Properties

Label 750.2.g.a.151.1
Level $750$
Weight $2$
Character 750.151
Analytic conductor $5.989$
Analytic rank $0$
Dimension $4$
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] = [750,2,Mod(151,750)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(750, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("750.151");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.g (of order \(5\), 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: \(5.98878015160\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 151.1
Root \(-0.309017 + 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 750.151
Dual form 750.2.g.a.601.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.809017 - 0.587785i) q^{6} -2.00000 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.809017 - 0.587785i) q^{6} -2.00000 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-1.61803 - 4.97980i) q^{11} +(0.309017 - 0.951057i) q^{12} +(1.50000 - 4.61653i) q^{13} +(-0.618034 - 1.90211i) q^{14} +(0.309017 - 0.951057i) q^{16} +(6.35410 + 4.61653i) q^{17} +1.00000 q^{18} +(2.23607 + 1.62460i) q^{19} +(1.61803 - 1.17557i) q^{21} +(4.23607 - 3.07768i) q^{22} +(-1.85410 - 5.70634i) q^{23} +1.00000 q^{24} +4.85410 q^{26} +(0.309017 + 0.951057i) q^{27} +(1.61803 - 1.17557i) q^{28} +(1.11803 - 0.812299i) q^{29} +(-3.00000 - 2.17963i) q^{31} +1.00000 q^{32} +(4.23607 + 3.07768i) q^{33} +(-2.42705 + 7.46969i) q^{34} +(0.309017 + 0.951057i) q^{36} +(0.663119 - 2.04087i) q^{37} +(-0.854102 + 2.62866i) q^{38} +(1.50000 + 4.61653i) q^{39} +(-1.88197 + 5.79210i) q^{41} +(1.61803 + 1.17557i) q^{42} +1.23607 q^{43} +(4.23607 + 3.07768i) q^{44} +(4.85410 - 3.52671i) q^{46} +(3.85410 - 2.80017i) q^{47} +(0.309017 + 0.951057i) q^{48} -3.00000 q^{49} -7.85410 q^{51} +(1.50000 + 4.61653i) q^{52} +(6.92705 - 5.03280i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(1.61803 + 1.17557i) q^{56} -2.76393 q^{57} +(1.11803 + 0.812299i) q^{58} +(2.76393 - 8.50651i) q^{59} +(-2.73607 - 8.42075i) q^{61} +(1.14590 - 3.52671i) q^{62} +(-0.618034 + 1.90211i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.61803 + 4.97980i) q^{66} +(-7.85410 - 5.70634i) q^{67} -7.85410 q^{68} +(4.85410 + 3.52671i) q^{69} +(11.4721 - 8.33499i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(0.972136 + 2.99193i) q^{73} +2.14590 q^{74} -2.76393 q^{76} +(3.23607 + 9.95959i) q^{77} +(-3.92705 + 2.85317i) q^{78} +(-0.809017 - 0.587785i) q^{81} -6.09017 q^{82} +(4.85410 + 3.52671i) q^{83} +(-0.618034 + 1.90211i) q^{84} +(0.381966 + 1.17557i) q^{86} +(-0.427051 + 1.31433i) q^{87} +(-1.61803 + 4.97980i) q^{88} +(0.427051 + 1.31433i) q^{89} +(-3.00000 + 9.23305i) q^{91} +(4.85410 + 3.52671i) q^{92} +3.70820 q^{93} +(3.85410 + 2.80017i) q^{94} +(-0.809017 + 0.587785i) q^{96} +(-11.2082 + 8.14324i) q^{97} +(-0.927051 - 2.85317i) q^{98} -5.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} - q^{3} - q^{4} - q^{6} - 8 q^{7} - q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} - q^{3} - q^{4} - q^{6} - 8 q^{7} - q^{8} - q^{9} - 2 q^{11} - q^{12} + 6 q^{13} + 2 q^{14} - q^{16} + 12 q^{17} + 4 q^{18} + 2 q^{21} + 8 q^{22} + 6 q^{23} + 4 q^{24} + 6 q^{26} - q^{27} + 2 q^{28} - 12 q^{31} + 4 q^{32} + 8 q^{33} - 3 q^{34} - q^{36} - 13 q^{37} + 10 q^{38} + 6 q^{39} - 12 q^{41} + 2 q^{42} - 4 q^{43} + 8 q^{44} + 6 q^{46} + 2 q^{47} - q^{48} - 12 q^{49} - 18 q^{51} + 6 q^{52} + 21 q^{53} - q^{54} + 2 q^{56} - 20 q^{57} + 20 q^{59} - 2 q^{61} + 18 q^{62} + 2 q^{63} - q^{64} - 2 q^{66} - 18 q^{67} - 18 q^{68} + 6 q^{69} + 28 q^{71} - q^{72} - 14 q^{73} + 22 q^{74} - 20 q^{76} + 4 q^{77} - 9 q^{78} - q^{81} - 2 q^{82} + 6 q^{83} + 2 q^{84} + 6 q^{86} + 5 q^{87} - 2 q^{88} - 5 q^{89} - 12 q^{91} + 6 q^{92} - 12 q^{93} + 2 q^{94} - q^{96} - 18 q^{97} + 3 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.309017 + 0.951057i 0.218508 + 0.672499i
\(3\) −0.809017 + 0.587785i −0.467086 + 0.339358i
\(4\) −0.809017 + 0.587785i −0.404508 + 0.293893i
\(5\) 0 0
\(6\) −0.809017 0.587785i −0.330280 0.239962i
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) −0.809017 0.587785i −0.286031 0.207813i
\(9\) 0.309017 0.951057i 0.103006 0.317019i
\(10\) 0 0
\(11\) −1.61803 4.97980i −0.487856 1.50147i −0.827802 0.561020i \(-0.810409\pi\)
0.339946 0.940445i \(-0.389591\pi\)
\(12\) 0.309017 0.951057i 0.0892055 0.274546i
\(13\) 1.50000 4.61653i 0.416025 1.28039i −0.495306 0.868719i \(-0.664944\pi\)
0.911331 0.411675i \(-0.135056\pi\)
\(14\) −0.618034 1.90211i −0.165177 0.508361i
\(15\) 0 0
\(16\) 0.309017 0.951057i 0.0772542 0.237764i
\(17\) 6.35410 + 4.61653i 1.54110 + 1.11967i 0.949644 + 0.313332i \(0.101445\pi\)
0.591452 + 0.806340i \(0.298555\pi\)
\(18\) 1.00000 0.235702
\(19\) 2.23607 + 1.62460i 0.512989 + 0.372708i 0.813956 0.580926i \(-0.197309\pi\)
−0.300967 + 0.953635i \(0.597309\pi\)
\(20\) 0 0
\(21\) 1.61803 1.17557i 0.353084 0.256531i
\(22\) 4.23607 3.07768i 0.903133 0.656164i
\(23\) −1.85410 5.70634i −0.386607 1.18985i −0.935308 0.353835i \(-0.884877\pi\)
0.548701 0.836019i \(-0.315123\pi\)
\(24\) 1.00000 0.204124
\(25\) 0 0
\(26\) 4.85410 0.951968
\(27\) 0.309017 + 0.951057i 0.0594703 + 0.183031i
\(28\) 1.61803 1.17557i 0.305780 0.222162i
\(29\) 1.11803 0.812299i 0.207614 0.150840i −0.479120 0.877750i \(-0.659044\pi\)
0.686733 + 0.726909i \(0.259044\pi\)
\(30\) 0 0
\(31\) −3.00000 2.17963i −0.538816 0.391473i 0.284829 0.958578i \(-0.408063\pi\)
−0.823645 + 0.567106i \(0.808063\pi\)
\(32\) 1.00000 0.176777
\(33\) 4.23607 + 3.07768i 0.737405 + 0.535756i
\(34\) −2.42705 + 7.46969i −0.416236 + 1.28104i
\(35\) 0 0
\(36\) 0.309017 + 0.951057i 0.0515028 + 0.158509i
\(37\) 0.663119 2.04087i 0.109016 0.335517i −0.881636 0.471930i \(-0.843557\pi\)
0.990652 + 0.136413i \(0.0435575\pi\)
\(38\) −0.854102 + 2.62866i −0.138554 + 0.426424i
\(39\) 1.50000 + 4.61653i 0.240192 + 0.739236i
\(40\) 0 0
\(41\) −1.88197 + 5.79210i −0.293914 + 0.904573i 0.689670 + 0.724123i \(0.257755\pi\)
−0.983584 + 0.180450i \(0.942245\pi\)
\(42\) 1.61803 + 1.17557i 0.249668 + 0.181394i
\(43\) 1.23607 0.188499 0.0942493 0.995549i \(-0.469955\pi\)
0.0942493 + 0.995549i \(0.469955\pi\)
\(44\) 4.23607 + 3.07768i 0.638611 + 0.463978i
\(45\) 0 0
\(46\) 4.85410 3.52671i 0.715698 0.519985i
\(47\) 3.85410 2.80017i 0.562179 0.408447i −0.270077 0.962839i \(-0.587049\pi\)
0.832256 + 0.554392i \(0.187049\pi\)
\(48\) 0.309017 + 0.951057i 0.0446028 + 0.137273i
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) −7.85410 −1.09979
\(52\) 1.50000 + 4.61653i 0.208013 + 0.640197i
\(53\) 6.92705 5.03280i 0.951504 0.691308i 0.000341607 1.00000i \(-0.499891\pi\)
0.951162 + 0.308692i \(0.0998913\pi\)
\(54\) −0.809017 + 0.587785i −0.110093 + 0.0799874i
\(55\) 0 0
\(56\) 1.61803 + 1.17557i 0.216219 + 0.157092i
