Properties

Label 475.2.j.d.49.9
Level $475$
Weight $2$
Character 475.49
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 49.9
Character \(\chi\) \(=\) 475.49
Dual form 475.2.j.d.349.9

$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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 0.879478 0.475939i \(-0.157892\pi\)
0.0275641 + 0.999620i \(0.491225\pi\)
\(3\) −0.157277 0.0908038i −0.0908038 0.0524256i 0.453910 0.891047i \(-0.350029\pi\)
−0.544714 + 0.838622i \(0.683362\pi\)
\(4\) 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 \(-0.920728\pi\)
0.969149 0.246474i \(-0.0792719\pi\)
\(8\) 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 −0.450431 0.892811i \(-0.648730\pi\)
0.547982 + 0.836490i \(0.315396\pi\)
\(14\) 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 0.760201 0.649688i \(-0.225100\pi\)
−0.182546 + 0.983197i \(0.558434\pi\)
\(18\) 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 −0.972357 0.233498i \(-0.924983\pi\)
−0.283964 + 0.958835i \(0.591650\pi\)
\(24\) −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 0.617243 0.786772i \(-0.288249\pi\)
−0.989986 + 0.141162i \(0.954916\pi\)
\(30\) 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 \(0.0987387\pi\)
−0.952274 + 0.305246i \(0.901261\pi\)
\(38\) 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 −0.814639 0.579969i \(-0.803065\pi\)
0.909587 + 0.415514i \(0.136398\pi\)
\(42\) −0.303827 + 0.175415i −0.0468816 + 0.0270671i
\(43\) 2.70426 + 1.56130i 0.412396 + 0.238097i 0.691819 0.722071i \(-0.256810\pi\)
−0.279423 + 0.960168i \(0.590143\pi\)
\(44\) 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 −0.851147 0.524927i \(-0.824093\pi\)
0.0290269 + 0.999579i \(0.490759\pi\)
\(48\) −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 −0.826429 0.563041i \(-0.809631\pi\)
0.0743934 + 0.997229i \(0.476298\pi\)
\(54\) −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 −0.225187 0.974315i \(-0.572299\pi\)
0.956376 0.292140i \(-0.0943672\pi\)
\(60\) 0 0
\(61\) −0.467072 0.808992i −0.0598024 0.103581i 0.834574 0.550896i \(-0.185714\pi\)
−0.894377 + 0.447315i \(0.852380\pi\)
\(62\) −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 −0.192995 0.981200i \(-0.561820\pi\)
0.753246 + 0.657739i \(0.228487\pi\)
\(68\) 0.533363i 0.0646797i
\(69\) 1.26348 0.152105
\(70\) 0 0
\(71\) 0.817659 1.41623i 0.0970383 0.168075i −0.813419 0.581678i \(-0.802396\pi\)
0.910457 + 0.413603i \(0.135730\pi\)
\(72\) −6.87378 + 3.96858i −0.810083 + 0.467702i
\(73\) 6.65794 + 3.84396i 0.779252 + 0.449902i 0.836165 0.548478i \(-0.184792\pi\)
−0.0569129 + 0.998379i \(0.518126\pi\)
\(74\) −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 0.0878971 + 0.996130i \(0.471985\pi\)
−0.906622 + 0.421944i \(0.861348\pi\)
\(80\) 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 \(0.316121\pi\)
−0.546077 + 0.837735i \(0.683879\pi\)
\(84\) −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 0.946181 + 0.323638i \(0.104906\pi\)
−0.192812 + 0.981236i \(0.561761\pi\)
\(90\) 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 −0.989909 0.141707i \(-0.954741\pi\)
−0.617676 0.786433i \(-0.711926\pi\)
\(98\) 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 0.922334 + 0.386394i \(0.126280\pi\)
−0.126540 + 0.991962i \(0.540387\pi\)
\(102\) 0.739791i 0.0732502i
\(103\) 5.30941i 0.523152i −0.965183 0.261576i \(-0.915758\pi\)
0.965183 0.261576i \(-0.0842422\pi\)
