Properties

Label 322.2.g.b.229.8
Level $322$
Weight $2$
Character 322.229
Analytic conductor $2.571$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [322,2,Mod(45,322)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(322, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("322.45");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 322 = 2 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 322.g (of order \(6\), degree \(2\), 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: \(2.57118294509\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 12x^{14} + 73x^{12} + 312x^{10} + 1045x^{8} + 2808x^{6} + 5913x^{4} + 8748x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 229.8
Root \(0.956239 - 1.44416i\) of defining polynomial
Character \(\chi\) \(=\) 322.229
Dual form 322.2.g.b.45.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(2.13508 - 1.23269i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.511122 - 0.885289i) q^{5} -2.46537i q^{6} +(-2.61593 + 0.396147i) q^{7} -1.00000 q^{8} +(1.53904 - 2.66569i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(2.13508 - 1.23269i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.511122 - 0.885289i) q^{5} -2.46537i q^{6} +(-2.61593 + 0.396147i) q^{7} -1.00000 q^{8} +(1.53904 - 2.66569i) q^{9} +(-0.511122 - 0.885289i) q^{10} +(1.28679 - 0.742931i) q^{11} +(-2.13508 - 1.23269i) q^{12} -0.0815813i q^{13} +(-0.964890 + 2.46353i) q^{14} -2.52021i q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.20592 + 2.08871i) q^{17} +(-1.53904 - 2.66569i) q^{18} +(1.03400 - 1.79095i) q^{19} -1.02224 q^{20} +(-5.09688 + 4.07042i) q^{21} -1.48586i q^{22} +(3.64481 + 3.11694i) q^{23} +(-2.13508 + 1.23269i) q^{24} +(1.97751 + 3.42515i) q^{25} +(-0.0706515 - 0.0407907i) q^{26} -0.192480i q^{27} +(1.65104 + 2.06738i) q^{28} -0.342432 q^{29} +(-2.18257 - 1.26011i) q^{30} +(-2.67411 + 1.54390i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.83160 - 3.17243i) q^{33} +2.41184 q^{34} +(-0.986353 + 2.51833i) q^{35} -3.07807 q^{36} +(0.135119 + 0.0780112i) q^{37} +(-1.03400 - 1.79095i) q^{38} +(-0.100564 - 0.174182i) q^{39} +(-0.511122 + 0.885289i) q^{40} +2.13767i q^{41} +(0.976650 + 6.44924i) q^{42} -6.69764i q^{43} +(-1.28679 - 0.742931i) q^{44} +(-1.57327 - 2.72498i) q^{45} +(4.52176 - 1.59803i) q^{46} +(-3.72680 - 2.15167i) q^{47} +2.46537i q^{48} +(6.68614 - 2.07258i) q^{49} +3.95502 q^{50} +(5.14946 + 2.97304i) q^{51} +(-0.0706515 + 0.0407907i) q^{52} +(-7.03856 + 4.06372i) q^{53} +(-0.166692 - 0.0962398i) q^{54} -1.51891i q^{55} +(2.61593 - 0.396147i) q^{56} -5.09841i q^{57} +(-0.171216 + 0.296554i) q^{58} +(2.48203 - 1.43300i) q^{59} +(-2.18257 + 1.26011i) q^{60} +(1.09121 - 1.89003i) q^{61} +3.08780i q^{62} +(-2.97000 + 7.58293i) q^{63} +1.00000 q^{64} +(-0.0722231 - 0.0416980i) q^{65} +(-1.83160 - 3.17243i) q^{66} +(-13.5852 + 7.84342i) q^{67} +(1.20592 - 2.08871i) q^{68} +(11.6242 + 2.16200i) q^{69} +(1.68776 + 2.11337i) q^{70} -7.61259 q^{71} +(-1.53904 + 2.66569i) q^{72} +(5.53281 - 3.19437i) q^{73} +(0.135119 - 0.0780112i) q^{74} +(8.44427 + 4.87530i) q^{75} -2.06801 q^{76} +(-3.07185 + 2.45321i) q^{77} -0.201129 q^{78} +(6.55870 + 3.78667i) q^{79} +(0.511122 + 0.885289i) q^{80} +(4.37984 + 7.58611i) q^{81} +(1.85128 + 1.06883i) q^{82} -3.61313 q^{83} +(6.07353 + 2.37882i) q^{84} +2.46549 q^{85} +(-5.80033 - 3.34882i) q^{86} +(-0.731118 + 0.422111i) q^{87} +(-1.28679 + 0.742931i) q^{88} +(7.27080 - 12.5934i) q^{89} -3.14654 q^{90} +(0.0323182 + 0.213411i) q^{91} +(0.876945 - 4.71497i) q^{92} +(-3.80629 + 6.59269i) q^{93} +(-3.72680 + 2.15167i) q^{94} +(-1.05700 - 1.83078i) q^{95} +(2.13508 + 1.23269i) q^{96} +15.5010 q^{97} +(1.54816 - 6.82665i) q^{98} -4.57359i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{2} - 6 q^{3} - 8 q^{4} - 16 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{2} - 6 q^{3} - 8 q^{4} - 16 q^{8} + 10 q^{9} + 6 q^{12} - 8 q^{16} - 10 q^{18} + 8 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{29} + 12 q^{31} + 8 q^{32} - 20 q^{36} - 2 q^{39} - 8 q^{46} - 6 q^{47} - 18 q^{49} + 4 q^{50} - 6 q^{52} + 18 q^{54} - 8 q^{58} + 36 q^{59} + 16 q^{64} - 12 q^{70} - 52 q^{71} - 10 q^{72} + 24 q^{73} + 30 q^{77} - 4 q^{78} - 20 q^{81} + 54 q^{82} + 80 q^{85} + 54 q^{87} - 16 q^{92} - 26 q^{93} - 6 q^{94} - 6 q^{95} - 6 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).

\(n\) \(185\) \(281\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 2.13508 1.23269i 1.23269 0.711692i 0.265098 0.964221i \(-0.414596\pi\)
0.967589 + 0.252529i \(0.0812623\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.511122 0.885289i 0.228581 0.395913i −0.728807 0.684719i \(-0.759925\pi\)
0.957388 + 0.288806i \(0.0932582\pi\)
\(6\) 2.46537i 1.00649i
\(7\) −2.61593 + 0.396147i −0.988727 + 0.149729i
\(8\) −1.00000 −0.353553
\(9\) 1.53904 2.66569i 0.513012 0.888563i
\(10\) −0.511122 0.885289i −0.161631 0.279953i
\(11\) 1.28679 0.742931i 0.387983 0.224002i −0.293303 0.956020i \(-0.594754\pi\)
0.681286 + 0.732018i \(0.261421\pi\)
\(12\) −2.13508 1.23269i −0.616344 0.355846i
\(13\) 0.0815813i 0.0226266i −0.999936 0.0113133i \(-0.996399\pi\)
0.999936 0.0113133i \(-0.00360121\pi\)
\(14\) −0.964890 + 2.46353i −0.257878 + 0.658406i
\(15\) 2.52021i 0.650716i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.20592 + 2.08871i 0.292478 + 0.506587i 0.974395 0.224842i \(-0.0721867\pi\)
−0.681917 + 0.731430i \(0.738853\pi\)
\(18\) −1.53904 2.66569i −0.362754 0.628309i
\(19\) 1.03400 1.79095i 0.237217 0.410872i −0.722698 0.691164i \(-0.757098\pi\)
0.959915 + 0.280293i \(0.0904315\pi\)
\(20\) −1.02224 −0.228581
\(21\) −5.09688 + 4.07042i −1.11223 + 0.888239i
\(22\) 1.48586i 0.316787i
\(23\) 3.64481 + 3.11694i 0.759996 + 0.649927i
\(24\) −2.13508 + 1.23269i −0.435821 + 0.251621i
\(25\) 1.97751 + 3.42515i 0.395502 + 0.685029i
\(26\) −0.0706515 0.0407907i −0.0138559 0.00799971i
\(27\) 0.192480i 0.0370427i
\(28\) 1.65104 + 2.06738i 0.312016 + 0.390699i
\(29\) −0.342432 −0.0635880 −0.0317940 0.999494i \(-0.510122\pi\)
−0.0317940 + 0.999494i \(0.510122\pi\)
\(30\) −2.18257 1.26011i −0.398481 0.230063i
\(31\) −2.67411 + 1.54390i −0.480285 + 0.277293i −0.720535 0.693418i \(-0.756104\pi\)
0.240250 + 0.970711i \(0.422770\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 1.83160 3.17243i 0.318841 0.552249i
\(34\) 2.41184 0.413627
\(35\) −0.986353 + 2.51833i −0.166724 + 0.425675i
\(36\) −3.07807 −0.513012
\(37\) 0.135119 + 0.0780112i 0.0222135 + 0.0128250i 0.511066 0.859542i \(-0.329251\pi\)
−0.488852 + 0.872367i \(0.662584\pi\)
\(38\) −1.03400 1.79095i −0.167738 0.290530i
\(39\) −0.100564 0.174182i −0.0161032 0.0278915i
\(40\) −0.511122 + 0.885289i −0.0808155 + 0.139976i
\(41\) 2.13767i 0.333848i 0.985970 + 0.166924i \(0.0533834\pi\)
−0.985970 + 0.166924i \(0.946617\pi\)
\(42\) 0.976650 + 6.44924i 0.150700 + 0.995139i
\(43\) 6.69764i 1.02138i −0.859765 0.510690i \(-0.829390\pi\)
0.859765 0.510690i \(-0.170610\pi\)
\(44\) −1.28679 0.742931i −0.193991 0.112001i
\(45\) −1.57327 2.72498i −0.234529 0.406217i
\(46\) 4.52176 1.59803i 0.666697 0.235617i
\(47\) −3.72680 2.15167i −0.543609 0.313853i 0.202931 0.979193i \(-0.434953\pi\)
−0.746540 + 0.665340i \(0.768287\pi\)
\(48\) 2.46537i 0.355846i
\(49\) 6.68614 2.07258i 0.955162 0.296083i
\(50\) 3.95502 0.559324
\(51\) 5.14946 + 2.97304i 0.721069 + 0.416309i
\(52\) −0.0706515 + 0.0407907i −0.00979760 + 0.00565665i
\(53\) −7.03856 + 4.06372i −0.966821 + 0.558195i −0.898266 0.439453i \(-0.855172\pi\)
