Properties

Label 432.2.v.a.35.15
Level $432$
Weight $2$
Character 432.35
Analytic conductor $3.450$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [432,2,Mod(35,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.v (of order \(12\), degree \(4\), 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: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 35.15
Character \(\chi\) \(=\) 432.35
Dual form 432.2.v.a.395.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.725676 - 1.21383i) q^{2} +(-0.946789 - 1.76170i) q^{4} +(-0.178044 + 0.664471i) q^{5} +(0.645693 - 1.11837i) q^{7} +(-2.82548 - 0.129179i) q^{8} +O(q^{10})\) \(q+(0.725676 - 1.21383i) q^{2} +(-0.946789 - 1.76170i) q^{4} +(-0.178044 + 0.664471i) q^{5} +(0.645693 - 1.11837i) q^{7} +(-2.82548 - 0.129179i) q^{8} +(0.677355 + 0.698307i) q^{10} +(-0.860301 - 3.21069i) q^{11} +(1.27203 - 4.74727i) q^{13} +(-0.888956 - 1.59534i) q^{14} +(-2.20718 + 3.33592i) q^{16} -5.58523i q^{17} +(-2.49649 + 2.49649i) q^{19} +(1.33917 - 0.315453i) q^{20} +(-4.52154 - 1.28565i) q^{22} +(2.36529 - 1.36560i) q^{23} +(3.92031 + 2.26339i) q^{25} +(-4.83933 - 4.98901i) q^{26} +(-2.58157 - 0.0786549i) q^{28} +(0.792277 + 2.95682i) q^{29} +(-5.28160 + 3.04933i) q^{31} +(2.44755 + 5.09995i) q^{32} +(-6.77954 - 4.05307i) q^{34} +(0.628165 + 0.628165i) q^{35} +(0.507420 - 0.507420i) q^{37} +(1.21868 + 4.84196i) q^{38} +(0.588896 - 1.85445i) q^{40} +(4.89892 + 8.48518i) q^{41} +(-0.949956 + 0.254540i) q^{43} +(-4.84175 + 4.55544i) q^{44} +(0.0588204 - 3.86205i) q^{46} +(6.13774 - 10.6309i) q^{47} +(2.66616 + 4.61793i) q^{49} +(5.59225 - 3.11611i) q^{50} +(-9.56762 + 2.25373i) q^{52} +(-0.601793 - 0.601793i) q^{53} +2.28658 q^{55} +(-1.96886 + 3.07653i) q^{56} +(4.16402 + 1.18400i) q^{58} +(-4.77715 - 1.28003i) q^{59} +(10.8292 - 2.90167i) q^{61} +(-0.131344 + 8.62382i) q^{62} +(7.96663 + 0.729984i) q^{64} +(2.92795 + 1.69045i) q^{65} +(0.110351 + 0.0295686i) q^{67} +(-9.83950 + 5.28803i) q^{68} +(1.21833 - 0.306644i) q^{70} +0.0447904i q^{71} +13.2931i q^{73} +(-0.247701 - 0.984146i) q^{74} +(6.76171 + 2.03442i) q^{76} +(-4.14624 - 1.11098i) q^{77} +(-2.50052 - 1.44368i) q^{79} +(-1.82364 - 2.06055i) q^{80} +(13.8546 + 0.211011i) q^{82} +(-3.79568 + 1.01705i) q^{83} +(3.71122 + 0.994419i) q^{85} +(-0.380391 + 1.33780i) q^{86} +(2.01601 + 9.18285i) q^{88} +12.7362 q^{89} +(-4.48788 - 4.48788i) q^{91} +(-4.64521 - 2.87400i) q^{92} +(-8.45011 - 15.1648i) q^{94} +(-1.21436 - 2.10333i) q^{95} +(4.41066 - 7.63949i) q^{97} +(7.54017 + 0.114840i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 40 q^{46} - 24 q^{49} - 72 q^{50} - 2 q^{52} - 16 q^{55} - 36 q^{56} + 16 q^{58} + 42 q^{59} - 2 q^{61} - 44 q^{64} + 12 q^{65} - 2 q^{67} - 96 q^{68} - 16 q^{70} - 78 q^{74} - 14 q^{76} + 6 q^{77} - 36 q^{82} - 54 q^{83} + 8 q^{85} - 54 q^{86} + 22 q^{88} + 20 q^{91} - 108 q^{92} + 6 q^{94} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.725676 1.21383i 0.513130 0.858311i
\(3\) 0 0
\(4\) −0.946789 1.76170i −0.473394 0.880851i
\(5\) −0.178044 + 0.664471i −0.0796239 + 0.297161i −0.994242 0.107158i \(-0.965825\pi\)
0.914618 + 0.404319i \(0.132491\pi\)
\(6\) 0 0
\(7\) 0.645693 1.11837i 0.244049 0.422705i −0.717815 0.696234i \(-0.754858\pi\)
0.961864 + 0.273529i \(0.0881909\pi\)
\(8\) −2.82548 0.129179i −0.998957 0.0456717i
\(9\) 0 0
\(10\) 0.677355 + 0.698307i 0.214199 + 0.220824i
\(11\) −0.860301 3.21069i −0.259390 0.968058i −0.965595 0.260051i \(-0.916261\pi\)
0.706205 0.708008i \(-0.250406\pi\)
\(12\) 0 0
\(13\) 1.27203 4.74727i 0.352797 1.31666i −0.530437 0.847725i \(-0.677972\pi\)
0.883234 0.468933i \(-0.155361\pi\)
\(14\) −0.888956 1.59534i −0.237584 0.426373i
\(15\) 0 0
\(16\) −2.20718 + 3.33592i −0.551795 + 0.833980i
\(17\) 5.58523i 1.35462i −0.735699 0.677308i \(-0.763146\pi\)
0.735699 0.677308i \(-0.236854\pi\)
\(18\) 0 0
\(19\) −2.49649 + 2.49649i −0.572733 + 0.572733i −0.932891 0.360158i \(-0.882723\pi\)
0.360158 + 0.932891i \(0.382723\pi\)
\(20\) 1.33917 0.315453i 0.299448 0.0705374i
\(21\) 0 0
\(22\) −4.52154 1.28565i −0.963996 0.274103i
\(23\) 2.36529 1.36560i 0.493197 0.284747i −0.232703 0.972548i \(-0.574757\pi\)
0.725900 + 0.687801i \(0.241424\pi\)
\(24\) 0 0
\(25\) 3.92031 + 2.26339i 0.784061 + 0.452678i
\(26\) −4.83933 4.98901i −0.949070 0.978426i
\(27\) 0 0
\(28\) −2.58157 0.0786549i −0.487872 0.0148644i
\(29\) 0.792277 + 2.95682i 0.147122 + 0.549067i 0.999652 + 0.0263884i \(0.00840066\pi\)
−0.852530 + 0.522679i \(0.824933\pi\)
\(30\) 0 0
\(31\) −5.28160 + 3.04933i −0.948604 + 0.547677i −0.892647 0.450757i \(-0.851154\pi\)
−0.0559568 + 0.998433i \(0.517821\pi\)
\(32\) 2.44755 + 5.09995i 0.432671 + 0.901552i
\(33\) 0 0
\(34\) −6.77954 4.05307i −1.16268 0.695095i
\(35\) 0.628165 + 0.628165i 0.106179 + 0.106179i
\(36\) 0 0
\(37\) 0.507420 0.507420i 0.0834193 0.0834193i −0.664166 0.747585i \(-0.731213\pi\)
0.747585 + 0.664166i \(0.231213\pi\)
\(38\) 1.21868 + 4.84196i 0.197696 + 0.785470i
\(39\) 0 0
\(40\) 0.588896 1.85445i 0.0931127 0.293214i
\(41\) 4.89892 + 8.48518i 0.765083 + 1.32516i 0.940203 + 0.340616i \(0.110635\pi\)
−0.175120 + 0.984547i \(0.556031\pi\)
\(42\) 0 0
\(43\) −0.949956 + 0.254540i −0.144867 + 0.0388170i −0.330524 0.943798i \(-0.607225\pi\)
0.185657 + 0.982615i \(0.440559\pi\)
\(44\) −4.84175 + 4.55544i −0.729921 + 0.686758i
\(45\) 0 0
\(46\) 0.0588204 3.86205i 0.00867260 0.569428i
\(47\) 6.13774 10.6309i 0.895281 1.55067i 0.0618250 0.998087i \(-0.480308\pi\)
0.833456 0.552586i \(-0.186359\pi\)
\(48\) 0 0
\(49\) 2.66616 + 4.61793i 0.380880 + 0.659704i
\(50\) 5.59225 3.11611i 0.790864 0.440685i
\(51\) 0 0
\(52\) −9.56762 + 2.25373i −1.32679 + 0.312537i
\(53\) −0.601793 0.601793i −0.0826626 0.0826626i 0.664567 0.747229i \(-0.268616\pi\)
−0.747229 + 0.664567i \(0.768616\pi\)
\(54\) 0 0
\(55\) 2.28658 0.308322
\(56\) −1.96886 + 3.07653i −0.263100 + 0.411118i
\(57\) 0 0
\(58\) 4.16402 + 1.18400i 0.546763 + 0.155467i
\(59\) −4.77715 1.28003i −0.621932 0.166646i −0.0659263 0.997824i \(-0.521000\pi\)
−0.556006 + 0.831178i \(0.687667\pi\)
\(60\) 0 0
\(61\) 10.8292 2.90167i 1.38653 0.371520i 0.513043 0.858363i \(-0.328518\pi\)
0.873490 + 0.486842i \(0.161851\pi\)
\(62\) −0.131344 + 8.62382i −0.0166807 + 1.09523i
\(63\) 0 0
\(64\) 7.96663 + 0.729984i 0.995828 + 0.0912480i
\(65\) 2.92795 + 1.69045i 0.363167 + 0.209675i
\(66\) 0 0
\(67\) 0.110351 + 0.0295686i 0.0134816 + 0.00361238i 0.265554 0.964096i \(-0.414445\pi\)