\(104\) −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 \(-0.783671\pi\)
0.777814 0.628494i \(-0.216329\pi\)
\(108\) −0.182004 + 0.105080i −0.0175134 + 0.0101114i
\(109\) −4.09697 + 7.09616i −0.392418 + 0.679689i −0.992768 0.120049i \(-0.961695\pi\)
0.600350 + 0.799738i \(0.295028\pi\)
\(110\) 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 \(0.0996536\pi\)
−0.951392 + 0.307982i \(0.900346\pi\)
\(114\) −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 0.209500 0.977809i \(-0.432817\pi\)
0.951557 + 0.307472i \(0.0994832\pi\)
\(128\) −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 −0.806406 0.591363i \(-0.798590\pi\)
0.915338 + 0.402686i \(0.131923\pi\)
\(132\) 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 −0.980886 0.194583i \(-0.937665\pi\)
−0.321930 + 0.946764i \(0.604331\pi\)
\(138\) 1.62073 + 0.935729i 0.137966 + 0.0796546i
\(139\) 1.57736 + 2.73207i 0.133790 + 0.231731i 0.925135 0.379639i \(-0.123952\pi\)
−0.791345 + 0.611370i \(0.790619\pi\)
\(140\) 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 −0.966530 0.256552i \(-0.917413\pi\)
0.705446 + 0.708764i \(0.250747\pi\)
\(150\) 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 0.570649 0.821194i \(-0.306692\pi\)
−0.425851 + 0.904793i \(0.640025\pi\)
\(158\) −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 \(-0.877873\pi\)
0.927296 0.374328i \(-0.122127\pi\)
\(164\) 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 0.179938 0.983678i \(-0.442410\pi\)
0.941859 + 0.336008i \(0.109077\pi\)
\(168\) 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 0.883691 0.468070i \(-0.155050\pi\)
0.0364853 + 0.999334i \(0.488384\pi\)
\(174\) −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 −0.998342 0.0575593i \(-0.981668\pi\)
0.449323 0.893369i \(-0.351665\pi\)
\(182\) 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 0.973866 0.227123i \(-0.0729320\pi\)
0.290238 + 0.956954i \(0.406265\pi\)
\(194\) −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 \(0.191907\pi\)
−0.823698 + 0.567028i \(0.808093\pi\)
\(198\) 21.8966i 1.55613i
\(199\) −6.61785 11.4625i −0.469127 0.812552i 0.530250 0.847841i \(-0.322098\pi\)
−0.999377 + 0.0352892i \(0.988765\pi\)
\(200\) 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 −0.647204 0.762317i \(-0.724062\pi\)
0.983788 + 0.179336i \(0.0573950\pi\)
\(212\) −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 −0.499822 0.866128i \(-0.666601\pi\)
−1.00000 0.000205308i \(0.999935\pi\)
\(224\) −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 \(0.0241684\pi\)
−0.997119 + 0.0758545i \(0.975832\pi\)
\(228\) 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 0.440605 0.897701i \(-0.354764\pi\)
−0.557130 + 0.830425i \(0.688097\pi\)
\(234\) −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 0.531146 0.847280i \(-0.321762\pi\)
−0.999339 + 0.0363455i \(0.988428\pi\)
\(242\) 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 0.730037 0.683407i \(-0.239503\pi\)
−0.956867 + 0.290527i \(0.906169\pi\)
\(252\) −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 −0.716366 0.697725i \(-0.754196\pi\)
0.246064 + 0.969254i \(0.420863\pi\)
\(258\) 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 0.984096 + 0.177639i \(0.0568461\pi\)
0.645888 + 0.763432i \(0.276487\pi\)
\(264\) −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 0.436230 + 0.899835i \(0.356313\pi\)
−0.997395 + 0.0721309i \(0.977020\pi\)
