Properties

Label 475.2.u.a.424.2
Level $475$
Weight $2$
Character 475.424
Analytic conductor $3.793$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(24,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.24");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.u (of order \(18\), degree \(6\), 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: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{18})\)
Coefficient field: \(\Q(\zeta_{36})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{6} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 19)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 424.2
Root \(-0.342020 + 0.939693i\) of defining polynomial
Character \(\chi\) \(=\) 475.424
Dual form 475.2.u.a.149.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.62760 + 1.93969i) q^{2} +(-0.223238 + 0.613341i) q^{3} +(-0.766044 + 4.34445i) q^{4} +(-1.55303 + 0.565258i) q^{6} +(1.32683 + 0.766044i) q^{7} +(-5.28801 + 3.05303i) q^{8} +(1.97178 + 1.65452i) q^{9} +O(q^{10})\) \(q+(1.62760 + 1.93969i) q^{2} +(-0.223238 + 0.613341i) q^{3} +(-0.766044 + 4.34445i) q^{4} +(-1.55303 + 0.565258i) q^{6} +(1.32683 + 0.766044i) q^{7} +(-5.28801 + 3.05303i) q^{8} +(1.97178 + 1.65452i) q^{9} +(0.592396 + 1.02606i) q^{11} +(-2.49362 - 1.43969i) q^{12} +(-0.929228 - 2.55303i) q^{13} +(0.673648 + 3.82045i) q^{14} +(-6.23783 - 2.27038i) q^{16} +(-2.49362 - 2.97178i) q^{17} +6.51754i q^{18} +(-0.819078 - 4.28125i) q^{19} +(-0.766044 + 0.642788i) q^{21} +(-1.02606 + 2.81908i) q^{22} +(-4.98724 - 0.879385i) q^{23} +(-0.692066 - 3.92490i) q^{24} +(3.43969 - 5.95772i) q^{26} +(-3.15074 + 1.81908i) q^{27} +(-4.34445 + 5.17752i) q^{28} +(3.56418 + 2.99070i) q^{29} +(1.91875 - 3.32337i) q^{31} +(-1.57202 - 4.31908i) q^{32} +(-0.761570 + 0.134285i) q^{33} +(1.70574 - 9.67372i) q^{34} +(-8.69846 + 7.29888i) q^{36} +4.10607i q^{37} +(6.97118 - 8.55690i) q^{38} +1.77332 q^{39} +(9.38326 + 3.41523i) q^{41} +(-2.49362 - 0.439693i) q^{42} +(8.57013 - 1.51114i) q^{43} +(-4.91147 + 1.78763i) q^{44} +(-6.41147 - 11.1050i) q^{46} +(0.368946 - 0.439693i) q^{47} +(2.78504 - 3.31908i) q^{48} +(-2.32635 - 4.02936i) q^{49} +(2.37939 - 0.866025i) q^{51} +(11.8034 - 2.08125i) q^{52} +(2.89884 + 0.511144i) q^{53} +(-8.65657 - 3.15074i) q^{54} -9.35504 q^{56} +(2.80872 + 0.453363i) q^{57} +11.7811i q^{58} +(3.01501 - 2.52990i) q^{59} +(-0.784463 + 4.44891i) q^{61} +(9.56926 - 1.68732i) q^{62} +(1.34878 + 3.70574i) q^{63} +(-0.819078 + 1.41868i) q^{64} +(-1.50000 - 1.25865i) q^{66} +(-2.49860 + 2.97771i) q^{67} +(14.8210 - 8.55690i) q^{68} +(1.65270 - 2.86257i) q^{69} +(-1.20439 - 6.83045i) q^{71} +(-15.4781 - 2.72921i) q^{72} +(2.09602 - 5.75877i) q^{73} +(-7.96451 + 6.68302i) q^{74} +(19.2271 - 0.278817i) q^{76} +1.81521i q^{77} +(2.88624 + 3.43969i) q^{78} +(9.21688 + 3.35467i) q^{79} +(0.928548 + 5.26606i) q^{81} +(8.64766 + 23.7592i) q^{82} +(-10.6679 - 6.15910i) q^{83} +(-2.20574 - 3.82045i) q^{84} +(16.8799 + 14.1639i) q^{86} +(-2.62998 + 1.51842i) q^{87} +(-6.26519 - 3.61721i) q^{88} +(-2.27972 + 0.829748i) q^{89} +(0.722811 - 4.09927i) q^{91} +(7.64090 - 20.9932i) q^{92} +(1.61002 + 1.91875i) q^{93} +1.45336 q^{94} +3.00000 q^{96} +(-4.73708 - 5.64543i) q^{97} +(4.02936 - 11.0706i) q^{98} +(-0.529563 + 3.00330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{6} - 6 q^{9} + 6 q^{14} - 36 q^{16} + 24 q^{19} - 30 q^{24} + 30 q^{26} + 6 q^{29} + 18 q^{31} - 48 q^{36} + 48 q^{39} + 42 q^{41} - 18 q^{44} - 36 q^{46} - 30 q^{49} + 6 q^{51} - 60 q^{54} - 12 q^{56} - 24 q^{59} - 24 q^{61} + 24 q^{64} - 18 q^{66} + 24 q^{69} - 12 q^{71} - 30 q^{74} + 72 q^{76} + 78 q^{79} + 12 q^{81} - 6 q^{84} + 48 q^{86} + 24 q^{89} + 30 q^{91} - 36 q^{94} + 36 q^{96} - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.62760 + 1.93969i 1.15088 + 1.37157i 0.916797 + 0.399354i \(0.130766\pi\)
0.234087 + 0.972216i \(0.424790\pi\)
\(3\) −0.223238 + 0.613341i −0.128886 + 0.354112i −0.987305 0.158838i \(-0.949225\pi\)
0.858418 + 0.512950i \(0.171448\pi\)
\(4\) −0.766044 + 4.34445i −0.383022 + 2.17223i
\(5\) 0 0
\(6\) −1.55303 + 0.565258i −0.634023 + 0.230766i
\(7\) 1.32683 + 0.766044i 0.501494 + 0.289538i 0.729330 0.684162i \(-0.239832\pi\)
−0.227836 + 0.973699i \(0.573165\pi\)
\(8\) −5.28801 + 3.05303i −1.86959 + 1.07941i
\(9\) 1.97178 + 1.65452i 0.657261 + 0.551507i
\(10\) 0 0
\(11\) 0.592396 + 1.02606i 0.178614 + 0.309369i 0.941406 0.337275i \(-0.109505\pi\)
−0.762792 + 0.646644i \(0.776172\pi\)
\(12\) −2.49362 1.43969i −0.719846 0.415603i
\(13\) −0.929228 2.55303i −0.257722 0.708084i −0.999307 0.0372256i \(-0.988148\pi\)
0.741585 0.670859i \(-0.234074\pi\)
\(14\) 0.673648 + 3.82045i 0.180040 + 1.02106i
\(15\) 0 0
\(16\) −6.23783 2.27038i −1.55946 0.567596i
\(17\) −2.49362 2.97178i −0.604792 0.720763i 0.373584 0.927596i \(-0.378129\pi\)
−0.978376 + 0.206833i \(0.933684\pi\)
\(18\) 6.51754i 1.53620i
\(19\) −0.819078 4.28125i −0.187909 0.982186i
\(20\) 0 0
\(21\) −0.766044 + 0.642788i −0.167165 + 0.140268i
\(22\) −1.02606 + 2.81908i −0.218757 + 0.601029i
\(23\) −4.98724 0.879385i −1.03991 0.183364i −0.372484 0.928039i \(-0.621494\pi\)
−0.667428 + 0.744674i \(0.732605\pi\)
\(24\) −0.692066 3.92490i −0.141267 0.801168i
\(25\) 0 0
\(26\) 3.43969 5.95772i 0.674579 1.16841i
\(27\) −3.15074 + 1.81908i −0.606359 + 0.350082i
\(28\) −4.34445 + 5.17752i −0.821025 + 0.978459i
\(29\) 3.56418 + 2.99070i 0.661851 + 0.555359i 0.910641 0.413198i \(-0.135588\pi\)
−0.248790 + 0.968557i \(0.580033\pi\)
\(30\) 0 0
\(31\) 1.91875 3.32337i 0.344617 0.596895i −0.640667 0.767819i \(-0.721342\pi\)
0.985284 + 0.170924i \(0.0546753\pi\)
\(32\) −1.57202 4.31908i −0.277896 0.763512i
\(33\) −0.761570 + 0.134285i −0.132572 + 0.0233761i
\(34\) 1.70574 9.67372i 0.292531 1.65903i
\(35\) 0 0
\(36\) −8.69846 + 7.29888i −1.44974 + 1.21648i
\(37\) 4.10607i 0.675033i 0.941320 + 0.337517i \(0.109587\pi\)
−0.941320 + 0.337517i \(0.890413\pi\)
\(38\) 6.97118 8.55690i 1.13088 1.38811i
\(39\) 1.77332 0.283958
\(40\) 0 0
\(41\) 9.38326 + 3.41523i 1.46542 + 0.533369i 0.946852 0.321669i \(-0.104244\pi\)
0.518566 + 0.855038i \(0.326466\pi\)
\(42\) −2.49362 0.439693i −0.384774 0.0678460i
\(43\) 8.57013 1.51114i 1.30693 0.230447i 0.523554 0.851993i \(-0.324606\pi\)
0.783378 + 0.621545i \(0.213495\pi\)
\(44\) −4.91147 + 1.78763i −0.740433 + 0.269495i
\(45\) 0 0
\(46\) −6.41147 11.1050i −0.945320 1.63734i
\(47\) 0.368946 0.439693i 0.0538163 0.0641358i −0.738465 0.674292i \(-0.764449\pi\)
0.792281 + 0.610156i \(0.208893\pi\)
\(48\) 2.78504 3.31908i 0.401985 0.479068i
\(49\) −2.32635 4.02936i −0.332336 0.575623i
\(50\) 0 0
\(51\) 2.37939 0.866025i 0.333181 0.121268i
\(52\) 11.8034 2.08125i 1.63683 0.288618i
\(53\) 2.89884 + 0.511144i 0.398187 + 0.0702111i 0.369156 0.929367i \(-0.379647\pi\)
0.0290308 + 0.999579i \(0.490758\pi\)
\(54\) −8.65657 3.15074i −1.17801 0.428761i
\(55\) 0 0
\(56\) −9.35504 −1.25012
\(57\) 2.80872 + 0.453363i 0.372023 + 0.0600494i
\(58\) 11.7811i 1.54693i
\(59\) 3.01501 2.52990i 0.392521 0.329365i −0.425073 0.905159i \(-0.639752\pi\)
0.817595 + 0.575794i \(0.195307\pi\)
\(60\) 0 0
\(61\) −0.784463 + 4.44891i −0.100440 + 0.569624i 0.892504 + 0.451040i \(0.148947\pi\)
