Properties

Label 441.2.w.a.188.13
Level $441$
Weight $2$
Character 441.188
Analytic conductor $3.521$
Analytic rank $0$
Dimension $120$
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(62,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([7, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.62");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.w (of order \(14\), degree \(6\), 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: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 188.13
Character \(\chi\) \(=\) 441.188
Dual form 441.2.w.a.251.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.920203 - 0.733838i) q^{2} +(-0.136785 + 0.599296i) q^{4} +(-1.46088 + 0.703524i) q^{5} +(-2.01956 + 1.70920i) q^{7} +(1.33526 + 2.77270i) q^{8} +O(q^{10})\) \(q+(0.920203 - 0.733838i) q^{2} +(-0.136785 + 0.599296i) q^{4} +(-1.46088 + 0.703524i) q^{5} +(-2.01956 + 1.70920i) q^{7} +(1.33526 + 2.77270i) q^{8} +(-0.828037 + 1.71944i) q^{10} +(2.35512 - 1.87814i) q^{11} +(-2.44072 + 1.94641i) q^{13} +(-0.604130 + 3.05484i) q^{14} +(2.15577 + 1.03816i) q^{16} +(0.882993 + 3.86864i) q^{17} +6.34682i q^{19} +(-0.221792 - 0.971733i) q^{20} +(0.788935 - 3.45655i) q^{22} +(-1.23051 - 0.280855i) q^{23} +(-1.47822 + 1.85362i) q^{25} +(-0.817612 + 3.58219i) q^{26} +(-0.748071 - 1.44411i) q^{28} +(7.25165 - 1.65514i) q^{29} -1.49304i q^{31} +(-3.25504 + 0.742941i) q^{32} +(3.65149 + 2.91197i) q^{34} +(1.74788 - 3.91776i) q^{35} +(-1.72116 - 7.54089i) q^{37} +(4.65754 + 5.84036i) q^{38} +(-3.90133 - 3.11121i) q^{40} +(9.09214 - 4.37855i) q^{41} +(-0.978095 - 0.471026i) q^{43} +(0.803418 + 1.66832i) q^{44} +(-1.33842 + 0.644549i) q^{46} +(-5.44608 - 6.82916i) q^{47} +(1.15725 - 6.90368i) q^{49} +2.79048i q^{50} +(-0.832622 - 1.72896i) q^{52} +(0.104261 + 0.0237970i) q^{53} +(-2.11923 + 4.40063i) q^{55} +(-7.43576 - 3.31741i) q^{56} +(5.45839 - 6.84461i) q^{58} +(1.54958 + 0.746240i) q^{59} +(-10.5852 + 2.41600i) q^{61} +(-1.09565 - 1.37390i) q^{62} +(-5.43377 + 6.81373i) q^{64} +(2.19626 - 4.56059i) q^{65} +11.0005 q^{67} -2.43924 q^{68} +(-1.26659 - 4.88779i) q^{70} +(3.29503 + 0.752069i) q^{71} +(8.80135 + 7.01884i) q^{73} +(-7.11761 - 5.67610i) q^{74} +(-3.80362 - 0.868152i) q^{76} +(-1.54618 + 7.81840i) q^{77} +14.5682 q^{79} -3.87969 q^{80} +(5.15348 - 10.7013i) q^{82} +(2.15744 - 2.70535i) q^{83} +(-4.01163 - 5.03043i) q^{85} +(-1.24570 + 0.284324i) q^{86} +(8.35225 + 4.02223i) q^{88} +(-7.65264 + 9.59610i) q^{89} +(1.60238 - 8.10259i) q^{91} +(0.336631 - 0.699021i) q^{92} +(-10.0230 - 2.28768i) q^{94} +(-4.46514 - 9.27196i) q^{95} +6.40900i q^{97} +(-4.00127 - 7.20202i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q + 24 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{5}{14}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.920203 0.733838i 0.650682 0.518902i −0.241602 0.970375i \(-0.577673\pi\)
0.892284 + 0.451474i \(0.149102\pi\)
\(3\) 0 0
\(4\) −0.136785 + 0.599296i −0.0683927 + 0.299648i
\(5\) −1.46088 + 0.703524i −0.653327 + 0.314626i −0.731024 0.682351i \(-0.760957\pi\)
0.0776976 + 0.996977i \(0.475243\pi\)
\(6\) 0 0
\(7\) −2.01956 + 1.70920i −0.763322 + 0.646018i
\(8\) 1.33526 + 2.77270i 0.472087 + 0.980299i
\(9\) 0 0
\(10\) −0.828037 + 1.71944i −0.261848 + 0.543734i
\(11\) 2.35512 1.87814i 0.710095 0.566282i −0.200444 0.979705i \(-0.564238\pi\)
0.910539 + 0.413423i \(0.135667\pi\)
\(12\) 0 0
\(13\) −2.44072 + 1.94641i −0.676935 + 0.539838i −0.900503 0.434851i \(-0.856801\pi\)
0.223567 + 0.974688i \(0.428230\pi\)
\(14\) −0.604130 + 3.05484i −0.161460 + 0.816441i
\(15\) 0 0
\(16\) 2.15577 + 1.03816i 0.538941 + 0.259540i
\(17\) 0.882993 + 3.86864i 0.214157 + 0.938284i 0.961707 + 0.274079i \(0.0883729\pi\)
−0.747550 + 0.664205i \(0.768770\pi\)
\(18\) 0 0
\(19\) 6.34682i 1.45606i 0.685545 + 0.728030i \(0.259564\pi\)
−0.685545 + 0.728030i \(0.740436\pi\)
\(20\) −0.221792 0.971733i −0.0495941 0.217286i
\(21\) 0 0
\(22\) 0.788935 3.45655i 0.168202 0.736939i
\(23\) −1.23051 0.280855i −0.256579 0.0585624i 0.0922967 0.995732i \(-0.470579\pi\)
−0.348875 + 0.937169i \(0.613436\pi\)
\(24\) 0 0
\(25\) −1.47822 + 1.85362i −0.295643 + 0.370725i
\(26\) −0.817612 + 3.58219i −0.160347 + 0.702526i
\(27\) 0 0
\(28\) −0.748071 1.44411i −0.141372 0.272911i
\(29\) 7.25165 1.65514i 1.34660 0.307352i 0.512367 0.858767i \(-0.328769\pi\)
0.834232 + 0.551414i \(0.185912\pi\)
\(30\) 0 0
\(31\) 1.49304i 0.268158i −0.990971 0.134079i \(-0.957192\pi\)
0.990971 0.134079i \(-0.0428076\pi\)
\(32\) −3.25504 + 0.742941i −0.575415 + 0.131335i
\(33\) 0 0
\(34\) 3.65149 + 2.91197i 0.626225 + 0.499398i
\(35\) 1.74788 3.91776i 0.295445 0.662221i
\(36\) 0 0
\(37\) −1.72116 7.54089i −0.282957 1.23971i −0.893982 0.448103i \(-0.852100\pi\)
0.611025 0.791611i \(-0.290757\pi\)
\(38\) 4.65754 + 5.84036i 0.755552 + 0.947432i
\(39\) 0 0
\(40\) −3.90133 3.11121i −0.616854 0.491925i
\(41\) 9.09214 4.37855i 1.41995 0.683814i 0.442854 0.896594i \(-0.353966\pi\)
0.977100 + 0.212780i \(0.0682516\pi\)
\(42\) 0 0
\(43\) −0.978095 0.471026i −0.149158 0.0718308i 0.357816 0.933792i \(-0.383522\pi\)
−0.506974 + 0.861961i \(0.669236\pi\)
\(44\) 0.803418 + 1.66832i 0.121120 + 0.251508i
\(45\) 0 0
\(46\) −1.33842 + 0.644549i −0.197339 + 0.0950336i
\(47\) −5.44608 6.82916i −0.794392 0.996136i −0.999847 0.0174695i \(-0.994439\pi\)
0.205455 0.978666i \(-0.434132\pi\)
\(48\) 0 0
\(49\) 1.15725 6.90368i 0.165322 0.986240i
\(50\) 2.79048i 0.394634i
\(51\) 0 0
\(52\) −0.832622 1.72896i −0.115464 0.239763i
\(53\) 0.104261 + 0.0237970i 0.0143214 + 0.00326877i 0.229676 0.973267i \(-0.426233\pi\)
−0.215354 + 0.976536i \(0.569091\pi\)
\(54\) 0 0
\(55\) −2.11923 + 4.40063i −0.285757 + 0.593381i
\(56\) −7.43576 3.31741i −0.993645 0.443308i
\(57\) 0 0
\(58\) 5.45839 6.84461i 0.716722 0.898741i
\(59\) 1.54958 + 0.746240i 0.201739 + 0.0971522i 0.532025 0.846728i \(-0.321431\pi\)
−0.330287 + 0.943881i \(0.607145\pi\)
\(60\) 0 0
\(61\) −10.5852 + 2.41600i −1.35529 + 0.309337i −0.837626 0.546244i \(-0.816057\pi\)
−0.517668 + 0.855581i \(0.673200\pi\)
\(62\) −1.09565 1.37390i −0.139148 0.174486i
\(63\) 0 0
\(64\) −5.43377 + 6.81373i −0.679221 + 0.851717i
\(65\) 2.19626 4.56059i 0.272413 0.565672i
\(66\) 0 0