\(270\) 0 0
\(271\) 5.73694 9.93668i 0.348494 0.603610i −0.637488 0.770460i \(-0.720026\pi\)
0.985982 + 0.166850i \(0.0533597\pi\)
\(272\) 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 \(0.0171914\pi\)
−0.998542 + 0.0539823i \(0.982809\pi\)
\(278\) 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 0.996258 0.0864258i \(-0.0275446\pi\)
−0.572976 + 0.819572i \(0.694211\pi\)
\(282\) 1.51611 + 0.875326i 0.0902830 + 0.0521249i
\(283\) −15.5094 8.95435i −0.921938 0.532281i −0.0376851 0.999290i \(-0.511998\pi\)
−0.884253 + 0.467009i \(0.845332\pi\)
\(284\) 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 \(-0.574190\pi\)
0.230970 0.972961i \(-0.425810\pi\)
\(294\) −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 0.832495 0.554033i \(-0.186912\pi\)
−0.0635594 + 0.997978i \(0.520245\pi\)
\(308\) 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 0.563774 0.825929i \(-0.309349\pi\)
0.997163 0.0752782i \(-0.0239845\pi\)
\(314\) 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 −0.132239 0.991218i \(-0.542217\pi\)
0.792300 + 0.610131i \(0.208883\pi\)
\(318\) 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 0.0872973 0.996182i \(-0.472177\pi\)
−0.819071 + 0.573693i \(0.805510\pi\)
\(338\) −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 −0.127434 0.991847i \(-0.540674\pi\)
−0.922682 + 0.385562i \(0.874008\pi\)
\(348\) −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 \(0.0883459\pi\)
−0.961730 + 0.273997i \(0.911654\pi\)
\(354\) −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 −0.838681 0.544623i \(-0.816673\pi\)
0.890998 + 0.454008i \(0.150006\pi\)
\(360\) 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 −0.376026 0.926609i \(-0.622710\pi\)
0.614454 + 0.788953i \(0.289376\pi\)
\(368\) 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 \(-0.693317\pi\)
0.570670 0.821179i \(-0.306683\pi\)
\(374\) 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 0.159044 0.987271i \(-0.449159\pi\)
−0.775480 + 0.631372i \(0.782492\pi\)
\(384\) 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 0.853827 0.520557i \(-0.174276\pi\)
−0.877729 + 0.479157i \(0.840943\pi\)
\(390\) 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 −0.272174 0.962248i \(-0.587743\pi\)
−0.969418 + 0.245414i \(0.921076\pi\)
\(398\) 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 −0.762565 0.646911i \(-0.776060\pi\)
0.941524 + 0.336945i \(0.109394\pi\)
\(402\) −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 0.705949 0.708263i \(-0.250521\pi\)
−0.966348 + 0.257238i \(0.917187\pi\)
\(410\) 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 −0.988336 0.152286i \(-0.951336\pi\)
0.626052 + 0.779781i \(0.284670\pi\)
\(422\) 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 0.911968 0.410261i \(-0.134562\pi\)
−0.811280 + 0.584657i \(0.801229\pi\)
\(432\) 4.08261 + 2.35709i 0.196425 + 0.113406i
\(433\) −21.9150 + 12.6527i −1.05317 + 0.608048i −0.923535 0.383514i \(-0.874714\pi\)
−0.129635 + 0.991562i \(0.541380\pi\)
\(434\) −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 −0.281904 0.959443i \(-0.590966\pi\)
0.971854 0.235585i \(-0.0757008\pi\)
\(440\) 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 −0.591423 0.806362i \(-0.701434\pi\)
0.402618 + 0.915368i \(0.368100\pi\)
\(444\) 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 \(0.187122\pi\)
−0.832128 + 0.554584i \(0.812878\pi\)
