Properties

Label 475.2.j.d.349.9
Level $475$
Weight $2$
Character 475.349
Analytic conductor $3.793$
Analytic rank $0$
Dimension $24$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(49,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 349.9
Character \(\chi\) \(=\) 475.349
Dual form 475.2.j.d.49.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.28275 - 0.740597i) q^{2} +(-0.157277 + 0.0908038i) q^{3} +(0.0969683 - 0.167954i) q^{4} +(-0.134498 + 0.232958i) q^{6} +1.30422i q^{7} +2.67513i q^{8} +(-1.48351 + 2.56951i) q^{9} +4.98247 q^{11} +0.0352204i q^{12} +(0.351723 + 0.203067i) q^{13} +(0.965899 + 1.67299i) q^{14} +(2.17513 + 3.76744i) q^{16} +(2.38173 - 1.37510i) q^{17} +4.39473i q^{18} +(4.35785 - 0.0955054i) q^{19} +(-0.118428 - 0.205123i) q^{21} +(6.39128 - 3.69001i) q^{22} +(-6.02510 - 3.47860i) q^{23} +(-0.242912 - 0.420736i) q^{24} +0.601564 q^{26} -1.08366i q^{27} +(0.219048 + 0.126468i) q^{28} +(-2.00728 + 3.47672i) q^{29} -2.57321 q^{31} +(0.946844 + 0.546661i) q^{32} +(-0.783628 + 0.452428i) q^{33} +(2.03678 - 3.52781i) q^{34} +(0.287707 + 0.498323i) q^{36} -3.71348i q^{37} +(5.51931 - 3.34992i) q^{38} -0.0737572 q^{39} +(0.607965 + 1.05303i) q^{41} +(-0.303827 - 0.175415i) q^{42} +(2.70426 - 1.56130i) q^{43} +(0.483142 - 0.836826i) q^{44} -10.3050 q^{46} +(-5.63617 - 3.25405i) q^{47} +(-0.684196 - 0.395020i) q^{48} +5.29902 q^{49} +(-0.249728 + 0.432541i) q^{51} +(0.0682119 - 0.0393822i) q^{52} +(-5.47490 - 3.16094i) q^{53} +(-0.802553 - 1.39006i) q^{54} -3.48895 q^{56} +(-0.676717 + 0.410731i) q^{57} +5.94636i q^{58} +(5.61636 + 9.72783i) q^{59} +(-0.467072 + 0.808992i) q^{61} +(-3.30079 + 1.90571i) q^{62} +(-3.35120 - 1.93482i) q^{63} -7.08110 q^{64} +(-0.670133 + 1.16071i) q^{66} +(4.58585 + 2.64764i) q^{67} -0.533363i q^{68} +1.26348 q^{69} +(0.817659 + 1.41623i) q^{71} +(-6.87378 - 3.96858i) q^{72} +(6.65794 - 3.84396i) q^{73} +(-2.75019 - 4.76347i) q^{74} +(0.406533 - 0.741180i) q^{76} +6.49822i q^{77} +(-0.0946121 + 0.0546243i) q^{78} +(-7.27699 - 12.6041i) q^{79} +(-4.35213 - 7.53811i) q^{81} +(1.55974 + 0.900514i) q^{82} -15.2643i q^{83} -0.0459350 q^{84} +(2.31260 - 4.00553i) q^{86} -0.729076i q^{87} +13.3288i q^{88} +(7.10727 - 12.3101i) q^{89} +(-0.264844 + 0.458723i) q^{91} +(-1.16849 + 0.674627i) q^{92} +(0.404707 - 0.233658i) q^{93} -9.63975 q^{94} -0.198556 q^{96} +(-15.8329 + 9.14111i) q^{97} +(6.79733 - 3.92444i) q^{98} +(-7.39155 + 12.8025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{4} + 2 q^{6} + 14 q^{9} - 4 q^{11} - 12 q^{14} + 12 q^{16} + 12 q^{19} - 6 q^{21} + 22 q^{24} + 76 q^{26} + 6 q^{29} - 12 q^{31} - 2 q^{34} - 26 q^{36} - 32 q^{39} - 22 q^{41} + 42 q^{44} - 48 q^{46}+ \cdots - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28275 0.740597i 0.907043 0.523681i 0.0275641 0.999620i \(-0.491225\pi\)
0.879478 + 0.475939i \(0.157892\pi\)
\(3\) −0.157277 + 0.0908038i −0.0908038 + 0.0524256i −0.544714 0.838622i \(-0.683362\pi\)
0.453910 + 0.891047i \(0.350029\pi\)
\(4\) 0.0969683 0.167954i 0.0484841 0.0839770i
\(5\) 0 0
\(6\) −0.134498 + 0.232958i −0.0549086 + 0.0951045i
\(7\) 1.30422i 0.492948i 0.969149 + 0.246474i \(0.0792719\pi\)
−0.969149 + 0.246474i \(0.920728\pi\)
\(8\) 2.67513i 0.945802i
\(9\) −1.48351 + 2.56951i −0.494503 + 0.856505i
\(10\) 0 0
\(11\) 4.98247 1.50227 0.751136 0.660147i \(-0.229506\pi\)
0.751136 + 0.660147i \(0.229506\pi\)
\(12\) 0.0352204i 0.0101672i
\(13\) 0.351723 + 0.203067i 0.0975504 + 0.0563207i 0.547982 0.836490i \(-0.315396\pi\)
−0.450431 + 0.892811i \(0.648730\pi\)
\(14\) 0.965899 + 1.67299i 0.258147 + 0.447124i
\(15\) 0 0
\(16\) 2.17513 + 3.76744i 0.543783 + 0.941859i
\(17\) 2.38173 1.37510i 0.577656 0.333510i −0.182546 0.983197i \(-0.558434\pi\)
0.760201 + 0.649688i \(0.225100\pi\)
\(18\) 4.39473i 1.03585i
\(19\) 4.35785 0.0955054i 0.999760 0.0219104i
\(20\) 0 0
\(21\) −0.118428 0.205123i −0.0258431 0.0447615i
\(22\) 6.39128 3.69001i 1.36262 0.786712i
\(23\) −6.02510 3.47860i −1.25632 0.725337i −0.283964 0.958835i \(-0.591650\pi\)
−0.972357 + 0.233498i \(0.924983\pi\)
\(24\) −0.242912 0.420736i −0.0495842 0.0858824i
\(25\) 0 0
\(26\) 0.601564 0.117976
\(27\) 1.08366i 0.208550i
\(28\) 0.219048 + 0.126468i 0.0413963 + 0.0239001i
\(29\) −2.00728 + 3.47672i −0.372743 + 0.645610i −0.989986 0.141162i \(-0.954916\pi\)
0.617243 + 0.786772i \(0.288249\pi\)
\(30\) 0 0
\(31\) −2.57321 −0.462163 −0.231081 0.972934i \(-0.574226\pi\)
−0.231081 + 0.972934i \(0.574226\pi\)
\(32\) 0.946844 + 0.546661i 0.167380 + 0.0966369i
\(33\) −0.783628 + 0.452428i −0.136412 + 0.0787576i
\(34\) 2.03678 3.52781i 0.349305 0.605015i
\(35\) 0 0
\(36\) 0.287707 + 0.498323i 0.0479511 + 0.0830538i
\(37\) 3.71348i 0.610492i −0.952274 0.305246i \(-0.901261\pi\)
0.952274 0.305246i \(-0.0987387\pi\)
\(38\) 5.51931 3.34992i 0.895351 0.543429i
\(39\) −0.0737572 −0.0118106
\(40\) 0 0
\(41\) 0.607965 + 1.05303i 0.0949482 + 0.164455i 0.909587 0.415514i \(-0.136398\pi\)
−0.814639 + 0.579969i \(0.803065\pi\)
\(42\) −0.303827 0.175415i −0.0468816 0.0270671i
\(43\) 2.70426 1.56130i 0.412396 0.238097i −0.279423 0.960168i \(-0.590143\pi\)
0.691819 + 0.722071i \(0.256810\pi\)
\(44\) 0.483142 0.836826i 0.0728364 0.126156i
\(45\) 0 0
\(46\) −10.3050 −1.51938
\(47\) −5.63617 3.25405i −0.822120 0.474651i 0.0290269 0.999579i \(-0.490759\pi\)
−0.851147 + 0.524927i \(0.824093\pi\)
\(48\) −0.684196 0.395020i −0.0987551 0.0570163i
\(49\) 5.29902 0.757003
\(50\) 0 0
\(51\) −0.249728 + 0.432541i −0.0349689 + 0.0605679i
\(52\) 0.0682119 0.0393822i 0.00945929 0.00546132i
\(53\) −5.47490 3.16094i −0.752036 0.434188i 0.0743934 0.997229i \(-0.476298\pi\)
−0.826429 + 0.563041i \(0.809631\pi\)
\(54\) −0.802553 1.39006i −0.109214 0.189164i
\(55\) 0 0
\(56\) −3.48895 −0.466231
\(57\) −0.676717 + 0.410731i −0.0896334 + 0.0544026i
\(58\) 5.94636i 0.780795i
\(59\) 5.61636 + 9.72783i 0.731188 + 1.26646i 0.956376 + 0.292140i \(0.0943672\pi\)
−0.225187 + 0.974315i \(0.572299\pi\)
\(60\) 0 0
\(61\) −0.467072 + 0.808992i −0.0598024 + 0.103581i −0.894377 0.447315i \(-0.852380\pi\)
0.834574 + 0.550896i \(0.185714\pi\)
\(62\) −3.30079 + 1.90571i −0.419201 + 0.242026i
\(63\) −3.35120 1.93482i −0.422212 0.243764i
\(64\) −7.08110 −0.885138
\(65\) 0 0
\(66\) −0.670133 + 1.16071i −0.0824877 + 0.142873i
\(67\) 4.58585 + 2.64764i 0.560251 + 0.323461i 0.753246 0.657739i \(-0.228487\pi\)
−0.192995 + 0.981200i \(0.561820\pi\)
\(68\) 0.533363i 0.0646797i
\(69\) 1.26348 0.152105
\(70\) 0 0