−0.0685556 + 0.997647i \(0.521839\pi\)
\(54\) −0.166692 0.0962398i −0.0226839 0.0130966i
\(55\) 1.51891i 0.204810i
\(56\) 2.61593 0.396147i 0.349568 0.0529373i
\(57\) 5.09841i 0.675302i
\(58\) −0.171216 + 0.296554i −0.0224817 + 0.0389395i
\(59\) 2.48203 1.43300i 0.323133 0.186561i −0.329655 0.944101i \(-0.606932\pi\)
0.652788 + 0.757540i \(0.273599\pi\)
\(60\) −2.18257 + 1.26011i −0.281768 + 0.162679i
\(61\) 1.09121 1.89003i 0.139715 0.241994i −0.787674 0.616093i \(-0.788715\pi\)
0.927389 + 0.374099i \(0.122048\pi\)
\(62\) 3.08780i 0.392151i
\(63\) −2.97000 + 7.58293i −0.374185 + 0.955359i
\(64\) 1.00000 0.125000
\(65\) −0.0722231 0.0416980i −0.00895817 0.00517200i
\(66\) −1.83160 3.17243i −0.225455 0.390499i
\(67\) −13.5852 + 7.84342i −1.65970 + 0.958227i −0.686844 + 0.726805i \(0.741004\pi\)
−0.972854 + 0.231422i \(0.925662\pi\)
\(68\) 1.20592 2.08871i 0.146239 0.253294i
\(69\) 11.6242 + 2.16200i 1.39939 + 0.260274i
\(70\) 1.68776 + 2.11337i 0.201726 + 0.252596i
\(71\) −7.61259 −0.903448 −0.451724 0.892158i \(-0.649191\pi\)
−0.451724 + 0.892158i \(0.649191\pi\)
\(72\) −1.53904 + 2.66569i −0.181377 + 0.314155i
\(73\) 5.53281 3.19437i 0.647567 0.373873i −0.139957 0.990158i \(-0.544696\pi\)
0.787523 + 0.616285i \(0.211363\pi\)
\(74\) 0.135119 0.0780112i 0.0157073 0.00906862i
\(75\) 8.44427 + 4.87530i 0.975060 + 0.562951i
\(76\) −2.06801 −0.237217
\(77\) −3.07185 + 2.45321i −0.350069 + 0.279569i
\(78\) −0.201129 −0.0227733
\(79\) 6.55870 + 3.78667i 0.737911 + 0.426033i 0.821309 0.570483i \(-0.193244\pi\)
−0.0833983 + 0.996516i \(0.526577\pi\)
\(80\) 0.511122 + 0.885289i 0.0571452 + 0.0989783i
\(81\) 4.37984 + 7.58611i 0.486649 + 0.842901i
\(82\) 1.85128 + 1.06883i 0.204439 + 0.118033i
\(83\) −3.61313 −0.396593 −0.198296 0.980142i \(-0.563541\pi\)
−0.198296 + 0.980142i \(0.563541\pi\)
\(84\) 6.07353 + 2.37882i 0.662676 + 0.259550i
\(85\) 2.46549 0.267420
\(86\) −5.80033 3.34882i −0.625465 0.361113i
\(87\) −0.731118 + 0.422111i −0.0783841 + 0.0452551i
\(88\) −1.28679 + 0.742931i −0.137173 + 0.0791967i
\(89\) 7.27080 12.5934i 0.770703 1.33490i −0.166475 0.986046i \(-0.553239\pi\)
0.937178 0.348851i \(-0.113428\pi\)
\(90\) −3.14654 −0.331675
\(91\) 0.0323182 + 0.213411i 0.00338787 + 0.0223715i
\(92\) 0.876945 4.71497i 0.0914278 0.491570i
\(93\) −3.80629 + 6.59269i −0.394694 + 0.683630i
\(94\) −3.72680 + 2.15167i −0.384390 + 0.221928i
\(95\) −1.05700 1.83078i −0.108446 0.187835i
\(96\) 2.13508 + 1.23269i 0.217910 + 0.125811i
\(97\) 15.5010 1.57389 0.786946 0.617022i \(-0.211661\pi\)
0.786946 + 0.617022i \(0.211661\pi\)
\(98\) 1.54816 6.82665i 0.156388 0.689596i
\(99\) 4.57359i 0.459663i
\(100\) 1.97751 3.42515i 0.197751 0.342515i
\(101\) −14.5106 + 8.37770i −1.44386 + 0.833612i −0.998104 0.0615432i \(-0.980398\pi\)
−0.445754 + 0.895155i \(0.647064\pi\)
\(102\) 5.14946 2.97304i 0.509873 0.294375i
\(103\) 3.89407 6.74472i 0.383694 0.664577i −0.607893 0.794019i \(-0.707985\pi\)
0.991587 + 0.129441i \(0.0413184\pi\)
\(104\) 0.0815813i 0.00799971i
\(105\) 0.998374 + 6.59269i 0.0974314 + 0.643381i
\(106\) 8.12743i 0.789406i
\(107\) −5.64261 3.25776i −0.545491 0.314940i 0.201810 0.979425i \(-0.435318\pi\)
−0.747302 + 0.664485i \(0.768651\pi\)
\(108\) −0.166692 + 0.0962398i −0.0160400 + 0.00926068i
\(109\) −14.9835 + 8.65070i −1.43515 + 0.828587i −0.997508 0.0705599i \(-0.977521\pi\)
−0.437647 + 0.899147i \(0.644188\pi\)
\(110\) −1.31542 0.759456i −0.125420 0.0724113i
\(111\) 0.384654 0.0365097
\(112\) 0.964890 2.46353i 0.0911735 0.232782i
\(113\) 15.6200i 1.46941i 0.678388 + 0.734703i \(0.262679\pi\)
−0.678388 + 0.734703i \(0.737321\pi\)
\(114\) −4.41536 2.54921i −0.413536 0.238755i
\(115\) 4.62234 1.63358i 0.431035 0.152332i
\(116\) 0.171216 + 0.296554i 0.0158970 + 0.0275344i
\(117\) −0.217471 0.125557i −0.0201052 0.0116077i
\(118\) 2.86600i 0.263837i
\(119\) −3.98203 4.98620i −0.365032 0.457084i
\(120\) 2.52021i 0.230063i
\(121\) −4.39611 + 7.61428i −0.399646 + 0.692207i
\(122\) −1.09121 1.89003i −0.0987936 0.171116i
\(123\) 2.63508 + 4.56409i 0.237597 + 0.411530i
\(124\) 2.67411 + 1.54390i 0.240143 + 0.138646i
\(125\) 9.15421 0.818778
\(126\) 5.08201 + 6.36356i 0.452741 + 0.566911i
\(127\) 6.12885 0.543848 0.271924 0.962319i \(-0.412340\pi\)
0.271924 + 0.962319i \(0.412340\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −8.25610 14.3000i −0.726909 1.25904i
\(130\) −0.0722231 + 0.0416980i −0.00633438 + 0.00365716i
\(131\) −11.3272 6.53974i −0.989658 0.571380i −0.0844863 0.996425i \(-0.526925\pi\)
−0.905172 + 0.425045i \(0.860258\pi\)
\(132\) −3.66321 −0.318841
\(133\) −1.99540 + 5.09460i −0.173023 + 0.441758i
\(134\) 15.6868i 1.35514i
\(135\) −0.170400 0.0983805i −0.0146657 0.00846725i
\(136\) −1.20592 2.08871i −0.103407 0.179106i
\(137\) −9.11197 + 5.26080i −0.778488 + 0.449460i −0.835894 0.548891i \(-0.815050\pi\)
0.0574061 + 0.998351i \(0.481717\pi\)
\(138\) 7.68443 8.98583i 0.654142 0.764925i
\(139\) 16.5716i 1.40558i −0.711396 0.702791i \(-0.751937\pi\)
0.711396 0.702791i \(-0.248063\pi\)
\(140\) 2.67411 0.404958i 0.226004 0.0342252i
\(141\) −10.6093 −0.893467
\(142\) −3.80629 + 6.59269i −0.319417 + 0.553247i
\(143\) −0.0606093 0.104978i −0.00506840 0.00877873i
\(144\) 1.53904 + 2.66569i 0.128253 + 0.222141i
\(145\) −0.175024 + 0.303151i −0.0145350 + 0.0251753i
\(146\) 6.38874i 0.528736i
\(147\) 11.7206 12.6670i 0.966696 1.04476i
\(148\) 0.156022i 0.0128250i
\(149\) −9.44175 5.45120i −0.773498 0.446580i 0.0606227 0.998161i \(-0.480691\pi\)
−0.834121 + 0.551581i \(0.814025\pi\)
\(150\) 8.44427 4.87530i 0.689472 0.398067i
\(151\) −8.58387 14.8677i −0.698545 1.20992i −0.968971 0.247175i \(-0.920498\pi\)
0.270425 0.962741i \(-0.412836\pi\)
\(152\) −1.03400 + 1.79095i −0.0838688 + 0.145265i
\(153\) 7.42382 0.600180
\(154\) 0.588619 + 3.88690i 0.0474323 + 0.313216i
\(155\) 3.15648i 0.253535i
\(156\) −0.100564 + 0.174182i −0.00805159 + 0.0139458i
\(157\) −0.180567 0.312751i −0.0144108 0.0249602i 0.858730 0.512428i \(-0.171254\pi\)
−0.873141 + 0.487468i \(0.837921\pi\)
\(158\) 6.55870 3.78667i 0.521782 0.301251i
\(159\) −10.0186 + 17.3527i −0.794526 + 1.37616i
\(160\) 1.02224 0.0808155
\(161\) −10.7693 6.70981i −0.848742 0.528807i
\(162\) 8.75969 0.688226
\(163\) 12.1574 21.0573i 0.952243 1.64933i 0.211687 0.977338i \(-0.432104\pi\)
0.740556 0.671995i \(-0.234562\pi\)
\(164\) 1.85128 1.06883i 0.144560 0.0834619i
\(165\) −1.87234 3.24300i −0.145762 0.252467i
\(166\) −1.80657 + 3.12907i −0.140217 + 0.242863i
\(167\) 13.1624i 1.01854i −0.860607 0.509270i \(-0.829915\pi\)
0.860607 0.509270i \(-0.170085\pi\)
\(168\) 5.09688 4.07042i 0.393233 0.314040i
\(169\) 12.9933 0.999488
\(170\) 1.23274 2.13517i 0.0945471 0.163760i
\(171\) −3.18274 5.51267i −0.243390 0.421564i
\(172\) −5.80033 + 3.34882i −0.442271 + 0.255345i
\(173\) −12.8768 7.43442i −0.979005 0.565229i −0.0770351 0.997028i \(-0.524545\pi\)
−0.901969 + 0.431800i \(0.857879\pi\)
\(174\) 0.844222i 0.0640003i
\(175\) −6.52988 8.17654i −0.493612 0.618089i
\(176\) 1.48586i 0.112001i
\(177\) 3.53289 6.11914i 0.265548 0.459943i
\(178\) −7.27080 12.5934i −0.544969 0.943914i
\(179\) −8.23112 14.2567i −0.615223 1.06560i −0.990345 0.138622i \(-0.955733\pi\)
0.375123 0.926975i \(-0.377601\pi\)
\(180\) −1.57327 + 2.72498i −0.117265 + 0.203108i
\(181\) 20.9810 1.55950 0.779751 0.626090i \(-0.215346\pi\)
0.779751 + 0.626090i \(0.215346\pi\)
\(182\) 0.200978 + 0.0787170i 0.0148975 + 0.00583489i
\(183\) 5.38049i 0.397737i
