Properties

Label 441.2.u.c.253.3
Level $441$
Weight $2$
Character 441.253
Analytic conductor $3.521$
Analytic rank $0$
Dimension $24$
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] = [441,2,Mod(64,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.u (of order \(7\), degree \(6\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{7})\)
Twist minimal: no (minimal twist has level 147)
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 253.3
Character \(\chi\) \(=\) 441.253
Dual form 441.2.u.c.190.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.309296 + 0.387845i) q^{2} +(0.390282 - 1.70994i) q^{4} +(-0.734303 + 0.353621i) q^{5} +(-2.35634 - 1.20320i) q^{7} +(1.67779 - 0.807983i) q^{8} +O(q^{10})\) \(q+(0.309296 + 0.387845i) q^{2} +(0.390282 - 1.70994i) q^{4} +(-0.734303 + 0.353621i) q^{5} +(-2.35634 - 1.20320i) q^{7} +(1.67779 - 0.807983i) q^{8} +(-0.364267 - 0.175422i) q^{10} +(-2.98698 - 3.74555i) q^{11} +(-1.29812 - 1.62779i) q^{13} +(-0.262151 - 1.28604i) q^{14} +(-2.32813 - 1.12117i) q^{16} +(-0.242546 - 1.06266i) q^{17} +7.79907 q^{19} +(0.318086 + 1.39362i) q^{20} +(0.528833 - 2.31697i) q^{22} +(-0.652310 + 2.85796i) q^{23} +(-2.70330 + 3.38983i) q^{25} +(0.229827 - 1.00694i) q^{26} +(-2.97703 + 3.55960i) q^{28} +(-2.37416 - 10.4019i) q^{29} -3.31585 q^{31} +(-1.11400 - 4.88077i) q^{32} +(0.337130 - 0.422748i) q^{34} +(2.15574 + 0.0502606i) q^{35} +(-0.439504 - 1.92559i) q^{37} +(2.41222 + 3.02483i) q^{38} +(-0.946288 + 1.18661i) q^{40} +(7.26508 - 3.49868i) q^{41} +(5.89689 + 2.83979i) q^{43} +(-7.57043 + 3.64573i) q^{44} +(-1.31020 + 0.630959i) q^{46} +(5.16833 + 6.48089i) q^{47} +(4.10463 + 5.67027i) q^{49} -2.15085 q^{50} +(-3.29006 + 1.58441i) q^{52} +(0.782663 - 3.42907i) q^{53} +(3.51786 + 1.69411i) q^{55} +(-4.92561 - 0.114839i) q^{56} +(3.29999 - 4.13806i) q^{58} +(7.50811 + 3.61571i) q^{59} +(-1.32716 - 5.81465i) q^{61} +(-1.02558 - 1.28603i) q^{62} +(-1.67381 + 2.09889i) q^{64} +(1.52884 + 0.736249i) q^{65} +1.24067 q^{67} -1.91175 q^{68} +(0.647268 + 0.851638i) q^{70} +(-1.67946 + 7.35819i) q^{71} +(3.69966 - 4.63923i) q^{73} +(0.610895 - 0.766038i) q^{74} +(3.04384 - 13.3359i) q^{76} +(2.53168 + 12.4197i) q^{77} -5.49325 q^{79} +2.10602 q^{80} +(3.60400 + 1.73560i) q^{82} +(-6.02154 + 7.55077i) q^{83} +(0.553883 + 0.694547i) q^{85} +(0.722485 + 3.16541i) q^{86} +(-8.03788 - 3.87084i) q^{88} +(-3.82643 + 4.79820i) q^{89} +(1.10025 + 5.39753i) q^{91} +(4.63234 + 2.23082i) q^{92} +(-0.915033 + 4.00902i) q^{94} +(-5.72687 + 2.75792i) q^{95} -10.2300 q^{97} +(-0.929641 + 3.34575i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - q^{2} - 3 q^{4} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - q^{2} - 3 q^{4} - 3 q^{8} - 30 q^{10} - 9 q^{11} + 21 q^{14} - 29 q^{16} - 5 q^{17} + 26 q^{19} + 13 q^{20} + 11 q^{22} - 4 q^{23} - 28 q^{25} + 22 q^{26} - 7 q^{28} - 6 q^{29} + 36 q^{31} - 14 q^{32} + 46 q^{34} + 7 q^{35} - 22 q^{37} + 45 q^{38} + 35 q^{40} + 11 q^{41} + 6 q^{43} - 82 q^{44} - 16 q^{46} - 29 q^{47} - 42 q^{49} + 48 q^{50} - 50 q^{52} - 28 q^{53} + 23 q^{55} - 21 q^{56} + 39 q^{58} + 15 q^{59} - 32 q^{61} + 8 q^{62} + 29 q^{64} + 21 q^{65} - 34 q^{67} + 22 q^{68} - 24 q^{71} - 15 q^{73} - 6 q^{74} + 7 q^{76} + 21 q^{77} - 34 q^{79} - 8 q^{80} + 14 q^{82} - 14 q^{83} + 20 q^{85} + 100 q^{86} - 108 q^{88} - 10 q^{89} + 84 q^{91} + 21 q^{92} + 99 q^{94} - 18 q^{95} - 64 q^{97} - 91 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{6}{7}\right)\) \(1\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.309296 + 0.387845i 0.218705 + 0.274248i 0.879065 0.476701i \(-0.158168\pi\)
−0.660360 + 0.750949i \(0.729596\pi\)
\(3\) 0 0
\(4\) 0.390282 1.70994i 0.195141 0.854969i
\(5\) −0.734303 + 0.353621i −0.328390 + 0.158144i −0.590813 0.806809i \(-0.701193\pi\)
0.262423 + 0.964953i \(0.415479\pi\)
\(6\) 0 0
\(7\) −2.35634 1.20320i −0.890611 0.454766i
\(8\) 1.67779 0.807983i 0.593190 0.285665i
\(9\) 0 0
\(10\) −0.364267 0.175422i −0.115191 0.0554732i
\(11\) −2.98698 3.74555i −0.900608 1.12933i −0.991059 0.133426i \(-0.957402\pi\)
0.0904503 0.995901i \(-0.471169\pi\)
\(12\) 0 0
\(13\) −1.29812 1.62779i −0.360034 0.451469i 0.568518 0.822671i \(-0.307517\pi\)
−0.928552 + 0.371202i \(0.878946\pi\)
\(14\) −0.262151 1.28604i −0.0700627 0.343708i
\(15\) 0 0
\(16\) −2.32813 1.12117i −0.582034 0.280293i
\(17\) −0.242546 1.06266i −0.0588261 0.257734i 0.936960 0.349435i \(-0.113627\pi\)
−0.995787 + 0.0917015i \(0.970769\pi\)
\(18\) 0 0
\(19\) 7.79907 1.78923 0.894614 0.446839i \(-0.147450\pi\)
0.894614 + 0.446839i \(0.147450\pi\)
\(20\) 0.318086 + 1.39362i 0.0711261 + 0.311624i
\(21\) 0 0
\(22\) 0.528833 2.31697i 0.112748 0.493980i
\(23\) −0.652310 + 2.85796i −0.136016 + 0.595925i 0.860271 + 0.509836i \(0.170294\pi\)
−0.996287 + 0.0860888i \(0.972563\pi\)
\(24\) 0 0
\(25\) −2.70330 + 3.38983i −0.540659 + 0.677965i
\(26\) 0.229827 1.00694i 0.0450729 0.197477i
\(27\) 0 0
\(28\) −2.97703 + 3.55960i −0.562606 + 0.672701i
\(29\) −2.37416 10.4019i −0.440870 1.93158i −0.353613 0.935392i \(-0.615047\pi\)
−0.0872565 0.996186i \(-0.527810\pi\)
\(30\) 0 0
\(31\) −3.31585 −0.595544 −0.297772 0.954637i \(-0.596243\pi\)
−0.297772 + 0.954637i \(0.596243\pi\)
\(32\) −1.11400 4.88077i −0.196930 0.862807i
\(33\) 0 0
\(34\) 0.337130 0.422748i 0.0578173 0.0725006i
\(35\) 2.15574 + 0.0502606i 0.364386 + 0.00849559i
\(36\) 0 0
\(37\) −0.439504 1.92559i −0.0722541 0.316566i 0.925866 0.377852i \(-0.123337\pi\)
−0.998120 + 0.0612858i \(0.980480\pi\)
\(38\) 2.41222 + 3.02483i 0.391314 + 0.490692i
\(39\) 0 0
\(40\) −0.946288 + 1.18661i −0.149621 + 0.187619i
\(41\) 7.26508 3.49868i 1.13461 0.546402i 0.230237 0.973135i \(-0.426050\pi\)
0.904378 + 0.426733i \(0.140336\pi\)
\(42\) 0 0
\(43\) 5.89689 + 2.83979i 0.899267 + 0.433064i 0.825624 0.564220i \(-0.190823\pi\)
0.0736429 + 0.997285i \(0.476537\pi\)
\(44\) −7.57043 + 3.64573i −1.14129 + 0.549614i
\(45\) 0 0
\(46\) −1.31020 + 0.630959i −0.193178 + 0.0930298i
\(47\) 5.16833 + 6.48089i 0.753879 + 0.945334i 0.999712 0.0239776i \(-0.00763304\pi\)
−0.245833 + 0.969312i \(0.579062\pi\)
\(48\) 0 0
\(49\) 4.10463 + 5.67027i 0.586376 + 0.810039i
\(50\) −2.15085 −0.304175
\(51\) 0 0
\(52\) −3.29006 + 1.58441i −0.456249 + 0.219718i
\(53\) 0.782663 3.42907i 0.107507 0.471019i −0.892301 0.451440i \(-0.850910\pi\)
