Properties

Label 1950.2.y.h.49.1
Level $1950$
Weight $2$
Character 1950.49
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1950,2,Mod(49,1950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1950.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.y (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.49
Dual form 1950.2.y.h.199.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(0.633975 - 1.09808i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(0.633975 - 1.09808i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.09808 + 0.633975i) q^{11} -1.00000i q^{12} +(3.23205 + 1.59808i) q^{13} +1.26795 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.50000 - 2.59808i) q^{17} +1.00000 q^{18} +(4.09808 + 2.36603i) q^{19} +1.26795i q^{21} +(-1.09808 - 0.633975i) q^{22} +(7.09808 - 4.09808i) q^{23} +(0.866025 - 0.500000i) q^{24} +(0.232051 + 3.59808i) q^{26} +1.00000i q^{27} +(0.633975 + 1.09808i) q^{28} +(-1.50000 - 2.59808i) q^{29} +9.46410i q^{31} +(0.500000 - 0.866025i) q^{32} +(0.633975 - 1.09808i) q^{33} -5.19615i q^{34} +(0.500000 + 0.866025i) q^{36} +(1.50000 + 2.59808i) q^{37} +4.73205i q^{38} +(-3.59808 + 0.232051i) q^{39} +(5.59808 - 3.23205i) q^{41} +(-1.09808 + 0.633975i) q^{42} +(-3.63397 - 2.09808i) q^{43} -1.26795i q^{44} +(7.09808 + 4.09808i) q^{46} +4.73205 q^{47} +(0.866025 + 0.500000i) q^{48} +(2.69615 + 4.66987i) q^{49} +5.19615 q^{51} +(-3.00000 + 2.00000i) q^{52} +3.00000i q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.633975 + 1.09808i) q^{56} -4.73205 q^{57} +(1.50000 - 2.59808i) q^{58} +(12.0000 + 6.92820i) q^{59} +(-7.59808 + 13.1603i) q^{61} +(-8.19615 + 4.73205i) q^{62} +(-0.633975 - 1.09808i) q^{63} +1.00000 q^{64} +1.26795 q^{66} +(-3.63397 - 6.29423i) q^{67} +(4.50000 - 2.59808i) q^{68} +(-4.09808 + 7.09808i) q^{69} +(1.90192 + 1.09808i) q^{71} +(-0.500000 + 0.866025i) q^{72} +12.1244 q^{73} +(-1.50000 + 2.59808i) q^{74} +(-4.09808 + 2.36603i) q^{76} +1.60770i q^{77} +(-2.00000 - 3.00000i) q^{78} -8.39230 q^{79} +(-0.500000 - 0.866025i) q^{81} +(5.59808 + 3.23205i) q^{82} -5.66025 q^{83} +(-1.09808 - 0.633975i) q^{84} -4.19615i q^{86} +(2.59808 + 1.50000i) q^{87} +(1.09808 - 0.633975i) q^{88} +(8.19615 - 4.73205i) q^{89} +(3.80385 - 2.53590i) q^{91} +8.19615i q^{92} +(-4.73205 - 8.19615i) q^{93} +(2.36603 + 4.09808i) q^{94} +1.00000i q^{96} +(-3.00000 + 5.19615i) q^{97} +(-2.69615 + 4.66987i) q^{98} +1.26795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} + 6 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} + 6 q^{7} - 4 q^{8} + 2 q^{9} + 6 q^{11} + 6 q^{13} + 12 q^{14} - 2 q^{16} - 18 q^{17} + 4 q^{18} + 6 q^{19} + 6 q^{22} + 18 q^{23} - 6 q^{26} + 6 q^{28} - 6 q^{29} + 2 q^{32} + 6 q^{33} + 2 q^{36} + 6 q^{37} - 4 q^{39} + 12 q^{41} + 6 q^{42} - 18 q^{43} + 18 q^{46} + 12 q^{47} - 10 q^{49} - 12 q^{52} - 6 q^{56} - 12 q^{57} + 6 q^{58} + 48 q^{59} - 20 q^{61} - 12 q^{62} - 6 q^{63} + 4 q^{64} + 12 q^{66} - 18 q^{67} + 18 q^{68} - 6 q^{69} + 18 q^{71} - 2 q^{72} - 6 q^{74} - 6 q^{76} - 8 q^{78} + 8 q^{79} - 2 q^{81} + 12 q^{82} + 12 q^{83} + 6 q^{84} - 6 q^{88} + 12 q^{89} + 36 q^{91} - 12 q^{93} + 6 q^{94} - 12 q^{97} + 10 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) 0.633975 1.09808i 0.239620 0.415034i −0.720985 0.692950i \(-0.756311\pi\)
0.960605 + 0.277916i \(0.0896439\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) −1.09808 + 0.633975i −0.331082 + 0.191151i −0.656322 0.754481i \(-0.727889\pi\)
0.325239 + 0.945632i \(0.394555\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 3.23205 + 1.59808i 0.896410 + 0.443227i
\(14\) 1.26795 0.338874
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −4.50000 2.59808i −1.09141 0.630126i −0.157459 0.987526i \(-0.550330\pi\)
−0.933952 + 0.357400i \(0.883663\pi\)
\(18\) 1.00000 0.235702
\(19\) 4.09808 + 2.36603i 0.940163 + 0.542803i 0.890011 0.455938i \(-0.150696\pi\)
0.0501517 + 0.998742i \(0.484030\pi\)
\(20\) 0 0
\(21\) 1.26795i 0.276689i
\(22\) −1.09808 0.633975i −0.234111 0.135164i
\(23\) 7.09808 4.09808i 1.48005 0.854508i 0.480306 0.877101i \(-0.340525\pi\)
0.999745 + 0.0225928i \(0.00719212\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) 0 0
\(26\) 0.232051 + 3.59808i 0.0455089 + 0.705641i
\(27\) 1.00000i 0.192450i
\(28\) 0.633975 + 1.09808i 0.119810 + 0.207517i
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 0 0
\(31\) 9.46410i 1.69980i 0.526942 + 0.849901i \(0.323339\pi\)
−0.526942 + 0.849901i \(0.676661\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0.633975 1.09808i 0.110361 0.191151i
\(34\) 5.19615i 0.891133i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 1.50000 + 2.59808i 0.246598 + 0.427121i 0.962580 0.270998i \(-0.0873538\pi\)
−0.715981 + 0.698119i \(0.754020\pi\)
\(38\) 4.73205i 0.767640i
\(39\) −3.59808 + 0.232051i −0.576153 + 0.0371579i
\(40\) 0 0
\(41\) 5.59808 3.23205i 0.874273 0.504762i 0.00550690 0.999985i \(-0.498247\pi\)
0.868766 + 0.495223i \(0.164914\pi\)
\(42\) −1.09808 + 0.633975i −0.169437 + 0.0978244i
\(43\) −3.63397 2.09808i −0.554176 0.319954i 0.196629 0.980478i \(-0.437001\pi\)
−0.750805 + 0.660524i \(0.770334\pi\)
\(44\) 1.26795i 0.191151i
\(45\) 0 0
\(46\) 7.09808 + 4.09808i 1.04655 + 0.604228i
\(47\) 4.73205 0.690241 0.345120 0.938558i \(-0.387838\pi\)
0.345120 + 0.938558i \(0.387838\pi\)
\(48\) 0.866025 + 0.500000i 0.125000 + 0.0721688i
\(49\) 2.69615 + 4.66987i 0.385165 + 0.667125i
\(50\) 0 0
\(51\) 5.19615 0.727607
\(52\) −3.00000 + 2.00000i −0.416025 + 0.277350i
\(53\) 3.00000i 0.412082i 0.978543 + 0.206041i \(0.0660580\pi\)
−0.978543 + 0.206041i \(0.933942\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) 0 0
\(56\) −0.633975 + 1.09808i −0.0847184 + 0.146737i
\(57\) −4.73205 −0.626775
\(58\) 1.50000 2.59808i 0.196960 0.341144i
\(59\) 12.0000 + 6.92820i 1.56227 + 0.901975i 0.997027 + 0.0770484i \(0.0245496\pi\)
0.565240 + 0.824927i \(0.308784\pi\)
\(60\) 0 0
\(61\) −7.59808 + 13.1603i −0.972834 + 1.68500i −0.285929 + 0.958251i \(0.592302\pi\)
−0.686905 + 0.726747i \(0.741031\pi\)
\(62\) −8.19615 + 4.73205i −1.04091 + 0.600971i
\(63\) −0.633975 1.09808i −0.0798733 0.138345i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.26795 0.156074
\(67\) −3.63397 6.29423i −0.443961 0.768962i 0.554019 0.832504i \(-0.313094\pi\)
−0.997979 + 0.0635419i \(0.979760\pi\)
\(68\) 4.50000 2.59808i 0.545705 0.315063i
\(69\) −4.09808 + 7.09808i −0.493350 + 0.854508i
\(70\) 0 0
\(71\) 1.90192 + 1.09808i 0.225717 + 0.130318i 0.608595 0.793481i \(-0.291734\pi\)
