Properties

Label 66.2.h.a.35.2
Level $66$
Weight $2$
Character 66.35
Analytic conductor $0.527$
Analytic rank $0$
Dimension $8$
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] = [66,2,Mod(17,66)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(66, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("66.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 66 = 2 \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 66.h (of order \(10\), 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: \(0.527012653340\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: 8.0.185640625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + x^{6} + x^{5} + 4x^{4} + 3x^{3} + 9x^{2} - 81x + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 35.2
Root \(-0.245684 - 1.71454i\) of defining polynomial
Character \(\chi\) \(=\) 66.35
Dual form 66.2.h.a.17.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.309017 - 0.951057i) q^{2} +(1.70654 - 0.296161i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.01556 + 0.654895i) q^{5} +(0.245684 - 1.71454i) q^{6} +(-2.01556 + 2.77418i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.82458 - 1.01082i) q^{9} +O(q^{10})\) \(q+(0.309017 - 0.951057i) q^{2} +(1.70654 - 0.296161i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.01556 + 0.654895i) q^{5} +(0.245684 - 1.71454i) q^{6} +(-2.01556 + 2.77418i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.82458 - 1.01082i) q^{9} +2.11929i q^{10} +(0.960858 - 3.17439i) q^{11} +(-1.55470 - 0.763481i) q^{12} +(-1.79505 - 0.583248i) q^{13} +(2.01556 + 2.77418i) q^{14} +(-3.24568 + 1.71454i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.59384 + 4.90534i) q^{17} +(-0.0885088 - 2.99869i) q^{18} +(-0.141616 - 0.194917i) q^{19} +(2.01556 + 0.654895i) q^{20} +(-2.61803 + 5.33119i) q^{21} +(-2.72210 - 1.89477i) q^{22} -4.97072i q^{23} +(-1.20654 + 1.24268i) q^{24} +(-0.411491 + 0.298966i) q^{25} +(-1.10940 + 1.52696i) q^{26} +(4.52089 - 2.56155i) q^{27} +(3.26124 - 1.05964i) q^{28} +(-3.37235 - 2.45016i) q^{29} +(0.627650 + 3.61665i) q^{30} +(2.02518 - 6.23285i) q^{31} +1.00000 q^{32} +(0.699614 - 5.70180i) q^{33} +5.15778 q^{34} +(2.24568 - 6.91151i) q^{35} +(-2.87928 - 0.842471i) q^{36} +(7.14052 + 5.18789i) q^{37} +(-0.229139 + 0.0744518i) q^{38} +(-3.23607 - 0.463712i) q^{39} +(1.24568 - 1.71454i) q^{40} +(-6.42001 + 4.66441i) q^{41} +(4.26124 + 4.13733i) q^{42} -6.51583i q^{43} +(-2.64321 + 2.00336i) q^{44} +(-5.03112 + 3.88718i) q^{45} +(-4.72744 - 1.53604i) q^{46} +(1.98077 + 2.72629i) q^{47} +(0.809017 + 1.53150i) q^{48} +(-1.47047 - 4.52566i) q^{49} +(0.157176 + 0.483737i) q^{50} +(4.17274 + 7.89915i) q^{51} +(1.10940 + 1.52696i) q^{52} +(5.91040 + 1.92040i) q^{53} +(-1.03914 - 5.09119i) q^{54} +(0.142225 + 7.02743i) q^{55} -3.42908i q^{56} +(-0.299400 - 0.290694i) q^{57} +(-3.37235 + 2.45016i) q^{58} +(-1.62931 + 2.24256i) q^{59} +(3.63359 + 0.520675i) q^{60} +(1.53975 - 0.500295i) q^{61} +(-5.30198 - 3.85211i) q^{62} +(-2.88889 + 9.87326i) q^{63} +(0.309017 - 0.951057i) q^{64} +4.00000 q^{65} +(-5.20654 - 2.42733i) q^{66} -9.98396 q^{67} +(1.59384 - 4.90534i) q^{68} +(-1.47214 - 8.48275i) q^{69} +(-5.87928 - 4.27155i) q^{70} +(-9.47214 + 3.07768i) q^{71} +(-1.69098 + 2.47802i) q^{72} +(-1.45756 + 2.00616i) q^{73} +(7.14052 - 5.18789i) q^{74} +(-0.613685 + 0.632066i) q^{75} +0.240931i q^{76} +(6.86966 + 9.06377i) q^{77} +(-1.44102 + 2.93439i) q^{78} +(10.7741 + 3.50072i) q^{79} +(-1.24568 - 1.71454i) q^{80} +(6.95647 - 5.71030i) q^{81} +(2.45223 + 7.54718i) q^{82} +(2.12232 + 6.53182i) q^{83} +(5.25163 - 2.77418i) q^{84} +(-6.42497 - 8.84322i) q^{85} +(-6.19693 - 2.01350i) q^{86} +(-6.48070 - 3.18254i) q^{87} +(1.08851 + 3.13291i) q^{88} -2.47254i q^{89} +(2.14222 + 5.98608i) q^{90} +(5.23607 - 3.80423i) q^{91} +(-2.92172 + 4.02140i) q^{92} +(1.61012 - 11.2364i) q^{93} +(3.20495 - 1.04135i) q^{94} +(0.413086 + 0.300124i) q^{95} +(1.70654 - 0.296161i) q^{96} +(-4.08582 + 12.5749i) q^{97} -4.75856 q^{98} +(-0.494732 - 9.93757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 3 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 3 q^{6} - 2 q^{8} + 2 q^{9} + q^{11} - 3 q^{12} - 21 q^{15} - 2 q^{16} + 10 q^{17} + 2 q^{18} - 15 q^{19} - 12 q^{21} + 6 q^{22} + 2 q^{24} - 6 q^{25} + 10 q^{26} + 20 q^{27} + 5 q^{28} - 23 q^{29} + 9 q^{30} + 13 q^{31} + 8 q^{32} + 20 q^{33} + 10 q^{34} + 13 q^{35} + 7 q^{36} + 6 q^{37} - 10 q^{38} - 8 q^{39} + 5 q^{40} - 2 q^{41} + 13 q^{42} - 9 q^{44} - 8 q^{45} - 10 q^{46} - 10 q^{47} + 2 q^{48} - 18 q^{49} - q^{50} + 15 q^{51} - 10 q^{52} - 15 q^{53} - 15 q^{54} - 14 q^{55} + 15 q^{57} - 23 q^{58} + 25 q^{59} + 4 q^{60} - 10 q^{61} - 2 q^{62} - 6 q^{63} - 2 q^{64} + 32 q^{65} - 30 q^{66} - 2 q^{67} + 10 q^{68} + 24 q^{69} - 17 q^{70} - 40 q^{71} - 18 q^{72} + 5 q^{73} + 6 q^{74} + q^{75} + 12 q^{77} - 8 q^{78} + 10 q^{79} - 5 q^{80} - 26 q^{81} + 3 q^{82} + 21 q^{83} + 8 q^{84} + 30 q^{85} - 25 q^{86} - 42 q^{87} + 6 q^{88} + 2 q^{90} + 24 q^{91} - 10 q^{92} + 27 q^{93} + 40 q^{94} - 20 q^{95} + 2 q^{96} + 9 q^{97} + 22 q^{98} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/66\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.309017 0.951057i 0.218508 0.672499i
\(3\) 1.70654 0.296161i 0.985273 0.170989i
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) −2.01556 + 0.654895i −0.901386 + 0.292878i −0.722809 0.691048i \(-0.757149\pi\)
−0.178577 + 0.983926i \(0.557149\pi\)
\(6\) 0.245684 1.71454i 0.100300 0.699957i
\(7\) −2.01556 + 2.77418i −0.761810 + 1.04854i 0.235251 + 0.971935i \(0.424409\pi\)
−0.997061 + 0.0766070i \(0.975591\pi\)
\(8\) −0.809017 + 0.587785i −0.286031 + 0.207813i
\(9\) 2.82458 1.01082i 0.941526 0.336941i
\(10\) 2.11929i 0.670177i
\(11\) 0.960858 3.17439i 0.289710 0.957115i
\(12\) −1.55470 0.763481i −0.448804 0.220398i
\(13\) −1.79505 0.583248i −0.497858 0.161764i 0.0493154 0.998783i \(-0.484296\pi\)
−0.547173 + 0.837019i \(0.684296\pi\)
\(14\) 2.01556 + 2.77418i 0.538681 + 0.741431i
\(15\) −3.24568 + 1.71454i −0.838032 + 0.442692i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) 1.59384 + 4.90534i 0.386564 + 1.18972i 0.935340 + 0.353751i \(0.115094\pi\)
−0.548776 + 0.835970i \(0.684906\pi\)
\(18\) −0.0885088 2.99869i −0.0208617 0.706799i
\(19\) −0.141616 0.194917i −0.0324889 0.0447171i 0.792464 0.609919i \(-0.208798\pi\)
−0.824952 + 0.565202i \(0.808798\pi\)
\(20\) 2.01556 + 0.654895i 0.450693 + 0.146439i
\(21\) −2.61803 + 5.33119i −0.571302 + 1.16336i
\(22\) −2.72210 1.89477i −0.580354 0.403967i
\(23\) 4.97072i 1.03647i −0.855239 0.518234i \(-0.826590\pi\)
0.855239 0.518234i \(-0.173410\pi\)
\(24\) −1.20654 + 1.24268i −0.246285 + 0.253661i
\(25\) −0.411491 + 0.298966i −0.0822982 + 0.0597932i
\(26\) −1.10940 + 1.52696i −0.217572 + 0.299462i
\(27\) 4.52089 2.56155i 0.870046 0.492970i
\(28\) 3.26124 1.05964i 0.616317 0.200254i
\(29\) −3.37235 2.45016i −0.626230 0.454982i 0.228862 0.973459i \(-0.426499\pi\)
−0.855092 + 0.518476i \(0.826499\pi\)
\(30\) 0.627650 + 3.61665i 0.114593 + 0.660307i
\(31\) 2.02518 6.23285i 0.363732 1.11945i −0.587039 0.809559i \(-0.699706\pi\)
0.950771 0.309894i \(-0.100294\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.699614 5.70180i 0.121787 0.992556i
\(34\) 5.15778 0.884553
\(35\) 2.24568 6.91151i 0.379590 1.16826i
\(36\) −2.87928 0.842471i −0.479880 0.140412i
\(37\) 7.14052 + 5.18789i 1.17389 + 0.852884i 0.991470 0.130335i \(-0.0416054\pi\)
0.182425 + 0.983220i \(0.441605\pi\)
\(38\) −0.229139 + 0.0744518i −0.0371713 + 0.0120777i
\(39\) −3.23607 0.463712i −0.518186 0.0742533i
\(40\) 1.24568 1.71454i 0.196960 0.271092i
\(41\) −6.42001 + 4.66441i −1.00264 + 0.728459i −0.962652 0.270741i \(-0.912731\pi\)
−0.0399856 + 0.999200i \(0.512731\pi\)
\(42\) 4.26124 + 4.13733i 0.657524 + 0.638403i
\(43\) 6.51583i 0.993655i −0.867849 0.496828i \(-0.834498\pi\)
0.867849 0.496828i \(-0.165502\pi\)
\(44\) −2.64321 + 2.00336i −0.398479 + 0.302017i
\(45\) −5.03112 + 3.88718i −0.749995 + 0.579466i
\(46\) −4.72744 1.53604i −0.697023 0.226476i
