Properties

Label 855.2.bs.b.586.3
Level $855$
Weight $2$
Character 855.586
Analytic conductor $6.827$
Analytic rank $0$
Dimension $18$
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] = [855,2,Mod(226,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 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("855.226");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.bs (of order \(9\), 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: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} + 12 x^{16} - 8 x^{15} + 96 x^{14} - 75 x^{13} + 448 x^{12} - 405 x^{11} + 1521 x^{10} - 1294 x^{9} + 3333 x^{8} - 2616 x^{7} + 5113 x^{6} - 3126 x^{5} + 4032 x^{4} + \cdots + 361 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 586.3
Root \(0.785237 - 1.36007i\) of defining polynomial
Character \(\chi\) \(=\) 855.586
Dual form 855.2.bs.b.766.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.20305 + 1.00948i) q^{2} +(0.0809872 + 0.459301i) q^{4} +(0.173648 - 0.984808i) q^{5} +(2.00668 + 3.47568i) q^{7} +(1.20425 - 2.08582i) q^{8} +O(q^{10})\) \(q+(1.20305 + 1.00948i) q^{2} +(0.0809872 + 0.459301i) q^{4} +(0.173648 - 0.984808i) q^{5} +(2.00668 + 3.47568i) q^{7} +(1.20425 - 2.08582i) q^{8} +(1.20305 - 1.00948i) q^{10} +(1.38310 - 2.39560i) q^{11} +(-2.61923 - 0.953321i) q^{13} +(-1.09448 + 6.20713i) q^{14} +(4.43089 - 1.61271i) q^{16} +(2.76292 + 2.31836i) q^{17} +(1.79089 + 3.97401i) q^{19} +0.466387 q^{20} +(4.08226 - 1.48582i) q^{22} +(-0.237457 - 1.34669i) q^{23} +(-0.939693 - 0.342020i) q^{25} +(-2.18871 - 3.79096i) q^{26} +(-1.43387 + 1.20316i) q^{28} +(7.28463 - 6.11253i) q^{29} +(-0.776853 - 1.34555i) q^{31} +(2.43210 + 0.885212i) q^{32} +(0.983591 + 5.57822i) q^{34} +(3.77133 - 1.37265i) q^{35} +8.51183 q^{37} +(-1.85715 + 6.58880i) q^{38} +(-1.84502 - 1.54815i) q^{40} +(-6.21041 + 2.26041i) q^{41} +(-1.08613 + 6.15974i) q^{43} +(1.21232 + 0.441247i) q^{44} +(1.07378 - 1.85984i) q^{46} +(-6.97857 + 5.85572i) q^{47} +(-4.55356 + 7.88699i) q^{49} +(-0.785237 - 1.36007i) q^{50} +(0.225738 - 1.28022i) q^{52} +(0.684965 + 3.88463i) q^{53} +(-2.11903 - 1.77808i) q^{55} +9.66619 q^{56} +14.9343 q^{58} +(-2.76682 - 2.32164i) q^{59} +(-1.30047 - 7.37531i) q^{61} +(0.423711 - 2.40298i) q^{62} +(-2.68292 - 4.64695i) q^{64} +(-1.39366 + 2.41389i) q^{65} +(-11.1628 + 9.36668i) q^{67} +(-0.841066 + 1.45677i) q^{68} +(5.92277 + 2.15571i) q^{70} +(0.576318 - 3.26846i) q^{71} +(9.40420 - 3.42285i) q^{73} +(10.2402 + 8.59253i) q^{74} +(-1.68023 + 1.14440i) q^{76} +11.1018 q^{77} +(1.82991 - 0.666034i) q^{79} +(-0.818796 - 4.64362i) q^{80} +(-9.75329 - 3.54991i) q^{82} +(0.809339 + 1.40182i) q^{83} +(2.76292 - 2.31836i) q^{85} +(-7.52481 + 6.31406i) q^{86} +(-3.33120 - 5.76980i) q^{88} +(-11.5122 - 4.19008i) q^{89} +(-1.94252 - 11.0166i) q^{91} +(0.599304 - 0.218129i) q^{92} -14.3068 q^{94} +(4.22462 - 1.07360i) q^{95} +(-8.87934 - 7.45065i) q^{97} +(-13.4399 + 4.89173i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8} - 3 q^{10} - 3 q^{13} - 24 q^{14} + 21 q^{16} + 24 q^{17} - 12 q^{19} + 12 q^{20} + 15 q^{22} - 21 q^{23} + 21 q^{26} - 24 q^{28} + 9 q^{29} + 30 q^{31} - 45 q^{32} + 24 q^{34} + 6 q^{35} - 60 q^{37} + 15 q^{38} - 6 q^{40} + 6 q^{41} - 6 q^{43} + 30 q^{44} + 21 q^{46} - 33 q^{47} - 3 q^{49} + 9 q^{52} - 24 q^{53} - 3 q^{55} + 72 q^{56} + 36 q^{58} - 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{64} - 3 q^{65} - 24 q^{67} + 3 q^{68} + 39 q^{70} - 24 q^{71} + 6 q^{73} + 39 q^{74} + 27 q^{76} - 24 q^{77} + 9 q^{79} - 33 q^{80} - 57 q^{82} + 24 q^{85} + 33 q^{86} + 39 q^{88} + 6 q^{89} - 6 q^{91} + 66 q^{92} - 66 q^{94} + 15 q^{95} - 87 q^{97} - 39 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.20305 + 1.00948i 0.850687 + 0.713811i 0.959941 0.280203i \(-0.0904018\pi\)
−0.109254 + 0.994014i \(0.534846\pi\)
\(3\) 0 0
\(4\) 0.0809872 + 0.459301i 0.0404936 + 0.229651i
\(5\) 0.173648 0.984808i 0.0776578 0.440419i
\(6\) 0 0
\(7\) 2.00668 + 3.47568i 0.758455 + 1.31368i 0.943638 + 0.330979i \(0.107379\pi\)
−0.185183 + 0.982704i \(0.559288\pi\)
\(8\) 1.20425 2.08582i 0.425766 0.737449i
\(9\) 0 0
\(10\) 1.20305 1.00948i 0.380439 0.319226i
\(11\) 1.38310 2.39560i 0.417021 0.722301i −0.578618 0.815599i \(-0.696408\pi\)
0.995638 + 0.0932980i \(0.0297409\pi\)
\(12\) 0 0
\(13\) −2.61923 0.953321i −0.726443 0.264404i −0.0477847 0.998858i \(-0.515216\pi\)
−0.678659 + 0.734454i \(0.737438\pi\)
\(14\) −1.09448 + 6.20713i −0.292513 + 1.65893i
\(15\) 0 0
\(16\) 4.43089 1.61271i 1.10772 0.403178i
\(17\) 2.76292 + 2.31836i 0.670106 + 0.562286i 0.913097 0.407743i \(-0.133684\pi\)
−0.242991 + 0.970029i \(0.578129\pi\)
\(18\) 0 0
\(19\) 1.79089 + 3.97401i 0.410858 + 0.911699i
\(20\) 0.466387 0.104287
\(21\) 0 0
\(22\) 4.08226 1.48582i 0.870340 0.316778i
\(23\) −0.237457 1.34669i −0.0495133 0.280804i 0.949991 0.312276i \(-0.101091\pi\)
−0.999505 + 0.0314725i \(0.989980\pi\)
\(24\) 0 0
\(25\) −0.939693 0.342020i −0.187939 0.0684040i
\(26\) −2.18871 3.79096i −0.429241 0.743468i
\(27\) 0 0
\(28\) −1.43387 + 1.20316i −0.270975 + 0.227375i
\(29\) 7.28463 6.11253i 1.35272 1.13507i 0.374564 0.927201i \(-0.377792\pi\)
0.978157 0.207866i \(-0.0666520\pi\)
\(30\) 0 0
\(31\) −0.776853 1.34555i −0.139527 0.241668i 0.787791 0.615943i \(-0.211225\pi\)
−0.927318 + 0.374275i \(0.877891\pi\)
\(32\) 2.43210 + 0.885212i 0.429939 + 0.156485i
\(33\) 0 0
\(34\) 0.983591 + 5.57822i 0.168685 + 0.956658i
\(35\) 3.77133 1.37265i 0.637471 0.232021i
\(36\) 0 0
\(37\) 8.51183 1.39934 0.699668 0.714468i \(-0.253331\pi\)
0.699668 + 0.714468i \(0.253331\pi\)
\(38\) −1.85715 + 6.58880i −0.301269 + 1.06885i
\(39\) 0 0
\(40\) −1.84502 1.54815i −0.291723 0.244785i
\(41\) −6.21041 + 2.26041i −0.969904 + 0.353016i −0.777907 0.628379i \(-0.783719\pi\)
−0.191997 + 0.981396i \(0.561496\pi\)
\(42\) 0 0
\(43\) −1.08613 + 6.15974i −0.165633 + 0.939351i 0.782776 + 0.622303i \(0.213803\pi\)
−0.948409 + 0.317048i \(0.897308\pi\)
\(44\) 1.21232 + 0.441247i 0.182764 + 0.0665205i
\(45\) 0 0
\(46\) 1.07378 1.85984i 0.158320 0.274219i
\(47\) −6.97857 + 5.85572i −1.01793 + 0.854144i −0.989366 0.145448i \(-0.953538\pi\)
−0.0285637 + 0.999592i \(0.509093\pi\)
\(48\) 0 0
\(49\) −4.55356 + 7.88699i −0.650508 + 1.12671i
\(50\) −0.785237 1.36007i −0.111049 0.192343i
\(51\) 0 0
\(52\) 0.225738 1.28022i 0.0313042 0.177535i
\(53\) 0.684965 + 3.88463i 0.0940872 + 0.533595i 0.995023 + 0.0996432i \(0.0317701\pi\)
