Properties

Label 495.2.n.e.136.1
Level $495$
Weight $2$
Character 495.136
Analytic conductor $3.953$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [495,2,Mod(91,495)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(495, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("495.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.n (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: \(3.95259490005\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 136.1
Root \(-0.227943 + 0.701538i\) of defining polynomial
Character \(\chi\) \(=\) 495.136
Dual form 495.2.n.e.91.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.596764 - 0.433574i) q^{2} +(-0.449894 - 1.38463i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.318714 + 0.980901i) q^{7} +(-0.787747 + 2.42443i) q^{8} +O(q^{10})\) \(q+(-0.596764 - 0.433574i) q^{2} +(-0.449894 - 1.38463i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.318714 + 0.980901i) q^{7} +(-0.787747 + 2.42443i) q^{8} +0.737640 q^{10} +(-1.93675 + 2.69240i) q^{11} +(-2.79029 - 2.02726i) q^{13} +(0.235096 - 0.723552i) q^{14} +(-0.834404 + 0.606230i) q^{16} +(1.94020 - 1.40964i) q^{17} +(-2.36979 + 7.29347i) q^{19} +(1.17784 + 0.855749i) q^{20} +(2.32313 - 0.767001i) q^{22} -2.45589 q^{23} +(0.309017 - 0.951057i) q^{25} +(0.786174 + 2.41960i) q^{26} +(1.21480 - 0.882602i) q^{28} +(1.83998 + 5.66289i) q^{29} +(2.98382 + 2.16787i) q^{31} +5.85919 q^{32} -1.76902 q^{34} +(-0.834404 - 0.606230i) q^{35} +(1.84130 + 5.66694i) q^{37} +(4.57646 - 3.32500i) q^{38} +(-0.787747 - 2.42443i) q^{40} +(-1.21637 + 3.74360i) q^{41} -7.64941 q^{43} +(4.59931 + 1.47039i) q^{44} +(1.46558 + 1.06481i) q^{46} +(-1.80557 + 5.55697i) q^{47} +(4.80253 - 3.48924i) q^{49} +(-0.596764 + 0.433574i) q^{50} +(-1.55168 + 4.77558i) q^{52} +(-9.58526 - 6.96410i) q^{53} +(-0.0156899 - 3.31659i) q^{55} -2.62920 q^{56} +(1.35725 - 4.17718i) q^{58} +(-0.910456 - 2.80210i) q^{59} +(-2.00666 + 1.45792i) q^{61} +(-0.840701 - 2.58741i) q^{62} +(-1.82774 - 1.32793i) q^{64} +3.44899 q^{65} -6.14702 q^{67} +(-2.82471 - 2.05227i) q^{68} +(0.235096 + 0.723552i) q^{70} +(1.63676 - 1.18918i) q^{71} +(-0.255207 - 0.785446i) q^{73} +(1.35822 - 4.18017i) q^{74} +11.1649 q^{76} +(-3.25824 - 1.04165i) q^{77} +(9.77146 + 7.09938i) q^{79} +(0.318714 - 0.980901i) q^{80} +(2.34901 - 1.70666i) q^{82} +(1.30253 - 0.946345i) q^{83} +(-0.741089 + 2.28084i) q^{85} +(4.56489 + 3.31659i) q^{86} +(-5.00188 - 6.81645i) q^{88} -8.16116 q^{89} +(1.09924 - 3.38312i) q^{91} +(1.10489 + 3.40050i) q^{92} +(3.48685 - 2.53335i) q^{94} +(-2.36979 - 7.29347i) q^{95} +(-1.97625 - 1.43583i) q^{97} -4.37882 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} - 4 q^{8} + 2 q^{10} - 3 q^{11} - 2 q^{13} + 16 q^{14} + 4 q^{16} + 13 q^{17} + 15 q^{19} + 3 q^{20} - 7 q^{22} - 10 q^{23} - 2 q^{25} - 10 q^{26} - 6 q^{28} + 9 q^{29} - 10 q^{31} - 16 q^{32} + 4 q^{34} + 4 q^{35} + 24 q^{37} - 4 q^{40} - 8 q^{41} - 38 q^{43} + 12 q^{44} + 3 q^{46} + q^{49} + 2 q^{50} - 28 q^{52} - 13 q^{53} + 7 q^{55} - 22 q^{56} + 12 q^{58} + 27 q^{59} + 6 q^{61} + 30 q^{62} - 26 q^{64} - 2 q^{65} - 38 q^{67} - 11 q^{68} + 16 q^{70} + 20 q^{71} + 13 q^{73} - 20 q^{74} - 34 q^{77} + 37 q^{79} - q^{80} + 28 q^{82} - 27 q^{83} - 12 q^{85} + 3 q^{86} - 36 q^{88} + 16 q^{89} + 44 q^{91} - 11 q^{92} + 17 q^{94} + 15 q^{95} + 24 q^{97} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(397\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.596764 0.433574i −0.421976 0.306583i 0.356457 0.934312i \(-0.383985\pi\)
−0.778432 + 0.627729i \(0.783985\pi\)
\(3\) 0 0
\(4\) −0.449894 1.38463i −0.224947 0.692315i
\(5\) −0.809017 + 0.587785i −0.361803 + 0.262866i
\(6\) 0 0
\(7\) 0.318714 + 0.980901i 0.120463 + 0.370746i 0.993047 0.117717i \(-0.0375577\pi\)
−0.872585 + 0.488463i \(0.837558\pi\)
\(8\) −0.787747 + 2.42443i −0.278510 + 0.857167i
\(9\) 0 0
\(10\) 0.737640 0.233262
\(11\) −1.93675 + 2.69240i −0.583951 + 0.811789i
\(12\) 0 0
\(13\) −2.79029 2.02726i −0.773887 0.562262i 0.129251 0.991612i \(-0.458743\pi\)
−0.903138 + 0.429350i \(0.858743\pi\)
\(14\) 0.235096 0.723552i 0.0628321 0.193377i
\(15\) 0 0
\(16\) −0.834404 + 0.606230i −0.208601 + 0.151557i
\(17\) 1.94020 1.40964i 0.470567 0.341887i −0.327095 0.944991i \(-0.606070\pi\)
0.797662 + 0.603105i \(0.206070\pi\)
\(18\) 0 0
\(19\) −2.36979 + 7.29347i −0.543668 + 1.67324i 0.180470 + 0.983581i \(0.442238\pi\)
−0.724137 + 0.689656i \(0.757762\pi\)
\(20\) 1.17784 + 0.855749i 0.263372 + 0.191351i
\(21\) 0 0
\(22\) 2.32313 0.767001i 0.495294 0.163525i
\(23\) −2.45589 −0.512088 −0.256044 0.966665i \(-0.582419\pi\)
−0.256044 + 0.966665i \(0.582419\pi\)
\(24\) 0 0
\(25\) 0.309017 0.951057i 0.0618034 0.190211i
\(26\) 0.786174 + 2.41960i 0.154181 + 0.474522i
\(27\) 0 0
\(28\) 1.21480 0.882602i 0.229575 0.166796i
\(29\) 1.83998 + 5.66289i 0.341677 + 1.05157i 0.963339 + 0.268287i \(0.0864575\pi\)
−0.621663 + 0.783285i \(0.713542\pi\)
\(30\) 0 0
\(31\) 2.98382 + 2.16787i 0.535909 + 0.389361i 0.822564 0.568673i \(-0.192543\pi\)
−0.286654 + 0.958034i \(0.592543\pi\)
\(32\) 5.85919 1.03577
\(33\) 0 0
\(34\) −1.76902 −0.303384
\(35\) −0.834404 0.606230i −0.141040 0.102472i
\(36\) 0 0
\(37\) 1.84130 + 5.66694i 0.302708 + 0.931640i 0.980523 + 0.196407i \(0.0629273\pi\)
−0.677814 + 0.735233i \(0.737073\pi\)
\(38\) 4.57646 3.32500i 0.742401 0.539386i
\(39\) 0 0
\(40\) −0.787747 2.42443i −0.124554 0.383337i
\(41\) −1.21637 + 3.74360i −0.189965 + 0.584652i −0.999999 0.00173135i \(-0.999449\pi\)
0.810033 + 0.586384i \(0.199449\pi\)
\(42\) 0 0
\(43\) −7.64941 −1.16652 −0.583262 0.812284i \(-0.698224\pi\)
−0.583262 + 0.812284i \(0.698224\pi\)
\(44\) 4.59931 + 1.47039i 0.693372 + 0.221669i
\(45\) 0 0
\(46\) 1.46558 + 1.06481i 0.216089 + 0.156998i
\(47\) −1.80557 + 5.55697i −0.263369 + 0.810567i 0.728695 + 0.684838i \(0.240127\pi\)
−0.992065 + 0.125729i \(0.959873\pi\)
\(48\) 0 0
\(49\) 4.80253 3.48924i 0.686076 0.498463i
\(50\) −0.596764 + 0.433574i −0.0843951 + 0.0613166i
\(51\) 0 0
\(52\) −1.55168 + 4.77558i −0.215179 + 0.662253i
\(53\) −9.58526 6.96410i −1.31664 0.956592i −0.999968 0.00805607i \(-0.997436\pi\)
−0.316669 0.948536i \(-0.602564\pi\)
\(54\) 0 0
\(55\) −0.0156899 3.31659i −0.00211563 0.447209i
\(56\) −2.62920 −0.351341
\(57\) 0 0
\(58\) 1.35725 4.17718i 0.178215 0.548490i