−0.252072 + 0.967708i \(0.581112\pi\)
\(68\) −9.83950 + 5.28803i −1.19321 + 0.641268i
\(69\) 0 0
\(70\) 1.21833 0.306644i 0.145619 0.0366510i
\(71\) 0.0447904i 0.00531565i 0.999996 + 0.00265782i \(0.000846013\pi\)
−0.999996 + 0.00265782i \(0.999154\pi\)
\(72\) 0 0
\(73\) 13.2931i 1.55585i 0.628360 + 0.777923i \(0.283726\pi\)
−0.628360 + 0.777923i \(0.716274\pi\)
\(74\) −0.247701 0.984146i −0.0287947 0.114405i
\(75\) 0 0
\(76\) 6.76171 + 2.03442i 0.775621 + 0.233364i
\(77\) −4.14624 1.11098i −0.472507 0.126608i
\(78\) 0 0
\(79\) −2.50052 1.44368i −0.281331 0.162426i 0.352695 0.935738i \(-0.385265\pi\)
−0.634026 + 0.773312i \(0.718599\pi\)
\(80\) −1.82364 2.06055i −0.203890 0.230377i
\(81\) 0 0
\(82\) 13.8546 + 0.211011i 1.52999 + 0.0233023i
\(83\) −3.79568 + 1.01705i −0.416630 + 0.111636i −0.461043 0.887378i \(-0.652525\pi\)
0.0444135 + 0.999013i \(0.485858\pi\)
\(84\) 0 0
\(85\) 3.71122 + 0.994419i 0.402539 + 0.107860i
\(86\) −0.380391 + 1.33780i −0.0410186 + 0.144259i
\(87\) 0 0
\(88\) 2.01601 + 9.18285i 0.214907 + 0.978895i
\(89\) 12.7362 1.35003 0.675017 0.737802i \(-0.264136\pi\)
0.675017 + 0.737802i \(0.264136\pi\)
\(90\) 0 0
\(91\) −4.48788 4.48788i −0.470458 0.470458i
\(92\) −4.64521 2.87400i −0.484296 0.299635i
\(93\) 0 0
\(94\) −8.45011 15.1648i −0.871563 1.56413i
\(95\) −1.21436 2.10333i −0.124590 0.215797i
\(96\) 0 0
\(97\) 4.41066 7.63949i 0.447835 0.775673i −0.550410 0.834895i \(-0.685529\pi\)
0.998245 + 0.0592215i \(0.0188618\pi\)
\(98\) 7.54017 + 0.114840i 0.761672 + 0.0116005i
\(99\) 0 0
\(100\) 0.275714 9.04936i 0.0275714 0.904936i
\(101\) 7.02523 1.88240i 0.699037 0.187306i 0.108238 0.994125i \(-0.465479\pi\)
0.590799 + 0.806819i \(0.298813\pi\)
\(102\) 0 0
\(103\) 9.50698 + 16.4666i 0.936750 + 1.62250i 0.771483 + 0.636250i \(0.219515\pi\)
0.165267 + 0.986249i \(0.447151\pi\)
\(104\) −4.20733 + 13.2490i −0.412563 + 1.29917i
\(105\) 0 0
\(106\) −1.16718 + 0.293770i −0.113367 + 0.0285335i
\(107\) −8.28797 + 8.28797i −0.801228 + 0.801228i −0.983287 0.182060i \(-0.941724\pi\)
0.182060 + 0.983287i \(0.441724\pi\)
\(108\) 0 0
\(109\) −14.3799 14.3799i −1.37735 1.37735i −0.849074 0.528273i \(-0.822840\pi\)
−0.528273 0.849074i \(-0.677160\pi\)
\(110\) 1.65932 2.77553i 0.158210 0.264636i
\(111\) 0 0
\(112\) 2.30564 + 4.62243i 0.217862 + 0.436779i
\(113\) 2.18778 1.26312i 0.205809 0.118824i −0.393553 0.919302i \(-0.628754\pi\)
0.599362 + 0.800478i \(0.295421\pi\)
\(114\) 0 0
\(115\) 0.486275 + 1.81480i 0.0453454 + 0.169231i
\(116\) 4.45891 4.19524i 0.413999 0.389518i
\(117\) 0 0
\(118\) −5.02042 + 4.86978i −0.462167 + 0.448300i
\(119\) −6.24637 3.60634i −0.572604 0.330593i
\(120\) 0 0
\(121\) −0.0421101 + 0.0243123i −0.00382819 + 0.00221021i
\(122\) 4.33632 15.2505i 0.392592 1.38071i
\(123\) 0 0
\(124\) 10.3726 + 6.41753i 0.931485 + 0.576311i
\(125\) −4.63408 + 4.63408i −0.414485 + 0.414485i
\(126\) 0 0
\(127\) 17.5157i 1.55427i −0.629333 0.777135i \(-0.716672\pi\)
0.629333 0.777135i \(-0.283328\pi\)
\(128\) 6.66727 9.14043i 0.589309 0.807908i
\(129\) 0 0
\(130\) 4.17667 2.32733i 0.366318 0.204120i
\(131\) −3.21241 + 11.9889i −0.280669 + 1.04747i 0.671277 + 0.741207i \(0.265746\pi\)
−0.951946 + 0.306266i \(0.900920\pi\)
\(132\) 0 0
\(133\) 1.18004 + 4.40397i 0.102322 + 0.381872i
\(134\) 0.115971 0.112491i 0.0100183 0.00971776i
\(135\) 0 0
\(136\) −0.721494 + 15.7809i −0.0618676 + 1.35320i
\(137\) −5.00063 + 8.66134i −0.427232 + 0.739988i −0.996626 0.0820768i \(-0.973845\pi\)
0.569394 + 0.822065i \(0.307178\pi\)
\(138\) 0 0
\(139\) −0.368654 + 1.37583i −0.0312688 + 0.116697i −0.979796 0.199998i \(-0.935906\pi\)
0.948528 + 0.316695i \(0.102573\pi\)
\(140\) 0.511899 1.70138i 0.0432634 0.143793i
\(141\) 0 0
\(142\) 0.0543682 + 0.0325034i 0.00456248 + 0.00272762i
\(143\) −16.3363 −1.36611
\(144\) 0 0
\(145\) −2.10578 −0.174876
\(146\) 16.1357 + 9.64652i 1.33540 + 0.798352i
\(147\) 0 0
\(148\) −1.37434 0.413503i −0.112970 0.0339897i
\(149\) −1.48172 + 5.52986i −0.121387 + 0.453024i −0.999685 0.0250901i \(-0.992013\pi\)
0.878298 + 0.478114i \(0.158679\pi\)
\(150\) 0 0
\(151\) 8.10127 14.0318i 0.659272 1.14189i −0.321533 0.946899i \(-0.604198\pi\)
0.980804 0.194994i \(-0.0624687\pi\)
\(152\) 7.37625 6.73127i 0.598293 0.545978i
\(153\) 0 0
\(154\) −4.35737 + 4.22663i −0.351127 + 0.340592i
\(155\) −1.08583 4.05239i −0.0872163 0.325496i
\(156\) 0 0
\(157\) −2.02762 + 7.56718i −0.161822 + 0.603927i 0.836602 + 0.547810i \(0.184538\pi\)
−0.998424 + 0.0561165i \(0.982128\pi\)
\(158\) −3.56695 + 1.98758i −0.283772 + 0.158123i
\(159\) 0 0
\(160\) −3.82454 + 0.718311i −0.302357 + 0.0567875i
\(161\) 3.52703i 0.277969i
\(162\) 0 0
\(163\) −4.89763 + 4.89763i −0.383612 + 0.383612i −0.872402 0.488789i \(-0.837439\pi\)
0.488789 + 0.872402i \(0.337439\pi\)
\(164\) 10.3101 16.6641i 0.805084 1.30125i
\(165\) 0 0
\(166\) −1.51990 + 5.34537i −0.117967 + 0.414882i
\(167\) 18.7832 10.8445i 1.45349 0.839174i 0.454814 0.890587i \(-0.349706\pi\)
0.998677 + 0.0514129i \(0.0163725\pi\)
\(168\) 0 0
\(169\) −9.66023 5.57734i −0.743095 0.429026i
\(170\) 3.90021 3.78318i 0.299132 0.290157i
\(171\) 0 0
\(172\) 1.34783 + 1.43254i 0.102771 + 0.109230i
\(173\) 2.05946 + 7.68601i 0.156578 + 0.584356i 0.998965 + 0.0454836i \(0.0144829\pi\)
−0.842387 + 0.538873i \(0.818850\pi\)
\(174\) 0 0
\(175\) 5.06263 2.92291i 0.382699 0.220951i
\(176\) 12.6094 + 4.21668i 0.950471 + 0.317844i
\(177\) 0 0
\(178\) 9.24236 15.4596i 0.692744 1.15875i
\(179\) 9.47991 + 9.47991i 0.708562 + 0.708562i 0.966233 0.257671i \(-0.0829551\pi\)
−0.257671 + 0.966233i \(0.582955\pi\)
\(180\) 0 0
\(181\) 8.00075 8.00075i 0.594691 0.594691i −0.344204 0.938895i \(-0.611851\pi\)
0.938895 + 0.344204i \(0.111851\pi\)
\(182\) −8.70430 + 2.19080i −0.645206 + 0.162393i
\(183\) 0 0
\(184\) −6.85947 + 3.55292i −0.505687 + 0.261925i
\(185\) 0.246822 + 0.427509i 0.0181467 + 0.0314311i
\(186\) 0 0
\(187\) −17.9324 + 4.80498i −1.31135 + 0.351375i
\(188\) −24.5396 0.747667i −1.78973 0.0545292i
\(189\) 0 0
\(190\) −3.43432 0.0523060i −0.249152 0.00379468i
\(191\) −9.22986 + 15.9866i −0.667850 + 1.15675i 0.310655 + 0.950523i \(0.399452\pi\)
−0.978504 + 0.206227i \(0.933882\pi\)
\(192\) 0 0
\(193\) 2.61643 + 4.53179i 0.188335 + 0.326205i 0.944695 0.327950i \(-0.106358\pi\)
−0.756360 + 0.654155i \(0.773024\pi\)
\(194\) −6.07237 10.8976i −0.435971 0.782403i
\(195\) 0 0
\(196\) 5.61111 9.06918i 0.400794 0.647799i