\(71\) 0.817659 + 1.41623i 0.0970383 + 0.168075i 0.910457 0.413603i \(-0.135730\pi\)
−0.813419 + 0.581678i \(0.802396\pi\)
\(72\) −6.87378 3.96858i −0.810083 0.467702i
\(73\) 6.65794 3.84396i 0.779252 0.449902i −0.0569129 0.998379i \(-0.518126\pi\)
0.836165 + 0.548478i \(0.184792\pi\)
\(74\) −2.75019 4.76347i −0.319703 0.553742i
\(75\) 0 0
\(76\) 0.406533 0.741180i 0.0466325 0.0850191i
\(77\) 6.49822i 0.740541i
\(78\) −0.0946121 + 0.0546243i −0.0107127 + 0.00618499i
\(79\) −7.27699 12.6041i −0.818725 1.41807i −0.906622 0.421944i \(-0.861348\pi\)
0.0878971 0.996130i \(-0.471985\pi\)
\(80\) 0 0
\(81\) −4.35213 7.53811i −0.483570 0.837567i
\(82\) 1.55974 + 0.900514i 0.172244 + 0.0994452i
\(83\) 15.2643i 1.67547i −0.546077 0.837735i \(-0.683879\pi\)
0.546077 0.837735i \(-0.316121\pi\)
\(84\) −0.0459350 −0.00501192
\(85\) 0 0
\(86\) 2.31260 4.00553i 0.249374 0.431928i
\(87\) 0.729076i 0.0781652i
\(88\) 13.3288i 1.42085i
\(89\) 7.10727 12.3101i 0.753369 1.30487i −0.192812 0.981236i \(-0.561761\pi\)
0.946181 0.323638i \(-0.104906\pi\)
\(90\) 0 0
\(91\) −0.264844 + 0.458723i −0.0277632 + 0.0480872i
\(92\) −1.16849 + 0.674627i −0.121823 + 0.0703347i
\(93\) 0.404707 0.233658i 0.0419661 0.0242292i
\(94\) −9.63975 −0.994264
\(95\) 0 0
\(96\) −0.198556 −0.0202650
\(97\) −15.8329 + 9.14111i −1.60758 + 0.928139i −0.617676 + 0.786433i \(0.711926\pi\)
−0.989909 + 0.141707i \(0.954741\pi\)
\(98\) 6.79733 3.92444i 0.686634 0.396428i
\(99\) −7.39155 + 12.8025i −0.742878 + 1.28670i
\(100\) 0 0
\(101\) 7.99763 13.8523i 0.795794 1.37836i −0.126540 0.991962i \(-0.540387\pi\)
0.922334 0.386394i \(-0.126280\pi\)
\(102\) 0.739791i 0.0732502i
\(103\) 5.30941i 0.523152i 0.965183 + 0.261576i \(0.0842422\pi\)
−0.965183 + 0.261576i \(0.915758\pi\)
\(104\) −0.543232 + 0.940905i −0.0532682 + 0.0922633i
\(105\) 0 0
\(106\) −9.36392 −0.909504
\(107\) 13.0024i 1.25699i 0.777814 + 0.628494i \(0.216329\pi\)
−0.777814 + 0.628494i \(0.783671\pi\)
\(108\) −0.182004 0.105080i −0.0175134 0.0101114i
\(109\) −4.09697 7.09616i −0.392418 0.679689i 0.600350 0.799738i \(-0.295028\pi\)
−0.992768 + 0.120049i \(0.961695\pi\)
\(110\) 0 0
\(111\) 0.337198 + 0.584044i 0.0320054 + 0.0554350i
\(112\) −4.91355 + 2.83684i −0.464287 + 0.268056i
\(113\) 6.54779i 0.615964i −0.951392 0.307982i \(-0.900346\pi\)
0.951392 0.307982i \(-0.0996536\pi\)
\(114\) −0.563874 + 1.02804i −0.0528117 + 0.0962848i
\(115\) 0 0
\(116\) 0.389286 + 0.674263i 0.0361443 + 0.0626037i
\(117\) −1.04357 + 0.602504i −0.0964779 + 0.0557016i
\(118\) 14.4088 + 8.31892i 1.32644 + 0.765819i
\(119\) 1.79342 + 3.10630i 0.164403 + 0.284754i
\(120\) 0 0
\(121\) 13.8250 1.25682
\(122\) 1.38365i 0.125270i
\(123\) −0.191238 0.110411i −0.0172433 0.00995544i
\(124\) −0.249520 + 0.432181i −0.0224076 + 0.0388110i
\(125\) 0 0
\(126\) −5.73168 −0.510619
\(127\) 13.0844 + 7.55431i 1.16106 + 0.670336i 0.951557 0.307472i \(-0.0994832\pi\)
0.209500 + 0.977809i \(0.432817\pi\)
\(128\) −10.9770 + 6.33757i −0.970238 + 0.560167i
\(129\) −0.283545 + 0.491114i −0.0249647 + 0.0432402i
\(130\) 0 0
\(131\) 1.24679 + 2.15950i 0.108933 + 0.188677i 0.915338 0.402686i \(-0.131923\pi\)
−0.806406 + 0.591363i \(0.798590\pi\)
\(132\) 0.175485i 0.0152740i
\(133\) 0.124560 + 5.68358i 0.0108007 + 0.492829i
\(134\) 7.84335 0.677562
\(135\) 0 0
\(136\) 3.67856 + 6.37145i 0.315434 + 0.546348i
\(137\) −15.2491 8.80405i −1.30282 0.752181i −0.321930 0.946764i \(-0.604331\pi\)
−0.980886 + 0.194583i \(0.937665\pi\)
\(138\) 1.62073 0.935729i 0.137966 0.0796546i
\(139\) 1.57736 2.73207i 0.133790 0.231731i −0.791345 0.611370i \(-0.790619\pi\)
0.925135 + 0.379639i \(0.123952\pi\)
\(140\) 0 0
\(141\) 1.18192 0.0995356
\(142\) 2.09771 + 1.21111i 0.176036 + 0.101634i
\(143\) 1.75245 + 1.01178i 0.146547 + 0.0846091i
\(144\) −12.9073 −1.07561
\(145\) 0 0
\(146\) 5.69365 9.86170i 0.471210 0.816160i
\(147\) −0.833413 + 0.481171i −0.0687388 + 0.0396863i
\(148\) −0.623693 0.360090i −0.0512673 0.0295992i
\(149\) −3.18694 5.51994i −0.261084 0.452211i 0.705446 0.708764i \(-0.250747\pi\)
−0.966530 + 0.256552i \(0.917413\pi\)
\(150\) 0 0
\(151\) 4.96340 0.403915 0.201958 0.979394i \(-0.435270\pi\)
0.201958 + 0.979394i \(0.435270\pi\)
\(152\) 0.255489 + 11.6578i 0.0207229 + 0.945575i
\(153\) 8.15987i 0.659686i
\(154\) 4.81257 + 8.33561i 0.387808 + 0.671703i
\(155\) 0 0
\(156\) −0.00715211 + 0.0123878i −0.000572627 + 0.000991819i
\(157\) 1.81432 1.04750i 0.144798 0.0835993i −0.425851 0.904793i \(-0.640025\pi\)
0.570649 + 0.821194i \(0.306692\pi\)
\(158\) −18.6691 10.7786i −1.48524 0.857502i
\(159\) 1.14810 0.0910503
\(160\) 0 0
\(161\) 4.53684 7.85804i 0.357553 0.619300i
\(162\) −11.1654 6.44635i −0.877237 0.506473i
\(163\) 9.55821i 0.748656i 0.927296 + 0.374328i \(0.122127\pi\)
−0.927296 + 0.374328i \(0.877873\pi\)
\(164\) 0.235813 0.0184139
\(165\) 0 0
\(166\) −11.3047 19.5803i −0.877412 1.51972i
\(167\) 14.4968 + 8.36974i 1.12180 + 0.647670i 0.941859 0.336008i \(-0.109077\pi\)
0.179938 + 0.983678i \(0.442410\pi\)
\(168\) 0.548731 0.316810i 0.0423355 0.0244424i
\(169\) −6.41753 11.1155i −0.493656 0.855037i
\(170\) 0 0
\(171\) −6.21951 + 11.3392i −0.475618 + 0.867134i
\(172\) 0.605588i 0.0461757i
\(173\) 12.1030 6.98769i 0.920177 0.531264i 0.0364853 0.999334i \(-0.488384\pi\)
0.883691 + 0.468070i \(0.155050\pi\)
\(174\) −0.539952 0.935224i −0.0409336 0.0708992i
\(175\) 0 0
\(176\) 10.8375 + 18.7712i 0.816910 + 1.41493i
\(177\) −1.76665 1.01997i −0.132789 0.0766660i
\(178\) 21.0545i 1.57810i
\(179\) 9.86133 0.737071 0.368535 0.929614i \(-0.379859\pi\)
0.368535 + 0.929614i \(0.379859\pi\)
\(180\) 0 0
\(181\) −7.38629 + 12.7934i −0.549019 + 0.950929i 0.449323 + 0.893369i \(0.351665\pi\)
−0.998342 + 0.0575593i \(0.981668\pi\)
\(182\) 0.784570i 0.0581562i
\(183\) 0.169648i 0.0125407i
\(184\) 9.30570 16.1179i 0.686025 1.18823i
\(185\) 0 0
\(186\) 0.346092 0.599450i 0.0253767 0.0439538i
\(187\) 11.8669 6.85138i 0.867796 0.501022i
\(188\) −1.09306 + 0.631078i −0.0797196 + 0.0460261i
\(189\) 1.41332 0.102804
\(190\) 0 0
\(191\) −20.6797 −1.49633 −0.748166 0.663512i \(-0.769065\pi\)
−0.748166 + 0.663512i \(0.769065\pi\)
\(192\) 1.11369 0.642991i 0.0803739 0.0464039i
\(193\) 17.5615 10.1391i 1.26410 0.729831i 0.290238 0.956954i \(-0.406265\pi\)
0.973866 + 0.227123i \(0.0729320\pi\)
\(194\) −13.5398 + 23.4516i −0.972099 + 1.68372i
\(195\) 0 0
\(196\) 0.513837 0.889991i 0.0367026 0.0635708i
\(197\) 15.9172i 1.13406i −0.823698 0.567028i \(-0.808093\pi\)
0.823698 0.567028i \(-0.191907\pi\)
\(198\) 21.8966i 1.55613i
