Properties

Label 729.2.g.d.28.6
Level $729$
Weight $2$
Character 729.28
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
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] = [729,2,Mod(28,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([44]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.g (of order \(27\), degree \(18\), 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: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: no (minimal twist has level 81)
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 28.6
Character \(\chi\) \(=\) 729.28
Dual form 729.2.g.d.703.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.890910 - 0.585961i) q^{2} +(-0.341789 + 0.792356i) q^{4} +(0.585850 - 0.620965i) q^{5} +(0.284505 + 0.0332539i) q^{7} +(0.530120 + 3.00646i) q^{8} +O(q^{10})\) \(q+(0.890910 - 0.585961i) q^{2} +(-0.341789 + 0.792356i) q^{4} +(0.585850 - 0.620965i) q^{5} +(0.284505 + 0.0332539i) q^{7} +(0.530120 + 3.00646i) q^{8} +(0.158079 - 0.896509i) q^{10} +(-0.519011 + 1.73362i) q^{11} +(-0.325075 + 5.58132i) q^{13} +(0.272954 - 0.137083i) q^{14} +(1.04960 + 1.11251i) q^{16} +(4.42908 - 1.61205i) q^{17} +(-1.75427 - 0.638503i) q^{19} +(0.291788 + 0.676441i) q^{20} +(0.553440 + 1.84862i) q^{22} +(1.34612 - 0.157339i) q^{23} +(0.248347 + 4.26396i) q^{25} +(2.98082 + 5.16294i) q^{26} +(-0.123590 + 0.214064i) q^{28} +(5.35083 + 2.68729i) q^{29} +(-2.54206 - 3.41458i) q^{31} +(-4.35412 - 1.03194i) q^{32} +(3.00131 - 4.03146i) q^{34} +(0.187327 - 0.157186i) q^{35} +(-5.46107 - 4.58238i) q^{37} +(-1.93704 + 0.459086i) q^{38} +(2.17748 + 1.43215i) q^{40} +(9.58849 + 6.30645i) q^{41} +(12.3767 - 2.93332i) q^{43} +(-1.19625 - 1.00377i) q^{44} +(1.10708 - 0.928949i) q^{46} +(-1.22397 + 1.64408i) q^{47} +(-6.73148 - 1.59539i) q^{49} +(2.71977 + 3.65328i) q^{50} +(-4.31129 - 2.16521i) q^{52} +(-1.54131 + 2.66962i) q^{53} +(0.772454 + 1.33793i) q^{55} +(0.0508455 + 0.872983i) q^{56} +(6.34175 - 0.741244i) q^{58} +(0.361763 + 1.20837i) q^{59} +(1.09744 + 2.54416i) q^{61} +(-4.26556 - 1.55254i) q^{62} +(-7.35831 + 2.67821i) q^{64} +(3.27536 + 3.47168i) q^{65} +(-5.61273 + 2.81882i) q^{67} +(-0.236491 + 4.06039i) q^{68} +(0.0747867 - 0.249805i) q^{70} +(2.24048 - 12.7064i) q^{71} +(-1.11508 - 6.32396i) q^{73} +(-7.55042 - 0.882517i) q^{74} +(1.10551 - 1.17178i) q^{76} +(-0.205311 + 0.475965i) q^{77} +(-5.95312 + 3.91543i) q^{79} +1.30574 q^{80} +12.2378 q^{82} +(11.3260 - 7.44925i) q^{83} +(1.59375 - 3.69472i) q^{85} +(9.30768 - 9.86557i) q^{86} +(-5.48720 - 0.641362i) q^{88} +(-0.0750415 - 0.425581i) q^{89} +(-0.278086 + 1.57711i) q^{91} +(-0.335421 + 1.12038i) q^{92} +(-0.127083 + 2.18193i) q^{94} +(-1.42423 + 0.715275i) q^{95} +(-6.92494 - 7.34001i) q^{97} +(-6.93197 + 2.52303i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{22}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.890910 0.585961i 0.629968 0.414337i −0.193977 0.981006i \(-0.562139\pi\)
0.823945 + 0.566669i \(0.191768\pi\)
\(3\) 0 0
\(4\) −0.341789 + 0.792356i −0.170894 + 0.396178i
\(5\) 0.585850 0.620965i 0.262000 0.277704i −0.582998 0.812474i \(-0.698120\pi\)
0.844998 + 0.534770i \(0.179602\pi\)
\(6\) 0 0
\(7\) 0.284505 + 0.0332539i 0.107533 + 0.0125688i 0.169689 0.985498i \(-0.445724\pi\)
−0.0621562 + 0.998066i \(0.519798\pi\)
\(8\) 0.530120 + 3.00646i 0.187426 + 1.06295i
\(9\) 0 0
\(10\) 0.158079 0.896509i 0.0499889 0.283501i
\(11\) −0.519011 + 1.73362i −0.156488 + 0.522706i −0.999894 0.0145710i \(-0.995362\pi\)
0.843406 + 0.537277i \(0.180547\pi\)
\(12\) 0 0
\(13\) −0.325075 + 5.58132i −0.0901596 + 1.54798i 0.585443 + 0.810714i \(0.300921\pi\)
−0.675602 + 0.737266i \(0.736116\pi\)
\(14\) 0.272954 0.137083i 0.0729501 0.0366369i
\(15\) 0 0
\(16\) 1.04960 + 1.11251i 0.262400 + 0.278128i
\(17\) 4.42908 1.61205i 1.07421 0.390980i 0.256460 0.966555i \(-0.417444\pi\)
0.817749 + 0.575574i \(0.195222\pi\)
\(18\) 0 0
\(19\) −1.75427 0.638503i −0.402458 0.146483i 0.132857 0.991135i \(-0.457585\pi\)
−0.535315 + 0.844652i \(0.679807\pi\)
\(20\) 0.291788 + 0.676441i 0.0652458 + 0.151257i
\(21\) 0 0
\(22\) 0.553440 + 1.84862i 0.117994 + 0.394127i
\(23\) 1.34612 0.157339i 0.280686 0.0328074i 0.0254146 0.999677i \(-0.491909\pi\)
0.255271 + 0.966870i \(0.417835\pi\)
\(24\) 0 0
\(25\) 0.248347 + 4.26396i 0.0496694 + 0.852791i
\(26\) 2.98082 + 5.16294i 0.584587 + 1.01254i
\(27\) 0 0
\(28\) −0.123590 + 0.214064i −0.0233563 + 0.0404542i
\(29\) 5.35083 + 2.68729i 0.993624 + 0.499017i 0.869862 0.493295i \(-0.164208\pi\)
0.123762 + 0.992312i \(0.460504\pi\)
\(30\) 0 0
\(31\) −2.54206 3.41458i −0.456568 0.613277i 0.512914 0.858440i \(-0.328566\pi\)
−0.969482 + 0.245163i \(0.921159\pi\)
\(32\) −4.35412 1.03194i −0.769706 0.182424i
\(33\) 0 0
\(34\) 3.00131 4.03146i 0.514721 0.691390i
\(35\) 0.187327 0.157186i 0.0316641 0.0265693i
\(36\) 0 0
\(37\) −5.46107 4.58238i −0.897794 0.753339i 0.0719637 0.997407i \(-0.477073\pi\)
−0.969758 + 0.244068i \(0.921518\pi\)
\(38\) −1.93704 + 0.459086i −0.314229 + 0.0744736i
\(39\) 0 0
\(40\) 2.17748 + 1.43215i 0.344290 + 0.226443i
\(41\) 9.58849 + 6.30645i 1.49747 + 0.984902i 0.992563 + 0.121728i \(0.0388437\pi\)
0.504907 + 0.863174i \(0.331527\pi\)
\(42\) 0 0
\(43\) 12.3767 2.93332i 1.88742 0.447328i 0.887514 0.460780i \(-0.152430\pi\)
0.999910 + 0.0134525i \(0.00428219\pi\)
\(44\) −1.19625 1.00377i −0.180342 0.151325i
\(45\) 0 0
\(46\) 1.10708 0.928949i 0.163230 0.136966i
\(47\) −1.22397 + 1.64408i −0.178535 + 0.239814i −0.882378 0.470542i \(-0.844059\pi\)
0.703843 + 0.710356i \(0.251466\pi\)
\(48\) 0 0
\(49\) −6.73148 1.59539i −0.961640 0.227913i
\(50\) 2.71977 + 3.65328i 0.384633 + 0.516652i
\(51\) 0 0
\(52\) −4.31129 2.16521i −0.597868 0.300261i
\(53\) −1.54131 + 2.66962i −0.211715 + 0.366701i −0.952251 0.305315i \(-0.901238\pi\)
0.740537 + 0.672016i \(0.234571\pi\)
\(54\) 0 0
\(55\) 0.772454 + 1.33793i 0.104158 + 0.180406i
\(56\) 0.0508455 + 0.872983i 0.00679452 + 0.116657i
\(57\) 0 0
\(58\) 6.34175 0.741244i 0.832713 0.0973301i
\(59\) 0.361763 + 1.20837i 0.0470975 + 0.157317i 0.978304 0.207177i \(-0.0664275\pi\)
−0.931206 + 0.364493i \(0.881242\pi\)
\(60\) 0 0
\(61\) 1.09744 + 2.54416i 0.140513 + 0.325747i 0.973912 0.226926i \(-0.0728674\pi\)
−0.833399 + 0.552672i \(0.813608\pi\)
\(62\) −4.26556 1.55254i −0.541726 0.197172i
\(63\) 0 0
\(64\) −7.35831 + 2.67821i −0.919789 + 0.334776i
\(65\) 3.27536 + 3.47168i 0.406258 + 0.430609i
\(66\) 0 0
\(67\) −5.61273 + 2.81882i −0.685705 + 0.344374i −0.757307 0.653060i \(-0.773485\pi\)