0.999808 0.0195786i \(-0.00623246\pi\)
\(54\) 0 0
\(55\) 3.51786 + 1.69411i 0.474348 + 0.228434i
\(56\) −4.92561 0.114839i −0.658212 0.0153461i
\(57\) 0 0
\(58\) 3.29999 4.13806i 0.433310 0.543354i
\(59\) 7.50811 + 3.61571i 0.977472 + 0.470726i 0.853235 0.521527i \(-0.174637\pi\)
0.124237 + 0.992253i \(0.460352\pi\)
\(60\) 0 0
\(61\) −1.32716 5.81465i −0.169925 0.744490i −0.986027 0.166583i \(-0.946727\pi\)
0.816102 0.577907i \(-0.196130\pi\)
\(62\) −1.02558 1.28603i −0.130249 0.163327i
\(63\) 0 0
\(64\) −1.67381 + 2.09889i −0.209227 + 0.262362i
\(65\) 1.52884 + 0.736249i 0.189629 + 0.0913205i
\(66\) 0 0
\(67\) 1.24067 0.151572 0.0757860 0.997124i \(-0.475853\pi\)
0.0757860 + 0.997124i \(0.475853\pi\)
\(68\) −1.91175 −0.231834
\(69\) 0 0
\(70\) 0.647268 + 0.851638i 0.0773633 + 0.101790i
\(71\) −1.67946 + 7.35819i −0.199315 + 0.873257i 0.772031 + 0.635585i \(0.219241\pi\)
−0.971346 + 0.237671i \(0.923616\pi\)
\(72\) 0 0
\(73\) 3.69966 4.63923i 0.433013 0.542981i −0.516674 0.856182i \(-0.672830\pi\)
0.949687 + 0.313202i \(0.101402\pi\)
\(74\) 0.610895 0.766038i 0.0710151 0.0890501i
\(75\) 0 0
\(76\) 3.04384 13.3359i 0.349152 1.52974i
\(77\) 2.53168 + 12.4197i 0.288512 + 1.41536i
\(78\) 0 0
\(79\) −5.49325 −0.618039 −0.309020 0.951056i \(-0.600001\pi\)
−0.309020 + 0.951056i \(0.600001\pi\)
\(80\) 2.10602 0.235461
\(81\) 0 0
\(82\) 3.60400 + 1.73560i 0.397996 + 0.191665i
\(83\) −6.02154 + 7.55077i −0.660950 + 0.828805i −0.993446 0.114299i \(-0.963538\pi\)
0.332496 + 0.943105i \(0.392109\pi\)
\(84\) 0 0
\(85\) 0.553883 + 0.694547i 0.0600770 + 0.0753342i
\(86\) 0.722485 + 3.16541i 0.0779076 + 0.341335i
\(87\) 0 0
\(88\) −8.03788 3.87084i −0.856841 0.412633i
\(89\) −3.82643 + 4.79820i −0.405601 + 0.508608i −0.942118 0.335282i \(-0.891168\pi\)
0.536517 + 0.843890i \(0.319740\pi\)
\(90\) 0 0
\(91\) 1.10025 + 5.39753i 0.115338 + 0.565814i
\(92\) 4.63234 + 2.23082i 0.482955 + 0.232579i
\(93\) 0 0
\(94\) −0.915033 + 4.00902i −0.0943785 + 0.413499i
\(95\) −5.72687 + 2.75792i −0.587565 + 0.282956i
\(96\) 0 0
\(97\) −10.2300 −1.03870 −0.519350 0.854562i \(-0.673826\pi\)
−0.519350 + 0.854562i \(0.673826\pi\)
\(98\) −0.929641 + 3.34575i −0.0939080 + 0.337972i
\(99\) 0 0
\(100\) 4.74135 + 5.94546i 0.474135 + 0.594546i
\(101\) 10.1408 4.88353i 1.00904 0.485930i 0.145045 0.989425i \(-0.453667\pi\)
0.863998 + 0.503495i \(0.167953\pi\)
\(102\) 0 0
\(103\) −0.0310048 + 0.0149311i −0.00305500 + 0.00147121i −0.435411 0.900232i \(-0.643397\pi\)
0.432356 + 0.901703i \(0.357683\pi\)
\(104\) −3.49321 1.68224i −0.342538 0.164957i
\(105\) 0 0
\(106\) 1.57202 0.757045i 0.152688 0.0735307i
\(107\) −3.33963 + 4.18777i −0.322854 + 0.404847i −0.916600 0.399807i \(-0.869077\pi\)
0.593745 + 0.804653i \(0.297649\pi\)
\(108\) 0 0
\(109\) 5.09968 + 6.39479i 0.488461 + 0.612510i 0.963583 0.267409i \(-0.0861676\pi\)
−0.475122 + 0.879920i \(0.657596\pi\)
\(110\) 0.431007 + 1.88836i 0.0410949 + 0.180048i
\(111\) 0 0
\(112\) 4.13687 + 5.44306i 0.390898 + 0.514321i
\(113\) 8.84577 11.0922i 0.832140 1.04347i −0.166212 0.986090i \(-0.553154\pi\)
0.998352 0.0573807i \(-0.0182749\pi\)
\(114\) 0 0
\(115\) −0.531642 2.32928i −0.0495759 0.217206i
\(116\) −18.7131 −1.73747
\(117\) 0 0
\(118\) 0.919891 + 4.03031i 0.0846828 + 0.371020i
\(119\) −0.707075 + 2.79582i −0.0648174 + 0.256293i
\(120\) 0 0
\(121\) −2.65940 + 11.6516i −0.241764 + 1.05924i
\(122\) 1.84470 2.31318i 0.167011 0.209425i
\(123\) 0 0
\(124\) −1.29412 + 5.66989i −0.116215 + 0.509172i
\(125\) 1.69311 7.41800i 0.151436 0.663486i
\(126\) 0 0
\(127\) 0.252598 + 1.10670i 0.0224144 + 0.0982041i 0.984898 0.173136i \(-0.0553902\pi\)
−0.962483 + 0.271341i \(0.912533\pi\)
\(128\) −11.3443 −1.00271
\(129\) 0 0
\(130\) 0.187313 + 0.820670i 0.0164284 + 0.0719776i
\(131\) 7.11942 + 3.42853i 0.622027 + 0.299552i 0.718226 0.695810i \(-0.244954\pi\)
−0.0961992 + 0.995362i \(0.530669\pi\)
\(132\) 0 0
\(133\) −18.3772 9.38382i −1.59351 0.813680i
\(134\) 0.383734 + 0.481187i 0.0331496 + 0.0415682i
\(135\) 0 0
\(136\) −1.26556 1.58696i −0.108521 0.136081i
\(137\) 13.8429 + 6.66641i 1.18268 + 0.569549i 0.918691 0.394976i \(-0.129247\pi\)
0.263990 + 0.964525i \(0.414961\pi\)
\(138\) 0 0
\(139\) −0.460998 + 0.222005i −0.0391014 + 0.0188302i −0.453332 0.891342i \(-0.649765\pi\)
0.414231 + 0.910172i \(0.364051\pi\)
\(140\) 0.927289 3.66657i 0.0783702 0.309881i
\(141\) 0 0
\(142\) −3.37329 + 1.62449i −0.283080 + 0.136324i
\(143\) −2.21953 + 9.72438i −0.185606 + 0.813193i
\(144\) 0 0
\(145\) 5.42167 + 6.79856i 0.450245 + 0.564590i
\(146\) 2.94359 0.243613
\(147\) 0 0
\(148\) −3.46418 −0.284754
\(149\) −8.71719 10.9310i −0.714140 0.895504i 0.283850 0.958869i \(-0.408388\pi\)
−0.997990 + 0.0633651i \(0.979817\pi\)
\(150\) 0 0
\(151\) 4.21510 18.4675i 0.343020 1.50287i −0.449644 0.893208i \(-0.648449\pi\)
0.792663 0.609660i \(-0.208694\pi\)
\(152\) 13.0852 6.30151i 1.06135 0.511120i
\(153\) 0 0
\(154\) −4.03388 + 4.82327i −0.325059 + 0.388670i
\(155\) 2.43484 1.17255i 0.195571 0.0941819i
\(156\) 0 0
\(157\) 17.6120 + 8.48150i 1.40559 + 0.676898i 0.974287 0.225309i \(-0.0723390\pi\)
0.431305 + 0.902206i \(0.358053\pi\)
\(158\) −1.69904 2.13053i −0.135168 0.169496i
\(159\) 0 0
\(160\) 2.54396 + 3.19003i 0.201118 + 0.252194i
\(161\) 4.97575 5.94944i 0.392144 0.468882i
\(162\) 0 0
\(163\) −13.7964 6.64398i −1.08062 0.520397i −0.193102 0.981179i \(-0.561855\pi\)
−0.887513 + 0.460782i \(0.847569\pi\)
\(164\) −3.14709 13.7883i −0.245747 1.07669i
\(165\) 0 0
\(166\) −4.79097 −0.371851
\(167\) −3.85674 16.8975i −0.298444 1.30757i −0.872445 0.488713i \(-0.837467\pi\)
0.574001 0.818855i \(-0.305391\pi\)
\(168\) 0 0
\(169\) 1.92818 8.44791i 0.148322 0.649839i
\(170\) −0.0980628 + 0.429641i −0.00752107 + 0.0329520i
\(171\) 0 0
\(172\) 7.15732 8.97500i 0.545741 0.684337i
\(173\) −4.24082 + 18.5802i −0.322423 + 1.41263i 0.510804 + 0.859697i \(0.329348\pi\)
−0.833227 + 0.552931i \(0.813509\pi\)
\(174\) 0 0
\(175\) 10.4485 4.73497i 0.789833 0.357930i
\(176\) 2.75469 + 12.0691i 0.207642 + 0.909740i
\(177\) 0 0
\(178\) −3.04446 −0.228192
\(179\) −2.54954 11.1703i −0.190561 0.834904i −0.976313 0.216362i \(-0.930581\pi\)
0.785752 0.618542i \(-0.212276\pi\)
\(180\) 0 0
\(181\) 2.67475 3.35403i 0.198813 0.249303i −0.672424 0.740166i \(-0.734747\pi\)
0.871237 + 0.490863i \(0.163318\pi\)
