Properties

Label 666.2.be.d.467.3
Level $666$
Weight $2$
Character 666.467
Analytic conductor $5.318$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [666,2,Mod(125,666)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(666, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("666.125");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 666.be (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.31803677462\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: 16.0.6040479020157644046336.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 7x^{12} - 32x^{8} - 567x^{4} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 467.3
Root \(0.0537601 - 1.73122i\) of defining polynomial
Character \(\chi\) \(=\) 666.467
Dual form 666.2.be.d.251.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-0.765290 - 0.205059i) q^{5} +(-0.896143 - 1.55217i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-0.765290 - 0.205059i) q^{5} +(-0.896143 - 1.55217i) q^{7} +(0.707107 - 0.707107i) q^{8} -0.792287 q^{10} +4.98417 q^{11} +(0.0278283 - 0.103857i) q^{13} +(-1.26734 - 1.26734i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.912166 + 3.40425i) q^{17} +(2.21397 - 8.26264i) q^{19} +(-0.765290 + 0.205059i) q^{20} +(4.81433 - 1.29000i) q^{22} +(5.99711 - 5.99711i) q^{23} +(-3.78651 - 2.18614i) q^{25} -0.107520i q^{26} +(-1.55217 - 0.896143i) q^{28} +(-4.02266 - 4.02266i) q^{29} +(-6.76493 + 6.76493i) q^{31} +(0.258819 - 0.965926i) q^{32} +(1.76217 + 3.05217i) q^{34} +(0.367525 + 1.37162i) q^{35} +(4.26613 - 4.33591i) q^{37} -8.55412i q^{38} +(-0.686141 + 0.396143i) q^{40} +(4.52147 + 7.83142i) q^{41} +(2.24060 + 2.24060i) q^{43} +(4.31641 - 2.49208i) q^{44} +(4.24060 - 7.34493i) q^{46} +8.63283i q^{47} +(1.89385 - 3.28025i) q^{49} +(-4.22330 - 1.13163i) q^{50} +(-0.0278283 - 0.103857i) q^{52} +(0.970349 + 0.560232i) q^{53} +(-3.81433 - 1.02205i) q^{55} +(-1.73122 - 0.463878i) q^{56} +(-4.92674 - 2.84445i) q^{58} +(3.06049 + 11.4219i) q^{59} +(-2.05217 - 0.549876i) q^{61} +(-4.78353 + 8.28532i) q^{62} -1.00000i q^{64} +(-0.0425934 + 0.0737740i) q^{65} +(-12.9290 + 7.46458i) q^{67} +(2.49208 + 2.49208i) q^{68} +(0.710003 + 1.22976i) q^{70} +(-5.01144 + 2.89335i) q^{71} +2.90818i q^{73} +(2.99855 - 5.29232i) q^{74} +(-2.21397 - 8.26264i) q^{76} +(-4.46653 - 7.73625i) q^{77} +(-0.0278283 + 0.103857i) q^{79} +(-0.560232 + 0.560232i) q^{80} +(6.39433 + 6.39433i) q^{82} +(3.41423 + 1.97121i) q^{83} -2.79229i q^{85} +(2.74416 + 1.58434i) q^{86} +(3.52434 - 3.52434i) q^{88} +(5.75830 - 1.54293i) q^{89} +(-0.186141 + 0.0498762i) q^{91} +(2.19509 - 8.19220i) q^{92} +(2.23434 + 8.33867i) q^{94} +(-3.38866 + 5.86933i) q^{95} +(-0.841688 - 0.841688i) q^{97} +(0.980331 - 3.65864i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 8 q^{7} + 4 q^{13} + 8 q^{16} + 16 q^{19} + 20 q^{22} + 12 q^{28} - 12 q^{31} + 8 q^{34} + 12 q^{37} + 12 q^{40} - 20 q^{43} + 12 q^{46} + 20 q^{49} - 4 q^{52} - 4 q^{55} + 4 q^{61} - 132 q^{67} + 28 q^{70} - 16 q^{76} - 4 q^{79} + 12 q^{82} + 16 q^{88} + 20 q^{91} + 12 q^{94} - 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/666\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 0.258819i 0.683013 0.183013i
\(3\) 0 0
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) −0.765290 0.205059i −0.342248 0.0917052i 0.0836009 0.996499i \(-0.473358\pi\)
−0.425849 + 0.904794i \(0.640025\pi\)
\(6\) 0 0
\(7\) −0.896143 1.55217i −0.338710 0.586664i 0.645480 0.763777i \(-0.276657\pi\)
−0.984190 + 0.177114i \(0.943324\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 0 0
\(10\) −0.792287 −0.250543
\(11\) 4.98417 1.50278 0.751391 0.659857i \(-0.229383\pi\)
0.751391 + 0.659857i \(0.229383\pi\)
\(12\) 0 0
\(13\) 0.0278283 0.103857i 0.00771817 0.0288046i −0.961959 0.273193i \(-0.911920\pi\)
0.969678 + 0.244388i \(0.0785870\pi\)
\(14\) −1.26734 1.26734i −0.338710 0.338710i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 0.912166 + 3.40425i 0.221233 + 0.825652i 0.983879 + 0.178836i \(0.0572331\pi\)
−0.762646 + 0.646816i \(0.776100\pi\)
\(18\) 0 0
\(19\) 2.21397 8.26264i 0.507919 1.89558i 0.0676637 0.997708i \(-0.478446\pi\)
0.440256 0.897872i \(-0.354888\pi\)
\(20\) −0.765290 + 0.205059i −0.171124 + 0.0458526i
\(21\) 0 0
\(22\) 4.81433 1.29000i 1.02642 0.275028i
\(23\) 5.99711 5.99711i 1.25048 1.25048i 0.294980 0.955503i \(-0.404687\pi\)
0.955503 0.294980i \(-0.0953131\pi\)
\(24\) 0 0
\(25\) −3.78651 2.18614i −0.757301 0.437228i
\(26\) 0.107520i 0.0210864i
\(27\) 0 0
\(28\) −1.55217 0.896143i −0.293332 0.169355i
\(29\) −4.02266 4.02266i −0.746990 0.746990i 0.226923 0.973913i \(-0.427133\pi\)
−0.973913 + 0.226923i \(0.927133\pi\)
\(30\) 0 0
\(31\) −6.76493 + 6.76493i −1.21502 + 1.21502i −0.245663 + 0.969355i \(0.579006\pi\)
−0.969355 + 0.245663i \(0.920994\pi\)
\(32\) 0.258819 0.965926i 0.0457532 0.170753i
\(33\) 0 0
\(34\) 1.76217 + 3.05217i 0.302209 + 0.523442i
\(35\) 0.367525 + 1.37162i 0.0621230 + 0.231846i
\(36\) 0 0
\(37\) 4.26613 4.33591i 0.701348 0.712819i
\(38\) 8.55412i 1.38766i
\(39\) 0 0
\(40\) −0.686141 + 0.396143i −0.108488 + 0.0626358i
\(41\) 4.52147 + 7.83142i 0.706136 + 1.22306i 0.966280 + 0.257493i \(0.0828964\pi\)
−0.260145 + 0.965570i \(0.583770\pi\)
\(42\) 0 0
\(43\) 2.24060 + 2.24060i 0.341688 + 0.341688i 0.857002 0.515314i \(-0.172325\pi\)
−0.515314 + 0.857002i \(0.672325\pi\)
\(44\) 4.31641 2.49208i 0.650724 0.375696i
\(45\) 0 0
\(46\) 4.24060 7.34493i 0.625242 1.08295i
\(47\) 8.63283i 1.25923i 0.776908 + 0.629614i \(0.216787\pi\)
−0.776908 + 0.629614i \(0.783213\pi\)
\(48\) 0 0
\(49\) 1.89385 3.28025i 0.270551 0.468607i
\(50\) −4.22330 1.13163i −0.597265 0.160037i
\(51\) 0 0
\(52\) −0.0278283 0.103857i −0.00385909 0.0144023i
\(53\) 0.970349 + 0.560232i 0.133288 + 0.0769537i 0.565161 0.824980i \(-0.308814\pi\)
−0.431873 + 0.901934i \(0.642147\pi\)
\(54\) 0 0
\(55\) −3.81433 1.02205i −0.514325 0.137813i
\(56\) −1.73122 0.463878i −0.231344 0.0619883i
\(57\) 0 0
\(58\) −4.92674 2.84445i −0.646912 0.373495i
\(59\) 3.06049 + 11.4219i 0.398442 + 1.48700i 0.815838 + 0.578280i \(0.196276\pi\)
−0.417396 + 0.908725i \(0.637057\pi\)
\(60\) 0 0
\(61\) −2.05217 0.549876i −0.262753 0.0704044i 0.125037 0.992152i \(-0.460095\pi\)