\(57\) −2.76393 −0.366092
\(58\) 1.11803 + 0.812299i 0.146805 + 0.106660i
\(59\) 2.76393 8.50651i 0.359833 1.10745i −0.593320 0.804966i \(-0.702183\pi\)
0.953154 0.302487i \(-0.0978167\pi\)
\(60\) 0 0
\(61\) −2.73607 8.42075i −0.350318 1.07817i −0.958675 0.284504i \(-0.908171\pi\)
0.608357 0.793663i \(-0.291829\pi\)
\(62\) 1.14590 3.52671i 0.145529 0.447893i
\(63\) −0.618034 + 1.90211i −0.0778650 + 0.239644i
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) 0 0
\(66\) −1.61803 + 4.97980i −0.199166 + 0.612971i
\(67\) −7.85410 5.70634i −0.959531 0.697140i −0.00648944 0.999979i \(-0.502066\pi\)
−0.953042 + 0.302839i \(0.902066\pi\)
\(68\) −7.85410 −0.952450
\(69\) 4.85410 + 3.52671i 0.584365 + 0.424566i
\(70\) 0 0
\(71\) 11.4721 8.33499i 1.36149 0.989182i 0.363144 0.931733i \(-0.381703\pi\)
0.998348 0.0574487i \(-0.0182966\pi\)
\(72\) −0.809017 + 0.587785i −0.0953436 + 0.0692712i
\(73\) 0.972136 + 2.99193i 0.113780 + 0.350179i 0.991691 0.128646i \(-0.0410631\pi\)
−0.877911 + 0.478824i \(0.841063\pi\)
\(74\) 2.14590 0.249456
\(75\) 0 0
\(76\) −2.76393 −0.317045
\(77\) 3.23607 + 9.95959i 0.368784 + 1.13500i
\(78\) −3.92705 + 2.85317i −0.444651 + 0.323058i
\(79\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) −6.09017 −0.672547
\(83\) 4.85410 + 3.52671i 0.532807 + 0.387107i 0.821407 0.570343i \(-0.193190\pi\)
−0.288600 + 0.957450i \(0.593190\pi\)
\(84\) −0.618034 + 1.90211i −0.0674330 + 0.207538i
\(85\) 0 0
\(86\) 0.381966 + 1.17557i 0.0411885 + 0.126765i
\(87\) −0.427051 + 1.31433i −0.0457847 + 0.140911i
\(88\) −1.61803 + 4.97980i −0.172483 + 0.530848i
\(89\) 0.427051 + 1.31433i 0.0452673 + 0.139318i 0.971136 0.238528i \(-0.0766648\pi\)
−0.925868 + 0.377846i \(0.876665\pi\)
\(90\) 0 0
\(91\) −3.00000 + 9.23305i −0.314485 + 0.967887i
\(92\) 4.85410 + 3.52671i 0.506075 + 0.367685i
\(93\) 3.70820 0.384523
\(94\) 3.85410 + 2.80017i 0.397520 + 0.288815i
\(95\) 0 0
\(96\) −0.809017 + 0.587785i −0.0825700 + 0.0599906i
\(97\) −11.2082 + 8.14324i −1.13802 + 0.826820i −0.986842 0.161686i \(-0.948307\pi\)
−0.151178 + 0.988506i \(0.548307\pi\)
\(98\) −0.927051 2.85317i −0.0936463 0.288214i
\(99\) −5.23607 −0.526245
\(100\) 0 0
\(101\) 1.67376 0.166546 0.0832728 0.996527i \(-0.473463\pi\)
0.0832728 + 0.996527i \(0.473463\pi\)
\(102\) −2.42705 7.46969i −0.240314 0.739610i
\(103\) −1.85410 + 1.34708i −0.182690 + 0.132732i −0.675372 0.737478i \(-0.736017\pi\)
0.492682 + 0.870210i \(0.336017\pi\)
\(104\) −3.92705 + 2.85317i −0.385079 + 0.279776i
\(105\) 0 0
\(106\) 6.92705 + 5.03280i 0.672815 + 0.488828i
\(107\) −10.9443 −1.05802 −0.529011 0.848615i \(-0.677437\pi\)
−0.529011 + 0.848615i \(0.677437\pi\)
\(108\) −0.809017 0.587785i −0.0778477 0.0565597i
\(109\) 0.791796 2.43690i 0.0758403 0.233412i −0.905949 0.423388i \(-0.860841\pi\)
0.981789 + 0.189975i \(0.0608408\pi\)
\(110\) 0 0
\(111\) 0.663119 + 2.04087i 0.0629405 + 0.193711i
\(112\) −0.618034 + 1.90211i −0.0583987 + 0.179733i
\(113\) 3.57295 10.9964i 0.336115 1.03445i −0.630056 0.776550i \(-0.716968\pi\)
0.966170 0.257905i \(-0.0830321\pi\)
\(114\) −0.854102 2.62866i −0.0799940 0.246196i
\(115\) 0 0
\(116\) −0.427051 + 1.31433i −0.0396507 + 0.122032i
\(117\) −3.92705 2.85317i −0.363056 0.263776i
\(118\) 8.94427 0.823387
\(119\) −12.7082 9.23305i −1.16496 0.846392i
\(120\) 0 0
\(121\) −13.2812 + 9.64932i −1.20738 + 0.877211i
\(122\) 7.16312 5.20431i 0.648518 0.471176i
\(123\) −1.88197 5.79210i −0.169691 0.522256i
\(124\) 3.70820 0.333007
\(125\) 0 0
\(126\) −2.00000 −0.178174
\(127\) −0.0901699 0.277515i −0.00800129 0.0246254i 0.946976 0.321304i \(-0.104121\pi\)
−0.954977 + 0.296678i \(0.904121\pi\)
\(128\) −0.809017 + 0.587785i −0.0715077 + 0.0519534i
\(129\) −1.00000 + 0.726543i −0.0880451 + 0.0639685i
\(130\) 0 0
\(131\) 0.618034 + 0.449028i 0.0539979 + 0.0392318i 0.614457 0.788950i \(-0.289375\pi\)
−0.560459 + 0.828182i \(0.689375\pi\)
\(132\) −5.23607 −0.455741
\(133\) −4.47214 3.24920i −0.387783 0.281741i
\(134\) 3.00000 9.23305i 0.259161 0.797614i
\(135\) 0 0
\(136\) −2.42705 7.46969i −0.208118 0.640521i
\(137\) 4.64590 14.2986i 0.396926 1.22161i −0.530526 0.847669i \(-0.678005\pi\)
0.927452 0.373943i \(-0.121995\pi\)
\(138\) −1.85410 + 5.70634i −0.157832 + 0.485756i
\(139\) −4.14590 12.7598i −0.351650 1.08227i −0.957926 0.287014i \(-0.907337\pi\)
0.606276 0.795254i \(-0.292663\pi\)
\(140\) 0 0
\(141\) −1.47214 + 4.53077i −0.123976 + 0.381560i
\(142\) 11.4721 + 8.33499i 0.962720 + 0.699457i
\(143\) −25.4164 −2.12543
\(144\) −0.809017 0.587785i −0.0674181 0.0489821i
\(145\) 0 0
\(146\) −2.54508 + 1.84911i −0.210633 + 0.153034i
\(147\) 2.42705 1.76336i 0.200180 0.145439i
\(148\) 0.663119 + 2.04087i 0.0545080 + 0.167759i
\(149\) 7.03444 0.576284 0.288142 0.957588i \(-0.406962\pi\)
0.288142 + 0.957588i \(0.406962\pi\)
\(150\) 0 0
\(151\) −6.94427 −0.565117 −0.282558 0.959250i \(-0.591183\pi\)
−0.282558 + 0.959250i \(0.591183\pi\)
\(152\) −0.854102 2.62866i −0.0692768 0.213212i
\(153\) 6.35410 4.61653i 0.513699 0.373224i
\(154\) −8.47214 + 6.15537i −0.682704 + 0.496014i
\(155\) 0 0
\(156\) −3.92705 2.85317i −0.314416 0.228436i
\(157\) −17.8541 −1.42491 −0.712456 0.701717i \(-0.752417\pi\)
−0.712456 + 0.701717i \(0.752417\pi\)
\(158\) 0 0
\(159\) −2.64590 + 8.14324i −0.209833 + 0.645801i
\(160\) 0 0
\(161\) 3.70820 + 11.4127i 0.292247 + 0.899445i
\(162\) 0.309017 0.951057i 0.0242787 0.0747221i
\(163\) −6.32624 + 19.4702i −0.495509 + 1.52502i 0.320652 + 0.947197i \(0.396098\pi\)
−0.816162 + 0.577824i \(0.803902\pi\)
\(164\) −1.88197 5.79210i −0.146957 0.452287i
\(165\) 0 0
\(166\) −1.85410 + 5.70634i −0.143906 + 0.442898i
\(167\) 5.23607 + 3.80423i 0.405179 + 0.294380i 0.771647 0.636051i \(-0.219433\pi\)
−0.366468 + 0.930431i \(0.619433\pi\)
\(168\) −2.00000 −0.154303
\(169\) −8.54508 6.20837i −0.657314 0.477567i
\(170\) 0 0
\(171\) 2.23607 1.62460i 0.170996 0.124236i
\(172\) −1.00000 + 0.726543i −0.0762493 + 0.0553983i
\(173\) 3.37132 + 10.3759i 0.256317 + 0.788862i 0.993567 + 0.113243i \(0.0361238\pi\)
−0.737250 + 0.675620i \(0.763876\pi\)
\(174\) −1.38197 −0.104767
\(175\) 0 0
\(176\) −5.23607 −0.394683
\(177\) 2.76393 + 8.50651i 0.207750 + 0.639388i
\(178\) −1.11803 + 0.812299i −0.0838002 + 0.0608844i
\(179\) 3.09017 2.24514i 0.230970 0.167810i −0.466281 0.884637i \(-0.654406\pi\)
0.697251 + 0.716827i \(0.254406\pi\)
\(180\) 0 0
\(181\) 16.2082 + 11.7759i 1.20475 + 0.875299i 0.994743 0.102401i \(-0.0326526\pi\)
0.210003 + 0.977701i \(0.432653\pi\)
\(182\) −9.70820 −0.719620
\(183\) 7.16312 + 5.20431i 0.529513 + 0.384714i
\(184\) −1.85410 + 5.70634i −0.136686 + 0.420677i
\(185\) 0 0
\(186\) 1.14590 + 3.52671i 0.0840213 + 0.258591i
\(187\) 12.7082 39.1118i 0.929316 2.86014i