−0.382878 + 0.923799i \(0.625067\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 12.1244 1.41905 0.709524 0.704681i \(-0.248910\pi\)
0.709524 + 0.704681i \(0.248910\pi\)
\(74\) −1.50000 + 2.59808i −0.174371 + 0.302020i
\(75\) 0 0
\(76\) −4.09808 + 2.36603i −0.470082 + 0.271402i
\(77\) 1.60770i 0.183214i
\(78\) −2.00000 3.00000i −0.226455 0.339683i
\(79\) −8.39230 −0.944208 −0.472104 0.881543i \(-0.656505\pi\)
−0.472104 + 0.881543i \(0.656505\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 5.59808 + 3.23205i 0.618204 + 0.356920i
\(83\) −5.66025 −0.621294 −0.310647 0.950525i \(-0.600546\pi\)
−0.310647 + 0.950525i \(0.600546\pi\)
\(84\) −1.09808 0.633975i −0.119810 0.0691723i
\(85\) 0 0
\(86\) 4.19615i 0.452483i
\(87\) 2.59808 + 1.50000i 0.278543 + 0.160817i
\(88\) 1.09808 0.633975i 0.117055 0.0675819i
\(89\) 8.19615 4.73205i 0.868790 0.501596i 0.00184433 0.999998i \(-0.499413\pi\)
0.866946 + 0.498402i \(0.166080\pi\)
\(90\) 0 0
\(91\) 3.80385 2.53590i 0.398752 0.265834i
\(92\) 8.19615i 0.854508i
\(93\) −4.73205 8.19615i −0.490691 0.849901i
\(94\) 2.36603 + 4.09808i 0.244037 + 0.422684i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −3.00000 + 5.19615i −0.304604 + 0.527589i −0.977173 0.212445i \(-0.931857\pi\)
0.672569 + 0.740034i \(0.265191\pi\)
\(98\) −2.69615 + 4.66987i −0.272353 + 0.471728i
\(99\) 1.26795i 0.127434i
\(100\) 0 0
\(101\) 9.69615 + 16.7942i 0.964803 + 1.67109i 0.710143 + 0.704058i \(0.248630\pi\)
0.254660 + 0.967031i \(0.418036\pi\)
\(102\) 2.59808 + 4.50000i 0.257248 + 0.445566i
\(103\) 6.19615i 0.610525i −0.952268 0.305263i \(-0.901256\pi\)
0.952268 0.305263i \(-0.0987442\pi\)
\(104\) −3.23205 1.59808i −0.316929 0.156704i
\(105\) 0 0
\(106\) −2.59808 + 1.50000i −0.252347 + 0.145693i
\(107\) 1.90192 1.09808i 0.183866 0.106155i −0.405242 0.914210i \(-0.632813\pi\)
0.589108 + 0.808054i \(0.299479\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) 4.39230i 0.420707i 0.977625 + 0.210353i \(0.0674614\pi\)
−0.977625 + 0.210353i \(0.932539\pi\)
\(110\) 0 0
\(111\) −2.59808 1.50000i −0.246598 0.142374i
\(112\) −1.26795 −0.119810
\(113\) −0.696152 0.401924i −0.0654885 0.0378098i 0.466898 0.884311i \(-0.345371\pi\)
−0.532387 + 0.846501i \(0.678705\pi\)
\(114\) −2.36603 4.09808i −0.221599 0.383820i
\(115\) 0 0
\(116\) 3.00000 0.278543
\(117\) 3.00000 2.00000i 0.277350 0.184900i
\(118\) 13.8564i 1.27559i
\(119\) −5.70577 + 3.29423i −0.523047 + 0.301981i
\(120\) 0 0
\(121\) −4.69615 + 8.13397i −0.426923 + 0.739452i
\(122\) −15.1962 −1.37579
\(123\) −3.23205 + 5.59808i −0.291424 + 0.504762i
\(124\) −8.19615 4.73205i −0.736036 0.424951i
\(125\) 0 0
\(126\) 0.633975 1.09808i 0.0564789 0.0978244i
\(127\) −3.46410 + 2.00000i −0.307389 + 0.177471i −0.645758 0.763542i \(-0.723458\pi\)
0.338368 + 0.941014i \(0.390125\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 4.19615 0.369451
\(130\) 0 0
\(131\) −4.39230 −0.383757 −0.191879 0.981419i \(-0.561458\pi\)
−0.191879 + 0.981419i \(0.561458\pi\)
\(132\) 0.633975 + 1.09808i 0.0551804 + 0.0955753i
\(133\) 5.19615 3.00000i 0.450564 0.260133i
\(134\) 3.63397 6.29423i 0.313928 0.543739i
\(135\) 0 0
\(136\) 4.50000 + 2.59808i 0.385872 + 0.222783i
\(137\) −4.50000 + 7.79423i −0.384461 + 0.665906i −0.991694 0.128618i \(-0.958946\pi\)
0.607233 + 0.794524i \(0.292279\pi\)
\(138\) −8.19615 −0.697703
\(139\) −2.00000 + 3.46410i −0.169638 + 0.293821i −0.938293 0.345843i \(-0.887593\pi\)
0.768655 + 0.639664i \(0.220926\pi\)
\(140\) 0 0
\(141\) −4.09808 + 2.36603i −0.345120 + 0.199255i
\(142\) 2.19615i 0.184297i
\(143\) −4.56218 + 0.294229i −0.381508 + 0.0246046i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 6.06218 + 10.5000i 0.501709 + 0.868986i
\(147\) −4.66987 2.69615i −0.385165 0.222375i
\(148\) −3.00000 −0.246598
\(149\) 5.30385 + 3.06218i 0.434508 + 0.250863i 0.701265 0.712900i \(-0.252619\pi\)
−0.266757 + 0.963764i \(0.585952\pi\)
\(150\) 0 0
\(151\) 10.7321i 0.873362i −0.899616 0.436681i \(-0.856154\pi\)
0.899616 0.436681i \(-0.143846\pi\)
\(152\) −4.09808 2.36603i −0.332398 0.191910i
\(153\) −4.50000 + 2.59808i −0.363803 + 0.210042i
\(154\) −1.39230 + 0.803848i −0.112195 + 0.0647759i
\(155\) 0 0
\(156\) 1.59808 3.23205i 0.127948 0.258771i
\(157\) 7.19615i 0.574315i −0.957883 0.287158i \(-0.907290\pi\)
0.957883 0.287158i \(-0.0927104\pi\)
\(158\) −4.19615 7.26795i −0.333828 0.578207i
\(159\) −1.50000 2.59808i −0.118958 0.206041i
\(160\) 0 0
\(161\) 10.3923i 0.819028i
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) −1.26795 + 2.19615i −0.0993134 + 0.172016i −0.911401 0.411520i \(-0.864998\pi\)
0.812087 + 0.583536i \(0.198331\pi\)
\(164\) 6.46410i 0.504762i
\(165\) 0 0
\(166\) −2.83013 4.90192i −0.219660 0.380463i
\(167\) −4.73205 8.19615i −0.366177 0.634237i 0.622787 0.782391i \(-0.286000\pi\)
−0.988964 + 0.148154i \(0.952667\pi\)
\(168\) 1.26795i 0.0978244i
\(169\) 7.89230 + 10.3301i 0.607100 + 0.794625i
\(170\) 0 0
\(171\) 4.09808 2.36603i 0.313388 0.180934i
\(172\) 3.63397 2.09808i 0.277088 0.159977i
\(173\) −3.80385 2.19615i −0.289201 0.166970i 0.348380 0.937353i \(-0.386732\pi\)
−0.637582 + 0.770383i \(0.720065\pi\)
\(174\) 3.00000i 0.227429i
\(175\) 0 0
\(176\) 1.09808 + 0.633975i 0.0827706 + 0.0477876i
\(177\) −13.8564 −1.04151
\(178\) 8.19615 + 4.73205i 0.614328 + 0.354682i
\(179\) −1.09808 1.90192i −0.0820741 0.142156i 0.822067 0.569391i \(-0.192821\pi\)
−0.904141 + 0.427235i \(0.859488\pi\)
\(180\) 0 0
\(181\) −19.5885 −1.45600 −0.727999 0.685578i \(-0.759550\pi\)
−0.727999 + 0.685578i \(0.759550\pi\)
\(182\) 4.09808 + 2.02628i 0.303770 + 0.150198i
\(183\) 15.1962i 1.12333i
\(184\) −7.09808 + 4.09808i −0.523277 + 0.302114i
\(185\) 0 0
\(186\) 4.73205 8.19615i 0.346971 0.600971i
\(187\) 6.58846 0.481796
\(188\) −2.36603 + 4.09808i −0.172560 + 0.298883i
\(189\) 1.09808 + 0.633975i 0.0798733 + 0.0461149i
\(190\) 0 0
\(191\) 10.3923 18.0000i 0.751961 1.30243i −0.194910 0.980821i \(-0.562442\pi\)
0.946871 0.321613i \(-0.104225\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) 11.5981 + 20.0885i 0.834848 + 1.44600i 0.894154 + 0.447759i \(0.147778\pi\)
−0.0593065 + 0.998240i \(0.518889\pi\)
\(194\) −6.00000 −0.430775
\(195\) 0 0
\(196\) −5.39230 −0.385165
\(197\) 3.46410 + 6.00000i 0.246807 + 0.427482i 0.962638 0.270791i \(-0.0872853\pi\)
−0.715831 + 0.698273i \(0.753952\pi\)
\(198\) −1.09808 + 0.633975i −0.0780369 + 0.0450546i
\(199\) 11.2942 19.5622i 0.800627 1.38673i −0.118578 0.992945i \(-0.537833\pi\)
0.919204 0.393781i \(-0.128833\pi\)
\(200\) 0 0
\(201\) 6.29423 + 3.63397i 0.443961 + 0.256321i