−0.387790 + 0.921748i \(0.626762\pi\)
\(62\) −4.78353 + 8.28532i −0.607509 + 1.05224i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −0.0425934 + 0.0737740i −0.00528306 + 0.00915053i
\(66\) 0 0
\(67\) −12.9290 + 7.46458i −1.57953 + 0.911943i −0.584608 + 0.811316i \(0.698752\pi\)
−0.994924 + 0.100627i \(0.967915\pi\)
\(68\) 2.49208 + 2.49208i 0.302209 + 0.302209i
\(69\) 0 0
\(70\) 0.710003 + 1.22976i 0.0848616 + 0.146985i
\(71\) −5.01144 + 2.89335i −0.594748 + 0.343378i −0.766973 0.641680i \(-0.778238\pi\)
0.172225 + 0.985058i \(0.444905\pi\)
\(72\) 0 0
\(73\) 2.90818i 0.340377i 0.985412 + 0.170188i \(0.0544376\pi\)
−0.985412 + 0.170188i \(0.945562\pi\)
\(74\) 2.99855 5.29232i 0.348575 0.615220i
\(75\) 0 0
\(76\) −2.21397 8.26264i −0.253960 0.947790i
\(77\) −4.46653 7.73625i −0.509008 0.881628i
\(78\) 0 0
\(79\) −0.0278283 + 0.103857i −0.00313092 + 0.0116848i −0.967474 0.252972i \(-0.918592\pi\)
0.964343 + 0.264657i \(0.0852586\pi\)
\(80\) −0.560232 + 0.560232i −0.0626358 + 0.0626358i
\(81\) 0 0
\(82\) 6.39433 + 6.39433i 0.706136 + 0.706136i
\(83\) 3.41423 + 1.97121i 0.374760 + 0.216368i 0.675536 0.737327i \(-0.263912\pi\)
−0.300776 + 0.953695i \(0.597246\pi\)
\(84\) 0 0
\(85\) 2.79229i 0.302866i
\(86\) 2.74416 + 1.58434i 0.295910 + 0.170844i
\(87\) 0 0
\(88\) 3.52434 3.52434i 0.375696 0.375696i
\(89\) 5.75830 1.54293i 0.610379 0.163551i 0.0596287 0.998221i \(-0.481008\pi\)
0.550750 + 0.834670i \(0.314342\pi\)
\(90\) 0 0
\(91\) −0.186141 + 0.0498762i −0.0195128 + 0.00522845i
\(92\) 2.19509 8.19220i 0.228854 0.854096i
\(93\) 0 0
\(94\) 2.23434 + 8.33867i 0.230455 + 0.860068i
\(95\) −3.38866 + 5.86933i −0.347669 + 0.602180i
\(96\) 0 0
\(97\) −0.841688 0.841688i −0.0854604 0.0854604i 0.663084 0.748545i \(-0.269247\pi\)
−0.748545 + 0.663084i \(0.769247\pi\)
\(98\) 0.980331 3.65864i 0.0990284 0.369579i
\(99\) 0 0
\(100\) −4.37228 −0.437228
\(101\) −3.67984 −0.366158 −0.183079 0.983098i \(-0.558606\pi\)
−0.183079 + 0.983098i \(0.558606\pi\)
\(102\) 0 0
\(103\) 4.16915 4.16915i 0.410798 0.410798i −0.471218 0.882017i \(-0.656186\pi\)
0.882017 + 0.471218i \(0.156186\pi\)
\(104\) −0.0537601 0.0931152i −0.00527161 0.00913070i
\(105\) 0 0
\(106\) 1.08228 + 0.289997i 0.105121 + 0.0281670i
\(107\) −6.57967 + 3.79878i −0.636081 + 0.367242i −0.783103 0.621892i \(-0.786364\pi\)
0.147022 + 0.989133i \(0.453031\pi\)
\(108\) 0 0
\(109\) −1.29854 + 0.347944i −0.124378 + 0.0333269i −0.320471 0.947258i \(-0.603841\pi\)
0.196093 + 0.980585i \(0.437175\pi\)
\(110\) −3.94889 −0.376512
\(111\) 0 0
\(112\) −1.79229 −0.169355
\(113\) −18.8250 + 5.04416i −1.77091 + 0.474514i −0.988879 0.148723i \(-0.952484\pi\)
−0.782033 + 0.623237i \(0.785817\pi\)
\(114\) 0 0
\(115\) −5.81929 + 3.35977i −0.542652 + 0.313300i
\(116\) −5.49506 1.47240i −0.510204 0.136709i
\(117\) 0 0
\(118\) 5.91241 + 10.2406i 0.544282 + 0.942723i
\(119\) 4.46653 4.46653i 0.409446 0.409446i
\(120\) 0 0
\(121\) 13.8419 1.25836
\(122\) −2.12456 −0.192349
\(123\) 0 0
\(124\) −2.47614 + 9.24107i −0.222364 + 0.829873i
\(125\) 5.25065 + 5.25065i 0.469632 + 0.469632i
\(126\) 0 0
\(127\) −4.78193 + 8.28254i −0.424327 + 0.734957i −0.996357 0.0852761i \(-0.972823\pi\)
0.572030 + 0.820233i \(0.306156\pi\)
\(128\) −0.258819 0.965926i −0.0228766 0.0853766i
\(129\) 0 0
\(130\) −0.0220480 + 0.0822842i −0.00193374 + 0.00721680i
\(131\) 8.80388 2.35899i 0.769198 0.206106i 0.147181 0.989110i \(-0.452980\pi\)
0.622017 + 0.783004i \(0.286313\pi\)
\(132\) 0 0
\(133\) −14.8090 + 3.96807i −1.28411 + 0.344075i
\(134\) −10.5565 + 10.5565i −0.911943 + 0.911943i
\(135\) 0 0
\(136\) 3.05217 + 1.76217i 0.261721 + 0.151105i
\(137\) 17.3708i 1.48409i −0.670351 0.742044i \(-0.733856\pi\)
0.670351 0.742044i \(-0.266144\pi\)
\(138\) 0 0
\(139\) 15.9125 + 9.18709i 1.34968 + 0.779239i 0.988204 0.153142i \(-0.0489392\pi\)
0.361477 + 0.932381i \(0.382273\pi\)
\(140\) 1.00410 + 1.00410i 0.0848616 + 0.0848616i
\(141\) 0 0
\(142\) −4.09182 + 4.09182i −0.343378 + 0.343378i
\(143\) 0.138701 0.517638i 0.0115987 0.0432871i
\(144\) 0 0
\(145\) 2.25362 + 3.90339i 0.187153 + 0.324159i
\(146\) 0.752692 + 2.80909i 0.0622933 + 0.232482i
\(147\) 0 0
\(148\) 1.52663 5.88807i 0.125488 0.483997i
\(149\) 1.20618i 0.0988143i −0.998779 0.0494072i \(-0.984267\pi\)
0.998779 0.0494072i \(-0.0157332\pi\)
\(150\) 0 0
\(151\) 6.05904 3.49819i 0.493077 0.284678i −0.232773 0.972531i \(-0.574780\pi\)
0.725850 + 0.687853i \(0.241447\pi\)
\(152\) −4.27706 7.40808i −0.346915 0.600875i
\(153\) 0 0
\(154\) −6.31662 6.31662i −0.509008 0.509008i
\(155\) 6.56435 3.78993i 0.527261 0.304414i
\(156\) 0 0
\(157\) −8.71820 + 15.1004i −0.695788 + 1.20514i 0.274126 + 0.961694i \(0.411611\pi\)
−0.969914 + 0.243447i \(0.921722\pi\)
\(158\) 0.107520i 0.00855385i
\(159\) 0 0
\(160\) −0.396143 + 0.686141i −0.0313179 + 0.0542442i
\(161\) −14.6828 3.93424i −1.15717 0.310061i
\(162\) 0 0
\(163\) 3.72217 + 13.8913i 0.291543 + 1.08805i 0.943925 + 0.330161i \(0.107103\pi\)
−0.652382 + 0.757890i \(0.726230\pi\)
\(164\) 7.83142 + 4.52147i 0.611531 + 0.353068i
\(165\) 0 0
\(166\) 3.80808 + 1.02037i 0.295564 + 0.0791962i
\(167\) −14.5054 3.88671i −1.12246 0.300763i −0.350582 0.936532i \(-0.614016\pi\)
−0.771879 + 0.635769i \(0.780683\pi\)
\(168\) 0 0
\(169\) 11.2483 + 6.49422i 0.865255 + 0.499555i
\(170\) −0.722697 2.69714i −0.0554283 0.206861i
\(171\) 0 0
\(172\) 3.06071 + 0.820115i 0.233377 + 0.0625332i
\(173\) −0.921013 + 1.59524i −0.0700233 + 0.121284i −0.898911 0.438131i \(-0.855641\pi\)
0.828888 + 0.559415i \(0.188974\pi\)
\(174\) 0 0
\(175\) 7.83638i 0.592375i
\(176\) 2.49208 4.31641i 0.187848 0.325362i
\(177\) 0 0
\(178\) 5.16275 2.98072i 0.386965 0.223414i
\(179\) −3.22506 3.22506i −0.241052 0.241052i 0.576233 0.817285i \(-0.304522\pi\)
−0.817285 + 0.576233i \(0.804522\pi\)
\(180\) 0 0
\(181\) −11.2596 19.5023i −0.836922 1.44959i −0.892456 0.451134i \(-0.851020\pi\)
0.0555345 0.998457i \(-0.482314\pi\)
\(182\) −0.166889 + 0.0963535i −0.0123706 + 0.00714220i
\(183\) 0 0
\(184\) 8.48119i 0.625242i
\(185\) −4.15395 + 2.44342i −0.305404 + 0.179644i
\(186\) 0 0
\(187\) 4.54639 + 16.9673i 0.332465 + 1.24077i
\(188\) 4.31641 + 7.47625i 0.314807 + 0.545262i
\(189\) 0 0
\(190\) −1.75410 + 6.54639i −0.127256 + 0.474925i
