Properties

Label 170.2.k.b.111.3
Level $170$
Weight $2$
Character 170.111
Analytic conductor $1.357$
Analytic rank $0$
Dimension $16$
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] = [170,2,Mod(111,170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(170, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("170.111");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 170 = 2 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 170.k (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.35745683436\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{8})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 28x^{14} + 286x^{12} + 1412x^{10} + 3709x^{8} + 5264x^{6} + 3780x^{4} + 1072x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 111.3
Root \(-2.47571i\) of defining polynomial
Character \(\chi\) \(=\) 170.111
Dual form 170.2.k.b.121.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(1.36338 + 0.564729i) q^{3} -1.00000i q^{4} +(0.382683 - 0.923880i) q^{5} +(1.36338 - 0.564729i) q^{6} +(1.35785 + 3.27815i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.581445 - 0.581445i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(1.36338 + 0.564729i) q^{3} -1.00000i q^{4} +(0.382683 - 0.923880i) q^{5} +(1.36338 - 0.564729i) q^{6} +(1.35785 + 3.27815i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.581445 - 0.581445i) q^{9} +(-0.382683 - 0.923880i) q^{10} +(-4.35013 + 1.80188i) q^{11} +(0.564729 - 1.36338i) q^{12} -5.47699i q^{13} +(3.27815 + 1.35785i) q^{14} +(1.04348 - 1.04348i) q^{15} -1.00000 q^{16} +(2.52894 + 3.25645i) q^{17} -0.822287 q^{18} +(0.857748 - 0.857748i) q^{19} +(-0.923880 - 0.382683i) q^{20} +5.23617i q^{21} +(-1.80188 + 4.35013i) q^{22} +(-5.28485 + 2.18906i) q^{23} +(-0.564729 - 1.36338i) q^{24} +(-0.707107 - 0.707107i) q^{25} +(-3.87282 - 3.87282i) q^{26} +(-2.15856 - 5.21121i) q^{27} +(3.27815 - 1.35785i) q^{28} +(-1.77710 + 4.29029i) q^{29} -1.47571i q^{30} +(6.72892 + 2.78721i) q^{31} +(-0.707107 + 0.707107i) q^{32} -6.94843 q^{33} +(4.09089 + 0.514430i) q^{34} +3.54824 q^{35} +(-0.581445 + 0.581445i) q^{36} +(-8.58444 - 3.55579i) q^{37} -1.21304i q^{38} +(3.09302 - 7.46720i) q^{39} +(-0.923880 + 0.382683i) q^{40} +(0.0547598 + 0.132202i) q^{41} +(3.70253 + 3.70253i) q^{42} +(-0.587013 - 0.587013i) q^{43} +(1.80188 + 4.35013i) q^{44} +(-0.759695 + 0.314676i) q^{45} +(-2.18906 + 5.28485i) q^{46} +5.85635i q^{47} +(-1.36338 - 0.564729i) q^{48} +(-3.95275 + 3.95275i) q^{49} -1.00000 q^{50} +(1.60888 + 5.86793i) q^{51} -5.47699 q^{52} +(6.54226 - 6.54226i) q^{53} +(-5.21121 - 2.15856i) q^{54} +4.70854i q^{55} +(1.35785 - 3.27815i) q^{56} +(1.65383 - 0.685038i) q^{57} +(1.77710 + 4.29029i) q^{58} +(-3.33507 - 3.33507i) q^{59} +(-1.04348 - 1.04348i) q^{60} +(4.76261 + 11.4980i) q^{61} +(6.72892 - 2.78721i) q^{62} +(1.11655 - 2.69558i) q^{63} +1.00000i q^{64} +(-5.06008 - 2.09595i) q^{65} +(-4.91328 + 4.91328i) q^{66} +8.66703 q^{67} +(3.25645 - 2.52894i) q^{68} -8.44146 q^{69} +(2.50899 - 2.50899i) q^{70} +(4.75235 + 1.96849i) q^{71} +0.822287i q^{72} +(6.17351 - 14.9042i) q^{73} +(-8.58444 + 3.55579i) q^{74} +(-0.564729 - 1.36338i) q^{75} +(-0.857748 - 0.857748i) q^{76} +(-11.8137 - 11.8137i) q^{77} +(-3.09302 - 7.46720i) q^{78} +(9.34587 - 3.87118i) q^{79} +(-0.382683 + 0.923880i) q^{80} -5.85698i q^{81} +(0.132202 + 0.0547598i) q^{82} +(2.40841 - 2.40841i) q^{83} +5.23617 q^{84} +(3.97635 - 1.09024i) q^{85} -0.830161 q^{86} +(-4.84570 + 4.84570i) q^{87} +(4.35013 + 1.80188i) q^{88} -2.24175i q^{89} +(-0.314676 + 0.759695i) q^{90} +(17.9544 - 7.43696i) q^{91} +(2.18906 + 5.28485i) q^{92} +(7.60004 + 7.60004i) q^{93} +(4.14106 + 4.14106i) q^{94} +(-0.464210 - 1.12070i) q^{95} +(-1.36338 + 0.564729i) q^{96} +(1.66675 - 4.02389i) q^{97} +5.59004i q^{98} +(3.57705 + 1.48166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 8 q^{11} - 8 q^{14} + 8 q^{15} - 16 q^{16} + 8 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{27} - 8 q^{28} + 8 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{34} + 16 q^{35} - 8 q^{37} - 32 q^{39} - 32 q^{41} + 32 q^{42} - 16 q^{43} + 8 q^{44} - 16 q^{45} - 24 q^{46} - 8 q^{49} - 16 q^{50} - 8 q^{51} - 8 q^{52} - 40 q^{53} - 16 q^{57} - 8 q^{58} + 16 q^{59} - 8 q^{60} - 24 q^{61} + 32 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} + 16 q^{67} - 16 q^{69} + 8 q^{70} + 8 q^{71} + 16 q^{73} - 8 q^{74} + 24 q^{77} + 32 q^{78} + 40 q^{79} + 16 q^{82} + 32 q^{83} + 16 q^{84} + 16 q^{85} - 32 q^{87} + 8 q^{88} + 24 q^{91} + 24 q^{92} - 32 q^{93} + 40 q^{94} + 16 q^{95} + 24 q^{97} - 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).

\(n\) \(71\) \(137\)
\(\chi(n)\) \(e\left(\frac{1}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 1.36338 + 0.564729i 0.787145 + 0.326046i 0.739795 0.672832i \(-0.234922\pi\)
0.0473502 + 0.998878i \(0.484922\pi\)
\(4\) 1.00000i 0.500000i
\(5\) 0.382683 0.923880i 0.171141 0.413171i
\(6\) 1.36338 0.564729i 0.556596 0.230550i
\(7\) 1.35785 + 3.27815i 0.513221 + 1.23902i 0.941999 + 0.335615i \(0.108944\pi\)
−0.428779 + 0.903410i \(0.641056\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −0.581445 0.581445i −0.193815 0.193815i
\(10\) −0.382683 0.923880i −0.121015 0.292156i
\(11\) −4.35013 + 1.80188i −1.31161 + 0.543288i −0.925354 0.379103i \(-0.876232\pi\)
−0.386258 + 0.922391i \(0.626232\pi\)
\(12\) 0.564729 1.36338i 0.163023 0.393573i
\(13\) 5.47699i 1.51904i −0.650481 0.759522i \(-0.725433\pi\)
0.650481 0.759522i \(-0.274567\pi\)
\(14\) 3.27815 + 1.35785i 0.876123 + 0.362902i
\(15\) 1.04348 1.04348i 0.269426 0.269426i
\(16\) −1.00000 −0.250000
\(17\) 2.52894 + 3.25645i 0.613358 + 0.789805i
\(18\) −0.822287 −0.193815
\(19\) 0.857748 0.857748i 0.196781 0.196781i −0.601838 0.798619i \(-0.705565\pi\)
0.798619 + 0.601838i \(0.205565\pi\)
\(20\) −0.923880 0.382683i −0.206586 0.0855706i
\(21\) 5.23617i 1.14263i
\(22\) −1.80188 + 4.35013i −0.384162 + 0.927450i
\(23\) −5.28485 + 2.18906i −1.10197 + 0.456450i −0.858165 0.513375i \(-0.828395\pi\)
−0.243803 + 0.969825i \(0.578395\pi\)
\(24\) −0.564729 1.36338i −0.115275 0.278298i
\(25\) −0.707107 0.707107i −0.141421 0.141421i
\(26\) −3.87282 3.87282i −0.759522 0.759522i
\(27\) −2.15856 5.21121i −0.415414 1.00290i
\(28\) 3.27815 1.35785i 0.619512 0.256610i
\(29\) −1.77710 + 4.29029i −0.329999 + 0.796687i 0.668593 + 0.743629i \(0.266897\pi\)
−0.998591 + 0.0530586i \(0.983103\pi\)
\(30\) 1.47571i 0.269426i
\(31\) 6.72892 + 2.78721i 1.20855 + 0.500598i 0.893752 0.448561i \(-0.148063\pi\)
0.314798 + 0.949159i \(0.398063\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −6.94843 −1.20957
\(34\) 4.09089 + 0.514430i 0.701581 + 0.0882239i
\(35\) 3.54824 0.599763
\(36\) −0.581445 + 0.581445i −0.0969075 + 0.0969075i
\(37\) −8.58444 3.55579i −1.41127 0.584569i −0.458622 0.888631i \(-0.651657\pi\)
−0.952652 + 0.304063i \(0.901657\pi\)
\(38\) 1.21304i 0.196781i
\(39\) 3.09302 7.46720i 0.495279 1.19571i
\(40\) −0.923880 + 0.382683i −0.146078 + 0.0605076i
\(41\) 0.0547598 + 0.132202i 0.00855205 + 0.0206465i 0.928098 0.372336i \(-0.121443\pi\)
−0.919546 + 0.392983i \(0.871443\pi\)
\(42\) 3.70253 + 3.70253i 0.571313 + 0.571313i
\(43\) −0.587013 0.587013i −0.0895186 0.0895186i 0.660929 0.750448i \(-0.270162\pi\)
−0.750448 + 0.660929i \(0.770162\pi\)
\(44\) 1.80188 + 4.35013i 0.271644 + 0.655806i
\(45\) −0.759695 + 0.314676i −0.113249 + 0.0469091i
\(46\) −2.18906 + 5.28485i −0.322759 + 0.779209i
\(47\) 5.85635i 0.854236i 0.904196 + 0.427118i \(0.140471\pi\)
−0.904196 + 0.427118i \(0.859529\pi\)
\(48\) −1.36338 0.564729i −0.196786 0.0815116i
