −0.267512 | − | 0.194359i | ||||
\(863\) | 8.23607 | + | 5.98385i | 0.280359 | + | 0.203693i | 0.719074 | − | 0.694934i | \(-0.244566\pi\) |
−0.438715 | + | 0.898626i | \(0.644566\pi\) | |||||||
\(864\) | −0.809017 | + | 0.587785i | −0.0275233 | + | 0.0199969i | ||||
\(865\) | 39.9615 | + | 29.0337i | 1.35873 | + | 0.987176i | ||||
\(866\) | −24.1525 | − | 17.5478i | −0.820735 | − | 0.596299i | ||||
\(867\) | 4.84752 | + | 14.9191i | 0.164631 | + | 0.506681i | ||||
\(868\) | −19.4164 | −0.659036 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2.50000 | − | 7.69421i | −0.0847579 | − | 0.260858i | ||||
\(871\) | 2.12461 | − | 6.53888i | 0.0719897 | − | 0.221562i | ||||
\(872\) | 5.42705 | − | 16.7027i | 0.183783 | − | 0.565626i | ||||
\(873\) | 5.78115 | − | 4.20025i | 0.195662 | − | 0.142157i | ||||
\(874\) | 43.4164 | 1.46858 | ||||||||
\(875\) | −18.0902 | − | 13.1433i | −0.611559 | − | 0.444324i | ||||
\(876\) | 9.85410 | 0.332939 | ||||||||
\(877\) | 23.4443 | − | 17.0333i | 0.791657 | − | 0.575172i | −0.116798 | − | 0.993156i | \(-0.537263\pi\) |
0.908455 | + | 0.417983i | \(0.137263\pi\) | |||||||
\(878\) | −4.67376 | + | 14.3844i | −0.157732 | + | 0.485449i | ||||
\(879\) | 1.29837 | − | 3.99598i | 0.0437931 | − | 0.134781i | ||||
\(880\) | −0.527864 | − | 1.62460i | −0.0177943 | − | 0.0547652i | ||||
\(881\) | −13.2016 | − | 40.6304i | −0.444774 | − | 1.36887i | −0.882731 | − | 0.469878i | \(-0.844298\pi\) |
0.437957 | − | 0.898996i | \(-0.355702\pi\) | |||||||
\(882\) | 3.00000 | 0.101015 | ||||||||
\(883\) | 6.12461 | + | 18.8496i | 0.206110 | + | 0.634340i | 0.999666 | + | 0.0258434i | \(0.00822713\pi\) |
−0.793556 | + | 0.608497i | \(0.791773\pi\) | |||||||
\(884\) | −1.71885 | − | 1.24882i | −0.0578111 | − | 0.0420022i | ||||
\(885\) | −16.1803 | − | 11.7557i | −0.543896 | − | 0.395164i | ||||
\(886\) | −22.7082 | + | 16.4985i | −0.762897 | + | 0.554277i | ||||
\(887\) | −38.9787 | − | 28.3197i | −1.30878 | − | 0.950882i | −0.308777 | − | 0.951134i | \(-0.599920\pi\) |
−1.00000 | 0.000252175i | \(0.999920\pi\) | ||||||||
\(888\) | 7.16312 | + | 5.20431i | 0.240379 | + | 0.174645i | ||||
\(889\) | −22.1803 | + | 16.1150i | −0.743905 | + | 0.540478i | ||||
\(890\) | −8.09017 | −0.271183 | ||||||||
\(891\) | 0.618034 | + | 0.449028i | 0.0207049 | + | 0.0150430i | ||||
\(892\) | −4.85410 | − | 14.9394i | −0.162527 | − | 0.500208i | ||||
\(893\) | −66.8328 | −2.23647 | ||||||||
\(894\) | −6.80902 | − | 20.9560i | −0.227728 | − | 0.700873i | ||||
\(895\) | −58.5410 | −1.95681 | ||||||||
\(896\) | −0.618034 | + | 1.90211i | −0.0206471 | + | 0.0635451i | ||||
\(897\) | −3.43769 | + | 10.5801i | −0.114781 | + | 0.353260i | ||||
\(898\) | −16.0172 | + | 11.6372i | −0.534502 | + | 0.388338i | ||||
\(899\) | 35.1246 | 1.17147 | ||||||||
\(900\) | 1.54508 | − | 4.75528i | 0.0515028 | − | 0.158509i | ||||
\(901\) | −13.2492 | −0.441396 | ||||||||