0.0716021 + 0.997433i \(0.477189\pi\)
\(68\) −0.236491 + 4.06039i −0.0286787 + 0.492395i
\(69\) 0 0
\(70\) 0.0747867 0.249805i 0.00893872 0.0298574i
\(71\) 2.24048 12.7064i 0.265896 1.50797i −0.500576 0.865693i \(-0.666878\pi\)
0.766472 0.642278i \(-0.222011\pi\)
\(72\) 0 0
\(73\) −1.11508 6.32396i −0.130511 0.740164i −0.977881 0.209161i \(-0.932927\pi\)
0.847370 0.531002i \(-0.178184\pi\)
\(74\) −7.55042 0.882517i −0.877718 0.102591i
\(75\) 0 0
\(76\) 1.10551 1.17178i 0.126811 0.134412i
\(77\) −0.205311 + 0.475965i −0.0233974 + 0.0542412i
\(78\) 0 0
\(79\) −5.95312 + 3.91543i −0.669778 + 0.440520i −0.838323 0.545174i \(-0.816464\pi\)
0.168545 + 0.985694i \(0.446093\pi\)
\(80\) 1.30574 0.145986
\(81\) 0 0
\(82\) 12.2378 1.35144
\(83\) 11.3260 7.44925i 1.24319 0.817661i 0.254421 0.967094i \(-0.418115\pi\)
0.988772 + 0.149433i \(0.0477447\pi\)
\(84\) 0 0
\(85\) 1.59375 3.69472i 0.172866 0.400749i
\(86\) 9.30768 9.86557i 1.00367 1.06383i
\(87\) 0 0
\(88\) −5.48720 0.641362i −0.584937 0.0683694i
\(89\) −0.0750415 0.425581i −0.00795438 0.0451115i 0.980572 0.196158i \(-0.0628467\pi\)
−0.988527 + 0.151047i \(0.951736\pi\)
\(90\) 0 0
\(91\) −0.278086 + 1.57711i −0.0291514 + 0.165326i
\(92\) −0.335421 + 1.12038i −0.0349700 + 0.116808i
\(93\) 0 0
\(94\) −0.127083 + 2.18193i −0.0131076 + 0.225049i
\(95\) −1.42423 + 0.715275i −0.146123 + 0.0733857i
\(96\) 0 0
\(97\) −6.92494 7.34001i −0.703121 0.745265i 0.273114 0.961982i \(-0.411947\pi\)
−0.976234 + 0.216717i \(0.930465\pi\)
\(98\) −6.93197 + 2.52303i −0.700235 + 0.254865i
\(99\) 0 0
\(100\) −3.46345 1.26059i −0.346345 0.126059i
\(101\) −3.67502 8.51965i −0.365678 0.847737i −0.997367 0.0725151i \(-0.976897\pi\)
0.631689 0.775222i \(-0.282362\pi\)
\(102\) 0 0
\(103\) −4.20365 14.0412i −0.414198 1.38352i −0.869831 0.493349i \(-0.835772\pi\)
0.455634 0.890167i \(-0.349413\pi\)
\(104\) −16.9524 + 1.98145i −1.66232 + 0.194297i
\(105\) 0 0
\(106\) 0.191128 + 3.28154i 0.0185640 + 0.318731i
\(107\) 0.0376376 + 0.0651902i 0.00363856 + 0.00630218i 0.867839 0.496846i \(-0.165508\pi\)
−0.864200 + 0.503148i \(0.832175\pi\)
\(108\) 0 0
\(109\) −2.64599 + 4.58298i −0.253440 + 0.438970i −0.964470 0.264191i \(-0.914895\pi\)
0.711031 + 0.703161i \(0.248229\pi\)
\(110\) 1.47216 + 0.739347i 0.140365 + 0.0704939i
\(111\) 0 0
\(112\) 0.261622 + 0.351419i 0.0247210 + 0.0332060i
\(113\) −18.0181 4.27037i −1.69500 0.401722i −0.734193 0.678941i \(-0.762439\pi\)
−0.960807 + 0.277219i \(0.910587\pi\)
\(114\) 0 0
\(115\) 0.690923 0.928071i 0.0644289 0.0865430i
\(116\) −3.95814 + 3.32128i −0.367504 + 0.308373i
\(117\) 0 0
\(118\) 1.03036 + 0.864571i 0.0948520 + 0.0795903i
\(119\) 1.31370 0.311354i 0.120427 0.0285417i
\(120\) 0 0
\(121\) 6.45430 + 4.24506i 0.586755 + 0.385915i
\(122\) 2.46850 + 1.62356i 0.223488 + 0.146990i
\(123\) 0 0
\(124\) 3.57441 0.847151i 0.320992 0.0760764i
\(125\) 6.06315 + 5.08759i 0.542305 + 0.455048i
\(126\) 0 0
\(127\) 8.52895 7.15664i 0.756822 0.635049i −0.180476 0.983579i \(-0.557764\pi\)
0.937297 + 0.348531i \(0.113319\pi\)
\(128\) 0.357982 0.480853i 0.0316414 0.0425018i
\(129\) 0 0
\(130\) 4.95232 + 1.17372i 0.434347 + 0.102942i
\(131\) 0.164790 + 0.221351i 0.0143977 + 0.0193395i 0.809264 0.587445i \(-0.199866\pi\)
−0.794866 + 0.606785i \(0.792459\pi\)
\(132\) 0 0
\(133\) −0.477868 0.239994i −0.0414364 0.0208101i
\(134\) −3.34872 + 5.80016i −0.289285 + 0.501057i
\(135\) 0 0
\(136\) 7.19452 + 12.4613i 0.616925 + 1.06855i
\(137\) −0.612702 10.5197i −0.0523466 0.898757i −0.917621 0.397458i \(-0.869893\pi\)
0.865274 0.501299i \(-0.167144\pi\)
\(138\) 0 0
\(139\) −0.538250 + 0.0629124i −0.0456537 + 0.00533616i −0.138889 0.990308i \(-0.544353\pi\)
0.0932354 + 0.995644i \(0.470279\pi\)
\(140\) 0.0605210 + 0.202154i 0.00511496 + 0.0170851i
\(141\) 0 0
\(142\) −5.44938 12.6331i −0.457302 1.06014i
\(143\) −9.50717 3.46033i −0.795029 0.289367i
\(144\) 0 0
\(145\) 4.80349 1.74833i 0.398908 0.145191i
\(146\) −4.69903 4.98068i −0.388895 0.412204i
\(147\) 0 0
\(148\) 5.49741 2.76090i 0.451884 0.226945i
\(149\) 1.14216 19.6101i 0.0935693 1.60652i −0.545997 0.837787i \(-0.683849\pi\)
0.639566 0.768736i \(-0.279114\pi\)
\(150\) 0 0
\(151\) −4.25389 + 14.2090i −0.346177 + 1.15631i 0.590770 + 0.806840i \(0.298824\pi\)
−0.936947 + 0.349471i \(0.886361\pi\)
\(152\) 0.989660 5.61264i 0.0802720 0.455245i
\(153\) 0 0
\(154\) 0.0959829 + 0.544346i 0.00773452 + 0.0438647i
\(155\) −3.60960 0.421902i −0.289930 0.0338880i
\(156\) 0 0
\(157\) −4.00801 + 4.24824i −0.319874 + 0.339047i −0.867280 0.497820i \(-0.834134\pi\)
0.547406 + 0.836867i \(0.315615\pi\)
\(158\) −3.00941 + 6.97659i −0.239415 + 0.555027i
\(159\) 0 0
\(160\) −3.19166 + 2.09919i −0.252323 + 0.165955i
\(161\) 0.388211 0.0305953
\(162\) 0 0
\(163\) −6.88988 −0.539657 −0.269828 0.962908i \(-0.586967\pi\)
−0.269828 + 0.962908i \(0.586967\pi\)
\(164\) −8.27419 + 5.44202i −0.646106 + 0.424951i
\(165\) 0 0
\(166\) 5.72551 13.2732i 0.444385 1.03020i
\(167\) 12.1766 12.9064i 0.942252 0.998728i −0.0577483 0.998331i \(-0.518392\pi\)
1.00000 0.000397221i \(-0.000126439\pi\)
\(168\) 0 0
\(169\) −18.1334 2.11949i −1.39488 0.163038i
\(170\) −0.745077 4.22554i −0.0571448 0.324084i
\(171\) 0 0
\(172\) −1.90597 + 10.8093i −0.145329 + 0.824202i
\(173\) −4.01157 + 13.3996i −0.304994 + 1.01875i 0.658848 + 0.752276i \(0.271044\pi\)
−0.963842 + 0.266474i \(0.914141\pi\)
\(174\) 0 0
\(175\) −0.0711371 + 1.22138i −0.00537746 + 0.0923274i
\(176\) −2.47343 + 1.24220i −0.186442 + 0.0936345i
\(177\) 0 0
\(178\) −0.316229 0.335183i −0.0237024 0.0251230i
\(179\) 9.85261 3.58606i 0.736418 0.268034i 0.0535392 0.998566i \(-0.482950\pi\)
0.682879 + 0.730531i \(0.260728\pi\)
\(180\) 0 0
\(181\) 11.6610 + 4.24426i 0.866755 + 0.315473i 0.736852 0.676054i \(-0.236311\pi\)
0.129903 + 0.991527i \(0.458533\pi\)
\(182\) 0.676372 + 1.56801i 0.0501361 + 0.116228i
\(183\) 0 0
\(184\) 1.18664 + 3.96365i 0.0874803 + 0.292204i
\(185\) −6.04487 + 0.706543i −0.444427 + 0.0519461i
\(186\) 0 0
\(187\) 0.495943 + 8.51501i 0.0362669 + 0.622679i
\(188\) −0.884358 1.53175i −0.0644984 0.111715i
\(189\) 0 0
\(190\) −0.849737 + 1.47179i −0.0616464 + 0.106775i
\(191\) −12.6284 6.34222i −0.913759 0.458907i −0.0711702 0.997464i \(-0.522673\pi\)
−0.842589 + 0.538557i \(0.818970\pi\)
\(192\) 0 0
\(193\) 13.1675 + 17.6871i 0.947820 + 1.27314i 0.961945 + 0.273243i \(0.0880965\pi\)
−0.0141245 + 0.999900i \(0.504496\pi\)
\(194\) −10.4705 2.48154i −0.751735 0.178164i
\(195\) 0 0
\(196\) 3.56486 4.78844i 0.254633 0.342031i