\(49\) −3.95275 + 3.95275i −0.564679 + 0.564679i
\(50\) −1.00000 −0.141421
\(51\) 1.60888 + 5.86793i 0.225288 + 0.821675i
\(52\) −5.47699 −0.759522
\(53\) 6.54226 6.54226i 0.898648 0.898648i −0.0966687 0.995317i \(-0.530819\pi\)
0.995317 + 0.0966687i \(0.0308187\pi\)
\(54\) −5.21121 2.15856i −0.709156 0.293742i
\(55\) 4.70854i 0.634900i
\(56\) 1.35785 3.27815i 0.181451 0.438061i
\(57\) 1.65383 0.685038i 0.219055 0.0907355i
\(58\) 1.77710 + 4.29029i 0.233344 + 0.563343i
\(59\) −3.33507 3.33507i −0.434189 0.434189i 0.455861 0.890051i \(-0.349331\pi\)
−0.890051 + 0.455861i \(0.849331\pi\)
\(60\) −1.04348 1.04348i −0.134713 0.134713i
\(61\) 4.76261 + 11.4980i 0.609790 + 1.47216i 0.863229 + 0.504812i \(0.168438\pi\)
−0.253439 + 0.967351i \(0.581562\pi\)
\(62\) 6.72892 2.78721i 0.854574 0.353976i
\(63\) 1.11655 2.69558i 0.140672 0.339611i
\(64\) 1.00000i 0.125000i
\(65\) −5.06008 2.09595i −0.627626 0.259971i
\(66\) −4.91328 + 4.91328i −0.604783 + 0.604783i
\(67\) 8.66703 1.05885 0.529423 0.848358i \(-0.322408\pi\)
0.529423 + 0.848358i \(0.322408\pi\)
\(68\) 3.25645 2.52894i 0.394903 0.306679i
\(69\) −8.44146 −1.01623
\(70\) 2.50899 2.50899i 0.299881 0.299881i
\(71\) 4.75235 + 1.96849i 0.564000 + 0.233617i 0.646421 0.762981i \(-0.276265\pi\)
−0.0824206 + 0.996598i \(0.526265\pi\)
\(72\) 0.822287i 0.0969075i
\(73\) 6.17351 14.9042i 0.722555 1.74440i 0.0566159 0.998396i \(-0.481969\pi\)
0.665939 0.746006i \(-0.268031\pi\)
\(74\) −8.58444 + 3.55579i −0.997921 + 0.413353i
\(75\) −0.564729 1.36338i −0.0652093 0.157429i
\(76\) −0.857748 0.857748i −0.0983905 0.0983905i
\(77\) −11.8137 11.8137i −1.34629 1.34629i
\(78\) −3.09302 7.46720i −0.350215 0.845494i
\(79\) 9.34587 3.87118i 1.05149 0.435542i 0.211068 0.977471i \(-0.432306\pi\)
0.840424 + 0.541929i \(0.182306\pi\)
\(80\) −0.382683 + 0.923880i −0.0427853 + 0.103293i
\(81\) 5.85698i 0.650776i
\(82\) 0.132202 + 0.0547598i 0.0145993 + 0.00604721i
\(83\) 2.40841 2.40841i 0.264358 0.264358i −0.562464 0.826822i \(-0.690147\pi\)
0.826822 + 0.562464i \(0.190147\pi\)
\(84\) 5.23617 0.571313
\(85\) 3.97635 1.09024i 0.431296 0.118254i
\(86\) −0.830161 −0.0895186
\(87\) −4.84570 + 4.84570i −0.519514 + 0.519514i
\(88\) 4.35013 + 1.80188i 0.463725 + 0.192081i
\(89\) 2.24175i 0.237625i −0.992917 0.118813i \(-0.962091\pi\)
0.992917 0.118813i \(-0.0379088\pi\)
\(90\) −0.314676 + 0.759695i −0.0331697 + 0.0800788i
\(91\) 17.9544 7.43696i 1.88213 0.779605i
\(92\) 2.18906 + 5.28485i 0.228225 + 0.550984i
\(93\) 7.60004 + 7.60004i 0.788087 + 0.788087i
\(94\) 4.14106 + 4.14106i 0.427118 + 0.427118i
\(95\) −0.464210 1.12070i −0.0476269 0.114982i
\(96\) −1.36338 + 0.564729i −0.139149 + 0.0576374i
\(97\) 1.66675 4.02389i 0.169233 0.408564i −0.816395 0.577493i \(-0.804031\pi\)
0.985628 + 0.168929i \(0.0540309\pi\)
\(98\) 5.59004i 0.564679i
\(99\) 3.57705 + 1.48166i 0.359507 + 0.148913i
\(100\) −0.707107 + 0.707107i −0.0707107 + 0.0707107i
\(101\) −10.7393 −1.06860 −0.534301 0.845294i \(-0.679425\pi\)
−0.534301 + 0.845294i \(0.679425\pi\)
\(102\) 5.28690 + 3.01160i 0.523482 + 0.298193i
\(103\) −7.43306 −0.732401 −0.366200 0.930536i \(-0.619342\pi\)
−0.366200 + 0.930536i \(0.619342\pi\)
\(104\) −3.87282 + 3.87282i −0.379761 + 0.379761i
\(105\) 4.83759 + 2.00380i 0.472101 + 0.195550i
\(106\) 9.25215i 0.898648i
\(107\) 6.01999 14.5335i 0.581974 1.40501i −0.309046 0.951047i \(-0.600010\pi\)
0.891020 0.453963i \(-0.149990\pi\)
\(108\) −5.21121 + 2.15856i −0.501449 + 0.207707i
\(109\) 2.46089 + 5.94112i 0.235711 + 0.569056i 0.996830 0.0795553i \(-0.0253500\pi\)
−0.761120 + 0.648611i \(0.775350\pi\)
\(110\) 3.32944 + 3.32944i 0.317450 + 0.317450i
\(111\) −9.69577 9.69577i −0.920281 0.920281i
\(112\) −1.35785 3.27815i −0.128305 0.309756i
\(113\) −8.90782 + 3.68974i −0.837978 + 0.347102i −0.760056 0.649858i \(-0.774828\pi\)
−0.0779218 + 0.996959i \(0.524828\pi\)
\(114\) 0.685038 1.65383i 0.0641597 0.154895i
\(115\) 5.72028i 0.533419i
\(116\) 4.29029 + 1.77710i 0.398344 + 0.164999i
\(117\) −3.18457 + 3.18457i −0.294414 + 0.294414i
\(118\) −4.71650 −0.434189
\(119\) −7.24121 + 12.7120i −0.663800 + 1.16531i
\(120\) −1.47571 −0.134713
\(121\) 7.89864 7.89864i 0.718058 0.718058i
\(122\) 11.4980 + 4.76261i 1.04098 + 0.431187i
\(123\) 0.211165i 0.0190401i
\(124\) 2.78721 6.72892i 0.250299 0.604275i
\(125\) −0.923880 + 0.382683i −0.0826343 + 0.0342282i
\(126\) −1.11655 2.69558i −0.0994699 0.240142i
\(127\) 2.26692 + 2.26692i 0.201157 + 0.201157i 0.800496 0.599339i \(-0.204570\pi\)
−0.599339 + 0.800496i \(0.704570\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) −0.468816 1.13182i −0.0412769 0.0996513i
\(130\) −5.06008 + 2.09595i −0.443798 + 0.183827i
\(131\) −1.36747 + 3.30136i −0.119476 + 0.288441i −0.972292 0.233771i \(-0.924893\pi\)
0.852815 + 0.522213i \(0.174893\pi\)
\(132\) 6.94843i 0.604783i
\(133\) 3.97653 + 1.64713i 0.344808 + 0.142824i
\(134\) 6.12852 6.12852i 0.529423 0.529423i
\(135\) −5.64058 −0.485464
\(136\) 0.514430 4.09089i 0.0441120 0.350791i
\(137\) 3.30950 0.282750 0.141375 0.989956i \(-0.454848\pi\)
0.141375 + 0.989956i \(0.454848\pi\)
\(138\) −5.96902 + 5.96902i −0.508116 + 0.508116i
\(139\) −1.66295 0.688816i −0.141049 0.0584246i 0.311042 0.950396i \(-0.399322\pi\)
−0.452092 + 0.891972i \(0.649322\pi\)
\(140\) 3.54824i 0.299881i
\(141\) −3.30725 + 7.98440i −0.278520 + 0.672408i
\(142\) 4.75235 1.96849i 0.398808 0.165192i
\(143\) 9.86889 + 23.8256i 0.825278 + 1.99240i
\(144\) 0.581445 + 0.581445i 0.0484538 + 0.0484538i
\(145\) 3.28365 + 3.28365i 0.272692 + 0.272692i
\(146\) −6.17351 14.9042i −0.510924 1.23348i
\(147\) −7.62132 + 3.15686i −0.628596 + 0.260373i
\(148\) −3.55579 + 8.58444i −0.292284 + 0.705637i
\(149\) 4.16768i 0.341430i 0.985320 + 0.170715i \(0.0546077\pi\)
−0.985320 + 0.170715i \(0.945392\pi\)
\(150\) −1.36338 0.564729i −0.111319 0.0461099i
\(151\) −3.24744 + 3.24744i −0.264273 + 0.264273i −0.826788 0.562514i \(-0.809834\pi\)
0.562514 + 0.826788i \(0.309834\pi\)
\(152\) −1.21304 −0.0983905
\(153\) 0.423009 3.36389i 0.0341982 0.271954i
\(154\) −16.7071 −1.34629
\(155\) 5.15010 5.15010i 0.413666 0.413666i
\(156\) −7.46720 3.09302i −0.597854 0.247639i
\(157\) 15.5482i 1.24088i 0.784253 + 0.620442i \(0.213047\pi\)
−0.784253 + 0.620442i \(0.786953\pi\)
\(158\) 3.87118 9.34587i 0.307975 0.743517i
\(159\) 12.6142 5.22495i 1.00037 0.414366i
\(160\) 0.382683 + 0.923880i 0.0302538 + 0.0730391i
\(161\) −14.3521 14.3521i −1.13111 1.13111i
\(162\) −4.14151 4.14151i −0.325388 0.325388i
\(163\) 3.87956 + 9.36608i 0.303870 + 0.733608i 0.999879 + 0.0155742i \(0.00495762\pi\)
−0.696008 + 0.718034i \(0.745042\pi\)
\(164\) 0.132202 0.0547598i 0.0103232 0.00427602i
\(165\) −2.65905 + 6.41951i −0.207007 + 0.499758i
\(166\) 3.40601i 0.264358i
\(167\) −11.5038 4.76501i −0.890187 0.368728i −0.109748 0.993959i \(-0.535004\pi\)
−0.780439 + 0.625232i \(0.785004\pi\)
\(168\) 3.70253 3.70253i 0.285657 0.285657i
\(169\) −16.9974 −1.30750
\(170\) 2.04079 3.58262i 0.156521 0.274775i
\(171\) −0.997467 −0.0762782
\(172\) −0.587013 + 0.587013i −0.0447593 + 0.0447593i
\(173\) −3.27672 1.35726i −0.249125 0.103191i 0.254627 0.967039i \(-0.418047\pi\)
−0.503752 + 0.863849i \(0.668047\pi\)
\(174\) 6.85286i 0.519514i
\(175\) 1.35785 3.27815i 0.102644 0.247805i
\(176\) 4.35013 1.80188i 0.327903 0.135822i
\(177\) −2.66354 6.43037i −0.200204 0.483336i
\(178\) −1.58516 1.58516i −0.118813 0.118813i
\(179\) −9.26485 9.26485i −0.692487 0.692487i 0.270291 0.962779i \(-0.412880\pi\)
−0.962779 + 0.270291i \(0.912880\pi\)
\(180\) 0.314676 + 0.759695i 0.0234545 + 0.0566243i