\(184\) −3.64481 3.11694i −0.268699 0.229784i
\(185\) 0.138125 0.0797465i 0.0101551 0.00586308i
\(186\) 3.80629 + 6.59269i 0.279091 + 0.483400i
\(187\) 3.10354 + 1.79183i 0.226953 + 0.131032i
\(188\) 4.30334i 0.313853i
\(189\) 0.0762501 + 0.503512i 0.00554638 + 0.0366251i
\(190\) −2.11401 −0.153366
\(191\) 8.61942 + 4.97643i 0.623680 + 0.360082i 0.778300 0.627892i \(-0.216082\pi\)
−0.154621 + 0.987974i \(0.549416\pi\)
\(192\) 2.13508 1.23269i 0.154086 0.0889616i
\(193\) 5.53019 + 9.57857i 0.398072 + 0.689481i 0.993488 0.113937i \(-0.0363461\pi\)
−0.595416 + 0.803418i \(0.703013\pi\)
\(194\) 7.75052 13.4243i 0.556455 0.963808i
\(195\) −0.205602 −0.0147235
\(196\) −5.13798 4.75407i −0.366998 0.339577i
\(197\) −11.3061 −0.805526 −0.402763 0.915304i \(-0.631950\pi\)
−0.402763 + 0.915304i \(0.631950\pi\)
\(198\) −3.96085 2.28680i −0.281485 0.162515i
\(199\) −6.69299 11.5926i −0.474454 0.821778i 0.525118 0.851029i \(-0.324021\pi\)
−0.999572 + 0.0292512i \(0.990688\pi\)
\(200\) −1.97751 3.42515i −0.139831 0.242194i
\(201\) −19.3370 + 33.4926i −1.36393 + 2.36239i
\(202\) 16.7554i 1.17891i
\(203\) 0.895776 0.135653i 0.0628711 0.00952098i
\(204\) 5.94609i 0.416309i
\(205\) 1.89245 + 1.09261i 0.132175 + 0.0763111i
\(206\) −3.89407 6.74472i −0.271313 0.469927i
\(207\) 13.9183 4.91885i 0.967389 0.341884i
\(208\) 0.0706515 + 0.0407907i 0.00489880 + 0.00282832i
\(209\) 3.07277i 0.212548i
\(210\) 6.20863 + 2.43173i 0.428436 + 0.167805i
\(211\) −13.3090 −0.916232 −0.458116 0.888892i \(-0.651476\pi\)
−0.458116 + 0.888892i \(0.651476\pi\)
\(212\) 7.03856 + 4.06372i 0.483411 + 0.279097i
\(213\) −16.2535 + 9.38394i −1.11367 + 0.642977i
\(214\) −5.64261 + 3.25776i −0.385721 + 0.222696i
\(215\) −5.92935 3.42331i −0.404378 0.233468i
\(216\) 0.192480i 0.0130966i
\(217\) 6.38367 5.09807i 0.433352 0.346080i
\(218\) 17.3014i 1.17180i
\(219\) 7.87532 13.6405i 0.532165 0.921736i
\(220\) −1.31542 + 0.759456i −0.0886854 + 0.0512025i
\(221\) 0.170400 0.0983805i 0.0114623 0.00661779i
\(222\) 0.192327 0.333120i 0.0129081 0.0223575i
\(223\) 13.7849i 0.923103i 0.887113 + 0.461551i \(0.152707\pi\)
−0.887113 + 0.461551i \(0.847293\pi\)
\(224\) −1.65104 2.06738i −0.110314 0.138133i
\(225\) 12.1738 0.811589
\(226\) 13.5273 + 7.81001i 0.899824 + 0.519514i
\(227\) 4.99408 + 8.65000i 0.331469 + 0.574120i 0.982800 0.184673i \(-0.0591226\pi\)
−0.651331 + 0.758793i \(0.725789\pi\)
\(228\) −4.41536 + 2.54921i −0.292414 + 0.168825i
\(229\) −7.15920 + 12.4001i −0.473093 + 0.819421i −0.999526 0.0307956i \(-0.990196\pi\)
0.526433 + 0.850217i \(0.323529\pi\)
\(230\) 0.896451 4.81985i 0.0591102 0.317812i
\(231\) −3.53459 + 9.02442i −0.232559 + 0.593763i
\(232\) 0.342432 0.0224817
\(233\) −9.06280 + 15.6972i −0.593724 + 1.02836i 0.400002 + 0.916514i \(0.369009\pi\)
−0.993726 + 0.111845i \(0.964324\pi\)
\(234\) −0.217471 + 0.125557i −0.0142165 + 0.00820790i
\(235\) −3.80970 + 2.19953i −0.248517 + 0.143481i
\(236\) −2.48203 1.43300i −0.161567 0.0932805i
\(237\) 18.6711 1.21282
\(238\) −6.30919 + 0.955442i −0.408964 + 0.0619321i
\(239\) 0.994204 0.0643097 0.0321549 0.999483i \(-0.489763\pi\)
0.0321549 + 0.999483i \(0.489763\pi\)
\(240\) 2.18257 + 1.26011i 0.140884 + 0.0813396i
\(241\) −8.98769 15.5671i −0.578948 1.00277i −0.995600 0.0937016i \(-0.970130\pi\)
0.416652 0.909066i \(-0.363203\pi\)
\(242\) 4.39611 + 7.61428i 0.282593 + 0.489465i
\(243\) 19.2027 + 11.0867i 1.23185 + 0.711210i
\(244\) −2.18242 −0.139715
\(245\) 1.58260 6.97850i 0.101108 0.445840i
\(246\) 5.27015 0.336013
\(247\) −0.146108 0.0843554i −0.00929662 0.00536741i
\(248\) 2.67411 1.54390i 0.169806 0.0980378i
\(249\) −7.71432 + 4.45386i −0.488875 + 0.282252i
\(250\) 4.57711 7.92778i 0.289482 0.501397i
\(251\) −20.0434 −1.26513 −0.632564 0.774508i \(-0.717997\pi\)
−0.632564 + 0.774508i \(0.717997\pi\)
\(252\) 8.05201 1.21937i 0.507229 0.0768130i
\(253\) 7.00580 + 1.30302i 0.440451 + 0.0819200i
\(254\) 3.06443 5.30774i 0.192279 0.333037i
\(255\) 5.26401 3.03917i 0.329645 0.190321i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 20.5193 + 11.8468i 1.27996 + 0.738984i 0.976841 0.213969i \(-0.0686391\pi\)
0.303118 + 0.952953i \(0.401972\pi\)
\(258\) −16.5122 −1.02800
\(259\) −0.384366 0.150544i −0.0238834 0.00935438i
\(260\) 0.0833960i 0.00517200i
\(261\) −0.527015 + 0.912816i −0.0326214 + 0.0565019i
\(262\) −11.3272 + 6.53974i −0.699794 + 0.404026i
\(263\) −3.14002 + 1.81289i −0.193622 + 0.111788i −0.593677 0.804703i \(-0.702324\pi\)
0.400055 + 0.916491i \(0.368991\pi\)
\(264\) −1.83160 + 3.17243i −0.112727 + 0.195249i
\(265\) 8.30822i 0.510370i
\(266\) 3.41436 + 4.27537i 0.209348 + 0.262140i
\(267\) 35.8505i 2.19401i
\(268\) 13.5852 + 7.84342i 0.829849 + 0.479113i
\(269\) 17.0267 9.83038i 1.03814 0.599369i 0.118832 0.992914i \(-0.462085\pi\)
0.919305 + 0.393546i \(0.128752\pi\)
\(270\) −0.170400 + 0.0983805i −0.0103702 + 0.00598725i
\(271\) 6.85141 + 3.95566i 0.416193 + 0.240289i 0.693447 0.720507i \(-0.256091\pi\)
−0.277254 + 0.960797i \(0.589424\pi\)
\(272\) −2.41184 −0.146239
\(273\) 0.332071 + 0.415810i 0.0200978 + 0.0251660i
\(274\) 10.5216i 0.635633i
\(275\) 5.08929 + 2.93830i 0.306896 + 0.177186i
\(276\) −3.93974 11.1478i −0.237145 0.671020i
\(277\) 7.97446 + 13.8122i 0.479139 + 0.829893i 0.999714 0.0239230i \(-0.00761567\pi\)
−0.520575 + 0.853816i \(0.674282\pi\)
\(278\) −14.3514 8.28579i −0.860740 0.496949i
\(279\) 9.50448i 0.569018i
\(280\) 0.986353 2.51833i 0.0589458 0.150499i
\(281\) 9.47524i 0.565246i 0.959231 + 0.282623i \(0.0912045\pi\)
−0.959231 + 0.282623i \(0.908796\pi\)
\(282\) −5.30467 + 9.18795i −0.315888 + 0.547135i
\(283\) 9.94962 + 17.2332i 0.591443 + 1.02441i 0.994038 + 0.109032i \(0.0347750\pi\)
−0.402595 + 0.915378i \(0.631892\pi\)
\(284\) 3.80629 + 6.59269i 0.225862 + 0.391204i
\(285\) −4.51357 2.60591i −0.267361 0.154361i
\(286\) −0.121219 −0.00716780
\(287\) −0.846830 5.59198i −0.0499868 0.330084i
\(288\) 3.07807 0.181377
\(289\) 5.59152 9.68479i 0.328913 0.569694i
\(290\) 0.175024 + 0.303151i 0.0102778 + 0.0178016i
\(291\) 33.0959 19.1079i 1.94012 1.12013i
\(292\) −5.53281 3.19437i −0.323783 0.186936i
\(293\) −5.49722 −0.321151 −0.160576 0.987024i \(-0.551335\pi\)
−0.160576 + 0.987024i \(0.551335\pi\)
\(294\) −5.10969 16.4838i −0.298003 0.961357i
\(295\) 2.92975i 0.170577i
\(296\) −0.135119 0.0780112i −0.00785366 0.00453431i
\(297\) −0.142999 0.247681i −0.00829764 0.0143719i
\(298\) −9.44175 + 5.45120i −0.546946 + 0.315779i
\(299\) 0.254284 0.297349i 0.0147056 0.0171961i
\(300\) 9.75060i 0.562951i
\(301\) 2.65325 + 17.5205i 0.152931 + 1.00987i
\(302\) −17.1677 −0.987892
\(303\) −20.6542 + 35.7741i −1.18655 + 2.05517i
\(304\) 1.03400 + 1.79095i 0.0593042 + 0.102718i
\(305\) −1.11548 1.93208i −0.0638724 0.110630i
\(306\) 3.71191 6.42921i 0.212196 0.367534i
\(307\) 13.1660i 0.751426i −0.926736 0.375713i \(-0.877398\pi\)
0.926736 0.375713i \(-0.122602\pi\)
\(308\) 3.66047 + 1.43369i 0.208574 + 0.0816922i
\(309\) 19.2007i 1.09229i
\(310\) 2.73360 + 1.57824i 0.155258 + 0.0896381i
\(311\) −7.00742 + 4.04574i −0.397354 + 0.229413i −0.685342 0.728222i \(-0.740347\pi\)
0.287987 + 0.957634i \(0.407014\pi\)
\(312\) 0.100564 + 0.174182i 0.00569333 + 0.00986114i
\(313\) 9.29473 16.0989i 0.525369 0.909966i −0.474194 0.880420i \(-0.657261\pi\)
0.999563 0.0295456i \(-0.00940604\pi\)
\(314\) −0.361133 −0.0203799
\(315\) 5.19505 + 6.50511i 0.292708 + 0.366522i
\(316\) 7.57333i 0.426033i
\(317\) 2.54483 4.40778i 0.142932 0.247566i −0.785667 0.618649i \(-0.787680\pi\)