\(47\) 1.98077 + 2.72629i 0.288925 + 0.397671i 0.928664 0.370921i \(-0.120958\pi\)
−0.639740 + 0.768591i \(0.720958\pi\)
\(48\) 0.809017 + 1.53150i 0.116772 + 0.221053i
\(49\) −1.47047 4.52566i −0.210068 0.646522i
\(50\) 0.157176 + 0.483737i 0.0222280 + 0.0684107i
\(51\) 4.17274 + 7.89915i 0.584300 + 1.10610i
\(52\) 1.10940 + 1.52696i 0.153847 + 0.211752i
\(53\) 5.91040 + 1.92040i 0.811856 + 0.263788i 0.685384 0.728182i \(-0.259635\pi\)
0.126472 + 0.991970i \(0.459635\pi\)
\(54\) −1.03914 5.09119i −0.141409 0.692823i
\(55\) 0.142225 + 7.02743i 0.0191776 + 0.947579i
\(56\) 3.42908i 0.458229i
\(57\) −0.299400 0.290694i −0.0396566 0.0385033i
\(58\) −3.37235 + 2.45016i −0.442811 + 0.321721i
\(59\) −1.62931 + 2.24256i −0.212118 + 0.291956i −0.901797 0.432160i \(-0.857752\pi\)
0.689679 + 0.724115i \(0.257752\pi\)
\(60\) 3.63359 + 0.520675i 0.469095 + 0.0672189i
\(61\) 1.53975 0.500295i 0.197145 0.0640563i −0.208780 0.977963i \(-0.566949\pi\)
0.405925 + 0.913906i \(0.366949\pi\)
\(62\) −5.30198 3.85211i −0.673352 0.489219i
\(63\) −2.88889 + 9.87326i −0.363967 + 1.24391i
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) 4.00000 0.496139
\(66\) −5.20654 2.42733i −0.640881 0.298783i
\(67\) −9.98396 −1.21973 −0.609867 0.792504i \(-0.708777\pi\)
−0.609867 + 0.792504i \(0.708777\pi\)
\(68\) 1.59384 4.90534i 0.193282 0.594860i
\(69\) −1.47214 8.48275i −0.177224 1.02120i
\(70\) −5.87928 4.27155i −0.702708 0.510547i
\(71\) −9.47214 + 3.07768i −1.12414 + 0.365254i −0.811345 0.584568i \(-0.801264\pi\)
−0.312791 + 0.949822i \(0.601264\pi\)
\(72\) −1.69098 + 2.47802i −0.199284 + 0.292037i
\(73\) −1.45756 + 2.00616i −0.170595 + 0.234803i −0.885751 0.464162i \(-0.846356\pi\)
0.715156 + 0.698965i \(0.246356\pi\)
\(74\) 7.14052 5.18789i 0.830069 0.603080i
\(75\) −0.613685 + 0.632066i −0.0708623 + 0.0729847i
\(76\) 0.240931i 0.0276367i
\(77\) 6.86966 + 9.06377i 0.782871 + 1.03291i
\(78\) −1.44102 + 2.93439i −0.163163 + 0.332254i
\(79\) 10.7741 + 3.50072i 1.21218 + 0.393862i 0.844229 0.535982i \(-0.180059\pi\)
0.367953 + 0.929844i \(0.380059\pi\)
\(80\) −1.24568 1.71454i −0.139272 0.191691i
\(81\) 6.95647 5.71030i 0.772941 0.634478i
\(82\) 2.45223 + 7.54718i 0.270803 + 0.833447i
\(83\) 2.12232 + 6.53182i 0.232954 + 0.716960i 0.997386 + 0.0722554i \(0.0230197\pi\)
−0.764432 + 0.644705i \(0.776980\pi\)
\(84\) 5.25163 2.77418i 0.573000 0.302688i
\(85\) −6.42497 8.84322i −0.696886 0.959181i
\(86\) −6.19693 2.01350i −0.668232 0.217122i
\(87\) −6.48070 3.18254i −0.694804 0.341204i
\(88\) 1.08851 + 3.13291i 0.116035 + 0.333970i
\(89\) 2.47254i 0.262088i −0.991377 0.131044i \(-0.958167\pi\)
0.991377 0.131044i \(-0.0418330\pi\)
\(90\) 2.14222 + 5.98608i 0.225810 + 0.630989i
\(91\) 5.23607 3.80423i 0.548889 0.398791i
\(92\) −2.92172 + 4.02140i −0.304610 + 0.419260i
\(93\) 1.61012 11.2364i 0.166962 1.16516i
\(94\) 3.20495 1.04135i 0.330565 0.107407i
\(95\) 0.413086 + 0.300124i 0.0423817 + 0.0307921i
\(96\) 1.70654 0.296161i 0.174173 0.0302268i
\(97\) −4.08582 + 12.5749i −0.414852 + 1.27678i 0.497531 + 0.867446i \(0.334240\pi\)
−0.912383 + 0.409338i \(0.865760\pi\)
\(98\) −4.75856 −0.480687
\(99\) −0.494732 9.93757i −0.0497225 0.998763i
\(100\) 0.508631 0.0508631
\(101\) 0.760259 2.33984i 0.0756486 0.232822i −0.906081 0.423105i \(-0.860940\pi\)
0.981729 + 0.190282i \(0.0609403\pi\)
\(102\) 8.80198 1.52754i 0.871526 0.151249i
\(103\) 3.72914 + 2.70938i 0.367443 + 0.266963i 0.756150 0.654399i \(-0.227078\pi\)
−0.388707 + 0.921361i \(0.627078\pi\)
\(104\) 1.79505 0.583248i 0.176019 0.0571921i
\(105\) 1.78544 12.4599i 0.174241 1.21596i
\(106\) 3.65283 5.02768i 0.354794 0.488332i
\(107\) 14.6716 10.6596i 1.41836 1.03050i 0.426322 0.904572i \(-0.359809\pi\)
0.992039 0.125928i \(-0.0401909\pi\)
\(108\) −5.16312 0.584981i −0.496821 0.0562898i
\(109\) 0.702783i 0.0673144i 0.999433 + 0.0336572i \(0.0107154\pi\)
−0.999433 + 0.0336572i \(0.989285\pi\)
\(110\) 6.72744 + 2.03633i 0.641436 + 0.194157i
\(111\) 13.7221 + 6.73861i 1.30244 + 0.639601i
\(112\) −3.26124 1.05964i −0.308159 0.100127i
\(113\) 2.51821 + 3.46601i 0.236893 + 0.326055i 0.910867 0.412700i \(-0.135414\pi\)
−0.673974 + 0.738755i \(0.735414\pi\)
\(114\) −0.368986 + 0.194917i −0.0345587 + 0.0182557i
\(115\) 3.25530 + 10.0188i 0.303558 + 0.934257i
\(116\) 1.28812 + 3.96443i 0.119599 + 0.368089i
\(117\) −5.65982 + 0.167054i −0.523251 + 0.0154442i
\(118\) 1.62931 + 2.24256i 0.149990 + 0.206444i
\(119\) −16.8208 5.46541i −1.54196 0.501013i
\(120\) 1.61803 3.29486i 0.147706 0.300778i
\(121\) −9.15350 6.10028i −0.832137 0.554571i
\(122\) 1.61899i 0.146576i
\(123\) −9.57461 + 9.86138i −0.863314 + 0.889171i
\(124\) −5.30198 + 3.85211i −0.476132 + 0.345930i
\(125\) 6.86202 9.44475i 0.613757 0.844765i
\(126\) 8.49731 + 5.79851i 0.757001 + 0.516572i
\(127\) −16.6803 + 5.41975i −1.48013 + 0.480925i −0.934153 0.356872i \(-0.883843\pi\)
−0.545982 + 0.837797i \(0.683843\pi\)
\(128\) −0.809017 0.587785i −0.0715077 0.0519534i
\(129\) −1.92974 11.1195i −0.169904 0.979022i
\(130\) 1.23607 3.80423i 0.108410 0.333653i
\(131\) 4.82298 0.421386 0.210693 0.977552i \(-0.432428\pi\)
0.210693 + 0.977552i \(0.432428\pi\)
\(132\) −3.91743 + 4.20163i −0.340969 + 0.365705i
\(133\) 0.826171 0.0716381
\(134\) −3.08521 + 9.49531i −0.266522 + 0.820270i
\(135\) −7.43459 + 8.12366i −0.639868 + 0.699173i
\(136\) −4.17274 3.03167i −0.357809 0.259964i
\(137\) −17.1743 + 5.58026i −1.46730 + 0.476754i −0.930291 0.366823i \(-0.880445\pi\)
−0.537008 + 0.843577i \(0.680445\pi\)
\(138\) −8.52249 1.22123i −0.725482 0.103958i
\(139\) 0.581539 0.800420i 0.0493255 0.0678907i −0.783642 0.621213i \(-0.786640\pi\)
0.832967 + 0.553322i \(0.186640\pi\)
\(140\) −5.87928 + 4.27155i −0.496890 + 0.361012i
\(141\) 4.18769 + 4.06591i 0.352667 + 0.342411i
\(142\) 9.95959i 0.835790i
\(143\) −3.57625 + 5.13778i −0.299061 + 0.429642i
\(144\) 1.83419 + 2.37397i 0.152849 + 0.197831i
\(145\) 8.40177 + 2.72990i 0.697729 + 0.226706i
\(146\) 1.45756 + 2.00616i 0.120629 + 0.166031i
\(147\) −3.84975 7.28773i −0.317522 0.601082i
\(148\) −2.72744 8.39419i −0.224194 0.689998i
\(149\) −4.32227 13.3026i −0.354094 1.08979i −0.956533 0.291624i \(-0.905804\pi\)
0.602439 0.798165i \(-0.294196\pi\)
\(150\) 0.411491 + 0.778968i 0.0335981 + 0.0636025i
\(151\) −3.71979 5.11985i −0.302712 0.416648i 0.630379 0.776288i \(-0.282900\pi\)
−0.933091 + 0.359640i \(0.882900\pi\)
\(152\) 0.229139 + 0.0744518i 0.0185856 + 0.00603884i
\(153\) 9.46037 + 12.2444i 0.764826 + 0.989903i
\(154\) 10.7430 3.73258i 0.865695 0.300780i
\(155\) 13.8890i 1.11559i
\(156\) 2.34547 + 2.27726i 0.187788 + 0.182327i
\(157\) 3.00000 2.17963i 0.239426 0.173953i −0.461601 0.887087i \(-0.652725\pi\)
0.701028 + 0.713134i \(0.252725\pi\)
\(158\) 6.65877 9.16501i 0.529743 0.729129i
\(159\) 10.6551 + 1.52682i 0.845004 + 0.121085i
\(160\) −2.01556 + 0.654895i −0.159344 + 0.0517740i
\(161\) 13.7897 + 10.0188i 1.08678 + 0.789591i
\(162\) −3.28115 8.38057i −0.257792 0.658440i
\(163\) 2.64222 8.13193i 0.206955 0.636942i −0.792672 0.609648i \(-0.791311\pi\)
0.999627 0.0272943i \(-0.00868912\pi\)
\(164\) 7.93557 0.619664
\(165\) 2.32397 + 11.9505i 0.180921 + 0.930345i
\(166\) 6.86796 0.533057
\(167\) 0.508631 1.56541i 0.0393591 0.121135i −0.929446 0.368957i \(-0.879715\pi\)
0.968805 + 0.247822i \(0.0797149\pi\)
\(168\) −1.01556 5.85186i −0.0783521 0.451481i
\(169\) −7.63519 5.54729i −0.587322 0.426715i
\(170\) −10.3958 + 3.37781i −0.797323 + 0.259066i
\(171\) −0.597032 0.407411i −0.0456562 0.0311555i
\(172\) −3.82991 + 5.27142i −0.292028 + 0.401942i
\(173\) 2.83854 2.06232i 0.215810 0.156795i −0.474628 0.880186i \(-0.657418\pi\)
0.690439 + 0.723391i \(0.257418\pi\)
\(174\) −5.02942 + 5.18005i −0.381279 + 0.392699i
\(175\) 1.74413i 0.131844i
\(176\) 3.31595 0.0671098i 0.249949 0.00505859i
\(177\) −2.11633 + 4.30956i −0.159073 + 0.323926i
\(178\) −2.35152 0.764056i −0.176254 0.0572684i
\(179\) −7.80160 10.7380i −0.583119 0.802595i 0.410914 0.911674i \(-0.365210\pi\)
−0.994033 + 0.109079i \(0.965210\pi\)
\(180\) 6.35509 0.187575i 0.473680 0.0139810i
