Properties

Label 342.2.f.g.7.9
Level $342$
Weight $2$
Character 342.7
Analytic conductor $2.731$
Analytic rank $0$
Dimension $18$
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] = [342,2,Mod(7,342)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(342, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("342.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 342.f (of order \(3\), 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: \(2.73088374913\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} + 4 x^{16} - 6 x^{15} + x^{14} - 21 x^{13} - 12 x^{12} + 9 x^{10} + 135 x^{9} + 27 x^{8} - 324 x^{6} - 1701 x^{5} + 243 x^{4} - 4374 x^{3} + 8748 x^{2} + 19683 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 7.9
Root \(0.339544 - 1.69844i\) of defining polynomial
Character \(\chi\) \(=\) 342.7
Dual form 342.2.f.g.49.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +(1.64067 - 0.555168i) q^{3} +1.00000 q^{4} +(0.467593 - 0.809895i) q^{5} +(-1.64067 + 0.555168i) q^{6} +(-0.568176 + 0.984110i) q^{7} -1.00000 q^{8} +(2.38358 - 1.82169i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(1.64067 - 0.555168i) q^{3} +1.00000 q^{4} +(0.467593 - 0.809895i) q^{5} +(-1.64067 + 0.555168i) q^{6} +(-0.568176 + 0.984110i) q^{7} -1.00000 q^{8} +(2.38358 - 1.82169i) q^{9} +(-0.467593 + 0.809895i) q^{10} +(0.0397925 - 0.0689226i) q^{11} +(1.64067 - 0.555168i) q^{12} +6.63538 q^{13} +(0.568176 - 0.984110i) q^{14} +(0.317537 - 1.58836i) q^{15} +1.00000 q^{16} +(-1.10797 - 1.91906i) q^{17} +(-2.38358 + 1.82169i) q^{18} +(-4.19489 - 1.18444i) q^{19} +(0.467593 - 0.809895i) q^{20} +(-0.385842 + 1.93003i) q^{21} +(-0.0397925 + 0.0689226i) q^{22} -0.138465 q^{23} +(-1.64067 + 0.555168i) q^{24} +(2.06271 + 3.57272i) q^{25} -6.63538 q^{26} +(2.89931 - 4.31207i) q^{27} +(-0.568176 + 0.984110i) q^{28} +(-2.94499 - 5.10087i) q^{29} +(-0.317537 + 1.58836i) q^{30} +(1.71503 + 2.97052i) q^{31} -1.00000 q^{32} +(0.0270226 - 0.135171i) q^{33} +(1.10797 + 1.91906i) q^{34} +(0.531351 + 0.920326i) q^{35} +(2.38358 - 1.82169i) q^{36} -1.58712 q^{37} +(4.19489 + 1.18444i) q^{38} +(10.8865 - 3.68375i) q^{39} +(-0.467593 + 0.809895i) q^{40} +(1.15143 - 1.99433i) q^{41} +(0.385842 - 1.93003i) q^{42} +3.30138 q^{43} +(0.0397925 - 0.0689226i) q^{44} +(-0.360834 - 2.78226i) q^{45} +0.138465 q^{46} +(-2.46002 - 4.26088i) q^{47} +(1.64067 - 0.555168i) q^{48} +(2.85435 + 4.94388i) q^{49} +(-2.06271 - 3.57272i) q^{50} +(-2.88321 - 2.53343i) q^{51} +6.63538 q^{52} +(-4.22378 + 7.31580i) q^{53} +(-2.89931 + 4.31207i) q^{54} +(-0.0372134 - 0.0644555i) q^{55} +(0.568176 - 0.984110i) q^{56} +(-7.53998 + 0.385604i) q^{57} +(2.94499 + 5.10087i) q^{58} +(-3.81301 + 6.60433i) q^{59} +(0.317537 - 1.58836i) q^{60} +(1.54050 + 2.66822i) q^{61} +(-1.71503 - 2.97052i) q^{62} +(0.438452 + 3.38074i) q^{63} +1.00000 q^{64} +(3.10266 - 5.37396i) q^{65} +(-0.0270226 + 0.135171i) q^{66} -10.8359 q^{67} +(-1.10797 - 1.91906i) q^{68} +(-0.227174 + 0.0768711i) q^{69} +(-0.531351 - 0.920326i) q^{70} +(6.23133 + 10.7930i) q^{71} +(-2.38358 + 1.82169i) q^{72} +(-6.81871 - 11.8104i) q^{73} +1.58712 q^{74} +(5.36769 + 4.71650i) q^{75} +(-4.19489 - 1.18444i) q^{76} +(0.0452183 + 0.0783203i) q^{77} +(-10.8865 + 3.68375i) q^{78} -6.12676 q^{79} +(0.467593 - 0.809895i) q^{80} +(2.36288 - 8.68428i) q^{81} +(-1.15143 + 1.99433i) q^{82} +(-4.76093 + 8.24617i) q^{83} +(-0.385842 + 1.93003i) q^{84} -2.07231 q^{85} -3.30138 q^{86} +(-7.66359 - 6.73387i) q^{87} +(-0.0397925 + 0.0689226i) q^{88} +(-4.11336 + 7.12456i) q^{89} +(0.360834 + 2.78226i) q^{90} +(-3.77006 + 6.52994i) q^{91} -0.138465 q^{92} +(4.46294 + 3.92151i) q^{93} +(2.46002 + 4.26088i) q^{94} +(-2.92077 + 2.84359i) q^{95} +(-1.64067 + 0.555168i) q^{96} -14.9427 q^{97} +(-2.85435 - 4.94388i) q^{98} +(-0.0307072 - 0.236772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9} + q^{11} - 2 q^{13} - 5 q^{14} + 18 q^{16} - 5 q^{17} - 4 q^{18} + 9 q^{19} - 4 q^{21} - q^{22} + 4 q^{23} - 9 q^{25} + 2 q^{26} - 18 q^{27} + 5 q^{28} - 9 q^{29} + 4 q^{31} - 18 q^{32} + 16 q^{33} + 5 q^{34} + 6 q^{35} + 4 q^{36} + 20 q^{37} - 9 q^{38} + 4 q^{39} + q^{41} + 4 q^{42} - 14 q^{43} + q^{44} + 30 q^{45} - 4 q^{46} + 19 q^{47} + 6 q^{49} + 9 q^{50} + 16 q^{51} - 2 q^{52} - 10 q^{53} + 18 q^{54} + 6 q^{55} - 5 q^{56} - 36 q^{57} + 9 q^{58} - 5 q^{59} + 18 q^{61} - 4 q^{62} - 15 q^{63} + 18 q^{64} - 45 q^{65} - 16 q^{66} - 44 q^{67} - 5 q^{68} - 26 q^{69} - 6 q^{70} + 11 q^{71} - 4 q^{72} + 44 q^{73} - 20 q^{74} + 9 q^{76} - 2 q^{77} - 4 q^{78} - 4 q^{79} - 32 q^{81} - q^{82} - 7 q^{83} - 4 q^{84} + 14 q^{86} + 3 q^{87} - q^{88} + q^{89} - 30 q^{90} - 25 q^{91} + 4 q^{92} + 10 q^{93} - 19 q^{94} - 24 q^{95} - 6 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(325\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.64067 0.555168i 0.947240 0.320526i
\(4\) 1.00000 0.500000
\(5\) 0.467593 0.809895i 0.209114 0.362196i −0.742322 0.670044i \(-0.766275\pi\)
0.951436 + 0.307848i \(0.0996087\pi\)
\(6\) −1.64067 + 0.555168i −0.669800 + 0.226646i
\(7\) −0.568176 + 0.984110i −0.214750 + 0.371959i −0.953195 0.302355i \(-0.902227\pi\)
0.738445 + 0.674314i \(0.235560\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.38358 1.82169i 0.794526 0.607230i
\(10\) −0.467593 + 0.809895i −0.147866 + 0.256111i
\(11\) 0.0397925 0.0689226i 0.0119979 0.0207809i −0.859964 0.510354i \(-0.829514\pi\)
0.871962 + 0.489574i \(0.162848\pi\)
\(12\) 1.64067 0.555168i 0.473620 0.160263i
\(13\) 6.63538 1.84032 0.920162 0.391539i \(-0.128057\pi\)
0.920162 + 0.391539i \(0.128057\pi\)
\(14\) 0.568176 0.984110i 0.151851 0.263014i
\(15\) 0.317537 1.58836i 0.0819877 0.410113i
\(16\) 1.00000 0.250000
\(17\) −1.10797 1.91906i −0.268722 0.465440i 0.699810 0.714329i \(-0.253268\pi\)
−0.968532 + 0.248889i \(0.919935\pi\)
\(18\) −2.38358 + 1.82169i −0.561815 + 0.429377i
\(19\) −4.19489 1.18444i −0.962374 0.271728i
\(20\) 0.467593 0.809895i 0.104557 0.181098i
\(21\) −0.385842 + 1.93003i −0.0841976 + 0.421167i
\(22\) −0.0397925 + 0.0689226i −0.00848378 + 0.0146943i
\(23\) −0.138465 −0.0288719 −0.0144359 0.999896i \(-0.504595\pi\)
−0.0144359 + 0.999896i \(0.504595\pi\)
\(24\) −1.64067 + 0.555168i −0.334900 + 0.113323i
\(25\) 2.06271 + 3.57272i 0.412543 + 0.714545i
\(26\) −6.63538 −1.30131
\(27\) 2.89931 4.31207i 0.557973 0.829859i
\(28\) −0.568176 + 0.984110i −0.107375 + 0.185979i
\(29\) −2.94499 5.10087i −0.546871 0.947208i −0.998487 0.0549955i \(-0.982486\pi\)
0.451616 0.892213i \(-0.350848\pi\)
\(30\) −0.317537 + 1.58836i −0.0579741 + 0.289994i
\(31\) 1.71503 + 2.97052i 0.308029 + 0.533522i 0.977931 0.208928i \(-0.0669973\pi\)
−0.669902 + 0.742449i \(0.733664\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.0270226 0.135171i 0.00470403 0.0235302i
\(34\) 1.10797 + 1.91906i 0.190015 + 0.329116i
\(35\) 0.531351 + 0.920326i 0.0898146 + 0.155564i
\(36\) 2.38358 1.82169i 0.397263 0.303615i
\(37\) −1.58712 −0.260922 −0.130461 0.991453i \(-0.541646\pi\)
−0.130461 + 0.991453i \(0.541646\pi\)
\(38\) 4.19489 + 1.18444i 0.680501 + 0.192141i
\(39\) 10.8865 3.68375i 1.74323 0.589872i
\(40\) −0.467593 + 0.809895i −0.0739330 + 0.128056i
\(41\) 1.15143 1.99433i 0.179823 0.311462i −0.761997 0.647581i \(-0.775781\pi\)
0.941820 + 0.336118i \(0.109114\pi\)
\(42\) 0.385842 1.93003i 0.0595367 0.297810i
\(43\) 3.30138 0.503456 0.251728 0.967798i \(-0.419001\pi\)
0.251728 + 0.967798i \(0.419001\pi\)
\(44\) 0.0397925 0.0689226i 0.00599894 0.0103905i
\(45\) −0.360834 2.78226i −0.0537900 0.414755i
\(46\) 0.138465 0.0204155
\(47\) −2.46002 4.26088i −0.358830 0.621513i 0.628935 0.777458i \(-0.283491\pi\)
−0.987766 + 0.155945i \(0.950158\pi\)
\(48\) 1.64067 0.555168i 0.236810 0.0801316i