\(197\) −1.28639 + 1.07941i −0.0916516 + 0.0769049i −0.687462 0.726220i \(-0.741275\pi\)
0.595811 + 0.803125i \(0.296831\pi\)
\(198\) 0 0
\(199\) 8.18059 + 6.86433i 0.579906 + 0.486599i 0.884916 0.465750i \(-0.154215\pi\)
−0.305010 + 0.952349i \(0.598660\pi\)
\(200\) −12.6878 + 3.00706i −0.897161 + 0.212631i
\(201\) 0 0
\(202\) −8.26629 5.43682i −0.581614 0.382534i
\(203\) 1.43298 + 0.942484i 0.100575 + 0.0661494i
\(204\) 0 0
\(205\) 9.53350 2.25948i 0.665849 0.157809i
\(206\) −11.9726 10.0462i −0.834173 0.699954i
\(207\) 0 0
\(208\) −6.55049 + 5.49652i −0.454195 + 0.381115i
\(209\) 2.01741 2.70985i 0.139547 0.187444i
\(210\) 0 0
\(211\) −10.1652 2.40919i −0.699798 0.165855i −0.134709 0.990885i \(-0.543010\pi\)
−0.565089 + 0.825030i \(0.691158\pi\)
\(212\) −1.58849 2.13371i −0.109098 0.146544i
\(213\) 0 0
\(214\) 0.0717306 + 0.0360245i 0.00490341 + 0.00246258i
\(215\) 5.42938 9.40396i 0.370281 0.641345i
\(216\) 0 0
\(217\) −0.609682 1.05600i −0.0413879 0.0716860i
\(218\) 0.328112 + 5.63347i 0.0222226 + 0.381547i
\(219\) 0 0
\(220\) −1.32413 + 0.154769i −0.0892730 + 0.0104345i
\(221\) 7.55761 + 25.2442i 0.508380 + 1.69811i
\(222\) 0 0
\(223\) 5.39966 + 12.5178i 0.361588 + 0.838256i 0.997772 + 0.0667182i \(0.0212528\pi\)
−0.636184 + 0.771538i \(0.719488\pi\)
\(224\) −1.20445 0.438385i −0.0804759 0.0292908i
\(225\) 0 0
\(226\) −18.5548 + 6.75338i −1.23424 + 0.449228i
\(227\) 8.98971 + 9.52854i 0.596668 + 0.632431i 0.953376 0.301785i \(-0.0975824\pi\)
−0.356708 + 0.934216i \(0.616101\pi\)
\(228\) 0 0
\(229\) 1.54142 0.774128i 0.101860 0.0511559i −0.397140 0.917758i \(-0.629997\pi\)
0.499000 + 0.866602i \(0.333701\pi\)
\(230\) 0.0717373 1.23168i 0.00473021 0.0812146i
\(231\) 0 0
\(232\) −5.24264 + 17.5116i −0.344196 + 1.14970i
\(233\) −4.21198 + 23.8873i −0.275936 + 1.56491i 0.460036 + 0.887900i \(0.347836\pi\)
−0.735972 + 0.677011i \(0.763275\pi\)
\(234\) 0 0
\(235\) 0.303852 + 1.72323i 0.0198211 + 0.112411i
\(236\) −1.08111 0.126363i −0.0703741 0.00822555i
\(237\) 0 0
\(238\) 0.987951 1.04717i 0.0640394 0.0678778i
\(239\) 8.77100 20.3335i 0.567349 1.31526i −0.357139 0.934051i \(-0.616248\pi\)
0.924488 0.381211i \(-0.124493\pi\)
\(240\) 0 0
\(241\) 15.1000 9.93144i 0.972677 0.639740i 0.0395241 0.999219i \(-0.487416\pi\)
0.933153 + 0.359479i \(0.117045\pi\)
\(242\) 8.23764 0.529536
\(243\) 0 0
\(244\) −2.39098 −0.153067
\(245\) −4.93432 + 3.24535i −0.315242 + 0.207338i
\(246\) 0 0
\(247\) 4.13396 9.58361i 0.263038 0.609790i
\(248\) 8.91821 9.45275i 0.566307 0.600250i
\(249\) 0 0
\(250\) 8.38285 + 0.979815i 0.530178 + 0.0619689i
\(251\) −1.74420 9.89185i −0.110093 0.624368i −0.989063 0.147492i \(-0.952880\pi\)
0.878970 0.476876i \(-0.158231\pi\)
\(252\) 0 0
\(253\) −0.425886 + 2.41532i −0.0267752 + 0.151850i
\(254\) 3.40502 11.3735i 0.213650 0.713640i
\(255\) 0 0
\(256\) 0.947781 16.2728i 0.0592363 1.01705i
\(257\) −8.19846 + 4.11742i −0.511406 + 0.256838i −0.685737 0.727849i \(-0.740520\pi\)
0.174331 + 0.984687i \(0.444224\pi\)
\(258\) 0 0
\(259\) −1.40132 1.48531i −0.0870739 0.0922929i
\(260\) −3.87029 + 1.40867i −0.240025 + 0.0873620i
\(261\) 0 0
\(262\) 0.276516 + 0.100643i 0.0170832 + 0.00621777i
\(263\) −9.41306 21.8219i −0.580434 1.34560i −0.915087 0.403257i \(-0.867878\pi\)
0.334653 0.942342i \(-0.391381\pi\)
\(264\) 0 0
\(265\) 0.754766 + 2.52109i 0.0463649 + 0.154870i
\(266\) −0.566364 + 0.0661985i −0.0347260 + 0.00405889i
\(267\) 0 0
\(268\) −0.315139 5.41072i −0.0192502 0.330513i
\(269\) 3.35091 + 5.80395i 0.204309 + 0.353873i 0.949912 0.312517i \(-0.101172\pi\)
−0.745604 + 0.666390i \(0.767839\pi\)
\(270\) 0 0
\(271\) 4.74494 8.21848i 0.288235 0.499237i −0.685154 0.728398i \(-0.740265\pi\)
0.973388 + 0.229161i \(0.0735984\pi\)
\(272\) 6.44220 + 3.23539i 0.390616 + 0.196175i
\(273\) 0 0
\(274\) −6.70998 9.01307i −0.405365 0.544499i
\(275\) −7.52097 1.78250i −0.453532 0.107489i
\(276\) 0 0
\(277\) −0.827868 + 1.11202i −0.0497418 + 0.0668148i −0.826298 0.563233i \(-0.809557\pi\)
0.776556 + 0.630048i \(0.216965\pi\)
\(278\) −0.442668 + 0.371442i −0.0265494 + 0.0222776i
\(279\) 0 0
\(280\) 0.571880 + 0.479864i 0.0341764 + 0.0286774i
\(281\) 15.5815 3.69287i 0.929512 0.220298i 0.262146 0.965028i \(-0.415570\pi\)
0.667366 + 0.744730i \(0.267422\pi\)
\(282\) 0 0
\(283\) 0.262449 + 0.172616i 0.0156010 + 0.0102609i 0.557286 0.830321i \(-0.311843\pi\)
−0.541685 + 0.840582i \(0.682213\pi\)
\(284\) 9.30221 + 6.11816i 0.551985 + 0.363046i
\(285\) 0 0
\(286\) −10.4976 + 2.48799i −0.620739 + 0.147118i
\(287\) 2.51826 + 2.11307i 0.148648 + 0.124731i
\(288\) 0 0
\(289\) 3.99528 3.35244i 0.235016 0.197202i
\(290\) 3.25503 4.37226i 0.191142 0.256748i
\(291\) 0 0
\(292\) 5.39195 + 1.27792i 0.315540 + 0.0747844i
\(293\) 11.1446 + 14.9698i 0.651076 + 0.874547i 0.997991 0.0633491i \(-0.0201782\pi\)
−0.346915 + 0.937897i \(0.612771\pi\)
\(294\) 0 0
\(295\) 0.962295 + 0.483283i 0.0560270 + 0.0281378i
\(296\) 10.8817 18.8477i 0.632488 1.09550i
\(297\) 0 0
\(298\) −10.4732 18.1401i −0.606696 1.05083i
\(299\) 0.440569 + 7.56428i 0.0254788 + 0.437454i
\(300\) 0 0
\(301\) 3.61877 0.422974i 0.208583 0.0243798i
\(302\) 4.53607 + 15.1515i 0.261022 + 0.871873i
\(303\) 0 0
\(304\) −1.13095 2.62183i −0.0648642 0.150372i
\(305\) 2.22277 + 0.809023i 0.127276 + 0.0463245i
\(306\) 0 0
\(307\) 25.4414 9.25992i 1.45202 0.528491i 0.508864 0.860847i \(-0.330066\pi\)
0.943154 + 0.332356i \(0.107843\pi\)
\(308\) −0.306960 0.325359i −0.0174907 0.0185391i
\(309\) 0 0
\(310\) −3.46305 + 1.73921i −0.196688 + 0.0987804i
\(311\) 0.719941 12.3609i 0.0408241 0.700923i −0.914359 0.404906i \(-0.867304\pi\)
0.955183 0.296017i \(-0.0956586\pi\)
\(312\) 0 0
\(313\) 6.15560 20.5611i 0.347935 1.16218i −0.587660 0.809108i \(-0.699951\pi\)
0.935595 0.353076i \(-0.114864\pi\)
\(314\) −1.08147 + 6.13334i −0.0610311 + 0.346124i
\(315\) 0 0
\(316\) −1.06770 6.05524i −0.0600629 0.340634i
\(317\) 23.4460 + 2.74044i 1.31686 + 0.153919i 0.745348 0.666676i \(-0.232283\pi\)
0.571511 + 0.820595i \(0.306358\pi\)
\(318\) 0 0
\(319\) −7.43587 + 7.88156i −0.416329 + 0.441283i
\(320\) −2.64780 + 6.13828i −0.148016 + 0.343140i
\(321\) 0 0
\(322\) 0.345861 0.227476i 0.0192741 0.0126768i
\(323\) −8.79912 −0.489596
\(324\) 0 0
\(325\) −23.8792 −1.32458
\(326\) −6.13826 + 4.03720i −0.339967 + 0.223600i
\(327\) 0 0
\(328\) −13.8770 + 32.1706i −0.766232 + 1.77633i
\(329\) −0.402900 + 0.427049i −0.0222126 + 0.0235439i
\(330\) 0 0
\(331\) 0.842076 + 0.0984246i 0.0462847 + 0.00540990i 0.139204 0.990264i \(-0.455546\pi\)
