Properties

Label 567.2.ba.a.143.12
Level $567$
Weight $2$
Character 567.143
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
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] = [567,2,Mod(143,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([7, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.ba (of order \(18\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 143.12
Character \(\chi\) \(=\) 567.143
Dual form 567.2.ba.a.341.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0103898 - 0.0123821i) q^{2} +(0.347251 + 1.96936i) q^{4} +(-3.05823 + 2.56616i) q^{5} +(-2.57348 + 0.614149i) q^{7} +(0.0559891 + 0.0323253i) q^{8} +O(q^{10})\) \(q+(0.0103898 - 0.0123821i) q^{2} +(0.347251 + 1.96936i) q^{4} +(-3.05823 + 2.56616i) q^{5} +(-2.57348 + 0.614149i) q^{7} +(0.0559891 + 0.0323253i) q^{8} +0.0645293i q^{10} +(3.31590 - 3.95174i) q^{11} +(0.220791 - 0.606618i) q^{13} +(-0.0191336 + 0.0382461i) q^{14} +(-3.75730 + 1.36754i) q^{16} -3.38766 q^{17} -0.379246i q^{19} +(-6.11565 - 5.13164i) q^{20} +(-0.0144792 - 0.0821158i) q^{22} +(-0.344877 + 0.947543i) q^{23} +(1.89935 - 10.7717i) q^{25} +(-0.00521724 - 0.00903653i) q^{26} +(-2.10312 - 4.85485i) q^{28} +(-1.97120 - 5.41582i) q^{29} +(-6.35598 + 1.12073i) q^{31} +(-0.0663282 + 0.182235i) q^{32} +(-0.0351973 + 0.0419465i) q^{34} +(6.29429 - 8.48217i) q^{35} +(-3.08407 + 5.34176i) q^{37} +(-0.00469587 - 0.00394030i) q^{38} +(-0.254179 + 0.0448186i) q^{40} +(0.266252 + 0.0969077i) q^{41} +(-1.45052 + 8.22633i) q^{43} +(8.93384 + 5.15796i) q^{44} +(0.00814938 + 0.0141151i) q^{46} +(-1.27739 + 7.24446i) q^{47} +(6.24564 - 3.16101i) q^{49} +(-0.113643 - 0.135434i) q^{50} +(1.27132 + 0.224168i) q^{52} +(1.71989 + 0.992981i) q^{53} +20.5944i q^{55} +(-0.163940 - 0.0488030i) q^{56} +(-0.0875398 - 0.0318619i) q^{58} +(3.21846 + 1.17142i) q^{59} +(-7.93400 - 1.39898i) q^{61} +(-0.0521605 + 0.0903447i) q^{62} +(-3.99687 - 6.92277i) q^{64} +(0.881448 + 2.42176i) q^{65} +(7.23088 - 6.06743i) q^{67} +(-1.17637 - 6.67152i) q^{68} +(-0.0396306 - 0.166065i) q^{70} +(-8.57363 + 4.94999i) q^{71} +(-6.13914 + 3.54444i) q^{73} +(0.0340994 + 0.0936874i) q^{74} +(0.746871 - 0.131693i) q^{76} +(-6.10647 + 12.2062i) q^{77} +(-0.980903 - 0.823075i) q^{79} +(7.98133 - 13.8241i) q^{80} +(0.00396624 - 0.00228991i) q^{82} +(-8.07527 + 2.93916i) q^{83} +(10.3602 - 8.69327i) q^{85} +(0.0867887 + 0.103431i) q^{86} +(0.313396 - 0.114067i) q^{88} +5.35698 q^{89} +(-0.195648 + 1.69672i) q^{91} +(-1.98581 - 0.350152i) q^{92} +(0.0764298 + 0.0910855i) q^{94} +(0.973203 + 1.15982i) q^{95} +(7.39427 + 1.30381i) q^{97} +(0.0257512 - 0.110177i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34} - 18 q^{35} + 3 q^{37} + 99 q^{38} - 54 q^{40} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 45 q^{47} - 24 q^{49} + 9 q^{50} - 9 q^{52} + 45 q^{53} - 3 q^{56} - 3 q^{58} - 36 q^{59} - 9 q^{61} + 99 q^{62} + 18 q^{64} - 69 q^{65} - 3 q^{67} - 36 q^{68} + 66 q^{70} - 18 q^{71} - 9 q^{73} - 75 q^{74} + 36 q^{76} - 15 q^{77} - 21 q^{79} - 72 q^{80} - 18 q^{82} + 90 q^{83} + 9 q^{85} + 105 q^{86} - 63 q^{88} + 18 q^{89} + 6 q^{91} - 150 q^{92} - 9 q^{94} - 45 q^{95} - 27 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{18}\right)\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0103898 0.0123821i 0.00734672 0.00875548i −0.762359 0.647155i \(-0.775959\pi\)
0.769705 + 0.638399i \(0.220403\pi\)
\(3\) 0 0
\(4\) 0.347251 + 1.96936i 0.173625 + 0.984679i
\(5\) −3.05823 + 2.56616i −1.36768 + 1.14762i −0.394154 + 0.919045i \(0.628962\pi\)
−0.973526 + 0.228575i \(0.926593\pi\)
\(6\) 0 0
\(7\) −2.57348 + 0.614149i −0.972686 + 0.232127i
\(8\) 0.0559891 + 0.0323253i 0.0197951 + 0.0114287i
\(9\) 0 0
\(10\) 0.0645293i 0.0204059i
\(11\) 3.31590 3.95174i 0.999782 1.19149i 0.0183214 0.999832i \(-0.494168\pi\)
0.981461 0.191662i \(-0.0613878\pi\)
\(12\) 0 0
\(13\) 0.220791 0.606618i 0.0612364 0.168246i −0.905301 0.424770i \(-0.860355\pi\)
0.966538 + 0.256524i \(0.0825773\pi\)
\(14\) −0.0191336 + 0.0382461i −0.00511367 + 0.0102217i
\(15\) 0 0
\(16\) −3.75730 + 1.36754i −0.939324 + 0.341886i
\(17\) −3.38766 −0.821629 −0.410815 0.911719i \(-0.634756\pi\)
−0.410815 + 0.911719i \(0.634756\pi\)
\(18\) 0 0
\(19\) 0.379246i 0.0870049i −0.999053 0.0435025i \(-0.986148\pi\)
0.999053 0.0435025i \(-0.0138516\pi\)
\(20\) −6.11565 5.13164i −1.36750 1.14747i
\(21\) 0 0
\(22\) −0.0144792 0.0821158i −0.00308698 0.0175072i
\(23\) −0.344877 + 0.947543i −0.0719119 + 0.197576i −0.970441 0.241337i \(-0.922414\pi\)
0.898530 + 0.438913i \(0.144636\pi\)
\(24\) 0 0
\(25\) 1.89935 10.7717i 0.379869 2.15434i
\(26\) −0.00521724 0.00903653i −0.00102318 0.00177221i
\(27\) 0 0
\(28\) −2.10312 4.85485i −0.397453 0.917480i
\(29\) −1.97120 5.41582i −0.366042 1.00569i −0.976852 0.213916i \(-0.931378\pi\)
0.610810 0.791777i \(-0.290844\pi\)
\(30\) 0 0
\(31\) −6.35598 + 1.12073i −1.14157 + 0.201289i −0.712291 0.701884i \(-0.752342\pi\)
−0.429276 + 0.903173i \(0.641231\pi\)
\(32\) −0.0663282 + 0.182235i −0.0117253 + 0.0322150i
\(33\) 0 0
\(34\) −0.0351973 + 0.0419465i −0.00603628 + 0.00719376i
\(35\) 6.29429 8.48217i 1.06393 1.43375i
\(36\) 0 0
\(37\) −3.08407 + 5.34176i −0.507018 + 0.878181i 0.492949 + 0.870058i \(0.335919\pi\)
−0.999967 + 0.00812261i \(0.997414\pi\)
\(38\) −0.00469587 0.00394030i −0.000761770 0.000639201i
\(39\) 0 0
\(40\) −0.254179 + 0.0448186i −0.0401892 + 0.00708645i
\(41\) 0.266252 + 0.0969077i 0.0415816 + 0.0151344i 0.362727 0.931895i \(-0.381846\pi\)
−0.321146 + 0.947030i \(0.604068\pi\)
\(42\) 0 0
\(43\) −1.45052 + 8.22633i −0.221203 + 1.25450i 0.648610 + 0.761121i \(0.275351\pi\)
−0.869812 + 0.493383i \(0.835760\pi\)
\(44\) 8.93384 + 5.15796i 1.34683 + 0.777591i
\(45\) 0 0
\(46\) 0.00814938 + 0.0141151i 0.00120156 + 0.00208116i
\(47\) −1.27739 + 7.24446i −0.186327 + 1.05671i 0.737912 + 0.674897i \(0.235812\pi\)
−0.924239 + 0.381815i \(0.875299\pi\)
\(48\) 0 0
\(49\) 6.24564 3.16101i 0.892235 0.451572i
\(50\) −0.113643 0.135434i −0.0160715 0.0191533i
\(51\) 0 0
\(52\) 1.27132 + 0.224168i 0.176300 + 0.0310865i
\(53\) 1.71989 + 0.992981i 0.236246 + 0.136396i 0.613450 0.789734i \(-0.289781\pi\)
−0.377204 + 0.926130i \(0.623115\pi\)
\(54\) 0 0
\(55\) 20.5944i 2.77695i
\(56\) −0.163940 0.0488030i −0.0219074 0.00652158i
\(57\) 0 0
\(58\) −0.0875398 0.0318619i −0.0114945 0.00418367i
\(59\) 3.21846 + 1.17142i 0.419007 + 0.152506i 0.542915 0.839788i \(-0.317321\pi\)
−0.123908 + 0.992294i \(0.539543\pi\)
\(60\) 0 0