\(458\) 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 0.0933568 + 0.995633i \(0.470240\pi\)
−0.908922 + 0.416967i \(0.863093\pi\)
\(462\) −1.51381 + 0.873999i −0.0704289 + 0.0406621i
\(463\) 20.4936i 0.952417i 0.879332 + 0.476209i \(0.157989\pi\)
−0.879332 + 0.476209i \(0.842011\pi\)
\(464\) −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 \(-0.931394\pi\)
0.976863 0.213868i \(-0.0686063\pi\)
\(468\) 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 0.905847 0.423604i \(-0.139235\pi\)
−0.819776 + 0.572685i \(0.805902\pi\)
\(480\) 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 \(-0.913865\pi\)
0.963610 0.267311i \(-0.0861349\pi\)
\(488\) −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 −0.940786 0.339002i \(-0.889911\pi\)
0.763977 + 0.645243i \(0.223244\pi\)
\(492\) −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 −0.853923 0.520399i \(-0.825783\pi\)
0.877640 + 0.479320i \(0.159117\pi\)
\(500\) 0 0
\(501\) −3.04002 −0.135818
\(502\) 10.6458i 0.475145i
\(503\) 4.65671 2.68855i 0.207633 0.119877i −0.392578 0.919719i \(-0.628417\pi\)
0.600211 + 0.799842i \(0.295083\pi\)
\(504\) 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 0.947753 + 0.319004i \(0.103348\pi\)
−0.197611 + 0.980280i \(0.563318\pi\)
\(510\) 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 −0.880604 0.473854i \(-0.842863\pi\)
−0.0299323 + 0.999552i \(0.509529\pi\)
\(524\) 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 0.997230 + 0.0743856i \(0.0236996\pi\)
−0.434195 + 0.900819i \(0.642967\pi\)
\(542\) 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 −0.750242 0.661164i \(-0.770063\pi\)
0.197464 + 0.980310i \(0.436730\pi\)
\(548\) −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 −0.593653 0.804721i \(-0.702315\pi\)
0.400083 + 0.916479i \(0.368981\pi\)
\(558\) 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 \(-0.876924\pi\)
0.926175 0.377093i \(-0.123076\pi\)
\(564\) 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 \(-0.797339\pi\)
0.804076 0.594527i \(-0.202661\pi\)
\(578\) 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 0.997945 0.0640822i \(-0.0204120\pi\)
0.443476 + 0.896286i \(0.353745\pi\)
\(588\) 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 0.0810610 0.996709i \(-0.474169\pi\)
0.903706 + 0.428154i \(0.140836\pi\)
\(594\) −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 0.837917 0.545797i \(-0.183773\pi\)
−0.891633 + 0.452759i \(0.850440\pi\)
\(600\) 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 \(-0.774444\pi\)
0.759271 0.650775i \(-0.225556\pi\)
\(608\) 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 0.701832 0.712343i \(-0.252366\pi\)
−0.265991 + 0.963976i \(0.585699\pi\)
\(614\) 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 −0.884594 0.466362i \(-0.845564\pi\)
−0.0384155 + 0.999262i \(0.512231\pi\)
\(618\) −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 −0.920542 0.390643i \(-0.872253\pi\)
0.121964 0.992535i \(-0.461081\pi\)
\(632\) 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 −0.870012 0.493031i \(-0.835889\pi\)
0.861983 + 0.506937i \(0.169222\pi\)
\(642\) −3.02901 + 1.74880i −0.119545 + 0.0690195i
\(643\) −21.7975 12.5848i −0.859610 0.496296i 0.00427137 0.999991i \(-0.498640\pi\)
−0.863882 + 0.503695i \(0.831974\pi\)
\(644\) −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 \(0.117534\pi\)
−0.932600 + 0.360911i \(0.882466\pi\)