\(188\) −1.47214 + 4.53077i −0.107367 + 0.330440i
\(189\) −0.618034 1.90211i −0.0449554 0.138358i
\(190\) 0 0
\(191\) −0.236068 + 0.726543i −0.0170813 + 0.0525708i −0.959234 0.282614i \(-0.908799\pi\)
0.942153 + 0.335184i \(0.108799\pi\)
\(192\) −0.809017 0.587785i −0.0583858 0.0424197i
\(193\) −2.38197 −0.171458 −0.0857288 0.996319i \(-0.527322\pi\)
−0.0857288 + 0.996319i \(0.527322\pi\)
\(194\) −11.2082 8.14324i −0.804702 0.584650i
\(195\) 0 0
\(196\) 2.42705 1.76336i 0.173361 0.125954i
\(197\) −10.7812 + 7.83297i −0.768125 + 0.558076i −0.901392 0.433005i \(-0.857453\pi\)
0.133266 + 0.991080i \(0.457453\pi\)
\(198\) −1.61803 4.97980i −0.114989 0.353899i
\(199\) −6.18034 −0.438113 −0.219056 0.975712i \(-0.570298\pi\)
−0.219056 + 0.975712i \(0.570298\pi\)
\(200\) 0 0
\(201\) 9.70820 0.684764
\(202\) 0.517221 + 1.59184i 0.0363915 + 0.112002i
\(203\) −2.23607 + 1.62460i −0.156941 + 0.114024i
\(204\) 6.35410 4.61653i 0.444876 0.323221i
\(205\) 0 0
\(206\) −1.85410 1.34708i −0.129181 0.0938558i
\(207\) −6.00000 −0.417029
\(208\) −3.92705 2.85317i −0.272292 0.197832i
\(209\) 4.47214 13.7638i 0.309344 0.952063i
\(210\) 0 0
\(211\) −2.47214 7.60845i −0.170189 0.523787i 0.829192 0.558963i \(-0.188801\pi\)
−0.999381 + 0.0351760i \(0.988801\pi\)
\(212\) −2.64590 + 8.14324i −0.181721 + 0.559280i
\(213\) −4.38197 + 13.4863i −0.300247 + 0.924066i
\(214\) −3.38197 10.4086i −0.231186 0.711519i
\(215\) 0 0
\(216\) 0.309017 0.951057i 0.0210259 0.0647112i
\(217\) 6.00000 + 4.35926i 0.407307 + 0.295926i
\(218\) 2.56231 0.173541
\(219\) −2.54508 1.84911i −0.171981 0.124951i
\(220\) 0 0
\(221\) 30.8435 22.4091i 2.07476 1.50740i
\(222\) −1.73607 + 1.26133i −0.116517 + 0.0846547i
\(223\) 0.708204 + 2.17963i 0.0474248 + 0.145959i 0.971965 0.235127i \(-0.0755505\pi\)
−0.924540 + 0.381085i \(0.875550\pi\)
\(224\) −2.00000 −0.133631
\(225\) 0 0
\(226\) 11.5623 0.769113
\(227\) 5.23607 + 16.1150i 0.347530 + 1.06959i 0.960215 + 0.279261i \(0.0900893\pi\)
−0.612685 + 0.790327i \(0.709911\pi\)
\(228\) 2.23607 1.62460i 0.148087 0.107592i
\(229\) 19.6353 14.2658i 1.29753 0.942714i 0.297606 0.954689i \(-0.403812\pi\)
0.999928 + 0.0119751i \(0.00381187\pi\)
\(230\) 0 0
\(231\) −8.47214 6.15537i −0.557426 0.404993i
\(232\) −1.38197 −0.0907305
\(233\) −17.8713 12.9843i −1.17079 0.850628i −0.179686 0.983724i \(-0.557508\pi\)
−0.991103 + 0.133096i \(0.957508\pi\)
\(234\) 1.50000 4.61653i 0.0980581 0.301792i
\(235\) 0 0
\(236\) 2.76393 + 8.50651i 0.179917 + 0.553727i
\(237\) 0 0
\(238\) 4.85410 14.9394i 0.314645 0.968377i
\(239\) 8.29180 + 25.5195i 0.536352 + 1.65072i 0.740710 + 0.671825i \(0.234489\pi\)
−0.204358 + 0.978896i \(0.565511\pi\)
\(240\) 0 0
\(241\) −4.28115 + 13.1760i −0.275773 + 0.848743i 0.713240 + 0.700919i \(0.247227\pi\)
−0.989014 + 0.147824i \(0.952773\pi\)
\(242\) −13.2812 9.64932i −0.853745 0.620282i
\(243\) 1.00000 0.0641500
\(244\) 7.16312 + 5.20431i 0.458572 + 0.333172i
\(245\) 0 0
\(246\) 4.92705 3.57971i 0.314137 0.228234i
\(247\) 10.8541 7.88597i 0.690630 0.501772i
\(248\) 1.14590 + 3.52671i 0.0727646 + 0.223946i
\(249\) −6.00000 −0.380235
\(250\) 0 0
\(251\) −12.4721 −0.787234 −0.393617 0.919274i \(-0.628776\pi\)
−0.393617 + 0.919274i \(0.628776\pi\)
\(252\) −0.618034 1.90211i −0.0389325 0.119822i
\(253\) −25.4164 + 18.4661i −1.59792 + 1.16095i
\(254\) 0.236068 0.171513i 0.0148122 0.0107617i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) 11.6180 0.724713 0.362357 0.932040i \(-0.381972\pi\)
0.362357 + 0.932040i \(0.381972\pi\)
\(258\) −1.00000 0.726543i −0.0622573 0.0452326i
\(259\) −1.32624 + 4.08174i −0.0824084 + 0.253627i
\(260\) 0 0
\(261\) −0.427051 1.31433i −0.0264338 0.0813548i
\(262\) −0.236068 + 0.726543i −0.0145843 + 0.0448859i
\(263\) −0.145898 + 0.449028i −0.00899646 + 0.0276883i −0.955454 0.295140i \(-0.904634\pi\)
0.946458 + 0.322828i \(0.104634\pi\)
\(264\) −1.61803 4.97980i −0.0995831 0.306485i
\(265\) 0 0
\(266\) 1.70820 5.25731i 0.104737 0.322346i
\(267\) −1.11803 0.812299i −0.0684226 0.0497119i
\(268\) 9.70820 0.593023
\(269\) 1.54508 + 1.12257i 0.0942055 + 0.0684443i 0.633891 0.773422i \(-0.281457\pi\)
−0.539685 + 0.841867i \(0.681457\pi\)
\(270\) 0 0
\(271\) −22.7984 + 16.5640i −1.38490 + 1.00619i −0.388500 + 0.921449i \(0.627007\pi\)
−0.996403 + 0.0847417i \(0.972993\pi\)
\(272\) 6.35410 4.61653i 0.385274 0.279918i
\(273\) −3.00000 9.23305i −0.181568 0.558810i
\(274\) 15.0344 0.908264
\(275\) 0 0
\(276\) −6.00000 −0.361158
\(277\) 6.84346 + 21.0620i 0.411184 + 1.26549i 0.915620 + 0.402044i \(0.131700\pi\)
−0.504437 + 0.863449i \(0.668300\pi\)
\(278\) 10.8541 7.88597i 0.650986 0.472969i
\(279\) −3.00000 + 2.17963i −0.179605 + 0.130491i
\(280\) 0 0
\(281\) 4.92705 + 3.57971i 0.293923 + 0.213548i 0.724968 0.688783i \(-0.241855\pi\)
−0.431044 + 0.902331i \(0.641855\pi\)
\(282\) −4.76393 −0.283688
\(283\) 2.61803 + 1.90211i 0.155626 + 0.113069i 0.662873 0.748732i \(-0.269337\pi\)
−0.507247 + 0.861801i \(0.669337\pi\)
\(284\) −4.38197 + 13.4863i −0.260022 + 0.800265i
\(285\) 0 0
\(286\) −7.85410 24.1724i −0.464423 1.42935i
\(287\) 3.76393 11.5842i 0.222178 0.683793i
\(288\) 0.309017 0.951057i 0.0182090 0.0560415i
\(289\) 13.8090 + 42.4998i 0.812295 + 2.49999i
\(290\) 0 0
\(291\) 4.28115 13.1760i 0.250966 0.772393i
\(292\) −2.54508 1.84911i −0.148940 0.108211i
\(293\) 28.7984 1.68242 0.841209 0.540709i \(-0.181844\pi\)
0.841209 + 0.540709i \(0.181844\pi\)
\(294\) 2.42705 + 1.76336i 0.141548 + 0.102841i
\(295\) 0 0
\(296\) −1.73607 + 1.26133i −0.100907 + 0.0733132i
\(297\) 4.23607 3.07768i 0.245802 0.178585i
\(298\) 2.17376 + 6.69015i 0.125923 + 0.387550i
\(299\) −29.1246 −1.68432
\(300\) 0 0
\(301\) −2.47214 −0.142492
\(302\) −2.14590 6.60440i −0.123483 0.380040i
\(303\) −1.35410 + 0.983813i −0.0777911 + 0.0565186i
\(304\) 2.23607 1.62460i 0.128247 0.0931771i
\(305\) 0 0
\(306\) 6.35410 + 4.61653i 0.363240 + 0.263909i
\(307\) 16.2918 0.929822 0.464911 0.885357i \(-0.346086\pi\)
0.464911 + 0.885357i \(0.346086\pi\)
\(308\) −8.47214 6.15537i −0.482745 0.350735i
\(309\) 0.708204 2.17963i 0.0402883 0.123995i
\(310\) 0 0
\(311\) −5.76393 17.7396i −0.326843 1.00592i −0.970602 0.240690i \(-0.922626\pi\)
0.643759 0.765228i \(-0.277374\pi\)
\(312\) 1.50000 4.61653i 0.0849208 0.261359i
\(313\) 8.14590 25.0705i 0.460433 1.41707i −0.404203 0.914669i \(-0.632451\pi\)
0.864636 0.502399i \(-0.167549\pi\)
\(314\) −5.51722 16.9803i −0.311355 0.958252i
\(315\) 0 0
\(316\) 0 0
\(317\) −5.61803 4.08174i −0.315540 0.229253i 0.418730 0.908111i \(-0.362475\pi\)
−0.734270 + 0.678857i \(0.762475\pi\)
\(318\) −8.56231 −0.480150
\(319\) −5.85410 4.25325i −0.327767 0.238137i
\(320\) 0 0
\(321\) 8.85410 6.43288i 0.494188 0.359048i
\(322\) −9.70820 + 7.05342i −0.541017 + 0.393072i