\(61\) −7.93400 1.39898i −1.01584 0.179121i −0.359152 0.933279i \(-0.616934\pi\)
−0.656692 + 0.754158i \(0.728045\pi\)
\(62\) −0.0521605 + 0.0903447i −0.00662439 + 0.0114738i
\(63\) 0 0
\(64\) −3.99687 6.92277i −0.499608 0.865347i
\(65\) 0.881448 + 2.42176i 0.109330 + 0.300382i
\(66\) 0 0
\(67\) 7.23088 6.06743i 0.883393 0.741255i −0.0834809 0.996509i \(-0.526604\pi\)
0.966874 + 0.255255i \(0.0821593\pi\)
\(68\) −1.17637 6.67152i −0.142656 0.809041i
\(69\) 0 0
\(70\) −0.0396306 0.166065i −0.00473676 0.0198486i
\(71\) −8.57363 + 4.94999i −1.01750 + 0.587456i −0.913380 0.407109i \(-0.866537\pi\)
−0.104123 + 0.994564i \(0.533204\pi\)
\(72\) 0 0
\(73\) −6.13914 + 3.54444i −0.718533 + 0.414845i −0.814212 0.580567i \(-0.802831\pi\)
0.0956798 + 0.995412i \(0.469498\pi\)
\(74\) 0.0340994 + 0.0936874i 0.00396398 + 0.0108909i
\(75\) 0 0
\(76\) 0.746871 0.131693i 0.0856719 0.0151063i
\(77\) −6.10647 + 12.2062i −0.695896 + 1.39103i
\(78\) 0 0
\(79\) −0.980903 0.823075i −0.110360 0.0926032i 0.585938 0.810356i \(-0.300726\pi\)
−0.696298 + 0.717753i \(0.745171\pi\)
\(80\) 7.98133 13.8241i 0.892340 1.54558i
\(81\) 0 0
\(82\) 0.00396624 0.00228991i 0.000437998 0.000252878i
\(83\) −8.07527 + 2.93916i −0.886376 + 0.322614i −0.744780 0.667310i \(-0.767446\pi\)
−0.141596 + 0.989925i \(0.545223\pi\)
\(84\) 0 0
\(85\) 10.3602 8.69327i 1.12373 0.942918i
\(86\) 0.0867887 + 0.103431i 0.00935867 + 0.0111532i
\(87\) 0 0
\(88\) 0.313396 0.114067i 0.0334081 0.0121595i
\(89\) 5.35698 0.567839 0.283920 0.958848i \(-0.408365\pi\)
0.283920 + 0.958848i \(0.408365\pi\)
\(90\) 0 0
\(91\) −0.195648 + 1.69672i −0.0205095 + 0.177865i
\(92\) −1.98581 0.350152i −0.207035 0.0365059i
\(93\) 0 0
\(94\) 0.0764298 + 0.0910855i 0.00788314 + 0.00939476i
\(95\) 0.973203 + 1.15982i 0.0998486 + 0.118995i
\(96\) 0 0
\(97\) 7.39427 + 1.30381i 0.750774 + 0.132382i 0.535925 0.844265i \(-0.319963\pi\)
0.214849 + 0.976647i \(0.431074\pi\)
\(98\) 0.0257512 0.110177i 0.00260127 0.0111295i
\(99\) 0 0
\(100\) 21.8729 2.18729
\(101\) −10.7151 + 3.89999i −1.06620 + 0.388064i −0.814753 0.579808i \(-0.803127\pi\)
−0.251443 + 0.967872i \(0.580905\pi\)
\(102\) 0 0
\(103\) 6.15395 + 7.33400i 0.606367 + 0.722640i 0.978663 0.205474i \(-0.0658736\pi\)
−0.372296 + 0.928114i \(0.621429\pi\)
\(104\) 0.0319710 0.0268269i 0.00313502 0.00263059i
\(105\) 0 0
\(106\) 0.0301646 0.0109790i 0.00292985 0.00106638i
\(107\) −12.0916 + 6.98107i −1.16894 + 0.674885i −0.953429 0.301617i \(-0.902474\pi\)
−0.215507 + 0.976502i \(0.569140\pi\)
\(108\) 0 0
\(109\) 0.912496 1.58049i 0.0874012 0.151383i −0.819011 0.573778i \(-0.805477\pi\)
0.906412 + 0.422395i \(0.138810\pi\)
\(110\) 0.255003 + 0.213973i 0.0243136 + 0.0204015i
\(111\) 0 0
\(112\) 8.82947 5.82689i 0.834306 0.550590i
\(113\) −4.07591 + 0.718692i −0.383429 + 0.0676089i −0.362041 0.932162i \(-0.617920\pi\)
−0.0213886 + 0.999771i \(0.506809\pi\)
\(114\) 0 0
\(115\) −1.37683 3.78281i −0.128390 0.352749i
\(116\) 9.98120 5.76265i 0.926731 0.535048i
\(117\) 0 0
\(118\) 0.0479439 0.0276804i 0.00441360 0.00254819i
\(119\) 8.71810 2.08053i 0.799187 0.190722i
\(120\) 0 0
\(121\) −2.71090 15.3743i −0.246446 1.39766i
\(122\) −0.0997552 + 0.0837046i −0.00903141 + 0.00757826i
\(123\) 0 0
\(124\) −4.41424 12.1280i −0.396410 1.08913i
\(125\) 11.8527 + 20.5295i 1.06014 + 1.83622i
\(126\) 0 0
\(127\) −3.16383 + 5.47991i −0.280744 + 0.486263i −0.971568 0.236760i \(-0.923915\pi\)
0.690824 + 0.723023i \(0.257248\pi\)
\(128\) −0.509214 0.0897883i −0.0450086 0.00793624i
\(129\) 0 0
\(130\) 0.0391446 + 0.0142475i 0.00343321 + 0.00124959i
\(131\) −3.68789 1.34228i −0.322212 0.117276i 0.175850 0.984417i \(-0.443733\pi\)
−0.498062 + 0.867141i \(0.665955\pi\)
\(132\) 0 0
\(133\) 0.232913 + 0.975983i 0.0201962 + 0.0846284i
\(134\) 0.152573i 0.0131803i
\(135\) 0 0
\(136\) −0.189672 0.109507i −0.0162643 0.00939017i
\(137\) 6.38590 + 1.12601i 0.545584 + 0.0962012i 0.439645 0.898171i \(-0.355104\pi\)
0.105939 + 0.994373i \(0.466215\pi\)
\(138\) 0 0
\(139\) 3.60990 + 4.30212i 0.306188 + 0.364901i 0.897094 0.441840i \(-0.145674\pi\)
−0.590906 + 0.806740i \(0.701230\pi\)
\(140\) 18.8901 + 9.45027i 1.59651 + 0.798694i
\(141\) 0 0
\(142\) −0.0277873 + 0.157589i −0.00233185 + 0.0132246i
\(143\) −1.66508 2.88400i −0.139241 0.241172i
\(144\) 0 0
\(145\) 19.9262 + 11.5044i 1.65478 + 0.955389i
\(146\) −0.0198970 + 0.112842i −0.00164669 + 0.00933885i
\(147\) 0 0
\(148\) −11.5908 4.21870i −0.952757 0.346775i
\(149\) 3.49363 0.616020i 0.286209 0.0504664i −0.0287006 0.999588i \(-0.509137\pi\)
0.314910 + 0.949122i \(0.398026\pi\)
\(150\) 0 0
\(151\) −12.2877 10.3106i −0.999958 0.839065i −0.0129798 0.999916i \(-0.504132\pi\)
−0.986979 + 0.160851i \(0.948576\pi\)
\(152\) 0.0122592 0.0212336i 0.000994355 0.00172227i
\(153\) 0 0
\(154\) 0.0876935 + 0.202431i 0.00706654 + 0.0163124i
\(155\) 16.5620 19.7379i 1.33030 1.58538i
\(156\) 0 0
\(157\) 2.09850 5.76559i 0.167479 0.460144i −0.827353 0.561683i \(-0.810154\pi\)
0.994832 + 0.101538i \(0.0323765\pi\)
\(158\) −0.0203828 + 0.00359404i −0.00162157 + 0.000285927i
\(159\) 0 0
\(160\) −0.264798 0.727525i −0.0209341 0.0575159i
\(161\) 0.305604 2.65029i 0.0240850 0.208872i
\(162\) 0 0
\(163\) −1.58197 2.74005i −0.123910 0.214618i 0.797397 0.603456i \(-0.206210\pi\)
−0.921306 + 0.388838i \(0.872877\pi\)
\(164\) −0.0983898 + 0.557997i −0.00768296 + 0.0435722i
\(165\) 0 0
\(166\) −0.0475077 + 0.130526i −0.00368731 + 0.0101308i
\(167\) 1.33048 + 7.54555i 0.102956 + 0.583892i 0.992017 + 0.126104i \(0.0402472\pi\)
−0.889061 + 0.457788i \(0.848642\pi\)
\(168\) 0 0
\(169\) 9.63934 + 8.08837i 0.741488 + 0.622182i
\(170\) 0.218603i 0.0167661i
\(171\) 0 0
\(172\) −16.7043 −1.27369
\(173\) −1.48665 + 0.541097i −0.113028 + 0.0411388i −0.397915 0.917422i \(-0.630266\pi\)
0.284887 + 0.958561i \(0.408044\pi\)
\(174\) 0 0
\(175\) 1.72751 + 28.8873i 0.130587 + 2.18368i
\(176\) −7.05465 + 19.3825i −0.531765 + 1.46101i
\(177\) 0 0
\(178\) 0.0556582 0.0663308i 0.00417176 0.00497171i
\(179\) 8.70775i 0.650848i 0.945568 + 0.325424i \(0.105507\pi\)
−0.945568 + 0.325424i \(0.894493\pi\)
\(180\) 0 0
\(181\) −1.08680 0.627465i −0.0807813 0.0466391i 0.459065 0.888403i \(-0.348184\pi\)
−0.539847 + 0.841763i \(0.681518\pi\)
\(182\) 0.0189763 + 0.0200512i 0.00140661 + 0.00148629i
\(183\) 0 0
\(184\) −0.0499390 + 0.0419038i −0.00368155 + 0.00308919i
\(185\) −4.27602 24.2505i −0.314379 1.78293i
\(186\) 0 0
\(187\) −11.2332 + 13.3872i −0.821450 + 0.978966i
\(188\) −14.7105 −1.07287
\(189\) 0 0
\(190\) 0.0244724 0.00177542