\(197\) −14.3573 14.3573i −1.02292 1.02292i −0.999731 0.0231869i \(-0.992619\pi\)
−0.0231869 0.999731i \(-0.507381\pi\)
\(198\) 0 0
\(199\) −13.8358 −0.980797 −0.490399 0.871498i \(-0.663149\pi\)
−0.490399 + 0.871498i \(0.663149\pi\)
\(200\) −10.7843 6.90157i −0.762568 0.488015i
\(201\) 0 0
\(202\) 2.81311 9.89348i 0.197930 0.696103i
\(203\) 3.81839 + 1.02314i 0.267999 + 0.0718100i
\(204\) 0 0
\(205\) −6.51038 + 1.74445i −0.454705 + 0.121838i
\(206\) 26.8867 + 0.409494i 1.87328 + 0.0285308i
\(207\) 0 0
\(208\) 13.0289 + 14.7215i 0.903393 + 1.02075i
\(209\) 10.1632 + 5.86770i 0.703001 + 0.405878i
\(210\) 0 0
\(211\) −25.6481 6.87239i −1.76569 0.473115i −0.777831 0.628473i \(-0.783680\pi\)
−0.987858 + 0.155358i \(0.950347\pi\)
\(212\) −0.490408 + 1.62995i −0.0336814 + 0.111945i
\(213\) 0 0
\(214\) 4.04584 + 16.0746i 0.276568 + 1.09884i
\(215\) 0.676538i 0.0461395i
\(216\) 0 0
\(217\) 7.87574i 0.534640i
\(218\) −27.8900 + 7.01969i −1.88895 + 0.475433i
\(219\) 0 0
\(220\) −2.16491 4.02827i −0.145958 0.271586i
\(221\) −26.5146 7.10457i −1.78357 0.477905i
\(222\) 0 0
\(223\) 2.77266 + 1.60079i 0.185671 + 0.107197i 0.589954 0.807437i \(-0.299146\pi\)
−0.404284 + 0.914634i \(0.632479\pi\)
\(224\) 7.28401 + 0.555723i 0.486684 + 0.0371308i
\(225\) 0 0
\(226\) 0.0544063 3.57222i 0.00361905 0.237621i
\(227\) −2.78291 + 0.745680i −0.184708 + 0.0494925i −0.349988 0.936754i \(-0.613814\pi\)
0.165279 + 0.986247i \(0.447148\pi\)
\(228\) 0 0
\(229\) −17.6277 4.72334i −1.16487 0.312127i −0.375963 0.926635i \(-0.622688\pi\)
−0.788911 + 0.614508i \(0.789355\pi\)
\(230\) 2.55575 + 0.726701i 0.168521 + 0.0479173i
\(231\) 0 0
\(232\) −1.85660 8.45676i −0.121892 0.555214i
\(233\) −6.00585 −0.393456 −0.196728 0.980458i \(-0.563032\pi\)
−0.196728 + 0.980458i \(0.563032\pi\)
\(234\) 0 0
\(235\) 5.97112 + 5.97112i 0.389513 + 0.389513i
\(236\) 2.26792 + 9.62784i 0.147629 + 0.626719i
\(237\) 0 0
\(238\) −8.91034 + 4.96502i −0.577572 + 0.321835i
\(239\) −6.00788 10.4059i −0.388617 0.673105i 0.603647 0.797252i \(-0.293714\pi\)
−0.992264 + 0.124147i \(0.960381\pi\)
\(240\) 0 0
\(241\) 1.51923 2.63138i 0.0978622 0.169502i −0.812937 0.582351i \(-0.802133\pi\)
0.910800 + 0.412849i \(0.135466\pi\)
\(242\) −0.00104720 + 0.0687575i −6.73167e−5 + 0.00441990i
\(243\) 0 0
\(244\) −15.3648 16.3305i −0.983631 1.04545i
\(245\) −3.54317 + 0.949391i −0.226365 + 0.0606543i
\(246\) 0 0
\(247\) 8.67590 + 15.0271i 0.552034 + 0.956152i
\(248\) 15.3169 7.93355i 0.972627 0.503781i
\(249\) 0 0
\(250\) 2.26217 + 8.98784i 0.143072 + 0.568441i
\(251\) −2.95387 + 2.95387i −0.186447 + 0.186447i −0.794158 0.607711i \(-0.792088\pi\)
0.607711 + 0.794158i \(0.292088\pi\)
\(252\) 0 0
\(253\) −6.41937 6.41937i −0.403582 0.403582i
\(254\) −21.2612 12.7108i −1.33405 0.797544i
\(255\) 0 0
\(256\) −6.25670 14.7260i −0.391044 0.920372i
\(257\) −1.67398 + 0.966474i −0.104420 + 0.0602870i −0.551301 0.834307i \(-0.685868\pi\)
0.446880 + 0.894594i \(0.352535\pi\)
\(258\) 0 0
\(259\) −0.239847 0.895122i −0.0149034 0.0556202i
\(260\) 0.205922 6.75867i 0.0127707 0.419155i
\(261\) 0 0
\(262\) 12.2213 + 12.5994i 0.755037 + 0.778392i
\(263\) 1.51993 + 0.877533i 0.0937230 + 0.0541110i 0.546129 0.837701i \(-0.316101\pi\)
−0.452406 + 0.891812i \(0.649434\pi\)
\(264\) 0 0
\(265\) 0.507020 0.292728i 0.0311460 0.0179821i
\(266\) 6.20201 + 1.76348i 0.380270 + 0.108126i
\(267\) 0 0
\(268\) −0.0523885 0.222401i −0.00320014 0.0135853i
\(269\) 14.2013 14.2013i 0.865871 0.865871i −0.126141 0.992012i \(-0.540259\pi\)
0.992012 + 0.126141i \(0.0402592\pi\)
\(270\) 0 0
\(271\) 11.3712i 0.690754i 0.938464 + 0.345377i \(0.112249\pi\)
−0.938464 + 0.345377i \(0.887751\pi\)
\(272\) 18.6319 + 12.3276i 1.12972 + 0.747471i
\(273\) 0 0
\(274\) 6.88460 + 12.3553i 0.415914 + 0.746409i
\(275\) 3.89439 14.5341i 0.234841 0.876437i
\(276\) 0 0
\(277\) 1.81439 + 6.77138i 0.109016 + 0.406853i 0.998770 0.0495877i \(-0.0157907\pi\)
−0.889754 + 0.456441i \(0.849124\pi\)
\(278\) 1.40251 + 1.44589i 0.0841171 + 0.0867190i
\(279\) 0 0
\(280\) −1.69372 1.85601i −0.101219 0.110918i
\(281\) −5.16379 + 8.94395i −0.308046 + 0.533552i −0.977935 0.208910i \(-0.933008\pi\)
0.669889 + 0.742461i \(0.266342\pi\)
\(282\) 0 0
\(283\) 6.25018 23.3260i 0.371535 1.38659i −0.486807 0.873509i \(-0.661839\pi\)
0.858342 0.513078i \(-0.171495\pi\)
\(284\) 0.0789074 0.0424071i 0.00468229 0.00251640i
\(285\) 0 0
\(286\) −11.8549 + 19.8296i −0.700994 + 1.17255i
\(287\) 12.6528 0.746871
\(288\) 0 0
\(289\) −14.1948 −0.834987
\(290\) −1.52811 + 2.55607i −0.0897340 + 0.150098i
\(291\) 0 0
\(292\) 23.4186 12.5858i 1.37047 0.736529i
\(293\) 5.04554 18.8302i 0.294763 1.10007i −0.646642 0.762794i \(-0.723827\pi\)
0.941405 0.337278i \(-0.109506\pi\)
\(294\) 0 0
\(295\) 1.70109 2.94638i 0.0990414 0.171545i
\(296\) −1.49925 + 1.36815i −0.0871421 + 0.0795224i
\(297\) 0 0
\(298\) 5.63709 + 5.81145i 0.326548 + 0.336648i
\(299\) −3.47416 12.9658i −0.200916 0.749829i
\(300\) 0 0
\(301\) −0.328709 + 1.22676i −0.0189465 + 0.0707093i
\(302\) −11.1534 20.0161i −0.641806 1.15180i
\(303\) 0 0
\(304\) −2.81787 13.8383i −0.161616 0.793679i
\(305\) 7.71230i 0.441605i
\(306\) 0 0
\(307\) −4.37646 + 4.37646i −0.249778 + 0.249778i −0.820879 0.571101i \(-0.806516\pi\)
0.571101 + 0.820879i \(0.306516\pi\)
\(308\) 1.96839 + 8.35629i 0.112160 + 0.476144i
\(309\) 0 0
\(310\) −5.70689 1.62270i −0.324130 0.0921630i
\(311\) 2.65273 1.53155i 0.150423 0.0868465i −0.422900 0.906177i \(-0.638988\pi\)
0.573322 + 0.819330i \(0.305654\pi\)
\(312\) 0 0
\(313\) −2.59526 1.49837i −0.146693 0.0846930i 0.424857 0.905260i \(-0.360324\pi\)
−0.571550 + 0.820567i \(0.693658\pi\)
\(314\) 7.71391 + 7.95252i 0.435321 + 0.448787i
\(315\) 0 0
\(316\) −0.175861 + 5.77203i −0.00989296 + 0.324702i
\(317\) −2.47692 9.24401i −0.139118 0.519195i −0.999947 0.0103009i \(-0.996721\pi\)
0.860829 0.508894i \(-0.169946\pi\)
\(318\) 0 0
\(319\) 8.81182 5.08751i 0.493367 0.284846i
\(320\) −1.90347 + 5.16362i −0.106407 + 0.288655i
\(321\) 0 0
\(322\) −4.28123 2.55948i −0.238584 0.142634i
\(323\) 13.9434 + 13.9434i 0.775834 + 0.775834i
\(324\) 0 0
\(325\) 15.7317 15.7317i 0.872636 0.872636i
\(326\) 2.39082 + 9.49901i 0.132415 + 0.526102i
\(327\) 0 0
\(328\) −12.7457 24.6075i −0.703762 1.35872i
\(329\) −7.92619 13.7286i −0.436985 0.756880i
\(330\) 0 0
\(331\) 14.5870 3.90856i 0.801772 0.214834i 0.165410 0.986225i \(-0.447105\pi\)
