Properties

Label 441.2.s.c.362.3
Level $441$
Weight $2$
Character 441.362
Analytic conductor $3.521$
Analytic rank $0$
Dimension $12$
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] = [441,2,Mod(362,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.362");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.s (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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 362.3
Root \(0.474636 - 0.274031i\) of defining polynomial
Character \(\chi\) \(=\) 441.362
Dual form 441.2.s.c.374.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.555632 - 0.320794i) q^{2} +(-0.175815 - 1.72310i) q^{3} +(-0.794182 + 1.37556i) q^{4} -2.21105 q^{5} +(-0.650451 - 0.901012i) q^{6} +2.30225i q^{8} +(-2.93818 + 0.605896i) q^{9} +O(q^{10})\) \(q+(0.555632 - 0.320794i) q^{2} +(-0.175815 - 1.72310i) q^{3} +(-0.794182 + 1.37556i) q^{4} -2.21105 q^{5} +(-0.650451 - 0.901012i) q^{6} +2.30225i q^{8} +(-2.93818 + 0.605896i) q^{9} +(-1.22853 + 0.709292i) q^{10} +3.39272i q^{11} +(2.50987 + 1.12661i) q^{12} +(-1.56060 + 0.901012i) q^{13} +(0.388736 + 3.80987i) q^{15} +(-0.849814 - 1.47192i) q^{16} +(2.98450 + 5.16931i) q^{17} +(-1.43818 + 1.27921i) q^{18} +(-1.42391 - 0.822093i) q^{19} +(1.75597 - 3.04144i) q^{20} +(1.08836 + 1.88510i) q^{22} +2.37364i q^{23} +(3.96702 - 0.404771i) q^{24} -0.111264 q^{25} +(-0.578079 + 1.00126i) q^{26} +(1.56060 + 4.95626i) q^{27} +(2.44437 + 1.41126i) q^{29} +(1.43818 + 1.99218i) q^{30} +(-9.28558 - 5.36103i) q^{31} +(-4.93199 - 2.84748i) q^{32} +(5.84600 - 0.596491i) q^{33} +(3.31657 + 1.91482i) q^{34} +(1.50000 - 4.52284i) q^{36} +(-0.849814 + 1.47192i) q^{37} -1.05489 q^{38} +(1.82691 + 2.53066i) q^{39} -5.09039i q^{40} +(-0.455074 - 0.788211i) q^{41} +(-1.96108 + 3.39669i) q^{43} +(-4.66690 - 2.69443i) q^{44} +(6.49645 - 1.33966i) q^{45} +(0.761450 + 1.31887i) q^{46} +(0.123005 + 0.213051i) q^{47} +(-2.38686 + 1.72310i) q^{48} +(-0.0618219 + 0.0356929i) q^{50} +(8.38255 - 6.05146i) q^{51} -2.86227i q^{52} +(6.82072 - 3.93795i) q^{53} +(2.45706 + 2.25323i) q^{54} -7.50146i q^{55} +(-1.16621 + 2.59808i) q^{57} +1.81089 q^{58} +(-5.39093 + 9.33736i) q^{59} +(-5.54944 - 2.49100i) q^{60} +(-1.22853 + 0.709292i) q^{61} -6.87916 q^{62} -0.254572 q^{64} +(3.45056 - 1.99218i) q^{65} +(3.05688 - 2.20679i) q^{66} +(3.99381 - 6.91748i) q^{67} -9.48096 q^{68} +(4.09003 - 0.417322i) q^{69} -12.1743i q^{71} +(-1.39493 - 6.76443i) q^{72} +(-0.369016 + 0.213051i) q^{73} +1.09046i q^{74} +(0.0195619 + 0.191720i) q^{75} +(2.26168 - 1.30578i) q^{76} +(1.82691 + 0.820053i) q^{78} +(2.49381 + 4.31941i) q^{79} +(1.87898 + 3.25449i) q^{80} +(8.26578 - 3.56046i) q^{81} +(-0.505707 - 0.291970i) q^{82} +(-4.28541 + 7.42254i) q^{83} +(-6.59888 - 11.4296i) q^{85} +2.51641i q^{86} +(2.00199 - 4.46002i) q^{87} -7.81089 q^{88} +(-5.26792 + 9.12431i) q^{89} +(3.17988 - 2.82839i) q^{90} +(-3.26509 - 1.88510i) q^{92} +(-7.60507 + 16.9426i) q^{93} +(0.136691 + 0.0789188i) q^{94} +(3.14833 + 1.81769i) q^{95} +(-4.03940 + 8.99896i) q^{96} +(-6.30108 - 3.63793i) q^{97} +(-2.05563 - 9.96840i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{2} + 2 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{2} + 2 q^{4} + 6 q^{15} + 2 q^{16} + 18 q^{18} - 10 q^{22} + 30 q^{29} - 18 q^{30} + 12 q^{32} + 18 q^{36} + 2 q^{37} - 12 q^{39} - 10 q^{43} - 54 q^{44} + 20 q^{46} - 36 q^{50} + 66 q^{51} + 12 q^{53} - 18 q^{57} - 4 q^{58} - 30 q^{60} + 16 q^{64} + 78 q^{65} + 12 q^{67} - 54 q^{72} - 12 q^{78} - 6 q^{79} + 24 q^{81} - 6 q^{85} - 68 q^{88} + 30 q^{92} - 54 q^{93} - 72 q^{95} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.555632 0.320794i 0.392891 0.226836i −0.290521 0.956869i \(-0.593829\pi\)
0.683412 + 0.730033i \(0.260495\pi\)
\(3\) −0.175815 1.72310i −0.101507 0.994835i
\(4\) −0.794182 + 1.37556i −0.397091 + 0.687782i
\(5\) −2.21105 −0.988811 −0.494405 0.869231i \(-0.664614\pi\)
−0.494405 + 0.869231i \(0.664614\pi\)
\(6\) −0.650451 0.901012i −0.265545 0.367836i
\(7\) 0 0
\(8\) 2.30225i 0.813970i
\(9\) −2.93818 + 0.605896i −0.979393 + 0.201965i
\(10\) −1.22853 + 0.709292i −0.388495 + 0.224298i
\(11\) 3.39272i 1.02294i 0.859300 + 0.511471i \(0.170899\pi\)
−0.859300 + 0.511471i \(0.829101\pi\)
\(12\) 2.50987 + 1.12661i 0.724537 + 0.325225i
\(13\) −1.56060 + 0.901012i −0.432832 + 0.249896i −0.700552 0.713601i \(-0.747063\pi\)
0.267720 + 0.963497i \(0.413730\pi\)
\(14\) 0 0
\(15\) 0.388736 + 3.80987i 0.100371 + 0.983704i
\(16\) −0.849814 1.47192i −0.212454 0.367980i
\(17\) 2.98450 + 5.16931i 0.723849 + 1.25374i 0.959446 + 0.281892i \(0.0909620\pi\)
−0.235597 + 0.971851i \(0.575705\pi\)
\(18\) −1.43818 + 1.27921i −0.338982 + 0.301512i
\(19\) −1.42391 0.822093i −0.326667 0.188601i 0.327694 0.944784i \(-0.393729\pi\)
−0.654360 + 0.756183i \(0.727062\pi\)
\(20\) 1.75597 3.04144i 0.392648 0.680086i
\(21\) 0 0
\(22\) 1.08836 + 1.88510i 0.232040 + 0.401905i
\(23\) 2.37364i 0.494938i 0.968896 + 0.247469i \(0.0795988\pi\)
−0.968896 + 0.247469i \(0.920401\pi\)
\(24\) 3.96702 0.404771i 0.809765 0.0826235i
\(25\) −0.111264 −0.0222528
\(26\) −0.578079 + 1.00126i −0.113371 + 0.196364i
\(27\) 1.56060 + 4.95626i 0.300337 + 0.953833i
\(28\) 0 0
\(29\) 2.44437 + 1.41126i 0.453908 + 0.262064i 0.709479 0.704726i \(-0.248930\pi\)
−0.255571 + 0.966790i \(0.582264\pi\)
\(30\) 1.43818 + 1.99218i 0.262574 + 0.363721i
\(31\) −9.28558 5.36103i −1.66774 0.962870i −0.968853 0.247638i \(-0.920346\pi\)
−0.698887 0.715232i \(-0.746321\pi\)
\(32\) −4.93199 2.84748i −0.871861 0.503369i
\(33\) 5.84600 0.596491i 1.01766 0.103836i
\(34\) 3.31657 + 1.91482i 0.568788 + 0.328390i
\(35\) 0 0
\(36\) 1.50000 4.52284i 0.250000 0.753807i
\(37\) −0.849814 + 1.47192i −0.139709 + 0.241982i −0.927386 0.374105i \(-0.877950\pi\)
0.787678 + 0.616088i \(0.211283\pi\)
\(38\) −1.05489 −0.171126
\(39\) 1.82691 + 2.53066i 0.292540 + 0.405230i
\(40\) 5.09039i 0.804862i
\(41\) −0.455074 0.788211i −0.0710706 0.123098i 0.828300 0.560285i \(-0.189308\pi\)
−0.899371 + 0.437187i \(0.855975\pi\)
\(42\) 0 0
\(43\) −1.96108 + 3.39669i −0.299062 + 0.517990i −0.975922 0.218122i \(-0.930007\pi\)
0.676860 + 0.736112i \(0.263340\pi\)
\(44\) −4.66690 2.69443i −0.703561 0.406201i
\(45\) 6.49645 1.33966i 0.968434 0.199705i
\(46\) 0.761450 + 1.31887i 0.112270 + 0.194457i
\(47\) 0.123005 + 0.213051i 0.0179422 + 0.0310767i 0.874857 0.484381i \(-0.160955\pi\)
−0.856915 + 0.515458i \(0.827622\pi\)
\(48\) −2.38686 + 1.72310i −0.344514 + 0.248709i
\(49\) 0 0
\(50\) −0.0618219 + 0.0356929i −0.00874294 + 0.00504774i
\(51\) 8.38255 6.05146i 1.17379 0.847373i
\(52\) 2.86227i 0.396925i
\(53\) 6.82072 3.93795i 0.936899 0.540919i 0.0479118 0.998852i \(-0.484743\pi\)
0.888987 + 0.457933i \(0.151410\pi\)
\(54\) 2.45706 + 2.25323i 0.334363 + 0.306625i
\(55\) 7.50146i 1.01150i
\(56\) 0 0
\(57\) −1.16621 + 2.59808i −0.154468 + 0.344124i
\(58\) 1.81089 0.237782
\(59\) −5.39093 + 9.33736i −0.701839 + 1.21562i 0.265981 + 0.963978i \(0.414304\pi\)
−0.967820 + 0.251643i \(0.919029\pi\)
\(60\) −5.54944 2.49100i −0.716430 0.321586i
\(61\) −1.22853 + 0.709292i −0.157297 + 0.0908155i −0.576582 0.817039i \(-0.695614\pi\)
