Properties

Label 187.2.g.f.69.4
Level $187$
Weight $2$
Character 187.69
Analytic conductor $1.493$
Analytic rank $0$
Dimension $36$
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] = [187,2,Mod(69,187)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(187, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("187.69");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 187 = 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 187.g (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.49320251780\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 69.4
Character \(\chi\) \(=\) 187.69
Dual form 187.2.g.f.103.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.28769 + 0.935561i) q^{2} +(0.00348887 + 0.0107376i) q^{3} +(0.164835 - 0.507309i) q^{4} +(2.53950 + 1.84506i) q^{5} +(-0.0145383 - 0.0105627i) q^{6} +(-0.112651 + 0.346704i) q^{7} +(-0.721344 - 2.22007i) q^{8} +(2.42695 - 1.76328i) q^{9} +O(q^{10})\) \(q+(-1.28769 + 0.935561i) q^{2} +(0.00348887 + 0.0107376i) q^{3} +(0.164835 - 0.507309i) q^{4} +(2.53950 + 1.84506i) q^{5} +(-0.0145383 - 0.0105627i) q^{6} +(-0.112651 + 0.346704i) q^{7} +(-0.721344 - 2.22007i) q^{8} +(2.42695 - 1.76328i) q^{9} -4.99625 q^{10} +(0.725045 + 3.23640i) q^{11} +0.00602239 q^{12} +(-4.04521 + 2.93902i) q^{13} +(-0.179303 - 0.551839i) q^{14} +(-0.0109516 + 0.0337055i) q^{15} +(3.86896 + 2.81096i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(-1.47550 + 4.54111i) q^{18} +(1.47444 + 4.53787i) q^{19} +(1.35461 - 0.984183i) q^{20} -0.00411581 q^{21} +(-3.96148 - 3.48916i) q^{22} -1.68786 q^{23} +(0.0213216 - 0.0154911i) q^{24} +(1.49976 + 4.61578i) q^{25} +(2.45934 - 7.56908i) q^{26} +(0.0548028 + 0.0398165i) q^{27} +(0.157317 + 0.114298i) q^{28} +(2.90382 - 8.93704i) q^{29} +(-0.0174313 - 0.0536480i) q^{30} +(-6.32486 + 4.59528i) q^{31} -2.94321 q^{32} +(-0.0322218 + 0.0190767i) q^{33} +1.59167 q^{34} +(-0.925767 + 0.672609i) q^{35} +(-0.494483 - 1.52186i) q^{36} +(2.53206 - 7.79288i) q^{37} +(-6.14408 - 4.46393i) q^{38} +(-0.0456714 - 0.0331822i) q^{39} +(2.26430 - 6.96880i) q^{40} +(-0.686013 - 2.11133i) q^{41} +(0.00529988 - 0.00385059i) q^{42} +9.31357 q^{43} +(1.76137 + 0.165650i) q^{44} +9.41660 q^{45} +(2.17344 - 1.57910i) q^{46} +(-1.25302 - 3.85638i) q^{47} +(-0.0166848 + 0.0513506i) q^{48} +(5.55561 + 4.03638i) q^{49} +(-6.24956 - 4.54057i) q^{50} +(0.00348887 - 0.0107376i) q^{51} +(0.824199 + 2.53662i) q^{52} +(10.1419 - 7.36855i) q^{53} -0.107820 q^{54} +(-4.13010 + 9.55661i) q^{55} +0.850967 q^{56} +(-0.0435819 + 0.0316641i) q^{57} +(4.62193 + 14.2248i) q^{58} +(1.12397 - 3.45922i) q^{59} +(0.0152939 + 0.0111117i) q^{60} +(-4.65285 - 3.38049i) q^{61} +(3.84529 - 11.8346i) q^{62} +(0.337939 + 1.04007i) q^{63} +(-3.94799 + 2.86838i) q^{64} -15.6955 q^{65} +(0.0236442 - 0.0547102i) q^{66} -8.99814 q^{67} +(-0.431543 + 0.313534i) q^{68} +(-0.00588874 - 0.0181237i) q^{69} +(0.562833 - 1.73222i) q^{70} +(4.79716 + 3.48534i) q^{71} +(-5.66527 - 4.11606i) q^{72} +(-2.27187 + 6.99211i) q^{73} +(4.03021 + 12.4037i) q^{74} +(-0.0443301 + 0.0322077i) q^{75} +2.54514 q^{76} +(-1.20375 - 0.113208i) q^{77} +0.0898545 q^{78} +(5.70100 - 4.14202i) q^{79} +(4.63885 + 14.2769i) q^{80} +(2.78080 - 8.55842i) q^{81} +(2.85865 + 2.07693i) q^{82} +(-10.5136 - 7.63855i) q^{83} +(-0.000678428 + 0.00208799i) q^{84} +(-0.970004 - 2.98537i) q^{85} +(-11.9930 + 8.71341i) q^{86} +0.106094 q^{87} +(6.66203 - 3.94421i) q^{88} +0.993612 q^{89} +(-12.1256 + 8.80980i) q^{90} +(-0.563273 - 1.73358i) q^{91} +(-0.278218 + 0.856267i) q^{92} +(-0.0714091 - 0.0518818i) q^{93} +(5.22138 + 3.79355i) q^{94} +(-4.62828 + 14.2444i) q^{95} +(-0.0102685 - 0.0316031i) q^{96} +(-10.3805 + 7.54187i) q^{97} -10.9302 q^{98} +(7.46633 + 6.57613i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9} - 10 q^{10} + 3 q^{11} + 28 q^{12} - 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 9 q^{17} + 2 q^{18} + 10 q^{19} + 19 q^{20} - 50 q^{21} - 25 q^{22} + 38 q^{23} - 17 q^{24} - 28 q^{25} + 20 q^{26} - 16 q^{27} + 31 q^{28} - 45 q^{29} + 68 q^{30} - 13 q^{31} - 40 q^{32} - 29 q^{33} - 4 q^{34} + 13 q^{35} - 25 q^{36} + q^{37} + 65 q^{38} - 34 q^{39} - 54 q^{40} + 37 q^{41} + 28 q^{42} - 8 q^{43} - 2 q^{44} + 42 q^{45} + 22 q^{46} - 35 q^{47} + 48 q^{48} - 2 q^{49} - 49 q^{50} - q^{51} + 56 q^{52} + 58 q^{53} - 58 q^{54} - 19 q^{55} - 28 q^{56} + 9 q^{57} - 52 q^{58} + 16 q^{59} + 97 q^{60} - 14 q^{61} - 64 q^{62} + 34 q^{63} - 33 q^{64} - 42 q^{65} - 28 q^{66} + 54 q^{67} - 14 q^{68} + 19 q^{69} + 4 q^{70} + 25 q^{71} - 72 q^{72} + 8 q^{73} + 84 q^{74} + 30 q^{75} - 140 q^{76} - 31 q^{77} - 48 q^{78} + 19 q^{79} - 19 q^{80} + 56 q^{81} + 48 q^{82} + 42 q^{83} - 91 q^{84} - 9 q^{85} + 30 q^{86} - 32 q^{87} + 126 q^{88} + 12 q^{89} + 160 q^{90} - 59 q^{91} + 69 q^{92} - 40 q^{93} - 77 q^{94} - 11 q^{95} + 192 q^{96} - 49 q^{97} - 212 q^{98} + 38 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).

\(n\) \(35\) \(122\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.28769 + 0.935561i −0.910533 + 0.661541i −0.941150 0.337990i \(-0.890253\pi\)
0.0306163 + 0.999531i \(0.490253\pi\)
\(3\) 0.00348887 + 0.0107376i 0.00201430 + 0.00619938i 0.952059 0.305916i \(-0.0989626\pi\)
−0.950044 + 0.312115i \(0.898963\pi\)
\(4\) 0.164835 0.507309i 0.0824173 0.253654i
\(5\) 2.53950 + 1.84506i 1.13570 + 0.825135i 0.986514 0.163674i \(-0.0523346\pi\)
0.149186 + 0.988809i \(0.452335\pi\)
\(6\) −0.0145383 0.0105627i −0.00593524 0.00431220i
\(7\) −0.112651 + 0.346704i −0.0425781 + 0.131042i −0.970086 0.242762i \(-0.921947\pi\)
0.927508 + 0.373804i \(0.121947\pi\)
\(8\) −0.721344 2.22007i −0.255034 0.784913i
\(9\) 2.42695 1.76328i 0.808983 0.587760i
\(10\) −4.99625 −1.57995
\(11\) 0.725045 + 3.23640i 0.218609 + 0.975812i
\(12\) 0.00602239 0.00173851
\(13\) −4.04521 + 2.93902i −1.12194 + 0.815137i −0.984502 0.175373i \(-0.943887\pi\)
−0.137438 + 0.990510i \(0.543887\pi\)
\(14\) −0.179303 0.551839i −0.0479208 0.147485i
\(15\) −0.0109516 + 0.0337055i −0.00282768 + 0.00870271i
\(16\) 3.86896 + 2.81096i 0.967240 + 0.702741i
\(17\) −0.809017 0.587785i −0.196215 0.142559i
\(18\) −1.47550 + 4.54111i −0.347778 + 1.07035i
\(19\) 1.47444 + 4.53787i 0.338261 + 1.04106i 0.965094 + 0.261905i \(0.0843508\pi\)
−0.626833 + 0.779154i \(0.715649\pi\)
\(20\) 1.35461 0.984183i 0.302900 0.220070i
\(21\) −0.00411581 −0.000898144
\(22\) −3.96148 3.48916i −0.844591 0.743891i
\(23\) −1.68786 −0.351944 −0.175972 0.984395i \(-0.556307\pi\)
−0.175972 + 0.984395i \(0.556307\pi\)
\(24\) 0.0213216 0.0154911i 0.00435226 0.00316210i
\(25\) 1.49976 + 4.61578i 0.299952 + 0.923156i
\(26\) 2.45934 7.56908i 0.482317 1.48442i
\(27\) 0.0548028 + 0.0398165i 0.0105468 + 0.00766270i
\(28\) 0.157317 + 0.114298i 0.0297302 + 0.0216002i
\(29\) 2.90382 8.93704i 0.539226 1.65957i −0.195110 0.980781i \(-0.562506\pi\)
0.734336 0.678786i \(-0.237494\pi\)
\(30\) −0.0174313 0.0536480i −0.00318250 0.00979474i
\(31\) −6.32486 + 4.59528i −1.13598 + 0.825337i −0.986554 0.163436i \(-0.947742\pi\)
−0.149425 + 0.988773i \(0.547742\pi\)
\(32\) −2.94321 −0.520291
\(33\) −0.0322218 + 0.0190767i −0.00560909 + 0.00332082i
\(34\) 1.59167 0.272969
\(35\) −0.925767 + 0.672609i −0.156483 + 0.113692i
\(36\) −0.494483 1.52186i −0.0824138 0.253644i
\(37\) 2.53206 7.79288i 0.416268 1.28114i −0.494843 0.868982i \(-0.664774\pi\)
0.911111 0.412160i \(-0.135226\pi\)
\(38\) −6.14408 4.46393i −0.996701 0.724146i
\(39\) −0.0456714 0.0331822i −0.00731327 0.00531340i
\(40\) 2.26430 6.96880i 0.358017 1.10186i
\(41\) −0.686013 2.11133i −0.107137 0.329735i 0.883089 0.469206i \(-0.155460\pi\)
−0.990226 + 0.139471i \(0.955460\pi\)
\(42\) 0.00529988 0.00385059i 0.000817790 0.000594159i
\(43\) 9.31357 1.42031 0.710153 0.704047i \(-0.248626\pi\)
0.710153 + 0.704047i \(0.248626\pi\)
\(44\) 1.76137 + 0.165650i 0.265536 + 0.0249726i
\(45\) 9.41660 1.40374
\(46\) 2.17344 1.57910i 0.320457 0.232825i
