Properties

Label 170.2.n.b.59.5
Level $170$
Weight $2$
Character 170.59
Analytic conductor $1.357$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [170,2,Mod(9,170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(170, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("170.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 170 = 2 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 170.n (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.35745683436\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{8})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 16 x^{15} + 52 x^{14} + 992 x^{13} + 6181 x^{12} + 8952 x^{11} + 6244 x^{10} - 11448 x^{9} - 14520 x^{8} + 27936 x^{7} + 27880 x^{6} - 121104 x^{5} + 187460 x^{4} + \cdots + 2048 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 59.5
Root \(-0.969032 + 2.33945i\) of defining polynomial
Character \(\chi\) \(=\) 170.59
Dual form 170.2.n.b.49.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(2.33945 + 0.969032i) q^{3} +1.00000i q^{4} +(-1.78490 + 1.34690i) q^{5} +(-0.969032 - 2.33945i) q^{6} +(1.26758 + 3.06021i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.41268 + 2.41268i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(2.33945 + 0.969032i) q^{3} +1.00000i q^{4} +(-1.78490 + 1.34690i) q^{5} +(-0.969032 - 2.33945i) q^{6} +(1.26758 + 3.06021i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.41268 + 2.41268i) q^{9} +(2.21452 + 0.309710i) q^{10} +(-0.949504 - 2.29231i) q^{11} +(-0.969032 + 2.33945i) q^{12} +0.777809 q^{13} +(1.26758 - 3.06021i) q^{14} +(-5.48087 + 1.42139i) q^{15} -1.00000 q^{16} +(-4.04502 - 0.798615i) q^{17} -3.41205i q^{18} +(4.13806 - 4.13806i) q^{19} +(-1.34690 - 1.78490i) q^{20} +8.38752i q^{21} +(-0.949504 + 2.29231i) q^{22} +(7.45510 - 3.08800i) q^{23} +(2.33945 - 0.969032i) q^{24} +(1.37171 - 4.80816i) q^{25} +(-0.549994 - 0.549994i) q^{26} +(0.399286 + 0.963960i) q^{27} +(-3.06021 + 1.26758i) q^{28} +(0.319339 + 0.132275i) q^{29} +(4.88063 + 2.87049i) q^{30} +(-0.719461 + 1.73693i) q^{31} +(0.707107 + 0.707107i) q^{32} -6.28283i q^{33} +(2.29556 + 3.42497i) q^{34} +(-6.38429 - 3.75485i) q^{35} +(-2.41268 + 2.41268i) q^{36} +(-4.26699 - 1.76745i) q^{37} -5.85211 q^{38} +(1.81964 + 0.753721i) q^{39} +(-0.309710 + 2.21452i) q^{40} +(2.17392 - 0.900466i) q^{41} +(5.93087 - 5.93087i) q^{42} +(-8.03592 + 8.03592i) q^{43} +(2.29231 - 0.949504i) q^{44} +(-7.55603 - 1.05674i) q^{45} +(-7.45510 - 3.08800i) q^{46} -9.25971 q^{47} +(-2.33945 - 0.969032i) q^{48} +(-2.80835 + 2.80835i) q^{49} +(-4.36983 + 2.42993i) q^{50} +(-8.68924 - 5.78807i) q^{51} +0.777809i q^{52} +(2.98917 + 2.98917i) q^{53} +(0.399286 - 0.963960i) q^{54} +(4.78228 + 2.81264i) q^{55} +(3.06021 + 1.26758i) q^{56} +(13.6907 - 5.67088i) q^{57} +(-0.132275 - 0.319339i) q^{58} +(-9.06612 - 9.06612i) q^{59} +(-1.42139 - 5.48087i) q^{60} +(12.7953 - 5.29999i) q^{61} +(1.73693 - 0.719461i) q^{62} +(-4.32504 + 10.4416i) q^{63} -1.00000i q^{64} +(-1.38831 + 1.04763i) q^{65} +(-4.44263 + 4.44263i) q^{66} -0.862303i q^{67} +(0.798615 - 4.04502i) q^{68} +20.4332 q^{69} +(1.85930 + 7.16945i) q^{70} +(-3.13819 + 7.57626i) q^{71} +3.41205 q^{72} +(-3.75104 + 9.05580i) q^{73} +(1.76745 + 4.26699i) q^{74} +(7.86831 - 9.91921i) q^{75} +(4.13806 + 4.13806i) q^{76} +(5.81136 - 5.81136i) q^{77} +(-0.753721 - 1.81964i) q^{78} +(3.33195 + 8.04403i) q^{79} +(1.78490 - 1.34690i) q^{80} -7.59408i q^{81} +(-2.17392 - 0.900466i) q^{82} +(2.56072 + 2.56072i) q^{83} -8.38752 q^{84} +(8.29560 - 4.02280i) q^{85} +11.3645 q^{86} +(0.618900 + 0.618900i) q^{87} +(-2.29231 - 0.949504i) q^{88} +3.67668i q^{89} +(4.59569 + 6.09015i) q^{90} +(0.985934 + 2.38025i) q^{91} +(3.08800 + 7.45510i) q^{92} +(-3.36628 + 3.36628i) q^{93} +(6.54760 + 6.54760i) q^{94} +(-1.81245 + 12.9596i) q^{95} +(0.969032 + 2.33945i) q^{96} +(1.05015 - 2.53530i) q^{97} +3.97161 q^{98} +(3.23975 - 7.82145i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 4 q^{5} + 8 q^{10} - 8 q^{11} + 24 q^{13} + 16 q^{15} - 20 q^{16} - 4 q^{20} - 8 q^{22} - 16 q^{23} + 8 q^{25} - 12 q^{26} - 24 q^{27} - 12 q^{29} + 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} + 8 q^{37} + 8 q^{38} - 4 q^{40} + 4 q^{41} - 8 q^{42} - 16 q^{43} - 8 q^{44} - 32 q^{45} + 16 q^{46} - 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} - 44 q^{53} - 24 q^{54} + 72 q^{57} + 16 q^{59} + 8 q^{60} + 8 q^{61} + 8 q^{62} + 24 q^{63} - 28 q^{65} - 8 q^{66} - 20 q^{68} - 16 q^{69} + 8 q^{71} + 28 q^{72} + 60 q^{73} + 28 q^{74} - 8 q^{78} + 56 q^{79} + 4 q^{80} - 4 q^{82} + 16 q^{84} + 84 q^{85} + 48 q^{86} + 72 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} + 8 q^{92} - 72 q^{93} + 32 q^{94} + 88 q^{95} - 48 q^{97} + 36 q^{98} + 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(71\) \(137\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) 2.33945 + 0.969032i 1.35068 + 0.559471i 0.936482 0.350715i \(-0.114062\pi\)
0.414200 + 0.910186i \(0.364062\pi\)
\(4\) 1.00000i 0.500000i
\(5\) −1.78490 + 1.34690i −0.798230 + 0.602353i
\(6\) −0.969032 2.33945i −0.395606 0.955076i
\(7\) 1.26758 + 3.06021i 0.479100 + 1.15665i 0.960032 + 0.279891i \(0.0902984\pi\)
−0.480932 + 0.876758i \(0.659702\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 2.41268 + 2.41268i 0.804227 + 0.804227i
\(10\) 2.21452 + 0.309710i 0.700291 + 0.0979388i
\(11\) −0.949504 2.29231i −0.286286 0.691156i 0.713670 0.700482i \(-0.247032\pi\)
−0.999957 + 0.00932562i \(0.997032\pi\)
\(12\) −0.969032 + 2.33945i −0.279735 + 0.675341i
\(13\) 0.777809 0.215725 0.107863 0.994166i \(-0.465599\pi\)
0.107863 + 0.994166i \(0.465599\pi\)
\(14\) 1.26758 3.06021i 0.338775 0.817874i
\(15\) −5.48087 + 1.42139i −1.41515 + 0.367000i
\(16\) −1.00000 −0.250000
\(17\) −4.04502 0.798615i −0.981062 0.193693i
\(18\) 3.41205i 0.804227i
\(19\) 4.13806 4.13806i 0.949337 0.949337i −0.0494400 0.998777i \(-0.515744\pi\)
0.998777 + 0.0494400i \(0.0157437\pi\)
\(20\) −1.34690 1.78490i −0.301176 0.399115i
\(21\) 8.38752i 1.83031i
\(22\) −0.949504 + 2.29231i −0.202435 + 0.488721i
\(23\) 7.45510 3.08800i 1.55450 0.643893i 0.570373 0.821386i \(-0.306799\pi\)
0.984122 + 0.177493i \(0.0567986\pi\)
\(24\) 2.33945 0.969032i 0.477538 0.197803i
\(25\) 1.37171 4.80816i 0.274343 0.961632i
\(26\) −0.549994 0.549994i −0.107863 0.107863i
\(27\) 0.399286 + 0.963960i 0.0768425 + 0.185514i
\(28\) −3.06021 + 1.26758i −0.578324 + 0.239550i
\(29\) 0.319339 + 0.132275i 0.0592998 + 0.0245628i 0.412136 0.911122i \(-0.364783\pi\)
−0.352836 + 0.935685i \(0.614783\pi\)
\(30\) 4.88063 + 2.87049i 0.891077 + 0.524077i
\(31\) −0.719461 + 1.73693i −0.129219 + 0.311962i −0.975226 0.221209i \(-0.929000\pi\)
0.846008 + 0.533171i \(0.179000\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 6.28283i 1.09370i
\(34\) 2.29556 + 3.42497i 0.393685 + 0.587377i
\(35\) −6.38429 3.75485i −1.07914 0.634685i
\(36\) −2.41268 + 2.41268i −0.402113 + 0.402113i
\(37\) −4.26699 1.76745i −0.701489 0.290566i 0.00328857 0.999995i \(-0.498953\pi\)
−0.704778 + 0.709428i \(0.748953\pi\)
\(38\) −5.85211 −0.949337
\(39\) 1.81964 + 0.753721i 0.291376 + 0.120692i
\(40\) −0.309710 + 2.21452i −0.0489694 + 0.350146i
\(41\) 2.17392 0.900466i 0.339509 0.140629i −0.206414 0.978465i \(-0.566179\pi\)
0.545923 + 0.837836i \(0.316179\pi\)
\(42\) 5.93087 5.93087i 0.915153 0.915153i
\(43\) −8.03592 + 8.03592i −1.22547 + 1.22547i −0.259805 + 0.965661i \(0.583658\pi\)
−0.965661 + 0.259805i \(0.916342\pi\)
\(44\) 2.29231 0.949504i 0.345578 0.143143i
\(45\) −7.55603 1.05674i −1.12639 0.157530i
\(46\) −7.45510 3.08800i −1.09919 0.455301i
\(47\) −9.25971 −1.35067 −0.675334 0.737512i \(-0.736000\pi\)
−0.675334 + 0.737512i \(0.736000\pi\)
