Properties

Label 125.2.e.b.74.1
Level $125$
Weight $2$
Character 125.74
Analytic conductor $0.998$
Analytic rank $0$
Dimension $8$
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] = [125,2,Mod(24,125)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(125, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("125.24");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 125 = 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 125.e (of order \(10\), degree \(4\), 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: \(0.998130025266\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: 8.0.58140625.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) 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 25)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 74.1
Root \(1.66637 + 0.917186i\) of defining polynomial
Character \(\chi\) \(=\) 125.74
Dual form 125.2.e.b.49.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.666375 - 0.917186i) q^{2} +(2.47539 + 0.804303i) q^{3} +(0.220859 - 0.679734i) q^{4} +(-0.911842 - 2.80636i) q^{6} +0.407162i q^{7} +(-2.92705 + 0.951057i) q^{8} +(3.05361 + 2.21858i) q^{9} +O(q^{10})\) \(q+(-0.666375 - 0.917186i) q^{2} +(2.47539 + 0.804303i) q^{3} +(0.220859 - 0.679734i) q^{4} +(-0.911842 - 2.80636i) q^{6} +0.407162i q^{7} +(-2.92705 + 0.951057i) q^{8} +(3.05361 + 2.21858i) q^{9} +(-1.61803 + 1.17557i) q^{11} +(1.09343 - 1.50497i) q^{12} +(0.411842 - 0.566852i) q^{13} +(0.373443 - 0.271322i) q^{14} +(1.66637 + 1.21069i) q^{16} +(-1.50527 + 0.489091i) q^{17} -4.27913i q^{18} +(-1.52988 - 4.70847i) q^{19} +(-0.327481 + 1.00788i) q^{21} +(2.15643 + 0.700668i) q^{22} +(0.706192 + 0.971990i) q^{23} -8.01054 q^{24} -0.794350 q^{26} +(1.18484 + 1.63079i) q^{27} +(0.276762 + 0.0899253i) q^{28} +(-1.70239 + 5.23943i) q^{29} +(2.53514 + 7.80237i) q^{31} +3.82022i q^{32} +(-4.95078 + 1.60861i) q^{33} +(1.45166 + 1.05469i) q^{34} +(2.18246 - 1.58565i) q^{36} +(-3.01846 + 4.15456i) q^{37} +(-3.29908 + 4.54079i) q^{38} +(1.47539 - 1.07193i) q^{39} +(-5.83802 - 4.24157i) q^{41} +(1.14264 - 0.371267i) q^{42} -9.16531i q^{43} +(0.441718 + 1.35947i) q^{44} +(0.420907 - 1.29542i) q^{46} +(-1.21092 - 0.393451i) q^{47} +(3.15117 + 4.33721i) q^{48} +6.83422 q^{49} -4.11950 q^{51} +(-0.294350 - 0.405138i) q^{52} +(4.83133 + 1.56979i) q^{53} +(0.706192 - 2.17344i) q^{54} +(-0.387234 - 1.19178i) q^{56} -12.8858i q^{57} +(5.93997 - 1.93001i) q^{58} +(-5.25838 - 3.82044i) q^{59} +(7.62101 - 5.53699i) q^{61} +(5.46687 - 7.52450i) q^{62} +(-0.903319 + 1.24331i) q^{63} +(6.83660 - 4.96708i) q^{64} +(4.77447 + 3.46885i) q^{66} +(2.93090 - 0.952307i) q^{67} +1.13120i q^{68} +(0.966327 + 2.97405i) q^{69} +(2.12183 - 6.53032i) q^{71} +(-11.0481 - 3.58973i) q^{72} +(0.320429 + 0.441032i) q^{73} +5.82193 q^{74} -3.53840 q^{76} +(-0.478647 - 0.658801i) q^{77} +(-1.96633 - 0.638898i) q^{78} +(-1.69390 + 5.21330i) q^{79} +(-1.87783 - 5.77938i) q^{81} +8.18102i q^{82} +(0.926457 - 0.301024i) q^{83} +(0.612766 + 0.445201i) q^{84} +(-8.40629 + 6.10753i) q^{86} +(-8.42819 + 11.6004i) q^{87} +(3.61803 - 4.97980i) q^{88} +(-1.83363 + 1.33221i) q^{89} +(0.230800 + 0.167686i) q^{91} +(0.816664 - 0.265350i) q^{92} +21.3529i q^{93} +(0.446057 + 1.37282i) q^{94} +(-3.07261 + 9.45653i) q^{96} +(14.4736 + 4.70276i) q^{97} +(-4.55415 - 6.26825i) q^{98} -7.54893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 5 q^{2} + 5 q^{3} - q^{4} - 9 q^{6} - 10 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 5 q^{2} + 5 q^{3} - q^{4} - 9 q^{6} - 10 q^{8} + q^{9} - 4 q^{11} - 15 q^{12} + 5 q^{13} + 13 q^{14} + 3 q^{16} + 10 q^{17} - 5 q^{19} - 4 q^{21} - 5 q^{23} - 20 q^{24} + 6 q^{26} + 5 q^{27} + 15 q^{28} - 5 q^{29} - 9 q^{31} - 10 q^{33} + 13 q^{34} + 23 q^{36} - 30 q^{37} - 15 q^{38} - 3 q^{39} - 4 q^{41} + 15 q^{42} - 2 q^{44} - 19 q^{46} + 30 q^{48} + 14 q^{49} - 4 q^{51} + 10 q^{52} + 10 q^{53} - 5 q^{54} + 10 q^{56} - 20 q^{58} - 9 q^{61} + 30 q^{62} - 10 q^{63} + 4 q^{64} + 12 q^{66} - 20 q^{67} + 17 q^{69} + 6 q^{71} - 5 q^{72} - 15 q^{73} - 12 q^{74} - 20 q^{76} - 10 q^{77} - 25 q^{78} + 15 q^{79} + 28 q^{81} + 45 q^{83} + 18 q^{84} - 9 q^{86} + 20 q^{87} + 20 q^{88} - 25 q^{89} + 6 q^{91} - 30 q^{92} - 27 q^{94} + 16 q^{96} + 60 q^{97} + 10 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/125\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.666375 0.917186i −0.471198 0.648548i 0.505586 0.862776i \(-0.331276\pi\)
−0.976784 + 0.214228i \(0.931276\pi\)
\(3\) 2.47539 + 0.804303i 1.42917 + 0.464365i 0.918503 0.395415i \(-0.129399\pi\)
0.510665 + 0.859780i \(0.329399\pi\)
\(4\) 0.220859 0.679734i 0.110430 0.339867i
\(5\) 0 0
\(6\) −0.911842 2.80636i −0.372258 1.14569i
\(7\) 0.407162i 0.153893i 0.997035 + 0.0769463i \(0.0245170\pi\)
−0.997035 + 0.0769463i \(0.975483\pi\)
\(8\) −2.92705 + 0.951057i −1.03487 + 0.336249i
\(9\) 3.05361 + 2.21858i 1.01787 + 0.739525i
\(10\) 0 0
\(11\) −1.61803 + 1.17557i −0.487856 + 0.354448i −0.804359 0.594144i \(-0.797491\pi\)
0.316503 + 0.948591i \(0.397491\pi\)
\(12\) 1.09343 1.50497i 0.315645 0.434448i
\(13\) 0.411842 0.566852i 0.114224 0.157216i −0.748077 0.663612i \(-0.769023\pi\)
0.862301 + 0.506396i \(0.169023\pi\)
\(14\) 0.373443 0.271322i 0.0998068 0.0725139i
\(15\) 0 0
\(16\) 1.66637 + 1.21069i 0.416594 + 0.302673i
\(17\) −1.50527 + 0.489091i −0.365081 + 0.118622i −0.485812 0.874063i \(-0.661476\pi\)
0.120731 + 0.992685i \(0.461476\pi\)
\(18\) 4.27913i 1.00860i
\(19\) −1.52988 4.70847i −0.350978 1.08020i −0.958305 0.285747i \(-0.907758\pi\)
0.607328 0.794452i \(-0.292242\pi\)
\(20\) 0 0
\(21\) −0.327481 + 1.00788i −0.0714623 + 0.219938i
\(22\) 2.15643 + 0.700668i 0.459753 + 0.149383i
\(23\) 0.706192 + 0.971990i 0.147251 + 0.202674i 0.876271 0.481819i \(-0.160024\pi\)
−0.729020 + 0.684493i \(0.760024\pi\)
\(24\) −8.01054 −1.63514
\(25\) 0 0
\(26\) −0.794350 −0.155785
\(27\) 1.18484 + 1.63079i 0.228022 + 0.313846i
\(28\) 0.276762 + 0.0899253i 0.0523030 + 0.0169943i
\(29\) −1.70239 + 5.23943i −0.316127 + 0.972938i 0.659161 + 0.752001i \(0.270911\pi\)
−0.975288 + 0.220937i \(0.929089\pi\)
\(30\) 0 0
\(31\) 2.53514 + 7.80237i 0.455325 + 1.40135i 0.870753 + 0.491721i \(0.163632\pi\)
−0.415428 + 0.909626i \(0.636368\pi\)
\(32\) 3.82022i 0.675325i
\(33\) −4.95078 + 1.60861i −0.861821 + 0.280023i
\(34\) 1.45166 + 1.05469i 0.248958 + 0.180878i
\(35\) 0 0
\(36\) 2.18246 1.58565i 0.363743 0.264275i
\(37\) −3.01846 + 4.15456i −0.496232 + 0.683005i −0.981522 0.191348i \(-0.938714\pi\)
0.485290 + 0.874353i \(0.338714\pi\)
\(38\) −3.29908 + 4.54079i −0.535181 + 0.736613i
\(39\) 1.47539 1.07193i 0.236252 0.171647i
\(40\) 0 0
\(41\) −5.83802 4.24157i −0.911745 0.662422i 0.0297106 0.999559i \(-0.490541\pi\)
−0.941456 + 0.337137i \(0.890541\pi\)
\(42\) 1.14264 0.371267i 0.176314 0.0572877i
\(43\) 9.16531i 1.39770i −0.715270 0.698848i \(-0.753696\pi\)
0.715270 0.698848i \(-0.246304\pi\)
\(44\) 0.441718 + 1.35947i 0.0665915 + 0.204948i
\(45\) 0 0
\(46\) 0.420907 1.29542i 0.0620593 0.190999i
