Properties

Label 243.2.g.a.37.2
Level $243$
Weight $2$
Character 243.37
Analytic conductor $1.940$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [243,2,Mod(10,243)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(243, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("243.10");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 243 = 3^{5} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 243.g (of order \(27\), degree \(18\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.94036476912\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: no (minimal twist has level 81)
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 37.2
Character \(\chi\) \(=\) 243.37
Dual form 243.2.g.a.46.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.587043 + 1.96086i) q^{2} +(-1.82938 - 1.20320i) q^{4} +(-0.00823679 + 0.0190950i) q^{5} +(0.0874756 + 1.50190i) q^{7} +(0.297287 - 0.249453i) q^{8} +O(q^{10})\) \(q+(-0.587043 + 1.96086i) q^{2} +(-1.82938 - 1.20320i) q^{4} +(-0.00823679 + 0.0190950i) q^{5} +(0.0874756 + 1.50190i) q^{7} +(0.297287 - 0.249453i) q^{8} +(-0.0326074 - 0.0273608i) q^{10} +(-3.58878 + 4.82057i) q^{11} +(-1.50763 + 1.59800i) q^{13} +(-2.99637 - 0.710152i) q^{14} +(-1.41989 - 3.29167i) q^{16} +(0.699765 - 3.96856i) q^{17} +(0.689869 + 3.91244i) q^{19} +(0.0380435 - 0.0250216i) q^{20} +(-7.34570 - 9.86699i) q^{22} +(0.0585660 - 1.00554i) q^{23} +(3.43091 + 3.63655i) q^{25} +(-2.24841 - 3.89435i) q^{26} +(1.64706 - 2.85280i) q^{28} +(5.47229 - 1.29696i) q^{29} +(2.66908 - 1.34046i) q^{31} +(8.05896 - 0.941957i) q^{32} +(7.37101 + 3.70186i) q^{34} +(-0.0293993 - 0.0107005i) q^{35} +(-6.49019 + 2.36224i) q^{37} +(-8.07674 - 0.944036i) q^{38} +(0.00231463 + 0.00773139i) q^{40} +(-1.41282 - 4.71915i) q^{41} +(-6.54159 - 0.764602i) q^{43} +(12.3654 - 4.50063i) q^{44} +(1.93734 + 0.705135i) q^{46} +(12.0829 + 6.06825i) q^{47} +(4.70462 - 0.549892i) q^{49} +(-9.14487 + 4.59273i) q^{50} +(4.68076 - 1.10936i) q^{52} +(-4.73855 + 8.20740i) q^{53} +(-0.0624889 - 0.108234i) q^{55} +(0.400658 + 0.424673i) q^{56} +(-0.669320 + 11.4918i) q^{58} +(1.04543 + 1.40425i) q^{59} +(7.43976 - 4.89321i) q^{61} +(1.06160 + 6.02061i) q^{62} +(-1.63891 + 9.29469i) q^{64} +(-0.0180958 - 0.0419507i) q^{65} +(13.2656 + 3.14400i) q^{67} +(-6.05513 + 6.41806i) q^{68} +(0.0382408 - 0.0513663i) q^{70} +(3.48681 + 2.92578i) q^{71} +(-7.30212 + 6.12720i) q^{73} +(-0.821995 - 14.1131i) q^{74} +(3.44543 - 7.98741i) q^{76} +(-7.55393 - 4.96830i) q^{77} +(0.913387 - 3.05093i) q^{79} +0.0745499 q^{80} +10.0830 q^{82} +(0.481396 - 1.60798i) q^{83} +(0.0700161 + 0.0460503i) q^{85} +(5.33948 - 12.3783i) q^{86} +(0.135609 + 2.32832i) q^{88} +(7.75680 - 6.50872i) q^{89} +(-2.53191 - 2.12452i) q^{91} +(-1.31701 + 1.76905i) q^{92} +(-18.9922 + 20.1305i) q^{94} +(-0.0803905 - 0.0190529i) q^{95} +(-2.62993 - 6.09687i) q^{97} +(-1.68356 + 9.54793i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26} - 9 q^{28} - 9 q^{29} - 18 q^{31} - 36 q^{32} - 18 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} - 18 q^{40} - 18 q^{43} - 54 q^{44} - 18 q^{46} - 36 q^{47} - 18 q^{49} - 99 q^{50} - 45 q^{53} - 9 q^{55} - 126 q^{56} - 18 q^{58} - 45 q^{59} - 18 q^{61} - 81 q^{62} - 18 q^{64} + 9 q^{67} + 99 q^{68} + 36 q^{70} + 90 q^{71} - 18 q^{73} + 162 q^{74} + 63 q^{76} + 162 q^{77} + 36 q^{79} + 288 q^{80} - 36 q^{82} + 90 q^{83} + 36 q^{85} + 162 q^{86} + 63 q^{88} + 81 q^{89} - 18 q^{91} + 144 q^{92} + 36 q^{94} - 18 q^{95} + 9 q^{97} - 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{16}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.587043 + 1.96086i −0.415102 + 1.38654i 0.453601 + 0.891205i \(0.350139\pi\)
−0.868703 + 0.495333i \(0.835046\pi\)
\(3\) 0 0
\(4\) −1.82938 1.20320i −0.914691 0.601602i
\(5\) −0.00823679 + 0.0190950i −0.00368361 + 0.00853956i −0.920048 0.391806i \(-0.871851\pi\)
0.916364 + 0.400345i \(0.131110\pi\)
\(6\) 0 0
\(7\) 0.0874756 + 1.50190i 0.0330627 + 0.567664i 0.973641 + 0.228087i \(0.0732469\pi\)
−0.940578 + 0.339577i \(0.889716\pi\)
\(8\) 0.297287 0.249453i 0.105107 0.0881950i
\(9\) 0 0
\(10\) −0.0326074 0.0273608i −0.0103114 0.00865225i
\(11\) −3.58878 + 4.82057i −1.08206 + 1.45346i −0.201518 + 0.979485i \(0.564588\pi\)
−0.880540 + 0.473972i \(0.842820\pi\)
\(12\) 0 0
\(13\) −1.50763 + 1.59800i −0.418142 + 0.443205i −0.901866 0.432016i \(-0.857802\pi\)
0.483724 + 0.875221i \(0.339284\pi\)
\(14\) −2.99637 0.710152i −0.800812 0.189796i
\(15\) 0 0
\(16\) −1.41989 3.29167i −0.354972 0.822918i
\(17\) 0.699765 3.96856i 0.169718 0.962518i −0.774348 0.632760i \(-0.781922\pi\)
0.944066 0.329758i \(-0.106967\pi\)
\(18\) 0 0
\(19\) 0.689869 + 3.91244i 0.158267 + 0.897576i 0.955738 + 0.294219i \(0.0950595\pi\)
−0.797471 + 0.603357i \(0.793829\pi\)
\(20\) 0.0380435 0.0250216i 0.00850678 0.00559500i
\(21\) 0 0
\(22\) −7.34570 9.86699i −1.56611 2.10365i
\(23\) 0.0585660 1.00554i 0.0122119 0.209670i −0.986682 0.162658i \(-0.947993\pi\)
0.998894 0.0470114i \(-0.0149697\pi\)
\(24\) 0 0
\(25\) 3.43091 + 3.63655i 0.686182 + 0.727311i
\(26\) −2.24841 3.89435i −0.440949 0.763746i
\(27\) 0 0
\(28\) 1.64706 2.85280i 0.311266 0.539128i
\(29\) 5.47229 1.29696i 1.01618 0.240839i 0.311410 0.950276i \(-0.399199\pi\)
0.704769 + 0.709437i \(0.251051\pi\)
\(30\) 0 0
\(31\) 2.66908 1.34046i 0.479382 0.240754i −0.192663 0.981265i \(-0.561713\pi\)
0.672045 + 0.740510i \(0.265416\pi\)
\(32\) 8.05896 0.941957i 1.42464 0.166516i
\(33\) 0 0
\(34\) 7.37101 + 3.70186i 1.26412 + 0.634864i
\(35\) −0.0293993 0.0107005i −0.00496939 0.00180871i
\(36\) 0 0
\(37\) −6.49019 + 2.36224i −1.06698 + 0.388349i −0.815047 0.579395i \(-0.803289\pi\)
−0.251934 + 0.967744i \(0.581067\pi\)
\(38\) −8.07674 0.944036i −1.31022 0.153143i
\(39\) 0 0
\(40\) 0.00231463 + 0.00773139i 0.000365975 + 0.00122244i
\(41\) −1.41282 4.71915i −0.220646 0.737008i −0.994601 0.103768i \(-0.966910\pi\)
0.773956 0.633240i \(-0.218275\pi\)
\(42\) 0 0
\(43\) −6.54159 0.764602i −0.997583 0.116601i −0.398399 0.917212i \(-0.630434\pi\)
−0.599184 + 0.800611i \(0.704508\pi\)
\(44\) 12.3654 4.50063i 1.86415 0.678496i
\(45\) 0 0
\(46\) 1.93734 + 0.705135i 0.285646 + 0.103967i
\(47\) 12.0829 + 6.06825i 1.76247 + 0.885145i 0.955735 + 0.294228i \(0.0950626\pi\)
0.806733 + 0.590916i \(0.201234\pi\)
\(48\) 0 0
\(49\) 4.70462 0.549892i 0.672089 0.0785560i
\(50\) −9.14487 + 4.59273i −1.29328 + 0.649510i
\(51\) 0 0
\(52\) 4.68076 1.10936i 0.649104 0.153840i
\(53\) −4.73855 + 8.20740i −0.650890 + 1.12737i 0.332018 + 0.943273i \(0.392271\pi\)
−0.982907 + 0.184101i \(0.941063\pi\)
\(54\) 0 0
\(55\) −0.0624889 0.108234i −0.00842600 0.0145943i