\(181\) 1.68821 0.699281i 0.125484 0.0519772i −0.319058 0.947735i \(-0.603366\pi\)
0.444542 + 0.895758i \(0.353366\pi\)
\(182\) 7.43696 17.9544i 0.551264 1.33087i
\(183\) 18.3656i 1.35763i
\(184\) 5.28485 + 2.18906i 0.389604 + 0.161379i
\(185\) −6.57025 + 6.57025i −0.483054 + 0.483054i
\(186\) 10.7481 0.788087
\(187\) −16.8689 9.60913i −1.23358 0.702689i
\(188\) 5.85635 0.427118
\(189\) 14.1521 14.1521i 1.02942 1.02942i
\(190\) −1.12070 0.464210i −0.0813043 0.0336773i
\(191\) 16.8319i 1.21791i 0.793205 + 0.608955i \(0.208411\pi\)
−0.793205 + 0.608955i \(0.791589\pi\)
\(192\) −0.564729 + 1.36338i −0.0407558 + 0.0983932i
\(193\) −5.38504 + 2.23056i −0.387624 + 0.160559i −0.567980 0.823042i \(-0.692275\pi\)
0.180356 + 0.983601i \(0.442275\pi\)
\(194\) −1.66675 4.02389i −0.119666 0.288899i
\(195\) −5.71515 5.71515i −0.409270 0.409270i
\(196\) 3.95275 + 3.95275i 0.282340 + 0.282340i
\(197\) 1.34760 + 3.25339i 0.0960123 + 0.231794i 0.964587 0.263763i \(-0.0849638\pi\)
−0.868575 + 0.495557i \(0.834964\pi\)
\(198\) 3.57705 1.48166i 0.254210 0.105297i
\(199\) −6.42910 + 15.5212i −0.455747 + 1.10027i 0.514356 + 0.857577i \(0.328031\pi\)
−0.970103 + 0.242694i \(0.921969\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 11.8164 + 4.89452i 0.833466 + 0.345233i
\(202\) −7.59384 + 7.59384i −0.534301 + 0.534301i
\(203\) −16.4773 −1.15648
\(204\) 5.86793 1.60888i 0.410837 0.112644i
\(205\) 0.143094 0.00999414
\(206\) −5.25597 + 5.25597i −0.366200 + 0.366200i
\(207\) 4.34567 + 1.80003i 0.302045 + 0.125111i
\(208\) 5.47699i 0.379761i
\(209\) −2.18575 + 5.27687i −0.151192 + 0.365009i
\(210\) 4.83759 2.00380i 0.333826 0.138275i
\(211\) −8.73280 21.0828i −0.601191 1.45140i −0.872357 0.488870i \(-0.837409\pi\)
0.271166 0.962533i \(-0.412591\pi\)
\(212\) −6.54226 6.54226i −0.449324 0.449324i
\(213\) 5.36758 + 5.36758i 0.367780 + 0.367780i
\(214\) −6.01999 14.5335i −0.411518 0.993492i
\(215\) −0.766969 + 0.317689i −0.0523068 + 0.0216662i
\(216\) −2.15856 + 5.21121i −0.146871 + 0.354578i
\(217\) 25.8431i 1.75434i
\(218\) 5.94112 + 2.46089i 0.402383 + 0.166673i
\(219\) 16.8336 16.8336i 1.13751 1.13751i
\(220\) 4.70854 0.317450
\(221\) 17.8356 13.8510i 1.19975 0.931717i
\(222\) −13.7119 −0.920281
\(223\) −6.41246 + 6.41246i −0.429410 + 0.429410i −0.888427 0.459017i \(-0.848202\pi\)
0.459017 + 0.888427i \(0.348202\pi\)
\(224\) −3.27815 1.35785i −0.219031 0.0907255i
\(225\) 0.822287i 0.0548192i
\(226\) −3.68974 + 8.90782i −0.245438 + 0.592540i
\(227\) 14.5491 6.02643i 0.965658 0.399988i 0.156564 0.987668i \(-0.449958\pi\)
0.809094 + 0.587679i \(0.199958\pi\)
\(228\) −0.685038 1.65383i −0.0453678 0.109527i
\(229\) 14.2262 + 14.2262i 0.940092 + 0.940092i 0.998304 0.0582124i \(-0.0185401\pi\)
−0.0582124 + 0.998304i \(0.518540\pi\)
\(230\) 4.04485 + 4.04485i 0.266710 + 0.266710i
\(231\) −9.43496 22.7780i −0.620775 1.49868i
\(232\) 4.29029 1.77710i 0.281672 0.116672i
\(233\) −7.37613 + 17.8076i −0.483227 + 1.16661i 0.474841 + 0.880071i \(0.342505\pi\)
−0.958068 + 0.286541i \(0.907495\pi\)
\(234\) 4.50366i 0.294414i
\(235\) 5.41056 + 2.24113i 0.352946 + 0.146195i
\(236\) −3.33507 + 3.33507i −0.217095 + 0.217095i
\(237\) 14.9281 0.969684
\(238\) 3.86845 + 14.1091i 0.250755 + 0.914555i
\(239\) 14.2040 0.918778 0.459389 0.888235i \(-0.348068\pi\)
0.459389 + 0.888235i \(0.348068\pi\)
\(240\) −1.04348 + 1.04348i −0.0673565 + 0.0673565i
\(241\) −4.22633 1.75060i −0.272242 0.112766i 0.242386 0.970180i \(-0.422070\pi\)
−0.514628 + 0.857414i \(0.672070\pi\)
\(242\) 11.1704i 0.718058i
\(243\) −3.16806 + 7.64838i −0.203231 + 0.490644i
\(244\) 11.4980 4.76261i 0.736082 0.304895i
\(245\) 2.13922 + 5.16452i 0.136669 + 0.329949i
\(246\) 0.149316 + 0.149316i 0.00952007 + 0.00952007i
\(247\) −4.69788 4.69788i −0.298919 0.298919i
\(248\) −2.78721 6.72892i −0.176988 0.427287i
\(249\) 4.64367 1.92347i 0.294281 0.121895i
\(250\) −0.382683 + 0.923880i −0.0242030 + 0.0584313i
\(251\) 9.00712i 0.568524i 0.958747 + 0.284262i \(0.0917486\pi\)
−0.958747 + 0.284262i \(0.908251\pi\)
\(252\) −2.69558 1.11655i −0.169806 0.0703358i
\(253\) 19.0453 19.0453i 1.19737 1.19737i
\(254\) 3.20591 0.201157
\(255\) 6.03695 + 0.759148i 0.378049 + 0.0475397i
\(256\) 1.00000 0.0625000
\(257\) 20.2643 20.2643i 1.26405 1.26405i 0.314938 0.949112i \(-0.398016\pi\)
0.949112 0.314938i \(-0.101984\pi\)
\(258\) −1.13182 0.468816i −0.0704641 0.0291872i
\(259\) 32.9693i 2.04862i
\(260\) −2.09595 + 5.06008i −0.129986 + 0.313813i
\(261\) 3.52785 1.46129i 0.218369 0.0904513i
\(262\) 1.36747 + 3.30136i 0.0844825 + 0.203959i
\(263\) −4.27498 4.27498i −0.263606 0.263606i 0.562911 0.826517i \(-0.309681\pi\)
−0.826517 + 0.562911i \(0.809681\pi\)
\(264\) 4.91328 + 4.91328i 0.302392 + 0.302392i
\(265\) −3.54064 8.54787i −0.217500 0.525091i
\(266\) 3.97653 1.64713i 0.243816 0.100992i
\(267\) 1.26598 3.05635i 0.0774769 0.187046i
\(268\) 8.66703i 0.529423i
\(269\) −15.6073 6.46477i −0.951596 0.394164i −0.147765 0.989022i \(-0.547208\pi\)
−0.803830 + 0.594858i \(0.797208\pi\)
\(270\) −3.98849 + 3.98849i −0.242732 + 0.242732i
\(271\) −22.9305 −1.39293 −0.696463 0.717593i \(-0.745244\pi\)
−0.696463 + 0.717593i \(0.745244\pi\)
\(272\) −2.52894 3.25645i −0.153339 0.197451i
\(273\) 28.6785 1.73570
\(274\) 2.34017 2.34017i 0.141375 0.141375i
\(275\) 4.35013 + 1.80188i 0.262322 + 0.108658i
\(276\) 8.44146i 0.508116i
\(277\) 7.65435 18.4792i 0.459905 1.11031i −0.508530 0.861044i \(-0.669811\pi\)
0.968435 0.249265i \(-0.0801891\pi\)
\(278\) −1.66295 + 0.688816i −0.0997370 + 0.0413124i
\(279\) −2.29189 5.53311i −0.137212 0.331259i
\(280\) −2.50899 2.50899i −0.149941 0.149941i
\(281\) 16.4633 + 16.4633i 0.982118 + 0.982118i 0.999843 0.0177247i \(-0.00564226\pi\)
−0.0177247 + 0.999843i \(0.505642\pi\)
\(282\) 3.30725 + 7.98440i 0.196944 + 0.475464i
\(283\) −23.2363 + 9.62478i −1.38125 + 0.572134i −0.944816 0.327601i \(-0.893760\pi\)
−0.436437 + 0.899735i \(0.643760\pi\)
\(284\) 1.96849 4.75235i 0.116808 0.282000i
\(285\) 1.79009i 0.106036i
\(286\) 23.8256 + 9.86889i 1.40884 + 0.583560i
\(287\) −0.359022 + 0.359022i −0.0211924 + 0.0211924i
\(288\) 0.822287 0.0484538
\(289\) −4.20895 + 16.4707i −0.247585 + 0.968866i
\(290\) 4.64378 0.272692
\(291\) 4.54481 4.54481i 0.266422 0.266422i
\(292\) −14.9042 6.17351i −0.872201 0.361278i
\(293\) 25.5251i 1.49119i −0.666399 0.745595i \(-0.732165\pi\)
0.666399 0.745595i \(-0.267835\pi\)
\(294\) −3.15686 + 7.62132i −0.184112 + 0.444485i
\(295\) −4.35748 + 1.80493i −0.253702 + 0.105087i
\(296\) 3.55579 + 8.58444i 0.206676 + 0.498961i
\(297\) 18.7800 + 18.7800i 1.08972 + 1.08972i
\(298\) 2.94700 + 2.94700i 0.170715 + 0.170715i
\(299\) 11.9894 + 28.9451i 0.693368 + 1.67394i
\(300\) −1.36338 + 0.564729i −0.0787145 + 0.0326046i
\(301\) 1.12724 2.72139i 0.0649729 0.156858i
\(302\) 4.59258i 0.264273i
\(303\) −14.6417 6.06480i −0.841145 0.348414i
\(304\) −0.857748 + 0.857748i −0.0491952 + 0.0491952i
\(305\) 12.4453 0.712616
\(306\) −2.07951 2.67774i −0.118878 0.153076i
\(307\) −14.2382 −0.812616 −0.406308 0.913736i \(-0.633184\pi\)
−0.406308 + 0.913736i \(0.633184\pi\)
\(308\) −11.8137 + 11.8137i −0.673147 + 0.673147i
\(309\) −10.1341 4.19766i −0.576506 0.238797i
\(310\) 7.28334i 0.413666i
\(311\) −4.65012 + 11.2264i −0.263684 + 0.636590i −0.999161 0.0409602i \(-0.986958\pi\)
0.735477 + 0.677550i \(0.236958\pi\)
\(312\) −7.46720 + 3.09302i −0.422747 + 0.175108i
\(313\) −8.33854 20.1310i −0.471322 1.13787i −0.963579 0.267422i \(-0.913828\pi\)
0.492257 0.870450i \(-0.336172\pi\)
\(314\) 10.9943 + 10.9943i 0.620442 + 0.620442i
\(315\) −2.06311 2.06311i −0.116243 0.116243i
