Properties

Label 930.2.n.d.481.1
Level $930$
Weight $2$
Character 930.481
Analytic conductor $7.426$
Analytic rank $0$
Dimension $12$
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] = [930,2,Mod(481,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.481");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.n (of order \(5\), 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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} + 13 x^{10} - 9 x^{9} + 60 x^{8} + x^{7} + 263 x^{6} + 823 x^{5} + 1931 x^{4} + 1170 x^{3} + 1340 x^{2} + 1000 x + 400 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 481.1
Root \(-0.781164 + 2.40418i\) of defining polynomial
Character \(\chi\) \(=\) 930.481
Dual form 930.2.n.d.901.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.809017 + 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(-0.482786 + 1.48586i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.809017 + 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(-0.482786 + 1.48586i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.809017 - 0.587785i) q^{10} +(0.945865 - 2.91107i) q^{11} +(0.809017 - 0.587785i) q^{12} +(-5.04097 - 3.66248i) q^{13} +(-0.482786 - 1.48586i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.20421 - 6.78386i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(5.71245 - 4.15034i) q^{19} +(-0.309017 + 0.951057i) q^{20} +(-1.26395 + 0.918314i) q^{21} +(0.945865 + 2.91107i) q^{22} +(0.457949 + 1.40942i) q^{23} +(-0.309017 + 0.951057i) q^{24} +1.00000 q^{25} +6.23099 q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.26395 + 0.918314i) q^{28} +(-6.07561 + 4.41419i) q^{29} +1.00000 q^{30} +(5.34781 + 1.54950i) q^{31} +1.00000 q^{32} +(2.47631 - 1.79914i) q^{33} +(5.77070 + 4.19266i) q^{34} +(0.482786 - 1.48586i) q^{35} +1.00000 q^{36} -0.145898 q^{37} +(-2.18196 + 6.71539i) q^{38} +(-1.92548 - 5.92602i) q^{39} +(-0.309017 - 0.951057i) q^{40} +(0.510889 - 0.371183i) q^{41} +(0.482786 - 1.48586i) q^{42} +(7.05602 - 5.12650i) q^{43} +(-2.47631 - 1.79914i) q^{44} +(-0.309017 - 0.951057i) q^{45} +(-1.19893 - 0.871071i) q^{46} +(-6.97476 - 5.06746i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(3.68841 + 2.67979i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(2.20421 - 6.78386i) q^{51} +(-5.04097 + 3.66248i) q^{52} +(-3.67237 - 11.3024i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-0.945865 + 2.91107i) q^{55} -1.56233 q^{56} +7.06098 q^{57} +(2.32067 - 7.14230i) q^{58} +(-2.94172 - 2.13729i) q^{59} +(-0.809017 + 0.587785i) q^{60} +11.2548 q^{61} +(-5.23724 + 1.88979i) q^{62} -1.56233 q^{63} +(-0.809017 + 0.587785i) q^{64} +(5.04097 + 3.66248i) q^{65} +(-0.945865 + 2.91107i) q^{66} -6.16263 q^{67} -7.13298 q^{68} +(-0.457949 + 1.40942i) q^{69} +(0.482786 + 1.48586i) q^{70} +(-1.16864 - 3.59670i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(4.45246 - 13.7033i) q^{73} +(0.118034 - 0.0857567i) q^{74} +(0.809017 + 0.587785i) q^{75} +(-2.18196 - 6.71539i) q^{76} +(3.86881 + 2.81085i) q^{77} +(5.04097 + 3.66248i) q^{78} +(1.21142 + 3.72835i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-0.195142 + 0.600586i) q^{82} +(2.65416 - 1.92836i) q^{83} +(0.482786 + 1.48586i) q^{84} +(2.20421 + 6.78386i) q^{85} +(-2.69516 + 8.29485i) q^{86} -7.50986 q^{87} +3.06088 q^{88} +(-1.97058 + 6.06481i) q^{89} +(0.809017 + 0.587785i) q^{90} +(7.87566 - 5.72200i) q^{91} +1.48195 q^{92} +(3.41569 + 4.39694i) q^{93} +8.62127 q^{94} +(-5.71245 + 4.15034i) q^{95} +(0.809017 + 0.587785i) q^{96} +(-4.33487 + 13.3414i) q^{97} -4.55913 q^{98} +3.06088 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} + 6 q^{11} + 3 q^{12} - 6 q^{13} - q^{14} - 3 q^{15} - 3 q^{16} - 13 q^{17} - 3 q^{18} - 10 q^{19} + 3 q^{20} + q^{21} + 6 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 14 q^{26} + 3 q^{27} - q^{28} + 7 q^{29} + 12 q^{30} + 16 q^{31} + 12 q^{32} + 9 q^{33} + 17 q^{34} + q^{35} + 12 q^{36} - 42 q^{37} + q^{39} + 3 q^{40} - 3 q^{41} + q^{42} + 5 q^{43} - 9 q^{44} + 3 q^{45} - 2 q^{46} - 16 q^{47} + 3 q^{48} + 28 q^{49} - 3 q^{50} + 13 q^{51} - 6 q^{52} - q^{53} + 3 q^{54} - 6 q^{55} + 4 q^{56} - 20 q^{57} - 3 q^{58} - 3 q^{59} - 3 q^{60} + 8 q^{61} - 14 q^{62} + 4 q^{63} - 3 q^{64} + 6 q^{65} - 6 q^{66} + 24 q^{67} - 8 q^{68} - 8 q^{69} + q^{70} - 19 q^{71} - 3 q^{72} + 10 q^{73} - 12 q^{74} + 3 q^{75} + 6 q^{78} + 3 q^{79} + 3 q^{80} - 3 q^{81} + 7 q^{82} - 36 q^{83} + q^{84} + 13 q^{85} + 20 q^{86} + 8 q^{87} + 6 q^{88} - 15 q^{89} + 3 q^{90} + 51 q^{91} - 12 q^{92} - q^{93} + 24 q^{94} + 10 q^{95} + 3 q^{96} - 14 q^{97} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.809017 + 0.587785i −0.572061 + 0.415627i
\(3\) 0.809017 + 0.587785i 0.467086 + 0.339358i
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) −1.00000 −0.447214
\(6\) −1.00000 −0.408248
\(7\) −0.482786 + 1.48586i −0.182476 + 0.561603i −0.999896 0.0144391i \(-0.995404\pi\)
0.817420 + 0.576043i \(0.195404\pi\)
\(8\) 0.309017 + 0.951057i 0.109254 + 0.336249i
\(9\) 0.309017 + 0.951057i 0.103006 + 0.317019i
\(10\) 0.809017 0.587785i 0.255834 0.185874i
\(11\) 0.945865 2.91107i 0.285189 0.877722i −0.701153 0.713011i \(-0.747331\pi\)
0.986342 0.164711i \(-0.0526690\pi\)
\(12\) 0.809017 0.587785i 0.233543 0.169679i
\(13\) −5.04097 3.66248i −1.39811 1.01579i −0.994919 0.100676i \(-0.967899\pi\)
−0.403195 0.915114i \(-0.632101\pi\)
\(14\) −0.482786 1.48586i −0.129030 0.397114i
\(15\) −0.809017 0.587785i −0.208887 0.151765i
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) −2.20421 6.78386i −0.534600 1.64533i −0.744513 0.667608i \(-0.767318\pi\)
0.209913 0.977720i \(-0.432682\pi\)
\(18\) −0.809017 0.587785i −0.190687 0.138542i
\(19\) 5.71245 4.15034i 1.31053 0.952153i 0.310528 0.950564i \(-0.399494\pi\)
0.999999 0.00158911i \(-0.000505829\pi\)
\(20\) −0.309017 + 0.951057i −0.0690983 + 0.212663i
\(21\) −1.26395 + 0.918314i −0.275817 + 0.200393i
\(22\) 0.945865 + 2.91107i 0.201659 + 0.620643i
\(23\) 0.457949 + 1.40942i 0.0954890 + 0.293885i 0.987381 0.158364i \(-0.0506219\pi\)
−0.891892 + 0.452249i \(0.850622\pi\)
\(24\) −0.309017 + 0.951057i −0.0630778 + 0.194134i
\(25\) 1.00000 0.200000
\(26\) 6.23099 1.22200
\(27\) −0.309017 + 0.951057i −0.0594703 + 0.183031i
\(28\) 1.26395 + 0.918314i 0.238864 + 0.173545i
\(29\) −6.07561 + 4.41419i −1.12821 + 0.819694i −0.985434 0.170061i \(-0.945604\pi\)
−0.142778 + 0.989755i \(0.545604\pi\)
\(30\) 1.00000 0.182574
\(31\) 5.34781 + 1.54950i 0.960495 + 0.278299i
\(32\) 1.00000 0.176777
\(33\) 2.47631 1.79914i 0.431070 0.313190i
\(34\) 5.77070 + 4.19266i 0.989667 + 0.719035i
\(35\) 0.482786 1.48586i 0.0816058 0.251157i
\(36\) 1.00000 0.166667
\(37\) −0.145898 −0.0239855 −0.0119927 0.999928i \(-0.503818\pi\)
−0.0119927 + 0.999928i \(0.503818\pi\)
\(38\) −2.18196 + 6.71539i −0.353961 + 1.08938i
\(39\) −1.92548 5.92602i −0.308324 0.948923i
\(40\) −0.309017 0.951057i −0.0488599 0.150375i
\(41\) 0.510889 0.371183i 0.0797875 0.0579690i −0.547176 0.837017i \(-0.684297\pi\)
0.626964 + 0.779048i \(0.284297\pi\)
\(42\) 0.482786 1.48586i 0.0744955 0.229274i
\(43\) 7.05602 5.12650i 1.07603 0.781784i 0.0990464 0.995083i \(-0.468421\pi\)
0.976987 + 0.213299i \(0.0684208\pi\)
\(44\) −2.47631 1.79914i −0.373317 0.271231i
\(45\) −0.309017 0.951057i −0.0460655 0.141775i
\(46\) −1.19893 0.871071i −0.176772 0.128432i
\(47\) −6.97476 5.06746i −1.01737 0.739164i −0.0516300 0.998666i \(-0.516442\pi\)
−0.965743 + 0.259502i \(0.916442\pi\)
\(48\) −0.309017 0.951057i −0.0446028 0.137273i
\(49\) 3.68841 + 2.67979i 0.526916 + 0.382827i
\(50\) −0.809017 + 0.587785i −0.114412 + 0.0831254i
\(51\) 2.20421 6.78386i 0.308651 0.949931i