\(182\) −1.75310 + 2.09616i −0.129948 + 0.155378i
\(183\) 0 0
\(184\) 1.21474 + 5.32212i 0.0895517 + 0.392352i
\(185\) 1.00366 + 1.25855i 0.0737906 + 0.0925305i
\(186\) 0 0
\(187\) −3.25578 + 4.08263i −0.238087 + 0.298551i
\(188\) 13.0990 6.30816i 0.955345 0.460070i
\(189\) 0 0
\(190\) −2.84094 1.36813i −0.206104 0.0992543i
\(191\) 2.00226 0.964238i 0.144878 0.0697698i −0.360040 0.932937i \(-0.617237\pi\)
0.504918 + 0.863167i \(0.331523\pi\)
\(192\) 0 0
\(193\) −11.6453 + 5.60808i −0.838247 + 0.403678i −0.803202 0.595707i \(-0.796872\pi\)
−0.0350454 + 0.999386i \(0.511158\pi\)
\(194\) −3.16410 3.96765i −0.227169 0.284861i
\(195\) 0 0
\(196\) 11.2978 4.80566i 0.806985 0.343261i
\(197\) 26.7968 1.90920 0.954598 0.297898i \(-0.0962857\pi\)
0.954598 + 0.297898i \(0.0962857\pi\)
\(198\) 0 0
\(199\) 17.1513 8.25963i 1.21582 0.585510i 0.287678 0.957727i \(-0.407117\pi\)
0.928146 + 0.372217i \(0.121402\pi\)
\(200\) −1.79665 + 7.87165i −0.127043 + 0.556610i
\(201\) 0 0
\(202\) 5.03055 + 2.42258i 0.353948 + 0.170452i
\(203\) −6.92119 + 27.3669i −0.485772 + 1.92078i
\(204\) 0 0
\(205\) −4.09756 + 5.13817i −0.286186 + 0.358866i
\(206\) −0.0153806 0.00740692i −0.00107162 0.000516065i
\(207\) 0 0
\(208\) 1.19717 + 5.24514i 0.0830087 + 0.363685i
\(209\) −23.2957 29.2118i −1.61139 2.02062i
\(210\) 0 0
\(211\) −0.620248 + 0.777766i −0.0426996 + 0.0535436i −0.802723 0.596352i \(-0.796616\pi\)
0.760023 + 0.649896i \(0.225188\pi\)
\(212\) −5.55804 2.67661i −0.381728 0.183830i
\(213\) 0 0
\(214\) −2.65714 −0.181638
\(215\) −5.33431 −0.363797
\(216\) 0 0
\(217\) 7.81325 + 3.98962i 0.530398 + 0.270833i
\(218\) −0.902878 + 3.95577i −0.0611506 + 0.267918i
\(219\) 0 0
\(220\) 4.26978 5.35413i 0.287869 0.360976i
\(221\) −1.41494 + 1.77428i −0.0951794 + 0.119351i
\(222\) 0 0
\(223\) 2.12351 9.30371i 0.142201 0.623023i −0.852721 0.522367i \(-0.825049\pi\)
0.994921 0.100655i \(-0.0320939\pi\)
\(224\) −3.24757 + 12.8411i −0.216987 + 0.857982i
\(225\) 0 0
\(226\) 7.03803 0.468163
\(227\) 6.33745 0.420632 0.210316 0.977634i \(-0.432551\pi\)
0.210316 + 0.977634i \(0.432551\pi\)
\(228\) 0 0
\(229\) −16.7559 8.06923i −1.10726 0.533229i −0.211328 0.977415i \(-0.567779\pi\)
−0.895935 + 0.444186i \(0.853493\pi\)
\(230\) 0.738963 0.926630i 0.0487257 0.0611002i
\(231\) 0 0
\(232\) −12.3879 15.5339i −0.813304 1.01985i
\(233\) −1.65102 7.23360i −0.108162 0.473889i −0.999777 0.0210952i \(-0.993285\pi\)
0.891615 0.452793i \(-0.149572\pi\)
\(234\) 0 0
\(235\) −6.08690 2.93130i −0.397066 0.191217i
\(236\) 9.11293 11.4272i 0.593201 0.743851i
\(237\) 0 0
\(238\) −1.30304 + 0.590501i −0.0844636 + 0.0382765i
\(239\) −22.5961 10.8817i −1.46162 0.703880i −0.477053 0.878875i \(-0.658295\pi\)
−0.984569 + 0.174994i \(0.944009\pi\)
\(240\) 0 0
\(241\) 2.00652 8.79115i 0.129251 0.566288i −0.868280 0.496074i \(-0.834775\pi\)
0.997532 0.0702140i \(-0.0223682\pi\)
\(242\) −5.34155 + 2.57236i −0.343368 + 0.165357i
\(243\) 0 0
\(244\) −10.4607 −0.669676
\(245\) −5.01917 2.71221i −0.320663 0.173277i
\(246\) 0 0
\(247\) −10.1241 12.6953i −0.644184 0.807781i
\(248\) −5.56331 + 2.67915i −0.353271 + 0.170126i
\(249\) 0 0
\(250\) 3.40071 1.63769i 0.215080 0.103577i
\(251\) −7.77165 3.74263i −0.490542 0.236233i 0.172226 0.985057i \(-0.444904\pi\)
−0.662768 + 0.748825i \(0.730618\pi\)
\(252\) 0 0
\(253\) 12.6531 6.09340i 0.795492 0.383089i
\(254\) −0.351102 + 0.440268i −0.0220301 + 0.0276249i
\(255\) 0 0
\(256\) −0.161129 0.202050i −0.0100706 0.0126281i
\(257\) 0.324772 + 1.42292i 0.0202587 + 0.0887592i 0.984047 0.177911i \(-0.0569338\pi\)
−0.963788 + 0.266670i \(0.914077\pi\)
\(258\) 0 0
\(259\) −1.28125 + 5.06616i −0.0796131 + 0.314796i
\(260\) 1.85562 2.32687i 0.115081 0.144306i
\(261\) 0 0
\(262\) 0.872270 + 3.82166i 0.0538890 + 0.236103i
\(263\) 2.23788 0.137993 0.0689967 0.997617i \(-0.478020\pi\)
0.0689967 + 0.997617i \(0.478020\pi\)
\(264\) 0 0
\(265\) 0.637881 + 2.79474i 0.0391847 + 0.171680i
\(266\) −2.04453 10.0299i −0.125358 0.614972i
\(267\) 0 0
\(268\) 0.484211 2.12147i 0.0295779 0.129589i
\(269\) 1.74064 2.18270i 0.106129 0.133081i −0.725930 0.687768i \(-0.758591\pi\)
0.832059 + 0.554687i \(0.187162\pi\)
\(270\) 0 0
\(271\) −4.64427 + 20.3479i −0.282119 + 1.23605i 0.612951 + 0.790121i \(0.289982\pi\)
−0.895071 + 0.445925i \(0.852875\pi\)
\(272\) −0.626747 + 2.74596i −0.0380021 + 0.166498i
\(273\) 0 0
\(274\) 1.69603 + 7.43080i 0.102461 + 0.448911i
\(275\) 20.7715 1.25257
\(276\) 0 0
\(277\) −2.49753 10.9424i −0.150062 0.657465i −0.992865 0.119243i \(-0.961953\pi\)
0.842803 0.538222i \(-0.180904\pi\)
\(278\) −0.228688 0.110131i −0.0137158 0.00660519i
\(279\) 0 0
\(280\) 3.65750 1.65747i 0.218577 0.0990530i
\(281\) −5.50298 6.90052i −0.328281 0.411651i 0.590112 0.807321i \(-0.299084\pi\)
−0.918392 + 0.395671i \(0.870512\pi\)
\(282\) 0 0
\(283\) 18.5289 + 23.2345i 1.10143 + 1.38115i 0.917277 + 0.398251i \(0.130383\pi\)
0.184153 + 0.982898i \(0.441046\pi\)
\(284\) 11.9266 + 5.74354i 0.707713 + 0.340817i
\(285\) 0 0
\(286\) −4.45804 + 2.14688i −0.263609 + 0.126948i
\(287\) −21.3286 0.497271i −1.25899 0.0293530i
\(288\) 0 0
\(289\) 14.2460 6.86053i 0.838003 0.403561i
\(290\) −0.959886 + 4.20553i −0.0563664 + 0.246957i
\(291\) 0 0
\(292\) −6.48888 8.13680i −0.379733 0.476170i
\(293\) 9.52198 0.556280 0.278140 0.960541i \(-0.410282\pi\)
0.278140 + 0.960541i \(0.410282\pi\)
\(294\) 0 0
\(295\) −6.79182 −0.395435
\(296\) −2.29325 2.87564i −0.133292 0.167143i
\(297\) 0 0
\(298\) 1.54334 6.76184i 0.0894036 0.391703i
\(299\) 5.49894 2.64815i 0.318012 0.153146i
\(300\) 0 0
\(301\) −10.4782 13.7866i −0.603954 0.794648i
\(302\) 8.46625 4.07713i 0.487178 0.234613i
\(303\) 0 0
\(304\) −18.1573 8.74408i −1.04139 0.501507i
\(305\) 3.03072 + 3.80040i 0.173539 + 0.217611i
\(306\) 0 0
\(307\) 20.5371 + 25.7527i 1.17211 + 1.46978i 0.852881 + 0.522105i \(0.174853\pi\)
0.319230 + 0.947677i \(0.396576\pi\)
\(308\) 22.2250 + 0.518171i 1.26639 + 0.0295255i
\(309\) 0 0
\(310\) 1.20785 + 0.581672i 0.0686015 + 0.0330367i
\(311\) −1.42368 6.23757i −0.0807298 0.353700i 0.918389 0.395679i \(-0.129491\pi\)
−0.999118 + 0.0419792i \(0.986634\pi\)
\(312\) 0 0
\(313\) −5.76875 −0.326069 −0.163035 0.986620i \(-0.552128\pi\)
−0.163035 + 0.986620i \(0.552128\pi\)
\(314\) 2.15782 + 9.45402i 0.121773 + 0.533521i
\(315\) 0 0
\(316\) −2.14392 + 9.39313i −0.120605 + 0.528405i