0.928600 + 0.371083i \(0.121014\pi\)
\(318\) 10.0186 + 17.3527i 0.561814 + 0.973091i
\(319\) −0.440639 + 0.254403i −0.0246710 + 0.0142438i
\(320\) 0.511122 0.885289i 0.0285726 0.0494892i
\(321\) −16.0632 −0.896560
\(322\) −11.1955 + 5.97161i −0.623903 + 0.332785i
\(323\) 4.98770 0.277523
\(324\) 4.37984 7.58611i 0.243325 0.421451i
\(325\) 0.279428 0.161328i 0.0154999 0.00894886i
\(326\) −12.1574 21.0573i −0.673337 1.16625i
\(327\) −21.3272 + 36.9398i −1.17940 + 2.04278i
\(328\) 2.13767i 0.118033i
\(329\) 10.6014 + 4.15224i 0.584474 + 0.228921i
\(330\) −3.74469 −0.206138
\(331\) −4.57645 + 7.92664i −0.251544 + 0.435688i −0.963951 0.266079i \(-0.914272\pi\)
0.712407 + 0.701767i \(0.247605\pi\)
\(332\) 1.80657 + 3.12907i 0.0991482 + 0.171730i
\(333\) 0.415907 0.240124i 0.0227916 0.0131587i
\(334\) −11.3990 6.58122i −0.623726 0.360108i
\(335\) 16.0358i 0.876128i
\(336\) −0.976650 6.44924i −0.0532806 0.351835i
\(337\) 20.4152i 1.11209i −0.831153 0.556044i \(-0.812319\pi\)
0.831153 0.556044i \(-0.187681\pi\)
\(338\) 6.49667 11.2526i 0.353372 0.612059i
\(339\) 19.2546 + 33.3499i 1.04577 + 1.81132i
\(340\) −1.23274 2.13517i −0.0668549 0.115796i
\(341\) −2.29402 + 3.97336i −0.124228 + 0.215170i
\(342\) −6.36548 −0.344206
\(343\) −16.6694 + 8.07041i −0.900062 + 0.435761i
\(344\) 6.69764i 0.361113i
\(345\) 7.85536 9.18571i 0.422919 0.494542i
\(346\) −12.8768 + 7.43442i −0.692261 + 0.399677i
\(347\) 15.5611 + 26.9526i 0.835364 + 1.44689i 0.893734 + 0.448597i \(0.148076\pi\)
−0.0583706 + 0.998295i \(0.518591\pi\)
\(348\) 0.731118 + 0.422111i 0.0391920 + 0.0226275i
\(349\) 10.4339i 0.558517i −0.960216 0.279258i \(-0.909911\pi\)
0.960216 0.279258i \(-0.0900886\pi\)
\(350\) −10.3460 + 1.56677i −0.553019 + 0.0837472i
\(351\) −0.0157027 −0.000838150
\(352\) 1.28679 + 0.742931i 0.0685863 + 0.0395983i
\(353\) −5.09731 + 2.94294i −0.271303 + 0.156637i −0.629479 0.777017i \(-0.716732\pi\)
0.358177 + 0.933654i \(0.383398\pi\)
\(354\) −3.53289 6.11914i −0.187771 0.325229i
\(355\) −3.89096 + 6.73934i −0.206511 + 0.357687i
\(356\) −14.5416 −0.770703
\(357\) −14.6484 5.73732i −0.775274 0.303651i
\(358\) −16.4622 −0.870056
\(359\) 3.49303 + 2.01670i 0.184355 + 0.106437i 0.589337 0.807887i \(-0.299389\pi\)
−0.404982 + 0.914325i \(0.632722\pi\)
\(360\) 1.57327 + 2.72498i 0.0829186 + 0.143619i
\(361\) 7.36167 + 12.7508i 0.387456 + 0.671094i
\(362\) 10.4905 18.1700i 0.551367 0.954996i
\(363\) 21.6761i 1.13770i
\(364\) 0.168660 0.134694i 0.00884019 0.00705987i
\(365\) 6.53085i 0.341840i
\(366\) −4.65964 2.69025i −0.243563 0.140621i
\(367\) 16.5648 + 28.6912i 0.864678 + 1.49767i 0.867367 + 0.497670i \(0.165811\pi\)
−0.00268854 + 0.999996i \(0.500856\pi\)
\(368\) −4.52176 + 1.59803i −0.235713 + 0.0833031i
\(369\) 5.69836 + 3.28995i 0.296645 + 0.171268i
\(370\) 0.159493i 0.00829164i
\(371\) 16.8025 13.4187i 0.872344 0.696664i
\(372\) 7.61259 0.394694
\(373\) 2.62443 + 1.51522i 0.135888 + 0.0784549i 0.566403 0.824129i \(-0.308335\pi\)
−0.430515 + 0.902583i \(0.641668\pi\)
\(374\) 3.10354 1.79183i 0.160480 0.0926533i
\(375\) 19.5449 11.2843i 1.00930 0.582718i
\(376\) 3.72680 + 2.15167i 0.192195 + 0.110964i
\(377\) 0.0279360i 0.00143878i
\(378\) 0.474179 + 0.185722i 0.0243892 + 0.00955249i
\(379\) 20.8285i 1.06989i −0.844888 0.534943i \(-0.820333\pi\)
0.844888 0.534943i \(-0.179667\pi\)
\(380\) −1.05700 + 1.83078i −0.0542232 + 0.0939173i
\(381\) 13.0856 7.55496i 0.670394 0.387052i
\(382\) 8.61942 4.97643i 0.441008 0.254616i
\(383\) 14.8397 25.7031i 0.758272 1.31337i −0.185458 0.982652i \(-0.559377\pi\)
0.943731 0.330714i \(-0.107290\pi\)
\(384\) 2.46537i 0.125811i
\(385\) 0.601712 + 3.97336i 0.0306661 + 0.202501i
\(386\) 11.0604 0.562959
\(387\) −17.8538 10.3079i −0.907561 0.523981i
\(388\) −7.75052 13.4243i −0.393473 0.681515i
\(389\) 8.91834 5.14901i 0.452178 0.261065i −0.256572 0.966525i \(-0.582593\pi\)
0.708750 + 0.705460i \(0.249260\pi\)
\(390\) −0.102801 + 0.178057i −0.00520554 + 0.00901626i
\(391\) −2.11505 + 11.3718i −0.106963 + 0.575094i
\(392\) −6.68614 + 2.07258i −0.337701 + 0.104681i
\(393\) −32.2458 −1.62659
\(394\) −5.65304 + 9.79136i −0.284796 + 0.493282i
\(395\) 6.70459 3.87089i 0.337344 0.194766i
\(396\) −3.96085 + 2.28680i −0.199040 + 0.114916i
\(397\) 24.4139 + 14.0954i 1.22530 + 0.707427i 0.966043 0.258381i \(-0.0831891\pi\)
0.259257 + 0.965808i \(0.416522\pi\)
\(398\) −13.3860 −0.670979
\(399\) 2.01972 + 13.3371i 0.101112 + 0.667689i
\(400\) −3.95502 −0.197751
\(401\) −8.50199 4.90863i −0.424569 0.245125i 0.272461 0.962167i \(-0.412162\pi\)
−0.697030 + 0.717042i \(0.745496\pi\)
\(402\) 19.3370 + 33.4926i 0.964441 + 1.67046i
\(403\) 0.125953 + 0.218158i 0.00627419 + 0.0108672i
\(404\) 14.5106 + 8.37770i 0.721929 + 0.416806i
\(405\) 8.95453 0.444954
\(406\) 0.330409 0.843591i 0.0163979 0.0418667i
\(407\) 0.231828 0.0114913
\(408\) −5.14946 2.97304i −0.254936 0.147188i
\(409\) 6.44300 3.71987i 0.318586 0.183936i −0.332176 0.943217i \(-0.607783\pi\)
0.650762 + 0.759282i \(0.274450\pi\)
\(410\) 1.89245 1.09261i 0.0934617 0.0539601i
\(411\) −12.9698 + 22.4644i −0.639755 + 1.10809i
\(412\) −7.78814 −0.383694
\(413\) −5.92513 + 4.73188i −0.291557 + 0.232840i
\(414\) 2.69930 14.5130i 0.132663 0.713277i
\(415\) −1.84675 + 3.19867i −0.0906535 + 0.157016i
\(416\) 0.0706515 0.0407907i 0.00346398 0.00199993i
\(417\) −20.4276 35.3816i −1.00034 1.73264i
\(418\) −2.66110 1.53639i −0.130159 0.0751471i
\(419\) −32.1651 −1.57137 −0.785684 0.618628i \(-0.787689\pi\)
−0.785684 + 0.618628i \(0.787689\pi\)
\(420\) 5.21025 4.16096i 0.254234 0.203034i
\(421\) 0.626009i 0.0305098i −0.999884 0.0152549i \(-0.995144\pi\)
0.999884 0.0152549i \(-0.00485597\pi\)
\(422\) −6.65452 + 11.5260i −0.323937 + 0.561075i
\(423\) −11.4714 + 6.62299i −0.557756 + 0.322021i
\(424\) 7.03856 4.06372i 0.341823 0.197352i
\(425\) −4.76943 + 8.26090i −0.231351 + 0.400712i
\(426\) 18.7679i 0.909307i
\(427\) −2.10580 + 5.37647i −0.101907 + 0.260186i
\(428\) 6.51552i 0.314940i
\(429\) −0.258811 0.149425i −0.0124955 0.00721429i
\(430\) −5.92935 + 3.42331i −0.285939 + 0.165087i
\(431\) 31.1064 17.9593i 1.49834 0.865068i 0.498343 0.866980i \(-0.333942\pi\)
0.999998 + 0.00191218i \(0.000608667\pi\)
\(432\) 0.166692 + 0.0962398i 0.00801998 + 0.00463034i
\(433\) −9.42386 −0.452882 −0.226441 0.974025i \(-0.572709\pi\)
−0.226441 + 0.974025i \(0.572709\pi\)
\(434\) −1.22322 8.07746i −0.0587165 0.387730i
\(435\) 0.863001i 0.0413777i
\(436\) 14.9835 + 8.65070i 0.717577 + 0.414293i
\(437\) 9.35103 3.30474i 0.447321 0.158087i
\(438\) −7.87532 13.6405i −0.376297 0.651766i
\(439\) −21.4226 12.3684i −1.02245 0.590309i −0.107634 0.994191i \(-0.534328\pi\)
−0.914811 + 0.403881i \(0.867661\pi\)
\(440\) 1.51891i 0.0724113i
\(441\) 4.76535 21.0129i 0.226921 1.00062i
\(442\) 0.196761i 0.00935897i
\(443\) −3.93090 + 6.80852i −0.186763 + 0.323483i −0.944169 0.329461i \(-0.893133\pi\)
0.757406 + 0.652944i \(0.226466\pi\)
\(444\) −0.192327 0.333120i −0.00912743 0.0158092i
\(445\) −7.43253 12.8735i −0.352336 0.610263i
\(446\) 11.9380 + 6.89243i 0.565283 + 0.326366i
\(447\) −26.8785 −1.27131
\(448\) −2.61593 + 0.396147i −0.123591 + 0.0187162i
\(449\) 19.7956 0.934213 0.467107 0.884201i \(-0.345296\pi\)
0.467107 + 0.884201i \(0.345296\pi\)
\(450\) 6.08692 10.5428i 0.286940 0.496995i
\(451\) 1.58814 + 2.75074i 0.0747826 + 0.129527i
\(452\) 13.5273 7.81001i 0.636272 0.367352i
\(453\) −36.6544 21.1625i −1.72218 0.994299i
\(454\) 9.98815 0.468767
\(455\) 0.205449 + 0.0804680i 0.00963158 + 0.00377240i