\(202\) −9.69615 + 16.7942i −0.682219 + 1.18164i
\(203\) −3.80385 −0.266978
\(204\) −2.59808 + 4.50000i −0.181902 + 0.315063i
\(205\) 0 0
\(206\) 5.36603 3.09808i 0.373869 0.215853i
\(207\) 8.19615i 0.569672i
\(208\) −0.232051 3.59808i −0.0160898 0.249482i
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) 12.1962 + 21.1244i 0.839618 + 1.45426i 0.890215 + 0.455541i \(0.150554\pi\)
−0.0505968 + 0.998719i \(0.516112\pi\)
\(212\) −2.59808 1.50000i −0.178437 0.103020i
\(213\) −2.19615 −0.150478
\(214\) 1.90192 + 1.09808i 0.130013 + 0.0750629i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 10.3923 + 6.00000i 0.705476 + 0.407307i
\(218\) −3.80385 + 2.19615i −0.257629 + 0.148742i
\(219\) −10.5000 + 6.06218i −0.709524 + 0.409644i
\(220\) 0 0
\(221\) −10.3923 15.5885i −0.699062 1.04859i
\(222\) 3.00000i 0.201347i
\(223\) −2.53590 4.39230i −0.169816 0.294130i 0.768539 0.639803i \(-0.220984\pi\)
−0.938355 + 0.345673i \(0.887651\pi\)
\(224\) −0.633975 1.09808i −0.0423592 0.0733683i
\(225\) 0 0
\(226\) 0.803848i 0.0534711i
\(227\) 10.0981 17.4904i 0.670233 1.16088i −0.307605 0.951514i \(-0.599528\pi\)
0.977838 0.209363i \(-0.0671391\pi\)
\(228\) 2.36603 4.09808i 0.156694 0.271402i
\(229\) 7.85641i 0.519166i −0.965721 0.259583i \(-0.916415\pi\)
0.965721 0.259583i \(-0.0835851\pi\)
\(230\) 0 0
\(231\) −0.803848 1.39230i −0.0528893 0.0916069i
\(232\) 1.50000 + 2.59808i 0.0984798 + 0.170572i
\(233\) 18.0000i 1.17922i 0.807688 + 0.589610i \(0.200718\pi\)
−0.807688 + 0.589610i \(0.799282\pi\)
\(234\) 3.23205 + 1.59808i 0.211286 + 0.104470i
\(235\) 0 0
\(236\) −12.0000 + 6.92820i −0.781133 + 0.450988i
\(237\) 7.26795 4.19615i 0.472104 0.272569i
\(238\) −5.70577 3.29423i −0.369850 0.213533i
\(239\) 6.58846i 0.426172i −0.977033 0.213086i \(-0.931649\pi\)
0.977033 0.213086i \(-0.0683514\pi\)
\(240\) 0 0
\(241\) 9.69615 + 5.59808i 0.624584 + 0.360604i 0.778652 0.627457i \(-0.215904\pi\)
−0.154068 + 0.988060i \(0.549237\pi\)
\(242\) −9.39230 −0.603760
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) −7.59808 13.1603i −0.486417 0.842499i
\(245\) 0 0
\(246\) −6.46410 −0.412136
\(247\) 9.46410 + 14.1962i 0.602186 + 0.903280i
\(248\) 9.46410i 0.600971i
\(249\) 4.90192 2.83013i 0.310647 0.179352i
\(250\) 0 0
\(251\) 8.19615 14.1962i 0.517337 0.896053i −0.482461 0.875918i \(-0.660257\pi\)
0.999797 0.0201356i \(-0.00640979\pi\)
\(252\) 1.26795 0.0798733
\(253\) −5.19615 + 9.00000i −0.326679 + 0.565825i
\(254\) −3.46410 2.00000i −0.217357 0.125491i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 20.0885 11.5981i 1.25308 0.723468i 0.281363 0.959601i \(-0.409214\pi\)
0.971721 + 0.236133i \(0.0758802\pi\)
\(258\) 2.09808 + 3.63397i 0.130621 + 0.226241i
\(259\) 3.80385 0.236360
\(260\) 0 0
\(261\) −3.00000 −0.185695
\(262\) −2.19615 3.80385i −0.135679 0.235002i
\(263\) 7.09808 4.09808i 0.437686 0.252698i −0.264930 0.964268i \(-0.585349\pi\)
0.702616 + 0.711570i \(0.252015\pi\)
\(264\) −0.633975 + 1.09808i −0.0390184 + 0.0675819i
\(265\) 0 0
\(266\) 5.19615 + 3.00000i 0.318597 + 0.183942i
\(267\) −4.73205 + 8.19615i −0.289597 + 0.501596i
\(268\) 7.26795 0.443961
\(269\) −3.80385 + 6.58846i −0.231925 + 0.401705i −0.958374 0.285514i \(-0.907836\pi\)
0.726450 + 0.687220i \(0.241169\pi\)
\(270\) 0 0
\(271\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(272\) 5.19615i 0.315063i
\(273\) −2.02628 + 4.09808i −0.122636 + 0.248027i
\(274\) −9.00000 −0.543710
\(275\) 0 0
\(276\) −4.09808 7.09808i −0.246675 0.427254i
\(277\) −4.16025 2.40192i −0.249965 0.144318i 0.369783 0.929118i \(-0.379432\pi\)
−0.619748 + 0.784801i \(0.712765\pi\)
\(278\) −4.00000 −0.239904
\(279\) 8.19615 + 4.73205i 0.490691 + 0.283300i
\(280\) 0 0
\(281\) 17.5359i 1.04610i −0.852301 0.523052i \(-0.824793\pi\)
0.852301 0.523052i \(-0.175207\pi\)
\(282\) −4.09808 2.36603i −0.244037 0.140895i
\(283\) 17.1506 9.90192i 1.01950 0.588608i 0.105541 0.994415i \(-0.466343\pi\)
0.913959 + 0.405807i \(0.133009\pi\)
\(284\) −1.90192 + 1.09808i −0.112858 + 0.0651588i
\(285\) 0 0
\(286\) −2.53590 3.80385i −0.149951 0.224926i
\(287\) 8.19615i 0.483804i
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) 5.00000 + 8.66025i 0.294118 + 0.509427i
\(290\) 0 0
\(291\) 6.00000i 0.351726i
\(292\) −6.06218 + 10.5000i −0.354762 + 0.614466i
\(293\) −1.33013 + 2.30385i −0.0777069 + 0.134592i −0.902260 0.431192i \(-0.858093\pi\)
0.824553 + 0.565784i \(0.191426\pi\)
\(294\) 5.39230i 0.314486i
\(295\) 0 0
\(296\) −1.50000 2.59808i −0.0871857 0.151010i
\(297\) −0.633975 1.09808i −0.0367869 0.0637168i
\(298\) 6.12436i 0.354774i
\(299\) 29.4904 1.90192i 1.70547 0.109991i
\(300\) 0 0
\(301\) −4.60770 + 2.66025i −0.265583 + 0.153334i
\(302\) 9.29423 5.36603i 0.534823 0.308780i
\(303\) −16.7942 9.69615i −0.964803 0.557029i
\(304\) 4.73205i 0.271402i
\(305\) 0 0
\(306\) −4.50000 2.59808i −0.257248 0.148522i
\(307\) −7.26795 −0.414804 −0.207402 0.978256i \(-0.566501\pi\)
−0.207402 + 0.978256i \(0.566501\pi\)
\(308\) −1.39230 0.803848i −0.0793339 0.0458035i
\(309\) 3.09808 + 5.36603i 0.176243 + 0.305263i
\(310\) 0 0
\(311\) 8.19615 0.464761 0.232381 0.972625i \(-0.425349\pi\)
0.232381 + 0.972625i \(0.425349\pi\)
\(312\) 3.59808 0.232051i 0.203701 0.0131373i
\(313\) 3.60770i 0.203919i −0.994789 0.101959i \(-0.967489\pi\)
0.994789 0.101959i \(-0.0325112\pi\)
\(314\) 6.23205 3.59808i 0.351695 0.203051i
\(315\) 0 0
\(316\) 4.19615 7.26795i 0.236052 0.408854i
\(317\) −18.1244 −1.01797 −0.508983 0.860777i \(-0.669978\pi\)
−0.508983 + 0.860777i \(0.669978\pi\)
\(318\) 1.50000 2.59808i 0.0841158 0.145693i
\(319\) 3.29423 + 1.90192i 0.184441 + 0.106487i
\(320\) 0 0
\(321\) −1.09808 + 1.90192i −0.0612886 + 0.106155i
\(322\) 9.00000 5.19615i 0.501550 0.289570i
\(323\) −12.2942 21.2942i −0.684069 1.18484i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −2.53590 −0.140450
\(327\) −2.19615 3.80385i −0.121448 0.210353i
\(328\) −5.59808 + 3.23205i −0.309102 + 0.178460i
\(329\) 3.00000 5.19615i 0.165395 0.286473i
\(330\) 0 0
\(331\) −10.3923 6.00000i −0.571213 0.329790i 0.186421 0.982470i \(-0.440311\pi\)
−0.757634 + 0.652680i \(0.773645\pi\)
\(332\) 2.83013 4.90192i 0.155323 0.269028i
\(333\) 3.00000 0.164399
\(334\) 4.73205 8.19615i 0.258926 0.448474i
\(335\) 0 0
\(336\) 1.09808 0.633975i 0.0599050 0.0345861i
\(337\) 31.0000i 1.68868i −0.535810 0.844339i \(-0.679994\pi\)
0.535810 0.844339i \(-0.320006\pi\)
\(338\) −5.00000 + 12.0000i −0.271964 + 0.652714i
\(339\) 0.803848 0.0436590
\(340\) 0 0
\(341\) −6.00000 10.3923i −0.324918 0.562775i