\(52\) −5.04097 + 3.66248i −0.699057 + 0.507895i
\(53\) −3.67237 11.3024i −0.504439 1.55250i −0.801711 0.597711i \(-0.796077\pi\)
0.297272 0.954793i \(-0.403923\pi\)
\(54\) −0.309017 0.951057i −0.0420519 0.129422i
\(55\) −0.945865 + 2.91107i −0.127540 + 0.392529i
\(56\) −1.56233 −0.208775
\(57\) 7.06098 0.935250
\(58\) 2.32067 7.14230i 0.304720 0.937830i
\(59\) −2.94172 2.13729i −0.382980 0.278251i 0.379593 0.925154i \(-0.376064\pi\)
−0.762573 + 0.646902i \(0.776064\pi\)
\(60\) −0.809017 + 0.587785i −0.104444 + 0.0758827i
\(61\) 11.2548 1.44103 0.720515 0.693439i \(-0.243905\pi\)
0.720515 + 0.693439i \(0.243905\pi\)
\(62\) −5.23724 + 1.88979i −0.665130 + 0.240003i
\(63\) −1.56233 −0.196835
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) 5.04097 + 3.66248i 0.625256 + 0.454275i
\(66\) −0.945865 + 2.91107i −0.116428 + 0.358328i
\(67\) −6.16263 −0.752885 −0.376443 0.926440i \(-0.622853\pi\)
−0.376443 + 0.926440i \(0.622853\pi\)
\(68\) −7.13298 −0.865000
\(69\) −0.457949 + 1.40942i −0.0551306 + 0.169675i
\(70\) 0.482786 + 1.48586i 0.0577040 + 0.177595i
\(71\) −1.16864 3.59670i −0.138692 0.426850i 0.857454 0.514561i \(-0.172045\pi\)
−0.996146 + 0.0877105i \(0.972045\pi\)
\(72\) −0.809017 + 0.587785i −0.0953436 + 0.0692712i
\(73\) 4.45246 13.7033i 0.521121 1.60385i −0.250741 0.968054i \(-0.580674\pi\)
0.771861 0.635791i \(-0.219326\pi\)
\(74\) 0.118034 0.0857567i 0.0137212 0.00996902i
\(75\) 0.809017 + 0.587785i 0.0934172 + 0.0678716i
\(76\) −2.18196 6.71539i −0.250288 0.770308i
\(77\) 3.86881 + 2.81085i 0.440891 + 0.320326i
\(78\) 5.04097 + 3.66248i 0.570778 + 0.414694i
\(79\) 1.21142 + 3.72835i 0.136295 + 0.419473i 0.995789 0.0916728i \(-0.0292214\pi\)
−0.859494 + 0.511145i \(0.829221\pi\)
\(80\) 0.809017 + 0.587785i 0.0904508 + 0.0657164i
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) −0.195142 + 0.600586i −0.0215499 + 0.0663236i
\(83\) 2.65416 1.92836i 0.291332 0.211665i −0.432513 0.901628i \(-0.642373\pi\)
0.723845 + 0.689963i \(0.242373\pi\)
\(84\) 0.482786 + 1.48586i 0.0526763 + 0.162121i
\(85\) 2.20421 + 6.78386i 0.239080 + 0.735813i
\(86\) −2.69516 + 8.29485i −0.290627 + 0.894457i
\(87\) −7.50986 −0.805142
\(88\) 3.06088 0.326291
\(89\) −1.97058 + 6.06481i −0.208881 + 0.642869i 0.790651 + 0.612267i \(0.209742\pi\)
−0.999532 + 0.0306017i \(0.990258\pi\)
\(90\) 0.809017 + 0.587785i 0.0852779 + 0.0619580i
\(91\) 7.87566 5.72200i 0.825593 0.599829i
\(92\) 1.48195 0.154504
\(93\) 3.41569 + 4.39694i 0.354191 + 0.455941i
\(94\) 8.62127 0.889216
\(95\) −5.71245 + 4.15034i −0.586085 + 0.425816i
\(96\) 0.809017 + 0.587785i 0.0825700 + 0.0599906i
\(97\) −4.33487 + 13.3414i −0.440140 + 1.35461i 0.447587 + 0.894240i \(0.352283\pi\)
−0.887727 + 0.460370i \(0.847717\pi\)
\(98\) −4.55913 −0.460542
\(99\) 3.06088 0.307630
\(100\) 0.309017 0.951057i 0.0309017 0.0951057i
\(101\) −1.26139 3.88216i −0.125513 0.386290i 0.868481 0.495722i \(-0.165097\pi\)
−0.993994 + 0.109433i \(0.965097\pi\)
\(102\) 2.20421 + 6.78386i 0.218249 + 0.671703i
\(103\) −8.40457 + 6.10628i −0.828127 + 0.601670i −0.919029 0.394190i \(-0.871025\pi\)
0.0909018 + 0.995860i \(0.471025\pi\)
\(104\) 1.92548 5.92602i 0.188809 0.581094i
\(105\) 1.26395 0.918314i 0.123349 0.0896183i
\(106\) 9.61440 + 6.98527i 0.933833 + 0.678469i
\(107\) 3.15650 + 9.71470i 0.305150 + 0.939155i 0.979621 + 0.200854i \(0.0643717\pi\)
−0.674471 + 0.738301i \(0.735628\pi\)
\(108\) 0.809017 + 0.587785i 0.0778477 + 0.0565597i
\(109\) −11.8925 8.64043i −1.13910 0.827603i −0.152105 0.988364i \(-0.548605\pi\)
−0.986993 + 0.160761i \(0.948605\pi\)
\(110\) −0.945865 2.91107i −0.0901847 0.277560i
\(111\) −0.118034 0.0857567i −0.0112033 0.00813967i
\(112\) 1.26395 0.918314i 0.119432 0.0867725i
\(113\) 4.25391 13.0922i 0.400174 1.23161i −0.524684 0.851297i \(-0.675816\pi\)
0.924858 0.380313i \(-0.124184\pi\)
\(114\) −5.71245 + 4.15034i −0.535020 + 0.388715i
\(115\) −0.457949 1.40942i −0.0427040 0.131429i
\(116\) 2.32067 + 7.14230i 0.215469 + 0.663146i
\(117\) 1.92548 5.92602i 0.178011 0.547861i
\(118\) 3.63617 0.334737
\(119\) 11.1441 1.02157
\(120\) 0.309017 0.951057i 0.0282093 0.0868192i
\(121\) 1.31950 + 0.958674i 0.119955 + 0.0871521i
\(122\) −9.10533 + 6.61541i −0.824358 + 0.598931i
\(123\) 0.631494 0.0569399
\(124\) 3.12623 4.60724i 0.280744 0.413743i
\(125\) −1.00000 −0.0894427
\(126\) 1.26395 0.918314i 0.112602 0.0818099i
\(127\) 6.67485 + 4.84956i 0.592297 + 0.430329i 0.843136 0.537700i \(-0.180707\pi\)
−0.250839 + 0.968029i \(0.580707\pi\)
\(128\) 0.309017 0.951057i 0.0273135 0.0840623i
\(129\) 8.72172 0.767905
\(130\) −6.23099 −0.546494
\(131\) 4.00580 12.3286i 0.349988 1.07715i −0.608871 0.793269i \(-0.708377\pi\)
0.958859 0.283883i \(-0.0916228\pi\)
\(132\) −0.945865 2.91107i −0.0823270 0.253376i
\(133\) 3.40894 + 10.4917i 0.295593 + 0.909741i
\(134\) 4.98567 3.62230i 0.430697 0.312919i
\(135\) 0.309017 0.951057i 0.0265959 0.0818539i
\(136\) 5.77070 4.19266i 0.494833 0.359517i
\(137\) 0.318811 + 0.231630i 0.0272379 + 0.0197895i 0.601321 0.799008i \(-0.294641\pi\)
−0.574083 + 0.818797i \(0.694641\pi\)
\(138\) −0.457949 1.40942i −0.0389832 0.119978i
\(139\) −13.2441 9.62242i −1.12335 0.816163i −0.138638 0.990343i \(-0.544273\pi\)
−0.984714 + 0.174180i \(0.944273\pi\)
\(140\) −1.26395 0.918314i −0.106823 0.0776117i
\(141\) −2.66412 8.19932i −0.224359 0.690507i
\(142\) 3.05954 + 2.22288i 0.256751 + 0.186540i
\(143\) −15.4298 + 11.2104i −1.29031 + 0.937463i
\(144\) 0.309017 0.951057i 0.0257514 0.0792547i
\(145\) 6.07561 4.41419i 0.504552 0.366578i
\(146\) 4.45246 + 13.7033i 0.368488 + 1.13409i
\(147\) 1.40885 + 4.33599i 0.116200 + 0.357626i
\(148\) −0.0450850 + 0.138757i −0.00370596 + 0.0114058i
\(149\) 8.72415 0.714710 0.357355 0.933969i \(-0.383679\pi\)
0.357355 + 0.933969i \(0.383679\pi\)
\(150\) −1.00000 −0.0816497
\(151\) 5.43249 16.7195i 0.442090 1.36061i −0.443554 0.896248i \(-0.646282\pi\)
0.885644 0.464365i \(-0.153718\pi\)
\(152\) 5.71245 + 4.15034i 0.463341 + 0.336637i
\(153\) 5.77070 4.19266i 0.466533 0.338956i
\(154\) −4.78211 −0.385353
\(155\) −5.34781 1.54950i −0.429546 0.124459i
\(156\) −6.23099 −0.498878
\(157\) −7.39870 + 5.37547i −0.590480 + 0.429009i −0.842487 0.538716i \(-0.818909\pi\)
0.252007 + 0.967725i \(0.418909\pi\)
\(158\) −3.17153 2.30425i −0.252313 0.183316i
\(159\) 3.67237 11.3024i 0.291238 0.896339i
\(160\) −1.00000 −0.0790569
\(161\) −2.31530 −0.182471
\(162\) 0.309017 0.951057i 0.0242787 0.0747221i
\(163\) −1.30056 4.00271i −0.101868 0.313517i 0.887115 0.461549i \(-0.152706\pi\)
−0.988983 + 0.148032i \(0.952706\pi\)
\(164\) −0.195142 0.600586i −0.0152380 0.0468979i
\(165\) −2.47631 + 1.79914i −0.192780 + 0.140063i
\(166\) −1.01380 + 3.12015i −0.0786860 + 0.242171i
\(167\) −0.584088 + 0.424365i −0.0451981 + 0.0328383i −0.610155 0.792282i \(-0.708893\pi\)
0.564957 + 0.825120i \(0.308893\pi\)
\(168\) −1.26395 0.918314i −0.0975159 0.0708495i
\(169\) 7.98043 + 24.5612i 0.613879 + 1.88932i
\(170\) −5.77070 4.19266i −0.442592 0.321562i
\(171\) 5.71245 + 4.15034i 0.436842 + 0.317384i
\(172\) −2.69516 8.29485i −0.205504 0.632477i
\(173\) 1.62481 + 1.18050i 0.123532 + 0.0897514i 0.647836 0.761780i \(-0.275674\pi\)
−0.524304 + 0.851531i \(0.675674\pi\)
\(174\) 6.07561 4.41419i 0.460590 0.334639i
\(175\) −0.482786 + 1.48586i −0.0364952 + 0.112321i
\(176\) −2.47631 + 1.79914i −0.186659 + 0.135615i
\(177\) −1.12364 3.45820i −0.0844579 0.259935i
\(178\) −1.97058 6.06481i −0.147701 0.454577i
\(179\) −2.42434 + 7.46134i −0.181203 + 0.557687i −0.999862 0.0165932i \(-0.994718\pi\)
0.818659 + 0.574280i \(0.194718\pi\)
\(180\) −1.00000 −0.0745356