\(47\) −1.21092 0.393451i −0.176631 0.0573907i 0.219367 0.975643i \(-0.429601\pi\)
−0.395997 + 0.918252i \(0.629601\pi\)
\(48\) 3.15117 + 4.33721i 0.454832 + 0.626022i
\(49\) 6.83422 0.976317
\(50\) 0 0
\(51\) −4.11950 −0.576846
\(52\) −0.294350 0.405138i −0.0408190 0.0561825i
\(53\) 4.83133 + 1.56979i 0.663634 + 0.215628i 0.621416 0.783481i \(-0.286558\pi\)
0.0422180 + 0.999108i \(0.486558\pi\)
\(54\) 0.706192 2.17344i 0.0961005 0.295767i
\(55\) 0 0
\(56\) −0.387234 1.19178i −0.0517463 0.159259i
\(57\) 12.8858i 1.70677i
\(58\) 5.93997 1.93001i 0.779956 0.253423i
\(59\) −5.25838 3.82044i −0.684583 0.497379i 0.190292 0.981728i \(-0.439057\pi\)
−0.874875 + 0.484349i \(0.839057\pi\)
\(60\) 0 0
\(61\) 7.62101 5.53699i 0.975770 0.708938i 0.0190107 0.999819i \(-0.493948\pi\)
0.956759 + 0.290881i \(0.0939483\pi\)
\(62\) 5.46687 7.52450i 0.694293 0.955612i
\(63\) −0.903319 + 1.24331i −0.113807 + 0.156643i
\(64\) 6.83660 4.96708i 0.854575 0.620885i
\(65\) 0 0
\(66\) 4.77447 + 3.46885i 0.587696 + 0.426986i
\(67\) 2.93090 0.952307i 0.358066 0.116343i −0.124459 0.992225i \(-0.539720\pi\)
0.482526 + 0.875882i \(0.339720\pi\)
\(68\) 1.13120i 0.137178i
\(69\) 0.966327 + 2.97405i 0.116332 + 0.358033i
\(70\) 0 0
\(71\) 2.12183 6.53032i 0.251815 0.775007i −0.742625 0.669707i \(-0.766420\pi\)
0.994440 0.105300i \(-0.0335803\pi\)
\(72\) −11.0481 3.58973i −1.30203 0.423054i
\(73\) 0.320429 + 0.441032i 0.0375033 + 0.0516189i 0.827357 0.561677i \(-0.189843\pi\)
−0.789854 + 0.613296i \(0.789843\pi\)
\(74\) 5.82193 0.676786
\(75\) 0 0
\(76\) −3.53840 −0.405882
\(77\) −0.478647 0.658801i −0.0545469 0.0750774i
\(78\) −1.96633 0.638898i −0.222643 0.0723410i
\(79\) −1.69390 + 5.21330i −0.190579 + 0.586542i −1.00000 0.000687140i \(-0.999781\pi\)
0.809421 + 0.587229i \(0.199781\pi\)
\(80\) 0 0
\(81\) −1.87783 5.77938i −0.208648 0.642153i
\(82\) 8.18102i 0.903442i
\(83\) 0.926457 0.301024i 0.101692 0.0330417i −0.257729 0.966217i \(-0.582974\pi\)
0.359421 + 0.933176i \(0.382974\pi\)
\(84\) 0.612766 + 0.445201i 0.0668583 + 0.0485754i
\(85\) 0 0
\(86\) −8.40629 + 6.10753i −0.906474 + 0.658592i
\(87\) −8.42819 + 11.6004i −0.903596 + 1.24369i
\(88\) 3.61803 4.97980i 0.385684 0.530848i
\(89\) −1.83363 + 1.33221i −0.194364 + 0.141214i −0.680711 0.732552i \(-0.738329\pi\)
0.486347 + 0.873766i \(0.338329\pi\)
\(90\) 0 0
\(91\) 0.230800 + 0.167686i 0.0241945 + 0.0175783i
\(92\) 0.816664 0.265350i 0.0851431 0.0276647i
\(93\) 21.3529i 2.21420i
\(94\) 0.446057 + 1.37282i 0.0460073 + 0.141596i
\(95\) 0 0
\(96\) −3.07261 + 9.45653i −0.313597 + 0.965153i
\(97\) 14.4736 + 4.70276i 1.46957 + 0.477493i 0.930979 0.365073i \(-0.118956\pi\)
0.538593 + 0.842566i \(0.318956\pi\)
\(98\) −4.55415 6.26825i −0.460039 0.633189i
\(99\) −7.54893 −0.758696
\(100\) 0 0
\(101\) 18.3965 1.83052 0.915261 0.402861i \(-0.131984\pi\)
0.915261 + 0.402861i \(0.131984\pi\)
\(102\) 2.74513 + 3.77835i 0.271809 + 0.374113i
\(103\) −11.3026 3.67243i −1.11368 0.361856i −0.306326 0.951927i \(-0.599100\pi\)
−0.807351 + 0.590071i \(0.799100\pi\)
\(104\) −0.666375 + 2.05089i −0.0653434 + 0.201106i
\(105\) 0 0
\(106\) −1.77968 5.47730i −0.172858 0.532002i
\(107\) 0.754919i 0.0729808i 0.999334 + 0.0364904i \(0.0116178\pi\)
−0.999334 + 0.0364904i \(0.988382\pi\)
\(108\) 1.37019 0.445201i 0.131846 0.0428395i
\(109\) −7.40859 5.38265i −0.709614 0.515565i 0.173435 0.984845i \(-0.444513\pi\)
−0.883049 + 0.469281i \(0.844513\pi\)
\(110\) 0 0
\(111\) −10.8134 + 7.85640i −1.02636 + 0.745697i
\(112\) −0.492947 + 0.678484i −0.0465791 + 0.0641107i
\(113\) 7.54710 10.3877i 0.709971 0.977191i −0.289827 0.957079i \(-0.593598\pi\)
0.999798 0.0201123i \(-0.00640237\pi\)
\(114\) −11.8187 + 8.58677i −1.10692 + 0.804225i
\(115\) 0 0
\(116\) 3.18543 + 2.31435i 0.295760 + 0.214882i
\(117\) 2.51521 0.817241i 0.232531 0.0755539i
\(118\) 7.36876i 0.678349i
\(119\) −0.199139 0.612887i −0.0182551 0.0561833i
\(120\) 0 0
\(121\) −2.16312 + 6.65740i −0.196647 + 0.605218i
\(122\) −10.1569 3.30017i −0.919562 0.298784i
\(123\) −11.0399 15.1951i −0.995432 1.37009i
\(124\) 5.86345 0.526553
\(125\) 0 0
\(126\) 1.74230 0.155216
\(127\) −4.17632 5.74821i −0.370588 0.510071i 0.582472 0.812850i \(-0.302085\pi\)
−0.953061 + 0.302780i \(0.902085\pi\)
\(128\) −1.84498 0.599472i −0.163075 0.0529863i
\(129\) 7.37169 22.6877i 0.649041 1.99754i
\(130\) 0 0
\(131\) 0.739865 + 2.27707i 0.0646423 + 0.198949i 0.978161 0.207848i \(-0.0666459\pi\)
−0.913519 + 0.406796i \(0.866646\pi\)
\(132\) 3.72049i 0.323827i
\(133\) 1.91711 0.622907i 0.166234 0.0540129i
\(134\) −2.82652 2.05359i −0.244174 0.177403i
\(135\) 0 0
\(136\) 3.94084 2.86319i 0.337924 0.245516i
\(137\) 11.1793 15.3870i 0.955111 1.31460i 0.00589176 0.999983i \(-0.498125\pi\)
0.949219 0.314615i \(-0.101875\pi\)
\(138\) 2.08382 2.86813i 0.177386 0.244152i
\(139\) −5.44849 + 3.95856i −0.462135 + 0.335761i −0.794368 0.607437i \(-0.792198\pi\)
0.332233 + 0.943197i \(0.392198\pi\)
\(140\) 0 0
\(141\) −2.68104 1.94789i −0.225784 0.164042i
\(142\) −7.40346 + 2.40553i −0.621284 + 0.201867i
\(143\) 1.40134i 0.117186i
\(144\) 2.40244 + 7.39396i 0.200204 + 0.616163i
\(145\) 0 0
\(146\) 0.190983 0.587785i 0.0158059 0.0486455i
\(147\) 16.9174 + 5.49679i 1.39532 + 0.453367i
\(148\) 2.15734 + 2.96933i 0.177332 + 0.244077i
\(149\) 0.720492 0.0590250 0.0295125 0.999564i \(-0.490605\pi\)
0.0295125 + 0.999564i \(0.490605\pi\)
\(150\) 0 0
\(151\) −15.5178 −1.26282 −0.631412 0.775447i \(-0.717524\pi\)
−0.631412 + 0.775447i \(0.717524\pi\)
\(152\) 8.95605 + 12.3269i 0.726432 + 0.999847i
\(153\) −5.68158 1.84606i −0.459329 0.149245i
\(154\) −0.285285 + 0.878017i −0.0229889 + 0.0707526i
\(155\) 0 0
\(156\) −0.402777 1.23962i −0.0322480 0.0992491i
\(157\) 2.78418i 0.222202i −0.993809 0.111101i \(-0.964562\pi\)
0.993809 0.111101i \(-0.0354376\pi\)
\(158\) 5.91034 1.92039i 0.470201 0.152778i
\(159\) 10.6968 + 7.77171i 0.848315 + 0.616337i
\(160\) 0 0
\(161\) −0.395757 + 0.287534i −0.0311900 + 0.0226609i
\(162\) −4.04942 + 5.57355i −0.318153 + 0.437900i
\(163\) −14.2287 + 19.5842i −1.11448 + 1.53395i −0.299835 + 0.953991i \(0.596932\pi\)
−0.814645 + 0.579960i \(0.803068\pi\)
\(164\) −4.17252 + 3.03151i −0.325819 + 0.236721i
\(165\) 0 0
\(166\) −0.893462 0.649138i −0.0693461 0.0503829i
\(167\) −18.1140 + 5.88559i −1.40170 + 0.455441i −0.909741 0.415176i \(-0.863720\pi\)
−0.491961 + 0.870617i \(0.663720\pi\)
\(168\) 3.26158i 0.251637i
\(169\) 3.86551 + 11.8968i 0.297347 + 0.915141i
\(170\) 0 0
\(171\) 5.77447 17.7720i 0.441585 1.35906i
\(172\) −6.22998 2.02424i −0.475031 0.154347i
\(173\) 7.78642 + 10.7171i 0.591991 + 0.814805i 0.994946 0.100415i \(-0.0320169\pi\)
−0.402955 + 0.915220i \(0.632017\pi\)
\(174\) 16.2561 1.23237
\(175\) 0 0
\(176\) −4.11950 −0.310519
\(177\) −9.94376 13.6864i −0.747419 1.02873i
\(178\) 2.44376 + 0.794027i 0.183168 + 0.0595148i
\(179\) 3.77772 11.6266i 0.282360 0.869016i −0.704817 0.709389i \(-0.748971\pi\)
0.987177 0.159627i \(-0.0510290\pi\)
\(180\) 0 0