\(316\) −3.87118 9.34587i −0.217771 0.525746i
\(317\) 9.47130 3.92314i 0.531961 0.220346i −0.100501 0.994937i \(-0.532044\pi\)
0.632462 + 0.774591i \(0.282044\pi\)
\(318\) 5.22495 12.6142i 0.293001 0.707367i
\(319\) 21.8654i 1.22423i
\(320\) 0.923880 + 0.382683i 0.0516464 + 0.0213927i
\(321\) 16.4150 16.4150i 0.916197 0.916197i
\(322\) −20.2970 −1.13111
\(323\) 4.96241 + 0.624023i 0.276116 + 0.0347216i
\(324\) −5.85698 −0.325388
\(325\) −3.87282 + 3.87282i −0.214825 + 0.214825i
\(326\) 9.36608 + 3.87956i 0.518739 + 0.214869i
\(327\) 9.48972i 0.524783i
\(328\) 0.0547598 0.132202i 0.00302360 0.00729963i
\(329\) −19.1980 + 7.95207i −1.05842 + 0.438412i
\(330\) 2.65905 + 6.41951i 0.146376 + 0.353383i
\(331\) −0.209438 0.209438i −0.0115117 0.0115117i 0.701327 0.712839i \(-0.252591\pi\)
−0.712839 + 0.701327i \(0.752591\pi\)
\(332\) −2.40841 2.40841i −0.132179 0.132179i
\(333\) 2.92388 + 7.05888i 0.160228 + 0.386824i
\(334\) −11.5038 + 4.76501i −0.629457 + 0.260730i
\(335\) 3.31673 8.00729i 0.181212 0.437485i
\(336\) 5.23617i 0.285657i
\(337\) −12.9824 5.37748i −0.707196 0.292930i −5.22341e−5 1.00000i \(-0.500017\pi\)
−0.707144 + 0.707070i \(0.750017\pi\)
\(338\) −12.0190 + 12.0190i −0.653748 + 0.653748i
\(339\) −14.2284 −0.772782
\(340\) −1.09024 3.97635i −0.0591268 0.215648i
\(341\) −34.2939 −1.85712
\(342\) −0.705316 + 0.705316i −0.0381391 + 0.0381391i
\(343\) 4.62206 + 1.91452i 0.249568 + 0.103374i
\(344\) 0.830161i 0.0447593i
\(345\) −3.23041 + 7.79889i −0.173919 + 0.419878i
\(346\) −3.27672 + 1.35726i −0.176158 + 0.0729669i
\(347\) −4.26669 10.3007i −0.229048 0.552971i 0.767014 0.641631i \(-0.221742\pi\)
−0.996062 + 0.0886594i \(0.971742\pi\)
\(348\) 4.84570 + 4.84570i 0.259757 + 0.259757i
\(349\) −1.77671 1.77671i −0.0951051 0.0951051i 0.657953 0.753059i \(-0.271422\pi\)
−0.753059 + 0.657953i \(0.771422\pi\)
\(350\) −1.35785 3.27815i −0.0725804 0.175225i
\(351\) −28.5418 + 11.8224i −1.52345 + 0.631033i
\(352\) 1.80188 4.35013i 0.0960406 0.231862i
\(353\) 10.0823i 0.536629i 0.963331 + 0.268314i \(0.0864666\pi\)
−0.963331 + 0.268314i \(0.913533\pi\)
\(354\) −6.43037 2.66354i −0.341770 0.141566i
\(355\) 3.63729 3.63729i 0.193047 0.193047i
\(356\) −2.24175 −0.118813
\(357\) −17.0513 + 13.2420i −0.902452 + 0.700838i
\(358\) −13.1025 −0.692487
\(359\) −17.4429 + 17.4429i −0.920599 + 0.920599i −0.997072 0.0764723i \(-0.975634\pi\)
0.0764723 + 0.997072i \(0.475634\pi\)
\(360\) 0.759695 + 0.314676i 0.0400394 + 0.0165849i
\(361\) 17.5285i 0.922555i
\(362\) 0.699281 1.68821i 0.0367534 0.0887306i
\(363\) 15.2294 6.30823i 0.799337 0.331096i
\(364\) −7.43696 17.9544i −0.389803 0.941067i
\(365\) −11.4072 11.4072i −0.597078 0.597078i
\(366\) 12.9865 + 12.9865i 0.678813 + 0.678813i
\(367\) 11.3939 + 27.5072i 0.594755 + 1.43587i 0.878863 + 0.477073i \(0.158302\pi\)
−0.284108 + 0.958792i \(0.591698\pi\)
\(368\) 5.28485 2.18906i 0.275492 0.114112i
\(369\) 0.0450283 0.108708i 0.00234408 0.00565911i
\(370\) 9.29174i 0.483054i
\(371\) 30.3299 + 12.5631i 1.57465 + 0.652242i
\(372\) 7.60004 7.60004i 0.394043 0.394043i
\(373\) 20.8039 1.07718 0.538592 0.842567i \(-0.318956\pi\)
0.538592 + 0.842567i \(0.318956\pi\)
\(374\) −18.7228 + 5.13346i −0.968134 + 0.265445i
\(375\) −1.47571 −0.0762052
\(376\) 4.14106 4.14106i 0.213559 0.213559i
\(377\) 23.4979 + 9.73315i 1.21020 + 0.501283i
\(378\) 20.0142i 1.02942i
\(379\) 3.99706 9.64974i 0.205315 0.495674i −0.787359 0.616494i \(-0.788552\pi\)
0.992674 + 0.120820i \(0.0385524\pi\)
\(380\) −1.12070 + 0.464210i −0.0574908 + 0.0238135i
\(381\) 1.81047 + 4.37087i 0.0927533 + 0.223926i
\(382\) 11.9019 + 11.9019i 0.608955 + 0.608955i
\(383\) −14.2495 14.2495i −0.728113 0.728113i 0.242130 0.970244i \(-0.422154\pi\)
−0.970244 + 0.242130i \(0.922154\pi\)
\(384\) 0.564729 + 1.36338i 0.0288187 + 0.0695745i
\(385\) −15.4353 + 6.39351i −0.786656 + 0.325844i
\(386\) −2.23056 + 5.38504i −0.113532 + 0.274091i
\(387\) 0.682631i 0.0347001i
\(388\) −4.02389 1.66675i −0.204282 0.0846164i
\(389\) −13.9058 + 13.9058i −0.705051 + 0.705051i −0.965490 0.260440i \(-0.916133\pi\)
0.260440 + 0.965490i \(0.416133\pi\)
\(390\) −8.08244 −0.409270
\(391\) −20.4936 11.6739i −1.03641 0.590373i
\(392\) 5.59004 0.282340
\(393\) −3.72875 + 3.72875i −0.188090 + 0.188090i
\(394\) 3.25339 + 1.34760i 0.163903 + 0.0678909i
\(395\) 10.1159i 0.508986i
\(396\) 1.48166 3.57705i 0.0744564 0.179754i
\(397\) −22.1250 + 9.16446i −1.11042 + 0.459951i −0.861083 0.508465i \(-0.830213\pi\)
−0.249338 + 0.968416i \(0.580213\pi\)
\(398\) 6.42910 + 15.5212i 0.322262 + 0.778009i
\(399\) 4.49132 + 4.49132i 0.224847 + 0.224847i
\(400\) 0.707107 + 0.707107i 0.0353553 + 0.0353553i
\(401\) −8.81734 21.2869i −0.440317 1.06302i −0.975838 0.218497i \(-0.929885\pi\)
0.535521 0.844522i \(-0.320115\pi\)
\(402\) 11.8164 4.89452i 0.589350 0.244117i
\(403\) 15.2655 36.8543i 0.760431 1.83584i
\(404\) 10.7393i 0.534301i
\(405\) −5.41114 2.24137i −0.268882 0.111375i
\(406\) −11.6512 + 11.6512i −0.578239 + 0.578239i
\(407\) 43.7505 2.16863
\(408\) 3.01160 5.28690i 0.149097 0.261741i
\(409\) 12.7488 0.630389 0.315195 0.949027i \(-0.397930\pi\)
0.315195 + 0.949027i \(0.397930\pi\)
\(410\) 0.101183 0.101183i 0.00499707 0.00499707i
\(411\) 4.51209 + 1.86897i 0.222565 + 0.0921895i
\(412\) 7.43306i 0.366200i
\(413\) 6.40432 15.4614i 0.315136 0.760806i
\(414\) 4.34567 1.80003i 0.213578 0.0884669i
\(415\) −1.30342 3.14674i −0.0639826 0.154468i
\(416\) 3.87282 + 3.87282i 0.189881 + 0.189881i
\(417\) −1.87823 1.87823i −0.0919773 0.0919773i
\(418\) 2.18575 + 5.27687i 0.106909 + 0.258100i
\(419\) 25.2883 10.4748i 1.23541 0.511725i 0.333136 0.942879i \(-0.391893\pi\)
0.902279 + 0.431153i \(0.141893\pi\)
\(420\) 2.00380 4.83759i 0.0977752 0.236050i
\(421\) 33.6813i 1.64153i −0.571268 0.820764i \(-0.693548\pi\)
0.571268 0.820764i \(-0.306452\pi\)
\(422\) −21.0828 8.73280i −1.02630 0.425106i
\(423\) 3.40514 3.40514i 0.165564 0.165564i
\(424\) −9.25215 −0.449324
\(425\) 0.514430 4.09089i 0.0249535 0.198437i
\(426\) 7.59090 0.367780
\(427\) −31.2251 + 31.2251i −1.51109 + 1.51109i
\(428\) −14.5335 6.01999i −0.702505 0.290987i
\(429\) 38.0565i 1.83739i
\(430\) −0.317689 + 0.766969i −0.0153203 + 0.0369865i
\(431\) −16.7963 + 6.95725i −0.809049 + 0.335119i −0.748575 0.663051i \(-0.769261\pi\)
−0.0604746 + 0.998170i \(0.519261\pi\)
\(432\) 2.15856 + 5.21121i 0.103854 + 0.250725i
\(433\) −5.73034 5.73034i −0.275382 0.275382i 0.555880 0.831262i \(-0.312381\pi\)
−0.831262 + 0.555880i \(0.812381\pi\)
\(434\) 18.2738 + 18.2738i 0.877170 + 0.877170i
\(435\) 2.62248 + 6.33122i 0.125738 + 0.303559i
\(436\) 5.94112 2.46089i 0.284528 0.117855i
\(437\) −2.65541 + 6.41073i −0.127026 + 0.306667i
\(438\) 23.8064i 1.13751i
\(439\) 22.1522 + 9.17574i 1.05727 + 0.437934i 0.842480 0.538727i \(-0.181095\pi\)
0.214786 + 0.976661i \(0.431095\pi\)
\(440\) 3.32944 3.32944i 0.158725 0.158725i
\(441\) 4.59662 0.218887
\(442\) 2.81753 22.4058i 0.134016 1.06573i
\(443\) 0.244075 0.0115964 0.00579819 0.999983i \(-0.498154\pi\)
0.00579819 + 0.999983i \(0.498154\pi\)
\(444\) −9.69577 + 9.69577i −0.460141 + 0.460141i
\(445\) −2.07111 0.857882i −0.0981800 0.0406675i
\(446\) 9.06859i 0.429410i
\(447\) −2.35361 + 5.68212i −0.111322 + 0.268755i
\(448\) −3.27815 + 1.35785i −0.154878 + 0.0641526i
\(449\) −0.0315454 0.0761574i −0.00148872 0.00359409i 0.923133 0.384480i \(-0.125619\pi\)
−0.924622 + 0.380886i \(0.875619\pi\)
\(450\) 0.581445 + 0.581445i 0.0274096 + 0.0274096i
\(451\) −0.476424 0.476424i −0.0224339 0.0224339i
\(452\) 3.68974 + 8.90782i 0.173551 + 0.418989i
\(453\) −6.26141 + 2.59356i −0.294187 + 0.121856i