\(199\) −6.61785 + 11.4625i −0.469127 + 0.812552i −0.999377 0.0352892i \(-0.988765\pi\)
0.530250 + 0.847841i \(0.322098\pi\)
\(200\) 0 0
\(201\) −0.961665 −0.0678306
\(202\) 23.6921i 1.66697i
\(203\) −4.53439 2.61793i −0.318252 0.183743i
\(204\) 0.0484314 + 0.0838856i 0.00339087 + 0.00587317i
\(205\) 0 0
\(206\) 3.93214 + 6.81066i 0.273965 + 0.474521i
\(207\) 17.8766 10.3211i 1.24251 0.717363i
\(208\) 1.76679i 0.122505i
\(209\) 21.7129 0.475853i 1.50191 0.0329154i
\(210\) 0 0
\(211\) 4.88917 + 8.46829i 0.336584 + 0.582981i 0.983788 0.179336i \(-0.0573950\pi\)
−0.647204 + 0.762317i \(0.724062\pi\)
\(212\) −1.06178 + 0.613021i −0.0729236 + 0.0421025i
\(213\) −0.257198 0.148493i −0.0176229 0.0101746i
\(214\) 9.62954 + 16.6788i 0.658262 + 1.14014i
\(215\) 0 0
\(216\) 2.89892 0.197247
\(217\) 3.35603i 0.227822i
\(218\) −10.5108 6.06841i −0.711880 0.411004i
\(219\) −0.698093 + 1.20913i −0.0471727 + 0.0817056i
\(220\) 0 0
\(221\) 1.11695 0.0751340
\(222\) 0.865083 + 0.499456i 0.0580606 + 0.0335213i
\(223\) −22.3971 + 12.9310i −1.49982 + 0.865923i −1.00000 0.000205308i \(-0.999935\pi\)
−0.499822 + 0.866128i \(0.666601\pi\)
\(224\) −0.712964 + 1.23489i −0.0476369 + 0.0825095i
\(225\) 0 0
\(226\) −4.84927 8.39918i −0.322569 0.558705i
\(227\) 2.28573i 0.151709i −0.997119 0.0758545i \(-0.975832\pi\)
0.997119 0.0758545i \(-0.0241684\pi\)
\(228\) 0.00336373 + 0.153485i 0.000222769 + 0.0101648i
\(229\) 21.8805 1.44590 0.722952 0.690898i \(-0.242785\pi\)
0.722952 + 0.690898i \(0.242785\pi\)
\(230\) 0 0
\(231\) −0.590064 1.02202i −0.0388233 0.0672440i
\(232\) −9.30068 5.36975i −0.610619 0.352541i
\(233\) −1.77868 + 1.02692i −0.116525 + 0.0672758i −0.557130 0.830425i \(-0.688097\pi\)
0.440605 + 0.897701i \(0.354764\pi\)
\(234\) −0.892426 + 1.54573i −0.0583397 + 0.101047i
\(235\) 0 0
\(236\) 2.17844 0.141804
\(237\) 2.28900 + 1.32156i 0.148687 + 0.0858443i
\(238\) 4.60103 + 2.65641i 0.298241 + 0.172189i
\(239\) −7.68110 −0.496849 −0.248425 0.968651i \(-0.579913\pi\)
−0.248425 + 0.968651i \(0.579913\pi\)
\(240\) 0 0
\(241\) −7.26832 + 12.5891i −0.468194 + 0.810935i −0.999339 0.0363455i \(-0.988428\pi\)
0.531146 + 0.847280i \(0.321762\pi\)
\(242\) 17.7341 10.2388i 1.13999 0.658174i
\(243\) 4.18440 + 2.41586i 0.268429 + 0.154978i
\(244\) 0.0905823 + 0.156893i 0.00579894 + 0.0100441i
\(245\) 0 0
\(246\) −0.327081 −0.0208539
\(247\) 1.55215 + 0.851346i 0.0987610 + 0.0541698i
\(248\) 6.88368i 0.437114i
\(249\) 1.38605 + 2.40072i 0.0878376 + 0.152139i
\(250\) 0 0
\(251\) −3.59365 + 6.22439i −0.226829 + 0.392880i −0.956867 0.290527i \(-0.906169\pi\)
0.730037 + 0.683407i \(0.239503\pi\)
\(252\) −0.649921 + 0.375232i −0.0409412 + 0.0236374i
\(253\) −30.0199 17.3320i −1.88734 1.08965i
\(254\) 22.3788 1.40417
\(255\) 0 0
\(256\) −2.30606 + 3.99422i −0.144129 + 0.249639i
\(257\) −7.53951 4.35294i −0.470302 0.271529i 0.246064 0.969254i \(-0.420863\pi\)
−0.716366 + 0.697725i \(0.754196\pi\)
\(258\) 0.839970i 0.0522943i
\(259\) 4.84318 0.300940
\(260\) 0 0
\(261\) −5.95565 10.3155i −0.368645 0.638513i
\(262\) 3.19864 + 1.84674i 0.197613 + 0.114092i
\(263\) 26.4339 15.2616i 1.62998 0.941072i 0.645888 0.763432i \(-0.276487\pi\)
0.984096 0.177639i \(-0.0568461\pi\)
\(264\) −1.21030 2.09631i −0.0744890 0.129019i
\(265\) 0 0
\(266\) 4.36903 + 7.19838i 0.267882 + 0.441361i
\(267\) 2.58147i 0.157983i
\(268\) 0.889365 0.513475i 0.0543266 0.0313655i
\(269\) −9.20379 15.9414i −0.561165 0.971966i −0.997395 0.0721309i \(-0.977020\pi\)
0.436230 0.899835i \(-0.356313\pi\)
\(270\) 0 0
\(271\) 5.73694 + 9.93668i 0.348494 + 0.603610i 0.985982 0.166850i \(-0.0533597\pi\)
−0.637488 + 0.770460i \(0.720026\pi\)
\(272\) 10.3612 + 5.98202i 0.628238 + 0.362714i
\(273\) 0.0961953i 0.00582201i
\(274\) −26.0810 −1.57561
\(275\) 0 0
\(276\) 0.122517 0.212206i 0.00737468 0.0127733i
\(277\) 1.79689i 0.107965i −0.998542 0.0539823i \(-0.982809\pi\)
0.998542 0.0539823i \(-0.0171914\pi\)
\(278\) 4.67276i 0.280253i
\(279\) 3.81739 6.61191i 0.228541 0.395844i
\(280\) 0 0
\(281\) 7.09550 12.2898i 0.423282 0.733146i −0.572976 0.819572i \(-0.694211\pi\)
0.996258 + 0.0864258i \(0.0275446\pi\)
\(282\) 1.51611 0.875326i 0.0902830 0.0521249i
\(283\) −15.5094 + 8.95435i −0.921938 + 0.532281i −0.884253 0.467009i \(-0.845332\pi\)
−0.0376851 + 0.999290i \(0.511998\pi\)
\(284\) 0.317148 0.0188193
\(285\) 0 0
\(286\) 2.99728 0.177233
\(287\) −1.37337 + 0.792918i −0.0810677 + 0.0468045i
\(288\) −2.80930 + 1.62195i −0.165540 + 0.0955744i
\(289\) −4.71823 + 8.17221i −0.277543 + 0.480718i
\(290\) 0 0
\(291\) 1.66010 2.87537i 0.0973166 0.168557i
\(292\) 1.49097i 0.0872524i
\(293\) 33.3088i 1.94592i 0.230970 + 0.972961i \(0.425810\pi\)
−0.230970 + 0.972961i \(0.574190\pi\)
\(294\) −0.712708 + 1.23445i −0.0415660 + 0.0719944i
\(295\) 0 0
\(296\) 9.93404 0.577404
\(297\) 5.39929i 0.313299i
\(298\) −8.17610 4.72048i −0.473629 0.273450i
\(299\) −1.41278 2.44700i −0.0817031 0.141514i
\(300\) 0 0
\(301\) 2.03628 + 3.52694i 0.117369 + 0.203289i
\(302\) 6.36681 3.67588i 0.366369 0.211523i
\(303\) 2.90486i 0.166880i
\(304\) 9.83871 + 16.2102i 0.564289 + 0.929719i
\(305\) 0 0
\(306\) 6.04317 + 10.4671i 0.345465 + 0.598363i
\(307\) 13.4728 7.77854i 0.768935 0.443945i −0.0635594 0.997978i \(-0.520245\pi\)
0.832495 + 0.554033i \(0.186912\pi\)
\(308\) 1.09140 + 0.630122i 0.0621884 + 0.0359045i
\(309\) −0.482115 0.835048i −0.0274266 0.0475042i
\(310\) 0 0
\(311\) 29.1959 1.65555 0.827773 0.561063i \(-0.189608\pi\)
0.827773 + 0.561063i \(0.189608\pi\)
\(312\) 0.197310i 0.0111705i
\(313\) 27.6158 + 15.9440i 1.56094 + 0.901207i 0.997163 + 0.0752782i \(0.0239845\pi\)
0.563774 + 0.825929i \(0.309349\pi\)
\(314\) 1.55155 2.68736i 0.0875588 0.151656i
\(315\) 0 0
\(316\) −2.82255 −0.158781
\(317\) 11.7520 + 6.78505i 0.660061 + 0.381086i 0.792300 0.610131i \(-0.208883\pi\)
−0.132239 + 0.991218i \(0.542217\pi\)
\(318\) 1.47273 0.850280i 0.0825865 0.0476813i
\(319\) −10.0012 + 17.3227i −0.559962 + 0.969882i
\(320\) 0 0
\(321\) −1.18067 2.04498i −0.0658984 0.114139i
\(322\) 13.4399i 0.748976i
\(323\) 10.2479 6.21993i 0.570210 0.346086i
\(324\) −1.68807 −0.0937819
\(325\) 0 0
\(326\) 7.07878 + 12.2608i 0.392057 + 0.679063i
\(327\) 1.28872 + 0.744041i 0.0712662 + 0.0411456i
\(328\) −2.81698 + 1.62639i −0.155542 + 0.0898022i
\(329\) 4.24398 7.35079i 0.233978 0.405262i
\(330\) 0 0
\(331\) −29.4274 −1.61747 −0.808737 0.588171i \(-0.799848\pi\)
−0.808737 + 0.588171i \(0.799848\pi\)
\(332\) −2.56369 1.48015i −0.140701 0.0812337i