−0.0929190 + 0.995674i \(0.529620\pi\)
\(332\) 2.03134 + 11.5203i 0.111484 + 0.632259i
\(333\) 0 0
\(334\) 3.28558 18.6334i 0.179779 1.01958i
\(335\) −1.53783 + 5.13672i −0.0840207 + 0.280649i
\(336\) 0 0
\(337\) −0.118835 + 2.04032i −0.00647336 + 0.111143i −0.999997 0.00248306i \(-0.999210\pi\)
0.993524 + 0.113626i \(0.0362467\pi\)
\(338\) −17.3971 + 8.73718i −0.946280 + 0.475240i
\(339\) 0 0
\(340\) 2.38281 + 2.52563i 0.129226 + 0.136972i
\(341\) 7.23894 2.63476i 0.392011 0.142680i
\(342\) 0 0
\(343\) −3.74626 1.36353i −0.202279 0.0736236i
\(344\) 15.3801 + 35.6550i 0.829237 + 1.92239i
\(345\) 0 0
\(346\) 4.27767 + 14.2884i 0.229969 + 0.768151i
\(347\) 6.45936 0.754991i 0.346757 0.0405300i 0.0590678 0.998254i \(-0.481187\pi\)
0.287689 + 0.957724i \(0.407113\pi\)
\(348\) 0 0
\(349\) −0.384965 6.60959i −0.0206067 0.353803i −0.992813 0.119677i \(-0.961814\pi\)
0.972206 0.234126i \(-0.0752229\pi\)
\(350\) 0.652302 + 1.12982i 0.0348670 + 0.0603914i
\(351\) 0 0
\(352\) 4.04883 7.01279i 0.215804 0.373783i
\(353\) −0.270111 0.135655i −0.0143765 0.00722017i 0.441596 0.897214i \(-0.354412\pi\)
−0.455973 + 0.889994i \(0.650709\pi\)
\(354\) 0 0
\(355\) −6.57763 8.83530i −0.349105 0.468929i
\(356\) 0.362860 + 0.0859995i 0.0192316 + 0.00455796i
\(357\) 0 0
\(358\) 6.67650 8.96809i 0.352864 0.473978i
\(359\) 3.14494 2.63892i 0.165984 0.139277i −0.556012 0.831174i \(-0.687669\pi\)
0.721996 + 0.691897i \(0.243225\pi\)
\(360\) 0 0
\(361\) −11.8851 9.97274i −0.625529 0.524881i
\(362\) 12.8759 3.05164i 0.676740 0.160390i
\(363\) 0 0
\(364\) −1.15458 0.759381i −0.0605166 0.0398024i
\(365\) −4.58023 3.01246i −0.239740 0.157680i
\(366\) 0 0
\(367\) −8.75239 + 2.07435i −0.456871 + 0.108280i −0.452606 0.891711i \(-0.649506\pi\)
−0.00426466 + 0.999991i \(0.501357\pi\)
\(368\) 1.58793 + 1.33243i 0.0827767 + 0.0694579i
\(369\) 0 0
\(370\) −4.97142 + 4.17152i −0.258452 + 0.216867i
\(371\) −0.527285 + 0.708267i −0.0273753 + 0.0367714i
\(372\) 0 0
\(373\) 5.11858 + 1.21313i 0.265030 + 0.0628133i 0.360982 0.932573i \(-0.382441\pi\)
−0.0959522 + 0.995386i \(0.530590\pi\)
\(374\) 5.43130 + 7.29550i 0.280846 + 0.377242i
\(375\) 0 0
\(376\) −5.59173 2.80827i −0.288371 0.144826i
\(377\) −16.7380 + 28.9911i −0.862053 + 1.49312i
\(378\) 0 0
\(379\) −3.76722 6.52502i −0.193509 0.335168i 0.752902 0.658133i \(-0.228654\pi\)
−0.946411 + 0.322965i \(0.895320\pi\)
\(380\) −0.0799664 1.37297i −0.00410219 0.0704319i
\(381\) 0 0
\(382\) −14.9671 + 1.74940i −0.765782 + 0.0895070i
\(383\) 10.2165 + 34.1256i 0.522040 + 1.74374i 0.657996 + 0.753022i \(0.271404\pi\)
−0.135955 + 0.990715i \(0.543410\pi\)
\(384\) 0 0
\(385\) 0.175276 + 0.406335i 0.00893288 + 0.0207088i
\(386\) 22.0950 + 8.04193i 1.12461 + 0.409324i
\(387\) 0 0
\(388\) 8.18276 2.97828i 0.415417 0.151199i
\(389\) −8.68991 9.21077i −0.440596 0.467005i 0.468577 0.883423i \(-0.344767\pi\)
−0.909173 + 0.416418i \(0.863285\pi\)
\(390\) 0 0
\(391\) 5.70844 2.86689i 0.288688 0.144985i
\(392\) 1.22798 21.0837i 0.0620226 1.06489i
\(393\) 0 0
\(394\) −0.513567 + 1.71543i −0.0258731 + 0.0864223i
\(395\) −1.05629 + 5.99053i −0.0531478 + 0.301416i
\(396\) 0 0
\(397\) 1.88601 + 10.6961i 0.0946564 + 0.536823i 0.994852 + 0.101337i \(0.0323122\pi\)
−0.900196 + 0.435486i \(0.856577\pi\)
\(398\) 11.3104 + 1.32200i 0.566939 + 0.0662656i
\(399\) 0 0
\(400\) −4.48304 + 4.75175i −0.224152 + 0.237587i
\(401\) 2.27311 5.26965i 0.113514 0.263154i −0.851983 0.523569i \(-0.824600\pi\)
0.965497 + 0.260415i \(0.0838594\pi\)
\(402\) 0 0
\(403\) 19.8842 13.0781i 0.990505 0.651465i
\(404\) 8.00667 0.398347
\(405\) 0 0
\(406\) 1.82891 0.0907674
\(407\) 10.7785 7.08910i 0.534268 0.351394i
\(408\) 0 0
\(409\) −11.7085 + 27.1434i −0.578948 + 1.34215i 0.337245 + 0.941417i \(0.390505\pi\)
−0.916193 + 0.400737i \(0.868754\pi\)
\(410\) 7.16952 7.59925i 0.354078 0.375300i
\(411\) 0 0
\(412\) 12.5624 + 1.46833i 0.618903 + 0.0723394i
\(413\) 0.0627404 + 0.355818i 0.00308725 + 0.0175087i
\(414\) 0 0
\(415\) 2.00964 11.3972i 0.0986491 0.559467i
\(416\) 7.17503 23.9663i 0.351785 1.17504i
\(417\) 0 0
\(418\) 0.209464 3.59636i 0.0102452 0.175904i
\(419\) −7.98438 + 4.00990i −0.390062 + 0.195897i −0.633012 0.774142i \(-0.718181\pi\)
0.242949 + 0.970039i \(0.421885\pi\)
\(420\) 0 0
\(421\) −1.73759 1.84173i −0.0846848 0.0897606i 0.683645 0.729814i \(-0.260394\pi\)
−0.768330 + 0.640054i \(0.778912\pi\)
\(422\) −10.4679 + 3.81001i −0.509570 + 0.185468i
\(423\) 0 0
\(424\) −8.84319 3.21866i −0.429463 0.156312i
\(425\) 7.97367 + 18.4851i 0.386780 + 0.896657i
\(426\) 0 0
\(427\) 0.227626 + 0.760322i 0.0110156 + 0.0367946i
\(428\) −0.0645180 + 0.00754107i −0.00311860 + 0.000364511i
\(429\) 0 0
\(430\) −0.673263 11.5595i −0.0324676 0.557448i
\(431\) −14.8594 25.7372i −0.715750 1.23972i −0.962669 0.270680i \(-0.912751\pi\)
0.246919 0.969036i \(-0.420582\pi\)
\(432\) 0 0
\(433\) 0.612994 1.06174i 0.0294586 0.0510238i −0.850920 0.525295i \(-0.823955\pi\)
0.880379 + 0.474271i \(0.157288\pi\)
\(434\) −1.16195 0.583551i −0.0557752 0.0280114i
\(435\) 0 0
\(436\) −2.72698 3.66298i −0.130599 0.175425i
\(437\) −2.46193 0.583487i −0.117770 0.0279120i
\(438\) 0 0
\(439\) −10.3661 + 13.9241i −0.494748 + 0.664562i −0.977436 0.211231i \(-0.932253\pi\)
0.482689 + 0.875792i \(0.339660\pi\)
\(440\) −3.61294 + 3.03162i −0.172240 + 0.144527i
\(441\) 0 0
\(442\) 21.5252 + 18.0618i 1.02385 + 0.859113i
\(443\) −11.6619 + 2.76392i −0.554073 + 0.131318i −0.498108 0.867115i \(-0.665972\pi\)
−0.0559651 + 0.998433i \(0.517824\pi\)
\(444\) 0 0
\(445\) −0.308234 0.202729i −0.0146117 0.00961027i
\(446\) 12.1456 + 7.98827i 0.575109 + 0.378255i
\(447\) 0 0
\(448\) −2.18254 + 0.517271i −0.103115 + 0.0244388i
\(449\) 15.0015 + 12.5878i 0.707965 + 0.594053i 0.924027 0.382327i \(-0.124877\pi\)
−0.216063 + 0.976380i \(0.569322\pi\)
\(450\) 0 0
\(451\) −15.9095 + 13.3497i −0.749150 + 0.628611i
\(452\) 9.54203 12.8172i 0.448820 0.602869i
\(453\) 0 0
\(454\) 13.5924 + 3.22145i 0.637921 + 0.151190i
\(455\) 0.816411 + 1.09663i 0.0382739 + 0.0514108i
\(456\) 0 0
\(457\) 21.4625 + 10.7789i 1.00397 + 0.504215i 0.873286 0.487208i \(-0.161985\pi\)
0.130689 + 0.991423i \(0.458281\pi\)
\(458\) 0.919654 1.59289i 0.0429726 0.0744308i
\(459\) 0 0
\(460\) 0.499212 + 0.864661i 0.0232759 + 0.0403150i
\(461\) 0.823736 + 14.1430i 0.0383652 + 0.658705i 0.961598 + 0.274463i \(0.0885001\pi\)
−0.923232 + 0.384242i \(0.874463\pi\)
\(462\) 0 0
\(463\) 10.9340 1.27800i 0.508147 0.0593938i 0.141843 0.989889i \(-0.454697\pi\)
