Properties

Label 441.2.s.c.362.4
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 362.4
Root \(-0.474636 + 0.274031i\) of defining polynomial
Character \(\chi\) \(=\) 441.362
Dual form 441.2.s.c.374.4

$q$-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 \(-0.335386\pi\)
0.494405 + 0.869231i \(0.335386\pi\)
\(6\) 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 −0.267720 0.963497i \(-0.586270\pi\)
0.700552 + 0.713601i \(0.252937\pi\)
\(14\) 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 \(-0.909038\pi\)
0.235597 0.971851i \(-0.424295\pi\)
\(18\) −1.43818 + 1.27921i −0.338982 + 0.301512i
\(19\) 1.42391 + 0.822093i 0.326667 + 0.188601i 0.654360 0.756183i \(-0.272938\pi\)
−0.327694 + 0.944784i \(0.606271\pi\)
\(20\) −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 \(0.0796544\pi\)
0.698887 + 0.715232i \(0.253679\pi\)
\(32\) −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 0.899371 0.437187i \(-0.144025\pi\)
−0.828300 + 0.560285i \(0.810692\pi\)
\(42\) 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 0.856915 0.515458i \(-0.172378\pi\)
−0.874857 + 0.484381i \(0.839045\pi\)
\(48\) 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 \(-0.585696\pi\)
0.967820 0.251643i \(-0.0809709\pi\)
\(60\) −5.54944 2.49100i −0.716430 0.321586i
\(61\) 1.22853 0.709292i 0.157297 0.0908155i −0.419285 0.907855i \(-0.637719\pi\)
0.576582 + 0.817039i \(0.304386\pi\)
\(62\) 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 −0.478250 0.878224i \(-0.658729\pi\)
0.521440 + 0.853288i \(0.325395\pi\)
\(74\) 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 −0.529042 0.848596i \(-0.677449\pi\)
0.999426 + 0.0338660i \(0.0107819\pi\)
\(84\) 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 \(-0.644749\pi\)
0.997630 0.0688014i \(-0.0219175\pi\)
\(90\) −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 0.784529 0.620092i \(-0.212905\pi\)
−0.144751 + 0.989468i \(0.546238\pi\)
\(98\) 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 \(-0.574608\pi\)
−0.232247 + 0.972657i \(0.574608\pi\)
\(102\) 2.71634 6.05146i 0.268958 0.599183i
\(103\) 6.24071i 0.614916i 0.951562 + 0.307458i \(0.0994783\pi\)
−0.951562 + 0.307458i \(0.900522\pi\)
\(104\) 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 \(-0.766935\pi\)
−0.743708 + 0.668505i \(0.766935\pi\)
\(132\) 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 −0.754934 0.655801i \(-0.772331\pi\)
0.190474 + 0.981692i \(0.438998\pi\)
\(140\) 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 0.289935 0.957046i \(-0.406366\pi\)
−0.683859 + 0.729614i \(0.739700\pi\)
\(158\) 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 0.787621 0.616160i \(-0.211312\pi\)
−0.927421 + 0.374020i \(0.877979\pi\)
\(168\) 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 \(-0.925477\pi\)
0.285453 0.958393i \(-0.407856\pi\)
\(174\) 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 \(-0.831889\pi\)
0.863747 0.503925i \(-0.168111\pi\)
\(182\) 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 −0.887870 0.460094i \(-0.847816\pi\)
−0.0454817 + 0.998965i \(0.514482\pi\)
\(200\) 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 0.939591 0.342300i \(-0.111206\pi\)
0.173354 + 0.984860i \(0.444539\pi\)
\(224\) 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 \(-0.407078\pi\)
0.287793 + 0.957693i \(0.407078\pi\)
\(228\) −2.64764 3.66754i −0.175344 0.242889i