−0.900936 + 0.433952i \(0.857119\pi\)
\(54\) 0 0
\(55\) −2.11903 1.77808i −0.285730 0.239756i
\(56\) 9.66619 1.29170
\(57\) 0 0
\(58\) 14.9343 1.96096
\(59\) −2.76682 2.32164i −0.360209 0.302251i 0.444665 0.895697i \(-0.353323\pi\)
−0.804874 + 0.593446i \(0.797767\pi\)
\(60\) 0 0
\(61\) −1.30047 7.37531i −0.166508 0.944311i −0.947496 0.319766i \(-0.896396\pi\)
0.780989 0.624545i \(-0.214716\pi\)
\(62\) 0.423711 2.40298i 0.0538113 0.305179i
\(63\) 0 0
\(64\) −2.68292 4.64695i −0.335365 0.580869i
\(65\) −1.39366 + 2.41389i −0.172863 + 0.299407i
\(66\) 0 0
\(67\) −11.1628 + 9.36668i −1.36375 + 1.14432i −0.388946 + 0.921261i \(0.627161\pi\)
−0.974804 + 0.223061i \(0.928395\pi\)
\(68\) −0.841066 + 1.45677i −0.101994 + 0.176659i
\(69\) 0 0
\(70\) 5.92277 + 2.15571i 0.707907 + 0.257657i
\(71\) 0.576318 3.26846i 0.0683964 0.387895i −0.931323 0.364195i \(-0.881344\pi\)
0.999719 0.0237002i \(-0.00754470\pi\)
\(72\) 0 0
\(73\) 9.40420 3.42285i 1.10068 0.400614i 0.273112 0.961982i \(-0.411947\pi\)
0.827566 + 0.561368i \(0.189725\pi\)
\(74\) 10.2402 + 8.59253i 1.19040 + 0.998862i
\(75\) 0 0
\(76\) −1.68023 + 1.14440i −0.192735 + 0.131272i
\(77\) 11.1018 1.26517
\(78\) 0 0
\(79\) 1.82991 0.666034i 0.205881 0.0749347i −0.237021 0.971505i \(-0.576171\pi\)
0.442902 + 0.896570i \(0.353949\pi\)
\(80\) −0.818796 4.64362i −0.0915441 0.519173i
\(81\) 0 0
\(82\) −9.75329 3.54991i −1.07707 0.392022i
\(83\) 0.809339 + 1.40182i 0.0888365 + 0.153869i 0.907020 0.421088i \(-0.138352\pi\)
−0.818183 + 0.574958i \(0.805018\pi\)
\(84\) 0 0
\(85\) 2.76292 2.31836i 0.299680 0.251462i
\(86\) −7.52481 + 6.31406i −0.811421 + 0.680863i
\(87\) 0 0
\(88\) −3.33120 5.76980i −0.355107 0.615063i
\(89\) −11.5122 4.19008i −1.22029 0.444148i −0.350025 0.936740i \(-0.613827\pi\)
−0.870260 + 0.492593i \(0.836049\pi\)
\(90\) 0 0
\(91\) −1.94252 11.0166i −0.203632 1.15485i
\(92\) 0.599304 0.218129i 0.0624818 0.0227415i
\(93\) 0 0
\(94\) −14.3068 −1.47564
\(95\) 4.22462 1.07360i 0.433436 0.110149i
\(96\) 0 0
\(97\) −8.87934 7.45065i −0.901560 0.756499i 0.0689344 0.997621i \(-0.478040\pi\)
−0.970495 + 0.241122i \(0.922485\pi\)
\(98\) −13.4399 + 4.89173i −1.35764 + 0.494140i
\(99\) 0 0
\(100\) 0.0809872 0.459301i 0.00809872 0.0459301i
\(101\) −6.56131 2.38812i −0.652874 0.237627i −0.00571740 0.999984i \(-0.501820\pi\)
−0.647157 + 0.762357i \(0.724042\pi\)
\(102\) 0 0
\(103\) −5.06688 + 8.77610i −0.499255 + 0.864735i −1.00000 0.000860217i \(-0.999726\pi\)
0.500745 + 0.865595i \(0.333060\pi\)
\(104\) −5.14266 + 4.31521i −0.504279 + 0.423141i
\(105\) 0 0
\(106\) −3.09741 + 5.36487i −0.300847 + 0.521083i
\(107\) −5.89176 10.2048i −0.569578 0.986538i −0.996608 0.0823003i \(-0.973773\pi\)
0.427030 0.904238i \(-0.359560\pi\)
\(108\) 0 0
\(109\) −0.278545 + 1.57971i −0.0266797 + 0.151308i −0.995237 0.0974809i \(-0.968922\pi\)
0.968558 + 0.248789i \(0.0800326\pi\)
\(110\) −0.754371 4.27825i −0.0719264 0.407915i
\(111\) 0 0
\(112\) 14.4967 + 12.1641i 1.36981 + 1.14940i
\(113\) −12.9449 −1.21775 −0.608876 0.793266i \(-0.708379\pi\)
−0.608876 + 0.793266i \(0.708379\pi\)
\(114\) 0 0
\(115\) −1.36746 −0.127517
\(116\) 3.39745 + 2.85080i 0.315445 + 0.264690i
\(117\) 0 0
\(118\) −0.984981 5.58610i −0.0906748 0.514242i
\(119\) −2.51358 + 14.2552i −0.230420 + 1.30677i
\(120\) 0 0
\(121\) 1.67406 + 2.89956i 0.152187 + 0.263596i
\(122\) 5.88070 10.1857i 0.532414 0.922168i
\(123\) 0 0
\(124\) 0.555097 0.465781i 0.0498492 0.0418284i
\(125\) −0.500000 + 0.866025i −0.0447214 + 0.0774597i
\(126\) 0 0
\(127\) 7.79759 + 2.83809i 0.691924 + 0.251840i 0.663959 0.747769i \(-0.268875\pi\)
0.0279654 + 0.999609i \(0.491097\pi\)
\(128\) 2.36218 13.3966i 0.208790 1.18410i
\(129\) 0 0
\(130\) −4.11343 + 1.49717i −0.360772 + 0.131310i
\(131\) 4.98836 + 4.18573i 0.435835 + 0.365709i 0.834148 0.551540i \(-0.185960\pi\)
−0.398313 + 0.917250i \(0.630404\pi\)
\(132\) 0 0
\(133\) −10.2186 + 14.1991i −0.886066 + 1.23122i
\(134\) −22.8849 −1.97695
\(135\) 0 0
\(136\) 8.16293 2.97106i 0.699966 0.254767i
\(137\) −2.58191 14.6427i −0.220587 1.25101i −0.870943 0.491384i \(-0.836491\pi\)
0.650356 0.759630i \(-0.274620\pi\)
\(138\) 0 0
\(139\) −9.35768 3.40592i −0.793708 0.288886i −0.0868313 0.996223i \(-0.527674\pi\)
−0.706876 + 0.707337i \(0.749896\pi\)
\(140\) 0.935890 + 1.62101i 0.0790972 + 0.137000i
\(141\) 0 0
\(142\) 3.99279 3.35035i 0.335068 0.281155i
\(143\) −5.90644 + 4.95609i −0.493921 + 0.414449i
\(144\) 0 0
\(145\) −4.75470 8.23538i −0.394856 0.683911i
\(146\) 14.7690 + 5.37549i 1.22229 + 0.444879i
\(147\) 0 0
\(148\) 0.689349 + 3.90949i 0.0566642 + 0.321358i
\(149\) −1.34529 + 0.489644i −0.110210 + 0.0401132i −0.396537 0.918019i \(-0.629788\pi\)
0.286326 + 0.958132i \(0.407566\pi\)
\(150\) 0 0
\(151\) −8.18383 −0.665990 −0.332995 0.942929i \(-0.608059\pi\)
−0.332995 + 0.942929i \(0.608059\pi\)
\(152\) 10.4457 + 1.05022i 0.847262 + 0.0851841i
\(153\) 0 0
\(154\) 13.3560 + 11.2070i 1.07626 + 0.903089i
\(155\) −1.46001 + 0.531399i −0.117270 + 0.0426830i
\(156\) 0 0
\(157\) −1.36055 + 7.71609i −0.108584 + 0.615811i 0.881144 + 0.472848i \(0.156774\pi\)
−0.989728 + 0.142963i \(0.954337\pi\)
\(158\) 2.87383 + 1.04599i 0.228630 + 0.0832144i
\(159\) 0 0
\(160\) 1.29409 2.24144i 0.102307 0.177201i
\(161\) 4.20415 3.52770i 0.331333 0.278022i
\(162\) 0 0
\(163\) 9.64968 16.7137i 0.755821 1.30912i −0.189144 0.981949i \(-0.560571\pi\)
0.944965 0.327171i \(-0.106095\pi\)
\(164\) −1.54117 2.66939i −0.120345 0.208444i
\(165\) 0 0
\(166\) −0.441429 + 2.50347i −0.0342616 + 0.194307i
\(167\) −1.63050 9.24703i −0.126172 0.715556i −0.980605 0.195995i \(-0.937206\pi\)
0.854433 0.519562i \(-0.173905\pi\)
\(168\) 0 0
\(169\) −4.00704 3.36231i −0.308234 0.258639i
\(170\) 5.66428 0.434430
\(171\) 0 0
\(172\) −2.91714 −0.222430
\(173\) −6.36647 5.34210i −0.484034 0.406153i 0.367849 0.929886i \(-0.380094\pi\)
−0.851882 + 0.523733i \(0.824539\pi\)
\(174\) 0 0
\(175\) −0.696914 3.95239i −0.0526817 0.298773i
\(176\) 2.26495 12.8452i 0.170727 0.968243i
\(177\) 0 0
\(178\) −9.61991 16.6622i −0.721043 1.24888i
\(179\) −9.26593 + 16.0491i −0.692568 + 1.19956i 0.278425 + 0.960458i \(0.410187\pi\)
−0.970994 + 0.239105i \(0.923146\pi\)
\(180\) 0 0
\(181\) 8.67868 7.28228i 0.645081 0.541288i −0.260493 0.965476i \(-0.583885\pi\)
0.905574 + 0.424188i \(0.139441\pi\)
\(182\) 8.78409 15.2145i 0.651120 1.12777i
\(183\) 0 0
\(184\) −3.09491 1.12645i −0.228160 0.0830433i