−0.992944 + 0.118585i \(0.962164\pi\)
\(62\) 9.56926 1.68732i 1.21530 0.214290i
\(63\) 1.34878 + 3.70574i 0.169930 + 0.466879i
\(64\) −0.819078 + 1.41868i −0.102385 + 0.177336i
\(65\) 0 0
\(66\) −1.50000 1.25865i −0.184637 0.154929i
\(67\) −2.49860 + 2.97771i −0.305252 + 0.363785i −0.896763 0.442512i \(-0.854087\pi\)
0.591510 + 0.806297i \(0.298532\pi\)
\(68\) 14.8210 8.55690i 1.79731 1.03768i
\(69\) 1.65270 2.86257i 0.198962 0.344613i
\(70\) 0 0
\(71\) −1.20439 6.83045i −0.142935 0.810625i −0.969002 0.247053i \(-0.920538\pi\)
0.826067 0.563572i \(-0.190573\pi\)
\(72\) −15.4781 2.72921i −1.82411 0.321640i
\(73\) 2.09602 5.75877i 0.245321 0.674013i −0.754522 0.656275i \(-0.772131\pi\)
0.999843 0.0177383i \(-0.00564657\pi\)
\(74\) −7.96451 + 6.68302i −0.925855 + 0.776885i
\(75\) 0 0
\(76\) 19.2271 0.278817i 2.20551 0.0319825i
\(77\) 1.81521i 0.206862i
\(78\) 2.88624 + 3.43969i 0.326803 + 0.389468i
\(79\) 9.21688 + 3.35467i 1.03698 + 0.377430i 0.803735 0.594988i \(-0.202843\pi\)
0.233246 + 0.972418i \(0.425065\pi\)
\(80\) 0 0
\(81\) 0.928548 + 5.26606i 0.103172 + 0.585118i
\(82\) 8.64766 + 23.7592i 0.954974 + 2.62377i
\(83\) −10.6679 6.15910i −1.17095 0.676049i −0.217047 0.976161i \(-0.569643\pi\)
−0.953904 + 0.300112i \(0.902976\pi\)
\(84\) −2.20574 3.82045i −0.240666 0.416845i
\(85\) 0 0
\(86\) 16.8799 + 14.1639i 1.82020 + 1.52733i
\(87\) −2.62998 + 1.51842i −0.281963 + 0.162792i
\(88\) −6.26519 3.61721i −0.667872 0.385596i
\(89\) −2.27972 + 0.829748i −0.241649 + 0.0879532i −0.460006 0.887916i \(-0.652153\pi\)
0.218356 + 0.975869i \(0.429930\pi\)
\(90\) 0 0
\(91\) 0.722811 4.09927i 0.0757712 0.429720i
\(92\) 7.64090 20.9932i 0.796619 2.18869i
\(93\) 1.61002 + 1.91875i 0.166951 + 0.198965i
\(94\) 1.45336 0.149903
\(95\) 0 0
\(96\) 3.00000 0.306186
\(97\) −4.73708 5.64543i −0.480977 0.573207i 0.469922 0.882708i \(-0.344282\pi\)
−0.950899 + 0.309502i \(0.899838\pi\)
\(98\) 4.02936 11.0706i 0.407027 1.11830i
\(99\) −0.529563 + 3.00330i −0.0532231 + 0.301843i
\(100\) 0 0
\(101\) −2.03936 + 0.742267i −0.202924 + 0.0738584i −0.441483 0.897270i \(-0.645547\pi\)
0.238559 + 0.971128i \(0.423325\pi\)
\(102\) 5.55250 + 3.20574i 0.549779 + 0.317415i
\(103\) −10.8042 + 6.23783i −1.06457 + 0.614631i −0.926694 0.375818i \(-0.877362\pi\)
−0.137879 + 0.990449i \(0.544029\pi\)
\(104\) 12.7083 + 10.6635i 1.24615 + 1.04564i
\(105\) 0 0
\(106\) 3.72668 + 6.45480i 0.361967 + 0.626946i
\(107\) −5.78509 3.34002i −0.559266 0.322892i 0.193585 0.981083i \(-0.437988\pi\)
−0.752851 + 0.658191i \(0.771322\pi\)
\(108\) −5.48930 15.0817i −0.528208 1.45124i
\(109\) −1.64156 9.30975i −0.157233 0.891712i −0.956716 0.291023i \(-0.906004\pi\)
0.799483 0.600689i \(-0.205107\pi\)
\(110\) 0 0
\(111\) −2.51842 0.916629i −0.239038 0.0870026i
\(112\) −6.53731 7.79086i −0.617717 0.736167i
\(113\) 1.31046i 0.123278i 0.998099 + 0.0616388i \(0.0196327\pi\)
−0.998099 + 0.0616388i \(0.980367\pi\)
\(114\) 3.69207 + 6.18594i 0.345794 + 0.579366i
\(115\) 0 0
\(116\) −15.7233 + 13.1934i −1.45987 + 1.22498i
\(117\) 2.39181 6.57145i 0.221123 0.607531i
\(118\) 9.81445 + 1.73055i 0.903493 + 0.159310i
\(119\) −1.03209 5.85327i −0.0946114 0.536568i
\(120\) 0 0
\(121\) 4.79813 8.31061i 0.436194 0.755510i
\(122\) −9.90630 + 5.71941i −0.896875 + 0.517811i
\(123\) −4.18939 + 4.99273i −0.377745 + 0.450179i
\(124\) 12.9684 + 10.8818i 1.16459 + 0.977211i
\(125\) 0 0
\(126\) −4.99273 + 8.64766i −0.444787 + 0.770394i
\(127\) −4.96032 13.6284i −0.440157 1.20932i −0.939389 0.342853i \(-0.888607\pi\)
0.499232 0.866468i \(-0.333615\pi\)
\(128\) −13.1378 + 2.31655i −1.16123 + 0.204756i
\(129\) −0.986329 + 5.59375i −0.0868415 + 0.492502i
\(130\) 0 0
\(131\) −15.1741 + 12.7326i −1.32577 + 1.11245i −0.340722 + 0.940164i \(0.610671\pi\)
−0.985047 + 0.172288i \(0.944884\pi\)
\(132\) 3.41147i 0.296931i
\(133\) 2.19285 6.30793i 0.190144 0.546967i
\(134\) −9.84255 −0.850267
\(135\) 0 0
\(136\) 22.2592 + 8.10170i 1.90871 + 0.694715i
\(137\) −10.0494 1.77197i −0.858575 0.151390i −0.273006 0.962012i \(-0.588018\pi\)
−0.585569 + 0.810622i \(0.699129\pi\)
\(138\) 8.24243 1.45336i 0.701642 0.123718i
\(139\) −1.56031 + 0.567905i −0.132344 + 0.0481691i −0.407343 0.913275i \(-0.633545\pi\)
0.274999 + 0.961444i \(0.411322\pi\)
\(140\) 0 0
\(141\) 0.187319 + 0.324446i 0.0157751 + 0.0273232i
\(142\) 11.2887 13.4534i 0.947328 1.12898i
\(143\) 2.06910 2.46585i 0.173026 0.206205i
\(144\) −8.54323 14.7973i −0.711936 1.23311i
\(145\) 0 0
\(146\) 14.5817 5.30731i 1.20679 0.439236i
\(147\) 2.99070 0.527341i 0.246669 0.0434944i
\(148\) −17.8386 3.14543i −1.46633 0.258553i
\(149\) 10.5312 + 3.83305i 0.862750 + 0.314015i 0.735228 0.677820i \(-0.237075\pi\)
0.127523 + 0.991836i \(0.459297\pi\)
\(150\) 0 0
\(151\) −11.0419 −0.898576 −0.449288 0.893387i \(-0.648322\pi\)
−0.449288 + 0.893387i \(0.648322\pi\)
\(152\) 17.4021 + 20.1386i 1.41150 + 1.63346i
\(153\) 9.98545i 0.807276i
\(154\) −3.52094 + 2.95442i −0.283726 + 0.238074i
\(155\) 0 0
\(156\) −1.35844 + 7.70410i −0.108762 + 0.616822i
\(157\) 10.8262 1.90895i 0.864023 0.152351i 0.275964 0.961168i \(-0.411003\pi\)
0.588060 + 0.808817i \(0.299892\pi\)
\(158\) 8.49432 + 23.3380i 0.675772 + 1.85667i
\(159\) −0.960637 + 1.66387i −0.0761835 + 0.131954i
\(160\) 0 0
\(161\) −5.94356 4.98724i −0.468418 0.393050i
\(162\) −8.70323 + 10.3721i −0.683791 + 0.814910i
\(163\) −5.48432 + 3.16637i −0.429565 + 0.248010i −0.699161 0.714964i \(-0.746443\pi\)
0.269596 + 0.962973i \(0.413110\pi\)
\(164\) −22.0253 + 38.1489i −1.71989 + 2.97893i
\(165\) 0 0
\(166\) −5.41622 30.7169i −0.420380 2.38410i
\(167\) 13.5690 + 2.39259i 1.05000 + 0.185144i 0.671917 0.740626i \(-0.265471\pi\)
0.378087 + 0.925770i \(0.376582\pi\)
\(168\) 2.08840 5.73783i 0.161123 0.442683i
\(169\) 4.30406 3.61154i 0.331082 0.277811i
\(170\) 0 0
\(171\) 5.46838 9.79687i 0.418177 0.749186i
\(172\) 38.3901i 2.92722i
\(173\) 16.2286 + 19.3405i 1.23384 + 1.47043i 0.832053 + 0.554696i \(0.187165\pi\)
0.401784 + 0.915734i \(0.368390\pi\)
\(174\) −7.22580 2.62998i −0.547787 0.199378i
\(175\) 0 0
\(176\) −1.36571 7.74535i −0.102945 0.583828i
\(177\) 0.878624 + 2.41400i 0.0660414 + 0.181447i
\(178\) −5.31991 3.07145i −0.398744 0.230215i
\(179\) 2.91534 + 5.04952i 0.217903 + 0.377419i 0.954167 0.299276i \(-0.0967450\pi\)
−0.736264 + 0.676695i \(0.763412\pi\)
\(180\) 0 0
\(181\) 10.3892 + 8.71756i 0.772222 + 0.647971i 0.941277 0.337635i \(-0.109627\pi\)
−0.169055 + 0.985607i \(0.554072\pi\)
\(182\) 9.12776 5.26991i 0.676595 0.390632i
\(183\) −2.55358 1.47431i −0.188766 0.108984i
\(184\) 29.0574 10.5760i 2.14214 0.779674i
\(185\) 0 0
\(186\) −1.10132 + 6.24589i −0.0807526 + 0.457971i
\(187\) 1.57202 4.31908i 0.114957 0.315842i
\(188\) 1.62760 + 1.93969i 0.118705 + 0.141467i
\(189\) −5.57398 −0.405447
\(190\) 0 0
\(191\) −10.2841 −0.744128 −0.372064 0.928207i \(-0.621350\pi\)
−0.372064 + 0.928207i \(0.621350\pi\)
\(192\) −0.687288 0.819078i −0.0496007 0.0591119i
\(193\) 4.72010 12.9684i 0.339760 0.933484i −0.645702 0.763590i \(-0.723435\pi\)
0.985462 0.169895i \(-0.0543427\pi\)
\(194\) 3.24035 18.3770i 0.232644 1.31939i
\(195\) 0 0
\(196\) 19.2875 7.02006i 1.37768 0.501433i
\(197\) −6.87700 3.97044i −0.489966 0.282882i 0.234594 0.972093i \(-0.424624\pi\)