0.366304 + 0.930495i \(0.380623\pi\)
\(464\) 2.62660 + 8.77345i 0.121937 + 0.407297i
\(465\) 0 0
\(466\) 10.2445 + 23.7495i 0.474569 + 1.10018i
\(467\) 36.6170 + 13.3275i 1.69443 + 0.616723i 0.995172 0.0981436i \(-0.0312904\pi\)
0.699261 + 0.714867i \(0.253513\pi\)
\(468\) 0 0
\(469\) −1.69059 + 0.615324i −0.0780642 + 0.0284130i
\(470\) 1.28045 + 1.35720i 0.0590628 + 0.0626029i
\(471\) 0 0
\(472\) −3.44115 + 1.72821i −0.158392 + 0.0795472i
\(473\) −1.33837 + 22.9789i −0.0615381 + 1.05657i
\(474\) 0 0
\(475\) 2.28688 7.63872i 0.104929 0.350488i
\(476\) −0.202307 + 1.14734i −0.00927272 + 0.0525882i
\(477\) 0 0
\(478\) −4.10044 23.2547i −0.187550 1.06365i
\(479\) −14.0251 1.63930i −0.640825 0.0749017i −0.210526 0.977588i \(-0.567518\pi\)
−0.430299 + 0.902686i \(0.641592\pi\)
\(480\) 0 0
\(481\) 27.3510 28.9904i 1.24710 1.32185i
\(482\) 7.63332 17.6960i 0.347688 0.806032i
\(483\) 0 0
\(484\) −5.56961 + 3.66319i −0.253164 + 0.166509i
\(485\) −8.61486 −0.391181
\(486\) 0 0
\(487\) −11.6224 −0.526663 −0.263332 0.964705i \(-0.584821\pi\)
−0.263332 + 0.964705i \(0.584821\pi\)
\(488\) −7.06715 + 4.64814i −0.319915 + 0.210411i
\(489\) 0 0
\(490\) −2.49438 + 5.78263i −0.112685 + 0.261233i
\(491\) 3.60508 3.82116i 0.162695 0.172447i −0.640898 0.767626i \(-0.721438\pi\)
0.803593 + 0.595180i \(0.202919\pi\)
\(492\) 0 0
\(493\) 28.0313 + 3.27639i 1.26247 + 0.147561i
\(494\) −1.93263 10.9605i −0.0869530 0.493135i
\(495\) 0 0
\(496\) 1.13061 6.41203i 0.0507660 0.287909i
\(497\) 1.05997 3.54053i 0.0475460 0.158815i
\(498\) 0 0
\(499\) −0.320759 + 5.50722i −0.0143592 + 0.246537i 0.983489 + 0.180968i \(0.0579232\pi\)
−0.997848 + 0.0655687i \(0.979114\pi\)
\(500\) −6.10350 + 3.06529i −0.272957 + 0.137084i
\(501\) 0 0
\(502\) −7.35016 7.79071i −0.328054 0.347717i
\(503\) −31.2754 + 11.3833i −1.39450 + 0.507557i −0.926541 0.376193i \(-0.877233\pi\)
−0.467959 + 0.883750i \(0.655011\pi\)
\(504\) 0 0
\(505\) −7.44341 2.70918i −0.331227 0.120557i
\(506\) 1.03586 + 2.40139i 0.0460495 + 0.106755i
\(507\) 0 0
\(508\) 2.75550 + 9.20402i 0.122256 + 0.408362i
\(509\) 21.9142 2.56140i 0.971328 0.113532i 0.384396 0.923168i \(-0.374410\pi\)
0.586932 + 0.809636i \(0.300336\pi\)
\(510\) 0 0
\(511\) −0.106951 1.83628i −0.00473124 0.0812323i
\(512\) −8.09134 14.0146i −0.357590 0.619364i
\(513\) 0 0
\(514\) −4.89144 + 8.47222i −0.215752 + 0.373694i
\(515\) −11.1818 5.61570i −0.492728 0.247457i
\(516\) 0 0
\(517\) −2.21496 2.97520i −0.0974137 0.130849i
\(518\) −2.11879 0.502162i −0.0930942 0.0220637i
\(519\) 0 0
\(520\) −8.70114 + 11.6877i −0.381570 + 0.512538i
\(521\) 21.4866 18.0294i 0.941345 0.789882i −0.0364742 0.999335i \(-0.511613\pi\)
0.977819 + 0.209453i \(0.0671682\pi\)
\(522\) 0 0
\(523\) −6.29841 5.28500i −0.275410 0.231097i 0.494612 0.869114i \(-0.335310\pi\)
−0.770022 + 0.638017i \(0.779755\pi\)
\(524\) −0.231712 + 0.0549167i −0.0101224 + 0.00239905i
\(525\) 0 0
\(526\) −21.1730 13.9257i −0.923186 0.607189i
\(527\) −16.7635 11.0255i −0.730229 0.480279i
\(528\) 0 0
\(529\) −20.5927 + 4.88057i −0.895337 + 0.212199i
\(530\) 2.14969 + 1.80381i 0.0933766 + 0.0783523i
\(531\) 0 0
\(532\) 0.353491 0.296614i 0.0153258 0.0128598i
\(533\) −38.3153 + 51.4664i −1.65962 + 2.22926i
\(534\) 0 0
\(535\) 0.0625308 + 0.0148201i 0.00270344 + 0.000640728i
\(536\) −11.4501 15.3802i −0.494569 0.664322i
\(537\) 0 0
\(538\) 6.38625 + 3.20729i 0.275331 + 0.138276i
\(539\) 6.25951 10.8418i 0.269616 0.466989i
\(540\) 0 0
\(541\) 0.833782 + 1.44415i 0.0358471 + 0.0620889i 0.883392 0.468634i \(-0.155254\pi\)
−0.847545 + 0.530723i \(0.821920\pi\)
\(542\) −0.588390 10.1023i −0.0252735 0.433930i
\(543\) 0 0
\(544\) −20.9483 + 2.44850i −0.898150 + 0.104979i
\(545\) 1.29572 + 4.32801i 0.0555025 + 0.185391i
\(546\) 0 0
\(547\) 7.06785 + 16.3851i 0.302199 + 0.700577i 0.999875 0.0158373i \(-0.00504139\pi\)
−0.697675 + 0.716414i \(0.745782\pi\)
\(548\) 8.54475 + 3.11003i 0.365013 + 0.132854i
\(549\) 0 0
\(550\) −7.74498 + 2.81894i −0.330247 + 0.120200i
\(551\) −7.67098 8.13076i −0.326795 0.346382i
\(552\) 0 0
\(553\) −1.82390 + 0.915996i −0.0775600 + 0.0389521i
\(554\) −0.0859560 + 1.47581i −0.00365192 + 0.0627010i
\(555\) 0 0
\(556\) 0.134119 0.447988i 0.00568790 0.0189989i
\(557\) 3.03540 17.2146i 0.128614 0.729407i −0.850481 0.526005i \(-0.823689\pi\)
0.979095 0.203402i \(-0.0651997\pi\)
\(558\) 0 0
\(559\) 12.3485 + 70.0317i 0.522285 + 2.96203i
\(560\) 0.371490 + 0.0434210i 0.0156983 + 0.00183487i
\(561\) 0 0
\(562\) 11.7178 12.4201i 0.494285 0.523912i
\(563\) 13.6909 31.7390i 0.577002 1.33764i −0.340626 0.940199i \(-0.610639\pi\)
0.917628 0.397441i \(-0.130102\pi\)
\(564\) 0 0
\(565\) −13.2076 + 8.68681i −0.555650 + 0.365457i
\(566\) 0.334965 0.0140796
\(567\) 0 0
\(568\) 39.3890 1.65273
\(569\) −21.3130 + 14.0178i −0.893489 + 0.587657i −0.911099 0.412188i \(-0.864765\pi\)
0.0176099 + 0.999845i \(0.494394\pi\)
\(570\) 0 0
\(571\) 8.79169 20.3814i 0.367921 0.852936i −0.629210 0.777235i \(-0.716621\pi\)
0.997131 0.0757007i \(-0.0241194\pi\)
\(572\) 5.99126 6.35036i 0.250507 0.265522i
\(573\) 0 0
\(574\) 3.48172 + 0.406955i 0.145324 + 0.0169860i
\(575\) 1.00519 + 5.70073i 0.0419194 + 0.237737i
\(576\) 0 0
\(577\) −3.76924 + 21.3764i −0.156915 + 0.889911i 0.800098 + 0.599869i \(0.204781\pi\)
−0.957014 + 0.290042i \(0.906331\pi\)
\(578\) 1.59504 5.32779i 0.0663448 0.221607i
\(579\) 0 0
\(580\) −0.256483 + 4.40364i −0.0106499 + 0.182851i
\(581\) 3.47003 1.74272i 0.143961 0.0723000i
\(582\) 0 0
\(583\) −3.82815 4.05760i −0.158546 0.168049i
\(584\) 18.4216 6.70492i 0.762292 0.277452i
\(585\) 0 0
\(586\) 18.7006 + 6.80646i 0.772515 + 0.281172i
\(587\) −8.05782 18.6801i −0.332582 0.771012i −0.999661 0.0260249i \(-0.991715\pi\)
0.667079 0.744987i \(-0.267544\pi\)
\(588\) 0 0
\(589\) 2.27925 + 7.61323i 0.0939149 + 0.313698i
\(590\) 1.14050 0.133306i 0.0469538 0.00548811i
\(591\) 0 0
\(592\) −0.633990 10.8852i −0.0260568 0.447378i
\(593\) 0.579087 + 1.00301i 0.0237803 + 0.0411886i 0.877671 0.479264i \(-0.159096\pi\)
−0.853890 + 0.520453i \(0.825763\pi\)
\(594\) 0 0
\(595\) 0.576294 0.998171i 0.0236258 0.0409210i
\(596\) 15.1478 + 7.60752i 0.620479 + 0.311616i
\(597\) 0 0
\(598\) 4.82488 + 6.48094i 0.197304 + 0.265025i
\(599\) −44.1467 10.4629i −1.80378 0.427505i −0.815326 0.579002i \(-0.803442\pi\)
−0.988458 + 0.151498i \(0.951590\pi\)
\(600\) 0 0
\(601\) −19.5190 + 26.2185i −0.796195 + 1.06948i 0.199780 + 0.979841i \(0.435977\pi\)
−0.995975 + 0.0896345i \(0.971430\pi\)
\(602\) 2.97615 2.49729i 0.121299 0.101782i
\(603\) 0 0