\(67\) 11.0005 1.34392 0.671961 0.740587i \(-0.265452\pi\)
0.671961 + 0.740587i \(0.265452\pi\)
\(68\) −2.43924 −0.295802
\(69\) 0 0
\(70\) −1.26659 4.88779i −0.151387 0.584203i
\(71\) 3.29503 + 0.752069i 0.391048 + 0.0892542i 0.413524 0.910493i \(-0.364298\pi\)
−0.0224758 + 0.999747i \(0.507155\pi\)
\(72\) 0 0
\(73\) 8.80135 + 7.01884i 1.03012 + 0.821493i 0.984130 0.177449i \(-0.0567844\pi\)
0.0459897 + 0.998942i \(0.485356\pi\)
\(74\) −7.11761 5.67610i −0.827405 0.659833i
\(75\) 0 0
\(76\) −3.80362 0.868152i −0.436305 0.0995838i
\(77\) −1.54618 + 7.81840i −0.176203 + 0.890990i
\(78\) 0 0
\(79\) 14.5682 1.63905 0.819525 0.573044i \(-0.194238\pi\)
0.819525 + 0.573044i \(0.194238\pi\)
\(80\) −3.87969 −0.433763
\(81\) 0 0
\(82\) 5.15348 10.7013i 0.569107 1.18176i
\(83\) 2.15744 2.70535i 0.236810 0.296950i −0.649199 0.760619i \(-0.724896\pi\)
0.886009 + 0.463668i \(0.153467\pi\)
\(84\) 0 0
\(85\) −4.01163 5.03043i −0.435123 0.545627i
\(86\) −1.24570 + 0.284324i −0.134328 + 0.0306594i
\(87\) 0 0
\(88\) 8.35225 + 4.02223i 0.890352 + 0.428771i
\(89\) −7.65264 + 9.59610i −0.811178 + 1.01718i 0.188207 + 0.982129i \(0.439732\pi\)
−0.999385 + 0.0350556i \(0.988839\pi\)
\(90\) 0 0
\(91\) 1.60238 8.10259i 0.167975 0.849382i
\(92\) 0.336631 0.699021i 0.0350962 0.0728780i
\(93\) 0 0
\(94\) −10.0230 2.28768i −1.03379 0.235957i
\(95\) −4.46514 9.27196i −0.458114 0.951283i
\(96\) 0 0
\(97\) 6.40900i 0.650736i 0.945587 + 0.325368i \(0.105488\pi\)
−0.945587 + 0.325368i \(0.894512\pi\)
\(98\) −4.00127 7.20202i −0.404189 0.727514i
\(99\) 0 0
\(100\) −0.908671 1.13944i −0.0908671 0.113944i
\(101\) 0.402455 0.193812i 0.0400458 0.0192850i −0.413754 0.910389i \(-0.635783\pi\)
0.453799 + 0.891104i \(0.350068\pi\)
\(102\) 0 0
\(103\) −1.04038 2.16038i −0.102512 0.212869i 0.843404 0.537280i \(-0.180548\pi\)
−0.945916 + 0.324411i \(0.894834\pi\)
\(104\) −8.65584 4.16843i −0.848775 0.408749i
\(105\) 0 0
\(106\) 0.113405 0.0546129i 0.0110149 0.00530447i
\(107\) −12.7985 10.2065i −1.23728 0.986698i −0.999883 0.0152850i \(-0.995134\pi\)
−0.237397 0.971413i \(-0.576294\pi\)
\(108\) 0 0
\(109\) 12.8699 + 16.1383i 1.23271 + 1.54577i 0.734292 + 0.678834i \(0.237515\pi\)
0.498419 + 0.866936i \(0.333914\pi\)
\(110\) 1.27923 + 5.60465i 0.121969 + 0.534383i
\(111\) 0 0
\(112\) −6.12813 + 1.58801i −0.579054 + 0.150053i
\(113\) 0.0806342 + 0.0643036i 0.00758543 + 0.00604918i 0.627275 0.778798i \(-0.284170\pi\)
−0.619690 + 0.784847i \(0.712742\pi\)
\(114\) 0 0
\(115\) 1.99522 0.455395i 0.186055 0.0424658i
\(116\) 4.57228i 0.424526i
\(117\) 0 0
\(118\) 1.97355 0.450450i 0.181680 0.0414673i
\(119\) −8.39555 6.30375i −0.769619 0.577864i
\(120\) 0 0
\(121\) −0.428573 + 1.87770i −0.0389612 + 0.170700i
\(122\) −7.96757 + 9.99102i −0.721350 + 0.904544i
\(123\) 0 0
\(124\) 0.894772 + 0.204226i 0.0803529 + 0.0183400i
\(125\) 2.65947 11.6519i 0.237870 1.04218i
\(126\) 0 0
\(127\) 2.10534 + 9.22408i 0.186818 + 0.818504i 0.978280 + 0.207286i \(0.0664631\pi\)
−0.791462 + 0.611218i \(0.790680\pi\)
\(128\) 3.58003i 0.316433i
\(129\) 0 0
\(130\) −1.32572 5.80837i −0.116274 0.509428i
\(131\) 9.38963 + 4.52181i 0.820376 + 0.395072i 0.796497 0.604643i \(-0.206684\pi\)
0.0238790 + 0.999715i \(0.492398\pi\)
\(132\) 0 0
\(133\) −10.8480 12.8178i −0.940641 1.11144i
\(134\) 10.1227 8.07256i 0.874466 0.697363i
\(135\) 0 0
\(136\) −9.54758 + 7.61394i −0.818698 + 0.652890i
\(137\) −0.174028 + 0.361374i −0.0148682 + 0.0308742i −0.908271 0.418383i \(-0.862597\pi\)
0.893402 + 0.449257i \(0.148311\pi\)
\(138\) 0 0
\(139\) −0.906271 1.88189i −0.0768689 0.159620i 0.858993 0.511988i \(-0.171091\pi\)
−0.935861 + 0.352368i \(0.885377\pi\)
\(140\) 2.10881 + 1.58339i 0.178227 + 0.133821i
\(141\) 0 0
\(142\) 3.58400 1.72596i 0.300762 0.144839i
\(143\) −2.09255 + 9.16807i −0.174988 + 0.766672i
\(144\) 0 0
\(145\) −9.42939 + 7.51968i −0.783068 + 0.624476i
\(146\) 13.2497 1.09655
\(147\) 0 0
\(148\) 4.75465 0.390830
\(149\) −6.31126 + 5.03306i −0.517038 + 0.412324i −0.846938 0.531692i \(-0.821557\pi\)
0.329900 + 0.944016i \(0.392985\pi\)
\(150\) 0 0
\(151\) 3.42041 14.9858i 0.278349 1.21953i −0.621532 0.783389i \(-0.713489\pi\)
0.899880 0.436137i \(-0.143654\pi\)
\(152\) −17.5979 + 8.47468i −1.42737 + 0.687387i
\(153\) 0 0
\(154\) 4.31464 + 8.32916i 0.347684 + 0.671183i
\(155\) 1.05039 + 2.18116i 0.0843693 + 0.175195i
\(156\) 0 0
\(157\) 4.33471 9.00113i 0.345948 0.718368i −0.653302 0.757097i \(-0.726617\pi\)
0.999250 + 0.0387294i \(0.0123311\pi\)
\(158\) 13.4057 10.6907i 1.06650 0.850505i
\(159\) 0 0
\(160\) 4.23255 3.37535i 0.334613 0.266845i
\(161\) 2.96513 1.53598i 0.233685 0.121052i
\(162\) 0 0
\(163\) 0.815328 + 0.392641i 0.0638614 + 0.0307540i 0.465542 0.885026i \(-0.345859\pi\)
−0.401680 + 0.915780i \(0.631574\pi\)
\(164\) 1.38037 + 6.04780i 0.107789 + 0.472254i
\(165\) 0 0
\(166\) 4.07268i 0.316101i
\(167\) 0.422648 + 1.85174i 0.0327055 + 0.143292i 0.988644 0.150273i \(-0.0480154\pi\)
−0.955939 + 0.293565i \(0.905158\pi\)
\(168\) 0 0
\(169\) −0.724159 + 3.17275i −0.0557045 + 0.244057i
\(170\) −7.38304 1.68513i −0.566253 0.129244i
\(171\) 0 0
\(172\) 0.416073 0.521739i 0.0317253 0.0397822i
\(173\) 1.64885 7.22409i 0.125360 0.549237i −0.872771 0.488129i \(-0.837679\pi\)
0.998131 0.0611080i \(-0.0194634\pi\)
\(174\) 0 0
\(175\) −0.182871 6.27008i −0.0138238 0.473973i
\(176\) 7.02690 1.60384i 0.529673 0.120894i
\(177\) 0 0
\(178\) 14.4462i 1.08279i
\(179\) 22.9124 5.22960i 1.71255 0.390879i 0.749885 0.661568i \(-0.230109\pi\)
0.962667 + 0.270689i \(0.0872514\pi\)
\(180\) 0 0
\(181\) 10.1147 + 8.06617i 0.751817 + 0.599554i 0.922601 0.385755i \(-0.126059\pi\)
−0.170785 + 0.985308i \(0.554630\pi\)
\(182\) −4.47147 8.63192i −0.331448 0.639840i
\(183\) 0 0
\(184\) −0.864324 3.78685i −0.0637188 0.279170i
\(185\) 7.81961 + 9.80548i 0.574909 + 0.720913i
\(186\) 0 0
\(187\) 9.34543 + 7.45273i 0.683405 + 0.544998i
\(188\) 4.83763 2.32968i 0.352821 0.169909i
\(189\) 0 0
\(190\) −10.9130 5.25540i −0.791709 0.381267i
\(191\) −8.84660 18.3702i −0.640118 1.32922i −0.928368 0.371663i \(-0.878788\pi\)
0.288250 0.957555i \(-0.406927\pi\)
\(192\) 0 0
\(193\) −3.34801 + 1.61232i −0.240995 + 0.116057i −0.550483 0.834846i \(-0.685557\pi\)