−0.724560 + 0.689211i \(0.757957\pi\)
\(198\) −6.68739 + 3.86097i −0.475252 + 0.274387i
\(199\) −20.7101 17.3778i −1.46810 1.23188i −0.917879 0.396861i \(-0.870100\pi\)
−0.550219 0.835020i \(-0.685456\pi\)
\(200\) 0 0
\(201\) −1.26857 2.19723i −0.0894781 0.154981i
\(202\) −4.75903 2.74763i −0.334844 0.193322i
\(203\) 2.43804 + 6.69846i 0.171117 + 0.470140i
\(204\) 1.93969 + 11.0005i 0.135806 + 0.770192i
\(205\) 0 0
\(206\) −29.6844 10.8042i −2.06821 0.752766i
\(207\) −8.37879 9.98545i −0.582366 0.694037i
\(208\) 18.0351i 1.25051i
\(209\) 3.90760 3.37662i 0.270295 0.233566i
\(210\) 0 0
\(211\) −6.18345 + 5.18853i −0.425686 + 0.357193i −0.830321 0.557285i \(-0.811843\pi\)
0.404635 + 0.914478i \(0.367399\pi\)
\(212\) −4.44129 + 12.2023i −0.305029 + 0.838060i
\(213\) 4.45826 + 0.786112i 0.305475 + 0.0538635i
\(214\) −2.93717 16.6575i −0.200781 1.13868i
\(215\) 0 0
\(216\) 11.1074 19.2386i 0.755764 1.30902i
\(217\) 5.09170 2.93969i 0.345647 0.199559i
\(218\) 15.3863 18.3366i 1.04209 1.24191i
\(219\) 3.06418 + 2.57115i 0.207058 + 0.173742i
\(220\) 0 0
\(221\) −5.26991 + 9.12776i −0.354493 + 0.614000i
\(222\) −2.32099 6.37686i −0.155774 0.427987i
\(223\) 15.2405 2.68732i 1.02058 0.179956i 0.361773 0.932266i \(-0.382172\pi\)
0.658809 + 0.752310i \(0.271060\pi\)
\(224\) 1.22281 6.93491i 0.0817025 0.463358i
\(225\) 0 0
\(226\) −2.54189 + 2.13290i −0.169084 + 0.141878i
\(227\) 9.87258i 0.655266i −0.944805 0.327633i \(-0.893749\pi\)
0.944805 0.327633i \(-0.106251\pi\)
\(228\) −4.12122 + 11.8550i −0.272934 + 0.785119i
\(229\) −20.1189 −1.32949 −0.664746 0.747070i \(-0.731460\pi\)
−0.664746 + 0.747070i \(0.731460\pi\)
\(230\) 0 0
\(231\) −1.11334 0.405223i −0.0732524 0.0266617i
\(232\) −27.9781 4.93330i −1.83685 0.323887i
\(233\) −3.48108 + 0.613808i −0.228053 + 0.0402119i −0.286507 0.958078i \(-0.592494\pi\)
0.0584538 + 0.998290i \(0.481383\pi\)
\(234\) 16.6395 6.05628i 1.08776 0.395912i
\(235\) 0 0
\(236\) 8.68139 + 15.0366i 0.565110 + 0.978800i
\(237\) −4.11511 + 4.90420i −0.267305 + 0.318562i
\(238\) 9.67372 11.5287i 0.627054 0.747294i
\(239\) 5.98680 + 10.3694i 0.387254 + 0.670743i 0.992079 0.125615i \(-0.0400904\pi\)
−0.604825 + 0.796358i \(0.706757\pi\)
\(240\) 0 0
\(241\) −12.1236 + 4.41263i −0.780950 + 0.284243i −0.701569 0.712602i \(-0.747517\pi\)
−0.0793814 + 0.996844i \(0.525294\pi\)
\(242\) 23.9294 4.21941i 1.53824 0.271234i
\(243\) −14.1858 2.50134i −0.910021 0.160461i
\(244\) −18.7271 6.81612i −1.19888 0.436358i
\(245\) 0 0
\(246\) −16.5030 −1.05219
\(247\) −10.1691 + 6.06939i −0.647042 + 0.386186i
\(248\) 23.4320i 1.48793i
\(249\) 6.15910 5.16810i 0.390317 0.327515i
\(250\) 0 0
\(251\) 2.49407 14.1446i 0.157424 0.892798i −0.799112 0.601183i \(-0.794696\pi\)
0.956536 0.291615i \(-0.0941925\pi\)
\(252\) −17.1326 + 3.02094i −1.07925 + 0.190302i
\(253\) −2.05212 5.63816i −0.129016 0.354468i
\(254\) 18.3614 31.8029i 1.15210 1.99549i
\(255\) 0 0
\(256\) −23.3666 19.6069i −1.46042 1.22543i
\(257\) 3.19961 3.81315i 0.199586 0.237858i −0.656963 0.753923i \(-0.728159\pi\)
0.856549 + 0.516065i \(0.172604\pi\)
\(258\) −12.4555 + 7.19119i −0.775446 + 0.447704i
\(259\) −3.14543 + 5.44804i −0.195447 + 0.338525i
\(260\) 0 0
\(261\) 2.07960 + 11.7940i 0.128724 + 0.730031i
\(262\) −49.3946 8.70961i −3.05161 0.538081i
\(263\) −8.22313 + 22.5929i −0.507060 + 1.39314i 0.377196 + 0.926133i \(0.376888\pi\)
−0.884256 + 0.467002i \(0.845334\pi\)
\(264\) 3.61721 3.03520i 0.222624 0.186804i
\(265\) 0 0
\(266\) 15.8045 6.01330i 0.969038 0.368699i
\(267\) 1.58347i 0.0969070i
\(268\) −11.0225 13.1361i −0.673306 0.802415i
\(269\) −12.3204 4.48427i −0.751189 0.273411i −0.0620832 0.998071i \(-0.519774\pi\)
−0.689106 + 0.724660i \(0.741997\pi\)
\(270\) 0 0
\(271\) −4.61381 26.1662i −0.280269 1.58948i −0.721711 0.692194i \(-0.756644\pi\)
0.441443 0.897290i \(-0.354467\pi\)
\(272\) 8.80769 + 24.1989i 0.534045 + 1.46728i
\(273\) 2.35289 + 1.35844i 0.142403 + 0.0822166i
\(274\) −12.9192 22.3767i −0.780478 1.35183i
\(275\) 0 0
\(276\) 11.1702 + 9.37295i 0.672370 + 0.564185i
\(277\) 14.2987 8.25537i 0.859127 0.496017i −0.00459317 0.999989i \(-0.501462\pi\)
0.863720 + 0.503973i \(0.168129\pi\)
\(278\) −3.64111 2.10220i −0.218379 0.126081i
\(279\) 9.28194 3.37835i 0.555695 0.202256i
\(280\) 0 0
\(281\) −3.36706 + 19.0955i −0.200862 + 1.13914i 0.702958 + 0.711231i \(0.251862\pi\)
−0.903820 + 0.427913i \(0.859249\pi\)
\(282\) −0.324446 + 0.891407i −0.0193205 + 0.0530825i
\(283\) −7.27022 8.66431i −0.432170 0.515040i 0.505377 0.862899i \(-0.331353\pi\)
−0.937547 + 0.347859i \(0.886909\pi\)
\(284\) 30.5972 1.81561
\(285\) 0 0
\(286\) 8.15064 0.481958
\(287\) 9.83375 + 11.7194i 0.580468 + 0.691775i
\(288\) 4.04633 11.1172i 0.238433 0.655088i
\(289\) 0.338678 1.92074i 0.0199222 0.112985i
\(290\) 0 0
\(291\) 4.52007 1.64517i 0.264971 0.0964416i
\(292\) 23.4131 + 13.5175i 1.37015 + 0.791054i
\(293\) 3.37662 1.94949i 0.197264 0.113891i −0.398115 0.917336i \(-0.630335\pi\)
0.595379 + 0.803445i \(0.297002\pi\)
\(294\) 5.89053 + 4.94274i 0.343543 + 0.288267i
\(295\) 0 0
\(296\) −12.5360 21.7129i −0.728638 1.26204i
\(297\) −3.73297 2.15523i −0.216609 0.125059i
\(298\) 9.70562 + 26.6660i 0.562231 + 1.54472i
\(299\) 2.38919 + 13.5497i 0.138170 + 0.783602i
\(300\) 0 0
\(301\) 12.5287 + 4.56007i 0.722141 + 0.262838i
\(302\) −17.9717 21.4179i −1.03416 1.23246i
\(303\) 1.41653i 0.0813773i
\(304\) −4.61081 + 28.5653i −0.264448 + 1.63833i
\(305\) 0 0
\(306\) 19.3687 16.2523i 1.10724 0.929081i
\(307\) −7.92642 + 21.7777i −0.452385 + 1.24292i 0.478657 + 0.878002i \(0.341124\pi\)
−0.931041 + 0.364914i \(0.881098\pi\)
\(308\) −7.88609 1.39053i −0.449351 0.0792328i
\(309\) −1.41400 8.01919i −0.0804397 0.456196i
\(310\) 0 0
\(311\) 1.73055 2.99740i 0.0981306 0.169967i −0.812780 0.582570i \(-0.802047\pi\)
0.910911 + 0.412603i \(0.135380\pi\)
\(312\) −9.37732 + 5.41400i −0.530886 + 0.306507i
\(313\) 14.7133 17.5346i 0.831644 0.991115i −0.168341 0.985729i \(-0.553841\pi\)
0.999985 0.00538626i \(-0.00171451\pi\)
\(314\) 21.3234 + 17.8925i 1.20335 + 1.00973i
\(315\) 0 0
\(316\) −21.6348 + 37.4725i −1.21705 + 2.10799i
\(317\) 8.93378 + 24.5453i 0.501771 + 1.37860i 0.889544 + 0.456849i \(0.151022\pi\)
−0.387773 + 0.921755i \(0.626756\pi\)
\(318\) −4.79093 + 0.844770i −0.268662 + 0.0473724i
\(319\) −0.957234 + 5.42874i −0.0535948 + 0.303951i
\(320\) 0 0
\(321\) 3.34002 2.80261i 0.186422 0.156427i
\(322\) 19.6459i 1.09482i
\(323\) −10.6805 + 13.1099i −0.594277 + 0.729456i
\(324\) −23.5895 −1.31053
\(325\) 0 0
\(326\) −15.0680 5.48432i −0.834542 0.303748i
\(327\) 6.07650 + 1.07145i 0.336031 + 0.0592514i
\(328\) −60.0455 + 10.5876i −3.31546 + 0.584605i
\(329\) 0.826352 0.300767i 0.0455583 0.0165818i
\(330\) 0 0
\(331\) −9.52229 16.4931i −0.523392 0.906542i −0.999629 0.0272251i \(-0.991333\pi\)
0.476237 0.879317i \(-0.342000\pi\)
\(332\) 34.9300 41.6279i 1.91703 2.28463i
\(333\) −6.79357 + 8.09627i −0.372286 + 0.443673i
\(334\) 17.4440 + 30.2139i 0.954495 + 1.65323i
\(335\) 0 0
\(336\) 6.23783 2.27038i 0.340301 0.123860i
\(337\) 1.67555 0.295445i 0.0912731 0.0160939i −0.127825 0.991797i \(-0.540800\pi\)
0.219098 + 0.975703i \(0.429688\pi\)