\(59\) −0.910456 2.80210i −0.118531 0.364802i 0.874136 0.485681i \(-0.161428\pi\)
−0.992667 + 0.120880i \(0.961428\pi\)
\(60\) 0 0
\(61\) −2.00666 + 1.45792i −0.256927 + 0.186668i −0.708791 0.705419i \(-0.750759\pi\)
0.451864 + 0.892087i \(0.350759\pi\)
\(62\) −0.840701 2.58741i −0.106769 0.328602i
\(63\) 0 0
\(64\) −1.82774 1.32793i −0.228468 0.165992i
\(65\) 3.44899 0.427794
\(66\) 0 0
\(67\) −6.14702 −0.750978 −0.375489 0.926827i \(-0.622525\pi\)
−0.375489 + 0.926827i \(0.622525\pi\)
\(68\) −2.82471 2.05227i −0.342546 0.248874i
\(69\) 0 0
\(70\) 0.235096 + 0.723552i 0.0280994 + 0.0864810i
\(71\) 1.63676 1.18918i 0.194248 0.141129i −0.486410 0.873731i \(-0.661694\pi\)
0.680658 + 0.732601i \(0.261694\pi\)
\(72\) 0 0
\(73\) −0.255207 0.785446i −0.0298697 0.0919295i 0.935010 0.354621i \(-0.115390\pi\)
−0.964880 + 0.262691i \(0.915390\pi\)
\(74\) 1.35822 4.18017i 0.157890 0.485934i
\(75\) 0 0
\(76\) 11.1649 1.28070
\(77\) −3.25824 1.04165i −0.371311 0.118707i
\(78\) 0 0
\(79\) 9.77146 + 7.09938i 1.09937 + 0.798742i 0.980958 0.194221i \(-0.0622180\pi\)
0.118417 + 0.992964i \(0.462218\pi\)
\(80\) 0.318714 0.980901i 0.0356333 0.109668i
\(81\) 0 0
\(82\) 2.34901 1.70666i 0.259405 0.188469i
\(83\) 1.30253 0.946345i 0.142971 0.103875i −0.514000 0.857790i \(-0.671837\pi\)
0.656972 + 0.753915i \(0.271837\pi\)
\(84\) 0 0
\(85\) −0.741089 + 2.28084i −0.0803824 + 0.247392i
\(86\) 4.56489 + 3.31659i 0.492245 + 0.357637i
\(87\) 0 0
\(88\) −5.00188 6.81645i −0.533202 0.726636i
\(89\) −8.16116 −0.865081 −0.432541 0.901614i \(-0.642383\pi\)
−0.432541 + 0.901614i \(0.642383\pi\)
\(90\) 0 0
\(91\) 1.09924 3.38312i 0.115232 0.354647i
\(92\) 1.10489 + 3.40050i 0.115193 + 0.354526i
\(93\) 0 0
\(94\) 3.48685 2.53335i 0.359642 0.261295i
\(95\) −2.36979 7.29347i −0.243136 0.748294i
\(96\) 0 0
\(97\) −1.97625 1.43583i −0.200658 0.145787i 0.482919 0.875665i \(-0.339577\pi\)
−0.683577 + 0.729879i \(0.739577\pi\)
\(98\) −4.37882 −0.442328
\(99\) 0 0
\(100\) −1.45589 −0.145589
\(101\) −6.08683 4.42234i −0.605662 0.440039i 0.242222 0.970221i \(-0.422124\pi\)
−0.847884 + 0.530182i \(0.822124\pi\)
\(102\) 0 0
\(103\) −2.93020 9.01821i −0.288721 0.888591i −0.985259 0.171071i \(-0.945277\pi\)
0.696538 0.717520i \(-0.254723\pi\)
\(104\) 7.11301 5.16791i 0.697488 0.506755i
\(105\) 0 0
\(106\) 2.70068 + 8.31184i 0.262313 + 0.807317i
\(107\) 1.43593 4.41935i 0.138817 0.427235i −0.857347 0.514739i \(-0.827889\pi\)
0.996164 + 0.0875039i \(0.0278890\pi\)
\(108\) 0 0
\(109\) −5.32826 −0.510355 −0.255178 0.966894i \(-0.582134\pi\)
−0.255178 + 0.966894i \(0.582134\pi\)
\(110\) −1.42862 + 1.98602i −0.136214 + 0.189360i
\(111\) 0 0
\(112\) −0.860587 0.625253i −0.0813179 0.0590809i
\(113\) −0.0942195 + 0.289978i −0.00886342 + 0.0272788i −0.955390 0.295346i \(-0.904565\pi\)
0.946527 + 0.322625i \(0.104565\pi\)
\(114\) 0 0
\(115\) 1.98685 1.44353i 0.185275 0.134610i
\(116\) 7.01321 5.09540i 0.651160 0.473096i
\(117\) 0 0
\(118\) −0.671589 + 2.06694i −0.0618248 + 0.190277i
\(119\) 2.00108 + 1.45387i 0.183439 + 0.133276i
\(120\) 0 0
\(121\) −3.49802 10.4290i −0.318001 0.948090i
\(122\) 1.82962 0.165646
\(123\) 0 0
\(124\) 1.65930 5.10680i 0.149009 0.458604i
\(125\) 0.309017 + 0.951057i 0.0276393 + 0.0850651i
\(126\) 0 0
\(127\) 9.63536 7.00050i 0.855000 0.621194i −0.0715199 0.997439i \(-0.522785\pi\)
0.926520 + 0.376245i \(0.122785\pi\)
\(128\) −3.10621 9.55992i −0.274552 0.844985i
\(129\) 0 0
\(130\) −2.05823 1.49539i −0.180519 0.131155i
\(131\) 11.1875 0.977452 0.488726 0.872437i \(-0.337462\pi\)
0.488726 + 0.872437i \(0.337462\pi\)
\(132\) 0 0
\(133\) −7.90945 −0.685837
\(134\) 3.66832 + 2.66519i 0.316894 + 0.230237i
\(135\) 0 0
\(136\) 1.88919 + 5.81432i 0.161996 + 0.498573i
\(137\) −3.46360 + 2.51645i −0.295915 + 0.214995i −0.725829 0.687875i \(-0.758544\pi\)
0.429914 + 0.902870i \(0.358544\pi\)
\(138\) 0 0
\(139\) −1.83964 5.66183i −0.156036 0.480230i 0.842228 0.539121i \(-0.181243\pi\)
−0.998264 + 0.0588913i \(0.981243\pi\)
\(140\) −0.464011 + 1.42808i −0.0392161 + 0.120695i
\(141\) 0 0
\(142\) −1.49235 −0.125236
\(143\) 10.8623 3.58627i 0.908351 0.299899i
\(144\) 0 0
\(145\) −4.81714 3.49986i −0.400042 0.290647i
\(146\) −0.188251 + 0.579377i −0.0155798 + 0.0479495i
\(147\) 0 0
\(148\) 7.01823 5.09905i 0.576895 0.419139i
\(149\) −3.06168 + 2.22444i −0.250823 + 0.182233i −0.706091 0.708121i \(-0.749543\pi\)
0.455269 + 0.890354i \(0.349543\pi\)
\(150\) 0 0
\(151\) −7.52661 + 23.1645i −0.612507 + 1.88510i −0.179348 + 0.983786i \(0.557399\pi\)
−0.433159 + 0.901317i \(0.642601\pi\)
\(152\) −15.8157 11.4908i −1.28283 0.932028i
\(153\) 0 0
\(154\) 1.49277 + 2.03431i 0.120291 + 0.163929i
\(155\) −3.68820 −0.296243
\(156\) 0 0
\(157\) 2.23484 6.87813i 0.178360 0.548935i −0.821411 0.570336i \(-0.806813\pi\)
0.999771 + 0.0214015i \(0.00681284\pi\)
\(158\) −2.75314 8.47330i −0.219028 0.674100i
\(159\) 0 0
\(160\) −4.74018 + 3.44395i −0.374744 + 0.272268i
\(161\) −0.782725 2.40898i −0.0616874 0.189854i
\(162\) 0 0
\(163\) −15.1198 10.9852i −1.18428 0.860428i −0.191630 0.981467i \(-0.561377\pi\)
−0.992648 + 0.121039i \(0.961377\pi\)
\(164\) 5.73074 0.447496
\(165\) 0 0
\(166\) −1.18761 −0.0921767
\(167\) 6.35343 + 4.61604i 0.491644 + 0.357200i 0.805816 0.592166i \(-0.201727\pi\)
−0.314172 + 0.949366i \(0.601727\pi\)
\(168\) 0 0
\(169\) −0.341302 1.05042i −0.0262540 0.0808014i
\(170\) 1.43117 1.03980i 0.109766 0.0797493i
\(171\) 0 0
\(172\) 3.44142 + 10.5916i 0.262406 + 0.807603i
\(173\) −3.46244 + 10.6563i −0.263244 + 0.810183i 0.728848 + 0.684675i \(0.240056\pi\)
−0.992093 + 0.125508i \(0.959944\pi\)
\(174\) 0 0
\(175\) 1.03138 0.0779650
\(176\) −0.0161823 3.42066i −0.00121979 0.257842i
\(177\) 0 0
\(178\) 4.87028 + 3.53847i 0.365043 + 0.265219i
\(179\) −0.452595 + 1.39295i −0.0338286 + 0.104114i −0.966545 0.256497i \(-0.917432\pi\)
0.932716 + 0.360611i \(0.117432\pi\)
\(180\) 0 0
\(181\) −7.51496 + 5.45994i −0.558583 + 0.405834i −0.830940 0.556362i \(-0.812197\pi\)
0.272357 + 0.962196i \(0.412197\pi\)
\(182\) −2.12282 + 1.54232i −0.157354 + 0.114324i
\(183\) 0 0
\(184\) 1.93462 5.95414i 0.142622 0.438945i
\(185\) −4.82059 3.50236i −0.354417 0.257499i
\(186\) 0 0
\(187\) 0.0376278 + 7.95389i 0.00275162 + 0.581646i
\(188\) 8.50666 0.620412
\(189\) 0 0
\(190\) −1.74805 + 5.37996i −0.126817 + 0.390303i
\(191\) 1.38222 + 4.25404i 0.100014 + 0.307811i 0.988528 0.151038i \(-0.0482617\pi\)