\(185\) 1.47806 8.38252i 0.108669 0.616295i
\(186\) 0 0
\(187\) 9.37527 3.41232i 0.685587 0.249533i
\(188\) −3.25471 2.73103i −0.237374 0.199181i
\(189\) 0 0
\(190\) 6.16622 + 2.97307i 0.447344 + 0.215689i
\(191\) −11.8879 −0.860175 −0.430088 0.902787i \(-0.641517\pi\)
−0.430088 + 0.902787i \(0.641517\pi\)
\(192\) 0 0
\(193\) 0.900069 0.327598i 0.0647884 0.0235810i −0.309423 0.950925i \(-0.600136\pi\)
0.374211 + 0.927344i \(0.377914\pi\)
\(194\) −3.16102 17.9270i −0.226948 1.28709i
\(195\) 0 0
\(196\) −3.99128 1.45271i −0.285092 0.103765i
\(197\) 7.13881 + 12.3648i 0.508619 + 0.880955i 0.999950 + 0.00998159i \(0.00317729\pi\)
−0.491331 + 0.870973i \(0.663489\pi\)
\(198\) 0 0
\(199\) −5.94888 + 4.99170i −0.421705 + 0.353852i −0.828811 0.559528i \(-0.810982\pi\)
0.407106 + 0.913381i \(0.366538\pi\)
\(200\) −1.84502 + 1.54815i −0.130462 + 0.109471i
\(201\) 0 0
\(202\) −5.48283 9.49655i −0.385771 0.668175i
\(203\) 35.8631 + 13.0531i 2.51710 + 0.916148i
\(204\) 0 0
\(205\) 1.14764 + 6.50858i 0.0801545 + 0.454579i
\(206\) −14.9550 + 5.44319i −1.04197 + 0.379245i
\(207\) 0 0
\(208\) −13.1430 −0.911300
\(209\) 11.9971 + 1.20620i 0.829858 + 0.0834343i
\(210\) 0 0
\(211\) 5.83936 + 4.89980i 0.401998 + 0.337316i 0.821265 0.570546i \(-0.193269\pi\)
−0.419267 + 0.907863i \(0.637713\pi\)
\(212\) −1.72874 + 0.629211i −0.118731 + 0.0432144i
\(213\) 0 0
\(214\) 3.21348 18.2246i 0.219669 1.24581i
\(215\) 5.87755 + 2.13925i 0.400846 + 0.145896i
\(216\) 0 0
\(217\) 3.11779 5.40018i 0.211650 0.366588i
\(218\) −1.92979 + 1.61928i −0.130702 + 0.109672i
\(219\) 0 0
\(220\) 0.645060 1.11728i 0.0434899 0.0753268i
\(221\) −5.02657 8.70627i −0.338123 0.585647i
\(222\) 0 0
\(223\) −1.38976 + 7.88173i −0.0930653 + 0.527799i 0.902258 + 0.431197i \(0.141909\pi\)
−0.995323 + 0.0966024i \(0.969202\pi\)
\(224\) 1.80374 + 10.2295i 0.120518 + 0.683490i
\(225\) 0 0
\(226\) −15.5734 13.0676i −1.03592 0.869244i
\(227\) 17.7409 1.17750 0.588752 0.808314i \(-0.299619\pi\)
0.588752 + 0.808314i \(0.299619\pi\)
\(228\) 0 0
\(229\) −24.2231 −1.60071 −0.800354 0.599528i \(-0.795355\pi\)
−0.800354 + 0.599528i \(0.795355\pi\)
\(230\) −1.64513 1.38043i −0.108477 0.0910227i
\(231\) 0 0
\(232\) −3.97713 22.5554i −0.261111 1.48084i
\(233\) −2.37014 + 13.4418i −0.155273 + 0.880598i 0.803262 + 0.595625i \(0.203096\pi\)
−0.958536 + 0.284973i \(0.908015\pi\)
\(234\) 0 0
\(235\) 4.55494 + 7.88939i 0.297132 + 0.514647i
\(236\) 0.842254 1.45883i 0.0548260 0.0949615i
\(237\) 0 0
\(238\) −17.4144 + 14.6124i −1.12880 + 0.947180i
\(239\) 1.86882 3.23689i 0.120884 0.209377i −0.799233 0.601022i \(-0.794760\pi\)
0.920117 + 0.391645i \(0.128094\pi\)
\(240\) 0 0
\(241\) 4.96295 + 1.80636i 0.319691 + 0.116358i 0.496881 0.867819i \(-0.334478\pi\)
−0.177190 + 0.984177i \(0.556701\pi\)
\(242\) −0.913066 + 5.17826i −0.0586941 + 0.332871i
\(243\) 0 0
\(244\) 3.28217 1.19461i 0.210119 0.0764771i
\(245\) 6.97645 + 5.85394i 0.445709 + 0.373994i
\(246\) 0 0
\(247\) −0.902244 12.1161i −0.0574084 0.770930i
\(248\) −3.74210 −0.237623
\(249\) 0 0
\(250\) −1.47576 + 0.537134i −0.0933354 + 0.0339713i
\(251\) 2.17833 + 12.3539i 0.137495 + 0.779772i 0.973090 + 0.230426i \(0.0740119\pi\)
−0.835595 + 0.549346i \(0.814877\pi\)
\(252\) 0 0
\(253\) −3.55455 1.29375i −0.223473 0.0813375i
\(254\) 6.51591 + 11.2859i 0.408845 + 0.708140i
\(255\) 0 0
\(256\) 8.14452 6.83406i 0.509032 0.427129i
\(257\) −6.58784 + 5.52786i −0.410938 + 0.344818i −0.824703 0.565565i \(-0.808658\pi\)
0.413765 + 0.910384i \(0.364214\pi\)
\(258\) 0 0
\(259\) 17.0806 + 29.5844i 1.06133 + 1.83828i
\(260\) −1.22157 0.444616i −0.0757587 0.0275739i
\(261\) 0 0
\(262\) 1.77584 + 10.0713i 0.109712 + 0.622208i
\(263\) 25.0807 9.12863i 1.54654 0.562895i 0.578939 0.815371i \(-0.303467\pi\)
0.967603 + 0.252475i \(0.0812447\pi\)
\(264\) 0 0
\(265\) 3.94456 0.242312
\(266\) −26.6273 + 6.76679i −1.63262 + 0.414899i
\(267\) 0 0
\(268\) −5.20617 4.36849i −0.318017 0.266848i
\(269\) −3.10399 + 1.12976i −0.189254 + 0.0688828i −0.434909 0.900475i \(-0.643219\pi\)
0.245655 + 0.969357i \(0.420997\pi\)
\(270\) 0 0
\(271\) −3.19296 + 18.1082i −0.193959 + 1.09999i 0.719935 + 0.694041i \(0.244172\pi\)
−0.913894 + 0.405953i \(0.866940\pi\)
\(272\) 15.9810 + 5.81662i 0.968993 + 0.352685i
\(273\) 0 0
\(274\) 11.6754 20.2224i 0.705336 1.22168i
\(275\) −2.11903 + 1.77808i −0.127783 + 0.107222i
\(276\) 0 0
\(277\) −13.3893 + 23.1910i −0.804488 + 1.39341i 0.112148 + 0.993691i \(0.464227\pi\)
−0.916636 + 0.399722i \(0.869107\pi\)
\(278\) −7.81957 13.5439i −0.468987 0.812308i
\(279\) 0 0
\(280\) 1.67852 9.51934i 0.100311 0.568889i
\(281\) −3.74145 21.2188i −0.223196 1.26581i −0.866103 0.499865i \(-0.833383\pi\)
0.642907 0.765945i \(-0.277728\pi\)
\(282\) 0 0
\(283\) 14.0547 + 11.7933i 0.835465 + 0.701038i 0.956539 0.291605i \(-0.0941894\pi\)
−0.121074 + 0.992643i \(0.538634\pi\)
\(284\) 1.54788 0.0918499
\(285\) 0 0
\(286\) −12.1088 −0.716010
\(287\) −20.3188 17.0495i −1.19938 1.00640i
\(288\) 0 0
\(289\) −0.693114 3.93084i −0.0407714 0.231226i
\(290\) 2.59331 14.7074i 0.152284 0.863647i
\(291\) 0 0
\(292\) 2.33374 + 4.04215i 0.136572 + 0.236549i
\(293\) −4.64436 + 8.04426i −0.271326 + 0.469951i −0.969202 0.246268i \(-0.920796\pi\)
0.697875 + 0.716219i \(0.254129\pi\)
\(294\) 0 0
\(295\) −2.76682 + 2.32164i −0.161090 + 0.135171i
\(296\) 10.2504 17.7542i 0.595791 1.03194i
\(297\) 0 0
\(298\) −2.11274 0.768973i −0.122388 0.0445454i
\(299\) −0.661871 + 3.75366i −0.0382770 + 0.217079i
\(300\) 0 0
\(301\) −23.5888 + 8.58561i −1.35963 + 0.494867i
\(302\) −9.84557 8.26142i −0.566549 0.475391i
\(303\) 0 0
\(304\) 14.3442 + 14.7202i 0.822694 + 0.844261i
\(305\) −7.48908 −0.428824
\(306\) 0 0
\(307\) 10.3508 3.76739i 0.590753 0.215017i −0.0293076 0.999570i \(-0.509330\pi\)
0.620061 + 0.784554i \(0.287108\pi\)
\(308\) 0.899102 + 5.09906i 0.0512311 + 0.290546i
\(309\) 0 0
\(310\) −2.29290 0.834547i −0.130228 0.0473991i
\(311\) 12.6911 + 21.9816i 0.719644 + 1.24646i 0.961141 + 0.276058i \(0.0890283\pi\)
−0.241497 + 0.970402i \(0.577638\pi\)
\(312\) 0 0
\(313\) 16.1297 13.5345i 0.911707 0.765013i −0.0607363 0.998154i \(-0.519345\pi\)
0.972443 + 0.233141i \(0.0749004\pi\)
\(314\) −9.42606 + 7.90940i −0.531943 + 0.446353i
\(315\) 0 0
\(316\) 0.454110 + 0.786541i 0.0255457 + 0.0442464i
\(317\) 3.76804 + 1.37145i 0.211634 + 0.0770285i 0.445662 0.895201i \(-0.352968\pi\)
−0.234028 + 0.972230i \(0.575191\pi\)