\(338\) 14.0105 + 2.47044i 0.762073 + 0.134374i
\(339\) −0.803758 0.292544i −0.0436542 0.0158888i
\(340\) 0 0
\(341\) 4.54664 0.246214
\(342\) 27.9032 5.33837i 1.50883 0.288666i
\(343\) 17.8530i 0.963970i
\(344\) −40.7053 + 34.1558i −2.19468 + 1.84156i
\(345\) 0 0
\(346\) −11.1010 + 62.9570i −0.596794 + 3.38459i
\(347\) −4.82721 + 0.851167i −0.259138 + 0.0456930i −0.301708 0.953400i \(-0.597557\pi\)
0.0425697 + 0.999094i \(0.486446\pi\)
\(348\) −4.58202 12.5890i −0.245622 0.674841i
\(349\) −14.0646 + 24.3607i −0.752863 + 1.30400i 0.193566 + 0.981087i \(0.437994\pi\)
−0.946430 + 0.322910i \(0.895339\pi\)
\(350\) 0 0
\(351\) 7.57192 + 6.35359i 0.404159 + 0.339130i
\(352\) 3.50038 4.17159i 0.186571 0.222346i
\(353\) −7.20529 + 4.15998i −0.383499 + 0.221413i −0.679340 0.733824i \(-0.737734\pi\)
0.295841 + 0.955237i \(0.404400\pi\)
\(354\) −3.25237 + 5.63328i −0.172862 + 0.299405i
\(355\) 0 0
\(356\) −1.85844 10.5397i −0.0984972 0.558605i
\(357\) 3.82045 + 0.673648i 0.202200 + 0.0356532i
\(358\) −5.04952 + 13.8735i −0.266876 + 0.733235i
\(359\) −19.0967 + 16.0241i −1.00789 + 0.845718i −0.988057 0.154086i \(-0.950757\pi\)
−0.0198296 + 0.999803i \(0.506312\pi\)
\(360\) 0 0
\(361\) −17.6582 + 7.01336i −0.929380 + 0.369124i
\(362\) 34.3405i 1.80490i
\(363\) 4.02611 + 4.79813i 0.211316 + 0.251837i
\(364\) 17.2554 + 6.28044i 0.904427 + 0.329184i
\(365\) 0 0
\(366\) −1.29648 7.35273i −0.0677683 0.384333i
\(367\) −0.884409 2.42989i −0.0461657 0.126839i 0.914467 0.404660i \(-0.132610\pi\)
−0.960633 + 0.277821i \(0.910388\pi\)
\(368\) 29.1130 + 16.8084i 1.51762 + 0.876198i
\(369\) 12.8512 + 22.2589i 0.669005 + 1.15875i
\(370\) 0 0
\(371\) 3.45471 + 2.89884i 0.179359 + 0.150500i
\(372\) −9.56926 + 5.52481i −0.496143 + 0.286448i
\(373\) 20.2505 + 11.6917i 1.04853 + 0.605371i 0.922238 0.386622i \(-0.126358\pi\)
0.126295 + 0.991993i \(0.459691\pi\)
\(374\) 10.9363 3.98048i 0.565502 0.205826i
\(375\) 0 0
\(376\) −0.608593 + 3.45150i −0.0313858 + 0.177998i
\(377\) 4.32342 11.8785i 0.222668 0.611774i
\(378\) −9.07218 10.8118i −0.466623 0.556099i
\(379\) −25.4388 −1.30670 −0.653352 0.757054i \(-0.726638\pi\)
−0.653352 + 0.757054i \(0.726638\pi\)
\(380\) 0 0
\(381\) 9.46616 0.484966
\(382\) −16.7383 19.9479i −0.856405 1.02062i
\(383\) −9.39895 + 25.8234i −0.480264 + 1.31951i 0.429003 + 0.903303i \(0.358865\pi\)
−0.909268 + 0.416212i \(0.863357\pi\)
\(384\) 1.51202 8.57510i 0.0771600 0.437596i
\(385\) 0 0
\(386\) 32.8371 11.9517i 1.67136 0.608327i
\(387\) 19.3986 + 11.1998i 0.986088 + 0.569318i
\(388\) 28.1551 16.2554i 1.42936 0.825241i
\(389\) 2.56031 + 2.14835i 0.129813 + 0.108926i 0.705383 0.708827i \(-0.250775\pi\)
−0.575570 + 0.817753i \(0.695220\pi\)
\(390\) 0 0
\(391\) 9.82295 + 17.0138i 0.496768 + 0.860427i
\(392\) 24.6035 + 14.2049i 1.24267 + 0.717454i
\(393\) −4.42198 12.1493i −0.223060 0.612851i
\(394\) −3.49154 19.8015i −0.175901 0.997587i
\(395\) 0 0
\(396\) −12.6420 4.60132i −0.635286 0.231225i
\(397\) 8.43550 + 10.0530i 0.423365 + 0.504547i 0.934996 0.354658i \(-0.115403\pi\)
−0.511631 + 0.859206i \(0.670958\pi\)
\(398\) 68.4552i 3.43135i
\(399\) 3.37939 + 2.75314i 0.169181 + 0.137829i
\(400\) 0 0
\(401\) 13.1099 11.0005i 0.654679 0.549341i −0.253808 0.967255i \(-0.581683\pi\)
0.908487 + 0.417914i \(0.137239\pi\)
\(402\) 2.19723 6.03684i 0.109588 0.301090i
\(403\) −10.2676 1.81046i −0.511467 0.0901854i
\(404\) −1.66250 9.42853i −0.0827127 0.469087i
\(405\) 0 0
\(406\) −9.02481 + 15.6314i −0.447894 + 0.775775i
\(407\) −4.21307 + 2.43242i −0.208834 + 0.120571i
\(408\) −9.93821 + 11.8439i −0.492015 + 0.586360i
\(409\) 6.73964 + 5.65523i 0.333254 + 0.279633i 0.794024 0.607886i \(-0.207982\pi\)
−0.460770 + 0.887519i \(0.652427\pi\)
\(410\) 0 0
\(411\) 3.33022 5.76811i 0.164268 0.284520i
\(412\) −18.8234 51.7169i −0.927364 2.54791i
\(413\) 5.93842 1.04710i 0.292211 0.0515246i
\(414\) 5.73143 32.5046i 0.281684 1.59751i
\(415\) 0 0
\(416\) −9.56599 + 8.02682i −0.469011 + 0.393547i
\(417\) 1.08378i 0.0530728i
\(418\) 12.9096 + 2.08378i 0.631429 + 0.101921i
\(419\) −6.84018 −0.334165 −0.167082 0.985943i \(-0.553435\pi\)
−0.167082 + 0.985943i \(0.553435\pi\)
\(420\) 0 0
\(421\) 4.53209 + 1.64955i 0.220880 + 0.0803939i 0.450090 0.892983i \(-0.351392\pi\)
−0.229210 + 0.973377i \(0.573614\pi\)
\(422\) −20.1283 3.54916i −0.979830 0.172771i
\(423\) 1.45496 0.256549i 0.0707426 0.0124738i
\(424\) −16.8897 + 6.14733i −0.820234 + 0.298541i
\(425\) 0 0
\(426\) 5.73143 + 9.92713i 0.277689 + 0.480971i
\(427\) −4.44891 + 5.30200i −0.215298 + 0.256582i
\(428\) 18.9422 22.5744i 0.915606 1.09118i
\(429\) 1.05051 + 1.81953i 0.0507190 + 0.0878478i
\(430\) 0 0
\(431\) −1.22503 + 0.445875i −0.0590077 + 0.0214771i −0.371355 0.928491i \(-0.621107\pi\)
0.312348 + 0.949968i \(0.398885\pi\)
\(432\) 23.7837 4.19372i 1.14430 0.201770i
\(433\) 19.5227 + 3.44238i 0.938202 + 0.165430i 0.621783 0.783189i \(-0.286409\pi\)
0.316419 + 0.948620i \(0.397520\pi\)
\(434\) 13.9893 + 5.09170i 0.671509 + 0.244409i
\(435\) 0 0
\(436\) 41.7033 1.99722
\(437\) 0.320070 + 22.0719i 0.0153110 + 1.05584i
\(438\) 10.1284i 0.483952i
\(439\) 26.4800 22.2193i 1.26382 1.06047i 0.268557 0.963264i \(-0.413453\pi\)
0.995264 0.0972078i \(-0.0309912\pi\)
\(440\) 0 0
\(441\) 2.07960 11.7940i 0.0990287 0.561620i
\(442\) −26.2823 + 4.63429i −1.25012 + 0.220430i
\(443\) −5.81780 15.9843i −0.276412 0.759436i −0.997762 0.0668650i \(-0.978700\pi\)
0.721350 0.692571i \(-0.243522\pi\)
\(444\) 5.91147 10.2390i 0.280546 0.485920i
\(445\) 0 0
\(446\) 30.0180 + 25.1881i 1.42139 + 1.19269i
\(447\) −4.70193 + 5.60354i −0.222394 + 0.265038i
\(448\) −2.17355 + 1.25490i −0.102691 + 0.0592885i
\(449\) 18.7049 32.3978i 0.882737 1.52895i 0.0344512 0.999406i \(-0.489032\pi\)
0.848286 0.529539i \(-0.177635\pi\)
\(450\) 0 0
\(451\) 2.05438 + 11.6510i 0.0967369 + 0.548622i
\(452\) −5.69323 1.00387i −0.267787 0.0472181i
\(453\) 2.46497 6.77244i 0.115814 0.318197i
\(454\) 19.1498 16.0686i 0.898743 0.754135i
\(455\) 0 0
\(456\) −16.2366 + 6.17771i −0.760351 + 0.289298i
\(457\) 9.11112i 0.426200i −0.977030 0.213100i \(-0.931644\pi\)
0.977030 0.213100i \(-0.0683560\pi\)
\(458\) −32.7454 39.0244i −1.53009 1.82349i
\(459\) 13.2626 + 4.82721i 0.619047 + 0.225315i
\(460\) 0 0
\(461\) −4.24540 24.0769i −0.197728 1.12137i −0.908480 0.417929i \(-0.862756\pi\)
0.710751 0.703443i \(-0.248355\pi\)
\(462\) −1.02606 2.81908i −0.0477367 0.131155i
\(463\) 0.217134 + 0.125362i 0.0100911 + 0.00582609i 0.505037 0.863098i \(-0.331479\pi\)
−0.494946 + 0.868924i \(0.664812\pi\)
\(464\) −15.4427 26.7475i −0.716909 1.24172i
\(465\) 0 0
\(466\) −6.85638 5.75319i −0.317616 0.266511i
\(467\) −13.3037 + 7.68092i −0.615624 + 0.355431i −0.775163 0.631761i \(-0.782332\pi\)
0.159539 + 0.987192i \(0.448999\pi\)
\(468\) 26.7171 + 15.4251i 1.23500 + 0.713028i
\(469\) −5.59627 + 2.03687i −0.258412 + 0.0940541i
\(470\) 0 0
\(471\) −1.24598 + 7.06629i −0.0574116 + 0.325597i
\(472\) −8.21956 + 22.5831i −0.378336 + 1.03947i
\(473\) 6.62744 + 7.89827i 0.304730 + 0.363163i
\(474\) −16.2104 −0.744567
\(475\) 0 0
\(476\) 26.2199 1.20179
\(477\) 4.87019 + 5.80406i 0.222991 + 0.265750i
\(478\) −10.3694 + 28.4898i −0.474287 + 1.30309i
