Properties

Label 693.2.m.k.64.4
Level $693$
Weight $2$
Character 693.64
Analytic conductor $5.534$
Analytic rank $0$
Dimension $32$
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] = [693,2,Mod(64,693)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(693, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("693.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 693.m (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.53363286007\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 64.4
Character \(\chi\) \(=\) 693.64
Dual form 693.2.m.k.379.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.123907 + 0.381345i) q^{2} +(1.48796 + 1.08107i) q^{4} +(0.712476 + 2.19277i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-1.24541 + 0.904845i) q^{8} +O(q^{10})\) \(q+(-0.123907 + 0.381345i) q^{2} +(1.48796 + 1.08107i) q^{4} +(0.712476 + 2.19277i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-1.24541 + 0.904845i) q^{8} -0.924485 q^{10} +(3.30642 + 0.259994i) q^{11} +(1.38796 - 4.27172i) q^{13} +(0.324392 - 0.235684i) q^{14} +(0.945959 + 2.91136i) q^{16} +(2.30765 + 7.10221i) q^{17} +(1.08998 - 0.791919i) q^{19} +(-1.31040 + 4.03300i) q^{20} +(-0.508834 + 1.22867i) q^{22} -4.27146 q^{23} +(-0.255555 + 0.185671i) q^{25} +(1.45702 + 1.05859i) q^{26} +(-0.568351 - 1.74920i) q^{28} +(-0.910862 - 0.661780i) q^{29} +(-2.50687 + 7.71535i) q^{31} -4.30627 q^{32} -2.99433 q^{34} +(0.712476 - 2.19277i) q^{35} +(-8.95237 - 6.50427i) q^{37} +(0.166938 + 0.513784i) q^{38} +(-2.87145 - 2.08623i) q^{40} +(0.939852 - 0.682843i) q^{41} +9.95451 q^{43} +(4.63876 + 3.96132i) q^{44} +(0.529262 - 1.62890i) q^{46} +(-10.3911 + 7.54956i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-0.0391400 - 0.120460i) q^{50} +(6.68326 - 4.85567i) q^{52} +(3.62469 - 11.1556i) q^{53} +(1.78564 + 7.43547i) q^{55} +1.53941 q^{56} +(0.365228 - 0.265354i) q^{58} +(0.848599 + 0.616543i) q^{59} +(-2.06929 - 6.36863i) q^{61} +(-2.63160 - 1.91197i) q^{62} +(-1.35834 + 4.18055i) q^{64} +10.3558 q^{65} -2.46445 q^{67} +(-4.24428 + 13.0626i) q^{68} +(0.747924 + 0.543398i) q^{70} +(2.60280 + 8.01059i) q^{71} +(8.71874 + 6.33453i) q^{73} +(3.58963 - 2.60802i) q^{74} +2.47797 q^{76} +(-2.52213 - 2.15380i) q^{77} +(0.837891 - 2.57876i) q^{79} +(-5.70999 + 4.14855i) q^{80} +(0.143945 + 0.443017i) q^{82} +(-2.82105 - 8.68231i) q^{83} +(-13.9294 + 10.1203i) q^{85} +(-1.23343 + 3.79610i) q^{86} +(-4.35311 + 2.66800i) q^{88} +5.28542 q^{89} +(-3.63374 + 2.64007i) q^{91} +(-6.35577 - 4.61774i) q^{92} +(-1.59147 - 4.89803i) q^{94} +(2.51309 + 1.82586i) q^{95} +(1.77561 - 5.46478i) q^{97} -0.400970 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 10 q^{4} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52} - 12 q^{55} - 104 q^{58} + 34 q^{61} - 52 q^{64} + 104 q^{67} + 18 q^{70} + 2 q^{73} - 28 q^{76} - 42 q^{79} - 172 q^{82} - 30 q^{85} - 16 q^{88} - 10 q^{91} + 150 q^{94} - 74 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(442\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.123907 + 0.381345i −0.0876152 + 0.269652i −0.985259 0.171070i \(-0.945278\pi\)
0.897644 + 0.440722i \(0.145278\pi\)
\(3\) 0 0
\(4\) 1.48796 + 1.08107i 0.743981 + 0.540534i
\(5\) 0.712476 + 2.19277i 0.318629 + 0.980639i 0.974235 + 0.225536i \(0.0724132\pi\)
−0.655606 + 0.755103i \(0.727587\pi\)
\(6\) 0 0
\(7\) −0.809017 0.587785i −0.305780 0.222162i
\(8\) −1.24541 + 0.904845i −0.440320 + 0.319911i
\(9\) 0 0
\(10\) −0.924485 −0.292348
\(11\) 3.30642 + 0.259994i 0.996923 + 0.0783910i
\(12\) 0 0
\(13\) 1.38796 4.27172i 0.384952 1.18476i −0.551563 0.834133i \(-0.685968\pi\)
0.936515 0.350628i \(-0.114032\pi\)
\(14\) 0.324392 0.235684i 0.0866973 0.0629893i
\(15\) 0 0
\(16\) 0.945959 + 2.91136i 0.236490 + 0.727840i
\(17\) 2.30765 + 7.10221i 0.559687 + 1.72254i 0.683232 + 0.730201i \(0.260574\pi\)
−0.123545 + 0.992339i \(0.539426\pi\)
\(18\) 0 0
\(19\) 1.08998 0.791919i 0.250059 0.181679i −0.455694 0.890137i \(-0.650609\pi\)
0.705753 + 0.708458i \(0.250609\pi\)
\(20\) −1.31040 + 4.03300i −0.293015 + 0.901807i
\(21\) 0 0
\(22\) −0.508834 + 1.22867i −0.108484 + 0.261954i
\(23\) −4.27146 −0.890661 −0.445330 0.895366i \(-0.646914\pi\)
−0.445330 + 0.895366i \(0.646914\pi\)
\(24\) 0 0
\(25\) −0.255555 + 0.185671i −0.0511109 + 0.0371342i
\(26\) 1.45702 + 1.05859i 0.285745 + 0.207606i
\(27\) 0 0
\(28\) −0.568351 1.74920i −0.107408 0.330569i
\(29\) −0.910862 0.661780i −0.169143 0.122889i 0.499993 0.866029i \(-0.333336\pi\)
−0.669136 + 0.743140i \(0.733336\pi\)
\(30\) 0 0
\(31\) −2.50687 + 7.71535i −0.450247 + 1.38572i 0.426378 + 0.904545i \(0.359789\pi\)
−0.876625 + 0.481173i \(0.840211\pi\)
\(32\) −4.30627 −0.761249
\(33\) 0 0
\(34\) −2.99433 −0.513523
\(35\) 0.712476 2.19277i 0.120430 0.370647i
\(36\) 0 0
\(37\) −8.95237 6.50427i −1.47176 1.06930i −0.980099 0.198509i \(-0.936390\pi\)
−0.491661 0.870787i \(-0.663610\pi\)
\(38\) 0.166938 + 0.513784i 0.0270810 + 0.0833467i
\(39\) 0 0
\(40\) −2.87145 2.08623i −0.454016 0.329862i
\(41\) 0.939852 0.682843i 0.146780 0.106642i −0.511972 0.859002i \(-0.671085\pi\)
0.658752 + 0.752360i \(0.271085\pi\)
\(42\) 0 0
\(43\) 9.95451 1.51805 0.759024 0.651063i \(-0.225676\pi\)
0.759024 + 0.651063i \(0.225676\pi\)
\(44\) 4.63876 + 3.96132i 0.699319 + 0.597192i
\(45\) 0 0
\(46\) 0.529262 1.62890i 0.0780354 0.240168i
\(47\) −10.3911 + 7.54956i −1.51569 + 1.10122i −0.552124 + 0.833762i \(0.686182\pi\)
−0.963571 + 0.267454i \(0.913818\pi\)
\(48\) 0 0
\(49\) 0.309017 + 0.951057i 0.0441453 + 0.135865i
\(50\) −0.0391400 0.120460i −0.00553523 0.0170357i
\(51\) 0 0
\(52\) 6.68326 4.85567i 0.926801 0.673360i
\(53\) 3.62469 11.1556i 0.497889 1.53235i −0.314515 0.949252i \(-0.601842\pi\)
0.812405 0.583094i \(-0.198158\pi\)
\(54\) 0 0
\(55\) 1.78564 + 7.43547i 0.240775 + 1.00260i
\(56\) 1.53941 0.205713
\(57\) 0 0
\(58\) 0.365228 0.265354i 0.0479568 0.0348427i
\(59\) 0.848599 + 0.616543i 0.110478 + 0.0802671i 0.641653 0.766995i \(-0.278249\pi\)
−0.531174 + 0.847263i \(0.678249\pi\)
\(60\) 0 0
\(61\) −2.06929 6.36863i −0.264946 0.815419i −0.991706 0.128528i \(-0.958975\pi\)
0.726760 0.686891i \(-0.241025\pi\)
\(62\) −2.63160 1.91197i −0.334213 0.242820i