0.309488 + 0.950903i \(0.399842\pi\)
\(194\) 4.70317 + 5.89759i 0.337668 + 0.423422i
\(195\) 0 0
\(196\) 3.97905 + 1.63786i 0.284218 + 0.116990i
\(197\) 22.4887i 1.60225i 0.598495 + 0.801127i \(0.295766\pi\)
−0.598495 + 0.801127i \(0.704234\pi\)
\(198\) 0 0
\(199\) −3.52589 7.32159i −0.249944 0.519014i 0.737815 0.675003i \(-0.235858\pi\)
−0.987759 + 0.155989i \(0.950143\pi\)
\(200\) −7.11336 1.62358i −0.502991 0.114804i
\(201\) 0 0
\(202\) 0.228114 0.473683i 0.0160500 0.0333282i
\(203\) −11.8162 + 15.7372i −0.829334 + 1.10454i
\(204\) 0 0
\(205\) −10.2021 + 12.7931i −0.712549 + 0.893508i
\(206\) −2.54274 1.22452i −0.177161 0.0853161i
\(207\) 0 0
\(208\) −7.28232 + 1.66214i −0.504938 + 0.115249i
\(209\) 11.9202 + 14.9475i 0.824540 + 1.03394i
\(210\) 0 0
\(211\) −7.04725 + 8.83697i −0.485153 + 0.608362i −0.962808 0.270185i \(-0.912915\pi\)
0.477656 + 0.878547i \(0.341487\pi\)
\(212\) −0.0285229 + 0.0592283i −0.00195896 + 0.00406782i
\(213\) 0 0
\(214\) −19.2671 −1.31708
\(215\) 1.76026 0.120049
\(216\) 0 0
\(217\) 2.55191 + 3.01528i 0.173235 + 0.204691i
\(218\) 23.6858 + 5.40613i 1.60421 + 0.366149i
\(219\) 0 0
\(220\) −2.34740 1.87199i −0.158262 0.126209i
\(221\) −9.68512 7.72363i −0.651492 0.519547i
\(222\) 0 0
\(223\) −14.7674 3.37056i −0.988899 0.225710i −0.302670 0.953095i \(-0.597878\pi\)
−0.686229 + 0.727386i \(0.740735\pi\)
\(224\) 5.30391 7.06393i 0.354382 0.471979i
\(225\) 0 0
\(226\) 0.121388 0.00807463
\(227\) 10.2172 0.678137 0.339068 0.940762i \(-0.389888\pi\)
0.339068 + 0.940762i \(0.389888\pi\)
\(228\) 0 0
\(229\) 8.72661 18.1210i 0.576670 1.19747i −0.384912 0.922953i \(-0.625768\pi\)
0.961583 0.274515i \(-0.0885173\pi\)
\(230\) 1.50182 1.88322i 0.0990270 0.124176i
\(231\) 0 0
\(232\) 14.2721 + 17.8966i 0.937009 + 1.17497i
\(233\) 13.2535 3.02504i 0.868269 0.198177i 0.234893 0.972021i \(-0.424526\pi\)
0.633376 + 0.773845i \(0.281669\pi\)
\(234\) 0 0
\(235\) 12.7606 + 6.14516i 0.832407 + 0.400866i
\(236\) −0.659179 + 0.826584i −0.0429089 + 0.0538060i
\(237\) 0 0
\(238\) −12.3515 + 0.360242i −0.800632 + 0.0233510i
\(239\) 4.93834 10.2546i 0.319434 0.663312i −0.677987 0.735073i \(-0.737148\pi\)
0.997422 + 0.0717611i \(0.0228619\pi\)
\(240\) 0 0
\(241\) −10.7608 2.45609i −0.693166 0.158211i −0.138598 0.990349i \(-0.544260\pi\)
−0.554569 + 0.832138i \(0.687117\pi\)
\(242\) 0.983553 + 2.04237i 0.0632252 + 0.131288i
\(243\) 0 0
\(244\) 6.67413i 0.427267i
\(245\) 3.16629 + 10.8996i 0.202287 + 0.696351i
\(246\) 0 0
\(247\) −12.3535 15.4908i −0.786036 0.985658i
\(248\) 4.13976 1.99360i 0.262875 0.126594i
\(249\) 0 0
\(250\) −6.10336 12.6738i −0.386010 0.801558i
\(251\) 8.68576 + 4.18284i 0.548240 + 0.264019i 0.687434 0.726246i \(-0.258737\pi\)
−0.139194 + 0.990265i \(0.544451\pi\)
\(252\) 0 0
\(253\) −3.42548 + 1.64962i −0.215358 + 0.103711i
\(254\) 8.70631 + 6.94305i 0.546283 + 0.435646i
\(255\) 0 0
\(256\) −8.24038 10.3331i −0.515024 0.645819i
\(257\) 4.54669 + 19.9204i 0.283615 + 1.24260i 0.893121 + 0.449817i \(0.148511\pi\)
−0.609506 + 0.792781i \(0.708632\pi\)
\(258\) 0 0
\(259\) 16.3649 + 12.2875i 1.01686 + 0.763507i
\(260\) 2.43273 + 1.94003i 0.150871 + 0.120316i
\(261\) 0 0
\(262\) 11.9586 2.72948i 0.738807 0.168628i
\(263\) 2.13098i 0.131402i 0.997839 + 0.0657008i \(0.0209283\pi\)
−0.997839 + 0.0657008i \(0.979072\pi\)
\(264\) 0 0
\(265\) −0.169055 + 0.0385858i −0.0103850 + 0.00237031i
\(266\) −19.3885 3.83430i −1.18879 0.235096i
\(267\) 0 0
\(268\) −1.50470 + 6.59254i −0.0919144 + 0.402703i
\(269\) 12.2811 15.4000i 0.748793 0.938957i −0.250784 0.968043i \(-0.580688\pi\)
0.999577 + 0.0290862i \(0.00925973\pi\)
\(270\) 0 0
\(271\) −9.93868 2.26844i −0.603732 0.137798i −0.0902801 0.995916i \(-0.528776\pi\)
−0.513452 + 0.858119i \(0.671633\pi\)
\(272\) −2.11275 + 9.25658i −0.128105 + 0.561263i
\(273\) 0 0
\(274\) 0.105048 + 0.460246i 0.00634619 + 0.0278045i
\(275\) 7.14181i 0.430667i
\(276\) 0 0
\(277\) 1.55911 + 6.83089i 0.0936776 + 0.410428i 0.999924 0.0123214i \(-0.00392213\pi\)
−0.906247 + 0.422750i \(0.861065\pi\)
\(278\) −2.21496 1.06667i −0.132844 0.0639744i
\(279\) 0 0
\(280\) 13.1967 0.384890i 0.788651 0.0230016i
\(281\) −19.0575 + 15.1979i −1.13688 + 0.906630i −0.996510 0.0834696i \(-0.973400\pi\)
−0.140368 + 0.990099i \(0.544828\pi\)
\(282\) 0 0
\(283\) −11.2353 + 8.95982i −0.667867 + 0.532606i −0.897691 0.440626i \(-0.854756\pi\)
0.229824 + 0.973232i \(0.426185\pi\)
\(284\) −0.901424 + 1.87183i −0.0534897 + 0.111072i
\(285\) 0 0
\(286\) 4.80230 + 9.97208i 0.283966 + 0.589661i
\(287\) −10.8783 + 24.3831i −0.642127 + 1.43929i
\(288\) 0 0
\(289\) 1.12974 0.544053i 0.0664552 0.0320031i
\(290\) −3.15873 + 13.8393i −0.185487 + 0.812671i
\(291\) 0 0
\(292\) −5.41026 + 4.31453i −0.316611 + 0.252489i
\(293\) 6.11482 0.357232 0.178616 0.983919i \(-0.442838\pi\)
0.178616 + 0.983919i \(0.442838\pi\)
\(294\) 0 0
\(295\) −2.78876 −0.162368
\(296\) 18.6105 14.8413i 1.08171 0.862636i
\(297\) 0 0
\(298\) −2.11419 + 9.26288i −0.122472 + 0.536584i
\(299\) 3.54999 1.70959i 0.205301 0.0988679i
\(300\) 0 0
\(301\) 2.78040 0.720497i 0.160260 0.0415288i
\(302\) −7.84966 16.3000i −0.451697 0.937959i
\(303\) 0 0
\(304\) −6.58903 + 13.6823i −0.377907 + 0.784731i
\(305\) 13.7640 10.9764i 0.788125 0.628508i
\(306\) 0 0
\(307\) 19.0106 15.1604i 1.08499 0.865253i 0.0935262 0.995617i \(-0.470186\pi\)
0.991466 + 0.130364i \(0.0416147\pi\)
\(308\) −4.47404 1.99606i −0.254932 0.113736i
\(309\) 0 0
\(310\) 2.56719 + 1.23629i 0.145806 + 0.0702167i
\(311\) −6.98480 30.6024i −0.396072 1.73530i −0.642632 0.766175i \(-0.722157\pi\)
0.246560 0.969128i \(-0.420700\pi\)
\(312\) 0 0
\(313\) 23.8964i 1.35070i 0.737496 + 0.675351i \(0.236008\pi\)
−0.737496 + 0.675351i \(0.763992\pi\)
\(314\) −2.61655 11.4638i −0.147660 0.646942i
\(315\) 0 0
\(316\) −1.99271 + 8.73065i −0.112099 + 0.491138i
\(317\) −28.8101 6.57572i −1.61814 0.369329i −0.684913 0.728625i \(-0.740160\pi\)
−0.933224 + 0.359296i \(0.883017\pi\)
\(318\) 0 0
\(319\) 13.9699 17.5177i 0.782165 0.980804i
\(320\) 3.14448 13.7769i 0.175782 0.770150i
\(321\) 0 0
\(322\) 1.60136 3.58934i 0.0892401 0.200026i
\(323\) −24.5536 + 5.60420i −1.36620 + 0.311826i
\(324\) 0 0
\(325\) 7.40140i 0.410556i
\(326\) 1.03840 0.237009i 0.0575118 0.0131267i