\(479\) 0.124896 0.708319i 0.00570663 0.0323639i −0.981821 0.189807i \(-0.939214\pi\)
0.987528 + 0.157443i \(0.0503250\pi\)
\(480\) 0 0
\(481\) 10.4829 3.81547i 0.477980 0.173971i
\(482\) −28.2915 16.3341i −1.28864 0.743998i
\(483\) 4.38571 2.53209i 0.199557 0.115214i
\(484\) 32.4295 + 27.2116i 1.47407 + 1.23689i
\(485\) 0 0
\(486\) −18.2369 31.5873i −0.827245 1.43283i
\(487\) 10.1731 + 5.87346i 0.460988 + 0.266152i 0.712460 0.701713i \(-0.247581\pi\)
−0.251471 + 0.967865i \(0.580914\pi\)
\(488\) −9.43442 25.9209i −0.427076 1.17338i
\(489\) −0.717759 4.07061i −0.0324582 0.184079i
\(490\) 0 0
\(491\) −0.0834734 0.0303818i −0.00376710 0.00137111i 0.340136 0.940376i \(-0.389527\pi\)
−0.343903 + 0.939005i \(0.611749\pi\)
\(492\) −18.4814 22.0253i −0.833206 0.992976i
\(493\) 18.0496i 0.812914i
\(494\) −28.3239 9.84635i −1.27435 0.443008i
\(495\) 0 0
\(496\) −19.5141 + 16.3743i −0.876211 + 0.735228i
\(497\) 3.63441 9.98545i 0.163025 0.447909i
\(498\) 20.0490 + 3.53519i 0.898419 + 0.158416i
\(499\) −2.55097 14.4673i −0.114197 0.647645i −0.987145 0.159830i \(-0.948905\pi\)
0.872947 0.487815i \(-0.162206\pi\)
\(500\) 0 0
\(501\) −4.49660 + 7.78833i −0.200893 + 0.347957i
\(502\) 31.4955 18.1839i 1.40571 0.811588i
\(503\) 3.15225 3.75671i 0.140552 0.167503i −0.691176 0.722686i \(-0.742907\pi\)
0.831728 + 0.555183i \(0.187352\pi\)
\(504\) −18.4461 15.4781i −0.821654 0.689450i
\(505\) 0 0
\(506\) 7.59627 13.1571i 0.337695 0.584905i
\(507\) 1.25427 + 3.44609i 0.0557043 + 0.153046i
\(508\) 63.0076 11.1099i 2.79551 0.492924i
\(509\) −1.11375 + 6.31640i −0.0493662 + 0.279969i −0.999491 0.0319002i \(-0.989844\pi\)
0.950125 + 0.311870i \(0.100955\pi\)
\(510\) 0 0
\(511\) 7.19253 6.03525i 0.318179 0.266984i
\(512\) 50.5553i 2.23425i
\(513\) 10.3686 + 11.9991i 0.457786 + 0.529774i
\(514\) 12.6040 0.555939
\(515\) 0 0
\(516\) −23.5462 8.57013i −1.03656 0.377279i
\(517\) 0.669713 + 0.118089i 0.0294540 + 0.00519353i
\(518\) −15.6870 + 2.76604i −0.689248 + 0.121533i
\(519\) −15.4851 + 5.63613i −0.679723 + 0.247399i
\(520\) 0 0
\(521\) 17.9067 + 31.0154i 0.784508 + 1.35881i 0.929293 + 0.369344i \(0.120418\pi\)
−0.144785 + 0.989463i \(0.546249\pi\)
\(522\) −19.4920 + 23.2297i −0.853142 + 1.01674i
\(523\) −24.9225 + 29.7015i −1.08978 + 1.29875i −0.138526 + 0.990359i \(0.544236\pi\)
−0.951258 + 0.308395i \(0.900208\pi\)
\(524\) −43.6921 75.6770i −1.90870 3.30596i
\(525\) 0 0
\(526\) −57.2071 + 20.8217i −2.49435 + 0.907869i
\(527\) −14.6610 + 2.58512i −0.638641 + 0.112610i
\(528\) 5.05542 + 0.891407i 0.220009 + 0.0387935i
\(529\) 2.48633 + 0.904950i 0.108101 + 0.0393456i
\(530\) 0 0
\(531\) 10.1307 0.439636
\(532\) 25.7247 + 14.3589i 1.11531 + 0.622538i
\(533\) 27.1293i 1.17510i
\(534\) 3.07145 2.57725i 0.132915 0.111529i
\(535\) 0 0
\(536\) 4.12155 23.3745i 0.178024 1.00962i
\(537\) −3.74789 + 0.660855i −0.161734 + 0.0285180i
\(538\) −11.3546 31.1964i −0.489530 1.34497i
\(539\) 2.75624 4.77396i 0.118720 0.205629i
\(540\) 0 0
\(541\) 7.26991 + 6.10018i 0.312558 + 0.262267i 0.785548 0.618800i \(-0.212381\pi\)
−0.472990 + 0.881068i \(0.656825\pi\)
\(542\) 43.2450 51.5374i 1.85753 2.21372i
\(543\) −7.66610 + 4.42602i −0.328984 + 0.189939i
\(544\) −8.91534 + 15.4418i −0.382242 + 0.662063i
\(545\) 0 0
\(546\) 1.19459 + 6.77487i 0.0511238 + 0.289938i
\(547\) −13.9962 2.46791i −0.598435 0.105520i −0.133779 0.991011i \(-0.542711\pi\)
−0.464657 + 0.885491i \(0.653822\pi\)
\(548\) 15.3965 42.3016i 0.657707 1.80703i
\(549\) −8.90760 + 7.47437i −0.380167 + 0.318998i
\(550\) 0 0
\(551\) 9.88460 17.7088i 0.421098 0.754418i
\(552\) 20.1830i 0.859047i
\(553\) 9.65939 + 11.5116i 0.410759 + 0.489524i
\(554\) 39.2854 + 14.2987i 1.66908 + 0.607494i
\(555\) 0 0
\(556\) −1.27197 7.21372i −0.0539437 0.305930i
\(557\) 7.70908 + 21.1805i 0.326644 + 0.897447i 0.988955 + 0.148218i \(0.0473537\pi\)
−0.662311 + 0.749229i \(0.730424\pi\)
\(558\) 21.6602 + 12.5055i 0.916949 + 0.529401i
\(559\) −11.8216 20.4756i −0.500001 0.866026i
\(560\) 0 0
\(561\) 2.29813 + 1.92836i 0.0970273 + 0.0814155i
\(562\) −42.5197 + 24.5488i −1.79358 + 1.03553i
\(563\) 37.2147 + 21.4859i 1.56841 + 0.905524i 0.996354 + 0.0853106i \(0.0271882\pi\)
0.572058 + 0.820213i \(0.306145\pi\)
\(564\) −1.55303 + 0.565258i −0.0653945 + 0.0238017i
\(565\) 0 0
\(566\) 4.97313 28.2040i 0.209036 1.18550i
\(567\) −2.80201 + 7.69846i −0.117673 + 0.323305i
\(568\) 27.2224 + 32.4424i 1.14223 + 1.36125i
\(569\) −7.42696 −0.311354 −0.155677 0.987808i \(-0.549756\pi\)
−0.155677 + 0.987808i \(0.549756\pi\)
\(570\) 0 0
\(571\) 4.04458 0.169260 0.0846301 0.996412i \(-0.473029\pi\)
0.0846301 + 0.996412i \(0.473029\pi\)
\(572\) 9.12776 + 10.8780i 0.381651 + 0.454834i
\(573\) 2.29579 6.30763i 0.0959080 0.263505i
\(574\) −6.72668 + 38.1489i −0.280766 + 1.59230i
\(575\) 0 0
\(576\) −3.96229 + 1.44215i −0.165095 + 0.0600898i
\(577\) 2.80109 + 1.61721i 0.116611 + 0.0673254i 0.557171 0.830398i \(-0.311887\pi\)
−0.440560 + 0.897723i \(0.645220\pi\)
\(578\) 4.27688 2.46926i 0.177895 0.102707i
\(579\) 6.90033 + 5.79006i 0.286768 + 0.240627i
\(580\) 0 0
\(581\) −9.43629 16.3441i −0.391483 0.678069i
\(582\) 10.5480 + 6.08987i 0.437227 + 0.252433i
\(583\) 1.19280 + 3.27719i 0.0494007 + 0.135727i
\(584\) 6.49794 + 36.8517i 0.268887 + 1.52493i
\(585\) 0 0
\(586\) 9.27719 + 3.37662i 0.383237 + 0.139487i
\(587\) 26.2311 + 31.2610i 1.08267 + 1.29028i 0.954396 + 0.298543i \(0.0965008\pi\)
0.128279 + 0.991738i \(0.459055\pi\)
\(588\) 13.3969i 0.552480i
\(589\) −15.7998 5.49254i −0.651019 0.226316i
\(590\) 0 0
\(591\) 3.97044 3.33159i 0.163322 0.137043i
\(592\) 9.32234 25.6129i 0.383146 1.05268i
\(593\) −10.8961 1.92127i −0.447449 0.0788973i −0.0546164 0.998507i \(-0.517394\pi\)
−0.392832 + 0.919610i \(0.628505\pi\)
\(594\) −1.89528 10.7487i −0.0777642 0.441023i
\(595\) 0 0
\(596\) −24.7199 + 42.8161i −1.01257 + 1.75381i
\(597\) 15.2818 8.82295i 0.625442 0.361099i
\(598\) −22.3937 + 26.6878i −0.915747 + 1.09134i
\(599\) 34.1332 + 28.6411i 1.39464 + 1.17024i 0.963419 + 0.268000i \(0.0863626\pi\)
0.431224 + 0.902245i \(0.358082\pi\)
\(600\) 0 0
\(601\) 2.49953 4.32932i 0.101958 0.176597i −0.810533 0.585693i \(-0.800823\pi\)
0.912491 + 0.409096i \(0.134156\pi\)
\(602\) 11.5465 + 31.7237i 0.470600 + 1.29296i
\(603\) −9.85337 + 1.73742i −0.401260 + 0.0707530i
\(604\) 8.45858 47.9710i 0.344175 1.95191i
\(605\) 0 0
\(606\) 2.74763 2.30553i 0.111615 0.0936558i
\(607\) 31.1881i 1.26589i 0.774199 + 0.632943i \(0.218153\pi\)
−0.774199 + 0.632943i \(0.781847\pi\)
\(608\) −17.2035 + 10.2679i −0.697692 + 0.416417i
\(609\) −4.65270 −0.188537
\(610\) 0 0
\(611\) −1.46538 0.533356i −0.0592831 0.0215773i
\(612\) 43.3813 + 7.64930i 1.75359 + 0.309205i
\(613\) −16.1209 + 2.84255i −0.651117 + 0.114809i −0.489444 0.872035i \(-0.662800\pi\)
−0.161673 + 0.986844i \(0.551689\pi\)
\(614\) −55.1430 + 20.0704i −2.22539 + 0.809975i
\(615\) 0 0
\(616\) −5.54189 9.59883i −0.223289 0.386748i
\(617\) 10.3221 12.3014i 0.415551 0.495235i −0.517145 0.855898i \(-0.673005\pi\)
0.932696 + 0.360663i \(0.117450\pi\)
\(618\) 13.2534 15.7947i 0.533128 0.635357i
\(619\) 11.9213 + 20.6483i 0.479156 + 0.829923i 0.999714 0.0239031i \(-0.00760931\pi\)
−0.520558 + 0.853826i \(0.674276\pi\)
\(620\) 0 0