0.419285 + 0.907855i \(0.362281\pi\)
\(62\) −6.87916 −0.873654
\(63\) 0 0
\(64\) −0.254572 −0.0318214
\(65\) 3.45056 1.99218i 0.427989 0.247100i
\(66\) 3.05688 2.20679i 0.376275 0.271638i
\(67\) 3.99381 6.91748i 0.487922 0.845105i −0.511982 0.858996i \(-0.671089\pi\)
0.999904 + 0.0138913i \(0.00442187\pi\)
\(68\) −9.48096 −1.14974
\(69\) 4.09003 0.417322i 0.492382 0.0502396i
\(70\) 0 0
\(71\) 12.1743i 1.44482i −0.691463 0.722412i \(-0.743034\pi\)
0.691463 0.722412i \(-0.256966\pi\)
\(72\) −1.39493 6.76443i −0.164394 0.797196i
\(73\) −0.369016 + 0.213051i −0.0431900 + 0.0249358i −0.521440 0.853288i \(-0.674605\pi\)
0.478250 + 0.878224i \(0.341271\pi\)
\(74\) 1.09046i 0.126764i
\(75\) 0.0195619 + 0.191720i 0.00225882 + 0.0221379i
\(76\) 2.26168 1.30578i 0.259433 0.149784i
\(77\) 0 0
\(78\) 1.82691 + 0.820053i 0.206857 + 0.0928527i
\(79\) 2.49381 + 4.31941i 0.280576 + 0.485971i 0.971527 0.236930i \(-0.0761413\pi\)
−0.690951 + 0.722902i \(0.742808\pi\)
\(80\) 1.87898 + 3.25449i 0.210076 + 0.363863i
\(81\) 8.26578 3.56046i 0.918420 0.395607i
\(82\) −0.505707 0.291970i −0.0558460 0.0322427i
\(83\) −4.28541 + 7.42254i −0.470384 + 0.814730i −0.999426 0.0338660i \(-0.989218\pi\)
0.529042 + 0.848596i \(0.322551\pi\)
\(84\) 0 0
\(85\) −6.59888 11.4296i −0.715750 1.23971i
\(86\) 2.51641i 0.271352i
\(87\) 2.00199 4.46002i 0.214635 0.478165i
\(88\) −7.81089 −0.832644
\(89\) −5.26792 + 9.12431i −0.558399 + 0.967175i 0.439231 + 0.898374i \(0.355251\pi\)
−0.997630 + 0.0688014i \(0.978083\pi\)
\(90\) 3.17988 2.82839i 0.335189 0.298138i
\(91\) 0 0
\(92\) −3.26509 1.88510i −0.340409 0.196535i
\(93\) −7.60507 + 16.9426i −0.788609 + 1.75686i
\(94\) 0.136691 + 0.0789188i 0.0140986 + 0.00813985i
\(95\) 3.14833 + 1.81769i 0.323012 + 0.186491i
\(96\) −4.03940 + 8.99896i −0.412269 + 0.918453i
\(97\) −6.30108 3.63793i −0.639777 0.369376i 0.144751 0.989468i \(-0.453762\pi\)
−0.784529 + 0.620092i \(0.787095\pi\)
\(98\) 0 0
\(99\) −2.05563 9.96840i −0.206599 1.00186i
\(100\) 0.0883640 0.153051i 0.00883640 0.0153051i
\(101\) 4.66811 0.464494 0.232247 0.972657i \(-0.425392\pi\)
0.232247 + 0.972657i \(0.425392\pi\)
\(102\) 2.71634 6.05146i 0.268958 0.599183i
\(103\) 6.24071i 0.614916i −0.951562 0.307458i \(-0.900522\pi\)
0.951562 0.307458i \(-0.0994783\pi\)
\(104\) −2.07436 3.59289i −0.203407 0.352312i
\(105\) 0 0
\(106\) 2.52654 4.37610i 0.245399 0.425044i
\(107\) −1.28985 0.744696i −0.124695 0.0719925i 0.436355 0.899774i \(-0.356269\pi\)
−0.561050 + 0.827782i \(0.689602\pi\)
\(108\) −8.05705 1.78947i −0.775290 0.172192i
\(109\) 2.19344 + 3.79915i 0.210093 + 0.363892i 0.951744 0.306895i \(-0.0992899\pi\)
−0.741650 + 0.670787i \(0.765957\pi\)
\(110\) −2.40643 4.16805i −0.229444 0.397408i
\(111\) 2.68568 + 1.20553i 0.254914 + 0.114424i
\(112\) 0 0
\(113\) −14.8764 + 8.58887i −1.39945 + 0.807973i −0.994335 0.106293i \(-0.966102\pi\)
−0.405115 + 0.914266i \(0.632769\pi\)
\(114\) 0.185466 + 1.81769i 0.0173705 + 0.170242i
\(115\) 5.24823i 0.489400i
\(116\) −3.88255 + 2.24159i −0.360485 + 0.208126i
\(117\) 4.03940 3.59289i 0.373442 0.332163i
\(118\) 6.91752i 0.636809i
\(119\) 0 0
\(120\) −8.77128 + 0.894969i −0.800705 + 0.0816991i
\(121\) −0.510520 −0.0464110
\(122\) −0.455074 + 0.788211i −0.0412004 + 0.0713612i
\(123\) −1.27816 + 0.922719i −0.115248 + 0.0831987i
\(124\) 14.7489 8.51527i 1.32449 0.764694i
\(125\) 11.3013 1.01081
\(126\) 0 0
\(127\) 6.32141 0.560935 0.280467 0.959864i \(-0.409511\pi\)
0.280467 + 0.959864i \(0.409511\pi\)
\(128\) 9.72253 5.61330i 0.859358 0.496151i
\(129\) 6.19763 + 2.78195i 0.545671 + 0.244937i
\(130\) 1.27816 2.21384i 0.112102 0.194167i
\(131\) 17.0243 1.48742 0.743708 0.668505i \(-0.233065\pi\)
0.743708 + 0.668505i \(0.233065\pi\)
\(132\) −3.82228 + 8.51527i −0.332687 + 0.741159i
\(133\) 0 0
\(134\) 5.12477i 0.442712i
\(135\) −3.45056 10.9585i −0.296977 0.943161i
\(136\) −11.9011 + 6.87109i −1.02051 + 0.589191i
\(137\) 6.26517i 0.535270i −0.963520 0.267635i \(-0.913758\pi\)
0.963520 0.267635i \(-0.0862421\pi\)
\(138\) 2.13868 1.54394i 0.182056 0.131429i
\(139\) 6.65488 3.84220i 0.564460 0.325891i −0.190474 0.981692i \(-0.561002\pi\)
0.754934 + 0.655801i \(0.227669\pi\)
\(140\) 0 0
\(141\) 0.345483 0.249409i 0.0290950 0.0210040i
\(142\) −3.90545 6.76443i −0.327738 0.567658i
\(143\) −3.05688 5.29467i −0.255629 0.442762i
\(144\) 3.38874 + 3.80987i 0.282395 + 0.317489i
\(145\) −5.40462 3.12036i −0.448829 0.259132i
\(146\) −0.136691 + 0.236756i −0.0113127 + 0.0195941i
\(147\) 0 0
\(148\) −1.34981 2.33795i −0.110954 0.192178i
\(149\) 15.4377i 1.26471i 0.774679 + 0.632355i \(0.217911\pi\)
−0.774679 + 0.632355i \(0.782089\pi\)
\(150\) 0.0723718 + 0.100250i 0.00590914 + 0.00818540i
\(151\) 11.6872 0.951095 0.475547 0.879690i \(-0.342250\pi\)
0.475547 + 0.879690i \(0.342250\pi\)
\(152\) 1.89267 3.27819i 0.153516 0.265897i
\(153\) −11.9011 13.3801i −0.962145 1.08171i
\(154\) 0 0
\(155\) 20.5309 + 11.8535i 1.64908 + 0.952096i
\(156\) −4.93199 + 0.503230i −0.394875 + 0.0402907i
\(157\) 4.93586 + 2.84972i 0.393924 + 0.227432i 0.683859 0.729614i \(-0.260300\pi\)
−0.289935 + 0.957046i \(0.593634\pi\)
\(158\) 2.77128 + 1.60000i 0.220471 + 0.127289i
\(159\) −7.98468 11.0605i −0.633226 0.877152i
\(160\) 10.9049 + 6.29593i 0.862105 + 0.497737i
\(161\) 0 0
\(162\) 3.45056 4.62992i 0.271101 0.363761i
\(163\) 5.10507 8.84225i 0.399860 0.692578i −0.593848 0.804577i \(-0.702392\pi\)
0.993708 + 0.111999i \(0.0357253\pi\)
\(164\) 1.44565 0.112886
\(165\) −12.9258 + 1.31887i −1.00627 + 0.102674i
\(166\) 5.49894i 0.426800i
\(167\) 1.80661 + 3.12914i 0.139800 + 0.242140i 0.927421 0.374020i \(-0.122021\pi\)
−0.787621 + 0.616160i \(0.788688\pi\)
\(168\) 0 0
\(169\) −4.87636 + 8.44610i −0.375104 + 0.649700i
\(170\) −7.33310 4.23377i −0.562423 0.324715i
\(171\) 4.68179 + 1.55272i 0.358026 + 0.118739i
\(172\) −3.11491 5.39518i −0.237509 0.411378i
\(173\) 9.03957 + 15.6570i 0.687266 + 1.19038i 0.972719 + 0.231987i \(0.0745226\pi\)
−0.285453 + 0.958393i \(0.592144\pi\)
\(174\) −0.318382 3.12036i −0.0241365 0.236554i
\(175\) 0 0
\(176\) 4.99381 2.88318i 0.376423 0.217328i
\(177\) 17.0371 + 7.64749i 1.28058 + 0.574820i
\(178\) 6.75968i 0.506660i
\(179\) −4.35779 + 2.51597i −0.325716 + 0.188052i −0.653938 0.756548i \(-0.726884\pi\)
0.328221 + 0.944601i \(0.393551\pi\)
\(180\) −3.31657 + 10.0002i −0.247203 + 0.745373i
\(181\) 13.5592i 1.00785i 0.863747 + 0.503925i \(0.168111\pi\)
−0.863747 + 0.503925i \(0.831889\pi\)
\(182\) 0 0
\(183\) 1.43818 + 1.99218i 0.106313 + 0.147266i
\(184\) −5.46472 −0.402865
\(185\) 1.87898 3.25449i 0.138145 0.239275i
\(186\) 1.20946 + 11.8535i 0.0886819 + 0.869141i
\(187\) −17.5380 + 10.1256i −1.28251 + 0.740455i
\(188\) −0.390754 −0.0284987
\(189\) 0 0
\(190\) 2.33242 0.169211
\(191\) 8.86948 5.12080i 0.641773 0.370528i −0.143524 0.989647i \(-0.545844\pi\)
0.785297 + 0.619119i \(0.212510\pi\)
\(192\) 0.0447575 + 0.438653i 0.00323010 + 0.0316571i
\(193\) −8.06615 + 13.9710i −0.580614 + 1.00565i 0.414792 + 0.909916i \(0.363854\pi\)
−0.995407 + 0.0957374i \(0.969479\pi\)
\(194\) −4.66811 −0.335151
\(195\) −4.03940 5.59542i −0.289267 0.400696i
\(196\) 0 0
\(197\) 3.86303i 0.275230i −0.990486 0.137615i \(-0.956056\pi\)