\(181\) 3.37348 + 10.3825i 0.250748 + 0.771724i 0.994638 + 0.103421i \(0.0329790\pi\)
−0.743889 + 0.668303i \(0.767021\pi\)
\(182\) 0.323429i 0.0239741i
\(183\) 23.3184 7.57661i 1.72375 0.560079i
\(184\) −2.99148 2.17344i −0.220535 0.160228i
\(185\) 0 0
\(186\) 19.5846 14.2291i 1.43601 1.04333i
\(187\) 1.86061 2.56091i 0.136062 0.187273i
\(188\) −0.534884 + 0.736205i −0.0390105 + 0.0536933i
\(189\) −0.663995 + 0.482421i −0.0482986 + 0.0350910i
\(190\) 0 0
\(191\) −1.26824 0.921429i −0.0917665 0.0666723i 0.540956 0.841051i \(-0.318063\pi\)
−0.632722 + 0.774379i \(0.718063\pi\)
\(192\) 20.9183 6.79677i 1.50965 0.490514i
\(193\) 1.65786i 0.119335i 0.998218 + 0.0596675i \(0.0190040\pi\)
−0.998218 + 0.0596675i \(0.980996\pi\)
\(194\) −5.33154 16.4088i −0.382782 1.17808i
\(195\) 0 0
\(196\) 1.50940 4.64545i 0.107814 0.331818i
\(197\) −12.6330 4.10470i −0.900061 0.292448i −0.177799 0.984067i \(-0.556898\pi\)
−0.722262 + 0.691619i \(0.756898\pi\)
\(198\) 5.03042 + 6.92378i 0.357496 + 0.492051i
\(199\) −12.1025 −0.857921 −0.428960 0.903323i \(-0.641120\pi\)
−0.428960 + 0.903323i \(0.641120\pi\)
\(200\) 0 0
\(201\) 8.02107 0.565763
\(202\) −12.2590 16.8730i −0.862539 1.18718i
\(203\) −2.13330 0.693150i −0.149728 0.0486496i
\(204\) −0.909830 + 2.80017i −0.0637008 + 0.196051i
\(205\) 0 0
\(206\) 4.16345 + 12.8138i 0.290082 + 0.892779i
\(207\) 4.53482i 0.315192i
\(208\) 1.37257 0.445974i 0.0951704 0.0309227i
\(209\) 8.01054 + 5.81999i 0.554100 + 0.402577i
\(210\) 0 0
\(211\) 5.42091 3.93852i 0.373191 0.271139i −0.385342 0.922774i \(-0.625917\pi\)
0.758533 + 0.651635i \(0.225917\pi\)
\(212\) 2.13409 2.93732i 0.146570 0.201736i
\(213\) 10.5047 14.4585i 0.719772 0.990681i
\(214\) 0.692401 0.503059i 0.0473316 0.0343884i
\(215\) 0 0
\(216\) −5.01906 3.64656i −0.341504 0.248117i
\(217\) −3.17683 + 1.03221i −0.215657 + 0.0700712i
\(218\) 10.3819i 0.703152i
\(219\) 0.438463 + 1.34945i 0.0296286 + 0.0911873i
\(220\) 0 0
\(221\) −0.342690 + 1.05469i −0.0230518 + 0.0709463i
\(222\) 14.4116 + 4.68260i 0.967241 + 0.314276i
\(223\) 6.22564 + 8.56885i 0.416900 + 0.573813i 0.964884 0.262675i \(-0.0846048\pi\)
−0.547985 + 0.836488i \(0.684605\pi\)
\(224\) −1.55545 −0.103928
\(225\) 0 0
\(226\) −14.5566 −0.968293
\(227\) 11.5272 + 15.8658i 0.765087 + 1.05305i 0.996774 + 0.0802612i \(0.0255755\pi\)
−0.231687 + 0.972790i \(0.574425\pi\)
\(228\) −8.75892 2.84595i −0.580074 0.188477i
\(229\) −2.73139 + 8.40637i −0.180496 + 0.555508i −0.999842 0.0177908i \(-0.994337\pi\)
0.819346 + 0.573299i \(0.194337\pi\)
\(230\) 0 0
\(231\) −0.654963 2.01577i −0.0430934 0.132628i
\(232\) 16.9552i 1.11316i
\(233\) −10.5210 + 3.41848i −0.689253 + 0.223952i −0.632642 0.774445i \(-0.718029\pi\)
−0.0566109 + 0.998396i \(0.518029\pi\)
\(234\) −2.42563 1.76233i −0.158569 0.115207i
\(235\) 0 0
\(236\) −3.75824 + 2.73052i −0.244641 + 0.177742i
\(237\) −8.38615 + 11.5425i −0.544739 + 0.749769i
\(238\) −0.429430 + 0.591060i −0.0278358 + 0.0383127i
\(239\) 13.0296 9.46655i 0.842814 0.612340i −0.0803411 0.996767i \(-0.525601\pi\)
0.923155 + 0.384427i \(0.125601\pi\)
\(240\) 0 0
\(241\) −4.84498 3.52009i −0.312093 0.226749i 0.420701 0.907199i \(-0.361784\pi\)
−0.732794 + 0.680451i \(0.761784\pi\)
\(242\) 7.54752 2.45234i 0.485173 0.157642i
\(243\) 21.8639i 1.40257i
\(244\) −2.08051 6.40315i −0.133191 0.409920i
\(245\) 0 0
\(246\) −6.58002 + 20.2512i −0.419527 + 1.29117i
\(247\) −3.29908 1.07193i −0.209915 0.0682056i
\(248\) −14.8410 20.4269i −0.942404 1.29711i
\(249\) 2.53546 0.160678
\(250\) 0 0
\(251\) 3.73176 0.235547 0.117773 0.993041i \(-0.462424\pi\)
0.117773 + 0.993041i \(0.462424\pi\)
\(252\) 0.645616 + 0.888614i 0.0406700 + 0.0559774i
\(253\) −2.28528 0.742534i −0.143675 0.0466827i
\(254\) −2.48918 + 7.66092i −0.156185 + 0.480689i
\(255\) 0 0
\(256\) −4.54307 13.9821i −0.283942 0.873884i
\(257\) 23.5935i 1.47172i 0.677132 + 0.735862i \(0.263223\pi\)
−0.677132 + 0.735862i \(0.736777\pi\)
\(258\) −25.7212 + 8.35731i −1.60133 + 0.520304i
\(259\) −1.69158 1.22900i −0.105109 0.0763665i
\(260\) 0 0
\(261\) −16.8225 + 12.2223i −1.04129 + 0.756540i
\(262\) 1.59547 2.19598i 0.0985685 0.135668i
\(263\) −3.90363 + 5.37289i −0.240708 + 0.331307i −0.912230 0.409678i \(-0.865641\pi\)
0.671522 + 0.740985i \(0.265641\pi\)
\(264\) 12.9613 9.41695i 0.797714 0.579573i
\(265\) 0 0
\(266\) −1.84883 1.34326i −0.113359 0.0823604i
\(267\) −5.61044 + 1.82294i −0.343353 + 0.111562i
\(268\) 2.20256i 0.134543i
\(269\) 4.03078 + 12.4055i 0.245761 + 0.756375i 0.995510 + 0.0946532i \(0.0301742\pi\)
−0.749749 + 0.661722i \(0.769826\pi\)
\(270\) 0 0
\(271\) −3.66147 + 11.2689i −0.222419 + 0.684534i 0.776125 + 0.630579i \(0.217183\pi\)
−0.998543 + 0.0539549i \(0.982817\pi\)
\(272\) −3.10048 1.00741i −0.187994 0.0610830i
\(273\) 0.436451 + 0.600723i 0.0264152 + 0.0363574i
\(274\) −21.5623 −1.30263
\(275\) 0 0
\(276\) 2.23498 0.134530
\(277\) 9.96641 + 13.7176i 0.598824 + 0.824210i 0.995600 0.0937053i \(-0.0298711\pi\)
−0.396776 + 0.917915i \(0.629871\pi\)
\(278\) 7.26147 + 2.35939i 0.435514 + 0.141507i
\(279\) −9.56882 + 29.4498i −0.572870 + 1.76311i
\(280\) 0 0
\(281\) −1.56826 4.82659i −0.0935543 0.287930i 0.893320 0.449421i \(-0.148370\pi\)
−0.986874 + 0.161491i \(0.948370\pi\)
\(282\) 3.75704i 0.223728i
\(283\) −11.2461 + 3.65408i −0.668511 + 0.217212i −0.623558 0.781777i \(-0.714314\pi\)
−0.0449525 + 0.998989i \(0.514314\pi\)
\(284\) −3.97026 2.88456i −0.235592 0.171167i
\(285\) 0 0
\(286\) 1.28528 0.933814i 0.0760005 0.0552176i
\(287\) 1.72700 2.37702i 0.101942 0.140311i
\(288\) −8.47544 + 11.6654i −0.499420 + 0.687393i
\(289\) −11.7267 + 8.51992i −0.689804 + 0.501172i
\(290\) 0 0
\(291\) 32.0454 + 23.2823i 1.87853 + 1.36484i
\(292\) 0.370554 0.120400i 0.0216851 0.00704590i
\(293\) 19.4348i 1.13540i −0.823237 0.567698i \(-0.807834\pi\)
0.823237 0.567698i \(-0.192166\pi\)
\(294\) −6.23173 19.1793i −0.363442 1.11856i
\(295\) 0 0
\(296\) 4.88398 15.0313i 0.283875 0.873679i
\(297\) −3.83422 1.24581i −0.222484 0.0722894i
\(298\) −0.480118 0.660825i −0.0278125 0.0382806i
\(299\) 0.841814 0.0486834
\(300\) 0 0
\(301\) 3.73176 0.215095
\(302\) 10.3407 + 14.2328i 0.595040 + 0.819003i
\(303\) 45.5386 + 14.7964i 2.61612 + 0.850030i
\(304\) 3.15117 9.69829i 0.180732 0.556235i
\(305\) 0 0
\(306\) 2.09288 + 6.44123i 0.119642 + 0.368221i
\(307\) 25.4169i 1.45062i −0.688423 0.725310i \(-0.741697\pi\)
0.688423 0.725310i \(-0.258303\pi\)
\(308\) −0.553523 + 0.179851i −0.0315399 + 0.0102479i
\(309\) −25.0246 18.1814i −1.42360 1.03431i
\(310\) 0 0
\(311\) −12.8292 + 9.32097i −0.727478 + 0.528544i −0.888765 0.458364i \(-0.848436\pi\)
0.161287 + 0.986908i \(0.448436\pi\)
\(312\) −3.29908 + 4.54079i −0.186773 + 0.257072i
\(313\) 4.12416 5.67642i 0.233111 0.320850i −0.676396 0.736538i \(-0.736459\pi\)
0.909507 + 0.415688i \(0.136459\pi\)
\(314\) −2.55361 + 1.85530i −0.144108 + 0.104701i
\(315\) 0 0
\(316\) 3.16955 + 2.30281i 0.178301 + 0.129543i
\(317\) 12.3958 4.02763i 0.696215 0.226214i 0.0605344 0.998166i \(-0.480720\pi\)