\(621\) 17.3131 6.30147i 0.694753 0.252869i
\(622\) 8.63068 1.52182i 0.346059 0.0610195i
\(623\) −3.66041 0.645430i −0.146651 0.0258586i
\(624\) −11.0617 4.02611i −0.442820 0.161173i
\(625\) 0 0
\(626\) 57.9590 2.31651
\(627\) 1.19869 + 3.15048i 0.0478712 + 0.125818i
\(628\) 48.4962i 1.93521i
\(629\) 12.2023 10.2390i 0.486539 0.408255i
\(630\) 0 0
\(631\) 3.72874 21.1467i 0.148439 0.841838i −0.816103 0.577907i \(-0.803870\pi\)
0.964541 0.263931i \(-0.0850193\pi\)
\(632\) −58.9809 + 10.3999i −2.34613 + 0.413687i
\(633\) −1.80196 4.95084i −0.0716214 0.196778i
\(634\) −33.0699 + 57.2787i −1.31337 + 2.27483i
\(635\) 0 0
\(636\) −6.49273 5.44804i −0.257453 0.216029i
\(637\) −8.12538 + 9.68345i −0.321939 + 0.383672i
\(638\) −12.0881 + 6.97906i −0.478572 + 0.276303i
\(639\) 8.92633 15.4609i 0.353120 0.611622i
\(640\) 0 0
\(641\) 2.21466 + 12.5600i 0.0874738 + 0.496089i 0.996795 + 0.0799944i \(0.0254902\pi\)
−0.909322 + 0.416094i \(0.863399\pi\)
\(642\) 10.8724 + 1.91710i 0.429100 + 0.0756619i
\(643\) 9.78456 26.8828i 0.385865 1.06016i −0.582979 0.812487i \(-0.698113\pi\)
0.968845 0.247669i \(-0.0796646\pi\)
\(644\) 26.2199 22.0011i 1.03321 0.866964i
\(645\) 0 0
\(646\) −42.8127 + 0.620838i −1.68444 + 0.0244265i
\(647\) 16.7128i 0.657046i −0.944496 0.328523i \(-0.893449\pi\)
0.944496 0.328523i \(-0.106551\pi\)
\(648\) −20.9876 25.0121i −0.824472 0.982567i
\(649\) 4.38191 + 1.59489i 0.172005 + 0.0626047i
\(650\) 0 0
\(651\) 0.666374 + 3.77920i 0.0261173 + 0.148118i
\(652\) −9.55493 26.2520i −0.374200 1.02811i
\(653\) −23.3827 13.5000i −0.915035 0.528296i −0.0329874 0.999456i \(-0.510502\pi\)
−0.882048 + 0.471160i \(0.843835\pi\)
\(654\) 7.81180 + 13.5304i 0.305466 + 0.529082i
\(655\) 0 0
\(656\) −50.7772 42.6072i −1.98252 1.66353i
\(657\) 13.6609 7.88713i 0.532963 0.307706i
\(658\) 1.92836 + 1.11334i 0.0751754 + 0.0434025i
\(659\) −41.2533 + 15.0150i −1.60700 + 0.584900i −0.980844 0.194797i \(-0.937595\pi\)
−0.626157 + 0.779697i \(0.715373\pi\)
\(660\) 0 0
\(661\) −1.86777 + 10.5927i −0.0726480 + 0.412007i 0.926697 + 0.375810i \(0.122636\pi\)
−0.999345 + 0.0361971i \(0.988476\pi\)
\(662\) 16.4931 45.3144i 0.641022 1.76119i
\(663\) −4.42198 5.26991i −0.171736 0.204667i
\(664\) 75.2158 2.91894
\(665\) 0 0
\(666\) −26.7615 −1.03699
\(667\) −15.1454 18.0496i −0.586434 0.698884i
\(668\) −20.7890 + 57.1173i −0.804350 + 2.20993i
\(669\) −1.75402 + 9.94756i −0.0678144 + 0.384595i
\(670\) 0 0
\(671\) −5.02956 + 1.83061i −0.194164 + 0.0706700i
\(672\) 3.98048 + 2.29813i 0.153550 + 0.0886524i
\(673\) 4.03374 2.32888i 0.155489 0.0897717i −0.420237 0.907415i \(-0.638053\pi\)
0.575726 + 0.817643i \(0.304720\pi\)
\(674\) 3.30019 + 2.76919i 0.127119 + 0.106665i
\(675\) 0 0
\(676\) 12.3931 + 21.4654i 0.476656 + 0.825592i
\(677\) 2.83067 + 1.63429i 0.108791 + 0.0628107i 0.553408 0.832910i \(-0.313327\pi\)
−0.444617 + 0.895721i \(0.646660\pi\)
\(678\) −0.740748 2.03519i −0.0284482 0.0781609i
\(679\) −1.96064 11.1193i −0.0752423 0.426721i
\(680\) 0 0
\(681\) 6.05525 + 2.20393i 0.232038 + 0.0844549i
\(682\) 7.40008 + 8.81908i 0.283364 + 0.337700i
\(683\) 6.21894i 0.237961i 0.992897 + 0.118981i \(0.0379626\pi\)
−0.992897 + 0.118981i \(0.962037\pi\)
\(684\) 38.3730 + 31.2620i 1.46723 + 1.19533i
\(685\) 0 0
\(686\) 34.6293 29.0574i 1.32215 1.10942i
\(687\) 4.49129 12.3397i 0.171353 0.470790i
\(688\) −56.8898 10.0312i −2.16890 0.382436i
\(689\) −1.38872 7.87581i −0.0529060 0.300045i
\(690\) 0 0
\(691\) −11.1088 + 19.2409i −0.422597 + 0.731959i −0.996193 0.0871792i \(-0.972215\pi\)
0.573596 + 0.819139i \(0.305548\pi\)
\(692\) −96.4557 + 55.6887i −3.66670 + 2.11697i
\(693\) −3.00330 + 3.57919i −0.114086 + 0.135962i
\(694\) −9.50774 7.97794i −0.360909 0.302839i
\(695\) 0 0
\(696\) 9.27156 16.0588i 0.351438 0.608708i
\(697\) −13.2490 36.4013i −0.501841 1.37880i
\(698\) −70.1438 + 12.3682i −2.65498 + 0.468145i
\(699\) 0.400634 2.27211i 0.0151534 0.0859391i
\(700\) 0 0
\(701\) −21.2750 + 17.8518i −0.803544 + 0.674254i −0.949058 0.315102i \(-0.897961\pi\)
0.145513 + 0.989356i \(0.453517\pi\)
\(702\) 25.0283i 0.944631i
\(703\) 17.5791 3.36319i 0.663008 0.126845i
\(704\) −1.94087 −0.0731495
\(705\) 0 0
\(706\) −19.7964 7.20529i −0.745047 0.271175i
\(707\) −3.27449 0.577382i −0.123150 0.0217147i
\(708\) −11.1606 + 1.96791i −0.419440 + 0.0739586i
\(709\) −5.73947 + 2.08900i −0.215551 + 0.0784540i −0.447538 0.894265i \(-0.647699\pi\)
0.231988 + 0.972719i \(0.425477\pi\)
\(710\) 0 0
\(711\) 12.6233 + 21.8642i 0.473411 + 0.819972i
\(712\) 9.52190 11.3478i 0.356848 0.425275i
\(713\) −12.4918 + 14.8871i −0.467821 + 0.557527i
\(714\) 4.91147 + 8.50692i 0.183807 + 0.318364i
\(715\) 0 0
\(716\) −24.1707 + 8.79742i −0.903302 + 0.328775i
\(717\) −7.69648 + 1.35710i −0.287430 + 0.0506817i
\(718\) −62.1635 10.9611i −2.31992 0.409065i
\(719\) 36.3885 + 13.2443i 1.35706 + 0.493930i 0.915144 0.403126i \(-0.132076\pi\)
0.441917 + 0.897056i \(0.354299\pi\)
\(720\) 0 0
\(721\) −19.1138 −0.711835
\(722\) −42.3442 22.8366i −1.57589 0.849891i
\(723\) 8.42097i 0.313179i
\(724\) −45.8316 + 38.4573i −1.70332 + 1.42925i
\(725\) 0 0
\(726\) −2.75402 + 15.6188i −0.102211 + 0.579669i
\(727\) −10.9096 + 1.92366i −0.404615 + 0.0713445i −0.372252 0.928132i \(-0.621414\pi\)
−0.0323628 + 0.999476i \(0.510303\pi\)
\(728\) 8.69296 + 23.8837i 0.322183 + 0.885190i
\(729\) −3.31996 + 5.75033i −0.122961 + 0.212975i
\(730\) 0 0
\(731\) −25.8614 21.7003i −0.956520 0.802615i
\(732\) 8.36121 9.96451i 0.309039 0.368299i
\(733\) −13.6897 + 7.90373i −0.505639 + 0.291931i −0.731039 0.682335i \(-0.760964\pi\)
0.225400 + 0.974266i \(0.427631\pi\)
\(734\) 3.27379 5.67036i 0.120838 0.209297i
\(735\) 0 0
\(736\) 4.04189 + 22.9227i 0.148986 + 0.844942i
\(737\) −4.53547 0.799726i −0.167066 0.0294583i
\(738\) −22.2589 + 61.1558i −0.819360 + 2.25117i
\(739\) −1.18685 + 0.995887i −0.0436591 + 0.0366343i −0.664356 0.747416i \(-0.731294\pi\)
0.620697 + 0.784050i \(0.286850\pi\)
\(740\) 0 0
\(741\) −1.45249 7.59202i −0.0533584 0.278900i
\(742\) 11.4192i 0.419213i
\(743\) 24.5310 + 29.2349i 0.899955 + 1.07252i 0.997012 + 0.0772453i \(0.0246125\pi\)
−0.0970576 + 0.995279i \(0.530943\pi\)
\(744\) −14.3718 5.23091i −0.526896 0.191774i
\(745\) 0 0
\(746\) 10.2815 + 58.3091i 0.376431 + 2.13485i
\(747\) −10.8444 29.7946i −0.396774 1.09013i
\(748\) 17.5598 + 10.1382i 0.642050 + 0.370688i
\(749\) −5.11721 8.86327i −0.186979 0.323857i
\(750\) 0 0
\(751\) −19.4179 16.2935i −0.708568 0.594559i 0.215629 0.976475i \(-0.430820\pi\)
−0.924197 + 0.381916i \(0.875264\pi\)
\(752\) −3.29969 + 1.90508i −0.120327 + 0.0694710i
\(753\) 8.11867 + 4.68732i 0.295861 + 0.170815i
\(754\) 30.0774 10.9473i 1.09536 0.398677i
\(755\) 0 0
\(756\) 4.26991 24.2159i 0.155295 0.880723i
\(757\) −14.4916 + 39.8153i −0.526705 + 1.44711i 0.336222 + 0.941783i \(0.390851\pi\)
−0.862927 + 0.505328i \(0.831372\pi\)
\(758\) −41.4041 49.3435i −1.50386 1.79224i
\(759\) 3.91622 0.142150
\(760\) 0 0
\(761\) −2.85710 −0.103570 −0.0517848 0.998658i \(-0.516491\pi\)
−0.0517848 + 0.998658i \(0.516491\pi\)
\(762\) 15.4071 + 18.3614i 0.558139 + 0.665165i
\(763\) 4.95361 13.6099i 0.179333 0.492713i
\(764\) 7.87804 44.6786i 0.285018 1.61641i
\(765\) 0 0