\(49\) 2.85435 + 4.94388i 0.407765 + 0.706269i
\(50\) −2.06271 3.57272i −0.291712 0.505259i
\(51\) −2.88321 2.53343i −0.403730 0.354751i
\(52\) 6.63538 0.920162
\(53\) −4.22378 + 7.31580i −0.580181 + 1.00490i 0.415277 + 0.909695i \(0.363685\pi\)
−0.995457 + 0.0952074i \(0.969649\pi\)
\(54\) −2.89931 + 4.31207i −0.394547 + 0.586799i
\(55\) −0.0372134 0.0644555i −0.00501785 0.00869117i
\(56\) 0.568176 0.984110i 0.0759257 0.131507i
\(57\) −7.53998 + 0.385604i −0.998695 + 0.0510745i
\(58\) 2.94499 + 5.10087i 0.386696 + 0.669777i
\(59\) −3.81301 + 6.60433i −0.496412 + 0.859810i −0.999991 0.00413867i \(-0.998683\pi\)
0.503580 + 0.863949i \(0.332016\pi\)
\(60\) 0.317537 1.58836i 0.0409939 0.205057i
\(61\) 1.54050 + 2.66822i 0.197240 + 0.341630i 0.947633 0.319363i \(-0.103469\pi\)
−0.750392 + 0.660993i \(0.770135\pi\)
\(62\) −1.71503 2.97052i −0.217809 0.377257i
\(63\) 0.438452 + 3.38074i 0.0552398 + 0.425934i
\(64\) 1.00000 0.125000
\(65\) 3.10266 5.37396i 0.384837 0.666558i
\(66\) −0.0270226 + 0.135171i −0.00332625 + 0.0166383i
\(67\) −10.8359 −1.32381 −0.661906 0.749587i \(-0.730252\pi\)
−0.661906 + 0.749587i \(0.730252\pi\)
\(68\) −1.10797 1.91906i −0.134361 0.232720i
\(69\) −0.227174 + 0.0768711i −0.0273486 + 0.00925420i
\(70\) −0.531351 0.920326i −0.0635085 0.110000i
\(71\) 6.23133 + 10.7930i 0.739523 + 1.28089i 0.952710 + 0.303880i \(0.0982821\pi\)
−0.213188 + 0.977011i \(0.568385\pi\)
\(72\) −2.38358 + 1.82169i −0.280907 + 0.214688i
\(73\) −6.81871 11.8104i −0.798070 1.38230i −0.920872 0.389866i \(-0.872521\pi\)
0.122802 0.992431i \(-0.460812\pi\)
\(74\) 1.58712 0.184499
\(75\) 5.36769 + 4.71650i 0.619807 + 0.544614i
\(76\) −4.19489 1.18444i −0.481187 0.135864i
\(77\) 0.0452183 + 0.0783203i 0.00515310 + 0.00892543i
\(78\) −10.8865 + 3.68375i −1.23265 + 0.417102i
\(79\) −6.12676 −0.689315 −0.344657 0.938729i \(-0.612005\pi\)
−0.344657 + 0.938729i \(0.612005\pi\)
\(80\) 0.467593 0.809895i 0.0522785 0.0905490i
\(81\) 2.36288 8.68428i 0.262543 0.964920i
\(82\) −1.15143 + 1.99433i −0.127154 + 0.220237i
\(83\) −4.76093 + 8.24617i −0.522580 + 0.905135i 0.477075 + 0.878863i \(0.341697\pi\)
−0.999655 + 0.0262725i \(0.991636\pi\)
\(84\) −0.385842 + 1.93003i −0.0420988 + 0.210583i
\(85\) −2.07231 −0.224774
\(86\) −3.30138 −0.355997
\(87\) −7.66359 6.73387i −0.821623 0.721947i
\(88\) −0.0397925 + 0.0689226i −0.00424189 + 0.00734717i
\(89\) −4.11336 + 7.12456i −0.436016 + 0.755201i −0.997378 0.0723688i \(-0.976944\pi\)
0.561362 + 0.827570i \(0.310277\pi\)
\(90\) 0.360834 + 2.78226i 0.0380352 + 0.293276i
\(91\) −3.77006 + 6.52994i −0.395210 + 0.684524i
\(92\) −0.138465 −0.0144359
\(93\) 4.46294 + 3.92151i 0.462785 + 0.406642i
\(94\) 2.46002 + 4.26088i 0.253731 + 0.439476i
\(95\) −2.92077 + 2.84359i −0.299665 + 0.291746i
\(96\) −1.64067 + 0.555168i −0.167450 + 0.0566616i
\(97\) −14.9427 −1.51720 −0.758601 0.651555i \(-0.774117\pi\)
−0.758601 + 0.651555i \(0.774117\pi\)
\(98\) −2.85435 4.94388i −0.288333 0.499408i
\(99\) −0.0307072 0.236772i −0.00308619 0.0237965i
\(100\) 2.06271 + 3.57272i 0.206271 + 0.357272i
\(101\) −0.318675 0.551961i −0.0317093 0.0549222i 0.849735 0.527210i \(-0.176762\pi\)
−0.881445 + 0.472287i \(0.843428\pi\)
\(102\) 2.88321 + 2.53343i 0.285480 + 0.250847i
\(103\) 2.96826 + 5.14118i 0.292472 + 0.506576i 0.974394 0.224849i \(-0.0721889\pi\)
−0.681922 + 0.731425i \(0.738856\pi\)
\(104\) −6.63538 −0.650653
\(105\) 1.38270 + 1.21496i 0.134938 + 0.118568i
\(106\) 4.22378 7.31580i 0.410250 0.710573i
\(107\) −16.7256 −1.61692 −0.808461 0.588550i \(-0.799699\pi\)
−0.808461 + 0.588550i \(0.799699\pi\)
\(108\) 2.89931 4.31207i 0.278987 0.414930i
\(109\) −1.01969 1.76615i −0.0976685 0.169167i 0.813051 0.582193i \(-0.197805\pi\)
−0.910719 + 0.413026i \(0.864472\pi\)
\(110\) 0.0372134 + 0.0644555i 0.00354816 + 0.00614559i
\(111\) −2.60394 + 0.881120i −0.247155 + 0.0836322i
\(112\) −0.568176 + 0.984110i −0.0536876 + 0.0929896i
\(113\) 8.92114 + 15.4519i 0.839231 + 1.45359i 0.890539 + 0.454907i \(0.150328\pi\)
−0.0513082 + 0.998683i \(0.516339\pi\)
\(114\) 7.53998 0.385604i 0.706184 0.0361151i
\(115\) −0.0647451 + 0.112142i −0.00603752 + 0.0104573i
\(116\) −2.94499 5.10087i −0.273435 0.473604i
\(117\) 15.8159 12.0876i 1.46218 1.11750i
\(118\) 3.81301 6.60433i 0.351016 0.607977i
\(119\) 2.51808 0.230832
\(120\) −0.317537 + 1.58836i −0.0289870 + 0.144997i
\(121\) 5.49683 + 9.52079i 0.499712 + 0.865527i
\(122\) −1.54050 2.66822i −0.139470 0.241569i
\(123\) 0.781921 3.91127i 0.0705034 0.352667i
\(124\) 1.71503 + 2.97052i 0.154015 + 0.266761i
\(125\) 8.53397 0.763302
\(126\) −0.438452 3.38074i −0.0390604 0.301181i
\(127\) 0.409265 0.708868i 0.0363164 0.0629019i −0.847296 0.531121i \(-0.821771\pi\)
0.883612 + 0.468219i \(0.155104\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 5.41647 1.83282i 0.476893 0.161371i
\(130\) −3.10266 + 5.37396i −0.272121 + 0.471328i
\(131\) 1.91686 3.32010i 0.167477 0.290079i −0.770055 0.637977i \(-0.779771\pi\)
0.937532 + 0.347899i \(0.113105\pi\)
\(132\) 0.0270226 0.135171i 0.00235202 0.0117651i
\(133\) 3.54905 3.45527i 0.307742 0.299610i
\(134\) 10.8359 0.936076
\(135\) −2.13663 4.36444i −0.183892 0.375631i
\(136\) 1.10797 + 1.91906i 0.0950075 + 0.164558i
\(137\) −1.47091 2.54770i −0.125669 0.217665i 0.796325 0.604868i \(-0.206774\pi\)
−0.921994 + 0.387204i \(0.873441\pi\)
\(138\) 0.227174 0.0768711i 0.0193384 0.00654370i
\(139\) −11.2341 −0.952867 −0.476433 0.879211i \(-0.658071\pi\)
−0.476433 + 0.879211i \(0.658071\pi\)
\(140\) 0.531351 + 0.920326i 0.0449073 + 0.0777818i
\(141\) −6.40157 5.62496i −0.539110 0.473707i
\(142\) −6.23133 10.7930i −0.522922 0.905727i
\(143\) 0.264038 0.457328i 0.0220800 0.0382436i
\(144\) 2.38358 1.82169i 0.198631 0.151808i
\(145\) −5.50823 −0.457433
\(146\) 6.81871 + 11.8104i 0.564320 + 0.977432i
\(147\) 7.42773 + 6.52662i 0.612628 + 0.538307i
\(148\) −1.58712 −0.130461
\(149\) 8.84481 15.3197i 0.724595 1.25503i −0.234546 0.972105i \(-0.575360\pi\)
0.959141 0.282930i \(-0.0913064\pi\)
\(150\) −5.36769 4.71650i −0.438270 0.385101i
\(151\) 6.93789 12.0168i 0.564597 0.977912i −0.432490 0.901639i \(-0.642365\pi\)
0.997087 0.0762726i \(-0.0243019\pi\)
\(152\) 4.19489 + 1.18444i 0.340251 + 0.0960704i
\(153\) −6.13686 2.55585i −0.496136 0.206628i
\(154\) −0.0452183 0.0783203i −0.00364379 0.00631123i
\(155\) 3.20775 0.257653
\(156\) 10.8865 3.68375i 0.871614 0.294936i
\(157\) 7.76796 13.4545i 0.619951 1.07379i −0.369543 0.929214i \(-0.620486\pi\)
0.989494 0.144573i \(-0.0461809\pi\)
\(158\) 6.12676 0.487419
\(159\) −2.86832 + 14.3477i −0.227473 + 1.13785i
\(160\) −0.467593 + 0.809895i −0.0369665 + 0.0640278i
\(161\) 0.0786723 0.136264i 0.00620025 0.0107391i
\(162\) −2.36288 + 8.68428i −0.185646 + 0.682302i
\(163\) −22.6136 −1.77124 −0.885618 0.464415i \(-0.846265\pi\)
−0.885618 + 0.464415i \(0.846265\pi\)
\(164\) 1.15143 1.99433i 0.0899114 0.155731i
\(165\) −0.0968384 0.0850903i −0.00753886 0.00662427i
\(166\) 4.76093 8.24617i 0.369520 0.640027i
\(167\) 6.88495 0.532773 0.266387 0.963866i \(-0.414170\pi\)
0.266387 + 0.963866i \(0.414170\pi\)
\(168\) 0.385842 1.93003i 0.0297683 0.148905i
\(169\) 31.0283 2.38679
\(170\) 2.07231 0.158939
\(171\) −12.1565 + 4.81860i −0.929633 + 0.368488i
\(172\) 3.30138 0.251728
\(173\) −0.888179 −0.0675270 −0.0337635 0.999430i \(-0.510749\pi\)
−0.0337635 + 0.999430i \(0.510749\pi\)
\(174\) 7.66359 + 6.73387i 0.580975 + 0.510493i
\(175\) −4.68794 −0.354375
\(176\) 0.0397925 0.0689226i 0.00299947 0.00519523i
\(177\) −2.58937 + 12.9524i −0.194629 + 0.973559i
\(178\) 4.11336 7.12456i 0.308310 0.534008i
\(179\) 11.8427 0.885162 0.442581 0.896729i \(-0.354063\pi\)
0.442581 + 0.896729i \(0.354063\pi\)