\(318\) 0 0
\(319\) −4.56780 25.9053i −0.255748 1.45042i
\(320\) −5.04224 + 1.83522i −0.281870 + 0.102592i
\(321\) 0 0
\(322\) 8.61896 0.480316
\(323\) −4.26511 + 15.1318i −0.237317 + 0.841955i
\(324\) 0 0
\(325\) 2.13521 + 1.79166i 0.118440 + 0.0993833i
\(326\) 28.4813 10.3663i 1.57743 0.574138i
\(327\) 0 0
\(328\) −2.76409 + 15.6759i −0.152621 + 0.865557i
\(329\) −34.3564 12.5047i −1.89413 0.689406i
\(330\) 0 0
\(331\) 16.0680 27.8306i 0.883176 1.52971i 0.0353860 0.999374i \(-0.488734\pi\)
0.847790 0.530332i \(-0.177933\pi\)
\(332\) −0.578309 + 0.485259i −0.0317389 + 0.0266321i
\(333\) 0 0
\(334\) 7.37312 12.7706i 0.403439 0.698777i
\(335\) 7.28598 + 12.6197i 0.398076 + 0.689488i
\(336\) 0 0
\(337\) 4.07164 23.0914i 0.221796 1.25787i −0.646920 0.762558i \(-0.723943\pi\)
0.868716 0.495310i \(-0.164946\pi\)
\(338\) −1.42650 8.09007i −0.0775912 0.440042i
\(339\) 0 0
\(340\) 1.28859 + 1.08125i 0.0698835 + 0.0586392i
\(341\) −4.29786 −0.232742
\(342\) 0 0
\(343\) −8.45661 −0.456614
\(344\) 11.5401 + 9.68333i 0.622203 + 0.522090i
\(345\) 0 0
\(346\) −2.26645 12.8537i −0.121845 0.691017i
\(347\) −1.12759 + 6.39487i −0.0605321 + 0.343295i 0.939468 + 0.342638i \(0.111320\pi\)
−1.00000 0.000657202i \(0.999791\pi\)
\(348\) 0 0
\(349\) 13.6004 + 23.5566i 0.728013 + 1.26096i 0.957722 + 0.287696i \(0.0928893\pi\)
−0.229709 + 0.973259i \(0.573777\pi\)
\(350\) 3.15144 5.45846i 0.168452 0.291767i
\(351\) 0 0
\(352\) 5.48446 4.60201i 0.292323 0.245288i
\(353\) −3.28062 + 5.68221i −0.174610 + 0.302433i −0.940026 0.341102i \(-0.889200\pi\)
0.765416 + 0.643536i \(0.222533\pi\)
\(354\) 0 0
\(355\) −3.11873 1.13513i −0.165525 0.0602462i
\(356\) 0.992172 5.62689i 0.0525850 0.298224i
\(357\) 0 0
\(358\) −27.3486 + 9.95408i −1.44542 + 0.526090i
\(359\) 2.09279 + 1.75606i 0.110453 + 0.0926813i 0.696342 0.717710i \(-0.254810\pi\)
−0.585888 + 0.810392i \(0.699254\pi\)
\(360\) 0 0
\(361\) −12.5854 + 14.2340i −0.662391 + 0.749158i
\(362\) 17.7922 0.935139
\(363\) 0 0
\(364\) 4.90262 1.78441i 0.256967 0.0935284i
\(365\) −1.73783 9.85570i −0.0909619 0.515871i
\(366\) 0 0
\(367\) −6.18227 2.25016i −0.322712 0.117457i 0.175584 0.984464i \(-0.443819\pi\)
−0.498296 + 0.867007i \(0.666041\pi\)
\(368\) −3.22397 5.58408i −0.168061 0.291090i
\(369\) 0 0
\(370\) 10.2402 8.59253i 0.532362 0.446704i
\(371\) −12.1272 + 10.1759i −0.629614 + 0.528309i
\(372\) 0 0
\(373\) 4.27996 + 7.41311i 0.221608 + 0.383836i 0.955296 0.295650i \(-0.0955361\pi\)
−0.733688 + 0.679486i \(0.762203\pi\)
\(374\) 14.7236 + 5.35896i 0.761340 + 0.277105i
\(375\) 0 0
\(376\) 3.81004 + 21.6078i 0.196488 + 1.11434i
\(377\) −24.9073 + 9.06551i −1.28279 + 0.466898i
\(378\) 0 0
\(379\) 14.2477 0.731856 0.365928 0.930643i \(-0.380752\pi\)
0.365928 + 0.930643i \(0.380752\pi\)
\(380\) 0.835247 + 1.85342i 0.0428472 + 0.0950786i
\(381\) 0 0
\(382\) −14.3017 12.0006i −0.731739 0.614002i
\(383\) 20.0778 7.30773i 1.02593 0.373408i 0.226399 0.974035i \(-0.427305\pi\)
0.799529 + 0.600627i \(0.205082\pi\)
\(384\) 0 0
\(385\) 1.92780 10.9331i 0.0982500 0.557204i
\(386\) 1.41353 + 0.514485i 0.0719470 + 0.0261866i
\(387\) 0 0
\(388\) 2.70298 4.68170i 0.137223 0.237677i
\(389\) −11.7148 + 9.82991i −0.593965 + 0.498396i −0.889500 0.456936i \(-0.848947\pi\)
0.295534 + 0.955332i \(0.404502\pi\)
\(390\) 0 0
\(391\) 2.46604 4.27130i 0.124713 0.216009i
\(392\) 10.9672 + 18.9958i 0.553929 + 0.959433i
\(393\) 0 0
\(394\) −3.89365 + 22.0820i −0.196159 + 1.11247i
\(395\) −0.338154 1.91777i −0.0170144 0.0964934i
\(396\) 0 0
\(397\) 24.9746 + 20.9562i 1.25344 + 1.05176i 0.996349 + 0.0853727i \(0.0272081\pi\)
0.257090 + 0.966387i \(0.417236\pi\)
\(398\) −12.1958 −0.611322
\(399\) 0 0
\(400\) −4.71526 −0.235763
\(401\) 13.2617 + 11.1279i 0.662258 + 0.555701i 0.910763 0.412930i \(-0.135495\pi\)
−0.248505 + 0.968631i \(0.579939\pi\)
\(402\) 0 0
\(403\) 0.752015 + 4.26489i 0.0374605 + 0.212449i
\(404\) 0.565485 3.20702i 0.0281339 0.159555i
\(405\) 0 0
\(406\) 29.9683 + 51.9067i 1.48730 + 2.57609i
\(407\) 11.7727 20.3910i 0.583552 1.01074i
\(408\) 0 0
\(409\) −8.29411 + 6.95959i −0.410117 + 0.344129i −0.824389 0.566024i \(-0.808481\pi\)
0.414271 + 0.910153i \(0.364036\pi\)
\(410\) −5.18962 + 8.98868i −0.256297 + 0.443919i
\(411\) 0 0
\(412\) −4.44123 1.61647i −0.218803 0.0796379i
\(413\) 2.51713 14.2754i 0.123860 0.702445i
\(414\) 0 0
\(415\) 1.52106 0.553620i 0.0746659 0.0271761i
\(416\) −5.52633 4.63715i −0.270951 0.227355i
\(417\) 0 0
\(418\) 13.2155 + 13.5620i 0.646392 + 0.663338i
\(419\) −33.9763 −1.65985 −0.829925 0.557876i \(-0.811617\pi\)
−0.829925 + 0.557876i \(0.811617\pi\)
\(420\) 0 0
\(421\) −7.80720 + 2.84159i −0.380500 + 0.138491i −0.525187 0.850987i \(-0.676005\pi\)
0.144687 + 0.989477i \(0.453782\pi\)
\(422\) 2.07880 + 11.7894i 0.101194 + 0.573901i
\(423\) 0 0
\(424\) 8.92752 + 3.24935i 0.433559 + 0.157802i
\(425\) −1.80337 3.12352i −0.0874761 0.151513i
\(426\) 0 0
\(427\) 23.0246 19.3199i 1.11424 0.934956i
\(428\) 4.20993 3.53255i 0.203495 0.170752i
\(429\) 0 0
\(430\) 4.91147 + 8.50691i 0.236852 + 0.410240i
\(431\) −11.3983 4.14863i −0.549035 0.199832i 0.0525827 0.998617i \(-0.483255\pi\)
−0.601618 + 0.798784i \(0.705477\pi\)
\(432\) 0 0
\(433\) −0.943849 5.35283i −0.0453585 0.257241i 0.953693 0.300781i \(-0.0972474\pi\)
−0.999052 + 0.0435404i \(0.986136\pi\)
\(434\) 9.20225 3.34934i 0.441722 0.160774i
\(435\) 0 0
\(436\) −0.748119 −0.0358284
\(437\) 4.92648 3.35542i 0.235666 0.160512i
\(438\) 0 0
\(439\) −19.4428 16.3144i −0.927952 0.778644i 0.0474965 0.998871i \(-0.484876\pi\)
−0.975449 + 0.220227i \(0.929320\pi\)
\(440\) −6.26060 + 2.27867i −0.298463 + 0.108632i
\(441\) 0 0
\(442\) 2.74159 15.5483i 0.130404 0.739558i
\(443\) −4.62446 1.68317i −0.219715 0.0799697i 0.229817 0.973234i \(-0.426187\pi\)
−0.449532 + 0.893264i \(0.648409\pi\)
\(444\) 0 0
\(445\) −6.12549 + 10.6097i −0.290376 + 0.502946i
\(446\) −9.62841 + 8.07919i −0.455918 + 0.382561i
\(447\) 0 0
\(448\) 10.7675 18.6499i 0.508718 0.881125i
\(449\) 2.03325 + 3.52169i 0.0959548 + 0.166199i 0.910007 0.414594i \(-0.136076\pi\)
−0.814052 + 0.580792i \(0.802743\pi\)
\(450\) 0 0
\(451\) −3.17460 + 18.0041i −0.149486 + 0.847778i
\(452\) −1.04837 5.94560i −0.0493111 0.279657i
\(453\) 0 0
\(454\) 21.3432 + 17.9091i 1.00169 + 0.840515i
\(455\) −11.1866 −0.524434
\(456\) 0 0
\(457\) −13.5517 −0.633922 −0.316961 0.948439i \(-0.602662\pi\)
−0.316961 + 0.948439i \(0.602662\pi\)