\(766\) −65.3872 + 23.7990i −2.36253 + 0.859892i
\(767\) −9.26055 5.34658i −0.334379 0.193054i
\(768\) 17.2421 9.95471i 0.622169 0.359210i
\(769\) −14.6472 12.2905i −0.528193 0.443207i 0.339284 0.940684i \(-0.389815\pi\)
−0.867477 + 0.497477i \(0.834260\pi\)
\(770\) 0 0
\(771\) 1.62449 + 2.81369i 0.0585044 + 0.101333i
\(772\) 52.7247 + 30.4406i 1.89760 + 1.09558i
\(773\) −0.860130 2.36319i −0.0309367 0.0849980i 0.923263 0.384169i \(-0.125512\pi\)
−0.954199 + 0.299171i \(0.903290\pi\)
\(774\) 9.84895 + 55.8561i 0.354013 + 2.00771i
\(775\) 0 0
\(776\) 42.2854 + 15.3906i 1.51796 + 0.552491i
\(777\) −2.63933 3.14543i −0.0946854 0.112842i
\(778\) 8.46286i 0.303408i
\(779\) 6.93582 42.9694i 0.248502 1.53954i
\(780\) 0 0
\(781\) 6.29498 5.28211i 0.225252 0.189009i
\(782\) −17.0138 + 46.7452i −0.608414 + 1.67160i
\(783\) −16.6701 2.93939i −0.595741 0.105045i
\(784\) 5.36319 + 30.4162i 0.191542 + 1.08629i
\(785\) 0 0
\(786\) 16.3687 28.3514i 0.583852 1.01126i
\(787\) −2.36083 + 1.36303i −0.0841545 + 0.0485866i −0.541487 0.840709i \(-0.682138\pi\)
0.457332 + 0.889296i \(0.348805\pi\)
\(788\) 22.5175 26.8353i 0.802152 0.955967i
\(789\) −12.0214 10.0872i −0.427974 0.359112i
\(790\) 0 0
\(791\) −1.00387 + 1.73875i −0.0356935 + 0.0618230i
\(792\) −6.36884 17.4982i −0.226307 0.621773i
\(793\) 12.0872 2.13129i 0.429228 0.0756844i
\(794\) −5.77022 + 32.7245i −0.204777 + 1.16135i
\(795\) 0 0
\(796\) 91.3620 76.6618i 3.23824 2.71720i
\(797\) 22.0327i 0.780439i −0.920722 0.390219i \(-0.872399\pi\)
0.920722 0.390219i \(-0.127601\pi\)
\(798\) 0.160035 + 11.0360i 0.00566518 + 0.390669i
\(799\) −2.22668 −0.0787743
\(800\) 0 0
\(801\) −5.86794 2.13575i −0.207333 0.0754632i
\(802\) 42.6753 + 7.52481i 1.50692 + 0.265710i
\(803\) 7.15052 1.26083i 0.252336 0.0444937i
\(804\) 10.5175 3.82807i 0.370925 0.135006i
\(805\) 0 0
\(806\) −13.1998 22.8627i −0.464943 0.805306i
\(807\) 5.50077 6.55556i 0.193636 0.230767i
\(808\) 8.51800 10.1514i 0.299662 0.357124i
\(809\) 27.3603 + 47.3893i 0.961935 + 1.66612i 0.717633 + 0.696422i \(0.245226\pi\)
0.244302 + 0.969699i \(0.421441\pi\)
\(810\) 0 0
\(811\) 2.17112 0.790224i 0.0762384 0.0277485i −0.303619 0.952793i \(-0.598195\pi\)
0.379858 + 0.925045i \(0.375973\pi\)
\(812\) −30.9688 + 5.46064i −1.08679 + 0.191631i
\(813\) 17.0788 + 3.01145i 0.598979 + 0.105616i
\(814\) −11.5753 4.21307i −0.405715 0.147668i
\(815\) 0 0
\(816\) −16.8084 −0.588412
\(817\) −13.4892 35.4531i −0.471927 1.24035i
\(818\) 22.2772i 0.778906i
\(819\) 8.20755 6.88695i 0.286795 0.240650i
\(820\) 0 0
\(821\) 0.192944 1.09424i 0.00673379 0.0381892i −0.981256 0.192710i \(-0.938272\pi\)
0.987990 + 0.154521i \(0.0493834\pi\)
\(822\) 16.6086 2.92855i 0.579292 0.102145i
\(823\) −7.06191 19.4024i −0.246163 0.676327i −0.999818 0.0190572i \(-0.993934\pi\)
0.753656 0.657270i \(-0.228289\pi\)
\(824\) 38.0886 65.9714i 1.32688 2.29822i
\(825\) 0 0
\(826\) 11.6964 + 9.81445i 0.406970 + 0.341488i
\(827\) 23.3367 27.8116i 0.811495 0.967103i −0.188392 0.982094i \(-0.560328\pi\)
0.999888 + 0.0149913i \(0.00477207\pi\)
\(828\) 49.7999 28.7520i 1.73066 0.999200i
\(829\) −3.57486 + 6.19183i −0.124160 + 0.215051i −0.921404 0.388606i \(-0.872957\pi\)
0.797244 + 0.603657i \(0.206290\pi\)
\(830\) 0 0
\(831\) 1.87134 + 10.6129i 0.0649161 + 0.368157i
\(832\) 4.38306 + 0.772852i 0.151955 + 0.0267938i
\(833\) −6.17334 + 16.9611i −0.213893 + 0.587667i
\(834\) 2.10220 1.76395i 0.0727931 0.0610807i
\(835\) 0 0
\(836\) 11.6762 + 19.5630i 0.403829 + 0.676602i
\(837\) 13.9614i 0.482577i
\(838\) −11.1331 13.2679i −0.384585 0.458330i
\(839\) −32.5197 11.8362i −1.12270 0.408631i −0.287065 0.957911i \(-0.592680\pi\)
−0.835638 + 0.549280i \(0.814902\pi\)
\(840\) 0 0
\(841\) −1.27672 7.24065i −0.0440249 0.249678i
\(842\) 4.17680 + 11.4757i 0.143942 + 0.395477i
\(843\) −10.9604 6.32800i −0.377497 0.217948i
\(844\) −17.8045 30.8384i −0.612857 1.06150i
\(845\) 0 0
\(846\) 2.86571 + 2.40462i 0.0985253 + 0.0826725i
\(847\) 12.7326 7.35117i 0.437497 0.252589i
\(848\) −16.9220 9.76991i −0.581103 0.335500i
\(849\) 6.93717 2.52492i 0.238083 0.0866551i
\(850\) 0 0
\(851\) 3.61081 20.4779i 0.123777 0.701975i
\(852\) −6.83045 + 18.7665i −0.234007 + 0.642930i
\(853\) 21.3732 + 25.4716i 0.731805 + 0.872132i 0.995721 0.0924142i \(-0.0294584\pi\)
−0.263915 + 0.964546i \(0.585014\pi\)
\(854\) −17.5253 −0.599703
\(855\) 0 0
\(856\) 40.7888 1.39413
\(857\) 2.49800 + 2.97700i 0.0853299 + 0.101692i 0.807020 0.590524i \(-0.201079\pi\)
−0.721690 + 0.692216i \(0.756634\pi\)
\(858\) −1.81953 + 4.99912i −0.0621178 + 0.170667i
\(859\) −0.287866 + 1.63257i −0.00982187 + 0.0557026i −0.989325 0.145727i \(-0.953448\pi\)
0.979503 + 0.201430i \(0.0645589\pi\)
\(860\) 0 0
\(861\) −9.38326 + 3.41523i −0.319780 + 0.116391i
\(862\) −2.85872 1.65048i −0.0973684 0.0562156i
\(863\) −45.6558 + 26.3594i −1.55414 + 0.897284i −0.556343 + 0.830953i \(0.687796\pi\)
−0.997798 + 0.0663308i \(0.978871\pi\)
\(864\) 12.8097 + 10.7487i 0.435796 + 0.365677i
\(865\) 0 0
\(866\) 25.0979 + 43.4709i 0.852862 + 1.47720i
\(867\) 1.10246 + 0.636507i 0.0374416 + 0.0216169i
\(868\) 8.87089 + 24.3726i 0.301098 + 0.827259i
\(869\) 2.01795 + 11.4444i 0.0684543 + 0.388224i
\(870\) 0 0
\(871\) 9.92396 + 3.61203i 0.336261 + 0.122389i
\(872\) 37.1035 + 44.2183i 1.25648 + 1.49742i
\(873\) 18.9691i 0.642008i
\(874\) −42.2918 + 36.5450i −1.43054 + 1.23615i
\(875\) 0 0
\(876\) −13.5175 + 11.3426i −0.456715 + 0.383230i
\(877\) 7.24735 19.9119i 0.244726 0.672378i −0.755133 0.655572i \(-0.772428\pi\)
0.999859 0.0168069i \(-0.00535004\pi\)
\(878\) 86.1974 + 15.1989i 2.90902 + 0.512939i
\(879\) 0.441914 + 2.50622i 0.0149054 + 0.0845327i
\(880\) 0 0
\(881\) −16.0505 + 27.8003i −0.540755 + 0.936616i 0.458106 + 0.888898i \(0.348528\pi\)
−0.998861 + 0.0477179i \(0.984805\pi\)
\(882\) 26.2615 15.1621i 0.884271 0.510534i
\(883\) 30.4018 36.2315i 1.02310 1.21929i 0.0476989 0.998862i \(-0.484811\pi\)
0.975404 0.220425i \(-0.0707444\pi\)
\(884\) −35.6181 29.8872i −1.19797 1.00521i
\(885\) 0 0
\(886\) 21.5355 37.3007i 0.723501 1.25314i
\(887\) 3.61278 + 9.92602i 0.121305 + 0.333283i 0.985451 0.169958i \(-0.0543631\pi\)
−0.864146 + 0.503241i \(0.832141\pi\)
\(888\) 16.1159 2.84167i 0.540815 0.0953602i
\(889\) 3.85844 21.8823i 0.129408 0.733909i
\(890\) 0 0
\(891\) −4.85323 + 4.07234i −0.162589 + 0.136429i
\(892\) 68.2704i 2.28586i
\(893\) −2.18463 1.21941i −0.0731059 0.0408059i
\(894\) −18.5220 −0.619468
\(895\) 0 0
\(896\) −19.2062 6.99049i −0.641634 0.233536i
\(897\) −8.84397 1.55943i −0.295291 0.0520679i
\(898\) 93.2857 16.4488i 3.11298 0.548903i
\(899\) 16.7780 6.10668i 0.559576 0.203669i
\(900\) 0 0
\(901\) −5.70961 9.88933i −0.190215 0.329461i
\(902\) −19.2556 + 22.9479i −0.641141 + 0.764081i
\(903\) −5.59375 + 6.66637i −0.186148 + 0.221843i
\(904\) −4.00088 6.92972i −0.133067 0.230479i
\(905\) 0 0
\(906\) 17.1484 6.24152i 0.569718 0.207360i
\(907\) 42.2684 7.45306i 1.40350 0.247475i 0.579919 0.814674i \(-0.303084\pi\)
0.823580 + 0.567200i \(0.191973\pi\)
\(908\) 42.8910 + 7.56283i 1.42339 + 0.250981i
\(909\) −5.24928 1.91058i −0.174107 0.0633699i
\(910\) 0 0
\(911\) −55.1411 −1.82691 −0.913454 0.406942i \(-0.866595\pi\)
−0.913454 + 0.406942i \(0.866595\pi\)