\(180\) −0.360834 2.78226i −0.0268950 0.207377i
\(181\) 8.04715 13.9381i 0.598140 1.03601i −0.394956 0.918700i \(-0.629240\pi\)
0.993096 0.117308i \(-0.0374265\pi\)
\(182\) 3.77006 6.52994i 0.279456 0.484032i
\(183\) 4.00875 + 3.52242i 0.296335 + 0.260385i
\(184\) 0.138465 0.0102078
\(185\) −0.742128 + 1.28540i −0.0545624 + 0.0945048i
\(186\) −4.46294 3.92151i −0.327238 0.287539i
\(187\) −0.176355 −0.0128964
\(188\) −2.46002 4.26088i −0.179415 0.310756i
\(189\) 2.59623 + 5.30326i 0.188848 + 0.385755i
\(190\) 2.92077 2.84359i 0.211895 0.206296i
\(191\) 0.636975 1.10327i 0.0460899 0.0798301i −0.842060 0.539384i \(-0.818657\pi\)
0.888150 + 0.459554i \(0.151991\pi\)
\(192\) 1.64067 0.555168i 0.118405 0.0400658i
\(193\) −4.05430 + 7.02226i −0.291835 + 0.505473i −0.974244 0.225498i \(-0.927599\pi\)
0.682409 + 0.730971i \(0.260932\pi\)
\(194\) 14.9427 1.07282
\(195\) 2.10698 10.5394i 0.150884 0.754741i
\(196\) 2.85435 + 4.94388i 0.203882 + 0.353134i
\(197\) 20.1767 1.43753 0.718767 0.695251i \(-0.244707\pi\)
0.718767 + 0.695251i \(0.244707\pi\)
\(198\) 0.0307072 + 0.236772i 0.00218227 + 0.0168266i
\(199\) 3.27803 5.67772i 0.232374 0.402483i −0.726132 0.687555i \(-0.758684\pi\)
0.958506 + 0.285072i \(0.0920174\pi\)
\(200\) −2.06271 3.57272i −0.145856 0.252630i
\(201\) −17.7780 + 6.01572i −1.25397 + 0.424316i
\(202\) 0.318675 + 0.551961i 0.0224219 + 0.0388359i
\(203\) 6.69309 0.469763
\(204\) −2.88321 2.53343i −0.201865 0.177375i
\(205\) −1.07680 1.86507i −0.0752069 0.130262i
\(206\) −2.96826 5.14118i −0.206809 0.358203i
\(207\) −0.330041 + 0.252240i −0.0229395 + 0.0175319i
\(208\) 6.63538 0.460081
\(209\) −0.248559 + 0.241991i −0.0171932 + 0.0167389i
\(210\) −1.38270 1.21496i −0.0954157 0.0838402i
\(211\) −5.53735 + 9.59098i −0.381207 + 0.660270i −0.991235 0.132110i \(-0.957825\pi\)
0.610028 + 0.792380i \(0.291158\pi\)
\(212\) −4.22378 + 7.31580i −0.290090 + 0.502451i
\(213\) 16.2155 + 14.2483i 1.11106 + 0.976274i
\(214\) 16.7256 1.14334
\(215\) 1.54370 2.67377i 0.105280 0.182350i
\(216\) −2.89931 + 4.31207i −0.197273 + 0.293399i
\(217\) −3.89776 −0.264597
\(218\) 1.01969 + 1.76615i 0.0690621 + 0.119619i
\(219\) −17.7440 15.5913i −1.19903 1.05356i
\(220\) −0.0372134 0.0644555i −0.00250893 0.00434559i
\(221\) −7.35179 12.7337i −0.494535 0.856560i
\(222\) 2.60394 0.881120i 0.174765 0.0591369i
\(223\) 0.747365 0.0500473 0.0250236 0.999687i \(-0.492034\pi\)
0.0250236 + 0.999687i \(0.492034\pi\)
\(224\) 0.568176 0.984110i 0.0379629 0.0657536i
\(225\) 11.4250 + 4.75824i 0.761669 + 0.317216i
\(226\) −8.92114 15.4519i −0.593426 1.02784i
\(227\) −14.1895 + 24.5769i −0.941790 + 1.63123i −0.179735 + 0.983715i \(0.557524\pi\)
−0.762054 + 0.647513i \(0.775809\pi\)
\(228\) −7.53998 + 0.385604i −0.499347 + 0.0255373i
\(229\) 3.63731 + 6.30001i 0.240360 + 0.416316i 0.960817 0.277184i \(-0.0894011\pi\)
−0.720457 + 0.693500i \(0.756068\pi\)
\(230\) 0.0647451 0.112142i 0.00426917 0.00739442i
\(231\) 0.117669 + 0.103394i 0.00774205 + 0.00680282i
\(232\) 2.94499 + 5.10087i 0.193348 + 0.334889i
\(233\) −8.86740 15.3588i −0.580923 1.00619i −0.995370 0.0961148i \(-0.969358\pi\)
0.414447 0.910073i \(-0.363975\pi\)
\(234\) −15.8159 + 12.0876i −1.03392 + 0.790192i
\(235\) −4.60115 −0.300146
\(236\) −3.81301 + 6.60433i −0.248206 + 0.429905i
\(237\) −10.0520 + 3.40138i −0.652946 + 0.220943i
\(238\) −2.51808 −0.163223
\(239\) 12.0318 + 20.8396i 0.778270 + 1.34800i 0.932938 + 0.360037i \(0.117236\pi\)
−0.154667 + 0.987967i \(0.549431\pi\)
\(240\) 0.317537 1.58836i 0.0204969 0.102528i
\(241\) −5.35131 9.26873i −0.344708 0.597052i 0.640593 0.767881i \(-0.278689\pi\)
−0.985301 + 0.170829i \(0.945355\pi\)
\(242\) −5.49683 9.52079i −0.353350 0.612020i
\(243\) −0.944527 15.5598i −0.0605914 0.998163i
\(244\) 1.54050 + 2.66822i 0.0986201 + 0.170815i
\(245\) 5.33870 0.341077
\(246\) −0.781921 + 3.91127i −0.0498535 + 0.249373i
\(247\) −27.8347 7.85918i −1.77108 0.500068i
\(248\) −1.71503 2.97052i −0.108905 0.188628i
\(249\) −3.23309 + 16.1723i −0.204889 + 1.02488i
\(250\) −8.53397 −0.539736
\(251\) 7.87511 13.6401i 0.497073 0.860955i −0.502921 0.864332i \(-0.667742\pi\)
0.999994 + 0.00337672i \(0.00107485\pi\)
\(252\) 0.438452 + 3.38074i 0.0276199 + 0.212967i
\(253\) −0.00550985 + 0.00954334i −0.000346401 + 0.000599985i
\(254\) −0.409265 + 0.708868i −0.0256796 + 0.0444783i
\(255\) −3.39998 + 1.15048i −0.212915 + 0.0720460i
\(256\) 1.00000 0.0625000
\(257\) −5.24788 −0.327353 −0.163677 0.986514i \(-0.552335\pi\)
−0.163677 + 0.986514i \(0.552335\pi\)
\(258\) −5.41647 + 1.83282i −0.337215 + 0.114106i
\(259\) 0.901766 1.56190i 0.0560330 0.0970520i
\(260\) 3.10266 5.37396i 0.192419 0.333279i
\(261\) −16.3118 6.79346i −1.00968 0.420505i
\(262\) −1.91686 + 3.32010i −0.118424 + 0.205117i
\(263\) −9.00516 −0.555282 −0.277641 0.960685i \(-0.589553\pi\)
−0.277641 + 0.960685i \(0.589553\pi\)
\(264\) −0.0270226 + 0.135171i −0.00166313 + 0.00831917i
\(265\) 3.95002 + 6.84164i 0.242648 + 0.420278i
\(266\) −3.54905 + 3.45527i −0.217606 + 0.211856i
\(267\) −2.79334 + 13.9726i −0.170950 + 0.855111i
\(268\) −10.8359 −0.661906
\(269\) 6.28989 + 10.8944i 0.383501 + 0.664243i 0.991560 0.129648i \(-0.0413849\pi\)
−0.608059 + 0.793892i \(0.708052\pi\)
\(270\) 2.13663 + 4.36444i 0.130031 + 0.265611i
\(271\) −2.79712 4.84476i −0.169913 0.294298i 0.768476 0.639879i \(-0.221015\pi\)
−0.938389 + 0.345581i \(0.887682\pi\)
\(272\) −1.10797 1.91906i −0.0671805 0.116360i
\(273\) −2.56021 + 12.8065i −0.154951 + 0.775083i
\(274\) 1.47091 + 2.54770i 0.0888612 + 0.153912i
\(275\) 0.328322 0.0197985
\(276\) −0.227174 + 0.0768711i −0.0136743 + 0.00462710i
\(277\) 7.72542 13.3808i 0.464175 0.803975i −0.534988 0.844859i \(-0.679684\pi\)
0.999164 + 0.0408839i \(0.0130174\pi\)
\(278\) 11.2341 0.673778
\(279\) 9.49929 + 3.95621i 0.568708 + 0.236852i
\(280\) −0.531351 0.920326i −0.0317543 0.0550000i
\(281\) −4.41799 7.65218i −0.263555 0.456491i 0.703629 0.710568i \(-0.251562\pi\)
−0.967184 + 0.254077i \(0.918228\pi\)
\(282\) 6.40157 + 5.62496i 0.381208 + 0.334961i
\(283\) 13.3232 23.0765i 0.791982 1.37175i −0.132756 0.991149i \(-0.542383\pi\)
0.924738 0.380604i \(-0.124284\pi\)
\(284\) 6.23133 + 10.7930i 0.369761 + 0.640445i
\(285\) −3.21334 + 6.28690i −0.190342 + 0.372404i
\(286\) −0.264038 + 0.457328i −0.0156129 + 0.0270423i
\(287\) 1.30843 + 2.26626i 0.0772340 + 0.133773i
\(288\) −2.38358 + 1.82169i −0.140454 + 0.107344i
\(289\) 6.04481 10.4699i 0.355577 0.615878i
\(290\) 5.50823 0.323454
\(291\) −24.5160 + 8.29571i −1.43715 + 0.486303i
\(292\) −6.81871 11.8104i −0.399035 0.691149i
\(293\) −4.55284 7.88575i −0.265980 0.460690i 0.701840 0.712335i \(-0.252362\pi\)
−0.967820 + 0.251644i \(0.919029\pi\)
\(294\) −7.42773 6.52662i −0.433194 0.380640i
\(295\) 3.56587 + 6.17628i 0.207613 + 0.359597i
\(296\) 1.58712 0.0922497
\(297\) −0.181828 0.371416i −0.0105508 0.0215518i
\(298\) −8.84481 + 15.3197i −0.512366 + 0.887444i
\(299\) −0.918766 −0.0531336
\(300\) 5.36769 + 4.71650i 0.309904 + 0.272307i
\(301\) −1.87577 + 3.24892i −0.108117 + 0.187265i
\(302\) −6.93789 + 12.0168i −0.399231 + 0.691488i
\(303\) −0.829271 0.728667i −0.0476403 0.0418608i
\(304\) −4.19489 1.18444i −0.240594 0.0679320i
\(305\) 2.88130 0.164983
\(306\) 6.13686 + 2.55585i 0.350821 + 0.146108i
\(307\) 4.46612 + 7.73555i 0.254895 + 0.441491i 0.964867 0.262739i \(-0.0846257\pi\)
−0.709972 + 0.704230i \(0.751292\pi\)
\(308\) 0.0452183 + 0.0783203i 0.00257655 + 0.00446271i
\(309\) 7.72415 + 6.78709i 0.439412 + 0.386104i
\(310\) −3.20775 −0.182188
\(311\) 0.795438 + 1.37774i 0.0451051 + 0.0781244i 0.887697 0.460429i \(-0.152304\pi\)
−0.842591 + 0.538553i \(0.818971\pi\)
\(312\) −10.8865 + 3.68375i −0.616324 + 0.208551i