0.990486 0.137615i \(-0.0439436\pi\)
\(198\) −4.33998 4.87933i −0.308429 0.346759i
\(199\) 13.1665 7.60171i 0.933352 0.538871i 0.0454817 0.998965i \(-0.485518\pi\)
0.887870 + 0.460094i \(0.152184\pi\)
\(200\) 0.256158i 0.0181131i
\(201\) −12.6217 5.66555i −0.890267 0.399617i
\(202\) 2.59375 1.49750i 0.182496 0.105364i
\(203\) 0 0
\(204\) 1.66690 + 16.3367i 0.116706 + 1.14380i
\(205\) 1.00619 + 1.74277i 0.0702753 + 0.121720i
\(206\) −2.00199 3.46754i −0.139485 0.241595i
\(207\) −1.43818 6.97418i −0.0999603 0.484739i
\(208\) 2.65244 + 1.53138i 0.183913 + 0.106182i
\(209\) 2.78913 4.83091i 0.192928 0.334161i
\(210\) 0 0
\(211\) 11.9523 + 20.7021i 0.822833 + 1.42519i 0.903564 + 0.428453i \(0.140941\pi\)
−0.0807311 + 0.996736i \(0.525726\pi\)
\(212\) 12.5098i 0.859176i
\(213\) −20.9776 + 2.14043i −1.43736 + 0.146660i
\(214\) −0.955577 −0.0653219
\(215\) 4.33604 7.51024i 0.295715 0.512194i
\(216\) −11.4106 + 3.59289i −0.776391 + 0.244465i
\(217\) 0 0
\(218\) 2.43749 + 1.40729i 0.165088 + 0.0953134i
\(219\) 0.431988 + 0.598395i 0.0291911 + 0.0404358i
\(220\) 10.3187 + 5.95752i 0.695689 + 0.401656i
\(221\) −9.31522 5.37815i −0.626610 0.361773i
\(222\) 1.87898 0.191720i 0.126109 0.0128674i
\(223\) −16.6198 9.59545i −1.11294 0.642559i −0.173354 0.984860i \(-0.555461\pi\)
−0.939591 + 0.342300i \(0.888794\pi\)
\(224\) 0 0
\(225\) 0.326914 0.0674145i 0.0217943 0.00449430i
\(226\) −5.51052 + 9.54450i −0.366554 + 0.634891i
\(227\) −8.67208 −0.575586 −0.287793 0.957693i \(-0.592922\pi\)
−0.287793 + 0.957693i \(0.592922\pi\)
\(228\) −2.64764 3.66754i −0.175344 0.242889i
\(229\) 14.3688i 0.949515i 0.880117 + 0.474758i \(0.157464\pi\)
−0.880117 + 0.474758i \(0.842536\pi\)
\(230\) −1.68360 2.91609i −0.111014 0.192281i
\(231\) 0 0
\(232\) −3.24907 + 5.62755i −0.213312 + 0.369467i
\(233\) −25.7348 14.8580i −1.68594 0.973381i −0.957570 0.288202i \(-0.906942\pi\)
−0.728375 0.685178i \(-0.759724\pi\)
\(234\) 1.09184 3.29214i 0.0713757 0.215214i
\(235\) −0.271971 0.471067i −0.0177414 0.0307290i
\(236\) −8.56276 14.8311i −0.557388 0.965425i
\(237\) 7.00434 5.05651i 0.454981 0.328456i
\(238\) 0 0
\(239\) −13.7101 + 7.91556i −0.886836 + 0.512015i −0.872906 0.487888i \(-0.837767\pi\)
−0.0139296 + 0.999903i \(0.504434\pi\)
\(240\) 5.27747 3.80987i 0.340659 0.245926i
\(241\) 5.02263i 0.323536i 0.986829 + 0.161768i \(0.0517196\pi\)
−0.986829 + 0.161768i \(0.948280\pi\)
\(242\) −0.283662 + 0.163772i −0.0182345 + 0.0105277i
\(243\) −7.58829 13.6168i −0.486789 0.873519i
\(244\) 2.25323i 0.144248i
\(245\) 0 0
\(246\) −0.414184 + 0.922719i −0.0264074 + 0.0588304i
\(247\) 2.96286 0.188522
\(248\) 12.3425 21.3778i 0.783747 1.35749i
\(249\) 13.5433 + 6.07921i 0.858269 + 0.385254i
\(250\) 6.27934 3.62538i 0.397140 0.229289i
\(251\) −7.29728 −0.460600 −0.230300 0.973120i \(-0.573971\pi\)
−0.230300 + 0.973120i \(0.573971\pi\)
\(252\) 0 0
\(253\) −8.05308 −0.506293
\(254\) 3.51238 2.02787i 0.220386 0.127240i
\(255\) −18.5342 + 13.3801i −1.16066 + 0.837892i
\(256\) 3.85600 6.67879i 0.241000 0.417425i
\(257\) 8.00794 0.499522 0.249761 0.968308i \(-0.419648\pi\)
0.249761 + 0.968308i \(0.419648\pi\)
\(258\) 4.33604 0.442423i 0.269950 0.0275441i
\(259\) 0 0
\(260\) 6.32862i 0.392484i
\(261\) −8.03706 2.66549i −0.497482 0.164990i
\(262\) 9.45922 5.46128i 0.584393 0.337399i
\(263\) 15.7098i 0.968707i 0.874872 + 0.484353i \(0.160945\pi\)
−0.874872 + 0.484353i \(0.839055\pi\)
\(264\) 1.37327 + 13.4590i 0.0845191 + 0.828343i
\(265\) −15.0810 + 8.70699i −0.926416 + 0.534866i
\(266\) 0 0
\(267\) 16.6483 + 7.47299i 1.01886 + 0.457340i
\(268\) 6.34362 + 10.9875i 0.387499 + 0.671167i
\(269\) −5.24619 9.08666i −0.319866 0.554024i 0.660594 0.750743i \(-0.270304\pi\)
−0.980460 + 0.196720i \(0.936971\pi\)
\(270\) −5.43268 4.98199i −0.330622 0.303195i
\(271\) 19.2722 + 11.1268i 1.17071 + 0.675907i 0.953846 0.300296i \(-0.0970853\pi\)
0.216859 + 0.976203i \(0.430419\pi\)
\(272\) 5.07255 8.78591i 0.307568 0.532724i
\(273\) 0 0
\(274\) −2.00983 3.48113i −0.121418 0.210303i
\(275\) 0.377488i 0.0227634i
\(276\) −2.67417 + 5.95752i −0.160966 + 0.358601i
\(277\) −22.8502 −1.37294 −0.686468 0.727160i \(-0.740840\pi\)
−0.686468 + 0.727160i \(0.740840\pi\)
\(278\) 2.46511 4.26970i 0.147848 0.256079i
\(279\) 30.5309 + 10.1256i 1.82784 + 0.606202i
\(280\) 0 0
\(281\) 0.796041 + 0.459595i 0.0474878 + 0.0274171i 0.523556 0.851991i \(-0.324605\pi\)
−0.476068 + 0.879408i \(0.657938\pi\)
\(282\) 0.111953 0.249409i 0.00666670 0.0148521i
\(283\) 19.1573 + 11.0605i 1.13878 + 0.657477i 0.946129 0.323790i \(-0.104957\pi\)
0.192654 + 0.981267i \(0.438290\pi\)
\(284\) 16.7465 + 9.66861i 0.993723 + 0.573726i
\(285\) 2.57854 5.74447i 0.152740 0.340273i
\(286\) −3.39700 1.96126i −0.200869 0.115972i
\(287\) 0 0
\(288\) 16.2163 + 5.37815i 0.955557 + 0.316910i
\(289\) −9.31453 + 16.1332i −0.547914 + 0.949014i
\(290\) −4.00397 −0.235121
\(291\) −5.16071 + 11.4970i −0.302526 + 0.673967i
\(292\) 0.676806i 0.0396071i
\(293\) 14.6259 + 25.3328i 0.854453 + 1.47996i 0.877152 + 0.480214i \(0.159441\pi\)
−0.0226986 + 0.999742i \(0.507226\pi\)
\(294\) 0 0
\(295\) 11.9196 20.6454i 0.693986 1.20202i
\(296\) −3.38874 1.95649i −0.196966 0.113719i
\(297\) −16.8152 + 5.29467i −0.975716 + 0.307228i
\(298\) 4.95234 + 8.57771i 0.286881 + 0.496893i
\(299\) −2.13868 3.70430i −0.123683 0.214225i
\(300\) −0.279258 0.125352i −0.0161230 0.00723718i
\(301\) 0 0
\(302\) 6.49381 3.74920i 0.373677 0.215742i
\(303\) −0.820724 8.04364i −0.0471494 0.462095i
\(304\) 2.79450i 0.160276i
\(305\) 2.71634 1.56828i 0.155537 0.0897994i
\(306\) −10.9049 3.61660i −0.623390 0.206747i
\(307\) 14.8451i 0.847254i −0.905837 0.423627i \(-0.860757\pi\)
0.905837 0.423627i \(-0.139243\pi\)
\(308\) 0 0
\(309\) −10.7534 + 1.09721i −0.611740 + 0.0624182i
\(310\) 15.2101 0.863878
\(311\) 9.69002 16.7836i 0.549471 0.951711i −0.448840 0.893612i \(-0.648163\pi\)
0.998311 0.0580991i \(-0.0185040\pi\)
\(312\) −5.82623 + 4.20602i −0.329845 + 0.238119i
\(313\) −12.6608 + 7.30974i −0.715633 + 0.413171i −0.813143 0.582064i \(-0.802245\pi\)
0.0975102 + 0.995235i \(0.468912\pi\)
\(314\) 3.65669 0.206359
\(315\) 0 0
\(316\) −7.92216 −0.445656
\(317\) 14.7046 8.48973i 0.825895 0.476831i −0.0265499 0.999647i \(-0.508452\pi\)
0.852445 + 0.522817i \(0.175119\pi\)
\(318\) −7.98468 3.58411i −0.447759 0.200987i
\(319\) −4.78799 + 8.29305i −0.268076 + 0.464321i
\(320\) 0.562870 0.0314654
\(321\) −1.05641 + 2.35348i −0.0589633 + 0.131358i
\(322\) 0 0
\(323\) 9.81416i 0.546074i
\(324\) −1.66690 + 14.1978i −0.0926053 + 0.788764i
\(325\) 0.173639 0.100250i 0.00963174 0.00556089i
\(326\) 6.55072i 0.362811i
\(327\) 6.16069 4.44747i 0.340687 0.245946i
\(328\) 1.81466 1.04769i 0.100198 0.0578493i
\(329\) 0 0
\(330\) −6.75890 + 4.87933i −0.372065 + 0.268598i
\(331\) −9.94801 17.2305i −0.546792 0.947072i −0.998492 0.0549016i \(-0.982515\pi\)
0.451700 0.892170i \(-0.350818\pi\)
\(332\) −6.80678 11.7897i −0.373571 0.647044i
\(333\) 1.60507 4.83967i 0.0879575 0.265212i
\(334\) 2.00762 + 1.15910i 0.109852 + 0.0634231i
\(335\) −8.83051 + 15.2949i −0.482462 + 0.835649i
\(336\) 0 0