\(317\) 1.37782 6.03663i 0.0773862 0.339051i −0.921383 0.388657i \(-0.872939\pi\)
0.998769 + 0.0496055i \(0.0157964\pi\)
\(318\) 0 0
\(319\) −31.8692 + 39.9627i −1.78433 + 2.23748i
\(320\) 0.486871 2.13312i 0.0272169 0.119245i
\(321\) 0 0
\(322\) 3.84644 + 0.0896789i 0.214354 + 0.00499761i
\(323\) −1.89163 8.28778i −0.105253 0.461145i
\(324\) 0 0
\(325\) 9.02715 0.500736
\(326\) −1.69033 7.40581i −0.0936186 0.410170i
\(327\) 0 0
\(328\) 9.36243 11.7401i 0.516954 0.648240i
\(329\) −4.38054 21.4897i −0.241507 1.18476i
\(330\) 0 0
\(331\) 1.74339 + 7.63830i 0.0958254 + 0.419839i 0.999973 0.00738214i \(-0.00234983\pi\)
−0.904147 + 0.427221i \(0.859493\pi\)
\(332\) 10.5613 + 13.2434i 0.579624 + 0.726826i
\(333\) 0 0
\(334\) 5.36073 6.72214i 0.293326 0.367819i
\(335\) −0.911027 + 0.438727i −0.0497747 + 0.0239702i
\(336\) 0 0
\(337\) 5.14108 + 2.47581i 0.280052 + 0.134866i 0.568638 0.822588i \(-0.307471\pi\)
−0.288585 + 0.957454i \(0.593185\pi\)
\(338\) 3.87286 1.86507i 0.210656 0.101446i
\(339\) 0 0
\(340\) 1.40380 0.676036i 0.0761319 0.0366632i
\(341\) 9.90437 + 12.4197i 0.536352 + 0.672564i
\(342\) 0 0
\(343\) −2.84942 18.2997i −0.153854 0.988094i
\(344\) 12.1883 0.657148
\(345\) 0 0
\(346\) −8.51791 + 4.10201i −0.457926 + 0.220525i
\(347\) −2.08346 + 9.12823i −0.111846 + 0.490029i 0.887715 + 0.460394i \(0.152292\pi\)
−0.999561 + 0.0296354i \(0.990565\pi\)
\(348\) 0 0
\(349\) −19.9865 9.62499i −1.06985 0.515214i −0.185793 0.982589i \(-0.559485\pi\)
−0.884059 + 0.467375i \(0.845200\pi\)
\(350\) 5.06811 + 2.58789i 0.270902 + 0.138329i
\(351\) 0 0
\(352\) −14.9537 + 18.7513i −0.797034 + 0.999449i
\(353\) −28.1253 13.5444i −1.49696 0.720897i −0.506959 0.861970i \(-0.669230\pi\)
−0.989999 + 0.141073i \(0.954945\pi\)
\(354\) 0 0
\(355\) −1.36878 5.99703i −0.0726475 0.318289i
\(356\) 6.71123 + 8.41562i 0.355695 + 0.446027i
\(357\) 0 0
\(358\) 3.54377 4.44374i 0.187294 0.234859i
\(359\) −7.69208 3.70431i −0.405973 0.195506i 0.219742 0.975558i \(-0.429478\pi\)
−0.625715 + 0.780052i \(0.715193\pi\)
\(360\) 0 0
\(361\) 41.8254 2.20134
\(362\) 2.12813 0.111852
\(363\) 0 0
\(364\) 9.65884 + 0.225194i 0.506261 + 0.0118034i
\(365\) −1.07614 + 4.71488i −0.0563277 + 0.246788i
\(366\) 0 0
\(367\) −12.8401 + 16.1009i −0.670246 + 0.840462i −0.994415 0.105537i \(-0.966344\pi\)
0.324169 + 0.945999i \(0.394915\pi\)
\(368\) 4.72292 5.92235i 0.246199 0.308724i
\(369\) 0 0
\(370\) −0.177694 + 0.778529i −0.00923788 + 0.0404738i
\(371\) −5.97006 + 7.13834i −0.309950 + 0.370604i
\(372\) 0 0
\(373\) −5.23130 −0.270867 −0.135433 0.990786i \(-0.543243\pi\)
−0.135433 + 0.990786i \(0.543243\pi\)
\(374\) −2.59043 −0.133948
\(375\) 0 0
\(376\) 13.9079 + 6.69767i 0.717243 + 0.345406i
\(377\) −13.8501 + 17.3675i −0.713319 + 0.894473i
\(378\) 0 0
\(379\) −13.5974 17.0506i −0.698452 0.875831i 0.298455 0.954424i \(-0.403529\pi\)
−0.996907 + 0.0785931i \(0.974957\pi\)
\(380\) 2.48077 + 10.8690i 0.127261 + 0.557566i
\(381\) 0 0
\(382\) 0.993265 + 0.478331i 0.0508199 + 0.0244736i
\(383\) −8.80378 + 11.0396i −0.449852 + 0.564097i −0.954110 0.299456i \(-0.903195\pi\)
0.504258 + 0.863553i \(0.331766\pi\)
\(384\) 0 0
\(385\) −6.25090 8.22457i −0.318575 0.419163i
\(386\) −5.77691 2.78201i −0.294037 0.141601i
\(387\) 0 0
\(388\) −3.99259 + 17.4927i −0.202693 + 0.888056i
\(389\) −21.6718 + 10.4366i −1.09881 + 0.529157i −0.893283 0.449495i \(-0.851604\pi\)
−0.205523 + 0.978652i \(0.565890\pi\)
\(390\) 0 0
\(391\) 3.19526 0.161591
\(392\) 11.4682 + 6.19708i 0.579232 + 0.313000i
\(393\) 0 0
\(394\) 8.28815 + 10.3930i 0.417551 + 0.523592i
\(395\) 4.03371 1.94253i 0.202958 0.0977394i
\(396\) 0 0
\(397\) 12.3693 5.95674i 0.620797 0.298960i −0.0969230 0.995292i \(-0.530900\pi\)
0.717720 + 0.696332i \(0.245186\pi\)
\(398\) 8.50828 + 4.09737i 0.426482 + 0.205383i
\(399\) 0 0
\(400\) 10.0942 4.86112i 0.504711 0.243056i
\(401\) 2.17712 2.73002i 0.108720 0.136331i −0.724494 0.689281i \(-0.757927\pi\)
0.833214 + 0.552950i \(0.186498\pi\)
\(402\) 0 0
\(403\) 4.30437 + 5.39752i 0.214416 + 0.268869i
\(404\) −4.39278 19.2460i −0.218549 0.957526i
\(405\) 0 0
\(406\) −12.7548 + 5.78011i −0.633010 + 0.286862i
\(407\) −5.89963 + 7.39790i −0.292434 + 0.366700i
\(408\) 0 0
\(409\) −4.53852 19.8845i −0.224415 0.983227i −0.954111 0.299455i \(-0.903195\pi\)
0.729695 0.683772i \(-0.239662\pi\)
\(410\) −3.26017 −0.161008
\(411\) 0 0
\(412\) 0.0134307 + 0.0588437i 0.000661682 + 0.00289902i
\(413\) −13.3412 17.5536i −0.656477 0.863755i
\(414\) 0 0
\(415\) 1.75152 7.67390i 0.0859786 0.376697i
\(416\) −6.49878 + 8.14921i −0.318629 + 0.399548i
\(417\) 0 0
\(418\) 4.12441 18.0702i 0.201731 0.883842i
\(419\) −7.12743 + 31.2273i −0.348198 + 1.52555i 0.433072 + 0.901359i \(0.357430\pi\)
−0.781270 + 0.624194i \(0.785428\pi\)
\(420\) 0 0
\(421\) 0.915710 + 4.01199i 0.0446290 + 0.195532i 0.992328 0.123633i \(-0.0394546\pi\)
−0.947699 + 0.319165i \(0.896597\pi\)
\(422\) −0.493493 −0.0240228
\(423\) 0 0
\(424\) −1.45748 6.38565i −0.0707816 0.310115i
\(425\) 4.25792 + 2.05051i 0.206539 + 0.0994642i
\(426\) 0 0
\(427\) −3.86895 + 15.2981i −0.187232 + 0.740327i
\(428\) 5.85742 + 7.34497i 0.283129 + 0.355033i
\(429\) 0 0
\(430\) −1.64988 2.06889i −0.0795643 0.0997705i
\(431\) 33.4595 + 16.1132i 1.61169 + 0.776147i 0.999889 0.0148684i \(-0.00473292\pi\)
0.611796 + 0.791015i \(0.290447\pi\)
\(432\) 0 0
\(433\) −22.7009 + 10.9322i −1.09094 + 0.525368i −0.890798 0.454399i \(-0.849854\pi\)
−0.200140 + 0.979767i \(0.564140\pi\)
\(434\) 0.869252 + 4.26430i 0.0417254 + 0.204693i
\(435\) 0 0
\(436\) 12.9250 6.22436i 0.618996 0.298093i
\(437\) −5.08741 + 22.2894i −0.243364 + 1.06625i
\(438\) 0 0
\(439\) 12.8829 + 16.1546i 0.614865 + 0.771016i 0.987612 0.156917i \(-0.0501555\pi\)
−0.372747 + 0.927933i \(0.621584\pi\)
\(440\) 7.27105 0.346634
\(441\) 0 0
\(442\) −1.12578 −0.0535480
\(443\) 22.2856 + 27.9453i 1.05882 + 1.32772i 0.942387 + 0.334524i \(0.108575\pi\)
0.116436 + 0.993198i \(0.462853\pi\)
\(444\) 0 0
\(445\) 1.11302 4.87644i 0.0527620 0.231165i
\(446\) 4.26519 2.05401i 0.201963 0.0972600i
\(447\) 0 0
\(448\) 6.46945 2.93177i 0.305653 0.138513i
\(449\) −7.08769 + 3.41325i −0.334489 + 0.161081i −0.593587 0.804770i \(-0.702289\pi\)
0.259099 + 0.965851i \(0.416575\pi\)
\(450\) 0 0
\(451\) −34.8051 16.7613i −1.63891 0.789257i
\(452\) −15.5147 19.4548i −0.729750 0.915078i