\(191\) −1.17684 + 1.17684i −0.0851531 + 0.0851531i −0.748400 0.663247i \(-0.769178\pi\)
0.663247 + 0.748400i \(0.269178\pi\)
\(192\) 0 0
\(193\) 8.26264 + 8.26264i 0.594758 + 0.594758i 0.938913 0.344155i \(-0.111834\pi\)
−0.344155 + 0.938913i \(0.611834\pi\)
\(194\) −1.03085 0.595163i −0.0740109 0.0427302i
\(195\) 0 0
\(196\) 3.78771i 0.270551i
\(197\) −9.14410 5.27935i −0.651490 0.376138i 0.137537 0.990497i \(-0.456081\pi\)
−0.789027 + 0.614359i \(0.789415\pi\)
\(198\) 0 0
\(199\) 16.6329 16.6329i 1.17908 1.17908i 0.199095 0.979980i \(-0.436200\pi\)
0.979980 0.199095i \(-0.0638002\pi\)
\(200\) −4.22330 + 1.13163i −0.298632 + 0.0800183i
\(201\) 0 0
\(202\) −3.55446 + 0.952414i −0.250091 + 0.0670116i
\(203\) −2.63896 + 9.84873i −0.185219 + 0.691245i
\(204\) 0 0
\(205\) −1.85434 6.92048i −0.129513 0.483347i
\(206\) 2.94803 5.10614i 0.205399 0.355762i
\(207\) 0 0
\(208\) −0.0760282 0.0760282i −0.00527161 0.00527161i
\(209\) 11.0348 41.1824i 0.763292 2.84865i
\(210\) 0 0
\(211\) −23.4651 −1.61540 −0.807700 0.589593i \(-0.799288\pi\)
−0.807700 + 0.589593i \(0.799288\pi\)
\(212\) 1.12046 0.0769537
\(213\) 0 0
\(214\) −5.37228 + 5.37228i −0.367242 + 0.367242i
\(215\) −1.25525 2.17416i −0.0856075 0.148277i
\(216\) 0 0
\(217\) 16.5627 + 4.43795i 1.12435 + 0.301268i
\(218\) −1.16424 + 0.672175i −0.0788524 + 0.0455255i
\(219\) 0 0
\(220\) −3.81433 + 1.02205i −0.257162 + 0.0689065i
\(221\) 0.378937 0.0254901
\(222\) 0 0
\(223\) −20.1248 −1.34765 −0.673827 0.738889i \(-0.735351\pi\)
−0.673827 + 0.738889i \(0.735351\pi\)
\(224\) −1.73122 + 0.463878i −0.115672 + 0.0309942i
\(225\) 0 0
\(226\) −16.8781 + 9.74456i −1.12271 + 0.648199i
\(227\) 26.7043 + 7.15539i 1.77242 + 0.474920i 0.989169 0.146780i \(-0.0468911\pi\)
0.783255 + 0.621700i \(0.213558\pi\)
\(228\) 0 0
\(229\) 3.12737 + 5.41676i 0.206662 + 0.357950i 0.950661 0.310231i \(-0.100406\pi\)
−0.743999 + 0.668181i \(0.767073\pi\)
\(230\) −4.75143 + 4.75143i −0.313300 + 0.313300i
\(231\) 0 0
\(232\) −5.68891 −0.373495
\(233\) −4.12762 −0.270409 −0.135205 0.990818i \(-0.543169\pi\)
−0.135205 + 0.990818i \(0.543169\pi\)
\(234\) 0 0
\(235\) 1.77024 6.60662i 0.115478 0.430968i
\(236\) 8.36141 + 8.36141i 0.544282 + 0.544282i
\(237\) 0 0
\(238\) 3.15831 5.47036i 0.204723 0.354591i
\(239\) 7.24419 + 27.0357i 0.468588 + 1.74879i 0.644713 + 0.764425i \(0.276977\pi\)
−0.176125 + 0.984368i \(0.556356\pi\)
\(240\) 0 0
\(241\) 3.35143 12.5077i 0.215885 0.805693i −0.769968 0.638082i \(-0.779728\pi\)
0.985853 0.167611i \(-0.0536053\pi\)
\(242\) 13.3703 3.58255i 0.859473 0.230295i
\(243\) 0 0
\(244\) −2.05217 + 0.549876i −0.131376 + 0.0352022i
\(245\) −2.12199 + 2.12199i −0.135569 + 0.135569i
\(246\) 0 0
\(247\) −0.796518 0.459870i −0.0506813 0.0292608i
\(248\) 9.56706i 0.607509i
\(249\) 0 0
\(250\) 6.43070 + 3.71277i 0.406713 + 0.234816i
\(251\) 8.30142 + 8.30142i 0.523981 + 0.523981i 0.918771 0.394790i \(-0.129183\pi\)
−0.394790 + 0.918771i \(0.629183\pi\)
\(252\) 0 0
\(253\) 29.8906 29.8906i 1.87921 1.87921i
\(254\) −2.47531 + 9.23797i −0.155315 + 0.579642i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 4.70514 + 17.5598i 0.293498 + 1.09535i 0.942403 + 0.334481i \(0.108561\pi\)
−0.648904 + 0.760870i \(0.724772\pi\)
\(258\) 0 0
\(259\) −10.5531 2.73615i −0.655739 0.170016i
\(260\) 0.0851868i 0.00528306i
\(261\) 0 0
\(262\) 7.89334 4.55722i 0.487652 0.281546i
\(263\) −9.28386 16.0801i −0.572467 0.991542i −0.996312 0.0858072i \(-0.972653\pi\)
0.423845 0.905735i \(-0.360680\pi\)
\(264\) 0 0
\(265\) −0.627719 0.627719i −0.0385605 0.0385605i
\(266\) −13.2774 + 7.66572i −0.814090 + 0.470015i
\(267\) 0 0
\(268\) −7.46458 + 12.9290i −0.455972 + 0.789766i
\(269\) 4.56704i 0.278457i −0.990260 0.139229i \(-0.955538\pi\)
0.990260 0.139229i \(-0.0444623\pi\)
\(270\) 0 0
\(271\) 2.34773 4.06639i 0.142615 0.247016i −0.785866 0.618397i \(-0.787782\pi\)
0.928480 + 0.371381i \(0.121116\pi\)
\(272\) 3.40425 + 0.912166i 0.206413 + 0.0553082i
\(273\) 0 0
\(274\) −4.49590 16.7789i −0.271607 1.01365i
\(275\) −18.8726 10.8961i −1.13806 0.657059i
\(276\) 0 0
\(277\) 18.4300 + 4.93830i 1.10735 + 0.296714i 0.765754 0.643133i \(-0.222366\pi\)
0.341596 + 0.939847i \(0.389033\pi\)
\(278\) 17.7481 + 4.75559i 1.06446 + 0.285221i
\(279\) 0 0
\(280\) 1.22976 + 0.710003i 0.0734923 + 0.0424308i
\(281\) −6.10881 22.7984i −0.364421 1.36004i −0.868204 0.496207i \(-0.834726\pi\)
0.503783 0.863830i \(-0.331941\pi\)
\(282\) 0 0
\(283\) −6.37604 1.70845i −0.379016 0.101557i 0.0642809 0.997932i \(-0.479525\pi\)
−0.443297 + 0.896375i \(0.646191\pi\)
\(284\) −2.89335 + 5.01144i −0.171689 + 0.297374i
\(285\) 0 0
\(286\) 0.535898i 0.0316883i
\(287\) 8.10378 14.0362i 0.478351 0.828528i
\(288\) 0 0
\(289\) 3.96557 2.28952i 0.233269 0.134678i
\(290\) 3.18710 + 3.18710i 0.187153 + 0.187153i
\(291\) 0 0
\(292\) 1.45409 + 2.51856i 0.0850942 + 0.147387i
\(293\) −0.583026 + 0.336610i −0.0340608 + 0.0196650i −0.516934 0.856025i \(-0.672927\pi\)
0.482873 + 0.875690i \(0.339593\pi\)
\(294\) 0 0
\(295\) 9.36865i 0.545464i
\(296\) −0.0493365 6.08256i −0.00286762 0.353542i
\(297\) 0 0
\(298\) −0.312183 1.16508i −0.0180843 0.0674915i
\(299\) −0.455950 0.789728i −0.0263682 0.0456711i
\(300\) 0 0
\(301\) 1.46988 5.48567i 0.0847226 0.316189i
\(302\) 4.94718 4.94718i 0.284678 0.284678i
\(303\) 0 0
\(304\) −6.04868 6.04868i −0.346915 0.346915i
\(305\) 1.45775 + 0.841630i 0.0834703 + 0.0481916i
\(306\) 0 0
\(307\) 5.44263i 0.310627i 0.987865 + 0.155314i \(0.0496388\pi\)
−0.987865 + 0.155314i \(0.950361\pi\)
\(308\) −7.73625 4.46653i −0.440814 0.254504i
\(309\) 0 0
\(310\) 5.35977 5.35977i 0.304414 0.304414i
\(311\) −10.4362 + 2.79638i −0.591784 + 0.158568i −0.542269 0.840205i \(-0.682434\pi\)
−0.0495157 + 0.998773i \(0.515768\pi\)
\(312\) 0 0
\(313\) −3.13623 + 0.840349i −0.177270 + 0.0474993i −0.346362 0.938101i \(-0.612583\pi\)
0.169092 + 0.985600i \(0.445916\pi\)
\(314\) −4.51287 + 16.8423i −0.254676 + 0.950464i
\(315\) 0 0
\(316\) 0.0278283 + 0.103857i 0.00156546 + 0.00584238i
\(317\) 5.83841 10.1124i 0.327918 0.567971i −0.654181 0.756338i \(-0.726986\pi\)
0.982099 + 0.188368i \(0.0603197\pi\)
\(318\) 0 0
\(319\) −20.0496 20.0496i −1.12256 1.12256i