\(323\) 6.70820 + 20.6457i 0.373254 + 1.14876i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −20.4721 −1.13385
\(327\) 0.791796 + 2.43690i 0.0437864 + 0.134761i
\(328\) 4.92705 3.57971i 0.272051 0.197657i
\(329\) −7.70820 + 5.60034i −0.424967 + 0.308757i
\(330\) 0 0
\(331\) 26.2705 + 19.0866i 1.44396 + 1.04910i 0.987197 + 0.159507i \(0.0509906\pi\)
0.456761 + 0.889589i \(0.349009\pi\)
\(332\) −6.00000 −0.329293
\(333\) −1.73607 1.26133i −0.0951359 0.0691203i
\(334\) −2.00000 + 6.15537i −0.109435 + 0.336807i
\(335\) 0 0
\(336\) −0.618034 1.90211i −0.0337165 0.103769i
\(337\) −8.90983 + 27.4216i −0.485349 + 1.49375i 0.346125 + 0.938188i \(0.387497\pi\)
−0.831474 + 0.555563i \(0.812503\pi\)
\(338\) 3.26393 10.0453i 0.177534 0.546395i
\(339\) 3.57295 + 10.9964i 0.194056 + 0.597243i
\(340\) 0 0
\(341\) −6.00000 + 18.4661i −0.324918 + 0.999995i
\(342\) 2.23607 + 1.62460i 0.120913 + 0.0878482i
\(343\) 20.0000 1.07990
\(344\) −1.00000 0.726543i −0.0539164 0.0391725i
\(345\) 0 0
\(346\) −8.82624 + 6.41264i −0.474501 + 0.344746i
\(347\) −4.23607 + 3.07768i −0.227404 + 0.165219i −0.695653 0.718378i \(-0.744885\pi\)
0.468249 + 0.883596i \(0.344885\pi\)
\(348\) −0.427051 1.31433i −0.0228923 0.0704554i
\(349\) 14.7984 0.792139 0.396069 0.918221i \(-0.370374\pi\)
0.396069 + 0.918221i \(0.370374\pi\)
\(350\) 0 0
\(351\) 4.85410 0.259093
\(352\) −1.61803 4.97980i −0.0862415 0.265424i
\(353\) 16.5623 12.0332i 0.881523 0.640464i −0.0521313 0.998640i \(-0.516601\pi\)
0.933654 + 0.358177i \(0.116601\pi\)
\(354\) −7.23607 + 5.25731i −0.384593 + 0.279423i
\(355\) 0 0
\(356\) −1.11803 0.812299i −0.0592557 0.0430518i
\(357\) 15.7082 0.831366
\(358\) 3.09017 + 2.24514i 0.163321 + 0.118659i
\(359\) −8.61803 + 26.5236i −0.454842 + 1.39986i 0.416478 + 0.909146i \(0.363264\pi\)
−0.871320 + 0.490715i \(0.836736\pi\)
\(360\) 0 0
\(361\) −3.51064 10.8046i −0.184771 0.568666i
\(362\) −6.19098 + 19.0539i −0.325391 + 1.00145i
\(363\) 5.07295 15.6129i 0.266261 0.819466i
\(364\) −3.00000 9.23305i −0.157243 0.483943i
\(365\) 0 0
\(366\) −2.73607 + 8.42075i −0.143017 + 0.440160i
\(367\) −10.0902 7.33094i −0.526703 0.382672i 0.292420 0.956290i \(-0.405539\pi\)
−0.819123 + 0.573618i \(0.805539\pi\)
\(368\) −6.00000 −0.312772
\(369\) 4.92705 + 3.57971i 0.256492 + 0.186352i
\(370\) 0 0
\(371\) −13.8541 + 10.0656i −0.719269 + 0.522580i
\(372\) −3.00000 + 2.17963i −0.155543 + 0.113008i
\(373\) −0.798374 2.45714i −0.0413382 0.127226i 0.928258 0.371938i \(-0.121307\pi\)
−0.969596 + 0.244712i \(0.921307\pi\)
\(374\) 41.1246 2.12650
\(375\) 0 0
\(376\) −4.76393 −0.245681
\(377\) −2.07295 6.37988i −0.106762 0.328581i
\(378\) 1.61803 1.17557i 0.0832227 0.0604648i
\(379\) 2.76393 2.00811i 0.141974 0.103150i −0.514531 0.857472i \(-0.672034\pi\)
0.656505 + 0.754322i \(0.272034\pi\)
\(380\) 0 0
\(381\) 0.236068 + 0.171513i 0.0120941 + 0.00878690i
\(382\) −0.763932 −0.0390862
\(383\) 16.5623 + 12.0332i 0.846294 + 0.614869i 0.924122 0.382098i \(-0.124798\pi\)
−0.0778275 + 0.996967i \(0.524798\pi\)
\(384\) 0.309017 0.951057i 0.0157695 0.0485334i
\(385\) 0 0
\(386\) −0.736068 2.26538i −0.0374649 0.115305i
\(387\) 0.381966 1.17557i 0.0194164 0.0597576i
\(388\) 4.28115 13.1760i 0.217343 0.668912i
\(389\) 4.93769 + 15.1967i 0.250351 + 0.770501i 0.994710 + 0.102722i \(0.0327551\pi\)
−0.744359 + 0.667780i \(0.767245\pi\)
\(390\) 0 0
\(391\) 14.5623 44.8182i 0.736447 2.26655i
\(392\) 2.42705 + 1.76336i 0.122585 + 0.0890629i
\(393\) −0.763932 −0.0385353
\(394\) −10.7812 7.83297i −0.543147 0.394619i
\(395\) 0 0
\(396\) 4.23607 3.07768i 0.212870 0.154659i
\(397\) 23.3262 16.9475i 1.17071 0.850571i 0.179617 0.983737i \(-0.442514\pi\)
0.991094 + 0.133166i \(0.0425143\pi\)
\(398\) −1.90983 5.87785i −0.0957311 0.294630i
\(399\) 5.52786 0.276739
\(400\) 0 0
\(401\) −26.0902 −1.30288 −0.651440 0.758700i \(-0.725835\pi\)
−0.651440 + 0.758700i \(0.725835\pi\)
\(402\) 3.00000 + 9.23305i 0.149626 + 0.460503i
\(403\) −14.5623 + 10.5801i −0.725400 + 0.527034i
\(404\) −1.35410 + 0.983813i −0.0673691 + 0.0489465i
\(405\) 0 0
\(406\) −2.23607 1.62460i −0.110974 0.0806275i
\(407\) −11.2361 −0.556951
\(408\) 6.35410 + 4.61653i 0.314575 + 0.228552i
\(409\) 6.48278 19.9519i 0.320553 0.986560i −0.652855 0.757483i \(-0.726429\pi\)
0.973408 0.229077i \(-0.0735709\pi\)
\(410\) 0 0
\(411\) 4.64590 + 14.2986i 0.229165 + 0.705298i
\(412\) 0.708204 2.17963i 0.0348907 0.107383i
\(413\) −5.52786 + 17.0130i −0.272008 + 0.837156i
\(414\) −1.85410 5.70634i −0.0911241 0.280451i
\(415\) 0 0
\(416\) 1.50000 4.61653i 0.0735436 0.226344i
\(417\) 10.8541 + 7.88597i 0.531528 + 0.386177i
\(418\) 14.4721 0.707855
\(419\) 30.6525 + 22.2703i 1.49747 + 1.08798i 0.971375 + 0.237552i \(0.0763450\pi\)
0.526097 + 0.850425i \(0.323655\pi\)
\(420\) 0 0
\(421\) 8.97214 6.51864i 0.437275 0.317699i −0.347276 0.937763i \(-0.612893\pi\)
0.784551 + 0.620064i \(0.212893\pi\)
\(422\) 6.47214 4.70228i 0.315059 0.228904i
\(423\) −1.47214 4.53077i −0.0715777 0.220294i
\(424\) −8.56231 −0.415822
\(425\) 0 0
\(426\) −14.1803 −0.687040
\(427\) 5.47214 + 16.8415i 0.264815 + 0.815017i
\(428\) 8.85410 6.43288i 0.427979 0.310945i
\(429\) 20.5623 14.9394i 0.992757 0.721281i
\(430\) 0 0
\(431\) −3.00000 2.17963i −0.144505 0.104989i 0.513184 0.858279i \(-0.328466\pi\)
−0.657689 + 0.753290i \(0.728466\pi\)
\(432\) 1.00000 0.0481125
\(433\) −18.7254 13.6048i −0.899886 0.653806i 0.0385504 0.999257i \(-0.487726\pi\)
−0.938437 + 0.345451i \(0.887726\pi\)
\(434\) −2.29180 + 7.05342i −0.110010 + 0.338575i
\(435\) 0 0
\(436\) 0.791796 + 2.43690i 0.0379202 + 0.116706i
\(437\) 5.12461 15.7719i 0.245143 0.754474i
\(438\) 0.972136 2.99193i 0.0464505 0.142960i
\(439\) −7.76393 23.8949i −0.370552 1.14044i −0.946431 0.322907i \(-0.895340\pi\)
0.575878 0.817535i \(-0.304660\pi\)
\(440\) 0 0
\(441\) −0.927051 + 2.85317i −0.0441453 + 0.135865i
\(442\) 30.8435 + 22.4091i 1.46707 + 1.06589i
\(443\) −30.0689 −1.42862 −0.714308 0.699832i \(-0.753258\pi\)
−0.714308 + 0.699832i \(0.753258\pi\)
\(444\) −1.73607 1.26133i −0.0823901 0.0598599i
\(445\) 0 0
\(446\) −1.85410 + 1.34708i −0.0877943 + 0.0637863i
\(447\) −5.69098 + 4.13474i −0.269174 + 0.195567i
\(448\) −0.618034 1.90211i −0.0291994 0.0898664i
\(449\) 4.79837 0.226449 0.113225 0.993569i \(-0.463882\pi\)
0.113225 + 0.993569i \(0.463882\pi\)
\(450\) 0 0
\(451\) 31.8885 1.50157
\(452\) 3.57295 + 10.9964i 0.168057 + 0.517227i
\(453\) 5.61803 4.08174i 0.263958 0.191777i
\(454\) −13.7082 + 9.95959i −0.643358 + 0.467427i
\(455\) 0 0
\(456\) 2.23607 + 1.62460i 0.104713 + 0.0760788i
\(457\) 12.4721 0.583422 0.291711 0.956507i \(-0.405775\pi\)
0.291711 + 0.956507i \(0.405775\pi\)
\(458\) 19.6353 + 14.2658i 0.917495 + 0.666599i
\(459\) −2.42705 + 7.46969i −0.113285 + 0.348655i