\(313\) 2.53074 + 4.38337i 0.143046 + 0.247763i 0.928642 0.370977i \(-0.120977\pi\)
−0.785596 + 0.618739i \(0.787644\pi\)
\(314\) −7.76796 + 13.4545i −0.438372 + 0.759282i
\(315\) 2.94306 + 1.22571i 0.165823 + 0.0690611i
\(316\) −6.12676 −0.344657
\(317\) −16.0375 27.7777i −0.900755 1.56015i −0.826516 0.562913i \(-0.809680\pi\)
−0.0742392 0.997240i \(-0.523653\pi\)
\(318\) 2.86832 14.3477i 0.160847 0.804579i
\(319\) −0.468754 −0.0262452
\(320\) 0.467593 0.809895i 0.0261393 0.0452745i
\(321\) −27.4411 + 9.28549i −1.53161 + 0.518266i
\(322\) −0.0786723 + 0.136264i −0.00438424 + 0.00759372i
\(323\) 2.37481 + 9.36256i 0.132138 + 0.520947i
\(324\) 2.36288 8.68428i 0.131271 0.482460i
\(325\) 13.6869 + 23.7064i 0.759212 + 1.31499i
\(326\) 22.6136 1.25245
\(327\) −2.65348 2.33157i −0.146738 0.128936i
\(328\) −1.15143 + 1.99433i −0.0635769 + 0.110118i
\(329\) 5.59089 0.308236
\(330\) 0.0968384 + 0.0850903i 0.00533078 + 0.00468407i
\(331\) −2.26128 + 3.91666i −0.124291 + 0.215279i −0.921456 0.388483i \(-0.872999\pi\)
0.797164 + 0.603762i \(0.206332\pi\)
\(332\) −4.76093 + 8.24617i −0.261290 + 0.452568i
\(333\) −3.78303 + 2.89125i −0.207309 + 0.158440i
\(334\) −6.88495 −0.376728
\(335\) −5.06677 + 8.77591i −0.276827 + 0.479479i
\(336\) −0.385842 + 1.93003i −0.0210494 + 0.105292i
\(337\) 0.468804 0.811992i 0.0255374 0.0442320i −0.852974 0.521953i \(-0.825204\pi\)
0.878512 + 0.477721i \(0.158537\pi\)
\(338\) −31.0283 −1.68772
\(339\) 23.2150 + 20.3987i 1.26087 + 1.10790i
\(340\) −2.07231 −0.112387
\(341\) 0.272982 0.0147828
\(342\) 12.1565 4.81860i 0.657350 0.260560i
\(343\) −14.4416 −0.779771
\(344\) −3.30138 −0.177999
\(345\) −0.0439677 + 0.219932i −0.00236714 + 0.0118407i
\(346\) 0.888179 0.0477488
\(347\) 8.49448 14.7129i 0.456008 0.789828i −0.542738 0.839902i \(-0.682612\pi\)
0.998746 + 0.0500739i \(0.0159457\pi\)
\(348\) −7.66359 6.73387i −0.410811 0.360973i
\(349\) 11.0932 19.2139i 0.593804 1.02850i −0.399910 0.916554i \(-0.630959\pi\)
0.993714 0.111945i \(-0.0357079\pi\)
\(350\) 4.68794 0.250581
\(351\) 19.2380 28.6123i 1.02685 1.52721i
\(352\) −0.0397925 + 0.0689226i −0.00212095 + 0.00367359i
\(353\) 8.74572 15.1480i 0.465488 0.806248i −0.533736 0.845651i \(-0.679212\pi\)
0.999223 + 0.0394032i \(0.0125457\pi\)
\(354\) 2.58937 12.9524i 0.137623 0.688410i
\(355\) 11.6549 0.618578
\(356\) −4.11336 + 7.12456i −0.218008 + 0.377601i
\(357\) 4.13134 1.39796i 0.218654 0.0739879i
\(358\) −11.8427 −0.625904
\(359\) 8.96717 + 15.5316i 0.473269 + 0.819726i 0.999532 0.0305960i \(-0.00974054\pi\)
−0.526263 + 0.850322i \(0.676407\pi\)
\(360\) 0.360834 + 2.78226i 0.0190176 + 0.146638i
\(361\) 16.1942 + 9.93715i 0.852328 + 0.523008i
\(362\) −8.04715 + 13.9381i −0.422949 + 0.732569i
\(363\) 14.3041 + 12.5688i 0.750771 + 0.659690i
\(364\) −3.77006 + 6.52994i −0.197605 + 0.342262i
\(365\) −12.7535 −0.667550
\(366\) −4.00875 3.52242i −0.209541 0.184120i
\(367\) −10.4730 18.1398i −0.546687 0.946889i −0.998499 0.0547761i \(-0.982556\pi\)
0.451812 0.892113i \(-0.350778\pi\)
\(368\) −0.138465 −0.00721797
\(369\) −0.888538 6.85119i −0.0462554 0.356658i
\(370\) 0.742128 1.28540i 0.0385814 0.0668250i
\(371\) −4.79970 8.31333i −0.249188 0.431606i
\(372\) 4.46294 + 3.92151i 0.231393 + 0.203321i
\(373\) 6.12723 + 10.6127i 0.317256 + 0.549503i 0.979914 0.199419i \(-0.0639053\pi\)
−0.662659 + 0.748922i \(0.730572\pi\)
\(374\) 0.176355 0.00911911
\(375\) 14.0014 4.73779i 0.723030 0.244658i
\(376\) 2.46002 + 4.26088i 0.126866 + 0.219738i
\(377\) −19.5411 33.8462i −1.00642 1.74317i
\(378\) −2.59623 5.30326i −0.133536 0.272770i
\(379\) 31.8645 1.63677 0.818384 0.574672i \(-0.194870\pi\)
0.818384 + 0.574672i \(0.194870\pi\)
\(380\) −2.92077 + 2.84359i −0.149832 + 0.145873i
\(381\) 0.277927 1.39023i 0.0142386 0.0712235i
\(382\) −0.636975 + 1.10327i −0.0325905 + 0.0564484i
\(383\) 16.3299 28.2842i 0.834419 1.44526i −0.0600844 0.998193i \(-0.519137\pi\)
0.894503 0.447062i \(-0.147530\pi\)
\(384\) −1.64067 + 0.555168i −0.0837249 + 0.0283308i
\(385\) 0.0845750 0.00431034
\(386\) 4.05430 7.02226i 0.206358 0.357423i
\(387\) 7.86910 6.01410i 0.400009 0.305714i
\(388\) −14.9427 −0.758601
\(389\) 18.4772 + 32.0034i 0.936830 + 1.62264i 0.771338 + 0.636426i \(0.219588\pi\)
0.165492 + 0.986211i \(0.447079\pi\)
\(390\) −2.10698 + 10.5394i −0.106691 + 0.533682i
\(391\) 0.153415 + 0.265722i 0.00775851 + 0.0134381i
\(392\) −2.85435 4.94388i −0.144167 0.249704i
\(393\) 1.30172 6.51137i 0.0656631 0.328455i
\(394\) −20.1767 −1.01649
\(395\) −2.86483 + 4.96204i −0.144145 + 0.249667i
\(396\) −0.0307072 0.236772i −0.00154309 0.0118982i
\(397\) 8.42840 + 14.5984i 0.423009 + 0.732673i 0.996232 0.0867261i \(-0.0276405\pi\)
−0.573223 + 0.819399i \(0.694307\pi\)
\(398\) −3.27803 + 5.67772i −0.164313 + 0.284599i
\(399\) 3.90456 7.63926i 0.195472 0.382441i
\(400\) 2.06271 + 3.57272i 0.103136 + 0.178636i
\(401\) −6.87472 + 11.9074i −0.343307 + 0.594625i −0.985045 0.172299i \(-0.944880\pi\)
0.641738 + 0.766924i \(0.278214\pi\)
\(402\) 17.7780 6.01572i 0.886688 0.300037i
\(403\) 11.3799 + 19.7106i 0.566873 + 0.981853i
\(404\) −0.318675 0.551961i −0.0158547 0.0274611i
\(405\) −5.92849 5.97440i −0.294589 0.296870i
\(406\) −6.69309 −0.332172
\(407\) −0.0631556 + 0.109389i −0.00313051 + 0.00542220i
\(408\) 2.88321 + 2.53343i 0.142740 + 0.125423i
\(409\) 14.4996 0.716961 0.358481 0.933537i \(-0.383295\pi\)
0.358481 + 0.933537i \(0.383295\pi\)
\(410\) 1.07680 + 1.86507i 0.0531793 + 0.0921093i
\(411\) −3.82768 3.36332i −0.188806 0.165900i
\(412\) 2.96826 + 5.14118i 0.146236 + 0.253288i
\(413\) −4.33292 7.50484i −0.213209 0.369289i
\(414\) 0.330041 0.252240i 0.0162206 0.0123969i
\(415\) 4.45236 + 7.71171i 0.218558 + 0.378553i
\(416\) −6.63538 −0.325326
\(417\) −18.4315 + 6.23683i −0.902593 + 0.305419i
\(418\) 0.248559 0.241991i 0.0121574 0.0118362i
\(419\) −0.703380 1.21829i −0.0343624 0.0595174i 0.848333 0.529463i \(-0.177607\pi\)
−0.882695 + 0.469946i \(0.844273\pi\)
\(420\) 1.38270 + 1.21496i 0.0674691 + 0.0592840i
\(421\) −29.2010 −1.42317 −0.711585 0.702600i \(-0.752022\pi\)
−0.711585 + 0.702600i \(0.752022\pi\)
\(422\) 5.53735 9.59098i 0.269554 0.466881i
\(423\) −13.6256 5.67474i −0.662501 0.275915i
\(424\) 4.22378 7.31580i 0.205125 0.355287i
\(425\) 4.57084 7.91693i 0.221718 0.384028i
\(426\) −16.2155 14.2483i −0.785641 0.690330i
\(427\) −3.50109 −0.169430
\(428\) −16.7256 −0.808461
\(429\) 0.179305 0.896908i 0.00865694 0.0433031i
\(430\) −1.54370 + 2.67377i −0.0744440 + 0.128941i
\(431\) −14.7626 + 25.5695i −0.711087 + 1.23164i 0.253362 + 0.967372i \(0.418464\pi\)
−0.964449 + 0.264268i \(0.914870\pi\)
\(432\) 2.89931 4.31207i 0.139493 0.207465i
\(433\) −0.0851720 + 0.147522i −0.00409310 + 0.00708946i −0.868065 0.496451i \(-0.834636\pi\)
0.863972 + 0.503541i \(0.167970\pi\)
\(434\) 3.89776 0.187099
\(435\) −9.03717 + 3.05799i −0.433299 + 0.146619i
\(436\) −1.01969 1.76615i −0.0488342 0.0845834i
\(437\) 0.580844 + 0.164002i 0.0277856 + 0.00784530i
\(438\) 17.7440 + 15.5913i 0.847839 + 0.744983i
\(439\) −4.15010 −0.198074 −0.0990368 0.995084i \(-0.531576\pi\)
−0.0990368 + 0.995084i \(0.531576\pi\)
\(440\) 0.0372134 + 0.0644555i 0.00177408 + 0.00307279i
\(441\) 15.8098 + 6.58438i 0.752847 + 0.313542i
\(442\) 7.35179 + 12.7337i 0.349689 + 0.605679i
\(443\) −11.7195 20.2988i −0.556810 0.964423i −0.997760 0.0668916i \(-0.978692\pi\)
0.440950 0.897532i \(-0.354642\pi\)
\(444\) −2.60394 + 0.881120i −0.123578 + 0.0418161i
\(445\) 3.84676 + 6.66279i 0.182354 + 0.315846i
\(446\) −0.747365 −0.0353888
\(447\) 6.00641 30.0448i 0.284093 1.42107i
\(448\) −0.568176 + 0.984110i −0.0268438 + 0.0464948i
\(449\) −37.0884 −1.75031 −0.875155 0.483842i \(-0.839241\pi\)
−0.875155 + 0.483842i \(0.839241\pi\)