\(453\) 0 0
\(454\) 1.96015 + 2.45795i 0.0919943 + 0.115357i
\(455\) −2.71660 3.57434i −0.127356 0.167568i
\(456\) 0 0
\(457\) 31.7115 + 15.2715i 1.48340 + 0.714368i 0.988023 0.154309i \(-0.0493150\pi\)
0.495379 + 0.868677i \(0.335029\pi\)
\(458\) −2.05293 8.99447i −0.0959271 0.420284i
\(459\) 0 0
\(460\) −4.19041 −0.195379
\(461\) 9.37727 + 41.0845i 0.436743 + 1.91350i 0.405768 + 0.913976i \(0.367004\pi\)
0.0309755 + 0.999520i \(0.490139\pi\)
\(462\) 0 0
\(463\) −3.93728 + 17.2504i −0.182981 + 0.801692i 0.797220 + 0.603688i \(0.206303\pi\)
−0.980201 + 0.198003i \(0.936554\pi\)
\(464\) −6.13490 + 26.8788i −0.284806 + 1.24782i
\(465\) 0 0
\(466\) 2.29486 2.87766i 0.106307 0.133305i
\(467\) −5.66633 + 24.8258i −0.262206 + 1.14880i 0.656646 + 0.754199i \(0.271975\pi\)
−0.918852 + 0.394602i \(0.870883\pi\)
\(468\) 0 0
\(469\) −2.92343 1.49277i −0.134992 0.0689298i
\(470\) −0.745765 3.26741i −0.0343996 0.150714i
\(471\) 0 0
\(472\) 15.5185 0.714297
\(473\) −6.97729 30.5695i −0.320816 1.40559i
\(474\) 0 0
\(475\) −21.0832 + 26.4375i −0.967363 + 1.21304i
\(476\) 4.50473 + 2.30021i 0.206474 + 0.105430i
\(477\) 0 0
\(478\) −2.76847 12.1295i −0.126627 0.554789i
\(479\) 18.1918 + 22.8118i 0.831203 + 1.04230i 0.998410 + 0.0563737i \(0.0179538\pi\)
−0.167207 + 0.985922i \(0.553475\pi\)
\(480\) 0 0
\(481\) −2.56394 + 3.21508i −0.116906 + 0.146595i
\(482\) 4.03021 1.94085i 0.183571 0.0884031i
\(483\) 0 0
\(484\) 18.8856 + 9.09482i 0.858436 + 0.413401i
\(485\) 7.51192 3.61755i 0.341099 0.164264i
\(486\) 0 0
\(487\) −6.21830 + 2.99458i −0.281778 + 0.135697i −0.569435 0.822036i \(-0.692838\pi\)
0.287657 + 0.957734i \(0.407124\pi\)
\(488\) −6.92484 8.68347i −0.313473 0.393082i
\(489\) 0 0
\(490\) −0.500492 2.78554i −0.0226099 0.125838i
\(491\) −7.47189 −0.337202 −0.168601 0.985684i \(-0.553925\pi\)
−0.168601 + 0.985684i \(0.553925\pi\)
\(492\) 0 0
\(493\) −10.4778 + 5.04586i −0.471898 + 0.227254i
\(494\) 1.79244 7.85319i 0.0806457 0.353332i
\(495\) 0 0
\(496\) 7.71974 + 3.71763i 0.346626 + 0.166926i
\(497\) 12.8107 15.3176i 0.574640 0.687090i
\(498\) 0 0
\(499\) 26.3626 33.0576i 1.18015 1.47986i 0.337564 0.941302i \(-0.390397\pi\)
0.842587 0.538560i \(-0.181032\pi\)
\(500\) −12.0235 5.79023i −0.537709 0.258947i
\(501\) 0 0
\(502\) −0.952180 4.17177i −0.0424979 0.186195i
\(503\) −4.63784 5.81567i −0.206791 0.259308i 0.667610 0.744511i \(-0.267317\pi\)
−0.874402 + 0.485203i \(0.838746\pi\)
\(504\) 0 0
\(505\) −5.71946 + 7.17198i −0.254513 + 0.319149i
\(506\) 6.27683 + 3.02276i 0.279039 + 0.134378i
\(507\) 0 0
\(508\) 1.99098 0.0883355
\(509\) −30.3188 −1.34386 −0.671928 0.740617i \(-0.734534\pi\)
−0.671928 + 0.740617i \(0.734534\pi\)
\(510\) 0 0
\(511\) −14.2996 + 6.48015i −0.632575 + 0.286665i
\(512\) −5.02017 + 21.9948i −0.221862 + 0.972043i
\(513\) 0 0
\(514\) −0.451421 + 0.566064i −0.0199113 + 0.0249680i
\(515\) 0.0174869 0.0219279i 0.000770567 0.000966260i
\(516\) 0 0
\(517\) 8.83680 38.7166i 0.388642 1.70275i
\(518\) −2.36117 + 1.07001i −0.103744 + 0.0470138i
\(519\) 0 0
\(520\) 3.15995 0.138573
\(521\) 20.7854 0.910625 0.455312 0.890332i \(-0.349528\pi\)
0.455312 + 0.890332i \(0.349528\pi\)
\(522\) 0 0
\(523\) 3.17478 + 1.52889i 0.138823 + 0.0668538i 0.502006 0.864864i \(-0.332596\pi\)
−0.363183 + 0.931718i \(0.618310\pi\)
\(524\) 8.64117 10.8357i 0.377491 0.473359i
\(525\) 0 0
\(526\) 0.692166 + 0.867949i 0.0301799 + 0.0378444i
\(527\) 0.804246 + 3.52363i 0.0350335 + 0.153492i
\(528\) 0 0
\(529\) 12.9799 + 6.25078i 0.564343 + 0.271773i
\(530\) −0.886631 + 1.11180i −0.0385128 + 0.0482935i
\(531\) 0 0
\(532\) −23.2181 + 27.7616i −1.00663 + 1.20362i
\(533\) −15.1261 7.28434i −0.655183 0.315520i
\(534\) 0 0
\(535\) 0.971416 4.25605i 0.0419980 0.184005i
\(536\) 2.08159 1.00244i 0.0899109 0.0432988i
\(537\) 0 0
\(538\) 1.38492 0.0597082
\(539\) 8.97788 32.3111i 0.386704 1.39174i
\(540\) 0 0
\(541\) −7.14665 8.96161i −0.307258 0.385290i 0.604097 0.796911i \(-0.293534\pi\)
−0.911355 + 0.411621i \(0.864963\pi\)
\(542\) −9.32827 + 4.49226i −0.400684 + 0.192959i
\(543\) 0 0
\(544\) −4.91642 + 2.36762i −0.210790 + 0.101511i
\(545\) −6.00604 2.89236i −0.257271 0.123895i
\(546\) 0 0
\(547\) 29.9504 14.4234i 1.28059 0.616699i 0.335047 0.942201i \(-0.391248\pi\)
0.945541 + 0.325503i \(0.105534\pi\)
\(548\) 16.8018 21.0688i 0.717737 0.900014i
\(549\) 0 0
\(550\) 6.42453 + 8.05611i 0.273943 + 0.343514i
\(551\) −18.5162 81.1248i −0.788817 3.45603i
\(552\) 0 0
\(553\) 12.9439 + 6.60947i 0.550433 + 0.281063i
\(554\) 3.47148 4.35310i 0.147489 0.184945i
\(555\) 0 0
\(556\) 0.199696 + 0.874923i 0.00846898 + 0.0371050i
\(557\) 22.6314 0.958922 0.479461 0.877563i \(-0.340832\pi\)
0.479461 + 0.877563i \(0.340832\pi\)
\(558\) 0 0
\(559\) −3.03229 13.2853i −0.128252 0.561909i
\(560\) −4.96250 2.53396i −0.209704 0.107080i
\(561\) 0 0
\(562\) 0.974282 4.26861i 0.0410976 0.180060i
\(563\) 11.1134 13.9358i 0.468375 0.587323i −0.490397 0.871499i \(-0.663148\pi\)
0.958772 + 0.284175i \(0.0917198\pi\)
\(564\) 0 0
\(565\) −2.57302 + 11.2731i −0.108248 + 0.474264i
\(566\) −3.28047 + 14.3727i −0.137888 + 0.604129i
\(567\) 0 0
\(568\) 3.12751 + 13.7025i 0.131227 + 0.574944i
\(569\) 1.61881 0.0678639 0.0339319 0.999424i \(-0.489197\pi\)
0.0339319 + 0.999424i \(0.489197\pi\)
\(570\) 0 0
\(571\) 6.07719 + 26.6259i 0.254322 + 1.11426i 0.927218 + 0.374522i \(0.122193\pi\)
−0.672896 + 0.739737i \(0.734950\pi\)
\(572\) 15.7618 + 7.59050i 0.659036 + 0.317375i
\(573\) 0 0
\(574\) −6.40397 8.42597i −0.267297 0.351693i
\(575\) −7.92459 9.93712i −0.330478 0.414407i
\(576\) 0 0
\(577\) −2.48245 3.11289i −0.103346 0.129591i 0.727469 0.686141i \(-0.240696\pi\)
−0.830815 + 0.556549i \(0.812125\pi\)
\(578\) 7.06707 + 3.40332i 0.293951 + 0.141559i
\(579\) 0 0
\(580\) 13.7411 6.61737i 0.570568 0.274771i
\(581\) 23.2738 10.5470i 0.965562 0.437565i
\(582\) 0 0
\(583\) −15.1816 + 7.31106i −0.628756 + 0.302793i
\(584\) 2.45885 10.7729i 0.101748 0.445787i
\(585\) 0 0
\(586\) 2.94511 + 3.69305i 0.121661 + 0.152558i
\(587\) 22.4755 0.927662 0.463831 0.885924i \(-0.346474\pi\)
0.463831 + 0.885924i \(0.346474\pi\)
\(588\) 0 0
\(589\) −25.8605 −1.06556
\(590\) −2.10068 2.63417i −0.0864837 0.108447i
\(591\) 0 0
\(592\) −1.13569 + 4.97580i −0.0466767 + 0.204504i
\(593\) −11.3952 + 5.48764i −0.467945 + 0.225350i −0.652970 0.757383i \(-0.726477\pi\)