\(191\) 5.70046 6.79355i 0.412471 0.491564i −0.519309 0.854586i \(-0.673811\pi\)
0.931780 + 0.363023i \(0.118255\pi\)
\(192\) 0 0
\(193\) 4.37792 + 24.8284i 0.315129 + 1.78719i 0.571493 + 0.820607i \(0.306364\pi\)
−0.256364 + 0.966580i \(0.582524\pi\)
\(194\) 0.0929692 0.0780104i 0.00667480 0.00560082i
\(195\) 0 0
\(196\) 8.39396 + 11.2022i 0.599568 + 0.800160i
\(197\) 11.0546 + 6.38238i 0.787608 + 0.454726i 0.839120 0.543947i \(-0.183071\pi\)
−0.0515117 + 0.998672i \(0.516404\pi\)
\(198\) 0 0
\(199\) 20.3712i 1.44408i −0.691853 0.722038i \(-0.743206\pi\)
0.691853 0.722038i \(-0.256794\pi\)
\(200\) 0.454542 0.541702i 0.0321410 0.0383041i
\(201\) 0 0
\(202\) −0.0630384 + 0.173196i −0.00443536 + 0.0121861i
\(203\) 8.39897 + 12.7269i 0.589492 + 0.893255i
\(204\) 0 0
\(205\) −1.06294 + 0.386878i −0.0742388 + 0.0270207i
\(206\) 0.154749 0.0107819
\(207\) 0 0
\(208\) 2.58119i 0.178973i
\(209\) −1.49868 1.25754i −0.103666 0.0869860i
\(210\) 0 0
\(211\) −0.149574 0.848277i −0.0102971 0.0583978i 0.979226 0.202771i \(-0.0649946\pi\)
−0.989523 + 0.144373i \(0.953884\pi\)
\(212\) −1.35830 + 3.73190i −0.0932885 + 0.256308i
\(213\) 0 0
\(214\) −0.0391889 + 0.222251i −0.00267890 + 0.0151928i
\(215\) −16.6740 28.8802i −1.13716 1.96962i
\(216\) 0 0
\(217\) 15.6687 6.78770i 1.06366 0.460779i
\(218\) −0.0100891 0.0277197i −0.000683322 0.00187741i
\(219\) 0 0
\(220\) −40.5578 + 7.15144i −2.73441 + 0.482150i
\(221\) −0.747966 + 2.05502i −0.0503136 + 0.138235i
\(222\) 0 0
\(223\) 10.1302 12.0727i 0.678367 0.808446i −0.311530 0.950236i \(-0.600841\pi\)
0.989897 + 0.141790i \(0.0452858\pi\)
\(224\) 0.0587750 0.509715i 0.00392707 0.0340568i
\(225\) 0 0
\(226\) −0.0334491 + 0.0579355i −0.00222500 + 0.00385381i
\(227\) −7.25051 6.08390i −0.481233 0.403803i 0.369639 0.929176i \(-0.379481\pi\)
−0.850872 + 0.525373i \(0.823926\pi\)
\(228\) 0 0
\(229\) −1.81290 + 0.319663i −0.119800 + 0.0211240i −0.233227 0.972422i \(-0.574928\pi\)
0.113427 + 0.993546i \(0.463817\pi\)
\(230\) −0.0611442 0.0222547i −0.00403173 0.00146743i
\(231\) 0 0
\(232\) 0.0647026 0.366947i 0.00424793 0.0240912i
\(233\) −9.13855 5.27615i −0.598686 0.345652i 0.169838 0.985472i \(-0.445675\pi\)
−0.768525 + 0.639820i \(0.779009\pi\)
\(234\) 0 0
\(235\) −14.6838 25.4332i −0.957868 1.65908i
\(236\) −1.18934 + 6.74507i −0.0774193 + 0.439067i
\(237\) 0 0
\(238\) 0.0648182 0.129565i 0.00420154 0.00839845i
\(239\) 3.07353 + 3.66289i 0.198810 + 0.236933i 0.856234 0.516588i \(-0.172798\pi\)
−0.657424 + 0.753521i \(0.728354\pi\)
\(240\) 0 0
\(241\) −8.59483 1.51550i −0.553642 0.0976219i −0.110174 0.993912i \(-0.535141\pi\)
−0.443468 + 0.896290i \(0.646252\pi\)
\(242\) −0.218532 0.126170i −0.0140478 0.00811049i
\(243\) 0 0
\(244\) 16.1107i 1.03138i
\(245\) −10.9889 + 25.6944i −0.702058 + 1.64155i
\(246\) 0 0
\(247\) −0.230057 0.0837340i −0.0146382 0.00532787i
\(248\) −0.392093 0.142710i −0.0248980 0.00906211i
\(249\) 0 0
\(250\) 0.377347 + 0.0665364i 0.0238655 + 0.00420813i
\(251\) 5.48464 9.49967i 0.346187 0.599614i −0.639382 0.768890i \(-0.720810\pi\)
0.985569 + 0.169276i \(0.0541429\pi\)
\(252\) 0 0
\(253\) 2.60086 + 4.50483i 0.163515 + 0.283216i
\(254\) 0.0349813 + 0.0961103i 0.00219492 + 0.00603049i
\(255\) 0 0
\(256\) 12.2407 10.2712i 0.765044 0.641948i
\(257\) −2.22842 12.6380i −0.139005 0.788337i −0.971987 0.235036i \(-0.924479\pi\)
0.832982 0.553301i \(-0.186632\pi\)
\(258\) 0 0
\(259\) 4.65616 15.6410i 0.289320 0.971886i
\(260\) −4.46323 + 2.57685i −0.276798 + 0.159809i
\(261\) 0 0
\(262\) −0.0549368 + 0.0317178i −0.00339401 + 0.00195953i
\(263\) −0.846006 2.32438i −0.0521670 0.143328i 0.910872 0.412688i \(-0.135410\pi\)
−0.963039 + 0.269360i \(0.913188\pi\)
\(264\) 0 0
\(265\) −7.80796 + 1.37675i −0.479639 + 0.0845734i
\(266\) 0.0145047 + 0.00725634i 0.000889338 + 0.000444915i
\(267\) 0 0
\(268\) 14.4599 + 12.1333i 0.883278 + 0.741158i
\(269\) −13.2754 + 22.9936i −0.809413 + 1.40195i 0.103858 + 0.994592i \(0.466881\pi\)
−0.913271 + 0.407353i \(0.866452\pi\)
\(270\) 0 0
\(271\) −17.4414 + 10.0698i −1.05949 + 0.611698i −0.925292 0.379257i \(-0.876180\pi\)
−0.134200 + 0.990954i \(0.542846\pi\)
\(272\) 12.7285 4.63278i 0.771776 0.280904i
\(273\) 0 0
\(274\) 0.0802908 0.0673720i 0.00485054 0.00407009i
\(275\) −36.2690 43.2237i −2.18710 2.60649i
\(276\) 0 0
\(277\) 21.9953 8.00564i 1.32157 0.481012i 0.417609 0.908627i \(-0.362868\pi\)
0.903961 + 0.427615i \(0.140646\pi\)
\(278\) 0.0907756 0.00544436
\(279\) 0 0
\(280\) 0.626600 0.271444i 0.0374465 0.0162219i
\(281\) −8.66178 1.52731i −0.516719 0.0911114i −0.0907933 0.995870i \(-0.528940\pi\)
−0.425925 + 0.904758i \(0.640051\pi\)
\(282\) 0 0
\(283\) 19.1846 + 22.8633i 1.14041 + 1.35908i 0.923823 + 0.382821i \(0.125047\pi\)
0.216585 + 0.976264i \(0.430508\pi\)
\(284\) −12.7255 15.1657i −0.755120 0.899917i
\(285\) 0 0
\(286\) −0.0530099 0.00934707i −0.00313454 0.000552704i
\(287\) −0.744711 0.0858722i −0.0439589 0.00506888i
\(288\) 0 0
\(289\) −5.52374 −0.324926
\(290\) 0.349479 0.127200i 0.0205221 0.00746944i
\(291\) 0 0
\(292\) −9.11209 10.8594i −0.533245 0.635496i
\(293\) 1.70777 1.43299i 0.0997691 0.0837162i −0.591539 0.806277i \(-0.701479\pi\)
0.691308 + 0.722560i \(0.257035\pi\)
\(294\) 0 0
\(295\) −12.8488 + 4.67659i −0.748087 + 0.272281i
\(296\) −0.345348 + 0.199387i −0.0200730 + 0.0115891i
\(297\) 0 0
\(298\) 0.0286706 0.0496589i 0.00166084 0.00287666i
\(299\) 0.498651 + 0.418418i 0.0288377 + 0.0241977i
\(300\) 0 0
\(301\) −1.31929 22.0612i −0.0760428 1.27158i
\(302\) −0.255334 + 0.0450223i −0.0146928 + 0.00259074i
\(303\) 0 0
\(304\) 0.518635 + 1.42494i 0.0297458 + 0.0817258i
\(305\) 27.8539 16.0815i 1.59491 0.920823i
\(306\) 0 0
\(307\) −12.9614 + 7.48325i −0.739744 + 0.427091i −0.821976 0.569522i \(-0.807128\pi\)
0.0822321 + 0.996613i \(0.473795\pi\)
\(308\) −26.1589 7.78721i −1.49054 0.443717i
\(309\) 0 0
\(310\) −0.0723199 0.410146i −0.00410749 0.0232948i
\(311\) 3.46916 2.91097i 0.196718 0.165066i −0.539108 0.842237i \(-0.681239\pi\)
0.735826 + 0.677171i \(0.236794\pi\)
\(312\) 0 0
\(313\) 4.15956 + 11.4283i 0.235112 + 0.645965i 0.999998 + 0.00179989i \(0.000572922\pi\)
−0.764886 + 0.644165i \(0.777205\pi\)
\(314\) −0.0495872 0.0858875i −0.00279836 0.00484691i
\(315\) 0 0
\(316\) 1.28031 2.21756i 0.0720231 0.124748i
\(317\) 33.4798 + 5.90340i 1.88041 + 0.331568i 0.991873 0.127230i \(-0.0406087\pi\)
0.888541 + 0.458798i \(0.151720\pi\)
\(318\) 0 0
\(319\) −27.9382 10.1687i −1.56424 0.569337i
\(320\) 29.9882 + 10.9148i 1.67639 + 0.610157i
\(321\) 0 0