0.636362 + 0.771391i \(0.280439\pi\)
\(332\) 5.38544 + 5.72392i 0.295565 + 0.314141i
\(333\) 0 0
\(334\) 0.467106 30.6694i 0.0255589 1.67815i
\(335\) −0.0392949 + 0.0680608i −0.00214691 + 0.00371856i
\(336\) 0 0
\(337\) 1.09448 + 1.89569i 0.0596200 + 0.103265i 0.894295 0.447478i \(-0.147678\pi\)
−0.834675 + 0.550743i \(0.814344\pi\)
\(338\) −13.7802 + 7.67858i −0.749542 + 0.417660i
\(339\) 0 0
\(340\) −1.76188 7.47957i −0.0955511 0.405637i
\(341\) 14.3342 + 14.3342i 0.776242 + 0.776242i
\(342\) 0 0
\(343\) 15.9258 0.859912
\(344\) 2.71696 0.596482i 0.146489 0.0321602i
\(345\) 0 0
\(346\) 10.8240 + 3.07771i 0.581904 + 0.165459i
\(347\) 27.6810 + 7.41711i 1.48599 + 0.398171i 0.908382 0.418140i \(-0.137318\pi\)
0.577612 + 0.816311i \(0.303985\pi\)
\(348\) 0 0
\(349\) −23.0850 + 6.18561i −1.23571 + 0.331108i −0.816801 0.576919i \(-0.804255\pi\)
−0.418911 + 0.908027i \(0.637588\pi\)
\(350\) 0.125898 8.26628i 0.00672955 0.441851i
\(351\) 0 0
\(352\) 14.2687 12.2458i 0.760524 0.652704i
\(353\) 0.355770 + 0.205404i 0.0189357 + 0.0109325i 0.509438 0.860507i \(-0.329853\pi\)
−0.490502 + 0.871440i \(0.663187\pi\)
\(354\) 0 0
\(355\) −0.0297620 0.00797469i −0.00157960 0.000423253i
\(356\) −12.0585 22.4374i −0.639099 1.18918i
\(357\) 0 0
\(358\) 18.3864 4.62770i 0.971750 0.244581i
\(359\) 1.19383i 0.0630078i −0.999504 0.0315039i \(-0.989970\pi\)
0.999504 0.0315039i \(-0.0100297\pi\)
\(360\) 0 0
\(361\) 6.53512i 0.343954i
\(362\) −3.90564 15.5175i −0.205276 0.815584i
\(363\) 0 0
\(364\) −3.65723 + 12.1554i −0.191691 + 0.637116i
\(365\) −8.83291 2.36677i −0.462336 0.123883i
\(366\) 0 0
\(367\) 16.1698 + 9.33562i 0.844055 + 0.487316i 0.858641 0.512578i \(-0.171310\pi\)
−0.0145854 + 0.999894i \(0.504643\pi\)
\(368\) −0.665092 + 10.9045i −0.0346703 + 0.568438i
\(369\) 0 0
\(370\) 0.698038 + 0.0106314i 0.0362893 + 0.000552699i
\(371\) −1.06160 + 0.284455i −0.0551156 + 0.0147682i
\(372\) 0 0
\(373\) 11.5442 + 3.09325i 0.597735 + 0.160163i 0.544986 0.838445i \(-0.316535\pi\)
0.0527491 + 0.998608i \(0.483202\pi\)
\(374\) −7.18068 + 25.2538i −0.371304 + 1.30585i
\(375\) 0 0
\(376\) −18.7153 + 29.2444i −0.965169 + 1.50817i
\(377\) 15.0446 0.774838
\(378\) 0 0
\(379\) 15.3650 + 15.3650i 0.789248 + 0.789248i 0.981371 0.192123i \(-0.0615372\pi\)
−0.192123 + 0.981371i \(0.561537\pi\)
\(380\) −2.55570 + 4.13074i −0.131104 + 0.211903i
\(381\) 0 0
\(382\) 12.7072 + 22.8046i 0.650156 + 1.16679i
\(383\) 11.1162 + 19.2539i 0.568013 + 0.983827i 0.996762 + 0.0804037i \(0.0256210\pi\)
−0.428750 + 0.903423i \(0.641046\pi\)
\(384\) 0 0
\(385\) 1.47643 2.55725i 0.0752458 0.130330i
\(386\) 7.39952 + 0.112697i 0.376626 + 0.00573615i
\(387\) 0 0
\(388\) −17.6345 0.537284i −0.895255 0.0272764i
\(389\) −15.6338 + 4.18905i −0.792663 + 0.212393i −0.632360 0.774675i \(-0.717914\pi\)
−0.160303 + 0.987068i \(0.551247\pi\)
\(390\) 0 0
\(391\) −7.62718 13.2107i −0.385723 0.668092i
\(392\) −6.93663 13.3923i −0.350353 0.676411i
\(393\) 0 0
\(394\) −27.8462 + 7.00866i −1.40287 + 0.353091i
\(395\) 1.40449 1.40449i 0.0706674 0.0706674i
\(396\) 0 0
\(397\) 14.5828 + 14.5828i 0.731887 + 0.731887i 0.970993 0.239106i \(-0.0768543\pi\)
−0.239106 + 0.970993i \(0.576854\pi\)
\(398\) −10.0403 + 16.7944i −0.503277 + 0.841829i
\(399\) 0 0
\(400\) −16.2033 + 8.08211i −0.810165 + 0.404105i
\(401\) −27.9585 + 16.1418i −1.39618 + 0.806085i −0.993990 0.109470i \(-0.965085\pi\)
−0.402191 + 0.915556i \(0.631751\pi\)
\(402\) 0 0
\(403\) 7.75768 + 28.9521i 0.386438 + 1.44220i
\(404\) −9.96764 10.5941i −0.495909 0.527077i
\(405\) 0 0
\(406\) 4.01283 3.89243i 0.199154 0.193178i
\(407\) −2.06570 1.19263i −0.102393 0.0591166i
\(408\) 0 0
\(409\) 12.9975 7.50409i 0.642683 0.371053i −0.142964 0.989728i \(-0.545663\pi\)
0.785647 + 0.618674i \(0.212330\pi\)
\(410\) −2.60695 + 9.16844i −0.128748 + 0.452797i
\(411\) 0 0
\(412\) 20.0081 32.3388i 0.985727 1.59322i
\(413\) −4.51613 + 4.51613i −0.222224 + 0.222224i
\(414\) 0 0
\(415\) 2.70320i 0.132695i
\(416\) 27.3242 5.13193i 1.33968 0.251614i
\(417\) 0 0
\(418\) 14.4976 8.07835i 0.709100 0.395125i
\(419\) −6.00718 + 22.4191i −0.293470 + 1.09525i 0.648955 + 0.760827i \(0.275206\pi\)
−0.942425 + 0.334418i \(0.891460\pi\)
\(420\) 0 0
\(421\) 4.05109 + 15.1189i 0.197438 + 0.736849i 0.991622 + 0.129172i \(0.0412319\pi\)
−0.794184 + 0.607677i \(0.792101\pi\)
\(422\) −26.9542 + 26.1454i −1.31211 + 1.27274i
\(423\) 0 0
\(424\) 1.62261 + 1.77809i 0.0788010 + 0.0863517i
\(425\) 12.6415 21.8958i 0.613205 1.06210i
\(426\) 0 0
\(427\) 3.74717 13.9846i 0.181338 0.676764i
\(428\) 22.4479 + 6.75396i 1.08506 + 0.326465i
\(429\) 0 0
\(430\) −0.821205 0.490947i −0.0396020 0.0236756i
\(431\) 1.63818 0.0789082 0.0394541 0.999221i \(-0.487438\pi\)
0.0394541 + 0.999221i \(0.487438\pi\)
\(432\) 0 0
\(433\) 24.1284 1.15954 0.579769 0.814781i \(-0.303143\pi\)
0.579769 + 0.814781i \(0.303143\pi\)
\(434\) 9.55984 + 5.71523i 0.458887 + 0.274340i
\(435\) 0 0
\(436\) −11.7184 + 38.9479i −0.561209 + 1.86527i
\(437\) −2.49571 + 9.31411i −0.119386 + 0.445554i
\(438\) 0 0
\(439\) 6.04546 10.4711i 0.288534 0.499756i −0.684926 0.728613i \(-0.740165\pi\)
0.973460 + 0.228857i \(0.0734987\pi\)
\(440\) −6.46068 0.295378i −0.308001 0.0140816i
\(441\) 0 0
\(442\) −27.8648 + 27.0287i −1.32539 + 1.28563i
\(443\) 4.35450 + 16.2512i 0.206889 + 0.772119i 0.988866 + 0.148811i \(0.0475448\pi\)
−0.781977 + 0.623307i \(0.785789\pi\)
\(444\) 0 0
\(445\) −2.26761 + 8.46284i −0.107495 + 0.401177i
\(446\) 3.95515 2.20389i 0.187282 0.104357i
\(447\) 0 0
\(448\) 5.96039 8.43831i 0.281602 0.398673i
\(449\) 31.8270i 1.50201i −0.660298 0.751004i \(-0.729570\pi\)
0.660298 0.751004i \(-0.270430\pi\)
\(450\) 0 0
\(451\) 23.0287 23.0287i 1.08438 1.08438i
\(452\) −4.29661 2.65832i −0.202095 0.125037i
\(453\) 0 0
\(454\) −1.11436 + 3.91912i −0.0522996 + 0.183933i
\(455\) 3.78111 2.18303i 0.177261 0.102342i
\(456\) 0 0
\(457\) −24.8553 14.3502i −1.16268 0.671275i −0.210737 0.977543i \(-0.567586\pi\)
−0.951945 + 0.306268i \(0.900920\pi\)
\(458\) −18.5254 + 17.9695i −0.865634 + 0.839661i
\(459\) 0 0
\(460\) 2.73674 2.57491i 0.127601 0.120056i
\(461\) −0.483918 1.80601i −0.0225383 0.0841141i 0.953741 0.300631i \(-0.0971971\pi\)
−0.976279 + 0.216517i \(0.930530\pi\)
\(462\) 0 0
\(463\) −4.71990 + 2.72503i −0.219352 + 0.126643i −0.605650 0.795731i \(-0.707087\pi\)
0.386298 + 0.922374i \(0.373754\pi\)
\(464\) −11.6124 3.88326i −0.539092 0.180276i
\(465\) 0 0