0.185026 + 0.982734i \(0.440763\pi\)
\(594\) 0 0
\(595\) −0.469456 2.30302i −0.0192458 0.0944145i
\(596\) −22.0935 + 10.6397i −0.904986 + 0.435818i
\(597\) 0 0
\(598\) 2.72787 + 1.31367i 0.111551 + 0.0537201i
\(599\) 13.7993 + 17.3037i 0.563823 + 0.707012i 0.979259 0.202611i \(-0.0649426\pi\)
−0.415436 + 0.909622i \(0.636371\pi\)
\(600\) 0 0
\(601\) 5.37281 + 6.73729i 0.219161 + 0.274820i 0.879242 0.476375i \(-0.158049\pi\)
−0.660081 + 0.751195i \(0.729478\pi\)
\(602\) 2.10620 8.32807i 0.0858424 0.339427i
\(603\) 0 0
\(604\) −29.9333 14.4151i −1.21797 0.586543i
\(605\) −2.16745 9.49621i −0.0881193 0.386076i
\(606\) 0 0
\(607\) −32.9540 −1.33756 −0.668780 0.743460i \(-0.733183\pi\)
−0.668780 + 0.743460i \(0.733183\pi\)
\(608\) −8.68819 38.0655i −0.352353 1.54376i
\(609\) 0 0
\(610\) −0.536577 + 2.35090i −0.0217254 + 0.0951851i
\(611\) 3.84042 16.8260i 0.155367 0.680706i
\(612\) 0 0
\(613\) −4.36592 + 5.47469i −0.176338 + 0.221121i −0.862144 0.506664i \(-0.830879\pi\)
0.685806 + 0.727785i \(0.259450\pi\)
\(614\) −3.63601 + 15.9304i −0.146737 + 0.642898i
\(615\) 0 0
\(616\) 14.2826 + 18.7922i 0.575461 + 0.757158i
\(617\) 0.0708000 + 0.310195i 0.00285030 + 0.0124880i 0.976333 0.216272i \(-0.0693899\pi\)
−0.973483 + 0.228760i \(0.926533\pi\)
\(618\) 0 0
\(619\) −16.8765 −0.678322 −0.339161 0.940728i \(-0.610143\pi\)
−0.339161 + 0.940728i \(0.610143\pi\)
\(620\) −1.05472 4.62104i −0.0423587 0.185586i
\(621\) 0 0
\(622\) 1.97887 2.48142i 0.0793454 0.0994960i
\(623\) 14.7895 6.70220i 0.592531 0.268518i
\(624\) 0 0
\(625\) −3.44407 15.0894i −0.137763 0.603578i
\(626\) −1.78425 2.23738i −0.0713131 0.0894238i
\(627\) 0 0
\(628\) 21.3765 26.8053i 0.853015 1.06965i
\(629\) −1.93966 + 0.934091i −0.0773393 + 0.0372446i
\(630\) 0 0
\(631\) −25.1532 12.1132i −1.00133 0.482217i −0.139943 0.990160i \(-0.544692\pi\)
−0.861391 + 0.507943i \(0.830406\pi\)
\(632\) −9.21655 + 4.43846i −0.366615 + 0.176552i
\(633\) 0 0
\(634\) 2.76743 1.33272i 0.109909 0.0529293i
\(635\) −0.576838 0.723332i −0.0228911 0.0287045i
\(636\) 0 0
\(637\) 3.90173 14.0422i 0.154592 0.556372i
\(638\) −25.3563 −1.00387
\(639\) 0 0
\(640\) 8.33017 4.01160i 0.329279 0.158572i
\(641\) −4.31012 + 18.8839i −0.170240 + 0.745869i 0.815660 + 0.578531i \(0.196374\pi\)
−0.985900 + 0.167337i \(0.946483\pi\)
\(642\) 0 0
\(643\) −9.03423 4.35065i −0.356275 0.171573i 0.247181 0.968969i \(-0.420496\pi\)
−0.603456 + 0.797396i \(0.706210\pi\)
\(644\) −8.23124 10.8302i −0.324356 0.426769i
\(645\) 0 0
\(646\) 2.62930 3.29704i 0.103448 0.129720i
\(647\) −0.597503 0.287742i −0.0234902 0.0113123i 0.422102 0.906548i \(-0.361292\pi\)
−0.445592 + 0.895236i \(0.647007\pi\)
\(648\) 0 0
\(649\) −8.88371 38.9221i −0.348716 1.52783i
\(650\) 2.79206 + 3.50113i 0.109514 + 0.137326i
\(651\) 0 0
\(652\) −16.7453 + 20.9979i −0.655796 + 0.822342i
\(653\) −19.5544 9.41689i −0.765221 0.368511i 0.0102060 0.999948i \(-0.496751\pi\)
−0.775427 + 0.631437i \(0.782466\pi\)
\(654\) 0 0
\(655\) −6.44021 −0.251640
\(656\) −20.8367 −0.813536
\(657\) 0 0
\(658\) 6.97977 8.34564i 0.272100 0.325347i
\(659\) −1.71657 + 7.52080i −0.0668682 + 0.292969i −0.997294 0.0735104i \(-0.976580\pi\)
0.930426 + 0.366479i \(0.119437\pi\)
\(660\) 0 0
\(661\) 5.14393 6.45028i 0.200076 0.250887i −0.671664 0.740855i \(-0.734420\pi\)
0.871740 + 0.489969i \(0.162992\pi\)
\(662\) −2.42325 + 3.03866i −0.0941823 + 0.118101i
\(663\) 0 0
\(664\) −4.00201 + 17.5340i −0.155308 + 0.680449i
\(665\) 16.8128 + 0.391986i 0.651971 + 0.0152005i
\(666\) 0 0
\(667\) 31.2768 1.21104
\(668\) −30.3989 −1.17617
\(669\) 0 0
\(670\) −0.451935 0.217640i −0.0174598 0.00840818i
\(671\) −17.8149 + 22.3392i −0.687737 + 0.862395i
\(672\) 0 0
\(673\) 27.2700 + 34.1955i 1.05118 + 1.31814i 0.946171 + 0.323666i \(0.104916\pi\)
0.105009 + 0.994471i \(0.466513\pi\)
\(674\) 0.629883 + 2.75970i 0.0242622 + 0.106300i
\(675\) 0 0
\(676\) −13.6929 6.59414i −0.526649 0.253621i
\(677\) 8.10949 10.1690i 0.311673 0.390826i −0.601180 0.799113i \(-0.705303\pi\)
0.912853 + 0.408288i \(0.133874\pi\)
\(678\) 0 0
\(679\) 24.1053 + 12.3087i 0.925077 + 0.472365i
\(680\) 1.49048 + 0.717779i 0.0571575 + 0.0275256i
\(681\) 0 0
\(682\) −1.75353 + 7.68272i −0.0671461 + 0.294186i
\(683\) −9.21676 + 4.43856i −0.352669 + 0.169837i −0.601827 0.798626i \(-0.705560\pi\)
0.249158 + 0.968463i \(0.419846\pi\)
\(684\) 0 0
\(685\) −12.5223 −0.478452
\(686\) 6.21615 6.76517i 0.237334 0.258295i
\(687\) 0 0
\(688\) −10.5449 13.2228i −0.402019 0.504116i
\(689\) −6.59781 + 3.17734i −0.251356 + 0.121047i
\(690\) 0 0
\(691\) 13.3160 6.41263i 0.506563 0.243948i −0.163104 0.986609i \(-0.552151\pi\)
0.669668 + 0.742661i \(0.266436\pi\)
\(692\) 30.1159 + 14.5031i 1.14484 + 0.551324i
\(693\) 0 0
\(694\) −4.18474 + 2.01527i −0.158851 + 0.0764984i
\(695\) 0.260006 0.326038i 0.00986261 0.0123673i
\(696\) 0 0
\(697\) −5.48003 6.87174i −0.207571 0.260286i
\(698\) −2.44874 10.7286i −0.0926861 0.406084i
\(699\) 0 0
\(700\) −4.01864 19.7143i −0.151890 0.745130i
\(701\) −7.16495 + 8.98456i −0.270616 + 0.339342i −0.898507 0.438959i \(-0.855347\pi\)
0.627890 + 0.778302i \(0.283919\pi\)
\(702\) 0 0
\(703\) −3.42772 15.0178i −0.129279 0.566409i
\(704\) 12.8612 0.484724
\(705\) 0 0
\(706\) −3.44590 15.0975i −0.129688 0.568201i
\(707\) −29.7709 0.694101i −1.11965 0.0261044i
\(708\) 0 0
\(709\) −3.27974 + 14.3695i −0.123173 + 0.539657i 0.875258 + 0.483657i \(0.160692\pi\)
−0.998431 + 0.0560000i \(0.982165\pi\)
\(710\) 1.90256 2.38573i 0.0714017 0.0895349i
\(711\) 0 0
\(712\) −2.54311 + 11.1421i −0.0953070 + 0.417567i
\(713\) 2.16296 9.47655i 0.0810035 0.354899i
\(714\) 0 0
\(715\) −1.80894 7.92551i −0.0676507 0.296397i
\(716\) −20.0955 −0.751004
\(717\) 0 0
\(718\) −0.942432 4.12906i −0.0351712 0.154095i
\(719\) −10.8617 5.23070i −0.405071 0.195072i 0.220243 0.975445i \(-0.429315\pi\)
−0.625314 + 0.780373i \(0.715029\pi\)
\(720\) 0 0
\(721\) 0.0910229 + 0.00212218i 0.00338987 + 7.90340e-5i
\(722\) 12.9364 + 16.2218i 0.481444 + 0.603712i
\(723\) 0 0
\(724\) −4.69128 5.88267i −0.174350 0.218628i
\(725\) 41.6786 + 20.0713i 1.54790 + 0.745431i
\(726\) 0 0
\(727\) 18.3337 8.82904i 0.679959 0.327451i −0.0618279 0.998087i \(-0.519693\pi\)
0.741787 + 0.670636i \(0.233979\pi\)
\(728\) 6.20711 + 8.16695i 0.230051 + 0.302687i
\(729\) 0 0