\(56\) 0.400658 + 0.424673i 0.0535402 + 0.0567493i
\(57\) 0 0
\(58\) −0.669320 + 11.4918i −0.0878860 + 1.50895i
\(59\) 1.04543 + 1.40425i 0.136103 + 0.182818i 0.864949 0.501859i \(-0.167350\pi\)
−0.728846 + 0.684678i \(0.759943\pi\)
\(60\) 0 0
\(61\) 7.43976 4.89321i 0.952564 0.626511i 0.0248056 0.999692i \(-0.492103\pi\)
0.927759 + 0.373181i \(0.121733\pi\)
\(62\) 1.06160 + 6.02061i 0.134823 + 0.764619i
\(63\) 0 0
\(64\) −1.63891 + 9.29469i −0.204863 + 1.16184i
\(65\) −0.0180958 0.0419507i −0.00224450 0.00520334i
\(66\) 0 0
\(67\) 13.2656 + 3.14400i 1.62065 + 0.384101i 0.937997 0.346644i \(-0.112679\pi\)
0.682651 + 0.730745i \(0.260827\pi\)
\(68\) −6.05513 + 6.41806i −0.734292 + 0.778305i
\(69\) 0 0
\(70\) 0.0382408 0.0513663i 0.00457065 0.00613945i
\(71\) 3.48681 + 2.92578i 0.413808 + 0.347226i 0.825802 0.563960i \(-0.190723\pi\)
−0.411994 + 0.911187i \(0.635167\pi\)
\(72\) 0 0
\(73\) −7.30212 + 6.12720i −0.854648 + 0.717135i −0.960808 0.277214i \(-0.910589\pi\)
0.106160 + 0.994349i \(0.466144\pi\)
\(74\) −0.821995 14.1131i −0.0955549 1.64061i
\(75\) 0 0
\(76\) 3.44543 7.98741i 0.395218 0.916219i
\(77\) −7.55393 4.96830i −0.860850 0.566190i
\(78\) 0 0
\(79\) 0.913387 3.05093i 0.102764 0.343256i −0.891108 0.453791i \(-0.850071\pi\)
0.993872 + 0.110535i \(0.0352565\pi\)
\(80\) 0.0745499 0.00833493
\(81\) 0 0
\(82\) 10.0830 1.11348
\(83\) 0.481396 1.60798i 0.0528401 0.176498i −0.927496 0.373833i \(-0.878043\pi\)
0.980336 + 0.197335i \(0.0632286\pi\)
\(84\) 0 0
\(85\) 0.0700161 + 0.0460503i 0.00759431 + 0.00499485i
\(86\) 5.33948 12.3783i 0.575770 1.33479i
\(87\) 0 0
\(88\) 0.135609 + 2.32832i 0.0144560 + 0.248200i
\(89\) 7.75680 6.50872i 0.822219 0.689923i −0.131272 0.991346i \(-0.541906\pi\)
0.953491 + 0.301423i \(0.0974616\pi\)
\(90\) 0 0
\(91\) −2.53191 2.12452i −0.265416 0.222711i
\(92\) −1.31701 + 1.76905i −0.137308 + 0.184436i
\(93\) 0 0
\(94\) −18.9922 + 20.1305i −1.95889 + 2.07630i
\(95\) −0.0803905 0.0190529i −0.00824790 0.00195479i
\(96\) 0 0
\(97\) −2.62993 6.09687i −0.267029 0.619043i 0.730961 0.682420i \(-0.239072\pi\)
−0.997990 + 0.0633767i \(0.979813\pi\)
\(98\) −1.68356 + 9.54793i −0.170065 + 0.964486i
\(99\) 0 0
\(100\) −1.90093 10.7807i −0.190093 1.07807i
\(101\) −2.33869 + 1.53818i −0.232709 + 0.153055i −0.660508 0.750819i \(-0.729659\pi\)
0.427800 + 0.903874i \(0.359289\pi\)
\(102\) 0 0
\(103\) 2.70182 + 3.62917i 0.266218 + 0.357593i 0.915051 0.403338i \(-0.132150\pi\)
−0.648833 + 0.760931i \(0.724743\pi\)
\(104\) −0.0495737 + 0.851147i −0.00486110 + 0.0834618i
\(105\) 0 0
\(106\) −13.3119 14.1097i −1.29296 1.37046i
\(107\) −2.05630 3.56161i −0.198790 0.344314i 0.749347 0.662178i \(-0.230368\pi\)
−0.948136 + 0.317864i \(0.897034\pi\)
\(108\) 0 0
\(109\) 4.81003 8.33121i 0.460717 0.797985i −0.538280 0.842766i \(-0.680926\pi\)
0.998997 + 0.0447810i \(0.0142590\pi\)
\(110\) 0.248916 0.0589941i 0.0237332 0.00562486i
\(111\) 0 0
\(112\) 4.81955 2.42047i 0.455404 0.228713i
\(113\) −1.83824 + 0.214859i −0.172927 + 0.0202122i −0.202116 0.979362i \(-0.564782\pi\)
0.0291888 + 0.999574i \(0.490708\pi\)
\(114\) 0 0
\(115\) 0.0187184 + 0.00940074i 0.00174550 + 0.000876624i
\(116\) −11.5714 4.21166i −1.07438 0.391042i
\(117\) 0 0
\(118\) −3.36726 + 1.22558i −0.309982 + 0.112824i
\(119\) 6.02159 + 0.703823i 0.551998 + 0.0645193i
\(120\) 0 0
\(121\) −7.20371 24.0621i −0.654883 2.18746i
\(122\) 5.22744 + 17.4609i 0.473270 + 1.58083i
\(123\) 0 0
\(124\) −6.49563 0.759230i −0.583325 0.0681809i
\(125\) −0.195408 + 0.0711227i −0.0174778 + 0.00636141i
\(126\) 0 0
\(127\) −17.8824 6.50866i −1.58681 0.577550i −0.610136 0.792296i \(-0.708885\pi\)
−0.976670 + 0.214746i \(0.931108\pi\)
\(128\) −2.76194 1.38710i −0.244123 0.122603i
\(129\) 0 0
\(130\) 0.0928825 0.0108564i 0.00814633 0.000952170i
\(131\) 0.710862 0.357008i 0.0621083 0.0311920i −0.417474 0.908689i \(-0.637085\pi\)
0.479582 + 0.877497i \(0.340788\pi\)
\(132\) 0 0
\(133\) −5.81574 + 1.37836i −0.504289 + 0.119519i
\(134\) −13.9524 + 24.1663i −1.20531 + 2.08765i
\(135\) 0 0
\(136\) −0.781940 1.35436i −0.0670508 0.116135i
\(137\) −2.90137 3.07527i −0.247880 0.262738i 0.591472 0.806326i \(-0.298547\pi\)
−0.839352 + 0.543588i \(0.817066\pi\)
\(138\) 0 0
\(139\) −0.318310 + 5.46516i −0.0269987 + 0.463549i 0.957531 + 0.288331i \(0.0931002\pi\)
−0.984530 + 0.175218i \(0.943937\pi\)
\(140\) 0.0409077 + 0.0549486i 0.00345733 + 0.00464401i
\(141\) 0 0
\(142\) −7.78396 + 5.11959i −0.653216 + 0.429627i
\(143\) −2.29269 13.0025i −0.191725 1.08733i
\(144\) 0 0
\(145\) −0.0203087 + 0.115176i −0.00168655 + 0.00956488i
\(146\) −7.72794 17.9154i −0.639569 1.48269i
\(147\) 0 0
\(148\) 14.7153 + 3.48759i 1.20959 + 0.286678i
\(149\) 5.33644 5.65630i 0.437178 0.463382i −0.470898 0.882188i \(-0.656070\pi\)
0.908076 + 0.418806i \(0.137551\pi\)
\(150\) 0 0
\(151\) −7.90781 + 10.6220i −0.643529 + 0.864409i −0.997487 0.0708524i \(-0.977428\pi\)
0.353958 + 0.935261i \(0.384835\pi\)
\(152\) 1.18106 + 0.991027i 0.0957966 + 0.0803829i
\(153\) 0 0
\(154\) 14.1766 11.8956i 1.14239 0.958575i
\(155\) 0.00361152 + 0.0620074i 0.000290084 + 0.00498055i
\(156\) 0 0
\(157\) −2.75454 + 6.38575i −0.219836 + 0.509638i −0.992068 0.125703i \(-0.959881\pi\)
0.772231 + 0.635341i \(0.219141\pi\)
\(158\) 5.44624 + 3.58205i 0.433280 + 0.284973i
\(159\) 0 0
\(160\) −0.0483933 + 0.161645i −0.00382583 + 0.0127791i
\(161\) 1.51534 0.119426
\(162\) 0 0
\(163\) 5.19903 0.407219 0.203610 0.979052i \(-0.434733\pi\)
0.203610 + 0.979052i \(0.434733\pi\)
\(164\) −3.09351 + 10.3331i −0.241563 + 0.806876i
\(165\) 0 0
\(166\) 2.87042 + 1.88790i 0.222788 + 0.146530i
\(167\) −3.74255 + 8.67620i −0.289607 + 0.671384i −0.999456 0.0329691i \(-0.989504\pi\)
0.709849 + 0.704353i \(0.248763\pi\)
\(168\) 0 0
\(169\) 0.475244 + 8.15962i 0.0365572 + 0.627663i
\(170\) −0.131401 + 0.110258i −0.0100780 + 0.00845642i
\(171\) 0 0
\(172\) 11.0471 + 9.26962i 0.842333 + 0.706802i
\(173\) −5.37651 + 7.22190i −0.408768 + 0.549071i −0.958063 0.286558i \(-0.907489\pi\)
0.549295 + 0.835629i \(0.314896\pi\)
\(174\) 0 0
\(175\) −5.16161 + 5.47099i −0.390181 + 0.413568i
\(176\) 20.9634 + 4.96842i 1.58018 + 0.374509i
\(177\) 0 0
\(178\) 8.20913 + 19.0309i 0.615300 + 1.42643i
\(179\) −1.67669 + 9.50897i −0.125321 + 0.710733i 0.855795 + 0.517315i \(0.173069\pi\)
−0.981116 + 0.193418i \(0.938043\pi\)
\(180\) 0 0
\(181\) −1.70395 9.66360i −0.126654 0.718290i −0.980312 0.197456i \(-0.936732\pi\)
0.853658 0.520834i \(-0.174379\pi\)
\(182\) 5.65224 3.71754i 0.418972 0.275562i
\(183\) 0 0
\(184\) −0.233424 0.313543i −0.0172083 0.0231147i
\(185\) 0.00835138 0.143388i 0.000614006 0.0105421i