\(912\) −16.4910 9.20486i −0.546071 0.304803i
\(913\) 14.5945i 0.483008i
\(914\) 17.6728 14.8292i 0.584563 0.490507i
\(915\) 0 0
\(916\) 15.4119 87.4055i 0.509225 2.88796i
\(917\) −29.8872 + 5.26991i −0.986961 + 0.174028i
\(918\) 12.2229 + 33.5822i 0.403416 + 1.10838i
\(919\) −12.2788 + 21.2676i −0.405041 + 0.701552i −0.994326 0.106373i \(-0.966076\pi\)
0.589285 + 0.807925i \(0.299410\pi\)
\(920\) 0 0
\(921\) −11.5876 9.72319i −0.381826 0.320390i
\(922\) 39.7920 47.4222i 1.31048 1.56177i
\(923\) −16.3192 + 9.42190i −0.537154 + 0.310126i
\(924\) 2.61334 4.52644i 0.0859726 0.148909i
\(925\) 0 0
\(926\) 0.110242 + 0.625213i 0.00362277 + 0.0205458i
\(927\) −31.6242 5.57620i −1.03867 0.183146i
\(928\) 7.31412 20.0954i 0.240098 0.659663i
\(929\) 17.0654 14.3195i 0.559896 0.469809i −0.318379 0.947963i \(-0.603139\pi\)
0.878276 + 0.478155i \(0.158694\pi\)
\(930\) 0 0
\(931\) −15.3452 + 13.2601i −0.502920 + 0.434581i
\(932\) 15.5936i 0.510785i
\(933\) 1.45211 + 1.73055i 0.0475398 + 0.0566557i
\(934\) −36.5517 13.3037i −1.19601 0.435312i
\(935\) 0 0
\(936\) 7.41493 + 42.0522i 0.242365 + 1.37452i
\(937\) −3.26687 8.97565i −0.106724 0.293222i 0.874823 0.484443i \(-0.160978\pi\)
−0.981547 + 0.191221i \(0.938755\pi\)
\(938\) −13.0594 7.53983i −0.426403 0.246184i
\(939\) 7.47013 + 12.9386i 0.243779 + 0.422237i
\(940\) 0 0
\(941\) −42.6883 35.8197i −1.39160 1.16769i −0.964688 0.263394i \(-0.915158\pi\)
−0.426909 0.904295i \(-0.640398\pi\)
\(942\) −15.7344 + 9.08424i −0.512654 + 0.295981i
\(943\) −43.7933 25.2841i −1.42610 0.823362i
\(944\) −24.5510 + 8.93582i −0.799066 + 0.290836i
\(945\) 0 0
\(946\) −4.53343 + 25.7104i −0.147395 + 0.835916i
\(947\) 9.24919 25.4119i 0.300558 0.825777i −0.693845 0.720125i \(-0.744085\pi\)
0.994403 0.105653i \(-0.0336931\pi\)
\(948\) −18.1537 21.6348i −0.589605 0.702664i
\(949\) −16.6500 −0.540482
\(950\) 0 0
\(951\) −17.0490 −0.552852
\(952\) 23.3279 + 27.8011i 0.756062 + 0.901040i
\(953\) 7.91128 21.7361i 0.256272 0.704100i −0.743118 0.669161i \(-0.766654\pi\)
0.999389 0.0349398i \(-0.0111240\pi\)
\(954\) −3.33140 + 18.8933i −0.107858 + 0.611694i
\(955\) 0 0
\(956\) −49.6357 + 18.0659i −1.60533 + 0.584293i
\(957\) −3.11598 1.79901i −0.100725 0.0581538i
\(958\) 1.57720 0.910597i 0.0509570 0.0294200i
\(959\) −11.9764 10.0494i −0.386737 0.324511i
\(960\) 0 0
\(961\) 8.13681 + 14.0934i 0.262478 + 0.454625i
\(962\) 24.4628 + 14.1236i 0.788713 + 0.455363i
\(963\) −5.88079 16.1573i −0.189506 0.520663i
\(964\) −9.88326 56.0507i −0.318318 1.80527i
\(965\) 0 0
\(966\) 12.0496 + 4.38571i 0.387690 + 0.141108i
\(967\) −25.0913 29.9026i −0.806881 0.961603i 0.192927 0.981213i \(-0.438202\pi\)
−0.999808 + 0.0196101i \(0.993758\pi\)
\(968\) 58.5954i 1.88333i
\(969\) −5.65657 9.47740i −0.181715 0.304458i
\(970\) 0 0
\(971\) −31.5631 + 26.4845i −1.01291 + 0.849930i −0.988720 0.149778i \(-0.952144\pi\)
−0.0241869 + 0.999707i \(0.507700\pi\)
\(972\) 21.7339 59.7135i 0.697117 1.91531i
\(973\) −2.50530 0.441752i −0.0803162 0.0141619i
\(974\) 5.16503 + 29.2923i 0.165498 + 0.938587i
\(975\) 0 0
\(976\) 14.9941 25.9705i 0.479948 0.831295i
\(977\) −19.4802 + 11.2469i −0.623227 + 0.359821i −0.778125 0.628110i \(-0.783829\pi\)
0.154897 + 0.987931i \(0.450495\pi\)
\(978\) 6.72752 8.01754i 0.215122 0.256373i
\(979\) −2.20187 1.84759i −0.0703720 0.0590491i
\(980\) 0 0
\(981\) 12.1664 21.0728i 0.388442 0.672802i
\(982\) −0.0769295 0.211362i −0.00245492 0.00674484i
\(983\) 43.8694 7.73536i 1.39922 0.246720i 0.577395 0.816465i \(-0.304069\pi\)
0.821821 + 0.569746i \(0.192958\pi\)
\(984\) 6.91060 39.1919i 0.220302 1.24939i
\(985\) 0 0
\(986\) 35.0107 29.3775i 1.11497 0.935570i
\(987\) 0.573978i 0.0182699i
\(988\) −18.5782 48.8285i −0.591052 1.55344i
\(989\) −44.0702 −1.40135
\(990\) 0 0
\(991\) 42.5959 + 15.5036i 1.35310 + 0.492489i 0.913915 0.405907i \(-0.133044\pi\)
0.439187 + 0.898395i \(0.355266\pi\)
\(992\) −17.3702 3.06283i −0.551504 0.0972451i
\(993\) 12.2416 2.15853i 0.388476 0.0684988i
\(994\) 25.2841 9.20264i 0.801961 0.291890i
\(995\) 0 0
\(996\) 17.7344 + 30.7169i 0.561937 + 0.973303i
\(997\) −6.74357 + 8.03667i −0.213571 + 0.254524i −0.862185 0.506593i \(-0.830905\pi\)
0.648614 + 0.761117i \(0.275349\pi\)
\(998\) 23.9101 28.4950i 0.756862 0.901994i
\(999\) −7.46926 12.9371i −0.236317 0.409313i
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.u.a.424.2 12
5.2 odd 4 19.2.e.a.6.1 6
5.3 odd 4 475.2.l.a.101.1 6
5.4 even 2 inner 475.2.u.a.424.1 12
15.2 even 4 171.2.u.c.82.1 6
19.16 even 9 inner 475.2.u.a.149.1 12
20.7 even 4 304.2.u.b.177.1 6
35.2 odd 12 931.2.x.a.557.1 6
35.12 even 12 931.2.x.b.557.1 6
35.17 even 12 931.2.v.a.177.1 6
35.27 even 4 931.2.w.a.785.1 6
35.32 odd 12 931.2.v.b.177.1 6
95.2 even 36 361.2.e.a.62.1 6
95.7 odd 12 361.2.e.f.28.1 6
95.12 even 12 361.2.e.b.28.1 6
95.17 odd 36 361.2.e.g.62.1 6
95.22 even 36 361.2.e.h.54.1 6
95.23 odd 36 9025.2.a.bd.1.3 3
95.27 even 12 361.2.e.a.99.1 6
95.32 even 36 361.2.c.h.292.1 6
95.37 even 4 361.2.e.h.234.1 6
95.42 odd 36 361.2.a.g.1.1 3
95.47 odd 36 361.2.c.i.68.3 6
95.52 even 36 361.2.e.b.245.1 6
95.53 even 36 9025.2.a.x.1.1 3
95.54 even 18 inner 475.2.u.a.149.2 12
95.62 odd 36 361.2.e.f.245.1 6
95.67 even 36 361.2.c.h.68.1 6
95.72 even 36 361.2.a.h.1.3 3
95.73 odd 36 475.2.l.a.301.1 6
95.82 odd 36 361.2.c.i.292.3 6
95.87 odd 12 361.2.e.g.99.1 6
95.92 odd 36 19.2.e.a.16.1 yes 6
285.92 even 36 171.2.u.c.73.1 6
285.137 even 36 3249.2.a.z.1.3 3
285.167 odd 36 3249.2.a.s.1.1 3
380.167 odd 36 5776.2.a.bi.1.2 3
380.187 even 36 304.2.u.b.225.1 6
380.327 even 36 5776.2.a.br.1.2 3
665.187 even 36 931.2.v.a.263.1 6
665.282 odd 36 931.2.v.b.263.1 6
665.377 even 36 931.2.w.a.491.1 6
665.472 even 36 931.2.x.b.814.1 6
665.662 odd 36 931.2.x.a.814.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
19.2.e.a.6.1 6 5.2 odd 4
19.2.e.a.16.1 yes 6 95.92 odd 36
171.2.u.c.73.1 6 285.92 even 36
171.2.u.c.82.1 6 15.2 even 4
304.2.u.b.177.1 6 20.7 even 4
304.2.u.b.225.1 6 380.187 even 36
361.2.a.g.1.1 3 95.42 odd 36
361.2.a.h.1.3 3 95.72 even 36
361.2.c.h.68.1 6 95.67 even 36
361.2.c.h.292.1 6 95.32 even 36
361.2.c.i.68.3 6 95.47 odd 36
361.2.c.i.292.3 6 95.82 odd 36
361.2.e.a.62.1 6 95.2 even 36
361.2.e.a.99.1 6 95.27 even 12
361.2.e.b.28.1 6 95.12 even 12
361.2.e.b.245.1 6 95.52 even 36
361.2.e.f.28.1 6 95.7 odd 12
361.2.e.f.245.1 6 95.62 odd 36
361.2.e.g.62.1 6 95.17 odd 36
361.2.e.g.99.1 6 95.87 odd 12
361.2.e.h.54.1 6 95.22 even 36
361.2.e.h.234.1 6 95.37 even 4
475.2.l.a.101.1 6 5.3 odd 4
475.2.l.a.301.1 6 95.73 odd 36
475.2.u.a.149.1 12 19.16 even 9 inner
475.2.u.a.149.2 12 95.54 even 18 inner
475.2.u.a.424.1 12 5.4 even 2 inner
475.2.u.a.424.2 12 1.1 even 1 trivial
931.2.v.a.177.1 6 35.17 even 12
931.2.v.a.263.1 6 665.187 even 36
931.2.v.b.177.1 6 35.32 odd 12
931.2.v.b.263.1 6 665.282 odd 36
931.2.w.a.491.1 6 665.377 even 36
931.2.w.a.785.1 6 35.27 even 4
931.2.x.a.557.1 6 35.2 odd 12
931.2.x.a.814.1 6 665.662 odd 36
931.2.x.b.557.1 6 35.12 even 12
931.2.x.b.814.1 6 665.472 even 36
3249.2.a.s.1.1 3 285.167 odd 36
3249.2.a.z.1.3 3 285.137 even 36
5776.2.a.bi.1.2 3 380.167 odd 36
5776.2.a.br.1.2 3 380.327 even 36
9025.2.a.x.1.1 3 95.53 even 36
9025.2.a.bd.1.3 3 95.23 odd 36