\(342\) 4.09808 + 2.36603i 0.221599 + 0.127940i
\(343\) 15.7128 0.848412
\(344\) 3.63397 + 2.09808i 0.195931 + 0.113121i
\(345\) 0 0
\(346\) 4.39230i 0.236132i
\(347\) 16.0981 + 9.29423i 0.864190 + 0.498940i 0.865413 0.501059i \(-0.167056\pi\)
−0.00122316 + 0.999999i \(0.500389\pi\)
\(348\) −2.59808 + 1.50000i −0.139272 + 0.0804084i
\(349\) 8.19615 4.73205i 0.438730 0.253301i −0.264329 0.964433i \(-0.585150\pi\)
0.703059 + 0.711132i \(0.251817\pi\)
\(350\) 0 0
\(351\) −1.59808 + 3.23205i −0.0852990 + 0.172514i
\(352\) 1.26795i 0.0675819i
\(353\) −17.8923 30.9904i −0.952311 1.64945i −0.740404 0.672162i \(-0.765366\pi\)
−0.211907 0.977290i \(-0.567967\pi\)
\(354\) −6.92820 12.0000i −0.368230 0.637793i
\(355\) 0 0
\(356\) 9.46410i 0.501596i
\(357\) 3.29423 5.70577i 0.174349 0.301981i
\(358\) 1.09808 1.90192i 0.0580351 0.100520i
\(359\) 16.0526i 0.847222i −0.905844 0.423611i \(-0.860762\pi\)
0.905844 0.423611i \(-0.139238\pi\)
\(360\) 0 0
\(361\) 1.69615 + 2.93782i 0.0892712 + 0.154622i
\(362\) −9.79423 16.9641i −0.514773 0.891613i
\(363\) 9.39230i 0.492968i
\(364\) 0.294229 + 4.56218i 0.0154218 + 0.239123i
\(365\) 0 0
\(366\) 13.1603 7.59808i 0.687897 0.397158i
\(367\) 11.9545 6.90192i 0.624019 0.360277i −0.154413 0.988006i \(-0.549349\pi\)
0.778432 + 0.627729i \(0.216015\pi\)
\(368\) −7.09808 4.09808i −0.370013 0.213627i
\(369\) 6.46410i 0.336508i
\(370\) 0 0
\(371\) 3.29423 + 1.90192i 0.171028 + 0.0987430i
\(372\) 9.46410 0.490691
\(373\) 24.2321 + 13.9904i 1.25469 + 0.724394i 0.972037 0.234828i \(-0.0754528\pi\)
0.282651 + 0.959223i \(0.408786\pi\)
\(374\) 3.29423 + 5.70577i 0.170341 + 0.295038i
\(375\) 0 0
\(376\) −4.73205 −0.244037
\(377\) −0.696152 10.7942i −0.0358537 0.555931i
\(378\) 1.26795i 0.0652163i
\(379\) −26.1962 + 15.1244i −1.34561 + 0.776886i −0.987624 0.156842i \(-0.949869\pi\)
−0.357982 + 0.933728i \(0.616535\pi\)
\(380\) 0 0
\(381\) 2.00000 3.46410i 0.102463 0.177471i
\(382\) 20.7846 1.06343
\(383\) −11.6603 + 20.1962i −0.595811 + 1.03198i 0.397621 + 0.917550i \(0.369836\pi\)
−0.993432 + 0.114425i \(0.963497\pi\)
\(384\) −0.866025 0.500000i −0.0441942 0.0255155i
\(385\) 0 0
\(386\) −11.5981 + 20.0885i −0.590327 + 1.02248i
\(387\) −3.63397 + 2.09808i −0.184725 + 0.106651i
\(388\) −3.00000 5.19615i −0.152302 0.263795i
\(389\) 7.39230 0.374805 0.187402 0.982283i \(-0.439993\pi\)
0.187402 + 0.982283i \(0.439993\pi\)
\(390\) 0 0
\(391\) −42.5885 −2.15379
\(392\) −2.69615 4.66987i −0.136176 0.235864i
\(393\) 3.80385 2.19615i 0.191879 0.110781i
\(394\) −3.46410 + 6.00000i −0.174519 + 0.302276i
\(395\) 0 0
\(396\) −1.09808 0.633975i −0.0551804 0.0318584i
\(397\) 2.19615 3.80385i 0.110222 0.190910i −0.805638 0.592408i \(-0.798177\pi\)
0.915860 + 0.401499i \(0.131511\pi\)
\(398\) 22.5885 1.13226
\(399\) −3.00000 + 5.19615i −0.150188 + 0.260133i
\(400\) 0 0
\(401\) −18.1865 + 10.5000i −0.908192 + 0.524345i −0.879849 0.475253i \(-0.842356\pi\)
−0.0283431 + 0.999598i \(0.509023\pi\)
\(402\) 7.26795i 0.362492i
\(403\) −15.1244 + 30.5885i −0.753398 + 1.52372i
\(404\) −19.3923 −0.964803
\(405\) 0 0
\(406\) −1.90192 3.29423i −0.0943909 0.163490i
\(407\) −3.29423 1.90192i −0.163289 0.0942749i
\(408\) −5.19615 −0.257248
\(409\) −17.8923 10.3301i −0.884718 0.510792i −0.0125066 0.999922i \(-0.503981\pi\)
−0.872211 + 0.489130i \(0.837314\pi\)
\(410\) 0 0
\(411\) 9.00000i 0.443937i
\(412\) 5.36603 + 3.09808i 0.264365 + 0.152631i
\(413\) 15.2154 8.78461i 0.748700 0.432262i
\(414\) 7.09808 4.09808i 0.348851 0.201409i
\(415\) 0 0
\(416\) 3.00000 2.00000i 0.147087 0.0980581i
\(417\) 4.00000i 0.195881i
\(418\) −3.00000 5.19615i −0.146735 0.254152i
\(419\) −2.19615 3.80385i −0.107289 0.185830i 0.807382 0.590029i \(-0.200884\pi\)
−0.914671 + 0.404199i \(0.867550\pi\)
\(420\) 0 0
\(421\) 6.46410i 0.315041i −0.987516 0.157521i \(-0.949650\pi\)
0.987516 0.157521i \(-0.0503500\pi\)
\(422\) −12.1962 + 21.1244i −0.593699 + 1.02832i
\(423\) 2.36603 4.09808i 0.115040 0.199255i
\(424\) 3.00000i 0.145693i
\(425\) 0 0
\(426\) −1.09808 1.90192i −0.0532020 0.0921485i
\(427\) 9.63397 + 16.6865i 0.466221 + 0.807518i
\(428\) 2.19615i 0.106155i
\(429\) 3.80385 2.53590i 0.183651 0.122434i
\(430\) 0 0
\(431\) 33.0788 19.0981i 1.59335 0.919922i 0.600625 0.799531i \(-0.294918\pi\)
0.992727 0.120391i \(-0.0384149\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 6.74167 + 3.89230i 0.323984 + 0.187052i 0.653167 0.757214i \(-0.273440\pi\)
−0.329183 + 0.944266i \(0.606773\pi\)
\(434\) 12.0000i 0.576018i
\(435\) 0 0
\(436\) −3.80385 2.19615i −0.182171 0.105177i
\(437\) 38.7846 1.85532
\(438\) −10.5000 6.06218i −0.501709 0.289662i
\(439\) 7.29423 + 12.6340i 0.348135 + 0.602987i 0.985918 0.167229i \(-0.0534819\pi\)
−0.637784 + 0.770216i \(0.720149\pi\)
\(440\) 0 0
\(441\) 5.39230 0.256776
\(442\) 8.30385 16.7942i 0.394974 0.798820i
\(443\) 16.3923i 0.778822i 0.921064 + 0.389411i \(0.127321\pi\)
−0.921064 + 0.389411i \(0.872679\pi\)
\(444\) 2.59808 1.50000i 0.123299 0.0711868i
\(445\) 0 0
\(446\) 2.53590 4.39230i 0.120078 0.207982i
\(447\) −6.12436 −0.289672
\(448\) 0.633975 1.09808i 0.0299525 0.0518792i
\(449\) −22.9808 13.2679i −1.08453 0.626153i −0.152415 0.988317i \(-0.548705\pi\)
−0.932115 + 0.362163i \(0.882038\pi\)
\(450\) 0 0
\(451\) −4.09808 + 7.09808i −0.192971 + 0.334235i
\(452\) 0.696152 0.401924i 0.0327443 0.0189049i
\(453\) 5.36603 + 9.29423i 0.252118 + 0.436681i
\(454\) 20.1962 0.947852
\(455\) 0 0
\(456\) 4.73205 0.221599
\(457\) 15.9904 + 27.6962i 0.747998 + 1.29557i 0.948781 + 0.315935i \(0.102318\pi\)
−0.200782 + 0.979636i \(0.564348\pi\)
\(458\) 6.80385 3.92820i 0.317923 0.183553i
\(459\) 2.59808 4.50000i 0.121268 0.210042i
\(460\) 0 0
\(461\) −27.6962 15.9904i −1.28994 0.744746i −0.311295 0.950313i \(-0.600763\pi\)
−0.978643 + 0.205567i \(0.934096\pi\)
\(462\) 0.803848 1.39230i 0.0373984 0.0647759i
\(463\) −15.8038 −0.734467 −0.367234 0.930129i \(-0.619695\pi\)
−0.367234 + 0.930129i \(0.619695\pi\)
\(464\) −1.50000 + 2.59808i −0.0696358 + 0.120613i
\(465\) 0 0
\(466\) −15.5885 + 9.00000i −0.722121 + 0.416917i
\(467\) 5.41154i 0.250416i 0.992130 + 0.125208i \(0.0399599\pi\)
−0.992130 + 0.125208i \(0.960040\pi\)
\(468\) 0.232051 + 3.59808i 0.0107266 + 0.166321i
\(469\) −9.21539 −0.425527
\(470\) 0 0
\(471\) 3.59808 + 6.23205i 0.165791 + 0.287158i
\(472\) −12.0000 6.92820i −0.552345 0.318896i
\(473\) 5.32051 0.244637
\(474\) 7.26795 + 4.19615i 0.333828 + 0.192736i
\(475\) 0 0
\(476\) 6.58846i 0.301981i
\(477\) 2.59808 + 1.50000i 0.118958 + 0.0686803i