\(327\) 0 0
\(328\) 24.2808 + 19.3633i 1.34068 + 1.06916i
\(329\) 22.6711 + 4.48347i 1.24990 + 0.247182i
\(330\) 0 0
\(331\) −2.23262 9.78176i −0.122716 0.537654i −0.998490 0.0549329i \(-0.982506\pi\)
0.875774 0.482721i \(-0.160352\pi\)
\(332\) 1.32620 + 1.66300i 0.0727845 + 0.0912688i
\(333\) 0 0
\(334\) 1.74780 + 1.39382i 0.0956353 + 0.0762666i
\(335\) −16.0704 + 7.73910i −0.878020 + 0.422832i
\(336\) 0 0
\(337\) 2.17525 + 1.04754i 0.118493 + 0.0570633i 0.492191 0.870487i \(-0.336196\pi\)
−0.373698 + 0.927550i \(0.621910\pi\)
\(338\) 1.66191 + 3.45099i 0.0903959 + 0.187709i
\(339\) 0 0
\(340\) 3.56345 1.71607i 0.193255 0.0930668i
\(341\) −2.80414 3.51629i −0.151853 0.190418i
\(342\) 0 0
\(343\) 9.46264 + 15.9204i 0.510934 + 0.859620i
\(344\) 3.34091i 0.180130i
\(345\) 0 0
\(346\) −3.78403 7.85762i −0.203431 0.422428i
\(347\) −21.6209 4.93483i −1.16067 0.264916i −0.401533 0.915845i \(-0.631522\pi\)
−0.759139 + 0.650929i \(0.774380\pi\)
\(348\) 0 0
\(349\) −12.3332 + 25.6101i −0.660180 + 1.37088i 0.254648 + 0.967034i \(0.418040\pi\)
−0.914828 + 0.403844i \(0.867674\pi\)
\(350\) −4.76950 5.63555i −0.254940 0.301233i
\(351\) 0 0
\(352\) −6.27065 + 7.86315i −0.334227 + 0.419107i
\(353\) −8.75844 4.21784i −0.466165 0.224493i 0.186031 0.982544i \(-0.440438\pi\)
−0.652195 + 0.758051i \(0.726152\pi\)
\(354\) 0 0
\(355\) −5.34276 + 1.21945i −0.283564 + 0.0647216i
\(356\) −4.70413 5.89880i −0.249319 0.312636i
\(357\) 0 0
\(358\) 17.2464 21.6263i 0.911500 1.14298i
\(359\) −5.14678 + 10.6874i −0.271637 + 0.564059i −0.991508 0.130049i \(-0.958487\pi\)
0.719871 + 0.694108i \(0.244201\pi\)
\(360\) 0 0
\(361\) −21.2821 −1.12011
\(362\) 15.2268 0.800303
\(363\) 0 0
\(364\) 4.63667 + 2.06861i 0.243027 + 0.108425i
\(365\) −17.7957 4.06174i −0.931468 0.212601i
\(366\) 0 0
\(367\) −24.7126 19.7076i −1.28999 1.02873i −0.997368 0.0725000i \(-0.976902\pi\)
−0.292618 0.956230i \(-0.594526\pi\)
\(368\) −2.36111 1.88292i −0.123082 0.0981543i
\(369\) 0 0
\(370\) 14.3913 + 3.28471i 0.748166 + 0.170764i
\(371\) −0.251236 + 0.130144i −0.0130435 + 0.00675676i
\(372\) 0 0
\(373\) 21.5782 1.11728 0.558638 0.829411i \(-0.311324\pi\)
0.558638 + 0.829411i \(0.311324\pi\)
\(374\) 14.0688 0.727480
\(375\) 0 0
\(376\) 11.6633 24.2191i 0.601489 1.24900i
\(377\) −14.4777 + 18.1545i −0.745639 + 0.935002i
\(378\) 0 0
\(379\) 5.85961 + 7.34772i 0.300988 + 0.377427i 0.909208 0.416341i \(-0.136688\pi\)
−0.608221 + 0.793768i \(0.708116\pi\)
\(380\) 6.16741 1.40767i 0.316382 0.0722120i
\(381\) 0 0
\(382\) −21.6214 10.4123i −1.10625 0.532740i
\(383\) 0.146422 0.183607i 0.00748181 0.00938190i −0.778077 0.628170i \(-0.783804\pi\)
0.785558 + 0.618788i \(0.212376\pi\)
\(384\) 0 0
\(385\) −3.24165 12.5095i −0.165210 0.637545i
\(386\) −1.89767 + 3.94056i −0.0965890 + 0.200569i
\(387\) 0 0
\(388\) −3.84089 0.876658i −0.194992 0.0445056i
\(389\) 10.9367 + 22.7103i 0.554513 + 1.15146i 0.970279 + 0.241987i \(0.0777992\pi\)
−0.415766 + 0.909472i \(0.636486\pi\)
\(390\) 0 0
\(391\) 5.00839i 0.253285i
\(392\) 20.6871 6.00951i 1.04486 0.303526i
\(393\) 0 0
\(394\) 16.5031 + 20.6942i 0.831412 + 1.04256i
\(395\) −21.2824 + 10.2491i −1.07083 + 0.515687i
\(396\) 0 0
\(397\) −10.6086 22.0291i −0.532432 1.10561i −0.977661 0.210190i \(-0.932592\pi\)
0.445229 0.895417i \(-0.353122\pi\)
\(398\) −8.61740 4.14992i −0.431951 0.208017i
\(399\) 0 0
\(400\) −5.11105 + 2.46135i −0.255552 + 0.123068i
\(401\) −13.1606 10.4952i −0.657209 0.524107i 0.237141 0.971475i \(-0.423790\pi\)
−0.894350 + 0.447369i \(0.852361\pi\)
\(402\) 0 0
\(403\) 2.90607 + 3.64410i 0.144762 + 0.181525i
\(404\) 0.0611008 + 0.267700i 0.00303988 + 0.0133186i
\(405\) 0 0
\(406\) 0.675262 + 23.1526i 0.0335127 + 1.14904i
\(407\) −18.2164 14.5271i −0.902954 0.720082i
\(408\) 0 0
\(409\) −8.16130 + 1.86276i −0.403550 + 0.0921077i −0.419478 0.907765i \(-0.637787\pi\)
0.0159278 + 0.999873i \(0.494930\pi\)
\(410\) 19.2590i 0.951132i
\(411\) 0 0
\(412\) 1.43702 0.327990i 0.0707967 0.0161589i
\(413\) −4.40495 + 1.14147i −0.216754 + 0.0561683i
\(414\) 0 0
\(415\) −1.24849 + 5.47001i −0.0612861 + 0.268512i
\(416\) 6.49858 8.14896i 0.318619 0.399536i
\(417\) 0 0
\(418\) 21.9381 + 5.00723i 1.07303 + 0.244912i
\(419\) 5.69223 24.9393i 0.278084 1.21836i −0.622129 0.782915i \(-0.713732\pi\)
0.900213 0.435450i \(-0.143411\pi\)
\(420\) 0 0
\(421\) 0.390341 + 1.71019i 0.0190240 + 0.0833497i 0.983549 0.180643i \(-0.0578178\pi\)
−0.964525 + 0.263992i \(0.914961\pi\)
\(422\) 13.3034i 0.647597i
\(423\) 0 0
\(424\) 0.0732345 + 0.320861i 0.00355658 + 0.0155824i
\(425\) −8.47627 4.08195i −0.411159 0.198004i
\(426\) 0 0
\(427\) 17.2480 22.9715i 0.834689 1.11167i
\(428\) 7.86735 6.27400i 0.380283 0.303265i
\(429\) 0 0
\(430\) 1.61980 1.29175i 0.0781136 0.0622935i
\(431\) 11.7556 24.4108i 0.566248 1.17583i −0.399593 0.916693i \(-0.630849\pi\)
0.965841 0.259134i \(-0.0834372\pi\)
\(432\) 0 0
\(433\) −13.8451 28.7496i −0.665351 1.38162i −0.911061 0.412273i \(-0.864735\pi\)
0.245709 0.969344i \(-0.420979\pi\)
\(434\) 4.56100 + 0.901990i 0.218935 + 0.0432969i
\(435\) 0 0
\(436\) −11.4320 + 5.50538i −0.547495 + 0.263660i
\(437\) 1.78254 7.80981i 0.0852704 0.373594i
\(438\) 0 0
\(439\) 23.1323 18.4474i 1.10405 0.880448i 0.110500 0.993876i \(-0.464755\pi\)
0.993546 + 0.113429i \(0.0361833\pi\)
\(440\) −15.0314 −0.716594
\(441\) 0 0
\(442\) −14.5802 −0.693508
\(443\) 2.08603 1.66356i 0.0991105 0.0790380i −0.572681 0.819778i \(-0.694097\pi\)
0.671791 + 0.740740i \(0.265525\pi\)
\(444\) 0 0
\(445\) 4.42852 19.4026i 0.209932 0.919771i
\(446\) −16.0625 + 7.73528i −0.760580 + 0.366276i
\(447\) 0 0
\(448\) −0.672217 23.0482i −0.0317593 1.08892i
\(449\) 7.81973 + 16.2378i 0.369036 + 0.766310i 0.999955 0.00953840i \(-0.00303621\pi\)
−0.630919 + 0.775849i \(0.717322\pi\)
\(450\) 0 0
\(451\) 13.1895 27.3884i 0.621071 1.28967i
\(452\) −0.0495665 + 0.0395279i −0.00233141 + 0.00185924i
\(453\) 0 0
\(454\) 9.40186 7.49774i 0.441251 0.351886i
\(455\) 3.35948 + 12.9643i 0.157495 + 0.607774i
\(456\) 0 0
\(457\) −17.2758 8.31958i −0.808127 0.389173i −0.0162604 0.999868i \(-0.505176\pi\)
−0.791866 + 0.610694i \(0.790890\pi\)
\(458\) −5.26761 23.0789i −0.246139 1.07841i
\(459\) 0 0