\(333\) 9.54183 + 5.50898i 0.522889 + 0.301890i
\(334\) 24.7944 1.35669
\(335\) 0 0
\(336\) 0.515192 0.892339i 0.0281060 0.0486811i
\(337\) −13.4336 + 7.75588i −0.731773 + 0.422489i −0.819071 0.573693i \(-0.805510\pi\)
0.0872973 + 0.996182i \(0.472177\pi\)
\(338\) −16.4642 9.50560i −0.895534 0.517037i
\(339\) 0.594564 + 1.02982i 0.0322923 + 0.0559319i
\(340\) 0 0
\(341\) −12.8210 −0.694294
\(342\) 0.419720 + 19.1516i 0.0226959 + 1.03560i
\(343\) 16.0406i 0.866110i
\(344\) 4.17669 + 7.23425i 0.225192 + 0.390044i
\(345\) 0 0
\(346\) 10.3501 17.9269i 0.556426 0.963759i
\(347\) −19.5615 + 11.2938i −1.05012 + 0.606285i −0.922682 0.385562i \(-0.874008\pi\)
−0.127434 + 0.991847i \(0.540674\pi\)
\(348\) −0.122451 0.0706973i −0.00656408 0.00378977i
\(349\) −25.4885 −1.36437 −0.682184 0.731181i \(-0.738970\pi\)
−0.682184 + 0.731181i \(0.738970\pi\)
\(350\) 0 0
\(351\) 0.220055 0.381147i 0.0117457 0.0203441i
\(352\) 4.71762 + 2.72372i 0.251450 + 0.145175i
\(353\) 10.2959i 0.547994i −0.961730 0.273997i \(-0.911654\pi\)
0.961730 0.273997i \(-0.0883459\pi\)
\(354\) −3.02156 −0.160594
\(355\) 0 0
\(356\) −1.37836 2.38739i −0.0730529 0.126531i
\(357\) −0.564128 0.325699i −0.0298568 0.0172378i
\(358\) 12.6496 7.30328i 0.668555 0.385990i
\(359\) 0.991256 + 1.71691i 0.0523165 + 0.0906148i 0.890998 0.454008i \(-0.150006\pi\)
−0.838681 + 0.544623i \(0.816673\pi\)
\(360\) 0 0
\(361\) 18.9818 0.832397i 0.999040 0.0438103i
\(362\) 21.8811i 1.15004i
\(363\) −2.17436 + 1.25537i −0.114124 + 0.0658897i
\(364\) 0.0513629 + 0.0889631i 0.00269215 + 0.00466294i
\(365\) 0 0
\(366\) −0.125641 0.217616i −0.00656734 0.0113750i
\(367\) 4.56763 + 2.63712i 0.238428 + 0.137657i 0.614454 0.788953i \(-0.289376\pi\)
−0.376026 + 0.926609i \(0.622710\pi\)
\(368\) 30.2656i 1.57770i
\(369\) −3.60769 −0.187809
\(370\) 0 0
\(371\) 4.12255 7.14046i 0.214032 0.370714i
\(372\) 0.0906295i 0.00469892i
\(373\) 31.7192i 1.64236i 0.570670 + 0.821179i \(0.306683\pi\)
−0.570670 + 0.821179i \(0.693317\pi\)
\(374\) 10.1482 17.5772i 0.524752 0.908897i
\(375\) 0 0
\(376\) 8.70500 15.0775i 0.448926 0.777563i
\(377\) −1.41202 + 0.815227i −0.0727225 + 0.0419863i
\(378\) 1.81294 1.04670i 0.0932477 0.0538366i
\(379\) −35.5119 −1.82412 −0.912062 0.410052i \(-0.865510\pi\)
−0.912062 + 0.410052i \(0.865510\pi\)
\(380\) 0 0
\(381\) −2.74384 −0.140571
\(382\) −26.5269 + 15.3153i −1.35724 + 0.783601i
\(383\) −12.0639 + 6.96509i −0.616436 + 0.355899i −0.775480 0.631372i \(-0.782492\pi\)
0.159044 + 0.987271i \(0.449159\pi\)
\(384\) 1.15095 1.99350i 0.0587342 0.101731i
\(385\) 0 0
\(386\) 15.0180 26.0120i 0.764398 1.32398i
\(387\) 9.26484i 0.470958i
\(388\) 3.54559i 0.180000i
\(389\) −0.471434 + 0.816548i −0.0239027 + 0.0414006i −0.877729 0.479157i \(-0.840943\pi\)
0.853827 + 0.520557i \(0.174276\pi\)
\(390\) 0 0
\(391\) −19.1336 −0.967628
\(392\) 14.1756i 0.715974i
\(393\) −0.392183 0.226427i −0.0197830 0.0114217i
\(394\) −11.7883 20.4179i −0.593884 1.02864i
\(395\) 0 0
\(396\) 1.43349 + 2.48288i 0.0720356 + 0.124769i
\(397\) −24.7386 + 14.2828i −1.24159 + 0.716834i −0.969418 0.245414i \(-0.921076\pi\)
−0.272174 + 0.962248i \(0.587743\pi\)
\(398\) 19.6047i 0.982693i
\(399\) −0.535682 0.882586i −0.0268176 0.0441846i
\(400\) 0 0
\(401\) 3.58365 + 6.20707i 0.178959 + 0.309966i 0.941524 0.336945i \(-0.109394\pi\)
−0.762565 + 0.646911i \(0.776060\pi\)
\(402\) −1.23358 + 0.712206i −0.0615252 + 0.0355216i
\(403\) −0.905058 0.522535i −0.0450841 0.0260293i
\(404\) −1.55103 2.68647i −0.0771668 0.133657i
\(405\) 0 0
\(406\) −7.75534 −0.384891
\(407\) 18.5023i 0.917125i
\(408\) −1.15710 0.668055i −0.0572852 0.0330736i
\(409\) −5.26624 + 9.12140i −0.260399 + 0.451024i −0.966348 0.257238i \(-0.917187\pi\)
0.705949 + 0.708263i \(0.250521\pi\)
\(410\) 0 0
\(411\) 3.19777 0.157734
\(412\) 0.891737 + 0.514845i 0.0439327 + 0.0253646i
\(413\) −12.6872 + 7.32495i −0.624296 + 0.360437i
\(414\) 15.2875 26.4787i 0.751339 1.30136i
\(415\) 0 0
\(416\) 0.222018 + 0.384546i 0.0108853 + 0.0188539i
\(417\) 0.572922i 0.0280561i
\(418\) 27.4998 16.6909i 1.34506 0.816379i
\(419\) −2.52693 −0.123448 −0.0617242 0.998093i \(-0.519660\pi\)
−0.0617242 + 0.998093i \(0.519660\pi\)
\(420\) 0 0
\(421\) −7.43346 12.8751i −0.362285 0.627495i 0.626052 0.779781i \(-0.284670\pi\)
−0.988336 + 0.152286i \(0.951336\pi\)
\(422\) 12.5432 + 7.24181i 0.610592 + 0.352526i
\(423\) 16.7226 9.65481i 0.813082 0.469433i
\(424\) 8.45592 14.6461i 0.410656 0.711276i
\(425\) 0 0
\(426\) −0.439895 −0.0213130
\(427\) −1.05510 0.609163i −0.0510599 0.0294794i
\(428\) 2.18380 + 1.26082i 0.105558 + 0.0609440i
\(429\) −0.367493 −0.0177427
\(430\) 0 0
\(431\) 2.09034 3.62057i 0.100688 0.174397i −0.811280 0.584657i \(-0.801229\pi\)
0.911968 + 0.410261i \(0.134562\pi\)
\(432\) 4.08261 2.35709i 0.196425 0.113406i
\(433\) −21.9150 12.6527i −1.05317 0.608048i −0.129635 0.991562i \(-0.541380\pi\)
−0.923535 + 0.383514i \(0.874714\pi\)
\(434\) −2.48546 4.30495i −0.119306 0.206644i
\(435\) 0 0
\(436\) −1.58910 −0.0761043
\(437\) −26.5887 14.5838i −1.27191 0.697637i
\(438\) 2.06802i 0.0988139i
\(439\) 14.4561 + 25.0386i 0.689950 + 1.19503i 0.971854 + 0.235585i \(0.0757008\pi\)
−0.281904 + 0.959443i \(0.590966\pi\)
\(440\) 0 0
\(441\) −7.86114 + 13.6159i −0.374340 + 0.648376i
\(442\) 1.43277 0.827208i 0.0681498 0.0393463i
\(443\) −3.97388 2.29432i −0.188805 0.109007i 0.402618 0.915368i \(-0.368100\pi\)
−0.591423 + 0.806362i \(0.701434\pi\)
\(444\) 0.130790 0.00620702
\(445\) 0 0
\(446\) −19.1533 + 33.1745i −0.906935 + 1.57086i
\(447\) 1.00246 + 0.578773i 0.0474149 + 0.0273750i
\(448\) 9.23529i 0.436327i
\(449\) −29.2171 −1.37884 −0.689420 0.724362i \(-0.742135\pi\)
−0.689420 + 0.724362i \(0.742135\pi\)
\(450\) 0 0
\(451\) 3.02917 + 5.24668i 0.142638 + 0.247056i
\(452\) −1.09973 0.634928i −0.0517268 0.0298645i
\(453\) −0.780628 + 0.450696i −0.0366771 + 0.0211755i
\(454\) −1.69280 2.93202i −0.0794471 0.137606i
\(455\) 0 0
\(456\) −1.09876 1.81031i −0.0514541 0.0847754i
\(457\) 23.7113i 1.10917i −0.832128 0.554584i \(-0.812878\pi\)
0.832128 0.554584i \(-0.187122\pi\)
\(458\) 28.0673 16.2046i 1.31150 0.757193i
\(459\) −1.49013 2.58098i −0.0695534 0.120470i
\(460\) 0 0
\(461\) −17.5109 30.3298i −0.815565 1.41260i −0.908922 0.416967i \(-0.863093\pi\)
0.0933568 0.995633i \(-0.470240\pi\)
\(462\) −1.51381 0.873999i −0.0704289 0.0406621i
\(463\) 20.4936i 0.952417i −0.879332 0.476209i \(-0.842011\pi\)
0.879332 0.476209i \(-0.157989\pi\)
\(464\) −17.4644 −0.810765