\(181\) −2.29709 7.06971i −0.170741 0.525488i 0.828672 0.559734i \(-0.189097\pi\)
−0.999413 + 0.0342467i \(0.989097\pi\)
\(182\) −2.00000 6.15537i −0.148250 0.456266i
\(183\) 2.47948 1.30979i 0.183289 0.0968225i
\(184\) 2.92172 + 4.02140i 0.215392 + 0.296461i
\(185\) −17.7897 5.78022i −1.30792 0.424970i
\(186\) −10.1889 5.00356i −0.747087 0.366879i
\(187\) 17.1029 0.346138i 1.25069 0.0253121i
\(188\) 3.36988i 0.245774i
\(189\) −2.00594 + 17.7047i −0.145911 + 1.28783i
\(190\) 0.413086 0.300124i 0.0299684 0.0217733i
\(191\) −1.52249 + 2.09553i −0.110163 + 0.151627i −0.860539 0.509385i \(-0.829873\pi\)
0.750375 + 0.661012i \(0.229873\pi\)
\(192\) 0.245684 1.71454i 0.0177307 0.123736i
\(193\) 18.5702 6.03383i 1.33671 0.434325i 0.448511 0.893777i \(-0.351954\pi\)
0.888202 + 0.459453i \(0.151954\pi\)
\(194\) 10.6968 + 7.77169i 0.767987 + 0.557975i
\(195\) 6.82617 1.18465i 0.488832 0.0848342i
\(196\) −1.47047 + 4.52566i −0.105034 + 0.323261i
\(197\) 5.38713 0.383817 0.191908 0.981413i \(-0.438532\pi\)
0.191908 + 0.981413i \(0.438532\pi\)
\(198\) −9.60407 2.60036i −0.682531 0.184799i
\(199\) 7.38713 0.523659 0.261830 0.965114i \(-0.415674\pi\)
0.261830 + 0.965114i \(0.415674\pi\)
\(200\) 0.157176 0.483737i 0.0111140 0.0342054i
\(201\) −17.0380 + 2.95686i −1.20177 + 0.208561i
\(202\) −1.99038 1.44610i −0.140043 0.101747i
\(203\) 13.5943 4.41707i 0.954136 0.310018i
\(204\) 1.26719 8.84322i 0.0887209 0.619149i
\(205\) 9.88522 13.6058i 0.690414 0.950273i
\(206\) 3.72914 2.70938i 0.259821 0.188771i
\(207\) −5.02453 14.0402i −0.349229 0.975860i
\(208\) 1.88743i 0.130870i
\(209\) −0.754817 + 0.262256i −0.0522118 + 0.0181406i
\(210\) −11.2983 5.54836i −0.779657 0.382873i
\(211\) −8.14317 2.64588i −0.560599 0.182150i 0.0149917 0.999888i \(-0.495228\pi\)
−0.575591 + 0.817738i \(0.695228\pi\)
\(212\) −3.65283 5.02768i −0.250877 0.345303i
\(213\) −15.2531 + 8.05748i −1.04513 + 0.552089i
\(214\) −5.60407 17.2475i −0.383086 1.17902i
\(215\) 4.26719 + 13.1331i 0.291020 + 0.895667i
\(216\) −2.15184 + 4.72965i −0.146414 + 0.321812i
\(217\) 13.2092 + 18.1809i 0.896698 + 1.23420i
\(218\) 0.668387 + 0.217172i 0.0452689 + 0.0147087i
\(219\) −1.89324 + 3.85527i −0.127934 + 0.260515i
\(220\) 4.01556 5.76891i 0.270729 0.388940i
\(221\) 9.73495i 0.654844i
\(222\) 10.6492 10.9681i 0.714724 0.736131i
\(223\) −0.0407361 + 0.0295965i −0.00272789 + 0.00198193i −0.589148 0.808025i \(-0.700537\pi\)
0.586420 + 0.810007i \(0.300537\pi\)
\(224\) −2.01556 + 2.77418i −0.134670 + 0.185358i
\(225\) −0.860086 + 1.26040i −0.0573391 + 0.0840265i
\(226\) 4.07454 1.32390i 0.271035 0.0880645i
\(227\) −11.5589 8.39806i −0.767194 0.557399i 0.133914 0.990993i \(-0.457245\pi\)
−0.901108 + 0.433594i \(0.857245\pi\)
\(228\) 0.0713545 + 0.411159i 0.00472557 + 0.0272297i
\(229\) −9.34547 + 28.7624i −0.617566 + 1.90067i −0.271783 + 0.962359i \(0.587613\pi\)
−0.345783 + 0.938314i \(0.612387\pi\)
\(230\) 10.5344 0.694616
\(231\) 14.4077 + 13.4332i 0.947958 + 0.883838i
\(232\) 4.16845 0.273672
\(233\) −0.874011 + 2.68993i −0.0572583 + 0.176223i −0.975595 0.219576i \(-0.929532\pi\)
0.918337 + 0.395799i \(0.129532\pi\)
\(234\) −1.59010 + 5.43443i −0.103948 + 0.355260i
\(235\) −5.77779 4.19781i −0.376901 0.273835i
\(236\) 2.63628 0.856580i 0.171607 0.0557586i
\(237\) 19.4233 + 2.78326i 1.26168 + 0.180792i
\(238\) −10.3958 + 14.3086i −0.673861 + 0.927490i
\(239\) −0.918528 + 0.667349i −0.0594146 + 0.0431672i −0.617096 0.786888i \(-0.711691\pi\)
0.557682 + 0.830055i \(0.311691\pi\)
\(240\) −2.63359 2.55701i −0.169998 0.165054i
\(241\) 15.0464i 0.969223i −0.874730 0.484611i \(-0.838961\pi\)
0.874730 0.484611i \(-0.161039\pi\)
\(242\) −8.63030 + 6.82041i −0.554777 + 0.438432i
\(243\) 10.1803 11.8051i 0.653069 0.757298i
\(244\) −1.53975 0.500295i −0.0985724 0.0320281i
\(245\) 5.92766 + 8.15872i 0.378704 + 0.521242i
\(246\) 6.42001 + 12.1533i 0.409325 + 0.774868i
\(247\) 0.140523 + 0.432484i 0.00894124 + 0.0275183i
\(248\) 2.02518 + 6.23285i 0.128599 + 0.395786i
\(249\) 5.55630 + 10.5183i 0.352116 + 0.666569i
\(250\) −6.86202 9.44475i −0.433992 0.597339i
\(251\) 9.16478 + 2.97782i 0.578476 + 0.187958i 0.583618 0.812029i \(-0.301637\pi\)
−0.00514185 + 0.999987i \(0.501637\pi\)
\(252\) 8.14052 6.28959i 0.512805 0.396207i
\(253\) −15.7790 4.77616i −0.992018 0.300275i
\(254\) 17.5387i 1.10047i
\(255\) −13.5835 13.1885i −0.850632 0.825896i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) −7.85036 + 10.8051i −0.489692 + 0.674003i −0.980331 0.197360i \(-0.936763\pi\)
0.490639 + 0.871363i \(0.336763\pi\)
\(258\) −11.1716 1.60084i −0.695516 0.0996639i
\(259\) −28.7843 + 9.35259i −1.78857 + 0.581141i
\(260\) −3.23607 2.35114i −0.200692 0.145812i
\(261\) −12.0021 3.51180i −0.742914 0.217375i
\(262\) 1.49038 4.58693i 0.0920762 0.283381i
\(263\) −9.33677 −0.575730 −0.287865 0.957671i \(-0.592945\pi\)
−0.287865 + 0.957671i \(0.592945\pi\)
\(264\) 2.78544 + 5.02408i 0.171432 + 0.309211i
\(265\) −13.1704 −0.809053
\(266\) 0.255301 0.785736i 0.0156535 0.0481765i
\(267\) −0.732270 4.21949i −0.0448142 0.258229i
\(268\) 8.07719 + 5.86842i 0.493393 + 0.358471i
\(269\) 12.9581 4.21035i 0.790071 0.256710i 0.113937 0.993488i \(-0.463654\pi\)
0.676134 + 0.736778i \(0.263654\pi\)
\(270\) 5.42865 + 9.58106i 0.330377 + 0.583085i
\(271\) 2.75734 3.79515i 0.167496 0.230539i −0.717015 0.697058i \(-0.754492\pi\)
0.884511 + 0.466519i \(0.154492\pi\)
\(272\) −4.17274 + 3.03167i −0.253009 + 0.183822i
\(273\) 7.80891 8.04280i 0.472617 0.486772i
\(274\) 18.0581i 1.09093i
\(275\) 0.553649 + 1.59350i 0.0333863 + 0.0960915i
\(276\) −3.79505 + 7.72799i −0.228435 + 0.465170i
\(277\) −7.87652 2.55924i −0.473254 0.153770i 0.0626723 0.998034i \(-0.480038\pi\)
−0.535927 + 0.844264i \(0.680038\pi\)
\(278\) −0.581539 0.800420i −0.0348784 0.0480060i
\(279\) −0.580052 19.6523i −0.0347268 1.17655i
\(280\) 2.24568 + 6.91151i 0.134205 + 0.413041i
\(281\) −3.91369 12.0451i −0.233471 0.718551i −0.997320 0.0731563i \(-0.976693\pi\)
0.763849 0.645395i \(-0.223307\pi\)
\(282\) 5.16097 2.72629i 0.307332 0.162348i
\(283\) 13.2896 + 18.2916i 0.789985 + 1.08732i 0.994110 + 0.108377i \(0.0345652\pi\)
−0.204125 + 0.978945i \(0.565435\pi\)
\(284\) 9.47214 + 3.07768i 0.562068 + 0.182627i
\(285\) 0.793834 + 0.389835i 0.0470226 + 0.0230918i
\(286\) 3.78119 + 4.98887i 0.223587 + 0.294998i
\(287\) 27.2117i 1.60625i
\(288\) 2.82458 1.01082i 0.166440 0.0595634i
\(289\) −7.76878 + 5.64435i −0.456987 + 0.332021i
\(290\) 5.19258 7.14697i 0.304919 0.419685i
\(291\) −3.24844 + 22.6696i −0.190427 + 1.32892i
\(292\) 2.35838 0.766285i 0.138014 0.0448435i
\(293\) −20.2998 14.7487i −1.18593 0.861626i −0.193099 0.981179i \(-0.561854\pi\)
−0.992828 + 0.119553i \(0.961854\pi\)
\(294\) −8.12068 + 1.40930i −0.473608 + 0.0821921i
\(295\) 1.81534 5.58703i 0.105693 0.325290i
\(296\) −8.82617 −0.513011
\(297\) −3.78741 16.8124i −0.219768 0.975552i
\(298\) −13.9871 −0.810254
\(299\) −2.89916 + 8.92270i −0.167663 + 0.516013i
\(300\) 0.868001 0.150637i 0.0501140 0.00869703i
\(301\) 18.0761 + 13.1331i 1.04189 + 0.756977i
\(302\) −6.01875 + 1.95561i −0.346340 + 0.112533i
\(303\) 0.604445 4.21819i 0.0347245 0.242329i
\(304\) 0.141616 0.194917i 0.00812222 0.0111793i
\(305\) −2.77582 + 2.01675i −0.158943 + 0.115479i
\(306\) 14.5686 5.21361i 0.832829 0.298042i
\(307\) 16.0682i 0.917058i −0.888679 0.458529i \(-0.848377\pi\)
0.888679 0.458529i \(-0.151623\pi\)
\(308\) −0.230125 11.3706i −0.0131126 0.647902i
\(309\) 7.16635 + 3.51924i 0.407679 + 0.200203i
\(310\) 13.2092 + 4.29193i 0.750232 + 0.243765i
\(311\) 5.65772 + 7.78718i 0.320820 + 0.441571i 0.938717 0.344688i \(-0.112015\pi\)
−0.617897 + 0.786259i \(0.712015\pi\)
\(312\) 2.89060 1.52696i 0.163648 0.0864472i
\(313\) 6.21555 + 19.1295i 0.351324 + 1.08126i 0.958111 + 0.286399i \(0.0924581\pi\)
−0.606787 + 0.794865i \(0.707542\pi\)
\(314\) −1.14590 3.52671i −0.0646668 0.199024i
\(315\) −0.643210 21.7921i −0.0362408 1.22784i
\(316\) −6.65877 9.16501i −0.374585 0.515572i
\(317\) 17.5481 + 5.70172i 0.985599 + 0.320241i 0.757097 0.653303i \(-0.226617\pi\)