\(458\) −29.1417 24.4528i −1.36170 1.14260i
\(459\) 0 0
\(460\) −0.110747 0.628077i −0.00516360 0.0292842i
\(461\) −3.10504 + 17.6096i −0.144616 + 0.820160i 0.823058 + 0.567957i \(0.192266\pi\)
−0.967674 + 0.252203i \(0.918845\pi\)
\(462\) 0 0
\(463\) −0.653477 1.13185i −0.0303696 0.0526017i 0.850441 0.526070i \(-0.176335\pi\)
−0.880811 + 0.473468i \(0.843002\pi\)
\(464\) 22.4196 38.8320i 1.04081 1.80273i
\(465\) 0 0
\(466\) −16.4206 + 13.7785i −0.760669 + 0.638277i
\(467\) 13.5133 23.4057i 0.625321 1.08309i −0.363158 0.931728i \(-0.618301\pi\)
0.988479 0.151360i \(-0.0483653\pi\)
\(468\) 0 0
\(469\) −54.9557 20.0022i −2.53762 0.923618i
\(470\) −2.48435 + 14.0895i −0.114595 + 0.649899i
\(471\) 0 0
\(472\) −8.17446 + 2.97526i −0.376260 + 0.136947i
\(473\) 13.2541 + 11.1215i 0.609422 + 0.511366i
\(474\) 0 0
\(475\) −0.323695 4.34686i −0.0148522 0.199448i
\(476\) −6.75101 −0.309432
\(477\) 0 0
\(478\) 5.51587 2.00761i 0.252290 0.0918261i
\(479\) −0.0502667 0.285076i −0.00229674 0.0130255i 0.983638 0.180157i \(-0.0576606\pi\)
−0.985935 + 0.167132i \(0.946550\pi\)
\(480\) 0 0
\(481\) −22.2944 8.11451i −1.01654 0.369990i
\(482\) 4.14719 + 7.18315i 0.188899 + 0.327184i
\(483\) 0 0
\(484\) −1.19619 + 1.00373i −0.0543724 + 0.0456239i
\(485\) −8.87934 + 7.45065i −0.403190 + 0.338317i
\(486\) 0 0
\(487\) −7.68554 13.3117i −0.348265 0.603212i 0.637676 0.770304i \(-0.279896\pi\)
−0.985941 + 0.167092i \(0.946562\pi\)
\(488\) −16.9497 6.16917i −0.767275 0.279265i
\(489\) 0 0
\(490\) 2.48360 + 14.0852i 0.112198 + 0.636304i
\(491\) 13.6351 4.96276i 0.615342 0.223966i −0.0154969 0.999880i \(-0.504933\pi\)
0.630839 + 0.775914i \(0.282711\pi\)
\(492\) 0 0
\(493\) 34.2979 1.54470
\(494\) 11.1455 15.4871i 0.501462 0.696799i
\(495\) 0 0
\(496\) −5.61213 4.70914i −0.251992 0.211447i
\(497\) 12.5166 4.55567i 0.561447 0.204350i
\(498\) 0 0
\(499\) −2.55922 + 14.5140i −0.114566 + 0.649737i 0.872398 + 0.488797i \(0.162564\pi\)
−0.986964 + 0.160941i \(0.948547\pi\)
\(500\) −0.438260 0.159514i −0.0195996 0.00713367i
\(501\) 0 0
\(502\) −9.85039 + 17.0614i −0.439644 + 0.761486i
\(503\) −3.33423 + 2.79775i −0.148666 + 0.124746i −0.714087 0.700057i \(-0.753158\pi\)
0.565421 + 0.824802i \(0.308714\pi\)
\(504\) 0 0
\(505\) −3.49120 + 6.04693i −0.155356 + 0.269085i
\(506\) −2.97030 5.14471i −0.132046 0.228710i
\(507\) 0 0
\(508\) −0.672034 + 3.81129i −0.0298167 + 0.169099i
\(509\) −1.49227 8.46308i −0.0661437 0.375119i −0.999854 0.0170899i \(-0.994560\pi\)
0.933710 0.358029i \(-0.116551\pi\)
\(510\) 0 0
\(511\) 30.7680 + 25.8174i 1.36109 + 1.14209i
\(512\) −10.5094 −0.464455
\(513\) 0 0
\(514\) −13.5058 −0.595715
\(515\) 7.76292 + 6.51386i 0.342075 + 0.287035i
\(516\) 0 0
\(517\) 4.37590 + 24.8169i 0.192452 + 1.09145i
\(518\) −9.31607 + 52.8341i −0.409325 + 2.32140i
\(519\) 0 0
\(520\) 3.35663 + 5.81386i 0.147198 + 0.254955i
\(521\) 1.03475 1.79225i 0.0453334 0.0785197i −0.842468 0.538746i \(-0.818898\pi\)
0.887802 + 0.460226i \(0.152232\pi\)
\(522\) 0 0
\(523\) 10.7338 9.00674i 0.469357 0.393837i −0.377203 0.926131i \(-0.623114\pi\)
0.846560 + 0.532293i \(0.178670\pi\)
\(524\) −1.51852 + 2.63015i −0.0663368 + 0.114899i
\(525\) 0 0
\(526\) 39.3886 + 14.3363i 1.71742 + 0.625091i
\(527\) 0.973090 5.51866i 0.0423884 0.240397i
\(528\) 0 0
\(529\) 19.8557 7.22690i 0.863293 0.314213i
\(530\) 4.74551 + 3.98196i 0.206132 + 0.172965i
\(531\) 0 0
\(532\) −7.34925 3.54347i −0.318630 0.153629i
\(533\) 18.4214 0.797919
\(534\) 0 0
\(535\) −11.0729 + 4.03020i −0.478723 + 0.174241i
\(536\) 6.09446 + 34.5634i 0.263240 + 1.49291i
\(537\) 0 0
\(538\) −4.87474 1.77426i −0.210165 0.0764938i
\(539\) 12.5961 + 21.8170i 0.542551 + 0.939725i
\(540\) 0 0
\(541\) −12.7311 + 10.6827i −0.547354 + 0.459285i −0.874044 0.485847i \(-0.838511\pi\)
0.326690 + 0.945132i \(0.394067\pi\)
\(542\) −22.1212 + 18.5619i −0.950186 + 0.797301i
\(543\) 0 0
\(544\) 4.66745 + 8.08426i 0.200115 + 0.346610i
\(545\) 1.50734 + 0.548626i 0.0645672 + 0.0235005i
\(546\) 0 0
\(547\) −1.04789 5.94288i −0.0448045 0.254099i 0.954176 0.299247i \(-0.0967353\pi\)
−0.998980 + 0.0451475i \(0.985624\pi\)
\(548\) 6.51632 2.37175i 0.278364 0.101316i
\(549\) 0 0
\(550\) −4.34425 −0.185239
\(551\) 37.3372 + 18.0023i 1.59062 + 0.766923i
\(552\) 0 0
\(553\) 5.98698 + 5.02367i 0.254592 + 0.213628i
\(554\) −39.5190 + 14.3837i −1.67900 + 0.611106i
\(555\) 0 0
\(556\) 0.806489 4.57383i 0.0342028 0.193973i
\(557\) −26.4311 9.62013i −1.11992 0.407618i −0.285298 0.958439i \(-0.592093\pi\)
−0.834623 + 0.550821i \(0.814315\pi\)
\(558\) 0 0
\(559\) 8.71703 15.0983i 0.368691 0.638591i
\(560\) 14.4967 12.1641i 0.612596 0.514029i
\(561\) 0 0
\(562\) 16.9188 29.3043i 0.713679 1.23613i
\(563\) −0.605777 1.04924i −0.0255305 0.0442201i 0.852978 0.521947i \(-0.174794\pi\)
−0.878508 + 0.477727i \(0.841461\pi\)
\(564\) 0 0
\(565\) −2.24785 + 12.7482i −0.0945679 + 0.536321i
\(566\) 5.00343 + 28.3759i 0.210310 + 1.19273i
\(567\) 0 0
\(568\) −6.12340 5.13814i −0.256932 0.215592i
\(569\) 17.5814 0.737049 0.368524 0.929618i \(-0.379863\pi\)
0.368524 + 0.929618i \(0.379863\pi\)
\(570\) 0 0
\(571\) 42.6982 1.78686 0.893432 0.449198i \(-0.148290\pi\)
0.893432 + 0.449198i \(0.148290\pi\)
\(572\) −2.75468 2.31145i −0.115179 0.0966467i
\(573\) 0 0
\(574\) −7.23343 41.0228i −0.301918 1.71226i
\(575\) −0.237457 + 1.34669i −0.00990266 + 0.0561608i
\(576\) 0 0
\(577\) −2.74678 4.75757i −0.114350 0.198060i 0.803170 0.595750i \(-0.203145\pi\)
−0.917520 + 0.397690i \(0.869812\pi\)
\(578\) 3.13426 5.42869i 0.130368 0.225804i
\(579\) 0 0
\(580\) 3.39745 2.85080i 0.141071 0.118373i
\(581\) −3.24817 + 5.62600i −0.134757 + 0.233406i
\(582\) 0 0
\(583\) 10.2534 + 3.73193i 0.424653 + 0.154561i
\(584\) 4.18555 23.7374i 0.173199 0.982262i
\(585\) 0 0
\(586\) −13.7079 + 4.98928i −0.566270 + 0.206105i
\(587\) 9.51705 + 7.98576i 0.392811 + 0.329607i 0.817707 0.575635i \(-0.195245\pi\)
−0.424896 + 0.905242i \(0.639689\pi\)
\(588\) 0 0
\(589\) 3.95596 5.49694i 0.163002 0.226498i
\(590\) −5.67228 −0.233524
\(591\) 0 0
\(592\) 37.7150 13.7271i 1.55008 0.564182i
\(593\) 0.194097 + 1.10078i 0.00797061 + 0.0452036i 0.988534 0.151001i \(-0.0482496\pi\)
−0.980563 + 0.196204i \(0.937138\pi\)
\(594\) 0 0
\(595\) 13.6022 + 4.95079i 0.557635 + 0.202963i
\(596\) −0.333845 0.578237i −0.0136748 0.0236855i
\(597\) 0 0
\(598\) −4.58551 + 3.84770i −0.187515 + 0.157344i
\(599\) 21.0736 17.6829i 0.861044 0.722502i −0.101149 0.994871i \(-0.532252\pi\)