\(320\) −0.205059 + 0.765290i −0.0114631 + 0.0427810i
\(321\) 0 0
\(322\) −15.2007 −0.847104
\(323\) 30.1476 1.67746
\(324\) 0 0
\(325\) −0.332417 + 0.332417i −0.0184392 + 0.0184392i
\(326\) 7.19067 + 12.4546i 0.398255 + 0.689797i
\(327\) 0 0
\(328\) 8.73482 + 2.34049i 0.482300 + 0.129232i
\(329\) 13.3996 7.73625i 0.738743 0.426513i
\(330\) 0 0
\(331\) 22.2516 5.96229i 1.22306 0.327717i 0.411184 0.911552i \(-0.365115\pi\)
0.811872 + 0.583835i \(0.198449\pi\)
\(332\) 3.94241 0.216368
\(333\) 0 0
\(334\) −15.0171 −0.821699
\(335\) 11.4251 3.06136i 0.624222 0.167260i
\(336\) 0 0
\(337\) 0.497068 0.286982i 0.0270770 0.0156329i −0.486400 0.873736i \(-0.661690\pi\)
0.513477 + 0.858103i \(0.328357\pi\)
\(338\) 12.5459 + 3.36166i 0.682405 + 0.182850i
\(339\) 0 0
\(340\) −1.39614 2.41819i −0.0757165 0.131145i
\(341\) −33.7176 + 33.7176i −1.82591 + 1.82591i
\(342\) 0 0
\(343\) −19.3347 −1.04397
\(344\) 3.16868 0.170844
\(345\) 0 0
\(346\) −0.476751 + 1.77926i −0.0256303 + 0.0956536i
\(347\) 8.37128 + 8.37128i 0.449394 + 0.449394i 0.895153 0.445759i \(-0.147066\pi\)
−0.445759 + 0.895153i \(0.647066\pi\)
\(348\) 0 0
\(349\) 5.94253 10.2928i 0.318096 0.550959i −0.661995 0.749509i \(-0.730290\pi\)
0.980091 + 0.198550i \(0.0636231\pi\)
\(350\) 2.02821 + 7.56936i 0.108412 + 0.404600i
\(351\) 0 0
\(352\) 1.29000 4.81433i 0.0687571 0.256605i
\(353\) −20.0086 + 5.36130i −1.06495 + 0.285353i −0.748417 0.663228i \(-0.769186\pi\)
−0.316535 + 0.948581i \(0.602519\pi\)
\(354\) 0 0
\(355\) 4.42851 1.18662i 0.235041 0.0629791i
\(356\) 4.21537 4.21537i 0.223414 0.223414i
\(357\) 0 0
\(358\) −3.94987 2.28046i −0.208757 0.120526i
\(359\) 14.1435i 0.746464i 0.927738 + 0.373232i \(0.121751\pi\)
−0.927738 + 0.373232i \(0.878249\pi\)
\(360\) 0 0
\(361\) −46.9152 27.0865i −2.46922 1.42560i
\(362\) −15.9235 15.9235i −0.836922 0.836922i
\(363\) 0 0
\(364\) −0.136264 + 0.136264i −0.00714220 + 0.00714220i
\(365\) 0.596348 2.22560i 0.0312143 0.116493i
\(366\) 0 0
\(367\) 5.73783 + 9.93821i 0.299512 + 0.518771i 0.976024 0.217661i \(-0.0698427\pi\)
−0.676512 + 0.736432i \(0.736509\pi\)
\(368\) −2.19509 8.19220i −0.114427 0.427048i
\(369\) 0 0
\(370\) −3.38000 + 3.43528i −0.175718 + 0.178592i
\(371\) 2.00819i 0.104260i
\(372\) 0 0
\(373\) −12.4379 + 7.18105i −0.644012 + 0.371820i −0.786158 0.618025i \(-0.787933\pi\)
0.142146 + 0.989846i \(0.454600\pi\)
\(374\) 8.78294 + 15.2125i 0.454155 + 0.786620i
\(375\) 0 0
\(376\) 6.10433 + 6.10433i 0.314807 + 0.314807i
\(377\) −0.529724 + 0.305836i −0.0272822 + 0.0157514i
\(378\) 0 0
\(379\) 9.82685 17.0206i 0.504771 0.874289i −0.495214 0.868771i \(-0.664910\pi\)
0.999985 0.00551811i \(-0.00175648\pi\)
\(380\) 6.77732i 0.347669i
\(381\) 0 0
\(382\) −0.832151 + 1.44133i −0.0425766 + 0.0737448i
\(383\) −6.70238 1.79590i −0.342476 0.0917660i 0.0834818 0.996509i \(-0.473396\pi\)
−0.425957 + 0.904743i \(0.640063\pi\)
\(384\) 0 0
\(385\) 1.83180 + 6.83638i 0.0933573 + 0.348414i
\(386\) 10.1196 + 5.84257i 0.515076 + 0.297379i
\(387\) 0 0
\(388\) −1.14977 0.308079i −0.0583706 0.0156403i
\(389\) 14.8872 + 3.98900i 0.754809 + 0.202251i 0.615650 0.788020i \(-0.288893\pi\)
0.139159 + 0.990270i \(0.455560\pi\)
\(390\) 0 0
\(391\) 25.8860 + 14.9453i 1.30911 + 0.755816i
\(392\) −0.980331 3.65864i −0.0495142 0.184789i
\(393\) 0 0
\(394\) −10.1989 2.73279i −0.513814 0.137676i
\(395\) 0.0425934 0.0737740i 0.00214311 0.00371197i
\(396\) 0 0
\(397\) 15.0940i 0.757546i 0.925490 + 0.378773i \(0.123654\pi\)
−0.925490 + 0.378773i \(0.876346\pi\)
\(398\) 11.7612 20.3711i 0.589538 1.02111i
\(399\) 0 0
\(400\) −3.78651 + 2.18614i −0.189325 + 0.109307i
\(401\) 11.2363 + 11.2363i 0.561116 + 0.561116i 0.929624 0.368508i \(-0.120131\pi\)
−0.368508 + 0.929624i \(0.620131\pi\)
\(402\) 0 0
\(403\) 0.514326 + 0.890839i 0.0256204 + 0.0443758i
\(404\) −3.18684 + 1.83992i −0.158551 + 0.0915395i
\(405\) 0 0
\(406\) 10.1962i 0.506027i
\(407\) 21.2631 21.6109i 1.05397 1.07121i
\(408\) 0 0
\(409\) −5.55070 20.7155i −0.274464 1.02432i −0.956199 0.292716i \(-0.905441\pi\)
0.681735 0.731599i \(-0.261226\pi\)
\(410\) −3.58230 6.20473i −0.176917 0.306430i
\(411\) 0 0
\(412\) 1.52601 5.69516i 0.0751813 0.280580i
\(413\) 14.9861 14.9861i 0.737415 0.737415i
\(414\) 0 0
\(415\) −2.20866 2.20866i −0.108419 0.108419i
\(416\) −0.0931152 0.0537601i −0.00456535 0.00263580i
\(417\) 0 0
\(418\) 42.6352i 2.08535i
\(419\) 16.1336 + 9.31474i 0.788178 + 0.455055i 0.839321 0.543637i \(-0.182953\pi\)
−0.0511427 + 0.998691i \(0.516286\pi\)
\(420\) 0 0
\(421\) 18.9146 18.9146i 0.921842 0.921842i −0.0753175 0.997160i \(-0.523997\pi\)
0.997160 + 0.0753175i \(0.0239970\pi\)
\(422\) −22.6655 + 6.07320i −1.10334 + 0.295639i
\(423\) 0 0
\(424\) 1.08228 0.289997i 0.0525604 0.0140835i
\(425\) 3.98825 14.8843i 0.193458 0.721996i
\(426\) 0 0
\(427\) 0.985536 + 3.67807i 0.0476934 + 0.177994i
\(428\) −3.79878 + 6.57967i −0.183621 + 0.318041i
\(429\) 0 0
\(430\) −1.77520 1.77520i −0.0856075 0.0856075i
\(431\) −0.477908 + 1.78358i −0.0230200 + 0.0859118i −0.976480 0.215607i \(-0.930827\pi\)
0.953460 + 0.301519i \(0.0974936\pi\)
\(432\) 0 0
\(433\) −23.4164 −1.12532 −0.562660 0.826689i \(-0.690222\pi\)
−0.562660 + 0.826689i \(0.690222\pi\)
\(434\) 17.1469 0.823079
\(435\) 0 0
\(436\) −0.950599 + 0.950599i −0.0455255 + 0.0455255i
\(437\) −36.2746 62.8294i −1.73525 3.00554i
\(438\) 0 0
\(439\) 13.0416 + 3.49449i 0.622441 + 0.166783i 0.556237 0.831023i \(-0.312245\pi\)
0.0662040 + 0.997806i \(0.478911\pi\)
\(440\) −3.41984 + 1.97445i −0.163034 + 0.0941280i
\(441\) 0 0
\(442\) 0.366025 0.0980762i 0.0174101 0.00466501i
\(443\) 12.3490 0.586718 0.293359 0.956002i \(-0.405227\pi\)
0.293359 + 0.956002i \(0.405227\pi\)
\(444\) 0 0
\(445\) −4.72317 −0.223900
\(446\) −19.4390 + 5.20868i −0.920465 + 0.246638i
\(447\) 0 0
\(448\) −1.55217 + 0.896143i −0.0733330 + 0.0423388i
\(449\) −8.02367 2.14994i −0.378660 0.101462i 0.0644684 0.997920i \(-0.479465\pi\)
−0.443129 + 0.896458i \(0.646132\pi\)
\(450\) 0 0
\(451\) 22.5358 + 39.0331i 1.06117 + 1.83800i
\(452\) −13.7809 + 13.7809i −0.648199 + 0.648199i
\(453\) 0 0
\(454\) 27.6463 1.29750
\(455\) 0.152679 0.00715771
\(456\) 0 0
\(457\) 6.24444 23.3045i 0.292102 1.09014i −0.651389 0.758744i \(-0.725813\pi\)