\(181\) −18.1308 −1.34765 −0.673827 0.738889i \(-0.735351\pi\)
−0.673827 + 0.738889i \(0.735351\pi\)
\(182\) −3.00823 + 9.25839i −0.222985 + 0.686278i
\(183\) 9.10533 + 6.61541i 0.673085 + 0.489025i
\(184\) −1.19893 + 0.871071i −0.0883860 + 0.0642162i
\(185\) 0.145898 0.0107266
\(186\) −5.34781 1.54950i −0.392120 0.113615i
\(187\) −21.8332 −1.59660
\(188\) −6.97476 + 5.06746i −0.508686 + 0.369582i
\(189\) −1.26395 0.918314i −0.0919389 0.0667975i
\(190\) 2.18196 6.71539i 0.158296 0.487186i
\(191\) −19.8009 −1.43274 −0.716371 0.697720i \(-0.754198\pi\)
−0.716371 + 0.697720i \(0.754198\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −6.52687 + 20.0877i −0.469815 + 1.44594i 0.383010 + 0.923744i \(0.374887\pi\)
−0.852825 + 0.522197i \(0.825113\pi\)
\(194\) −4.33487 13.3414i −0.311226 0.957854i
\(195\) 1.92548 + 5.92602i 0.137887 + 0.424371i
\(196\) 3.68841 2.67979i 0.263458 0.191413i
\(197\) −7.02740 + 21.6281i −0.500681 + 1.54094i 0.307230 + 0.951635i \(0.400598\pi\)
−0.807912 + 0.589304i \(0.799402\pi\)
\(198\) −2.47631 + 1.79914i −0.175983 + 0.127859i
\(199\) −5.99062 4.35244i −0.424664 0.308536i 0.354848 0.934924i \(-0.384533\pi\)
−0.779512 + 0.626388i \(0.784533\pi\)
\(200\) 0.309017 + 0.951057i 0.0218508 + 0.0672499i
\(201\) −4.98567 3.62230i −0.351662 0.255498i
\(202\) 3.30237 + 2.39931i 0.232354 + 0.168815i
\(203\) −3.62566 11.1586i −0.254471 0.783182i
\(204\) −5.77070 4.19266i −0.404030 0.293545i
\(205\) −0.510889 + 0.371183i −0.0356820 + 0.0259245i
\(206\) 3.21026 9.88017i 0.223669 0.688384i
\(207\) −1.19893 + 0.871071i −0.0833312 + 0.0605436i
\(208\) 1.92548 + 5.92602i 0.133508 + 0.410896i
\(209\) −6.67873 20.5550i −0.461978 1.42182i
\(210\) −0.482786 + 1.48586i −0.0333154 + 0.102534i
\(211\) −4.07178 −0.280313 −0.140157 0.990129i \(-0.544761\pi\)
−0.140157 + 0.990129i \(0.544761\pi\)
\(212\) −11.8840 −0.816200
\(213\) 1.16864 3.59670i 0.0800739 0.246442i
\(214\) −8.26381 6.00401i −0.564903 0.410426i
\(215\) −7.05602 + 5.12650i −0.481217 + 0.349624i
\(216\) −1.00000 −0.0680414
\(217\) −4.88420 + 7.19803i −0.331561 + 0.488634i
\(218\) 14.7000 0.995608
\(219\) 11.6567 8.46908i 0.787686 0.572287i
\(220\) 2.47631 + 1.79914i 0.166953 + 0.121298i
\(221\) −13.7344 + 42.2702i −0.923876 + 2.84340i
\(222\) 0.145898 0.00979203
\(223\) 19.6521 1.31600 0.658000 0.753018i \(-0.271403\pi\)
0.658000 + 0.753018i \(0.271403\pi\)
\(224\) −0.482786 + 1.48586i −0.0322575 + 0.0992784i
\(225\) 0.309017 + 0.951057i 0.0206011 + 0.0634038i
\(226\) 4.25391 + 13.0922i 0.282966 + 0.870880i
\(227\) −19.6412 + 14.2702i −1.30363 + 0.947145i −0.999984 0.00563890i \(-0.998205\pi\)
−0.303649 + 0.952784i \(0.598205\pi\)
\(228\) 2.18196 6.71539i 0.144504 0.444738i
\(229\) 20.3631 14.7946i 1.34563 0.977657i 0.346413 0.938082i \(-0.387400\pi\)
0.999217 0.0395751i \(-0.0126004\pi\)
\(230\) 1.19893 + 0.871071i 0.0790549 + 0.0574367i
\(231\) 1.47775 + 4.54805i 0.0972290 + 0.299240i
\(232\) −6.07561 4.41419i −0.398883 0.289805i
\(233\) −2.27586 1.65351i −0.149096 0.108325i 0.510736 0.859737i \(-0.329373\pi\)
−0.659833 + 0.751413i \(0.729373\pi\)
\(234\) 1.92548 + 5.92602i 0.125873 + 0.387396i
\(235\) 6.97476 + 5.06746i 0.454983 + 0.330564i
\(236\) −2.94172 + 2.13729i −0.191490 + 0.139126i
\(237\) −1.21142 + 3.72835i −0.0786899 + 0.242183i
\(238\) −9.01573 + 6.55031i −0.584403 + 0.424594i
\(239\) 6.50773 + 20.0287i 0.420950 + 1.29555i 0.906820 + 0.421519i \(0.138503\pi\)
−0.485870 + 0.874031i \(0.661497\pi\)
\(240\) 0.309017 + 0.951057i 0.0199470 + 0.0613904i
\(241\) 0.00164170 0.00505264i 0.000105751 0.000325469i −0.951004 0.309180i \(-0.899946\pi\)
0.951109 + 0.308854i \(0.0999455\pi\)
\(242\) −1.63099 −0.104844
\(243\) −1.00000 −0.0641500
\(244\) 3.47793 10.7040i 0.222651 0.685250i
\(245\) −3.68841 2.67979i −0.235644 0.171205i
\(246\) −0.510889 + 0.371183i −0.0325731 + 0.0236657i
\(247\) −43.9969 −2.79945
\(248\) 0.178899 + 5.56489i 0.0113601 + 0.353371i
\(249\) 3.28072 0.207907
\(250\) 0.809017 0.587785i 0.0511667 0.0371748i
\(251\) 4.38998 + 3.18950i 0.277093 + 0.201320i 0.717648 0.696406i \(-0.245219\pi\)
−0.440556 + 0.897725i \(0.645219\pi\)
\(252\) −0.482786 + 1.48586i −0.0304127 + 0.0936006i
\(253\) 4.53609 0.285182
\(254\) −8.25056 −0.517686
\(255\) −2.20421 + 6.78386i −0.138033 + 0.424822i
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) −2.93485 9.03252i −0.183071 0.563433i 0.816839 0.576865i \(-0.195724\pi\)
−0.999910 + 0.0134321i \(0.995724\pi\)
\(258\) −7.05602 + 5.12650i −0.439289 + 0.319162i
\(259\) 0.0704376 0.216784i 0.00437678 0.0134703i
\(260\) 5.04097 3.66248i 0.312628 0.227138i
\(261\) −6.07561 4.41419i −0.376071 0.273231i
\(262\) 4.00580 + 12.3286i 0.247479 + 0.761662i
\(263\) 21.7705 + 15.8172i 1.34243 + 0.975330i 0.999351 + 0.0360226i \(0.0114688\pi\)
0.343076 + 0.939308i \(0.388531\pi\)
\(264\) 2.47631 + 1.79914i 0.152406 + 0.110730i
\(265\) 3.67237 + 11.3024i 0.225592 + 0.694301i
\(266\) −8.92473 6.48420i −0.547210 0.397572i
\(267\) −5.15904 + 3.74826i −0.315728 + 0.229390i
\(268\) −1.90436 + 5.86101i −0.116327 + 0.358018i
\(269\) 7.49025 5.44198i 0.456688 0.331804i −0.335542 0.942025i \(-0.608920\pi\)
0.792231 + 0.610222i \(0.208920\pi\)
\(270\) 0.309017 + 0.951057i 0.0188062 + 0.0578795i
\(271\) −0.620319 1.90915i −0.0376817 0.115972i 0.930446 0.366428i \(-0.119419\pi\)
−0.968128 + 0.250456i \(0.919419\pi\)
\(272\) −2.20421 + 6.78386i −0.133650 + 0.411332i
\(273\) 9.73485 0.589180
\(274\) −0.394072 −0.0238068
\(275\) 0.945865 2.91107i 0.0570378 0.175544i
\(276\) 1.19893 + 0.871071i 0.0721669 + 0.0524323i
\(277\) 22.6245 16.4377i 1.35938 0.987645i 0.360893 0.932607i \(-0.382472\pi\)
0.998484 0.0550378i \(-0.0175279\pi\)
\(278\) 16.3706 0.981846
\(279\) 0.178899 + 5.56489i 0.0107104 + 0.333161i
\(280\) 1.56233 0.0933670
\(281\) 15.4684 11.2385i 0.922769 0.670431i −0.0214429 0.999770i \(-0.506826\pi\)
0.944212 + 0.329339i \(0.106826\pi\)
\(282\) 6.97476 + 5.06746i 0.415341 + 0.301763i
\(283\) 8.26050 25.4232i 0.491036 1.51125i −0.332009 0.943276i \(-0.607727\pi\)
0.823045 0.567976i \(-0.192273\pi\)
\(284\) −3.78180 −0.224408
\(285\) −7.06098 −0.418256
\(286\) 5.89367 18.1389i 0.348500 1.07257i
\(287\) 0.304876 + 0.938313i 0.0179963 + 0.0553869i
\(288\) 0.309017 + 0.951057i 0.0182090 + 0.0560415i
\(289\) −27.4090 + 19.9138i −1.61229 + 1.17140i
\(290\) −2.32067 + 7.14230i −0.136275 + 0.419410i
\(291\) −11.3488 + 8.24542i −0.665281 + 0.483355i
\(292\) −11.6567 8.46908i −0.682156 0.495615i
\(293\) 3.58864 + 11.0447i 0.209651 + 0.645238i 0.999490 + 0.0319248i \(0.0101637\pi\)
−0.789840 + 0.613313i \(0.789836\pi\)
\(294\) −3.68841 2.67979i −0.215113 0.156288i
\(295\) 2.94172 + 2.13729i 0.171274 + 0.124438i
\(296\) −0.0450850 0.138757i −0.00262051 0.00806510i
\(297\) 2.47631 + 1.79914i 0.143690 + 0.104397i
\(298\) −7.05799 + 5.12793i −0.408858 + 0.297053i
\(299\) 2.85348 8.78209i 0.165021 0.507882i
\(300\) 0.809017 0.587785i 0.0467086 0.0339358i
\(301\) 4.21073 + 12.9593i 0.242702 + 0.746961i
\(302\) 5.43249 + 16.7195i 0.312605 + 0.962099i
\(303\) 1.26139 3.88216i 0.0724651 0.223024i
\(304\) −7.06098 −0.404975
\(305\) −11.2548 −0.644448
\(306\) −2.20421 + 6.78386i −0.126006 + 0.387808i
\(307\) −13.3480 9.69790i −0.761812 0.553489i 0.137654 0.990480i \(-0.456044\pi\)
−0.899465 + 0.436992i \(0.856044\pi\)
\(308\) 3.86881 2.81085i 0.220446 0.160163i
\(309\) −10.3886 −0.590988
\(310\) 5.23724 1.88979i 0.297455 0.107333i
\(311\) 3.47195 0.196876 0.0984380 0.995143i \(-0.468615\pi\)
0.0984380 + 0.995143i \(0.468615\pi\)
\(312\) 5.04097 3.66248i 0.285389 0.207347i
\(313\) −6.74389 4.89972i −0.381187 0.276949i 0.380648 0.924720i \(-0.375701\pi\)