0.962193 + 0.272370i \(0.0878073\pi\)
\(600\) 0 0
\(601\) −7.02686 12.1709i −0.286631 0.496460i 0.686372 0.727251i \(-0.259202\pi\)
−0.973004 + 0.230790i \(0.925869\pi\)
\(602\) −37.0455 13.4835i −1.50986 0.549545i
\(603\) 0 0
\(604\) −0.662785 3.75884i −0.0269683 0.152945i
\(605\) 3.14621 1.14513i 0.127912 0.0465560i
\(606\) 0 0
\(607\) −16.1942 −0.657304 −0.328652 0.944451i \(-0.606594\pi\)
−0.328652 + 0.944451i \(0.606594\pi\)
\(608\) 0.837784 + 11.2505i 0.0339766 + 0.456268i
\(609\) 0 0
\(610\) −9.00976 7.56008i −0.364794 0.306099i
\(611\) 23.8609 8.68464i 0.965307 0.351343i
\(612\) 0 0
\(613\) 4.80621 27.2574i 0.194121 1.10091i −0.719544 0.694447i \(-0.755649\pi\)
0.913665 0.406468i \(-0.133240\pi\)
\(614\) 16.2557 + 5.91659i 0.656027 + 0.238774i
\(615\) 0 0
\(616\) 13.3693 23.1563i 0.538665 0.932995i
\(617\) −4.66949 + 3.91817i −0.187987 + 0.157739i −0.731924 0.681386i \(-0.761377\pi\)
0.543937 + 0.839126i \(0.316933\pi\)
\(618\) 0 0
\(619\) 5.85935 10.1487i 0.235507 0.407910i −0.723913 0.689891i \(-0.757658\pi\)
0.959420 + 0.281981i \(0.0909916\pi\)
\(620\) −0.362314 0.627546i −0.0145509 0.0252028i
\(621\) 0 0
\(622\) −6.92195 + 39.2564i −0.277545 + 1.57404i
\(623\) −8.53787 48.4207i −0.342063 1.93993i
\(624\) 0 0
\(625\) 0.766044 + 0.642788i 0.0306418 + 0.0257115i
\(626\) 33.0677 1.32165
\(627\) 0 0
\(628\) −3.65419 −0.145818
\(629\) 23.5175 + 19.7335i 0.937704 + 0.786827i
\(630\) 0 0
\(631\) 3.63291 + 20.6033i 0.144624 + 0.820203i 0.967668 + 0.252226i \(0.0811626\pi\)
−0.823045 + 0.567977i \(0.807726\pi\)
\(632\) 0.814445 4.61895i 0.0323969 0.183732i
\(633\) 0 0
\(634\) 3.14869 + 5.45369i 0.125050 + 0.216594i
\(635\) 4.14901 7.18630i 0.164649 0.285180i
\(636\) 0 0
\(637\) 19.4456 16.3168i 0.770464 0.646496i
\(638\) 20.6556 35.7765i 0.817763 1.41641i
\(639\) 0 0
\(640\) −12.7829 4.65259i −0.505288 0.183910i
\(641\) 1.64737 9.34270i 0.0650672 0.369015i −0.934836 0.355081i \(-0.884453\pi\)
0.999903 0.0139340i \(-0.00443547\pi\)
\(642\) 0 0
\(643\) −11.7831 + 4.28868i −0.464678 + 0.169129i −0.563740 0.825952i \(-0.690638\pi\)
0.0990618 + 0.995081i \(0.468416\pi\)
\(644\) 1.96076 + 1.64527i 0.0772647 + 0.0648328i
\(645\) 0 0
\(646\) −20.4064 + 13.8988i −0.802879 + 0.546840i
\(647\) 15.6504 0.615281 0.307640 0.951503i \(-0.400461\pi\)
0.307640 + 0.951503i \(0.400461\pi\)
\(648\) 0 0
\(649\) −9.38851 + 3.41714i −0.368531 + 0.134134i
\(650\) 0.760131 + 4.31092i 0.0298148 + 0.169088i
\(651\) 0 0
\(652\) 8.45814 + 3.07851i 0.331246 + 0.120564i
\(653\) 9.54528 + 16.5329i 0.373536 + 0.646983i 0.990107 0.140317i \(-0.0448120\pi\)
−0.616571 + 0.787299i \(0.711479\pi\)
\(654\) 0 0
\(655\) 4.98836 4.18573i 0.194911 0.163550i
\(656\) −23.8723 + 20.0312i −0.932056 + 0.782088i
\(657\) 0 0
\(658\) −28.7093 49.7259i −1.11920 1.93852i
\(659\) −9.83688 3.58033i −0.383190 0.139470i 0.143240 0.989688i \(-0.454248\pi\)
−0.526431 + 0.850218i \(0.676470\pi\)
\(660\) 0 0
\(661\) −5.06045 28.6992i −0.196829 1.11627i −0.909791 0.415068i \(-0.863758\pi\)
0.712962 0.701203i \(-0.247353\pi\)
\(662\) 47.4250 17.2613i 1.84323 0.670880i
\(663\) 0 0
\(664\) 3.89858 0.151294
\(665\) 12.2090 + 12.5290i 0.473443 + 0.485855i
\(666\) 0 0
\(667\) −9.96145 8.35865i −0.385709 0.323648i
\(668\) 4.11512 1.49778i 0.159219 0.0579509i
\(669\) 0 0
\(670\) −3.97392 + 22.5372i −0.153526 + 0.870689i
\(671\) −19.4670 7.08540i −0.751514 0.273529i
\(672\) 0 0
\(673\) 7.27748 12.6050i 0.280526 0.485886i −0.690988 0.722866i \(-0.742824\pi\)
0.971514 + 0.236980i \(0.0761577\pi\)
\(674\) 28.2087 23.6699i 1.08656 0.911731i
\(675\) 0 0
\(676\) 1.21979 2.11274i 0.0469151 0.0812594i
\(677\) −5.48999 9.50895i −0.210998 0.365459i 0.741029 0.671473i \(-0.234338\pi\)
−0.952027 + 0.306014i \(0.901005\pi\)
\(678\) 0 0
\(679\) 8.07804 45.8128i 0.310007 1.75813i
\(680\) −1.50845 8.55484i −0.0578464 0.328063i
\(681\) 0 0
\(682\) −5.17055 4.33861i −0.197991 0.166134i
\(683\) 43.3449 1.65854 0.829272 0.558844i \(-0.188755\pi\)
0.829272 + 0.558844i \(0.188755\pi\)
\(684\) 0 0
\(685\) −14.8686 −0.568101
\(686\) −10.1737 8.53678i −0.388435 0.325936i
\(687\) 0 0
\(688\) 5.12137 + 29.0447i 0.195251 + 1.10732i
\(689\) 1.90922 10.8277i 0.0727355 0.412504i
\(690\) 0 0
\(691\) −15.2029 26.3321i −0.578344 1.00172i −0.995669 0.0929641i \(-0.970366\pi\)
0.417325 0.908757i \(-0.362968\pi\)
\(692\) 1.93803 3.35677i 0.0736729 0.127605i
\(693\) 0 0
\(694\) −7.81205 + 6.55509i −0.296541 + 0.248828i
\(695\) −4.97912 + 8.62408i −0.188869 + 0.327130i
\(696\) 0 0
\(697\) −22.3993 8.15268i −0.848434 0.308805i
\(698\) −7.41793 + 42.0692i −0.280773 + 1.59234i
\(699\) 0 0
\(700\) 1.75890 0.640187i 0.0664801 0.0241968i
\(701\) −16.3694 13.7356i −0.618266 0.518786i 0.278992 0.960293i \(-0.410000\pi\)
−0.897258 + 0.441507i \(0.854444\pi\)
\(702\) 0 0
\(703\) 15.2437 + 33.8261i 0.574929 + 1.27577i
\(704\) −14.8430 −0.559416
\(705\) 0 0
\(706\) −9.68284 + 3.52427i −0.364419 + 0.132638i
\(707\) −4.86613 27.5972i −0.183010 1.03790i
\(708\) 0 0
\(709\) 18.8045 + 6.84427i 0.706217 + 0.257042i 0.670063 0.742304i \(-0.266267\pi\)
0.0361542 + 0.999346i \(0.488489\pi\)
\(710\) −2.60611 4.51391i −0.0978055 0.169404i
\(711\) 0 0
\(712\) −22.6033 + 18.9664i −0.847093 + 0.710795i
\(713\) −1.62756 + 1.36569i −0.0609527 + 0.0511454i
\(714\) 0 0
\(715\) 3.85515 + 6.67732i 0.144175 + 0.249718i
\(716\) −8.12177 2.95608i −0.303525 0.110474i
\(717\) 0 0
\(718\) 0.745028 + 4.22526i 0.0278042 + 0.157685i
\(719\) −3.85410 + 1.40278i −0.143734 + 0.0523147i −0.412885 0.910783i \(-0.635479\pi\)
0.269152 + 0.963098i \(0.413257\pi\)
\(720\) 0 0
\(721\) −40.6705 −1.51465
\(722\) −29.5099 + 4.41950i −1.09824 + 0.164477i
\(723\) 0 0
\(724\) 4.04762 + 3.39636i 0.150429 + 0.126225i
\(725\) −8.93592 + 3.25241i −0.331872 + 0.120791i
\(726\) 0 0
\(727\) −6.20784 + 35.2064i −0.230236 + 1.30573i 0.622182 + 0.782872i \(0.286246\pi\)
−0.852418 + 0.522861i \(0.824865\pi\)
\(728\) −25.3180 9.21498i −0.938346 0.341530i
\(729\) 0 0
\(730\) 7.85844 13.6112i 0.290854 0.503774i
\(731\) −17.2814 + 14.5008i −0.639175 + 0.536332i
\(732\) 0 0
\(733\) 15.6472 27.1018i 0.577943 1.00103i −0.417772 0.908552i \(-0.637189\pi\)
0.995715 0.0924752i \(-0.0294779\pi\)
\(734\) −5.16610 8.94794i −0.190684 0.330274i
\(735\) 0 0
\(736\) 0.614584 3.48548i 0.0226539 0.128476i
\(737\) 6.99959 + 39.6966i 0.257833 + 1.46224i
\(738\) 0 0