\(186\) 0 0
\(187\) 16.6194 + 17.6156i 1.21533 + 1.28818i
\(188\) −14.8029 25.6393i −1.07961 1.86994i
\(189\) 0 0
\(190\) 0.0845529 0.146450i 0.00613411 0.0106246i
\(191\) 3.43575 0.814287i 0.248602 0.0589197i −0.104426 0.994533i \(-0.533300\pi\)
0.353027 + 0.935613i \(0.385152\pi\)
\(192\) 0 0
\(193\) 19.3015 9.69357i 1.38935 0.697759i 0.412357 0.911022i \(-0.364706\pi\)
0.976995 + 0.213264i \(0.0684094\pi\)
\(194\) 13.4990 1.57781i 0.969171 0.113280i
\(195\) 0 0
\(196\) −9.26819 4.65466i −0.662014 0.332476i
\(197\) −15.5802 5.67071i −1.11004 0.404022i −0.279032 0.960282i \(-0.590014\pi\)
−0.831008 + 0.556260i \(0.812236\pi\)
\(198\) 0 0
\(199\) 19.4015 7.06158i 1.37534 0.500582i 0.454576 0.890708i \(-0.349791\pi\)
0.920761 + 0.390126i \(0.127569\pi\)
\(200\) 1.92711 + 0.225247i 0.136268 + 0.0159274i
\(201\) 0 0
\(202\) −1.64325 5.48883i −0.115619 0.386193i
\(203\) 2.42659 + 8.10537i 0.170313 + 0.568886i
\(204\) 0 0
\(205\) 0.101750 + 0.0118928i 0.00710650 + 0.000830630i
\(206\) −8.70238 + 3.16741i −0.606324 + 0.220684i
\(207\) 0 0
\(208\) 7.40076 + 2.69365i 0.513150 + 0.186771i
\(209\) −21.3360 10.7153i −1.47584 0.741195i
\(210\) 0 0
\(211\) −2.15943 + 0.252402i −0.148662 + 0.0173760i −0.190098 0.981765i \(-0.560881\pi\)
0.0414366 + 0.999141i \(0.486807\pi\)
\(212\) 18.5438 9.31305i 1.27359 0.639623i
\(213\) 0 0
\(214\) 8.19096 1.94129i 0.559922 0.132704i
\(215\) 0.0684818 0.118614i 0.00467042 0.00808941i
\(216\) 0 0
\(217\) 2.24672 + 3.89143i 0.152517 + 0.264168i
\(218\) 13.5127 + 14.3226i 0.915193 + 0.970047i
\(219\) 0 0
\(220\) −0.0159114 + 0.273188i −0.00107275 + 0.0184183i
\(221\) 5.28677 + 7.10136i 0.355627 + 0.477689i
\(222\) 0 0
\(223\) −18.8624 + 12.4060i −1.26312 + 0.830766i −0.991305 0.131584i \(-0.957994\pi\)
−0.271813 + 0.962350i \(0.587623\pi\)
\(224\) 2.11969 + 12.0213i 0.141627 + 0.803209i
\(225\) 0 0
\(226\) 0.657816 3.73066i 0.0437573 0.248160i
\(227\) 7.30925 + 16.9447i 0.485132 + 1.12466i 0.968448 + 0.249216i \(0.0801729\pi\)
−0.483316 + 0.875446i \(0.660568\pi\)
\(228\) 0 0
\(229\) −10.9915 2.60504i −0.726340 0.172146i −0.149219 0.988804i \(-0.547676\pi\)
−0.577121 + 0.816658i \(0.695824\pi\)
\(230\) −0.0294221 + 0.0311856i −0.00194003 + 0.00205632i
\(231\) 0 0
\(232\) 1.30331 1.75065i 0.0855665 0.114936i
\(233\) −12.6194 10.5889i −0.826724 0.693703i 0.127813 0.991798i \(-0.459204\pi\)
−0.954536 + 0.298095i \(0.903649\pi\)
\(234\) 0 0
\(235\) −0.215398 + 0.180740i −0.0140510 + 0.0117902i
\(236\) −0.222885 3.82678i −0.0145086 0.249102i
\(237\) 0 0
\(238\) −4.91503 + 11.3943i −0.318594 + 0.738585i
\(239\) −9.15402 6.02070i −0.592125 0.389446i 0.217789 0.975996i \(-0.430116\pi\)
−0.809913 + 0.586549i \(0.800486\pi\)
\(240\) 0 0
\(241\) 5.72108 19.1097i 0.368527 1.23097i −0.549851 0.835263i \(-0.685316\pi\)
0.918378 0.395704i \(-0.129499\pi\)
\(242\) 51.4113 3.30484
\(243\) 0 0
\(244\) −19.4977 −1.24821
\(245\) −0.0282508 + 0.0943643i −0.00180488 + 0.00602872i
\(246\) 0 0
\(247\) −7.29214 4.79612i −0.463988 0.305170i
\(248\) 0.459100 1.06431i 0.0291529 0.0675840i
\(249\) 0 0
\(250\) −0.0247488 0.424920i −0.00156525 0.0268743i
\(251\) 15.8375 13.2893i 0.999656 0.838811i 0.0127196 0.999919i \(-0.495951\pi\)
0.986937 + 0.161108i \(0.0515067\pi\)
\(252\) 0 0
\(253\) 4.63709 + 3.89098i 0.291532 + 0.244624i
\(254\) 23.2603 31.2440i 1.45948 1.96043i
\(255\) 0 0
\(256\) −8.61231 + 9.12852i −0.538270 + 0.570533i
\(257\) −11.4743 2.71945i −0.715744 0.169635i −0.143420 0.989662i \(-0.545810\pi\)
−0.572324 + 0.820027i \(0.693958\pi\)
\(258\) 0 0
\(259\) −4.11557 9.54096i −0.255729 0.592847i
\(260\) −0.0173712 + 0.0985168i −0.00107731 + 0.00610975i
\(261\) 0 0
\(262\) 0.282737 + 1.60348i 0.0174676 + 0.0990634i
\(263\) 1.63557 1.07573i 0.100854 0.0663326i −0.498080 0.867131i \(-0.665962\pi\)
0.598934 + 0.800798i \(0.295591\pi\)
\(264\) 0 0
\(265\) −0.117690 0.158085i −0.00722965 0.00971111i
\(266\) 0.711327 12.2130i 0.0436143 0.748828i
\(267\) 0 0
\(268\) −20.4849 21.7128i −1.25132 1.32632i
\(269\) 10.6534 + 18.4522i 0.649547 + 1.12505i 0.983231 + 0.182364i \(0.0583749\pi\)
−0.333684 + 0.942685i \(0.608292\pi\)
\(270\) 0 0
\(271\) −6.85691 + 11.8765i −0.416528 + 0.721447i −0.995587 0.0938378i \(-0.970086\pi\)
0.579060 + 0.815285i \(0.303420\pi\)
\(272\) −14.0568 + 3.33152i −0.852319 + 0.202003i
\(273\) 0 0
\(274\) 7.73340 3.88386i 0.467192 0.234633i
\(275\) −29.8431 + 3.48815i −1.79960 + 0.210344i
\(276\) 0 0
\(277\) 4.28071 + 2.14985i 0.257203 + 0.129172i 0.572729 0.819745i \(-0.305885\pi\)
−0.315526 + 0.948917i \(0.602181\pi\)
\(278\) −10.5296 3.83245i −0.631522 0.229855i
\(279\) 0 0
\(280\) −0.0114093 + 0.00415264i −0.000681835 + 0.000248168i
\(281\) −13.8337 1.61692i −0.825247 0.0964576i −0.307023 0.951702i \(-0.599333\pi\)
−0.518225 + 0.855245i \(0.673407\pi\)
\(282\) 0 0
\(283\) −0.860245 2.87342i −0.0511363 0.170807i 0.928607 0.371065i \(-0.121007\pi\)
−0.979743 + 0.200258i \(0.935822\pi\)
\(284\) −2.85840 9.54772i −0.169615 0.566553i
\(285\) 0 0
\(286\) 26.8420 + 3.13739i 1.58720 + 0.185517i
\(287\) 6.96410 2.53472i 0.411078 0.149620i
\(288\) 0 0
\(289\) 0.714943 + 0.260218i 0.0420555 + 0.0153069i
\(290\) −0.213923 0.107436i −0.0125620 0.00630887i
\(291\) 0 0
\(292\) 20.7306 2.42307i 1.21317 0.141799i
\(293\) 21.5690 10.8324i 1.26007 0.632833i 0.311759 0.950161i \(-0.399082\pi\)
0.948316 + 0.317328i \(0.102786\pi\)
\(294\) 0 0
\(295\) −0.0354253 + 0.00839595i −0.00206254 + 0.000488831i
\(296\) −1.34018 + 2.32126i −0.0778964 + 0.134920i
\(297\) 0 0
\(298\) 7.95849 + 13.7845i 0.461023 + 0.798515i
\(299\) 1.51855 + 1.60957i 0.0878203 + 0.0930840i
\(300\) 0 0
\(301\) 0.576125 9.89168i 0.0332073 0.570147i
\(302\) −16.1861 21.7417i −0.931406 1.25110i
\(303\) 0 0
\(304\) 11.8989 7.82606i 0.682451 0.448855i
\(305\) 0.0321562 + 0.182367i 0.00184126 + 0.0104423i
\(306\) 0 0
\(307\) 3.34825 18.9889i 0.191095 1.08375i −0.726776 0.686874i \(-0.758982\pi\)
0.917871 0.396879i \(-0.129907\pi\)
\(308\) 7.84116 + 18.1778i 0.446791 + 1.03578i
\(309\) 0 0
\(310\) −0.123708 0.0293193i −0.00702614 0.00166523i
\(311\) −7.85065 + 8.32121i −0.445170 + 0.471852i −0.910634 0.413215i \(-0.864406\pi\)
0.465464 + 0.885067i \(0.345887\pi\)
\(312\) 0 0
\(313\) 3.36282 4.51705i 0.190078 0.255319i −0.696861 0.717207i \(-0.745420\pi\)
0.886938 + 0.461888i \(0.152828\pi\)
\(314\) −10.9045 9.14999i −0.615378 0.516364i
\(315\) 0 0
\(316\) −5.34182 + 4.48232i −0.300501 + 0.252150i
\(317\) 0.352180 + 6.04669i 0.0197804 + 0.339616i 0.993651 + 0.112511i \(0.0358892\pi\)
−0.973870 + 0.227106i \(0.927074\pi\)
\(318\) 0 0
\(319\) −13.3868 + 31.0341i −0.749517 + 1.73757i