\(450\) −11.4250 4.75824i −0.538581 0.224306i
\(451\) −0.0916363 0.158719i −0.00431498 0.00747377i
\(452\) 8.92114 + 15.4519i 0.419615 + 0.726795i
\(453\) 4.71144 23.5672i 0.221363 1.10728i
\(454\) 14.1895 24.5769i 0.665946 1.15345i
\(455\) 3.52571 + 6.10671i 0.165288 + 0.286287i
\(456\) 7.53998 0.385604i 0.353092 0.0180576i
\(457\) −17.9019 + 31.0069i −0.837413 + 1.45044i 0.0546368 + 0.998506i \(0.482600\pi\)
−0.892050 + 0.451936i \(0.850733\pi\)
\(458\) −3.63731 6.30001i −0.169960 0.294380i
\(459\) −11.4875 0.786308i −0.536189 0.0367017i
\(460\) −0.0647451 + 0.112142i −0.00301876 + 0.00522864i
\(461\) 5.84450 0.272205 0.136103 0.990695i \(-0.456542\pi\)
0.136103 + 0.990695i \(0.456542\pi\)
\(462\) −0.117669 0.103394i −0.00547446 0.00481032i
\(463\) −0.657422 1.13869i −0.0305530 0.0529194i 0.850345 0.526226i \(-0.176394\pi\)
−0.880898 + 0.473307i \(0.843060\pi\)
\(464\) −2.94499 5.10087i −0.136718 0.236802i
\(465\) 5.26285 1.78084i 0.244059 0.0825845i
\(466\) 8.86740 + 15.3588i 0.410775 + 0.711482i
\(467\) 16.6029 0.768290 0.384145 0.923273i \(-0.374496\pi\)
0.384145 + 0.923273i \(0.374496\pi\)
\(468\) 15.8159 12.0876i 0.731092 0.558750i
\(469\) 6.15668 10.6637i 0.284289 0.492403i
\(470\) 4.60115 0.212235
\(471\) 5.27513 26.3869i 0.243065 1.21584i
\(472\) 3.81301 6.60433i 0.175508 0.303989i
\(473\) 0.131370 0.227540i 0.00604041 0.0104623i
\(474\) 10.0520 3.40138i 0.461703 0.156231i
\(475\) −4.42120 17.4303i −0.202858 0.799759i
\(476\) 2.51808 0.115416
\(477\) 3.25942 + 25.1322i 0.149239 + 1.15072i
\(478\) −12.0318 20.8396i −0.550320 0.953183i
\(479\) 16.6278 + 28.8001i 0.759742 + 1.31591i 0.942982 + 0.332843i \(0.108008\pi\)
−0.183240 + 0.983068i \(0.558659\pi\)
\(480\) −0.317537 + 1.58836i −0.0144935 + 0.0724984i
\(481\) −10.5312 −0.480180
\(482\) 5.35131 + 9.26873i 0.243745 + 0.422179i
\(483\) 0.0534255 0.267241i 0.00243094 0.0121599i
\(484\) 5.49683 + 9.52079i 0.249856 + 0.432763i
\(485\) −6.98711 + 12.1020i −0.317268 + 0.549525i
\(486\) 0.944527 + 15.5598i 0.0428446 + 0.705808i
\(487\) −10.0490 −0.455366 −0.227683 0.973735i \(-0.573115\pi\)
−0.227683 + 0.973735i \(0.573115\pi\)
\(488\) −1.54050 2.66822i −0.0697350 0.120785i
\(489\) −37.1014 + 12.5544i −1.67778 + 0.567727i
\(490\) −5.33870 −0.241178
\(491\) 19.3339 33.4873i 0.872527 1.51126i 0.0131528 0.999913i \(-0.495813\pi\)
0.859374 0.511347i \(-0.170853\pi\)
\(492\) 0.781921 3.91127i 0.0352517 0.176334i
\(493\) −6.52591 + 11.3032i −0.293912 + 0.509071i
\(494\) 27.8347 + 7.85918i 1.25234 + 0.353601i
\(495\) −0.206119 0.0858433i −0.00926436 0.00385837i
\(496\) 1.71503 + 2.97052i 0.0770073 + 0.133380i
\(497\) −14.1620 −0.635251
\(498\) 3.23309 16.1723i 0.144878 0.724700i
\(499\) 17.8984 31.0009i 0.801240 1.38779i −0.117560 0.993066i \(-0.537507\pi\)
0.918800 0.394723i \(-0.129159\pi\)
\(500\) 8.53397 0.381651
\(501\) 11.2959 3.82230i 0.504664 0.170768i
\(502\) −7.87511 + 13.6401i −0.351484 + 0.608787i
\(503\) −11.6716 + 20.2158i −0.520410 + 0.901377i 0.479308 + 0.877647i \(0.340888\pi\)
−0.999718 + 0.0237301i \(0.992446\pi\)
\(504\) −0.438452 3.38074i −0.0195302 0.150590i
\(505\) −0.596041 −0.0265235
\(506\) 0.00550985 0.00954334i 0.000244943 0.000424253i
\(507\) 50.9071 17.2259i 2.26086 0.765029i
\(508\) 0.409265 0.708868i 0.0181582 0.0314509i
\(509\) −43.7873 −1.94084 −0.970419 0.241427i \(-0.922384\pi\)
−0.970419 + 0.241427i \(0.922384\pi\)
\(510\) 3.39998 1.15048i 0.150554 0.0509442i
\(511\) 15.4969 0.685543
\(512\) −1.00000 −0.0441942
\(513\) −17.2697 + 14.6546i −0.762475 + 0.647018i
\(514\) 5.24788 0.231474
\(515\) 5.55176 0.244640
\(516\) 5.41647 1.83282i 0.238447 0.0806854i
\(517\) −0.391561 −0.0172208
\(518\) −0.901766 + 1.56190i −0.0396213 + 0.0686261i
\(519\) −1.45721 + 0.493089i −0.0639643 + 0.0216442i
\(520\) −3.10266 + 5.37396i −0.136061 + 0.235664i
\(521\) 14.0255 0.614470 0.307235 0.951634i \(-0.400596\pi\)
0.307235 + 0.951634i \(0.400596\pi\)
\(522\) 16.3118 + 6.79346i 0.713949 + 0.297342i
\(523\) −1.68513 + 2.91874i −0.0736858 + 0.127627i −0.900514 0.434827i \(-0.856810\pi\)
0.826828 + 0.562454i \(0.190143\pi\)
\(524\) 1.91686 3.32010i 0.0837385 0.145039i
\(525\) −7.69134 + 2.60259i −0.335678 + 0.113586i
\(526\) 9.00516 0.392644
\(527\) 3.80040 6.58249i 0.165548 0.286738i
\(528\) 0.0270226 0.135171i 0.00117601 0.00588254i
\(529\) −22.9808 −0.999166
\(530\) −3.95002 6.84164i −0.171578 0.297182i
\(531\) 2.94244 + 22.6880i 0.127691 + 0.984577i
\(532\) 3.54905 3.45527i 0.153871 0.149805i
\(533\) 7.64016 13.2331i 0.330932 0.573191i
\(534\) 2.79334 13.9726i 0.120880 0.604655i
\(535\) −7.82076 + 13.5460i −0.338121 + 0.585643i
\(536\) 10.8359 0.468038
\(537\) 19.4299 6.57466i 0.838460 0.283718i
\(538\) −6.28989 10.8944i −0.271176 0.469691i
\(539\) 0.454327 0.0195692
\(540\) −2.13663 4.36444i −0.0919459 0.187815i
\(541\) −4.05201 + 7.01829i −0.174210 + 0.301740i −0.939887 0.341484i \(-0.889070\pi\)
0.765678 + 0.643224i \(0.222404\pi\)
\(542\) 2.79712 + 4.84476i 0.120147 + 0.208100i
\(543\) 5.46472 27.3352i 0.234514 1.17307i
\(544\) 1.10797 + 1.91906i 0.0475038 + 0.0822789i
\(545\) −1.90720 −0.0816954
\(546\) 2.56021 12.8065i 0.109567 0.548067i
\(547\) 17.8887 + 30.9841i 0.764865 + 1.32479i 0.940318 + 0.340298i \(0.110528\pi\)
−0.175452 + 0.984488i \(0.556139\pi\)
\(548\) −1.47091 2.54770i −0.0628344 0.108832i
\(549\) 8.53256 + 3.55359i 0.364161 + 0.151664i
\(550\) −0.328322 −0.0139997
\(551\) 6.31226 + 24.8857i 0.268911 + 1.06017i
\(552\) 0.227174 0.0768711i 0.00966919 0.00327185i
\(553\) 3.48108 6.02941i 0.148031 0.256396i
\(554\) −7.72542 + 13.3808i −0.328222 + 0.568497i
\(555\) −0.503971 + 2.52093i −0.0213924 + 0.107007i
\(556\) −11.2341 −0.476433
\(557\) 12.8280 22.2187i 0.543538 0.941436i −0.455159 0.890410i \(-0.650418\pi\)
0.998697 0.0510256i \(-0.0162490\pi\)
\(558\) −9.49929 3.95621i −0.402137 0.167480i
\(559\) 21.9059 0.926522
\(560\) 0.531351 + 0.920326i 0.0224537 + 0.0388909i
\(561\) −0.289340 + 0.0979067i −0.0122160 + 0.00413363i
\(562\) 4.41799 + 7.65218i 0.186362 + 0.322788i
\(563\) −19.7952 34.2862i −0.834267 1.44499i −0.894626 0.446816i \(-0.852558\pi\)
0.0603587 0.998177i \(-0.480776\pi\)
\(564\) −6.40157 5.62496i −0.269555 0.236853i
\(565\) 16.6859 0.701980
\(566\) −13.3232 + 23.0765i −0.560016 + 0.969976i
\(567\) 7.20375 + 7.25954i 0.302529 + 0.304872i
\(568\) −6.23133 10.7930i −0.261461 0.452863i
\(569\) 8.34476 14.4535i 0.349830 0.605924i −0.636389 0.771369i \(-0.719573\pi\)
0.986219 + 0.165445i \(0.0529059\pi\)
\(570\) 3.21334 6.28690i 0.134592 0.263329i
\(571\) 17.0306 + 29.4979i 0.712710 + 1.23445i 0.963836 + 0.266496i \(0.0858659\pi\)
−0.251126 + 0.967954i \(0.580801\pi\)
\(572\) 0.264038 0.457328i 0.0110400 0.0191218i
\(573\) 0.432563 2.16373i 0.0180706 0.0903912i
\(574\) −1.30843 2.26626i −0.0546127 0.0945919i
\(575\) −0.285613 0.494696i −0.0119109 0.0206303i
\(576\) 2.38358 1.82169i 0.0993157 0.0759038i
\(577\) 13.8354 0.575975 0.287987 0.957634i \(-0.407014\pi\)
0.287987 + 0.957634i \(0.407014\pi\)
\(578\) −6.04481 + 10.4699i −0.251431 + 0.435491i
\(579\) −2.75323 + 13.7720i −0.114420 + 0.572345i
\(580\) −5.50823 −0.228717
\(581\) −5.41009 9.37056i −0.224449 0.388756i
\(582\) 24.5160 8.29571i 1.01622 0.343868i
\(583\) 0.336149 + 0.582228i 0.0139219 + 0.0241134i
\(584\) 6.81871 + 11.8104i 0.282160 + 0.488716i
\(585\) −2.39427 18.4613i −0.0989909 0.763283i
\(586\) 4.55284 + 7.88575i 0.188076 + 0.325757i
\(587\) −32.5972 −1.34543 −0.672716 0.739901i \(-0.734872\pi\)
−0.672716 + 0.739901i \(0.734872\pi\)
\(588\) 7.42773 + 6.52662i 0.306314 + 0.269153i
\(589\) −3.67598 14.4924i −0.151466 0.597148i
\(590\) −3.56587 6.17628i −0.146805 0.254273i
\(591\) 33.1033 11.2015i 1.36169 0.460767i
\(592\) −1.58712 −0.0652304
