Properties

Label 475.2.e.f.201.6
Level $475$
Weight $2$
Character 475.201
Analytic conductor $3.793$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(26,475)]
 
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([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.e (of order \(3\), degree \(2\), 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: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} - 552 x^{3} + 1107 x^{2} + 33 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.6
Root \(0.590804 + 1.02330i\) of defining polynomial
Character \(\chi\) \(=\) 475.201
Dual form 475.2.e.f.26.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.740597 - 1.28275i) q^{2} +(0.0908038 - 0.157277i) q^{3} +(-0.0969683 - 0.167954i) q^{4} +(-0.134498 - 0.232958i) q^{6} -1.30422 q^{7} +2.67513 q^{8} +(1.48351 + 2.56951i) q^{9} +O(q^{10})\) \(q+(0.740597 - 1.28275i) q^{2} +(0.0908038 - 0.157277i) q^{3} +(-0.0969683 - 0.167954i) q^{4} +(-0.134498 - 0.232958i) q^{6} -1.30422 q^{7} +2.67513 q^{8} +(1.48351 + 2.56951i) q^{9} +4.98247 q^{11} -0.0352204 q^{12} +(0.203067 + 0.351723i) q^{13} +(-0.965899 + 1.67299i) q^{14} +(2.17513 - 3.76744i) q^{16} +(1.37510 - 2.38173i) q^{17} +4.39473 q^{18} +(-4.35785 - 0.0955054i) q^{19} +(-0.118428 + 0.205123i) q^{21} +(3.69001 - 6.39128i) q^{22} +(-3.47860 - 6.02510i) q^{23} +(0.242912 - 0.420736i) q^{24} +0.601564 q^{26} +1.08366 q^{27} +(0.126468 + 0.219048i) q^{28} +(2.00728 + 3.47672i) q^{29} -2.57321 q^{31} +(-0.546661 - 0.946844i) q^{32} +(0.452428 - 0.783628i) q^{33} +(-2.03678 - 3.52781i) q^{34} +(0.287707 - 0.498323i) q^{36} +3.71348 q^{37} +(-3.34992 + 5.51931i) q^{38} +0.0737572 q^{39} +(0.607965 - 1.05303i) q^{41} +(0.175415 + 0.303827i) q^{42} +(-1.56130 + 2.70426i) q^{43} +(-0.483142 - 0.836826i) q^{44} -10.3050 q^{46} +(3.25405 + 5.63617i) q^{47} +(-0.395020 - 0.684196i) q^{48} -5.29902 q^{49} +(-0.249728 - 0.432541i) q^{51} +(0.0393822 - 0.0682119i) q^{52} +(-3.16094 - 5.47490i) q^{53} +(0.802553 - 1.39006i) q^{54} -3.48895 q^{56} +(-0.410731 + 0.676717i) q^{57} +5.94636 q^{58} +(-5.61636 + 9.72783i) q^{59} +(-0.467072 - 0.808992i) q^{61} +(-1.90571 + 3.30079i) q^{62} +(-1.93482 - 3.35120i) q^{63} +7.08110 q^{64} +(-0.670133 - 1.16071i) q^{66} +(-2.64764 - 4.58585i) q^{67} -0.533363 q^{68} -1.26348 q^{69} +(0.817659 - 1.41623i) q^{71} +(3.96858 + 6.87378i) q^{72} +(-3.84396 + 6.65794i) q^{73} +(2.75019 - 4.76347i) q^{74} +(0.406533 + 0.741180i) q^{76} -6.49822 q^{77} +(0.0546243 - 0.0946121i) q^{78} +(7.27699 - 12.6041i) q^{79} +(-4.35213 + 7.53811i) q^{81} +(-0.900514 - 1.55974i) q^{82} -15.2643 q^{83} +0.0459350 q^{84} +(2.31260 + 4.00553i) q^{86} +0.729076 q^{87} +13.3288 q^{88} +(-7.10727 - 12.3101i) q^{89} +(-0.264844 - 0.458723i) q^{91} +(-0.674627 + 1.16849i) q^{92} +(-0.233658 + 0.404707i) q^{93} +9.63975 q^{94} -0.198556 q^{96} +(-9.14111 + 15.8329i) q^{97} +(-3.92444 + 6.79733i) q^{98} +(7.39155 + 12.8025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24} + 38 q^{26} + 36 q^{27} + 4 q^{28} - 3 q^{29} - 6 q^{31} + 6 q^{32} + 18 q^{33} + q^{34} - 13 q^{36} - 12 q^{37} - 18 q^{38} + 16 q^{39} - 11 q^{41} + 11 q^{42} - 13 q^{43} - 21 q^{44} - 24 q^{46} + 6 q^{47} + 19 q^{48} + 8 q^{49} + 17 q^{51} + q^{52} - 18 q^{53} - 18 q^{54} + 8 q^{56} - 20 q^{57} + 10 q^{58} - 4 q^{59} - 25 q^{61} + 21 q^{62} - 43 q^{63} - 44 q^{64} - 34 q^{66} - 6 q^{67} - 2 q^{68} + 26 q^{69} - 18 q^{71} - 13 q^{72} - q^{73} + 6 q^{74} + 24 q^{76} - 22 q^{77} - 72 q^{78} - 3 q^{79} - 2 q^{81} - 31 q^{82} - 46 q^{83} + 74 q^{84} - 9 q^{86} + 22 q^{87} + 22 q^{88} - 12 q^{89} + 11 q^{91} - 28 q^{92} + 13 q^{93} + 16 q^{94} - 26 q^{96} - 3 q^{97} + 22 q^{98} + 20 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.740597 1.28275i 0.523681 0.907043i −0.475939 0.879478i \(-0.657892\pi\)
0.999620 0.0275641i \(-0.00877505\pi\)
\(3\) 0.0908038 0.157277i 0.0524256 0.0908038i −0.838622 0.544714i \(-0.816638\pi\)
0.891047 + 0.453910i \(0.149971\pi\)
\(4\) −0.0969683 0.167954i −0.0484841 0.0839770i
\(5\) 0 0
\(6\) −0.134498 0.232958i −0.0549086 0.0951045i
\(7\) −1.30422 −0.492948 −0.246474 0.969149i \(-0.579272\pi\)
−0.246474 + 0.969149i \(0.579272\pi\)
\(8\) 2.67513 0.945802
\(9\) 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 \(0.229506\pi\)
\(12\) −0.0352204 −0.0101672
\(13\) 0.203067 + 0.351723i 0.0563207 + 0.0975504i 0.892811 0.450431i \(-0.148730\pi\)
−0.836490 + 0.547982i \(0.815396\pi\)
\(14\) −0.965899 + 1.67299i −0.258147 + 0.447124i
\(15\) 0 0
\(16\) 2.17513 3.76744i 0.543783 0.941859i
\(17\) 1.37510 2.38173i 0.333510 0.577656i −0.649688 0.760201i \(-0.725100\pi\)
0.983197 + 0.182546i \(0.0584337\pi\)
\(18\) 4.39473 1.03585
\(19\) −4.35785 0.0955054i −0.999760 0.0219104i
\(20\) 0 0
\(21\) −0.118428 + 0.205123i −0.0258431 + 0.0447615i
\(22\) 3.69001 6.39128i 0.786712 1.36262i
\(23\) −3.47860 6.02510i −0.725337 1.25632i −0.958835 0.283964i \(-0.908350\pi\)
0.233498 0.972357i \(-0.424983\pi\)
\(24\) 0.242912 0.420736i 0.0495842 0.0858824i
\(25\) 0 0
\(26\) 0.601564 0.117976
\(27\) 1.08366 0.208550
\(28\) 0.126468 + 0.219048i 0.0239001 + 0.0413963i
\(29\) 2.00728 + 3.47672i 0.372743 + 0.645610i 0.989986 0.141162i \(-0.0450839\pi\)
−0.617243 + 0.786772i \(0.711751\pi\)
\(30\) 0 0
\(31\) −2.57321 −0.462163 −0.231081 0.972934i \(-0.574226\pi\)
−0.231081 + 0.972934i \(0.574226\pi\)
\(32\) −0.546661 0.946844i −0.0966369 0.167380i
\(33\) 0.452428 0.783628i 0.0787576 0.136412i
\(34\) −2.03678 3.52781i −0.349305 0.605015i
\(35\) 0 0
\(36\) 0.287707 0.498323i 0.0479511 0.0830538i
\(37\) 3.71348 0.610492 0.305246 0.952274i \(-0.401261\pi\)
0.305246 + 0.952274i \(0.401261\pi\)
\(38\) −3.34992 + 5.51931i −0.543429 + 0.895351i
\(39\) 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 \(0.136398\pi\)
\(42\) 0.175415 + 0.303827i 0.0270671 + 0.0468816i
\(43\) −1.56130 + 2.70426i −0.238097 + 0.412396i −0.960168 0.279423i \(-0.909857\pi\)
0.722071 + 0.691819i \(0.243190\pi\)
\(44\) −0.483142 0.836826i −0.0728364 0.126156i
\(45\) 0 0
\(46\) −10.3050 −1.51938
\(47\) 3.25405 + 5.63617i 0.474651 + 0.822120i 0.999579 0.0290269i \(-0.00924083\pi\)
−0.524927 + 0.851147i \(0.675907\pi\)
\(48\) −0.395020 0.684196i −0.0570163 0.0987551i
\(49\) −5.29902 −0.757003
\(50\) 0 0