\(47\) −1.25302 3.85638i −0.182771 0.562512i 0.817132 0.576451i \(-0.195563\pi\)
−0.999903 + 0.0139394i \(0.995563\pi\)
\(48\) −0.0166848 + 0.0513506i −0.00240825 + 0.00741183i
\(49\) 5.55561 + 4.03638i 0.793658 + 0.576626i
\(50\) −6.24956 4.54057i −0.883822 0.642134i
\(51\) 0.00348887 0.0107376i 0.000488540 0.00150357i
\(52\) 0.824199 + 2.53662i 0.114296 + 0.351766i
\(53\) 10.1419 7.36855i 1.39310 1.01215i 0.397585 0.917565i \(-0.369848\pi\)
0.995517 0.0945830i \(-0.0301518\pi\)
\(54\) −0.107820 −0.0146724
\(55\) −4.13010 + 9.55661i −0.556902 + 1.28861i
\(56\) 0.850967 0.113715
\(57\) −0.0435819 + 0.0316641i −0.00577256 + 0.00419401i
\(58\) 4.62193 + 14.2248i 0.606889 + 1.86781i
\(59\) 1.12397 3.45922i 0.146328 0.450352i −0.850851 0.525407i \(-0.823913\pi\)
0.997179 + 0.0750549i \(0.0239132\pi\)
\(60\) 0.0152939 + 0.0111117i 0.00197443 + 0.00143451i
\(61\) −4.65285 3.38049i −0.595736 0.432828i 0.248627 0.968599i \(-0.420021\pi\)
−0.844363 + 0.535772i \(0.820021\pi\)
\(62\) 3.84529 11.8346i 0.488352 1.50299i
\(63\) 0.337939 + 1.04007i 0.0425763 + 0.131036i
\(64\) −3.94799 + 2.86838i −0.493498 + 0.358548i
\(65\) −15.6955 −1.94679
\(66\) 0.0236442 0.0547102i 0.00291040 0.00673436i
\(67\) −8.99814 −1.09930 −0.549649 0.835396i \(-0.685238\pi\)
−0.549649 + 0.835396i \(0.685238\pi\)
\(68\) −0.431543 + 0.313534i −0.0523322 + 0.0380216i
\(69\) −0.00588874 0.0181237i −0.000708921 0.00218183i
\(70\) 0.562833 1.73222i 0.0672714 0.207040i
\(71\) 4.79716 + 3.48534i 0.569318 + 0.413634i 0.834857 0.550466i \(-0.185550\pi\)
−0.265539 + 0.964100i \(0.585550\pi\)
\(72\) −5.66527 4.11606i −0.667659 0.485082i
\(73\) −2.27187 + 6.99211i −0.265903 + 0.818364i 0.725581 + 0.688136i \(0.241571\pi\)
−0.991484 + 0.130228i \(0.958429\pi\)
\(74\) 4.03021 + 12.4037i 0.468502 + 1.44190i
\(75\) −0.0443301 + 0.0322077i −0.00511880 + 0.00371903i
\(76\) 2.54514 0.291948
\(77\) −1.20375 0.113208i −0.137180 0.0129013i
\(78\) 0.0898545 0.0101740
\(79\) 5.70100 4.14202i 0.641412 0.466013i −0.218923 0.975742i \(-0.570254\pi\)
0.860335 + 0.509729i \(0.170254\pi\)
\(80\) 4.63885 + 14.2769i 0.518639 + 1.59621i
\(81\) 2.78080 8.55842i 0.308978 0.950935i
\(82\) 2.85865 + 2.07693i 0.315685 + 0.229359i
\(83\) −10.5136 7.63855i −1.15401 0.838440i −0.165004 0.986293i \(-0.552764\pi\)
−0.989009 + 0.147853i \(0.952764\pi\)
\(84\) −0.000678428 0.00208799i −7.40226e−5 0.000227818i
\(85\) −0.970004 2.98537i −0.105212 0.323808i
\(86\) −11.9930 + 8.71341i −1.29324 + 0.939591i
\(87\) 0.106094 0.0113745
\(88\) 6.66203 3.94421i 0.710175 0.420454i
\(89\) 0.993612 0.105323 0.0526613 0.998612i \(-0.483230\pi\)
0.0526613 + 0.998612i \(0.483230\pi\)
\(90\) −12.1256 + 8.80980i −1.27816 + 0.928634i
\(91\) −0.563273 1.73358i −0.0590470 0.181728i
\(92\) −0.278218 + 0.856267i −0.0290062 + 0.0892721i
\(93\) −0.0714091 0.0518818i −0.00740478 0.00537989i
\(94\) 5.22138 + 3.79355i 0.538544 + 0.391275i
\(95\) −4.62828 + 14.2444i −0.474851 + 1.46144i
\(96\) −0.0102685 0.0316031i −0.00104802 0.00322548i
\(97\) −10.3805 + 7.54187i −1.05398 + 0.765761i −0.972965 0.230952i \(-0.925816\pi\)
−0.0810141 + 0.996713i \(0.525816\pi\)
\(98\) −10.9302 −1.10411
\(99\) 7.46633 + 6.57613i 0.750395 + 0.660926i
\(100\) 2.58884 0.258884
\(101\) 5.77069 4.19265i 0.574205 0.417184i −0.262425 0.964952i \(-0.584522\pi\)
0.836630 + 0.547768i \(0.184522\pi\)
\(102\) 0.00555314 + 0.0170908i 0.000549842 + 0.00169224i
\(103\) 3.97535 12.2349i 0.391703 1.20554i −0.539797 0.841795i \(-0.681499\pi\)
0.931500 0.363742i \(-0.118501\pi\)
\(104\) 9.44282 + 6.86061i 0.925944 + 0.672738i
\(105\) −0.0104521 0.00759391i −0.00102002 0.000741090i
\(106\) −6.16593 + 18.9768i −0.598889 + 1.84319i
\(107\) 0.518107 + 1.59457i 0.0500873 + 0.154153i 0.972972 0.230924i \(-0.0741749\pi\)
−0.922884 + 0.385077i \(0.874175\pi\)
\(108\) 0.0292327 0.0212388i 0.00281291 0.00204370i
\(109\) 8.86758 0.849360 0.424680 0.905343i \(-0.360387\pi\)
0.424680 + 0.905343i \(0.360387\pi\)
\(110\) −3.62251 16.1699i −0.345393 1.54174i
\(111\) 0.0925113 0.00878078
\(112\) −1.41042 + 1.02473i −0.133272 + 0.0968276i
\(113\) 2.47171 + 7.60713i 0.232519 + 0.715619i 0.997441 + 0.0714960i \(0.0227773\pi\)
−0.764922 + 0.644123i \(0.777223\pi\)
\(114\) 0.0264962 0.0815470i 0.00248160 0.00763758i
\(115\) −4.28633 3.11420i −0.399703 0.290401i
\(116\) −4.05519 2.94627i −0.376515 0.273554i
\(117\) −4.63520 + 14.2657i −0.428525 + 1.31886i
\(118\) 1.78899 + 5.50593i 0.164690 + 0.506862i
\(119\) 0.294924 0.214275i 0.0270357 0.0196426i
\(120\) 0.0827283 0.00755203
\(121\) −9.94862 + 4.69308i −0.904420 + 0.426643i
\(122\) 9.15408 0.828771
\(123\) 0.0202773 0.0147323i 0.00182834 0.00132837i
\(124\) 1.28867 + 3.96612i 0.115726 + 0.356168i
\(125\) 0.142283 0.437901i 0.0127262 0.0391671i
\(126\) −1.40821 1.02312i −0.125453 0.0911470i
\(127\) −0.0451792 0.0328246i −0.00400901 0.00291272i 0.585779 0.810471i \(-0.300789\pi\)
−0.589788 + 0.807558i \(0.700789\pi\)
\(128\) 4.21924 12.9855i 0.372931 1.14776i
\(129\) 0.0324939 + 0.100006i 0.00286093 + 0.00880502i
\(130\) 20.2109 14.6841i 1.77261 1.28788i
\(131\) 1.06635 0.0931678 0.0465839 0.998914i \(-0.485167\pi\)
0.0465839 + 0.998914i \(0.485167\pi\)
\(132\) 0.00436650 + 0.0194909i 0.000380055 + 0.00169646i
\(133\) −1.73940 −0.150825
\(134\) 11.5868 8.41831i 1.00095 0.727231i
\(135\) 0.0657080 + 0.202228i 0.00565525 + 0.0174051i
\(136\) −0.721344 + 2.22007i −0.0618548 + 0.190369i
\(137\) −8.41936 6.11702i −0.719314 0.522613i 0.166851 0.985982i \(-0.446640\pi\)
−0.886165 + 0.463370i \(0.846640\pi\)
\(138\) 0.0245387 + 0.0178284i 0.00208887 + 0.00151765i
\(139\) 0.900584 2.77171i 0.0763865 0.235093i −0.905571 0.424194i \(-0.860557\pi\)
0.981958 + 0.189101i \(0.0605573\pi\)
\(140\) 0.188622 + 0.580519i 0.0159415 + 0.0490628i
\(141\) 0.0370369 0.0269089i 0.00311907 0.00226614i
\(142\) −9.43799 −0.792019
\(143\) −12.4448 10.9610i −1.04069 0.916606i
\(144\) 14.3463 1.19552
\(145\) 23.8636 17.3379i 1.98177 1.43984i
\(146\) −3.61607 11.1291i −0.299268 0.921054i
\(147\) −0.0239585 + 0.0737366i −0.00197606 + 0.00608169i
\(148\) −3.53603 2.56907i −0.290660 0.211177i
\(149\) 7.32688 + 5.32329i 0.600242 + 0.436101i 0.845965 0.533239i \(-0.179025\pi\)
−0.245723 + 0.969340i \(0.579025\pi\)
\(150\) 0.0269511 0.0829471i 0.00220055 0.00677260i
\(151\) −6.26267 19.2745i −0.509649 1.56854i −0.792812 0.609467i \(-0.791384\pi\)
0.283163 0.959072i \(-0.408616\pi\)
\(152\) 9.01081 6.54673i 0.730873 0.531010i
\(153\) −2.99987 −0.242525
\(154\) 1.65597 0.980406i 0.133442 0.0790034i
\(155\) −24.5406 −1.97115
\(156\) −0.0243618 + 0.0176999i −0.00195051 + 0.00141713i
\(157\) −0.543073 1.67141i −0.0433420 0.133393i 0.927044 0.374953i \(-0.122341\pi\)
−0.970386 + 0.241560i \(0.922341\pi\)
\(158\) −3.46600 + 10.6673i −0.275740 + 0.848641i
\(159\) 0.114505 + 0.0831926i 0.00908082 + 0.00659760i
\(160\) −7.47429 5.43039i −0.590894 0.429310i
\(161\) 0.190139 0.585189i 0.0149851 0.0461194i
\(162\) 4.42612 + 13.6222i 0.347748 + 1.07026i
\(163\) −13.7013 + 9.95460i −1.07317 + 0.779704i −0.976479 0.215610i \(-0.930826\pi\)
−0.0966912 + 0.995314i \(0.530826\pi\)
\(164\) −1.18418 −0.0924686
\(165\) −0.117025 0.0110057i −0.00911037 0.000856795i
\(166\) 20.6845 1.60543
\(167\) −2.34022 + 1.70027i −0.181092 + 0.131571i −0.674638 0.738149i \(-0.735700\pi\)
0.493547 + 0.869719i \(0.335700\pi\)
\(168\) 0.00296892 + 0.00913739i 0.000229057 + 0.000704965i
\(169\) 3.70869 11.4142i 0.285284 0.878013i
\(170\) 4.04205 + 2.93672i 0.310011 + 0.225236i
\(171\) 11.5799 + 8.41332i 0.885540 + 0.643382i
\(172\) 1.53520 4.72486i 0.117058 0.360267i
\(173\) 2.03089 + 6.25044i 0.154406 + 0.475212i 0.998100 0.0616117i \(-0.0196240\pi\)
−0.843694 + 0.536824i \(0.819624\pi\)
\(174\) −0.136616 + 0.0992573i −0.0103568 + 0.00752467i
\(175\) −1.76926 −0.133743
\(176\) −6.29225 + 14.5596i −0.474296 + 1.09747i
\(177\) 0.0410652 0.00308665
\(178\) −1.27946 + 0.929584i −0.0958998 + 0.0696753i