\(48\) −2.33945 0.969032i −0.337670 0.139868i
\(49\) −2.80835 + 2.80835i −0.401193 + 0.401193i
\(50\) −4.36983 + 2.42993i −0.617987 + 0.343645i
\(51\) −8.68924 5.78807i −1.21674 0.810493i
\(52\) 0.777809i 0.107863i
\(53\) 2.98917 + 2.98917i 0.410594 + 0.410594i 0.881945 0.471352i \(-0.156234\pi\)
−0.471352 + 0.881945i \(0.656234\pi\)
\(54\) 0.399286 0.963960i 0.0543359 0.131178i
\(55\) 4.78228 + 2.81264i 0.644842 + 0.379256i
\(56\) 3.06021 + 1.26758i 0.408937 + 0.169387i
\(57\) 13.6907 5.67088i 1.81338 0.751126i
\(58\) −0.132275 0.319339i −0.0173685 0.0419313i
\(59\) −9.06612 9.06612i −1.18031 1.18031i −0.979664 0.200644i \(-0.935697\pi\)
−0.200644 0.979664i \(-0.564303\pi\)
\(60\) −1.42139 5.48087i −0.183500 0.707577i
\(61\) 12.7953 5.29999i 1.63827 0.678595i 0.642151 0.766579i \(-0.278042\pi\)
0.996122 + 0.0879839i \(0.0280424\pi\)
\(62\) 1.73693 0.719461i 0.220590 0.0913716i
\(63\) −4.32504 + 10.4416i −0.544903 + 1.31551i
\(64\) 1.00000i 0.125000i
\(65\) −1.38831 + 1.04763i −0.172198 + 0.129943i
\(66\) −4.44263 + 4.44263i −0.546850 + 0.546850i
\(67\) 0.862303i 0.105347i −0.998612 0.0526736i \(-0.983226\pi\)
0.998612 0.0526736i \(-0.0167743\pi\)
\(68\) 0.798615 4.04502i 0.0968463 0.490531i
\(69\) 20.4332 2.45987
\(70\) 1.85930 + 7.16945i 0.222229 + 0.856914i
\(71\) −3.13819 + 7.57626i −0.372435 + 0.899137i 0.620902 + 0.783888i \(0.286767\pi\)
−0.993337 + 0.115249i \(0.963233\pi\)
\(72\) 3.41205 0.402113
\(73\) −3.75104 + 9.05580i −0.439026 + 1.05990i 0.537260 + 0.843417i \(0.319459\pi\)
−0.976286 + 0.216485i \(0.930541\pi\)
\(74\) 1.76745 + 4.26699i 0.205461 + 0.496028i
\(75\) 7.86831 9.91921i 0.908555 1.14537i
\(76\) 4.13806 + 4.13806i 0.474669 + 0.474669i
\(77\) 5.81136 5.81136i 0.662265 0.662265i
\(78\) −0.753721 1.81964i −0.0853421 0.206034i
\(79\) 3.33195 + 8.04403i 0.374873 + 0.905024i 0.992909 + 0.118874i \(0.0379286\pi\)
−0.618036 + 0.786150i \(0.712071\pi\)
\(80\) 1.78490 1.34690i 0.199558 0.150588i
\(81\) 7.59408i 0.843787i
\(82\) −2.17392 0.900466i −0.240069 0.0994399i
\(83\) 2.56072 + 2.56072i 0.281075 + 0.281075i 0.833538 0.552462i \(-0.186312\pi\)
−0.552462 + 0.833538i \(0.686312\pi\)
\(84\) −8.38752 −0.915153
\(85\) 8.29560 4.02280i 0.899785 0.436334i
\(86\) 11.3645 1.22547
\(87\) 0.618900 + 0.618900i 0.0663530 + 0.0663530i
\(88\) −2.29231 0.949504i −0.244361 0.101217i
\(89\) 3.67668i 0.389728i 0.980830 + 0.194864i \(0.0624265\pi\)
−0.980830 + 0.194864i \(0.937574\pi\)
\(90\) 4.59569 + 6.09015i 0.484428 + 0.641958i
\(91\) 0.985934 + 2.38025i 0.103354 + 0.249519i
\(92\) 3.08800 + 7.45510i 0.321947 + 0.777248i
\(93\) −3.36628 + 3.36628i −0.349067 + 0.349067i
\(94\) 6.54760 + 6.54760i 0.675334 + 0.675334i
\(95\) −1.81245 + 12.9596i −0.185954 + 1.32963i
\(96\) 0.969032 + 2.33945i 0.0989014 + 0.238769i
\(97\) 1.05015 2.53530i 0.106627 0.257420i −0.861556 0.507662i \(-0.830510\pi\)
0.968183 + 0.250241i \(0.0805100\pi\)
\(98\) 3.97161 0.401193
\(99\) 3.23975 7.82145i 0.325607 0.786086i
\(100\) 4.80816 + 1.37171i 0.480816 + 0.137171i
\(101\) −9.51804 −0.947080 −0.473540 0.880772i \(-0.657024\pi\)
−0.473540 + 0.880772i \(0.657024\pi\)
\(102\) 2.05144 + 10.2370i 0.203123 + 1.01362i
\(103\) 12.8896i 1.27005i −0.772490 0.635027i \(-0.780989\pi\)
0.772490 0.635027i \(-0.219011\pi\)
\(104\) 0.549994 0.549994i 0.0539313 0.0539313i
\(105\) −11.2972 14.9709i −1.10249 1.46101i
\(106\) 4.22732i 0.410594i
\(107\) 1.95011 4.70799i 0.188525 0.455139i −0.801151 0.598462i \(-0.795779\pi\)
0.989676 + 0.143323i \(0.0457788\pi\)
\(108\) −0.963960 + 0.399286i −0.0927571 + 0.0384213i
\(109\) 0.169155 0.0700661i 0.0162021 0.00671112i −0.374568 0.927200i \(-0.622209\pi\)
0.390770 + 0.920488i \(0.372209\pi\)
\(110\) −1.39274 5.37042i −0.132793 0.512049i
\(111\) −8.26970 8.26970i −0.784925 0.784925i
\(112\) −1.26758 3.06021i −0.119775 0.289162i
\(113\) 11.1347 4.61213i 1.04746 0.433873i 0.208477 0.978027i \(-0.433149\pi\)
0.838985 + 0.544154i \(0.183149\pi\)
\(114\) −13.6907 5.67088i −1.28225 0.531126i
\(115\) −9.14734 + 15.5530i −0.852994 + 1.45033i
\(116\) −0.132275 + 0.319339i −0.0122814 + 0.0296499i
\(117\) 1.87660 + 1.87660i 0.173492 + 0.173492i
\(118\) 12.8214i 1.18031i
\(119\) −2.68346 13.3909i −0.245992 1.22754i
\(120\) −2.87049 + 4.88063i −0.262038 + 0.445538i
\(121\) 3.42507 3.42507i 0.311370 0.311370i
\(122\) −12.7953 5.29999i −1.15843 0.479839i
\(123\) 5.95835 0.537246
\(124\) −1.73693 0.719461i −0.155981 0.0646095i
\(125\) 4.02775 + 10.4296i 0.360253 + 0.932855i
\(126\) 10.4416 4.32504i 0.930208 0.385305i
\(127\) −13.6948 + 13.6948i −1.21522 + 1.21522i −0.245934 + 0.969286i \(0.579095\pi\)
−0.969286 + 0.245934i \(0.920905\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) −26.5867 + 11.0126i −2.34083 + 0.969602i
\(130\) 1.72247 + 0.240895i 0.151071 + 0.0211279i
\(131\) 6.17744 + 2.55878i 0.539725 + 0.223561i 0.635857 0.771807i \(-0.280647\pi\)
−0.0961315 + 0.995369i \(0.530647\pi\)
\(132\) 6.28283 0.546850
\(133\) 17.9086 + 7.41801i 1.55288 + 0.643223i
\(134\) −0.609741 + 0.609741i −0.0526736 + 0.0526736i
\(135\) −2.01104 1.18277i −0.173083 0.101797i
\(136\) −3.42497 + 2.29556i −0.293689 + 0.196842i
\(137\) 2.17815i 0.186092i 0.995662 + 0.0930461i \(0.0296604\pi\)
−0.995662 + 0.0930461i \(0.970340\pi\)
\(138\) −14.4485 14.4485i −1.22993 1.22993i
\(139\) 3.84818 9.29033i 0.326398 0.787995i −0.672456 0.740137i \(-0.734761\pi\)
0.998854 0.0478580i \(-0.0152395\pi\)
\(140\) 3.75485 6.38429i 0.317343 0.539571i
\(141\) −21.6626 8.97295i −1.82432 0.755659i
\(142\) 7.57626 3.13819i 0.635786 0.263351i
\(143\) −0.738533 1.78298i −0.0617592 0.149100i
\(144\) −2.41268 2.41268i −0.201057 0.201057i
\(145\) −0.748149 + 0.194022i −0.0621304 + 0.0161126i
\(146\) 9.05580 3.75104i 0.749464 0.310438i
\(147\) −9.29139 + 3.84862i −0.766341 + 0.317429i
\(148\) 1.76745 4.26699i 0.145283 0.350745i
\(149\) 12.2117i 1.00043i 0.865903 + 0.500213i \(0.166745\pi\)
−0.865903 + 0.500213i \(0.833255\pi\)
\(150\) −12.5777 + 1.45021i −1.02696 + 0.118409i
\(151\) −8.45256 + 8.45256i −0.687860 + 0.687860i −0.961759 0.273899i \(-0.911687\pi\)
0.273899 + 0.961759i \(0.411687\pi\)
\(152\) 5.85211i 0.474669i
\(153\) −7.83255 11.6862i −0.633224 0.944769i
\(154\) −8.21850 −0.662265
\(155\) −1.05531 4.06929i −0.0847647 0.326853i
\(156\) −0.753721 + 1.81964i −0.0603460 + 0.145688i
\(157\) 8.98017 0.716696 0.358348 0.933588i \(-0.383340\pi\)
0.358348 + 0.933588i \(0.383340\pi\)
\(158\) 3.33195 8.04403i 0.265075 0.639949i
\(159\) 4.09641 + 9.88961i 0.324866 + 0.784297i
\(160\) −2.21452 0.309710i −0.175073 0.0244847i
\(161\) 18.8998 + 18.8998i 1.48952 + 1.48952i
\(162\) −5.36983 + 5.36983i −0.421893 + 0.421893i
\(163\) −4.06748 9.81976i −0.318589 0.769143i −0.999329 0.0366176i \(-0.988342\pi\)
0.680740 0.732525i \(-0.261658\pi\)
\(164\) 0.900466 + 2.17392i 0.0703146 + 0.169754i
\(165\) 8.46236 + 11.2142i 0.658794 + 0.873025i
\(166\) 3.62140i 0.281075i
\(167\) −4.96753 2.05762i −0.384399 0.159223i 0.182111 0.983278i \(-0.441707\pi\)
−0.566510 + 0.824055i \(0.691707\pi\)
\(168\) 5.93087 + 5.93087i 0.457577 + 0.457577i
\(169\) −12.3950 −0.953463
\(170\) −8.71043 3.02133i −0.668059 0.231725i
\(171\) 19.9677 1.52696
\(172\) −8.03592 8.03592i −0.612733 0.612733i
\(173\) 3.90622 + 1.61801i 0.296985 + 0.123015i 0.526201 0.850361i \(-0.323616\pi\)
−0.229216 + 0.973376i \(0.573616\pi\)
\(174\) 0.875257i 0.0663530i
\(175\) 16.4527 1.89700i 1.24371 0.143399i
\(176\) 0.949504 + 2.29231i 0.0715716 + 0.172789i
\(177\) −12.4244 29.9951i −0.933873 2.25457i
\(178\) 2.59981 2.59981i 0.194864 0.194864i
\(179\) 3.76205 + 3.76205i 0.281189 + 0.281189i 0.833583 0.552394i \(-0.186286\pi\)
−0.552394 + 0.833583i \(0.686286\pi\)