\(604\) −9.80464 8.22707i −0.398945 0.334755i
\(605\) 6.41729 1.52093i 0.260900 0.0618344i
\(606\) 0 0
\(607\) −0.512985 0.337395i −0.0208214 0.0136945i 0.539056 0.842270i \(-0.318781\pi\)
−0.559877 + 0.828576i \(0.689152\pi\)
\(608\) 6.97941 + 4.59043i 0.283052 + 0.186167i
\(609\) 0 0
\(610\) 2.45435 0.581691i 0.0993736 0.0235520i
\(611\) −8.77827 7.36585i −0.355131 0.297990i
\(612\) 0 0
\(613\) −15.6352 + 13.1195i −0.631499 + 0.529891i −0.901394 0.432999i \(-0.857455\pi\)
0.269895 + 0.962890i \(0.413011\pi\)
\(614\) 17.2401 23.1574i 0.695752 0.934557i
\(615\) 0 0
\(616\) −1.53981 0.364942i −0.0620407 0.0147039i
\(617\) 5.77352 + 7.75518i 0.232433 + 0.312212i 0.903003 0.429635i \(-0.141358\pi\)
−0.670570 + 0.741847i \(0.733950\pi\)
\(618\) 0 0
\(619\) −24.0046 12.0556i −0.964828 0.484555i −0.104628 0.994511i \(-0.533365\pi\)
−0.860200 + 0.509957i \(0.829661\pi\)
\(620\) 1.56802 2.71589i 0.0629732 0.109073i
\(621\) 0 0
\(622\) −6.60160 11.4343i −0.264700 0.458474i
\(623\) −0.00719746 0.123576i −0.000288360 0.00495095i
\(624\) 0 0
\(625\) −14.5002 + 1.69483i −0.580008 + 0.0677932i
\(626\) −6.56393 21.9251i −0.262347 0.876302i
\(627\) 0 0
\(628\) −1.99623 4.62778i −0.0796581 0.184668i
\(629\) −31.5746 11.4922i −1.25896 0.458224i
\(630\) 0 0
\(631\) 29.6208 10.7811i 1.17918 0.429188i 0.323270 0.946307i \(-0.395218\pi\)
0.855914 + 0.517119i \(0.172996\pi\)
\(632\) −14.9275 15.8222i −0.593782 0.629372i
\(633\) 0 0
\(634\) 22.4941 11.2969i 0.893354 0.448659i
\(635\) 0.552665 9.48889i 0.0219318 0.376555i
\(636\) 0 0
\(637\) 11.0926 37.0519i 0.439505 1.46805i
\(638\) −2.00641 + 11.3789i −0.0794344 + 0.450495i
\(639\) 0 0
\(640\) −0.0888692 0.504002i −0.00351286 0.0199224i
\(641\) 11.2656 + 1.31676i 0.444965 + 0.0520089i 0.335625 0.941996i \(-0.391052\pi\)
0.109339 + 0.994004i \(0.465126\pi\)
\(642\) 0 0
\(643\) −9.07210 + 9.61586i −0.357769 + 0.379213i −0.881111 0.472910i \(-0.843204\pi\)
0.523342 + 0.852123i \(0.324685\pi\)
\(644\) −0.132686 + 0.307601i −0.00522857 + 0.0121212i
\(645\) 0 0
\(646\) −7.83922 + 5.15594i −0.308430 + 0.202858i
\(647\) −36.5943 −1.43867 −0.719336 0.694663i \(-0.755554\pi\)
−0.719336 + 0.694663i \(0.755554\pi\)
\(648\) 0 0
\(649\) −2.28261 −0.0896005
\(650\) −21.2743 + 13.9923i −0.834445 + 0.548823i
\(651\) 0 0
\(652\) 2.35488 5.45923i 0.0922244 0.213800i
\(653\) −18.7327 + 19.8555i −0.733069 + 0.777008i −0.981463 0.191651i \(-0.938616\pi\)
0.248394 + 0.968659i \(0.420097\pi\)
\(654\) 0 0
\(655\) 0.233993 + 0.0273499i 0.00914287 + 0.00106865i
\(656\) 3.04809 + 17.2866i 0.119008 + 0.674928i
\(657\) 0 0
\(658\) −0.108714 + 0.616545i −0.00423809 + 0.0240354i
\(659\) 4.23303 14.1393i 0.164895 0.550789i −0.835104 0.550091i \(-0.814593\pi\)
1.00000 0.000697383i \(-0.000221984\pi\)
\(660\) 0 0
\(661\) 1.61762 27.7734i 0.0629181 1.08026i −0.808111 0.589030i \(-0.799510\pi\)
0.871029 0.491232i \(-0.163453\pi\)
\(662\) 0.807887 0.405736i 0.0313994 0.0157694i
\(663\) 0 0
\(664\) 28.4000 + 30.1023i 1.10214 + 1.16820i
\(665\) −0.428987 + 0.156138i −0.0166354 + 0.00605479i
\(666\) 0 0
\(667\) 7.62568 + 2.77552i 0.295267 + 0.107469i
\(668\) 6.06466 + 14.0595i 0.234649 + 0.543977i
\(669\) 0 0
\(670\) 1.63984 + 5.47746i 0.0633527 + 0.211613i
\(671\) −4.98019 + 0.582101i −0.192258 + 0.0224718i
\(672\) 0 0
\(673\) −1.91225 32.8321i −0.0737118 1.26558i −0.808992 0.587820i \(-0.799986\pi\)
0.735280 0.677763i \(-0.237051\pi\)
\(674\) 1.08967 + 1.88737i 0.0419727 + 0.0726989i
\(675\) 0 0
\(676\) 7.87718 13.6437i 0.302968 0.524757i
\(677\) −21.5460 10.8208i −0.828081 0.415878i −0.0163192 0.999867i \(-0.505195\pi\)
−0.811762 + 0.583989i \(0.801491\pi\)
\(678\) 0 0
\(679\) −1.72610 2.31855i −0.0662416 0.0889779i
\(680\) 11.9529 + 2.83290i 0.458374 + 0.108637i
\(681\) 0 0
\(682\) 4.90538 6.58907i 0.187837 0.252308i
\(683\) −10.1873 + 8.54816i −0.389806 + 0.327086i −0.816538 0.577292i \(-0.804109\pi\)
0.426731 + 0.904378i \(0.359665\pi\)
\(684\) 0 0
\(685\) −6.89130 5.78249i −0.263303 0.220938i
\(686\) −4.13656 + 0.980382i −0.157934 + 0.0374311i
\(687\) 0 0
\(688\) 16.2539 + 10.6904i 0.619675 + 0.407567i
\(689\) −14.3990 9.47035i −0.548557 0.360792i
\(690\) 0 0
\(691\) −42.6555 + 10.1095i −1.62269 + 0.384585i −0.938654 0.344862i \(-0.887926\pi\)
−0.684038 + 0.729447i \(0.739778\pi\)
\(692\) −9.24612 7.75841i −0.351485 0.294931i
\(693\) 0 0
\(694\) 5.31231 4.45756i 0.201653 0.169207i
\(695\) −0.276267 + 0.371091i −0.0104794 + 0.0140763i
\(696\) 0 0
\(697\) 52.6345 + 12.4746i 1.99367 + 0.472510i
\(698\) −4.21593 5.66297i −0.159575 0.214347i
\(699\) 0 0
\(700\) −0.943452 0.473819i −0.0356591 0.0179087i
\(701\) −3.65194 + 6.32534i −0.137932 + 0.238905i −0.926714 0.375768i \(-0.877379\pi\)
0.788782 + 0.614673i \(0.210712\pi\)
\(702\) 0 0
\(703\) 6.65434 + 11.5257i 0.250973 + 0.434699i
\(704\) −0.823941 14.1465i −0.0310535 0.533167i
\(705\) 0 0
\(706\) −0.320133 + 0.0374181i −0.0120484 + 0.00140825i
\(707\) −0.762251 2.54609i −0.0286674 0.0957558i
\(708\) 0 0
\(709\) −17.3188 40.1494i −0.650420 1.50784i −0.849350 0.527829i \(-0.823006\pi\)
0.198931 0.980014i \(-0.436253\pi\)
\(710\) −11.0372 4.01722i −0.414219 0.150764i
\(711\) 0 0
\(712\) 1.23971 0.451219i 0.0464602 0.0169101i
\(713\) −3.95917 4.19647i −0.148272 0.157159i
\(714\) 0 0
\(715\) −7.71852 + 3.87638i −0.288656 + 0.144969i
\(716\) −0.526080 + 9.03245i −0.0196605 + 0.337558i
\(717\) 0 0
\(718\) 1.25556 4.19385i 0.0468569 0.156513i
\(719\) −1.93615 + 10.9804i −0.0722061 + 0.409501i 0.927185 + 0.374604i \(0.122221\pi\)
−0.999391 + 0.0348968i \(0.988890\pi\)
\(720\) 0 0
\(721\) −0.729037 4.13457i −0.0271508 0.153980i
\(722\) −16.4321 1.92064i −0.611541 0.0714789i
\(723\) 0 0
\(724\) −7.34856 + 7.78902i −0.273107 + 0.289477i
\(725\) −10.1296 + 23.4831i −0.376204 + 0.872140i
\(726\) 0 0
\(727\) −24.3067 + 15.9867i −0.901484 + 0.592916i −0.913422 0.407013i \(-0.866570\pi\)
0.0119379 + 0.999929i \(0.496200\pi\)
\(728\) −4.88893 −0.181196
\(729\) 0 0
\(730\) −5.84576 −0.216361
\(731\) 50.0886 32.9438i 1.85259 1.21847i
\(732\) 0 0
\(733\) 6.87604 15.9405i 0.253972 0.588774i −0.742759 0.669559i \(-0.766483\pi\)
0.996732 + 0.0807844i \(0.0257425\pi\)
\(734\) −6.58210 + 6.97662i −0.242950 + 0.257512i
\(735\) 0 0
\(736\) −6.02353 0.704050i −0.222030 0.0259516i
\(737\) −1.97369 11.1933i −0.0727017 0.412312i
\(738\) 0 0
\(739\) 3.59215 20.3721i 0.132139 0.749400i −0.844670 0.535288i \(-0.820203\pi\)
0.976809 0.214112i \(-0.0686857\pi\)
\(740\) 1.50623 5.03117i 0.0553703 0.184950i
\(741\) 0 0