\(179\) −0.0593318 0.182604i −0.00443467 0.0136485i 0.948815 0.315833i \(-0.102284\pi\)
−0.953249 + 0.302185i \(0.902284\pi\)
\(180\) 1.55218 4.77712i 0.115693 0.356066i
\(181\) −15.3281 11.1365i −1.13933 0.827769i −0.152301 0.988334i \(-0.548668\pi\)
−0.987025 + 0.160565i \(0.948668\pi\)
\(182\) 2.34718 + 1.70533i 0.173985 + 0.126407i
\(183\) 0.0200653 0.0617548i 0.00148327 0.00456504i
\(184\) 1.21753 + 3.74717i 0.0897575 + 0.276245i
\(185\) 20.8085 15.1183i 1.52987 1.11152i
\(186\) 0.140491 0.0103013
\(187\) 1.31574 3.04448i 0.0962162 0.222634i
\(188\) −2.16292 −0.157747
\(189\) −0.0199781 + 0.0145150i −0.00145320 + 0.00105581i
\(190\) −7.36669 22.6724i −0.534436 1.64483i
\(191\) −5.12112 + 15.7612i −0.370551 + 1.14044i 0.575880 + 0.817534i \(0.304660\pi\)
−0.946431 + 0.322905i \(0.895340\pi\)
\(192\) −0.0445737 0.0323847i −0.00321683 0.00233716i
\(193\) 8.10382 + 5.88777i 0.583326 + 0.423811i 0.839922 0.542708i \(-0.182601\pi\)
−0.256596 + 0.966519i \(0.582601\pi\)
\(194\) 6.31097 19.4232i 0.453101 1.39450i
\(195\) −0.0547596 0.168533i −0.00392141 0.0120689i
\(196\) 2.96345 2.15307i 0.211675 0.153791i
\(197\) −2.26647 −0.161479 −0.0807397 0.996735i \(-0.525728\pi\)
−0.0807397 + 0.996735i \(0.525728\pi\)
\(198\) −15.7667 1.48279i −1.12049 0.105378i
\(199\) 8.59133 0.609023 0.304512 0.952509i \(-0.401507\pi\)
0.304512 + 0.952509i \(0.401507\pi\)
\(200\) 9.16551 6.65913i 0.648099 0.470872i
\(201\) −0.0313934 0.0966188i −0.00221432 0.00681497i
\(202\) −3.50837 + 10.7977i −0.246848 + 0.759721i
\(203\) 2.77139 + 2.01353i 0.194514 + 0.141322i
\(204\) −0.00487221 0.00353987i −0.000341123 0.000247841i
\(205\) 2.15339 6.62747i 0.150400 0.462882i
\(206\) 6.32745 + 19.4739i 0.440854 + 1.35681i
\(207\) −4.09636 + 2.97618i −0.284716 + 0.206859i
\(208\) −23.9122 −1.65802
\(209\) −13.6173 + 8.06205i −0.941931 + 0.557664i
\(210\) 0.0205636 0.00141903
\(211\) −17.4174 + 12.6545i −1.19906 + 0.871170i −0.994192 0.107619i \(-0.965677\pi\)
−0.204870 + 0.978789i \(0.565677\pi\)
\(212\) −2.06639 6.35968i −0.141920 0.436785i
\(213\) −0.0206877 + 0.0636701i −0.00141750 + 0.00436260i
\(214\) −2.15898 1.56859i −0.147585 0.107226i
\(215\) 23.6519 + 17.1841i 1.61304 + 1.17194i
\(216\) 0.0488638 0.150387i 0.00332476 0.0102326i
\(217\) −0.880701 2.71052i −0.0597859 0.184002i
\(218\) −11.4187 + 8.29616i −0.773371 + 0.561887i
\(219\) −0.0830051 −0.00560896
\(220\) 4.16737 + 3.67049i 0.280964 + 0.247465i
\(221\) 5.00016 0.336347
\(222\) −0.119126 + 0.0865499i −0.00799520 + 0.00580885i
\(223\) −3.36897 10.3686i −0.225603 0.694334i −0.998230 0.0594739i \(-0.981058\pi\)
0.772627 0.634860i \(-0.218942\pi\)
\(224\) 0.331555 1.02042i 0.0221530 0.0681798i
\(225\) 11.7787 + 8.55776i 0.785250 + 0.570517i
\(226\) −10.2997 7.48318i −0.685127 0.497774i
\(227\) 1.32255 4.07038i 0.0877804 0.270160i −0.897525 0.440964i \(-0.854636\pi\)
0.985305 + 0.170804i \(0.0546365\pi\)
\(228\) 0.00887967 + 0.0273288i 0.000588070 + 0.00180989i
\(229\) −12.8769 + 9.35560i −0.850928 + 0.618235i −0.925402 0.378988i \(-0.876272\pi\)
0.0744738 + 0.997223i \(0.476272\pi\)
\(230\) 8.43299 0.556055
\(231\) −0.00298415 0.0133204i −0.000196343 0.000876420i
\(232\) −21.9355 −1.44014
\(233\) −11.7385 + 8.52855i −0.769018 + 0.558724i −0.901663 0.432439i \(-0.857653\pi\)
0.132645 + 0.991164i \(0.457653\pi\)
\(234\) −7.37772 22.7063i −0.482296 1.48436i
\(235\) 3.93321 12.1052i 0.256575 0.789655i
\(236\) −1.56962 1.14040i −0.102174 0.0742335i
\(237\) 0.0643656 + 0.0467643i 0.00418099 + 0.00303767i
\(238\) −0.179303 + 0.551839i −0.0116225 + 0.0357704i
\(239\) 1.78360 + 5.48935i 0.115371 + 0.355077i 0.992024 0.126047i \(-0.0402289\pi\)
−0.876653 + 0.481123i \(0.840229\pi\)
\(240\) −0.137116 + 0.0996207i −0.00885080 + 0.00643049i
\(241\) 15.0632 0.970303 0.485152 0.874430i \(-0.338764\pi\)
0.485152 + 0.874430i \(0.338764\pi\)
\(242\) 8.42007 15.3508i 0.541263 0.986784i
\(243\) 0.304819 0.0195541
\(244\) −2.48190 + 1.80321i −0.158888 + 0.115439i
\(245\) 6.66112 + 20.5008i 0.425563 + 1.30975i
\(246\) −0.0123279 + 0.0379413i −0.000785997 + 0.00241905i
\(247\) −19.3013 14.0232i −1.22811 0.892277i
\(248\) 14.7642 + 10.7268i 0.937530 + 0.681156i
\(249\) 0.0453396 0.139541i 0.00287328 0.00884304i
\(250\) 0.226467 + 0.696995i 0.0143231 + 0.0440818i
\(251\) −1.53636 + 1.11623i −0.0969742 + 0.0704559i −0.635216 0.772335i \(-0.719089\pi\)
0.538242 + 0.842791i \(0.319089\pi\)
\(252\) 0.583340 0.0367469
\(253\) −1.22378 5.46261i −0.0769382 0.343431i
\(254\) 0.0888862 0.00557722
\(255\) 0.0286716 0.0208311i 0.00179548 0.00130450i
\(256\) 3.69964 + 11.3863i 0.231228 + 0.711646i
\(257\) 0.396910 1.22156i 0.0247586 0.0761991i −0.937914 0.346868i \(-0.887245\pi\)
0.962672 + 0.270669i \(0.0872450\pi\)
\(258\) −0.135404 0.0983764i −0.00842985 0.00612465i
\(259\) 2.41659 + 1.75575i 0.150159 + 0.109097i
\(260\) −2.58716 + 7.96246i −0.160449 + 0.493811i
\(261\) −8.71109 26.8100i −0.539203 1.65950i
\(262\) −1.37313 + 0.997639i −0.0848324 + 0.0616343i
\(263\) 21.2568 1.31075 0.655375 0.755304i \(-0.272511\pi\)
0.655375 + 0.755304i \(0.272511\pi\)
\(264\) 0.0655945 + 0.0577737i 0.00403706 + 0.00355573i
\(265\) 39.3509 2.41731
\(266\) 2.23980 1.62731i 0.137331 0.0997768i
\(267\) 0.00346658 + 0.0106691i 0.000212152 + 0.000652935i
\(268\) −1.48320 + 4.56483i −0.0906011 + 0.278842i
\(269\) 0.167278 + 0.121534i 0.0101991 + 0.00741007i 0.592873 0.805296i \(-0.297994\pi\)
−0.582674 + 0.812706i \(0.697994\pi\)
\(270\) −0.273808 0.198934i −0.0166635 0.0121067i
\(271\) −7.82050 + 24.0690i −0.475061 + 1.46209i 0.370814 + 0.928707i \(0.379079\pi\)
−0.845875 + 0.533381i \(0.820921\pi\)
\(272\) −1.47781 4.54824i −0.0896055 0.275777i
\(273\) 0.0166493 0.0120964i 0.00100766 0.000732110i
\(274\) 16.5644 1.00069
\(275\) −13.8511 + 8.20047i −0.835255 + 0.494507i
\(276\) −0.0101650 −0.000611859
\(277\) 11.1915 8.13108i 0.672431 0.488550i −0.198407 0.980120i \(-0.563577\pi\)
0.870838 + 0.491570i \(0.163577\pi\)
\(278\) 1.43343 + 4.41165i 0.0859716 + 0.264593i
\(279\) −7.24734 + 22.3050i −0.433887 + 1.33537i
\(280\) 2.16103 + 1.57008i 0.129147 + 0.0938305i
\(281\) −15.7974 11.4775i −0.942393 0.684688i 0.00660280 0.999978i \(-0.497898\pi\)
−0.948995 + 0.315290i \(0.897898\pi\)
\(282\) −0.0225171 + 0.0693005i −0.00134087 + 0.00412678i
\(283\) 2.11190 + 6.49975i 0.125539 + 0.386370i 0.993999 0.109390i \(-0.0348896\pi\)
−0.868460 + 0.495760i \(0.834890\pi\)
\(284\) 2.55888 1.85914i 0.151842 0.110319i
\(285\) −0.169098 −0.0100165
\(286\) 26.2797 + 2.47151i 1.55395 + 0.146143i
\(287\) 0.809287 0.0477707
\(288\) −7.14301 + 5.18970i −0.420906 + 0.305806i
\(289\) 0.309017 + 0.951057i 0.0181775 + 0.0559445i
\(290\) −14.5082 + 44.6517i −0.851953 + 2.62204i
\(291\) −0.117198 0.0851494i −0.00687028 0.00499155i
\(292\) 3.17267 + 2.30508i 0.185667 + 0.134895i
\(293\) −0.542866 + 1.67077i −0.0317146 + 0.0976075i −0.965661 0.259806i \(-0.916341\pi\)
0.933946 + 0.357414i \(0.116341\pi\)
\(294\) −0.0381340 0.117364i −0.00222402 0.00684483i
\(295\) 9.23677 6.71091i 0.537786 0.390724i
\(296\) −19.1272 −1.11175
\(297\) −0.0891279 + 0.206233i −0.00517173 + 0.0119668i
\(298\) −14.4150 −0.835039
\(299\) 6.82776 4.96066i 0.394860 0.286882i
\(300\) 0.00903212 + 0.0277980i 0.000521470 + 0.00160492i
\(301\) −1.04918 + 3.22905i −0.0604739 + 0.186120i
\(302\) 26.0969 + 18.9605i 1.50171 + 1.09105i
\(303\) 0.0651524 + 0.0473360i 0.00374291 + 0.00271938i
\(304\) −7.05123 + 21.7015i −0.404416 + 1.24466i
\(305\) −5.57873 17.1696i −0.319437 0.983126i
\(306\) 3.86290 2.80656i 0.220827 0.160441i
\(307\) −18.4396 −1.05240 −0.526201 0.850360i \(-0.676384\pi\)
−0.526201 + 0.850360i \(0.676384\pi\)
\(308\) −0.255851 + 0.592013i −0.0145785 + 0.0337331i
\(309\) 0.145243 0.00826259
\(310\) 31.6006 22.9592i 1.79479 1.30399i
\(311\) −5.83674 17.9636i −0.330971 1.01862i −0.968673 0.248341i \(-0.920115\pi\)
0.637702 0.770284i \(-0.279885\pi\)