\(478\) 5.70577 3.29423i 0.260976 0.150675i
\(479\) −0.588457 + 0.339746i −0.0268873 + 0.0155234i −0.513383 0.858159i \(-0.671608\pi\)
0.486496 + 0.873683i \(0.338275\pi\)
\(480\) 0 0
\(481\) 0.696152 + 10.7942i 0.0317418 + 0.492174i
\(482\) 11.1962i 0.509971i
\(483\) 5.19615 + 9.00000i 0.236433 + 0.409514i
\(484\) −4.69615 8.13397i −0.213461 0.369726i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 7.56218 13.0981i 0.342675 0.593530i −0.642254 0.766492i \(-0.722000\pi\)
0.984929 + 0.172962i \(0.0553337\pi\)
\(488\) 7.59808 13.1603i 0.343949 0.595737i
\(489\) 2.53590i 0.114677i
\(490\) 0 0
\(491\) −15.2942 26.4904i −0.690219 1.19549i −0.971766 0.235947i \(-0.924181\pi\)
0.281547 0.959547i \(-0.409152\pi\)
\(492\) −3.23205 5.59808i −0.145712 0.252381i
\(493\) 15.5885i 0.702069i
\(494\) −7.56218 + 15.2942i −0.340238 + 0.688120i
\(495\) 0 0
\(496\) 8.19615 4.73205i 0.368018 0.212475i
\(497\) 2.41154 1.39230i 0.108172 0.0624534i
\(498\) 4.90192 + 2.83013i 0.219660 + 0.126821i
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 8.19615 + 4.73205i 0.366177 + 0.211412i
\(502\) 16.3923 0.731624
\(503\) −10.9019 6.29423i −0.486093 0.280646i 0.236859 0.971544i \(-0.423882\pi\)
−0.722952 + 0.690898i \(0.757215\pi\)
\(504\) 0.633975 + 1.09808i 0.0282395 + 0.0489122i
\(505\) 0 0
\(506\) −10.3923 −0.461994
\(507\) −12.0000 5.00000i −0.532939 0.222058i
\(508\) 4.00000i 0.177471i
\(509\) −23.0885 + 13.3301i −1.02338 + 0.590847i −0.915081 0.403271i \(-0.867873\pi\)
−0.108297 + 0.994119i \(0.534540\pi\)
\(510\) 0 0
\(511\) 7.68653 13.3135i 0.340032 0.588953i
\(512\) −1.00000 −0.0441942
\(513\) −2.36603 + 4.09808i −0.104463 + 0.180934i
\(514\) 20.0885 + 11.5981i 0.886064 + 0.511569i
\(515\) 0 0
\(516\) −2.09808 + 3.63397i −0.0923627 + 0.159977i
\(517\) −5.19615 + 3.00000i −0.228527 + 0.131940i
\(518\) 1.90192 + 3.29423i 0.0835657 + 0.144740i
\(519\) 4.39230 0.192801
\(520\) 0 0
\(521\) −29.1962 −1.27911 −0.639553 0.768747i \(-0.720881\pi\)
−0.639553 + 0.768747i \(0.720881\pi\)
\(522\) −1.50000 2.59808i −0.0656532 0.113715i
\(523\) 28.2224 16.2942i 1.23408 0.712497i 0.266203 0.963917i \(-0.414231\pi\)
0.967878 + 0.251420i \(0.0808976\pi\)
\(524\) 2.19615 3.80385i 0.0959394 0.166172i
\(525\) 0 0
\(526\) 7.09808 + 4.09808i 0.309491 + 0.178685i
\(527\) 24.5885 42.5885i 1.07109 1.85518i
\(528\) −1.26795 −0.0551804
\(529\) 22.0885 38.2583i 0.960368 1.66341i
\(530\) 0 0
\(531\) 12.0000 6.92820i 0.520756 0.300658i
\(532\) 6.00000i 0.260133i
\(533\) 23.2583 1.50000i 1.00743 0.0649722i
\(534\) −9.46410 −0.409552
\(535\) 0 0
\(536\) 3.63397 + 6.29423i 0.156964 + 0.271869i
\(537\) 1.90192 + 1.09808i 0.0820741 + 0.0473855i
\(538\) −7.60770 −0.327991
\(539\) −5.92116 3.41858i −0.255042 0.147249i
\(540\) 0 0
\(541\) 10.8564i 0.466753i 0.972386 + 0.233377i \(0.0749775\pi\)
−0.972386 + 0.233377i \(0.925022\pi\)
\(542\) 0 0
\(543\) 16.9641 9.79423i 0.727999 0.420311i
\(544\) −4.50000 + 2.59808i −0.192936 + 0.111392i
\(545\) 0 0
\(546\) −4.56218 + 0.294229i −0.195243 + 0.0125918i
\(547\) 4.19615i 0.179415i −0.995968 0.0897073i \(-0.971407\pi\)
0.995968 0.0897073i \(-0.0285931\pi\)
\(548\) −4.50000 7.79423i −0.192230 0.332953i
\(549\) 7.59808 + 13.1603i 0.324278 + 0.561666i
\(550\) 0 0
\(551\) 14.1962i 0.604776i
\(552\) 4.09808 7.09808i 0.174426 0.302114i
\(553\) −5.32051 + 9.21539i −0.226251 + 0.391878i
\(554\) 4.80385i 0.204096i
\(555\) 0 0
\(556\) −2.00000 3.46410i −0.0848189 0.146911i
\(557\) 12.8660 + 22.2846i 0.545151 + 0.944229i 0.998597 + 0.0529457i \(0.0168610\pi\)
−0.453446 + 0.891284i \(0.649806\pi\)
\(558\) 9.46410i 0.400647i
\(559\) −8.39230 12.5885i −0.354957 0.532435i
\(560\) 0 0
\(561\) −5.70577 + 3.29423i −0.240898 + 0.139082i
\(562\) 15.1865 8.76795i 0.640605 0.369854i
\(563\) −28.3923 16.3923i −1.19659 0.690853i −0.236799 0.971559i \(-0.576098\pi\)
−0.959794 + 0.280705i \(0.909432\pi\)
\(564\) 4.73205i 0.199255i
\(565\) 0 0
\(566\) 17.1506 + 9.90192i 0.720895 + 0.416209i
\(567\) −1.26795 −0.0532489
\(568\) −1.90192 1.09808i −0.0798029 0.0460743i
\(569\) −4.39230 7.60770i −0.184135 0.318931i 0.759150 0.650916i \(-0.225615\pi\)
−0.943285 + 0.331985i \(0.892282\pi\)
\(570\) 0 0
\(571\) 24.1962 1.01258 0.506289 0.862364i \(-0.331017\pi\)
0.506289 + 0.862364i \(0.331017\pi\)
\(572\) 2.02628 4.09808i 0.0847230 0.171349i
\(573\) 20.7846i 0.868290i
\(574\) 7.09808 4.09808i 0.296268 0.171050i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) −19.7321 −0.821456 −0.410728 0.911758i \(-0.634725\pi\)
−0.410728 + 0.911758i \(0.634725\pi\)
\(578\) −5.00000 + 8.66025i −0.207973 + 0.360219i
\(579\) −20.0885 11.5981i −0.834848 0.482000i
\(580\) 0 0
\(581\) −3.58846 + 6.21539i −0.148874 + 0.257858i
\(582\) 5.19615 3.00000i 0.215387 0.124354i
\(583\) −1.90192 3.29423i −0.0787696 0.136433i
\(584\) −12.1244 −0.501709
\(585\) 0 0
\(586\) −2.66025 −0.109894
\(587\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(588\) 4.66987 2.69615i 0.192582 0.111187i
\(589\) −22.3923 + 38.7846i −0.922659 + 1.59809i
\(590\) 0 0
\(591\) −6.00000 3.46410i −0.246807 0.142494i
\(592\) 1.50000 2.59808i 0.0616496 0.106780i
\(593\) −19.1436 −0.786133 −0.393067 0.919510i \(-0.628586\pi\)
−0.393067 + 0.919510i \(0.628586\pi\)
\(594\) 0.633975 1.09808i 0.0260123 0.0450546i
\(595\) 0 0
\(596\) −5.30385 + 3.06218i −0.217254 + 0.125432i
\(597\) 22.5885i 0.924484i
\(598\) 16.3923 + 24.5885i 0.670331 + 1.00550i
\(599\) −16.3923 −0.669771 −0.334886 0.942259i \(-0.608698\pi\)
−0.334886 + 0.942259i \(0.608698\pi\)
\(600\) 0 0
\(601\) 9.89230 + 17.1340i 0.403516 + 0.698909i 0.994147 0.108032i \(-0.0344548\pi\)
−0.590632 + 0.806941i \(0.701121\pi\)
\(602\) −4.60770 2.66025i −0.187796 0.108424i
\(603\) −7.26795 −0.295974
\(604\) 9.29423 + 5.36603i 0.378177 + 0.218340i
\(605\) 0 0
\(606\) 19.3923i 0.787759i
\(607\) −6.24871 3.60770i −0.253627 0.146432i 0.367797 0.929906i \(-0.380112\pi\)
−0.621424 + 0.783474i \(0.713446\pi\)
\(608\) 4.09808 2.36603i 0.166199 0.0959550i
\(609\) 3.29423 1.90192i 0.133489 0.0770698i
\(610\) 0 0
\(611\) 15.2942 + 7.56218i 0.618738 + 0.305933i
\(612\) 5.19615i 0.210042i
\(613\) −6.57180 11.3827i −0.265432 0.459742i 0.702244 0.711936i \(-0.252181\pi\)
−0.967677 + 0.252194i \(0.918848\pi\)
\(614\) −3.63397 6.29423i −0.146655 0.254014i
\(615\) 0 0
\(616\) 1.60770i 0.0647759i
\(617\) −15.6962 + 27.1865i −0.631903 + 1.09449i 0.355259 + 0.934768i \(0.384393\pi\)
−0.987162 + 0.159721i \(0.948941\pi\)
\(618\) −3.09808 + 5.36603i −0.124623 + 0.215853i
\(619\) 28.3923i 1.14118i −0.821234 0.570592i \(-0.806714\pi\)