\(229\) 14.3688i 0.949515i −0.880117 0.474758i \(-0.842536\pi\)
0.880117 0.474758i \(-0.157464\pi\)
\(230\) 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 \(-0.948280\pi\)
0.986829 0.161768i \(-0.0517196\pi\)
\(242\) −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 \(-0.426029\pi\)
0.230300 + 0.973120i \(0.426029\pi\)
\(252\) 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 \(-0.580352\pi\)
−0.249761 + 0.968308i \(0.580352\pi\)
\(258\) −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 0.980460 0.196720i \(-0.0630289\pi\)
−0.660594 + 0.750743i \(0.729696\pi\)
\(270\) −5.43268 4.98199i −0.330622 0.303195i
\(271\) −19.2722 11.1268i −1.17071 0.675907i −0.216859 0.976203i \(-0.569581\pi\)
−0.953846 + 0.300296i \(0.902915\pi\)
\(272\) −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 −0.192654 0.981267i \(-0.561710\pi\)
−0.946129 + 0.323790i \(0.895043\pi\)
\(284\) 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 \(-0.840559\pi\)
0.0226986 0.999742i \(-0.492774\pi\)
\(294\) 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 \(0.139243\pi\)
−0.905837 + 0.423627i \(0.860757\pi\)
\(308\) 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 \(0.351837\pi\)
−0.998311 + 0.0580991i \(0.981496\pi\)
\(312\) −5.82623 + 4.20602i −0.329845 + 0.238119i
\(313\) 12.6608 7.30974i 0.715633 0.413171i −0.0975102 0.995235i \(-0.531088\pi\)
0.813143 + 0.582064i \(0.197755\pi\)
\(314\) −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 0.248755 0.968566i \(-0.419979\pi\)
−0.714426 + 0.699711i \(0.753312\pi\)
\(350\) 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 \(-0.476713\pi\)
0.0730920 + 0.997325i \(0.476713\pi\)
\(354\) 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 \(-0.951506\pi\)
0.988417 0.151760i \(-0.0484941\pi\)
\(368\) 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 \(-0.528376\pi\)
−0.0890268 + 0.996029i \(0.528376\pi\)
\(384\) 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 0.856639 0.515917i \(-0.172549\pi\)
−0.0184778 + 0.999829i \(0.505882\pi\)
\(398\) −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 0.866774 0.498701i \(-0.166189\pi\)
0.00149954 + 0.999999i \(0.499523\pi\)
\(410\) 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 0.969145 0.246492i \(-0.0792779\pi\)
−0.698041 + 0.716058i \(0.745945\pi\)
\(420\) 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 \(0.0255411\pi\)
−0.996783 + 0.0801537i \(0.974459\pi\)
\(434\) 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 −0.352282 0.935894i \(-0.614594\pi\)
0.634367 + 0.773032i \(0.281261\pi\)
\(440\) −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 \(0.400725\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(462\) 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 \(-0.631593\pi\)
0.993936 0.109964i \(-0.0350735\pi\)
\(468\) −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 \(-0.503894\pi\)
−0.0122338 + 0.999925i \(0.503894\pi\)
\(480\) 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 \(-0.478943\pi\)
0.0661055 + 0.997813i \(0.478943\pi\)
\(504\) 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 \(-0.543147\pi\)
−0.135137 + 0.990827i \(0.543147\pi\)
\(510\) 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 \(-0.912569\pi\)
0.246364 0.969177i \(-0.420764\pi\)
\(522\) −5.32072 + 1.09721i −0.232882 + 0.0480237i
\(523\) 1.73424 + 1.00126i 0.0758329 + 0.0437821i 0.537437 0.843304i \(-0.319393\pi\)