\(51\) −0.249728 0.432541i −0.0349689 0.0605679i
\(52\) 0.0393822 0.0682119i 0.00546132 0.00945929i
\(53\) −3.16094 5.47490i −0.434188 0.752036i 0.563041 0.826429i \(-0.309631\pi\)
−0.997229 + 0.0743934i \(0.976298\pi\)
\(54\) 0.802553 1.39006i 0.109214 0.189164i
\(55\) 0 0
\(56\) −3.48895 −0.466231
\(57\) −0.410731 + 0.676717i −0.0544026 + 0.0896334i
\(58\) 5.94636 0.780795
\(59\) −5.61636 + 9.72783i −0.731188 + 1.26646i 0.225187 + 0.974315i \(0.427701\pi\)
−0.956376 + 0.292140i \(0.905633\pi\)
\(60\) 0 0
\(61\) −0.467072 0.808992i −0.0598024 0.103581i 0.834574 0.550896i \(-0.185714\pi\)
−0.894377 + 0.447315i \(0.852380\pi\)
\(62\) −1.90571 + 3.30079i −0.242026 + 0.419201i
\(63\) −1.93482 3.35120i −0.243764 0.422212i
\(64\) 7.08110 0.885138
\(65\) 0 0
\(66\) −0.670133 1.16071i −0.0824877 0.142873i
\(67\) −2.64764 4.58585i −0.323461 0.560251i 0.657739 0.753246i \(-0.271513\pi\)
−0.981200 + 0.192995i \(0.938180\pi\)
\(68\) −0.533363 −0.0646797
\(69\) −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 \(0.135730\pi\)
\(72\) 3.96858 + 6.87378i 0.467702 + 0.810083i
\(73\) −3.84396 + 6.65794i −0.449902 + 0.779252i −0.998379 0.0569129i \(-0.981874\pi\)
0.548478 + 0.836165i \(0.315208\pi\)
\(74\) 2.75019 4.76347i 0.319703 0.553742i
\(75\) 0 0
\(76\) 0.406533 + 0.741180i 0.0466325 + 0.0850191i
\(77\) −6.49822 −0.740541
\(78\) 0.0546243 0.0946121i 0.00618499 0.0107127i
\(79\) 7.27699 12.6041i 0.818725 1.41807i −0.0878971 0.996130i \(-0.528015\pi\)
0.906622 0.421944i \(-0.138652\pi\)
\(80\) 0 0
\(81\) −4.35213 + 7.53811i −0.483570 + 0.837567i
\(82\) −0.900514 1.55974i −0.0994452 0.172244i
\(83\) −15.2643 −1.67547 −0.837735 0.546077i \(-0.816121\pi\)
−0.837735 + 0.546077i \(0.816121\pi\)
\(84\) 0.0459350 0.00501192
\(85\) 0 0
\(86\) 2.31260 + 4.00553i 0.249374 + 0.431928i
\(87\) 0.729076 0.0781652
\(88\) 13.3288 1.42085
\(89\) −7.10727 12.3101i −0.753369 1.30487i −0.946181 0.323638i \(-0.895094\pi\)
0.192812 0.981236i \(-0.438239\pi\)
\(90\) 0 0
\(91\) −0.264844 0.458723i −0.0277632 0.0480872i
\(92\) −0.674627 + 1.16849i −0.0703347 + 0.121823i
\(93\) −0.233658 + 0.404707i −0.0242292 + 0.0419661i
\(94\) 9.63975 0.994264
\(95\) 0 0
\(96\) −0.198556 −0.0202650
\(97\) −9.14111 + 15.8329i −0.928139 + 1.60758i −0.141707 + 0.989909i \(0.545259\pi\)
−0.786433 + 0.617676i \(0.788074\pi\)
\(98\) −3.92444 + 6.79733i −0.396428 + 0.686634i
\(99\) 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 \(0.540387\pi\)
\(102\) −0.739791 −0.0732502
\(103\) 5.30941 0.523152 0.261576 0.965183i \(-0.415758\pi\)
0.261576 + 0.965183i \(0.415758\pi\)
\(104\) 0.543232 + 0.940905i 0.0532682 + 0.0922633i
\(105\) 0 0
\(106\) −9.36392 −0.909504
\(107\) −13.0024 −1.25699 −0.628494 0.777814i \(-0.716329\pi\)
−0.628494 + 0.777814i \(0.716329\pi\)
\(108\) −0.105080 0.182004i −0.0101114 0.0175134i
\(109\) 4.09697 7.09616i 0.392418 0.679689i −0.600350 0.799738i \(-0.704972\pi\)
0.992768 + 0.120049i \(0.0383052\pi\)
\(110\) 0 0
\(111\) 0.337198 0.584044i 0.0320054 0.0554350i
\(112\) −2.83684 + 4.91355i −0.268056 + 0.464287i
\(113\) −6.54779 −0.615964 −0.307982 0.951392i \(-0.599654\pi\)
−0.307982 + 0.951392i \(0.599654\pi\)
\(114\) 0.563874 + 1.02804i 0.0528117 + 0.0962848i
\(115\) 0 0
\(116\) 0.389286 0.674263i 0.0361443 0.0626037i
\(117\) −0.602504 + 1.04357i −0.0557016 + 0.0964779i
\(118\) 8.31892 + 14.4088i 0.765819 + 1.32644i
\(119\) −1.79342 + 3.10630i −0.164403 + 0.284754i
\(120\) 0 0
\(121\) 13.8250 1.25682
\(122\) −1.38365 −0.125270
\(123\) −0.110411 0.191238i −0.00995544 0.0172433i
\(124\) 0.249520 + 0.432181i 0.0224076 + 0.0388110i
\(125\) 0 0
\(126\) −5.73168 −0.510619
\(127\) −7.55431 13.0844i −0.670336 1.16106i −0.977809 0.209500i \(-0.932817\pi\)
0.307472 0.951557i \(-0.400517\pi\)
\(128\) 6.33757 10.9770i 0.560167 0.970238i
\(129\) 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 \(0.131923\pi\)
\(132\) −0.175485 −0.0152740
\(133\) 5.68358 + 0.124560i 0.492829 + 0.0108007i
\(134\) −7.84335 −0.677562
\(135\) 0 0
\(136\) 3.67856 6.37145i 0.315434 0.546348i
\(137\) 8.80405 + 15.2491i 0.752181 + 1.30282i 0.946764 + 0.321930i \(0.104331\pi\)
−0.194583 + 0.980886i \(0.562335\pi\)
\(138\) −0.935729 + 1.62073i −0.0796546 + 0.137966i
\(139\) −1.57736 2.73207i −0.133790 0.231731i 0.791345 0.611370i \(-0.209381\pi\)
−0.925135 + 0.379639i \(0.876048\pi\)
\(140\) 0 0
\(141\) 1.18192 0.0995356
\(142\) −1.21111 2.09771i −0.101634 0.176036i
\(143\) 1.01178 + 1.75245i 0.0846091 + 0.146547i
\(144\) 12.9073 1.07561
\(145\) 0 0
\(146\) 5.69365 + 9.86170i 0.471210 + 0.816160i
\(147\) −0.481171 + 0.833413i −0.0396863 + 0.0687388i
\(148\) −0.360090 0.623693i −0.0295992 0.0512673i
\(149\) 3.18694 5.51994i 0.261084 0.452211i −0.705446 0.708764i \(-0.749253\pi\)
0.966530 + 0.256552i \(0.0825866\pi\)
\(150\) 0 0
\(151\) 4.96340 0.403915 0.201958 0.979394i \(-0.435270\pi\)
0.201958 + 0.979394i \(0.435270\pi\)
\(152\) −11.6578 0.255489i −0.945575 0.0207229i
\(153\) 8.15987 0.659686
\(154\) −4.81257 + 8.33561i −0.387808 + 0.671703i
\(155\) 0 0
\(156\) −0.00715211 0.0123878i −0.000572627 0.000991819i
\(157\) 1.04750 1.81432i 0.0835993 0.144798i −0.821194 0.570649i \(-0.806692\pi\)
0.904793 + 0.425851i \(0.140025\pi\)
\(158\) −10.7786 18.6691i −0.857502 1.48524i
\(159\) −1.14810 −0.0910503
\(160\) 0 0
\(161\) 4.53684 + 7.85804i 0.357553 + 0.619300i
\(162\) 6.44635 + 11.1654i 0.506473 + 0.877237i
\(163\) 9.55821 0.748656 0.374328 0.927296i \(-0.377873\pi\)
0.374328 + 0.927296i \(0.377873\pi\)
\(164\) −0.235813 −0.0184139
\(165\) 0 0
\(166\) −11.3047 + 19.5803i −0.877412 + 1.51972i
\(167\) −8.36974 14.4968i −0.647670 1.12180i −0.983678 0.179938i \(-0.942410\pi\)
0.336008 0.941859i \(-0.390923\pi\)
\(168\) −0.316810 + 0.548731i −0.0244424 + 0.0423355i
\(169\) 6.41753 11.1155i 0.493656 0.855037i
\(170\) 0 0
\(171\) −6.21951 11.3392i −0.475618 0.867134i
\(172\) 0.605588 0.0461757
\(173\) −6.98769 + 12.1030i −0.531264 + 0.920177i 0.468070 + 0.883691i \(0.344950\pi\)
−0.999334 + 0.0364853i \(0.988384\pi\)
\(174\) 0.539952 0.935224i 0.0409336 0.0708992i
\(175\) 0 0
\(176\) 10.8375 18.7712i 0.816910 1.41493i
\(177\) 1.01997 + 1.76665i 0.0766660 + 0.132789i
\(178\) −21.0545 −1.57810
\(179\) −9.86133 −0.737071 −0.368535 0.929614i \(-0.620141\pi\)
−0.368535 + 0.929614i \(0.620141\pi\)