−0.761835 + 0.647772i \(0.775701\pi\)
\(314\) 2.82605 8.69769i 0.159483 0.490839i
\(315\) 1.56233 0.0880273
\(316\) 3.92022 0.220530
\(317\) 2.99288 9.21114i 0.168097 0.517349i −0.831154 0.556042i \(-0.812319\pi\)
0.999251 + 0.0386928i \(0.0123194\pi\)
\(318\) 3.67237 + 11.3024i 0.205936 + 0.633807i
\(319\) 7.10331 + 21.8618i 0.397709 + 1.22402i
\(320\) 0.809017 0.587785i 0.0452254 0.0328582i
\(321\) −3.15650 + 9.71470i −0.176178 + 0.542221i
\(322\) 1.87312 1.36090i 0.104385 0.0758400i
\(323\) −40.7468 29.6043i −2.26721 1.64723i
\(324\) 0.309017 + 0.951057i 0.0171676 + 0.0528365i
\(325\) −5.04097 3.66248i −0.279623 0.203158i
\(326\) 3.40491 + 2.47381i 0.188580 + 0.137012i
\(327\) −4.54254 13.9805i −0.251203 0.773124i
\(328\) 0.510889 + 0.371183i 0.0282091 + 0.0204951i
\(329\) 10.8969 7.91703i 0.600763 0.436480i
\(330\) 0.945865 2.91107i 0.0520682 0.160249i
\(331\) −15.8268 + 11.4989i −0.869921 + 0.632035i −0.930566 0.366125i \(-0.880684\pi\)
0.0606446 + 0.998159i \(0.480684\pi\)
\(332\) −1.01380 3.12015i −0.0556394 0.171241i
\(333\) −0.0450850 0.138757i −0.00247064 0.00760385i
\(334\) 0.223102 0.686637i 0.0122076 0.0375711i
\(335\) 6.16263 0.336701
\(336\) 1.56233 0.0852320
\(337\) −7.91353 + 24.3554i −0.431078 + 1.32672i 0.465975 + 0.884798i \(0.345704\pi\)
−0.897053 + 0.441923i \(0.854296\pi\)
\(338\) −20.8930 15.1797i −1.13643 0.825665i
\(339\) 11.1369 8.09142i 0.604873 0.439466i
\(340\) 7.13298 0.386840
\(341\) 9.56902 14.1022i 0.518191 0.763679i
\(342\) −7.06098 −0.381814
\(343\) −14.6102 + 10.6149i −0.788875 + 0.573151i
\(344\) 7.05602 + 5.12650i 0.380435 + 0.276402i
\(345\) 0.457949 1.40942i 0.0246552 0.0758808i
\(346\) −2.00838 −0.107971
\(347\) 24.2157 1.29997 0.649984 0.759947i \(-0.274775\pi\)
0.649984 + 0.759947i \(0.274775\pi\)
\(348\) −2.32067 + 7.14230i −0.124401 + 0.382868i
\(349\) 7.39056 + 22.7458i 0.395608 + 1.21756i 0.928487 + 0.371364i \(0.121110\pi\)
−0.532879 + 0.846191i \(0.678890\pi\)
\(350\) −0.482786 1.48586i −0.0258060 0.0794227i
\(351\) 5.04097 3.66248i 0.269067 0.195489i
\(352\) 0.945865 2.91107i 0.0504148 0.155161i
\(353\) 0.558968 0.406114i 0.0297509 0.0216153i −0.572810 0.819688i \(-0.694147\pi\)
0.602561 + 0.798073i \(0.294147\pi\)
\(354\) 2.94172 + 2.13729i 0.156351 + 0.113596i
\(355\) 1.16864 + 3.59670i 0.0620249 + 0.190893i
\(356\) 5.15904 + 3.74826i 0.273428 + 0.198657i
\(357\) 9.01573 + 6.55031i 0.477163 + 0.346679i
\(358\) −2.42434 7.46134i −0.128130 0.394344i
\(359\) −3.09155 2.24614i −0.163166 0.118547i 0.503206 0.864166i \(-0.332154\pi\)
−0.666372 + 0.745620i \(0.732154\pi\)
\(360\) 0.809017 0.587785i 0.0426389 0.0309790i
\(361\) 9.53548 29.3472i 0.501867 1.54459i
\(362\) 14.6681 10.6570i 0.770941 0.560121i
\(363\) 0.504005 + 1.55117i 0.0264534 + 0.0814151i
\(364\) −3.00823 9.25839i −0.157674 0.485272i
\(365\) −4.45246 + 13.7033i −0.233052 + 0.717261i
\(366\) −11.2548 −0.588298
\(367\) −27.3527 −1.42780 −0.713900 0.700247i \(-0.753073\pi\)
−0.713900 + 0.700247i \(0.753073\pi\)
\(368\) 0.457949 1.40942i 0.0238723 0.0734712i
\(369\) 0.510889 + 0.371183i 0.0265958 + 0.0193230i
\(370\) −0.118034 + 0.0857567i −0.00613629 + 0.00445828i
\(371\) 18.5668 0.963940
\(372\) 5.23724 1.88979i 0.271538 0.0979810i
\(373\) 6.21206 0.321648 0.160824 0.986983i \(-0.448585\pi\)
0.160824 + 0.986983i \(0.448585\pi\)
\(374\) 17.6634 12.8332i 0.913355 0.663591i
\(375\) −0.809017 0.587785i −0.0417775 0.0303531i
\(376\) 2.66412 8.19932i 0.137391 0.422847i
\(377\) 46.7938 2.41001
\(378\) 1.56233 0.0803575
\(379\) −0.189287 + 0.582564i −0.00972300 + 0.0299243i −0.955800 0.294017i \(-0.905008\pi\)
0.946077 + 0.323941i \(0.105008\pi\)
\(380\) 2.18196 + 6.71539i 0.111932 + 0.344492i
\(381\) 2.54956 + 7.84675i 0.130618 + 0.402001i
\(382\) 16.0192 11.6387i 0.819616 0.595486i
\(383\) −6.06165 + 18.6558i −0.309736 + 0.953268i 0.668132 + 0.744043i \(0.267094\pi\)
−0.977867 + 0.209225i \(0.932906\pi\)
\(384\) 0.809017 0.587785i 0.0412850 0.0299953i
\(385\) −3.86881 2.81085i −0.197173 0.143254i
\(386\) −6.52687 20.0877i −0.332209 1.02243i
\(387\) 7.05602 + 5.12650i 0.358678 + 0.260595i
\(388\) 11.3488 + 8.24542i 0.576150 + 0.418598i
\(389\) −1.07478 3.30783i −0.0544935 0.167714i 0.920106 0.391670i \(-0.128103\pi\)
−0.974599 + 0.223957i \(0.928103\pi\)
\(390\) −5.04097 3.66248i −0.255260 0.185457i
\(391\) 8.55191 6.21333i 0.432489 0.314222i
\(392\) −1.40885 + 4.33599i −0.0711576 + 0.219001i
\(393\) 10.4873 7.61948i 0.529015 0.384352i
\(394\) −7.02740 21.6281i −0.354035 1.08961i
\(395\) −1.21142 3.72835i −0.0609529 0.187594i
\(396\) 0.945865 2.91107i 0.0475315 0.146287i
\(397\) 27.8724 1.39888 0.699438 0.714693i \(-0.253434\pi\)
0.699438 + 0.714693i \(0.253434\pi\)
\(398\) 7.40481 0.371170
\(399\) −3.40894 + 10.4917i −0.170661 + 0.525239i
\(400\) −0.809017 0.587785i −0.0404508 0.0293893i
\(401\) 1.69825 1.23385i 0.0848065 0.0616155i −0.544574 0.838713i \(-0.683309\pi\)
0.629381 + 0.777097i \(0.283309\pi\)
\(402\) 6.16263 0.307364
\(403\) −21.2831 27.3973i −1.06019 1.36475i
\(404\) −4.08195 −0.203085
\(405\) 0.809017 0.587785i 0.0402004 0.0292073i
\(406\) 9.49209 + 6.89641i 0.471085 + 0.342263i
\(407\) −0.138000 + 0.424720i −0.00684040 + 0.0210526i
\(408\) 7.13298 0.353135
\(409\) 30.2260 1.49458 0.747291 0.664497i \(-0.231354\pi\)
0.747291 + 0.664497i \(0.231354\pi\)
\(410\) 0.195142 0.600586i 0.00963739 0.0296608i
\(411\) 0.121775 + 0.374785i 0.00600672 + 0.0184868i
\(412\) 3.21026 + 9.88017i 0.158158 + 0.486761i
\(413\) 4.59594 3.33915i 0.226151 0.164309i
\(414\) 0.457949 1.40942i 0.0225070 0.0692693i
\(415\) −2.65416 + 1.92836i −0.130288 + 0.0946594i
\(416\) −5.04097 3.66248i −0.247154 0.179568i
\(417\) −5.05881 15.5694i −0.247731 0.762437i
\(418\) 17.4852 + 12.7037i 0.855227 + 0.621359i
\(419\) −2.20176 1.59967i −0.107563 0.0781490i 0.532704 0.846302i \(-0.321176\pi\)
−0.640266 + 0.768153i \(0.721176\pi\)
\(420\) −0.482786 1.48586i −0.0235576 0.0725027i
\(421\) 6.32078 + 4.59232i 0.308056 + 0.223816i 0.731062 0.682311i \(-0.239025\pi\)
−0.423006 + 0.906127i \(0.639025\pi\)
\(422\) 3.29414 2.39333i 0.160356 0.116506i
\(423\) 2.66412 8.19932i 0.129534 0.398664i
\(424\) 9.61440 6.98527i 0.466916 0.339235i
\(425\) −2.20421 6.78386i −0.106920 0.329066i
\(426\) 1.16864 + 3.59670i 0.0566208 + 0.174261i
\(427\) −5.43366 + 16.7231i −0.262953 + 0.809287i
\(428\) 10.2146 0.493743
\(429\) −19.0723 −0.920821
\(430\) 2.69516 8.29485i 0.129972 0.400013i
\(431\) −22.9440 16.6698i −1.10517 0.802954i −0.123275 0.992372i \(-0.539340\pi\)
−0.981897 + 0.189418i \(0.939340\pi\)
\(432\) 0.809017 0.587785i 0.0389238 0.0282798i
\(433\) −12.6166 −0.606316 −0.303158 0.952940i \(-0.598041\pi\)
−0.303158 + 0.952940i \(0.598041\pi\)
\(434\) −0.279499 8.69419i −0.0134164 0.417334i
\(435\) 7.50986 0.360070
\(436\) −11.8925 + 8.64043i −0.569549 + 0.413802i
\(437\) 8.46560 + 6.15062i 0.404964 + 0.294224i
\(438\) −4.45246 + 13.7033i −0.212747 + 0.654767i
\(439\) −16.8449 −0.803961 −0.401981 0.915648i \(-0.631678\pi\)
−0.401981 + 0.915648i \(0.631678\pi\)
\(440\) −3.06088 −0.145922
\(441\) −1.40885 + 4.33599i −0.0670880 + 0.206476i
\(442\) −13.7344 42.2702i −0.653279 2.01059i
\(443\) 5.89639 + 18.1472i 0.280146 + 0.862201i 0.987812 + 0.155654i \(0.0497484\pi\)
−0.707666 + 0.706548i \(0.750252\pi\)
\(444\) −0.118034 + 0.0857567i −0.00560165 + 0.00406983i
\(445\) 1.97058 6.06481i 0.0934143 0.287500i
\(446\) −15.8989 + 11.5512i −0.752833 + 0.546965i
\(447\) 7.05799 + 5.12793i 0.333831 + 0.242543i
\(448\) −0.482786 1.48586i −0.0228095 0.0702004i
\(449\) −22.4111 16.2826i −1.05765 0.768424i −0.0839942 0.996466i \(-0.526768\pi\)
−0.973651 + 0.228042i \(0.926768\pi\)