\(312\) −0.0407220 + 0.125329i −0.00230543 + 0.00709538i
\(313\) −1.65974 1.20587i −0.0938142 0.0681600i 0.539889 0.841736i \(-0.318466\pi\)
−0.633704 + 0.773576i \(0.718466\pi\)
\(314\) 2.26301 + 1.64417i 0.127709 + 0.0927861i
\(315\) −1.06079 + 3.26477i −0.0597687 + 0.183949i
\(316\) −1.16156 3.57491i −0.0653428 0.201105i
\(317\) −14.0184 + 10.1849i −0.787349 + 0.572043i −0.907176 0.420752i \(-0.861766\pi\)
0.119826 + 0.992795i \(0.461766\pi\)
\(318\) −0.225278 −0.0126330
\(319\) 31.0293 + 2.91818i 1.73731 + 0.163387i
\(320\) −15.3183 −0.856317
\(321\) −0.0153143 + 0.0111265i −0.000854761 + 0.000621020i
\(322\) 0.302639 + 0.931428i 0.0168654 + 0.0519065i
\(323\) 1.47444 4.53787i 0.0820402 0.252494i
\(324\) −3.88339 2.82145i −0.215744 0.156747i
\(325\) −19.6327 14.2640i −1.08903 0.791224i
\(326\) 8.32991 25.6368i 0.461351 1.41989i
\(327\) 0.0309379 + 0.0952170i 0.00171087 + 0.00526551i
\(328\) −4.19245 + 3.04599i −0.231489 + 0.168187i
\(329\) 1.47818 0.0814946
\(330\) 0.160988 0.0953119i 0.00886211 0.00524675i
\(331\) 24.8844 1.36777 0.683885 0.729590i \(-0.260289\pi\)
0.683885 + 0.729590i \(0.260289\pi\)
\(332\) −5.60810 + 4.07453i −0.307785 + 0.223619i
\(333\) −7.59586 23.3777i −0.416251 1.28109i
\(334\) 1.42277 4.37883i 0.0778504 0.239599i
\(335\) −22.8508 16.6021i −1.24847 0.907069i
\(336\) −0.0159239 0.0115694i −0.000868721 0.000631163i
\(337\) −6.26447 + 19.2801i −0.341248 + 1.05025i 0.622314 + 0.782767i \(0.286193\pi\)
−0.963562 + 0.267485i \(0.913807\pi\)
\(338\) 5.90301 + 18.1676i 0.321081 + 0.988187i
\(339\) −0.0730592 + 0.0530806i −0.00396803 + 0.00288294i
\(340\) −1.67439 −0.0908067
\(341\) −19.4580 17.1380i −1.05371 0.928076i
\(342\) −22.7825 −1.23194
\(343\) −4.08974 + 2.97137i −0.220825 + 0.160439i
\(344\) −6.71829 20.6768i −0.362226 1.11482i
\(345\) 0.0184847 0.0568902i 0.000995185 0.00306287i
\(346\) −8.46282 6.14860i −0.454964 0.330551i
\(347\) 25.4175 + 18.4669i 1.36448 + 0.991356i 0.998145 + 0.0608745i \(0.0193889\pi\)
0.366339 + 0.930481i \(0.380611\pi\)
\(348\) 0.0174879 0.0538223i 0.000937452 0.00288518i
\(349\) 1.27756 + 3.93193i 0.0683864 + 0.210472i 0.979410 0.201884i \(-0.0647063\pi\)
−0.911023 + 0.412355i \(0.864706\pi\)
\(350\) 2.27825 1.65525i 0.121778 0.0884768i
\(351\) −0.338710 −0.0180790
\(352\) −2.13396 9.52541i −0.113740 0.507706i
\(353\) −10.2593 −0.546048 −0.273024 0.962007i \(-0.588024\pi\)
−0.273024 + 0.962007i \(0.588024\pi\)
\(354\) −0.0528792 + 0.0384190i −0.00281050 + 0.00204195i
\(355\) 5.75175 + 17.7021i 0.305271 + 0.939528i
\(356\) 0.163782 0.504068i 0.00868041 0.0267155i
\(357\) 0.00332976 + 0.00241921i 0.000176230 + 0.000128038i
\(358\) 0.247238 + 0.179629i 0.0130670 + 0.00949370i
\(359\) −0.301624 + 0.928303i −0.0159191 + 0.0489939i −0.958701 0.284417i \(-0.908200\pi\)
0.942781 + 0.333411i \(0.108200\pi\)
\(360\) −6.79261 20.9055i −0.358002 1.10182i
\(361\) −3.04696 + 2.21375i −0.160366 + 0.116513i
\(362\) 30.1566 1.58500
\(363\) −0.0851021 0.0904512i −0.00446670 0.00474746i
\(364\) −0.972304 −0.0509626
\(365\) −18.6703 + 13.5647i −0.977247 + 0.710011i
\(366\) 0.0319374 + 0.0982933i 0.00166940 + 0.00513787i
\(367\) −7.48352 + 23.0319i −0.390637 + 1.20226i 0.541671 + 0.840590i \(0.317792\pi\)
−0.932308 + 0.361665i \(0.882208\pi\)
\(368\) −6.53028 4.74452i −0.340414 0.247325i
\(369\) −5.38779 3.91446i −0.280477 0.203779i
\(370\) −12.6508 + 38.9352i −0.657685 + 2.02415i
\(371\) 1.41221 + 4.34633i 0.0733181 + 0.225650i
\(372\) −0.0380908 + 0.0276746i −0.00197491 + 0.00143486i
\(373\) 16.3450 0.846311 0.423155 0.906057i \(-0.360922\pi\)
0.423155 + 0.906057i \(0.360922\pi\)
\(374\) 1.15403 + 5.15129i 0.0596736 + 0.266367i
\(375\) 0.00519844 0.000268446
\(376\) −7.65759 + 5.56356i −0.394910 + 0.286919i
\(377\) 14.5196 + 44.6866i 0.747796 + 2.30148i
\(378\) 0.0121460 0.0373815i 0.000624723 0.00192270i
\(379\) −5.37438 3.90472i −0.276063 0.200572i 0.441135 0.897441i \(-0.354576\pi\)
−0.717199 + 0.696869i \(0.754576\pi\)
\(380\) 6.46339 + 4.69593i 0.331565 + 0.240896i
\(381\) 0.000194835 0 0.000599640i 9.98169e−6 0 3.07205e-5i
\(382\) −8.15114 25.0866i −0.417049 1.28354i
\(383\) −1.98010 + 1.43863i −0.101178 + 0.0735104i −0.637224 0.770679i \(-0.719917\pi\)
0.536046 + 0.844189i \(0.319917\pi\)
\(384\) 0.154154 0.00786663
\(385\) −2.84806 2.50848i −0.145150 0.127844i
\(386\) −15.9436 −0.811506
\(387\) 22.6036 16.4224i 1.14900 0.834800i
\(388\) 2.11499 + 6.50927i 0.107372 + 0.330458i
\(389\) 5.56665 17.1324i 0.282240 0.868646i −0.704972 0.709235i \(-0.749040\pi\)
0.987212 0.159411i \(-0.0509595\pi\)
\(390\) 0.228186 + 0.165787i 0.0115546 + 0.00839493i
\(391\) 1.36551 + 0.992101i 0.0690568 + 0.0501727i
\(392\) 4.95355 15.2455i 0.250192 0.770012i
\(393\) 0.00372037 + 0.0114501i 0.000187668 + 0.000577583i
\(394\) 2.91851 2.12042i 0.147032 0.106825i
\(395\) 22.1200 1.11298
\(396\) 4.56684 2.70376i 0.229492 0.135869i
\(397\) 8.93729 0.448550 0.224275 0.974526i \(-0.427999\pi\)
0.224275 + 0.974526i \(0.427999\pi\)
\(398\) −11.0630 + 8.03771i −0.554536 + 0.402894i
\(399\) −0.00606853 0.0186770i −0.000303807 0.000935020i
\(400\) −7.17229 + 22.0740i −0.358614 + 1.10370i
\(401\) 13.0041 + 9.44805i 0.649395 + 0.471813i 0.863065 0.505093i \(-0.168542\pi\)
−0.213670 + 0.976906i \(0.568542\pi\)
\(402\) 0.130818 + 0.0950446i 0.00652459 + 0.00474039i
\(403\) 12.0798 37.1778i 0.601737 1.85196i
\(404\) −1.17576 3.61861i −0.0584962 0.180033i
\(405\) 22.8526 16.6034i 1.13556 0.825030i
\(406\) −5.45247 −0.270602
\(407\) 27.0568 + 2.54458i 1.34115 + 0.126130i
\(408\) −0.0263550 −0.00130477
\(409\) −5.52798 + 4.01631i −0.273341 + 0.198594i −0.716008 0.698092i \(-0.754033\pi\)
0.442667 + 0.896686i \(0.354033\pi\)
\(410\) 3.42750 + 10.5487i 0.169272 + 0.520966i
\(411\) 0.0363084 0.111746i 0.00179096 0.00551201i
\(412\) −5.55158 4.03346i −0.273507 0.198714i
\(413\) 1.07271 + 0.779369i 0.0527845 + 0.0383502i
\(414\) 2.49044 7.66478i 0.122398 0.376703i
\(415\) −12.6057 38.7963i −0.618788 1.90443i
\(416\) 11.9059 8.65014i 0.583735 0.424108i
\(417\) 0.0329037 0.00161130
\(418\) 9.99236 23.1213i 0.488742 1.13090i
\(419\) −38.2885 −1.87052 −0.935258 0.353966i \(-0.884833\pi\)
−0.935258 + 0.353966i \(0.884833\pi\)
\(420\) −0.00557533 + 0.00405071i −0.000272048 + 0.000197654i
\(421\) −5.96412 18.3557i −0.290673 0.894600i −0.984641 0.174594i \(-0.944139\pi\)
0.693967 0.720006i \(-0.255861\pi\)
\(422\) 10.5891 32.5900i 0.515472 1.58646i
\(423\) −9.84089 7.14983i −0.478481 0.347636i
\(424\) −23.6745 17.2005i −1.14974 0.835332i
\(425\) 1.49976 4.61578i 0.0727489 0.223898i
\(426\) −0.0329280 0.101342i −0.00159536 0.00491003i
\(427\) 1.69618 1.23235i 0.0820839 0.0596374i
\(428\) 0.894341 0.0432296
\(429\) 0.0742772 0.171870i 0.00358614 0.00829794i
\(430\) −46.5330 −2.24402
\(431\) −27.3054 + 19.8385i −1.31525 + 0.955587i −0.315275 + 0.949001i \(0.602097\pi\)
−0.999978 + 0.00658663i \(0.997903\pi\)
\(432\) 0.100107 + 0.308097i 0.00481639 + 0.0148233i
\(433\) −5.28554 + 16.2672i −0.254007 + 0.781753i 0.740017 + 0.672588i \(0.234817\pi\)
−0.994024 + 0.109164i \(0.965183\pi\)
\(434\) 3.66992 + 2.66635i 0.176162 + 0.127989i
\(435\) 0.269426 + 0.195749i 0.0129180 + 0.00938546i
\(436\) 1.46168 4.49860i 0.0700020 0.215444i
\(437\) −2.48866 7.65930i −0.119049 0.366394i
\(438\) 0.106885 0.0776563i 0.00510715 0.00371056i
\(439\) 29.1790 1.39264 0.696318 0.717733i \(-0.254820\pi\)
0.696318 + 0.717733i \(0.254820\pi\)
\(440\) 24.1956 + 2.27550i 1.15348 + 0.108480i
\(441\) 20.6004 0.980973
\(442\) −6.43865 + 4.67795i −0.306255 + 0.222507i
\(443\) −2.73559 8.41928i −0.129972 0.400012i 0.864802 0.502112i \(-0.167444\pi\)
−0.994774 + 0.102101i \(0.967444\pi\)
\(444\) 0.0152491 0.0469318i 0.000723688 0.00222728i
\(445\) 2.52328 + 1.83327i 0.119615 + 0.0869054i
\(446\) 14.0387 + 10.1997i 0.664750 + 0.482969i
\(447\) −0.0315971 + 0.0972458i −0.00149449 + 0.00459957i
\(448\) −0.549735 1.69191i −0.0259725 0.0799352i