0.635681 + 0.771952i \(0.280720\pi\)
\(318\) 14.9899i 0.840590i
\(319\) −3.40479 10.4789i −0.190632 0.586704i
\(320\) 0 0
\(321\) −0.607184 + 1.86872i −0.0338897 + 0.104302i
\(322\) 0.527445 + 0.171377i 0.0293933 + 0.00955047i
\(323\) 4.60575 + 6.33927i 0.256271 + 0.352726i
\(324\) −4.34318 −0.241288
\(325\) 0 0
\(326\) 27.4440 1.51998
\(327\) −14.0099 19.2829i −0.774747 1.06635i
\(328\) 21.1221 + 6.86300i 1.16628 + 0.378946i
\(329\) 0.160198 0.493039i 0.00883201 0.0271821i
\(330\) 0 0
\(331\) −5.45225 16.7803i −0.299683 0.922329i −0.981608 0.190907i \(-0.938857\pi\)
0.681925 0.731422i \(-0.261143\pi\)
\(332\) 0.696229i 0.0382105i
\(333\) −18.4344 + 5.98970i −1.01020 + 0.328234i
\(334\) 17.4689 + 12.6919i 0.955855 + 0.694469i
\(335\) 0 0
\(336\) −1.76594 + 1.28303i −0.0963401 + 0.0699952i
\(337\) −14.6062 + 20.1037i −0.795649 + 1.09512i 0.197733 + 0.980256i \(0.436642\pi\)
−0.993382 + 0.114860i \(0.963358\pi\)
\(338\) 8.33572 11.4731i 0.453404 0.624056i
\(339\) 27.0369 19.6434i 1.46844 1.06689i
\(340\) 0 0
\(341\) −13.2742 9.64426i −0.718837 0.522266i
\(342\) −20.1482 + 6.54654i −1.08949 + 0.353996i
\(343\) 5.63276i 0.304141i
\(344\) 8.71673 + 26.8273i 0.469974 + 1.44643i
\(345\) 0 0
\(346\) 4.64089 14.2832i 0.249496 0.767869i
\(347\) −12.6276 4.10297i −0.677887 0.220259i −0.0502171 0.998738i \(-0.515991\pi\)
−0.627670 + 0.778479i \(0.715991\pi\)
\(348\) 6.02375 + 8.29098i 0.322907 + 0.444443i
\(349\) 18.1283 0.970385 0.485192 0.874407i \(-0.338750\pi\)
0.485192 + 0.874407i \(0.338750\pi\)
\(350\) 0 0
\(351\) 1.41238 0.0753875
\(352\) −4.49094 6.18124i −0.239368 0.329461i
\(353\) −16.8377 5.47091i −0.896182 0.291187i −0.175522 0.984476i \(-0.556161\pi\)
−0.720660 + 0.693288i \(0.756161\pi\)
\(354\) −5.92672 + 18.2406i −0.315001 + 0.969475i
\(355\) 0 0
\(356\) 0.500574 + 1.54061i 0.0265304 + 0.0816521i
\(357\) 1.67730i 0.0887723i
\(358\) −13.1812 + 4.28282i −0.696646 + 0.226354i
\(359\) 26.3289 + 19.1291i 1.38959 + 1.00959i 0.995910 + 0.0903458i \(0.0287972\pi\)
0.393677 + 0.919249i \(0.371203\pi\)
\(360\) 0 0
\(361\) −4.45789 + 3.23885i −0.234626 + 0.170466i
\(362\) 7.27467 10.0127i 0.382348 0.526257i
\(363\) −10.7091 + 14.7399i −0.562084 + 0.773642i
\(364\) 0.164956 0.119848i 0.00864607 0.00628174i
\(365\) 0 0
\(366\) −22.4879 16.3384i −1.17546 0.854024i
\(367\) 31.3355 10.1815i 1.63570 0.531472i 0.660129 0.751152i \(-0.270501\pi\)
0.975572 + 0.219680i \(0.0705014\pi\)
\(368\) 2.47468i 0.129002i
\(369\) −8.41677 25.9042i −0.438160 1.34852i
\(370\) 0 0
\(371\) −0.639160 + 1.96713i −0.0331835 + 0.102128i
\(372\) 14.5143 + 4.71599i 0.752533 + 0.244513i
\(373\) −2.03754 2.80444i −0.105500 0.145208i 0.753003 0.658018i \(-0.228605\pi\)
−0.858503 + 0.512809i \(0.828605\pi\)
\(374\) −3.58870 −0.185567
\(375\) 0 0
\(376\) 3.91861 0.202087
\(377\) 2.26886 + 3.12282i 0.116852 + 0.160834i
\(378\) 0.884939 + 0.287534i 0.0455164 + 0.0147892i
\(379\) 0.595979 1.83424i 0.0306134 0.0942183i −0.934582 0.355747i \(-0.884227\pi\)
0.965196 + 0.261528i \(0.0842265\pi\)
\(380\) 0 0
\(381\) −5.71472 17.5881i −0.292774 0.901065i
\(382\) 1.77723i 0.0909309i
\(383\) 4.68874 1.52346i 0.239583 0.0778454i −0.186764 0.982405i \(-0.559800\pi\)
0.426348 + 0.904559i \(0.359800\pi\)
\(384\) −4.08490 2.96786i −0.208457 0.151453i
\(385\) 0 0
\(386\) 1.52056 1.10475i 0.0773945 0.0562304i
\(387\) 20.3339 27.9873i 1.03363 1.42267i
\(388\) 6.39326 8.79956i 0.324568 0.446730i
\(389\) 10.8295 7.86809i 0.549077 0.398928i −0.278368 0.960475i \(-0.589793\pi\)
0.827445 + 0.561547i \(0.189793\pi\)
\(390\) 0 0
\(391\) −1.53840 1.11771i −0.0778002 0.0565252i
\(392\) −20.0041 + 6.49973i −1.01036 + 0.328286i
\(393\) 6.23172i 0.314349i
\(394\) 4.65351 + 14.3220i 0.234441 + 0.721534i
\(395\) 0 0
\(396\) −1.66725 + 5.13127i −0.0837825 + 0.257856i
\(397\) −2.03418 0.660946i −0.102093 0.0331719i 0.257525 0.966272i \(-0.417093\pi\)
−0.359618 + 0.933100i \(0.617093\pi\)
\(398\) 8.06477 + 11.1002i 0.404250 + 0.556403i
\(399\) 5.24660 0.262659
\(400\) 0 0
\(401\) −26.8213 −1.33939 −0.669696 0.742635i \(-0.733576\pi\)
−0.669696 + 0.742635i \(0.733576\pi\)
\(402\) −5.34504 7.35681i −0.266586 0.366924i
\(403\) 5.46687 + 1.77629i 0.272324 + 0.0884835i
\(404\) 4.06304 12.5048i 0.202144 0.622135i
\(405\) 0 0
\(406\) 0.785827 + 2.41853i 0.0389999 + 0.120029i
\(407\) 10.2706i 0.509097i
\(408\) 12.0580 3.91788i 0.596960 0.193964i
\(409\) 11.3248 + 8.22796i 0.559976 + 0.406847i 0.831450 0.555599i \(-0.187511\pi\)
−0.271474 + 0.962446i \(0.587511\pi\)
\(410\) 0 0
\(411\) 40.0489 29.0972i 1.97547 1.43526i
\(412\) −4.99256 + 6.87167i −0.245966 + 0.338543i
\(413\) 1.55554 2.14101i 0.0765429 0.105352i
\(414\) 4.15927 3.02189i 0.204417 0.148518i
\(415\) 0 0
\(416\) 2.16550 + 1.57333i 0.106172 + 0.0771387i
\(417\) −16.6710 + 5.41674i −0.816384 + 0.265259i
\(418\) 11.2254i 0.549055i
\(419\) −9.54925 29.3896i −0.466511 1.43577i −0.857072 0.515197i \(-0.827719\pi\)
0.390560 0.920577i \(-0.372281\pi\)
\(420\) 0 0
\(421\) −2.54622 + 7.83646i −0.124095 + 0.381926i −0.993735 0.111761i \(-0.964351\pi\)
0.869640 + 0.493687i \(0.164351\pi\)
\(422\) −7.22471 2.34745i −0.351693 0.114272i
\(423\) −2.82477 3.88796i −0.137345 0.189039i
\(424\) −15.6345 −0.759279
\(425\) 0 0
\(426\) −20.2612 −0.981660
\(427\) 2.25445 + 3.10298i 0.109100 + 0.150164i
\(428\) 0.513144 + 0.166731i 0.0248038 + 0.00805923i
\(429\) −1.12710 + 3.46885i −0.0544168 + 0.167478i
\(430\) 0 0
\(431\) 8.38925 + 25.8194i 0.404096 + 1.24368i 0.921648 + 0.388027i \(0.126843\pi\)
−0.517552 + 0.855652i \(0.673157\pi\)
\(432\) 4.15198i 0.199762i
\(433\) 20.4387 6.64093i 0.982220 0.319143i 0.226481 0.974016i \(-0.427278\pi\)
0.755739 + 0.654873i \(0.227278\pi\)
\(434\) 3.06369 + 2.22590i 0.147062 + 0.106847i
\(435\) 0 0
\(436\) −5.29503 + 3.84706i −0.253586 + 0.184241i
\(437\) 3.49620 4.81211i 0.167246 0.230194i
\(438\) 0.945515 1.30139i 0.0451785 0.0621828i
\(439\) −20.8691 + 15.1623i −0.996027 + 0.723656i −0.961233 0.275739i \(-0.911078\pi\)
−0.0347942 + 0.999394i \(0.511078\pi\)
\(440\) 0 0
\(441\) 20.8690 + 15.1622i 0.993763 + 0.722011i
\(442\) 1.19571 0.388509i 0.0568741 0.0184795i
\(443\) 3.18479i 0.151314i −0.997134 0.0756570i \(-0.975895\pi\)
0.997134 0.0756570i \(-0.0241054\pi\)
\(444\) 2.95203 + 9.08540i 0.140097 + 0.431174i
\(445\) 0 0
\(446\) 3.71063 11.4201i 0.175703 0.540759i
\(447\) 1.78350 + 0.579494i 0.0843566 + 0.0274091i
\(448\) 2.02240 + 2.78360i 0.0955496 + 0.131513i
\(449\) −36.0785 −1.70265 −0.851325 0.524639i \(-0.824200\pi\)
−0.851325 + 0.524639i \(0.824200\pi\)
\(450\) 0 0
\(451\) 14.4324 0.679594
\(452\) −5.39402 7.42424i −0.253714 0.349207i
\(453\) −38.4127 12.4811i −1.80479 0.586411i
\(454\) 6.87048 21.1452i 0.322448 0.992392i
\(455\) 0 0
\(456\) 12.2551 + 37.7174i 0.573899 + 1.76628i
\(457\) 25.5245i 1.19399i 0.802246 + 0.596994i \(0.203638\pi\)
−0.802246 + 0.596994i \(0.796362\pi\)
\(458\) 9.53033 3.09659i 0.445323 0.144694i
\(459\) −2.58111 1.87528i −0.120476 0.0875307i
\(460\) 0 0