\(593\) −22.3884 + 38.7779i −0.919383 + 1.59242i −0.119028 + 0.992891i \(0.537978\pi\)
−0.800355 + 0.599526i \(0.795356\pi\)
\(594\) 0.181828 + 0.371416i 0.00746051 + 0.0152394i
\(595\) 1.17744 2.03938i 0.0482703 0.0836066i
\(596\) 8.84481 15.3197i 0.362297 0.627517i
\(597\) 2.22608 11.1351i 0.0911072 0.455730i
\(598\) 0.918766 0.0375711
\(599\) 13.1482 0.537222 0.268611 0.963249i \(-0.413435\pi\)
0.268611 + 0.963249i \(0.413435\pi\)
\(600\) −5.36769 4.71650i −0.219135 0.192550i
\(601\) −5.57735 + 9.66025i −0.227505 + 0.394050i −0.957068 0.289864i \(-0.906390\pi\)
0.729563 + 0.683913i \(0.239723\pi\)
\(602\) 1.87577 3.24892i 0.0764505 0.132416i
\(603\) −25.8281 + 19.7396i −1.05180 + 0.803858i
\(604\) 6.93789 12.0168i 0.282299 0.488956i
\(605\) 10.2811 0.417987
\(606\) 0.829271 + 0.728667i 0.0336868 + 0.0296001i
\(607\) −22.8386 39.5577i −0.926991 1.60560i −0.788327 0.615257i \(-0.789052\pi\)
−0.138665 0.990339i \(-0.544281\pi\)
\(608\) 4.19489 + 1.18444i 0.170125 + 0.0480352i
\(609\) 10.9811 3.71579i 0.444978 0.150571i
\(610\) −2.88130 −0.116660
\(611\) −16.3232 28.2725i −0.660364 1.14378i
\(612\) −6.13686 2.55585i −0.248068 0.103314i
\(613\) −8.80325 15.2477i −0.355560 0.615848i 0.631654 0.775251i \(-0.282376\pi\)
−0.987214 + 0.159403i \(0.949043\pi\)
\(614\) −4.46612 7.73555i −0.180238 0.312181i
\(615\) −2.80210 2.46216i −0.112991 0.0992837i
\(616\) −0.0452183 0.0783203i −0.00182190 0.00315562i
\(617\) −17.9178 −0.721344 −0.360672 0.932693i \(-0.617453\pi\)
−0.360672 + 0.932693i \(0.617453\pi\)
\(618\) −7.72415 6.78709i −0.310711 0.273017i
\(619\) −8.69227 + 15.0555i −0.349372 + 0.605130i −0.986138 0.165927i \(-0.946938\pi\)
0.636766 + 0.771057i \(0.280272\pi\)
\(620\) 3.20775 0.128826
\(621\) −0.401453 + 0.597070i −0.0161097 + 0.0239596i
\(622\) −0.795438 1.37774i −0.0318942 0.0552423i
\(623\) −4.67423 8.09600i −0.187269 0.324360i
\(624\) 10.8865 3.68375i 0.435807 0.147468i
\(625\) −6.32314 + 10.9520i −0.252926 + 0.438080i
\(626\) −2.53074 4.38337i −0.101149 0.175195i
\(627\) −0.273458 + 0.535019i −0.0109208 + 0.0213666i
\(628\) 7.76796 13.4545i 0.309975 0.536893i
\(629\) 1.75848 + 3.04578i 0.0701153 + 0.121443i
\(630\) −2.94306 1.22571i −0.117255 0.0488335i
\(631\) −15.6412 + 27.0914i −0.622668 + 1.07849i 0.366319 + 0.930489i \(0.380618\pi\)
−0.988987 + 0.148003i \(0.952715\pi\)
\(632\) 6.12676 0.243710
\(633\) −3.76035 + 18.8098i −0.149461 + 0.747621i
\(634\) 16.0375 + 27.7777i 0.636930 + 1.10320i
\(635\) −0.382739 0.662924i −0.0151885 0.0263073i
\(636\) −2.86832 + 14.3477i −0.113736 + 0.568923i
\(637\) 18.9397 + 32.8045i 0.750419 + 1.29976i
\(638\) 0.468754 0.0185581
\(639\) 34.5143 + 14.3743i 1.36537 + 0.568640i
\(640\) −0.467593 + 0.809895i −0.0184832 + 0.0320139i
\(641\) −9.47055 −0.374064 −0.187032 0.982354i \(-0.559887\pi\)
−0.187032 + 0.982354i \(0.559887\pi\)
\(642\) 27.4411 9.28549i 1.08301 0.366469i
\(643\) 4.13256 7.15781i 0.162972 0.282277i −0.772961 0.634454i \(-0.781225\pi\)
0.935933 + 0.352177i \(0.114559\pi\)
\(644\) 0.0786723 0.136264i 0.00310012 0.00536957i
\(645\) 1.04831 5.24379i 0.0412772 0.206474i
\(646\) −2.37481 9.36256i −0.0934356 0.368365i
\(647\) −19.0963 −0.750754 −0.375377 0.926872i \(-0.622487\pi\)
−0.375377 + 0.926872i \(0.622487\pi\)
\(648\) −2.36288 + 8.68428i −0.0928229 + 0.341151i
\(649\) 0.303458 + 0.525605i 0.0119118 + 0.0206318i
\(650\) −13.6869 23.7064i −0.536844 0.929841i
\(651\) −6.39493 + 2.16391i −0.250637 + 0.0848104i
\(652\) −22.6136 −0.885618
\(653\) 4.14981 + 7.18769i 0.162395 + 0.281276i 0.935727 0.352725i \(-0.114745\pi\)
−0.773332 + 0.634001i \(0.781412\pi\)
\(654\) 2.65348 + 2.33157i 0.103759 + 0.0911716i
\(655\) −1.79262 3.10492i −0.0700436 0.121319i
\(656\) 1.15143 1.99433i 0.0449557 0.0778655i
\(657\) −37.7677 15.7293i −1.47346 0.613659i
\(658\) −5.59089 −0.217956
\(659\) 4.91963 + 8.52104i 0.191641 + 0.331933i 0.945794 0.324766i \(-0.105286\pi\)
−0.754153 + 0.656699i \(0.771952\pi\)
\(660\) −0.0968384 0.0850903i −0.00376943 0.00331213i
\(661\) 44.1357 1.71668 0.858340 0.513082i \(-0.171496\pi\)
0.858340 + 0.513082i \(0.171496\pi\)
\(662\) 2.26128 3.91666i 0.0878873 0.152225i
\(663\) −19.1312 16.8103i −0.742993 0.652856i
\(664\) 4.76093 8.24617i 0.184760 0.320014i
\(665\) −1.13889 4.49002i −0.0441643 0.174115i
\(666\) 3.78303 2.89125i 0.146590 0.112034i
\(667\) 0.407777 + 0.706291i 0.0157892 + 0.0273477i
\(668\) 6.88495 0.266387
\(669\) 1.22618 0.414913i 0.0474068 0.0160415i
\(670\) 5.06677 8.77591i 0.195747 0.339043i
\(671\) 0.245201 0.00946586
\(672\) 0.385842 1.93003i 0.0148842 0.0744525i
\(673\) −12.6558 + 21.9205i −0.487845 + 0.844972i −0.999902 0.0139794i \(-0.995550\pi\)
0.512058 + 0.858951i \(0.328883\pi\)
\(674\) −0.468804 + 0.811992i −0.0180577 + 0.0312768i
\(675\) 21.3863 + 1.46388i 0.823159 + 0.0563446i
\(676\) 31.0283 1.19340
\(677\) 14.4291 24.9919i 0.554554 0.960516i −0.443384 0.896332i \(-0.646222\pi\)
0.997938 0.0641840i \(-0.0204445\pi\)
\(678\) −23.2150 20.3987i −0.891567 0.783406i
\(679\) 8.49009 14.7053i 0.325820 0.564336i
\(680\) 2.07231 0.0794696
\(681\) −9.63592 + 48.2001i −0.369249 + 1.84703i
\(682\) −0.272982 −0.0104530
\(683\) 24.9816 0.955893 0.477947 0.878389i \(-0.341381\pi\)
0.477947 + 0.878389i \(0.341381\pi\)
\(684\) −12.1565 + 4.81860i −0.464816 + 0.184244i
\(685\) −2.75116 −0.105116
\(686\) 14.4416 0.551381
\(687\) 9.46518 + 8.31690i 0.361119 + 0.317309i
\(688\) 3.30138 0.125864
\(689\) −28.0264 + 48.5431i −1.06772 + 1.84935i
\(690\) 0.0439677 0.219932i 0.00167382 0.00837267i
\(691\) 9.20873 15.9500i 0.350317 0.606766i −0.635988 0.771699i \(-0.719407\pi\)
0.986305 + 0.164933i \(0.0527407\pi\)
\(692\) −0.888179 −0.0337635
\(693\) 0.250457 + 0.104309i 0.00951406 + 0.00396237i
\(694\) −8.49448 + 14.7129i −0.322446 + 0.558493i
\(695\) −5.25300 + 9.09847i −0.199258 + 0.345125i
\(696\) 7.66359 + 6.73387i 0.290487 + 0.255247i
\(697\) −5.10298 −0.193289
\(698\) −11.0932 + 19.2139i −0.419883 + 0.727258i
\(699\) −23.0752 20.2758i −0.872783 0.766900i
\(700\) −4.68794 −0.177187
\(701\) −9.04527 15.6669i −0.341635 0.591729i 0.643101 0.765781i \(-0.277647\pi\)
−0.984737 + 0.174052i \(0.944314\pi\)
\(702\) −19.2380 + 28.6123i −0.726093 + 1.07990i
\(703\) 6.65781 + 1.87985i 0.251104 + 0.0708997i
\(704\) 0.0397925 0.0689226i 0.00149974 0.00259762i
\(705\) −7.54896 + 2.55441i −0.284310 + 0.0962047i
\(706\) −8.74572 + 15.1480i −0.329149 + 0.570103i
\(707\) 0.724254 0.0272384
\(708\) −2.58937 + 12.9524i −0.0973145 + 0.486780i
\(709\) −11.6354 20.1531i −0.436977 0.756866i 0.560478 0.828169i \(-0.310618\pi\)
−0.997455 + 0.0713033i \(0.977284\pi\)
\(710\) −11.6549 −0.437401
\(711\) −14.6036 + 11.1611i −0.547678 + 0.418573i
\(712\) 4.11336 7.12456i 0.154155 0.267004i
\(713\) −0.237471 0.411313i −0.00889338 0.0154038i
\(714\) −4.13134 + 1.39796i −0.154611 + 0.0523173i
\(715\) −0.246925 0.427686i −0.00923447 0.0159946i
\(716\) 11.8427 0.442581
\(717\) 31.3096 + 27.5113i 1.16928 + 1.02743i
\(718\) −8.96717 15.5316i −0.334652 0.579634i
\(719\) 12.5242 + 21.6926i 0.467075 + 0.808997i 0.999292 0.0376103i \(-0.0119745\pi\)
−0.532218 + 0.846608i \(0.678641\pi\)
\(720\) −0.360834 2.78226i −0.0134475 0.103689i
\(721\) −6.74599 −0.251234
\(722\) −16.1942 9.93715i −0.602687 0.369823i
\(723\) −13.9254 12.2360i −0.517892 0.455063i
\(724\) 8.04715 13.9381i 0.299070 0.518004i
\(725\) 12.1493 21.0433i 0.451215 0.781527i
\(726\) −14.3041 12.5688i −0.530875 0.466472i
\(727\) −28.6838 −1.06382 −0.531911 0.846800i \(-0.678526\pi\)
−0.531911 + 0.846800i \(0.678526\pi\)
\(728\) 3.77006 6.52994i 0.139728 0.242016i
\(729\) −10.1880 25.0041i −0.377332 0.926078i
\(730\) 12.7535 0.472029
\(731\) −3.65783 6.33554i −0.135290 0.234328i
\(732\) 4.00875 + 3.52242i 0.148168 + 0.130192i
