Properties

Label 216.2.l.b.179.8
Level $216$
Weight $2$
Character 216.179
Analytic conductor $1.725$
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] = [216,2,Mod(35,216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(216, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("216.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 216.l (of order \(6\), degree \(2\), 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: \(1.72476868366\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + \cdots + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 179.8
Root \(0.608741 + 1.27649i\) of defining polynomial
Character \(\chi\) \(=\) 216.179
Dual form 216.2.l.b.35.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.40985 + 0.111062i) q^{2} +(1.97533 + 0.313160i) q^{4} +(-1.74322 + 3.01934i) q^{5} +(1.80802 - 1.04386i) q^{7} +(2.75013 + 0.660890i) q^{8} +O(q^{10})\) \(q+(1.40985 + 0.111062i) q^{2} +(1.97533 + 0.313160i) q^{4} +(-1.74322 + 3.01934i) q^{5} +(1.80802 - 1.04386i) q^{7} +(2.75013 + 0.660890i) q^{8} +(-2.79300 + 4.06320i) q^{10} +(0.116985 - 0.0675415i) q^{11} +(-2.63890 - 1.52357i) q^{13} +(2.66496 - 1.27088i) q^{14} +(3.80386 + 1.23719i) q^{16} -4.19800i q^{17} +0.919111 q^{19} +(-4.38897 + 5.41829i) q^{20} +(0.172432 - 0.0822305i) q^{22} +(-0.689877 + 1.19490i) q^{23} +(-3.57762 - 6.19662i) q^{25} +(-3.55124 - 2.44108i) q^{26} +(3.89833 - 1.49577i) q^{28} +(-4.24111 - 7.34582i) q^{29} +(-4.39877 - 2.53963i) q^{31} +(5.22546 + 2.16671i) q^{32} +(0.466236 - 5.91853i) q^{34} +7.27870i q^{35} +1.61676i q^{37} +(1.29580 + 0.102078i) q^{38} +(-6.78953 + 7.15151i) q^{40} +(-1.79408 - 1.03581i) q^{41} +(5.41106 + 9.37224i) q^{43} +(0.252236 - 0.0967817i) q^{44} +(-1.10533 + 1.60801i) q^{46} +(0.205809 + 0.356471i) q^{47} +(-1.32071 + 2.28754i) q^{49} +(-4.35568 - 9.13361i) q^{50} +(-4.73559 - 3.83596i) q^{52} +0.968137 q^{53} +0.470958i q^{55} +(5.66217 - 1.67585i) q^{56} +(-5.16348 - 10.8275i) q^{58} +(-3.88770 - 2.24457i) q^{59} +(-7.44553 + 4.29868i) q^{61} +(-5.91953 - 4.06902i) q^{62} +(7.12645 + 3.63507i) q^{64} +(9.20037 - 5.31183i) q^{65} +(3.15416 - 5.46316i) q^{67} +(1.31464 - 8.29243i) q^{68} +(-0.808385 + 10.2618i) q^{70} +11.9687 q^{71} -4.06264 q^{73} +(-0.179560 + 2.27939i) q^{74} +(1.81555 + 0.287828i) q^{76} +(0.141008 - 0.244232i) q^{77} +(10.8672 - 6.27416i) q^{79} +(-10.3665 + 9.32847i) q^{80} +(-2.41434 - 1.65959i) q^{82} +(-5.23875 + 3.02459i) q^{83} +(12.6752 + 7.31802i) q^{85} +(6.58787 + 13.8144i) q^{86} +(0.366362 - 0.108434i) q^{88} +8.35848i q^{89} -6.36158 q^{91} +(-1.73693 + 2.14428i) q^{92} +(0.250568 + 0.525426i) q^{94} +(-1.60221 + 2.77511i) q^{95} +(-0.477065 - 0.826300i) q^{97} +(-2.11606 + 3.07840i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 3 q^{2} - 5 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 3 q^{2} - 5 q^{4} - 12 q^{11} + 18 q^{14} + 7 q^{16} - 4 q^{19} - 18 q^{20} - q^{22} - 14 q^{25} - 12 q^{28} - 27 q^{32} - 13 q^{34} + 15 q^{38} - 12 q^{40} + 36 q^{41} + 8 q^{43} + 12 q^{46} + 10 q^{49} - 51 q^{50} - 18 q^{52} + 66 q^{56} + 12 q^{58} - 12 q^{59} + 34 q^{64} + 6 q^{65} - 16 q^{67} + 9 q^{68} + 18 q^{70} - 4 q^{73} + 60 q^{74} - 7 q^{76} - 22 q^{82} - 54 q^{83} + 51 q^{86} - 13 q^{88} - 36 q^{91} - 84 q^{92} + 24 q^{94} + 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.40985 + 0.111062i 0.996912 + 0.0785324i
\(3\) 0 0
\(4\) 1.97533 + 0.313160i 0.987665 + 0.156580i
\(5\) −1.74322 + 3.01934i −0.779591 + 1.35029i 0.152587 + 0.988290i \(0.451240\pi\)
−0.932178 + 0.362001i \(0.882094\pi\)
\(6\) 0 0
\(7\) 1.80802 1.04386i 0.683367 0.394542i −0.117756 0.993043i \(-0.537570\pi\)
0.801122 + 0.598501i \(0.204237\pi\)
\(8\) 2.75013 + 0.660890i 0.972318 + 0.233660i
\(9\) 0 0
\(10\) −2.79300 + 4.06320i −0.883225 + 1.28490i
\(11\) 0.116985 0.0675415i 0.0352724 0.0203645i −0.482260 0.876028i \(-0.660184\pi\)
0.517533 + 0.855664i \(0.326851\pi\)
\(12\) 0 0
\(13\) −2.63890 1.52357i −0.731900 0.422563i 0.0872168 0.996189i \(-0.472203\pi\)
−0.819117 + 0.573627i \(0.805536\pi\)
\(14\) 2.66496 1.27088i 0.712241 0.339657i
\(15\) 0 0
\(16\) 3.80386 + 1.23719i 0.950966 + 0.309297i
\(17\) 4.19800i 1.01816i −0.860718 0.509082i \(-0.829985\pi\)
0.860718 0.509082i \(-0.170015\pi\)
\(18\) 0 0
\(19\) 0.919111 0.210858 0.105429 0.994427i \(-0.466378\pi\)
0.105429 + 0.994427i \(0.466378\pi\)
\(20\) −4.38897 + 5.41829i −0.981403 + 1.21157i
\(21\) 0 0
\(22\) 0.172432 0.0822305i 0.0367627 0.0175316i
\(23\) −0.689877 + 1.19490i −0.143849 + 0.249154i −0.928943 0.370223i \(-0.879281\pi\)
0.785094 + 0.619377i \(0.212615\pi\)
\(24\) 0 0
\(25\) −3.57762 6.19662i −0.715524 1.23932i
\(26\) −3.55124 2.44108i −0.696455 0.478736i
\(27\) 0 0
\(28\) 3.89833 1.49577i 0.736715 0.282674i
\(29\) −4.24111 7.34582i −0.787555 1.36409i −0.927461 0.373921i \(-0.878013\pi\)
0.139906 0.990165i \(-0.455320\pi\)
\(30\) 0 0
\(31\) −4.39877 2.53963i −0.790042 0.456131i 0.0499352 0.998752i \(-0.484099\pi\)
−0.839977 + 0.542621i \(0.817432\pi\)
\(32\) 5.22546 + 2.16671i 0.923739 + 0.383023i
\(33\) 0 0
\(34\) 0.466236 5.91853i 0.0799589 1.01502i
\(35\) 7.27870i 1.23033i
\(36\) 0 0
\(37\) 1.61676i 0.265794i 0.991130 + 0.132897i \(0.0424280\pi\)
−0.991130 + 0.132897i \(0.957572\pi\)
\(38\) 1.29580 + 0.102078i 0.210207 + 0.0165592i
\(39\) 0 0
\(40\) −6.78953 + 7.15151i −1.07352 + 1.13075i
\(41\) −1.79408 1.03581i −0.280188 0.161767i 0.353320 0.935502i \(-0.385053\pi\)
−0.633509 + 0.773736i \(0.718386\pi\)
\(42\) 0 0
\(43\) 5.41106 + 9.37224i 0.825180 + 1.42925i 0.901782 + 0.432191i \(0.142259\pi\)
−0.0766025 + 0.997062i \(0.524407\pi\)
\(44\) 0.252236 0.0967817i 0.0380260 0.0145904i
\(45\) 0 0
\(46\) −1.10533 + 1.60801i −0.162972 + 0.237088i
\(47\) 0.205809 + 0.356471i 0.0300203 + 0.0519966i 0.880645 0.473776i \(-0.157109\pi\)
−0.850625 + 0.525773i \(0.823776\pi\)
\(48\) 0 0
\(49\) −1.32071 + 2.28754i −0.188673 + 0.326791i
\(50\) −4.35568 9.13361i −0.615987 1.29169i
\(51\) 0 0
\(52\) −4.73559 3.83596i −0.656708 0.531951i
\(53\) 0.968137 0.132984 0.0664919 0.997787i \(-0.478819\pi\)
0.0664919 + 0.997787i \(0.478819\pi\)
\(54\) 0 0
\(55\) 0.470958i 0.0635040i
\(56\) 5.66217 1.67585i 0.756639 0.223945i
\(57\) 0 0
\(58\) −5.16348 10.8275i −0.677998 1.42172i
\(59\) −3.88770 2.24457i −0.506136 0.292218i 0.225108 0.974334i \(-0.427726\pi\)
−0.731244 + 0.682116i \(0.761060\pi\)