\(337\) 0.490168 + 0.848996i 0.0267012 + 0.0462478i 0.879067 0.476698i \(-0.158166\pi\)
−0.852366 + 0.522946i \(0.824833\pi\)
\(338\) 6.25723i 0.340348i
\(339\) 17.4150 + 24.1235i 0.945853 + 1.31021i
\(340\) 20.9629 1.13687
\(341\) 18.1885 31.5033i 0.984960 1.70600i
\(342\) 3.09946 0.639154i 0.167599 0.0345615i
\(343\) 0 0
\(344\) −7.82004 4.51490i −0.421628 0.243427i
\(345\) −9.04325 + 0.922719i −0.486872 + 0.0496775i
\(346\) 10.0454 + 5.79969i 0.540041 + 0.311793i
\(347\) −18.3702 10.6060i −0.986162 0.569361i −0.0820373 0.996629i \(-0.526143\pi\)
−0.904125 + 0.427268i \(0.859476\pi\)
\(348\) 4.54510 + 6.29593i 0.243643 + 0.337497i
\(349\) 8.69945 + 5.02263i 0.465671 + 0.268855i 0.714426 0.699711i \(-0.246688\pi\)
−0.248755 + 0.968566i \(0.580021\pi\)
\(350\) 0 0
\(351\) −6.90112 6.32862i −0.368354 0.337797i
\(352\) 9.66071 16.7328i 0.514917 0.891863i
\(353\) −2.74655 −0.146184 −0.0730920 0.997325i \(-0.523287\pi\)
−0.0730920 + 0.997325i \(0.523287\pi\)
\(354\) 11.9196 1.21620i 0.633520 0.0646406i
\(355\) 26.9180i 1.42866i
\(356\) −8.36738 14.4927i −0.443470 0.768113i
\(357\) 0 0
\(358\) −1.61422 + 2.79591i −0.0853140 + 0.147768i
\(359\) 8.66140 + 5.00066i 0.457131 + 0.263925i 0.710837 0.703357i \(-0.248316\pi\)
−0.253706 + 0.967281i \(0.581650\pi\)
\(360\) 3.08425 + 14.9565i 0.162554 + 0.788276i
\(361\) −8.14833 14.1133i −0.428859 0.742806i
\(362\) 4.34973 + 7.53395i 0.228616 + 0.395975i
\(363\) 0.0897572 + 0.879680i 0.00471103 + 0.0461712i
\(364\) 0 0
\(365\) 0.815912 0.471067i 0.0427068 0.0246568i
\(366\) 1.43818 + 0.645560i 0.0751748 + 0.0337440i
\(367\) 5.81461i 0.303520i 0.988417 + 0.151760i \(0.0484941\pi\)
−0.988417 + 0.151760i \(0.951506\pi\)
\(368\) 3.49381 2.01715i 0.182127 0.105151i
\(369\) 1.81466 + 2.04018i 0.0944675 + 0.106207i
\(370\) 2.41106i 0.125345i
\(371\) 0 0
\(372\) −17.2658 23.9168i −0.895189 1.24003i
\(373\) −15.5192 −0.803553 −0.401776 0.915738i \(-0.631607\pi\)
−0.401776 + 0.915738i \(0.631607\pi\)
\(374\) −6.49645 + 11.2522i −0.335924 + 0.581837i
\(375\) −1.98693 19.4732i −0.102605 1.00559i
\(376\) −0.490498 + 0.283189i −0.0252955 + 0.0146044i
\(377\) −5.08623 −0.261954
\(378\) 0 0
\(379\) 2.79714 0.143679 0.0718396 0.997416i \(-0.477113\pi\)
0.0718396 + 0.997416i \(0.477113\pi\)
\(380\) −5.00069 + 2.88715i −0.256530 + 0.148108i
\(381\) −1.11140 10.8925i −0.0569388 0.558037i
\(382\) 3.28544 5.69056i 0.168098 0.291154i
\(383\) 3.48458 0.178054 0.0890268 0.996029i \(-0.471624\pi\)
0.0890268 + 0.996029i \(0.471624\pi\)
\(384\) −11.3817 15.7660i −0.580819 0.804557i
\(385\) 0 0
\(386\) 10.3503i 0.526817i
\(387\) 3.70396 11.1683i 0.188283 0.567716i
\(388\) 10.0084 5.77835i 0.508100 0.293352i
\(389\) 7.35563i 0.372945i 0.982460 + 0.186473i \(0.0597056\pi\)
−0.982460 + 0.186473i \(0.940294\pi\)
\(390\) −4.03940 1.81318i −0.204543 0.0918138i
\(391\) −12.2701 + 7.08414i −0.620525 + 0.358260i
\(392\) 0 0
\(393\) −2.99312 29.3346i −0.150983 1.47973i
\(394\) −1.23924 2.14642i −0.0624319 0.108135i
\(395\) −5.51394 9.55042i −0.277436 0.480534i
\(396\) 15.3447 + 5.08907i 0.771101 + 0.255736i
\(397\) −16.7002 9.64189i −0.838161 0.483912i 0.0184778 0.999829i \(-0.494118\pi\)
−0.856639 + 0.515917i \(0.827451\pi\)
\(398\) 4.87717 8.44751i 0.244470 0.423435i
\(399\) 0 0
\(400\) 0.0945538 + 0.163772i 0.00472769 + 0.00818860i
\(401\) 11.0918i 0.553897i 0.960885 + 0.276949i \(0.0893232\pi\)
−0.960885 + 0.276949i \(0.910677\pi\)
\(402\) −8.83051 + 0.901012i −0.440426 + 0.0449384i
\(403\) 19.3214 0.962468
\(404\) −3.70733 + 6.42128i −0.184446 + 0.319471i
\(405\) −18.2760 + 7.87235i −0.908144 + 0.391180i
\(406\) 0 0
\(407\) −4.99381 2.88318i −0.247534 0.142914i
\(408\) 13.9320 + 19.2987i 0.689736 + 0.955430i
\(409\) −17.5597 10.1381i −0.868274 0.501298i −0.00149954 0.999999i \(-0.500477\pi\)
−0.866774 + 0.498701i \(0.833811\pi\)
\(410\) 1.11814 + 0.645560i 0.0552211 + 0.0318819i
\(411\) −10.7955 + 1.10151i −0.532505 + 0.0543336i
\(412\) 8.58450 + 4.95626i 0.422928 + 0.244178i
\(413\) 0 0
\(414\) −3.03637 3.41372i −0.149230 0.167775i
\(415\) 9.47524 16.4116i 0.465121 0.805614i
\(416\) 10.2625 0.503159
\(417\) −7.79054 10.7915i −0.381504 0.528464i
\(418\) 3.57895i 0.175052i
\(419\) −5.54936 9.61177i −0.271104 0.469566i 0.698041 0.716058i \(-0.254055\pi\)
−0.969145 + 0.246492i \(0.920722\pi\)
\(420\) 0 0
\(421\) 4.59269 7.95478i 0.223834 0.387692i −0.732135 0.681160i \(-0.761476\pi\)
0.955969 + 0.293467i \(0.0948092\pi\)
\(422\) 13.2822 + 7.66849i 0.646568 + 0.373296i
\(423\) −0.490498 0.551454i −0.0238488 0.0268126i
\(424\) 9.06615 + 15.7030i 0.440291 + 0.762607i
\(425\) −0.332068 0.575159i −0.0161077 0.0278993i
\(426\) −10.9692 + 7.91878i −0.531459 + 0.383666i
\(427\) 0 0
\(428\) 2.04875 1.18285i 0.0990302 0.0571751i
\(429\) −8.58582 + 6.19820i −0.414527 + 0.299252i
\(430\) 5.56391i 0.268315i
\(431\) 13.0858 7.55510i 0.630322 0.363916i −0.150555 0.988602i \(-0.548106\pi\)
0.780877 + 0.624685i \(0.214773\pi\)
\(432\) 5.96901 6.50898i 0.287184 0.313163i
\(433\) 3.33578i 0.160307i −0.996783 0.0801537i \(-0.974459\pi\)
0.996783 0.0801537i \(-0.0255411\pi\)
\(434\) 0 0
\(435\) −4.42649 + 9.86132i −0.212234 + 0.472814i
\(436\) −6.96796 −0.333705
\(437\) 1.95135 3.37984i 0.0933458 0.161680i
\(438\) 0.431988 + 0.193908i 0.0206412 + 0.00926529i
\(439\) −5.91032 + 3.41233i −0.282084 + 0.162861i −0.634367 0.773032i \(-0.718739\pi\)
0.352282 + 0.935894i \(0.385406\pi\)
\(440\) 17.2703 0.823327
\(441\) 0 0
\(442\) −6.90112 −0.328253
\(443\) −9.77747 + 5.64503i −0.464542 + 0.268203i −0.713952 0.700195i \(-0.753097\pi\)
0.249410 + 0.968398i \(0.419763\pi\)
\(444\) −3.79121 + 2.73692i −0.179923 + 0.129888i
\(445\) 11.6476 20.1743i 0.552151 0.956354i
\(446\) −12.3127 −0.583022
\(447\) 26.6008 2.71419i 1.25818 0.128377i
\(448\) 0 0
\(449\) 24.8554i 1.17300i −0.809950 0.586498i \(-0.800506\pi\)
0.809950 0.586498i \(-0.199494\pi\)
\(450\) 0.160018 0.142330i 0.00754331 0.00670949i
\(451\) 2.67417 1.54394i 0.125922 0.0727011i
\(452\) 27.2845i 1.28335i
\(453\) −2.05480 20.1384i −0.0965427 0.946182i
\(454\) −4.81849 + 2.78195i −0.226143 + 0.130564i
\(455\) 0 0
\(456\) −5.98143 2.68491i −0.280106 0.125732i
\(457\) 6.30470 + 10.9201i 0.294922 + 0.510819i 0.974967 0.222351i \(-0.0713732\pi\)
−0.680045 + 0.733170i \(0.738040\pi\)
\(458\) 4.60942 + 7.98375i 0.215384 + 0.373056i
\(459\) −20.9629 + 22.8592i −0.978463 + 1.06698i
\(460\) 7.21928 + 4.16805i 0.336601 + 0.194336i
\(461\) 14.4031 24.9470i 0.670821 1.16190i −0.306851 0.951758i \(-0.599275\pi\)
0.977672 0.210138i \(-0.0673913\pi\)
\(462\) 0 0
\(463\) −12.5858 21.7993i −0.584912 1.01310i −0.994886 0.101001i \(-0.967796\pi\)
0.409974 0.912097i \(-0.365538\pi\)
\(464\) 4.79722i 0.222705i
\(465\) 16.8152 37.4609i 0.779786 1.73721i
\(466\) −19.0655 −0.883191
\(467\) −12.7975 + 22.1660i −0.592199 + 1.02572i 0.401736 + 0.915755i \(0.368407\pi\)
−0.993936 + 0.109964i \(0.964927\pi\)
\(468\) 1.73424 + 8.40986i 0.0801651 + 0.388746i
\(469\) 0 0
\(470\) −0.302231 0.174493i −0.0139409 0.00804877i
\(471\) 4.04256 9.00602i 0.186272 0.414976i
\(472\) −21.4970 12.4113i −0.989479 0.571276i
\(473\) −11.5240 6.65338i −0.529874 0.305923i
\(474\) 2.26973 5.05651i 0.104252 0.232253i