\(454\) 6.02643 14.5491i 0.282835 0.682823i
\(455\) 19.4337i 0.911066i
\(456\) −1.65383 0.685038i −0.0774476 0.0320799i
\(457\) 17.2461 17.2461i 0.806737 0.806737i −0.177402 0.984139i \(-0.556769\pi\)
0.984139 + 0.177402i \(0.0567692\pi\)
\(458\) 20.1188 0.940092
\(459\) 11.5112 20.2081i 0.537297 0.943232i
\(460\) 5.72028 0.266710
\(461\) 20.5839 20.5839i 0.958687 0.958687i −0.0404924 0.999180i \(-0.512893\pi\)
0.999180 + 0.0404924i \(0.0128926\pi\)
\(462\) −22.7780 9.43496i −1.05973 0.438954i
\(463\) 27.9762i 1.30016i −0.759865 0.650081i \(-0.774735\pi\)
0.759865 0.650081i \(-0.225265\pi\)
\(464\) 1.77710 4.29029i 0.0824997 0.199172i
\(465\) 9.92992 4.11311i 0.460489 0.190741i
\(466\) 7.37613 + 17.8076i 0.341693 + 0.824919i
\(467\) 22.1173 + 22.1173i 1.02347 + 1.02347i 0.999718 + 0.0237504i \(0.00756069\pi\)
0.0237504 + 0.999718i \(0.492439\pi\)
\(468\) 3.18457 + 3.18457i 0.147207 + 0.147207i
\(469\) 11.7686 + 28.4118i 0.543422 + 1.31194i
\(470\) 5.41056 2.24113i 0.249570 0.103375i
\(471\) −8.78053 + 21.1981i −0.404586 + 0.976756i
\(472\) 4.71650i 0.217095i
\(473\) 3.61131 + 1.49585i 0.166048 + 0.0687793i
\(474\) 10.5558 10.5558i 0.484842 0.484842i
\(475\) −1.21304 −0.0556581
\(476\) 12.7120 + 7.24121i 0.582655 + 0.331900i
\(477\) −7.60792 −0.348343
\(478\) 10.0437 10.0437i 0.459389 0.459389i
\(479\) −11.1564 4.62112i −0.509748 0.211144i 0.112959 0.993600i \(-0.463967\pi\)
−0.622707 + 0.782455i \(0.713967\pi\)
\(480\) 1.47571i 0.0673565i
\(481\) −19.4751 + 47.0169i −0.887986 + 2.14379i
\(482\) −4.22633 + 1.75060i −0.192504 + 0.0797378i
\(483\) −11.4623 27.6724i −0.521552 1.25914i
\(484\) −7.89864 7.89864i −0.359029 0.359029i
\(485\) −3.07975 3.07975i −0.139844 0.139844i
\(486\) 3.16806 + 7.64838i 0.143706 + 0.346937i
\(487\) 4.63377 1.91937i 0.209976 0.0869749i −0.275217 0.961382i \(-0.588750\pi\)
0.485192 + 0.874407i \(0.338750\pi\)
\(488\) 4.76261 11.4980i 0.215593 0.520488i
\(489\) 14.9604i 0.676532i
\(490\) 5.16452 + 2.13922i 0.233309 + 0.0966399i
\(491\) −18.6988 + 18.6988i −0.843865 + 0.843865i −0.989359 0.145494i \(-0.953523\pi\)
0.145494 + 0.989359i \(0.453523\pi\)
\(492\) 0.211165 0.00952007
\(493\) −18.4653 + 5.06285i −0.831635 + 0.228019i
\(494\) −6.64381 −0.298919
\(495\) 2.73776 2.73776i 0.123053 0.123053i
\(496\) −6.72892 2.78721i −0.302138 0.125150i
\(497\) 18.2518i 0.818707i
\(498\) 1.92347 4.64367i 0.0861929 0.208088i
\(499\) −27.6595 + 11.4569i −1.23821 + 0.512882i −0.903154 0.429317i \(-0.858754\pi\)
−0.335053 + 0.942199i \(0.608754\pi\)
\(500\) 0.382683 + 0.923880i 0.0171141 + 0.0413171i
\(501\) −12.9930 12.9930i −0.580484 0.580484i
\(502\) 6.36899 + 6.36899i 0.284262 + 0.284262i
\(503\) 13.0499 + 31.5052i 0.581865 + 1.40475i 0.891120 + 0.453768i \(0.149920\pi\)
−0.309255 + 0.950979i \(0.600080\pi\)
\(504\) −2.69558 + 1.11655i −0.120071 + 0.0497349i
\(505\) −4.10976 + 9.92183i −0.182882 + 0.441516i
\(506\) 26.9342i 1.19737i
\(507\) −23.1739 9.59895i −1.02919 0.426304i
\(508\) 2.26692 2.26692i 0.100578 0.100578i
\(509\) 28.0939 1.24524 0.622620 0.782525i \(-0.286068\pi\)
0.622620 + 0.782525i \(0.286068\pi\)
\(510\) 4.80557 3.73197i 0.212794 0.165255i
\(511\) 57.2409 2.53219
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −6.32141 2.61841i −0.279097 0.115606i
\(514\) 28.6580i 1.26405i
\(515\) −2.84451 + 6.86725i −0.125344 + 0.302607i
\(516\) −1.13182 + 0.468816i −0.0498257 + 0.0206385i
\(517\) −10.5524 25.4758i −0.464096 1.12043i
\(518\) −23.3129 23.3129i −1.02431 1.02431i
\(519\) −3.70092 3.70092i −0.162452 0.162452i
\(520\) 2.09595 + 5.06008i 0.0919137 + 0.221899i
\(521\) 17.6215 7.29907i 0.772013 0.319778i 0.0383252 0.999265i \(-0.487798\pi\)
0.733687 + 0.679487i \(0.237798\pi\)
\(522\) 1.46129 3.52785i 0.0639587 0.154410i
\(523\) 6.69653i 0.292819i −0.989224 0.146409i \(-0.953228\pi\)
0.989224 0.146409i \(-0.0467717\pi\)
\(524\) 3.30136 + 1.36747i 0.144221 + 0.0597381i
\(525\) 3.70253 3.70253i 0.161592 0.161592i
\(526\) −6.04573 −0.263606
\(527\) 7.94061 + 28.9611i 0.345899 + 1.26157i
\(528\) 6.94843 0.302392
\(529\) 6.87423 6.87423i 0.298879 0.298879i
\(530\) −8.54787 3.54064i −0.371296 0.153796i
\(531\) 3.87832i 0.168305i
\(532\) 1.64713 3.97653i 0.0714122 0.172404i
\(533\) 0.724069 0.299919i 0.0313629 0.0129909i
\(534\) −1.26598 3.05635i −0.0547844 0.132261i
\(535\) −11.1235 11.1235i −0.480910 0.480910i
\(536\) −6.12852 6.12852i −0.264712 0.264712i
\(537\) −7.39935 17.8636i −0.319305 0.770871i
\(538\) −15.6073 + 6.46477i −0.672880 + 0.278716i
\(539\) 10.0726 24.3174i 0.433857 1.04742i
\(540\) 5.64058i 0.242732i
\(541\) −6.32639 2.62047i −0.271993 0.112663i 0.242518 0.970147i \(-0.422027\pi\)
−0.514511 + 0.857484i \(0.672027\pi\)
\(542\) −16.2143 + 16.2143i −0.696463 + 0.696463i
\(543\) 2.69657 0.115721
\(544\) −4.09089 0.514430i −0.175395 0.0220560i
\(545\) 6.43062 0.275458
\(546\) 20.2787 20.2787i 0.867850 0.867850i
\(547\) −3.26202 1.35117i −0.139474 0.0577719i 0.311855 0.950130i \(-0.399050\pi\)
−0.451329 + 0.892358i \(0.649050\pi\)
\(548\) 3.30950i 0.141375i
\(549\) 3.91624 9.45463i 0.167141 0.403514i
\(550\) 4.35013 1.80188i 0.185490 0.0768325i
\(551\) 2.15569 + 5.20429i 0.0918355 + 0.221710i
\(552\) 5.96902 + 5.96902i 0.254058 + 0.254058i
\(553\) 25.3806 + 25.3806i 1.07929 + 1.07929i
\(554\) −7.65435 18.4792i −0.325202 0.785108i
\(555\) −12.6681 + 5.24731i −0.537732 + 0.222736i
\(556\) −0.688816 + 1.66295i −0.0292123 + 0.0705247i
\(557\) 45.7591i 1.93888i −0.245338 0.969438i \(-0.578899\pi\)
0.245338 0.969438i \(-0.421101\pi\)
\(558\) −5.53311 2.29189i −0.234235 0.0970234i
\(559\) −3.21506 + 3.21506i −0.135983 + 0.135983i
\(560\) −3.54824 −0.149941
\(561\) −17.5721 22.6272i −0.741897 0.955322i
\(562\) 23.2826 0.982118
\(563\) −7.05601 + 7.05601i −0.297375 + 0.297375i −0.839985 0.542610i \(-0.817436\pi\)
0.542610 + 0.839985i \(0.317436\pi\)
\(564\) 7.98440 + 3.30725i 0.336204 + 0.139260i
\(565\) 9.64176i 0.405632i
\(566\) −9.62478 + 23.2363i −0.404560 + 0.976693i
\(567\) 19.2001 7.95293i 0.806327 0.333992i
\(568\) −1.96849 4.75235i −0.0825959 0.199404i
\(569\) −9.56020 9.56020i −0.400784 0.400784i 0.477725 0.878509i \(-0.341462\pi\)
−0.878509 + 0.477725i \(0.841462\pi\)
\(570\) −1.26579 1.26579i −0.0530179 0.0530179i
\(571\) 6.49469 + 15.6796i 0.271794 + 0.656169i 0.999560 0.0296562i \(-0.00944125\pi\)
−0.727766 + 0.685826i \(0.759441\pi\)
\(572\) 23.8256 9.86889i 0.996199 0.412639i
\(573\) −9.50543 + 22.9481i −0.397095 + 0.958673i
\(574\) 0.507734i 0.0211924i
\(575\) 5.28485 + 2.18906i 0.220394 + 0.0912900i
\(576\) 0.581445 0.581445i 0.0242269 0.0242269i
\(577\) −9.67374 −0.402723 −0.201361 0.979517i \(-0.564537\pi\)
−0.201361 + 0.979517i \(0.564537\pi\)
\(578\) 8.67039 + 14.6227i 0.360641 + 0.608226i
\(579\) −8.60150 −0.357466
\(580\) 3.28365 3.28365i 0.136346 0.136346i
\(581\) 11.1654 + 4.62487i 0.463220 + 0.191872i
\(582\) 6.42734i 0.266422i
\(583\) −16.6713 + 40.2480i −0.690453 + 1.66690i
\(584\) −14.9042 + 6.17351i −0.616739 + 0.255462i
\(585\) 1.72348 + 4.16084i 0.0712570 + 0.172030i
\(586\) −18.0489 18.0489i −0.745595 0.745595i
\(587\) 3.24694 + 3.24694i 0.134015 + 0.134015i 0.770932 0.636917i \(-0.219791\pi\)
−0.636917 + 0.770932i \(0.719791\pi\)
\(588\) 3.15686 + 7.62132i 0.130187 + 0.314298i
\(589\) 8.16245 3.38100i 0.336328 0.139312i
\(590\) −1.80493 + 4.35748i −0.0743077 + 0.179395i
\(591\) 5.19661i 0.213760i
\(592\) 8.58444 + 3.55579i 0.352818 + 0.146142i
\(593\) −0.550724 + 0.550724i −0.0226155 + 0.0226155i −0.718324 0.695709i \(-0.755090\pi\)
0.695709 + 0.718324i \(0.255090\pi\)
\(594\) 26.5589 1.08972
\(595\) 8.97329 + 11.5547i 0.367869 + 0.473696i