\(63\) 0 0
\(64\) −1.35834 + 4.18055i −0.169793 + 0.522568i
\(65\) 10.3558 1.28448
\(66\) 0 0
\(67\) −2.46445 −0.301080 −0.150540 0.988604i \(-0.548101\pi\)
−0.150540 + 0.988604i \(0.548101\pi\)
\(68\) −4.24428 + 13.0626i −0.514695 + 1.58407i
\(69\) 0 0
\(70\) 0.747924 + 0.543398i 0.0893940 + 0.0649485i
\(71\) 2.60280 + 8.01059i 0.308895 + 0.950682i 0.978195 + 0.207689i \(0.0665943\pi\)
−0.669300 + 0.742993i \(0.733406\pi\)
\(72\) 0 0
\(73\) 8.71874 + 6.33453i 1.02045 + 0.741401i 0.966375 0.257136i \(-0.0827788\pi\)
0.0540756 + 0.998537i \(0.482779\pi\)
\(74\) 3.58963 2.60802i 0.417286 0.303176i
\(75\) 0 0
\(76\) 2.47797 0.284243
\(77\) −2.52213 2.15380i −0.287423 0.245449i
\(78\) 0 0
\(79\) 0.837891 2.57876i 0.0942702 0.290134i −0.892793 0.450468i \(-0.851257\pi\)
0.987063 + 0.160334i \(0.0512572\pi\)
\(80\) −5.70999 + 4.14855i −0.638396 + 0.463822i
\(81\) 0 0
\(82\) 0.143945 + 0.443017i 0.0158961 + 0.0489230i
\(83\) −2.82105 8.68231i −0.309651 0.953007i −0.977901 0.209070i \(-0.932956\pi\)
0.668250 0.743937i \(-0.267044\pi\)
\(84\) 0 0
\(85\) −13.9294 + 10.1203i −1.51086 + 1.09770i
\(86\) −1.23343 + 3.79610i −0.133004 + 0.409344i
\(87\) 0 0
\(88\) −4.35311 + 2.66800i −0.464043 + 0.284409i
\(89\) 5.28542 0.560253 0.280126 0.959963i \(-0.409624\pi\)
0.280126 + 0.959963i \(0.409624\pi\)
\(90\) 0 0
\(91\) −3.63374 + 2.64007i −0.380919 + 0.276754i
\(92\) −6.35577 4.61774i −0.662635 0.481433i
\(93\) 0 0
\(94\) −1.59147 4.89803i −0.164147 0.505193i
\(95\) 2.51309 + 1.82586i 0.257837 + 0.187330i
\(96\) 0 0
\(97\) 1.77561 5.46478i 0.180286 0.554864i −0.819549 0.573009i \(-0.805776\pi\)
0.999835 + 0.0181449i \(0.00577600\pi\)
\(98\) −0.400970 −0.0405041
\(99\) 0 0
\(100\) −0.580979 −0.0580979
\(101\) 2.95530 9.09549i 0.294064 0.905035i −0.689470 0.724314i \(-0.742157\pi\)
0.983534 0.180722i \(-0.0578433\pi\)
\(102\) 0 0
\(103\) 0.653358 + 0.474692i 0.0643773 + 0.0467728i 0.619508 0.784990i \(-0.287332\pi\)
−0.555131 + 0.831763i \(0.687332\pi\)
\(104\) 2.13665 + 6.57594i 0.209516 + 0.644824i
\(105\) 0 0
\(106\) 3.80503 + 2.76452i 0.369577 + 0.268514i
\(107\) 13.6302 9.90291i 1.31768 0.957351i 0.317722 0.948184i \(-0.397082\pi\)
0.999958 0.00916669i \(-0.00291789\pi\)
\(108\) 0 0
\(109\) 9.41870 0.902147 0.451074 0.892487i \(-0.351041\pi\)
0.451074 + 0.892487i \(0.351041\pi\)
\(110\) −3.05673 0.240360i −0.291448 0.0229174i
\(111\) 0 0
\(112\) 0.945959 2.91136i 0.0893847 0.275098i
\(113\) 3.52035 2.55768i 0.331166 0.240606i −0.409759 0.912194i \(-0.634387\pi\)
0.740925 + 0.671587i \(0.234387\pi\)
\(114\) 0 0
\(115\) −3.04331 9.36635i −0.283790 0.873417i
\(116\) −0.639899 1.96941i −0.0594131 0.182855i
\(117\) 0 0
\(118\) −0.340263 + 0.247215i −0.0313237 + 0.0227580i
\(119\) 2.30765 7.10221i 0.211542 0.651059i
\(120\) 0 0
\(121\) 10.8648 + 1.71930i 0.987710 + 0.156300i
\(122\) 2.68504 0.243093
\(123\) 0 0
\(124\) −12.0710 + 8.77006i −1.08400 + 0.787575i
\(125\) 8.73722 + 6.34796i 0.781480 + 0.567779i
\(126\) 0 0
\(127\) −1.96145 6.03673i −0.174051 0.535673i 0.825538 0.564346i \(-0.190872\pi\)
−0.999589 + 0.0286733i \(0.990872\pi\)
\(128\) −8.39362 6.09832i −0.741898 0.539021i
\(129\) 0 0
\(130\) −1.28315 + 3.94914i −0.112540 + 0.346362i
\(131\) −15.2292 −1.33058 −0.665290 0.746585i \(-0.731692\pi\)
−0.665290 + 0.746585i \(0.731692\pi\)
\(132\) 0 0
\(133\) −1.34729 −0.116825
\(134\) 0.305361 0.939805i 0.0263792 0.0811868i
\(135\) 0 0
\(136\) −9.30037 6.75712i −0.797501 0.579418i
\(137\) −5.90200 18.1645i −0.504241 1.55190i −0.802042 0.597268i \(-0.796253\pi\)
0.297801 0.954628i \(-0.403747\pi\)
\(138\) 0 0
\(139\) 3.18676 + 2.31532i 0.270297 + 0.196382i 0.714674 0.699457i \(-0.246575\pi\)
−0.444377 + 0.895840i \(0.646575\pi\)
\(140\) 3.43068 2.49253i 0.289945 0.210657i
\(141\) 0 0
\(142\) −3.37730 −0.283417
\(143\) 5.69981 13.7632i 0.476642 1.15094i
\(144\) 0 0
\(145\) 0.802167 2.46882i 0.0666163 0.205024i
\(146\) −3.49595 + 2.53996i −0.289327 + 0.210208i
\(147\) 0 0
\(148\) −6.28922 19.3562i −0.516971 1.59107i
\(149\) −6.29823 19.3840i −0.515971 1.58800i −0.781508 0.623895i \(-0.785549\pi\)
0.265537 0.964101i \(-0.414451\pi\)
\(150\) 0 0
\(151\) 3.97808 2.89024i 0.323732 0.235205i −0.414035 0.910261i \(-0.635881\pi\)
0.737766 + 0.675056i \(0.235881\pi\)
\(152\) −0.640914 + 1.97253i −0.0519850 + 0.159993i
\(153\) 0 0
\(154\) 1.13385 0.694931i 0.0913683 0.0559992i
\(155\) −18.7041 −1.50235
\(156\) 0 0
\(157\) −1.81381 + 1.31781i −0.144758 + 0.105173i −0.657807 0.753186i \(-0.728516\pi\)
0.513049 + 0.858359i \(0.328516\pi\)
\(158\) 0.879579 + 0.639052i 0.0699756 + 0.0508402i
\(159\) 0 0
\(160\) −3.06811 9.44268i −0.242556 0.746510i
\(161\) 3.45568 + 2.51070i 0.272346 + 0.197871i
\(162\) 0 0
\(163\) −3.03994 + 9.35597i −0.238107 + 0.732816i 0.758588 + 0.651571i \(0.225890\pi\)
−0.996694 + 0.0812454i \(0.974110\pi\)
\(164\) 2.13666 0.166845
\(165\) 0 0
\(166\) 3.66050 0.284110
\(167\) 2.67139 8.22170i 0.206719 0.636214i −0.792920 0.609326i \(-0.791440\pi\)
0.999638 0.0268885i \(-0.00855990\pi\)
\(168\) 0 0
\(169\) −5.80389 4.21677i −0.446453 0.324367i
\(170\) −2.13339 6.56589i −0.163623 0.503581i
\(171\) 0 0
\(172\) 14.8119 + 10.7615i 1.12940 + 0.820557i
\(173\) −12.9178 + 9.38531i −0.982120 + 0.713552i −0.958181 0.286161i \(-0.907621\pi\)
−0.0239388 + 0.999713i \(0.507621\pi\)
\(174\) 0 0
\(175\) 0.315883 0.0238785
\(176\) 2.37080 + 9.87212i 0.178706 + 0.744139i
\(177\) 0 0
\(178\) −0.654898 + 2.01557i −0.0490867 + 0.151073i
\(179\) 14.2192 10.3308i 1.06279 0.772163i 0.0881881 0.996104i \(-0.471892\pi\)
0.974603 + 0.223941i \(0.0718923\pi\)
\(180\) 0 0
\(181\) 6.41658 + 19.7482i 0.476941 + 1.46787i 0.843322 + 0.537409i \(0.180597\pi\)
−0.366381 + 0.930465i \(0.619403\pi\)
\(182\) −0.556532 1.71283i −0.0412529 0.126963i
\(183\) 0 0
\(184\) 5.31973 3.86501i 0.392175 0.284932i
\(185\) 7.88407 24.2647i 0.579648 1.78397i
\(186\) 0 0
\(187\) 5.78352 + 24.0829i 0.422933 + 1.76111i
\(188\) −23.6231 −1.72289
\(189\) 0 0
\(190\) −1.00767 + 0.732117i −0.0731042 + 0.0531133i
\(191\) −8.49477 6.17181i −0.614660 0.446577i 0.236392 0.971658i \(-0.424035\pi\)
−0.851052 + 0.525081i \(0.824035\pi\)
\(192\) 0 0