\(460\) 0 0
\(461\) 7.75329 + 23.8622i 0.361107 + 1.11137i 0.952383 + 0.304903i \(0.0986241\pi\)
−0.591277 + 0.806469i \(0.701376\pi\)
\(462\) 3.23607 9.95959i 0.150556 0.463362i
\(463\) 3.79837 11.6902i 0.176525 0.543289i −0.823174 0.567789i \(-0.807799\pi\)
0.999700 + 0.0244992i \(0.00779912\pi\)
\(464\) −0.427051 1.31433i −0.0198253 0.0610161i
\(465\) 0 0
\(466\) 6.82624 21.0090i 0.316219 0.973223i
\(467\) 12.7984 + 9.29856i 0.592238 + 0.430286i 0.843115 0.537733i \(-0.180719\pi\)
−0.250877 + 0.968019i \(0.580719\pi\)
\(468\) 4.85410 0.224381
\(469\) 15.7082 + 11.4127i 0.725337 + 0.526989i
\(470\) 0 0
\(471\) 14.4443 10.4944i 0.665557 0.483555i
\(472\) −7.23607 + 5.25731i −0.333067 + 0.241987i
\(473\) −2.00000 6.15537i −0.0919601 0.283024i
\(474\) 0 0
\(475\) 0 0
\(476\) 15.7082 0.719984
\(477\) −2.64590 8.14324i −0.121147 0.372853i
\(478\) −21.7082 + 15.7719i −0.992910 + 0.721391i
\(479\) −3.61803 + 2.62866i −0.165312 + 0.120106i −0.667366 0.744730i \(-0.732578\pi\)
0.502053 + 0.864837i \(0.332578\pi\)
\(480\) 0 0
\(481\) −8.42705 6.12261i −0.384240 0.279167i
\(482\) −13.8541 −0.631037
\(483\) −9.70820 7.05342i −0.441739 0.320942i
\(484\) 5.07295 15.6129i 0.230589 0.709679i
\(485\) 0 0
\(486\) 0.309017 + 0.951057i 0.0140173 + 0.0431408i
\(487\) −3.18034 + 9.78808i −0.144115 + 0.443540i −0.996896 0.0787282i \(-0.974914\pi\)
0.852781 + 0.522268i \(0.174914\pi\)
\(488\) −2.73607 + 8.42075i −0.123856 + 0.381190i
\(489\) −6.32624 19.4702i −0.286082 0.880471i
\(490\) 0 0
\(491\) 9.23607 28.4257i 0.416818 1.28283i −0.493797 0.869577i \(-0.664391\pi\)
0.910615 0.413256i \(-0.135609\pi\)
\(492\) 4.92705 + 3.57971i 0.222129 + 0.161386i
\(493\) 10.8541 0.488844
\(494\) 10.8541 + 7.88597i 0.488349 + 0.354806i
\(495\) 0 0
\(496\) −3.00000 + 2.17963i −0.134704 + 0.0978682i
\(497\) −22.9443 + 16.6700i −1.02919 + 0.747751i
\(498\) −1.85410 5.70634i −0.0830843 0.255707i
\(499\) −33.4164 −1.49592 −0.747962 0.663742i \(-0.768967\pi\)
−0.747962 + 0.663742i \(0.768967\pi\)
\(500\) 0 0
\(501\) −6.47214 −0.289154
\(502\) −3.85410 11.8617i −0.172017 0.529414i
\(503\) 17.4164 12.6538i 0.776559 0.564203i −0.127385 0.991853i \(-0.540658\pi\)
0.903944 + 0.427650i \(0.140658\pi\)
\(504\) 1.61803 1.17557i 0.0720730 0.0523641i
\(505\) 0 0
\(506\) −25.4164 18.4661i −1.12990 0.820918i
\(507\) 10.5623 0.469088
\(508\) 0.236068 + 0.171513i 0.0104738 + 0.00760968i
\(509\) −4.24671 + 13.0700i −0.188232 + 0.579319i −0.999989 0.00467647i \(-0.998511\pi\)
0.811757 + 0.583995i \(0.198511\pi\)
\(510\) 0 0
\(511\) −1.94427 5.98385i −0.0860095 0.264710i
\(512\) 0.309017 0.951057i 0.0136568 0.0420312i
\(513\) −0.854102 + 2.62866i −0.0377095 + 0.116058i
\(514\) 3.59017 + 11.0494i 0.158356 + 0.487368i
\(515\) 0 0
\(516\) 0.381966 1.17557i 0.0168151 0.0517516i
\(517\) −20.1803 14.6619i −0.887530 0.644829i
\(518\) −4.29180 −0.188571
\(519\) −8.82624 6.41264i −0.387429 0.281484i
\(520\) 0 0
\(521\) −5.07295 + 3.68571i −0.222250 + 0.161474i −0.693339 0.720612i \(-0.743861\pi\)
0.471089 + 0.882086i \(0.343861\pi\)
\(522\) 1.11803 0.812299i 0.0489350 0.0355534i
\(523\) 0.708204 + 2.17963i 0.0309676 + 0.0953085i 0.965346 0.260975i \(-0.0840439\pi\)
−0.934378 + 0.356283i \(0.884044\pi\)
\(524\) −0.763932 −0.0333725
\(525\) 0 0
\(526\) −0.472136 −0.0205861
\(527\) −9.00000 27.6992i −0.392046 1.20659i
\(528\) 4.23607 3.07768i 0.184351 0.133939i
\(529\) −10.5172 + 7.64121i −0.457270 + 0.332226i
\(530\) 0 0
\(531\) −7.23607 5.25731i −0.314019 0.228148i
\(532\) 5.52786 0.239663
\(533\) 23.9164 + 17.3763i 1.03593 + 0.752651i
\(534\) 0.427051 1.31433i 0.0184803 0.0568765i
\(535\) 0 0
\(536\) 3.00000 + 9.23305i 0.129580 + 0.398807i
\(537\) −1.18034 + 3.63271i −0.0509354 + 0.156763i
\(538\) −0.590170 + 1.81636i −0.0254440 + 0.0783087i
\(539\) 4.85410 + 14.9394i 0.209081 + 0.643485i
\(540\) 0 0
\(541\) 6.57295 20.2295i 0.282593 0.869732i −0.704517 0.709688i \(-0.748836\pi\)
0.987110 0.160045i \(-0.0511639\pi\)
\(542\) −22.7984 16.5640i −0.979274 0.711484i
\(543\) −20.0344 −0.859760
\(544\) 6.35410 + 4.61653i 0.272430 + 0.197932i
\(545\) 0 0
\(546\) 7.85410 5.70634i 0.336125 0.244209i
\(547\) 1.61803 1.17557i 0.0691821 0.0502638i −0.552657 0.833409i \(-0.686386\pi\)
0.621839 + 0.783145i \(0.286386\pi\)
\(548\) 4.64590 + 14.2986i 0.198463 + 0.610806i
\(549\) −8.85410 −0.377884
\(550\) 0 0
\(551\) 3.81966 0.162723
\(552\) −1.85410 5.70634i −0.0789158 0.242878i
\(553\) 0 0
\(554\) −17.9164 + 13.0170i −0.761195 + 0.553041i
\(555\) 0 0
\(556\) 10.8541 + 7.88597i 0.460316 + 0.334439i
\(557\) 27.2705 1.15549 0.577744 0.816218i \(-0.303933\pi\)
0.577744 + 0.816218i \(0.303933\pi\)
\(558\) −3.00000 2.17963i −0.127000 0.0922710i
\(559\) 1.85410 5.70634i 0.0784202 0.241352i
\(560\) 0 0
\(561\) 12.7082 + 39.1118i 0.536541 + 1.65130i
\(562\) −1.88197 + 5.79210i −0.0793859 + 0.244325i
\(563\) −3.23607 + 9.95959i −0.136384 + 0.419747i −0.995803 0.0915256i \(-0.970826\pi\)
0.859419 + 0.511272i \(0.170826\pi\)
\(564\) −1.47214 4.53077i −0.0619881 0.190780i
\(565\) 0 0
\(566\) −1.00000 + 3.07768i −0.0420331 + 0.129365i
\(567\) 1.61803 + 1.17557i 0.0679510 + 0.0493693i
\(568\) −14.1803 −0.594994
\(569\) −17.2984 12.5680i −0.725186 0.526878i 0.162851 0.986651i \(-0.447931\pi\)
−0.888037 + 0.459772i \(0.847931\pi\)
\(570\) 0 0
\(571\) −27.2705 + 19.8132i −1.14124 + 0.829156i −0.987291 0.158924i \(-0.949198\pi\)
−0.153944 + 0.988080i \(0.549198\pi\)
\(572\) 20.5623 14.9394i 0.859753 0.624647i
\(573\) −0.236068 0.726543i −0.00986188 0.0303517i
\(574\) 12.1803 0.508398
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) −8.90983 27.4216i −0.370921 1.14158i −0.946190 0.323613i \(-0.895102\pi\)
0.575268 0.817965i \(-0.304898\pi\)
\(578\) −36.1525 + 26.2663i −1.50374 + 1.09253i
\(579\) 1.92705 1.40008i 0.0800855 0.0581855i
\(580\) 0 0
\(581\) −9.70820 7.05342i −0.402764 0.292625i
\(582\) 13.8541 0.574271
\(583\) −36.2705 26.3521i −1.50217 1.09139i
\(584\) 0.972136 2.99193i 0.0402273 0.123807i
\(585\) 0 0
\(586\) 8.89919 + 27.3889i 0.367622 + 1.13142i
\(587\) 4.90983 15.1109i 0.202650 0.623694i −0.797151 0.603780i \(-0.793661\pi\)
0.999802 0.0199141i \(-0.00633929\pi\)
\(588\) −0.927051 + 2.85317i −0.0382309 + 0.117663i
\(589\) −3.16718 9.74759i −0.130502 0.401642i
\(590\) 0 0
\(591\) 4.11803 12.6740i 0.169393 0.521339i
\(592\) −1.73607 1.26133i −0.0713520 0.0518402i
\(593\) 6.03444 0.247805 0.123902 0.992294i \(-0.460459\pi\)
0.123902 + 0.992294i \(0.460459\pi\)
\(594\) 4.23607 + 3.07768i 0.173808 + 0.126279i
\(595\) 0 0
\(596\) −5.69098 + 4.13474i −0.233112 + 0.169366i
\(597\) 5.00000 3.63271i 0.204636 0.148677i
\(598\) −9.00000 27.6992i −0.368037 1.13270i
\(599\) 1.05573 0.0431359 0.0215679 0.999767i \(-0.493134\pi\)