\(322\) −0.0296411 0.0313201i −0.00165183 0.00174540i
\(323\) 1.28476i 0.0714858i
\(324\) 0 0
\(325\) −6.11497 3.53048i −0.339197 0.195836i
\(326\) −0.0503641 0.00888055i −0.00278941 0.000491848i
\(327\) 0 0
\(328\) 0.0117746 + 0.0140325i 0.000650145 + 0.000774813i
\(329\) −1.16183 19.4280i −0.0640535 1.07110i
\(330\) 0 0
\(331\) −5.78063 + 32.7836i −0.317732 + 1.80195i 0.238743 + 0.971083i \(0.423265\pi\)
−0.556475 + 0.830864i \(0.687846\pi\)
\(332\) −8.59240 14.8825i −0.471569 0.816782i
\(333\) 0 0
\(334\) 0.107253 + 0.0619228i 0.00586865 + 0.00338826i
\(335\) −6.54370 + 37.1111i −0.357520 + 2.02760i
\(336\) 0 0
\(337\) −26.0769 9.49121i −1.42050 0.517019i −0.486306 0.873789i \(-0.661656\pi\)
−0.934192 + 0.356770i \(0.883878\pi\)
\(338\) 0.200302 0.0353187i 0.0108950 0.00192108i
\(339\) 0 0
\(340\) 20.7178 + 17.3843i 1.12358 + 0.942794i
\(341\) −16.6470 + 28.8334i −0.901484 + 1.56142i
\(342\) 0 0
\(343\) −14.1317 + 11.9706i −0.763042 + 0.646349i
\(344\) −0.347132 + 0.413696i −0.0187161 + 0.0223050i
\(345\) 0 0
\(346\) −0.00874614 + 0.0240298i −0.000470195 + 0.00129185i
\(347\) 12.0266 2.12061i 0.645620 0.113840i 0.158756 0.987318i \(-0.449252\pi\)
0.486864 + 0.873478i \(0.338141\pi\)
\(348\) 0 0
\(349\) 3.80673 + 10.4589i 0.203770 + 0.559853i 0.998915 0.0465660i \(-0.0148278\pi\)
−0.795145 + 0.606419i \(0.792606\pi\)
\(350\) 0.375635 + 0.278744i 0.0200785 + 0.0148995i
\(351\) 0 0
\(352\) 0.500209 + 0.866387i 0.0266612 + 0.0461786i
\(353\) 3.40999 19.3390i 0.181496 1.02931i −0.748880 0.662706i \(-0.769408\pi\)
0.930376 0.366608i \(-0.119481\pi\)
\(354\) 0 0
\(355\) 13.5177 37.1395i 0.717443 1.97116i
\(356\) 1.86022 + 10.5498i 0.0985913 + 0.559139i
\(357\) 0 0
\(358\) 0.107820 + 0.0904721i 0.00569849 + 0.00478160i
\(359\) 30.0037i 1.58354i 0.610821 + 0.791768i \(0.290839\pi\)
−0.610821 + 0.791768i \(0.709161\pi\)
\(360\) 0 0
\(361\) 18.8562 0.992430
\(362\) −0.0190610 + 0.00693765i −0.00100183 + 0.000364635i
\(363\) 0 0
\(364\) −3.40939 + 0.203887i −0.178701 + 0.0106866i
\(365\) 9.67931 26.5937i 0.506638 1.39198i
\(366\) 0 0
\(367\) 0.0174386 0.0207825i 0.000910286 0.00108484i −0.765589 0.643330i \(-0.777552\pi\)
0.766499 + 0.642245i \(0.221997\pi\)
\(368\) 4.03184i 0.210174i
\(369\) 0 0
\(370\) −0.344700 0.199013i −0.0179201 0.0103462i
\(371\) −5.03596 1.49915i −0.261454 0.0778320i
\(372\) 0 0
\(373\) −21.5425 + 18.0763i −1.11543 + 0.935957i −0.998365 0.0571672i \(-0.981793\pi\)
−0.117066 + 0.993124i \(0.537349\pi\)
\(374\) 0.0490508 + 0.278181i 0.00253636 + 0.0143844i
\(375\) 0 0
\(376\) −0.305699 + 0.364318i −0.0157652 + 0.0187883i
\(377\) −3.72056 −0.191619
\(378\) 0 0
\(379\) 0.592745 0.0304473 0.0152236 0.999884i \(-0.495154\pi\)
0.0152236 + 0.999884i \(0.495154\pi\)
\(380\) −1.94615 + 2.31933i −0.0998355 + 0.118979i
\(381\) 0 0
\(382\) −0.0248917 0.141168i −0.00127357 0.00722276i
\(383\) 8.98969 7.54325i 0.459352 0.385442i −0.383541 0.923524i \(-0.625295\pi\)
0.842892 + 0.538082i \(0.180851\pi\)
\(384\) 0 0
\(385\) −12.6481 52.9994i −0.644604 2.70110i
\(386\) 0.352914 + 0.203755i 0.0179629 + 0.0103709i
\(387\) 0 0
\(388\) 15.0147i 0.762257i
\(389\) 9.84805 11.7364i 0.499316 0.595062i −0.456245 0.889854i \(-0.650806\pi\)
0.955561 + 0.294792i \(0.0952505\pi\)
\(390\) 0 0
\(391\) 1.16833 3.20996i 0.0590849 0.162335i
\(392\) 0.451868 + 0.0249105i 0.0228228 + 0.00125817i
\(393\) 0 0
\(394\) 0.193883 0.0705676i 0.00976768 0.00355515i
\(395\) 5.11196 0.257211
\(396\) 0 0
\(397\) 22.7982i 1.14421i 0.820181 + 0.572104i \(0.193873\pi\)
−0.820181 + 0.572104i \(0.806127\pi\)
\(398\) −0.252239 0.211653i −0.0126436 0.0106092i
\(399\) 0 0
\(400\) 7.59440 + 43.0700i 0.379720 + 2.15350i
\(401\) 1.00298 2.75565i 0.0500862 0.137611i −0.912127 0.409907i \(-0.865561\pi\)
0.962213 + 0.272297i \(0.0877832\pi\)
\(402\) 0 0
\(403\) −0.723487 + 4.10310i −0.0360395 + 0.204390i
\(404\) −11.4013 19.7477i −0.567237 0.982483i
\(405\) 0 0
\(406\) 0.244850 + 0.0282336i 0.0121517 + 0.00140121i
\(407\) 10.8828 + 29.9002i 0.539440 + 1.48210i
\(408\) 0 0
\(409\) 19.8273 3.49609i 0.980398 0.172871i 0.339591 0.940573i \(-0.389711\pi\)
0.640806 + 0.767702i \(0.278600\pi\)
\(410\) −0.00625338 + 0.0171810i −0.000308833 + 0.000848511i
\(411\) 0 0
\(412\) −12.3063 + 14.6661i −0.606288 + 0.722546i
\(413\) −9.00207 1.03802i −0.442963 0.0510778i
\(414\) 0 0
\(415\) 17.1537 29.7110i 0.842040 1.45846i
\(416\) 0.0959026 + 0.0804718i 0.00470201 + 0.00394546i
\(417\) 0 0
\(418\) −0.0311421 + 0.00549119i −0.00152321 + 0.000268583i
\(419\) −13.5738 4.94048i −0.663126 0.241358i −0.0115404 0.999933i \(-0.503674\pi\)
−0.651585 + 0.758575i \(0.725896\pi\)
\(420\) 0 0
\(421\) 1.54410 8.75701i 0.0752547 0.426791i −0.923782 0.382918i \(-0.874919\pi\)
0.999037 0.0438728i \(-0.0139696\pi\)
\(422\) −0.0120575 0.00696141i −0.000586951 0.000338876i
\(423\) 0 0
\(424\) 0.0641968 + 0.111192i 0.00311767 + 0.00539997i
\(425\) −6.43434 + 36.4910i −0.312111 + 1.77007i
\(426\) 0 0
\(427\) 21.2772 1.27241i 1.02968 0.0615762i
\(428\) −17.9470 21.3884i −0.867503 1.03385i
\(429\) 0 0
\(430\) −0.530839 0.0936012i −0.0255993 0.00451385i
\(431\) −27.2881 15.7548i −1.31442 0.758881i −0.331595 0.943422i \(-0.607587\pi\)
−0.982825 + 0.184541i \(0.940920\pi\)
\(432\) 0 0
\(433\) 35.8271i 1.72174i −0.508824 0.860870i \(-0.669920\pi\)
0.508824 0.860870i \(-0.330080\pi\)
\(434\) 0.0787492 0.264535i 0.00378008 0.0126981i
\(435\) 0 0
\(436\) 3.42941 + 1.24820i 0.164239 + 0.0597782i
\(437\) 0.359352 + 0.130793i 0.0171901 + 0.00625669i
\(438\) 0 0
\(439\) −35.6506 6.28616i −1.70151 0.300022i −0.763288 0.646058i \(-0.776416\pi\)
−0.938221 + 0.346036i \(0.887528\pi\)
\(440\) −0.665722 + 1.15306i −0.0317370 + 0.0549701i
\(441\) 0 0
\(442\) 0.0176743 + 0.0306127i 0.000840678 + 0.00145610i
\(443\) 8.20728 + 22.5493i 0.389940 + 1.07135i 0.967028 + 0.254669i \(0.0819665\pi\)
−0.577089 + 0.816682i \(0.695811\pi\)
\(444\) 0 0
\(445\) −16.3829 + 13.7469i −0.776622 + 0.651663i
\(446\) −0.0442345 0.250866i −0.00209456 0.0118789i
\(447\) 0 0
\(448\) 14.5375 + 15.3610i 0.686832 + 0.725738i
\(449\) 27.8837 16.0987i 1.31591 0.759743i 0.332845 0.942981i \(-0.391991\pi\)
0.983069 + 0.183238i \(0.0586580\pi\)
\(450\) 0 0
\(451\) 1.26582 0.730821i 0.0596051 0.0344130i
\(452\) −2.83073 7.77736i −0.133146 0.365816i
\(453\) 0 0
\(454\) −0.150663 + 0.0265660i −0.00707098 + 0.00124680i
\(455\) −3.75571 5.69102i −0.176071 0.266799i
\(456\) 0 0
\(457\) 0.847636 + 0.711251i 0.0396507 + 0.0332709i 0.662398 0.749152i \(-0.269539\pi\)