−0.888514 + 0.458850i \(0.848262\pi\)
\(192\) 0 0
\(193\) 18.3372 13.3227i 1.31994 0.958992i 0.320007 0.947415i \(-0.396315\pi\)
0.999933 0.0115772i \(-0.00368521\pi\)
\(194\) 0.556816 + 1.71370i 0.0399771 + 0.123037i
\(195\) 0 0
\(196\) −6.99194 5.07994i −0.499424 0.362853i
\(197\) 11.2080 0.798535 0.399267 0.916835i \(-0.369265\pi\)
0.399267 + 0.916835i \(0.369265\pi\)
\(198\) 0 0
\(199\) −7.81979 −0.554330 −0.277165 0.960822i \(-0.589395\pi\)
−0.277165 + 0.960822i \(0.589395\pi\)
\(200\) 2.06235 + 1.49838i 0.145830 + 0.105952i
\(201\) 0 0
\(202\) 1.71499 + 5.27818i 0.120666 + 0.371372i
\(203\) −4.96830 + 3.60968i −0.348707 + 0.253350i
\(204\) 0 0
\(205\) −1.21637 3.74360i −0.0849550 0.261464i
\(206\) −2.16143 + 6.65220i −0.150594 + 0.463481i
\(207\) 0 0
\(208\) 3.55722 0.246649
\(209\) −15.0472 20.5060i −1.04084 1.41843i
\(210\) 0 0
\(211\) 18.4189 + 13.3821i 1.26801 + 0.921262i 0.999121 0.0419098i \(-0.0133442\pi\)
0.268887 + 0.963172i \(0.413344\pi\)
\(212\) −5.33035 + 16.4051i −0.366090 + 1.12671i
\(213\) 0 0
\(214\) −2.77303 + 2.01472i −0.189560 + 0.137724i
\(215\) 6.18851 4.49621i 0.422053 0.306639i
\(216\) 0 0
\(217\) −1.17548 + 3.61776i −0.0797969 + 0.245589i
\(218\) 3.17971 + 2.31020i 0.215357 + 0.156466i
\(219\) 0 0
\(220\) −4.58519 + 1.51384i −0.309133 + 0.102063i
\(221\) −8.27142 −0.556396
\(222\) 0 0
\(223\) −4.95746 + 15.2575i −0.331976 + 1.02172i 0.636216 + 0.771511i \(0.280499\pi\)
−0.968192 + 0.250207i \(0.919501\pi\)
\(224\) 1.86741 + 5.74728i 0.124771 + 0.384006i
\(225\) 0 0
\(226\) 0.181954 0.132197i 0.0121034 0.00879361i
\(227\) 7.46468 + 22.9739i 0.495448 + 1.52483i 0.816257 + 0.577689i \(0.196045\pi\)
−0.320809 + 0.947144i \(0.603955\pi\)
\(228\) 0 0
\(229\) 12.1468 + 8.82517i 0.802684 + 0.583184i 0.911700 0.410856i \(-0.134770\pi\)
−0.109017 + 0.994040i \(0.534770\pi\)
\(230\) −1.81156 −0.119451
\(231\) 0 0
\(232\) −15.1787 −0.996534
\(233\) 9.24378 + 6.71600i 0.605580 + 0.439980i 0.847855 0.530228i \(-0.177894\pi\)
−0.242275 + 0.970208i \(0.577894\pi\)
\(234\) 0 0
\(235\) −1.80557 5.55697i −0.117782 0.362497i
\(236\) −3.47026 + 2.52129i −0.225895 + 0.164122i
\(237\) 0 0
\(238\) −0.563811 1.73523i −0.0365465 0.112478i
\(239\) −8.46914 + 26.0653i −0.547823 + 1.68603i 0.166358 + 0.986065i \(0.446799\pi\)
−0.714181 + 0.699961i \(0.753201\pi\)
\(240\) 0 0
\(241\) 10.9387 0.704624 0.352312 0.935883i \(-0.385396\pi\)
0.352312 + 0.935883i \(0.385396\pi\)
\(242\) −2.43425 + 7.74029i −0.156480 + 0.497565i
\(243\) 0 0
\(244\) 2.92147 + 2.12257i 0.187028 + 0.135884i
\(245\) −1.83440 + 5.64571i −0.117196 + 0.360691i
\(246\) 0 0
\(247\) 21.3982 15.5467i 1.36154 0.989213i
\(248\) −7.60635 + 5.52634i −0.483004 + 0.350923i
\(249\) 0 0
\(250\) 0.227943 0.701538i 0.0144164 0.0443691i
\(251\) 13.9403 + 10.1282i 0.879902 + 0.639286i 0.933225 0.359291i \(-0.116982\pi\)
−0.0533238 + 0.998577i \(0.516982\pi\)
\(252\) 0 0
\(253\) 4.75643 6.61222i 0.299034 0.415707i
\(254\) −8.78527 −0.551237
\(255\) 0 0
\(256\) −3.68753 + 11.3491i −0.230471 + 0.709316i
\(257\) −5.71540 17.5902i −0.356517 1.09725i −0.955125 0.296204i \(-0.904279\pi\)
0.598608 0.801042i \(-0.295721\pi\)
\(258\) 0 0
\(259\) −4.97186 + 3.61227i −0.308936 + 0.224455i
\(260\) −1.55168 4.77558i −0.0962310 0.296169i
\(261\) 0 0
\(262\) −6.67626 4.85059i −0.412461 0.299670i
\(263\) −3.69135 −0.227618 −0.113809 0.993503i \(-0.536305\pi\)
−0.113809 + 0.993503i \(0.536305\pi\)
\(264\) 0 0
\(265\) 11.8480 0.727819
\(266\) 4.72007 + 3.42933i 0.289406 + 0.210266i
\(267\) 0 0
\(268\) 2.76550 + 8.51135i 0.168930 + 0.519913i
\(269\) −8.04575 + 5.84558i −0.490558 + 0.356411i −0.805399 0.592733i \(-0.798049\pi\)
0.314841 + 0.949145i \(0.398049\pi\)
\(270\) 0 0
\(271\) 0.387400 + 1.19229i 0.0235329 + 0.0724267i 0.962133 0.272580i \(-0.0878768\pi\)
−0.938600 + 0.345006i \(0.887877\pi\)
\(272\) −0.764345 + 2.35241i −0.0463452 + 0.142636i
\(273\) 0 0
\(274\) 3.15802 0.190783
\(275\) 1.96213 + 2.67395i 0.118321 + 0.161245i
\(276\) 0 0
\(277\) 6.54763 + 4.75713i 0.393409 + 0.285828i 0.766851 0.641825i \(-0.221823\pi\)
−0.373442 + 0.927654i \(0.621823\pi\)
\(278\) −1.35699 + 4.17639i −0.0813870 + 0.250483i
\(279\) 0 0
\(280\) 2.12706 1.54540i 0.127116 0.0923554i
\(281\) 20.5250 14.9123i 1.22442 0.889591i 0.227958 0.973671i \(-0.426795\pi\)
0.996459 + 0.0840804i \(0.0267953\pi\)
\(282\) 0 0
\(283\) −6.31705 + 19.4419i −0.375510 + 1.15570i 0.567624 + 0.823288i \(0.307863\pi\)
−0.943134 + 0.332412i \(0.892137\pi\)
\(284\) −2.38294 1.73131i −0.141401 0.102734i
\(285\) 0 0
\(286\) −8.03714 2.56945i −0.475246 0.151935i
\(287\) −4.05977 −0.239641
\(288\) 0 0
\(289\) −3.47600 + 10.6980i −0.204470 + 0.629295i
\(290\) 1.35725 + 4.17718i 0.0797003 + 0.245292i
\(291\) 0 0
\(292\) −0.972737 + 0.706734i −0.0569251 + 0.0413585i
\(293\) −0.787705 2.42431i −0.0460182 0.141630i 0.925407 0.378974i \(-0.123723\pi\)
−0.971426 + 0.237344i \(0.923723\pi\)
\(294\) 0 0
\(295\) 2.38361 + 1.73179i 0.138779 + 0.100829i
\(296\) −15.1896 −0.882878
\(297\) 0 0
\(298\) 2.79156 0.161711
\(299\) 6.85264 + 4.97873i 0.396298 + 0.287928i
\(300\) 0 0
\(301\) −2.43797 7.50331i −0.140523 0.432484i
\(302\) 14.5352 10.5604i 0.836404 0.607683i
\(303\) 0 0
\(304\) −2.44416 7.52234i −0.140182 0.431436i
\(305\) 0.766476 2.35897i 0.0438883 0.135074i
\(306\) 0 0
\(307\) 8.99273 0.513242 0.256621 0.966512i \(-0.417391\pi\)
0.256621 + 0.966512i \(0.417391\pi\)
\(308\) 0.0235596 + 4.98010i 0.00134243 + 0.283767i
\(309\) 0 0
\(310\) 2.20098 + 1.59911i 0.125008 + 0.0908233i
\(311\) 6.21840 19.1383i 0.352613 1.08523i −0.604767 0.796402i \(-0.706734\pi\)
0.957380 0.288830i \(-0.0932662\pi\)
\(312\) 0 0
\(313\) −5.74792 + 4.17611i −0.324892 + 0.236048i −0.738260 0.674516i \(-0.764352\pi\)
0.413368 + 0.910564i \(0.364352\pi\)
\(314\) −4.31585 + 3.13565i −0.243558 + 0.176955i
\(315\) 0 0
\(316\) 5.43390 16.7238i 0.305681 0.940789i
\(317\) 1.85526 + 1.34793i 0.104202 + 0.0757071i 0.638666 0.769484i \(-0.279487\pi\)
−0.534464 + 0.845191i \(0.679487\pi\)
\(318\) 0 0
\(319\) −18.8103 6.01362i −1.05318 0.336698i
\(320\) 2.25922 0.126294
\(321\) 0 0
\(322\) −0.577370 + 1.77696i −0.0321756 + 0.0990262i
\(323\) 5.68327 + 17.4913i 0.316226 + 0.973242i
\(324\) 0 0
\(325\) −2.79029 + 2.02726i −0.154777 + 0.112452i
\(326\) 4.26007 + 13.1111i 0.235943 + 0.726159i
\(327\) 0 0