0.228503 + 0.973543i \(0.426617\pi\)
\(318\) 4.74470 9.66179i 0.266070 0.541806i
\(319\) −11.0181 + 8.35090i −0.616895 + 0.467561i
\(320\) 2.11929i 0.118472i
\(321\) 21.8808 22.5362i 1.22127 1.25785i
\(322\) 13.7897 10.0188i 0.768469 0.558325i
\(323\) 0.730424 1.00534i 0.0406419 0.0559387i
\(324\) −8.98433 + 0.530822i −0.499130 + 0.0294901i
\(325\) 0.913019 0.296658i 0.0506452 0.0164556i
\(326\) −6.91743 5.02581i −0.383121 0.278354i
\(327\) 0.208137 + 1.19933i 0.0115100 + 0.0663231i
\(328\) 2.45223 7.54718i 0.135402 0.416723i
\(329\) −11.5556 −0.637080
\(330\) 12.0837 + 1.48268i 0.665188 + 0.0816189i
\(331\) −5.03641 −0.276826 −0.138413 0.990375i \(-0.544200\pi\)
−0.138413 + 0.990375i \(0.544200\pi\)
\(332\) 2.12232 6.53182i 0.116477 0.358480i
\(333\) 25.4130 + 7.43579i 1.39262 + 0.407479i
\(334\) −1.33161 0.967474i −0.0728626 0.0529378i
\(335\) 20.1233 6.53844i 1.09945 0.357233i
\(336\) −5.87928 0.842471i −0.320741 0.0459605i
\(337\) 10.3769 14.2826i 0.565267 0.778024i −0.426717 0.904385i \(-0.640330\pi\)
0.991984 + 0.126361i \(0.0403299\pi\)
\(338\) −7.63519 + 5.54729i −0.415299 + 0.301733i
\(339\) 5.32393 + 5.16911i 0.289156 + 0.280747i
\(340\) 10.9308i 0.592807i
\(341\) −17.8396 12.4176i −0.966068 0.672450i
\(342\) −0.571964 + 0.441914i −0.0309282 + 0.0238960i
\(343\) −7.30989 2.37513i −0.394697 0.128245i
\(344\) 3.82991 + 5.27142i 0.206495 + 0.284216i
\(345\) 8.52249 + 16.1334i 0.458835 + 0.868593i
\(346\) −1.08423 3.33691i −0.0582884 0.179393i
\(347\) 4.64355 + 14.2914i 0.249279 + 0.767201i 0.994903 + 0.100834i \(0.0321512\pi\)
−0.745625 + 0.666366i \(0.767849\pi\)
\(348\) 3.37235 + 6.38399i 0.180777 + 0.342218i
\(349\) 2.05443 + 2.82768i 0.109971 + 0.151362i 0.860455 0.509527i \(-0.170179\pi\)
−0.750484 + 0.660889i \(0.770179\pi\)
\(350\) −1.65877 0.538967i −0.0886650 0.0288090i
\(351\) −9.60925 + 1.96131i −0.512904 + 0.104687i
\(352\) 0.960858 3.17439i 0.0512139 0.169196i
\(353\) 25.2674i 1.34485i 0.740167 + 0.672423i \(0.234747\pi\)
−0.740167 + 0.672423i \(0.765253\pi\)
\(354\) 3.44465 + 3.34448i 0.183081 + 0.177757i
\(355\) 17.0761 12.4065i 0.906305 0.658469i
\(356\) −1.45332 + 2.00032i −0.0770258 + 0.106017i
\(357\) −30.3241 4.34528i −1.60492 0.229977i
\(358\) −12.6233 + 4.10155i −0.667160 + 0.216773i
\(359\) 15.6095 + 11.3409i 0.823836 + 0.598552i 0.917809 0.397023i \(-0.129957\pi\)
−0.0939725 + 0.995575i \(0.529957\pi\)
\(360\) 1.78544 6.10201i 0.0941007 0.321604i
\(361\) 5.85339 18.0149i 0.308073 0.948151i
\(362\) −7.43354 −0.390698
\(363\) −17.4275 7.69947i −0.914707 0.404117i
\(364\) −6.47214 −0.339232
\(365\) 1.62398 4.99809i 0.0850029 0.261612i
\(366\) −0.479482 2.76288i −0.0250629 0.144418i
\(367\) 0.726385 + 0.527749i 0.0379170 + 0.0275483i 0.606582 0.795021i \(-0.292540\pi\)
−0.568665 + 0.822569i \(0.692540\pi\)
\(368\) 4.72744 1.53604i 0.246435 0.0800715i
\(369\) −13.4189 + 19.6645i −0.698561 + 1.02369i
\(370\) −10.9946 + 15.1328i −0.571583 + 0.786717i
\(371\) −17.2403 + 12.5258i −0.895072 + 0.650308i
\(372\) −7.90721 + 8.14404i −0.409970 + 0.422249i
\(373\) 26.3407i 1.36387i 0.731413 + 0.681935i \(0.238861\pi\)
−0.731413 + 0.681935i \(0.761139\pi\)
\(374\) 4.95590 16.3728i 0.256264 0.846618i
\(375\) 8.91315 18.1501i 0.460273 0.937269i
\(376\) −3.20495 1.04135i −0.165283 0.0537036i
\(377\) 4.62449 + 6.36507i 0.238174 + 0.327818i
\(378\) 16.2183 + 7.37883i 0.834180 + 0.379526i
\(379\) −0.823525 2.53455i −0.0423016 0.130191i 0.927675 0.373388i \(-0.121804\pi\)
−0.969977 + 0.243197i \(0.921804\pi\)
\(380\) −0.157785 0.485611i −0.00809418 0.0249113i
\(381\) −26.8605 + 14.1891i −1.37610 + 0.726929i
\(382\) 1.52249 + 2.09553i 0.0778973 + 0.107216i
\(383\) 31.1072 + 10.1073i 1.58950 + 0.516461i 0.964483 0.264146i \(-0.0850901\pi\)
0.625022 + 0.780607i \(0.285090\pi\)
\(384\) −1.55470 0.763481i −0.0793380 0.0389612i
\(385\) −19.7820 13.7697i −1.00819 0.701767i
\(386\) 19.5259i 0.993841i
\(387\) −6.58636 18.4045i −0.334804 0.935552i
\(388\) 10.6968 7.77169i 0.543049 0.394548i
\(389\) −0.990218 + 1.36292i −0.0502060 + 0.0691027i −0.833382 0.552698i \(-0.813598\pi\)
0.783176 + 0.621800i \(0.213598\pi\)
\(390\) 0.982738 6.85815i 0.0497629 0.347276i
\(391\) 24.3831 7.92255i 1.23311 0.400661i
\(392\) 3.84975 + 2.79701i 0.194442 + 0.141270i
\(393\) 8.23063 1.42838i 0.415180 0.0720523i
\(394\) 1.66471 5.12346i 0.0838671 0.258116i
\(395\) −24.0085 −1.20800
\(396\) −5.44091 + 8.33046i −0.273416 + 0.418621i
\(397\) −8.89235 −0.446294 −0.223147 0.974785i \(-0.571633\pi\)
−0.223147 + 0.974785i \(0.571633\pi\)
\(398\) 2.28275 7.02557i 0.114424 0.352160i
\(399\) 1.40990 0.244680i 0.0705831 0.0122493i
\(400\) −0.411491 0.298966i −0.0205746 0.0149483i
\(401\) 18.6014 6.04398i 0.928912 0.301822i 0.194794 0.980844i \(-0.437596\pi\)
0.734118 + 0.679022i \(0.237596\pi\)
\(402\) −2.45290 + 17.1179i −0.122340 + 0.853762i
\(403\) −7.27059 + 10.0071i −0.362174 + 0.498490i
\(404\) −1.99038 + 1.44610i −0.0990253 + 0.0719461i
\(405\) −10.2815 + 16.0652i −0.510893 + 0.798287i
\(406\) 14.2939i 0.709396i
\(407\) 23.3294 17.6820i 1.15640 0.876463i
\(408\) −8.01882 3.93787i −0.396991 0.194954i
\(409\) 23.5359 + 7.64727i 1.16377 + 0.378133i 0.826315 0.563208i \(-0.190433\pi\)
0.337458 + 0.941341i \(0.390433\pi\)
\(410\) −9.88522 13.6058i −0.488196 0.671945i
\(411\) −27.6560 + 14.6093i −1.36417 + 0.720625i
\(412\) −1.42440 4.38387i −0.0701754 0.215978i
\(413\) −2.93728 9.04001i −0.144534 0.444830i
\(414\) −14.9057 + 0.439953i −0.732574 + 0.0216225i
\(415\) −8.55531 11.7754i −0.419964 0.578030i
\(416\) −1.79505 0.583248i −0.0880096 0.0285961i
\(417\) 0.755368 1.53818i 0.0369905 0.0753250i
\(418\) 0.0161689 + 0.798915i 0.000790845 + 0.0390762i
\(419\) 34.8462i 1.70235i 0.524883 + 0.851174i \(0.324109\pi\)
−0.524883 + 0.851174i \(0.675891\pi\)
\(420\) −8.76817 + 9.03079i −0.427843 + 0.440657i
\(421\) −14.1996 + 10.3166i −0.692045 + 0.502800i −0.877332 0.479884i \(-0.840679\pi\)
0.185287 + 0.982684i \(0.440679\pi\)
\(422\) −5.03276 + 6.92699i −0.244991 + 0.337201i
\(423\) 8.35063 + 5.69841i 0.406022 + 0.277066i
\(424\) −5.91040 + 1.92040i −0.287034 + 0.0932631i
\(425\) −2.12238 1.54200i −0.102951 0.0747981i
\(426\) 2.94965 + 16.9965i 0.142911 + 0.823482i
\(427\) −1.71555 + 5.27992i −0.0830213 + 0.255513i
\(428\) −18.1351 −0.876595
\(429\) −4.58141 + 9.82698i −0.221192 + 0.474451i
\(430\) 13.8089 0.665925
\(431\) −10.3275 + 31.7846i −0.497456 + 1.53101i 0.315638 + 0.948880i \(0.397782\pi\)
−0.813094 + 0.582133i \(0.802218\pi\)
\(432\) 3.83321 + 3.50806i 0.184425 + 0.168782i
\(433\) −21.9952 15.9805i −1.05702 0.767973i −0.0834881 0.996509i \(-0.526606\pi\)
−0.973535 + 0.228536i \(0.926606\pi\)
\(434\) 21.3729 6.94448i 1.02593 0.333346i
\(435\) 15.1465 + 2.17041i 0.726217 + 0.104063i
\(436\) 0.413086 0.568564i 0.0197832 0.0272293i
\(437\) −0.968880 + 0.703933i −0.0463478 + 0.0336737i
\(438\) 3.08154 + 2.99193i 0.147242 + 0.142960i
\(439\) 13.4068i 0.639873i −0.947439 0.319936i \(-0.896338\pi\)
0.947439 0.319936i \(-0.103662\pi\)
\(440\) −4.24568 5.60172i −0.202405 0.267051i
\(441\) −8.72811 11.2967i −0.415624 0.537937i
\(442\) −9.25849 3.00827i −0.440381 0.143089i
\(443\) −10.8348 14.9128i −0.514777 0.708530i 0.469939 0.882699i \(-0.344276\pi\)
−0.984716 + 0.174169i \(0.944276\pi\)
\(444\) −7.14052 13.5173i −0.338874 0.641502i
\(445\) 1.61925 + 4.98355i 0.0767599 + 0.236243i
\(446\) 0.0155598 + 0.0478882i 0.000736779 + 0.00226757i
\(447\) −11.3158 21.4213i −0.535221 1.01319i
\(448\) 2.01556 + 2.77418i 0.0952263 + 0.131068i
\(449\) 28.8836 + 9.38485i 1.36310 + 0.442898i 0.897077 0.441874i \(-0.145686\pi\)
0.466024 + 0.884772i \(0.345686\pi\)
\(450\) 0.932928 + 1.20748i 0.0439786 + 0.0569209i
\(451\) 8.63794 + 24.8615i 0.406745 + 1.17068i
\(452\) 4.28423i 0.201513i
\(453\) −7.86429 7.63559i −0.369496 0.358751i
\(454\) −11.5589 + 8.39806i −0.542488 + 0.394141i
\(455\) −8.06224 + 11.0967i −0.377964 + 0.520222i
\(456\) 0.413086 + 0.0591931i 0.0193445 + 0.00277197i
\(457\) 32.9901 10.7191i 1.54321 0.501419i 0.590950 0.806708i \(-0.298753\pi\)