\(742\) −0.0547471 + 0.939971i −0.00200983 + 0.0345074i
\(743\) −34.0508 + 17.1009i −1.24920 + 0.627373i −0.945571 0.325417i \(-0.894495\pi\)
−0.303632 + 0.952790i \(0.598199\pi\)
\(744\) 0 0
\(745\) −11.5081 12.1978i −0.421623 0.446894i
\(746\) 5.27104 1.91850i 0.192986 0.0702413i
\(747\) 0 0
\(748\) −6.91643 2.51737i −0.252890 0.0920443i
\(749\) 0.00854027 + 0.0197986i 0.000312055 + 0.000723424i
\(750\) 0 0
\(751\) −9.82318 32.8117i −0.358453 1.19732i −0.927125 0.374752i \(-0.877728\pi\)
0.568672 0.822564i \(-0.307457\pi\)
\(752\) −3.11375 + 0.363945i −0.113547 + 0.0132717i
\(753\) 0 0
\(754\) 2.07558 + 35.6363i 0.0755881 + 1.29780i
\(755\) 6.33114 + 10.9659i 0.230414 + 0.399088i
\(756\) 0 0
\(757\) −14.5877 + 25.2666i −0.530198 + 0.918330i 0.469181 + 0.883102i \(0.344549\pi\)
−0.999379 + 0.0352284i \(0.988784\pi\)
\(758\) −7.17966 3.60576i −0.260777 0.130967i
\(759\) 0 0
\(760\) −2.90546 3.90271i −0.105392 0.141566i
\(761\) 12.0070 + 2.84572i 0.435255 + 0.103157i 0.442401 0.896817i \(-0.354127\pi\)
−0.00714662 + 0.999974i \(0.502275\pi\)
\(762\) 0 0
\(763\) −0.905200 + 1.21589i −0.0327704 + 0.0440183i
\(764\) 9.34155 7.83849i 0.337965 0.283587i
\(765\) 0 0
\(766\) 29.0983 + 24.4163i 1.05136 + 0.882198i
\(767\) −6.86191 + 1.62630i −0.247769 + 0.0587224i
\(768\) 0 0
\(769\) −2.31777 1.52442i −0.0835810 0.0549721i 0.507031 0.861928i \(-0.330743\pi\)
−0.590612 + 0.806956i \(0.701113\pi\)
\(770\) 0.394251 + 0.259303i 0.0142078 + 0.00934464i
\(771\) 0 0
\(772\) −18.5150 + 4.38813i −0.666369 + 0.157932i
\(773\) −21.3606 17.9237i −0.768287 0.644669i 0.171983 0.985100i \(-0.444983\pi\)
−0.940270 + 0.340431i \(0.889427\pi\)
\(774\) 0 0
\(775\) 13.9283 11.6872i 0.500320 0.419818i
\(776\) 18.3964 24.7107i 0.660392 0.887061i
\(777\) 0 0
\(778\) −13.1391 3.11402i −0.471059 0.111643i
\(779\) −12.7941 17.1855i −0.458398 0.615735i
\(780\) 0 0
\(781\) 20.8652 + 10.4789i 0.746616 + 0.374964i
\(782\) 3.40582 5.89906i 0.121792 0.210950i
\(783\) 0 0
\(784\) −5.29048 9.16338i −0.188946 0.327263i
\(785\) 0.289916 + 4.97767i 0.0103476 + 0.177661i
\(786\) 0 0
\(787\) 1.39131 0.162621i 0.0495950 0.00579682i −0.0912592 0.995827i \(-0.529089\pi\)
0.140854 + 0.990030i \(0.455015\pi\)
\(788\) −0.415603 1.38821i −0.0148052 0.0494530i
\(789\) 0 0
\(790\) 2.56915 + 5.95597i 0.0914064 + 0.211904i
\(791\) −4.98424 1.81411i −0.177219 0.0645025i
\(792\) 0 0
\(793\) −14.5565 + 5.29815i −0.516918 + 0.188143i
\(794\) 7.94778 + 8.42415i 0.282056 + 0.298962i
\(795\) 0 0
\(796\) −8.23503 + 4.13579i −0.291883 + 0.146589i
\(797\) 0.651880 11.1924i 0.0230908 0.396453i −0.966885 0.255214i \(-0.917854\pi\)
0.989975 0.141240i \(-0.0451088\pi\)
\(798\) 0 0
\(799\) −2.77073 + 9.25489i −0.0980214 + 0.327414i
\(800\) 3.31883 18.8220i 0.117338 0.665460i
\(801\) 0 0
\(802\) −1.06268 6.02674i −0.0375244 0.212812i
\(803\) 11.5421 + 1.34908i 0.407311 + 0.0476078i
\(804\) 0 0
\(805\) 0.227433 0.241065i 0.00801597 0.00849643i
\(806\) 10.0518 23.3028i 0.354061 0.820805i
\(807\) 0 0
\(808\) 23.6658 15.5652i 0.832560 0.547583i
\(809\) 2.44943 0.0861173 0.0430587 0.999073i \(-0.486290\pi\)
0.0430587 + 0.999073i \(0.486290\pi\)
\(810\) 0 0
\(811\) 11.9053 0.418050 0.209025 0.977910i \(-0.432971\pi\)
0.209025 + 0.977910i \(0.432971\pi\)
\(812\) −1.23656 + 0.813297i −0.0433947 + 0.0285411i
\(813\) 0 0
\(814\) 5.44870 12.6315i 0.190977 0.442734i
\(815\) −4.03644 + 4.27837i −0.141390 + 0.149865i
\(816\) 0 0
\(817\) −23.5850 2.75669i −0.825135 0.0964444i
\(818\) 5.47372 + 31.0430i 0.191384 + 1.08539i
\(819\) 0 0
\(820\) −1.46813 + 8.32619i −0.0512694 + 0.290763i
\(821\) −6.96784 + 23.2742i −0.243179 + 0.812275i 0.746049 + 0.665891i \(0.231949\pi\)
−0.989228 + 0.146384i \(0.953237\pi\)
\(822\) 0 0
\(823\) −1.80431 + 30.9788i −0.0628944 + 1.07985i 0.808254 + 0.588834i \(0.200413\pi\)
−0.871148 + 0.491020i \(0.836624\pi\)
\(824\) 39.9858 20.0816i 1.39297 0.699576i
\(825\) 0 0
\(826\) 0.264392 + 0.280239i 0.00919936 + 0.00975075i
\(827\) 9.52144 3.46552i 0.331093 0.120508i −0.171124 0.985249i \(-0.554740\pi\)
0.502217 + 0.864741i \(0.332518\pi\)
\(828\) 0 0
\(829\) −16.7991 6.11438i −0.583458 0.212361i 0.0333918 0.999442i \(-0.489369\pi\)
−0.616850 + 0.787081i \(0.711591\pi\)
\(830\) −4.88791 11.3315i −0.169662 0.393320i
\(831\) 0 0
\(832\) −12.5559 41.9397i −0.435298 1.45400i
\(833\) −32.3861 + 3.78539i −1.12211 + 0.131156i
\(834\) 0 0
\(835\) −0.880782 15.1224i −0.0304807 0.523334i
\(836\) 1.45764 + 2.52470i 0.0504135 + 0.0873187i
\(837\) 0 0
\(838\) −4.76371 + 8.25099i −0.164560 + 0.285026i
\(839\) 22.0336 + 11.0657i 0.760685 + 0.382030i 0.786463 0.617637i \(-0.211910\pi\)
−0.0257780 + 0.999668i \(0.508206\pi\)
\(840\) 0 0
\(841\) 4.09225 + 5.49684i 0.141112 + 0.189546i
\(842\) −2.62722 0.622662i −0.0905399 0.0214583i
\(843\) 0 0
\(844\) 5.38327 7.23098i 0.185300 0.248901i
\(845\) −11.9396 + 10.0185i −0.410734 + 0.344647i
\(846\) 0 0
\(847\) 1.69512 + 1.42237i 0.0582450 + 0.0488734i
\(848\) −4.58775 + 1.08732i −0.157544 + 0.0373386i
\(849\) 0 0
\(850\) 17.9353 + 11.7963i 0.615177 + 0.404608i
\(851\) −8.07225 5.30920i −0.276713 0.181997i
\(852\) 0 0
\(853\) 2.02471 0.479866i 0.0693249 0.0164303i −0.195807 0.980642i \(-0.562733\pi\)
0.265132 + 0.964212i \(0.414584\pi\)
\(854\) 0.648313 + 0.543999i 0.0221848 + 0.0186153i
\(855\) 0 0
\(856\) −0.176040 + 0.147715i −0.00601691 + 0.00504879i
\(857\) −7.38060 + 9.91387i −0.252117 + 0.338651i −0.910106 0.414376i \(-0.864000\pi\)
0.657989 + 0.753027i \(0.271407\pi\)
\(858\) 0 0
\(859\) −38.1158 9.03362i −1.30050 0.308223i −0.478686 0.877986i \(-0.658887\pi\)
−0.821809 + 0.569763i \(0.807035\pi\)
\(860\) 5.59558 + 7.51617i 0.190808 + 0.256299i
\(861\) 0 0
\(862\) −28.3193 14.2225i −0.964560 0.484420i
\(863\) 12.2220 21.1691i 0.416040 0.720603i −0.579497 0.814975i \(-0.696751\pi\)
0.995537 + 0.0943715i \(0.0300842\pi\)
\(864\) 0 0
\(865\) 5.97048 + 10.3412i 0.203003 + 0.351611i
\(866\) −0.0760135 1.30510i −0.00258304 0.0443491i
\(867\) 0 0
\(868\) 1.04511 0.122156i 0.0354734 0.00414624i
\(869\) −3.69812 12.3526i −0.125450 0.419033i
\(870\) 0 0
\(871\) −13.9082 32.2428i −0.471261 1.09251i
\(872\) −15.1813 5.52553i −0.514102 0.187118i
\(873\) 0 0
\(874\) −2.53525 + 0.922757i −0.0857563 + 0.0312127i
\(875\) 1.55582 + 1.64907i 0.0525962 + 0.0557488i
\(876\) 0 0
\(877\) −12.1192 + 6.08649i −0.409236 + 0.205526i −0.641494 0.767128i \(-0.721685\pi\)
0.232258 + 0.972654i \(0.425389\pi\)
\(878\) −1.07629 + 18.4793i −0.0363232 + 0.623645i
\(879\) 0 0
\(880\) −0.677694 + 2.26366i −0.0228451 + 0.0763079i