\(461\) 13.4614 9.78026i 0.626959 0.455512i −0.228387 0.973571i \(-0.573345\pi\)
0.855345 + 0.518058i \(0.173345\pi\)
\(462\) −1.41238 + 1.94398i −0.0657100 + 0.0904421i
\(463\) −10.4730 + 14.4149i −0.486723 + 0.669916i −0.979779 0.200081i \(-0.935880\pi\)
0.493057 + 0.869997i \(0.335880\pi\)
\(464\) −9.18017 + 6.66978i −0.426178 + 0.309637i
\(465\) 0 0
\(466\) 10.1463 + 7.37171i 0.470018 + 0.341488i
\(467\) 13.5507 4.40289i 0.627051 0.203741i 0.0217829 0.999763i \(-0.493066\pi\)
0.605269 + 0.796021i \(0.293066\pi\)
\(468\) 1.89017i 0.0873731i
\(469\) 0.387743 + 1.19335i 0.0179043 + 0.0551038i
\(470\) 0 0
\(471\) 2.23932 6.89193i 0.103183 0.317563i
\(472\) 19.0250 + 6.18160i 0.875697 + 0.284531i
\(473\) 10.7745 + 14.8298i 0.495411 + 0.681874i
\(474\) 16.1750 0.742941
\(475\) 0 0
\(476\) −0.460582 −0.0211107
\(477\) 11.2703 + 15.5122i 0.516031 + 0.710255i
\(478\) −17.3652 5.64229i −0.794265 0.258072i
\(479\) −0.898820 + 2.76628i −0.0410681 + 0.126395i −0.969489 0.245137i \(-0.921167\pi\)
0.928420 + 0.371531i \(0.121167\pi\)
\(480\) 0 0
\(481\) 1.11189 + 3.42205i 0.0506978 + 0.156032i
\(482\) 6.78945i 0.309251i
\(483\) −1.21092 + 0.393451i −0.0550987 + 0.0179026i
\(484\) 4.04752 + 2.94069i 0.183978 + 0.133668i
\(485\) 0 0
\(486\) −20.0532 + 14.5695i −0.909633 + 0.660887i
\(487\) −10.0307 + 13.8060i −0.454533 + 0.625612i −0.973364 0.229266i \(-0.926368\pi\)
0.518831 + 0.854877i \(0.326368\pi\)
\(488\) −17.0411 + 23.4550i −0.771414 + 1.06176i
\(489\) −50.9733 + 37.0343i −2.30509 + 1.67475i
\(490\) 0 0
\(491\) −24.8990 18.0902i −1.12368 0.816398i −0.138913 0.990305i \(-0.544361\pi\)
−0.984762 + 0.173906i \(0.944361\pi\)
\(492\) −12.7669 + 4.14821i −0.575575 + 0.187016i
\(493\) 8.71937i 0.392701i
\(494\) 1.21526 + 3.74018i 0.0546770 + 0.168278i
\(495\) 0 0
\(496\) −5.22177 + 16.0709i −0.234464 + 0.721607i
\(497\) 2.65890 + 0.863928i 0.119268 + 0.0387525i
\(498\) −1.68956 2.32549i −0.0757112 0.104208i
\(499\) 11.8824 0.531927 0.265964 0.963983i \(-0.414310\pi\)
0.265964 + 0.963983i \(0.414310\pi\)
\(500\) 0 0
\(501\) −49.5730 −2.21476
\(502\) −2.48675 3.42272i −0.110989 0.152763i
\(503\) 2.83247 + 0.920324i 0.126293 + 0.0410352i 0.371482 0.928440i \(-0.378850\pi\)
−0.245188 + 0.969475i \(0.578850\pi\)
\(504\) 1.46160 4.49834i 0.0651049 0.200372i
\(505\) 0 0
\(506\) 0.841814 + 2.59084i 0.0374232 + 0.115177i
\(507\) 32.5584i 1.44597i
\(508\) −4.82963 + 1.56924i −0.214280 + 0.0696239i
\(509\) −29.7038 21.5811i −1.31660 0.956564i −0.999968 0.00801464i \(-0.997449\pi\)
−0.316629 0.948549i \(-0.602551\pi\)
\(510\) 0 0
\(511\) −0.179571 + 0.130466i −0.00794377 + 0.00577149i
\(512\) −12.0774 + 16.6231i −0.533749 + 0.734642i
\(513\) 5.86588 8.07369i 0.258985 0.356462i
\(514\) 21.6396 15.7221i 0.954484 0.693473i
\(515\) 0 0
\(516\) −13.7935 10.0216i −0.607226 0.441176i
\(517\) 2.42184 0.786902i 0.106512 0.0346079i
\(518\) 2.37047i 0.104152i
\(519\) 10.6546 + 32.7916i 0.467687 + 1.43939i
\(520\) 0 0
\(521\) 0.772662 2.37801i 0.0338509 0.104182i −0.932703 0.360644i \(-0.882557\pi\)
0.966554 + 0.256462i \(0.0825568\pi\)
\(522\) 22.4202 + 7.28477i 0.981306 + 0.318846i
\(523\) −24.7609 34.0805i −1.08272 1.49024i −0.856491 0.516162i \(-0.827360\pi\)
−0.226229 0.974074i \(-0.572640\pi\)
\(524\) 1.71121 0.0747545
\(525\) 0 0
\(526\) 7.52922 0.328290
\(527\) −7.63214 10.5047i −0.332461 0.457594i
\(528\) −10.1974 3.31333i −0.443784 0.144194i
\(529\) 6.66133 20.5015i 0.289623 0.891369i
\(530\) 0 0
\(531\) −7.58111 23.3322i −0.328992 1.01253i
\(532\) 1.44070i 0.0624623i
\(533\) −4.80868 + 1.56244i −0.208287 + 0.0676766i
\(534\) 5.41063 + 3.93105i 0.234141 + 0.170113i
\(535\) 0 0
\(536\) −7.67320 + 5.57490i −0.331432 + 0.240799i
\(537\) 18.7027 25.7420i 0.807080 1.11085i
\(538\) 8.69212 11.9637i 0.374744 0.515791i
\(539\) −11.0580 + 8.03411i −0.476302 + 0.346053i
\(540\) 0 0
\(541\) 22.1259 + 16.0754i 0.951268 + 0.691137i 0.951107 0.308863i \(-0.0999485\pi\)
0.000161922 1.00000i \(0.499948\pi\)
\(542\) 12.7756 4.15103i 0.548757 0.178302i
\(543\) 28.4140i 1.21936i
\(544\) −1.86843 5.75045i −0.0801085 0.246549i
\(545\) 0 0
\(546\) 0.260135 0.800613i 0.0111327 0.0342631i
\(547\) −19.3437 6.28515i −0.827077 0.268734i −0.135263 0.990810i \(-0.543188\pi\)
−0.691814 + 0.722076i \(0.743188\pi\)
\(548\) −7.99001 10.9973i −0.341316 0.469781i
\(549\) 35.5558 1.51748
\(550\) 0 0
\(551\) 27.2742 1.16192
\(552\) −5.65697 7.78616i −0.240777 0.331401i
\(553\) −2.12266 0.689692i −0.0902645 0.0293287i
\(554\) 5.94022 18.2821i 0.252376 0.776732i
\(555\) 0 0
\(556\) 1.48742 + 4.57781i 0.0630807 + 0.194142i
\(557\) 28.2605i 1.19744i −0.800960 0.598718i \(-0.795677\pi\)
0.800960 0.598718i \(-0.204323\pi\)
\(558\) 33.3873 10.8482i 1.41340 0.459241i
\(559\) −5.19537 3.77466i −0.219741 0.159651i
\(560\) 0 0
\(561\) 6.66550 4.84277i 0.281418 0.204462i
\(562\) −3.38184 + 4.65470i −0.142654 + 0.196347i
\(563\) 7.59738 10.4569i 0.320192 0.440706i −0.618334 0.785915i \(-0.712192\pi\)
0.938526 + 0.345210i \(0.112192\pi\)
\(564\) −1.91618 + 1.39219i −0.0806858 + 0.0586216i
\(565\) 0 0
\(566\) 10.8456 + 7.87977i 0.455874 + 0.331212i
\(567\) 2.35314 0.764582i 0.0988226 0.0321094i
\(568\) 21.1326i 0.886703i
\(569\) 0.953142 + 2.93347i 0.0399578 + 0.122977i 0.969046 0.246882i \(-0.0794059\pi\)
−0.929088 + 0.369859i \(0.879406\pi\)
\(570\) 0 0
\(571\) −1.27552 + 3.92564i −0.0533788 + 0.164283i −0.974192 0.225721i \(-0.927526\pi\)
0.920813 + 0.390004i \(0.127526\pi\)
\(572\) 0.952536 + 0.309498i 0.0398275 + 0.0129407i
\(573\) −2.39828 3.30095i −0.100190 0.137899i
\(574\) −3.33100 −0.139033
\(575\) 0 0
\(576\) 31.8961 1.32901
\(577\) 3.73579 + 5.14187i 0.155523 + 0.214059i 0.879667 0.475589i \(-0.157765\pi\)
−0.724145 + 0.689648i \(0.757765\pi\)
\(578\) 15.6287 + 5.07807i 0.650068 + 0.211220i
\(579\) −1.33342 + 4.10384i −0.0554150 + 0.170550i
\(580\) 0 0
\(581\) 0.122565 + 0.377218i 0.00508487 + 0.0156496i
\(582\) 44.9063i 1.86143i
\(583\) −9.66266 + 3.13959i −0.400187 + 0.130028i
\(584\) −1.35736 0.986178i −0.0561679 0.0408083i
\(585\) 0 0
\(586\) −17.8254 + 12.9509i −0.736359 + 0.534996i
\(587\) 12.4046 17.0735i 0.511992 0.704697i −0.472261 0.881459i \(-0.656562\pi\)
0.984254 + 0.176761i \(0.0565621\pi\)
\(588\) 7.47271 10.2853i 0.308169 0.424159i
\(589\) 32.8588 23.8733i 1.35392 0.983683i
\(590\) 0 0
\(591\) −27.9701 20.3215i −1.15054 0.835913i
\(592\) −10.0598 + 3.26862i −0.413455 + 0.134340i
\(593\) 21.6529i 0.889177i 0.895735 + 0.444589i \(0.146650\pi\)
−0.895735 + 0.444589i \(0.853350\pi\)
\(594\) 1.41238 + 4.34687i 0.0579508 + 0.178354i
\(595\) 0 0
\(596\) 0.159127 0.489743i 0.00651810 0.0200607i
\(597\) −29.9583 9.73405i −1.22611 0.398388i
\(598\) −0.560963 0.772100i −0.0229395 0.0315735i
\(599\) 3.38501 0.138308 0.0691539 0.997606i \(-0.477970\pi\)
0.0691539 + 0.997606i \(0.477970\pi\)
\(600\) 0 0
\(601\) 28.8265 1.17586 0.587928 0.808913i \(-0.299944\pi\)
0.587928 + 0.808913i \(0.299944\pi\)
\(602\) −2.48675 3.42272i −0.101352 0.139500i
\(603\) 11.0626 + 3.59445i 0.450503 + 0.146377i