\(475\) 0.158430 + 0.0914695i 0.00726926 + 0.00419691i
\(476\) 0 0
\(477\) −17.6545 + 15.7030i −0.808345 + 0.718993i
\(478\) −5.07853 + 8.79628i −0.232287 + 0.402332i
\(479\) 0.535498 0.0244675 0.0122338 0.999925i \(-0.496106\pi\)
0.0122338 + 0.999925i \(0.496106\pi\)
\(480\) 8.93130 19.8971i 0.407656 0.908176i
\(481\) 3.06277i 0.139650i
\(482\) 1.61123 + 2.79073i 0.0733896 + 0.127114i
\(483\) 0 0
\(484\) 0.405446 0.702253i 0.0184294 0.0319206i
\(485\) 13.9320 + 8.04364i 0.632619 + 0.365243i
\(486\) −8.58450 5.13166i −0.389401 0.232777i
\(487\) −17.0662 29.5594i −0.773341 1.33947i −0.935722 0.352738i \(-0.885251\pi\)
0.162381 0.986728i \(-0.448083\pi\)
\(488\) −1.63297 2.82839i −0.0739211 0.128035i
\(489\) −16.1337 7.24198i −0.729590 0.327493i
\(490\) 0 0
\(491\) 5.86948 3.38874i 0.264886 0.152932i −0.361675 0.932304i \(-0.617795\pi\)
0.626561 + 0.779372i \(0.284462\pi\)
\(492\) −0.254166 2.49100i −0.0114587 0.112303i
\(493\) 16.8476i 0.758778i
\(494\) 1.64626 0.950469i 0.0740688 0.0427636i
\(495\) 4.54510 + 22.0406i 0.204287 + 0.990652i
\(496\) 18.2235i 0.818260i
\(497\) 0 0
\(498\) 9.47524 0.966796i 0.424596 0.0433232i
\(499\) 8.60074 0.385022 0.192511 0.981295i \(-0.438337\pi\)
0.192511 + 0.981295i \(0.438337\pi\)
\(500\) −8.97525 + 15.5456i −0.401385 + 0.695220i
\(501\) 5.07420 3.66312i 0.226699 0.163656i
\(502\) −4.05460 + 2.34093i −0.180966 + 0.104481i
\(503\) −2.96518 −0.132211 −0.0661055 0.997813i \(-0.521057\pi\)
−0.0661055 + 0.997813i \(0.521057\pi\)
\(504\) 0 0
\(505\) −10.3214 −0.459297
\(506\) −4.47455 + 2.58338i −0.198918 + 0.114845i
\(507\) 15.4108 + 6.91752i 0.684420 + 0.307218i
\(508\) −5.02035 + 8.69551i −0.222742 + 0.385801i
\(509\) 6.09765 0.270273 0.135137 0.990827i \(-0.456853\pi\)
0.135137 + 0.990827i \(0.456853\pi\)
\(510\) −6.00596 + 13.3801i −0.265948 + 0.592479i
\(511\) 0 0
\(512\) 17.5053i 0.773631i
\(513\) 1.85236 8.34021i 0.0817838 0.368229i
\(514\) 4.44947 2.56890i 0.196258 0.113309i
\(515\) 13.7985i 0.608035i
\(516\) −8.74880 + 6.31586i −0.385145 + 0.278040i
\(517\) −0.722823 + 0.417322i −0.0317897 + 0.0183538i
\(518\) 0 0
\(519\) 25.3893 18.3289i 1.11447 0.804548i
\(520\) 4.58650 + 7.94406i 0.201132 + 0.348370i
\(521\) 16.3464 + 28.3128i 0.716150 + 1.24041i 0.962514 + 0.271231i \(0.0874307\pi\)
−0.246364 + 0.969177i \(0.579236\pi\)
\(522\) −5.32072 + 1.09721i −0.232882 + 0.0480237i
\(523\) −1.73424 1.00126i −0.0758329 0.0437821i 0.461604 0.887086i \(-0.347274\pi\)
−0.537437 + 0.843304i \(0.680607\pi\)
\(524\) −13.5204 + 23.4179i −0.590639 + 1.02302i
\(525\) 0 0
\(526\) 5.03961 + 8.72886i 0.219737 + 0.380596i
\(527\) 64.0001i 2.78789i
\(528\) −5.84600 8.09795i −0.254415 0.352418i
\(529\) 17.3658 0.755036
\(530\) −5.58631 + 9.67577i −0.242654 + 0.420289i
\(531\) 10.1820 30.7012i 0.441863 1.33232i
\(532\) 0 0
\(533\) 1.42037 + 0.820053i 0.0615232 + 0.0355204i
\(534\) 11.6476 1.18845i 0.504043 0.0514295i
\(535\) 2.85192 + 1.64656i 0.123299 + 0.0711870i
\(536\) 15.9258 + 9.19476i 0.687890 + 0.397153i
\(537\) 5.10144 + 7.06658i 0.220144 + 0.304945i
\(538\) −5.82990 3.36589i −0.251345 0.145114i
\(539\) 0 0
\(540\) 17.8145 + 3.95661i 0.766615 + 0.170265i
\(541\) 5.72253 9.91171i 0.246031 0.426138i −0.716390 0.697700i \(-0.754207\pi\)
0.962421 + 0.271562i \(0.0875403\pi\)
\(542\) 14.2777 0.613280
\(543\) 23.3640 2.38392i 1.00264 0.102304i
\(544\) 33.9933i 1.45745i
\(545\) −4.84980 8.40010i −0.207743 0.359821i
\(546\) 0 0
\(547\) −3.91961 + 6.78896i −0.167590 + 0.290275i −0.937572 0.347791i \(-0.886932\pi\)
0.769982 + 0.638066i \(0.220265\pi\)
\(548\) 8.61814 + 4.97569i 0.368149 + 0.212551i
\(549\) 3.17988 2.82839i 0.135714 0.120713i
\(550\) −0.121096 0.209744i −0.00516355 0.00894353i
\(551\) −2.32037 4.01899i −0.0988510 0.171215i
\(552\) 0.960781 + 9.41628i 0.0408935 + 0.400784i
\(553\) 0 0
\(554\) −12.6963 + 7.33022i −0.539415 + 0.311431i
\(555\) −5.93818 2.66549i −0.252062 0.113144i
\(556\) 12.2056i 0.517634i
\(557\) −0.0116910 + 0.00674980i −0.000495364 + 0.000285998i −0.500248 0.865882i \(-0.666758\pi\)
0.499752 + 0.866168i \(0.333424\pi\)
\(558\) 20.2122 4.16805i 0.855650 0.176448i
\(559\) 7.06782i 0.298937i
\(560\) 0 0
\(561\) 20.5309 + 28.4396i 0.866814 + 1.20072i
\(562\) 0.589741 0.0248767
\(563\) −9.54528 + 16.5329i −0.402286 + 0.696779i −0.994001 0.109368i \(-0.965117\pi\)
0.591716 + 0.806147i \(0.298451\pi\)
\(564\) 0.0687005 + 0.673310i 0.00289281 + 0.0283515i
\(565\) 32.8923 18.9904i 1.38379 0.798932i
\(566\) 14.1925 0.596557
\(567\) 0 0
\(568\) 28.0283 1.17604
\(569\) −32.3406 + 18.6719i −1.35579 + 0.782765i −0.989053 0.147561i \(-0.952858\pi\)
−0.366735 + 0.930325i \(0.619525\pi\)
\(570\) −0.410074 4.01899i −0.0171761 0.168337i
\(571\) −22.6421 + 39.2173i −0.947544 + 1.64119i −0.196968 + 0.980410i \(0.563110\pi\)
−0.750576 + 0.660784i \(0.770224\pi\)
\(572\) 9.71086 0.406032
\(573\) −10.3831 14.3827i −0.433758 0.600847i
\(574\) 0 0
\(575\) 0.264101i 0.0110138i
\(576\) 0.747976 0.154244i 0.0311657 0.00642683i
\(577\) −32.1285 + 18.5494i −1.33753 + 0.772221i −0.986440 0.164123i \(-0.947521\pi\)
−0.351086 + 0.936343i \(0.614187\pi\)
\(578\) 11.9522i 0.497146i
\(579\) 25.4916 + 11.4425i 1.05940 + 0.475535i
\(580\) 8.58450 4.95626i 0.356452 0.205798i
\(581\) 0 0
\(582\) 0.820724 + 8.04364i 0.0340201 + 0.333419i
\(583\) 13.3603 + 23.1408i 0.553329 + 0.958393i
\(584\) −0.490498 0.849568i −0.0202970 0.0351554i
\(585\) −8.93130 + 7.94406i −0.369264 + 0.328446i
\(586\) 16.2532 + 9.38380i 0.671414 + 0.387641i
\(587\) −17.0612 + 29.5509i −0.704191 + 1.21969i 0.262792 + 0.964853i \(0.415357\pi\)
−0.966983 + 0.254842i \(0.917977\pi\)
\(588\) 0 0
\(589\) 8.81453 + 15.2672i 0.363197 + 0.629075i
\(590\) 15.2950i 0.629684i
\(591\) −6.65641 + 0.679179i −0.273808 + 0.0279377i
\(592\) 2.88874 0.118726
\(593\) −9.84997 + 17.0607i −0.404490 + 0.700597i −0.994262 0.106973i \(-0.965884\pi\)
0.589772 + 0.807570i \(0.299218\pi\)
\(594\) −7.64456 + 8.33610i −0.313660 + 0.342034i
\(595\) 0 0
\(596\) −21.2356 12.2604i −0.869844 0.502205i
\(597\) −15.4134 21.3508i −0.630829 0.873832i
\(598\) −2.37663 1.37215i −0.0971878 0.0561114i
\(599\) 9.74033 + 5.62358i 0.397979 + 0.229773i 0.685612 0.727967i \(-0.259535\pi\)
−0.287632 + 0.957741i \(0.592868\pi\)
\(600\) −0.441388 + 0.0450365i −0.0180196 + 0.00183861i
\(601\) 29.7646 + 17.1846i 1.21412 + 0.700975i 0.963655 0.267150i \(-0.0860818\pi\)
0.250469 + 0.968125i \(0.419415\pi\)
\(602\) 0 0
\(603\) −7.54325 + 22.7446i −0.307185 + 0.926233i
\(604\) −9.28180 + 16.0766i −0.377671 + 0.654146i
\(605\) 1.12879 0.0458917
\(606\) −3.03637 4.20602i −0.123344 0.170858i
\(607\) 39.0160i 1.58361i −0.610775 0.791804i \(-0.709142\pi\)
0.610775 0.791804i \(-0.290858\pi\)
\(608\) 4.68179 + 8.10910i 0.189872 + 0.328868i
\(609\) 0 0
\(610\) 1.00619 1.74277i 0.0407394 0.0705628i
\(611\) −0.383923 0.221658i −0.0155319 0.00896733i
\(612\) 27.8567 5.74447i 1.12604 0.232207i
\(613\) 8.05494 + 13.9516i 0.325336 + 0.563499i 0.981580 0.191050i \(-0.0611892\pi\)
−0.656244 + 0.754549i \(0.727856\pi\)
\(614\) −4.76222 8.24840i −0.192187 0.332878i
\(615\) 2.82607 2.04018i 0.113958 0.0822678i
\(616\) 0 0
\(617\) 7.03569 4.06205i 0.283246 0.163532i −0.351646 0.936133i \(-0.614378\pi\)