\(60\) 0 0
\(61\) −7.44553 + 4.29868i −0.953303 + 0.550390i −0.894105 0.447857i \(-0.852188\pi\)
−0.0591976 + 0.998246i \(0.518854\pi\)
\(62\) −5.91953 4.06902i −0.751781 0.516766i
\(63\) 0 0
\(64\) 7.12645 + 3.63507i 0.890806 + 0.454384i
\(65\) 9.20037 5.31183i 1.14117 0.658852i
\(66\) 0 0
\(67\) 3.15416 5.46316i 0.385342 0.667432i −0.606475 0.795103i \(-0.707417\pi\)
0.991817 + 0.127671i \(0.0407502\pi\)
\(68\) 1.31464 8.29243i 0.159424 1.00561i
\(69\) 0 0
\(70\) −0.808385 + 10.2618i −0.0966205 + 1.22653i
\(71\) 11.9687 1.42042 0.710210 0.703990i \(-0.248600\pi\)
0.710210 + 0.703990i \(0.248600\pi\)
\(72\) 0 0
\(73\) −4.06264 −0.475496 −0.237748 0.971327i \(-0.576409\pi\)
−0.237748 + 0.971327i \(0.576409\pi\)
\(74\) −0.179560 + 2.27939i −0.0208735 + 0.264973i
\(75\) 0 0
\(76\) 1.81555 + 0.287828i 0.208258 + 0.0330162i
\(77\) 0.141008 0.244232i 0.0160693 0.0278329i
\(78\) 0 0
\(79\) 10.8672 6.27416i 1.22265 0.705899i 0.257170 0.966366i \(-0.417210\pi\)
0.965483 + 0.260468i \(0.0838768\pi\)
\(80\) −10.3665 + 9.32847i −1.15900 + 1.04296i
\(81\) 0 0
\(82\) −2.41434 1.65959i −0.266619 0.183271i
\(83\) −5.23875 + 3.02459i −0.575027 + 0.331992i −0.759155 0.650910i \(-0.774387\pi\)
0.184128 + 0.982902i \(0.441054\pi\)
\(84\) 0 0
\(85\) 12.6752 + 7.31802i 1.37482 + 0.793751i
\(86\) 6.58787 + 13.8144i 0.710388 + 1.48964i
\(87\) 0 0
\(88\) 0.366362 0.108434i 0.0390544 0.0115591i
\(89\) 8.35848i 0.885997i 0.896522 + 0.442999i \(0.146085\pi\)
−0.896522 + 0.442999i \(0.853915\pi\)
\(90\) 0 0
\(91\) −6.36158 −0.666875
\(92\) −1.73693 + 2.14428i −0.181087 + 0.223557i
\(93\) 0 0
\(94\) 0.250568 + 0.525426i 0.0258441 + 0.0541936i
\(95\) −1.60221 + 2.77511i −0.164383 + 0.284720i
\(96\) 0 0
\(97\) −0.477065 0.826300i −0.0484386 0.0838981i 0.840790 0.541362i \(-0.182091\pi\)
−0.889228 + 0.457464i \(0.848758\pi\)
\(98\) −2.11606 + 3.07840i −0.213754 + 0.310965i
\(99\) 0 0
\(100\) −5.12645 13.3607i −0.512645 1.33607i
\(101\) 5.35926 + 9.28250i 0.533266 + 0.923644i 0.999245 + 0.0388479i \(0.0123688\pi\)
−0.465979 + 0.884796i \(0.654298\pi\)
\(102\) 0 0
\(103\) 7.46070 + 4.30743i 0.735124 + 0.424424i 0.820294 0.571942i \(-0.193810\pi\)
−0.0851696 + 0.996366i \(0.527143\pi\)
\(104\) −6.25042 5.93405i −0.612904 0.581881i
\(105\) 0 0
\(106\) 1.36492 + 0.107523i 0.132573 + 0.0104435i
\(107\) 4.80774i 0.464781i −0.972623 0.232391i \(-0.925345\pi\)
0.972623 0.232391i \(-0.0746548\pi\)
\(108\) 0 0
\(109\) 7.16698i 0.686472i −0.939249 0.343236i \(-0.888477\pi\)
0.939249 0.343236i \(-0.111523\pi\)
\(110\) −0.0523054 + 0.663978i −0.00498712 + 0.0633078i
\(111\) 0 0
\(112\) 8.16891 1.73384i 0.771889 0.163833i
\(113\) 0.213928 + 0.123511i 0.0201246 + 0.0116190i 0.510029 0.860157i \(-0.329635\pi\)
−0.489904 + 0.871776i \(0.662968\pi\)
\(114\) 0 0
\(115\) −2.40521 4.16595i −0.224287 0.388477i
\(116\) −6.07719 15.8386i −0.564253 1.47058i
\(117\) 0 0
\(118\) −5.23178 3.59627i −0.481624 0.331063i
\(119\) −4.38212 7.59006i −0.401708 0.695779i
\(120\) 0 0
\(121\) −5.49088 + 9.51048i −0.499171 + 0.864589i
\(122\) −10.9745 + 5.23356i −0.993582 + 0.473825i
\(123\) 0 0
\(124\) −7.89371 6.39413i −0.708876 0.574210i
\(125\) 7.51409 0.672081
\(126\) 0 0
\(127\) 17.6276i 1.56420i 0.623156 + 0.782098i \(0.285850\pi\)
−0.623156 + 0.782098i \(0.714150\pi\)
\(128\) 9.64348 + 5.91636i 0.852371 + 0.522938i
\(129\) 0 0
\(130\) 13.5610 6.46706i 1.18938 0.567199i
\(131\) 12.7802 + 7.37864i 1.11661 + 0.644675i 0.940533 0.339702i \(-0.110326\pi\)
0.176076 + 0.984377i \(0.443659\pi\)
\(132\) 0 0
\(133\) 1.66177 0.959423i 0.144094 0.0831925i
\(134\) 5.05362 7.35191i 0.436567 0.635108i
\(135\) 0 0
\(136\) 2.77442 11.5450i 0.237904 0.989979i
\(137\) −14.8589 + 8.57878i −1.26948 + 0.732934i −0.974889 0.222689i \(-0.928516\pi\)
−0.294590 + 0.955624i \(0.595183\pi\)
\(138\) 0 0
\(139\) −0.607862 + 1.05285i −0.0515581 + 0.0893013i −0.890653 0.454684i \(-0.849752\pi\)
0.839095 + 0.543986i \(0.183085\pi\)
\(140\) −2.27940 + 14.3778i −0.192644 + 1.21515i
\(141\) 0 0
\(142\) 16.8740 + 1.32926i 1.41603 + 0.111549i
\(143\) −0.411617 −0.0344211
\(144\) 0 0
\(145\) 29.5727 2.45588
\(146\) −5.72770 0.451204i −0.474028 0.0373419i
\(147\) 0 0
\(148\) −0.506305 + 3.19364i −0.0416180 + 0.262516i
\(149\) 4.46357 7.73113i 0.365670 0.633359i −0.623214 0.782052i \(-0.714173\pi\)
0.988883 + 0.148693i \(0.0475066\pi\)
\(150\) 0 0
\(151\) −18.9453 + 10.9381i −1.54175 + 0.890127i −0.543017 + 0.839722i \(0.682718\pi\)
−0.998729 + 0.0504058i \(0.983949\pi\)
\(152\) 2.52768 + 0.607431i 0.205022 + 0.0492692i
\(153\) 0 0
\(154\) 0.225924 0.328670i 0.0182055 0.0264850i
\(155\) 15.3360 8.85426i 1.23182 0.711191i
\(156\) 0 0
\(157\) 4.85478 + 2.80291i 0.387454 + 0.223697i 0.681056 0.732231i \(-0.261521\pi\)
−0.293602 + 0.955928i \(0.594854\pi\)
\(158\) 16.0179 7.63868i 1.27431 0.607701i
\(159\) 0 0
\(160\) −15.6511 + 12.0004i −1.23733 + 0.948714i
\(161\) 2.88054i 0.227018i
\(162\) 0 0
\(163\) −17.1763 −1.34535 −0.672676 0.739937i \(-0.734855\pi\)
−0.672676 + 0.739937i \(0.734855\pi\)
\(164\) −3.21952 2.60790i −0.251403 0.203643i
\(165\) 0 0
\(166\) −7.72174 + 3.68238i −0.599323 + 0.285808i
\(167\) −2.31249 + 4.00535i −0.178946 + 0.309943i −0.941520 0.336958i \(-0.890602\pi\)
0.762574 + 0.646901i \(0.223935\pi\)
\(168\) 0 0
\(169\) −1.85746 3.21721i −0.142881 0.247478i
\(170\) 17.0573 + 11.7250i 1.30824 + 0.899267i
\(171\) 0 0
\(172\) 7.75363 + 20.2078i 0.591209 + 1.54083i
\(173\) 1.52076 + 2.63404i 0.115621 + 0.200262i 0.918028 0.396516i \(-0.129781\pi\)
−0.802407 + 0.596778i \(0.796447\pi\)
\(174\) 0 0
\(175\) −12.9368 7.46907i −0.977930 0.564608i
\(176\) 0.528557 0.112186i 0.0398415 0.00845632i
\(177\) 0 0
\(178\) −0.928307 + 11.7842i −0.0695795 + 0.883261i
\(179\) 17.9997i 1.34536i −0.739935 0.672679i \(-0.765144\pi\)
0.739935 0.672679i \(-0.234856\pi\)
\(180\) 0 0
\(181\) 15.9507i 1.18561i −0.805347 0.592804i \(-0.798021\pi\)
0.805347 0.592804i \(-0.201979\pi\)
\(182\) −8.96885 0.706528i −0.664815 0.0523713i
\(183\) 0 0
\(184\) −2.68695 + 2.83020i −0.198085 + 0.208645i
\(185\) −4.88156 2.81837i −0.358899 0.207211i
\(186\) 0 0
\(187\) −0.283539 0.491104i −0.0207344 0.0359131i
\(188\) 0.294908 + 0.768599i 0.0215084 + 0.0560558i
\(189\) 0 0
\(190\) −2.56708 + 3.73453i −0.186235 + 0.270931i
\(191\) −2.21964 3.84452i −0.160607 0.278180i 0.774479 0.632599i \(-0.218012\pi\)