−0.622747 + 0.782423i \(0.713983\pi\)
\(458\) −0.0148776 + 0.0257688i −0.000695186 + 0.00120410i
\(459\) 0 0
\(460\) 6.97160 4.02506i 0.325053 0.187669i
\(461\) 19.7443 7.18634i 0.919584 0.334701i 0.161511 0.986871i \(-0.448363\pi\)
0.758073 + 0.652170i \(0.226141\pi\)
\(462\) 0 0
\(463\) −17.5556 + 14.7309i −0.815876 + 0.684601i −0.952003 0.306090i \(-0.900979\pi\)
0.136126 + 0.990691i \(0.456535\pi\)
\(464\) 14.8128 + 17.6532i 0.687665 + 0.819527i
\(465\) 0 0
\(466\) −0.160278 + 0.0583364i −0.00742473 + 0.00270238i
\(467\) −34.0177 −1.57415 −0.787076 0.616855i \(-0.788406\pi\)
−0.787076 + 0.616855i \(0.788406\pi\)
\(468\) 0 0
\(469\) −14.8823 + 20.0553i −0.687199 + 0.926067i
\(470\) −0.467479 0.0824292i −0.0215632 0.00380218i
\(471\) 0 0
\(472\) 0.142332 + 0.169624i 0.00655135 + 0.00780760i
\(473\) 27.6985 + 33.0098i 1.27358 + 1.51779i
\(474\) 0 0
\(475\) −4.08513 0.720319i −0.187439 0.0330505i
\(476\) 7.12468 + 16.4466i 0.326559 + 0.753828i
\(477\) 0 0
\(478\) 0.0772879 0.00353507
\(479\) 35.7900 13.0265i 1.63529 0.595195i 0.649080 0.760720i \(-0.275154\pi\)
0.986206 + 0.165525i \(0.0529317\pi\)
\(480\) 0 0
\(481\) 2.55948 + 3.05027i 0.116702 + 0.139080i
\(482\) −0.108064 + 0.0906764i −0.00492218 + 0.00413020i
\(483\) 0 0
\(484\) 29.3361 10.6775i 1.33346 0.485340i
\(485\) −25.9591 + 14.9875i −1.17874 + 0.680548i
\(486\) 0 0
\(487\) 10.4173 18.0433i 0.472053 0.817619i −0.527436 0.849595i \(-0.676847\pi\)
0.999489 + 0.0319755i \(0.0101799\pi\)
\(488\) −0.398995 0.334796i −0.0180616 0.0151555i
\(489\) 0 0
\(490\) 0.203977 + 0.403027i 0.00921476 + 0.0182069i
\(491\) −2.73237 + 0.481790i −0.123310 + 0.0217429i −0.234962 0.972004i \(-0.575497\pi\)
0.111653 + 0.993747i \(0.464386\pi\)
\(492\) 0 0
\(493\) 6.67776 + 18.3470i 0.300751 + 0.826307i
\(494\) −0.00342706 + 0.00197862i −0.000154191 + 8.90221e-5i
\(495\) 0 0
\(496\) 22.3486 12.9030i 1.00348 0.579362i
\(497\) 19.0241 18.0042i 0.853347 0.807599i
\(498\) 0 0
\(499\) −0.706689 4.00783i −0.0316358 0.179415i 0.964896 0.262634i \(-0.0845911\pi\)
−0.996531 + 0.0832186i \(0.973480\pi\)
\(500\) −36.3141 + 30.4711i −1.62402 + 1.36271i
\(501\) 0 0
\(502\) −0.0606416 0.166611i −0.00270657 0.00743623i
\(503\) −20.5736 35.6344i −0.917329 1.58886i −0.803455 0.595366i \(-0.797007\pi\)
−0.113875 0.993495i \(-0.536326\pi\)
\(504\) 0 0
\(505\) 22.7613 39.4238i 1.01287 1.75433i
\(506\) 0.0828019 + 0.0146002i 0.00368099 + 0.000649058i
\(507\) 0 0
\(508\) −11.8905 4.32781i −0.527558 0.192015i
\(509\) 36.1173 + 13.1456i 1.60087 + 0.582669i 0.979605 0.200932i \(-0.0643969\pi\)
0.621265 + 0.783601i \(0.286619\pi\)
\(510\) 0 0
\(511\) 13.6222 12.8919i 0.602610 0.570304i
\(512\) 1.29242i 0.0571175i
\(513\) 0 0
\(514\) −0.179638 0.103714i −0.00792350 0.00457463i
\(515\) −37.6403 6.63701i −1.65863 0.292462i
\(516\) 0 0
\(517\) 24.3925 + 29.0698i 1.07278 + 1.27849i
\(518\) −0.145292 0.220161i −0.00638378 0.00967331i
\(519\) 0 0
\(520\) −0.0289326 + 0.164085i −0.00126878 + 0.00719561i
\(521\) 13.6287 + 23.6056i 0.597084 + 1.03418i 0.993249 + 0.116001i \(0.0370076\pi\)
−0.396165 + 0.918179i \(0.629659\pi\)
\(522\) 0 0
\(523\) −12.1701 7.02641i −0.532162 0.307244i 0.209735 0.977758i \(-0.432740\pi\)
−0.741896 + 0.670515i \(0.766073\pi\)
\(524\) 1.36281 7.72887i 0.0595346 0.337637i
\(525\) 0 0
\(526\) −0.0375707 0.0136746i −0.00163816 0.000596241i
\(527\) 21.5319 3.79666i 0.937945 0.165385i
\(528\) 0 0
\(529\) 16.8401 + 14.1305i 0.732179 + 0.614371i
\(530\) −0.0640763 + 0.110983i −0.00278330 + 0.00482081i
\(531\) 0 0
\(532\) −1.84118 + 0.797601i −0.0798253 + 0.0345804i
\(533\) 0.117572 0.140117i 0.00509261 0.00606914i
\(534\) 0 0
\(535\) 19.0642 52.3785i 0.824218 2.26452i
\(536\) 0.600982 0.105969i 0.0259585 0.00457718i
\(537\) 0 0
\(538\) 0.146781 + 0.403277i 0.00632817 + 0.0173865i
\(539\) 8.21847 35.1627i 0.353995 1.51457i
\(540\) 0 0
\(541\) 10.7693 + 18.6530i 0.463010 + 0.801957i 0.999109 0.0421981i \(-0.0134361\pi\)
−0.536099 + 0.844155i \(0.680103\pi\)
\(542\) −0.0565279 + 0.320586i −0.00242808 + 0.0137703i
\(543\) 0 0
\(544\) 0.224698 0.617352i 0.00963384 0.0264687i
\(545\) 1.26516 + 7.17510i 0.0541936 + 0.307347i
\(546\) 0 0
\(547\) −20.2027 16.9521i −0.863805 0.724819i 0.0989790 0.995090i \(-0.468442\pi\)
−0.962784 + 0.270271i \(0.912887\pi\)
\(548\) 12.9671i 0.553928i
\(549\) 0 0
\(550\) −0.912030 −0.0388891
\(551\) −2.05393 + 0.747568i −0.0875003 + 0.0318475i
\(552\) 0 0
\(553\) 3.02983 + 1.51575i 0.128841 + 0.0644563i
\(554\) 0.129401 0.355526i 0.00549771 0.0151048i
\(555\) 0 0
\(556\) −7.21887 + 8.60311i −0.306148 + 0.364853i
\(557\) 30.7772i 1.30407i 0.758188 + 0.652036i \(0.226085\pi\)
−0.758188 + 0.652036i \(0.773915\pi\)
\(558\) 0 0
\(559\) 4.66998 + 2.69621i 0.197519 + 0.114038i
\(560\) −12.0498 + 40.4777i −0.509196 + 1.71050i
\(561\) 0 0
\(562\) −0.108906 + 0.0913828i −0.00459391 + 0.00385475i
\(563\) 3.36336 + 19.0746i 0.141749 + 0.803898i 0.969920 + 0.243423i \(0.0782703\pi\)
−0.828171 + 0.560475i \(0.810619\pi\)
\(564\) 0 0
\(565\) 10.6208 12.6573i 0.446819 0.532498i
\(566\) 0.482422 0.0202777
\(567\) 0 0
\(568\) −0.640040 −0.0268555
\(569\) 27.3462 32.5900i 1.14641 1.36624i 0.226553 0.973999i \(-0.427254\pi\)
0.919861 0.392245i \(-0.128301\pi\)
\(570\) 0 0
\(571\) 5.30750 + 30.1004i 0.222112 + 1.25966i 0.868129 + 0.496338i \(0.165322\pi\)
−0.646017 + 0.763323i \(0.723567\pi\)
\(572\) 5.10142 4.28060i 0.213301 0.178981i
\(573\) 0 0
\(574\) −0.00880070 + 0.00832890i −0.000367334 + 0.000347642i
\(575\) 9.55163 + 5.51464i 0.398331 + 0.229976i
\(576\) 0 0
\(577\) 7.18870i 0.299269i 0.988741 + 0.149635i \(0.0478097\pi\)
−0.988741 + 0.149635i \(0.952190\pi\)
\(578\) −0.0573907 + 0.0683956i −0.00238714 + 0.00284488i
\(579\) 0 0
\(580\) −15.7369 + 43.2368i −0.653439 + 1.79531i
\(581\) 18.9765 12.5233i 0.787278 0.519554i
\(582\) 0 0
\(583\) 9.62700 3.50394i 0.398710 0.145118i
\(584\) −0.458300 −0.0189646
\(585\) 0 0
\(586\) 0.0360344i 0.00148857i
\(587\) −17.1076 14.3550i −0.706107 0.592495i 0.217396 0.976083i \(-0.430244\pi\)
−0.923504 + 0.383589i \(0.874688\pi\)
\(588\) 0 0
\(589\) 0.425032 + 2.41048i 0.0175131 + 0.0993220i
\(590\) −0.0755910 + 0.207685i −0.00311203 + 0.00855024i
\(591\) 0 0
\(592\) 4.28267 24.2882i 0.176016 0.998239i
\(593\) 17.8613 + 30.9367i 0.733476 + 1.27042i 0.955389 + 0.295351i \(0.0954364\pi\)
−0.221913 + 0.975066i \(0.571230\pi\)
\(594\) 0 0
\(595\) −21.3229 + 28.7347i −0.874155 + 1.17801i
\(596\) 2.42633 + 6.66629i 0.0993863 + 0.273062i
\(597\) 0 0