0.943491 0.331397i \(-0.107520\pi\)
\(458\) 4.42277 + 4.42277i 0.206662 + 0.206662i
\(459\) 0 0
\(460\) −3.35977 + 5.81929i −0.156650 + 0.271326i
\(461\) 7.27574 + 27.1534i 0.338865 + 1.26466i 0.899618 + 0.436678i \(0.143845\pi\)
−0.560753 + 0.827983i \(0.689488\pi\)
\(462\) 0 0
\(463\) 5.06434 18.9004i 0.235360 0.878375i −0.742626 0.669706i \(-0.766420\pi\)
0.977986 0.208669i \(-0.0669131\pi\)
\(464\) −5.49506 + 1.47240i −0.255102 + 0.0683543i
\(465\) 0 0
\(466\) −3.98697 + 1.06831i −0.184693 + 0.0494883i
\(467\) 7.16747 7.16747i 0.331671 0.331671i −0.521550 0.853221i \(-0.674646\pi\)
0.853221 + 0.521550i \(0.174646\pi\)
\(468\) 0 0
\(469\) 23.1725 + 13.3787i 1.07001 + 0.617769i
\(470\) 6.83968i 0.315491i
\(471\) 0 0
\(472\) 10.2406 + 5.91241i 0.471362 + 0.272141i
\(473\) 11.1675 + 11.1675i 0.513482 + 0.513482i
\(474\) 0 0
\(475\) −26.4465 + 26.4465i −1.21345 + 1.21345i
\(476\) 1.63486 6.10139i 0.0749338 0.279657i
\(477\) 0 0
\(478\) 13.9947 + 24.2395i 0.640102 + 1.10869i
\(479\) −4.30956 16.0835i −0.196909 0.734874i −0.991764 0.128075i \(-0.959120\pi\)
0.794855 0.606799i \(-0.207547\pi\)
\(480\) 0 0
\(481\) −0.331593 0.563727i −0.0151193 0.0257037i
\(482\) 12.9489i 0.589808i
\(483\) 0 0
\(484\) 11.9874 6.92096i 0.544884 0.314589i
\(485\) 0.471540 + 0.816731i 0.0214115 + 0.0370858i
\(486\) 0 0
\(487\) −2.35061 2.35061i −0.106516 0.106516i 0.651840 0.758356i \(-0.273997\pi\)
−0.758356 + 0.651840i \(0.773997\pi\)
\(488\) −1.83992 + 1.06228i −0.0832893 + 0.0480871i
\(489\) 0 0
\(490\) −1.50048 + 2.59890i −0.0677846 + 0.117406i
\(491\) 21.6729i 0.978086i 0.872260 + 0.489043i \(0.162654\pi\)
−0.872260 + 0.489043i \(0.837346\pi\)
\(492\) 0 0
\(493\) 10.0248 17.3635i 0.451495 0.782012i
\(494\) −0.888401 0.238046i −0.0399710 0.0107102i
\(495\) 0 0
\(496\) 2.47614 + 9.24107i 0.111182 + 0.414936i
\(497\) 8.98193 + 5.18572i 0.402895 + 0.232611i
\(498\) 0 0
\(499\) −12.7053 3.40437i −0.568766 0.152400i −0.0370355 0.999314i \(-0.511791\pi\)
−0.531731 + 0.846914i \(0.678458\pi\)
\(500\) 7.17252 + 1.92187i 0.320765 + 0.0859487i
\(501\) 0 0
\(502\) 10.1671 + 5.86999i 0.453781 + 0.261991i
\(503\) 5.22764 + 19.5098i 0.233089 + 0.869900i 0.979001 + 0.203855i \(0.0653473\pi\)
−0.745912 + 0.666045i \(0.767986\pi\)
\(504\) 0 0
\(505\) 2.81615 + 0.754585i 0.125317 + 0.0335786i
\(506\) 21.1358 36.6083i 0.939603 1.62744i
\(507\) 0 0
\(508\) 9.56385i 0.424327i
\(509\) −12.2010 + 21.1327i −0.540799 + 0.936691i 0.458060 + 0.888921i \(0.348545\pi\)
−0.998858 + 0.0477694i \(0.984789\pi\)
\(510\) 0 0
\(511\) 4.51398 2.60615i 0.199687 0.115289i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 0 0
\(514\) 9.08963 + 15.7437i 0.400926 + 0.694425i
\(515\) −4.04553 + 2.33569i −0.178267 + 0.102923i
\(516\) 0 0
\(517\) 43.0275i 1.89235i
\(518\) −10.9017 + 0.0884251i −0.478993 + 0.00388518i
\(519\) 0 0
\(520\) 0.0220480 + 0.0822842i 0.000966868 + 0.00360840i
\(521\) −4.59382 7.95672i −0.201259 0.348590i 0.747676 0.664064i \(-0.231170\pi\)
−0.948934 + 0.315474i \(0.897837\pi\)
\(522\) 0 0
\(523\) 4.67977 17.4652i 0.204632 0.763698i −0.784929 0.619586i \(-0.787301\pi\)
0.989561 0.144112i \(-0.0460326\pi\)
\(524\) 6.44488 6.44488i 0.281546 0.281546i
\(525\) 0 0
\(526\) −13.1294 13.1294i −0.572467 0.572467i
\(527\) −29.2003 16.8588i −1.27198 0.734380i
\(528\) 0 0
\(529\) 48.9306i 2.12742i
\(530\) −0.768795 0.443864i −0.0333943 0.0192802i
\(531\) 0 0
\(532\) −10.8410 + 10.8410i −0.470015 + 0.470015i
\(533\) 0.939169 0.251650i 0.0406799 0.0109002i
\(534\) 0 0
\(535\) 5.81433 1.55795i 0.251376 0.0673559i
\(536\) −3.86395 + 14.4205i −0.166897 + 0.622869i
\(537\) 0 0
\(538\) −1.18204 4.41142i −0.0509612 0.190190i
\(539\) 9.43928 16.3493i 0.406579 0.704215i
\(540\) 0 0
\(541\) −2.60437 2.60437i −0.111971 0.111971i 0.648902 0.760872i \(-0.275229\pi\)
−0.760872 + 0.648902i \(0.775229\pi\)
\(542\) 1.21528 4.53547i 0.0522006 0.194815i
\(543\) 0 0
\(544\) 3.52434 0.151105
\(545\) 1.06511 0.0456244
\(546\) 0 0
\(547\) −26.6204 + 26.6204i −1.13821 + 1.13821i −0.149434 + 0.988772i \(0.547745\pi\)
−0.988772 + 0.149434i \(0.952255\pi\)
\(548\) −8.68540 15.0436i −0.371022 0.642629i
\(549\) 0 0
\(550\) −21.0496 5.64023i −0.897559 0.240500i
\(551\) −42.1439 + 24.3318i −1.79539 + 1.03657i
\(552\) 0 0
\(553\) 0.186141 0.0498762i 0.00791551 0.00212095i
\(554\) 19.0801 0.810637
\(555\) 0 0
\(556\) 18.3742 0.779239
\(557\) 22.5007 6.02905i 0.953386 0.255459i 0.251587 0.967835i \(-0.419047\pi\)
0.701798 + 0.712376i \(0.252381\pi\)
\(558\) 0 0
\(559\) 0.295052 0.170349i 0.0124794 0.00720498i
\(560\) 1.37162 + 0.367525i 0.0579615 + 0.0155307i
\(561\) 0 0
\(562\) −11.8013 20.4405i −0.497808 0.862229i
\(563\) −2.51051 + 2.51051i −0.105805 + 0.105805i −0.758028 0.652222i \(-0.773837\pi\)
0.652222 + 0.758028i \(0.273837\pi\)
\(564\) 0 0
\(565\) 15.4410 0.649607
\(566\) −6.60096 −0.277459
\(567\) 0 0
\(568\) −1.49771 + 5.58953i −0.0628425 + 0.234531i
\(569\) −14.5450 14.5450i −0.609760 0.609760i 0.333123 0.942883i \(-0.391898\pi\)
−0.942883 + 0.333123i \(0.891898\pi\)
\(570\) 0 0
\(571\) −15.7795 + 27.3309i −0.660353 + 1.14376i 0.320170 + 0.947360i \(0.396260\pi\)
−0.980523 + 0.196404i \(0.937074\pi\)
\(572\) −0.138701 0.517638i −0.00579937 0.0216435i
\(573\) 0 0
\(574\) 4.19482 15.6553i 0.175089 0.653439i
\(575\) −35.8186 + 9.59757i −1.49374 + 0.400246i
\(576\) 0 0
\(577\) −32.2224 + 8.63397i −1.34144 + 0.359437i −0.856967 0.515371i \(-0.827654\pi\)
−0.484470 + 0.874808i \(0.660988\pi\)
\(578\) 3.23787 3.23787i 0.134678 0.134678i
\(579\) 0 0
\(580\) 3.90339 + 2.25362i 0.162079 + 0.0935766i
\(581\) 7.06594i 0.293144i
\(582\) 0 0
\(583\) 4.83638 + 2.79229i 0.200303 + 0.115645i
\(584\) 2.05639 + 2.05639i 0.0850942 + 0.0850942i
\(585\) 0 0
\(586\) −0.476039 + 0.476039i −0.0196650 + 0.0196650i
\(587\) −3.35254 + 12.5119i −0.138374 + 0.516420i 0.861587 + 0.507610i \(0.169471\pi\)
−0.999961 + 0.00880962i \(0.997196\pi\)
\(588\) 0 0
\(589\) 40.9189 + 70.8736i 1.68603 + 2.92030i
\(590\) −2.42479 9.04942i −0.0998269 0.372559i
\(591\) 0 0
\(592\) −1.62194 5.86253i −0.0666613 0.240949i
\(593\) 3.82605i 0.157117i −0.996910 0.0785584i \(-0.974968\pi\)
0.996910 0.0785584i \(-0.0250317\pi\)
\(594\) 0 0
\(595\) −4.33409 + 2.50229i −0.177680 + 0.102584i