−0.935087 + 0.354419i \(0.884679\pi\)
\(192\) 0 0
\(193\) 0.673862 1.16716i 0.0485057 0.0840143i −0.840753 0.541419i \(-0.817887\pi\)
0.889259 + 0.457404i \(0.151221\pi\)
\(194\) −0.580817 1.21794i −0.0417003 0.0874430i
\(195\) 0 0
\(196\) −3.32521 + 4.10505i −0.237515 + 0.293218i
\(197\) −9.16835 −0.653218 −0.326609 0.945160i \(-0.605906\pi\)
−0.326609 + 0.945160i \(0.605906\pi\)
\(198\) 0 0
\(199\) 24.0240i 1.70301i −0.524344 0.851507i \(-0.675689\pi\)
0.524344 0.851507i \(-0.324311\pi\)
\(200\) −5.74364 19.4059i −0.406136 1.37221i
\(201\) 0 0
\(202\) 6.52479 + 13.6821i 0.459083 + 0.962670i
\(203\) −15.3360 8.85426i −1.07638 0.621447i
\(204\) 0 0
\(205\) 6.25494 3.61129i 0.436864 0.252224i
\(206\) 10.0400 + 6.90142i 0.699523 + 0.480844i
\(207\) 0 0
\(208\) −8.15308 9.06028i −0.565314 0.628217i
\(209\) 0.107522 0.0620781i 0.00743748 0.00429403i
\(210\) 0 0
\(211\) 10.1275 17.5414i 0.697208 1.20760i −0.272223 0.962234i \(-0.587759\pi\)
0.969431 0.245365i \(-0.0789078\pi\)
\(212\) 1.91239 + 0.303181i 0.131344 + 0.0208226i
\(213\) 0 0
\(214\) 0.533955 6.77817i 0.0365004 0.463346i
\(215\) −37.7307 −2.57321
\(216\) 0 0
\(217\) −10.6041 −0.719852
\(218\) 0.795977 10.1043i 0.0539104 0.684352i
\(219\) 0 0
\(220\) −0.147485 + 0.930298i −0.00994344 + 0.0627207i
\(221\) −6.39595 + 11.0781i −0.430238 + 0.745194i
\(222\) 0 0
\(223\) 0.521119 0.300868i 0.0348967 0.0201476i −0.482450 0.875923i \(-0.660253\pi\)
0.517347 + 0.855776i \(0.326920\pi\)
\(224\) 11.7095 1.53720i 0.782371 0.102708i
\(225\) 0 0
\(226\) 0.287888 + 0.197891i 0.0191500 + 0.0131635i
\(227\) −9.23720 + 5.33310i −0.613095 + 0.353970i −0.774176 0.632971i \(-0.781835\pi\)
0.161081 + 0.986941i \(0.448502\pi\)
\(228\) 0 0
\(229\) −22.1574 12.7926i −1.46420 0.845356i −0.464998 0.885312i \(-0.653945\pi\)
−0.999201 + 0.0399555i \(0.987278\pi\)
\(230\) −2.92830 6.14047i −0.193086 0.404891i
\(231\) 0 0
\(232\) −6.80884 23.0049i −0.447022 1.51035i
\(233\) 4.71086i 0.308619i 0.988023 + 0.154309i \(0.0493152\pi\)
−0.988023 + 0.154309i \(0.950685\pi\)
\(234\) 0 0
\(235\) −1.43508 −0.0936141
\(236\) −6.97659 5.65123i −0.454137 0.367864i
\(237\) 0 0
\(238\) −5.33515 11.1875i −0.345827 0.725178i
\(239\) 7.51034 13.0083i 0.485803 0.841436i −0.514064 0.857752i \(-0.671861\pi\)
0.999867 + 0.0163162i \(0.00519384\pi\)
\(240\) 0 0
\(241\) 12.8731 + 22.2969i 0.829230 + 1.43627i 0.898643 + 0.438681i \(0.144554\pi\)
−0.0694129 + 0.997588i \(0.522113\pi\)
\(242\) −8.79754 + 12.7985i −0.565527 + 0.822717i
\(243\) 0 0
\(244\) −16.0536 + 6.15968i −1.02772 + 0.394333i
\(245\) −4.60458 7.97536i −0.294176 0.509527i
\(246\) 0 0
\(247\) −2.42544 1.40033i −0.154327 0.0891009i
\(248\) −10.4188 9.89142i −0.661593 0.628106i
\(249\) 0 0
\(250\) 10.5937 + 0.834527i 0.670005 + 0.0527801i
\(251\) 5.30436i 0.334808i 0.985888 + 0.167404i \(0.0535385\pi\)
−0.985888 + 0.167404i \(0.946462\pi\)
\(252\) 0 0
\(253\) 0.186381i 0.0117177i
\(254\) −1.95775 + 24.8522i −0.122840 + 1.55936i
\(255\) 0 0
\(256\) 12.9387 + 9.41218i 0.808671 + 0.588261i
\(257\) 21.4984 + 12.4121i 1.34104 + 0.774248i 0.986959 0.160969i \(-0.0514619\pi\)
0.354077 + 0.935216i \(0.384795\pi\)
\(258\) 0 0
\(259\) 1.68767 + 2.92314i 0.104867 + 0.181635i
\(260\) 19.8372 7.61145i 1.23025 0.472042i
\(261\) 0 0
\(262\) 17.1986 + 11.8221i 1.06253 + 0.730374i
\(263\) 9.95859 + 17.2488i 0.614073 + 1.06361i 0.990546 + 0.137178i \(0.0438033\pi\)
−0.376473 + 0.926427i \(0.622863\pi\)
\(264\) 0 0
\(265\) −1.68767 + 2.92314i −0.103673 + 0.179567i
\(266\) 2.44939 1.16808i 0.150182 0.0716196i
\(267\) 0 0
\(268\) 7.94135 9.80380i 0.485095 0.598862i
\(269\) −2.35540 −0.143611 −0.0718057 0.997419i \(-0.522876\pi\)
−0.0718057 + 0.997419i \(0.522876\pi\)
\(270\) 0 0
\(271\) 12.0774i 0.733648i 0.930290 + 0.366824i \(0.119555\pi\)
−0.930290 + 0.366824i \(0.880445\pi\)
\(272\) 5.19371 15.9686i 0.314915 0.968239i
\(273\) 0 0
\(274\) −21.9015 + 10.4445i −1.32312 + 0.630975i
\(275\) −0.837057 0.483275i −0.0504764 0.0291426i
\(276\) 0 0
\(277\) −14.5504 + 8.40069i −0.874250 + 0.504748i −0.868758 0.495237i \(-0.835081\pi\)
−0.00549164 + 0.999985i \(0.501748\pi\)
\(278\) −0.973922 + 1.41684i −0.0584120 + 0.0849765i
\(279\) 0 0
\(280\) −4.81042 + 20.0174i −0.287478 + 1.19627i
\(281\) −11.9853 + 6.91973i −0.714984 + 0.412796i −0.812904 0.582398i \(-0.802115\pi\)
0.0979194 + 0.995194i \(0.468781\pi\)
\(282\) 0 0
\(283\) 2.58123 4.47082i 0.153438 0.265763i −0.779051 0.626960i \(-0.784299\pi\)
0.932489 + 0.361198i \(0.117632\pi\)
\(284\) 23.6421 + 3.74810i 1.40290 + 0.222409i
\(285\) 0 0
\(286\) −0.580317 0.0457149i −0.0343148 0.00270318i
\(287\) −4.32497 −0.255295
\(288\) 0 0
\(289\) −0.623177 −0.0366574
\(290\) 41.6930 + 3.28440i 2.44830 + 0.192866i
\(291\) 0 0
\(292\) −8.02506 1.27226i −0.469631 0.0744531i
\(293\) 5.41881 9.38566i 0.316571 0.548316i −0.663200 0.748443i \(-0.730802\pi\)
0.979770 + 0.200126i \(0.0641353\pi\)
\(294\) 0 0
\(295\) 13.5542 7.82554i 0.789158 0.455620i
\(296\) −1.06850 + 4.44631i −0.0621054 + 0.258436i
\(297\) 0 0
\(298\) 7.15158 10.4040i 0.414280 0.602686i
\(299\) 3.64104 2.10215i 0.210567 0.121571i
\(300\) 0 0
\(301\) 19.5666 + 11.2968i 1.12780 + 0.651136i
\(302\) −27.9247 + 13.3169i −1.60689 + 0.766301i
\(303\) 0 0
\(304\) 3.49617 + 1.13711i 0.200519 + 0.0652179i
\(305\) 29.9742i 1.71632i
\(306\) 0 0
\(307\) 16.6551 0.950557 0.475279 0.879835i \(-0.342347\pi\)
0.475279 + 0.879835i \(0.342347\pi\)
\(308\) 0.355021 0.438282i 0.0202292 0.0249734i
\(309\) 0 0
\(310\) 22.6048 10.7799i 1.28387 0.612257i
\(311\) 6.47216 11.2101i 0.367002 0.635667i −0.622093 0.782943i \(-0.713717\pi\)
0.989095 + 0.147277i \(0.0470508\pi\)
\(312\) 0 0
\(313\) −13.3593 23.1390i −0.755112 1.30789i −0.945318 0.326149i \(-0.894249\pi\)
0.190206 0.981744i \(-0.439084\pi\)
\(314\) 6.53320 + 4.49085i 0.368690 + 0.253433i
\(315\) 0 0
\(316\) 23.4311 8.99039i 1.31810 0.505749i
\(317\) 12.5342 + 21.7098i 0.703990 + 1.21935i 0.967055 + 0.254568i \(0.0819332\pi\)
−0.263065 + 0.964778i \(0.584733\pi\)
\(318\) 0 0
\(319\) −0.992296 0.572902i −0.0555579 0.0320764i
\(320\) −23.3985 + 15.1805i −1.30801 + 0.848614i
\(321\) 0 0
\(322\) −0.319918 + 4.06112i −0.0178283 + 0.226317i
\(323\) 3.85842i 0.214688i
\(324\) 0 0
\(325\) 21.8030i 1.20941i
\(326\) −24.2160 1.90763i −1.34120 0.105654i
\(327\) 0 0
\(328\) −4.24940 4.03431i −0.234634 0.222757i