\(598\) 0.0103618 0.00182707i 0.000423726 7.47143e-5i
\(599\) −12.6673 + 34.8032i −0.517572 + 1.42202i 0.355615 + 0.934633i \(0.384272\pi\)
−0.873187 + 0.487386i \(0.837951\pi\)
\(600\) 0 0
\(601\) −1.43732 + 1.71293i −0.0586295 + 0.0698719i −0.794562 0.607183i \(-0.792300\pi\)
0.735933 + 0.677055i \(0.236744\pi\)
\(602\) −0.286871 0.212876i −0.0116920 0.00867619i
\(603\) 0 0
\(604\) 16.0384 27.7792i 0.652591 1.13032i
\(605\) 47.7433 + 40.0614i 1.94104 + 1.62873i
\(606\) 0 0
\(607\) 31.4589 5.54705i 1.27688 0.225148i 0.506223 0.862403i \(-0.331041\pi\)
0.770653 + 0.637255i \(0.219930\pi\)
\(608\) 0.0691120 + 0.0251547i 0.00280286 + 0.00102016i
\(609\) 0 0
\(610\) 0.0902750 0.511975i 0.00365513 0.0207293i
\(611\) 4.11258 + 2.37440i 0.166377 + 0.0960580i
\(612\) 0 0
\(613\) 5.02179 + 8.69800i 0.202828 + 0.351309i 0.949439 0.313953i \(-0.101653\pi\)
−0.746610 + 0.665262i \(0.768320\pi\)
\(614\) −0.0420080 + 0.238239i −0.00169530 + 0.00961454i
\(615\) 0 0
\(616\) −0.736465 + 0.486020i −0.0296730 + 0.0195823i
\(617\) −20.1274 23.9869i −0.810298 0.965675i 0.189571 0.981867i \(-0.439290\pi\)
−0.999869 + 0.0161920i \(0.994846\pi\)
\(618\) 0 0
\(619\) 28.4246 + 5.01202i 1.14248 + 0.201450i 0.712690 0.701479i \(-0.247477\pi\)
0.429790 + 0.902929i \(0.358588\pi\)
\(620\) 44.6221 + 25.7626i 1.79207 + 1.03465i
\(621\) 0 0
\(622\) 0.0732000i 0.00293505i
\(623\) −13.7861 + 3.28999i −0.552329 + 0.131811i
\(624\) 0 0
\(625\) −37.5389 13.6630i −1.50156 0.546522i
\(626\) 0.184724 + 0.0672339i 0.00738304 + 0.00268721i
\(627\) 0 0
\(628\) 12.0832 + 2.13060i 0.482173 + 0.0850201i
\(629\) 10.4478 18.0961i 0.416581 0.721539i
\(630\) 0 0
\(631\) 4.47416 + 7.74947i 0.178113 + 0.308501i 0.941234 0.337754i \(-0.109667\pi\)
−0.763121 + 0.646256i \(0.776334\pi\)
\(632\) −0.0283137 0.0777912i −0.00112626 0.00309437i
\(633\) 0 0
\(634\) 0.420946 0.353216i 0.0167179 0.0140280i
\(635\) −4.38660 24.8777i −0.174077 0.987240i
\(636\) 0 0
\(637\) −0.538543 4.48664i −0.0213378 0.177767i
\(638\) −0.416183 + 0.240284i −0.0164769 + 0.00951292i
\(639\) 0 0
\(640\) 1.78770 1.03213i 0.0706652 0.0407986i
\(641\) −9.90209 27.2058i −0.391109 1.07456i −0.966496 0.256682i \(-0.917371\pi\)
0.575387 0.817881i \(-0.304851\pi\)
\(642\) 0 0
\(643\) 12.3352 2.17502i 0.486451 0.0857744i 0.0749567 0.997187i \(-0.476118\pi\)
0.411494 + 0.911412i \(0.365007\pi\)
\(644\) 5.32550 0.318473i 0.209854 0.0125496i
\(645\) 0 0
\(646\) 0.0159080 + 0.0133484i 0.000625892 + 0.000525186i
\(647\) −4.53468 + 7.85429i −0.178277 + 0.308784i −0.941290 0.337598i \(-0.890385\pi\)
0.763014 + 0.646382i \(0.223719\pi\)
\(648\) 0 0
\(649\) 15.3012 8.83418i 0.600626 0.346772i
\(650\) −0.107248 + 0.0390352i −0.00420662 + 0.00153109i
\(651\) 0 0
\(652\) 4.84681 4.06695i 0.189816 0.159274i
\(653\) −15.2001 18.1147i −0.594824 0.708884i 0.381701 0.924286i \(-0.375338\pi\)
−0.976525 + 0.215402i \(0.930894\pi\)
\(654\) 0 0
\(655\) 14.7229 5.35869i 0.575271 0.209381i
\(656\) −1.13291 −0.0442328
\(657\) 0 0
\(658\) −0.252631 0.187468i −0.00984859 0.00730826i
\(659\) −42.5738 7.50690i −1.65844 0.292427i −0.735543 0.677478i \(-0.763073\pi\)
−0.922895 + 0.385051i \(0.874184\pi\)
\(660\) 0 0
\(661\) −10.0610 11.9902i −0.391327 0.466366i 0.534028 0.845467i \(-0.320678\pi\)
−0.925355 + 0.379101i \(0.876233\pi\)
\(662\) 0.345870 + 0.412192i 0.0134426 + 0.0160203i
\(663\) 0 0
\(664\) −0.547136 0.0964749i −0.0212330 0.00374395i
\(665\) −3.21682 2.38708i −0.124743 0.0925671i
\(666\) 0 0
\(667\) 5.81155 0.225024
\(668\) −14.3979 + 5.24040i −0.557070 + 0.202757i
\(669\) 0 0
\(670\) 0.391527 + 0.466603i 0.0151260 + 0.0180265i
\(671\) −31.8368 + 26.7142i −1.22904 + 1.03129i
\(672\) 0 0
\(673\) 0.784137 0.285403i 0.0302263 0.0110015i −0.326863 0.945072i \(-0.605991\pi\)
0.357089 + 0.934070i \(0.383769\pi\)
\(674\) −0.388456 + 0.224275i −0.0149628 + 0.00863875i
\(675\) 0 0
\(676\) −12.5816 + 21.7920i −0.483909 + 0.838154i
\(677\) −15.9582 13.3905i −0.613325 0.514641i 0.282373 0.959305i \(-0.408879\pi\)
−0.895697 + 0.444664i \(0.853323\pi\)
\(678\) 0 0
\(679\) −19.8298 + 1.18585i −0.760997 + 0.0455088i
\(680\) 0.861073 0.151830i 0.0330206 0.00582243i
\(681\) 0 0
\(682\) 0.184059 + 0.505699i 0.00704800 + 0.0193642i
\(683\) −15.2002 + 8.77584i −0.581619 + 0.335798i −0.761777 0.647840i \(-0.775673\pi\)
0.180157 + 0.983638i \(0.442339\pi\)
\(684\) 0 0
\(685\) −22.4190 + 12.9436i −0.856587 + 0.494551i
\(686\) 0.00139453 + 0.299353i 5.32433e−5 + 0.0114293i
\(687\) 0 0
\(688\) −5.79982 32.8924i −0.221116 1.25401i
\(689\) 0.982097 0.824077i 0.0374149 0.0313949i
\(690\) 0 0
\(691\) 8.98305 + 24.6807i 0.341731 + 0.938899i 0.984892 + 0.173168i \(0.0554004\pi\)
−0.643161 + 0.765731i \(0.722377\pi\)
\(692\) −1.58186 2.73985i −0.0601331 0.104154i
\(693\) 0 0
\(694\) 0.0986965 0.170947i 0.00374647 0.00648907i
\(695\) −22.0798 3.89326i −0.837535 0.147680i
\(696\) 0 0
\(697\) −0.901972 0.328291i −0.0341646 0.0124349i
\(698\) 0.169055 + 0.0615309i 0.00639882 + 0.00232898i
\(699\) 0 0
\(700\) −56.2896 + 13.4332i −2.12755 + 0.507729i
\(701\) 8.38616i 0.316741i 0.987380 + 0.158370i \(0.0506240\pi\)
−0.987380 + 0.158370i \(0.949376\pi\)
\(702\) 0 0
\(703\) 2.02584 + 1.16962i 0.0764060 + 0.0441130i
\(704\) −40.6102 7.16068i −1.53056 0.269878i
\(705\) 0 0
\(706\) −0.204029 0.243152i −0.00767874 0.00915116i
\(707\) 25.1801 16.6173i 0.946994 0.624956i
\(708\) 0 0
\(709\) −1.38512 + 7.85540i −0.0520193 + 0.295016i −0.999708 0.0241813i \(-0.992302\pi\)
0.947688 + 0.319197i \(0.103413\pi\)
\(710\) −0.319419 0.553250i −0.0119876 0.0207631i
\(711\) 0 0
\(712\) 0.299933 + 0.173166i 0.0112404 + 0.00648968i
\(713\) 1.13009 6.40908i 0.0423223 0.240022i
\(714\) 0 0
\(715\) 12.4930 + 4.54706i 0.467210 + 0.170051i
\(716\) −17.1487 + 3.02378i −0.640876 + 0.113004i
\(717\) 0 0
\(718\) 0.371510 + 0.311734i 0.0138646 + 0.0116338i
\(719\) 24.8364 43.0180i 0.926243 1.60430i 0.136694 0.990613i \(-0.456352\pi\)
0.789549 0.613687i \(-0.210314\pi\)
\(720\) 0 0
\(721\) −20.3413 15.0945i −0.757548 0.562148i
\(722\) 0.195913 0.233479i 0.00729111 0.00868921i
\(723\) 0 0
\(724\) 0.858310 2.35819i 0.0318988 0.0876413i
\(725\) −62.0817 + 10.9467i −2.30566 + 0.406550i
\(726\) 0 0
\(727\) −10.9113 29.9786i −0.404678 1.11184i −0.959949 0.280174i \(-0.909608\pi\)
0.555271 0.831669i \(-0.312614\pi\)
\(728\) −0.0658012 + 0.0886735i −0.00243875 + 0.00328646i
\(729\) 0 0
\(730\) −0.228720 0.396154i −0.00846530 0.0146623i
\(731\) 4.91389 27.8680i 0.181747 1.03074i
\(732\) 0 0
\(733\) 12.7466 35.0211i 0.470808 1.29353i −0.446296 0.894885i \(-0.647257\pi\)