\(180\) 0 0
\(181\) −7.38629 12.7934i −0.549019 0.950929i −0.998342 0.0575593i \(-0.981668\pi\)
0.449323 0.893369i \(-0.351665\pi\)
\(182\) −0.784570 −0.0581562
\(183\) −0.169648 −0.0125407
\(184\) −9.30570 16.1179i −0.686025 1.18823i
\(185\) 0 0
\(186\) 0.346092 + 0.599450i 0.0253767 + 0.0439538i
\(187\) 6.85138 11.8669i 0.501022 0.867796i
\(188\) 0.631078 1.09306i 0.0460261 0.0797196i
\(189\) −1.41332 −0.102804
\(190\) 0 0
\(191\) −20.6797 −1.49633 −0.748166 0.663512i \(-0.769065\pi\)
−0.748166 + 0.663512i \(0.769065\pi\)
\(192\) 0.642991 1.11369i 0.0464039 0.0803739i
\(193\) −10.1391 + 17.5615i −0.729831 + 1.26410i 0.227123 + 0.973866i \(0.427068\pi\)
−0.956954 + 0.290238i \(0.906265\pi\)
\(194\) 13.5398 + 23.4516i 0.972099 + 1.68372i
\(195\) 0 0
\(196\) 0.513837 + 0.889991i 0.0367026 + 0.0635708i
\(197\) 15.9172 1.13406 0.567028 0.823698i \(-0.308093\pi\)
0.567028 + 0.823698i \(0.308093\pi\)
\(198\) 21.8966 1.55613
\(199\) 6.61785 + 11.4625i 0.469127 + 0.812552i 0.999377 0.0352892i \(-0.0112352\pi\)
−0.530250 + 0.847841i \(0.677902\pi\)
\(200\) 0 0
\(201\) −0.961665 −0.0678306
\(202\) 23.6921 1.66697
\(203\) −2.61793 4.53439i −0.183743 0.318252i
\(204\) −0.0484314 + 0.0838856i −0.00339087 + 0.00587317i
\(205\) 0 0
\(206\) 3.93214 6.81066i 0.273965 0.474521i
\(207\) 10.3211 17.8766i 0.717363 1.24251i
\(208\) 1.76679 0.122505
\(209\) −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 \(0.0573950\pi\)
\(212\) −0.613021 + 1.06178i −0.0421025 + 0.0729236i
\(213\) −0.148493 0.257198i −0.0101746 0.0176229i
\(214\) −9.62954 + 16.6788i −0.658262 + 1.14014i
\(215\) 0 0
\(216\) 2.89892 0.197247
\(217\) 3.35603 0.227822
\(218\) −6.06841 10.5108i −0.411004 0.711880i
\(219\) 0.698093 + 1.20913i 0.0471727 + 0.0817056i
\(220\) 0 0
\(221\) 1.11695 0.0751340
\(222\) −0.499456 0.865083i −0.0335213 0.0580606i
\(223\) 12.9310 22.3971i 0.865923 1.49982i −0.000205308 1.00000i \(-0.500065\pi\)
0.866128 0.499822i \(-0.166601\pi\)
\(224\) 0.712964 + 1.23489i 0.0476369 + 0.0825095i
\(225\) 0 0
\(226\) −4.84927 + 8.39918i −0.322569 + 0.558705i
\(227\) 2.28573 0.151709 0.0758545 0.997119i \(-0.475832\pi\)
0.0758545 + 0.997119i \(0.475832\pi\)
\(228\) 0.153485 + 0.00336373i 0.0101648 + 0.000222769i
\(229\) −21.8805 −1.44590 −0.722952 0.690898i \(-0.757215\pi\)
−0.722952 + 0.690898i \(0.757215\pi\)
\(230\) 0 0
\(231\) −0.590064 + 1.02202i −0.0388233 + 0.0672440i
\(232\) 5.36975 + 9.30068i 0.352541 + 0.610619i
\(233\) 1.02692 1.77868i 0.0672758 0.116525i −0.830425 0.557130i \(-0.811903\pi\)
0.897701 + 0.440605i \(0.145236\pi\)
\(234\) 0.892426 + 1.54573i 0.0583397 + 0.101047i
\(235\) 0 0
\(236\) 2.17844 0.141804
\(237\) −1.32156 2.28900i −0.0858443 0.148687i
\(238\) 2.65641 + 4.60103i 0.172189 + 0.298241i
\(239\) 7.68110 0.496849 0.248425 0.968651i \(-0.420087\pi\)
0.248425 + 0.968651i \(0.420087\pi\)
\(240\) 0 0
\(241\) −7.26832 12.5891i −0.468194 0.810935i 0.531146 0.847280i \(-0.321762\pi\)
−0.999339 + 0.0363455i \(0.988428\pi\)
\(242\) 10.2388 17.7341i 0.658174 1.13999i
\(243\) 2.41586 + 4.18440i 0.154978 + 0.268429i
\(244\) −0.0905823 + 0.156893i −0.00579894 + 0.0100441i
\(245\) 0 0
\(246\) −0.327081 −0.0208539
\(247\) −0.851346 1.55215i −0.0541698 0.0987610i
\(248\) −6.88368 −0.437114
\(249\) −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 \(0.906169\pi\)
\(252\) −0.375232 + 0.649921i −0.0236374 + 0.0409412i
\(253\) −17.3320 30.0199i −1.08965 1.88734i
\(254\) −22.3788 −1.40417
\(255\) 0 0
\(256\) −2.30606 3.99422i −0.144129 0.249639i
\(257\) 4.35294 + 7.53951i 0.271529 + 0.470302i 0.969254 0.246064i \(-0.0791374\pi\)
−0.697725 + 0.716366i \(0.745804\pi\)
\(258\) 0.839970 0.0522943
\(259\) −4.84318 −0.300940
\(260\) 0 0
\(261\) −5.95565 + 10.3155i −0.368645 + 0.638513i
\(262\) −1.84674 3.19864i −0.114092 0.197613i
\(263\) −15.2616 + 26.4339i −0.941072 + 1.62998i −0.177639 + 0.984096i \(0.556846\pi\)
−0.763432 + 0.645888i \(0.776487\pi\)
\(264\) 1.21030 2.09631i 0.0744890 0.129019i
\(265\) 0 0
\(266\) 4.36903 7.19838i 0.267882 0.441361i
\(267\) −2.58147 −0.157983
\(268\) −0.513475 + 0.889365i −0.0313655 + 0.0543266i
\(269\) 9.20379 15.9414i 0.561165 0.971966i −0.436230 0.899835i \(-0.643687\pi\)
0.997395 0.0721309i \(-0.0229800\pi\)
\(270\) 0 0
\(271\) 5.73694 9.93668i 0.348494 0.603610i −0.637488 0.770460i \(-0.720026\pi\)
0.985982 + 0.166850i \(0.0533597\pi\)
\(272\) −5.98202 10.3612i −0.362714 0.628238i
\(273\) −0.0961953 −0.00582201
\(274\) 26.0810 1.57561
\(275\) 0 0
\(276\) 0.122517 + 0.212206i 0.00737468 + 0.0127733i
\(277\) 1.79689 0.107965 0.0539823 0.998542i \(-0.482809\pi\)
0.0539823 + 0.998542i \(0.482809\pi\)
\(278\) −4.67276 −0.280253
\(279\) −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 \(0.694211\pi\)
\(282\) 0.875326 1.51611i 0.0521249 0.0902830i
\(283\) 8.95435 15.5094i 0.532281 0.921938i −0.467009 0.884253i \(-0.654668\pi\)
0.999290 0.0376851i \(-0.0119984\pi\)
\(284\) −0.317148 −0.0188193
\(285\) 0 0
\(286\) 2.99728 0.177233
\(287\) −0.792918 + 1.37337i −0.0468045 + 0.0810677i
\(288\) 1.62195 2.80930i 0.0955744 0.165540i
\(289\) 4.71823 + 8.17221i 0.277543 + 0.480718i
\(290\) 0 0
\(291\) 1.66010 + 2.87537i 0.0973166 + 0.168557i
\(292\) 1.49097 0.0872524
\(293\) 33.3088 1.94592 0.972961 0.230970i \(-0.0741900\pi\)
0.972961 + 0.230970i \(0.0741900\pi\)
\(294\) 0.712708 + 1.23445i 0.0415660 + 0.0719944i
\(295\) 0 0
\(296\) 9.93404 0.577404
\(297\) 5.39929 0.313299
\(298\) −4.72048 8.17610i −0.273450 0.473629i
\(299\) 1.41278 2.44700i 0.0817031 0.141514i
\(300\) 0 0
\(301\) 2.03628 3.52694i 0.117369 0.203289i
\(302\) 3.67588 6.36681i 0.211523 0.366369i
\(303\) 2.90486 0.166880
\(304\) −9.83871 + 16.2102i −0.564289 + 0.929719i
\(305\) 0 0
\(306\) 6.04317 10.4671i 0.345465 0.598363i
\(307\) 7.77854 13.4728i 0.443945 0.768935i −0.554033 0.832495i \(-0.686912\pi\)
0.997978 + 0.0635594i \(0.0202452\pi\)
\(308\) 0.630122 + 1.09140i 0.0359045 + 0.0621884i
\(309\) 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 \(0.189608\pi\)
\(312\) 0.197310 0.0111705
\(313\) 15.9440 + 27.6158i 0.901207 + 1.56094i 0.825929 + 0.563774i \(0.190651\pi\)
0.0752782 + 0.997163i \(0.476016\pi\)
\(314\) −1.55155 2.68736i −0.0875588 0.151656i
\(315\) 0 0
\(316\) −2.82255 −0.158781