\(193\) −4.00178 12.3162i −0.288054 0.886541i −0.985466 0.169870i \(-0.945665\pi\)
0.697412 0.716670i \(-0.254335\pi\)
\(194\) 1.86396 + 1.35424i 0.133824 + 0.0972290i
\(195\) 0 0
\(196\) −0.568351 + 1.74920i −0.0405965 + 0.124943i
\(197\) 0.664214 0.0473233 0.0236617 0.999720i \(-0.492468\pi\)
0.0236617 + 0.999720i \(0.492468\pi\)
\(198\) 0 0
\(199\) 13.3550 0.946710 0.473355 0.880872i \(-0.343043\pi\)
0.473355 + 0.880872i \(0.343043\pi\)
\(200\) 0.150267 0.462474i 0.0106255 0.0327019i
\(201\) 0 0
\(202\) 3.10234 + 2.25398i 0.218280 + 0.158590i
\(203\) 0.347918 + 1.07078i 0.0244191 + 0.0751542i
\(204\) 0 0
\(205\) 2.16694 + 1.57438i 0.151346 + 0.109959i
\(206\) −0.261977 + 0.190337i −0.0182528 + 0.0132614i
\(207\) 0 0
\(208\) 13.7495 0.953354
\(209\) 3.80983 2.33503i 0.263532 0.161517i
\(210\) 0 0
\(211\) 4.04178 12.4393i 0.278247 0.856358i −0.710094 0.704106i \(-0.751348\pi\)
0.988342 0.152251i \(-0.0486522\pi\)
\(212\) 17.4534 12.6807i 1.19871 0.870911i
\(213\) 0 0
\(214\) 2.08756 + 6.42484i 0.142703 + 0.439193i
\(215\) 7.09234 + 21.8280i 0.483694 + 1.48866i
\(216\) 0 0
\(217\) 6.56307 4.76835i 0.445530 0.323697i
\(218\) −1.16704 + 3.59177i −0.0790418 + 0.243266i
\(219\) 0 0
\(220\) −5.38129 + 12.9941i −0.362807 + 0.876062i
\(221\) 33.5416 2.25625
\(222\) 0 0
\(223\) −8.27567 + 6.01263i −0.554180 + 0.402635i −0.829324 0.558768i \(-0.811274\pi\)
0.275144 + 0.961403i \(0.411274\pi\)
\(224\) 3.48385 + 2.53116i 0.232774 + 0.169120i
\(225\) 0 0
\(226\) 0.539166 + 1.65938i 0.0358648 + 0.110380i
\(227\) 2.41788 + 1.75669i 0.160480 + 0.116596i 0.665127 0.746730i \(-0.268377\pi\)
−0.504647 + 0.863326i \(0.668377\pi\)
\(228\) 0 0
\(229\) 6.21177 19.1179i 0.410485 1.26334i −0.505742 0.862685i \(-0.668781\pi\)
0.916227 0.400659i \(-0.131219\pi\)
\(230\) 3.94890 0.260383
\(231\) 0 0
\(232\) 1.73321 0.113791
\(233\) −1.44327 + 4.44193i −0.0945518 + 0.291001i −0.987137 0.159879i \(-0.948890\pi\)
0.892585 + 0.450880i \(0.148890\pi\)
\(234\) 0 0
\(235\) −23.9579 17.4064i −1.56284 1.13547i
\(236\) 0.596158 + 1.83479i 0.0388066 + 0.119434i
\(237\) 0 0
\(238\) 2.42246 + 1.76002i 0.157025 + 0.114085i
\(239\) −18.4191 + 13.3823i −1.19143 + 0.865628i −0.993415 0.114570i \(-0.963451\pi\)
−0.198019 + 0.980198i \(0.563451\pi\)
\(240\) 0 0
\(241\) −4.83714 −0.311587 −0.155794 0.987790i \(-0.549793\pi\)
−0.155794 + 0.987790i \(0.549793\pi\)
\(242\) −2.00187 + 3.93021i −0.128685 + 0.252643i
\(243\) 0 0
\(244\) 3.80589 11.7133i 0.243647 0.749869i
\(245\) −1.86529 + 1.35521i −0.119169 + 0.0865811i
\(246\) 0 0
\(247\) −1.86999 5.75525i −0.118985 0.366198i
\(248\) −3.85911 11.8771i −0.245054 0.754198i
\(249\) 0 0
\(250\) −3.50336 + 2.54534i −0.221572 + 0.160982i
\(251\) −4.96145 + 15.2698i −0.313164 + 0.963819i 0.663340 + 0.748318i \(0.269138\pi\)
−0.976504 + 0.215501i \(0.930862\pi\)
\(252\) 0 0
\(253\) −14.1232 1.11055i −0.887920 0.0698198i
\(254\) 2.54512 0.159695
\(255\) 0 0
\(256\) −3.74678 + 2.72220i −0.234174 + 0.170137i
\(257\) −9.84920 7.15587i −0.614376 0.446371i 0.236576 0.971613i \(-0.423975\pi\)
−0.850953 + 0.525242i \(0.823975\pi\)
\(258\) 0 0
\(259\) 3.41950 + 10.5241i 0.212477 + 0.653938i
\(260\) 15.4090 + 11.1953i 0.955629 + 0.694305i
\(261\) 0 0
\(262\) 1.88700 5.80758i 0.116579 0.358793i
\(263\) −18.8786 −1.16411 −0.582053 0.813151i \(-0.697750\pi\)
−0.582053 + 0.813151i \(0.697750\pi\)
\(264\) 0 0
\(265\) 27.0443 1.66132
\(266\) 0.166938 0.513784i 0.0102356 0.0315021i
\(267\) 0 0
\(268\) −3.66701 2.66424i −0.223998 0.162744i
\(269\) −0.219722 0.676236i −0.0133967 0.0412308i 0.944135 0.329560i \(-0.106900\pi\)
−0.957531 + 0.288329i \(0.906900\pi\)
\(270\) 0 0
\(271\) −11.9118 8.65441i −0.723588 0.525718i 0.163940 0.986470i \(-0.447580\pi\)
−0.887529 + 0.460753i \(0.847580\pi\)
\(272\) −18.4942 + 13.4368i −1.12137 + 0.814726i
\(273\) 0 0
\(274\) 7.65823 0.462651
\(275\) −0.893244 + 0.547464i −0.0538646 + 0.0330133i
\(276\) 0 0
\(277\) 5.43342 16.7223i 0.326462 1.00475i −0.644314 0.764761i \(-0.722857\pi\)
0.970776 0.239987i \(-0.0771430\pi\)
\(278\) −1.27779 + 0.928372i −0.0766370 + 0.0556801i
\(279\) 0 0
\(280\) 1.09679 + 3.37559i 0.0655460 + 0.201730i
\(281\) 4.62684 + 14.2399i 0.276014 + 0.849484i 0.988949 + 0.148254i \(0.0473654\pi\)
−0.712935 + 0.701230i \(0.752635\pi\)
\(282\) 0 0
\(283\) −14.1107 + 10.2520i −0.838795 + 0.609421i −0.922034 0.387109i \(-0.873474\pi\)
0.0832385 + 0.996530i \(0.473474\pi\)
\(284\) −4.78713 + 14.7333i −0.284064 + 0.874258i
\(285\) 0 0
\(286\) 4.54229 + 3.87895i 0.268591 + 0.229367i
\(287\) −1.16172 −0.0685742
\(288\) 0 0
\(289\) −31.3629 + 22.7865i −1.84488 + 1.34038i
\(290\) 0.842078 + 0.611805i 0.0494485 + 0.0359264i
\(291\) 0 0
\(292\) 6.12509 + 18.8511i 0.358444 + 1.10318i
\(293\) 21.0444 + 15.2897i 1.22943 + 0.893231i 0.996847 0.0793461i \(-0.0252832\pi\)
0.232580 + 0.972577i \(0.425283\pi\)
\(294\) 0 0
\(295\) −0.747334 + 2.30006i −0.0435115 + 0.133915i
\(296\) 17.0347 0.990124
\(297\) 0 0
\(298\) 8.17237 0.473413
\(299\) −5.92864 + 18.2465i −0.342862 + 1.05522i
\(300\) 0 0
\(301\) −8.05337 5.85111i −0.464188 0.337253i
\(302\) 0.609271 + 1.87514i 0.0350596 + 0.107902i
\(303\) 0 0
\(304\) 3.33664 + 2.42421i 0.191369 + 0.139038i
\(305\) 12.4906 9.07498i 0.715212 0.519632i
\(306\) 0 0
\(307\) −23.5921 −1.34647 −0.673236 0.739428i \(-0.735096\pi\)
−0.673236 + 0.739428i \(0.735096\pi\)
\(308\) −1.42442 5.93137i −0.0811641 0.337971i
\(309\) 0 0
\(310\) 2.31756 7.13273i 0.131629 0.405112i
\(311\) 3.68257 2.67555i 0.208820 0.151716i −0.478460 0.878109i \(-0.658805\pi\)
0.687279 + 0.726393i \(0.258805\pi\)
\(312\) 0 0
\(313\) −4.05657 12.4848i −0.229291 0.705684i −0.997828 0.0658787i \(-0.979015\pi\)
0.768537 0.639805i \(-0.220985\pi\)
\(314\) −0.277798 0.854974i −0.0156770 0.0482490i
\(315\) 0 0
\(316\) 4.03457 2.93129i 0.226962 0.164898i
\(317\) 2.76370 8.50580i 0.155225 0.477733i −0.842959 0.537978i \(-0.819188\pi\)
0.998184 + 0.0602451i \(0.0191882\pi\)
\(318\) 0 0
\(319\) −2.83963 2.42494i −0.158989 0.135770i
\(320\) −10.1348 −0.566552
\(321\) 0 0
\(322\) −1.38563 + 1.00672i −0.0772179 + 0.0561021i
\(323\) 8.13967 + 5.91382i 0.452904 + 0.329054i
\(324\) 0 0