\(320\) −0.163983 0.107853i −0.00916694 0.00602919i
\(321\) 0 0
\(322\) −0.889571 + 2.97137i −0.0495738 + 0.165588i
\(323\) 16.0095 0.890794
\(324\) 0 0
\(325\) −10.9838 −0.609269
\(326\) −3.05206 + 10.1946i −0.169038 + 0.564626i
\(327\) 0 0
\(328\) −1.59722 1.05051i −0.0881918 0.0580046i
\(329\) −8.05693 + 18.6781i −0.444193 + 1.02975i
\(330\) 0 0
\(331\) −0.594022 10.1990i −0.0326504 0.560586i −0.974477 0.224487i \(-0.927929\pi\)
0.941827 0.336099i \(-0.109108\pi\)
\(332\) −2.81538 + 2.36238i −0.154514 + 0.129653i
\(333\) 0 0
\(334\) −14.8158 12.4319i −0.810684 0.680244i
\(335\) −0.169301 + 0.227410i −0.00924988 + 0.0124247i
\(336\) 0 0
\(337\) 6.25087 6.62553i 0.340506 0.360916i −0.534380 0.845245i \(-0.679455\pi\)
0.874886 + 0.484329i \(0.160936\pi\)
\(338\) −16.2789 3.85816i −0.885454 0.209856i
\(339\) 0 0
\(340\) −0.0726783 0.168487i −0.00394153 0.00913750i
\(341\) −3.11696 + 17.6771i −0.168793 + 0.957271i
\(342\) 0 0
\(343\) 3.06613 + 17.3889i 0.165555 + 0.938911i
\(344\) −2.13546 + 1.40451i −0.115136 + 0.0757263i
\(345\) 0 0
\(346\) −11.0049 14.7822i −0.591628 0.794694i
\(347\) 0.167828 2.88149i 0.00900946 0.154686i −0.990803 0.135313i \(-0.956796\pi\)
0.999812 0.0193731i \(-0.00616704\pi\)
\(348\) 0 0
\(349\) 18.8015 + 19.9284i 1.00642 + 1.06674i 0.997768 + 0.0667806i \(0.0212728\pi\)
0.00865259 + 0.999963i \(0.497246\pi\)
\(350\) −7.69776 13.3329i −0.411463 0.712674i
\(351\) 0 0
\(352\) −24.3811 + 42.2293i −1.29952 + 2.25083i
\(353\) −2.70304 + 0.640631i −0.143868 + 0.0340974i −0.301919 0.953334i \(-0.597627\pi\)
0.158051 + 0.987431i \(0.449479\pi\)
\(354\) 0 0
\(355\) −0.0845881 + 0.0424817i −0.00448947 + 0.00225470i
\(356\) −22.0215 + 2.57394i −1.16714 + 0.136419i
\(357\) 0 0
\(358\) −17.6615 8.86993i −0.933438 0.468790i
\(359\) 17.4937 + 6.36718i 0.923281 + 0.336047i 0.759543 0.650457i \(-0.225423\pi\)
0.163738 + 0.986504i \(0.447645\pi\)
\(360\) 0 0
\(361\) 3.02287 1.10024i 0.159099 0.0579071i
\(362\) 19.9493 + 2.33174i 1.04851 + 0.122553i
\(363\) 0 0
\(364\) 2.07560 + 6.93297i 0.108791 + 0.363387i
\(365\) −0.0568531 0.189903i −0.00297583 0.00993996i
\(366\) 0 0
\(367\) 4.10848 + 0.480212i 0.214461 + 0.0250669i 0.222645 0.974900i \(-0.428531\pi\)
−0.00818400 + 0.999967i \(0.502605\pi\)
\(368\) −3.39306 + 1.23497i −0.176876 + 0.0643775i
\(369\) 0 0
\(370\) 0.276261 + 0.100551i 0.0143621 + 0.00522738i
\(371\) −12.7412 6.39886i −0.661489 0.332212i
\(372\) 0 0
\(373\) 3.87344 0.452740i 0.200559 0.0234420i −0.0152202 0.999884i \(-0.504845\pi\)
0.215779 + 0.976442i \(0.430771\pi\)
\(374\) −44.2980 + 22.2473i −2.29060 + 1.15038i
\(375\) 0 0
\(376\) 5.10582 1.21010i 0.263313 0.0624062i
\(377\) −6.17768 + 10.7001i −0.318167 + 0.551081i
\(378\) 0 0
\(379\) −15.6974 27.1887i −0.806321 1.39659i −0.915395 0.402556i \(-0.868122\pi\)
0.109074 0.994034i \(-0.465211\pi\)
\(380\) 0.124141 + 0.131581i 0.00636828 + 0.00674998i
\(381\) 0 0
\(382\) −0.420229 + 7.21505i −0.0215008 + 0.369154i
\(383\) 13.5437 + 18.1923i 0.692050 + 0.929585i 0.999760 0.0218955i \(-0.00697012\pi\)
−0.307710 + 0.951480i \(0.599563\pi\)
\(384\) 0 0
\(385\) 0.157090 0.103320i 0.00800605 0.00526566i
\(386\) 7.67694 + 43.5381i 0.390746 + 2.21603i
\(387\) 0 0
\(388\) −2.52462 + 14.3178i −0.128168 + 0.726879i
\(389\) −6.33140 14.6778i −0.321015 0.744195i −0.999950 0.00999750i \(-0.996818\pi\)
0.678935 0.734198i \(-0.262442\pi\)
\(390\) 0 0
\(391\) −3.94957 0.936065i −0.199738 0.0473388i
\(392\) 1.26145 1.33706i 0.0637128 0.0675317i
\(393\) 0 0
\(394\) 20.2657 27.2216i 1.02097 1.37140i
\(395\) 0.0507341 + 0.0425710i 0.00255271 + 0.00214198i
\(396\) 0 0
\(397\) −19.5239 + 16.3825i −0.979876 + 0.822214i −0.984071 0.177778i \(-0.943109\pi\)
0.00419466 + 0.999991i \(0.498665\pi\)
\(398\) 2.45724 + 42.1892i 0.123170 + 2.11475i
\(399\) 0 0
\(400\) 7.09883 16.4569i 0.354941 0.822847i
\(401\) 8.21664 + 5.40417i 0.410320 + 0.269871i 0.737844 0.674971i \(-0.235844\pi\)
−0.327524 + 0.944843i \(0.606214\pi\)
\(402\) 0 0
\(403\) −1.88194 + 6.28612i −0.0937461 + 0.313134i
\(404\) 6.12911 0.304935
\(405\) 0 0
\(406\) −17.3180 −0.859479
\(407\) 11.9046 39.7640i 0.590087 1.97103i
\(408\) 0 0
\(409\) −20.4267 13.4348i −1.01004 0.664311i −0.0672585 0.997736i \(-0.521425\pi\)
−0.942777 + 0.333425i \(0.891796\pi\)
\(410\) −0.0830516 + 0.192535i −0.00410163 + 0.00950864i
\(411\) 0 0
\(412\) −0.576025 9.88997i −0.0283787 0.487244i
\(413\) −2.01760 + 1.69296i −0.0992795 + 0.0833054i
\(414\) 0 0
\(415\) 0.0267392 + 0.0224368i 0.00131257 + 0.00110138i
\(416\) −10.6447 + 14.2983i −0.521900 + 0.701033i
\(417\) 0 0
\(418\) 33.5365 35.5466i 1.64032 1.73864i
\(419\) 4.23901 + 1.00466i 0.207089 + 0.0490810i 0.332851 0.942979i \(-0.391989\pi\)
−0.125762 + 0.992060i \(0.540138\pi\)
\(420\) 0 0
\(421\) 0.501821 + 1.16335i 0.0244573 + 0.0566983i 0.930007 0.367542i \(-0.119801\pi\)
−0.905550 + 0.424240i \(0.860541\pi\)
\(422\) 0.772757 4.38252i 0.0376172 0.213338i
\(423\) 0 0
\(424\) 0.638656 + 3.62200i 0.0310159 + 0.175900i
\(425\) 16.8327 11.0711i 0.816507 0.537025i
\(426\) 0 0
\(427\) 7.99990 + 10.7457i 0.387142 + 0.520022i
\(428\) −0.523590 + 8.98969i −0.0253087 + 0.434533i
\(429\) 0 0
\(430\) 0.192384 + 0.203915i 0.00927757 + 0.00983365i
\(431\) −17.8588 30.9323i −0.860227 1.48996i −0.871709 0.490023i \(-0.836988\pi\)
0.0114820 0.999934i \(-0.496345\pi\)
\(432\) 0 0
\(433\) 16.1789 28.0227i 0.777509 1.34668i −0.155865 0.987778i \(-0.549816\pi\)
0.933374 0.358906i \(-0.116850\pi\)
\(434\) −8.94948 + 2.12107i −0.429589 + 0.101814i
\(435\) 0 0
\(436\) −18.8235 + 9.45353i −0.901483 + 0.452742i
\(437\) 3.97452 0.464555i 0.190127 0.0222227i
\(438\) 0 0
\(439\) 7.93828 + 3.98676i 0.378874 + 0.190277i 0.628036 0.778184i \(-0.283859\pi\)
−0.249163 + 0.968462i \(0.580155\pi\)
\(440\) −0.0455764 0.0165885i −0.00217277 0.000790824i
\(441\) 0 0
\(442\) −17.0284 + 6.19781i −0.809956 + 0.294800i
\(443\) 13.3588 + 1.56142i 0.634695 + 0.0741852i 0.427355 0.904084i \(-0.359445\pi\)
0.207340 + 0.978269i \(0.433519\pi\)
\(444\) 0 0
\(445\) 0.0603932 + 0.201727i 0.00286291 + 0.00956279i
\(446\) −13.2534 44.2694i −0.627565 2.09621i
\(447\) 0 0
\(448\) −14.1030 1.64841i −0.666306 0.0778800i
\(449\) 16.7390 6.09251i 0.789964 0.287524i 0.0846431 0.996411i \(-0.473025\pi\)
0.705321 + 0.708888i \(0.250803\pi\)
\(450\) 0 0
\(451\) 27.8193 + 10.1254i 1.30996 + 0.476787i
\(452\) 3.62136 + 1.81871i 0.170334 + 0.0855451i
\(453\) 0 0
\(454\) −37.5171 + 4.38512i −1.76077 + 0.205804i
\(455\) 0.0614227 0.0308476i 0.00287954 0.00144616i
\(456\) 0 0
\(457\) 1.21419 0.287769i 0.0567976 0.0134613i −0.202119 0.979361i \(-0.564783\pi\)