0.952260 + 0.305289i \(0.0987530\pi\)
\(458\) 24.4668 + 17.7761i 1.14326 + 0.830625i
\(459\) 19.7709 + 18.0938i 0.922825 + 0.844548i
\(460\) 3.25530 10.0188i 0.151779 0.467128i
\(461\) 20.8777 0.972370 0.486185 0.873856i \(-0.338388\pi\)
0.486185 + 0.873856i \(0.338388\pi\)
\(462\) 17.2279 9.55147i 0.801516 0.444374i
\(463\) 6.14371 0.285522 0.142761 0.989757i \(-0.454402\pi\)
0.142761 + 0.989757i \(0.454402\pi\)
\(464\) 1.28812 3.96443i 0.0597996 0.184044i
\(465\) 4.11338 + 23.7021i 0.190753 + 1.09916i
\(466\) 2.28819 + 1.66247i 0.105998 + 0.0770123i
\(467\) −33.1013 + 10.7553i −1.53174 + 0.497694i −0.949084 0.315022i \(-0.897988\pi\)
−0.582660 + 0.812716i \(0.697988\pi\)
\(468\) 4.67708 + 3.19161i 0.216198 + 0.147532i
\(469\) 20.1233 27.6973i 0.929206 1.27894i
\(470\) −5.77779 + 4.19781i −0.266510 + 0.193631i
\(471\) 4.47411 4.60811i 0.206156 0.212331i
\(472\) 2.77195i 0.127589i
\(473\) −20.6838 6.26079i −0.951042 0.287872i
\(474\) 8.64915 17.6126i 0.397269 0.808971i
\(475\) 0.116547 + 0.0378685i 0.00534756 + 0.00173753i
\(476\) 10.3958 + 14.3086i 0.476492 + 0.655835i
\(477\) 18.6356 0.550043i 0.853264 0.0251848i
\(478\) 0.350846 + 1.07979i 0.0160473 + 0.0493886i
\(479\) −10.7639 33.1280i −0.491817 1.51366i −0.821860 0.569690i \(-0.807063\pi\)
0.330043 0.943966i \(-0.392937\pi\)
\(480\) −3.24568 + 1.71454i −0.148145 + 0.0782576i
\(481\) −9.79178 13.4772i −0.446467 0.614509i
\(482\) −14.3100 4.64959i −0.651801 0.211783i
\(483\) 26.4999 + 13.0135i 1.20578 + 0.592136i
\(484\) 3.81969 + 10.3155i 0.173622 + 0.468887i
\(485\) 28.0212i 1.27238i
\(486\) −8.08143 13.3301i −0.366581 0.604664i
\(487\) 4.66471 3.38911i 0.211378 0.153575i −0.477059 0.878871i \(-0.658297\pi\)
0.688437 + 0.725296i \(0.258297\pi\)
\(488\) −0.951618 + 1.30979i −0.0430777 + 0.0592914i
\(489\) 2.10071 14.6600i 0.0949972 0.662949i
\(490\) 9.59116 3.11636i 0.433284 0.140783i
\(491\) −8.42871 6.12382i −0.380382 0.276364i 0.381121 0.924525i \(-0.375538\pi\)
−0.761503 + 0.648161i \(0.775538\pi\)
\(492\) 13.5424 2.35021i 0.610538 0.105956i
\(493\) 6.64386 20.4477i 0.299224 0.920918i
\(494\) 0.454741 0.0204597
\(495\) 7.50523 + 19.7058i 0.337335 + 0.885708i
\(496\) 6.55361 0.294266
\(497\) 10.5536 32.4807i 0.473394 1.45696i
\(498\) 11.7205 2.03402i 0.525207 0.0911468i
\(499\) 17.7151 + 12.8708i 0.793038 + 0.576176i 0.908864 0.417094i \(-0.136951\pi\)
−0.115825 + 0.993270i \(0.536951\pi\)
\(500\) −11.1030 + 3.60758i −0.496540 + 0.161336i
\(501\) 0.404388 2.82207i 0.0180667 0.126081i
\(502\) 5.66415 7.79603i 0.252803 0.347954i
\(503\) −15.8347 + 11.5045i −0.706032 + 0.512962i −0.881891 0.471453i \(-0.843730\pi\)
0.175859 + 0.984415i \(0.443730\pi\)
\(504\) −3.46619 9.68569i −0.154396 0.431435i
\(505\) 5.21397i 0.232019i
\(506\) −9.41838 + 13.5308i −0.418698 + 0.601518i
\(507\) −14.6727 7.20544i −0.651636 0.320005i
\(508\) 16.6803 + 5.41975i 0.740067 + 0.240462i
\(509\) −21.3064 29.3257i −0.944389 1.29984i −0.953975 0.299886i \(-0.903051\pi\)
0.00958605 0.999954i \(-0.496949\pi\)
\(510\) −16.7405 + 8.84322i −0.741284 + 0.391584i
\(511\) −2.62765 8.08708i −0.116240 0.357751i
\(512\) 0.309017 + 0.951057i 0.0136568 + 0.0420312i
\(513\) −1.13952 0.518446i −0.0503110 0.0228899i
\(514\) 7.85036 + 10.8051i 0.346265 + 0.476592i
\(515\) −9.29066 3.01872i −0.409395 0.133021i
\(516\) −4.97472 + 10.1302i −0.219000 + 0.445956i
\(517\) 10.5575 3.66815i 0.464321 0.161325i
\(518\) 30.2656i 1.32979i
\(519\) 4.23331 4.36011i 0.185822 0.191387i
\(520\) −3.23607 + 2.35114i −0.141911 + 0.103104i
\(521\) 10.6363 14.6396i 0.465985 0.641373i −0.509751 0.860322i \(-0.670263\pi\)
0.975736 + 0.218948i \(0.0702626\pi\)
\(522\) −7.04878 + 10.3295i −0.308517 + 0.452110i
\(523\) −23.8450 + 7.74771i −1.04267 + 0.338784i −0.779787 0.626045i \(-0.784673\pi\)
−0.262881 + 0.964828i \(0.584673\pi\)
\(524\) −3.90187 2.83488i −0.170454 0.123842i
\(525\) −0.516545 2.97644i −0.0225439 0.129902i
\(526\) −2.88522 + 8.87980i −0.125802 + 0.387178i
\(527\) 33.8021 1.47244
\(528\) 5.63893 1.09658i 0.245403 0.0477226i
\(529\) −1.70807 −0.0742639
\(530\) −4.06988 + 12.5258i −0.176785 + 0.544087i
\(531\) −2.33529 + 7.98122i −0.101343 + 0.346355i
\(532\) −0.668387 0.485611i −0.0289782 0.0210539i
\(533\) 14.2448 4.62840i 0.617009 0.200478i
\(534\) −4.23926 0.607464i −0.183451 0.0262875i
\(535\) −22.5907 + 31.0934i −0.976680 + 1.34428i
\(536\) 8.07719 5.86842i 0.348881 0.253477i
\(537\) −16.4939 16.0143i −0.711766 0.691068i
\(538\) 13.6250i 0.587415i
\(539\) −15.7791 + 0.319346i −0.679655 + 0.0137552i
\(540\) 10.7897 2.20224i 0.464314 0.0947692i
\(541\) −37.4648 12.1730i −1.61074 0.523360i −0.641006 0.767536i \(-0.721483\pi\)
−0.969731 + 0.244176i \(0.921483\pi\)
\(542\) −2.75734 3.79515i −0.118438 0.163016i
\(543\) −6.01386 11.3845i −0.258079 0.488554i
\(544\) 1.59384 + 4.90534i 0.0683355 + 0.210315i
\(545\) −0.460249 1.41650i −0.0197149 0.0606763i
\(546\) −5.23607 9.91207i −0.224083 0.424198i
\(547\) 1.05599 + 1.45344i 0.0451507 + 0.0621446i 0.830995 0.556279i \(-0.187772\pi\)
−0.785845 + 0.618424i \(0.787772\pi\)
\(548\) 17.1743 + 5.58026i 0.733649 + 0.238377i
\(549\) 3.84343 2.96954i 0.164034 0.126737i
\(550\) 1.68659 0.0341341i 0.0719166 0.00145548i
\(551\) 1.00431i 0.0427851i
\(552\) 6.17702 + 5.99739i 0.262911 + 0.255266i
\(553\) −31.4275 + 22.8334i −1.33643 + 0.970976i
\(554\) −4.86796 + 6.70017i −0.206820 + 0.284663i
\(555\) −32.0707 4.59557i −1.36133 0.195071i
\(556\) −0.940950 + 0.305733i −0.0399052 + 0.0129660i
\(557\) 34.6574 + 25.1801i 1.46848 + 1.06691i 0.981051 + 0.193750i \(0.0620652\pi\)
0.487429 + 0.873163i \(0.337935\pi\)
\(558\) −18.8697 5.52122i −0.798816 0.233732i
\(559\) −3.80034 + 11.6963i −0.160737 + 0.494699i
\(560\) 7.26719 0.307095
\(561\) 29.0844 5.65593i 1.22794 0.238794i
\(562\) −12.6650 −0.534240
\(563\) −5.33623 + 16.4232i −0.224895 + 0.692157i 0.773407 + 0.633910i \(0.218551\pi\)
−0.998302 + 0.0582467i \(0.981449\pi\)
\(564\) −0.998029 5.75085i −0.0420246 0.242154i
\(565\) −7.34547 5.33680i −0.309026 0.224521i
\(566\) 21.5030 6.98676i 0.903840 0.293675i
\(567\) 1.82023 + 30.8080i 0.0764424 + 1.29381i
\(568\) 5.85410 8.05748i 0.245633 0.338084i
\(569\) −4.41418 + 3.20709i −0.185052 + 0.134448i −0.676454 0.736484i \(-0.736484\pi\)
0.491402 + 0.870933i \(0.336484\pi\)
\(570\) 0.616063 0.634515i 0.0258040 0.0265769i
\(571\) 18.8259i 0.787838i 0.919145 + 0.393919i \(0.128881\pi\)
−0.919145 + 0.393919i \(0.871119\pi\)
\(572\) 5.91315 2.05448i 0.247241 0.0859023i
\(573\) −1.97758 + 4.02701i −0.0826145 + 0.168231i
\(574\) −25.8798 8.40887i −1.08020 0.350980i
\(575\) 1.48608 + 2.04541i 0.0619736 + 0.0852994i
\(576\) −0.0885088 2.99869i −0.00368787 0.124946i
\(577\) 4.84849 + 14.9221i 0.201845 + 0.621216i 0.999828 + 0.0185361i \(0.00590056\pi\)
−0.797983 + 0.602680i \(0.794099\pi\)
\(578\) 2.96741 + 9.13275i 0.123428 + 0.379872i
\(579\) 29.9039 15.7968i 1.24276 0.656491i
\(580\) −5.19258 7.14697i −0.215610 0.296762i
\(581\) −22.3981 7.27758i −0.929230 0.301925i
\(582\) 20.5563 + 10.0947i 0.852084 + 0.418441i
\(583\) 11.7752 16.9167i 0.487678 0.700617i
\(584\) 2.47975i 0.102613i
\(585\) 11.2983 4.04330i 0.467128 0.167170i
\(586\) −20.2998 + 14.7487i −0.838577 + 0.609262i
\(587\) −1.74399 + 2.40039i −0.0719821 + 0.0990748i −0.843490 0.537145i \(-0.819503\pi\)
0.771508 + 0.636220i \(0.219503\pi\)
\(588\) −1.16910 + 8.15872i −0.0482130 + 0.336460i
\(589\) −1.50169 + 0.487928i −0.0618760 + 0.0201047i
\(590\) −4.75261 3.45298i −0.195662 0.142157i
\(591\) 9.19336 1.59546i 0.378164 0.0656284i
\(592\) −2.72744 + 8.39419i −0.112097 + 0.344999i
\(593\) −43.4839 −1.78567 −0.892836 0.450383i \(-0.851288\pi\)
−0.892836 + 0.450383i \(0.851288\pi\)
\(594\) −17.1599 1.59327i −0.704078 0.0653726i
\(595\) 37.4826 1.53664
\(596\) −4.32227 + 13.3026i −0.177047 + 0.544894i
\(597\) 12.6064 2.18778i 0.515948 0.0895399i
\(598\) 7.59010 + 5.51453i 0.310382 + 0.225506i
\(599\) 24.7770 8.05055i 1.01236 0.328936i 0.244567 0.969632i \(-0.421354\pi\)
0.767795 + 0.640696i \(0.221354\pi\)
\(600\) 0.124963 0.872067i 0.00510158 0.0356020i