\(317\) −6.78505 11.7520i −0.381086 0.660061i 0.610131 0.792300i \(-0.291117\pi\)
−0.991218 + 0.132239i \(0.957783\pi\)
\(318\) −0.850280 + 1.47273i −0.0476813 + 0.0825865i
\(319\) 10.0012 + 17.3227i 0.559962 + 0.969882i
\(320\) 0 0
\(321\) −1.18067 + 2.04498i −0.0658984 + 0.114139i
\(322\) 13.4399 0.748976
\(323\) −6.21993 + 10.2479i −0.346086 + 0.570210i
\(324\) 1.68807 0.0937819
\(325\) 0 0
\(326\) 7.07878 12.2608i 0.392057 0.679063i
\(327\) −0.744041 1.28872i −0.0411456 0.0712662i
\(328\) 1.62639 2.81698i 0.0898022 0.155542i
\(329\) −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 \(0.799848\pi\)
\(332\) 1.48015 + 2.56369i 0.0812337 + 0.140701i
\(333\) 5.50898 + 9.54183i 0.301890 + 0.522889i
\(334\) −24.7944 −1.35669
\(335\) 0 0
\(336\) 0.515192 + 0.892339i 0.0281060 + 0.0486811i
\(337\) −7.75588 + 13.4336i −0.422489 + 0.731773i −0.996182 0.0872973i \(-0.972177\pi\)
0.573693 + 0.819071i \(0.305510\pi\)
\(338\) −9.50560 16.4642i −0.517037 0.895534i
\(339\) −0.594564 + 1.02982i −0.0322923 + 0.0559319i
\(340\) 0 0
\(341\) −12.8210 −0.694294
\(342\) −19.1516 0.419720i −1.03560 0.0226959i
\(343\) 16.0406 0.866110
\(344\) −4.17669 + 7.23425i −0.225192 + 0.390044i
\(345\) 0 0
\(346\) 10.3501 + 17.9269i 0.556426 + 0.963759i
\(347\) −11.2938 + 19.5615i −0.606285 + 1.05012i 0.385562 + 0.922682i \(0.374008\pi\)
−0.991847 + 0.127434i \(0.959326\pi\)
\(348\) −0.0706973 0.122451i −0.00378977 0.00656408i
\(349\) 25.4885 1.36437 0.682184 0.731181i \(-0.261030\pi\)
0.682184 + 0.731181i \(0.261030\pi\)
\(350\) 0 0
\(351\) 0.220055 + 0.381147i 0.0117457 + 0.0203441i
\(352\) −2.72372 4.71762i −0.145175 0.251450i
\(353\) −10.2959 −0.547994 −0.273997 0.961730i \(-0.588346\pi\)
−0.273997 + 0.961730i \(0.588346\pi\)
\(354\) 3.02156 0.160594
\(355\) 0 0
\(356\) −1.37836 + 2.38739i −0.0730529 + 0.126531i
\(357\) 0.325699 + 0.564128i 0.0172378 + 0.0298568i
\(358\) −7.30328 + 12.6496i −0.385990 + 0.668555i
\(359\) −0.991256 + 1.71691i −0.0523165 + 0.0906148i −0.890998 0.454008i \(-0.849994\pi\)
0.838681 + 0.544623i \(0.183327\pi\)
\(360\) 0 0
\(361\) 18.9818 + 0.832397i 0.999040 + 0.0438103i
\(362\) −21.8811 −1.15004
\(363\) 1.25537 2.17436i 0.0658897 0.114124i
\(364\) −0.0513629 + 0.0889631i −0.00269215 + 0.00466294i
\(365\) 0 0
\(366\) −0.125641 + 0.217616i −0.00656734 + 0.0113750i
\(367\) −2.63712 4.56763i −0.137657 0.238428i 0.788953 0.614454i \(-0.210624\pi\)
−0.926609 + 0.376026i \(0.877290\pi\)
\(368\) −30.2656 −1.57770
\(369\) 3.60769 0.187809
\(370\) 0 0
\(371\) 4.12255 + 7.14046i 0.214032 + 0.370714i
\(372\) 0.0906295 0.00469892
\(373\) 31.7192 1.64236 0.821179 0.570670i \(-0.193317\pi\)
0.821179 + 0.570670i \(0.193317\pi\)
\(374\) −10.1482 17.5772i −0.524752 0.908897i
\(375\) 0 0
\(376\) 8.70500 + 15.0775i 0.448926 + 0.777563i
\(377\) −0.815227 + 1.41202i −0.0419863 + 0.0727225i
\(378\) −1.04670 + 1.81294i −0.0538366 + 0.0932477i
\(379\) 35.5119 1.82412 0.912062 0.410052i \(-0.134490\pi\)
0.912062 + 0.410052i \(0.134490\pi\)
\(380\) 0 0
\(381\) −2.74384 −0.140571
\(382\) −15.3153 + 26.5269i −0.783601 + 1.35724i
\(383\) 6.96509 12.0639i 0.355899 0.616436i −0.631372 0.775480i \(-0.717508\pi\)
0.987271 + 0.159044i \(0.0508412\pi\)
\(384\) −1.15095 1.99350i −0.0587342 0.101731i
\(385\) 0 0
\(386\) 15.0180 + 26.0120i 0.764398 + 1.32398i
\(387\) −9.26484 −0.470958
\(388\) 3.54559 0.180000
\(389\) 0.471434 + 0.816548i 0.0239027 + 0.0414006i 0.877729 0.479157i \(-0.159057\pi\)
−0.853827 + 0.520557i \(0.825724\pi\)
\(390\) 0 0
\(391\) −19.1336 −0.967628
\(392\) −14.1756 −0.715974
\(393\) −0.226427 0.392183i −0.0114217 0.0197830i
\(394\) 11.7883 20.4179i 0.593884 1.02864i
\(395\) 0 0
\(396\) 1.43349 2.48288i 0.0720356 0.124769i
\(397\) −14.2828 + 24.7386i −0.716834 + 1.24159i 0.245414 + 0.969418i \(0.421076\pi\)
−0.962248 + 0.272174i \(0.912257\pi\)
\(398\) 19.6047 0.982693
\(399\) 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 \(0.109394\pi\)
\(402\) −0.712206 + 1.23358i −0.0355216 + 0.0615252i
\(403\) −0.522535 0.905058i −0.0260293 0.0450841i
\(404\) 1.55103 2.68647i 0.0771668 0.133657i
\(405\) 0 0
\(406\) −7.75534 −0.384891
\(407\) 18.5023 0.917125
\(408\) −0.668055 1.15710i −0.0330736 0.0572852i
\(409\) 5.26624 + 9.12140i 0.260399 + 0.451024i 0.966348 0.257238i \(-0.0828126\pi\)
−0.705949 + 0.708263i \(0.749479\pi\)
\(410\) 0 0
\(411\) 3.19777 0.157734
\(412\) −0.514845 0.891737i −0.0253646 0.0439327i
\(413\) 7.32495 12.6872i 0.360437 0.624296i
\(414\) −15.2875 26.4787i −0.751339 1.30136i
\(415\) 0 0
\(416\) 0.222018 0.384546i 0.0108853 0.0188539i
\(417\) −0.572922 −0.0280561
\(418\) −16.6909 + 27.4998i −0.816379 + 1.34506i
\(419\) 2.52693 0.123448 0.0617242 0.998093i \(-0.480340\pi\)
0.0617242 + 0.998093i \(0.480340\pi\)
\(420\) 0 0
\(421\) −7.43346 + 12.8751i −0.362285 + 0.627495i −0.988336 0.152286i \(-0.951336\pi\)
0.626052 + 0.779781i \(0.284670\pi\)
\(422\) −7.24181 12.5432i −0.352526 0.610592i
\(423\) −9.65481 + 16.7226i −0.469433 + 0.813082i
\(424\) −8.45592 14.6461i −0.410656 0.711276i
\(425\) 0 0
\(426\) −0.439895 −0.0213130
\(427\) 0.609163 + 1.05510i 0.0294794 + 0.0510599i
\(428\) 1.26082 + 2.18380i 0.0609440 + 0.105558i
\(429\) 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 \(0.801229\pi\)
\(432\) 2.35709 4.08261i 0.113406 0.196425i
\(433\) −12.6527 21.9150i −0.608048 1.05317i −0.991562 0.129635i \(-0.958620\pi\)
0.383514 0.923535i \(-0.374714\pi\)
\(434\) 2.48546 4.30495i 0.119306 0.206644i
\(435\) 0 0
\(436\) −1.58910 −0.0761043
\(437\) 14.5838 + 26.5887i 0.697637 + 1.27191i
\(438\) 2.06802 0.0988139
\(439\) −14.4561 + 25.0386i −0.689950 + 1.19503i 0.281904 + 0.959443i \(0.409034\pi\)
−0.971854 + 0.235585i \(0.924299\pi\)
\(440\) 0 0
\(441\) −7.86114 13.6159i −0.374340 0.648376i
\(442\) 0.827208 1.43277i 0.0393463 0.0681498i
\(443\) −2.29432 3.97388i −0.109007 0.188805i 0.806362 0.591423i \(-0.201434\pi\)
−0.915368 + 0.402618i \(0.868100\pi\)
\(444\) −0.130790 −0.00620702
\(445\) 0 0
\(446\) −19.1533 33.1745i −0.906935 1.57086i
\(447\) −0.578773 1.00246i −0.0273750 0.0474149i
\(448\) −9.23529 −0.436327
\(449\) 29.2171 1.37884 0.689420 0.724362i \(-0.257865\pi\)
0.689420 + 0.724362i \(0.257865\pi\)
\(450\) 0 0
\(451\) 3.02917 5.24668i 0.142638 0.247056i
\(452\) 0.634928 + 1.09973i 0.0298645 + 0.0517268i