\(466\) −4.35830 + 7.29011i −0.201894 + 0.337708i
\(467\) −8.95228 8.95228i −0.414262 0.414262i 0.468958 0.883220i \(-0.344630\pi\)
−0.883220 + 0.468958i \(0.844630\pi\)
\(468\) 0 0
\(469\) 0.104322 0.104322i 0.00481713 0.00481713i
\(470\) 11.5810 2.91485i 0.534194 0.134452i
\(471\) 0 0
\(472\) 13.3324 + 4.23381i 0.613672 + 0.194877i
\(473\) 1.63450 + 2.83103i 0.0751542 + 0.130171i
\(474\) 0 0
\(475\) −15.4375 + 4.13647i −0.708321 + 0.189794i
\(476\) −0.439306 + 14.4187i −0.0201355 + 0.660879i
\(477\) 0 0
\(478\) −16.9909 0.258777i −0.777144 0.0118362i
\(479\) 4.27809 7.40987i 0.195471 0.338566i −0.751584 0.659638i \(-0.770710\pi\)
0.947055 + 0.321072i \(0.104043\pi\)
\(480\) 0 0
\(481\) −1.76341 3.05431i −0.0804045 0.139265i
\(482\) −2.09160 3.75363i −0.0952696 0.170973i
\(483\) 0 0
\(484\) 0.0827003 + 0.0511668i 0.00375911 + 0.00232576i
\(485\) 4.29093 + 4.29093i 0.194841 + 0.194841i
\(486\) 0 0
\(487\) −13.1689 −0.596738 −0.298369 0.954451i \(-0.596443\pi\)
−0.298369 + 0.954451i \(0.596443\pi\)
\(488\) −30.9724 + 6.79969i −1.40205 + 0.307808i
\(489\) 0 0
\(490\) −1.41879 + 4.98978i −0.0640945 + 0.225415i
\(491\) −8.09692 2.16956i −0.365409 0.0979110i 0.0714425 0.997445i \(-0.477240\pi\)
−0.436851 + 0.899534i \(0.643906\pi\)
\(492\) 0 0
\(493\) 16.5145 4.42505i 0.743776 0.199294i
\(494\) 24.5363 + 0.373697i 1.10394 + 0.0168134i
\(495\) 0 0
\(496\) 1.48513 24.3494i 0.0666841 1.09332i
\(497\) 0.0500924 + 0.0289209i 0.00224695 + 0.00129728i
\(498\) 0 0
\(499\) 31.2957 + 8.38567i 1.40099 + 0.375394i 0.878700 0.477374i \(-0.158411\pi\)
0.522289 + 0.852768i \(0.325078\pi\)
\(500\) 12.5514 + 3.77637i 0.561314 + 0.168884i
\(501\) 0 0
\(502\) 1.44196 + 5.72906i 0.0643577 + 0.255701i
\(503\) 20.8126i 0.927989i 0.885838 + 0.463994i \(0.153584\pi\)
−0.885838 + 0.463994i \(0.846416\pi\)
\(504\) 0 0
\(505\) 5.00321i 0.222640i
\(506\) −12.4504 + 3.13367i −0.553489 + 0.139309i
\(507\) 0 0
\(508\) −30.8575 + 16.5837i −1.36908 + 0.735783i
\(509\) 20.7078 + 5.54865i 0.917859 + 0.245940i 0.686670 0.726969i \(-0.259072\pi\)
0.231189 + 0.972909i \(0.425738\pi\)
\(510\) 0 0
\(511\) 14.8667 + 8.58329i 0.657664 + 0.379703i
\(512\) −22.4152 3.09167i −0.990622 0.136634i
\(513\) 0 0
\(514\) −0.0416289 + 2.73329i −0.00183617 + 0.120560i
\(515\) −12.6342 + 3.38533i −0.556730 + 0.149175i
\(516\) 0 0
\(517\) −39.4127 10.5606i −1.73337 0.464455i
\(518\) −1.26058 0.358434i −0.0553868 0.0157487i
\(519\) 0 0
\(520\) −8.05448 5.15456i −0.353212 0.226042i
\(521\) −20.1534 −0.882938 −0.441469 0.897277i \(-0.645542\pi\)
−0.441469 + 0.897277i \(0.645542\pi\)
\(522\) 0 0
\(523\) 14.7713 + 14.7713i 0.645905 + 0.645905i 0.952001 0.306096i \(-0.0990228\pi\)
−0.306096 + 0.952001i \(0.599023\pi\)
\(524\) 24.1623 5.69163i 1.05553 0.248640i
\(525\) 0 0
\(526\) 2.16816 1.20814i 0.0945362 0.0526775i
\(527\) 17.0312 + 29.4990i 0.741892 + 1.28499i
\(528\) 0 0
\(529\) −7.77028 + 13.4585i −0.337838 + 0.585153i
\(530\) 0.0126087 0.827864i 0.000547686 0.0359601i
\(531\) 0 0
\(532\) 6.64122 6.24850i 0.287934 0.270907i
\(533\) 46.5131 12.4631i 2.01470 0.539838i
\(534\) 0 0
\(535\) −4.03149 6.98274i −0.174296 0.301890i
\(536\) −0.307976 0.0978004i −0.0133025 0.00422433i
\(537\) 0 0
\(538\) −6.93251 27.5437i −0.298882 1.18749i
\(539\) 12.5330 12.5330i 0.539835 0.539835i
\(540\) 0 0
\(541\) 11.1739 + 11.1739i 0.480403 + 0.480403i 0.905260 0.424857i \(-0.139676\pi\)
−0.424857 + 0.905260i \(0.639676\pi\)
\(542\) 13.8028 + 8.25184i 0.592882 + 0.354447i
\(543\) 0 0
\(544\) 28.4844 13.6701i 1.22126 0.586103i
\(545\) 12.1153 6.99478i 0.518963 0.299624i
\(546\) 0 0
\(547\) −3.23236 12.0633i −0.138206 0.515791i −0.999964 0.00847177i \(-0.997303\pi\)
0.861758 0.507319i \(-0.169363\pi\)
\(548\) 19.9932 + 0.609150i 0.854068 + 0.0260216i
\(549\) 0 0
\(550\) −14.8159 15.2742i −0.631751 0.651293i
\(551\) −9.35956 5.40375i −0.398731 0.230207i
\(552\) 0 0
\(553\) −3.22914 + 1.86435i −0.137317 + 0.0792800i
\(554\) 9.53600 + 2.71146i 0.405146 + 0.115199i
\(555\) 0 0
\(556\) 2.77285 0.653167i 0.117595 0.0277004i
\(557\) 4.41323 4.41323i 0.186995 0.186995i −0.607401 0.794395i \(-0.707788\pi\)
0.794395 + 0.607401i \(0.207788\pi\)
\(558\) 0 0
\(559\) 4.83349i 0.204435i
\(560\) −3.48198 + 0.709032i −0.147140 + 0.0299621i
\(561\) 0 0
\(562\) 7.10924 + 12.7584i 0.299885 + 0.538181i
\(563\) 9.09152 33.9300i 0.383162 1.42998i −0.457882 0.889013i \(-0.651392\pi\)
0.841044 0.540967i \(-0.181942\pi\)
\(564\) 0 0
\(565\) 0.449782 + 1.67861i 0.0189225 + 0.0706197i
\(566\) −23.7783 24.5138i −0.999477 1.03039i
\(567\) 0 0
\(568\) 0.00578599 0.126554i 0.000242775 0.00531010i
\(569\) 10.8432 18.7810i 0.454572 0.787342i −0.544091 0.839026i \(-0.683126\pi\)
0.998663 + 0.0516841i \(0.0164589\pi\)
\(570\) 0 0
\(571\) 2.69081 10.0422i 0.112607 0.420255i −0.886490 0.462748i \(-0.846863\pi\)
0.999097 + 0.0424934i \(0.0135301\pi\)
\(572\) 15.4671 + 28.7797i 0.646710 + 1.20334i
\(573\) 0 0
\(574\) 9.18183 15.3584i 0.383242 0.641047i
\(575\) 12.3635 0.515595
\(576\) 0 0
\(577\) −33.2014 −1.38219 −0.691096 0.722763i \(-0.742872\pi\)
−0.691096 + 0.722763i \(0.742872\pi\)
\(578\) −10.3008 + 17.2301i −0.428457 + 0.716678i
\(579\) 0 0
\(580\) 1.99373 + 3.70976i 0.0827851 + 0.154039i
\(581\) −1.31340 + 4.90169i −0.0544891 + 0.203356i
\(582\) 0 0
\(583\) −1.41444 + 2.44989i −0.0585803 + 0.101464i
\(584\) 1.71720 37.5595i 0.0710581 1.55422i
\(585\) 0 0
\(586\) −19.1953 19.7891i −0.792951 0.817479i
\(587\) 0.554497 + 2.06941i 0.0228865 + 0.0854137i 0.976425 0.215859i \(-0.0692552\pi\)
−0.953538 + 0.301273i \(0.902589\pi\)
\(588\) 0 0
\(589\) 5.57282 20.7981i 0.229624 0.856969i
\(590\) −2.34197 4.20296i −0.0964175 0.173033i
\(591\) 0 0
\(592\) 0.572743 + 2.81268i 0.0235396 + 0.115600i
\(593\) 13.9278i 0.571945i 0.958238 + 0.285973i \(0.0923166\pi\)
−0.958238 + 0.285973i \(0.907683\pi\)
\(594\) 0 0
\(595\) 3.50844 3.50844i 0.143832 0.143832i
\(596\) 11.1448 2.62526i 0.456510 0.107535i
\(597\) 0 0
\(598\) −18.2594 5.19187i −0.746682 0.212312i
\(599\) −20.2130 + 11.6700i −0.825881 + 0.476823i −0.852440 0.522825i \(-0.824878\pi\)
0.0265594 + 0.999647i \(0.491545\pi\)
\(600\) 0 0
\(601\) −10.3379 5.96857i −0.421691 0.243463i 0.274110 0.961698i \(-0.411617\pi\)
−0.695800 + 0.718235i \(0.744950\pi\)
\(602\) 1.25055 + 1.28923i 0.0509685 + 0.0525451i
\(603\) 0 0
\(604\) −32.3900 0.986853i −1.31793 0.0401545i
\(605\) −0.00865733 0.0323096i −0.000351971 0.00131357i
\(606\) 0 0