\(902\) | −3.14590 | + | 2.28563i | −0.104747 | + | 0.0761031i | ||||
\(903\) | −2.00000 | + | 6.15537i | −0.0665558 | + | 0.204838i | ||||
\(904\) | −2.64590 | + | 8.14324i | −0.0880013 | + | 0.270840i | ||||
\(905\) | −16.3435 | + | 11.8742i | −0.543275 | + | 0.394712i | ||||
\(906\) | 3.38197 | + | 10.4086i | 0.112358 | + | 0.345803i | ||||
\(907\) | 33.7082 | 1.11926 | 0.559631 | − | 0.828742i | \(-0.310943\pi\) | ||||
0.559631 | + | 0.828742i | \(0.310943\pi\) | |||||||
\(908\) | 0.291796 | + | 0.898056i | 0.00968359 | + | 0.0298030i | ||||
\(909\) | −14.0172 | − | 10.1841i | −0.464922 | − | 0.337786i | ||||
\(910\) | −2.56231 | − | 7.88597i | −0.0849396 | − | 0.261417i | ||||
\(911\) | 1.67376 | − | 1.21606i | 0.0554542 | − | 0.0402898i | −0.559713 | − | 0.828687i | \(-0.689089\pi\) |
0.615167 | + | 0.788397i | \(0.289089\pi\) | |||||||
\(912\) | −5.85410 | − | 4.25325i | −0.193849 | − | 0.140839i | ||||
\(913\) | 3.70820 | + | 2.69417i | 0.122724 | + | 0.0891639i | ||||
\(914\) | −2.85410 | + | 2.07363i | −0.0944053 | + | 0.0685895i | ||||
\(915\) | −3.88197 | + | 2.82041i | −0.128334 | + | 0.0932400i | ||||
\(916\) | −7.50000 | − | 5.44907i | −0.247807 | − | 0.180042i | ||||
\(917\) | −3.23607 | − | 9.95959i | −0.106864 | − | 0.328895i | ||||
\(918\) | 1.14590 | 0.0378203 | ||||||||
\(919\) | −5.85410 | − | 18.0171i | −0.193109 | − | 0.594328i | −0.999993 | − | 0.00361909i | \(-0.998848\pi\) |
0.806884 | − | 0.590709i | \(-0.201152\pi\) | |||||||
\(920\) | −4.14590 | + | 12.7598i | −0.136686 | + | 0.420677i | ||||
\(921\) | 9.18034 | − | 28.2542i | 0.302502 | − | 0.931007i | ||||
\(922\) | −4.29837 | + | 13.2290i | −0.141559 | + | 0.435675i | ||||
\(923\) | −12.2705 | + | 8.91505i | −0.403889 | + | 0.293442i | ||||
\(924\) | 1.52786 | 0.0502630 | ||||||||
\(925\) | −44.2705 | −1.45561 | ||||||||
\(926\) | 25.7082 | 0.844824 | ||||||||
\(927\) | 12.7082 | − | 9.23305i | 0.417392 | − | 0.303253i | ||||
\(928\) | 1.11803 | − | 3.44095i | 0.0367013 | − | 0.112955i | ||||
\(929\) | 4.93769 | − | 15.1967i | 0.162000 | − | 0.498586i | −0.836802 | − | 0.547505i | \(-0.815578\pi\) |
0.998803 | + | 0.0489190i | \(0.0155776\pi\) | |||||||
\(930\) | 17.5623 | + | 12.7598i | 0.575891 | + | 0.418409i | ||||
\(931\) | 6.70820 | + | 20.6457i | 0.219853 | + | 0.676636i | ||||
\(932\) | −10.9098 | −0.357363 | ||||||||
\(933\) | −3.90983 | − | 12.0332i | −0.128002 | − | 0.393950i | ||||
\(934\) | 30.8885 | + | 22.4418i | 1.01070 | + | 0.734319i | ||||
\(935\) | −0.604878 | + | 1.86162i | −0.0197816 | + | 0.0608816i | ||||
\(936\) | 1.50000 | − | 1.08981i | 0.0490290 | − | 0.0356217i | ||||
\(937\) | −19.3435 | − | 14.0538i | −0.631923 | − | 0.459119i | 0.225143 | − | 0.974326i | \(-0.427715\pi\) |
−0.857066 | + | 0.515207i | \(0.827715\pi\) | |||||||
\(938\) | 6.00000 | + | 4.35926i | 0.195907 | + | 0.142335i | ||||
\(939\) | 14.8541 | − | 10.7921i | 0.484745 | − | 0.352188i | ||||
\(940\) | 6.38197 | − | 19.6417i | 0.208157 | − | 0.640641i | ||||