\(453\) 0.450696 0.780628i 0.0211755 0.0366771i
\(454\) 1.69280 2.93202i 0.0794471 0.137606i
\(455\) 0 0
\(456\) −1.09876 + 1.81031i −0.0514541 + 0.0847754i
\(457\) 23.7113 1.10917 0.554584 0.832128i \(-0.312878\pi\)
0.554584 + 0.832128i \(0.312878\pi\)
\(458\) −16.2046 + 28.0673i −0.757193 + 1.31150i
\(459\) 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 \(0.863093\pi\)
\(462\) 0.873999 + 1.51381i 0.0406621 + 0.0704289i
\(463\) −20.4936 −0.952417 −0.476209 0.879332i \(-0.657989\pi\)
−0.476209 + 0.879332i \(0.657989\pi\)
\(464\) 17.4644 0.810765
\(465\) 0 0
\(466\) −1.52107 2.63457i −0.0704621 0.122044i
\(467\) −9.24346 −0.427736 −0.213868 0.976863i \(-0.568606\pi\)
−0.213868 + 0.976863i \(0.568606\pi\)
\(468\) 0.233695 0.0108026
\(469\) 3.45310 + 5.98095i 0.159449 + 0.276174i
\(470\) 0 0
\(471\) −0.190233 0.329494i −0.00876549 0.0151823i
\(472\) −15.0245 + 26.0232i −0.691559 + 1.19782i
\(473\) −7.77916 + 13.4739i −0.357686 + 0.619530i
\(474\) −3.91496 −0.179820
\(475\) 0 0
\(476\) 0.695620 0.0318837
\(477\) 9.37856 16.2441i 0.429415 0.743768i
\(478\) 5.68860 9.85295i 0.260191 0.450663i
\(479\) −1.88377 3.26278i −0.0860715 0.149080i 0.819776 0.572685i \(-0.194098\pi\)
−0.905847 + 0.423604i \(0.860765\pi\)
\(480\) 0 0
\(481\) 0.754086 + 1.30611i 0.0343834 + 0.0595537i
\(482\) −21.5316 −0.980737
\(483\) 1.64785 0.0749798
\(484\) −1.34059 2.32197i −0.0609359 0.105544i
\(485\) 0 0
\(486\) 7.15673 0.324636
\(487\) −11.7981 −0.534621 −0.267311 0.963610i \(-0.586135\pi\)
−0.267311 + 0.963610i \(0.586135\pi\)
\(488\) −1.24948 2.16416i −0.0565612 0.0979669i
\(489\) 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 \(0.223244\pi\)
\(492\) −0.0214128 + 0.0370880i −0.000965362 + 0.00167206i
\(493\) 11.0408 0.497254
\(494\) −2.62153 0.0574526i −0.117948 0.00258491i
\(495\) 0 0
\(496\) −5.59707 + 9.69442i −0.251316 + 0.435292i
\(497\) −1.06641 + 1.84707i −0.0478348 + 0.0828523i
\(498\) 2.05301 + 3.55593i 0.0919978 + 0.159345i
\(499\) −0.529796 + 0.917633i −0.0237169 + 0.0410789i −0.877640 0.479320i \(-0.840883\pi\)
0.853923 + 0.520399i \(0.174217\pi\)
\(500\) 0 0
\(501\) −3.04002 −0.135818
\(502\) −10.6458 −0.475145
\(503\) 2.68855 + 4.65671i 0.119877 + 0.207633i 0.919719 0.392578i \(-0.128417\pi\)
−0.799842 + 0.600211i \(0.795083\pi\)
\(504\) −5.17589 8.96490i −0.230552 0.399329i
\(505\) 0 0
\(506\) −51.3441 −2.28253
\(507\) −1.16547 2.01866i −0.0517604 0.0896517i
\(508\) −1.46506 + 2.53755i −0.0650014 + 0.112586i
\(509\) −16.9240 29.3132i −0.750142 1.29928i −0.947753 0.319004i \(-0.896652\pi\)
0.197611 0.980280i \(-0.436682\pi\)
\(510\) 0 0
\(511\) 5.01336 8.68339i 0.221778 0.384131i
\(512\) 18.5188 0.818423
\(513\) −4.72242 0.103495i −0.208500 0.00456942i
\(514\) 12.8951 0.568778
\(515\) 0 0
\(516\) 0.0549897 0.0952450i 0.00242079 0.00419293i
\(517\) 16.2132 + 28.0821i 0.713056 + 1.23505i
\(518\) −3.58684 + 6.21260i −0.157597 + 0.272966i
\(519\) 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 \(0.724325\pi\)
\(522\) 8.82147 + 15.2792i 0.386105 + 0.668754i
\(523\) −12.0223 20.8232i −0.525698 0.910536i −0.999552 0.0299323i \(-0.990471\pi\)
0.473854 0.880604i \(-0.342863\pi\)
\(524\) −0.483596 −0.0211260
\(525\) 0 0
\(526\) 22.6054 + 39.1537i 0.985643 + 1.70718i
\(527\) −3.53841 + 6.12871i −0.154136 + 0.266971i
\(528\) −1.96818 3.40899i −0.0856540 0.148357i
\(529\) −12.7013 + 21.9992i −0.552228 + 0.956488i
\(530\) 0 0
\(531\) −33.3277 −1.44630
\(532\) −0.530207 0.966659i −0.0229874 0.0419100i
\(533\) 0.493831 0.0213902
\(534\) −1.91183 + 3.31138i −0.0827329 + 0.143298i
\(535\) 0 0
\(536\) −7.08279 12.2678i −0.305930 0.529886i
\(537\) −0.895447 + 1.55096i −0.0386414 + 0.0669289i
\(538\) −13.6326 23.6124i −0.587743 1.01800i
\(539\) −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 \(0.642967\pi\)
\(542\) −8.49753 14.7181i −0.365000 0.632199i
\(543\) −2.68282 −0.115131
\(544\) −3.00684 −0.128917
\(545\) 0 0
\(546\) −0.0712420 + 0.123395i −0.00304888 + 0.00528081i
\(547\) 7.46421 + 12.9284i 0.319146 + 0.552778i 0.980310 0.197464i \(-0.0632705\pi\)
−0.661164 + 0.750242i \(0.729937\pi\)
\(548\) 1.70743 2.95735i 0.0729377 0.126332i
\(549\) 1.38581 2.40029i 0.0591449 0.102442i
\(550\) 0 0
\(551\) −8.41540 15.3427i −0.358508 0.653622i
\(552\) −3.37997 −0.143861
\(553\) −9.49077 + 16.4385i −0.403588 + 0.699036i
\(554\) 1.33077 2.30496i 0.0565390 0.0979284i
\(555\) 0 0
\(556\) −0.305908 + 0.529848i −0.0129734 + 0.0224706i
\(557\) 2.63757 + 4.56841i 0.111758 + 0.193570i 0.916479 0.400083i \(-0.131019\pi\)
−0.804721 + 0.593653i \(0.797685\pi\)
\(558\) −11.3086 −0.478730
\(559\) −1.26820 −0.0536391
\(560\) 0 0
\(561\) −1.24426 2.15513i −0.0525328 0.0909895i
\(562\) 21.0196 0.886660
\(563\) 17.8950 0.754186 0.377093 0.926175i \(-0.376924\pi\)
0.377093 + 0.926175i \(0.376924\pi\)
\(564\) −0.114609 0.198508i −0.00482590 0.00835870i
\(565\) 0 0
\(566\) −13.2631 22.9724i −0.557491 0.965603i
\(567\) 5.67612 9.83132i 0.238375 0.412877i
\(568\) 2.18735 3.78859i 0.0917790 0.158966i
\(569\) 6.81848 0.285846 0.142923 0.989734i \(-0.454350\pi\)
0.142923 + 0.989734i \(0.454350\pi\)
\(570\) 0 0
\(571\) 5.16915 0.216322 0.108161 0.994133i \(-0.465504\pi\)
0.108161 + 0.994133i \(0.465504\pi\)
\(572\) 0.196221 0.339864i 0.00820440 0.0142104i
\(573\) −1.87780 + 3.25244i −0.0784461 + 0.135873i
\(574\) 1.17447 + 2.03423i 0.0490213 + 0.0849073i
\(575\) 0 0
\(576\) 10.5049 + 18.1950i 0.437703 + 0.758125i
\(577\) −28.5621 −1.18905 −0.594527 0.804076i \(-0.702661\pi\)
−0.594527 + 0.804076i \(0.702661\pi\)
\(578\) 13.9772 0.581376
\(579\) 1.84135 + 3.18930i 0.0765237 + 0.132543i
\(580\) 0 0
\(581\) 19.9079 0.825919
\(582\) 4.91785 0.203851
\(583\) −15.7493 27.2786i −0.652269 1.12976i
\(584\) −10.2831 + 17.8108i −0.425518 + 0.737018i
\(585\) 0 0
\(586\) 24.6684 42.7269i 1.01904 1.76503i
\(587\) 20.1627 34.9228i 0.832204 1.44142i −0.0640822 0.997945i \(-0.520412\pi\)
0.896286 0.443476i \(-0.146255\pi\)
\(588\) 0.186633 0.00769663
\(589\) 11.2137 + 0.245756i 0.462052 + 0.0101262i
\(590\) 0 0
\(591\) 1.44535 2.50341i 0.0594536 0.102977i
\(592\) 8.07730 13.9903i 0.331975 0.574997i
\(593\) 13.8452 + 23.9806i 0.568555 + 0.984767i 0.996709 + 0.0810610i \(0.0258308\pi\)
−0.428154 + 0.903706i \(0.640836\pi\)
\(594\) 3.99870 6.92595i 0.164069 0.284175i