−0.461604 + 0.887086i \(0.652726\pi\)
\(524\) 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 −0.591716 0.806147i \(-0.701549\pi\)
0.994001 + 0.109368i \(0.0348826\pi\)
\(564\) 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 0.351086 0.936343i \(-0.385813\pi\)
0.986440 + 0.164123i \(0.0524793\pi\)
\(578\) 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 \(-0.584643\pi\)
0.966983 0.254842i \(-0.0820235\pi\)
\(588\) 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 −0.589772 0.807570i \(-0.700782\pi\)
0.994262 + 0.106973i \(0.0341157\pi\)
\(594\) 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 −0.250469 0.968125i \(-0.580585\pi\)
−0.963655 + 0.267150i \(0.913918\pi\)
\(602\) 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 \(0.290858\pi\)
−0.610775 + 0.791804i \(0.709142\pi\)
\(608\) −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 \(0.270866\pi\)
−0.659270 + 0.751906i \(0.729134\pi\)
\(620\) −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 −0.997373 0.0724332i \(-0.976924\pi\)
−0.435958 + 0.899967i \(0.643590\pi\)
\(644\) 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 0.921170 0.389161i \(-0.127235\pi\)
−0.797608 + 0.603176i \(0.793902\pi\)
\(648\) 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 0.801841 0.597538i \(-0.203854\pi\)
−0.116563 + 0.993183i \(0.537188\pi\)
\(662\) −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 \(-0.982798\pi\)
0.452492 0.891769i \(-0.350535\pi\)
\(678\) −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 −0.840299 0.542123i \(-0.817621\pi\)
0.0493424 + 0.998782i \(0.484287\pi\)
\(692\) 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 −0.643459 0.765481i \(-0.722501\pi\)
0.984655 + 0.174512i \(0.0558347\pi\)
\(720\) 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 0.922756 0.385384i \(-0.125931\pi\)
0.127626 + 0.991822i \(0.459264\pi\)
\(728\) 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 \(-0.997069\pi\)
0.999958 0.00920836i \(-0.00293115\pi\)
\(734\) −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 \(-0.212480\pi\)
0.785355 + 0.619045i \(0.212480\pi\)
\(762\) 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 −0.600111 0.799917i \(-0.704877\pi\)
0.392693 + 0.919670i \(0.371544\pi\)
\(770\) 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 \(-0.871514\pi\)
0.119660 0.992815i \(-0.461819\pi\)
\(774\) −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 0.120665 0.992693i \(-0.461497\pi\)
−0.799365 + 0.600846i \(0.794831\pi\)
\(788\) 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 0.985219 0.171297i \(-0.0547959\pi\)
−0.640958 + 0.767576i \(0.721463\pi\)
\(798\) 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 \(-0.772500\pi\)
0.755281 0.655401i \(-0.227500\pi\)
\(812\) 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 −0.222709 0.974885i \(-0.571490\pi\)
0.732921 + 0.680314i \(0.238157\pi\)
\(830\) 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 −0.537986 0.842954i \(-0.680815\pi\)
0.999012 + 0.0444321i \(0.0141478\pi\)
\(840\) 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 −0.310017 0.950731i \(-0.600335\pi\)
−0.978366 + 0.206883i \(0.933668\pi\)
\(854\) 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 \(-0.586235\pi\)
−0.267615 + 0.963526i \(0.586235\pi\)
\(858\) −2.78221 + 6.19820i −0.0949830 + 0.211603i
\(859\) 20.0431i 0.683862i 0.939725 + 0.341931i \(0.111081\pi\)