\(180\) 1.05674 7.55603i 0.0787650 0.563193i
\(181\) −6.05136 14.6093i −0.449794 1.08590i −0.972399 0.233324i \(-0.925040\pi\)
0.522605 0.852575i \(-0.324960\pi\)
\(182\) 0.985934 2.38025i 0.0730823 0.176436i
\(183\) 35.0699 2.59244
\(184\) 3.08800 7.45510i 0.227651 0.549597i
\(185\) 9.99671 2.59251i 0.734973 0.190605i
\(186\) 4.76064 0.349067
\(187\) 2.01010 + 10.0307i 0.146993 + 0.733519i
\(188\) 9.25971i 0.675334i
\(189\) −2.44379 + 2.44379i −0.177760 + 0.177760i
\(190\) 10.4454 7.88221i 0.757789 0.571836i
\(191\) 26.3384i 1.90578i 0.303318 + 0.952890i \(0.401906\pi\)
−0.303318 + 0.952890i \(0.598094\pi\)
\(192\) 0.969032 2.33945i 0.0699338 0.168835i
\(193\) −12.6427 + 5.23679i −0.910044 + 0.376953i −0.788074 0.615581i \(-0.788921\pi\)
−0.121971 + 0.992534i \(0.538921\pi\)
\(194\) −2.53530 + 1.05015i −0.182024 + 0.0753967i
\(195\) −4.26307 + 1.10557i −0.305285 + 0.0791713i
\(196\) −2.80835 2.80835i −0.200597 0.200597i
\(197\) −2.48851 6.00780i −0.177299 0.428038i 0.810099 0.586293i \(-0.199413\pi\)
−0.987398 + 0.158255i \(0.949413\pi\)
\(198\) −7.82145 + 3.23975i −0.555846 + 0.230239i
\(199\) −10.2616 4.25049i −0.727424 0.301309i −0.0119313 0.999929i \(-0.503798\pi\)
−0.715493 + 0.698620i \(0.753798\pi\)
\(200\) −2.42993 4.36983i −0.171822 0.308994i
\(201\) 0.835599 2.01732i 0.0589386 0.142290i
\(202\) 6.73027 + 6.73027i 0.473540 + 0.473540i
\(203\) 1.14491i 0.0803571i
\(204\) 5.78807 8.68924i 0.405246 0.608369i
\(205\) −2.66738 + 4.53529i −0.186298 + 0.316759i
\(206\) −9.11435 + 9.11435i −0.635027 + 0.635027i
\(207\) 25.4371 + 10.5364i 1.76800 + 0.732331i
\(208\) −0.777809 −0.0539313
\(209\) −13.4148 5.55660i −0.927922 0.384358i
\(210\) −2.59769 + 18.5743i −0.179258 + 1.28175i
\(211\) −4.39176 + 1.81913i −0.302342 + 0.125234i −0.528697 0.848811i \(-0.677319\pi\)
0.226355 + 0.974045i \(0.427319\pi\)
\(212\) −2.98917 + 2.98917i −0.205297 + 0.205297i
\(213\) −14.6833 + 14.6833i −1.00608 + 1.00608i
\(214\) −4.70799 + 1.95011i −0.321832 + 0.133307i
\(215\) 3.51969 25.1669i 0.240041 1.71637i
\(216\) 0.963960 + 0.399286i 0.0655892 + 0.0271679i
\(217\) −6.22734 −0.422739
\(218\) −0.169155 0.0700661i −0.0114566 0.00474548i
\(219\) −17.5507 + 17.5507i −1.18597 + 1.18597i
\(220\) −2.81264 + 4.78228i −0.189628 + 0.322421i
\(221\) −3.14626 0.621170i −0.211640 0.0417844i
\(222\) 11.6951i 0.784925i
\(223\) −13.4824 13.4824i −0.902845 0.902845i 0.0928360 0.995681i \(-0.470407\pi\)
−0.995681 + 0.0928360i \(0.970407\pi\)
\(224\) −1.26758 + 3.06021i −0.0846937 + 0.204469i
\(225\) 14.9101 8.29105i 0.994004 0.552737i
\(226\) −11.1347 4.61213i −0.740667 0.306794i
\(227\) −16.6070 + 6.87885i −1.10225 + 0.456565i −0.858261 0.513214i \(-0.828455\pi\)
−0.243985 + 0.969779i \(0.578455\pi\)
\(228\) 5.67088 + 13.6907i 0.375563 + 0.906689i
\(229\) 0.797989 + 0.797989i 0.0527326 + 0.0527326i 0.732981 0.680249i \(-0.238128\pi\)
−0.680249 + 0.732981i \(0.738128\pi\)
\(230\) 17.4658 4.52952i 1.15166 0.298667i
\(231\) 19.2268 7.96398i 1.26503 0.523992i
\(232\) 0.319339 0.132275i 0.0209657 0.00868426i
\(233\) −8.55988 + 20.6654i −0.560776 + 1.35383i 0.348370 + 0.937357i \(0.386735\pi\)
−0.909146 + 0.416477i \(0.863265\pi\)
\(234\) 2.65392i 0.173492i
\(235\) 16.5276 12.4719i 1.07814 0.813578i
\(236\) 9.06612 9.06612i 0.590154 0.590154i
\(237\) 22.0474i 1.43213i
\(238\) −7.57131 + 11.3663i −0.490775 + 0.736768i
\(239\) −11.2657 −0.728714 −0.364357 0.931259i \(-0.618711\pi\)
−0.364357 + 0.931259i \(0.618711\pi\)
\(240\) 5.48087 1.42139i 0.353788 0.0917501i
\(241\) −0.166358 + 0.401624i −0.0107161 + 0.0258709i −0.929147 0.369710i \(-0.879457\pi\)
0.918431 + 0.395581i \(0.129457\pi\)
\(242\) −4.84378 −0.311370
\(243\) 8.55676 20.6578i 0.548916 1.32520i
\(244\) 5.29999 + 12.7953i 0.339297 + 0.819136i
\(245\) 1.23005 8.79520i 0.0785848 0.561905i
\(246\) −4.21319 4.21319i −0.268623 0.268623i
\(247\) 3.21862 3.21862i 0.204796 0.204796i
\(248\) 0.719461 + 1.73693i 0.0456858 + 0.110295i
\(249\) 3.50926 + 8.47209i 0.222390 + 0.536897i
\(250\) 4.52681 10.2229i 0.286301 0.646554i
\(251\) 23.8942i 1.50819i −0.656767 0.754094i \(-0.728077\pi\)
0.656767 0.754094i \(-0.271923\pi\)
\(252\) −10.4416 4.32504i −0.657757 0.272452i
\(253\) −14.1573 14.1573i −0.890061 0.890061i
\(254\) 19.3674 1.21522
\(255\) 23.3054 1.37244i 1.45944 0.0859455i
\(256\) 1.00000 0.0625000
\(257\) 20.7578 + 20.7578i 1.29483 + 1.29483i 0.931761 + 0.363073i \(0.118273\pi\)
0.363073 + 0.931761i \(0.381727\pi\)
\(258\) 26.5867 + 11.0126i 1.65521 + 0.685612i
\(259\) 15.2982i 0.950587i
\(260\) −1.04763 1.38831i −0.0649714 0.0860992i
\(261\) 0.451327 + 1.08960i 0.0279365 + 0.0674446i
\(262\) −2.55878 6.17744i −0.158082 0.381643i
\(263\) −14.2208 + 14.2208i −0.876892 + 0.876892i −0.993212 0.116320i \(-0.962890\pi\)
0.116320 + 0.993212i \(0.462890\pi\)
\(264\) −4.44263 4.44263i −0.273425 0.273425i
\(265\) −9.36147 1.30924i −0.575071 0.0804261i
\(266\) −7.41801 17.9086i −0.454827 1.09805i
\(267\) −3.56282 + 8.60141i −0.218041 + 0.526398i
\(268\) 0.862303 0.0526736
\(269\) 1.10168 2.65969i 0.0671707 0.162164i −0.886729 0.462289i \(-0.847028\pi\)
0.953900 + 0.300125i \(0.0970283\pi\)
\(270\) 0.585676 + 2.25837i 0.0356431 + 0.137440i
\(271\) 18.7793 1.14076 0.570380 0.821381i \(-0.306796\pi\)
0.570380 + 0.821381i \(0.306796\pi\)
\(272\) 4.04502 + 0.798615i 0.245266 + 0.0484231i
\(273\) 6.52389i 0.394844i
\(274\) 1.54019 1.54019i 0.0930461 0.0930461i
\(275\) −12.3242 + 1.42098i −0.743178 + 0.0856884i
\(276\) 20.4332i 1.22993i
\(277\) 3.35394 8.09712i 0.201519 0.486509i −0.790521 0.612435i \(-0.790190\pi\)
0.992040 + 0.125926i \(0.0401902\pi\)
\(278\) −9.29033 + 3.84818i −0.557197 + 0.230798i
\(279\) −5.92649 + 2.45483i −0.354810 + 0.146967i
\(280\) −7.16945 + 1.85930i −0.428457 + 0.111114i
\(281\) 21.5263 + 21.5263i 1.28415 + 1.28415i 0.938284 + 0.345866i \(0.112415\pi\)
0.345866 + 0.938284i \(0.387585\pi\)
\(282\) 8.97295 + 21.6626i 0.534332 + 1.28999i
\(283\) 8.83075 3.65782i 0.524934 0.217435i −0.104449 0.994530i \(-0.533308\pi\)
0.629383 + 0.777096i \(0.283308\pi\)
\(284\) −7.57626 3.13819i −0.449569 0.186217i
\(285\) −16.7984 + 28.5620i −0.995051 + 1.69186i
\(286\) −0.738533 + 1.78298i −0.0436704 + 0.105430i
\(287\) 5.51122 + 5.51122i 0.325317 + 0.325317i
\(288\) 3.41205i 0.201057i
\(289\) 15.7244 + 6.46083i 0.924966 + 0.380049i
\(290\) 0.666215 + 0.391827i 0.0391215 + 0.0230089i
\(291\) 4.91357 4.91357i 0.288038 0.288038i
\(292\) −9.05580 3.75104i −0.529951 0.219513i
\(293\) −5.34949 −0.312521 −0.156260 0.987716i \(-0.549944\pi\)
−0.156260 + 0.987716i \(0.549944\pi\)
\(294\) 9.29139 + 3.84862i 0.541885 + 0.224456i
\(295\) 28.3933 + 3.97092i 1.65312 + 0.231196i
\(296\) −4.26699 + 1.76745i −0.248014 + 0.102731i
\(297\) 1.83057 1.83057i 0.106220 0.106220i
\(298\) 8.63501 8.63501i 0.500213 0.500213i
\(299\) 5.79864 2.40188i 0.335344 0.138904i
\(300\) 9.91921 + 7.86831i 0.572686 + 0.454277i
\(301\) −34.7777 14.4054i −2.00455 0.830313i
\(302\) 11.9537 0.687860
\(303\) −22.2670 9.22328i −1.27920 0.529864i
\(304\) −4.13806 + 4.13806i −0.237334 + 0.237334i
\(305\) −15.6998 + 26.6940i −0.898965 + 1.52849i
\(306\) −2.72491 + 13.8018i −0.155773 + 0.788997i
\(307\) 19.6367i 1.12073i −0.828247 0.560363i \(-0.810662\pi\)
0.828247 0.560363i \(-0.189338\pi\)
\(308\) 5.81136 + 5.81136i 0.331133 + 0.331133i
\(309\) 12.4905 30.1547i 0.710558 1.71544i
\(310\) −2.13120 + 3.62364i −0.121044 + 0.205809i
\(311\) 12.6908 + 5.25670i 0.719629 + 0.298080i 0.712283 0.701893i \(-0.247661\pi\)
0.00734657 + 0.999973i \(0.497661\pi\)
\(312\) 1.81964 0.753721i 0.103017 0.0426711i
\(313\) 2.35732 + 5.69107i 0.133244 + 0.321678i 0.976393 0.216001i \(-0.0693013\pi\)
−0.843150 + 0.537679i \(0.819301\pi\)