\(739\) 24.9062 + 20.8988i 0.916188 + 0.768773i 0.973286 0.229596i \(-0.0737403\pi\)
−0.0570981 + 0.998369i \(0.518185\pi\)
\(740\) 3.96980 0.145933
\(741\) 0 0
\(742\) −24.8621 −0.912716
\(743\) −29.7586 24.9704i −1.09174 0.916076i −0.0948946 0.995487i \(-0.530251\pi\)
−0.996842 + 0.0794116i \(0.974696\pi\)
\(744\) 0 0
\(745\) 0.248599 + 1.40987i 0.00910796 + 0.0516538i
\(746\) −2.33438 + 13.2389i −0.0854676 + 0.484711i
\(747\) 0 0
\(748\) 2.32656 + 4.02972i 0.0850674 + 0.147341i
\(749\) 23.6458 40.9557i 0.863998 1.49649i
\(750\) 0 0
\(751\) −1.38487 + 1.16204i −0.0505345 + 0.0424035i −0.667705 0.744426i \(-0.732723\pi\)
0.617171 + 0.786829i \(0.288279\pi\)
\(752\) −21.4777 + 37.2005i −0.783212 + 1.35656i
\(753\) 0 0
\(754\) −39.1162 14.2371i −1.42453 0.518486i
\(755\) −1.42111 + 8.05950i −0.0517194 + 0.293315i
\(756\) 0 0
\(757\) −21.2025 + 7.71707i −0.770617 + 0.280482i −0.697254 0.716824i \(-0.745595\pi\)
−0.0733625 + 0.997305i \(0.523373\pi\)
\(758\) 17.1408 + 14.3828i 0.622580 + 0.522407i
\(759\) 0 0
\(760\) 2.84815 10.1047i 0.103313 0.366535i
\(761\) −2.85080 −0.103341 −0.0516707 0.998664i \(-0.516455\pi\)
−0.0516707 + 0.998664i \(0.516455\pi\)
\(762\) 0 0
\(763\) −6.04950 + 2.20184i −0.219006 + 0.0797118i
\(764\) −0.962764 5.46011i −0.0348316 0.197540i
\(765\) 0 0
\(766\) 31.5317 + 11.4766i 1.13929 + 0.414666i
\(767\) 5.03367 + 8.71856i 0.181755 + 0.314809i
\(768\) 0 0
\(769\) 4.68799 3.93369i 0.169053 0.141852i −0.554336 0.832293i \(-0.687028\pi\)
0.723389 + 0.690441i \(0.242583\pi\)
\(770\) 13.3560 11.2070i 0.481318 0.403874i
\(771\) 0 0
\(772\) 0.223360 + 0.386872i 0.00803892 + 0.0139238i
\(773\) 47.1328 + 17.1549i 1.69525 + 0.617020i 0.995270 0.0971441i \(-0.0309708\pi\)
0.699978 + 0.714164i \(0.253193\pi\)
\(774\) 0 0
\(775\) 0.269798 + 1.53010i 0.00969143 + 0.0549629i
\(776\) −26.2337 + 9.54827i −0.941734 + 0.342763i
\(777\) 0 0
\(778\) −24.0167 −0.861039
\(779\) −20.1050 20.6321i −0.720337 0.739221i
\(780\) 0 0
\(781\) −7.03283 5.90124i −0.251654 0.211163i
\(782\) 7.27856 2.64918i 0.260281 0.0947345i
\(783\) 0 0
\(784\) −7.45686 + 42.2900i −0.266317 + 1.51036i
\(785\) 7.36260 + 2.67977i 0.262783 + 0.0956450i
\(786\) 0 0
\(787\) 16.5102 28.5964i 0.588524 1.01935i −0.405902 0.913917i \(-0.633043\pi\)
0.994426 0.105437i \(-0.0336240\pi\)
\(788\) −5.10101 + 4.28025i −0.181716 + 0.152478i
\(789\) 0 0
\(790\) 1.52913 2.64854i 0.0544041 0.0942307i
\(791\) −25.9763 44.9922i −0.923610 1.59974i
\(792\) 0 0
\(793\) −3.62482 + 20.5574i −0.128721 + 0.730014i
\(794\) 8.89089 + 50.4227i 0.315526 + 1.78944i
\(795\) 0 0
\(796\) −2.77448 2.32806i −0.0983388 0.0825160i
\(797\) −47.2358 −1.67318 −0.836590 0.547830i \(-0.815454\pi\)
−0.836590 + 0.547830i \(0.815454\pi\)
\(798\) 0 0
\(799\) −32.8569 −1.16239
\(800\) −1.98267 1.66365i −0.0700978 0.0588191i
\(801\) 0 0
\(802\) 4.72113 + 26.7749i 0.166709 + 0.945454i
\(803\) 4.80718 27.2629i 0.169642 0.962085i
\(804\) 0 0
\(805\) −2.74406 4.75286i −0.0967156 0.167516i
\(806\) −3.40061 + 5.89003i −0.119781 + 0.207467i
\(807\) 0 0
\(808\) −12.8826 + 10.8098i −0.453210 + 0.380288i
\(809\) 2.19118 3.79524i 0.0770378 0.133433i −0.824933 0.565231i \(-0.808787\pi\)
0.901971 + 0.431797i \(0.142120\pi\)
\(810\) 0 0
\(811\) 31.9131 + 11.6154i 1.12062 + 0.407873i 0.834879 0.550433i \(-0.185537\pi\)
0.285743 + 0.958306i \(0.407760\pi\)
\(812\) −3.09085 + 17.5291i −0.108468 + 0.615151i
\(813\) 0 0
\(814\) 34.7475 12.6471i 1.21790 0.443279i
\(815\) −14.7842 12.4054i −0.517867 0.434542i
\(816\) 0 0
\(817\) −26.4240 + 6.71513i −0.924458 + 0.234933i
\(818\) −17.0038 −0.594525
\(819\) 0 0
\(820\) −2.89645 + 1.05422i −0.101149 + 0.0368151i
\(821\) −6.96961 39.5266i −0.243241 1.37949i −0.824542 0.565800i \(-0.808567\pi\)
0.581301 0.813688i \(-0.302544\pi\)
\(822\) 0 0
\(823\) −5.93493 2.16014i −0.206879 0.0752976i 0.236502 0.971631i \(-0.423999\pi\)
−0.443381 + 0.896333i \(0.646221\pi\)
\(824\) 12.2036 + 21.1372i 0.425132 + 0.736350i
\(825\) 0 0
\(826\) 17.4389 14.6330i 0.606779 0.509148i
\(827\) −16.3638 + 13.7308i −0.569024 + 0.477468i −0.881322 0.472516i \(-0.843346\pi\)
0.312298 + 0.949984i \(0.398901\pi\)
\(828\) 0 0
\(829\) −24.5301 42.4874i −0.851966 1.47565i −0.879432 0.476025i \(-0.842077\pi\)
0.0274658 0.999623i \(-0.491256\pi\)
\(830\) 2.38878 + 0.869446i 0.0829159 + 0.0301789i
\(831\) 0 0
\(832\) 2.59714 + 14.7291i 0.0900396 + 0.510640i
\(833\) −30.8660 + 11.2343i −1.06944 + 0.389246i
\(834\) 0 0
\(835\) −9.38968 −0.324943
\(836\) 0.417606 + 5.60797i 0.0144432 + 0.193956i
\(837\) 0 0
\(838\) −40.8752 34.2984i −1.41201 1.18482i
\(839\) −6.94430 + 2.52752i −0.239744 + 0.0872597i −0.459098 0.888386i \(-0.651827\pi\)
0.219354 + 0.975645i \(0.429605\pi\)
\(840\) 0 0
\(841\) 10.6670 60.4955i 0.367827 2.08605i
\(842\) −12.2610 4.46264i −0.422542 0.153793i
\(843\) 0 0
\(844\) −1.77757 + 3.07884i −0.0611865 + 0.105978i
\(845\) −4.00704 + 3.36231i −0.137846 + 0.115667i
\(846\) 0 0
\(847\) −6.71862 + 11.6370i −0.230855 + 0.399852i
\(848\) 9.29980 + 16.1077i 0.319357 + 0.553142i
\(849\) 0 0
\(850\) 0.983591 5.57822i 0.0337369 0.191332i
\(851\) −2.02120 11.4628i −0.0692858 0.392939i
\(852\) 0 0
\(853\) 2.10899 + 1.76966i 0.0722106 + 0.0605919i 0.678179 0.734897i \(-0.262770\pi\)
−0.605968 + 0.795489i \(0.707214\pi\)
\(854\) 47.2028 1.61525
\(855\) 0 0
\(856\) −28.3806 −0.970029
\(857\) 33.8025 + 28.3637i 1.15467 + 0.968885i 0.999818 0.0190524i \(-0.00606493\pi\)
0.154854 + 0.987937i \(0.450509\pi\)
\(858\) 0 0
\(859\) −2.04090 11.5745i −0.0696347 0.394918i −0.999626 0.0273372i \(-0.991297\pi\)
0.929992 0.367581i \(-0.119814\pi\)
\(860\) −0.506556 + 2.87282i −0.0172734 + 0.0979623i
\(861\) 0 0
\(862\) −9.52474 16.4973i −0.324414 0.561902i
\(863\) −17.1415 + 29.6900i −0.583504 + 1.01066i 0.411556 + 0.911385i \(0.364986\pi\)
−0.995060 + 0.0992746i \(0.968348\pi\)
\(864\) 0 0
\(865\) −6.36647 + 5.34210i −0.216466 + 0.181637i
\(866\) 4.26808 7.39254i 0.145035 0.251209i
\(867\) 0 0
\(868\) 2.73281 + 0.994661i 0.0927576 + 0.0337610i
\(869\) 0.935404 5.30494i 0.0317314 0.179958i
\(870\) 0 0
\(871\) 38.1673 13.8918i 1.29325 0.470704i
\(872\) 2.95955 + 2.48335i 0.100223 + 0.0840970i
\(873\) 0 0
\(874\) 9.31406 + 0.936439i 0.315053 + 0.0316755i
\(875\) −4.01337 −0.135677
\(876\) 0 0
\(877\) 22.7444 8.27828i 0.768023 0.279537i 0.0718537 0.997415i \(-0.477109\pi\)
0.696169 + 0.717878i \(0.254886\pi\)
\(878\) −6.92157 39.2542i −0.233592 1.32476i
\(879\) 0 0