\(601\) −27.1211 + 37.3290i −1.10629 + 1.52268i −0.279529 + 0.960137i \(0.590178\pi\)
−0.826766 + 0.562546i \(0.809822\pi\)
\(602\) 18.0761 13.1331i 0.736727 0.535263i
\(603\) −28.2005 + 10.0920i −1.14841 + 0.410979i
\(604\) 6.32849i 0.257502i
\(605\) 22.4445 + 6.30089i 0.912498 + 0.256168i
\(606\) −3.82495 1.87835i −0.155378 0.0763029i
\(607\) −9.07413 2.94836i −0.368307 0.119670i 0.119015 0.992892i \(-0.462026\pi\)
−0.487322 + 0.873222i \(0.662026\pi\)
\(608\) −0.141616 0.194917i −0.00574328 0.00790495i
\(609\) 21.8912 11.5640i 0.887075 0.468599i
\(610\) 1.06027 + 3.26317i 0.0429290 + 0.132122i
\(611\) −1.96548 6.04911i −0.0795146 0.244721i
\(612\) −0.456510 15.4666i −0.0184533 0.625201i
\(613\) −6.16173 8.48089i −0.248870 0.342540i 0.666245 0.745733i \(-0.267900\pi\)
−0.915115 + 0.403193i \(0.867900\pi\)
\(614\) −15.2817 4.96533i −0.616720 0.200384i
\(615\) 12.8400 26.1466i 0.517760 1.05433i
\(616\) −10.8852 3.29486i −0.438578 0.132754i
\(617\) 26.7867i 1.07839i 0.842180 + 0.539196i \(0.181272\pi\)
−0.842180 + 0.539196i \(0.818728\pi\)
\(618\) 5.56152 5.72810i 0.223717 0.230418i
\(619\) 6.51821 4.73575i 0.261989 0.190346i −0.449035 0.893514i \(-0.648232\pi\)
0.711023 + 0.703168i \(0.248232\pi\)
\(620\) 8.16373 11.2364i 0.327863 0.451265i
\(621\) −12.7327 22.4721i −0.510947 0.901775i
\(622\) 9.15438 2.97444i 0.367057 0.119264i
\(623\) 6.85926 + 4.98355i 0.274811 + 0.199662i
\(624\) −0.558984 3.22098i −0.0223773 0.128942i
\(625\) −6.85960 + 21.1117i −0.274384 + 0.844467i
\(626\) 20.1139 0.803915
\(627\) −1.21046 + 0.671098i −0.0483410 + 0.0268011i
\(628\) −3.70820 −0.147973
\(629\) −14.0675 + 43.2954i −0.560909 + 1.72630i
\(630\) −20.9243 6.12239i −0.833642 0.243922i
\(631\) 16.5719 + 12.0402i 0.659718 + 0.479313i 0.866568 0.499060i \(-0.166321\pi\)
−0.206850 + 0.978373i \(0.566321\pi\)
\(632\) −10.7741 + 3.50072i −0.428571 + 0.139251i
\(633\) −14.6803 2.10361i −0.583488 0.0836109i
\(634\) 10.8453 14.9273i 0.430723 0.592839i
\(635\) 30.0707 21.8477i 1.19332 0.866998i
\(636\) −7.72271 7.49813i −0.306225 0.297320i
\(637\) 8.98144i 0.355858i
\(638\) 4.53740 + 13.0594i 0.179637 + 0.517027i
\(639\) −23.6438 + 18.2678i −0.935333 + 0.722664i
\(640\) 2.01556 + 0.654895i 0.0796720 + 0.0258870i
\(641\) 1.82529 + 2.51229i 0.0720946 + 0.0992296i 0.843541 0.537064i \(-0.180467\pi\)
−0.771447 + 0.636294i \(0.780467\pi\)
\(642\) −14.6716 27.7740i −0.579044 1.09615i
\(643\) −12.1432 37.3728i −0.478880 1.47384i −0.840653 0.541574i \(-0.817828\pi\)
0.361773 0.932266i \(-0.382172\pi\)
\(644\) −5.26719 16.2107i −0.207556 0.638793i
\(645\) 11.1716 + 21.1483i 0.439883 + 0.832715i
\(646\) −0.730424 1.00534i −0.0287381 0.0395547i
\(647\) −34.1070 11.0820i −1.34088 0.435680i −0.451268 0.892388i \(-0.649028\pi\)
−0.889616 + 0.456709i \(0.849028\pi\)
\(648\) −2.27147 + 8.70864i −0.0892318 + 0.342108i
\(649\) 5.55321 + 7.32685i 0.217982 + 0.287604i
\(650\) 0.960005i 0.0376545i
\(651\) 27.9265 + 27.1144i 1.09453 + 1.06270i
\(652\) −6.91743 + 5.02581i −0.270908 + 0.196826i
\(653\) 1.38621 1.90795i 0.0542465 0.0746639i −0.781032 0.624491i \(-0.785306\pi\)
0.835278 + 0.549827i \(0.185306\pi\)
\(654\) 1.20495 + 0.172663i 0.0471172 + 0.00675166i
\(655\) −9.72101 + 3.15855i −0.379831 + 0.123415i
\(656\) −6.42001 4.66441i −0.250659 0.182115i
\(657\) −2.08912 + 7.13990i −0.0815043 + 0.278554i
\(658\) −3.57087 + 10.9900i −0.139207 + 0.428435i
\(659\) −8.51039 −0.331518 −0.165759 0.986166i \(-0.553007\pi\)
−0.165759 + 0.986166i \(0.553007\pi\)
\(660\) 5.14420 11.0341i 0.200238 0.429504i
\(661\) 42.4546 1.65129 0.825646 0.564189i \(-0.190811\pi\)
0.825646 + 0.564189i \(0.190811\pi\)
\(662\) −1.55634 + 4.78991i −0.0604888 + 0.186165i
\(663\) −2.88312 16.6131i −0.111971 0.645200i
\(664\) −5.55630 4.03689i −0.215626 0.156662i
\(665\) −1.66520 + 0.541056i −0.0645736 + 0.0209812i
\(666\) 14.9249 21.8714i 0.578328 0.847500i
\(667\) −12.1790 + 16.7630i −0.471574 + 0.649066i
\(668\) −1.33161 + 0.967474i −0.0515217 + 0.0374327i
\(669\) −0.0607526 + 0.0625722i −0.00234883 + 0.00241918i
\(670\) 21.1588i 0.817438i
\(671\) −0.108650 5.36848i −0.00419439 0.207248i
\(672\) −2.61803 + 5.33119i −0.100993 + 0.205655i
\(673\) 45.4817 + 14.7779i 1.75319 + 0.569646i 0.996459 0.0840801i \(-0.0267952\pi\)
0.756731 + 0.653726i \(0.226795\pi\)
\(674\) −10.3769 14.2826i −0.399704 0.550146i
\(675\) −1.09449 + 2.40565i −0.0421271 + 0.0925934i
\(676\) 2.91638 + 8.97570i 0.112169 + 0.345219i
\(677\) 1.70016 + 5.23254i 0.0653423 + 0.201103i 0.978397 0.206734i \(-0.0662833\pi\)
−0.913055 + 0.407837i \(0.866283\pi\)
\(678\) 6.56130 3.46601i 0.251985 0.133111i
\(679\) −26.6497 36.6802i −1.02272 1.40766i
\(680\) 10.3958 + 3.37781i 0.398662 + 0.129533i
\(681\) −22.2130 10.9083i −0.851205 0.418009i
\(682\) −17.3226 + 13.1292i −0.663315 + 0.502744i
\(683\) 40.1110i 1.53480i −0.641166 0.767402i \(-0.721549\pi\)
0.641166 0.767402i \(-0.278451\pi\)
\(684\) 0.243539 + 0.680529i 0.00931195 + 0.0260207i
\(685\) 30.9613 22.4947i 1.18297 0.859479i
\(686\) −4.51776 + 6.21817i −0.172489 + 0.237411i
\(687\) −7.43013 + 51.8520i −0.283477 + 1.97828i
\(688\) 6.19693 2.01350i 0.236256 0.0767641i
\(689\) −9.48940 6.89445i −0.361517 0.262658i
\(690\) 17.9774 3.11988i 0.684386 0.118772i
\(691\) 9.77418 30.0818i 0.371827 1.14437i −0.573767 0.819019i \(-0.694518\pi\)
0.945594 0.325348i \(-0.105482\pi\)
\(692\) −3.50863 −0.133378
\(693\) 28.5658 + 18.6573i 1.08512 + 0.708732i
\(694\) 15.0268 0.570411
\(695\) −0.647936 + 1.99414i −0.0245776 + 0.0756421i
\(696\) 7.11364 1.23454i 0.269642 0.0467949i
\(697\) −33.1131 24.0580i −1.25425 0.911263i
\(698\) 3.32413 1.08008i 0.125820 0.0408815i
\(699\) −0.694884 + 4.84933i −0.0262829 + 0.183418i
\(700\) −1.02518 + 1.41103i −0.0387480 + 0.0533321i
\(701\) 12.7136 9.23696i 0.480185 0.348875i −0.321212 0.947007i \(-0.604090\pi\)
0.801397 + 0.598132i \(0.204090\pi\)
\(702\) −1.10411 + 9.74502i −0.0416719 + 0.367802i
\(703\) 2.12650i 0.0802025i
\(704\) −2.72210 1.89477i −0.102593 0.0714119i
\(705\) −11.1033 5.45258i −0.418174 0.205356i
\(706\) 24.0307 + 7.80805i 0.904407 + 0.293860i
\(707\) 4.95878 + 6.82517i 0.186494 + 0.256687i
\(708\) 4.24524 2.24256i 0.159546 0.0842804i
\(709\) 1.83617 + 5.65115i 0.0689588 + 0.212233i 0.979597 0.200971i \(-0.0644096\pi\)
−0.910638 + 0.413204i \(0.864410\pi\)
\(710\) −6.52249 20.0742i −0.244785 0.753370i
\(711\) 33.9709 1.00268i 1.27401 0.0376034i
\(712\) 1.45332 + 2.00032i 0.0544655 + 0.0749653i
\(713\) −30.9818 10.0666i −1.16028 0.376997i
\(714\) −13.5033 + 27.4971i −0.505347 + 1.02905i
\(715\) 3.84343 12.6976i 0.143736 0.474862i
\(716\) 13.2729i 0.496031i
\(717\) −1.36986 + 1.41089i −0.0511585 + 0.0526908i
\(718\) 15.6095 11.3409i 0.582540 0.423240i
\(719\) 18.1483 24.9789i 0.676816 0.931557i −0.323075 0.946373i \(-0.604716\pi\)
0.999890 + 0.0148168i \(0.00471649\pi\)
\(720\) −5.25163 3.58367i −0.195717 0.133556i
\(721\) −15.0326 + 4.88439i −0.559844 + 0.181904i
\(722\) −15.3244 11.1338i −0.570314 0.414357i
\(723\) −4.45616 25.6773i −0.165726 0.954949i
\(724\) −2.29709 + 7.06971i −0.0853706 + 0.262744i
\(725\) 2.12020 0.0787424
\(726\) −12.7080 + 14.1953i −0.471639 + 0.526836i
\(727\) −23.3566 −0.866249 −0.433124 0.901334i \(-0.642589\pi\)
−0.433124 + 0.901334i \(0.642589\pi\)
\(728\) −2.00000 + 6.15537i −0.0741249 + 0.228133i
\(729\) 13.8770 23.1610i 0.513962 0.857813i
\(730\) −4.25163 3.08899i −0.157360 0.114329i
\(731\) 31.9624 10.3852i 1.18217 0.384111i
\(732\) −2.77582 0.397761i −0.102597 0.0147017i
\(733\) 24.3752 33.5495i 0.900317 1.23918i −0.0700499 0.997543i \(-0.522316\pi\)
0.970367 0.241636i \(-0.0776842\pi\)
\(734\) 0.726385 0.527749i 0.0268114 0.0194796i
\(735\) 12.5321 + 12.1677i 0.462254 + 0.448811i
\(736\) 4.97072i 0.183223i
\(737\) −9.59317 + 31.6930i −0.353369 + 1.16743i
\(738\) 14.5554 + 18.8388i 0.535791 + 0.693466i
\(739\) 29.5635 + 9.60577i 1.08751 + 0.353354i 0.797284 0.603604i \(-0.206269\pi\)
0.290227 + 0.956958i \(0.406269\pi\)
\(740\) 10.9946 + 15.1328i 0.404170 + 0.556293i
\(741\) 0.367893 + 0.696435i 0.0135149 + 0.0255842i