\(465\) 0 0
\(466\) −1.52107 + 2.63457i −0.0704621 + 0.122044i
\(467\) 9.24346i 0.427736i 0.976863 + 0.213868i \(0.0686063\pi\)
−0.976863 + 0.213868i \(0.931394\pi\)
\(468\) 0.233695i 0.0108026i
\(469\) −3.45310 + 5.98095i −0.159449 + 0.276174i
\(470\) 0 0
\(471\) −0.190233 + 0.329494i −0.00876549 + 0.0151823i
\(472\) −26.0232 + 15.0245i −1.19782 + 0.691559i
\(473\) 13.4739 7.77916i 0.619530 0.357686i
\(474\) 3.91496 0.179820
\(475\) 0 0
\(476\) 0.695620 0.0318837
\(477\) 16.2441 9.37856i 0.743768 0.429415i
\(478\) −9.85295 + 5.68860i −0.450663 + 0.260191i
\(479\) 1.88377 3.26278i 0.0860715 0.149080i −0.819776 0.572685i \(-0.805902\pi\)
0.905847 + 0.423604i \(0.139235\pi\)
\(480\) 0 0
\(481\) 0.754086 1.30611i 0.0343834 0.0595537i
\(482\) 21.5316i 0.980737i
\(483\) 1.64785i 0.0749798i
\(484\) 1.34059 2.32197i 0.0609359 0.105544i
\(485\) 0 0
\(486\) 7.15673 0.324636
\(487\) 11.7981i 0.534621i 0.963610 + 0.267311i \(0.0861349\pi\)
−0.963610 + 0.267311i \(0.913865\pi\)
\(488\) −2.16416 1.24948i −0.0979669 0.0565612i
\(489\) −0.867922 1.50328i −0.0392488 0.0679809i
\(490\) 0 0
\(491\) −3.91782 6.78586i −0.176809 0.306241i 0.763977 0.645243i \(-0.223244\pi\)
−0.940786 + 0.339002i \(0.889911\pi\)
\(492\) −0.0370880 + 0.0214128i −0.00167206 + 0.000965362i
\(493\) 11.0408i 0.497254i
\(494\) 2.62153 0.0574526i 0.117948 0.00258491i
\(495\) 0 0
\(496\) −5.59707 9.69442i −0.251316 0.435292i
\(497\) −1.84707 + 1.06641i −0.0828523 + 0.0478348i
\(498\) 3.55593 + 2.05301i 0.159345 + 0.0919978i
\(499\) 0.529796 + 0.917633i 0.0237169 + 0.0410789i 0.877640 0.479320i \(-0.159117\pi\)
−0.853923 + 0.520399i \(0.825783\pi\)
\(500\) 0 0
\(501\) −3.04002 −0.135818
\(502\) 10.6458i 0.475145i
\(503\) 4.65671 + 2.68855i 0.207633 + 0.119877i 0.600211 0.799842i \(-0.295083\pi\)
−0.392578 + 0.919719i \(0.628417\pi\)
\(504\) 5.17589 8.96490i 0.230552 0.399329i
\(505\) 0 0
\(506\) −51.3441 −2.28253
\(507\) 2.01866 + 1.16547i 0.0896517 + 0.0517604i
\(508\) 2.53755 1.46506i 0.112586 0.0650014i
\(509\) 16.9240 29.3132i 0.750142 1.29928i −0.197611 0.980280i \(-0.563318\pi\)
0.947753 0.319004i \(-0.103348\pi\)
\(510\) 0 0
\(511\) 5.01336 + 8.68339i 0.221778 + 0.384131i
\(512\) 18.5188i 0.818423i
\(513\) −0.103495 4.72242i −0.00456942 0.208500i
\(514\) −12.8951 −0.568778
\(515\) 0 0
\(516\) 0.0549897 + 0.0952450i 0.00242079 + 0.00419293i
\(517\) −28.0821 16.2132i −1.23505 0.713056i
\(518\) 6.21260 3.58684i 0.272966 0.157597i
\(519\) −1.26902 + 2.19800i −0.0557037 + 0.0964817i
\(520\) 0 0
\(521\) −29.5742 −1.29567 −0.647834 0.761782i \(-0.724325\pi\)
−0.647834 + 0.761782i \(0.724325\pi\)
\(522\) −15.2792 8.82147i −0.668754 0.386105i
\(523\) −20.8232 12.0223i −0.910536 0.525698i −0.0299323 0.999552i \(-0.509529\pi\)
−0.880604 + 0.473854i \(0.842863\pi\)
\(524\) 0.483596 0.0211260
\(525\) 0 0
\(526\) 22.6054 39.1537i 0.985643 1.70718i
\(527\) −6.12871 + 3.53841i −0.266971 + 0.154136i
\(528\) −3.40899 1.96818i −0.148357 0.0856540i
\(529\) 12.7013 + 21.9992i 0.552228 + 0.956488i
\(530\) 0 0
\(531\) −33.3277 −1.44630
\(532\) 0.966659 + 0.530207i 0.0419100 + 0.0229874i
\(533\) 0.493831i 0.0213902i
\(534\) 1.91183 + 3.31138i 0.0827329 + 0.143298i
\(535\) 0 0
\(536\) −7.08279 + 12.2678i −0.305930 + 0.529886i
\(537\) −1.55096 + 0.895447i −0.0669289 + 0.0386414i
\(538\) −23.6124 13.6326i −1.01800 0.587743i
\(539\) 26.4022 1.13722
\(540\) 0 0
\(541\) 13.0959 22.6827i 0.563035 0.975205i −0.434195 0.900819i \(-0.642967\pi\)
0.997230 0.0743856i \(-0.0236996\pi\)
\(542\) 14.7181 + 8.49753i 0.632199 + 0.365000i
\(543\) 2.68282i 0.115131i
\(544\) 3.00684 0.128917
\(545\) 0 0
\(546\) −0.0712420 0.123395i −0.00304888 0.00528081i
\(547\) −12.9284 7.46421i −0.552778 0.319146i 0.197464 0.980310i \(-0.436730\pi\)
−0.750242 + 0.661164i \(0.770063\pi\)
\(548\) −2.95735 + 1.70743i −0.126332 + 0.0729377i
\(549\) −1.38581 2.40029i −0.0591449 0.102442i
\(550\) 0 0
\(551\) −8.41540 + 15.3427i −0.358508 + 0.653622i
\(552\) 3.37997i 0.143861i
\(553\) 16.4385 9.49077i 0.699036 0.403588i
\(554\) −1.33077 2.30496i −0.0565390 0.0979284i
\(555\) 0 0
\(556\) −0.305908 0.529848i −0.0129734 0.0224706i
\(557\) −4.56841 2.63757i −0.193570 0.111758i 0.400083 0.916479i \(-0.368981\pi\)
−0.593653 + 0.804721i \(0.702315\pi\)
\(558\) 11.3086i 0.478730i
\(559\) 1.26820 0.0536391
\(560\) 0 0
\(561\) −1.24426 + 2.15513i −0.0525328 + 0.0909895i
\(562\) 21.0196i 0.886660i
\(563\) 17.8950i 0.754186i 0.926175 + 0.377093i \(0.123076\pi\)
−0.926175 + 0.377093i \(0.876924\pi\)
\(564\) 0.114609 0.198508i 0.00482590 0.00835870i
\(565\) 0 0
\(566\) −13.2631 + 22.9724i −0.557491 + 0.965603i
\(567\) 9.83132 5.67612i 0.412877 0.238375i
\(568\) −3.78859 + 2.18735i −0.158966 + 0.0917790i
\(569\) −6.81848 −0.285846 −0.142923 0.989734i \(-0.545650\pi\)
−0.142923 + 0.989734i \(0.545650\pi\)
\(570\) 0 0
\(571\) 5.16915 0.216322 0.108161 0.994133i \(-0.465504\pi\)
0.108161 + 0.994133i \(0.465504\pi\)
\(572\) 0.339864 0.196221i 0.0142104 0.00820440i
\(573\) 3.25244 1.87780i 0.135873 0.0784461i
\(574\) −1.17447 + 2.03423i −0.0490213 + 0.0849073i
\(575\) 0 0
\(576\) 10.5049 18.1950i 0.437703 0.758125i
\(577\) 28.5621i 1.18905i 0.804076 + 0.594527i \(0.202661\pi\)
−0.804076 + 0.594527i \(0.797339\pi\)
\(578\) 13.9772i 0.581376i
\(579\) −1.84135 + 3.18930i −0.0765237 + 0.132543i
\(580\) 0 0
\(581\) 19.9079 0.825919
\(582\) 4.91785i 0.203851i
\(583\) −27.2786 15.7493i −1.12976 0.652269i
\(584\) 10.2831 + 17.8108i 0.425518 + 0.737018i
\(585\) 0 0
\(586\) 24.6684 + 42.7269i 1.01904 + 1.76503i
\(587\) 34.9228 20.1627i 1.44142 0.832204i 0.443476 0.896286i \(-0.353745\pi\)
0.997945 + 0.0640822i \(0.0204120\pi\)
\(588\) 0.186633i 0.00769663i
\(589\) −11.2137 + 0.245756i −0.462052 + 0.0101262i
\(590\) 0 0
\(591\) 1.44535 + 2.50341i 0.0594536 + 0.102977i
\(592\) 13.9903 8.07730i 0.574997 0.331975i
\(593\) 23.9806 + 13.8452i 0.984767 + 0.568555i 0.903706 0.428154i \(-0.140836\pi\)
0.0810610 + 0.996709i \(0.474169\pi\)
\(594\) −3.99870 6.92595i −0.164069 0.284175i
\(595\) 0 0
\(596\) −1.23613 −0.0506338
\(597\) 2.40371i 0.0983771i
\(598\) −3.62449 2.09260i −0.148216 0.0855727i
\(599\) −1.31466 + 2.27706i −0.0537156 + 0.0930382i −0.891633 0.452759i \(-0.850440\pi\)
0.837917 + 0.545797i \(0.183773\pi\)
\(600\) 0 0
\(601\) 27.7009 1.12994 0.564972 0.825110i \(-0.308887\pi\)
0.564972 + 0.825110i \(0.308887\pi\)
\(602\) 5.22408 + 3.01613i 0.212918 + 0.122928i
\(603\) −13.6063 + 7.85561i −0.554092 + 0.319905i
\(604\) 0.481292 0.833622i 0.0195835 0.0339196i