\(733\) −9.80946 16.9905i −0.362321 0.627558i 0.626022 0.779806i \(-0.284682\pi\)
−0.988342 + 0.152248i \(0.951349\pi\)
\(734\) 10.4730 + 18.1398i 0.386566 + 0.669552i
\(735\) 8.75903 2.96388i 0.323082 0.109324i
\(736\) 0.138465 0.00510388
\(737\) −0.431186 + 0.746835i −0.0158829 + 0.0275100i
\(738\) 0.888538 + 6.85119i 0.0327075 + 0.252196i
\(739\) 7.81031 + 13.5278i 0.287307 + 0.497630i 0.973166 0.230104i \(-0.0739067\pi\)
−0.685859 + 0.727734i \(0.740573\pi\)
\(740\) −0.742128 + 1.28540i −0.0272812 + 0.0472524i
\(741\) −50.0306 + 2.55863i −1.83792 + 0.0939936i
\(742\) 4.79970 + 8.31333i 0.176203 + 0.305192i
\(743\) 16.2184 28.0912i 0.594997 1.03056i −0.398551 0.917146i \(-0.630487\pi\)
0.993547 0.113418i \(-0.0361800\pi\)
\(744\) −4.46294 3.92151i −0.163619 0.143770i
\(745\) −8.27154 14.3267i −0.303046 0.524891i
\(746\) −6.12723 10.6127i −0.224334 0.388557i
\(747\) 3.67393 + 28.3283i 0.134422 + 1.03648i
\(748\) −0.176355 −0.00644819
\(749\) 9.50306 16.4598i 0.347234 0.601428i
\(750\) −14.0014 + 4.73779i −0.511259 + 0.173000i
\(751\) −17.0078 −0.620623 −0.310312 0.950635i \(-0.600433\pi\)
−0.310312 + 0.950635i \(0.600433\pi\)
\(752\) −2.46002 4.26088i −0.0897076 0.155378i
\(753\) 5.34790 26.7509i 0.194888 0.974856i
\(754\) 19.5411 + 33.8462i 0.711646 + 1.23261i
\(755\) −6.48822 11.2379i −0.236131 0.408990i
\(756\) 2.59623 + 5.30326i 0.0944241 + 0.192878i
\(757\) 17.2273 + 29.8386i 0.626139 + 1.08450i 0.988320 + 0.152396i \(0.0486989\pi\)
−0.362181 + 0.932108i \(0.617968\pi\)
\(758\) −31.8645 −1.15737
\(759\) −0.00374168 + 0.0187163i −0.000135814 + 0.000679360i
\(760\) 2.92077 2.84359i 0.105948 0.103148i
\(761\) 15.8669 + 27.4822i 0.575174 + 0.996230i 0.996023 + 0.0890994i \(0.0283989\pi\)
−0.420849 + 0.907131i \(0.638268\pi\)
\(762\) −0.277927 + 1.39023i −0.0100682 + 0.0503626i
\(763\) 2.31745 0.0838974
\(764\) 0.636975 1.10327i 0.0230450 0.0399150i
\(765\) −4.93952 + 3.77512i −0.178589 + 0.136490i
\(766\) −16.3299 + 28.2842i −0.590023 + 1.02195i
\(767\) −25.3008 + 43.8222i −0.913558 + 1.58233i
\(768\) 1.64067 0.555168i 0.0592025 0.0200329i
\(769\) −30.1599 −1.08759 −0.543797 0.839217i \(-0.683014\pi\)
−0.543797 + 0.839217i \(0.683014\pi\)
\(770\) −0.0845750 −0.00304787
\(771\) −8.61002 + 2.91345i −0.310082 + 0.104925i
\(772\) −4.05430 + 7.02226i −0.145917 + 0.252736i
\(773\) −20.0303 + 34.6935i −0.720440 + 1.24784i 0.240384 + 0.970678i \(0.422727\pi\)
−0.960824 + 0.277161i \(0.910607\pi\)
\(774\) −7.86910 + 6.01410i −0.282849 + 0.216172i
\(775\) −7.07524 + 12.2547i −0.254150 + 0.440201i
\(776\) 14.9427 0.536412
\(777\) 0.612379 3.06320i 0.0219690 0.109892i
\(778\) −18.4772 32.0034i −0.662439 1.14738i
\(779\) −7.19227 + 7.00221i −0.257690 + 0.250880i
\(780\) 2.10698 10.5394i 0.0754420 0.377370i
\(781\) 0.991840 0.0354908
\(782\) −0.153415 0.265722i −0.00548609 0.00950219i
\(783\) −30.5338 2.09001i −1.09119 0.0746910i
\(784\) 2.85435 + 4.94388i 0.101941 + 0.176567i
\(785\) −7.26449 12.5825i −0.259281 0.449088i
\(786\) −1.30172 + 6.51137i −0.0464308 + 0.232253i
\(787\) −3.20276 5.54735i −0.114166 0.197742i 0.803280 0.595602i \(-0.203086\pi\)
−0.917446 + 0.397860i \(0.869753\pi\)
\(788\) 20.1767 0.718767
\(789\) −14.7745 + 4.99938i −0.525985 + 0.177983i
\(790\) 2.86483 4.96204i 0.101926 0.176541i
\(791\) −20.2751 −0.720900
\(792\) 0.0307072 + 0.236772i 0.00109113 + 0.00841332i
\(793\) 10.2218 + 17.7046i 0.362986 + 0.628710i
\(794\) −8.42840 14.5984i −0.299113 0.518078i
\(795\) 10.2789 + 9.03193i 0.364556 + 0.320329i
\(796\) 3.27803 5.67772i 0.116187 0.201242i
\(797\) 22.6941 + 39.3074i 0.803867 + 1.39234i 0.917053 + 0.398764i \(0.130561\pi\)
−0.113187 + 0.993574i \(0.536106\pi\)
\(798\) −3.90456 + 7.63926i −0.138220 + 0.270427i
\(799\) −5.45124 + 9.44183i −0.192851 + 0.334028i
\(800\) −2.06271 3.57272i −0.0729279 0.126315i
\(801\) 3.17422 + 24.4752i 0.112155 + 0.864789i
\(802\) 6.87472 11.9074i 0.242755 0.420464i
\(803\) −1.08533 −0.0383006
\(804\) −17.7780 + 6.01572i −0.626983 + 0.212158i
\(805\) −0.0735733 0.127433i −0.00259312 0.00449141i
\(806\) −11.3799 19.7106i −0.400840 0.694275i
\(807\) 16.3678 + 14.3821i 0.576175 + 0.506276i
\(808\) 0.318675 + 0.551961i 0.0112109 + 0.0194179i
\(809\) −37.1208 −1.30510 −0.652548 0.757747i \(-0.726300\pi\)
−0.652548 + 0.757747i \(0.726300\pi\)
\(810\) 5.92849 + 5.97440i 0.208306 + 0.209919i
\(811\) 13.6434 23.6311i 0.479085 0.829799i −0.520628 0.853784i \(-0.674302\pi\)
0.999712 + 0.0239847i \(0.00763531\pi\)
\(812\) 6.69309 0.234881
\(813\) −7.27880 6.39576i −0.255279 0.224309i
\(814\) 0.0631556 0.109389i 0.00221360 0.00383407i
\(815\) −10.5740 + 18.3147i −0.370390 + 0.641535i
\(816\) −2.88321 2.53343i −0.100932 0.0886877i
\(817\) −13.8489 3.91027i −0.484513 0.136803i
\(818\) −14.4996 −0.506968
\(819\) 2.90930 + 22.4325i 0.101659 + 0.783856i
\(820\) −1.07680 1.86507i −0.0376035 0.0651311i
\(821\) −7.78257 13.4798i −0.271614 0.470449i 0.697662 0.716428i \(-0.254224\pi\)
−0.969275 + 0.245979i \(0.920891\pi\)
\(822\) 3.82768 + 3.36332i 0.133506 + 0.117309i
\(823\) −6.77770 −0.236256 −0.118128 0.992998i \(-0.537689\pi\)
−0.118128 + 0.992998i \(0.537689\pi\)
\(824\) −2.96826 5.14118i −0.103404 0.179102i
\(825\) 0.538667 0.182274i 0.0187540 0.00634595i
\(826\) 4.33292 + 7.50484i 0.150762 + 0.261127i
\(827\) 22.2662 38.5662i 0.774272 1.34108i −0.160931 0.986966i \(-0.551450\pi\)
0.935203 0.354112i \(-0.115217\pi\)
\(828\) −0.330041 + 0.252240i −0.0114697 + 0.00876594i
\(829\) 13.0200 0.452204 0.226102 0.974104i \(-0.427402\pi\)
0.226102 + 0.974104i \(0.427402\pi\)
\(830\) −4.45236 7.71171i −0.154544 0.267677i
\(831\) 5.24624 26.2424i 0.181990 0.910338i
\(832\) 6.63538 0.230040
\(833\) 6.32506 10.9553i 0.219150 0.379580i
\(834\) 18.4315 6.23683i 0.638230 0.215964i
\(835\) 3.21936 5.57609i 0.111410 0.192968i
\(836\) −0.248559 + 0.241991i −0.00859661 + 0.00836944i
\(837\) 17.7815 + 1.21713i 0.614620 + 0.0420702i
\(838\) 0.703380 + 1.21829i 0.0242979 + 0.0420852i
\(839\) −2.58115 −0.0891113 −0.0445557 0.999007i \(-0.514187\pi\)
−0.0445557 + 0.999007i \(0.514187\pi\)
\(840\) −1.38270 1.21496i −0.0477078 0.0419201i
\(841\) −2.84592 + 4.92929i −0.0981353 + 0.169975i
\(842\) 29.2010 1.00633
\(843\) −11.4967 10.1020i −0.395967 0.347930i
\(844\) −5.53735 + 9.59098i −0.190604 + 0.330135i
\(845\) 14.5086 25.1296i 0.499111 0.864486i
\(846\) 13.6256 + 5.67474i 0.468459 + 0.195101i
\(847\) −12.4927 −0.429253
\(848\) −4.22378 + 7.31580i −0.145045 + 0.251226i
\(849\) 9.04763 45.2574i 0.310514 1.55323i
\(850\) −4.57084 + 7.91693i −0.156779 + 0.271549i
\(851\) 0.219761 0.00753330
\(852\) 16.2155 + 14.2483i 0.555532 + 0.488137i
\(853\) 45.6154 1.56184 0.780921 0.624630i \(-0.214750\pi\)
0.780921 + 0.624630i \(0.214750\pi\)
\(854\) 3.50109 0.119805
\(855\) −1.78175 + 12.0987i −0.0609344 + 0.413765i
\(856\) 16.7256 0.571668
\(857\) −1.78120 −0.0608448 −0.0304224 0.999537i \(-0.509685\pi\)
−0.0304224 + 0.999537i \(0.509685\pi\)
\(858\) −0.179305 + 0.896908i −0.00612138 + 0.0306199i
\(859\) 27.2935 0.931244 0.465622 0.884984i \(-0.345831\pi\)
0.465622 + 0.884984i \(0.345831\pi\)
\(860\) 1.54370 2.67377i 0.0526399 0.0911749i
\(861\) 3.40485 + 2.99178i 0.116037 + 0.101960i
\(862\) 14.7626 25.5695i 0.502815 0.870901i
\(863\) 44.6491 1.51987 0.759937 0.649997i \(-0.225230\pi\)
0.759937 + 0.649997i \(0.225230\pi\)
\(864\) −2.89931 + 4.31207i −0.0986366 + 0.146700i
\(865\) −0.415307 + 0.719332i −0.0141209 + 0.0244580i
\(866\) 0.0851720 0.147522i 0.00289426 0.00501301i
\(867\) 4.10496 20.5335i 0.139412 0.697356i
\(868\) −3.89776 −0.132299
\(869\) −0.243799 + 0.422272i −0.00827031 + 0.0143246i
\(870\) 9.03717 3.05799i 0.306389 0.103676i
\(871\) −71.9001 −2.43624