\(314\) −6.34994 6.34994i −0.358348 0.358348i
\(315\) −6.34401 24.4625i −0.357444 1.37831i
\(316\) −8.04403 + 3.33195i −0.452512 + 0.187437i
\(317\) 4.69756 1.94579i 0.263841 0.109287i −0.246842 0.969056i \(-0.579393\pi\)
0.510683 + 0.859769i \(0.329393\pi\)
\(318\) 4.09641 9.88961i 0.229715 0.554582i
\(319\) 0.857619i 0.0480174i
\(320\) 1.34690 + 1.78490i 0.0752941 + 0.0997788i
\(321\) 9.12439 9.12439i 0.509274 0.509274i
\(322\) 26.7284i 1.48952i
\(323\) −20.0433 + 13.4338i −1.11524 + 0.747479i
\(324\) 7.59408 0.421893
\(325\) 1.06693 3.73983i 0.0591827 0.207448i
\(326\) −4.06748 + 9.81976i −0.225277 + 0.543866i
\(327\) 0.463625 0.0256385
\(328\) 0.900466 2.17392i 0.0497199 0.120035i
\(329\) −11.7374 28.3366i −0.647104 1.56225i
\(330\) 1.94585 13.9134i 0.107116 0.765909i
\(331\) 2.30132 + 2.30132i 0.126492 + 0.126492i 0.767519 0.641027i \(-0.221491\pi\)
−0.641027 + 0.767519i \(0.721491\pi\)
\(332\) −2.56072 + 2.56072i −0.140538 + 0.140538i
\(333\) −6.03061 14.5592i −0.330475 0.797838i
\(334\) 2.05762 + 4.96753i 0.112588 + 0.271811i
\(335\) 1.16144 + 1.53912i 0.0634561 + 0.0840913i
\(336\) 8.38752i 0.457577i
\(337\) 5.37723 + 2.22732i 0.292917 + 0.121330i 0.524303 0.851532i \(-0.324326\pi\)
−0.231386 + 0.972862i \(0.574326\pi\)
\(338\) 8.76460 + 8.76460i 0.476731 + 0.476731i
\(339\) 30.5183 1.65753
\(340\) 4.02280 + 8.29560i 0.218167 + 0.449892i
\(341\) 4.66471 0.252608
\(342\) −14.1193 14.1193i −0.763482 0.763482i
\(343\) 9.26749 + 3.83872i 0.500397 + 0.207271i
\(344\) 11.3645i 0.612733i
\(345\) −36.4711 + 27.5215i −1.96354 + 1.48171i
\(346\) −1.61801 3.90622i −0.0869848 0.210000i
\(347\) −4.68855 11.3192i −0.251695 0.607645i 0.746646 0.665221i \(-0.231663\pi\)
−0.998341 + 0.0575764i \(0.981663\pi\)
\(348\) −0.618900 + 0.618900i −0.0331765 + 0.0331765i
\(349\) −4.08452 4.08452i −0.218640 0.218640i 0.589285 0.807925i \(-0.299409\pi\)
−0.807925 + 0.589285i \(0.799409\pi\)
\(350\) −12.9752 10.2924i −0.693554 0.550154i
\(351\) 0.310568 + 0.749777i 0.0165769 + 0.0400201i
\(352\) 0.949504 2.29231i 0.0506087 0.122180i
\(353\) −12.5280 −0.666797 −0.333398 0.942786i \(-0.608195\pi\)
−0.333398 + 0.942786i \(0.608195\pi\)
\(354\) −12.4244 + 29.9951i −0.660348 + 1.59422i
\(355\) −4.60313 17.7497i −0.244309 0.942055i
\(356\) −3.67668 −0.194864
\(357\) 6.69840 33.9277i 0.354517 1.79564i
\(358\) 5.32034i 0.281189i
\(359\) −4.29559 + 4.29559i −0.226713 + 0.226713i −0.811318 0.584605i \(-0.801249\pi\)
0.584605 + 0.811318i \(0.301249\pi\)
\(360\) −6.09015 + 4.59569i −0.320979 + 0.242214i
\(361\) 15.2472i 0.802482i
\(362\) −6.05136 + 14.6093i −0.318052 + 0.767847i
\(363\) 11.3318 4.69377i 0.594764 0.246359i
\(364\) −2.38025 + 0.985934i −0.124759 + 0.0516770i
\(365\) −5.50206 21.2160i −0.287991 1.11049i
\(366\) −24.7981 24.7981i −1.29622 1.29622i
\(367\) −3.76510 9.08975i −0.196536 0.474481i 0.794632 0.607092i \(-0.207664\pi\)
−0.991168 + 0.132611i \(0.957664\pi\)
\(368\) −7.45510 + 3.08800i −0.388624 + 0.160973i
\(369\) 7.41751 + 3.07243i 0.386140 + 0.159944i
\(370\) −8.90192 5.23556i −0.462789 0.272184i
\(371\) −5.35846 + 12.9365i −0.278198 + 0.671628i
\(372\) −3.36628 3.36628i −0.174534 0.174534i
\(373\) 10.2057i 0.528431i −0.964464 0.264215i \(-0.914887\pi\)
0.964464 0.264215i \(-0.0851130\pi\)
\(374\) 5.67144 8.51414i 0.293263 0.440256i
\(375\) −0.683924 + 28.3026i −0.0353177 + 1.46154i
\(376\) −6.54760 + 6.54760i −0.337667 + 0.337667i
\(377\) 0.248385 + 0.102884i 0.0127925 + 0.00529882i
\(378\) 3.45604 0.177760
\(379\) 20.4751 + 8.48108i 1.05174 + 0.435644i 0.840512 0.541793i \(-0.182254\pi\)
0.211226 + 0.977437i \(0.432254\pi\)
\(380\) −12.9596 1.81245i −0.664813 0.0929769i
\(381\) −45.3091 + 18.7677i −2.32126 + 0.961496i
\(382\) 18.6241 18.6241i 0.952890 0.952890i
\(383\) 7.19636 7.19636i 0.367717 0.367717i −0.498927 0.866644i \(-0.666273\pi\)
0.866644 + 0.498927i \(0.166273\pi\)
\(384\) −2.33945 + 0.969032i −0.119385 + 0.0494507i
\(385\) −2.54535 + 18.2000i −0.129723 + 0.927558i
\(386\) 12.6427 + 5.23679i 0.643498 + 0.266546i
\(387\) −38.7762 −1.97111
\(388\) 2.53530 + 1.05015i 0.128710 + 0.0533135i
\(389\) −6.49707 + 6.49707i −0.329414 + 0.329414i −0.852364 0.522949i \(-0.824832\pi\)
0.522949 + 0.852364i \(0.324832\pi\)
\(390\) 3.79620 + 2.23269i 0.192228 + 0.113057i
\(391\) −32.6222 + 6.53729i −1.64977 + 0.330605i
\(392\) 3.97161i 0.200597i
\(393\) 11.9723 + 11.9723i 0.603921 + 0.603921i
\(394\) −2.48851 + 6.00780i −0.125370 + 0.302669i
\(395\) −16.7817 9.86996i −0.844379 0.496612i
\(396\) 7.82145 + 3.23975i 0.393043 + 0.162804i
\(397\) −23.5614 + 9.75944i −1.18251 + 0.489812i −0.885309 0.465003i \(-0.846053\pi\)
−0.297202 + 0.954815i \(0.596053\pi\)
\(398\) 4.25049 + 10.2616i 0.213058 + 0.514367i
\(399\) 34.7081 + 34.7081i 1.73758 + 1.73758i
\(400\) −1.37171 + 4.80816i −0.0685857 + 0.240408i
\(401\) 33.7790 13.9917i 1.68684 0.698712i 0.687226 0.726444i \(-0.258828\pi\)
0.999615 + 0.0277317i \(0.00882842\pi\)
\(402\) −2.01732 + 0.835599i −0.100615 + 0.0416759i
\(403\) −0.559603 + 1.35100i −0.0278758 + 0.0672981i
\(404\) 9.51804i 0.473540i
\(405\) 10.2285 + 13.5547i 0.508257 + 0.673536i
\(406\) 0.809575 0.809575i 0.0401786 0.0401786i
\(407\) 11.4594i 0.568024i
\(408\) −10.2370 + 2.05144i −0.506808 + 0.101561i
\(409\) −14.9024 −0.736875 −0.368438 0.929652i \(-0.620107\pi\)
−0.368438 + 0.929652i \(0.620107\pi\)
\(410\) 5.09306 1.32081i 0.251528 0.0652303i
\(411\) −2.11070 + 5.09568i −0.104113 + 0.251351i
\(412\) 12.8896 0.635027
\(413\) 16.2522 39.2362i 0.799717 1.93069i
\(414\) −10.5364 25.4371i −0.517836 1.25017i
\(415\) −8.01966 1.12158i −0.393669 0.0550564i
\(416\) 0.549994 + 0.549994i 0.0269657 + 0.0269657i
\(417\) 18.0052 18.0052i 0.881720 0.881720i
\(418\) 5.55660 + 13.4148i 0.271782 + 0.656140i
\(419\) 0.678866 + 1.63893i 0.0331648 + 0.0800668i 0.939594 0.342291i \(-0.111203\pi\)
−0.906429 + 0.422357i \(0.861203\pi\)
\(420\) 14.9709 11.2972i 0.730503 0.551245i
\(421\) 25.1213i 1.22434i 0.790728 + 0.612168i \(0.209702\pi\)
−0.790728 + 0.612168i \(0.790298\pi\)
\(422\) 4.39176 + 1.81913i 0.213788 + 0.0885538i
\(423\) −22.3407 22.3407i −1.08624 1.08624i
\(424\) 4.22732 0.205297
\(425\) −9.38848 + 18.3536i −0.455408 + 0.890283i
\(426\) 20.7653 1.00608
\(427\) 32.4381 + 32.4381i 1.56979 + 1.56979i
\(428\) 4.70799 + 1.95011i 0.227569 + 0.0942623i
\(429\) 4.88684i 0.235939i
\(430\) −20.2845 + 15.3069i −0.978204 + 0.738163i
\(431\) −8.98389 21.6890i −0.432739 1.04472i −0.978400 0.206718i \(-0.933722\pi\)
0.545662 0.838006i \(-0.316278\pi\)
\(432\) −0.399286 0.963960i −0.0192106 0.0463786i
\(433\) 20.4541 20.4541i 0.982961 0.982961i −0.0168966 0.999857i \(-0.505379\pi\)
0.999857 + 0.0168966i \(0.00537861\pi\)
\(434\) 4.40339 + 4.40339i 0.211370 + 0.211370i
\(435\) −1.93827 0.271075i −0.0929329 0.0129971i
\(436\) 0.0700661 + 0.169155i 0.00335556 + 0.00810103i
\(437\) 18.0713 43.6280i 0.864468 2.08701i
\(438\) 24.8205 1.18597
\(439\) −0.391020 + 0.944005i −0.0186624 + 0.0450549i −0.932936 0.360042i \(-0.882762\pi\)
0.914274 + 0.405097i \(0.132762\pi\)
\(440\) 5.37042 1.39274i 0.256025 0.0663964i
\(441\) −13.5513 −0.645301
\(442\) 1.78551 + 2.66397i 0.0849278 + 0.126712i
\(443\) 23.1860i 1.10160i −0.834637 0.550801i \(-0.814322\pi\)
0.834637 0.550801i \(-0.185678\pi\)
\(444\) 8.26970 8.26970i 0.392463 0.392463i
\(445\) −4.95213 6.56250i −0.234753 0.311092i
\(446\) 19.0669i 0.902845i
\(447\) −11.8336 + 28.5688i −0.559709 + 1.35126i
\(448\) 3.06021 1.26758i 0.144581 0.0598875i
\(449\) 25.7449 10.6639i 1.21498 0.503259i 0.319166 0.947699i \(-0.396597\pi\)
0.895809 + 0.444440i \(0.146597\pi\)
\(450\) −16.4057 4.68035i −0.773370 0.220634i
\(451\) −4.12829 4.12829i −0.194393 0.194393i