\(596\) −0.603091 1.04458i −0.0247036 0.0427879i
\(597\) 0 0
\(598\) −0.644810 0.644810i −0.0263682 0.0263682i
\(599\) 21.0110 12.1307i 0.858486 0.495647i −0.00501889 0.999987i \(-0.501598\pi\)
0.863505 + 0.504340i \(0.168264\pi\)
\(600\) 0 0
\(601\) −15.3406 + 26.5707i −0.625757 + 1.08384i 0.362637 + 0.931930i \(0.381876\pi\)
−0.988394 + 0.151912i \(0.951457\pi\)
\(602\) 5.67919i 0.231466i
\(603\) 0 0
\(604\) 3.49819 6.05904i 0.142339 0.246539i
\(605\) −10.5931 2.83841i −0.430670 0.115398i
\(606\) 0 0
\(607\) 3.36991 + 12.5767i 0.136780 + 0.510471i 0.999984 + 0.00561578i \(0.00178757\pi\)
−0.863204 + 0.504856i \(0.831546\pi\)
\(608\) −7.40808 4.27706i −0.300437 0.173458i
\(609\) 0 0
\(610\) 1.62590 + 0.435660i 0.0658309 + 0.0176393i
\(611\) 0.896575 + 0.240237i 0.0362716 + 0.00971894i
\(612\) 0 0
\(613\) 2.61099 + 1.50746i 0.105457 + 0.0608856i 0.551801 0.833976i \(-0.313941\pi\)
−0.446344 + 0.894862i \(0.647274\pi\)
\(614\) 1.40866 + 5.25718i 0.0568487 + 0.212162i
\(615\) 0 0
\(616\) −8.62867 2.31205i −0.347659 0.0931550i
\(617\) −18.8360 + 32.6249i −0.758308 + 1.31343i 0.185405 + 0.982662i \(0.440640\pi\)
−0.943713 + 0.330765i \(0.892693\pi\)
\(618\) 0 0
\(619\) 22.5053i 0.904563i −0.891875 0.452281i \(-0.850610\pi\)
0.891875 0.452281i \(-0.149390\pi\)
\(620\) 3.78993 6.56435i 0.152207 0.263631i
\(621\) 0 0
\(622\) −9.35687 + 5.40219i −0.375176 + 0.216608i
\(623\) −7.55515 7.55515i −0.302691 0.302691i
\(624\) 0 0
\(625\) 7.98913 + 13.8376i 0.319565 + 0.553503i
\(626\) −2.81186 + 1.62343i −0.112385 + 0.0648853i
\(627\) 0 0
\(628\) 17.4364i 0.695788i
\(629\) 18.6519 + 10.5679i 0.743701 + 0.421371i
\(630\) 0 0
\(631\) 0.374964 + 1.39938i 0.0149271 + 0.0557086i 0.972988 0.230857i \(-0.0741530\pi\)
−0.958061 + 0.286566i \(0.907486\pi\)
\(632\) 0.0537601 + 0.0931152i 0.00213846 + 0.00370392i
\(633\) 0 0
\(634\) 3.02219 11.2790i 0.120026 0.447944i
\(635\) 5.35797 5.35797i 0.212625 0.212625i
\(636\) 0 0
\(637\) −0.287973 0.287973i −0.0114099 0.0114099i
\(638\) −24.5557 14.1772i −0.972169 0.561282i
\(639\) 0 0
\(640\) 0.792287i 0.0313179i
\(641\) 9.43096 + 5.44497i 0.372500 + 0.215063i 0.674550 0.738229i \(-0.264338\pi\)
−0.302050 + 0.953292i \(0.597671\pi\)
\(642\) 0 0
\(643\) 17.0252 17.0252i 0.671409 0.671409i −0.286632 0.958041i \(-0.592536\pi\)
0.958041 + 0.286632i \(0.0925357\pi\)
\(644\) −14.6828 + 3.93424i −0.578583 + 0.155031i
\(645\) 0 0
\(646\) 29.1204 7.80277i 1.14572 0.306996i
\(647\) −4.01905 + 14.9993i −0.158005 + 0.589683i 0.840824 + 0.541308i \(0.182071\pi\)
−0.998829 + 0.0483749i \(0.984596\pi\)
\(648\) 0 0
\(649\) 15.2540 + 56.9287i 0.598771 + 2.23465i
\(650\) −0.235054 + 0.407126i −0.00921958 + 0.0159688i
\(651\) 0 0
\(652\) 10.1691 + 10.1691i 0.398255 + 0.398255i
\(653\) 0.221964 0.828380i 0.00868611 0.0324170i −0.961447 0.274991i \(-0.911325\pi\)
0.970133 + 0.242574i \(0.0779918\pi\)
\(654\) 0 0
\(655\) −7.22125 −0.282158
\(656\) 9.04295 0.353068
\(657\) 0 0
\(658\) 10.9407 10.9407i 0.426513 0.426513i
\(659\) −2.26089 3.91597i −0.0880717 0.152545i 0.818624 0.574329i \(-0.194737\pi\)
−0.906696 + 0.421785i \(0.861404\pi\)
\(660\) 0 0
\(661\) −47.2167 12.6517i −1.83652 0.492093i −0.837957 0.545736i \(-0.816250\pi\)
−0.998560 + 0.0536429i \(0.982917\pi\)
\(662\) 19.9502 11.5183i 0.775387 0.447670i
\(663\) 0 0
\(664\) 3.80808 1.02037i 0.147782 0.0395981i
\(665\) 12.1469 0.471036
\(666\) 0 0
\(667\) −48.2487 −1.86820
\(668\) −14.5054 + 3.88671i −0.561231 + 0.150381i
\(669\) 0 0
\(670\) 10.2435 5.91409i 0.395741 0.228481i
\(671\) −10.2283 2.74067i −0.394861 0.105803i
\(672\) 0 0
\(673\) 12.7612 + 22.1031i 0.491909 + 0.852012i 0.999957 0.00931715i \(-0.00296578\pi\)
−0.508047 + 0.861329i \(0.669632\pi\)
\(674\) 0.405854 0.405854i 0.0156329 0.0156329i
\(675\) 0 0
\(676\) 12.9884 0.499555
\(677\) −12.0765 −0.464139 −0.232070 0.972699i \(-0.574550\pi\)
−0.232070 + 0.972699i \(0.574550\pi\)
\(678\) 0 0
\(679\) −0.552166 + 2.06071i −0.0211902 + 0.0790829i
\(680\) −1.97445 1.97445i −0.0757165 0.0757165i
\(681\) 0 0
\(682\) −23.8419 + 41.2954i −0.912954 + 1.58128i
\(683\) 8.08028 + 30.1560i 0.309183 + 1.15389i 0.929284 + 0.369366i \(0.120425\pi\)
−0.620101 + 0.784522i \(0.712908\pi\)
\(684\) 0 0
\(685\) −3.56204 + 13.2937i −0.136099 + 0.507927i
\(686\) −18.6759 + 5.00418i −0.713047 + 0.191060i
\(687\) 0 0
\(688\) 3.06071 0.820115i 0.116689 0.0312666i
\(689\) 0.0851868 0.0851868i 0.00324536 0.00324536i
\(690\) 0 0
\(691\) 8.41072 + 4.85593i 0.319959 + 0.184728i 0.651374 0.758757i \(-0.274193\pi\)
−0.331415 + 0.943485i \(0.607526\pi\)
\(692\) 1.84203i 0.0700233i
\(693\) 0 0
\(694\) 10.2527 + 5.91939i 0.389187 + 0.224697i
\(695\) −10.2938 10.2938i −0.390466 0.390466i
\(696\) 0 0
\(697\) −22.5358 + 22.5358i −0.853603 + 0.853603i
\(698\) 3.07608 11.4801i 0.116431 0.434528i
\(699\) 0 0
\(700\) 3.91819 + 6.78651i 0.148094 + 0.256506i
\(701\) 2.50113 + 9.33433i 0.0944662 + 0.352553i 0.996938 0.0781963i \(-0.0249161\pi\)
−0.902472 + 0.430749i \(0.858249\pi\)
\(702\) 0 0
\(703\) −26.3810 44.8491i −0.994977 1.69152i
\(704\) 4.98417i 0.187848i
\(705\) 0 0
\(706\) −17.9392 + 10.3572i −0.675153 + 0.389800i
\(707\) 3.29767 + 5.71173i 0.124022 + 0.214812i
\(708\) 0 0
\(709\) −22.0107 22.0107i −0.826630 0.826630i 0.160419 0.987049i \(-0.448715\pi\)
−0.987049 + 0.160419i \(0.948715\pi\)
\(710\) 3.97050 2.29237i 0.149010 0.0860310i
\(711\) 0 0
\(712\) 2.98072 5.16275i 0.111707 0.193482i
\(713\) 81.1401i 3.03872i
\(714\) 0 0
\(715\) −0.212293 + 0.367702i −0.00793930 + 0.0137513i
\(716\) −4.40551 1.18045i −0.164642 0.0441156i
\(717\) 0 0
\(718\) 3.66060 + 13.6616i 0.136612 + 0.509845i
\(719\) −41.0502 23.7004i −1.53091 0.883874i −0.999320 0.0368750i \(-0.988260\pi\)
−0.531595 0.846999i \(-0.678407\pi\)
\(720\) 0 0
\(721\) −10.2074 2.73506i −0.380142 0.101859i
\(722\) −52.3271 14.0210i −1.94741 0.521807i
\(723\) 0 0
\(724\) −19.5023 11.2596i −0.724795 0.418461i
\(725\) 6.43773 + 24.0260i 0.239091 + 0.892302i
\(726\) 0 0
\(727\) −10.1143 2.71013i −0.375120 0.100513i 0.0663327 0.997798i \(-0.478870\pi\)
−0.441453 + 0.897284i \(0.645537\pi\)
\(728\) −0.0963535 + 0.166889i −0.00357110 + 0.00618532i
\(729\) 0 0
\(730\) 2.30411i 0.0852790i
\(731\) −5.58375 + 9.67134i −0.206523 + 0.357708i