0.821234 0.570592i \(-0.193286\pi\)
\(620\) 0 0
\(621\) 4.09808 + 7.09808i 0.164450 + 0.284836i
\(622\) 4.09808 + 7.09808i 0.164318 + 0.284607i
\(623\) 12.0000i 0.480770i
\(624\) 2.00000 + 3.00000i 0.0800641 + 0.120096i
\(625\) 0 0
\(626\) 3.12436 1.80385i 0.124874 0.0720962i
\(627\) 5.19615 3.00000i 0.207514 0.119808i
\(628\) 6.23205 + 3.59808i 0.248686 + 0.143579i
\(629\) 15.5885i 0.621552i
\(630\) 0 0
\(631\) −1.60770 0.928203i −0.0640013 0.0369512i 0.467658 0.883910i \(-0.345098\pi\)
−0.531659 + 0.846958i \(0.678431\pi\)
\(632\) 8.39230 0.333828
\(633\) −21.1244 12.1962i −0.839618 0.484754i
\(634\) −9.06218 15.6962i −0.359905 0.623374i
\(635\) 0 0
\(636\) 3.00000 0.118958
\(637\) 1.25129 + 19.4019i 0.0495779 + 0.768732i
\(638\) 3.80385i 0.150596i
\(639\) 1.90192 1.09808i 0.0752389 0.0434392i
\(640\) 0 0
\(641\) −20.5981 + 35.6769i −0.813575 + 1.40915i 0.0967715 + 0.995307i \(0.469148\pi\)
−0.910347 + 0.413847i \(0.864185\pi\)
\(642\) −2.19615 −0.0866752
\(643\) 13.8564 24.0000i 0.546443 0.946468i −0.452071 0.891982i \(-0.649315\pi\)
0.998515 0.0544858i \(-0.0173519\pi\)
\(644\) 9.00000 + 5.19615i 0.354650 + 0.204757i
\(645\) 0 0
\(646\) 12.2942 21.2942i 0.483710 0.837810i
\(647\) −42.5885 + 24.5885i −1.67433 + 0.966672i −0.709153 + 0.705054i \(0.750923\pi\)
−0.965172 + 0.261618i \(0.915744\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −17.5692 −0.689652
\(650\) 0 0
\(651\) −12.0000 −0.470317
\(652\) −1.26795 2.19615i −0.0496567 0.0860080i
\(653\) 11.4115 6.58846i 0.446568 0.257826i −0.259812 0.965659i \(-0.583660\pi\)
0.706380 + 0.707833i \(0.250327\pi\)
\(654\) 2.19615 3.80385i 0.0858764 0.148742i
\(655\) 0 0
\(656\) −5.59808 3.23205i −0.218568 0.126190i
\(657\) 6.06218 10.5000i 0.236508 0.409644i
\(658\) 6.00000 0.233904
\(659\) −18.5885 + 32.1962i −0.724103 + 1.25418i 0.235238 + 0.971938i \(0.424413\pi\)
−0.959342 + 0.282246i \(0.908920\pi\)
\(660\) 0 0
\(661\) −7.79423 + 4.50000i −0.303160 + 0.175030i −0.643862 0.765142i \(-0.722669\pi\)
0.340701 + 0.940172i \(0.389335\pi\)
\(662\) 12.0000i 0.466393i
\(663\) 16.7942 + 8.30385i 0.652234 + 0.322495i
\(664\) 5.66025 0.219660
\(665\) 0 0
\(666\) 1.50000 + 2.59808i 0.0581238 + 0.100673i
\(667\) −21.2942 12.2942i −0.824516 0.476034i
\(668\) 9.46410 0.366177
\(669\) 4.39230 + 2.53590i 0.169816 + 0.0980435i
\(670\) 0 0
\(671\) 19.2679i 0.743831i
\(672\) 1.09808 + 0.633975i 0.0423592 + 0.0244561i
\(673\) −0.866025 + 0.500000i −0.0333828 + 0.0192736i −0.516599 0.856228i \(-0.672802\pi\)
0.483216 + 0.875501i \(0.339469\pi\)
\(674\) 26.8468 15.5000i 1.03410 0.597038i
\(675\) 0 0
\(676\) −12.8923 + 1.66987i −0.495858 + 0.0642259i
\(677\) 16.3923i 0.630007i 0.949090 + 0.315004i \(0.102006\pi\)
−0.949090 + 0.315004i \(0.897994\pi\)
\(678\) 0.401924 + 0.696152i 0.0154358 + 0.0267356i
\(679\) 3.80385 + 6.58846i 0.145978 + 0.252842i
\(680\) 0 0
\(681\) 20.1962i 0.773918i
\(682\) 6.00000 10.3923i 0.229752 0.397942i
\(683\) 13.8564 24.0000i 0.530201 0.918334i −0.469179 0.883103i \(-0.655450\pi\)
0.999379 0.0352311i \(-0.0112167\pi\)
\(684\) 4.73205i 0.180934i
\(685\) 0 0
\(686\) 7.85641 + 13.6077i 0.299959 + 0.519544i
\(687\) 3.92820 + 6.80385i 0.149870 + 0.259583i
\(688\) 4.19615i 0.159977i
\(689\) −4.79423 + 9.69615i −0.182646 + 0.369394i
\(690\) 0 0
\(691\) 22.0981 12.7583i 0.840650 0.485350i −0.0168348 0.999858i \(-0.505359\pi\)
0.857485 + 0.514509i \(0.172026\pi\)
\(692\) 3.80385 2.19615i 0.144601 0.0834852i
\(693\) 1.39230 + 0.803848i 0.0528893 + 0.0305356i
\(694\) 18.5885i 0.705608i
\(695\) 0 0
\(696\) −2.59808 1.50000i −0.0984798 0.0568574i
\(697\) −33.5885 −1.27225
\(698\) 8.19615 + 4.73205i 0.310229 + 0.179111i
\(699\) −9.00000 15.5885i −0.340411 0.589610i
\(700\) 0 0
\(701\) 16.3923 0.619129 0.309564 0.950878i \(-0.399817\pi\)
0.309564 + 0.950878i \(0.399817\pi\)
\(702\) −3.59808 + 0.232051i −0.135801 + 0.00875819i
\(703\) 14.1962i 0.535418i
\(704\) −1.09808 + 0.633975i −0.0413853 + 0.0238938i
\(705\) 0 0
\(706\) 17.8923 30.9904i 0.673386 1.16634i
\(707\) 24.5885 0.924744
\(708\) 6.92820 12.0000i 0.260378 0.450988i
\(709\) 39.1865 + 22.6244i 1.47168 + 0.849676i 0.999494 0.0318226i \(-0.0101311\pi\)
0.472188 + 0.881498i \(0.343464\pi\)
\(710\) 0 0
\(711\) −4.19615 + 7.26795i −0.157368 + 0.272569i
\(712\) −8.19615 + 4.73205i −0.307164 + 0.177341i
\(713\) 38.7846 + 67.1769i 1.45250 + 2.51580i
\(714\) 6.58846 0.246567
\(715\) 0 0
\(716\) 2.19615 0.0820741
\(717\) 3.29423 + 5.70577i 0.123025 + 0.213086i
\(718\) 13.9019 8.02628i 0.518815 0.299538i
\(719\) −15.8038 + 27.3731i −0.589384 + 1.02084i 0.404929 + 0.914348i \(0.367296\pi\)
−0.994313 + 0.106495i \(0.966037\pi\)
\(720\) 0 0
\(721\) −6.80385 3.92820i −0.253389 0.146294i
\(722\) −1.69615 + 2.93782i −0.0631243 + 0.109334i
\(723\) −11.1962 −0.416389
\(724\) 9.79423 16.9641i 0.364000 0.630466i
\(725\) 0 0
\(726\) 8.13397 4.69615i 0.301880 0.174291i
\(727\) 13.8038i 0.511956i −0.966683 0.255978i \(-0.917602\pi\)
0.966683 0.255978i \(-0.0823975\pi\)
\(728\) −3.80385 + 2.53590i −0.140980 + 0.0939866i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 10.9019 + 18.8827i 0.403222 + 0.698401i
\(732\) 13.1603 + 7.59808i 0.486417 + 0.280833i
\(733\) −20.3205 −0.750555 −0.375278 0.926912i \(-0.622453\pi\)
−0.375278 + 0.926912i \(0.622453\pi\)
\(734\) 11.9545 + 6.90192i 0.441248 + 0.254755i
\(735\) 0 0
\(736\) 8.19615i 0.302114i
\(737\) 7.98076 + 4.60770i 0.293975 + 0.169727i
\(738\) 5.59808 3.23205i 0.206068 0.118973i
\(739\) −4.39230 + 2.53590i −0.161574 + 0.0932845i −0.578607 0.815607i \(-0.696403\pi\)
0.417033 + 0.908891i \(0.363070\pi\)
\(740\) 0 0
\(741\) −15.2942 7.56218i −0.561848 0.277804i
\(742\) 3.80385i 0.139644i
\(743\) −8.19615 14.1962i −0.300688 0.520806i 0.675604 0.737264i \(-0.263883\pi\)
−0.976292 + 0.216458i \(0.930550\pi\)
\(744\) 4.73205 + 8.19615i 0.173485 + 0.300486i
\(745\) 0 0
\(746\) 27.9808i 1.02445i
\(747\) −2.83013 + 4.90192i −0.103549 + 0.179352i
\(748\) −3.29423 + 5.70577i −0.120449 + 0.208624i
\(749\) 2.78461i 0.101747i
\(750\) 0 0
\(751\) 13.4904 + 23.3660i 0.492271 + 0.852638i 0.999960 0.00890181i \(-0.00283357\pi\)
−0.507689 + 0.861540i \(0.669500\pi\)
\(752\) −2.36603 4.09808i −0.0862801 0.149441i
\(753\) 16.3923i 0.597369i
\(754\) 9.00000 6.00000i 0.327761 0.218507i
\(755\) 0 0
\(756\) −1.09808 + 0.633975i −0.0399366 + 0.0230574i
\(757\) 19.7321 11.3923i 0.717174 0.414060i −0.0965379 0.995329i \(-0.530777\pi\)
0.813712 + 0.581269i \(0.197444\pi\)
\(758\) −26.1962 15.1244i −0.951487 0.549341i
\(759\) 10.3923i 0.377217i