\(449\) −3.64510 + 2.64832i −0.172023 + 0.124982i −0.670465 0.741941i \(-0.733905\pi\)
0.498443 + 0.866923i \(0.333905\pi\)
\(450\) −23.1737 −1.09242
\(451\) 6.33573 3.75103i 0.298338 0.176629i
\(452\) 4.26658 0.200683
\(453\) 0.185113 0.134493i 0.00869738 0.00631902i
\(454\) 2.10506 + 6.47870i 0.0987952 + 0.304061i
\(455\) 1.76811 5.44169i 0.0828904 0.255110i
\(456\) 0.101734 + 0.0739141i 0.00476413 + 0.00346135i
\(457\) 20.8441 + 15.1441i 0.975047 + 0.708413i 0.956596 0.291417i \(-0.0941267\pi\)
0.0184504 + 0.999830i \(0.494127\pi\)
\(458\) 7.82868 24.0942i 0.365810 1.12585i
\(459\) −0.0209328 0.0644245i −0.000977059 0.00300708i
\(460\) −2.28640 + 1.66117i −0.106604 + 0.0774523i
\(461\) 14.3574 0.668691 0.334346 0.942451i \(-0.391485\pi\)
0.334346 + 0.942451i \(0.391485\pi\)
\(462\) 0.0163047 + 0.0143607i 0.000758564 + 0.000668121i
\(463\) 15.6118 0.725541 0.362771 0.931879i \(-0.381831\pi\)
0.362771 + 0.931879i \(0.381831\pi\)
\(464\) 36.3565 26.4145i 1.68781 1.22626i
\(465\) −0.0856189 0.263508i −0.00397048 0.0122199i
\(466\) 7.13662 21.9642i 0.330597 1.01747i
\(467\) 5.81360 + 4.22383i 0.269021 + 0.195455i 0.714115 0.700029i \(-0.246830\pi\)
−0.445093 + 0.895484i \(0.646830\pi\)
\(468\) 6.47307 + 4.70296i 0.299218 + 0.217394i
\(469\) 1.01365 3.11969i 0.0468060 0.144054i
\(470\) 6.26038 + 19.2675i 0.288770 + 0.888742i
\(471\) 0.0160523 0.0116627i 0.000739649 0.000537387i
\(472\) −8.49047 −0.390806
\(473\) 6.75276 + 30.1425i 0.310492 + 1.38595i
\(474\) −0.126634 −0.00581648
\(475\) −18.7345 + 13.6114i −0.859598 + 0.624534i
\(476\) −0.0600898 0.184937i −0.00275421 0.00847660i
\(477\) 11.6211 35.7662i 0.532095 1.63762i
\(478\) −7.43234 5.39991i −0.339947 0.246986i
\(479\) −18.6826 13.5737i −0.853629 0.620197i 0.0725155 0.997367i \(-0.476897\pi\)
−0.926144 + 0.377170i \(0.876897\pi\)
\(480\) 0.0322327 0.0992022i 0.00147122 0.00452794i
\(481\) 12.6607 + 38.9656i 0.577279 + 1.77668i
\(482\) −19.3967 + 14.0925i −0.883494 + 0.641896i
\(483\) 0.00694693 0.000316096
\(484\) 0.740961 + 5.82060i 0.0336801 + 0.264573i
\(485\) −40.2765 −1.82886
\(486\) −0.392512 + 0.285177i −0.0178047 + 0.0129359i
\(487\) 0.417602 + 1.28525i 0.0189234 + 0.0582401i 0.960072 0.279752i \(-0.0902523\pi\)
−0.941149 + 0.337992i \(0.890252\pi\)
\(488\) −4.14862 + 12.7681i −0.187799 + 0.577987i
\(489\) −0.154691 0.112390i −0.00699537 0.00508244i
\(490\) −27.7572 20.1668i −1.25394 0.911043i
\(491\) 10.8012 33.2426i 0.487450 1.50022i −0.340951 0.940081i \(-0.610749\pi\)
0.828401 0.560136i \(-0.189251\pi\)
\(492\) −0.00413144 0.0127153i −0.000186260 0.000573248i
\(493\) −7.60230 + 5.52340i −0.342391 + 0.248761i
\(494\) 37.9737 1.70852
\(495\) 6.82746 + 30.4759i 0.306871 + 1.36979i
\(496\) −37.3878 −1.67876
\(497\) −1.74879 + 1.27057i −0.0784438 + 0.0569927i
\(498\) 0.0721657 + 0.222103i 0.00323382 + 0.00995268i
\(499\) −1.70016 + 5.23256i −0.0761097 + 0.234242i −0.981872 0.189544i \(-0.939299\pi\)
0.905762 + 0.423786i \(0.139299\pi\)
\(500\) −0.198698 0.144363i −0.00888605 0.00645609i
\(501\) −0.0264216 0.0191964i −0.00118043 0.000857633i
\(502\) 0.934052 2.87472i 0.0416888 0.128305i
\(503\) −12.3627 38.0486i −0.551227 1.69650i −0.705704 0.708506i \(-0.749369\pi\)
0.154477 0.987996i \(-0.450631\pi\)
\(504\) 2.06525 1.50049i 0.0919937 0.0668373i
\(505\) 22.3904 0.996358
\(506\) 6.68644 + 5.88922i 0.297249 + 0.261808i
\(507\) 0.135500 0.00601779
\(508\) −0.0240993 + 0.0175092i −0.00106923 + 0.000776844i
\(509\) −0.0632846 0.194770i −0.00280504 0.00863303i 0.949644 0.313330i \(-0.101445\pi\)
−0.952449 + 0.304697i \(0.901445\pi\)
\(510\) −0.0174313 + 0.0536480i −0.000771871 + 0.00237557i
\(511\) −2.16826 1.57534i −0.0959183 0.0696888i
\(512\) 6.67562 + 4.85012i 0.295024 + 0.214347i
\(513\) −0.0998787 + 0.307395i −0.00440975 + 0.0135718i
\(514\) 0.631751 + 1.94433i 0.0278653 + 0.0857607i
\(515\) 32.6694 23.7357i 1.43959 1.04592i
\(516\) 0.0560899 0.00246922
\(517\) 11.5723 6.85132i 0.508950 0.301321i
\(518\) −4.75442 −0.208897
\(519\) −0.0600295 + 0.0436140i −0.00263500 + 0.00191444i
\(520\) 11.3219 + 34.8451i 0.496496 + 1.52806i
\(521\) −12.5964 + 38.7678i −0.551859 + 1.69845i 0.152238 + 0.988344i \(0.451352\pi\)
−0.704097 + 0.710104i \(0.748648\pi\)
\(522\) 36.2996 + 26.3732i 1.58879 + 1.15432i
\(523\) −15.5638 11.3078i −0.680559 0.494455i 0.192984 0.981202i \(-0.438183\pi\)
−0.873543 + 0.486747i \(0.838183\pi\)
\(524\) 0.175772 0.540970i 0.00767863 0.0236324i
\(525\) −0.00617272 0.0189977i −0.000269400 0.000829127i
\(526\) −27.3721 + 19.8870i −1.19348 + 0.867115i
\(527\) 7.81796 0.340556
\(528\) −0.178289 0.0167673i −0.00775902 0.000729705i
\(529\) −20.1511 −0.876136
\(530\) −50.6717 + 36.8151i −2.20104 + 1.59915i
\(531\) −3.37176 10.3772i −0.146322 0.450333i
\(532\) −0.286713 + 0.882411i −0.0124306 + 0.0382574i
\(533\) 8.98031 + 6.52458i 0.388980 + 0.282611i
\(534\) −0.0144454 0.0104952i −0.000625115 0.000454172i
\(535\) −1.62634 + 5.00535i −0.0703127 + 0.216400i
\(536\) 6.49076 + 19.9765i 0.280358 + 0.862853i
\(537\) 0.00175374 0.00127417i 7.56795e−5 5.49844e-5i
\(538\) −0.329104 −0.0141887
\(539\) −9.03530 + 20.9067i −0.389178 + 0.900517i
\(540\) 0.113423 0.00488096
\(541\) −16.8343 + 12.2309i −0.723764 + 0.525845i −0.887585 0.460645i \(-0.847618\pi\)
0.163820 + 0.986490i \(0.447618\pi\)
\(542\) −12.4477 38.3099i −0.534673 1.64555i
\(543\) 0.0661020 0.203441i 0.00283671 0.00873049i
\(544\) 2.38111 + 1.72997i 0.102089 + 0.0741720i
\(545\) 22.5193 + 16.3612i 0.964619 + 0.700837i
\(546\) −0.0101222 + 0.0311529i −0.000433190 + 0.00133322i
\(547\) 6.59780 + 20.3059i 0.282102 + 0.868219i 0.987252 + 0.159162i \(0.0508792\pi\)
−0.705151 + 0.709057i \(0.749121\pi\)
\(548\) −4.49102 + 3.26292i −0.191847 + 0.139385i
\(549\) −17.2530 −0.736339
\(550\) 10.1639 23.5182i 0.433391 1.00282i
\(551\) 44.8367 1.91011
\(552\) −0.0359880 + 0.0261468i −0.00153175 + 0.00111288i
\(553\) 0.793831 + 2.44316i 0.0337571 + 0.103894i
\(554\) −6.80402 + 20.9406i −0.289075 + 0.889681i
\(555\) 0.234933 + 0.170689i 0.00997234 + 0.00724533i
\(556\) −1.25767 0.913748i −0.0533369 0.0387515i
\(557\) −13.8399 + 42.5950i −0.586417 + 1.80481i 0.00708505 + 0.999975i \(0.497745\pi\)
−0.593502 + 0.804832i \(0.702255\pi\)
\(558\) −11.5354 35.5022i −0.488331 1.50293i
\(559\) −37.6754 + 27.3728i −1.59350 + 1.15774i
\(560\) −5.47244 −0.231253
\(561\) 0.0372809 + 0.00350613i 0.00157400 + 0.000148029i
\(562\) 31.0800 1.31103
\(563\) 12.3526 8.97469i 0.520600 0.378238i −0.296230 0.955117i \(-0.595729\pi\)
0.816830 + 0.576879i \(0.195729\pi\)
\(564\) −0.00754614 0.0232246i −0.000317750 0.000977934i
\(565\) −7.75868 + 23.8788i −0.326410 + 1.00459i
\(566\) −8.80038 6.39385i −0.369908 0.268754i
\(567\) 2.65398 + 1.92823i 0.111457 + 0.0809780i
\(568\) 4.27729 13.1642i 0.179471 0.552356i
\(569\) −0.632495 1.94662i −0.0265156 0.0816066i 0.936923 0.349536i \(-0.113661\pi\)
−0.963439 + 0.267929i \(0.913661\pi\)
\(570\) 0.217746 0.158202i 0.00912039 0.00662635i
\(571\) −24.7020 −1.03375 −0.516874 0.856062i \(-0.672904\pi\)
−0.516874 + 0.856062i \(0.672904\pi\)
\(572\) −7.61195 + 4.50661i −0.318272 + 0.188431i
\(573\) −0.187105 −0.00781643
\(574\) −1.04211 + 0.757137i −0.0434968 + 0.0316023i
\(575\) −2.53139 7.79080i −0.105566 0.324899i
\(576\) −4.52380 + 13.9228i −0.188492 + 0.580118i
\(577\) 19.8512 + 14.4227i 0.826416 + 0.600426i 0.918543 0.395321i \(-0.129367\pi\)
−0.0921273 + 0.995747i \(0.529367\pi\)
\(578\) −1.28769 0.935561i −0.0535608 0.0389142i
\(579\) −0.0349476 + 0.107558i −0.00145237 + 0.00446994i
\(580\) −4.86214 14.9641i −0.201889 0.621351i
\(581\) 3.83268 2.78461i 0.159006 0.115525i
\(582\) 0.230577 0.00955773
\(583\) 31.2010 + 27.4809i 1.29221 + 1.13814i
\(584\) 17.1618 0.710159
\(585\) −38.0921 + 27.6756i −1.57492 + 1.14424i
\(586\) −0.864064 2.65932i −0.0356942 0.109855i
\(587\) −0.477688 + 1.47017i −0.0197163 + 0.0606805i −0.960431 0.278519i \(-0.910156\pi\)