\(595\) 0 0
\(596\) −1.23613 −0.0506338
\(597\) 2.40371 0.0983771
\(598\) −2.09260 3.62449i −0.0855727 0.148216i
\(599\) 1.31466 + 2.27706i 0.0537156 + 0.0930382i 0.891633 0.452759i \(-0.149560\pi\)
−0.837917 + 0.545797i \(0.816227\pi\)
\(600\) 0 0
\(601\) 27.7009 1.12994 0.564972 0.825110i \(-0.308887\pi\)
0.564972 + 0.825110i \(0.308887\pi\)
\(602\) −3.01613 5.22408i −0.122928 0.212918i
\(603\) 7.85561 13.6063i 0.319905 0.554092i
\(604\) −0.481292 0.833622i −0.0195835 0.0339196i
\(605\) 0 0
\(606\) 2.15133 3.72622i 0.0873919 0.151367i
\(607\) −32.0668 −1.30155 −0.650775 0.759271i \(-0.725556\pi\)
−0.650775 + 0.759271i \(0.725556\pi\)
\(608\) 2.29184 + 4.17842i 0.0929463 + 0.169457i
\(609\) −0.950874 −0.0385313
\(610\) 0 0
\(611\) −1.32158 + 2.28904i −0.0534654 + 0.0926048i
\(612\) −0.791248 1.37048i −0.0319843 0.0553985i
\(613\) −6.23014 + 10.7909i −0.251633 + 0.435841i −0.963976 0.265991i \(-0.914301\pi\)
0.712343 + 0.701832i \(0.247634\pi\)
\(614\) −11.5215 19.9559i −0.464971 0.805354i
\(615\) 0 0
\(616\) −17.3836 −0.700405
\(617\) 13.2370 + 22.9271i 0.532900 + 0.923009i 0.999262 + 0.0384155i \(0.0122311\pi\)
−0.466362 + 0.884594i \(0.654436\pi\)
\(618\) −0.714106 1.23687i −0.0287256 0.0497541i
\(619\) 33.3766 1.34152 0.670760 0.741674i \(-0.265968\pi\)
0.670760 + 0.741674i \(0.265968\pi\)
\(620\) 0 0
\(621\) −3.76960 6.52914i −0.151269 0.262005i
\(622\) 21.6224 37.4511i 0.866978 1.50165i
\(623\) 9.26942 + 16.0551i 0.371371 + 0.643234i
\(624\) 0.160431 0.277875i 0.00642240 0.0111239i
\(625\) 0 0
\(626\) 47.2323 1.88778
\(627\) −2.04645 + 3.37173i −0.0817275 + 0.134654i
\(628\) −0.406296 −0.0162130
\(629\) 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 \(-0.461081\pi\)
\(632\) 19.4669 33.7176i 0.774351 1.34122i
\(633\) −0.887911 1.53791i −0.0352913 0.0611263i
\(634\) −20.1000 −0.798271
\(635\) 0 0
\(636\) 0.111329 + 0.192828i 0.00441450 + 0.00764613i
\(637\) −1.07606 1.86379i −0.0426349 0.0738459i
\(638\) 29.6276 1.17297
\(639\) 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 \(0.169222\pi\)
\(642\) 1.74880 + 3.02901i 0.0690195 + 0.119545i
\(643\) 12.5848 21.7975i 0.496296 0.859610i −0.503695 0.863882i \(-0.668026\pi\)
0.999991 + 0.00427137i \(0.00135962\pi\)
\(644\) 0.879860 1.52396i 0.0346713 0.0600525i
\(645\) 0 0
\(646\) 8.53908 + 15.5682i 0.335965 + 0.612523i
\(647\) 18.3604 0.721821 0.360911 0.932600i \(-0.382466\pi\)
0.360911 + 0.932600i \(0.382466\pi\)
\(648\) −11.6425 + 20.1654i −0.457361 + 0.792173i
\(649\) −27.9834 + 48.4686i −1.09844 + 1.90256i
\(650\) 0 0
\(651\) 0.304740 0.527825i 0.0119437 0.0206871i
\(652\) −0.926843 1.60534i −0.0362980 0.0628699i
\(653\) 33.0301 1.29257 0.646284 0.763097i \(-0.276322\pi\)
0.646284 + 0.763097i \(0.276322\pi\)
\(654\) −2.20414 −0.0861886
\(655\) 0 0
\(656\) −2.64481 4.58094i −0.103262 0.178856i
\(657\) −22.8102 −0.889911
\(658\) −12.5723 −0.490120
\(659\) 13.2310 + 22.9167i 0.515406 + 0.892709i 0.999840 + 0.0178814i \(0.00569212\pi\)
−0.484434 + 0.874828i \(0.660975\pi\)
\(660\) 0 0
\(661\) 7.79673 + 13.5043i 0.303258 + 0.525258i 0.976872 0.213825i \(-0.0685924\pi\)
−0.673614 + 0.739083i \(0.735259\pi\)
\(662\) −21.7938 + 37.7480i −0.847041 + 1.46712i
\(663\) 0.101423 0.175670i 0.00393895 0.00682246i
\(664\) −40.8339 −1.58466
\(665\) 0 0
\(666\) 16.3197 0.632377
\(667\) 13.9651 24.1882i 0.540729 0.936570i
\(668\) −1.62320 + 2.81146i −0.0628034 + 0.108779i
\(669\) −2.34837 4.06749i −0.0907931 0.157258i
\(670\) 0 0
\(671\) −2.32717 4.03078i −0.0898395 0.155607i
\(672\) 0.258959 0.00998958
\(673\) −6.13645 −0.236543 −0.118271 0.992981i \(-0.537735\pi\)
−0.118271 + 0.992981i \(0.537735\pi\)
\(674\) 11.4880 + 19.8977i 0.442500 + 0.766432i
\(675\) 0 0
\(676\) −2.48919 −0.0957379
\(677\) 22.2754 0.856112 0.428056 0.903752i \(-0.359199\pi\)
0.428056 + 0.903752i \(0.359199\pi\)
\(678\) 0.880665 + 1.52536i 0.0338217 + 0.0585810i
\(679\) 11.9220 20.6495i 0.457524 0.792455i
\(680\) 0 0
\(681\) 0.207553 0.359492i 0.00795344 0.0137758i
\(682\) −9.49517 + 16.4461i −0.363589 + 0.629754i
\(683\) 16.7397 0.640527 0.320264 0.947328i \(-0.396228\pi\)
0.320264 + 0.947328i \(0.396228\pi\)
\(684\) −1.30138 + 2.14414i −0.0497594 + 0.0819832i
\(685\) 0 0
\(686\) 11.8796 20.5761i 0.453566 0.785599i
\(687\) −1.98683 + 3.44130i −0.0758024 + 0.131294i
\(688\) 6.79208 + 11.7642i 0.258946 + 0.448507i
\(689\) 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 \(0.253573\pi\)
\(692\) 2.71034 0.103032
\(693\) −9.64018 16.6973i −0.366200 0.634277i
\(694\) 16.7284 + 28.9744i 0.635000 + 1.09985i
\(695\) 0 0
\(696\) 1.95037 0.0739288
\(697\) −1.67202 2.89602i −0.0633323 0.109695i
\(698\) 18.8767 32.6954i 0.714494 1.23754i
\(699\) −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 \(0.933509\pi\)
\(702\) 0.651889 0.0246040
\(703\) −16.1828 0.354657i −0.610345 0.0133761i
\(704\) 35.2814 1.32972
\(705\) 0 0
\(706\) −7.62510 + 13.2071i −0.286974 + 0.497054i
\(707\) −10.4306 18.0664i −0.392285 0.679457i
\(708\) 0.197810 0.342618i 0.00743417 0.0128764i
\(709\) −16.9184 29.3036i −0.635386 1.10052i −0.986433 0.164163i \(-0.947508\pi\)
0.351048 0.936358i \(-0.385826\pi\)
\(710\) 0 0
\(711\) 43.1819 1.61945
\(712\) −19.0129 32.9313i −0.712538 1.23415i
\(713\) 8.95117 + 15.5039i 0.335224 + 0.580625i
\(714\) 0.964848 0.0361085
\(715\) 0 0
\(716\) 0.956237 + 1.65625i 0.0357362 + 0.0618970i
\(717\) 0.697474 1.20806i 0.0260476 0.0451158i
\(718\) 1.46824 + 2.54307i 0.0547943 + 0.0949066i
\(719\) −13.4970 + 23.3775i −0.503353 + 0.871833i 0.496640 + 0.867957i \(0.334567\pi\)
−0.999992 + 0.00387581i \(0.998766\pi\)
\(720\) 0 0
\(721\) −6.92463 −0.257887
\(722\) 15.1256 23.7324i 0.562916 0.883229i
\(723\) −2.63997 −0.0981814
\(724\) −1.43247 + 2.48111i −0.0532374 + 0.0922099i
\(725\) 0 0
\(726\) −1.85944 3.22065i −0.0690104 0.119529i
\(727\) −10.8016 + 18.7090i −0.400610 + 0.693878i −0.993800 0.111185i \(-0.964535\pi\)
0.593189 + 0.805063i \(0.297869\pi\)
\(728\) −0.708492 1.22714i −0.0262584 0.0454810i
\(729\) −25.2353 −0.934640
\(730\) 0 0
\(731\) 4.29388 + 7.43723i 0.158815 + 0.275076i
\(732\) 0.0164504 + 0.0284930i 0.000608026 + 0.00105313i
\(733\) 17.2551 0.637332 0.318666 0.947867i \(-0.396765\pi\)
0.318666 + 0.947867i \(0.396765\pi\)
\(734\) −7.81217 −0.288353
\(735\) 0 0