\(607\) −10.3919 + 5.99979i −0.421796 + 0.243524i −0.695845 0.718192i \(-0.744970\pi\)
0.274050 + 0.961716i \(0.411637\pi\)
\(608\) −18.8422 6.62167i −0.764153 0.268544i
\(609\) 0 0
\(610\) 9.36145 + 5.59663i 0.379034 + 0.226601i
\(611\) −42.6603 42.6603i −1.72585 1.72585i
\(612\) 0 0
\(613\) −18.1803 + 18.1803i −0.734296 + 0.734296i −0.971468 0.237172i \(-0.923780\pi\)
0.237172 + 0.971468i \(0.423780\pi\)
\(614\) 2.13641 + 8.48820i 0.0862185 + 0.342556i
\(615\) 0 0
\(616\) 11.5716 + 3.67466i 0.466232 + 0.148056i
\(617\) −18.9672 32.8521i −0.763589 1.32257i −0.940989 0.338436i \(-0.890102\pi\)
0.177401 0.984139i \(-0.443231\pi\)
\(618\) 0 0
\(619\) −0.00230201 0.000616823i −9.25258e−5 2.47922e-5i −0.258865 0.965913i \(-0.583349\pi\)
0.258773 + 0.965938i \(0.416682\pi\)
\(620\) −6.11104 + 5.74967i −0.245425 + 0.230912i
\(621\) 0 0
\(622\) 0.0659686 4.33139i 0.00264510 0.173673i
\(623\) 8.22368 14.2438i 0.329475 0.570667i
\(624\) 0 0
\(625\) 9.06281 + 15.6972i 0.362512 + 0.627890i
\(626\) −3.70209 + 2.06288i −0.147965 + 0.0824493i
\(627\) 0 0
\(628\) 15.2508 3.59246i 0.608575 0.143355i
\(629\) −2.83406 2.83406i −0.113001 0.113001i
\(630\) 0 0
\(631\) −39.2643 −1.56309 −0.781543 0.623852i \(-0.785567\pi\)
−0.781543 + 0.623852i \(0.785567\pi\)
\(632\) 6.87867 + 4.40209i 0.273619 + 0.175106i
\(633\) 0 0
\(634\) −13.0181 3.70158i −0.517016 0.147008i
\(635\) 11.6387 + 3.11858i 0.461868 + 0.123757i
\(636\) 0 0
\(637\) 25.3140 6.78286i 1.00298 0.268747i
\(638\) 0.219134 14.3880i 0.00867560 0.569625i
\(639\) 0 0
\(640\) 4.88648 + 6.05761i 0.193155 + 0.239448i
\(641\) −15.2983 8.83246i −0.604245 0.348861i 0.166465 0.986047i \(-0.446765\pi\)
−0.770710 + 0.637186i \(0.780098\pi\)
\(642\) 0 0
\(643\) −6.60298 1.76926i −0.260396 0.0697729i 0.126259 0.991997i \(-0.459703\pi\)
−0.386655 + 0.922224i \(0.626370\pi\)
\(644\) −6.21358 + 3.33935i −0.244849 + 0.131589i
\(645\) 0 0
\(646\) 27.0435 6.80661i 1.06401 0.267803i
\(647\) 4.24252i 0.166791i 0.996517 + 0.0833953i \(0.0265764\pi\)
−0.996517 + 0.0833953i \(0.973424\pi\)
\(648\) 0 0
\(649\) 16.4392i 0.645293i
\(650\) −7.67955 30.5117i −0.301217 1.19677i
\(651\) 0 0
\(652\) 13.2652 + 3.99114i 0.519505 + 0.156305i
\(653\) 26.6484 + 7.14041i 1.04283 + 0.279426i 0.739286 0.673391i \(-0.235163\pi\)
0.303545 + 0.952817i \(0.401830\pi\)
\(654\) 0 0
\(655\) −7.39431 4.26911i −0.288919 0.166808i
\(656\) −39.1187 2.38594i −1.52733 0.0931551i
\(657\) 0 0
\(658\) −22.4161 0.341405i −0.873869 0.0133093i
\(659\) 10.1504 2.71978i 0.395402 0.105948i −0.0556391 0.998451i \(-0.517720\pi\)
0.451041 + 0.892503i \(0.351053\pi\)
\(660\) 0 0
\(661\) −28.3410 7.59396i −1.10234 0.295371i −0.338622 0.940922i \(-0.609961\pi\)
−0.763717 + 0.645552i \(0.776628\pi\)
\(662\) 5.84105 20.5425i 0.227019 0.798407i
\(663\) 0 0
\(664\) 10.8560 2.38333i 0.421294 0.0924910i
\(665\) −3.13641 −0.121625
\(666\) 0 0
\(667\) 5.91179 + 5.91179i 0.228905 + 0.228905i
\(668\) −36.8886 22.8230i −1.42726 0.883049i
\(669\) 0 0
\(670\) 0.0540992 + 0.0970876i 0.00209003 + 0.00375082i
\(671\) −18.6327 32.2728i −0.719307 1.24588i
\(672\) 0 0
\(673\) −5.32418 + 9.22175i −0.205232 + 0.355472i −0.950207 0.311621i \(-0.899128\pi\)
0.744975 + 0.667093i \(0.232462\pi\)
\(674\) 3.09529 + 0.0471425i 0.119226 + 0.00181586i
\(675\) 0 0
\(676\) −0.679401 + 22.2990i −0.0261308 + 0.857654i
\(677\) −21.2938 + 5.70565i −0.818387 + 0.219286i −0.643641 0.765327i \(-0.722577\pi\)
−0.174746 + 0.984614i \(0.555910\pi\)
\(678\) 0 0
\(679\) −5.69587 9.86554i −0.218587 0.378605i
\(680\) −10.3575 3.28912i −0.397192 0.126132i
\(681\) 0 0
\(682\) 27.8014 6.99738i 1.06457 0.267943i
\(683\) −1.68202 + 1.68202i −0.0643609 + 0.0643609i −0.738555 0.674194i \(-0.764491\pi\)
0.674194 + 0.738555i \(0.264491\pi\)
\(684\) 0 0
\(685\) −4.86488 4.86488i −0.185877 0.185877i
\(686\) 11.5570 19.3313i 0.441247 0.738071i
\(687\) 0 0
\(688\) 1.24760 3.73079i 0.0475644 0.142235i
\(689\) −3.62237 + 2.09138i −0.138001 + 0.0796751i
\(690\) 0 0
\(691\) −0.595784 2.22350i −0.0226647 0.0845858i 0.953667 0.300864i \(-0.0972749\pi\)
−0.976332 + 0.216278i \(0.930608\pi\)
\(692\) 11.5906 10.9052i 0.440607 0.414553i
\(693\) 0 0
\(694\) 29.0906 28.2178i 1.10426 1.07113i
\(695\) −0.848565 0.489919i −0.0321879 0.0185837i
\(696\) 0 0
\(697\) 47.3917 27.3616i 1.79509 1.03639i
\(698\) −9.24393 + 32.5101i −0.349888 + 1.23053i
\(699\) 0 0
\(700\) −9.94253 6.15146i −0.375792 0.232503i
\(701\) −10.2728 + 10.2728i −0.387997 + 0.387997i −0.873972 0.485976i \(-0.838464\pi\)
0.485976 + 0.873972i \(0.338464\pi\)
\(702\) 0 0
\(703\) 2.53353i 0.0955540i
\(704\) −4.50994 26.2063i −0.169975 0.987689i
\(705\) 0 0
\(706\) 0.507500 0.282789i 0.0191000 0.0106429i
\(707\) 2.43091 9.07228i 0.0914238 0.341198i
\(708\) 0 0
\(709\) 1.30925 + 4.88619i 0.0491700 + 0.183505i 0.986143 0.165896i \(-0.0530517\pi\)
−0.936973 + 0.349401i \(0.886385\pi\)
\(710\) −0.0312775 + 0.0303391i −0.00117382 + 0.00113860i
\(711\) 0 0
\(712\) −35.9858 1.64525i −1.34863 0.0616584i
\(713\) −8.32834 + 14.4251i −0.311899 + 0.540224i
\(714\) 0 0
\(715\) 2.90859 10.8550i 0.108775 0.405955i
\(716\) 7.72529 25.6762i 0.288708 0.959566i
\(717\) 0 0
\(718\) −1.44911 0.866331i −0.0540802 0.0323312i
\(719\) −6.73858 −0.251307 −0.125653 0.992074i \(-0.540103\pi\)
−0.125653 + 0.992074i \(0.540103\pi\)
\(720\) 0 0
\(721\) 24.5544 0.914452
\(722\) 7.93255 + 4.74238i 0.295219 + 0.176493i
\(723\) 0 0
\(724\) −21.6700 6.51991i −0.805358 0.242311i
\(725\) −3.58646 + 13.3849i −0.133198 + 0.497101i
\(726\) 0 0
\(727\) −4.14056 + 7.17166i −0.153565 + 0.265982i −0.932536 0.361078i \(-0.882409\pi\)
0.778971 + 0.627060i \(0.215742\pi\)
\(728\) 12.1007 + 13.2601i 0.448481 + 0.491454i
\(729\) 0 0
\(730\) −9.28270 + 9.00419i −0.343568 + 0.333260i
\(731\) 1.42166 + 5.30572i 0.0525821 + 0.196239i
\(732\) 0 0
\(733\) −11.7070 + 43.6909i −0.432406 + 1.61376i 0.314792 + 0.949161i \(0.398065\pi\)
−0.747198 + 0.664601i \(0.768601\pi\)
\(734\) 23.0659 12.8528i 0.851378 0.474405i
\(735\) 0 0
\(736\) 12.7537 + 8.72047i 0.470106 + 0.321441i
\(737\) 0.379742i 0.0139880i
\(738\) 0 0
\(739\) 22.0530 22.0530i 0.811234 0.811234i −0.173585 0.984819i \(-0.555535\pi\)
0.984819 + 0.173585i \(0.0555352\pi\)
\(740\) 0.519454 0.839588i 0.0190955 0.0308639i
\(741\) 0 0
\(742\) −0.425097 + 1.49503i −0.0156058 + 0.0548843i
\(743\) −29.9386 + 17.2851i −1.09834 + 0.634128i −0.935785 0.352571i \(-0.885307\pi\)