\(452\) 4.61213 + 11.1347i 0.216936 + 0.523731i
\(453\) −27.9651 + 11.5835i −1.31392 + 0.544242i
\(454\) 16.6070 + 6.87885i 0.779405 + 0.322840i
\(455\) −4.96576 2.92055i −0.232798 0.136918i
\(456\) 5.67088 13.6907i 0.265563 0.641126i
\(457\) 21.7244 + 21.7244i 1.01623 + 1.01623i 0.999866 + 0.0163596i \(0.00520767\pi\)
0.0163596 + 0.999866i \(0.494792\pi\)
\(458\) 1.12853i 0.0527326i
\(459\) −0.845286 4.21812i −0.0394546 0.196885i
\(460\) −15.5530 9.14734i −0.725165 0.426497i
\(461\) 2.37157 2.37157i 0.110455 0.110455i −0.649719 0.760174i \(-0.725114\pi\)
0.760174 + 0.649719i \(0.225114\pi\)
\(462\) −19.2268 7.96398i −0.894510 0.370518i
\(463\) −25.7516 −1.19678 −0.598389 0.801206i \(-0.704192\pi\)
−0.598389 + 0.801206i \(0.704192\pi\)
\(464\) −0.319339 0.132275i −0.0148250 0.00614070i
\(465\) 1.47442 10.5425i 0.0683744 0.488898i
\(466\) 20.6654 8.55988i 0.957305 0.396529i
\(467\) −9.24427 + 9.24427i −0.427774 + 0.427774i −0.887869 0.460096i \(-0.847815\pi\)
0.460096 + 0.887869i \(0.347815\pi\)
\(468\) −1.87660 + 1.87660i −0.0867461 + 0.0867461i
\(469\) 2.63883 1.09304i 0.121850 0.0504718i
\(470\) −20.5058 2.86782i −0.945861 0.132283i
\(471\) 21.0087 + 8.70207i 0.968028 + 0.400970i
\(472\) −12.8214 −0.590154
\(473\) 26.0509 + 10.7906i 1.19782 + 0.496154i
\(474\) 15.5898 15.5898i 0.716065 0.716065i
\(475\) −14.2202 25.5727i −0.652469 1.17336i
\(476\) 13.3909 2.68346i 0.613771 0.122996i
\(477\) 14.4238i 0.660421i
\(478\) 7.96602 + 7.96602i 0.364357 + 0.364357i
\(479\) −10.0693 + 24.3093i −0.460076 + 1.11072i 0.508290 + 0.861186i \(0.330278\pi\)
−0.968366 + 0.249535i \(0.919722\pi\)
\(480\) −4.88063 2.87049i −0.222769 0.131019i
\(481\) −3.31890 1.37473i −0.151329 0.0626825i
\(482\) 0.401624 0.166358i 0.0182935 0.00757741i
\(483\) 25.9007 + 62.5298i 1.17852 + 2.84520i
\(484\) 3.42507 + 3.42507i 0.155685 + 0.155685i
\(485\) 1.54038 + 5.93970i 0.0699450 + 0.269708i
\(486\) −20.6578 + 8.55676i −0.937059 + 0.388143i
\(487\) 19.0022 7.87096i 0.861071 0.356667i 0.0919445 0.995764i \(-0.470692\pi\)
0.769126 + 0.639097i \(0.220692\pi\)
\(488\) 5.29999 12.7953i 0.239919 0.579217i
\(489\) 26.9143i 1.21711i
\(490\) −7.08892 + 5.34937i −0.320245 + 0.241660i
\(491\) 2.44344 2.44344i 0.110271 0.110271i −0.649818 0.760089i \(-0.725155\pi\)
0.760089 + 0.649818i \(0.225155\pi\)
\(492\) 5.95835i 0.268623i
\(493\) −1.18610 0.790083i −0.0534192 0.0355836i
\(494\) −4.55182 −0.204796
\(495\) 4.75210 + 18.3241i 0.213591 + 0.823608i
\(496\) 0.719461 1.73693i 0.0323047 0.0779905i
\(497\) −27.1628 −1.21842
\(498\) 3.50926 8.47209i 0.157253 0.379643i
\(499\) 2.11896 + 5.11563i 0.0948579 + 0.229007i 0.964185 0.265229i \(-0.0854477\pi\)
−0.869327 + 0.494237i \(0.835448\pi\)
\(500\) −10.4296 + 4.02775i −0.466427 + 0.180126i
\(501\) −9.62739 9.62739i −0.430120 0.430120i
\(502\) −16.8957 + 16.8957i −0.754094 + 0.754094i
\(503\) 6.60394 + 15.9433i 0.294455 + 0.710878i 0.999998 + 0.00221001i \(0.000703468\pi\)
−0.705542 + 0.708668i \(0.749297\pi\)
\(504\) 4.32504 + 10.4416i 0.192652 + 0.465104i
\(505\) 16.9887 12.8199i 0.755988 0.570476i
\(506\) 20.0214i 0.890061i
\(507\) −28.9975 12.0112i −1.28782 0.533434i
\(508\) −13.6948 13.6948i −0.607610 0.607610i
\(509\) −11.3910 −0.504899 −0.252450 0.967610i \(-0.581236\pi\)
−0.252450 + 0.967610i \(0.581236\pi\)
\(510\) −17.4498 15.5089i −0.772692 0.686747i
\(511\) −32.4674 −1.43627
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 5.64120 + 2.33666i 0.249065 + 0.103166i
\(514\) 29.3559i 1.29483i
\(515\) 17.3611 + 23.0067i 0.765020 + 1.01379i
\(516\) −11.0126 26.5867i −0.484801 1.17041i
\(517\) 8.79213 + 21.2261i 0.386678 + 0.933522i
\(518\) −10.8175 + 10.8175i −0.475293 + 0.475293i
\(519\) 7.57051 + 7.57051i 0.332309 + 0.332309i
\(520\) −0.240895 + 1.72247i −0.0105639 + 0.0755353i
\(521\) 14.4478 + 34.8802i 0.632972 + 1.52813i 0.835869 + 0.548929i \(0.184964\pi\)
−0.202897 + 0.979200i \(0.565036\pi\)
\(522\) 0.451327 1.08960i 0.0197541 0.0476905i
\(523\) 17.2841 0.755782 0.377891 0.925850i \(-0.376649\pi\)
0.377891 + 0.925850i \(0.376649\pi\)
\(524\) −2.55878 + 6.17744i −0.111781 + 0.269863i
\(525\) 40.3285 + 11.5053i 1.76008 + 0.502131i
\(526\) 20.1112 0.876892
\(527\) 4.29737 6.45136i 0.187197 0.281025i
\(528\) 6.28283i 0.273425i
\(529\) 29.7793 29.7793i 1.29475 1.29475i
\(530\) 5.69379 + 7.54534i 0.247322 + 0.327748i
\(531\) 43.7473i 1.89847i
\(532\) −7.41801 + 17.9086i −0.321611 + 0.776438i
\(533\) 1.69089 0.700391i 0.0732407 0.0303373i
\(534\) 8.60141 3.56282i 0.372220 0.154178i
\(535\) 2.86045 + 11.0299i 0.123668 + 0.476864i
\(536\) −0.609741 0.609741i −0.0263368 0.0263368i
\(537\) 5.15558 + 12.4467i 0.222480 + 0.537113i
\(538\) −2.65969 + 1.10168i −0.114668 + 0.0474969i
\(539\) 9.10415 + 3.77106i 0.392144 + 0.162431i
\(540\) 1.18277 2.01104i 0.0508984 0.0865415i
\(541\) −1.67743 + 4.04967i −0.0721182 + 0.174109i −0.955828 0.293926i \(-0.905038\pi\)
0.883710 + 0.468035i \(0.155038\pi\)
\(542\) −13.2789 13.2789i −0.570380 0.570380i
\(543\) 40.0416i 1.71835i
\(544\) −2.29556 3.42497i −0.0984212 0.146844i
\(545\) −0.207551 + 0.352895i −0.00889052 + 0.0151164i
\(546\) 4.61308 4.61308i 0.197422 0.197422i
\(547\) 11.6639 + 4.83135i 0.498713 + 0.206574i 0.617838 0.786306i \(-0.288009\pi\)
−0.119125 + 0.992879i \(0.538009\pi\)
\(548\) −2.17815 −0.0930461
\(549\) 43.6582 + 18.0838i 1.86329 + 0.771799i
\(550\) 9.71933 + 7.70975i 0.414433 + 0.328745i
\(551\) 1.86881 0.774086i 0.0796139 0.0329772i
\(552\) 14.4485 14.4485i 0.614967 0.614967i
\(553\) −20.3929 + 20.3929i −0.867194 + 0.867194i
\(554\) −8.09712 + 3.35394i −0.344014 + 0.142495i
\(555\) 25.8990 + 3.62209i 1.09935 + 0.153749i
\(556\) 9.29033 + 3.84818i 0.393998 + 0.163199i
\(557\) 33.3916 1.41485 0.707423 0.706790i \(-0.249857\pi\)
0.707423 + 0.706790i \(0.249857\pi\)
\(558\) 5.92649 + 2.45483i 0.250888 + 0.103921i
\(559\) −6.25041 + 6.25041i −0.264364 + 0.264364i
\(560\) 6.38429 + 3.75485i 0.269786 + 0.158671i
\(561\) −5.01756 + 25.4142i −0.211842 + 1.07299i
\(562\) 30.4428i 1.28415i
\(563\) 3.53877 + 3.53877i 0.149141 + 0.149141i 0.777734 0.628593i \(-0.216369\pi\)
−0.628593 + 0.777734i \(0.716369\pi\)
\(564\) 8.97295 21.6626i 0.377829 0.912161i
\(565\) −13.6622 + 23.2295i −0.574771 + 0.977272i
\(566\) −8.83075 3.65782i −0.371184 0.153749i
\(567\) 23.2394 9.62609i 0.975965 0.404258i
\(568\) 3.13819 + 7.57626i 0.131676 + 0.317893i
\(569\) −0.875778 0.875778i −0.0367145 0.0367145i 0.688511 0.725226i \(-0.258265\pi\)
−0.725226 + 0.688511i \(0.758265\pi\)
\(570\) 32.0746 8.31810i 1.34346 0.348407i
\(571\) −21.1567 + 8.76339i −0.885380 + 0.366736i −0.778581 0.627544i \(-0.784060\pi\)
−0.106799 + 0.994281i \(0.534060\pi\)
\(572\) 1.78298 0.738533i 0.0745500 0.0308796i
\(573\) −25.5227 + 61.6173i −1.06623 + 2.57410i
\(574\) 7.79405i 0.325317i
\(575\) −4.62135 40.0812i −0.192724 1.67150i
\(576\) 2.41268 2.41268i 0.100528 0.100528i
\(577\) 8.94035i 0.372192i −0.982532 0.186096i \(-0.940416\pi\)
0.982532 0.186096i \(-0.0595835\pi\)
\(578\) −6.55035 15.6873i −0.272459 0.652508i
\(579\) −34.6517 −1.44007
\(580\) −0.194022 0.748149i −0.00805632 0.0310652i
\(581\) −4.59041 + 11.0822i −0.190442 + 0.459769i
\(582\) −6.94883 −0.288038
\(583\) 4.01386 9.69032i 0.166237 0.401332i
\(584\) 3.75104 + 9.05580i 0.155219 + 0.374732i
\(585\) −5.87715 0.821944i −0.242990 0.0339832i
\(586\) 3.78266 + 3.78266i 0.156260 + 0.156260i
\(587\) 2.61621 2.61621i 0.107983 0.107983i −0.651051 0.759034i \(-0.725672\pi\)
0.759034 + 0.651051i \(0.225672\pi\)
\(588\) −3.84862 9.29139i −0.158714 0.383170i
\(589\) 4.21036 + 10.1647i 0.173485 + 0.418829i
\(590\) −17.2692 22.8849i −0.710962 0.942158i
\(591\) 16.4664i 0.677337i