\(328\) −8.11793 5.89802i −0.448237 0.325664i
\(329\) −6.02629 −0.332240
\(330\) 0 0
\(331\) 15.3951 0.846192 0.423096 0.906085i \(-0.360943\pi\)
0.423096 + 0.906085i \(0.360943\pi\)
\(332\) −1.89634 1.37777i −0.104075 0.0756150i
\(333\) 0 0
\(334\) −1.79010 5.50937i −0.0979501 0.301459i
\(335\) 4.97304 3.61313i 0.271706 0.197406i
\(336\) 0 0
\(337\) −6.02485 18.5426i −0.328195 1.01008i −0.969978 0.243193i \(-0.921805\pi\)
0.641783 0.766886i \(-0.278195\pi\)
\(338\) −0.251758 + 0.774831i −0.0136938 + 0.0421453i
\(339\) 0 0
\(340\) 3.49153 0.189355
\(341\) −11.6157 + 3.83501i −0.629024 + 0.207677i
\(342\) 0 0
\(343\) 10.7941 + 7.84234i 0.582825 + 0.423447i
\(344\) 6.02580 18.5455i 0.324889 0.999907i
\(345\) 0 0
\(346\) 6.68655 4.85806i 0.359471 0.261171i
\(347\) −1.75479 + 1.27493i −0.0942023 + 0.0684420i −0.633889 0.773424i \(-0.718543\pi\)
0.539687 + 0.841866i \(0.318543\pi\)
\(348\) 0 0
\(349\) −7.74150 + 23.8259i −0.414393 + 1.27537i 0.498400 + 0.866947i \(0.333921\pi\)
−0.912793 + 0.408423i \(0.866079\pi\)
\(350\) −0.615490 0.447180i −0.0328993 0.0239028i
\(351\) 0 0
\(352\) −11.3478 + 15.7753i −0.604838 + 0.840825i
\(353\) 23.2532 1.23764 0.618821 0.785532i \(-0.287611\pi\)
0.618821 + 0.785532i \(0.287611\pi\)
\(354\) 0 0
\(355\) −0.625187 + 1.92413i −0.0331815 + 0.102122i
\(356\) 3.67166 + 11.3002i 0.194597 + 0.598909i
\(357\) 0 0
\(358\) 0.874037 0.635025i 0.0461943 0.0335621i
\(359\) −3.12799 9.62695i −0.165089 0.508091i 0.833954 0.551834i \(-0.186072\pi\)
−0.999043 + 0.0437429i \(0.986072\pi\)
\(360\) 0 0
\(361\) −32.2075 23.4001i −1.69513 1.23158i
\(362\) 6.85194 0.360130
\(363\) 0 0
\(364\) −5.17891 −0.271448
\(365\) 0.668140 + 0.485432i 0.0349721 + 0.0254087i
\(366\) 0 0
\(367\) 1.14622 + 3.52770i 0.0598322 + 0.184145i 0.976505 0.215493i \(-0.0691359\pi\)
−0.916673 + 0.399638i \(0.869136\pi\)
\(368\) 2.04920 1.48883i 0.106822 0.0776107i
\(369\) 0 0
\(370\) 1.35822 + 4.18017i 0.0706104 + 0.217316i
\(371\) 3.77613 11.6217i 0.196047 0.603371i
\(372\) 0 0
\(373\) −9.34017 −0.483616 −0.241808 0.970324i \(-0.577740\pi\)
−0.241808 + 0.970324i \(0.577740\pi\)
\(374\) 3.42615 4.76291i 0.177162 0.246284i
\(375\) 0 0
\(376\) −12.0502 8.75496i −0.621440 0.451503i
\(377\) 6.34609 19.5312i 0.326840 1.00591i
\(378\) 0 0
\(379\) 7.93783 5.76717i 0.407739 0.296240i −0.364947 0.931028i \(-0.618913\pi\)
0.772686 + 0.634789i \(0.218913\pi\)
\(380\) −9.03261 + 6.56257i −0.463363 + 0.336653i
\(381\) 0 0
\(382\) 1.01958 3.13795i 0.0521663 0.160552i
\(383\) −14.6002 10.6076i −0.746034 0.542025i 0.148561 0.988903i \(-0.452536\pi\)
−0.894595 + 0.446878i \(0.852536\pi\)
\(384\) 0 0
\(385\) 3.24824 1.07243i 0.165546 0.0546562i
\(386\) −16.7194 −0.850993
\(387\) 0 0
\(388\) −1.09899 + 3.38235i −0.0557929 + 0.171713i
\(389\) −9.63871 29.6649i −0.488702 1.50407i −0.826546 0.562869i \(-0.809698\pi\)
0.337844 0.941202i \(-0.390302\pi\)
\(390\) 0 0
\(391\) −4.76490 + 3.46191i −0.240972 + 0.175076i
\(392\) 4.67626 + 14.3921i 0.236187 + 0.726909i
\(393\) 0 0
\(394\) −6.68851 4.85948i −0.336962 0.244817i
\(395\) −12.0782 −0.607719
\(396\) 0 0
\(397\) −10.6212 −0.533062 −0.266531 0.963826i \(-0.585877\pi\)
−0.266531 + 0.963826i \(0.585877\pi\)
\(398\) 4.66657 + 3.39046i 0.233914 + 0.169948i
\(399\) 0 0
\(400\) 0.318714 + 0.980901i 0.0159357 + 0.0490450i
\(401\) −22.3029 + 16.2040i −1.11375 + 0.809190i −0.983251 0.182258i \(-0.941659\pi\)
−0.130503 + 0.991448i \(0.541659\pi\)
\(402\) 0 0
\(403\) −3.93087 12.0980i −0.195811 0.602643i
\(404\) −3.38488 + 10.4176i −0.168404 + 0.518295i
\(405\) 0 0
\(406\) 4.52997 0.224818
\(407\) −18.8238 6.01792i −0.933061 0.298297i
\(408\) 0 0
\(409\) −11.6241 8.44540i −0.574774 0.417598i 0.262062 0.965051i \(-0.415598\pi\)
−0.836836 + 0.547453i \(0.815598\pi\)
\(410\) −0.897243 + 2.76143i −0.0443117 + 0.136377i
\(411\) 0 0
\(412\) −11.1686 + 8.11448i −0.550238 + 0.399772i
\(413\) 2.45840 1.78613i 0.120970 0.0878899i
\(414\) 0 0
\(415\) −0.497523 + 1.53122i −0.0244224 + 0.0751645i
\(416\) −16.3488 11.8781i −0.801568 0.582373i
\(417\) 0 0
\(418\) 0.0887552 + 18.7613i 0.00434116 + 0.917647i
\(419\) 31.4707 1.53744 0.768722 0.639584i \(-0.220893\pi\)
0.768722 + 0.639584i \(0.220893\pi\)
\(420\) 0 0
\(421\) 8.21095 25.2707i 0.400177 1.23162i −0.524679 0.851300i \(-0.675815\pi\)
0.924856 0.380318i \(-0.124185\pi\)
\(422\) −5.18959 15.9719i −0.252625 0.777500i
\(423\) 0 0
\(424\) 24.4348 17.7529i 1.18666 0.862156i
\(425\) −0.741089 2.28084i −0.0359481 0.110637i
\(426\) 0 0
\(427\) −2.06963 1.50367i −0.100156 0.0727679i
\(428\) −6.76518 −0.327008
\(429\) 0 0
\(430\) −5.64252 −0.272106
\(431\) −3.12984 2.27397i −0.150759 0.109533i 0.509849 0.860264i \(-0.329701\pi\)
−0.660608 + 0.750731i \(0.729701\pi\)
\(432\) 0 0
\(433\) 12.4036 + 38.1743i 0.596077 + 1.83454i 0.549288 + 0.835633i \(0.314899\pi\)
0.0467895 + 0.998905i \(0.485101\pi\)
\(434\) 2.27005 1.64929i 0.108966 0.0791684i
\(435\) 0 0
\(436\) 2.39715 + 7.37768i 0.114803 + 0.353327i
\(437\) 5.81994 17.9119i 0.278406 0.856844i
\(438\) 0 0
\(439\) 1.02336 0.0488425 0.0244212 0.999702i \(-0.492226\pi\)
0.0244212 + 0.999702i \(0.492226\pi\)
\(440\) 8.05321 + 2.57459i 0.383922 + 0.122739i
\(441\) 0 0
\(442\) 4.93608 + 3.58627i 0.234785 + 0.170582i
\(443\) 4.96678 15.2862i 0.235979 0.726268i −0.761011 0.648739i \(-0.775297\pi\)
0.996990 0.0775295i \(-0.0247032\pi\)
\(444\) 0 0
\(445\) 6.60252 4.79701i 0.312989 0.227400i
\(446\) 9.57368 6.95569i 0.453327 0.329361i
\(447\) 0 0
\(448\) 0.720043 2.21607i 0.0340188 0.104699i
\(449\) 28.9969 + 21.0675i 1.36845 + 0.994235i 0.997857 + 0.0654379i \(0.0208444\pi\)
0.370590 + 0.928797i \(0.379156\pi\)
\(450\) 0 0
\(451\) −7.72346 10.5254i −0.363684 0.495620i
\(452\) 0.443901 0.0208793
\(453\) 0 0
\(454\) 5.50625 16.9465i 0.258421 0.795338i
\(455\) 1.09924 + 3.38312i 0.0515332 + 0.158603i
\(456\) 0 0
\(457\) 20.3488 14.7842i 0.951875 0.691578i 0.000625413 1.00000i \(-0.499801\pi\)
0.951250 + 0.308422i \(0.0998009\pi\)
\(458\) −3.42241 10.5331i −0.159919 0.492179i
\(459\) 0 0
\(460\) −2.89263 2.10162i −0.134870 0.0979886i
\(461\) −6.65631 −0.310015 −0.155008 0.987913i \(-0.549540\pi\)
−0.155008 + 0.987913i \(0.549540\pi\)
\(462\) 0 0
\(463\) 38.7730 1.80194 0.900968 0.433886i \(-0.142858\pi\)
0.900968 + 0.433886i \(0.142858\pi\)
\(464\) −4.96830 3.60968i −0.230648 0.167575i
\(465\) 0 0
\(466\) −2.60447 8.01573i −0.120650 0.371321i