−0.162557 + 0.986699i \(0.551974\pi\)
\(744\) 0 0
\(745\) −3.41062 1.96912i −0.124955 0.0721431i
\(746\) 12.1320 11.7680i 0.444185 0.430858i
\(747\) 0 0
\(748\) 25.4431 + 27.0423i 0.930293 + 0.988763i
\(749\) 3.91756 + 14.6205i 0.143144 + 0.534222i
\(750\) 0 0
\(751\) −38.8676 + 22.4402i −1.41830 + 0.818855i −0.996149 0.0876713i \(-0.972057\pi\)
−0.422149 + 0.906526i \(0.638724\pi\)
\(752\) 21.9166 + 43.9393i 0.799217 + 1.60230i
\(753\) 0 0
\(754\) 10.9175 18.2617i 0.397593 0.665051i
\(755\) 7.88134 + 7.88134i 0.286832 + 0.286832i
\(756\) 0 0
\(757\) 27.6111 27.6111i 1.00354 1.00354i 0.00354931 0.999994i \(-0.498870\pi\)
0.999994 0.00354931i \(-0.00112978\pi\)
\(758\) 29.8006 7.50057i 1.08241 0.272433i
\(759\) 0 0
\(760\) 3.15943 + 6.09977i 0.114605 + 0.221262i
\(761\) 17.8578 + 30.9307i 0.647346 + 1.12124i 0.983754 + 0.179520i \(0.0574545\pi\)
−0.336408 + 0.941716i \(0.609212\pi\)
\(762\) 0 0
\(763\) −25.3672 + 6.79711i −0.918353 + 0.246072i
\(764\) 36.9023 + 1.12433i 1.33508 + 0.0406769i
\(765\) 0 0
\(766\) 31.4378 + 0.478809i 1.13589 + 0.0173001i
\(767\) −12.1534 + 21.0502i −0.438832 + 0.760079i
\(768\) 0 0
\(769\) −22.6077 39.1577i −0.815254 1.41206i −0.909145 0.416479i \(-0.863264\pi\)
0.0938910 0.995582i \(-0.470069\pi\)
\(770\) −2.03267 3.64788i −0.0732523 0.131460i
\(771\) 0 0
\(772\) 5.50645 8.90002i 0.198182 0.320319i
\(773\) −5.57961 5.57961i −0.200685 0.200685i 0.599609 0.800293i \(-0.295323\pi\)
−0.800293 + 0.599609i \(0.795323\pi\)
\(774\) 0 0
\(775\) −27.6073 −0.991684
\(776\) −13.4491 + 21.0154i −0.482794 + 0.754410i
\(777\) 0 0
\(778\) −6.26022 + 22.0167i −0.224440 + 0.789336i
\(779\) −33.4132 8.95305i −1.19715 0.320776i
\(780\) 0 0
\(781\) 0.143808 0.0385333i 0.00514586 0.00137883i
\(782\) −21.5704 0.328526i −0.771357 0.0117481i
\(783\) 0 0
\(784\) −21.2897 1.29851i −0.760347 0.0463753i
\(785\) −4.66717 2.69459i −0.166578 0.0961741i
\(786\) 0 0
\(787\) 8.95529 + 2.39956i 0.319221 + 0.0855351i 0.414872 0.909880i \(-0.363826\pi\)
−0.0956504 + 0.995415i \(0.530493\pi\)
\(788\) −11.7000 + 38.8867i −0.416794 + 1.38528i
\(789\) 0 0
\(790\) −0.685612 2.72402i −0.0243930 0.0969161i
\(791\) 3.26235i 0.115996i
\(792\) 0 0
\(793\) 55.1001i 1.95666i
\(794\) 28.2834 7.11870i 1.00374 0.252633i
\(795\) 0 0
\(796\) 13.0996 + 24.3746i 0.464304 + 0.863936i
\(797\) 24.5310 + 6.57307i 0.868934 + 0.232830i 0.665627 0.746285i \(-0.268164\pi\)
0.203307 + 0.979115i \(0.434831\pi\)
\(798\) 0 0
\(799\) −59.3759 34.2807i −2.10057 1.21276i
\(800\) −1.94801 + 25.5331i −0.0688726 + 0.902732i
\(801\) 0 0
\(802\) −0.695278 + 45.6508i −0.0245511 + 1.61198i
\(803\) 42.6801 11.4361i 1.50615 0.403571i
\(804\) 0 0
\(805\) 2.34361 + 0.627969i 0.0826014 + 0.0221330i
\(806\) 40.7726 + 11.5933i 1.43615 + 0.408355i
\(807\) 0 0
\(808\) −20.0928 + 4.41118i −0.706862 + 0.155185i
\(809\) −33.1931 −1.16701 −0.583503 0.812111i \(-0.698318\pi\)
−0.583503 + 0.812111i \(0.698318\pi\)
\(810\) 0 0
\(811\) 7.35128 + 7.35128i 0.258138 + 0.258138i 0.824297 0.566158i \(-0.191571\pi\)
−0.566158 + 0.824297i \(0.691571\pi\)
\(812\) −1.81275 7.69556i −0.0636152 0.270061i
\(813\) 0 0
\(814\) −2.94669 + 1.64195i −0.103281 + 0.0575504i
\(815\) −2.38234 4.12633i −0.0834497 0.144539i
\(816\) 0 0
\(817\) 1.73610 3.00701i 0.0607383 0.105202i
\(818\) 0.323224 21.2223i 0.0113013 0.742021i
\(819\) 0 0
\(820\) 9.23716 + 9.81772i 0.322576 + 0.342850i
\(821\) −38.6179 + 10.3476i −1.34777 + 0.361135i −0.859313 0.511450i \(-0.829109\pi\)
−0.488462 + 0.872585i \(0.662442\pi\)
\(822\) 0 0
\(823\) 11.8717 + 20.5623i 0.413821 + 0.716758i 0.995304 0.0968000i \(-0.0308607\pi\)
−0.581483 + 0.813558i \(0.697527\pi\)
\(824\) −24.7346 47.7540i −0.861670 1.66359i
\(825\) 0 0
\(826\) 2.20459 + 8.75908i 0.0767075 + 0.304768i
\(827\) −25.1545 + 25.1545i −0.874708 + 0.874708i −0.992981 0.118273i \(-0.962264\pi\)
0.118273 + 0.992981i \(0.462264\pi\)
\(828\) 0 0
\(829\) 6.12372 + 6.12372i 0.212686 + 0.212686i 0.805407 0.592722i \(-0.201947\pi\)
−0.592722 + 0.805407i \(0.701947\pi\)
\(830\) −3.28124 1.96165i −0.113893 0.0680897i
\(831\) 0 0
\(832\) 13.5992 36.8912i 0.471468 1.27897i
\(833\) 25.7922 14.8911i 0.893646 0.515947i
\(834\) 0 0
\(835\) 3.86161 + 14.4117i 0.133637 + 0.498739i
\(836\) 0.714772 23.4599i 0.0247209 0.811379i
\(837\) 0 0
\(838\) 22.8538 + 23.5607i 0.789472 + 0.813892i
\(839\) 35.2084 + 20.3276i 1.21553 + 0.701786i 0.963958 0.266054i \(-0.0857198\pi\)
0.251570 + 0.967839i \(0.419053\pi\)
\(840\) 0 0
\(841\) 16.9997 9.81476i 0.586195 0.338440i
\(842\) 21.2916 + 6.05405i 0.733757 + 0.208636i
\(843\) 0 0
\(844\) 12.1763 + 51.6910i 0.419124 + 1.77928i
\(845\) 5.42593 5.42593i 0.186658 0.186658i
\(846\) 0 0
\(847\) 0.0627931i 0.00215760i
\(848\) 3.33580 0.679265i 0.114552 0.0233261i
\(849\) 0 0
\(850\) −17.4042 31.2340i −0.596960 1.07132i
\(851\) 0.507262 1.89313i 0.0173887 0.0648955i
\(852\) 0 0
\(853\) 11.1499 + 41.6120i 0.381765 + 1.42477i 0.843203 + 0.537595i \(0.180667\pi\)
−0.461437 + 0.887173i \(0.652666\pi\)
\(854\) −14.2558 14.6968i −0.487824 0.502913i
\(855\) 0 0
\(856\) 24.4881 22.3468i 0.836985 0.763798i
\(857\) −4.72246 + 8.17953i −0.161316 + 0.279408i −0.935341 0.353748i \(-0.884907\pi\)
0.774025 + 0.633155i \(0.218241\pi\)
\(858\) 0 0
\(859\) −5.87045 + 21.9088i −0.200297 + 0.747519i 0.790535 + 0.612417i \(0.209803\pi\)
−0.990832 + 0.135102i \(0.956864\pi\)
\(860\) −1.19186 + 0.640539i −0.0406420 + 0.0218422i
\(861\) 0 0
\(862\) 1.18878 1.98847i 0.0404902 0.0677277i
\(863\) 3.58147 0.121915 0.0609573 0.998140i \(-0.480585\pi\)
0.0609573 + 0.998140i \(0.480585\pi\)
\(864\) 0 0
\(865\) −5.47380 −0.186115
\(866\) 17.5094 29.2879i 0.594994 0.995243i
\(867\) 0 0
\(868\) 13.8747 7.45666i 0.470938 0.253096i
\(869\) −2.48399 + 9.27039i −0.0842637 + 0.314476i
\(870\) 0 0
\(871\) 0.280740 0.486256i 0.00951252 0.0164762i
\(872\) 38.7726 + 42.4877i 1.31300 + 1.43882i
\(873\) 0 0
\(874\) 9.49471 + 9.78840i 0.321163 + 0.331098i
\(875\) 2.19044 + 8.17482i 0.0740503 + 0.276359i
\(876\) 0 0
\(877\) 4.52743 16.8966i 0.152881 0.570558i −0.846397 0.532553i \(-0.821233\pi\)
0.999278 0.0380056i \(-0.0121005\pi\)
\(878\) −8.32308 14.9368i −0.280890 0.504092i
\(879\) 0 0
\(880\) −5.04690 + 7.62784i −0.170131 + 0.257135i
\(881\) 46.1363i 1.55437i 0.629272 + 0.777185i \(0.283353\pi\)
−0.629272 + 0.777185i \(0.716647\pi\)
\(882\) 0 0
\(883\) 19.7311 19.7311i 0.664003 0.664003i −0.292318 0.956321i \(-0.594427\pi\)