\(456\) 5.09841i 0.238755i
\(457\) −6.77168 3.90963i −0.316766 0.182885i 0.333184 0.942862i \(-0.391877\pi\)
−0.649950 + 0.759977i \(0.725210\pi\)
\(458\) 7.15920 + 12.4001i 0.334527 + 0.579418i
\(459\) 0.402035 0.232115i 0.0187654 0.0108342i
\(460\) −3.72589 3.18628i −0.173720 0.148561i
\(461\) 5.25112i 0.244569i −0.992495 0.122284i \(-0.960978\pi\)
0.992495 0.122284i \(-0.0390220\pi\)
\(462\) 6.04808 + 7.57326i 0.281382 + 0.352340i
\(463\) −6.73239 −0.312881 −0.156440 0.987687i \(-0.550002\pi\)
−0.156440 + 0.987687i \(0.550002\pi\)
\(464\) 0.171216 0.296554i 0.00794849 0.0137672i
\(465\) 3.89096 + 6.73934i 0.180439 + 0.312529i
\(466\) 9.06280 + 15.6972i 0.419826 + 0.727160i
\(467\) 6.40963 11.1018i 0.296602 0.513730i −0.678754 0.734366i \(-0.737480\pi\)
0.975356 + 0.220636i \(0.0708131\pi\)
\(468\) 0.251113i 0.0116077i
\(469\) 32.4308 25.8995i 1.49751 1.19593i
\(470\) 4.39906i 0.202913i
\(471\) −0.771048 0.445165i −0.0355280 0.0205121i
\(472\) −2.48203 + 1.43300i −0.114245 + 0.0659593i
\(473\) −4.97588 8.61848i −0.228791 0.396278i
\(474\) 9.33555 16.1696i 0.428796 0.742696i
\(475\) 8.17901 0.375279
\(476\) −2.32716 + 5.94164i −0.106665 + 0.272335i
\(477\) 25.0168i 1.14544i
\(478\) 0.497102 0.861006i 0.0227369 0.0393815i
\(479\) 3.59812 + 6.23212i 0.164402 + 0.284753i 0.936443 0.350820i \(-0.114097\pi\)
−0.772041 + 0.635573i \(0.780764\pi\)
\(480\) 2.18257 1.26011i 0.0996202 0.0575158i
\(481\) 0.00636426 0.0110232i 0.000290185 0.000502616i
\(482\) −17.9754 −0.818756
\(483\) −31.2644 1.05075i −1.42258 0.0478106i
\(484\) 8.79222 0.399646
\(485\) 7.92292 13.7229i 0.359761 0.623125i
\(486\) 19.2027 11.0867i 0.871051 0.502902i
\(487\) −7.22065 12.5065i −0.327199 0.566725i 0.654756 0.755840i \(-0.272771\pi\)
−0.981955 + 0.189115i \(0.939438\pi\)
\(488\) −1.09121 + 1.89003i −0.0493968 + 0.0855578i
\(489\) 59.9452i 2.71082i
\(490\) −5.25226 4.85982i −0.237273 0.219544i
\(491\) 36.8916 1.66490 0.832448 0.554103i \(-0.186939\pi\)
0.832448 + 0.554103i \(0.186939\pi\)
\(492\) 2.63508 4.56409i 0.118798 0.205765i
\(493\) −0.412945 0.715242i −0.0185981 0.0322129i
\(494\) −0.146108 + 0.0843554i −0.00657370 + 0.00379533i
\(495\) −4.04895 2.33766i −0.181987 0.105070i
\(496\) 3.08780i 0.138646i
\(497\) 19.9140 3.01570i 0.893263 0.135273i
\(498\) 8.90773i 0.399165i
\(499\) 2.83621 4.91245i 0.126966 0.219912i −0.795534 0.605909i \(-0.792809\pi\)
0.922500 + 0.385998i \(0.126143\pi\)
\(500\) −4.57711 7.92778i −0.204694 0.354541i
\(501\) −16.2252 28.1028i −0.724887 1.25554i
\(502\) −10.0217 + 17.3581i −0.447290 + 0.774729i
\(503\) −27.9984 −1.24839 −0.624194 0.781269i \(-0.714573\pi\)
−0.624194 + 0.781269i \(0.714573\pi\)
\(504\) 2.97000 7.58293i 0.132294 0.337771i
\(505\) 17.1281i 0.762190i
\(506\) 4.63134 5.41569i 0.205888 0.240757i
\(507\) 27.7418 16.0167i 1.23206 0.711328i
\(508\) −3.06443 5.30774i −0.135962 0.235493i
\(509\) 27.6822 + 15.9823i 1.22699 + 0.708403i 0.966399 0.257046i \(-0.0827491\pi\)
0.260592 + 0.965449i \(0.416082\pi\)
\(510\) 6.07835i 0.269154i
\(511\) −13.2080 + 10.5480i −0.584287 + 0.466618i
\(512\) −1.00000 −0.0441942
\(513\) −0.344721 0.199025i −0.0152198 0.00878715i
\(514\) 20.5193 11.8468i 0.905067 0.522541i
\(515\) −3.98069 6.89475i −0.175410 0.303819i
\(516\) −8.25610 + 14.3000i −0.363454 + 0.629522i
\(517\) −6.39416 −0.281215
\(518\) −0.322558 + 0.257599i −0.0141724 + 0.0113182i
\(519\) −36.6573 −1.60908
\(520\) 0.0722231 + 0.0416980i 0.00316719 + 0.00182858i
\(521\) −15.6394 27.0883i −0.685175 1.18676i −0.973382 0.229190i \(-0.926392\pi\)
0.288207 0.957568i \(-0.406941\pi\)
\(522\) 0.527015 + 0.912816i 0.0230668 + 0.0399529i
\(523\) 15.2538 26.4204i 0.667004 1.15528i −0.311734 0.950169i \(-0.600910\pi\)
0.978738 0.205115i \(-0.0657569\pi\)
\(524\) 13.0795i 0.571380i
\(525\) −24.0209 9.40826i −1.04836 0.410610i
\(526\) 3.62578i 0.158092i
\(527\) −6.44953 3.72364i −0.280946 0.162204i
\(528\) 1.83160 + 3.17243i 0.0797103 + 0.138062i
\(529\) 3.56934 + 22.7214i 0.155189 + 0.987885i
\(530\) 7.19513 + 4.15411i 0.312536 + 0.180443i
\(531\) 8.82177i 0.382832i
\(532\) 5.40976 0.819234i 0.234543 0.0355183i
\(533\) 0.174394 0.00755384
\(534\) −31.0474 17.9252i −1.34355 0.775701i
\(535\) −5.76812 + 3.33022i −0.249378 + 0.143978i
\(536\) 13.5852 7.84342i 0.586792 0.338784i
\(537\) −35.1481 20.2928i −1.51675 0.875699i
\(538\) 19.6608i 0.847635i
\(539\) 7.06389 7.63432i 0.304263 0.328833i
\(540\) 0.196761i 0.00846725i
\(541\) 18.7925 32.5496i 0.807953 1.39941i −0.106327 0.994331i \(-0.533909\pi\)
0.914280 0.405084i \(-0.132758\pi\)
\(542\) 6.85141 3.95566i 0.294293 0.169910i
\(543\) 44.7960 25.8630i 1.92238 1.10989i
\(544\) −1.20592 + 2.08871i −0.0517034 + 0.0895529i
\(545\) 17.6863i 0.757596i
\(546\) 0.526137 0.0796764i 0.0225166 0.00340984i
\(547\) 0.838058 0.0358328 0.0179164 0.999839i \(-0.494297\pi\)
0.0179164 + 0.999839i \(0.494297\pi\)
\(548\) 9.11197 + 5.26080i 0.389244 + 0.224730i
\(549\) −3.35883 5.81766i −0.143351 0.248292i
\(550\) 5.08929 2.93830i 0.217008 0.125290i
\(551\) −0.354076 + 0.613277i −0.0150841 + 0.0261265i
\(552\) −11.6242 2.16200i −0.494758 0.0920207i
\(553\) −18.6571 7.30743i −0.793382 0.310744i
\(554\) 15.9489 0.677605
\(555\) 0.196605 0.340530i 0.00834542 0.0144547i
\(556\) −14.3514 + 8.28579i −0.608635 + 0.351396i
\(557\) −14.2817 + 8.24557i −0.605137 + 0.349376i −0.771060 0.636763i \(-0.780273\pi\)
0.165923 + 0.986139i \(0.446940\pi\)
\(558\) 8.23112 + 4.75224i 0.348451 + 0.201178i
\(559\) −0.546403 −0.0231104
\(560\) −1.68776 2.11337i −0.0713209 0.0893062i
\(561\) 8.83506 0.373017
\(562\) 8.20580 + 4.73762i 0.346141 + 0.199845i
\(563\) 16.6530 + 28.8438i 0.701840 + 1.21562i 0.967820 + 0.251645i \(0.0809714\pi\)
−0.265979 + 0.963979i \(0.585695\pi\)
\(564\) 5.30467 + 9.18795i 0.223367 + 0.386883i
\(565\) 13.8282 + 7.98373i 0.581758 + 0.335878i
\(566\) 19.8992 0.836427
\(567\) −14.4626 18.1096i −0.607370 0.760533i
\(568\) 7.61259 0.319417
\(569\) 19.6304 + 11.3336i 0.822951 + 0.475131i 0.851433 0.524463i \(-0.175734\pi\)
−0.0284820 + 0.999594i \(0.509067\pi\)
\(570\) −4.51357 + 2.60591i −0.189053 + 0.109150i
\(571\) −4.61506 + 2.66451i −0.193134 + 0.111506i −0.593449 0.804872i \(-0.702234\pi\)
0.400315 + 0.916378i \(0.368901\pi\)
\(572\) −0.0606093 + 0.104978i −0.00253420 + 0.00438937i
\(573\) 24.5375 1.02507
\(574\) −5.26621 2.06261i −0.219808 0.0860919i
\(575\) −3.46833 + 18.6478i −0.144639 + 0.777667i
\(576\) 1.53904 2.66569i 0.0641265 0.111070i
\(577\) 4.66357 2.69251i 0.194147 0.112091i −0.399776 0.916613i \(-0.630912\pi\)
0.593922 + 0.804522i \(0.297579\pi\)
\(578\) −5.59152 9.68479i −0.232576 0.402834i
\(579\) 23.6148 + 13.6340i 0.981397 + 0.566610i
\(580\) 0.350049 0.0145350
\(581\) 9.45169 1.43133i 0.392122 0.0593816i
\(582\) 38.2159i 1.58410i
\(583\) −6.03812 + 10.4583i −0.250073 + 0.433140i
\(584\) −5.53281 + 3.19437i −0.228949 + 0.132184i
\(585\) −0.222308 + 0.128350i −0.00919130 + 0.00530660i
\(586\) −2.74861 + 4.76074i −0.113544 + 0.196664i
\(587\) 29.0516i 1.19909i 0.800342 + 0.599543i \(0.204651\pi\)
−0.800342 + 0.599543i \(0.795349\pi\)
\(588\) −16.8303 3.81680i −0.694068 0.157402i
\(589\) 6.38560i 0.263114i
\(590\) −2.53724 1.46488i −0.104457 0.0603081i
\(591\) −24.1394 + 13.9369i −0.992961 + 0.573286i
\(592\) −0.135119 + 0.0780112i −0.00555337 + 0.00320624i
\(593\) −11.5856 6.68893i −0.475762 0.274682i 0.242886 0.970055i \(-0.421906\pi\)
−0.718649 + 0.695373i \(0.755239\pi\)
\(594\) −0.285998 −0.0117346