\(941\) | −30.1976 | − | 21.9398i | −0.984412 | − | 0.715217i | −0.0257220 | − | 0.999669i | \(-0.508188\pi\) |
−0.958690 | + | 0.284452i | \(0.908188\pi\) | |||||||
\(942\) | 3.44427 | + | 10.6004i | 0.112220 | + | 0.345379i | ||||
\(943\) | 30.5410 | 0.994552 | ||||||||
\(944\) | −2.76393 | − | 8.50651i | −0.0899583 | − | 0.276863i | ||||
\(945\) | 3.61803 | + | 2.62866i | 0.117695 | + | 0.0855102i | ||||
\(946\) | 0.763932 | − | 2.35114i | 0.0248376 | − | 0.0764422i | ||||
\(947\) | −2.14590 | + | 6.60440i | −0.0697323 | + | 0.214614i | −0.979850 | − | 0.199737i | \(-0.935991\pi\) |
0.910117 | + | 0.414351i | \(0.135991\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.2705 | −0.593086 | ||||||||
\(950\) | 36.1803 | 1.17385 | ||||||||
\(951\) | −10.9443 | −0.354892 | ||||||||
\(952\) | 1.85410 | − | 1.34708i | 0.0600918 | − | 0.0436592i | ||||
\(953\) | 15.4098 | − | 47.4266i | 0.499173 | − | 1.53630i | −0.311177 | − | 0.950352i | \(-0.600723\pi\) |
0.810350 | − | 0.585946i | \(-0.199277\pi\) | |||||||
\(954\) | 3.57295 | − | 10.9964i | 0.115678 | − | 0.356022i | ||||
\(955\) | −3.61803 | + | 11.1352i | −0.117077 | + | 0.360325i | ||||
\(956\) | −8.29180 | − | 25.5195i | −0.268176 | − | 0.825360i | ||||
\(957\) | −2.76393 | −0.0893452 | ||||||||
\(958\) | 1.38197 | + | 4.25325i | 0.0446493 | + | 0.137416i | ||||
\(959\) | −22.7082 | − | 16.4985i | −0.733286 | − | 0.532764i | ||||
\(960\) | 1.80902 | − | 1.31433i | 0.0583858 | − | 0.0424197i | ||||
\(961\) | −51.1697 | + | 37.1770i | −1.65064 | + | 1.19926i | ||||
\(962\) | −13.2812 | − | 9.64932i | −0.428202 | − | 0.311107i | ||||
\(963\) | 5.61803 | + | 4.08174i | 0.181039 | + | 0.131532i | ||||
\(964\) | 5.78115 | − | 4.20025i | 0.186198 | − | 0.135281i | ||||
\(965\) | 3.19098 | + | 9.82084i | 0.102721 | + | 0.316144i | ||||
\(966\) | −9.70820 | − | 7.05342i | −0.312356 | − | 0.226940i | ||||
\(967\) | 7.12461 | + | 21.9273i | 0.229112 | + | 0.705134i | 0.997848 | + | 0.0655682i | \(0.0208860\pi\) |
−0.768736 | + | 0.639566i | \(0.779114\pi\) | |||||||
\(968\) | 10.4164 | 0.334796 | ||||||||
\(969\) | 2.56231 | + | 7.88597i | 0.0823131 | + | 0.253334i | ||||
\(970\) | −12.9271 | + | 9.39205i | −0.415063 | + | 0.301561i | ||||
\(971\) | 11.6738 | − | 35.9281i | 0.374629 | − | 1.15299i | −0.569100 | − | 0.822268i | \(-0.692708\pi\) |
0.943729 | − | 0.330721i | \(-0.107292\pi\) | |||||||
\(972\) | −0.309017 | + | 0.951057i | −0.00991172 | + | 0.0305052i | ||||
\(973\) | −21.7082 | + | 15.7719i | −0.695933 | + | 0.505625i | ||||
\(974\) | −23.7082 | −0.759660 | ||||||||
\(975\) | −2.86475 | + | 8.81678i | −0.0917453 | + | 0.282363i | ||||
\(976\) | −2.14590 | −0.0686885 | ||||||||
\(977\) | 0.354102 | − | 0.257270i | 0.0113287 | − | 0.00823080i | −0.582106 | − | 0.813113i | \(-0.697771\pi\) |
0.593435 | + | 0.804882i | \(0.297771\pi\) | |||||||
\(978\) | 3.56231 | − | 10.9637i | 0.113910 | − | 0.350579i | ||||