\(460\) 1.25802i 0.0586553i
\(461\) 3.12162 + 13.6767i 0.145389 + 0.636989i 0.994131 + 0.108182i \(0.0345031\pi\)
−0.848743 + 0.528806i \(0.822640\pi\)
\(462\) 0 0
\(463\) 4.48852 19.6655i 0.208599 0.913932i −0.756901 0.653529i \(-0.773288\pi\)
0.965500 0.260403i \(-0.0838553\pi\)
\(464\) 17.3512 + 3.96029i 0.805508 + 0.183852i
\(465\) 0 0
\(466\) 9.97607 12.5096i 0.462133 0.579496i
\(467\) 8.78197 38.4763i 0.406381 1.78047i −0.194257 0.980951i \(-0.562229\pi\)
0.600638 0.799521i \(-0.294913\pi\)
\(468\) 0 0
\(469\) −22.2161 + 18.8020i −1.02585 + 0.868197i
\(470\) 16.2519 3.70938i 0.749643 0.171101i
\(471\) 0 0
\(472\) 5.29296i 0.243628i
\(473\) −3.18819 + 0.727683i −0.146593 + 0.0334589i
\(474\) 0 0
\(475\) −11.7646 9.38197i −0.539798 0.430474i
\(476\) 4.92620 4.16916i 0.225792 0.191093i
\(477\) 0 0
\(478\) −2.98091 13.0602i −0.136344 0.597360i
\(479\) −15.8455 19.8697i −0.724001 0.907869i 0.274556 0.961571i \(-0.411469\pi\)
−0.998557 + 0.0537025i \(0.982898\pi\)
\(480\) 0 0
\(481\) 18.8786 + 15.0551i 0.860788 + 0.686456i
\(482\) −11.7045 + 5.63660i −0.533127 + 0.256740i
\(483\) 0 0
\(484\) −1.06667 0.513684i −0.0484852 0.0233493i
\(485\) −4.50889 9.36281i −0.204738 0.425143i
\(486\) 0 0
\(487\) −4.73926 + 2.28231i −0.214757 + 0.103421i −0.538170 0.842837i \(-0.680884\pi\)
0.323413 + 0.946258i \(0.395170\pi\)
\(488\) −20.8329 26.1236i −0.943060 1.18256i
\(489\) 0 0
\(490\) 10.9122 + 7.70633i 0.492962 + 0.348136i
\(491\) 32.1882i 1.45263i −0.687361 0.726316i \(-0.741231\pi\)
0.687361 0.726316i \(-0.258769\pi\)
\(492\) 0 0
\(493\) 12.8063 + 26.5926i 0.576768 + 1.19767i
\(494\) −22.7355 5.18923i −1.02292 0.233475i
\(495\) 0 0
\(496\) 1.55002 3.21864i 0.0695978 0.144521i
\(497\) −7.93996 + 4.11303i −0.356156 + 0.184494i
\(498\) 0 0
\(499\) −16.9252 + 21.2236i −0.757677 + 0.950097i −0.999797 0.0201497i \(-0.993586\pi\)
0.242120 + 0.970246i \(0.422157\pi\)
\(500\) 6.61916 + 3.18762i 0.296018 + 0.142555i
\(501\) 0 0
\(502\) 11.0622 2.52487i 0.493730 0.112691i
\(503\) 24.4642 + 30.6772i 1.09081 + 1.36783i 0.924247 + 0.381796i \(0.124694\pi\)
0.166559 + 0.986031i \(0.446734\pi\)
\(504\) 0 0
\(505\) −0.451588 + 0.566274i −0.0200954 + 0.0251988i
\(506\) −1.94158 + 4.03174i −0.0863138 + 0.179233i
\(507\) 0 0
\(508\) −5.81593 −0.258040
\(509\) 43.5926 1.93221 0.966104 0.258153i \(-0.0831139\pi\)
0.966104 + 0.258153i \(0.0831139\pi\)
\(510\) 0 0
\(511\) −29.7715 + 0.868307i −1.31701 + 0.0384116i
\(512\) −22.1462 5.05472i −0.978733 0.223389i
\(513\) 0 0
\(514\) 18.8022 + 14.9943i 0.829329 + 0.661368i
\(515\) 3.03976 + 2.42413i 0.133948 + 0.106820i
\(516\) 0 0
\(517\) −25.6523 5.85497i −1.12819 0.257501i
\(518\) 24.0760 0.702196i 1.05784 0.0308527i
\(519\) 0 0
\(520\) 15.5778 0.683130
\(521\) 8.32018 0.364514 0.182257 0.983251i \(-0.441660\pi\)
0.182257 + 0.983251i \(0.441660\pi\)
\(522\) 0 0
\(523\) −12.8076 + 26.5953i −0.560039 + 1.16293i 0.408197 + 0.912894i \(0.366158\pi\)
−0.968236 + 0.250039i \(0.919557\pi\)
\(524\) −3.99426 + 5.00865i −0.174490 + 0.218804i
\(525\) 0 0
\(526\) 1.56379 + 1.96093i 0.0681845 + 0.0855007i
\(527\) 5.77604 1.31834i 0.251608 0.0574279i
\(528\) 0 0
\(529\) −19.2870 9.28814i −0.838566 0.403832i
\(530\) −0.127250 + 0.159566i −0.00552737 + 0.00693111i
\(531\) 0 0
\(532\) 9.16549 4.74787i 0.397375 0.205846i
\(533\) −13.6690 + 28.3839i −0.592068 + 1.22944i
\(534\) 0 0
\(535\) 25.8777 + 5.90641i 1.11879 + 0.255356i
\(536\) 14.6885 + 30.5011i 0.634448 + 1.31745i
\(537\) 0 0
\(538\) 23.1835i 0.999513i
\(539\) −10.2406 18.4325i −0.441095 0.793943i
\(540\) 0 0
\(541\) −26.2932 32.9706i −1.13043 1.41752i −0.895250 0.445565i \(-0.853003\pi\)
−0.235182 0.971951i \(-0.575569\pi\)
\(542\) −10.8103 + 5.20595i −0.464341 + 0.223615i
\(543\) 0 0
\(544\) −5.74835 11.9366i −0.246458 0.511776i
\(545\) −30.1551 14.5219i −1.29170 0.622051i
\(546\) 0 0
\(547\) 22.5823 10.8751i 0.965549 0.464984i 0.116438 0.993198i \(-0.462852\pi\)
0.849111 + 0.528214i \(0.177138\pi\)
\(548\) −0.192765 0.153725i −0.00823452 0.00656681i
\(549\) 0 0
\(550\) 5.24093 + 6.57192i 0.223474 + 0.280227i
\(551\) 10.5049 + 46.0249i 0.447523 + 1.96073i
\(552\) 0 0
\(553\) −29.4213 + 24.9000i −1.25112 + 1.05885i
\(554\) 6.44746 + 5.14168i 0.273926 + 0.218449i
\(555\) 0 0
\(556\) 1.25177 0.285709i 0.0530870 0.0121168i
\(557\) 38.6766i 1.63878i 0.573237 + 0.819389i \(0.305687\pi\)
−0.573237 + 0.819389i \(0.694313\pi\)
\(558\) 0 0
\(559\) 3.30407 0.754133i 0.139747 0.0318964i
\(560\) 7.83528 6.63118i 0.331101 0.280219i
\(561\) 0 0
\(562\) −6.38404 + 27.9703i −0.269294 + 1.17986i
\(563\) 16.3519 20.5046i 0.689150 0.864167i −0.307011 0.951706i \(-0.599329\pi\)
0.996161 + 0.0875387i \(0.0279001\pi\)
\(564\) 0 0
\(565\) −0.163036 0.0372120i −0.00685899 0.00156552i
\(566\) −3.76367 + 16.4897i −0.158199 + 0.693114i
\(567\) 0 0
\(568\) 2.31447 + 10.1404i 0.0971131 + 0.425480i
\(569\) 0.617863i 0.0259022i 0.999916 + 0.0129511i \(0.00412257\pi\)
−0.999916 + 0.0129511i \(0.995877\pi\)
\(570\) 0 0
\(571\) 7.72061 + 33.8262i 0.323098 + 1.41558i 0.832008 + 0.554763i \(0.187191\pi\)
−0.508911 + 0.860819i \(0.669952\pi\)
\(572\) −5.20815 2.50811i −0.217764 0.104870i
\(573\) 0 0
\(574\) 7.88294 + 30.4203i 0.329028 + 1.26972i
\(575\) 2.33956 1.86573i 0.0975663 0.0778065i
\(576\) 0 0
\(577\) 20.0054 15.9538i 0.832837 0.664165i −0.111275 0.993790i \(-0.535494\pi\)
0.944112 + 0.329624i \(0.106922\pi\)
\(578\) 0.640342 1.32968i 0.0266347 0.0553076i
\(579\) 0 0
\(580\) −3.21671 6.67957i −0.133567 0.277354i
\(581\) 0.266899 + 9.15112i 0.0110728 + 0.379652i
\(582\) 0 0
\(583\) 0.290242 0.139773i 0.0120206 0.00578882i
\(584\) −7.70905 + 33.7755i −0.319003 + 1.39764i
\(585\) 0 0
\(586\) 5.62688 4.48729i 0.232444 0.185368i
\(587\) 28.4634 1.17481 0.587405 0.809293i \(-0.300150\pi\)
0.587405 + 0.809293i \(0.300150\pi\)
\(588\) 0 0
\(589\) 9.47605 0.390454
\(590\) −2.56622 + 2.04650i −0.105650 + 0.0842529i
\(591\) 0 0
\(592\) 4.11825 18.0432i 0.169259 0.741572i
\(593\) 19.9794 9.62156i 0.820455 0.395110i 0.0239281 0.999714i \(-0.492383\pi\)
0.796527 + 0.604604i \(0.206668\pi\)
\(594\) 0 0
\(595\) 16.6998 + 3.30257i 0.684624 + 0.135392i
\(596\) −2.15300 4.47076i −0.0881905 0.183129i
\(597\) 0 0
\(598\) 2.01216 4.17829i 0.0822832 0.170863i