\(329\) 0.744211 + 0.429671i 0.0410297 + 0.0236885i
\(330\) 0 0
\(331\) −8.47956 14.6870i −0.466079 0.807272i 0.533171 0.846008i \(-0.321000\pi\)
−0.999249 + 0.0387357i \(0.987667\pi\)
\(332\) −11.2954 + 4.33400i −0.619917 + 0.237859i
\(333\) 0 0
\(334\) −3.70510 + 5.39010i −0.202734 + 0.294933i
\(335\) 10.9968 + 19.0470i 0.600818 + 1.04065i
\(336\) 0 0
\(337\) 4.47220 7.74608i 0.243616 0.421956i −0.718125 0.695914i \(-0.755000\pi\)
0.961742 + 0.273958i \(0.0883329\pi\)
\(338\) −2.26142 4.74207i −0.123005 0.257934i
\(339\) 0 0
\(340\) 22.7460 + 18.4249i 1.23357 + 0.999229i
\(341\) −0.686122 −0.0371556
\(342\) 0 0
\(343\) 20.1286i 1.08684i
\(344\) 8.68712 + 29.3510i 0.468378 + 1.58250i
\(345\) 0 0
\(346\) 1.85150 + 3.88248i 0.0995372 + 0.208724i
\(347\) 4.29330 + 2.47874i 0.230476 + 0.133066i 0.610792 0.791791i \(-0.290851\pi\)
−0.380315 + 0.924857i \(0.624185\pi\)
\(348\) 0 0
\(349\) 22.9731 13.2635i 1.22972 0.709980i 0.262749 0.964864i \(-0.415371\pi\)
0.966972 + 0.254884i \(0.0820374\pi\)
\(350\) −17.4094 11.9670i −0.930570 0.639664i
\(351\) 0 0
\(352\) 0.757644 0.0994621i 0.0403825 0.00530135i
\(353\) 28.7458 16.5964i 1.52998 0.883337i 0.530623 0.847608i \(-0.321958\pi\)
0.999362 0.0357291i \(-0.0113753\pi\)
\(354\) 0 0
\(355\) −20.8640 + 36.1375i −1.10735 + 1.91798i
\(356\) −2.61754 + 16.5108i −0.138729 + 0.875069i
\(357\) 0 0
\(358\) 1.99907 25.3767i 0.105654 1.34120i
\(359\) 20.6138 1.08795 0.543977 0.839100i \(-0.316918\pi\)
0.543977 + 0.839100i \(0.316918\pi\)
\(360\) 0 0
\(361\) −18.1552 −0.955539
\(362\) 1.77151 22.4881i 0.0931087 1.18195i
\(363\) 0 0
\(364\) −12.5662 1.99219i −0.658649 0.104419i
\(365\) 7.08207 12.2665i 0.370693 0.642058i
\(366\) 0 0
\(367\) 10.1478 5.85881i 0.529708 0.305827i −0.211189 0.977445i \(-0.567734\pi\)
0.740898 + 0.671618i \(0.234400\pi\)
\(368\) −4.10251 + 3.69174i −0.213858 + 0.192445i
\(369\) 0 0
\(370\) −6.56923 4.51562i −0.341518 0.234756i
\(371\) 1.75041 1.01060i 0.0908767 0.0524677i
\(372\) 0 0
\(373\) −3.02771 1.74805i −0.156769 0.0905105i 0.419563 0.907726i \(-0.362183\pi\)
−0.576332 + 0.817216i \(0.695517\pi\)
\(374\) −0.345203 0.723871i −0.0178500 0.0374305i
\(375\) 0 0
\(376\) 0.330412 + 1.11636i 0.0170397 + 0.0575718i
\(377\) 25.8466i 1.33117i
\(378\) 0 0
\(379\) 20.1604 1.03557 0.517785 0.855511i \(-0.326757\pi\)
0.517785 + 0.855511i \(0.326757\pi\)
\(380\) −4.03395 + 4.98001i −0.206937 + 0.255469i
\(381\) 0 0
\(382\) −2.70237 5.66670i −0.138265 0.289934i
\(383\) −5.33120 + 9.23391i −0.272412 + 0.471831i −0.969479 0.245175i \(-0.921155\pi\)
0.697067 + 0.717006i \(0.254488\pi\)
\(384\) 0 0
\(385\) 0.491614 + 0.851501i 0.0250550 + 0.0433965i
\(386\) 1.07967 1.57068i 0.0549537 0.0799455i
\(387\) 0 0
\(388\) −0.683597 1.78161i −0.0347044 0.0904477i
\(389\) −8.34122 14.4474i −0.422917 0.732513i 0.573307 0.819341i \(-0.305660\pi\)
−0.996223 + 0.0868277i \(0.972327\pi\)
\(390\) 0 0
\(391\) 5.01619 + 2.89610i 0.253680 + 0.146462i
\(392\) −5.14394 + 5.41819i −0.259808 + 0.273660i
\(393\) 0 0
\(394\) −12.9260 1.01825i −0.651200 0.0512988i
\(395\) 43.7489i 2.20125i
\(396\) 0 0
\(397\) 22.9869i 1.15368i 0.816857 + 0.576840i \(0.195715\pi\)
−0.816857 + 0.576840i \(0.804285\pi\)
\(398\) 2.66814 33.8701i 0.133742 1.69775i
\(399\) 0 0
\(400\) −5.94239 27.9973i −0.297119 1.39986i
\(401\) −27.3094 15.7671i −1.36377 0.787371i −0.373644 0.927572i \(-0.621892\pi\)
−0.990123 + 0.140201i \(0.955225\pi\)
\(402\) 0 0
\(403\) 7.73862 + 13.4037i 0.385488 + 0.667685i
\(404\) 7.67940 + 20.0143i 0.382064 + 0.995749i
\(405\) 0 0
\(406\) −20.6381 14.1864i −1.02425 0.704058i
\(407\) 0.109199 + 0.189137i 0.00541277 + 0.00937519i
\(408\) 0 0
\(409\) 3.59259 6.22255i 0.177642 0.307686i −0.763430 0.645890i \(-0.776486\pi\)
0.941073 + 0.338205i \(0.109820\pi\)
\(410\) 9.21958 4.39668i 0.455323 0.217137i
\(411\) 0 0
\(412\) 13.3884 + 10.8450i 0.659600 + 0.534295i
\(413\) −9.37205 −0.461169
\(414\) 0 0
\(415\) 21.0901i 1.03527i
\(416\) −10.4883 13.6791i −0.514233 0.670672i
\(417\) 0 0
\(418\) 0.158485 0.0755789i 0.00775173 0.00369669i
\(419\) 12.5999 + 7.27453i 0.615543 + 0.355384i 0.775132 0.631800i \(-0.217683\pi\)
−0.159589 + 0.987184i \(0.551017\pi\)
\(420\) 0 0
\(421\) 9.38587 5.41893i 0.457439 0.264103i −0.253528 0.967328i \(-0.581591\pi\)
0.710967 + 0.703225i \(0.248258\pi\)
\(422\) 16.2264 23.6059i 0.789890 1.14912i
\(423\) 0 0
\(424\) 2.66250 + 0.639832i 0.129303 + 0.0310730i
\(425\) −26.0134 + 15.0188i −1.26183 + 0.728520i
\(426\) 0 0
\(427\) −8.97444 + 15.5442i −0.434304 + 0.752236i
\(428\) 1.50559 9.49687i 0.0727754 0.459048i
\(429\) 0 0
\(430\) −53.1944 4.19043i −2.56526 0.202080i
\(431\) 10.8604 0.523129 0.261565 0.965186i \(-0.415762\pi\)
0.261565 + 0.965186i \(0.415762\pi\)
\(432\) 0 0
\(433\) 9.41382 0.452399 0.226200 0.974081i \(-0.427370\pi\)
0.226200 + 0.974081i \(0.427370\pi\)
\(434\) −14.9501 1.17771i −0.717628 0.0565317i
\(435\) 0 0
\(436\) 2.24441 14.1572i 0.107488 0.678005i
\(437\) −0.634073 + 1.09825i −0.0303318 + 0.0525363i
\(438\) 0 0
\(439\) −9.25745 + 5.34479i −0.441834 + 0.255093i −0.704375 0.709828i \(-0.748773\pi\)
0.262541 + 0.964921i \(0.415439\pi\)
\(440\) −0.311252 + 1.29520i −0.0148383 + 0.0617461i
\(441\) 0 0
\(442\) −10.2477 + 14.9081i −0.487431 + 0.709105i
\(443\) −18.9818 + 10.9592i −0.901854 + 0.520686i −0.877801 0.479025i \(-0.840990\pi\)
−0.0240526 + 0.999711i \(0.507657\pi\)
\(444\) 0 0
\(445\) −25.2371 14.5707i −1.19635 0.690715i
\(446\) 0.768113 0.366302i 0.0363712 0.0173449i
\(447\) 0 0
\(448\) 16.6793 0.866739i 0.788021 0.0409496i
\(449\) 18.7436i 0.884565i −0.896876 0.442282i \(-0.854169\pi\)
0.896876 0.442282i \(-0.145831\pi\)
\(450\) 0 0
\(451\) −0.279841 −0.0131772
\(452\) 0.383899 + 0.310969i 0.0180571 + 0.0146267i
\(453\) 0 0
\(454\) −13.6153 + 6.49295i −0.638999 + 0.304729i
\(455\) 11.0896 19.2078i 0.519890 0.900475i
\(456\) 0 0
\(457\) −0.00912370 0.0158027i −0.000426789 0.000739220i 0.865812 0.500370i \(-0.166803\pi\)
−0.866239 + 0.499630i \(0.833469\pi\)
\(458\) −29.8177 20.4964i −1.39329 0.957732i
\(459\) 0 0
\(460\) −3.44648 8.98234i −0.160693 0.418804i
\(461\) 1.25915 + 2.18091i 0.0586444 + 0.101575i 0.893857 0.448352i \(-0.147989\pi\)
−0.835213 + 0.549927i \(0.814656\pi\)
\(462\) 0 0
\(463\) 23.9003 + 13.7988i 1.11074 + 0.641286i 0.939021 0.343860i \(-0.111735\pi\)
0.171719 + 0.985146i \(0.445068\pi\)