\(467\) 18.2429 13.2542i 0.844179 0.613332i −0.0793559 0.996846i \(-0.525286\pi\)
0.923535 + 0.383514i \(0.125286\pi\)
\(468\) 0 0
\(469\) −1.95914 6.02961i −0.0904647 0.278422i
\(470\) −1.33186 + 4.09904i −0.0614341 + 0.189075i
\(471\) 0 0
\(472\) 7.51071 0.345708
\(473\) 14.8150 20.5953i 0.681194 0.946971i
\(474\) 0 0
\(475\) 6.20420 + 4.50761i 0.284668 + 0.206823i
\(476\) 1.11280 3.42484i 0.0510051 0.156977i
\(477\) 0 0
\(478\) 16.3553 11.8828i 0.748075 0.543509i
\(479\) −1.32021 + 0.959186i −0.0603218 + 0.0438263i −0.617538 0.786541i \(-0.711870\pi\)
0.557216 + 0.830368i \(0.311870\pi\)
\(480\) 0 0
\(481\) 6.35063 19.5452i 0.289564 0.891186i
\(482\) −6.52782 4.74274i −0.297334 0.216026i
\(483\) 0 0
\(484\) −12.8666 + 9.53540i −0.584844 + 0.433427i
\(485\) 2.44278 0.110921
\(486\) 0 0
\(487\) 0.324560 0.998894i 0.0147072 0.0452642i −0.943434 0.331562i \(-0.892425\pi\)
0.958141 + 0.286297i \(0.0924245\pi\)
\(488\) −1.95390 6.01349i −0.0884490 0.272218i
\(489\) 0 0
\(490\) 3.54254 2.57381i 0.160036 0.116273i
\(491\) 4.29969 + 13.2331i 0.194042 + 0.597201i 0.999986 + 0.00520928i \(0.00165817\pi\)
−0.805944 + 0.591992i \(0.798342\pi\)
\(492\) 0 0
\(493\) 11.5525 + 8.39341i 0.520300 + 0.378020i
\(494\) −19.5103 −0.877811
\(495\) 0 0
\(496\) −3.80394 −0.170802
\(497\) 1.68812 + 1.22649i 0.0757226 + 0.0550157i
\(498\) 0 0
\(499\) 5.36679 + 16.5173i 0.240250 + 0.739415i 0.996381 + 0.0849943i \(0.0270872\pi\)
−0.756131 + 0.654420i \(0.772913\pi\)
\(500\) 1.17784 0.855749i 0.0526745 0.0382702i
\(501\) 0 0
\(502\) −3.92772 12.0883i −0.175303 0.539526i
\(503\) −11.0794 + 34.0988i −0.494005 + 1.52039i 0.324498 + 0.945887i \(0.394805\pi\)
−0.818502 + 0.574503i \(0.805195\pi\)
\(504\) 0 0
\(505\) 7.52373 0.334802
\(506\) −5.70536 + 1.88367i −0.253634 + 0.0837393i
\(507\) 0 0
\(508\) −14.0280 10.1919i −0.622392 0.452194i
\(509\) −0.660921 + 2.03410i −0.0292948 + 0.0901601i −0.964635 0.263590i \(-0.915094\pi\)
0.935340 + 0.353750i \(0.115094\pi\)
\(510\) 0 0
\(511\) 0.689106 0.500665i 0.0304843 0.0221481i
\(512\) −9.14306 + 6.64282i −0.404070 + 0.293574i
\(513\) 0 0
\(514\) −4.21591 + 12.9752i −0.185956 + 0.572313i
\(515\) 7.67135 + 5.57356i 0.338040 + 0.245601i
\(516\) 0 0
\(517\) −11.4646 15.6238i −0.504214 0.687132i
\(518\) 4.53321 0.199178
\(519\) 0 0
\(520\) −2.71693 + 8.36185i −0.119145 + 0.366691i
\(521\) 3.93540 + 12.1119i 0.172413 + 0.530633i 0.999506 0.0314326i \(-0.0100070\pi\)
−0.827093 + 0.562065i \(0.810007\pi\)
\(522\) 0 0
\(523\) −19.3426 + 14.0532i −0.845793 + 0.614504i −0.923983 0.382434i \(-0.875086\pi\)
0.0781901 + 0.996938i \(0.475086\pi\)
\(524\) −5.03317 15.4905i −0.219875 0.676705i
\(525\) 0 0
\(526\) 2.20286 + 1.60047i 0.0960493 + 0.0697839i
\(527\) 8.84510 0.385299
\(528\) 0 0
\(529\) −16.9686 −0.737766
\(530\) −7.07047 5.13700i −0.307122 0.223137i
\(531\) 0 0
\(532\) 3.55841 + 10.9517i 0.154277 + 0.474815i
\(533\) 10.9833 7.97983i 0.475739 0.345645i
\(534\) 0 0
\(535\) 1.43593 + 4.41935i 0.0620808 + 0.191065i
\(536\) 4.84229 14.9030i 0.209155 0.643713i
\(537\) 0 0
\(538\) 7.33590 0.316273
\(539\) 0.0931395 + 19.6881i 0.00401180 + 0.848027i
\(540\) 0 0
\(541\) −1.06726 0.775410i −0.0458851 0.0333375i 0.564606 0.825360i \(-0.309028\pi\)
−0.610491 + 0.792023i \(0.709028\pi\)
\(542\) 0.285762 0.879484i 0.0122745 0.0377771i
\(543\) 0 0
\(544\) 11.3680 8.25932i 0.487398 0.354116i
\(545\) 4.31066 3.13188i 0.184648 0.134155i
\(546\) 0 0
\(547\) 2.88044 8.86507i 0.123159 0.379043i −0.870403 0.492341i \(-0.836141\pi\)
0.993561 + 0.113298i \(0.0361414\pi\)
\(548\) 5.04261 + 3.66367i 0.215410 + 0.156504i
\(549\) 0 0
\(550\) −0.0115735 2.44645i −0.000493497 0.104317i
\(551\) −45.6625 −1.94529
\(552\) 0 0
\(553\) −3.84949 + 11.8475i −0.163697 + 0.503807i
\(554\) −1.84482 5.67776i −0.0783788 0.241225i
\(555\) 0 0
\(556\) −7.01190 + 5.09444i −0.297371 + 0.216052i
\(557\) −12.1497 37.3929i −0.514798 1.58439i −0.783648 0.621205i \(-0.786644\pi\)
0.268850 0.963182i \(-0.413356\pi\)
\(558\) 0 0
\(559\) 21.3441 + 15.5074i 0.902759 + 0.655893i
\(560\) 1.06374 0.0449514
\(561\) 0 0
\(562\) −18.7141 −0.789407
\(563\) 16.1649 + 11.7445i 0.681271 + 0.494972i 0.873779 0.486323i \(-0.161662\pi\)
−0.192508 + 0.981295i \(0.561662\pi\)
\(564\) 0 0
\(565\) −0.0942195 0.289978i −0.00396384 0.0121995i
\(566\) 12.1993 8.86330i 0.512774 0.372552i
\(567\) 0 0
\(568\) 1.59373 + 4.90499i 0.0668713 + 0.205809i
\(569\) 10.6811 32.8730i 0.447775 1.37811i −0.431637 0.902047i \(-0.642064\pi\)
0.879412 0.476061i \(-0.157936\pi\)
\(570\) 0 0
\(571\) 3.15090 0.131861 0.0659306 0.997824i \(-0.478998\pi\)
0.0659306 + 0.997824i \(0.478998\pi\)
\(572\) −9.85254 13.4268i −0.411955 0.561404i
\(573\) 0 0
\(574\) 2.42273 + 1.76021i 0.101123 + 0.0734699i
\(575\) −0.758911 + 2.33569i −0.0316488 + 0.0974049i
\(576\) 0 0
\(577\) −22.1044 + 16.0598i −0.920220 + 0.668579i −0.943579 0.331148i \(-0.892564\pi\)
0.0233590 + 0.999727i \(0.492564\pi\)
\(578\) 6.71273 4.87709i 0.279213 0.202860i
\(579\) 0 0
\(580\) −2.67881 + 8.24453i −0.111231 + 0.342335i
\(581\) 1.34340 + 0.976041i 0.0557338 + 0.0404930i
\(582\) 0 0
\(583\) 37.3143 12.3196i 1.54540 0.510227i
\(584\) 2.10530 0.0871180
\(585\) 0 0
\(586\) −0.581043 + 1.78827i −0.0240027 + 0.0738726i
\(587\) 14.2667 + 43.9082i 0.588848 + 1.81229i 0.583236 + 0.812303i \(0.301786\pi\)
0.00561158 + 0.999984i \(0.498214\pi\)
\(588\) 0 0
\(589\) −22.8823 + 16.6250i −0.942850 + 0.685020i
\(590\) −0.671589 2.06694i −0.0276489 0.0850945i
\(591\) 0 0
\(592\) −4.97186 3.61227i −0.204342 0.148463i
\(593\) −39.4265 −1.61905 −0.809525 0.587085i \(-0.800275\pi\)
−0.809525 + 0.587085i \(0.800275\pi\)
\(594\) 0 0
\(595\) −2.47347 −0.101402
\(596\) 4.45746 + 3.23853i 0.182585 + 0.132656i
\(597\) 0 0
\(598\) −1.93075 5.94225i −0.0789544 0.242997i
\(599\) 0.848455 0.616438i 0.0346669 0.0251870i −0.570317 0.821425i \(-0.693180\pi\)
0.604984 + 0.796238i \(0.293180\pi\)
\(600\) 0 0
\(601\) 8.42065 + 25.9161i 0.343485 + 1.05714i 0.962390 + 0.271673i \(0.0875768\pi\)
−0.618904 + 0.785466i \(0.712423\pi\)
\(602\) −1.79835 + 5.53475i −0.0732952 + 0.225579i
\(603\) 0 0
\(604\) 35.4605 1.44287
\(605\) 8.95996 + 6.38115i 0.364274 + 0.259431i
\(606\) 0 0
\(607\) −17.7350 12.8852i −0.719842 0.522996i 0.166492 0.986043i \(-0.446756\pi\)
−0.886334 + 0.463047i \(0.846756\pi\)
\(608\) −13.8851 + 42.7338i −0.563114 + 1.73309i