0.634892 + 0.772601i \(0.281045\pi\)
\(618\) −5.62296 + 4.05928i −0.226188 + 0.163288i
\(619\) 37.4144i 1.50381i −0.659270 0.751906i \(-0.729134\pi\)
0.659270 0.751906i \(-0.270866\pi\)
\(620\) −32.6105 + 18.8277i −1.30967 + 0.756138i
\(621\) −11.7644 + 3.70430i −0.472088 + 0.148648i
\(622\) 12.4340i 0.498559i
\(623\) 0 0
\(624\) 2.17240 4.83967i 0.0869655 0.193742i
\(625\) −24.4313 −0.977252
\(626\) −4.68985 + 8.12305i −0.187444 + 0.324662i
\(627\) −8.81453 3.95661i −0.352019 0.158012i
\(628\) −7.83994 + 4.52639i −0.312848 + 0.180623i
\(629\) −10.1451 −0.404511
\(630\) 0 0
\(631\) −19.8268 −0.789294 −0.394647 0.918833i \(-0.629133\pi\)
−0.394647 + 0.918833i \(0.629133\pi\)
\(632\) −9.94437 + 5.74138i −0.395566 + 0.228380i
\(633\) 33.5704 24.2349i 1.33430 0.963249i
\(634\) 5.44692 9.43434i 0.216325 0.374685i
\(635\) −13.9770 −0.554658
\(636\) 21.5557 2.19941i 0.854738 0.0872123i
\(637\) 0 0
\(638\) 6.14384i 0.243237i
\(639\) 7.37636 + 35.7703i 0.291804 + 1.41505i
\(640\) −21.4970 + 12.4113i −0.849743 + 0.490599i
\(641\) 9.25896i 0.365707i 0.983140 + 0.182853i \(0.0585334\pi\)
−0.983140 + 0.182853i \(0.941467\pi\)
\(642\) 0.168005 + 1.64656i 0.00663063 + 0.0649845i
\(643\) 36.3456 20.9841i 1.43333 0.827534i 0.435958 0.899967i \(-0.356410\pi\)
0.997373 + 0.0724332i \(0.0230764\pi\)
\(644\) 0 0
\(645\) −13.7033 6.15103i −0.539566 0.242197i
\(646\) −3.14833 5.45306i −0.123869 0.214548i
\(647\) −3.14293 5.44372i −0.123561 0.214015i 0.797608 0.603176i \(-0.206098\pi\)
−0.921170 + 0.389161i \(0.872765\pi\)
\(648\) 8.19708 + 19.0299i 0.322012 + 0.747566i
\(649\) −31.6790 18.2899i −1.24351 0.717941i
\(650\) 0.0643195 0.111405i 0.00252282 0.00436965i
\(651\) 0 0
\(652\) 8.10872 + 14.0447i 0.317562 + 0.550033i
\(653\) 23.2866i 0.911277i 0.890165 + 0.455638i \(0.150589\pi\)
−0.890165 + 0.455638i \(0.849411\pi\)
\(654\) 1.99635 4.44747i 0.0780635 0.173910i
\(655\) −37.6414 −1.47077
\(656\) −0.773456 + 1.33966i −0.0301984 + 0.0523051i
\(657\) 0.955147 0.849568i 0.0372638 0.0331448i
\(658\) 0 0
\(659\) 25.8880 + 14.9464i 1.00845 + 0.582230i 0.910738 0.412984i \(-0.135514\pi\)
0.0977141 + 0.995215i \(0.468847\pi\)
\(660\) 8.45125 18.8277i 0.328964 0.732866i
\(661\) −17.6184 10.1720i −0.685278 0.395645i 0.116563 0.993183i \(-0.462812\pi\)
−0.801841 + 0.597538i \(0.796146\pi\)
\(662\) −11.0549 6.38253i −0.429660 0.248064i
\(663\) −7.62935 + 16.9967i −0.296299 + 0.660096i
\(664\) −17.0886 9.86609i −0.663165 0.382879i
\(665\) 0 0
\(666\) −0.660706 3.20397i −0.0256019 0.124151i
\(667\) −3.34981 + 5.80205i −0.129705 + 0.224656i
\(668\) −5.73910 −0.222053
\(669\) −13.6120 + 30.3247i −0.526269 + 1.17242i
\(670\) 11.3311i 0.437759i
\(671\) −2.40643 4.16805i −0.0928990 0.160906i
\(672\) 0 0
\(673\) −8.55996 + 14.8263i −0.329962 + 0.571511i −0.982504 0.186241i \(-0.940369\pi\)
0.652542 + 0.757753i \(0.273703\pi\)
\(674\) 0.544706 + 0.314486i 0.0209813 + 0.0121136i
\(675\) −0.173639 0.551454i −0.00668335 0.0212255i
\(676\) −7.74543 13.4155i −0.297901 0.515980i
\(677\) 14.2078 + 24.6085i 0.546048 + 0.945783i 0.998540 + 0.0540148i \(0.0172018\pi\)
−0.452492 + 0.891769i \(0.649465\pi\)
\(678\) 17.4150 + 7.81713i 0.668819 + 0.300215i
\(679\) 0 0
\(680\) 26.3138 15.1923i 1.00909 0.582598i
\(681\) 1.52468 + 14.9429i 0.0584260 + 0.572613i
\(682\) 23.3390i 0.893697i
\(683\) 18.1236 10.4637i 0.693482 0.400382i −0.111433 0.993772i \(-0.535544\pi\)
0.804915 + 0.593390i \(0.202211\pi\)
\(684\) −5.85406 + 5.20697i −0.223835 + 0.199093i
\(685\) 13.8526i 0.529281i
\(686\) 0 0
\(687\) 24.7589 2.52625i 0.944611 0.0963824i
\(688\) 6.66621 0.254147
\(689\) −7.09627 + 12.2911i −0.270346 + 0.468254i
\(690\) −4.72872 + 3.41372i −0.180019 + 0.129958i
\(691\) 20.7918 12.0041i 0.790957 0.456659i −0.0493424 0.998782i \(-0.515713\pi\)
0.840299 + 0.542123i \(0.182379\pi\)
\(692\) −28.7163 −1.09163
\(693\) 0 0
\(694\) −13.6094 −0.516606
\(695\) −14.7143 + 8.49529i −0.558144 + 0.322245i
\(696\) 10.2681 + 4.60908i 0.389211 + 0.174707i
\(697\) 2.71634 4.70484i 0.102889 0.178208i
\(698\) 6.44493 0.243944
\(699\) −21.0773 + 46.9561i −0.797218 + 1.77604i
\(700\) 0 0
\(701\) 42.0117i 1.58676i 0.608728 + 0.793379i \(0.291680\pi\)
−0.608728 + 0.793379i \(0.708320\pi\)
\(702\) −5.86467 1.30254i −0.221348 0.0491613i
\(703\) 2.42011 1.39725i 0.0912762 0.0526984i
\(704\) 0.863689i 0.0325515i
\(705\) −0.763881 + 0.551454i −0.0287694 + 0.0207690i
\(706\) −1.52607 + 0.881077i −0.0574344 + 0.0331598i
\(707\) 0 0
\(708\) −24.0501 + 17.3621i −0.903859 + 0.652506i
\(709\) −18.6094 32.2324i −0.698891 1.21051i −0.968851 0.247643i \(-0.920344\pi\)
0.269960 0.962871i \(-0.412989\pi\)
\(710\) 8.63513 + 14.9565i 0.324071 + 0.561307i
\(711\) −9.94437 11.1802i −0.372943 0.419290i
\(712\) −21.0065 12.1281i −0.787251 0.454520i
\(713\) 12.7252 22.0406i 0.476561 0.825428i
\(714\) 0 0
\(715\) 6.75890 + 11.7068i 0.252769 + 0.437808i
\(716\) 7.99255i 0.298696i
\(717\) 16.0498 + 22.2323i 0.599390 + 0.830282i
\(718\) 6.41673 0.239470
\(719\) −9.14889 + 15.8463i −0.341196 + 0.590969i −0.984655 0.174512i \(-0.944165\pi\)
0.643459 + 0.765481i \(0.277499\pi\)
\(720\) −7.49266 8.42380i −0.279235 0.313937i
\(721\) 0 0
\(722\) −9.05494 5.22787i −0.336990 0.194561i
\(723\) 8.65452 0.883054i 0.321865 0.0328411i
\(724\) −18.6516 10.7685i −0.693181 0.400208i
\(725\) −0.271971 0.157022i −0.0101007 0.00583166i
\(726\) 0.332068 + 0.459985i 0.0123242 + 0.0170716i
\(727\) −28.3214 16.3514i −1.05038 0.606439i −0.127626 0.991822i \(-0.540736\pi\)
−0.922756 + 0.385384i \(0.874069\pi\)
\(728\) 0 0
\(729\) −22.1291 + 15.4695i −0.819595 + 0.572943i
\(730\) 0.302231 0.523480i 0.0111861 0.0193749i
\(731\) −23.4114 −0.865901
\(732\) −3.88255 + 0.396151i −0.143503 + 0.0146422i
\(733\) 0.498614i 0.0184167i 0.999958 + 0.00920836i \(0.00293115\pi\)
−0.999958 + 0.00920836i \(0.997069\pi\)
\(734\) 1.86529 + 3.23078i 0.0688493 + 0.119250i
\(735\) 0 0
\(736\) 6.75890 11.7068i 0.249136 0.431517i
\(737\) 23.4691 + 13.5499i 0.864494 + 0.499116i
\(738\) 1.66276 + 0.551454i 0.0612071 + 0.0202993i
\(739\) 23.8523 + 41.3134i 0.877421 + 1.51974i 0.854162 + 0.520007i \(0.174071\pi\)
0.0232588 + 0.999729i \(0.492596\pi\)
\(740\) 2.98450 + 5.16931i 0.109713 + 0.190028i
\(741\) −0.520916 5.10532i −0.0191363 0.187549i
\(742\) 0 0
\(743\) 9.20534 5.31470i 0.337711 0.194978i −0.321548 0.946893i \(-0.604203\pi\)
0.659259 + 0.751916i \(0.270870\pi\)
\(744\) −39.0061 17.5088i −1.43003 0.641904i
\(745\) 34.1336i 1.25056i
\(746\) −8.62296 + 4.97847i −0.315709 + 0.182275i
\(747\) 8.09400 24.4053i 0.296144 0.892942i
\(748\) 32.1662i 1.17611i
\(749\) 0 0
\(750\) −7.35091 10.1826i −0.268417 0.371815i
\(751\) 19.1185 0.697646 0.348823 0.937189i \(-0.386581\pi\)
0.348823 + 0.937189i \(0.386581\pi\)
\(752\) 0.209063 0.362108i 0.00762375 0.0132047i
\(753\) 1.28297 + 12.5740i 0.0467541 + 0.458221i
\(754\) −2.82607 + 1.63164i −0.102920 + 0.0594206i
\(755\) −25.8411 −0.940453
\(756\) 0 0
\(757\) 28.5388 1.03726 0.518631 0.854998i \(-0.326442\pi\)
0.518631 + 0.854998i \(0.326442\pi\)
\(758\) 1.55418 0.897305i 0.0564503 0.0325916i
\(759\) 1.41585 + 13.8763i 0.0513923 + 0.503678i