0.940714 + 0.339200i \(0.110156\pi\)
\(588\) 0.0334580 + 0.0243087i 0.00137979 + 0.00100247i
\(589\) −30.1784 21.9259i −1.24348 0.903442i
\(590\) −5.61563 + 17.2831i −0.231192 + 0.711535i
\(591\) −0.00790743 0.0243366i −0.000325268 0.00100107i
\(592\) 31.7020 23.0328i 1.30294 0.946644i
\(593\) −5.53691 −0.227373 −0.113687 0.993517i \(-0.536266\pi\)
−0.113687 + 0.993517i \(0.536266\pi\)
\(594\) −0.0781741 0.348948i −0.00320752 0.0143175i
\(595\) 1.14431 0.0469122
\(596\) 3.90828 2.83953i 0.160089 0.116312i
\(597\) 0.0299741 + 0.0922507i 0.00122676 + 0.00377557i
\(598\) −4.15104 + 12.7756i −0.169748 + 0.522432i
\(599\) −28.5936 20.7745i −1.16830 0.848821i −0.177497 0.984121i \(-0.556800\pi\)
−0.990805 + 0.135300i \(0.956800\pi\)
\(600\) 0.103481 + 0.0751831i 0.00422458 + 0.00306934i
\(601\) 2.12799 6.54927i 0.0868024 0.267150i −0.898228 0.439529i \(-0.855145\pi\)
0.985031 + 0.172379i \(0.0551453\pi\)
\(602\) −1.66995 5.13959i −0.0680623 0.209474i
\(603\) −21.8380 + 15.8662i −0.889313 + 0.646124i
\(604\) −10.8104 −0.439870
\(605\) −33.9236 6.43769i −1.37919 0.261729i
\(606\) −0.128182 −0.00520702
\(607\) −16.5966 + 12.0581i −0.673634 + 0.489424i −0.871240 0.490858i \(-0.836684\pi\)
0.197605 + 0.980282i \(0.436684\pi\)
\(608\) −4.33959 13.3559i −0.175994 0.541653i
\(609\) −0.0119516 + 0.0367832i −0.000484303 + 0.00149053i
\(610\) 23.2468 + 16.8898i 0.941236 + 0.683848i
\(611\) 16.4027 + 11.9173i 0.663582 + 0.482121i
\(612\) −0.494483 + 1.52186i −0.0199883 + 0.0615176i
\(613\) −10.0164 30.8273i −0.404558 1.24510i −0.921264 0.388939i \(-0.872842\pi\)
0.516705 0.856163i \(-0.327158\pi\)
\(614\) 23.7444 17.2513i 0.958247 0.696207i
\(615\) 0.0786763 0.00317254
\(616\) 0.616990 + 2.75407i 0.0248592 + 0.110965i
\(617\) −8.31960 −0.334935 −0.167467 0.985878i \(-0.553559\pi\)
−0.167467 + 0.985878i \(0.553559\pi\)
\(618\) −0.187028 + 0.135884i −0.00752337 + 0.00546605i
\(619\) −3.63457 11.1861i −0.146086 0.449606i 0.851063 0.525063i \(-0.175958\pi\)
−0.997149 + 0.0754574i \(0.975958\pi\)
\(620\) −4.04513 + 12.4496i −0.162456 + 0.499990i
\(621\) −0.0924995 0.0672049i −0.00371188 0.00269684i
\(622\) 24.3220 + 17.6709i 0.975222 + 0.708540i
\(623\) −0.111931 + 0.344489i −0.00448444 + 0.0138017i
\(624\) −0.0834268 0.256761i −0.00333974 0.0102787i
\(625\) 20.8014 15.1131i 0.832054 0.604523i
\(626\) 3.26540 0.130512
\(627\) −0.134077 0.118091i −0.00535451 0.00471609i
\(628\) −0.937437 −0.0374078
\(629\) −6.62902 + 4.81627i −0.264316 + 0.192037i
\(630\) −1.68843 5.19644i −0.0672685 0.207031i
\(631\) 14.4710 44.5372i 0.576082 1.77300i −0.0563838 0.998409i \(-0.517957\pi\)
0.632466 0.774588i \(-0.282043\pi\)
\(632\) −13.3079 9.66879i −0.529362 0.384604i
\(633\) −0.196646 0.142872i −0.00781599 0.00567865i
\(634\) 8.52266 26.2300i 0.338478 1.04173i
\(635\) −0.0541695 0.166717i −0.00214965 0.00661595i
\(636\) 0.0610787 0.0443763i 0.00242193 0.00175963i
\(637\) −34.3366 −1.36047
\(638\) −42.6862 + 25.2721i −1.68996 + 1.00053i
\(639\) 17.7881 0.703686
\(640\) 34.6737 25.1919i 1.37060 0.995799i
\(641\) −0.245277 0.754884i −0.00968785 0.0298161i 0.946096 0.323887i \(-0.104990\pi\)
−0.955784 + 0.294071i \(0.904990\pi\)
\(642\) 0.00931055 0.0286549i 0.000367458 0.00113092i
\(643\) 39.5362 + 28.7247i 1.55916 + 1.13279i 0.936698 + 0.350139i \(0.113866\pi\)
0.622457 + 0.782654i \(0.286134\pi\)
\(644\) −0.265530 0.192919i −0.0104633 0.00760206i
\(645\) −0.101998 + 0.313918i −0.00401618 + 0.0123605i
\(646\) 2.34683 + 7.22280i 0.0923347 + 0.284177i
\(647\) 25.4820 18.5138i 1.00180 0.727851i 0.0393273 0.999226i \(-0.487478\pi\)
0.962474 + 0.271375i \(0.0874785\pi\)
\(648\) −21.0062 −0.825201
\(649\) 12.0104 + 1.12953i 0.471447 + 0.0443378i
\(650\) 38.6256 1.51502
\(651\) 0.0260319 0.0189133i 0.00102027 0.000741271i
\(652\) 2.79160 + 8.59166i 0.109328 + 0.336475i
\(653\) 10.1644 31.2829i 0.397765 1.22420i −0.529022 0.848608i \(-0.677441\pi\)
0.926787 0.375587i \(-0.122559\pi\)
\(654\) −0.128920 0.0936655i −0.00504115 0.00366261i
\(655\) 2.70801 + 1.96748i 0.105811 + 0.0768760i
\(656\) 3.28072 10.0970i 0.128091 0.394222i
\(657\) 6.81533 + 20.9754i 0.265891 + 0.818330i
\(658\) −1.90343 + 1.38293i −0.0742035 + 0.0539120i
\(659\) −23.8822 −0.930320 −0.465160 0.885227i \(-0.654003\pi\)
−0.465160 + 0.885227i \(0.654003\pi\)
\(660\) −0.0248730 + 0.0575536i −0.000968182 + 0.00224027i
\(661\) −44.2541 −1.72129 −0.860643 0.509209i \(-0.829938\pi\)
−0.860643 + 0.509209i \(0.829938\pi\)
\(662\) −32.0434 + 23.2809i −1.24540 + 0.904837i
\(663\) 0.0174449 + 0.0536899i 0.000677504 + 0.00208514i
\(664\) −9.37422 + 28.8509i −0.363790 + 1.11963i
\(665\) −4.41720 3.20929i −0.171292 0.124451i
\(666\) 31.6523 + 22.9968i 1.22650 + 0.891106i
\(667\) −4.90125 + 15.0845i −0.189777 + 0.584074i
\(668\) 0.476812 + 1.46748i 0.0184484 + 0.0567784i
\(669\) 0.0995807 0.0723496i 0.00385001 0.00279720i
\(670\) 44.9570 1.73684
\(671\) 7.56712 17.5095i 0.292125 0.675947i
\(672\) 0.0121137 0.000467296
\(673\) 0.653008 0.474438i 0.0251716 0.0182882i −0.575128 0.818063i \(-0.695048\pi\)
0.600300 + 0.799775i \(0.295048\pi\)
\(674\) −9.97098 30.6875i −0.384068 1.18204i
\(675\) −0.101593 + 0.312673i −0.00391033 + 0.0120348i
\(676\) −5.17919 3.76290i −0.199199 0.144727i
\(677\) −27.9192 20.2845i −1.07302 0.779596i −0.0965690 0.995326i \(-0.530787\pi\)
−0.976453 + 0.215730i \(0.930787\pi\)
\(678\) 0.0444174 0.136703i 0.00170584 0.00525003i
\(679\) −1.44542 4.44856i −0.0554703 0.170720i
\(680\) −5.92801 + 4.30695i −0.227329 + 0.165164i
\(681\) 0.0483205 0.00185164
\(682\) 41.0895 + 3.86430i 1.57340 + 0.147972i
\(683\) 27.2372 1.04220 0.521100 0.853495i \(-0.325522\pi\)
0.521100 + 0.853495i \(0.325522\pi\)
\(684\) 6.17692 4.48780i 0.236181 0.171595i
\(685\) −10.0947 31.0684i −0.385700 1.18706i
\(686\) 2.48642 7.65241i 0.0949319 0.292170i
\(687\) −0.145383 0.105627i −0.00554670 0.00402992i
\(688\) 36.0339 + 26.1801i 1.37378 + 0.998108i
\(689\) −19.3700 + 59.6147i −0.737938 + 2.27114i
\(690\) 0.0294216 + 0.0905505i 0.00112006 + 0.00344720i
\(691\) 24.0798 17.4950i 0.916039 0.665542i −0.0264956 0.999649i \(-0.508435\pi\)
0.942535 + 0.334107i \(0.108435\pi\)
\(692\) 3.50566 0.133265
\(693\) −3.12106 + 1.84780i −0.118559 + 0.0701922i
\(694\) −50.0068 −1.89823
\(695\) 7.40100 5.37714i 0.280736 0.203967i
\(696\) −0.0765302 0.235536i −0.00290087 0.00892796i
\(697\) −0.686013 + 2.11133i −0.0259846 + 0.0799724i
\(698\) −5.32366 3.86787i −0.201504 0.146401i
\(699\) −0.132531 0.0962893i −0.00501278 0.00364200i
\(700\) −0.291635 + 0.897560i −0.0110228 + 0.0339246i
\(701\) −1.35861 4.18137i −0.0513139 0.157928i 0.922116 0.386914i \(-0.126459\pi\)
−0.973430 + 0.228986i \(0.926459\pi\)
\(702\) 0.436153 0.316884i 0.0164616 0.0119600i
\(703\) 39.0965 1.47455
\(704\) −12.1457 10.6976i −0.457759 0.403180i
\(705\) 0.143704 0.00541220
\(706\) 13.2108 9.59820i 0.497195 0.361233i
\(707\) 0.803535 + 2.47303i 0.0302201 + 0.0930078i
\(708\) 0.00676897 0.0208327i 0.000254393 0.000782943i
\(709\) 13.7400 + 9.98269i 0.516016 + 0.374908i 0.815101 0.579319i \(-0.196681\pi\)
−0.299085 + 0.954227i \(0.596681\pi\)
\(710\) −23.9678 17.4136i −0.899496 0.653522i
\(711\) 6.53248 20.1049i 0.244987 0.753993i
\(712\) −0.716736 2.20589i −0.0268608 0.0826691i
\(713\) 10.6755 7.75620i 0.399800 0.290472i
\(714\) −0.00655102 −0.000245166
\(715\) −11.3799 50.7969i −0.425585 1.89970i
\(716\) −0.102417 −0.00382749
\(717\) −0.0527200 + 0.0383033i −0.00196886 + 0.00143046i
\(718\) −0.480086 1.47755i −0.0179166 0.0551418i
\(719\) 14.5171 44.6789i 0.541395 1.66624i −0.188014 0.982166i \(-0.560205\pi\)
0.729410 0.684077i \(-0.239795\pi\)
\(720\) 36.4325 + 26.4697i 1.35776 + 0.986469i
\(721\) 3.79405 + 2.75654i 0.141298 + 0.102659i
\(722\) 1.85244 5.70123i 0.0689408 0.212178i
\(723\) 0.0525534 + 0.161743i 0.00195448 + 0.00601528i
\(724\) −8.17623 + 5.94038i −0.303867 + 0.220773i
\(725\) 45.6064 1.69378
\(726\) 0.194208 + 0.0368549i 0.00720772 + 0.00136781i