\(730\) −2.16149 + 1.04092i −0.0800002 + 0.0385261i
\(731\) 1.58748 6.95519i 0.0587149 0.257247i
\(732\) 0 0
\(733\) −11.6372 14.5926i −0.429832 0.538992i 0.519000 0.854774i \(-0.326304\pi\)
−0.948832 + 0.315782i \(0.897733\pi\)
\(734\) −10.2160 −0.377081
\(735\) 0 0
\(736\) 14.6757 0.540954
\(737\) −3.70586 4.64700i −0.136507 0.171174i
\(738\) 0 0
\(739\) 5.04720 22.1132i 0.185664 0.813449i −0.793204 0.608956i \(-0.791588\pi\)
0.978868 0.204493i \(-0.0655544\pi\)
\(740\) 2.54376 1.22501i 0.0935103 0.0450322i
\(741\) 0 0
\(742\) −4.61508 0.107600i −0.169425 0.00395011i
\(743\) −7.28844 + 3.50993i −0.267387 + 0.128767i −0.562774 0.826611i \(-0.690266\pi\)
0.295387 + 0.955378i \(0.404551\pi\)
\(744\) 0 0
\(745\) 10.2665 + 4.94408i 0.376135 + 0.181137i
\(746\) −1.61802 2.02893i −0.0592400 0.0742845i
\(747\) 0 0
\(748\) 5.71036 + 7.16057i 0.208792 + 0.261816i
\(749\) 12.9080 5.84954i 0.471648 0.213738i
\(750\) 0 0
\(751\) 2.51328 + 1.21033i 0.0917108 + 0.0441656i 0.479177 0.877718i \(-0.340935\pi\)
−0.387466 + 0.921884i \(0.626650\pi\)
\(752\) −4.76640 20.8830i −0.173813 0.761523i
\(753\) 0 0
\(754\) −11.0197 −0.401314
\(755\) 3.43536 + 15.0513i 0.125026 + 0.547773i
\(756\) 0 0
\(757\) 1.59439 6.98550i 0.0579492 0.253892i −0.937653 0.347573i \(-0.887006\pi\)
0.995602 + 0.0936803i \(0.0298632\pi\)
\(758\) 2.40737 10.5474i 0.0874395 0.383097i
\(759\) 0 0
\(760\) −7.38017 + 9.25444i −0.267707 + 0.335694i
\(761\) −1.18442 + 5.18929i −0.0429352 + 0.188112i −0.991848 0.127427i \(-0.959328\pi\)
0.948913 + 0.315539i \(0.102185\pi\)
\(762\) 0 0
\(763\) −4.32235 21.2042i −0.156480 0.767644i
\(764\) −0.867340 3.80007i −0.0313793 0.137482i
\(765\) 0 0
\(766\) −7.00462 −0.253087
\(767\) −3.86080 16.9153i −0.139406 0.610776i
\(768\) 0 0
\(769\) 7.30139 9.15565i 0.263295 0.330161i −0.632557 0.774514i \(-0.717995\pi\)
0.895852 + 0.444352i \(0.146566\pi\)
\(770\) 1.25648 4.96820i 0.0452804 0.179042i
\(771\) 0 0
\(772\) 5.04452 + 22.1015i 0.181556 + 0.795450i
\(773\) −23.1847 29.0727i −0.833895 1.04567i −0.998242 0.0592688i \(-0.981123\pi\)
0.164347 0.986403i \(-0.447448\pi\)
\(774\) 0 0
\(775\) 8.96372 11.2401i 0.321986 0.403758i
\(776\) −17.1638 + 8.26567i −0.616146 + 0.296720i
\(777\) 0 0
\(778\) −10.7508 5.17731i −0.385435 0.185616i
\(779\) 56.6608 27.2864i 2.03008 0.977637i
\(780\) 0 0
\(781\) 32.5770 15.6883i 1.16570 0.561370i
\(782\) 0.988281 + 1.23927i 0.0353409 + 0.0443160i
\(783\) 0 0
\(784\) −3.19879 17.8031i −0.114242 0.635827i
\(785\) −15.9318 −0.568630
\(786\) 0 0
\(787\) −38.3856 + 18.4856i −1.36830 + 0.658939i −0.966471 0.256776i \(-0.917340\pi\)
−0.401829 + 0.915715i \(0.631625\pi\)
\(788\) 10.4583 45.8209i 0.372562 1.63230i
\(789\) 0 0
\(790\) 2.00101 + 0.963636i 0.0711928 + 0.0342846i
\(791\) −34.1898 + 15.4938i −1.21565 + 0.550897i
\(792\) 0 0
\(793\) −7.74225 + 9.70847i −0.274935 + 0.344758i
\(794\) 6.13606 + 2.95497i 0.217761 + 0.104868i
\(795\) 0 0
\(796\) −7.42961 32.5513i −0.263336 1.15375i
\(797\) 24.5798 + 30.8221i 0.870662 + 1.09178i 0.995034 + 0.0995399i \(0.0317371\pi\)
−0.124372 + 0.992236i \(0.539691\pi\)
\(798\) 0 0
\(799\) 5.63344 7.06412i 0.199297 0.249910i
\(800\) 19.5565 + 9.41789i 0.691425 + 0.332973i
\(801\) 0 0
\(802\) 1.73220 0.0611661
\(803\) −28.4273 −1.00318
\(804\) 0 0
\(805\) −1.54985 + 6.12822i −0.0546251 + 0.215991i
\(806\) −0.762073 + 3.33886i −0.0268429 + 0.117606i
\(807\) 0 0
\(808\) 13.0683 16.3871i 0.459741 0.576497i
\(809\) −20.0972 + 25.2010i −0.706579 + 0.886022i −0.997496 0.0707267i \(-0.977468\pi\)
0.290917 + 0.956748i \(0.406040\pi\)
\(810\) 0 0
\(811\) −4.58766 + 20.0999i −0.161095 + 0.705802i 0.828268 + 0.560332i \(0.189326\pi\)
−0.989363 + 0.145470i \(0.953531\pi\)
\(812\) 44.0944 + 22.5156i 1.54741 + 0.790143i
\(813\) 0 0
\(814\) −4.69397 −0.164524
\(815\) 12.4802 0.437161
\(816\) 0 0
\(817\) 45.9902 + 22.1477i 1.60899 + 0.774851i
\(818\) 6.30837 7.91045i 0.220567 0.276582i
\(819\) 0 0
\(820\) 7.18676 + 9.01191i 0.250972 + 0.314710i
\(821\) −5.83792 25.5776i −0.203745 0.892665i −0.968632 0.248500i \(-0.920062\pi\)
0.764887 0.644165i \(-0.222795\pi\)
\(822\) 0 0
\(823\) 38.9295 + 18.7475i 1.35700 + 0.653495i 0.963965 0.266030i \(-0.0857120\pi\)
0.393032 + 0.919525i \(0.371426\pi\)
\(824\) −0.0399556 + 0.0501027i −0.00139192 + 0.00174541i
\(825\) 0 0
\(826\) 2.68168 10.6036i 0.0933077 0.368945i
\(827\) 32.2737 + 15.5422i 1.12227 + 0.540456i 0.900592 0.434665i \(-0.143133\pi\)
0.221675 + 0.975121i \(0.428847\pi\)
\(828\) 0 0
\(829\) −0.313146 + 1.37198i −0.0108760 + 0.0476509i −0.980075 0.198629i \(-0.936351\pi\)
0.969199 + 0.246280i \(0.0792083\pi\)
\(830\) 3.51802 1.69419i 0.122112 0.0588061i
\(831\) 0 0
\(832\) 5.58938 0.193777
\(833\) 5.03003 5.73714i 0.174280 0.198780i
\(834\) 0 0
\(835\) 8.80733 + 11.0440i 0.304790 + 0.382195i
\(836\) −59.0423 + 28.4333i −2.04202 + 0.983385i
\(837\) 0 0
\(838\) −14.3158 + 6.89414i −0.494532 + 0.238154i
\(839\) −32.2917 15.5509i −1.11483 0.536876i −0.216542 0.976273i \(-0.569478\pi\)
−0.898293 + 0.439397i \(0.855192\pi\)
\(840\) 0 0
\(841\) −76.4340 + 36.8087i −2.63566 + 1.26927i
\(842\) −1.27280 + 1.59604i −0.0438637 + 0.0550033i
\(843\) 0 0
\(844\) 1.08786 + 1.36413i 0.0374457 + 0.0469554i
\(845\) 1.57150 + 6.88517i 0.0540611 + 0.236857i
\(846\) 0 0
\(847\) 20.2856 24.2553i 0.697022 0.833421i
\(848\) −5.66671 + 7.10583i −0.194596 + 0.244015i
\(849\) 0 0
\(850\) 0.521679 + 2.28563i 0.0178934 + 0.0783963i
\(851\) 5.78996 0.198477
\(852\) 0 0
\(853\) 12.4139 + 54.3887i 0.425043 + 1.86224i 0.501493 + 0.865162i \(0.332784\pi\)
−0.0764498 + 0.997073i \(0.524359\pi\)
\(854\) −7.12994 + 3.23109i −0.243982 + 0.110566i
\(855\) 0 0
\(856\) −2.21957 + 9.72458i −0.0758634 + 0.332379i
\(857\) 30.8107 38.6354i 1.05247 1.31976i 0.106928 0.994267i \(-0.465899\pi\)
0.945545 0.325492i \(-0.105530\pi\)
\(858\) 0 0
\(859\) −5.45591 + 23.9039i −0.186153 + 0.815590i 0.792467 + 0.609915i \(0.208796\pi\)
−0.978620 + 0.205675i \(0.934061\pi\)
\(860\) −2.08189 + 9.12134i −0.0709918 + 0.311035i
\(861\) 0 0
\(862\) 4.09944 + 17.9608i 0.139628 + 0.611749i
\(863\) 14.7600 0.502438 0.251219 0.967930i \(-0.419169\pi\)
0.251219 + 0.967930i \(0.419169\pi\)
\(864\) 0 0
\(865\) −3.45633 15.1432i −0.117519 0.514883i
\(866\) −11.2613 5.42316i −0.382675 0.184286i
\(867\) 0 0
\(868\) 9.87138 11.8031i 0.335056 0.400623i