\(599\) −11.2925 + 9.00546i −0.461398 + 0.367953i −0.826427 0.563043i \(-0.809630\pi\)
0.365029 + 0.930996i \(0.381059\pi\)
\(600\) 0 0
\(601\) 3.05140 2.43341i 0.124469 0.0992610i −0.559277 0.828981i \(-0.688921\pi\)
0.683746 + 0.729720i \(0.260350\pi\)
\(602\) 2.02981 2.70337i 0.0827288 0.110181i
\(603\) 0 0
\(604\) 8.51305 + 4.09967i 0.346391 + 0.166813i
\(605\) −0.694913 3.04461i −0.0282522 0.123781i
\(606\) 0 0
\(607\) 40.6191i 1.64868i 0.566097 + 0.824338i \(0.308453\pi\)
−0.566097 + 0.824338i \(0.691547\pi\)
\(608\) −4.71531 20.6591i −0.191231 0.837839i
\(609\) 0 0
\(610\) 4.61077 20.2011i 0.186685 0.817918i
\(611\) 26.5847 + 6.06779i 1.07550 + 0.245477i
\(612\) 0 0
\(613\) −6.96530 + 8.73421i −0.281326 + 0.352771i −0.902338 0.431030i \(-0.858150\pi\)
0.621012 + 0.783801i \(0.286722\pi\)
\(614\) 6.36831 27.9014i 0.257004 1.12601i
\(615\) 0 0
\(616\) −23.7427 + 6.15254i −0.956620 + 0.247893i
\(617\) −26.4798 + 6.04385i −1.06604 + 0.243316i −0.719338 0.694660i \(-0.755555\pi\)
−0.346699 + 0.937976i \(0.612698\pi\)
\(618\) 0 0
\(619\) 13.0186i 0.523262i 0.965168 + 0.261631i \(0.0842603\pi\)
−0.965168 + 0.261631i \(0.915740\pi\)
\(620\) −1.45084 + 0.331144i −0.0582670 + 0.0132991i
\(621\) 0 0
\(622\) −28.8846 23.0347i −1.15817 0.923608i
\(623\) −0.946715 32.4598i −0.0379293 1.30048i
\(624\) 0 0
\(625\) 1.67438 + 7.33593i 0.0669751 + 0.293437i
\(626\) 17.5361 + 21.9895i 0.700882 + 0.878878i
\(627\) 0 0
\(628\) 4.80141 + 3.82900i 0.191597 + 0.152794i
\(629\) 27.6532 13.3171i 1.10261 0.530988i
\(630\) 0 0
\(631\) −13.3941 6.45024i −0.533209 0.256780i 0.147848 0.989010i \(-0.452765\pi\)
−0.681057 + 0.732230i \(0.738480\pi\)
\(632\) 19.4524 + 40.3933i 0.773774 + 1.60676i
\(633\) 0 0
\(634\) −31.3367 + 15.0909i −1.24454 + 0.599338i
\(635\) −9.56501 11.9941i −0.379576 0.475973i
\(636\) 0 0
\(637\) 10.6129 + 19.1025i 0.420497 + 0.756867i
\(638\) 26.3715i 1.04406i
\(639\) 0 0
\(640\) −2.51864 5.23001i −0.0995580 0.206734i
\(641\) 3.54318 + 0.808708i 0.139947 + 0.0319420i 0.291921 0.956443i \(-0.405706\pi\)
−0.151973 + 0.988385i \(0.548563\pi\)
\(642\) 0 0
\(643\) −9.21696 + 19.1392i −0.363482 + 0.754777i −0.999862 0.0165979i \(-0.994716\pi\)
0.636381 + 0.771375i \(0.280431\pi\)
\(644\) 0.514922 + 1.98709i 0.0202908 + 0.0783022i
\(645\) 0 0
\(646\) −18.4817 + 23.1753i −0.727154 + 0.911822i
\(647\) −39.8148 19.1738i −1.56528 0.753799i −0.567695 0.823239i \(-0.692165\pi\)
−0.997586 + 0.0694398i \(0.977879\pi\)
\(648\) 0 0
\(649\) 5.05100 1.15286i 0.198269 0.0452536i
\(650\) −5.43143 6.81080i −0.213038 0.267141i
\(651\) 0 0
\(652\) −0.346833 + 0.434915i −0.0135830 + 0.0170326i
\(653\) −10.1195 + 21.0133i −0.396006 + 0.822314i 0.603679 + 0.797227i \(0.293701\pi\)
−0.999685 + 0.0250873i \(0.992014\pi\)
\(654\) 0 0
\(655\) −16.8984 −0.660273
\(656\) 24.1462 0.942750
\(657\) 0 0
\(658\) 24.1522 12.5112i 0.941550 0.487738i
\(659\) 1.63674 + 0.373574i 0.0637582 + 0.0145524i 0.254281 0.967130i \(-0.418161\pi\)
−0.190523 + 0.981683i \(0.561018\pi\)
\(660\) 0 0
\(661\) 19.4053 + 15.4752i 0.754778 + 0.601915i 0.923433 0.383760i \(-0.125371\pi\)
−0.168655 + 0.985675i \(0.553942\pi\)
\(662\) −9.23270 7.36283i −0.358839 0.286164i
\(663\) 0 0
\(664\) 10.3819 + 2.36960i 0.402895 + 0.0919582i
\(665\) 24.8653 + 11.0935i 0.964234 + 0.430186i
\(666\) 0 0
\(667\) −9.38807 −0.363508
\(668\) −1.16755 −0.0451739
\(669\) 0 0
\(670\) −9.10880 + 18.9146i −0.351904 + 0.730736i
\(671\) −20.3918 + 25.5705i −0.787216 + 0.987137i
\(672\) 0 0
\(673\) −28.7486 36.0496i −1.10818 1.38961i −0.912566 0.408930i \(-0.865902\pi\)
−0.195612 0.980681i \(-0.562669\pi\)
\(674\) 2.77040 0.632325i 0.106712 0.0243562i
\(675\) 0 0
\(676\) −1.80236 0.867971i −0.0693215 0.0333835i
\(677\) −13.8596 + 17.3794i −0.532669 + 0.667945i −0.973245 0.229770i \(-0.926203\pi\)
0.440576 + 0.897715i \(0.354774\pi\)
\(678\) 0 0
\(679\) −10.9543 12.9434i −0.420387 0.496721i
\(680\) 8.59131 17.8400i 0.329462 0.684134i
\(681\) 0 0
\(682\) −5.16077 1.17791i −0.197616 0.0451046i
\(683\) 6.17866 + 12.8301i 0.236420 + 0.490931i 0.985096 0.172005i \(-0.0550245\pi\)
−0.748676 + 0.662936i \(0.769310\pi\)
\(684\) 0 0
\(685\) 0.650358i 0.0248489i
\(686\) 20.3905 + 7.70595i 0.778514 + 0.294215i
\(687\) 0 0
\(688\) −1.61954 2.03084i −0.0617445 0.0774252i
\(689\) −0.300792 + 0.144854i −0.0114593 + 0.00551849i
\(690\) 0 0
\(691\) 11.3856 + 23.6425i 0.433130 + 0.899404i 0.997278 + 0.0737304i \(0.0234904\pi\)
−0.564148 + 0.825674i \(0.690795\pi\)
\(692\) 4.10383 + 1.97630i 0.156004 + 0.0751276i
\(693\) 0 0
\(694\) −23.5170 + 11.3252i −0.892693 + 0.429898i
\(695\) 2.64791 + 2.11164i 0.100441 + 0.0800990i
\(696\) 0 0
\(697\) 24.9673 + 31.3080i 0.945705 + 1.18588i
\(698\) 7.44463 + 32.6171i 0.281784 + 1.23457i
\(699\) 0 0
\(700\) 3.78264 + 0.748061i 0.142971 + 0.0282740i
\(701\) −6.68543 5.33145i −0.252505 0.201366i 0.489054 0.872253i \(-0.337342\pi\)
−0.741559 + 0.670887i \(0.765913\pi\)
\(702\) 0 0
\(703\) 47.8607 10.9239i 1.80510 0.412002i
\(704\) 26.2526i 0.989431i
\(705\) 0 0
\(706\) −11.1548 + 2.54600i −0.419815 + 0.0958200i
\(707\) −0.481518 + 1.07929i −0.0181094 + 0.0405910i
\(708\) 0 0
\(709\) −2.32873 + 10.2028i −0.0874573 + 0.383176i −0.999646 0.0265942i \(-0.991534\pi\)
0.912189 + 0.409770i \(0.134391\pi\)
\(710\) −4.02154 + 5.04286i −0.150926 + 0.189255i
\(711\) 0 0
\(712\) −36.8255 8.40517i −1.38009 0.314997i
\(713\) −0.419328 + 1.83720i −0.0157040 + 0.0688036i
\(714\) 0 0
\(715\) −3.39298 14.8656i −0.126890 0.555943i
\(716\) 14.4466i 0.539896i
\(717\) 0 0
\(718\) 3.10673 + 13.6115i 0.115942 + 0.507976i
\(719\) −24.6264 11.8595i −0.918411 0.442283i −0.0859072 0.996303i \(-0.527379\pi\)
−0.832503 + 0.554020i \(0.813093\pi\)
\(720\) 0 0
\(721\) 5.79365 + 2.58479i 0.215767 + 0.0962628i
\(722\) −19.5839 + 15.6176i −0.728836 + 0.581228i
\(723\) 0 0
\(724\) −6.21756 + 4.95834i −0.231074 + 0.184275i
\(725\) −7.65150 + 15.8885i −0.284169 + 0.590084i
\(726\) 0 0
\(727\) −8.59104 17.8395i −0.318624 0.661629i 0.678725 0.734392i \(-0.262533\pi\)
−0.997349 + 0.0727629i \(0.976818\pi\)
\(728\) 24.6057 6.37618i 0.911948 0.236317i
\(729\) 0 0
\(730\) −19.3563 + 9.32150i −0.716408 + 0.345004i
\(731\) 0.958581 4.19982i 0.0354544 0.155336i