\(325\) 0.438434 + 1.34936i 0.0243200 + 0.0748491i
\(326\) −3.19119 2.31853i −0.176744 0.128412i
\(327\) 0 0
\(328\) −0.552637 + 1.70084i −0.0305143 + 0.0939132i
\(329\) 12.8441 0.708117
\(330\) 0 0
\(331\) 25.9302 1.42525 0.712627 0.701543i \(-0.247505\pi\)
0.712627 + 0.701543i \(0.247505\pi\)
\(332\) 5.18854 15.9687i 0.284758 0.876396i
\(333\) 0 0
\(334\) 2.80430 + 2.03745i 0.153445 + 0.111484i
\(335\) −1.75586 5.40398i −0.0959328 0.295251i
\(336\) 0 0
\(337\) 12.7469 + 9.26115i 0.694367 + 0.504487i 0.878093 0.478490i \(-0.158816\pi\)
−0.183726 + 0.982978i \(0.558816\pi\)
\(338\) 2.32719 1.69080i 0.126582 0.0919674i
\(339\) 0 0
\(340\) −31.6672 −1.71739
\(341\) −10.2947 + 24.8584i −0.557490 + 1.34616i
\(342\) 0 0
\(343\) 0.309017 0.951057i 0.0166853 0.0513522i
\(344\) −12.3975 + 9.00728i −0.668426 + 0.485640i
\(345\) 0 0
\(346\) −1.97845 6.08903i −0.106362 0.327349i
\(347\) 0.689010 + 2.12055i 0.0369880 + 0.113837i 0.967846 0.251544i \(-0.0809385\pi\)
−0.930858 + 0.365382i \(0.880938\pi\)
\(348\) 0 0
\(349\) −7.78134 + 5.65347i −0.416525 + 0.302623i −0.776238 0.630440i \(-0.782875\pi\)
0.359713 + 0.933063i \(0.382875\pi\)
\(350\) −0.0391400 + 0.120460i −0.00209212 + 0.00643888i
\(351\) 0 0
\(352\) −14.2383 1.11960i −0.758906 0.0596750i
\(353\) −9.98576 −0.531488 −0.265744 0.964044i \(-0.585618\pi\)
−0.265744 + 0.964044i \(0.585618\pi\)
\(354\) 0 0
\(355\) −15.7110 + 11.4147i −0.833852 + 0.605829i
\(356\) 7.86450 + 5.71389i 0.416818 + 0.302836i
\(357\) 0 0
\(358\) 2.17777 + 6.70247i 0.115098 + 0.354237i
\(359\) 8.28988 + 6.02295i 0.437523 + 0.317879i 0.784650 0.619939i \(-0.212843\pi\)
−0.347127 + 0.937818i \(0.612843\pi\)
\(360\) 0 0
\(361\) −5.31040 + 16.3437i −0.279495 + 0.860196i
\(362\) −8.32595 −0.437602
\(363\) 0 0
\(364\) −8.26096 −0.432992
\(365\) −7.67832 + 23.6314i −0.401901 + 1.23693i
\(366\) 0 0
\(367\) −2.98740 2.17047i −0.155941 0.113298i 0.507079 0.861900i \(-0.330725\pi\)
−0.663020 + 0.748602i \(0.730725\pi\)
\(368\) −4.04063 12.4358i −0.210632 0.648259i
\(369\) 0 0
\(370\) 8.27632 + 6.01310i 0.430266 + 0.312606i
\(371\) −9.48956 + 6.89457i −0.492673 + 0.357948i
\(372\) 0 0
\(373\) 17.2657 0.893986 0.446993 0.894538i \(-0.352495\pi\)
0.446993 + 0.894538i \(0.352495\pi\)
\(374\) −9.90050 0.778506i −0.511943 0.0402556i
\(375\) 0 0
\(376\) 6.10999 18.8046i 0.315099 0.969774i
\(377\) −4.09118 + 2.97242i −0.210706 + 0.153087i
\(378\) 0 0
\(379\) −1.60365 4.93553i −0.0823740 0.253521i 0.901384 0.433020i \(-0.142552\pi\)
−0.983758 + 0.179499i \(0.942552\pi\)
\(380\) 1.76549 + 5.43363i 0.0905679 + 0.278739i
\(381\) 0 0
\(382\) 3.40615 2.47471i 0.174274 0.126617i
\(383\) −5.44524 + 16.7587i −0.278239 + 0.856331i 0.710105 + 0.704095i \(0.248647\pi\)
−0.988344 + 0.152236i \(0.951353\pi\)
\(384\) 0 0
\(385\) 2.92585 7.06499i 0.149115 0.360065i
\(386\) 5.19258 0.264295
\(387\) 0 0
\(388\) 8.54984 6.21183i 0.434053 0.315358i
\(389\) −8.59081 6.24159i −0.435571 0.316461i 0.348302 0.937383i \(-0.386759\pi\)
−0.783873 + 0.620922i \(0.786759\pi\)
\(390\) 0 0
\(391\) −9.85703 30.3368i −0.498492 1.53420i
\(392\) −1.24541 0.904845i −0.0629028 0.0457016i
\(393\) 0 0
\(394\) −0.0823005 + 0.253295i −0.00414624 + 0.0127608i
\(395\) 6.25163 0.314554
\(396\) 0 0
\(397\) 22.6262 1.13557 0.567787 0.823175i \(-0.307800\pi\)
0.567787 + 0.823175i \(0.307800\pi\)
\(398\) −1.65477 + 5.09286i −0.0829462 + 0.255282i
\(399\) 0 0
\(400\) −0.782300 0.568374i −0.0391150 0.0284187i
\(401\) 1.42441 + 4.38389i 0.0711318 + 0.218921i 0.980302 0.197503i \(-0.0632832\pi\)
−0.909170 + 0.416424i \(0.863283\pi\)
\(402\) 0 0
\(403\) 29.4784 + 21.4173i 1.46842 + 1.06687i
\(404\) 14.2302 10.3389i 0.707980 0.514378i
\(405\) 0 0
\(406\) −0.451447 −0.0224049
\(407\) −27.9092 23.8334i −1.38341 1.18138i
\(408\) 0 0
\(409\) 6.50438 20.0184i 0.321621 0.989848i −0.651322 0.758802i \(-0.725785\pi\)
0.972943 0.231046i \(-0.0742149\pi\)
\(410\) −0.868879 + 0.631278i −0.0429109 + 0.0311766i
\(411\) 0 0
\(412\) 0.458997 + 1.41265i 0.0226132 + 0.0695962i
\(413\) −0.324136 0.997588i −0.0159497 0.0490881i
\(414\) 0 0
\(415\) 17.0284 12.3719i 0.835892 0.607311i
\(416\) −5.97695 + 18.3952i −0.293044 + 0.901897i
\(417\) 0 0
\(418\) 0.418388 + 1.74219i 0.0204640 + 0.0852131i
\(419\) 14.0827 0.687984 0.343992 0.938973i \(-0.388221\pi\)
0.343992 + 0.938973i \(0.388221\pi\)
\(420\) 0 0
\(421\) −22.3026 + 16.2038i −1.08696 + 0.789725i −0.978884 0.204417i \(-0.934470\pi\)
−0.108080 + 0.994142i \(0.534470\pi\)
\(422\) 4.24287 + 3.08263i 0.206540 + 0.150060i
\(423\) 0 0
\(424\) 5.57990 + 17.1732i 0.270984 + 0.834002i
\(425\) −1.90841 1.38654i −0.0925714 0.0672570i
\(426\) 0 0
\(427\) −2.06929 + 6.36863i −0.100140 + 0.308199i
\(428\) 30.9869 1.49781
\(429\) 0 0
\(430\) −9.20279 −0.443798
\(431\) −10.6424 + 32.7540i −0.512627 + 1.57770i 0.274931 + 0.961464i \(0.411345\pi\)
−0.787558 + 0.616240i \(0.788655\pi\)
\(432\) 0 0
\(433\) −13.0563 9.48594i −0.627445 0.455865i 0.228069 0.973645i \(-0.426759\pi\)
−0.855514 + 0.517780i \(0.826759\pi\)
\(434\) 1.00518 + 3.09363i 0.0482502 + 0.148499i
\(435\) 0 0
\(436\) 14.0147 + 10.1823i 0.671181 + 0.487641i
\(437\) −4.65582 + 3.38265i −0.222718 + 0.161814i
\(438\) 0 0
\(439\) 19.3036 0.921309 0.460655 0.887580i \(-0.347615\pi\)
0.460655 + 0.887580i \(0.347615\pi\)
\(440\) −8.95180 7.64450i −0.426760 0.364437i
\(441\) 0 0
\(442\) −4.15602 + 12.7909i −0.197682 + 0.608402i
\(443\) −10.6233 + 7.71830i −0.504730 + 0.366708i −0.810821 0.585295i \(-0.800979\pi\)
0.306091 + 0.952002i \(0.400979\pi\)
\(444\) 0 0
\(445\) 3.76573 + 11.5897i 0.178513 + 0.549406i
\(446\) −1.26748 3.90089i −0.0600168 0.184713i
\(447\) 0 0
\(448\) 3.55619 2.58372i 0.168014 0.122069i
\(449\) −3.94032 + 12.1270i −0.185955 + 0.572311i −0.999964 0.00854221i \(-0.997281\pi\)
0.814008 + 0.580853i \(0.197281\pi\)
\(450\) 0 0
\(451\) 3.28508 2.01341i 0.154688 0.0948077i
\(452\) 8.00317 0.376437
\(453\) 0 0
\(454\) −0.969498 + 0.704382i −0.0455008 + 0.0330583i
\(455\) −8.37802 6.08699i −0.392768 0.285362i
\(456\) 0 0
\(457\) −2.84121 8.74436i −0.132906 0.409044i 0.862352 0.506309i \(-0.168991\pi\)
−0.995259 + 0.0972652i \(0.968991\pi\)
\(458\) 6.52083 + 4.73766i 0.304698 + 0.221376i