\(880\) −12.2567 4.46109i −0.413175 0.150383i
\(881\) −19.5867 33.9251i −0.659892 1.14297i −0.980643 0.195802i \(-0.937269\pi\)
0.320752 0.947163i \(-0.396064\pi\)
\(882\) 0 0
\(883\) 24.7964 20.8067i 0.834467 0.700201i −0.121845 0.992549i \(-0.538881\pi\)
0.956312 + 0.292348i \(0.0944366\pi\)
\(884\) 3.59171 3.01380i 0.120802 0.101365i
\(885\) 0 0
\(886\) −3.86435 6.69325i −0.129825 0.224864i
\(887\) 0.357853 + 0.130248i 0.0120155 + 0.00437329i 0.348021 0.937487i \(-0.386854\pi\)
−0.336005 + 0.941860i \(0.609076\pi\)
\(888\) 0 0
\(889\) 5.78301 + 32.7971i 0.193956 + 1.09998i
\(890\) −18.0795 + 6.58041i −0.606027 + 0.220576i
\(891\) 0 0
\(892\) −3.73264 −0.124978
\(893\) −35.7685 17.2459i −1.19695 0.577114i
\(894\) 0 0
\(895\) 14.1962 + 11.9121i 0.474528 + 0.398176i
\(896\) 51.3024 18.6726i 1.71389 0.623807i
\(897\) 0 0
\(898\) −1.10897 + 6.28930i −0.0370069 + 0.209877i
\(899\) −13.8838 5.05328i −0.463050 0.168536i
\(900\) 0 0
\(901\) −7.11348 + 12.3209i −0.236984 + 0.410469i
\(902\) −21.9940 + 18.4551i −0.732319 + 0.614488i
\(903\) 0 0
\(904\) −15.5889 + 27.0007i −0.518478 + 0.898030i
\(905\) −5.66461 9.81139i −0.188298 0.326142i
\(906\) 0 0
\(907\) −0.855419 + 4.85132i −0.0284037 + 0.161086i −0.995710 0.0925237i \(-0.970507\pi\)
0.967307 + 0.253609i \(0.0816177\pi\)
\(908\) 1.43678 + 8.14841i 0.0476814 + 0.270415i
\(909\) 0 0
\(910\) −13.4580 11.2926i −0.446129 0.374346i
\(911\) −20.6775 −0.685075 −0.342537 0.939504i \(-0.611286\pi\)
−0.342537 + 0.939504i \(0.611286\pi\)
\(912\) 0 0
\(913\) 4.47759 0.148187
\(914\) −16.3034 13.6802i −0.539269 0.452500i
\(915\) 0 0
\(916\) −1.96176 11.1257i −0.0648184 0.367604i
\(917\) −4.53819 + 25.7374i −0.149864 + 0.849923i
\(918\) 0 0
\(919\) 30.2934 + 52.4697i 0.999287 + 1.73082i 0.532344 + 0.846528i \(0.321311\pi\)
0.466943 + 0.884287i \(0.345355\pi\)
\(920\) −1.64677 + 2.85228i −0.0542923 + 0.0940370i
\(921\) 0 0
\(922\) −21.5121 + 18.0508i −0.708462 + 0.594470i
\(923\) −4.62540 + 8.01143i −0.152247 + 0.263699i
\(924\) 0 0
\(925\) −7.99851 2.91122i −0.262989 0.0957203i
\(926\) 0.356419 2.02135i 0.0117127 0.0664258i
\(927\) 0 0
\(928\) 23.1278 8.41784i 0.759208 0.276329i
\(929\) 0.222628 + 0.186807i 0.00730419 + 0.00612894i 0.646432 0.762971i \(-0.276260\pi\)
−0.639128 + 0.769100i \(0.720705\pi\)
\(930\) 0 0
\(931\) −39.4978 3.97113i −1.29449 0.130149i
\(932\) −6.36576 −0.208517
\(933\) 0 0
\(934\) 39.8848 14.5169i 1.30507 0.475007i
\(935\) −1.73248 9.82538i −0.0566581 0.321324i
\(936\) 0 0
\(937\) −4.98587 1.81471i −0.162881 0.0592839i 0.259293 0.965799i \(-0.416511\pi\)
−0.422174 + 0.906515i \(0.638733\pi\)
\(938\) −45.9227 79.5405i −1.49943 2.59709i
\(939\) 0 0
\(940\) −3.25471 + 2.73103i −0.106157 + 0.0890763i
\(941\) 21.7752 18.2716i 0.709852 0.595637i −0.214706 0.976679i \(-0.568879\pi\)
0.924558 + 0.381042i \(0.124435\pi\)
\(942\) 0 0
\(943\) 4.51877 + 7.82674i 0.147151 + 0.254874i
\(944\) −16.0036 5.82484i −0.520873 0.189582i
\(945\) 0 0
\(946\) 4.71841 + 26.7594i 0.153409 + 0.870024i
\(947\) −46.9649 + 17.0938i −1.52615 + 0.555474i −0.962676 0.270657i \(-0.912759\pi\)
−0.563478 + 0.826131i \(0.690537\pi\)
\(948\) 0 0
\(949\) −27.8948 −0.905504
\(950\) 3.99865 5.55627i 0.129733 0.180269i
\(951\) 0 0
\(952\) 26.7069 + 22.4097i 0.865575 + 0.726304i
\(953\) −11.3705 + 4.13854i −0.368328 + 0.134060i −0.519551 0.854439i \(-0.673901\pi\)
0.151224 + 0.988500i \(0.451679\pi\)
\(954\) 0 0
\(955\) −2.06430 + 11.7073i −0.0667993 + 0.378838i
\(956\) 1.63806 + 0.596205i 0.0529786 + 0.0192826i
\(957\) 0 0
\(958\) 0.227306 0.393705i 0.00734391 0.0127200i
\(959\) 45.7124 38.3572i 1.47613 1.23862i
\(960\) 0 0
\(961\) 14.2930 24.7562i 0.461065 0.798587i
\(962\) −18.6299 32.2680i −0.600653 1.04036i
\(963\) 0 0
\(964\) −0.427730 + 2.42578i −0.0137763 + 0.0781291i
\(965\) −0.166326 0.943282i −0.00535423 0.0303653i
\(966\) 0 0
\(967\) 10.0879 + 8.46474i 0.324404 + 0.272208i 0.790415 0.612571i \(-0.209865\pi\)
−0.466011 + 0.884779i \(0.654309\pi\)
\(968\) 8.06395 0.259185
\(969\) 0 0
\(970\) −18.2036 −0.584482
\(971\) 13.4161 + 11.2575i 0.430544 + 0.361269i 0.832157 0.554540i \(-0.187106\pi\)
−0.401613 + 0.915809i \(0.631550\pi\)
\(972\) 0 0
\(973\) −6.94003 39.3589i −0.222487 1.26179i
\(974\) 4.19184 23.7731i 0.134315 0.761740i
\(975\) 0 0
\(976\) −17.6565 30.5819i −0.565170 0.978903i
\(977\) −5.26807 + 9.12457i −0.168541 + 0.291921i −0.937907 0.346887i \(-0.887239\pi\)
0.769366 + 0.638808i \(0.220572\pi\)
\(978\) 0 0
\(979\) −25.9602 + 21.7832i −0.829693 + 0.696195i
\(980\) −2.12372 + 3.67839i −0.0678397 + 0.117502i
\(981\) 0 0
\(982\) 21.4135 + 7.79388i 0.683333 + 0.248713i
\(983\) −9.02591 + 51.1885i −0.287882 + 1.63266i 0.406925 + 0.913462i \(0.366601\pi\)
−0.694807 + 0.719197i \(0.744510\pi\)
\(984\) 0 0
\(985\) 13.4166 4.88324i 0.427488 0.155593i
\(986\) 41.2621 + 34.6230i 1.31405 + 1.10262i
\(987\) 0 0
\(988\) 5.49188 1.39565i 0.174720 0.0444016i
\(989\) 8.55315 0.271974
\(990\) 0 0
\(991\) −6.36762 + 2.31763i −0.202274 + 0.0736218i −0.441171 0.897423i \(-0.645437\pi\)
0.238896 + 0.971045i \(0.423214\pi\)
\(992\) −0.698288 3.96019i −0.0221707 0.125736i
\(993\) 0 0
\(994\) 19.6570 + 7.15456i 0.623482 + 0.226929i
\(995\) 3.88286 + 6.72530i 0.123095 + 0.213206i
\(996\) 0 0
\(997\) −30.8481 + 25.8846i −0.976968 + 0.819774i −0.983629 0.180204i \(-0.942324\pi\)
0.00666090 + 0.999978i \(0.497880\pi\)
\(998\) −17.7305 + 14.8777i −0.561250 + 0.470944i
\(999\) 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 855.2.bs.b.586.3 18
3.2 odd 2 95.2.k.b.16.1 yes 18
15.2 even 4 475.2.u.c.149.5 36
15.8 even 4 475.2.u.c.149.2 36
15.14 odd 2 475.2.l.b.301.3 18
19.6 even 9 inner 855.2.bs.b.766.3 18
57.5 odd 18 1805.2.a.t.1.2 9
57.14 even 18 1805.2.a.u.1.8 9
57.44 odd 18 95.2.k.b.6.1 18
285.14 even 18 9025.2.a.cd.1.2 9
285.44 odd 18 475.2.l.b.101.3 18
285.119 odd 18 9025.2.a.ce.1.8 9
285.158 even 36 475.2.u.c.424.5 36
285.272 even 36 475.2.u.c.424.2 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.k.b.6.1 18 57.44 odd 18
95.2.k.b.16.1 yes 18 3.2 odd 2
475.2.l.b.101.3 18 285.44 odd 18
475.2.l.b.301.3 18 15.14 odd 2
475.2.u.c.149.2 36 15.8 even 4
475.2.u.c.149.5 36 15.2 even 4
475.2.u.c.424.2 36 285.272 even 36
475.2.u.c.424.5 36 285.158 even 36
855.2.bs.b.586.3 18 1.1 even 1 trivial
855.2.bs.b.766.3 18 19.6 even 9 inner
1805.2.a.t.1.2 9 57.5 odd 18
1805.2.a.u.1.8 9 57.14 even 18
9025.2.a.cd.1.2 9 285.14 even 18
9025.2.a.ce.1.8 9 285.119 odd 18