\(592\) 4.26699 + 1.76745i 0.175372 + 0.0726416i
\(593\) −29.8060 29.8060i −1.22399 1.22399i −0.966202 0.257785i \(-0.917007\pi\)
−0.257785 0.966202i \(-0.582993\pi\)
\(594\) −2.58882 −0.106220
\(595\) 22.8259 + 20.2870i 0.935772 + 0.831687i
\(596\) −12.2117 −0.500213
\(597\) −19.8876 19.8876i −0.813945 0.813945i
\(598\) −5.79864 2.40188i −0.237124 0.0982200i
\(599\) 18.0176i 0.736178i −0.929790 0.368089i \(-0.880012\pi\)
0.929790 0.368089i \(-0.119988\pi\)
\(600\) −1.45021 12.5777i −0.0592044 0.513482i
\(601\) 3.49949 + 8.44852i 0.142747 + 0.344622i 0.979042 0.203657i \(-0.0652829\pi\)
−0.836295 + 0.548280i \(0.815283\pi\)
\(602\) 14.4054 + 34.7777i 0.587120 + 1.41743i
\(603\) 2.08046 2.08046i 0.0847230 0.0847230i
\(604\) −8.45256 8.45256i −0.343930 0.343930i
\(605\) −1.50016 + 10.7266i −0.0609903 + 0.436099i
\(606\) 9.22328 + 22.2670i 0.374670 + 0.904534i
\(607\) −5.67532 + 13.7014i −0.230354 + 0.556124i −0.996219 0.0868777i \(-0.972311\pi\)
0.765865 + 0.643001i \(0.222311\pi\)
\(608\) 5.85211 0.237334
\(609\) −1.10946 + 2.67847i −0.0449574 + 0.108537i
\(610\) 29.9769 7.77409i 1.21373 0.314764i
\(611\) −7.20228 −0.291373
\(612\) 11.6862 7.83255i 0.472385 0.316612i
\(613\) 21.3405i 0.861933i −0.902368 0.430967i \(-0.858173\pi\)
0.902368 0.430967i \(-0.141827\pi\)
\(614\) −13.8852 + 13.8852i −0.560363 + 0.560363i
\(615\) −10.6350 + 8.02531i −0.428846 + 0.323612i
\(616\) 8.21850i 0.331133i
\(617\) 5.10375 12.3215i 0.205469 0.496047i −0.787230 0.616659i \(-0.788486\pi\)
0.992700 + 0.120612i \(0.0384858\pi\)
\(618\) −30.1547 + 12.4905i −1.21300 + 0.502440i
\(619\) −15.1303 + 6.26719i −0.608139 + 0.251900i −0.665433 0.746458i \(-0.731753\pi\)
0.0572934 + 0.998357i \(0.481753\pi\)
\(620\) 4.06929 1.05531i 0.163426 0.0423824i
\(621\) 5.95342 + 5.95342i 0.238903 + 0.238903i
\(622\) −5.25670 12.6908i −0.210774 0.508855i
\(623\) −11.2514 + 4.66048i −0.450778 + 0.186718i
\(624\) −1.81964 0.753721i −0.0728441 0.0301730i
\(625\) −21.2368 13.1908i −0.849472 0.527633i
\(626\) 2.35732 5.69107i 0.0942174 0.227461i
\(627\) −25.9988 25.9988i −1.03829 1.03829i
\(628\) 8.98017i 0.358348i
\(629\) 15.8486 + 10.5570i 0.631924 + 0.420937i
\(630\) −12.8117 + 21.7835i −0.510431 + 0.867875i
\(631\) 9.58945 9.58945i 0.381750 0.381750i −0.489982 0.871732i \(-0.662997\pi\)
0.871732 + 0.489982i \(0.162997\pi\)
\(632\) 8.04403 + 3.33195i 0.319974 + 0.132538i
\(633\) −12.0371 −0.478432
\(634\) −4.69756 1.94579i −0.186564 0.0772773i
\(635\) 5.99828 42.8895i 0.238034 1.70202i
\(636\) −9.88961 + 4.09641i −0.392149 + 0.162433i
\(637\) −2.18436 + 2.18436i −0.0865476 + 0.0865476i
\(638\) −0.606428 + 0.606428i −0.0240087 + 0.0240087i
\(639\) −25.8506 + 10.7077i −1.02263 + 0.423588i
\(640\) 0.309710 2.21452i 0.0122423 0.0875364i
\(641\) 22.9560 + 9.50869i 0.906707 + 0.375571i 0.786795 0.617214i \(-0.211739\pi\)
0.119912 + 0.992785i \(0.461739\pi\)
\(642\) −12.9038 −0.509274
\(643\) 6.62075 + 2.74240i 0.261097 + 0.108150i 0.509392 0.860535i \(-0.329870\pi\)
−0.248295 + 0.968684i \(0.579870\pi\)
\(644\) −18.8998 + 18.8998i −0.744758 + 0.744758i
\(645\) 32.6216 55.4659i 1.28448 2.18397i
\(646\) 23.6719 + 4.67358i 0.931359 + 0.183880i
\(647\) 32.6880i 1.28510i 0.766244 + 0.642550i \(0.222123\pi\)
−0.766244 + 0.642550i \(0.777877\pi\)
\(648\) −5.36983 5.36983i −0.210947 0.210947i
\(649\) −12.1740 + 29.3906i −0.477871 + 1.15368i
\(650\) −3.39889 + 1.89002i −0.133316 + 0.0741329i
\(651\) −14.5685 6.03449i −0.570986 0.236510i
\(652\) 9.81976 4.06748i 0.384571 0.159295i
\(653\) −3.25759 7.86453i −0.127480 0.307763i 0.847234 0.531219i \(-0.178266\pi\)
−0.974714 + 0.223456i \(0.928266\pi\)
\(654\) −0.327832 0.327832i −0.0128193 0.0128193i
\(655\) −14.4725 + 3.75324i −0.565488 + 0.146651i
\(656\) −2.17392 + 0.900466i −0.0848772 + 0.0351573i
\(657\) −30.8988 + 12.7987i −1.20548 + 0.499325i
\(658\) −11.7374 + 28.3366i −0.457572 + 1.10468i
\(659\) 10.0536i 0.391632i −0.980641 0.195816i \(-0.937264\pi\)
0.980641 0.195816i \(-0.0627355\pi\)
\(660\) −11.2142 + 8.46236i −0.436512 + 0.329397i
\(661\) 19.9368 19.9368i 0.775451 0.775451i −0.203603 0.979054i \(-0.565265\pi\)
0.979054 + 0.203603i \(0.0652650\pi\)
\(662\) 3.25455i 0.126492i
\(663\) −6.75857 4.50202i −0.262481 0.174844i
\(664\) 3.62140 0.140538
\(665\) −41.9564 + 10.8808i −1.62700 + 0.421940i
\(666\) −6.03061 + 14.5592i −0.233681 + 0.564156i
\(667\) 2.78917 0.107997
\(668\) 2.05762 4.96753i 0.0796116 0.192200i
\(669\) −18.4765 44.6061i −0.714341 1.72457i
\(670\) 0.267064 1.90958i 0.0103176 0.0737737i
\(671\) −24.2984 24.2984i −0.938030 0.938030i
\(672\) −5.93087 + 5.93087i −0.228788 + 0.228788i
\(673\) 1.83418 + 4.42810i 0.0707025 + 0.170691i 0.955280 0.295702i \(-0.0955534\pi\)
−0.884578 + 0.466393i \(0.845553\pi\)
\(674\) −2.22732 5.37723i −0.0857933 0.207123i
\(675\) 5.18258 0.597551i 0.199478 0.0229998i
\(676\) 12.3950i 0.476731i
\(677\) 11.5273 + 4.77476i 0.443030 + 0.183509i 0.593036 0.805176i \(-0.297929\pi\)
−0.150006 + 0.988685i \(0.547929\pi\)
\(678\) −21.5797 21.5797i −0.828763 0.828763i
\(679\) 9.08968 0.348830
\(680\) 3.02133 8.71043i 0.115863 0.334030i
\(681\) −45.5171 −1.74422
\(682\) −3.29845 3.29845i −0.126304 0.126304i
\(683\) 10.4418 + 4.32512i 0.399543 + 0.165496i 0.573401 0.819275i \(-0.305624\pi\)
−0.173858 + 0.984771i \(0.555624\pi\)
\(684\) 19.9677i 0.763482i
\(685\) −2.93376 3.88778i −0.112093 0.148544i
\(686\) −3.83872 9.26749i −0.146563 0.353834i
\(687\) 1.09358 + 2.64013i 0.0417226 + 0.100727i
\(688\) 8.03592 8.03592i 0.306366 0.306366i
\(689\) 2.32500 + 2.32500i 0.0885755 + 0.0885755i
\(690\) 45.2496 + 6.32836i 1.72262 + 0.240916i
\(691\) −9.79890 23.6566i −0.372768 0.899941i −0.993279 0.115744i \(-0.963075\pi\)
0.620511 0.784197i \(-0.286925\pi\)
\(692\) −1.61801 + 3.90622i −0.0615076 + 0.148492i
\(693\) 28.0419 1.06522
\(694\) −4.68855 + 11.3192i −0.177975 + 0.429670i
\(695\) 5.64455 + 21.7654i 0.214110 + 0.825608i
\(696\) 0.875257 0.0331765
\(697\) −9.51267 + 1.90628i −0.360318 + 0.0722056i
\(698\) 5.77639i 0.218640i
\(699\) −40.0508 + 40.0508i −1.51486 + 1.51486i
\(700\) 1.89700 + 16.4527i 0.0716997 + 0.621854i
\(701\) 22.2922i 0.841966i −0.907068 0.420983i \(-0.861685\pi\)
0.907068 0.420983i \(-0.138315\pi\)
\(702\) 0.310568 0.749777i 0.0117216 0.0282985i
\(703\) −24.9709 + 10.3433i −0.941795 + 0.390104i
\(704\) −2.29231 + 0.949504i −0.0863945 + 0.0357858i
\(705\) 50.7512 13.1616i 1.91140 0.495695i
\(706\) 8.85861 + 8.85861i 0.333398 + 0.333398i
\(707\) −12.0649 29.1272i −0.453746 1.09544i
\(708\) 29.9951 12.4244i 1.12728 0.466936i
\(709\) −27.3200 11.3163i −1.02602 0.424993i −0.194748 0.980853i \(-0.562389\pi\)
−0.831276 + 0.555860i \(0.812389\pi\)
\(710\) −9.29602 + 15.8058i −0.348873 + 0.593182i
\(711\) −11.3688 + 27.4466i −0.426362 + 1.02933i
\(712\) 2.59981 + 2.59981i 0.0974319 + 0.0974319i
\(713\) 15.1707i 0.568147i
\(714\) −28.7270 + 19.2540i −1.07508 + 0.720564i
\(715\) 3.71970 + 2.18770i 0.139109 + 0.0818152i
\(716\) −3.76205 + 3.76205i −0.140594 + 0.140594i
\(717\) −26.3554 10.9168i −0.984261 0.407694i
\(718\) 6.07488 0.226713
\(719\) −17.1054 7.08529i −0.637924 0.264237i 0.0401916 0.999192i \(-0.487203\pi\)
−0.678116 + 0.734955i \(0.737203\pi\)
\(720\) 7.55603 + 1.05674i 0.281597 + 0.0393825i
\(721\) 39.4449 16.3386i 1.46901 0.608482i
\(722\) −10.7814 + 10.7814i −0.401241 + 0.401241i
\(723\) −0.778374 + 0.778374i −0.0289480 + 0.0289480i
\(724\) 14.6093 6.05136i 0.542949 0.224897i
\(725\) 1.07404 1.35399i 0.0398888 0.0502860i
\(726\) −11.3318 4.69377i −0.420561 0.174202i
\(727\) −18.3747 −0.681480 −0.340740 0.940158i \(-0.610678\pi\)
−0.340740 + 0.940158i \(0.610678\pi\)
\(728\) 2.38025 + 0.985934i 0.0882181 + 0.0365411i
\(729\) 23.9267 23.9267i 0.886176 0.886176i