0.258916 + 0.965900i \(0.416635\pi\)
\(458\) 11.5606 20.0236i 0.540192 0.935640i
\(459\) 0 0
\(460\) −0.0229321 0.0397196i −0.00106922 0.00185194i
\(461\) −12.9468 13.7228i −0.602993 0.639135i 0.351917 0.936031i \(-0.385530\pi\)
−0.954910 + 0.296896i \(0.904049\pi\)
\(462\) 0 0
\(463\) 0.691589 11.8741i 0.0321409 0.551838i −0.943350 0.331799i \(-0.892345\pi\)
0.975491 0.220039i \(-0.0706184\pi\)
\(464\) −12.0392 16.1715i −0.558906 0.750741i
\(465\) 0 0
\(466\) 28.1715 18.5287i 1.30502 0.858326i
\(467\) −1.20388 6.82753i −0.0557088 0.315940i 0.944201 0.329370i \(-0.106836\pi\)
−0.999910 + 0.0134295i \(0.995725\pi\)
\(468\) 0 0
\(469\) −3.56155 + 20.1986i −0.164457 + 0.932683i
\(470\) −0.227958 0.528467i −0.0105149 0.0243764i
\(471\) 0 0
\(472\) 0.661088 + 0.156681i 0.0304290 + 0.00721181i
\(473\) 27.1621 28.7902i 1.24892 1.32377i
\(474\) 0 0
\(475\) −11.8609 + 15.9320i −0.544217 + 0.731010i
\(476\) −10.1689 8.53276i −0.466093 0.391098i
\(477\) 0 0
\(478\) 17.1796 14.4154i 0.785775 0.659343i
\(479\) 2.11898 + 36.3814i 0.0968185 + 1.66231i 0.601402 + 0.798946i \(0.294609\pi\)
−0.504584 + 0.863363i \(0.668354\pi\)
\(480\) 0 0
\(481\) 6.00998 13.9327i 0.274031 0.635276i
\(482\) 34.1130 + 22.4365i 1.55381 + 1.02195i
\(483\) 0 0
\(484\) −15.7732 + 52.6863i −0.716965 + 2.39483i
\(485\) 0.138082 0.00626998
\(486\) 0 0
\(487\) 35.1072 1.59086 0.795429 0.606046i \(-0.207245\pi\)
0.795429 + 0.606046i \(0.207245\pi\)
\(488\) 0.991116 3.31056i 0.0448657 0.149862i
\(489\) 0 0
\(490\) −0.168451 0.110792i −0.00760984 0.00500507i
\(491\) 9.92481 23.0083i 0.447900 1.03835i −0.533400 0.845863i \(-0.679086\pi\)
0.981300 0.192486i \(-0.0616550\pi\)
\(492\) 0 0
\(493\) −1.31774 22.6247i −0.0593480 1.01897i
\(494\) 13.6853 11.4834i 0.615732 0.516661i
\(495\) 0 0
\(496\) −8.20217 6.88244i −0.368288 0.309031i
\(497\) −4.08921 + 5.49277i −0.183426 + 0.246384i
\(498\) 0 0
\(499\) 14.5510 15.4232i 0.651393 0.690436i −0.314535 0.949246i \(-0.601849\pi\)
0.965928 + 0.258810i \(0.0833302\pi\)
\(500\) 0.443051 + 0.105005i 0.0198139 + 0.00469597i
\(501\) 0 0
\(502\) 16.7611 + 38.8566i 0.748084 + 1.73425i
\(503\) 4.86905 27.6138i 0.217100 1.23124i −0.660124 0.751156i \(-0.729496\pi\)
0.877225 0.480080i \(-0.159392\pi\)
\(504\) 0 0
\(505\) −0.0101083 0.0573271i −0.000449814 0.00255102i
\(506\) −10.3519 + 6.80852i −0.460196 + 0.302676i
\(507\) 0 0
\(508\) 24.8825 + 33.4230i 1.10398 + 1.48291i
\(509\) −1.26445 + 21.7097i −0.0560456 + 0.962265i 0.846695 + 0.532079i \(0.178589\pi\)
−0.902740 + 0.430186i \(0.858448\pi\)
\(510\) 0 0
\(511\) −9.84119 10.4311i −0.435349 0.461443i
\(512\) −15.9347 27.5996i −0.704219 1.21974i
\(513\) 0 0
\(514\) 12.0683 20.9030i 0.532312 0.921992i
\(515\) −0.0915534 + 0.0216986i −0.00403432 + 0.000956153i
\(516\) 0 0
\(517\) −72.6152 + 36.4687i −3.19361 + 1.60389i
\(518\) 21.1245 2.46910i 0.928159 0.108486i
\(519\) 0 0
\(520\) −0.0158444 0.00795734i −0.000694821 0.000348952i
\(521\) 1.12952 + 0.411112i 0.0494852 + 0.0180112i 0.366644 0.930361i \(-0.380507\pi\)
−0.317159 + 0.948372i \(0.602729\pi\)
\(522\) 0 0
\(523\) −11.8149 + 4.30029i −0.516631 + 0.188038i −0.587159 0.809471i \(-0.699754\pi\)
0.0705281 + 0.997510i \(0.477532\pi\)
\(524\) −1.72999 0.202207i −0.0755751 0.00883346i
\(525\) 0 0
\(526\) 1.14921 + 3.83864i 0.0501081 + 0.167373i
\(527\) −3.45199 11.5304i −0.150371 0.502274i
\(528\) 0 0
\(529\) 21.8368 + 2.55236i 0.949426 + 0.110972i
\(530\) 0.379073 0.137971i 0.0164659 0.00599309i
\(531\) 0 0
\(532\) 12.2977 + 4.47598i 0.533171 + 0.194058i
\(533\) 9.67122 + 4.85707i 0.418907 + 0.210383i
\(534\) 0 0
\(535\) 0.0849463 0.00992880i 0.00367255 0.000429260i
\(536\) 4.72796 2.37447i 0.204217 0.102561i
\(537\) 0 0
\(538\) −42.4361 + 10.0576i −1.82955 + 0.433612i
\(539\) −14.2331 + 24.6524i −0.613062 + 1.06185i
\(540\) 0 0
\(541\) 18.1901 + 31.5062i 0.782053 + 1.35456i 0.930744 + 0.365672i \(0.119161\pi\)
−0.148691 + 0.988884i \(0.547506\pi\)
\(542\) −19.2629 20.4175i −0.827413 0.877006i
\(543\) 0 0
\(544\) 1.90116 32.6417i 0.0815116 1.39950i
\(545\) 0.119466 + 0.160470i 0.00511734 + 0.00687378i
\(546\) 0 0
\(547\) −9.60436 + 6.31689i −0.410653 + 0.270091i −0.737983 0.674819i \(-0.764221\pi\)
0.327330 + 0.944910i \(0.393851\pi\)
\(548\) 1.60753 + 9.11678i 0.0686705 + 0.389450i
\(549\) 0 0
\(550\) 10.6794 60.5658i 0.455370 2.58253i
\(551\) 8.84944 + 20.5153i 0.376999 + 0.873981i
\(552\) 0 0
\(553\) 4.66208 + 1.10493i 0.198252 + 0.0469865i
\(554\) −6.72853 + 7.13183i −0.285868 + 0.303002i
\(555\) 0 0
\(556\) 7.15802 9.61489i 0.303568 0.407762i
\(557\) 24.9391 + 20.9264i 1.05670 + 0.886679i 0.993782 0.111340i \(-0.0355142\pi\)
0.0629202 + 0.998019i \(0.479959\pi\)
\(558\) 0 0
\(559\) 11.0841 9.30071i 0.468810 0.393378i
\(560\) 0.00652130 + 0.111966i 0.000275575 + 0.00473144i
\(561\) 0 0
\(562\) 11.2915 26.1767i 0.476304 1.10420i
\(563\) −6.73953 4.43266i −0.284037 0.186814i 0.399493 0.916736i \(-0.369186\pi\)
−0.683531 + 0.729922i \(0.739556\pi\)
\(564\) 0 0
\(565\) 0.0110384 0.0368709i 0.000464390 0.00155117i
\(566\) 6.13938 0.258057
\(567\) 0 0
\(568\) 1.76643 0.0741177
\(569\) 3.00013 10.0211i 0.125772 0.420107i −0.871791 0.489878i \(-0.837041\pi\)
0.997563 + 0.0697702i \(0.0222266\pi\)
\(570\) 0 0
\(571\) 20.5356 + 13.5065i 0.859389 + 0.565229i 0.900958 0.433907i \(-0.142865\pi\)
−0.0415690 + 0.999136i \(0.513236\pi\)
\(572\) −11.4505 + 26.5452i −0.478768 + 1.10991i
\(573\) 0 0
\(574\) 0.882016 + 15.1436i 0.0368146 + 0.632083i
\(575\) 3.85763 3.23694i 0.160874 0.134990i
\(576\) 0 0
\(577\) 16.7824 + 14.0821i 0.698659 + 0.586244i 0.921392 0.388635i \(-0.127053\pi\)
−0.222733 + 0.974880i \(0.571498\pi\)
\(578\) −0.929954 + 1.24915i −0.0386810 + 0.0519576i
\(579\) 0 0
\(580\) 0.175733 0.186266i 0.00729692 0.00773429i
\(581\) 2.45712 + 0.582349i 0.101939 + 0.0241599i
\(582\) 0 0
\(583\) −22.5588 52.2971i −0.934288 2.16592i
\(584\) −0.642372 + 3.64307i −0.0265815 + 0.150751i
\(585\) 0 0
\(586\) 8.57882 + 48.6529i 0.354388 + 2.00983i
\(587\) −37.2045 + 24.4698i −1.53559 + 1.00998i −0.551125 + 0.834423i \(0.685801\pi\)
−0.984470 + 0.175553i \(0.943829\pi\)
\(588\) 0 0
\(589\) 7.08581 + 9.51789i 0.291966 + 0.392178i
\(590\) 0.00433289 0.0743929i 0.000178382 0.00306271i
\(591\) 0 0
\(592\) 16.9911 + 18.0095i 0.698328 + 0.740185i
\(593\) 0.181983 + 0.315204i 0.00747314 + 0.0129439i 0.869738 0.493514i \(-0.164288\pi\)
−0.862265 + 0.506458i \(0.830955\pi\)
\(594\) 0 0
\(595\) −0.0630381 + 0.109185i −0.00258431 + 0.00447616i
\(596\) −16.5681 + 3.92670i −0.678655 + 0.160844i
\(597\) 0 0
\(598\) −4.04761 + 2.03279i −0.165519 + 0.0831268i