\(464\) −7.04445 33.1896i −0.327030 1.54079i
\(465\) 0 0
\(466\) −0.523196 + 6.64159i −0.0242366 + 0.307666i
\(467\) 28.4629i 1.31711i −0.752533 0.658554i \(-0.771168\pi\)
0.752533 0.658554i \(-0.228832\pi\)
\(468\) 0 0
\(469\) 13.1700i 0.608134i
\(470\) −2.02324 0.159382i −0.0933250 0.00735174i
\(471\) 0 0
\(472\) −9.20828 8.74220i −0.423846 0.402392i
\(473\) 1.26603 + 0.730942i 0.0582121 + 0.0336088i
\(474\) 0 0
\(475\) −3.28823 5.69538i −0.150874 0.261322i
\(476\) −6.27924 16.3652i −0.287808 0.750097i
\(477\) 0 0
\(478\) 12.0331 17.5056i 0.550383 0.800686i
\(479\) −19.1602 33.1865i −0.875454 1.51633i −0.856279 0.516514i \(-0.827229\pi\)
−0.0191747 0.999816i \(-0.506104\pi\)
\(480\) 0 0
\(481\) 2.46325 4.26648i 0.112315 0.194535i
\(482\) 15.6728 + 32.8649i 0.713875 + 1.49695i
\(483\) 0 0
\(484\) −13.8246 + 17.0668i −0.628391 + 0.775764i
\(485\) 3.32651 0.151049
\(486\) 0 0
\(487\) 2.25659i 0.102256i −0.998692 0.0511280i \(-0.983718\pi\)
0.998692 0.0511280i \(-0.0162817\pi\)
\(488\) −23.3172 + 6.90126i −1.05552 + 0.312405i
\(489\) 0 0
\(490\) −5.60599 11.7554i −0.253253 0.531056i
\(491\) 17.7659 + 10.2572i 0.801765 + 0.462899i 0.844088 0.536205i \(-0.180142\pi\)
−0.0423228 + 0.999104i \(0.513476\pi\)
\(492\) 0 0
\(493\) −30.8377 + 17.8042i −1.38886 + 0.801860i
\(494\) −3.26398 2.24362i −0.146853 0.100945i
\(495\) 0 0
\(496\) −13.5903 15.1025i −0.610223 0.678123i
\(497\) 21.6396 12.4936i 0.970667 0.560415i
\(498\) 0 0
\(499\) 1.87815 3.25306i 0.0840777 0.145627i −0.820920 0.571043i \(-0.806539\pi\)
0.904998 + 0.425416i \(0.139872\pi\)
\(500\) 14.8428 + 2.35311i 0.663791 + 0.105234i
\(501\) 0 0
\(502\) −0.589111 + 7.47833i −0.0262933 + 0.333774i
\(503\) 33.3322 1.48621 0.743104 0.669175i \(-0.233353\pi\)
0.743104 + 0.669175i \(0.233353\pi\)
\(504\) 0 0
\(505\) −37.3694 −1.66292
\(506\) −0.0206998 + 0.262769i −0.000920219 + 0.0116815i
\(507\) 0 0
\(508\) −5.52025 + 34.8203i −0.244921 + 1.54490i
\(509\) −3.41788 + 5.91994i −0.151495 + 0.262397i −0.931777 0.363031i \(-0.881742\pi\)
0.780282 + 0.625427i \(0.215075\pi\)
\(510\) 0 0
\(511\) −7.34533 + 4.24083i −0.324938 + 0.187603i
\(512\) 17.1963 + 14.7067i 0.759976 + 0.649951i
\(513\) 0 0
\(514\) 28.9310 + 19.8868i 1.27609 + 0.877171i
\(515\) −26.0112 + 15.0176i −1.14619 + 0.661754i
\(516\) 0 0
\(517\) 0.0481531 + 0.0278012i 0.00211777 + 0.00122270i
\(518\) 2.05471 + 4.30861i 0.0902788 + 0.189309i
\(519\) 0 0
\(520\) 28.8128 8.52781i 1.26352 0.373969i
\(521\) 19.9468i 0.873887i −0.899489 0.436943i \(-0.856061\pi\)
0.899489 0.436943i \(-0.143939\pi\)
\(522\) 0 0
\(523\) −5.50358 −0.240655 −0.120327 0.992734i \(-0.538394\pi\)
−0.120327 + 0.992734i \(0.538394\pi\)
\(524\) 22.9344 + 18.5775i 1.00189 + 0.811561i
\(525\) 0 0
\(526\) 12.1244 + 25.4241i 0.528649 + 1.10855i
\(527\) −10.6614 + 18.4660i −0.464416 + 0.804392i
\(528\) 0 0
\(529\) 10.5481 + 18.2699i 0.458615 + 0.794344i
\(530\) −2.70401 + 3.93374i −0.117455 + 0.170871i
\(531\) 0 0
\(532\) 3.58300 1.37478i 0.155343 0.0596042i
\(533\) 3.15627 + 5.46682i 0.136713 + 0.236794i
\(534\) 0 0
\(535\) 14.5162 + 8.38093i 0.627590 + 0.362339i
\(536\) 12.2849 12.9399i 0.530627 0.558917i
\(537\) 0 0
\(538\) −3.32075 0.261595i −0.143168 0.0112782i
\(539\) 0.356811i 0.0153690i
\(540\) 0 0
\(541\) 12.1375i 0.521831i 0.965362 + 0.260915i \(0.0840243\pi\)
−0.965362 + 0.260915i \(0.915976\pi\)
\(542\) −1.34133 + 17.0272i −0.0576152 + 0.731382i
\(543\) 0 0
\(544\) 9.09583 21.9364i 0.389980 0.940517i
\(545\) 21.6396 + 12.4936i 0.926937 + 0.535167i
\(546\) 0 0
\(547\) 5.02439 + 8.70250i 0.214827 + 0.372092i 0.953219 0.302280i \(-0.0977477\pi\)
−0.738392 + 0.674372i \(0.764414\pi\)
\(548\) −32.0377 + 12.2927i −1.36858 + 0.525119i
\(549\) 0 0
\(550\) −1.12645 0.774308i −0.0480319 0.0330166i
\(551\) −3.89805 6.75163i −0.166063 0.287629i
\(552\) 0 0
\(553\) 13.0987 22.6876i 0.557013 0.964775i
\(554\) −21.4468 + 10.2277i −0.911189 + 0.434533i
\(555\) 0 0
\(556\) −1.53044 + 1.88936i −0.0649050 + 0.0801269i
\(557\) −15.4323 −0.653887 −0.326944 0.945044i \(-0.606019\pi\)
−0.326944 + 0.945044i \(0.606019\pi\)
\(558\) 0 0
\(559\) 32.9766i 1.39476i
\(560\) −9.00512 + 27.6872i −0.380536 + 1.17000i
\(561\) 0 0
\(562\) −17.6660 + 8.42464i −0.745194 + 0.355372i
\(563\) −5.08901 2.93814i −0.214476 0.123828i 0.388914 0.921274i \(-0.372850\pi\)
−0.603390 + 0.797446i \(0.706184\pi\)
\(564\) 0 0
\(565\) −0.745845 + 0.430614i −0.0313779 + 0.0181161i
\(566\) 4.13567 6.01649i 0.173835 0.252892i
\(567\) 0 0
\(568\) 32.9154 + 7.90997i 1.38110 + 0.331895i
\(569\) 28.3228 16.3522i 1.18735 0.685519i 0.229650 0.973273i \(-0.426242\pi\)
0.957704 + 0.287754i \(0.0929087\pi\)
\(570\) 0 0
\(571\) 16.4253 28.4495i 0.687377 1.19057i −0.285306 0.958437i \(-0.592095\pi\)
0.972683 0.232136i \(-0.0745715\pi\)
\(572\) −0.813080 0.128902i −0.0339966 0.00538966i
\(573\) 0 0
\(574\) −6.09754 0.480338i −0.254507 0.0200489i
\(575\) 9.87246 0.411710
\(576\) 0 0
\(577\) −16.7158 −0.695887 −0.347943 0.937516i \(-0.613120\pi\)
−0.347943 + 0.937516i \(0.613120\pi\)
\(578\) −0.878583 0.0692110i −0.0365442 0.00287880i
\(579\) 0 0
\(580\) 58.4159 + 9.26099i 2.42559 + 0.384542i
\(581\) −6.31450 + 10.9370i −0.261970 + 0.453745i
\(582\) 0 0
\(583\) 0.113258 0.0653894i 0.00469066 0.00270815i
\(584\) −11.1728 2.68496i −0.462334 0.111104i
\(585\) 0 0
\(586\) 8.68208 12.6305i 0.358653 0.521762i
\(587\) 23.7005 13.6835i 0.978222 0.564777i 0.0764895 0.997070i \(-0.475629\pi\)
0.901733 + 0.432293i \(0.142296\pi\)
\(588\) 0 0
\(589\) −4.04296 2.33420i −0.166587 0.0961791i
\(590\) 19.9785 9.52744i 0.822501 0.392239i
\(591\) 0 0
\(592\) −2.00024 + 6.14994i −0.0822093 + 0.252761i
\(593\) 25.6865i 1.05482i 0.849612 + 0.527408i \(0.176836\pi\)
−0.849612 + 0.527408i \(0.823164\pi\)
\(594\) 0 0
\(595\) 30.5560 1.25267
\(596\) 11.2381 13.8737i 0.460331 0.568290i
\(597\) 0 0
\(598\) 5.36677 2.55933i 0.219464 0.104659i
\(599\) −19.9859 + 34.6166i −0.816601 + 1.41439i 0.0915718 + 0.995798i \(0.470811\pi\)
−0.908173 + 0.418596i \(0.862522\pi\)
\(600\) 0 0
\(601\) 2.01867 + 3.49645i 0.0823434 + 0.142623i 0.904256 0.426991i \(-0.140426\pi\)
−0.821913 + 0.569613i \(0.807093\pi\)
\(602\) 26.3313 + 18.0998i 1.07318 + 0.737694i
\(603\) 0 0
\(604\) −40.8486 + 15.6734i −1.66210 + 0.637742i
\(605\) −19.1436 33.1577i −0.778298 1.34805i
\(606\) 0 0
\(607\) −11.2251 6.48081i −0.455612 0.263048i 0.254585 0.967050i \(-0.418061\pi\)