\(869\) 16.4082 + 20.5753i 0.556612 + 0.697969i
\(870\) 0 0
\(871\) −1.61054 2.01955i −0.0545711 0.0684300i
\(872\) 13.7231 + 6.60870i 0.464723 + 0.223799i
\(873\) 0 0
\(874\) −10.2183 + 4.92089i −0.345640 + 0.166452i
\(875\) −12.9149 + 15.4422i −0.436602 + 0.522040i
\(876\) 0 0
\(877\) 6.14263 2.95814i 0.207422 0.0998891i −0.327289 0.944924i \(-0.606135\pi\)
0.534711 + 0.845035i \(0.320421\pi\)
\(878\) −2.28086 + 9.99309i −0.0769752 + 0.337251i
\(879\) 0 0
\(880\) −6.29065 7.88823i −0.212058 0.265912i
\(881\) −6.79163 −0.228816 −0.114408 0.993434i \(-0.536497\pi\)
−0.114408 + 0.993434i \(0.536497\pi\)
\(882\) 0 0
\(883\) 17.5817 0.591670 0.295835 0.955239i \(-0.404402\pi\)
0.295835 + 0.955239i \(0.404402\pi\)
\(884\) 2.48169 + 3.11194i 0.0834681 + 0.104666i
\(885\) 0 0
\(886\) −3.94559 + 17.2867i −0.132555 + 0.580760i
\(887\) 43.7551 21.0713i 1.46915 0.707506i 0.483351 0.875427i \(-0.339419\pi\)
0.985801 + 0.167920i \(0.0537052\pi\)
\(888\) 0 0
\(889\) 0.736379 2.91169i 0.0246973 0.0976550i
\(890\) 2.23555 1.07659i 0.0749359 0.0360872i
\(891\) 0 0
\(892\) −15.0800 7.26215i −0.504916 0.243155i
\(893\) 40.3082 + 50.5449i 1.34886 + 1.69142i
\(894\) 0 0
\(895\) 5.82218 + 7.30078i 0.194614 + 0.244038i
\(896\) 26.7310 + 13.6495i 0.893021 + 0.455997i
\(897\) 0 0
\(898\) −3.51600 1.69322i −0.117331 0.0565034i
\(899\) 7.87234 + 34.4910i 0.262557 + 1.15034i
\(900\) 0 0
\(901\) −3.83378 −0.127722
\(902\) −4.26431 18.6832i −0.141986 0.622082i
\(903\) 0 0
\(904\) 5.87904 25.7577i 0.195534 0.856690i
\(905\) −0.778018 + 3.40872i −0.0258622 + 0.113310i
\(906\) 0 0
\(907\) 14.3312 17.9707i 0.475859 0.596709i −0.484736 0.874661i \(-0.661084\pi\)
0.960595 + 0.277952i \(0.0896557\pi\)
\(908\) 2.47340 10.8367i 0.0820825 0.359627i
\(909\) 0 0
\(910\) 0.546057 2.15915i 0.0181016 0.0715751i
\(911\) 3.13432 + 13.7324i 0.103845 + 0.454974i 0.999938 + 0.0111084i \(0.00353600\pi\)
−0.896094 + 0.443865i \(0.853607\pi\)
\(912\) 0 0
\(913\) 46.2681 1.53125
\(914\) 3.88528 + 17.0225i 0.128514 + 0.563056i
\(915\) 0 0
\(916\) −20.3374 + 25.5023i −0.671967 + 0.842620i
\(917\) −12.6505 16.6449i −0.417758 0.549661i
\(918\) 0 0
\(919\) 6.53244 + 28.6205i 0.215485 + 0.944102i 0.960768 + 0.277354i \(0.0894574\pi\)
−0.745283 + 0.666749i \(0.767685\pi\)
\(920\) −2.77400 3.47849i −0.0914561 0.114682i
\(921\) 0 0
\(922\) −13.0341 + 16.3442i −0.429254 + 0.538267i
\(923\) 14.1578 6.81802i 0.466008 0.224418i
\(924\) 0 0
\(925\) 7.71554 + 3.71561i 0.253686 + 0.122169i
\(926\) −7.90824 + 3.80841i −0.259881 + 0.125152i
\(927\) 0 0
\(928\) −48.1243 + 23.1754i −1.57976 + 0.760771i
\(929\) 34.4742 + 43.2293i 1.13106 + 1.41831i 0.894715 + 0.446637i \(0.147379\pi\)
0.236346 + 0.971669i \(0.424050\pi\)
\(930\) 0 0
\(931\) 32.0123 + 44.2228i 1.04916 + 1.44935i
\(932\) −13.0134 −0.426267
\(933\) 0 0
\(934\) −11.3811 + 5.48086i −0.372402 + 0.179339i
\(935\) 0.947027 4.14920i 0.0309711 0.135693i
\(936\) 0 0
\(937\) −2.37609 1.14426i −0.0776233 0.0373814i 0.394669 0.918823i \(-0.370859\pi\)
−0.472293 + 0.881442i \(0.656573\pi\)
\(938\) −0.325242 1.59555i −0.0106195 0.0520964i
\(939\) 0 0
\(940\) −7.38795 + 9.26419i −0.240968 + 0.302165i
\(941\) −44.0223 21.2000i −1.43509 0.691101i −0.455150 0.890415i \(-0.650414\pi\)
−0.979936 + 0.199314i \(0.936129\pi\)
\(942\) 0 0
\(943\) 5.25998 + 23.0455i 0.171289 + 0.750465i
\(944\) −13.4260 16.8357i −0.436981 0.547956i
\(945\) 0 0
\(946\) 9.69818 12.1611i 0.315315 0.395393i
\(947\) 14.4965 + 6.98113i 0.471072 + 0.226856i 0.654331 0.756208i \(-0.272950\pi\)
−0.183259 + 0.983065i \(0.558665\pi\)
\(948\) 0 0
\(949\) −12.3543 −0.401038
\(950\) −16.7746 −0.544239
\(951\) 0 0
\(952\) 1.07265 + 5.26212i 0.0347648 + 0.170546i
\(953\) 5.44008 23.8346i 0.176222 0.772077i −0.807131 0.590372i \(-0.798981\pi\)
0.983353 0.181706i \(-0.0581618\pi\)
\(954\) 0 0
\(955\) −1.12929 + 1.41608i −0.0365429 + 0.0458234i
\(956\) −27.4259 + 34.3910i −0.887019 + 1.11229i
\(957\) 0 0
\(958\) −3.22078 + 14.1112i −0.104059 + 0.455911i
\(959\) −24.5976 32.3641i −0.794297 1.04509i
\(960\) 0 0
\(961\) −20.0052 −0.645328
\(962\) −2.03997 −0.0657712
\(963\) 0 0
\(964\) −14.2492 6.86206i −0.458936 0.221012i
\(965\) 6.56804 8.23606i 0.211433 0.265128i
\(966\) 0 0
\(967\) −20.1339 25.2471i −0.647463 0.811893i 0.344451 0.938804i \(-0.388065\pi\)
−0.991914 + 0.126911i \(0.959494\pi\)
\(968\) 4.95236 + 21.6977i 0.159175 + 0.697391i
\(969\) 0 0
\(970\) 3.72645 + 1.79457i 0.119649 + 0.0576200i
\(971\) 31.0779 38.9705i 0.997338 1.25062i 0.0293649 0.999569i \(-0.490652\pi\)
0.967973 0.251054i \(-0.0807770\pi\)
\(972\) 0 0
\(973\) 1.35338 + 0.0315538i 0.0433875 + 0.00101157i
\(974\) −3.08473 1.48553i −0.0988410 0.0475993i
\(975\) 0 0
\(976\) −3.42942 + 15.0253i −0.109773 + 0.480947i
\(977\) −38.3046 + 18.4465i −1.22547 + 0.590156i −0.930830 0.365451i \(-0.880915\pi\)
−0.294642 + 0.955608i \(0.595200\pi\)
\(978\) 0 0
\(979\) 29.4014 0.939673
\(980\) −6.59661 + 7.52394i −0.210721 + 0.240344i
\(981\) 0 0
\(982\) −2.31103 2.89793i −0.0737478 0.0924768i
\(983\) −40.6323 + 19.5675i −1.29597 + 0.624106i −0.949444 0.313935i \(-0.898352\pi\)
−0.346524 + 0.938041i \(0.612638\pi\)
\(984\) 0 0
\(985\) −19.6770 + 9.47593i −0.626961 + 0.301928i
\(986\) −5.19776 2.50311i −0.165531 0.0797153i
\(987\) 0 0
\(988\) −25.6594 + 12.3569i −0.816334 + 0.393126i
\(989\) −11.9626 + 15.0006i −0.380389 + 0.476992i
\(990\) 0 0
\(991\) −13.6218 17.0813i −0.432712 0.542604i 0.516894 0.856049i \(-0.327088\pi\)
−0.949606 + 0.313445i \(0.898517\pi\)
\(992\) 3.69387 + 16.1839i 0.117280 + 0.513839i
\(993\) 0 0
\(994\) 9.90317 + 0.230890i 0.314110 + 0.00732339i
\(995\) −9.67346 + 12.1301i −0.306669 + 0.384551i
\(996\) 0 0
\(997\) −3.22013 14.1083i −0.101983 0.446815i −0.999977 0.00680784i \(-0.997833\pi\)
0.897994 0.440007i \(-0.145024\pi\)
\(998\) 20.9751 0.663954
\(999\) 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 441.2.u.c.253.3 24
3.2 odd 2 147.2.i.a.106.2 yes 24
49.43 even 7 inner 441.2.u.c.190.3 24
147.71 odd 14 7203.2.a.a.1.6 12
147.92 odd 14 147.2.i.a.43.2 24
147.125 even 14 7203.2.a.b.1.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
147.2.i.a.43.2 24 147.92 odd 14
147.2.i.a.106.2 yes 24 3.2 odd 2
441.2.u.c.190.3 24 49.43 even 7 inner
441.2.u.c.253.3 24 1.1 even 1 trivial
7203.2.a.a.1.6 12 147.71 odd 14
7203.2.a.b.1.6 12 147.125 even 14