\(727\) −38.8372 −1.44039 −0.720197 0.693770i \(-0.755949\pi\)
−0.720197 + 0.693770i \(0.755949\pi\)
\(728\) −3.44234 + 2.50101i −0.127582 + 0.0926936i
\(729\) −8.34133 25.6720i −0.308938 0.950814i
\(730\) 11.3509 34.9343i 0.420114 1.29298i
\(731\) −7.53484 5.47438i −0.278686 0.202477i
\(732\) −0.0280213 0.0203586i −0.00103570 0.000752477i
\(733\) 8.42146 25.9186i 0.311054 0.957325i −0.666295 0.745688i \(-0.732121\pi\)
0.977348 0.211636i \(-0.0678792\pi\)
\(734\) −11.9113 36.6592i −0.439654 1.35312i
\(735\) −0.196891 + 0.143050i −0.00726243 + 0.00527646i
\(736\) 4.96773 0.183113
\(737\) −6.52405 29.1216i −0.240317 1.07271i
\(738\) 10.6000 0.390192
\(739\) 19.8216 14.4013i 0.729151 0.529759i −0.160144 0.987094i \(-0.551196\pi\)
0.889295 + 0.457334i \(0.151196\pi\)
\(740\) −4.23966 13.0483i −0.155853 0.479667i
\(741\) 0.0832366 0.256176i 0.00305777 0.00941086i
\(742\) −5.88474 4.27551i −0.216035 0.156959i
\(743\) −12.3238 8.95375i −0.452116 0.328481i 0.338315 0.941033i \(-0.390143\pi\)
−0.790430 + 0.612552i \(0.790143\pi\)
\(744\) −0.0636706 + 0.195958i −0.00233428 + 0.00718416i
\(745\) 8.78487 + 27.0370i 0.321853 + 0.990561i
\(746\) −21.0472 + 15.2917i −0.770594 + 0.559869i
\(747\) −38.9848 −1.42638
\(748\) −1.32761 1.16932i −0.0485422 0.0427546i
\(749\) −0.611209 −0.0223331
\(750\) −0.00669397 + 0.00486345i −0.000244429 + 0.000177588i
\(751\) 11.5401 + 35.5166i 0.421103 + 1.29602i 0.906677 + 0.421825i \(0.138610\pi\)
−0.485575 + 0.874195i \(0.661390\pi\)
\(752\) 5.99229 18.4424i 0.218516 0.672525i
\(753\) −0.0173459 0.0126025i −0.000632118 0.000459261i
\(754\) −60.5037 43.9585i −2.20342 1.60088i
\(755\) 19.6585 60.5027i 0.715447 2.20192i
\(756\) 0.00407048 + 0.0125277i 0.000148042 + 0.000455626i
\(757\) 4.28604 3.11399i 0.155779 0.113180i −0.507165 0.861849i \(-0.669307\pi\)
0.662944 + 0.748669i \(0.269307\pi\)
\(758\) 10.5736 0.384052
\(759\) 0.0543859 0.0321988i 0.00197408 0.00116874i
\(760\) 34.9621 1.26821
\(761\) −6.20444 + 4.50779i −0.224911 + 0.163407i −0.694534 0.719459i \(-0.744390\pi\)
0.469624 + 0.882867i \(0.344390\pi\)
\(762\) 0.000310113 0 0.000954429i 1.12342e−5 0 3.45753e-5i
\(763\) −0.998942 + 3.07443i −0.0361641 + 0.111302i
\(764\) 7.15165 + 5.19598i 0.258738 + 0.187984i
\(765\) −7.61819 5.53494i −0.275436 0.200116i
\(766\) 1.20383 3.70501i 0.0434962 0.133867i
\(767\) 5.62001 + 17.2966i 0.202927 + 0.624545i
\(768\) −0.109355 + 0.0794509i −0.00394600 + 0.00286694i
\(769\) 2.26805 0.0817879 0.0408940 0.999163i \(-0.486979\pi\)
0.0408940 + 0.999163i \(0.486979\pi\)
\(770\) 6.01425 + 0.565616i 0.216738 + 0.0203834i
\(771\) 0.0145015 0.000522259
\(772\) 4.32271 3.14063i 0.155578 0.113034i
\(773\) 13.0105 + 40.0423i 0.467956 + 1.44022i 0.855227 + 0.518254i \(0.173418\pi\)
−0.387271 + 0.921966i \(0.626582\pi\)
\(774\) −13.7422 + 42.2940i −0.493951 + 1.52023i
\(775\) −30.6966 22.3024i −1.10265 0.801124i
\(776\) 24.2314 + 17.6051i 0.869856 + 0.631987i
\(777\) −0.0104215 + 0.0320740i −0.000373869 + 0.00115065i
\(778\) 8.86027 + 27.2691i 0.317656 + 0.977645i
\(779\) 8.56946 6.22608i 0.307033 0.223072i
\(780\) −0.0945243 −0.00338451
\(781\) −7.80181 + 18.0526i −0.279171 + 0.645972i
\(782\) −2.68652 −0.0960698
\(783\) 0.514980 0.374155i 0.0184039 0.0133712i
\(784\) 10.1483 + 31.2332i 0.362439 + 1.11547i
\(785\) 1.70471 5.24655i 0.0608436 0.187257i
\(786\) −0.0155030 0.0112636i −0.000552973 0.000401758i
\(787\) 22.0839 + 16.0449i 0.787208 + 0.571940i 0.907133 0.420843i \(-0.138266\pi\)
−0.119926 + 0.992783i \(0.538266\pi\)
\(788\) −0.373593 + 1.14980i −0.0133087 + 0.0409599i
\(789\) 0.0741622 + 0.228248i 0.00264025 + 0.00812584i
\(790\) −28.4836 + 20.6946i −1.01340 + 0.736280i
\(791\) −2.91586 −0.103676
\(792\) 9.21366 21.3194i 0.327393 0.757553i
\(793\) 28.7571 1.02119
\(794\) −11.5084 + 8.36137i −0.408419 + 0.296734i
\(795\) 0.137290 + 0.422536i 0.00486918 + 0.0149858i
\(796\) 1.41615 4.35846i 0.0501941 0.154481i
\(797\) −41.7333 30.3211i −1.47827 1.07403i −0.978109 0.208095i \(-0.933274\pi\)
−0.500162 0.865932i \(-0.666726\pi\)
\(798\) 0.0252879 + 0.0183727i 0.000895181 + 0.000650387i
\(799\) −1.25302 + 3.85638i −0.0443285 + 0.136429i
\(800\) −4.41410 13.5852i −0.156062 0.480309i
\(801\) 2.41144 1.75202i 0.0852042 0.0619045i
\(802\) −25.5845 −0.903420
\(803\) −24.2765 2.28311i −0.856699 0.0805691i
\(804\) −0.0541903 −0.00191114
\(805\) 1.56257 1.13527i 0.0550733 0.0400131i
\(806\) 19.2270 + 59.1748i 0.677244 + 2.08434i
\(807\) −0.000721382 0.00222018i −2.53938e−5 7.81542e-5i
\(808\) −13.4706 9.78698i −0.473895 0.344305i
\(809\) −13.0863 9.50775i −0.460090 0.334275i 0.333477 0.942758i \(-0.391778\pi\)
−0.793566 + 0.608484i \(0.791778\pi\)
\(810\) −13.8936 + 42.7600i −0.488170 + 1.50243i
\(811\) −9.59674 29.5357i −0.336987 1.03714i −0.965735 0.259530i \(-0.916432\pi\)
0.628748 0.777609i \(-0.283568\pi\)
\(812\) 1.47830 1.07405i 0.0518783 0.0376918i
\(813\) −0.285729 −0.0100210
\(814\) −37.2213 + 22.0366i −1.30461 + 0.772383i
\(815\) −53.1614 −1.86216
\(816\) 0.0436815 0.0317364i 0.00152916 0.00111100i
\(817\) 13.7323 + 42.2638i 0.480434 + 1.47862i
\(818\) 3.36081 10.3435i 0.117508 0.361653i
\(819\) −4.42381 3.21409i −0.154581 0.112309i
\(820\) −3.00722 2.18487i −0.105017 0.0762990i
\(821\) −4.90683 + 15.1017i −0.171249 + 0.527052i −0.999442 0.0333915i \(-0.989369\pi\)
0.828193 + 0.560443i \(0.189369\pi\)
\(822\) 0.0577909 + 0.177862i 0.00201569 + 0.00620366i
\(823\) −29.1988 + 21.2142i −1.01781 + 0.739479i −0.965832 0.259169i \(-0.916551\pi\)
−0.0519741 + 0.998648i \(0.516551\pi\)
\(824\) −30.0298 −1.04614
\(825\) −0.136379 0.120118i −0.00474809 0.00418198i
\(826\) −2.11046 −0.0734323
\(827\) −0.873180 + 0.634402i −0.0303634 + 0.0220603i −0.602863 0.797844i \(-0.705974\pi\)
0.572500 + 0.819905i \(0.305974\pi\)
\(828\) 0.834619 + 2.56869i 0.0290050 + 0.0892683i
\(829\) −9.23274 + 28.4155i −0.320666 + 0.986909i 0.652693 + 0.757623i \(0.273639\pi\)
−0.973359 + 0.229287i \(0.926361\pi\)
\(830\) 52.5284 + 38.1641i 1.82329 + 1.32470i
\(831\) 0.126354 + 0.0918018i 0.00438318 + 0.00318457i
\(832\) 7.54022 23.2064i 0.261410 0.804538i
\(833\) −2.12205 6.53101i −0.0735248 0.226286i
\(834\) −0.0423697 + 0.0307834i −0.00146714 + 0.00106594i
\(835\) −9.08009 −0.314229
\(836\) 1.84534 + 8.23710i 0.0638224 + 0.284886i
\(837\) −0.529588 −0.0183052
\(838\) 49.3037 35.8212i 1.70317 1.23742i
\(839\) 10.4342 + 32.1131i 0.360228 + 1.10867i 0.952916 + 0.303235i \(0.0980669\pi\)
−0.592688 + 0.805432i \(0.701933\pi\)
\(840\) −0.00931943 + 0.0286823i −0.000321551 + 0.000989632i
\(841\) −47.9771 34.8574i −1.65438 1.20198i
\(842\) 24.8528 + 18.0566i 0.856483 + 0.622271i
\(843\) 0.0681259 0.209670i 0.00234638 0.00722142i
\(844\) 3.54874 + 10.9219i 0.122153 + 0.375947i
\(845\) 30.4780 22.1436i 1.04848 0.761762i
\(846\) 19.3611 0.665648
\(847\) −0.506387 3.97791i −0.0173997 0.136683i
\(848\) 59.9515 2.05874
\(849\) −0.0624239 + 0.0453536i −0.00214238 + 0.00155653i
\(850\) 2.38712 + 7.34680i 0.0818775 + 0.251993i
\(851\) −4.27377 + 13.1533i −0.146503 + 0.450890i
\(852\) 0.0288903 + 0.0209901i 0.000989767 + 0.000719108i
\(853\) −21.8299 15.8604i −0.747442 0.543049i 0.147591 0.989049i \(-0.452848\pi\)
−0.895033 + 0.446000i \(0.852848\pi\)
\(854\) −1.03122 + 3.17376i −0.0352875 + 0.108604i
\(855\) 13.8842 + 42.7313i 0.474831 + 1.46138i
\(856\) 3.16632 2.30047i 0.108223 0.0786283i
\(857\) −10.4807 −0.358014 −0.179007 0.983848i \(-0.557288\pi\)
−0.179007 + 0.983848i \(0.557288\pi\)
\(858\) 0.0651485 + 0.290805i 0.00222413 + 0.00992793i
\(859\) 21.2764 0.725940 0.362970 0.931801i \(-0.381763\pi\)
0.362970 + 0.931801i \(0.381763\pi\)
\(860\) 12.6163 9.16626i 0.430211 0.312567i
\(861\) 0.00282350 + 0.00868984i 9.62246e−5 + 0.000296149i
\(862\) 16.6007 51.0916i 0.565421 1.74019i
\(863\) −35.6902 25.9304i −1.21491 0.882682i −0.219240 0.975671i \(-0.570358\pi\)
−0.995667 + 0.0929889i \(0.970358\pi\)