\(648\) 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 \(-0.776322\pi\)
0.763097 0.646284i \(-0.223678\pi\)
\(654\) 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 −0.999840 0.0178814i \(-0.994308\pi\)
0.484434 0.874828i \(-0.339025\pi\)
\(660\) 0 0
\(661\) 7.79673 + 13.5043i 0.303258 + 0.525258i 0.976872 0.213825i \(-0.0685924\pi\)
−0.673614 + 0.739083i \(0.735259\pi\)
\(662\) −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 \(0.0377353\pi\)
−0.992981 + 0.118271i \(0.962265\pi\)
\(674\) −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 \(0.140801\pi\)
−0.903752 + 0.428056i \(0.859199\pi\)
\(678\) 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 \(-0.896228\pi\)
0.947328 0.320264i \(-0.103772\pi\)
\(684\) 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 0.309541 + 0.950886i \(0.399824\pi\)
−0.978262 + 0.207372i \(0.933509\pi\)
\(702\) 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 0.986433 + 0.164163i \(0.0524922\pi\)
−0.351048 + 0.936358i \(0.614174\pi\)
\(710\) 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 −0.496640 0.867957i \(-0.665433\pi\)
0.999992 0.00387581i \(-0.00123371\pi\)
\(720\) 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 0.111185 0.993800i \(-0.464535\pi\)
−0.805063 + 0.593189i \(0.797869\pi\)
\(728\) −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 \(-0.896765\pi\)
0.947867 0.318666i \(-0.103235\pi\)
\(734\) 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 −0.818596 0.574370i \(-0.805247\pi\)
0.906717 + 0.421740i \(0.138580\pi\)
\(740\) 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 0.251878 0.967759i \(-0.418952\pi\)
−0.712165 + 0.702012i \(0.752285\pi\)
\(744\) 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 0.801137 0.598482i \(-0.204229\pi\)
−0.918869 + 0.394564i \(0.870896\pi\)
\(752\) 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 0.952100 0.305788i \(-0.0989197\pi\)
0.211230 + 0.977436i \(0.432253\pi\)
\(758\) −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 0.949208 + 0.314649i \(0.101887\pi\)
−0.202110 + 0.979363i \(0.564780\pi\)
\(770\) 0 0
\(771\) 1.58105 0.0569403
\(772\) 3.93270i 0.141541i
\(773\) −33.6285 + 19.4154i −1.20953 + 0.698325i −0.962658 0.270722i \(-0.912738\pi\)
−0.246877 + 0.969047i \(0.579404\pi\)
\(774\) 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 \(0.370038\pi\)
−0.397037 + 0.917803i \(0.629962\pi\)
\(788\) −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 \(-0.957568\pi\)
0.991128 0.132908i \(-0.0424316\pi\)
\(798\) −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 0.817264 0.576263i \(-0.195490\pi\)
−0.907690 + 0.419640i \(0.862156\pi\)
\(812\) −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 0.877824 0.478984i \(-0.158995\pi\)
−0.853724 + 0.520726i \(0.825661\pi\)
\(822\) 4.10194 + 2.36826i 0.143072 + 0.0826025i
\(823\) 12.4846 7.20798i 0.435185 0.251254i −0.266368 0.963871i \(-0.585824\pi\)
0.701553 + 0.712617i \(0.252490\pi\)
\(824\) −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 −0.635812 0.771844i \(-0.719335\pi\)
0.350530 + 0.936552i \(0.386001\pi\)
\(828\) 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 −0.737382 0.675476i \(-0.763938\pi\)
0.953670 + 0.300853i \(0.0972714\pi\)
\(840\) 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 0.447624 0.894222i \(-0.352270\pi\)
−0.550606 + 0.834765i \(0.685603\pi\)
\(854\) −1.80458 −0.0617513
\(855\) 0 0