\(450\) −0.809017 0.587785i −0.0381374 0.0277085i
\(451\) −0.597308 1.83832i −0.0281261 0.0865633i
\(452\) −11.1369 8.09142i −0.523835 0.380588i
\(453\) 14.2225 10.3332i 0.668229 0.485497i
\(454\) 7.50228 23.0896i 0.352099 1.08365i
\(455\) −7.87566 + 5.72200i −0.369217 + 0.268252i
\(456\) 2.18196 + 6.71539i 0.102180 + 0.314477i
\(457\) 8.33575 + 25.6548i 0.389930 + 1.20008i 0.932840 + 0.360290i \(0.117322\pi\)
−0.542910 + 0.839791i \(0.682678\pi\)
\(458\) −7.77800 + 23.9382i −0.363442 + 1.11856i
\(459\) 7.13298 0.332939
\(460\) −1.48195 −0.0690965
\(461\) 5.32443 16.3869i 0.247984 0.763215i −0.747148 0.664658i \(-0.768577\pi\)
0.995131 0.0985571i \(-0.0314227\pi\)
\(462\) −3.86881 2.81085i −0.179993 0.130773i
\(463\) 25.4248 18.4722i 1.18159 0.858475i 0.189240 0.981931i \(-0.439398\pi\)
0.992350 + 0.123455i \(0.0393976\pi\)
\(464\) 7.50986 0.348637
\(465\) −3.41569 4.39694i −0.158399 0.203903i
\(466\) 2.81312 0.130315
\(467\) 20.1650 14.6507i 0.933124 0.677955i −0.0136314 0.999907i \(-0.504339\pi\)
0.946756 + 0.321952i \(0.104339\pi\)
\(468\) −5.04097 3.66248i −0.233019 0.169298i
\(469\) 2.97523 9.15683i 0.137384 0.422823i
\(470\) −8.62127 −0.397670
\(471\) −9.14529 −0.421393
\(472\) 1.12364 3.45820i 0.0517197 0.159177i
\(473\) −8.24957 25.3896i −0.379316 1.16741i
\(474\) −1.21142 3.72835i −0.0556422 0.171249i
\(475\) 5.71245 4.15034i 0.262105 0.190431i
\(476\) 3.44370 10.5986i 0.157842 0.485787i
\(477\) 9.61440 6.98527i 0.440213 0.319833i
\(478\) −17.0374 12.3784i −0.779275 0.566176i
\(479\) 10.5601 + 32.5006i 0.482503 + 1.48499i 0.835565 + 0.549392i \(0.185141\pi\)
−0.353061 + 0.935600i \(0.614859\pi\)
\(480\) −0.809017 0.587785i −0.0369264 0.0268286i
\(481\) 0.735468 + 0.534349i 0.0335345 + 0.0243642i
\(482\) 0.00164170 + 0.00505264i 7.47775e−5 + 0.000230142i
\(483\) −1.87312 1.36090i −0.0852298 0.0619231i
\(484\) 1.31950 0.958674i 0.0599773 0.0435761i
\(485\) 4.33487 13.3414i 0.196836 0.605800i
\(486\) 0.809017 0.587785i 0.0366978 0.0266625i
\(487\) −1.81438 5.58409i −0.0822174 0.253039i 0.901495 0.432790i \(-0.142471\pi\)
−0.983712 + 0.179751i \(0.942471\pi\)
\(488\) 3.47793 + 10.7040i 0.157438 + 0.484545i
\(489\) 1.30056 4.00271i 0.0588133 0.181009i
\(490\) 4.55913 0.205960
\(491\) −3.40548 −0.153687 −0.0768435 0.997043i \(-0.524484\pi\)
−0.0768435 + 0.997043i \(0.524484\pi\)
\(492\) 0.195142 0.600586i 0.00879769 0.0270765i
\(493\) 43.3371 + 31.4863i 1.95181 + 1.41807i
\(494\) 35.5942 25.8607i 1.60146 1.16353i
\(495\) −3.06088 −0.137576
\(496\) −3.41569 4.39694i −0.153369 0.197428i
\(497\) 5.90841 0.265028
\(498\) −2.65416 + 1.92836i −0.118936 + 0.0864119i
\(499\) −27.5699 20.0307i −1.23420 0.896696i −0.236999 0.971510i \(-0.576164\pi\)
−0.997198 + 0.0748139i \(0.976164\pi\)
\(500\) −0.309017 + 0.951057i −0.0138197 + 0.0425325i
\(501\) −0.721973 −0.0322554
\(502\) −5.42631 −0.242188
\(503\) 10.0442 30.9129i 0.447849 1.37834i −0.431479 0.902123i \(-0.642008\pi\)
0.879329 0.476215i \(-0.157992\pi\)
\(504\) −0.482786 1.48586i −0.0215050 0.0661856i
\(505\) 1.26139 + 3.88216i 0.0561312 + 0.172754i
\(506\) −3.66977 + 2.66625i −0.163141 + 0.118529i
\(507\) −7.98043 + 24.5612i −0.354423 + 1.09080i
\(508\) 6.67485 4.84956i 0.296148 0.215164i
\(509\) 22.8756 + 16.6201i 1.01394 + 0.736674i 0.965033 0.262129i \(-0.0844246\pi\)
0.0489120 + 0.998803i \(0.484425\pi\)
\(510\) −2.20421 6.78386i −0.0976041 0.300395i
\(511\) 18.2116 + 13.2315i 0.805633 + 0.585327i
\(512\) −0.809017 0.587785i −0.0357538 0.0259767i
\(513\) 2.18196 + 6.71539i 0.0963360 + 0.296492i
\(514\) 7.68352 + 5.58241i 0.338906 + 0.246229i
\(515\) 8.40457 6.10628i 0.370350 0.269075i
\(516\) 2.69516 8.29485i 0.118648 0.365161i
\(517\) −21.3489 + 15.5109i −0.938924 + 0.682168i
\(518\) 0.0704376 + 0.216784i 0.00309485 + 0.00952496i
\(519\) 0.620623 + 1.91008i 0.0272423 + 0.0838433i
\(520\) −1.92548 + 5.92602i −0.0844379 + 0.259873i
\(521\) 29.1228 1.27589 0.637946 0.770081i \(-0.279784\pi\)
0.637946 + 0.770081i \(0.279784\pi\)
\(522\) 7.50986 0.328698
\(523\) 0.961645 2.95964i 0.0420498 0.129416i −0.927828 0.373009i \(-0.878326\pi\)
0.969878 + 0.243593i \(0.0783261\pi\)
\(524\) −10.4873 7.61948i −0.458140 0.332858i
\(525\) −1.26395 + 0.918314i −0.0551633 + 0.0400785i
\(526\) −26.9098 −1.17332
\(527\) −1.27608 39.6942i −0.0555870 1.72911i
\(528\) −3.06088 −0.133208
\(529\) 16.8306 12.2282i 0.731767 0.531660i
\(530\) −9.61440 6.98527i −0.417623 0.303421i
\(531\) 1.12364 3.45820i 0.0487618 0.150073i
\(532\) 11.0316 0.478279
\(533\) −3.93483 −0.170436
\(534\) 1.97058 6.06481i 0.0852752 0.262450i
\(535\) −3.15650 9.71470i −0.136467 0.420003i
\(536\) −1.90436 5.86101i −0.0822557 0.253157i
\(537\) −6.34700 + 4.61136i −0.273893 + 0.198995i
\(538\) −2.86102 + 8.80531i −0.123347 + 0.379624i
\(539\) 11.2898 8.20252i 0.486286 0.353308i
\(540\) −0.809017 0.587785i −0.0348145 0.0252942i
\(541\) −2.51474 7.73959i −0.108117 0.332751i 0.882332 0.470627i \(-0.155972\pi\)
−0.990449 + 0.137876i \(0.955972\pi\)
\(542\) 1.62402 + 1.17992i 0.0697575 + 0.0506818i
\(543\) −14.6681 10.6570i −0.629470 0.457337i
\(544\) −2.20421 6.78386i −0.0945048 0.290856i
\(545\) 11.8925 + 8.64043i 0.509420 + 0.370115i
\(546\) −7.87566 + 5.72200i −0.337047 + 0.244879i
\(547\) −6.96745 + 21.4436i −0.297907 + 0.916862i 0.684323 + 0.729179i \(0.260098\pi\)
−0.982230 + 0.187683i \(0.939902\pi\)
\(548\) 0.318811 0.231630i 0.0136189 0.00989473i
\(549\) 3.47793 + 10.7040i 0.148434 + 0.456834i
\(550\) 0.945865 + 2.91107i 0.0403318 + 0.124129i
\(551\) −16.3862 + 50.4317i −0.698077 + 2.14846i
\(552\) −1.48195 −0.0630762
\(553\) −6.12468 −0.260448
\(554\) −8.64181 + 26.5967i −0.367155 + 1.12999i
\(555\) 0.118034 + 0.0857567i 0.00501026 + 0.00364017i
\(556\) −13.2441 + 9.62242i −0.561676 + 0.408082i
\(557\) 31.2385 1.32362 0.661808 0.749673i \(-0.269789\pi\)
0.661808 + 0.749673i \(0.269789\pi\)
\(558\) −3.41569 4.39694i −0.144598 0.186137i
\(559\) −54.3449 −2.29855
\(560\) −1.26395 + 0.918314i −0.0534117 + 0.0388058i
\(561\) −17.6634 12.8332i −0.745751 0.541820i
\(562\) −5.90841 + 18.1842i −0.249231 + 0.767055i
\(563\) 21.2403 0.895173 0.447586 0.894241i \(-0.352284\pi\)
0.447586 + 0.894241i \(0.352284\pi\)
\(564\) −8.62127 −0.363021
\(565\) −4.25391 + 13.0922i −0.178963 + 0.550793i
\(566\) 8.26050 + 25.4232i 0.347215 + 1.06862i
\(567\) −0.482786 1.48586i −0.0202751 0.0624004i
\(568\) 3.05954 2.22288i 0.128375 0.0932702i
\(569\) −2.70936 + 8.33855i −0.113582 + 0.349570i −0.991649 0.128968i \(-0.958833\pi\)
0.878066 + 0.478539i \(0.158833\pi\)
\(570\) 5.71245 4.15034i 0.239268 0.173839i
\(571\) 7.23696 + 5.25796i 0.302857 + 0.220039i 0.728826 0.684699i \(-0.240066\pi\)
−0.425968 + 0.904738i \(0.640066\pi\)
\(572\) 5.89367 + 18.1389i 0.246427 + 0.758424i
\(573\) −16.0192 11.6387i −0.669214 0.486212i
\(574\) −0.798177 0.579909i −0.0333152 0.0242049i
\(575\) 0.457949 + 1.40942i 0.0190978 + 0.0587770i
\(576\) −0.809017 0.587785i −0.0337090 0.0244911i
\(577\) −4.11770 + 2.99168i −0.171422 + 0.124545i −0.670188 0.742191i \(-0.733787\pi\)
0.498766 + 0.866737i \(0.333787\pi\)
\(578\) 10.4693 32.2212i 0.435465 1.34022i
\(579\) −17.0876 + 12.4149i −0.710136 + 0.515944i
\(580\) −2.32067 7.14230i −0.0963608 0.296568i
\(581\) 1.58389 + 4.87470i 0.0657107 + 0.202237i
\(582\) 4.33487 13.3414i 0.179686 0.553017i
\(583\) −36.3757 −1.50653
\(584\) 14.4085 0.596226
\(585\) −1.92548 + 5.92602i −0.0796088 + 0.245011i
\(586\) −9.39518 6.82600i −0.388111 0.281979i
\(587\) 37.2730 27.0804i 1.53842 1.11773i 0.587103 0.809512i \(-0.300268\pi\)
0.951317 0.308215i \(-0.0997317\pi\)
\(588\) 4.55913 0.188015
\(589\) 36.9801 13.3438i 1.52374 0.549820i
\(590\) −3.63617 −0.149699