\(604\) −3.42726 + 10.5480i −0.139453 + 0.429193i
\(605\) 0 0
\(606\) −16.7747 51.6273i −0.681427 2.09722i
\(607\) 15.6708i 0.636059i 0.948081 + 0.318029i \(0.103021\pi\)
−0.948081 + 0.318029i \(0.896979\pi\)
\(608\) 17.9874 5.84446i 0.729485 0.237024i
\(609\) −4.72324 3.43163i −0.191395 0.139057i
\(610\) 0 0
\(611\) −0.721736 + 0.524372i −0.0291983 + 0.0212138i
\(612\) −2.50966 + 3.45425i −0.101447 + 0.139630i
\(613\) 22.4537 30.9048i 0.906896 1.24823i −0.0613201 0.998118i \(-0.519531\pi\)
0.968216 0.250117i \(-0.0804690\pi\)
\(614\) −23.3120 + 16.9372i −0.940797 + 0.683529i
\(615\) 0 0
\(616\) 2.02758 + 1.47312i 0.0816936 + 0.0593539i
\(617\) −12.5842 + 4.08884i −0.506619 + 0.164611i −0.551164 0.834397i \(-0.685816\pi\)
0.0445449 + 0.999007i \(0.485816\pi\)
\(618\) 35.0678i 1.41064i
\(619\) −1.86789 5.74878i −0.0750770 0.231063i 0.906475 0.422260i \(-0.138763\pi\)
−0.981552 + 0.191197i \(0.938763\pi\)
\(620\) 0 0
\(621\) −0.748388 + 2.30330i −0.0300318 + 0.0924284i
\(622\) 17.0981 + 5.55552i 0.685572 + 0.222756i
\(623\) −0.542423 0.746582i −0.0217317 0.0299112i
\(624\) 3.75634 0.150374
\(625\) 0 0
\(626\) −7.95456 −0.317928
\(627\) 15.1482 + 20.8497i 0.604960 + 0.832655i
\(628\) −1.89250 0.614911i −0.0755190 0.0245376i
\(629\) 2.51164 7.73003i 0.100146 0.308216i
\(630\) 0 0
\(631\) −11.6763 35.9361i −0.464828 1.43059i −0.859199 0.511642i \(-0.829037\pi\)
0.394371 0.918952i \(-0.370963\pi\)
\(632\) 16.8706i 0.671076i
\(633\) 16.5866 5.38932i 0.659259 0.214206i
\(634\) −11.9543 8.68531i −0.474766 0.344938i
\(635\) 0 0
\(636\) 7.64520 5.55456i 0.303152 0.220253i
\(637\) 2.81462 3.87399i 0.111519 0.153493i
\(638\) −7.34220 + 10.1057i −0.290681 + 0.400087i
\(639\) 20.9673 15.2336i 0.829452 0.602632i
\(640\) 0 0
\(641\) 16.8737 + 12.2594i 0.666470 + 0.484219i 0.868842 0.495090i \(-0.164865\pi\)
−0.202372 + 0.979309i \(0.564865\pi\)
\(642\) 2.11858 0.688367i 0.0836135 0.0271677i
\(643\) 37.5552i 1.48103i 0.672039 + 0.740516i \(0.265419\pi\)
−0.672039 + 0.740516i \(0.734581\pi\)
\(644\) 0.108040 + 0.332514i 0.00425739 + 0.0131029i
\(645\) 0 0
\(646\) 2.74513 8.44865i 0.108006 0.332408i
\(647\) −26.0592 8.46714i −1.02449 0.332878i −0.251882 0.967758i \(-0.581049\pi\)
−0.772611 + 0.634880i \(0.781049\pi\)
\(648\) 10.9930 + 15.1306i 0.431847 + 0.594387i
\(649\) 12.9994 0.510272
\(650\) 0 0
\(651\) −8.69410 −0.340749
\(652\) 10.1695 + 13.9971i 0.398268 + 0.548169i
\(653\) −21.9182 7.12164i −0.857724 0.278691i −0.153046 0.988219i \(-0.548908\pi\)
−0.704678 + 0.709528i \(0.748908\pi\)
\(654\) −8.35021 + 25.6993i −0.326519 + 1.00492i
\(655\) 0 0
\(656\) −4.59309 14.1361i −0.179330 0.551921i
\(657\) 2.05763i 0.0802760i
\(658\) −0.558961 + 0.181617i −0.0217906 + 0.00708018i
\(659\) 16.5717 + 12.0400i 0.645540 + 0.469012i 0.861749 0.507335i \(-0.169369\pi\)
−0.216209 + 0.976347i \(0.569369\pi\)
\(660\) 0 0
\(661\) −11.3181 + 8.22311i −0.440224 + 0.319842i −0.785724 0.618577i \(-0.787709\pi\)
0.345500 + 0.938419i \(0.387709\pi\)
\(662\) −11.7574 + 16.1827i −0.456965 + 0.628959i
\(663\) −1.69659 + 2.33515i −0.0658899 + 0.0906897i
\(664\) −2.42550 + 1.76223i −0.0941275 + 0.0683876i
\(665\) 0 0
\(666\) 17.7779 + 12.9164i 0.688880 + 0.500500i
\(667\) −6.29489 + 2.04533i −0.243739 + 0.0791957i
\(668\) 13.6126i 0.526687i
\(669\) 8.51893 + 26.2186i 0.329361 + 1.01367i
\(670\) 0 0
\(671\) −5.82193 + 17.9181i −0.224753 + 0.691719i
\(672\) −3.85034 1.25105i −0.148530 0.0482603i
\(673\) 4.61160 + 6.34732i 0.177764 + 0.244671i 0.888596 0.458691i \(-0.151681\pi\)
−0.710832 + 0.703362i \(0.751681\pi\)
\(674\) 28.1720 1.08514
\(675\) 0 0
\(676\) 8.94042 0.343862
\(677\) −8.46310 11.6485i −0.325263 0.447687i 0.614802 0.788682i \(-0.289236\pi\)
−0.940065 + 0.340995i \(0.889236\pi\)
\(678\) −36.0334 11.7080i −1.38385 0.449641i
\(679\) −1.91478 + 5.89310i −0.0734826 + 0.226156i
\(680\) 0 0
\(681\) 15.7734 + 48.5455i 0.604437 + 1.86027i
\(682\) 18.6016i 0.712291i
\(683\) −12.0537 + 3.91647i −0.461221 + 0.149860i −0.530405 0.847744i \(-0.677960\pi\)
0.0691847 + 0.997604i \(0.477960\pi\)
\(684\) −10.8049 7.85021i −0.413135 0.300160i
\(685\) 0 0
\(686\) 5.16629 3.75353i 0.197250 0.143310i
\(687\) −13.5225 + 18.6122i −0.515917 + 0.710099i
\(688\) 11.0964 15.2728i 0.423045 0.582271i
\(689\) 2.87959 2.09214i 0.109704 0.0797043i
\(690\) 0 0
\(691\) −4.64805 3.37700i −0.176820 0.128467i 0.495855 0.868405i \(-0.334855\pi\)
−0.672675 + 0.739938i \(0.734855\pi\)
\(692\) 9.00448 2.92573i 0.342299 0.111220i
\(693\) 3.07364i 0.116758i
\(694\) 4.65155 + 14.3160i 0.176571 + 0.543428i
\(695\) 0 0
\(696\) 13.6371 41.9707i 0.516913 1.59089i
\(697\) 10.8623 + 3.52937i 0.411439 + 0.133685i
\(698\) −12.0802 16.6270i −0.457243 0.629342i
\(699\) −28.7931 −1.08905
\(700\) 0 0
\(701\) −30.5834 −1.15512 −0.577560 0.816348i \(-0.695995\pi\)
−0.577560 + 0.816348i \(0.695995\pi\)
\(702\) −0.941177 1.29542i −0.0355224 0.0488924i
\(703\) 24.1795 + 7.85640i 0.911948 + 0.296310i
\(704\) −5.22270 + 16.0738i −0.196838 + 0.605804i
\(705\) 0 0
\(706\) 6.20239 + 19.0890i 0.233430 + 0.718424i
\(707\) 7.49036i 0.281704i
\(708\) −11.4993 + 3.73635i −0.432170 + 0.140421i
\(709\) −21.8998 15.9111i −0.822464 0.597555i 0.0949536 0.995482i \(-0.469730\pi\)
−0.917417 + 0.397927i \(0.869730\pi\)
\(710\) 0 0
\(711\) −16.7386 + 12.1613i −0.627747 + 0.456085i
\(712\) 4.10011 5.64332i 0.153658 0.211492i
\(713\) −5.79353 + 7.97410i −0.216969 + 0.298633i
\(714\) −1.53840 + 1.11771i −0.0575731 + 0.0418293i
\(715\) 0 0
\(716\) −7.06868 5.13570i −0.264169 0.191930i
\(717\) 39.8673 12.9537i 1.48887 0.483764i
\(718\) 36.8957i 1.37693i
\(719\) 5.16263 + 15.8889i 0.192534 + 0.592557i 0.999997 + 0.00263916i \(0.000840071\pi\)
−0.807463 + 0.589918i \(0.799160\pi\)
\(720\) 0 0
\(721\) 1.49527 4.60198i 0.0556869 0.171387i
\(722\) 5.94125 + 1.93043i 0.221110 + 0.0718431i
\(723\) −9.16202 12.6104i −0.340739 0.468987i
\(724\) 7.80240 0.289974
\(725\) 0 0
\(726\) 20.6555 0.766597
\(727\) −6.87743 9.46598i −0.255070 0.351074i 0.662209 0.749319i \(-0.269619\pi\)
−0.917279 + 0.398246i \(0.869619\pi\)
\(728\) −0.835044 0.271322i −0.0309488 0.0100559i
\(729\) 11.9517 36.7835i 0.442655 1.36235i
\(730\) 0 0
\(731\) 4.48267 + 13.7962i 0.165798 + 0.510272i
\(732\) 17.5237i 0.647694i
\(733\) 32.4385 10.5399i 1.19814 0.389300i 0.359065 0.933312i \(-0.383096\pi\)
0.839077 + 0.544012i \(0.183096\pi\)
\(734\) −30.2196 21.9558i −1.11542 0.810403i
\(735\) 0 0
\(736\) −3.71321 + 2.69781i −0.136871 + 0.0994425i
\(737\) −3.62279 + 4.98635i −0.133447 + 0.183674i
\(738\) −18.1502 + 24.9816i −0.668119 + 0.919586i
\(739\) 4.64794 3.37693i 0.170977 0.124222i −0.499006 0.866599i \(-0.666301\pi\)
0.669983 + 0.742376i \(0.266301\pi\)
\(740\) 0 0
\(741\) −7.30434 5.30692i −0.268332 0.194954i
\(742\) 2.23015 0.724618i 0.0818712 0.0266016i
\(743\) 36.4348i 1.33666i −0.743863 0.668332i \(-0.767009\pi\)
0.743863 0.668332i \(-0.232991\pi\)
\(744\) −20.3079 62.5012i −0.744522 2.29140i
\(745\) 0 0
\(746\) −1.21442 + 3.73761i −0.0444632 + 0.136844i