\(760\) 0 0
\(761\) 14.1962 + 8.19615i 0.514610 + 0.297110i 0.734727 0.678363i \(-0.237310\pi\)
−0.220117 + 0.975474i \(0.570644\pi\)
\(762\) 4.00000 0.144905
\(763\) 4.82309 + 2.78461i 0.174607 + 0.100810i
\(764\) 10.3923 + 18.0000i 0.375980 + 0.651217i
\(765\) 0 0
\(766\) −23.3205 −0.842604
\(767\) 27.7128 + 41.5692i 1.00065 + 1.50098i
\(768\) 1.00000i 0.0360844i
\(769\) 18.8038 10.8564i 0.678084 0.391492i −0.121049 0.992647i \(-0.538626\pi\)
0.799133 + 0.601155i \(0.205292\pi\)
\(770\) 0 0
\(771\) −11.5981 + 20.0885i −0.417695 + 0.723468i
\(772\) −23.1962 −0.834848
\(773\) −4.60770 + 7.98076i −0.165727 + 0.287048i −0.936913 0.349562i \(-0.886330\pi\)
0.771186 + 0.636610i \(0.219664\pi\)
\(774\) −3.63397 2.09808i −0.130621 0.0754138i
\(775\) 0 0
\(776\) 3.00000 5.19615i 0.107694 0.186531i
\(777\) −3.29423 + 1.90192i −0.118180 + 0.0682311i
\(778\) 3.69615 + 6.40192i 0.132513 + 0.229520i
\(779\) 30.5885 1.09595
\(780\) 0 0
\(781\) −2.78461 −0.0996412
\(782\) −21.2942 36.8827i −0.761480 1.31892i
\(783\) 2.59808 1.50000i 0.0928477 0.0536056i
\(784\) 2.69615 4.66987i 0.0962912 0.166781i
\(785\) 0 0
\(786\) 3.80385 + 2.19615i 0.135679 + 0.0783342i
\(787\) −10.7321 + 18.5885i −0.382556 + 0.662607i −0.991427 0.130663i \(-0.958290\pi\)
0.608871 + 0.793270i \(0.291623\pi\)
\(788\) −6.92820 −0.246807
\(789\) −4.09808 + 7.09808i −0.145895 + 0.252698i
\(790\) 0 0
\(791\) −0.882686 + 0.509619i −0.0313847 + 0.0181200i
\(792\) 1.26795i 0.0450546i
\(793\) −45.5885 + 30.3923i −1.61889 + 1.07926i
\(794\) 4.39230 0.155877
\(795\) 0 0
\(796\) 11.2942 + 19.5622i 0.400313 + 0.693363i
\(797\) −5.19615 3.00000i −0.184057 0.106265i 0.405140 0.914255i \(-0.367223\pi\)
−0.589197 + 0.807989i \(0.700556\pi\)
\(798\) −6.00000 −0.212398
\(799\) −21.2942 12.2942i −0.753336 0.434939i
\(800\) 0 0
\(801\) 9.46410i 0.334398i
\(802\) −18.1865 10.5000i −0.642189 0.370768i
\(803\) −13.3135 + 7.68653i −0.469822 + 0.271252i
\(804\) −6.29423 + 3.63397i −0.221980 + 0.128160i
\(805\) 0 0
\(806\) −34.0526 + 2.19615i −1.19945 + 0.0773562i
\(807\) 7.60770i 0.267804i
\(808\) −9.69615 16.7942i −0.341109 0.590819i
\(809\) −18.4019 31.8731i −0.646977 1.12060i −0.983841 0.179044i \(-0.942700\pi\)
0.336864 0.941553i \(-0.390634\pi\)
\(810\) 0 0
\(811\) 16.3923i 0.575612i −0.957689 0.287806i \(-0.907074\pi\)
0.957689 0.287806i \(-0.0929258\pi\)
\(812\) 1.90192 3.29423i 0.0667444 0.115605i
\(813\) 0 0
\(814\) 3.80385i 0.133325i
\(815\) 0 0
\(816\) −2.59808 4.50000i −0.0909509 0.157532i
\(817\) −9.92820 17.1962i −0.347344 0.601617i
\(818\) 20.6603i 0.722369i
\(819\) −0.294229 4.56218i −0.0102812 0.159415i
\(820\) 0 0
\(821\) 24.8038 14.3205i 0.865660 0.499789i −0.000243419 1.00000i \(-0.500077\pi\)
0.865904 + 0.500211i \(0.166744\pi\)
\(822\) 7.79423 4.50000i 0.271855 0.156956i
\(823\) −27.7128 16.0000i −0.966008 0.557725i −0.0679910 0.997686i \(-0.521659\pi\)
−0.898017 + 0.439961i \(0.854992\pi\)
\(824\) 6.19615i 0.215853i
\(825\) 0 0
\(826\) 15.2154 + 8.78461i 0.529411 + 0.305656i
\(827\) −44.1051 −1.53369 −0.766843 0.641835i \(-0.778173\pi\)
−0.766843 + 0.641835i \(0.778173\pi\)
\(828\) 7.09808 + 4.09808i 0.246675 + 0.142418i
\(829\) −19.9904 34.6244i −0.694295 1.20255i −0.970418 0.241431i \(-0.922383\pi\)
0.276123 0.961122i \(-0.410950\pi\)
\(830\) 0 0
\(831\) 4.80385 0.166644
\(832\) 3.23205 + 1.59808i 0.112051 + 0.0554033i
\(833\) 28.0192i 0.970809i
\(834\) 3.46410 2.00000i 0.119952 0.0692543i
\(835\) 0 0
\(836\) 3.00000 5.19615i 0.103757 0.179713i
\(837\) −9.46410 −0.327127
\(838\) 2.19615 3.80385i 0.0758648 0.131402i
\(839\) 10.3923 + 6.00000i 0.358782 + 0.207143i 0.668546 0.743670i \(-0.266917\pi\)
−0.309764 + 0.950813i \(0.600250\pi\)
\(840\) 0 0
\(841\) 10.0000 17.3205i 0.344828 0.597259i
\(842\) 5.59808 3.23205i 0.192922 0.111384i
\(843\) 8.76795 + 15.1865i 0.301984 + 0.523052i
\(844\) −24.3923 −0.839618
\(845\) 0 0
\(846\) 4.73205 0.162691
\(847\) 5.95448 + 10.3135i 0.204598 + 0.354375i
\(848\) 2.59808 1.50000i 0.0892183 0.0515102i
\(849\) −9.90192 + 17.1506i −0.339833 + 0.588608i
\(850\) 0 0
\(851\) 21.2942 + 12.2942i 0.729957 + 0.421441i
\(852\) 1.09808 1.90192i 0.0376195 0.0651588i
\(853\) 9.00000 0.308154 0.154077 0.988059i \(-0.450760\pi\)
0.154077 + 0.988059i \(0.450760\pi\)
\(854\) −9.63397 + 16.6865i −0.329668 + 0.571001i
\(855\) 0 0
\(856\) −1.90192 + 1.09808i −0.0650064 + 0.0375315i
\(857\) 18.3731i 0.627612i 0.949487 + 0.313806i \(0.101604\pi\)
−0.949487 + 0.313806i \(0.898396\pi\)
\(858\) 4.09808 + 2.02628i 0.139906 + 0.0691760i
\(859\) 20.5885 0.702469 0.351235 0.936288i \(-0.385762\pi\)
0.351235 + 0.936288i \(0.385762\pi\)
\(860\) 0 0
\(861\) 4.09808 + 7.09808i 0.139662 + 0.241902i
\(862\) 33.0788 + 19.0981i 1.12667 + 0.650483i
\(863\) −49.5167 −1.68557 −0.842783 0.538253i \(-0.819085\pi\)
−0.842783 + 0.538253i \(0.819085\pi\)
\(864\) 0.866025 + 0.500000i 0.0294628 + 0.0170103i
\(865\) 0 0
\(866\) 7.78461i 0.264532i
\(867\) −8.66025 5.00000i −0.294118 0.169809i
\(868\) −10.3923 + 6.00000i −0.352738 + 0.203653i
\(869\) 9.21539 5.32051i 0.312611 0.180486i
\(870\) 0 0
\(871\) −1.68653 26.1506i −0.0571460 0.886080i
\(872\) 4.39230i 0.148742i
\(873\) 3.00000 + 5.19615i 0.101535 + 0.175863i
\(874\) 19.3923 + 33.5885i 0.655954 + 1.13615i
\(875\) 0 0
\(876\) 12.1244i 0.409644i
\(877\) −11.3038 + 19.5788i −0.381704 + 0.661130i −0.991306 0.131577i \(-0.957996\pi\)
0.609602 + 0.792708i \(0.291329\pi\)
\(878\) −7.29423 + 12.6340i −0.246168 + 0.426376i
\(879\) 2.66025i 0.0897281i
\(880\) 0 0
\(881\) −6.99038 12.1077i −0.235512 0.407919i 0.723909 0.689895i \(-0.242343\pi\)
−0.959421 + 0.281976i \(0.909010\pi\)
\(882\) 2.69615 + 4.66987i 0.0907842 + 0.157243i
\(883\) 16.7846i 0.564847i −0.959290 0.282424i \(-0.908862\pi\)
0.959290 0.282424i \(-0.0911383\pi\)
\(884\) 18.6962 1.20577i 0.628820 0.0405545i
\(885\) 0 0
\(886\) −14.1962 + 8.19615i −0.476929 + 0.275355i
\(887\) −41.5692 + 24.0000i −1.39576 + 0.805841i −0.993945 0.109881i \(-0.964953\pi\)
−0.401813 + 0.915722i \(0.631620\pi\)
\(888\) 2.59808 + 1.50000i 0.0871857 + 0.0503367i
\(889\) 5.07180i 0.170103i
\(890\) 0 0
\(891\) 1.09808 + 0.633975i 0.0367869 + 0.0212389i
\(892\) 5.07180 0.169816
\(893\) 19.3923 + 11.1962i 0.648939 + 0.374665i
\(894\) −3.06218 5.30385i −0.102415 0.177387i
\(895\) 0 0
\(896\) 1.26795 0.0423592
\(897\) −24.5885 + 16.3923i −0.820985 + 0.547323i
\(898\) 26.5359i 0.885514i
\(899\) 24.5885 14.1962i 0.820071 0.473468i
\(900\) 0 0
\(901\) 7.79423 13.5000i 0.259663 0.449750i
\(902\) −8.19615 −0.272902