\(605\) 0 0
\(606\) 2.15133 + 3.72622i 0.0873919 + 0.151367i
\(607\) 32.0668i 1.30155i 0.759271 + 0.650775i \(0.225556\pi\)
−0.759271 + 0.650775i \(0.774444\pi\)
\(608\) 4.17842 + 2.29184i 0.169457 + 0.0929463i
\(609\) 0.950874 0.0385313
\(610\) 0 0
\(611\) −1.32158 2.28904i −0.0534654 0.0926048i
\(612\) 1.37048 + 0.791248i 0.0553985 + 0.0319843i
\(613\) 10.7909 6.23014i 0.435841 0.251633i −0.265991 0.963976i \(-0.585699\pi\)
0.701832 + 0.712343i \(0.252366\pi\)
\(614\) 11.5215 19.9559i 0.464971 0.805354i
\(615\) 0 0
\(616\) −17.3836 −0.700405
\(617\) −22.9271 13.2370i −0.923009 0.532900i −0.0384155 0.999262i \(-0.512231\pi\)
−0.884594 + 0.466362i \(0.845564\pi\)
\(618\) −1.23687 0.714106i −0.0497541 0.0287256i
\(619\) −33.3766 −1.34152 −0.670760 0.741674i \(-0.734032\pi\)
−0.670760 + 0.741674i \(0.734032\pi\)
\(620\) 0 0
\(621\) −3.76960 + 6.52914i −0.151269 + 0.262005i
\(622\) 37.4511 21.6224i 1.50165 0.866978i
\(623\) 16.0551 + 9.26942i 0.643234 + 0.371371i
\(624\) −0.160431 0.277875i −0.00642240 0.0111239i
\(625\) 0 0
\(626\) 47.2323 1.88778
\(627\) −3.37173 + 2.04645i −0.134654 + 0.0817275i
\(628\) 0.406296i 0.0162130i
\(629\) −5.10638 8.84452i −0.203605 0.352654i
\(630\) 0 0
\(631\) −20.0601 + 34.7450i −0.798578 + 1.38318i 0.121964 + 0.992535i \(0.461081\pi\)
−0.920542 + 0.390643i \(0.872253\pi\)
\(632\) 33.7176 19.4669i 1.34122 0.774351i
\(633\) −1.53791 0.887911i −0.0611263 0.0352913i
\(634\) 20.1000 0.798271
\(635\) 0 0
\(636\) 0.111329 0.192828i 0.00441450 0.00764613i
\(637\) 1.86379 + 1.07606i 0.0738459 + 0.0426349i
\(638\) 29.6276i 1.17297i
\(639\) −4.85202 −0.191943
\(640\) 0 0
\(641\) −0.203273 0.352079i −0.00802880 0.0139063i 0.861983 0.506937i \(-0.169222\pi\)
−0.870012 + 0.493031i \(0.835889\pi\)
\(642\) −3.02901 1.74880i −0.119545 0.0690195i
\(643\) −21.7975 + 12.5848i −0.859610 + 0.496296i −0.863882 0.503695i \(-0.831974\pi\)
0.00427137 + 0.999991i \(0.498640\pi\)
\(644\) −0.879860 1.52396i −0.0346713 0.0600525i
\(645\) 0 0
\(646\) 8.53908 15.5682i 0.335965 0.612523i
\(647\) 18.3604i 0.721821i −0.932600 0.360911i \(-0.882466\pi\)
0.932600 0.360911i \(-0.117534\pi\)
\(648\) 20.1654 11.6425i 0.792173 0.457361i
\(649\) 27.9834 + 48.4686i 1.09844 + 1.90256i
\(650\) 0 0
\(651\) 0.304740 + 0.527825i 0.0119437 + 0.0206871i
\(652\) 1.60534 + 0.926843i 0.0628699 + 0.0362980i
\(653\) 33.0301i 1.29257i 0.763097 + 0.646284i \(0.223678\pi\)
−0.763097 + 0.646284i \(0.776322\pi\)
\(654\) 2.20414 0.0861886
\(655\) 0 0
\(656\) −2.64481 + 4.58094i −0.103262 + 0.178856i
\(657\) 22.8102i 0.889911i
\(658\) 12.5723i 0.490120i
\(659\) −13.2310 + 22.9167i −0.515406 + 0.892709i 0.484434 + 0.874828i \(0.339025\pi\)
−0.999840 + 0.0178814i \(0.994308\pi\)
\(660\) 0 0
\(661\) 7.79673 13.5043i 0.303258 0.525258i −0.673614 0.739083i \(-0.735259\pi\)
0.976872 + 0.213825i \(0.0685924\pi\)
\(662\) −37.7480 + 21.7938i −1.46712 + 0.847041i
\(663\) −0.175670 + 0.101423i −0.00682246 + 0.00393895i
\(664\) 40.8339 1.58466
\(665\) 0 0
\(666\) 16.3197 0.632377
\(667\) 24.1882 13.9651i 0.936570 0.540729i
\(668\) 2.81146 1.62320i 0.108779 0.0628034i
\(669\) 2.34837 4.06749i 0.0907931 0.157258i
\(670\) 0 0
\(671\) −2.32717 + 4.03078i −0.0898395 + 0.155607i
\(672\) 0.258959i 0.00998958i
\(673\) 6.13645i 0.236543i −0.992981 0.118271i \(-0.962265\pi\)
0.992981 0.118271i \(-0.0377353\pi\)
\(674\) −11.4880 + 19.8977i −0.442500 + 0.766432i
\(675\) 0 0
\(676\) −2.48919 −0.0957379
\(677\) 22.2754i 0.856112i −0.903752 0.428056i \(-0.859199\pi\)
0.903752 0.428056i \(-0.140801\pi\)
\(678\) 1.52536 + 0.880665i 0.0585810 + 0.0338217i
\(679\) −11.9220 20.6495i −0.457524 0.792455i
\(680\) 0 0
\(681\) 0.207553 + 0.359492i 0.00795344 + 0.0137758i
\(682\) −16.4461 + 9.49517i −0.629754 + 0.363589i
\(683\) 16.7397i 0.640527i 0.947328 + 0.320264i \(0.103772\pi\)
−0.947328 + 0.320264i \(0.896228\pi\)
\(684\) 1.30138 + 2.14414i 0.0497594 + 0.0819832i
\(685\) 0 0
\(686\) 11.8796 + 20.5761i 0.453566 + 0.785599i
\(687\) −3.44130 + 1.98683i −0.131294 + 0.0758024i
\(688\) 11.7642 + 6.79208i 0.448507 + 0.258946i
\(689\) −1.28377 2.22355i −0.0489076 0.0847104i
\(690\) 0 0
\(691\) 36.7557 1.39825 0.699126 0.714999i \(-0.253573\pi\)
0.699126 + 0.714999i \(0.253573\pi\)
\(692\) 2.71034i 0.103032i
\(693\) −16.6973 9.64018i −0.634277 0.366200i
\(694\) −16.7284 + 28.9744i −0.635000 + 1.09985i
\(695\) 0 0
\(696\) 1.95037 0.0739288
\(697\) 2.89602 + 1.67202i 0.109695 + 0.0633323i
\(698\) −32.6954 + 18.8767i −1.23754 + 0.714494i
\(699\) 0.186497 0.323021i 0.00705395 0.0122178i
\(700\) 0 0
\(701\) −17.7053 30.6665i −0.668721 1.15826i −0.978262 0.207372i \(-0.933509\pi\)
0.309541 0.950886i \(-0.399824\pi\)
\(702\) 0.651889i 0.0246040i
\(703\) −0.354657 16.1828i −0.0133761 0.610345i
\(704\) −35.2814 −1.32972
\(705\) 0 0
\(706\) −7.62510 13.2071i −0.286974 0.497054i
\(707\) 18.0664 + 10.4306i 0.679457 + 0.392285i
\(708\) −0.342618 + 0.197810i −0.0128764 + 0.00743417i
\(709\) 16.9184 29.3036i 0.635386 1.10052i −0.351048 0.936358i \(-0.614174\pi\)
0.986433 0.164163i \(-0.0524922\pi\)
\(710\) 0 0
\(711\) 43.1819 1.61945
\(712\) 32.9313 + 19.0129i 1.23415 + 0.712538i
\(713\) 15.5039 + 8.95117i 0.580625 + 0.335224i
\(714\) −0.964848 −0.0361085
\(715\) 0 0
\(716\) 0.956237 1.65625i 0.0357362 0.0618970i
\(717\) 1.20806 0.697474i 0.0451158 0.0260476i
\(718\) 2.54307 + 1.46824i 0.0949066 + 0.0547943i
\(719\) 13.4970 + 23.3775i 0.503353 + 0.871833i 0.999992 + 0.00387581i \(0.00123371\pi\)
−0.496640 + 0.867957i \(0.665433\pi\)
\(720\) 0 0
\(721\) −6.92463 −0.257887
\(722\) 23.7324 15.1256i 0.883229 0.562916i
\(723\) 2.63997i 0.0981814i
\(724\) 1.43247 + 2.48111i 0.0532374 + 0.0922099i
\(725\) 0 0
\(726\) −1.85944 + 3.22065i −0.0690104 + 0.119529i
\(727\) −18.7090 + 10.8016i −0.693878 + 0.400610i −0.805063 0.593189i \(-0.797869\pi\)
0.111185 + 0.993800i \(0.464535\pi\)
\(728\) −1.22714 0.708492i −0.0454810 0.0262584i
\(729\) 25.2353 0.934640
\(730\) 0 0
\(731\) 4.29388 7.43723i 0.158815 0.275076i
\(732\) −0.0284930 0.0164504i −0.00105313 0.000608026i
\(733\) 17.2551i 0.637332i 0.947867 + 0.318666i \(0.103235\pi\)
−0.947867 + 0.318666i \(0.896765\pi\)
\(734\) 7.81217 0.288353
\(735\) 0 0
\(736\) −3.80322 6.58737i −0.140189 0.242814i
\(737\) 22.8489 + 13.1918i 0.841650 + 0.485927i
\(738\) −4.62777 + 2.67184i −0.170350 + 0.0983519i
\(739\) 2.39553 + 4.14918i 0.0881210 + 0.152630i 0.906717 0.421740i \(-0.138580\pi\)
−0.818596 + 0.574370i \(0.805247\pi\)
\(740\) 0 0