0.956321 + 0.292318i \(0.0944265\pi\)
\(884\) 12.5876 + 53.4373i 0.423367 + 1.79729i
\(885\) 0 0
\(886\) 22.8863 + 6.50748i 0.768879 + 0.218623i
\(887\) −29.7760 + 17.1912i −0.999780 + 0.577223i −0.908183 0.418573i \(-0.862530\pi\)
−0.0915965 + 0.995796i \(0.529197\pi\)
\(888\) 0 0
\(889\) −19.5891 11.3098i −0.656999 0.379318i
\(890\) 8.62694 + 8.89378i 0.289176 + 0.298120i
\(891\) 0 0
\(892\) 0.195000 6.40020i 0.00652909 0.214295i
\(893\) 11.2171 + 41.8626i 0.375364 + 1.40088i
\(894\) 0 0
\(895\) −7.98697 + 4.61128i −0.266975 + 0.154138i
\(896\) −5.91741 13.3584i −0.197687 0.446273i
\(897\) 0 0
\(898\) −38.6327 23.0961i −1.28919 0.770726i
\(899\) −13.2008 13.2008i −0.440272 0.440272i
\(900\) 0 0
\(901\) −3.36115 + 3.36115i −0.111976 + 0.111976i
\(902\) −11.2417 44.6644i −0.374306 1.48716i
\(903\) 0 0
\(904\) −6.34470 + 3.28629i −0.211022 + 0.109300i
\(905\) 3.89178 + 6.74076i 0.129367 + 0.224070i
\(906\) 0 0
\(907\) −53.7121 + 14.3921i −1.78348 + 0.477883i −0.991211 0.132287i \(-0.957768\pi\)
−0.792271 + 0.610170i \(0.791101\pi\)
\(908\) 3.94850 + 4.19666i 0.131035 + 0.139271i
\(909\) 0 0
\(910\) 0.0940295 6.17382i 0.00311705 0.204660i
\(911\) 6.01435 10.4172i 0.199264 0.345136i −0.749026 0.662541i \(-0.769478\pi\)
0.948290 + 0.317405i \(0.102811\pi\)
\(912\) 0 0
\(913\) 6.53085 + 11.3118i 0.216140 + 0.374365i
\(914\) −35.4557 + 19.7566i −1.17277 + 0.653491i
\(915\) 0 0
\(916\) 8.36863 + 35.5268i 0.276507 + 1.17384i
\(917\) 11.3338 + 11.3338i 0.374275 + 0.374275i
\(918\) 0 0
\(919\) −11.8860 −0.392084 −0.196042 0.980595i \(-0.562809\pi\)
−0.196042 + 0.980595i \(0.562809\pi\)
\(920\) −1.13952 5.19050i −0.0375690 0.171126i
\(921\) 0 0
\(922\) −2.54336 0.723179i −0.0837611 0.0238166i
\(923\) 0.212633 + 0.0569747i 0.00699889 + 0.00187535i
\(924\) 0 0
\(925\) 3.13773 0.840752i 0.103168 0.0276438i
\(926\) −0.117375 + 7.70666i −0.00385719 + 0.253257i
\(927\) 0 0
\(928\) −13.1405 + 11.2775i −0.431357 + 0.370204i
\(929\) 3.44934 + 1.99148i 0.113169 + 0.0653382i 0.555516 0.831506i \(-0.312521\pi\)
−0.442347 + 0.896844i \(0.645854\pi\)
\(930\) 0 0
\(931\) −18.1846 4.87255i −0.595977 0.159692i
\(932\) 5.68627 + 10.5805i 0.186260 + 0.346576i
\(933\) 0 0
\(934\) −17.3630 + 4.37013i −0.568136 + 0.142995i
\(935\) 12.7711i 0.417659i
\(936\) 0 0
\(937\) 26.0017i 0.849438i 0.905325 + 0.424719i \(0.139627\pi\)
−0.905325 + 0.424719i \(0.860373\pi\)
\(938\) −0.0509256 0.202333i −0.00166278 0.00660642i
\(939\) 0 0
\(940\) 4.86594 16.1727i 0.158709 0.527496i
\(941\) 41.3717 + 11.0855i 1.34868 + 0.361378i 0.859648 0.510888i \(-0.170683\pi\)
0.489033 + 0.872265i \(0.337350\pi\)
\(942\) 0 0
\(943\) 23.1747 + 13.3799i 0.754673 + 0.435710i
\(944\) 14.8141 13.1109i 0.482159 0.426724i
\(945\) 0 0
\(946\) 4.62252 + 0.0704026i 0.150291 + 0.00228899i
\(947\) −17.6066 + 4.71769i −0.572139 + 0.153304i −0.533277 0.845940i \(-0.679040\pi\)
−0.0388617 + 0.999245i \(0.512373\pi\)
\(948\) 0 0
\(949\) 63.1062 + 16.9093i 2.04851 + 0.548898i
\(950\) −6.18164 + 21.7403i −0.200559 + 0.705349i
\(951\) 0 0
\(952\) 17.1831 + 10.9965i 0.556908 + 0.356400i
\(953\) −16.9031 −0.547545 −0.273772 0.961795i \(-0.588271\pi\)
−0.273772 + 0.961795i \(0.588271\pi\)
\(954\) 0 0
\(955\) −8.97930 8.97930i −0.290563 0.290563i
\(956\) −12.6440 + 20.4363i −0.408936 + 0.660958i
\(957\) 0 0
\(958\) −5.88985 10.5701i −0.190292 0.341503i
\(959\) 6.45774 + 11.1851i 0.208531 + 0.361187i
\(960\) 0 0
\(961\) 3.09688 5.36395i 0.0998993 0.173031i
\(962\) −4.98709 0.0759553i −0.160790 0.00244890i
\(963\) 0 0
\(964\) −6.07410 0.185065i −0.195634 0.00596053i
\(965\) −3.47708 + 0.931682i −0.111931 + 0.0299919i
\(966\) 0 0
\(967\) 1.50617 + 2.60876i 0.0484351 + 0.0838921i 0.889227 0.457467i \(-0.151243\pi\)
−0.840791 + 0.541359i \(0.817910\pi\)
\(968\) 0.122122 0.0632540i 0.00392514 0.00203306i
\(969\) 0 0
\(970\) 8.32230 2.09465i 0.267213 0.0672553i
\(971\) 35.4934 35.4934i 1.13904 1.13904i 0.150413 0.988623i \(-0.451940\pi\)
0.988623 0.150413i \(-0.0480604\pi\)
\(972\) 0 0
\(973\) 1.30066 + 1.30066i 0.0416972 + 0.0416972i
\(974\) −9.55632 + 15.9848i −0.306204 + 0.512186i
\(975\) 0 0
\(976\) −14.2222 + 42.5297i −0.455242 + 1.36134i
\(977\) −8.03784 + 4.64065i −0.257153 + 0.148467i −0.623035 0.782194i \(-0.714101\pi\)
0.365882 + 0.930661i \(0.380767\pi\)
\(978\) 0 0
\(979\) −10.9570 40.8920i −0.350186 1.30691i
\(980\) 5.02718 + 5.34314i 0.160587 + 0.170680i
\(981\) 0 0
\(982\) −8.50923 + 8.25392i −0.271540 + 0.263393i
\(983\) −11.0480 6.37856i −0.352376 0.203444i 0.313355 0.949636i \(-0.398547\pi\)
−0.665731 + 0.746192i \(0.731880\pi\)
\(984\) 0 0
\(985\) 12.0963 6.98379i 0.385420 0.222522i
\(986\) 6.61290 23.2570i 0.210598 0.740655i
\(987\) 0 0
\(988\) 18.2590 29.5118i 0.580897 0.938897i
\(989\) −1.89932 + 1.89932i −0.0603949 + 0.0603949i
\(990\) 0 0
\(991\) 6.60967i 0.209963i −0.994474 0.104982i \(-0.966522\pi\)
0.994474 0.104982i \(-0.0334784\pi\)
\(992\) −28.4785 19.4725i −0.904192 0.618252i
\(993\) 0 0
\(994\) 0.0714560 0.0398167i 0.00226645 0.00126291i
\(995\) 2.46340 9.19352i 0.0780949 0.291454i
\(996\) 0 0
\(997\) −9.80194 36.5814i −0.310431 1.15854i −0.928169 0.372159i \(-0.878618\pi\)
0.617738 0.786384i \(-0.288049\pi\)
\(998\) 32.8894 31.9026i 1.04109 1.00986i
\(999\) 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 432.2.v.a.35.15 88
3.2 odd 2 144.2.u.a.83.8 yes 88
4.3 odd 2 1728.2.z.a.1007.10 88
9.4 even 3 144.2.u.a.131.15 yes 88
9.5 odd 6 inner 432.2.v.a.179.8 88
12.11 even 2 576.2.y.a.47.5 88
16.5 even 4 1728.2.z.a.143.10 88
16.11 odd 4 inner 432.2.v.a.251.8 88
36.23 even 6 1728.2.z.a.1583.10 88
36.31 odd 6 576.2.y.a.239.7 88
48.5 odd 4 576.2.y.a.335.7 88
48.11 even 4 144.2.u.a.11.15 88
144.5 odd 12 1728.2.z.a.719.10 88
144.59 even 12 inner 432.2.v.a.395.15 88
144.85 even 12 576.2.y.a.527.5 88
144.139 odd 12 144.2.u.a.59.8 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.u.a.11.15 88 48.11 even 4
144.2.u.a.59.8 yes 88 144.139 odd 12
144.2.u.a.83.8 yes 88 3.2 odd 2
144.2.u.a.131.15 yes 88 9.4 even 3
432.2.v.a.35.15 88 1.1 even 1 trivial
432.2.v.a.179.8 88 9.5 odd 6 inner
432.2.v.a.251.8 88 16.11 odd 4 inner
432.2.v.a.395.15 88 144.59 even 12 inner
576.2.y.a.47.5 88 12.11 even 2
576.2.y.a.239.7 88 36.31 odd 6
576.2.y.a.335.7 88 48.5 odd 4
576.2.y.a.527.5 88 144.85 even 12
1728.2.z.a.143.10 88 16.5 even 4
1728.2.z.a.719.10 88 144.5 odd 12
1728.2.z.a.1007.10 88 4.3 odd 2
1728.2.z.a.1583.10 88 36.23 even 6