\(596\) 4.16768 0.170715
\(597\) −17.5306 + 17.5306i −0.717478 + 0.717478i
\(598\) 28.9451 + 11.9894i 1.18365 + 0.490285i
\(599\) 10.4846i 0.428391i 0.976791 + 0.214196i \(0.0687130\pi\)
−0.976791 + 0.214196i \(0.931287\pi\)
\(600\) −0.564729 + 1.36338i −0.0230550 + 0.0556596i
\(601\) −14.1755 + 5.87170i −0.578233 + 0.239512i −0.652579 0.757721i \(-0.726313\pi\)
0.0743464 + 0.997232i \(0.476313\pi\)
\(602\) −1.12724 2.72139i −0.0459428 0.110916i
\(603\) −5.03940 5.03940i −0.205220 0.205220i
\(604\) 3.24744 + 3.24744i 0.132137 + 0.132137i
\(605\) −4.27471 10.3201i −0.173792 0.419571i
\(606\) −14.6417 + 6.06480i −0.594779 + 0.246366i
\(607\) 8.27458 19.9766i 0.335855 0.810825i −0.662250 0.749283i \(-0.730398\pi\)
0.998105 0.0615418i \(-0.0196018\pi\)
\(608\) 1.21304i 0.0491952i
\(609\) −22.4647 9.30519i −0.910316 0.377065i
\(610\) 8.80016 8.80016i 0.356308 0.356308i
\(611\) 32.0752 1.29762
\(612\) −3.36389 0.423009i −0.135977 0.0170991i
\(613\) −18.6071 −0.751535 −0.375768 0.926714i \(-0.622621\pi\)
−0.375768 + 0.926714i \(0.622621\pi\)
\(614\) −10.0679 + 10.0679i −0.406308 + 0.406308i
\(615\) 0.195091 + 0.0808095i 0.00786684 + 0.00325855i
\(616\) 16.7071i 0.673147i
\(617\) 2.18286 5.26989i 0.0878787 0.212158i −0.873830 0.486231i \(-0.838371\pi\)
0.961709 + 0.274074i \(0.0883712\pi\)
\(618\) −10.1341 + 4.19766i −0.407651 + 0.168855i
\(619\) 11.1868 + 27.0073i 0.449635 + 1.08552i 0.972459 + 0.233075i \(0.0748787\pi\)
−0.522823 + 0.852441i \(0.675121\pi\)
\(620\) −5.15010 5.15010i −0.206833 0.206833i
\(621\) 22.8153 + 22.8153i 0.915546 + 0.915546i
\(622\) 4.65012 + 11.2264i 0.186453 + 0.450137i
\(623\) 7.34881 3.04397i 0.294424 0.121954i
\(624\) −3.09302 + 7.46720i −0.123820 + 0.298927i
\(625\) 1.00000i 0.0400000i
\(626\) −20.1310 8.33854i −0.804597 0.333275i
\(627\) −5.96000 + 5.96000i −0.238020 + 0.238020i
\(628\) 15.5482 0.620442
\(629\) −10.1303 36.9472i −0.403920 1.47318i
\(630\) −2.91768 −0.116243
\(631\) 30.9574 30.9574i 1.23239 1.23239i 0.269351 0.963042i \(-0.413191\pi\)
0.963042 0.269351i \(-0.0868092\pi\)
\(632\) −9.34587 3.87118i −0.371759 0.153987i
\(633\) 33.6755i 1.33848i
\(634\) 3.92314 9.47130i 0.155808 0.376153i
\(635\) 2.96188 1.22685i 0.117539 0.0486861i
\(636\) −5.22495 12.6142i −0.207183 0.500184i
\(637\) 21.6492 + 21.6492i 0.857773 + 0.857773i
\(638\) −15.4612 15.4612i −0.612115 0.612115i
\(639\) −1.61866 3.90780i −0.0640333 0.154590i
\(640\) 0.923880 0.382683i 0.0365195 0.0151269i
\(641\) −16.6913 + 40.2963i −0.659265 + 1.59161i 0.139676 + 0.990197i \(0.455394\pi\)
−0.798941 + 0.601410i \(0.794606\pi\)
\(642\) 23.2143i 0.916197i
\(643\) −5.12401 2.12244i −0.202071 0.0837007i 0.279353 0.960189i \(-0.409880\pi\)
−0.481424 + 0.876488i \(0.659880\pi\)
\(644\) −14.3521 + 14.3521i −0.565553 + 0.565553i
\(645\) −1.22508 −0.0482373
\(646\) 3.95020 3.06770i 0.155419 0.120697i
\(647\) −25.3893 −0.998155 −0.499078 0.866557i \(-0.666328\pi\)
−0.499078 + 0.866557i \(0.666328\pi\)
\(648\) −4.14151 + 4.14151i −0.162694 + 0.162694i
\(649\) 20.5174 + 8.49858i 0.805378 + 0.333598i
\(650\) 5.47699i 0.214825i
\(651\) −14.5943 + 35.2338i −0.571996 + 1.38092i
\(652\) 9.36608 3.87956i 0.366804 0.151935i
\(653\) 15.0457 + 36.3236i 0.588784 + 1.42145i 0.884666 + 0.466226i \(0.154387\pi\)
−0.295882 + 0.955225i \(0.595613\pi\)
\(654\) 6.71024 + 6.71024i 0.262391 + 0.262391i
\(655\) 2.52675 + 2.52675i 0.0987284 + 0.0987284i
\(656\) −0.0547598 0.132202i −0.00213801 0.00516162i
\(657\) −12.2555 + 5.07640i −0.478133 + 0.198049i
\(658\) −7.95207 + 19.1980i −0.310004 + 0.748415i
\(659\) 39.5179i 1.53940i −0.638408 0.769698i \(-0.720407\pi\)
0.638408 0.769698i \(-0.279593\pi\)
\(660\) 6.41951 + 2.65905i 0.249879 + 0.103503i
\(661\) −2.21986 + 2.21986i −0.0863427 + 0.0863427i −0.748959 0.662616i \(-0.769446\pi\)
0.662616 + 0.748959i \(0.269446\pi\)
\(662\) −0.296190 −0.0115117
\(663\) 32.1386 8.81183i 1.24816 0.342223i
\(664\) −3.40601 −0.132179
\(665\) 3.04350 3.04350i 0.118022 0.118022i
\(666\) 7.05888 + 2.92388i 0.273526 + 0.113298i
\(667\) 26.5637i 1.02855i
\(668\) −4.76501 + 11.5038i −0.184364 + 0.445093i
\(669\) −12.3639 + 5.12129i −0.478016 + 0.198001i
\(670\) −3.31673 8.00729i −0.128136 0.309349i
\(671\) −41.4359 41.4359i −1.59962 1.59962i
\(672\) −3.70253 3.70253i −0.142828 0.142828i
\(673\) −8.91195 21.5153i −0.343530 0.829355i −0.997353 0.0727079i \(-0.976836\pi\)
0.653823 0.756647i \(-0.273164\pi\)
\(674\) −12.9824 + 5.37748i −0.500063 + 0.207133i
\(675\) −2.15856 + 5.21121i −0.0830829 + 0.200580i
\(676\) 16.9974i 0.653748i
\(677\) −38.1349 15.7960i −1.46564 0.607089i −0.499782 0.866151i \(-0.666587\pi\)
−0.965861 + 0.259062i \(0.916587\pi\)
\(678\) −10.0610 + 10.0610i −0.386391 + 0.386391i
\(679\) 15.4541 0.593075
\(680\) −3.58262 2.04079i −0.137387 0.0782606i
\(681\) 23.2392 0.890528
\(682\) −24.2494 + 24.2494i −0.928559 + 0.928559i
\(683\) 5.77636 + 2.39265i 0.221026 + 0.0915521i 0.490449 0.871470i \(-0.336833\pi\)
−0.269423 + 0.963022i \(0.586833\pi\)
\(684\) 0.997467i 0.0381391i
\(685\) 1.26649 3.05758i 0.0483901 0.116824i
\(686\) 4.62206 1.91452i 0.176471 0.0730968i
\(687\) 11.3617 + 27.4295i 0.433476 + 1.04650i
\(688\) 0.587013 + 0.587013i 0.0223796 + 0.0223796i
\(689\) −35.8319 35.8319i −1.36509 1.36509i
\(690\) 3.23041 + 7.79889i 0.122980 + 0.296899i
\(691\) −29.6992 + 12.3018i −1.12981 + 0.467983i −0.867716 0.497060i \(-0.834413\pi\)
−0.262094 + 0.965042i \(0.584413\pi\)
\(692\) −1.35726 + 3.27672i −0.0515954 + 0.124562i
\(693\) 13.7380i 0.521864i
\(694\) −10.3007 4.26669i −0.391010 0.161961i
\(695\) −1.27277 + 1.27277i −0.0482788 + 0.0482788i
\(696\) 6.85286 0.259757
\(697\) −0.292025 + 0.512653i −0.0110612 + 0.0194181i
\(698\) −2.51265 −0.0951051
\(699\) −20.1129 + 20.1129i −0.760739 + 0.760739i
\(700\) −3.27815 1.35785i −0.123902 0.0513221i
\(701\) 12.7609i 0.481972i 0.970529 + 0.240986i \(0.0774708\pi\)
−0.970529 + 0.240986i \(0.922529\pi\)
\(702\) −11.8224 + 28.5418i −0.446208 + 1.07724i
\(703\) −10.4133 + 4.31332i −0.392744 + 0.162680i
\(704\) −1.80188 4.35013i −0.0679109 0.163952i
\(705\) 6.11100 + 6.11100i 0.230153 + 0.230153i
\(706\) 7.12929 + 7.12929i 0.268314 + 0.268314i
\(707\) −14.5824 35.2051i −0.548429 1.32402i
\(708\) −6.43037 + 2.66354i −0.241668 + 0.100102i
\(709\) 12.8274 30.9681i 0.481744 1.16303i −0.477036 0.878884i \(-0.658289\pi\)
0.958780 0.284149i \(-0.0917110\pi\)
\(710\) 5.14391i 0.193047i
\(711\) −7.68499 3.18323i −0.288210 0.119380i
\(712\) −1.58516 + 1.58516i −0.0594063 + 0.0594063i
\(713\) −41.6627 −1.56028
\(714\) −2.69364 + 21.4206i −0.100807 + 0.801645i
\(715\) 25.7886 0.964441
\(716\) −9.26485 + 9.26485i −0.346244 + 0.346244i
\(717\) 19.3653 + 8.02139i 0.723212 + 0.299564i
\(718\) 24.6679i 0.920599i
\(719\) −10.9707 + 26.4857i −0.409140 + 0.987750i 0.576225 + 0.817291i \(0.304525\pi\)
−0.985365 + 0.170459i \(0.945475\pi\)
\(720\) 0.759695 0.314676i 0.0283121 0.0117273i
\(721\) −10.0930 24.3667i −0.375883 0.907463i
\(722\) 12.3945 + 12.3945i 0.461277 + 0.461277i
\(723\) −4.77346 4.77346i −0.177527 0.177527i
\(724\) −0.699281 1.68821i −0.0259886 0.0627420i
\(725\) 4.29029 1.77710i 0.159337 0.0659998i
\(726\) 6.30823 15.2294i 0.234120 0.565216i
\(727\) 21.0302i 0.779966i −0.920822 0.389983i \(-0.872481\pi\)
0.920822 0.389983i \(-0.127519\pi\)
\(728\) −17.9544 7.43696i −0.665435 0.275632i
\(729\) −21.0631 + 21.0631i −0.780113 + 0.780113i
\(730\) −16.1322 −0.597078
\(731\) 0.427059 3.39610i 0.0157954 0.125609i
\(732\) 18.3656 0.678813
\(733\) −6.38248 + 6.38248i −0.235742 + 0.235742i −0.815084 0.579342i \(-0.803310\pi\)
0.579342 + 0.815084i \(0.303310\pi\)