\(591\) −18.3980 + 13.3669i −0.756791 + 0.549841i
\(592\) 0.118034 + 0.0857567i 0.00485117 + 0.00352458i
\(593\) −0.0141339 + 0.0434996i −0.000580409 + 0.00178632i −0.951346 0.308124i \(-0.900299\pi\)
0.950766 + 0.309910i \(0.100299\pi\)
\(594\) −3.06088 −0.125590
\(595\) −11.1441 −0.456862
\(596\) 2.69591 8.29716i 0.110429 0.339865i
\(597\) −2.28821 7.04239i −0.0936503 0.288226i
\(598\) 2.85348 + 8.78209i 0.116687 + 0.359127i
\(599\) 18.9543 13.7711i 0.774454 0.562673i −0.128856 0.991663i \(-0.541130\pi\)
0.903309 + 0.428990i \(0.141130\pi\)
\(600\) −0.309017 + 0.951057i −0.0126156 + 0.0388267i
\(601\) 2.63758 1.91631i 0.107589 0.0781680i −0.532690 0.846311i \(-0.678819\pi\)
0.640279 + 0.768143i \(0.278819\pi\)
\(602\) −11.0238 8.00928i −0.449298 0.326434i
\(603\) −1.90436 5.86101i −0.0775515 0.238679i
\(604\) −14.2225 10.3332i −0.578703 0.420453i
\(605\) −1.31950 0.958674i −0.0536453 0.0389756i
\(606\) 1.26139 + 3.88216i 0.0512405 + 0.157702i
\(607\) −7.05094 5.12281i −0.286189 0.207928i 0.435423 0.900226i \(-0.356599\pi\)
−0.721612 + 0.692297i \(0.756599\pi\)
\(608\) 5.71245 4.15034i 0.231671 0.168319i
\(609\) 3.62566 11.1586i 0.146919 0.452170i
\(610\) 9.10533 6.61541i 0.368664 0.267850i
\(611\) 16.6001 + 51.0898i 0.671568 + 2.06687i
\(612\) −2.20421 6.78386i −0.0890999 0.274221i
\(613\) −1.36100 + 4.18872i −0.0549702 + 0.169181i −0.974772 0.223202i \(-0.928349\pi\)
0.919802 + 0.392383i \(0.128349\pi\)
\(614\) 16.4991 0.665848
\(615\) −0.631494 −0.0254643
\(616\) −1.47775 + 4.54805i −0.0595403 + 0.183246i
\(617\) −5.36453 3.89756i −0.215968 0.156910i 0.474542 0.880233i \(-0.342614\pi\)
−0.690510 + 0.723323i \(0.742614\pi\)
\(618\) 8.40457 6.10628i 0.338081 0.245631i
\(619\) 6.96062 0.279771 0.139885 0.990168i \(-0.455327\pi\)
0.139885 + 0.990168i \(0.455327\pi\)
\(620\) −3.12623 + 4.60724i −0.125552 + 0.185031i
\(621\) −1.48195 −0.0594688
\(622\) −2.80886 + 2.04076i −0.112625 + 0.0818270i
\(623\) −8.06011 5.85602i −0.322922 0.234616i
\(624\) −1.92548 + 5.92602i −0.0770809 + 0.237231i
\(625\) 1.00000 0.0400000
\(626\) 8.33590 0.333170
\(627\) 6.67873 20.5550i 0.266723 0.820889i
\(628\) 2.82605 + 8.69769i 0.112772 + 0.347076i
\(629\) 0.321590 + 0.989752i 0.0128226 + 0.0394640i
\(630\) −1.26395 + 0.918314i −0.0503570 + 0.0365865i
\(631\) 4.27325 13.1517i 0.170115 0.523561i −0.829261 0.558861i \(-0.811239\pi\)
0.999377 + 0.0352998i \(0.0112386\pi\)
\(632\) −3.17153 + 2.30425i −0.126157 + 0.0916581i
\(633\) −3.29414 2.39333i −0.130930 0.0951265i
\(634\) 2.99288 + 9.21114i 0.118862 + 0.365821i
\(635\) −6.67485 4.84956i −0.264883 0.192449i
\(636\) −9.61440 6.98527i −0.381236 0.276984i
\(637\) −8.77851 27.0175i −0.347817 1.07047i
\(638\) −18.5967 13.5113i −0.736251 0.534918i
\(639\) 3.05954 2.22288i 0.121033 0.0879360i
\(640\) −0.309017 + 0.951057i −0.0122150 + 0.0375938i
\(641\) −33.9221 + 24.6458i −1.33984 + 0.973452i −0.340392 + 0.940284i \(0.610560\pi\)
−0.999450 + 0.0331681i \(0.989440\pi\)
\(642\) −3.15650 9.71470i −0.124577 0.383408i
\(643\) 10.6518 + 32.7830i 0.420068 + 1.29284i 0.907639 + 0.419752i \(0.137883\pi\)
−0.487571 + 0.873083i \(0.662117\pi\)
\(644\) −0.715467 + 2.20198i −0.0281934 + 0.0867702i
\(645\) −8.72172 −0.343418
\(646\) 50.3658 1.98162
\(647\) 13.9599 42.9643i 0.548822 1.68910i −0.162904 0.986642i \(-0.552086\pi\)
0.711726 0.702458i \(-0.247914\pi\)
\(648\) −0.809017 0.587785i −0.0317812 0.0230904i
\(649\) −9.00428 + 6.54199i −0.353449 + 0.256796i
\(650\) 6.23099 0.244399
\(651\) −8.18229 + 2.95247i −0.320689 + 0.115716i
\(652\) −4.20870 −0.164825
\(653\) −31.7816 + 23.0907i −1.24371 + 0.903607i −0.997840 0.0656961i \(-0.979073\pi\)
−0.245869 + 0.969303i \(0.579073\pi\)
\(654\) 11.8925 + 8.64043i 0.465035 + 0.337868i
\(655\) −4.00580 + 12.3286i −0.156519 + 0.481717i
\(656\) −0.631494 −0.0246557
\(657\) 14.4085 0.562128
\(658\) −4.16223 + 12.8100i −0.162261 + 0.499387i
\(659\) 2.41976 + 7.44725i 0.0942603 + 0.290104i 0.987060 0.160350i \(-0.0512623\pi\)
−0.892800 + 0.450454i \(0.851262\pi\)
\(660\) 0.945865 + 2.91107i 0.0368177 + 0.113313i
\(661\) 34.8377 25.3111i 1.35503 0.984487i 0.356286 0.934377i \(-0.384043\pi\)
0.998744 0.0501095i \(-0.0159570\pi\)
\(662\) 6.04531 18.6056i 0.234958 0.723125i
\(663\) −35.9572 + 26.1244i −1.39646 + 1.01459i
\(664\) 2.65416 + 1.92836i 0.103001 + 0.0748349i
\(665\) −3.40894 10.4917i −0.132193 0.406849i
\(666\) 0.118034 + 0.0857567i 0.00457372 + 0.00332301i
\(667\) −9.00377 6.54162i −0.348627 0.253293i
\(668\) 0.223102 + 0.686637i 0.00863207 + 0.0265668i
\(669\) 15.8989 + 11.5512i 0.614685 + 0.446595i
\(670\) −4.98567 + 3.62230i −0.192613 + 0.139942i
\(671\) 10.6455 32.7636i 0.410966 1.26482i
\(672\) −1.26395 + 0.918314i −0.0487580 + 0.0354247i
\(673\) 6.98740 + 21.5050i 0.269345 + 0.828958i 0.990661 + 0.136351i \(0.0435376\pi\)
−0.721316 + 0.692606i \(0.756462\pi\)
\(674\) −7.91353 24.3554i −0.304818 0.938133i
\(675\) −0.309017 + 0.951057i −0.0118941 + 0.0366062i
\(676\) 25.8252 0.993277
\(677\) −1.18096 −0.0453882 −0.0226941 0.999742i \(-0.507224\pi\)
−0.0226941 + 0.999742i \(0.507224\pi\)
\(678\) −4.25391 + 13.0922i −0.163370 + 0.502803i
\(679\) −17.7306 12.8821i −0.680439 0.494368i
\(680\) −5.77070 + 4.19266i −0.221296 + 0.160781i
\(681\) −24.2779 −0.930330
\(682\) 0.547588 + 17.0335i 0.0209682 + 0.652246i
\(683\) 40.4963 1.54955 0.774774 0.632239i \(-0.217864\pi\)
0.774774 + 0.632239i \(0.217864\pi\)
\(684\) 5.71245 4.15034i 0.218421 0.158692i
\(685\) −0.318811 0.231630i −0.0121811 0.00885012i
\(686\) 5.58059 17.1753i 0.213068 0.655755i
\(687\) 25.1701 0.960301
\(688\) −8.72172 −0.332513
\(689\) −22.8825 + 70.4251i −0.871754 + 2.68298i
\(690\) 0.457949 + 1.40942i 0.0174338 + 0.0536558i
\(691\) −0.0881680 0.271353i −0.00335407 0.0103228i 0.949365 0.314174i \(-0.101727\pi\)
−0.952720 + 0.303851i \(0.901727\pi\)
\(692\) 1.62481 1.18050i 0.0617661 0.0448757i
\(693\) −1.47775 + 4.54805i −0.0561352 + 0.172766i
\(694\) −19.5909 + 14.2337i −0.743662 + 0.540302i
\(695\) 13.2441 + 9.62242i 0.502378 + 0.364999i
\(696\) −2.32067 7.14230i −0.0879649 0.270728i
\(697\) −3.64416 2.64764i −0.138032 0.100286i
\(698\) −19.3487 14.0577i −0.732361 0.532091i
\(699\) −0.869301 2.67543i −0.0328800 0.101194i
\(700\) 1.26395 + 0.918314i 0.0477728 + 0.0347090i
\(701\) −4.54407 + 3.30146i −0.171627 + 0.124694i −0.670283 0.742106i \(-0.733827\pi\)
0.498656 + 0.866800i \(0.333827\pi\)
\(702\) −1.92548 + 5.92602i −0.0726726 + 0.223663i
\(703\) −0.833436 + 0.605526i −0.0314336 + 0.0228379i
\(704\) 0.945865 + 2.91107i 0.0356486 + 0.109715i
\(705\) 2.66412 + 8.19932i 0.100337 + 0.308804i
\(706\) −0.213507 + 0.657106i −0.00803543 + 0.0247305i
\(707\) 6.37735 0.239845
\(708\) −3.63617 −0.136656
\(709\) −13.3828 + 41.1881i −0.502602 + 1.54685i 0.302163 + 0.953256i \(0.402291\pi\)
−0.804765 + 0.593594i \(0.797709\pi\)
\(710\) −3.05954 2.22288i −0.114822 0.0834234i
\(711\) −3.17153 + 2.30425i −0.118942 + 0.0864161i
\(712\) −6.37692 −0.238985
\(713\) 0.265120 + 8.24691i 0.00992882 + 0.308849i
\(714\) −11.1441 −0.417056
\(715\) 15.4298 11.2104i 0.577043 0.419246i
\(716\) 6.34700 + 4.61136i 0.237198 + 0.172335i
\(717\) −6.50773 + 20.0287i −0.243035 + 0.747986i
\(718\) 3.82137 0.142612
\(719\) −15.4612 −0.576604 −0.288302 0.957539i \(-0.593091\pi\)
−0.288302 + 0.957539i \(0.593091\pi\)
\(720\) −0.309017 + 0.951057i −0.0115164 + 0.0354438i
\(721\) −5.01548 15.4361i −0.186786 0.574869i
\(722\) 9.53548 + 29.3472i 0.354874 + 1.09219i
\(723\) 0.00429803 0.00312270i 0.000159846 0.000116135i
\(724\) −5.60273 + 17.2434i −0.208224 + 0.640847i
\(725\) −6.07561 + 4.41419i −0.225642 + 0.163939i