0.0215679 + 0.999767i \(0.493134\pi\)
\(600\) 0 0
\(601\) 7.32624 0.298843 0.149422 0.988774i \(-0.452259\pi\)
0.149422 + 0.988774i \(0.452259\pi\)
\(602\) −0.763932 2.35114i −0.0311355 0.0958254i
\(603\) −7.85410 + 5.70634i −0.319844 + 0.232380i
\(604\) 5.61803 4.08174i 0.228595 0.166084i
\(605\) 0 0
\(606\) −1.35410 0.983813i −0.0550066 0.0399647i
\(607\) 1.81966 0.0738577 0.0369289 0.999318i \(-0.488243\pi\)
0.0369289 + 0.999318i \(0.488243\pi\)
\(608\) 2.23607 + 1.62460i 0.0906845 + 0.0658862i
\(609\) 0.854102 2.62866i 0.0346100 0.106518i
\(610\) 0 0
\(611\) −7.14590 21.9928i −0.289092 0.889734i
\(612\) −2.42705 + 7.46969i −0.0981077 + 0.301945i
\(613\) 6.66312 20.5070i 0.269121 0.828269i −0.721594 0.692316i \(-0.756590\pi\)
0.990715 0.135953i \(-0.0434096\pi\)
\(614\) 5.03444 + 15.4944i 0.203174 + 0.625304i
\(615\) 0 0
\(616\) 3.23607 9.95959i 0.130385 0.401283i
\(617\) 6.78115 + 4.92680i 0.272999 + 0.198345i 0.715858 0.698246i \(-0.246036\pi\)
−0.442859 + 0.896591i \(0.646036\pi\)
\(618\) 2.29180 0.0921896
\(619\) −2.76393 2.00811i −0.111092 0.0807129i 0.530852 0.847464i \(-0.321872\pi\)
−0.641944 + 0.766751i \(0.721872\pi\)
\(620\) 0 0
\(621\) 4.85410 3.52671i 0.194788 0.141522i
\(622\) 15.0902 10.9637i 0.605061 0.439602i
\(623\) −0.854102 2.62866i −0.0342189 0.105315i
\(624\) 4.85410 0.194320
\(625\) 0 0
\(626\) 26.3607 1.05358
\(627\) 4.47214 + 13.7638i 0.178600 + 0.549674i
\(628\) 14.4443 10.4944i 0.576389 0.418771i
\(629\) 13.6353 9.90659i 0.543673 0.395002i
\(630\) 0 0
\(631\) 34.8885 + 25.3480i 1.38889 + 1.00909i 0.995986 + 0.0895093i \(0.0285299\pi\)
0.392905 + 0.919579i \(0.371470\pi\)
\(632\) 0 0
\(633\) 6.47214 + 4.70228i 0.257244 + 0.186899i
\(634\) 2.14590 6.60440i 0.0852245 0.262294i
\(635\) 0 0
\(636\) −2.64590 8.14324i −0.104917 0.322900i
\(637\) −4.50000 + 13.8496i −0.178296 + 0.548740i
\(638\) 2.23607 6.88191i 0.0885268 0.272457i
\(639\) −4.38197 13.4863i −0.173348 0.533510i
\(640\) 0 0
\(641\) −8.32624 + 25.6255i −0.328867 + 1.01215i 0.640798 + 0.767709i \(0.278603\pi\)
−0.969665 + 0.244438i \(0.921397\pi\)
\(642\) 8.85410 + 6.43288i 0.349444 + 0.253886i
\(643\) 39.7771 1.56866 0.784328 0.620347i \(-0.213008\pi\)
0.784328 + 0.620347i \(0.213008\pi\)
\(644\) −9.70820 7.05342i −0.382557 0.277944i
\(645\) 0 0
\(646\) −17.5623 + 12.7598i −0.690980 + 0.502026i
\(647\) −29.0344 + 21.0948i −1.14146 + 0.829320i −0.987322 0.158729i \(-0.949261\pi\)
−0.154139 + 0.988049i \(0.549261\pi\)
\(648\) 0.309017 + 0.951057i 0.0121393 + 0.0373610i
\(649\) −46.8328 −1.83835
\(650\) 0 0
\(651\) −7.41641 −0.290672
\(652\) −6.32624 19.4702i −0.247755 0.762510i
\(653\) −26.0623 + 18.9354i −1.01990 + 0.740998i −0.966262 0.257562i \(-0.917081\pi\)
−0.0536351 + 0.998561i \(0.517081\pi\)
\(654\) −2.07295 + 1.50609i −0.0810587 + 0.0588926i
\(655\) 0 0
\(656\) 4.92705 + 3.57971i 0.192369 + 0.139764i
\(657\) 3.14590 0.122733
\(658\) −7.70820 5.60034i −0.300497 0.218324i
\(659\) 12.0344 37.0382i 0.468795 1.44280i −0.385351 0.922770i \(-0.625920\pi\)
0.854146 0.520033i \(-0.174080\pi\)
\(660\) 0 0
\(661\) −7.27051 22.3763i −0.282790 0.870338i −0.987052 0.160398i \(-0.948722\pi\)
0.704262 0.709940i \(-0.251278\pi\)
\(662\) −10.0344 + 30.8828i −0.390000 + 1.20030i
\(663\) −11.7812 + 36.2587i −0.457542 + 1.40817i
\(664\) −1.85410 5.70634i −0.0719531 0.221449i
\(665\) 0 0
\(666\) 0.663119 2.04087i 0.0256953 0.0790821i
\(667\) −6.70820 4.87380i −0.259743 0.188714i
\(668\) −6.47214 −0.250414
\(669\) −1.85410 1.34708i −0.0716837 0.0520813i
\(670\) 0 0
\(671\) −37.5066 + 27.2501i −1.44793 + 1.05198i
\(672\) 1.61803 1.17557i 0.0624170 0.0453486i
\(673\) 5.80902 + 17.8783i 0.223921 + 0.689158i 0.998399 + 0.0565578i \(0.0180125\pi\)
−0.774478 + 0.632601i \(0.781987\pi\)
\(674\) −28.8328 −1.11060
\(675\) 0 0
\(676\) 10.5623 0.406243
\(677\) −11.2705 34.6871i −0.433161 1.33313i −0.894960 0.446147i \(-0.852796\pi\)
0.461799 0.886985i \(-0.347204\pi\)
\(678\) −9.35410 + 6.79615i −0.359242 + 0.261005i
\(679\) 22.4164 16.2865i 0.860263 0.625017i
\(680\) 0 0
\(681\) −13.7082 9.95959i −0.525300 0.381652i
\(682\) −19.4164 −0.743493
\(683\) 15.7082 + 11.4127i 0.601058 + 0.436694i 0.846254 0.532779i \(-0.178852\pi\)
−0.245196 + 0.969473i \(0.578852\pi\)
\(684\) −0.854102 + 2.62866i −0.0326574 + 0.100509i
\(685\) 0 0
\(686\) 6.18034 + 19.0211i 0.235966 + 0.726230i
\(687\) −7.50000 + 23.0826i −0.286143 + 0.880657i
\(688\) 0.381966 1.17557i 0.0145623 0.0448182i
\(689\) −12.8435 39.5281i −0.489297 1.50590i
\(690\) 0 0
\(691\) −7.47214 + 22.9969i −0.284253 + 0.874842i 0.702368 + 0.711814i \(0.252126\pi\)
−0.986621 + 0.163028i \(0.947874\pi\)
\(692\) −8.82624 6.41264i −0.335523 0.243772i
\(693\) 10.4721 0.397804
\(694\) −4.23607 3.07768i −0.160799 0.116827i
\(695\) 0 0
\(696\) 1.11803 0.812299i 0.0423790 0.0307901i
\(697\) −38.6976 + 28.1154i −1.46577 + 1.06495i
\(698\) 4.57295 + 14.0741i 0.173089 + 0.532712i
\(699\) 22.0902 0.835527
\(700\) 0 0
\(701\) −20.1591 −0.761397 −0.380698 0.924699i \(-0.624316\pi\)
−0.380698 + 0.924699i \(0.624316\pi\)
\(702\) 1.50000 + 4.61653i 0.0566139 + 0.174240i
\(703\) 4.79837 3.48622i 0.180974 0.131485i
\(704\) 4.23607 3.07768i 0.159653 0.115995i
\(705\) 0 0
\(706\) 16.5623 + 12.0332i 0.623331 + 0.452876i
\(707\) −3.34752 −0.125897
\(708\) −7.23607 5.25731i −0.271948 0.197582i
\(709\) −9.20820 + 28.3399i −0.345821 + 1.06433i 0.615321 + 0.788276i \(0.289026\pi\)
−0.961143 + 0.276052i \(0.910974\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.427051 1.31433i 0.0160044 0.0492565i
\(713\) −6.87539 + 21.1603i −0.257485 + 0.792458i
\(714\) 4.85410 + 14.9394i 0.181660 + 0.559093i
\(715\) 0 0
\(716\) −1.18034 + 3.63271i −0.0441114 + 0.135761i
\(717\) −21.7082 15.7719i −0.810708 0.589014i
\(718\) −27.8885 −1.04079
\(719\) −18.0902 13.1433i −0.674649 0.490162i 0.196929 0.980418i \(-0.436903\pi\)
−0.871578 + 0.490256i \(0.836903\pi\)
\(720\) 0 0
\(721\) 3.70820 2.69417i 0.138101 0.100336i
\(722\) 9.19098 6.67764i 0.342053 0.248516i
\(723\) −4.28115 13.1760i −0.159218 0.490022i
\(724\) −20.0344 −0.744574
\(725\) 0 0
\(726\) 16.4164 0.609270
\(727\) −3.18034 9.78808i −0.117952 0.363020i 0.874599 0.484847i \(-0.161125\pi\)
−0.992551 + 0.121827i \(0.961125\pi\)
\(728\) 7.85410 5.70634i 0.291092 0.211491i
\(729\) −0.809017 + 0.587785i −0.0299636 + 0.0217698i
\(730\) 0 0
\(731\) 7.85410 + 5.70634i 0.290494 + 0.211057i
\(732\) −8.85410 −0.327257
\(733\) −5.14590 3.73871i −0.190068 0.138093i 0.488682 0.872462i \(-0.337478\pi\)
−0.678750 + 0.734370i \(0.737478\pi\)
\(734\) 3.85410 11.8617i 0.142257 0.437824i
\(735\) 0 0
\(736\) −1.85410 5.70634i −0.0683431 0.210338i
\(737\) −15.7082 + 48.3449i −0.578619 + 1.78081i
\(738\) −1.88197 + 5.79210i −0.0692761 + 0.213210i