\(732\) 0 0
\(733\) 4.46629 3.56175i 0.164966 0.131556i −0.537527 0.843246i \(-0.680641\pi\)
0.702493 + 0.711690i \(0.252070\pi\)
\(734\) −37.2028 −1.37318
\(735\) 0 0
\(736\) 4.21401 0.155330
\(737\) 25.9074 20.6605i 0.954312 0.761039i
\(738\) 0 0
\(739\) 1.07259 4.69931i 0.0394558 0.172867i −0.951361 0.308078i \(-0.900314\pi\)
0.990817 + 0.135211i \(0.0431713\pi\)
\(740\) −6.94599 + 3.34501i −0.255340 + 0.122965i
\(741\) 0 0
\(742\) −0.135684 + 0.304126i −0.00498110 + 0.0111648i
\(743\) 4.67324 + 9.70408i 0.171444 + 0.356008i 0.968932 0.247327i \(-0.0795523\pi\)
−0.797488 + 0.603335i \(0.793838\pi\)
\(744\) 0 0
\(745\) 5.67913 11.7928i 0.208067 0.432056i
\(746\) 19.8563 15.8349i 0.726992 0.579757i
\(747\) 0 0
\(748\) −5.74471 + 4.58125i −0.210047 + 0.167507i
\(749\) 43.2923 1.26265i 1.58187 0.0461363i
\(750\) 0 0
\(751\) 41.2195 + 19.8503i 1.50412 + 0.724346i 0.990986 0.133962i \(-0.0427700\pi\)
0.513134 + 0.858308i \(0.328484\pi\)
\(752\) −4.65069 20.3760i −0.169593 0.743036i
\(753\) 0 0
\(754\) 27.3301i 0.995303i
\(755\) 5.54605 + 24.2988i 0.201841 + 0.884324i
\(756\) 0 0
\(757\) −4.65249 + 20.3839i −0.169098 + 0.740866i 0.817263 + 0.576265i \(0.195491\pi\)
−0.986360 + 0.164600i \(0.947367\pi\)
\(758\) 10.7841 + 2.46139i 0.391695 + 0.0894018i
\(759\) 0 0
\(760\) 19.7463 24.7610i 0.716272 0.898177i
\(761\) 10.3439 45.3197i 0.374967 1.64284i −0.337641 0.941275i \(-0.609629\pi\)
0.712608 0.701562i \(-0.247514\pi\)
\(762\) 0 0
\(763\) −53.5752 10.5951i −1.93955 0.383568i
\(764\) 12.2192 2.78896i 0.442077 0.100901i
\(765\) 0 0
\(766\) 0.276406i 0.00998696i
\(767\) −5.23460 + 1.19476i −0.189010 + 0.0431404i
\(768\) 0 0
\(769\) 33.0698 + 26.3723i 1.19253 + 0.951009i 0.999544 0.0301926i \(-0.00961206\pi\)
0.192984 + 0.981202i \(0.438183\pi\)
\(770\) −12.1630 9.13248i −0.438323 0.329112i
\(771\) 0 0
\(772\) −0.508296 2.22699i −0.0182940 0.0801511i
\(773\) 11.8115 + 14.8111i 0.424829 + 0.532719i 0.947475 0.319831i \(-0.103626\pi\)
−0.522645 + 0.852550i \(0.675055\pi\)
\(774\) 0 0
\(775\) 2.76753 + 2.20703i 0.0994128 + 0.0792790i
\(776\) −17.7703 + 8.55772i −0.637916 + 0.307204i
\(777\) 0 0
\(778\) 26.7297 + 12.8723i 0.958306 + 0.461496i
\(779\) 27.7898 + 57.7062i 0.995674 + 2.06754i
\(780\) 0 0
\(781\) 9.17269 4.41733i 0.328225 0.158065i
\(782\) −3.67535 4.60874i −0.131430 0.164808i
\(783\) 0 0
\(784\) 9.66190 13.6813i 0.345068 0.488618i
\(785\) 16.1992i 0.578173i
\(786\) 0 0
\(787\) −8.74293 18.1549i −0.311652 0.647152i 0.685033 0.728512i \(-0.259788\pi\)
−0.996685 + 0.0813603i \(0.974074\pi\)
\(788\) −13.4774 3.07612i −0.480112 0.109582i
\(789\) 0 0
\(790\) −12.0630 + 25.0491i −0.429182 + 0.891206i
\(791\) −0.272754 + 0.00795506i −0.00969800 + 0.000282849i
\(792\) 0 0
\(793\) 21.1330 26.4999i 0.750454 0.941040i
\(794\) −25.9279 12.4862i −0.920145 0.443119i
\(795\) 0 0
\(796\) 4.87009 1.11157i 0.172616 0.0393984i
\(797\) −19.9227 24.9823i −0.705700 0.884919i 0.291735 0.956499i \(-0.405767\pi\)
−0.997435 + 0.0715797i \(0.977196\pi\)
\(798\) 0 0
\(799\) 21.6108 27.0990i 0.764534 0.958695i
\(800\) 3.43452 7.13184i 0.121428 0.252149i
\(801\) 0 0
\(802\) −19.8122 −0.699594
\(803\) 33.9106 1.19668
\(804\) 0 0
\(805\) −3.25110 + 4.32993i −0.114586 + 0.152610i
\(806\) 5.34835 + 1.22073i 0.188388 + 0.0429983i
\(807\) 0 0
\(808\) 1.07477 + 0.857098i 0.0378102 + 0.0301526i
\(809\) −28.6281 22.8302i −1.00651 0.802666i −0.0261062 0.999659i \(-0.508311\pi\)
−0.980405 + 0.196993i \(0.936882\pi\)
\(810\) 0 0
\(811\) −31.4471 7.17759i −1.10426 0.252039i −0.368731 0.929536i \(-0.620207\pi\)
−0.735525 + 0.677497i \(0.763065\pi\)
\(812\) −7.81496 9.23401i −0.274251 0.324050i
\(813\) 0 0
\(814\) −27.4233 −0.961188
\(815\) −1.46733 −0.0513984
\(816\) 0 0
\(817\) 2.98952 6.20779i 0.104590 0.217183i
\(818\) −6.14309 + 7.70319i −0.214788 + 0.269336i
\(819\) 0 0
\(820\) −6.27134 7.86401i −0.219005 0.274623i
\(821\) 1.83900 0.419740i 0.0641816 0.0146490i −0.190310 0.981724i \(-0.560949\pi\)
0.254491 + 0.967075i \(0.418092\pi\)
\(822\) 0 0
\(823\) 8.90635 + 4.28907i 0.310456 + 0.149508i 0.582623 0.812742i \(-0.302026\pi\)
−0.272168 + 0.962250i \(0.587741\pi\)
\(824\) 4.60091 5.76936i 0.160280 0.200985i
\(825\) 0 0
\(826\) −3.21580 + 4.28291i −0.111892 + 0.149021i
\(827\) −0.402679 + 0.836172i −0.0140025 + 0.0290765i −0.907853 0.419289i \(-0.862279\pi\)
0.893850 + 0.448366i \(0.147994\pi\)
\(828\) 0 0
\(829\) 13.6428 + 3.11387i 0.473833 + 0.108149i 0.452767 0.891629i \(-0.350437\pi\)
0.0210656 + 0.999778i \(0.493294\pi\)
\(830\) 2.86523 + 5.94971i 0.0994536 + 0.206518i
\(831\) 0 0
\(832\) 27.2068i 0.943226i
\(833\) 27.7297 1.61889i 0.960778 0.0560913i
\(834\) 0 0
\(835\) −1.92018 2.40783i −0.0664507 0.0833265i
\(836\) −10.5885 + 5.09915i −0.366211 + 0.176358i
\(837\) 0 0
\(838\) −13.0634 27.1264i −0.451267 0.937066i
\(839\) −35.6979 17.1912i −1.23243 0.593507i −0.299683 0.954039i \(-0.596881\pi\)
−0.932747 + 0.360532i \(0.882595\pi\)
\(840\) 0 0
\(841\) 23.7189 11.4224i 0.817893 0.393876i
\(842\) 1.61420 + 1.28728i 0.0556289 + 0.0443626i
\(843\) 0 0
\(844\) −4.33200 5.43216i −0.149114 0.186983i
\(845\) −1.17419 5.14448i −0.0403935 0.176975i
\(846\) 0 0
\(847\) −2.34384 4.52465i −0.0805353 0.155469i
\(848\) 0.200058 + 0.159541i 0.00687002 + 0.00547866i
\(849\) 0 0
\(850\) −10.7954 + 2.46398i −0.370279 + 0.0845137i
\(851\) 9.76252i 0.334655i
\(852\) 0 0
\(853\) −17.8729 + 4.07937i −0.611955 + 0.139675i −0.517255 0.855831i \(-0.673046\pi\)
−0.0946999 + 0.995506i \(0.530189\pi\)
\(854\) −0.985675 33.7957i −0.0337291 1.15646i
\(855\) 0 0
\(856\) 11.2102 49.1149i 0.383155 1.67871i
\(857\) 34.8821 43.7407i 1.19155 1.49416i 0.365263 0.930904i \(-0.380979\pi\)
0.826286 0.563251i \(-0.190449\pi\)
\(858\) 0 0
\(859\) 41.0178 + 9.36205i 1.39951 + 0.319429i 0.854696 0.519128i \(-0.173743\pi\)
0.544814 + 0.838557i \(0.316600\pi\)
\(860\) −0.240778 + 1.05492i −0.00821046 + 0.0359724i
\(861\) 0 0
\(862\) −7.09600 31.0896i −0.241691 1.05892i
\(863\) 32.2608i 1.09817i 0.835766 + 0.549085i \(0.185024\pi\)
−0.835766 + 0.549085i \(0.814976\pi\)
\(864\) 0 0
\(865\) 2.67354 + 11.7136i 0.0909032 + 0.398273i
\(866\) −33.8378 16.2954i −1.14986 0.553741i
\(867\) 0 0
\(868\) −2.15611 + 1.11690i −0.0731832 + 0.0379101i