\(760\) −4.18478 + 7.24825i −0.151798 + 0.262922i
\(761\) −43.3300 −1.57071 −0.785355 0.619045i \(-0.787520\pi\)
−0.785355 + 0.619045i \(0.787520\pi\)
\(762\) −4.11177 5.69567i −0.148954 0.206332i
\(763\) 0 0
\(764\) 16.2674i 0.588533i
\(765\) 26.3138 + 29.5840i 0.951379 + 1.06961i
\(766\) 1.93614 1.11783i 0.0699557 0.0403889i
\(767\) 19.4292i 0.701546i
\(768\) −12.1862 5.47006i −0.439732 0.197384i
\(769\) 5.75189 3.32086i 0.207419 0.119753i −0.392693 0.919670i \(-0.628456\pi\)
0.600111 + 0.799917i \(0.295123\pi\)
\(770\) 0 0
\(771\) −1.40792 13.7985i −0.0507049 0.496942i
\(772\) −12.8120 22.1910i −0.461113 0.798672i
\(773\) 22.2415 + 38.5235i 0.799973 + 1.38559i 0.919633 + 0.392779i \(0.128486\pi\)
−0.119660 + 0.992815i \(0.538181\pi\)
\(774\) −1.52468 7.39366i −0.0548036 0.265760i
\(775\) 1.03315 + 0.596491i 0.0371119 + 0.0214266i
\(776\) 8.37543 14.5067i 0.300661 0.520759i
\(777\) 0 0
\(778\) 2.35965 + 4.08703i 0.0845974 + 0.146527i
\(779\) 1.49645i 0.0536159i
\(780\) 10.9049 1.11267i 0.390457 0.0398399i
\(781\) 41.3039 1.47797
\(782\) −4.54510 + 7.87235i −0.162533 + 0.281515i
\(783\) −3.17988 + 14.3173i −0.113640 + 0.511660i
\(784\) 0 0
\(785\) −10.9134 6.30087i −0.389517 0.224888i
\(786\) −11.0734 15.3390i −0.394976 0.547126i
\(787\) 19.0399 + 10.9927i 0.678700 + 0.391848i 0.799365 0.600846i \(-0.205169\pi\)
−0.120665 + 0.992693i \(0.538503\pi\)
\(788\) 5.31385 + 3.06795i 0.189298 + 0.109291i
\(789\) 27.0696 2.76202i 0.963703 0.0983305i
\(790\) −6.12744 3.53768i −0.218004 0.125865i
\(791\) 0 0
\(792\) 22.9498 4.73259i 0.815485 0.168165i
\(793\) 1.27816 2.21384i 0.0453888 0.0786157i
\(794\) −12.3722 −0.439075
\(795\) 17.6545 + 24.4552i 0.626141 + 0.867338i
\(796\) 24.1486i 0.855923i
\(797\) −9.71892 16.8337i −0.344262 0.596279i 0.640958 0.767576i \(-0.278537\pi\)
−0.985219 + 0.171297i \(0.945204\pi\)
\(798\) 0 0
\(799\) −0.734219 + 1.27171i −0.0259748 + 0.0449897i
\(800\) 0.548754 + 0.316823i 0.0194014 + 0.0112014i
\(801\) 9.94972 30.0007i 0.351556 1.06002i
\(802\) 3.55818 + 6.16295i 0.125644 + 0.217621i
\(803\) −0.722823 1.25197i −0.0255079 0.0441809i
\(804\) 17.8173 12.8625i 0.628367 0.453625i
\(805\) 0 0
\(806\) 10.7356 6.19820i 0.378145 0.218322i
\(807\) −14.7349 + 10.6373i −0.518693 + 0.374451i
\(808\) 10.7472i 0.378084i
\(809\) −18.1916 + 10.5029i −0.639582 + 0.369263i −0.784453 0.620188i \(-0.787056\pi\)
0.144872 + 0.989450i \(0.453723\pi\)
\(810\) −7.62935 + 10.2370i −0.268068 + 0.359691i
\(811\) 37.3291i 1.31080i 0.755281 + 0.655401i \(0.227500\pi\)
−0.755281 + 0.655401i \(0.772500\pi\)
\(812\) 0 0
\(813\) 15.7844 35.1644i 0.553581 1.23327i
\(814\) −3.69963 −0.129672
\(815\) −11.2876 + 19.5506i −0.395386 + 0.684829i
\(816\) −16.0309 7.19583i −0.561193 0.251905i
\(817\) 5.58478 3.22438i 0.195387 0.112807i
\(818\) −13.0090 −0.454849
\(819\) 0 0
\(820\) −3.19639 −0.111623
\(821\) 10.9017 6.29412i 0.380473 0.219666i −0.297551 0.954706i \(-0.596170\pi\)
0.678024 + 0.735040i \(0.262837\pi\)
\(822\) −5.64499 + 4.07519i −0.196892 + 0.142138i
\(823\) 22.4189 38.8307i 0.781474 1.35355i −0.149608 0.988745i \(-0.547801\pi\)
0.931083 0.364808i \(-0.118865\pi\)
\(824\) 14.3677 0.500523
\(825\) −0.650451 + 0.0663681i −0.0226458 + 0.00231064i
\(826\) 0 0
\(827\) 25.7293i 0.894695i 0.894360 + 0.447347i \(0.147631\pi\)
−0.894360 + 0.447347i \(0.852369\pi\)
\(828\) 10.7356 + 3.56046i 0.373088 + 0.123735i
\(829\) −14.6902 + 8.48139i −0.510212 + 0.294571i −0.732921 0.680314i \(-0.761843\pi\)
0.222709 + 0.974885i \(0.428510\pi\)
\(830\) 12.1584i 0.422025i
\(831\) 4.01741 + 39.3733i 0.139363 + 1.36585i
\(832\) 0.397284 0.229372i 0.0137733 0.00795204i
\(833\) 0 0
\(834\) −7.79054 3.49697i −0.269764 0.121090i
\(835\) −3.99450 6.91867i −0.138235 0.239431i
\(836\) 4.43015 + 7.67324i 0.153220 + 0.265385i
\(837\) 12.0796 54.3882i 0.417533 1.87993i
\(838\) −6.16680 3.56041i −0.213029 0.122992i
\(839\) −13.3539 + 23.1296i −0.461027 + 0.798522i −0.999012 0.0444321i \(-0.985852\pi\)
0.537986 + 0.842954i \(0.319185\pi\)
\(840\) 0 0
\(841\) −10.5167 18.2155i −0.362645 0.628120i
\(842\) 5.89324i 0.203095i
\(843\) 0.651973 1.45247i 0.0224552 0.0500256i
\(844\) −37.9693 −1.30696
\(845\) 10.7819 18.6747i 0.370907 0.642430i
\(846\) −0.449440 0.149057i −0.0154521 0.00512467i
\(847\) 0 0
\(848\) −11.5927 6.69305i −0.398095 0.229840i
\(849\) 15.6902 34.9546i 0.538486 1.19964i
\(850\) −0.369016 0.213051i −0.0126571 0.00730760i
\(851\) −3.49381 2.01715i −0.119766 0.0691471i
\(852\) 13.7157 30.5559i 0.469893 1.04683i
\(853\) 37.6287 + 21.7249i 1.28838 + 0.743848i 0.978366 0.206883i \(-0.0663319\pi\)
0.310017 + 0.950731i \(0.399665\pi\)
\(854\) 0 0
\(855\) −10.3517 3.43313i −0.354020 0.117411i
\(856\) 1.71448 2.96957i 0.0585997 0.101498i
\(857\) 15.6686 0.535229 0.267615 0.963526i \(-0.413765\pi\)
0.267615 + 0.963526i \(0.413765\pi\)
\(858\) −2.78221 + 6.19820i −0.0949830 + 0.211603i
\(859\) 20.0431i 0.683862i −0.939725 0.341931i \(-0.888919\pi\)
0.939725 0.341931i \(-0.111081\pi\)
\(860\) 6.88721 + 11.9290i 0.234852 + 0.406775i
\(861\) 0 0
\(862\) 4.84727 8.39571i 0.165099 0.285959i
\(863\) 34.6600 + 20.0110i 1.17984 + 0.681181i 0.955978 0.293439i \(-0.0947998\pi\)
0.223863 + 0.974621i \(0.428133\pi\)
\(864\) 6.41603 28.8880i 0.218278 0.982790i
\(865\) −19.9869 34.6184i −0.679576 1.17706i
\(866\) −1.07010 1.85347i −0.0363635 0.0629834i
\(867\) 29.4369 + 13.2134i 0.999730 + 0.448752i
\(868\) 0 0
\(869\) −14.6545 + 8.46079i −0.497120 + 0.287013i
\(870\) 0.703959 + 6.89926i 0.0238664 + 0.233907i
\(871\) 14.3939i 0.487718i
\(872\) −8.74660 + 5.04985i −0.296197 + 0.171010i
\(873\) 20.7179 + 6.87109i 0.701194 + 0.232551i
\(874\) 2.50393i 0.0846967i
\(875\) 0 0
\(876\) −1.16621 + 0.118993i −0.0394025 + 0.00402039i
\(877\) 45.2705 1.52868 0.764338 0.644815i \(-0.223066\pi\)
0.764338 + 0.644815i \(0.223066\pi\)
\(878\) −2.18931 + 3.79200i −0.0738856 + 0.127974i
\(879\) 41.0795 29.6558i 1.38558 1.00027i
\(880\) −11.0416 + 6.37485i −0.372211 + 0.214896i
\(881\) 45.3385 1.52749 0.763746 0.645517i \(-0.223358\pi\)
0.763746 + 0.645517i \(0.223358\pi\)
\(882\) 0 0
\(883\) 12.5650 0.422845 0.211423 0.977395i \(-0.432190\pi\)
0.211423 + 0.977395i \(0.432190\pi\)
\(884\) 14.7960 8.54245i 0.497642 0.287314i
\(885\) −37.6698 16.9090i −1.26626 0.568389i
\(886\) −3.62178 + 6.27311i −0.121676 + 0.210749i
\(887\) −35.7241 −1.19950 −0.599748 0.800189i \(-0.704733\pi\)
−0.599748 + 0.800189i \(0.704733\pi\)
\(888\) −2.77544 + 6.18313i −0.0931377 + 0.207492i
\(889\) 0 0
\(890\) 14.9460i 0.500991i
\(891\) 12.0796 + 28.0434i 0.404683 + 0.939491i
\(892\) 26.3983 15.2411i 0.883881 0.510309i
\(893\) 0.404487i 0.0135356i
\(894\) 13.9096 10.0415i 0.465206 0.335838i
\(895\) 9.63528 5.56293i 0.322072 0.185948i
\(896\) 0 0
\(897\) −6.00688 + 4.33643i −0.200564 + 0.144789i
\(898\) −7.97346 13.8104i −0.266078 0.460860i
\(899\) −15.1316 26.2087i −0.504667 0.874108i
\(900\) −0.166896 + 0.503230i −0.00556321 + 0.0167743i
\(901\) 40.7130 + 23.5056i 1.35635 + 0.783086i
\(902\) 0.990571 1.71572i 0.0329824 0.0571272i
\(903\) 0 0
\(904\) −19.7738 34.2491i −0.657665 1.13911i
\(905\) 29.9801i 0.996573i
\(906\) −7.60198 10.5303i −0.252559 0.349847i