\(736\) −3.80322 + 6.58737i −0.140189 + 0.242814i
\(737\) −13.1918 22.8489i −0.485927 0.841650i
\(738\) 2.67184 4.62777i 0.0983519 0.170350i
\(739\) −2.39553 + 4.14918i −0.0881210 + 0.152630i −0.906717 0.421740i \(-0.861420\pi\)
0.818596 + 0.574370i \(0.194753\pi\)
\(740\) 0 0
\(741\) −0.321423 0.00704420i −0.0118078 0.000258775i
\(742\) 12.2126 0.448338
\(743\) 7.24373 12.5465i 0.265747 0.460287i −0.702012 0.712165i \(-0.747715\pi\)
0.967759 + 0.251878i \(0.0810482\pi\)
\(744\) −0.625065 + 1.08264i −0.0229160 + 0.0396917i
\(745\) 0 0
\(746\) 23.4912 40.6879i 0.860072 1.48969i
\(747\) −22.6447 39.2217i −0.828525 1.43505i
\(748\) −2.65746 −0.0971665
\(749\) 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 \(0.870896\pi\)
\(752\) 28.3119 1.03243
\(753\) −1.30527 −0.0475667
\(754\) 1.20751 + 2.09147i 0.0439749 + 0.0761668i
\(755\) 0 0
\(756\) 0.137047 + 0.237373i 0.00498437 + 0.00863318i
\(757\) 18.4795 32.0074i 0.671649 1.16333i −0.305788 0.952100i \(-0.598920\pi\)
0.977436 0.211230i \(-0.0677469\pi\)
\(758\) 26.3000 45.5530i 0.955260 1.65456i
\(759\) −6.29525 −0.228503
\(760\) 0 0
\(761\) 48.3893 1.75411 0.877055 0.480389i \(-0.159505\pi\)
0.877055 + 0.480389i \(0.159505\pi\)
\(762\) −2.03208 + 3.51967i −0.0736145 + 0.127504i
\(763\) −5.34333 + 9.25493i −0.193442 + 0.335051i
\(764\) 2.00528 + 3.47324i 0.0725484 + 0.125657i
\(765\) 0 0
\(766\) −10.3167 17.8690i −0.372756 0.645632i
\(767\) −4.56200 −0.164724
\(768\) −0.837598 −0.0302242
\(769\) −20.7177 35.8841i −0.747098 1.29401i −0.949208 0.314649i \(-0.898113\pi\)
0.202110 0.979363i \(-0.435220\pi\)
\(770\) 0 0
\(771\) 1.58105 0.0569403
\(772\) 3.93270 0.141541
\(773\) −19.4154 33.6285i −0.698325 1.20953i −0.969047 0.246877i \(-0.920596\pi\)
0.270722 0.962658i \(-0.412738\pi\)
\(774\) −6.86151 + 11.8845i −0.246632 + 0.427179i
\(775\) 0 0
\(776\) −24.4537 + 42.3550i −0.877836 + 1.52046i
\(777\) −0.439779 + 0.761720i −0.0157770 + 0.0273266i
\(778\) 1.39657 0.0500695
\(779\) −2.74999 + 4.53087i −0.0985287 + 0.162335i
\(780\) 0 0
\(781\) 4.07397 7.05632i 0.145778 0.252495i
\(782\) −14.1703 + 24.5437i −0.506729 + 0.877680i
\(783\) 2.17521 + 3.76757i 0.0777355 + 0.134642i
\(784\) −11.5261 + 19.9637i −0.411645 + 0.712990i
\(785\) 0 0
\(786\) −0.670764 −0.0239254
\(787\) 51.4952 1.83561 0.917803 0.397037i \(-0.129962\pi\)
0.917803 + 0.397037i \(0.129962\pi\)
\(788\) −1.54347 2.67336i −0.0549838 0.0952347i
\(789\) 2.77163 + 4.80060i 0.0986725 + 0.170906i
\(790\) 0 0
\(791\) 8.53973 0.303638
\(792\) 19.7734 + 34.2485i 0.702615 + 1.21697i
\(793\) 0.189694 0.328560i 0.00673623 0.0116675i
\(794\) 21.1556 + 36.6426i 0.750785 + 1.30040i
\(795\) 0 0
\(796\) 1.28344 2.22299i 0.0454905 0.0787918i
\(797\) −7.50433 −0.265817 −0.132908 0.991128i \(-0.542432\pi\)
−0.132908 + 0.991128i \(0.542432\pi\)
\(798\) −0.735414 1.34079i −0.0260334 0.0474634i
\(799\) 17.8985 0.633203
\(800\) 0 0
\(801\) 21.0874 36.5244i 0.745087 1.29053i
\(802\) −5.30809 9.19387i −0.187435 0.324647i
\(803\) −19.1524 + 33.1730i −0.675875 + 1.17065i
\(804\) 0.0932510 + 0.161515i 0.00328871 + 0.00569621i
\(805\) 0 0
\(806\) −1.54795 −0.0545243
\(807\) −1.67148 2.89509i −0.0588388 0.101912i
\(808\) 21.3947 + 37.0567i 0.752663 + 1.30365i
\(809\) −17.9109 −0.629714 −0.314857 0.949139i \(-0.601957\pi\)
−0.314857 + 0.949139i \(0.601957\pi\)
\(810\) 0 0
\(811\) −2.57516 4.46030i −0.0904260 0.156622i 0.817264 0.576263i \(-0.195490\pi\)
−0.907690 + 0.419640i \(0.862156\pi\)
\(812\) −0.507713 + 0.879385i −0.0178172 + 0.0308604i
\(813\) −1.04187 1.80458i −0.0365401 0.0632893i
\(814\) 13.7028 23.7339i 0.480281 0.831871i
\(815\) 0 0
\(816\) −2.17276 −0.0760619
\(817\) 7.06221 11.6356i 0.247075 0.407080i
\(818\) 15.6007 0.545464
\(819\) 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 \(0.825661\pi\)
\(822\) 2.36826 4.10194i 0.0826025 0.143072i
\(823\) 7.20798 + 12.4846i 0.251254 + 0.435185i 0.963871 0.266368i \(-0.0858236\pi\)
−0.712617 + 0.701553i \(0.752490\pi\)
\(824\) 14.2034 0.494798
\(825\) 0 0
\(826\) −10.8497 18.7922i −0.377509 0.653864i
\(827\) 4.73660 + 8.20404i 0.164708 + 0.285282i 0.936552 0.350530i \(-0.113999\pi\)
−0.771844 + 0.635812i \(0.780665\pi\)
\(828\) −4.00326 −0.139123
\(829\) −12.3950 −0.430497 −0.215248 0.976559i \(-0.569056\pi\)
−0.215248 + 0.976559i \(0.569056\pi\)
\(830\) 0 0
\(831\) 0.163164 0.282609i 0.00566011 0.00980359i
\(832\) 1.43794 + 2.49059i 0.0498516 + 0.0863455i
\(833\) −7.28666 + 12.6209i −0.252468 + 0.437287i
\(834\) −0.424304 + 0.734916i −0.0146925 + 0.0254481i
\(835\) 0 0
\(836\) 2.02554 + 3.69291i 0.0700548 + 0.127722i
\(837\) −2.78848 −0.0963839
\(838\) 1.87144 3.24142i 0.0646477 0.111973i
\(839\) −6.26491 + 10.8511i −0.216289 + 0.374623i −0.953670 0.300853i \(-0.902729\pi\)
0.737382 + 0.675476i \(0.236062\pi\)
\(840\) 0 0
\(841\) 6.44162 11.1572i 0.222125 0.384732i
\(842\) 11.0104 + 19.0706i 0.379443 + 0.657215i
\(843\) 2.57720 0.0887633
\(844\) −1.89638 −0.0652760
\(845\) 0 0
\(846\) 14.3007 + 24.7695i 0.491667 + 0.851592i
\(847\) −18.0308 −0.619547
\(848\) −27.5018 −0.944416
\(849\) −1.62618 2.81663i −0.0558103 0.0966663i
\(850\) 0 0
\(851\) −12.9177 22.3741i −0.442813 0.766974i
\(852\) −0.0287983 + 0.0498801i −0.000986613 + 0.00170886i
\(853\) 1.73650 3.00771i 0.0594567 0.102982i −0.834765 0.550606i \(-0.814397\pi\)
0.894222 + 0.447624i \(0.147730\pi\)
\(854\) 1.80458 0.0617513
\(855\) 0 0
\(856\) −34.7831 −1.18886
\(857\) −8.33085 + 14.4295i −0.284577 + 0.492901i −0.972506 0.232876i \(-0.925186\pi\)
0.687930 + 0.725777i \(0.258520\pi\)
\(858\) 0.272164 0.471402i 0.00929154 0.0160934i
\(859\) −20.4042 35.3412i −0.696183 1.20583i −0.969780 0.243981i \(-0.921547\pi\)
0.273597 0.961844i \(-0.411787\pi\)
\(860\) 0 0
\(861\) 0.144000 + 0.249415i 0.00490751 + 0.00850005i
\(862\) 6.19239 0.210914
\(863\) −4.07050 −0.138561 −0.0692806 0.997597i \(-0.522070\pi\)
−0.0692806 + 0.997597i \(0.522070\pi\)
\(864\) −0.592392 1.02605i −0.0201536 0.0349071i
\(865\) 0 0
\(866\) −37.4821 −1.27369
\(867\) 1.71373 0.0582014
\(868\) −0.325428 0.563658i −0.0110458 0.0191318i
\(869\) 36.2574 62.7996i 1.22995 2.13033i
\(870\) 0 0
\(871\) 1.07530 1.86247i 0.0364351 0.0631075i
\(872\) 10.9599 18.9831i 0.371150 0.642851i
\(873\) −54.2437 −1.83587
\(874\) 44.9075 + 0.984178i 1.51902 + 0.0332903i