\(609\) 0 0
\(610\) −1.48019 + 1.07542i −0.0599313 + 0.0435426i
\(611\) 16.3035 11.8452i 0.659569 0.479205i
\(612\) 0 0
\(613\) 3.27313 10.0736i 0.132200 0.406871i −0.862944 0.505300i \(-0.831382\pi\)
0.995144 + 0.0984293i \(0.0313818\pi\)
\(614\) −5.36653 3.89901i −0.216576 0.157351i
\(615\) 0 0
\(616\) 5.09209 7.07884i 0.205166 0.285215i
\(617\) −4.60402 −0.185351 −0.0926755 0.995696i \(-0.529542\pi\)
−0.0926755 + 0.995696i \(0.529542\pi\)
\(618\) 0 0
\(619\) 11.4348 35.1926i 0.459603 1.41451i −0.406043 0.913854i \(-0.633092\pi\)
0.865645 0.500657i \(-0.166908\pi\)
\(620\) 1.65930 + 5.10680i 0.0666390 + 0.205094i
\(621\) 0 0
\(622\) −12.0088 + 8.72489i −0.481508 + 0.349836i
\(623\) −2.60108 8.00529i −0.104210 0.320725i
\(624\) 0 0
\(625\) −0.809017 0.587785i −0.0323607 0.0235114i
\(626\) 5.24081 0.209465
\(627\) 0 0
\(628\) −10.5291 −0.420157
\(629\) 11.5608 + 8.39942i 0.460960 + 0.334907i
\(630\) 0 0
\(631\) −7.67617 23.6248i −0.305583 0.940489i −0.979459 0.201644i \(-0.935372\pi\)
0.673875 0.738845i \(-0.264628\pi\)
\(632\) −24.9094 + 18.0977i −0.990843 + 0.719890i
\(633\) 0 0
\(634\) −0.522727 1.60879i −0.0207601 0.0638931i
\(635\) −3.68038 + 11.3270i −0.146051 + 0.449500i
\(636\) 0 0
\(637\) −20.4741 −0.811213
\(638\) 8.61798 + 11.7444i 0.341189 + 0.464965i
\(639\) 0 0
\(640\) 8.13215 + 5.90835i 0.321452 + 0.233548i
\(641\) 13.7294 42.2547i 0.542278 1.66896i −0.185096 0.982720i \(-0.559260\pi\)
0.727374 0.686241i \(-0.240740\pi\)
\(642\) 0 0
\(643\) −20.9220 + 15.2007i −0.825082 + 0.599457i −0.918164 0.396201i \(-0.870328\pi\)
0.0930818 + 0.995658i \(0.470328\pi\)
\(644\) −2.98341 + 2.16757i −0.117563 + 0.0854143i
\(645\) 0 0
\(646\) 4.19221 12.9023i 0.164940 0.507634i
\(647\) 15.7649 + 11.4539i 0.619782 + 0.450298i 0.852845 0.522163i \(-0.174875\pi\)
−0.233063 + 0.972462i \(0.574875\pi\)
\(648\) 0 0
\(649\) 9.30768 + 2.97564i 0.365358 + 0.116804i
\(650\) 2.54411 0.0997883
\(651\) 0 0
\(652\) −8.40814 + 25.8776i −0.329288 + 1.01344i
\(653\) 5.16979 + 15.9110i 0.202310 + 0.622645i 0.999813 + 0.0193305i \(0.00615349\pi\)
−0.797504 + 0.603314i \(0.793847\pi\)
\(654\) 0 0
\(655\) −9.05084 + 6.57582i −0.353646 + 0.256939i
\(656\) −1.25454 3.86108i −0.0489815 0.150750i
\(657\) 0 0
\(658\) 3.59627 + 2.61284i 0.140197 + 0.101859i
\(659\) 1.66127 0.0647137 0.0323569 0.999476i \(-0.489699\pi\)
0.0323569 + 0.999476i \(0.489699\pi\)
\(660\) 0 0
\(661\) −44.0130 −1.71191 −0.855953 0.517053i \(-0.827029\pi\)
−0.855953 + 0.517053i \(0.827029\pi\)
\(662\) −9.18724 6.67492i −0.357072 0.259428i
\(663\) 0 0
\(664\) 1.26829 + 3.90338i 0.0492190 + 0.151481i
\(665\) 6.39888 4.64906i 0.248138 0.180283i
\(666\) 0 0
\(667\) −4.51879 13.9074i −0.174968 0.538497i
\(668\) 3.53314 10.8739i 0.136701 0.420723i
\(669\) 0 0
\(670\) −4.53429 −0.175175
\(671\) −0.0389168 8.22636i −0.00150237 0.317575i
\(672\) 0 0
\(673\) 31.2239 + 22.6855i 1.20359 + 0.874462i 0.994633 0.103462i \(-0.0329920\pi\)
0.208961 + 0.977924i \(0.432992\pi\)
\(674\) −4.44417 + 13.6778i −0.171183 + 0.526848i
\(675\) 0 0
\(676\) −1.30089 + 0.945154i −0.0500343 + 0.0363521i
\(677\) −31.2271 + 22.6878i −1.20016 + 0.871964i −0.994300 0.106619i \(-0.965998\pi\)
−0.205855 + 0.978582i \(0.565998\pi\)
\(678\) 0 0
\(679\) 0.778549 2.39613i 0.0298780 0.0919549i
\(680\) −4.94595 3.59344i −0.189669 0.137802i
\(681\) 0 0
\(682\) 8.59457 + 2.74766i 0.329103 + 0.105213i
\(683\) 0.748158 0.0286275 0.0143137 0.999898i \(-0.495444\pi\)
0.0143137 + 0.999898i \(0.495444\pi\)
\(684\) 0 0
\(685\) 1.32298 4.07170i 0.0505484 0.155572i
\(686\) −3.04126 9.36005i −0.116116 0.357368i
\(687\) 0 0
\(688\) 6.38270 4.63730i 0.243338 0.176796i
\(689\) 12.6276 + 38.8637i 0.481073 + 1.48059i
\(690\) 0 0
\(691\) −4.22456 3.06932i −0.160710 0.116763i 0.504524 0.863398i \(-0.331668\pi\)
−0.665234 + 0.746635i \(0.731668\pi\)
\(692\) 16.3128 0.620118
\(693\) 0 0
\(694\) 1.59998 0.0607342
\(695\) 4.81624 + 3.49920i 0.182690 + 0.132732i
\(696\) 0 0
\(697\) 2.91712 + 8.97796i 0.110494 + 0.340065i
\(698\) 14.9501 10.8619i 0.565871 0.411129i
\(699\) 0 0
\(700\) −0.464011 1.42808i −0.0175380 0.0539764i
\(701\) 4.37506 13.4650i 0.165244 0.508568i −0.833811 0.552051i \(-0.813845\pi\)
0.999054 + 0.0434831i \(0.0138455\pi\)
\(702\) 0 0
\(703\) −45.6952 −1.72343
\(704\) 7.11520 2.34914i 0.268164 0.0885366i
\(705\) 0 0
\(706\) −13.8766 10.0820i −0.522255 0.379440i
\(707\) 2.39792 7.38004i 0.0901830 0.277555i
\(708\) 0 0
\(709\) 13.9267 10.1183i 0.523028 0.380002i −0.294715 0.955585i \(-0.595225\pi\)
0.817744 + 0.575583i \(0.195225\pi\)
\(710\) 1.20734 0.877184i 0.0453107 0.0329201i
\(711\) 0 0
\(712\) 6.42893 19.7862i 0.240934 0.741519i
\(713\) −7.32792 5.32404i −0.274433 0.199387i
\(714\) 0 0
\(715\) −6.67982 + 9.28605i −0.249811 + 0.347279i
\(716\) 2.13233 0.0796891
\(717\) 0 0
\(718\) −2.30733 + 7.10123i −0.0861087 + 0.265015i
\(719\) 8.20624 + 25.2562i 0.306041 + 0.941897i 0.979287 + 0.202478i \(0.0648996\pi\)
−0.673246 + 0.739419i \(0.735100\pi\)
\(720\) 0 0
\(721\) 7.91208 5.74846i 0.294661 0.214084i
\(722\) 9.07457 + 27.9286i 0.337720 + 1.03940i
\(723\) 0 0
\(724\) 10.9409 + 7.94905i 0.406617 + 0.295424i
\(725\) 5.95431 0.221138
\(726\) 0 0
\(727\) 44.1917 1.63898 0.819490 0.573094i \(-0.194257\pi\)
0.819490 + 0.573094i \(0.194257\pi\)
\(728\) 7.33622 + 5.33007i 0.271898 + 0.197546i
\(729\) 0 0
\(730\) −0.188251 0.579377i −0.00696748 0.0214437i
\(731\) −14.8414 + 10.7829i −0.548928 + 0.398819i
\(732\) 0 0
\(733\) 7.71320 + 23.7388i 0.284894 + 0.876812i 0.986431 + 0.164179i \(0.0524975\pi\)
−0.701537 + 0.712633i \(0.747502\pi\)
\(734\) 0.845498 2.60218i 0.0312079 0.0960480i
\(735\) 0 0
\(736\) −14.3895 −0.530404
\(737\) 11.9052 16.5502i 0.438534 0.609635i
\(738\) 0 0
\(739\) −17.1789 12.4812i −0.631934 0.459127i 0.225135 0.974327i \(-0.427718\pi\)
−0.857070 + 0.515200i \(0.827718\pi\)
\(740\) −2.68073 + 8.25043i −0.0985455 + 0.303292i
\(741\) 0 0
\(742\) −7.29234 + 5.29820i −0.267710 + 0.194503i
\(743\) −24.7986 + 18.0172i −0.909772 + 0.660988i −0.940957 0.338526i \(-0.890072\pi\)
0.0311852 + 0.999514i \(0.490072\pi\)
\(744\) 0 0
\(745\) 1.16946 3.59922i 0.0428456 0.131865i
\(746\) 5.57387 + 4.04965i 0.204074 + 0.148268i
\(747\) 0 0
\(748\) 10.9963 3.63051i 0.402064 0.132744i
\(749\) 4.79259 0.175118
\(750\) 0 0
\(751\) −9.36548 + 28.8240i −0.341751 + 1.05180i 0.621549 + 0.783375i \(0.286504\pi\)