\(595\) −6.44953 + 0.976694i −0.264405 + 0.0400406i
\(596\) 10.9024i 0.446580i
\(597\) −28.5801 16.5007i −1.16971 0.675330i
\(598\) −0.130369 0.368891i −0.00533120 0.0150851i
\(599\) 13.1165 + 22.7184i 0.535925 + 0.928249i 0.999118 + 0.0419915i \(0.0133702\pi\)
−0.463193 + 0.886257i \(0.653296\pi\)
\(600\) −8.44427 4.87530i −0.344736 0.199033i
\(601\) 6.64915i 0.271225i 0.990762 + 0.135612i \(0.0433002\pi\)
−0.990762 + 0.135612i \(0.956700\pi\)
\(602\) 16.4999 + 6.46249i 0.672484 + 0.263391i
\(603\) 48.2853i 1.96633i
\(604\) −8.58387 + 14.8677i −0.349273 + 0.604958i
\(605\) 4.49389 + 7.78365i 0.182703 + 0.316450i
\(606\) 20.6542 + 35.7741i 0.839018 + 1.45322i
\(607\) −7.01860 4.05219i −0.284876 0.164473i 0.350753 0.936468i \(-0.385926\pi\)
−0.635629 + 0.771995i \(0.719259\pi\)
\(608\) 2.06801 0.0838688
\(609\) 1.74533 1.39384i 0.0707244 0.0564813i
\(610\) −2.23097 −0.0903293
\(611\) −0.175536 + 0.304037i −0.00710142 + 0.0123000i
\(612\) −3.71191 6.42921i −0.150045 0.259886i
\(613\) −6.10873 + 3.52688i −0.246729 + 0.142449i −0.618266 0.785969i \(-0.712164\pi\)
0.371536 + 0.928418i \(0.378831\pi\)
\(614\) −11.4021 6.58302i −0.460153 0.265669i
\(615\) 5.38738 0.217240
\(616\) 3.07185 2.45321i 0.123768 0.0988427i
\(617\) 25.1391i 1.01206i 0.862515 + 0.506032i \(0.168888\pi\)
−0.862515 + 0.506032i \(0.831112\pi\)
\(618\) −16.6283 9.60034i −0.668887 0.386182i
\(619\) 1.93440 + 3.35049i 0.0777503 + 0.134667i 0.902279 0.431153i \(-0.141893\pi\)
−0.824529 + 0.565820i \(0.808560\pi\)
\(620\) 2.73360 1.57824i 0.109784 0.0633837i
\(621\) 0.599948 0.701552i 0.0240751 0.0281523i
\(622\) 8.09147i 0.324439i
\(623\) −14.0310 + 35.8237i −0.562142 + 1.43525i
\(624\) 0.201129 0.00805159
\(625\) −5.20863 + 9.02161i −0.208345 + 0.360864i
\(626\) −9.29473 16.0989i −0.371492 0.643443i
\(627\) −3.78777 6.56061i −0.151269 0.262005i
\(628\) −0.180567 + 0.312751i −0.00720539 + 0.0124801i
\(629\) 0.376301i 0.0150041i
\(630\) 8.23112 1.24649i 0.327936 0.0496614i
\(631\) 9.33314i 0.371546i 0.982593 + 0.185773i \(0.0594790\pi\)
−0.982593 + 0.185773i \(0.940521\pi\)
\(632\) −6.55870 3.78667i −0.260891 0.150625i
\(633\) −28.4158 + 16.4059i −1.12943 + 0.652076i
\(634\) −2.54483 4.40778i −0.101068 0.175055i
\(635\) 3.13259 5.42581i 0.124313 0.215317i
\(636\) 20.0372 0.794526
\(637\) −0.169084 0.545464i −0.00669935 0.0216121i
\(638\) 0.508806i 0.0201438i
\(639\) −11.7160 + 20.2928i −0.463480 + 0.802770i
\(640\) −0.511122 0.885289i −0.0202039 0.0349941i
\(641\) 19.6315 11.3343i 0.775398 0.447676i −0.0593988 0.998234i \(-0.518918\pi\)
0.834797 + 0.550558i \(0.185585\pi\)
\(642\) −8.03160 + 13.9111i −0.316982 + 0.549029i
\(643\) −2.18923 −0.0863347 −0.0431673 0.999068i \(-0.513745\pi\)
−0.0431673 + 0.999068i \(0.513745\pi\)
\(644\) −0.426201 + 12.6814i −0.0167947 + 0.499718i
\(645\) −16.8795 −0.664629
\(646\) 2.49385 4.31948i 0.0981192 0.169948i
\(647\) −3.21752 + 1.85764i −0.126494 + 0.0730313i −0.561912 0.827197i \(-0.689934\pi\)
0.435418 + 0.900228i \(0.356601\pi\)
\(648\) −4.37984 7.58611i −0.172056 0.298011i
\(649\) 2.12924 3.68796i 0.0835801 0.144765i
\(650\) 0.322656i 0.0126556i
\(651\) 7.34531 18.7538i 0.287885 0.735021i
\(652\) −24.3148 −0.952243
\(653\) −16.1362 + 27.9487i −0.631458 + 1.09372i 0.355795 + 0.934564i \(0.384210\pi\)
−0.987254 + 0.159154i \(0.949123\pi\)
\(654\) 21.3272 + 36.9398i 0.833960 + 1.44446i
\(655\) −11.5791 + 6.68521i −0.452434 + 0.261213i
\(656\) −1.85128 1.06883i −0.0722802 0.0417310i
\(657\) 19.6650i 0.767205i
\(658\) 8.89665 7.10496i 0.346828 0.276980i
\(659\) 21.0261i 0.819060i −0.912297 0.409530i \(-0.865693\pi\)
0.912297 0.409530i \(-0.134307\pi\)
\(660\) −1.87234 + 3.24300i −0.0728809 + 0.126233i
\(661\) −1.01116 1.75138i −0.0393295 0.0681207i 0.845691 0.533674i \(-0.179189\pi\)
−0.885020 + 0.465553i \(0.845856\pi\)
\(662\) 4.57645 + 7.92664i 0.177869 + 0.308078i
\(663\) 0.242545 0.420100i 0.00941966 0.0163153i
\(664\) 3.61313 0.140217
\(665\) 3.49030 + 4.37047i 0.135348 + 0.169480i
\(666\) 0.480248i 0.0186093i
\(667\) −1.24810 1.06734i −0.0483266 0.0413276i
\(668\) −11.3990 + 6.58122i −0.441041 + 0.254635i
\(669\) 16.9924 + 29.4317i 0.656965 + 1.13790i
\(670\) 13.8874 + 8.01789i 0.536517 + 0.309758i
\(671\) 3.24278i 0.125186i
\(672\) −6.07353 2.37882i −0.234291 0.0917648i
\(673\) −24.9185 −0.960538 −0.480269 0.877121i \(-0.659461\pi\)
−0.480269 + 0.877121i \(0.659461\pi\)
\(674\) −17.6801 10.2076i −0.681012 0.393183i
\(675\) 0.659271 0.380630i 0.0253753 0.0146505i
\(676\) −6.49667 11.2526i −0.249872 0.432791i
\(677\) 14.4527 25.0329i 0.555464 0.962092i −0.442403 0.896816i \(-0.645874\pi\)
0.997867 0.0652757i \(-0.0207927\pi\)
\(678\) 38.5092 1.47894
\(679\) −40.5496 + 6.14068i −1.55615 + 0.235658i
\(680\) −2.46549 −0.0945471
\(681\) 21.3255 + 12.3123i 0.817194 + 0.471807i
\(682\) 2.29402 + 3.97336i 0.0878426 + 0.152148i
\(683\) 14.6289 + 25.3379i 0.559757 + 0.969528i 0.997516 + 0.0704359i \(0.0224390\pi\)
−0.437759 + 0.899092i \(0.644228\pi\)
\(684\) −3.18274 + 5.51267i −0.121695 + 0.210782i
\(685\) 10.7556i 0.410952i
\(686\) −1.34552 + 18.4713i −0.0513721 + 0.705238i
\(687\) 35.3002i 1.34679i
\(688\) 5.80033 + 3.34882i 0.221135 + 0.127673i
\(689\) 0.331524 + 0.574216i 0.0126300 + 0.0218759i
\(690\) −4.02738 11.3958i −0.153320 0.433831i
\(691\) −21.6346 12.4907i −0.823018 0.475170i 0.0284381 0.999596i \(-0.490947\pi\)
−0.851456 + 0.524426i \(0.824280\pi\)
\(692\) 14.8688i 0.565229i
\(693\) 1.81181 + 11.9642i 0.0688251 + 0.454481i
\(694\) 31.1222 1.18138
\(695\) −14.6706 8.47009i −0.556489 0.321289i
\(696\) 0.731118 0.422111i 0.0277130 0.0160001i
\(697\) −4.46498 + 2.57786i −0.169123 + 0.0976433i
\(698\) −9.03607 5.21697i −0.342020 0.197465i
\(699\) 44.6864i 1.69019i
\(700\) −3.81616 + 9.74331i −0.144237 + 0.368263i
\(701\) 8.46507i 0.319721i 0.987140 + 0.159861i \(0.0511045\pi\)
−0.987140 + 0.159861i \(0.948896\pi\)
\(702\) −0.00785137 + 0.0135990i −0.000296331 + 0.000513260i
\(703\) 0.279428 0.161328i 0.0105388 0.00608459i
\(704\) 1.28679 0.742931i 0.0484979 0.0280003i
\(705\) −5.42266 + 9.39233i −0.204229 + 0.353736i
\(706\) 5.88587i 0.221518i
\(707\) 34.6399 27.6638i 1.30277 1.04040i
\(708\) −7.06577 −0.265548
\(709\) −23.3960 13.5077i −0.878655 0.507292i −0.00844049 0.999964i \(-0.502687\pi\)
−0.870215 + 0.492673i \(0.836020\pi\)
\(710\) 3.89096 + 6.73934i 0.146025 + 0.252923i
\(711\) 20.1881 11.6556i 0.757115 0.437120i
\(712\) −7.27080 + 12.5934i −0.272485 + 0.471957i
\(713\) −14.5589 2.70783i −0.545235 0.101409i
\(714\) −12.2928 + 9.81720i −0.460048 + 0.367400i
\(715\) −0.123915 −0.00463416
\(716\) −8.23112 + 14.2567i −0.307611 + 0.532798i
\(717\) 2.12270 1.22554i 0.0792738 0.0457687i
\(718\) 3.49303 2.01670i 0.130359 0.0752626i
\(719\) 27.7231 + 16.0059i 1.03390 + 0.596921i 0.918099 0.396352i \(-0.129724\pi\)
0.115799 + 0.993273i \(0.463057\pi\)
\(720\) 3.14654 0.117265
\(721\) −7.51469 + 19.1863i −0.279862 + 0.714536i
\(722\) 14.7233 0.547946
\(723\) −38.3788 22.1580i −1.42732 0.824066i
\(724\) −10.4905 18.1700i −0.389876 0.675284i
\(725\) −0.677162 1.17288i −0.0251491 0.0435596i
\(726\) 18.7721 + 10.8381i 0.696696 + 0.402238i
\(727\) 31.7477 1.17746 0.588728 0.808331i \(-0.299629\pi\)
0.588728 + 0.808331i \(0.299629\pi\)
\(728\) −0.0323182 0.213411i −0.00119779 0.00790953i
\(729\) 28.3866 1.05135
\(730\) −5.65588 3.26542i −0.209334 0.120859i
\(731\) 13.9895 8.07682i 0.517419 0.298732i
\(732\) −4.65964 + 2.69025i −0.172225 + 0.0994343i