\(741\) −0.321423 + 0.00704420i −0.0118078 + 0.000258775i
\(742\) 12.2126i 0.448338i
\(743\) −12.5465 + 7.24373i −0.460287 + 0.265747i −0.712165 0.702012i \(-0.752285\pi\)
0.251878 + 0.967759i \(0.418952\pi\)
\(744\) 0.625065 + 1.08264i 0.0229160 + 0.0396917i
\(745\) 0 0
\(746\) 23.4912 + 40.6879i 0.860072 + 1.48969i
\(747\) 39.2217 + 22.6447i 1.43505 + 0.828525i
\(748\) 2.65746i 0.0971665i
\(749\) −16.9579 −0.619630
\(750\) 0 0
\(751\) −3.22637 + 5.58824i −0.117732 + 0.203918i −0.918869 0.394564i \(-0.870896\pi\)
0.801137 + 0.598482i \(0.204229\pi\)
\(752\) 28.3119i 1.03243i
\(753\) 1.30527i 0.0475667i
\(754\) −1.20751 + 2.09147i −0.0439749 + 0.0761668i
\(755\) 0 0
\(756\) 0.137047 0.237373i 0.00498437 0.00863318i
\(757\) 32.0074 18.4795i 1.16333 0.671649i 0.211230 0.977436i \(-0.432253\pi\)
0.952100 + 0.305788i \(0.0989197\pi\)
\(758\) −45.5530 + 26.3000i −1.65456 + 0.955260i
\(759\) 6.29525 0.228503
\(760\) 0 0
\(761\) 48.3893 1.75411 0.877055 0.480389i \(-0.159505\pi\)
0.877055 + 0.480389i \(0.159505\pi\)
\(762\) −3.51967 + 2.03208i −0.127504 + 0.0736145i
\(763\) 9.25493 5.34333i 0.335051 0.193442i
\(764\) −2.00528 + 3.47324i −0.0725484 + 0.125657i
\(765\) 0 0
\(766\) −10.3167 + 17.8690i −0.372756 + 0.645632i
\(767\) 4.56200i 0.164724i
\(768\) 0.837598i 0.0302242i
\(769\) 20.7177 35.8841i 0.747098 1.29401i −0.202110 0.979363i \(-0.564780\pi\)
0.949208 0.314649i \(-0.101887\pi\)
\(770\) 0 0
\(771\) 1.58105 0.0569403
\(772\) 3.93270i 0.141541i
\(773\) −33.6285 19.4154i −1.20953 0.698325i −0.246877 0.969047i \(-0.579404\pi\)
−0.962658 + 0.270722i \(0.912738\pi\)
\(774\) 6.86151 + 11.8845i 0.246632 + 0.427179i
\(775\) 0 0
\(776\) −24.4537 42.3550i −0.877836 1.52046i
\(777\) −0.761720 + 0.439779i −0.0273266 + 0.0157770i
\(778\) 1.39657i 0.0500695i
\(779\) 2.74999 + 4.53087i 0.0985287 + 0.162335i
\(780\) 0 0
\(781\) 4.07397 + 7.05632i 0.145778 + 0.252495i
\(782\) −24.5437 + 14.1703i −0.877680 + 0.506729i
\(783\) 3.76757 + 2.17521i 0.134642 + 0.0777355i
\(784\) 11.5261 + 19.9637i 0.411645 + 0.712990i
\(785\) 0 0
\(786\) −0.670764 −0.0239254
\(787\) 51.4952i 1.83561i −0.397037 0.917803i \(-0.629962\pi\)
0.397037 0.917803i \(-0.370038\pi\)
\(788\) −2.67336 1.54347i −0.0952347 0.0549838i
\(789\) −2.77163 + 4.80060i −0.0986725 + 0.170906i
\(790\) 0 0
\(791\) 8.53973 0.303638
\(792\) −34.2485 19.7734i −1.21697 0.702615i
\(793\) −0.328560 + 0.189694i −0.0116675 + 0.00673623i
\(794\) −21.1556 + 36.6426i −0.750785 + 1.30040i
\(795\) 0 0
\(796\) 1.28344 + 2.22299i 0.0454905 + 0.0787918i
\(797\) 7.50433i 0.265817i 0.991128 + 0.132908i \(0.0424316\pi\)
−0.991128 + 0.132908i \(0.957568\pi\)
\(798\) −1.34079 0.735414i −0.0474634 0.0260334i
\(799\) −17.8985 −0.633203
\(800\) 0 0
\(801\) 21.0874 + 36.5244i 0.745087 + 1.29053i
\(802\) 9.19387 + 5.30809i 0.324647 + 0.187435i
\(803\) 33.1730 19.1524i 1.17065 0.675875i
\(804\) −0.0932510 + 0.161515i −0.00328871 + 0.00569621i
\(805\) 0 0
\(806\) −1.54795 −0.0545243
\(807\) 2.89509 + 1.67148i 0.101912 + 0.0588388i
\(808\) 37.0567 + 21.3947i 1.30365 + 0.752663i
\(809\) 17.9109 0.629714 0.314857 0.949139i \(-0.398043\pi\)
0.314857 + 0.949139i \(0.398043\pi\)
\(810\) 0 0
\(811\) −2.57516 + 4.46030i −0.0904260 + 0.156622i −0.907690 0.419640i \(-0.862156\pi\)
0.817264 + 0.576263i \(0.195490\pi\)
\(812\) −0.879385 + 0.507713i −0.0308604 + 0.0178172i
\(813\) −1.80458 1.04187i −0.0632893 0.0365401i
\(814\) −13.7028 23.7339i −0.480281 0.831871i
\(815\) 0 0
\(816\) −2.17276 −0.0760619
\(817\) 11.6356 7.06221i 0.407080 0.247075i
\(818\) 15.6007i 0.545464i
\(819\) −0.785796 1.36104i −0.0274579 0.0475586i
\(820\) 0 0
\(821\) 0.690525 1.19602i 0.0240995 0.0417415i −0.853724 0.520726i \(-0.825661\pi\)
0.877824 + 0.478984i \(0.158995\pi\)
\(822\) 4.10194 2.36826i 0.143072 0.0826025i
\(823\) 12.4846 + 7.20798i 0.435185 + 0.251254i 0.701553 0.712617i \(-0.252490\pi\)
−0.266368 + 0.963871i \(0.585824\pi\)
\(824\) −14.2034 −0.494798
\(825\) 0 0
\(826\) −10.8497 + 18.7922i −0.377509 + 0.653864i
\(827\) −8.20404 4.73660i −0.285282 0.164708i 0.350530 0.936552i \(-0.386001\pi\)
−0.635812 + 0.771844i \(0.719335\pi\)
\(828\) 4.00326i 0.139123i
\(829\) 12.3950 0.430497 0.215248 0.976559i \(-0.430944\pi\)
0.215248 + 0.976559i \(0.430944\pi\)
\(830\) 0 0
\(831\) 0.163164 + 0.282609i 0.00566011 + 0.00980359i
\(832\) −2.49059 1.43794i −0.0863455 0.0498516i
\(833\) 12.6209 7.28666i 0.437287 0.252468i
\(834\) 0.424304 + 0.734916i 0.0146925 + 0.0254481i
\(835\) 0 0
\(836\) 2.02554 3.69291i 0.0700548 0.127722i
\(837\) 2.78848i 0.0963839i
\(838\) −3.24142 + 1.87144i −0.111973 + 0.0646477i
\(839\) 6.26491 + 10.8511i 0.216289 + 0.374623i 0.953670 0.300853i \(-0.0972714\pi\)
−0.737382 + 0.675476i \(0.763938\pi\)
\(840\) 0 0
\(841\) 6.44162 + 11.1572i 0.222125 + 0.384732i
\(842\) −19.0706 11.0104i −0.657215 0.379443i
\(843\) 2.57720i 0.0887633i
\(844\) 1.89638 0.0652760
\(845\) 0 0
\(846\) 14.3007 24.7695i 0.491667 0.851592i
\(847\) 18.0308i 0.619547i
\(848\) 27.5018i 0.944416i
\(849\) 1.62618 2.81663i 0.0558103 0.0966663i
\(850\) 0 0
\(851\) −12.9177 + 22.3741i −0.442813 + 0.766974i
\(852\) −0.0498801 + 0.0287983i −0.00170886 + 0.000986613i
\(853\) −3.00771 + 1.73650i −0.102982 + 0.0594567i −0.550606 0.834765i \(-0.685603\pi\)
0.447624 + 0.894222i \(0.352270\pi\)
\(854\) −1.80458 −0.0617513
\(855\) 0 0
\(856\) −34.7831 −1.18886
\(857\) −14.4295 + 8.33085i −0.492901 + 0.284577i −0.725777 0.687930i \(-0.758520\pi\)
0.232876 + 0.972506i \(0.425186\pi\)
\(858\) −0.471402 + 0.272164i −0.0160934 + 0.00929154i
\(859\) 20.4042 35.3412i 0.696183 1.20583i −0.273597 0.961844i \(-0.588213\pi\)
0.969780 0.243981i \(-0.0784533\pi\)
\(860\) 0 0
\(861\) 0.144000 0.249415i 0.00490751 0.00850005i
\(862\) 6.19239i 0.210914i
\(863\) 4.07050i 0.138561i −0.997597 0.0692806i \(-0.977930\pi\)
0.997597 0.0692806i \(-0.0220704\pi\)
\(864\) 0.592392 1.02605i 0.0201536 0.0349071i
\(865\) 0 0
\(866\) −37.4821 −1.27369
\(867\) 1.71373i 0.0582014i
\(868\) −0.563658 0.325428i −0.0191318 0.0110458i
\(869\) −36.2574 62.7996i −1.22995 2.13033i
\(870\) 0 0
\(871\) 1.07530 + 1.86247i 0.0364351 + 0.0631075i
\(872\) 18.9831 10.9599i 0.642851 0.371150i
\(873\) 54.2437i 1.83587i
\(874\) −44.9075 + 0.984178i −1.51902 + 0.0332903i
\(875\) 0 0
\(876\) 0.135386 + 0.234495i 0.00457426 + 0.00792285i
\(877\) −22.9621 + 13.2572i −0.775376 + 0.447663i −0.834789 0.550570i \(-0.814410\pi\)
0.0594132 + 0.998233i \(0.481077\pi\)
\(878\) 37.0871 + 21.4122i 1.25163 + 0.722628i