−0.963300 + 0.268427i \(0.913496\pi\)
\(752\) −1.86223 5.73134i −0.0679084 0.209001i
\(753\) 0 0
\(754\) −12.2554 + 8.90404i −0.446314 + 0.324266i
\(755\) −7.52661 23.1645i −0.273922 0.843044i
\(756\) 0 0
\(757\) 28.2099 + 20.4957i 1.02531 + 0.744929i 0.967364 0.253391i \(-0.0815459\pi\)
0.0579427 + 0.998320i \(0.481546\pi\)
\(758\) −7.23750 −0.262878
\(759\) 0 0
\(760\) 19.5493 0.709129
\(761\) −2.17603 1.58098i −0.0788809 0.0573104i 0.547646 0.836710i \(-0.315524\pi\)
−0.626527 + 0.779400i \(0.715524\pi\)
\(762\) 0 0
\(763\) −1.69819 5.22650i −0.0614787 0.189212i
\(764\) 5.26842 3.82773i 0.190605 0.138482i
\(765\) 0 0
\(766\) 4.11365 + 12.6605i 0.148632 + 0.457443i
\(767\) −3.14015 + 9.66440i −0.113384 + 0.348961i
\(768\) 0 0
\(769\) −32.5735 −1.17463 −0.587315 0.809359i \(-0.699815\pi\)
−0.587315 + 0.809359i \(0.699815\pi\)
\(770\) −2.40341 0.768365i −0.0866129 0.0276899i
\(771\) 0 0
\(772\) −26.6969 19.3964i −0.960841 0.698092i
\(773\) −12.8748 + 39.6246i −0.463074 + 1.42520i 0.398314 + 0.917249i \(0.369595\pi\)
−0.861388 + 0.507947i \(0.830405\pi\)
\(774\) 0 0
\(775\) 2.98382 2.16787i 0.107182 0.0778722i
\(776\) 5.03787 3.66022i 0.180849 0.131394i
\(777\) 0 0
\(778\) −7.10990 + 21.8820i −0.254902 + 0.784509i
\(779\) −24.4213 17.7431i −0.874984 0.635713i
\(780\) 0 0
\(781\) 0.0317431 + 6.70994i 0.00113586 + 0.240101i
\(782\) 4.34451 0.155359
\(783\) 0 0
\(784\) −1.89197 + 5.82288i −0.0675703 + 0.207960i
\(785\) 2.23484 + 6.87813i 0.0797649 + 0.245491i
\(786\) 0 0
\(787\) 29.0605 21.1137i 1.03589 0.752622i 0.0664148 0.997792i \(-0.478844\pi\)
0.969480 + 0.245170i \(0.0788439\pi\)
\(788\) −5.04239 15.5189i −0.179628 0.552838i
\(789\) 0 0
\(790\) 7.20782 + 5.23679i 0.256443 + 0.186317i
\(791\) −0.314468 −0.0111812
\(792\) 0 0
\(793\) 8.55476 0.303789
\(794\) 6.33833 + 4.60507i 0.224939 + 0.163428i
\(795\) 0 0
\(796\) 3.51808 + 10.8275i 0.124695 + 0.383771i
\(797\) −25.6618 + 18.6444i −0.908987 + 0.660418i −0.940759 0.339077i \(-0.889885\pi\)
0.0317713 + 0.999495i \(0.489885\pi\)
\(798\) 0 0
\(799\) 4.33014 + 13.3268i 0.153189 + 0.471468i
\(800\) 1.81059 5.57242i 0.0640140 0.197015i
\(801\) 0 0
\(802\) 20.3352 0.718061
\(803\) 2.60900 + 0.834092i 0.0920698 + 0.0294345i
\(804\) 0 0
\(805\) 2.04920 + 1.48883i 0.0722249 + 0.0524744i
\(806\) −2.89957 + 8.92396i −0.102133 + 0.314333i
\(807\) 0 0
\(808\) 15.5166 11.2734i 0.545870 0.396598i
\(809\) −6.88936 + 5.00541i −0.242217 + 0.175981i −0.702270 0.711910i \(-0.747830\pi\)
0.460053 + 0.887891i \(0.347830\pi\)
\(810\) 0 0
\(811\) 2.79052 8.58832i 0.0979882 0.301577i −0.890033 0.455897i \(-0.849319\pi\)
0.988021 + 0.154320i \(0.0493186\pi\)
\(812\) 7.23329 + 5.25529i 0.253839 + 0.184425i
\(813\) 0 0
\(814\) 8.62415 + 11.7528i 0.302276 + 0.411935i
\(815\) 18.6892 0.654653
\(816\) 0 0
\(817\) 18.1275 55.7908i 0.634202 1.95187i
\(818\) 3.27513 + 10.0798i 0.114512 + 0.352432i
\(819\) 0 0
\(820\) −4.63627 + 3.36845i −0.161906 + 0.117631i
\(821\) 16.7866 + 51.6638i 0.585856 + 1.80308i 0.595806 + 0.803129i \(0.296833\pi\)
−0.00994979 + 0.999950i \(0.503167\pi\)
\(822\) 0 0
\(823\) −14.4486 10.4975i −0.503646 0.365920i 0.306762 0.951786i \(-0.400755\pi\)
−0.810408 + 0.585866i \(0.800755\pi\)
\(824\) 24.1723 0.842083
\(825\) 0 0
\(826\) −2.24151 −0.0779920
\(827\) −42.0280 30.5351i −1.46146 1.06181i −0.982981 0.183708i \(-0.941190\pi\)
−0.478474 0.878102i \(-0.658810\pi\)
\(828\) 0 0
\(829\) −6.10185 18.7796i −0.211926 0.652241i −0.999358 0.0358392i \(-0.988590\pi\)
0.787431 0.616402i \(-0.211410\pi\)
\(830\) 0.960800 0.698062i 0.0333498 0.0242301i
\(831\) 0 0
\(832\) 2.40786 + 7.41064i 0.0834776 + 0.256918i
\(833\) 4.39930 13.5396i 0.152427 0.469121i
\(834\) 0 0
\(835\) −7.85328 −0.271774
\(836\) −21.6236 + 30.0604i −0.747869 + 1.03966i
\(837\) 0 0
\(838\) −18.7806 13.6449i −0.648763 0.471354i
\(839\) 1.27207 3.91502i 0.0439166 0.135162i −0.926694 0.375817i \(-0.877362\pi\)
0.970611 + 0.240655i \(0.0773623\pi\)
\(840\) 0 0
\(841\) −5.22128 + 3.79348i −0.180044 + 0.130810i
\(842\) −15.8567 + 11.5206i −0.546458 + 0.397025i
\(843\) 0 0
\(844\) 10.2427 31.5239i 0.352569 1.08510i
\(845\) 0.893540 + 0.649194i 0.0307387 + 0.0223330i
\(846\) 0 0
\(847\) 9.11494 6.75507i 0.313193 0.232107i
\(848\) 12.2198 0.419630
\(849\) 0 0
\(850\) −0.546657 + 1.68244i −0.0187502 + 0.0577072i
\(851\) −4.52203 13.9174i −0.155013 0.477081i
\(852\) 0 0
\(853\) −4.45190 + 3.23449i −0.152430 + 0.110747i −0.661386 0.750046i \(-0.730032\pi\)
0.508956 + 0.860792i \(0.330032\pi\)
\(854\) 0.583125 + 1.79468i 0.0199541 + 0.0614125i
\(855\) 0 0
\(856\) 9.58327 + 6.96265i 0.327549 + 0.237979i
\(857\) 26.9281 0.919847 0.459924 0.887959i \(-0.347877\pi\)
0.459924 + 0.887959i \(0.347877\pi\)
\(858\) 0 0
\(859\) 19.1519 0.653456 0.326728 0.945118i \(-0.394054\pi\)
0.326728 + 0.945118i \(0.394054\pi\)
\(860\) −9.00976 6.54598i −0.307230 0.223216i
\(861\) 0 0
\(862\) 0.881845 + 2.71404i 0.0300358 + 0.0924405i
\(863\) 4.01394 2.91630i 0.136636 0.0992720i −0.517368 0.855763i \(-0.673088\pi\)
0.654004 + 0.756491i \(0.273088\pi\)
\(864\) 0 0
\(865\) −3.46244 10.6563i −0.117726 0.362325i
\(866\) 9.14937 28.1589i 0.310908 0.956877i
\(867\) 0 0
\(868\) 5.53810 0.187975
\(869\) −38.0392 + 12.5589i −1.29039 + 0.426033i
\(870\) 0 0
\(871\) 17.1520 + 12.4616i 0.581172 + 0.422246i
\(872\) 4.19732 12.9180i 0.142139 0.437460i
\(873\) 0 0
\(874\) −11.2393 + 8.16581i −0.380174 + 0.276213i
\(875\) −0.834404 + 0.606230i −0.0282080 + 0.0204943i
\(876\) 0 0
\(877\) −8.40691 + 25.8738i −0.283881 + 0.873696i 0.702851 + 0.711338i \(0.251910\pi\)
−0.986732 + 0.162359i \(0.948090\pi\)
\(878\) −0.610706 0.443704i −0.0206103 0.0149743i
\(879\) 0 0
\(880\) 2.02371 + 2.75786i 0.0682191 + 0.0929675i
\(881\) −10.3570 −0.348935 −0.174467 0.984663i \(-0.555820\pi\)
−0.174467 + 0.984663i \(0.555820\pi\)
\(882\) 0 0
\(883\) 2.28515 7.03296i 0.0769014 0.236678i −0.905215 0.424954i \(-0.860290\pi\)
0.982116 + 0.188276i \(0.0602901\pi\)
\(884\) 3.72126 + 11.4529i 0.125159 + 0.385201i
\(885\) 0 0
\(886\) −9.59168 + 6.96877i −0.322239 + 0.234120i
\(887\) 5.58054 + 17.1752i 0.187376 + 0.576685i 0.999981 0.00612989i \(-0.00195122\pi\)
−0.812605 + 0.582815i \(0.801951\pi\)
\(888\) 0 0
\(889\) 9.93772 + 7.22018i 0.333300 + 0.242157i
\(890\) −6.02000 −0.201791
\(891\) 0 0
\(892\) 23.3563 0.782027