−0.710198 + 0.704002i \(0.751394\pi\)
\(608\) 4.80277 + 1.99144i 0.194778 + 0.0807637i
\(609\) 0 0
\(610\) 3.32898 42.2589i 0.134786 1.71101i
\(611\) 1.25426i 0.0507418i
\(612\) 0 0
\(613\) 22.0890i 0.892167i 0.894991 + 0.446084i \(0.147182\pi\)
−0.894991 + 0.446084i \(0.852818\pi\)
\(614\) 23.4811 + 1.84974i 0.947622 + 0.0746496i
\(615\) 0 0
\(616\) 0.549201 0.578481i 0.0221279 0.0233077i
\(617\) −20.0171 11.5569i −0.805859 0.465263i 0.0396569 0.999213i \(-0.487374\pi\)
−0.845516 + 0.533951i \(0.820707\pi\)
\(618\) 0 0
\(619\) −2.24675 3.89149i −0.0903046 0.156412i 0.817335 0.576163i \(-0.195451\pi\)
−0.907639 + 0.419751i \(0.862117\pi\)
\(620\) 33.0665 12.6875i 1.32798 0.509541i
\(621\) 0 0
\(622\) 10.3698 15.0857i 0.415789 0.604882i
\(623\) 8.72509 + 15.1123i 0.349563 + 0.605461i
\(624\) 0 0
\(625\) 4.78939 8.29547i 0.191576 0.331819i
\(626\) −16.2647 34.1061i −0.650068 1.36315i
\(627\) 0 0
\(628\) 8.71204 + 7.05700i 0.347648 + 0.281605i
\(629\) 6.78716 0.270622
\(630\) 0 0
\(631\) 30.8693i 1.22889i −0.788961 0.614443i \(-0.789381\pi\)
0.788961 0.614443i \(-0.210619\pi\)
\(632\) 34.0327 10.0728i 1.35375 0.400673i
\(633\) 0 0
\(634\) 15.2601 + 31.9996i 0.606057 + 1.27087i
\(635\) −53.2237 30.7287i −2.11212 1.21943i
\(636\) 0 0
\(637\) 6.97046 4.02440i 0.276180 0.159452i
\(638\) −1.33536 0.917910i −0.0528673 0.0363404i
\(639\) 0 0
\(640\) −34.6742 + 18.8034i −1.37062 + 0.743271i
\(641\) −23.7137 + 13.6911i −0.936633 + 0.540766i −0.888903 0.458095i \(-0.848532\pi\)
−0.0477300 + 0.998860i \(0.515199\pi\)
\(642\) 0 0
\(643\) −19.9857 + 34.6162i −0.788158 + 1.36513i 0.138937 + 0.990301i \(0.455631\pi\)
−0.927094 + 0.374828i \(0.877702\pi\)
\(644\) −0.902069 + 5.69002i −0.0355465 + 0.224218i
\(645\) 0 0
\(646\) 0.428523 5.43978i 0.0168600 0.214025i
\(647\) −30.9768 −1.21782 −0.608912 0.793238i \(-0.708394\pi\)
−0.608912 + 0.793238i \(0.708394\pi\)
\(648\) 0 0
\(649\) −0.606405 −0.0238035
\(650\) −2.42148 + 30.7389i −0.0949783 + 1.20568i
\(651\) 0 0
\(652\) −33.9289 5.37893i −1.32876 0.210655i
\(653\) 2.78891 4.83053i 0.109138 0.189033i −0.806283 0.591530i \(-0.798524\pi\)
0.915421 + 0.402497i \(0.131857\pi\)
\(654\) 0 0
\(655\) −44.5573 + 25.7252i −1.74100 + 1.00517i
\(656\) −5.54294 6.15970i −0.216415 0.240496i
\(657\) 0 0
\(658\) 1.00150 + 0.688423i 0.0390427 + 0.0268375i
\(659\) 5.69959 3.29066i 0.222025 0.128186i −0.384863 0.922974i \(-0.625751\pi\)
0.606887 + 0.794788i \(0.292418\pi\)
\(660\) 0 0
\(661\) 26.9562 + 15.5632i 1.04847 + 0.605337i 0.922222 0.386661i \(-0.126372\pi\)
0.126253 + 0.991998i \(0.459705\pi\)
\(662\) −10.3237 21.6482i −0.401242 0.841381i
\(663\) 0 0
\(664\) −16.4062 + 4.85579i −0.636683 + 0.188441i
\(665\) 6.68993i 0.259425i
\(666\) 0 0
\(667\) 11.7034 0.453157
\(668\) −5.82225 + 7.18771i −0.225270 + 0.278101i
\(669\) 0 0
\(670\) 13.3884 + 28.0746i 0.517238 + 1.08462i
\(671\) −0.580679 + 1.00576i −0.0224168 + 0.0388271i
\(672\) 0 0
\(673\) −3.54087 6.13297i −0.136491 0.236409i 0.789675 0.613525i \(-0.210249\pi\)
−0.926166 + 0.377116i \(0.876916\pi\)
\(674\) 7.16541 10.4241i 0.276001 0.401521i
\(675\) 0 0
\(676\) −2.66159 6.93674i −0.102369 0.266798i
\(677\) 3.18253 + 5.51231i 0.122315 + 0.211855i 0.920680 0.390318i \(-0.127635\pi\)
−0.798365 + 0.602173i \(0.794302\pi\)
\(678\) 0 0
\(679\) −1.72508 0.995978i −0.0662026 0.0382221i
\(680\) 30.0220 + 28.5024i 1.15129 + 1.09302i
\(681\) 0 0
\(682\) −0.967326 0.0762018i −0.0370408 0.00291792i
\(683\) 51.9104i 1.98630i 0.116864 + 0.993148i \(0.462716\pi\)
−0.116864 + 0.993148i \(0.537284\pi\)
\(684\) 0 0
\(685\) 59.8187i 2.28556i
\(686\) −2.23552 + 28.3782i −0.0853524 + 1.08349i
\(687\) 0 0
\(688\) 8.98773 + 42.3452i 0.342654 + 1.61440i
\(689\) −2.55482 1.47503i −0.0973309 0.0561940i
\(690\) 0 0
\(691\) −17.9150 31.0297i −0.681519 1.18043i −0.974517 0.224313i \(-0.927986\pi\)
0.292998 0.956113i \(-0.405347\pi\)
\(692\) 2.17913 + 5.67933i 0.0828382 + 0.215896i
\(693\) 0 0
\(694\) 5.77760 + 3.97146i 0.219315 + 0.150755i
\(695\) −2.11927 3.67068i −0.0803885 0.139237i
\(696\) 0 0
\(697\) −4.34834 + 7.53154i −0.164705 + 0.285277i
\(698\) 33.8616 16.1481i 1.28168 0.611214i
\(699\) 0 0
\(700\) −23.2154 18.8052i −0.877461 0.710768i
\(701\) 19.0081 0.717927 0.358964 0.933352i \(-0.383130\pi\)
0.358964 + 0.933352i \(0.383130\pi\)
\(702\) 0 0
\(703\) 1.48598i 0.0560449i
\(704\) 1.07921 0.0560811i 0.0406742 0.00211364i
\(705\) 0 0
\(706\) 42.3704 20.2058i 1.59463 0.760455i
\(707\) 19.3793 + 11.1886i 0.728832 + 0.420792i
\(708\) 0 0
\(709\) 38.5758 22.2717i 1.44874 0.836433i 0.450337 0.892859i \(-0.351304\pi\)
0.998407 + 0.0564260i \(0.0179705\pi\)
\(710\) −33.4285 + 48.6311i −1.25455 + 1.82509i
\(711\) 0 0
\(712\) −5.52404 + 22.9869i −0.207022 + 0.861472i
\(713\) 6.06922 3.50407i 0.227294 0.131228i
\(714\) 0 0
\(715\) 0.717538 1.24281i 0.0268344 0.0464786i
\(716\) 5.63676 35.5553i 0.210656 1.32876i
\(717\) 0 0
\(718\) 29.0623 + 2.28940i 1.08459 + 0.0854397i
\(719\) −40.5385 −1.51183 −0.755915 0.654670i \(-0.772808\pi\)
−0.755915 + 0.654670i \(0.772808\pi\)
\(720\) 0 0
\(721\) 17.9854 0.669813
\(722\) −25.5961 2.01635i −0.952588 0.0750408i
\(723\) 0 0
\(724\) 4.99512 31.5080i 0.185642 1.17098i
\(725\) −30.3462 + 52.5611i −1.12703 + 1.95207i
\(726\) 0 0
\(727\) 16.5719 9.56779i 0.614618 0.354850i −0.160153 0.987092i \(-0.551199\pi\)
0.774770 + 0.632243i \(0.217865\pi\)
\(728\) −17.4952 4.20431i −0.648415 0.155822i
\(729\) 0 0
\(730\) 11.3470 16.5073i 0.419970 0.610964i
\(731\) 39.3446 22.7156i 1.45521 0.840168i
\(732\) 0 0
\(733\) −25.4597 14.6992i −0.940377 0.542927i −0.0502985 0.998734i \(-0.516017\pi\)
−0.890078 + 0.455807i \(0.849351\pi\)
\(734\) 14.9575 7.13299i 0.552090 0.263283i
\(735\) 0 0
\(736\) −6.19392 + 4.74915i −0.228311 + 0.175056i
\(737\) 0.852146i 0.0313892i
\(738\) 0 0
\(739\) −0.807511 −0.0297048 −0.0148524 0.999890i \(-0.504728\pi\)
−0.0148524 + 0.999890i \(0.504728\pi\)
\(740\) −8.76009 7.09592i −0.322027 0.260851i
\(741\) 0 0
\(742\) 2.58005 1.23039i 0.0947165 0.0451689i
\(743\) −13.2127 + 22.8850i −0.484725 + 0.839569i −0.999846 0.0175489i \(-0.994414\pi\)
0.515121 + 0.857118i \(0.327747\pi\)
\(744\) 0 0
\(745\) 15.5620 + 26.9541i 0.570146 + 0.987521i
\(746\) −4.07446 2.80074i −0.149177 0.102542i
\(747\) 0 0
\(748\) −0.406289 1.05889i −0.0148554 0.0387167i
\(749\) −5.01860 8.69248i −0.183376 0.317616i