\(734\) 27.5072 + 11.3939i 1.01531 + 0.420555i
\(735\) 8.24926i 0.304279i
\(736\) 2.18906 5.28485i 0.0806897 0.194802i
\(737\) −37.7027 + 15.6170i −1.38880 + 0.575258i
\(738\) −0.0450283 0.108708i −0.00165751 0.00400160i
\(739\) 10.1850 + 10.1850i 0.374662 + 0.374662i 0.869172 0.494510i \(-0.164653\pi\)
−0.494510 + 0.869172i \(0.664653\pi\)
\(740\) 6.57025 + 6.57025i 0.241527 + 0.241527i
\(741\) −3.75195 9.05801i −0.137831 0.332754i
\(742\) 30.3299 12.5631i 1.11345 0.461205i
\(743\) 12.6717 30.5921i 0.464879 1.12232i −0.501492 0.865162i \(-0.667215\pi\)
0.966370 0.257154i \(-0.0827847\pi\)
\(744\) 10.7481i 0.394043i
\(745\) 3.85044 + 1.59490i 0.141069 + 0.0584327i
\(746\) 14.7106 14.7106i 0.538592 0.538592i
\(747\) −2.80072 −0.102473
\(748\) −9.60913 + 16.8689i −0.351344 + 0.616789i
\(749\) 55.8174 2.03952
\(750\) −1.04348 + 1.04348i −0.0381026 + 0.0381026i
\(751\) −5.92242 2.45315i −0.216112 0.0895166i 0.272001 0.962297i \(-0.412315\pi\)
−0.488113 + 0.872780i \(0.662315\pi\)
\(752\) 5.85635i 0.213559i
\(753\) −5.08658 + 12.2801i −0.185365 + 0.447511i
\(754\) 23.4979 9.73315i 0.855743 0.354460i
\(755\) 1.75750 + 4.24299i 0.0639621 + 0.154418i
\(756\) −14.1521 14.1521i −0.514708 0.514708i
\(757\) 34.6660 + 34.6660i 1.25996 + 1.25996i 0.951112 + 0.308847i \(0.0999430\pi\)
0.308847 + 0.951112i \(0.400057\pi\)
\(758\) −3.99706 9.64974i −0.145180 0.350495i
\(759\) 36.7214 15.2105i 1.33290 0.552107i
\(760\) −0.464210 + 1.12070i −0.0168387 + 0.0406521i
\(761\) 42.6819i 1.54722i −0.633662 0.773610i \(-0.718449\pi\)
0.633662 0.773610i \(-0.281551\pi\)
\(762\) 4.37087 + 1.81047i 0.158340 + 0.0655865i
\(763\) −16.1344 + 16.1344i −0.584103 + 0.584103i
\(764\) 16.8319 0.608955
\(765\) −2.94595 1.67811i −0.106511 0.0606723i
\(766\) −20.1518 −0.728113
\(767\) −18.2662 + 18.2662i −0.659553 + 0.659553i
\(768\) 1.36338 + 0.564729i 0.0491966 + 0.0203779i
\(769\) 14.6429i 0.528035i −0.964518 0.264018i \(-0.914952\pi\)
0.964518 0.264018i \(-0.0850477\pi\)
\(770\) −6.39351 + 15.4353i −0.230406 + 0.556250i
\(771\) 39.0716 16.1840i 1.40713 0.582853i
\(772\) 2.23056 + 5.38504i 0.0802795 + 0.193812i
\(773\) 10.5010 + 10.5010i 0.377696 + 0.377696i 0.870270 0.492575i \(-0.163944\pi\)
−0.492575 + 0.870270i \(0.663944\pi\)
\(774\) 0.482693 + 0.482693i 0.0173500 + 0.0173500i
\(775\) −2.78721 6.72892i −0.100120 0.241710i
\(776\) −4.02389 + 1.66675i −0.144449 + 0.0598328i
\(777\) 18.6187 44.9496i 0.667944 1.61256i
\(778\) 19.6657i 0.705051i
\(779\) 0.160366 + 0.0664258i 0.00574571 + 0.00237995i
\(780\) −5.71515 + 5.71515i −0.204635 + 0.204635i
\(781\) −24.2203 −0.866670
\(782\) −22.7458 + 6.23650i −0.813390 + 0.223017i
\(783\) 26.1936 0.936083
\(784\) 3.95275 3.95275i 0.141170 0.141170i
\(785\) 14.3647 + 5.95005i 0.512698 + 0.212366i
\(786\) 5.27324i 0.188090i
\(787\) 8.22589 19.8591i 0.293221 0.707899i −0.706779 0.707435i \(-0.749852\pi\)
1.00000 0.000464022i \(-0.000147703\pi\)
\(788\) 3.25339 1.34760i 0.115897 0.0480061i
\(789\) −3.41420 8.24261i −0.121549 0.293445i
\(790\) −7.15302 7.15302i −0.254493 0.254493i
\(791\) −24.1911 24.1911i −0.860135 0.860135i
\(792\) −1.48166 3.57705i −0.0526486 0.127105i
\(793\) 62.9743 26.0848i 2.23628 0.926298i
\(794\) −9.16446 + 22.1250i −0.325235 + 0.785186i
\(795\) 13.6535i 0.484238i
\(796\) 15.5212 + 6.42910i 0.550135 + 0.227874i
\(797\) 14.8934 14.8934i 0.527550 0.527550i −0.392291 0.919841i \(-0.628317\pi\)
0.919841 + 0.392291i \(0.128317\pi\)
\(798\) 6.35168 0.224847
\(799\) −19.0709 + 14.8103i −0.674680 + 0.523952i
\(800\) 1.00000 0.0353553
\(801\) −1.30346 + 1.30346i −0.0460554 + 0.0460554i
\(802\) −21.2869 8.81734i −0.751668 0.311351i
\(803\) 75.9590i 2.68053i
\(804\) 4.89452 11.8164i 0.172617 0.416733i
\(805\) −18.7519 + 7.76731i −0.660919 + 0.273762i
\(806\) −15.2655 36.8543i −0.537706 1.29814i
\(807\) −17.6278 17.6278i −0.620529 0.620529i
\(808\) 7.59384 + 7.59384i 0.267150 + 0.267150i
\(809\) −6.98690 16.8679i −0.245646 0.593042i 0.752179 0.658959i \(-0.229003\pi\)
−0.997825 + 0.0659166i \(0.979003\pi\)
\(810\) −5.41114 + 2.24137i −0.190128 + 0.0787537i
\(811\) −5.56638 + 13.4384i −0.195462 + 0.471887i −0.990975 0.134050i \(-0.957202\pi\)
0.795512 + 0.605937i \(0.207202\pi\)
\(812\) 16.4773i 0.578239i
\(813\) −31.2628 12.9495i −1.09644 0.454158i
\(814\) 30.9363 30.9363i 1.08432 1.08432i
\(815\) 10.1378 0.355111
\(816\) −1.60888 5.86793i −0.0563221 0.205419i
\(817\) −1.00702 −0.0352311
\(818\) 9.01479 9.01479i 0.315195 0.315195i
\(819\) −14.7637 6.11532i −0.515885 0.213686i
\(820\) 0.143094i 0.00499707i
\(821\) 15.6230 37.7172i 0.545246 1.31634i −0.375733 0.926728i \(-0.622609\pi\)
0.920979 0.389613i \(-0.127391\pi\)
\(822\) 4.51209 1.86897i 0.157377 0.0651878i
\(823\) 0.697439 + 1.68377i 0.0243112 + 0.0586925i 0.935569 0.353144i \(-0.114887\pi\)
−0.911258 + 0.411837i \(0.864887\pi\)
\(824\) 5.25597 + 5.25597i 0.183100 + 0.183100i
\(825\) 4.91328 + 4.91328i 0.171059 + 0.171059i
\(826\) −6.40432 15.4614i −0.222835 0.537971i
\(827\) 42.9008 17.7701i 1.49181 0.617927i 0.520098 0.854107i \(-0.325896\pi\)
0.971709 + 0.236180i \(0.0758955\pi\)
\(828\) 1.80003 4.34567i 0.0625555 0.151022i
\(829\) 34.9749i 1.21473i 0.794424 + 0.607364i \(0.207773\pi\)
−0.794424 + 0.607364i \(0.792227\pi\)
\(830\) −3.14674 1.30342i −0.109225 0.0452425i
\(831\) 20.8715 20.8715i 0.724025 0.724025i
\(832\) 5.47699 0.189881
\(833\) −22.8682 2.87568i −0.792337 0.0996365i
\(834\) −2.65622 −0.0919773
\(835\) −8.80459 + 8.80459i −0.304695 + 0.304695i
\(836\) 5.27687 + 2.18575i 0.182504 + 0.0755958i
\(837\) 41.0822i 1.42001i
\(838\) 10.4748 25.2883i 0.361845 0.873570i
\(839\) 39.6860 16.4385i 1.37011 0.567520i 0.428294 0.903639i \(-0.359115\pi\)
0.941819 + 0.336120i \(0.109115\pi\)
\(840\) −2.00380 4.83759i −0.0691375 0.166913i
\(841\) 5.25756 + 5.25756i 0.181295 + 0.181295i
\(842\) −23.8163 23.8163i −0.820764 0.820764i
\(843\) 13.1484 + 31.7430i 0.452854 + 1.09329i
\(844\) −21.0828 + 8.73280i −0.725701 + 0.300595i
\(845\) −6.50464 + 15.7036i −0.223766 + 0.540220i
\(846\) 4.81560i 0.165564i
\(847\) 36.6181 + 15.1677i 1.25821 + 0.521169i
\(848\) −6.54226 + 6.54226i −0.224662 + 0.224662i
\(849\) −37.1152 −1.27379
\(850\) −2.52894 3.25645i −0.0867419 0.111695i
\(851\) 53.1513 1.82200
\(852\) 5.36758 5.36758i 0.183890 0.183890i
\(853\) −8.59031 3.55822i −0.294127 0.121831i 0.230741 0.973015i \(-0.425885\pi\)
−0.524867 + 0.851184i \(0.675885\pi\)
\(854\) 44.1590i 1.51109i
\(855\) −0.381714 + 0.921539i −0.0130543 + 0.0315160i
\(856\) −14.5335 + 6.01999i −0.496746 + 0.205759i
\(857\) −11.8527 28.6150i −0.404881 0.977469i −0.986463 0.163982i \(-0.947566\pi\)
0.581582 0.813488i \(-0.302434\pi\)
\(858\) 26.9100 + 26.9100i 0.918693 + 0.918693i
\(859\) 13.1008 + 13.1008i 0.446994 + 0.446994i 0.894354 0.447360i \(-0.147636\pi\)
−0.447360 + 0.894354i \(0.647636\pi\)
\(860\) 0.317689 + 0.766969i 0.0108331 + 0.0261534i
\(861\) −0.692232 + 0.286732i −0.0235912 + 0.00977179i
\(862\) −6.95725 + 16.7963i −0.236965 + 0.572084i
\(863\) 18.5377i 0.631030i 0.948921 + 0.315515i \(0.102177\pi\)
−0.948921 + 0.315515i \(0.897823\pi\)
\(864\) 5.21121 + 2.15856i 0.177289 + 0.0734356i
\(865\) −2.50790 + 2.50790i −0.0852710 + 0.0852710i
\(866\) −8.10392 −0.275382
\(867\) −15.0399 + 20.0789i −0.510781 + 0.681914i
\(868\) 25.8431 0.877170
\(869\) −33.6803 + 33.6803i −1.14253 + 1.14253i
\(870\) 6.33122 + 2.62248i 0.214648 + 0.0889103i
\(871\) 47.4693i 1.60843i
\(872\) 2.46089 5.94112i 0.0833363 0.201192i
\(873\) −3.30880 + 1.37055i −0.111986 + 0.0463860i
\(874\) 2.65541 + 6.41073i 0.0898207 + 0.216846i