\(459\) 0 0
\(460\) 5.59733 17.2268i 0.260977 0.803204i
\(461\) 16.0714 0.748521 0.374260 0.927324i \(-0.377897\pi\)
0.374260 + 0.927324i \(0.377897\pi\)
\(462\) 0 0
\(463\) 32.9203 1.52994 0.764968 0.644068i \(-0.222755\pi\)
0.764968 + 0.644068i \(0.222755\pi\)
\(464\) 1.06504 3.27786i 0.0494434 0.152171i
\(465\) 0 0
\(466\) −1.51508 1.10077i −0.0701847 0.0509921i
\(467\) −2.62969 8.09336i −0.121688 0.374516i 0.871595 0.490226i \(-0.163086\pi\)
−0.993283 + 0.115710i \(0.963086\pi\)
\(468\) 0 0
\(469\) 1.99378 + 1.44857i 0.0920642 + 0.0668886i
\(470\) 9.60639 6.97945i 0.443110 0.321938i
\(471\) 0 0
\(472\) −1.61473 −0.0743240
\(473\) 32.9138 + 2.58811i 1.51338 + 0.119001i
\(474\) 0 0
\(475\) −0.131513 + 0.404757i −0.00603425 + 0.0185715i
\(476\) 11.1117 8.07310i 0.509303 0.370030i
\(477\) 0 0
\(478\) −2.82102 8.68220i −0.129030 0.397115i
\(479\) −2.94258 9.05634i −0.134450 0.413795i 0.861054 0.508513i \(-0.169805\pi\)
−0.995504 + 0.0947188i \(0.969805\pi\)
\(480\) 0 0
\(481\) −40.2100 + 29.2143i −1.83342 + 1.33206i
\(482\) 0.599353 1.84462i 0.0272998 0.0840201i
\(483\) 0 0
\(484\) 14.3078 + 14.3038i 0.650352 + 0.650175i
\(485\) 13.2481 0.601566
\(486\) 0 0
\(487\) 0.885370 0.643259i 0.0401199 0.0291488i −0.567545 0.823343i \(-0.692107\pi\)
0.607665 + 0.794194i \(0.292107\pi\)
\(488\) 8.33974 + 6.05918i 0.377522 + 0.274286i
\(489\) 0 0
\(490\) −0.285681 0.879237i −0.0129058 0.0397199i
\(491\) −16.7211 12.1486i −0.754611 0.548257i 0.142642 0.989774i \(-0.454440\pi\)
−0.897253 + 0.441517i \(0.854440\pi\)
\(492\) 0 0
\(493\) 2.59815 7.99629i 0.117015 0.360135i
\(494\) 2.42644 0.109171
\(495\) 0 0
\(496\) −24.8336 −1.11506
\(497\) 2.60280 8.01059i 0.116751 0.359324i
\(498\) 0 0
\(499\) −19.2829 14.0099i −0.863222 0.627167i 0.0655377 0.997850i \(-0.479124\pi\)
−0.928760 + 0.370683i \(0.879124\pi\)
\(500\) 6.13808 + 18.8911i 0.274503 + 0.844834i
\(501\) 0 0
\(502\) −5.20830 3.78405i −0.232458 0.168890i
\(503\) −12.2240 + 8.88123i −0.545039 + 0.395994i −0.825953 0.563739i \(-0.809362\pi\)
0.280914 + 0.959733i \(0.409362\pi\)
\(504\) 0 0
\(505\) 22.0500 0.981210
\(506\) 2.17347 5.24822i 0.0966223 0.233312i
\(507\) 0 0
\(508\) 3.60755 11.1029i 0.160059 0.492611i
\(509\) −1.35615 + 0.985301i −0.0601103 + 0.0436727i −0.617435 0.786622i \(-0.711828\pi\)
0.557324 + 0.830295i \(0.311828\pi\)
\(510\) 0 0
\(511\) −3.33026 10.2495i −0.147322 0.453411i
\(512\) −6.98600 21.5007i −0.308740 0.950206i
\(513\) 0 0
\(514\) 3.94924 2.86929i 0.174193 0.126559i
\(515\) −0.575392 + 1.77087i −0.0253548 + 0.0780340i
\(516\) 0 0
\(517\) −36.3201 + 22.2604i −1.59736 + 0.979011i
\(518\) −4.43703 −0.194952
\(519\) 0 0
\(520\) −12.8972 + 9.37039i −0.565581 + 0.410919i
\(521\) 29.1017 + 21.1436i 1.27497 + 0.926319i 0.999389 0.0349596i \(-0.0111302\pi\)
0.275580 + 0.961278i \(0.411130\pi\)
\(522\) 0 0
\(523\) −4.93227 15.1800i −0.215673 0.663774i −0.999105 0.0422964i \(-0.986533\pi\)
0.783432 0.621478i \(-0.213467\pi\)
\(524\) −22.6605 16.4638i −0.989927 0.719224i
\(525\) 0 0
\(526\) 2.33919 7.19927i 0.101993 0.313903i
\(527\) −60.5811 −2.63895
\(528\) 0 0
\(529\) −4.75463 −0.206723
\(530\) −3.35097 + 10.3132i −0.145557 + 0.447978i
\(531\) 0 0
\(532\) −2.00472 1.45651i −0.0869157 0.0631479i
\(533\) −1.61243 4.96254i −0.0698420 0.214952i
\(534\) 0 0
\(535\) 31.4260 + 22.8323i 1.35867 + 0.987129i
\(536\) 3.06925 2.22994i 0.132571 0.0963188i
\(537\) 0 0
\(538\) 0.285104 0.0122917
\(539\) 0.774471 + 3.22493i 0.0333588 + 0.138908i
\(540\) 0 0
\(541\) −2.37528 + 7.31035i −0.102121 + 0.314296i −0.989044 0.147621i \(-0.952838\pi\)
0.886923 + 0.461917i \(0.152838\pi\)
\(542\) 4.77626 3.47016i 0.205158 0.149056i
\(543\) 0 0
\(544\) −9.93737 30.5841i −0.426061 1.31128i
\(545\) 6.71059 + 20.6531i 0.287450 + 0.884681i
\(546\) 0 0
\(547\) −12.3328 + 8.96030i −0.527312 + 0.383115i −0.819351 0.573292i \(-0.805666\pi\)
0.292039 + 0.956406i \(0.405666\pi\)
\(548\) 10.8551 33.4085i 0.463706 1.42714i
\(549\) 0 0
\(550\) −0.0980941 0.408469i −0.00418275 0.0174172i
\(551\) −1.51690 −0.0646221
\(552\) 0 0
\(553\) −2.19363 + 1.59376i −0.0932826 + 0.0677738i
\(554\) 5.70375 + 4.14401i 0.242329 + 0.176062i
\(555\) 0 0
\(556\) 2.23876 + 6.89020i 0.0949447 + 0.292210i
\(557\) 1.69483 + 1.23137i 0.0718123 + 0.0521747i 0.623112 0.782132i \(-0.285868\pi\)
−0.551300 + 0.834307i \(0.685868\pi\)
\(558\) 0 0
\(559\) 13.8165 42.5228i 0.584376 1.79852i
\(560\) 7.05793 0.298252
\(561\) 0 0
\(562\) −6.00363 −0.253248
\(563\) 3.04944 9.38523i 0.128519 0.395540i −0.866007 0.500032i \(-0.833322\pi\)
0.994526 + 0.104492i \(0.0333216\pi\)
\(564\) 0 0
\(565\) 8.11658 + 5.89704i 0.341467 + 0.248090i
\(566\) −2.16116 6.65135i −0.0908401 0.279577i
\(567\) 0 0
\(568\) −10.4899 7.62135i −0.440146 0.319785i
\(569\) −12.3543 + 8.97596i −0.517921 + 0.376292i −0.815820 0.578306i \(-0.803714\pi\)
0.297899 + 0.954597i \(0.403714\pi\)
\(570\) 0 0
\(571\) −20.5400 −0.859573 −0.429787 0.902930i \(-0.641411\pi\)
−0.429787 + 0.902930i \(0.641411\pi\)
\(572\) 23.3601 14.3173i 0.976734 0.598635i
\(573\) 0 0
\(574\) 0.143945 0.443017i 0.00600815 0.0184912i
\(575\) 1.09159 0.793087i 0.0455225 0.0330740i
\(576\) 0 0
\(577\) 13.6765 + 42.0920i 0.569362 + 1.75231i 0.654622 + 0.755956i \(0.272828\pi\)
−0.0852608 + 0.996359i \(0.527172\pi\)
\(578\) −4.80345 14.7835i −0.199797 0.614912i
\(579\) 0 0
\(580\) 3.86255 2.80631i 0.160384 0.116526i
\(581\) −2.82105 + 8.68231i −0.117037 + 0.360203i
\(582\) 0 0
\(583\) 14.8851 35.9428i 0.616479 1.48860i
\(584\) −16.5902 −0.686507
\(585\) 0 0
\(586\) −8.43818 + 6.13069i −0.348578 + 0.253257i
\(587\) −2.88772 2.09805i −0.119189 0.0865959i 0.526594 0.850117i \(-0.323469\pi\)
−0.645783 + 0.763521i \(0.723469\pi\)
\(588\) 0 0
\(589\) 3.37749 + 10.3948i 0.139167 + 0.428312i
\(590\) −0.784517 0.569985i −0.0322980 0.0234659i
\(591\) 0 0
\(592\) 10.4677 32.2164i 0.430221 1.32408i
\(593\) 11.2563 0.462240 0.231120 0.972925i \(-0.425761\pi\)
0.231120 + 0.972925i \(0.425761\pi\)
\(594\) 0 0
\(595\) 17.2177 0.705857
\(596\) 11.5838 35.6514i 0.474493 1.46034i
\(597\) 0 0
\(598\) −6.22361 4.52171i −0.254502 0.184907i
\(599\) −13.4813 41.4911i −0.550830 1.69528i −0.706708 0.707505i \(-0.749821\pi\)