\(747\) 3.49688 + 1.13621i 0.127944 + 0.0415716i
\(748\) −1.32981 1.83032i −0.0486226 0.0669233i
\(749\) −0.307374 −0.0112312
\(750\) 0 0
\(751\) 1.48912 0.0543387 0.0271693 0.999631i \(-0.491351\pi\)
0.0271693 + 0.999631i \(0.491351\pi\)
\(752\) −1.54149 2.12169i −0.0562125 0.0773699i
\(753\) 9.23757 + 3.00147i 0.336636 + 0.109380i
\(754\) 1.35230 4.16194i 0.0492477 0.151569i
\(755\) 0 0
\(756\) 0.181269 + 0.557888i 0.00659268 + 0.0202902i
\(757\) 5.53316i 0.201106i −0.994932 0.100553i \(-0.967939\pi\)
0.994932 0.100553i \(-0.0320612\pi\)
\(758\) −2.07948 + 0.675664i −0.0755301 + 0.0245412i
\(759\) −5.05975 3.67613i −0.183657 0.133435i
\(760\) 0 0
\(761\) 15.1041 10.9738i 0.547523 0.397799i −0.279348 0.960190i \(-0.590118\pi\)
0.826871 + 0.562391i \(0.190118\pi\)
\(762\) −12.3234 + 16.9617i −0.446430 + 0.614458i
\(763\) 2.19161 3.01649i 0.0793416 0.109204i
\(764\) −0.906429 + 0.658559i −0.0327935 + 0.0238258i
\(765\) 0 0
\(766\) −4.52176 3.28525i −0.163378 0.118701i
\(767\) −4.33125 + 1.40731i −0.156392 + 0.0508149i
\(768\) 38.2653i 1.38078i
\(769\) 4.06150 + 12.5000i 0.146462 + 0.450763i 0.997196 0.0748333i \(-0.0238425\pi\)
−0.850734 + 0.525596i \(0.823842\pi\)
\(770\) 0 0
\(771\) −18.9764 + 58.4032i −0.683417 + 2.10334i
\(772\) 1.12690 + 0.366152i 0.0405581 + 0.0131781i
\(773\) 16.4425 + 22.6311i 0.591394 + 0.813984i 0.994887 0.100999i \(-0.0322039\pi\)
−0.403493 + 0.914983i \(0.632204\pi\)
\(774\) −39.2195 −1.40972
\(775\) 0 0
\(776\) −46.8376 −1.68137
\(777\) −3.19882 4.40280i −0.114757 0.157950i
\(778\) −14.4330 4.68957i −0.517448 0.168129i
\(779\) −11.0399 + 33.9772i −0.395544 + 1.21736i
\(780\) 0 0
\(781\) 4.24366 + 13.0606i 0.151850 + 0.467347i
\(782\) 2.15581i 0.0770917i
\(783\) −10.5615 + 3.43163i −0.377437 + 0.122637i
\(784\) 11.3884 + 8.27413i 0.406727 + 0.295505i
\(785\) 0 0
\(786\) 5.71564 4.15266i 0.203870 0.148120i
\(787\) 19.6126 26.9944i 0.699114 0.962248i −0.300849 0.953672i \(-0.597270\pi\)
0.999963 0.00857605i \(-0.00272988\pi\)
\(788\) −5.58021 + 7.68050i −0.198787 + 0.273606i
\(789\) −13.9845 + 10.1603i −0.497860 + 0.361716i
\(790\) 0 0
\(791\) 4.22947 + 3.07289i 0.150383 + 0.109259i
\(792\) 22.0961 7.17946i 0.785151 0.255111i
\(793\) 6.60035i 0.234385i
\(794\) 0.749317 + 2.30616i 0.0265923 + 0.0818426i
\(795\) 0 0
\(796\) −2.67294 + 8.22646i −0.0947398 + 0.291579i
\(797\) 35.5682 + 11.5568i 1.25989 + 0.409363i 0.861455 0.507833i \(-0.169553\pi\)
0.398435 + 0.917197i \(0.369553\pi\)
\(798\) −3.49620 4.81211i −0.123764 0.170347i
\(799\) 2.01519 0.0712923
\(800\) 0 0
\(801\) −8.55478 −0.302268
\(802\) 17.8730 + 24.6001i 0.631119 + 0.868660i
\(803\) −1.03693 0.336919i −0.0365924 0.0118896i
\(804\) 1.77153 5.45220i 0.0624769 0.192284i
\(805\) 0 0
\(806\) −2.01379 6.19781i −0.0709328 0.218309i
\(807\) 33.9504i 1.19511i
\(808\) −53.8476 + 17.4961i −1.89435 + 0.615512i
\(809\) 27.1844 + 19.7506i 0.955751 + 0.694394i 0.952160 0.305600i \(-0.0988569\pi\)
0.00359108 + 0.999994i \(0.498857\pi\)
\(810\) 0 0
\(811\) 30.7471 22.3391i 1.07968 0.784432i 0.102051 0.994779i \(-0.467459\pi\)
0.977627 + 0.210347i \(0.0674594\pi\)
\(812\) −0.942315 + 1.29699i −0.0330688 + 0.0455153i
\(813\) −18.1272 + 24.9499i −0.635747 + 0.875031i
\(814\) −9.42008 + 6.84409i −0.330174 + 0.239885i
\(815\) 0 0
\(816\) −6.86464 4.98745i −0.240310 0.174596i
\(817\) −43.1546 + 14.0218i −1.50979 + 0.490560i
\(818\) 15.8699i 0.554877i
\(819\) 0.332749 + 1.02410i 0.0116272 + 0.0357848i
\(820\) 0 0
\(821\) 7.70479 23.7129i 0.268899 0.827587i −0.721870 0.692028i \(-0.756717\pi\)
0.990769 0.135558i \(-0.0432827\pi\)
\(822\) −53.3751 17.3426i −1.86167 0.604894i
\(823\) −14.9653 20.5980i −0.521659 0.718002i 0.464172 0.885745i \(-0.346352\pi\)
−0.985831 + 0.167743i \(0.946352\pi\)
\(824\) 36.5760 1.27418
\(825\) 0 0
\(826\) −3.00027 −0.104393
\(827\) 19.0082 + 26.1626i 0.660980 + 0.909761i 0.999513 0.0311933i \(-0.00993074\pi\)
−0.338533 + 0.940954i \(0.609931\pi\)
\(828\) 3.08247 + 1.00156i 0.107123 + 0.0348065i
\(829\) −7.71962 + 23.7585i −0.268113 + 0.825168i 0.722846 + 0.691009i \(0.242833\pi\)
−0.990960 + 0.134159i \(0.957167\pi\)
\(830\) 0 0
\(831\) 13.6377 + 41.9724i 0.473085 + 1.45601i
\(832\) 5.92099i 0.205273i
\(833\) −10.2873 + 3.34256i −0.356435 + 0.115813i
\(834\) 16.0773 + 11.6808i 0.556712 + 0.404475i
\(835\) 0 0
\(836\) 5.72525 4.15964i 0.198012 0.143864i
\(837\) −9.72030 + 13.3788i −0.335983 + 0.462440i
\(838\) −20.5923 + 28.3429i −0.711350 + 0.979089i
\(839\) 15.6566 11.3752i 0.540524 0.392714i −0.283755 0.958897i \(-0.591580\pi\)
0.824280 + 0.566183i \(0.191580\pi\)
\(840\) 0 0
\(841\) −1.09201 0.793390i −0.0376554 0.0273583i
\(842\) 8.88423 2.88666i 0.306171 0.0994809i
\(843\) 13.2091i 0.454944i
\(844\) −1.47989 4.55463i −0.0509399 0.156777i
\(845\) 0 0
\(846\) −1.68363 + 5.18167i −0.0578843 + 0.178150i
\(847\) −2.71064 0.880739i −0.0931385 0.0302625i
\(848\) 6.15027 + 8.46512i 0.211201 + 0.290693i
\(849\) −30.7775 −1.05628
\(850\) 0 0
\(851\) −6.16980 −0.211498
\(852\) −7.50789 10.3337i −0.257216 0.354027i
\(853\) 25.4765 + 8.27783i 0.872300 + 0.283427i 0.710756 0.703438i \(-0.248353\pi\)
0.161543 + 0.986866i \(0.448353\pi\)
\(854\) 1.34370 4.13550i 0.0459806 0.141514i
\(855\) 0 0
\(856\) −0.717971 2.20969i −0.0245397 0.0755255i
\(857\) 47.5186i 1.62320i 0.584210 + 0.811602i \(0.301404\pi\)
−0.584210 + 0.811602i \(0.698596\pi\)
\(858\) 3.93265 1.27780i 0.134259 0.0436233i
\(859\) 9.32717 + 6.77658i 0.318239 + 0.231214i 0.735424 0.677608i \(-0.236983\pi\)
−0.417185 + 0.908822i \(0.636983\pi\)
\(860\) 0 0
\(861\) 6.18685 4.49501i 0.210847 0.153190i
\(862\) 18.0908 24.8999i 0.616177 0.848095i
\(863\) 10.5835 14.5669i 0.360266 0.495864i −0.589957 0.807435i \(-0.700855\pi\)
0.950223 + 0.311571i \(0.100855\pi\)
\(864\) −6.22998 + 4.52634i −0.211948 + 0.153989i
\(865\) 0 0
\(866\) −19.7108 14.3207i −0.669799 0.486638i
\(867\) −35.8807 + 11.6583i −1.21857 + 0.395938i
\(868\) 2.38737i 0.0810327i
\(869\) −3.38781 10.4266i −0.114924 0.353698i
\(870\) 0 0
\(871\) 0.667251 2.05359i 0.0226089 0.0695831i
\(872\) 26.8045 + 8.70932i 0.907716 + 0.294935i
\(873\) 33.7633 + 46.4712i 1.14271 + 1.57281i
\(874\) −6.74338 −0.228098
\(875\) 0 0
\(876\) 1.01411 0.0342635
\(877\) −10.0495 13.8320i −0.339349 0.467074i 0.604902 0.796300i \(-0.293212\pi\)
−0.944251 + 0.329226i \(0.893212\pi\)
\(878\) 27.8132 + 9.03707i 0.938652 + 0.304986i
\(879\) 15.6315 48.1088i 0.527238 1.62267i
\(880\) 0 0
\(881\) −11.7516 36.1678i −0.395923 1.21853i −0.928240 0.371981i \(-0.878679\pi\)
0.532318 0.846545i \(-0.321321\pi\)
\(882\) 29.2445i 0.984714i
\(883\) 35.0458 11.3871i 1.17939 0.383206i 0.347247 0.937774i \(-0.387116\pi\)
0.832138 + 0.554568i \(0.187116\pi\)
\(884\) 0.641224 + 0.465877i 0.0215667 + 0.0156691i
\(885\) 0 0
\(886\) −2.92104 + 2.12226i −0.0981344 + 0.0712988i
\(887\) −17.5594 + 24.1684i −0.589586 + 0.811495i −0.994705 0.102769i \(-0.967230\pi\)
0.405120 + 0.914264i \(0.367230\pi\)
\(888\) 24.1795 33.2802i 0.811411 1.11681i