\(739\) 2.56231 + 7.88597i 0.0942559 + 0.290090i 0.987059 0.160357i \(-0.0512646\pi\)
−0.892803 + 0.450447i \(0.851265\pi\)
\(740\) 0 0
\(741\) −4.14590 + 12.7598i −0.152303 + 0.468742i
\(742\) −13.8541 10.0656i −0.508600 0.369520i
\(743\) −6.65248 −0.244056 −0.122028 0.992527i \(-0.538940\pi\)
−0.122028 + 0.992527i \(0.538940\pi\)
\(744\) −3.00000 2.17963i −0.109985 0.0799090i
\(745\) 0 0
\(746\) 2.09017 1.51860i 0.0765266 0.0555998i
\(747\) 4.85410 3.52671i 0.177602 0.129036i
\(748\) 12.7082 + 39.1118i 0.464658 + 1.43007i
\(749\) 21.8885 0.799790
\(750\) 0 0
\(751\) 14.7639 0.538744 0.269372 0.963036i \(-0.413184\pi\)
0.269372 + 0.963036i \(0.413184\pi\)
\(752\) −1.47214 4.53077i −0.0536833 0.165220i
\(753\) 10.0902 7.33094i 0.367706 0.267154i
\(754\) 5.42705 3.94298i 0.197642 0.143595i
\(755\) 0 0
\(756\) 1.61803 + 1.17557i 0.0588473 + 0.0427551i
\(757\) 28.8541 1.04872 0.524360 0.851497i \(-0.324305\pi\)
0.524360 + 0.851497i \(0.324305\pi\)
\(758\) 2.76393 + 2.00811i 0.100391 + 0.0729380i
\(759\) 9.70820 29.8788i 0.352385 1.08453i
\(760\) 0 0
\(761\) 7.46556 + 22.9766i 0.270626 + 0.832902i 0.990344 + 0.138635i \(0.0442714\pi\)
−0.719717 + 0.694267i \(0.755729\pi\)
\(762\) −0.0901699 + 0.277515i −0.00326651 + 0.0100533i
\(763\) −1.58359 + 4.87380i −0.0573299 + 0.176443i
\(764\) −0.236068 0.726543i −0.00854064 0.0262854i
\(765\) 0 0
\(766\) −6.32624 + 19.4702i −0.228576 + 0.703485i
\(767\) −35.1246 25.5195i −1.26828 0.921457i
\(768\) 1.00000 0.0360844
\(769\) 1.90983 + 1.38757i 0.0688702 + 0.0500372i 0.621688 0.783265i \(-0.286447\pi\)
−0.552817 + 0.833302i \(0.686447\pi\)
\(770\) 0 0
\(771\) −9.39919 + 6.82891i −0.338503 + 0.245937i
\(772\) 1.92705 1.40008i 0.0693561 0.0503901i
\(773\) −4.35410 13.4005i −0.156606 0.481984i 0.841714 0.539924i \(-0.181547\pi\)
−0.998320 + 0.0579395i \(0.981547\pi\)
\(774\) 1.23607 0.0444295
\(775\) 0 0
\(776\) 13.8541 0.497333
\(777\) −1.32624 4.08174i −0.0475785 0.146432i
\(778\) −12.9271 + 9.39205i −0.463457 + 0.336721i
\(779\) −13.6180 + 9.89408i −0.487917 + 0.354492i
\(780\) 0 0
\(781\) −60.0689 43.6426i −2.14943 1.56165i
\(782\) 47.1246 1.68517
\(783\) 1.11803 + 0.812299i 0.0399553 + 0.0290292i
\(784\) −0.927051 + 2.85317i −0.0331090 + 0.101899i
\(785\) 0 0
\(786\) −0.236068 0.726543i −0.00842027 0.0259149i
\(787\) −9.43769 + 29.0462i −0.336417 + 1.03539i 0.629602 + 0.776918i \(0.283218\pi\)
−0.966020 + 0.258469i \(0.916782\pi\)
\(788\) 4.11803 12.6740i 0.146699 0.451493i
\(789\) −0.145898 0.449028i −0.00519411 0.0159858i
\(790\) 0 0
\(791\) −7.14590 + 21.9928i −0.254079 + 0.781974i
\(792\) 4.23607 + 3.07768i 0.150522 + 0.109361i
\(793\) −42.9787 −1.52622
\(794\) 23.3262 + 16.9475i 0.827817 + 0.601444i
\(795\) 0 0
\(796\) 5.00000 3.63271i 0.177220 0.128758i
\(797\) −10.7812 + 7.83297i −0.381888 + 0.277458i −0.762123 0.647432i \(-0.775843\pi\)
0.380235 + 0.924890i \(0.375843\pi\)
\(798\) 1.70820 + 5.25731i 0.0604698 + 0.186107i
\(799\) 37.4164 1.32370
\(800\) 0 0
\(801\) 1.38197 0.0488294
\(802\) −8.06231 24.8132i −0.284690 0.876185i
\(803\) 13.3262 9.68208i 0.470273 0.341673i
\(804\) −7.85410 + 5.70634i −0.276993 + 0.201247i
\(805\) 0 0
\(806\) −14.5623 10.5801i −0.512935 0.372669i
\(807\) −1.90983 −0.0672292
\(808\) −1.35410 0.983813i −0.0476371 0.0346104i
\(809\) 2.53851 7.81272i 0.0892492 0.274681i −0.896463 0.443118i \(-0.853872\pi\)
0.985712 + 0.168438i \(0.0538722\pi\)
\(810\) 0 0
\(811\) 3.18034 + 9.78808i 0.111677 + 0.343706i 0.991239 0.132077i \(-0.0421647\pi\)
−0.879563 + 0.475783i \(0.842165\pi\)
\(812\) 0.854102 2.62866i 0.0299731 0.0922477i
\(813\) 8.70820 26.8011i 0.305410 0.939955i
\(814\) −3.47214 10.6861i −0.121698 0.374549i
\(815\) 0 0
\(816\) −2.42705 + 7.46969i −0.0849638 + 0.261492i
\(817\) 2.76393 + 2.00811i 0.0966977 + 0.0702550i
\(818\) 20.9787 0.733504
\(819\) 7.85410 + 5.70634i 0.274445 + 0.199396i
\(820\) 0 0
\(821\) 36.2705 26.3521i 1.26585 0.919694i 0.266820 0.963746i \(-0.414027\pi\)
0.999029 + 0.0440528i \(0.0140270\pi\)
\(822\) −12.1631 + 8.83702i −0.424237 + 0.308227i
\(823\) 7.29180 + 22.4418i 0.254176 + 0.782273i 0.993991 + 0.109463i \(0.0349131\pi\)
−0.739815 + 0.672811i \(0.765087\pi\)
\(824\) 2.29180 0.0798385
\(825\) 0 0
\(826\) −17.8885 −0.622422
\(827\) −4.56231 14.0413i −0.158647 0.488265i 0.839865 0.542795i \(-0.182634\pi\)
−0.998512 + 0.0545300i \(0.982634\pi\)
\(828\) 4.85410 3.52671i 0.168692 0.122562i
\(829\) −31.6697 + 23.0094i −1.09993 + 0.799149i −0.981049 0.193759i \(-0.937932\pi\)
−0.118885 + 0.992908i \(0.537932\pi\)
\(830\) 0 0
\(831\) −17.9164 13.0170i −0.621513 0.451556i
\(832\) 4.85410 0.168286
\(833\) −19.0623 13.8496i −0.660470 0.479859i
\(834\) −4.14590 + 12.7598i −0.143561 + 0.441834i
\(835\) 0 0
\(836\) 4.47214 + 13.7638i 0.154672 + 0.476032i
\(837\) 1.14590 3.52671i 0.0396080 0.121901i
\(838\) −11.7082 + 36.0341i −0.404453 + 1.24478i
\(839\) −1.58359 4.87380i −0.0546717 0.168262i 0.919992 0.391937i \(-0.128195\pi\)
−0.974664 + 0.223674i \(0.928195\pi\)
\(840\) 0 0
\(841\) −8.37132 + 25.7643i −0.288666 + 0.888424i
\(842\) 8.97214 + 6.51864i 0.309200 + 0.224647i
\(843\) −6.09017 −0.209757
\(844\) 6.47214 + 4.70228i 0.222780 + 0.161859i
\(845\) 0 0
\(846\) 3.85410 2.80017i 0.132507 0.0962718i
\(847\) 26.5623 19.2986i 0.912692 0.663109i
\(848\) −2.64590 8.14324i −0.0908605 0.279640i
\(849\) −3.23607 −0.111062
\(850\) 0 0
\(851\) −12.8754 −0.441363
\(852\) −4.38197 13.4863i −0.150124 0.462033i
\(853\) 13.3090 9.66957i 0.455692 0.331080i −0.336147 0.941810i \(-0.609124\pi\)
0.791839 + 0.610730i \(0.209124\pi\)
\(854\) −14.3262 + 10.4086i −0.490234 + 0.356176i
\(855\) 0 0
\(856\) 8.85410 + 6.43288i 0.302627 + 0.219871i
\(857\) −23.3050 −0.796082 −0.398041 0.917368i \(-0.630310\pi\)
−0.398041 + 0.917368i \(0.630310\pi\)
\(858\) 20.5623 + 14.9394i 0.701986 + 0.510022i
\(859\) 14.0689 43.2996i 0.480024 1.47736i −0.359036 0.933324i \(-0.616894\pi\)
0.839060 0.544039i \(-0.183106\pi\)
\(860\) 0 0
\(861\) 3.76393 + 11.5842i 0.128274 + 0.394788i
\(862\) 1.14590 3.52671i 0.0390294 0.120120i
\(863\) −3.76393 + 11.5842i −0.128126 + 0.394330i −0.994458 0.105138i \(-0.966471\pi\)
0.866332 + 0.499469i \(0.166471\pi\)
\(864\) 0.309017 + 0.951057i 0.0105130 + 0.0323556i
\(865\) 0 0
\(866\) 7.15248 22.0131i 0.243051 0.748034i
\(867\) −36.1525 26.2663i −1.22780 0.892051i
\(868\) −7.41641 −0.251729
\(869\) 0 0
\(870\) 0 0
\(871\) −38.1246 + 27.6992i −1.29180 + 0.938550i
\(872\) −2.07295 + 1.50609i −0.0701989 + 0.0510025i
\(873\) 4.28115 + 13.1760i 0.144895 + 0.445941i
\(874\) 16.5836 0.560948
\(875\) 0 0
\(876\) 3.14590 0.106290
\(877\) −5.55573 17.0988i −0.187604 0.577385i 0.812380 0.583129i \(-0.198172\pi\)
−0.999984 + 0.00574402i \(0.998172\pi\)
\(878\) 20.3262 14.7679i 0.685977 0.498392i