0.917104 0.398648i \(-0.130521\pi\)
\(734\) −7.61473e−5 0 0.000431853i −2.81065e−6 0 1.59400e-5i
\(735\) 0 0
\(736\) −0.149801 0.125698i −0.00552173 0.00463328i
\(737\) 48.6936i 1.79365i
\(738\) 0 0
\(739\) −48.9604 −1.80104 −0.900518 0.434818i \(-0.856813\pi\)
−0.900518 + 0.434818i \(0.856813\pi\)
\(740\) 46.2731 16.8420i 1.70103 0.619126i
\(741\) 0 0
\(742\) −0.0708854 + 0.0467799i −0.00260229 + 0.00171734i
\(743\) −13.1684 + 36.1798i −0.483100 + 1.32731i 0.423721 + 0.905793i \(0.360724\pi\)
−0.906821 + 0.421515i \(0.861499\pi\)
\(744\) 0 0
\(745\) −9.10349 + 10.8491i −0.333526 + 0.397481i
\(746\) 0.454552i 0.0166423i
\(747\) 0 0
\(748\) −30.2648 17.4734i −1.10659 0.638891i
\(749\) 26.8300 25.3917i 0.980348 0.927792i
\(750\) 0 0
\(751\) −3.36026 + 2.81959i −0.122618 + 0.102888i −0.702035 0.712143i \(-0.747725\pi\)
0.579417 + 0.815031i \(0.303280\pi\)
\(752\) −5.10757 28.9665i −0.186254 1.05630i
\(753\) 0 0
\(754\) −0.0386560 + 0.0460684i −0.00140777 + 0.00167771i
\(755\) 64.0371 2.33055
\(756\) 0 0
\(757\) 2.14305 0.0778906 0.0389453 0.999241i \(-0.487600\pi\)
0.0389453 + 0.999241i \(0.487600\pi\)
\(758\) 0.00615852 0.00733944i 0.000223688 0.000266580i
\(759\) 0 0
\(760\) 0.0169973 + 0.0963963i 0.000616556 + 0.00349666i
\(761\) 18.1810 15.2557i 0.659062 0.553018i −0.250744 0.968053i \(-0.580675\pi\)
0.909805 + 0.415035i \(0.136231\pi\)
\(762\) 0 0
\(763\) −1.37764 + 4.62777i −0.0498738 + 0.167537i
\(764\) 15.3584 + 8.86719i 0.555648 + 0.320804i
\(765\) 0 0
\(766\) 0.189685i 0.00685358i
\(767\) 1.42121 1.69373i 0.0513170 0.0611572i
\(768\) 0 0
\(769\) 15.4284 42.3891i 0.556362 1.52859i −0.268513 0.963276i \(-0.586532\pi\)
0.824875 0.565315i \(-0.191245\pi\)
\(770\) −0.787657 0.394046i −0.0283852 0.0142004i
\(771\) 0 0
\(772\) −47.3758 + 17.2434i −1.70509 + 0.620603i
\(773\) −6.19919 −0.222969 −0.111485 0.993766i \(-0.535561\pi\)
−0.111485 + 0.993766i \(0.535561\pi\)
\(774\) 0 0
\(775\) 70.5935i 2.53579i
\(776\) 0.371852 + 0.312021i 0.0133487 + 0.0112009i
\(777\) 0 0
\(778\) −0.0430025 0.243880i −0.00154172 0.00874351i
\(779\) 0.0367518 0.100975i 0.00131677 0.00361780i
\(780\) 0 0
\(781\) −8.86827 + 50.2944i −0.317332 + 1.79968i
\(782\) −0.0276073 0.0478173i −0.000987236 0.00170994i
\(783\) 0 0
\(784\) −19.1439 + 20.4180i −0.683711 + 0.729215i
\(785\) 8.37771 + 23.0176i 0.299013 + 0.821532i
\(786\) 0 0
\(787\) −2.35268 + 0.414840i −0.0838638 + 0.0147875i −0.215423 0.976521i \(-0.569113\pi\)
0.131559 + 0.991308i \(0.458002\pi\)
\(788\) −8.73047 + 23.9868i −0.311010 + 0.854493i
\(789\) 0 0
\(790\) 0.0531124 0.0632969i 0.00188966 0.00225200i
\(791\) 10.0479 4.35276i 0.357262 0.154766i
\(792\) 0 0
\(793\) −2.60040 + 4.50403i −0.0923429 + 0.159943i
\(794\) 0.282290 + 0.236869i 0.0100181 + 0.00840618i
\(795\) 0 0
\(796\) 40.1182 7.07392i 1.42195 0.250728i
\(797\) −3.93456 1.43206i −0.139369 0.0507263i 0.271394 0.962468i \(-0.412515\pi\)
−0.410763 + 0.911742i \(0.634738\pi\)
\(798\) 0 0
\(799\) 4.32738 24.5418i 0.153092 0.868226i
\(800\) 1.83701 + 1.06060i 0.0649481 + 0.0374978i
\(801\) 0 0
\(802\) −0.0237001 0.0410498i −0.000836879 0.00144952i
\(803\) −6.35012 + 36.0133i −0.224091 + 1.27088i
\(804\) 0 0
\(805\) 5.86646 + 8.88942i 0.206766 + 0.313311i
\(806\) 0.0432882 + 0.0515888i 0.00152476 + 0.00181714i
\(807\) 0 0
\(808\) −0.725999 0.128013i −0.0255406 0.00450349i
\(809\) 30.6187 + 17.6777i 1.07650 + 0.621516i 0.929949 0.367688i \(-0.119851\pi\)
0.146547 + 0.989204i \(0.453184\pi\)
\(810\) 0 0
\(811\) 30.5126i 1.07144i 0.844395 + 0.535722i \(0.179960\pi\)
−0.844395 + 0.535722i \(0.820040\pi\)
\(812\) −22.1473 + 20.9600i −0.777219 + 0.735553i
\(813\) 0 0
\(814\) 0.483298 + 0.175906i 0.0169396 + 0.00616551i
\(815\) 11.8694 + 4.32012i 0.415768 + 0.151327i
\(816\) 0 0
\(817\) 3.11980 + 0.550105i 0.109148 + 0.0192457i
\(818\) 0.162714 0.281828i 0.00568915 0.00985389i
\(819\) 0 0
\(820\) −1.13101 1.95896i −0.0394965 0.0684099i
\(821\) −2.76913 7.60811i −0.0966432 0.265525i 0.881945 0.471352i \(-0.156234\pi\)
−0.978588 + 0.205827i \(0.934012\pi\)
\(822\) 0 0
\(823\) −11.6207 + 9.75094i −0.405073 + 0.339896i −0.822451 0.568837i \(-0.807394\pi\)
0.417378 + 0.908733i \(0.362949\pi\)
\(824\) 0.107481 + 0.609552i 0.00374426 + 0.0212348i
\(825\) 0 0
\(826\) −0.106383 + 0.100680i −0.00370154 + 0.00350310i
\(827\) −28.1258 + 16.2385i −0.978031 + 0.564667i −0.901675 0.432414i \(-0.857662\pi\)
−0.0763561 + 0.997081i \(0.524329\pi\)
\(828\) 0 0
\(829\) 46.4304 26.8066i 1.61260 0.931033i 0.623830 0.781560i \(-0.285576\pi\)
0.988766 0.149472i \(-0.0477575\pi\)
\(830\) −0.189662 0.521091i −0.00658325 0.0180873i
\(831\) 0 0
\(832\) −5.08195 + 0.896085i −0.176185 + 0.0310662i
\(833\) −21.1581 + 10.7084i −0.733086 + 0.371025i
\(834\) 0 0
\(835\) −23.4320 19.6618i −0.810897 0.680423i
\(836\) 1.95613 3.38812i 0.0676542 0.117181i
\(837\) 0 0
\(838\) −0.202204 + 0.116742i −0.00698501 + 0.00403280i
\(839\) 45.4329 16.5362i 1.56852 0.570893i 0.595849 0.803096i \(-0.296816\pi\)
0.972667 + 0.232203i \(0.0745934\pi\)
\(840\) 0 0
\(841\) −3.23023 + 2.71049i −0.111387 + 0.0934651i
\(842\) −0.0923875 0.110103i −0.00318388 0.00379440i
\(843\) 0 0
\(844\) 1.61862 0.589130i 0.0557153 0.0202787i
\(845\) −50.2353 −1.72815
\(846\) 0 0
\(847\) 16.4186 + 37.9006i 0.564148 + 1.30228i
\(848\) −7.82010 1.37889i −0.268543 0.0473514i
\(849\) 0 0
\(850\) 0.384984 + 0.458806i 0.0132048 + 0.0157369i
\(851\) −3.99793 4.76454i −0.137047 0.163326i
\(852\) 0 0
\(853\) −23.9167 4.21716i −0.818892 0.144393i −0.251518 0.967853i \(-0.580930\pi\)
−0.567374 + 0.823460i \(0.692041\pi\)
\(854\) 0.205311 0.276677i 0.00702561 0.00946769i
\(855\) 0 0
\(856\) −0.902661 −0.0308523
\(857\) −37.5356 + 13.6618i −1.28219 + 0.466679i −0.891156 0.453697i \(-0.850105\pi\)
−0.391034 + 0.920376i \(0.627883\pi\)
\(858\) 0 0
\(859\) 3.72944 + 4.44457i 0.127247 + 0.151647i 0.825906 0.563808i \(-0.190664\pi\)
−0.698659 + 0.715455i \(0.746220\pi\)
\(860\) 51.0855 42.8658i 1.74200 1.46171i
\(861\) 0 0
\(862\) −0.478596 + 0.174195i −0.0163011 + 0.00593310i
\(863\) 18.5008 10.6815i 0.629776 0.363601i −0.150889 0.988551i \(-0.548214\pi\)
0.780665 + 0.624949i \(0.214880\pi\)
\(864\) 0 0
\(865\) 3.15798 5.46978i 0.107374 0.185978i
\(866\) −0.443616 0.372238i −0.0150747 0.0126492i
\(867\) 0 0
\(868\) 18.8084 + 28.5003i 0.638398 + 0.967362i
\(869\) −6.50516 + 1.14703i −0.220672 + 0.0389105i
\(870\) 0 0
\(871\) −2.08410 5.72602i −0.0706171 0.194019i
\(872\) 0.102180 0.0589934i 0.00346024 0.00199777i