\(889\) 2.34045 1.70044i 0.0784961 0.0570308i
\(890\) 0 0
\(891\) 9.83247 + 7.14371i 0.329400 + 0.239323i
\(892\) 7.19953 2.33927i 0.241058 0.0783246i
\(893\) 6.30351i 0.210939i
\(894\) −0.656975 2.02196i −0.0219725 0.0676245i
\(895\) 0 0
\(896\) 0.244082 0.751207i 0.00815420 0.0250961i
\(897\) 2.08382 + 0.677074i 0.0695767 + 0.0226068i
\(898\) 24.0418 + 33.0907i 0.802285 + 1.10425i
\(899\) −45.1958 −1.50736
\(900\) 0 0
\(901\) −8.04022 −0.267859
\(902\) −9.61736 13.2372i −0.320223 0.440749i
\(903\) 9.23757 + 3.00147i 0.307407 + 0.0998826i
\(904\) −12.2115 + 37.5830i −0.406147 + 1.24999i
\(905\) 0 0
\(906\) 14.1498 + 43.5487i 0.470097 + 1.44681i
\(907\) 43.4897i 1.44405i −0.691866 0.722026i \(-0.743211\pi\)
0.691866 0.722026i \(-0.256789\pi\)
\(908\) 13.3304 4.33132i 0.442386 0.143740i
\(909\) 56.1758 + 40.8141i 1.86323 + 1.35372i
\(910\) 0 0
\(911\) 19.7150 14.3238i 0.653186 0.474568i −0.211169 0.977450i \(-0.567727\pi\)
0.864355 + 0.502882i \(0.167727\pi\)
\(912\) 15.6007 21.4726i 0.516592 0.711028i
\(913\) −1.14516 + 1.57618i −0.0378994 + 0.0521640i
\(914\) 23.4107 17.0089i 0.774358 0.562604i
\(915\) 0 0
\(916\) 5.11084 + 3.71325i 0.168867 + 0.122689i
\(917\) −0.927136 + 0.301245i −0.0306167 + 0.00994797i
\(918\) 3.61699i 0.119379i
\(919\) −14.0647 43.2867i −0.463952 1.42790i −0.860296 0.509795i \(-0.829721\pi\)
0.396344 0.918102i \(-0.370279\pi\)
\(920\) 0 0
\(921\) 20.4429 62.9168i 0.673617 2.07318i
\(922\) −17.9406 5.82926i −0.590843 0.191977i
\(923\) −2.82787 3.89223i −0.0930804 0.128114i
\(924\) −1.51484 −0.0498346
\(925\) 0 0
\(926\) 20.2001 0.663816
\(927\) −26.3661 36.2898i −0.865977 1.19191i
\(928\) −20.0158 6.50352i −0.657050 0.213488i
\(929\) −2.79288 + 8.59560i −0.0916314 + 0.282012i −0.986361 0.164596i \(-0.947368\pi\)
0.894730 + 0.446608i \(0.147368\pi\)
\(930\) 0 0
\(931\) −10.4555 32.1787i −0.342665 1.05462i
\(932\) 7.90648i 0.258985i
\(933\) −39.2542 + 12.7545i −1.28513 + 0.417562i
\(934\) −13.0681 9.49453i −0.427601 0.310671i
\(935\) 0 0
\(936\) −6.58490 + 4.78421i −0.215234 + 0.156377i
\(937\) 19.5892 26.9623i 0.639953 0.880819i −0.358661 0.933468i \(-0.616766\pi\)
0.998613 + 0.0526490i \(0.0167664\pi\)
\(938\) 0.836142 1.15085i 0.0273010 0.0375766i
\(939\) 14.7745 10.7343i 0.482147 0.350300i
\(940\) 0 0
\(941\) 23.7050 + 17.2227i 0.772762 + 0.561444i 0.902798 0.430065i \(-0.141509\pi\)
−0.130036 + 0.991509i \(0.541509\pi\)
\(942\) −7.81341 + 2.53873i −0.254575 + 0.0827163i
\(943\) 8.66985i 0.282329i
\(944\) −4.13706 12.7326i −0.134650 0.414410i
\(945\) 0 0
\(946\) 6.42184 19.7644i 0.208792 0.642595i
\(947\) 54.0634 + 17.5663i 1.75682 + 0.570827i 0.996863 0.0791426i \(-0.0252182\pi\)
0.759961 + 0.649969i \(0.225218\pi\)
\(948\) 5.99371 + 8.24963i 0.194667 + 0.267936i
\(949\) 0.381966 0.0123991
\(950\) 0 0
\(951\) 33.9238 1.10005
\(952\) 1.16578 + 1.60456i 0.0377832 + 0.0520041i
\(953\) −18.1051 5.88270i −0.586481 0.190559i 0.000720915 1.00000i \(-0.499771\pi\)
−0.587202 + 0.809441i \(0.699771\pi\)
\(954\) 6.71735 20.6739i 0.217482 0.669342i
\(955\) 0 0
\(956\) −3.55704 10.9474i −0.115043 0.354065i
\(957\) 28.6778i 0.927021i
\(958\) 3.13615 1.01900i 0.101324 0.0329223i
\(959\) 6.26498 + 4.55178i 0.202307 + 0.146985i
\(960\) 0 0
\(961\) −29.3705 + 21.3389i −0.947435 + 0.688352i
\(962\) 2.39772 3.30017i 0.0773055 0.106402i
\(963\) −1.67485 + 2.30523i −0.0539711 + 0.0742849i
\(964\) −3.46278 + 2.51586i −0.111529 + 0.0810304i
\(965\) 0 0
\(966\) 1.16779 + 0.848451i 0.0375731 + 0.0272985i
\(967\) 13.9905 4.54580i 0.449906 0.146183i −0.0752956 0.997161i \(-0.523990\pi\)
0.525201 + 0.850978i \(0.323990\pi\)
\(968\) 21.5438i 0.692443i
\(969\) 6.30233 + 19.3966i 0.202460 + 0.623108i
\(970\) 0 0
\(971\) −12.0039 + 36.9441i −0.385223 + 1.18559i 0.551096 + 0.834442i \(0.314210\pi\)
−0.936319 + 0.351151i \(0.885790\pi\)
\(972\) −14.8616 4.82884i −0.476687 0.154885i
\(973\) −1.61177 2.21842i −0.0516711 0.0711191i
\(974\) 19.3469 0.619914
\(975\) 0 0
\(976\) 19.4030 0.621076
\(977\) −34.3586 47.2906i −1.09923 1.51296i −0.836402 0.548116i \(-0.815345\pi\)
−0.262827 0.964843i \(-0.584655\pi\)
\(978\) 67.9346 + 22.0733i 2.17231 + 0.705826i
\(979\) 1.40077 4.31111i 0.0447687 0.137784i
\(980\) 0 0
\(981\) −10.6811 32.8730i −0.341021 1.04955i
\(982\) 34.8918i 1.11344i
\(983\) −26.7812 + 8.70175i −0.854189 + 0.277543i −0.703199 0.710993i \(-0.748246\pi\)
−0.150989 + 0.988535i \(0.548246\pi\)
\(984\) 46.7656 + 33.9772i 1.49083 + 1.08315i
\(985\) 0 0
\(986\) −7.99729 + 5.81037i −0.254685 + 0.185040i
\(987\) 0.793106 1.09162i 0.0252449 0.0347466i
\(988\) −1.45726 + 2.00575i −0.0463617 + 0.0638114i
\(989\) 8.90859 6.47247i 0.283277 0.205812i
\(990\) 0 0
\(991\) −31.8297 23.1256i −1.01110 0.734610i −0.0466640 0.998911i \(-0.514859\pi\)
−0.964440 + 0.264300i \(0.914859\pi\)
\(992\) −29.8068 + 9.68480i −0.946365 + 0.307493i
\(993\) 45.9231i 1.45733i
\(994\) −0.979439 3.01440i −0.0310659 0.0956110i
\(995\) 0 0
\(996\) 0.559979 1.72344i 0.0177436 0.0546092i
\(997\) −41.0074 13.3241i −1.29872 0.421979i −0.423583 0.905857i \(-0.639228\pi\)
−0.875136 + 0.483878i \(0.839228\pi\)
\(998\) −7.91810 10.8983i −0.250643 0.344980i
\(999\) −10.3516 −0.327511
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 125.2.e.b.74.1 8
5.2 odd 4 125.2.d.b.51.3 16
5.3 odd 4 125.2.d.b.51.2 16
5.4 even 2 25.2.e.a.14.2 yes 8
15.14 odd 2 225.2.m.a.64.1 8
20.19 odd 2 400.2.y.c.289.2 8
25.2 odd 20 625.2.d.o.126.2 16
25.3 odd 20 625.2.a.f.1.6 8
25.4 even 10 625.2.b.c.624.3 8
25.6 even 5 625.2.e.i.124.2 8
25.8 odd 20 625.2.d.o.501.3 16
25.9 even 10 inner 125.2.e.b.49.1 8
25.11 even 5 625.2.e.a.499.1 8
25.12 odd 20 125.2.d.b.76.3 16
25.13 odd 20 125.2.d.b.76.2 16
25.14 even 10 625.2.e.i.499.2 8
25.16 even 5 25.2.e.a.9.2 8
25.17 odd 20 625.2.d.o.501.2 16
25.19 even 10 625.2.e.a.124.1 8
25.21 even 5 625.2.b.c.624.6 8
25.22 odd 20 625.2.a.f.1.3 8
25.23 odd 20 625.2.d.o.126.3 16
75.41 odd 10 225.2.m.a.109.1 8
75.47 even 20 5625.2.a.x.1.6 8
75.53 even 20 5625.2.a.x.1.3 8
100.3 even 20 10000.2.a.bj.1.8 8
100.47 even 20 10000.2.a.bj.1.1 8
100.91 odd 10 400.2.y.c.209.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.2.e.a.9.2 8 25.16 even 5
25.2.e.a.14.2 yes 8 5.4 even 2
125.2.d.b.51.2 16 5.3 odd 4
125.2.d.b.51.3 16 5.2 odd 4
125.2.d.b.76.2 16 25.13 odd 20
125.2.d.b.76.3 16 25.12 odd 20
125.2.e.b.49.1 8 25.9 even 10 inner
125.2.e.b.74.1 8 1.1 even 1 trivial
225.2.m.a.64.1 8 15.14 odd 2
225.2.m.a.109.1 8 75.41 odd 10
400.2.y.c.209.2 8 100.91 odd 10
400.2.y.c.289.2 8 20.19 odd 2
625.2.a.f.1.3 8 25.22 odd 20
625.2.a.f.1.6 8 25.3 odd 20
625.2.b.c.624.3 8 25.4 even 10
625.2.b.c.624.6 8 25.21 even 5
625.2.d.o.126.2 16 25.2 odd 20
625.2.d.o.126.3 16 25.23 odd 20
625.2.d.o.501.2 16 25.17 odd 20
625.2.d.o.501.3 16 25.8 odd 20
625.2.e.a.124.1 8 25.19 even 10
625.2.e.a.499.1 8 25.11 even 5
625.2.e.i.124.2 8 25.6 even 5
625.2.e.i.499.2 8 25.14 even 10
5625.2.a.x.1.3 8 75.53 even 20
5625.2.a.x.1.6 8 75.47 even 20
10000.2.a.bj.1.1 8 100.47 even 20
10000.2.a.bj.1.8 8 100.3 even 20