\(599\) 27.7478 3.24326i 1.13375 0.132516i 0.471544 0.881842i \(-0.343697\pi\)
0.662201 + 0.749326i \(0.269623\pi\)
\(600\) 0 0
\(601\) 18.8668 + 9.47526i 0.769593 + 0.386504i 0.789857 0.613291i \(-0.210155\pi\)
−0.0202646 + 0.999795i \(0.506451\pi\)
\(602\) 19.0580 + 6.93655i 0.776746 + 0.282713i
\(603\) 0 0
\(604\) 27.2469 9.91706i 1.10866 0.403519i
\(605\) 0.518801 + 0.0606392i 0.0210923 + 0.00246533i
\(606\) 0 0
\(607\) 11.9393 + 39.8800i 0.484600 + 1.61868i 0.754857 + 0.655889i \(0.227706\pi\)
−0.270257 + 0.962788i \(0.587109\pi\)
\(608\) 9.24498 + 30.8804i 0.374934 + 1.25237i
\(609\) 0 0
\(610\) −0.376473 0.0440034i −0.0152430 0.00178165i
\(611\) −27.9136 + 10.1597i −1.12926 + 0.411018i
\(612\) 0 0
\(613\) −14.2653 5.19214i −0.576170 0.209709i 0.0374659 0.999298i \(-0.488071\pi\)
−0.613636 + 0.789589i \(0.710294\pi\)
\(614\) 35.2690 + 17.7128i 1.42334 + 0.714829i
\(615\) 0 0
\(616\) −3.48504 + 0.407343i −0.140416 + 0.0164123i
\(617\) 32.6914 16.4183i 1.31611 0.660974i 0.354411 0.935090i \(-0.384681\pi\)
0.961697 + 0.274116i \(0.0883852\pi\)
\(618\) 0 0
\(619\) −19.6748 + 4.66302i −0.790799 + 0.187423i −0.606117 0.795376i \(-0.707274\pi\)
−0.184682 + 0.982798i \(0.559125\pi\)
\(620\) 0.0680007 0.117781i 0.00273097 0.00473018i
\(621\) 0 0
\(622\) −11.7081 20.2790i −0.469450 0.813112i
\(623\) 10.4540 + 11.0806i 0.418829 + 0.443933i
\(624\) 0 0
\(625\) −1.45324 + 24.9512i −0.0581297 + 0.998049i
\(626\) 6.88319 + 9.24573i 0.275108 + 0.369534i
\(627\) 0 0
\(628\) 12.7225 8.36770i 0.507682 0.333908i
\(629\) 4.83308 + 27.4098i 0.192707 + 1.09290i
\(630\) 0 0
\(631\) −1.06905 + 6.06286i −0.0425580 + 0.241358i −0.998665 0.0516602i \(-0.983549\pi\)
0.956107 + 0.293019i \(0.0946598\pi\)
\(632\) −0.489525 1.13485i −0.0194723 0.0451418i
\(633\) 0 0
\(634\) −12.0635 2.85910i −0.479102 0.113549i
\(635\) 0.271577 0.287855i 0.0107772 0.0114232i
\(636\) 0 0
\(637\) −6.21412 + 8.34702i −0.246213 + 0.330721i
\(638\) −52.9949 44.4680i −2.09809 1.76051i
\(639\) 0 0
\(640\) 0.0492363 0.0413141i 0.00194623 0.00163308i
\(641\) −2.38177 40.8934i −0.0940742 1.61519i −0.633900 0.773415i \(-0.718547\pi\)
0.539826 0.841776i \(-0.318490\pi\)
\(642\) 0 0
\(643\) 9.72465 22.5443i 0.383503 0.889060i −0.611687 0.791099i \(-0.709509\pi\)
0.995190 0.0979601i \(-0.0312317\pi\)
\(644\) −2.77214 1.82326i −0.109238 0.0718467i
\(645\) 0 0
\(646\) −9.39829 + 31.3925i −0.369771 + 1.23512i
\(647\) −44.0995 −1.73373 −0.866866 0.498542i \(-0.833869\pi\)
−0.866866 + 0.498542i \(0.833869\pi\)
\(648\) 0 0
\(649\) −10.5211 −0.412990
\(650\) 6.44795 21.5376i 0.252909 0.844776i
\(651\) 0 0
\(652\) −9.51102 6.25549i −0.372480 0.244984i
\(653\) 3.90101 9.04355i 0.152658 0.353902i −0.824675 0.565606i \(-0.808642\pi\)
0.977334 + 0.211705i \(0.0679015\pi\)
\(654\) 0 0
\(655\) 0.000961862 0.0165145i 3.75831e−5 0.000645276i
\(656\) −13.5279 + 11.3512i −0.528174 + 0.443191i
\(657\) 0 0
\(658\) −31.8953 26.7634i −1.24341 1.04334i
\(659\) 22.8178 30.6496i 0.888855 1.19394i −0.0913231 0.995821i \(-0.529110\pi\)
0.980178 0.198118i \(-0.0634830\pi\)
\(660\) 0 0
\(661\) 21.7200 23.0219i 0.844810 0.895447i −0.150845 0.988557i \(-0.548200\pi\)
0.995656 + 0.0931107i \(0.0296810\pi\)
\(662\) 20.3475 + 4.82244i 0.790827 + 0.187429i
\(663\) 0 0
\(664\) −0.258002 0.598115i −0.0100124 0.0232114i
\(665\) 0.0215833 0.122405i 0.000836965 0.00474666i
\(666\) 0 0
\(667\) −0.983652 5.57857i −0.0380872 0.216003i
\(668\) 17.2858 11.3690i 0.668807 0.439881i
\(669\) 0 0
\(670\) −0.346533 0.465475i −0.0133877 0.0179829i
\(671\) −3.11163 + 53.4246i −0.120123 + 2.06243i
\(672\) 0 0
\(673\) 6.28061 + 6.65706i 0.242100 + 0.256611i 0.837018 0.547176i \(-0.184297\pi\)
−0.594918 + 0.803786i \(0.702816\pi\)
\(674\) 9.32222 + 16.1466i 0.359079 + 0.621942i
\(675\) 0 0
\(676\) 8.94828 15.4989i 0.344165 0.596111i
\(677\) 1.30114 0.308376i 0.0500069 0.0118519i −0.205536 0.978649i \(-0.565894\pi\)
0.255543 + 0.966798i \(0.417746\pi\)
\(678\) 0 0
\(679\) 8.92681 4.48321i 0.342580 0.172050i
\(680\) 0.0323022 0.00377559i 0.00123873 0.000144787i
\(681\) 0 0
\(682\) −32.8326 16.4892i −1.25723 0.631403i
\(683\) −13.8418 5.03800i −0.529642 0.192774i 0.0633367 0.997992i \(-0.479826\pi\)
−0.592978 + 0.805218i \(0.702048\pi\)
\(684\) 0 0
\(685\) 0.0826203 0.0300713i 0.00315676 0.00114897i
\(686\) −35.8971 4.19577i −1.37056 0.160195i
\(687\) 0 0
\(688\) 6.77151 + 22.6184i 0.258161 + 0.862319i
\(689\) −5.97142 19.9459i −0.227493 0.759880i
\(690\) 0 0
\(691\) −15.9253 1.86141i −0.605828 0.0708112i −0.192352 0.981326i \(-0.561612\pi\)
−0.413476 + 0.910515i \(0.635686\pi\)
\(692\) 18.5251 6.74259i 0.704219 0.256315i
\(693\) 0 0
\(694\) 5.55168 + 2.02065i 0.210739 + 0.0767027i
\(695\) −0.101736 0.0510936i −0.00385905 0.00193809i
\(696\) 0 0
\(697\) −19.7169 + 2.30458i −0.746831 + 0.0872921i
\(698\) −50.1141 + 25.1683i −1.89685 + 0.952633i
\(699\) 0 0
\(700\) 16.0253 3.79806i 0.605698 0.143553i
\(701\) 1.43354 2.48297i 0.0541441 0.0937804i −0.837683 0.546157i \(-0.816090\pi\)
0.891827 + 0.452376i \(0.149424\pi\)
\(702\) 0 0
\(703\) −13.7195 23.7629i −0.517441 0.896234i
\(704\) −38.9240 41.2571i −1.46701 1.55493i
\(705\) 0 0
\(706\) 0.330610 5.67636i 0.0124427 0.213633i
\(707\) −2.51477 3.37792i −0.0945777 0.127040i
\(708\) 0 0
\(709\) −18.2414 + 11.9975i −0.685069 + 0.450577i −0.843738 0.536755i \(-0.819650\pi\)
0.158669 + 0.987332i \(0.449280\pi\)
\(710\) −0.0336439 0.190804i −0.00126263 0.00716075i
\(711\) 0 0
\(712\) 0.682370 3.86991i 0.0255729 0.145031i
\(713\) −1.19157 2.76238i −0.0446247 0.103452i
\(714\) 0 0
\(715\) 0.267168 + 0.0633200i 0.00999152 + 0.00236803i
\(716\) 14.5085 15.3781i 0.542209 0.574708i
\(717\) 0 0
\(718\) −22.7547 + 30.5649i −0.849198 + 1.14067i
\(719\) 11.5460 + 9.68821i 0.430591 + 0.361309i 0.832175 0.554513i \(-0.187096\pi\)
−0.401583 + 0.915822i \(0.631540\pi\)
\(720\) 0 0
\(721\) −5.21430 + 4.37531i −0.194191 + 0.162945i
\(722\) 0.382852 + 6.57332i 0.0142483 + 0.244634i
\(723\) 0 0
\(724\) −8.51010 + 19.7286i −0.316275 + 0.733209i
\(725\) 23.4914 + 15.4505i 0.872449 + 0.573819i
\(726\) 0 0
\(727\) 15.3809 51.3757i 0.570445 1.90542i 0.184788 0.982778i \(-0.440840\pi\)
0.385657 0.922642i \(-0.373975\pi\)
\(728\) −1.28267 −0.0475390
\(729\) 0 0
\(730\) 0.405748 0.0150174
\(731\) −7.61195 + 25.4257i −0.281538 + 0.940402i
\(732\) 0 0
\(733\) 8.05165 + 5.29565i 0.297394 + 0.195599i 0.689433 0.724349i \(-0.257860\pi\)
−0.392039 + 0.919949i \(0.628230\pi\)
\(734\) −3.35348 + 7.77425i −0.123779 + 0.286953i
\(735\) 0 0
\(736\) −0.475194 8.15877i −0.0175159 0.300736i
\(737\) −62.7631 + 52.6645i −2.31191 + 1.93992i
\(738\) 0 0