\(730\) −11.1114 + 18.8925i −0.411251 + 0.699242i
\(731\) 38.9231 26.0879i 1.43962 0.964895i
\(732\) 35.0699i 1.29622i
\(733\) −0.587977 0.587977i −0.0217174 0.0217174i 0.696165 0.717882i \(-0.254888\pi\)
−0.717882 + 0.696165i \(0.754888\pi\)
\(734\) −3.76510 + 9.08975i −0.138972 + 0.335509i
\(735\) 11.4005 19.3840i 0.420512 0.714988i
\(736\) 7.45510 + 3.08800i 0.274799 + 0.113825i
\(737\) −1.97666 + 0.818761i −0.0728113 + 0.0301594i
\(738\) −3.07243 7.41751i −0.113098 0.273042i
\(739\) −2.33228 2.33228i −0.0857943 0.0857943i 0.662907 0.748702i \(-0.269322\pi\)
−0.748702 + 0.662907i \(0.769322\pi\)
\(740\) 2.59251 + 9.99671i 0.0953025 + 0.367487i
\(741\) 10.6488 4.41086i 0.391192 0.162037i
\(742\) 12.9365 5.35846i 0.474913 0.196715i
\(743\) 7.05841 17.0405i 0.258948 0.625156i −0.739922 0.672693i \(-0.765137\pi\)
0.998869 + 0.0475376i \(0.0151374\pi\)
\(744\) 4.76064i 0.174534i
\(745\) −16.4480 21.7967i −0.602609 0.798570i
\(746\) −7.21651 + 7.21651i −0.264215 + 0.264215i
\(747\) 12.3564i 0.452097i
\(748\) −10.0307 + 2.01010i −0.366759 + 0.0734964i
\(749\) 16.8793 0.616758
\(750\) 20.4966 19.5294i 0.748429 0.713112i
\(751\) 6.27632 15.1524i 0.229026 0.552918i −0.767033 0.641607i \(-0.778268\pi\)
0.996059 + 0.0886896i \(0.0282679\pi\)
\(752\) 9.25971 0.337667
\(753\) 23.1542 55.8992i 0.843786 2.03708i
\(754\) −0.102884 0.248385i −0.00374683 0.00904565i
\(755\) 3.70218 26.4717i 0.134736 0.963405i
\(756\) −2.44379 2.44379i −0.0888798 0.0888798i
\(757\) 1.27297 1.27297i 0.0462668 0.0462668i −0.683595 0.729862i \(-0.739584\pi\)
0.729862 + 0.683595i \(0.239584\pi\)
\(758\) −8.48108 20.4751i −0.308047 0.743691i
\(759\) −19.4014 46.8391i −0.704226 1.70015i
\(760\) 7.88221 + 10.4454i 0.285918 + 0.378895i
\(761\) 9.64351i 0.349577i 0.984606 + 0.174788i \(0.0559241\pi\)
−0.984606 + 0.174788i \(0.944076\pi\)
\(762\) 45.3091 + 18.7677i 1.64138 + 0.679881i
\(763\) 0.428833 + 0.428833i 0.0155248 + 0.0155248i
\(764\) −26.3384 −0.952890
\(765\) 29.7204 + 10.3089i 1.07454 + 0.372719i
\(766\) −10.1772 −0.367717
\(767\) −7.05171 7.05171i −0.254622 0.254622i
\(768\) 2.33945 + 0.969032i 0.0844176 + 0.0349669i
\(769\) 33.9195i 1.22317i 0.791179 + 0.611585i \(0.209468\pi\)
−0.791179 + 0.611585i \(0.790532\pi\)
\(770\) 14.6692 11.0695i 0.528640 0.398917i
\(771\) 28.4468 + 68.6767i 1.02449 + 2.47333i
\(772\) −5.23679 12.6427i −0.188476 0.455022i
\(773\) −16.9057 + 16.9057i −0.608055 + 0.608055i −0.942438 0.334382i \(-0.891472\pi\)
0.334382 + 0.942438i \(0.391472\pi\)
\(774\) 27.4189 + 27.4189i 0.985553 + 0.985553i
\(775\) 7.36455 + 5.84185i 0.264542 + 0.209846i
\(776\) −1.05015 2.53530i −0.0376983 0.0910119i
\(777\) 14.8245 35.7895i 0.531825 1.28394i
\(778\) 9.18824 0.329414
\(779\) 5.26962 12.7220i 0.188804 0.455813i
\(780\) −1.10557 4.26307i −0.0395856 0.152642i
\(781\) 20.3468 0.728067
\(782\) 27.6899 + 18.4448i 0.990189 + 0.659584i
\(783\) 0.360646i 0.0128884i
\(784\) 2.80835 2.80835i 0.100298 0.100298i
\(785\) −16.0287 + 12.0954i −0.572088 + 0.431704i
\(786\) 16.9313i 0.603921i
\(787\) −13.9830 + 33.7579i −0.498439 + 1.20334i 0.451885 + 0.892076i \(0.350752\pi\)
−0.950324 + 0.311262i \(0.899248\pi\)
\(788\) 6.00780 2.48851i 0.214019 0.0886496i
\(789\) −47.0492 + 19.4884i −1.67500 + 0.693807i
\(790\) 4.88734 + 18.8456i 0.173884 + 0.670495i
\(791\) 28.2281 + 28.2281i 1.00368 + 1.00368i
\(792\) −3.23975 7.82145i −0.115120 0.277923i
\(793\) 9.95231 4.12238i 0.353417 0.146390i
\(794\) 23.5614 + 9.75944i 0.836162 + 0.346349i
\(795\) −20.6320 12.1345i −0.731742 0.430365i
\(796\) 4.25049 10.2616i 0.150655 0.363712i
\(797\) −10.0544 10.0544i −0.356147 0.356147i 0.506244 0.862390i \(-0.331034\pi\)
−0.862390 + 0.506244i \(0.831034\pi\)
\(798\) 49.0847i 1.73758i
\(799\) 37.4557 + 7.39494i 1.32509 + 0.261614i
\(800\) 4.36983 2.42993i 0.154497 0.0859112i
\(801\) −8.87066 + 8.87066i −0.313429 + 0.313429i
\(802\) −33.7790 13.9917i −1.19278 0.494064i
\(803\) 24.3203 0.858245
\(804\) 2.01732 + 0.835599i 0.0711452 + 0.0294693i
\(805\) −59.1905 8.27804i −2.08619 0.291763i
\(806\) 1.35100 0.559603i 0.0475870 0.0197112i
\(807\) 5.15466 5.15466i 0.181453 0.181453i
\(808\) −6.73027 + 6.73027i −0.236770 + 0.236770i
\(809\) −4.32037 + 1.78955i −0.151896 + 0.0629174i −0.457336 0.889294i \(-0.651196\pi\)
0.305440 + 0.952211i \(0.401196\pi\)
\(810\) 2.35196 16.8172i 0.0826394 0.590897i
\(811\) 40.2894 + 16.6884i 1.41475 + 0.586009i 0.953536 0.301280i \(-0.0974137\pi\)
0.461215 + 0.887288i \(0.347414\pi\)
\(812\) −1.14491 −0.0401786
\(813\) 43.9332 + 18.1977i 1.54080 + 0.638221i
\(814\) 8.10305 8.10305i 0.284012 0.284012i
\(815\) 20.4863 + 12.0488i 0.717603 + 0.422050i
\(816\) 8.68924 + 5.78807i 0.304184 + 0.202623i
\(817\) 66.5063i 2.32676i
\(818\) 10.5376 + 10.5376i 0.368438 + 0.368438i
\(819\) −3.36405 + 8.12154i −0.117549 + 0.283790i
\(820\) −4.53529 2.66738i −0.158379 0.0931489i
\(821\) 32.1854 + 13.3316i 1.12328 + 0.465277i 0.865490 0.500925i \(-0.167007\pi\)
0.257786 + 0.966202i \(0.417007\pi\)
\(822\) 5.09568 2.11070i 0.177732 0.0736191i
\(823\) 11.8633 + 28.6405i 0.413528 + 0.998344i 0.984183 + 0.177154i \(0.0566892\pi\)
−0.570656 + 0.821190i \(0.693311\pi\)
\(824\) −9.11435 9.11435i −0.317513 0.317513i
\(825\) −30.2089 8.61825i −1.05174 0.300049i
\(826\) −39.2362 + 16.2522i −1.36520 + 0.565485i
\(827\) 24.0440 9.95934i 0.836091 0.346320i 0.0767796 0.997048i \(-0.475536\pi\)
0.759311 + 0.650728i \(0.225536\pi\)
\(828\) −10.5364 + 25.4371i −0.366165 + 0.884002i
\(829\) 31.3054i 1.08728i 0.839318 + 0.543641i \(0.182955\pi\)
−0.839318 + 0.543641i \(0.817045\pi\)
\(830\) 4.87767 + 6.46383i 0.169307 + 0.224363i
\(831\) 15.6927 15.6927i 0.544375 0.544375i
\(832\) 0.777809i 0.0269657i
\(833\) 13.6027 9.11707i 0.471304 0.315888i
\(834\) −25.4633 −0.881720
\(835\) 11.6379 3.01814i 0.402747 0.104447i
\(836\) 5.55660 13.4148i 0.192179 0.463961i
\(837\) −1.96160 −0.0678029
\(838\) 0.678866 1.63893i 0.0234510 0.0566158i
\(839\) −11.2215 27.0910i −0.387408 0.935285i −0.990487 0.137604i \(-0.956060\pi\)
0.603080 0.797681i \(-0.293940\pi\)
\(840\) −18.5743 2.59769i −0.640874 0.0896290i
\(841\) −20.4216 20.4216i −0.704194 0.704194i
\(842\) 17.7634 17.7634i 0.612168 0.612168i
\(843\) 29.5000 + 71.2193i 1.01603 + 2.45292i
\(844\) −1.81913 4.39176i −0.0626170 0.151171i
\(845\) 22.1238 16.6949i 0.761083 0.574321i
\(846\) 31.5946i 1.08624i
\(847\) 14.8229 + 6.13987i 0.509323 + 0.210968i
\(848\) −2.98917 2.98917i −0.102648 0.102648i
\(849\) 24.2036 0.830666
\(850\) 19.6166 6.33933i 0.672845 0.217437i
\(851\) −37.2687 −1.27755
\(852\) −14.6833 14.6833i −0.503041 0.503041i
\(853\) 48.0043 + 19.8840i 1.64364 + 0.680816i 0.996658 0.0816920i \(-0.0260324\pi\)
0.646978 + 0.762508i \(0.276032\pi\)
\(854\) 45.8745i 1.56979i
\(855\) −35.6402 + 26.8945i −1.21887 + 0.919771i
\(856\) −1.95011 4.70799i −0.0666535 0.160916i
\(857\) −22.0112 53.1397i −0.751888 1.81522i −0.548567 0.836107i \(-0.684826\pi\)
−0.203321 0.979112i \(-0.565174\pi\)
\(858\) −3.45552 + 3.45552i −0.117970 + 0.117970i
\(859\) −34.5161 34.5161i −1.17768 1.17768i −0.980335 0.197341i \(-0.936769\pi\)
−0.197341 0.980335i \(-0.563231\pi\)
\(860\) 25.1669 + 3.51969i 0.858183 + 0.120021i
\(861\) 7.55268 + 18.2338i 0.257395 + 0.621405i
\(862\) −8.98389 + 21.6890i −0.305993 + 0.738731i
\(863\) 19.9590 0.679414 0.339707 0.940531i \(-0.389672\pi\)
0.339707 + 0.940531i \(0.389672\pi\)
\(864\) −0.399286 + 0.963960i −0.0135840 + 0.0327946i
\(865\) −9.15151 + 2.37332i −0.311161 + 0.0806952i
\(866\) −28.9264 −0.982961
\(867\) 30.5258 + 30.3523i 1.03671 + 1.03082i
\(868\) 6.22734i 0.211370i
\(869\) 15.2757 15.2757i 0.518192 0.518192i
\(870\) 1.17888 + 1.56224i 0.0399679 + 0.0529650i