\(864\) −0.161296 0.117188i −0.00548740 0.00398683i
\(865\) −6.37496 + 19.6201i −0.216755 + 0.667104i
\(866\) −8.41284 25.8921i −0.285880 0.879848i
\(867\) −0.00913399 + 0.00663623i −0.000310206 + 0.000225378i
\(868\) −1.52024 −0.0516003
\(869\) 17.5387 + 15.4476i 0.594960 + 0.524023i
\(870\) −0.530072 −0.0179711
\(871\) 36.3994 26.4457i 1.23335 0.896078i
\(872\) −6.39658 19.6866i −0.216615 0.666674i
\(873\) −11.8945 + 36.6074i −0.402567 + 1.23897i
\(874\) 10.3704 + 7.53451i 0.350783 + 0.254859i
\(875\) 0.135794 + 0.0986601i 0.00459067 + 0.00333532i
\(876\) −0.0136821 + 0.0421092i −0.000462275 + 0.00142274i
\(877\) 2.56777 + 7.90278i 0.0867074 + 0.266858i 0.985004 0.172532i \(-0.0551948\pi\)
−0.898297 + 0.439390i \(0.855195\pi\)
\(878\) −37.5734 + 27.2987i −1.26804 + 0.921286i
\(879\) −0.0198341 −0.000668989
\(880\) −42.8425 + 25.3646i −1.44422 + 0.855040i
\(881\) −28.5726 −0.962634 −0.481317 0.876547i \(-0.659841\pi\)
−0.481317 + 0.876547i \(0.659841\pi\)
\(882\) −26.5270 + 19.2730i −0.893209 + 0.648954i
\(883\) 12.4641 + 38.3606i 0.419451 + 1.29094i 0.908209 + 0.418518i \(0.137450\pi\)
−0.488758 + 0.872419i \(0.662550\pi\)
\(884\) 0.824199 2.53662i 0.0277208 0.0853159i
\(885\) 0.104285 + 0.0757677i 0.00350551 + 0.00254690i
\(886\) 11.3993 + 8.28210i 0.382968 + 0.278242i
\(887\) −6.40492 + 19.7123i −0.215056 + 0.661875i 0.784094 + 0.620643i \(0.213128\pi\)
−0.999150 + 0.0412319i \(0.986872\pi\)
\(888\) −0.0667325 0.205381i −0.00223940 0.00689215i
\(889\) 0.0164699 0.0119661i 0.000552384 0.000401330i
\(890\) −4.96434 −0.166405
\(891\) 29.7147 + 2.79455i 0.995480 + 0.0936210i
\(892\) −5.81541 −0.194714
\(893\) 15.6523 11.3720i 0.523783 0.380551i
\(894\) −0.0502921 0.154783i −0.00168202 0.00517673i
\(895\) 0.186242 0.573195i 0.00622540 0.0191598i
\(896\) 4.02682 + 2.92565i 0.134527 + 0.0977392i
\(897\) 0.0770870 + 0.0560070i 0.00257386 + 0.00187002i
\(898\) 2.21609 6.82042i 0.0739518 0.227600i
\(899\) 22.7020 + 69.8694i 0.757153 + 2.33028i
\(900\) 6.28297 4.56485i 0.209432 0.152162i
\(901\) −12.5361 −0.417639
\(902\) −4.64914 + 10.7576i −0.154799 + 0.358189i
\(903\) −0.0383329 −0.00127564
\(904\) 15.1054 10.9747i 0.502398 0.365014i
\(905\) −18.3782 56.5623i −0.610912 1.88020i
\(906\) −0.112542 + 0.346369i −0.00373897 + 0.0115074i
\(907\) −19.6017 14.2415i −0.650864 0.472880i 0.212701 0.977117i \(-0.431774\pi\)
−0.863565 + 0.504237i \(0.831774\pi\)
\(908\) −1.84694 1.34188i −0.0612927 0.0445318i
\(909\) 6.61234 20.3507i 0.219317 0.674990i
\(910\) 2.81425 + 8.66138i 0.0932916 + 0.287122i
\(911\) −28.8260 + 20.9433i −0.955049 + 0.693884i −0.951996 0.306112i \(-0.900972\pi\)
−0.00305335 + 0.999995i \(0.500972\pi\)
\(912\) −0.257623 −0.00853076
\(913\) 17.0986 39.5644i 0.565882 1.30939i
\(914\) −41.0090 −1.35646
\(915\) 0.164897 0.119805i 0.00545133 0.00396062i
\(916\) 2.62362 + 8.07468i 0.0866869 + 0.266795i
\(917\) −0.120126 + 0.369709i −0.00396690 + 0.0122089i
\(918\) 0.0872280 + 0.0633748i 0.00287895 + 0.00209168i
\(919\) 14.3841 + 10.4507i 0.474489 + 0.344736i 0.799188 0.601081i \(-0.205263\pi\)
−0.324699 + 0.945817i \(0.605263\pi\)
\(920\) −3.82183 + 11.7624i −0.126002 + 0.387794i
\(921\) −0.0643333 0.197998i −0.00211985 0.00652424i
\(922\) −18.4879 + 13.4322i −0.608866 + 0.442367i
\(923\) −29.6490 −0.975909
\(924\) −0.00724946 0.000681783i −0.000238490 2.24290e-5i
\(925\) 39.7677 1.30755
\(926\) −20.1031 + 14.6058i −0.660629 + 0.479975i
\(927\) −11.9255 36.7030i −0.391686 1.20549i
\(928\) −8.54655 + 26.3036i −0.280554 + 0.863457i
\(929\) −7.35843 5.34621i −0.241422 0.175403i 0.460494 0.887663i \(-0.347672\pi\)
−0.701917 + 0.712259i \(0.747672\pi\)
\(930\) 0.356778 + 0.259214i 0.0116992 + 0.00849998i
\(931\) −10.1252 + 31.1620i −0.331839 + 1.02129i
\(932\) 2.39169 + 7.36087i 0.0783424 + 0.241113i
\(933\) 0.172524 0.125346i 0.00564817 0.00410363i
\(934\) −11.4378 −0.374255
\(935\) 8.95855 5.30385i 0.292976 0.173454i
\(936\) 35.0144 1.14448
\(937\) 26.3744 19.1621i 0.861615 0.626000i −0.0667091 0.997772i \(-0.521250\pi\)
0.928324 + 0.371773i \(0.121250\pi\)
\(938\) 1.61340 + 4.96552i 0.0526793 + 0.162130i
\(939\) 0.00715761 0.0220289i 0.000233580 0.000718885i
\(940\) −5.49274 3.99071i −0.179153 0.130163i
\(941\) 9.38413 + 6.81797i 0.305914 + 0.222260i 0.730141 0.683296i \(-0.239454\pi\)
−0.424227 + 0.905556i \(0.639454\pi\)
\(942\) −0.00975920 + 0.0300357i −0.000317972 + 0.000978617i
\(943\) 1.15790 + 3.56364i 0.0377063 + 0.116048i
\(944\) 14.0723 10.2241i 0.458015 0.332768i
\(945\) −0.0775155 −0.00252158
\(946\) −36.8956 32.4965i −1.19958 1.05655i
\(947\) 16.2101 0.526759 0.263379 0.964692i \(-0.415163\pi\)
0.263379 + 0.964692i \(0.415163\pi\)
\(948\) 0.0343336 0.0249448i 0.00111510 0.000810170i
\(949\) −11.3597 34.9616i −0.368752 1.13490i
\(950\) 11.3899 35.0545i 0.369537 1.13732i
\(951\) −0.158270 0.114990i −0.00513227 0.00372881i
\(952\) −0.688447 0.500186i −0.0223127 0.0162111i
\(953\) −14.2456 + 43.8434i −0.461459 + 1.42023i 0.401922 + 0.915674i \(0.368342\pi\)
−0.863381 + 0.504552i \(0.831658\pi\)
\(954\) 18.4970 + 56.9280i 0.598863 + 1.84311i
\(955\) −42.0854 + 30.5768i −1.36185 + 0.989443i
\(956\) 3.07879 0.0995753
\(957\) 0.0769228 + 0.343363i 0.00248656 + 0.0110993i
\(958\) 36.7563 1.18754
\(959\) 3.06925 2.22994i 0.0991111 0.0720085i
\(960\) −0.0534434 0.164482i −0.00172488 0.00530863i
\(961\) 9.30773 28.6463i 0.300249 0.924073i
\(962\) −52.7578 38.3308i −1.70098 1.23583i
\(963\) 4.06909 + 2.95637i 0.131125 + 0.0952676i
\(964\) 2.48293 7.64167i 0.0799698 0.246122i
\(965\) 9.71641 + 29.9040i 0.312782 + 0.962645i
\(966\) −0.00894548 + 0.00649927i −0.000287816 + 0.000209111i
\(967\) 21.8136 0.701477 0.350739 0.936473i \(-0.385931\pi\)
0.350739 + 0.936473i \(0.385931\pi\)
\(968\) 17.5953 + 18.7013i 0.565535 + 0.601083i
\(969\) 0.0538702 0.00173056
\(970\) 51.8636 37.6811i 1.66524 1.20987i
\(971\) −18.7210 57.6172i −0.600784 1.84902i −0.523521 0.852013i \(-0.675382\pi\)
−0.0772630 0.997011i \(-0.524618\pi\)
\(972\) 0.0502447 0.154637i 0.00161160 0.00495999i
\(973\) 0.859512 + 0.624472i 0.0275547 + 0.0200197i
\(974\) −1.74017 1.26431i −0.0557586 0.0405110i
\(975\) 0.0846657 0.260574i 0.00271147 0.00834505i
\(976\) −8.49925 26.1580i −0.272054 0.837297i
\(977\) 24.8263 18.0374i 0.794265 0.577067i −0.114961 0.993370i \(-0.536674\pi\)
0.909226 + 0.416303i \(0.136674\pi\)
\(978\) 0.304341 0.00973176
\(979\) 0.720413 + 3.21573i 0.0230245 + 0.102775i
\(980\) 11.4982 0.367297
\(981\) 21.5212 15.6360i 0.687118 0.499220i
\(982\) 17.1919 + 52.9113i 0.548616 + 1.68847i
\(983\) 2.41453 7.43115i 0.0770115 0.237017i −0.905138 0.425117i \(-0.860233\pi\)
0.982150 + 0.188100i \(0.0602329\pi\)
\(984\) −0.0473337 0.0343900i −0.00150894 0.00109631i
\(985\) −5.75571 4.18177i −0.183392 0.133242i
\(986\) 4.62193 14.2248i 0.147192 0.453011i
\(987\) 0.00515717 + 0.0158722i 0.000164155 + 0.000505216i
\(988\) −10.2956 + 7.48021i −0.327548 + 0.237977i
\(989\) −15.7200 −0.499868
\(990\) −37.3037 32.8560i −1.18559 1.04423i
\(991\) 9.72063 0.308786 0.154393 0.988010i \(-0.450658\pi\)
0.154393 + 0.988010i \(0.450658\pi\)
\(992\) 18.6154 13.5249i 0.591039 0.429415i
\(993\) 0.0868185 + 0.267200i 0.00275510 + 0.00847933i
\(994\) 1.06320 3.27219i 0.0337226 0.103788i
\(995\) 21.8177 + 15.8515i 0.691668 + 0.502526i
\(996\) −0.0633168 0.0460023i −0.00200627 0.00145764i
\(997\) −16.5802 + 51.0285i −0.525099 + 1.61609i 0.239022 + 0.971014i \(0.423173\pi\)
−0.764120 + 0.645074i \(0.776827\pi\)
\(998\) −2.70610 8.32852i −0.0856601 0.263635i
\(999\) 0.449050 0.326254i 0.0142073 0.0103222i
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 187.2.g.f.69.4 36
11.2 odd 10 2057.2.a.be.1.6 18
11.4 even 5 inner 187.2.g.f.103.4 yes 36
11.9 even 5 2057.2.a.bd.1.13 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
187.2.g.f.69.4 36 1.1 even 1 trivial
187.2.g.f.103.4 yes 36 11.4 even 5 inner
2057.2.a.bd.1.13 18 11.9 even 5
2057.2.a.be.1.6 18 11.2 odd 10