\(907\) −9.04208 −0.300237 −0.150119 0.988668i \(-0.547966\pi\)
−0.150119 + 0.988668i \(0.547966\pi\)
\(908\) 6.88721 11.9290i 0.228560 0.395878i
\(909\) −13.7157 + 2.82839i −0.454922 + 0.0938117i
\(910\) 0 0
\(911\) −35.5171 20.5058i −1.17673 0.679388i −0.221478 0.975165i \(-0.571088\pi\)
−0.955257 + 0.295777i \(0.904421\pi\)
\(912\) 4.81522 0.491316i 0.159448 0.0162691i
\(913\) −25.1826 14.5392i −0.833421 0.481176i
\(914\) 7.00619 + 4.04503i 0.231744 + 0.133798i
\(915\) −3.17988 4.40481i −0.105124 0.145618i
\(916\) −19.7652 11.4114i −0.653059 0.377044i
\(917\) 0 0
\(918\) −4.31453 + 19.4261i −0.142401 + 0.641156i
\(919\) −5.11628 + 8.86166i −0.168771 + 0.292319i −0.937988 0.346668i \(-0.887313\pi\)
0.769217 + 0.638987i \(0.220646\pi\)
\(920\) 12.0828 0.398357
\(921\) −25.5796 + 2.60999i −0.842877 + 0.0860021i
\(922\) 18.4818i 0.608665i
\(923\) 10.9692 + 18.9992i 0.361055 + 0.625366i
\(924\) 0 0
\(925\) 0.0945538 0.163772i 0.00310891 0.00538479i
\(926\) −13.9862 8.07492i −0.459614 0.265358i
\(927\) 3.78122 + 18.3363i 0.124192 + 0.602244i
\(928\) −8.03706 13.9206i −0.263830 0.456966i
\(929\) −12.8330 22.2273i −0.421036 0.729255i 0.575005 0.818150i \(-0.305000\pi\)
−0.996041 + 0.0888945i \(0.971667\pi\)
\(930\) −2.67417 26.2087i −0.0876896 0.859416i
\(931\) 0 0
\(932\) 40.8763 23.5999i 1.33895 0.773041i
\(933\) −30.6236 13.7461i −1.00257 0.450027i
\(934\) 16.4215i 0.537328i
\(935\) 38.7774 22.3881i 1.26816 0.732170i
\(936\) 8.27175 + 9.29971i 0.270371 + 0.303971i
\(937\) 15.9276i 0.520333i 0.965564 + 0.260167i \(0.0837775\pi\)
−0.965564 + 0.260167i \(0.916223\pi\)
\(938\) 0 0
\(939\) 14.8214 + 20.5308i 0.483679 + 0.669997i
\(940\) 0.863976 0.0281798
\(941\) 19.6767 34.0810i 0.641442 1.11101i −0.343669 0.939091i \(-0.611670\pi\)
0.985111 0.171919i \(-0.0549967\pi\)
\(942\) −0.642902 6.30087i −0.0209469 0.205293i
\(943\) 1.87093 1.08018i 0.0609258 0.0351755i
\(944\) 18.3252 0.596433
\(945\) 0 0
\(946\) −8.53747 −0.277577
\(947\) −28.9086 + 16.6904i −0.939403 + 0.542365i −0.889773 0.456403i \(-0.849138\pi\)
−0.0496302 + 0.998768i \(0.515804\pi\)
\(948\) 1.39284 + 13.6507i 0.0452372 + 0.443354i
\(949\) 0.383923 0.664975i 0.0124627 0.0215860i
\(950\) 0.117372 0.00380804
\(951\) −17.2140 23.8450i −0.558202 0.773228i
\(952\) 0 0
\(953\) 44.4622i 1.44027i −0.693832 0.720137i \(-0.744079\pi\)
0.693832 0.720137i \(-0.255921\pi\)
\(954\) −4.77197 + 14.3886i −0.154498 + 0.465847i
\(955\) −19.6108 + 11.3223i −0.634592 + 0.366382i
\(956\) 25.1456i 0.813266i
\(957\) 15.1316 + 6.79217i 0.489135 + 0.219560i
\(958\) 0.297540 0.171785i 0.00961307 0.00555011i
\(959\) 0 0
\(960\) −0.0989611 0.969884i −0.00319395 0.0313029i
\(961\) 41.9814 + 72.7138i 1.35424 + 2.34561i
\(962\) −0.982519 1.70177i −0.0316777 0.0548674i
\(963\) 4.24102 + 1.40653i 0.136665 + 0.0453249i
\(964\) −6.90895 3.98888i −0.222522 0.128473i
\(965\) 17.8347 30.8905i 0.574118 0.994401i
\(966\) 0 0
\(967\) −20.0556 34.7372i −0.644943 1.11707i −0.984315 0.176422i \(-0.943548\pi\)
0.339371 0.940652i \(-0.389786\pi\)
\(968\) 1.17535i 0.0377771i
\(969\) −16.9108 + 1.72548i −0.543254 + 0.0554303i
\(970\) 10.3214 0.331401
\(971\) 23.0013 39.8394i 0.738147 1.27851i −0.215181 0.976574i \(-0.569034\pi\)
0.953329 0.301934i \(-0.0976324\pi\)
\(972\) 24.7573 + 0.376055i 0.794090 + 0.0120620i
\(973\) 0 0
\(974\) −18.9650 10.9494i −0.607678 0.350843i
\(975\) −0.203270 0.281572i −0.00650985 0.00901752i
\(976\) 2.08804 + 1.20553i 0.0668366 + 0.0385882i
\(977\) 46.8323 + 27.0386i 1.49830 + 0.865042i 0.999998 0.00196335i \(-0.000624955\pi\)
0.498299 + 0.867005i \(0.333958\pi\)
\(978\) −11.2876 + 1.15172i −0.360937 + 0.0368278i
\(979\) −30.9562 17.8726i −0.989365 0.571210i
\(980\) 0 0
\(981\) −8.74660 9.83357i −0.279257 0.313962i
\(982\) 2.17418 3.76579i 0.0693809 0.120171i
\(983\) 13.9578 0.445185 0.222592 0.974912i \(-0.428548\pi\)
0.222592 + 0.974912i \(0.428548\pi\)
\(984\) −2.12433 2.94265i −0.0677212 0.0938082i
\(985\) 8.54135i 0.272150i
\(986\) 5.40462 + 9.36107i 0.172118 + 0.298117i
\(987\) 0 0
\(988\) −2.35305 + 4.07560i −0.0748605 + 0.129662i
\(989\) −8.06251 4.65489i −0.256373 0.148017i
\(990\) 9.59591 + 10.7884i 0.304978 + 0.342879i
\(991\) 18.5149 + 32.0687i 0.588144 + 1.01869i 0.994475 + 0.104969i \(0.0334744\pi\)
−0.406332 + 0.913726i \(0.633192\pi\)
\(992\) 30.5309 + 52.8811i 0.969358 + 1.67898i
\(993\) −27.9409 + 20.1708i −0.886677 + 0.640102i
\(994\) 0 0
\(995\) −29.1119 + 16.8077i −0.922909 + 0.532841i
\(996\) −19.1181 + 13.8016i −0.605782 + 0.437321i
\(997\) 50.1466i 1.58816i 0.607815 + 0.794079i \(0.292046\pi\)
−0.607815 + 0.794079i \(0.707954\pi\)
\(998\) 4.77885 2.75907i 0.151272 0.0873368i
\(999\) −8.62145 1.91482i −0.272770 0.0605824i
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 441.2.s.c.362.3 12
3.2 odd 2 1323.2.s.c.656.4 12
7.2 even 3 63.2.o.a.20.4 yes 12
7.3 odd 6 441.2.i.c.227.4 12
7.4 even 3 441.2.i.c.227.3 12
7.5 odd 6 63.2.o.a.20.3 12
7.6 odd 2 inner 441.2.s.c.362.4 12
9.4 even 3 1323.2.i.c.1097.4 12
9.5 odd 6 441.2.i.c.68.4 12
21.2 odd 6 189.2.o.a.62.3 12
21.5 even 6 189.2.o.a.62.4 12
21.11 odd 6 1323.2.i.c.521.3 12
21.17 even 6 1323.2.i.c.521.4 12
21.20 even 2 1323.2.s.c.656.3 12
28.19 even 6 1008.2.cc.a.209.6 12
28.23 odd 6 1008.2.cc.a.209.1 12
63.2 odd 6 567.2.c.c.566.6 12
63.4 even 3 1323.2.s.c.962.3 12
63.5 even 6 63.2.o.a.41.4 yes 12
63.13 odd 6 1323.2.i.c.1097.3 12
63.16 even 3 567.2.c.c.566.7 12
63.23 odd 6 63.2.o.a.41.3 yes 12
63.31 odd 6 1323.2.s.c.962.4 12
63.32 odd 6 inner 441.2.s.c.374.4 12
63.40 odd 6 189.2.o.a.125.3 12
63.41 even 6 441.2.i.c.68.3 12
63.47 even 6 567.2.c.c.566.5 12
63.58 even 3 189.2.o.a.125.4 12
63.59 even 6 inner 441.2.s.c.374.3 12
63.61 odd 6 567.2.c.c.566.8 12
84.23 even 6 3024.2.cc.a.2897.2 12
84.47 odd 6 3024.2.cc.a.2897.5 12
252.23 even 6 1008.2.cc.a.545.6 12
252.103 even 6 3024.2.cc.a.881.2 12
252.131 odd 6 1008.2.cc.a.545.1 12
252.247 odd 6 3024.2.cc.a.881.5 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.o.a.20.3 12 7.5 odd 6
63.2.o.a.20.4 yes 12 7.2 even 3
63.2.o.a.41.3 yes 12 63.23 odd 6
63.2.o.a.41.4 yes 12 63.5 even 6
189.2.o.a.62.3 12 21.2 odd 6
189.2.o.a.62.4 12 21.5 even 6
189.2.o.a.125.3 12 63.40 odd 6
189.2.o.a.125.4 12 63.58 even 3
441.2.i.c.68.3 12 63.41 even 6
441.2.i.c.68.4 12 9.5 odd 6
441.2.i.c.227.3 12 7.4 even 3
441.2.i.c.227.4 12 7.3 odd 6
441.2.s.c.362.3 12 1.1 even 1 trivial
441.2.s.c.362.4 12 7.6 odd 2 inner
441.2.s.c.374.3 12 63.59 even 6 inner
441.2.s.c.374.4 12 63.32 odd 6 inner
567.2.c.c.566.5 12 63.47 even 6
567.2.c.c.566.6 12 63.2 odd 6
567.2.c.c.566.7 12 63.16 even 3
567.2.c.c.566.8 12 63.61 odd 6
1008.2.cc.a.209.1 12 28.23 odd 6
1008.2.cc.a.209.6 12 28.19 even 6
1008.2.cc.a.545.1 12 252.131 odd 6
1008.2.cc.a.545.6 12 252.23 even 6
1323.2.i.c.521.3 12 21.11 odd 6
1323.2.i.c.521.4 12 21.17 even 6
1323.2.i.c.1097.3 12 63.13 odd 6
1323.2.i.c.1097.4 12 9.4 even 3
1323.2.s.c.656.3 12 21.20 even 2
1323.2.s.c.656.4 12 3.2 odd 2
1323.2.s.c.962.3 12 63.4 even 3
1323.2.s.c.962.4 12 63.31 odd 6
3024.2.cc.a.881.2 12 252.103 even 6
3024.2.cc.a.881.5 12 252.247 odd 6
3024.2.cc.a.2897.2 12 84.23 even 6
3024.2.cc.a.2897.5 12 84.47 odd 6