\(903\) 2.66025 4.60770i 0.0885277 0.153334i
\(904\) 0.696152 + 0.401924i 0.0231537 + 0.0133678i
\(905\) 0 0
\(906\) −5.36603 + 9.29423i −0.178274 + 0.308780i
\(907\) 18.3397 10.5885i 0.608961 0.351584i −0.163598 0.986527i \(-0.552310\pi\)
0.772559 + 0.634943i \(0.218977\pi\)
\(908\) 10.0981 + 17.4904i 0.335116 + 0.580439i
\(909\) 19.3923 0.643202
\(910\) 0 0
\(911\) −25.1769 −0.834148 −0.417074 0.908872i \(-0.636944\pi\)
−0.417074 + 0.908872i \(0.636944\pi\)
\(912\) 2.36603 + 4.09808i 0.0783469 + 0.135701i
\(913\) 6.21539 3.58846i 0.205699 0.118761i
\(914\) −15.9904 + 27.6962i −0.528915 + 0.916107i
\(915\) 0 0
\(916\) 6.80385 + 3.92820i 0.224805 + 0.129791i
\(917\) −2.78461 + 4.82309i −0.0919559 + 0.159272i
\(918\) 5.19615 0.171499
\(919\) 5.80385 10.0526i 0.191451 0.331603i −0.754280 0.656553i \(-0.772014\pi\)
0.945731 + 0.324949i \(0.105347\pi\)
\(920\) 0 0
\(921\) 6.29423 3.63397i 0.207402 0.119744i
\(922\) 31.9808i 1.05323i
\(923\) 4.39230 + 6.58846i 0.144574 + 0.216862i
\(924\) 1.60770 0.0528893
\(925\) 0 0
\(926\) −7.90192 13.6865i −0.259673 0.449767i
\(927\) −5.36603 3.09808i −0.176243 0.101754i
\(928\) −3.00000 −0.0984798
\(929\) −47.9711 27.6962i −1.57388 0.908681i −0.995686 0.0927833i \(-0.970424\pi\)
−0.578196 0.815898i \(-0.696243\pi\)
\(930\) 0 0
\(931\) 25.5167i 0.836275i
\(932\) −15.5885 9.00000i −0.510617 0.294805i
\(933\) −7.09808 + 4.09808i −0.232381 + 0.134165i
\(934\) −4.68653 + 2.70577i −0.153348 + 0.0885355i
\(935\) 0 0
\(936\) −3.00000 + 2.00000i −0.0980581 + 0.0653720i
\(937\) 15.3923i 0.502845i 0.967877 + 0.251422i \(0.0808983\pi\)
−0.967877 + 0.251422i \(0.919102\pi\)
\(938\) −4.60770 7.98076i −0.150447 0.260581i
\(939\) 1.80385 + 3.12436i 0.0588663 + 0.101959i
\(940\) 0 0
\(941\) 38.7846i 1.26434i −0.774829 0.632171i \(-0.782164\pi\)
0.774829 0.632171i \(-0.217836\pi\)
\(942\) −3.59808 + 6.23205i −0.117232 + 0.203051i
\(943\) 26.4904 45.8827i 0.862645 1.49415i
\(944\) 13.8564i 0.450988i
\(945\) 0 0
\(946\) 2.66025 + 4.60770i 0.0864923 + 0.149809i
\(947\) −14.5359 25.1769i −0.472353 0.818140i 0.527146 0.849775i \(-0.323262\pi\)
−0.999499 + 0.0316348i \(0.989929\pi\)
\(948\) 8.39230i 0.272569i
\(949\) 39.1865 + 19.3756i 1.27205 + 0.628960i
\(950\) 0 0
\(951\) 15.6962 9.06218i 0.508983 0.293861i
\(952\) 5.70577 3.29423i 0.184925 0.106767i
\(953\) −20.7846 12.0000i −0.673280 0.388718i 0.124039 0.992277i \(-0.460415\pi\)
−0.797318 + 0.603559i \(0.793749\pi\)
\(954\) 3.00000i 0.0971286i
\(955\) 0 0
\(956\) 5.70577 + 3.29423i 0.184538 + 0.106543i
\(957\) −3.80385 −0.122961
\(958\) −0.588457 0.339746i −0.0190122 0.0109767i
\(959\) 5.70577 + 9.88269i 0.184249 + 0.319129i
\(960\) 0 0
\(961\) −58.5692 −1.88933
\(962\) −9.00000 + 6.00000i −0.290172 + 0.193448i
\(963\) 2.19615i 0.0707700i
\(964\) −9.69615 + 5.59808i −0.312292 + 0.180302i
\(965\) 0 0
\(966\) −5.19615 + 9.00000i −0.167183 + 0.289570i
\(967\) −39.1244 −1.25815 −0.629077 0.777343i \(-0.716567\pi\)
−0.629077 + 0.777343i \(0.716567\pi\)
\(968\) 4.69615 8.13397i 0.150940 0.261436i
\(969\) 21.2942 + 12.2942i 0.684069 + 0.394948i
\(970\) 0 0
\(971\) −24.5885 + 42.5885i −0.789081 + 1.36673i 0.137449 + 0.990509i \(0.456110\pi\)
−0.926530 + 0.376220i \(0.877224\pi\)
\(972\) −0.866025 + 0.500000i −0.0277778 + 0.0160375i
\(973\) 2.53590 + 4.39230i 0.0812972 + 0.140811i
\(974\) 15.1244 0.484616
\(975\) 0 0
\(976\) 15.1962 0.486417
\(977\) −5.42820 9.40192i −0.173664 0.300794i 0.766034 0.642800i \(-0.222227\pi\)
−0.939698 + 0.342005i \(0.888894\pi\)
\(978\) 2.19615 1.26795i 0.0702252 0.0405445i
\(979\) −6.00000 + 10.3923i −0.191761 + 0.332140i
\(980\) 0 0
\(981\) 3.80385 + 2.19615i 0.121448 + 0.0701178i
\(982\) 15.2942 26.4904i 0.488058 0.845342i
\(983\) 20.7846 0.662926 0.331463 0.943468i \(-0.392458\pi\)
0.331463 + 0.943468i \(0.392458\pi\)
\(984\) 3.23205 5.59808i 0.103034 0.178460i
\(985\) 0 0
\(986\) −13.5000 + 7.79423i −0.429928 + 0.248219i
\(987\) 6.00000i 0.190982i
\(988\) −17.0263 + 1.09808i −0.541678 + 0.0349345i
\(989\) −34.3923 −1.09361
\(990\) 0 0
\(991\) 21.6865 + 37.5622i 0.688895 + 1.19320i 0.972196 + 0.234171i \(0.0752374\pi\)
−0.283300 + 0.959031i \(0.591429\pi\)
\(992\) 8.19615 + 4.73205i 0.260228 + 0.150243i
\(993\) 12.0000 0.380808
\(994\) 2.41154 + 1.39230i 0.0764895 + 0.0441612i
\(995\) 0 0
\(996\) 5.66025i 0.179352i
\(997\) 2.42820 + 1.40192i 0.0769020 + 0.0443994i 0.537958 0.842972i \(-0.319196\pi\)
−0.461056 + 0.887371i \(0.652529\pi\)
\(998\) 0 0
\(999\) −2.59808 + 1.50000i −0.0821995 + 0.0474579i
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 1950.2.y.h.49.1 4
5.2 odd 4 78.2.i.b.49.1 yes 4
5.3 odd 4 1950.2.bc.c.751.2 4
5.4 even 2 1950.2.y.a.49.2 4
13.4 even 6 1950.2.y.a.199.2 4
15.2 even 4 234.2.l.a.127.2 4
20.7 even 4 624.2.bv.d.49.1 4
60.47 odd 4 1872.2.by.k.1297.1 4
65.2 even 12 1014.2.a.h.1.2 2
65.4 even 6 inner 1950.2.y.h.199.1 4
65.7 even 12 1014.2.e.h.529.1 4
65.12 odd 4 1014.2.i.f.361.2 4
65.17 odd 12 78.2.i.b.43.1 4
65.22 odd 12 1014.2.i.f.823.2 4
65.32 even 12 1014.2.e.j.529.2 4
65.37 even 12 1014.2.a.j.1.1 2
65.42 odd 12 1014.2.b.d.337.2 4
65.43 odd 12 1950.2.bc.c.901.2 4
65.47 even 4 1014.2.e.h.991.1 4
65.57 even 4 1014.2.e.j.991.2 4
65.62 odd 12 1014.2.b.d.337.3 4
195.2 odd 12 3042.2.a.v.1.1 2
195.17 even 12 234.2.l.a.199.2 4
195.62 even 12 3042.2.b.l.1351.2 4
195.107 even 12 3042.2.b.l.1351.3 4
195.167 odd 12 3042.2.a.s.1.2 2
260.67 odd 12 8112.2.a.bq.1.2 2
260.147 even 12 624.2.bv.d.433.1 4
260.167 odd 12 8112.2.a.bx.1.1 2
780.407 odd 12 1872.2.by.k.433.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.2.i.b.43.1 4 65.17 odd 12
78.2.i.b.49.1 yes 4 5.2 odd 4
234.2.l.a.127.2 4 15.2 even 4
234.2.l.a.199.2 4 195.17 even 12
624.2.bv.d.49.1 4 20.7 even 4
624.2.bv.d.433.1 4 260.147 even 12
1014.2.a.h.1.2 2 65.2 even 12
1014.2.a.j.1.1 2 65.37 even 12
1014.2.b.d.337.2 4 65.42 odd 12
1014.2.b.d.337.3 4 65.62 odd 12
1014.2.e.h.529.1 4 65.7 even 12
1014.2.e.h.991.1 4 65.47 even 4
1014.2.e.j.529.2 4 65.32 even 12
1014.2.e.j.991.2 4 65.57 even 4
1014.2.i.f.361.2 4 65.12 odd 4
1014.2.i.f.823.2 4 65.22 odd 12
1872.2.by.k.433.1 4 780.407 odd 12
1872.2.by.k.1297.1 4 60.47 odd 4
1950.2.y.a.49.2 4 5.4 even 2
1950.2.y.a.199.2 4 13.4 even 6
1950.2.y.h.49.1 4 1.1 even 1 trivial
1950.2.y.h.199.1 4 65.4 even 6 inner
1950.2.bc.c.751.2 4 5.3 odd 4
1950.2.bc.c.901.2 4 65.43 odd 12
3042.2.a.s.1.2 2 195.167 odd 12
3042.2.a.v.1.1 2 195.2 odd 12
3042.2.b.l.1351.2 4 195.62 even 12
3042.2.b.l.1351.3 4 195.107 even 12
8112.2.a.bq.1.2 2 260.67 odd 12
8112.2.a.bx.1.1 2 260.167 odd 12