\(879\) −23.2984 + 16.9273i −0.785835 + 0.570942i
\(880\) 0 0
\(881\) −37.7984 27.4621i −1.27346 0.925223i −0.274125 0.961694i \(-0.588388\pi\)
−0.999335 + 0.0364716i \(0.988388\pi\)
\(882\) −3.00000 −0.101015
\(883\) 34.1246 + 24.7930i 1.14838 + 0.834350i 0.988265 0.152747i \(-0.0488121\pi\)
0.160119 + 0.987098i \(0.448812\pi\)
\(884\) −11.7812 + 36.2587i −0.396243 + 1.21951i
\(885\) 0 0
\(886\) −9.29180 28.5972i −0.312164 0.960742i
\(887\) −7.97871 + 24.5560i −0.267899 + 0.824508i 0.723112 + 0.690730i \(0.242711\pi\)
−0.991011 + 0.133778i \(0.957289\pi\)
\(888\) 0.663119 2.04087i 0.0222528 0.0684871i
\(889\) 0.180340 + 0.555029i 0.00604841 + 0.0186151i
\(890\) 0 0
\(891\) −1.61803 + 4.97980i −0.0542062 + 0.166829i
\(892\) −1.85410 1.34708i −0.0620799 0.0451037i
\(893\) 13.1672 0.440623
\(894\) −5.69098 4.13474i −0.190335 0.138286i
\(895\) 0 0
\(896\) 1.61803 1.17557i 0.0540547 0.0392731i
\(897\) 23.5623 17.1190i 0.786722 0.571587i
\(898\) 1.48278 + 4.56352i 0.0494810 + 0.152287i
\(899\) −5.12461 −0.170915
\(900\) 0 0
\(901\) 67.2492 2.24040
\(902\) 9.85410 + 30.3278i 0.328106 + 1.00981i
\(903\) 2.00000 1.45309i 0.0665558 0.0483556i
\(904\) −9.35410 + 6.79615i −0.311113 + 0.226037i
\(905\) 0 0
\(906\) 5.61803 + 4.08174i 0.186647 + 0.135607i
\(907\) −20.2918 −0.673778 −0.336889 0.941544i \(-0.609375\pi\)
−0.336889 + 0.941544i \(0.609375\pi\)
\(908\) −13.7082 9.95959i −0.454923 0.330521i
\(909\) 0.517221 1.59184i 0.0171551 0.0527981i
\(910\) 0 0
\(911\) 17.3262 + 53.3247i 0.574044 + 1.76673i 0.639412 + 0.768864i \(0.279178\pi\)
−0.0653683 + 0.997861i \(0.520822\pi\)
\(912\) −0.854102 + 2.62866i −0.0282821 + 0.0870435i
\(913\) 9.70820 29.8788i 0.321295 0.988843i
\(914\) 3.85410 + 11.8617i 0.127482 + 0.392350i
\(915\) 0 0
\(916\) −7.50000 + 23.0826i −0.247807 + 0.762671i
\(917\) −1.23607 0.898056i −0.0408186 0.0296564i
\(918\) −7.85410 −0.259224
\(919\) 0.854102 + 0.620541i 0.0281742 + 0.0204698i 0.601783 0.798659i \(-0.294457\pi\)
−0.573609 + 0.819129i \(0.694457\pi\)
\(920\) 0 0
\(921\) −13.1803 + 9.57608i −0.434307 + 0.315542i
\(922\) −20.2984 + 14.7476i −0.668491 + 0.485687i
\(923\) −21.2705 65.4639i −0.700127 2.15477i
\(924\) 10.4721 0.344508
\(925\) 0 0
\(926\) 12.2918 0.403933
\(927\) 0.708204 + 2.17963i 0.0232605 + 0.0715884i
\(928\) 1.11803 0.812299i 0.0367013 0.0266650i
\(929\) 25.0623 18.2088i 0.822268 0.597412i −0.0950935 0.995468i \(-0.530315\pi\)
0.917361 + 0.398056i \(0.130315\pi\)
\(930\) 0 0
\(931\) −6.70820 4.87380i −0.219853 0.159732i
\(932\) 22.0902 0.723588
\(933\) 15.0902 + 10.9637i 0.494030 + 0.358934i
\(934\) −4.88854 + 15.0454i −0.159958 + 0.492300i
\(935\) 0 0
\(936\) 1.50000 + 4.61653i 0.0490290 + 0.150896i
\(937\) −10.8435 + 33.3727i −0.354240 + 1.09024i 0.602208 + 0.798339i \(0.294288\pi\)
−0.956449 + 0.291901i \(0.905712\pi\)
\(938\) −6.00000 + 18.4661i −0.195907 + 0.602940i
\(939\) 8.14590 + 25.0705i 0.265831 + 0.818145i
\(940\) 0 0
\(941\) 6.69756 20.6130i 0.218334 0.671964i −0.780566 0.625074i \(-0.785069\pi\)
0.998900 0.0468901i \(-0.0149311\pi\)
\(942\) 14.4443 + 10.4944i 0.470620 + 0.341925i
\(943\) 36.5410 1.18994
\(944\) −7.23607 5.25731i −0.235514 0.171111i
\(945\) 0 0
\(946\) 5.23607 3.80423i 0.170239 0.123686i
\(947\) 8.85410 6.43288i 0.287720 0.209041i −0.434558 0.900644i \(-0.643095\pi\)
0.722278 + 0.691603i \(0.243095\pi\)
\(948\) 0 0
\(949\) 15.2705 0.495702
\(950\) 0 0
\(951\) 6.94427 0.225183
\(952\) 4.85410 + 14.9394i 0.157322 + 0.484188i
\(953\) −26.5902 + 19.3189i −0.861340 + 0.625800i −0.928249 0.371959i \(-0.878686\pi\)
0.0669091 + 0.997759i \(0.478686\pi\)
\(954\) 6.92705 5.03280i 0.224272 0.162943i
\(955\) 0 0
\(956\) −21.7082 15.7719i −0.702093 0.510101i
\(957\) 7.23607 0.233909
\(958\) −3.61803 2.62866i −0.116893 0.0849280i
\(959\) −9.29180 + 28.5972i −0.300048 + 0.923452i
\(960\) 0 0
\(961\) −5.33030 16.4050i −0.171945 0.529193i
\(962\) 3.21885 9.90659i 0.103780 0.319401i
\(963\) −3.38197 + 10.4086i −0.108982 + 0.335413i
\(964\) −4.28115 13.1760i −0.137887 0.424371i
\(965\) 0 0
\(966\) 3.70820 11.4127i 0.119310 0.367197i
\(967\) 33.1246 + 24.0664i 1.06522 + 0.773925i 0.975046 0.222002i \(-0.0712591\pi\)
0.0901695 + 0.995926i \(0.471259\pi\)
\(968\) 16.4164 0.527643
\(969\) −17.5623 12.7598i −0.564183 0.409903i
\(970\) 0 0
\(971\) 27.3262 19.8537i 0.876941 0.637135i −0.0554996 0.998459i \(-0.517675\pi\)
0.932440 + 0.361324i \(0.117675\pi\)
\(972\) −0.809017 + 0.587785i −0.0259492 + 0.0188532i
\(973\) 8.29180 + 25.5195i 0.265823 + 0.818118i
\(974\) −10.2918 −0.329770
\(975\) 0 0
\(976\) −8.85410 −0.283413
\(977\) 6.35410 + 19.5559i 0.203286 + 0.625649i 0.999779 + 0.0210023i \(0.00668574\pi\)
−0.796494 + 0.604647i \(0.793314\pi\)
\(978\) 16.5623 12.0332i 0.529604 0.384780i
\(979\) 5.85410 4.25325i 0.187098 0.135935i
\(980\) 0 0
\(981\) −2.07295 1.50609i −0.0661842 0.0480856i
\(982\) 29.8885 0.953782
\(983\) −34.4164 25.0050i −1.09771 0.797535i −0.117028 0.993129i \(-0.537337\pi\)
−0.980685 + 0.195594i \(0.937337\pi\)
\(984\) −1.88197 + 5.79210i −0.0599949 + 0.184645i
\(985\) 0 0
\(986\) 3.35410 + 10.3229i 0.106816 + 0.328747i
\(987\) 2.94427 9.06154i 0.0937172 0.288432i
\(988\) −4.14590 + 12.7598i −0.131899 + 0.405942i
\(989\) −2.29180 7.05342i −0.0728749 0.224286i
\(990\) 0 0
\(991\) 18.7082 57.5779i 0.594286 1.82902i 0.0360356 0.999351i \(-0.488527\pi\)
0.558250 0.829673i \(-0.311473\pi\)
\(992\) −3.00000 2.17963i −0.0952501 0.0692032i
\(993\) −32.4721 −1.03047
\(994\) −22.9443 16.6700i −0.727748 0.528740i
\(995\) 0 0
\(996\) 4.85410 3.52671i 0.153808 0.111748i
\(997\) −1.14590 + 0.832544i −0.0362910 + 0.0263669i −0.605783 0.795630i \(-0.707140\pi\)
0.569492 + 0.821997i \(0.307140\pi\)
\(998\) −10.3262 31.7809i −0.326871 1.00601i
\(999\) 2.14590 0.0678932
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 750.2.g.a.151.1 4
5.2 odd 4 750.2.h.a.349.1 8
5.3 odd 4 750.2.h.a.349.2 8
5.4 even 2 150.2.g.b.31.1 4
15.14 odd 2 450.2.h.b.181.1 4
25.2 odd 20 3750.2.c.c.1249.3 4
25.3 odd 20 750.2.h.a.649.1 8
25.4 even 10 150.2.g.b.121.1 yes 4
25.11 even 5 3750.2.a.g.1.1 2
25.14 even 10 3750.2.a.b.1.1 2
25.21 even 5 inner 750.2.g.a.601.1 4
25.22 odd 20 750.2.h.a.649.2 8
25.23 odd 20 3750.2.c.c.1249.1 4
75.29 odd 10 450.2.h.b.271.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.2.g.b.31.1 4 5.4 even 2
150.2.g.b.121.1 yes 4 25.4 even 10
450.2.h.b.181.1 4 15.14 odd 2
450.2.h.b.271.1 4 75.29 odd 10
750.2.g.a.151.1 4 1.1 even 1 trivial
750.2.g.a.601.1 4 25.21 even 5 inner
750.2.h.a.349.1 8 5.2 odd 4
750.2.h.a.349.2 8 5.3 odd 4
750.2.h.a.649.1 8 25.3 odd 20
750.2.h.a.649.2 8 25.22 odd 20
3750.2.a.b.1.1 2 25.14 even 10
3750.2.a.g.1.1 2 25.11 even 5
3750.2.c.c.1249.1 4 25.23 odd 20
3750.2.c.c.1249.3 4 25.2 odd 20