\(750\) 0 0
\(751\) 2.08658 + 1.20469i 0.0761405 + 0.0439597i 0.537587 0.843208i \(-0.319336\pi\)
−0.461446 + 0.887168i \(0.652669\pi\)
\(752\) 0.341846 + 1.61059i 0.0124658 + 0.0587322i
\(753\) 0 0
\(754\) −2.87056 + 36.4397i −0.104540 + 1.32705i
\(755\) 76.2698i 2.77574i
\(756\) 0 0
\(757\) 3.61528i 0.131400i −0.997839 0.0656998i \(-0.979072\pi\)
0.997839 0.0656998i \(-0.0209280\pi\)
\(758\) 28.4231 + 2.23905i 1.03237 + 0.0813258i
\(759\) 0 0
\(760\) −6.24033 + 6.57303i −0.226361 + 0.238429i
\(761\) −7.79878 4.50263i −0.282706 0.163220i 0.351942 0.936022i \(-0.385521\pi\)
−0.634648 + 0.772802i \(0.718855\pi\)
\(762\) 0 0
\(763\) −7.48133 12.9580i −0.270842 0.469112i
\(764\) −3.18057 8.28930i −0.115069 0.299896i
\(765\) 0 0
\(766\) −8.54171 + 12.4263i −0.308624 + 0.448981i
\(767\) 6.83951 + 11.8464i 0.246961 + 0.427748i
\(768\) 0 0
\(769\) 7.58489 13.1374i 0.273518 0.473747i −0.696242 0.717807i \(-0.745146\pi\)
0.969760 + 0.244060i \(0.0784794\pi\)
\(770\) 0.598531 + 1.25508i 0.0215696 + 0.0452301i
\(771\) 0 0
\(772\) 1.69661 2.09451i 0.0610623 0.0753830i
\(773\) 31.6926 1.13990 0.569952 0.821678i \(-0.306962\pi\)
0.569952 + 0.821678i \(0.306962\pi\)
\(774\) 0 0
\(775\) 36.3433i 1.30549i
\(776\) −0.765897 2.58772i −0.0274941 0.0928938i
\(777\) 0 0
\(778\) −10.1553 21.2950i −0.364084 0.763463i
\(779\) −1.64896 0.952026i −0.0590800 0.0341099i
\(780\) 0 0
\(781\) 1.40016 0.808381i 0.0501016 0.0289262i
\(782\) 6.75042 + 4.64016i 0.241394 + 0.165932i
\(783\) 0 0
\(784\) −7.85392 + 7.06752i −0.280497 + 0.252411i
\(785\) −16.9259 + 9.77217i −0.604111 + 0.348784i
\(786\) 0 0
\(787\) 10.3290 17.8904i 0.368189 0.637723i −0.621093 0.783737i \(-0.713311\pi\)
0.989283 + 0.146014i \(0.0466444\pi\)
\(788\) −18.1105 2.87116i −0.645161 0.102281i
\(789\) 0 0
\(790\) −4.85883 + 61.6793i −0.172869 + 2.19445i
\(791\) 0.515713 0.0183367
\(792\) 0 0
\(793\) 26.1974 0.930297
\(794\) −2.55297 + 32.4080i −0.0906014 + 1.15012i
\(795\) 0 0
\(796\) 7.52333 47.4553i 0.266657 1.68201i
\(797\) 17.8453 30.9089i 0.632112 1.09485i −0.355007 0.934864i \(-0.615521\pi\)
0.987119 0.159987i \(-0.0511452\pi\)
\(798\) 0 0
\(799\) 1.49646 0.863984i 0.0529411 0.0305655i
\(800\) −5.26843 40.1318i −0.186267 1.41887i
\(801\) 0 0
\(802\) −36.7510 25.2622i −1.29772 0.892040i
\(803\) −0.475269 + 0.274397i −0.0167719 + 0.00968325i
\(804\) 0 0
\(805\) −8.69734 5.02141i −0.306541 0.176981i
\(806\) 9.42162 + 19.7566i 0.331863 + 0.695896i
\(807\) 0 0
\(808\) 8.60394 + 29.0700i 0.302686 + 1.02268i
\(809\) 18.7528i 0.659314i 0.944101 + 0.329657i \(0.106933\pi\)
−0.944101 + 0.329657i \(0.893067\pi\)
\(810\) 0 0
\(811\) −33.9206 −1.19111 −0.595556 0.803314i \(-0.703068\pi\)
−0.595556 + 0.803314i \(0.703068\pi\)
\(812\) −27.5209 22.2927i −0.965795 0.782321i
\(813\) 0 0
\(814\) 0.132947 + 0.278782i 0.00465980 + 0.00977131i
\(815\) 29.9421 51.8612i 1.04882 1.81662i
\(816\) 0 0
\(817\) 4.97337 + 8.61412i 0.173996 + 0.301370i
\(818\) 5.75609 8.37384i 0.201257 0.292785i
\(819\) 0 0
\(820\) 13.4865 5.17470i 0.470969 0.180708i
\(821\) 5.34636 + 9.26017i 0.186589 + 0.323182i 0.944111 0.329628i \(-0.106923\pi\)
−0.757522 + 0.652810i \(0.773590\pi\)
\(822\) 0 0
\(823\) −33.4172 19.2934i −1.16485 0.672527i −0.212390 0.977185i \(-0.568125\pi\)
−0.952462 + 0.304658i \(0.901458\pi\)
\(824\) 17.6712 + 16.7767i 0.615604 + 0.584445i
\(825\) 0 0
\(826\) −13.2131 1.04088i −0.459744 0.0362167i
\(827\) 0.214418i 0.00745604i −0.999993 0.00372802i \(-0.998813\pi\)
0.999993 0.00372802i \(-0.00118667\pi\)
\(828\) 0 0
\(829\) 35.5733i 1.23551i 0.786369 + 0.617757i \(0.211958\pi\)
−0.786369 + 0.617757i \(0.788042\pi\)
\(830\) 2.34230 29.7338i 0.0813024 1.03207i
\(831\) 0 0
\(832\) −13.2677 20.4503i −0.459975 0.708985i
\(833\) 9.60309 + 5.54434i 0.332727 + 0.192100i
\(834\) 0 0
\(835\) −8.06235 13.9644i −0.279009 0.483258i
\(836\) 0.231833 0.0889531i 0.00801810 0.00307651i
\(837\) 0 0
\(838\) 16.9559 + 11.6553i 0.585733 + 0.402627i
\(839\) −20.5867 35.6571i −0.710730 1.23102i −0.964583 0.263778i \(-0.915031\pi\)
0.253853 0.967243i \(-0.418302\pi\)
\(840\) 0 0
\(841\) −21.4741 + 37.1942i −0.740486 + 1.28256i
\(842\) 13.8345 6.59745i 0.476767 0.227363i
\(843\) 0 0
\(844\) 25.4985 31.4785i 0.877693 1.08353i
\(845\) 12.9518 0.445556
\(846\) 0 0
\(847\) 22.9268i 0.787775i
\(848\) 3.68266 + 1.19777i 0.126463 + 0.0411315i
\(849\) 0 0
\(850\) −38.3429 + 18.2851i −1.31515 + 0.627175i
\(851\) −1.93187 1.11537i −0.0662237 0.0382343i
\(852\) 0 0
\(853\) −30.9858 + 17.8897i −1.06093 + 0.612530i −0.925690 0.378282i \(-0.876515\pi\)
−0.135243 + 0.990812i \(0.543181\pi\)
\(854\) −14.3789 + 20.9182i −0.492037 + 0.715806i
\(855\) 0 0
\(856\) 3.17739 13.2219i 0.108601 0.451915i
\(857\) −26.3688 + 15.2241i −0.900742 + 0.520044i −0.877441 0.479685i \(-0.840751\pi\)
−0.0233014 + 0.999728i \(0.507418\pi\)
\(858\) 0 0
\(859\) −11.7147 + 20.2904i −0.399700 + 0.692301i −0.993689 0.112172i \(-0.964219\pi\)
0.593989 + 0.804473i \(0.297552\pi\)
\(860\) −74.5305 11.8157i −2.54147 0.402913i
\(861\) 0 0
\(862\) 15.3115 + 1.20618i 0.521513 + 0.0410826i
\(863\) 32.2240 1.09692 0.548458 0.836178i \(-0.315215\pi\)
0.548458 + 0.836178i \(0.315215\pi\)
\(864\) 0 0
\(865\) −10.6041 −0.360549
\(866\) 13.2720 + 1.04551i 0.451002 + 0.0355280i
\(867\) 0 0
\(868\) −20.9466 3.32077i −0.710972 0.112714i
\(869\) 0.847532 1.46797i 0.0287506 0.0497974i
\(870\) 0 0
\(871\) −16.6470 + 9.61117i −0.564063 + 0.325662i
\(872\) 4.73659 19.7101i 0.160401 0.667470i
\(873\) 0 0
\(874\) −1.01592 + 1.47794i −0.0343640 + 0.0499920i
\(875\) 13.5856 7.84366i 0.459278 0.265164i
\(876\) 0 0
\(877\) −1.74081 1.00506i −0.0587829 0.0339384i 0.470320 0.882496i \(-0.344138\pi\)
−0.529103 + 0.848557i \(0.677472\pi\)
\(878\) −13.6452 + 6.50718i −0.460502 + 0.219607i
\(879\) 0 0
\(880\) −0.582663 + 1.79146i −0.0196416 + 0.0603901i
\(881\) 21.6545i 0.729558i 0.931094 + 0.364779i \(0.118855\pi\)
−0.931094 + 0.364779i \(0.881145\pi\)
\(882\) 0 0
\(883\) −23.3462 −0.785664 −0.392832 0.919610i \(-0.628505\pi\)
−0.392832 + 0.919610i \(0.628505\pi\)
\(884\) −16.1033 + 19.8800i −0.541614 + 0.668636i
\(885\) 0 0
\(886\) −27.9786 + 13.3426i −0.939959 + 0.448253i
\(887\) 24.4901 42.4181i 0.822297 1.42426i −0.0816710 0.996659i \(-0.526026\pi\)
0.903968 0.427600i \(-0.140641\pi\)
\(888\) 0 0
\(889\) 18.4007 + 31.8710i 0.617141 + 1.06892i