\(875\) 0 0
\(876\) 0.135386 0.234495i 0.00457426 0.00792285i
\(877\) −13.2572 + 22.9621i −0.447663 + 0.775376i −0.998233 0.0594132i \(-0.981077\pi\)
0.550570 + 0.834789i \(0.314410\pi\)
\(878\) 21.4122 + 37.0871i 0.722628 + 1.25163i
\(879\) 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 \(0.623004\pi\)
\(882\) −23.2878 −0.784140
\(883\) 9.85689 + 17.0726i 0.331711 + 0.574540i 0.982847 0.184421i \(-0.0590408\pi\)
−0.651137 + 0.758961i \(0.725708\pi\)
\(884\) −0.108308 0.187596i −0.00364281 0.00630953i
\(885\) 0 0
\(886\) −6.79667 −0.228339
\(887\) 5.71080 + 9.89139i 0.191750 + 0.332120i 0.945830 0.324662i \(-0.105250\pi\)
−0.754080 + 0.656782i \(0.771917\pi\)
\(888\) 0.902049 1.56239i 0.0302708 0.0524305i
\(889\) 9.85245 + 17.0649i 0.330441 + 0.572340i
\(890\) 0 0
\(891\) −21.6844 + 37.5584i −0.726453 + 1.25825i
\(892\) −5.01558 −0.167934
\(893\) −13.6424 24.8724i −0.456524 0.832323i
\(894\) −1.71455 −0.0573431
\(895\) 0 0
\(896\) −8.26556 + 14.3164i −0.276133 + 0.478276i
\(897\) −0.256571 0.444395i −0.00856667 0.0148379i
\(898\) 21.6381 37.4783i 0.722073 1.25067i
\(899\) −5.16517 8.94634i −0.172268 0.298377i
\(900\) 0 0
\(901\) −17.3864 −0.579223
\(902\) −4.48679 7.77135i −0.149394 0.258758i
\(903\) −0.369804 0.640519i −0.0123063 0.0213151i
\(904\) −17.5162 −0.582580
\(905\) 0 0
\(906\) −0.667568 1.15626i −0.0221784 0.0384142i
\(907\) −5.36915 + 9.29964i −0.178280 + 0.308789i −0.941291 0.337595i \(-0.890387\pi\)
0.763012 + 0.646385i \(0.223720\pi\)
\(908\) −0.221643 0.383897i −0.00735548 0.0127401i
\(909\) −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 \(0.651124\pi\)
\(912\) 1.65610 + 3.01935i 0.0548388 + 0.0999807i
\(913\) −76.0538 −2.51701
\(914\) 17.5605 30.4157i 0.580850 1.00606i
\(915\) 0 0
\(916\) 2.12171 + 3.67492i 0.0701034 + 0.121423i
\(917\) −1.62608 + 2.81646i −0.0536980 + 0.0930077i
\(918\) −2.20717 3.82294i −0.0728476 0.126176i
\(919\) −49.2639 −1.62507 −0.812533 0.582915i \(-0.801912\pi\)
−0.812533 + 0.582915i \(0.801912\pi\)
\(920\) 0 0
\(921\) −1.41264 2.44677i −0.0465482 0.0806238i
\(922\) 25.9371 + 44.9243i 0.854192 + 1.47950i
\(923\) 0.664160 0.0218611
\(924\) 0.228870 0.00752927
\(925\) 0 0
\(926\) −15.1775 + 26.2882i −0.498763 + 0.863883i
\(927\) 7.87657 + 13.6426i 0.258700 + 0.448082i
\(928\) 2.19461 3.80117i 0.0720415 0.124779i
\(929\) −21.5374 + 37.3039i −0.706619 + 1.22390i 0.259485 + 0.965747i \(0.416447\pi\)
−0.966104 + 0.258153i \(0.916886\pi\)
\(930\) 0 0
\(931\) 23.0923 + 0.506085i 0.756821 + 0.0165863i
\(932\) −0.398315 −0.0130472
\(933\) 2.65110 4.59183i 0.0867930 0.150330i
\(934\) −6.84568 + 11.8571i −0.223998 + 0.387975i
\(935\) 0 0
\(936\) −1.61178 + 2.79168i −0.0526826 + 0.0912490i
\(937\) −21.7222 37.6239i −0.709633 1.22912i −0.964993 0.262275i \(-0.915527\pi\)
0.255360 0.966846i \(-0.417806\pi\)
\(938\) 10.2294 0.334003
\(939\) 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 \(0.991783\pi\)
\(942\) −0.563545 −0.0183613
\(943\) −8.45946 −0.275478
\(944\) 24.4326 + 42.3186i 0.795215 + 1.37735i
\(945\) 0 0
\(946\) 11.5224 + 19.9575i 0.374627 + 0.648873i
\(947\) 1.00294 1.73715i 0.0325913 0.0564498i −0.849270 0.527959i \(-0.822957\pi\)
0.881861 + 0.471509i \(0.156291\pi\)
\(948\) −0.256298 + 0.443921i −0.00832418 + 0.0144179i
\(949\) −3.12233 −0.101355
\(950\) 0 0
\(951\) −2.46443 −0.0799148
\(952\) −4.79764 + 8.30975i −0.155492 + 0.269321i
\(953\) 9.61946 16.6614i 0.311605 0.539716i −0.667105 0.744964i \(-0.732467\pi\)
0.978710 + 0.205248i \(0.0658001\pi\)
\(954\) −13.8915 24.0607i −0.449753 0.778995i
\(955\) 0 0
\(956\) −0.744823 1.29007i −0.0240893 0.0417239i
\(957\) 3.63260 0.117425
\(958\) −5.58045 −0.180296
\(959\) −11.4824 19.8881i −0.370786 0.642220i
\(960\) 0 0
\(961\) −24.3786 −0.786406
\(962\) 2.23390 0.0720237
\(963\) −19.2892 33.4098i −0.621585 1.07662i
\(964\) −1.40959 + 2.44149i −0.0453999 + 0.0786350i
\(965\) 0 0
\(966\) 1.22039 2.11378i 0.0392655 0.0680099i
\(967\) −14.2071 + 24.6075i −0.456871 + 0.791324i −0.998794 0.0491047i \(-0.984363\pi\)
0.541923 + 0.840428i \(0.317697\pi\)
\(968\) 36.9838 1.18870
\(969\) 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 \(0.259804\pi\)
\(972\) 0.468524 0.811508i 0.0150279 0.0260291i
\(973\) 2.05722 + 3.56321i 0.0659515 + 0.114231i
\(974\) −8.73761 + 15.1340i −0.279971 + 0.484924i
\(975\) 0 0
\(976\) −4.06377 −0.130078
\(977\) 13.2288 0.423226 0.211613 0.977354i \(-0.432128\pi\)
0.211613 + 0.977354i \(0.432128\pi\)
\(978\) −1.28556 2.22666i −0.0411077 0.0712006i
\(979\) −35.4118 61.3350i −1.13177 1.96027i
\(980\) 0 0
\(981\) 24.3116 0.776208
\(982\) 5.80305 + 10.0512i 0.185183 + 0.320746i
\(983\) −24.2617 + 42.0225i −0.773828 + 1.34031i 0.161623 + 0.986853i \(0.448327\pi\)
−0.935451 + 0.353457i \(0.885006\pi\)
\(984\) −0.295364 0.511586i −0.00941587 0.0163088i
\(985\) 0 0
\(986\) 8.17680 14.1626i 0.260403 0.451030i
\(987\) −1.54148 −0.0490658
\(988\) −0.178136 + 0.293496i −0.00566727 + 0.00933736i
\(989\) 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 \(0.945695\pi\)
\(992\) 1.40667 + 2.43643i 0.0446619 + 0.0773568i
\(993\) −2.67212 + 4.62824i −0.0847971 + 0.146873i
\(994\) 1.57955 + 2.73587i 0.0501004 + 0.0867764i
\(995\) 0 0
\(996\) 0.537613 0.0170349
\(997\) −13.7795 23.8668i −0.436401 0.755869i 0.561008 0.827811i \(-0.310414\pi\)
−0.997409 + 0.0719414i \(0.977081\pi\)
\(998\) 0.784730 + 1.35919i 0.0248402 + 0.0430245i
\(999\) 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.e.f.201.6 yes 12
5.2 odd 4 475.2.j.d.49.9 24
5.3 odd 4 475.2.j.d.49.4 24
5.4 even 2 475.2.e.h.201.1 yes 12
19.7 even 3 inner 475.2.e.f.26.6 12
19.8 odd 6 9025.2.a.bs.1.6 6
19.11 even 3 9025.2.a.bz.1.1 6
95.7 odd 12 475.2.j.d.349.4 24
95.49 even 6 9025.2.a.br.1.6 6
95.64 even 6 475.2.e.h.26.1 yes 12
95.83 odd 12 475.2.j.d.349.9 24
95.84 odd 6 9025.2.a.by.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
475.2.e.f.26.6 12 19.7 even 3 inner
475.2.e.f.201.6 yes 12 1.1 even 1 trivial
475.2.e.h.26.1 yes 12 95.64 even 6
475.2.e.h.201.1 yes 12 5.4 even 2
475.2.j.d.49.4 24 5.3 odd 4
475.2.j.d.49.9 24 5.2 odd 4
475.2.j.d.349.4 24 95.7 odd 12
475.2.j.d.349.9 24 95.83 odd 12
9025.2.a.br.1.6 6 95.49 even 6
9025.2.a.bs.1.6 6 19.8 odd 6
9025.2.a.by.1.1 6 95.84 odd 6
9025.2.a.bz.1.1 6 19.11 even 3