\(732\) 0 0
\(733\) 20.0631 11.5834i 0.741048 0.427844i −0.0814022 0.996681i \(-0.525940\pi\)
0.822450 + 0.568837i \(0.192606\pi\)
\(734\) 8.11452 + 8.11452i 0.299512 + 0.299512i
\(735\) 0 0
\(736\) −4.24060 7.34493i −0.156310 0.270738i
\(737\) −64.4404 + 37.2047i −2.37369 + 1.37045i
\(738\) 0 0
\(739\) 31.6978i 1.16602i 0.812464 + 0.583011i \(0.198126\pi\)
−0.812464 + 0.583011i \(0.801874\pi\)
\(740\) −2.37572 + 4.19304i −0.0873330 + 0.154139i
\(741\) 0 0
\(742\) −0.519758 1.93976i −0.0190809 0.0712110i
\(743\) 7.17719 + 12.4313i 0.263305 + 0.456058i 0.967118 0.254327i \(-0.0818540\pi\)
−0.703813 + 0.710385i \(0.748521\pi\)
\(744\) 0 0
\(745\) −0.247339 + 0.923080i −0.00906178 + 0.0338190i
\(746\) −10.1555 + 10.1555i −0.371820 + 0.371820i
\(747\) 0 0
\(748\) 12.4210 + 12.4210i 0.454155 + 0.454155i
\(749\) 11.7927 + 6.80850i 0.430895 + 0.248777i
\(750\) 0 0
\(751\) 31.5531i 1.15139i −0.817665 0.575694i \(-0.804732\pi\)
0.817665 0.575694i \(-0.195268\pi\)
\(752\) 7.47625 + 4.31641i 0.272631 + 0.157403i
\(753\) 0 0
\(754\) −0.432518 + 0.432518i −0.0157514 + 0.0157514i
\(755\) −5.35426 + 1.43467i −0.194861 + 0.0522129i
\(756\) 0 0
\(757\) 2.75841 0.739115i 0.100256 0.0268636i −0.208342 0.978056i \(-0.566807\pi\)
0.308598 + 0.951192i \(0.400140\pi\)
\(758\) 5.08675 18.9840i 0.184759 0.689530i
\(759\) 0 0
\(760\) 1.75410 + 6.54639i 0.0636279 + 0.237462i
\(761\) 13.9132 24.0984i 0.504354 0.873567i −0.495633 0.868532i \(-0.665064\pi\)
0.999987 0.00503492i \(-0.00160267\pi\)
\(762\) 0 0
\(763\) 1.70375 + 1.70375i 0.0616798 + 0.0616798i
\(764\) −0.430753 + 1.60759i −0.0155841 + 0.0581607i
\(765\) 0 0
\(766\) −6.93881 −0.250709
\(767\) 1.27141 0.0459078
\(768\) 0 0
\(769\) 6.45747 6.45747i 0.232862 0.232862i −0.581024 0.813886i \(-0.697348\pi\)
0.813886 + 0.581024i \(0.197348\pi\)
\(770\) 3.53877 + 6.12933i 0.127528 + 0.220886i
\(771\) 0 0
\(772\) 11.2870 + 3.02434i 0.406227 + 0.108848i
\(773\) 11.2931 6.52009i 0.406186 0.234511i −0.282964 0.959131i \(-0.591318\pi\)
0.689149 + 0.724619i \(0.257984\pi\)
\(774\) 0 0
\(775\) 40.4046 10.8264i 1.45137 0.388895i
\(776\) −1.19033 −0.0427302
\(777\) 0 0
\(778\) 15.4123 0.552559
\(779\) 74.7187 20.0208i 2.67707 0.717320i
\(780\) 0 0
\(781\) −24.9778 + 14.4210i −0.893777 + 0.516022i
\(782\) 28.8721 + 7.73625i 1.03246 + 0.276648i
\(783\) 0 0
\(784\) −1.89385 3.28025i −0.0676376 0.117152i
\(785\) 9.76842 9.76842i 0.348650 0.348650i
\(786\) 0 0
\(787\) 12.3019 0.438514 0.219257 0.975667i \(-0.429637\pi\)
0.219257 + 0.975667i \(0.429637\pi\)
\(788\) −10.5587 −0.376138
\(789\) 0 0
\(790\) 0.0220480 0.0822842i 0.000784432 0.00292754i
\(791\) 24.6993 + 24.6993i 0.878207 + 0.878207i
\(792\) 0 0
\(793\) −0.114216 + 0.197829i −0.00405594 + 0.00702510i
\(794\) 3.90661 + 14.5797i 0.138641 + 0.517414i
\(795\) 0 0
\(796\) 6.08806 22.7210i 0.215786 0.805323i
\(797\) 16.1588 4.32974i 0.572375 0.153367i 0.0389893 0.999240i \(-0.487586\pi\)
0.533386 + 0.845872i \(0.320920\pi\)
\(798\) 0 0
\(799\) −29.3883 + 7.87457i −1.03968 + 0.278582i
\(800\) −3.09167 + 3.09167i −0.109307 + 0.109307i
\(801\) 0 0
\(802\) 13.7617 + 7.94529i 0.485941 + 0.280558i
\(803\) 14.4949i 0.511512i
\(804\) 0 0
\(805\) 10.4298 + 6.02167i 0.367604 + 0.212236i
\(806\) 0.727367 + 0.727367i 0.0256204 + 0.0256204i
\(807\) 0 0
\(808\) −2.60204 + 2.60204i −0.0915395 + 0.0915395i
\(809\) 8.46249 31.5825i 0.297525 1.11038i −0.641666 0.766985i \(-0.721756\pi\)
0.939191 0.343395i \(-0.111577\pi\)
\(810\) 0 0
\(811\) −13.1780 22.8250i −0.462743 0.801495i 0.536353 0.843994i \(-0.319801\pi\)
−0.999097 + 0.0424987i \(0.986468\pi\)
\(812\) 2.63896 + 9.84873i 0.0926093 + 0.345623i
\(813\) 0 0
\(814\) 14.9453 26.3778i 0.523832 0.924542i
\(815\) 11.3942i 0.399120i
\(816\) 0 0
\(817\) 23.4739 13.5526i 0.821247 0.474147i
\(818\) −10.7231 18.5730i −0.374925 0.649390i
\(819\) 0 0
\(820\) −5.06614 5.06614i −0.176917 0.176917i
\(821\) 16.7391 9.66433i 0.584199 0.337288i −0.178601 0.983922i \(-0.557157\pi\)
0.762800 + 0.646634i \(0.223824\pi\)
\(822\) 0 0
\(823\) −14.8848 + 25.7812i −0.518852 + 0.898678i 0.480908 + 0.876771i \(0.340307\pi\)
−0.999760 + 0.0219068i \(0.993026\pi\)
\(824\) 5.89607i 0.205399i
\(825\) 0 0
\(826\) 10.5967 18.3541i 0.368708 0.638620i
\(827\) −17.7198 4.74800i −0.616177 0.165104i −0.0627876 0.998027i \(-0.519999\pi\)
−0.553389 + 0.832923i \(0.686666\pi\)
\(828\) 0 0
\(829\) −10.3968 38.8015i −0.361097 1.34763i −0.872636 0.488372i \(-0.837591\pi\)
0.511539 0.859260i \(-0.329076\pi\)
\(830\) −2.70505 1.56176i −0.0938937 0.0542095i
\(831\) 0 0
\(832\) −0.103857 0.0278283i −0.00360058 0.000964772i
\(833\) 12.8943 + 3.45502i 0.446761 + 0.119709i
\(834\) 0 0
\(835\) 10.3038 + 5.94892i 0.356579 + 0.205871i
\(836\) −11.0348 41.1824i −0.381646 1.42432i
\(837\) 0 0
\(838\) 17.9947 + 4.82166i 0.621616 + 0.166562i
\(839\) −8.50761 + 14.7356i −0.293715 + 0.508730i −0.974685 0.223581i \(-0.928225\pi\)
0.680970 + 0.732312i \(0.261558\pi\)
\(840\) 0 0
\(841\) 3.36365i 0.115988i
\(842\) 13.3747 23.1656i 0.460921 0.798339i
\(843\) 0 0
\(844\) −20.3213 + 11.7325i −0.699489 + 0.403850i
\(845\) −7.27653 7.27653i −0.250320 0.250320i
\(846\) 0 0
\(847\) −12.4043 21.4849i −0.426218 0.738232i
\(848\) 0.970349 0.560232i 0.0333219 0.0192384i
\(849\) 0 0
\(850\) 15.4094i 0.528538i
\(851\) −0.418432 51.5874i −0.0143437 1.76839i
\(852\) 0 0
\(853\) −6.77831 25.2970i −0.232085 0.866153i −0.979441 0.201729i \(-0.935344\pi\)
0.747356 0.664423i \(-0.231323\pi\)
\(854\) 1.90391 + 3.29767i 0.0651504 + 0.112844i
\(855\) 0 0
\(856\) −1.96639 + 7.33867i −0.0672099 + 0.250831i
\(857\) −19.9710 + 19.9710i −0.682197 + 0.682197i −0.960495 0.278298i \(-0.910230\pi\)
0.278298 + 0.960495i \(0.410230\pi\)
\(858\) 0 0
\(859\) 7.23411 + 7.23411i 0.246825 + 0.246825i 0.819666 0.572841i \(-0.194159\pi\)
−0.572841 + 0.819666i \(0.694159\pi\)
\(860\) −2.17416 1.25525i −0.0741383 0.0428038i
\(861\) 0 0
\(862\) 1.84649i 0.0628918i
\(863\) −47.0658 27.1735i −1.60214 0.924996i −0.991059 0.133427i \(-0.957402\pi\)
−0.611081 0.791568i \(-0.709265\pi\)
\(864\) 0 0
\(865\) 1.03196 1.03196i 0.0350877 0.0350877i
\(866\) −22.6185 + 6.06060i −0.768607 + 0.205948i
\(867\) 0 0
\(868\) 16.5627 4.43795i 0.562173 0.150634i