\(871\) 0.670707i 0.0227260i
\(872\) 0.0700661 0.169155i 0.00237274 0.00572830i
\(873\) 8.65055 3.58317i 0.292777 0.121272i
\(874\) −43.6280 + 18.0713i −1.47574 + 0.611271i
\(875\) −26.8113 + 25.5461i −0.906388 + 0.863617i
\(876\) −17.5507 17.5507i −0.592984 0.592984i
\(877\) 5.21753 + 12.5962i 0.176184 + 0.425345i 0.987160 0.159734i \(-0.0510636\pi\)
−0.810977 + 0.585079i \(0.801064\pi\)
\(878\) 0.944005 0.391020i 0.0318586 0.0131963i
\(879\) −12.5149 5.18383i −0.422116 0.174846i
\(880\) −4.78228 2.81264i −0.161211 0.0948141i
\(881\) 6.20068 14.9698i 0.208906 0.504344i −0.784345 0.620324i \(-0.787001\pi\)
0.993251 + 0.115980i \(0.0370010\pi\)
\(882\) 9.58223 + 9.58223i 0.322651 + 0.322651i
\(883\) 5.19724i 0.174901i 0.996169 + 0.0874506i \(0.0278720\pi\)
−0.996169 + 0.0874506i \(0.972128\pi\)
\(884\) 0.621170 3.14626i 0.0208922 0.105820i
\(885\) 62.5766 + 36.8037i 2.10349 + 1.23714i
\(886\) −16.3950 + 16.3950i −0.550801 + 0.550801i
\(887\) 3.27376 + 1.35604i 0.109922 + 0.0455312i 0.436967 0.899478i \(-0.356053\pi\)
−0.327045 + 0.945009i \(0.606053\pi\)
\(888\) −11.6951 −0.392463
\(889\) −59.2683 24.5497i −1.98780 0.823372i
\(890\) −1.13870 + 8.14207i −0.0381694 + 0.272923i
\(891\) −17.4080 + 7.21061i −0.583188 + 0.241565i
\(892\) 13.4824 13.4824i 0.451423 0.451423i
\(893\) −38.3173 + 38.3173i −1.28224 + 1.28224i
\(894\) 28.5688 11.8336i 0.955482 0.395774i
\(895\) −11.7820 1.64776i −0.393828 0.0550785i
\(896\) −3.06021 1.26758i −0.102234 0.0423468i
\(897\) 15.8931 0.530656
\(898\) −25.7449 10.6639i −0.859117 0.355858i
\(899\) −0.459504 + 0.459504i −0.0153253 + 0.0153253i
\(900\) 8.29105 + 14.9101i 0.276368 + 0.497002i
\(901\) −9.70406 14.4785i −0.323289 0.482347i
\(902\) 5.83828i 0.194393i
\(903\) −67.4014 67.4014i −2.24298 2.24298i
\(904\) 4.61213 11.1347i 0.153397 0.370334i
\(905\) 30.4783 + 17.9255i 1.01313 + 0.595863i
\(906\) 27.9651 + 11.5835i 0.929080 + 0.384837i
\(907\) −40.4620 + 16.7599i −1.34352 + 0.556504i −0.934481 0.356013i \(-0.884136\pi\)
−0.409038 + 0.912517i \(0.634136\pi\)
\(908\) −6.87885 16.6070i −0.228283 0.551123i
\(909\) −22.9640 22.9640i −0.761668 0.761668i
\(910\) 1.44618 + 5.57647i 0.0479404 + 0.184858i
\(911\) −21.0931 + 8.73705i −0.698846 + 0.289471i −0.703680 0.710517i \(-0.748461\pi\)
0.00483423 + 0.999988i \(0.498461\pi\)
\(912\) −13.6907 + 5.67088i −0.453345 + 0.187781i
\(913\) 3.43854 8.30136i 0.113799 0.274735i
\(914\) 30.7230i 1.01623i
\(915\) −62.5961 + 47.2356i −2.06936 + 1.56156i
\(916\) −0.797989 + 0.797989i −0.0263663 + 0.0263663i
\(917\) 22.1477i 0.731381i
\(918\) −2.38495 + 3.58037i −0.0787152 + 0.118170i
\(919\) 46.6106 1.53754 0.768771 0.639524i \(-0.220868\pi\)
0.768771 + 0.639524i \(0.220868\pi\)
\(920\) 4.52952 + 17.4658i 0.149334 + 0.575831i
\(921\) 19.0286 45.9391i 0.627013 1.51374i
\(922\) −3.35390 −0.110455
\(923\) −2.44091 + 5.89289i −0.0803436 + 0.193967i
\(924\) 7.96398 + 19.2268i 0.261996 + 0.632514i
\(925\) −14.3512 + 18.0919i −0.471866 + 0.594860i
\(926\) 18.2091 + 18.2091i 0.598389 + 0.598389i
\(927\) 31.0986 31.0986i 1.02141 1.02141i
\(928\) 0.132275 + 0.319339i 0.00434213 + 0.0104828i
\(929\) 2.87430 + 6.93918i 0.0943028 + 0.227667i 0.963991 0.265934i \(-0.0856803\pi\)
−0.869688 + 0.493601i \(0.835680\pi\)
\(930\) −8.49726 + 6.41212i −0.278636 + 0.210262i
\(931\) 23.2423i 0.761736i
\(932\) −20.6654 8.55988i −0.676917 0.280388i
\(933\) 24.5956 + 24.5956i 0.805223 + 0.805223i
\(934\) 13.0734 0.427774
\(935\) −17.0982 15.1964i −0.559171 0.496975i
\(936\) 2.65392 0.0867461
\(937\) −29.2503 29.2503i −0.955567 0.955567i 0.0434874 0.999054i \(-0.486153\pi\)
−0.999054 + 0.0434874i \(0.986153\pi\)
\(938\) −2.63883 1.09304i −0.0861607 0.0356889i
\(939\) 15.5983i 0.509031i
\(940\) 12.4719 + 16.5276i 0.406789 + 0.539072i
\(941\) −7.76691 18.7510i −0.253194 0.611264i 0.745264 0.666769i \(-0.232323\pi\)
−0.998458 + 0.0555046i \(0.982323\pi\)
\(942\) −8.70207 21.0087i −0.283529 0.684499i
\(943\) 13.4261 13.4261i 0.437215 0.437215i
\(944\) 9.06612 + 9.06612i 0.295077 + 0.295077i
\(945\) 1.07037 7.65346i 0.0348191 0.248967i
\(946\) −10.7906 26.0509i −0.350834 0.846988i
\(947\) 10.0051 24.1545i 0.325123 0.784915i −0.673818 0.738897i \(-0.735347\pi\)
0.998941 0.0460180i \(-0.0146531\pi\)
\(948\) −22.0474 −0.716065
\(949\) −2.91759 + 7.04369i −0.0947090 + 0.228648i
\(950\) −8.02741 + 28.1379i −0.260444 + 0.912913i
\(951\) 12.8752 0.417508
\(952\) −11.3663 7.57131i −0.368384 0.245388i
\(953\) 10.2410i 0.331738i −0.986148 0.165869i \(-0.946957\pi\)
0.986148 0.165869i \(-0.0530430\pi\)
\(954\) 10.1992 10.1992i 0.330211 0.330211i
\(955\) −35.4752 47.0113i −1.14795 1.52125i
\(956\) 11.2657i 0.364357i
\(957\) 0.831060 2.00636i 0.0268643 0.0648563i
\(958\) 24.3093 10.0693i 0.785399 0.325323i
\(959\) −6.66559 + 2.76098i −0.215243 + 0.0891567i
\(960\) 1.42139 + 5.48087i 0.0458750 + 0.176894i
\(961\) 19.4210 + 19.4210i 0.626484 + 0.626484i
\(962\) 1.37473 + 3.31890i 0.0443232 + 0.107006i
\(963\) 16.0639 6.65388i 0.517651 0.214418i
\(964\) −0.401624 0.166358i −0.0129355 0.00535804i
\(965\) 15.5125 26.3757i 0.499366 0.849062i
\(966\) 25.9007 62.5298i 0.833341 2.01186i
\(967\) 1.61879 + 1.61879i 0.0520569 + 0.0520569i 0.732656 0.680599i \(-0.238280\pi\)
−0.680599 + 0.732656i \(0.738280\pi\)
\(968\) 4.84378i 0.155685i
\(969\) −59.9081 + 12.0052i −1.92452 + 0.385663i
\(970\) 3.11079 5.28921i 0.0998814 0.169826i
\(971\) −9.60331 + 9.60331i −0.308185 + 0.308185i −0.844205 0.536020i \(-0.819927\pi\)
0.536020 + 0.844205i \(0.319927\pi\)
\(972\) 20.6578 + 8.55676i 0.662601 + 0.274458i
\(973\) 33.3082 1.06781
\(974\) −19.0022 7.87096i −0.608869 0.252202i
\(975\) 6.12004 7.71525i 0.195998 0.247086i
\(976\) −12.7953 + 5.29999i −0.409568 + 0.169649i
\(977\) 17.0701 17.0701i 0.546120 0.546120i −0.379196 0.925316i \(-0.623799\pi\)
0.925316 + 0.379196i \(0.123799\pi\)
\(978\) −19.0313 + 19.0313i −0.608554 + 0.608554i
\(979\) 8.42808 3.49103i 0.269363 0.111574i
\(980\) 8.79520 + 1.23005i 0.280952 + 0.0392924i
\(981\) 0.577163 + 0.239069i 0.0184274 + 0.00763288i
\(982\) −3.45555 −0.110271
\(983\) −51.6554 21.3964i −1.64755 0.682439i −0.650525 0.759485i \(-0.725451\pi\)
−0.997028 + 0.0770464i \(0.975451\pi\)
\(984\) 4.21319 4.21319i 0.134312 0.134312i
\(985\) 12.5337 + 7.37153i 0.399356 + 0.234876i
\(986\) 0.280025 + 1.39737i 0.00891781 + 0.0445014i
\(987\) 77.6660i 2.47214i
\(988\) 3.21862 + 3.21862i 0.102398 + 0.102398i
\(989\) −35.0936 + 84.7235i −1.11591 + 2.69405i
\(990\) 9.59686 16.3173i 0.305008 0.518599i
\(991\) 28.9890 + 12.0076i 0.920866 + 0.381435i 0.792206 0.610253i \(-0.208932\pi\)
0.128660 + 0.991689i \(0.458932\pi\)
\(992\) −1.73693 + 0.719461i −0.0551476 + 0.0228429i
\(993\) 3.15376 + 7.61386i 0.100082 + 0.241618i
\(994\) 19.2070 + 19.2070i 0.609210 + 0.609210i
\(995\) 24.0409 6.23466i 0.762146 0.197652i
\(996\) −8.47209 + 3.50926i −0.268448 + 0.111195i
\(997\) 44.1910 18.3045i 1.39954 0.579710i 0.449910 0.893074i \(-0.351456\pi\)
0.949633 + 0.313365i \(0.101456\pi\)
\(998\) 2.11896 5.11563i 0.0670746 0.161933i
\(999\) 4.81893i 0.152464i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 170.2.n.b.59.5 yes 20
5.2 odd 4 850.2.l.h.501.5 20
5.3 odd 4 850.2.l.i.501.1 20
5.4 even 2 170.2.n.a.59.1 yes 20
17.15 even 8 170.2.n.a.49.1 20
85.32 odd 8 850.2.l.h.151.5 20
85.49 even 8 inner 170.2.n.b.49.5 yes 20
85.83 odd 8 850.2.l.i.151.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.n.a.49.1 20 17.15 even 8
170.2.n.a.59.1 yes 20 5.4 even 2
170.2.n.b.49.5 yes 20 85.49 even 8 inner
170.2.n.b.59.5 yes 20 1.1 even 1 trivial
850.2.l.h.151.5 20 85.32 odd 8
850.2.l.h.501.5 20 5.2 odd 4
850.2.l.i.151.1 20 85.83 odd 8
850.2.l.i.501.1 20 5.3 odd 4