\(726\) −1.31950 0.958674i −0.0489713 0.0355797i
\(727\) 2.11091 + 6.49672i 0.0782894 + 0.240950i 0.982540 0.186053i \(-0.0595695\pi\)
−0.904250 + 0.427003i \(0.859569\pi\)
\(728\) 7.87566 + 5.72200i 0.291891 + 0.212071i
\(729\) −0.809017 0.587785i −0.0299636 0.0217698i
\(730\) −4.45246 13.7033i −0.164793 0.507180i
\(731\) −50.3304 36.5672i −1.86154 1.35249i
\(732\) 9.10533 6.61541i 0.336543 0.244512i
\(733\) 1.36450 4.19949i 0.0503989 0.155112i −0.922690 0.385544i \(-0.874014\pi\)
0.973088 + 0.230432i \(0.0740139\pi\)
\(734\) 22.1288 16.0775i 0.816790 0.593433i
\(735\) −1.40885 4.33599i −0.0519661 0.159935i
\(736\) 0.457949 + 1.40942i 0.0168802 + 0.0519520i
\(737\) −5.82902 + 17.9399i −0.214715 + 0.660824i
\(738\) −0.631494 −0.0232456
\(739\) 45.1243 1.65992 0.829962 0.557820i \(-0.188362\pi\)
0.829962 + 0.557820i \(0.188362\pi\)
\(740\) 0.0450850 0.138757i 0.00165736 0.00510082i
\(741\) −35.5942 25.8607i −1.30759 0.950017i
\(742\) −15.0208 + 10.9133i −0.551433 + 0.400639i
\(743\) −8.89623 −0.326371 −0.163185 0.986595i \(-0.552177\pi\)
−0.163185 + 0.986595i \(0.552177\pi\)
\(744\) −3.12623 + 4.60724i −0.114613 + 0.168910i
\(745\) −8.72415 −0.319628
\(746\) −5.02566 + 3.65136i −0.184002 + 0.133686i
\(747\) 2.65416 + 1.92836i 0.0971106 + 0.0705550i
\(748\) −6.74683 + 20.7646i −0.246689 + 0.759230i
\(749\) −15.9586 −0.583115
\(750\) 1.00000 0.0365148
\(751\) −0.633678 + 1.95026i −0.0231233 + 0.0711661i −0.961952 0.273218i \(-0.911912\pi\)
0.938829 + 0.344384i \(0.111912\pi\)
\(752\) 2.66412 + 8.19932i 0.0971504 + 0.298998i
\(753\) 1.67682 + 5.16073i 0.0611068 + 0.188067i
\(754\) −37.8570 + 27.5047i −1.37867 + 1.00166i
\(755\) −5.43249 + 16.7195i −0.197709 + 0.608485i
\(756\) −1.26395 + 0.918314i −0.0459694 + 0.0333988i
\(757\) −1.08133 0.785632i −0.0393016 0.0285543i 0.567961 0.823055i \(-0.307732\pi\)
−0.607263 + 0.794501i \(0.707732\pi\)
\(758\) −0.189287 0.582564i −0.00687520 0.0211597i
\(759\) 3.66977 + 2.66625i 0.133204 + 0.0967786i
\(760\) −5.71245 4.15034i −0.207212 0.150549i
\(761\) 11.0687 + 34.0660i 0.401241 + 1.23489i 0.923994 + 0.382408i \(0.124905\pi\)
−0.522753 + 0.852484i \(0.675095\pi\)
\(762\) −6.67485 4.84956i −0.241804 0.175681i
\(763\) 18.5801 13.4992i 0.672643 0.488704i
\(764\) −6.11881 + 18.8318i −0.221371 + 0.681309i
\(765\) −5.77070 + 4.19266i −0.208640 + 0.151586i
\(766\) −6.06165 18.6558i −0.219016 0.674062i
\(767\) 7.00138 + 21.5480i 0.252805 + 0.778054i
\(768\) −0.309017 + 0.951057i −0.0111507 + 0.0343183i
\(769\) 11.5483 0.416441 0.208220 0.978082i \(-0.433233\pi\)
0.208220 + 0.978082i \(0.433233\pi\)
\(770\) 4.78211 0.172335
\(771\) 2.93485 9.03252i 0.105696 0.325298i
\(772\) 17.0876 + 12.4149i 0.614995 + 0.446820i
\(773\) 28.4794 20.6915i 1.02433 0.744222i 0.0571668 0.998365i \(-0.481793\pi\)
0.967167 + 0.254143i \(0.0817933\pi\)
\(774\) −8.72172 −0.313496
\(775\) 5.34781 + 1.54950i 0.192099 + 0.0556598i
\(776\) −14.0279 −0.503574
\(777\) 0.184408 0.133980i 0.00661560 0.00480651i
\(778\) 2.81381 + 2.04435i 0.100880 + 0.0732936i
\(779\) 1.37790 4.24073i 0.0493682 0.151940i
\(780\) 6.23099 0.223105
\(781\) −11.5756 −0.414209
\(782\) −3.26654 + 10.0534i −0.116811 + 0.359508i
\(783\) −2.32067 7.14230i −0.0829341 0.255245i
\(784\) −1.40885 4.33599i −0.0503160 0.154857i
\(785\) 7.39870 5.37547i 0.264071 0.191859i
\(786\) −4.00580 + 12.3286i −0.142882 + 0.439746i
\(787\) −7.22037 + 5.24590i −0.257378 + 0.186996i −0.708990 0.705218i \(-0.750849\pi\)
0.451612 + 0.892214i \(0.350849\pi\)
\(788\) 18.3980 + 13.3669i 0.655400 + 0.476176i
\(789\) 8.31559 + 25.5928i 0.296043 + 0.911127i
\(790\) 3.17153 + 2.30425i 0.112838 + 0.0819815i
\(791\) 17.3995 + 12.6415i 0.618654 + 0.449479i
\(792\) 0.945865 + 2.91107i 0.0336098 + 0.103440i
\(793\) −56.7352 41.2205i −2.01473 1.46378i
\(794\) −22.5493 + 16.3830i −0.800243 + 0.581411i
\(795\) −3.67237 + 11.3024i −0.130246 + 0.400855i
\(796\) −5.99062 + 4.35244i −0.212332 + 0.154268i
\(797\) −0.156744 0.482410i −0.00555217 0.0170878i 0.948242 0.317548i \(-0.102860\pi\)
−0.953794 + 0.300461i \(0.902860\pi\)
\(798\) −3.40894 10.4917i −0.120675 0.371400i
\(799\) −19.0031 + 58.4855i −0.672281 + 2.06907i
\(800\) 1.00000 0.0353553
\(801\) −6.37692 −0.225317
\(802\) −0.648673 + 1.99641i −0.0229054 + 0.0704957i
\(803\) −35.6798 25.9229i −1.25911 0.914798i
\(804\) −4.98567 + 3.62230i −0.175831 + 0.127749i
\(805\) 2.31530 0.0816036
\(806\) 33.3221 + 9.65493i 1.17372 + 0.340080i
\(807\) 9.25845 0.325913
\(808\) 3.30237 2.39931i 0.116177 0.0844074i
\(809\) 5.26480 + 3.82510i 0.185101 + 0.134483i 0.676477 0.736464i \(-0.263506\pi\)
−0.491376 + 0.870947i \(0.663506\pi\)
\(810\) −0.309017 + 0.951057i −0.0108578 + 0.0334167i
\(811\) 14.6774 0.515394 0.257697 0.966226i \(-0.417036\pi\)
0.257697 + 0.966226i \(0.417036\pi\)
\(812\) −11.7329 −0.411743
\(813\) 0.620319 1.90915i 0.0217555 0.0669567i
\(814\) −0.138000 0.424720i −0.00483689 0.0148864i
\(815\) 1.30056 + 4.00271i 0.0455566 + 0.140209i
\(816\) −5.77070 + 4.19266i −0.202015 + 0.146772i
\(817\) 19.0305 58.5698i 0.665792 2.04910i
\(818\) −24.4534 + 17.7664i −0.854993 + 0.621188i
\(819\) 7.87566 + 5.72200i 0.275198 + 0.199943i
\(820\) 0.195142 + 0.600586i 0.00681466 + 0.0209734i
\(821\) −40.2749 29.2614i −1.40560 1.02123i −0.993943 0.109892i \(-0.964949\pi\)
−0.411659 0.911338i \(-0.635051\pi\)
\(822\) −0.318811 0.231630i −0.0111198 0.00807902i
\(823\) −9.95968 30.6527i −0.347173 1.06849i −0.960410 0.278589i \(-0.910133\pi\)
0.613238 0.789898i \(-0.289867\pi\)
\(824\) −8.40457 6.10628i −0.292787 0.212722i
\(825\) 2.47631 1.79914i 0.0862139 0.0626381i
\(826\) −1.75549 + 5.40285i −0.0610814 + 0.187989i
\(827\) 7.63332 5.54593i 0.265436 0.192851i −0.447104 0.894482i \(-0.647545\pi\)
0.712540 + 0.701631i \(0.247545\pi\)
\(828\) 0.457949 + 1.40942i 0.0159148 + 0.0489808i
\(829\) −0.840238 2.58599i −0.0291827 0.0898151i 0.935404 0.353580i \(-0.115036\pi\)
−0.964587 + 0.263765i \(0.915036\pi\)
\(830\) 1.01380 3.12015i 0.0351895 0.108302i
\(831\) 27.9655 0.970111
\(832\) 6.23099 0.216021
\(833\) 10.0493 30.9285i 0.348187 1.07161i
\(834\) 13.2441 + 9.62242i 0.458607 + 0.333197i
\(835\) 0.584088 0.424365i 0.0202132 0.0146858i
\(836\) −21.6128 −0.747496
\(837\) −3.12623 + 4.60724i −0.108058 + 0.159250i
\(838\) 2.72152 0.0940134
\(839\) −44.7163 + 32.4883i −1.54378 + 1.12162i −0.595869 + 0.803082i \(0.703192\pi\)
−0.947910 + 0.318539i \(0.896808\pi\)
\(840\) 1.26395 + 0.918314i 0.0436104 + 0.0316848i
\(841\) 8.46645 26.0571i 0.291947 0.898519i
\(842\) −7.81292 −0.269251
\(843\) 19.1200 0.658528
\(844\) −1.25825 + 3.87250i −0.0433108 + 0.133297i
\(845\) −7.98043 24.5612i −0.274535 0.844932i
\(846\) 2.66412 + 8.19932i 0.0915943 + 0.281898i
\(847\) −2.06149 + 1.49776i −0.0708338 + 0.0514638i
\(848\) −3.67237 + 11.3024i −0.126110 + 0.388126i
\(849\) 21.6263 15.7124i 0.742211 0.539248i
\(850\) 5.77070 + 4.19266i 0.197933 + 0.143807i
\(851\) −0.0668139 0.205632i −0.00229035 0.00704897i
\(852\) −3.05954 2.22288i −0.104818 0.0761548i
\(853\) 45.8536 + 33.3146i 1.57000 + 1.14067i 0.927158 + 0.374672i \(0.122245\pi\)
0.642841 + 0.765999i \(0.277755\pi\)
\(854\) −5.43366 16.7231i −0.185936 0.572253i
\(855\) −5.71245 4.15034i −0.195362 0.141939i
\(856\) −8.26381 + 6.00401i −0.282451 + 0.205213i
\(857\) 5.09114 15.6689i 0.173910 0.535240i −0.825672 0.564151i \(-0.809204\pi\)
0.999582 + 0.0289105i \(0.00920377\pi\)
\(858\) 15.4298 11.2104i 0.526766 0.382718i
\(859\) −13.2398 40.7480i −0.451737 1.39030i −0.874924 0.484260i \(-0.839089\pi\)
0.423187 0.906042i \(-0.360911\pi\)
\(860\) 2.69516 + 8.29485i 0.0919042 + 0.282852i
\(861\) −0.304876 + 0.938313i −0.0103902 + 0.0319776i
\(862\) 28.3603 0.965956