\(856\) −34.7831 −1.18886
\(857\) −14.4295 8.33085i −0.492901 0.284577i 0.232876 0.972506i \(-0.425186\pi\)
−0.725777 + 0.687930i \(0.758520\pi\)
\(858\) −0.471402 0.272164i −0.0160934 0.00929154i
\(859\) 20.4042 + 35.3412i 0.696183 + 1.20583i 0.969780 + 0.243981i \(0.0784533\pi\)
−0.273597 + 0.961844i \(0.588213\pi\)
\(860\) 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 \(0.0220704\pi\)
−0.997597 + 0.0692806i \(0.977930\pi\)
\(864\) 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 0.0594132 0.998233i \(-0.481077\pi\)
−0.834789 + 0.550570i \(0.814410\pi\)
\(878\) 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 −0.184421 0.982847i \(-0.559041\pi\)
0.758961 + 0.651137i \(0.225708\pi\)
\(884\) 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 −0.656782 0.754080i \(-0.728083\pi\)
0.324662 + 0.945830i \(0.394750\pi\)
\(888\) −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 0.337595 0.941291i \(-0.390387\pi\)
−0.646385 + 0.763012i \(0.723720\pi\)
\(908\) −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 −0.259485 0.965747i \(-0.583553\pi\)
0.966104 0.258153i \(-0.0831138\pi\)
\(930\) 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 0.262275 0.964993i \(-0.415527\pi\)
0.966846 + 0.255360i \(0.0821941\pi\)
\(938\) 10.2294i 0.334003i
\(939\) −5.79110 −0.188985
\(940\) 0 0
\(941\) −14.6471 25.3694i −0.477480 0.827020i 0.522186 0.852831i \(-0.325117\pi\)
−0.999667 + 0.0258111i \(0.991783\pi\)
\(942\) 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 0.527959 0.849270i \(-0.322957\pi\)
−0.471509 + 0.881861i \(0.656291\pi\)
\(948\) 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 0.205248 0.978710i \(-0.434200\pi\)
−0.744964 + 0.667105i \(0.767533\pi\)
\(954\) 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 0.0491047 0.998794i \(-0.484363\pi\)
−0.840428 + 0.541923i \(0.817697\pi\)
\(968\) 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 −0.973438 0.228950i \(-0.926471\pi\)
0.684996 + 0.728547i \(0.259804\pi\)
\(972\) 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 \(0.0678716\pi\)
−0.977354 + 0.211613i \(0.932128\pi\)
\(978\) −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 0.986853 0.161623i \(-0.0516727\pi\)
0.353457 + 0.935451i \(0.385006\pi\)
\(984\) 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 0.345709 + 0.938342i \(0.387638\pi\)
−0.985482 + 0.169778i \(0.945695\pi\)
\(992\) −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 −0.0719414 0.997409i \(-0.522919\pi\)
0.827811 + 0.561008i \(0.189586\pi\)
\(998\) 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.49.9 24
5.2 odd 4 475.2.e.h.201.1 yes 12
5.3 odd 4 475.2.e.f.201.6 yes 12
5.4 even 2 inner 475.2.j.d.49.4 24
19.7 even 3 inner 475.2.j.d.349.4 24
95.7 odd 12 475.2.e.h.26.1 yes 12
95.8 even 12 9025.2.a.bs.1.6 6
95.27 even 12 9025.2.a.by.1.1 6
95.64 even 6 inner 475.2.j.d.349.9 24
95.68 odd 12 9025.2.a.bz.1.1 6
95.83 odd 12 475.2.e.f.26.6 12
95.87 odd 12 9025.2.a.br.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
475.2.e.f.26.6 12 95.83 odd 12
475.2.e.f.201.6 yes 12 5.3 odd 4
475.2.e.h.26.1 yes 12 95.7 odd 12
475.2.e.h.201.1 yes 12 5.2 odd 4
475.2.j.d.49.4 24 5.4 even 2 inner
475.2.j.d.49.9 24 1.1 even 1 trivial
475.2.j.d.349.4 24 19.7 even 3 inner
475.2.j.d.349.9 24 95.64 even 6 inner
9025.2.a.br.1.6 6 95.87 odd 12
9025.2.a.bs.1.6 6 95.8 even 12
9025.2.a.by.1.1 6 95.27 even 12
9025.2.a.bz.1.1 6 95.68 odd 12