\(742\) 6.58521 + 20.2672i 0.241751 + 0.744032i
\(743\) −9.47940 29.1746i −0.347765 1.07031i −0.960087 0.279703i \(-0.909764\pi\)
0.612321 0.790609i \(-0.290236\pi\)
\(744\) 5.30198 + 10.0368i 0.194380 + 0.367969i
\(745\) 17.4236 + 23.9815i 0.638350 + 0.878614i
\(746\) 25.0515 + 8.13972i 0.917200 + 0.298016i
\(747\) 12.5972 + 16.3043i 0.460906 + 0.596544i
\(748\) −14.0400 9.77282i −0.513354 0.357330i
\(749\) 62.1868i 2.27226i
\(750\) −14.5075 14.0856i −0.529739 0.514334i
\(751\) 6.03982 4.38818i 0.220396 0.160127i −0.472109 0.881540i \(-0.656507\pi\)
0.692505 + 0.721413i \(0.256507\pi\)
\(752\) −1.98077 + 2.72629i −0.0722311 + 0.0994176i
\(753\) 16.5220 + 2.36752i 0.602095 + 0.0862772i
\(754\) 7.48259 2.43124i 0.272500 0.0885406i
\(755\) 10.8504 + 7.88330i 0.394888 + 0.286903i
\(756\) 12.0294 13.1444i 0.437506 0.478056i
\(757\) −7.21548 + 22.2070i −0.262251 + 0.807126i 0.730063 + 0.683380i \(0.239491\pi\)
−0.992314 + 0.123746i \(0.960509\pi\)
\(758\) −2.66498 −0.0967965
\(759\) −28.3421 3.47759i −1.02875 0.126228i
\(760\) −0.510602 −0.0185215
\(761\) −2.97052 + 9.14231i −0.107681 + 0.331408i −0.990350 0.138586i \(-0.955744\pi\)
0.882669 + 0.469995i \(0.155744\pi\)
\(762\) 5.19428 + 29.9305i 0.188169 + 1.08427i
\(763\) −1.94965 1.41650i −0.0705820 0.0512808i
\(764\) 2.46344 0.800420i 0.0891241 0.0289582i
\(765\) −27.0868 18.4838i −0.979324 0.668284i
\(766\) 19.2253 26.4614i 0.694639 0.956088i
\(767\) 4.23266 3.07521i 0.152833 0.111039i
\(768\) −1.20654 + 1.24268i −0.0435374 + 0.0448414i
\(769\) 34.6298i 1.24878i −0.781112 0.624391i \(-0.785347\pi\)
0.781112 0.624391i \(-0.214653\pi\)
\(770\) −19.2087 + 14.5588i −0.692234 + 0.524662i
\(771\) −10.1969 + 20.7643i −0.367233 + 0.747809i
\(772\) −18.5702 6.03383i −0.668357 0.217162i
\(773\) −7.96896 10.9683i −0.286624 0.394504i 0.641290 0.767299i \(-0.278400\pi\)
−0.927914 + 0.372795i \(0.878400\pi\)
\(774\) −19.5390 + 0.576709i −0.702315 + 0.0207294i
\(775\) 1.03007 + 3.17022i 0.0370011 + 0.113878i
\(776\) −4.08582 12.5749i −0.146672 0.451411i
\(777\) −46.3518 + 24.4854i −1.66286 + 0.878408i
\(778\) 0.990218 + 1.36292i 0.0355010 + 0.0488630i
\(779\) 1.81835 + 0.590818i 0.0651492 + 0.0211683i
\(780\) −6.21881 3.05392i −0.222669 0.109348i
\(781\) 0.668387 + 33.0255i 0.0239168 + 1.18174i
\(782\) 25.6379i 0.916810i
\(783\) −21.5222 2.43847i −0.769141 0.0871436i
\(784\) 3.84975 2.79701i 0.137491 0.0998932i
\(785\) −4.61925 + 6.35786i −0.164868 + 0.226922i
\(786\) 1.18493 8.26918i 0.0422651 0.294952i
\(787\) −17.6164 + 5.72391i −0.627957 + 0.204036i −0.605670 0.795716i \(-0.707095\pi\)
−0.0222870 + 0.999752i \(0.507095\pi\)
\(788\) −4.35828 3.16647i −0.155257 0.112801i
\(789\) −15.9336 + 2.76519i −0.567251 + 0.0984434i
\(790\) −7.41903 + 22.8334i −0.263957 + 0.812377i
\(791\) −14.6909 −0.522350
\(792\) 6.24140 + 7.74886i 0.221779 + 0.275344i
\(793\) −3.05573 −0.108512
\(794\) −2.74789 + 8.45713i −0.0975189 + 0.300132i
\(795\) −22.4759 + 3.90057i −0.797138 + 0.138339i
\(796\) −5.97631 4.34204i −0.211825 0.153900i
\(797\) −49.0135 + 15.9254i −1.73615 + 0.564108i −0.994315 0.106479i \(-0.966042\pi\)
−0.741831 + 0.670587i \(0.766042\pi\)
\(798\) 0.202977 1.41650i 0.00718532 0.0501436i
\(799\) −10.2164 + 14.0616i −0.361429 + 0.497465i
\(800\) −0.411491 + 0.298966i −0.0145484 + 0.0105700i
\(801\) −2.49930 6.98387i −0.0883084 0.246763i
\(802\) 19.5587i 0.690642i
\(803\) 4.96783 + 6.55451i 0.175311 + 0.231303i
\(804\) 15.5221 + 7.62256i 0.547421 + 0.268827i
\(805\) −34.3552 11.1627i −1.21086 0.393432i
\(806\) 7.27059 + 10.0071i 0.256096 + 0.352485i
\(807\) 20.8667 11.0228i 0.734541 0.388022i
\(808\) 0.760259 + 2.33984i 0.0267458 + 0.0823151i
\(809\) 10.8032 + 33.2488i 0.379820 + 1.16897i 0.940169 + 0.340709i \(0.110667\pi\)
−0.560348 + 0.828257i \(0.689333\pi\)
\(810\) 12.1018 + 14.7427i 0.425212 + 0.518007i
\(811\) −10.5779 14.5592i −0.371440 0.511243i 0.581852 0.813295i \(-0.302328\pi\)
−0.953291 + 0.302052i \(0.902328\pi\)
\(812\) −13.5943 4.41707i −0.477068 0.155009i
\(813\) 3.58154 7.29320i 0.125610 0.255784i
\(814\) −9.60737 27.6516i −0.336738 0.969189i
\(815\) 18.1208i 0.634743i
\(816\) −6.22309 + 6.40948i −0.217852 + 0.224377i
\(817\) −1.27005 + 0.922745i −0.0444334 + 0.0322828i
\(818\) 14.5460 20.0208i 0.508588 0.700011i
\(819\) 10.9443 16.0381i 0.382424 0.560416i
\(820\) −15.9946 + 5.19697i −0.558557 + 0.181486i
\(821\) −7.34398 5.33572i −0.256307 0.186218i 0.452210 0.891911i \(-0.350636\pi\)
−0.708517 + 0.705693i \(0.750636\pi\)
\(822\) 5.34812 + 30.8169i 0.186537 + 1.07486i
\(823\) −0.237770 + 0.731782i −0.00828815 + 0.0255083i −0.955115 0.296235i \(-0.904269\pi\)
0.946827 + 0.321743i \(0.104269\pi\)
\(824\) −4.60947 −0.160578
\(825\) 1.41676 + 2.55540i 0.0493252 + 0.0889677i
\(826\) −9.50523 −0.330729
\(827\) 15.2780 47.0207i 0.531267 1.63507i −0.220314 0.975429i \(-0.570708\pi\)
0.751581 0.659641i \(-0.229292\pi\)
\(828\) −4.18769 + 14.3121i −0.145532 + 0.497380i
\(829\) 14.2060 + 10.3212i 0.493393 + 0.358471i 0.806488 0.591251i \(-0.201366\pi\)
−0.313095 + 0.949722i \(0.601366\pi\)
\(830\) −13.8428 + 4.49779i −0.480490 + 0.156121i
\(831\) −14.1996 2.03473i −0.492578 0.0705839i
\(832\) −1.10940 + 1.52696i −0.0384616 + 0.0529379i
\(833\) 19.8562 14.4264i 0.687976 0.499844i
\(834\) −1.22947 1.19372i −0.0425732 0.0413352i
\(835\) 3.48827i 0.120717i
\(836\) 0.764810 + 0.231501i 0.0264515 + 0.00800662i
\(837\) −6.81013 33.3656i −0.235392 1.15329i
\(838\) 33.1407 + 10.7681i 1.14483 + 0.371977i
\(839\) −0.712228 0.980298i −0.0245888 0.0338436i 0.796546 0.604578i \(-0.206658\pi\)
−0.821134 + 0.570735i \(0.806658\pi\)
\(840\) 5.87928 + 11.1297i 0.202854 + 0.384011i
\(841\) −3.59201 11.0551i −0.123863 0.381210i
\(842\) 5.42375 + 16.6926i 0.186915 + 0.575265i
\(843\) −10.2462 19.3964i −0.352897 0.668048i
\(844\) 5.03276 + 6.92699i 0.173235 + 0.238437i
\(845\) 19.0221 + 6.18065i 0.654379 + 0.212621i
\(846\) 8.00000 6.18102i 0.275046 0.212508i
\(847\) 35.3727 13.0980i 1.21542 0.450052i
\(848\) 6.21456i 0.213409i
\(849\) 28.0965 + 27.2795i 0.964271 + 0.936230i
\(850\) −2.12238 + 1.54200i −0.0727971 + 0.0528902i
\(851\) 25.7876 35.4935i 0.883987 1.21670i
\(852\) 17.0761 + 2.44692i 0.585017 + 0.0838300i
\(853\) 2.04187 0.663444i 0.0699123 0.0227159i −0.273852 0.961772i \(-0.588298\pi\)
0.343764 + 0.939056i \(0.388298\pi\)
\(854\) 4.49137 + 3.26317i 0.153691 + 0.111663i
\(855\) 1.47017 + 0.430167i 0.0502786 + 0.0147114i
\(856\) −5.60407 + 17.2475i −0.191543 + 0.589509i
\(857\) 55.7274 1.90361 0.951805 0.306704i \(-0.0992260\pi\)
0.951805 + 0.306704i \(0.0992260\pi\)
\(858\) 7.93028 + 7.39388i 0.270735 + 0.252423i
\(859\) −36.2927 −1.23829 −0.619146 0.785276i \(-0.712521\pi\)
−0.619146 + 0.785276i \(0.712521\pi\)
\(860\) 4.26719 13.1331i 0.145510 0.447833i
\(861\) −8.05905 46.4379i −0.274652 1.58260i
\(862\) 27.0376 + 19.6440i 0.920905 + 0.669077i
\(863\) −29.6543 + 9.63527i −1.00944 + 0.327988i −0.766633 0.642085i \(-0.778070\pi\)
−0.242811 + 0.970074i \(0.578070\pi\)
\(864\) 4.52089 2.56155i 0.153804 0.0871456i
\(865\) −4.37065 + 6.01568i −0.148606 + 0.204539i
\(866\) −21.9952 + 15.9805i −0.747428 + 0.543039i
\(867\) −11.5861 + 11.9331i −0.393485 + 0.405271i
\(868\) 22.4728i 0.762777i
\(869\) 21.4651 30.8375i 0.728152 1.04609i
\(870\) 6.74470 13.7345i 0.228667 0.465642i
\(871\) 17.9217 + 5.82312i 0.607254 + 0.197309i
\(872\) −0.413086 0.568564i −0.0139888 0.0192540i
\(873\) 1.17026 + 39.6487i 0.0396074 + 1.34191i
\(874\) 0.370079 + 1.13899i 0.0125181 + 0.0385268i
\(875\) 12.3706 + 38.0729i 0.418204 + 1.28710i
\(876\) 3.79774 2.00616i 0.128314 0.0677819i
\(877\) −10.8949 14.9956i −0.367895 0.506365i 0.584432 0.811443i \(-0.301317\pi\)
−0.952327 + 0.305078i \(0.901317\pi\)
\(878\) −12.7506 4.14293i −0.430313 0.139817i
\(879\) −39.0105 19.1572i −1.31579 0.646157i
\(880\) −6.63954 + 2.30686i −0.223819 + 0.0777643i
\(881\) 22.0893i 0.744207i −0.928191 0.372103i \(-0.878637\pi\)
0.928191 0.372103i \(-0.121363\pi\)
\(882\) −13.4409 + 4.81006i −0.452579 + 0.161963i