\(875\) −2.50899 2.50899i −0.0848193 0.0848193i
\(876\) −16.8336 16.8336i −0.568756 0.568756i
\(877\) 16.3998 + 39.5926i 0.553781 + 1.33695i 0.914619 + 0.404318i \(0.132491\pi\)
−0.360837 + 0.932629i \(0.617509\pi\)
\(878\) 22.1522 9.17574i 0.747600 0.309666i
\(879\) 14.4147 34.8003i 0.486197 1.17378i
\(880\) 4.70854i 0.158725i
\(881\) 37.7646 + 15.6426i 1.27232 + 0.527014i 0.913670 0.406457i \(-0.133236\pi\)
0.358653 + 0.933471i \(0.383236\pi\)
\(882\) 3.25030 3.25030i 0.109443 0.109443i
\(883\) 52.3174 1.76062 0.880310 0.474398i \(-0.157334\pi\)
0.880310 + 0.474398i \(0.157334\pi\)
\(884\) −13.8510 17.8356i −0.465859 0.599875i
\(885\) −6.96018 −0.233964
\(886\) 0.172587 0.172587i 0.00579819 0.00579819i
\(887\) −13.9607 5.78272i −0.468755 0.194165i 0.135787 0.990738i \(-0.456644\pi\)
−0.604542 + 0.796573i \(0.706644\pi\)
\(888\) 13.7119i 0.460141i
\(889\) −4.35317 + 10.5095i −0.146000 + 0.352476i
\(890\) −2.07111 + 0.857882i −0.0694238 + 0.0287563i
\(891\) 10.5536 + 25.4786i 0.353558 + 0.853565i
\(892\) 6.41246 + 6.41246i 0.214705 + 0.214705i
\(893\) 5.02327 + 5.02327i 0.168097 + 0.168097i
\(894\) 2.35361 + 5.68212i 0.0787165 + 0.190038i
\(895\) −12.1051 + 5.01410i −0.404629 + 0.167603i
\(896\) −1.35785 + 3.27815i −0.0453627 + 0.109515i
\(897\) 46.2338i 1.54370i
\(898\) −0.0761574 0.0315454i −0.00254140 0.00105268i
\(899\) −23.9159 + 23.9159i −0.797640 + 0.797640i
\(900\) 0.822287 0.0274096
\(901\) 37.8495 + 4.75958i 1.26095 + 0.158565i
\(902\) −0.673765 −0.0224339
\(903\) 3.07370 3.07370i 0.102286 0.102286i
\(904\) 8.90782 + 3.68974i 0.296270 + 0.122719i
\(905\) 1.82731i 0.0607418i
\(906\) −2.59356 + 6.26141i −0.0861653 + 0.208022i
\(907\) −23.1561 + 9.59155i −0.768884 + 0.318482i −0.732420 0.680853i \(-0.761609\pi\)
−0.0364638 + 0.999335i \(0.511609\pi\)
\(908\) −6.02643 14.5491i −0.199994 0.482829i
\(909\) 6.24432 + 6.24432i 0.207111 + 0.207111i
\(910\) −13.7417 13.7417i −0.455533 0.455533i
\(911\) −1.10387 2.66499i −0.0365730 0.0882950i 0.904538 0.426394i \(-0.140216\pi\)
−0.941111 + 0.338099i \(0.890216\pi\)
\(912\) −1.65383 + 0.685038i −0.0547637 + 0.0226839i
\(913\) −6.13723 + 14.8166i −0.203113 + 0.490357i
\(914\) 24.3896i 0.806737i
\(915\) 16.9676 + 7.02822i 0.560933 + 0.232346i
\(916\) 14.2262 14.2262i 0.470046 0.470046i
\(917\) −12.6792 −0.418703
\(918\) −6.14961 22.4289i −0.202967 0.740265i
\(919\) −48.0746 −1.58584 −0.792918 0.609328i \(-0.791439\pi\)
−0.792918 + 0.609328i \(0.791439\pi\)
\(920\) 4.04485 4.04485i 0.133355 0.133355i
\(921\) −19.4120 8.04071i −0.639647 0.264950i
\(922\) 29.1100i 0.958687i
\(923\) 10.7814 26.0286i 0.354874 0.856741i
\(924\) −22.7780 + 9.43496i −0.749341 + 0.310387i
\(925\) 3.55579 + 8.58444i 0.116914 + 0.282255i
\(926\) −19.7821 19.7821i −0.650081 0.650081i
\(927\) 4.32191 + 4.32191i 0.141950 + 0.141950i
\(928\) −1.77710 4.29029i −0.0583361 0.140836i
\(929\) 25.3430 10.4974i 0.831478 0.344409i 0.0739901 0.997259i \(-0.476427\pi\)
0.757487 + 0.652850i \(0.226427\pi\)
\(930\) 4.11311 9.92992i 0.134874 0.325615i
\(931\) 6.78094i 0.222236i
\(932\) 17.8076 + 7.37613i 0.583306 + 0.241613i
\(933\) −12.6797 + 12.6797i −0.415116 + 0.415116i
\(934\) 31.2786 1.02347
\(935\) −15.3331 + 11.9076i −0.501447 + 0.389420i
\(936\) 4.50366 0.147207
\(937\) −10.3762 + 10.3762i −0.338975 + 0.338975i −0.855981 0.517007i \(-0.827046\pi\)
0.517007 + 0.855981i \(0.327046\pi\)
\(938\) 28.4118 + 11.7686i 0.927679 + 0.384257i
\(939\) 32.1552i 1.04934i
\(940\) 2.24113 5.41056i 0.0730975 0.176473i
\(941\) 22.8397 9.46050i 0.744552 0.308404i 0.0220356 0.999757i \(-0.492985\pi\)
0.722517 + 0.691354i \(0.242985\pi\)
\(942\) 8.78053 + 21.1981i 0.286085 + 0.690671i
\(943\) −0.578795 0.578795i −0.0188482 0.0188482i
\(944\) 3.33507 + 3.33507i 0.108547 + 0.108547i
\(945\) −7.65908 18.4907i −0.249150 0.601501i
\(946\) 3.61131 1.49585i 0.117414 0.0486343i
\(947\) −2.49335 + 6.01947i −0.0810228 + 0.195606i −0.959200 0.282730i \(-0.908760\pi\)
0.878177 + 0.478336i \(0.158760\pi\)
\(948\) 14.9281i 0.484842i
\(949\) −81.6301 33.8123i −2.64982 1.09759i
\(950\) −0.857748 + 0.857748i −0.0278290 + 0.0278290i
\(951\) 15.1285 0.490574
\(952\) 14.1091 3.86845i 0.457277 0.125377i
\(953\) 13.6944 0.443607 0.221803 0.975091i \(-0.428806\pi\)
0.221803 + 0.975091i \(0.428806\pi\)
\(954\) −5.37961 + 5.37961i −0.174171 + 0.174171i
\(955\) 15.5506 + 6.44127i 0.503206 + 0.208435i
\(956\) 14.2040i 0.459389i
\(957\) 12.3480 29.8108i 0.399155 0.963646i
\(958\) −11.1564 + 4.62112i −0.360446 + 0.149302i
\(959\) 4.49382 + 10.8490i 0.145113 + 0.350334i
\(960\) 1.04348 + 1.04348i 0.0336783 + 0.0336783i
\(961\) 15.5896 + 15.5896i 0.502889 + 0.502889i
\(962\) 19.4751 + 47.0169i 0.627901 + 1.51589i
\(963\) −11.9507 + 4.95016i −0.385107 + 0.159517i
\(964\) −1.75060 + 4.22633i −0.0563832 + 0.136121i
\(965\) 5.82873i 0.187633i
\(966\) −27.6724 11.4623i −0.890344 0.368793i
\(967\) 11.5376 11.5376i 0.371026 0.371026i −0.496825 0.867851i \(-0.665501\pi\)
0.867851 + 0.496825i \(0.165501\pi\)
\(968\) −11.1704 −0.359029
\(969\) 6.41322 + 3.65319i 0.206022 + 0.117357i
\(970\) −4.35543 −0.139844
\(971\) −19.0136 + 19.0136i −0.610176 + 0.610176i −0.942992 0.332816i \(-0.892001\pi\)
0.332816 + 0.942992i \(0.392001\pi\)
\(972\) 7.64838 + 3.16806i 0.245322 + 0.101616i
\(973\) 6.38671i 0.204748i
\(974\) 1.91937 4.63377i 0.0615005 0.148475i
\(975\) −7.46720 + 3.09302i −0.239142 + 0.0990558i
\(976\) −4.76261 11.4980i −0.152448 0.368041i
\(977\) −14.1423 14.1423i −0.452451 0.452451i 0.443716 0.896167i \(-0.353660\pi\)
−0.896167 + 0.443716i \(0.853660\pi\)
\(978\) 10.5786 + 10.5786i 0.338266 + 0.338266i
\(979\) 4.03937 + 9.75191i 0.129099 + 0.311672i
\(980\) 5.16452 2.13922i 0.164975 0.0683347i
\(981\) 2.02356 4.88531i 0.0646073 0.155976i
\(982\) 26.4441i 0.843865i
\(983\) −26.6406 11.0349i −0.849704 0.351959i −0.0850316 0.996378i \(-0.527099\pi\)
−0.764672 + 0.644419i \(0.777099\pi\)
\(984\) 0.149316 0.149316i 0.00476003 0.00476003i
\(985\) 3.52144 0.112202
\(986\) −9.47696 + 16.6369i −0.301808 + 0.529827i
\(987\) −30.6648 −0.976072
\(988\) −4.69788 + 4.69788i −0.149460 + 0.149460i
\(989\) 4.38728 + 1.81727i 0.139507 + 0.0577858i
\(990\) 3.87177i 0.123053i
\(991\) −10.2929 + 24.8494i −0.326966 + 0.789366i 0.671848 + 0.740689i \(0.265501\pi\)
−0.998815 + 0.0486775i \(0.984499\pi\)
\(992\) −6.72892 + 2.78721i −0.213644 + 0.0884941i
\(993\) −0.167267 0.403818i −0.00530805 0.0128148i
\(994\) 12.9060 + 12.9060i 0.409353 + 0.409353i
\(995\) 11.8794 + 11.8794i 0.376603 + 0.376603i
\(996\) −1.92347 4.64367i −0.0609476 0.147140i
\(997\) 28.1434 11.6574i 0.891310 0.369193i 0.110437 0.993883i \(-0.464775\pi\)
0.780872 + 0.624690i \(0.214775\pi\)
\(998\) −11.4569 + 27.6595i −0.362663 + 0.875545i
\(999\) 52.4108i 1.65820i
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 170.2.k.b.111.3 16
5.2 odd 4 850.2.o.j.349.3 16
5.3 odd 4 850.2.o.g.349.2 16
5.4 even 2 850.2.l.e.451.2 16
17.2 even 8 inner 170.2.k.b.121.3 yes 16
17.6 odd 16 2890.2.a.bi.1.7 8
17.7 odd 16 2890.2.b.r.2311.5 16
17.10 odd 16 2890.2.b.r.2311.12 16
17.11 odd 16 2890.2.a.bj.1.2 8
85.2 odd 8 850.2.o.g.699.2 16
85.19 even 8 850.2.l.e.801.2 16
85.53 odd 8 850.2.o.j.699.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.k.b.111.3 16 1.1 even 1 trivial
170.2.k.b.121.3 yes 16 17.2 even 8 inner
850.2.l.e.451.2 16 5.4 even 2
850.2.l.e.801.2 16 85.19 even 8
850.2.o.g.349.2 16 5.3 odd 4
850.2.o.g.699.2 16 85.2 odd 8
850.2.o.j.349.3 16 5.2 odd 4
850.2.o.j.699.3 16 85.53 odd 8
2890.2.a.bi.1.7 8 17.6 odd 16
2890.2.a.bj.1.2 8 17.11 odd 16
2890.2.b.r.2311.5 16 17.7 odd 16
2890.2.b.r.2311.12 16 17.10 odd 16