\(979\) | −0.854102 | + | 2.62866i | −0.0272972 | + | 0.0840122i | ||||
\(980\) | −6.70820 | −0.214286 | ||||||||
\(981\) | −5.42705 | − | 16.7027i | −0.173272 | − | 0.533278i | ||||
\(982\) | 5.88854 | 0.187911 | ||||||||
\(983\) | 7.58359 | + | 23.3399i | 0.241879 | + | 0.744427i | 0.996134 | + | 0.0878456i | \(0.0279982\pi\) |
−0.754255 | + | 0.656582i | \(0.772002\pi\) | |||||||
\(984\) | −4.11803 | − | 2.99193i | −0.131278 | − | 0.0953791i | ||||
\(985\) | 5.20163 | 0.165738 | ||||||||
\(986\) | −3.35410 | + | 2.43690i | −0.106816 | + | 0.0776066i | ||||
\(987\) | 14.9443 | + | 10.8576i | 0.475681 | + | 0.345603i | ||||
\(988\) | 10.8541 | + | 7.88597i | 0.345315 | + | 0.250886i | ||||
\(989\) | −15.7082 | + | 11.4127i | −0.499492 | + | 0.362902i | ||||
\(990\) | −1.38197 | − | 1.00406i | −0.0439218 | − | 0.0319110i | ||||
\(991\) | 5.29180 | + | 3.84471i | 0.168099 | + | 0.122131i | 0.668654 | − | 0.743573i | \(-0.266871\pi\) |
−0.500555 | + | 0.865705i | \(0.666871\pi\) | |||||||
\(992\) | 3.00000 | + | 9.23305i | 0.0952501 | + | 0.293150i | ||||
\(993\) | 23.5279 | 0.746634 | ||||||||
\(994\) | −5.05573 | − | 15.5599i | −0.160358 | − | 0.493531i | ||||
\(995\) | 11.1803 | + | 34.4095i | 0.354441 | + | 1.09086i | ||||
\(996\) | −1.85410 | + | 5.70634i | −0.0587495 | + | 0.180812i | ||||
\(997\) | 7.85410 | − | 24.1724i | 0.248742 | − | 0.765549i | −0.746257 | − | 0.665658i | \(-0.768151\pi\) |
0.994998 | − | 0.0998904i | \(-0.0318492\pi\) | |||||||
\(998\) | −5.32624 | + | 3.86974i | −0.168599 | + | 0.122494i | ||||
\(999\) | 8.85410 | 0.280131 |
(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 | 150.2.g.b.61.1 | ✓ | 4 | |
3.2 | odd | 2 | 450.2.h.b.361.1 | 4 | |||
5.2 | odd | 4 | 750.2.h.a.199.2 | 8 | |||
5.3 | odd | 4 | 750.2.h.a.199.1 | 8 | |||
5.4 | even | 2 | 750.2.g.a.301.1 | 4 | |||
25.3 | odd | 20 | 3750.2.c.c.1249.4 | 4 | |||
25.4 | even | 10 | 3750.2.a.g.1.2 | 2 | |||
25.9 | even | 10 | 750.2.g.a.451.1 | 4 | |||
25.12 | odd | 20 | 750.2.h.a.49.1 | 8 | |||
25.13 | odd | 20 | 750.2.h.a.49.2 | 8 | |||
25.16 | even | 5 | inner | 150.2.g.b.91.1 | yes | 4 | |
25.21 | even | 5 | 3750.2.a.b.1.2 | 2 | |||
25.22 | odd | 20 | 3750.2.c.c.1249.2 | 4 | |||
75.41 | odd | 10 | 450.2.h.b.91.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.g.b.61.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
150.2.g.b.91.1 | yes | 4 | 25.16 | even | 5 | inner | |
450.2.h.b.91.1 | 4 | 75.41 | odd | 10 | |||
450.2.h.b.361.1 | 4 | 3.2 | odd | 2 | |||
750.2.g.a.301.1 | 4 | 5.4 | even | 2 | |||
750.2.g.a.451.1 | 4 | 25.9 | even | 10 | |||
750.2.h.a.49.1 | 8 | 25.12 | odd | 20 | |||
750.2.h.a.49.2 | 8 | 25.13 | odd | 20 | |||
750.2.h.a.199.1 | 8 | 5.3 | odd | 4 | |||
750.2.h.a.199.2 | 8 | 5.2 | odd | 4 | |||
3750.2.a.b.1.2 | 2 | 25.21 | even | 5 | |||
3750.2.a.g.1.2 | 2 | 25.4 | even | 10 | |||
3750.2.c.c.1249.2 | 4 | 25.22 | odd | 20 | |||
3750.2.c.c.1249.4 | 4 | 25.3 | odd | 20 |