\(890\) −33.9622 23.3453i −1.13842 0.782535i
\(891\) 0 0
\(892\) 1.12360 0.431121i 0.0376210 0.0144350i
\(893\) 0.189161 + 0.327636i 0.00633003 + 0.0109639i
\(894\) 0 0
\(895\) 54.3471 + 31.3773i 1.81662 + 1.04883i
\(896\) 23.6114 + 0.630457i 0.788803 + 0.0210621i
\(897\) 0 0
\(898\) 2.08169 26.4256i 0.0694670 0.881833i
\(899\) 43.0834i 1.43691i
\(900\) 0 0
\(901\) 4.06424i 0.135399i
\(902\) −0.394533 0.0310796i −0.0131365 0.00103484i
\(903\) 0 0
\(904\) 0.506702 + 0.481055i 0.0168526 + 0.0159996i
\(905\) 48.1607 + 27.8056i 1.60092 + 0.924289i
\(906\) 0 0
\(907\) −9.93443 17.2069i −0.329867 0.571347i 0.652618 0.757687i \(-0.273671\pi\)
−0.982485 + 0.186340i \(0.940337\pi\)
\(908\) −19.9166 + 7.64192i −0.660957 + 0.253606i
\(909\) 0 0
\(910\) 17.7679 25.8484i 0.589001 0.856866i
\(911\) −24.0672 41.6857i −0.797383 1.38111i −0.921315 0.388817i \(-0.872884\pi\)
0.123932 0.992291i \(-0.460450\pi\)
\(912\) 0 0
\(913\) −0.408571 + 0.707665i −0.0135217 + 0.0234203i
\(914\) −0.0111079 0.0232927i −0.000367418 0.000770453i
\(915\) 0 0
\(916\) −39.7620 32.2083i −1.31377 1.06419i
\(917\) 30.8091 1.01741
\(918\) 0 0
\(919\) 34.3644i 1.13358i 0.823864 + 0.566788i \(0.191814\pi\)
−0.823864 + 0.566788i \(0.808186\pi\)
\(920\) −3.86141 13.0465i −0.127307 0.430130i
\(921\) 0 0
\(922\) 1.53299 + 3.21459i 0.0504864 + 0.105867i
\(923\) −31.5841 18.2351i −1.03960 0.600216i
\(924\) 0 0
\(925\) 10.0185 5.78416i 0.329405 0.190182i
\(926\) 32.1632 + 22.1086i 1.05695 + 0.726535i
\(927\) 0 0
\(928\) −6.24550 47.5745i −0.205019 1.56171i
\(929\) −15.1165 + 8.72750i −0.495955 + 0.286340i −0.727042 0.686593i \(-0.759105\pi\)
0.231086 + 0.972933i \(0.425772\pi\)
\(930\) 0 0
\(931\) −1.21388 + 2.10250i −0.0397833 + 0.0689067i
\(932\) −1.47525 + 9.30551i −0.0483235 + 0.304812i
\(933\) 0 0
\(934\) 3.16114 40.1284i 0.103436 1.31304i
\(935\) 1.97708 0.0646574
\(936\) 0 0
\(937\) 42.3068 1.38210 0.691051 0.722806i \(-0.257148\pi\)
0.691051 + 0.722806i \(0.257148\pi\)
\(938\) 1.46268 18.5677i 0.0477583 0.606256i
\(939\) 0 0
\(940\) −2.83475 0.449408i −0.0924594 0.0146581i
\(941\) −11.6752 + 20.2221i −0.380602 + 0.659222i −0.991148 0.132758i \(-0.957617\pi\)
0.610546 + 0.791980i \(0.290950\pi\)
\(942\) 0 0
\(943\) 2.47539 1.42917i 0.0806097 0.0465400i
\(944\) −12.0113 13.3478i −0.390936 0.434435i
\(945\) 0 0
\(946\) 1.70373 + 1.17112i 0.0553929 + 0.0380765i
\(947\) −28.1206 + 16.2354i −0.913796 + 0.527580i −0.881651 0.471903i \(-0.843567\pi\)
−0.0321454 + 0.999483i \(0.510234\pi\)
\(948\) 0 0
\(949\) 10.7209 + 6.18973i 0.348016 + 0.200927i
\(950\) −4.00335 8.39480i −0.129886 0.272363i
\(951\) 0 0
\(952\) −7.03522 23.7698i −0.228013 0.770382i
\(953\) 11.0705i 0.358607i −0.983794 0.179304i \(-0.942616\pi\)
0.983794 0.179304i \(-0.0573844\pi\)
\(954\) 0 0
\(955\) 15.4772 0.500832
\(956\) 18.9091 23.3437i 0.611563 0.754990i
\(957\) 0 0
\(958\) −23.3272 48.9158i −0.753669 1.58040i
\(959\) −17.9101 + 31.0212i −0.578347 + 1.00173i
\(960\) 0 0
\(961\) −2.60055 4.50429i −0.0838888 0.145300i
\(962\) 3.94665 5.74151i 0.127245 0.185114i
\(963\) 0 0
\(964\) 18.4462 + 48.0751i 0.594111 + 1.54839i
\(965\) 2.34938 + 4.06924i 0.0756291 + 0.130993i
\(966\) 0 0
\(967\) −40.9201 23.6252i −1.31590 0.759736i −0.332835 0.942985i \(-0.608005\pi\)
−0.983066 + 0.183249i \(0.941338\pi\)
\(968\) −21.3860 + 22.5262i −0.687373 + 0.724019i
\(969\) 0 0
\(970\) 4.68987 + 0.369448i 0.150583 + 0.0118623i
\(971\) 33.9428i 1.08928i −0.838671 0.544638i \(-0.816667\pi\)
0.838671 0.544638i \(-0.183333\pi\)
\(972\) 0 0
\(973\) 2.53809i 0.0813674i
\(974\) 0.250621 3.18145i 0.00803042 0.101940i
\(975\) 0 0
\(976\) −33.6401 + 7.14007i −1.07679 + 0.228548i
\(977\) −26.9476 15.5582i −0.862131 0.497752i 0.00259421 0.999997i \(-0.499174\pi\)
−0.864725 + 0.502245i \(0.832508\pi\)
\(978\) 0 0
\(979\) 0.564544 + 0.977819i 0.0180429 + 0.0312512i
\(980\) −6.59800 17.1959i −0.210765 0.549304i
\(981\) 0 0
\(982\) 23.9080 + 16.4341i 0.762936 + 0.524434i
\(983\) 18.2288 + 31.5733i 0.581410 + 1.00703i 0.995313 + 0.0967103i \(0.0308320\pi\)
−0.413903 + 0.910321i \(0.635835\pi\)
\(984\) 0 0
\(985\) 15.9824 27.6824i 0.509243 0.882034i
\(986\) −45.4538 + 21.6763i −1.44754 + 0.690313i
\(987\) 0 0
\(988\) −4.35253 3.52567i −0.138472 0.112166i
\(989\) −14.9319 −0.474806
\(990\) 0 0
\(991\) 21.5164i 0.683490i −0.939793 0.341745i \(-0.888982\pi\)
0.939793 0.341745i \(-0.111018\pi\)
\(992\) −17.4829 22.8016i −0.555084 0.723951i
\(993\) 0 0
\(994\) 31.8960 15.2107i 1.01168 0.482455i
\(995\) 72.5365 + 41.8790i 2.29956 + 1.32765i
\(996\) 0 0
\(997\) 49.4923 28.5744i 1.56744 0.904961i 0.570971 0.820970i \(-0.306567\pi\)
0.996467 0.0839906i \(-0.0267666\pi\)
\(998\) 3.00920 4.37772i 0.0952544 0.138574i
\(999\) 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 216.2.l.b.179.8 16
3.2 odd 2 72.2.l.b.59.1 yes 16
4.3 odd 2 864.2.p.b.719.1 16
8.3 odd 2 inner 216.2.l.b.179.5 16
8.5 even 2 864.2.p.b.719.8 16
9.2 odd 6 inner 216.2.l.b.35.5 16
9.4 even 3 648.2.f.b.323.8 16
9.5 odd 6 648.2.f.b.323.9 16
9.7 even 3 72.2.l.b.11.4 yes 16
12.11 even 2 288.2.p.b.239.8 16
24.5 odd 2 288.2.p.b.239.7 16
24.11 even 2 72.2.l.b.59.4 yes 16
36.7 odd 6 288.2.p.b.47.7 16
36.11 even 6 864.2.p.b.143.8 16
36.23 even 6 2592.2.f.b.1295.1 16
36.31 odd 6 2592.2.f.b.1295.15 16
72.5 odd 6 2592.2.f.b.1295.16 16
72.11 even 6 inner 216.2.l.b.35.8 16
72.13 even 6 2592.2.f.b.1295.2 16
72.29 odd 6 864.2.p.b.143.1 16
72.43 odd 6 72.2.l.b.11.1 16
72.59 even 6 648.2.f.b.323.7 16
72.61 even 6 288.2.p.b.47.8 16
72.67 odd 6 648.2.f.b.323.10 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.2.l.b.11.1 16 72.43 odd 6
72.2.l.b.11.4 yes 16 9.7 even 3
72.2.l.b.59.1 yes 16 3.2 odd 2
72.2.l.b.59.4 yes 16 24.11 even 2
216.2.l.b.35.5 16 9.2 odd 6 inner
216.2.l.b.35.8 16 72.11 even 6 inner
216.2.l.b.179.5 16 8.3 odd 2 inner
216.2.l.b.179.8 16 1.1 even 1 trivial
288.2.p.b.47.7 16 36.7 odd 6
288.2.p.b.47.8 16 72.61 even 6
288.2.p.b.239.7 16 24.5 odd 2
288.2.p.b.239.8 16 12.11 even 2
648.2.f.b.323.7 16 72.59 even 6
648.2.f.b.323.8 16 9.4 even 3
648.2.f.b.323.9 16 9.5 odd 6
648.2.f.b.323.10 16 72.67 odd 6
864.2.p.b.143.1 16 72.29 odd 6
864.2.p.b.143.8 16 36.11 even 6
864.2.p.b.719.1 16 4.3 odd 2
864.2.p.b.719.8 16 8.5 even 2
2592.2.f.b.1295.1 16 36.23 even 6
2592.2.f.b.1295.2 16 72.13 even 6
2592.2.f.b.1295.15 16 36.31 odd 6
2592.2.f.b.1295.16 16 72.5 odd 6