0.155878 0.987776i \(-0.450179\pi\)
\(600\) 0 0
\(601\) 14.3428 + 10.4206i 0.585054 + 0.425066i 0.840543 0.541746i \(-0.182236\pi\)
−0.255489 + 0.966812i \(0.582236\pi\)
\(602\) 3.22916 2.34612i 0.131611 0.0956208i
\(603\) 0 0
\(604\) 9.04378 0.367986
\(605\) 3.97088 + 25.0490i 0.161439 + 1.01839i
\(606\) 0 0
\(607\) −2.21483 + 6.81655i −0.0898972 + 0.276675i −0.985890 0.167393i \(-0.946465\pi\)
0.895993 + 0.444068i \(0.146465\pi\)
\(608\) −4.69376 + 3.41022i −0.190357 + 0.138303i
\(609\) 0 0
\(610\) 1.91303 + 5.88770i 0.0774563 + 0.238386i
\(611\) 17.8271 + 54.8662i 0.721208 + 2.21965i
\(612\) 0 0
\(613\) 10.0143 7.27582i 0.404474 0.293868i −0.366887 0.930266i \(-0.619576\pi\)
0.771361 + 0.636398i \(0.219576\pi\)
\(614\) 2.92321 8.99673i 0.117971 0.363078i
\(615\) 0 0
\(616\) 5.08995 + 0.400238i 0.205080 + 0.0161260i
\(617\) 6.11777 0.246292 0.123146 0.992389i \(-0.460702\pi\)
0.123146 + 0.992389i \(0.460702\pi\)
\(618\) 0 0
\(619\) −31.4088 + 22.8198i −1.26243 + 0.917207i −0.998874 0.0474378i \(-0.984894\pi\)
−0.263553 + 0.964645i \(0.584894\pi\)
\(620\) −27.8310 20.2204i −1.11772 0.812072i
\(621\) 0 0
\(622\) 0.564012 + 1.73585i 0.0226148 + 0.0696012i
\(623\) −4.27599 3.10669i −0.171314 0.124467i
\(624\) 0 0
\(625\) −8.18266 + 25.1836i −0.327306 + 1.00735i
\(626\) 5.26366 0.210378
\(627\) 0 0
\(628\) −4.12353 −0.164547
\(629\) 25.5358 78.5912i 1.01818 3.13364i
\(630\) 0 0
\(631\) 7.85393 + 5.70621i 0.312660 + 0.227161i 0.733037 0.680189i \(-0.238102\pi\)
−0.420377 + 0.907350i \(0.638102\pi\)
\(632\) 1.28986 + 3.96979i 0.0513079 + 0.157910i
\(633\) 0 0
\(634\) 2.90120 + 2.10785i 0.115222 + 0.0837134i
\(635\) 11.8397 8.60205i 0.469844 0.341362i
\(636\) 0 0
\(637\) 4.49155 0.177962
\(638\) 1.27659 0.782414i 0.0505406 0.0309761i
\(639\) 0 0
\(640\) 7.39199 22.7502i 0.292194 0.899281i
\(641\) 12.0125 8.72762i 0.474467 0.344720i −0.324713 0.945813i \(-0.605268\pi\)
0.799179 + 0.601093i \(0.205268\pi\)
\(642\) 0 0
\(643\) −0.327423 1.00771i −0.0129123 0.0397400i 0.944393 0.328820i \(-0.106651\pi\)
−0.957305 + 0.289080i \(0.906651\pi\)
\(644\) 2.42769 + 7.47166i 0.0956644 + 0.294425i
\(645\) 0 0
\(646\) −3.26377 + 2.37126i −0.128411 + 0.0932962i
\(647\) −3.88194 + 11.9474i −0.152615 + 0.469700i −0.997911 0.0645974i \(-0.979424\pi\)
0.845297 + 0.534297i \(0.179424\pi\)
\(648\) 0 0
\(649\) 2.64553 + 2.25918i 0.103846 + 0.0886806i
\(650\) −0.568898 −0.0223140
\(651\) 0 0
\(652\) −14.6378 + 10.6350i −0.573259 + 0.416497i
\(653\) −23.9585 17.4069i −0.937568 0.681183i 0.0102659 0.999947i \(-0.496732\pi\)
−0.947834 + 0.318764i \(0.896732\pi\)
\(654\) 0 0
\(655\) −10.8504 33.3942i −0.423961 1.30482i
\(656\) 2.87706 + 2.09031i 0.112330 + 0.0816129i
\(657\) 0 0
\(658\) −1.59147 + 4.89803i −0.0620418 + 0.190945i
\(659\) −9.45208 −0.368201 −0.184100 0.982907i \(-0.558937\pi\)
−0.184100 + 0.982907i \(0.558937\pi\)
\(660\) 0 0
\(661\) −8.94284 −0.347836 −0.173918 0.984760i \(-0.555643\pi\)
−0.173918 + 0.984760i \(0.555643\pi\)
\(662\) −3.21292 + 9.88836i −0.124874 + 0.384322i
\(663\) 0 0
\(664\) 11.3695 + 8.26043i 0.441223 + 0.320567i
\(665\) −0.959913 2.95431i −0.0372238 0.114563i
\(666\) 0 0
\(667\) 3.89071 + 2.82677i 0.150649 + 0.109453i
\(668\) 12.8632 9.34563i 0.497690 0.361593i
\(669\) 0 0
\(670\) 2.27834 0.0880201
\(671\) −5.18614 21.5953i −0.200209 0.833679i
\(672\) 0 0
\(673\) 2.37389 7.30609i 0.0915068 0.281629i −0.894821 0.446426i \(-0.852697\pi\)
0.986328 + 0.164797i \(0.0526968\pi\)
\(674\) −5.11112 + 3.71345i −0.196873 + 0.143037i
\(675\) 0 0
\(676\) −4.07735 12.5488i −0.156821 0.482646i
\(677\) −10.8302 33.3320i −0.416240 1.28105i −0.911138 0.412102i \(-0.864795\pi\)
0.494898 0.868951i \(-0.335205\pi\)
\(678\) 0 0
\(679\) −4.64862 + 3.37742i −0.178398 + 0.129613i
\(680\) 8.19055 25.2079i 0.314093 0.966679i
\(681\) 0 0
\(682\) −8.20406 7.00596i −0.314150 0.268272i
\(683\) −23.5098 −0.899577 −0.449789 0.893135i \(-0.648501\pi\)
−0.449789 + 0.893135i \(0.648501\pi\)
\(684\) 0 0
\(685\) 35.6256 25.8835i 1.36118 0.988957i
\(686\) 0.324392 + 0.235684i 0.0123853 + 0.00899847i
\(687\) 0 0
\(688\) 9.41655 + 28.9812i 0.359003 + 1.10490i
\(689\) −42.6228 30.9673i −1.62380 1.17976i
\(690\) 0 0
\(691\) −5.01981 + 15.4494i −0.190963 + 0.587723i −1.00000 3.45787e-5i \(-0.999989\pi\)
0.809037 + 0.587757i \(0.199989\pi\)
\(692\) −29.3673 −1.11638
\(693\) 0 0
\(694\) −0.894036 −0.0339371
\(695\) −2.80648 + 8.63745i −0.106456 + 0.327637i
\(696\) 0 0
\(697\) 7.01855 + 5.09927i 0.265846 + 0.193149i
\(698\) −1.19177 3.66788i −0.0451090 0.138831i
\(699\) 0 0
\(700\) 0.470022 + 0.341491i 0.0177652 + 0.0129071i
\(701\) 18.2371 13.2501i 0.688808 0.500448i −0.187460 0.982272i \(-0.560026\pi\)
0.876268 + 0.481824i \(0.160026\pi\)
\(702\) 0 0
\(703\) −14.9088 −0.562295
\(704\) −5.57816 + 13.4695i −0.210235 + 0.507650i
\(705\) 0 0
\(706\) 1.23730 3.80802i 0.0465664 0.143317i
\(707\) −7.73709 + 5.62132i −0.290983 + 0.211412i
\(708\) 0 0
\(709\) 7.45304 + 22.9381i 0.279905 + 0.861458i 0.987880 + 0.155221i \(0.0496089\pi\)
−0.707975 + 0.706238i \(0.750391\pi\)
\(710\) −2.40625 7.40567i −0.0903048 0.277930i
\(711\) 0 0
\(712\) −6.58252 + 4.78248i −0.246690 + 0.179231i
\(713\) 10.7080 32.9558i 0.401018 1.23421i
\(714\) 0 0
\(715\) 34.2406 + 2.69244i 1.28053 + 0.100692i
\(716\) 32.3259 1.20808
\(717\) 0 0
\(718\) −3.32399 + 2.41502i −0.124050 + 0.0901279i
\(719\) −26.0574 18.9318i −0.971776 0.706037i −0.0159203 0.999873i \(-0.505068\pi\)
−0.955856 + 0.293837i \(0.905068\pi\)
\(720\) 0 0
\(721\) −0.249560 0.768068i −0.00929412 0.0286044i
\(722\) −5.57461 4.05019i −0.207465 0.150732i
\(723\) 0 0
\(724\) −11.8015 + 36.3214i −0.438600 + 1.34987i
\(725\) 0.355648 0.0132084
\(726\) 0 0
\(727\) 7.29214 0.270450 0.135225 0.990815i \(-0.456824\pi\)
0.135225 + 0.990815i \(0.456824\pi\)
\(728\) 2.13665 6.57594i 0.0791896 0.243720i
\(729\) 0 0
\(730\) −8.06034 5.85618i −0.298326 0.216747i
\(731\) 22.9715 + 70.6990i 0.849632 + 2.61490i
\(732\) 0 0
\(733\) −4.70741 3.42014i −0.173872 0.126326i 0.497446 0.867495i \(-0.334271\pi\)
−0.671318 + 0.741170i \(0.734271\pi\)
\(734\) 1.19786 0.870295i 0.0442138 0.0321232i
\(735\) 0 0