\(863\) 21.4906 0.731547 0.365774 0.930704i \(-0.380804\pi\)
0.365774 + 0.930704i \(0.380804\pi\)
\(864\) −0.309017 + 0.951057i −0.0105130 + 0.0323556i
\(865\) −1.62481 1.18050i −0.0552453 0.0401380i
\(866\) 10.2071 7.41586i 0.346850 0.252001i
\(867\) −33.8793 −1.15060
\(868\) 5.33643 + 6.86946i 0.181130 + 0.233165i
\(869\) 11.9993 0.407050
\(870\) −6.07561 + 4.41419i −0.205982 + 0.149655i
\(871\) 31.0657 + 22.5705i 1.05262 + 0.764773i
\(872\) 4.54254 13.9805i 0.153830 0.473440i
\(873\) −14.0279 −0.474774
\(874\) −10.4641 −0.353952
\(875\) 0.482786 1.48586i 0.0163212 0.0502313i
\(876\) −4.45246 13.7033i −0.150435 0.462990i
\(877\) 0.979968 + 3.01603i 0.0330912 + 0.101844i 0.966238 0.257652i \(-0.0829487\pi\)
−0.933147 + 0.359496i \(0.882949\pi\)
\(878\) 13.6278 9.90116i 0.459915 0.334148i
\(879\) −3.58864 + 11.0447i −0.121042 + 0.372528i
\(880\) 2.47631 1.79914i 0.0834763 0.0606491i
\(881\) −7.83413 5.69183i −0.263939 0.191763i 0.447943 0.894062i \(-0.352157\pi\)
−0.711882 + 0.702299i \(0.752157\pi\)
\(882\) −1.40885 4.33599i −0.0474384 0.146000i
\(883\) −26.1095 18.9696i −0.878654 0.638379i 0.0542411 0.998528i \(-0.482726\pi\)
−0.932895 + 0.360148i \(0.882726\pi\)
\(884\) 35.9572 + 26.1244i 1.20937 + 0.878659i
\(885\) 1.12364 + 3.45820i 0.0377707 + 0.116246i
\(886\) −15.4370 11.2156i −0.518615 0.376796i
\(887\) −25.8740 + 18.7986i −0.868766 + 0.631195i −0.930255 0.366913i \(-0.880415\pi\)
0.0614899 + 0.998108i \(0.480415\pi\)
\(888\) 0.0450850 0.138757i 0.00151295 0.00465639i
\(889\) −10.4283 + 7.57661i −0.349754 + 0.254111i
\(890\) 1.97058 + 6.06481i 0.0660539 + 0.203293i
\(891\) 0.945865 + 2.91107i 0.0316877 + 0.0975246i
\(892\) 6.07282 18.6902i 0.203333 0.625795i
\(893\) −60.8746 −2.03709
\(894\) −8.72415 −0.291779
\(895\) 2.42434 7.46134i 0.0810367 0.249405i
\(896\) 1.26395 + 0.918314i 0.0422256 + 0.0306787i
\(897\) 7.47050 5.42763i 0.249433 0.181223i
\(898\) 27.7017 0.924416
\(899\) −39.3310 + 14.1920i −1.31176 + 0.473331i
\(900\) 1.00000 0.0333333
\(901\) −68.5793 + 49.8257i −2.28471 + 1.65994i
\(902\) 1.56377 + 1.13615i 0.0520679 + 0.0378295i
\(903\) −4.21073 + 12.9593i −0.140124 + 0.431258i
\(904\) 13.7659 0.457849
\(905\) 18.1308 0.602689
\(906\) −5.43249 + 16.7195i −0.180482 + 0.555468i
\(907\) −7.38312 22.7229i −0.245152 0.754501i −0.995611 0.0935844i \(-0.970168\pi\)
0.750459 0.660917i \(-0.229832\pi\)
\(908\) 7.50228 + 23.0896i 0.248972 + 0.766256i
\(909\) 3.30237 2.39931i 0.109533 0.0795801i
\(910\) 3.00823 9.25839i 0.0997220 0.306913i
\(911\) 12.0984 8.79000i 0.400838 0.291226i −0.369044 0.929412i \(-0.620315\pi\)
0.769882 + 0.638186i \(0.220315\pi\)
\(912\) −5.71245 4.15034i −0.189158 0.137432i
\(913\) −3.10312 9.55042i −0.102698 0.316073i
\(914\) −21.8233 15.8555i −0.721850 0.524455i
\(915\) −9.10533 6.61541i −0.301013 0.218699i
\(916\) −7.77800 23.9382i −0.256992 0.790941i
\(917\) 16.3846 + 11.9041i 0.541068 + 0.393109i
\(918\) −5.77070 + 4.19266i −0.190461 + 0.138378i
\(919\) 5.03837 15.5065i 0.166201 0.511513i −0.832922 0.553390i \(-0.813334\pi\)
0.999123 + 0.0418773i \(0.0133339\pi\)
\(920\) 1.19893 0.871071i 0.0395274 0.0287184i
\(921\) −5.09849 15.6915i −0.168001 0.517054i
\(922\) 5.32443 + 16.3869i 0.175351 + 0.539674i
\(923\) −7.28178 + 22.4110i −0.239683 + 0.737667i
\(924\) 4.78211 0.157320
\(925\) −0.145898 −0.00479710
\(926\) −9.71140 + 29.8886i −0.319137 + 0.982201i
\(927\) −8.40457 6.10628i −0.276042 0.200557i
\(928\) −6.07561 + 4.41419i −0.199442 + 0.144903i
\(929\) 46.0922 1.51224 0.756119 0.654435i \(-0.227093\pi\)
0.756119 + 0.654435i \(0.227093\pi\)
\(930\) 5.34781 + 1.54950i 0.175362 + 0.0508102i
\(931\) 32.1919 1.05505
\(932\) −2.27586 + 1.65351i −0.0745482 + 0.0541625i
\(933\) 2.80886 + 2.04076i 0.0919581 + 0.0668115i
\(934\) −7.70234 + 23.7054i −0.252028 + 0.775663i
\(935\) 21.8332 0.714022
\(936\) 6.23099 0.203666
\(937\) −4.54937 + 14.0015i −0.148622 + 0.457410i −0.997459 0.0712440i \(-0.977303\pi\)
0.848837 + 0.528654i \(0.177303\pi\)
\(938\) 2.97523 + 9.15683i 0.0971448 + 0.298981i
\(939\) −2.57594 7.92792i −0.0840625 0.258718i
\(940\) 6.97476 5.06746i 0.227491 0.165282i
\(941\) 5.55287 17.0900i 0.181018 0.557117i −0.818839 0.574024i \(-0.805382\pi\)
0.999857 + 0.0169063i \(0.00538171\pi\)
\(942\) 7.39870 5.37547i 0.241063 0.175142i
\(943\) 0.757114 + 0.550076i 0.0246550 + 0.0179129i
\(944\) 1.12364 + 3.45820i 0.0365713 + 0.112555i
\(945\) 1.26395 + 0.918314i 0.0411163 + 0.0298728i
\(946\) 21.5977 + 15.6916i 0.702201 + 0.510179i
\(947\) −8.34377 25.6795i −0.271136 0.834471i −0.990216 0.139543i \(-0.955437\pi\)
0.719080 0.694927i \(-0.244563\pi\)
\(948\) 3.17153 + 2.30425i 0.103006 + 0.0748386i
\(949\) −72.6327 + 52.7707i −2.35776 + 1.71301i
\(950\) −2.18196 + 6.71539i −0.0707922 + 0.217876i
\(951\) 7.83546 5.69280i 0.254082 0.184602i
\(952\) 3.44370 + 10.5986i 0.111611 + 0.343503i
\(953\) −8.32380 25.6180i −0.269634 0.829849i −0.990589 0.136867i \(-0.956297\pi\)
0.720955 0.692982i \(-0.243703\pi\)
\(954\) −3.67237 + 11.3024i −0.118897 + 0.365929i
\(955\) 19.8009 0.640741
\(956\) 21.0594 0.681111
\(957\) −7.10331 + 21.8618i −0.229618 + 0.706690i
\(958\) −27.6467 20.0865i −0.893224 0.648965i
\(959\) −0.498088 + 0.361882i −0.0160841 + 0.0116858i
\(960\) 1.00000 0.0322749
\(961\) 26.1981 + 16.5729i 0.845099 + 0.534609i
\(962\) −0.909089 −0.0293102
\(963\) −8.26381 + 6.00401i −0.266298 + 0.193477i
\(964\) −0.00429803 0.00312270i −0.000138430 0.000100576i
\(965\) 6.52687 20.0877i 0.210108 0.646645i
\(966\) 2.31530 0.0744936
\(967\) 4.33890 0.139530 0.0697648 0.997563i \(-0.477775\pi\)
0.0697648 + 0.997563i \(0.477775\pi\)
\(968\) −0.504005 + 1.55117i −0.0161993 + 0.0498564i
\(969\) −15.5639 47.9007i −0.499984 1.53879i
\(970\) 4.33487 + 13.3414i 0.139184 + 0.428365i
\(971\) 10.4141 7.56628i 0.334204 0.242813i −0.408008 0.912978i \(-0.633777\pi\)
0.742212 + 0.670165i \(0.233777\pi\)
\(972\) −0.309017 + 0.951057i −0.00991172 + 0.0305052i
\(973\) 20.6917 15.0334i 0.663345 0.481948i
\(974\) 4.75011 + 3.45115i 0.152203 + 0.110582i
\(975\) −1.92548 5.92602i −0.0616647 0.189785i
\(976\) −9.10533 6.61541i −0.291454 0.211754i
\(977\) −8.67888 6.30557i −0.277662 0.201733i 0.440235 0.897883i \(-0.354895\pi\)
−0.717897 + 0.696149i \(0.754895\pi\)
\(978\) 1.30056 + 4.00271i 0.0415873 + 0.127993i
\(979\) 15.7912 + 11.4730i 0.504689 + 0.366678i
\(980\) −3.68841 + 2.67979i −0.117822 + 0.0856027i
\(981\) 4.54254 13.9805i 0.145032 0.446363i
\(982\) 2.75509 2.00169i 0.0879184 0.0638764i
\(983\) 7.95923 + 24.4960i 0.253860 + 0.781301i 0.994052 + 0.108905i \(0.0347345\pi\)
−0.740192 + 0.672395i \(0.765265\pi\)
\(984\) 0.195142 + 0.600586i 0.00622091 + 0.0191460i
\(985\) 7.02740 21.6281i 0.223912 0.689129i
\(986\) −53.5677 −1.70594
\(987\) 13.4693 0.428731
\(988\) −13.5958 + 41.8435i −0.432539 + 1.33122i
\(989\) 10.4567 + 7.59724i 0.332504 + 0.241578i
\(990\) 2.47631 1.79914i 0.0787022 0.0571805i
\(991\) 37.5355 1.19235 0.596177 0.802853i \(-0.296686\pi\)
0.596177 + 0.802853i \(0.296686\pi\)
\(992\) 5.34781 + 1.54950i 0.169793 + 0.0491968i
\(993\) −19.5630 −0.620814
\(994\) −4.78000 + 3.47288i −0.151613 + 0.110153i
\(995\) 5.99062 + 4.35244i 0.189915 + 0.137982i
\(996\) 1.01380 3.12015i 0.0321234 0.0988658i
\(997\) 22.3831 0.708880 0.354440 0.935079i \(-0.384671\pi\)
0.354440 + 0.935079i \(0.384671\pi\)
\(998\) 34.0782 1.07873
\(999\) 0.0450850 0.138757i 0.00142643 0.00439009i
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 930.2.n.d.481.1 12
31.2 even 5 inner 930.2.n.d.901.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.n.d.481.1 12 1.1 even 1 trivial
930.2.n.d.901.1 yes 12 31.2 even 5 inner