\(739\) −15.1436 12.7070i −0.557067 0.467435i 0.320259 0.947330i \(-0.396230\pi\)
−0.877326 + 0.479895i \(0.840675\pi\)
\(740\) −0.187803 + 0.252263i −0.00690376 + 0.00927336i
\(741\) 0 0
\(742\) 20.0269 21.2273i 0.735211 0.779278i
\(743\) −49.5365 11.7404i −1.81732 0.430712i −0.826163 0.563432i \(-0.809481\pi\)
−0.991154 + 0.132720i \(0.957629\pi\)
\(744\) 0 0
\(745\) 0.0640520 + 0.148489i 0.00234668 + 0.00544022i
\(746\) −1.38612 + 7.86105i −0.0507493 + 0.287814i
\(747\) 0 0
\(748\) −9.20818 52.2222i −0.336685 1.90943i
\(749\) 5.16929 3.39990i 0.188882 0.124230i
\(750\) 0 0
\(751\) 1.48620 + 1.99632i 0.0542323 + 0.0728466i 0.828412 0.560119i \(-0.189245\pi\)
−0.774180 + 0.632966i \(0.781837\pi\)
\(752\) 2.81834 48.3891i 0.102774 1.76457i
\(753\) 0 0
\(754\) −17.3548 18.3950i −0.632023 0.669905i
\(755\) −0.137693 0.238491i −0.00501116 0.00867959i
\(756\) 0 0
\(757\) −12.1617 + 21.0647i −0.442025 + 0.765610i −0.997840 0.0656966i \(-0.979073\pi\)
0.555815 + 0.831306i \(0.312406\pi\)
\(758\) 62.5283 14.8195i 2.27113 0.538268i
\(759\) 0 0
\(760\) −0.0286518 + 0.0143895i −0.00103931 + 0.000521962i
\(761\) −20.5191 + 2.39833i −0.743815 + 0.0869395i −0.479555 0.877512i \(-0.659202\pi\)
−0.264260 + 0.964451i \(0.585128\pi\)
\(762\) 0 0
\(763\) 12.9334 + 6.49539i 0.468220 + 0.235149i
\(764\) −7.26505 2.64426i −0.262840 0.0956660i
\(765\) 0 0
\(766\) −43.6234 + 15.8776i −1.57618 + 0.573681i
\(767\) −3.82012 0.446508i −0.137937 0.0161225i
\(768\) 0 0
\(769\) 8.76211 + 29.2675i 0.315970 + 1.05541i 0.957529 + 0.288338i \(0.0931028\pi\)
−0.641559 + 0.767074i \(0.721712\pi\)
\(770\) 0.110377 + 0.368685i 0.00397771 + 0.0132865i
\(771\) 0 0
\(772\) −46.9732 5.49038i −1.69060 0.197603i
\(773\) 10.0042 3.64122i 0.359825 0.130966i −0.155780 0.987792i \(-0.549789\pi\)
0.515606 + 0.856826i \(0.327567\pi\)
\(774\) 0 0
\(775\) 14.0321 + 5.10725i 0.504046 + 0.183458i
\(776\) −2.30273 1.15647i −0.0826630 0.0415149i
\(777\) 0 0
\(778\) 32.4980 3.79847i 1.16511 0.136182i
\(779\) 17.4888 8.78318i 0.626600 0.314690i
\(780\) 0 0
\(781\) −26.6173 + 6.30843i −0.952443 + 0.225733i
\(782\) 4.15406 7.19504i 0.148549 0.257294i
\(783\) 0 0
\(784\) −8.49011 14.7053i −0.303218 0.525189i
\(785\) −0.0992475 0.105196i −0.00354230 0.00375461i
\(786\) 0 0
\(787\) 0.661014 11.3492i 0.0235626 0.404555i −0.965819 0.259216i \(-0.916536\pi\)
0.989382 0.145339i \(-0.0464271\pi\)
\(788\) 21.6790 + 29.1200i 0.772284 + 1.03736i
\(789\) 0 0
\(790\) −0.113259 + 0.0744916i −0.00402957 + 0.00265029i
\(791\) −0.483497 2.74205i −0.0171912 0.0974960i
\(792\) 0 0
\(793\) −3.39710 + 19.2659i −0.120634 + 0.684152i
\(794\) −20.6624 47.9009i −0.733282 1.69994i
\(795\) 0 0
\(796\) −43.9893 10.4257i −1.55916 0.369528i
\(797\) −21.7922 + 23.0984i −0.771919 + 0.818186i −0.987387 0.158325i \(-0.949391\pi\)
0.215468 + 0.976511i \(0.430872\pi\)
\(798\) 0 0
\(799\) 32.5374 43.7053i 1.15109 1.54618i
\(800\) 31.0751 + 26.0751i 1.09867 + 0.921893i
\(801\) 0 0
\(802\) −15.4204 + 12.9392i −0.544512 + 0.456900i
\(803\) −3.33091 57.1896i −0.117545 2.01818i
\(804\) 0 0
\(805\) −0.0124815 + 0.0289355i −0.000439917 + 0.00101984i
\(806\) −11.2214 7.38045i −0.395258 0.259965i
\(807\) 0 0
\(808\) −0.311558 + 1.04068i −0.0109606 + 0.0366108i
\(809\) 13.8022 0.485261 0.242630 0.970119i \(-0.421990\pi\)
0.242630 + 0.970119i \(0.421990\pi\)
\(810\) 0 0
\(811\) −45.3121 −1.59112 −0.795562 0.605873i \(-0.792824\pi\)
−0.795562 + 0.605873i \(0.792824\pi\)
\(812\) 5.31326 17.7475i 0.186459 0.622816i
\(813\) 0 0
\(814\) 70.9832 + 46.6864i 2.48796 + 1.63636i
\(815\) −0.0428233 + 0.0992757i −0.00150004 + 0.00347747i
\(816\) 0 0
\(817\) −1.52138 26.1211i −0.0532263 0.913860i
\(818\) 38.3352 32.1671i 1.34036 1.12470i
\(819\) 0 0
\(820\) −0.171829 0.144182i −0.00600054 0.00503505i
\(821\) −16.8517 + 22.6358i −0.588129 + 0.789994i −0.992190 0.124738i \(-0.960191\pi\)
0.404061 + 0.914732i \(0.367598\pi\)
\(822\) 0 0
\(823\) 1.36217 1.44381i 0.0474822 0.0503282i −0.703197 0.710995i \(-0.748245\pi\)
0.750679 + 0.660667i \(0.229726\pi\)
\(824\) 1.70852 + 0.404927i 0.0595192 + 0.0141063i
\(825\) 0 0
\(826\) −2.13525 4.95007i −0.0742950 0.172235i
\(827\) −5.08225 + 28.8229i −0.176727 + 1.00227i 0.759404 + 0.650619i \(0.225491\pi\)
−0.936131 + 0.351650i \(0.885621\pi\)
\(828\) 0 0
\(829\) 4.01243 + 22.7556i 0.139358 + 0.790336i 0.971726 + 0.236113i \(0.0758734\pi\)
−0.832368 + 0.554223i \(0.813015\pi\)
\(830\) −0.0596926 + 0.0392604i −0.00207196 + 0.00136275i
\(831\) 0 0
\(832\) −12.3820 16.6320i −0.429270 0.576609i
\(833\) 1.10985 19.0554i 0.0384540 0.660230i
\(834\) 0 0
\(835\) −0.134846 0.142928i −0.00466653 0.00494623i
\(836\) 26.1390 + 45.2740i 0.904035 + 1.56583i
\(837\) 0 0
\(838\) −4.45849 + 7.72233i −0.154016 + 0.266763i
\(839\) 4.80613 1.13907i 0.165926 0.0393252i −0.146813 0.989164i \(-0.546902\pi\)
0.312739 + 0.949839i \(0.398753\pi\)
\(840\) 0 0
\(841\) 2.34856 1.17949i 0.0809849 0.0406722i
\(842\) −2.57576 + 0.301063i −0.0887666 + 0.0103753i
\(843\) 0 0
\(844\) 4.25412 + 2.13650i 0.146433 + 0.0735414i
\(845\) −0.159723 0.0581343i −0.00549463 0.00199988i
\(846\) 0 0
\(847\) 35.5086 12.9241i 1.22009 0.444076i
\(848\) 33.7443 + 3.94414i 1.15878 + 0.135442i
\(849\) 0 0
\(850\) 11.8273 + 39.5058i 0.405672 + 1.35504i
\(851\) 1.99522 + 6.66449i 0.0683952 + 0.228456i
\(852\) 0 0
\(853\) 33.4776 + 3.91297i 1.14625 + 0.133978i 0.667942 0.744213i \(-0.267175\pi\)
0.478310 + 0.878191i \(0.341249\pi\)
\(854\) −25.7672 + 9.37848i −0.881734 + 0.320925i
\(855\) 0 0
\(856\) −1.49976 0.545869i −0.0512609 0.0186574i
\(857\) 11.9854 + 6.01928i 0.409413 + 0.205615i 0.641572 0.767063i \(-0.278283\pi\)
−0.232159 + 0.972678i \(0.574579\pi\)
\(858\) 0 0
\(859\) −24.9583 + 2.91721i −0.851567 + 0.0995339i −0.530668 0.847580i \(-0.678059\pi\)
−0.320899 + 0.947114i \(0.603985\pi\)
\(860\) −0.267996 + 0.134593i −0.00913860 + 0.00458958i
\(861\) 0 0
\(862\) 71.1379 16.8600i 2.42297 0.574253i
\(863\) 6.50193 11.2617i 0.221328 0.383352i −0.733883 0.679276i \(-0.762294\pi\)
0.955212 + 0.295924i \(0.0956274\pi\)
\(864\) 0 0
\(865\) −0.0936173 0.162150i −0.00318308 0.00551326i
\(866\) 45.4509 + 48.1752i 1.54448 + 1.63706i
\(867\) 0 0
\(868\) 0.572077 9.82218i 0.0194176 0.333387i
\(869\) 11.4293 + 15.3522i 0.387711 + 0.520786i
\(870\) 0 0
\(871\) −25.0237 + 16.4584i −0.847896 + 0.557670i
\(872\) −0.648290 3.67663i −0.0219539 0.124507i
\(873\) 0 0
\(874\) −1.42229 + 8.06620i −0.0481096 + 0.272843i
\(875\) −0.123912 0.287261i −0.00418901 0.00971121i
\(876\) 0 0
\(877\) −8.95662 2.12276i −0.302443 0.0716804i 0.0765922 0.997063i \(-0.475596\pi\)
−0.379036 + 0.925382i \(0.623744\pi\)