\(736\) 18.3941 0.678014
\(737\) −8.14849 0.640740i −0.300154 0.0236020i
\(738\) 0 0
\(739\) −4.36063 + 13.4206i −0.160408 + 0.493686i −0.998669 0.0515840i \(-0.983573\pi\)
0.838260 + 0.545270i \(0.183573\pi\)
\(740\) 37.9629 27.5817i 1.39555 1.01392i
\(741\) 0 0
\(742\) −1.45339 4.47308i −0.0533557 0.164212i
\(743\) 0.704889 + 2.16943i 0.0258599 + 0.0795885i 0.963154 0.268952i \(-0.0866773\pi\)
−0.937294 + 0.348541i \(0.886677\pi\)
\(744\) 0 0
\(745\) 38.0173 27.6212i 1.39285 1.01196i
\(746\) −2.13934 + 6.58420i −0.0783267 + 0.241065i
\(747\) 0 0
\(748\) −17.4296 + 42.0868i −0.637288 + 1.53885i
\(749\) −16.8478 −0.615607
\(750\) 0 0
\(751\) 20.6194 14.9809i 0.752412 0.546659i −0.144161 0.989554i \(-0.546048\pi\)
0.896574 + 0.442895i \(0.146048\pi\)
\(752\) −31.8090 23.1106i −1.15996 0.842757i
\(753\) 0 0
\(754\) −0.626592 1.92845i −0.0228192 0.0702301i
\(755\) 9.17194 + 6.66380i 0.333801 + 0.242521i
\(756\) 0 0
\(757\) 7.77059 23.9154i 0.282427 0.869221i −0.704731 0.709475i \(-0.748932\pi\)
0.987158 0.159746i \(-0.0510677\pi\)
\(758\) 2.08084 0.0755796
\(759\) 0 0
\(760\) −4.78195 −0.173460
\(761\) 8.79224 27.0597i 0.318718 0.980914i −0.655478 0.755214i \(-0.727533\pi\)
0.974197 0.225700i \(-0.0724670\pi\)
\(762\) 0 0
\(763\) −7.61988 5.53617i −0.275858 0.200423i
\(764\) −5.96775 18.3668i −0.215906 0.664489i
\(765\) 0 0
\(766\) −5.71616 4.15303i −0.206533 0.150055i
\(767\) 3.81152 2.76923i 0.137626 0.0999912i
\(768\) 0 0
\(769\) −45.0119 −1.62317 −0.811586 0.584233i \(-0.801395\pi\)
−0.811586 + 0.584233i \(0.801395\pi\)
\(770\) 2.33167 + 1.99116i 0.0840275 + 0.0717564i
\(771\) 0 0
\(772\) 7.36017 22.6523i 0.264898 0.815273i
\(773\) −24.9705 + 18.1422i −0.898128 + 0.652528i −0.937984 0.346677i \(-0.887310\pi\)
0.0398566 + 0.999205i \(0.487310\pi\)
\(774\) 0 0
\(775\) −0.791877 2.43715i −0.0284451 0.0875449i
\(776\) 2.73340 + 8.41255i 0.0981235 + 0.301993i
\(777\) 0 0
\(778\) 3.44466 2.50269i 0.123497 0.0897258i
\(779\) 0.483667 1.48857i 0.0173292 0.0533337i
\(780\) 0 0
\(781\) 6.52324 + 27.1631i 0.233420 + 0.971971i
\(782\) 12.7902 0.457375
\(783\) 0 0
\(784\) −2.47655 + 1.79932i −0.0884483 + 0.0642614i
\(785\) −4.18196 3.03837i −0.149261 0.108444i
\(786\) 0 0
\(787\) −11.0176 33.9085i −0.392733 1.20871i −0.930713 0.365751i \(-0.880812\pi\)
0.537980 0.842958i \(-0.319188\pi\)
\(788\) 0.988326 + 0.718061i 0.0352077 + 0.0255799i
\(789\) 0 0
\(790\) −0.774618 + 2.38403i −0.0275597 + 0.0848199i
\(791\) −4.35139 −0.154718
\(792\) 0 0
\(793\) −30.0771 −1.06807
\(794\) −2.80353 + 8.62838i −0.0994935 + 0.306210i
\(795\) 0 0
\(796\) 19.8717 + 14.4376i 0.704334 + 0.511729i
\(797\) 13.7032 + 42.1740i 0.485391 + 1.49388i 0.831414 + 0.555653i \(0.187532\pi\)
−0.346023 + 0.938226i \(0.612468\pi\)
\(798\) 0 0
\(799\) −77.5975 56.3779i −2.74520 1.99451i
\(800\) 1.10049 0.799551i 0.0389081 0.0282684i
\(801\) 0 0
\(802\) −1.84827 −0.0652647
\(803\) 27.1809 + 23.2114i 0.959191 + 0.819114i
\(804\) 0 0
\(805\) −3.04331 + 9.36635i −0.107263 + 0.330120i
\(806\) −11.8199 + 8.58769i −0.416340 + 0.302488i
\(807\) 0 0
\(808\) 4.54944 + 14.0017i 0.160049 + 0.492579i
\(809\) 1.98179 + 6.09932i 0.0696760 + 0.214441i 0.979831 0.199827i \(-0.0640379\pi\)
−0.910155 + 0.414267i \(0.864038\pi\)
\(810\) 0 0
\(811\) −27.9849 + 20.3322i −0.982683 + 0.713961i −0.958307 0.285742i \(-0.907760\pi\)
−0.0243767 + 0.999703i \(0.507760\pi\)
\(812\) −0.639899 + 1.96941i −0.0224561 + 0.0691126i
\(813\) 0 0
\(814\) 12.5469 7.68992i 0.439768 0.269532i
\(815\) −22.6814 −0.794496
\(816\) 0 0
\(817\) 10.8502 7.88316i 0.379602 0.275797i
\(818\) 6.82800 + 4.96083i 0.238735 + 0.173451i
\(819\) 0 0
\(820\) 1.52232 + 4.68522i 0.0531618 + 0.163615i
\(821\) 11.1679 + 8.11394i 0.389762 + 0.283178i 0.765358 0.643605i \(-0.222562\pi\)
−0.375596 + 0.926783i \(0.622562\pi\)
\(822\) 0 0
\(823\) −17.5513 + 54.0174i −0.611801 + 1.88293i −0.171168 + 0.985242i \(0.554754\pi\)
−0.440633 + 0.897687i \(0.645246\pi\)
\(824\) −1.24322 −0.0433097
\(825\) 0 0
\(826\) 0.420588 0.0146341
\(827\) 1.63590 5.03480i 0.0568860 0.175077i −0.918576 0.395244i \(-0.870660\pi\)
0.975462 + 0.220167i \(0.0706601\pi\)
\(828\) 0 0
\(829\) −24.8059 18.0225i −0.861544 0.625948i 0.0667606 0.997769i \(-0.478734\pi\)
−0.928305 + 0.371821i \(0.878734\pi\)
\(830\) 2.60802 + 8.02666i 0.0905257 + 0.278609i
\(831\) 0 0
\(832\) 15.9728 + 11.6049i 0.553757 + 0.402328i
\(833\) −6.04150 + 4.38941i −0.209326 + 0.152084i
\(834\) 0 0
\(835\) 19.9316 0.689763
\(836\) 8.19321 + 0.644257i 0.283368 + 0.0222821i
\(837\) 0 0
\(838\) −1.74494 + 5.37036i −0.0602778 + 0.185516i
\(839\) 12.5166 9.09388i 0.432123 0.313956i −0.350374 0.936610i \(-0.613946\pi\)
0.782497 + 0.622654i \(0.213946\pi\)
\(840\) 0 0
\(841\) −8.56978 26.3751i −0.295510 0.909485i
\(842\) −3.41580 10.5128i −0.117716 0.362294i
\(843\) 0 0
\(844\) 19.4618 14.1398i 0.669901 0.486712i
\(845\) 5.11130 15.7310i 0.175834 0.541162i
\(846\) 0 0
\(847\) −7.77924 7.77711i −0.267298 0.267225i
\(848\) 35.9069 1.23305
\(849\) 0 0
\(850\) 0.765214 0.555961i 0.0262466 0.0190693i
\(851\) 38.2397 + 27.7827i 1.31084 + 0.952380i
\(852\) 0 0
\(853\) −11.2368 34.5834i −0.384741 1.18411i −0.936668 0.350219i \(-0.886107\pi\)
0.551927 0.833893i \(-0.313893\pi\)
\(854\) −2.17225 1.57823i −0.0743327 0.0540059i
\(855\) 0 0
\(856\) −8.01460 + 24.6664i −0.273933 + 0.843080i
\(857\) 17.0833 0.583554 0.291777 0.956486i \(-0.405754\pi\)
0.291777 + 0.956486i \(0.405754\pi\)
\(858\) 0 0
\(859\) 21.3315 0.727822 0.363911 0.931434i \(-0.381441\pi\)
0.363911 + 0.931434i \(0.381441\pi\)
\(860\) −13.0444 + 40.1465i −0.444810 + 1.36899i
\(861\) 0 0
\(862\) −11.1719 8.11687i −0.380517 0.276462i
\(863\) 4.61965 + 14.2178i 0.157255 + 0.483980i 0.998382 0.0568564i \(-0.0181077\pi\)
−0.841128 + 0.540837i \(0.818108\pi\)
\(864\) 0 0
\(865\) −29.7835 21.6390i −1.01267 0.735747i
\(866\) 5.23518 3.80358i 0.177899 0.129251i
\(867\) 0 0
\(868\) 14.9205 0.506435
\(869\) 3.44088 8.30863i 0.116724 0.281851i
\(870\) 0 0
\(871\) −3.42057 + 10.5274i −0.115901 + 0.356708i
\(872\) −11.7302 + 8.52246i −0.397233 + 0.288607i
\(873\) 0 0
\(874\) −0.713071 2.19461i −0.0241200 0.0742336i
\(875\) −3.33732 10.2712i −0.112822 0.347230i