\(879\) −3.02457 5.23871i −0.102016 0.176697i
\(880\) 0 0
\(881\) −22.3730 −0.753766 −0.376883 0.926261i \(-0.623004\pi\)
−0.376883 + 0.926261i \(0.623004\pi\)
\(882\) 23.2878i 0.784140i
\(883\) 17.0726 + 9.85689i 0.574540 + 0.331711i 0.758961 0.651137i \(-0.225708\pi\)
−0.184421 + 0.982847i \(0.559041\pi\)
\(884\) 0.108308 0.187596i 0.00364281 0.00630953i
\(885\) 0 0
\(886\) −6.79667 −0.228339
\(887\) −9.89139 5.71080i −0.332120 0.191750i 0.324662 0.945830i \(-0.394750\pi\)
−0.656782 + 0.754080i \(0.728083\pi\)
\(888\) −1.56239 + 0.902049i −0.0524305 + 0.0302708i
\(889\) −9.85245 + 17.0649i −0.330441 + 0.572340i
\(890\) 0 0
\(891\) −21.6844 37.5584i −0.726453 1.25825i
\(892\) 5.01558i 0.167934i
\(893\) −24.8724 13.6424i −0.832323 0.456524i
\(894\) 1.71455 0.0573431
\(895\) 0 0
\(896\) −8.26556 14.3164i −0.276133 0.478276i
\(897\) 0.444395 + 0.256571i 0.0148379 + 0.00856667i
\(898\) −37.4783 + 21.6381i −1.25067 + 0.722073i
\(899\) 5.16517 8.94634i 0.172268 0.298377i
\(900\) 0 0
\(901\) −17.3864 −0.579223
\(902\) 7.77135 + 4.48679i 0.258758 + 0.149394i
\(903\) −0.640519 0.369804i −0.0213151 0.0123063i
\(904\) 17.5162 0.582580
\(905\) 0 0
\(906\) −0.667568 + 1.15626i −0.0221784 + 0.0384142i
\(907\) −9.29964 + 5.36915i −0.308789 + 0.178280i −0.646385 0.763012i \(-0.723720\pi\)
0.337595 + 0.941291i \(0.390387\pi\)
\(908\) −0.383897 0.221643i −0.0127401 0.00735548i
\(909\) 23.7291 + 41.1000i 0.787045 + 1.36320i
\(910\) 0 0
\(911\) −27.5952 −0.914269 −0.457134 0.889398i \(-0.651124\pi\)
−0.457134 + 0.889398i \(0.651124\pi\)
\(912\) −3.01935 1.65610i −0.0999807 0.0548388i
\(913\) 76.0538i 2.51701i
\(914\) −17.5605 30.4157i −0.580850 1.00606i
\(915\) 0 0
\(916\) 2.12171 3.67492i 0.0701034 0.121423i
\(917\) −2.81646 + 1.62608i −0.0930077 + 0.0536980i
\(918\) −3.82294 2.20717i −0.126176 0.0728476i
\(919\) 49.2639 1.62507 0.812533 0.582915i \(-0.198088\pi\)
0.812533 + 0.582915i \(0.198088\pi\)
\(920\) 0 0
\(921\) −1.41264 + 2.44677i −0.0465482 + 0.0806238i
\(922\) −44.9243 25.9371i −1.47950 0.854192i
\(923\) 0.664160i 0.0218611i
\(924\) −0.228870 −0.00752927
\(925\) 0 0
\(926\) −15.1775 26.2882i −0.498763 0.863883i
\(927\) −13.6426 7.87657i −0.448082 0.258700i
\(928\) −3.80117 + 2.19461i −0.124779 + 0.0720415i
\(929\) 21.5374 + 37.3039i 0.706619 + 1.22390i 0.966104 + 0.258153i \(0.0831138\pi\)
−0.259485 + 0.965747i \(0.583553\pi\)
\(930\) 0 0
\(931\) 23.0923 0.506085i 0.756821 0.0165863i
\(932\) 0.398315i 0.0130472i
\(933\) −4.59183 + 2.65110i −0.150330 + 0.0867930i
\(934\) 6.84568 + 11.8571i 0.223998 + 0.387975i
\(935\) 0 0
\(936\) −1.61178 2.79168i −0.0526826 0.0912490i
\(937\) 37.6239 + 21.7222i 1.22912 + 0.709633i 0.966846 0.255360i \(-0.0821941\pi\)
0.262275 + 0.964993i \(0.415527\pi\)
\(938\) 10.2294i 0.334003i
\(939\) −5.79110 −0.188985
\(940\) 0 0
\(941\) −14.6471 + 25.3694i −0.477480 + 0.827020i −0.999667 0.0258111i \(-0.991783\pi\)
0.522186 + 0.852831i \(0.325117\pi\)
\(942\) 0.563545i 0.0183613i
\(943\) 8.45946i 0.275478i
\(944\) −24.4326 + 42.3186i −0.795215 + 1.37735i
\(945\) 0 0
\(946\) 11.5224 19.9575i 0.374627 0.648873i
\(947\) 1.73715 1.00294i 0.0564498 0.0325913i −0.471509 0.881861i \(-0.656291\pi\)
0.527959 + 0.849270i \(0.322957\pi\)
\(948\) 0.443921 0.256298i 0.0144179 0.00832418i
\(949\) 3.12233 0.101355
\(950\) 0 0
\(951\) −2.46443 −0.0799148
\(952\) −8.30975 + 4.79764i −0.269321 + 0.155492i
\(953\) −16.6614 + 9.61946i −0.539716 + 0.311605i −0.744964 0.667105i \(-0.767533\pi\)
0.205248 + 0.978710i \(0.434200\pi\)
\(954\) 13.8915 24.0607i 0.449753 0.778995i
\(955\) 0 0
\(956\) −0.744823 + 1.29007i −0.0240893 + 0.0417239i
\(957\) 3.63260i 0.117425i
\(958\) 5.58045i 0.180296i
\(959\) 11.4824 19.8881i 0.370786 0.642220i
\(960\) 0 0
\(961\) −24.3786 −0.786406
\(962\) 2.23390i 0.0720237i
\(963\) −33.4098 19.2892i −1.07662 0.621585i
\(964\) 1.40959 + 2.44149i 0.0453999 + 0.0786350i
\(965\) 0 0
\(966\) 1.22039 + 2.11378i 0.0392655 + 0.0680099i
\(967\) −24.6075 + 14.2071i −0.791324 + 0.456871i −0.840428 0.541923i \(-0.817697\pi\)
0.0491047 + 0.998794i \(0.484363\pi\)
\(968\) 36.9838i 1.18870i
\(969\) −1.04697 + 1.90880i −0.0336334 + 0.0613196i
\(970\) 0 0
\(971\) −8.98811 15.5679i −0.288442 0.499597i 0.684996 0.728547i \(-0.259804\pi\)
−0.973438 + 0.228950i \(0.926471\pi\)
\(972\) 0.811508 0.468524i 0.0260291 0.0150279i
\(973\) 3.56321 + 2.05722i 0.114231 + 0.0659515i
\(974\) 8.73761 + 15.1340i 0.279971 + 0.484924i
\(975\) 0 0
\(976\) −4.06377 −0.130078
\(977\) 13.2288i 0.423226i −0.977354 0.211613i \(-0.932128\pi\)
0.977354 0.211613i \(-0.0678716\pi\)
\(978\) −2.22666 1.28556i −0.0712006 0.0411077i
\(979\) 35.4118 61.3350i 1.13177 1.96027i
\(980\) 0 0
\(981\) 24.3116 0.776208
\(982\) −10.0512 5.80305i −0.320746 0.185183i
\(983\) 42.0225 24.2617i 1.34031 0.773828i 0.353457 0.935451i \(-0.385006\pi\)
0.986853 + 0.161623i \(0.0516727\pi\)
\(984\) 0.295364 0.511586i 0.00941587 0.0163088i
\(985\) 0 0
\(986\) 8.17680 + 14.1626i 0.260403 + 0.451030i
\(987\) 1.54148i 0.0490658i
\(988\) 0.293496 0.178136i 0.00933736 0.00566727i
\(989\) −21.7246 −0.690802
\(990\) 0 0
\(991\) −20.1402 34.8838i −0.639773 1.10812i −0.985482 0.169778i \(-0.945695\pi\)
0.345709 0.938342i \(-0.387638\pi\)
\(992\) −2.43643 1.40667i −0.0773568 0.0446619i
\(993\) 4.62824 2.67212i 0.146873 0.0847971i
\(994\) −1.57955 + 2.73587i −0.0501004 + 0.0867764i
\(995\) 0 0
\(996\) 0.537613 0.0170349
\(997\) 23.8668 + 13.7795i 0.755869 + 0.436401i 0.827811 0.561008i \(-0.189586\pi\)
−0.0719414 + 0.997409i \(0.522919\pi\)
\(998\) 1.35919 + 0.784730i 0.0430245 + 0.0248402i
\(999\) −4.02413 −0.127318
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 475.2.j.d.349.9 24
5.2 odd 4 475.2.e.f.26.6 12
5.3 odd 4 475.2.e.h.26.1 yes 12
5.4 even 2 inner 475.2.j.d.349.4 24
19.11 even 3 inner 475.2.j.d.49.4 24
95.7 odd 12 9025.2.a.bz.1.1 6
95.12 even 12 9025.2.a.bs.1.6 6
95.49 even 6 inner 475.2.j.d.49.9 24
95.68 odd 12 475.2.e.h.201.1 yes 12
95.83 odd 12 9025.2.a.br.1.6 6
95.87 odd 12 475.2.e.f.201.6 yes 12
95.88 even 12 9025.2.a.by.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
475.2.e.f.26.6 12 5.2 odd 4
475.2.e.f.201.6 yes 12 95.87 odd 12
475.2.e.h.26.1 yes 12 5.3 odd 4
475.2.e.h.201.1 yes 12 95.68 odd 12
475.2.j.d.49.4 24 19.11 even 3 inner
475.2.j.d.49.9 24 95.49 even 6 inner
475.2.j.d.349.4 24 5.4 even 2 inner
475.2.j.d.349.9 24 1.1 even 1 trivial
9025.2.a.br.1.6 6 95.83 odd 12
9025.2.a.bs.1.6 6 95.12 even 12
9025.2.a.by.1.1 6 95.88 even 12
9025.2.a.bz.1.1 6 95.7 odd 12