\(878\) −12.4776 + 13.2255i −0.421098 + 0.446338i
\(879\) 0 0
\(880\) −0.267543 + 0.359373i −0.00901889 + 0.0121145i
\(881\) −13.6126 11.4223i −0.458619 0.384827i 0.384004 0.923331i \(-0.374545\pi\)
−0.842622 + 0.538505i \(0.818989\pi\)
\(882\) 0 0
\(883\) 30.2693 25.3990i 1.01864 0.854744i 0.0291877 0.999574i \(-0.490708\pi\)
0.989457 + 0.144830i \(0.0462635\pi\)
\(884\) −1.12714 19.3522i −0.0379097 0.650884i
\(885\) 0 0
\(886\) −10.9039 + 25.2781i −0.366324 + 0.849235i
\(887\) −44.5438 29.2969i −1.49563 0.983694i −0.992861 0.119275i \(-0.961943\pi\)
−0.502773 0.864419i \(-0.667687\pi\)
\(888\) 0 0
\(889\) 8.21107 27.4269i 0.275390 0.919868i
\(890\) −0.431013 −0.0144476
\(891\) 0 0
\(892\) 49.4334 1.65515
\(893\) −15.4061 + 51.4598i −0.515544 + 1.72204i
\(894\) 0 0
\(895\) −0.167764 0.110340i −0.00560772 0.00368825i
\(896\) 1.84168 4.26949i 0.0615262 0.142634i
\(897\) 0 0
\(898\) 2.12003 + 36.3995i 0.0707463 + 1.21467i
\(899\) 12.8675 10.7971i 0.429155 0.360104i
\(900\) 0 0
\(901\) 29.2557 + 24.5485i 0.974650 + 0.817829i
\(902\) −36.1857 + 48.6058i −1.20485 + 1.61840i
\(903\) 0 0
\(904\) −0.492886 + 0.522429i −0.0163931 + 0.0173757i
\(905\) 0.198562 + 0.0470600i 0.00660042 + 0.00156433i
\(906\) 0 0
\(907\) −1.21010 2.80532i −0.0401807 0.0931493i 0.896944 0.442145i \(-0.145782\pi\)
−0.937124 + 0.348995i \(0.886523\pi\)
\(908\) 7.01657 39.7929i 0.232853 1.32057i
\(909\) 0 0
\(910\) 0.0244302 + 0.138550i 0.000809852 + 0.00459290i
\(911\) −12.9761 + 8.53455i −0.429919 + 0.282762i −0.745969 0.665980i \(-0.768013\pi\)
0.316050 + 0.948742i \(0.397643\pi\)
\(912\) 0 0
\(913\) 6.02373 + 8.09128i 0.199356 + 0.267782i
\(914\) −0.148509 + 2.54980i −0.00491224 + 0.0843399i
\(915\) 0 0
\(916\) 16.9733 + 17.9907i 0.560814 + 0.594428i
\(917\) 0.598373 + 1.03641i 0.0197600 + 0.0342253i
\(918\) 0 0
\(919\) −4.19749 + 7.27027i −0.138462 + 0.239824i −0.926915 0.375272i \(-0.877549\pi\)
0.788452 + 0.615096i \(0.210883\pi\)
\(920\) 0.00790978 0.00187465i 0.000260778 6.18055e-5i
\(921\) 0 0
\(922\) 34.5089 17.3310i 1.13649 0.570766i
\(923\) −9.93223 + 1.16091i −0.326923 + 0.0382118i
\(924\) 0 0
\(925\) −30.8577 15.4973i −1.01459 0.509548i
\(926\) 22.8775 + 8.32674i 0.751802 + 0.273634i
\(927\) 0 0
\(928\) 42.8793 15.6068i 1.40758 0.512318i
\(929\) 25.5551 + 2.98697i 0.838436 + 0.0979992i 0.524464 0.851433i \(-0.324266\pi\)
0.313973 + 0.949432i \(0.398340\pi\)
\(930\) 0 0
\(931\) 5.39700 + 18.0272i 0.176879 + 0.590818i
\(932\) 10.3451 + 34.5549i 0.338864 + 1.13188i
\(933\) 0 0
\(934\) 14.0946 + 1.64742i 0.461188 + 0.0539052i
\(935\) −0.473261 + 0.172253i −0.0154773 + 0.00563327i
\(936\) 0 0
\(937\) −28.5906 10.4061i −0.934015 0.339954i −0.170215 0.985407i \(-0.554446\pi\)
−0.763800 + 0.645453i \(0.776668\pi\)
\(938\) −37.5158 18.8411i −1.22493 0.615185i
\(939\) 0 0
\(940\) 0.611512 0.0714755i 0.0199453 0.00233127i
\(941\) 48.9474 24.5823i 1.59564 0.801360i 0.595640 0.803251i \(-0.296898\pi\)
0.999998 + 0.00189180i \(0.000602179\pi\)
\(942\) 0 0
\(943\) −4.82804 + 1.14427i −0.157223 + 0.0372625i
\(944\) 3.13795 5.43509i 0.102132 0.176897i
\(945\) 0 0
\(946\) 40.5082 + 70.1623i 1.31704 + 2.28117i
\(947\) −13.2900 14.0866i −0.431868 0.457753i 0.474492 0.880260i \(-0.342632\pi\)
−0.906360 + 0.422507i \(0.861150\pi\)
\(948\) 0 0
\(949\) 1.21766 20.9063i 0.0395268 0.678649i
\(950\) −24.2775 32.6104i −0.787668 1.05802i
\(951\) 0 0
\(952\) 1.96571 1.29287i 0.0637090 0.0419021i
\(953\) −1.98648 11.2659i −0.0643484 0.364938i −0.999930 0.0118276i \(-0.996235\pi\)
0.935582 0.353110i \(-0.114876\pi\)
\(954\) 0 0
\(955\) −0.0127507 + 0.0723128i −0.000412603 + 0.00233999i
\(956\) 9.50209 + 22.0283i 0.307320 + 0.712447i
\(957\) 0 0
\(958\) −72.5828 17.2024i −2.34504 0.555786i
\(959\) 4.36494 4.62657i 0.140951 0.149400i
\(960\) 0 0
\(961\) −13.1848 + 17.7102i −0.425315 + 0.571297i
\(962\) 23.7920 + 19.9638i 0.767084 + 0.643660i
\(963\) 0 0
\(964\) −33.4590 + 28.0754i −1.07764 + 0.904248i
\(965\) 0.0261167 + 0.448407i 0.000840727 + 0.0144347i
\(966\) 0 0
\(967\) −2.28298 + 5.29254i −0.0734157 + 0.170197i −0.950972 0.309277i \(-0.899913\pi\)
0.877556 + 0.479473i \(0.159172\pi\)
\(968\) −8.14392 5.35634i −0.261756 0.172159i
\(969\) 0 0
\(970\) −0.0810602 + 0.270760i −0.00260269 + 0.00869358i
\(971\) −4.83812 −0.155263 −0.0776313 0.996982i \(-0.524736\pi\)
−0.0776313 + 0.996982i \(0.524736\pi\)
\(972\) 0 0
\(973\) −8.23596 −0.264033
\(974\) −20.6094 + 68.8404i −0.660369 + 2.20579i
\(975\) 0 0
\(976\) −26.6705 17.5414i −0.853701 0.561488i
\(977\) 17.3215 40.1557i 0.554163 1.28469i −0.379052 0.925375i \(-0.623750\pi\)
0.933215 0.359319i \(-0.116991\pi\)
\(978\) 0 0
\(979\) 3.53832 + 60.7506i 0.113085 + 1.94160i
\(980\) 0.165221 0.138637i 0.00527779 0.00442860i
\(981\) 0 0
\(982\) 39.2898 + 32.9680i 1.25379 + 1.05205i
\(983\) 25.2437 33.9082i 0.805150 1.08150i −0.189868 0.981810i \(-0.560806\pi\)
0.995018 0.0996948i \(-0.0317866\pi\)
\(984\) 0 0
\(985\) 0.236613 0.250795i 0.00753912 0.00799100i
\(986\) 45.1375 + 10.6978i 1.43747 + 0.340687i
\(987\) 0 0
\(988\) 7.56941 + 17.5479i 0.240815 + 0.558272i
\(989\) −1.15195 + 6.53305i −0.0366300 + 0.207739i
\(990\) 0 0
\(991\) −4.65706 26.4115i −0.147936 0.838989i −0.964962 0.262388i \(-0.915490\pi\)
0.817026 0.576601i \(-0.195621\pi\)
\(992\) 20.2474 13.3169i 0.642855 0.422812i
\(993\) 0 0
\(994\) −8.37001 11.2429i −0.265481 0.356602i
\(995\) −0.0249653 + 0.428638i −0.000791453 + 0.0135887i
\(996\) 0 0
\(997\) −15.1727 16.0821i −0.480523 0.509325i 0.441075 0.897470i \(-0.354597\pi\)
−0.921598 + 0.388146i \(0.873116\pi\)
\(998\) 21.7006 + 37.5866i 0.686922 + 1.18978i
\(999\) 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 243.2.g.a.37.2 144
3.2 odd 2 81.2.g.a.49.7 yes 144
9.2 odd 6 729.2.g.d.595.2 144
9.4 even 3 729.2.g.b.109.2 144
9.5 odd 6 729.2.g.c.109.7 144
9.7 even 3 729.2.g.a.595.7 144
81.11 odd 54 729.2.g.d.136.2 144
81.16 even 27 729.2.g.b.622.2 144
81.23 odd 54 6561.2.a.c.1.13 72
81.38 odd 54 81.2.g.a.43.7 144
81.43 even 27 inner 243.2.g.a.46.2 144
81.58 even 27 6561.2.a.d.1.60 72
81.65 odd 54 729.2.g.c.622.7 144
81.70 even 27 729.2.g.a.136.7 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.43.7 144 81.38 odd 54
81.2.g.a.49.7 yes 144 3.2 odd 2
243.2.g.a.37.2 144 1.1 even 1 trivial
243.2.g.a.46.2 144 81.43 even 27 inner
729.2.g.a.136.7 144 81.70 even 27
729.2.g.a.595.7 144 9.7 even 3
729.2.g.b.109.2 144 9.4 even 3
729.2.g.b.622.2 144 81.16 even 27
729.2.g.c.109.7 144 9.5 odd 6
729.2.g.c.622.7 144 81.65 odd 54
729.2.g.d.136.2 144 81.11 odd 54
729.2.g.d.595.2 144 9.2 odd 6
6561.2.a.c.1.13 72 81.23 odd 54
6561.2.a.d.1.60 72 81.58 even 27