\(733\) 19.2615 33.3619i 0.711440 1.23225i −0.252877 0.967498i \(-0.581377\pi\)
0.964317 0.264751i \(-0.0852899\pi\)
\(734\) 33.1297 1.22284
\(735\) −5.22335 16.8505i −0.192666 0.621540i
\(736\) −0.876945 + 4.71497i −0.0323246 + 0.173796i
\(737\) −11.6542 + 20.1857i −0.429289 + 0.743551i
\(738\) 5.69836 3.28995i 0.209760 0.121105i
\(739\) −19.9020 34.4712i −0.732106 1.26805i −0.955981 0.293427i \(-0.905204\pi\)
0.223875 0.974618i \(-0.428129\pi\)
\(740\) −0.138125 0.0797465i −0.00507757 0.00293154i
\(741\) −0.415936 −0.0152798
\(742\) −3.21966 21.2608i −0.118197 0.780507i
\(743\) 39.5642i 1.45147i 0.687974 + 0.725735i \(0.258500\pi\)
−0.687974 + 0.725735i \(0.741500\pi\)
\(744\) 3.80629 6.59269i 0.139545 0.241700i
\(745\) −9.65177 + 5.57245i −0.353614 + 0.204159i
\(746\) 2.62443 1.51522i 0.0960872 0.0554760i
\(747\) −5.56075 + 9.63149i −0.203457 + 0.352398i
\(748\) 3.58366i 0.131032i
\(749\) 16.0512 + 6.28676i 0.586498 + 0.229713i
\(750\) 22.5686i 0.824087i
\(751\) −7.65953 4.42223i −0.279500 0.161369i 0.353697 0.935360i \(-0.384924\pi\)
−0.633197 + 0.773991i \(0.718258\pi\)
\(752\) 3.72680 2.15167i 0.135902 0.0784632i
\(753\) −42.7942 + 24.7072i −1.55951 + 0.900382i
\(754\) 0.0241933 + 0.0139680i 0.000881068 + 0.000508685i
\(755\) −17.5496 −0.638696
\(756\) 0.397929 0.317791i 0.0144725 0.0115579i
\(757\) 19.5400i 0.710195i −0.934829 0.355098i \(-0.884448\pi\)
0.934829 0.355098i \(-0.115552\pi\)
\(758\) −18.0380 10.4142i −0.655169 0.378262i
\(759\) 16.5641 5.85391i 0.601240 0.212484i
\(760\) 1.05700 + 1.83078i 0.0383416 + 0.0664095i
\(761\) −14.6407 8.45283i −0.530726 0.306415i 0.210586 0.977575i \(-0.432463\pi\)
−0.741312 + 0.671161i \(0.765796\pi\)
\(762\) 15.1099i 0.547375i
\(763\) 35.7687 28.5652i 1.29491 1.03413i
\(764\) 9.95285i 0.360082i
\(765\) 3.79447 6.57222i 0.137190 0.237619i
\(766\) −14.8397 25.7031i −0.536180 0.928690i
\(767\) −0.116906 0.202488i −0.00422124 0.00731140i
\(768\) −2.13508 1.23269i −0.0770430 0.0444808i
\(769\) 44.2342 1.59513 0.797563 0.603236i \(-0.206122\pi\)
0.797563 + 0.603236i \(0.206122\pi\)
\(770\) 3.74189 + 1.46558i 0.134848 + 0.0528160i
\(771\) 58.4137 2.10372
\(772\) 5.53019 9.57857i 0.199036 0.344740i
\(773\) 19.1314 + 33.1365i 0.688108 + 1.19184i 0.972449 + 0.233115i \(0.0748917\pi\)
−0.284341 + 0.958723i \(0.591775\pi\)
\(774\) −17.8538 + 10.3079i −0.641743 + 0.370510i
\(775\) −10.5762 6.10615i −0.379907 0.219339i
\(776\) −15.5010 −0.556455
\(777\) −1.00623 + 0.152379i −0.0360981 + 0.00546658i
\(778\) 10.2980i 0.369202i
\(779\) 3.82845 + 2.21036i 0.137169 + 0.0791943i
\(780\) 0.102801 + 0.178057i 0.00368087 + 0.00637546i
\(781\) −9.79583 + 5.65562i −0.350522 + 0.202374i
\(782\) 8.79070 + 7.51756i 0.314355 + 0.268828i
\(783\) 0.0659111i 0.00235547i
\(784\) −1.54816 + 6.82665i −0.0552914 + 0.243809i
\(785\) −0.369166 −0.0131761
\(786\) −16.1229 + 27.9257i −0.575085 + 0.996076i
\(787\) 20.5080 + 35.5209i 0.731031 + 1.26618i 0.956443 + 0.291920i \(0.0942940\pi\)
−0.225412 + 0.974264i \(0.572373\pi\)
\(788\) 5.65304 + 9.79136i 0.201381 + 0.348803i
\(789\) −4.46946 + 7.74132i −0.159117 + 0.275598i
\(790\) 7.74179i 0.275441i
\(791\) −6.18782 40.8608i −0.220013 1.45284i
\(792\) 4.57359i 0.162515i
\(793\) −0.154191 0.0890225i −0.00547550 0.00316128i
\(794\) 24.4139 14.0954i 0.866418 0.500227i
\(795\) 10.2414 + 17.7387i 0.363226 + 0.629127i
\(796\) −6.69299 + 11.5926i −0.237227 + 0.410889i
\(797\) −32.1997 −1.14057 −0.570286 0.821446i \(-0.693168\pi\)
−0.570286 + 0.821446i \(0.693168\pi\)
\(798\) 12.5601 + 4.91941i 0.444623 + 0.174145i
\(799\) 10.3790i 0.367181i
\(800\) −1.97751 + 3.42515i −0.0699155 + 0.121097i
\(801\) −22.3800 38.7634i −0.790760 1.36964i
\(802\) −8.50199 + 4.90863i −0.300216 + 0.173330i
\(803\) 4.74639 8.22099i 0.167496 0.290112i
\(804\) 38.6740 1.36393
\(805\) −11.4446 + 6.10444i −0.403368 + 0.215153i
\(806\) 0.251907 0.00887304
\(807\) 24.2356 41.9772i 0.853132 1.47767i
\(808\) 14.5106 8.37770i 0.510481 0.294726i
\(809\) −0.597463 1.03484i −0.0210057 0.0363829i 0.855331 0.518081i \(-0.173353\pi\)
−0.876337 + 0.481698i \(0.840020\pi\)
\(810\) 4.47727 7.75485i 0.157315 0.272478i
\(811\) 32.5133i 1.14170i −0.821055 0.570849i \(-0.806614\pi\)
0.821055 0.570849i \(-0.193386\pi\)
\(812\) −0.565367 0.707938i −0.0198405 0.0248438i
\(813\) 19.5044 0.684048
\(814\) 0.115914 0.200769i 0.00406278 0.00703694i
\(815\) −12.4278 21.5257i −0.435328 0.754011i
\(816\) −5.14946 + 2.97304i −0.180267 + 0.104077i
\(817\) −11.9951 6.92539i −0.419656 0.242289i
\(818\) 7.43973i 0.260124i
\(819\) 0.618626 + 0.242297i 0.0216165 + 0.00846653i
\(820\) 2.18522i 0.0763111i
\(821\) 13.0689 22.6360i 0.456107 0.790000i −0.542644 0.839963i \(-0.682577\pi\)
0.998751 + 0.0499623i \(0.0159101\pi\)
\(822\) 12.9698 + 22.4644i 0.452375 + 0.783537i
\(823\) −8.14872 14.1140i −0.284047 0.491983i 0.688331 0.725397i \(-0.258344\pi\)
−0.972378 + 0.233414i \(0.925010\pi\)
\(824\) −3.89407 + 6.74472i −0.135656 + 0.234964i
\(825\) 14.4880 0.504409
\(826\) 1.13536 + 7.49725i 0.0395042 + 0.260863i
\(827\) 0.742014i 0.0258024i −0.999917 0.0129012i \(-0.995893\pi\)
0.999917 0.0129012i \(-0.00410669\pi\)
\(828\) −11.2190 9.59418i −0.389887 0.333421i
\(829\) 41.4331 23.9214i 1.43903 0.830825i 0.441248 0.897385i \(-0.354536\pi\)
0.997782 + 0.0665603i \(0.0212025\pi\)
\(830\) 1.84675 + 3.19867i 0.0641017 + 0.111027i
\(831\) 34.0522 + 19.6600i 1.18126 + 0.681999i
\(832\) 0.0815813i 0.00282832i
\(833\) 12.3920 + 11.4661i 0.429356 + 0.397275i
\(834\) −40.8551 −1.41470
\(835\) −11.6526 6.72761i −0.403254 0.232819i
\(836\) −2.66110 + 1.53639i −0.0920361 + 0.0531370i
\(837\) 0.297169 + 0.514712i 0.0102717 + 0.0177911i
\(838\) −16.0825 + 27.8558i −0.555562 + 0.962262i
\(839\) −22.5059 −0.776990 −0.388495 0.921451i \(-0.627005\pi\)
−0.388495 + 0.921451i \(0.627005\pi\)
\(840\) −0.998374 6.59269i −0.0344472 0.227470i
\(841\) −28.8827 −0.995957
\(842\) −0.542139 0.313004i −0.0186834 0.0107868i
\(843\) 11.6800 + 20.2304i 0.402281 + 0.696771i
\(844\) 6.65452 + 11.5260i 0.229058 + 0.396740i
\(845\) 6.64118 11.5029i 0.228464 0.395711i
\(846\) 13.2460i 0.455406i
\(847\) 8.48352 21.6599i 0.291497 0.744243i
\(848\) 8.12743i 0.279097i
\(849\) 42.4864 + 24.5295i 1.45813 + 0.841852i
\(850\) 4.76943 + 8.26090i 0.163590 + 0.283347i
\(851\) 0.249329 + 0.705496i 0.00854687 + 0.0241841i
\(852\) 16.2535 + 9.38394i 0.556834 + 0.321488i
\(853\) 16.5459i 0.566520i −0.959043 0.283260i \(-0.908584\pi\)
0.959043 0.283260i \(-0.0914159\pi\)
\(854\) 3.60326 + 4.51191i 0.123301 + 0.154394i
\(855\) −6.50707 −0.222537
\(856\) 5.64261 + 3.25776i 0.192860 + 0.111348i
\(857\) −47.8740 + 27.6401i −1.63535 + 0.944167i −0.652940 + 0.757410i \(0.726464\pi\)
−0.982406 + 0.186757i \(0.940202\pi\)
\(858\) −0.258811 + 0.149425i −0.00883566 + 0.00510127i
\(859\) −22.5929 13.0440i −0.770860 0.445056i 0.0623211 0.998056i \(-0.480150\pi\)
−0.833181 + 0.553000i \(0.813483\pi\)
\(860\) 6.84662i 0.233468i
\(861\) −8.70121 10.8954i −0.296537 0.371316i
\(862\) 35.9185i 1.22339i
\(863\) 21.4647 37.1780i 0.730667 1.26555i −0.225931 0.974143i \(-0.572543\pi\)
0.956598 0.291409i \(-0.0941241\pi\)
\(864\) 0.166692 0.0962398i 0.00567098 0.00327414i
\(865\) −13.1632 + 7.59979i −0.447563 + 0.258401i
\(866\) −4.71193 + 8.16131i −0.160118 + 0.277332i
\(867\) 27.5704i 0.936339i
\(868\) −7.60689 2.97939i −0.258195 0.101127i
\(869\) 11.2529 0.381729
\(870\) 0.747381 + 0.431500i 0.0253386 + 0.0146292i
\(871\) 0.639877 + 1.10830i 0.0216814 + 0.0375533i
\(872\) 14.9835 8.65070i 0.507404 0.292950i