\(872\) 1.01969 + 1.76615i 0.0345310 + 0.0598095i
\(873\) −35.6171 + 27.2210i −1.20546 + 0.921291i
\(874\) −0.580844 0.164002i −0.0196474 0.00554747i
\(875\) −4.84880 + 8.39837i −0.163919 + 0.283917i
\(876\) −17.7440 15.5913i −0.599513 0.526782i
\(877\) −14.8318 + 25.6894i −0.500833 + 0.867468i 0.499167 + 0.866506i \(0.333639\pi\)
−1.00000 0.000961840i \(0.999694\pi\)
\(878\) 4.15010 0.140059
\(879\) −11.8476 10.4103i −0.399610 0.351131i
\(880\) −0.0372134 0.0644555i −0.00125446 0.00217279i
\(881\) 46.3343 1.56104 0.780521 0.625130i \(-0.214954\pi\)
0.780521 + 0.625130i \(0.214954\pi\)
\(882\) −15.8098 6.58438i −0.532344 0.221708i
\(883\) 11.1195 19.2595i 0.374201 0.648135i −0.616006 0.787741i \(-0.711250\pi\)
0.990207 + 0.139606i \(0.0445838\pi\)
\(884\) −7.35179 12.7337i −0.247268 0.428280i
\(885\) 9.27928 + 8.15355i 0.311920 + 0.274079i
\(886\) 11.7195 + 20.2988i 0.393724 + 0.681950i
\(887\) −24.2952 −0.815753 −0.407876 0.913037i \(-0.633731\pi\)
−0.407876 + 0.913037i \(0.633731\pi\)
\(888\) 2.60394 0.881120i 0.0873826 0.0295685i
\(889\) 0.465069 + 0.805524i 0.0155979 + 0.0270164i
\(890\) −3.84676 6.66279i −0.128944 0.223337i
\(891\) −0.504518 0.508425i −0.0169020 0.0170329i
\(892\) 0.747365 0.0250236
\(893\) 5.27278 + 20.7876i 0.176447 + 0.695632i
\(894\) −6.00641 + 30.0448i −0.200884 + 1.00485i
\(895\) 5.53755 9.59131i 0.185100 0.320602i
\(896\) 0.568176 0.984110i 0.0189814 0.0328768i
\(897\) −1.50739 + 0.510069i −0.0503303 + 0.0170307i
\(898\) 37.0884 1.23766
\(899\) 10.1015 17.4963i 0.336904 0.583535i
\(900\) 11.4250 + 4.75824i 0.380835 + 0.158608i
\(901\) 18.7193 0.623629
\(902\) 0.0916363 + 0.158719i 0.00305115 + 0.00528475i
\(903\) −1.27381 + 6.37176i −0.0423898 + 0.212039i
\(904\) −8.92114 15.4519i −0.296713 0.513922i
\(905\) −7.52558 13.0347i −0.250159 0.433288i
\(906\) −4.71144 + 23.5672i −0.156527 + 0.782969i
\(907\) 22.9849 0.763202 0.381601 0.924327i \(-0.375373\pi\)
0.381601 + 0.924327i \(0.375373\pi\)
\(908\) −14.1895 + 24.5769i −0.470895 + 0.815614i
\(909\) −1.76509 0.735115i −0.0585443 0.0243822i
\(910\) −3.52571 6.10671i −0.116876 0.202436i
\(911\) 26.8163 46.4473i 0.888465 1.53887i 0.0467748 0.998905i \(-0.485106\pi\)
0.841690 0.539961i \(-0.181561\pi\)
\(912\) −7.53998 + 0.385604i −0.249674 + 0.0127686i
\(913\) 0.378898 + 0.656271i 0.0125397 + 0.0217194i
\(914\) 17.9019 31.0069i 0.592141 1.02562i
\(915\) 4.72726 1.59961i 0.156278 0.0528813i
\(916\) 3.63731 + 6.30001i 0.120180 + 0.208158i
\(917\) 2.17823 + 3.77281i 0.0719315 + 0.124589i
\(918\) 11.4875 + 0.786308i 0.379143 + 0.0259520i
\(919\) −40.1397 −1.32409 −0.662043 0.749466i \(-0.730310\pi\)
−0.662043 + 0.749466i \(0.730310\pi\)
\(920\) 0.0647451 0.112142i 0.00213458 0.00369721i
\(921\) 11.6220 + 10.2120i 0.382956 + 0.336497i
\(922\) −5.84450 −0.192478
\(923\) 41.3472 + 71.6155i 1.36096 + 2.35725i
\(924\) 0.117669 + 0.103394i 0.00387103 + 0.00340141i
\(925\) −3.27378 5.67036i −0.107641 0.186440i
\(926\) 0.657422 + 1.13869i 0.0216042 + 0.0374196i
\(927\) 16.4407 + 6.84715i 0.539985 + 0.224890i
\(928\) 2.94499 + 5.10087i 0.0966740 + 0.167444i
\(929\) 35.5441 1.16616 0.583082 0.812413i \(-0.301847\pi\)
0.583082 + 0.812413i \(0.301847\pi\)
\(930\) −5.26285 + 1.78084i −0.172576 + 0.0583960i
\(931\) −6.11799 24.1198i −0.200509 0.790496i
\(932\) −8.86740 15.3588i −0.290461 0.503094i
\(933\) 2.06993 + 1.81881i 0.0677663 + 0.0595452i
\(934\) −16.6029 −0.543263
\(935\) −0.0824625 + 0.142829i −0.00269681 + 0.00467102i
\(936\) −15.8159 + 12.0876i −0.516960 + 0.395096i
\(937\) 22.6726 39.2701i 0.740682 1.28290i −0.211503 0.977377i \(-0.567836\pi\)
0.952185 0.305522i \(-0.0988309\pi\)
\(938\) −6.15668 + 10.6637i −0.201023 + 0.348181i
\(939\) 6.58561 + 5.78667i 0.214913 + 0.188841i
\(940\) −4.60115 −0.150073
\(941\) 12.8040 0.417398 0.208699 0.977980i \(-0.433077\pi\)
0.208699 + 0.977980i \(0.433077\pi\)
\(942\) −5.27513 + 26.3869i −0.171873 + 0.859731i
\(943\) −0.159432 + 0.276144i −0.00519182 + 0.00899250i
\(944\) −3.81301 + 6.60433i −0.124103 + 0.214952i
\(945\) 5.50907 + 0.377091i 0.179210 + 0.0122668i
\(946\) −0.131370 + 0.227540i −0.00427121 + 0.00739796i
\(947\) −28.4759 −0.925344 −0.462672 0.886530i \(-0.653109\pi\)
−0.462672 + 0.886530i \(0.653109\pi\)
\(948\) −10.0520 + 3.40138i −0.326473 + 0.110472i
\(949\) −45.2447 78.3662i −1.46871 2.54387i
\(950\) 4.42120 + 17.4303i 0.143443 + 0.565515i
\(951\) −41.7335 36.6705i −1.35330 1.18912i
\(952\) −2.51808 −0.0816116
\(953\) −4.47160 7.74504i −0.144849 0.250887i 0.784467 0.620170i \(-0.212936\pi\)
−0.929317 + 0.369284i \(0.879603\pi\)
\(954\) −3.25942 25.1322i −0.105528 0.813685i
\(955\) −0.595691 1.03177i −0.0192761 0.0333872i
\(956\) 12.0318 + 20.8396i 0.389135 + 0.674002i
\(957\) −0.769069 + 0.260237i −0.0248605 + 0.00841226i
\(958\) −16.6278 28.8001i −0.537219 0.930490i
\(959\) 3.34295 0.107950
\(960\) 0.317537 1.58836i 0.0102485 0.0512641i
\(961\) 9.61732 16.6577i 0.310236 0.537345i
\(962\) 10.5312 0.339539
\(963\) −39.8667 + 30.4688i −1.28469 + 0.981843i
\(964\) −5.35131 9.26873i −0.172354 0.298526i
\(965\) 3.79153 + 6.56712i 0.122054 + 0.211403i
\(966\) −0.0534255 + 0.267241i −0.00171894 + 0.00859834i
\(967\) −20.6993 + 35.8522i −0.665643 + 1.15293i 0.313467 + 0.949599i \(0.398509\pi\)
−0.979110 + 0.203329i \(0.934824\pi\)
\(968\) −5.49683 9.52079i −0.176675 0.306010i
\(969\) 9.09406 + 14.0424i 0.292143 + 0.451108i
\(970\) 6.98711 12.1020i 0.224343 0.388573i
\(971\) −1.82451 3.16014i −0.0585513 0.101414i 0.835264 0.549849i \(-0.185315\pi\)
−0.893815 + 0.448435i \(0.851981\pi\)
\(972\) −0.944527 15.5598i −0.0302957 0.499081i
\(973\) 6.38296 11.0556i 0.204628 0.354427i
\(974\) 10.0490 0.321992
\(975\) 35.6166 + 31.2958i 1.14065 + 1.00227i
\(976\) 1.54050 + 2.66822i 0.0493101 + 0.0854075i
\(977\) 21.3672 + 37.0091i 0.683597 + 1.18403i 0.973875 + 0.227083i \(0.0729189\pi\)
−0.290278 + 0.956942i \(0.593748\pi\)
\(978\) 37.1014 12.5544i 1.18637 0.401444i
\(979\) 0.327362 + 0.567007i 0.0104625 + 0.0181216i
\(980\) 5.33870 0.170539
\(981\) −5.64789 2.35220i −0.180323 0.0751001i
\(982\) −19.3339 + 33.4873i −0.616970 + 1.06862i
\(983\) 42.7076 1.36216 0.681081 0.732208i \(-0.261510\pi\)
0.681081 + 0.732208i \(0.261510\pi\)
\(984\) −0.781921 + 3.91127i −0.0249267 + 0.124687i
\(985\) 9.43451 16.3411i 0.300609 0.520669i
\(986\) 6.52591 11.3032i 0.207827 0.359968i
\(987\) 9.17279 3.10388i 0.291973 0.0987977i
\(988\) −27.8347 7.85918i −0.885540 0.250034i
\(989\) −0.457125 −0.0145357
\(990\) 0.206119 + 0.0858433i 0.00655089 + 0.00272828i
\(991\) −14.7910 25.6187i −0.469851 0.813806i 0.529555 0.848276i \(-0.322359\pi\)
−0.999406 + 0.0344699i \(0.989026\pi\)
\(992\) −1.71503 2.97052i −0.0544523 0.0943142i
\(993\) −1.53561 + 7.68132i −0.0487312 + 0.243759i
\(994\) 14.1620 0.449190
\(995\) −3.06557 5.30973i −0.0971852 0.168330i
\(996\) −3.23309 + 16.1723i −0.102444 + 0.512440i
\(997\) 0.991736 + 1.71774i 0.0314086 + 0.0544013i 0.881302 0.472553i \(-0.156667\pi\)
−0.849894 + 0.526954i \(0.823334\pi\)
\(998\) −17.8984 + 31.0009i −0.566562 + 0.981315i
\(999\) −4.60157 + 6.84380i −0.145587 + 0.216528i
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 342.2.f.g.7.9 18
3.2 odd 2 1026.2.f.g.235.4 18
9.4 even 3 342.2.h.g.121.3 yes 18
9.5 odd 6 1026.2.h.g.577.6 18
19.11 even 3 342.2.h.g.277.3 yes 18
57.11 odd 6 1026.2.h.g.505.6 18
171.49 even 3 inner 342.2.f.g.49.9 yes 18
171.68 odd 6 1026.2.f.g.847.4 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
342.2.f.g.7.9 18 1.1 even 1 trivial
342.2.f.g.49.9 yes 18 171.49 even 3 inner
342.2.h.g.121.3 yes 18 9.4 even 3
342.2.h.g.277.3 yes 18 19.11 even 3
1026.2.f.g.235.4 18 3.2 odd 2
1026.2.f.g.847.4 18 171.68 odd 6
1026.2.h.g.505.6 18 57.11 odd 6
1026.2.h.g.577.6 18 9.5 odd 6