\(873\) 0 0
\(874\) 0.00535310 0.00309062i 0.000181071 0.000104542i
\(875\) −43.1110 45.5530i −1.45742 1.53997i
\(876\) 0 0
\(877\) −1.72048 9.75733i −0.0580965 0.329482i 0.941883 0.335942i \(-0.109055\pi\)
−0.999979 + 0.00646042i \(0.997944\pi\)
\(878\) −0.448240 + 0.376118i −0.0151274 + 0.0126934i
\(879\) 0 0
\(880\) −28.1638 77.3794i −0.949402 2.60846i
\(881\) −4.16378 7.21189i −0.140281 0.242975i 0.787321 0.616543i \(-0.211467\pi\)
−0.927603 + 0.373569i \(0.878134\pi\)
\(882\) 0 0
\(883\) −8.57726 + 14.8562i −0.288648 + 0.499953i −0.973487 0.228741i \(-0.926539\pi\)
0.684839 + 0.728694i \(0.259872\pi\)
\(884\) −4.30680 0.759405i −0.144853 0.0255415i
\(885\) 0 0
\(886\) 0.364481 + 0.132660i 0.0122450 + 0.00445680i
\(887\) 14.1405 + 5.14672i 0.474791 + 0.172810i 0.568321 0.822807i \(-0.307593\pi\)
−0.0935304 + 0.995616i \(0.529815\pi\)
\(888\) 0 0
\(889\) 4.77658 16.0455i 0.160201 0.538150i
\(890\) 0.345682i 0.0115873i
\(891\) 0 0
\(892\) 27.2931 + 15.7577i 0.913842 + 0.527607i
\(893\) 2.74743 + 0.484446i 0.0919392 + 0.0162114i
\(894\) 0 0
\(895\) −22.3454 26.6303i −0.746926 0.890152i
\(896\) 1.36560 0.0816650i 0.0456215 0.00272824i
\(897\) 0 0
\(898\) 0.0903715 0.512522i 0.00301573 0.0171031i
\(899\) 18.5986 + 32.2137i 0.620297 + 1.07439i
\(900\) 0 0
\(901\) −5.82642 3.36388i −0.194106 0.112067i
\(902\) 0.00410254 0.0232666i 0.000136600 0.000774694i
\(903\) 0 0
\(904\) −0.251438 0.0915161i −0.00836271 0.00304378i
\(905\) 4.93385 0.869971i 0.164007 0.0289188i
\(906\) 0 0
\(907\) −20.4212 17.1354i −0.678076 0.568973i 0.237368 0.971420i \(-0.423715\pi\)
−0.915443 + 0.402447i \(0.868160\pi\)
\(908\) 9.46364 16.3915i 0.314062 0.543971i
\(909\) 0 0
\(910\) −0.109488 0.0126250i −0.00362950 0.000418515i
\(911\) 0.769727 0.917325i 0.0255022 0.0303923i −0.753143 0.657857i \(-0.771463\pi\)
0.778645 + 0.627465i \(0.215907\pi\)
\(912\) 0 0
\(913\) −15.1620 + 41.6573i −0.501790 + 1.37866i
\(914\) 0.0176136 0.00310575i 0.000582606 0.000102729i
\(915\) 0 0
\(916\) −1.25906 3.45925i −0.0416006 0.114297i
\(917\) 10.3151 + 1.18943i 0.340634 + 0.0392783i
\(918\) 0 0
\(919\) −19.4234 33.6423i −0.640718 1.10976i −0.985273 0.170990i \(-0.945303\pi\)
0.344555 0.938766i \(-0.388030\pi\)
\(920\) 0.0451931 0.256303i 0.00148997 0.00845004i
\(921\) 0 0
\(922\) 0.116158 0.319141i 0.00382546 0.0105104i
\(923\) 1.10977 + 6.29384i 0.0365286 + 0.207164i
\(924\) 0 0
\(925\) 51.6823 + 43.3666i 1.69930 + 1.42589i
\(926\) 0.370426i 0.0121730i
\(927\) 0 0
\(928\) 1.11770 0.0366903
\(929\) 18.2313 6.63565i 0.598150 0.217709i −0.0251605 0.999683i \(-0.508010\pi\)
0.623310 + 0.781975i \(0.285787\pi\)
\(930\) 0 0
\(931\) −1.19880 2.36863i −0.0392890 0.0776288i
\(932\) 7.21725 19.8292i 0.236409 0.649528i
\(933\) 0 0
\(934\) −0.353439 + 0.421212i −0.0115649 + 0.0137825i
\(935\) 69.7670i 2.28162i
\(936\) 0 0
\(937\) 6.25895 + 3.61361i 0.204471 + 0.118051i 0.598739 0.800944i \(-0.295669\pi\)
−0.394268 + 0.918995i \(0.629002\pi\)
\(938\) 0.0937028 + 0.392645i 0.00305950 + 0.0128203i
\(939\) 0 0
\(940\) 44.9880 37.7494i 1.46735 1.23125i
\(941\) 6.31346 + 35.8054i 0.205813 + 1.16722i 0.896155 + 0.443741i \(0.146349\pi\)
−0.690342 + 0.723483i \(0.742540\pi\)
\(942\) 0 0
\(943\) −0.183649 + 0.218864i −0.00598042 + 0.00712719i
\(944\) −13.6947 −0.445723
\(945\) 0 0
\(946\) 0.696515 0.0226456
\(947\) −28.0388 + 33.4153i −0.911138 + 1.08585i 0.0848523 + 0.996394i \(0.472958\pi\)
−0.995991 + 0.0894587i \(0.971486\pi\)
\(948\) 0 0
\(949\) 0.794652 + 4.50670i 0.0257955 + 0.146294i
\(950\) −0.0513629 + 0.0430986i −0.00166643 + 0.00139830i
\(951\) 0 0
\(952\) 0.555372 + 0.165328i 0.0179997 + 0.00535832i
\(953\) −43.3242 25.0133i −1.40341 0.810259i −0.408669 0.912683i \(-0.634007\pi\)
−0.994741 + 0.102424i \(0.967340\pi\)
\(954\) 0 0
\(955\) 35.4045i 1.14566i
\(956\) −6.14626 + 7.32483i −0.198784 + 0.236902i
\(957\) 0 0
\(958\) 0.210556 0.578499i 0.00680277 0.0186905i
\(959\) −17.1255 + 1.02414i −0.553013 + 0.0330710i
\(960\) 0 0
\(961\) 10.0119 3.64405i 0.322966 0.117550i
\(962\) 0.0643613 0.00207509
\(963\) 0 0
\(964\) 17.4526i 0.562109i
\(965\) −77.1022 64.6964i −2.48201 2.08265i
\(966\) 0 0
\(967\) −3.26924 18.5408i −0.105132 0.596231i −0.991168 0.132615i \(-0.957663\pi\)
0.886036 0.463616i \(-0.153448\pi\)
\(968\) 0.345198 0.948423i 0.0110951 0.0304835i
\(969\) 0 0
\(970\) −0.0841338 + 0.477147i −0.00270137 + 0.0153203i
\(971\) 2.80491 + 4.85825i 0.0900140 + 0.155909i 0.907517 0.420016i \(-0.137975\pi\)
−0.817503 + 0.575925i \(0.804642\pi\)
\(972\) 0 0
\(973\) −11.9322 8.85441i −0.382528 0.283859i
\(974\) −0.115180 0.316455i −0.00369061 0.0101399i
\(975\) 0 0
\(976\) 31.7235 5.59372i 1.01545 0.179051i
\(977\) −9.45867 + 25.9875i −0.302610 + 0.831413i 0.691435 + 0.722439i \(0.256979\pi\)
−0.994045 + 0.108974i \(0.965243\pi\)
\(978\) 0 0
\(979\) 17.7632 21.1694i 0.567715 0.676577i
\(980\) −54.4173 12.7188i −1.73830 0.406286i
\(981\) 0 0
\(982\) −0.0224232 + 0.0388382i −0.000715554 + 0.00123938i
\(983\) −25.9918 21.8097i −0.829009 0.695622i 0.126054 0.992023i \(-0.459769\pi\)
−0.955063 + 0.296402i \(0.904213\pi\)
\(984\) 0 0
\(985\) −50.1857 + 8.84909i −1.59905 + 0.281955i
\(986\) 0.296555 + 0.107937i 0.00944425 + 0.00343743i
\(987\) 0 0
\(988\) 0.0850146 0.482142i 0.00270468 0.0153390i
\(989\) −7.29455 4.21151i −0.231953 0.133918i
\(990\) 0 0
\(991\) 12.4282 + 21.5264i 0.394796 + 0.683807i 0.993075 0.117481i \(-0.0374818\pi\)
−0.598279 + 0.801288i \(0.704148\pi\)
\(992\) 0.217344 1.23262i 0.00690068 0.0391357i
\(993\) 0 0
\(994\) −0.0252733 0.422619i −0.000801620 0.0134047i
\(995\) 52.2757 + 62.2997i 1.65725 + 1.97503i
\(996\) 0 0
\(997\) −57.2855 10.1010i −1.81425 0.319901i −0.839527 0.543318i \(-0.817168\pi\)
−0.974723 + 0.223417i \(0.928279\pi\)
\(998\) −0.0569679 0.0328904i −0.00180329 0.00104113i
\(999\) 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 567.2.ba.a.143.12 132
3.2 odd 2 189.2.ba.a.101.11 132
7.5 odd 6 567.2.bd.a.467.11 132
21.5 even 6 189.2.bd.a.47.12 yes 132
27.4 even 9 189.2.bd.a.185.12 yes 132
27.23 odd 18 567.2.bd.a.17.11 132
189.131 even 18 inner 567.2.ba.a.341.12 132
189.166 odd 18 189.2.ba.a.131.11 yes 132
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
189.2.ba.a.101.11 132 3.2 odd 2
189.2.ba.a.131.11 yes 132 189.166 odd 18
189.2.bd.a.47.12 yes 132 21.5 even 6
189.2.bd.a.185.12 yes 132 27.4 even 9
567.2.ba.a.143.12 132 1.1 even 1 trivial
567.2.ba.a.341.12 132 189.131 even 18 inner
567.2.bd.a.17.11 132 27.23 odd 18
567.2.bd.a.467.11 132 7.5 odd 6