\(883\) −35.3330 + 25.6709i −1.18905 + 0.863894i −0.993163 0.116733i \(-0.962758\pi\)
−0.195885 + 0.980627i \(0.562758\pi\)
\(884\) −5.72206 + 7.87574i −0.192454 + 0.264890i
\(885\) 1.44329 10.0721i 0.0485155 0.338571i
\(886\) −17.5311 + 5.69619i −0.588968 + 0.191367i
\(887\) 6.82936 + 4.96182i 0.229307 + 0.166602i 0.696506 0.717551i \(-0.254737\pi\)
−0.467199 + 0.884152i \(0.654737\pi\)
\(888\) −15.0622 + 2.61397i −0.505456 + 0.0877191i
\(889\) 18.5847 57.1979i 0.623312 1.91836i
\(890\) 5.24001 0.175646
\(891\) −11.4425 27.5693i −0.383340 0.923607i
\(892\) 0.0503526 0.00168593
\(893\) 0.250894 0.772172i 0.00839585 0.0258398i
\(894\) −23.8697 + 4.14245i −0.798321 + 0.138544i
\(895\) 22.7569 + 16.5338i 0.760678 + 0.552665i
\(896\) 3.26124 1.05964i 0.108951 0.0354002i
\(897\) −2.30498 + 16.0856i −0.0769611 + 0.537082i
\(898\) 17.8510 24.5698i 0.595697 0.819906i
\(899\) −22.1011 + 16.0574i −0.737112 + 0.535543i
\(900\) 1.43667 0.514137i 0.0478889 0.0171379i
\(901\) 32.0534i 1.06785i
\(902\) 26.3139 0.532555i 0.876158 0.0177321i
\(903\) 34.7371 + 17.0587i 1.15598 + 0.567677i
\(904\) −4.07454 1.32390i −0.135517 0.0440322i
\(905\) 9.25984 + 12.7451i 0.307808 + 0.423661i
\(906\) −9.69208 + 5.11985i −0.321998 + 0.170096i
\(907\) −3.70460 11.4016i −0.123009 0.378583i 0.870524 0.492126i \(-0.163780\pi\)
−0.993533 + 0.113543i \(0.963780\pi\)
\(908\) 4.41512 + 13.5884i 0.146521 + 0.450945i
\(909\) −0.217754 7.37754i −0.00722244 0.244697i
\(910\) 8.06224 + 11.0967i 0.267261 + 0.367853i
\(911\) −27.1492 8.82132i −0.899494 0.292263i −0.177466 0.984127i \(-0.556790\pi\)
−0.722028 + 0.691864i \(0.756790\pi\)
\(912\) 0.183946 0.374576i 0.00609108 0.0124035i
\(913\) 22.7738 0.460908i 0.753702 0.0152538i
\(914\) 34.6878i 1.14737i
\(915\) −4.13977 + 4.26376i −0.136857 + 0.140956i
\(916\) 24.4668 17.7761i 0.808405 0.587340i
\(917\) −9.72101 + 13.3798i −0.321016 + 0.441841i
\(918\) 23.3178 13.2119i 0.769602 0.436058i
\(919\) 52.3547 17.0111i 1.72702 0.561143i 0.734008 0.679141i \(-0.237648\pi\)
0.993014 + 0.117998i \(0.0376475\pi\)
\(920\) −8.52249 6.19195i −0.280978 0.204143i
\(921\) −4.75877 27.4210i −0.156807 0.903552i
\(922\) 6.45155 19.8558i 0.212471 0.653917i
\(923\) 18.7980 0.618745
\(924\) −3.76026 19.3363i −0.123703 0.636118i
\(925\) −4.48926 −0.147606
\(926\) 1.89851 5.84302i 0.0623890 0.192013i
\(927\) 13.2719 + 3.88334i 0.435908 + 0.127546i
\(928\) −3.37235 2.45016i −0.110703 0.0804303i
\(929\) 10.6108 3.44764i 0.348128 0.113114i −0.129734 0.991549i \(-0.541412\pi\)
0.477861 + 0.878435i \(0.341412\pi\)
\(930\) 23.8132 + 3.41230i 0.780864 + 0.111894i
\(931\) −0.673887 + 0.927526i −0.0220858 + 0.0303984i
\(932\) 2.28819 1.66247i 0.0749521 0.0544559i
\(933\) 11.9614 + 11.6136i 0.391599 + 0.380211i
\(934\) 34.8047i 1.13885i
\(935\) −34.2453 + 11.8983i −1.11994 + 0.389116i
\(936\) 4.48070 3.46191i 0.146456 0.113156i
\(937\) −30.0019 9.74821i −0.980120 0.318460i −0.225225 0.974307i \(-0.572312\pi\)
−0.754894 + 0.655847i \(0.772312\pi\)
\(938\) −20.1233 27.6973i −0.657048 0.904349i
\(939\) 16.2725 + 30.8045i 0.531034 + 1.00527i
\(940\) 2.20692 + 6.79220i 0.0719818 + 0.221537i
\(941\) 15.7950 + 48.6119i 0.514901 + 1.58470i 0.783462 + 0.621440i \(0.213452\pi\)
−0.268560 + 0.963263i \(0.586548\pi\)
\(942\) −3.00000 5.67911i −0.0977453 0.185036i
\(943\) 23.1855 + 31.9121i 0.755024 + 1.03920i
\(944\) −2.63628 0.856580i −0.0858037 0.0278793i
\(945\) −7.55164 36.9986i −0.245655 1.20356i
\(946\) −12.3460 + 17.7368i −0.401404 + 0.576672i
\(947\) 23.9467i 0.778162i −0.921204 0.389081i \(-0.872793\pi\)
0.921204 0.389081i \(-0.127207\pi\)
\(948\) −14.0778 13.6684i −0.457226 0.443929i
\(949\) 3.78649 2.75104i 0.122915 0.0893027i
\(950\) 0.0720302 0.0991411i 0.00233697 0.00321656i
\(951\) 31.6352 + 4.53316i 1.02584 + 0.146998i
\(952\) 16.8208 5.46541i 0.545165 0.177135i
\(953\) 16.1924 + 11.7645i 0.524524 + 0.381089i 0.818306 0.574784i \(-0.194914\pi\)
−0.293781 + 0.955873i \(0.594914\pi\)
\(954\) 5.23558 17.8934i 0.169508 0.579322i
\(955\) 1.69632 5.22073i 0.0548915 0.168939i
\(956\) 1.13536 0.0367203
\(957\) −16.3296 + 17.5143i −0.527862 + 0.566157i
\(958\) −34.8328 −1.12540
\(959\) 19.1351 58.8919i 0.617906 1.90172i
\(960\) 0.627650 + 3.61665i 0.0202573 + 0.116727i
\(961\) −9.66758 7.02390i −0.311857 0.226578i
\(962\) −15.8434 + 5.14784i −0.510813 + 0.165973i
\(963\) 30.6662 44.9392i 0.988205 1.44815i
\(964\) −8.84404 + 12.1728i −0.284847 + 0.392059i
\(965\) −33.4779 + 24.3231i −1.07769 + 0.782988i
\(966\) 20.5655 21.1815i 0.661684 0.681502i
\(967\) 48.8703i 1.57156i 0.618505 + 0.785781i \(0.287739\pi\)
−0.618505 + 0.785781i \(0.712261\pi\)
\(968\) 10.9910 0.445065i 0.353264 0.0143049i
\(969\) 0.948756 1.93198i 0.0304784 0.0620642i
\(970\) −26.6497 8.65902i −0.855671 0.278024i
\(971\) 16.0664 + 22.1135i 0.515595 + 0.709656i 0.984850 0.173407i \(-0.0554775\pi\)
−0.469255 + 0.883063i \(0.655478\pi\)
\(972\) −15.1749 + 3.56668i −0.486736 + 0.114401i
\(973\) 1.04838 + 3.22659i 0.0336096 + 0.103440i
\(974\) −1.78176 5.48370i −0.0570913 0.175709i
\(975\) 1.47025 0.776660i 0.0470856 0.0248730i
\(976\) 0.951618 + 1.30979i 0.0304606 + 0.0419254i
\(977\) 14.7096 + 4.77945i 0.470603 + 0.152908i 0.534711 0.845035i \(-0.320420\pi\)
−0.0641084 + 0.997943i \(0.520420\pi\)
\(978\) −13.2933 6.52808i −0.425074 0.208745i
\(979\) −7.84880 2.37576i −0.250849 0.0759295i
\(980\) 10.0847i 0.322145i
\(981\) 0.710390 + 1.98507i 0.0226810 + 0.0633783i
\(982\) −8.42871 + 6.12382i −0.268971 + 0.195419i
\(983\) −25.9872 + 35.7683i −0.828863 + 1.14083i 0.159271 + 0.987235i \(0.449086\pi\)
−0.988134 + 0.153597i \(0.950914\pi\)
\(984\) 1.94965 13.6058i 0.0621525 0.433738i
\(985\) −10.8581 + 3.52800i −0.345967 + 0.112411i
\(986\) −17.3939 12.6374i −0.553933 0.402456i
\(987\) −19.7201 + 3.42232i −0.627697 + 0.108934i
\(988\) 0.140523 0.432484i 0.00447062 0.0137591i
\(989\) −32.3884 −1.02989
\(990\) 21.0605 1.04848i 0.669348 0.0333228i
\(991\) −36.1335 −1.14782 −0.573909 0.818919i \(-0.694574\pi\)
−0.573909 + 0.818919i \(0.694574\pi\)
\(992\) 2.02518 6.23285i 0.0642994 0.197893i
\(993\) −8.59485 + 1.49159i −0.272749 + 0.0473342i
\(994\) −27.6297 20.0742i −0.876361 0.636714i
\(995\) −14.8892 + 4.83779i −0.472019 + 0.153368i
\(996\) 1.68735 11.7754i 0.0534658 0.373117i
\(997\) 4.77670 6.57457i 0.151280 0.208219i −0.726650 0.687007i \(-0.758924\pi\)
0.877930 + 0.478789i \(0.158924\pi\)
\(998\) 17.7151 12.8708i 0.560763 0.407418i
\(999\) 45.5706 + 5.16314i 1.44179 + 0.163355i
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 66.2.h.a.35.2 yes 8
3.2 odd 2 66.2.h.b.35.1 yes 8
4.3 odd 2 528.2.bn.b.497.1 8
11.2 odd 10 726.2.h.f.239.2 8
11.3 even 5 726.2.h.c.161.1 8
11.4 even 5 726.2.b.e.725.3 8
11.5 even 5 726.2.h.d.215.2 8
11.6 odd 10 66.2.h.b.17.2 yes 8
11.7 odd 10 726.2.b.c.725.3 8
11.8 odd 10 726.2.h.h.161.1 8
11.9 even 5 726.2.h.a.239.2 8
11.10 odd 2 726.2.h.j.233.2 8
12.11 even 2 528.2.bn.a.497.2 8
33.2 even 10 726.2.h.c.239.1 8
33.5 odd 10 726.2.h.j.215.2 8
33.8 even 10 726.2.h.a.161.2 8
33.14 odd 10 726.2.h.f.161.2 8
33.17 even 10 inner 66.2.h.a.17.2 8
33.20 odd 10 726.2.h.h.239.1 8
33.26 odd 10 726.2.b.c.725.4 8
33.29 even 10 726.2.b.e.725.4 8
33.32 even 2 726.2.h.d.233.1 8
44.39 even 10 528.2.bn.a.17.1 8
132.83 odd 10 528.2.bn.b.17.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
66.2.h.a.17.2 8 33.17 even 10 inner
66.2.h.a.35.2 yes 8 1.1 even 1 trivial
66.2.h.b.17.2 yes 8 11.6 odd 10
66.2.h.b.35.1 yes 8 3.2 odd 2
528.2.bn.a.17.1 8 44.39 even 10
528.2.bn.a.497.2 8 12.11 even 2
528.2.bn.b.17.1 8 132.83 odd 10
528.2.bn.b.497.1 8 4.3 odd 2
726.2.b.c.725.3 8 11.7 odd 10
726.2.b.c.725.4 8 33.26 odd 10
726.2.b.e.725.3 8 11.4 even 5
726.2.b.e.725.4 8 33.29 even 10
726.2.h.a.161.2 8 33.8 even 10
726.2.h.a.239.2 8 11.9 even 5
726.2.h.c.161.1 8 11.3 even 5
726.2.h.c.239.1 8 33.2 even 10
726.2.h.d.215.2 8 11.5 even 5
726.2.h.d.233.1 8 33.32 even 2
726.2.h.f.161.2 8 33.14 odd 10
726.2.h.f.239.2 8 11.2 odd 10
726.2.h.h.161.1 8 11.8 odd 10
726.2.h.h.239.1 8 33.20 odd 10
726.2.h.j.215.2 8 33.5 odd 10
726.2.h.j.233.2 8 11.10 odd 2