−0.939725 + 0.341931i \(0.888919\pi\)
\(860\) −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 \(-0.776642\pi\)
−0.763746 + 0.645517i \(0.776642\pi\)
\(882\) 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 \(-0.295267\pi\)
0.599748 + 0.800189i \(0.295267\pi\)
\(888\) 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 0.996041 0.0888945i \(-0.0283334\pi\)
−0.575005 + 0.818150i \(0.695000\pi\)
\(930\) 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 \(-0.916223\pi\)
0.965564 0.260167i \(-0.0837775\pi\)
\(938\) 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 \(0.388330\pi\)
−0.985111 + 0.171919i \(0.945003\pi\)
\(942\) −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 \(0.430966\pi\)
−0.953329 + 0.301934i \(0.902368\pi\)
\(972\) −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 \(-0.571452\pi\)
−0.222592 + 0.974912i \(0.571452\pi\)
\(984\) −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 \(-0.707954\pi\)
0.607815 0.794079i \(-0.292046\pi\)
\(998\) 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.362.4 12
3.2 odd 2 1323.2.s.c.656.3 12
7.2 even 3 63.2.o.a.20.3 12
7.3 odd 6 441.2.i.c.227.3 12
7.4 even 3 441.2.i.c.227.4 12
7.5 odd 6 63.2.o.a.20.4 yes 12
7.6 odd 2 inner 441.2.s.c.362.3 12
9.4 even 3 1323.2.i.c.1097.3 12
9.5 odd 6 441.2.i.c.68.3 12
21.2 odd 6 189.2.o.a.62.4 12
21.5 even 6 189.2.o.a.62.3 12
21.11 odd 6 1323.2.i.c.521.4 12
21.17 even 6 1323.2.i.c.521.3 12
21.20 even 2 1323.2.s.c.656.4 12
28.19 even 6 1008.2.cc.a.209.1 12
28.23 odd 6 1008.2.cc.a.209.6 12
63.2 odd 6 567.2.c.c.566.5 12
63.4 even 3 1323.2.s.c.962.4 12
63.5 even 6 63.2.o.a.41.3 yes 12
63.13 odd 6 1323.2.i.c.1097.4 12
63.16 even 3 567.2.c.c.566.8 12
63.23 odd 6 63.2.o.a.41.4 yes 12
63.31 odd 6 1323.2.s.c.962.3 12
63.32 odd 6 inner 441.2.s.c.374.3 12
63.40 odd 6 189.2.o.a.125.4 12
63.41 even 6 441.2.i.c.68.4 12
63.47 even 6 567.2.c.c.566.6 12
63.58 even 3 189.2.o.a.125.3 12
63.59 even 6 inner 441.2.s.c.374.4 12
63.61 odd 6 567.2.c.c.566.7 12
84.23 even 6 3024.2.cc.a.2897.5 12
84.47 odd 6 3024.2.cc.a.2897.2 12
252.23 even 6 1008.2.cc.a.545.1 12
252.103 even 6 3024.2.cc.a.881.5 12
252.131 odd 6 1008.2.cc.a.545.6 12
252.247 odd 6 3024.2.cc.a.881.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.o.a.20.3 12 7.2 even 3
63.2.o.a.20.4 yes 12 7.5 odd 6
63.2.o.a.41.3 yes 12 63.5 even 6
63.2.o.a.41.4 yes 12 63.23 odd 6
189.2.o.a.62.3 12 21.5 even 6
189.2.o.a.62.4 12 21.2 odd 6
189.2.o.a.125.3 12 63.58 even 3
189.2.o.a.125.4 12 63.40 odd 6
441.2.i.c.68.3 12 9.5 odd 6
441.2.i.c.68.4 12 63.41 even 6
441.2.i.c.227.3 12 7.3 odd 6
441.2.i.c.227.4 12 7.4 even 3
441.2.s.c.362.3 12 7.6 odd 2 inner
441.2.s.c.362.4 12 1.1 even 1 trivial
441.2.s.c.374.3 12 63.32 odd 6 inner
441.2.s.c.374.4 12 63.59 even 6 inner
567.2.c.c.566.5 12 63.2 odd 6
567.2.c.c.566.6 12 63.47 even 6
567.2.c.c.566.7 12 63.61 odd 6
567.2.c.c.566.8 12 63.16 even 3
1008.2.cc.a.209.1 12 28.19 even 6
1008.2.cc.a.209.6 12 28.23 odd 6
1008.2.cc.a.545.1 12 252.23 even 6
1008.2.cc.a.545.6 12 252.131 odd 6
1323.2.i.c.521.3 12 21.17 even 6
1323.2.i.c.521.4 12 21.11 odd 6
1323.2.i.c.1097.3 12 9.4 even 3
1323.2.i.c.1097.4 12 63.13 odd 6
1323.2.s.c.656.3 12 3.2 odd 2
1323.2.s.c.656.4 12 21.20 even 2
1323.2.s.c.962.3 12 63.31 odd 6
1323.2.s.c.962.4 12 63.4 even 3
3024.2.cc.a.881.2 12 252.247 odd 6
3024.2.cc.a.881.5 12 252.103 even 6
3024.2.cc.a.2897.2 12 84.47 odd 6
3024.2.cc.a.2897.5 12 84.23 even 6