\(893\) −36.2507 26.3377i −1.21309 0.881358i
\(894\) 0 0
\(895\) −0.452595 1.39295i −0.0151286 0.0465610i
\(896\) 8.38734 6.09376i 0.280201 0.203578i
\(897\) 0 0
\(898\) −8.16997 25.1446i −0.272635 0.839085i
\(899\) −6.78623 + 20.8859i −0.226334 + 0.696583i
\(900\) 0 0
\(901\) −28.4141 −0.946612
\(902\) 0.0455564 + 9.62985i 0.00151686 + 0.320639i
\(903\) 0 0
\(904\) −0.628811 0.456858i −0.0209139 0.0151949i
\(905\) 2.87046 8.83437i 0.0954173 0.293664i
\(906\) 0 0
\(907\) −21.2748 + 15.4570i −0.706417 + 0.513242i −0.882016 0.471220i \(-0.843814\pi\)
0.175599 + 0.984462i \(0.443814\pi\)
\(908\) 28.4521 20.6716i 0.944215 0.686013i
\(909\) 0 0
\(910\) 0.810844 2.49552i 0.0268792 0.0827258i
\(911\) 23.1774 + 16.8394i 0.767902 + 0.557913i 0.901324 0.433146i \(-0.142597\pi\)
−0.133422 + 0.991059i \(0.542597\pi\)
\(912\) 0 0
\(913\) 0.0252611 + 5.33976i 0.000836020 + 0.176720i
\(914\) −18.5535 −0.613694
\(915\) 0 0
\(916\) 6.75483 20.7892i 0.223186 0.686896i
\(917\) 3.56560 + 10.9738i 0.117746 + 0.362386i
\(918\) 0 0
\(919\) −31.4358 + 22.8394i −1.03697 + 0.753404i −0.969692 0.244330i \(-0.921432\pi\)
−0.0672794 + 0.997734i \(0.521432\pi\)
\(920\) 1.93462 + 5.95414i 0.0637824 + 0.196302i
\(921\) 0 0
\(922\) 3.97224 + 2.88600i 0.130819 + 0.0950455i
\(923\) −6.97781 −0.229677
\(924\) 0 0
\(925\) 5.95858 0.195917
\(926\) −23.1383 16.8110i −0.760373 0.552443i
\(927\) 0 0
\(928\) 10.7808 + 33.1799i 0.353898 + 1.08919i
\(929\) 6.00397 4.36214i 0.196984 0.143117i −0.484921 0.874558i \(-0.661152\pi\)
0.681905 + 0.731441i \(0.261152\pi\)
\(930\) 0 0
\(931\) 14.0677 + 43.2959i 0.461050 + 1.41897i
\(932\) 5.14046 15.8207i 0.168381 0.518224i
\(933\) 0 0
\(934\) −16.6334 −0.544260
\(935\) −4.70562 6.41272i −0.153890 0.209718i
\(936\) 0 0
\(937\) 12.0834 + 8.77914i 0.394749 + 0.286802i 0.767399 0.641170i \(-0.221551\pi\)
−0.372650 + 0.927972i \(0.621551\pi\)
\(938\) −1.44514 + 4.44768i −0.0471855 + 0.145222i
\(939\) 0 0
\(940\) −6.88203 + 5.00009i −0.224467 + 0.163085i
\(941\) −42.3447 + 30.7652i −1.38040 + 1.00292i −0.383554 + 0.923518i \(0.625300\pi\)
−0.996843 + 0.0793986i \(0.974700\pi\)
\(942\) 0 0
\(943\) 2.98727 9.19386i 0.0972788 0.299393i
\(944\) 2.45840 + 1.78613i 0.0800142 + 0.0581337i
\(945\) 0 0
\(946\) −17.7706 + 5.86711i −0.577773 + 0.190756i
\(947\) 3.69553 0.120088 0.0600442 0.998196i \(-0.480876\pi\)
0.0600442 + 0.998196i \(0.480876\pi\)
\(948\) 0 0
\(949\) −0.880206 + 2.70899i −0.0285727 + 0.0879377i
\(950\) −1.74805 5.37996i −0.0567144 0.174549i
\(951\) 0 0
\(952\) −5.10116 + 3.70621i −0.165329 + 0.120119i
\(953\) −13.3349 41.0406i −0.431959 1.32943i −0.896171 0.443709i \(-0.853662\pi\)
0.464211 0.885724i \(-0.346338\pi\)
\(954\) 0 0
\(955\) −3.61870 2.62914i −0.117098 0.0850770i
\(956\) 39.9011 1.29049
\(957\) 0 0
\(958\) 1.20373 0.0388907
\(959\) −3.57229 2.59542i −0.115355 0.0838104i
\(960\) 0 0
\(961\) −5.37602 16.5457i −0.173420 0.533732i
\(962\) −12.2641 + 8.91041i −0.395411 + 0.287283i
\(963\) 0 0
\(964\) −4.92126 15.1461i −0.158503 0.487822i
\(965\) −7.00418 + 21.5567i −0.225473 + 0.693933i
\(966\) 0 0
\(967\) −29.2144 −0.939471 −0.469736 0.882807i \(-0.655651\pi\)
−0.469736 + 0.882807i \(0.655651\pi\)
\(968\) 28.0400 0.265306i 0.901238 0.00852725i
\(969\) 0 0
\(970\) −1.45776 1.05913i −0.0468060 0.0340065i
\(971\) 8.15948 25.1123i 0.261850 0.805892i −0.730552 0.682857i \(-0.760737\pi\)
0.992402 0.123035i \(-0.0392628\pi\)
\(972\) 0 0
\(973\) 4.96737 3.60901i 0.159247 0.115699i
\(974\) −0.626780 + 0.455382i −0.0200833 + 0.0145914i
\(975\) 0 0
\(976\) 0.790528 2.43300i 0.0253042 0.0778783i
\(977\) −12.8176 9.31251i −0.410070 0.297934i 0.363560 0.931571i \(-0.381561\pi\)
−0.773630 + 0.633637i \(0.781561\pi\)
\(978\) 0 0
\(979\) 15.8061 21.9731i 0.505166 0.702263i
\(980\) 8.64252 0.276075
\(981\) 0 0
\(982\) 3.17163 9.76126i 0.101211 0.311494i
\(983\) −10.8477 33.3858i −0.345988 1.06484i −0.961053 0.276365i \(-0.910870\pi\)
0.615064 0.788477i \(-0.289130\pi\)
\(984\) 0 0
\(985\) −9.06744 + 6.58788i −0.288913 + 0.209907i
\(986\) −3.25497 10.0178i −0.103659 0.319031i
\(987\) 0 0
\(988\) −31.1534 22.6342i −0.991120 0.720091i
\(989\) 18.7861 0.597363
\(990\) 0 0
\(991\) 18.9700 0.602600 0.301300 0.953529i \(-0.402579\pi\)
0.301300 + 0.953529i \(0.402579\pi\)
\(992\) 17.4828 + 12.7020i 0.555078 + 0.403288i
\(993\) 0 0
\(994\) −0.475634 1.46385i −0.0150862 0.0464306i
\(995\) 6.32635 4.59636i 0.200559 0.145714i
\(996\) 0 0
\(997\) 9.31213 + 28.6598i 0.294918 + 0.907665i 0.983249 + 0.182268i \(0.0583438\pi\)
−0.688331 + 0.725397i \(0.741656\pi\)
\(998\) 3.95876 12.1838i 0.125312 0.385672i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 495.2.n.e.136.1 8
3.2 odd 2 55.2.g.b.26.2 8
11.3 even 5 inner 495.2.n.e.91.1 8
11.5 even 5 5445.2.a.bp.1.3 4
11.6 odd 10 5445.2.a.bi.1.2 4
12.11 even 2 880.2.bo.h.81.2 8
15.2 even 4 275.2.z.a.224.2 16
15.8 even 4 275.2.z.a.224.3 16
15.14 odd 2 275.2.h.a.26.1 8
33.2 even 10 605.2.g.e.511.2 8
33.5 odd 10 605.2.a.j.1.2 4
33.8 even 10 605.2.g.k.366.1 8
33.14 odd 10 55.2.g.b.36.2 yes 8
33.17 even 10 605.2.a.k.1.3 4
33.20 odd 10 605.2.g.m.511.1 8
33.26 odd 10 605.2.g.m.251.1 8
33.29 even 10 605.2.g.e.251.2 8
33.32 even 2 605.2.g.k.81.1 8
132.47 even 10 880.2.bo.h.641.2 8
132.71 even 10 9680.2.a.cn.1.4 4
132.83 odd 10 9680.2.a.cm.1.4 4
165.14 odd 10 275.2.h.a.201.1 8
165.47 even 20 275.2.z.a.124.3 16
165.104 odd 10 3025.2.a.bd.1.3 4
165.113 even 20 275.2.z.a.124.2 16
165.149 even 10 3025.2.a.w.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.g.b.26.2 8 3.2 odd 2
55.2.g.b.36.2 yes 8 33.14 odd 10
275.2.h.a.26.1 8 15.14 odd 2
275.2.h.a.201.1 8 165.14 odd 10
275.2.z.a.124.2 16 165.113 even 20
275.2.z.a.124.3 16 165.47 even 20
275.2.z.a.224.2 16 15.2 even 4
275.2.z.a.224.3 16 15.8 even 4
495.2.n.e.91.1 8 11.3 even 5 inner
495.2.n.e.136.1 8 1.1 even 1 trivial
605.2.a.j.1.2 4 33.5 odd 10
605.2.a.k.1.3 4 33.17 even 10
605.2.g.e.251.2 8 33.29 even 10
605.2.g.e.511.2 8 33.2 even 10
605.2.g.k.81.1 8 33.32 even 2
605.2.g.k.366.1 8 33.8 even 10
605.2.g.m.251.1 8 33.26 odd 10
605.2.g.m.511.1 8 33.20 odd 10
880.2.bo.h.81.2 8 12.11 even 2
880.2.bo.h.641.2 8 132.47 even 10
3025.2.a.w.1.2 4 165.149 even 10
3025.2.a.bd.1.3 4 165.104 odd 10
5445.2.a.bi.1.2 4 11.6 odd 10
5445.2.a.bp.1.3 4 11.5 even 5
9680.2.a.cm.1.4 4 132.83 odd 10
9680.2.a.cn.1.4 4 132.71 even 10