\(873\) 23.8567 41.3210i 0.807426 1.39850i
\(874\) 1.81353 9.75060i 0.0613435 0.329819i
\(875\) −23.9467 + 3.62641i −0.809547 + 0.122595i
\(876\) −15.7506 −0.532165
\(877\) −22.0658 + 38.2191i −0.745110 + 1.29057i 0.205033 + 0.978755i \(0.434270\pi\)
−0.950143 + 0.311814i \(0.899064\pi\)
\(878\) −21.4226 + 12.3684i −0.722978 + 0.417412i
\(879\) −11.7370 + 6.77636i −0.395879 + 0.228561i
\(880\) 1.31542 + 0.759456i 0.0443427 + 0.0256013i
\(881\) −2.81759 −0.0949270 −0.0474635 0.998873i \(-0.515114\pi\)
−0.0474635 + 0.998873i \(0.515114\pi\)
\(882\) −15.8151 14.6334i −0.532521 0.492732i
\(883\) 11.0067 0.370403 0.185202 0.982701i \(-0.440706\pi\)
0.185202 + 0.982701i \(0.440706\pi\)
\(884\) −0.170400 0.0983805i −0.00573117 0.00330889i
\(885\) −3.61147 6.25525i −0.121398 0.210268i
\(886\) 3.93090 + 6.80852i 0.132061 + 0.228737i
\(887\) 7.71627 + 4.45499i 0.259087 + 0.149584i 0.623918 0.781490i \(-0.285540\pi\)
−0.364831 + 0.931074i \(0.618873\pi\)
\(888\) −0.384654 −0.0129081
\(889\) −16.0326 + 2.42792i −0.537717 + 0.0814300i
\(890\) −14.8651 −0.498278
\(891\) 11.2719 + 6.50784i 0.377623 + 0.218021i
\(892\) 11.9380 6.89243i 0.399715 0.230776i
\(893\) −7.70705 + 4.44967i −0.257907 + 0.148902i
\(894\) −13.4392 + 23.2775i −0.449476 + 0.778515i
\(895\) −16.8284 −0.562512
\(896\) −0.964890 + 2.46353i −0.0322347 + 0.0823008i
\(897\) 0.176379 0.948316i 0.00588911 0.0316633i
\(898\) 9.89781 17.1435i 0.330294 0.572086i
\(899\) 0.915701 0.528680i 0.0305403 0.0176325i
\(900\) −6.08692 10.5428i −0.202897 0.351428i
\(901\) −16.9759 9.80103i −0.565549 0.326520i
\(902\) 3.17628 0.105759
\(903\) 27.2622 + 34.1371i 0.907230 + 1.13601i
\(904\) 15.6200i 0.519514i
\(905\) 10.7238 18.5742i 0.356472 0.617428i
\(906\) −36.6544 + 21.1625i −1.21776 + 0.703075i
\(907\) −19.4132 + 11.2082i −0.644603 + 0.372162i −0.786385 0.617736i \(-0.788050\pi\)
0.141782 + 0.989898i \(0.454717\pi\)
\(908\) 4.99408 8.65000i 0.165734 0.287060i
\(909\) 51.5743i 1.71061i
\(910\) 0.172412 0.137690i 0.00571539 0.00456437i
\(911\) 45.4326i 1.50525i 0.658450 + 0.752624i \(0.271212\pi\)
−0.658450 + 0.752624i \(0.728788\pi\)
\(912\) 4.41536 + 2.54921i 0.146207 + 0.0844127i
\(913\) −4.64936 + 2.68431i −0.153871 + 0.0888376i
\(914\) −6.77168 + 3.90963i −0.223987 + 0.129319i
\(915\) −4.76329 2.75009i −0.157469 0.0909151i
\(916\) 14.3184 0.473093
\(917\) 32.2217 + 12.6203i 1.06405 + 0.416757i
\(918\) 0.464230i 0.0153219i
\(919\) 45.5151 + 26.2782i 1.50141 + 0.866837i 0.999999 + 0.00162549i \(0.000517409\pi\)
0.501407 + 0.865212i \(0.332816\pi\)
\(920\) −4.62234 + 1.63358i −0.152394 + 0.0538574i
\(921\) −16.2296 28.1105i −0.534784 0.926273i
\(922\) −4.54760 2.62556i −0.149767 0.0864682i
\(923\) 0.621045i 0.0204419i
\(924\) 9.58267 1.45117i 0.315247 0.0477399i
\(925\) 0.617071i 0.0202892i
\(926\) −3.36620 + 5.83042i −0.110620 + 0.191600i
\(927\) −11.9862 20.7608i −0.393679 0.681873i
\(928\) −0.171216 0.296554i −0.00562043 0.00973488i
\(929\) 3.52984 + 2.03795i 0.115810 + 0.0668631i 0.556786 0.830656i \(-0.312034\pi\)
−0.440976 + 0.897519i \(0.645368\pi\)
\(930\) 7.78192 0.255179
\(931\) 3.20161 14.1176i 0.104928 0.462685i
\(932\) 18.1256 0.593724
\(933\) −9.97426 + 17.2759i −0.326543 + 0.565588i
\(934\) −6.40963 11.1018i −0.209729 0.363262i
\(935\) 3.17257 1.83169i 0.103754 0.0599025i
\(936\) 0.217471 + 0.125557i 0.00710825 + 0.00410395i
\(937\) −18.5316 −0.605402 −0.302701 0.953086i \(-0.597888\pi\)
−0.302701 + 0.953086i \(0.597888\pi\)
\(938\) −6.21429 41.0356i −0.202904 1.33986i
\(939\) 45.8300i 1.49560i
\(940\) 3.80970 + 2.19953i 0.124259 + 0.0717407i
\(941\) −18.1217 31.3878i −0.590752 1.02321i −0.994131 0.108179i \(-0.965498\pi\)
0.403380 0.915033i \(-0.367835\pi\)
\(942\) −0.771048 + 0.445165i −0.0251221 + 0.0145042i
\(943\) −6.66299 + 7.79140i −0.216977 + 0.253723i
\(944\) 2.86600i 0.0932805i
\(945\) 0.484727 + 0.189853i 0.0157682 + 0.00617591i
\(946\) −9.95177 −0.323560
\(947\) −8.25770 + 14.3028i −0.268339 + 0.464777i −0.968433 0.249274i \(-0.919808\pi\)
0.700094 + 0.714051i \(0.253141\pi\)
\(948\) −9.33555 16.1696i −0.303205 0.525166i
\(949\) −0.260601 0.451374i −0.00845947 0.0146522i
\(950\) 4.08950 7.08323i 0.132681 0.229810i
\(951\) 12.5479i 0.406895i
\(952\) 3.98203 + 4.98620i 0.129058 + 0.161604i
\(953\) 55.5834i 1.80052i −0.435349 0.900262i \(-0.643375\pi\)
0.435349 0.900262i \(-0.356625\pi\)
\(954\) 21.6652 + 12.5084i 0.701437 + 0.404975i
\(955\) 8.81115 5.08712i 0.285122 0.164615i
\(956\) −0.497102 0.861006i −0.0160774 0.0278469i
\(957\) −0.627199 + 1.08634i −0.0202745 + 0.0351164i
\(958\) 7.19624 0.232500
\(959\) 21.7522 17.3715i 0.702415 0.560956i
\(960\) 2.52021i 0.0813396i
\(961\) −10.7327 + 18.5897i −0.346218 + 0.599666i
\(962\) −0.00636426 0.0110232i −0.000205192 0.000355403i
\(963\) −17.3684 + 10.0276i −0.559687 + 0.323136i
\(964\) −8.98769 + 15.5671i −0.289474 + 0.501384i
\(965\) 11.3064 0.363966
\(966\) −16.5422 + 26.5504i −0.532236 + 0.854246i
\(967\) −17.2521 −0.554789 −0.277394 0.960756i \(-0.589471\pi\)
−0.277394 + 0.960756i \(0.589471\pi\)
\(968\) 4.39611 7.61428i 0.141296 0.244732i
\(969\) 10.6491 6.14828i 0.342099 0.197511i
\(970\) −7.92292 13.7229i −0.254390 0.440616i
\(971\) −0.288764 + 0.500154i −0.00926687 + 0.0160507i −0.870622 0.491953i \(-0.836283\pi\)
0.861355 + 0.508004i \(0.169616\pi\)
\(972\) 22.1733i 0.711210i
\(973\) 6.56477 + 43.3500i 0.210457 + 1.38974i
\(974\) −14.4413 −0.462729
\(975\) 0.397734 0.688895i 0.0127377 0.0220623i
\(976\) 1.09121 + 1.89003i 0.0349288 + 0.0604985i
\(977\) −6.76955 + 3.90840i −0.216577 + 0.125041i −0.604364 0.796708i \(-0.706573\pi\)
0.387787 + 0.921749i \(0.373240\pi\)
\(978\) −51.9141 29.9726i −1.66003 0.958418i
\(979\) 21.6068i 0.690556i
\(980\) −6.83486 + 2.11868i −0.218332 + 0.0676788i
\(981\) 53.2550i 1.70030i
\(982\) 18.4458 31.9491i 0.588630 1.01954i
\(983\) −24.1184 41.7743i −0.769258 1.33239i −0.937966 0.346728i \(-0.887293\pi\)
0.168708 0.985666i \(-0.446041\pi\)
\(984\) −2.63508 4.56409i −0.0840032 0.145498i
\(985\) −5.77879 + 10.0092i −0.184128 + 0.318918i
\(986\) −0.825890 −0.0263017
\(987\) 27.7532 4.20285i 0.883395 0.133778i
\(988\) 0.168711i 0.00536741i
\(989\) 20.8762 24.4117i 0.663823 0.776245i
\(990\) −4.04895 + 2.33766i −0.128684 + 0.0742958i
\(991\) 8.92320 + 15.4554i 0.283455 + 0.490958i 0.972233 0.234014i \(-0.0751861\pi\)
−0.688779 + 0.724972i \(0.741853\pi\)
\(992\) −2.67411 1.54390i −0.0849032 0.0490189i
\(993\) 22.5653i 0.716089i
\(994\) 7.34531 18.7538i 0.232979 0.594836i
\(995\) −13.6837 −0.433804
\(996\) 7.71432 + 4.45386i 0.244438 + 0.141126i
\(997\) −2.81054 + 1.62267i −0.0890107 + 0.0513903i −0.543845 0.839186i \(-0.683032\pi\)
0.454834 + 0.890576i \(0.349699\pi\)
\(998\) −2.83621 4.91245i −0.0897785 0.155501i
\(999\) 0.0150156 0.0260077i 0.000475071 0.000822848i
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 322.2.g.b.229.8 yes 16
7.2 even 3 2254.2.c.b.2253.13 16
7.3 odd 6 inner 322.2.g.b.45.7 16
7.5 odd 6 2254.2.c.b.2253.4 16
23.22 odd 2 inner 322.2.g.b.229.7 yes 16
161.45 even 6 inner 322.2.g.b.45.8 yes 16
161.68 even 6 2254.2.c.b.2253.3 16
161.114 odd 6 2254.2.c.b.2253.14 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
322.2.g.b.45.7 16 7.3 odd 6 inner
322.2.g.b.45.8 yes 16 161.45 even 6 inner
322.2.g.b.229.7 yes 16 23.22 odd 2 inner
322.2.g.b.229.8 yes 16 1.1 even 1 trivial
2254.2.c.b.2253.3 16 161.68 even 6
2254.2.c.b.2253.4 16 7.5 odd 6
2254.2.c.b.2253.13 16 7.2 even 3
2254.2.c.b.2253.14 16 161.114 odd 6