\(869\) 34.3098 27.3612i 1.16388 0.928164i
\(870\) 0 0
\(871\) −26.8491 + 21.4115i −0.909748 + 0.725500i
\(872\) −27.5621 + 57.2333i −0.933370 + 1.93816i
\(873\) 0 0
\(874\) −4.09084 8.49471i −0.138375 0.287338i
\(875\) 14.5445 + 28.0773i 0.491694 + 0.949187i
\(876\) 0 0
\(877\) 36.2669 17.4652i 1.22465 0.589758i 0.294044 0.955792i \(-0.404999\pi\)
0.930602 + 0.366034i \(0.119285\pi\)
\(878\) 7.74904 33.9508i 0.261517 1.14578i
\(879\) 0 0
\(880\) −9.13714 + 7.28663i −0.308013 + 0.245632i
\(881\) −13.8361 −0.466150 −0.233075 0.972459i \(-0.574879\pi\)
−0.233075 + 0.972459i \(0.574879\pi\)
\(882\) 0 0
\(883\) 8.08344 0.272029 0.136015 0.990707i \(-0.456571\pi\)
0.136015 + 0.990707i \(0.456571\pi\)
\(884\) 5.95352 4.74777i 0.200239 0.159685i
\(885\) 0 0
\(886\) 0.698795 3.06162i 0.0234765 0.102857i
\(887\) 3.19597 1.53910i 0.107310 0.0516778i −0.379459 0.925209i \(-0.623890\pi\)
0.486769 + 0.873531i \(0.338175\pi\)
\(888\) 0 0
\(889\) −20.0177 15.0301i −0.671371 0.504095i
\(890\) −10.1632 21.1042i −0.340672 0.707413i
\(891\) 0 0
\(892\) 4.03993 8.38900i 0.135267 0.280885i
\(893\) 43.3435 34.5653i 1.45043 1.15668i
\(894\) 0 0
\(895\) −29.7932 + 23.7593i −0.995876 + 0.794185i
\(896\) −6.11900 7.23009i −0.204421 0.241540i
\(897\) 0 0
\(898\) 19.1117 + 9.20369i 0.637765 + 0.307131i
\(899\) −2.47119 10.8270i −0.0824189 0.361101i
\(900\) 0 0
\(901\) 0.424363i 0.0141376i
\(902\) −7.96155 34.8818i −0.265091 1.16144i
\(903\) 0 0
\(904\) −0.0706270 + 0.309437i −0.00234902 + 0.0102917i
\(905\) −20.4511 4.66782i −0.679817 0.155164i
\(906\) 0 0
\(907\) 7.87768 9.87830i 0.261574 0.328003i −0.633650 0.773620i \(-0.718444\pi\)
0.895224 + 0.445616i \(0.147015\pi\)
\(908\) −1.39756 + 6.12310i −0.0463796 + 0.203202i
\(909\) 0 0
\(910\) 12.6051 + 9.46444i 0.417854 + 0.313743i
\(911\) 14.2777 3.25879i 0.473041 0.107969i 0.0206474 0.999787i \(-0.493427\pi\)
0.452394 + 0.891818i \(0.350570\pi\)
\(912\) 0 0
\(913\) 10.4234i 0.344964i
\(914\) −22.0024 + 5.02192i −0.727776 + 0.166110i
\(915\) 0 0
\(916\) 9.66616 + 7.70850i 0.319379 + 0.254696i
\(917\) −26.6916 + 6.91671i −0.881435 + 0.228410i
\(918\) 0 0
\(919\) −5.83118 25.5481i −0.192353 0.842753i −0.975339 0.220714i \(-0.929161\pi\)
0.782986 0.622040i \(-0.213696\pi\)
\(920\) 3.92682 + 4.92408i 0.129463 + 0.162342i
\(921\) 0 0
\(922\) 12.9090 + 10.2946i 0.425136 + 0.339035i
\(923\) −9.50610 + 4.57790i −0.312897 + 0.150683i
\(924\) 0 0
\(925\) 16.5222 + 7.95668i 0.543247 + 0.261614i
\(926\) −10.3009 21.3901i −0.338509 0.702922i
\(927\) 0 0
\(928\) −22.3747 + 10.7751i −0.734487 + 0.353710i
\(929\) −19.2409 24.1274i −0.631274 0.791593i 0.358607 0.933489i \(-0.383252\pi\)
−0.989882 + 0.141895i \(0.954680\pi\)
\(930\) 0 0
\(931\) 43.8164 + 7.34488i 1.43602 + 0.240719i
\(932\) 8.35657i 0.273729i
\(933\) 0 0
\(934\) −20.1542 41.8506i −0.659465 1.36939i
\(935\) −18.8958 4.31283i −0.617957 0.141045i
\(936\) 0 0
\(937\) 17.1374 35.5862i 0.559855 1.16255i −0.408451 0.912780i \(-0.633931\pi\)
0.968305 0.249770i \(-0.0803550\pi\)
\(938\) −6.64572 + 33.6047i −0.216990 + 1.09723i
\(939\) 0 0
\(940\) −5.42823 + 6.80678i −0.177049 + 0.222013i
\(941\) −8.05728 3.88018i −0.262660 0.126490i 0.297920 0.954591i \(-0.403707\pi\)
−0.560579 + 0.828101i \(0.689422\pi\)
\(942\) 0 0
\(943\) −12.4177 + 2.83426i −0.404376 + 0.0922961i
\(944\) 2.56582 + 3.21744i 0.0835103 + 0.104719i
\(945\) 0 0
\(946\) −2.39978 + 3.00923i −0.0780235 + 0.0978384i
\(947\) 6.37741 13.2428i 0.207238 0.430334i −0.771280 0.636496i \(-0.780383\pi\)
0.978518 + 0.206162i \(0.0660974\pi\)
\(948\) 0 0
\(949\) −35.1432 −1.14080
\(950\) −17.7107 −0.574610
\(951\) 0 0
\(952\) 6.26816 31.6956i 0.203152 1.02726i
\(953\) −26.9110 6.14226i −0.871733 0.198967i −0.236823 0.971553i \(-0.576106\pi\)
−0.634911 + 0.772585i \(0.718963\pi\)
\(954\) 0 0
\(955\) 25.8477 + 20.6129i 0.836412 + 0.667016i
\(956\) 5.47002 + 4.36220i 0.176913 + 0.141084i
\(957\) 0 0
\(958\) −29.1622 6.65609i −0.942189 0.215049i
\(959\) −0.266200 1.02727i −0.00859604 0.0331721i
\(960\) 0 0
\(961\) 28.7708 0.928091
\(962\) 28.4202 0.916302
\(963\) 0 0
\(964\) 2.94385 6.11296i 0.0948150 0.196885i
\(965\) 3.75675 4.71081i 0.120934 0.151646i
\(966\) 0 0
\(967\) −20.2313 25.3692i −0.650594 0.815819i 0.341689 0.939813i \(-0.389001\pi\)
−0.992283 + 0.123994i \(0.960430\pi\)
\(968\) −5.77857 + 1.31892i −0.185730 + 0.0423917i
\(969\) 0 0
\(970\) −11.0199 5.30689i −0.353827 0.170394i
\(971\) 27.1145 34.0005i 0.870146 1.09113i −0.124945 0.992164i \(-0.539875\pi\)
0.995091 0.0989652i \(-0.0315533\pi\)
\(972\) 0 0
\(973\) 5.04680 + 2.25159i 0.161793 + 0.0721828i
\(974\) −2.68624 + 5.57804i −0.0860727 + 0.178732i
\(975\) 0 0
\(976\) −25.3274 5.78081i −0.810709 0.185039i
\(977\) 9.09110 + 18.8779i 0.290850 + 0.603957i 0.994280 0.106808i \(-0.0340632\pi\)
−0.703429 + 0.710765i \(0.748349\pi\)
\(978\) 0 0
\(979\) 36.9727i 1.18165i
\(980\) −6.96520 + 0.406636i −0.222495 + 0.0129895i
\(981\) 0 0
\(982\) −23.6209 29.6197i −0.753774 0.945202i
\(983\) −40.4338 + 19.4719i −1.28964 + 0.621057i −0.947849 0.318720i \(-0.896747\pi\)
−0.341789 + 0.939777i \(0.611033\pi\)
\(984\) 0 0
\(985\) −15.8213 32.8534i −0.504110 1.04680i
\(986\) 31.2991 + 15.0728i 0.996765 + 0.480017i
\(987\) 0 0
\(988\) 10.9734 5.28450i 0.349110 0.168122i
\(989\) 1.07126 + 0.854305i 0.0340642 + 0.0271653i
\(990\) 0 0
\(991\) 33.7996 + 42.3833i 1.07368 + 1.34635i 0.934452 + 0.356090i \(0.115890\pi\)
0.139227 + 0.990261i \(0.455538\pi\)
\(992\) 1.10924 + 4.85990i 0.0352184 + 0.154302i
\(993\) 0 0
\(994\) −4.28808 + 9.61146i −0.136010 + 0.304857i
\(995\) 10.3018 + 8.21544i 0.326590 + 0.260447i
\(996\) 0 0
\(997\) 22.8150 5.20738i 0.722559 0.164919i 0.154601 0.987977i \(-0.450591\pi\)
0.567958 + 0.823058i \(0.307734\pi\)
\(998\) 31.9503i 1.01137i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 441.2.w.a.188.13 yes 120
3.2 odd 2 inner 441.2.w.a.188.8 120
49.6 odd 14 inner 441.2.w.a.251.8 yes 120
147.104 even 14 inner 441.2.w.a.251.13 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.w.a.188.8 120 3.2 odd 2 inner
441.2.w.a.188.13 yes 120 1.1 even 1 trivial
441.2.w.a.251.8 yes 120 49.6 odd 14 inner
441.2.w.a.251.13 yes 120 147.104 even 14 inner