\(881\) −2.84380 + 16.1280i −0.0958101 + 0.543366i 0.898686 + 0.438593i \(0.144523\pi\)
−0.994496 + 0.104774i \(0.966588\pi\)
\(882\) 0 0
\(883\) −7.98860 45.3056i −0.268838 1.52465i −0.757880 0.652394i \(-0.773765\pi\)
0.489042 0.872260i \(-0.337347\pi\)
\(884\) −22.5855 2.63986i −0.759631 0.0887882i
\(885\) 0 0
\(886\) −8.77015 + 9.29581i −0.294639 + 0.312299i
\(887\) −19.5768 + 45.3842i −0.657325 + 1.52385i 0.183773 + 0.982969i \(0.441169\pi\)
−0.841098 + 0.540882i \(0.818090\pi\)
\(888\) 0 0
\(889\) 2.66452 1.75248i 0.0893651 0.0587763i
\(890\) −0.393400 −0.0131868
\(891\) 0 0
\(892\) −11.7641 −0.393892
\(893\) 3.19694 2.10266i 0.106981 0.0703628i
\(894\) 0 0
\(895\) 3.54534 8.21901i 0.118508 0.274731i
\(896\) 0.117838 0.124901i 0.00393669 0.00417265i
\(897\) 0 0
\(898\) 20.7409 + 2.42427i 0.692133 + 0.0808988i
\(899\) −4.42618 25.1021i −0.147621 0.837201i
\(900\) 0 0
\(901\) −2.52300 + 14.3086i −0.0840532 + 0.476690i
\(902\) −6.35156 + 21.2157i −0.211484 + 0.706406i
\(903\) 0 0
\(904\) 3.28694 56.4345i 0.109322 1.87698i
\(905\) 9.46713 4.75457i 0.314698 0.158047i
\(906\) 0 0
\(907\) 32.8053 + 34.7716i 1.08928 + 1.15457i 0.987149 + 0.159802i \(0.0510856\pi\)
0.102134 + 0.994771i \(0.467433\pi\)
\(908\) −10.6226 + 3.86630i −0.352523 + 0.128308i
\(909\) 0 0
\(910\) 1.36993 + 0.498614i 0.0454127 + 0.0165289i
\(911\) −13.1560 30.4989i −0.435876 1.01047i −0.984656 0.174508i \(-0.944167\pi\)
0.548780 0.835967i \(-0.315093\pi\)
\(912\) 0 0
\(913\) 7.03582 + 23.5013i 0.232852 + 0.777778i
\(914\) 25.4372 2.97318i 0.841387 0.0983441i
\(915\) 0 0
\(916\) 0.0865461 + 1.48594i 0.00285956 + 0.0490968i
\(917\) 0.0395228 + 0.0684554i 0.00130516 + 0.00226060i
\(918\) 0 0
\(919\) 13.4983 23.3798i 0.445268 0.771228i −0.552802 0.833312i \(-0.686442\pi\)
0.998071 + 0.0620848i \(0.0197749\pi\)
\(920\) 3.15648 + 1.58525i 0.104066 + 0.0522640i
\(921\) 0 0
\(922\) 9.02111 + 12.1175i 0.297094 + 0.399067i
\(923\) 70.1901 + 16.6354i 2.31034 + 0.547560i
\(924\) 0 0
\(925\) 18.1828 24.4238i 0.597848 0.803049i
\(926\) 8.99236 7.54549i 0.295507 0.247960i
\(927\) 0 0
\(928\) −20.5250 17.2225i −0.673766 0.565357i
\(929\) 0.850096 0.201476i 0.0278907 0.00661023i −0.216647 0.976250i \(-0.569512\pi\)
0.244538 + 0.969640i \(0.421364\pi\)
\(930\) 0 0
\(931\) 10.7902 + 7.09682i 0.353634 + 0.232589i
\(932\) −17.4877 11.5018i −0.572828 0.376755i
\(933\) 0 0
\(934\) 40.4318 9.58252i 1.32297 0.313550i
\(935\) 5.57807 + 4.68056i 0.182422 + 0.153071i
\(936\) 0 0
\(937\) 12.6271 10.5954i 0.412511 0.346138i −0.412795 0.910824i \(-0.635447\pi\)
0.825306 + 0.564686i \(0.191003\pi\)
\(938\) −1.14561 + 1.53882i −0.0374054 + 0.0502442i
\(939\) 0 0
\(940\) −1.46927 0.348222i −0.0479222 0.0113578i
\(941\) 18.1527 + 24.3833i 0.591760 + 0.794872i 0.992620 0.121267i \(-0.0386959\pi\)
−0.400860 + 0.916140i \(0.631288\pi\)
\(942\) 0 0
\(943\) 13.8995 + 6.98060i 0.452631 + 0.227320i
\(944\) −0.964622 + 1.67077i −0.0313958 + 0.0543791i
\(945\) 0 0
\(946\) 12.2723 + 21.2563i 0.399008 + 0.691102i
\(947\) 0.743799 + 12.7705i 0.0241702 + 0.414987i 0.988592 + 0.150618i \(0.0481265\pi\)
−0.964422 + 0.264368i \(0.914837\pi\)
\(948\) 0 0
\(949\) 35.6585 4.16789i 1.15753 0.135295i
\(950\) −2.43858 8.14543i −0.0791181 0.264273i
\(951\) 0 0
\(952\) 1.63249 + 3.78455i 0.0529095 + 0.122658i
\(953\) −28.8328 10.4943i −0.933986 0.339943i −0.170198 0.985410i \(-0.554441\pi\)
−0.763788 + 0.645467i \(0.776663\pi\)
\(954\) 0 0
\(955\) −11.3367 + 4.12620i −0.366845 + 0.133521i
\(956\) 13.1135 + 13.8995i 0.424121 + 0.449542i
\(957\) 0 0
\(958\) −13.4557 + 6.75771i −0.434734 + 0.218332i
\(959\) 0.175504 3.01328i 0.00566731 0.0973039i
\(960\) 0 0
\(961\) 3.69361 12.3375i 0.119149 0.397985i
\(962\) 7.38006 41.8544i 0.237943 1.34944i
\(963\) 0 0
\(964\) 2.70821 + 15.3590i 0.0872257 + 0.494681i
\(965\) 18.6973 + 2.18540i 0.601886 + 0.0703504i
\(966\) 0 0
\(967\) −11.6005 + 12.2958i −0.373047 + 0.395407i −0.886513 0.462703i \(-0.846880\pi\)
0.513466 + 0.858110i \(0.328361\pi\)
\(968\) −9.34106 + 21.6550i −0.300233 + 0.696019i
\(969\) 0 0
\(970\) −7.67506 + 5.04797i −0.246431 + 0.162081i
\(971\) 53.7751 1.72572 0.862862 0.505439i \(-0.168670\pi\)
0.862862 + 0.505439i \(0.168670\pi\)
\(972\) 0 0
\(973\) −0.155227 −0.00497635
\(974\) −10.3545 + 6.81029i −0.331781 + 0.218216i
\(975\) 0 0
\(976\) −1.67853 + 3.89128i −0.0537286 + 0.124557i
\(977\) 10.1987 10.8100i 0.326285 0.345841i −0.543378 0.839488i \(-0.682855\pi\)
0.869663 + 0.493647i \(0.164336\pi\)
\(978\) 0 0
\(979\) 0.776743 + 0.0907883i 0.0248248 + 0.00290161i
\(980\) −0.884978 5.01896i −0.0282696 0.160325i
\(981\) 0 0
\(982\) 0.972752 5.51675i 0.0310418 0.176047i
\(983\) −5.10312 + 17.0456i −0.162764 + 0.543671i −0.999995 0.00317929i \(-0.998988\pi\)
0.837231 + 0.546850i \(0.184173\pi\)
\(984\) 0 0
\(985\) −0.0833566 + 1.43118i −0.00265596 + 0.0456011i
\(986\) 26.8932 13.5063i 0.856454 0.430127i
\(987\) 0 0
\(988\) 6.18068 + 6.55114i 0.196634 + 0.208420i
\(989\) 16.1990 5.89594i 0.515097 0.187480i
\(990\) 0 0
\(991\) 12.0174 + 4.37398i 0.381746 + 0.138944i 0.525763 0.850631i \(-0.323780\pi\)
−0.144017 + 0.989575i \(0.546002\pi\)
\(992\) 7.54477 + 17.4907i 0.239547 + 0.555332i
\(993\) 0 0
\(994\) −1.13028 3.77539i −0.0358503 0.119748i
\(995\) 9.05510 1.05839i 0.287066 0.0335532i
\(996\) 0 0
\(997\) 3.57455 + 61.3726i 0.113207 + 1.94369i 0.284940 + 0.958545i \(0.408026\pi\)
−0.171733 + 0.985144i \(0.554937\pi\)
\(998\) 2.94125 + 5.09439i 0.0931036 + 0.161260i
\(999\) 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 729.2.g.d.28.6 144
3.2 odd 2 729.2.g.a.28.3 144
9.2 odd 6 729.2.g.b.271.6 144
9.4 even 3 81.2.g.a.40.6 144
9.5 odd 6 243.2.g.a.91.3 144
9.7 even 3 729.2.g.c.271.3 144
81.2 odd 54 729.2.g.b.460.6 144
81.25 even 27 81.2.g.a.79.6 yes 144
81.29 odd 54 729.2.g.a.703.3 144
81.32 odd 54 6561.2.a.d.1.46 72
81.49 even 27 6561.2.a.c.1.27 72
81.52 even 27 inner 729.2.g.d.703.6 144
81.56 odd 54 243.2.g.a.235.3 144
81.79 even 27 729.2.g.c.460.3 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.40.6 144 9.4 even 3
81.2.g.a.79.6 yes 144 81.25 even 27
243.2.g.a.91.3 144 9.5 odd 6
243.2.g.a.235.3 144 81.56 odd 54
729.2.g.a.28.3 144 3.2 odd 2
729.2.g.a.703.3 144 81.29 odd 54
729.2.g.b.271.6 144 9.2 odd 6
729.2.g.b.460.6 144 81.2 odd 54
729.2.g.c.271.3 144 9.7 even 3
729.2.g.c.460.3 144 81.79 even 27
729.2.g.d.28.6 144 1.1 even 1 trivial
729.2.g.d.703.6 144 81.52 even 27 inner
6561.2.a.c.1.27 72 81.49 even 27
6561.2.a.d.1.46 72 81.32 odd 54