\(876\) 0 0
\(877\) −13.9555 + 10.1392i −0.471242 + 0.342378i −0.797925 0.602756i \(-0.794069\pi\)
0.326683 + 0.945134i \(0.394069\pi\)
\(878\) −2.39184 + 7.36132i −0.0807207 + 0.248433i
\(879\) 0 0
\(880\) −19.9582 + 12.2323i −0.672791 + 0.412350i
\(881\) −2.58251 −0.0870069 −0.0435035 0.999053i \(-0.513852\pi\)
−0.0435035 + 0.999053i \(0.513852\pi\)
\(882\) 0 0
\(883\) −29.2922 + 21.2821i −0.985762 + 0.716198i −0.958989 0.283443i \(-0.908523\pi\)
−0.0267732 + 0.999642i \(0.508523\pi\)
\(884\) 49.9086 + 36.2607i 1.67861 + 1.21958i
\(885\) 0 0
\(886\) −1.62704 5.00751i −0.0546614 0.168230i
\(887\) −43.0200 31.2559i −1.44447 1.04947i −0.987084 0.160202i \(-0.948785\pi\)
−0.457387 0.889268i \(-0.651215\pi\)
\(888\) 0 0
\(889\) −1.96145 + 6.03673i −0.0657850 + 0.202465i
\(890\) −4.88629 −0.163789
\(891\) 0 0
\(892\) −18.8140 −0.629938
\(893\) −5.34745 + 16.4578i −0.178946 + 0.550738i
\(894\) 0 0
\(895\) 32.7840 + 23.8190i 1.09585 + 0.796180i
\(896\) 3.20608 + 9.86729i 0.107108 + 0.329643i
\(897\) 0 0
\(898\) −4.13636 3.00524i −0.138032 0.100286i
\(899\) 7.38928 5.36862i 0.246446 0.179054i
\(900\) 0 0
\(901\) 87.5943 2.91819
\(902\) 0.360761 + 1.50222i 0.0120120 + 0.0500186i
\(903\) 0 0
\(904\) −2.06998 + 6.37073i −0.0688464 + 0.211887i
\(905\) −38.7317 + 28.1402i −1.28749 + 0.935414i
\(906\) 0 0
\(907\) 15.1300 + 46.5653i 0.502382 + 1.54617i 0.805127 + 0.593102i \(0.202097\pi\)
−0.302745 + 0.953072i \(0.597903\pi\)
\(908\) 1.69861 + 5.22779i 0.0563704 + 0.173490i
\(909\) 0 0
\(910\) 3.35934 2.44070i 0.111361 0.0809084i
\(911\) 0.308429 0.949246i 0.0102187 0.0314499i −0.945817 0.324700i \(-0.894737\pi\)
0.956036 + 0.293250i \(0.0947368\pi\)
\(912\) 0 0
\(913\) −7.07024 29.4408i −0.233991 0.974348i
\(914\) 3.68667 0.121944
\(915\) 0 0
\(916\) 29.9106 21.7313i 0.988274 0.718023i
\(917\) 12.3207 + 8.95149i 0.406864 + 0.295604i
\(918\) 0 0
\(919\) 16.4871 + 50.7420i 0.543859 + 1.67382i 0.723688 + 0.690127i \(0.242445\pi\)
−0.179830 + 0.983698i \(0.557555\pi\)
\(920\) 12.2653 + 8.91124i 0.404374 + 0.293795i
\(921\) 0 0
\(922\) −1.99136 + 6.12876i −0.0655818 + 0.201840i
\(923\) 37.8315 1.24524
\(924\) 0 0
\(925\) 3.49547 0.114930
\(926\) −4.07904 + 12.5540i −0.134046 + 0.412550i
\(927\) 0 0
\(928\) 3.92242 + 2.84980i 0.128760 + 0.0935494i
\(929\) 0.842763 + 2.59376i 0.0276501 + 0.0850984i 0.963929 0.266158i \(-0.0857544\pi\)
−0.936279 + 0.351257i \(0.885754\pi\)
\(930\) 0 0
\(931\) 1.08998 + 0.791919i 0.0357227 + 0.0259541i
\(932\) −6.94956 + 5.04915i −0.227641 + 0.165391i
\(933\) 0 0
\(934\) 3.41220 0.111651
\(935\) −48.6877 + 29.8404i −1.59226 + 0.975886i
\(936\) 0 0
\(937\) 3.91631 12.0532i 0.127940 0.393760i −0.866485 0.499203i \(-0.833626\pi\)
0.994425 + 0.105443i \(0.0336261\pi\)
\(938\) −0.799446 + 0.580832i −0.0261028 + 0.0189648i
\(939\) 0 0
\(940\) −16.8309 51.8002i −0.548963 1.68954i
\(941\) −1.85489 5.70877i −0.0604677 0.186101i 0.916260 0.400585i \(-0.131193\pi\)
−0.976727 + 0.214484i \(0.931193\pi\)
\(942\) 0 0
\(943\) −4.01454 + 2.91674i −0.130731 + 0.0949820i
\(944\) −0.992241 + 3.05380i −0.0322947 + 0.0993928i
\(945\) 0 0
\(946\) −5.06520 + 12.2308i −0.164684 + 0.397658i
\(947\) −20.2935 −0.659450 −0.329725 0.944077i \(-0.606956\pi\)
−0.329725 + 0.944077i \(0.606956\pi\)
\(948\) 0 0
\(949\) 39.1606 28.4519i 1.27121 0.923586i
\(950\) −0.138057 0.100304i −0.00447915 0.00325429i
\(951\) 0 0
\(952\) 3.55243 + 10.9332i 0.115135 + 0.354349i
\(953\) 20.7822 + 15.0991i 0.673201 + 0.489109i 0.871095 0.491115i \(-0.163410\pi\)
−0.197894 + 0.980223i \(0.563410\pi\)
\(954\) 0 0
\(955\) 7.48108 23.0244i 0.242082 0.745052i
\(956\) −41.8741 −1.35431
\(957\) 0 0
\(958\) 3.81820 0.123360
\(959\) −5.90200 + 18.1645i −0.190585 + 0.586561i
\(960\) 0 0
\(961\) −28.1628 20.4614i −0.908476 0.660047i
\(962\) −6.15844 18.9537i −0.198556 0.611093i
\(963\) 0 0
\(964\) −7.19748 5.22927i −0.231815 0.168424i
\(965\) 24.1555 17.5500i 0.777594 0.564955i
\(966\) 0 0
\(967\) −3.86788 −0.124383 −0.0621914 0.998064i \(-0.519809\pi\)
−0.0621914 + 0.998064i \(0.519809\pi\)
\(968\) −15.0869 + 7.68973i −0.484910 + 0.247157i
\(969\) 0 0
\(970\) −1.64153 + 5.05210i −0.0527063 + 0.162213i
\(971\) 20.8901 15.1776i 0.670397 0.487072i −0.199761 0.979845i \(-0.564017\pi\)
0.870158 + 0.492773i \(0.164017\pi\)
\(972\) 0 0
\(973\) −1.21723 3.74626i −0.0390227 0.120100i
\(974\) 0.135601 + 0.417336i 0.00434492 + 0.0133723i
\(975\) 0 0
\(976\) 16.5839 12.0489i 0.530838 0.385676i
\(977\) −16.1377 + 49.6667i −0.516291 + 1.58898i 0.264631 + 0.964350i \(0.414750\pi\)
−0.780921 + 0.624630i \(0.785250\pi\)
\(978\) 0 0
\(979\) 17.4758 + 1.37417i 0.558529 + 0.0439188i
\(980\) −4.24055 −0.135459
\(981\) 0 0
\(982\) 6.70465 4.87121i 0.213954 0.155447i
\(983\) 26.2894 + 19.1004i 0.838502 + 0.609208i 0.921952 0.387304i \(-0.126594\pi\)
−0.0834495 + 0.996512i \(0.526594\pi\)
\(984\) 0 0
\(985\) 0.473237 + 1.45647i 0.0150786 + 0.0464071i
\(986\) 2.72742 + 1.98159i 0.0868587 + 0.0631065i
\(987\) 0 0
\(988\) 3.43934 10.5852i 0.109420 0.336760i
\(989\) −42.5203 −1.35207
\(990\) 0 0
\(991\) 1.37062 0.0435391 0.0217695 0.999763i \(-0.493070\pi\)
0.0217695 + 0.999763i \(0.493070\pi\)
\(992\) 10.7953 33.2244i 0.342750 1.05488i
\(993\) 0 0
\(994\) 2.73230 + 1.98513i 0.0866632 + 0.0629645i
\(995\) 9.51510 + 29.2845i 0.301649 + 0.928380i
\(996\) 0 0
\(997\) −6.99282 5.08058i −0.221465 0.160904i 0.471521 0.881855i \(-0.343705\pi\)
−0.692986 + 0.720951i \(0.743705\pi\)
\(998\) 7.73187 5.61753i 0.244748 0.177820i
\(999\) 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 693.2.m.k.64.4 32
3.2 odd 2 inner 693.2.m.k.64.5 yes 32
11.4 even 5 7623.2.a.dc.1.8 16
11.5 even 5 inner 693.2.m.k.379.4 yes 32
11.7 odd 10 7623.2.a.db.1.9 16
33.5 odd 10 inner 693.2.m.k.379.5 yes 32
33.26 odd 10 7623.2.a.dc.1.9 16
33.29 even 10 7623.2.a.db.1.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
693.2.m.k.64.4 32 1.1 even 1 trivial
693.2.m.k.64.5 yes 32 3.2 odd 2 inner
693.2.m.k.379.4 yes 32 11.5 even 5 inner
693.2.m.k.379.5 yes 32 33.5 odd 10 inner
7623.2.a.db.1.8 16 33.29 even 10
7623.2.a.db.1.9 16 11.7 odd 10
7623.2.a.dc.1.8 16 11.4 even 5
7623.2.a.dc.1.9 16 33.26 odd 10