\(869\) −0.138701 + 0.517638i −0.00470510 + 0.0175597i
\(870\) 0 0
\(871\) 0.415452 + 1.55049i 0.0140771 + 0.0525363i
\(872\) −0.672175 + 1.16424i −0.0227627 + 0.0394262i
\(873\) 0 0
\(874\) −51.3000 51.3000i −1.73525 1.73525i
\(875\) 3.44454 12.8552i 0.116447 0.434585i
\(876\) 0 0
\(877\) −35.8379 −1.21016 −0.605079 0.796165i \(-0.706859\pi\)
−0.605079 + 0.796165i \(0.706859\pi\)
\(878\) 13.5017 0.455659
\(879\) 0 0
\(880\) −2.79229 + 2.79229i −0.0941280 + 0.0941280i
\(881\) 14.6808 + 25.4279i 0.494609 + 0.856688i 0.999981 0.00621358i \(-0.00197786\pi\)
−0.505371 + 0.862902i \(0.668645\pi\)
\(882\) 0 0
\(883\) 40.8471 + 10.9449i 1.37461 + 0.368327i 0.869162 0.494528i \(-0.164659\pi\)
0.505452 + 0.862854i \(0.331326\pi\)
\(884\) 0.328169 0.189469i 0.0110375 0.00637252i
\(885\) 0 0
\(886\) 11.9282 3.19615i 0.400736 0.107377i
\(887\) −29.9674 −1.00621 −0.503103 0.864227i \(-0.667808\pi\)
−0.503103 + 0.864227i \(0.667808\pi\)
\(888\) 0 0
\(889\) 17.1412 0.574896
\(890\) −4.56223 + 1.22245i −0.152926 + 0.0409765i
\(891\) 0 0
\(892\) −17.4286 + 10.0624i −0.583552 + 0.336914i
\(893\) 71.3300 + 19.1128i 2.38697 + 0.639586i
\(894\) 0 0
\(895\) 1.80678 + 3.12943i 0.0603940 + 0.104605i
\(896\) −1.26734 + 1.26734i −0.0423388 + 0.0423388i
\(897\) 0 0
\(898\) −8.30671 −0.277199
\(899\) 54.4261 1.81521
\(900\) 0 0
\(901\) −1.02205 + 3.81433i −0.0340494 + 0.127074i
\(902\) 31.8704 + 31.8704i 1.06117 + 1.06117i
\(903\) 0 0
\(904\) −9.74456 + 16.8781i −0.324099 + 0.561357i
\(905\) 4.61778 + 17.2338i 0.153500 + 0.572870i
\(906\) 0 0
\(907\) 3.76598 14.0548i 0.125047 0.466683i −0.874794 0.484495i \(-0.839003\pi\)
0.999841 + 0.0178120i \(0.00567003\pi\)
\(908\) 26.7043 7.15539i 0.886212 0.237460i
\(909\) 0 0
\(910\) 0.147477 0.0395163i 0.00488881 0.00130995i
\(911\) −3.47075 + 3.47075i −0.114991 + 0.114991i −0.762261 0.647270i \(-0.775911\pi\)
0.647270 + 0.762261i \(0.275911\pi\)
\(912\) 0 0
\(913\) 17.0171 + 9.82482i 0.563184 + 0.325154i
\(914\) 24.1266i 0.798038i
\(915\) 0 0
\(916\) 5.41676 + 3.12737i 0.178975 + 0.103331i
\(917\) −11.5511 11.5511i −0.381450 0.381450i
\(918\) 0 0
\(919\) 22.0066 22.0066i 0.725932 0.725932i −0.243875 0.969807i \(-0.578419\pi\)
0.969807 + 0.243875i \(0.0784186\pi\)
\(920\) −1.73914 + 6.49058i −0.0573379 + 0.213988i
\(921\) 0 0
\(922\) 14.0557 + 24.3451i 0.462898 + 0.801764i
\(923\) 0.161034 + 0.600987i 0.00530050 + 0.0197817i
\(924\) 0 0
\(925\) −25.6327 + 7.09157i −0.842796 + 0.233169i
\(926\) 19.5671i 0.643015i
\(927\) 0 0
\(928\) −4.92674 + 2.84445i −0.161728 + 0.0933737i
\(929\) 8.13078 + 14.0829i 0.266762 + 0.462046i 0.968024 0.250858i \(-0.0807128\pi\)
−0.701262 + 0.712904i \(0.747379\pi\)
\(930\) 0 0
\(931\) −22.9106 22.9106i −0.750865 0.750865i
\(932\) −3.57462 + 2.06381i −0.117091 + 0.0676023i
\(933\) 0 0
\(934\) 5.06817 8.77833i 0.165836 0.287236i
\(935\) 13.9172i 0.455142i
\(936\) 0 0
\(937\) −8.09651 + 14.0236i −0.264501 + 0.458130i −0.967433 0.253128i \(-0.918541\pi\)
0.702931 + 0.711258i \(0.251874\pi\)
\(938\) 25.8456 + 6.92531i 0.843889 + 0.226119i
\(939\) 0 0
\(940\) −1.77024 6.60662i −0.0577388 0.215484i
\(941\) −28.5919 16.5075i −0.932068 0.538130i −0.0446030 0.999005i \(-0.514202\pi\)
−0.887465 + 0.460875i \(0.847536\pi\)
\(942\) 0 0
\(943\) 74.0817 + 19.8501i 2.41243 + 0.646409i
\(944\) 11.4219 + 3.06049i 0.371751 + 0.0996104i
\(945\) 0 0
\(946\) 13.6773 + 7.89662i 0.444689 + 0.256741i
\(947\) −5.47080 20.4173i −0.177777 0.663474i −0.996062 0.0886605i \(-0.971741\pi\)
0.818285 0.574813i \(-0.194925\pi\)
\(948\) 0 0
\(949\) 0.302033 + 0.0809296i 0.00980442 + 0.00262709i
\(950\) −18.7005 + 32.3902i −0.606725 + 1.05088i
\(951\) 0 0
\(952\) 6.31662i 0.204723i
\(953\) 8.15315 14.1217i 0.264106 0.457446i −0.703223 0.710970i \(-0.748256\pi\)
0.967329 + 0.253524i \(0.0815897\pi\)
\(954\) 0 0
\(955\) 1.14195 0.659303i 0.0369525 0.0213345i
\(956\) 19.7915 + 19.7915i 0.640102 + 0.640102i
\(957\) 0 0
\(958\) −8.32544 14.4201i −0.268983 0.465892i
\(959\) −26.9624 + 15.5667i −0.870661 + 0.502676i
\(960\) 0 0
\(961\) 60.5287i 1.95254i
\(962\) −0.466197 0.458696i −0.0150308 0.0147889i
\(963\) 0 0
\(964\) −3.35143 12.5077i −0.107942 0.402847i
\(965\) −4.62899 8.01765i −0.149013 0.258097i
\(966\) 0 0
\(967\) 7.10431 26.5136i 0.228459 0.852621i −0.752530 0.658558i \(-0.771167\pi\)
0.980989 0.194063i \(-0.0621666\pi\)
\(968\) 9.78771 9.78771i 0.314589 0.314589i
\(969\) 0 0
\(970\) 0.666858 + 0.666858i 0.0214115 + 0.0214115i
\(971\) 7.18762 + 4.14977i 0.230662 + 0.133173i 0.610877 0.791725i \(-0.290817\pi\)
−0.380216 + 0.924898i \(0.624150\pi\)
\(972\) 0 0
\(973\) 32.9318i 1.05575i
\(974\) −2.87890 1.66213i −0.0922458 0.0532582i
\(975\) 0 0
\(976\) −1.50229 + 1.50229i −0.0480871 + 0.0480871i
\(977\) 7.66321 2.05335i 0.245168 0.0656925i −0.134142 0.990962i \(-0.542828\pi\)
0.379310 + 0.925270i \(0.376161\pi\)
\(978\) 0 0
\(979\) 28.7003 7.69023i 0.917267 0.245781i
\(980\) −0.776703 + 2.89870i −0.0248109 + 0.0925955i
\(981\) 0 0
\(982\) 5.60937 + 20.9345i 0.179002 + 0.668045i
\(983\) −10.1378 + 17.5593i −0.323347 + 0.560053i −0.981176 0.193114i \(-0.938141\pi\)
0.657830 + 0.753167i \(0.271475\pi\)
\(984\) 0 0
\(985\) 5.91531 + 5.91531i 0.188478 + 0.188478i
\(986\) 5.18923 19.3665i 0.165259 0.616753i
\(987\) 0 0
\(988\) −0.919740 −0.0292608
\(989\) 26.8742 0.854550
\(990\) 0 0
\(991\) −4.99520 + 4.99520i −0.158678 + 0.158678i −0.781981 0.623303i \(-0.785790\pi\)
0.623303 + 0.781981i \(0.285790\pi\)
\(992\) 4.78353 + 8.28532i 0.151877 + 0.263059i
\(993\) 0 0
\(994\) 10.0180 + 2.68433i 0.317753 + 0.0851417i
\(995\) −16.1397 + 9.31828i −0.511664 + 0.295409i
\(996\) 0 0
\(997\) −53.8898 + 14.4397i −1.70671 + 0.457311i −0.974614 0.223894i \(-0.928123\pi\)
−0.732093 + 0.681205i \(0.761456\pi\)
\(998\) −13.1535 −0.416366
\(999\) 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 666.2.be.d.467.3 yes 16
3.2 odd 2 inner 666.2.be.d.467.2 yes 16
37.29 odd 12 inner 666.2.be.d.251.2 16
111.29 even 12 inner 666.2.be.d.251.3 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
666.2.be.d.251.2 16 37.29 odd 12 inner
666.2.be.d.251.3 yes 16 111.29 even 12 inner
666.2.be.d.467.2 yes 16 3.2 odd 2 inner
666.2.be.d.467.3 yes 16 1.1 even 1 trivial